LMFDB - Embedded newform 152.2.c.b.77.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(77,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("152.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.15
Root			$-0.466170 + 1.33517i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33517 - 0.466170i) q^{2} +0.579017i q^{3} +(1.56537 - 1.24484i) q^{4} -2.10882i q^{5} +(0.269921 + 0.773088i) q^{6} -2.73436 q^{7} +(1.50973 - 2.39180i) q^{8} +2.66474 q^{9} +O(q^{10})$	\(q+(1.33517 - 0.466170i) q^{2} +0.579017i q^{3} +(1.56537 - 1.24484i) q^{4} -2.10882i q^{5} +(0.269921 + 0.773088i) q^{6} -2.73436 q^{7} +(1.50973 - 2.39180i) q^{8} +2.66474 q^{9} +(-0.983067 - 2.81563i) q^{10} +4.66474i q^{11} +(0.720781 + 0.906377i) q^{12} +4.47791i q^{13} +(-3.65084 + 1.27468i) q^{14} +1.22104 q^{15} +(0.900771 - 3.89726i) q^{16} -6.85237 q^{17} +(3.55789 - 1.24222i) q^{18} -1.00000i q^{19} +(-2.62513 - 3.30108i) q^{20} -1.58324i q^{21} +(2.17456 + 6.22823i) q^{22} -1.20416 q^{23} +(1.38489 + 0.874162i) q^{24} +0.552894 q^{25} +(2.08747 + 5.97878i) q^{26} +3.27998i q^{27} +(-4.28028 + 3.40382i) q^{28} -9.57484i q^{29} +(1.63030 - 0.569213i) q^{30} -5.35842 q^{31} +(-0.614101 - 5.62342i) q^{32} -2.70096 q^{33} +(-9.14909 + 3.19437i) q^{34} +5.76625i q^{35} +(4.17130 - 3.31716i) q^{36} +1.09693i q^{37} +(-0.466170 - 1.33517i) q^{38} -2.59279 q^{39} +(-5.04386 - 3.18375i) q^{40} +7.33797 q^{41} +(-0.738059 - 2.11390i) q^{42} +7.64408i q^{43} +(5.80683 + 7.30205i) q^{44} -5.61945i q^{45} +(-1.60777 + 0.561345i) q^{46} +7.56486 q^{47} +(2.25658 + 0.521562i) q^{48} +0.476702 q^{49} +(0.738208 - 0.257743i) q^{50} -3.96764i q^{51} +(5.57426 + 7.00959i) q^{52} +3.11949i q^{53} +(1.52903 + 4.37934i) q^{54} +9.83708 q^{55} +(-4.12815 + 6.54003i) q^{56} +0.579017 q^{57} +(-4.46351 - 12.7841i) q^{58} -10.2442i q^{59} +(1.91138 - 1.51999i) q^{60} +0.722061i q^{61} +(-7.15441 + 2.49793i) q^{62} -7.28634 q^{63} +(-3.44140 - 7.22196i) q^{64} +9.44309 q^{65} +(-3.60625 + 1.25911i) q^{66} -6.13698i q^{67} +(-10.7265 + 8.53007i) q^{68} -0.697232i q^{69} +(2.68806 + 7.69894i) q^{70} +4.62247 q^{71} +(4.02305 - 6.37352i) q^{72} -6.19270 q^{73} +(0.511358 + 1.46460i) q^{74} +0.320135i q^{75} +(-1.24484 - 1.56537i) q^{76} -12.7551i q^{77} +(-3.46182 + 1.20868i) q^{78} -3.26723 q^{79} +(-8.21860 - 1.89956i) q^{80} +6.09505 q^{81} +(9.79746 - 3.42075i) q^{82} -8.97934i q^{83} +(-1.97087 - 2.47836i) q^{84} +14.4504i q^{85} +(3.56344 + 10.2062i) q^{86} +5.54400 q^{87} +(11.1571 + 7.04252i) q^{88} +0.620707 q^{89} +(-2.61962 - 7.50293i) q^{90} -12.2442i q^{91} +(-1.88496 + 1.49899i) q^{92} -3.10262i q^{93} +(10.1004 - 3.52651i) q^{94} -2.10882 q^{95} +(3.25606 - 0.355575i) q^{96} -1.67284 q^{97} +(0.636479 - 0.222224i) q^{98} +12.4303i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.33517	−	0.466170i	0.944109	−	0.329632i
$2$	1.33517	−	0.466170i	0.944109	−	0.329632i
$3$			0.579017i			0.334296i	0.985932	+	0.167148i	$0.0534557\pi$
$3$			0.579017i			0.334296i	−0.985932	+	0.167148i	$0.946544\pi$
$4$	1.56537	−	1.24484i	0.782685	−	0.622418i
$5$		−	2.10882i		−	0.943091i	−0.881842	−	0.471546i	$-0.843696\pi$
$5$		−	2.10882i		−	0.943091i	0.881842	−	0.471546i	$-0.156304\pi$
$6$	0.269921	+	0.773088i	0.110195	+	0.315612i
$7$	−2.73436			−1.03349			−0.516745	−	0.856140i	$-0.672856\pi$
$7$	−2.73436			−1.03349			−0.516745	+	0.856140i	$0.672856\pi$
$8$	1.50973	−	2.39180i	0.533772	−	0.845629i
$9$	2.66474			0.888246
$10$	−0.983067	−	2.81563i	−0.310873	−	0.890381i
$11$			4.66474i			1.40647i	0.710957	+	0.703236i	$0.248262\pi$
$11$			4.66474i			1.40647i	−0.710957	+	0.703236i	$0.751738\pi$
$12$	0.720781	+	0.906377i	0.208072	+	0.261648i
$13$			4.47791i			1.24195i	0.783831	+	0.620974i	$0.213263\pi$
$13$			4.47791i			1.24195i	−0.783831	+	0.620974i	$0.786737\pi$
$14$	−3.65084	+	1.27468i	−0.975727	+	0.340671i
$15$	1.22104			0.315271
$16$	0.900771	−	3.89726i	0.225193	−	0.974314i
$17$	−6.85237			−1.66194			−0.830972	−	0.556314i	$-0.812215\pi$
$17$	−6.85237			−1.66194			−0.830972	+	0.556314i	$0.812215\pi$
$18$	3.55789	−	1.24222i	0.838602	−	0.292795i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−2.62513	−	3.30108i	−0.586997	−	0.738144i
$21$		−	1.58324i		−	0.345491i
$22$	2.17456	+	6.22823i	0.463618	+	1.32786i
$23$	−1.20416			−0.251085			−0.125543	−	0.992088i	$-0.540067\pi$
$23$	−1.20416			−0.251085			−0.125543	+	0.992088i	$0.540067\pi$
$24$	1.38489	+	0.874162i	0.282690	+	0.178438i
$25$	0.552894			0.110579
$26$	2.08747	+	5.97878i	0.409386	+	1.17254i
$27$			3.27998i			0.631233i
$28$	−4.28028	+	3.40382i	−0.808897	+	0.643262i
$29$		−	9.57484i		−	1.77800i	−0.457904	−	0.889002i	$-0.651400\pi$
$29$		−	9.57484i		−	1.77800i	0.457904	−	0.889002i	$-0.348600\pi$
$30$	1.63030	−	0.569213i	0.297651	−	0.103924i
$31$	−5.35842			−0.962400			−0.481200	−	0.876611i	$-0.659799\pi$
$31$	−5.35842			−0.962400			−0.481200	+	0.876611i	$0.659799\pi$
$32$	−0.614101	−	5.62342i	−0.108559	−	0.994090i
$33$	−2.70096			−0.470178
$34$	−9.14909	+	3.19437i	−1.56906	+	0.547830i
$35$			5.76625i			0.974675i
$36$	4.17130	−	3.31716i	0.695217	−	0.552860i
$37$			1.09693i			0.180335i	0.995927	+	0.0901674i	$0.0287402\pi$
$37$			1.09693i			0.180335i	−0.995927	+	0.0901674i	$0.971260\pi$
$38$	−0.466170	−	1.33517i	−0.0756228	−	0.216594i
$39$	−2.59279			−0.415178
$40$	−5.04386	−	3.18375i	−0.797505	−	0.503396i
$41$	7.33797			1.14600			0.573000	−	0.819556i	$-0.305780\pi$
$41$	7.33797			1.14600			0.573000	+	0.819556i	$0.305780\pi$
$42$	−0.738059	−	2.11390i	−0.113885	−	0.326181i
$43$			7.64408i			1.16571i	0.812576	+	0.582856i	$0.198065\pi$
$43$			7.64408i			1.16571i	−0.812576	+	0.582856i	$0.801935\pi$
$44$	5.80683	+	7.30205i	0.875413	+	1.10082i
$45$		−	5.61945i		−	0.837697i
$46$	−1.60777	+	0.561345i	−0.237052	+	0.0827658i
$47$	7.56486			1.10345			0.551724	−	0.834027i	$-0.313970\pi$
$47$	7.56486			1.10345			0.551724	+	0.834027i	$0.313970\pi$
$48$	2.25658	+	0.521562i	0.325709	+	0.0752810i
$49$	0.476702			0.0681003
$50$	0.738208	−	0.257743i	0.104398	−	0.0364503i
$51$		−	3.96764i		−	0.555581i
$52$	5.57426	+	7.00959i	0.773011	+	0.972055i
$53$			3.11949i			0.428495i	0.976779	+	0.214248i	$0.0687300\pi$
$53$			3.11949i			0.428495i	−0.976779	+	0.214248i	$0.931270\pi$
$54$	1.52903	+	4.37934i	0.208075	+	0.595953i
$55$	9.83708			1.32643
$56$	−4.12815	+	6.54003i	−0.551648	+	0.873948i
$57$	0.579017			0.0766927
$58$	−4.46351	−	12.7841i	−0.586087	−	1.67863i
$59$		−	10.2442i		−	1.33368i	−0.745201	−	0.666840i	$-0.767646\pi$
$59$		−	10.2442i		−	1.33368i	0.745201	−	0.666840i	$-0.232354\pi$
$60$	1.91138	−	1.51999i	0.246758	−	0.196230i
$61$			0.722061i			0.0924504i	0.998931	+	0.0462252i	$0.0147192\pi$
$61$			0.722061i			0.0924504i	−0.998931	+	0.0462252i	$0.985281\pi$
$62$	−7.15441	+	2.49793i	−0.908611	+	0.317238i
$63$	−7.28634			−0.917993
$64$	−3.44140	−	7.22196i	−0.430175	−	0.902745i
$65$	9.44309			1.17127
$66$	−3.60625	+	1.25911i	−0.443899	+	0.154986i
$67$		−	6.13698i		−	0.749752i	−0.927075	−	0.374876i	$-0.877685\pi$
$67$		−	6.13698i		−	0.749752i	0.927075	−	0.374876i	$-0.122315\pi$
$68$	−10.7265	+	8.53007i	−1.30078	+	1.03442i
$69$		−	0.697232i		−	0.0839368i
$70$	2.68806	+	7.69894i	0.321284	+	0.920200i
$71$	4.62247			0.548587			0.274293	−	0.961646i	$-0.411556\pi$
$71$	4.62247			0.548587			0.274293	+	0.961646i	$0.411556\pi$
$72$	4.02305	−	6.37352i	0.474121	−	0.751126i
$73$	−6.19270			−0.724801			−0.362400	−	0.932022i	$-0.618043\pi$
$73$	−6.19270			−0.724801			−0.362400	+	0.932022i	$0.618043\pi$
$74$	0.511358	+	1.46460i	0.0594441	+	0.170256i
$75$			0.320135i			0.0369660i
$76$	−1.24484	−	1.56537i	−0.142792	−	0.179560i
$77$		−	12.7551i		−	1.45357i
$78$	−3.46182	+	1.20868i	−0.391974	+	0.136856i
