LMFDB - Embedded newform 140.2.w.b.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("140.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05431 - 0.942570i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(0.223125 + 1.98751i) q^{4} +(2.09885 - 0.771256i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-0.451584 - 2.60693i) q^{7} +(1.63813 - 2.30576i) q^{8} +(-1.25225 - 0.722989i) q^{9} +O(q^{10})$	\(q+(-1.05431 - 0.942570i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(0.223125 + 1.98751i) q^{4} +(2.09885 - 0.771256i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-0.451584 - 2.60693i) q^{7} +(1.63813 - 2.30576i) q^{8} +(-1.25225 - 0.722989i) q^{9} +(-2.93979 - 1.16517i) q^{10} +(0.824629 - 0.476100i) q^{11} +(0.372591 - 2.46521i) q^{12} +(-3.15680 - 3.15680i) q^{13} +(-1.98110 + 3.17415i) q^{14} +(-2.77612 + 0.251508i) q^{15} +(-3.90043 + 0.886929i) q^{16} +(2.56885 + 0.688322i) q^{17} +(0.638792 + 1.94259i) q^{18} +(1.99048 - 3.44760i) q^{19} +(2.00119 + 3.99941i) q^{20} +(-0.297348 + 3.28477i) q^{21} +(-1.31817 - 0.275315i) q^{22} +(-0.141582 - 0.528392i) q^{23} +(-2.71646 + 2.24790i) q^{24} +(3.81033 - 3.23750i) q^{25} +(0.352732 + 6.30375i) q^{26} +(3.91905 + 3.91905i) q^{27} +(5.08055 - 1.47920i) q^{28} +7.23080i q^{29} +(3.16395 + 2.35152i) q^{30} +(3.41863 - 1.97375i) q^{31} +(4.94824 + 2.74133i) q^{32} +(-1.14657 + 0.307222i) q^{33} +(-2.05957 - 3.14702i) q^{34} +(-2.95842 - 5.12326i) q^{35} +(1.15754 - 2.65019i) q^{36} +(0.269180 + 1.00460i) q^{37} +(-5.34818 + 1.75867i) q^{38} +(2.78267 + 4.81972i) q^{39} +(1.65985 - 6.10286i) q^{40} +3.71449 q^{41} +(3.40962 - 3.18289i) q^{42} +(-8.73324 + 8.73324i) q^{43} +(1.13025 + 1.53273i) q^{44} +(-3.18590 - 0.551635i) q^{45} +(-0.348775 + 0.690538i) q^{46} +(3.09794 - 0.830089i) q^{47} +(4.98278 + 0.190479i) q^{48} +(-6.59214 + 2.35449i) q^{49} +(-7.06882 - 0.178182i) q^{50} +(-2.87114 - 1.65765i) q^{51} +(5.56983 - 6.97856i) q^{52} +(-0.760768 + 2.83923i) q^{53} +(-0.437903 - 7.82586i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-6.75070 - 3.22924i) q^{56} +(-3.50914 + 3.50914i) q^{57} +(6.81553 - 7.62348i) q^{58} +(6.30084 + 10.9134i) q^{59} +(-1.11930 - 5.46147i) q^{60} +(3.01183 - 5.21665i) q^{61} +(-5.46468 - 1.14136i) q^{62} +(-1.31928 + 3.59102i) q^{63} +(-2.63307 - 7.55427i) q^{64} +(-9.06036 - 4.19095i) q^{65} +(1.49841 + 0.756815i) q^{66} +(-3.85605 + 14.3910i) q^{67} +(-0.794874 + 5.25921i) q^{68} +0.681932i q^{69} +(-1.70995 + 8.19000i) q^{70} -7.60710i q^{71} +(-3.71839 + 1.70305i) q^{72} +(3.80964 - 14.2178i) q^{73} +(0.663102 - 1.31287i) q^{74} +(-5.63268 + 2.66898i) q^{75} +(7.29629 + 3.18685i) q^{76} +(-1.61355 - 1.93475i) q^{77} +(1.60914 - 7.70432i) q^{78} +(5.34864 - 9.26412i) q^{79} +(-7.50236 + 4.86976i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(-3.91621 - 3.50117i) q^{82} +(5.72446 - 5.72446i) q^{83} +(-6.59488 + 0.141933i) q^{84} +(5.92250 - 0.536560i) q^{85} +(17.4392 - 0.975826i) q^{86} +(2.33298 - 8.70680i) q^{87} +(0.253076 - 2.68131i) q^{88} +(-1.83403 - 1.05888i) q^{89} +(2.83896 + 3.58452i) q^{90} +(-6.80400 + 9.65512i) q^{91} +(1.01860 - 0.399294i) q^{92} +(-4.75329 + 1.27364i) q^{93} +(-4.04859 - 2.04485i) q^{94} +(1.51872 - 8.77117i) q^{95} +(-5.07384 - 4.89744i) q^{96} +(-3.08588 + 3.08588i) q^{97} +(9.16941 + 3.73120i) q^{98} -1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.05431	−	0.942570i	−0.745507	−	0.666497i
$2$	−1.05431	−	0.942570i	−0.745507	−	0.666497i
$3$	−1.20413	−	0.322645i	−0.695203	−	0.186279i	−0.106122	−	0.994353i	$-0.533843\pi$
$3$	−1.20413	−	0.322645i	−0.695203	−	0.186279i	−0.589081	+	0.808074i	$0.700510\pi$
$4$	0.223125	+	1.98751i	0.111563	+	0.993757i
$5$	2.09885	−	0.771256i	0.938633	−	0.344916i
$5$	2.09885	−	0.771256i	0.938633	−	0.344916i
$6$	0.965404	+	1.47514i	0.394125	+	0.602224i
$7$	−0.451584	−	2.60693i	−0.170683	−	0.985326i
$7$	−0.451584	−	2.60693i	−0.170683	−	0.985326i
$8$	1.63813	−	2.30576i	0.579166	−	0.815210i
$9$	−1.25225	−	0.722989i	−0.417418	−	0.240996i
$10$	−2.93979	−	1.16517i	−0.929644	−	0.368459i
$11$	0.824629	−	0.476100i	0.248635	−	0.143549i	−0.370504	−	0.928831i	$-0.620815\pi$
$11$	0.824629	−	0.476100i	0.248635	−	0.143549i	0.619139	+	0.785281i	$0.287482\pi$
$12$	0.372591	−	2.46521i	0.107558	−	0.711645i
$13$	−3.15680	−	3.15680i	−0.875540	−	0.875540i	0.117529	−	0.993069i	$-0.462503\pi$
$13$	−3.15680	−	3.15680i	−0.875540	−	0.875540i	−0.993069	+	0.117529i	$0.962503\pi$
$14$	−1.98110	+	3.17415i	−0.529472	+	0.848327i
$15$	−2.77612	+	0.251508i	−0.716792	+	0.0649391i
$16$	−3.90043	+	0.886929i	−0.975108	+	0.221732i
$17$	2.56885	+	0.688322i	0.623038	+	0.166943i	0.556508	−	0.830842i	$-0.312141\pi$
$17$	2.56885	+	0.688322i	0.623038	+	0.166943i	0.0665295	+	0.997784i	$0.478807\pi$
$18$	0.638792	+	1.94259i	0.150565	+	0.457872i
$19$	1.99048	−	3.44760i	0.456646	−	0.790935i	−0.542135	−	0.840292i	$-0.682384\pi$
$19$	1.99048	−	3.44760i	0.456646	−	0.790935i	0.998781	+	0.0493567i	$0.0157171\pi$
$20$	2.00119	+	3.99941i	0.447479	+	0.894294i
$21$	−0.297348	+	3.28477i	−0.0648866	+	0.716797i
$22$	−1.31817	−	0.275315i	−0.281034	−	0.0586973i
$23$	−0.141582	−	0.528392i	−0.0295219	−	0.110177i	0.949593	−	0.313486i	$-0.101497\pi$
$23$	−0.141582	−	0.528392i	−0.0295219	−	0.110177i	−0.979115	+	0.203309i	$0.934830\pi$
$24$	−2.71646	+	2.24790i	−0.554495	+	0.458850i
$25$	3.81033	−	3.23750i	0.762066	−	0.647500i
$26$	0.352732	+	6.30375i	0.0691765	+	1.23627i
$27$	3.91905	+	3.91905i	0.754222	+	0.754222i
$28$	5.08055	−	1.47920i	0.960133	−	0.279543i
$29$			7.23080i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$29$			7.23080i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$30$	3.16395	+	2.35152i	0.577655	+	0.429327i
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	−0.160527	−	0.987031i	$-0.551319\pi$
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	0.774531	+	0.632536i	$0.217986\pi$
$32$	4.94824	+	2.74133i	0.874734	+	0.484604i
$33$	−1.14657	+	0.307222i	−0.199592	+	0.0534805i
$34$	−2.05957	−	3.14702i	−0.353213	−	0.539710i
$35$	−2.95842	−	5.12326i	−0.500063	−	0.865989i
$36$	1.15754	−	2.65019i	0.192924	−	0.441698i
$37$	0.269180	+	1.00460i	0.0442530	+	0.165154i	0.984516	−	0.175294i	$-0.0560877\pi$
$37$	0.269180	+	1.00460i	0.0442530	+	0.165154i	−0.940263	+	0.340449i	$0.889421\pi$
$38$	−5.34818	+	1.75867i	−0.867589	+	0.285294i
$39$	2.78267	+	4.81972i	0.445584	+	0.771773i
$40$	1.65985	−	6.10286i	0.262446	−	0.964947i
$41$	3.71449			0.580106			0.290053	−	0.957011i	$-0.406327\pi$
$41$	3.71449			0.580106			0.290053	+	0.957011i	$0.406327\pi$
$42$	3.40962	−	3.18289i	0.526116	−	0.491130i
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.428052	+	0.903754i	$0.640800\pi$
$43$	−8.73324	+	8.73324i	−1.33181	+	1.33181i	−0.903754	+	0.428052i	$0.859200\pi$
$44$	1.13025	+	1.53273i	0.170392	+	0.231068i
$45$	−3.18590	−	0.551635i	−0.474926	−	0.0822329i
$46$	−0.348775	+	0.690538i	−0.0514241	+	0.101814i
$47$	3.09794	−	0.830089i	0.451880	−	0.121081i	−0.0256988	−	0.999670i	$-0.508181\pi$
$47$	3.09794	−	0.830089i	0.451880	−	0.121081i	0.477579	+	0.878589i	$0.341514\pi$
$48$	4.98278	+	0.190479i	0.719202	+	0.0274933i
$49$	−6.59214	+	2.35449i	−0.941735	+	0.336356i
$50$	−7.06882	−	0.178182i	−0.999682	−	0.0251987i
$51$	−2.87114	−	1.65765i	−0.402040	−	0.232118i
$52$	5.56983	−	6.97856i	0.772397	−	0.967752i
$53$	−0.760768	+	2.83923i	−0.104500	+	0.389998i	−0.998288	−	0.0584914i	$-0.981371\pi$
$53$	−0.760768	+	2.83923i	−0.104500	+	0.389998i	0.893788	+	0.448489i	$0.148038\pi$
$54$	−0.437903	−	7.82586i	−0.0595911	−	1.06496i
$55$	1.36358	−	1.63526i	0.183864	−	0.220498i
$56$	−6.75070	−	3.22924i	−0.902101	−	0.431525i
$57$	−3.50914	+	3.50914i	−0.464797	+	0.464797i
$58$	6.81553	−	7.62348i	0.894923	−	1.00101i
$59$	6.30084	+	10.9134i	0.820300	+	1.42080i	0.905459	+	0.424433i	$0.139527\pi$
$59$	6.30084	+	10.9134i	0.820300	+	1.42080i	−0.0851594	+	0.996367i	$0.527140\pi$
$60$	−1.11930	−	5.46147i	−0.144501	−	0.705072i
$61$	3.01183	−	5.21665i	0.385626	−	0.667923i	−0.606230	−	0.795289i	$-0.707319\pi$
$61$	3.01183	−	5.21665i	0.385626	−	0.667923i	0.991856	+	0.127366i	$0.0406523\pi$
$62$	−5.46468	−	1.14136i	−0.694015	−	0.144953i
$63$	−1.31928	+	3.59102i	−0.166214	+	0.452426i
$64$	−2.63307	−	7.55427i	−0.329134	−	0.944283i
$65$	−9.06036	−	4.19095i	−1.12380	−	0.519823i
$66$	1.49841	+	0.756815i	0.184442	+	0.0931574i
$67$	−3.85605	+	14.3910i	−0.471092	+	1.75814i	0.164766	+	0.986333i	$0.447313\pi$
$67$	−3.85605	+	14.3910i	−0.471092	+	1.75814i	−0.635858	+	0.771806i	$0.719353\pi$
$68$	−0.794874	+	5.25921i	−0.0963927	+	0.637773i
$69$			0.681932i			0.0820949i
$70$	−1.70995	+	8.19000i	−0.204378	+	0.978892i
$71$		−	7.60710i		−	0.902797i	−0.892322	−	0.451399i	$-0.850925\pi$
$71$		−	7.60710i		−	0.902797i	0.892322	−	0.451399i	$-0.149075\pi$
$72$	−3.71839	+	1.70305i	−0.438216	+	0.200706i
$73$	3.80964	−	14.2178i	0.445885	−	1.66406i	−0.267705	−	0.963501i	$-0.586265\pi$
$73$	3.80964	−	14.2178i	0.445885	−	1.66406i	0.713590	−	0.700564i	$-0.247068\pi$
$74$	0.663102	−	1.31287i	0.0770841	−	0.152618i
$75$	−5.63268	+	2.66898i	−0.650406	+	0.308187i
$76$	7.29629	+	3.18685i	0.836942	+	0.365557i
$77$	−1.61355	−	1.93475i	−0.183881	−	0.220485i
$78$	1.60914	−	7.70432i	0.182199	−	0.872343i
$79$	5.34864	−	9.26412i	0.601769	−	1.04230i	−0.390784	−	0.920483i	$-0.627796\pi$
$79$	5.34864	−	9.26412i	0.601769	−	1.04230i	0.992553	−	0.121813i	$-0.0388707\pi$
$80$	−7.50236	+	4.86976i	−0.838790	+	0.544456i
