LMFDB - Embedded newform 1638.2.x.b.811.1

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			811.1
Root			$1.91681i$ of defining polynomial
Character	$\chi$	$=$	1638.811
Dual form			1638.2.x.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.56510 - 2.56510i) q^{5} +(2.56510 - 0.648285i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.56510 - 2.56510i) q^{5} +(2.56510 - 0.648285i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.62760 q^{10} +(1.64828 + 1.64828i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(-1.35539 + 2.27220i) q^{14} -1.00000 q^{16} -7.15945 q^{17} +(2.86167 + 2.86167i) q^{19} +(-2.56510 + 2.56510i) q^{20} -2.33103 q^{22} +4.45602i q^{23} +8.15945i q^{25} +(-0.707107 - 3.53553i) q^{26} +(-0.648285 - 2.56510i) q^{28} +9.75259 q^{29} +(-3.91681 - 3.91681i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.06250 - 5.06250i) q^{34} +(-8.24264 - 4.91681i) q^{35} +(2.48191 + 2.48191i) q^{37} -4.04701 q^{38} -3.62760i q^{40} +(7.53921 + 7.53921i) q^{41} -8.62240i q^{43} +(1.64828 - 1.64828i) q^{44} +(-3.15088 - 3.15088i) q^{46} +(-0.703431 + 0.703431i) q^{47} +(6.15945 - 3.32583i) q^{49} +(-5.76961 - 5.76961i) q^{50} +(3.00000 + 2.00000i) q^{52} -2.42677 q^{53} -8.45602i q^{55} +(2.27220 + 1.35539i) q^{56} +(-6.89612 + 6.89612i) q^{58} +(10.4560 - 10.4560i) q^{59} +7.15945i q^{61} +5.53921 q^{62} +1.00000i q^{64} +(12.8255 - 2.56510i) q^{65} +(-4.53921 + 4.53921i) q^{67} +7.15945i q^{68} +(9.30514 - 2.35172i) q^{70} +(0.456023 - 0.456023i) q^{71} +(-2.48191 + 2.48191i) q^{73} -3.50995 q^{74} +(2.86167 - 2.86167i) q^{76} +(5.29657 + 3.15945i) q^{77} +12.0422 q^{79} +(2.56510 + 2.56510i) q^{80} -10.6621 q^{82} +(2.70343 + 2.70343i) q^{83} +(18.3647 + 18.3647i) q^{85} +(6.09696 + 6.09696i) q^{86} +2.33103i q^{88} +(4.75044 - 4.75044i) q^{89} +(-3.18534 + 8.99186i) q^{91} +4.45602 q^{92} -0.994801i q^{94} -14.6809i q^{95} +(4.49220 + 4.49220i) q^{97} +(-2.00368 + 6.70711i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.56510	−	2.56510i	−1.14715	−	1.14715i	−0.987111	−	0.160035i	$-0.948839\pi$
$5$	−2.56510	−	2.56510i	−1.14715	−	1.14715i	−0.160035	−	0.987111i	$-0.551161\pi$
$6$		0			0
$7$	2.56510	−	0.648285i	0.969516	−	0.245029i
$7$	2.56510	−	0.648285i	0.969516	−	0.245029i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	3.62760			1.14715
$11$	1.64828	+	1.64828i	0.496977	+	0.496977i	0.910496	−	0.413519i	$-0.135700\pi$
$11$	1.64828	+	1.64828i	0.496977	+	0.496977i	−0.413519	+	0.910496i	$0.635700\pi$
$12$		0			0
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$	−1.35539	+	2.27220i	−0.362244	+	0.607272i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−7.15945			−1.73642			−0.868211	−	0.496195i	$-0.834730\pi$
$17$	−7.15945			−1.73642			−0.868211	+	0.496195i	$0.834730\pi$
$18$		0			0
$19$	2.86167	+	2.86167i	0.656512	+	0.656512i	0.954553	−	0.298041i	$-0.0963334\pi$
$19$	2.86167	+	2.86167i	0.656512	+	0.656512i	−0.298041	+	0.954553i	$0.596333\pi$
$20$	−2.56510	+	2.56510i	−0.573573	+	0.573573i
$21$		0			0
$22$	−2.33103			−0.496977
$23$			4.45602i			0.929145i	0.885535	+	0.464573i	$0.153792\pi$
$23$			4.45602i			0.929145i	−0.885535	+	0.464573i	$0.846208\pi$
$24$		0			0
$25$			8.15945i			1.63189i
$26$	−0.707107	−	3.53553i	−0.138675	−	0.693375i
$27$		0			0
$28$	−0.648285	−	2.56510i	−0.122514	−	0.484758i
$29$	9.75259			1.81101			0.905506	−	0.424335i	$-0.139492\pi$
$29$	9.75259			1.81101			0.905506	+	0.424335i	$0.139492\pi$
$30$		0			0
$31$	−3.91681	−	3.91681i	−0.703480	−	0.703480i	0.261676	−	0.965156i	$-0.415725\pi$
$31$	−3.91681	−	3.91681i	−0.703480	−	0.703480i	−0.965156	+	0.261676i	$0.915725\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	5.06250	−	5.06250i	0.868211	−	0.868211i
$35$	−8.24264	−	4.91681i	−1.39326	−	0.831093i
$36$		0			0
$37$	2.48191	+	2.48191i	0.408024	+	0.408024i	0.881049	−	0.473025i	$-0.156838\pi$
$37$	2.48191	+	2.48191i	0.408024	+	0.408024i	−0.473025	+	0.881049i	$0.656838\pi$
$38$	−4.04701			−0.656512
$39$		0			0
$40$		−	3.62760i		−	0.573573i
$41$	7.53921	+	7.53921i	1.17743	+	1.17743i	0.980398	+	0.197029i	$0.0631294\pi$
$41$	7.53921	+	7.53921i	1.17743	+	1.17743i	0.197029	+	0.980398i	$0.436871\pi$
$42$		0			0
$43$		−	8.62240i		−	1.31490i	−0.753497	−	0.657452i	$-0.771634\pi$
$43$		−	8.62240i		−	1.31490i	0.753497	−	0.657452i	$-0.228366\pi$
$44$	1.64828	−	1.64828i	0.248488	−	0.248488i
$45$		0			0
$46$	−3.15088	−	3.15088i	−0.464573	−	0.464573i
$47$	−0.703431	+	0.703431i	−0.102606	+	0.102606i	−0.756546	−	0.653940i	$-0.773115\pi$
$47$	−0.703431	+	0.703431i	−0.102606	+	0.102606i	0.653940	+	0.756546i	$0.273115\pi$
$48$		0			0
$49$	6.15945	−	3.32583i	0.879922	−	0.475118i
$50$	−5.76961	−	5.76961i	−0.815945	−	0.815945i
$51$		0			0
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$	−2.42677			−0.333342			−0.166671	−	0.986013i	$-0.553302\pi$
$53$	−2.42677			−0.333342			−0.166671	+	0.986013i	$0.553302\pi$
$54$		0			0
$55$		−	8.45602i		−	1.14021i
$56$	2.27220	+	1.35539i	0.303636	+	0.181122i
$57$		0			0
$58$	−6.89612	+	6.89612i	−0.905506	+	0.905506i
$59$	10.4560	−	10.4560i	1.36126	−	1.36126i	0.488942	−	0.872316i	$-0.337383\pi$
$59$	10.4560	−	10.4560i	1.36126	−	1.36126i	0.872316	−	0.488942i	$-0.162617\pi$
$60$		0			0
$61$			7.15945i			0.916674i	0.888778	+	0.458337i	$0.151555\pi$
$61$			7.15945i			0.916674i	−0.888778	+	0.458337i	$0.848445\pi$
$62$	5.53921			0.703480
$63$		0			0
$64$			1.00000i			0.125000i
$65$	12.8255	−	2.56510i	1.59081	−	0.318161i
$66$		0			0
$67$	−4.53921	+	4.53921i	−0.554553	+	0.554553i	−0.927751	−	0.373199i	$-0.878261\pi$
$67$	−4.53921	+	4.53921i	−0.554553	+	0.554553i	0.373199	+	0.927751i	$0.378261\pi$
$68$			7.15945i			0.868211i
$69$		0			0
$70$	9.30514	−	2.35172i	1.11218	−	0.281084i
$71$	0.456023	−	0.456023i	0.0541200	−	0.0541200i	−0.679529	−	0.733649i	$-0.737816\pi$
$71$	0.456023	−	0.456023i	0.0541200	−	0.0541200i	0.733649	+	0.679529i	$0.237816\pi$
$72$		0			0
$73$	−2.48191	+	2.48191i	−0.290486	+	0.290486i	−0.837272	−	0.546786i	$-0.815851\pi$
$73$	−2.48191	+	2.48191i	−0.290486	+	0.290486i	0.546786	+	0.837272i	$0.315851\pi$
$74$	−3.50995			−0.408024
$75$		0			0
$76$	2.86167	−	2.86167i	0.328256	−	0.328256i
$77$	5.29657	+	3.15945i	0.603600	+	0.360053i
$78$		0			0
$79$	12.0422			1.35486			0.677429	−	0.735588i	$-0.263094\pi$
$79$	12.0422			1.35486			0.677429	+	0.735588i	$0.263094\pi$
$80$	2.56510	+	2.56510i	0.286787	+	0.286787i
$81$		0			0
$82$	−10.6621			−1.17743
$83$	2.70343	+	2.70343i	0.296740	+	0.296740i	0.839736	−	0.542996i	$-0.182710\pi$
$83$	2.70343	+	2.70343i	0.296740	+	0.296740i	−0.542996	+	0.839736i	$0.682710\pi$
$84$		0			0
$85$	18.3647	+	18.3647i	1.99193	+	1.99193i
