LMFDB - Embedded newform 804.2.bd.a.23.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			23.10
Character	$\chi$	$=$	804.23
Dual form			804.2.bd.a.35.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38414 - 0.290119i) q^{2} +(1.40173 - 1.01742i) q^{3} +(1.83166 + 0.803128i) q^{4} +(-0.809462 + 0.369669i) q^{5} +(-2.23536 + 1.00158i) q^{6} +(-0.477128 - 0.500397i) q^{7} +(-2.30227 - 1.64304i) q^{8} +(0.929699 - 2.85231i) q^{9} +O(q^{10})$	\(q+(-1.38414 - 0.290119i) q^{2} +(1.40173 - 1.01742i) q^{3} +(1.83166 + 0.803128i) q^{4} +(-0.809462 + 0.369669i) q^{5} +(-2.23536 + 1.00158i) q^{6} +(-0.477128 - 0.500397i) q^{7} +(-2.30227 - 1.64304i) q^{8} +(0.929699 - 2.85231i) q^{9} +(1.22765 - 0.276832i) q^{10} +(-4.02459 - 0.384302i) q^{11} +(3.38462 - 0.737807i) q^{12} +(-5.25964 - 1.01371i) q^{13} +(0.515235 + 0.831041i) q^{14} +(-0.758538 + 1.34174i) q^{15} +(2.70997 + 2.94212i) q^{16} +(-2.70337 + 5.24380i) q^{17} +(-2.11434 + 3.67826i) q^{18} +(-0.345251 + 0.362089i) q^{19} +(-1.77955 + 0.0270071i) q^{20} +(-1.17792 - 0.215981i) q^{21} +(5.45908 + 1.69953i) q^{22} +(1.16552 - 0.466603i) q^{23} +(-4.89882 + 0.0392830i) q^{24} +(-2.75573 + 3.18028i) q^{25} +(6.98596 + 2.92904i) q^{26} +(-1.59882 - 4.94407i) q^{27} +(-0.472054 - 1.29975i) q^{28} +(1.91985 + 1.10842i) q^{29} +(1.43918 - 1.63709i) q^{30} +(0.952117 + 4.94005i) q^{31} +(-2.89740 - 4.85850i) q^{32} +(-6.03239 + 3.55602i) q^{33} +(5.26315 - 6.47383i) q^{34} +(0.571198 + 0.228673i) q^{35} +(3.99366 - 4.47780i) q^{36} +(-4.06524 - 7.04120i) q^{37} +(0.582923 - 0.401016i) q^{38} +(-8.40398 + 3.93033i) q^{39} +(2.47098 + 0.478900i) q^{40} +(-10.3180 + 0.491508i) q^{41} +(1.56774 + 0.640684i) q^{42} +(-3.50400 - 5.45233i) q^{43} +(-7.06304 - 3.93617i) q^{44} +(0.301854 + 2.65252i) q^{45} +(-1.74861 + 0.307703i) q^{46} +(6.05134 + 4.75882i) q^{47} +(6.79203 + 1.36687i) q^{48} +(0.310327 - 6.51456i) q^{49} +(4.73696 - 3.60245i) q^{50} +(1.54577 + 10.1009i) q^{51} +(-8.81975 - 6.08094i) q^{52} +(3.58094 - 5.57205i) q^{53} +(0.778613 + 7.30710i) q^{54} +(3.39982 - 1.17669i) q^{55} +(0.276304 + 1.93599i) q^{56} +(-0.115551 + 0.858817i) q^{57} +(-2.33575 - 2.09119i) q^{58} +(0.625246 + 0.721572i) q^{59} +(-2.46698 + 1.84841i) q^{60} +(7.02345 - 0.670658i) q^{61} +(0.115344 - 7.11393i) q^{62} +(-1.87087 + 0.895697i) q^{63} +(2.60086 + 7.56542i) q^{64} +(4.63222 - 1.12376i) q^{65} +(9.38131 - 3.17191i) q^{66} +(6.84326 + 4.49108i) q^{67} +(-9.16310 + 7.43372i) q^{68} +(1.15901 - 1.83988i) q^{69} +(-0.724273 - 0.482230i) q^{70} +(6.61185 - 3.40864i) q^{71} +(-6.82686 + 5.03924i) q^{72} +(-9.38415 + 0.896078i) q^{73} +(3.58405 + 10.9254i) q^{74} +(-0.627098 + 7.26164i) q^{75} +(-0.923186 + 0.385944i) q^{76} +(1.72794 + 2.19725i) q^{77} +(12.7725 - 3.00196i) q^{78} +(-11.0118 + 3.81121i) q^{79} +(-3.28123 - 1.37974i) q^{80} +(-7.27132 - 5.30358i) q^{81} +(14.4241 + 2.31314i) q^{82} +(-7.64186 + 10.7315i) q^{83} +(-1.98409 - 1.34163i) q^{84} +(0.249803 - 5.24401i) q^{85} +(3.26818 + 8.56334i) q^{86} +(3.81884 - 0.399585i) q^{87} +(8.63425 + 7.49732i) q^{88} +(-7.28704 + 1.04772i) q^{89} +(0.351739 - 3.75901i) q^{90} +(2.00226 + 3.11558i) q^{91} +(2.50958 + 0.0814009i) q^{92} +(6.36074 + 5.95592i) q^{93} +(-6.99524 - 8.34246i) q^{94} +(0.145615 - 0.420726i) q^{95} +(-9.00454 - 3.86243i) q^{96} +(-5.39631 - 9.34668i) q^{97} +(-2.31953 + 8.92701i) q^{98} +(-4.83780 + 11.1221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{14}{33}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.38414	−	0.290119i	−0.978732	−	0.205145i
$2$	−1.38414	−	0.290119i	−0.978732	−	0.205145i
$3$	1.40173	−	1.01742i	0.809290	−	0.587410i
$3$	1.40173	−	1.01742i	0.809290	−	0.587410i
$4$	1.83166	+	0.803128i	0.915831	+	0.401564i
$5$	−0.809462	+	0.369669i	−0.362002	+	0.165321i	−0.588109	−	0.808782i	$-0.700127\pi$
$5$	−0.809462	+	0.369669i	−0.362002	+	0.165321i	0.226107	+	0.974103i	$0.427400\pi$
$6$	−2.23536	+	1.00158i	−0.912582	+	0.408895i
$7$	−0.477128	−	0.500397i	−0.180337	−	0.189132i	0.627361	−	0.778729i	$-0.284135\pi$
$7$	−0.477128	−	0.500397i	−0.180337	−	0.189132i	−0.807698	+	0.589597i	$0.799287\pi$
$8$	−2.30227	−	1.64304i	−0.813974	−	0.580901i
$9$	0.929699	−	2.85231i	0.309900	−	0.950769i
$10$	1.22765	−	0.276832i	0.388218	−	0.0875418i
$11$	−4.02459	−	0.384302i	−1.21346	−	0.115871i	−0.531370	−	0.847140i	$-0.678323\pi$
$11$	−4.02459	−	0.384302i	−1.21346	−	0.115871i	−0.682090	+	0.731269i	$0.738929\pi$
$12$	3.38462	−	0.737807i	0.977055	−	0.212987i
$13$	−5.25964	−	1.01371i	−1.45876	−	0.281153i	−0.602676	−	0.797986i	$-0.705899\pi$
$13$	−5.25964	−	1.01371i	−1.45876	−	0.281153i	−0.856086	+	0.516833i	$0.827111\pi$
$14$	0.515235	+	0.831041i	0.137702	+	0.222105i
$15$	−0.758538	+	1.34174i	−0.195854	+	0.346436i
$16$	2.70997	+	2.94212i	0.677493	+	0.735529i
$17$	−2.70337	+	5.24380i	−0.655663	+	1.27181i	0.293179	+	0.956057i	$0.405287\pi$
$17$	−2.70337	+	5.24380i	−0.655663	+	1.27181i	−0.948842	+	0.315751i	$0.897744\pi$
$18$	−2.11434	+	3.67826i	−0.498354	+	0.866974i
$19$	−0.345251	+	0.362089i	−0.0792060	+	0.0830688i	−0.762144	−	0.647407i	$-0.775853\pi$
$19$	−0.345251	+	0.362089i	−0.0792060	+	0.0830688i	0.682938	+	0.730476i	$0.260702\pi$
$20$	−1.77955	+	0.0270071i	−0.397920	+	0.00603897i
$21$	−1.17792	−	0.215981i	−0.257043	−	0.0471310i
$22$	5.45908	+	1.69953i	1.16388	+	0.362342i
$23$	1.16552	−	0.466603i	0.243027	−	0.0972935i	−0.246951	−	0.969028i	$-0.579429\pi$
$23$	1.16552	−	0.466603i	0.243027	−	0.0972935i	0.489979	+	0.871734i	$0.337005\pi$
$24$	−4.89882	+	0.0392830i	−0.999968	+	0.00801861i
$25$	−2.75573	+	3.18028i	−0.551146	+	0.636056i
$26$	6.98596	+	2.92904i	1.37006	+	0.574432i
$27$	−1.59882	−	4.94407i	−0.307692	−	0.951486i
$28$	−0.472054	−	1.29975i	−0.0892098	−	0.245630i
$29$	1.91985	+	1.10842i	0.356506	+	0.205829i	0.667547	−	0.744568i	$-0.267344\pi$
$29$	1.91985	+	1.10842i	0.356506	+	0.205829i	−0.311041	+	0.950397i	$0.600678\pi$
$30$	1.43918	−	1.63709i	0.262758	−	0.298890i
$31$	0.952117	+	4.94005i	0.171005	+	0.887259i	0.961503	+	0.274794i	$0.0886098\pi$
$31$	0.952117	+	4.94005i	0.171005	+	0.887259i	−0.790498	+	0.612465i	$0.790178\pi$
$32$	−2.89740	−	4.85850i	−0.512194	−	0.858870i
$33$	−6.03239	+	3.55602i	−1.05010	+	0.619024i
$34$	5.26315	−	6.47383i	0.902623	−	1.11025i
$35$	0.571198	+	0.228673i	0.0965501	+	0.0386528i
$36$	3.99366	−	4.47780i	0.665610	−	0.746299i
$37$	−4.06524	−	7.04120i	−0.668321	−	1.15757i	−0.978374	−	0.206846i	$-0.933680\pi$
$37$	−4.06524	−	7.04120i	−0.668321	−	1.15757i	0.310053	−	0.950719i	$-0.399653\pi$
$38$	0.582923	−	0.401016i	0.0945625	−	0.0650534i
$39$	−8.40398	+	3.93033i	−1.34571	+	0.629357i
$40$	2.47098	+	0.478900i	0.390696	+	0.0757208i
$41$	−10.3180	+	0.491508i	−1.61140	+	0.0767606i	−0.833827	−	0.552026i	$-0.813855\pi$
$41$	−10.3180	+	0.491508i	−1.61140	+	0.0767606i	−0.777578	+	0.628787i	$0.783552\pi$
$42$	1.56774	+	0.640684i	0.241908	+	0.0988597i
$43$	−3.50400	−	5.45233i	−0.534355	−	0.831472i	0.464171	−	0.885745i	$-0.346352\pi$
$43$	−3.50400	−	5.45233i	−0.534355	−	0.831472i	−0.998526	+	0.0542733i	$0.982716\pi$
$44$	−7.06304	−	3.93617i	−1.06479	−	0.593400i
$45$	0.301854	+	2.65252i	0.0449977	+	0.395414i
$46$	−1.74861	+	0.307703i	−0.257818	+	0.0453684i
$47$	6.05134	+	4.75882i	0.882678	+	0.694146i	0.952867	−	0.303388i	$-0.0981178\pi$
$47$	6.05134	+	4.75882i	0.882678	+	0.694146i	−0.0701890	+	0.997534i	$0.522360\pi$
$48$	6.79203	+	1.36687i	0.980345	+	0.197290i
$49$	0.310327	−	6.51456i	0.0443324	−	0.930652i
$50$	4.73696	−	3.60245i	0.669908	−	0.509464i
$51$	1.54577	+	10.1009i	0.216451	+	1.41440i
$52$	−8.81975	−	6.08094i	−1.22308	−	0.843275i
$53$	3.58094	−	5.57205i	0.491879	−	0.765379i	−0.503231	−	0.864152i	$-0.667855\pi$
$53$	3.58094	−	5.57205i	0.491879	−	0.765379i	0.995110	+	0.0987728i	$0.0314917\pi$
$54$	0.778613	+	7.30710i	0.105956	+	0.994371i
$55$	3.39982	−	1.17669i	0.458431	−	0.158665i
$56$	0.276304	+	1.93599i	0.0369226	+	0.258707i
$57$	−0.115551	+	0.858817i	−0.0153051	+	0.113753i
$58$	−2.33575	−	2.09119i	−0.306699	−	0.274587i
$59$	0.625246	+	0.721572i	0.0814001	+	0.0939407i	0.794989	−	0.606624i	$-0.207477\pi$
$59$	0.625246	+	0.721572i	0.0814001	+	0.0939407i	−0.713589	+	0.700565i	$0.752931\pi$
$60$	−2.46698	+	1.84841i	−0.318485	+	0.238629i
$61$	7.02345	−	0.670658i	0.899261	−	0.0858690i	0.364823	−	0.931077i	$-0.381129\pi$
$61$	7.02345	−	0.670658i	0.899261	−	0.0858690i	0.534438	+	0.845208i	$0.320523\pi$
$62$	0.115344	−	7.11393i	0.0146487	−	0.903470i
$63$	−1.87087	+	0.895697i	−0.235708	+	0.112847i
$64$	2.60086	+	7.56542i	0.325107	+	0.945677i
$65$	4.63222	−	1.12376i	0.574556	−	0.139386i
$66$	9.38131	−	3.17191i	1.15476	−	0.390435i
$67$	6.84326	+	4.49108i	0.836038	+	0.548672i
$67$	6.84326	+	4.49108i	0.836038	+	0.548672i
$68$	−9.16310	+	7.43372i	−1.11119	+	0.901471i
$69$	1.15901	−	1.83988i	0.139528	−	0.221495i
$70$	−0.724273	−	0.482230i	−0.0865672	−	0.0576375i
$71$	6.61185	−	3.40864i	0.784682	−	0.404532i	−0.0188283	−	0.999823i	$-0.505994\pi$
$71$	6.61185	−	3.40864i	0.784682	−	0.404532i	0.803510	+	0.595291i	$0.202963\pi$
$72$	−6.82686	+	5.03924i	−0.804553	+	0.593880i
$73$	−9.38415	+	0.896078i	−1.09833	+	0.104878i	−0.628449	−	0.777851i	$-0.716310\pi$
$73$	−9.38415	+	0.896078i	−1.09833	+	0.104878i	−0.469883	+	0.882729i	$0.655704\pi$
$74$	3.58405	+	10.9254i	0.416638	+	1.27005i
$75$	−0.627098	+	7.26164i	−0.0724111	+	0.838502i
$76$	−0.923186	+	0.385944i	−0.105897	+	0.0442708i
$77$	1.72794	+	2.19725i	0.196917	+	0.250400i
