LMFDB - Embedded newform 770.2.l.c.573.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, degree $2$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.18
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.49597 - 1.49597i) q^{3} -1.00000i q^{4} +(0.446287 - 2.19108i) q^{5} -2.11563i q^{6} +(2.36936 + 1.17733i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.47587i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.49597 - 1.49597i) q^{3} -1.00000i q^{4} +(0.446287 - 2.19108i) q^{5} -2.11563i q^{6} +(2.36936 + 1.17733i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.47587i q^{9} +(-1.23375 - 1.86490i) q^{10} -1.00000 q^{11} +(-1.49597 - 1.49597i) q^{12} +(0.153605 - 0.153605i) q^{13} +(2.50789 - 0.842892i) q^{14} +(-2.61016 - 3.94543i) q^{15} -1.00000 q^{16} +(-0.185285 - 0.185285i) q^{17} +(-1.04360 - 1.04360i) q^{18} +3.14044 q^{19} +(-2.19108 - 0.446287i) q^{20} +(5.30577 - 1.78324i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(-2.00976 - 2.00976i) q^{23} -2.11563 q^{24} +(-4.60166 - 1.95570i) q^{25} -0.217230i q^{26} +(2.28005 + 2.28005i) q^{27} +(1.17733 - 2.36936i) q^{28} -1.96277i q^{29} +(-4.63550 - 0.944177i) q^{30} +8.77551i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.49597 + 1.49597i) q^{33} -0.262033 q^{34} +(3.63705 - 4.66603i) q^{35} -1.47587 q^{36} +(-4.87931 + 4.87931i) q^{37} +(2.22062 - 2.22062i) q^{38} -0.459577i q^{39} +(-1.86490 + 1.23375i) q^{40} +7.00275i q^{41} +(2.49080 - 5.01269i) q^{42} +(-4.12206 - 4.12206i) q^{43} +1.00000i q^{44} +(-3.23376 - 0.658664i) q^{45} -2.84223 q^{46} +(2.57824 + 2.57824i) q^{47} +(-1.49597 + 1.49597i) q^{48} +(4.22777 + 5.57907i) q^{49} +(-4.63675 + 1.87097i) q^{50} -0.554364 q^{51} +(-0.153605 - 0.153605i) q^{52} +(-4.52481 - 4.52481i) q^{53} +3.22448 q^{54} +(-0.446287 + 2.19108i) q^{55} +(-0.842892 - 2.50789i) q^{56} +(4.69801 - 4.69801i) q^{57} +(-1.38789 - 1.38789i) q^{58} -7.31725 q^{59} +(-3.94543 + 2.61016i) q^{60} -8.14009i q^{61} +(6.20523 + 6.20523i) q^{62} +(1.73760 - 3.49688i) q^{63} +1.00000i q^{64} +(-0.268008 - 0.405112i) q^{65} +2.11563i q^{66} +(-2.91752 + 2.91752i) q^{67} +(-0.185285 + 0.185285i) q^{68} -6.01309 q^{69} +(-0.727601 - 5.87117i) q^{70} +10.0742 q^{71} +(-1.04360 + 1.04360i) q^{72} +(3.13825 - 3.13825i) q^{73} +6.90039i q^{74} +(-9.80963 + 3.95828i) q^{75} -3.14044i q^{76} +(-2.36936 - 1.17733i) q^{77} +(-0.324970 - 0.324970i) q^{78} +11.0470i q^{79} +(-0.446287 + 2.19108i) q^{80} +11.2494 q^{81} +(4.95169 + 4.95169i) q^{82} +(8.41021 - 8.41021i) q^{83} +(-1.78324 - 5.30577i) q^{84} +(-0.488665 + 0.323284i) q^{85} -5.82948 q^{86} +(-2.93625 - 2.93625i) q^{87} +(0.707107 + 0.707107i) q^{88} -2.17845 q^{89} +(-2.75236 + 1.82087i) q^{90} +(0.544789 - 0.183101i) q^{91} +(-2.00976 + 2.00976i) q^{92} +(13.1279 + 13.1279i) q^{93} +3.64619 q^{94} +(1.40154 - 6.88095i) q^{95} +2.11563i q^{96} +(12.3704 + 12.3704i) q^{97} +(6.93448 + 0.955514i) q^{98} +1.47587i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.49597	−	1.49597i	0.863701	−	0.863701i	−0.128065	−	0.991766i	$-0.540877\pi$
$3$	1.49597	−	1.49597i	0.863701	−	0.863701i	0.991766	+	0.128065i	$0.0408766\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.446287	−	2.19108i	0.199586	−	0.979880i
$5$	0.446287	−	2.19108i	0.199586	−	0.979880i
$6$		−	2.11563i		−	0.863701i
$7$	2.36936	+	1.17733i	0.895535	+	0.444991i
$7$	2.36936	+	1.17733i	0.895535	+	0.444991i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.47587i		−	0.491958i
$10$	−1.23375	−	1.86490i	−0.390147	−	0.589733i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−1.49597	−	1.49597i	−0.431850	−	0.431850i
$13$	0.153605	−	0.153605i	0.0426023	−	0.0426023i	−0.685485	−	0.728087i	$-0.740410\pi$
$13$	0.153605	−	0.153605i	0.0426023	−	0.0426023i	0.728087	+	0.685485i	$0.240410\pi$
$14$	2.50789	−	0.842892i	0.670263	−	0.225272i
$15$	−2.61016	−	3.94543i	−0.673941	−	1.01871i
$16$	−1.00000			−0.250000
$17$	−0.185285	−	0.185285i	−0.0449383	−	0.0449383i	0.684281	−	0.729219i	$-0.260116\pi$
$17$	−0.185285	−	0.185285i	−0.0449383	−	0.0449383i	−0.729219	+	0.684281i	$0.760116\pi$
$18$	−1.04360	−	1.04360i	−0.245979	−	0.245979i
$19$	3.14044			0.720466			0.360233	−	0.932862i	$-0.382697\pi$
$19$	3.14044			0.720466			0.360233	+	0.932862i	$0.382697\pi$
$20$	−2.19108	−	0.446287i	−0.489940	−	0.0997929i
$21$	5.30577	−	1.78324i	1.15781	−	0.389136i
$22$	−0.707107	+	0.707107i	−0.150756	+	0.150756i
$23$	−2.00976	−	2.00976i	−0.419064	−	0.419064i	0.465817	−	0.884881i	$-0.345760\pi$
$23$	−2.00976	−	2.00976i	−0.419064	−	0.419064i	−0.884881	+	0.465817i	$0.845760\pi$
$24$	−2.11563			−0.431850
$25$	−4.60166	−	1.95570i	−0.920331	−	0.391140i
$26$		−	0.217230i		−	0.0426023i
$27$	2.28005	+	2.28005i	0.438796	+	0.438796i
$28$	1.17733	−	2.36936i	0.222495	−	0.447768i
$29$		−	1.96277i		−	0.364477i	−0.983254	−	0.182238i	$-0.941666\pi$
$29$		−	1.96277i		−	0.364477i	0.983254	−	0.182238i	$-0.0583342\pi$
$30$	−4.63550	−	0.944177i	−0.846324	−	0.172382i
$31$			8.77551i			1.57613i	0.615593	+	0.788064i	$0.288917\pi$
$31$			8.77551i			1.57613i	−0.615593	+	0.788064i	$0.711083\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.49597	+	1.49597i	−0.260416	+	0.260416i
$34$	−0.262033			−0.0449383
$35$	3.63705	−	4.66603i	0.614774	−	0.788704i
$36$	−1.47587			−0.245979
$37$	−4.87931	+	4.87931i	−0.802154	+	0.802154i	−0.983432	−	0.181278i	$-0.941977\pi$
$37$	−4.87931	+	4.87931i	−0.802154	+	0.802154i	0.181278	+	0.983432i	$0.441977\pi$
$38$	2.22062	−	2.22062i	0.360233	−	0.360233i
$39$		−	0.459577i		−	0.0735912i
$40$	−1.86490	+	1.23375i	−0.294867	+	0.195074i
$41$			7.00275i			1.09365i	0.837248	+	0.546823i	$0.184163\pi$
$41$			7.00275i			1.09365i	−0.837248	+	0.546823i	$0.815837\pi$
$42$	2.49080	−	5.01269i	0.384339	−	0.773475i
$43$	−4.12206	−	4.12206i	−0.628609	−	0.628609i	0.319109	−	0.947718i	$-0.396616\pi$
$43$	−4.12206	−	4.12206i	−0.628609	−	0.628609i	−0.947718	+	0.319109i	$0.896616\pi$
$44$			1.00000i			0.150756i
$45$	−3.23376	−	0.658664i	−0.482060	−	0.0981879i
$46$	−2.84223			−0.419064
$47$	2.57824	+	2.57824i	0.376075	+	0.376075i	0.869684	−	0.493609i	$-0.164322\pi$
$47$	2.57824	+	2.57824i	0.376075	+	0.376075i	−0.493609	+	0.869684i	$0.664322\pi$
$48$	−1.49597	+	1.49597i	−0.215925	+	0.215925i
$49$	4.22777	+	5.57907i	0.603967	+	0.797010i
$50$	−4.63675	+	1.87097i	−0.655736	+	0.264595i
$51$	−0.554364			−0.0776265
$52$	−0.153605	−	0.153605i	−0.0213011	−	0.0213011i
$53$	−4.52481	−	4.52481i	−0.621530	−	0.621530i	0.324392	−	0.945923i	$-0.394840\pi$
$53$	−4.52481	−	4.52481i	−0.621530	−	0.621530i	−0.945923	+	0.324392i	$0.894840\pi$
$54$	3.22448			0.438796
$55$	−0.446287	+	2.19108i	−0.0601774	+	0.295445i
$56$	−0.842892	−	2.50789i	−0.112636	−	0.335131i
$57$	4.69801	−	4.69801i	0.622267	−	0.622267i
$58$	−1.38789	−	1.38789i	−0.182238	−	0.182238i
$59$	−7.31725			−0.952625			−0.476312	−	0.879276i	$-0.658027\pi$
$59$	−7.31725			−0.952625			−0.476312	+	0.879276i	$0.658027\pi$
$60$	−3.94543	+	2.61016i	−0.509353	+	0.336971i
$61$		−	8.14009i		−	1.04223i	−0.853486	−	0.521116i	$-0.825516\pi$
$61$		−	8.14009i		−	1.04223i	0.853486	−	0.521116i	$-0.174484\pi$
$62$	6.20523	+	6.20523i	0.788064	+	0.788064i
$63$	1.73760	−	3.49688i	0.218917	−	0.440566i
$64$			1.00000i			0.125000i
$65$	−0.268008	−	0.405112i	−0.0332423	−	0.0502479i
$66$			2.11563i			0.260416i
$67$	−2.91752	+	2.91752i	−0.356432	+	0.356432i	−0.862496	−	0.506064i	$-0.831100\pi$
$67$	−2.91752	+	2.91752i	−0.356432	+	0.356432i	0.506064	+	0.862496i	$0.331100\pi$
$68$	−0.185285	+	0.185285i	−0.0224691	+	0.0224691i
$69$	−6.01309			−0.723891
$70$	−0.727601	−	5.87117i	−0.0869650	−	0.701739i
$71$	10.0742			1.19558			0.597791	−	0.801652i	$-0.296045\pi$
$71$	10.0742			1.19558			0.597791	+	0.801652i	$0.296045\pi$
$72$	−1.04360	+	1.04360i	−0.122990	+	0.122990i
$73$	3.13825	−	3.13825i	0.367305	−	0.367305i	−0.499189	−	0.866493i	$-0.666369\pi$
$73$	3.13825	−	3.13825i	0.367305	−	0.367305i	0.866493	+	0.499189i	$0.166369\pi$
$74$			6.90039i			0.802154i
$75$	−9.80963	+	3.95828i	−1.13272	+	0.457063i
$76$		−	3.14044i		−	0.360233i
$77$	−2.36936	−	1.17733i	−0.270014	−	0.134170i
$78$	−0.324970	−	0.324970i	−0.0367956	−	0.0367956i
$79$			11.0470i			1.24288i	0.783462	+	0.621440i	$0.213452\pi$
$79$			11.0470i			1.24288i	−0.783462	+	0.621440i	$0.786548\pi$