$86$	6.09696	+	6.09696i	0.657452	+	0.657452i
$87$		0			0
$88$			2.33103i			0.248488i
$89$	4.75044	−	4.75044i	0.503546	−	0.503546i	−0.408992	−	0.912538i	$-0.634120\pi$
$89$	4.75044	−	4.75044i	0.503546	−	0.503546i	0.912538	+	0.408992i	$0.134120\pi$
$90$		0			0
$91$	−3.18534	+	8.99186i	−0.333915	+	0.942603i
$92$	4.45602			0.464573
$93$		0			0
$94$		−	0.994801i		−	0.102606i
$95$		−	14.6809i		−	1.50623i
$96$		0			0
$97$	4.49220	+	4.49220i	0.456114	+	0.456114i	0.897378	−	0.441264i	$-0.145470\pi$
$97$	4.49220	+	4.49220i	0.456114	+	0.456114i	−0.441264	+	0.897378i	$0.645470\pi$
$98$	−2.00368	+	6.70711i	−0.202402	+	0.677520i
$99$		0			0
$100$	8.15945			0.815945
$101$	3.55696			0.353931			0.176965	−	0.984217i	$-0.443372\pi$
$101$	3.55696			0.353931			0.176965	+	0.984217i	$0.443372\pi$
$102$		0			0
$103$	9.80437			0.966053			0.483027	−	0.875606i	$-0.339537\pi$
$103$	9.80437			0.966053			0.483027	+	0.875606i	$0.339537\pi$
$104$	−3.53553	+	0.707107i	−0.346688	+	0.0693375i
$105$		0			0
$106$	1.71598	−	1.71598i	0.166671	−	0.166671i
$107$	0.332748			0.0321679			0.0160840	−	0.999871i	$-0.494880\pi$
$107$	0.332748			0.0321679			0.0160840	+	0.999871i	$0.494880\pi$
$108$		0			0
$109$	−12.9672	+	12.9672i	−1.24203	+	1.24203i	−0.282875	+	0.959157i	$0.591288\pi$
$109$	−12.9672	+	12.9672i	−1.24203	+	1.24203i	−0.959157	+	0.282875i	$0.908712\pi$
$110$	5.97931	+	5.97931i	0.570105	+	0.570105i
$111$		0			0
$112$	−2.56510	+	0.648285i	−0.242379	+	0.0612572i
$113$	12.6872			1.19351			0.596754	−	0.802425i	$-0.296457\pi$
$113$	12.6872			1.19351			0.596754	+	0.802425i	$0.296457\pi$
$114$		0			0
$115$	11.4301	−	11.4301i	1.06587	−	1.06587i
$116$		−	9.75259i		−	0.905506i
$117$		0			0
$118$			14.7870i			1.36126i
$119$	−18.3647	+	4.64136i	−1.68349	+	0.425473i
$120$		0			0
$121$		−	5.56631i		−	0.506029i
$122$	−5.06250	−	5.06250i	−0.458337	−	0.458337i
$123$		0			0
$124$	−3.91681	+	3.91681i	−0.351740	+	0.351740i
$125$	8.10431	−	8.10431i	0.724871	−	0.724871i
$126$		0			0
$127$			5.94822i			0.527820i	0.964547	+	0.263910i	$0.0850121\pi$
$127$			5.94822i			0.527820i	−0.964547	+	0.263910i	$0.914988\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−7.25519	+	10.8828i	−0.636322	+	0.954484i
$131$		−	0.0292581i		−	0.00255629i	−0.999999	−	0.00127815i	$-0.999593\pi$
$131$		−	0.0292581i		−	0.00255629i	0.999999	−	0.00127815i	$-0.000406847\pi$
$132$		0			0
$133$	9.19563	+	5.48528i	0.797362	+	0.475634i
$134$		−	6.41941i		−	0.554553i
$135$		0			0
$136$	−5.06250	−	5.06250i	−0.434106	−	0.434106i
$137$	−4.56510	−	4.56510i	−0.390023	−	0.390023i	0.484673	−	0.874695i	$-0.338939\pi$
$137$	−4.56510	−	4.56510i	−0.390023	−	0.390023i	−0.874695	+	0.484673i	$0.838939\pi$
$138$		0			0
$139$			12.6872i			1.07611i	0.842910	+	0.538055i	$0.180841\pi$
$139$			12.6872i			1.07611i	−0.842910	+	0.538055i	$0.819159\pi$
$140$	−4.91681	+	8.24264i	−0.415547	+	0.696630i
$141$		0			0
$142$			0.644914i			0.0541200i
$143$	−8.24142	+	1.64828i	−0.689182	+	0.137836i
$144$		0			0
$145$	−25.0164	−	25.0164i	−2.07750	−	2.07750i
$146$		−	3.50995i		−	0.290486i
$147$		0			0
$148$	2.48191	−	2.48191i	0.204012	−	0.204012i
$149$	−13.4021	+	13.4021i	−1.09794	+	1.09794i	−0.103291	+	0.994651i	$0.532937\pi$
$149$	−13.4021	+	13.4021i	−1.09794	+	1.09794i	−0.994651	+	0.103291i	$0.967063\pi$
$150$		0			0
$151$	3.02804	+	3.02804i	0.246418	+	0.246418i	0.819499	−	0.573081i	$-0.194252\pi$
$151$	3.02804	+	3.02804i	0.246418	+	0.246418i	−0.573081	+	0.819499i	$0.694252\pi$
$152$			4.04701i			0.328256i
$153$		0			0
$154$	−5.97931	+	1.51117i	−0.481827	+	0.121773i
$155$			20.0940i			1.61399i
$156$		0			0
$157$		−	11.4198i		−	0.911403i	−0.890133	−	0.455701i	$-0.849388\pi$
$157$		−	11.4198i		−	0.911403i	0.890133	−	0.455701i	$-0.150612\pi$
$158$	−8.51515	+	8.51515i	−0.677429	+	0.677429i
$159$		0			0
$160$	−3.62760			−0.286787
$161$	2.88877	+	11.4301i	0.227667	+	0.900821i
$162$		0			0
$163$	−9.07627	−	9.07627i	−0.710908	−	0.710908i	0.255817	−	0.966725i	$-0.417656\pi$
$163$	−9.07627	−	9.07627i	−0.710908	−	0.710908i	−0.966725	+	0.255817i	$0.917656\pi$
$164$	7.53921	−	7.53921i	0.588713	−	0.588713i
$165$		0			0
$166$	−3.82323			−0.296740
$167$	3.31554	−	3.31554i	0.256564	−	0.256564i	−0.567091	−	0.823655i	$-0.691931\pi$
$167$	3.31554	−	3.31554i	0.256564	−	0.256564i	0.823655	+	0.567091i	$0.191931\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−25.9716			−1.99193
$171$		0			0
$172$	−8.62240			−0.657452
$173$	−6.05852			−0.460620			−0.230310	−	0.973117i	$-0.573974\pi$
$173$	−6.05852			−0.460620			−0.230310	+	0.973117i	$0.573974\pi$
$174$		0			0
$175$	5.28965	+	20.9298i	0.399860	+	1.58214i
$176$	−1.64828	−	1.64828i	−0.124244	−	0.124244i
$177$		0			0
$178$			6.71814i			0.503546i
$179$			13.5570i			1.01329i	0.862153	+	0.506647i	$0.169115\pi$
$179$			13.5570i			1.01329i	−0.862153	+	0.506647i	$0.830885\pi$
$180$		0			0
$181$	14.5793			1.08367			0.541835	−	0.840485i	$-0.317730\pi$
$181$	14.5793			1.08367			0.541835	+	0.840485i	$0.317730\pi$
$182$	−4.10583	−	8.61058i	−0.304344	−	0.638259i
$183$		0			0
$184$	−3.15088	+	3.15088i	−0.232286	+	0.232286i
$185$		−	12.7327i		−	0.936126i
$186$		0			0
$187$	−11.8008	−	11.8008i	−0.862961	−	0.862961i
$188$	0.703431	+	0.703431i	0.0513029	+	0.0513029i
$189$		0			0
$190$	10.3810	+	10.3810i	0.753115	+	0.753115i
$191$	26.3837			1.90906			0.954528	−	0.298123i	$-0.0963604\pi$
$191$	26.3837			1.90906			0.954528	+	0.298123i	$0.0963604\pi$
$192$		0			0
$193$	2.86288	+	2.86288i	0.206075	+	0.206075i	0.802597	−	0.596522i	$-0.203451\pi$
$193$	2.86288	+	2.86288i	0.206075	+	0.206075i	−0.596522	+	0.802597i	$0.703451\pi$
$194$	−6.35293			−0.456114
$195$		0			0
$196$	−3.32583	−	6.15945i	−0.237559	−	0.439961i
$197$	6.21338	−	6.21338i	0.442685	−	0.442685i	−0.450228	−	0.892913i	$-0.648657\pi$
$197$	6.21338	−	6.21338i	0.442685	−	0.442685i	0.892913	+	0.450228i	$0.148657\pi$
$198$		0			0
$199$	1.63799			0.116114			0.0580572	−	0.998313i	$-0.481509\pi$
$199$	1.63799			0.116114			0.0580572	+	0.998313i	$0.481509\pi$
$200$	−5.76961	+	5.76961i	−0.407973	+	0.407973i
$201$		0			0
$202$	−2.51515	+	2.51515i	−0.176965	+	0.176965i
$203$	25.0164	−	6.32246i	1.75580	−	0.443749i
$204$		0			0
$205$		−	38.6776i		−	2.70136i
$206$	−6.93274	+	6.93274i	−0.483027	+	0.483027i
$207$		0			0
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$			9.43369i			0.652542i
$210$		0			0
$211$	0.622397			0.0428476			0.0214238	−	0.999770i	$-0.493180\pi$
$211$	0.622397			0.0428476			0.0214238	+	0.999770i	$0.493180\pi$
$212$			2.42677i			0.166671i
$213$		0			0
$214$	−0.235288	+	0.235288i	−0.0160840	+	0.0160840i
$215$	−22.1173	+	22.1173i	−1.50839	+	1.50839i
$216$		0			0