$78$	12.7725	−	3.00196i	1.44620	−	0.339905i
$79$	−11.0118	+	3.81121i	−1.23892	+	0.428795i	−0.866457	−	0.499252i	$-0.833608\pi$
$79$	−11.0118	+	3.81121i	−1.23892	+	0.428795i	−0.372464	+	0.928047i	$0.621487\pi$
$80$	−3.28123	−	1.37974i	−0.366852	−	0.154260i
$81$	−7.27132	−	5.30358i	−0.807924	−	0.589286i
$82$	14.4241	+	2.31314i	1.59288	+	0.255444i
$83$	−7.64186	+	10.7315i	−0.838803	+	1.17793i	0.143317	+	0.989677i	$0.454223\pi$
$83$	−7.64186	+	10.7315i	−0.838803	+	1.17793i	−0.982120	+	0.188257i	$0.939716\pi$
$84$	−1.98409	−	1.34163i	−0.216482	−	0.146383i
$85$	0.249803	−	5.24401i	0.0270949	−	0.568793i
$86$	3.26818	+	8.56334i	0.352417	+	0.923408i
$87$	3.81884	−	0.399585i	0.409423	−	0.0428400i
$88$	8.63425	+	7.49732i	0.920414	+	0.799216i
$89$	−7.28704	+	1.04772i	−0.772425	+	0.111058i	−0.517247	−	0.855836i	$-0.673043\pi$
$89$	−7.28704	+	1.04772i	−0.772425	+	0.111058i	−0.255178	+	0.966894i	$0.582134\pi$
$90$	0.351739	−	3.75901i	0.0370765	−	0.396235i
$91$	2.00226	+	3.11558i	0.209894	+	0.326602i
$92$	2.50958	+	0.0814009i	0.261642	+	0.00848663i
$93$	6.36074	+	5.95592i	0.659578	+	0.617600i
$94$	−6.99524	−	8.34246i	−0.721504	−	0.860459i
$95$	0.145615	−	0.420726i	0.0149397	−	0.0431655i
$96$	−9.00454	−	3.86243i	−0.919022	−	0.394207i
$97$	−5.39631	−	9.34668i	−0.547912	−	0.949011i	−0.998417	−	0.0562377i	$-0.982090\pi$
$97$	−5.39631	−	9.34668i	−0.547912	−	0.949011i	0.450505	−	0.892774i	$-0.351244\pi$
$98$	−2.31953	+	8.92701i	−0.234308	+	0.901764i
$99$	−4.83780	+	11.1221i	−0.486218	+	1.11781i
$100$	−7.60174	+	3.61200i	−0.760174	+	0.361200i
$101$	−8.31734	−	2.01777i	−0.827606	−	0.200775i	−0.200485	−	0.979697i	$-0.564252\pi$
$101$	−8.31734	−	2.01777i	−0.827606	−	0.200775i	−0.627121	+	0.778922i	$0.715767\pi$
$102$	0.790894	−	14.4294i	0.0783101	−	1.42873i
$103$	0.613959	+	3.18552i	0.0604952	+	0.313879i	0.999554	−	0.0298790i	$-0.00951219\pi$
$103$	0.613959	+	3.18552i	0.0604952	+	0.313879i	−0.939058	+	0.343758i	$0.888300\pi$
$104$	10.4435	+	10.9756i	1.02407	+	1.07625i
$105$	1.03332	−	0.260612i	0.100842	−	0.0254331i
$106$	−6.57306	+	6.67357i	−0.638432	+	0.648194i
$107$	8.51069	−	18.6358i	0.822759	−	1.80159i	0.284897	−	0.958558i	$-0.408041\pi$
$107$	8.51069	−	18.6358i	0.822759	−	1.80159i	0.537862	−	0.843033i	$-0.319232\pi$
$108$	1.04222	−	10.3399i	0.100288	−	0.994958i
$109$	7.74646	−	8.93989i	0.741976	−	0.856286i	−0.251789	−	0.967782i	$-0.581019\pi$
$109$	7.74646	−	8.93989i	0.741976	−	0.856286i	0.993765	+	0.111496i	$0.0355643\pi$
$110$	−5.04719	+	0.642344i	−0.481230	+	0.0612451i
$111$	−12.8622	−	5.73379i	−1.22083	−	0.544228i
$112$	0.179225	−	2.75983i	0.0169351	−	0.260779i
$113$	−10.0851	+	7.18157i	−0.948726	+	0.675585i	−0.945916	−	0.324411i	$-0.894834\pi$
$113$	−10.0851	+	7.18157i	−0.948726	+	0.675585i	−0.00281023	+	0.999996i	$0.500895\pi$
$114$	0.409098	−	1.15520i	0.0383155	−	0.108194i
$115$	−0.770954	+	0.808554i	−0.0718919	+	0.0753980i
$116$	2.62630	+	3.57214i	0.243846	+	0.331665i
$117$	−7.78131	+	14.0597i	−0.719382	+	1.29982i
$118$	−0.656083	−	1.18015i	−0.0603974	−	0.108642i
$119$	3.91384	−	1.14921i	0.358781	−	0.105348i
$120$	3.95089	−	1.84274i	0.360665	−	0.168218i
$121$	5.24841	+	1.01155i	0.477129	+	0.0919590i
$122$	−9.91598	−	1.10935i	−0.897750	−	0.100436i
$123$	−13.9630	+	11.1868i	−1.25900	+	1.00868i
$124$	−2.22354	+	9.81318i	−0.199679	+	0.881249i
$125$	2.30855	−	7.86219i	0.206483	−	0.703215i
$126$	2.84940	−	0.696990i	0.253845	−	0.0620928i
$127$	3.06196	+	3.21129i	0.271705	+	0.284956i	0.845423	−	0.534097i	$-0.179348\pi$
$127$	3.06196	+	3.21129i	0.271705	+	0.284956i	−0.573719	+	0.819052i	$0.694500\pi$
$128$	−1.40507	−	11.2261i	−0.124191	−	0.992258i
$129$	−10.4590	−	4.07765i	−0.920862	−	0.359017i
$130$	−6.73764	+	0.211548i	−0.590930	+	0.0185539i
$131$	−0.708966	+	4.93097i	−0.0619427	+	0.430821i	0.935126	+	0.354314i	$0.115286\pi$
$131$	−0.708966	+	4.93097i	−0.0619427	+	0.430821i	−0.997069	+	0.0765064i	$0.975623\pi$
$132$	−13.9052	+	1.66866i	−1.21030	+	0.145238i
$133$	0.345917			0.0299948
$134$	−8.16906	−	8.20162i	−0.705699	−	0.708512i
$135$	3.12185	+	3.41100i	0.268686	+	0.293572i
$136$	14.8396	−	7.63089i	1.27249	−	0.654343i
$137$	−7.07673	−	1.01748i	−0.604606	−	0.0869293i	−0.166788	−	0.985993i	$-0.553340\pi$
$137$	−7.07673	−	1.01748i	−0.604606	−	0.0869293i	−0.437818	+	0.899064i	$0.644249\pi$
$138$	−2.13801	+	2.21039i	−0.182000	+	0.188161i
$139$	14.0859	−	6.43280i	1.19475	−	0.545623i	0.284096	−	0.958796i	$-0.408307\pi$
$139$	14.0859	−	6.43280i	1.19475	−	0.545623i	0.910653	+	0.413173i	$0.135579\pi$
$140$	0.862588	+	0.877597i	0.0729020	+	0.0741705i
$141$	13.3241	+	0.513818i	1.12209	+	0.0432713i
$142$	−10.1406	+	2.79980i	−0.850981	+	0.234954i
$143$	20.7783	+	6.10107i	1.73757	+	0.510197i
$144$	10.9113	−	4.99439i	0.909273	−	0.416199i
$145$	−1.96379	−	0.187519i	−0.163084	−	0.0155726i
$146$	13.2489	+	1.48223i	1.09649	+	0.122670i
$147$	−6.19308	−	9.44740i	−0.510796	−	0.779208i
$148$	−1.79116	−	16.1620i	−0.147232	−	1.32851i
$149$	5.24559	+	17.8648i	0.429736	+	1.46354i	0.835461	+	0.549550i	$0.185201\pi$
$149$	5.24559	+	17.8648i	0.429736	+	1.46354i	−0.405725	+	0.913995i	$0.632981\pi$
$150$	2.97473	−	9.86917i	0.242886	−	0.805814i
$151$	−0.581576	+	1.12810i	−0.0473280	+	0.0918035i	−0.911313	−	0.411713i	$-0.864931\pi$
$151$	−0.581576	+	1.12810i	−0.0473280	+	0.0918035i	0.863985	+	0.503517i	$0.167961\pi$
$152$	1.38978	−	0.266364i	0.112726	−	0.0216050i
$153$	12.4436	+	12.5860i	1.00601	+	1.01752i
$154$	−1.75424	−	3.54261i	−0.141361	−	0.285471i
$155$	−2.59689	−	3.64682i	−0.208587	−	0.292919i
$156$	−18.5498	+	0.449569i	−1.48517	+	0.0359943i
$157$	−9.88225	+	3.95626i	−0.788689	+	0.315744i	−0.730811	−	0.682580i	$-0.760858\pi$
$157$	−9.88225	+	3.95626i	−0.788689	+	0.315744i	−0.0578785	+	0.998324i	$0.518434\pi$
$158$	16.3475	−	2.08051i	1.30054	−	0.165516i
$159$	−0.649621	−	11.4538i	−0.0515183	−	0.908348i
$160$	4.14138	+	2.86169i	0.327405	+	0.226237i
$161$	−0.789588	−	0.360593i	−0.0622283	−	0.0284187i
$162$	8.52582	+	9.45041i	0.669852	+	0.742495i
$163$	−18.8735	−	10.8966i	−1.47828	−	0.853487i	−0.478585	−	0.878041i	$-0.658850\pi$
$163$	−18.8735	−	10.8966i	−1.47828	−	0.853487i	−0.999699	+	0.0245540i	$0.992183\pi$
$164$	−19.2939	−	7.38641i	−1.50660	−	0.576782i
$165$	3.56844	−	5.10845i	0.277803	−	0.397693i
$166$	13.6908	−	12.6368i	1.06261	−	0.980805i
$167$	1.20694	−	4.97508i	0.0933959	−	0.384983i	−0.905859	−	0.423579i	$-0.860773\pi$
$167$	1.20694	−	4.97508i	0.0933959	−	0.384983i	0.999255	+	0.0385962i	$0.0122886\pi$
$168$	2.35702	+	2.43261i	0.181848	+	0.187680i
$169$	14.5674	+	5.83192i	1.12057	+	0.448609i
$170$	−1.86715	+	7.18595i	−0.143204	+	0.551137i
$171$	0.711809	+	1.32140i	0.0544334	+	0.101050i
$172$	−2.03922	−	12.8010i	−0.155489	−	0.976065i
$173$	3.11426	+	1.07786i	0.236773	+	0.0819480i	0.442878	−	0.896582i	$-0.353958\pi$
$173$	3.11426	+	1.07786i	0.236773	+	0.0819480i	−0.206105	+	0.978530i	$0.566079\pi$
$174$	−5.40172	−	0.554839i	−0.409504	−	0.0420623i
$175$	2.90624	−	0.138441i	0.219691	−	0.0104652i
$176$	−9.77586	−	12.8823i	−0.736883	−	0.971037i
$177$	1.61057	+	0.375310i	0.121058	+	0.0282100i
$178$	10.3902	+	0.663924i	0.778780	+	0.0497632i
$179$	−0.317602	−	2.20897i	−0.0237387	−	0.165106i	0.974504	−	0.224372i	$-0.0720331\pi$
$179$	−0.317602	−	2.20897i	−0.0237387	−	0.165106i	−0.998242	+	0.0592659i	$0.981124\pi$
$180$	−1.57742	+	5.10094i	−0.117574	+	0.380202i
$181$	7.69698	+	6.05297i	0.572112	+	0.449914i	0.861829	−	0.507198i	$-0.169319\pi$
$181$	7.69698	+	6.05297i	0.572112	+	0.449914i	−0.289717	+	0.957112i	$0.593561\pi$
$182$	−1.86751	−	4.89328i	−0.138429	−	0.362714i
$183$	9.16264	−	8.08591i	0.677322	−	0.597727i
$184$	−3.44998	−	0.840746i	−0.254336	−	0.0619806i
$185$	5.89357	+	4.19679i	0.433304	+	0.308554i
$186$	−7.07620	−	10.0892i	−0.518852	−	0.739773i
$187$	12.8951	−	20.0652i	0.942986	−	1.46732i
$188$	7.26206	+	13.5766i	0.529640	+	0.990172i
$189$	−1.71116	+	3.15899i	−0.124468	+	0.229783i
$190$	−0.323611	+	0.540096i	−0.0234772	+	0.0391827i
$191$	17.2737	−	13.5842i	1.24988	−	0.982917i	0.249988	−	0.968249i	$-0.419573\pi$
$191$	17.2737	−	13.5842i	1.24988	−	0.982917i	0.999892	−	0.0146676i	$-0.00466901\pi$
$192$	11.3429	+	7.95851i	0.818606	+	0.574356i
$193$	−8.98633	−	10.3708i	−0.646850	−	0.746505i	0.333720	−	0.942672i	$-0.391696\pi$
$193$	−8.98633	−	10.3708i	−0.646850	−	0.746505i	−0.980570	+	0.196167i	$0.937150\pi$
$194$	4.75757	+	14.5026i	0.341574	+	1.04123i
$195$	5.34978	−	6.28814i	0.383106	−	0.450303i
$196$	5.80044	−	11.6832i	0.414317	−	0.834518i
$197$	−2.04374	−	3.96430i	−0.145610	−	0.282444i	0.804740	−	0.593628i	$-0.202305\pi$
$197$	−2.04374	−	3.96430i	−0.145610	−	0.282444i	−0.950350	+	0.311184i	$0.899275\pi$
$198$	9.92290	−	13.9909i	0.705190	−	0.994292i
$199$	18.8658	−	4.57680i	1.33736	−	0.324441i	0.497606	−	0.867403i	$-0.334213\pi$
$199$	18.8658	−	4.57680i	1.33736	−	0.324441i	0.839757	+	0.542962i	$0.182697\pi$
$200$	11.5697	−	2.79409i	0.818105	−	0.197572i
$201$	14.1617	−	0.667215i	0.998892	−	0.0470617i
$202$	10.9269	+	5.20588i	0.768816	+	0.366284i
$203$	−0.361360	−	1.48955i	−0.0253625	−	0.104546i
$204$	−5.28095	+	19.7428i	−0.369741	+	1.38227i
$205$	8.17035	−	4.21211i	0.570642	−	0.294186i
$206$	0.0743777	−	4.58732i	0.00518214	−	0.319613i
$207$	−0.247315	−	3.75822i	−0.0171896	−	0.261214i
$208$	−11.2710	−	18.2216i	−0.781505	−	1.26344i
$209$	1.52864	−	1.32458i	0.105739	−	0.0916229i
$210$	−1.50587	+	0.0609357i	−0.103915	+	0.00420496i
$211$	4.65497	+	5.91928i	0.320461	+	0.407500i	0.919418	−	0.393282i	$-0.128660\pi$
