LMFDB - Embedded newform 416.2.bf.a.157.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			157.18
Character	$\chi$	$=$	416.157
Dual form			416.2.bf.a.53.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.705052 - 1.22593i) q^{2} +(3.06559 + 1.26981i) q^{3} +(-1.00580 + 1.72869i) q^{4} +(0.112862 + 0.272473i) q^{5} +(-0.604704 - 4.65347i) q^{6} +(-1.80857 + 1.80857i) q^{7} +(2.82839 + 0.0142285i) q^{8} +(5.66408 + 5.66408i) q^{9} +O(q^{10})$	\(q+(-0.705052 - 1.22593i) q^{2} +(3.06559 + 1.26981i) q^{3} +(-1.00580 + 1.72869i) q^{4} +(0.112862 + 0.272473i) q^{5} +(-0.604704 - 4.65347i) q^{6} +(-1.80857 + 1.80857i) q^{7} +(2.82839 + 0.0142285i) q^{8} +(5.66408 + 5.66408i) q^{9} +(0.254459 - 0.330468i) q^{10} +(-2.10606 + 0.872359i) q^{11} +(-5.27848 + 4.02226i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(3.49231 + 0.942042i) q^{14} +0.978601i q^{15} +(-1.97672 - 3.47744i) q^{16} +3.28489i q^{17} +(2.95029 - 10.9372i) q^{18} +(2.88448 - 6.96374i) q^{19} +(-0.584537 - 0.0789510i) q^{20} +(-7.84086 + 3.24779i) q^{21} +(2.55433 + 1.96682i) q^{22} +(1.45336 + 1.45336i) q^{23} +(8.65261 + 3.63513i) q^{24} +(3.47403 - 3.47403i) q^{25} +(1.40242 - 0.182241i) q^{26} +(6.36202 + 15.3593i) q^{27} +(-1.30739 - 4.94551i) q^{28} +(-7.19503 - 2.98028i) q^{29} +(1.19970 - 0.689965i) q^{30} +1.16991 q^{31} +(-2.86940 + 4.87509i) q^{32} -7.56404 q^{33} +(4.02704 - 2.31602i) q^{34} +(-0.696904 - 0.288667i) q^{35} +(-15.4884 + 4.09448i) q^{36} +(1.93528 + 4.67218i) q^{37} +(-10.5708 + 1.37364i) q^{38} +(-2.34630 + 2.34630i) q^{39} +(0.315341 + 0.772265i) q^{40} +(-1.89890 - 1.89890i) q^{41} +(9.50977 + 7.32247i) q^{42} +(9.69546 - 4.01599i) q^{43} +(0.610247 - 4.51814i) q^{44} +(-0.904049 + 2.18257i) q^{45} +(0.757019 - 2.80640i) q^{46} -10.8738i q^{47} +(-1.64413 - 13.1704i) q^{48} +0.458157i q^{49} +(-6.70829 - 1.80954i) q^{50} +(-4.17117 + 10.0701i) q^{51} +(-1.21219 - 1.59078i) q^{52} +(6.82302 - 2.82619i) q^{53} +(14.3438 - 18.6285i) q^{54} +(-0.475388 - 0.475388i) q^{55} +(-5.14107 + 5.08961i) q^{56} +(17.6852 - 17.6852i) q^{57} +(1.41926 + 10.9219i) q^{58} +(-1.41929 - 3.42646i) q^{59} +(-1.69170 - 0.984280i) q^{60} +(-3.10660 - 1.28679i) q^{61} +(-0.824851 - 1.43423i) q^{62} -20.4878 q^{63} +(7.99960 + 0.0804878i) q^{64} -0.294922 q^{65} +(5.33304 + 9.27298i) q^{66} +(-2.33286 - 0.966304i) q^{67} +(-5.67854 - 3.30395i) q^{68} +(2.60991 + 6.30087i) q^{69} +(0.137468 + 1.05788i) q^{70} +(3.12139 - 3.12139i) q^{71} +(15.9397 + 16.1008i) q^{72} +(1.58685 + 1.58685i) q^{73} +(4.36329 - 5.66665i) q^{74} +(15.0613 - 6.23859i) q^{75} +(9.13691 + 11.9905i) q^{76} +(2.23124 - 5.38668i) q^{77} +(4.53066 + 1.22213i) q^{78} -15.9814i q^{79} +(0.724410 - 0.931072i) q^{80} +31.1330i q^{81} +(-0.989095 + 3.66675i) q^{82} +(1.02714 - 2.47975i) q^{83} +(2.27195 - 16.8210i) q^{84} +(-0.895042 + 0.370739i) q^{85} +(-11.7591 - 9.05446i) q^{86} +(-18.2726 - 18.2726i) q^{87} +(-5.96918 + 2.43741i) q^{88} +(-5.24144 + 5.24144i) q^{89} +(3.31307 - 0.430524i) q^{90} +(-0.978790 - 2.36301i) q^{91} +(-3.97419 + 1.05061i) q^{92} +(3.58647 + 1.48557i) q^{93} +(-13.3305 + 7.66660i) q^{94} +2.22298 q^{95} +(-14.9868 + 11.3014i) q^{96} -5.34042 q^{97} +(0.561668 - 0.323025i) q^{98} +(-16.8700 - 6.98780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.705052	−	1.22593i	−0.498547	−	0.866863i
$2$	−0.705052	−	1.22593i	−0.498547	−	0.866863i
$3$	3.06559	+	1.26981i	1.76992	+	0.733124i	0.994863	+	0.101228i	$0.0322771\pi$
$3$	3.06559	+	1.26981i	1.76992	+	0.733124i	0.775053	+	0.631896i	$0.217723\pi$
$4$	−1.00580	+	1.72869i	−0.502902	+	0.864344i
$5$	0.112862	+	0.272473i	0.0504734	+	0.121853i	0.947105	−	0.320924i	$-0.103993\pi$
$5$	0.112862	+	0.272473i	0.0504734	+	0.121853i	−0.896632	+	0.442777i	$0.853993\pi$
$6$	−0.604704	−	4.65347i	−0.246869	−	1.89977i
$7$	−1.80857	+	1.80857i	−0.683575	+	0.683575i	−0.960804	−	0.277229i	$-0.910584\pi$
$7$	−1.80857	+	1.80857i	−0.683575	+	0.683575i	0.277229	+	0.960804i	$0.410584\pi$
$8$	2.82839	+	0.0142285i	0.999987	+	0.00503055i
$9$	5.66408	+	5.66408i	1.88803	+	1.88803i
$10$	0.254459	−	0.330468i	0.0804669	−	0.104503i
$11$	−2.10606	+	0.872359i	−0.635002	+	0.263026i	−0.676877	−	0.736097i	$-0.736667\pi$
$11$	−2.10606	+	0.872359i	−0.635002	+	0.263026i	0.0418749	+	0.999123i	$0.486667\pi$