$217$	−12.5862	−	7.50780i	−0.854408	−	0.509663i
$218$		−	18.3384i		−	1.24203i
$219$		0			0
$220$	−8.45602			−0.570105
$221$	14.3189	−	21.4784i	0.963194	−	1.44479i
$222$		0			0
$223$	15.5615	+	15.5615i	1.04208	+	1.04208i	0.999075	+	0.0430034i	$0.0136926\pi$
$223$	15.5615	+	15.5615i	1.04208	+	1.04208i	0.0430034	+	0.999075i	$0.486307\pi$
$224$	1.35539	−	2.27220i	0.0905609	−	0.151818i
$225$		0			0
$226$	−8.97117	+	8.97117i	−0.596754	+	0.596754i
$227$	1.15945	+	1.15945i	0.0769556	+	0.0769556i	0.744537	−	0.667581i	$-0.232670\pi$
$227$	1.15945	+	1.15945i	0.0769556	+	0.0769556i	−0.667581	+	0.744537i	$0.732670\pi$
$228$		0			0
$229$	−4.15945	+	4.15945i	−0.274864	+	0.274864i	−0.831055	−	0.556190i	$-0.812263\pi$
$229$	−4.15945	+	4.15945i	−0.274864	+	0.274864i	0.556190	+	0.831055i	$0.312263\pi$
$230$			16.1647i			1.06587i
$231$		0			0
$232$	6.89612	+	6.89612i	0.452753	+	0.452753i
$233$		−	10.7974i		−	0.707364i	−0.935366	−	0.353682i	$-0.884929\pi$
$233$		−	10.7974i		−	0.707364i	0.935366	−	0.353682i	$-0.115071\pi$
$234$		0			0
$235$	3.60874			0.235408
$236$	−10.4560	−	10.4560i	−0.680629	−	0.680629i
$237$		0			0
$238$	9.70386	−	16.2677i	0.629008	−	1.05448i
$239$	−16.1501	+	16.1501i	−1.04466	+	1.04466i	−0.0457083	+	0.998955i	$0.514554\pi$
$239$	−16.1501	+	16.1501i	−1.04466	+	1.04466i	−0.998955	+	0.0457083i	$0.985446\pi$
$240$		0			0
$241$	−3.45602	+	3.45602i	−0.222622	+	0.222622i	−0.809602	−	0.586980i	$-0.800317\pi$
$241$	−3.45602	+	3.45602i	−0.222622	+	0.222622i	0.586980	+	0.809602i	$0.300317\pi$
$242$	3.93598	+	3.93598i	0.253014	+	0.253014i
$243$		0			0
$244$	7.15945			0.458337
$245$	−24.3307	−	7.26853i	−1.55443	−	0.464369i
$246$		0			0
$247$	−14.3083	+	2.86167i	−0.910418	+	0.182084i
$248$		−	5.53921i		−	0.351740i
$249$		0			0
$250$			11.4612i			0.724871i
$251$	−5.64230			−0.356139			−0.178069	−	0.984018i	$-0.556985\pi$
$251$	−5.64230			−0.356139			−0.178069	+	0.984018i	$0.556985\pi$
$252$		0			0
$253$	−7.34480	+	7.34480i	−0.461763	+	0.461763i
$254$	−4.20603	−	4.20603i	−0.263910	−	0.263910i
$255$		0			0
$256$	1.00000			0.0625000
$257$	25.0199			1.56070			0.780349	−	0.625344i	$-0.215041\pi$
$257$	25.0199			1.56070			0.780349	+	0.625344i	$0.215041\pi$
$258$		0			0
$259$	7.97533	+	4.75736i	0.495563	+	0.295608i
$260$	−2.56510	−	12.8255i	−0.159081	−	0.795403i
$261$		0			0
$262$	0.0206886	+	0.0206886i	0.00127815	+	0.00127815i
$263$	12.1525			0.749357			0.374679	−	0.927155i	$-0.377753\pi$
$263$	12.1525			0.749357			0.374679	+	0.927155i	$0.377753\pi$
$264$		0			0
$265$	6.22489	+	6.22489i	0.382392	+	0.382392i
$266$	−10.3810	+	2.62361i	−0.636498	+	0.160864i
$267$		0			0
$268$	4.53921	+	4.53921i	0.277276	+	0.277276i
$269$			19.9482i			1.21626i	0.793836	+	0.608132i	$0.208081\pi$
$269$			19.9482i			1.21626i	−0.793836	+	0.608132i	$0.791919\pi$
$270$		0			0
$271$	8.31432	−	8.31432i	0.505059	−	0.505059i	−0.407947	−	0.913006i	$-0.633755\pi$
$271$	8.31432	−	8.31432i	0.505059	−	0.505059i	0.913006	+	0.407947i	$0.133755\pi$
$272$	7.15945			0.434106
$273$		0			0
$274$	6.45602			0.390023
$275$	−13.4491	+	13.4491i	−0.811011	+	0.811011i
$276$		0			0
$277$		−	5.55696i		−	0.333885i	−0.985967	−	0.166943i	$-0.946611\pi$
$277$		−	5.55696i		−	0.333885i	0.985967	−	0.166943i	$-0.0533895\pi$
$278$	−8.97117	−	8.97117i	−0.538055	−	0.538055i
$279$		0			0
$280$	−2.35172	−	9.30514i	−0.140542	−	0.556088i
$281$	11.4807	+	11.4807i	0.684881	+	0.684881i	0.961096	−	0.276215i	$-0.0890802\pi$
$281$	11.4807	+	11.4807i	0.684881	+	0.684881i	−0.276215	+	0.961096i	$0.589080\pi$
$282$		0			0
$283$	−6.44735			−0.383255			−0.191627	−	0.981468i	$-0.561377\pi$
$283$	−6.44735			−0.383255			−0.191627	+	0.981468i	$0.561377\pi$
$284$	−0.456023	−	0.456023i	−0.0270600	−	0.0270600i
$285$		0			0
$286$	4.66205	−	6.99308i	0.275673	−	0.413509i
$287$	24.2264	+	14.4513i	1.43004	+	0.853031i
$288$		0			0
$289$	34.2578			2.01516
$290$	35.3785			2.07750
$291$		0			0
$292$	2.48191	+	2.48191i	0.145243	+	0.145243i
$293$	−22.1703	+	22.1703i	−1.29520	+	1.29520i	−0.363677	+	0.931525i	$0.618479\pi$
$293$	−22.1703	+	22.1703i	−1.29520	+	1.29520i	−0.931525	+	0.363677i	$0.881521\pi$
$294$		0			0
$295$	−53.6414			−3.12313
$296$			3.50995i			0.204012i
$297$		0			0
$298$		−	18.9534i		−	1.09794i
$299$	−13.3681	−	8.91205i	−0.773095	−	0.515397i
$300$		0			0
$301$	−5.58977	−	22.1173i	−0.322189	−	1.27482i
$302$	−4.28230			−0.246418
$303$		0			0
$304$	−2.86167	−	2.86167i	−0.164128	−	0.164128i
$305$	18.3647	−	18.3647i	1.05156	−	1.05156i
$306$		0			0
$307$	−5.54613	+	5.54613i	−0.316534	+	0.316534i	−0.847434	−	0.530900i	$-0.821854\pi$
$307$	−5.54613	+	5.54613i	−0.316534	+	0.316534i	0.530900	+	0.847434i	$0.321854\pi$
$308$	3.15945	−	5.29657i	0.180027	−	0.301800i
$309$		0			0
$310$	−14.2086	−	14.2086i	−0.806995	−	0.806995i
$311$	−15.6648			−0.888270			−0.444135	−	0.895960i	$-0.646489\pi$
$311$	−15.6648			−0.888270			−0.444135	+	0.895960i	$0.646489\pi$
$312$		0			0
$313$			2.58640i			0.146192i	0.997325	+	0.0730959i	$0.0232879\pi$
$313$			2.58640i			0.146192i	−0.997325	+	0.0730959i	$0.976712\pi$
$314$	8.07505	+	8.07505i	0.455701	+	0.455701i
$315$		0			0
$316$		−	12.0422i		−	0.677429i
$317$	−5.33059	+	5.33059i	−0.299396	+	0.299396i	−0.840777	−	0.541381i	$-0.817902\pi$
$317$	−5.33059	+	5.33059i	−0.299396	+	0.299396i	0.541381	+	0.840777i	$0.317902\pi$
$318$		0			0
$319$	16.0750	+	16.0750i	0.900030	+	0.900030i
$320$	2.56510	−	2.56510i	0.143393	−	0.143393i
$321$		0			0
$322$	−10.1250	−	6.03966i	−0.564244	−	0.336577i
$323$	−20.4880	−	20.4880i	−1.13998	−	1.13998i
$324$		0			0
$325$	−24.4784	−	16.3189i	−1.35782	−	0.905210i
$326$	12.8358			0.710908
$327$		0			0
$328$			10.6621i			0.588713i
$329$	−1.34834	+	2.26039i	−0.0743367	+	0.124619i
$330$		0			0
$331$	17.3927	−	17.3927i	0.955991	−	0.955991i	−0.0430801	−	0.999072i	$-0.513717\pi$
$331$	17.3927	−	17.3927i	0.955991	−	0.955991i	0.999072	+	0.0430801i	$0.0137171\pi$
$332$	2.70343	−	2.70343i	0.148370	−	0.148370i
$333$		0			0
$334$			4.68888i			0.256564i
$335$	23.2870			1.27231
$336$		0			0
$337$		−	9.75259i		−	0.531258i	−0.964075	−	0.265629i	$-0.914420\pi$
$337$		−	9.75259i		−	0.531258i	0.964075	−	0.265629i	$-0.0855795\pi$
$338$	12.0208	+	4.94975i	0.653846	+	0.269231i
$339$		0			0
$340$	18.3647	−	18.3647i	0.995966	−	0.995966i
$341$		−	12.9120i		−	0.699227i
$342$		0			0
$343$	13.6435	−	12.5242i	0.736681	−	0.676241i
$344$	6.09696	−	6.09696i	0.328726	−	0.328726i
$345$		0			0
$346$	4.28402	−	4.28402i	0.230310	−	0.230310i
$347$	−2.38696			−0.128139			−0.0640693	−	0.997945i	$-0.520408\pi$
$347$	−2.38696			−0.128139			−0.0640693	+	0.997945i	$0.520408\pi$
$348$		0			0
$349$	−1.27667	+	1.27667i	−0.0683383	+	0.0683383i	−0.740450	−	0.672112i	$-0.765388\pi$
