LMFDB - Embedded newform 702.2.bb.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.2
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.62665 - 0.435860i) q^{5} +(0.290365 + 0.0778030i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.62665 - 0.435860i) q^{5} +(0.290365 + 0.0778030i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.45842 - 0.842018i) q^{10} +(1.12392 + 1.12392i) q^{11} +(-3.56563 + 0.535061i) q^{13} +(-0.260334 + 0.150304i) q^{14} -1.00000 q^{16} +(-1.26545 + 2.19182i) q^{17} +(4.16702 - 1.11655i) q^{19} +(-0.435860 + 1.62665i) q^{20} -1.58947 q^{22} +(-0.660949 + 1.14480i) q^{23} +(-1.87410 - 1.08201i) q^{25} +(2.14293 - 2.89963i) q^{26} +(0.0778030 - 0.290365i) q^{28} +7.48368i q^{29} +(-2.78151 + 10.3807i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.655045 - 2.44466i) q^{34} +(-0.438411 - 0.253117i) q^{35} +(-2.37887 - 0.637416i) q^{37} +(-2.15701 + 3.73605i) q^{38} +(-0.842018 - 1.45842i) q^{40} +(0.974309 + 3.63617i) q^{41} +(-6.42917 + 3.71188i) q^{43} +(1.12392 - 1.12392i) q^{44} +(-0.342133 - 1.27686i) q^{46} +(-3.46610 + 0.928739i) q^{47} +(-5.98392 - 3.45482i) q^{49} +(2.09029 - 0.560091i) q^{50} +(0.535061 + 3.56563i) q^{52} +3.63112i q^{53} +(-1.33836 - 2.31811i) q^{55} +(0.150304 + 0.260334i) q^{56} +(-5.29176 - 5.29176i) q^{58} +(0.512425 + 0.512425i) q^{59} +(5.62852 + 9.74888i) q^{61} +(-5.37346 - 9.30710i) q^{62} +1.00000i q^{64} +(6.03325 + 0.683757i) q^{65} +(0.943886 - 0.252913i) q^{67} +(2.19182 + 1.26545i) q^{68} +(0.488984 - 0.131023i) q^{70} +(-1.84126 - 6.87167i) q^{71} +(3.38109 - 3.38109i) q^{73} +(2.13284 - 1.23139i) q^{74} +(-1.11655 - 4.16702i) q^{76} +(0.238903 + 0.413792i) q^{77} +(-3.69530 + 6.40045i) q^{79} +(1.62665 + 0.435860i) q^{80} +(-3.26010 - 1.88222i) q^{82} +(-3.18219 - 11.8761i) q^{83} +(3.01378 - 3.01378i) q^{85} +(1.92141 - 7.17081i) q^{86} +1.58947i q^{88} +(-0.512119 + 1.91125i) q^{89} +(-1.07696 - 0.122054i) q^{91} +(1.14480 + 0.660949i) q^{92} +(1.79419 - 3.10762i) q^{94} -7.26495 q^{95} +(1.61645 - 6.03268i) q^{97} +(6.67419 - 1.78835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.62665	−	0.435860i	−0.727461	−	0.194923i	−0.123963	−	0.992287i	$-0.539560\pi$
$5$	−1.62665	−	0.435860i	−0.727461	−	0.194923i	−0.603498	+	0.797364i	$0.706227\pi$
$6$		0			0
$7$	0.290365	+	0.0778030i	0.109748	+	0.0294068i	0.313275	−	0.949663i	$-0.398574\pi$
$7$	0.290365	+	0.0778030i	0.109748	+	0.0294068i	−0.203527	+	0.979069i	$0.565241\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.45842	−	0.842018i	0.461192	−	0.266269i
$11$	1.12392	+	1.12392i	0.338876	+	0.338876i	0.855944	−	0.517068i	$-0.172977\pi$
$11$	1.12392	+	1.12392i	0.338876	+	0.338876i	−0.517068	+	0.855944i	$0.672977\pi$
$12$		0			0
$13$	−3.56563	+	0.535061i	−0.988928	+	0.148399i
$13$	−3.56563	+	0.535061i	−0.988928	+	0.148399i
$14$	−0.260334	+	0.150304i	−0.0695771	+	0.0401704i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.26545	+	2.19182i	−0.306917	+	0.531595i	−0.977686	−	0.210071i	$-0.932631\pi$
$17$	−1.26545	+	2.19182i	−0.306917	+	0.531595i	0.670770	+	0.741666i	$0.265964\pi$
$18$		0			0
$19$	4.16702	−	1.11655i	0.955980	−	0.256154i	0.253082	−	0.967445i	$-0.418556\pi$
$19$	4.16702	−	1.11655i	0.955980	−	0.256154i	0.702898	+	0.711291i	$0.251889\pi$
$20$	−0.435860	+	1.62665i	−0.0974613	+	0.363731i
$21$		0			0
$22$	−1.58947			−0.338876
$23$	−0.660949	+	1.14480i	−0.137817	+	0.238707i	−0.926670	−	0.375875i	$-0.877342\pi$
$23$	−0.660949	+	1.14480i	−0.137817	+	0.238707i	0.788853	+	0.614582i	$0.210675\pi$
$24$		0			0
$25$	−1.87410	−	1.08201i	−0.374820	−	0.216403i
$26$	2.14293	−	2.89963i	0.420264	−	0.568663i
$27$		0			0
$28$	0.0778030	−	0.290365i	0.0147034	−	0.0548738i
$29$			7.48368i			1.38969i	0.719162	+	0.694843i	$0.244526\pi$
$29$			7.48368i			1.38969i	−0.719162	+	0.694843i	$0.755474\pi$
$30$		0			0
$31$	−2.78151	+	10.3807i	−0.499573	+	1.86443i	0.00316697	+	0.999995i	$0.498992\pi$
$31$	−2.78151	+	10.3807i	−0.499573	+	1.86443i	−0.502740	+	0.864438i	$0.667675\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.655045	−	2.44466i	−0.112339	−	0.419256i
$35$	−0.438411	−	0.253117i	−0.0741050	−	0.0427846i
$36$		0			0
$37$	−2.37887	−	0.637416i	−0.391084	−	0.104791i	0.0579183	−	0.998321i	$-0.481554\pi$
$37$	−2.37887	−	0.637416i	−0.391084	−	0.104791i	−0.449002	+	0.893531i	$0.648220\pi$
$38$	−2.15701	+	3.73605i	−0.349913	+	0.606067i
$39$		0			0
$40$	−0.842018	−	1.45842i	−0.133135	−	0.230596i
$41$	0.974309	+	3.63617i	0.152161	+	0.567874i	0.999332	+	0.0365529i	$0.0116377\pi$
$41$	0.974309	+	3.63617i	0.152161	+	0.567874i	−0.847170	+	0.531322i	$0.821696\pi$
$42$		0			0
$43$	−6.42917	+	3.71188i	−0.980439	+	0.566057i	−0.902403	−	0.430894i	$-0.858198\pi$
$43$	−6.42917	+	3.71188i	−0.980439	+	0.566057i	−0.0780366	+	0.996950i	$0.524865\pi$
$44$	1.12392	−	1.12392i	0.169438	−	0.169438i
$45$		0			0
$46$	−0.342133	−	1.27686i	−0.0504447	−	0.188262i
$47$	−3.46610	+	0.928739i	−0.505583	+	0.135470i	−0.502590	−	0.864525i	$-0.667619\pi$
$47$	−3.46610	+	0.928739i	−0.505583	+	0.135470i	−0.00299296	+	0.999996i	$0.500953\pi$
$48$		0			0
$49$	−5.98392	−	3.45482i	−0.854846	−	0.493545i
$50$	2.09029	−	0.560091i	0.295611	−	0.0792088i
$51$		0			0
$52$	0.535061	+	3.56563i	0.0741997	+	0.494464i
$53$			3.63112i			0.498772i	0.968404	+	0.249386i	$0.0802288\pi$
$53$			3.63112i			0.498772i	−0.968404	+	0.249386i	$0.919771\pi$
$54$		0			0
$55$	−1.33836	−	2.31811i	−0.180464	−	0.312574i
$56$	0.150304	+	0.260334i	0.0200852	+	0.0347886i
$57$		0			0
$58$	−5.29176	−	5.29176i	−0.694843	−	0.694843i
$59$	0.512425	+	0.512425i	0.0667121	+	0.0667121i	0.739676	−	0.672964i	$-0.234979\pi$
$59$	0.512425	+	0.512425i	0.0667121	+	0.0667121i	−0.672964	+	0.739676i	$0.734979\pi$
$60$		0			0
$61$	5.62852	+	9.74888i	0.720658	+	1.24822i	0.960736	+	0.277463i	$0.0894935\pi$
$61$	5.62852	+	9.74888i	0.720658	+	1.24822i	−0.240078	+	0.970754i	$0.577173\pi$
