LMFDB - Embedded newform 690.2.d.c.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(139,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.5
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	690.139
Dual form			690.2.d.c.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.17009 - 0.539189i) q^{10} -1.07838 q^{11} -1.00000i q^{12} +2.34017i q^{13} -4.34017 q^{14} +(2.17009 - 0.539189i) q^{15} +1.00000 q^{16} +0.921622i q^{17} -1.00000i q^{18} -2.34017 q^{19} +(0.539189 + 2.17009i) q^{20} -4.34017 q^{21} -1.07838i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(-4.41855 + 2.34017i) q^{25} -2.34017 q^{26} -1.00000i q^{27} -4.34017i q^{28} -10.4969 q^{29} +(0.539189 + 2.17009i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -1.07838i q^{33} -0.921622 q^{34} +(9.41855 - 2.34017i) q^{35} +1.00000 q^{36} +2.58145i q^{37} -2.34017i q^{38} -2.34017 q^{39} +(-2.17009 + 0.539189i) q^{40} +0.156755 q^{41} -4.34017i q^{42} -0.738205i q^{43} +1.07838 q^{44} +(0.539189 + 2.17009i) q^{45} +1.00000 q^{46} +6.83710i q^{47} +1.00000i q^{48} -11.8371 q^{49} +(-2.34017 - 4.41855i) q^{50} -0.921622 q^{51} -2.34017i q^{52} +0.340173i q^{53} +1.00000 q^{54} +(0.581449 + 2.34017i) q^{55} +4.34017 q^{56} -2.34017i q^{57} -10.4969i q^{58} +8.83710 q^{59} +(-2.17009 + 0.539189i) q^{60} -11.5753 q^{61} -4.00000i q^{62} -4.34017i q^{63} -1.00000 q^{64} +(5.07838 - 1.26180i) q^{65} +1.07838 q^{66} +2.58145i q^{67} -0.921622i q^{68} +1.00000 q^{69} +(2.34017 + 9.41855i) q^{70} +15.1773 q^{71} +1.00000i q^{72} +4.68035i q^{73} -2.58145 q^{74} +(-2.34017 - 4.41855i) q^{75} +2.34017 q^{76} -4.68035i q^{77} -2.34017i q^{78} +11.9155 q^{79} +(-0.539189 - 2.17009i) q^{80} +1.00000 q^{81} +0.156755i q^{82} -11.4186i q^{83} +4.34017 q^{84} +(2.00000 - 0.496928i) q^{85} +0.738205 q^{86} -10.4969i q^{87} +1.07838i q^{88} +4.68035 q^{89} +(-2.17009 + 0.539189i) q^{90} -10.1568 q^{91} +1.00000i q^{92} -4.00000i q^{93} -6.83710 q^{94} +(1.26180 + 5.07838i) q^{95} -1.00000 q^{96} +9.02052i q^{97} -11.8371i q^{98} +1.07838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 4 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} - 4 q^{21} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 28 q^{29} - 24 q^{31} - 12 q^{34} + 28 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{46} - 14 q^{49} + 8 q^{50} - 12 q^{51} + 6 q^{54} + 32 q^{55} + 4 q^{56} - 4 q^{59} - 2 q^{60} - 28 q^{61} - 6 q^{64} + 24 q^{65} + 6 q^{69} - 8 q^{70} + 12 q^{71} - 44 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{79} + 6 q^{81} + 4 q^{84} + 12 q^{85} + 20 q^{86} - 16 q^{89} - 2 q^{90} - 48 q^{91} + 16 q^{94} - 8 q^{95} - 6 q^{96}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 4 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 - 4 * q^21 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 28 * q^29 - 24 * q^31 - 12 * q^34 + 28 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^46 - 14 * q^49 + 8 * q^50 - 12 * q^51 + 6 * q^54 + 32 * q^55 + 4 * q^56 - 4 * q^59 - 2 * q^60 - 28 * q^61 - 6 * q^64 + 24 * q^65 + 6 * q^69 - 8 * q^70 + 12 * q^71 - 44 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^79 + 6 * q^81 + 4 * q^84 + 12 * q^85 + 20 * q^86 - 16 * q^89 - 2 * q^90 - 48 * q^91 + 16 * q^94 - 8 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	−0.539189	−	2.17009i	−0.241133	−	0.970492i
$5$	−0.539189	−	2.17009i	−0.241133	−	0.970492i
$6$	−1.00000			−0.408248
$7$			4.34017i			1.64043i	0.572055	+	0.820216i	$0.306147\pi$
$7$			4.34017i			1.64043i	−0.572055	+	0.820216i	$0.693853\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	2.17009	−	0.539189i	0.686242	−	0.170506i
$11$	−1.07838			−0.325143			−0.162572	−	0.986697i	$-0.551979\pi$
$11$	−1.07838			−0.325143			−0.162572	+	0.986697i	$0.551979\pi$
$12$		−	1.00000i		−	0.288675i
$13$			2.34017i			0.649047i	0.945878	+	0.324524i	$0.105204\pi$
$13$			2.34017i			0.649047i	−0.945878	+	0.324524i	$0.894796\pi$
$14$	−4.34017			−1.15996
$15$	2.17009	−	0.539189i	0.560314	−	0.139218i
$16$	1.00000			0.250000
$17$			0.921622i			0.223526i	0.993735	+	0.111763i	$0.0356498\pi$
$17$			0.921622i			0.223526i	−0.993735	+	0.111763i	$0.964350\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−2.34017			−0.536873			−0.268436	−	0.963297i	$-0.586507\pi$
$19$	−2.34017			−0.536873			−0.268436	+	0.963297i	$0.586507\pi$
$20$	0.539189	+	2.17009i	0.120566	+	0.485246i
$21$	−4.34017			−0.947103
$22$		−	1.07838i		−	0.229911i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.00000			0.204124
$25$	−4.41855	+	2.34017i	−0.883710	+	0.468035i
$26$	−2.34017			−0.458946
$27$		−	1.00000i		−	0.192450i
$28$		−	4.34017i		−	0.820216i
$29$	−10.4969			−1.94923			−0.974615	−	0.223886i	$-0.928126\pi$
$29$	−10.4969			−1.94923			−0.974615	+	0.223886i	$0.928126\pi$
$30$	0.539189	+	2.17009i	0.0984420	+	0.396202i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			1.00000i			0.176777i
$33$		−	1.07838i		−	0.187721i
$34$	−0.921622			−0.158057
$35$	9.41855	−	2.34017i	1.59203	−	0.395561i
$36$	1.00000			0.166667
$37$			2.58145i			0.424388i	0.977228	+	0.212194i	$0.0680608\pi$
$37$			2.58145i			0.424388i	−0.977228	+	0.212194i	$0.931939\pi$
$38$		−	2.34017i		−	0.379626i
$39$	−2.34017			−0.374728
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$	0.156755			0.0244811			0.0122405	−	0.999925i	$-0.496104\pi$
$41$	0.156755			0.0244811			0.0122405	+	0.999925i	$0.496104\pi$
$42$		−	4.34017i		−	0.669703i
$43$		−	0.738205i		−	0.112575i	−0.998415	−	0.0562876i	$-0.982074\pi$
$43$		−	0.738205i		−	0.112575i	0.998415	−	0.0562876i	$-0.0179264\pi$
$44$	1.07838			0.162572
$45$	0.539189	+	2.17009i	0.0803775	+	0.323497i
$46$	1.00000			0.147442
$47$			6.83710i			0.997294i	0.866805	+	0.498647i	$0.166170\pi$
$47$			6.83710i			0.997294i	−0.866805	+	0.498647i	$0.833830\pi$
$48$			1.00000i			0.144338i
$49$	−11.8371			−1.69101
$50$	−2.34017	−	4.41855i	−0.330950	−	0.624877i
$51$	−0.921622			−0.129053
$52$		−	2.34017i		−	0.324524i
$53$			0.340173i			0.0467264i	0.999727	+	0.0233632i	$0.00743741\pi$
$53$			0.340173i			0.0467264i	−0.999727	+	0.0233632i	$0.992563\pi$
$54$	1.00000			0.136083
$55$	0.581449	+	2.34017i	0.0784026	+	0.315549i
$56$	4.34017			0.579980
$57$		−	2.34017i		−	0.309963i
$58$		−	10.4969i		−	1.37831i
$59$	8.83710			1.15049			0.575246	−	0.817980i	$-0.304906\pi$
$59$	8.83710			1.15049			0.575246	+	0.817980i	$0.304906\pi$
$60$	−2.17009	+	0.539189i	−0.280157	+	0.0696090i
$61$	−11.5753			−1.48207			−0.741033	−	0.671469i	$-0.765664\pi$
$61$	−11.5753			−1.48207			−0.741033	+	0.671469i	$0.765664\pi$
$62$		−	4.00000i		−	0.508001i
$63$		−	4.34017i		−	0.546810i
$64$	−1.00000			−0.125000
$65$	5.07838	−	1.26180i	0.629895	−	0.156506i
$66$	1.07838			0.132739
$67$			2.58145i			0.315374i	0.987489	+	0.157687i	$0.0504037\pi$
$67$			2.58145i			0.315374i	−0.987489	+	0.157687i	$0.949596\pi$
$68$		−	0.921622i		−	0.111763i
$69$	1.00000			0.120386
$70$	2.34017	+	9.41855i	0.279704	+	1.12573i
$71$	15.1773			1.80121			0.900606	−	0.434637i	$-0.143123\pi$