$80$	−0.446287	+	2.19108i	−0.0498964	+	0.244970i
$81$	11.2494			1.24994
$82$	4.95169	+	4.95169i	0.546823	+	0.546823i
$83$	8.41021	−	8.41021i	0.923140	−	0.923140i	−0.0741097	−	0.997250i	$-0.523611\pi$
$83$	8.41021	−	8.41021i	0.923140	−	0.923140i	0.997250	+	0.0741097i	$0.0236115\pi$
$84$	−1.78324	−	5.30577i	−0.194568	−	0.578907i
$85$	−0.488665	+	0.323284i	−0.0530032	+	0.0350651i
$86$	−5.82948			−0.628609
$87$	−2.93625	−	2.93625i	−0.314799	−	0.314799i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	−2.17845			−0.230915			−0.115457	−	0.993312i	$-0.536833\pi$
$89$	−2.17845			−0.230915			−0.115457	+	0.993312i	$0.536833\pi$
$90$	−2.75236	+	1.82087i	−0.290124	+	0.191936i
$91$	0.544789	−	0.183101i	0.0571095	−	0.0191942i
$92$	−2.00976	+	2.00976i	−0.209532	+	0.209532i
$93$	13.1279	+	13.1279i	1.36130	+	1.36130i
$94$	3.64619			0.376075
$95$	1.40154	−	6.88095i	0.143795	−	0.705970i
$96$			2.11563i			0.215925i
$97$	12.3704	+	12.3704i	1.25602	+	1.25602i	0.952975	+	0.303048i	$0.0980042\pi$
$97$	12.3704	+	12.3704i	1.25602	+	1.25602i	0.303048	+	0.952975i	$0.401996\pi$
$98$	6.93448	+	0.955514i	0.700488	+	0.0965215i
$99$			1.47587i			0.148331i
$100$	−1.95570	+	4.60166i	−0.195570	+	0.460166i
$101$		−	14.7396i		−	1.46664i	−0.679883	−	0.733321i	$-0.737969\pi$
$101$		−	14.7396i		−	1.46664i	0.679883	−	0.733321i	$-0.262031\pi$
$102$	−0.391995	+	0.391995i	−0.0388132	+	0.0388132i
$103$	5.18522	−	5.18522i	0.510914	−	0.510914i	−0.403892	−	0.914807i	$-0.632343\pi$
$103$	5.18522	−	5.18522i	0.510914	−	0.510914i	0.914807	+	0.403892i	$0.132343\pi$
$104$	−0.217230			−0.0213011
$105$	−1.53933	−	12.4212i	−0.150223	−	1.21218i
$106$	−6.39905			−0.621530
$107$	−2.39215	+	2.39215i	−0.231258	+	0.231258i	−0.813217	−	0.581960i	$-0.802286\pi$
$107$	−2.39215	+	2.39215i	−0.231258	+	0.231258i	0.581960	+	0.813217i	$0.302286\pi$
$108$	2.28005	−	2.28005i	0.219398	−	0.219398i
$109$			8.52321i			0.816375i	0.912898	+	0.408188i	$0.133839\pi$
$109$			8.52321i			0.816375i	−0.912898	+	0.408188i	$0.866161\pi$
$110$	1.23375	+	1.86490i	0.117634	+	0.177811i
$111$			14.5987i			1.38564i
$112$	−2.36936	−	1.17733i	−0.223884	−	0.111248i
$113$	−1.18886	−	1.18886i	−0.111838	−	0.111838i	0.648973	−	0.760811i	$-0.275199\pi$
$113$	−1.18886	−	1.18886i	−0.111838	−	0.111838i	−0.760811	+	0.648973i	$0.775199\pi$
$114$		−	6.64399i		−	0.622267i
$115$	−5.30047	+	3.50661i	−0.494271	+	0.326993i
$116$	−1.96277			−0.182238
$117$	−0.226701	−	0.226701i	−0.0209585	−	0.0209585i
$118$	−5.17408	+	5.17408i	−0.476312	+	0.476312i
$119$	−0.220865	−	0.657151i	−0.0202467	−	0.0602409i
$120$	−0.944177	+	4.63550i	−0.0861912	+	0.423162i
$121$	1.00000			0.0909091
$122$	−5.75591	−	5.75591i	−0.521116	−	0.521116i
$123$	10.4759	+	10.4759i	0.944583	+	0.944583i
$124$	8.77551			0.788064
$125$	−6.33876	+	9.20979i	−0.566956	+	0.823748i
$126$	−1.24400	−	3.70134i	−0.110825	−	0.329741i
$127$	12.4727	−	12.4727i	1.10677	−	1.10677i	0.113197	−	0.993573i	$-0.463891\pi$
$127$	12.4727	−	12.4727i	1.10677	−	1.10677i	0.993573	−	0.113197i	$-0.0361091\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−12.3330			−1.08586
$130$	−0.475968	−	0.0969469i	−0.0417451	−	0.00850281i
$131$		−	5.36124i		−	0.468413i	−0.972187	−	0.234207i	$-0.924751\pi$
$131$		−	5.36124i		−	0.468413i	0.972187	−	0.234207i	$-0.0752492\pi$
$132$	1.49597	+	1.49597i	0.130208	+	0.130208i
$133$	7.44084	+	3.69734i	0.645202	+	0.320600i
$134$			4.12600i			0.356432i
$135$	6.01333	−	3.97821i	0.517545	−	0.342390i
$136$			0.262033i			0.0224691i
$137$	−0.417393	+	0.417393i	−0.0356603	+	0.0356603i	−0.724712	−	0.689052i	$-0.758027\pi$
$137$	−0.417393	+	0.417393i	−0.0356603	+	0.0356603i	0.689052	+	0.724712i	$0.258027\pi$
$138$	−4.25190	+	4.25190i	−0.361946	+	0.361946i
$139$	−12.4160			−1.05311			−0.526556	−	0.850140i	$-0.676517\pi$
$139$	−12.4160			−1.05311			−0.526556	+	0.850140i	$0.676517\pi$
$140$	−4.66603	−	3.63705i	−0.394352	−	0.307387i
$141$	7.71397			0.649633
$142$	7.12350	−	7.12350i	0.597791	−	0.597791i
$143$	−0.153605	+	0.153605i	−0.0128451	+	0.0128451i
$144$			1.47587i			0.122990i
$145$	−4.30058	−	0.875958i	−0.357143	−	0.0727443i
$146$		−	4.43816i		−	0.367305i
$147$	14.6708	+	2.02151i	1.21002	+	0.166731i
$148$	4.87931	+	4.87931i	0.401077	+	0.401077i
$149$			3.97559i			0.325693i	0.986651	+	0.162846i	$0.0520675\pi$
$149$			3.97559i			0.325693i	−0.986651	+	0.162846i	$0.947932\pi$
$150$	−4.13753	+	9.73538i	−0.337828	+	0.794891i
$151$	−15.5391			−1.26456			−0.632278	−	0.774741i	$-0.717880\pi$
$151$	−15.5391			−1.26456			−0.632278	+	0.774741i	$0.717880\pi$
$152$	−2.22062	−	2.22062i	−0.180116	−	0.180116i
$153$	−0.273458	+	0.273458i	−0.0221078	+	0.0221078i
$154$	−2.50789	+	0.842892i	−0.202092	+	0.0679221i
$155$	19.2278	+	3.91640i	1.54442	+	0.314573i
$156$	−0.459577			−0.0367956
$157$	−5.67596	−	5.67596i	−0.452991	−	0.452991i	0.443355	−	0.896346i	$-0.353788\pi$
$157$	−5.67596	−	5.67596i	−0.452991	−	0.452991i	−0.896346	+	0.443355i	$0.853788\pi$
$158$	7.81138	+	7.81138i	0.621440	+	0.621440i
$159$	−13.5380			−1.07363
$160$	1.23375	+	1.86490i	0.0975368	+	0.147433i
$161$	−2.39569	−	7.12801i	−0.188807	−	0.561766i
$162$	7.95454	−	7.95454i	0.624968	−	0.624968i
$163$	−5.71289	−	5.71289i	−0.447468	−	0.447468i	0.447044	−	0.894512i	$-0.352477\pi$
$163$	−5.71289	−	5.71289i	−0.447468	−	0.447468i	−0.894512	+	0.447044i	$0.852477\pi$
$164$	7.00275			0.546823
$165$	2.61016	+	3.94543i	0.203201	+	0.307151i
$166$		−	11.8938i		−	0.923140i
$167$	7.18133	+	7.18133i	0.555708	+	0.555708i	0.928083	−	0.372375i	$-0.121456\pi$
$167$	7.18133	+	7.18133i	0.555708	+	0.555708i	−0.372375	+	0.928083i	$0.621456\pi$
$168$	−5.01269	−	2.49080i	−0.386737	−	0.192169i
$169$			12.9528i			0.996370i
$170$	−0.116942	+	0.574135i	−0.00896904	+	0.0440342i
$171$		−	4.63489i		−	0.354439i
$172$	−4.12206	+	4.12206i	−0.314304	+	0.314304i
$173$	−0.964940	+	0.964940i	−0.0733630	+	0.0733630i	−0.742836	−	0.669473i	$-0.766520\pi$
$173$	−0.964940	+	0.964940i	−0.0733630	+	0.0733630i	0.669473	+	0.742836i	$0.266520\pi$
$174$	−4.15248			−0.314799
$175$	−8.60048	−	10.0515i	−0.650135	−	0.759819i
$176$	1.00000			0.0753778
$177$	−10.9464	+	10.9464i	−0.822783	+	0.822783i
$178$	−1.54039	+	1.54039i	−0.115457	+	0.115457i
$179$		−	24.4782i		−	1.82959i	−0.403922	−	0.914794i	$-0.632353\pi$
$179$		−	24.4782i		−	1.82959i	0.403922	−	0.914794i	$-0.367647\pi$
$180$	−0.658664	+	3.23376i	−0.0490939	+	0.241030i
$181$			11.0910i			0.824388i	0.911096	+	0.412194i	$0.135237\pi$
$181$			11.0910i			0.824388i	−0.911096	+	0.412194i	$0.864763\pi$
$182$	0.255752	−	0.514696i	0.0189576	−	0.0381518i
$183$	−12.1774	−	12.1774i	−0.900176	−	0.900176i
$184$			2.84223i			0.209532i
$185$	8.51339	+	12.8685i	0.625917	+	0.946114i
$186$	18.5657			1.36130
$187$	0.185285	+	0.185285i	0.0135494	+	0.0135494i
$188$	2.57824	−	2.57824i	0.188038	−	0.188038i
$189$	2.71789	+	8.08665i	0.197697	+	0.588217i
$190$	−3.87453	−	5.85660i	−0.281088	−	0.424882i
$191$	−21.1039			−1.52702			−0.763511	−	0.645795i	$-0.776526\pi$
$191$	−21.1039			−1.52702			−0.763511	+	0.645795i	$0.776526\pi$
$192$	1.49597	+	1.49597i	0.107963	+	0.107963i
$193$	4.58952	+	4.58952i	0.330361	+	0.330361i	0.852723	−	0.522363i	$-0.174949\pi$
$193$	4.58952	+	4.58952i	0.330361	+	0.330361i	−0.522363	+	0.852723i	$0.674949\pi$
$194$	17.4944			1.25602
$195$	−1.00697	−	0.205103i	−0.0721106	−	0.0146878i
$196$	5.57907	−	4.22777i	0.398505	−	0.301983i
$197$	−1.32312	+	1.32312i	−0.0942684	+	0.0942684i	−0.752668	−	0.658400i	$-0.771234\pi$
$197$	−1.32312	+	1.32312i	−0.0942684	+	0.0942684i	0.658400	+	0.752668i	$0.271234\pi$
$198$	1.04360	+	1.04360i	0.0741655	+	0.0741655i
$199$	4.68453			0.332077			0.166039	−	0.986119i	$-0.446902\pi$
$199$	4.68453			0.332077			0.166039	+	0.986119i	$0.446902\pi$
$200$	1.87097	+	4.63675i	0.132298	+	0.327868i
$201$			8.72908i			0.615702i
$202$	−10.4224	−	10.4224i	−0.733321	−	0.733321i
$203$	2.31083	−	4.65051i	0.162189	−	0.326402i
$204$			0.554364i			0.0388132i
$205$	15.3436	+	3.12524i	1.07164	+	0.218276i
$206$		−	7.33300i		−	0.510914i
$207$	−2.96615	+	2.96615i	−0.206162	+	0.206162i
$208$	−0.153605	+	0.153605i	−0.0106506	+	0.0106506i
$209$	−3.14044			−0.217229
$210$	−9.87158	−	7.69464i	−0.681204	−	0.530981i
$211$	11.0663			0.761837			0.380919	−	0.924609i	$-0.375608\pi$