$211$	4.65497	+	5.91928i	0.320461	+	0.407500i	−0.598957	+	0.800781i	$0.704418\pi$
$212$	11.0341	−	7.33016i	0.757827	−	0.503437i
$213$	5.80000	−	11.5050i	0.397409	−	0.788313i
$214$	−17.1865	+	23.3254i	−1.17485	+	1.59449i
$215$	4.85191	+	3.11813i	0.330897	+	0.212655i
$216$	−4.44238	+	14.0095i	−0.302266	+	0.953224i
$217$	2.01771	−	2.83347i	0.136971	−	0.192349i
$218$	−13.3158	+	10.1266i	−0.901858	+	0.685861i
$219$	−12.2424	+	10.8037i	−0.827262	+	0.730047i
$220$	7.17235	+	0.575192i	0.483559	+	0.0387795i
$221$	19.5345	−	24.8401i	1.31403	−	1.67092i
$222$	16.1396	+	11.6679i	1.08322	+	0.783100i
$223$	−3.21469	+	0.462203i	−0.215272	+	0.0309514i	−0.249107	−	0.968476i	$-0.580137\pi$
$223$	−3.21469	+	0.462203i	−0.215272	+	0.0309514i	0.0338351	+	0.999427i	$0.489228\pi$
$224$	−1.04875	+	3.76798i	−0.0700725	+	0.251759i
$225$	6.50914	+	10.8169i	0.433943	+	0.721126i
$226$	16.0427	−	7.01438i	1.06714	−	0.466590i
$227$	−0.578412	−	12.1424i	−0.0383905	−	0.805917i	−0.933176	−	0.359420i	$-0.882975\pi$
$227$	−0.578412	−	12.1424i	−0.0383905	−	0.805917i	0.894785	−	0.446497i	$-0.147329\pi$
$228$	−0.901391	+	1.48026i	−0.0596961	+	0.0980326i
$229$	−5.44482	+	15.7318i	−0.359804	+	1.03958i	0.609302	+	0.792938i	$0.291450\pi$
$229$	−5.44482	+	15.7318i	−0.359804	+	1.03958i	−0.969106	+	0.246646i	$0.920671\pi$
$230$	1.30168	−	0.895479i	0.0858304	−	0.0590462i
$231$	4.65764	+	1.32191i	0.306451	+	0.0869755i
$232$	−2.59881	−	5.70626i	−0.170620	−	0.374635i
$233$	10.2135	−	25.5122i	0.669111	−	1.67136i	−0.0698057	−	0.997561i	$-0.522238\pi$
$233$	10.2135	−	25.5122i	0.669111	−	1.67136i	0.738916	−	0.673797i	$-0.235338\pi$
$234$	14.8494	−	17.2030i	0.970733	−	1.12459i
$235$	−6.65752	−	1.61510i	−0.434288	−	0.105357i
$236$	0.565724	+	1.82383i	0.0368255	+	0.118721i
$237$	−11.5579	+	16.5459i	−0.750768	+	1.07477i
$238$	−5.75068	+	0.455179i	−0.372762	+	0.0295049i
$239$	−11.9692	+	20.7312i	−0.774223	+	1.34099i	0.161008	+	0.986953i	$0.448526\pi$
$239$	−11.9692	+	20.7312i	−0.774223	+	1.34099i	−0.935230	+	0.354040i	$0.884808\pi$
$240$	−6.00318	+	1.40437i	−0.387504	+	0.0906520i
$241$	−2.11506	+	4.63133i	−0.136243	+	0.298330i	−0.965440	−	0.260626i	$-0.916071\pi$
$241$	−2.11506	+	4.63133i	−0.136243	+	0.298330i	0.829197	+	0.558957i	$0.188798\pi$
$242$	−6.97105	−	2.92278i	−0.448116	−	0.187884i
$243$	−15.5884	−	0.0361743i	−0.999997	−	0.00232058i
$244$	13.4032	+	4.41231i	0.858053	+	0.282469i
$245$	2.15703	+	5.38801i	0.137808	+	0.344227i
$246$	22.5722	−	11.4331i	1.43915	−	0.728945i
$247$	2.18295	−	1.55447i	0.138898	−	0.0989087i
$248$	5.92466	−	12.9377i	0.376216	−	0.821543i
$249$	0.206639	+	22.8177i	0.0130952	+	1.44601i
$250$	−5.47631	+	10.2126i	−0.346352	+	0.645900i
$251$	1.81520	+	0.935802i	0.114575	+	0.0590673i	0.514561	−	0.857454i	$-0.327955\pi$
$251$	1.81520	+	0.935802i	0.114575	+	0.0590673i	−0.399987	+	0.916521i	$0.630985\pi$
$252$	−4.14616	+	0.138064i	−0.261184	+	0.00869721i
$253$	−4.87005	+	1.42998i	−0.306177	+	0.0899018i
$254$	−3.30651	−	5.33319i	−0.207469	−	0.334634i
$255$	−4.98522	−	7.60484i	−0.312187	−	0.476234i
$256$	−1.31211	+	15.9461i	−0.0820067	+	0.996632i
$257$	−0.422291	+	4.42243i	−0.0263418	+	0.275864i	0.972699	+	0.232071i	$0.0745502\pi$
$257$	−0.422291	+	4.42243i	−0.0263418	+	0.275864i	−0.999041	+	0.0437927i	$0.986056\pi$
$258$	13.2937	+	8.67836i	0.827627	+	0.540291i
$259$	−1.58376	+	5.39378i	−0.0984099	+	0.335153i
$260$	9.38719	+	1.66191i	0.582169	+	0.103067i
$261$	4.94644	−	4.44549i	0.306177	−	0.275169i
$262$	2.41187	−	6.61944i	0.149006	−	0.408951i
$263$	−10.7879	−	23.6221i	−0.665207	−	1.45660i	−0.877589	−	0.479414i	$-0.840849\pi$
$263$	−10.7879	−	23.6221i	−0.665207	−	1.45660i	0.212381	−	0.977187i	$-0.431878\pi$
$264$	19.7308	+	1.72453i	1.21435	+	0.106137i
$265$	−0.838820	+	5.83412i	−0.0515283	+	0.358387i
$266$	−0.478796	−	0.100357i	−0.0293569	−	0.00615329i
$267$	−9.14850	+	8.88263i	−0.559879	+	0.543608i
$268$	8.92764	+	13.7221i	0.545342	+	0.838214i
$269$		−	14.8779i		−	0.907120i	−0.891226	−	0.453560i	$-0.850154\pi$
$269$		−	14.8779i		−	0.907120i	0.891226	−	0.453560i	$-0.149846\pi$
$270$	−3.33147	−	5.62699i	−0.202747	−	0.342448i
$271$	−6.82600	−	0.981430i	−0.414650	−	0.0596176i	−0.0681669	−	0.997674i	$-0.521715\pi$
$271$	−6.82600	−	0.981430i	−0.414650	−	0.0596176i	−0.346483	+	0.938056i	$0.612624\pi$
$272$	−22.7539	+	6.25693i	−1.37966	+	0.379382i
$273$	5.97650	+	2.33006i	0.361714	+	0.141022i
$274$	9.49997	+	3.46143i	0.573914	+	0.209112i
$275$	12.3129	−	11.7403i	0.742494	−	0.707967i
$276$	3.60057	−	2.43920i	0.216729	−	0.146823i
$277$	−6.16135	−	1.80914i	−0.370200	−	0.108700i	0.0913404	−	0.995820i	$-0.470885\pi$
$277$	−6.16135	−	1.80914i	−0.370200	−	0.108700i	−0.461540	+	0.887119i	$0.652703\pi$
$278$	−21.3630	+	4.81729i	−1.28127	+	0.288922i
$279$	14.9757	+	1.87703i	0.896573	+	0.112375i
$280$	−0.939331	−	1.46497i	−0.0561358	−	0.0875485i
$281$	0.120921	−	0.627400i	0.00721356	−	0.0374275i	−0.978144	−	0.207931i	$-0.933327\pi$
$281$	0.120921	−	0.627400i	0.00721356	−	0.0374275i	0.985357	+	0.170503i	$0.0545393\pi$
$282$	−18.2933	−	4.57676i	−1.08935	−	0.272542i
$283$	1.40240	+	4.77613i	0.0833639	+	0.283911i	0.990616	−	0.136676i	$-0.0436421\pi$
$283$	1.40240	+	4.77613i	0.0833639	+	0.283911i	−0.907252	+	0.420588i	$0.861824\pi$
$284$	14.8482	−	0.933326i	0.881081	−	0.0553827i
$285$	−0.223944	−	0.737896i	−0.0132653	−	0.0437092i
$286$	−26.9900	−	14.4729i	−1.59595	−	0.855800i
$287$	5.16896	+	4.92860i	0.305114	+	0.290926i
$288$	−16.5517	+	3.74734i	−0.975316	+	0.220814i
$289$	−10.3283	−	14.5040i	−0.607546	−	0.853179i
$290$	2.66375	+	0.829285i	0.156421	+	0.0486973i
$291$	−17.0737	−	7.61120i	−1.00088	−	0.446176i
$292$	−17.9083	−	5.89536i	−1.04800	−	0.345000i
$293$	−8.51381	−	7.37726i	−0.497382	−	0.430984i	0.369698	−	0.929152i	$-0.379461\pi$
$293$	−8.51381	−	7.37726i	−0.497382	−	0.430984i	−0.867081	+	0.498168i	$0.834006\pi$
$294$	5.83119	+	14.8732i	0.340082	+	0.867423i
$295$	−0.772856	−	0.352951i	−0.0449974	−	0.0205496i
$296$	−2.20969	+	22.8900i	−0.128436	+	1.33046i
$297$	4.53457	+	20.5123i	0.263122	+	1.19024i
$298$	−2.07768	−	26.2492i	−0.120357	−	1.52058i
$299$	−6.60321	+	1.27266i	−0.381874	+	0.0736001i
$300$	−6.98066	+	12.7972i	−0.403029	+	0.738849i
$301$	−1.05647	+	4.35485i	−0.0608942	+	0.251009i
$302$	1.13226	−	1.39272i	0.0651544	−	0.0801419i
$303$	−13.7116	+	5.63389i	−0.787711	+	0.323659i
$304$	−2.00093	−	0.0345185i	−0.114761	−	0.00197977i
$305$	−5.43729	+	3.13922i	−0.311339	+	0.179751i
$306$	−13.5722	−	21.0308i	−0.775872	−	1.20225i
$307$	2.03072	+	0.702839i	0.115899	+	0.0401131i	0.384402	−	0.923166i	$-0.374408\pi$
$307$	2.03072	+	0.702839i	0.115899	+	0.0401131i	−0.268503	+	0.963279i	$0.586529\pi$
$308$	1.40033	+	5.41238i	0.0797910	+	0.308399i
$309$	4.10163	+	3.84059i	0.233334	+	0.218483i
$310$	2.53643	+	5.80109i	0.144060	+	0.329480i
$311$	2.38373	−	1.53193i	0.135169	−	0.0868679i	−0.471309	−	0.881968i	$-0.656218\pi$
$311$	2.38373	−	1.53193i	0.135169	−	0.0868679i	0.606478	+	0.795100i	$0.292582\pi$
$312$	25.8059	+	4.75938i	1.46097	+	0.269447i
$313$	1.73431	+	12.0624i	0.0980292	+	0.681808i	0.978278	+	0.207296i	$0.0664664\pi$
$313$	1.73431	+	12.0624i	0.0980292	+	0.681808i	−0.880249	+	0.474512i	$0.842625\pi$
$314$	14.8262	−	2.60897i	0.836688	−	0.147232i
$315$	1.18329	−	1.41664i	0.0666708	−	0.0798184i
$316$	−23.2307	−	1.86301i	−1.30683	−	0.104802i
$317$	5.38121	+	0.256339i	0.302239	+	0.0143974i	0.198154	−	0.980171i	$-0.436506\pi$
$317$	5.38121	+	0.256339i	0.302239	+	0.0143974i	0.104085	+	0.994568i	$0.466809\pi$
$318$	−2.42381	+	16.0421i	−0.135921	+	0.899598i
$319$	−7.30062	−	5.19875i	−0.408756	−	0.291074i
$320$	−4.90199	−	5.16246i	−0.274030	−	0.288590i
$321$	−7.03081	−	34.7814i	−0.392422	−	1.94131i
$322$	0.988282	+	0.728184i	0.0550748	+	0.0405801i
$323$	−0.965381	−	2.78929i	−0.0537152	−	0.155200i
$324$	−9.05915	−	15.5542i	−0.503286	−	0.864120i
$325$	17.7180	−	13.9336i	0.982820	−	0.772899i
$326$	22.9621	+	20.5579i	1.27175	+	1.13860i
$327$	1.76280	−	20.4127i	0.0974829	−	1.12883i
$328$	24.5624	+	15.8213i	1.35623	+	0.873586i
$329$	−0.505959	−	5.29864i	−0.0278944	−	0.292123i
$330$	−6.42126	+	6.03552i	−0.353479	+	0.332244i
$331$	−6.72771	−	13.0499i	−0.369789	−	0.717290i	0.628372	−	0.777913i	$-0.283722\pi$
$331$	−6.72771	−	13.0499i	−0.369789	−	0.717290i	−0.998161	+	0.0606231i	$0.980691\pi$
$332$	−22.6161	+	13.5191i	−1.24122	+	0.741956i
$333$	−23.8631	+	5.04911i	−1.30769	+	0.276690i
$334$	−3.11394	+	6.53603i	−0.170387	+	0.357636i
$335$	−7.19957	−	1.10561i	−0.393355	−	0.0604062i
$336$	−2.55669	−	4.05088i	−0.139479	−	0.220994i
$337$	7.78653	+	32.0965i	0.424159	+	1.74841i	0.636562	+	0.771225i	$0.280356\pi$
$337$	7.78653	+	32.0965i	0.424159	+	1.74841i	−0.212403	+	0.977182i	$0.568129\pi$
$338$	−18.4714	−	12.2985i	−1.00471	−	0.668948i
$339$	−6.82990	+	20.3274i	−0.370949	+	1.10404i
$340$	4.66916	−	9.40463i	0.253221	−	0.510038i
$341$	−1.93341	−	20.2476i	−0.104700	−	1.09647i
$342$	−0.601878	−	2.03550i	−0.0325459	−	0.110067i
$343$	−7.06567	+	6.12244i	−0.381510	+	0.330580i
$344$	−0.891243	+	18.3099i	−0.0480526	+	0.987204i
$345$	−0.258029	+	1.91776i	−0.0138918	+	0.103249i
$346$	−3.99786	−	2.39541i	−0.214926	−	0.128778i
$347$	7.02829	+	20.3069i	0.377298	+	1.09013i	0.960614	+	0.277886i	$0.0896338\pi$
$347$	7.02829	+	20.3069i	0.377298	+	1.09013i	−0.583316	+	0.812245i	$0.698245\pi$
$348$	7.31575	+	2.33511i	0.392165	+	0.125175i
$349$	17.8874	+	11.4956i	0.957492	+	0.615343i	0.923303	−	0.384073i	$-0.125479\pi$