$349$	−1.27667	+	1.27667i	−0.0683383	+	0.0683383i	0.672112	+	0.740450i	$0.265388\pi$
$350$	−18.5399	−	11.0593i	−0.991002	−	0.591142i
$351$		0			0
$352$	2.33103			0.124244
$353$	−16.3074	−	16.3074i	−0.867955	−	0.867955i	0.124291	−	0.992246i	$-0.460335\pi$
$353$	−16.3074	−	16.3074i	−0.867955	−	0.867955i	−0.992246	+	0.124291i	$0.960335\pi$
$354$		0			0
$355$	−2.33949			−0.124167
$356$	−4.75044	−	4.75044i	−0.251773	−	0.251773i
$357$		0			0
$358$	−9.58622	−	9.58622i	−0.506647	−	0.506647i
$359$	−16.0130	−	16.0130i	−0.845133	−	0.845133i	0.144388	−	0.989521i	$-0.453879\pi$
$359$	−16.0130	−	16.0130i	−0.845133	−	0.845133i	−0.989521	+	0.144388i	$0.953879\pi$
$360$		0			0
$361$		−	2.62172i		−	0.137985i
$362$	−10.3091	+	10.3091i	−0.541835	+	0.541835i
$363$		0			0
$364$	8.99186	+	3.18534i	0.471302	+	0.166957i
$365$	12.7327			0.666459
$366$		0			0
$367$			2.42677i			0.126676i	0.997992	+	0.0633381i	$0.0201746\pi$
$367$			2.42677i			0.126676i	−0.997992	+	0.0633381i	$0.979825\pi$
$368$		−	4.45602i		−	0.232286i
$369$		0			0
$370$	9.00337	+	9.00337i	0.468063	+	0.468063i
$371$	−6.22489	+	1.57323i	−0.323180	+	0.0816783i
$372$		0			0
$373$	−11.8759			−0.614909			−0.307455	−	0.951563i	$-0.599477\pi$
$373$	−11.8759			−0.614909			−0.307455	+	0.951563i	$0.599477\pi$
$374$	16.6889			0.862961
$375$		0			0
$376$	−0.994801			−0.0513029
$377$	−19.5052	+	29.2578i	−1.00457	+	1.50685i
$378$		0			0
$379$	14.4021	−	14.4021i	0.739786	−	0.739786i	−0.232751	−	0.972536i	$-0.574773\pi$
$379$	14.4021	−	14.4021i	0.739786	−	0.739786i	0.972536	+	0.232751i	$0.0747726\pi$
$380$	−14.6809			−0.753115
$381$		0			0
$382$	−18.6561	+	18.6561i	−0.954528	+	0.954528i
$383$	18.6121	+	18.6121i	0.951034	+	0.951034i	0.998856	−	0.0478217i	$-0.0152279\pi$
$383$	18.6121	+	18.6121i	0.951034	+	0.951034i	−0.0478217	+	0.998856i	$0.515228\pi$
$384$		0			0
$385$	−5.48191	−	21.6905i	−0.279384	−	1.10545i
$386$	−4.04873			−0.206075
$387$		0			0
$388$	4.49220	−	4.49220i	0.228057	−	0.228057i
$389$		−	0.107858i		−	0.00546860i	−0.999996	−	0.00273430i	$-0.999130\pi$
$389$		−	0.107858i		−	0.00546860i	0.999996	−	0.00273430i	$-0.000870356\pi$
$390$		0			0
$391$		−	31.9027i		−	1.61339i
$392$	6.70711	+	2.00368i	0.338760	+	0.101201i
$393$		0			0
$394$			8.78705i			0.442685i
$395$	−30.8895	−	30.8895i	−1.55422	−	1.55422i
$396$		0			0
$397$	−18.9320	+	18.9320i	−0.950167	+	0.950167i	−0.998816	−	0.0486486i	$-0.984509\pi$
$397$	−18.9320	+	18.9320i	−0.950167	+	0.950167i	0.0486486	+	0.998816i	$0.484509\pi$
$398$	−1.15824	+	1.15824i	−0.0580572	+	0.0580572i
$399$		0			0
$400$		−	8.15945i		−	0.407973i
$401$	−1.33059	−	1.33059i	−0.0664467	−	0.0664467i	0.673103	−	0.739549i	$-0.264961\pi$
$401$	−1.33059	−	1.33059i	−0.0664467	−	0.0664467i	−0.739549	+	0.673103i	$0.764961\pi$
$402$		0			0
$403$	19.5841	−	3.91681i	0.975552	−	0.195110i
$404$		−	3.55696i		−	0.176965i
$405$		0			0
$406$	−13.2186	+	22.1599i	−0.656027	+	1.09978i
$407$			8.18179i			0.405556i
$408$		0			0
$409$	21.6543	+	21.6543i	1.07074	+	1.07074i	0.997300	+	0.0734389i	$0.0233974\pi$
$409$	21.6543	+	21.6543i	1.07074	+	1.07074i	0.0734389	+	0.997300i	$0.476603\pi$
$410$	27.3492	+	27.3492i	1.35068	+	1.35068i
$411$		0			0
$412$		−	9.80437i		−	0.483027i
$413$	20.0422	−	33.5992i	0.986214	−	1.65331i
$414$		0			0
$415$		−	13.8691i		−	0.680809i
$416$	0.707107	+	3.53553i	0.0346688	+	0.173344i
$417$		0			0
$418$	−6.67062	−	6.67062i	−0.326271	−	0.326271i
$419$		−	3.41741i		−	0.166951i	−0.996510	−	0.0834757i	$-0.973398\pi$
$419$		−	3.41741i		−	0.166951i	0.996510	−	0.0834757i	$-0.0266021\pi$
$420$		0			0
$421$	−1.36201	+	1.36201i	−0.0663801	+	0.0663801i	−0.739517	−	0.673137i	$-0.764946\pi$
$421$	−1.36201	+	1.36201i	−0.0663801	+	0.0663801i	0.673137	+	0.739517i	$0.264946\pi$
$422$	−0.440101	+	0.440101i	−0.0214238	+	0.0214238i
$423$		0			0
$424$	−1.71598	−	1.71598i	−0.0833355	−	0.0833355i
$425$		−	58.4172i		−	2.83365i
$426$		0			0
$427$	4.64136	+	18.3647i	0.224611	+	0.888730i
$428$		−	0.332748i		−	0.0160840i
$429$		0			0
$430$		−	31.2786i		−	1.50839i
$431$	−11.1302	+	11.1302i	−0.536123	+	0.536123i	−0.922388	−	0.386265i	$-0.873765\pi$
$431$	−11.1302	+	11.1302i	−0.536123	+	0.536123i	0.386265	+	0.922388i	$0.373765\pi$
$432$		0			0
$433$	19.7843			0.950772			0.475386	−	0.879777i	$-0.342308\pi$
$433$	19.7843			0.950772			0.475386	+	0.879777i	$0.342308\pi$
$434$	14.2086	−	3.59099i	0.682035	−	0.172373i
$435$		0			0
$436$	12.9672	+	12.9672i	0.621016	+	0.621016i
$437$	−12.7517	+	12.7517i	−0.609994	+	0.609994i
$438$		0			0
$439$	−26.7749			−1.27790			−0.638949	−	0.769249i	$-0.720630\pi$
$439$	−26.7749			−1.27790			−0.638949	+	0.769249i	$0.720630\pi$
$440$	5.97931	−	5.97931i	0.285052	−	0.285052i
$441$		0			0
$442$	5.06250	+	25.3125i	0.240798	+	1.20399i
$443$	−28.3587			−1.34736			−0.673682	−	0.739022i	$-0.735288\pi$
$443$	−28.3587			−1.34736			−0.673682	+	0.739022i	$0.735288\pi$
$444$		0			0
$445$	−24.3707			−1.15528
$446$	−22.0074			−1.04208
$447$		0			0
$448$	0.648285	+	2.56510i	0.0306286	+	0.121189i
$449$	−2.28843	−	2.28843i	−0.107998	−	0.107998i	0.651043	−	0.759041i	$-0.274332\pi$
$449$	−2.28843	−	2.28843i	−0.107998	−	0.107998i	−0.759041	+	0.651043i	$0.774332\pi$
$450$		0			0
$451$			24.8535i			1.17031i
$452$		−	12.6872i		−	0.596754i
$453$		0			0
$454$	−1.63972			−0.0769556
$455$	31.2357	−	14.8943i	1.46435	−	0.698255i
$456$		0			0
$457$	−5.68091	+	5.68091i	−0.265742	+	0.265742i	−0.827382	−	0.561640i	$-0.810171\pi$
$457$	−5.68091	+	5.68091i	−0.265742	+	0.265742i	0.561640	+	0.827382i	$0.310171\pi$
$458$		−	5.88236i		−	0.274864i
$459$		0			0
$460$	−11.4301	−	11.4301i	−0.532933	−	0.532933i
$461$	−15.6953	−	15.6953i	−0.731003	−	0.731003i	0.239816	−	0.970818i	$-0.422913\pi$
$461$	−15.6953	−	15.6953i	−0.731003	−	0.731003i	−0.970818	+	0.239816i	$0.922913\pi$
$462$		0			0
$463$	−11.2324	−	11.2324i	−0.522012	−	0.522012i	0.396167	−	0.918179i	$-0.370340\pi$
$463$	−11.2324	−	11.2324i	−0.522012	−	0.522012i	−0.918179	+	0.396167i	$0.870340\pi$
$464$	−9.75259			−0.452753
$465$		0			0
$466$	7.63495	+	7.63495i	0.353682	+	0.353682i
$467$	2.81997			0.130492			0.0652462	−	0.997869i	$-0.479217\pi$
$467$	2.81997			0.130492			0.0652462	+	0.997869i	$0.479217\pi$
$468$		0			0
$469$	−8.70082	+	14.5862i	−0.401766	+	0.673529i
$470$	−2.55176	+	2.55176i	−0.117704	+	0.117704i
$471$		0			0
$472$	14.7870			0.680629
$473$	14.2122	−	14.2122i	0.653476	−	0.653476i
$474$		0			0
$475$	−23.3496	+	23.3496i	−1.07136	+	1.07136i
$476$	4.64136	+	18.3647i	0.212737	+	0.841745i
$477$		0			0
$478$		−	22.8397i		−	1.04466i
$479$	−23.0456	+	23.0456i	−1.05298	+	1.05298i	−0.0544653	+	0.998516i	$0.517345\pi$