$71$	15.1773			1.80121			0.900606	+	0.434637i	$0.143123\pi$
$72$			1.00000i			0.117851i
$73$			4.68035i			0.547793i	0.961759	+	0.273897i	$0.0883126\pi$
$73$			4.68035i			0.547793i	−0.961759	+	0.273897i	$0.911687\pi$
$74$	−2.58145			−0.300087
$75$	−2.34017	−	4.41855i	−0.270220	−	0.510210i
$76$	2.34017			0.268436
$77$		−	4.68035i		−	0.533375i
$78$		−	2.34017i		−	0.264972i
$79$	11.9155			1.34060			0.670298	−	0.742092i	$-0.266166\pi$
$79$	11.9155			1.34060			0.670298	+	0.742092i	$0.266166\pi$
$80$	−0.539189	−	2.17009i	−0.0602831	−	0.242623i
$81$	1.00000			0.111111
$82$			0.156755i			0.0173107i
$83$		−	11.4186i		−	1.25335i	−0.779281	−	0.626674i	$-0.784416\pi$
$83$		−	11.4186i		−	1.25335i	0.779281	−	0.626674i	$-0.215584\pi$
$84$	4.34017			0.473552
$85$	2.00000	−	0.496928i	0.216930	−	0.0538995i
$86$	0.738205			0.0796027
$87$		−	10.4969i		−	1.12539i
$88$			1.07838i			0.114955i
$89$	4.68035			0.496116			0.248058	−	0.968745i	$-0.420208\pi$
$89$	4.68035			0.496116			0.248058	+	0.968745i	$0.420208\pi$
$90$	−2.17009	+	0.539189i	−0.228747	+	0.0568355i
$91$	−10.1568			−1.06472
$92$			1.00000i			0.104257i
$93$		−	4.00000i		−	0.414781i
$94$	−6.83710			−0.705193
$95$	1.26180	+	5.07838i	0.129457	+	0.521031i
$96$	−1.00000			−0.102062
$97$			9.02052i			0.915895i	0.888979	+	0.457947i	$0.151415\pi$
$97$			9.02052i			0.915895i	−0.888979	+	0.457947i	$0.848585\pi$
$98$		−	11.8371i		−	1.19573i
$99$	1.07838			0.108381
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	1.50307			0.149561			0.0747806	−	0.997200i	$-0.476174\pi$
$101$	1.50307			0.149561			0.0747806	+	0.997200i	$0.476174\pi$
$102$		−	0.921622i		−	0.0912542i
$103$			2.49693i			0.246030i	0.992405	+	0.123015i	$0.0392563\pi$
$103$			2.49693i			0.246030i	−0.992405	+	0.123015i	$0.960744\pi$
$104$	2.34017			0.229473
$105$	2.34017	+	9.41855i	0.228377	+	0.919156i
$106$	−0.340173			−0.0330405
$107$			9.57531i			0.925680i	0.886442	+	0.462840i	$0.153170\pi$
$107$			9.57531i			0.925680i	−0.886442	+	0.462840i	$0.846830\pi$
$108$			1.00000i			0.0962250i
$109$	9.78539			0.937270			0.468635	−	0.883392i	$-0.344746\pi$
$109$	9.78539			0.937270			0.468635	+	0.883392i	$0.344746\pi$
$110$	−2.34017	+	0.581449i	−0.223127	+	0.0554390i
$111$	−2.58145			−0.245020
$112$			4.34017i			0.410108i
$113$		−	8.92162i		−	0.839276i	−0.907692	−	0.419638i	$-0.862157\pi$
$113$		−	8.92162i		−	0.839276i	0.907692	−	0.419638i	$-0.137843\pi$
$114$	2.34017			0.219177
$115$	−2.17009	+	0.539189i	−0.202362	+	0.0502796i
$116$	10.4969			0.974615
$117$		−	2.34017i		−	0.216349i
$118$			8.83710i			0.813521i
$119$	−4.00000			−0.366679
$120$	−0.539189	−	2.17009i	−0.0492210	−	0.198101i
$121$	−9.83710			−0.894282
$122$		−	11.5753i		−	1.04798i
$123$			0.156755i			0.0141342i
$124$	4.00000			0.359211
$125$	7.46081	+	8.32684i	0.667315	+	0.744775i
$126$	4.34017			0.386653
$127$			17.1773i			1.52424i	0.647438	+	0.762118i	$0.275841\pi$
$127$			17.1773i			1.52424i	−0.647438	+	0.762118i	$0.724159\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.738205			0.0649953
$130$	1.26180	+	5.07838i	0.110667	+	0.445403i
$131$	−6.68035			−0.583665			−0.291832	−	0.956470i	$-0.594265\pi$
$131$	−6.68035			−0.583665			−0.291832	+	0.956470i	$0.594265\pi$
$132$			1.07838i			0.0938607i
$133$		−	10.1568i		−	0.880702i
$134$	−2.58145			−0.223003
$135$	−2.17009	+	0.539189i	−0.186771	+	0.0464060i
$136$	0.921622			0.0790285
$137$			22.2823i			1.90371i	0.306554	+	0.951853i	$0.400824\pi$
$137$			22.2823i			1.90371i	−0.306554	+	0.951853i	$0.599176\pi$
$138$			1.00000i			0.0851257i
$139$	10.5236			0.892599			0.446300	−	0.894884i	$-0.352742\pi$
$139$	10.5236			0.892599			0.446300	+	0.894884i	$0.352742\pi$
$140$	−9.41855	+	2.34017i	−0.796013	+	0.197781i
$141$	−6.83710			−0.575788
$142$			15.1773i			1.27365i
$143$		−	2.52359i		−	0.211033i
$144$	−1.00000			−0.0833333
$145$	5.65983	+	22.7792i	0.470023	+	1.89171i
$146$	−4.68035			−0.387348
$147$		−	11.8371i		−	0.976308i
$148$		−	2.58145i		−	0.212194i
$149$	−6.92162			−0.567041			−0.283521	−	0.958966i	$-0.591502\pi$
$149$	−6.92162			−0.567041			−0.283521	+	0.958966i	$0.591502\pi$
$150$	4.41855	−	2.34017i	0.360773	−	0.191074i
$151$	6.15676			0.501030			0.250515	−	0.968113i	$-0.419400\pi$
$151$	6.15676			0.501030			0.250515	+	0.968113i	$0.419400\pi$
$152$			2.34017i			0.189813i
$153$		−	0.921622i		−	0.0745087i
$154$	4.68035			0.377153
$155$	2.15676	+	8.68035i	0.173235	+	0.697222i
$156$	2.34017			0.187364
$157$			2.89496i			0.231043i	0.993305	+	0.115521i	$0.0368539\pi$
$157$			2.89496i			0.231043i	−0.993305	+	0.115521i	$0.963146\pi$
$158$			11.9155i			0.947945i
$159$	−0.340173			−0.0269775
$160$	2.17009	−	0.539189i	0.171560	−	0.0426266i
$161$	4.34017			0.342054
$162$			1.00000i			0.0785674i
$163$		−	6.52359i		−	0.510967i	−0.966813	−	0.255484i	$-0.917765\pi$
$163$		−	6.52359i		−	0.510967i	0.966813	−	0.255484i	$-0.0822347\pi$
$164$	−0.156755			−0.0122405
$165$	−2.34017	+	0.581449i	−0.182182	+	0.0452658i
$166$	11.4186			0.886251
$167$			5.47641i			0.423777i	0.977294	+	0.211889i	$0.0679614\pi$
$167$			5.47641i			0.423777i	−0.977294	+	0.211889i	$0.932039\pi$
$168$			4.34017i			0.334852i
$169$	7.52359			0.578738
$170$	0.496928	+	2.00000i	0.0381127	+	0.153393i
$171$	2.34017			0.178958
$172$			0.738205i			0.0562876i
$173$			15.6742i			1.19169i	0.803100	+	0.595844i	$0.203182\pi$
$173$			15.6742i			1.19169i	−0.803100	+	0.595844i	$0.796818\pi$
$174$	10.4969			0.795770
$175$	−10.1568	−	19.1773i	−0.767779	−	1.44967i
$176$	−1.07838			−0.0812858
$177$			8.83710i			0.664237i
$178$			4.68035i			0.350807i
$179$	−15.3607			−1.14811			−0.574056	−	0.818816i	$-0.694631\pi$
$179$	−15.3607			−1.14811			−0.574056	+	0.818816i	$0.694631\pi$
$180$	−0.539189	−	2.17009i	−0.0401888	−	0.161749i
$181$	21.6163			1.60673			0.803365	−	0.595487i	$-0.203041\pi$
$181$	21.6163			1.60673			0.803365	+	0.595487i	$0.203041\pi$
$182$		−	10.1568i		−	0.752869i
$183$		−	11.5753i		−	0.855671i
$184$	−1.00000			−0.0737210
$185$	5.60197	−	1.39189i	0.411865	−	0.102334i
$186$	4.00000			0.293294
$187$		−	0.993857i		−	0.0726780i
$188$		−	6.83710i		−	0.498647i
$189$	4.34017			0.315701
$190$	−5.07838	+	1.26180i	−0.368424	+	0.0915402i
$191$	4.36683			0.315973			0.157987	−	0.987441i	$-0.449500\pi$
$191$	4.36683			0.315973			0.157987	+	0.987441i	$0.449500\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			8.68035i			0.624825i	0.949947	+	0.312412i	$0.101137\pi$
$193$			8.68035i			0.624825i	−0.949947	+	0.312412i	$0.898863\pi$
$194$	−9.02052			−0.647636
$195$	1.26180	+	5.07838i	0.0903590	+	0.363670i
$196$	11.8371			0.845507
$197$		−	22.6803i		−	1.61591i	−0.589246	−	0.807954i	$-0.700575\pi$
$197$		−	22.6803i		−	1.61591i	0.589246	−	0.807954i	$-0.299425\pi$
$198$			1.07838i			0.0766370i
$199$	5.44521			0.386001			0.193000	−	0.981199i	$-0.438178\pi$
$199$	5.44521			0.386001			0.193000	+	0.981199i	$0.438178\pi$
$200$	2.34017	+	4.41855i	0.165475	+	0.312439i
$201$	−2.58145			−0.182081
$202$			1.50307i			0.105756i
$203$		−	45.5585i		−	3.19758i
$204$	0.921622			0.0645265
