LMFDB - Embedded newform 1638.2.x.b.811.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(307,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1638.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.2
Root			$-0.916813i$ of defining polynomial
Character	$\chi$	$=$	1638.811
Dual form			1638.2.x.b.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.27220 + 2.27220i) q^{5} +(-2.27220 + 1.35539i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.27220 + 2.27220i) q^{5} +(-2.27220 + 1.35539i) q^{7} +(0.707107 + 0.707107i) q^{8} -3.21338 q^{10} +(-0.355392 - 0.355392i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(0.648285 - 2.56510i) q^{14} -1.00000 q^{16} -4.32583 q^{17} +(-5.98299 - 5.98299i) q^{19} +(2.27220 - 2.27220i) q^{20} +0.502600 q^{22} -2.38496i q^{23} +5.32583i q^{25} +(-0.707107 - 3.53553i) q^{26} +(1.35539 + 2.27220i) q^{28} -1.09574 q^{29} +(-1.08319 - 1.08319i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.05882 - 3.05882i) q^{34} +(-8.24264 - 2.08319i) q^{35} +(-5.18902 - 5.18902i) q^{37} +8.46122 q^{38} +3.21338i q^{40} +(3.53186 + 3.53186i) q^{41} -7.44867i q^{43} +(-0.355392 + 0.355392i) q^{44} +(1.68642 + 1.68642i) q^{46} +(-4.71078 + 4.71078i) q^{47} +(3.32583 - 6.15945i) q^{49} +(-3.76593 - 3.76593i) q^{50} +(3.00000 + 2.00000i) q^{52} +11.2552 q^{53} -1.61504i q^{55} +(-2.56510 - 0.648285i) q^{56} +(0.774804 - 0.774804i) q^{58} +(3.61504 - 3.61504i) q^{59} +4.32583i q^{61} +1.53186 q^{62} +1.00000i q^{64} +(-11.3610 + 2.27220i) q^{65} +(-0.531858 + 0.531858i) q^{67} +4.32583i q^{68} +(7.30146 - 4.35539i) q^{70} +(-6.38496 + 6.38496i) q^{71} +(5.18902 - 5.18902i) q^{73} +7.33838 q^{74} +(-5.98299 + 5.98299i) q^{76} +(1.28922 + 0.325828i) q^{77} -11.3143 q^{79} +(-2.27220 - 2.27220i) q^{80} -4.99480 q^{82} +(6.71078 + 6.71078i) q^{83} +(-9.82917 - 9.82917i) q^{85} +(5.26701 + 5.26701i) q^{86} -0.502600i q^{88} +(-3.75044 + 3.75044i) q^{89} +(0.478235 - 9.52740i) q^{91} -2.38496 q^{92} -6.66205i q^{94} -27.1891i q^{95} +(12.9931 + 12.9931i) q^{97} +(2.00368 + 6.70711i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + 4 * q^7	$ 8 q - 4 q^{5} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{16} - 12 q^{17} - 4 q^{19} - 4 q^{20} + 4 q^{22} + 12 q^{29} - 20 q^{31} + 24 q^{34} - 32 q^{35} - 8 q^{37} + 12 q^{38} + 16 q^{41} + 8 q^{44} - 20 q^{46} - 16 q^{47} + 4 q^{49} - 24 q^{50} + 24 q^{52} + 24 q^{53} - 4 q^{56} - 16 q^{58} + 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} + 8 q^{73} + 4 q^{74} - 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} - 40 q^{82} + 32 q^{83} + 20 q^{85} + 20 q^{86} + 4 q^{89} - 8 q^{91} - 20 q^{92} + 36 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^16 - 12 * q^17 - 4 * q^19 - 4 * q^20 + 4 * q^22 + 12 * q^29 - 20 * q^31 + 24 * q^34 - 32 * q^35 - 8 * q^37 + 12 * q^38 + 16 * q^41 + 8 * q^44 - 20 * q^46 - 16 * q^47 + 4 * q^49 - 24 * q^50 + 24 * q^52 + 24 * q^53 - 4 * q^56 - 16 * q^58 + 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 + 8 * q^73 + 4 * q^74 - 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 - 40 * q^82 + 32 * q^83 + 20 * q^85 + 20 * q^86 + 4 * q^89 - 8 * q^91 - 20 * q^92 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.27220	+	2.27220i	1.01616	+	1.01616i	0.999867	+	0.0162935i	$0.00518663\pi$
$5$	2.27220	+	2.27220i	1.01616	+	1.01616i	0.0162935	+	0.999867i	$0.494813\pi$
$6$		0			0
$7$	−2.27220	+	1.35539i	−0.858813	+	0.512290i
$7$	−2.27220	+	1.35539i	−0.858813	+	0.512290i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−3.21338			−1.01616
$11$	−0.355392	−	0.355392i	−0.107155	−	0.107155i	0.651497	−	0.758651i	$-0.274141\pi$
$11$	−0.355392	−	0.355392i	−0.107155	−	0.107155i	−0.758651	+	0.651497i	$0.774141\pi$
$12$		0			0
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$	0.648285	−	2.56510i	0.173261	−	0.685551i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.32583			−1.04917			−0.524584	−	0.851359i	$-0.675779\pi$
$17$	−4.32583			−1.04917			−0.524584	+	0.851359i	$0.675779\pi$
$18$		0			0
$19$	−5.98299	−	5.98299i	−1.37259	−	1.37259i	−0.856584	−	0.516007i	$-0.827418\pi$
$19$	−5.98299	−	5.98299i	−1.37259	−	1.37259i	−0.516007	−	0.856584i	$-0.672582\pi$
$20$	2.27220	−	2.27220i	0.508080	−	0.508080i
$21$		0			0
$22$	0.502600			0.107155
$23$		−	2.38496i		−	0.497298i	−0.968594	−	0.248649i	$-0.920014\pi$
$23$		−	2.38496i		−	0.497298i	0.968594	−	0.248649i	$-0.0799865\pi$
$24$		0			0
$25$			5.32583i			1.06517i
$26$	−0.707107	−	3.53553i	−0.138675	−	0.693375i
$27$		0			0
$28$	1.35539	+	2.27220i	0.256145	+	0.429406i
$29$	−1.09574			−0.203474			−0.101737	−	0.994811i	$-0.532440\pi$
$29$	−1.09574			−0.203474			−0.101737	+	0.994811i	$0.532440\pi$
$30$		0			0
$31$	−1.08319	−	1.08319i	−0.194546	−	0.194546i	0.603111	−	0.797657i	$-0.293928\pi$
$31$	−1.08319	−	1.08319i	−0.194546	−	0.194546i	−0.797657	+	0.603111i	$0.793928\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	3.05882	−	3.05882i	0.524584	−	0.524584i
$35$	−8.24264	−	2.08319i	−1.39326	−	0.352123i
$36$		0			0
$37$	−5.18902	−	5.18902i	−0.853069	−	0.853069i	0.137441	−	0.990510i	$-0.456112\pi$
$37$	−5.18902	−	5.18902i	−0.853069	−	0.853069i	−0.990510	+	0.137441i	$0.956112\pi$
$38$	8.46122			1.37259
$39$		0			0
$40$			3.21338i			0.508080i
$41$	3.53186	+	3.53186i	0.551583	+	0.551583i	0.926898	−	0.375314i	$-0.122465\pi$
$41$	3.53186	+	3.53186i	0.551583	+	0.551583i	−0.375314	+	0.926898i	$0.622465\pi$
$42$		0			0
$43$		−	7.44867i		−	1.13591i	−0.823059	−	0.567956i	$-0.807734\pi$
$43$		−	7.44867i		−	1.13591i	0.823059	−	0.567956i	$-0.192266\pi$
$44$	−0.355392	+	0.355392i	−0.0535773	+	0.0535773i
$45$		0			0
$46$	1.68642	+	1.68642i	0.248649	+	0.248649i
$47$	−4.71078	+	4.71078i	−0.687138	+	0.687138i	−0.961598	−	0.274460i	$-0.911501\pi$
$47$	−4.71078	+	4.71078i	−0.687138	+	0.687138i	0.274460	+	0.961598i	$0.411501\pi$
$48$		0			0
$49$	3.32583	−	6.15945i	0.475118	−	0.879922i
$50$	−3.76593	−	3.76593i	−0.532583	−	0.532583i
$51$		0			0
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$	11.2552			1.54602			0.773010	−	0.634394i	$-0.218750\pi$
$53$	11.2552			1.54602			0.773010	+	0.634394i	$0.218750\pi$
$54$		0			0
$55$		−	1.61504i		−	0.217773i
$56$	−2.56510	−	0.648285i	−0.342776	−	0.0866307i
$57$		0			0
$58$	0.774804	−	0.774804i	0.101737	−	0.101737i
$59$	3.61504	−	3.61504i	0.470639	−	0.470639i	−0.431483	−	0.902121i	$-0.642009\pi$
$59$	3.61504	−	3.61504i	0.470639	−	0.470639i	0.902121	+	0.431483i	$0.142009\pi$
$60$		0			0
$61$			4.32583i			0.553865i	0.960889	+	0.276933i	$0.0893179\pi$
$61$			4.32583i			0.553865i	−0.960889	+	0.276933i	$0.910682\pi$
$62$	1.53186			0.194546
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−11.3610	+	2.27220i	−1.40916	+	0.281832i
$66$		0			0
$67$	−0.531858	+	0.531858i	−0.0649768	+	0.0649768i	−0.738848	−	0.673872i	$-0.764630\pi$
$67$	−0.531858	+	0.531858i	−0.0649768	+	0.0649768i	0.673872	+	0.738848i	$0.264630\pi$
$68$			4.32583i			0.524584i
$69$		0			0
$70$	7.30146	−	4.35539i	0.872692	−	0.520569i