$479$	−23.0456	+	23.0456i	−1.05298	+	1.05298i	−0.998516	+	0.0544653i	$0.982655\pi$
$480$		0			0
$481$	−12.4096	+	2.48191i	−0.565827	+	0.113165i
$482$		−	4.88755i		−	0.222622i
$483$		0			0
$484$	−5.56631			−0.253014
$485$		−	23.0459i		−	1.04646i
$486$		0			0
$487$	26.3503	−	26.3503i	1.19405	−	1.19405i	0.218126	−	0.975921i	$-0.430005\pi$
$487$	26.3503	−	26.3503i	1.19405	−	1.19405i	0.975921	−	0.218126i	$-0.0699945\pi$
$488$	−5.06250	+	5.06250i	−0.229169	+	0.229169i
$489$		0			0
$490$	22.3440	−	12.0648i	1.00940	−	0.545030i
$491$			11.7819i			0.531707i	0.964013	+	0.265854i	$0.0856538\pi$
$491$			11.7819i			0.531707i	−0.964013	+	0.265854i	$0.914346\pi$
$492$		0			0
$493$	−69.8232			−3.14468
$494$	8.09402	−	12.1410i	0.364167	−	0.546251i
$495$		0			0
$496$	3.91681	+	3.91681i	0.175870	+	0.175870i
$497$	0.874111	−	1.46538i	0.0392093	−	0.0657312i
$498$		0			0
$499$	−25.6014	+	25.6014i	−1.14607	+	1.14607i	−0.158756	+	0.987318i	$0.550748\pi$
$499$	−25.6014	+	25.6014i	−1.14607	+	1.14607i	−0.987318	+	0.158756i	$0.949252\pi$
$500$	−8.10431	−	8.10431i	−0.362436	−	0.362436i
$501$		0			0
$502$	3.98971	−	3.98971i	0.178069	−	0.178069i
$503$			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
$505$	−9.12395	−	9.12395i	−0.406011	−	0.406011i
$506$		−	10.3871i		−	0.461763i
$507$		0			0
$508$	5.94822			0.263910
$509$	−24.4927	−	24.4927i	−1.08562	−	1.08562i	−0.995973	−	0.0896482i	$-0.971426\pi$
$509$	−24.4927	−	24.4927i	−1.08562	−	1.08562i	−0.0896482	−	0.995973i	$-0.528574\pi$
$510$		0			0
$511$	−4.75736	+	7.97533i	−0.210453	+	0.352808i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−17.6917	+	17.6917i	−0.780349	+	0.780349i
$515$	−25.1492	−	25.1492i	−1.10820	−	1.10820i
$516$		0			0
$517$	−2.31891			−0.101985
$518$	−9.00337	+	2.27545i	−0.395585	+	0.0999775i
$519$		0			0
$520$	10.8828	+	7.25519i	0.477242	+	0.318161i
$521$		−	24.7188i		−	1.08295i	−0.840716	−	0.541476i	$-0.817866\pi$
$521$		−	24.7188i		−	1.08295i	0.840716	−	0.541476i	$-0.182134\pi$
$522$		0			0
$523$		−	8.22489i		−	0.359649i	−0.983699	−	0.179825i	$-0.942447\pi$
$523$		−	8.22489i		−	0.359649i	0.983699	−	0.179825i	$-0.0575530\pi$
$524$	−0.0292581			−0.00127815
$525$		0			0
$526$	−8.59314	+	8.59314i	−0.374679	+	0.374679i
$527$	28.0422	+	28.0422i	1.22154	+	1.22154i
$528$		0			0
$529$	3.14386			0.136689
$530$	−8.80332			−0.382392
$531$		0			0
$532$	5.48528	−	9.19563i	0.237817	−	0.398681i
$533$	−37.6961	+	7.53921i	−1.63280	+	0.326559i
$534$		0			0
$535$	−0.853530	−	0.853530i	−0.0369013	−	0.0369013i
$536$	−6.41941			−0.277276
$537$		0			0
$538$	−14.1055	−	14.1055i	−0.608132	−	0.608132i
$539$	15.6344	+	4.67062i	0.673423	+	0.201178i
$540$		0			0
$541$	15.1691	+	15.1691i	0.652169	+	0.652169i	0.953515	−	0.301346i	$-0.0974358\pi$
$541$	15.1691	+	15.1691i	0.652169	+	0.652169i	−0.301346	+	0.953515i	$0.597436\pi$
$542$			11.7582i			0.505059i
$543$		0			0
$544$	−5.06250	+	5.06250i	−0.217053	+	0.217053i
$545$	66.5242			2.84959
$546$		0			0
$547$	−15.2261			−0.651020			−0.325510	−	0.945539i	$-0.605536\pi$
$547$	−15.2261			−0.651020			−0.325510	+	0.945539i	$0.605536\pi$
$548$	−4.56510	+	4.56510i	−0.195011	+	0.195011i
$549$		0			0
$550$		−	19.0199i		−	0.811011i
$551$	27.9087	+	27.9087i	1.18895	+	1.18895i
$552$		0			0
$553$	30.8895	−	7.80680i	1.31356	−	0.331979i
$554$	3.92936	+	3.92936i	0.166943	+	0.166943i
$555$		0			0
$556$	12.6872			0.538055
$557$	−24.0893	−	24.0893i	−1.02069	−	1.02069i	−0.999781	−	0.0209130i	$-0.993343\pi$
$557$	−24.0893	−	24.0893i	−1.02069	−	1.02069i	−0.0209130	−	0.999781i	$-0.506657\pi$
$558$		0			0
$559$	25.8672	+	17.2448i	1.09407	+	0.729377i
$560$	8.24264	+	4.91681i	0.348315	+	0.207773i
$561$		0			0
$562$	−16.2362			−0.684881
$563$	31.8346			1.34167			0.670835	−	0.741607i	$-0.265936\pi$
$563$	31.8346			1.34167			0.670835	+	0.741607i	$0.265936\pi$
$564$		0			0
$565$	−32.5438	−	32.5438i	−1.36913	−	1.36913i
$566$	4.55896	−	4.55896i	0.191627	−	0.191627i
$567$		0			0
$568$	0.644914			0.0270600
$569$			15.2218i			0.638130i	0.947733	+	0.319065i	$0.103369\pi$
$569$			15.2218i			0.638130i	−0.947733	+	0.319065i	$0.896631\pi$
$570$		0			0
$571$		−	2.53462i		−	0.106071i	−0.998593	−	0.0530353i	$-0.983110\pi$
$571$		−	2.53462i		−	0.106071i	0.998593	−	0.0530353i	$-0.0168896\pi$
$572$	1.64828	+	8.24142i	0.0689182	+	0.344591i
$573$		0			0
$574$	−27.3492	+	6.91205i	−1.14153	+	0.288503i
$575$	−36.3587			−1.51626
$576$		0			0
$577$	−14.6380	−	14.6380i	−0.609388	−	0.609388i	0.333398	−	0.942786i	$-0.391805\pi$
$577$	−14.6380	−	14.6380i	−0.609388	−	0.609388i	−0.942786	+	0.333398i	$0.891805\pi$
$578$	−24.2239	+	24.2239i	−1.00758	+	1.00758i
$579$		0			0
$580$	−25.0164	+	25.0164i	−1.03875	+	1.03875i
$581$	8.68716	+	5.18197i	0.360404	+	0.214984i
$582$		0			0
$583$	−4.00000	−	4.00000i	−0.165663	−	0.165663i
$584$	−3.50995			−0.145243
$585$		0			0
$586$		−	31.3535i		−	1.29520i
$587$	21.2017	+	21.2017i	0.875088	+	0.875088i	0.993021	−	0.117934i	$-0.0376271\pi$
$587$	21.2017	+	21.2017i	0.875088	+	0.875088i	−0.117934	+	0.993021i	$0.537627\pi$
$588$		0			0
$589$		−	22.4172i		−	0.923686i
$590$	37.9302	−	37.9302i	1.56156	−	1.56156i
$591$		0			0
$592$	−2.48191	−	2.48191i	−0.102006	−	0.102006i
$593$	−13.9952	+	13.9952i	−0.574715	+	0.574715i	−0.933442	−	0.358727i	$-0.883211\pi$
$593$	−13.9952	+	13.9952i	−0.574715	+	0.574715i	0.358727	+	0.933442i	$0.383211\pi$
$594$		0			0
$595$	59.0128	+	35.2017i	2.41929	+	1.44313i
$596$	13.4021	+	13.4021i	0.548971	+	0.548971i
$597$		0			0
$598$	15.7544	−	3.15088i	0.644246	−	0.128849i
$599$	−26.4603			−1.08114			−0.540570	−	0.841299i	$-0.681791\pi$
$599$	−26.4603			−1.08114			−0.540570	+	0.841299i	$0.681791\pi$
$600$		0			0
$601$		−	8.65166i		−	0.352908i	−0.984309	−	0.176454i	$-0.943537\pi$
$601$		−	8.65166i		−	0.352908i	0.984309	−	0.176454i	$-0.0564627\pi$
$602$	19.5919	+	11.6867i	0.798504	+	0.476315i
$603$		0			0
$604$	3.02804	−	3.02804i	0.123209	−	0.123209i
$605$	−14.2781	+	14.2781i	−0.580489	+	0.580489i
$606$		0			0
$607$			2.46556i			0.100074i	0.998747	+	0.0500369i	$0.0159339\pi$
$607$			2.46556i			0.100074i	−0.998747	+	0.0500369i	$0.984066\pi$
$608$	4.04701			0.164128
$609$		0			0
$610$			25.9716i			1.05156i
$611$	−0.703431	−	3.51715i	−0.0284578	−	0.142289i
$612$		0			0
$613$	−6.36488	+	6.36488i	−0.257075	+	0.257075i	−0.823863	−	0.566788i	$-0.808186\pi$
$613$	−6.36488	+	6.36488i	−0.257075	+	0.257075i	0.566788	+	0.823863i	$0.308186\pi$
$614$		−	7.84341i		−	0.316534i
$615$		0			0
$616$	1.51117	+	5.97931i	0.0608867	+	0.240913i
$617$	21.1065	−	21.1065i	0.849714	−	0.849714i	−0.140383	−	0.990097i	$-0.544833\pi$
$617$	21.1065	−	21.1065i	0.849714	−	0.849714i	0.990097	+	0.140383i	$0.0448334\pi$