$211$	11.0663			0.761837			0.380919	+	0.924609i	$0.375608\pi$
$212$	−4.52481	+	4.52481i	−0.310765	+	0.310765i
$213$	15.0707	−	15.0707i	1.03263	−	1.03263i
$214$			3.38301i			0.231258i
$215$	−10.8714	+	7.19214i	−0.741423	+	0.490500i
$216$		−	3.22448i		−	0.219398i
$217$	−10.3317	+	20.7924i	−0.701363	+	1.41148i
$218$	6.02682	+	6.02682i	0.408188	+	0.408188i
$219$		−	9.38949i		−	0.634483i
$220$	2.19108	+	0.446287i	0.147723	+	0.0300887i
$221$	−0.0569214			−0.00382895
$222$	10.3228	+	10.3228i	0.692821	+	0.692821i
$223$	−3.68907	+	3.68907i	−0.247038	+	0.247038i	−0.819754	−	0.572716i	$-0.805890\pi$
$223$	−3.68907	+	3.68907i	−0.247038	+	0.247038i	0.572716	+	0.819754i	$0.305890\pi$
$224$	−2.50789	+	0.842892i	−0.167566	+	0.0563181i
$225$	−2.88637	+	6.79147i	−0.192425	+	0.452765i
$226$	−1.68130			−0.111838
$227$	2.49164	+	2.49164i	0.165376	+	0.165376i	0.784943	−	0.619567i	$-0.212692\pi$
$227$	2.49164	+	2.49164i	0.165376	+	0.165376i	−0.619567	+	0.784943i	$0.712692\pi$
$228$	−4.69801	−	4.69801i	−0.311133	−	0.311133i
$229$	15.3573			1.01484			0.507420	−	0.861699i	$-0.330599\pi$
$229$	15.3573			1.01484			0.507420	+	0.861699i	$0.330599\pi$
$230$	−1.26845	+	6.22755i	−0.0836391	+	0.410632i
$231$	−5.30577	+	1.78324i	−0.349094	+	0.117329i
$232$	−1.38789	+	1.38789i	−0.0911191	+	0.0911191i
$233$	19.9984	+	19.9984i	1.31014	+	1.31014i	0.921309	+	0.388831i	$0.127121\pi$
$233$	19.9984	+	19.9984i	1.31014	+	1.31014i	0.388831	+	0.921309i	$0.372879\pi$
$234$	−0.320604			−0.0209585
$235$	6.79977	−	4.49850i	0.443568	−	0.293450i
$236$			7.31725i			0.476312i
$237$	16.5260	+	16.5260i	1.07348	+	1.07348i
$238$	−0.620852	−	0.308501i	−0.0402438	−	0.0199971i
$239$		−	5.63084i		−	0.364229i	−0.983277	−	0.182114i	$-0.941706\pi$
$239$		−	5.63084i		−	0.364229i	0.983277	−	0.182114i	$-0.0582941\pi$
$240$	2.61016	+	3.94543i	0.168485	+	0.254676i
$241$		−	0.733892i		−	0.0472742i	−0.999721	−	0.0236371i	$-0.992475\pi$
$241$		−	0.733892i		−	0.0472742i	0.999721	−	0.0236371i	$-0.00752462\pi$
$242$	0.707107	−	0.707107i	0.0454545	−	0.0454545i
$243$	9.98868	−	9.98868i	0.640774	−	0.640774i
$244$	−8.14009			−0.521116
$245$	14.1110	−	6.77350i	0.901517	−	0.432743i
$246$	14.8152			0.944583
$247$	0.482386	−	0.482386i	0.0306935	−	0.0306935i
$248$	6.20523	−	6.20523i	0.394032	−	0.394032i
$249$		−	25.1629i		−	1.59463i
$250$	2.03012	+	10.9945i	0.128396	+	0.695352i
$251$			27.3956i			1.72919i	0.502467	+	0.864597i	$0.332426\pi$
$251$			27.3956i			1.72919i	−0.502467	+	0.864597i	$0.667574\pi$
$252$	−3.49688	−	1.73760i	−0.220283	−	0.109458i
$253$	2.00976	+	2.00976i	0.126352	+	0.126352i
$254$		−	17.6390i		−	1.10677i
$255$	−0.247406	+	1.21466i	−0.0154931	+	0.0760647i
$256$	1.00000			0.0625000
$257$	10.4532	+	10.4532i	0.652050	+	0.652050i	0.953486	−	0.301436i	$-0.0974660\pi$
$257$	10.4532	+	10.4532i	0.652050	+	0.652050i	−0.301436	+	0.953486i	$0.597466\pi$
$258$	−8.72075	+	8.72075i	−0.542930	+	0.542930i
$259$	−17.3055	+	5.81628i	−1.07531	+	0.361406i
$260$	−0.405112	+	0.268008i	−0.0251240	+	0.0166212i
$261$	−2.89680			−0.179307
$262$	−3.79097	−	3.79097i	−0.234207	−	0.234207i
$263$	−12.5045	−	12.5045i	−0.771060	−	0.771060i	0.207232	−	0.978292i	$-0.433555\pi$
$263$	−12.5045	−	12.5045i	−0.771060	−	0.771060i	−0.978292	+	0.207232i	$0.933555\pi$
$264$	2.11563			0.130208
$265$	−11.9336	+	7.89485i	−0.733074	+	0.484977i
$266$	7.87588	−	2.64705i	0.482901	−	0.162301i
$267$	−3.25890	+	3.25890i	−0.199441	+	0.199441i
$268$	2.91752	+	2.91752i	0.178216	+	0.178216i
$269$	−31.9774			−1.94970			−0.974849	−	0.222868i	$-0.928458\pi$
$269$	−31.9774			−1.94970			−0.974849	+	0.222868i	$0.928458\pi$
$270$	1.43904	−	7.06509i	0.0875774	−	0.429968i
$271$		−	22.9881i		−	1.39643i	−0.715890	−	0.698213i	$-0.753979\pi$
$271$		−	22.9881i		−	1.39643i	0.715890	−	0.698213i	$-0.246021\pi$
$272$	0.185285	+	0.185285i	0.0112346	+	0.0112346i
$273$	0.541076	−	1.08891i	0.0327474	−	0.0659036i
$274$			0.590283i			0.0356603i
$275$	4.60166	+	1.95570i	0.277490	+	0.117933i
$276$			6.01309i			0.361946i
$277$	−11.8887	+	11.8887i	−0.714325	+	0.714325i	−0.967437	−	0.253112i	$-0.918546\pi$
$277$	−11.8887	+	11.8887i	−0.714325	+	0.714325i	0.253112	+	0.967437i	$0.418546\pi$
$278$	−8.77945	+	8.77945i	−0.526556	+	0.526556i
$279$	12.9516			0.775390
$280$	−5.87117	+	0.727601i	−0.350869	+	0.0434825i
$281$	−24.4432			−1.45816			−0.729078	−	0.684430i	$-0.760051\pi$
$281$	−24.4432			−1.45816			−0.729078	+	0.684430i	$0.760051\pi$
$282$	5.45460	−	5.45460i	0.324817	−	0.324817i
$283$	13.4434	−	13.4434i	0.799126	−	0.799126i	−0.183832	−	0.982958i	$-0.558850\pi$
$283$	13.4434	−	13.4434i	0.799126	−	0.799126i	0.982958	+	0.183832i	$0.0588502\pi$
$284$		−	10.0742i		−	0.597791i
$285$	−8.19705	−	12.3904i	−0.485551	−	0.733943i
$286$			0.217230i			0.0128451i
$287$	−8.24458	+	16.5921i	−0.486662	+	0.979398i
$288$	1.04360	+	1.04360i	0.0614948	+	0.0614948i
$289$		−	16.9313i		−	0.995961i
$290$	−3.66036	+	2.42157i	−0.214944	+	0.142200i
$291$	37.0116			2.16966
$292$	−3.13825	−	3.13825i	−0.183652	−	0.183652i
$293$	−1.71069	+	1.71069i	−0.0999397	+	0.0999397i	−0.755309	−	0.655369i	$-0.772513\pi$
$293$	−1.71069	+	1.71069i	−0.0999397	+	0.0999397i	0.655369	+	0.755309i	$0.272513\pi$
$294$	11.8032	−	8.94437i	0.688378	−	0.521646i
$295$	−3.26560	+	16.0327i	−0.190130	+	0.933458i
$296$	6.90039			0.401077
$297$	−2.28005	−	2.28005i	−0.132302	−	0.132302i
$298$	2.81117	+	2.81117i	0.162846	+	0.162846i
$299$	−0.617417			−0.0357061
$300$	3.95828	+	9.80963i	0.228531	+	0.566359i
$301$	−4.91362	−	14.6197i	−0.283216	−	0.842666i
$302$	−10.9878	+	10.9878i	−0.632278	+	0.632278i
$303$	−22.0500	−	22.0500i	−1.26674	−	1.26674i
$304$	−3.14044			−0.180116
$305$	−17.8356	−	3.63282i	−1.02126	−	0.208015i
$306$			0.386728i			0.0221078i
$307$	−5.76020	−	5.76020i	−0.328752	−	0.328752i	0.523360	−	0.852112i	$-0.324678\pi$
$307$	−5.76020	−	5.76020i	−0.328752	−	0.328752i	−0.852112	+	0.523360i	$0.824678\pi$
$308$	−1.17733	+	2.36936i	−0.0670849	+	0.135007i
$309$		−	15.5139i		−	0.882554i
$310$	16.3655	−	10.8268i	0.929495	−	0.614922i
$311$		−	8.22772i		−	0.466551i	−0.972411	−	0.233276i	$-0.925056\pi$
$311$		−	8.22772i		−	0.466551i	0.972411	−	0.233276i	$-0.0749444\pi$
$312$	−0.324970	+	0.324970i	−0.0183978	+	0.0183978i
$313$	−18.7486	+	18.7486i	−1.05974	+	1.05974i	−0.0616377	+	0.998099i	$0.519632\pi$
$313$	−18.7486	+	18.7486i	−1.05974	+	1.05974i	−0.998099	+	0.0616377i	$0.980368\pi$
$314$	−8.02702			−0.452991
$315$	−6.88648	−	5.36783i	−0.388009	−	0.302443i
$316$	11.0470			0.621440
$317$	−4.09250	+	4.09250i	−0.229858	+	0.229858i	−0.812633	−	0.582776i	$-0.801967\pi$
$317$	−4.09250	+	4.09250i	−0.229858	+	0.229858i	0.582776	+	0.812633i	$0.301967\pi$
$318$	−9.57280	+	9.57280i	−0.536816	+	0.536816i
$319$			1.96277i			0.109894i
$320$	2.19108	+	0.446287i	0.122485	+	0.0249482i
$321$			7.15718i			0.399475i
$322$	−6.73427	−	3.34625i	−0.375286	−	0.186479i
$323$	−0.581877	−	0.581877i	−0.0323765	−	0.0323765i
$324$		−	11.2494i		−	0.624968i
$325$	−1.00724	+	0.406431i	−0.0558717	+	0.0225447i
$326$	−8.07924			−0.447468
$327$	12.7505	+	12.7505i	0.705104	+	0.705104i
$328$	4.95169	−	4.95169i	0.273411	−	0.273411i
$329$	3.07334	+	9.14425i	0.169439	+	0.504139i
$330$	4.63550	+	0.944177i	0.255176	+	0.0519752i
$331$	−19.2530			−1.05824			−0.529121	−	0.848547i	$-0.677478\pi$
$331$	−19.2530			−1.05824			−0.529121	+	0.848547i	$0.677478\pi$
$332$	−8.41021	−	8.41021i	−0.461570	−	0.461570i
$333$	7.20126	+	7.20126i	0.394626	+	0.394626i
$334$	10.1559			0.555708
$335$	5.09047	+	7.69458i	0.278122	+	0.420400i
$336$	−5.30577	+	1.78324i	−0.289453	+	0.0972839i
$337$	−22.2127	+	22.2127i	−1.21000	+	1.21000i	−0.238975	+	0.971026i	$0.576811\pi$
$337$	−22.2127	+	22.2127i	−1.21000	+	1.21000i	−0.971026	+	0.238975i	$0.923189\pi$
$338$	9.15902	+	9.15902i	0.498185	+	0.498185i
$339$	−3.55700			−0.193190
$340$	0.323284	+	0.488665i	0.0175326	+	0.0265016i
$341$		−	8.77551i		−	0.475221i
$342$	−3.27736	−	3.27736i	−0.177220	−	0.177220i
$343$	3.44869	+	18.1963i	0.186212	+	0.982510i
$344$			5.82948i			0.314304i
$345$	−2.68357	+	13.1752i	−0.144478	+	0.709327i
$346$			1.36463i			0.0733630i
$347$	21.7616	−	21.7616i	1.16822	−	1.16822i	0.185597	−	0.982626i	$-0.440578\pi$
$347$	21.7616	−	21.7616i	1.16822	−	1.16822i	0.982626	−	0.185597i	$-0.0594218\pi$
$348$	−2.93625	+	2.93625i	−0.157399	+	0.157399i