$81$	−1.28561	−	2.22674i	−0.142846	−	0.247416i
$82$	−3.91621	−	3.50117i	−0.432473	−	0.386639i
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	−0.319309	−	0.947651i	$-0.603451\pi$
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	0.947651	+	0.319309i	$0.103451\pi$
$84$	−6.59488	+	0.141933i	−0.719561	+	0.0154861i
$85$	5.92250	−	0.536560i	0.642386	−	0.0581981i
$86$	17.4392	−	0.975826i	1.88052	−	0.105226i
$87$	2.33298	−	8.70680i	0.250122	−	0.933467i
$88$	0.253076	−	2.68131i	0.0269780	−	0.285828i
$89$	−1.83403	−	1.05888i	−0.194407	−	0.112241i	0.399637	−	0.916673i	$-0.369136\pi$
$89$	−1.83403	−	1.05888i	−0.194407	−	0.112241i	−0.594044	+	0.804433i	$0.702469\pi$
$90$	2.83896	+	3.58452i	0.299253	+	0.377842i
$91$	−6.80400	+	9.65512i	−0.713253	+	1.01213i
$92$	1.01860	−	0.399294i	0.106196	−	0.0416293i
$93$	−4.75329	+	1.27364i	−0.492893	+	0.132070i
$94$	−4.04859	−	2.04485i	−0.417580	−	0.210910i
$95$	1.51872	−	8.77117i	0.155817	−	0.899903i
$96$	−5.07384	−	4.89744i	−0.517846	−	0.499843i
$97$	−3.08588	+	3.08588i	−0.313324	+	0.313324i	−0.846196	−	0.532872i	$-0.821113\pi$
$97$	−3.08588	+	3.08588i	−0.313324	+	0.313324i	0.532872	+	0.846196i	$0.321113\pi$
$98$	9.16941	+	3.73120i	0.926251	+	0.376908i
$99$	−1.37686			−0.138379
$100$	7.28476	+	6.85072i	0.728476	+	0.685072i
$101$	0.715074	+	1.23854i	0.0711525	+	0.123240i	0.899407	−	0.437113i	$-0.143999\pi$
$101$	0.715074	+	1.23854i	0.0711525	+	0.123240i	−0.828254	+	0.560353i	$0.810666\pi$
$102$	1.46461	+	4.45393i	0.145018	+	0.441004i
$103$	2.63366	+	9.82894i	0.259502	+	0.968474i	0.965530	+	0.260291i	$0.0838184\pi$
$103$	2.63366	+	9.82894i	0.259502	+	0.968474i	−0.706028	+	0.708183i	$0.749515\pi$
$104$	−12.4501	+	2.10758i	−1.22083	+	0.206666i
$105$	1.90932	+	7.12357i	0.186330	+	0.695190i
$106$	3.47825	−	2.27634i	0.337838	−	0.221097i
$107$	−0.0388547	+	0.0104111i	−0.00375622	+	0.00100648i	−0.260697	−	0.965421i	$-0.583952\pi$
$107$	−0.0388547	+	0.0104111i	−0.00375622	+	0.00100648i	0.256940	+	0.966427i	$0.417286\pi$
$108$	−6.91473	+	8.66361i	−0.665371	+	0.833656i
$109$	5.44983	−	3.14646i	0.521999	−	0.301376i	−0.215753	−	0.976448i	$-0.569221\pi$
$109$	5.44983	−	3.14646i	0.521999	−	0.301376i	0.737752	+	0.675072i	$0.235887\pi$
$110$	−2.97897	+	0.438801i	−0.284034	+	0.0418381i
$111$		−	1.29651i		−	0.123059i
$112$	4.07353	+	9.76762i	0.384912	+	0.922953i
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.999779	+	0.0210265i	$0.00669344\pi$
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.0210265	+	0.999779i	$0.493307\pi$
$114$	7.00732	−	0.392101i	0.656295	−	0.0367236i
$115$	−0.704685	−	0.999818i	−0.0657122	−	0.0932335i
$116$	−14.3713	+	1.61337i	−1.33434	+	0.149798i
$117$	1.67078	+	6.23545i	0.154464	+	0.576468i
$118$	3.64360	−	17.4450i	0.335420	−	1.60595i
$119$	0.634353	−	7.00765i	0.0581511	−	0.642390i
$120$	−3.96773	+	6.81308i	−0.362202	+	0.621946i
$121$	−5.04666	+	8.74107i	−0.458787	+	0.794643i
$122$	−8.09245	+	2.66108i	−0.732656	+	0.240923i
$123$	−4.47272	−	1.19846i	−0.403292	−	0.108062i
$124$	4.68563	+	6.35419i	0.420782	+	0.570623i
$125$	5.50036	−	9.73376i	0.491967	−	0.870614i
$126$	4.77572	−	2.54252i	0.425455	−	0.226506i
$127$	−1.22418	−	1.22418i	−0.108629	−	0.108629i	0.650703	−	0.759332i	$-0.274474\pi$
$127$	−1.22418	−	1.22418i	−0.108629	−	0.108629i	−0.759332	+	0.650703i	$0.774474\pi$
$128$	−4.34436	+	10.4464i	−0.383991	+	0.923337i
$129$	13.3337	−	7.69820i	1.17396	−	0.677788i
$130$	5.60214	+	12.9586i	0.491340	+	1.13654i
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	0.449831	−	0.893114i	$-0.351484\pi$
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	−0.548544	+	0.836122i	$0.684818\pi$
$132$	−0.866437	−	2.21027i	−0.0754137	−	0.192380i
$133$	−9.88652	−	3.63214i	−0.857270	−	0.314947i
$134$	17.6300	−	11.5379i	1.52300	−	0.996724i
$135$	11.2481	+	5.20290i	0.968081	+	0.447794i
$136$	5.79522	−	4.79560i	0.496936	−	0.411219i
$137$	−1.12037	−	0.300203i	−0.0957198	−	0.0256480i	0.210641	−	0.977563i	$-0.432445\pi$
$137$	−1.12037	−	0.300203i	−0.0957198	−	0.0256480i	−0.306361	+	0.951915i	$0.599111\pi$
$138$	0.642768	−	0.718965i	0.0547161	−	0.0612024i
$139$	−17.4513			−1.48020			−0.740099	−	0.672498i	$-0.765221\pi$
$139$	−17.4513			−1.48020			−0.740099	+	0.672498i	$0.765221\pi$
$140$	9.52246	−	7.02302i	0.804794	−	0.593554i
$141$	−3.99813			−0.336704
$142$	−7.17023	+	8.02022i	−0.601712	+	0.673042i
$143$	−4.10614	−	1.10024i	−0.343373	−	0.0920065i
$144$	5.52556	+	1.70931i	0.460464	+	0.142442i
$145$	5.57680	+	15.1763i	0.463128	+	1.26033i
$146$	−17.4178	+	11.3990i	−1.44151	+	0.943392i
$147$	8.69745	−	0.708187i	0.717353	−	0.0584103i
$148$	−1.93659	+	0.759151i	−0.159186	+	0.0624018i
$149$	9.70894	+	5.60546i	0.795387	+	0.459217i	0.841856	−	0.539703i	$-0.181463\pi$
$149$	9.70894	+	5.60546i	0.795387	+	0.459217i	−0.0464684	+	0.998920i	$0.514797\pi$
$150$	8.45427	+	2.49527i	0.690289	+	0.203738i
$151$	13.0081	−	7.51022i	1.05858	−	0.611173i	0.133543	−	0.991043i	$-0.457365\pi$
$151$	13.0081	−	7.51022i	1.05858	−	0.611173i	0.925040	+	0.379870i	$0.124031\pi$
$152$	−4.68870	−	10.2372i	−0.380304	−	0.830345i
$153$	−2.71920	−	2.71920i	−0.219835	−	0.219835i
$154$	−0.122463	+	3.56070i	−0.00986832	+	0.286929i
$155$	5.65292	−	6.77924i	0.454054	−	0.544521i
$156$	−8.95839	+	6.60600i	−0.717245	+	0.528903i
$157$	−7.27171	−	1.94845i	−0.580345	−	0.155503i	−0.0433084	−	0.999062i	$-0.513790\pi$
$157$	−7.27171	−	1.94845i	−0.580345	−	0.155503i	−0.537037	+	0.843559i	$0.680456\pi$
$158$	−14.3712	+	4.72576i	−1.14331	+	0.375961i
$159$	1.83212	−	3.17333i	0.145297	−	0.251662i
$160$	12.4999	+	1.93728i	0.988202	+	0.153155i
$161$	−1.31354	+	0.607707i	−0.103522	+	0.0478941i
$162$	−0.743432	+	3.55944i	−0.0584095	+	0.279656i
$163$	−1.72089	−	6.42243i	−0.134790	−	0.503044i	−0.999999	−	0.00163153i	$-0.999481\pi$
$163$	−1.72089	−	6.42243i	−0.134790	−	0.503044i	0.865208	−	0.501412i	$-0.167186\pi$
$164$	0.828796	+	7.38261i	0.0647181	+	0.576485i
$165$	−2.16953	+	1.52911i	−0.168897	+	0.119041i
$166$	−11.4310	+	0.639635i	−0.887221	+	0.0496453i
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	0.439276	−	0.898352i	$-0.355235\pi$
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	−0.898352	+	0.439276i	$0.855235\pi$
$168$	7.08681	+	6.06650i	0.546759	+	0.468040i
$169$			6.93083i			0.533141i
$170$	−6.74988	−	5.01667i	−0.517692	−	0.384761i
$171$	−4.98516	+	2.87818i	−0.381225	+	0.220100i
$172$	−19.3060	−	15.4088i	−1.47207	−	1.17491i
$173$	2.13818	−	0.572923i	0.162563	−	0.0435585i	−0.176620	−	0.984279i	$-0.556516\pi$
$173$	2.13818	−	0.572923i	0.162563	−	0.0435585i	0.339182	+	0.940721i	$0.389850\pi$
$174$	−10.6664	+	6.98064i	−0.808621	+	0.529201i
$175$	−10.1606	−	8.47125i	−0.768070	−	0.640366i
$176$	−2.79414	+	2.58838i	−0.210616	+	0.195106i
$177$	−4.06587	−	15.1740i	−0.305610	−	1.14055i
$178$	0.935563	+	2.84508i	0.0701234	+	0.213248i
$179$	−8.23493	−	14.2633i	−0.615507	−	1.06609i	−0.990295	−	0.138980i	$-0.955618\pi$
$179$	−8.23493	−	14.2633i	−0.615507	−	1.06609i	0.374788	−	0.927111i	$-0.377716\pi$
$180$	0.385530	−	6.45510i	0.0287357	−	0.481135i
$181$	−5.97636			−0.444219			−0.222110	−	0.975022i	$-0.571294\pi$
$181$	−5.97636			−0.444219			−0.222110	+	0.975022i	$0.571294\pi$
$182$	16.2741	−	3.76622i	1.20632	−	0.279171i
$183$	−5.30976	+	5.30976i	−0.392508	+	0.392508i
$184$	−1.45027	−	0.539119i	−0.106916	−	0.0397444i
$185$	1.33977	+	1.90089i	0.0985018	+	0.139756i
$186$	6.21192	+	3.13750i	0.455480	+	0.230052i
$187$	2.44606	−	0.655419i	0.178873	−	0.0479290i
$188$	2.34104	+	5.97198i	0.170738	+	0.435551i
$189$	8.44690	−	11.9865i	0.614422	−	0.871887i
$190$	−9.86863	+	7.81600i	−0.715946	+	0.567032i
$191$	−6.96830	−	4.02315i	−0.504209	−	0.291105i	0.226241	−	0.974071i	$-0.427356\pi$
$191$	−6.96830	−	4.02315i	−0.504209	−	0.291105i	−0.730450	+	0.682966i	$0.760690\pi$
$192$	0.733203	+	9.94585i	0.0529144	+	0.717780i
$193$	−3.76831	+	14.0635i	−0.271249	+	1.01231i	0.687065	+	0.726596i	$0.258899\pi$
$193$	−3.76831	+	14.0635i	−0.271249	+	1.01231i	−0.958314	+	0.285718i	$0.907768\pi$
$194$	6.16213	−	0.344807i	0.442415	−	0.0247557i
$195$	9.55764	+	7.96972i	0.684437	+	0.570723i
$196$	−6.15046	−	12.5766i	−0.439319	−	0.898331i
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.194001	−	0.981001i	$-0.437854\pi$
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.981001	−	0.194001i	$-0.0621465\pi$
$198$	1.45163	+	1.29778i	0.103163	+	0.0922295i
$199$	4.82793	+	8.36222i	0.342243	+	0.592782i	0.984849	−	0.173415i	$-0.0554801\pi$
$199$	4.82793	+	8.36222i	0.342243	+	0.592782i	−0.642606	+	0.766197i	$0.722147\pi$
$200$	−1.22309	−	14.0891i	−0.0864857	−	0.996253i
$201$	9.28636	−	16.0844i	0.655009	−	1.13451i
$202$	0.413507	−	1.97981i	0.0290943	−	0.139299i
$203$	18.8502	−	3.26531i	1.32302	−	0.229180i
$204$	2.65399	−	6.07630i	0.185816	−	0.425426i
$205$	7.79615	−	2.86482i	0.544507	−	0.200088i
$206$	6.48778	−	12.8451i	0.452025	−	0.894962i
$207$	−0.204725	+	0.764042i	−0.0142293	+	0.0531046i
$208$	15.1128	+	9.51304i	1.04788	+	0.659610i
$209$		−	3.79066i		−	0.262205i
$210$	4.70146	−	9.31009i	0.324432	−	0.642458i
$211$			10.4344i			0.718333i	0.933274	+	0.359166i	$0.116939\pi$
$211$			10.4344i			0.718333i	−0.933274	+	0.359166i	$0.883061\pi$
$212$	−5.81275	−	0.878535i	−0.399221	−	0.0603381i
$213$	−2.45439	+	9.15992i	−0.168172	+	0.627628i
$214$	0.0507779	+	0.0256468i	0.00347111	+	0.00175318i
$215$	−11.5942	+	25.0653i	−0.790716	+	1.70944i
$216$	15.4563	−	2.61649i	1.05167	−	0.178029i