$205$	−0.0845208	−	0.340173i	−0.00590319	−	0.0237587i
$206$	−2.49693			−0.173969
$207$			1.00000i			0.0695048i
$208$			2.34017i			0.162262i
$209$	2.52359			0.174560
$210$	−9.41855	+	2.34017i	−0.649942	+	0.161487i
$211$	−22.0410			−1.51737			−0.758684	−	0.651459i	$-0.774157\pi$
$211$	−22.0410			−1.51737			−0.758684	+	0.651459i	$0.774157\pi$
$212$		−	0.340173i		−	0.0233632i
$213$			15.1773i			1.03993i
$214$	−9.57531			−0.654554
$215$	−1.60197	+	0.398032i	−0.109253	+	0.0271455i
$216$	−1.00000			−0.0680414
$217$		−	17.3607i		−	1.17852i
$218$			9.78539i			0.662750i
$219$	−4.68035			−0.316268
$220$	−0.581449	−	2.34017i	−0.0392013	−	0.157774i
$221$	−2.15676			−0.145079
$222$		−	2.58145i		−	0.173256i
$223$		−	21.1773i		−	1.41814i	−0.705141	−	0.709068i	$-0.749116\pi$
$223$		−	21.1773i		−	1.41814i	0.705141	−	0.709068i	$-0.250884\pi$
$224$	−4.34017			−0.289990
$225$	4.41855	−	2.34017i	0.294570	−	0.156012i
$226$	8.92162			0.593457
$227$		−	11.7854i		−	0.782224i	−0.920343	−	0.391112i	$-0.872091\pi$
$227$		−	11.7854i		−	0.782224i	0.920343	−	0.391112i	$-0.127909\pi$
$228$			2.34017i			0.154982i
$229$	−1.78539			−0.117982			−0.0589908	−	0.998259i	$-0.518788\pi$
$229$	−1.78539			−0.117982			−0.0589908	+	0.998259i	$0.518788\pi$
$230$	−0.539189	−	2.17009i	−0.0355531	−	0.143091i
$231$	4.68035			0.307944
$232$			10.4969i			0.689157i
$233$		−	18.3135i		−	1.19976i	−0.800091	−	0.599879i	$-0.795215\pi$
$233$		−	18.3135i		−	1.19976i	0.800091	−	0.599879i	$-0.204785\pi$
$234$	2.34017			0.152982
$235$	14.8371	−	3.68649i	0.967866	−	0.240480i
$236$	−8.83710			−0.575246
$237$			11.9155i			0.773994i
$238$		−	4.00000i		−	0.259281i
$239$	5.33403			0.345030			0.172515	−	0.985007i	$-0.444811\pi$
$239$	5.33403			0.345030			0.172515	+	0.985007i	$0.444811\pi$
$240$	2.17009	−	0.539189i	0.140078	−	0.0348045i
$241$	26.1978			1.68755			0.843774	−	0.536698i	$-0.180329\pi$
$241$	26.1978			1.68755			0.843774	+	0.536698i	$0.180329\pi$
$242$		−	9.83710i		−	0.632353i
$243$			1.00000i			0.0641500i
$244$	11.5753			0.741033
$245$	6.38243	+	25.6875i	0.407759	+	1.64112i
$246$	−0.156755			−0.00999437
$247$		−	5.47641i		−	0.348456i
$248$			4.00000i			0.254000i
$249$	11.4186			0.723621
$250$	−8.32684	+	7.46081i	−0.526636	+	0.471863i
$251$	27.4329			1.73155			0.865775	−	0.500433i	$-0.166826\pi$
$251$	27.4329			1.73155			0.865775	+	0.500433i	$0.166826\pi$
$252$			4.34017i			0.273405i
$253$			1.07838i			0.0677970i
$254$	−17.1773			−1.07780
$255$	0.496928	+	2.00000i	0.0311189	+	0.125245i
$256$	1.00000			0.0625000
$257$		−	10.3135i		−	0.643339i	−0.946852	−	0.321670i	$-0.895756\pi$
$257$		−	10.3135i		−	0.643339i	0.946852	−	0.321670i	$-0.104244\pi$
$258$			0.738205i			0.0459586i
$259$	−11.2039			−0.696179
$260$	−5.07838	+	1.26180i	−0.314948	+	0.0782532i
$261$	10.4969			0.649744
$262$		−	6.68035i		−	0.412713i
$263$			20.9939i			1.29454i	0.762262	+	0.647268i	$0.224089\pi$
$263$			20.9939i			1.29454i	−0.762262	+	0.647268i	$0.775911\pi$
$264$	−1.07838			−0.0663696
$265$	0.738205	−	0.183417i	0.0453476	−	0.0112672i
$266$	10.1568			0.622751
$267$			4.68035i			0.286433i
$268$		−	2.58145i		−	0.157687i
$269$	−25.3874			−1.54789			−0.773947	−	0.633250i	$-0.781720\pi$
$269$	−25.3874			−1.54789			−0.773947	+	0.633250i	$0.781720\pi$
$270$	−0.539189	−	2.17009i	−0.0328140	−	0.132067i
$271$	−32.5646			−1.97816			−0.989080	−	0.147379i	$-0.952916\pi$
$271$	−32.5646			−1.97816			−0.989080	+	0.147379i	$0.952916\pi$
$272$			0.921622i			0.0558816i
$273$		−	10.1568i		−	0.614715i
$274$	−22.2823			−1.34612
$275$	4.76487	−	2.52359i	0.287332	−	0.152178i
$276$	−1.00000			−0.0601929
$277$			15.7009i			0.943374i	0.881766	+	0.471687i	$0.156355\pi$
$277$			15.7009i			0.943374i	−0.881766	+	0.471687i	$0.843645\pi$
$278$			10.5236i			0.631163i
$279$	4.00000			0.239474
$280$	−2.34017	−	9.41855i	−0.139852	−	0.562866i
$281$	−9.36069			−0.558412			−0.279206	−	0.960231i	$-0.590071\pi$
$281$	−9.36069			−0.558412			−0.279206	+	0.960231i	$0.590071\pi$
$282$		−	6.83710i		−	0.407143i
$283$			17.4186i			1.03543i	0.855555	+	0.517713i	$0.173216\pi$
$283$			17.4186i			1.03543i	−0.855555	+	0.517713i	$0.826784\pi$
$284$	−15.1773			−0.900606
$285$	−5.07838	+	1.26180i	−0.300817	+	0.0747423i
$286$	2.52359			0.149223
$287$			0.680346i			0.0401596i
$288$		−	1.00000i		−	0.0589256i
$289$	16.1506			0.950036
$290$	−22.7792	+	5.65983i	−1.33764	+	0.332356i
$291$	−9.02052			−0.528792
$292$		−	4.68035i		−	0.273897i
$293$			16.3402i			0.954603i	0.878740	+	0.477302i	$0.158385\pi$
$293$			16.3402i			0.954603i	−0.878740	+	0.477302i	$0.841615\pi$
$294$	11.8371			0.690354
$295$	−4.76487	−	19.1773i	−0.277421	−	1.11654i
$296$	2.58145			0.150044
$297$			1.07838i			0.0625738i
$298$		−	6.92162i		−	0.400959i
$299$	2.34017			0.135336
$300$	2.34017	+	4.41855i	0.135110	+	0.255105i
$301$	3.20394			0.184672
$302$			6.15676i			0.354281i
$303$			1.50307i			0.0863492i
$304$	−2.34017			−0.134218
$305$	6.24128	+	25.1194i	0.357374	+	1.43833i
$306$	0.921622			0.0526856
$307$		−	3.20394i		−	0.182858i	−0.995812	−	0.0914292i	$-0.970856\pi$
$307$		−	3.20394i		−	0.182858i	0.995812	−	0.0914292i	$-0.0291435\pi$
$308$			4.68035i			0.266687i
$309$	−2.49693			−0.142045
$310$	−8.68035	+	2.15676i	−0.493011	+	0.122495i
$311$	12.6537			0.717525			0.358762	−	0.933429i	$-0.383199\pi$
$311$	12.6537			0.717525			0.358762	+	0.933429i	$0.383199\pi$
$312$			2.34017i			0.132486i
$313$		−	33.2183i		−	1.87761i	−0.344449	−	0.938805i	$-0.611934\pi$
$313$		−	33.2183i		−	1.87761i	0.344449	−	0.938805i	$-0.388066\pi$
$314$	−2.89496			−0.163372
$315$	−9.41855	+	2.34017i	−0.530675	+	0.131854i
$316$	−11.9155			−0.670298
$317$		−	6.99386i		−	0.392814i	−0.980522	−	0.196407i	$-0.937073\pi$
$317$		−	6.99386i		−	0.392814i	0.980522	−	0.196407i	$-0.0629274\pi$
$318$		−	0.340173i		−	0.0190760i
$319$	11.3197			0.633779
$320$	0.539189	+	2.17009i	0.0301416	+	0.121312i
$321$	−9.57531			−0.534441
$322$			4.34017i			0.241868i
$323$		−	2.15676i		−	0.120005i
$324$	−1.00000			−0.0555556
$325$	−5.47641	−	10.3402i	−0.303777	−	0.573570i
$326$	6.52359			0.361308
$327$			9.78539i			0.541133i
$328$		−	0.156755i		−	0.00865537i
$329$	−29.6742			−1.63599
$330$	−0.581449	−	2.34017i	−0.0320077	−	0.128822i
$331$	−29.7275			−1.63397			−0.816986	−	0.576657i	$-0.804357\pi$
$331$	−29.7275			−1.63397			−0.816986	+	0.576657i	$0.804357\pi$
$332$			11.4186i			0.626674i
$333$		−	2.58145i		−	0.141463i
$334$	−5.47641			−0.299656
$335$	5.60197	−	1.39189i	0.306068	−	0.0760470i
$336$	−4.34017			−0.236776
$337$			28.3402i			1.54379i	0.635751	+	0.771894i	$0.280690\pi$
$337$			28.3402i			1.54379i	−0.635751	+	0.771894i	$0.719310\pi$
$338$			7.52359i			0.409229i
$339$	8.92162			0.484556
$340$	−2.00000	+	0.496928i	−0.108465	+	0.0269497i
$341$	4.31351			0.233590
$342$			2.34017i			0.126542i
$343$		−	20.9939i		−	1.13356i
$344$	−0.738205			−0.0398013
$345$	−0.539189	−	2.17009i	−0.0290290	−	0.116834i
$346$	−15.6742			−0.842650
$347$		−	22.5236i		−	1.20913i	−0.796556	−	0.604565i	$-0.793347\pi$