$12$	−5.27848	+	4.02226i	−1.52376	+	1.16113i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$14$	3.49231	+	0.942042i	0.933360	+	0.251771i
$15$			0.978601i			0.252674i
$16$	−1.97672	−	3.47744i	−0.494180	−	0.869360i
$17$			3.28489i			0.796702i	0.917233	+	0.398351i	$0.130417\pi$
$17$			3.28489i			0.796702i	−0.917233	+	0.398351i	$0.869583\pi$
$18$	2.95029	−	10.9372i	0.695390	−	2.57793i
$19$	2.88448	−	6.96374i	0.661744	−	1.59759i	−0.133325	−	0.991072i	$-0.542565\pi$
$19$	2.88448	−	6.96374i	0.661744	−	1.59759i	0.795069	−	0.606519i	$-0.207435\pi$
$20$	−0.584537	−	0.0789510i	−0.130706	−	0.0176540i
$21$	−7.84086	+	3.24779i	−1.71102	+	0.708726i
$22$	2.55433	+	1.96682i	0.544586	+	0.419328i
$23$	1.45336	+	1.45336i	0.303046	+	0.303046i	0.842204	−	0.539159i	$-0.181258\pi$
$23$	1.45336	+	1.45336i	0.303046	+	0.303046i	−0.539159	+	0.842204i	$0.681258\pi$
$24$	8.65261	+	3.63513i	1.76621	+	0.742018i
$25$	3.47403	−	3.47403i	0.694806	−	0.694806i
$26$	1.40242	−	0.182241i	0.275038	−	0.0357403i
$27$	6.36202	+	15.3593i	1.22437	+	2.95589i
$28$	−1.30739	−	4.94551i	−0.247073	−	0.934614i
$29$	−7.19503	−	2.98028i	−1.33608	−	0.553424i	−0.403700	−	0.914892i	$-0.632276\pi$
$29$	−7.19503	−	2.98028i	−1.33608	−	0.553424i	−0.932385	+	0.361467i	$0.882276\pi$
$30$	1.19970	−	0.689965i	0.219033	−	0.125970i
$31$	1.16991			0.210123			0.105061	−	0.994466i	$-0.466496\pi$
$31$	1.16991			0.210123			0.105061	+	0.994466i	$0.466496\pi$
$32$	−2.86940	+	4.87509i	−0.507243	+	0.861803i
$33$	−7.56404			−1.31673
$34$	4.02704	−	2.31602i	0.690631	−	0.397194i
$35$	−0.696904	−	0.288667i	−0.117798	−	0.0487936i
$36$	−15.4884	+	4.09448i	−2.58140	+	0.682413i
$37$	1.93528	+	4.67218i	0.318158	+	0.768102i	0.999352	+	0.0359985i	$0.0114612\pi$
$37$	1.93528	+	4.67218i	0.318158	+	0.768102i	−0.681194	+	0.732103i	$0.738539\pi$
$38$	−10.5708	+	1.37364i	−1.71480	+	0.222833i
$39$	−2.34630	+	2.34630i	−0.375708	+	0.375708i
$40$	0.315341	+	0.772265i	0.0498597	+	0.122106i
$41$	−1.89890	−	1.89890i	−0.296559	−	0.296559i	0.543106	−	0.839664i	$-0.317248\pi$
$41$	−1.89890	−	1.89890i	−0.296559	−	0.296559i	−0.839664	+	0.543106i	$0.817248\pi$
$42$	9.50977	+	7.32247i	1.46739	+	1.12988i
$43$	9.69546	−	4.01599i	1.47854	−	0.612433i	0.509754	−	0.860320i	$-0.329736\pi$
$43$	9.69546	−	4.01599i	1.47854	−	0.612433i	0.968789	+	0.247887i	$0.0797363\pi$
$44$	0.610247	−	4.51814i	0.0919982	−	0.681136i
$45$	−0.904049	+	2.18257i	−0.134768	+	0.325358i
$46$	0.757019	−	2.80640i	0.111616	−	0.413782i
$47$		−	10.8738i		−	1.58611i	−0.609152	−	0.793054i	$-0.708490\pi$
$47$		−	10.8738i		−	1.58611i	0.609152	−	0.793054i	$-0.291510\pi$
$48$	−1.64413	−	13.1704i	−0.237309	−	1.90099i
$49$			0.458157i			0.0654510i
$50$	−6.70829	−	1.80954i	−0.948695	−	0.255908i
$51$	−4.17117	+	10.0701i	−0.584081	+	1.41010i
$52$	−1.21219	−	1.59078i	−0.168101	−	0.220602i
$53$	6.82302	−	2.82619i	0.937214	−	0.388207i	0.138803	−	0.990320i	$-0.455674\pi$
$53$	6.82302	−	2.82619i	0.937214	−	0.388207i	0.798411	+	0.602113i	$0.205674\pi$
$54$	14.3438	−	18.6285i	1.95195	−	2.53501i
$55$	−0.475388	−	0.475388i	−0.0641013	−	0.0641013i
$56$	−5.14107	+	5.08961i	−0.687005	+	0.680127i
$57$	17.6852	−	17.6852i	2.34246	−	2.34246i
$58$	1.41926	+	10.9219i	0.186358	+	1.43411i
$59$	−1.41929	−	3.42646i	−0.184775	−	0.446087i	0.804164	−	0.594408i	$-0.202613\pi$
$59$	−1.41929	−	3.42646i	−0.184775	−	0.446087i	−0.988939	+	0.148320i	$0.952613\pi$
$60$	−1.69170	−	0.984280i	−0.218397	−	0.127070i
$61$	−3.10660	−	1.28679i	−0.397759	−	0.164757i	0.174832	−	0.984598i	$-0.444062\pi$
$61$	−3.10660	−	1.28679i	−0.397759	−	0.164757i	−0.572591	+	0.819841i	$0.694062\pi$
$62$	−0.824851	−	1.43423i	−0.104756	−	0.182148i
$63$	−20.4878			−2.58122
$64$	7.99960	+	0.0804878i	0.999949	+	0.0100610i
$65$	−0.294922			−0.0365806
$66$	5.33304	+	9.27298i	0.656452	+	1.14142i
$67$	−2.33286	−	0.966304i	−0.285005	−	0.118053i	0.235601	−	0.971850i	$-0.424294\pi$
$67$	−2.33286	−	0.966304i	−0.285005	−	0.118053i	−0.520606	+	0.853797i	$0.674294\pi$
$68$	−5.67854	−	3.30395i	−0.688625	−	0.400663i
$69$	2.60991	+	6.30087i	0.314196	+	0.758536i
$70$	0.137468	+	1.05788i	0.0164306	+	0.126441i
$71$	3.12139	−	3.12139i	0.370441	−	0.370441i	−0.497197	−	0.867638i	$-0.665637\pi$
$71$	3.12139	−	3.12139i	0.370441	−	0.370441i	0.867638	+	0.497197i	$0.165637\pi$
$72$	15.9397	+	16.1008i	1.87851	+	1.89750i
$73$	1.58685	+	1.58685i	0.185727	+	0.185727i	0.793846	−	0.608119i	$-0.208076\pi$