$217$	−6.68921	−	8.02081i	−0.454093	−	0.544488i
$218$	−8.71155	−	1.81951i	−0.590020	−	0.123233i
$219$	−9.17459	+	15.8909i	−0.619961	+	1.07380i
$220$	3.55435	+	2.34526i	0.239634	+	0.158117i
$221$	−5.93647	−	10.2823i	−0.399330	−	0.691660i
$222$	−1.22205	+	1.36692i	−0.0820187	+	0.0917416i
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	−0.249973	−	0.968253i	$-0.580422\pi$
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	0.968253	+	0.249973i	$0.0804218\pi$
$224$	4.91191	−	14.1377i	0.328191	−	0.944611i
$225$	−7.11217	+	1.29934i	−0.474145	+	0.0866230i
$226$	−1.21249	−	21.6687i	−0.0806539	−	1.44138i
$227$	−2.59397	+	9.68083i	−0.172168	+	0.642539i	0.824849	+	0.565353i	$0.191260\pi$
$227$	−2.59397	+	9.68083i	−0.172168	+	0.642539i	−0.997017	+	0.0771860i	$0.975406\pi$
$228$	−7.75744	−	6.19149i	−0.513749	−	0.410041i
$229$	−14.7989	−	8.54416i	−0.977940	−	0.564614i	−0.0762921	−	0.997086i	$-0.524308\pi$
$229$	−14.7989	−	8.54416i	−0.977940	−	0.564614i	−0.901647	+	0.432472i	$0.857641\pi$
$230$	−0.199444	+	1.71833i	−0.0131510	+	0.113303i
$231$	1.31868	+	2.85029i	0.0867627	+	0.187535i
$232$	16.6725	+	11.8450i	1.09460	+	0.777661i
$233$	1.81156	−	0.485407i	0.118680	−	0.0318001i	−0.198990	−	0.980001i	$-0.563766\pi$
$233$	1.81156	−	0.485407i	0.118680	−	0.0318001i	0.317670	+	0.948201i	$0.397100\pi$
$234$	4.11583	−	8.14891i	0.269060	−	0.532711i
$235$	5.86188	−	4.13153i	0.382387	−	0.269512i
$236$	−20.2846	+	14.9581i	−1.32042	+	0.973687i
$237$	−9.42947	+	9.42947i	−0.612510	+	0.612510i
$238$	−7.27400	+	6.79029i	−0.471503	+	0.440149i
$239$	15.2182			0.984385			0.492193	−	0.870486i	$-0.336196\pi$
$239$	15.2182			0.984385			0.492193	+	0.870486i	$0.336196\pi$
$240$	10.6050	−	3.44321i	0.684550	−	0.222258i
$241$	6.58780	+	11.4104i	0.424357	+	0.735008i	0.996360	−	0.0852432i	$-0.0271667\pi$
$241$	6.58780	+	11.4104i	0.424357	+	0.735008i	−0.572003	+	0.820252i	$0.693833\pi$
$242$	13.5598	−	4.45894i	0.871656	−	0.286632i
$243$	−3.47383	−	12.9645i	−0.222846	−	0.831673i
$244$	11.0402	+	4.82210i	0.706775	+	0.308703i
$245$	−12.0200	+	10.0260i	−0.767929	+	0.640535i
$246$	3.58599	+	5.47940i	0.228634	+	0.349354i
$247$	−17.1670	+	4.59987i	−1.09231	+	0.292683i
$248$	1.04917	−	11.1158i	0.0666222	−	0.705854i
$249$	−8.73995	+	5.04601i	−0.553872	+	0.319778i
$250$	−14.9738	+	5.07790i	−0.947027	+	0.321154i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$	−7.43158	−	1.82084i	−0.468145	−	0.114702i
$253$	−0.368320	−	0.368320i	−0.0231561	−	0.0231561i
$254$	0.136786	+	2.44454i	0.00858275	+	0.153384i
$255$	−7.30457	−	1.26478i	−0.457430	−	0.0792035i
$256$	14.4267	−	6.91881i	0.901670	−	0.432426i
$257$	3.42109	+	12.7677i	0.213402	+	0.796426i	0.986723	+	0.162412i	$0.0519273\pi$
$257$	3.42109	+	12.7677i	0.213402	+	0.796426i	−0.773321	+	0.634014i	$0.781406\pi$
$258$	−21.3139	−	4.45165i	−1.32694	−	0.277148i
$259$	2.49735	−	1.15539i	0.155178	−	0.0717926i
$260$	6.30798	−	18.9427i	0.391204	−	1.17478i
$261$	5.22778	−	9.05478i	0.323592	−	0.560477i
$262$	0.576336	+	1.75266i	0.0356061	+	0.108279i
$263$	−10.2083	−	2.73529i	−0.629468	−	0.168665i	−0.0700398	−	0.997544i	$-0.522313\pi$
$263$	−10.2083	−	2.73529i	−0.629468	−	0.168665i	−0.559428	+	0.828879i	$0.688979\pi$
$264$	−1.16985	+	3.14698i	−0.0719991	+	0.193683i
$265$	0.593033	+	6.54585i	0.0364298	+	0.402108i
$266$	6.99988	+	13.1481i	0.429190	+	0.806164i
$267$	1.86676	+	1.86676i	0.114244	+	0.114244i
$268$	−29.4627	−	4.45297i	−1.79972	−	0.272009i
$269$	−10.5625	+	6.09826i	−0.644007	+	0.371818i	−0.786156	−	0.618027i	$-0.787932\pi$
$269$	−10.5625	+	6.09826i	−0.644007	+	0.371818i	0.142149	+	0.989845i	$0.454599\pi$
$270$	−6.95484	−	16.0876i	−0.423258	−	0.979058i
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	0.663036	−	0.748588i	$-0.269268\pi$
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	−0.316778	+	0.948500i	$0.602601\pi$
$272$	−10.6301	−	0.406362i	−0.644546	−	0.0246393i
$273$	11.3081	−	9.43072i	0.684395	−	0.570773i
$274$	0.898253	+	1.37253i	0.0542655	+	0.0829178i
$275$	1.60073	−	4.48383i	0.0965278	−	0.270385i
$276$	−1.35535	+	0.152156i	−0.0815824	+	0.00915872i
$277$	3.96687	+	1.06292i	0.238346	+	0.0638646i	0.376015	−	0.926614i	$-0.377294\pi$
$277$	3.96687	+	1.06292i	0.238346	+	0.0638646i	−0.137669	+	0.990478i	$0.543961\pi$
$278$	18.3990	+	16.4490i	1.10350	+	0.986548i
$279$	−5.70799			−0.341728
$280$	−16.6593	−	1.57116i	−0.995582	−	0.0938947i
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	4.21526	+	3.76852i	0.251015	+	0.224412i
$283$	18.8626	+	5.05423i	1.12127	+	0.300443i	0.771396	−	0.636355i	$-0.219559\pi$
$283$	18.8626	+	5.05423i	1.12127	+	0.300443i	0.349872	+	0.936798i	$0.386225\pi$
$284$	15.1192	−	1.69734i	0.897161	−	0.100718i
$285$	−4.65870	+	10.0716i	−0.275958	+	0.596590i
$286$	3.29208	+	5.03032i	0.194665	+	0.297449i
$287$	−1.67740	−	9.68341i	−0.0990140	−	0.571594i
$288$	−4.21450	−	7.01036i	−0.248342	−	0.413090i
$289$	−8.59722	−	4.96361i	−0.505719	−	0.291977i
$290$	8.42511	−	21.2570i	0.494739	−	1.24826i
$291$	4.71144	−	2.72015i	0.276190	−	0.159458i
$292$	29.1081	+	4.39938i	1.70342	+	0.257454i
$293$	12.6859	+	12.6859i	0.741121	+	0.741121i	0.972794	−	0.231673i	$-0.0744200\pi$
$293$	12.6859	+	12.6859i	0.741121	+	0.741121i	−0.231673	+	0.972794i	$0.574420\pi$
$294$	−9.83729	−	7.45130i	−0.573723	−	0.434569i
$295$	21.6415	+	18.0460i	1.26002	+	1.05068i
$296$	2.75731	+	1.02499i	0.160265	+	0.0595764i
$297$	5.09762	+	1.36590i	0.295794	+	0.0792577i
$298$	−4.95266	−	15.0612i	−0.286900	−	0.872473i
$299$	−1.22108	+	2.11498i	−0.0706170	+	0.122312i
$300$	−6.56143	−	10.5995i	−0.378824	−	0.611964i
$301$	26.7107	+	18.8231i	1.53958	+	1.08495i
$302$	−20.7934	−	4.34295i	−1.19653	−	0.249909i
$303$	−0.461430	−	1.72208i	−0.0265085	−	0.0989309i
$304$	−4.70593	+	15.2126i	−0.269904	+	0.872500i
$305$	2.29801	−	13.2718i	0.131584	−	0.759944i
$306$	0.303836	+	5.42991i	0.0173691	+	0.310407i
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	0.362387	−	0.932028i	$-0.381962\pi$
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	−0.932028	+	0.362387i	$0.881962\pi$
$308$	3.48532	−	3.63864i	0.198594	−	0.207331i
$309$		−	12.6850i		−	0.721626i
$310$	−12.3498	+	1.81912i	−0.701422	+	0.103319i
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	−0.801544	−	0.597935i	$-0.795988\pi$
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	0.117055	+	0.993125i	$0.462655\pi$
$312$	15.6715	+	1.47916i	0.887224	+	0.0837409i
$313$	−4.74109	+	1.27037i	−0.267982	+	0.0718056i	−0.390308	−	0.920684i	$-0.627631\pi$
$313$	−4.74109	+	1.27037i	−0.267982	+	0.0718056i	0.122326	+	0.992490i	$0.460965\pi$
$314$	5.83006	+	8.90835i	0.329009	+	0.502727i
$315$	0.000626383		8.55452i	3.52927e−5		0.481992i
$316$	19.6060	+	8.56345i	1.10292	+	0.481732i
$317$	8.90414	+	33.2307i	0.500106	+	1.86642i	0.499312	+	0.866423i	$0.333586\pi$
$317$	8.90414	+	33.2307i	0.500106	+	1.86642i	0.000794747		1.00000i	$0.499747\pi$
$318$	−4.92271	+	1.61876i	−0.276052	+	0.0907756i
$319$	3.44258	+	5.96272i	0.192747	+	0.333848i
$320$	−11.3527	−	13.8245i	−0.634634	−	0.772812i
$321$	0.0501451			0.00279883
$322$	1.95768	+	0.597395i	0.109097	+	0.0332915i
$323$	7.48630	−	7.48630i	0.416549	−	0.416549i
$324$	4.13883	−	3.05201i	0.229935	−	0.169556i
$325$	−22.2486	−	1.80831i	−1.23413	−	0.100307i
$326$	−4.23925	+	8.39327i	−0.234790	+	0.464860i
$327$	−7.57748	+	2.03038i	−0.419035	+	0.112280i
$328$	6.08482	−	8.56473i	0.335978	−	0.472908i
$329$	−3.56296	−	7.70124i	−0.196432	−	0.424583i
$330$	3.72864	+	0.432778i	0.205255	+	0.0238237i
$331$	11.2201	+	6.47792i	0.616712	+	0.356059i	0.775588	−	0.631240i	$-0.217454\pi$
$331$	11.2201	+	6.47792i	0.616712	+	0.356059i	−0.158876	+	0.987299i	$0.550787\pi$
$332$	12.6547	+	10.1002i	0.694518	+	0.554320i
$333$	0.389229	−	1.45262i	0.0213296	−	0.0796032i
$334$	0.662889	+	11.8466i	0.0362717	+	0.648219i
$335$	3.00587	+	33.1785i	0.164228	+	1.81274i
$336$	−1.75358	−	13.0758i	−0.0956655	−	0.713341i
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	−0.475136	−	0.879912i	$-0.657601\pi$
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	0.879912	+	0.475136i	$0.157601\pi$
$338$	6.53279	−	7.30722i	0.355337	−	0.397461i
$339$	−9.56524	−	16.5675i	−0.519513	−	0.899822i
$340$	2.38788	+	11.6513i	0.129501	+	0.631883i
$341$	1.87940	−	3.25522i	0.101775	−	0.176280i
$342$	7.96877	+	1.66437i	0.430902	+	0.0899989i
$343$	9.11490	+	16.1220i	0.492158	+	0.870506i
$344$	5.83059	+	34.4429i	0.314364	+	1.85704i
$345$	0.525944	+	1.43127i	0.0283159	+	0.0770571i
$346$	−2.79431	−	1.41134i	−0.150223	−	0.0758743i
$347$	2.37153	−	8.85066i	0.127310	−	0.475128i	−0.872601	−	0.488433i	$-0.837569\pi$
$347$	2.37153	−	8.85066i	0.127310	−	0.475128i	0.999911	+	0.0133050i	$0.00423525\pi$
$348$	17.8254	+	2.69413i	0.955544	+	0.144420i
$349$			19.9513i			1.06797i	0.845495	+	0.533984i	$0.179306\pi$
$349$			19.9513i			1.06797i	−0.845495	+	0.533984i	$0.820694\pi$
$350$	2.72766	+	18.5084i	0.145799	+	0.989314i
$351$		−	24.7434i		−	1.32070i
$352$	5.38561	−	0.0952748i	0.287054	−	0.00507817i
$353$	0.641552	−	2.39430i	0.0341464	−	0.127436i	−0.946749	−	0.321973i	$-0.895654\pi$
$353$	0.641552	−	2.39430i	0.0341464	−	0.127436i	0.980895	+	0.194537i	$0.0623205\pi$
$354$	−10.0159	+	19.8305i	−0.532340	+	1.05398i
$355$	−5.86703	−	15.9662i	−0.311389	−	0.847396i
$356$	1.69532	−	3.88142i	0.0898516	−	0.205715i
$357$	−3.02482	+	8.23343i	−0.160091	+	0.435759i
$358$	−4.76203	+	22.7999i	−0.251681	+	1.20501i
$359$	−7.94645	+	13.7637i	−0.419398	+	0.726418i	−0.995879	−	0.0906921i	$-0.971092\pi$