$349$	−12.1689			−0.651387			−0.325694	−	0.945475i	$-0.605598\pi$
$349$	−12.1689			−0.651387			−0.325694	+	0.945475i	$0.605598\pi$
$350$	−13.1889	−	1.02600i	−0.704977	−	0.0548418i
$351$	0.700453			0.0373874
$352$	0.707107	−	0.707107i	0.0376889	−	0.0376889i
$353$	9.63724	−	9.63724i	0.512939	−	0.512939i	−0.402487	−	0.915426i	$-0.631854\pi$
$353$	9.63724	−	9.63724i	0.512939	−	0.512939i	0.915426	+	0.402487i	$0.131854\pi$
$354$			15.4806i			0.822783i
$355$	4.49597	−	22.0733i	0.238621	−	1.17153i
$356$			2.17845i			0.115457i
$357$	−1.31349	−	0.652672i	−0.0695173	−	0.0345431i
$358$	−17.3087	−	17.3087i	−0.914794	−	0.914794i
$359$		−	33.2168i		−	1.75311i	−0.481298	−	0.876557i	$-0.659834\pi$
$359$		−	33.2168i		−	1.75311i	0.481298	−	0.876557i	$-0.340166\pi$
$360$	1.82087	+	2.75236i	0.0959681	+	0.145062i
$361$	−9.13766			−0.480929
$362$	7.84253	+	7.84253i	0.412194	+	0.412194i
$363$	1.49597	−	1.49597i	0.0785183	−	0.0785183i
$364$	−0.183101	−	0.544789i	−0.00959711	−	0.0285547i
$365$	−5.47560	−	8.27672i	−0.286606	−	0.433223i
$366$	−17.2214			−0.900176
$367$	−11.7615	−	11.7615i	−0.613946	−	0.613946i	0.330026	−	0.943972i	$-0.392942\pi$
$367$	−11.7615	−	11.7615i	−0.613946	−	0.613946i	−0.943972	+	0.330026i	$0.892942\pi$
$368$	2.00976	+	2.00976i	0.104766	+	0.104766i
$369$	10.3352			0.538028
$370$	15.1193	+	3.07956i	0.786015	+	0.160099i
$371$	−5.39370	−	16.0481i	−0.280027	−	0.833177i
$372$	13.1279	−	13.1279i	0.680652	−	0.680652i
$373$	1.70485	+	1.70485i	0.0882735	+	0.0882735i	0.749865	−	0.661591i	$-0.230119\pi$
$373$	1.70485	+	1.70485i	0.0882735	+	0.0882735i	−0.661591	+	0.749865i	$0.730119\pi$
$374$	0.262033			0.0135494
$375$	4.29499	+	23.2602i	0.221792	+	1.20115i
$376$		−	3.64619i		−	0.188038i
$377$	−0.301490	−	0.301490i	−0.0155275	−	0.0155275i
$378$	7.63996	+	3.79629i	0.392957	+	0.195260i
$379$			16.5169i			0.848417i	0.905565	+	0.424209i	$0.139448\pi$
$379$			16.5169i			0.848417i	−0.905565	+	0.424209i	$0.860552\pi$
$380$	−6.88095	−	1.40154i	−0.352985	−	0.0718973i
$381$		−	37.3175i		−	1.91184i
$382$	−14.9227	+	14.9227i	−0.763511	+	0.763511i
$383$	13.9765	−	13.9765i	0.714165	−	0.714165i	−0.253239	−	0.967404i	$-0.581496\pi$
$383$	13.9765	−	13.9765i	0.714165	−	0.714165i	0.967404	+	0.253239i	$0.0814958\pi$
$384$	2.11563			0.107963
$385$	−3.63705	+	4.66603i	−0.185361	+	0.237803i
$386$	6.49056			0.330361
$387$	−6.08365	+	6.08365i	−0.309249	+	0.309249i
$388$	12.3704	−	12.3704i	0.628012	−	0.628012i
$389$		−	31.0719i		−	1.57541i	−0.616054	−	0.787704i	$-0.711270\pi$
$389$		−	31.0719i		−	1.57541i	0.616054	−	0.787704i	$-0.288730\pi$
$390$	−0.857065	+	0.567005i	−0.0433992	+	0.0287114i
$391$			0.744758i			0.0376640i
$392$	0.955514	−	6.93448i	0.0482607	−	0.350244i
$393$	−8.02027	−	8.02027i	−0.404569	−	0.404569i
$394$			1.87117i			0.0942684i
$395$	24.2048	+	4.93012i	1.21787	+	0.248061i
$396$	1.47587			0.0741655
$397$	−11.7917	−	11.7917i	−0.591808	−	0.591808i	0.346312	−	0.938120i	$-0.387434\pi$
$397$	−11.7917	−	11.7917i	−0.591808	−	0.591808i	−0.938120	+	0.346312i	$0.887434\pi$
$398$	3.31246	−	3.31246i	0.166039	−	0.166039i
$399$	16.6624	−	5.60016i	0.834165	−	0.280359i
$400$	4.60166	+	1.95570i	0.230083	+	0.0977851i
$401$	35.2263			1.75912			0.879559	−	0.475789i	$-0.157837\pi$
$401$	35.2263			1.75912			0.879559	+	0.475789i	$0.157837\pi$
$402$	6.17239	+	6.17239i	0.307851	+	0.307851i
$403$	1.34796	+	1.34796i	0.0671467	+	0.0671467i
$404$	−14.7396			−0.733321
$405$	5.02047	−	24.6484i	0.249469	−	1.22479i
$406$	−1.65440	−	4.92241i	−0.0821065	−	0.244295i
$407$	4.87931	−	4.87931i	0.241859	−	0.241859i
$408$	0.391995	+	0.391995i	0.0194066	+	0.0194066i
$409$	−3.32979			−0.164647			−0.0823237	−	0.996606i	$-0.526234\pi$
$409$	−3.32979			−0.164647			−0.0823237	+	0.996606i	$0.526234\pi$
$410$	13.0594	−	8.63967i	0.644959	−	0.426683i
$411$			1.24882i			0.0615997i
$412$	−5.18522	−	5.18522i	−0.255457	−	0.255457i
$413$	−17.3372	−	8.61485i	−0.853109	−	0.423909i
$414$			4.19477i			0.206162i
$415$	−14.6741	−	22.1808i	−0.720322	−	1.08881i
$416$			0.217230i			0.0106506i
$417$	−18.5740	+	18.5740i	−0.909574	+	0.909574i
$418$	−2.22062	+	2.22062i	−0.108614	+	0.108614i
$419$	23.6712			1.15641			0.578207	−	0.815890i	$-0.303752\pi$
$419$	23.6712			1.15641			0.578207	+	0.815890i	$0.303752\pi$
$420$	−12.4212	+	1.53933i	−0.606092	+	0.0751117i
$421$	−37.6425			−1.83458			−0.917292	−	0.398214i	$-0.869630\pi$
$421$	−37.6425			−1.83458			−0.917292	+	0.398214i	$0.869630\pi$
$422$	7.82507	−	7.82507i	0.380919	−	0.380919i
$423$	3.80517	−	3.80517i	0.185013	−	0.185013i
$424$			6.39905i			0.310765i
$425$	0.490256	+	1.21498i	0.0237809	+	0.0589353i
$426$		−	21.3131i		−	1.03263i
$427$	9.58361	−	19.2868i	0.463783	−	0.933355i
$428$	2.39215	+	2.39215i	0.115629	+	0.115629i
$429$			0.459577i			0.0221886i
$430$	−2.60162	+	12.7728i	−0.125461	+	0.615961i
$431$	−19.4858			−0.938598			−0.469299	−	0.883039i	$-0.655493\pi$
$431$	−19.4858			−0.938598			−0.469299	+	0.883039i	$0.655493\pi$
$432$	−2.28005	−	2.28005i	−0.109699	−	0.109699i
$433$	−14.3376	+	14.3376i	−0.689020	+	0.689020i	−0.962015	−	0.272996i	$-0.911986\pi$
$433$	−14.3376	+	14.3376i	−0.689020	+	0.689020i	0.272996	+	0.962015i	$0.411986\pi$
$434$	7.39681	+	22.0081i	0.355058	+	1.05642i
$435$	−7.74396	+	5.12314i	−0.371294	+	0.245636i
$436$	8.52321			0.408188
$437$	−6.31152	−	6.31152i	−0.301921	−	0.301921i
$438$	−6.63937	−	6.63937i	−0.317241	−	0.317241i
$439$	2.51820			0.120187			0.0600935	−	0.998193i	$-0.480860\pi$
$439$	2.51820			0.120187			0.0600935	+	0.998193i	$0.480860\pi$
$440$	1.86490	−	1.23375i	0.0889056	−	0.0588169i
$441$	8.23401	−	6.23965i	0.392096	−	0.297126i
$442$	−0.0402495	+	0.0402495i	−0.00191447	+	0.00191447i
$443$	4.33639	+	4.33639i	0.206028	+	0.206028i	0.802577	−	0.596549i	$-0.203462\pi$
$443$	4.33639	+	4.33639i	0.206028	+	0.206028i	−0.596549	+	0.802577i	$0.703462\pi$
$444$	14.5987			0.692821
$445$	−0.972212	+	4.77315i	−0.0460873	+	0.226269i
$446$			5.21713i			0.247038i
$447$	5.94738	+	5.94738i	0.281301	+	0.281301i
$448$	−1.17733	+	2.36936i	−0.0556238	+	0.111942i
$449$			21.7107i			1.02459i	0.858808	+	0.512297i	$0.171205\pi$
$449$			21.7107i			1.02459i	−0.858808	+	0.512297i	$0.828795\pi$
$450$	2.76132	+	6.84327i	0.130170	+	0.322595i
$451$		−	7.00275i		−	0.329747i
$452$	−1.18886	+	1.18886i	−0.0559191	+	0.0559191i
$453$	−23.2461	+	23.2461i	−1.09220	+	1.09220i
$454$	3.52371			0.165376
$455$	−0.158057	−	1.27539i	−0.00740981	−	0.0597913i
$456$	−6.64399			−0.311133
$457$	10.7185	−	10.7185i	0.501389	−	0.501389i	−0.410481	−	0.911869i	$-0.634639\pi$
$457$	10.7185	−	10.7185i	0.501389	−	0.501389i	0.911869	+	0.410481i	$0.134639\pi$
$458$	10.8593	−	10.8593i	0.507420	−	0.507420i
$459$		−	0.844920i		−	0.0394375i
$460$	3.50661	+	5.30047i	0.163497	+	0.247136i
$461$			21.7792i			1.01436i	0.861841	+	0.507178i	$0.169311\pi$
$461$			21.7792i			1.01436i	−0.861841	+	0.507178i	$0.830689\pi$
$462$	−2.49080	+	5.01269i	−0.115883	+	0.233211i
$463$	−6.85868	−	6.85868i	−0.318750	−	0.318750i	0.529537	−	0.848287i	$-0.322366\pi$
$463$	−6.85868	−	6.85868i	−0.318750	−	0.318750i	−0.848287	+	0.529537i	$0.822366\pi$
$464$			1.96277i			0.0911191i
$465$	34.6232	−	22.9055i	1.60561	−	1.06222i
$466$	28.2820			1.31014
$467$	−4.23119	−	4.23119i	−0.195796	−	0.195796i	0.602399	−	0.798195i	$-0.294212\pi$
$467$	−4.23119	−	4.23119i	−0.195796	−	0.195796i	−0.798195	+	0.602399i	$0.794212\pi$
$468$	−0.226701	+	0.226701i	−0.0104793	+	0.0104793i
$469$	−10.3476	+	3.47777i	−0.477807	+	0.160589i
$470$	1.62725	−	7.98908i	0.0750593	−	0.368509i
$471$	−16.9822			−0.782497
$472$	5.17408	+	5.17408i	0.238156	+	0.238156i
$473$	4.12206	+	4.12206i	0.189533	+	0.189533i
$474$	23.3712			1.07348
$475$	−14.4512	−	6.14176i	−0.663067	−	0.281803i
$476$	−0.657151	+	0.220865i	−0.0301205	+	0.0101234i
$477$	−6.67805	+	6.67805i	−0.305767	+	0.305767i
$478$	−3.98160	−	3.98160i	−0.182114	−	0.182114i
$479$	−36.2242			−1.65512			−0.827562	−	0.561374i	$-0.810273\pi$
$479$	−36.2242			−1.65512			−0.827562	+	0.561374i	$0.810273\pi$
$480$	4.63550	+	0.944177i	0.211581	+	0.0430956i
$481$			1.49897i			0.0683472i
$482$	−0.518940	−	0.518940i	−0.0236371	−	0.0236371i
$483$	−14.2472	−	7.07942i	−0.648270	−	0.322125i
$484$		−	1.00000i		−	0.0454545i
$485$	32.6253	−	21.5838i	1.48144	−	0.980068i