$73$	1.58685	+	1.58685i	0.185727	+	0.185727i	−0.608119	+	0.793846i	$0.708076\pi$
$74$	4.36329	−	5.66665i	0.507222	−	0.658734i
$75$	15.0613	−	6.23859i	1.73913	−	0.720370i
$76$	9.13691	+	11.9905i	1.04808	+	1.37541i
$77$	2.23124	−	5.38668i	0.254273	−	0.613869i
$78$	4.53066	+	1.22213i	0.512996	+	0.138379i
$79$		−	15.9814i		−	1.79805i	−0.437894	−	0.899026i	$-0.644276\pi$
$79$		−	15.9814i		−	1.79805i	0.437894	−	0.899026i	$-0.355724\pi$
$80$	0.724410	−	0.931072i	0.0809916	−	0.104097i
$81$			31.1330i			3.45923i
$82$	−0.989095	+	3.66675i	−0.109227	+	0.404924i
$83$	1.02714	−	2.47975i	0.112744	−	0.272187i	−0.857429	−	0.514602i	$-0.827940\pi$
$83$	1.02714	−	2.47975i	0.112744	−	0.272187i	0.970173	+	0.242415i	$0.0779395\pi$
$84$	2.27195	−	16.8210i	0.247890	−	1.83532i
$85$	−0.895042	+	0.370739i	−0.0970809	+	0.0402122i
$86$	−11.7591	−	9.05446i	−1.26802	−	0.976367i
$87$	−18.2726	−	18.2726i	−1.95903	−	1.95903i
$88$	−5.96918	+	2.43741i	−0.636317	+	0.259829i
$89$	−5.24144	+	5.24144i	−0.555591	+	0.555591i	−0.928049	−	0.372458i	$-0.878515\pi$
$89$	−5.24144	+	5.24144i	−0.555591	+	0.555591i	0.372458	+	0.928049i	$0.378515\pi$
$90$	3.31307	−	0.430524i	0.349229	−	0.0453812i
$91$	−0.978790	−	2.36301i	−0.102605	−	0.247711i
$92$	−3.97419	+	1.05061i	−0.414338	+	0.109533i
$93$	3.58647	+	1.48557i	0.371900	+	0.154046i
$94$	−13.3305	+	7.66660i	−1.37494	+	0.790749i
$95$	2.22298			0.228072
$96$	−14.9868	+	11.3014i	−1.52959	+	1.15345i
$97$	−5.34042			−0.542237			−0.271119	−	0.962546i	$-0.587394\pi$
$97$	−5.34042			−0.542237			−0.271119	+	0.962546i	$0.587394\pi$
$98$	0.561668	−	0.323025i	0.0567370	−	0.0326304i
$99$	−16.8700	−	6.98780i	−1.69550	−	0.702300i
$100$	2.51132	+	9.49970i	0.251132	+	0.949970i
$101$	2.64931	+	6.39601i	0.263617	+	0.636427i	0.999157	−	0.0410541i	$-0.0130716\pi$
$101$	2.64931	+	6.39601i	0.263617	+	0.636427i	−0.735540	+	0.677481i	$0.763072\pi$
$102$	15.2861	−	1.98639i	1.51355	−	0.196681i
$103$	−8.11516	+	8.11516i	−0.799611	+	0.799611i	−0.983034	−	0.183423i	$-0.941282\pi$
$103$	−8.11516	+	8.11516i	−0.799611	+	0.799611i	0.183423	+	0.983034i	$0.441282\pi$
$104$	−1.09552	+	2.60765i	−0.107425	+	0.255701i
$105$	−1.76987	−	1.76987i	−0.172721	−	0.172721i
$106$	−8.27529	−	6.37193i	−0.803767	−	0.618896i
$107$	−18.6266	+	7.71540i	−1.80070	+	0.745876i	−0.814538	+	0.580111i	$0.803009\pi$
$107$	−18.6266	+	7.71540i	−1.80070	+	0.745876i	−0.986165	+	0.165765i	$0.946991\pi$
$108$	−32.9503	−	4.45046i	−3.17065	−	0.428246i
$109$	0.199014	−	0.480461i	0.0190620	−	0.0460198i	−0.914062	−	0.405575i	$-0.867071\pi$
$109$	0.199014	−	0.480461i	0.0190620	−	0.0460198i	0.933124	+	0.359555i	$0.117071\pi$
$110$	−0.247619	+	0.917965i	−0.0236095	+	0.0875246i
$111$			16.7804i			1.59273i
$112$	9.86422	+	2.71415i	0.932081	+	0.256463i
$113$		−	1.21029i		−	0.113854i	−0.998378	−	0.0569272i	$-0.981870\pi$
$113$		−	1.21029i		−	0.113854i	0.998378	−	0.0569272i	$-0.0181303\pi$
$114$	−34.1498	−	9.21182i	−3.19842	−	0.862766i
$115$	−0.231971	+	0.560028i	−0.0216314	+	0.0522229i
$116$	12.3888	−	9.44039i	1.15027	−	0.876518i
$117$	−7.40048	+	3.06538i	−0.684175	+	0.283395i
$118$	−3.19993	+	4.15578i	−0.294577	+	0.382570i
$119$	−5.94095	−	5.94095i	−0.544606	−	0.544606i
$120$	−0.0139241	+	2.76787i	−0.00127109	+	0.252670i
$121$	−4.10369	+	4.10369i	−0.373063	+	0.373063i
$122$	0.612794	+	4.71572i	0.0554797	+	0.426941i
$123$	−3.41001	−	8.23249i	−0.307470	−	0.742299i
$124$	−1.17670	+	2.02242i	−0.105671	+	0.181618i
$125$	2.70103	+	1.11880i	0.241587	+	0.100069i
$126$	14.4449	+	25.1166i	1.28686	+	2.23756i
$127$	−3.14069			−0.278691			−0.139346	−	0.990244i	$-0.544500\pi$
$127$	−3.14069			−0.278691			−0.139346	+	0.990244i	$0.544500\pi$
$128$	−5.54146	−	9.86368i	−0.489800	−	0.871835i
$129$	34.8218			3.06589
$130$	0.207936	+	0.361554i	0.0182372	+	0.0317104i
$131$	−8.84413	−	3.66336i	−0.772715	−	0.320069i	−0.0387436	−	0.999249i	$-0.512336\pi$
$131$	−8.84413	−	3.66336i	−0.772715	−	0.320069i	−0.733972	+	0.679180i	$0.762336\pi$
$132$	7.60794	−	13.0759i	0.662186	−	1.13811i
$133$	7.37763	+	17.8112i	0.639722	+	1.54442i
$134$	0.460171	+	3.54122i	0.0397527	+	0.305915i
$135$	−3.46695	+	3.46695i	−0.298388	+	0.298388i
$136$	−0.0467392	+	9.29095i	−0.00400785	+	0.796692i
$137$	5.62836	+	5.62836i	0.480864	+	0.480864i	0.905407	−	0.424544i	$-0.139566\pi$
$137$	5.62836	+	5.62836i	0.480864	+	0.480864i	−0.424544	+	0.905407i	$0.639566\pi$