$71$	−6.38496	+	6.38496i	−0.757755	+	0.757755i	−0.975913	−	0.218159i	$-0.929995\pi$
$71$	−6.38496	+	6.38496i	−0.757755	+	0.757755i	0.218159	+	0.975913i	$0.429995\pi$
$72$		0			0
$73$	5.18902	−	5.18902i	0.607329	−	0.607329i	−0.334919	−	0.942247i	$-0.608709\pi$
$73$	5.18902	−	5.18902i	0.607329	−	0.607329i	0.942247	+	0.334919i	$0.108709\pi$
$74$	7.33838			0.853069
$75$		0			0
$76$	−5.98299	+	5.98299i	−0.686296	+	0.686296i
$77$	1.28922	+	0.325828i	0.146920	+	0.0371315i
$78$		0			0
$79$	−11.3143			−1.27296			−0.636480	−	0.771293i	$-0.719610\pi$
$79$	−11.3143			−1.27296			−0.636480	+	0.771293i	$0.719610\pi$
$80$	−2.27220	−	2.27220i	−0.254040	−	0.254040i
$81$		0			0
$82$	−4.99480			−0.551583
$83$	6.71078	+	6.71078i	0.736604	+	0.736604i	0.971919	−	0.235315i	$-0.0756122\pi$
$83$	6.71078	+	6.71078i	0.736604	+	0.736604i	−0.235315	+	0.971919i	$0.575612\pi$
$84$		0			0
$85$	−9.82917	−	9.82917i	−1.06612	−	1.06612i
$86$	5.26701	+	5.26701i	0.567956	+	0.567956i
$87$		0			0
$88$		−	0.502600i		−	0.0535773i
$89$	−3.75044	+	3.75044i	−0.397546	+	0.397546i	−0.877367	−	0.479821i	$-0.840702\pi$
$89$	−3.75044	+	3.75044i	−0.397546	+	0.397546i	0.479821	+	0.877367i	$0.340702\pi$
$90$		0			0
$91$	0.478235	−	9.52740i	0.0501326	−	0.998743i
$92$	−2.38496			−0.248649
$93$		0			0
$94$		−	6.66205i		−	0.687138i
$95$		−	27.1891i		−	2.78955i
$96$		0			0
$97$	12.9931	+	12.9931i	1.31925	+	1.31925i	0.914372	+	0.404876i	$0.132685\pi$
$97$	12.9931	+	12.9931i	1.31925	+	1.31925i	0.404876	+	0.914372i	$0.367315\pi$
$98$	2.00368	+	6.70711i	0.202402	+	0.677520i
$99$		0			0
$100$	5.32583			0.532583
$101$	−19.7996			−1.97013			−0.985067	−	0.172171i	$-0.944922\pi$
$101$	−19.7996			−1.97013			−0.985067	+	0.172171i	$0.944922\pi$
$102$		0			0
$103$	−2.70386			−0.266420			−0.133210	−	0.991088i	$-0.542528\pi$
$103$	−2.70386			−0.266420			−0.133210	+	0.991088i	$0.542528\pi$
$104$	−3.53553	+	0.707107i	−0.346688	+	0.0693375i
$105$		0			0
$106$	−7.95862	+	7.95862i	−0.773010	+	0.773010i
$107$	11.6673			1.12792			0.563958	−	0.825804i	$-0.309278\pi$
$107$	11.6673			1.12792			0.563958	+	0.825804i	$0.309278\pi$
$108$		0			0
$109$	−5.29626	+	5.29626i	−0.507290	+	0.507290i	−0.913694	−	0.406404i	$-0.866783\pi$
$109$	−5.29626	+	5.29626i	−0.507290	+	0.507290i	0.406404	+	0.913694i	$0.366783\pi$
$110$	1.14201	+	1.14201i	0.108886	+	0.108886i
$111$		0			0
$112$	2.27220	−	1.35539i	0.214703	−	0.128072i
$113$	−20.3440			−1.91380			−0.956902	−	0.290412i	$-0.906208\pi$
$113$	−20.3440			−1.91380			−0.956902	+	0.290412i	$0.906208\pi$
$114$		0			0
$115$	5.41911	−	5.41911i	0.505334	−	0.505334i
$116$			1.09574i			0.101737i
$117$		0			0
$118$			5.11245i			0.470639i
$119$	9.82917	−	5.86319i	0.901038	−	0.537478i
$120$		0			0
$121$		−	10.7474i		−	0.977036i
$122$	−3.05882	−	3.05882i	−0.276933	−	0.276933i
$123$		0			0
$124$	−1.08319	+	1.08319i	−0.0972731	+	0.0972731i
$125$	−0.740347	+	0.740347i	−0.0662186	+	0.0662186i
$126$		0			0
$127$			7.60812i			0.675112i	0.941305	+	0.337556i	$0.109600\pi$
$127$			7.60812i			0.675112i	−0.941305	+	0.337556i	$0.890400\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	6.42677	−	9.64015i	0.563665	−	0.845497i
$131$		−	6.87024i		−	0.600255i	−0.953899	−	0.300128i	$-0.902971\pi$
$131$		−	6.87024i		−	0.600255i	0.953899	−	0.300128i	$-0.0970293\pi$
$132$		0			0
$133$	21.7039	+	5.48528i	1.88196	+	0.475634i
$134$		−	0.752160i		−	0.0649768i
$135$		0			0
$136$	−3.05882	−	3.05882i	−0.262292	−	0.262292i
$137$	0.272205	+	0.272205i	0.0232560	+	0.0232560i	0.718639	−	0.695383i	$-0.244765\pi$
$137$	0.272205	+	0.272205i	0.0232560	+	0.0232560i	−0.695383	+	0.718639i	$0.744765\pi$
$138$		0			0
$139$		−	20.3440i		−	1.72556i	−0.505583	−	0.862778i	$-0.668722\pi$
$139$		−	20.3440i		−	1.72556i	0.505583	−	0.862778i	$-0.331278\pi$
$140$	−2.08319	+	8.24264i	−0.176061	+	0.696630i
$141$		0			0
$142$		−	9.02969i		−	0.757755i
$143$	1.77696	−	0.355392i	0.148597	−	0.0297193i
$144$		0			0
$145$	−2.48974	−	2.48974i	−0.206762	−	0.206762i
$146$			7.33838i			0.607329i
$147$		0			0
$148$	−5.18902	+	5.18902i	−0.426535	+	0.426535i
$149$	−10.5685	+	10.5685i	−0.865803	+	0.865803i	−0.992005	−	0.126202i	$-0.959721\pi$
$149$	−10.5685	+	10.5685i	−0.865803	+	0.865803i	0.126202	+	0.992005i	$0.459721\pi$
$150$		0			0
$151$	−0.149362	−	0.149362i	−0.0121549	−	0.0121549i	0.701003	−	0.713158i	$-0.252736\pi$
$151$	−0.149362	−	0.149362i	−0.0121549	−	0.0121549i	−0.713158	+	0.701003i	$0.752736\pi$
$152$		−	8.46122i		−	0.686296i
$153$		0			0
$154$	−1.14201	+	0.681219i	−0.0920257	+	0.0548942i
$155$		−	4.92244i		−	0.395380i
$156$		0			0
$157$			10.7630i			0.858980i	0.903072	+	0.429490i	$0.141307\pi$
$157$			10.7630i			0.858980i	−0.903072	+	0.429490i	$0.858693\pi$
$158$	8.00043	−	8.00043i	0.636480	−	0.636480i
$159$		0			0
$160$	3.21338			0.254040
$161$	3.23255	+	5.41911i	0.254761	+	0.427085i
$162$		0			0
$163$	−3.40901	−	3.40901i	−0.267015	−	0.267015i	0.560881	−	0.827896i	$-0.310462\pi$
$163$	−3.40901	−	3.40901i	−0.267015	−	0.267015i	−0.827896	+	0.560881i	$0.810462\pi$
$164$	3.53186	−	3.53186i	0.275792	−	0.275792i
$165$		0			0
$166$	−9.49048			−0.736604
$167$	−10.0226	+	10.0226i	−0.775575	+	0.775575i	−0.979075	−	0.203500i	$-0.934768\pi$
$167$	−10.0226	+	10.0226i	−0.775575	+	0.775575i	0.203500	+	0.979075i	$0.434768\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	13.9005			1.06612
$171$		0			0
$172$	−7.44867			−0.567956
$173$	−19.7405			−1.50084			−0.750420	−	0.660961i	$-0.770149\pi$
$173$	−19.7405			−1.50084			−0.750420	+	0.660961i	$0.770149\pi$
$174$		0			0
$175$	−7.21858	−	12.1014i	−0.545673	−	0.914778i
$176$	0.355392	+	0.355392i	0.0267886	+	0.0267886i
$177$		0			0
$178$		−	5.30392i		−	0.397546i
$179$		−	9.79960i		−	0.732457i	−0.930525	−	0.366228i	$-0.880649\pi$
$179$		−	9.79960i		−	0.732457i	0.930525	−	0.366228i	$-0.119351\pi$
$180$		0			0
$181$	−10.4372			−0.775788			−0.387894	−	0.921704i	$-0.626797\pi$
$181$	−10.4372			−0.775788			−0.387894	+	0.921704i	$0.626797\pi$
$182$	6.39872	+	7.07505i	0.474305	+	0.524438i
$183$		0			0
$184$	1.68642	−	1.68642i	0.124324	−	0.124324i
$185$		−	23.5810i		−	1.73371i
$186$		0			0
$187$	1.53736	+	1.53736i	0.112423	+	0.112423i
$188$	4.71078	+	4.71078i	0.343569	+	0.343569i
$189$		0			0
$190$	19.2256	+	19.2256i	1.39477	+	1.39477i
$191$	−11.1410			−0.806136			−0.403068	−	0.915170i	$-0.632056\pi$
$191$	−11.1410			−0.806136			−0.403068	+	0.915170i	$0.632056\pi$
$192$		0			0
$193$	4.03661	+	4.03661i	0.290562	+	0.290562i	0.837302	−	0.546741i	$-0.184132\pi$
$193$	4.03661	+	4.03661i	0.290562	+	0.290562i	−0.546741	+	0.837302i	$0.684132\pi$
$194$	−18.3750			−1.31925
$195$		0			0
$196$	−6.15945	−	3.32583i	−0.439961	−	0.237559i
$197$	−0.627596	+	0.627596i	−0.0447144	+	0.0447144i	−0.729110	−	0.684396i	$-0.760066\pi$
$197$	−0.627596	+	0.627596i	−0.0447144	+	0.0447144i	0.684396	+	0.729110i	$0.260066\pi$
$198$		0			0
$199$	−16.5375			−1.17231			−0.586156	−	0.810198i	$-0.699359\pi$
$199$	−16.5375			−1.17231			−0.586156	+	0.810198i	$0.699359\pi$
$200$	−3.76593	+	3.76593i	−0.266291	+	0.266291i