$79$	−3.26723			−0.367592			−0.183796	−	0.982964i	$-0.558839\pi$
$79$	−3.26723			−0.367592			−0.183796	+	0.982964i	$0.558839\pi$
$80$	−8.21860	−	1.89956i	−0.918867	−	0.212377i
$81$	6.09505			0.677228
$82$	9.79746	−	3.42075i	1.08195	−	0.377758i
$83$		−	8.97934i		−	0.985611i	−0.870140	−	0.492805i	$-0.835971\pi$
$83$		−	8.97934i		−	0.985611i	0.870140	−	0.492805i	$-0.164029\pi$
$84$	−1.97087	−	2.47836i	−0.215040	−	0.270411i
$85$			14.4504i			1.56736i
$86$	3.56344	+	10.2062i	0.384256	+	1.10056i
$87$	5.54400			0.594379
$88$	11.1571	+	7.04252i	1.18935	+	0.750735i
$89$	0.620707			0.0657948			0.0328974	−	0.999459i	$-0.489527\pi$
$89$	0.620707			0.0657948			0.0328974	+	0.999459i	$0.489527\pi$
$90$	−2.61962	−	7.50293i	−0.276132	−	0.790878i
$91$		−	12.2442i		−	1.28354i
$92$	−1.88496	+	1.49899i	−0.196521	+	0.156280i
$93$		−	3.10262i		−	0.321726i
$94$	10.1004	−	3.52651i	1.04178	−	0.363732i
$95$	−2.10882			−0.216360
$96$	3.25606	−	0.355575i	0.332320	−	0.0362907i
$97$	−1.67284			−0.169851			−0.0849257	−	0.996387i	$-0.527065\pi$
$97$	−1.67284			−0.169851			−0.0849257	+	0.996387i	$0.527065\pi$
$98$	0.636479	−	0.222224i	0.0642941	−	0.0224480i
$99$			12.4303i			1.24929i
$100$	0.865484	−	0.688261i	0.0865484	−	0.0688261i
$101$			7.30571i			0.726946i	0.931605	+	0.363473i	$0.118409\pi$
$101$			7.30571i			0.726946i	−0.931605	+	0.363473i	$0.881591\pi$
$102$	−1.84960	−	5.29748i	−0.183137	−	0.524529i
$103$	−8.77332			−0.864461			−0.432231	−	0.901763i	$-0.642273\pi$
$103$	−8.77332			−0.864461			−0.432231	+	0.901763i	$0.642273\pi$
$104$	10.7103	+	6.76045i	1.05023	+	0.662917i
$105$	−3.33876			−0.325830
$106$	1.45421	+	4.16506i	0.141246	+	0.404546i
$107$		−	9.91355i		−	0.958379i	−0.877711	−	0.479190i	$-0.840931\pi$
$107$		−	9.91355i		−	0.958379i	0.877711	−	0.479190i	$-0.159069\pi$
$108$	4.08304	+	5.13439i	0.392890	+	0.494057i
$109$			2.84589i			0.272587i	0.990669	+	0.136293i	$0.0435189\pi$
$109$			2.84589i			0.272587i	−0.990669	+	0.136293i	$0.956481\pi$
$110$	13.1342	−	4.58575i	1.25230	−	0.437234i
$111$	−0.635143			−0.0602851
$112$	−2.46303	+	10.6565i	−0.232734	+	1.00694i
$113$	−1.58487			−0.149092			−0.0745462	−	0.997218i	$-0.523751\pi$
$113$	−1.58487			−0.149092			−0.0745462	+	0.997218i	$0.523751\pi$
$114$	0.773088	−	0.269921i	0.0724063	−	0.0252804i
$115$			2.53936i			0.236797i
$116$	−11.9191	−	14.9882i	−1.10666	−	1.39162i
$117$			11.9325i			1.10316i
$118$	−4.77554	−	13.6778i	−0.439624	−	1.25914i
$119$	18.7368			1.71760
$120$	1.84345	−	2.92048i	0.168283	−	0.266603i
$121$	−10.7598			−0.978163
$122$	0.336603	+	0.964075i	0.0304746	+	0.0872833i
$123$			4.24881i			0.383103i
$124$	−8.38791	+	6.67034i	−0.753256	+	0.599015i
$125$		−	11.7100i		−	1.04738i
$126$	−9.72853	+	3.39668i	−0.866686	+	0.302600i
$127$	14.2933			1.26833			0.634163	−	0.773199i	$-0.281345\pi$
$127$	14.2933			1.26833			0.634163	+	0.773199i	$0.281345\pi$
$128$	−7.96153	−	8.03829i	−0.703706	−	0.710491i
$129$	−4.42605			−0.389692
$130$	12.6081	−	4.40209i	1.10581	−	0.386088i
$131$		−	0.609006i		−	0.0532091i	−0.999646	−	0.0266046i	$-0.991531\pi$
$131$		−	0.609006i		−	0.0532091i	0.999646	−	0.0266046i	$-0.00846949\pi$
$132$	−4.22801	+	3.36226i	−0.368001	+	0.292647i
$133$			2.73436i			0.237099i
$134$	−2.86088	−	8.19393i	−0.247142	−	0.707848i
$135$	6.91688			0.595310
$136$	−10.3453	+	16.3895i	−0.887099	+	1.40539i
$137$	18.1589			1.55142			0.775710	−	0.631089i	$-0.217392\pi$
$137$	18.1589			1.55142			0.775710	+	0.631089i	$0.217392\pi$
$138$	−0.325029	−	0.930924i	−0.0276683	−	0.0792455i
$139$			1.93421i			0.164058i	0.996630	+	0.0820289i	$0.0261400\pi$
$139$			1.93421i			0.164058i	−0.996630	+	0.0820289i	$0.973860\pi$
$140$	7.17804	+	9.02633i	0.606655	+	0.762864i
$141$			4.38018i			0.368878i
$142$	6.17180	−	2.15486i	0.517926	−	0.180832i
$143$	−20.8883			−1.74677
$144$	2.40032	−	10.3852i	0.200027	−	0.865431i
$145$	−20.1916			−1.67682
$146$	−8.26832	+	2.88685i	−0.684291	+	0.238918i
$147$			0.276019i			0.0227656i
$148$	1.36550	+	1.71711i	0.112244	+	0.141145i
$149$			15.5775i			1.27616i	0.769970	+	0.638080i	$0.220271\pi$
$149$			15.5775i			1.27616i	−0.769970	+	0.638080i	$0.779729\pi$
$150$	0.149237	+	0.427435i	0.0121852	+	0.0349000i
$151$	−19.9746			−1.62551			−0.812756	−	0.582605i	$-0.802034\pi$
$151$	−19.9746			−1.62551			−0.812756	+	0.582605i	$0.802034\pi$
$152$	−2.39180	−	1.50973i	−0.194000	−	0.122456i
$153$	−18.2598			−1.47622
$154$	−5.94603	−	17.0302i	−0.479145	−	1.37233i
$155$			11.2999i			0.907631i
$156$	−4.05867	+	3.22759i	−0.324954	+	0.258414i
$157$			20.8872i			1.66698i	0.552536	+	0.833489i	$0.313660\pi$
$157$			20.8872i			1.66698i	−0.552536	+	0.833489i	$0.686340\pi$
$158$	−4.36232	+	1.52309i	−0.347047	+	0.121170i
$159$	−1.80624			−0.143244
$160$	−11.8588	+	1.29503i	−0.937518	+	0.102381i
$161$	3.29261			0.259494
$162$	8.13794	−	2.84133i	0.639377	−	0.223236i
$163$			2.54835i			0.199602i	0.995007	+	0.0998010i	$0.0318206\pi$
$163$			2.54835i			0.199602i	−0.995007	+	0.0998010i	$0.968179\pi$
$164$	11.4867	−	9.13457i	0.896957	−	0.713290i
$165$			5.69584i			0.443420i
$166$	−4.18590	−	11.9890i	−0.324889	−	0.930524i
$167$	−18.6644			−1.44429			−0.722146	−	0.691740i	$-0.756844\pi$
$167$	−18.6644			−1.44429			−0.722146	+	0.691740i	$0.756844\pi$
$168$	−3.78679	−	2.39027i	−0.292157	−	0.184413i
$169$	−7.05167			−0.542436
$170$	6.73634	+	19.2938i	0.516654	+	1.47976i
$171$		−	2.66474i		−	0.203778i
$172$	9.51562	+	11.9658i	0.725559	+	0.912385i
$173$			8.42370i			0.640442i	0.947343	+	0.320221i	$0.103757\pi$
$173$			8.42370i			0.640442i	−0.947343	+	0.320221i	$0.896243\pi$
$174$	7.40219	−	2.58445i	0.561159	−	0.195926i
$175$	−1.51181			−0.114282
$176$	18.1797	+	4.20186i	1.37035	+	0.316727i
$177$	5.93157			0.445844
$178$	0.828751	−	0.289355i	0.0621175	−	0.0216881i
$179$		−	16.6809i		−	1.24679i	−0.781908	−	0.623394i	$-0.785753\pi$
$179$		−	16.6809i		−	1.24679i	0.781908	−	0.623394i	$-0.214247\pi$
$180$	−6.99528	−	8.79651i	−0.521398	−	0.655654i
$181$			4.65888i			0.346292i	0.984896	+	0.173146i	$0.0553932\pi$
$181$			4.65888i			0.346292i	−0.984896	+	0.173146i	$0.944607\pi$
$182$	−5.70788	−	16.3481i	−0.423096	−	1.21180i
$183$	−0.418086			−0.0309058
$184$	−1.81797	+	2.88012i	−0.134022	+	0.212325i
$185$	2.31323			0.170072
$186$	−1.44635	−	4.14253i	−0.106051	−	0.303745i
$187$		−	31.9645i		−	2.33748i
$188$	11.8418	−	9.41700i	0.863653	−	0.686805i
$189$		−	8.96864i		−	0.652372i
$190$	−2.81563	+	0.983067i	−0.204268	+	0.0713192i
$191$	20.0609			1.45155			0.725777	−	0.687930i	$-0.241480\pi$
$191$	20.0609			1.45155			0.725777	+	0.687930i	$0.241480\pi$
$192$	4.18164	−	1.99263i	0.301784	−	0.143806i
$193$	1.85117			0.133250			0.0666251	−	0.997778i	$-0.478777\pi$
$193$	1.85117			0.133250			0.0666251	+	0.997778i	$0.478777\pi$
$194$	−2.23353	+	0.779829i	−0.160358	+	0.0559885i
$195$			5.46771i			0.391551i
$196$	0.746215	−	0.593416i	0.0533011	−	0.0423868i
$197$			0.224883i			0.0160222i	0.999968	+	0.00801112i	$0.00255005\pi$
$197$			0.224883i			0.0160222i	−0.999968	+	0.00801112i	$0.997450\pi$
$198$	5.79464	+	16.5966i	0.411807	+	1.17947i
$199$	−1.77685			−0.125957			−0.0629787	−	0.998015i	$-0.520060\pi$
$199$	−1.77685			−0.125957			−0.0629787	+	0.998015i	$0.520060\pi$
$200$	0.834723	−	1.32241i	0.0590238	−	0.0935085i
$201$	3.55342			0.250639
$202$	3.40571	+	9.75439i	0.239625	+	0.686316i
$203$			26.1810i			1.83755i
$204$	−4.93906	−	6.21083i	−0.345803	−	0.434845i
$205$		−	15.4744i		−	1.08078i
$206$	−11.7139	+	4.08986i	−0.816146	+	0.284954i
$207$	−3.20878			−0.223026
$208$	17.4516	+	4.03357i	1.21005	+	0.279678i
$209$	4.66474			0.322667
$210$	−4.45782	+	1.55643i	−0.307619	+	0.107404i
$211$			17.0194i			1.17166i	0.810433	+	0.585831i	$0.199232\pi$