$138$	5.88430	−	7.64200i	0.500905	−	0.650530i
$139$	10.7803	−	4.46534i	0.914371	−	0.378745i	0.124643	−	0.992202i	$-0.460222\pi$
$139$	10.7803	−	4.46534i	0.914371	−	0.378745i	0.789728	+	0.613457i	$0.210222\pi$
$140$	1.19996	−	0.914387i	0.101415	−	0.0772798i
$141$	13.8076	−	33.3346i	1.16281	−	2.80728i
$142$	−6.02734	−	1.62586i	−0.505803	−	0.136439i
$143$		−	2.27959i		−	0.190628i
$144$	8.50020	−	30.8928i	0.708350	−	2.57440i
$145$		−	2.29681i		−	0.190740i
$146$	0.826554	−	3.06418i	0.0684061	−	0.253593i
$147$	−0.581771	+	1.40452i	−0.0479837	+	0.115843i
$148$	−10.0233	−	1.35380i	−0.823906	−	0.111282i
$149$	−7.28001	+	3.01548i	−0.596402	+	0.247038i	−0.660402	−	0.750912i	$-0.729614\pi$
$149$	−7.28001	+	3.01548i	−0.596402	+	0.247038i	0.0640003	+	0.997950i	$0.479614\pi$
$150$	−18.2671	−	14.0655i	−1.49150	−	1.14845i
$151$	9.17952	+	9.17952i	0.747019	+	0.747019i	0.973918	−	0.226899i	$-0.0728588\pi$
$151$	9.17952	+	9.17952i	0.747019	+	0.747019i	−0.226899	+	0.973918i	$0.572859\pi$
$152$	8.25751	−	19.6551i	0.669772	−	1.59424i
$153$	−18.6059	+	18.6059i	−1.50420	+	1.50420i
$154$	−8.17682	+	1.06255i	−0.658907	+	0.0856230i
$155$	0.132039	+	0.318770i	0.0106056	+	0.0256042i
$156$	−1.69610	−	6.41593i	−0.135797	−	0.513685i
$157$	15.2711	+	6.32549i	1.21876	+	0.504829i	0.897017	−	0.441997i	$-0.145730\pi$
$157$	15.2711	+	6.32549i	1.21876	+	0.504829i	0.321748	+	0.946825i	$0.395730\pi$
$158$	−19.5921	+	11.2677i	−1.55866	+	0.896414i
$159$	24.5053			1.94339
$160$	−1.65218	−	0.231621i	−0.130616	−	0.0183113i
$161$	−5.25699			−0.414309
$162$	38.1669	−	21.9504i	2.99867	−	1.72459i
$163$	−6.31309	−	2.61497i	−0.494480	−	0.204820i	0.121486	−	0.992593i	$-0.461234\pi$
$163$	−6.31309	−	2.61497i	−0.494480	−	0.204820i	−0.615966	+	0.787773i	$0.711234\pi$
$164$	5.19253	−	1.37269i	0.405469	−	0.107189i
$165$	−0.853692	−	2.06099i	−0.0664598	−	0.160448i
$166$	−3.76418	+	0.489144i	−0.292157	+	0.0379649i
$167$	−12.8397	+	12.8397i	−0.993568	+	0.993568i	−0.999979	−	0.00641173i	$-0.997959\pi$
$167$	−12.8397	+	12.8397i	−0.993568	+	0.993568i	0.00641173	+	0.999979i	$0.497959\pi$
$168$	−22.2232	+	9.07445i	−1.71456	+	0.700109i
$169$	−0.707107	−	0.707107i	−0.0543928	−	0.0543928i
$170$	1.08555	+	0.835868i	0.0832579	+	0.0641081i
$171$	55.7811	−	23.1053i	4.26569	−	1.76691i
$172$	−2.80933	+	20.7997i	−0.214209	+	1.58596i
$173$	5.87725	−	14.1889i	0.446839	−	1.07876i	−0.526661	−	0.850075i	$-0.676556\pi$
$173$	5.87725	−	14.1889i	0.446839	−	1.07876i	0.973500	−	0.228689i	$-0.0734438\pi$
$174$	−9.51778	+	35.2841i	−0.721541	+	2.67488i
$175$			12.5660i			0.949904i
$176$	7.19667	+	5.59929i	0.542469	+	0.422062i
$177$		−	12.3063i		−	0.925001i
$178$	10.1211	+	2.73014i	0.758610	+	0.204633i
$179$	7.19276	−	17.3649i	0.537612	−	1.29791i	−0.388773	−	0.921334i	$-0.627101\pi$
$179$	7.19276	−	17.3649i	0.537612	−	1.29791i	0.926385	−	0.376578i	$-0.122899\pi$
$180$	−2.86368	−	3.75805i	−0.213446	−	0.280109i
$181$	−4.79726	+	1.98709i	−0.356577	+	0.147699i	−0.553779	−	0.832664i	$-0.686815\pi$
$181$	−4.79726	+	1.98709i	−0.356577	+	0.147699i	0.197202	+	0.980363i	$0.436815\pi$
$182$	−2.20678	+	2.86597i	−0.163578	+	0.212440i
$183$	−7.88955	−	7.88955i	−0.583213	−	0.583213i
$184$	4.08998	+	4.13134i	0.301517	+	0.304566i
$185$	−1.05462	+	1.05462i	−0.0775373	+	0.0775373i
$186$	−0.707452	−	5.44416i	−0.0518729	−	0.399185i
$187$	−2.86560	−	6.91818i	−0.209554	−	0.505907i
$188$	18.7974	+	10.9369i	1.37094	+	0.797656i
$189$	−39.2845	−	16.2722i	−2.85752	−	1.18363i
$190$	−1.56731	−	2.72521i	−0.113705	−	0.197707i
$191$	−23.2262			−1.68059			−0.840294	−	0.542131i	$-0.817618\pi$
$191$	−23.2262			−1.68059			−0.840294	+	0.542131i	$0.817618\pi$
$192$	24.4212	+	10.4047i	1.76245	+	0.750893i
$193$	−2.92664			−0.210664			−0.105332	−	0.994437i	$-0.533591\pi$
$193$	−2.92664			−0.210664			−0.105332	+	0.994437i	$0.533591\pi$
$194$	3.76527	+	6.54697i	0.270331	+	0.470045i
$195$	−0.904109	−	0.374494i	−0.0647446	−	0.0268181i
$196$	−0.792010	−	0.460816i	−0.0565722	−	0.0329154i
$197$	−2.48720	−	6.00463i	−0.177206	−	0.427812i	0.810173	−	0.586191i	$-0.199373\pi$
$197$	−2.48720	−	6.00463i	−0.177206	−	0.427812i	−0.987378	+	0.158379i	$0.949373\pi$
$198$	3.32771	+	25.6082i	0.236490	+	1.81990i
$199$	1.25671	−	1.25671i	0.0890859	−	0.0890859i	−0.661159	−	0.750245i	$-0.729935\pi$
$199$	1.25671	−	1.25671i	0.0890859	−	0.0890859i	0.750245	+	0.661159i	$0.229935\pi$
$200$	9.87535	−	9.77649i	0.698293	−	0.691302i