$347$		−	22.5236i		−	1.20913i	0.796556	−	0.604565i	$-0.206653\pi$
$348$			10.4969i			0.562694i
$349$	−15.6742			−0.839021			−0.419510	−	0.907751i	$-0.637798\pi$
$349$	−15.6742			−0.839021			−0.419510	+	0.907751i	$0.637798\pi$
$350$	19.1773	−	10.1568i	1.02507	−	0.542901i
$351$	2.34017			0.124909
$352$		−	1.07838i		−	0.0574777i
$353$		−	26.3135i		−	1.40053i	−0.713885	−	0.700263i	$-0.753066\pi$
$353$		−	26.3135i		−	1.40053i	0.713885	−	0.700263i	$-0.246934\pi$
$354$	−8.83710			−0.469687
$355$	−8.18342	−	32.9360i	−0.434331	−	1.74806i
$356$	−4.68035			−0.248058
$357$		−	4.00000i		−	0.211702i
$358$		−	15.3607i		−	0.811838i
$359$	0.796064			0.0420146			0.0210073	−	0.999779i	$-0.493313\pi$
$359$	0.796064			0.0420146			0.0210073	+	0.999779i	$0.493313\pi$
$360$	2.17009	−	0.539189i	0.114374	−	0.0284177i
$361$	−13.5236			−0.711768
$362$			21.6163i			1.13613i
$363$		−	9.83710i		−	0.516314i
$364$	10.1568			0.532359
$365$	10.1568	−	2.52359i	0.531629	−	0.132091i
$366$	11.5753			0.605051
$367$			13.7009i			0.715179i	0.933879	+	0.357590i	$0.116401\pi$
$367$			13.7009i			0.715179i	−0.933879	+	0.357590i	$0.883599\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	−0.156755			−0.00816036
$370$	1.39189	+	5.60197i	0.0723608	+	0.291232i
$371$	−1.47641			−0.0766514
$372$			4.00000i			0.207390i
$373$		−	4.25565i		−	0.220349i	−0.993912	−	0.110175i	$-0.964859\pi$
$373$		−	4.25565i		−	0.220349i	0.993912	−	0.110175i	$-0.0351410\pi$
$374$	0.993857			0.0513911
$375$	−8.32684	+	7.46081i	−0.429996	+	0.385275i
$376$	6.83710			0.352597
$377$		−	24.5646i		−	1.26514i
$378$			4.34017i			0.223234i
$379$	30.6537			1.57457			0.787287	−	0.616587i	$-0.211485\pi$
$379$	30.6537			1.57457			0.787287	+	0.616587i	$0.211485\pi$
$380$	−1.26180	−	5.07838i	−0.0647287	−	0.260515i
$381$	−17.1773			−0.880018
$382$			4.36683i			0.223427i
$383$			20.8781i			1.06682i	0.845856	+	0.533412i	$0.179090\pi$
$383$			20.8781i			1.06682i	−0.845856	+	0.533412i	$0.820910\pi$
$384$	1.00000			0.0510310
$385$	−10.1568	+	2.52359i	−0.517636	+	0.128614i
$386$	−8.68035			−0.441818
$387$			0.738205i			0.0375251i
$388$		−	9.02052i		−	0.457947i
$389$	16.9627			0.860041			0.430021	−	0.902819i	$-0.358506\pi$
$389$	16.9627			0.860041			0.430021	+	0.902819i	$0.358506\pi$
$390$	−5.07838	+	1.26180i	−0.257154	+	0.0638935i
$391$	0.921622			0.0466084
$392$			11.8371i			0.597864i
$393$		−	6.68035i		−	0.336979i
$394$	22.6803			1.14262
$395$	−6.42469	−	25.8576i	−0.323261	−	1.30104i
$396$	−1.07838			−0.0541905
$397$		−	16.4969i		−	0.827957i	−0.910287	−	0.413979i	$-0.864139\pi$
$397$		−	16.4969i		−	0.827957i	0.910287	−	0.413979i	$-0.135861\pi$
$398$			5.44521i			0.272944i
$399$	10.1568			0.508474
$400$	−4.41855	+	2.34017i	−0.220928	+	0.117009i
$401$	−35.2039			−1.75800			−0.879000	−	0.476821i	$-0.841789\pi$
$401$	−35.2039			−1.75800			−0.879000	+	0.476821i	$0.841789\pi$
$402$		−	2.58145i		−	0.128751i
$403$		−	9.36069i		−	0.466289i
$404$	−1.50307			−0.0747806
$405$	−0.539189	−	2.17009i	−0.0267925	−	0.107832i
$406$	45.5585			2.26103
$407$		−	2.78378i		−	0.137987i
$408$			0.921622i			0.0456271i
$409$	−11.3607			−0.561750			−0.280875	−	0.959744i	$-0.590625\pi$
$409$	−11.3607			−0.561750			−0.280875	+	0.959744i	$0.590625\pi$
$410$	0.340173	−	0.0845208i	0.0167999	−	0.00417419i
$411$	−22.2823			−1.09911
$412$		−	2.49693i		−	0.123015i
$413$			38.3545i			1.88730i
$414$	−1.00000			−0.0491473
$415$	−24.7792	+	6.15676i	−1.21637	+	0.302223i
$416$	−2.34017			−0.114736
$417$			10.5236i			0.515342i
$418$			2.52359i			0.123433i
$419$	18.1256			0.885491			0.442746	−	0.896647i	$-0.354004\pi$
$419$	18.1256			0.885491			0.442746	+	0.896647i	$0.354004\pi$
$420$	−2.34017	−	9.41855i	−0.114189	−	0.459578i
$421$	2.58145			0.125812			0.0629061	−	0.998019i	$-0.479963\pi$
$421$	2.58145			0.125812			0.0629061	+	0.998019i	$0.479963\pi$
$422$		−	22.0410i		−	1.07294i
$423$		−	6.83710i		−	0.332431i
$424$	0.340173			0.0165203
$425$	−2.15676	−	4.07223i	−0.104618	−	0.197532i
$426$	−15.1773			−0.735341
$427$		−	50.2388i		−	2.43123i
$428$		−	9.57531i		−	0.462840i
$429$	2.52359			0.121840
$430$	−0.398032	−	1.60197i	−0.0191948	−	0.0772538i
$431$	−33.9877			−1.63713			−0.818565	−	0.574414i	$-0.805230\pi$
$431$	−33.9877			−1.63713			−0.818565	+	0.574414i	$0.805230\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			8.28685i			0.398241i	0.979975	+	0.199120i	$0.0638084\pi$
$433$			8.28685i			0.398241i	−0.979975	+	0.199120i	$0.936192\pi$
$434$	17.3607			0.833340
$435$	−22.7792	+	5.65983i	−1.09218	+	0.271368i
$436$	−9.78539			−0.468635
$437$			2.34017i			0.111946i
$438$		−	4.68035i		−	0.223636i
$439$	28.9939			1.38380			0.691901	−	0.721993i	$-0.256774\pi$
$439$	28.9939			1.38380			0.691901	+	0.721993i	$0.256774\pi$
$440$	2.34017	−	0.581449i	0.111563	−	0.0277195i
$441$	11.8371			0.563671
$442$		−	2.15676i		−	0.102586i
$443$			3.20394i			0.152224i	0.997099	+	0.0761118i	$0.0242506\pi$
$443$			3.20394i			0.152224i	−0.997099	+	0.0761118i	$0.975749\pi$
$444$	2.58145			0.122510
$445$	−2.52359	−	10.1568i	−0.119630	−	0.481476i
$446$	21.1773			1.00277
$447$		−	6.92162i		−	0.327381i
$448$		−	4.34017i		−	0.205054i
$449$	−28.1568			−1.32880			−0.664400	−	0.747377i	$-0.731313\pi$
$449$	−28.1568			−1.32880			−0.664400	+	0.747377i	$0.731313\pi$
$450$	2.34017	+	4.41855i	0.110317	+	0.208292i
$451$	−0.169042			−0.00795986
$452$			8.92162i			0.419638i
$453$			6.15676i			0.289270i
$454$	11.7854			0.553116
$455$	5.47641	+	22.0410i	0.256738	+	1.03330i
$456$	−2.34017			−0.109589
$457$		−	23.1773i		−	1.08419i	−0.840318	−	0.542094i	$-0.817632\pi$
$457$		−	23.1773i		−	1.08419i	0.840318	−	0.542094i	$-0.182368\pi$
$458$		−	1.78539i		−	0.0834256i
$459$	0.921622			0.0430176
$460$	2.17009	−	0.539189i	0.101181	−	0.0251398i
$461$	−42.3279			−1.97141			−0.985703	−	0.168491i	$-0.946110\pi$
$461$	−42.3279			−1.97141			−0.985703	+	0.168491i	$0.946110\pi$
$462$			4.68035i			0.217749i
$463$			34.9048i			1.62216i	0.584933	+	0.811082i	$0.301121\pi$
$463$			34.9048i			1.62216i	−0.584933	+	0.811082i	$0.698879\pi$
$464$	−10.4969			−0.487308
$465$	−8.68035	+	2.15676i	−0.402541	+	0.100017i
$466$	18.3135			0.848357
$467$		−	37.7731i		−	1.74793i	−0.485988	−	0.873965i	$-0.661540\pi$
$467$		−	37.7731i		−	1.74793i	0.485988	−	0.873965i	$-0.338460\pi$
$468$			2.34017i			0.108175i
$469$	−11.2039			−0.517350
$470$	3.68649	+	14.8371i	0.170045	+	0.684384i
$471$	−2.89496			−0.133393
$472$		−	8.83710i		−	0.406761i
$473$			0.796064i			0.0366030i
$474$	−11.9155			−0.547296
$475$	10.3402	−	5.47641i	0.474440	−	0.251275i
$476$	4.00000			0.183340
$477$		−	0.340173i		−	0.0155755i
$478$			5.33403i			0.243973i
$479$	28.1978			1.28839			0.644195	−	0.764861i	$-0.277193\pi$
$479$	28.1978			1.28839			0.644195	+	0.764861i	$0.277193\pi$
$480$	0.539189	+	2.17009i	0.0246105	+	0.0990504i
$481$	−6.04104			−0.275448
$482$			26.1978i			1.19328i
$483$			4.34017i			0.197485i
$484$	9.83710			0.447141
$485$	19.5753	−	4.86376i	0.888869	−	0.220852i
$486$	−1.00000			−0.0453609
$487$			38.2245i			1.73212i	0.499944	+	0.866058i	$0.333354\pi$