$359$	−7.94645	+	13.7637i	−0.419398	+	0.726418i	0.576481	+	0.817110i	$0.304425\pi$
$360$	−6.49085	+	6.44227i	−0.342098	+	0.339537i
$361$	1.57601	+	2.72973i	0.0829481	+	0.143670i
$362$	6.30091	+	5.63313i	0.331169	+	0.296071i
$363$	8.89708	−	8.89708i	0.466976	−	0.466976i
$364$	−20.7078	−	11.3688i	−1.08539	−	0.595884i
$365$	−2.96969	−	32.7792i	−0.155441	−	1.71574i
$366$	10.6029	−	0.593297i	0.554224	−	0.0310121i
$367$	2.78634	−	10.3988i	0.145446	−	0.542812i	−0.854289	−	0.519798i	$-0.826007\pi$
$367$	2.78634	−	10.3988i	0.145446	−	0.542812i	0.999735	−	0.0230136i	$-0.00732610\pi$
$368$	1.02088	+	1.93538i	0.0532169	+	0.100889i
$369$	−4.65148	−	2.68553i	−0.242147	−	0.139803i
$370$	0.379189	−	3.26694i	0.0197131	−	0.169840i
$371$	7.74521	+	0.701119i	0.402111	+	0.0364003i
$372$	−3.59195	−	9.16305i	−0.186234	−	0.475082i
$373$	14.2618	−	3.82144i	0.738448	−	0.197867i	0.130060	−	0.991506i	$-0.458483\pi$
$373$	14.2618	−	3.82144i	0.738448	−	0.197867i	0.608388	+	0.793640i	$0.291816\pi$
$374$	−3.19667	−	1.61457i	−0.165296	−	0.0834873i
$375$	−9.76368	+	9.94602i	−0.504194	+	0.513610i
$376$	3.16083	−	8.50289i	0.163007	−	0.438503i
$377$	22.8262	−	22.8262i	1.17561	−	1.17561i
$378$	−20.2037	+	4.67561i	−1.03917	+	0.240488i
$379$	−26.4563			−1.35897			−0.679483	−	0.733691i	$-0.737796\pi$
$379$	−26.4563			−1.35897			−0.679483	+	0.733691i	$0.737796\pi$
$380$	17.7717	+	1.06141i	0.911668	+	0.0544492i
$381$	1.07909	+	1.86905i	0.0552837	+	0.0957542i
$382$	3.55463	+	10.8097i	0.181871	+	0.553075i
$383$	−7.60437	−	28.3799i	−0.388565	−	1.45015i	−0.832470	−	0.554071i	$-0.813074\pi$
$383$	−7.60437	−	28.3799i	−0.388565	−	1.45015i	0.443904	−	0.896074i	$-0.353593\pi$
$384$	8.60163	−	11.1771i	0.438950	−	0.570377i
$385$	−4.87877	−	2.81629i	−0.248645	−	0.143531i
$386$	17.2288	−	11.2754i	0.876922	−	0.573901i
$387$	17.2503	−	4.62219i	0.876880	−	0.234959i
$388$	−6.82177	−	5.44470i	−0.346323	−	0.276413i
$389$	−8.09963	+	4.67632i	−0.410667	+	0.237099i	−0.691076	−	0.722782i	$-0.742863\pi$
$389$	−8.09963	+	4.67632i	−0.410667	+	0.237099i	0.280409	+	0.959881i	$0.409530\pi$
$390$	−2.56467	−	17.4113i	−0.129867	−	0.881654i
$391$		−	1.45481i		−	0.0735731i
$392$	−5.36988	+	19.0569i	−0.271220	+	0.962517i
$393$	1.14998	+	1.14998i	0.0580090	+	0.0580090i
$394$	−32.9324	+	1.84276i	−1.65911	+	0.0928370i
$395$	4.08098	−	23.5692i	0.205336	−	1.18589i
$396$	−0.307212	−	2.73653i	−0.0154380	−	0.137516i
$397$	−4.59912	−	17.1641i	−0.230823	−	0.861443i	−0.979987	−	0.199059i	$-0.936211\pi$
$397$	−4.59912	−	17.1641i	−0.230823	−	0.861443i	0.749164	−	0.662384i	$-0.230455\pi$
$398$	2.79186	−	13.3670i	0.139943	−	0.670028i
$399$	10.7327	+	7.56340i	0.537309	+	0.378644i
$400$	−11.9905	+	16.0071i	−0.599524	+	0.800357i
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	−0.932564	−	0.361004i	$-0.882434\pi$
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	0.778921	+	0.627122i	$0.215767\pi$
$402$	−24.9514	+	8.20490i	−1.24446	+	0.409223i
$403$	−17.0227	−	4.56121i	−0.847960	−	0.227210i
$404$	−2.30207	+	1.69757i	−0.114532	+	0.0844573i
$405$	−4.41569	−	3.68206i	−0.219417	−	0.182963i
$406$	−22.9516	−	14.3250i	−1.13907	−	0.710935i
$407$	0.700261	+	0.700261i	0.0347107	+	0.0347107i
$408$	−8.52545	+	3.90471i	−0.422073	+	0.193312i
$409$	5.66917	−	3.27310i	0.280322	−	0.161844i	−0.353247	−	0.935530i	$-0.614922\pi$
$409$	5.66917	−	3.27310i	0.280322	−	0.161844i	0.633569	+	0.773686i	$0.281589\pi$
$410$	−10.9198	−	4.32801i	−0.539292	−	0.213745i
$411$	1.25221	+	0.722965i	0.0617670	+	0.0356612i
$412$	−18.9475	+	7.42751i	−0.933478	+	0.365927i
$413$	25.6050	−	21.3541i	1.25994	−	1.05077i
$414$	0.936005	−	0.612568i	0.0460022	−	0.0301061i
$415$	7.59975	−	16.4298i	0.373057	−	0.806508i
$416$	−6.96678	−	24.2745i	−0.341575	−	1.19015i
$417$	21.0136	+	5.63057i	1.02904	+	0.275730i
$418$	−3.57296	+	3.99652i	−0.174759	+	0.195476i
$419$	−17.7908			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$419$	−17.7908			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$420$	−13.7322	+	5.38424i	−0.670062	+	0.262724i
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	9.83513	−	11.0010i	0.478767	−	0.535522i
$423$	−4.47954	−	1.20029i	−0.217803	−	0.0583601i
$424$	5.30034	+	6.40517i	0.257407	+	0.311062i
$425$	12.0166	−	5.69392i	0.582891	−	0.276196i
$426$	11.2215	−	7.34393i	0.543686	−	0.355815i
$427$	−14.9595	−	5.49588i	−0.723942	−	0.265964i
$428$	−0.0293616	−	0.0749013i	−0.00141925	−	0.00362049i
$429$	4.58934	+	2.64965i	0.221575	+	0.127926i
$430$	35.8496	−	15.4982i	1.72882	−	0.747389i
$431$	−13.1055	+	7.56644i	−0.631268	+	0.364463i	−0.781243	−	0.624227i	$-0.785414\pi$
$431$	−13.1055	+	7.56644i	−0.631268	+	0.364463i	0.149975	+	0.988690i	$0.452081\pi$
$432$	−18.7619	−	11.8101i	−0.902683	−	0.568212i
$433$	−5.45382	−	5.45382i	−0.262094	−	0.262094i	0.563811	−	0.825904i	$-0.309335\pi$
$433$	−5.45382	−	5.45382i	−0.262094	−	0.262094i	−0.825904	+	0.563811i	$0.809335\pi$
$434$	−0.507689	+	14.7614i	−0.0243698	+	0.708572i
$435$	−1.81860	−	20.0736i	−0.0871953	−	0.962454i
$436$	7.46963	+	10.1296i	0.357730	+	0.485118i
$437$	−2.10350	−	0.563632i	−0.100624	−	0.0269622i
$438$	24.6511	−	8.10614i	1.17787	−	0.387327i
$439$	12.8732	−	22.2970i	0.614402	−	1.06418i	−0.376087	−	0.926585i	$-0.622730\pi$
$439$	12.8732	−	22.2970i	0.614402	−	1.06418i	0.990489	−	0.137592i	$-0.0439362\pi$
$440$	−1.53681	−	5.82285i	−0.0732644	−	0.277593i
$441$	9.95730	+	1.81762i	0.474157	+	0.0865536i
$442$	−3.43289	+	16.4362i	−0.163286	+	0.781790i
$443$	4.47481	+	16.7002i	0.212605	+	0.793452i	0.986996	+	0.160745i	$0.0513897\pi$
$443$	4.47481	+	16.7002i	0.212605	+	0.793452i	−0.774391	+	0.632707i	$0.781944\pi$
$444$	2.57683	−	0.289284i	0.122291	−	0.0137288i
$445$	−4.66601	−	0.807916i	−0.221190	−	0.0382989i
$446$	−21.4189	+	1.19851i	−1.01421	+	0.0567513i
$447$	−9.88223	−	9.88223i	−0.467413	−	0.467413i
$448$	−18.5044	+	10.2756i	−0.874250	+	0.485477i
$449$			11.0999i			0.523839i	0.965090	+	0.261919i	$0.0843555\pi$
$449$			11.0999i			0.523839i	−0.965090	+	0.261919i	$0.915645\pi$
$450$	8.72313	+	5.33381i	0.411212	+	0.251438i
$451$	3.06308	−	1.76847i	0.144235	−	0.0832739i
$452$	−19.1459	+	23.9883i	−0.900549	+	1.12832i
$453$	−18.0865	+	4.84627i	−0.849779	+	0.227698i
$454$	11.8597	−	7.76157i	0.556603	−	0.364268i
$455$	−6.83399	+	25.5123i	−0.320382	+	1.19603i
$456$	2.34281	+	13.8397i	0.109712	+	0.648101i
$457$	−5.49672	−	20.5140i	−0.257126	−	0.959606i	−0.966896	−	0.255172i	$-0.917868\pi$
$457$	−5.49672	−	20.5140i	−0.257126	−	0.959606i	0.709770	−	0.704434i	$-0.248799\pi$
$458$	7.54913	+	22.9572i	0.352748	+	1.07272i
$459$	7.36989	+	12.7650i	0.343997	+	0.595821i
$460$	1.82992	−	1.62366i	0.0853205	−	0.0757033i
$461$	−8.61652			−0.401311			−0.200656	−	0.979662i	$-0.564307\pi$
$461$	−8.61652			−0.401311			−0.200656	+	0.979662i	$0.564307\pi$
$462$	1.29630	−	4.24802i	0.0603094	−	0.197636i
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	−0.744043	−	0.668132i	$-0.767094\pi$
$463$	−1.63340	+	1.63340i	−0.0759103	+	0.0759103i	0.668132	+	0.744043i	$0.267094\pi$
$464$	−6.41320	−	28.2032i	−0.297725	−	1.30930i
$465$	−8.99413	+	6.33918i	−0.417093	+	0.293972i
$466$	−2.36747	−	1.19576i	−0.109671	−	0.0553924i
$467$	24.6125	−	6.59489i	1.13893	−	0.305175i	0.360409	−	0.932794i	$-0.382637\pi$
$467$	24.6125	−	6.59489i	1.13893	−	0.305175i	0.778521	+	0.627619i	$0.215970\pi$
$468$	−12.0203	+	4.71199i	−0.555637	+	0.217812i
$469$	39.2576	+	3.55372i	1.81275	+	0.164095i
$470$	−10.0745	−	1.16933i	−0.464701	−	0.0539372i
$471$	8.12741	+	4.69236i	0.374491	+	0.216213i
$472$	35.4852	+	3.34928i	1.63334	+	0.154163i
$473$	−3.04379	+	11.3596i	−0.139953	+	0.522313i
$474$	18.8295	−	1.05362i	0.864867	−	0.0483944i
$475$	−3.57726	−	19.5807i	−0.164136	−	0.898423i
$476$	14.0693	−	0.302795i	0.644867	−	0.0138786i
$477$	3.00540	−	3.00540i	0.137608	−	0.137608i
$478$	−16.0447	−	14.3442i	−0.733867	−	0.656090i
$479$	−4.63924	−	8.03541i	−0.211972	−	0.367147i	0.740359	−	0.672211i	$-0.234655\pi$
$479$	−4.63924	−	8.03541i	−0.211972	−	0.367147i	−0.952332	+	0.305064i	$0.901322\pi$
$480$	−14.4264	−	6.36575i	−0.658472	−	0.290556i
$481$	2.32156	−	4.02106i	0.105854	−	0.183345i
$482$	3.80954	−	18.2395i	0.173520	−	0.830787i
$483$	1.77775	−	0.307949i	0.0808903	−	0.0140122i
$484$	−18.4990	−	8.07996i	−0.840865	−	0.367271i
$485$	−4.09679	+	8.85680i	−0.186026	+	0.402167i
$486$	−8.55746	+	16.9429i	−0.388174	+	0.768544i
$487$	−4.60932	+	17.2022i	−0.208868	+	0.779506i	0.779368	+	0.626567i	$0.215541\pi$
$487$	−4.60932	+	17.2022i	−0.208868	+	0.779506i	−0.988236	+	0.152939i	$0.951126\pi$
$488$	−7.09457	−	15.4901i	−0.321156	−	0.701204i
$489$			8.28866i			0.374826i
$490$	22.1229	+	0.759249i	0.999412	+	0.0342994i
$491$			2.49970i			0.112810i	0.998408	+	0.0564049i	$0.0179638\pi$
$491$			2.49970i			0.112810i	−0.998408	+	0.0564049i	$0.982036\pi$
$492$	1.38398	−	9.15701i	0.0623949	−	0.412830i
$493$	−4.97711	+	18.5748i	−0.224158	+	0.836569i
$494$	22.4349	+	11.3314i	1.00940	+	0.509823i
$495$	−2.88982	+	1.06191i	−0.129888	+	0.0477293i
$496$	−11.5836	+	10.7305i	−0.520117	+	0.481816i
$497$	−19.8312	+	3.43524i	−0.889550	+	0.154092i
$498$	13.9708	+	2.91797i	0.626047	+	0.130757i
$499$	−3.26199	+	5.64993i	−0.146027	+	0.252926i	−0.929756	−	0.368178i	$-0.879982\pi$
$499$	−3.26199	+	5.64993i	−0.146027	+	0.252926i	0.783729	+	0.621103i	$0.213315\pi$
$500$	20.5733	+	8.76020i	0.920064	+	0.391768i
$501$	5.22947	+	9.05770i	0.233635	+	0.404668i
$502$	13.8603	−	15.5034i	0.618617	−	0.691951i