$618$		0			0
$619$	−20.3108	+	20.3108i	−0.816359	+	0.816359i	−0.985578	−	0.169220i	$-0.945875\pi$
$619$	−20.3108	+	20.3108i	−0.816359	+	0.816359i	0.169220	+	0.985578i	$0.445875\pi$
$620$	20.0940			0.806995
$621$		0			0
$622$	11.0767	−	11.0767i	0.444135	−	0.444135i
$623$	9.10570	−	15.2650i	0.364812	−	0.611578i
$624$		0			0
$625$	−0.779417			−0.0311767
$626$	−1.82886	−	1.82886i	−0.0730959	−	0.0730959i
$627$		0			0
$628$	−11.4198			−0.455701
$629$	−17.7691	−	17.7691i	−0.708501	−	0.708501i
$630$		0			0
$631$	−10.3788	−	10.3788i	−0.413174	−	0.413174i	0.469669	−	0.882843i	$-0.344373\pi$
$631$	−10.3788	−	10.3788i	−0.413174	−	0.413174i	−0.882843	+	0.469669i	$0.844373\pi$
$632$	8.51515	+	8.51515i	0.338715	+	0.338715i
$633$		0			0
$634$		−	7.53860i		−	0.299396i
$635$	15.2578	−	15.2578i	0.605486	−	0.605486i
$636$		0			0
$637$	−2.34142	+	25.1300i	−0.0927706	+	0.995688i
$638$	−22.7336			−0.900030
$639$		0			0
$640$			3.62760i			0.143393i
$641$			0.168808i			0.00666750i	0.999994	+	0.00333375i	$0.00106117\pi$
$641$			0.168808i			0.00666750i	−0.999994	+	0.00333375i	$0.998939\pi$
$642$		0			0
$643$	23.4995	+	23.4995i	0.926729	+	0.926729i	0.997493	−	0.0707640i	$-0.0225437\pi$
$643$	23.4995	+	23.4995i	0.926729	+	0.926729i	−0.0707640	+	0.997493i	$0.522544\pi$
$644$	11.4301	−	2.88877i	0.450410	−	0.113834i
$645$		0			0
$646$	28.9744			1.13998
$647$	−7.68783			−0.302240			−0.151120	−	0.988515i	$-0.548288\pi$
$647$	−7.68783			−0.302240			−0.151120	+	0.988515i	$0.548288\pi$
$648$		0			0
$649$	34.4690			1.35303
$650$	28.8480	−	5.76961i	1.13151	−	0.226303i
$651$		0			0
$652$	−9.07627	+	9.07627i	−0.355454	+	0.355454i
$653$	−15.9545			−0.624347			−0.312173	−	0.950025i	$-0.601057\pi$
$653$	−15.9545			−0.624347			−0.312173	+	0.950025i	$0.601057\pi$
$654$		0			0
$655$	−0.0750499	+	0.0750499i	−0.00293244	+	0.00293244i
$656$	−7.53921	−	7.53921i	−0.294357	−	0.294357i
$657$		0			0
$658$	−0.644914	−	2.55176i	−0.0251414	−	0.0994780i
$659$	24.5438			0.956091			0.478045	−	0.878335i	$-0.341345\pi$
$659$	24.5438			0.956091			0.478045	+	0.878335i	$0.341345\pi$
$660$		0			0
$661$	3.34817	−	3.34817i	0.130229	−	0.130229i	−0.638988	−	0.769217i	$-0.720647\pi$
$661$	3.34817	−	3.34817i	0.130229	−	0.130229i	0.769217	+	0.638988i	$0.220647\pi$
$662$			24.5970i			0.955991i
$663$		0			0
$664$			3.82323i			0.148370i
$665$	−9.51741	−	37.6580i	−0.369069	−	1.46031i
$666$		0			0
$667$			43.4578i			1.68269i
$668$	−3.31554	−	3.31554i	−0.128282	−	0.128282i
$669$		0			0
$670$	−16.4664	+	16.4664i	−0.636153	+	0.636153i
$671$	−11.8008	+	11.8008i	−0.455566	+	0.455566i
$672$		0			0
$673$			11.5369i			0.444714i	0.974965	+	0.222357i	$0.0713750\pi$
$673$			11.5369i			0.444714i	−0.974965	+	0.222357i	$0.928625\pi$
$674$	6.89612	+	6.89612i	0.265629	+	0.265629i
$675$		0			0
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$			12.8958i			0.495625i	0.968808	+	0.247812i	$0.0797117\pi$
$677$			12.8958i			0.495625i	−0.968808	+	0.247812i	$0.920288\pi$
$678$		0			0
$679$	14.4352	+	8.61071i	0.553971	+	0.330449i
$680$			25.9716i			0.995966i
$681$		0			0
$682$	9.13020	+	9.13020i	0.349613	+	0.349613i
$683$	−14.7785	−	14.7785i	−0.565483	−	0.565483i	0.365377	−	0.930860i	$-0.380940\pi$
$683$	−14.7785	−	14.7785i	−0.565483	−	0.565483i	−0.930860	+	0.365377i	$0.880940\pi$
$684$		0			0
$685$			23.4198i			0.894826i
$686$	−0.791511	+	18.5033i	−0.0302200	+	0.706461i
$687$		0			0
$688$			8.62240i			0.328726i
$689$	4.85353	−	7.28030i	0.184905	−	0.277357i
$690$		0			0
$691$	−13.4220	−	13.4220i	−0.510597	−	0.510597i	0.404112	−	0.914709i	$-0.367580\pi$
$691$	−13.4220	−	13.4220i	−0.510597	−	0.510597i	−0.914709	+	0.404112i	$0.867580\pi$
$692$			6.05852i			0.230310i
$693$		0			0
$694$	1.68783	−	1.68783i	0.0640693	−	0.0640693i
$695$	32.5438	−	32.5438i	1.23446	−	1.23446i
$696$		0			0
$697$	−53.9766	−	53.9766i	−2.04451	−	2.04451i
$698$		−	1.80548i		−	0.0683383i
$699$		0			0
$700$	20.9298	−	5.28965i	0.791072	−	0.199930i
$701$		−	19.5009i		−	0.736538i	−0.929719	−	0.368269i	$-0.879951\pi$
$701$		−	19.5009i		−	0.736538i	0.929719	−	0.368269i	$-0.120049\pi$
$702$		0			0
$703$			14.2048i			0.535744i
$704$	−1.64828	+	1.64828i	−0.0621221	+	0.0621221i
$705$		0			0
$706$	23.0621			0.867955
$707$	9.12395	−	2.30592i	0.343142	−	0.0867232i
$708$		0			0
$709$	36.2084	+	36.2084i	1.35984	+	1.35984i	0.874112	+	0.485724i	$0.161444\pi$
$709$	36.2084	+	36.2084i	1.35984	+	1.35984i	0.485724	+	0.874112i	$0.338556\pi$
$710$	1.65427	−	1.65427i	0.0620836	−	0.0620836i
$711$		0			0
$712$	6.71814			0.251773
$713$	17.4534	−	17.4534i	0.653635	−	0.653635i
$714$		0			0
$715$	25.3681	+	16.9120i	0.948712	+	0.632475i
$716$	13.5570			0.506647
$717$		0			0
$718$	22.6458			0.845133
$719$	31.8404			1.18745			0.593723	−	0.804670i	$-0.297658\pi$
$719$	31.8404			1.18745			0.593723	+	0.804670i	$0.297658\pi$
$720$		0			0
$721$	25.1492	−	6.35602i	0.936604	−	0.236711i
$722$	1.85384	+	1.85384i	0.0689926	+	0.0689926i
$723$		0			0
$724$		−	14.5793i		−	0.541835i
$725$			79.5758i			2.95537i
$726$		0			0
$727$	−0.263681			−0.00977940			−0.00488970	−	0.999988i	$-0.501556\pi$
$727$	−0.263681			−0.00977940			−0.00488970	+	0.999988i	$0.501556\pi$
$728$	−8.61058	+	4.10583i	−0.319129	+	0.152172i
$729$		0			0
$730$	−9.00337	+	9.00337i	−0.333230	+	0.333230i
$731$			61.7317i			2.28323i
$732$		0			0
$733$	−14.4266	−	14.4266i	−0.532858	−	0.532858i	0.388564	−	0.921422i	$-0.372971\pi$
$733$	−14.4266	−	14.4266i	−0.532858	−	0.532858i	−0.921422	+	0.388564i	$0.872971\pi$
$734$	−1.71598	−	1.71598i	−0.0633381	−	0.0633381i
$735$		0			0
$736$	3.15088	+	3.15088i	0.116143	+	0.116143i
$737$	−14.9638			−0.551199
$738$		0			0
$739$	6.59099	+	6.59099i	0.242453	+	0.242453i	0.817864	−	0.575411i	$-0.195158\pi$
$739$	6.59099	+	6.59099i	0.242453	+	0.242453i	−0.575411	+	0.817864i	$0.695158\pi$
$740$	−12.7327			−0.468063
$741$		0			0
$742$	3.28922	−	5.51411i	0.120751	−	0.202429i
$743$	−18.2311	+	18.2311i	−0.668835	+	0.668835i	−0.957446	−	0.288611i	$-0.906807\pi$
$743$	−18.2311	+	18.2311i	−0.668835	+	0.668835i	0.288611	+	0.957446i	$0.406807\pi$
$744$		0			0
$745$	68.7554			2.51900
$746$	8.39751	−	8.39751i	0.307455	−	0.307455i
$747$		0			0
$748$	−11.8008	+	11.8008i	−0.431481	+	0.431481i
$749$	0.853530	−	0.215715i	0.0311873	−	0.00788206i
$750$		0			0
$751$		−	17.5282i		−	0.639613i	−0.947483	−	0.319807i	$-0.896382\pi$
$751$		−	17.5282i		−	0.639613i	0.947483	−	0.319807i	$-0.103618\pi$
$752$	0.703431	−	0.703431i	0.0256515	−	0.0256515i
$753$		0			0
$754$	−6.89612	−	34.4806i	−0.251142	−	1.25571i
$755$		−	15.5344i		−	0.565356i
$756$		0			0
$757$	31.7843			1.15522			0.577610	−	0.816313i	$-0.303986\pi$