$62$	−5.37346	−	9.30710i	−0.682430	−	1.18200i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	6.03325	+	0.683757i	0.748333	+	0.0848096i
$66$		0			0
$67$	0.943886	−	0.252913i	0.115314	−	0.0308983i	−0.200701	−	0.979653i	$-0.564322\pi$
$67$	0.943886	−	0.252913i	0.115314	−	0.0308983i	0.316015	+	0.948754i	$0.397655\pi$
$68$	2.19182	+	1.26545i	0.265798	+	0.153458i
$69$		0			0
$70$	0.488984	−	0.131023i	0.0584448	−	0.0156602i
$71$	−1.84126	−	6.87167i	−0.218517	−	0.815518i	−0.984899	−	0.173132i	$-0.944611\pi$
$71$	−1.84126	−	6.87167i	−0.218517	−	0.815518i	0.766381	−	0.642386i	$-0.222055\pi$
$72$		0			0
$73$	3.38109	−	3.38109i	0.395727	−	0.395727i	−0.480996	−	0.876723i	$-0.659725\pi$
$73$	3.38109	−	3.38109i	0.395727	−	0.395727i	0.876723	+	0.480996i	$0.159725\pi$
$74$	2.13284	−	1.23139i	0.247937	−	0.143147i
$75$		0			0
$76$	−1.11655	−	4.16702i	−0.128077	−	0.477990i
$77$	0.238903	+	0.413792i	0.0272255	+	0.0471560i
$78$		0			0
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	−0.995507	−	0.0946854i	$-0.969815\pi$
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	0.579754	+	0.814792i	$0.303149\pi$
$80$	1.62665	+	0.435860i	0.181865	+	0.0487307i
$81$		0			0
$82$	−3.26010	−	1.88222i	−0.360018	−	0.207856i
$83$	−3.18219	−	11.8761i	−0.349291	−	1.30357i	−0.887518	−	0.460773i	$-0.847572\pi$
$83$	−3.18219	−	11.8761i	−0.349291	−	1.30357i	0.538227	−	0.842800i	$-0.319094\pi$
$84$		0			0
$85$	3.01378	−	3.01378i	0.326890	−	0.326890i
$86$	1.92141	−	7.17081i	0.207191	−	0.773248i
$87$		0			0
$88$			1.58947i			0.169438i
$89$	−0.512119	+	1.91125i	−0.0542845	+	0.202592i	−0.987742	−	0.156096i	$-0.950109\pi$
$89$	−0.512119	+	1.91125i	−0.0542845	+	0.202592i	0.933457	+	0.358688i	$0.116776\pi$
$90$		0			0
$91$	−1.07696	−	0.122054i	−0.112896	−	0.0127947i
$92$	1.14480	+	0.660949i	0.119353	+	0.0689087i
$93$		0			0
$94$	1.79419	−	3.10762i	0.185056	−	0.320527i
$95$	−7.26495			−0.745368
$96$		0			0
$97$	1.61645	−	6.03268i	0.164126	−	0.612526i	−0.834024	−	0.551728i	$-0.813969\pi$
$97$	1.61645	−	6.03268i	0.164126	−	0.612526i	0.998150	−	0.0607982i	$-0.0193646\pi$
$98$	6.67419	−	1.78835i	0.674196	−	0.180650i
$99$		0			0
$100$	−1.08201	+	1.87410i	−0.108201	+	0.187410i
$101$	−8.59259			−0.854995			−0.427498	−	0.904017i	$-0.640605\pi$
$101$	−8.59259			−0.854995			−0.427498	+	0.904017i	$0.640605\pi$
$102$		0			0
$103$	0.228107	−	0.131698i	0.0224761	−	0.0129766i	−0.488720	−	0.872441i	$-0.662536\pi$
$103$	0.228107	−	0.131698i	0.0224761	−	0.0129766i	0.511196	+	0.859464i	$0.329203\pi$
$104$	−2.89963	−	2.14293i	−0.284332	−	0.210132i
$105$		0			0
$106$	−2.56759	−	2.56759i	−0.249386	−	0.249386i
$107$	−11.4443	+	6.60737i	−1.10636	+	0.638759i	−0.937885	−	0.346947i	$-0.887218\pi$
$107$	−11.4443	+	6.60737i	−1.10636	+	0.638759i	−0.168478	+	0.985705i	$0.553885\pi$
$108$		0			0
$109$	11.1164	+	11.1164i	1.06475	+	1.06475i	0.997753	+	0.0670011i	$0.0213431\pi$
$109$	11.1164	+	11.1164i	1.06475	+	1.06475i	0.0670011	+	0.997753i	$0.478657\pi$
$110$	2.58551	+	0.692786i	0.246519	+	0.0660546i
$111$		0			0
$112$	−0.290365	−	0.0778030i	−0.0274369	−	0.00735169i
$113$			9.74067i			0.916325i	0.888868	+	0.458163i	$0.151492\pi$
$113$			9.74067i			0.916325i	−0.888868	+	0.458163i	$0.848508\pi$
$114$		0			0
$115$	1.57411	−	1.57411i	0.146786	−	0.146786i
$116$	7.48368			0.694843
$117$		0			0
$118$	−0.724678			−0.0667121
$119$	−0.537972	+	0.537972i	−0.0493158	+	0.0493158i
$120$		0			0
$121$		−	8.47359i		−	0.770326i
$122$	−10.8735	−	2.91354i	−0.984437	−	0.263779i
$123$		0			0
$124$	10.3807	+	2.78151i	0.932216	+	0.249787i
$125$	8.53087	+	8.53087i	0.763024	+	0.763024i
$126$		0			0
$127$	15.1666	−	8.75644i	1.34582	−	0.777009i	0.358164	−	0.933659i	$-0.383403\pi$
$127$	15.1666	−	8.75644i	1.34582	−	0.777009i	0.987654	+	0.156650i	$0.0500694\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−4.74964	+	3.78266i	−0.416571	+	0.331762i
$131$	−13.4168	+	7.74619i	−1.17223	+	0.676788i	−0.954205	−	0.299155i	$-0.903295\pi$
$131$	−13.4168	+	7.74619i	−1.17223	+	0.676788i	−0.218027	+	0.975943i	$0.569962\pi$
$132$		0			0
$133$	1.29683			0.112449
$134$	−0.488591	+	0.846265i	−0.0422079	+	0.0731062i
$135$		0			0
$136$	−2.44466	+	0.655045i	−0.209628	+	0.0561697i
$137$	5.53629	−	20.6617i	0.472997	−	1.76525i	−0.155913	−	0.987771i	$-0.549832\pi$
$137$	5.53629	−	20.6617i	0.472997	−	1.76525i	0.628910	−	0.777478i	$-0.283501\pi$
$138$		0			0
$139$	9.22919			0.782810			0.391405	−	0.920219i	$-0.371989\pi$
$139$	9.22919			0.782810			0.391405	+	0.920219i	$0.371989\pi$
$140$	−0.253117	+	0.438411i	−0.0213923	+	0.0370525i
$141$		0			0
$142$	6.16098	+	3.55704i	0.517018	+	0.298500i
$143$	−4.60886	−	3.40613i	−0.385413	−	0.284835i
$144$		0			0
$145$	3.26184	−	12.1734i	0.270881	−	1.01094i
$146$			4.78159i			0.395727i
$147$		0			0
$148$	−0.637416	+	2.37887i	−0.0523953	+	0.195542i
$149$	15.7059	−	15.7059i	1.28668	−	1.28668i	0.349891	−	0.936790i	$-0.386219\pi$
$149$	15.7059	−	15.7059i	1.28668	−	1.28668i	0.936790	−	0.349891i	$-0.113781\pi$
$150$		0			0
$151$	4.46564	+	16.6660i	0.363409	+	1.35626i	0.869565	+	0.493818i	$0.164399\pi$
$151$	4.46564	+	16.6660i	0.363409	+	1.35626i	−0.506157	+	0.862441i	$0.668934\pi$
$152$	3.73605	+	2.15701i	0.303033	+	0.174956i
$153$		0			0
$154$	−0.461525	−	0.123665i	−0.0371908	−	0.00996524i
$155$	9.04909	−	15.6735i	0.726840	−	1.25892i
$156$		0			0
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	0.877770	−	0.479082i	$-0.159030\pi$
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	−0.853782	+	0.520631i	$0.825697\pi$
$158$	−1.91283	−	7.13877i	−0.152176	−	0.567930i
$159$		0			0
$160$	−1.45842	+	0.842018i	−0.115298	+	0.0665673i
$161$	−0.280985	+	0.280985i	−0.0221447	+	0.0221447i
$162$		0			0
$163$	0.929908	+	3.47046i	0.0728360	+	0.271828i	0.992734	−	0.120330i	$-0.0383953\pi$
$163$	0.929908	+	3.47046i	0.0728360	+	0.271828i	−0.919898	+	0.392158i	$0.871729\pi$