$349$	17.8874	+	11.4956i	0.957492	+	0.615343i	0.0341891	+	0.999415i	$0.489115\pi$
$350$	−4.06279	−	0.651534i	−0.217165	−	0.0348259i
$351$	3.39734	+	27.6248i	0.181337	+	1.47450i
$352$	9.79373	+	20.6670i	0.522008	+	1.10155i
$353$	4.20321	+	0.200224i	0.223714	+	0.0106568i	0.159140	−	0.987256i	$-0.449128\pi$
$353$	4.20321	+	0.200224i	0.223714	+	0.0106568i	0.0645745	+	0.997913i	$0.479431\pi$
$354$	−2.12036	−	0.986737i	−0.112696	−	0.0524445i
$355$	−4.09197	+	5.20336i	−0.217179	+	0.276166i
$356$	−14.1888	−	3.93336i	−0.752007	−	0.208468i
$357$	4.31691	−	5.59290i	0.228475	−	0.296008i
$358$	−0.201260	+	3.14966i	−0.0106369	+	0.166465i
$359$	16.4525	−	10.5734i	0.868328	−	0.558041i	−0.0289128	−	0.999582i	$-0.509205\pi$
$359$	16.4525	−	10.5734i	0.868328	−	0.558041i	0.897241	+	0.441541i	$0.145568\pi$
$360$	3.66324	−	6.60275i	0.193069	−	0.347996i
$361$	0.892146	+	18.7285i	0.0469551	+	0.985708i
$362$	−8.89758	−	10.6112i	−0.467647	−	0.557711i
$363$	8.38604	−	3.92194i	0.440153	−	0.205848i
$364$	1.16526	+	7.31476i	0.0610761	+	0.383398i
$365$	7.26486	−	4.19437i	0.380260	−	0.219543i
$366$	−15.0282	+	8.53373i	−0.785537	+	0.446065i
$367$	−8.64121	+	21.5847i	−0.451067	+	1.12671i	0.512367	+	0.858767i	$0.328769\pi$
$367$	−8.64121	+	21.5847i	−0.451067	+	1.12671i	−0.963434	+	0.267945i	$0.913655\pi$
$368$	4.53132	+	2.16461i	0.236212	+	0.112838i
$369$	−8.19072	+	29.8871i	−0.426392	+	1.55586i
$370$	−6.93992	−	7.51876i	−0.360790	−	0.390882i
$371$	−4.49680	+	0.866687i	−0.233462	+	0.0449962i
$372$	6.86736	+	16.0177i	0.356056	+	0.830480i
$373$	15.6164	−	27.0485i	0.808588	−	1.40052i	−0.105253	−	0.994445i	$-0.533565\pi$
$373$	15.6164	−	27.0485i	0.808588	−	1.40052i	0.913842	−	0.406071i	$-0.133101\pi$
$374$	−23.6699	+	24.0319i	−1.22394	+	1.24266i
$375$	−4.76321	−	13.3694i	−0.245971	−	0.690395i
$376$	−6.11286	−	20.8986i	−0.315247	−	1.07777i
$377$	−8.97408	−	7.77608i	−0.462189	−	0.400489i
$378$	3.28496	−	3.87604i	0.168960	−	0.199362i
$379$	4.46815	+	11.1609i	0.229513	+	0.573297i	0.997763	−	0.0668538i	$-0.0212961\pi$
$379$	4.46815	+	11.1609i	0.229513	+	0.573297i	−0.768249	+	0.640151i	$0.778872\pi$
$380$	0.604613	−	0.653680i	0.0310160	−	0.0335331i
$381$	7.55928	+	1.38605i	0.387274	+	0.0710097i
$382$	−27.8502	+	13.7909i	−1.42494	+	0.705605i
$383$	−21.4967	−	20.4971i	−1.09843	−	1.04735i	−0.998629	−	0.0523432i	$-0.983331\pi$
$383$	−21.4967	−	20.4971i	−1.09843	−	1.04735i	−0.0998006	−	0.995007i	$-0.531820\pi$
$384$	−13.3912	−	14.3065i	−0.683369	−	0.730073i
$385$	−2.21096	−	1.13983i	−0.112681	−	0.0580910i
$386$	9.42954	+	16.9617i	0.479951	+	0.863326i
$387$	−18.8094	+	4.92546i	−0.956134	+	0.250375i
$388$	−2.37763	−	21.4539i	−0.120706	−	1.08916i
$389$	−4.90290	+	25.4386i	−0.248587	+	1.28979i	0.616176	+	0.787609i	$0.288681\pi$
$389$	−4.90290	+	25.4386i	−0.248587	+	1.28979i	−0.864762	+	0.502181i	$0.832531\pi$
$390$	−9.22913	+	7.15157i	−0.467335	+	0.362134i
$391$	−0.704050	+	7.37315i	−0.0356053	+	0.372876i
$392$	−11.4181	+	14.4884i	−0.576703	+	0.731774i
$393$	4.02310	+	7.63321i	0.202939	+	0.385044i
$394$	1.67869	+	6.08005i	0.0845712	+	0.306309i
$395$	7.50473	−	7.15574i	0.377604	−	0.360044i
$396$	−17.7937	+	16.4865i	−0.894166	+	0.828479i
$397$	−6.01411	−	13.1691i	−0.301840	−	0.660937i	0.696559	−	0.717499i	$-0.254713\pi$
$397$	−6.01411	−	13.1691i	−0.301840	−	0.660937i	−0.998399	+	0.0565625i	$0.981986\pi$
$398$	−27.4407	+	0.861578i	−1.37548	+	0.0431870i
$399$	0.484882	−	0.351944i	0.0242745	−	0.0176192i
$400$	−16.8247	+	0.510793i	−0.841236	+	0.0255397i
$401$		−	13.7389i		−	0.686089i	−0.939319	−	0.343045i	$-0.888542\pi$
$401$		−	13.7389i		−	0.686089i	0.939319	−	0.343045i	$-0.111458\pi$
$402$	−19.7953	−	3.18507i	−0.987302	−	0.158857i
$403$		−	26.9481i		−	1.34238i
$404$	−13.6140	−	10.3758i	−0.677324	−	0.516213i
$405$	7.84642	+	1.60506i	0.389892	+	0.0797562i
$406$	0.0680256	+	2.16657i	0.00337605	+	0.107525i
$407$	13.6550	+	29.9002i	0.676851	+	1.48210i
$408$	13.0373	−	25.7946i	0.645444	−	1.27703i
$409$	−26.0160	+	24.8063i	−1.28641	+	1.22659i	−0.326854	+	0.945075i	$0.605989\pi$
$409$	−26.0160	+	24.8063i	−1.28641	+	1.22659i	−0.959557	+	0.281515i	$0.909163\pi$
$410$	−12.5309	+	3.45976i	−0.618856	+	0.170865i
$411$	−10.9549	+	5.77380i	−0.540365	+	0.284801i
$412$	−1.43382	+	6.32789i	−0.0706390	+	0.311753i
$413$	0.0627505	−	0.657153i	0.00308775	−	0.0323364i
$414$	−0.748013	+	5.27363i	−0.0367628	+	0.259185i
$415$	2.21870	−	11.5117i	0.108912	−	0.565087i
$416$	10.3142	+	28.4911i	0.505694	+	1.39689i
$417$	13.1997	−	23.3484i	0.646393	−	1.14337i
$418$	−2.50014	+	1.38991i	−0.122286	+	0.0679825i
$419$	5.83914	+	3.01029i	0.285261	+	0.147062i	0.594919	−	0.803786i	$-0.297184\pi$
$419$	5.83914	+	3.01029i	0.285261	+	0.147062i	−0.309658	+	0.950848i	$0.600215\pi$
$420$	2.10200	+	0.352538i	0.102567	+	0.0172021i
$421$	−5.62792	−	5.36621i	−0.274288	−	0.261533i	0.540432	−	0.841388i	$-0.318261\pi$
$421$	−5.62792	−	5.36621i	−0.274288	−	0.261533i	−0.814720	+	0.579855i	$0.803109\pi$
$422$	−4.72582	−	9.54358i	−0.230049	−	0.464574i
$423$	19.1996	−	12.8360i	0.933514	−	0.624108i
$424$	−17.3993	+	6.94472i	−0.844987	+	0.337265i
$425$	−9.22701	−	23.0480i	−0.447576	−	1.11799i
$426$	−11.3658	+	14.2419i	−0.550675	+	0.690020i
$427$	−3.68668	−	3.19453i	−0.178411	−	0.154594i
$428$	30.5556	−	27.2993i	1.47696	−	1.31956i
$429$	35.3330	−	12.5883i	1.70589	−	0.607769i
$430$	−5.81107	−	5.72355i	−0.280235	−	0.276014i
$431$	−10.4268	+	18.0597i	−0.502239	+	0.869904i	0.497757	+	0.867316i	$0.334157\pi$
$431$	−10.4268	+	18.0597i	−0.502239	+	0.869904i	−0.999997	+	0.00258764i	$0.999176\pi$
$432$	10.2133	−	18.1022i	0.491386	−	0.870942i
$433$	23.4412	−	4.51791i	1.12651	−	0.217117i	0.408236	−	0.912877i	$-0.366144\pi$
$433$	23.4412	−	4.51791i	1.12651	−	0.217117i	0.718275	+	0.695760i	$0.244932\pi$
$434$	−3.61482	+	3.33653i	−0.173517	+	0.160159i
$435$	−2.94349	+	1.73516i	−0.141130	+	0.0831944i
$436$	21.3688	−	10.1535i	1.02338	−	0.486262i
$437$	−0.233445	+	0.583116i	−0.0111672	+	0.0278942i
$438$	20.0794	−	11.4021i	0.959433	−	0.544812i
$439$	−24.3437	+	14.0548i	−1.16186	+	0.670800i	−0.951749	−	0.306878i	$-0.900716\pi$
$439$	−24.3437	+	14.0548i	−1.16186	+	0.670800i	−0.210111	+	0.977678i	$0.567382\pi$
$440$	−9.76062	−	2.87698i	−0.465319	−	0.137155i
$441$	−18.2930	−	6.94173i	−0.871097	−	0.330559i
$442$	−34.2449	+	28.7147i	−1.62886	+	1.36582i
$443$	−0.454120	−	9.53315i	−0.0215759	−	0.452934i	−0.983644	−	0.180124i	$-0.942350\pi$
$443$	−0.454120	−	9.53315i	−0.0215759	−	0.452934i	0.962068	−	0.272810i	$-0.0879529\pi$
$444$	−18.9543	−	20.8324i	−0.899532	−	0.988662i
$445$	5.51127	−	3.54188i	0.261259	−	0.167901i
$446$	4.58366	+	0.292891i	0.217043	+	0.0138688i
$447$	25.5290	+	19.7047i	1.20748	+	0.932001i
$448$	2.54477	−	4.91113i	0.120229	−	0.232029i
$449$	8.74427	−	11.1192i	0.412668	−	0.524750i	−0.534638	−	0.845081i	$-0.679552\pi$
$449$	8.74427	−	11.1192i	0.412668	−	0.524750i	0.947305	+	0.320332i	$0.103794\pi$
$450$	−5.87135	−	16.8605i	−0.276778	−	0.794810i
$451$	41.7147	+	1.98712i	1.96427	+	0.0935696i
$452$	−24.2402	+	5.05458i	−1.14016	+	0.237747i
$453$	0.332542	+	2.17300i	0.0156242	+	0.102097i
$454$	−2.72213	+	16.9745i	−0.127756	+	0.796652i
$455$	−2.77249	−	1.78177i	−0.129976	−	0.0835307i
$456$	1.67710	−	1.78737i	0.0785373	−	0.0837013i
$457$	4.74900	+	13.7213i	0.222149	+	0.641857i	0.999912	+	0.0132990i	$0.00423333\pi$
$457$	4.74900	+	13.7213i	0.222149	+	0.641857i	−0.777763	+	0.628558i	$0.783645\pi$
$458$	12.1004	−	20.1953i	0.565417	−	0.943662i
$459$	30.2479	+	4.98175i	1.41185	+	0.232528i
$460$	−2.06150	+	0.861822i	−0.0961179	+	0.0401827i
$461$	−22.5226	+	19.5159i	−1.04898	+	0.908947i	−0.995974	−	0.0896476i	$-0.971426\pi$
$461$	−22.5226	+	19.5159i	−1.04898	+	0.908947i	−0.0530067	+	0.998594i	$0.516880\pi$
$462$	−6.06330	−	3.18098i	−0.282090	−	0.147992i
$463$	−2.80712	−	29.3975i	−0.130458	−	1.36622i	−0.789332	−	0.613966i	$-0.789573\pi$
$463$	−2.80712	−	29.3975i	−0.130458	−	1.36622i	0.658874	−	0.752253i	$-0.271033\pi$
$464$	1.94162	+	8.65221i	0.0901372	+	0.401669i
$465$	−7.35049	−	2.46972i	−0.340871	−	0.114531i
$466$	−21.5385	+	32.3492i	−0.997751	+	1.49855i
$467$	1.68804	+	6.95819i	0.0781132	+	0.321987i	0.997440	−	0.0715079i	$-0.0227811\pi$
$467$	1.68804	+	6.95819i	0.0781132	+	0.321987i	−0.919327	+	0.393495i	$0.871266\pi$
$468$	−25.5444	+	19.5032i	−1.18079	+	0.901535i
$469$	−1.01779	−	5.56717i	−0.0469971	−	0.257068i
$470$	8.74633	+	4.16698i	0.403438	+	0.192209i
$471$	−9.82707	+	15.6000i	−0.452807	+	0.718812i
$472$	−0.253912	−	2.68855i	−0.0116873	−	0.123751i
$473$	12.0068	+	23.2900i	0.552074	+	1.07087i
$474$	20.7980	−	19.5486i	0.955285	−	0.897899i
$475$	−0.200126	−	2.09581i	−0.00918241	−	0.0961625i
$476$	8.09178	+	1.03835i	0.370886	+	0.0475928i
$477$	−12.5640	−	15.3943i	−0.575266	−	0.704855i
$478$	22.5815	−	25.2224i	1.03285	−	1.15364i
$479$	8.58684	−	6.75276i	0.392343	−	0.308542i	−0.402428	−	0.915452i	$-0.631834\pi$
$479$	8.58684	−	6.75276i	0.392343	−	0.308542i	0.794771	+	0.606910i	$0.207591\pi$
$480$	8.71665	−	0.202209i	0.397859	−	0.00922954i
$481$	14.2439	+	41.1552i	0.649468	+	1.87651i
$482$	4.27116	−	5.79677i	0.194546	−	0.264036i
$483$	−1.47367	+	0.297891i	−0.0670541	+	0.0135545i
$484$	8.80092	+	6.06796i	0.400042	+	0.275816i
$485$	7.82328	+	5.57093i	0.355237	+	0.252963i
$486$	21.5660	+	4.57256i	0.978253	+	0.207416i
$487$	24.7166	+	1.17740i	1.12001	+	0.0533529i	0.599408	−	0.800444i	$-0.295403\pi$
$487$	24.7166	+	1.17740i	1.12001	+	0.0533529i	0.520607	+	0.853797i	$0.325706\pi$