$201$		0			0
$202$	14.0004	−	14.0004i	0.985067	−	0.985067i
$203$	2.48974	−	1.48515i	0.174746	−	0.104237i
$204$		0			0
$205$			16.0502i			1.12100i
$206$	1.91192	−	1.91192i	0.133210	−	0.133210i
$207$		0			0
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$			4.25261i			0.294159i
$210$		0			0
$211$	−0.551329			−0.0379551			−0.0189775	−	0.999820i	$-0.506041\pi$
$211$	−0.551329			−0.0379551			−0.0189775	+	0.999820i	$0.506041\pi$
$212$		−	11.2552i		−	0.773010i
$213$		0			0
$214$	−8.24999	+	8.24999i	−0.563958	+	0.563958i
$215$	16.9249	−	16.9249i	1.15427	−	1.15427i
$216$		0			0
$217$	3.92936	+	0.993080i	0.266743	+	0.0674147i
$218$		−	7.49005i		−	0.507290i
$219$		0			0
$220$	−1.61504			−0.108886
$221$	8.65166	−	12.9775i	0.581973	−	0.872960i
$222$		0			0
$223$	9.89430	+	9.89430i	0.662571	+	0.662571i	0.955985	−	0.293414i	$-0.0947915\pi$
$223$	9.89430	+	9.89430i	0.662571	+	0.662571i	−0.293414	+	0.955985i	$0.594792\pi$
$224$	−0.648285	+	2.56510i	−0.0433153	+	0.171388i
$225$		0			0
$226$	14.3854	−	14.3854i	0.956902	−	0.956902i
$227$	−1.67417	−	1.67417i	−0.111119	−	0.111119i	0.649361	−	0.760480i	$-0.275036\pi$
$227$	−1.67417	−	1.67417i	−0.111119	−	0.111119i	−0.760480	+	0.649361i	$0.775036\pi$
$228$		0			0
$229$	−1.32583	+	1.32583i	−0.0876132	+	0.0876132i	−0.749555	−	0.661942i	$-0.769733\pi$
$229$	−1.32583	+	1.32583i	−0.0876132	+	0.0876132i	0.661942	+	0.749555i	$0.269733\pi$
$230$			7.66377i			0.505334i
$231$		0			0
$232$	−0.774804	−	0.774804i	−0.0508684	−	0.0508684i
$233$			10.2117i			0.668988i	0.942398	+	0.334494i	$0.108565\pi$
$233$			10.2117i			0.668988i	−0.942398	+	0.334494i	$0.891435\pi$
$234$		0			0
$235$	−21.4077			−1.39649
$236$	−3.61504	−	3.61504i	−0.235319	−	0.235319i
$237$		0			0
$238$	−2.80437	+	11.0962i	−0.181780	+	0.719258i
$239$	15.2212	−	15.2212i	0.984575	−	0.984575i	−0.0153074	−	0.999883i	$-0.504873\pi$
$239$	15.2212	−	15.2212i	0.984575	−	0.984575i	0.999883	+	0.0153074i	$0.00487267\pi$
$240$		0			0
$241$	3.38496	−	3.38496i	0.218044	−	0.218044i	−0.589630	−	0.807674i	$-0.700726\pi$
$241$	3.38496	−	3.38496i	0.218044	−	0.218044i	0.807674	+	0.589630i	$0.200726\pi$
$242$	7.59955	+	7.59955i	0.488518	+	0.488518i
$243$		0			0
$244$	4.32583			0.276933
$245$	21.5525	−	6.43858i	1.37694	−	0.411346i
$246$		0			0
$247$	29.9149	−	5.98299i	1.90344	−	0.380688i
$248$		−	1.53186i		−	0.0972731i
$249$		0			0
$250$		−	1.04701i		−	0.0662186i
$251$	17.2281			1.08743			0.543714	−	0.839271i	$-0.317018\pi$
$251$	17.2281			1.08743			0.543714	+	0.839271i	$0.317018\pi$
$252$		0			0
$253$	−0.847593	+	0.847593i	−0.0532877	+	0.0532877i
$254$	−5.37976	−	5.37976i	−0.337556	−	0.337556i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.32324			0.207298			0.103649	−	0.994614i	$-0.466948\pi$
$257$	3.32324			0.207298			0.103649	+	0.994614i	$0.466948\pi$
$258$		0			0
$259$	18.8237	+	4.75736i	1.16965	+	0.295608i
$260$	2.27220	+	11.3610i	0.140916	+	0.704581i
$261$		0			0
$262$	4.85799	+	4.85799i	0.300128	+	0.300128i
$263$	0.818029			0.0504418			0.0252209	−	0.999682i	$-0.491971\pi$
$263$	0.818029			0.0504418			0.0252209	+	0.999682i	$0.491971\pi$
$264$		0			0
$265$	25.5741	+	25.5741i	1.57100	+	1.57100i
$266$	−19.2256	+	11.4683i	−1.17880	+	0.703165i
$267$		0			0
$268$	0.531858	+	0.531858i	0.0324884	+	0.0324884i
$269$			21.6081i			1.31747i	0.752375	+	0.658735i	$0.228908\pi$
$269$			21.6081i			1.31747i	−0.752375	+	0.658735i	$0.771092\pi$
$270$		0			0
$271$	−15.0422	+	15.0422i	−0.913751	+	0.913751i	−0.996565	−	0.0828139i	$-0.973609\pi$
$271$	−15.0422	+	15.0422i	−0.913751	+	0.913751i	0.0828139	+	0.996565i	$0.473609\pi$
$272$	4.32583			0.262292
$273$		0			0
$274$	−0.384955			−0.0232560
$275$	1.89275	−	1.89275i	0.114137	−	0.114137i
$276$		0			0
$277$			17.7996i			1.06947i	0.845018	+	0.534737i	$0.179589\pi$
$277$			17.7996i			1.06947i	−0.845018	+	0.534737i	$0.820411\pi$
$278$	14.3854	+	14.3854i	0.862778	+	0.862778i
$279$		0			0
$280$	−4.35539	−	7.30146i	−0.260284	−	0.436346i
$281$	−6.20862	−	6.20862i	−0.370375	−	0.370375i	0.497239	−	0.867614i	$-0.334347\pi$
$281$	−6.20862	−	6.20862i	−0.370375	−	0.370375i	−0.867614	+	0.497239i	$0.834347\pi$
$282$		0			0
$283$	−25.1090			−1.49258			−0.746288	−	0.665624i	$-0.768166\pi$
$283$	−25.1090			−1.49258			−0.746288	+	0.665624i	$0.768166\pi$
$284$	6.38496	+	6.38496i	0.378877	+	0.378877i
$285$		0			0
$286$	−1.00520	+	1.50780i	−0.0594387	+	0.0891580i
$287$	−12.8122	−	3.23805i	−0.756277	−	0.191136i
$288$		0			0
$289$	1.71278			0.100752
$290$	3.52103			0.206762
$291$		0			0
$292$	−5.18902	−	5.18902i	−0.303664	−	0.303664i
$293$	8.51343	−	8.51343i	0.497360	−	0.497360i	−0.413255	−	0.910615i	$-0.635608\pi$
$293$	8.51343	−	8.51343i	0.497360	−	0.497360i	0.910615	+	0.413255i	$0.135608\pi$
$294$		0			0
$295$	16.4282			0.956489
$296$		−	7.33838i		−	0.426535i
$297$		0			0
$298$		−	14.9461i		−	0.865803i
$299$	7.15487	+	4.76991i	0.413777	+	0.275851i
$300$		0			0
$301$	10.0959	+	16.9249i	0.581916	+	0.975535i
$302$	0.211229			0.0121549
$303$		0			0
$304$	5.98299	+	5.98299i	0.343148	+	0.343148i
$305$	−9.82917	+	9.82917i	−0.562816	+	0.562816i
$306$		0			0
$307$	−10.0397	+	10.0397i	−0.572993	+	0.572993i	−0.932964	−	0.359970i	$-0.882787\pi$
$307$	−10.0397	+	10.0397i	−0.572993	+	0.572993i	0.359970	+	0.932964i	$0.382787\pi$
$308$	0.325828	−	1.28922i	0.0185658	−	0.0734600i
$309$		0			0
$310$	3.48069	+	3.48069i	0.197690	+	0.197690i
$311$	15.7064			0.890631			0.445316	−	0.895374i	$-0.353092\pi$
$311$	15.7064			0.890631			0.445316	+	0.895374i	$0.353092\pi$
$312$		0			0
$313$		−	20.7702i		−	1.17400i	−0.809587	−	0.587000i	$-0.800309\pi$
$313$		−	20.7702i		−	1.17400i	0.809587	−	0.587000i	$-0.199691\pi$
$314$	−7.61058	−	7.61058i	−0.429490	−	0.429490i
$315$		0			0
$316$			11.3143i			0.636480i
$317$	−19.0126	+	19.0126i	−1.06785	+	1.06785i	−0.0703273	+	0.997524i	$0.522404\pi$
$317$	−19.0126	+	19.0126i	−1.06785	+	1.06785i	−0.997524	+	0.0703273i	$0.977596\pi$
$318$		0			0
$319$	0.389416	+	0.389416i	0.0218031	+	0.0218031i
$320$	−2.27220	+	2.27220i	−0.127020	+	0.127020i
$321$		0			0
$322$	−6.11764	−	1.54613i	−0.340923	−	0.0861625i
$323$	25.8814	+	25.8814i	1.44008	+	1.44008i
$324$		0			0
$325$	−15.9775	−	10.6517i	−0.886271	−	0.590848i
$326$	4.82107			0.267015
$327$		0			0
$328$			4.99480i			0.275792i
$329$	4.31891	−	17.0888i	0.238109	−	0.942137i
$330$		0			0
$331$	−13.9785	+	13.9785i	−0.768329	+	0.768329i	−0.977812	−	0.209483i	$-0.932822\pi$
$331$	−13.9785	+	13.9785i	−0.768329	+	0.768329i	0.209483	+	0.977812i	$0.432822\pi$
$332$	6.71078	−	6.71078i	0.368302	−	0.368302i
$333$		0			0
$334$		−	14.1742i		−	0.775575i
$335$	−2.41698			−0.132054
$336$		0			0
$337$			1.09574i			0.0596887i	0.999555	+	0.0298443i	$0.00950116\pi$
$337$			1.09574i			0.0596887i	−0.999555	+	0.0298443i	$0.990499\pi$
$338$	12.0208	+	4.94975i	0.653846	+	0.269231i
$339$		0			0
$340$	−9.82917	+	9.82917i	−0.533061	+	0.533061i
$341$			0.769911i			0.0416930i
$342$		0			0
$343$	0.791511	+	18.5033i	0.0427376	+	0.999086i
$344$	5.26701	−	5.26701i	0.283978	−	0.283978i
$345$		0			0