$487$			38.2245i			1.73212i	−0.499944	+	0.866058i	$0.666646\pi$
$488$			11.5753i			0.523989i
$489$	6.52359			0.295007
$490$	−25.6875	+	6.38243i	−1.16044	+	0.288329i
$491$	11.3074			0.510294			0.255147	−	0.966902i	$-0.417876\pi$
$491$	11.3074			0.510294			0.255147	+	0.966902i	$0.417876\pi$
$492$		−	0.156755i		−	0.00706708i
$493$		−	9.67420i		−	0.435704i
$494$	5.47641			0.246395
$495$	−0.581449	−	2.34017i	−0.0261342	−	0.105183i
$496$	−4.00000			−0.179605
$497$			65.8720i			2.95476i
$498$			11.4186i			0.511677i
$499$	2.47027			0.110584			0.0552922	−	0.998470i	$-0.482391\pi$
$499$	2.47027			0.110584			0.0552922	+	0.998470i	$0.482391\pi$
$500$	−7.46081	−	8.32684i	−0.333658	−	0.372388i
$501$	−5.47641			−0.244668
$502$			27.4329i			1.22439i
$503$			20.6270i			0.919713i	0.887993	+	0.459857i	$0.152099\pi$
$503$			20.6270i			0.919713i	−0.887993	+	0.459857i	$0.847901\pi$
$504$	−4.34017			−0.193327
$505$	−0.810439	−	3.26180i	−0.0360641	−	0.145148i
$506$	−1.07838			−0.0479397
$507$			7.52359i			0.334134i
$508$		−	17.1773i		−	0.762118i
$509$	32.2245			1.42832			0.714162	−	0.699981i	$-0.246808\pi$
$509$	32.2245			1.42832			0.714162	+	0.699981i	$0.246808\pi$
$510$	−2.00000	+	0.496928i	−0.0885615	+	0.0220044i
$511$	−20.3135			−0.898617
$512$			1.00000i			0.0441942i
$513$			2.34017i			0.103321i
$514$	10.3135			0.454909
$515$	5.41855	−	1.34632i	0.238770	−	0.0593258i
$516$	−0.738205			−0.0324977
$517$		−	7.37298i		−	0.324263i
$518$		−	11.2039i		−	0.492273i
$519$	−15.6742			−0.688021
$520$	−1.26180	−	5.07838i	−0.0553334	−	0.222702i
$521$	−3.51745			−0.154102			−0.0770511	−	0.997027i	$-0.524550\pi$
$521$	−3.51745			−0.154102			−0.0770511	+	0.997027i	$0.524550\pi$
$522$			10.4969i			0.459438i
$523$			35.9421i			1.57164i	0.618455	+	0.785820i	$0.287759\pi$
$523$			35.9421i			1.57164i	−0.618455	+	0.785820i	$0.712241\pi$
$524$	6.68035			0.291832
$525$	19.1773	−	10.1568i	0.836965	−	0.443277i
$526$	−20.9939			−0.915376
$527$		−	3.68649i		−	0.160586i
$528$		−	1.07838i		−	0.0469304i
$529$	−1.00000			−0.0434783
$530$	0.183417	+	0.738205i	0.00796715	+	0.0320656i
$531$	−8.83710			−0.383498
$532$			10.1568i			0.440351i
$533$			0.366835i			0.0158894i
$534$	−4.68035			−0.202538
$535$	20.7792	−	5.16290i	0.898365	−	0.223212i
$536$	2.58145			0.111502
$537$		−	15.3607i		−	0.662863i
$538$		−	25.3874i		−	1.09453i
$539$	12.7649			0.549822
$540$	2.17009	−	0.539189i	0.0933857	−	0.0232030i
$541$	31.7275			1.36407			0.682036	−	0.731318i	$-0.261095\pi$
$541$	31.7275			1.36407			0.682036	+	0.731318i	$0.261095\pi$
$542$		−	32.5646i		−	1.39877i
$543$			21.6163i			0.927646i
$544$	−0.921622			−0.0395142
$545$	−5.27617	−	21.2351i	−0.226006	−	0.909613i
$546$	10.1568			0.434669
$547$		−	9.84324i		−	0.420867i	−0.977608	−	0.210433i	$-0.932512\pi$
$547$		−	9.84324i		−	0.420867i	0.977608	−	0.210433i	$-0.0674875\pi$
$548$		−	22.2823i		−	0.951853i
$549$	11.5753			0.494022
$550$	2.52359	+	4.76487i	0.107606	+	0.203175i
$551$	24.5646			1.04649
$552$		−	1.00000i		−	0.0425628i
$553$			51.7152i			2.19916i
$554$	−15.7009			−0.667066
$555$	1.39189	+	5.60197i	0.0590824	+	0.237790i
$556$	−10.5236			−0.446300
$557$			26.3279i			1.11555i	0.829993	+	0.557774i	$0.188344\pi$
$557$			26.3279i			1.11555i	−0.829993	+	0.557774i	$0.811656\pi$
$558$			4.00000i			0.169334i
$559$	1.72753			0.0730666
$560$	9.41855	−	2.34017i	0.398006	−	0.0988904i
$561$	0.993857			0.0419607
$562$		−	9.36069i		−	0.394857i
$563$			30.2557i			1.27512i	0.770399	+	0.637562i	$0.220057\pi$
$563$			30.2557i			1.27512i	−0.770399	+	0.637562i	$0.779943\pi$
$564$	6.83710			0.287894
$565$	−19.3607	+	4.81044i	−0.814510	+	0.202377i
$566$	−17.4186			−0.732156
$567$			4.34017i			0.182270i
$568$		−	15.1773i		−	0.636824i
$569$	−33.8720			−1.41999			−0.709994	−	0.704208i	$-0.751302\pi$
$569$	−33.8720			−1.41999			−0.709994	+	0.704208i	$0.751302\pi$
$570$	−1.26180	−	5.07838i	−0.0528508	−	0.212710i
$571$	35.1650			1.47161			0.735804	−	0.677194i	$-0.236804\pi$
$571$	35.1650			1.47161			0.735804	+	0.677194i	$0.236804\pi$
$572$			2.52359i			0.105517i
$573$			4.36683i			0.182427i
$574$	−0.680346			−0.0283971
$575$	2.34017	+	4.41855i	0.0975920	+	0.184266i
$576$	1.00000			0.0416667
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$			16.1506i			0.671777i
$579$	−8.68035			−0.360743
$580$	−5.65983	−	22.7792i	−0.235012	−	0.945857i
$581$	49.5585			2.05603
$582$		−	9.02052i		−	0.373913i
$583$		−	0.366835i		−	0.0151928i
$584$	4.68035			0.193674
$585$	−5.07838	+	1.26180i	−0.209965	+	0.0521688i
$586$	−16.3402			−0.675006
$587$			9.30737i			0.384156i	0.981380	+	0.192078i	$0.0615227\pi$
$587$			9.30737i			0.384156i	−0.981380	+	0.192078i	$0.938477\pi$
$588$			11.8371i			0.488154i
$589$	9.36069			0.385701
$590$	19.1773	−	4.76487i	0.789516	−	0.196166i
$591$	22.6803			0.932945
$592$			2.58145i			0.106097i
$593$		−	33.0349i		−	1.35658i	−0.734794	−	0.678290i	$-0.762721\pi$
$593$		−	33.0349i		−	1.35658i	0.734794	−	0.678290i	$-0.237279\pi$
$594$	−1.07838			−0.0442464
$595$	2.15676	+	8.68035i	0.0884184	+	0.355859i
$596$	6.92162			0.283521
$597$			5.44521i			0.222858i
$598$			2.34017i			0.0956968i
$599$	−13.6475			−0.557623			−0.278812	−	0.960346i	$-0.589941\pi$
$599$	−13.6475			−0.557623			−0.278812	+	0.960346i	$0.589941\pi$
$600$	−4.41855	+	2.34017i	−0.180387	+	0.0955372i
$601$	1.68649			0.0687933			0.0343967	−	0.999408i	$-0.489049\pi$
$601$	1.68649			0.0687933			0.0343967	+	0.999408i	$0.489049\pi$
$602$			3.20394i			0.130583i
$603$		−	2.58145i		−	0.105125i
$604$	−6.15676			−0.250515
$605$	5.30406	+	21.3474i	0.215641	+	0.867894i
$606$	−1.50307			−0.0610581
$607$		−	47.2183i		−	1.91653i	−0.285878	−	0.958266i	$-0.592285\pi$
$607$		−	47.2183i		−	1.91653i	0.285878	−	0.958266i	$-0.407715\pi$
$608$		−	2.34017i		−	0.0949065i
$609$	45.5585			1.84612
$610$	−25.1194	+	6.24128i	−1.01706	+	0.252702i
$611$	−16.0000			−0.647291
$612$			0.921622i			0.0372544i
$613$			7.45959i			0.301290i	0.988588	+	0.150645i	$0.0481350\pi$
$613$			7.45959i			0.301290i	−0.988588	+	0.150645i	$0.951865\pi$
$614$	3.20394			0.129300
$615$	0.340173	−	0.0845208i	0.0137171	−	0.00340821i
$616$	−4.68035			−0.188577
$617$			15.8120i			0.636569i	0.947995	+	0.318285i	$0.103107\pi$
$617$			15.8120i			0.636569i	−0.947995	+	0.318285i	$0.896893\pi$
$618$		−	2.49693i		−	0.100441i
$619$	26.3402			1.05870			0.529350	−	0.848403i	$-0.322436\pi$
$619$	26.3402			1.05870			0.529350	+	0.848403i	$0.322436\pi$
$620$	−2.15676	−	8.68035i	−0.0866174	−	0.348611i
$621$	−1.00000			−0.0401286
$622$			12.6537i			0.507367i
$623$			20.3135i			0.813844i
$624$	−2.34017			−0.0936819
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	33.2183			1.32767
$627$			2.52359i			0.100782i
$628$		−	2.89496i		−	0.115521i
$629$	−2.37912			−0.0948618
$630$	−2.34017	−	9.41855i	−0.0932347	−	0.375244i
$631$	−14.4391			−0.574810			−0.287405	−	0.957809i	$-0.592793\pi$
$631$	−14.4391			−0.574810			−0.287405	+	0.957809i	$0.592793\pi$
$632$		−	11.9155i		−	0.473972i
$633$		−	22.0410i		−	0.876053i