$211$			17.0194i			1.17166i	−0.810433	+	0.585831i	$0.800768\pi$
$212$	3.88325	+	4.88316i	0.266703	+	0.335377i
$213$			2.67649i			0.183390i
$214$	−4.62140	−	13.2363i	−0.315913	−	0.904815i
$215$	16.1200			1.09937
$216$	7.84506	+	4.95190i	0.533788	+	0.336934i
$217$	14.6518			0.994630
$218$	1.32667	+	3.79975i	0.0898533	+	0.257352i
$219$		−	3.58568i		−	0.242298i
$220$	15.3987	−	12.2455i	1.03818	−	0.825594i
$221$		−	30.6843i		−	2.06405i
$222$	−0.848026	+	0.296085i	−0.0569158	+	0.0198719i
$223$	13.6634			0.914971			0.457486	−	0.889217i	$-0.348750\pi$
$223$	13.6634			0.914971			0.457486	+	0.889217i	$0.348750\pi$
$224$	1.67917	+	15.3764i	0.112194	+	1.02738i
$225$	1.47332			0.0982212
$226$	−2.11608	+	0.738821i	−0.140760	+	0.0491457i
$227$		−	5.46152i		−	0.362494i	−0.983438	−	0.181247i	$-0.941987\pi$
$227$		−	5.46152i		−	0.362494i	0.983438	−	0.181247i	$-0.0580133\pi$
$228$	0.906377	−	0.720781i	0.0600263	−	0.0477349i
$229$			3.22791i			0.213306i	0.994296	+	0.106653i	$0.0340135\pi$
$229$			3.22791i			0.213306i	−0.994296	+	0.106653i	$0.965987\pi$
$230$	1.18377	+	3.39048i	0.0780557	+	0.223562i
$231$	7.38540			0.485923
$232$	−22.9011	−	14.4555i	−1.50353	−	0.949048i
$233$	−17.8344			−1.16837			−0.584185	−	0.811621i	$-0.698586\pi$
$233$	−17.8344			−1.16837			−0.584185	+	0.811621i	$0.698586\pi$
$234$	5.56256	+	15.9319i	0.363636	+	1.04150i
$235$		−	15.9529i		−	1.04065i
$236$	−12.7523	−	16.0360i	−0.830106	−	1.04385i
$237$		−	1.89178i		−	0.122884i
$238$	25.0169	−	8.73455i	1.62160	−	0.566176i
$239$	1.82556			0.118086			0.0590428	−	0.998255i	$-0.481195\pi$
$239$	1.82556			0.118086			0.0590428	+	0.998255i	$0.481195\pi$
$240$	1.09988	−	4.75871i	0.0709968	−	0.307173i
$241$	6.47608			0.417161			0.208581	−	0.978005i	$-0.433116\pi$
$241$	6.47608			0.417161			0.208581	+	0.978005i	$0.433116\pi$
$242$	−14.3662	+	5.01589i	−0.923493	+	0.322434i
$243$			13.3691i			0.857627i
$244$	0.898846	+	1.13029i	0.0575427	+	0.0723596i
$245$		−	1.00528i		−	0.0642248i
$246$	1.98067	+	5.67290i	0.126283	+	0.361691i
$247$	4.47791			0.284923
$248$	−8.08979	+	12.8163i	−0.513702	+	0.813833i
$249$	5.19919			0.329485
$250$	−5.45887	−	15.6349i	−0.345249	−	0.988839i
$251$			3.10899i			0.196238i	0.995175	+	0.0981189i	$0.0312825\pi$
$251$			3.10899i			0.196238i	−0.995175	+	0.0981189i	$0.968717\pi$
$252$	−11.4058	+	9.07030i	−0.718500	+	0.571375i
$253$		−	5.61711i		−	0.353145i
$254$	19.0840	−	6.66312i	1.19744	−	0.418081i
$255$	−8.36702			−0.523963
$256$	−14.3772	−	7.02107i	−0.898576	−	0.438817i
$257$	5.75606			0.359053			0.179526	−	0.983753i	$-0.442543\pi$
$257$	5.75606			0.359053			0.179526	+	0.983753i	$0.442543\pi$
$258$	−5.90955	+	2.06329i	−0.367912	+	0.128455i
$259$		−	2.99941i		−	0.186374i
$260$	14.7819	−	11.7551i	0.916737	−	0.729020i
$261$		−	25.5145i		−	1.57931i
$262$	−0.283900	−	0.813128i	−0.0175394	−	0.0502352i
$263$	−4.58595			−0.282782			−0.141391	−	0.989954i	$-0.545157\pi$
$263$	−4.58595			−0.282782			−0.141391	+	0.989954i	$0.545157\pi$
$264$	−4.07774	+	6.46016i	−0.250968	+	0.397596i
$265$	6.57844			0.404110
$266$	1.27468	+	3.65084i	0.0781554	+	0.223847i
$267$			0.359400i			0.0219949i
$268$	−7.63953	−	9.60665i	−0.466659	−	0.586820i
$269$		−	11.3913i		−	0.694542i	−0.937765	−	0.347271i	$-0.887108\pi$
$269$		−	11.3913i		−	0.694542i	0.937765	−	0.347271i	$-0.112892\pi$
$270$	9.23523	−	3.22444i	0.562038	−	0.196233i
$271$	25.1252			1.52625			0.763124	−	0.646252i	$-0.223664\pi$
$271$	25.1252			1.52625			0.763124	+	0.646252i	$0.223664\pi$
$272$	−6.17241	+	26.7054i	−0.374258	+	1.61926i
$273$	7.08960			0.429082
$274$	24.2453	−	8.46514i	1.46471	−	0.511398i
$275$			2.57910i			0.155526i
$276$	−0.867938	−	1.09143i	−0.0522437	−	0.0656961i
$277$			18.2998i			1.09953i	0.835321	+	0.549763i	$0.185282\pi$
$277$			18.2998i			1.09953i	−0.835321	+	0.549763i	$0.814718\pi$
$278$	0.901672	+	2.58251i	0.0540787	+	0.154888i
$279$	−14.2788			−0.854848
$280$	13.7917	+	8.70551i	0.824213	+	0.520254i
$281$	−18.0708			−1.07802			−0.539008	−	0.842301i	$-0.681201\pi$
$281$	−18.0708			−1.07802			−0.539008	+	0.842301i	$0.681201\pi$
$282$	2.04191	+	5.84830i	0.121594	+	0.348261i
$283$			15.3972i			0.915269i	0.889140	+	0.457634i	$0.151303\pi$
$283$			15.3972i			0.915269i	−0.889140	+	0.457634i	$0.848697\pi$
$284$	7.23589	−	5.75422i	0.429371	−	0.341450i
$285$		−	1.22104i		−	0.0723282i
$286$	−27.8894	+	9.73749i	−1.64914	+	0.575790i
$287$	−20.0646			−1.18438
$288$	−1.63642	−	14.9850i	−0.0964269	−	0.882997i
$289$	29.9550			1.76206
$290$	−26.9592	+	9.41271i	−1.58310	+	0.552734i
$291$		−	0.968605i		−	0.0567806i
$292$	−9.69387	+	7.70889i	−0.567291	+	0.451129i
$293$			11.4407i			0.668374i	0.942507	+	0.334187i	$0.108462\pi$
$293$			11.4407i			0.668374i	−0.942507	+	0.334187i	$0.891538\pi$
$294$	0.128672	+	0.368533i	0.00750429	+	0.0214933i
$295$	−21.6031			−1.25778
$296$	2.62364	+	1.65608i	0.152496	+	0.0962576i
$297$	−15.3003			−0.887811
$298$	7.26178	+	20.7987i	0.420664	+	1.20484i
$299$		−	5.39214i		−	0.311835i
$300$	0.398515	+	0.501130i	0.0230083	+	0.0289327i
$301$		−	20.9016i		−	1.20475i
$302$	−26.6696	+	9.31157i	−1.53466	+	0.535821i
$303$	−4.23013			−0.243015
$304$	−3.89726	−	0.900771i	−0.223523	−	0.0516628i
$305$	1.52269			0.0871892
$306$	−24.3799	+	8.51216i	−1.39371	+	0.486608i
$307$		−	21.3453i		−	1.21824i	−0.793077	−	0.609122i	$-0.791522\pi$
$307$		−	21.3453i		−	1.21824i	0.793077	−	0.609122i	$-0.208478\pi$
$308$	−15.8779	−	19.9664i	−0.904730	−	1.13769i
$309$		−	5.07991i		−	0.288986i
$310$	5.26768	+	15.0873i	0.299184	+	0.856903i
$311$	−21.7295			−1.23216			−0.616082	−	0.787682i	$-0.711281\pi$
$311$	−21.7295			−1.23216			−0.616082	+	0.787682i	$0.711281\pi$
$312$	−3.91442	+	6.20142i	−0.221610	+	0.351086i
$313$	34.1009			1.92750			0.963748	−	0.266814i	$-0.0859710\pi$
$313$	34.1009			1.92750			0.963748	+	0.266814i	$0.0859710\pi$
$314$	9.73698	+	27.8880i	0.549490	+	1.57381i
$315$			15.3656i			0.865751i
$316$	−5.11443	+	4.06716i	−0.287709	+	0.228796i
$317$		−	22.2281i		−	1.24845i	−0.781244	−	0.624226i	$-0.785414\pi$
$317$		−	22.2281i		−	1.24845i	0.781244	−	0.624226i	$-0.214586\pi$
$318$	−2.41164	+	0.842015i	−0.135238	+	0.0472179i
$319$	44.6641			2.50071
$320$	−15.2298	+	7.25729i	−0.851371	+	0.405695i
$321$	5.74012			0.320382
$322$	4.39620	−	1.53492i	0.244991	−	0.0855376i
$323$			6.85237i			0.381276i
$324$	9.54101	−	7.58733i	0.530056	−	0.421519i
$325$			2.47581i			0.137333i
$326$	1.18796	+	3.40248i	0.0657952	+	0.188446i
$327$	−1.64782			−0.0911245
$328$	11.0784	−	17.5510i	0.611702	−	0.969090i
$329$	−20.6850			−1.14040
$330$	2.65523	+	7.60493i	0.146166	+	0.418637i
$331$			24.1969i			1.32998i	0.746852	+	0.664991i	$0.231564\pi$
$331$			24.1969i			1.32998i	−0.746852	+	0.664991i	$0.768436\pi$
$332$	−11.1778	−	14.0560i	−0.613461	−	0.771423i
$333$			2.92304i			0.160182i
$334$	−24.9202	+	8.70077i	−1.36357	+	0.476085i
$335$	−12.9418			−0.707084
$336$	−6.17029	−	1.42614i	−0.336617	−	0.0778021i
$337$	−34.2735			−1.86700			−0.933498	−	0.358583i	$-0.883260\pi$
$337$	−34.2735			−1.86700			−0.933498	+	0.358583i	$0.883260\pi$
$338$	−9.41519	+	3.28728i	−0.512119	+	0.178804i
$339$		−	0.917670i		−	0.0498410i
$340$	17.9884	+	22.6202i	0.975555	+	1.22675i
$341$		−	24.9956i		−	1.35359i
$342$	−1.24222	−	3.55789i	−0.0671717	−	0.192388i
$343$	17.8370			0.963108
$344$	18.2831	+	11.5405i	0.985759	+	0.622224i
$345$	−1.47033			−0.0791601
$346$	3.92688	+	11.2471i	0.211110	+	0.604647i
$347$			26.9233i			1.44532i	0.691206	+	0.722658i	$0.257080\pi$
$347$			26.9233i			1.44532i	−0.691206	+	0.722658i	$0.742920\pi$
$348$	8.67841	−	6.90136i	0.465212	−	0.369952i
$349$			8.65769i			0.463436i	0.972783	+	0.231718i	$0.0744346\pi$
$349$			8.65769i			0.463436i	−0.972783	+	0.231718i	$0.925565\pi$
$350$	−2.01852	+	0.704760i	−0.107895	+	0.0376710i