$346$	13.9586	−	13.9586i	0.750420	−	0.750420i
$347$	−32.0983			−1.72313			−0.861564	−	0.507649i	$-0.830515\pi$
$347$	−32.0983			−1.72313			−0.861564	+	0.507649i	$0.830515\pi$
$348$		0			0
$349$	−18.9660	+	18.9660i	−1.01523	+	1.01523i	−0.0153431	+	0.999882i	$0.504884\pi$
$349$	−18.9660	+	18.9660i	−1.01523	+	1.01523i	−0.999882	+	0.0153431i	$0.995116\pi$
$350$	13.6613	+	3.45265i	0.730226	+	0.184552i
$351$		0			0
$352$	−0.502600			−0.0267886
$353$	15.5500	+	15.5500i	0.827645	+	0.827645i	0.987191	−	0.159545i	$-0.0510028\pi$
$353$	15.5500	+	15.5500i	0.827645	+	0.827645i	−0.159545	+	0.987191i	$0.551003\pi$
$354$		0			0
$355$	−29.0159			−1.54000
$356$	3.75044	+	3.75044i	0.198773	+	0.198773i
$357$		0			0
$358$	6.92936	+	6.92936i	0.366228	+	0.366228i
$359$	14.1846	+	14.1846i	0.748632	+	0.748632i	0.974222	−	0.225590i	$-0.0724310\pi$
$359$	14.1846	+	14.1846i	0.748632	+	0.748632i	−0.225590	+	0.974222i	$0.572431\pi$
$360$		0			0
$361$			52.5923i			2.76801i
$362$	7.38019	−	7.38019i	0.387894	−	0.387894i
$363$		0			0
$364$	−9.52740	−	0.478235i	−0.499371	−	0.0250663i
$365$	23.5810			1.23429
$366$		0			0
$367$		−	11.2552i		−	0.587516i	−0.955880	−	0.293758i	$-0.905094\pi$
$367$		−	11.2552i		−	0.587516i	0.955880	−	0.293758i	$-0.0949060\pi$
$368$			2.38496i			0.124324i
$369$		0			0
$370$	16.6743	+	16.6743i	0.866856	+	0.866856i
$371$	−25.5741	+	15.2552i	−1.32774	+	0.792010i
$372$		0			0
$373$	17.1479			0.887887			0.443944	−	0.896055i	$-0.353579\pi$
$373$	17.1479			0.887887			0.443944	+	0.896055i	$0.353579\pi$
$374$	−2.17416			−0.112423
$375$		0			0
$376$	−6.66205			−0.343569
$377$	2.19148	−	3.28722i	0.112867	−	0.169300i
$378$		0			0
$379$	11.5685	−	11.5685i	0.594232	−	0.594232i	−0.344540	−	0.938772i	$-0.611965\pi$
$379$	11.5685	−	11.5685i	0.594232	−	0.594232i	0.938772	+	0.344540i	$0.111965\pi$
$380$	−27.1891			−1.39477
$381$		0			0
$382$	7.87790	−	7.87790i	0.403068	−	0.403068i
$383$	1.26657	+	1.26657i	0.0647189	+	0.0647189i	0.738725	−	0.674007i	$-0.235428\pi$
$383$	1.26657	+	1.26657i	0.0647189	+	0.0647189i	−0.674007	+	0.738725i	$0.735428\pi$
$384$		0			0
$385$	2.18902	+	3.66971i	0.111563	+	0.187026i
$386$	−5.70863			−0.290562
$387$		0			0
$388$	12.9931	−	12.9931i	0.659624	−	0.659624i
$389$			7.90685i			0.400893i	0.979705	+	0.200447i	$0.0642393\pi$
$389$			7.90685i			0.400893i	−0.979705	+	0.200447i	$0.935761\pi$
$390$		0			0
$391$			10.3169i			0.521748i
$392$	6.70711	−	2.00368i	0.338760	−	0.101201i
$393$		0			0
$394$		−	0.887555i		−	0.0447144i
$395$	−25.7085	−	25.7085i	−1.29353	−	1.29353i
$396$		0			0
$397$	16.4467	−	16.4467i	0.825435	−	0.825435i	−0.161447	−	0.986881i	$-0.551616\pi$
$397$	16.4467	−	16.4467i	0.825435	−	0.825435i	0.986881	+	0.161447i	$0.0516160\pi$
$398$	11.6938	−	11.6938i	0.586156	−	0.586156i
$399$		0			0
$400$		−	5.32583i		−	0.266291i
$401$	−15.0126	−	15.0126i	−0.749691	−	0.749691i	0.224730	−	0.974421i	$-0.427850\pi$
$401$	−15.0126	−	15.0126i	−0.749691	−	0.749691i	−0.974421	+	0.224730i	$0.927850\pi$
$402$		0			0
$403$	5.41593	−	1.08319i	0.269787	−	0.0539574i
$404$			19.7996i			0.985067i
$405$		0			0
$406$	−0.710351	+	2.81068i	−0.0352541	+	0.139492i
$407$			3.68827i			0.182821i
$408$		0			0
$409$	−19.0477	−	19.0477i	−0.941850	−	0.941850i	0.0565493	−	0.998400i	$-0.481990\pi$
$409$	−19.0477	−	19.0477i	−0.941850	−	0.941850i	−0.998400	+	0.0565493i	$0.981990\pi$
$410$	−11.3492	−	11.3492i	−0.560498	−	0.560498i
$411$		0			0
$412$			2.70386i			0.133210i
$413$	−3.31432	+	13.1139i	−0.163087	+	0.645294i
$414$		0			0
$415$			30.4965i			1.49702i
$416$	0.707107	+	3.53553i	0.0346688	+	0.173344i
$417$		0			0
$418$	−3.00705	−	3.00705i	−0.147079	−	0.147079i
$419$			38.8022i			1.89561i	0.318849	+	0.947805i	$0.396704\pi$
$419$			38.8022i			1.89561i	−0.318849	+	0.947805i	$0.603296\pi$
$420$		0			0
$421$	−19.5375	+	19.5375i	−0.952199	+	0.952199i	−0.998909	−	0.0467096i	$-0.985126\pi$
$421$	−19.5375	+	19.5375i	−0.952199	+	0.952199i	0.0467096	+	0.998909i	$0.485126\pi$
$422$	0.389849	−	0.389849i	0.0189775	−	0.0189775i
$423$		0			0
$424$	7.95862	+	7.95862i	0.386505	+	0.386505i
$425$		−	23.0386i		−	1.11754i
$426$		0			0
$427$	−5.86319	−	9.82917i	−0.283740	−	0.475667i
$428$		−	11.6673i		−	0.563958i
$429$		0			0
$430$			23.9354i			1.15427i
$431$	−1.45559	+	1.45559i	−0.0701133	+	0.0701133i	−0.741294	−	0.671181i	$-0.765788\pi$
$431$	−1.45559	+	1.45559i	−0.0701133	+	0.0701133i	0.671181	+	0.741294i	$0.265788\pi$
$432$		0			0
$433$	35.8137			1.72110			0.860548	−	0.509369i	$-0.170121\pi$
$433$	35.8137			1.72110			0.860548	+	0.509369i	$0.170121\pi$
$434$	−3.48069	+	2.07627i	−0.167079	+	0.0996640i
$435$		0			0
$436$	5.29626	+	5.29626i	0.253645	+	0.253645i
$437$	−14.2692	+	14.2692i	−0.682586	+	0.682586i
$438$		0			0
$439$	−14.2667			−0.680912			−0.340456	−	0.940260i	$-0.610582\pi$
$439$	−14.2667			−0.680912			−0.340456	+	0.940260i	$0.610582\pi$
$440$	1.14201	−	1.14201i	0.0544431	−	0.0544431i
$441$		0			0
$442$	3.05882	+	15.2941i	0.145493	+	0.727467i
$443$	20.7019			0.983575			0.491788	−	0.870715i	$-0.336344\pi$
$443$	20.7019			0.983575			0.491788	+	0.870715i	$0.336344\pi$
$444$		0			0
$445$	−17.0435			−0.807941
$446$	−13.9926			−0.662571
$447$		0			0
$448$	−1.35539	−	2.27220i	−0.0640362	−	0.107352i
$449$	20.2382	+	20.2382i	0.955099	+	0.955099i	0.999034	−	0.0439356i	$-0.0139896\pi$
$449$	20.2382	+	20.2382i	0.955099	+	0.955099i	−0.0439356	+	0.999034i	$0.513990\pi$
$450$		0			0
$451$		−	2.51038i		−	0.118209i
$452$			20.3440i			0.956902i
$453$		0			0
$454$	2.36764			0.111119
$455$	22.7348	−	20.5615i	1.06583	−	0.963940i
$456$		0			0
$457$	−18.1891	+	18.1891i	−0.850852	+	0.850852i	−0.990238	−	0.139386i	$-0.955487\pi$
$457$	−18.1891	+	18.1891i	−0.850852	+	0.850852i	0.139386	+	0.990238i	$0.455487\pi$
$458$		−	1.87500i		−	0.0876132i
$459$		0			0
$460$	−5.41911	−	5.41911i	−0.252667	−	0.252667i
$461$	−1.18339	−	1.18339i	−0.0551158	−	0.0551158i	0.679012	−	0.734127i	$-0.262409\pi$
$461$	−1.18339	−	1.18339i	−0.0551158	−	0.0551158i	−0.734127	+	0.679012i	$0.762409\pi$
$462$		0			0
$463$	4.93946	+	4.93946i	0.229556	+	0.229556i	0.812507	−	0.582951i	$-0.198102\pi$
$463$	4.93946	+	4.93946i	0.229556	+	0.229556i	−0.582951	+	0.812507i	$0.698102\pi$
$464$	1.09574			0.0508684
$465$		0			0
$466$	−7.22074	−	7.22074i	−0.334494	−	0.334494i
$467$	−26.6900			−1.23507			−0.617533	−	0.786545i	$-0.711868\pi$
$467$	−26.6900			−1.23507			−0.617533	+	0.786545i	$0.711868\pi$
$468$		0			0
$469$	0.487614	−	1.92936i	0.0225159	−	0.0890898i
$470$	15.1375	−	15.1375i	0.698243	−	0.698243i
$471$		0			0
$472$	5.11245			0.235319
$473$	−2.64719	+	2.64719i	−0.121718	+	0.121718i
$474$		0			0
$475$	31.8644	−	31.8644i	1.46204	−	1.46204i
$476$	−5.86319	−	9.82917i	−0.268739	−	0.450519i
$477$		0			0
$478$			21.5260i			0.984575i
$479$	−7.35998	+	7.35998i	−0.336286	+	0.336286i	−0.854968	−	0.518682i	$-0.826423\pi$
$479$	−7.35998	+	7.35998i	−0.336286	+	0.336286i	0.518682	+	0.854968i	$0.326423\pi$
$480$		0			0
$481$	25.9451	−	5.18902i	1.18299	−	0.236599i
$482$			4.78705i			0.218044i
$483$		0			0