$634$	6.99386			0.277762
$635$	37.2762	−	9.26180i	1.47926	−	0.367543i
$636$	0.340173			0.0134887
$637$		−	27.7009i		−	1.09755i
$638$			11.3197i			0.448149i
$639$	−15.1773			−0.600404
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	−5.78992			−0.228688			−0.114344	−	0.993441i	$-0.536477\pi$
$641$	−5.78992			−0.228688			−0.114344	+	0.993441i	$0.536477\pi$
$642$		−	9.57531i		−	0.377907i
$643$		−	23.4063i		−	0.923053i	−0.887126	−	0.461526i	$-0.847302\pi$
$643$		−	23.4063i		−	0.923053i	0.887126	−	0.461526i	$-0.152698\pi$
$644$	−4.34017			−0.171027
$645$	−0.398032	−	1.60197i	−0.0156725	−	0.0630774i
$646$	2.15676			0.0848564
$647$			25.9877i			1.02168i	0.859675	+	0.510841i	$0.170666\pi$
$647$			25.9877i			1.02168i	−0.859675	+	0.510841i	$0.829334\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−9.52973			−0.374075
$650$	10.3402	−	5.47641i	0.405575	−	0.214802i
$651$	17.3607			0.680419
$652$			6.52359i			0.255484i
$653$			0.325797i			0.0127494i	0.999980	+	0.00637471i	$0.00202915\pi$
$653$			0.325797i			0.0127494i	−0.999980	+	0.00637471i	$0.997971\pi$
$654$	−9.78539			−0.382639
$655$	3.60197	+	14.4969i	0.140741	+	0.566442i
$656$	0.156755			0.00612027
$657$		−	4.68035i		−	0.182598i
$658$		−	29.6742i		−	1.15682i
$659$	3.11942			0.121515			0.0607576	−	0.998153i	$-0.480648\pi$
$659$	3.11942			0.121515			0.0607576	+	0.998153i	$0.480648\pi$
$660$	2.34017	−	0.581449i	0.0910911	−	0.0226329i
$661$	24.1399			0.938935			0.469467	−	0.882950i	$-0.344446\pi$
$661$	24.1399			0.938935			0.469467	+	0.882950i	$0.344446\pi$
$662$		−	29.7275i		−	1.15539i
$663$		−	2.15676i		−	0.0837614i
$664$	−11.4186			−0.443126
$665$	−22.0410	+	5.47641i	−0.854715	+	0.212366i
$666$	2.58145			0.100029
$667$			10.4969i			0.406443i
$668$		−	5.47641i		−	0.211889i
$669$	21.1773			0.818761
$670$	1.39189	+	5.60197i	0.0537734	+	0.216423i
$671$	12.4826			0.481884
$672$		−	4.34017i		−	0.167426i
$673$			45.6742i			1.76061i	0.474407	+	0.880306i	$0.342662\pi$
$673$			45.6742i			1.76061i	−0.474407	+	0.880306i	$0.657338\pi$
$674$	−28.3402			−1.09162
$675$	2.34017	+	4.41855i	0.0900733	+	0.170070i
$676$	−7.52359			−0.289369
$677$			9.38735i			0.360785i	0.983595	+	0.180393i	$0.0577368\pi$
$677$			9.38735i			0.360785i	−0.983595	+	0.180393i	$0.942263\pi$
$678$			8.92162i			0.342633i
$679$	−39.1506			−1.50246
$680$	−0.496928	−	2.00000i	−0.0190563	−	0.0766965i
$681$	11.7854			0.451617
$682$			4.31351i			0.165173i
$683$		−	20.9939i		−	0.803308i	−0.915792	−	0.401654i	$-0.868436\pi$
$683$		−	20.9939i		−	0.803308i	0.915792	−	0.401654i	$-0.131564\pi$
$684$	−2.34017			−0.0894788
$685$	48.3545	−	12.0144i	1.84753	−	0.459046i
$686$	20.9939			0.801549
$687$		−	1.78539i		−	0.0681167i
$688$		−	0.738205i		−	0.0281438i
$689$	−0.796064			−0.0303276
$690$	2.17009	−	0.539189i	0.0826138	−	0.0205266i
$691$	−44.1445			−1.67933			−0.839667	−	0.543101i	$-0.817250\pi$
$691$	−44.1445			−1.67933			−0.839667	+	0.543101i	$0.817250\pi$
$692$		−	15.6742i		−	0.595844i
$693$			4.68035i			0.177792i
$694$	22.5236			0.854984
$695$	−5.67420	−	22.8371i	−0.215235	−	0.866261i
$696$	−10.4969			−0.397885
$697$			0.144469i			0.00547217i
$698$		−	15.6742i		−	0.593277i
$699$	18.3135			0.692681
$700$	10.1568	+	19.1773i	0.383889	+	0.724833i
$701$	−27.7998			−1.04998			−0.524991	−	0.851108i	$-0.675931\pi$
$701$	−27.7998			−1.04998			−0.524991	+	0.851108i	$0.675931\pi$
$702$			2.34017i			0.0883241i
$703$		−	6.04104i		−	0.227842i
$704$	1.07838			0.0406429
$705$	3.68649	+	14.8371i	0.138841	+	0.558798i
$706$	26.3135			0.990322
$707$			6.52359i			0.245345i
$708$		−	8.83710i		−	0.332119i
$709$	−4.30898			−0.161827			−0.0809135	−	0.996721i	$-0.525784\pi$
$709$	−4.30898			−0.161827			−0.0809135	+	0.996721i	$0.525784\pi$
$710$	32.9360	−	8.18342i	1.23607	−	0.307118i
$711$	−11.9155			−0.446865
$712$		−	4.68035i		−	0.175403i
$713$			4.00000i			0.149801i
$714$	4.00000			0.149696
$715$	−5.47641	+	1.36069i	−0.204806	+	0.0508870i
$716$	15.3607			0.574056
$717$			5.33403i			0.199203i
$718$			0.796064i			0.0297088i
$719$	−15.9733			−0.595705			−0.297852	−	0.954612i	$-0.596270\pi$
$719$	−15.9733			−0.595705			−0.297852	+	0.954612i	$0.596270\pi$
$720$	0.539189	+	2.17009i	0.0200944	+	0.0808743i
$721$	−10.8371			−0.403595
$722$		−	13.5236i		−	0.503296i
$723$			26.1978i			0.974306i
$724$	−21.6163			−0.803365
$725$	46.3812	−	24.5646i	1.72255	−	0.912307i
$726$	9.83710			0.365089
$727$		−	0.340173i		−	0.0126163i	−0.999980	−	0.00630816i	$-0.997992\pi$
$727$		−	0.340173i		−	0.0126163i	0.999980	−	0.00630816i	$-0.00200796\pi$
$728$			10.1568i			0.376434i
$729$	−1.00000			−0.0370370
$730$	2.52359	+	10.1568i	0.0934023	+	0.375918i
$731$	0.680346			0.0251635
$732$			11.5753i			0.427836i
$733$			19.2618i			0.711451i	0.934591	+	0.355725i	$0.115766\pi$
$733$			19.2618i			0.711451i	−0.934591	+	0.355725i	$0.884234\pi$
$734$	−13.7009			−0.505708
$735$	−25.6875	+	6.38243i	−0.947499	+	0.235420i
$736$	1.00000			0.0368605
$737$		−	2.78378i		−	0.102542i
$738$		−	0.156755i		−	0.00577025i
$739$	−25.5585			−0.940184			−0.470092	−	0.882617i	$-0.655779\pi$
$739$	−25.5585			−0.940184			−0.470092	+	0.882617i	$0.655779\pi$
$740$	−5.60197	+	1.39189i	−0.205932	+	0.0511668i
$741$	5.47641			0.201181
$742$		−	1.47641i		−	0.0542007i
$743$			36.8781i			1.35293i	0.736476	+	0.676464i	$0.236489\pi$
$743$			36.8781i			1.35293i	−0.736476	+	0.676464i	$0.763511\pi$
$744$	−4.00000			−0.146647
$745$	3.73206	+	15.0205i	0.136732	+	0.550309i
$746$	4.25565			0.155810
$747$			11.4186i			0.417783i
$748$			0.993857i			0.0363390i
$749$	−41.5585			−1.51851
$750$	−7.46081	−	8.32684i	−0.272430	−	0.304053i
$751$	18.1256			0.661411			0.330706	−	0.943734i	$-0.392713\pi$
$751$	18.1256			0.661411			0.330706	+	0.943734i	$0.392713\pi$
$752$			6.83710i			0.249323i
$753$			27.4329i			0.999711i
$754$	24.5646			0.894591
$755$	−3.31965	−	13.3607i	−0.120815	−	0.486245i
$756$	−4.34017			−0.157851
$757$		−	17.4186i		−	0.633088i	−0.948578	−	0.316544i	$-0.897478\pi$
$757$		−	17.4186i		−	0.633088i	0.948578	−	0.316544i	$-0.102522\pi$
$758$			30.6537i			1.11339i
$759$	−1.07838			−0.0391426
$760$	5.07838	−	1.26180i	0.184212	−	0.0457701i
$761$	−23.4140			−0.848757			−0.424379	−	0.905485i	$-0.639507\pi$
$761$	−23.4140			−0.848757			−0.424379	+	0.905485i	$0.639507\pi$
$762$		−	17.1773i		−	0.622267i
$763$			42.4703i			1.53753i
$764$	−4.36683			−0.157987
$765$	−2.00000	+	0.496928i	−0.0723102	+	0.0179665i
$766$	−20.8781			−0.754358
$767$			20.6803i			0.746724i
$768$			1.00000i			0.0360844i
$769$	29.7152			1.07156			0.535779	−	0.844358i	$-0.320018\pi$
$769$	29.7152			1.07156			0.535779	+	0.844358i	$0.320018\pi$
$770$	−2.52359	−	10.1568i	−0.0909439	−	0.366024i
$771$	10.3135			0.371432
$772$		−	8.68035i		−	0.312412i
$773$		−	15.3463i		−	0.551969i	−0.961162	−	0.275984i	$-0.910996\pi$
$773$		−	15.3463i		−	0.551969i	0.961162	−	0.275984i	$-0.0890038\pi$
$774$	−0.738205			−0.0265342
$775$	17.6742	−	9.36069i	0.634876	−	0.336246i
$776$	9.02052			0.323818
$777$		−	11.2039i		−	0.401939i
$778$			16.9627i			0.608141i