$201$	−5.92457	−	5.92457i	−0.417887	−	0.417887i
$202$	5.97315	−	7.75739i	0.420269	−	0.545808i
$203$	18.4028	−	7.62267i	1.29162	−	0.535007i
$204$	−13.2127	−	17.3392i	−0.925073	−	1.21399i
$205$	0.303085	−	0.731713i	0.0211684	−	0.0511051i
$206$	15.6702	+	4.22700i	1.09180	+	0.294509i
$207$			16.4639i			1.14432i
$208$	3.96919	−	0.495493i	0.275214	−	0.0343563i
$209$			17.1824i			1.18853i
$210$	−0.921883	+	3.41758i	−0.0636160	+	0.235835i
$211$	6.61863	−	15.9788i	0.455645	−	1.10003i	−0.514498	−	0.857492i	$-0.672022\pi$
$211$	6.61863	−	15.9788i	0.455645	−	1.10003i	0.970143	−	0.242533i	$-0.0779784\pi$
$212$	−1.97702	+	14.6375i	−0.135782	+	1.00530i
$213$	13.5325	−	5.60532i	0.927228	−	0.384071i
$214$	22.5913	+	17.3951i	1.54431	+	1.18911i
$215$	2.18849	+	2.18849i	0.149254	+	0.149254i
$216$	17.7757	+	43.5326i	1.20949	+	2.96202i
$217$	−2.11587	+	2.11587i	−0.143635	+	0.143635i
$218$	−0.729326	+	0.0947737i	−0.0493962	+	0.00641888i
$219$	2.84963	+	6.87963i	0.192560	+	0.464882i
$220$	1.29994	−	0.343651i	0.0876422	−	0.0231689i
$221$	−3.03484	−	1.25707i	−0.204145	−	0.0845598i
$222$	20.5716	−	11.8311i	1.38067	−	0.794049i
$223$	25.9443			1.73736			0.868680	−	0.495374i	$-0.164969\pi$
$223$	25.9443			1.73736			0.868680	+	0.495374i	$0.164969\pi$
$224$	−3.62743	−	14.0065i	−0.242368	−	0.935845i
$225$	39.3544			2.62363
$226$	−1.48373	+	0.853317i	−0.0986962	+	0.0567618i
$227$	−12.7273	−	5.27184i	−0.844743	−	0.349904i	−0.0820213	−	0.996631i	$-0.526138\pi$
$227$	−12.7273	−	5.27184i	−0.844743	−	0.349904i	−0.762722	+	0.646726i	$0.776138\pi$
$228$	12.7844	+	48.3600i	0.846665	+	3.20272i
$229$	3.11942	+	7.53094i	0.206137	+	0.497658i	0.992809	−	0.119713i	$-0.0381975\pi$
$229$	3.11942	+	7.53094i	0.206137	+	0.497658i	−0.786672	+	0.617372i	$0.788197\pi$
$230$	0.850107	−	0.110469i	0.0560544	−	0.00728409i
$231$	13.6801	−	13.6801i	0.900084	−	0.900084i
$232$	−20.3080	−	8.53178i	−1.33328	−	0.560139i
$233$	−6.70028	−	6.70028i	−0.438950	−	0.438950i	0.452709	−	0.891658i	$-0.350458\pi$
$233$	−6.70028	−	6.70028i	−0.438950	−	0.438950i	−0.891658	+	0.452709i	$0.850458\pi$
$234$	8.97566	+	6.91121i	0.586758	+	0.451800i
$235$	2.96281	−	1.22724i	0.193273	−	0.0800561i
$236$	7.35081	+	0.992843i	0.478497	+	0.0646286i
$237$	20.2934	−	48.9925i	1.31819	−	3.18240i
$238$	−3.09450	+	11.4719i	−0.200587	+	0.743610i
$239$			28.3318i			1.83263i	0.400454	+	0.916317i	$0.368853\pi$
$239$			28.3318i			1.83263i	−0.400454	+	0.916317i	$0.631147\pi$
$240$	3.40302	−	1.93442i	0.219664	−	0.124866i
$241$			30.2391i			1.94787i	0.226825	+	0.973936i	$0.427166\pi$
$241$			30.2391i			1.94787i	−0.226825	+	0.973936i	$0.572834\pi$
$242$	7.92414	+	2.13752i	0.509383	+	0.137405i
$243$	−20.4469	+	49.3632i	−1.31167	+	3.16665i
$244$	5.34909	−	4.07607i	0.342440	−	0.260944i
$245$	−0.124835	+	0.0517084i	−0.00797543	+	0.00330353i
$246$	−7.68822	+	9.98477i	−0.490183	+	0.636606i
$247$	5.32982	+	5.32982i	0.339128	+	0.339128i
$248$	3.30898	+	0.0166462i	0.210120	+	0.00105703i
$249$	6.29760	−	6.29760i	0.399094	−	0.399094i
$250$	−0.532793	−	4.10008i	−0.0336968	−	0.259312i
$251$	4.71241	+	11.3768i	0.297445	+	0.718095i	0.999979	+	0.00644558i	$0.00205171\pi$
$251$	4.71241	+	11.3768i	0.297445	+	0.718095i	−0.702534	+	0.711650i	$0.747948\pi$
$252$	20.6067	−	35.4170i	1.29810	−	2.23106i
$253$	−4.32871	−	1.79301i	−0.272143	−	0.112726i
$254$	2.21435	+	3.85027i	0.138941	+	0.241587i
$255$	−3.21459			−0.201306
$256$	−8.18516	+	13.7478i	−0.511572	+	0.859240i
$257$	−16.8862			−1.05334			−0.526668	−	0.850071i	$-0.676559\pi$
$257$	−16.8862			−1.05334			−0.526668	+	0.850071i	$0.676559\pi$
$258$	−24.5512	−	42.6890i	−1.52849	−	2.65770i
$259$	−11.9500	−	4.94987i	−0.742540	−	0.307570i
$260$	0.296634	−	0.509828i	0.0183964	−	0.0316182i
$261$	−23.8727	−	57.6339i	−1.47768	−	3.56745i
$262$	1.74456	+	13.4251i	0.107779	+	0.829408i
$263$	5.64090	−	5.64090i	0.347833	−	0.347833i	−0.511469	−	0.859302i	$-0.670898\pi$
$263$	5.64090	−	5.64090i	0.347833	−	0.347833i	0.859302	+	0.511469i	$0.170898\pi$
$264$	−21.3941	−	0.107625i	−1.31671	−	0.00662388i
$265$	1.54012	+	1.54012i	0.0946087	+	0.0946087i
$266$	16.6336	−	21.6023i	1.01987	−	1.32452i
$267$	−22.7237	+	9.41246i	−1.39067	+	0.576033i
$268$	4.01684	−	3.06088i	0.245367	−	0.186973i
$269$	1.73236	−	4.18230i	0.105624	−	0.254999i	−0.862227	−	0.506521i	$-0.830931\pi$
$269$	1.73236	−	4.18230i	0.105624	−	0.254999i	0.967852	+	0.251522i	$0.0809312\pi$