$164$	3.63617	−	0.974309i	0.283937	−	0.0760807i
$165$		0			0
$166$	10.6478	+	6.14753i	0.826432	+	0.477141i
$167$	8.72138	−	2.33689i	0.674881	−	0.180834i	0.0949283	−	0.995484i	$-0.469738\pi$
$167$	8.72138	−	2.33689i	0.674881	−	0.180834i	0.579952	+	0.814650i	$0.303071\pi$
$168$		0			0
$169$	12.4274	−	3.81566i	0.955955	−	0.293512i
$170$			4.26212i			0.326890i
$171$		0			0
$172$	3.71188	+	6.42917i	0.283028	+	0.490220i
$173$	7.86600	+	13.6243i	0.598041	+	1.03584i	0.993110	+	0.117186i	$0.0373873\pi$
$173$	7.86600	+	13.6243i	0.598041	+	1.03584i	−0.395069	+	0.918651i	$0.629279\pi$
$174$		0			0
$175$	−0.459989	−	0.459989i	−0.0347719	−	0.0347719i
$176$	−1.12392	−	1.12392i	−0.0847190	−	0.0847190i
$177$		0			0
$178$	−0.989338	−	1.71358i	−0.0741540	−	0.128438i
$179$	−3.29562	−	5.70819i	−0.246326	−	0.426650i	0.716177	−	0.697918i	$-0.245890\pi$
$179$	−3.29562	−	5.70819i	−0.246326	−	0.426650i	−0.962504	+	0.271268i	$0.912557\pi$
$180$		0			0
$181$			11.2750i			0.838063i	0.907972	+	0.419031i	$0.137630\pi$
$181$			11.2750i			0.838063i	−0.907972	+	0.419031i	$0.862370\pi$
$182$	0.847832	−	0.675222i	0.0628455	−	0.0500508i
$183$		0			0
$184$	−1.27686	+	0.342133i	−0.0941311	+	0.0252223i
$185$	3.59177	+	2.07371i	0.264072	+	0.152462i
$186$		0			0
$187$	−3.88571	+	1.04117i	−0.284151	+	0.0761382i
$188$	0.928739	+	3.46610i	0.0677352	+	0.252791i
$189$		0			0
$190$	5.13710	−	5.13710i	0.372684	−	0.372684i
$191$	9.49618	−	5.48262i	0.687120	−	0.396709i	−0.115412	−	0.993318i	$-0.536819\pi$
$191$	9.49618	−	5.48262i	0.687120	−	0.396709i	0.802532	+	0.596609i	$0.203486\pi$
$192$		0			0
$193$	−3.61591	−	13.4948i	−0.260279	−	0.971374i	−0.965077	−	0.261966i	$-0.915629\pi$
$193$	−3.61591	−	13.4948i	−0.260279	−	0.971374i	0.704798	−	0.709408i	$-0.251038\pi$
$194$	3.12275	+	5.40876i	0.224200	+	0.388326i
$195$		0			0
$196$	−3.45482	+	5.98392i	−0.246773	+	0.427423i
$197$	−4.59113	−	1.23019i	−0.327105	−	0.0876474i	0.0915295	−	0.995802i	$-0.470824\pi$
$197$	−4.59113	−	1.23019i	−0.327105	−	0.0876474i	−0.418634	+	0.908155i	$0.637491\pi$
$198$		0			0
$199$	−20.1187	−	11.6155i	−1.42618	−	0.823403i	−0.429359	−	0.903134i	$-0.641260\pi$
$199$	−20.1187	−	11.6155i	−1.42618	−	0.823403i	−0.996816	+	0.0797315i	$0.974594\pi$
$200$	−0.560091	−	2.09029i	−0.0396044	−	0.147806i
$201$		0			0
$202$	6.07588	−	6.07588i	0.427498	−	0.427498i
$203$	−0.582253	+	2.17300i	−0.0408661	+	0.152514i
$204$		0			0
$205$		−	6.33945i		−	0.442766i
$206$	−0.0681718	+	0.254421i	−0.00474975	+	0.0177263i
$207$		0			0
$208$	3.56563	−	0.535061i	0.247232	−	0.0370998i
$209$	5.93833	+	3.42850i	0.410763	+	0.237154i
$210$		0			0
$211$	1.02671	−	1.77832i	0.0706817	−	0.122424i	−0.828519	−	0.559962i	$-0.810816\pi$
$211$	1.02671	−	1.77832i	0.0706817	−	0.122424i	0.899200	+	0.437537i	$0.144149\pi$
$212$	3.63112			0.249386
$213$		0			0
$214$	3.42023	−	12.7645i	0.233802	−	0.872560i
$215$	12.0759	−	3.23573i	0.823569	−	0.220675i
$216$		0			0
$217$	−1.61530	+	2.79778i	−0.109654	+	0.189926i
$218$	−15.7209			−1.06475
$219$		0			0
$220$	−2.31811	+	1.33836i	−0.156287	+	0.0902322i
$221$	3.33936	−	8.49232i	0.224630	−	0.571255i
$222$		0			0
$223$	−0.420741	−	0.420741i	−0.0281749	−	0.0281749i	0.692879	−	0.721054i	$-0.256342\pi$
$223$	−0.420741	−	0.420741i	−0.0281749	−	0.0281749i	−0.721054	+	0.692879i	$0.756342\pi$
$224$	0.260334	−	0.150304i	0.0173943	−	0.0100426i
$225$		0			0
$226$	−6.88769	−	6.88769i	−0.458163	−	0.458163i
$227$	−17.6264	−	4.72299i	−1.16991	−	0.313476i	−0.378992	−	0.925400i	$-0.623729\pi$
$227$	−17.6264	−	4.72299i	−1.16991	−	0.313476i	−0.790916	+	0.611924i	$0.790396\pi$
$228$		0			0
$229$	9.93612	+	2.66237i	0.656597	+	0.175935i	0.571710	−	0.820456i	$-0.306280\pi$
$229$	9.93612	+	2.66237i	0.656597	+	0.175935i	0.0848872	+	0.996391i	$0.472947\pi$
$230$			2.22612i			0.146786i
$231$		0			0
$232$	−5.29176	+	5.29176i	−0.347421	+	0.347421i
$233$	21.7770			1.42666			0.713328	−	0.700830i	$-0.247187\pi$
$233$	21.7770			1.42666			0.713328	+	0.700830i	$0.247187\pi$
$234$		0			0
$235$	6.04294			0.394198
$236$	0.512425	−	0.512425i	0.0333560	−	0.0333560i
$237$		0			0
$238$		−	0.760808i		−	0.0493158i
$239$	18.0937	+	4.84819i	1.17038	+	0.313603i	0.791106	−	0.611679i	$-0.209506\pi$
$239$	18.0937	+	4.84819i	1.17038	+	0.313603i	0.379278	+	0.925283i	$0.376172\pi$
$240$		0			0
$241$	4.27560	+	1.14564i	0.275416	+	0.0737974i	0.393883	−	0.919160i	$-0.371131\pi$
$241$	4.27560	+	1.14564i	0.275416	+	0.0737974i	−0.118467	+	0.992958i	$0.537798\pi$
$242$	5.99173	+	5.99173i	0.385163	+	0.385163i
$243$		0			0
$244$	9.74888	−	5.62852i	0.624108	−	0.360329i
$245$	8.22794	+	8.22794i	0.525664	+	0.525664i
$246$		0			0
$247$	−14.2606	+	6.21081i	−0.907381	+	0.395184i
$248$	−9.30710	+	5.37346i	−0.591001	+	0.341215i
$249$		0			0
$250$	−12.0645			−0.763024
$251$	−14.8094	+	25.6507i	−0.934763	+	1.61906i	−0.159706	+	0.987165i	$0.551055\pi$
$251$	−14.8094	+	25.6507i	−0.934763	+	1.61906i	−0.775057	+	0.631892i	$0.782279\pi$
$252$		0			0
$253$	−2.02952	+	0.543809i	−0.127595	+	0.0341890i
$254$	−4.53267	+	16.9162i	−0.284405	+	1.06141i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.32426	−	14.4180i	0.519253	−	0.899373i	−0.480496	−	0.876997i	$-0.659543\pi$
$257$	8.32426	−	14.4180i	0.519253	−	0.899373i	0.999750	−	0.0223764i	$-0.00712323\pi$
$258$		0			0
$259$	−0.641147	−	0.370166i	−0.0398389	−	0.0230010i
$260$	0.683757	−	6.03325i	0.0424048	−	0.374166i
$261$		0			0
$262$	4.00972	−	14.9645i	0.247722	−	0.924510i
$263$		−	28.0711i		−	1.73094i	−0.500963	−	0.865469i	$-0.667021\pi$
$263$		−	28.0711i		−	1.73094i	0.500963	−	0.865469i	$-0.332979\pi$
$264$		0			0
$265$	1.58266	−	5.90657i	0.0972220	−	0.362838i
$266$	−0.916994	+	0.916994i	−0.0562245	+	0.0562245i
$267$		0			0
$268$	−0.252913	−	0.943886i	−0.0154491	−	0.0576570i
$269$	−16.1655	−	9.33318i	−0.985631	−	0.569054i	−0.0816654	−	0.996660i	$-0.526024\pi$
$269$	−16.1655	−	9.33318i	−0.985631	−	0.569054i	−0.903965	+	0.427606i	$0.859357\pi$