$779$	−0.366835			−0.0131432
$780$	−1.26180	−	5.07838i	−0.0451795	−	0.181835i
$781$	−16.3668			−0.585651
$782$			0.921622i			0.0329571i
$783$			10.4969i			0.375130i
$784$	−11.8371			−0.422754
$785$	6.28231	−	1.56093i	0.224225	−	0.0557120i
$786$	6.68035			0.238280
$787$		−	22.8950i		−	0.816117i	−0.912956	−	0.408059i	$-0.866206\pi$
$787$		−	22.8950i		−	0.816117i	0.912956	−	0.408059i	$-0.133794\pi$
$788$			22.6803i			0.807954i
$789$	−20.9939			−0.747401
$790$	25.8576	−	6.42469i	0.919973	−	0.228580i
$791$	38.7214			1.37677
$792$		−	1.07838i		−	0.0383185i
$793$		−	27.0882i		−	0.961931i
$794$	16.4969			0.585454
$795$	0.183417	+	0.738205i	0.00650515	+	0.0261814i
$796$	−5.44521			−0.193000
$797$		−	7.60650i		−	0.269436i	−0.990884	−	0.134718i	$-0.956987\pi$
$797$		−	7.60650i		−	0.269436i	0.990884	−	0.134718i	$-0.0430129\pi$
$798$			10.1568i			0.359545i
$799$	−6.30122			−0.222921
$800$	−2.34017	−	4.41855i	−0.0827376	−	0.156219i
$801$	−4.68035			−0.165372
$802$		−	35.2039i		−	1.24309i
$803$		−	5.04718i		−	0.178111i
$804$	2.58145			0.0910407
$805$	−2.34017	−	9.41855i	−0.0824803	−	0.331960i
$806$	9.36069			0.329716
$807$		−	25.3874i		−	0.893677i
$808$		−	1.50307i		−	0.0528779i
$809$	−43.7275			−1.53738			−0.768689	−	0.639623i	$-0.779091\pi$
$809$	−43.7275			−1.53738			−0.768689	+	0.639623i	$0.779091\pi$
$810$	2.17009	−	0.539189i	0.0762491	−	0.0189452i
$811$	−4.79606			−0.168413			−0.0842063	−	0.996448i	$-0.526835\pi$
$811$	−4.79606			−0.168413			−0.0842063	+	0.996448i	$0.526835\pi$
$812$			45.5585i			1.59879i
$813$		−	32.5646i		−	1.14209i
$814$	2.78378			0.0975713
$815$	−14.1568	+	3.51745i	−0.495890	+	0.123211i
$816$	−0.921622			−0.0322632
$817$			1.72753i			0.0604385i
$818$		−	11.3607i		−	0.397217i
$819$	10.1568			0.354906
$820$	0.0845208	+	0.340173i	0.00295159	+	0.0118794i
$821$	−12.2245			−0.426636			−0.213318	−	0.976983i	$-0.568427\pi$
$821$	−12.2245			−0.426636			−0.213318	+	0.976983i	$0.568427\pi$
$822$		−	22.2823i		−	0.777185i
$823$			37.5441i			1.30871i	0.756189	+	0.654353i	$0.227059\pi$
$823$			37.5441i			1.30871i	−0.756189	+	0.654353i	$0.772941\pi$
$824$	2.49693			0.0869846
$825$	2.52359	+	4.76487i	0.0878601	+	0.165891i
$826$	−38.3545			−1.33453
$827$		−	38.3090i		−	1.33213i	−0.745892	−	0.666067i	$-0.767977\pi$
$827$		−	38.3090i		−	1.33213i	0.745892	−	0.666067i	$-0.232023\pi$
$828$		−	1.00000i		−	0.0347524i
$829$	31.4140			1.09105			0.545527	−	0.838093i	$-0.316330\pi$
$829$	31.4140			1.09105			0.545527	+	0.838093i	$0.316330\pi$
$830$	−6.15676	−	24.7792i	−0.213704	−	0.860100i
$831$	−15.7009			−0.544657
$832$		−	2.34017i		−	0.0811309i
$833$		−	10.9093i		−	0.377986i
$834$	−10.5236			−0.364402
$835$	11.8843	−	2.95282i	0.411273	−	0.102187i
$836$	−2.52359			−0.0872802
$837$			4.00000i			0.138260i
$838$			18.1256i			0.626137i
$839$	−23.1506			−0.799248			−0.399624	−	0.916679i	$-0.630859\pi$
$839$	−23.1506			−0.799248			−0.399624	+	0.916679i	$0.630859\pi$
$840$	9.41855	−	2.34017i	0.324971	−	0.0807436i
$841$	81.1855			2.79950
$842$			2.58145i			0.0889626i
$843$		−	9.36069i		−	0.322399i
$844$	22.0410			0.758684
$845$	−4.05664	−	16.3268i	−0.139553	−	0.561660i
$846$	6.83710			0.235064
$847$		−	42.6947i		−	1.46701i
$848$			0.340173i			0.0116816i
$849$	−17.4186			−0.597803
$850$	4.07223	−	2.15676i	0.139676	−	0.0739761i
$851$	2.58145			0.0884909
$852$		−	15.1773i		−	0.519965i
$853$			32.4969i			1.11267i	0.830957	+	0.556337i	$0.187794\pi$
$853$			32.4969i			1.11267i	−0.830957	+	0.556337i	$0.812206\pi$
$854$	50.2388			1.71914
$855$	−1.26180	−	5.07838i	−0.0431525	−	0.173677i
$856$	9.57531			0.327277
$857$			37.8310i			1.29228i	0.763219	+	0.646140i	$0.223618\pi$
$857$			37.8310i			1.29228i	−0.763219	+	0.646140i	$0.776382\pi$
$858$			2.52359i			0.0861540i
$859$	28.1978			0.962096			0.481048	−	0.876694i	$-0.340256\pi$
$859$	28.1978			0.962096			0.481048	+	0.876694i	$0.340256\pi$
$860$	1.60197	−	0.398032i	0.0546267	−	0.0135728i
$861$	−0.680346			−0.0231861
$862$		−	33.9877i		−	1.15763i
$863$		−	32.0288i		−	1.09027i	−0.838348	−	0.545136i	$-0.816478\pi$
$863$		−	32.0288i		−	1.09027i	0.838348	−	0.545136i	$-0.183522\pi$
$864$	1.00000			0.0340207
$865$	34.0144	−	8.45136i	1.15652	−	0.287355i
$866$	−8.28685			−0.281599
$867$			16.1506i			0.548504i
$868$			17.3607i			0.589260i
$869$	−12.8494			−0.435886
$870$	−5.65983	−	22.7792i	−0.191886	−	0.772289i
$871$	−6.04104			−0.204693
$872$		−	9.78539i		−	0.331375i
$873$		−	9.02052i		−	0.305298i
$874$	−2.34017			−0.0791575
$875$	−36.1399	+	32.3812i	−1.22175	+	1.09468i
$876$	4.68035			0.158134
$877$			27.7009i			0.935392i	0.883889	+	0.467696i	$0.154916\pi$
$877$			27.7009i			0.935392i	−0.883889	+	0.467696i	$0.845084\pi$
$878$			28.9939i			0.978495i
$879$	−16.3402			−0.551140
$880$	0.581449	+	2.34017i	0.0196007	+	0.0788872i
$881$	12.3135			0.414853			0.207426	−	0.978251i	$-0.433491\pi$
$881$	12.3135			0.414853			0.207426	+	0.978251i	$0.433491\pi$
$882$			11.8371i			0.398576i
$883$		−	7.15061i		−	0.240637i	−0.992735	−	0.120319i	$-0.961608\pi$
$883$		−	7.15061i		−	0.240637i	0.992735	−	0.120319i	$-0.0383916\pi$
$884$	2.15676			0.0725395
$885$	19.1773	−	4.76487i	0.644637	−	0.160169i
$886$	−3.20394			−0.107638
$887$			9.19165i			0.308625i	0.988022	+	0.154313i	$0.0493163\pi$
$887$			9.19165i			0.308625i	−0.988022	+	0.154313i	$0.950684\pi$
$888$			2.58145i			0.0866278i
$889$	−74.5523			−2.50041
$890$	10.1568	−	2.52359i	0.340455	−	0.0845909i
$891$	−1.07838			−0.0361270
$892$			21.1773i			0.709068i
$893$		−	16.0000i		−	0.535420i
$894$	6.92162			0.231494
$895$	8.28231	+	33.3340i	0.276847	+	1.11423i
$896$	4.34017			0.144995
$897$			2.34017i			0.0781361i
$898$		−	28.1568i		−	0.939603i
$899$	41.9877			1.40037
$900$	−4.41855	+	2.34017i	−0.147285	+	0.0780058i
$901$	−0.313511			−0.0104446
$902$		−	0.169042i		−	0.00562847i
$903$			3.20394i			0.106620i
$904$	−8.92162			−0.296729
$905$	−11.6553	−	46.9093i	−0.387435	−	1.55932i
$906$	−6.15676			−0.204545
$907$		−	14.0989i		−	0.468146i	−0.972219	−	0.234073i	$-0.924794\pi$
$907$		−	14.0989i		−	0.468146i	0.972219	−	0.234073i	$-0.0752055\pi$
$908$			11.7854i			0.391112i
$909$	−1.50307			−0.0498537
$910$	−22.0410	+	5.47641i	−0.730653	+	0.181541i
$911$	−20.9939			−0.695558			−0.347779	−	0.937577i	$-0.613064\pi$
$911$	−20.9939			−0.695558			−0.347779	+	0.937577i	$0.613064\pi$
$912$		−	2.34017i		−	0.0774909i
$913$			12.3135i			0.407518i
$914$	23.1773			0.766636
$915$	−25.1194	+	6.24128i	−0.830422	+	0.206330i
$916$	1.78539			0.0589908
$917$		−	28.9939i		−	0.957462i
$918$			0.921622i			0.0304181i
$919$	1.92777			0.0635911			0.0317956	−	0.999494i	$-0.489877\pi$
$919$	1.92777			0.0635911			0.0317956	+	0.999494i	$0.489877\pi$
$920$	0.539189	+	2.17009i	0.0177765	+	0.0715456i
$921$	3.20394			0.105573
$922$		−	42.3279i		−	1.39399i
$923$			35.5174i			1.16907i
$924$	−4.68035			−0.153972
$925$	−6.04104	−	11.4063i	−0.198628	−	0.375036i
$926$	−34.9048			−1.14704
$927$		−	2.49693i		−	0.0820099i
$928$		−	10.4969i		−	0.344579i
$929$	−18.5646			−0.609086			−0.304543	−	0.952499i	$-0.598504\pi$