$270$	6.69462	+	1.80586i	0.407422	+	0.109901i
$271$		−	29.3694i		−	1.78406i	−0.451974	−	0.892031i	$-0.649280\pi$
$271$		−	29.3694i		−	1.78406i	0.451974	−	0.892031i	$-0.350720\pi$
$272$	11.4230	−	6.49330i	0.692621	−	0.393714i
$273$		−	8.48688i		−	0.513649i
$274$	2.93168	−	10.8683i	0.177109	−	0.656576i
$275$	−4.28592	+	10.3471i	−0.258451	+	0.623955i
$276$	−13.5173	−	1.82572i	−0.813645	−	0.109896i
$277$	4.45007	−	1.84328i	0.267378	−	0.110752i	−0.244966	−	0.969532i	$-0.578777\pi$
$277$	4.45007	−	1.84328i	0.267378	−	0.110752i	0.512345	+	0.858780i	$0.328777\pi$
$278$	−13.0748	−	10.0676i	−0.784177	−	0.603812i
$279$	6.62649	+	6.62649i	0.396718	+	0.396718i
$280$	−1.96701	−	0.826379i	−0.117551	−	0.0493856i
$281$	−4.24709	+	4.24709i	−0.253360	+	0.253360i	−0.822347	−	0.568986i	$-0.807336\pi$
$281$	−4.24709	+	4.24709i	−0.253360	+	0.253360i	0.568986	+	0.822347i	$0.307336\pi$
$282$	−50.6009	+	6.57543i	−3.01324	+	0.391561i
$283$	−0.595770	−	1.43832i	−0.0354149	−	0.0854991i	0.905183	−	0.425023i	$-0.139734\pi$
$283$	−0.595770	−	1.43832i	−0.0354149	−	0.0854991i	−0.940597	+	0.339524i	$0.889734\pi$
$284$	2.25640	+	8.53541i	0.133893	+	0.506483i
$285$	6.81472	+	2.82275i	0.403669	+	0.167205i
$286$	−2.79461	+	1.60723i	−0.165249	+	0.0950373i
$287$	6.86860			0.405440
$288$	−43.8655	+	11.3604i	−2.58480	+	0.669418i
$289$	6.20951			0.365265
$290$	−2.81573	+	1.61937i	−0.165345	+	0.0950927i
$291$	−16.3715	−	6.78130i	−0.959714	−	0.397527i
$292$	−4.33923	+	1.14711i	−0.253934	+	0.0671296i
$293$	−5.08058	−	12.2656i	−0.296811	−	0.716564i	−0.999985	−	0.00554657i	$-0.998234\pi$
$293$	−5.08058	−	12.2656i	−0.296811	−	0.716564i	0.703174	−	0.711018i	$-0.251766\pi$
$294$	2.13202	−	0.277049i	0.124342	−	0.0161579i
$295$	0.773434	−	0.773434i	0.0450311	−	0.0450311i
$296$	5.40725	+	13.2423i	0.314290	+	0.769693i
$297$	−26.7976	−	26.7976i	−1.55496	−	1.55496i
$298$	8.82955	+	6.79871i	0.511482	+	0.393839i
$299$	−1.89890	+	0.786551i	−0.109816	+	0.0454874i
$300$	−4.36412	+	32.3110i	−0.251963	+	1.86548i
$301$	−10.2717	+	24.7981i	−0.592051	+	1.42934i
$302$	4.78140	−	17.7255i	0.275139	−	1.01999i
$303$			22.9716i			1.31969i
$304$	−29.9178	+	3.73478i	−1.71590	+	0.214204i
$305$		−	0.991692i		−	0.0567841i
$306$	35.9276	+	9.69137i	2.05384	+	0.554019i
$307$	10.6715	−	25.7633i	0.609054	−	1.47039i	−0.254976	−	0.966947i	$-0.582068\pi$
$307$	10.6715	−	25.7633i	0.609054	−	1.47039i	0.864031	−	0.503439i	$-0.167932\pi$
$308$	7.06770	+	9.27505i	0.402720	+	0.528495i
$309$	−35.1824	+	14.5730i	−2.00146	+	0.829031i
$310$	0.297695	−	0.386619i	0.0169079	−	0.0219585i
$311$	13.1578	+	13.1578i	0.746108	+	0.746108i	0.973746	−	0.227638i	$-0.0731003\pi$
$311$	13.1578	+	13.1578i	0.746108	+	0.746108i	−0.227638	+	0.973746i	$0.573100\pi$
$312$	−6.66963	+	6.60286i	−0.377594	+	0.373814i
$313$	−5.55875	+	5.55875i	−0.314199	+	0.314199i	−0.846534	−	0.532335i	$-0.821315\pi$
$313$	−5.55875	+	5.55875i	−0.314199	+	0.314199i	0.532335	+	0.846534i	$0.321315\pi$
$314$	−3.01231	−	23.1811i	−0.169994	−	1.30818i
$315$	−2.31229	−	5.58236i	−0.130283	−	0.314530i
$316$	27.6269	+	16.0742i	1.55414	+	0.904244i
$317$	18.2311	+	7.55156i	1.02396	+	0.424138i	0.830529	−	0.556976i	$-0.188038\pi$
$317$	18.2311	+	7.55156i	1.02396	+	0.424138i	0.193431	+	0.981114i	$0.438038\pi$
$318$	−17.2775	−	30.0417i	−0.968874	−	1.68466i
$319$	17.7531			0.993981
$320$	0.880918	+	2.18875i	0.0492448	+	0.122355i
$321$	−66.8986			−3.73391
$322$	3.70645	+	6.44469i	0.206552	+	0.359149i
$323$	22.8751	+	9.47518i	1.27280	+	0.527213i
$324$	−53.8193	−	31.3137i	−2.98996	−	1.73965i
$325$	1.88013	+	4.53904i	0.104291	+	0.251781i
$326$	1.24529	+	9.58309i	0.0689705	+	0.530759i
$327$	1.22019	−	1.22019i	0.0674764	−	0.0674764i
$328$	−5.34382	−	5.39786i	−0.295063	−	0.298047i
$329$	19.6660	+	19.6660i	1.08422	+	1.08422i
$330$	−1.92474	+	2.49967i	−0.105953	+	0.137603i
$331$	−11.6121	+	4.80991i	−0.638261	+	0.264377i	−0.678259	−	0.734823i	$-0.737265\pi$
$331$	−11.6121	+	4.80991i	−0.638261	+	0.264377i	0.0399972	+	0.999200i	$0.487265\pi$
$332$	3.25360	+	4.26975i	0.178565	+	0.234333i
$333$	−15.5020	+	37.4252i	−0.849506	+	2.05089i
$334$	24.7933	+	6.68791i	1.35663	+	0.365946i
$335$		−	0.744700i		−	0.0406873i
$336$	26.7932	+	20.8461i	1.46169	+	1.13725i
$337$		−	19.6182i		−	1.06867i	−0.845272	−	0.534336i	$-0.820562\pi$
$337$		−	19.6182i		−	1.06867i	0.845272	−	0.534336i	$-0.179438\pi$