$484$	−10.7474			−0.488518
$485$			59.0459i			2.68113i
$486$		0			0
$487$	25.1766	−	25.1766i	1.14086	−	1.14086i	0.152567	−	0.988293i	$-0.451246\pi$
$487$	25.1766	−	25.1766i	1.14086	−	1.14086i	0.988293	−	0.152567i	$-0.0487541\pi$
$488$	−3.05882	+	3.05882i	−0.138466	+	0.138466i
$489$		0			0
$490$	−10.6872	+	19.7927i	−0.482797	+	0.894142i
$491$			7.77450i			0.350858i	0.984492	+	0.175429i	$0.0561313\pi$
$491$			7.77450i			0.350858i	−0.984492	+	0.175429i	$0.943869\pi$
$492$		0			0
$493$	4.73998			0.213478
$494$	−16.9224	+	25.3837i	−0.761377	+	1.14207i
$495$		0			0
$496$	1.08319	+	1.08319i	0.0486365	+	0.0486365i
$497$	5.85381	−	23.1620i	0.262579	−	1.03896i
$498$		0			0
$499$	23.4592	−	23.4592i	1.05018	−	1.05018i	0.0515063	−	0.998673i	$-0.483598\pi$
$499$	23.4592	−	23.4592i	1.05018	−	1.05018i	0.998673	−	0.0515063i	$-0.0164022\pi$
$500$	0.740347	+	0.740347i	0.0331093	+	0.0331093i
$501$		0			0
$502$	−12.1821	+	12.1821i	−0.543714	+	0.543714i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	−44.9887	−	44.9887i	−2.00197	−	2.00197i
$506$		−	1.19868i		−	0.0532877i
$507$		0			0
$508$	7.60812			0.337556
$509$	11.0283	+	11.0283i	0.488820	+	0.488820i	0.907934	−	0.419114i	$-0.137659\pi$
$509$	11.0283	+	11.0283i	0.488820	+	0.488820i	−0.419114	+	0.907934i	$0.637659\pi$
$510$		0			0
$511$	−4.75736	+	18.8237i	−0.210453	+	0.832710i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−2.34989	+	2.34989i	−0.103649	+	0.103649i
$515$	−6.14373	−	6.14373i	−0.270725	−	0.270725i
$516$		0			0
$517$	3.34834			0.147260
$518$	−16.6743	+	9.94638i	−0.732627	+	0.437019i
$519$		0			0
$520$	−9.64015	−	6.42677i	−0.422748	−	0.281832i
$521$		−	18.5654i		−	0.813366i	−0.913569	−	0.406683i	$-0.866685\pi$
$521$		−	18.5654i		−	0.813366i	0.913569	−	0.406683i	$-0.133315\pi$
$522$		0			0
$523$		−	27.5741i		−	1.20573i	−0.797843	−	0.602866i	$-0.794026\pi$
$523$		−	27.5741i		−	1.20573i	0.797843	−	0.602866i	$-0.205974\pi$
$524$	−6.87024			−0.300128
$525$		0			0
$526$	−0.578434	+	0.578434i	−0.0252209	+	0.0252209i
$527$	4.68568	+	4.68568i	0.204111	+	0.204111i
$528$		0			0
$529$	17.3120			0.752695
$530$	−36.1672			−1.57100
$531$		0			0
$532$	5.48528	−	21.7039i	0.237817	−	0.940982i
$533$	−17.6593	+	3.53186i	−0.764909	+	0.152982i
$534$		0			0
$535$	26.5104	+	26.5104i	1.14614	+	1.14614i
$536$	−0.752160			−0.0324884
$537$		0			0
$538$	−15.2793	−	15.2793i	−0.658735	−	0.658735i
$539$	−3.37099	+	1.00705i	−0.145199	+	0.0433766i
$540$		0			0
$541$	−25.5330	−	25.5330i	−1.09775	−	1.09775i	−0.994673	−	0.103077i	$-0.967131\pi$
$541$	−25.5330	−	25.5330i	−1.09775	−	1.09775i	−0.103077	−	0.994673i	$-0.532869\pi$
$542$		−	21.2729i		−	0.913751i
$543$		0			0
$544$	−3.05882	+	3.05882i	−0.131146	+	0.131146i
$545$	−24.0684			−1.03098
$546$		0			0
$547$	44.1966			1.88971			0.944856	−	0.327486i	$-0.106201\pi$
$547$	44.1966			1.88971			0.944856	+	0.327486i	$0.106201\pi$
$548$	0.272205	−	0.272205i	0.0116280	−	0.0116280i
$549$		0			0
$550$			2.67676i			0.114137i
$551$	6.55579	+	6.55579i	0.279286	+	0.279286i
$552$		0			0
$553$	25.7085	−	15.3353i	1.09323	−	0.652125i
$554$	−12.5862	−	12.5862i	−0.534737	−	0.534737i
$555$		0			0
$556$	−20.3440			−0.862778
$557$	11.7755	+	11.7755i	0.498946	+	0.498946i	0.911110	−	0.412164i	$-0.135227\pi$
$557$	11.7755	+	11.7755i	0.498946	+	0.498946i	−0.412164	+	0.911110i	$0.635227\pi$
$558$		0			0
$559$	22.3460	+	14.8973i	0.945136	+	0.630090i
$560$	8.24264	+	2.08319i	0.348315	+	0.0880307i
$561$		0			0
$562$	8.78031			0.370375
$563$	−45.7636			−1.92870			−0.964352	−	0.264621i	$-0.914753\pi$
$563$	−45.7636			−1.92870			−0.964352	+	0.264621i	$0.914753\pi$
$564$		0			0
$565$	−46.2258	−	46.2258i	−1.94473	−	1.94473i
$566$	17.7547	−	17.7547i	0.746288	−	0.746288i
$567$		0			0
$568$	−9.02969			−0.378877
$569$		−	39.5061i		−	1.65618i	−0.560595	−	0.828090i	$-0.689428\pi$
$569$		−	39.5061i		−	1.65618i	0.560595	−	0.828090i	$-0.310572\pi$
$570$		0			0
$571$			19.1620i			0.801906i	0.916099	+	0.400953i	$0.131321\pi$
$571$			19.1620i			0.801906i	−0.916099	+	0.400953i	$0.868679\pi$
$572$	−0.355392	−	1.77696i	−0.0148597	−	0.0742983i
$573$		0			0
$574$	11.3492	−	6.76991i	0.473707	−	0.282571i
$575$	12.7019			0.529704
$576$		0			0
$577$	3.53749	+	3.53749i	0.147268	+	0.147268i	0.776896	−	0.629629i	$-0.216793\pi$
$577$	3.53749	+	3.53749i	0.147268	+	0.147268i	−0.629629	+	0.776896i	$0.716793\pi$
$578$	−1.21112	+	1.21112i	−0.0503760	+	0.0503760i
$579$		0			0
$580$	−2.48974	+	2.48974i	−0.103381	+	0.103381i
$581$	−24.3440	−	6.15253i	−1.00996	−	0.255250i
$582$		0			0
$583$	−4.00000	−	4.00000i	−0.165663	−	0.165663i
$584$	7.33838			0.303664
$585$		0			0
$586$			12.0398i			0.497360i
$587$	−4.98849	−	4.98849i	−0.205897	−	0.205897i	0.596624	−	0.802521i	$-0.296508\pi$
$587$	−4.98849	−	4.98849i	−0.205897	−	0.205897i	−0.802521	+	0.596624i	$0.796508\pi$
$588$		0			0
$589$			12.9614i			0.534065i
$590$	−11.6165	+	11.6165i	−0.478245	+	0.478245i
$591$		0			0
$592$	5.18902	+	5.18902i	0.213267	+	0.213267i
$593$	−3.14690	+	3.14690i	−0.129228	+	0.129228i	−0.768762	−	0.639535i	$-0.779127\pi$
$593$	−3.14690	+	3.14690i	−0.129228	+	0.129228i	0.639535	+	0.768762i	$0.279127\pi$
$594$		0			0
$595$	35.6562	+	9.01151i	1.46176	+	0.369436i
$596$	10.5685	+	10.5685i	0.432901	+	0.432901i
$597$		0			0
$598$	−8.43209	+	1.68642i	−0.344814	+	0.0689628i
$599$	−14.9244			−0.609796			−0.304898	−	0.952385i	$-0.598622\pi$
$599$	−14.9244			−0.609796			−0.304898	+	0.952385i	$0.598622\pi$
$600$		0			0
$601$		−	14.3189i		−	0.584080i	−0.956406	−	0.292040i	$-0.905666\pi$
$601$		−	14.3189i		−	0.584080i	0.956406	−	0.292040i	$-0.0943341\pi$
$602$	−19.1066	−	4.82886i	−0.778726	−	0.196810i
$603$		0			0
$604$	−0.149362	+	0.149362i	−0.00607743	+	0.00607743i
$605$	24.4203	−	24.4203i	0.992825	−	0.992825i
$606$		0			0
$607$			17.3212i			0.703047i	0.936179	+	0.351524i	$0.114336\pi$
$607$			17.3212i			0.703047i	−0.936179	+	0.351524i	$0.885664\pi$
$608$	−8.46122			−0.343148
$609$		0			0
$610$		−	13.9005i		−	0.562816i
$611$	−4.71078	−	23.5539i	−0.190578	−	0.952889i
$612$		0			0
$613$	28.6700	−	28.6700i	1.15797	−	1.15797i	0.173057	−	0.984912i	$-0.444635\pi$
$613$	28.6700	−	28.6700i	1.15797	−	1.15797i	0.984912	−	0.173057i	$-0.0553646\pi$
$614$		−	14.1982i		−	0.572993i
$615$		0			0
$616$	0.681219	+	1.14201i	0.0274471	+	0.0460129i
$617$	9.91435	−	9.91435i	0.399137	−	0.399137i	−0.478792	−	0.877929i	$-0.658925\pi$
$617$	9.91435	−	9.91435i	0.399137	−	0.399137i	0.877929	+	0.478792i	$0.158925\pi$
$618$		0			0
$619$	3.87574	−	3.87574i	0.155779	−	0.155779i	−0.624914	−	0.780693i	$-0.714866\pi$
$619$	3.87574	−	3.87574i	0.155779	−	0.155779i	0.780693	+	0.624914i	$0.214866\pi$
$620$	−4.92244			−0.197690
$621$		0			0
$622$	−11.1061	+	11.1061i	−0.445316	+	0.445316i
$623$	3.43845	−	13.6051i	0.137759	−	0.545076i
$624$		0			0
$625$	23.2647			0.930588
$626$	14.6867	+	14.6867i	0.587000	+	0.587000i
$627$		0			0
$628$	10.7630			0.429490
$629$	22.4468	+	22.4468i	0.895012	+	0.895012i
$630$		0			0
$631$	−21.5709	−	21.5709i	−0.858725	−	0.858725i	0.132463	−	0.991188i	$-0.457711\pi$