$488$	−17.2718	−	9.99576i	−0.781856	−	0.452487i
$489$	−37.5420	+	3.92820i	−1.69771	+	0.177640i
$490$	−1.42246	−	8.08353i	−0.0642604	−	0.365177i
$491$	−3.73295	−	25.9632i	−0.168466	−	1.17170i	−0.882057	−	0.471142i	$-0.843842\pi$
$491$	−3.73295	−	25.9632i	−0.168466	−	1.17170i	0.713592	−	0.700562i	$-0.247067\pi$
$492$	−34.5599	+	9.27627i	−1.55808	+	0.418207i
$493$	−11.0024	+	7.07081i	−0.495523	+	0.318453i
$494$	−3.47248	+	1.51828i	−0.156234	+	0.0683108i
$495$	−0.195470	−	10.7913i	−0.00878573	−	0.485032i
$496$	−11.9540	+	16.1886i	−0.536750	+	0.726891i
$497$	−4.86037	−	1.68219i	−0.218017	−	0.0754566i
$498$	6.33382	−	31.6427i	0.283825	−	1.41794i
$499$	−37.6939	+	21.7626i	−1.68741	+	0.974228i	−0.730924	+	0.682459i	$0.760911\pi$
$499$	−37.6939	+	21.7626i	−1.68741	+	0.974228i	−0.956489	+	0.291769i	$0.905756\pi$
$500$	10.5428	−	12.5468i	0.471489	−	0.561110i
$501$	−3.36996	−	8.20170i	−0.150559	−	0.366425i
$502$	−2.24099	−	1.82190i	−0.100020	−	0.0813154i
$503$	1.26615	−	5.21913i	0.0564547	−	0.232709i	−0.936594	−	0.350418i	$-0.886040\pi$
$503$	1.26615	−	5.21913i	0.0564547	−	0.232709i	0.993048	+	0.117708i	$0.0375548\pi$
$504$	5.77891	+	1.01178i	0.257413	+	0.0450683i
$505$	7.47848	−	1.44136i	0.332788	−	0.0641396i
$506$	7.15567	−	0.566386i	0.318108	−	0.0251789i
$507$	26.3532	−	6.64647i	1.17039	−	0.295180i
$508$	3.02940	+	8.34114i	0.134408	+	0.370078i
$509$	2.27447	+	1.03872i	0.100814	+	0.0460403i	0.465184	−	0.885214i	$-0.345988\pi$
$509$	2.27447	+	1.03872i	0.100814	+	0.0460403i	−0.364370	+	0.931254i	$0.618715\pi$
$510$	4.69391	+	11.9724i	0.207850	+	0.530149i
$511$	4.92583	+	4.26826i	0.217906	+	0.188817i
$512$	6.44240	−	21.6909i	0.284717	−	0.958612i
$513$	2.34218	+	1.12803i	0.103410	+	0.0498037i
$514$	1.86754	−	5.99873i	0.0823736	−	0.264593i
$515$	−1.67457	−	2.35160i	−0.0737902	−	0.103624i
$516$	−15.8825	−	15.8688i	−0.699186	−	0.698584i
$517$	−22.5253	−	21.4778i	−0.990662	−	0.944595i
$518$	3.75697	−	7.00625i	0.165072	−	0.307837i
$519$	5.46200	−	1.65766i	0.239755	−	0.0727632i
$520$	−12.5110	−	5.02371i	−0.548643	−	0.220304i
$521$	−5.14575	−	17.5248i	−0.225439	−	0.767775i	−0.992070	−	0.125687i	$-0.959886\pi$
$521$	−5.14575	−	17.5248i	−0.225439	−	0.767775i	0.766631	−	0.642088i	$-0.221932\pi$
$522$	−8.13627	+	4.71810i	−0.356115	+	0.206506i
$523$	0.414611	−	2.15121i	0.0181297	−	0.0940657i	−0.971737	−	0.236067i	$-0.924142\pi$
$523$	0.414611	−	2.15121i	0.0181297	−	0.0940657i	0.989866	+	0.142001i	$0.0453537\pi$
$524$	−5.25878	+	8.46248i	−0.229731	+	0.369685i
$525$	3.93291	−	3.15093i	0.171646	−	0.137518i
$526$	8.07863	+	35.8259i	0.352245	+	1.56209i
$527$	−28.4786	−	8.36206i	−1.24055	−	0.364257i
$528$	−26.8098	−	8.11127i	−1.16675	−	0.352998i
$529$	−15.5052	+	14.7841i	−0.674138	+	0.642789i
$530$	2.85363	−	7.83186i	0.123954	−	0.340194i
$531$	2.63944	−	1.11255i	0.114542	−	0.0482805i
$532$	0.633603	+	0.277815i	0.0274702	+	0.0120448i
$533$	54.7673	+	7.87436i	2.37224	+	0.341076i
$534$	15.2398	−	9.64060i	0.659490	−	0.417190i
$535$			18.2311i			0.788200i
$536$	−8.37600	−	21.5834i	−0.361788	−	0.932260i
$537$	−2.69265	−	2.77325i	−0.116196	−	0.119674i
$538$	−4.31635	+	20.5930i	−0.186091	+	0.887827i
$539$	−3.75250	+	26.0992i	−0.161631	+	1.12417i
$540$	2.97870	+	8.75504i	0.128183	+	0.376757i
$541$	4.37646	+	9.58311i	0.188159	+	0.412010i	0.980077	−	0.198617i	$-0.0636448\pi$
$541$	4.37646	+	9.58311i	0.188159	+	0.412010i	−0.791919	+	0.610627i	$0.790918\pi$
$542$	9.16337	+	3.33878i	0.393601	+	0.143413i
$543$	16.9475	+	0.653550i	0.727288	+	0.0280465i
$544$	33.3098	−	2.05909i	1.42814	−	0.0882828i
$545$	−2.96566	+	10.1001i	−0.127035	+	0.432642i
$546$	−7.59629	−	4.95901i	−0.325091	−	0.212226i
$547$	−3.83078	+	40.1177i	−0.163792	+	1.71531i	0.423466	+	0.905912i	$0.360813\pi$
$547$	−3.83078	+	40.1177i	−0.163792	+	1.71531i	−0.587259	+	0.809399i	$0.699793\pi$
$548$	−12.1450	−	7.54720i	−0.518809	−	0.322401i
$549$	4.61677	−	20.6566i	0.197039	−	0.881600i
$550$	−20.4488	+	12.6780i	−0.871938	+	0.540590i
$551$	−1.06418	+	0.312470i	−0.0453354	+	0.0133117i
$552$	−5.69134	+	2.33159i	−0.242239	+	0.0992391i
$553$	7.16114	+	3.69183i	0.304523	+	0.156992i
$554$	8.00328	+	4.29162i	0.340027	+	0.182333i
$555$	12.5311	−	0.113483i	0.531916	−	0.00481709i
$556$	30.9669	−	0.469965i	1.31329	−	0.0199310i
$557$	2.48371	−	1.76864i	0.105238	−	0.0749396i	−0.526226	−	0.850344i	$-0.676394\pi$
$557$	2.48371	−	1.76864i	0.105238	−	0.0749396i	0.631464	+	0.775405i	$0.282454\pi$
$558$	−20.1839	−	6.94281i	−0.854452	−	0.293912i
$559$	12.9027	+	32.2293i	0.545725	+	1.36316i
$560$	0.875147	+	2.30023i	0.0369817	+	0.0972025i
$561$	−2.33932	−	41.2459i	−0.0987662	−	1.74140i
$562$	−0.349392	+	0.833324i	−0.0147382	+	0.0351517i
$563$	−7.36666	+	16.1307i	−0.310468	+	0.679829i	−0.998969	−	0.0454061i	$-0.985542\pi$
$563$	−7.36666	+	16.1307i	−0.310468	+	0.679829i	0.688501	+	0.725235i	$0.258269\pi$
$564$	23.9926	+	11.6421i	1.01027	+	0.490220i
$565$	5.50870	−	9.54135i	0.231753	−	0.401408i
$566$	−0.555463	−	7.01767i	−0.0233479	−	0.294975i
$567$	0.815454	+	6.16903i	0.0342459	+	0.259075i
$568$	−20.8228	−	3.01591i	−0.873703	−	0.126545i
$569$	−11.8973	−	2.88626i	−0.498762	−	0.120998i	−0.0215169	−	0.999768i	$-0.506850\pi$
$569$	−11.8973	−	2.88626i	−0.498762	−	0.120998i	−0.477245	+	0.878770i	$0.658365\pi$
$570$	0.0958909	+	1.08632i	0.00401643	+	0.0455008i
$571$	13.5116	−	33.7502i	0.565441	−	1.41240i	−0.319896	−	0.947453i	$-0.603648\pi$
$571$	13.5116	−	33.7502i	0.565441	−	1.41240i	0.885337	−	0.464951i	$-0.153928\pi$
$572$	33.1589	+	27.8627i	1.38644	+	1.16500i
$573$	10.3922	−	36.6160i	0.434140	−	1.52966i
$574$	−5.72467	−	8.32146i	−0.238943	−	0.347331i
$575$	−1.72792	+	4.99251i	−0.0720594	+	0.208202i
$576$	23.9969	−	0.384881i	0.999871	−	0.0160367i
$577$	0.124481	+	2.61319i	0.00518223	+	0.108788i	0.999976	+	0.00688290i	$0.00219091\pi$
$577$	0.124481	+	2.61319i	0.00518223	+	0.108788i	−0.994794	+	0.101906i	$0.967506\pi$
$578$	10.0878	+	23.0720i	0.419599	+	0.959669i
$579$	−23.1479	−	5.39414i	−0.961993	−	0.224173i
$580$	−3.44640	−	1.92065i	−0.143104	−	0.0797506i
$581$	9.01615	−	1.29633i	0.374053	−	0.0537807i
$582$	21.4242	+	15.4883i	0.888060	+	0.642012i
$583$	−16.5531	+	21.0490i	−0.685561	+	0.871762i
$584$	23.0771	+	13.3555i	0.954937	+	0.552655i
$585$	1.10125	−	14.2573i	0.0455310	−	0.589466i
$586$	9.64399	+	12.6811i	0.398389	+	0.523853i
$587$	−0.795898	+	1.11768i	−0.0328502	+	0.0461317i	−0.830674	−	0.556758i	$-0.812045\pi$
$587$	−0.795898	+	1.11768i	−0.0328502	+	0.0461317i	0.797824	+	0.602890i	$0.205984\pi$
$588$	−3.75615	−	22.2783i	−0.154901	−	0.918741i
$589$	−2.11746	−	1.36081i	−0.0872482	−	0.0560710i
$590$	0.967339	+	0.712752i	0.0398247	+	0.0293436i
$591$	−6.89814	−	3.47753i	−0.283751	−	0.143047i
$592$	9.69935	−	31.0418i	0.398641	−	1.27581i
$593$	2.02085	+	2.56973i	0.0829865	+	0.105526i	0.825774	−	0.564002i	$-0.190739\pi$
$593$	2.02085	+	2.56973i	0.0829865	+	0.105526i	−0.742787	+	0.669528i	$0.766496\pi$
$594$	−0.325463	−	29.7073i	−0.0133539	−	1.21891i
$595$	−2.74328	+	2.37706i	−0.112463	+	0.0974500i
$596$	−4.73960	+	36.9352i	−0.194142	+	1.51293i
$597$	21.7883	−	25.6100i	0.891734	−	1.04815i
$598$	9.50896	+	0.154176i	0.388850	+	0.00630473i
$599$	−7.99503	+	4.12172i	−0.326668	+	0.168409i	−0.613757	−	0.789495i	$-0.710343\pi$
$599$	−7.99503	+	4.12172i	−0.326668	+	0.168409i	0.287089	+	0.957904i	$0.407312\pi$
$600$	13.3749	−	15.6879i	0.546028	−	0.640455i
$601$	9.18877	+	37.8766i	0.374818	+	1.54502i	0.777024	+	0.629470i	$0.216728\pi$
$601$	9.18877	+	37.8766i	0.374818	+	1.54502i	−0.402207	+	0.915549i	$0.631757\pi$
$602$	2.72573	−	5.72120i	0.111092	−	0.233179i
$603$	19.1721	−	15.3437i	0.780748	−	0.624845i
$604$	−1.97126	+	1.59922i	−0.0802094	+	0.0650713i
$605$	−4.62233	+	1.12137i	−0.187924	+	0.0455900i
$606$	20.6132	−	3.82008i	0.837354	−	0.155180i
$607$	−6.91957	−	13.4221i	−0.280857	−	0.544786i	0.705639	−	0.708571i	$-0.250660\pi$
$607$	−6.91957	−	13.4221i	−0.280857	−	0.544786i	−0.986496	+	0.163785i	$0.947630\pi$
$608$	2.75954	+	0.628285i	0.111914	+	0.0254803i
$609$	−2.02203	−	1.72029i	−0.0819367	−	0.0697095i
$610$	8.43670	−	2.76765i	0.341592	−	0.112059i
$611$	−27.0038	−	31.1640i	−1.09246	−	1.26076i
$612$	12.6843	+	33.0471i	0.512734	+	1.33585i
$613$	0.105143	−	0.0826852i	0.00424667	−	0.00333962i	−0.616033	−	0.787720i	$-0.711261\pi$
$613$	0.105143	−	0.0826852i	0.00424667	−	0.00333962i	0.620280	+	0.784380i	$0.287019\pi$
$614$	−2.60688	−	1.56197i	−0.105205	−	0.0630361i
$615$	7.16714	−	14.2169i	0.289007	−	0.573283i
$616$	−0.368006	−	7.89773i	−0.0148274	−	0.318209i
$617$	−15.7018	+	24.4325i	−0.632132	+	0.983617i	0.366453	+	0.930437i	$0.380572\pi$
$617$	−15.7018	+	24.4325i	−0.632132	+	0.983617i	−0.998585	+	0.0531804i	$0.983064\pi$
$618$	−4.56298	−	6.50586i	−0.183550	−	0.261704i
$619$	−12.4744	−	8.88295i	−0.501387	−	0.357036i	0.301210	−	0.953558i	$-0.402609\pi$
$619$	−12.4744	−	8.88295i	−0.501387	−	0.357036i	−0.802597	+	0.596522i	$0.796549\pi$
$620$	−1.82776	−	8.76536i	−0.0734045	−	0.352026i
$621$	−4.17037	−	5.01639i	−0.167351	−	0.201301i
$622$	−3.74385	+	1.42884i	−0.150115	+	0.0572911i
$623$	4.00113	+	3.14652i	0.160302	+	0.126063i
$624$	−34.3380	−	14.0744i	−1.37462	−	0.563427i
$625$	−1.95666	−	13.6089i	−0.0782665	−	0.544355i
$626$	1.09901	−	17.1992i	0.0439253	−	0.687418i
$627$	0.795091	−	3.41198i	0.0317529	−	0.136261i
$628$	−21.2783	−	0.690185i	−0.849097	−	0.0275414i
$629$	47.9125	−	2.28235i	1.91039	−	0.0910033i
$630$	−2.04882	+	1.61752i	−0.0816271	+	0.0644436i