$757$	31.7843			1.15522			0.577610	+	0.816313i	$0.303986\pi$
$758$			20.3676i			0.739786i
$759$		0			0
$760$	10.3810	−	10.3810i	0.376557	−	0.376557i
$761$	−1.82886	+	1.82886i	−0.0662961	+	0.0662961i	−0.739477	−	0.673181i	$-0.764927\pi$
$761$	−1.82886	+	1.82886i	−0.0662961	+	0.0662961i	0.673181	+	0.739477i	$0.264927\pi$
$762$		0			0
$763$	−24.8557	+	41.6685i	−0.899836	+	1.50850i
$764$		−	26.3837i		−	0.954528i
$765$		0			0
$766$	−26.3215			−0.951034
$767$	10.4560	+	52.2801i	0.377545	+	1.88773i
$768$		0			0
$769$	−1.20162	−	1.20162i	−0.0433314	−	0.0433314i	0.685109	−	0.728440i	$-0.259755\pi$
$769$	−1.20162	−	1.20162i	−0.0433314	−	0.0433314i	−0.728440	+	0.685109i	$0.759755\pi$
$770$	19.2138	+	11.4612i	0.692418	+	0.413034i
$771$		0			0
$772$	2.86288	−	2.86288i	0.103037	−	0.103037i
$773$	2.61687	+	2.61687i	0.0941224	+	0.0941224i	0.752600	−	0.658478i	$-0.228799\pi$
$773$	2.61687	+	2.61687i	0.0941224	+	0.0941224i	−0.658478	+	0.752600i	$0.728799\pi$
$774$		0			0
$775$	31.9591	−	31.9591i	1.14800	−	1.14800i
$776$			6.35293i			0.228057i
$777$		0			0
$778$	0.0762669	+	0.0762669i	0.00273430	+	0.00273430i
$779$			43.1494i			1.54599i
$780$		0			0
$781$	1.50331			0.0537927
$782$	22.5586	+	22.5586i	0.806694	+	0.806694i
$783$		0			0
$784$	−6.15945	+	3.32583i	−0.219980	+	0.118780i
$785$	−29.2930	+	29.2930i	−1.04551	+	1.04551i
$786$		0			0
$787$	−23.2324	+	23.2324i	−0.828144	+	0.828144i	−0.987260	−	0.159116i	$-0.949136\pi$
$787$	−23.2324	+	23.2324i	−0.828144	+	0.828144i	0.159116	+	0.987260i	$0.449136\pi$
$788$	−6.21338	−	6.21338i	−0.221343	−	0.221343i
$789$		0			0
$790$	43.6844			1.55422
$791$	32.5438	−	8.22489i	1.15712	−	0.292443i
$792$		0			0
$793$	−21.4784	−	14.3189i	−0.762719	−	0.508479i
$794$		−	26.7738i		−	0.950167i
$795$		0			0
$796$		−	1.63799i		−	0.0580572i
$797$	−33.6371			−1.19149			−0.595744	−	0.803174i	$-0.703143\pi$
$797$	−33.6371			−1.19149			−0.595744	+	0.803174i	$0.703143\pi$
$798$		0			0
$799$	5.03618	−	5.03618i	0.178167	−	0.178167i
$800$	5.76961	+	5.76961i	0.203986	+	0.203986i
$801$		0			0
$802$	1.88174			0.0664467
$803$	−8.18179			−0.288729
$804$		0			0
$805$	21.9094	−	36.7294i	0.772206	−	1.29454i
$806$	−11.0784	+	16.6176i	−0.390221	+	0.585331i
$807$		0			0
$808$	2.51515	+	2.51515i	0.0884827	+	0.0884827i
$809$	20.3165			0.714289			0.357145	−	0.934049i	$-0.383750\pi$
$809$	20.3165			0.714289			0.357145	+	0.934049i	$0.383750\pi$
$810$		0			0
$811$	−11.7152	−	11.7152i	−0.411376	−	0.411376i	0.470842	−	0.882218i	$-0.343950\pi$
$811$	−11.7152	−	11.7152i	−0.411376	−	0.411376i	−0.882218	+	0.470842i	$0.843950\pi$
$812$	−6.32246	−	25.0164i	−0.221875	−	0.877902i
$813$		0			0
$814$	−5.78540	−	5.78540i	−0.202778	−	0.202778i
$815$			46.5630i			1.63103i
$816$		0			0
$817$	24.6744	−	24.6744i	0.863249	−	0.863249i
$818$	−30.6239			−1.07074
$819$		0			0
$820$	−38.6776			−1.35068
$821$	−3.79529	+	3.79529i	−0.132457	+	0.132457i	−0.770227	−	0.637770i	$-0.779857\pi$
$821$	−3.79529	+	3.79529i	−0.132457	+	0.132457i	0.637770	+	0.770227i	$0.279857\pi$
$822$		0			0
$823$			42.2235i			1.47182i	0.677079	+	0.735910i	$0.263245\pi$
$823$			42.2235i			1.47182i	−0.677079	+	0.735910i	$0.736755\pi$
$824$	6.93274	+	6.93274i	0.241513	+	0.241513i
$825$		0			0
$826$	9.58622	+	37.9302i	0.333547	+	1.31976i
$827$	−8.55602	−	8.55602i	−0.297522	−	0.297522i	0.542520	−	0.840043i	$-0.317470\pi$
$827$	−8.55602	−	8.55602i	−0.297522	−	0.297522i	−0.840043	+	0.542520i	$0.817470\pi$
$828$		0			0
$829$	40.5026			1.40671			0.703356	−	0.710838i	$-0.251684\pi$
$829$	40.5026			1.40671			0.703356	+	0.710838i	$0.251684\pi$
$830$	9.80695	+	9.80695i	0.340404	+	0.340404i
$831$		0			0
$832$	−3.00000	−	2.00000i	−0.104006	−	0.0693375i
$833$	−44.0983	+	23.8111i	−1.52792	+	0.825006i
$834$		0			0
$835$	−17.0094			−0.588633
$836$	9.43369			0.326271
$837$		0			0
$838$	2.41647	+	2.41647i	0.0834757	+	0.0834757i
$839$	−13.3882	+	13.3882i	−0.462210	+	0.462210i	−0.899379	−	0.437169i	$-0.855981\pi$
$839$	−13.3882	+	13.3882i	−0.462210	+	0.462210i	0.437169	+	0.899379i	$0.355981\pi$
$840$		0			0
$841$	66.1131			2.27976
$842$		−	1.92617i		−	0.0663801i
$843$		0			0
$844$		−	0.622397i		−	0.0214238i
$845$	−17.9557	+	43.6067i	−0.617694	+	1.50011i
$846$		0			0
$847$	−3.60856	−	14.2781i	−0.123991	−	0.490603i
$848$	2.42677			0.0833355
$849$		0			0
$850$	41.3072	+	41.3072i	1.41683	+	1.41683i
$851$	−11.0595	+	11.0595i	−0.379113	+	0.379113i
$852$		0			0
$853$	3.51211	−	3.51211i	0.120252	−	0.120252i	−0.644420	−	0.764672i	$-0.722901\pi$
$853$	3.51211	−	3.51211i	0.120252	−	0.120252i	0.764672	+	0.644420i	$0.222901\pi$
$854$	−16.2677	−	9.70386i	−0.556671	−	0.332059i
$855$		0			0
$856$	0.235288	+	0.235288i	0.00804198	+	0.00804198i
$857$	24.3679			0.832391			0.416196	−	0.909275i	$-0.363363\pi$
$857$	24.3679			0.832391			0.416196	+	0.909275i	$0.363363\pi$
$858$		0			0
$859$			2.26749i			0.0773658i	0.999252	+	0.0386829i	$0.0123162\pi$
$859$			2.26749i			0.0773658i	−0.999252	+	0.0386829i	$0.987684\pi$
$860$	22.1173	+	22.1173i	0.754193	+	0.754193i
$861$		0			0
$862$		−	15.7405i		−	0.536123i
$863$	24.0154	−	24.0154i	0.817494	−	0.817494i	−0.168250	−	0.985744i	$-0.553812\pi$
$863$	24.0154	−	24.0154i	0.817494	−	0.817494i	0.985744	+	0.168250i	$0.0538116\pi$
$864$		0			0
$865$	15.5407	+	15.5407i	0.528399	+	0.528399i
$866$	−13.9896	+	13.9896i	−0.475386	+	0.475386i
$867$		0			0
$868$	−7.50780	+	12.5862i	−0.254831	+	0.427204i
$869$	19.8490	+	19.8490i	0.673333	+	0.673333i
$870$		0			0
$871$	−4.53921	−	22.6961i	−0.153805	−	0.769026i
$872$	−18.3384			−0.621016
$873$		0			0
$874$		−	18.0336i		−	0.609994i
$875$	15.5344	−	26.0422i	0.525160	−	0.880388i
$876$		0			0
$877$	−38.9474	+	38.9474i	−1.31516	+	1.31516i	−0.397601	+	0.917559i	$0.630157\pi$
$877$	−38.9474	+	38.9474i	−1.31516	+	1.31516i	−0.917559	+	0.397601i	$0.869843\pi$
$878$	18.9327	−	18.9327i	0.638949	−	0.638949i
$879$		0			0
$880$			8.45602i			0.285052i
$881$	−19.7569			−0.665627			−0.332813	−	0.942993i	$-0.607998\pi$
$881$	−19.7569			−0.665627			−0.332813	+	0.942993i	$0.607998\pi$
$882$		0			0
$883$		−	19.9027i		−	0.669779i	−0.942257	−	0.334889i	$-0.891301\pi$
$883$		−	19.9027i		−	0.669779i	0.942257	−	0.334889i	$-0.108699\pi$
$884$	−21.4784	−	14.3189i	−0.722395	−	0.481597i
$885$		0			0
$886$	20.0526	−	20.0526i	0.673682	−	0.673682i
$887$			1.87156i			0.0628409i	0.999506	+	0.0314204i	$0.0100031\pi$
$887$			1.87156i			0.0628409i	−0.999506	+	0.0314204i	$0.989997\pi$
$888$		0			0
$889$	3.85614	+	15.2578i	0.129331	+	0.511729i
$890$	17.2327	−	17.2327i	0.577641	−	0.577641i
$891$		0			0
$892$	15.5615	−	15.5615i	0.521039	−	0.521039i
$893$	−4.02597			−0.134724
$894$		0			0
$895$	34.7749	−	34.7749i	1.16240	−	1.16240i