$929$	−18.5646			−0.609086			−0.304543	+	0.952499i	$0.598504\pi$
$930$	−2.15676	−	8.68035i	−0.0707228	−	0.284640i
$931$	27.7009			0.907859
$932$			18.3135i			0.599879i
$933$			12.6537i			0.414263i
$934$	37.7731			1.23597
$935$	−2.15676	+	0.535877i	−0.0705334	+	0.0175250i
$936$	−2.34017			−0.0764909
$937$			22.3279i			0.729420i	0.931121	+	0.364710i	$0.118832\pi$
$937$			22.3279i			0.729420i	−0.931121	+	0.364710i	$0.881168\pi$
$938$		−	11.2039i		−	0.365821i
$939$	33.2183			1.08404
$940$	−14.8371	+	3.68649i	−0.483933	+	0.120240i
$941$	−11.0661			−0.360744			−0.180372	−	0.983598i	$-0.557730\pi$
$941$	−11.0661			−0.360744			−0.180372	+	0.983598i	$0.557730\pi$
$942$		−	2.89496i		−	0.0943229i
$943$		−	0.156755i		−	0.00510466i
$944$	8.83710			0.287623
$945$	−2.34017	−	9.41855i	−0.0761258	−	0.306385i
$946$	−0.796064			−0.0258823
$947$			8.05332i			0.261698i	0.991402	+	0.130849i	$0.0417703\pi$
$947$			8.05332i			0.261698i	−0.991402	+	0.130849i	$0.958230\pi$
$948$		−	11.9155i		−	0.386997i
$949$	−10.9528			−0.355544
$950$	5.47641	+	10.3402i	0.177678	+	0.335480i
$951$	6.99386			0.226791
$952$			4.00000i			0.129641i
$953$		−	39.5897i		−	1.28244i	−0.767359	−	0.641218i	$-0.778430\pi$
$953$		−	39.5897i		−	1.28244i	0.767359	−	0.641218i	$-0.221570\pi$
$954$	0.340173			0.0110135
$955$	−2.35455	−	9.47641i	−0.0761914	−	0.306649i
$956$	−5.33403			−0.172515
$957$			11.3197i			0.365912i
$958$			28.1978i			0.911029i
$959$	−96.7091			−3.12290
$960$	−2.17009	+	0.539189i	−0.0700392	+	0.0174022i
$961$	−15.0000			−0.483871
$962$		−	6.04104i		−	0.194771i
$963$		−	9.57531i		−	0.308560i
$964$	−26.1978			−0.843774
$965$	18.8371	−	4.68035i	0.606388	−	0.150666i
$966$	−4.34017			−0.139643
$967$			48.2655i			1.55211i	0.630663	+	0.776057i	$0.282783\pi$
$967$			48.2655i			1.55211i	−0.630663	+	0.776057i	$0.717217\pi$
$968$			9.83710i			0.316176i
$969$	2.15676			0.0692850
$970$	4.86376	+	19.5753i	0.156166	+	0.628525i
$971$	18.0722			0.579966			0.289983	−	0.957032i	$-0.406350\pi$
$971$	18.0722			0.579966			0.289983	+	0.957032i	$0.406350\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			45.6742i			1.46425i
$974$	−38.2245			−1.22479
$975$	10.3402	−	5.47641i	0.331151	−	0.175385i
$976$	−11.5753			−0.370517
$977$		−	45.9442i		−	1.46989i	−0.678129	−	0.734943i	$-0.737209\pi$
$977$		−	45.9442i		−	1.46989i	0.678129	−	0.734943i	$-0.262791\pi$
$978$			6.52359i			0.208601i
$979$	−5.04718			−0.161309
$980$	−6.38243	−	25.6875i	−0.203879	−	0.820558i
$981$	−9.78539			−0.312423
$982$			11.3074i			0.360833i
$983$		−	1.78992i		−	0.0570896i	−0.999593	−	0.0285448i	$-0.990913\pi$
$983$		−	1.78992i		−	0.0570896i	0.999593	−	0.0285448i	$-0.00908733\pi$
$984$	0.156755			0.00499718
$985$	−49.2183	+	12.2290i	−1.56823	+	0.389648i
$986$	9.67420			0.308089
$987$		−	29.6742i		−	0.944540i
$988$			5.47641i			0.174228i
$989$	−0.738205			−0.0234735
$990$	2.34017	−	0.581449i	0.0743756	−	0.0184797i
$991$	7.68649			0.244169			0.122085	−	0.992520i	$-0.461042\pi$
$991$	7.68649			0.244169			0.122085	+	0.992520i	$0.461042\pi$
$992$		−	4.00000i		−	0.127000i
$993$		−	29.7275i		−	0.943375i
$994$	−65.8720			−2.08933
$995$	−2.93600	−	11.8166i	−0.0930774	−	0.374611i
$996$	−11.4186			−0.361811
$997$		−	21.4908i		−	0.680620i	−0.940313	−	0.340310i	$-0.889468\pi$
$997$		−	21.4908i		−	0.680620i	0.940313	−	0.340310i	$-0.110532\pi$
$998$			2.47027i			0.0781949i
$999$	2.58145			0.0816734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.d.c.139.5	yes	6
3.2	odd	2		2070.2.d.e.829.2		6
5.2	odd	4		3450.2.a.bo.1.1		3
5.3	odd	4		3450.2.a.bt.1.3		3
5.4	even	2	inner	690.2.d.c.139.2	✓	6
15.14	odd	2		2070.2.d.e.829.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.2	✓	6	5.4	even	2	inner
690.2.d.c.139.5	yes	6	1.1	even	1	trivial
2070.2.d.e.829.2		6	3.2	odd	2
2070.2.d.e.829.5		6	15.14	odd	2
3450.2.a.bo.1.1		3	5.2	odd	4
3450.2.a.bt.1.3		3	5.3	odd	4

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.17009 - 0.539189i) q^{10} -1.07838 q^{11} -1.00000i q^{12} +2.34017i q^{13} -4.34017 q^{14} +(2.17009 - 0.539189i) q^{15} +1.00000 q^{16} +0.921622i q^{17} -1.00000i q^{18} -2.34017 q^{19} +(0.539189 + 2.17009i) q^{20} -4.34017 q^{21} -1.07838i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(-4.41855 + 2.34017i) q^{25} -2.34017 q^{26} -1.00000i q^{27} -4.34017i q^{28} -10.4969 q^{29} +(0.539189 + 2.17009i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -1.07838i q^{33} -0.921622 q^{34} +(9.41855 - 2.34017i) q^{35} +1.00000 q^{36} +2.58145i q^{37} -2.34017i q^{38} -2.34017 q^{39} +(-2.17009 + 0.539189i) q^{40} +0.156755 q^{41} -4.34017i q^{42} -0.738205i q^{43} +1.07838 q^{44} +(0.539189 + 2.17009i) q^{45} +1.00000 q^{46} +6.83710i q^{47} +1.00000i q^{48} -11.8371 q^{49} +(-2.34017 - 4.41855i) q^{50} -0.921622 q^{51} -2.34017i q^{52} +0.340173i q^{53} +1.00000 q^{54} +(0.581449 + 2.34017i) q^{55} +4.34017 q^{56} -2.34017i q^{57} -10.4969i q^{58} +8.83710 q^{59} +(-2.17009 + 0.539189i) q^{60} -11.5753 q^{61} -4.00000i q^{62} -4.34017i q^{63} -1.00000 q^{64} +(5.07838 - 1.26180i) q^{65} +1.07838 q^{66} +2.58145i q^{67} -0.921622i q^{68} +1.00000 q^{69} +(2.34017 + 9.41855i) q^{70} +15.1773 q^{71} +1.00000i q^{72} +4.68035i q^{73} -2.58145 q^{74} +(-2.34017 - 4.41855i) q^{75} +2.34017 q^{76} -4.68035i q^{77} -2.34017i q^{78} +11.9155 q^{79} +(-0.539189 - 2.17009i) q^{80} +1.00000 q^{81} +0.156755i q^{82} -11.4186i q^{83} +4.34017 q^{84} +(2.00000 - 0.496928i) q^{85} +0.738205 q^{86} -10.4969i q^{87} +1.07838i q^{88} +4.68035 q^{89} +(-2.17009 + 0.539189i) q^{90} -10.1568 q^{91} +1.00000i q^{92} -4.00000i q^{93} -6.83710 q^{94} +(1.26180 + 5.07838i) q^{95} -1.00000 q^{96} +9.02052i q^{97} -11.8371i q^{98} +1.07838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 4 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} - 4 q^{21} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 28 q^{29} - 24 q^{31} - 12 q^{34} + 28 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{46} - 14 q^{49} + 8 q^{50} - 12 q^{51} + 6 q^{54} + 32 q^{55} + 4 q^{56} - 4 q^{59} - 2 q^{60} - 28 q^{61} - 6 q^{64} + 24 q^{65} + 6 q^{69} - 8 q^{70} + 12 q^{71} - 44 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{79} + 6 q^{81} + 4 q^{84} + 12 q^{85} + 20 q^{86} - 16 q^{89} - 2 q^{90} - 48 q^{91} + 16 q^{94} - 8 q^{95} - 6 q^{96}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 4 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 - 4 * q^21 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 28 * q^29 - 24 * q^31 - 12 * q^34 + 28 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^46 - 14 * q^49 + 8 * q^50 - 12 * q^51 + 6 * q^54 + 32 * q^55 + 4 * q^56 - 4 * q^59 - 2 * q^60 - 28 * q^61 - 6 * q^64 + 24 * q^65 + 6 * q^69 - 8 * q^70 + 12 * q^71 - 44 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^79 + 6 * q^81 + 4 * q^84 + 12 * q^85 + 20 * q^86 - 16 * q^89 - 2 * q^90 - 48 * q^91 + 16 * q^94 - 8 * q^95 - 6 * q^96

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