$631$	13.3975	+	4.63693i	0.533347	+	0.184593i	0.580448	−	0.814297i	$-0.302877\pi$
$631$	13.3975	+	4.63693i	0.533347	+	0.184593i	−0.0471017	+	0.998890i	$0.514999\pi$
$632$	31.6140	+	9.31833i	1.25754	+	0.370663i
$633$	12.5474	+	3.56116i	0.498715	+	0.141543i
$634$	−7.37395	−	1.91600i	−0.292857	−	0.0760940i
$635$	−3.66565	−	1.46751i	−0.145467	−	0.0582362i
$636$	8.00901	−	21.5013i	0.317578	−	0.852582i
$637$	−8.23611	+	33.9497i	−0.326326	+	1.34514i
$638$	8.59679	+	9.31382i	0.340350	+	0.368738i
$639$	−3.57547	−	22.0280i	−0.141444	−	0.871416i
$640$	5.28730	+	8.56771i	0.208999	+	0.338668i
$641$	−10.4188	−	6.01532i	−0.411520	−	0.237591i	0.279923	−	0.960023i	$-0.409691\pi$
$641$	−10.4188	−	6.01532i	−0.411520	−	0.237591i	−0.691442	+	0.722432i	$0.743024\pi$
$642$	−0.359132	+	50.1819i	−0.0141738	+	1.98052i
$643$	11.3068	+	5.16362i	0.445895	+	0.203633i	0.625692	−	0.780070i	$-0.284817\pi$
$643$	11.3068	+	5.16362i	0.445895	+	0.203633i	−0.179797	+	0.983704i	$0.557544\pi$
$644$	−1.15666	−	1.29462i	−0.0455787	−	0.0510154i
$645$	9.97353	−	0.565663i	0.392707	−	0.0222730i
$646$	0.526994	+	4.14082i	0.0207343	+	0.162919i
$647$	−13.8087	+	5.52818i	−0.542877	+	0.217335i	−0.626860	−	0.779132i	$-0.715660\pi$
$647$	−13.8087	+	5.52818i	−0.542877	+	0.217335i	0.0839828	+	0.996467i	$0.473236\pi$
$648$	8.02654	+	24.1573i	0.315312	+	0.948988i
$649$	−2.23906	−	3.14431i	−0.0878906	−	0.123425i
$650$	−28.5666	+	14.1457i	−1.12047	+	0.554839i
$651$	−0.0545597	−	6.02463i	−0.00213836	−	0.236124i
$652$	−25.8184	−	35.1167i	−1.01113	−	1.37528i
$653$	−20.2284	+	39.2377i	−0.791600	+	1.53549i	0.0520797	+	0.998643i	$0.483415\pi$
$653$	−20.2284	+	39.2377i	−0.791600	+	1.53549i	−0.843680	+	0.536847i	$0.819615\pi$
$654$	−8.36207	+	27.7426i	−0.326983	+	1.08482i
$655$	−1.24894	−	4.25351i	−0.0488003	−	0.166199i
$656$	−29.4076	−	29.0249i	−1.14817	−	1.13323i
$657$	−6.16854	+	27.5996i	−0.240658	+	1.07676i
$658$	−0.836920	+	7.48082i	−0.0326265	+	0.291633i
$659$	24.1879	+	2.30967i	0.942229	+	0.0899719i	0.554851	−	0.831949i	$-0.312775\pi$
$659$	24.1879	+	2.30967i	0.942229	+	0.0899719i	0.387377	+	0.921921i	$0.373381\pi$
$660$	10.6389	−	6.49105i	0.414119	−	0.252664i
$661$	−10.0914	−	2.96311i	−0.392511	−	0.115252i	0.0795206	−	0.996833i	$-0.474661\pi$
$661$	−10.0914	−	2.96311i	−0.392511	−	0.115252i	−0.472032	+	0.881582i	$0.656479\pi$
$662$	5.52603	+	20.0147i	0.214775	+	0.777894i
$663$	2.10917	−	54.6939i	0.0819133	−	2.12414i
$664$	35.2258	−	12.1509i	1.36703	−	0.471546i
$665$	−0.280007	+	0.127875i	−0.0108582	+	0.00495877i
$666$	34.4946	−	0.0655181i	1.33664	−	0.00253878i
$667$	2.75481	+	0.396082i	0.106667	+	0.0153364i
$668$	6.20633	−	8.14334i	0.240130	−	0.315075i
$669$	−4.03588	+	3.91859i	−0.156036	+	0.151501i
$670$	9.64442	+	3.61905i	0.372597	+	0.139816i
$671$	−28.5242			−1.10117
$672$	2.36357	+	6.34872i	0.0911766	+	0.244907i
$673$	−1.07857	+	7.50161i	−0.0415758	+	0.289166i	0.958417	+	0.285371i	$0.0921169\pi$
$673$	−1.07857	+	7.50161i	−0.0415758	+	0.289166i	−0.999993	+	0.00379448i	$0.998792\pi$
$674$	−1.46581	−	46.6849i	−0.0564607	−	1.79824i
$675$	20.1294	+	8.53982i	0.774782	+	0.328698i
$676$	21.9988	+	22.3816i	0.846110	+	0.860832i
$677$	−6.52664	−	6.84494i	−0.250839	−	0.263073i	0.586261	−	0.810122i	$-0.300599\pi$
$677$	−6.52664	−	6.84494i	−0.250839	−	0.263073i	−0.837100	+	0.547050i	$0.815751\pi$
$678$	15.3509	−	26.1545i	0.589547	−	1.00446i
$679$	−2.10232	+	7.15986i	−0.0806798	+	0.274770i
$680$	−9.19121	+	11.6627i	−0.352467	+	0.447243i
$681$	−13.1647	−	16.4318i	−0.504472	−	0.629669i
$682$	−3.19810	+	28.5863i	−0.122462	+	1.09463i
$683$	44.9135	+	8.65636i	1.71857	+	0.331226i	0.950871	−	0.309588i	$-0.100191\pi$
$683$	44.9135	+	8.65636i	1.71857	+	0.331226i	0.767695	+	0.640815i	$0.221403\pi$
$684$	0.242544	+	2.99202i	0.00927391	+	0.114403i
$685$	6.10448	−	1.79244i	0.233240	−	0.0684855i
$686$	11.5561	−	6.42440i	0.441213	−	0.245285i
$687$	8.37370	+	27.5914i	0.319477	+	1.05268i
$688$	6.54565	−	25.0848i	0.249551	−	0.956350i
$689$	−24.4829	+	25.6769i	−0.932724	+	0.978213i
$690$	0.913526	−	2.57958i	0.0347773	−	0.0982030i
$691$	26.5761	−	18.9248i	1.01100	−	0.719933i	0.0506501	−	0.998716i	$-0.483871\pi$
$691$	26.5761	−	18.9248i	1.01100	−	0.719933i	0.960354	+	0.278784i	$0.0899313\pi$
$692$	4.83862	+	4.47542i	0.183937	+	0.170130i
$693$	7.87371	−	2.88583i	0.299098	−	0.109624i
$694$	−3.83669	−	30.1465i	−0.145639	−	1.14435i
$695$	−9.02397	+	10.4142i	−0.342299	+	0.395034i
$696$	−9.44852	−	5.35455i	−0.358145	−	0.202964i
$697$	25.3160	−	55.4344i	0.958913	−	2.09973i
$698$	−21.4235	−	21.1009i	−0.810893	−	0.798680i
$699$	−11.6401	−	46.1527i	−0.440267	−	1.74565i
$700$	5.43444	+	2.08050i	0.205402	+	0.0786357i
$701$	6.15687	+	31.9449i	0.232542	+	1.20654i	0.891028	+	0.453949i	$0.149985\pi$
$701$	6.15687	+	31.9449i	0.232542	+	1.20654i	−0.658486	+	0.752593i	$0.728803\pi$
$702$	3.31208	−	39.2220i	0.125006	−	1.48034i
$703$	3.95306	+	0.959003i	0.149093	+	0.0361695i
$704$	−7.55997	−	31.4472i	−0.284927	−	1.18521i
$705$	−10.9753	+	4.50958i	−0.413353	+	0.169841i
$706$	−5.75972	−	1.49657i	−0.216770	−	0.0563240i
$707$	2.95875	+	5.12471i	0.111275	+	0.192734i
$708$	2.64860	+	1.98094i	0.0995405	+	0.0744481i
$709$	−1.60562	+	4.63912i	−0.0603001	+	0.174226i	−0.971127	−	0.238562i	$-0.923324\pi$
$709$	−1.60562	+	4.63912i	−0.0603001	+	0.174226i	0.910827	+	0.412788i	$0.135445\pi$
$710$	7.17343	−	6.01500i	0.269214	−	0.225739i
$711$	0.633115	+	34.9522i	0.0237437	+	1.31081i
$712$	18.4981	+	9.56075i	0.693247	+	0.358304i
$713$	3.41475	+	5.31346i	0.127884	+	0.198991i
$714$	−7.59780	+	6.48892i	−0.284341	+	0.242842i
$715$	−19.0746	+	2.74252i	−0.713351	+	0.102564i
$716$	1.19235	−	4.30116i	0.0445601	−	0.160742i
$717$	4.31487	+	41.2374i	0.161142	+	1.54004i
$718$	−25.8400	+	9.86179i	−0.964339	+	0.368039i
$719$	−0.401345	+	8.42527i	−0.0149676	+	0.314209i	0.978951	+	0.204094i	$0.0654249\pi$
$719$	−0.401345	+	8.42527i	−0.0149676	+	0.314209i	−0.993919	+	0.110115i	$0.964878\pi$
$720$	−6.98600	+	8.07633i	−0.260353	+	0.300987i
$721$	1.30109	−	1.82712i	0.0484551	−	0.0680457i
$722$	4.19863	−	26.1815i	0.156257	−	0.974376i
$723$	1.74728	+	8.64379i	0.0649822	+	0.321466i
$724$	9.23696	+	17.2687i	0.343289	+	0.641785i
$725$	−8.81568	+	3.05113i	−0.327406	+	0.113316i
$726$	−12.7452	+	2.99555i	−0.473020	+	0.111175i
$727$	−23.2516	−	29.5668i	−0.862353	−	1.09657i	−0.994437	−	0.105333i	$-0.966409\pi$
$727$	−23.2516	−	29.5668i	−0.862353	−	1.09657i	0.132084	−	0.991239i	$-0.457833\pi$
$728$	0.509276	−	10.4627i	0.0188750	−	0.387773i
$729$	−21.8876	+	15.8093i	−0.810651	+	0.585530i
$730$	−11.2724	+	3.69790i	−0.417211	+	0.136865i
$731$	38.0635	−	3.63462i	1.40783	−	0.134431i
$732$	23.2769	−	7.45187i	0.860338	−	0.275429i
$733$	42.8928	−	22.1128i	1.58428	−	0.816753i	0.584294	−	0.811542i	$-0.301372\pi$
$733$	42.8928	−	22.1128i	1.58428	−	0.816753i	0.999986	−	0.00521089i	$-0.00165869\pi$
$734$	18.2227	−	27.3692i	0.672613	−	1.01021i
$735$	8.50547	+	5.35792i	0.313729	+	0.197630i
$736$	−5.64397	−	4.31074i	−0.208040	−	0.158896i
$737$	−25.8154	−	20.7046i	−0.950922	−	0.762664i
$738$	20.0079	−	38.9915i	0.736501	−	1.43530i
$739$	−7.53440	+	1.82783i	−0.277157	+	0.0672376i	−0.371928	−	0.928261i	$-0.621303\pi$
$739$	−7.53440	+	1.82783i	−0.277157	+	0.0672376i	0.0947710	+	0.995499i	$0.469788\pi$
$740$	7.42446	+	12.4204i	0.272929	+	0.456582i
$741$	1.47835	−	4.39994i	0.0543086	−	0.161636i
$742$	6.47562	+	0.104994i	0.237728	+	0.00385446i
$743$	−31.8998	+	3.04606i	−1.17029	+	0.111749i	−0.662045	−	0.749464i	$-0.730311\pi$
$743$	−31.8998	+	3.04606i	−1.17029	+	0.111749i	−0.508244	+	0.861213i	$0.669705\pi$
$744$	−4.85831	−	24.1630i	−0.178114	−	0.885860i
$745$	−10.8502	−	12.5218i	−0.397520	−	0.458762i
$746$	−29.4625	+	32.9081i	−1.07870	+	1.20485i
$747$	23.5049	+	31.7740i	0.859999	+	1.16255i
$748$	39.7345	−	26.3963i	1.45284	−	0.965144i
$749$	−13.3860	+	4.63294i	−0.489113	+	0.169284i
$750$	2.71420	+	19.8870i	0.0991087	+	0.726171i
$751$	20.3859	−	31.7211i	0.743893	−	1.15752i	−0.238581	−	0.971123i	$-0.576682\pi$
$751$	20.3859	−	31.7211i	0.743893	−	1.15752i	0.982474	−	0.186398i	$-0.0596814\pi$
$752$	2.39793	+	30.7000i	0.0874436	+	1.11951i
$753$	3.49653	−	0.535087i	0.127421	−	0.0194997i
$754$	10.1654	+	13.3667i	0.370200	+	0.486787i
$755$	0.0537402	−	1.12814i	0.00195580	−	0.0410574i
$756$	−5.67134	+	4.41193i	−0.206265	+	0.160460i
$757$	−16.0669	−	12.6352i	−0.583961	−	0.459232i	0.281950	−	0.959429i	$-0.409019\pi$
$757$	−16.0669	−	12.6352i	−0.583961	−	0.459232i	−0.865912	+	0.500197i	$0.833261\pi$
$758$	−2.94654	−	16.7445i	−0.107023	−	0.608187i
$759$	−5.37161	+	6.95934i	−0.194977	+	0.252608i
$760$	−1.02651	+	0.729372i	−0.0372355	+	0.0264571i
$761$	−20.6752	−	32.1713i	−0.749476	−	1.16621i	−0.981119	−	0.193406i	$-0.938047\pi$
$761$	−20.6752	−	32.1713i	−0.749476	−	1.16621i	0.231643	−	0.972801i	$-0.425590\pi$
$762$	−10.0609	−	4.11158i	−0.364470	−	0.148947i
$763$	−8.16955	+	0.389163i	−0.295757	+	0.0140887i
$764$	42.5494	−	11.0086i	1.53938	−	0.398279i
$765$	−14.7253	−	5.58786i	−0.532394	−	0.202030i
$766$	23.8078	+	34.6073i	0.860209	+	1.25041i
$767$	−2.55710	−	4.42903i	−0.0923316	−	0.159923i
$768$	14.3847	+	23.6871i	0.519064	+	0.854735i
$769$	−34.3422	−	13.7485i	−1.23841	−	0.495785i	−0.342290	−	0.939594i	$-0.611203\pi$
$769$	−34.3422	−	13.7485i	−1.23841	−	0.495785i	−0.896121	+	0.443809i	$0.853627\pi$
$770$	2.72958	+	2.21912i	0.0983672	+	0.0799714i
$771$	3.90755	+	6.62871i	0.140727	+	0.238727i
$772$	−8.13086	−	26.2129i	−0.292636	−	0.943424i