$486$		−	14.1261i		−	0.640774i
$487$	−8.78548	+	8.78548i	−0.398108	+	0.398108i	−0.877565	−	0.479457i	$-0.840834\pi$
$487$	−8.78548	+	8.78548i	−0.398108	+	0.398108i	0.479457	+	0.877565i	$0.340834\pi$
$488$	−5.75591	+	5.75591i	−0.260558	+	0.260558i
$489$	−17.0927			−0.772957
$490$	5.18838	−	14.7676i	0.234387	−	0.667130i
$491$	−33.3733			−1.50612			−0.753058	−	0.657954i	$-0.771422\pi$
$491$	−33.3733			−1.50612			−0.753058	+	0.657954i	$0.771422\pi$
$492$	10.4759	−	10.4759i	0.472291	−	0.472291i
$493$	−0.363672	+	0.363672i	−0.0163790	+	0.0163790i
$494$		−	0.682197i		−	0.0306935i
$495$	3.23376	+	0.658664i	0.145347	+	0.0296048i
$496$		−	8.77551i		−	0.394032i
$497$	23.8693	+	11.8606i	1.07069	+	0.532023i
$498$	−17.7929	−	17.7929i	−0.797317	−	0.797317i
$499$			6.48509i			0.290312i	0.989409	+	0.145156i	$0.0463685\pi$
$499$			6.48509i			0.290312i	−0.989409	+	0.145156i	$0.953632\pi$
$500$	9.20979	+	6.33876i	0.411874	+	0.283478i
$501$	21.4862			0.959931
$502$	19.3716	+	19.3716i	0.864597	+	0.864597i
$503$	28.6233	−	28.6233i	1.27625	−	1.27625i	0.333501	−	0.942750i	$-0.391770\pi$
$503$	28.6233	−	28.6233i	1.27625	−	1.27625i	0.942750	−	0.333501i	$-0.108230\pi$
$504$	−3.70134	+	1.24400i	−0.164871	+	0.0554123i
$505$	−32.2955	−	6.57808i	−1.43713	−	0.292721i
$506$	2.84223			0.126352
$507$	19.3771	+	19.3771i	0.860566	+	0.860566i
$508$	−12.4727	−	12.4727i	−0.553385	−	0.553385i
$509$	−21.0914			−0.934858			−0.467429	−	0.884031i	$-0.654820\pi$
$509$	−21.0914			−0.934858			−0.467429	+	0.884031i	$0.654820\pi$
$510$	0.683949	+	1.03383i	0.0302858	+	0.0457789i
$511$	11.1304	−	3.74089i	0.492381	−	0.165487i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	7.16036	+	7.16036i	0.316137	+	0.316137i
$514$	14.7830			0.652050
$515$	−9.04712	−	13.6753i	−0.398664	−	0.602606i
$516$			12.3330i			0.542930i
$517$	−2.57824	−	2.57824i	−0.113391	−	0.113391i
$518$	−8.12407	+	16.3495i	−0.356951	+	0.718357i
$519$			2.88705i			0.126727i
$520$	−0.0969469	+	0.475968i	−0.00425140	+	0.0208726i
$521$			22.9440i			1.00519i	0.864521	+	0.502597i	$0.167622\pi$
$521$			22.9440i			1.00519i	−0.864521	+	0.502597i	$0.832378\pi$
$522$	−2.04835	+	2.04835i	−0.0896536	+	0.0896536i
$523$	−31.5116	+	31.5116i	−1.37791	+	1.37791i	−0.529757	+	0.848149i	$0.677717\pi$
$523$	−31.5116	+	31.5116i	−1.37791	+	1.37791i	−0.848149	+	0.529757i	$0.822283\pi$
$524$	−5.36124			−0.234207
$525$	−27.9028	−	2.17062i	−1.21778	−	0.0947337i
$526$	−17.6840			−0.771060
$527$	1.62597	−	1.62597i	0.0708285	−	0.0708285i
$528$	1.49597	−	1.49597i	0.0651039	−	0.0651039i
$529$		−	14.9217i		−	0.648771i
$530$	−2.85581	+	14.0208i	−0.124049	+	0.609025i
$531$			10.7993i			0.468652i
$532$	3.69734	−	7.44084i	0.160300	−	0.322601i
$533$	1.07566	+	1.07566i	0.0465918	+	0.0465918i
$534$			4.60878i			0.199441i
$535$	4.17380	+	6.30897i	0.180449	+	0.272761i
$536$	4.12600			0.178216
$537$	−36.6188	−	36.6188i	−1.58022	−	1.58022i
$538$	−22.6114	+	22.6114i	−0.974849	+	0.974849i
$539$	−4.22777	−	5.57907i	−0.182103	−	0.240307i
$540$	−3.97821	−	6.01333i	−0.171195	−	0.258773i
$541$	−5.16536			−0.222076			−0.111038	−	0.993816i	$-0.535418\pi$
$541$	−5.16536			−0.222076			−0.111038	+	0.993816i	$0.535418\pi$
$542$	−16.2550	−	16.2550i	−0.698213	−	0.698213i
$543$	16.5919	+	16.5919i	0.712025	+	0.712025i
$544$	0.262033			0.0112346
$545$	18.6750	+	3.80380i	0.799950	+	0.162937i
$546$	−0.387374	−	1.15257i	−0.0165781	−	0.0493255i
$547$	31.4944	−	31.4944i	1.34660	−	1.34660i	0.457279	−	0.889323i	$-0.348824\pi$
$547$	31.4944	−	31.4944i	1.34660	−	1.34660i	0.889323	−	0.457279i	$-0.151176\pi$
$548$	0.417393	+	0.417393i	0.0178302	+	0.0178302i
$549$	−12.0138			−0.512735
$550$	4.63675	−	1.87097i	0.197712	−	0.0797785i
$551$		−	6.16394i		−	0.262593i
$552$	4.25190	+	4.25190i	0.180973	+	0.180973i
$553$	−13.0060	+	26.1743i	−0.553070	+	1.11304i
$554$			16.8132i			0.714325i
$555$	31.9868	+	6.51519i	1.35776	+	0.276555i
$556$			12.4160i			0.526556i
$557$	3.98735	−	3.98735i	0.168950	−	0.168950i	−0.617568	−	0.786518i	$-0.711882\pi$
$557$	3.98735	−	3.98735i	0.168950	−	0.168950i	0.786518	+	0.617568i	$0.211882\pi$
$558$	9.15814	−	9.15814i	0.387695	−	0.387695i
$559$	−1.26634			−0.0535603
$560$	−3.63705	+	4.66603i	−0.153693	+	0.197176i
$561$	0.554364			0.0234053
$562$	−17.2839	+	17.2839i	−0.729078	+	0.729078i
$563$	13.3351	−	13.3351i	0.562005	−	0.562005i	−0.367871	−	0.929877i	$-0.619913\pi$
$563$	13.3351	−	13.3351i	0.562005	−	0.562005i	0.929877	+	0.367871i	$0.119913\pi$
$564$		−	7.71397i		−	0.324817i
$565$	−3.13545	+	2.07431i	−0.131909	+	0.0872668i
$566$		−	19.0118i		−	0.799126i
$567$	26.6540	+	13.2443i	1.11936	+	0.556210i
$568$	−7.12350	−	7.12350i	−0.298895	−	0.298895i
$569$		−	38.9011i		−	1.63082i	−0.578884	−	0.815410i	$-0.696512\pi$
$569$		−	38.9011i		−	1.63082i	0.578884	−	0.815410i	$-0.303488\pi$
$570$	−14.5575	−	2.96513i	−0.609747	−	0.124196i
$571$	−19.4425			−0.813643			−0.406822	−	0.913508i	$-0.633363\pi$
$571$	−19.4425			−0.813643			−0.406822	+	0.913508i	$0.633363\pi$
$572$	0.153605	+	0.153605i	0.00642253	+	0.00642253i
$573$	−31.5708	+	31.5708i	−1.31889	+	1.31889i
$574$	5.90256	+	17.5622i	0.246368	+	0.733030i
$575$	5.31773	+	13.1787i	0.221765	+	0.549590i
$576$	1.47587			0.0614948
$577$	21.7123	+	21.7123i	0.903893	+	0.903893i	0.995770	−	0.0918772i	$-0.0292867\pi$
$577$	21.7123	+	21.7123i	0.903893	+	0.903893i	−0.0918772	+	0.995770i	$0.529287\pi$
$578$	−11.9723	−	11.9723i	−0.497981	−	0.497981i
$579$	13.7316			0.570665
$580$	−0.875958	+	4.30058i	−0.0363722	+	0.178572i
$581$	29.8285	−	10.0252i	1.23749	−	0.415916i
$582$	26.1711	−	26.1711i	1.08483	−	1.08483i
$583$	4.52481	+	4.52481i	0.187398	+	0.187398i
$584$	−4.43816			−0.183652
$585$	−0.597894	+	0.395547i	−0.0247199	+	0.0163538i
$586$			2.41928i			0.0999397i
$587$	13.4278	+	13.4278i	0.554226	+	0.554226i	0.927658	−	0.373431i	$-0.121819\pi$
$587$	13.4278	+	13.4278i	0.554226	+	0.554226i	−0.373431	+	0.927658i	$0.621819\pi$
$588$	2.02151	−	14.6708i	0.0833657	−	0.605012i
$589$			27.5589i			1.13555i
$590$	9.02769	+	13.6459i	0.371664	+	0.561794i
$591$			3.95870i			0.162839i
$592$	4.87931	−	4.87931i	0.200539	−	0.200539i
$593$	−21.2080	+	21.2080i	−0.870909	+	0.870909i	−0.992572	−	0.121662i	$-0.961177\pi$
$593$	−21.2080	+	21.2080i	−0.870909	+	0.870909i	0.121662	+	0.992572i	$0.461177\pi$
$594$	−3.22448			−0.132302
$595$	−1.53844	+	0.190656i	−0.0630699	+	0.00781611i
$596$	3.97559			0.162846
$597$	7.00793	−	7.00793i	0.286816	−	0.286816i
$598$	−0.436580	+	0.436580i	−0.0178531	+	0.0178531i
$599$			11.4227i			0.466721i	0.972390	+	0.233360i	$0.0749722\pi$
$599$			11.4227i			0.466721i	−0.972390	+	0.233360i	$0.925028\pi$
$600$	9.73538	+	4.13753i	0.397445	+	0.168914i
$601$		−	5.17383i		−	0.211045i	−0.994417	−	0.105522i	$-0.966349\pi$
$601$		−	5.17383i		−	0.211045i	0.994417	−	0.105522i	$-0.0336515\pi$
$602$	−13.8122	−	6.86325i	−0.562941	−	0.279725i
$603$	4.30590	+	4.30590i	0.175350	+	0.175350i
$604$			15.5391i			0.632278i
$605$	0.446287	−	2.19108i	0.0181442	−	0.0890800i
$606$	−31.1834			−1.26674
$607$	8.01010	+	8.01010i	0.325120	+	0.325120i	0.850727	−	0.525607i	$-0.176162\pi$
$607$	8.01010	+	8.01010i	0.325120	+	0.325120i	−0.525607	+	0.850727i	$0.676162\pi$
$608$	−2.22062	+	2.22062i	−0.0900582	+	0.0900582i
$609$	−3.50009	−	10.4140i	−0.141831	−	0.421996i
$610$	−15.1805	+	10.0429i	−0.614639	+	0.406624i
$611$	0.792061			0.0320433
$612$	0.273458	+	0.273458i	0.0110539	+	0.0110539i
$613$	−23.9273	−	23.9273i	−0.966415	−	0.966415i	0.0330392	−	0.999454i	$-0.489481\pi$
$613$	−23.9273	−	23.9273i	−0.966415	−	0.966415i	−0.999454	+	0.0330392i	$0.989481\pi$
$614$	−8.14615			−0.328752
$615$	27.6289	−	18.2783i	1.11410	−	0.737053i
$616$	0.842892	+	2.50789i	0.0339611	+	0.101046i
$617$	27.4224	−	27.4224i	1.10398	−	1.10398i	0.110059	−	0.993925i	$-0.464896\pi$
$617$	27.4224	−	27.4224i	1.10398	−	1.10398i	0.993925	−	0.110059i	$-0.0351039\pi$
$618$	−10.9700	−	10.9700i	−0.441277	−	0.441277i
$619$	22.2558			0.894535			0.447268	−	0.894400i	$-0.352397\pi$
$619$	22.2558			0.894535			0.447268	+	0.894400i	$0.352397\pi$
$620$	3.91640	−	19.2278i	0.157286	−	0.772209i
$621$		−	9.16471i		−	0.367767i
$622$	−5.81788	−	5.81788i	−0.233276	−	0.233276i
$623$	−5.16153	−	2.56476i	−0.206792	−	0.102755i
$624$			0.459577i			0.0183978i
$625$	17.3505	+	17.9989i	0.694019	+	0.719957i