$270$		0			0
$271$	−24.6548	−	6.60622i	−1.49767	−	0.401299i	−0.585351	−	0.810780i	$-0.699043\pi$
$271$	−24.6548	−	6.60622i	−1.49767	−	0.401299i	−0.912319	+	0.409481i	$0.865710\pi$
$272$	1.26545	−	2.19182i	0.0767292	−	0.132899i
$273$		0			0
$274$	10.6953	+	18.5248i	0.646126	+	1.11912i
$275$	−0.890247	−	3.32245i	−0.0536839	−	0.200351i
$276$		0			0
$277$	−13.6852	+	7.90117i	−0.822265	+	0.474735i	−0.851197	−	0.524846i	$-0.824123\pi$
$277$	−13.6852	+	7.90117i	−0.822265	+	0.474735i	0.0289317	+	0.999581i	$0.490789\pi$
$278$	−6.52602	+	6.52602i	−0.391405	+	0.391405i
$279$		0			0
$280$	−0.131023	−	0.488984i	−0.00783012	−	0.0292224i
$281$	−26.0117	+	6.96981i	−1.55173	+	0.415784i	−0.930033	−	0.367477i	$-0.880222\pi$
$281$	−26.0117	+	6.96981i	−1.55173	+	0.415784i	−0.621694	+	0.783261i	$0.713555\pi$
$282$		0			0
$283$	−20.1578	−	11.6381i	−1.19826	−	0.691813i	−0.238089	−	0.971243i	$-0.576521\pi$
$283$	−20.1578	−	11.6381i	−1.19826	−	0.691813i	−0.960166	+	0.279430i	$0.909854\pi$
$284$	−6.87167	+	1.84126i	−0.407759	+	0.109259i
$285$		0			0
$286$	5.66746	−	0.850463i	0.335124	−	0.0502890i
$287$			1.13162i			0.0667974i
$288$		0			0
$289$	5.29727	+	9.17515i	0.311604	+	0.539714i
$290$	6.30139	+	10.9143i	0.370031	+	0.640912i
$291$		0			0
$292$	−3.38109	−	3.38109i	−0.197864	−	0.197864i
$293$	16.5979	+	16.5979i	0.969662	+	0.969662i	0.999553	−	0.0298907i	$-0.00951592\pi$
$293$	16.5979	+	16.5979i	0.969662	+	0.969662i	−0.0298907	+	0.999553i	$0.509516\pi$
$294$		0			0
$295$	−0.610192	−	1.05688i	−0.0355267	−	0.0615341i
$296$	−1.23139	−	2.13284i	−0.0715733	−	0.123969i
$297$		0			0
$298$			22.2116i			1.28668i
$299$	1.74416	−	4.43557i	0.100868	−	0.256516i
$300$		0			0
$301$	−2.15560	+	0.577591i	−0.124247	+	0.0332918i
$302$	−14.9423	−	8.62695i	−0.859834	−	0.496425i
$303$		0			0
$304$	−4.16702	+	1.11655i	−0.238995	+	0.0640385i
$305$	−4.90650	−	18.3113i	−0.280945	−	1.04850i
$306$		0			0
$307$	−15.1916	+	15.1916i	−0.867028	+	0.867028i	−0.992142	−	0.125115i	$-0.960070\pi$
$307$	−15.1916	+	15.1916i	−0.867028	+	0.867028i	0.125115	+	0.992142i	$0.460070\pi$
$308$	0.413792	−	0.238903i	0.0235780	−	0.0136128i
$309$		0			0
$310$	4.68415	+	17.4815i	0.266042	+	0.992882i
$311$	−5.02062	−	8.69597i	−0.284693	−	0.493103i	0.687841	−	0.725861i	$-0.258558\pi$
$311$	−5.02062	−	8.69597i	−0.284693	−	0.493103i	−0.972535	+	0.232758i	$0.925225\pi$
$312$		0			0
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	−0.955565	−	0.294779i	$-0.904754\pi$
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	0.733069	+	0.680154i	$0.238087\pi$
$314$	−0.580663	−	0.155588i	−0.0327687	−	0.00878035i
$315$		0			0
$316$	6.40045	+	3.69530i	0.360053	+	0.207877i
$317$	2.84693	+	10.6249i	0.159900	+	0.596753i	0.998636	+	0.0522155i	$0.0166283\pi$
$317$	2.84693	+	10.6249i	0.159900	+	0.596753i	−0.838736	+	0.544538i	$0.816705\pi$
$318$		0			0
$319$	−8.41109	+	8.41109i	−0.470931	+	0.470931i
$320$	0.435860	−	1.62665i	0.0243653	−	0.0909327i
$321$		0			0
$322$		−	0.397373i		−	0.0221447i
$323$	−2.82587	+	10.5463i	−0.157236	+	0.586812i
$324$		0			0
$325$	7.26129	+	2.85530i	0.402784	+	0.158383i
$326$	−3.11153	−	1.79644i	−0.172332	−	0.0994958i
$327$		0			0
$328$	−1.88222	+	3.26010i	−0.103928	+	0.180009i
$329$	−1.07869			−0.0594702
$330$		0			0
$331$	5.82719	−	21.7474i	0.320292	−	1.19534i	−0.598669	−	0.800996i	$-0.704304\pi$
$331$	5.82719	−	21.7474i	0.320292	−	1.19534i	0.918961	−	0.394348i	$-0.129030\pi$
$332$	−11.8761	+	3.18219i	−0.651786	+	0.174646i
$333$		0			0
$334$	−4.51452	+	7.81938i	−0.247023	+	0.427857i
$335$	−1.64561			−0.0899093
$336$		0			0
$337$	12.2213	−	7.05595i	0.665734	−	0.384362i	−0.128724	−	0.991680i	$-0.541088\pi$
$337$	12.2213	−	7.05595i	0.665734	−	0.384362i	0.794458	+	0.607318i	$0.207755\pi$
$338$	−6.08943	+	11.4856i	−0.331221	+	0.624734i
$339$		0			0
$340$	−3.01378	−	3.01378i	−0.163445	−	0.163445i
$341$	−14.7933	+	8.54094i	−0.801105	+	0.462518i
$342$		0			0
$343$	−2.95666	−	2.95666i	−0.159644	−	0.159644i
$344$	−7.17081	−	1.92141i	−0.386624	−	0.103596i
$345$		0			0
$346$	−15.1959	−	4.07174i	−0.816939	−	0.218898i
$347$			24.6130i			1.32130i	0.750696	+	0.660648i	$0.229718\pi$
$347$			24.6130i			1.32130i	−0.750696	+	0.660648i	$0.770282\pi$
$348$		0			0
$349$	15.8417	−	15.8417i	0.847984	−	0.847984i	−0.141897	−	0.989881i	$-0.545320\pi$
$349$	15.8417	−	15.8417i	0.847984	−	0.847984i	0.989881	+	0.141897i	$0.0453203\pi$
$350$	0.650523			0.0347719
$351$		0			0
$352$	1.58947			0.0847190
$353$	−12.5669	+	12.5669i	−0.668870	+	0.668870i	−0.957455	−	0.288584i	$-0.906816\pi$
$353$	−12.5669	+	12.5669i	−0.668870	+	0.668870i	0.288584	+	0.957455i	$0.406816\pi$
$354$		0			0
$355$			11.9804i			0.635852i
$356$	1.91125	+	0.512119i	0.101296	+	0.0271422i
$357$		0			0
$358$	6.36666	+	1.70594i	0.336488	+	0.0901618i
$359$	−9.00574	−	9.00574i	−0.475305	−	0.475305i	0.428322	−	0.903626i	$-0.359105\pi$
$359$	−9.00574	−	9.00574i	−0.475305	−	0.475305i	−0.903626	+	0.428322i	$0.859105\pi$
$360$		0			0
$361$	−0.337122	+	0.194638i	−0.0177433	+	0.0102441i
$362$	−7.97262	−	7.97262i	−0.419031	−	0.419031i
$363$		0			0
$364$	−0.122054	+	1.07696i	−0.00639735	+	0.0564481i
$365$	−6.97355	+	4.02618i	−0.365012	+	0.210740i
$366$		0			0
$367$	−35.7209			−1.86462			−0.932308	−	0.361667i	$-0.882208\pi$
$367$	−35.7209			−1.86462			−0.932308	+	0.361667i	$0.882208\pi$
$368$	0.660949	−	1.14480i	0.0344544	−	0.0596767i
$369$		0			0
$370$	−4.00610	+	1.07343i	−0.208267	+	0.0558050i
$371$	−0.282512	+	1.05435i	−0.0146673	+	0.0547390i
$372$		0			0
$373$	−10.8592			−0.562267			−0.281134	−	0.959669i	$-0.590710\pi$
$373$	−10.8592			−0.562267			−0.281134	+	0.959669i	$0.590710\pi$
$374$	2.01139	−	3.48384i	0.104007	−	0.180145i
$375$		0			0
$376$	−3.10762	−	1.79419i	−0.160263	−	0.0925281i
$377$	−4.00423	−	26.6840i	−0.206228	−	1.37430i
$378$		0			0
$379$	3.41411	−	12.7416i	0.175371	−	0.654494i	−0.821117	−	0.570760i	$-0.806649\pi$