$351$	−14.6875			−0.783959
$352$	26.2318	−	2.86462i	1.39816	−	0.152685i
$353$	−9.11265			−0.485018			−0.242509	−	0.970149i	$-0.577970\pi$
$353$	−9.11265			−0.485018			−0.242509	+	0.970149i	$0.577970\pi$
$354$	7.91966	−	2.76512i	0.420925	−	0.146964i
$355$		−	9.74795i		−	0.517367i
$356$	0.971636	−	0.772678i	0.0514966	−	0.0409518i
$357$			10.8489i			0.574187i
$358$	−7.77613	−	22.2719i	−0.410981	−	1.17710i
$359$	4.29978			0.226934			0.113467	−	0.993542i	$-0.463804\pi$
$359$	4.29978			0.226934			0.113467	+	0.993542i	$0.463804\pi$
$360$	−13.4406	−	8.48387i	−0.708381	−	0.447139i
$361$	−1.00000			−0.0526316
$362$	2.17183	+	6.22041i	0.114149	+	0.326938i
$363$		−	6.23010i		−	0.326996i
$364$	−15.2420	−	19.1667i	−0.798898	−	1.00461i
$365$			13.0593i			0.683553i
$366$	−0.558216	+	0.194899i	−0.0291784	+	0.0101875i
$367$	−21.2873			−1.11119			−0.555594	−	0.831454i	$-0.687509\pi$
$367$	−21.2873			−1.11119			−0.555594	+	0.831454i	$0.687509\pi$
$368$	−1.08468	+	4.69294i	−0.0565426	+	0.244636i
$369$	19.5538			1.01793
$370$	3.08856	−	1.07836i	0.160567	−	0.0560612i
$371$		−	8.52980i		−	0.442845i
$372$	−3.86224	−	4.85674i	−0.200248	−	0.251810i
$373$		−	11.1076i		−	0.575129i	−0.957761	−	0.287565i	$-0.907154\pi$
$373$		−	11.1076i		−	0.575129i	0.957761	−	0.287565i	$-0.0928456\pi$
$374$	−14.9009	−	42.6781i	−0.770507	−	2.20683i
$375$	6.78031			0.350134
$376$	11.4209	−	18.0936i	0.588990	−	0.933107i
$377$	42.8753			2.20819
$378$	−4.18091	−	11.9747i	−0.215043	−	0.615911i
$379$		−	20.6908i		−	1.06281i	−0.847117	−	0.531407i	$-0.821664\pi$
$379$		−	20.6908i		−	1.06281i	0.847117	−	0.531407i	$-0.178336\pi$
$380$	−3.30108	+	2.62513i	−0.169342	+	0.134666i
$381$			8.27608i			0.423996i
$382$	26.7847	−	9.35178i	1.37043	−	0.478479i
$383$	−12.1869			−0.622720			−0.311360	−	0.950292i	$-0.600785\pi$
$383$	−12.1869			−0.622720			−0.311360	+	0.950292i	$0.600785\pi$
$384$	4.65431	−	4.60986i	0.237514	−	0.235246i
$385$	−26.8981			−1.37085
$386$	2.47163	−	0.862960i	0.125803	−	0.0439235i
$387$			20.3695i			1.03544i
$388$	−2.61862	+	2.08241i	−0.132940	+	0.105719i
$389$			26.1769i			1.32722i	0.748078	+	0.663611i	$0.230977\pi$
$389$			26.1769i			1.32722i	−0.748078	+	0.663611i	$0.769023\pi$
$390$	2.54888	+	7.30034i	0.129068	+	0.369667i
$391$	8.25137			0.417290
$392$	0.719694	−	1.14018i	0.0363500	−	0.0575876i
$393$	0.352625			0.0177876
$394$	0.104834	+	0.300257i	0.00528145	+	0.0151268i
$395$			6.88999i			0.346673i
$396$	15.4737	+	19.4580i	0.777582	+	0.977804i
$397$		−	14.8451i		−	0.745055i	−0.928021	−	0.372528i	$-0.878491\pi$
$397$		−	14.8451i		−	0.745055i	0.928021	−	0.372528i	$-0.121509\pi$
$398$	−2.37240	+	0.828314i	−0.118918	+	0.0415196i
$399$	−1.58324			−0.0792611
$400$	0.498030	−	2.15477i	0.0249015	−	0.107738i
$401$	34.4111			1.71841			0.859205	−	0.511632i	$-0.170959\pi$
$401$	34.4111			1.71841			0.859205	+	0.511632i	$0.170959\pi$
$402$	4.74443	−	1.65650i	0.236630	−	0.0826186i
$403$		−	23.9945i		−	1.19525i
$404$	9.09441	+	11.4361i	0.452464	+	0.568970i
$405$		−	12.8533i		−	0.638688i
$406$	12.2048	+	34.9562i	0.605715	+	1.73485i
$407$	−5.11691			−0.253636
$408$	−9.48980	−	5.99008i	−0.469815	−	0.296553i
$409$	1.43283			0.0708487			0.0354243	−	0.999372i	$-0.488722\pi$
$409$	1.43283			0.0708487			0.0354243	+	0.999372i	$0.488722\pi$
$410$	−7.21372	−	20.6610i	−0.356260	−	1.02038i
$411$			10.5143i			0.518633i
$412$	−13.7335	+	10.9213i	−0.676601	+	0.538056i
$413$			28.0113i			1.37834i
$414$	−4.28428	+	1.49584i	−0.210561	+	0.0735165i
$415$	−18.9358			−0.929521
$416$	25.1812	−	2.74989i	1.23461	−	0.134824i
$417$	−1.11994			−0.0548438
$418$	6.22823	−	2.17456i	0.304633	−	0.106361i
$419$			33.6886i			1.64579i	0.568190	+	0.822897i	$0.307644\pi$
$419$			33.6886i			1.64579i	−0.568190	+	0.822897i	$0.692356\pi$
$420$	−5.22640	+	4.15621i	−0.255022	+	0.202802i
$421$			0.237430i			0.0115716i	0.999983	+	0.00578582i	$0.00184169\pi$
$421$			0.237430i			0.0115716i	−0.999983	+	0.00578582i	$0.998158\pi$
$422$	7.93393	+	22.7238i	0.386218	+	1.10618i
$423$	20.1584			0.980134
$424$	7.46120	+	4.70961i	0.362348	+	0.228719i
$425$	−3.78863			−0.183776
$426$	1.24770	+	3.57358i	0.0604513	+	0.173140i
$427$		−	1.97437i		−	0.0955465i
$428$	−12.3407	−	15.5184i	−0.596512	−	0.750109i
$429$		−	12.0947i		−	0.583936i
$430$	21.5229	−	7.51464i	1.03793	−	0.362388i
$431$	13.0743			0.629766			0.314883	−	0.949130i	$-0.398035\pi$
$431$	13.0743			0.629766			0.314883	+	0.949130i	$0.398035\pi$
$432$	12.7829	+	2.95451i	0.615019	+	0.142149i
$433$	−9.67718			−0.465056			−0.232528	−	0.972590i	$-0.574700\pi$
$433$	−9.67718			−0.465056			−0.232528	+	0.972590i	$0.574700\pi$
$434$	19.5627	−	6.83024i	0.939040	−	0.327862i
$435$		−	11.6913i		−	0.560554i
$436$	3.54266	+	4.45487i	0.169663	+	0.213350i
$437$			1.20416i			0.0576030i
$438$	−1.67154	−	4.78750i	−0.0798692	−	0.228756i
$439$	17.7983			0.849468			0.424734	−	0.905318i	$-0.360368\pi$
$439$	17.7983			0.849468			0.424734	+	0.905318i	$0.360368\pi$
$440$	14.8514	−	23.5283i	0.708012	−	1.12167i
$441$	1.27029			0.0604898
$442$	−14.3041	−	40.9688i	−0.680377	−	1.94869i
$443$		−	3.30468i		−	0.157010i	−0.996914	−	0.0785050i	$-0.974985\pi$
$443$		−	3.30468i		−	0.157010i	0.996914	−	0.0785050i	$-0.0250147\pi$
$444$	−0.994235	+	0.790649i	−0.0471843	+	0.0375225i
$445$		−	1.30896i		−	0.0620505i
$446$	18.2430	−	6.36949i	0.863833	−	0.301604i
$447$	−9.01966			−0.426615
$448$	9.41002	+	19.7474i	0.444582	+	0.932978i
$449$	−29.6543			−1.39947			−0.699735	−	0.714402i	$-0.746699\pi$
$449$	−29.6543			−1.39947			−0.699735	+	0.714402i	$0.746699\pi$
$450$	1.96713	−	0.686817i	0.0927315	−	0.0323768i
$451$			34.2297i			1.61182i
$452$	−2.48092	+	1.97291i	−0.116692	+	0.0927978i
$453$		−	11.5656i		−	0.543402i
$454$	−2.54600	−	7.29207i	−0.119490	−	0.342234i
$455$	−25.8208			−1.21050
$456$	0.874162	−	1.38489i	0.0409364	−	0.0648535i
$457$	−20.2310			−0.946368			−0.473184	−	0.880964i	$-0.656895\pi$
$457$	−20.2310			−0.946368			−0.473184	+	0.880964i	$0.656895\pi$
$458$	1.50476	+	4.30982i	0.0703126	+	0.201385i
$459$		−	22.4756i		−	1.04907i
$460$	3.16108	+	3.97504i	0.147386	+	0.185337i
$461$		−	41.2429i		−	1.92087i	−0.278502	−	0.960436i	$-0.589838\pi$
$461$		−	41.2429i		−	1.92087i	0.278502	−	0.960436i	$-0.410162\pi$
$462$	9.86078	−	3.44285i	0.458765	−	0.160176i
$463$	−16.5232			−0.767896			−0.383948	−	0.923355i	$-0.625436\pi$
$463$	−16.5232			−0.767896			−0.383948	+	0.923355i	$0.625436\pi$
$464$	−37.3156	−	8.62474i	−1.73233	−	0.400393i
$465$	−6.54285			−0.303417
$466$	−23.8120	+	8.31386i	−1.10307	+	0.385132i
$467$		−	24.9967i		−	1.15671i	−0.815786	−	0.578355i	$-0.803695\pi$
$467$		−	24.9967i		−	1.15671i	0.815786	−	0.578355i	$-0.196305\pi$
$468$	14.8539	+	18.6787i	0.686624	+	0.863424i
$469$			16.7807i			0.774860i
$470$	−7.43677	−	21.2999i	−0.343032	−	0.982490i
$471$	−12.0940			−0.557264
$472$	−24.5021	−	15.4660i	−1.12780	−	0.711881i
$473$	−35.6576			−1.63954
$474$	−0.881893	−	2.52586i	−0.0405067	−	0.116016i
$475$		−	0.552894i		−	0.0253685i
$476$	29.3301	−	23.3242i	1.34434	−	1.06907i
$477$			8.31263i			0.380609i
$478$	2.43744	−	0.851022i	0.111486	−	0.0389248i
$479$	10.0298			0.458273			0.229137	−	0.973394i	$-0.426410\pi$
$479$	10.0298			0.458273			0.229137	+	0.973394i	$0.426410\pi$
$480$	−0.749842	−	6.86643i	−0.0342255	−	0.313408i
$481$	−4.91197			−0.223966
$482$	8.64669	−	3.01896i	0.393846	−	0.137510i
$483$			1.90648i			0.0867478i
$484$	−16.8431	+	13.3942i	−0.765594	+	0.608826i
$485$			3.52772i			0.160185i
$486$	6.23227	+	17.8500i	0.282701	+	0.809694i
$487$	41.6248			1.88620			0.943101	−	0.332508i	$-0.107895\pi$
$487$	41.6248			1.88620			0.943101	+	0.332508i	$0.107895\pi$
$488$	1.72702	+	1.09012i	0.0781787	+	0.0493474i