$626$			26.5146i			1.05974i
$627$	−4.69801	+	4.69801i	−0.187620	+	0.187620i
$628$	−5.67596	+	5.67596i	−0.226495	+	0.226495i
$629$	1.80813			0.0720949
$630$	−8.66511	+	1.07385i	−0.345226	+	0.0427831i
$631$	−12.7398			−0.507163			−0.253581	−	0.967314i	$-0.581609\pi$
$631$	−12.7398			−0.507163			−0.253581	+	0.967314i	$0.581609\pi$
$632$	7.81138	−	7.81138i	0.310720	−	0.310720i
$633$	16.5549	−	16.5549i	0.657999	−	0.657999i
$634$			5.78766i			0.229858i
$635$	−21.7622	−	32.8950i	−0.863606	−	1.30540i
$636$			13.5380i			0.536816i
$637$	1.50638	+	0.207566i	0.0596848	+	0.00822407i
$638$	1.38789	+	1.38789i	0.0549469	+	0.0549469i
$639$		−	14.8682i		−	0.588176i
$640$	1.86490	−	1.23375i	0.0737166	−	0.0487684i
$641$	5.21837			0.206113			0.103057	−	0.994675i	$-0.467138\pi$
$641$	5.21837			0.206113			0.103057	+	0.994675i	$0.467138\pi$
$642$	5.06089	+	5.06089i	0.199737	+	0.199737i
$643$	24.4615	−	24.4615i	0.964667	−	0.964667i	−0.0347296	−	0.999397i	$-0.511057\pi$
$643$	24.4615	−	24.4615i	0.964667	−	0.964667i	0.999397	+	0.0347296i	$0.0110570\pi$
$644$	−7.12801	+	2.39569i	−0.280883	+	0.0944034i
$645$	−5.50406	+	27.0226i	−0.216722	+	1.06401i
$646$	−0.822898			−0.0323765
$647$	−26.9903	−	26.9903i	−1.06110	−	1.06110i	−0.998008	−	0.0630903i	$-0.979904\pi$
$647$	−26.9903	−	26.9903i	−1.06110	−	1.06110i	−0.0630903	−	0.998008i	$-0.520096\pi$
$648$	−7.95454	−	7.95454i	−0.312484	−	0.312484i
$649$	7.31725			0.287227
$650$	−0.424837	+	0.999617i	−0.0166635	+	0.0392082i
$651$	15.6489	+	46.5608i	0.613328	+	1.82486i
$652$	−5.71289	+	5.71289i	−0.223734	+	0.223734i
$653$	−7.46092	−	7.46092i	−0.291968	−	0.291968i	0.545889	−	0.837857i	$-0.316192\pi$
$653$	−7.46092	−	7.46092i	−0.291968	−	0.291968i	−0.837857	+	0.545889i	$0.816192\pi$
$654$	18.0319			0.705104
$655$	−11.7469	−	2.39265i	−0.458989	−	0.0934886i
$656$		−	7.00275i		−	0.273411i
$657$	−4.63167	−	4.63167i	−0.180699	−	0.180699i
$658$	8.63914	+	4.29278i	0.336789	+	0.167350i
$659$			39.6713i			1.54537i	0.634787	+	0.772687i	$0.281088\pi$
$659$			39.6713i			1.54537i	−0.634787	+	0.772687i	$0.718912\pi$
$660$	3.94543	−	2.61016i	0.153576	−	0.101600i
$661$			31.0296i			1.20691i	0.797397	+	0.603455i	$0.206210\pi$
$661$			31.0296i			1.20691i	−0.797397	+	0.603455i	$0.793790\pi$
$662$	−13.6139	+	13.6139i	−0.529121	+	0.529121i
$663$	−0.0851529	+	0.0851529i	−0.00330707	+	0.00330707i
$664$	−11.8938			−0.461570
$665$	11.4219	−	14.6534i	0.442923	−	0.568234i
$666$	10.1841			0.394626
$667$	−3.94469	+	3.94469i	−0.152739	+	0.152739i
$668$	7.18133	−	7.18133i	0.277854	−	0.277854i
$669$			11.0375i			0.426735i
$670$	9.04040	+	1.84138i	0.349261	+	0.0711388i
$671$			8.14009i			0.314245i
$672$	−2.49080	+	5.01269i	−0.0960847	+	0.193369i
$673$	16.4605	+	16.4605i	0.634505	+	0.634505i	0.949195	−	0.314690i	$-0.101900\pi$
$673$	16.4605	+	16.4605i	0.634505	+	0.634505i	−0.314690	+	0.949195i	$0.601900\pi$
$674$			31.4134i			1.21000i
$675$	−6.03291	−	14.9511i	−0.232207	−	0.575468i
$676$	12.9528			0.498185
$677$	7.30098	+	7.30098i	0.280599	+	0.280599i	0.833348	−	0.552749i	$-0.186421\pi$
$677$	7.30098	+	7.30098i	0.280599	+	0.280599i	−0.552749	+	0.833348i	$0.686421\pi$
$678$	−2.51518	+	2.51518i	−0.0965948	+	0.0965948i
$679$	14.7459	+	43.8741i	0.565894	+	1.68373i
$680$	0.574135	+	0.116942i	0.0220171	+	0.00448452i
$681$	7.45486			0.285671
$682$	−6.20523	−	6.20523i	−0.237610	−	0.237610i
$683$	15.8922	+	15.8922i	0.608098	+	0.608098i	0.942449	−	0.334351i	$-0.108517\pi$
$683$	15.8922	+	15.8922i	0.608098	+	0.608098i	−0.334351	+	0.942449i	$0.608517\pi$
$684$	−4.63489			−0.177220
$685$	0.728264	+	1.10082i	0.0278255	+	0.0420601i
$686$	15.3053	+	10.4282i	0.584361	+	0.398149i
$687$	22.9741	−	22.9741i	0.876518	−	0.876518i
$688$	4.12206	+	4.12206i	0.157152	+	0.157152i
$689$	−1.39006			−0.0529572
$690$	7.41868	+	11.2138i	0.282424	+	0.426903i
$691$			15.1927i			0.577956i	0.957336	+	0.288978i	$0.0933155\pi$
$691$			15.1927i			0.577956i	−0.957336	+	0.288978i	$0.906685\pi$
$692$	0.964940	+	0.964940i	0.0366815	+	0.0366815i
$693$	−1.73760	+	3.49688i	−0.0660059	+	0.132836i
$694$		−	30.7755i		−	1.16822i
$695$	−5.54111	+	27.2045i	−0.210186	+	1.03192i
$696$			4.15248i			0.157399i
$697$	1.29751	−	1.29751i	0.0491466	−	0.0491466i
$698$	−8.60473	+	8.60473i	−0.325694	+	0.325694i
$699$	59.8342			2.26314
$700$	−10.0515	+	8.60048i	−0.379909	+	0.325068i
$701$	45.1929			1.70691			0.853456	−	0.521166i	$-0.174503\pi$
$701$	45.1929			1.70691			0.853456	+	0.521166i	$0.174503\pi$
$702$	0.495295	−	0.495295i	0.0186937	−	0.0186937i
$703$	−15.3232	+	15.3232i	−0.577925	+	0.577925i
$704$		−	1.00000i		−	0.0376889i
$705$	3.44265	−	16.9019i	0.129658	−	0.636563i
$706$		−	13.6291i		−	0.512939i
$707$	17.3534	−	34.9234i	0.652642	−	1.31343i
$708$	10.9464	+	10.9464i	0.411391	+	0.411391i
$709$			46.9892i			1.76472i	0.470579	+	0.882358i	$0.344045\pi$
$709$			46.9892i			1.76472i	−0.470579	+	0.882358i	$0.655955\pi$
$710$	−12.4290	−	18.7873i	−0.466453	−	0.705074i
$711$	16.3039			0.611445
$712$	1.54039	+	1.54039i	0.0577287	+	0.0577287i
$713$	17.6367	−	17.6367i	0.660498	−	0.660498i
$714$	−1.39029	+	0.467269i	−0.0520302	+	0.0174871i
$715$	0.268008	+	0.405112i	0.0100229	+	0.0151503i
$716$	−24.4782			−0.914794
$717$	−8.42358	−	8.42358i	−0.314585	−	0.314585i
$718$	−23.4878	−	23.4878i	−0.876557	−	0.876557i
$719$	−46.2286			−1.72403			−0.862017	−	0.506879i	$-0.830799\pi$
$719$	−46.2286			−1.72403			−0.862017	+	0.506879i	$0.830799\pi$
$720$	3.23376	+	0.658664i	0.120515	+	0.0245470i
$721$	18.3904	−	6.18093i	0.684894	−	0.230190i
$722$	−6.46130	+	6.46130i	−0.240465	+	0.240465i
$723$	−1.09788	−	1.09788i	−0.0408307	−	0.0408307i
$724$	11.0910			0.412194
$725$	−3.83858	+	9.03197i	−0.142561	+	0.335439i
$726$		−	2.11563i		−	0.0785183i
$727$	−16.1608	−	16.1608i	−0.599370	−	0.599370i	0.340775	−	0.940145i	$-0.389310\pi$
$727$	−16.1608	−	16.1608i	−0.599370	−	0.599370i	−0.940145	+	0.340775i	$0.889310\pi$
$728$	−0.514696	−	0.255752i	−0.0190759	−	0.00947881i
$729$			3.86264i			0.143061i
$730$	−9.72436	−	1.98069i	−0.359915	−	0.0733088i
$731$			1.52752i			0.0564972i
$732$	−12.1774	+	12.1774i	−0.450088	+	0.450088i
$733$	6.66562	−	6.66562i	0.246200	−	0.246200i	−0.573209	−	0.819409i	$-0.694302\pi$
$733$	6.66562	−	6.66562i	0.246200	−	0.246200i	0.819409	+	0.573209i	$0.194302\pi$
$734$	−16.6333			−0.613946
$735$	10.9767	−	31.2426i	0.404880	−	1.15240i
$736$	2.84223			0.104766
$737$	2.91752	−	2.91752i	0.107468	−	0.107468i
$738$	7.30808	−	7.30808i	0.269014	−	0.269014i
$739$		−	7.37970i		−	0.271467i	−0.990745	−	0.135733i	$-0.956661\pi$
$739$		−	7.37970i		−	0.271467i	0.990745	−	0.135733i	$-0.0433390\pi$
$740$	12.8685	−	8.51339i	0.473057	−	0.312958i
$741$		−	1.44327i		−	0.0530200i
$742$	−15.1617	−	7.53382i	−0.556602	−	0.276575i
$743$	3.59480	+	3.59480i	0.131881	+	0.131881i	0.769966	−	0.638085i	$-0.220273\pi$
$743$	3.59480	+	3.59480i	0.131881	+	0.131881i	−0.638085	+	0.769966i	$0.720273\pi$
$744$		−	18.5657i		−	0.680652i
$745$	8.71083	+	1.77425i	0.319140	+	0.0650037i
$746$	2.41102			0.0882735
$747$	−12.4124	−	12.4124i	−0.454147	−	0.454147i
$748$	0.185285	−	0.185285i	0.00677470	−	0.00677470i
$749$	−8.48422	+	2.85151i	−0.310007	+	0.104192i
$750$	19.4845	+	13.4104i	0.711472	+	0.489680i
$751$	−13.4394			−0.490410			−0.245205	−	0.969471i	$-0.578855\pi$
$751$	−13.4394			−0.490410			−0.245205	+	0.969471i	$0.578855\pi$
$752$	−2.57824	−	2.57824i	−0.0940189	−	0.0940189i
$753$	40.9831	+	40.9831i	1.49351	+	1.49351i
$754$	−0.426371			−0.0155275
$755$	−6.93492	+	34.0475i	−0.252387	+	1.23911i
$756$	8.08665	−	2.71789i	0.294109	−	0.0988486i
$757$	17.4748	−	17.4748i	0.635131	−	0.635131i	−0.314219	−	0.949350i	$-0.601743\pi$
$757$	17.4748	−	17.4748i	0.635131	−	0.635131i	0.949350	+	0.314219i	$0.101743\pi$
$758$	11.6792	+	11.6792i	0.424209	+	0.424209i
$759$	6.01309			0.218261
$760$	−5.85660	+	3.87453i	−0.212441	+	0.140544i
$761$			34.0908i			1.23579i	0.786260	+	0.617896i	$0.212015\pi$
$761$			34.0908i			1.23579i	−0.786260	+	0.617896i	$0.787985\pi$
$762$	−26.3875	−	26.3875i	−0.955918	−	0.955918i
$763$	−10.0347	+	20.1946i	−0.363279	+	0.731093i
$764$			21.1039i			0.763511i
$765$	0.477127	+	0.721209i	0.0172506	+	0.0260754i
$766$		−	19.7657i		−	0.714165i
$767$	−1.12396	+	1.12396i	−0.0405840	+	0.0405840i
$768$	1.49597	−	1.49597i	0.0539813	−	0.0539813i