$379$	3.41411	−	12.7416i	0.175371	−	0.654494i	0.996488	−	0.0837342i	$-0.0266847\pi$
$380$			7.26495i			0.372684i
$381$		0			0
$382$	−2.83802	+	10.5916i	−0.145206	+	0.541914i
$383$	−9.74254	+	9.74254i	−0.497820	+	0.497820i	−0.910759	−	0.412938i	$-0.864502\pi$
$383$	−9.74254	+	9.74254i	−0.497820	+	0.497820i	0.412938	+	0.910759i	$0.364502\pi$
$384$		0			0
$385$	−0.208257	−	0.777225i	−0.0106138	−	0.0396111i
$386$	12.0991	+	6.98540i	0.615826	+	0.355548i
$387$		0			0
$388$	−6.03268	−	1.61645i	−0.306263	−	0.0820629i
$389$	−10.3218	+	17.8779i	−0.523336	+	0.906445i	0.476295	+	0.879286i	$0.341980\pi$
$389$	−10.3218	+	17.8779i	−0.523336	+	0.906445i	−0.999631	+	0.0271595i	$0.991354\pi$
$390$		0			0
$391$	−1.67280	−	2.89737i	−0.0845970	−	0.146526i
$392$	−1.78835	−	6.67419i	−0.0903251	−	0.337098i
$393$		0			0
$394$	4.11630	−	2.37655i	0.207376	−	0.119729i
$395$	8.80067	−	8.80067i	0.442810	−	0.442810i
$396$		0			0
$397$	2.46047	+	9.18259i	0.123487	+	0.460861i	0.999781	−	0.0209159i	$-0.00665821\pi$
$397$	2.46047	+	9.18259i	0.123487	+	0.460861i	−0.876294	+	0.481777i	$0.839992\pi$
$398$	22.4395	−	6.01264i	1.12479	−	0.301386i
$399$		0			0
$400$	1.87410	+	1.08201i	0.0937051	+	0.0541006i
$401$	11.4410	−	3.06561i	0.571337	−	0.153089i	0.0384272	−	0.999261i	$-0.487765\pi$
$401$	11.4410	−	3.06561i	0.571337	−	0.153089i	0.532910	+	0.846172i	$0.321099\pi$
$402$		0			0
$403$	4.36349	−	38.5021i	0.217361	−	1.91792i
$404$			8.59259i			0.427498i
$405$		0			0
$406$	−1.12483	−	1.94826i	−0.0558242	−	0.0966903i
$407$	−1.95726	−	3.39008i	−0.0970178	−	0.168040i
$408$		0			0
$409$	27.1747	+	27.1747i	1.34370	+	1.34370i	0.892340	+	0.451364i	$0.149062\pi$
$409$	27.1747	+	27.1747i	1.34370	+	1.34370i	0.451364	+	0.892340i	$0.350938\pi$
$410$	4.48267	+	4.48267i	0.221383	+	0.221383i
$411$		0			0
$412$	−0.131698	−	0.228107i	−0.00648828	−	0.0112380i
$413$	0.108922	+	0.188658i	0.00535970	+	0.00928327i
$414$		0			0
$415$			20.7053i			1.01638i
$416$	−2.14293	+	2.89963i	−0.105066	+	0.142166i
$417$		0			0
$418$	−6.62335	+	1.77472i	−0.323958	+	0.0868044i
$419$	18.2166	+	10.5173i	0.889937	+	0.513805i	0.873922	−	0.486066i	$-0.161569\pi$
$419$	18.2166	+	10.5173i	0.889937	+	0.513805i	0.0160151	+	0.999872i	$0.494902\pi$
$420$		0			0
$421$	25.7609	−	6.90262i	1.25551	−	0.336413i	0.431048	−	0.902329i	$-0.358144\pi$
$421$	25.7609	−	6.90262i	1.25551	−	0.336413i	0.824463	+	0.565916i	$0.191477\pi$
$422$	0.531465	+	1.98345i	0.0258713	+	0.0965530i
$423$		0			0
$424$	−2.56759	+	2.56759i	−0.124693	+	0.124693i
$425$	4.74316	−	2.73847i	0.230077	−	0.132835i
$426$		0			0
$427$	0.875831	+	3.26865i	0.0423844	+	0.158181i
$428$	6.60737	+	11.4443i	0.319379	+	0.553181i
$429$		0			0
$430$	−6.25094	+	10.8269i	−0.301447	+	0.522122i
$431$	−30.6200	−	8.20459i	−1.47491	−	0.395201i	−0.570299	−	0.821437i	$-0.693173\pi$
$431$	−30.6200	−	8.20459i	−1.47491	−	0.395201i	−0.904612	+	0.426236i	$0.859839\pi$
$432$		0			0
$433$	−32.6337	−	18.8411i	−1.56827	−	0.905444i	−0.996370	−	0.0851235i	$-0.972872\pi$
$433$	−32.6337	−	18.8411i	−1.56827	−	0.905444i	−0.571904	−	0.820320i	$-0.693795\pi$
$434$	−0.836142	−	3.12052i	−0.0401361	−	0.149790i
$435$		0			0
$436$	11.1164	−	11.1164i	0.532377	−	0.532377i
$437$	−1.47596	+	5.50838i	−0.0706050	+	0.263501i
$438$		0			0
$439$			2.96173i			0.141356i	0.997499	+	0.0706779i	$0.0225162\pi$
$439$			2.96173i			0.141356i	−0.997499	+	0.0706779i	$0.977484\pi$
$440$	0.692786	−	2.58551i	0.0330273	−	0.123260i
$441$		0			0
$442$	3.64369	+	8.36627i	0.173313	+	0.397943i
$443$	23.4384	+	13.5322i	1.11359	+	0.642933i	0.939757	−	0.341842i	$-0.111051\pi$
$443$	23.4384	+	13.5322i	1.11359	+	0.642933i	0.173835	+	0.984775i	$0.444384\pi$
$444$		0			0
$445$	1.66608	−	2.88573i	0.0789797	−	0.136797i
$446$	0.595018			0.0281749
$447$		0			0
$448$	−0.0778030	+	0.290365i	−0.00367584	+	0.0137184i
$449$	38.6090	−	10.3453i	1.82207	−	0.488223i	0.825030	−	0.565088i	$-0.191158\pi$
$449$	38.6090	−	10.3453i	1.82207	−	0.488223i	0.997041	+	0.0768655i	$0.0244912\pi$
$450$		0			0
$451$	−2.99173	+	5.18183i	−0.140875	+	0.244003i
$452$	9.74067			0.458163
$453$		0			0
$454$	15.8034	−	9.12412i	0.741692	−	0.428216i
$455$	1.69864	+	0.667944i	0.0796337	+	0.0313137i
$456$		0			0
$457$	−22.8591	−	22.8591i	−1.06930	−	1.06930i	−0.997413	−	0.0718891i	$-0.977097\pi$
$457$	−22.8591	−	22.8591i	−1.06930	−	1.06930i	−0.0718891	−	0.997413i	$-0.522903\pi$
$458$	−8.90848	+	5.14331i	−0.416266	+	0.240331i
$459$		0			0
$460$	−1.57411	−	1.57411i	−0.0733931	−	0.0733931i
$461$	−10.0612	−	2.69590i	−0.468598	−	0.125560i	0.0167904	−	0.999859i	$-0.494655\pi$
$461$	−10.0612	−	2.69590i	−0.468598	−	0.125560i	−0.485389	+	0.874299i	$0.661322\pi$
$462$		0			0
$463$	12.6632	+	3.39310i	0.588509	+	0.157691i	0.540772	−	0.841169i	$-0.318132\pi$
$463$	12.6632	+	3.39310i	0.588509	+	0.157691i	0.0477376	+	0.998860i	$0.484799\pi$
$464$		−	7.48368i		−	0.347421i
$465$		0			0
$466$	−15.3986	+	15.3986i	−0.713328	+	0.713328i
$467$	−1.37176			−0.0634775			−0.0317388	−	0.999496i	$-0.510104\pi$
$467$	−1.37176			−0.0634775			−0.0317388	+	0.999496i	$0.510104\pi$
$468$		0			0
$469$	0.293749			0.0135640
$470$	−4.27301	+	4.27301i	−0.197099	+	0.197099i
$471$		0			0
$472$			0.724678i			0.0333560i
$473$	−11.3978	−	3.05402i	−0.524070	−	0.140424i
$474$		0			0
$475$	−9.01754	−	2.41624i	−0.413753	−	0.110865i
$476$	0.537972	+	0.537972i	0.0246579	+	0.0246579i
$477$		0			0
$478$	−16.2224	+	9.36599i	−0.741994	+	0.428390i
$479$	6.56789	+	6.56789i	0.300094	+	0.300094i	0.841051	−	0.540956i	$-0.181938\pi$
$479$	6.56789	+	6.56789i	0.300094	+	0.300094i	−0.540956	+	0.841051i	$0.681938\pi$
$480$		0			0
$481$	8.82322	+	0.999948i	0.402304	+	0.0455937i
$482$	−3.83340	+	2.21322i	−0.174607	+	0.100809i
$483$		0			0
$484$	−8.47359			−0.385163
$485$	−5.25881	+	9.10853i	−0.238790	+	0.413597i
$486$		0			0
$487$	−11.7546	+	3.14965i	−0.532654	+	0.142724i	−0.515113	−	0.857122i	$-0.672250\pi$