$631$	−21.5709	−	21.5709i	−0.858725	−	0.858725i	−0.991188	+	0.132463i	$0.957711\pi$
$632$	−8.00043	−	8.00043i	−0.318240	−	0.318240i
$633$		0			0
$634$		−	26.8878i		−	1.06785i
$635$	−17.2872	+	17.2872i	−0.686022	+	0.686022i
$636$		0			0
$637$	11.8267	+	22.2964i	0.468591	+	0.883415i
$638$	−0.550718			−0.0218031
$639$		0			0
$640$		−	3.21338i		−	0.127020i
$641$			25.8728i			1.02192i	0.859606	+	0.510958i	$0.170709\pi$
$641$			25.8728i			1.02192i	−0.859606	+	0.510958i	$0.829291\pi$
$642$		0			0
$643$	3.32032	+	3.32032i	0.130941	+	0.130941i	0.769540	−	0.638599i	$-0.220486\pi$
$643$	3.32032	+	3.32032i	0.130941	+	0.130941i	−0.638599	+	0.769540i	$0.720486\pi$
$644$	5.41911	−	3.23255i	0.213543	−	0.127380i
$645$		0			0
$646$	−36.6018			−1.44008
$647$	−28.6969			−1.12819			−0.564097	−	0.825709i	$-0.690775\pi$
$647$	−28.6969			−1.12819			−0.564097	+	0.825709i	$0.690775\pi$
$648$		0			0
$649$	−2.56951			−0.100862
$650$	18.8296	−	3.76593i	0.738559	−	0.147712i
$651$		0			0
$652$	−3.40901	+	3.40901i	−0.133507	+	0.133507i
$653$	27.9250			1.09279			0.546395	−	0.837527i	$-0.316000\pi$
$653$	27.9250			1.09279			0.546395	+	0.837527i	$0.316000\pi$
$654$		0			0
$655$	15.6106	−	15.6106i	0.609956	−	0.609956i
$656$	−3.53186	−	3.53186i	−0.137896	−	0.137896i
$657$		0			0
$658$	9.02969	+	15.1375i	0.352014	+	0.590123i
$659$	38.2258			1.48906			0.744532	−	0.667587i	$-0.232673\pi$
$659$	38.2258			1.48906			0.744532	+	0.667587i	$0.232673\pi$
$660$		0			0
$661$	4.52189	−	4.52189i	0.175881	−	0.175881i	−0.613676	−	0.789558i	$-0.710310\pi$
$661$	4.52189	−	4.52189i	0.175881	−	0.175881i	0.789558	+	0.613676i	$0.210310\pi$
$662$		−	19.7686i		−	0.768329i
$663$		0			0
$664$			9.49048i			0.368302i
$665$	36.8519	+	61.7793i	1.42906	+	2.39570i
$666$		0			0
$667$			2.61329i			0.101187i
$668$	10.0226	+	10.0226i	0.387788	+	0.387788i
$669$		0			0
$670$	1.70906	−	1.70906i	0.0660268	−	0.0660268i
$671$	1.53736	−	1.53736i	0.0593492	−	0.0593492i
$672$		0			0
$673$			16.7180i			0.644430i	0.946667	+	0.322215i	$0.104427\pi$
$673$			16.7180i			0.644430i	−0.946667	+	0.322215i	$0.895573\pi$
$674$	−0.774804	−	0.774804i	−0.0298443	−	0.0298443i
$675$		0			0
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$		−	37.8247i		−	1.45372i	−0.686785	−	0.726861i	$-0.740979\pi$
$677$		−	37.8247i		−	1.45372i	0.686785	−	0.726861i	$-0.259021\pi$
$678$		0			0
$679$	−47.1336	−	11.9122i	−1.80882	−	0.457149i
$680$		−	13.9005i		−	0.533061i
$681$		0			0
$682$	−0.544409	−	0.544409i	−0.0208465	−	0.0208465i
$683$	−3.10020	−	3.10020i	−0.118626	−	0.118626i	0.645302	−	0.763928i	$-0.276732\pi$
$683$	−3.10020	−	3.10020i	−0.118626	−	0.118626i	−0.763928	+	0.645302i	$0.776732\pi$
$684$		0			0
$685$			1.23701i			0.0472637i
$686$	−13.6435	−	12.5242i	−0.520912	−	0.478174i
$687$		0			0
$688$			7.44867i			0.283978i
$689$	−22.5104	+	33.7656i	−0.857577	+	1.28637i
$690$		0			0
$691$	11.1083	+	11.1083i	0.422579	+	0.422579i	0.886091	−	0.463512i	$-0.153411\pi$
$691$	11.1083	+	11.1083i	0.422579	+	0.422579i	−0.463512	+	0.886091i	$0.653411\pi$
$692$			19.7405i			0.750420i
$693$		0			0
$694$	22.6969	−	22.6969i	0.861564	−	0.861564i
$695$	46.2258	−	46.2258i	1.75344	−	1.75344i
$696$		0			0
$697$	−15.2782	−	15.2782i	−0.578703	−	0.578703i
$698$		−	26.8219i		−	1.01523i
$699$		0			0
$700$	−12.1014	+	7.21858i	−0.457389	+	0.272837i
$701$		−	2.49912i		−	0.0943905i	−0.998886	−	0.0471953i	$-0.984972\pi$
$701$		−	2.49912i		−	0.0943905i	0.998886	−	0.0471953i	$-0.0150283\pi$
$702$		0			0
$703$			62.0917i			2.34183i
$704$	0.355392	−	0.355392i	0.0133943	−	0.0133943i
$705$		0			0
$706$	−21.9911			−0.827645
$707$	44.9887	−	26.8362i	1.69198	−	1.00928i
$708$		0			0
$709$	25.3601	+	25.3601i	0.952419	+	0.952419i	0.998918	−	0.0464996i	$-0.0148066\pi$
$709$	25.3601	+	25.3601i	0.952419	+	0.952419i	−0.0464996	+	0.998918i	$0.514807\pi$
$710$	20.5173	−	20.5173i	0.770001	−	0.770001i
$711$		0			0
$712$	−5.30392			−0.198773
$713$	−2.58335	+	2.58335i	−0.0967473	+	0.0967473i
$714$		0			0
$715$	4.84513	+	3.23009i	0.181198	+	0.120798i
$716$	−9.79960			−0.366228
$717$		0			0
$718$	−20.0600			−0.748632
$719$	41.5150			1.54825			0.774124	−	0.633034i	$-0.218191\pi$
$719$	41.5150			1.54825			0.774124	+	0.633034i	$0.218191\pi$
$720$		0			0
$721$	6.14373	−	3.66479i	0.228804	−	0.136484i
$722$	−37.1884	−	37.1884i	−1.38401	−	1.38401i
$723$		0			0
$724$			10.4372i			0.387894i
$725$		−	5.83571i		−	0.216733i
$726$		0			0
$727$	−48.1505			−1.78580			−0.892902	−	0.450251i	$-0.851335\pi$
$727$	−48.1505			−1.78580			−0.892902	+	0.450251i	$0.851335\pi$
$728$	7.07505	−	6.39872i	0.262219	−	0.237152i
$729$		0			0
$730$	−16.6743	+	16.6743i	−0.617143	+	0.617143i
$731$			32.2217i			1.19176i
$732$		0			0
$733$	−7.58561	−	7.58561i	−0.280181	−	0.280181i	0.553000	−	0.833181i	$-0.313483\pi$
$733$	−7.58561	−	7.58561i	−0.280181	−	0.280181i	−0.833181	+	0.553000i	$0.813483\pi$
$734$	7.95862	+	7.95862i	0.293758	+	0.293758i
$735$		0			0
$736$	−1.68642	−	1.68642i	−0.0621622	−	0.0621622i
$737$	0.378035			0.0139251
$738$		0			0
$739$	0.923733	+	0.923733i	0.0339801	+	0.0339801i	0.723893	−	0.689913i	$-0.242351\pi$
$739$	0.923733	+	0.923733i	0.0339801	+	0.0339801i	−0.689913	+	0.723893i	$0.742351\pi$
$740$	−23.5810			−0.866856
$741$		0			0
$742$	7.29657	−	28.8707i	0.267865	−	1.05988i
$743$	7.95906	−	7.95906i	0.291989	−	0.291989i	−0.545876	−	0.837866i	$-0.683803\pi$
$743$	7.95906	−	7.95906i	0.291989	−	0.291989i	0.837866	+	0.545876i	$0.183803\pi$
$744$		0			0
$745$	−48.0274			−1.75959
$746$	−12.1254	+	12.1254i	−0.443944	+	0.443944i
$747$		0			0
$748$	1.53736	−	1.53736i	0.0562115	−	0.0562115i
$749$	−26.5104	+	15.8137i	−0.968668	+	0.577820i
$750$		0			0
$751$		−	48.2119i		−	1.75928i	−0.475642	−	0.879639i	$-0.657784\pi$
$751$		−	48.2119i		−	1.75928i	0.475642	−	0.879639i	$-0.342216\pi$
$752$	4.71078	−	4.71078i	0.171785	−	0.171785i
$753$		0			0
$754$	0.774804	+	3.87402i	0.0282167	+	0.141084i
$755$		−	0.678760i		−	0.0247026i
$756$		0			0
$757$	47.8137			1.73782			0.868909	−	0.494972i	$-0.164822\pi$
$757$	47.8137			1.73782			0.868909	+	0.494972i	$0.164822\pi$
$758$			16.3603i			0.594232i
$759$		0			0
$760$	19.2256	−	19.2256i	0.697387	−	0.697387i
$761$	14.6867	−	14.6867i	0.532393	−	0.532393i	−0.388891	−	0.921284i	$-0.627142\pi$
$761$	14.6867	−	14.6867i	0.532393	−	0.532393i	0.921284	+	0.388891i	$0.127142\pi$
$762$		0			0
$763$	4.85568	−	19.2127i	0.175788	−	0.695547i
$764$			11.1410i			0.403068i
$765$		0			0
$766$	−1.79120			−0.0647189
$767$	3.61504	+	18.0752i	0.130532	+	0.652658i
$768$		0			0
$769$	−34.5766	−	34.5766i	−1.24686	−	1.24686i	−0.957098	−	0.289765i	$-0.906423\pi$
$769$	−34.5766	−	34.5766i	−1.24686	−	1.24686i	−0.289765	−	0.957098i	$-0.593577\pi$
$770$	−4.14275	−	1.04701i	−0.149294	−	0.0377316i
$771$		0			0
$772$	4.03661	−	4.03661i	0.145281	−	0.145281i
$773$	−3.88033	−	3.88033i	−0.139566	−	0.139566i	0.633872	−	0.773438i	$-0.281465\pi$
$773$	−3.88033	−	3.88033i	−0.139566	−	0.139566i	−0.773438	+	0.633872i	$0.781465\pi$
$774$		0			0