$489$	−1.47554			−0.0667261
$490$	−0.468630	−	1.34222i	−0.0211706	−	0.0606352i
$491$			34.6939i			1.56572i	0.622200	+	0.782858i	$0.286239\pi$
$491$			34.6939i			1.56572i	−0.622200	+	0.782858i	$0.713761\pi$
$492$	5.28907	+	6.65097i	0.238450	+	0.299849i
$493$			65.6104i			2.95494i
$494$	5.97878	−	2.08747i	0.268998	−	0.0939196i
$495$	26.2132			1.17820
$496$	−4.82671	+	20.8831i	−0.216725	+	0.937680i
$497$	−12.6395			−0.566959
$498$	6.94182	−	2.42371i	0.311070	−	0.108609i
$499$		−	14.1270i		−	0.632413i	−0.948690	−	0.316207i	$-0.897591\pi$
$499$		−	14.1270i		−	0.632413i	0.948690	−	0.316207i	$-0.102409\pi$
$500$	−14.5771	−	18.3305i	−0.651906	−	0.819767i
$501$		−	10.8070i		−	0.482821i
$502$	1.44932	+	4.15104i	0.0646863	+	0.185270i
$503$	3.01157			0.134279			0.0671395	−	0.997744i	$-0.478613\pi$
$503$	3.01157			0.134279			0.0671395	+	0.997744i	$0.478613\pi$
$504$	−11.0004	+	17.4275i	−0.489999	+	0.776281i
$505$	15.4064			0.685576
$506$	−2.61853	−	7.49981i	−0.116408	−	0.333407i
$507$		−	4.08304i		−	0.181334i
$508$	22.3743	−	17.7928i	0.992701	−	0.789429i
$509$		−	2.38122i		−	0.105546i	−0.998607	−	0.0527730i	$-0.983194\pi$
$509$		−	2.38122i		−	0.105546i	0.998607	−	0.0527730i	$-0.0168060\pi$
$510$	−11.1714	+	3.90046i	−0.494679	+	0.172715i
$511$	16.9330			0.749074
$512$	−22.4691	−	2.67211i	−0.993003	−	0.118092i
$513$	3.27998			0.144815
$514$	7.68533	−	2.68330i	0.338985	−	0.118355i
$515$			18.5013i			0.815266i
$516$	−6.92842	+	5.50971i	−0.305006	+	0.242551i
$517$			35.2881i			1.55197i
$518$	−1.39823	−	4.00472i	−0.0614349	−	0.175957i
$519$	−4.87747			−0.214097
$520$	14.2566	−	22.5860i	0.625191	−	0.990460i
$521$	17.9133			0.784798			0.392399	−	0.919795i	$-0.371645\pi$
$521$	17.9133			0.784798			0.392399	+	0.919795i	$0.371645\pi$
$522$	−11.8941	−	34.0662i	−0.520590	−	1.49104i
$523$		−	18.9602i		−	0.829071i	−0.910033	−	0.414536i	$-0.863944\pi$
$523$		−	18.9602i		−	0.829071i	0.910033	−	0.414536i	$-0.136056\pi$
$524$	−0.758112	−	0.953320i	−0.0331183	−	0.0416460i
$525$		−	0.875363i		−	0.0382040i
$526$	−6.12304	+	2.13783i	−0.266977	+	0.0932140i
$527$	36.7178			1.59945
$528$	−2.43295	+	10.5264i	−0.105881	+	0.458101i
$529$	−21.5500			−0.936956
$530$	8.78335	−	3.06667i	0.381524	−	0.133208i
$531$		−	27.2981i		−	1.18464i
$532$	3.40382	+	4.28028i	0.147574	+	0.185574i
$533$			32.8588i			1.42327i
$534$	0.167542	+	0.479861i	0.00725023	+	0.0207656i
$535$	−20.9059			−0.903839
$536$	−14.6784	−	9.26521i	−0.634011	−	0.400196i
$537$	9.65852			0.416796
$538$	−5.31030	−	15.2094i	−0.228943	−	0.655724i
$539$			2.22369i			0.0957811i
$540$	10.8275	−	8.61037i	0.465941	−	0.370531i
$541$		−	34.2027i		−	1.47049i	−0.677802	−	0.735245i	$-0.737067\pi$
$541$		−	34.2027i		−	1.47049i	0.677802	−	0.735245i	$-0.262933\pi$
$542$	33.5465	−	11.7126i	1.44095	−	0.503100i
$543$	−2.69757			−0.115764
$544$	4.20804	+	38.5338i	0.180418	+	1.65212i
$545$	6.00145			0.257074
$546$	9.46584	−	3.30496i	0.405101	−	0.141439i
$547$		−	0.645113i		−	0.0275830i	−0.999905	−	0.0137915i	$-0.995610\pi$
$547$		−	0.645113i		−	0.0275830i	0.999905	−	0.0137915i	$-0.00439011\pi$
$548$	28.4254	−	22.6049i	1.21427	−	0.965632i
$549$			1.92410i			0.0821187i
$550$	1.20230	+	3.44355i	0.0512663	+	0.146833i
$551$	−9.57484			−0.407902
$552$	−1.66764	−	1.05263i	−0.0709794	−	0.0448031i
$553$	8.93377			0.379903
$554$	8.53080	+	24.4333i	0.362439	+	1.03807i
$555$			1.33940i			0.0568544i
$556$	2.40778	+	3.02776i	0.102112	+	0.128406i
$557$			10.2596i			0.434714i	0.976092	+	0.217357i	$0.0697436\pi$
$557$			10.2596i			0.434714i	−0.976092	+	0.217357i	$0.930256\pi$
$558$	−19.0646	+	6.65634i	−0.807070	+	0.281785i
$559$	−34.2295			−1.44775
$560$	22.4726	+	5.19407i	0.949640	+	0.219490i
$561$	18.5080			0.781409
$562$	−24.1277	+	8.42408i	−1.01776	+	0.355349i
$563$		−	12.9293i		−	0.544906i	−0.962169	−	0.272453i	$-0.912165\pi$
$563$		−	12.9293i		−	0.544906i	0.962169	−	0.272453i	$-0.0878350\pi$
$564$	5.45261	+	6.85661i	0.229596	+	0.288715i
$565$			3.34221i			0.140608i
$566$	7.17772	+	20.5579i	0.301702	+	0.864114i
$567$	−16.6660			−0.699908
$568$	6.97871	−	11.0560i	0.292820	−	0.463901i
$569$	6.32637			0.265215			0.132608	−	0.991169i	$-0.457665\pi$
$569$	6.32637			0.265215			0.132608	+	0.991169i	$0.457665\pi$
$570$	−0.569213	−	1.63030i	−0.0238417	−	0.0682858i
$571$		−	31.1997i		−	1.30566i	−0.757502	−	0.652832i	$-0.773581\pi$
$571$		−	31.1997i		−	1.30566i	0.757502	−	0.652832i	$-0.226419\pi$
$572$	−32.6979	+	26.0025i	−1.36717	+	1.08722i
$573$			11.6156i			0.485248i
$574$	−26.7897	+	9.35353i	−1.11818	+	0.390409i
$575$	−0.665774			−0.0277647
$576$	−9.17044	−	19.2446i	−0.382102	−	0.801860i
$577$	5.48996			0.228550			0.114275	−	0.993449i	$-0.463545\pi$
$577$	5.48996			0.228550			0.114275	+	0.993449i	$0.463545\pi$
$578$	39.9950	−	13.9641i	1.66357	−	0.580830i
$579$			1.07186i			0.0445450i
$580$	−31.6073	+	25.1352i	−1.31242	+	1.04368i
$581$			24.5527i			1.01862i
$582$	−0.451535	−	1.29325i	−0.0187167	−	0.0536071i
$583$	−14.5516			−0.602666
$584$	−9.34934	+	14.8117i	−0.386878	+	0.612912i
$585$	25.1634			1.04038
$586$	5.33332	+	15.2753i	0.220318	+	0.631018i
$587$		−	17.4576i		−	0.720552i	−0.932846	−	0.360276i	$-0.882683\pi$
$587$		−	17.4576i		−	0.720552i	0.932846	−	0.360276i	$-0.117317\pi$
$588$	0.343598	+	0.432072i	0.0141697	+	0.0178183i
$589$			5.35842i			0.220790i
$590$	−28.8439	+	10.0707i	−1.18748	+	0.414606i
$591$	−0.130211			−0.00535617
$592$	4.27503	+	0.988086i	0.175703	+	0.0406101i
$593$	−16.7657			−0.688486			−0.344243	−	0.938881i	$-0.611864\pi$
$593$	−16.7657			−0.688486			−0.344243	+	0.938881i	$0.611864\pi$
$594$	−20.4285	+	7.13252i	−0.838191	+	0.292651i
$595$		−	39.5125i		−	1.61985i
$596$	19.3915	+	24.3846i	0.794305	+	0.998832i
$597$		−	1.02883i		−	0.0421070i
$598$	−2.51365	−	7.19943i	−0.102791	−	0.294407i
$599$	−0.357982			−0.0146267			−0.00731337	−	0.999973i	$-0.502328\pi$
$599$	−0.357982			−0.0146267			−0.00731337	+	0.999973i	$0.502328\pi$
$600$	0.765698	+	0.483319i	0.0312595	+	0.0197314i
$601$	22.8949			0.933903			0.466952	−	0.884283i	$-0.345352\pi$
$601$	22.8949			0.933903			0.466952	+	0.884283i	$0.345352\pi$
$602$	−9.74372	−	27.9073i	−0.397124	−	1.13742i
$603$		−	16.3535i		−	0.665964i
$604$	−31.2677	+	24.8651i	−1.27226	+	1.01175i
$605$			22.6904i			0.922497i
$606$	−5.64796	+	1.97196i	−0.229433	+	0.0801055i
$607$	1.33917			0.0543551			0.0271775	−	0.999631i	$-0.491348\pi$
$607$	1.33917			0.0543551			0.0271775	+	0.999631i	$0.491348\pi$
$608$	−5.62342	+	0.614101i	−0.228060	+	0.0249051i
$609$	−15.1593			−0.614284
$610$	2.03306	−	0.709834i	0.0823161	−	0.0287403i
$611$			33.8747i			1.37043i
$612$	−28.5833	+	22.7304i	−1.15541	+	0.918822i
$613$		−	29.8667i		−	1.20631i	−0.797625	−	0.603153i	$-0.793911\pi$
$613$		−	29.8667i		−	1.20631i	0.797625	−	0.603153i	$-0.206089\pi$
$614$	−9.95056	−	28.4997i	−0.401572	−	1.15015i
$615$	8.95997			0.361301
$616$	−30.5075	−	19.2568i	−1.22918	−	0.775877i
$617$	−36.4935			−1.46917			−0.734587	−	0.678514i	$-0.762624\pi$
$617$	−36.4935			−1.46917			−0.734587	+	0.678514i	$0.762624\pi$
$618$	−2.36810	−	6.78255i	−0.0952590	−	0.272834i
$619$		−	8.88669i		−	0.357186i	−0.983923	−	0.178593i	$-0.942845\pi$
$619$		−	8.88669i		−	0.357186i	0.983923	−	0.178593i	$-0.0571546\pi$
$620$	14.0665	+	17.6886i	0.564926	+	0.710390i
$621$		−	3.94963i		−	0.158493i
$622$	−29.0126	+	10.1296i	−1.16330	+	0.406161i
$623$	−1.69723			−0.0679982
$624$	−2.33551	+	10.1048i	−0.0934951	+	0.404514i
$625$	−21.9298			−0.877194
$626$	45.5306	−	15.8968i	1.81977	−	0.635365i
$627$			2.70096i			0.107866i
$628$	26.0011	+	32.6962i	1.03756	+	1.30472i
$629$		−	7.51659i		−	0.299706i
$630$	7.16297	+	20.5157i	0.285379	+	0.817364i
$631$	−28.1724			−1.12153			−0.560763	−	0.827977i	$-0.689492\pi$