$487$	−11.7546	+	3.14965i	−0.532654	+	0.142724i	−0.0175402	+	0.999846i	$0.505584\pi$
$488$	−2.91354	+	10.8735i	−0.131890	+	0.492219i
$489$		0			0
$490$	−11.6361			−0.525664
$491$	3.72316	−	6.44870i	0.168024	−	0.291026i	−0.769701	−	0.638404i	$-0.779595\pi$
$491$	3.72316	−	6.44870i	0.168024	−	0.291026i	0.937725	+	0.347378i	$0.112928\pi$
$492$		0			0
$493$	−16.4029	−	9.47023i	−0.738750	−	0.426518i
$494$	5.69207	−	14.4755i	0.256098	−	0.651283i
$495$		0			0
$496$	2.78151	−	10.3807i	0.124893	−	0.466108i
$497$		−	2.13855i		−	0.0959269i
$498$		0			0
$499$	−1.27227	+	4.74819i	−0.0569548	+	0.212558i	−0.988539	−	0.150968i	$-0.951761\pi$
$499$	−1.27227	+	4.74819i	−0.0569548	+	0.212558i	0.931584	+	0.363527i	$0.118427\pi$
$500$	8.53087	−	8.53087i	0.381512	−	0.381512i
$501$		0			0
$502$	−7.66592	−	28.6096i	−0.342147	−	1.27691i
$503$	24.0111	+	13.8628i	1.07060	+	0.618112i	0.928346	−	0.371718i	$-0.121231\pi$
$503$	24.0111	+	13.8628i	1.07060	+	0.618112i	0.142255	+	0.989830i	$0.454565\pi$
$504$		0			0
$505$	13.9772	+	3.74517i	0.621976	+	0.166658i
$506$	1.05056	−	1.81962i	0.0467030	−	0.0808920i
$507$		0			0
$508$	−8.75644	−	15.1666i	−0.388504	−	0.672909i
$509$	2.37610	+	8.86772i	0.105319	+	0.393055i	0.998381	−	0.0568780i	$-0.0181146\pi$
$509$	2.37610	+	8.86772i	0.105319	+	0.393055i	−0.893062	+	0.449933i	$0.851448\pi$
$510$		0			0
$511$	1.24481	−	0.718691i	0.0550671	−	0.0317930i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	4.30896	+	16.0812i	0.190060	+	0.709313i
$515$	−0.428453	+	0.114804i	−0.0188799	+	0.00505885i
$516$		0			0
$517$	−4.93947	−	2.85180i	−0.217237	−	0.125422i
$518$	0.715106	−	0.191612i	0.0314200	−	0.00841895i
$519$		0			0
$520$	3.78266	+	4.74964i	0.165881	+	0.208286i
$521$			29.1318i			1.27629i	0.769918	+	0.638143i	$0.220297\pi$
$521$			29.1318i			1.27629i	−0.769918	+	0.638143i	$0.779703\pi$
$522$		0			0
$523$	1.29854	+	2.24913i	0.0567811	+	0.0983478i	0.893019	−	0.450019i	$-0.148583\pi$
$523$	1.29854	+	2.24913i	0.0567811	+	0.0983478i	−0.836238	+	0.548367i	$0.815250\pi$
$524$	7.74619	+	13.4168i	0.338394	+	0.586116i
$525$		0			0
$526$	19.8493	+	19.8493i	0.865469	+	0.865469i
$527$	−19.2329	−	19.2329i	−0.837796	−	0.837796i
$528$		0			0
$529$	10.6263	+	18.4053i	0.462013	+	0.800229i
$530$	3.05746	+	5.29568i	0.132808	+	0.230030i
$531$		0			0
$532$		−	1.29683i		−	0.0562245i
$533$	−5.41960	−	12.4439i	−0.234749	−	0.539006i
$534$		0			0
$535$	21.4958	−	5.75978i	0.929344	−	0.249017i
$536$	0.846265	+	0.488591i	0.0365531	+	0.0211039i
$537$		0			0
$538$	18.0303	−	4.83121i	0.777343	−	0.208288i
$539$	−2.84252	−	10.6084i	−0.122436	−	0.456937i
$540$		0			0
$541$	−4.52095	+	4.52095i	−0.194371	+	0.194371i	−0.797582	−	0.603211i	$-0.793888\pi$
$541$	−4.52095	+	4.52095i	−0.194371	+	0.194371i	0.603211	+	0.797582i	$0.293888\pi$
$542$	22.1049	−	12.7622i	0.949485	−	0.548185i
$543$		0			0
$544$	0.655045	+	2.44466i	0.0280848	+	0.104814i
$545$	−13.2373	−	22.9276i	−0.567023	−	0.982112i
$546$		0			0
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	−0.976777	−	0.214259i	$-0.931267\pi$
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	0.673942	+	0.738784i	$0.264600\pi$
$548$	−20.6617	−	5.53629i	−0.882624	−	0.236498i
$549$		0			0
$550$	2.97883	+	1.71983i	0.127018	+	0.0733336i
$551$	8.35590	+	31.1846i	0.355973	+	1.32851i
$552$		0			0
$553$	−1.57096	+	1.57096i	−0.0668039	+	0.0668039i
$554$	4.08995	−	15.2639i	0.173765	−	0.648500i
$555$		0			0
$556$		−	9.22919i		−	0.391405i
$557$	2.54976	−	9.51584i	0.108037	−	0.403199i	−0.890635	−	0.454719i	$-0.849740\pi$
$557$	2.54976	−	9.51584i	0.108037	−	0.403199i	0.998672	+	0.0515195i	$0.0164064\pi$
$558$		0			0
$559$	20.9380	−	16.6752i	0.885581	−	0.705286i
$560$	0.438411	+	0.253117i	0.0185263	+	0.0106961i
$561$		0			0
$562$	13.4646	−	23.3214i	0.567971	−	0.983755i
$563$	−33.4682			−1.41051			−0.705257	−	0.708951i	$-0.749169\pi$
$563$	−33.4682			−1.41051			−0.705257	+	0.708951i	$0.749169\pi$
$564$		0			0
$565$	4.24557	−	15.8447i	0.178613	−	0.666591i
$566$	22.4831	−	6.02432i	0.945034	−	0.253221i
$567$		0			0
$568$	3.55704	−	6.16098i	0.149250	−	0.258509i
$569$	10.6707			0.447337			0.223669	−	0.974665i	$-0.428197\pi$
$569$	10.6707			0.447337			0.223669	+	0.974665i	$0.428197\pi$
$570$		0			0
$571$	31.5424	−	18.2110i	1.32001	−	0.762107i	0.336279	−	0.941763i	$-0.390832\pi$
$571$	31.5424	−	18.2110i	1.32001	−	0.762107i	0.983730	+	0.179656i	$0.0574983\pi$
$572$	−3.40613	+	4.60886i	−0.142417	+	0.192706i
$573$		0			0
$574$	−0.800176	−	0.800176i	−0.0333987	−	0.0333987i
$575$	2.47737	−	1.43031i	0.103314	−	0.0596481i
$576$		0			0
$577$	−17.7894	−	17.7894i	−0.740581	−	0.740581i	0.232109	−	0.972690i	$-0.425437\pi$
$577$	−17.7894	−	17.7894i	−0.740581	−	0.740581i	−0.972690	+	0.232109i	$0.925437\pi$
$578$	−10.2335	−	2.74207i	−0.425659	−	0.114055i
$579$		0			0
$580$	−12.1734	−	3.26184i	−0.505471	−	0.135441i
$581$		−	3.69599i		−	0.153335i
$582$		0			0
$583$	−4.08110	+	4.08110i	−0.169022	+	0.169022i
$584$	4.78159			0.197864
$585$		0			0
$586$	−23.4730			−0.969662
$587$	14.6657	−	14.6657i	0.605317	−	0.605317i	−0.336401	−	0.941719i	$-0.609210\pi$
$587$	14.6657	−	14.6657i	0.605317	−	0.605317i	0.941719	+	0.336401i	$0.109210\pi$
$588$		0			0
$589$			46.3623i			1.91033i
$590$	1.17880	+	0.315859i	0.0485304	+	0.0130037i
$591$		0			0
$592$	2.37887	+	0.637416i	0.0977709	+	0.0261976i
$593$	25.1984	+	25.1984i	1.03477	+	1.03477i	0.999373	+	0.0353990i	$0.0112702\pi$
$593$	25.1984	+	25.1984i	1.03477	+	1.03477i	0.0353990	+	0.999373i	$0.488730\pi$
$594$		0			0
$595$	1.10958	−	0.640613i	0.0454881	−	0.0262626i
$596$	−15.7059	−	15.7059i	−0.643341	−	0.643341i
$597$		0			0
$598$	1.90311	+	4.36973i	0.0778241	+	0.178692i
$599$	27.2170	−	15.7138i	1.11206	−	0.642047i	0.172697	−	0.984975i	$-0.444752\pi$
$599$	27.2170	−	15.7138i	1.11206	−	0.642047i	0.939362	+	0.342928i	$0.111419\pi$
$600$		0			0
$601$	25.4826			1.03946			0.519728	−	0.854332i	$-0.326033\pi$