$773$	3.84875	+	19.9692i	0.138430	+	0.718243i	0.983116	+	0.182981i	$0.0585747\pi$
$773$	3.84875	+	19.9692i	0.138430	+	0.718243i	−0.844687	+	0.535261i	$0.820213\pi$
$774$	27.4637	−	1.36054i	0.987162	−	0.0489037i
$775$	−18.3345	−	10.5854i	−0.658596	−	0.380240i
$776$	−2.93321	+	30.3849i	−0.105296	+	1.09075i
$777$	3.26776	+	9.17198i	0.117230	+	0.329043i
$778$	14.1665	−	33.7881i	0.507894	−	1.21136i
$779$	3.38434	−	3.90573i	0.121256	−	0.139937i
$780$	14.8492	−	7.22120i	0.531686	−	0.258560i
$781$	−27.9199	+	11.1774i	−0.999053	+	0.399960i
$782$	3.11359	−	10.0012i	0.111342	−	0.357641i
$783$	2.41064	−	11.2640i	0.0861491	−	0.402543i
$784$	20.0076	−	16.7413i	0.714557	−	0.597902i
$785$	6.53680	−	6.85560i	0.233308	−	0.244687i
$786$	−3.35398	−	11.7326i	−0.119633	−	0.418487i
$787$	15.5322	−	30.1283i	0.553663	−	1.07396i	−0.431464	−	0.902130i	$-0.642003\pi$
$787$	15.5322	−	30.1283i	0.553663	−	1.07396i	0.985127	−	0.171827i	$-0.0549670\pi$
$788$	−0.559599	−	8.90263i	−0.0199349	−	0.317143i
$789$	−39.1553	−	22.1360i	−1.39397	−	0.788063i
$790$	−12.4636	+	7.72725i	−0.443434	+	0.274923i
$791$	8.40552	+	1.62003i	0.298866	+	0.0576017i
$792$	29.4119	−	17.6573i	1.04511	−	0.627425i
$793$	−37.6207	−	3.59234i	−1.33595	−	0.127568i
$794$	4.50375	+	19.9726i	0.159832	+	0.708800i
$795$	4.75997	+	9.03130i	0.168819	+	0.320307i
$796$	38.2316	+	6.76852i	1.35508	+	0.239904i
$797$	12.7636	+	13.3861i	0.452111	+	0.474161i	0.909857	−	0.414923i	$-0.136191\pi$
$797$	12.7636	+	13.3861i	0.452111	+	0.474161i	−0.457745	+	0.889083i	$0.651343\pi$
$798$	−0.773249	+	0.346465i	−0.0273727	+	0.0122647i
$799$	−41.3133	+	18.8672i	−1.46156	+	0.667472i
$800$	23.4359	+	4.17416i	0.828583	+	0.147579i
$801$	−3.78634	+	21.7589i	−0.133784	+	0.768815i
$802$	−3.98592	+	19.0165i	−0.140748	+	0.671497i
$803$	38.1117			1.34493
$804$	26.4754	+	10.1516i	0.933715	+	0.358018i
$805$	0.772442			0.0272250
$806$	−7.81815	+	37.2998i	−0.275382	+	1.31383i
$807$	−15.1371	−	20.8548i	−0.532851	−	0.734123i
$808$	15.8335	+	18.3111i	0.557019	+	0.644183i
$809$	−43.6411	+	19.9302i	−1.53434	+	0.700710i	−0.990376	−	0.138399i	$-0.955804\pi$
$809$	−43.6411	+	19.9302i	−1.53434	+	0.700710i	−0.543963	+	0.839109i	$0.683077\pi$
$810$	−10.3949	−	4.49802i	−0.365238	−	0.158044i
$811$	−28.1359	−	29.5081i	−0.987985	−	1.03617i	−0.999343	−	0.0362338i	$-0.988464\pi$
$811$	−28.1359	−	29.5081i	−0.987985	−	1.03617i	0.0113580	−	0.999935i	$-0.496385\pi$
$812$	0.534406	−	3.01856i	0.0187540	−	0.105931i
$813$	−10.5667	+	5.56923i	−0.370592	+	0.195321i
$814$	−10.2257	−	45.3475i	−0.358411	−	1.58943i
$815$	19.3055	+	1.84345i	0.676242	+	0.0645732i
$816$	−25.5289	+	31.9209i	−0.893691	+	1.11746i
$817$	3.18398	+	0.613663i	0.111393	+	0.0214693i
$818$	43.2065	−	26.7875i	1.51068	−	0.936602i
$819$	10.7481	−	2.81452i	0.375569	−	0.0983472i
$820$	18.3482	−	1.15332i	0.640746	−	0.0402758i
$821$	−4.79755	+	9.30594i	−0.167436	+	0.324780i	−0.957593	−	0.288124i	$-0.906968\pi$
$821$	−4.79755	+	9.30594i	−0.167436	+	0.324780i	0.790158	+	0.612904i	$0.209999\pi$
$822$	16.8381	−	4.81350i	0.587297	−	0.167890i
$823$	−4.81373	+	5.04849i	−0.167796	+	0.175979i	−0.802263	−	0.596970i	$-0.796371\pi$
$823$	−4.81373	+	5.04849i	−0.167796	+	0.175979i	0.634467	+	0.772950i	$0.281220\pi$
$824$	3.82044	−	8.34268i	0.133091	−	0.290631i
$825$	5.31448	−	28.9841i	0.185026	−	1.00910i
$826$	−0.277508	+	0.891384i	−0.00965573	+	0.0310152i
$827$	−4.26848	+	1.70884i	−0.148430	+	0.0594223i	−0.444688	−	0.895686i	$-0.646685\pi$
$827$	−4.26848	+	1.70884i	−0.148430	+	0.0594223i	0.296258	+	0.955108i	$0.404261\pi$
$828$	2.56533	−	7.08241i	0.0891515	−	0.246131i
$829$	2.77816	−	3.20616i	0.0964894	−	0.111355i	−0.705451	−	0.708759i	$-0.749256\pi$
$829$	2.77816	−	3.20616i	0.0964894	−	0.111355i	0.801941	+	0.597404i	$0.203801\pi$
$830$	−6.41074	+	15.2901i	−0.222520	+	0.530726i
$831$	−10.4772	+	3.73278i	−0.363451	+	0.129489i
$832$	−6.01041	−	42.4279i	−0.208373	−	1.47092i
$833$	33.3222	+	19.2386i	1.15454	+	0.666576i
$834$	−25.0440	+	28.4878i	−0.867203	+	0.986452i
$835$	0.862159	+	4.47331i	0.0298363	+	0.154805i
$836$	3.86376	−	1.19848i	0.133631	−	0.0414504i
$837$	22.9017	−	12.6056i	0.791598	−	0.435712i
$838$	−7.20882	−	5.86069i	−0.249025	−	0.202454i
$839$	15.0904	+	6.04127i	0.520977	+	0.208568i	0.617221	−	0.786790i	$-0.288259\pi$
$839$	15.0904	+	6.04127i	0.520977	+	0.208568i	−0.0962436	+	0.995358i	$0.530683\pi$
$840$	−2.80718	−	1.09779i	−0.0968569	−	0.0378774i
$841$	−12.0428	−	20.8587i	−0.415269	−	0.719267i
$842$	6.23297	+	9.06034i	0.214802	+	0.312240i
$843$	−0.468832	−	1.00247i	−0.0161474	−	0.0345270i
$844$	3.77240	+	14.5807i	0.129851	+	0.501887i
$845$	−13.9477	+	0.664409i	−0.479814	+	0.0228564i
$846$	−30.2987	+	12.1966i	−1.04169	+	0.419328i
$847$	−1.99799	−	3.10893i	−0.0686517	−	0.106824i
$848$	26.0978	−	4.56455i	0.896204	−	0.156747i
$849$	6.82513	+	5.26801i	0.234238	+	0.180798i
$850$	6.08479	+	34.5784i	0.208706	+	1.18603i
$851$	−8.02355	−	6.30979i	−0.275044	−	0.216297i
$852$	19.8637	−	16.4152i	0.680518	−	0.562376i
$853$	0.651315	−	13.6728i	0.0223006	−	0.468147i	−0.959904	−	0.280331i	$-0.909556\pi$
$853$	0.651315	−	13.6728i	0.0223006	−	0.468147i	0.982204	−	0.187817i	$-0.0601411\pi$
$854$	4.17607	+	5.49123i	0.142902	+	0.187906i
$855$	−1.06466	−	0.806486i	−0.0364106	−	0.0275812i
$856$	−50.2132	+	28.9212i	−1.71625	+	0.988506i
$857$	−14.9557	+	23.2716i	−0.510878	+	0.794941i	−0.996873	−	0.0790201i	$-0.974821\pi$
$857$	−14.9557	+	23.2716i	−0.510878	+	0.794941i	0.485995	+	0.873961i	$0.338457\pi$
$858$	−52.5578	+	7.17315i	−1.79429	+	0.244887i
$859$	−6.61905	+	2.29088i	−0.225839	+	0.0781637i	−0.437644	−	0.899148i	$-0.644187\pi$
$859$	−6.61905	+	2.29088i	−0.225839	+	0.0781637i	0.211805	+	0.977312i	$0.432066\pi$
$860$	6.38280	+	9.60807i	0.217652	+	0.327632i
$861$	12.2600	+	1.64954i	0.417819	+	0.0562162i
$862$	19.6715	−	21.9720i	0.670014	−	0.748371i
$863$	−25.0105	−	28.8637i	−0.851368	−	0.982531i	0.148611	−	0.988896i	$-0.452520\pi$
$863$	−25.0105	−	28.8637i	−0.851368	−	0.982531i	−0.999980	+	0.00636419i	$0.997974\pi$
$864$	−19.3883	+	22.0928i	−0.659605	+	0.751613i
$865$	−2.91933	+	0.278762i	−0.0992602	+	0.00947820i
$866$	−33.7565	−	0.547320i	−1.14709	−	0.0185987i
$867$	−29.2342	−	9.82253i	−0.992847	−	0.333591i
$868$	5.97140	−	3.56949i	0.202682	−	0.121156i
$869$	45.7825	−	11.1067i	1.55307	−	0.376770i
$870$	4.57760	−	1.54773i	0.155195	−	0.0524729i
$871$	−31.4404	−	30.5586i	−1.06532	−	1.03544i
$872$	−32.5230	+	7.85428i	−1.10137	+	0.265979i
$873$	−31.6765	+	6.70233i	−1.07209	+	0.226840i
$874$	0.492292	−	0.739385i	0.0166520	−	0.0250101i
$875$	−5.03569	+	2.59608i	−0.170237	+	0.0877634i
$876$	−31.1006	+	9.95657i	−1.05079	+	0.336401i
$877$	−42.3986	+	4.04858i	−1.43170	+	0.136711i	−0.781904	−	0.623398i	$-0.785751\pi$
$877$	−42.3986	+	4.04858i	−1.43170	+	0.136711i	−0.649795	+	0.760109i	$0.725145\pi$
$878$	37.7725	−	12.3912i	1.27476	−	0.418183i
$879$	−19.4399	−	1.67878i	−0.655691	−	0.0566239i
$880$	12.6754	+	6.81387i	0.427286	+	0.229695i
$881$	29.8255	+	37.9262i	1.00485	+	1.27777i	0.960362	+	0.278756i	$0.0899219\pi$
$881$	29.8255	+	37.9262i	1.00485	+	1.27777i	0.0444839	+	0.999010i	$0.485836\pi$
$882$	23.3061	+	14.9155i	0.784757	+	0.502229i
$883$	−51.7853	+	17.9231i	−1.74272	+	0.603160i	−0.997940	−	0.0641555i	$-0.979565\pi$
$883$	−51.7853	+	17.9231i	−1.74272	+	0.603160i	−0.744775	+	0.667315i	$0.767443\pi$
$884$	55.7303	−	29.8100i	1.87441	−	1.00262i
$885$	−1.44244	+	0.291579i	−0.0484870	+	0.00980131i
$886$	−2.13718	+	13.3269i	−0.0718001	+	0.447727i
$887$	2.85470	−	4.00886i	0.0958514	−	0.134605i	−0.763865	−	0.645376i	$-0.776701\pi$
$887$	2.85470	−	4.00886i	0.0958514	−	0.134605i	0.859717	+	0.510771i	$0.170640\pi$
$888$	20.1915	+	34.3339i	0.677581	+	1.15217i
$889$	0.145975	−	3.06439i	0.00489584	−	0.102776i
$890$	−8.65592	+	3.30352i	−0.290147	+	0.110734i
$891$	27.2259	+	24.1391i	0.912102	+	0.808690i
$892$	−6.25943	−	1.73521i	−0.209581	−	0.0580991i
$893$	−3.81234	+	0.548132i	−0.127575	+	0.0183426i
$894$	−29.6189	−	34.6804i	−0.990604	−	1.15989i
$895$	1.07367	+	1.67067i	0.0358890	+	0.0558443i
$896$	−4.94712	+	6.05939i	−0.165272	+	0.202430i
$897$	−7.96109	+	8.50220i	−0.265813	+	0.283880i
$898$	−15.3292	+	12.8537i	−0.511541	+	0.428932i
$899$	−3.64775	+	10.5395i	−0.121659	+	0.351511i
$900$	3.23520	+	25.0406i	0.107840	+	0.834686i
$901$	19.5381	+	33.8410i	0.650909	+	1.12741i
$902$	−57.1623	−	14.8527i	−1.90330	−	0.494539i
$903$	2.94983	+	7.17921i	0.0981642	+	0.238909i
$904$	35.0182	+	0.0363197i	1.16469	+	0.00120798i
$905$	−8.46801	−	2.05432i	−0.281486	−	0.0682878i
$906$	0.170145	−	3.10421i	0.00565269	−	0.103130i
$907$	1.25757	+	6.52490i	0.0417570	+	0.216656i	0.996813	−	0.0797682i	$-0.0254180\pi$
$907$	1.25757	+	6.52490i	0.0417570	+	0.216656i	−0.955056	+	0.296424i	$0.904206\pi$
$908$	8.69241	−	22.7052i	0.288468	−	0.753500i
$909$	−13.4879	+	21.8477i	−0.447366	+	0.724643i
$910$	3.32058	+	3.27056i	0.110076	+	0.108418i
$911$	−5.80121	+	12.7029i	−0.192203	+	0.420865i	−0.981058	−	0.193714i	$-0.937947\pi$
$911$	−5.80121	+	12.7029i	−0.192203	+	0.420865i	0.788856	+	0.614579i	$0.210674\pi$
$912$	−2.83988	+	1.98740i	−0.0940379	+	0.0658095i
$913$	34.8795	−	40.2531i	1.15434	−	1.33218i
$914$	−2.59244	−	20.3700i	−0.0857503	−	0.673779i
$915$	−4.42770	+	9.93238i	−0.146375	+	0.328354i
$916$	−22.6077	+	24.4424i	−0.746979	+	0.807599i
$917$	2.80571	−	1.99794i	0.0926527	−	0.0659777i
$918$	−40.4219	−	15.6709i	−1.33412	−	0.517217i