$631$	−28.1724			−1.12153			−0.560763	+	0.827977i	$0.689492\pi$
$632$	−4.93265	+	7.81456i	−0.196210	+	0.310846i
$633$	−9.85452			−0.391682
$634$	−10.3621	−	29.6783i	−0.411530	−	1.17868i
$635$		−	30.1420i		−	1.19615i
$636$	−2.82744	+	2.24847i	−0.112115	+	0.0891577i
$637$			2.13463i			0.0845771i
$638$	59.6343	−	20.8211i	2.36095	−	0.824315i
$639$	12.3177			0.487280
$640$	−16.9513	+	16.7894i	−0.670058	+	0.663659i
$641$	3.58435			0.141573			0.0707867	−	0.997491i	$-0.477449\pi$
$641$	3.58435			0.141573			0.0707867	+	0.997491i	$0.477449\pi$
$642$	7.66405	−	2.67587i	0.302476	−	0.105608i
$643$			19.8837i			0.784137i	0.919936	+	0.392069i	$0.128240\pi$
$643$			19.8837i			0.784137i	−0.919936	+	0.392069i	$0.871760\pi$
$644$	5.15416	−	4.09876i	0.203102	−	0.161514i
$645$			9.33373i			0.367515i
$646$	3.19437	+	9.14909i	0.125681	+	0.359966i
$647$	35.7712			1.40631			0.703156	−	0.711036i	$-0.251774\pi$
$647$	35.7712			1.40631			0.703156	+	0.711036i	$0.251774\pi$
$648$	9.20191	−	14.5781i	0.361485	−	0.572683i
$649$	47.7865			1.87578
$650$	1.15415	+	3.30563i	0.0452694	+	0.129657i
$651$			8.48365i			0.332501i
$652$	3.17227	+	3.98911i	0.124236	+	0.156226i
$653$		−	8.57378i		−	0.335518i	−0.985828	−	0.167759i	$-0.946347\pi$
$653$		−	8.57378i		−	0.335518i	0.985828	−	0.167759i	$-0.0536531\pi$
$654$	−2.20012	+	0.768164i	−0.0860315	+	0.0300376i
$655$	−1.28428			−0.0501810
$656$	6.60983	−	28.5980i	0.258071	−	1.11656i
$657$	−16.5019			−0.643802
$658$	−27.6181	+	9.64274i	−1.07666	+	0.375913i
$659$		−	22.9993i		−	0.895927i	−0.894052	−	0.447964i	$-0.852149\pi$
$659$		−	22.9993i		−	0.895927i	0.894052	−	0.447964i	$-0.147851\pi$
$660$	7.09038	+	8.91610i	0.275993	+	0.347059i
$661$		−	28.4720i		−	1.10743i	−0.832706	−	0.553716i	$-0.813209\pi$
$661$		−	28.4720i		−	1.10743i	0.832706	−	0.553716i	$-0.186791\pi$
$662$	11.2799	+	32.3070i	0.438405	+	1.25565i
$663$	17.7667			0.690003
$664$	−21.4768	−	13.5564i	−0.833461	−	0.526091i
$665$	5.76625			0.223606
$666$	1.36263	+	3.90276i	0.0528010	+	0.151229i
$667$			11.5297i			0.446431i
$668$	−29.2167	+	23.2341i	−1.13043	+	0.898953i
$669$			7.91136i			0.305871i
$670$	−17.2795	+	6.03307i	−0.667565	+	0.233078i
$671$	−3.36822			−0.130029
$672$	−8.90322	+	0.972268i	−0.343449	+	0.0375061i
$673$	6.63685			0.255832			0.127916	−	0.991785i	$-0.459171\pi$
$673$	6.63685			0.255832			0.127916	+	0.991785i	$0.459171\pi$
$674$	−45.7610	+	15.9773i	−1.76265	+	0.615422i
$675$			1.81348i			0.0698009i
$676$	−11.0385	+	8.77816i	−0.424557	+	0.337622i
$677$			29.0823i			1.11772i	0.829261	+	0.558862i	$0.188762\pi$
$677$			29.0823i			1.11772i	−0.829261	+	0.558862i	$0.811238\pi$
$678$	−0.427790	−	1.22525i	−0.0164292	−	0.0470553i
$679$	4.57415			0.175540
$680$	34.5624	+	21.8163i	1.32541	+	0.836615i
$681$	3.16231			0.121180
$682$	−11.6522	−	33.3735i	−0.446186	−	1.27794i
$683$			4.63939i			0.177521i	0.996053	+	0.0887607i	$0.0282906\pi$
$683$			4.63939i			0.177521i	−0.996053	+	0.0887607i	$0.971709\pi$
$684$	−3.31716	−	4.17130i	−0.126835	−	0.159494i
$685$		−	38.2938i		−	1.46313i
$686$	23.8155	−	8.31509i	0.909280	−	0.317471i
$687$	−1.86902			−0.0713074
$688$	29.7909	+	6.88556i	1.13577	+	0.262510i
$689$	−13.9688			−0.532169
$690$	−1.96315	+	0.685426i	−0.0747358	+	0.0260937i
$691$			5.11245i			0.194487i	0.995261	+	0.0972434i	$0.0310025\pi$
$691$			5.11245i			0.194487i	−0.995261	+	0.0972434i	$0.968997\pi$
$692$	10.4861	+	13.1862i	0.398622	+	0.501264i
$693$		−	33.9889i		−	1.29113i
$694$	12.5508	+	35.9472i	0.476423	+	1.36454i
$695$	4.07890			0.154721
$696$	8.36997	−	13.2601i	0.317263	−	0.502624i
$697$	−50.2825			−1.90459
$698$	4.03596	+	11.5595i	0.152763	+	0.437534i
$699$		−	10.3264i		−	0.390581i
$700$	−2.36654	+	1.88195i	−0.0894468	+	0.0711311i
$701$			5.27938i			0.199399i	0.995018	+	0.0996997i	$0.0317882\pi$
$701$			5.27938i			0.199399i	−0.995018	+	0.0996997i	$0.968212\pi$
$702$	−19.6103	+	6.84686i	−0.740143	+	0.258418i
$703$	1.09693			0.0413716
$704$	33.6886	−	16.0532i	1.26969	−	0.605029i
$705$	9.23700			0.347886
$706$	−12.1670	+	4.24805i	−0.457910	+	0.159877i
$707$		−	19.9764i		−	0.751290i
$708$	9.28510	−	7.38382i	0.348955	−	0.277501i
$709$		−	28.1441i		−	1.05697i	−0.848942	−	0.528486i	$-0.822760\pi$
$709$		−	28.1441i		−	1.05697i	0.848942	−	0.528486i	$-0.177240\pi$
$710$	−4.54420	−	13.0152i	−0.170541	−	0.488451i
$711$	−8.70632			−0.326512
$712$	0.937103	−	1.48461i	0.0351194	−	0.0556379i
$713$	6.45241			0.241645
$714$	5.05745	+	14.4852i	0.189270	+	0.542095i
$715$			44.0495i			1.64736i
$716$	−20.7650	−	26.1118i	−0.776023	−	0.975843i
$717$			1.05703i			0.0394755i
$718$	5.74094	−	2.00443i	0.214250	−	0.0748046i
$719$	9.51160			0.354723			0.177361	−	0.984146i	$-0.443244\pi$
$719$	9.51160			0.354723			0.177361	+	0.984146i	$0.443244\pi$
$720$	−21.9004	−	5.06183i	−0.816181	−	0.188643i
$721$	23.9894			0.893412
$722$	−1.33517	+	0.466170i	−0.0496900	+	0.0173491i
$723$			3.74976i			0.139455i
$724$	5.79954	+	7.29288i	0.215538	+	0.271038i
$725$		−	5.29387i		−	0.196609i
$726$	−2.90429	−	8.31826i	−0.107788	−	0.308720i
$727$	7.06196			0.261914			0.130957	−	0.991388i	$-0.458195\pi$
$727$	7.06196			0.261914			0.130957	+	0.991388i	$0.458195\pi$
$728$	−29.2857	−	18.4855i	−1.08540	−	0.685118i
$729$	10.5442			0.390527
$730$	6.08784	+	17.4364i	0.225321	+	0.645349i
$731$		−	52.3801i		−	1.93735i
$732$	−0.654459	+	0.520448i	−0.0241895	+	0.0192363i
$733$			7.62443i			0.281615i	0.990037	+	0.140807i	$0.0449698\pi$
$733$			7.62443i			0.281615i	−0.990037	+	0.140807i	$0.955030\pi$
$734$	−28.4222	+	9.92350i	−1.04908	+	0.366283i
$735$	0.582073			0.0214701
$736$	0.739478	+	6.77152i	0.0272575	+	0.249602i
$737$	28.6274			1.05450
$738$	26.1077	−	9.11539i	0.961037	−	0.335542i
$739$			45.0131i			1.65583i	0.560851	+	0.827917i	$0.310474\pi$
$739$			45.0131i			1.65583i	−0.560851	+	0.827917i	$0.689526\pi$
$740$	3.62106	−	2.87959i	0.133113	−	0.105856i
$741$			2.59279i			0.0952484i
$742$	−3.97634	−	11.3888i	−0.145976	−	0.418094i
$743$	15.3137			0.561805			0.280903	−	0.959736i	$-0.409366\pi$
$743$	15.3137			0.561805			0.280903	+	0.959736i	$0.409366\pi$
$744$	−7.42083	−	4.68413i	−0.272061	−	0.171728i
$745$	32.8501			1.20354
$746$	−5.17803	−	14.8306i	−0.189581	−	0.542985i
$747$		−	23.9276i		−	0.875465i
$748$	−39.7906	−	50.0363i	−1.45489	−	1.82951i
$749$			27.1072i			0.990475i
$750$	9.05288	−	3.16078i	0.330565	−	0.115415i
$751$	4.09580			0.149458			0.0747290	−	0.997204i	$-0.476191\pi$
$751$	4.09580			0.149458			0.0747290	+	0.997204i	$0.476191\pi$
$752$	6.81420	−	29.4822i	0.248488	−	1.07511i
$753$	−1.80016			−0.0656015
$754$	57.2459	−	19.9872i	2.08477	−	0.727890i
$755$			42.1228i			1.53301i
$756$	−11.1645	−	14.0392i	−0.406048	−	0.510602i
$757$		−	9.51720i		−	0.345909i	−0.984930	−	0.172954i	$-0.944669\pi$
$757$		−	9.51720i		−	0.345909i	0.984930	−	0.172954i	$-0.0553313\pi$
$758$	−9.64542	−	27.6258i	−0.350338	−	1.00341i
$759$	3.25240			0.118055
$760$	−3.18375	+	5.04386i	−0.115487	+	0.182960i
$761$	−38.4841			−1.39505			−0.697523	−	0.716562i	$-0.745715\pi$
$761$	−38.4841			−1.39505			−0.697523	+	0.716562i	$0.745715\pi$
$762$	3.85806	+	11.0500i	0.139763	+	0.400299i
$763$		−	7.78167i		−	0.281715i
$764$	31.4027	−	24.9725i	1.13611	−	0.903473i
$765$			38.5065i			1.39221i
$766$	−16.2716	+	5.68116i	−0.587916	+	0.205269i
$767$	45.8726			1.65636
$768$	4.06532	−	8.32466i	0.146695	−	0.300390i
$769$	15.0210			0.541670			0.270835	−	0.962626i	$-0.412700\pi$
$769$	15.0210			0.541670			0.270835	+	0.962626i	$0.412700\pi$
$770$	−35.9136	+	12.5391i	−1.29423	+	0.451877i
$771$			3.33286i			0.120030i
$772$	2.89777	−	2.30440i	0.104293	−	0.0829372i
$773$		−	38.4471i		−	1.38285i	−0.722451	−	0.691423i	$-0.756984\pi$
$773$		−	38.4471i		−	1.38285i	0.722451	−	0.691423i	$-0.243016\pi$