$769$	16.7689			0.604703			0.302352	−	0.953196i	$-0.402228\pi$
$769$	16.7689			0.604703			0.302352	+	0.953196i	$0.402228\pi$
$770$	0.727601	+	5.87117i	0.0262209	+	0.211582i
$771$	31.2753			1.12635
$772$	4.58952	−	4.58952i	0.165180	−	0.165180i
$773$	−5.05808	+	5.05808i	−0.181927	+	0.181927i	−0.792195	−	0.610268i	$-0.791062\pi$
$773$	−5.05808	+	5.05808i	−0.181927	+	0.181927i	0.610268	+	0.792195i	$0.291062\pi$
$774$			8.60358i			0.309249i
$775$	17.1623	−	40.3819i	0.616488	−	1.45056i
$776$		−	17.4944i		−	0.628012i
$777$	−17.1875	+	34.5895i	−0.616598	+	1.24089i
$778$	−21.9711	−	21.9711i	−0.787704	−	0.787704i
$779$			21.9917i			0.787934i
$780$	−0.205103	+	1.00697i	−0.00734388	+	0.0360553i
$781$	−10.0742			−0.360481
$782$	0.526623	+	0.526623i	0.0188320	+	0.0188320i
$783$	4.47521	−	4.47521i	0.159931	−	0.159931i
$784$	−4.22777	−	5.57907i	−0.150992	−	0.199252i
$785$	−14.9696	+	9.90336i	−0.534287	+	0.353466i
$786$	−11.3424			−0.404569
$787$	−28.2062	−	28.2062i	−1.00544	−	1.00544i	−0.999985	−	0.00545628i	$-0.998263\pi$
$787$	−28.2062	−	28.2062i	−1.00544	−	1.00544i	−0.00545628	−	0.999985i	$-0.501737\pi$
$788$	1.32312	+	1.32312i	0.0471342	+	0.0471342i
$789$	−37.4128			−1.33193
$790$	20.6015	−	13.6292i	0.732967	−	0.484906i
$791$	−1.41715	−	4.21652i	−0.0503881	−	0.149922i
$792$	1.04360	−	1.04360i	0.0370828	−	0.0370828i
$793$	−1.25036	−	1.25036i	−0.0444014	−	0.0444014i
$794$	−16.6760			−0.591808
$795$	−6.04183	+	29.6628i	−0.214282	+	1.05203i
$796$		−	4.68453i		−	0.166039i
$797$	−2.98711	−	2.98711i	−0.105809	−	0.105809i	0.652220	−	0.758029i	$-0.273838\pi$
$797$	−2.98711	−	2.98711i	−0.105809	−	0.105809i	−0.758029	+	0.652220i	$0.773838\pi$
$798$	7.82220	−	15.7420i	0.276903	−	0.557262i
$799$		−	0.955422i		−	0.0338004i
$800$	4.63675	−	1.87097i	0.163934	−	0.0661488i
$801$			3.21511i			0.113600i
$802$	24.9088	−	24.9088i	0.879559	−	0.879559i
$803$	−3.13825	+	3.13825i	−0.110747	+	0.110747i
$804$	8.72908			0.307851
$805$	−16.6872	+	2.06801i	−0.588146	+	0.0728877i
$806$	1.90630			0.0671467
$807$	−47.8374	+	47.8374i	−1.68396	+	1.68396i
$808$	−10.4224	+	10.4224i	−0.366660	+	0.366660i
$809$			26.5323i			0.932825i	0.884567	+	0.466412i	$0.154454\pi$
$809$			26.5323i			0.932825i	−0.884567	+	0.466412i	$0.845546\pi$
$810$	−13.8790	−	20.9790i	−0.487659	−	0.737128i
$811$			1.02559i			0.0360132i	0.999838	+	0.0180066i	$0.00573200\pi$
$811$			1.02559i			0.0360132i	−0.999838	+	0.0180066i	$0.994268\pi$
$812$	−4.65051	−	2.31083i	−0.163201	−	0.0810943i
$813$	−34.3896	−	34.3896i	−1.20609	−	1.20609i
$814$		−	6.90039i		−	0.241859i
$815$	−15.0670	+	9.96780i	−0.527773	+	0.349157i
$816$	0.554364			0.0194066
$817$	−12.9451	−	12.9451i	−0.452891	−	0.452891i
$818$	−2.35452	+	2.35452i	−0.0823237	+	0.0823237i
$819$	−0.270235	−	0.804041i	−0.00944276	−	0.0280955i
$820$	3.12524	−	15.3436i	0.109138	−	0.535821i
$821$	7.27994			0.254072			0.127036	−	0.991898i	$-0.459454\pi$
$821$	7.27994			0.254072			0.127036	+	0.991898i	$0.459454\pi$
$822$	0.883048	+	0.883048i	0.0307998	+	0.0307998i
$823$	23.4904	+	23.4904i	0.818825	+	0.818825i	0.985938	−	0.167112i	$-0.0534443\pi$
$823$	23.4904	+	23.4904i	0.818825	+	0.818825i	−0.167112	+	0.985938i	$0.553444\pi$
$824$	−7.33300			−0.255457
$825$	9.80963	−	3.95828i	0.341528	−	0.137810i
$826$	−18.3509	+	6.16765i	−0.638509	+	0.214600i
$827$	39.8657	−	39.8657i	1.38627	−	1.38627i	0.553253	−	0.833013i	$-0.313386\pi$
$827$	39.8657	−	39.8657i	1.38627	−	1.38627i	0.833013	−	0.553253i	$-0.186614\pi$
$828$	2.96615	+	2.96615i	0.103081	+	0.103081i
$829$	1.37937			0.0479076			0.0239538	−	0.999713i	$-0.492375\pi$
$829$	1.37937			0.0479076			0.0239538	+	0.999713i	$0.492375\pi$
$830$	−26.0603	−	5.30807i	−0.904567	−	0.184246i
$831$			35.5705i			1.23393i
$832$	0.153605	+	0.153605i	0.00532528	+	0.00532528i
$833$	0.250376	−	1.81706i	0.00867502	−	0.0629575i
$834$			26.2677i			0.909574i
$835$	18.9398	−	12.5299i	0.655439	−	0.433616i
$836$			3.14044i			0.108614i
$837$	−20.0086	+	20.0086i	−0.691599	+	0.691599i
$838$	16.7381	−	16.7381i	0.578207	−	0.578207i
$839$	13.2410			0.457129			0.228564	−	0.973529i	$-0.426597\pi$
$839$	13.2410			0.457129			0.228564	+	0.973529i	$0.426597\pi$
$840$	−7.69464	+	9.87158i	−0.265490	+	0.340602i
$841$	25.1475			0.867157
$842$	−26.6173	+	26.6173i	−0.917292	+	0.917292i
$843$	−36.5663	+	36.5663i	−1.25941	+	1.25941i
$844$		−	11.0663i		−	0.380919i
$845$	28.3806	+	5.78067i	0.976323	+	0.198861i
$846$		−	5.38132i		−	0.185013i
$847$	2.36936	+	1.17733i	0.0814123	+	0.0404537i
$848$	4.52481	+	4.52481i	0.155383	+	0.155383i
$849$		−	40.2219i		−	1.38041i
$850$	1.20579	+	0.512458i	0.0413581	+	0.0175772i
$851$	19.6125			0.672308
$852$	−15.0707	−	15.0707i	−0.516313	−	0.516313i
$853$	19.0070	−	19.0070i	0.650788	−	0.650788i	−0.302395	−	0.953183i	$-0.597786\pi$
$853$	19.0070	−	19.0070i	0.650788	−	0.650788i	0.953183	+	0.302395i	$0.0977861\pi$
$854$	−6.86121	−	20.4145i	−0.234786	−	0.698569i
$855$	−10.1554	−	2.06849i	−0.347308	−	0.0707410i
$856$	3.38301			0.115629
$857$	3.92037	+	3.92037i	0.133917	+	0.133917i	0.770888	−	0.636971i	$-0.219813\pi$
$857$	3.92037	+	3.92037i	0.133917	+	0.133917i	−0.636971	+	0.770888i	$0.719813\pi$
$858$	0.324970	+	0.324970i	0.0110943	+	0.0110943i
$859$	38.3418			1.30820			0.654102	−	0.756406i	$-0.273047\pi$
$859$	38.3418			1.30820			0.654102	+	0.756406i	$0.273047\pi$
$860$	7.19214	+	10.8714i	0.245250	+	0.370711i
$861$	12.4876	+	37.1550i	0.425577	+	1.26624i
$862$	−13.7785	+	13.7785i	−0.469299	+	0.469299i
$863$	−2.74694	−	2.74694i	−0.0935070	−	0.0935070i	0.658806	−	0.752313i	$-0.271062\pi$
$863$	−2.74694	−	2.74694i	−0.0935070	−	0.0935070i	−0.752313	+	0.658806i	$0.771062\pi$
$864$	−3.22448			−0.109699
$865$	1.68362	+	2.54490i	0.0572448	+	0.0865292i
$866$			20.2764i			0.689020i
$867$	−25.3288	−	25.3288i	−0.860212	−	0.860212i
$868$	20.7924	+	10.3317i	0.705739	+	0.350681i
$869$		−	11.0470i		−	0.374742i
$870$	−1.85320	+	9.09841i	−0.0628293	+	0.308465i
$871$			0.896291i			0.0303697i
$872$	6.02682	−	6.02682i	0.204094	−	0.204094i
$873$	18.2572	−	18.2572i	0.617911	−	0.617911i
$874$	−8.92584			−0.301921
$875$	−25.8618	+	14.3585i	−0.874289	+	0.485406i
$876$	−9.38949			−0.317241
$877$	−6.68984	+	6.68984i	−0.225900	+	0.225900i	−0.810977	−	0.585078i	$-0.801064\pi$
$877$	−6.68984	+	6.68984i	−0.225900	+	0.225900i	0.585078	+	0.810977i	$0.301064\pi$
$878$	1.78063	−	1.78063i	0.0600935	−	0.0600935i
$879$			5.11830i			0.172636i
$880$	0.446287	−	2.19108i	0.0150443	−	0.0738613i
$881$			23.5714i			0.794141i	0.917788	+	0.397070i	$0.129973\pi$
$881$			23.5714i			0.794141i	−0.917788	+	0.397070i	$0.870027\pi$
$882$	1.41022	−	10.2344i	0.0474845	−	0.344611i
$883$	35.5643	+	35.5643i	1.19683	+	1.19683i	0.975109	+	0.221724i	$0.0711684\pi$
$883$	35.5643	+	35.5643i	1.19683	+	1.19683i	0.221724	+	0.975109i	$0.428832\pi$
$884$			0.0569214i			0.00191447i
$885$	19.0992	+	28.8697i	0.642013	+	0.970445i
$886$	6.13259			0.206028
$887$	9.73335	+	9.73335i	0.326814	+	0.326814i	0.851374	−	0.524560i	$-0.175770\pi$
$887$	9.73335	+	9.73335i	0.326814	+	0.326814i	−0.524560	+	0.851374i	$0.675770\pi$
$888$	10.3228	−	10.3228i	0.346411	−	0.346411i
$889$	44.2368	−	14.8678i	1.48365	−	0.498649i
$890$	2.68767	+	4.06258i	0.0900908	+	0.136178i
$891$	−11.2494			−0.376870
$892$	3.68907	+	3.68907i	0.123519	+	0.123519i
$893$	8.09681	+	8.09681i	0.270949	+	0.270949i
$894$	8.41086			0.281301
$895$	−53.6337	−	10.9243i	−1.79278	−	0.365159i
$896$	0.842892	+	2.50789i	0.0281590	+	0.0837829i
$897$	−0.923639	+	0.923639i	−0.0308394	+	0.0308394i
$898$	15.3518	+	15.3518i	0.512297	+	0.512297i
$899$	17.2243			0.574462
$900$	6.79147	+	2.88637i	0.226382	+	0.0962124i
$901$			1.67676i			0.0558610i
$902$	−4.95169	−	4.95169i	−0.164873	−	0.164873i
$903$	−29.2214	−	14.5201i	−0.972426	−	0.483197i
$904$			1.68130i			0.0559191i
$905$	24.3013	+	4.94978i	0.807802	+	0.164536i
$906$			32.8750i			1.09220i
$907$	1.98285	−	1.98285i	0.0658395	−	0.0658395i	−0.673420	−	0.739260i	$-0.735176\pi$
$907$	1.98285	−	1.98285i	0.0658395	−	0.0658395i	0.739260	+	0.673420i	$0.235176\pi$
$908$	2.49164	−	2.49164i	0.0826880	−	0.0826880i
$909$	−21.7538			−0.721526
$910$	−1.01360	−	0.790076i	−0.0336006	−	0.0261908i
$911$	−21.2572			−0.704283			−0.352141	−	0.935947i	$-0.614546\pi$
$911$	−21.2572			−0.704283			−0.352141	+	0.935947i	$0.614546\pi$