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	−0.953313	−	0.301985i	$-0.902351\pi$
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	0.301985	+	0.953313i	$0.402351\pi$
$504$	6.11889	+	8.92451i	0.272557	+	0.397529i
$505$	2.45607	+	2.04801i	0.109294	+	0.0911353i
$506$	0.0411550	+	0.735489i	0.00182956	+	0.0326965i
$507$	2.23620	−	8.34561i	0.0993131	−	0.370641i
$508$	2.15993	−	2.70623i	0.0958316	−	0.120069i
$509$	−29.8459	−	17.2316i	−1.32290	−	0.763775i	−0.338708	−	0.940892i	$-0.609990\pi$
$509$	−29.8459	−	17.2316i	−1.32290	−	0.763775i	−0.984190	+	0.177116i	$0.943323\pi$
$510$	6.50911	+	8.21853i	0.288228	+	0.363922i
$511$	−38.7851	−	3.51094i	−1.71575	−	0.155315i
$512$	−21.7316	−	6.30364i	−0.960412	−	0.278584i
$513$	21.3121	−	5.71056i	0.940953	−	0.252128i
$514$	8.42755	−	16.6857i	0.371723	−	0.735973i
$515$	13.1083	+	18.5982i	0.577620	+	0.819536i
$516$	18.2754	+	24.7832i	0.804528	+	1.09102i
$517$	2.15944	−	2.15944i	0.0949721	−	0.0949721i
$518$	−3.72201	−	1.13579i	−0.163536	−	0.0499036i
$519$	−2.75949			−0.121128
$520$	−24.5054	+	14.0257i	−1.07463	+	0.615068i
$521$	16.9526	+	29.3627i	0.742705	+	1.28640i	0.951259	+	0.308392i	$0.0997908\pi$
$521$	16.9526	+	29.3627i	0.742705	+	1.28640i	−0.208555	+	0.978011i	$0.566876\pi$
$522$	−14.0465	+	4.61897i	−0.614796	+	0.202167i
$523$	4.77618	+	17.8250i	0.208848	+	0.779431i	0.988242	+	0.152897i	$0.0488604\pi$
$523$	4.77618	+	17.8250i	0.208848	+	0.779431i	−0.779394	+	0.626534i	$0.784473\pi$
$524$	1.04437	−	2.39107i	0.0456233	−	0.104455i
$525$	9.50146	+	13.4787i	0.414678	+	0.588260i
$526$	8.18443	+	12.5058i	0.356858	+	0.545280i
$527$	10.1405	−	2.71715i	0.441728	−	0.118361i
$528$	4.19963	−	2.21522i	0.182765	−	0.0964053i
$529$	19.6594	−	11.3504i	0.854758	−	0.493495i
$530$	5.54468	−	7.46031i	0.240846	−	0.324055i
$531$		−	18.2217i		−	0.790756i
$532$	5.01301	−	20.4600i	0.217341	−	0.887055i
$533$	−11.7259	−	11.7259i	−0.507906	−	0.507906i
$534$	−0.208587	−	3.72769i	−0.00902643	−	0.161313i
$535$	−0.0735205	+	0.0518182i	−0.00317857	+	0.00224030i
$536$	26.8655	+	32.4654i	1.16041	+	1.40229i
$537$	5.31392	+	19.8318i	0.229312	+	0.855806i
$538$	16.8842	+	3.52645i	0.727928	+	0.152036i
$539$	−4.31510	+	5.08010i	−0.185864	+	0.218815i
$540$	−7.83111	+	23.5166i	−0.336997	+	1.01199i
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	−0.898208	−	0.439572i	$-0.855130\pi$
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	0.829784	+	0.558085i	$0.188464\pi$
$542$	−2.90771	−	8.84244i	−0.124897	−	0.379815i
$543$	7.19630	+	1.92824i	0.308823	+	0.0827488i
$544$	10.8244	+	10.4481i	0.464092	+	0.447957i
$545$	9.01164	−	10.8072i	0.386016	−	0.462928i
$546$	−20.8113	−	0.715760i	−0.890640	−	0.0306317i
$547$	15.6791	+	15.6791i	0.670391	+	0.670391i	0.957806	−	0.287415i	$-0.0927960\pi$
$547$	15.6791	+	15.6791i	0.670391	+	0.670391i	−0.287415	+	0.957806i	$0.592796\pi$
$548$	0.346674	−	2.29374i	0.0148092	−	0.0979836i
$549$	−7.54315	+	4.35504i	−0.321934	+	0.185869i
$550$	−5.91398	+	3.21853i	−0.252173	+	0.137239i
$551$	24.9289	+	14.3927i	1.06201	+	0.613151i
$552$	1.57237	+	1.11709i	0.0669246	+	0.0475466i
$553$	−26.5663	−	9.76000i	−1.12971	−	0.415037i
$554$	−3.18042	−	4.85969i	−0.135123	−	0.206469i
$555$	−0.999942	−	2.72118i	−0.0424452	−	0.115508i
$556$	−3.89382	−	34.6847i	−0.165135	−	1.47096i
$557$	−20.6171	−	5.52434i	−0.873575	−	0.234074i	−0.205942	−	0.978564i	$-0.566026\pi$
$557$	−20.6171	−	5.52434i	−0.873575	−	0.234074i	−0.667633	+	0.744491i	$0.732692\pi$
$558$	6.01797	+	5.38017i	0.254761	+	0.227761i
$559$	55.1382			2.33210
$560$	16.0831	+	17.3590i	0.679633	+	0.733552i
$561$	−3.15683			−0.133282
$562$	34.0302	+	30.4236i	1.43548	+	1.28334i
$563$	−13.1487	−	3.52319i	−0.554153	−	0.148485i	−0.0291340	−	0.999576i	$-0.509275\pi$
$563$	−13.1487	−	3.52319i	−0.554153	−	0.148485i	−0.525019	+	0.851091i	$0.675942\pi$
$564$	−0.892084	−	7.94635i	−0.0375635	−	0.334602i
$565$	31.1444	+	14.4061i	1.31025	+	0.606070i
$566$	−15.1231	−	23.1081i	−0.635669	−	0.971305i
$567$	−5.22439	+	4.35705i	−0.219404	+	0.182979i
$568$	−17.5402	−	12.4614i	−0.735969	−	0.522869i
$569$	20.3421	+	11.7445i	0.852787	+	0.492357i	0.861590	−	0.507605i	$-0.169469\pi$
$569$	20.3421	+	11.7445i	0.852787	+	0.492357i	−0.00880335	+	0.999961i	$0.502802\pi$
$570$	14.4049	−	6.22740i	0.603354	−	0.260837i
$571$	23.4830	−	13.5579i	0.982734	−	0.567382i	0.0796395	−	0.996824i	$-0.474623\pi$
$571$	23.4830	−	13.5579i	0.982734	−	0.567382i	0.903094	+	0.429442i	$0.141290\pi$
$572$	1.27056	−	8.40651i	0.0531246	−	0.351494i
$573$	7.09267	+	7.09267i	0.296301	+	0.296301i
$574$	−7.35879	+	11.7904i	−0.307150	+	0.492120i
$575$	−2.25014	−	1.55497i	−0.0938374	−	0.0648469i
$576$	−2.16438	+	11.3635i	−0.0901826	+	0.473480i
$577$	−26.9522	−	7.22183i	−1.12204	−	0.300649i	−0.350329	−	0.936627i	$-0.613930\pi$
$577$	−26.9522	−	7.22183i	−1.12204	−	0.300649i	−0.771707	+	0.635978i	$0.780597\pi$
$578$	4.38556	+	13.3366i	0.182415	+	0.554731i
$579$	9.07505	−	15.7184i	0.377146	−	0.653236i
$580$	−28.9189	+	14.4702i	−1.20079	+	0.600842i
$581$	−17.5083	−	12.3382i	−0.726368	−	0.511874i
$582$	−7.53124	−	1.57299i	−0.312180	−	0.0652024i
$583$	0.724403	+	2.70351i	0.0300017	+	0.111968i
$584$	−26.5421	−	32.0747i	−1.09832	−	1.32726i
$585$	8.31585	+	11.7987i	0.343818	+	0.487815i
$586$	−1.41749	−	25.3323i	−0.0585560	−	1.04647i
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	0.998423	−	0.0561427i	$-0.0178802\pi$
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	−0.0561427	+	0.998423i	$0.517880\pi$
$588$	3.34815	+	17.1283i	0.138075	+	0.706359i
$589$		−	15.7148i		−	0.647516i
$590$	−5.80723	−	39.4246i	−0.239080	−	1.62309i
$591$	−25.1794	+	14.5374i	−1.03574	+	0.597987i
$592$	−1.94092	−	3.67961i	−0.0797715	−	0.151231i
$593$	−36.8872	+	9.88391i	−1.51478	+	0.405883i	−0.918019	−	0.396537i	$-0.870212\pi$
$593$	−36.8872	+	9.88391i	−1.51478	+	0.405883i	−0.596759	+	0.802421i	$0.703545\pi$
$594$	−4.08700	−	6.24494i	−0.167691	−	0.256233i
$595$	−4.07328	−	15.1972i	−0.166988	−	0.623026i
$596$	−8.97462	+	20.5474i	−0.367615	+	0.841653i
$597$	−3.11542	−	11.6269i	−0.127506	−	0.475857i
$598$	3.28091	−	1.07888i	0.134166	−	0.0441186i
$599$	14.4801	+	25.0802i	0.591640	+	1.02475i	0.994012	+	0.109274i	$0.0348526\pi$
$599$	14.4801	+	25.0802i	0.591640	+	1.02475i	−0.402372	+	0.915476i	$0.631814\pi$
$600$	−3.07303	+	17.3598i	−0.125456	+	0.708709i
$601$	−8.88262			−0.362330			−0.181165	−	0.983453i	$-0.557987\pi$
$601$	−8.88262			−0.362330			−0.181165	+	0.983453i	$0.557987\pi$
$602$	−10.4192	−	45.0220i	−0.424653	−	1.83496i
$603$	15.2333	−	15.2333i	0.620347	−	0.620347i
$604$	17.8291	+	24.1780i	0.725456	+	0.983791i
$605$	−3.85057	+	22.2384i	−0.156548	+	0.904121i
$606$	−1.13669	+	2.25053i	−0.0461749	+	0.0914215i
$607$	−44.3709	+	11.8891i	−1.80096	+	0.482565i	−0.994127	−	0.108218i	$-0.965485\pi$
$607$	−44.3709	+	11.8891i	−1.80096	+	0.482565i	−0.806830	+	0.590783i	$0.798819\pi$
$608$	19.3004	−	11.6030i	0.782734	−	0.470565i
$609$	−23.7515	−	2.15006i	−0.962461	−	0.0871249i
$610$	−14.9324	+	11.8266i	−0.604597	+	0.478844i
$611$	−12.4000	−	7.15915i	−0.501651	−	0.289628i
$612$	4.79773	−	6.01118i	0.193937	−	0.242988i
$613$	0.0600047	−	0.223941i	0.00242357	−	0.00904487i	−0.964703	−	0.263339i	$-0.915176\pi$
$613$	0.0600047	−	0.223941i	0.00242357	−	0.00904487i	0.967127	+	0.254294i	$0.0818430\pi$
$614$	1.11524	+	19.9306i	0.0450073	+	0.804335i
$615$	−10.3119	+	0.934224i	−0.415815	+	0.0376716i
$616$	−7.10426	+	0.551085i	−0.286239	+	0.0222038i
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.0957517	+	0.995405i	$0.530525\pi$
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.995405	+	0.0957517i	$0.969475\pi$
$618$	−11.9565	+	13.3739i	−0.480962	+	0.537978i
$619$	−7.14970	−	12.3836i	−0.287371	−	0.497741i	0.685811	−	0.727780i	$-0.259448\pi$
$619$	−7.14970	−	12.3836i	−0.287371	−	0.497741i	−0.973181	+	0.230039i	$0.926115\pi$
$620$	14.7351	+	9.72265i	0.591778	+	0.390471i
$621$	1.51593	−	2.62566i	0.0608320	−	0.105364i
$622$	19.2957	+	4.03012i	0.773685	+	0.161593i
$623$	−1.93220	+	5.25935i	−0.0774119	+	0.210711i
$624$	−15.1284	−	16.3310i	−0.605619	−	0.653762i
$625$	4.03719	−	24.6719i	0.161488	−	0.986875i
$626$	6.19597	+	3.12944i	0.247641	+	0.125078i
$627$	−1.22304	+	4.56444i	−0.0488434	+	0.182286i
$628$	2.25007	−	14.8874i	0.0897875	−	0.594071i
$629$			2.76594i			0.110285i
$630$	8.06257	−	9.01967i	0.321220	−	0.359352i
$631$		−	30.7128i		−	1.22266i	−0.791377	−	0.611328i	$-0.790636\pi$
$631$		−	30.7128i		−	1.22266i	0.791377	−	0.611328i	$-0.209364\pi$
$632$	−12.5991	−	27.5085i	−0.501165	−	1.09423i
$633$	3.36660	−	12.5643i	0.133810	−	0.499387i
$634$	21.9346	−	43.4281i	0.871132	−	1.72475i
$635$	−3.51353	−	1.62521i	−0.139430	−	0.0644946i
$636$	6.71584	+	2.93332i	0.266300	+	0.116314i
$637$	28.2428	+	13.3774i	1.11902	+	0.530033i
$638$	1.99075	−	9.53141i	0.0788144	−	0.377352i
$639$	−5.49985	+	9.52602i	−0.217571	+	0.376843i
$640$	−1.06133	+	25.2759i	−0.0419528	+	0.999120i
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	−0.905257	−	0.424864i	$-0.860322\pi$
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	0.0846851	−	0.996408i	$-0.473012\pi$
$642$	−0.0528683	−	0.0472652i	−0.00208655	−	0.00186541i
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	−0.910090	−	0.414410i	$-0.863988\pi$
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	0.414410	+	0.910090i	$0.363988\pi$
$644$	−1.50091	−	2.47509i	−0.0591442	−	0.0975322i
$645$	22.0481	−	26.4410i	0.868142	−	1.04111i