$774$	9.49564	+	27.1968i	0.341314	+	0.977568i
$775$	−2.96263			−0.106421
$776$	−2.52555	+	4.00110i	−0.0906619	+	0.143631i
$777$	1.73671			0.0623040
$778$	12.2029	+	34.9507i	0.437495	+	1.25304i
$779$		−	7.33797i		−	0.262910i
$780$	6.80640	+	8.55899i	0.243708	+	0.306461i
$781$			21.5626i			0.771572i
$782$	11.0170	−	3.84654i	0.393967	−	0.137552i
$783$	31.4053			1.12233
$784$	0.429399	−	1.85783i	0.0153357	−	0.0663511i
$785$	44.0472			1.57211
$786$	0.470815	−	0.164383i	0.0167934	−	0.00586336i
$787$		−	30.8457i		−	1.09953i	−0.835319	−	0.549765i	$-0.814717\pi$
$787$		−	30.8457i		−	1.09953i	0.835319	−	0.549765i	$-0.185283\pi$
$788$	0.279942	+	0.352025i	0.00997253	+	0.0125404i
$789$		−	2.65535i		−	0.0945328i
$790$	3.21191	+	9.19932i	0.114275	+	0.327297i
$791$	4.33361			0.154085
$792$	29.7308	+	18.7665i	1.05644	+	0.666838i
$793$	−3.23332			−0.114819
$794$	−6.92035	−	19.8208i	−0.245594	−	0.703414i
$795$			3.80903i			0.135092i
$796$	−2.78143	+	2.21188i	−0.0985850	+	0.0783981i
$797$		−	34.1285i		−	1.20889i	−0.796646	−	0.604446i	$-0.793394\pi$
$797$		−	34.1285i		−	1.20889i	0.796646	−	0.604446i	$-0.206606\pi$
$798$	−2.11390	+	0.738059i	−0.0748312	+	0.0261270i
$799$	−51.8372			−1.83387
$800$	−0.339532	−	3.10915i	−0.0120043	−	0.109925i
$801$	1.65402			0.0584420
$802$	45.9448	−	16.0414i	1.62237	−	0.566443i
$803$		−	28.8873i		−	1.01941i
$804$	5.56242	−	4.42342i	0.196171	−	0.156002i
$805$		−	6.94351i		−	0.244727i
$806$	−11.1855	−	32.0368i	−0.393993	−	1.12845i
$807$	6.59578			0.232182
$808$	17.4738	+	11.0297i	0.614726	+	0.388023i
$809$	−25.9170			−0.911192			−0.455596	−	0.890187i	$-0.650574\pi$
$809$	−25.9170			−0.911192			−0.455596	+	0.890187i	$0.650574\pi$
$810$	−5.99185	−	17.1614i	−0.210532	−	0.602991i
$811$			33.7874i			1.18644i	0.805041	+	0.593219i	$0.202143\pi$
$811$			33.7874i			1.18644i	−0.805041	+	0.593219i	$0.797857\pi$
$812$	32.5911	+	40.9830i	1.14372	+	1.43822i
$813$			14.5479i			0.510218i
$814$	−6.83195	+	2.38535i	−0.239460	+	0.0836065i
$815$	5.37400			0.188243
$816$	−15.4629	−	3.57393i	−0.541310	−	0.125113i
$817$	7.64408			0.267432
$818$	1.91307	−	0.667941i	0.0668889	−	0.0233540i
$819$		−	32.6276i		−	1.14010i
$820$	−19.2631	−	24.2232i	−0.672698	−	0.845912i
$821$		−	27.6475i		−	0.964903i	−0.875923	−	0.482451i	$-0.839746\pi$
$821$		−	27.6475i		−	0.964903i	0.875923	−	0.482451i	$-0.160254\pi$
$822$	4.90146	+	14.0384i	0.170958	+	0.489647i
$823$	−12.4983			−0.435665			−0.217832	−	0.975986i	$-0.569899\pi$
$823$	−12.4983			−0.435665			−0.217832	+	0.975986i	$0.569899\pi$
$824$	−13.2454	+	20.9840i	−0.461425	+	0.731013i
$825$	−1.49335			−0.0519916
$826$	13.0580	+	37.3999i	0.454347	+	1.30131i
$827$			9.03084i			0.314033i	0.987596	+	0.157017i	$0.0501876\pi$
$827$			9.03084i			0.314033i	−0.987596	+	0.157017i	$0.949812\pi$
$828$	−5.02293	+	3.99440i	−0.174559	+	0.138815i
$829$			55.7684i			1.93692i	0.249175	+	0.968458i	$0.419841\pi$
$829$			55.7684i			1.93692i	−0.249175	+	0.968458i	$0.580159\pi$
$830$	−25.2825	+	8.82730i	−0.877569	+	0.306400i
$831$	−10.5959			−0.367567
$832$	32.3393	−	15.4103i	1.12116	−	0.534256i
$833$	−3.26654			−0.113179
$834$	−1.49532	+	0.522084i	−0.0517786	+	0.0180783i
$835$			39.3597i			1.36210i
$836$	7.30205	−	5.80683i	0.252547	−	0.200833i
$837$		−	17.5755i		−	0.607498i
$838$	15.7046	+	44.9800i	0.542507	+	1.55381i
$839$	−14.3128			−0.494134			−0.247067	−	0.968998i	$-0.579467\pi$
$839$	−14.3128			−0.494134			−0.247067	+	0.968998i	$0.579467\pi$
$840$	−5.04064	+	7.98564i	−0.173919	+	0.275531i
$841$	−62.6776			−2.16130
$842$	0.110683	+	0.317010i	0.00381438	+	0.0109249i
$843$		−	10.4633i		−	0.360376i
$844$	21.1863	+	26.6416i	0.729264	+	0.917043i
$845$			14.8707i			0.511567i
$846$	26.9149	−	9.39723i	0.925354	−	0.323084i
$847$	29.4211			1.01092
$848$	12.1575	+	2.80995i	0.417489	+	0.0964940i
$849$	−8.91525			−0.305971
$850$	−5.05848	+	1.76615i	−0.173504	+	0.0605783i
$851$		−	1.32089i		−	0.0452794i
$852$	3.33179	+	4.18970i	0.114145	+	0.143537i
$853$		−	38.0325i		−	1.30221i	−0.758988	−	0.651105i	$-0.774306\pi$
$853$		−	38.0325i		−	1.30221i	0.758988	−	0.651105i	$-0.225694\pi$
$854$	−0.920393	−	2.63612i	−0.0314952	−	0.0902063i
$855$	−5.61945			−0.192181
$856$	−23.7112	−	14.9668i	−0.810433	−	0.511556i
$857$	−23.1869			−0.792048			−0.396024	−	0.918240i	$-0.629610\pi$
$857$	−23.1869			−0.792048			−0.396024	+	0.918240i	$0.629610\pi$
$858$	−5.63818	−	16.1485i	−0.192484	−	0.551300i
$859$			46.5870i			1.58953i	0.606919	+	0.794764i	$0.292405\pi$
$859$			46.5870i			1.58953i	−0.606919	+	0.794764i	$0.707595\pi$
$860$	25.2337	−	20.0667i	0.860462	−	0.684269i
$861$		−	11.6178i		−	0.395933i
$862$	17.4564	−	6.09484i	0.594568	−	0.207591i
$863$	−54.3149			−1.84890			−0.924451	−	0.381301i	$-0.875476\pi$
$863$	−54.3149			−1.84890			−0.924451	+	0.381301i	$0.875476\pi$
$864$	18.4447	−	2.01424i	0.627502	−	0.0685258i
$865$	17.7640			0.603995
$866$	−12.9207	+	4.51121i	−0.439063	+	0.153297i
$867$			17.3444i			0.589048i
$868$	22.9355	−	18.2391i	0.778482	−	0.619075i
$869$		−	15.2408i		−	0.517008i
$870$	−5.45012	−	15.6099i	−0.184777	−	0.529224i
$871$	27.4808			0.931153
$872$	6.80679	+	4.29653i	0.230507	+	0.145499i
$873$	−4.45769			−0.150870
$874$	0.561345	+	1.60777i	0.0189878	+	0.0543835i
$875$			32.0194i			1.08245i
$876$	−4.46358	−	5.61292i	−0.150810	−	0.189643i
$877$			1.80324i			0.0608910i	0.999536	+	0.0304455i	$0.00969260\pi$
$877$			1.80324i			0.0608910i	−0.999536	+	0.0304455i	$0.990307\pi$
$878$	23.7639	−	8.29705i	0.801991	−	0.280012i
$879$	−6.62438			−0.223435
$880$	8.86095	−	38.3376i	0.298703	−	1.29236i
$881$	12.6372			0.425759			0.212880	−	0.977078i	$-0.431716\pi$
$881$	12.6372			0.425759			0.212880	+	0.977078i	$0.431716\pi$
$882$	1.69605	−	0.592170i	0.0571090	−	0.0199394i
$883$			39.9276i			1.34367i	0.740700	+	0.671835i	$0.234494\pi$
$883$			39.9276i			1.34367i	−0.740700	+	0.671835i	$0.765506\pi$
$884$	−38.1969	−	48.0323i	−1.28470	−	1.61550i
$885$		−	12.5086i		−	0.420471i
$886$	−1.54054	−	4.41232i	−0.0517555	−	0.148235i
$887$	−14.3642			−0.482304			−0.241152	−	0.970487i	$-0.577525\pi$
$887$	−14.3642			−0.482304			−0.241152	+	0.970487i	$0.577525\pi$
$888$	−0.958898	+	1.51913i	−0.0321785	+	0.0509788i
$889$	−39.0830			−1.31080
$890$	−0.610197	−	1.74768i	−0.0204538	−	0.0585825i
$891$			28.4318i			0.952502i
$892$	21.3883	−	17.0087i	0.716135	−	0.569494i
$893$		−	7.56486i		−	0.253148i
$894$	−12.0428	+	4.20470i	−0.402771	+	0.140626i
$895$	−35.1769			−1.17584
$896$	21.7697	+	21.9795i	0.727273	+	0.734285i
$897$	3.12214			0.104245
$898$	−39.5935	+	13.8239i	−1.32125	+	0.461311i
$899$			51.3060i			1.71115i
$900$	2.30629	−	1.83404i	0.0768763	−	0.0611346i
$901$		−	21.3759i		−	0.712135i
$902$	15.9569	+	45.7026i	0.531306	+	1.52173i
$903$	12.1024			0.402743
$904$	−2.39274	+	3.79070i	−0.0795814	+	0.126077i
$905$	9.82473			0.326585
$906$	−5.39156	−	15.4421i	−0.179123	−	0.513031i
$907$		−	3.32787i		−	0.110500i	−0.998473	−	0.0552501i	$-0.982404\pi$
$907$		−	3.32787i		−	0.110500i	0.998473	−	0.0552501i	$-0.0175956\pi$
$908$	−6.79869	−	8.54930i	−0.225623	−	0.283719i
$909$			19.4678i			0.645707i
$910$	−34.4752	+	12.0369i	−1.14284	+	0.399018i
$911$	−35.8252			−1.18694			−0.593471	−	0.804855i	$-0.702243\pi$
$911$	−35.8252			−1.18694			−0.593471	+	0.804855i	$0.702243\pi$
$912$	0.521562	−	2.25658i	0.0172706	−	0.0747228i
$913$	41.8863			1.38623
$914$	−27.0119	+	9.43111i	−0.893475	+	0.311953i
$915$			0.881666i			0.0291470i
$916$	4.01822	+	5.05288i	0.132766	+	0.166952i
$917$			1.66524i			0.0549910i
$918$	−10.4775	−	30.0089i	−0.345808	−	0.990440i
$919$	−48.3186			−1.59388			−0.796942	−	0.604055i	$-0.793551\pi$
$919$	−48.3186			−1.59388			−0.796942	+	0.604055i	$0.793551\pi$
$920$	6.07364	+	3.83376i	0.200242	+	0.126395i