$912$	−4.69801	+	4.69801i	−0.155567	+	0.155567i
$913$	−8.41021	+	8.41021i	−0.278337	+	0.278337i
$914$		−	15.1582i		−	0.501389i
$915$	−32.1162	+	21.2470i	−1.06173	+	0.702403i
$916$		−	15.3573i		−	0.507420i
$917$	6.31197	−	12.7027i	0.208440	−	0.419481i
$918$	−0.597449	−	0.597449i	−0.0197187	−	0.0197187i
$919$		−	23.8915i		−	0.788106i	−0.919088	−	0.394053i	$-0.871073\pi$
$919$		−	23.8915i		−	0.788106i	0.919088	−	0.394053i	$-0.128927\pi$
$920$	6.22755	+	1.26845i	0.205316	+	0.0418196i
$921$	−17.2342			−0.567887
$922$	15.4002	+	15.4002i	0.507178	+	0.507178i
$923$	1.54744	−	1.54744i	0.0509345	−	0.0509345i
$924$	1.78324	+	5.30577i	0.0586644	+	0.174547i
$925$	31.9954	−	12.9104i	1.05200	−	0.424493i
$926$	−9.69964			−0.318750
$927$	−7.65273	−	7.65273i	−0.251349	−	0.251349i
$928$	1.38789	+	1.38789i	0.0455596	+	0.0455596i
$929$	−25.9362			−0.850939			−0.425469	−	0.904973i	$-0.639891\pi$
$929$	−25.9362			−0.850939			−0.425469	+	0.904973i	$0.639891\pi$
$930$	8.28564	−	40.6789i	0.271697	−	1.33391i
$931$	13.2770	+	17.5207i	0.435137	+	0.574218i
$932$	19.9984	−	19.9984i	0.655070	−	0.655070i
$933$	−12.3085	−	12.3085i	−0.402961	−	0.402961i
$934$	−5.98381			−0.195796
$935$	0.488665	−	0.323284i	0.0159811	−	0.0105725i
$936$			0.320604i			0.0104793i
$937$	−12.6406	−	12.6406i	−0.412952	−	0.412952i	0.469814	−	0.882766i	$-0.344321\pi$
$937$	−12.6406	−	12.6406i	−0.412952	−	0.412952i	−0.882766	+	0.469814i	$0.844321\pi$
$938$	−4.85768	+	9.77600i	−0.158609	+	0.319198i
$939$			56.0950i			1.83059i
$940$	−4.49850	−	6.79977i	−0.146725	−	0.221784i
$941$		−	17.6316i		−	0.574774i	−0.957815	−	0.287387i	$-0.907213\pi$
$941$		−	17.6316i		−	0.574774i	0.957815	−	0.287387i	$-0.0927866\pi$
$942$	−12.0082	+	12.0082i	−0.391248	+	0.391248i
$943$	14.0738	−	14.0738i	0.458307	−	0.458307i
$944$	7.31725			0.238156
$945$	18.9315	−	2.34613i	0.615840	−	0.0763198i
$946$	5.82948			0.189533
$947$	10.0489	−	10.0489i	0.326545	−	0.326545i	−0.524726	−	0.851271i	$-0.675832\pi$
$947$	10.0489	−	10.0489i	0.326545	−	0.326545i	0.851271	+	0.524726i	$0.175832\pi$
$948$	16.5260	−	16.5260i	0.536738	−	0.536738i
$949$		−	0.964101i		−	0.0312960i
$950$	−14.5614	+	5.87567i	−0.472435	+	0.190632i
$951$			12.2445i			0.397056i
$952$	−0.308501	+	0.620852i	−0.00999856	+	0.0201219i
$953$	15.0348	+	15.0348i	0.487025	+	0.487025i	0.907366	−	0.420341i	$-0.138090\pi$
$953$	15.0348	+	15.0348i	0.487025	+	0.487025i	−0.420341	+	0.907366i	$0.638090\pi$
$954$			9.44419i			0.305767i
$955$	−9.41838	+	46.2402i	−0.304772	+	1.49630i
$956$	−5.63084			−0.182114
$957$	2.93625	+	2.93625i	0.0949154	+	0.0949154i
$958$	−25.6144	+	25.6144i	−0.827562	+	0.827562i
$959$	−1.48037	+	0.497545i	−0.0478036	+	0.0160666i
$960$	3.94543	−	2.61016i	0.127338	−	0.0842426i
$961$	−46.0097			−1.48418
$962$	1.05993	+	1.05993i	0.0341736	+	0.0341736i
$963$	3.53051	+	3.53051i	0.113769	+	0.113769i
$964$	−0.733892			−0.0236371
$965$	12.1042	−	8.00775i	0.389649	−	0.257779i
$966$	−15.0802	+	5.06839i	−0.485198	+	0.163073i
$967$	25.5131	−	25.5131i	0.820446	−	0.820446i	−0.165726	−	0.986172i	$-0.552997\pi$
$967$	25.5131	−	25.5131i	0.820446	−	0.820446i	0.986172	+	0.165726i	$0.0529968\pi$
$968$	−0.707107	−	0.707107i	−0.0227273	−	0.0227273i
$969$	−1.74095			−0.0559272
$970$	7.80752	−	38.3316i	0.250684	−	1.23075i
$971$			55.1300i			1.76921i	0.466346	+	0.884603i	$0.345570\pi$
$971$			55.1300i			1.76921i	−0.466346	+	0.884603i	$0.654430\pi$
$972$	−9.98868	−	9.98868i	−0.320387	−	0.320387i
$973$	−29.4181	−	14.6178i	−0.943100	−	0.468625i
$974$			12.4245i			0.398108i
$975$	−0.898796	+	2.11482i	−0.0287845	+	0.0677283i
$976$			8.14009i			0.260558i
$977$	3.87924	−	3.87924i	0.124108	−	0.124108i	−0.642325	−	0.766433i	$-0.722030\pi$
$977$	3.87924	−	3.87924i	0.124108	−	0.124108i	0.766433	+	0.642325i	$0.222030\pi$
$978$	−12.0863	+	12.0863i	−0.386478	+	0.386478i
$979$	2.17845			0.0696234
$980$	−6.77350	−	14.1110i	−0.216372	−	0.450759i
$981$	12.5792			0.401623
$982$	−23.5985	+	23.5985i	−0.753058	+	0.753058i
$983$	11.9573	−	11.9573i	0.381377	−	0.381377i	−0.490221	−	0.871598i	$-0.663084\pi$
$983$	11.9573	−	11.9573i	0.381377	−	0.381377i	0.871598	+	0.490221i	$0.163084\pi$
$984$		−	14.8152i		−	0.472291i
$985$	2.30857	+	3.48955i	0.0735571	+	0.111186i
$986$			0.514310i			0.0163790i
$987$	18.2772	+	9.08192i	0.581770	+	0.289081i
$988$	−0.482386	−	0.482386i	−0.0153467	−	0.0153467i
$989$			16.5687i			0.526854i
$990$	2.75236	−	1.82087i	0.0874757	−	0.0578709i
$991$	−39.5377			−1.25596			−0.627978	−	0.778231i	$-0.716117\pi$
$991$	−39.5377			−1.25596			−0.627978	+	0.778231i	$0.716117\pi$
$992$	−6.20523	−	6.20523i	−0.197016	−	0.197016i
$993$	−28.8020	+	28.8020i	−0.914004	+	0.914004i
$994$	25.2649	−	8.49142i	0.801354	−	0.269331i
$995$	2.09065	−	10.2642i	0.0662779	−	0.325396i
$996$	−25.1629			−0.797317
$997$	20.9164	+	20.9164i	0.662428	+	0.662428i	0.955952	−	0.293524i	$-0.0948280\pi$
$997$	20.9164	+	20.9164i	0.662428	+	0.662428i	−0.293524	+	0.955952i	$0.594828\pi$
$998$	4.58565	+	4.58565i	0.145156	+	0.145156i
$999$	−22.2502			−0.703964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.18	yes	40
5.2	odd	4	inner	770.2.l.c.727.13	yes	40
7.6	odd	2	inner	770.2.l.c.573.13	✓	40
35.27	even	4	inner	770.2.l.c.727.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.13	✓	40	7.6	odd	2	inner
770.2.l.c.573.18	yes	40	1.1	even	1	trivial
770.2.l.c.727.13	yes	40	5.2	odd	4	inner
770.2.l.c.727.18	yes	40	35.27	even	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.49597 - 1.49597i) q^{3} -1.00000i q^{4} +(0.446287 - 2.19108i) q^{5} -2.11563i q^{6} +(2.36936 + 1.17733i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.47587i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.49597 - 1.49597i) q^{3} -1.00000i q^{4} +(0.446287 - 2.19108i) q^{5} -2.11563i q^{6} +(2.36936 + 1.17733i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.47587i q^{9} +(-1.23375 - 1.86490i) q^{10} -1.00000 q^{11} +(-1.49597 - 1.49597i) q^{12} +(0.153605 - 0.153605i) q^{13} +(2.50789 - 0.842892i) q^{14} +(-2.61016 - 3.94543i) q^{15} -1.00000 q^{16} +(-0.185285 - 0.185285i) q^{17} +(-1.04360 - 1.04360i) q^{18} +3.14044 q^{19} +(-2.19108 - 0.446287i) q^{20} +(5.30577 - 1.78324i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(-2.00976 - 2.00976i) q^{23} -2.11563 q^{24} +(-4.60166 - 1.95570i) q^{25} -0.217230i q^{26} +(2.28005 + 2.28005i) q^{27} +(1.17733 - 2.36936i) q^{28} -1.96277i q^{29} +(-4.63550 - 0.944177i) q^{30} +8.77551i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.49597 + 1.49597i) q^{33} -0.262033 q^{34} +(3.63705 - 4.66603i) q^{35} -1.47587 q^{36} +(-4.87931 + 4.87931i) q^{37} +(2.22062 - 2.22062i) q^{38} -0.459577i q^{39} +(-1.86490 + 1.23375i) q^{40} +7.00275i q^{41} +(2.49080 - 5.01269i) q^{42} +(-4.12206 - 4.12206i) q^{43} +1.00000i q^{44} +(-3.23376 - 0.658664i) q^{45} -2.84223 q^{46} +(2.57824 + 2.57824i) q^{47} +(-1.49597 + 1.49597i) q^{48} +(4.22777 + 5.57907i) q^{49} +(-4.63675 + 1.87097i) q^{50} -0.554364 q^{51} +(-0.153605 - 0.153605i) q^{52} +(-4.52481 - 4.52481i) q^{53} +3.22448 q^{54} +(-0.446287 + 2.19108i) q^{55} +(-0.842892 - 2.50789i) q^{56} +(4.69801 - 4.69801i) q^{57} +(-1.38789 - 1.38789i) q^{58} -7.31725 q^{59} +(-3.94543 + 2.61016i) q^{60} -8.14009i q^{61} +(6.20523 + 6.20523i) q^{62} +(1.73760 - 3.49688i) q^{63} +1.00000i q^{64} +(-0.268008 - 0.405112i) q^{65} +2.11563i q^{66} +(-2.91752 + 2.91752i) q^{67} +(-0.185285 + 0.185285i) q^{68} -6.01309 q^{69} +(-0.727601 - 5.87117i) q^{70} +10.0742 q^{71} +(-1.04360 + 1.04360i) q^{72} +(3.13825 - 3.13825i) q^{73} +6.90039i q^{74} +(-9.80963 + 3.95828i) q^{75} -3.14044i q^{76} +(-2.36936 - 1.17733i) q^{77} +(-0.324970 - 0.324970i) q^{78} +11.0470i q^{79} +(-0.446287 + 2.19108i) q^{80} +11.2494 q^{81} +(4.95169 + 4.95169i) q^{82} +(8.41021 - 8.41021i) q^{83} +(-1.78324 - 5.30577i) q^{84} +(-0.488665 + 0.323284i) q^{85} -5.82948 q^{86} +(-2.93625 - 2.93625i) q^{87} +(0.707107 + 0.707107i) q^{88} -2.17845 q^{89} +(-2.75236 + 1.82087i) q^{90} +(0.544789 - 0.183101i) q^{91} +(-2.00976 + 2.00976i) q^{92} +(13.1279 + 13.1279i) q^{93} +3.64619 q^{94} +(1.40154 - 6.88095i) q^{95} +2.11563i q^{96} +(12.3704 + 12.3704i) q^{97} +(6.93448 + 0.955514i) q^{98} +1.47587i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more