$646$	−14.9492	+	0.836497i	−0.588169	+	0.0329115i
$647$	−9.22084	+	34.4127i	−0.362509	+	1.35290i	0.508258	+	0.861205i	$0.330290\pi$
$647$	−9.22084	+	34.4127i	−0.362509	+	1.35290i	−0.870767	+	0.491696i	$0.836377\pi$
$648$	−7.24033	−	0.683380i	−0.284427	−	0.0268457i
$649$	10.3917	+	5.99966i	0.407910	+	0.235507i
$650$	21.7524	+	22.8774i	0.853200	+	0.897325i
$651$	5.46679	+	11.8163i	0.214261	+	0.463118i
$652$	12.3807	−	4.85329i	0.484866	−	0.190070i
$653$	−12.7132	+	3.40648i	−0.497505	+	0.133306i	−0.498842	−	0.866693i	$-0.666241\pi$
$653$	−12.7132	+	3.40648i	−0.497505	+	0.133306i	0.00133684	+	0.999999i	$0.499574\pi$
$654$	9.90276	+	5.00166i	0.387229	+	0.195580i
$655$	−2.87441	−	0.497701i	−0.112312	−	0.0194468i
$656$	−14.4881	+	3.29449i	−0.565666	+	0.128628i
$657$	−15.0499	+	15.0499i	−0.587153	+	0.587153i
$658$	−3.50250	+	11.4778i	−0.136542	+	0.447451i
$659$	−10.3786			−0.404294			−0.202147	−	0.979355i	$-0.564792\pi$
$659$	−10.3786			−0.404294			−0.202147	+	0.979355i	$0.564792\pi$
$660$	−3.52321	−	3.97078i	−0.137141	−	0.154563i
$661$	−11.5282	−	19.9675i	−0.448397	−	0.776646i	0.549885	−	0.835240i	$-0.314671\pi$
$661$	−11.5282	−	19.9675i	−0.448397	−	0.776646i	−0.998282	+	0.0585946i	$0.981338\pi$
$662$	−5.72352	−	17.4054i	−0.222451	−	0.676481i
$663$	3.83074	+	14.2965i	0.148774	+	0.555231i
$664$	−3.82184	−	22.5767i	−0.148316	−	0.876144i
$665$	−23.5516	+	0.00172451i	−0.913293	+	6.68736e-5i
$666$	−1.77956	+	1.16463i	−0.0689567	+	0.0451286i
$667$	3.82069	−	1.02375i	0.147938	−	0.0396398i
$668$	10.4674	−	13.1148i	0.404995	−	0.507427i
$669$	−16.3765	+	9.45496i	−0.633151	+	0.365550i
$670$	28.1039	−	37.8136i	1.08575	−	1.46087i
$671$		−	5.73573i		−	0.221425i
$672$	−10.4760	+	15.4387i	−0.404121	+	0.595562i
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.996700	+	0.0811716i	$0.0258662\pi$
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.0811716	+	0.996700i	$0.474134\pi$
$674$	−14.8382	+	0.830285i	−0.571546	+	0.0319814i
$675$	27.6208	+	2.24494i	1.06312	+	0.0864079i
$676$	−13.7751	+	1.54644i	−0.529813	+	0.0594786i
$677$	−8.86132	−	33.0709i	−0.340568	−	1.27102i	−0.897705	−	0.440597i	$-0.854767\pi$
$677$	−8.86132	−	33.0709i	−0.340568	−	1.27102i	0.557137	−	0.830421i	$-0.311900\pi$
$678$	−5.53131	+	26.4831i	−0.212429	+	1.01708i
$679$	9.43821	+	6.65114i	0.362205	+	0.255247i
$680$	8.46464	−	14.5348i	0.324604	−	0.557385i
$681$	6.24694	−	10.8200i	0.239383	−	0.414624i
$682$	−5.04973	+	1.66053i	−0.193364	+	0.0635850i
$683$	1.86138	+	0.498756i	0.0712239	+	0.0190844i	0.294255	−	0.955727i	$-0.404928\pi$
$683$	1.86138	+	0.498756i	0.0712239	+	0.0190844i	−0.223031	+	0.974811i	$0.571595\pi$
$684$	−6.83274	−	9.26588i	−0.261256	−	0.354290i
$685$	−2.58302	+	0.234014i	−0.0986922	+	0.00894120i
$686$	5.58620	−	25.5889i	0.213282	−	0.976991i
$687$	15.0630	+	15.0630i	0.574691	+	0.574691i
$688$	26.3176	−	41.8091i	1.00335	−	1.59396i
$689$	11.3645	−	6.56128i	0.432952	−	0.249965i
$690$	0.794566	−	2.00474i	0.0302486	−	0.0763191i
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.954800	−	0.297248i	$-0.0960688\pi$
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.219976	+	0.975505i	$0.429402\pi$
$692$	1.61577	+	4.12182i	0.0614225	+	0.156688i
$693$	0.621767	+	3.58937i	0.0236190	+	0.136349i
$694$	−10.8427	+	7.09598i	−0.411582	+	0.269360i
$695$	−36.6276	+	13.4594i	−1.38936	+	0.510544i
$696$	−16.2541	−	19.6422i	−0.616109	−	0.744534i
$697$	9.54198	+	2.55677i	0.361428	+	0.0968444i
$698$	18.8055	−	21.0348i	0.711797	−	0.796177i
$699$	−2.33797			−0.0884301
$700$	14.5696	−	22.0845i	0.550681	−	0.834716i
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	−23.3223	+	26.0871i	−0.880245	+	0.984594i
$703$	3.99924	+	1.07159i	0.150834	+	0.0404159i
$704$	−5.76789	−	4.97586i	−0.217385	−	0.187535i
$705$	−8.39147	+	3.08359i	−0.316041	+	0.116135i
$706$	−2.93319	+	1.91962i	−0.110392	+	0.0722460i
$707$	2.90588	−	2.42345i	0.109287	−	0.0911433i
$708$	29.2514	−	11.4667i	1.09934	−	0.430944i
$709$	7.92917	+	4.57791i	0.297786	+	0.171927i	0.641448	−	0.767167i	$-0.278334\pi$
$709$	7.92917	+	4.57791i	0.297786	+	0.171927i	−0.343662	+	0.939093i	$0.611667\pi$
$710$	−8.86357	+	22.3633i	−0.332644	+	0.839280i
$711$	−13.3957	+	7.73401i	−0.502378	+	0.290048i
$712$	−5.44589	+	2.49425i	−0.204093	+	0.0934762i
$713$	−1.52693	−	1.52693i	−0.0571839	−	0.0571839i
$714$	10.9497	−	5.82945i	0.409781	−	0.218162i
$715$	−9.46674	+	0.857657i	−0.354036	+	0.0320745i
$716$	26.5111	−	19.5495i	0.990767	−	0.730601i
$717$	−18.3247	−	4.91009i	−0.684348	−	0.183370i
$718$	21.3512	−	7.02104i	0.796820	−	0.262023i
$719$	6.67322	−	11.5584i	0.248869	−	0.431054i	−0.714343	−	0.699796i	$-0.753274\pi$
$719$	6.67322	−	11.5584i	0.248869	−	0.431054i	0.963212	+	0.268742i	$0.0866078\pi$
$720$	12.9156	−	0.674050i	0.481337	−	0.0251203i
$721$	24.4340	−	11.3043i	0.909970	−	0.420996i
$722$	0.911364	−	4.36348i	0.0339175	−	0.162392i
$723$	−4.25104	−	15.8651i	−0.158098	−	0.590029i
$724$	−1.33348	−	11.8781i	−0.0495582	−	0.441446i
$725$	23.4097	+	27.5517i	0.869414	+	1.02324i
$726$	−17.7664	+	0.994134i	−0.659372	+	0.0368958i
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	0.583602	−	0.812040i	$-0.301643\pi$
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	−0.812040	+	0.583602i	$0.801643\pi$
$728$	11.1166	+	31.5047i	0.412008	+	1.16764i
$729$			24.4454i			0.905384i
$730$	−27.7657	+	37.3584i	−1.02765	+	1.38270i
$731$	−28.4457	+	16.4231i	−1.05210	+	0.607431i
$732$	−11.7380	−	9.36848i	−0.433847	−	0.346269i
$733$	−9.92223	+	2.65865i	−0.366486	+	0.0981996i	−0.437362	−	0.899286i	$-0.644087\pi$
$733$	−9.92223	+	2.65865i	−0.366486	+	0.0981996i	0.0708761	+	0.997485i	$0.477420\pi$
$734$	−12.7392	+	8.33717i	−0.470213	+	0.307731i
$735$	17.7084	−	8.19434i	0.653185	−	0.302253i
$736$	0.747914	−	3.00273i	0.0275685	−	0.110682i
$737$	3.67173	+	13.7031i	0.135250	+	0.504760i
$738$	2.37279	+	7.21572i	0.0873435	+	0.265614i
$739$	−21.8583	−	37.8597i	−0.804070	−	1.39269i	−0.916917	−	0.399078i	$-0.869330\pi$
$739$	−21.8583	−	37.8597i	−0.804070	−	1.39269i	0.112847	−	0.993612i	$-0.464003\pi$
$740$	−3.47910	+	3.08695i	−0.127894	+	0.113478i
$741$	22.1553			0.813897
$742$	−7.50497	−	8.03959i	−0.275516	−	0.295143i
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	−0.999010	−	0.0444813i	$-0.985836\pi$
$743$	−26.0186	+	26.0186i	−0.954529	+	0.954529i	0.0444813	+	0.999010i	$0.485836\pi$
$744$	−4.84979	+	13.0463i	−0.177802	+	0.478302i
$745$	24.7008	+	4.27693i	0.904969	+	0.156694i
$746$	−18.6383	−	9.41377i	−0.682396	−	0.344663i
$747$	−11.3072	+	3.02975i	−0.413709	+	0.110853i
$748$	1.84843	+	4.71534i	0.0675854	+	0.172410i
$749$	0.0446871	+	0.0965899i	0.00163283	+	0.00352932i
$750$	19.6687	−	1.28321i	0.718201	−	0.0468562i
$751$	−7.30460	−	4.21731i	−0.266548	−	0.153892i	0.360770	−	0.932655i	$-0.382514\pi$
$751$	−7.30460	−	4.21731i	−0.266548	−	0.153892i	−0.627318	+	0.778763i	$0.715847\pi$
$752$	−11.3471	+	5.98535i	−0.413784	+	0.218263i
$753$	4.74444	−	17.7065i	0.172897	−	0.645260i
$754$	−45.5811	+	2.55053i	−1.65997	+	0.0928850i
$755$	21.5097	−	25.7954i	0.782818	−	0.938790i
$756$	25.7080	+	14.1139i	0.934991	+	0.513316i
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	−0.643981	−	0.765041i	$-0.722718\pi$
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	0.765041	+	0.643981i	$0.222718\pi$
$758$	27.8930	+	24.9369i	1.01312	+	0.905748i
$759$	0.324667	+	0.562340i	0.0117847	+	0.0204117i
$760$	−17.7364	−	17.8701i	−0.643365	−	0.648217i
$761$	17.2317	−	29.8462i	0.624649	−	1.08192i	−0.363959	−	0.931415i	$-0.618575\pi$
$761$	17.2317	−	29.8462i	0.624649	−	1.08192i	0.988609	−	0.150509i	$-0.0480913\pi$
$762$	0.624010	−	2.98767i	0.0226055	−	0.108232i
$763$	−10.6636	−	12.7864i	−0.386050	−	0.462899i
$764$	6.44127	−	14.7473i	0.233037	−	0.533537i
$765$	−7.80440	−	3.60999i	−0.282169	−	0.130520i
$766$	−18.7327	+	37.0888i	−0.676840	+	1.34007i
$767$	14.5609	−	54.3419i	0.525763	−	1.96217i
$768$	−19.6039	+	3.67642i	−0.707396	+	0.132661i
$769$		−	18.7498i		−	0.676135i	−0.941122	−	0.338067i	$-0.890227\pi$
$769$		−	18.7498i		−	0.676135i	0.941122	−	0.338067i	$-0.109773\pi$
$770$	2.48918	+	7.56781i	0.0897038	+	0.272725i
$771$		−	16.4777i		−	0.593431i
$772$	−28.7922	−	4.35164i	−1.03626	−	0.156619i
$773$	11.5075	−	42.9466i	0.413896	−	1.54468i	−0.373140	−	0.927775i	$-0.621719\pi$
$773$	11.5075	−	42.9466i	0.413896	−	1.54468i	0.787036	−	0.616907i	$-0.211614\pi$
$774$	−22.5438	−	11.3864i	−0.810320	−	0.409274i
$775$	6.63610	−	18.5884i	0.238376	−	0.667716i
$776$	2.06023	+	12.1704i	0.0739581	+	0.436891i
$777$	−3.37991	+	0.585483i	−0.121254	+	0.0210041i
$778$	12.9472	+	2.70418i	0.464181	+	0.0969497i
$779$	7.39361	−	12.8061i	0.264903	−	0.458826i
$780$	−13.7074	+	20.7742i	−0.490803	+	0.743835i
$781$	−3.62174	−	6.27304i	−0.129596	−	0.224467i
$782$	−1.37126	+	1.53382i	−0.0490363	+	0.0548493i
$783$	−28.3379	+	28.3379i	−1.01271	+	1.01271i
$784$	23.6239	−	15.0303i	0.843712	−	0.536796i
$785$	−16.7650	+	1.51885i	−0.598367	+	0.0542102i
$786$	−0.128496	−	2.29637i	−0.00458329	−	0.0819089i
$787$	0.279451	−	1.04293i	0.00996136	−	0.0371763i	−0.960766	−	0.277359i	$-0.910541\pi$
$787$	0.279451	−	1.04293i	0.00996136	−	0.0371763i	0.970728	+	0.240183i	$0.0772074\pi$
$788$	36.4577	+	29.0982i	1.29875	+	1.03658i
$789$	11.4095	+	6.58729i	0.406189	+	0.234514i
$790$	−26.5182	+	21.0025i	−0.943474	+	0.747236i
$791$	23.3883	−	33.1889i	0.831592	−	1.18006i
$792$	−2.25547	+	3.17471i	−0.0801447	+	0.112808i
$793$	−25.9757	+	6.96017i	−0.922424	+	0.247163i