$338$	−0.368316	+	1.36541i	−0.0200337	+	0.0742685i
$339$	1.53683	−	3.71025i	0.0834694	−	0.201513i
$340$	0.259345	−	1.92014i	0.0140650	−	0.104134i
$341$	−2.46391	+	1.02059i	−0.133428	+	0.0552678i
$342$	−67.6540	−	52.0932i	−3.65831	−	2.81688i
$343$	−13.4886	−	13.4886i	−0.728315	−	0.728315i
$344$	27.4797	−	11.2208i	1.48161	−	0.604987i
$345$	−1.42226	+	1.42226i	−0.0765717	+	0.0765717i
$346$	−21.5384	+	2.79885i	−1.15791	+	0.150467i
$347$	0.0945569	+	0.228280i	0.00507608	+	0.0122547i	0.926397	−	0.376548i	$-0.122889\pi$
$347$	0.0945569	+	0.228280i	0.00507608	+	0.0122547i	−0.921321	+	0.388802i	$0.872889\pi$
$348$	49.9663	−	13.2090i	2.67847	−	0.708076i
$349$	32.9217	+	13.6366i	1.76226	+	0.729952i	0.996191	+	0.0871930i	$0.0277897\pi$
$349$	32.9217	+	13.6366i	1.76226	+	0.729952i	0.766068	+	0.642759i	$0.222210\pi$
$350$	15.4051	−	8.85972i	0.823436	−	0.473572i
$351$	−16.6248			−0.887364
$352$	1.79030	−	12.7704i	0.0954235	−	0.680664i
$353$	−7.16380			−0.381291			−0.190645	−	0.981659i	$-0.561058\pi$
$353$	−7.16380			−0.381291			−0.190645	+	0.981659i	$0.561058\pi$
$354$	−15.0867	+	8.67661i	−0.801849	+	0.461156i
$355$	1.20278	+	0.498207i	0.0638369	+	0.0264421i
$356$	−3.78895	−	14.3327i	−0.200814	−	0.759630i
$357$	−10.6686	−	25.7563i	−0.564643	−	1.36317i
$358$	−26.3594	+	3.42532i	−1.39314	+	0.181034i
$359$	4.09252	−	4.09252i	0.215995	−	0.215995i	−0.590813	−	0.806808i	$-0.701193\pi$
$359$	4.09252	−	4.09252i	0.215995	−	0.215995i	0.806808	+	0.590813i	$0.201193\pi$
$360$	−2.58806	+	6.16029i	−0.136403	+	0.324676i
$361$	−26.7384	−	26.7384i	−1.40729	−	1.40729i
$362$	5.81834	+	4.48009i	0.305805	+	0.235468i
$363$	−17.7911	+	7.36932i	−0.933791	+	0.386789i
$364$	5.06937	+	0.684699i	0.265707	+	0.0358880i
$365$	−0.253279	+	0.611469i	−0.0132572	+	0.0320057i
$366$	−4.10949	+	15.2346i	−0.214806	+	0.796324i
$367$		−	11.0737i		−	0.578041i	−0.957323	−	0.289021i	$-0.906670\pi$
$367$		−	11.0737i		−	0.578041i	0.957323	−	0.289021i	$-0.0933296\pi$
$368$	2.18108	−	7.92683i	0.113697	−	0.413215i
$369$		−	21.5111i		−	1.11982i
$370$	2.03645	+	0.549328i	0.105870	+	0.0285582i
$371$	−7.22855	+	17.4513i	−0.375288	+	0.906024i
$372$	−6.17536	+	4.70570i	−0.320178	+	0.243979i
$373$	19.3482	−	8.01427i	1.00181	−	0.414963i	0.179349	−	0.983785i	$-0.442601\pi$
$373$	19.3482	−	8.01427i	1.00181	−	0.414963i	0.822460	+	0.568822i	$0.192601\pi$
$374$	−6.46079	+	8.39070i	−0.334080	+	0.433873i
$375$	6.85957	+	6.85957i	0.354226	+	0.354226i
$376$	0.154718	−	30.7554i	0.00797899	−	1.58609i
$377$	5.50684	−	5.50684i	0.283617	−	0.283617i
$378$	7.74908	+	59.6327i	0.398570	+	3.06717i
$379$	8.39719	+	20.2726i	0.431335	+	1.04133i	0.978858	+	0.204543i	$0.0655709\pi$
$379$	8.39719	+	20.2726i	0.431335	+	1.04133i	−0.547523	+	0.836791i	$0.684429\pi$
$380$	−2.23588	+	3.84283i	−0.114698	+	0.197133i
$381$	−9.62806	−	3.98808i	−0.493261	−	0.204315i
$382$	16.3757	+	28.4736i	0.837852	+	1.45684i
$383$	−0.916516			−0.0468318			−0.0234159	−	0.999726i	$-0.507454\pi$
$383$	−0.916516			−0.0468318			−0.0234159	+	0.999726i	$0.507454\pi$
$384$	−4.46284	−	37.2745i	−0.227743	−	1.90216i
$385$	1.71954			0.0876361
$386$	2.06343	+	3.58785i	0.105026	+	0.182617i
$387$	77.6628	+	32.1690i	3.94782	+	1.63524i
$388$	5.37141	−	9.23191i	0.272692	−	0.468679i
$389$	9.18515	+	22.1749i	0.465706	+	1.12431i	0.966020	+	0.258469i	$0.0832179\pi$
$389$	9.18515	+	22.1749i	0.465706	+	1.12431i	−0.500314	+	0.865844i	$0.666782\pi$
$390$	0.178341	+	1.37241i	0.00903063	+	0.0694948i
$391$	−4.77411	+	4.77411i	−0.241437	+	0.241437i
$392$	−0.00651890	+	1.29585i	−0.000329254	+	0.0654502i
$393$	−22.4607	−	22.4607i	−1.13299	−	1.13299i
$394$	−5.60765	+	7.28271i	−0.282509	+	0.366898i
$395$	4.35451	−	1.80370i	0.219099	−	0.0907538i
$396$	29.0476	−	22.1347i	1.45970	−	1.11231i
$397$	−4.84479	+	11.6964i	−0.243153	+	0.587024i	−0.997593	−	0.0693458i	$-0.977909\pi$
$397$	−4.84479	+	11.6964i	−0.243153	+	0.587024i	0.754439	+	0.656370i	$0.227909\pi$
$398$	−2.42669	−	0.654592i	−0.121639	−	0.0328117i
$399$			63.9698i			3.20250i
$400$	−18.9479	−	5.21354i	−0.947396	−	0.260677i
$401$			14.1566i			0.706948i	0.935444	+	0.353474i	$0.115000\pi$
$401$			14.1566i			0.706948i	−0.935444	+	0.353474i	$0.885000\pi$
$402$	−3.08597	+	11.4402i	−0.153914	+	0.570587i
$403$	−0.447707	+	1.08086i	−0.0223019	+	0.0538415i
$404$	−13.7214	−	1.85329i	−0.682665	−	0.0922047i