$775$	5.76887	−	5.76887i	0.207224	−	0.207224i
$776$			18.3750i			0.659624i
$777$		0			0
$778$	−5.59099	−	5.59099i	−0.200447	−	0.200447i
$779$		−	42.2621i		−	1.51420i
$780$		0			0
$781$	4.53832			0.162394
$782$	−7.29515	−	7.29515i	−0.260874	−	0.260874i
$783$		0			0
$784$	−3.32583	+	6.15945i	−0.118780	+	0.219980i
$785$	−24.4557	+	24.4557i	−0.872862	+	0.872862i
$786$		0			0
$787$	−7.06054	+	7.06054i	−0.251681	+	0.251681i	−0.821660	−	0.569978i	$-0.806952\pi$
$787$	−7.06054	+	7.06054i	−0.251681	+	0.251681i	0.569978	+	0.821660i	$0.306952\pi$
$788$	0.627596	+	0.627596i	0.0223572	+	0.0223572i
$789$		0			0
$790$	36.3572			1.29353
$791$	46.2258	−	27.5741i	1.64360	−	0.980422i
$792$		0			0
$793$	−12.9775	−	8.65166i	−0.460844	−	0.307229i
$794$			23.2591i			0.825435i
$795$		0			0
$796$			16.5375i			0.586156i
$797$	31.7376			1.12421			0.562103	−	0.827068i	$-0.309993\pi$
$797$	31.7376			1.12421			0.562103	+	0.827068i	$0.309993\pi$
$798$		0			0
$799$	20.3780	−	20.3780i	0.720923	−	0.720923i
$800$	3.76593	+	3.76593i	0.133146	+	0.133146i
$801$		0			0
$802$	21.2310			0.749691
$803$	−3.68827			−0.130156
$804$		0			0
$805$	−4.96831	+	19.6583i	−0.175110	+	0.692865i
$806$	−3.06372	+	4.59557i	−0.107915	+	0.161872i
$807$		0			0
$808$	−14.0004	−	14.0004i	−0.492533	−	0.492533i
$809$	−5.38754			−0.189416			−0.0947079	−	0.995505i	$-0.530192\pi$
$809$	−5.38754			−0.189416			−0.0947079	+	0.995505i	$0.530192\pi$
$810$		0			0
$811$	24.4934	+	24.4934i	0.860079	+	0.860079i	0.991347	−	0.131268i	$-0.0419049\pi$
$811$	24.4934	+	24.4934i	0.860079	+	0.860079i	−0.131268	+	0.991347i	$0.541905\pi$
$812$	−1.48515	−	2.48974i	−0.0521187	−	0.0873728i
$813$		0			0
$814$	−2.60800	−	2.60800i	−0.0914103	−	0.0914103i
$815$		−	15.4920i		−	0.542660i
$816$		0			0
$817$	−44.5653	+	44.5653i	−1.55914	+	1.55914i
$818$	26.9376			0.941850
$819$		0			0
$820$	16.0502			0.560498
$821$	14.8664	−	14.8664i	0.518840	−	0.518840i	−0.398381	−	0.917220i	$-0.630428\pi$
$821$	14.8664	−	14.8664i	0.518840	−	0.518840i	0.917220	+	0.398381i	$0.130428\pi$
$822$		0			0
$823$		−	46.5078i		−	1.62116i	−0.585628	−	0.810580i	$-0.699152\pi$
$823$		−	46.5078i		−	1.62116i	0.585628	−	0.810580i	$-0.300848\pi$
$824$	−1.91192	−	1.91192i	−0.0666049	−	0.0666049i
$825$		0			0
$826$	−6.92936	−	11.6165i	−0.241103	−	0.404190i
$827$	2.43470	+	2.43470i	0.0846630	+	0.0846630i	0.748170	−	0.663507i	$-0.230933\pi$
$827$	2.43470	+	2.43470i	0.0846630	+	0.0846630i	−0.663507	+	0.748170i	$0.730933\pi$
$828$		0			0
$829$	5.61013			0.194848			0.0974239	−	0.995243i	$-0.468940\pi$
$829$	5.61013			0.194848			0.0974239	+	0.995243i	$0.468940\pi$
$830$	−21.5643	−	21.5643i	−0.748508	−	0.748508i
$831$		0			0
$832$	−3.00000	−	2.00000i	−0.104006	−	0.0693375i
$833$	−14.3870	+	26.6447i	−0.498479	+	0.923185i
$834$		0			0
$835$	−45.5470			−1.57622
$836$	4.25261			0.147079
$837$		0			0
$838$	−27.4373	−	27.4373i	−0.947805	−	0.947805i
$839$	35.6724	−	35.6724i	1.23155	−	1.23155i	0.268180	−	0.963369i	$-0.413578\pi$
$839$	35.6724	−	35.6724i	1.23155	−	1.23155i	0.963369	−	0.268180i	$-0.0864222\pi$
$840$		0			0
$841$	−27.7994			−0.958599
$842$		−	27.6302i		−	0.952199i
$843$		0			0
$844$			0.551329i			0.0189775i
$845$	15.9054	−	38.6275i	0.547164	−	1.32883i
$846$		0			0
$847$	14.5669	+	24.4203i	0.500526	+	0.839091i
$848$	−11.2552			−0.386505
$849$		0			0
$850$	16.2908	+	16.2908i	0.558768	+	0.558768i
$851$	−12.3756	+	12.3756i	−0.424229	+	0.424229i
$852$		0			0
$853$	−9.68368	+	9.68368i	−0.331563	+	0.331563i	−0.853180	−	0.521617i	$-0.825329\pi$
$853$	−9.68368	+	9.68368i	−0.331563	+	0.331563i	0.521617	+	0.853180i	$0.325329\pi$
$854$	11.0962	+	2.80437i	0.379703	+	0.0959635i
$855$		0			0
$856$	8.24999	+	8.24999i	0.281979	+	0.281979i
$857$	10.6859			0.365025			0.182512	−	0.983204i	$-0.441577\pi$
$857$	10.6859			0.365025			0.182512	+	0.983204i	$0.441577\pi$
$858$		0			0
$859$		−	15.4218i		−	0.526186i	−0.964771	−	0.263093i	$-0.915257\pi$
$859$		−	15.4218i		−	0.526186i	0.964771	−	0.263093i	$-0.0847426\pi$
$860$	−16.9249	−	16.9249i	−0.577134	−	0.577134i
$861$		0			0
$862$		−	2.05852i		−	0.0701133i
$863$	13.8546	−	13.8546i	0.471617	−	0.471617i	−0.430820	−	0.902438i	$-0.641776\pi$
$863$	13.8546	−	13.8546i	0.471617	−	0.471617i	0.902438	+	0.430820i	$0.141776\pi$
$864$		0			0
$865$	−44.8544	−	44.8544i	−1.52510	−	1.52510i
$866$	−25.3241	+	25.3241i	−0.860548	+	0.860548i
$867$		0			0
$868$	0.993080	−	3.92936i	0.0337073	−	0.133371i
$869$	4.02101	+	4.02101i	0.136404	+	0.136404i
$870$		0			0
$871$	−0.531858	−	2.65929i	−0.0180213	−	0.0901065i
$872$	−7.49005			−0.253645
$873$		0			0
$874$		−	20.1796i		−	0.682586i
$875$	0.678760	−	2.68568i	0.0229463	−	0.0907926i
$876$		0			0
$877$	6.59203	−	6.59203i	0.222597	−	0.222597i	−0.586994	−	0.809591i	$-0.699689\pi$
$877$	6.59203	−	6.59203i	0.222597	−	0.222597i	0.809591	+	0.586994i	$0.199689\pi$
$878$	10.0881	−	10.0881i	0.340456	−	0.340456i
$879$		0			0
$880$			1.61504i			0.0544431i
$881$	−4.21366			−0.141962			−0.0709810	−	0.997478i	$-0.522613\pi$
$881$	−4.21366			−0.141962			−0.0709810	+	0.997478i	$0.522613\pi$
$882$		0			0
$883$			22.3169i			0.751024i	0.926818	+	0.375512i	$0.122533\pi$
$883$			22.3169i			0.751024i	−0.926818	+	0.375512i	$0.877467\pi$
$884$	−12.9775	−	8.65166i	−0.436480	−	0.290987i
$885$		0			0
$886$	−14.6384	+	14.6384i	−0.491788	+	0.491788i
$887$		−	22.4573i		−	0.754044i	−0.926204	−	0.377022i	$-0.876948\pi$
$887$		−	22.4573i		−	0.754044i	0.926204	−	0.377022i	$-0.123052\pi$
$888$		0			0
$889$	−10.3120	−	17.2872i	−0.345853	−	0.579795i
$890$	12.0516	−	12.0516i	0.403970	−	0.403970i
$891$		0			0
$892$	9.89430	−	9.89430i	0.331286	−	0.331286i
$893$	56.3691			1.88632
$894$		0			0
$895$	22.2667	−	22.2667i	0.744294	−	0.744294i
$896$	2.56510	+	0.648285i	0.0856939	+	0.0216577i
$897$		0			0
$898$	−28.6211			−0.955099
$899$	1.18689	+	1.18689i	0.0395850	+	0.0395850i
$900$		0			0
$901$	−48.6880			−1.62203
$902$	1.77511	+	1.77511i	0.0591047	+	0.0591047i
$903$		0			0
$904$	−14.3854	−	14.3854i	−0.478451	−	0.478451i
$905$	−23.7154	−	23.7154i	−0.788326	−	0.788326i
$906$		0			0
$907$		−	27.5490i		−	0.914749i	−0.889274	−	0.457375i	$-0.848790\pi$
$907$		−	27.5490i		−	0.914749i	0.889274	−	0.457375i	$-0.151210\pi$
$908$	−1.67417	+	1.67417i	−0.0555594	+	0.0555594i
$909$		0			0
$910$	−1.53675	+	30.6152i	−0.0509428	+	1.01488i
$911$	−50.9409			−1.68775			−0.843873	−	0.536542i	$-0.819730\pi$
$911$	−50.9409			−1.68775			−0.843873	+	0.536542i	$0.819730\pi$
$912$		0			0
$913$		−	4.76991i		−	0.157861i
$914$		−	25.7233i		−	0.850852i
$915$		0			0
$916$	1.32583	+	1.32583i	0.0438066	+	0.0438066i
$917$	9.31186	+	15.6106i	0.307505	+	0.515507i
$918$		0			0
$919$	−7.00433			−0.231052			−0.115526	−	0.993304i	$-0.536855\pi$
$919$	−7.00433			−0.231052			−0.115526	+	0.993304i	$0.536855\pi$
$920$	7.66377			0.252667
$921$		0			0
$922$	1.67356			0.0551158
$923$	−6.38496	−	31.9248i	−0.210163	−	1.05082i
$924$		0			0
$925$	27.6358	−	27.6358i	0.908660	−	0.908660i
$926$	−6.98545			−0.229556
$927$		0			0
$928$	−0.774804	+	0.774804i	−0.0254342	+	0.0254342i