$794$	−11.3295	+	22.4312i	−0.402069	+	0.796055i
$795$	1.39790	−	8.07338i	0.0495783	−	0.286333i
$796$	−15.5428	+	11.4614i	−0.550900	+	0.406239i
$797$	−13.9414	+	13.9414i	−0.493829	+	0.493829i	−0.909510	−	0.415681i	$-0.863543\pi$
$797$	−13.9414	+	13.9414i	−0.493829	+	0.493829i	0.415681	+	0.909510i	$0.363543\pi$
$798$	−4.18657	−	18.0905i	−0.148203	−	0.640397i
$799$	8.52950			0.301752
$800$	27.7295	−	5.57456i	0.980385	−	0.197090i
$801$	1.53111	+	2.65196i	0.0540992	+	0.0937025i
$802$	8.26676	−	2.71841i	0.291910	−	0.0959902i
$803$	−3.62754	−	13.5382i	−0.128013	−	0.477751i
$804$	34.0401	+	14.8679i	1.20050	+	0.524352i
$805$	−2.28823	+	2.28856i	−0.0806495	+	0.0806613i
$806$	13.6479	+	20.8540i	0.480726	+	0.734550i
$807$	14.6862	−	3.93515i	0.516978	−	0.138524i
$808$	4.02717	+	0.380106i	0.141675	+	0.0133721i
$809$	−4.37439	+	2.52555i	−0.153795	+	0.0887937i	−0.574923	−	0.818208i	$-0.694968\pi$
$809$	−4.37439	+	2.52555i	−0.153795	+	0.0887937i	0.421127	+	0.907001i	$0.361635\pi$
$810$	1.18489	+	8.04411i	0.0416329	+	0.282641i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$	10.6958	+	36.7364i	0.375349	+	1.28919i
$813$	−5.80185	−	5.80185i	−0.203480	−	0.203480i
$814$	−0.0782451	−	1.39833i	−0.00274249	−	0.0490116i
$815$	−8.56522	−	12.1525i	−0.300027	−	0.425682i
$816$	12.6689	+	3.91907i	0.443501	+	0.137195i
$817$	12.7255	+	47.4920i	0.445207	+	1.66154i
$818$	−9.06216	−	1.89274i	−0.316851	−	0.0661781i
$819$	15.5009	−	7.17144i	0.541644	−	0.250590i
$820$	7.43340	+	14.8558i	0.259586	+	0.518786i
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	0.204402	+	0.978887i	$0.434475\pi$
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	−0.949942	+	0.312426i	$0.898858\pi$
$822$	−0.638770	−	1.94252i	−0.0222797	−	0.0677533i
$823$	−4.61152	−	1.23565i	−0.160748	−	0.0430722i	0.177548	−	0.984112i	$-0.443184\pi$
$823$	−4.61152	−	1.23565i	−0.160748	−	0.0430722i	−0.338295	+	0.941040i	$0.609850\pi$
$824$	26.9775	+	10.0285i	0.939804	+	0.349359i
$825$	−3.37417	+	4.88263i	−0.117474	+	0.169992i
$826$	−47.1233	−	1.62071i	−1.63963	−	0.0563916i
$827$	6.21884	+	6.21884i	0.216250	+	0.216250i	0.806916	−	0.590666i	$-0.201135\pi$
$827$	6.21884	+	6.21884i	0.216250	+	0.216250i	−0.590666	+	0.806916i	$0.701135\pi$
$828$	−1.56422	−	0.236416i	−0.0543606	−	0.00821602i
$829$	33.7077	−	19.4612i	1.17072	−	0.675915i	0.216869	−	0.976201i	$-0.430415\pi$
$829$	33.7077	−	19.4612i	1.17072	−	0.675915i	0.953849	+	0.300286i	$0.0970821\pi$
$830$	−23.4987	+	10.1588i	−0.815652	+	0.352616i
$831$	−4.43367	−	2.55978i	−0.153802	−	0.0887978i
$832$	−15.5353	+	32.1594i	−0.538588	+	1.11493i
$833$	−18.5549	+	1.51083i	−0.642889	+	0.0523470i
$834$	−16.8475	−	25.7431i	−0.583383	−	0.891410i
$835$	−17.0271	−	7.87605i	−0.589248	−	0.272562i
$836$	7.53399	−	0.845791i	0.260568	−	0.0292523i
$837$	21.1330	+	5.66257i	0.730464	+	0.195727i
$838$	18.7570	+	16.7691i	0.647949	+	0.579279i
$839$	15.0742			0.520418			0.260209	−	0.965552i	$-0.416209\pi$
$839$	15.0742			0.520418			0.260209	+	0.965552i	$0.416209\pi$
$840$	19.5530	+	7.26691i	0.674641	+	0.250732i
$841$	−23.2844			−0.802910
$842$	17.3621	+	15.5220i	0.598337	+	0.534925i
$843$	38.8660	+	10.4141i	1.33862	+	0.358681i
$844$	−20.7385	+	2.32817i	−0.713848	+	0.0801390i
$845$	5.34545	+	14.5468i	0.183889	+	0.500424i
$846$	3.59146	+	5.48776i	0.123477	+	0.188673i
$847$	25.0663	+	9.20895i	0.861289	+	0.316423i
$848$	0.449132	−	11.7489i	0.0154233	−	0.403461i
$849$	−21.0823	−	12.1719i	−0.723543	−	0.417738i
$850$	−18.0361	−	5.32335i	−0.618633	−	0.182589i
$851$	0.492709	−	0.284465i	0.0168898	−	0.00975135i
$852$	−18.7531	−	2.83434i	−0.642471	−	0.0971028i
$853$	−14.0097	−	14.0097i	−0.479684	−	0.479684i	0.425346	−	0.905031i	$-0.360152\pi$
$853$	−14.0097	−	14.0097i	−0.479684	−	0.479684i	−0.905031	+	0.425346i	$0.860152\pi$
$854$	10.5917	+	19.8947i	0.362440	+	0.680784i
$855$	−8.24327	+	9.88570i	−0.281914	+	0.338084i
$856$	−0.0396435	+	0.106644i	−0.00135499	+	0.00364503i
$857$	34.4324	+	9.22615i	1.17619	+	0.315159i	0.793414	−	0.608682i	$-0.208302\pi$
$857$	34.4324	+	9.22615i	1.17619	+	0.315159i	0.382776	+	0.923841i	$0.374968\pi$
$858$	−2.34108	−	7.11932i	−0.0799233	−	0.243049i
$859$	−26.2004	+	45.3805i	−0.893947	+	1.54836i	−0.0588442	+	0.998267i	$0.518742\pi$
$859$	−26.2004	+	45.3805i	−0.893947	+	1.54836i	−0.835103	+	0.550094i	$0.814592\pi$
$860$	−52.4046	−	17.4509i	−1.78698	−	0.595071i
$861$	−1.10450	+	12.2013i	−0.0376411	+	0.415818i
$862$	20.9491	+	4.37546i	0.713528	+	0.149029i
$863$	1.36585	+	5.09743i	0.0464941	+	0.173518i	0.985269	−	0.171014i	$-0.0547042\pi$
$863$	1.36585	+	5.09743i	0.0464941	+	0.173518i	−0.938775	+	0.344532i	$0.888038\pi$
$864$	8.64899	+	30.1358i	0.294245	+	1.02524i
$865$	4.04584	−	2.85156i	0.137563	−	0.0969559i
$866$	0.609393	+	10.8906i	0.0207080	+	0.370077i
$867$	8.75067	+	8.75067i	0.297188	+	0.297188i
$868$	14.4489	−	15.0846i	0.490429	−	0.512003i
$869$		−	10.1859i		−	0.345535i
$870$	−17.0034	+	22.8779i	−0.576469	+	0.775632i
$871$	57.6023	−	33.2567i	1.95178	−	1.12686i
$872$	1.67254	−	17.7203i	0.0566392	−	0.600085i
$873$	6.09536	−	1.63325i	0.206297	−	0.0552771i
$874$	1.68647	+	2.57694i	0.0570458	+	0.0871662i
$875$	−27.8591	−	9.94343i	−0.941809	−	0.336149i
$876$	−33.6304	−	14.6890i	−1.13627	−	0.496295i
$877$	−2.89005	−	10.7858i	−0.0975901	−	0.364211i	0.899809	−	0.436283i	$-0.143705\pi$
$877$	−2.89005	−	10.7858i	−0.0975901	−	0.364211i	−0.997399	+	0.0720722i	$0.977039\pi$
$878$	−34.5887	+	11.3740i	−1.16731	+	0.383854i
$879$	−11.1824	−	19.3685i	−0.377174	−	0.653285i
$880$	−3.86817	+	7.58761i	−0.130396	+	0.255778i
$881$	22.0701			0.743561			0.371781	−	0.928321i	$-0.378747\pi$
$881$	22.0701			0.743561			0.371781	+	0.928321i	$0.378747\pi$
$882$	−8.78481	−	11.3018i	−0.295800	−	0.380551i
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	−0.790959	−	0.611869i	$-0.790418\pi$
$883$	−5.32169	+	5.32169i	−0.179089	+	0.179089i	0.611869	+	0.790959i	$0.290418\pi$
$884$	19.1116	−	14.0930i	0.642792	−	0.474000i
$885$	−20.2367	−	28.7122i	−0.680250	−	0.965149i
$886$	11.0233	−	21.8250i	0.370335	−	0.733225i
$887$	4.89193	−	1.31079i	0.164255	−	0.0440120i	−0.175754	−	0.984434i	$-0.556236\pi$
$887$	4.89193	−	1.31079i	0.164255	−	0.0440120i	0.340009	+	0.940422i	$0.389570\pi$
$888$	−2.98944	−	2.12385i	−0.100319	−	0.0712718i
$889$	−2.63853	+	3.74417i	−0.0884936	+	0.125576i
$890$	4.15789	+	5.24983i	0.139373	+	0.175975i
$891$	−2.12030	−	1.22416i	−0.0710327	−	0.0410108i
$892$	23.7118	+	18.9252i	0.793929	+	0.633662i
$893$	3.30454	−	12.3327i	0.110582	−	0.412699i
$894$	1.10421	+	19.7336i	0.0369303	+	0.659990i
$895$	−28.2845	−	23.5853i	−0.945448	−	0.788369i
$896$	29.1948	+	6.60803i	0.975328	+	0.220759i
$897$	2.15273	−	2.15273i	0.0718774	−	0.0718774i
$898$	10.4625	−	11.7028i	0.349137	−	0.390526i
$899$	14.2718	+	24.7194i	0.475990	+	0.824439i
$900$	−4.16937	−	13.8456i	−0.138979	−	0.461521i
$901$	−3.90860	+	6.76989i	−0.130214	+	0.225538i
$902$	−4.89633	−	1.02265i	−0.163030	−	0.0340507i
$903$	−26.0899	−	31.2835i	−0.868218	−	1.04105i
$904$	42.7964	−	7.24469i	1.42339	−	0.240955i
$905$	−12.5435	+	4.60930i	−0.416959	+	0.153218i
$906$	23.6367	+	11.9384i	0.785277	+	0.396625i
$907$	−0.876735	+	3.27202i	−0.0291115	+	0.108646i	−0.978953	−	0.204087i	$-0.934578\pi$
$907$	−0.876735	+	3.27202i	−0.0291115	+	0.108646i	0.949841	+	0.312732i	$0.101244\pi$
$908$	−19.8196	−	2.99552i	−0.657736	−	0.0994098i
$909$		−	2.06796i		−	0.0685899i
$910$	31.2522	−	20.4562i	1.03600	−	0.678118i
$911$			31.5983i			1.04690i	0.852057	+	0.523449i	$0.175355\pi$
$911$			31.5983i			1.04690i	−0.852057	+	0.523449i	$0.824645\pi$
$912$	10.5748	−	16.7995i	0.350166	−	0.556287i
$913$	1.99514	−	7.44597i	0.0660295	−	0.246426i
$914$	−13.5407	+	26.8091i	−0.447886	+	0.886767i
$915$	−7.04919	+	15.2396i	−0.233039	+	0.503804i
$916$	13.6796	−	31.3195i	0.451988	−	1.03482i
$917$	−1.19029	+	3.23992i	−0.0393069	+	0.106992i
$918$	4.26180	−	20.4049i	0.140660	−	0.673462i
$919$	23.1351	−	40.0712i	0.763157	−	1.32183i	−0.178058	−	0.984020i	$-0.556982\pi$
$919$	23.1351	−	40.0712i	0.763157	−	1.32183i	0.941215	−	0.337807i	$-0.109685\pi$
$920$	−3.45971	−	0.0129957i	−0.114063	−	0.000428455i
$921$	8.79800	+	15.2386i	0.289904	+	0.502128i
$922$	9.08446	+	8.12167i	0.299181	+	0.267473i
$923$	−24.0141	+	24.0141i	−0.790435	+	0.790435i
$924$	−5.37076	+	3.25686i	−0.176685	+	0.107143i
$925$	4.27804	+	2.95637i	0.140661	+	0.0972047i
$926$	3.26169	−	0.182511i	0.107186	−	0.00599768i
$927$	3.80821	−	14.2124i	0.125078	−	0.466797i
$928$	−19.8220	+	35.7797i	−0.650689	+	1.17453i
$929$	37.0594	+	21.3962i	1.21588	+	0.701987i	0.964034	−	0.265780i	$-0.0856296\pi$
$929$	37.0594	+	21.3962i	1.21588	+	0.701987i	0.251844	+	0.967768i	$0.418963\pi$
$930$	15.4577	+	1.79415i	0.506877	+	0.0588326i
$931$	−5.00414	+	27.4137i	−0.164004	+	0.898447i
$932$	1.36896	+	3.49220i	0.0448418	+	0.114391i
$933$	16.7837	−	4.49719i	0.549475	−	0.147231i
$934$	−32.1652	−	16.2459i	−1.05248	−	0.531583i
$935$	4.62841	−	3.26216i	0.151365	−	0.106684i
$936$	17.1144	+	6.36204i	0.559402	+	0.207950i
$937$	18.9957	−	18.9957i	0.620561	−	0.620561i	−0.325114	−	0.945675i	$-0.605403\pi$
$937$	18.9957	−	18.9957i	0.620561	−	0.620561i	0.945675	+	0.325114i	$0.105403\pi$
$938$	−38.0399	−	40.7497i	−1.24205	−	1.33053i
$939$	6.11875			0.199678
$940$	9.51942	+	10.7287i	0.310489	+	0.349933i
$941$	10.8404	+	18.7762i	0.353388	+	0.612086i	0.986841	−	0.161696i	$-0.0516963\pi$
$941$	10.8404	+	18.7762i	0.353388	+	0.612086i	−0.633453	+	0.773781i	$0.718363\pi$