$919$	−10.8866	+	11.4176i	−0.359117	+	0.376631i	−0.878363	−	0.477994i	$-0.841364\pi$
$919$	−10.8866	+	11.4176i	−0.359117	+	0.376631i	0.519247	+	0.854624i	$0.326213\pi$
$920$	3.10343	−	0.594799i	0.102317	−	0.0196099i
$921$	3.56161	−	1.08091i	0.117359	−	0.0356172i
$922$	36.8362	−	20.4784i	1.21314	−	0.674422i
$923$	−38.2313	+	11.2257i	−1.25840	+	0.369499i
$924$	7.46957	+	6.16198i	0.245731	+	0.202714i
$925$	33.5957	+	6.47504i	1.10462	+	0.212898i
$926$	−4.64334	+	41.5046i	−0.152590	+	1.36392i
$927$	9.65689	+	1.21038i	0.317174	+	0.0397540i
$928$	−0.177290	−	12.5391i	−0.00581984	−	0.411617i
$929$	3.47030	−	11.8188i	0.113857	−	0.387761i	−0.882772	−	0.469802i	$-0.844325\pi$
$929$	3.47030	−	11.8188i	0.113857	−	0.387761i	0.996629	+	0.0820404i	$0.0261437\pi$
$930$	9.45756	+	5.55095i	0.310126	+	0.182023i
$931$	2.25171	+	2.36152i	0.0737968	+	0.0773958i
$932$	39.1973	−	38.5269i	1.28395	−	1.26199i
$933$	1.78273	−	4.57262i	0.0583639	−	0.149701i
$934$	−0.317772	−	10.1208i	−0.0103978	−	0.331163i
$935$	−3.02064	+	21.0090i	−0.0987853	+	0.687067i
$936$	41.0152	−	19.5841i	1.34062	−	0.640127i
$937$	13.4363			0.438946			0.219473	−	0.975619i	$-0.429566\pi$
$937$	13.4363			0.438946			0.219473	+	0.975619i	$0.429566\pi$
$938$	−0.206383	+	8.00099i	−0.00673865	+	0.261242i
$939$	14.7036	+	15.1437i	0.479835	+	0.494197i
$940$	−10.8972	−	8.30515i	−0.355427	−	0.270884i
$941$	−39.8283	−	5.72645i	−1.29837	−	0.186677i	−0.541752	−	0.840538i	$-0.682239\pi$
$941$	−39.8283	−	5.72645i	−1.29837	−	0.186677i	−0.756614	+	0.653861i	$0.773148\pi$
$942$	18.1279	−	18.7415i	0.590637	−	0.610633i
$943$	−11.7965	+	5.38728i	−0.384147	+	0.175434i
$944$	−0.428551	+	3.79499i	−0.0139482	+	0.123516i
$945$	0.217334	−	3.18965i	0.00706988	−	0.103759i
$946$	−9.86220	−	35.7199i	−0.320648	−	1.16135i
$947$	−40.1618	−	11.7926i	−1.30508	−	0.383207i	−0.445995	−	0.895036i	$-0.647150\pi$
$947$	−40.1618	−	11.7926i	−1.30508	−	0.383207i	−0.859087	+	0.511829i	$0.828968\pi$
$948$	−34.4587	+	21.0241i	−1.11917	+	0.682830i
$949$	50.2656	+	4.79979i	1.63169	+	0.155808i
$950$	−0.331034	+	2.95895i	−0.0107402	+	0.0960010i
$951$	7.80381	−	5.11565i	0.253056	−	0.165886i
$952$	−10.8989	−	3.78480i	−0.353235	−	0.122666i
$953$	−7.68431	−	26.1704i	−0.248919	−	0.847741i	−0.985250	−	0.171120i	$-0.945262\pi$
$953$	−7.68431	−	26.1704i	−0.248919	−	0.847741i	0.736331	−	0.676622i	$-0.236557\pi$
$954$	12.9241	+	24.9528i	0.418433	+	0.807876i
$955$	−8.96075	+	17.3814i	−0.289963	+	0.562450i
$956$	−38.5734	+	28.3598i	−1.24755	+	0.917223i
$957$	−15.5228	+	0.140576i	−0.501782	+	0.00454419i
$958$	−13.8445	+	6.85554i	−0.447294	+	0.221492i
$959$	2.86736	+	4.02665i	0.0925920	+	0.130027i
$960$	−12.1237	−	2.24898i	−0.391290	−	0.0725855i
$961$	5.28183	−	2.11452i	0.170382	−	0.0682105i
$962$	−7.77565	−	61.0967i	−0.250697	−	1.96984i
$963$	−45.2427	−	41.6008i	−1.45792	−	1.34057i
$964$	−7.59362	+	6.78437i	−0.244574	+	0.218510i
$965$	11.1078	+	5.07278i	0.357574	+	0.163299i
$966$	2.12618	+	0.0152162i	0.0684086	+	0.000489574i
$967$	50.5905	+	29.2084i	1.62688	+	0.939279i	0.985017	+	0.172460i	$0.0551716\pi$
$967$	50.5905	+	29.2084i	1.62688	+	0.939279i	0.641863	+	0.766819i	$0.278162\pi$
$968$	−10.4212	−	10.9522i	−0.334951	−	0.352017i
$969$	−4.19109	−	2.92763i	−0.134637	−	0.0940489i
$970$	−9.21225	−	9.98061i	−0.295787	−	0.320458i
$971$	−10.0917	+	41.5987i	−0.323859	+	1.33497i	0.544388	+	0.838834i	$0.316762\pi$
$971$	−10.0917	+	41.5987i	−0.323859	+	1.33497i	−0.868247	+	0.496132i	$0.834753\pi$
$972$	−28.5237	−	12.5857i	−0.914897	−	0.403688i
$973$	−9.93972	−	3.97926i	−0.318653	−	0.127569i
$974$	−33.8695	−	8.80042i	−1.08525	−	0.281984i
$975$	10.6595	−	37.5580i	0.341378	−	1.20282i
$976$	21.0065	+	18.8463i	0.672402	+	0.603257i
$977$	−6.09391	−	2.10912i	−0.194961	−	0.0674768i	0.227842	−	0.973698i	$-0.426833\pi$
$977$	−6.09391	−	2.10912i	−0.194961	−	0.0674768i	−0.422804	+	0.906221i	$0.638954\pi$
$978$	53.1028	+	5.45447i	1.69804	+	0.174415i
$979$	29.7300	−	1.41621i	0.950174	−	0.0452624i
$980$	−0.376303	+	11.6014i	−0.0120206	+	0.370593i
$981$	−18.2974	−	30.4067i	−0.584192	−	0.970811i
$982$	−2.36552	+	37.0196i	−0.0754866	+	1.18134i
$983$	7.58771	+	52.7737i	0.242010	+	1.68322i	0.642004	+	0.766701i	$0.278103\pi$
$983$	7.58771	+	52.7737i	0.242010	+	1.68322i	−0.399993	+	0.916518i	$0.630988\pi$
$984$	50.5268	−	2.81313i	1.61074	−	0.0896794i
$985$	3.11980	+	2.45344i	0.0994052	+	0.0781731i
$986$	17.2802	−	6.59496i	0.550313	−	0.210026i
$987$	−6.10018	−	6.91249i	−0.194171	−	0.220027i
$988$	5.24687	−	1.09408i	0.166925	−	0.0348073i
$989$	−6.62805	−	4.71981i	−0.210760	−	0.150081i
$990$	−2.86020	+	14.9933i	−0.0909031	+	0.476519i
$991$	−2.25455	+	3.50816i	−0.0716183	+	0.111440i	−0.875215	−	0.483733i	$-0.839280\pi$
$991$	−2.25455	+	3.50816i	−0.0716183	+	0.111440i	0.803597	+	0.595174i	$0.202917\pi$
$992$	21.2426	−	18.9392i	0.674453	−	0.601320i
$993$	−22.7078	−	11.4476i	−0.720609	−	0.363278i
$994$	6.23938	+	3.73847i	0.197901	+	0.118577i
$995$	−13.5793	+	10.6789i	−0.430492	+	0.338542i
$996$	−17.9470	+	41.9602i	−0.568673	+	1.32956i
$997$	−38.7175	−	44.6824i	−1.22620	−	1.41510i	−0.878667	−	0.477435i	$-0.841567\pi$
$997$	−38.7175	−	44.6824i	−1.22620	−	1.41510i	−0.347528	−	0.937670i	$-0.612979\pi$
$998$	58.4873	−	19.1867i	1.85138	−	0.607344i
$999$	−28.3126	+	31.3564i	−0.895770	+	0.992072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.23.10	✓	2640
3.2	odd	2	inner	804.2.bd.a.23.123	yes	2640
4.3	odd	2	inner	804.2.bd.a.23.29	yes	2640
12.11	even	2	inner	804.2.bd.a.23.104	yes	2640
67.35	even	33	inner	804.2.bd.a.35.104	yes	2640
201.35	odd	66	inner	804.2.bd.a.35.29	yes	2640
268.35	odd	66	inner	804.2.bd.a.35.123	yes	2640
804.35	even	66	inner	804.2.bd.a.35.10	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.10	✓	2640	1.1	even	1	trivial
804.2.bd.a.23.29	yes	2640	4.3	odd	2	inner
804.2.bd.a.23.104	yes	2640	12.11	even	2	inner
804.2.bd.a.23.123	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.10	yes	2640	804.35	even	66	inner
804.2.bd.a.35.29	yes	2640	201.35	odd	66	inner
804.2.bd.a.35.104	yes	2640	67.35	even	33	inner
804.2.bd.a.35.123	yes	2640	268.35	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38414 - 0.290119i) q^{2} +(1.40173 - 1.01742i) q^{3} +(1.83166 + 0.803128i) q^{4} +(-0.809462 + 0.369669i) q^{5} +(-2.23536 + 1.00158i) q^{6} +(-0.477128 - 0.500397i) q^{7} +(-2.30227 - 1.64304i) q^{8} +(0.929699 - 2.85231i) q^{9} +O(q^{10})\)	\(q+(-1.38414 - 0.290119i) q^{2} +(1.40173 - 1.01742i) q^{3} +(1.83166 + 0.803128i) q^{4} +(-0.809462 + 0.369669i) q^{5} +(-2.23536 + 1.00158i) q^{6} +(-0.477128 - 0.500397i) q^{7} +(-2.30227 - 1.64304i) q^{8} +(0.929699 - 2.85231i) q^{9} +(1.22765 - 0.276832i) q^{10} +(-4.02459 - 0.384302i) q^{11} +(3.38462 - 0.737807i) q^{12} +(-5.25964 - 1.01371i) q^{13} +(0.515235 + 0.831041i) q^{14} +(-0.758538 + 1.34174i) q^{15} +(2.70997 + 2.94212i) q^{16} +(-2.70337 + 5.24380i) q^{17} +(-2.11434 + 3.67826i) q^{18} +(-0.345251 + 0.362089i) q^{19} +(-1.77955 + 0.0270071i) q^{20} +(-1.17792 - 0.215981i) q^{21} +(5.45908 + 1.69953i) q^{22} +(1.16552 - 0.466603i) q^{23} +(-4.89882 + 0.0392830i) q^{24} +(-2.75573 + 3.18028i) q^{25} +(6.98596 + 2.92904i) q^{26} +(-1.59882 - 4.94407i) q^{27} +(-0.472054 - 1.29975i) q^{28} +(1.91985 + 1.10842i) q^{29} +(1.43918 - 1.63709i) q^{30} +(0.952117 + 4.94005i) q^{31} +(-2.89740 - 4.85850i) q^{32} +(-6.03239 + 3.55602i) q^{33} +(5.26315 - 6.47383i) q^{34} +(0.571198 + 0.228673i) q^{35} +(3.99366 - 4.47780i) q^{36} +(-4.06524 - 7.04120i) q^{37} +(0.582923 - 0.401016i) q^{38} +(-8.40398 + 3.93033i) q^{39} +(2.47098 + 0.478900i) q^{40} +(-10.3180 + 0.491508i) q^{41} +(1.56774 + 0.640684i) q^{42} +(-3.50400 - 5.45233i) q^{43} +(-7.06304 - 3.93617i) q^{44} +(0.301854 + 2.65252i) q^{45} +(-1.74861 + 0.307703i) q^{46} +(6.05134 + 4.75882i) q^{47} +(6.79203 + 1.36687i) q^{48} +(0.310327 - 6.51456i) q^{49} +(4.73696 - 3.60245i) q^{50} +(1.54577 + 10.1009i) q^{51} +(-8.81975 - 6.08094i) q^{52} +(3.58094 - 5.57205i) q^{53} +(0.778613 + 7.30710i) q^{54} +(3.39982 - 1.17669i) q^{55} +(0.276304 + 1.93599i) q^{56} +(-0.115551 + 0.858817i) q^{57} +(-2.33575 - 2.09119i) q^{58} +(0.625246 + 0.721572i) q^{59} +(-2.46698 + 1.84841i) q^{60} +(7.02345 - 0.670658i) q^{61} +(0.115344 - 7.11393i) q^{62} +(-1.87087 + 0.895697i) q^{63} +(2.60086 + 7.56542i) q^{64} +(4.63222 - 1.12376i) q^{65} +(9.38131 - 3.17191i) q^{66} +(6.84326 + 4.49108i) q^{67} +(-9.16310 + 7.43372i) q^{68} +(1.15901 - 1.83988i) q^{69} +(-0.724273 - 0.482230i) q^{70} +(6.61185 - 3.40864i) q^{71} +(-6.82686 + 5.03924i) q^{72} +(-9.38415 + 0.896078i) q^{73} +(3.58405 + 10.9254i) q^{74} +(-0.627098 + 7.26164i) q^{75} +(-0.923186 + 0.385944i) q^{76} +(1.72794 + 2.19725i) q^{77} +(12.7725 - 3.00196i) q^{78} +(-11.0118 + 3.81121i) q^{79} +(-3.28123 - 1.37974i) q^{80} +(-7.27132 - 5.30358i) q^{81} +(14.4241 + 2.31314i) q^{82} +(-7.64186 + 10.7315i) q^{83} +(-1.98409 - 1.34163i) q^{84} +(0.249803 - 5.24401i) q^{85} +(3.26818 + 8.56334i) q^{86} +(3.81884 - 0.399585i) q^{87} +(8.63425 + 7.49732i) q^{88} +(-7.28704 + 1.04772i) q^{89} +(0.351739 - 3.75901i) q^{90} +(2.00226 + 3.11558i) q^{91} +(2.50958 + 0.0814009i) q^{92} +(6.36074 + 5.95592i) q^{93} +(-6.99524 - 8.34246i) q^{94} +(0.145615 - 0.420726i) q^{95} +(-9.00454 - 3.86243i) q^{96} +(-5.39631 - 9.34668i) q^{97} +(-2.31953 + 8.92701i) q^{98} +(-4.83780 + 11.1221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

Modular forms

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