$929$	−7.38650	−	7.38650i	−0.242343	−	0.242343i	0.575476	−	0.817819i	$-0.304817\pi$
$929$	−7.38650	−	7.38650i	−0.242343	−	0.242343i	−0.817819	+	0.575476i	$0.804817\pi$
$930$		0			0
$931$	−56.7503	+	16.9536i	−1.85992	+	0.555630i
$932$	10.2117			0.334494
$933$		0			0
$934$	18.8727	−	18.8727i	0.617533	−	0.617533i
$935$			6.98640i			0.228480i
$936$		0			0
$937$			47.1203i			1.53935i	0.638435	+	0.769676i	$0.279582\pi$
$937$			47.1203i			1.53935i	−0.638435	+	0.769676i	$0.720418\pi$
$938$	1.01947	+	1.70906i	0.0332869	+	0.0558029i
$939$		0			0
$940$			21.4077i			0.698243i
$941$	−18.1495	−	18.1495i	−0.591656	−	0.591656i	0.346422	−	0.938079i	$-0.387396\pi$
$941$	−18.1495	−	18.1495i	−0.591656	−	0.591656i	−0.938079	+	0.346422i	$0.887396\pi$
$942$		0			0
$943$	8.42332	−	8.42332i	0.274301	−	0.274301i
$944$	−3.61504	+	3.61504i	−0.117660	+	0.117660i
$945$		0			0
$946$		−	3.74370i		−	0.121718i
$947$	2.89980	+	2.89980i	0.0942309	+	0.0942309i	0.752651	−	0.658420i	$-0.228775\pi$
$947$	2.89980	+	2.89980i	0.0942309	+	0.0942309i	−0.658420	+	0.752651i	$0.728775\pi$
$948$		0			0
$949$	5.18902	+	25.9451i	0.168443	+	0.842213i
$950$			45.0630i			1.46204i
$951$		0			0
$952$	11.0962	+	2.80437i	0.359629	+	0.0908901i
$953$			39.8477i			1.29079i	0.763847	+	0.645397i	$0.223308\pi$
$953$			39.8477i			1.29079i	−0.763847	+	0.645397i	$0.776692\pi$
$954$		0			0
$955$	−25.3147	−	25.3147i	−0.819164	−	0.819164i
$956$	−15.2212	−	15.2212i	−0.492288	−	0.492288i
$957$		0			0
$958$		−	10.4086i		−	0.336286i
$959$	−0.987448	−	0.249561i	−0.0318864	−	0.00805874i
$960$		0			0
$961$		−	28.6534i		−	0.924304i
$962$	−14.6768	+	22.0151i	−0.473198	+	0.709797i
$963$		0			0
$964$	−3.38496	−	3.38496i	−0.109022	−	0.109022i
$965$			18.3440i			0.590515i
$966$		0			0
$967$	−19.7373	+	19.7373i	−0.634709	+	0.634709i	−0.949245	−	0.314537i	$-0.898151\pi$
$967$	−19.7373	+	19.7373i	−0.634709	+	0.634709i	0.314537	+	0.949245i	$0.398151\pi$
$968$	7.59955	−	7.59955i	0.244259	−	0.244259i
$969$		0			0
$970$	−41.7517	−	41.7517i	−1.34057	−	1.34057i
$971$			12.5416i			0.402478i	0.979542	+	0.201239i	$0.0644969\pi$
$971$			12.5416i			0.402478i	−0.979542	+	0.201239i	$0.935503\pi$
$972$		0			0
$973$	27.5741	+	46.2258i	0.883985	+	1.48193i
$974$			35.6051i			1.14086i
$975$		0			0
$976$		−	4.32583i		−	0.138466i
$977$	−13.8123	+	13.8123i	−0.441894	+	0.441894i	−0.892648	−	0.450754i	$-0.851155\pi$
$977$	−13.8123	+	13.8123i	−0.441894	+	0.441894i	0.450754	+	0.892648i	$0.351155\pi$
$978$		0			0
$979$	2.66575			0.0851977
$980$	−6.43858	−	21.5525i	−0.205673	−	0.688469i
$981$		0			0
$982$	−5.49740	−	5.49740i	−0.175429	−	0.175429i
$983$	−26.1069	+	26.1069i	−0.832680	+	0.832680i	−0.987883	−	0.155203i	$-0.950397\pi$
$983$	−26.1069	+	26.1069i	−0.832680	+	0.832680i	0.155203	+	0.987883i	$0.450397\pi$
$984$		0			0
$985$	−2.85205			−0.0908740
$986$	−3.35167	+	3.35167i	−0.106739	+	0.106739i
$987$		0			0
$988$	−5.98299	−	29.9149i	−0.190344	−	0.951721i
$989$	−17.7647			−0.564886
$990$		0			0
$991$	7.35727			0.233711			0.116856	−	0.993149i	$-0.462719\pi$
$991$	7.35727			0.233711			0.116856	+	0.993149i	$0.462719\pi$
$992$	−1.53186			−0.0486365
$993$		0			0
$994$	12.2388	+	20.5173i	0.388190	+	0.650769i
$995$	−37.5766	−	37.5766i	−1.19126	−	1.19126i
$996$		0			0
$997$		−	14.1274i		−	0.447420i	−0.974656	−	0.223710i	$-0.928183\pi$
$997$		−	14.1274i		−	0.447420i	0.974656	−	0.223710i	$-0.0718169\pi$
$998$			33.1763i			1.05018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.b.811.2		8
3.2	odd	2		546.2.o.d.265.3	yes	8
7.6	odd	2		1638.2.x.d.811.1		8
13.8	odd	4		1638.2.x.d.307.1		8
21.20	even	2		546.2.o.a.265.4	✓	8
39.8	even	4		546.2.o.a.307.4	yes	8
91.34	even	4	inner	1638.2.x.b.307.2		8
273.125	odd	4		546.2.o.d.307.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.4	✓	8	21.20	even	2
546.2.o.a.307.4	yes	8	39.8	even	4
546.2.o.d.265.3	yes	8	3.2	odd	2
546.2.o.d.307.3	yes	8	273.125	odd	4
1638.2.x.b.307.2		8	91.34	even	4	inner
1638.2.x.b.811.2		8	1.1	even	1	trivial
1638.2.x.d.307.1		8	13.8	odd	4
1638.2.x.d.811.1		8	7.6	odd	2

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.27220 + 2.27220i) q^{5} +(-2.27220 + 1.35539i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.27220 + 2.27220i) q^{5} +(-2.27220 + 1.35539i) q^{7} +(0.707107 + 0.707107i) q^{8} -3.21338 q^{10} +(-0.355392 - 0.355392i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(0.648285 - 2.56510i) q^{14} -1.00000 q^{16} -4.32583 q^{17} +(-5.98299 - 5.98299i) q^{19} +(2.27220 - 2.27220i) q^{20} +0.502600 q^{22} -2.38496i q^{23} +5.32583i q^{25} +(-0.707107 - 3.53553i) q^{26} +(1.35539 + 2.27220i) q^{28} -1.09574 q^{29} +(-1.08319 - 1.08319i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.05882 - 3.05882i) q^{34} +(-8.24264 - 2.08319i) q^{35} +(-5.18902 - 5.18902i) q^{37} +8.46122 q^{38} +3.21338i q^{40} +(3.53186 + 3.53186i) q^{41} -7.44867i q^{43} +(-0.355392 + 0.355392i) q^{44} +(1.68642 + 1.68642i) q^{46} +(-4.71078 + 4.71078i) q^{47} +(3.32583 - 6.15945i) q^{49} +(-3.76593 - 3.76593i) q^{50} +(3.00000 + 2.00000i) q^{52} +11.2552 q^{53} -1.61504i q^{55} +(-2.56510 - 0.648285i) q^{56} +(0.774804 - 0.774804i) q^{58} +(3.61504 - 3.61504i) q^{59} +4.32583i q^{61} +1.53186 q^{62} +1.00000i q^{64} +(-11.3610 + 2.27220i) q^{65} +(-0.531858 + 0.531858i) q^{67} +4.32583i q^{68} +(7.30146 - 4.35539i) q^{70} +(-6.38496 + 6.38496i) q^{71} +(5.18902 - 5.18902i) q^{73} +7.33838 q^{74} +(-5.98299 + 5.98299i) q^{76} +(1.28922 + 0.325828i) q^{77} -11.3143 q^{79} +(-2.27220 - 2.27220i) q^{80} -4.99480 q^{82} +(6.71078 + 6.71078i) q^{83} +(-9.82917 - 9.82917i) q^{85} +(5.26701 + 5.26701i) q^{86} -0.502600i q^{88} +(-3.75044 + 3.75044i) q^{89} +(0.478235 - 9.52740i) q^{91} -2.38496 q^{92} -6.66205i q^{94} -27.1891i q^{95} +(12.9931 + 12.9931i) q^{97} +(2.00368 + 6.70711i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + 4 * q^7	\( 8 q - 4 q^{5} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{16} - 12 q^{17} - 4 q^{19} - 4 q^{20} + 4 q^{22} + 12 q^{29} - 20 q^{31} + 24 q^{34} - 32 q^{35} - 8 q^{37} + 12 q^{38} + 16 q^{41} + 8 q^{44} - 20 q^{46} - 16 q^{47} + 4 q^{49} - 24 q^{50} + 24 q^{52} + 24 q^{53} - 4 q^{56} - 16 q^{58} + 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} + 8 q^{73} + 4 q^{74} - 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} - 40 q^{82} + 32 q^{83} + 20 q^{85} + 20 q^{86} + 4 q^{89} - 8 q^{91} - 20 q^{92} + 36 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^16 - 12 * q^17 - 4 * q^19 - 4 * q^20 + 4 * q^22 + 12 * q^29 - 20 * q^31 + 24 * q^34 - 32 * q^35 - 8 * q^37 + 12 * q^38 + 16 * q^41 + 8 * q^44 - 20 * q^46 - 16 * q^47 + 4 * q^49 - 24 * q^50 + 24 * q^52 + 24 * q^53 - 4 * q^56 - 16 * q^58 + 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 + 8 * q^73 + 4 * q^74 - 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 - 40 * q^82 + 32 * q^83 + 20 * q^85 + 20 * q^86 + 4 * q^89 - 8 * q^91 - 20 * q^92 + 36 * q^97

Introduction

L-functions

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