$601$	25.4826			1.03946			0.519728	+	0.854332i	$0.326033\pi$
$602$	1.11582	−	1.93266i	0.0454774	−	0.0787692i
$603$		0			0
$604$	16.6660	−	4.46564i	0.678130	−	0.181704i
$605$	−3.69330	+	13.7836i	−0.150154	+	0.560383i
$606$		0			0
$607$	14.5125			0.589045			0.294522	−	0.955645i	$-0.404839\pi$
$607$	14.5125			0.589045			0.294522	+	0.955645i	$0.404839\pi$
$608$	2.15701	−	3.73605i	0.0874782	−	0.151517i
$609$		0			0
$610$	16.4175	+	9.47862i	0.664723	+	0.383778i
$611$	11.8619	−	5.16611i	0.479881	−	0.208999i
$612$		0			0
$613$	1.08903	−	4.06431i	0.0439855	−	0.164156i	−0.940440	−	0.339961i	$-0.889586\pi$
$613$	1.08903	−	4.06431i	0.0439855	−	0.164156i	0.984425	+	0.175805i	$0.0562528\pi$
$614$		−	21.4841i		−	0.867028i
$615$		0			0
$616$	−0.123665	+	0.461525i	−0.00498262	+	0.0185954i
$617$	−1.56048	+	1.56048i	−0.0628225	+	0.0628225i	−0.737820	−	0.674997i	$-0.764145\pi$
$617$	−1.56048	+	1.56048i	−0.0628225	+	0.0628225i	0.674997	+	0.737820i	$0.264145\pi$
$618$		0			0
$619$	6.37151	+	23.7788i	0.256092	+	0.955750i	0.967479	+	0.252950i	$0.0814007\pi$
$619$	6.37151	+	23.7788i	0.256092	+	0.955750i	−0.711387	+	0.702800i	$0.751933\pi$
$620$	−15.6735	−	9.04909i	−0.629462	−	0.363420i
$621$		0			0
$622$	9.69909	+	2.59886i	0.388898	+	0.104205i
$623$	−0.297402	+	0.515116i	−0.0119152	+	0.0206377i
$624$		0			0
$625$	−4.74843	−	8.22452i	−0.189937	−	0.328981i
$626$	−2.03761	−	7.60448i	−0.0814394	−	0.303936i
$627$		0			0
$628$	0.520608	−	0.300573i	0.0207745	−	0.0119942i
$629$	4.40744	−	4.40744i	0.175736	−	0.175736i
$630$		0			0
$631$	9.44199	+	35.2380i	0.375880	+	1.40280i	0.852055	+	0.523452i	$0.175356\pi$
$631$	9.44199	+	35.2380i	0.375880	+	1.40280i	−0.476176	+	0.879350i	$0.657977\pi$
$632$	−7.13877	+	1.91283i	−0.283965	+	0.0760882i
$633$		0			0
$634$	−9.52602	−	5.49985i	−0.378326	−	0.218427i
$635$	−28.4874	+	7.63317i	−1.13049	+	0.302913i
$636$		0			0
$637$	23.1850	+	9.11683i	0.918622	+	0.361222i
$638$		−	11.8951i		−	0.470931i
$639$		0			0
$640$	0.842018	+	1.45842i	0.0332837	+	0.0576490i
$641$	−10.4318	−	18.0685i	−0.412033	−	0.713663i	0.583079	−	0.812416i	$-0.301848\pi$
$641$	−10.4318	−	18.0685i	−0.412033	−	0.713663i	−0.995112	+	0.0987531i	$0.968515\pi$
$642$		0			0
$643$	0.982746	+	0.982746i	0.0387557	+	0.0387557i	0.726219	−	0.687463i	$-0.241276\pi$
$643$	0.982746	+	0.982746i	0.0387557	+	0.0387557i	−0.687463	+	0.726219i	$0.741276\pi$
$644$	0.280985	+	0.280985i	0.0110724	+	0.0110724i
$645$		0			0
$646$	−5.45917	−	9.45556i	−0.214788	−	0.372024i
$647$	5.20265	+	9.01126i	0.204537	+	0.354269i	0.949985	−	0.312295i	$-0.101098\pi$
$647$	5.20265	+	9.01126i	0.204537	+	0.354269i	−0.745448	+	0.666564i	$0.767764\pi$
$648$		0			0
$649$			1.15185i			0.0452142i
$650$	−7.15351	+	3.11551i	−0.280584	+	0.122200i
$651$		0			0
$652$	3.47046	−	0.929908i	0.135914	−	0.0364180i
$653$	−23.5364	−	13.5887i	−0.921050	−	0.531769i	−0.0370803	−	0.999312i	$-0.511806\pi$
$653$	−23.5364	−	13.5887i	−0.921050	−	0.531769i	−0.883970	+	0.467544i	$0.845139\pi$
$654$		0			0
$655$	25.2007	−	6.75252i	0.984674	−	0.263843i
$656$	−0.974309	−	3.63617i	−0.0380404	−	0.141969i
$657$		0			0
$658$	0.762750	−	0.762750i	0.0297351	−	0.0297351i
$659$	20.1845	−	11.6535i	0.786277	−	0.453957i	−0.0523733	−	0.998628i	$-0.516679\pi$
$659$	20.1845	−	11.6535i	0.786277	−	0.453957i	0.838650	+	0.544670i	$0.183345\pi$
$660$		0			0
$661$	0.131680	+	0.491436i	0.00512175	+	0.0191146i	0.968439	−	0.249249i	$-0.0801838\pi$
$661$	0.131680	+	0.491436i	0.00512175	+	0.0191146i	−0.963318	+	0.268364i	$0.913517\pi$
$662$	11.2573	+	19.4982i	0.437526	+	0.757818i
$663$		0			0
$664$	6.14753	−	10.6478i	0.238570	−	0.413216i
$665$	−2.10949	−	0.565235i	−0.0818023	−	0.0219189i
$666$		0			0
$667$	−8.56730	−	4.94634i	−0.331727	−	0.191523i
$668$	−2.33689	−	8.72138i	−0.0904169	−	0.337440i
$669$		0			0
$670$	1.16362	−	1.16362i	0.0449546	−	0.0449546i
$671$	−4.63097	+	17.2830i	−0.178777	+	0.667204i
$672$		0			0
$673$			8.41494i			0.324372i	0.986760	+	0.162186i	$0.0518545\pi$
$673$			8.41494i			0.324372i	−0.986760	+	0.162186i	$0.948146\pi$
$674$	−3.65243	+	13.6310i	−0.140686	+	0.525048i
$675$		0			0
$676$	−3.81566	−	12.4274i	−0.146756	−	0.477978i
$677$	17.7008	+	10.2196i	0.680297	+	0.392770i	0.799967	−	0.600044i	$-0.204850\pi$
$677$	17.7008	+	10.2196i	0.680297	+	0.392770i	−0.119670	+	0.992814i	$0.538184\pi$
$678$		0			0
$679$	0.938721	−	1.62591i	0.0360248	−	0.0623968i
$680$	4.26212			0.163445
$681$		0			0
$682$	4.42112	−	16.4998i	0.169293	−	0.631811i
$683$	−16.8568	+	4.51677i	−0.645008	+	0.172829i	−0.566471	−	0.824082i	$-0.691692\pi$
$683$	−16.8568	+	4.51677i	−0.645008	+	0.172829i	−0.0785371	+	0.996911i	$0.525025\pi$
$684$		0			0
$685$	−18.0112	+	31.1964i	−0.688174	+	1.19195i
$686$	4.18134			0.159644
$687$		0			0
$688$	6.42917	−	3.71188i	0.245110	−	0.141514i
$689$	−1.94287	−	12.9472i	−0.0740175	−	0.493250i
$690$		0			0
$691$	5.28654	+	5.28654i	0.201110	+	0.201110i	0.800475	−	0.599366i	$-0.204580\pi$
$691$	5.28654	+	5.28654i	0.201110	+	0.201110i	−0.599366	+	0.800475i	$0.704580\pi$
$692$	13.6243	−	7.86600i	0.517919	−	0.299020i
$693$		0			0
$694$	−17.4040	−	17.4040i	−0.660648	−	0.660648i
$695$	−15.0127	−	4.02264i	−0.569464	−	0.152587i
$696$		0			0
$697$	−9.20278	−	2.46588i	−0.348580	−	0.0934018i
$698$			22.4035i			0.847984i
$699$		0			0
$700$	−0.459989	+	0.459989i	−0.0173859	+	0.0173859i
$701$	31.1840			1.17780			0.588901	−	0.808205i	$-0.299561\pi$
$701$	31.1840			1.17780			0.588901	+	0.808205i	$0.299561\pi$
$702$		0			0
$703$	−10.6245			−0.400711
$704$	−1.12392	+	1.12392i	−0.0423595	+	0.0423595i
$705$		0			0
$706$		−	17.7723i		−	0.668870i
$707$	−2.49499	−	0.668529i	−0.0938336	−	0.0251426i
$708$		0			0
$709$	−8.04984	−	2.15695i	−0.302318	−	0.0810059i	0.104471	−	0.994528i	$-0.466685\pi$
$709$	−8.04984	−	2.15695i	−0.302318	−	0.0810059i	−0.406789	+	0.913522i	$0.633352\pi$
$710$	−8.47140	−	8.47140i	−0.317926	−	0.317926i