$896$	−2.27220	−	1.35539i	−0.0759090	−	0.0452805i
$897$		0			0
$898$	3.23633			0.107998
$899$	−38.1991	−	38.1991i	−1.27401	−	1.27401i
$900$		0			0
$901$	17.3743			0.578822
$902$	−17.5741	−	17.5741i	−0.585154	−	0.585154i
$903$		0			0
$904$	8.97117	+	8.97117i	0.298377	+	0.298377i
$905$	−37.3973	−	37.3973i	−1.24313	−	1.24313i
$906$		0			0
$907$		−	35.5637i		−	1.18087i	−0.807084	−	0.590437i	$-0.798956\pi$
$907$		−	35.5637i		−	1.18087i	0.807084	−	0.590437i	$-0.201044\pi$
$908$	1.15945	−	1.15945i	0.0384778	−	0.0384778i
$909$		0			0
$910$	−11.5551	+	32.6188i	−0.383049	+	1.08130i
$911$	19.6150			0.649873			0.324937	−	0.945736i	$-0.394657\pi$
$911$	19.6150			0.649873			0.324937	+	0.945736i	$0.394657\pi$
$912$		0			0
$913$			8.91205i			0.294946i
$914$		−	8.03402i		−	0.265742i
$915$		0			0
$916$	4.15945	+	4.15945i	0.137432	+	0.137432i
$917$	−0.0189676	−	0.0750499i	−0.000626365	−	0.00247837i
$918$		0			0
$919$	−34.3682			−1.13370			−0.566852	−	0.823820i	$-0.691839\pi$
$919$	−34.3682			−1.13370			−0.566852	+	0.823820i	$0.691839\pi$
$920$	16.1647			0.532933
$921$		0			0
$922$	22.1965			0.731003
$923$	0.456023	+	2.28012i	0.0150102	+	0.0750509i
$924$		0			0
$925$	−20.2510	+	20.2510i	−0.665850	+	0.665850i
$926$	15.8849			0.522012
$927$		0			0
$928$	6.89612	−	6.89612i	0.226376	−	0.226376i
$929$	−21.5546	−	21.5546i	−0.707184	−	0.707184i	0.258758	−	0.965942i	$-0.416687\pi$
$929$	−21.5546	−	21.5546i	−0.707184	−	0.707184i	−0.965942	+	0.258758i	$0.916687\pi$
$930$		0			0
$931$	27.1437	+	8.10890i	0.889599	+	0.265758i
$932$	−10.7974			−0.353682
$933$		0			0
$934$	−1.99402	+	1.99402i	−0.0652462	+	0.0652462i
$935$			60.5405i			1.97989i
$936$		0			0
$937$		−	15.9071i		−	0.519661i	−0.965654	−	0.259831i	$-0.916333\pi$
$937$		−	15.9071i		−	0.519661i	0.965654	−	0.259831i	$-0.0836667\pi$
$938$	−4.16161	−	16.4664i	−0.135881	−	0.537648i
$939$		0			0
$940$		−	3.60874i		−	0.117704i
$941$	−10.1348	−	10.1348i	−0.330384	−	0.330384i	0.522348	−	0.852732i	$-0.325056\pi$
$941$	−10.1348	−	10.1348i	−0.330384	−	0.330384i	−0.852732	+	0.522348i	$0.825056\pi$
$942$		0			0
$943$	−33.5949	+	33.5949i	−1.09400	+	1.09400i
$944$	−10.4560	+	10.4560i	−0.340315	+	0.340315i
$945$		0			0
$946$			20.0990i			0.653476i
$947$	−8.77848	−	8.77848i	−0.285262	−	0.285262i	0.549941	−	0.835203i	$-0.314650\pi$
$947$	−8.77848	−	8.77848i	−0.285262	−	0.285262i	−0.835203	+	0.549941i	$0.814650\pi$
$948$		0			0
$949$	−2.48191	−	12.4096i	−0.0805662	−	0.402831i
$950$		−	33.0214i		−	1.07136i
$951$		0			0
$952$	−16.2677	−	9.70386i	−0.527241	−	0.314504i
$953$			41.5076i			1.34456i	0.740295	+	0.672282i	$0.234686\pi$
$953$			41.5076i			1.34456i	−0.740295	+	0.672282i	$0.765314\pi$
$954$		0			0
$955$	−67.6767	−	67.6767i	−2.18997	−	2.18997i
$956$	16.1501	+	16.1501i	0.522332	+	0.522332i
$957$		0			0
$958$		−	32.5914i		−	1.05298i
$959$	−14.6694	−	8.75044i	−0.473700	−	0.282566i
$960$		0			0
$961$		−	0.317151i		−	0.0102307i
$962$	7.01990	−	10.5299i	0.226331	−	0.339496i
$963$		0			0
$964$	3.45602	+	3.45602i	0.111311	+	0.111311i
$965$		−	14.6872i		−	0.472796i
$966$		0			0
$967$	−14.2124	+	14.2124i	−0.457041	+	0.457041i	−0.897683	−	0.440642i	$-0.854751\pi$
$967$	−14.2124	+	14.2124i	−0.457041	+	0.457041i	0.440642	+	0.897683i	$0.354751\pi$
$968$	3.93598	−	3.93598i	0.126507	−	0.126507i
$969$		0			0
$970$	16.2959	+	16.2959i	0.523230	+	0.523230i
$971$		−	48.8259i		−	1.56690i	−0.621457	−	0.783448i	$-0.713459\pi$
$971$		−	48.8259i		−	1.56690i	0.621457	−	0.783448i	$-0.286541\pi$
$972$		0			0
$973$	8.22489	+	32.5438i	0.263678	+	1.04331i
$974$			37.2650i			1.19405i
$975$		0			0
$976$		−	7.15945i		−	0.229169i
$977$	28.0635	−	28.0635i	0.897832	−	0.897832i	−0.0974119	−	0.995244i	$-0.531056\pi$
$977$	28.0635	−	28.0635i	0.897832	−	0.897832i	0.995244	+	0.0974119i	$0.0310564\pi$
$978$		0			0
$979$	15.6602			0.500501
$980$	−7.26853	+	24.3307i	−0.232185	+	0.777215i
$981$		0			0
$982$	−8.33103	−	8.33103i	−0.265854	−	0.265854i
$983$	24.2698	−	24.2698i	0.774087	−	0.774087i	−0.204731	−	0.978818i	$-0.565632\pi$
$983$	24.2698	−	24.2698i	0.774087	−	0.774087i	0.978818	+	0.204731i	$0.0656320\pi$
$984$		0			0
$985$	−31.8759			−1.01565
$986$	49.3725	−	49.3725i	1.57234	−	1.57234i
$987$		0			0
$988$	2.86167	+	14.3083i	0.0910418	+	0.455209i
$989$	38.4216			1.22174
$990$		0			0
$991$	46.7432			1.48485			0.742424	−	0.669930i	$-0.233676\pi$
$991$	46.7432			1.48485			0.742424	+	0.669930i	$0.233676\pi$
$992$	−5.53921			−0.175870
$993$		0			0
$994$	0.418088	+	1.65427i	0.0132609	+	0.0524702i
$995$	−4.20162	−	4.20162i	−0.133200	−	0.133200i
$996$		0			0
$997$		−	30.1568i		−	0.955077i	−0.878611	−	0.477538i	$-0.841529\pi$
$997$		−	30.1568i		−	0.955077i	0.878611	−	0.477538i	$-0.158471\pi$
$998$		−	36.2058i		−	1.14607i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.56510 - 2.56510i) q^{5} +(2.56510 - 0.648285i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.56510 - 2.56510i) q^{5} +(2.56510 - 0.648285i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.62760 q^{10} +(1.64828 + 1.64828i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(-1.35539 + 2.27220i) q^{14} -1.00000 q^{16} -7.15945 q^{17} +(2.86167 + 2.86167i) q^{19} +(-2.56510 + 2.56510i) q^{20} -2.33103 q^{22} +4.45602i q^{23} +8.15945i q^{25} +(-0.707107 - 3.53553i) q^{26} +(-0.648285 - 2.56510i) q^{28} +9.75259 q^{29} +(-3.91681 - 3.91681i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.06250 - 5.06250i) q^{34} +(-8.24264 - 4.91681i) q^{35} +(2.48191 + 2.48191i) q^{37} -4.04701 q^{38} -3.62760i q^{40} +(7.53921 + 7.53921i) q^{41} -8.62240i q^{43} +(1.64828 - 1.64828i) q^{44} +(-3.15088 - 3.15088i) q^{46} +(-0.703431 + 0.703431i) q^{47} +(6.15945 - 3.32583i) q^{49} +(-5.76961 - 5.76961i) q^{50} +(3.00000 + 2.00000i) q^{52} -2.42677 q^{53} -8.45602i q^{55} +(2.27220 + 1.35539i) q^{56} +(-6.89612 + 6.89612i) q^{58} +(10.4560 - 10.4560i) q^{59} +7.15945i q^{61} +5.53921 q^{62} +1.00000i q^{64} +(12.8255 - 2.56510i) q^{65} +(-4.53921 + 4.53921i) q^{67} +7.15945i q^{68} +(9.30514 - 2.35172i) q^{70} +(0.456023 - 0.456023i) q^{71} +(-2.48191 + 2.48191i) q^{73} -3.50995 q^{74} +(2.86167 - 2.86167i) q^{76} +(5.29657 + 3.15945i) q^{77} +12.0422 q^{79} +(2.56510 + 2.56510i) q^{80} -10.6621 q^{82} +(2.70343 + 2.70343i) q^{83} +(18.3647 + 18.3647i) q^{85} +(6.09696 + 6.09696i) q^{86} +2.33103i q^{88} +(4.75044 - 4.75044i) q^{89} +(-3.18534 + 8.99186i) q^{91} +4.45602 q^{92} -0.994801i q^{94} -14.6809i q^{95} +(4.49220 + 4.49220i) q^{97} +(-2.00368 + 6.70711i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 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

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