$942$	−4.14590	−	12.6078i	−0.135081	−	0.410785i
$943$	−0.525906	−	1.96271i	−0.0171258	−	0.0639145i
$944$	−34.2554	−	36.9785i	−1.11492	−	1.20355i
$945$	8.48413	−	31.6725i	0.275989	−	1.03031i
$946$	13.9163	−	9.10749i	0.452457	−	0.296110i
$947$	−14.8363	+	3.97536i	−0.482114	+	0.129182i	−0.491687	−	0.870772i	$-0.663619\pi$
$947$	−14.8363	+	3.97536i	−0.482114	+	0.129182i	0.00957300	+	0.999954i	$0.496953\pi$
$948$	−20.8452	−	16.6373i	−0.677019	−	0.540353i
$949$	−56.9090	+	32.8564i	−1.84735	+	1.06657i
$950$	−14.6846	+	24.0158i	−0.476432	+	0.779177i
$951$		−	42.8869i		−	1.39070i
$952$	−15.1188	−	12.9421i	−0.490003	−	0.419456i
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	0.967147	−	0.254216i	$-0.0818174\pi$
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	−0.254216	+	0.967147i	$0.581817\pi$
$954$	−6.00141	+	0.335815i	−0.194303	+	0.0108724i
$955$	−17.7283	−	3.06964i	−0.573674	−	0.0993311i
$956$	3.39557	+	30.2465i	0.109821	+	0.978240i
$957$	−2.22146	−	8.29061i	−0.0718096	−	0.267997i
$958$	−2.68274	+	12.8446i	−0.0866755	+	0.414990i
$959$	−0.276665	+	3.05629i	−0.00893398	+	0.0986929i
$960$	9.20968	+	20.3093i	0.297241	+	0.655481i
$961$	−7.70864	+	13.3518i	−0.248666	+	0.430702i
$962$	−6.23777	+	2.05120i	−0.201114	+	0.0661333i
$963$	0.0561830	+	0.0150542i	0.00181047	+	0.000485114i
$964$	−21.2084	+	15.6393i	−0.683078	+	0.503708i
$965$	2.93747	+	32.4235i	0.0945604	+	1.04375i
$966$	−2.16455	−	1.35098i	−0.0696434	−	0.0434670i
$967$	−16.9281	−	16.9281i	−0.544372	−	0.544372i	0.380435	−	0.924807i	$-0.375774\pi$
$967$	−16.9281	−	16.9281i	−0.544372	−	0.544372i	−0.924807	+	0.380435i	$0.875774\pi$
$968$	11.8877	+	25.9554i	0.382086	+	0.834238i
$969$	−11.4299	+	6.59904i	−0.367180	+	0.211992i
$970$	12.6674	−	5.47628i	0.406727	−	0.175833i
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.113568	−	0.993530i	$-0.536228\pi$
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.917206	+	0.398412i	$0.869561\pi$
$972$	24.9920	−	9.79698i	0.801620	−	0.314238i
$973$	7.88071	+	45.4942i	0.252644	+	1.45848i
$974$	21.0739	−	13.7918i	0.675251	−	0.441918i
$975$	26.2067	+	9.35584i	0.839287	+	0.299627i
$976$	−7.12065	+	23.0185i	−0.227926	+	0.736803i
$977$	−22.5762	−	6.04928i	−0.722277	−	0.193534i	−0.121090	−	0.992642i	$-0.538639\pi$
$977$	−22.5762	−	6.04928i	−0.722277	−	0.193534i	−0.601188	+	0.799108i	$0.705306\pi$
$978$	7.81264	−	8.73879i	0.249821	−	0.279436i
$979$	−2.01652			−0.0644484
$980$	−22.6087	−	21.6529i	−0.722208	−	0.691676i
$981$	−9.09942			−0.290522
$982$	2.35614	−	2.63545i	0.0751875	−	0.0841006i
$983$	19.2069	+	5.14648i	0.612606	+	0.164147i	0.551764	−	0.834000i	$-0.313955\pi$
$983$	19.2069	+	5.14648i	0.612606	+	0.164147i	0.0608417	+	0.998147i	$0.480622\pi$
$984$	−10.0903	+	8.34979i	−0.321666	+	0.266182i
$985$	21.8946	−	47.3336i	0.697619	−	1.50817i
$986$	22.7555	−	14.8923i	0.724682	−	0.474268i
$987$	1.80549	+	10.4228i	0.0574694	+	0.331763i
$988$	−12.9727	−	33.0932i	−0.412716	−	1.05284i
$989$	5.85104	+	3.37810i	0.186052	+	0.107417i
$990$	4.04768	+	1.60427i	0.128644	+	0.0509872i
$991$	−19.5362	+	11.2792i	−0.620586	+	0.358296i	−0.777097	−	0.629380i	$-0.783309\pi$
$991$	−19.5362	+	11.2792i	−0.620586	+	0.358296i	0.156511	+	0.987676i	$0.449975\pi$
$992$	22.3269	−	0.394977i	0.708880	−	0.0125405i
$993$	−11.4204	−	11.4204i	−0.362414	−	0.362414i
$994$	24.1461	+	15.0705i	0.765868	+	0.478006i
$995$	16.5825	+	13.8275i	0.525701	+	0.438360i
$996$	−11.9791	−	16.2449i	−0.379573	−	0.514739i
$997$	−16.6372	−	4.45792i	−0.526905	−	0.141184i	−0.0144466	−	0.999896i	$-0.504599\pi$
$997$	−16.6372	−	4.45792i	−0.526905	−	0.141184i	−0.512459	+	0.858712i	$0.671265\pi$
$998$	8.76459	−	2.88211i	0.277438	−	0.0912315i
$999$	−2.88213	+	4.99199i	−0.0911865	+	0.157940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.5	✓	72
4.3	odd	2	inner	140.2.w.b.23.11	yes	72
5.2	odd	4	inner	140.2.w.b.107.14	yes	72
5.3	odd	4		700.2.be.e.107.5		72
5.4	even	2		700.2.be.e.443.14		72
7.2	even	3		980.2.k.k.883.8		36
7.3	odd	6		980.2.x.m.263.17		72
7.4	even	3	inner	140.2.w.b.123.17	yes	72
7.5	odd	6		980.2.k.j.883.8		36
7.6	odd	2		980.2.x.m.863.5		72
20.3	even	4		700.2.be.e.107.2		72
20.7	even	4	inner	140.2.w.b.107.17	yes	72
20.19	odd	2		700.2.be.e.443.8		72
28.3	even	6		980.2.x.m.263.14		72
28.11	odd	6	inner	140.2.w.b.123.14	yes	72
28.19	even	6		980.2.k.j.883.1		36
28.23	odd	6		980.2.k.k.883.1		36
28.27	even	2		980.2.x.m.863.11		72
35.2	odd	12		980.2.k.k.687.1		36
35.4	even	6		700.2.be.e.543.2		72
35.12	even	12		980.2.k.j.687.1		36
35.17	even	12		980.2.x.m.67.11		72
35.18	odd	12		700.2.be.e.207.8		72
35.27	even	4		980.2.x.m.667.14		72
35.32	odd	12	inner	140.2.w.b.67.11	yes	72
140.27	odd	4		980.2.x.m.667.17		72
140.39	odd	6		700.2.be.e.543.5		72
140.47	odd	12		980.2.k.j.687.8		36
140.67	even	12	inner	140.2.w.b.67.5	yes	72
140.87	odd	12		980.2.x.m.67.5		72
140.107	even	12		980.2.k.k.687.8		36
140.123	even	12		700.2.be.e.207.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	1.1	even	1	trivial
140.2.w.b.23.11	yes	72	4.3	odd	2	inner
140.2.w.b.67.5	yes	72	140.67	even	12	inner
140.2.w.b.67.11	yes	72	35.32	odd	12	inner
140.2.w.b.107.14	yes	72	5.2	odd	4	inner
140.2.w.b.107.17	yes	72	20.7	even	4	inner
140.2.w.b.123.14	yes	72	28.11	odd	6	inner
140.2.w.b.123.17	yes	72	7.4	even	3	inner
700.2.be.e.107.2		72	20.3	even	4
700.2.be.e.107.5		72	5.3	odd	4
700.2.be.e.207.8		72	35.18	odd	12
700.2.be.e.207.14		72	140.123	even	12
700.2.be.e.443.8		72	20.19	odd	2
700.2.be.e.443.14		72	5.4	even	2
700.2.be.e.543.2		72	35.4	even	6
700.2.be.e.543.5		72	140.39	odd	6
980.2.k.j.687.1		36	35.12	even	12
980.2.k.j.687.8		36	140.47	odd	12
980.2.k.j.883.1		36	28.19	even	6
980.2.k.j.883.8		36	7.5	odd	6
980.2.k.k.687.1		36	35.2	odd	12
980.2.k.k.687.8		36	140.107	even	12
980.2.k.k.883.1		36	28.23	odd	6
980.2.k.k.883.8		36	7.2	even	3
980.2.x.m.67.5		72	140.87	odd	12
980.2.x.m.67.11		72	35.17	even	12
980.2.x.m.263.14		72	28.3	even	6
980.2.x.m.263.17		72	7.3	odd	6
980.2.x.m.667.14		72	35.27	even	4
980.2.x.m.667.17		72	140.27	odd	4
980.2.x.m.863.5		72	7.6	odd	2
980.2.x.m.863.11		72	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05431 - 0.942570i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(0.223125 + 1.98751i) q^{4} +(2.09885 - 0.771256i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-0.451584 - 2.60693i) q^{7} +(1.63813 - 2.30576i) q^{8} +(-1.25225 - 0.722989i) q^{9} +O(q^{10})\)	\(q+(-1.05431 - 0.942570i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(0.223125 + 1.98751i) q^{4} +(2.09885 - 0.771256i) q^{5} +(0.965404 + 1.47514i) q^{6} +(-0.451584 - 2.60693i) q^{7} +(1.63813 - 2.30576i) q^{8} +(-1.25225 - 0.722989i) q^{9} +(-2.93979 - 1.16517i) q^{10} +(0.824629 - 0.476100i) q^{11} +(0.372591 - 2.46521i) q^{12} +(-3.15680 - 3.15680i) q^{13} +(-1.98110 + 3.17415i) q^{14} +(-2.77612 + 0.251508i) q^{15} +(-3.90043 + 0.886929i) q^{16} +(2.56885 + 0.688322i) q^{17} +(0.638792 + 1.94259i) q^{18} +(1.99048 - 3.44760i) q^{19} +(2.00119 + 3.99941i) q^{20} +(-0.297348 + 3.28477i) q^{21} +(-1.31817 - 0.275315i) q^{22} +(-0.141582 - 0.528392i) q^{23} +(-2.71646 + 2.24790i) q^{24} +(3.81033 - 3.23750i) q^{25} +(0.352732 + 6.30375i) q^{26} +(3.91905 + 3.91905i) q^{27} +(5.08055 - 1.47920i) q^{28} +7.23080i q^{29} +(3.16395 + 2.35152i) q^{30} +(3.41863 - 1.97375i) q^{31} +(4.94824 + 2.74133i) q^{32} +(-1.14657 + 0.307222i) q^{33} +(-2.05957 - 3.14702i) q^{34} +(-2.95842 - 5.12326i) q^{35} +(1.15754 - 2.65019i) q^{36} +(0.269180 + 1.00460i) q^{37} +(-5.34818 + 1.75867i) q^{38} +(2.78267 + 4.81972i) q^{39} +(1.65985 - 6.10286i) q^{40} +3.71449 q^{41} +(3.40962 - 3.18289i) q^{42} +(-8.73324 + 8.73324i) q^{43} +(1.13025 + 1.53273i) q^{44} +(-3.18590 - 0.551635i) q^{45} +(-0.348775 + 0.690538i) q^{46} +(3.09794 - 0.830089i) q^{47} +(4.98278 + 0.190479i) q^{48} +(-6.59214 + 2.35449i) q^{49} +(-7.06882 - 0.178182i) q^{50} +(-2.87114 - 1.65765i) q^{51} +(5.56983 - 6.97856i) q^{52} +(-0.760768 + 2.83923i) q^{53} +(-0.437903 - 7.82586i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-6.75070 - 3.22924i) q^{56} +(-3.50914 + 3.50914i) q^{57} +(6.81553 - 7.62348i) q^{58} +(6.30084 + 10.9134i) q^{59} +(-1.11930 - 5.46147i) q^{60} +(3.01183 - 5.21665i) q^{61} +(-5.46468 - 1.14136i) q^{62} +(-1.31928 + 3.59102i) q^{63} +(-2.63307 - 7.55427i) q^{64} +(-9.06036 - 4.19095i) q^{65} +(1.49841 + 0.756815i) q^{66} +(-3.85605 + 14.3910i) q^{67} +(-0.794874 + 5.25921i) q^{68} +0.681932i q^{69} +(-1.70995 + 8.19000i) q^{70} -7.60710i q^{71} +(-3.71839 + 1.70305i) q^{72} +(3.80964 - 14.2178i) q^{73} +(0.663102 - 1.31287i) q^{74} +(-5.63268 + 2.66898i) q^{75} +(7.29629 + 3.18685i) q^{76} +(-1.61355 - 1.93475i) q^{77} +(1.60914 - 7.70432i) q^{78} +(5.34864 - 9.26412i) q^{79} +(-7.50236 + 4.86976i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(-3.91621 - 3.50117i) q^{82} +(5.72446 - 5.72446i) q^{83} +(-6.59488 + 0.141933i) q^{84} +(5.92250 - 0.536560i) q^{85} +(17.4392 - 0.975826i) q^{86} +(2.33298 - 8.70680i) q^{87} +(0.253076 - 2.68131i) q^{88} +(-1.83403 - 1.05888i) q^{89} +(2.83896 + 3.58452i) q^{90} +(-6.80400 + 9.65512i) q^{91} +(1.01860 - 0.399294i) q^{92} +(-4.75329 + 1.27364i) q^{93} +(-4.04859 - 2.04485i) q^{94} +(1.51872 - 8.77117i) q^{95} +(-5.07384 - 4.89744i) q^{96} +(-3.08588 + 3.08588i) q^{97} +(9.16941 + 3.73120i) q^{98} -1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

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