$711$		0			0
$712$	−1.71358	+	0.989338i	−0.0642192	+	0.0370770i
$713$	−10.0454	−	10.0454i	−0.376203	−	0.376203i
$714$		0			0
$715$	6.01243	+	7.54941i	0.224852	+	0.282332i
$716$	−5.70819	+	3.29562i	−0.213325	+	0.123163i
$717$		0			0
$718$	12.7360			0.475305
$719$	5.63051	−	9.75233i	0.209983	−	0.363701i	−0.741726	−	0.670703i	$-0.765993\pi$
$719$	5.63051	−	9.75233i	0.209983	−	0.363701i	0.951709	+	0.307002i	$0.0993259\pi$
$720$		0			0
$721$	0.0764807	−	0.0204930i	0.00284829	−	0.000763197i
$722$	0.100752	−	0.376011i	0.00374959	−	0.0139937i
$723$		0			0
$724$	11.2750			0.419031
$725$	8.09744	−	14.0252i	0.300731	−	0.520882i
$726$		0			0
$727$	5.52426	+	3.18943i	0.204883	+	0.118290i	0.598931	−	0.800800i	$-0.295592\pi$
$727$	5.52426	+	3.18943i	0.204883	+	0.118290i	−0.394048	+	0.919090i	$0.628926\pi$
$728$	−0.675222	−	0.847832i	−0.0250254	−	0.0314227i
$729$		0			0
$730$	2.08410	−	7.77798i	0.0771362	−	0.287876i
$731$		−	18.7888i		−	0.694929i
$732$		0			0
$733$	6.48221	−	24.1919i	0.239426	−	0.893550i	−0.736678	−	0.676244i	$-0.763606\pi$
$733$	6.48221	−	24.1919i	0.239426	−	0.893550i	0.976104	−	0.217306i	$-0.0697268\pi$
$734$	25.2585	−	25.2585i	0.932308	−	0.932308i
$735$		0			0
$736$	0.342133	+	1.27686i	0.0126112	+	0.0470655i
$737$	1.34511	+	0.776601i	0.0495478	+	0.0286065i
$738$		0			0
$739$	42.5336	+	11.3968i	1.56462	+	0.419240i	0.934124	−	0.356950i	$-0.116183\pi$
$739$	42.5336	+	11.3968i	1.56462	+	0.419240i	0.630500	+	0.776189i	$0.282850\pi$
$740$	2.07371	−	3.59177i	0.0762311	−	0.132036i
$741$		0			0
$742$	−0.545771	−	0.945302i	−0.0200359	−	0.0347031i
$743$	1.38387	+	5.16468i	0.0507693	+	0.189474i	0.986653	−	0.162834i	$-0.0520636\pi$
$743$	1.38387	+	5.16468i	0.0507693	+	0.189474i	−0.935884	+	0.352308i	$0.885397\pi$
$744$		0			0
$745$	−32.3937	+	18.7025i	−1.18681	+	0.685208i
$746$	7.67860	−	7.67860i	0.281134	−	0.281134i
$747$		0			0
$748$	1.04117	+	3.88571i	0.0380691	+	0.142076i
$749$	−3.83709	+	1.02815i	−0.140204	+	0.0375676i
$750$		0			0
$751$	−16.4494	−	9.49704i	−0.600246	−	0.346552i	0.168892	−	0.985634i	$-0.445981\pi$
$751$	−16.4494	−	9.49704i	−0.600246	−	0.346552i	−0.769138	+	0.639082i	$0.779314\pi$
$752$	3.46610	−	0.928739i	0.126396	−	0.0338676i
$753$		0			0
$754$	21.6999	+	16.0370i	0.790263	+	0.584035i
$755$		−	29.0562i		−	1.05746i
$756$		0			0
$757$	16.5655	+	28.6922i	0.602082	+	1.04284i	0.992505	+	0.122202i	$0.0389954\pi$
$757$	16.5655	+	28.6922i	0.602082	+	1.04284i	−0.390423	+	0.920636i	$0.627671\pi$
$758$	6.59556	+	11.4238i	0.239562	+	0.414933i
$759$		0			0
$760$	−5.13710	−	5.13710i	−0.186342	−	0.186342i
$761$	−31.7060	−	31.7060i	−1.14934	−	1.14934i	−0.986683	−	0.162658i	$-0.947993\pi$
$761$	−31.7060	−	31.7060i	−1.14934	−	1.14934i	−0.162658	−	0.986683i	$-0.552007\pi$
$762$		0			0
$763$	2.36291	+	4.09268i	0.0855431	+	0.148165i
$764$	−5.48262	−	9.49618i	−0.198354	−	0.343560i
$765$		0			0
$766$		−	13.7780i		−	0.497820i
$767$	−2.10130	−	1.55294i	−0.0758734	−	0.0560734i
$768$		0			0
$769$	−7.46852	+	2.00118i	−0.269322	+	0.0721645i	−0.390952	−	0.920411i	$-0.627854\pi$
$769$	−7.46852	+	2.00118i	−0.269322	+	0.0721645i	0.121631	+	0.992575i	$0.461188\pi$
$770$	0.696841	+	0.402321i	0.0251124	+	0.0144987i
$771$		0			0
$772$	−13.4948	+	3.61591i	−0.485687	+	0.130139i
$773$	8.41217	+	31.3946i	0.302565	+	1.12919i	0.935021	+	0.354591i	$0.115380\pi$
$773$	8.41217	+	31.3946i	0.302565	+	1.12919i	−0.632457	+	0.774596i	$0.717953\pi$
$774$		0			0
$775$	16.4449	−	16.4449i	0.590718	−	0.590718i
$776$	5.40876	−	3.12275i	0.194163	−	0.112100i
$777$		0			0
$778$	−5.34296	−	19.9402i	−0.191554	−	0.714891i
$779$	8.11993	+	14.0641i	0.290927	+	0.503900i
$780$		0			0
$781$	5.65380	−	9.79268i	0.202309	−	0.350410i
$782$	3.23159	+	0.865903i	0.115562	+	0.0309646i
$783$		0			0
$784$	5.98392	+	3.45482i

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.62665 - 0.435860i) q^{5} +(0.290365 + 0.0778030i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.62665 - 0.435860i) q^{5} +(0.290365 + 0.0778030i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.45842 - 0.842018i) q^{10} +(1.12392 + 1.12392i) q^{11} +(-3.56563 + 0.535061i) q^{13} +(-0.260334 + 0.150304i) q^{14} -1.00000 q^{16} +(-1.26545 + 2.19182i) q^{17} +(4.16702 - 1.11655i) q^{19} +(-0.435860 + 1.62665i) q^{20} -1.58947 q^{22} +(-0.660949 + 1.14480i) q^{23} +(-1.87410 - 1.08201i) q^{25} +(2.14293 - 2.89963i) q^{26} +(0.0778030 - 0.290365i) q^{28} +7.48368i q^{29} +(-2.78151 + 10.3807i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.655045 - 2.44466i) q^{34} +(-0.438411 - 0.253117i) q^{35} +(-2.37887 - 0.637416i) q^{37} +(-2.15701 + 3.73605i) q^{38} +(-0.842018 - 1.45842i) q^{40} +(0.974309 + 3.63617i) q^{41} +(-6.42917 + 3.71188i) q^{43} +(1.12392 - 1.12392i) q^{44} +(-0.342133 - 1.27686i) q^{46} +(-3.46610 + 0.928739i) q^{47} +(-5.98392 - 3.45482i) q^{49} +(2.09029 - 0.560091i) q^{50} +(0.535061 + 3.56563i) q^{52} +3.63112i q^{53} +(-1.33836 - 2.31811i) q^{55} +(0.150304 + 0.260334i) q^{56} +(-5.29176 - 5.29176i) q^{58} +(0.512425 + 0.512425i) q^{59} +(5.62852 + 9.74888i) q^{61} +(-5.37346 - 9.30710i) q^{62} +1.00000i q^{64} +(6.03325 + 0.683757i) q^{65} +(0.943886 - 0.252913i) q^{67} +(2.19182 + 1.26545i) q^{68} +(0.488984 - 0.131023i) q^{70} +(-1.84126 - 6.87167i) q^{71} +(3.38109 - 3.38109i) q^{73} +(2.13284 - 1.23139i) q^{74} +(-1.11655 - 4.16702i) q^{76} +(0.238903 + 0.413792i) q^{77} +(-3.69530 + 6.40045i) q^{79} +(1.62665 + 0.435860i) q^{80} +(-3.26010 - 1.88222i) q^{82} +(-3.18219 - 11.8761i) q^{83} +(3.01378 - 3.01378i) q^{85} +(1.92141 - 7.17081i) q^{86} +1.58947i q^{88} +(-0.512119 + 1.91125i) q^{89} +(-1.07696 - 0.122054i) q^{91} +(1.14480 + 0.660949i) q^{92} +(1.79419 - 3.10762i) q^{94} -7.26495 q^{95} +(1.61645 - 6.03268i) q^{97} +(6.67419 - 1.78835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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