$921$	12.3593			0.407254
$922$	−19.2262	−	55.0663i	−0.633181	−	1.81351i
$923$			20.6990i			0.681316i
$924$	11.5609	−	9.19360i	0.380325	−	0.302447i
$925$			0.606487i			0.0199412i
$926$	−22.0613	+	7.70261i	−0.724978	+	0.253123i
$927$	−23.3786			−0.767855
$928$	−53.8434	+	5.87992i	−1.76750	+	0.193018i
$929$	−23.2127			−0.761585			−0.380792	−	0.924661i	$-0.624349\pi$
$929$	−23.2127			−0.761585			−0.380792	+	0.924661i	$0.624349\pi$
$930$	−8.73583	+	3.05008i	−0.286459	+	0.100016i
$931$		−	0.476702i		−	0.0156233i
$932$	−27.9174	+	22.2009i	−0.914466	+	0.727214i
$933$		−	12.5817i		−	0.411908i
$934$	−11.6527	−	33.3749i	−0.381288	−	1.09206i
$935$	−67.4073			−2.20445
$936$	28.5400	+	18.0148i	0.932860	+	0.588834i
$937$	7.10467			0.232099			0.116050	−	0.993243i	$-0.462977\pi$
$937$	7.10467			0.232099			0.116050	+	0.993243i	$0.462977\pi$
$938$	7.82266	+	22.4051i	0.255419	+	0.731553i
$939$			19.7450i			0.644354i
$940$	−19.8587	−	24.9722i	−0.647720	−	0.814503i
$941$			55.5352i			1.81040i	0.424989	+	0.905199i	$0.360278\pi$
$941$			55.5352i			1.81040i	−0.424989	+	0.905199i	$0.639722\pi$
$942$	−16.1476	+	5.63788i	−0.526118	+	0.183692i
$943$	−8.83612			−0.287744
$944$	−39.9243	−	9.22767i	−1.29942	−	0.300335i
$945$	−18.9132			−0.615247
$946$	−47.6091	+	16.6225i	−1.54791	+	0.540445i
$947$		−	15.5988i		−	0.506894i	−0.967349	−	0.253447i	$-0.918436\pi$
$947$		−	15.5988i		−	0.506894i	0.967349	−	0.253447i	$-0.0815643\pi$
$948$	−2.35496	−	2.96134i	−0.0764855	−	0.0961799i
$949$		−	27.7304i		−	0.900165i
$950$	−0.257743	−	0.738208i	−0.00836227	−	0.0239506i
$951$	12.8704			0.417352
$952$	28.2876	−	44.8147i	0.916807	−	1.45245i
$953$	21.1243			0.684282			0.342141	−	0.939649i	$-0.388848\pi$
$953$	21.1243			0.684282			0.342141	+	0.939649i	$0.388848\pi$
$954$	3.87510	+	11.0988i	0.125461	+	0.359337i
$955$		−	42.3047i		−	1.36895i
$956$	2.85768	−	2.27252i	0.0924239	−	0.0734986i
$957$			25.8613i			0.835977i
$958$	13.3915	−	4.67560i	0.432660	−	0.151062i
$959$	−49.6529			−1.60338
$960$	−4.20209	−	8.81831i	−0.135622	−	0.284610i
$961$	−2.28738			−0.0737863
$962$	−6.55832	+	2.28981i	−0.211449	+	0.0738265i
$963$		−	26.4170i		−	0.851277i
$964$	10.1375	−	8.06165i	0.326506	−	0.259648i
$965$		−	3.90378i		−	0.125667i
$966$	0.888744	+	2.54548i	0.0285949	+	0.0818994i
$967$	46.1207			1.48314			0.741570	−	0.670875i	$-0.234081\pi$
$967$	46.1207			1.48314			0.741570	+	0.670875i	$0.234081\pi$
$968$	−16.2444	+	25.7353i	−0.522116	+	0.827162i
$969$	−3.96764			−0.127459
$970$	1.64452	+	4.71011i	0.0528022	+	0.151233i
$971$			22.3253i			0.716454i	0.933635	+	0.358227i	$0.116619\pi$
$971$			22.3253i			0.716454i	−0.933635	+	0.358227i	$0.883381\pi$
$972$	16.6423	+	20.9276i	0.533802	+	0.671252i
$973$		−	5.28882i		−	0.169552i
$974$	55.5763	−	19.4043i	1.78078	−	0.621752i
$975$	−1.43354			−0.0459099
$976$	2.81406	+	0.650411i	0.0900757	+	0.0208192i
$977$	14.2650			0.456379			0.228190	−	0.973617i	$-0.426719\pi$
$977$	14.2650			0.456379			0.228190	+	0.973617i	$0.426719\pi$
$978$	−1.97010	+	0.687851i	−0.0629967	+	0.0219951i
$979$			2.89544i			0.0925385i
$980$	−1.25140	−	1.57363i	−0.0399746	−	0.0502678i
$981$			7.58355i			0.242124i
$982$	16.1733	+	46.3224i	0.516110	+	1.47821i
$983$	12.7242			0.405838			0.202919	−	0.979196i	$-0.434957\pi$
$983$	12.7242			0.405838			0.202919	+	0.979196i	$0.434957\pi$
$984$	10.1623	+	6.41458i	0.323963	+	0.204489i
$985$	0.474237			0.0151104
$986$	30.5856	+	87.6011i	0.974044	+	2.78979i
$987$		−	11.9770i		−	0.381232i
$988$	7.00959	−	5.57426i	0.223005	−	0.177341i
$989$		−	9.20472i		−	0.292693i
$990$	34.9992	−	12.2198i	1.11235	−	0.388372i
$991$	−10.8169			−0.343611			−0.171806	−	0.985131i	$-0.554960\pi$
$991$	−10.8169			−0.343611			−0.171806	+	0.985131i	$0.554960\pi$
$992$	3.29061	+	30.1326i	0.104477	+	0.956712i
$993$	−14.0104			−0.444607
$994$	−16.8759	+	5.89215i	−0.535271	+	0.186888i
$995$			3.74705i			0.118789i
$996$	8.13866	−	6.47214i	0.257883	−	0.205078i
$997$			5.39134i			0.170746i	0.996349	+	0.0853728i	$0.0272081\pi$
$997$			5.39134i			0.170746i	−0.996349	+	0.0853728i	$0.972792\pi$
$998$	−6.58561	−	18.8620i	−0.208464	−	0.597067i
$999$	−3.59792			−0.113833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.15	✓	16
3.2	odd	2		1368.2.g.b.685.2		16
4.3	odd	2		608.2.c.b.305.8		16
8.3	odd	2		608.2.c.b.305.9		16
8.5	even	2	inner	152.2.c.b.77.16	yes	16
12.11	even	2		5472.2.g.b.2737.12		16
16.3	odd	4		4864.2.a.bp.1.5		8
16.5	even	4		4864.2.a.bo.1.5		8
16.11	odd	4		4864.2.a.bn.1.4		8
16.13	even	4		4864.2.a.bq.1.4		8
24.5	odd	2		1368.2.g.b.685.1		16
24.11	even	2		5472.2.g.b.2737.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.15	✓	16	1.1	even	1	trivial
152.2.c.b.77.16	yes	16	8.5	even	2	inner
608.2.c.b.305.8		16	4.3	odd	2
608.2.c.b.305.9		16	8.3	odd	2
1368.2.g.b.685.1		16	24.5	odd	2
1368.2.g.b.685.2		16	3.2	odd	2
4864.2.a.bn.1.4		8	16.11	odd	4
4864.2.a.bo.1.5		8	16.5	even	4
4864.2.a.bp.1.5		8	16.3	odd	4
4864.2.a.bq.1.4		8	16.13	even	4
5472.2.g.b.2737.5		16	24.11	even	2
5472.2.g.b.2737.12		16	12.11	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33517 - 0.466170i) q^{2} +0.579017i q^{3} +(1.56537 - 1.24484i) q^{4} -2.10882i q^{5} +(0.269921 + 0.773088i) q^{6} -2.73436 q^{7} +(1.50973 - 2.39180i) q^{8} +2.66474 q^{9} +O(q^{10})\)	\(q+(1.33517 - 0.466170i) q^{2} +0.579017i q^{3} +(1.56537 - 1.24484i) q^{4} -2.10882i q^{5} +(0.269921 + 0.773088i) q^{6} -2.73436 q^{7} +(1.50973 - 2.39180i) q^{8} +2.66474 q^{9} +(-0.983067 - 2.81563i) q^{10} +4.66474i q^{11} +(0.720781 + 0.906377i) q^{12} +4.47791i q^{13} +(-3.65084 + 1.27468i) q^{14} +1.22104 q^{15} +(0.900771 - 3.89726i) q^{16} -6.85237 q^{17} +(3.55789 - 1.24222i) q^{18} -1.00000i q^{19} +(-2.62513 - 3.30108i) q^{20} -1.58324i q^{21} +(2.17456 + 6.22823i) q^{22} -1.20416 q^{23} +(1.38489 + 0.874162i) q^{24} +0.552894 q^{25} +(2.08747 + 5.97878i) q^{26} +3.27998i q^{27} +(-4.28028 + 3.40382i) q^{28} -9.57484i q^{29} +(1.63030 - 0.569213i) q^{30} -5.35842 q^{31} +(-0.614101 - 5.62342i) q^{32} -2.70096 q^{33} +(-9.14909 + 3.19437i) q^{34} +5.76625i q^{35} +(4.17130 - 3.31716i) q^{36} +1.09693i q^{37} +(-0.466170 - 1.33517i) q^{38} -2.59279 q^{39} +(-5.04386 - 3.18375i) q^{40} +7.33797 q^{41} +(-0.738059 - 2.11390i) q^{42} +7.64408i q^{43} +(5.80683 + 7.30205i) q^{44} -5.61945i q^{45} +(-1.60777 + 0.561345i) q^{46} +7.56486 q^{47} +(2.25658 + 0.521562i) q^{48} +0.476702 q^{49} +(0.738208 - 0.257743i) q^{50} -3.96764i q^{51} +(5.57426 + 7.00959i) q^{52} +3.11949i q^{53} +(1.52903 + 4.37934i) q^{54} +9.83708 q^{55} +(-4.12815 + 6.54003i) q^{56} +0.579017 q^{57} +(-4.46351 - 12.7841i) q^{58} -10.2442i q^{59} +(1.91138 - 1.51999i) q^{60} +0.722061i q^{61} +(-7.15441 + 2.49793i) q^{62} -7.28634 q^{63} +(-3.44140 - 7.22196i) q^{64} +9.44309 q^{65} +(-3.60625 + 1.25911i) q^{66} -6.13698i q^{67} +(-10.7265 + 8.53007i) q^{68} -0.697232i q^{69} +(2.68806 + 7.69894i) q^{70} +4.62247 q^{71} +(4.02305 - 6.37352i) q^{72} -6.19270 q^{73} +(0.511358 + 1.46460i) q^{74} +0.320135i q^{75} +(-1.24484 - 1.56537i) q^{76} -12.7551i q^{77} +(-3.46182 + 1.20868i) q^{78} -3.26723 q^{79} +(-8.21860 - 1.89956i) q^{80} +6.09505 q^{81} +(9.79746 - 3.42075i) q^{82} -8.97934i q^{83} +(-1.97087 - 2.47836i) q^{84} +14.4504i q^{85} +(3.56344 + 10.2062i) q^{86} +5.54400 q^{87} +(11.1571 + 7.04252i) q^{88} +0.620707 q^{89} +(-2.61962 - 7.50293i) q^{90} -12.2442i q^{91} +(-1.88496 + 1.49899i) q^{92} -3.10262i q^{93} +(10.1004 - 3.52651i) q^{94} -2.10882 q^{95} +(3.25606 - 0.355575i) q^{96} -1.67284 q^{97} +(0.636479 - 0.222224i) q^{98} +12.4303i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Introduction

L-functions

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