$405$	−8.48290	+	3.51373i	−0.421519	+	0.174599i
$406$	−22.3198	−	17.1861i	−1.10771	−	0.852931i
$407$	−8.15164	−	8.15164i	−0.404062	−	0.404062i
$408$	−11.9410	+	28.4228i	−0.591167	+	1.40714i
$409$	−11.6998	+	11.6998i	−0.578516	+	0.578516i	−0.934494	−	0.355978i	$-0.884148\pi$
$409$	−11.6998	+	11.6998i	−0.578516	+	0.578516i	0.355978	+	0.934494i	$0.384148\pi$
$410$	−1.11072	+	0.144335i	−0.0548545	+	0.00712818i
$411$	10.1073	+	24.4012i	0.498556	+	1.20362i
$412$	−5.86632	−	22.1908i	−0.289013	−	1.09326i
$413$	8.76387	+	3.63011i	0.431242	+	0.178626i
$414$	20.1835	−	11.6079i	0.991966	−	0.570496i
$415$	0.791588			0.0388575
$416$	−3.40593	−	4.51660i	−0.166989	−	0.221444i
$417$	38.7180			1.89603
$418$	21.0644	−	12.1145i	1.03029	−	0.592538i
$419$	−1.25827	−	0.521191i	−0.0614703	−	0.0254618i	0.351736	−	0.936099i	$-0.385591\pi$
$419$	−1.25827	−	0.521191i	−0.0614703	−	0.0254618i	−0.413207	+	0.910637i	$0.635591\pi$
$420$	4.83969	−	1.27941i	0.236152	−	0.0624288i
$421$	−7.05827	−	17.0402i	−0.343999	−	0.830487i	−0.997303	−	0.0733914i	$-0.976618\pi$
$421$	−7.05827	−	17.0402i	−0.343999	−	0.830487i	0.653304	−	0.757095i	$-0.273382\pi$
$422$	−24.2553	+	3.15191i	−1.18073	+	0.153432i
$423$	61.5901	−	61.5901i	2.99462	−	2.99462i
$424$	19.3384	−	7.89648i	0.939155	−	0.383487i
$425$	11.4118	+	11.4118i	0.553554	+	0.553554i
$426$	−16.4128	−	12.6378i	−0.795203	−	0.612302i
$427$	7.94575	−	3.29124i	0.384522	−	0.159274i
$428$	5.39720	−	39.9598i	0.260884	−	1.93153i
$429$	2.89463	−	6.98826i	0.139754	−	0.337397i
$430$	1.13994	−	4.22594i	0.0549726	−	0.203793i
$431$			25.7588i			1.24076i	0.784302	+	0.620379i	$0.213021\pi$
$431$			25.7588i			1.24076i	−0.784302	+	0.620379i	$0.786979\pi$
$432$	40.8350	−	52.4845i	1.96468	−	2.52516i
$433$			8.12124i			0.390282i	0.980775	+	0.195141i	$0.0625164\pi$
$433$			8.12124i			0.390282i	−0.980775	+	0.195141i	$0.937484\pi$
$434$	4.08571	+	1.10211i	0.196120	+	0.0529029i
$435$	2.91651	−	7.04107i	0.139836	−	0.337593i
$436$	0.630399	+	0.827281i	0.0301906	+	0.0396196i
$437$	14.3130	−	5.92862i	0.684682	−	0.283604i
$438$	6.42479	−	8.34394i	0.306988	−	0.398689i
$439$	−7.35595	−	7.35595i	−0.351080	−	0.351080i	0.509431	−	0.860511i	$-0.329856\pi$
$439$	−7.35595	−	7.35595i	−0.351080	−	0.351080i	−0.860511	+	0.509431i	$0.829856\pi$
$440$	−1.33782	−	1.35135i	−0.0637780	−	0.0644230i
$441$	−2.59504	+	2.59504i	−0.123573	+	0.123573i
$442$	0.598640	+	4.60680i	0.0284744	+	0.219123i
$443$	5.55781	+	13.4177i	0.264060	+	0.637496i	0.999182	−	0.0404380i	$-0.0128753\pi$
$443$	5.55781	+	13.4177i	0.264060	+	0.637496i	−0.735122	+	0.677934i	$0.762875\pi$
$444$	−29.0081	−	16.8778i	−1.37666	−	0.800984i
$445$	−2.01971	−	0.836590i	−0.0957433	−	0.0396582i
$446$	−18.2921	−	31.8059i	−0.866155	−	1.50605i
$447$	−26.1466			−1.23669
$448$	−14.6134	+	14.3223i	−0.690418	+	0.676663i
$449$	−25.9902			−1.22655			−0.613277	−	0.789868i	$-0.710149\pi$
$449$	−25.9902			−1.22655			−0.613277	+	0.789868i	$0.710149\pi$
$450$	−27.7469	−	48.2457i	−1.30800	−	2.27432i
$451$	5.65574	+	2.34268i	0.266318	+	0.110313i
$452$	2.09221	+	1.21731i	0.0984094	+	0.0572576i
$453$	16.4844	+	39.7968i	0.774504	+	1.86982i
$454$	2.51054	+	19.3197i	0.117826	+	0.906720i
$455$	0.533387	−	0.533387i	0.0250056	−	0.0250056i
$456$	50.2723	−	49.7691i	2.35422	−	2.33065i
$457$	23.6455	+	23.6455i	1.10609	+	1.10609i	0.993660	+	0.112429i	$0.0358632\pi$
$457$	23.6455	+	23.6455i	1.10609	+	1.10609i	0.112429	+	0.993660i	$0.464137\pi$
$458$	7.03304	−	9.13389i	0.328633	−	0.426799i
$459$	−50.4535	+	20.8985i	−2.35497	+	0.975459i
$460$	−0.734796	−	0.964284i	−0.0342601	−	0.0449600i
$461$	−0.546667	+	1.31977i	−0.0254608	+	0.0614679i	−0.936099	−	0.351738i	$-0.885591\pi$
$461$	−0.546667	+	1.31977i	−0.0254608	+	0.0614679i	0.910638	+	0.413206i	$0.135591\pi$
$462$	−26.4160	−	7.12564i	−1.22898	−	0.331515i
$463$			5.59612i			0.260074i	0.991509	+	0.130037i	$0.0415096\pi$
$463$			5.59612i			0.260074i	−0.991509	+	0.130037i	$0.958490\pi$
$464$	3.85883	+	30.9115i	0.179141	+	1.43503i
$465$			1.14488i			0.0530925i
$466$	−3.49002	+	12.9381i	−0.161672	+	0.599346i
$467$	8.66794	−	20.9263i	0.401105	−	0.968352i	−0.586294	−	0.810098i	$-0.699414\pi$
$467$	8.66794	−	20.9263i	0.401105	−	0.968352i	0.987398	−	0.158254i	$-0.0505864\pi$
$468$	2.14434	−	15.8763i	0.0991224	−	0.733882i
$469$	5.96677	−	2.47152i	0.275520	−	0.114124i
$470$	−3.59344	−	2.76693i	−0.165753	−	0.127629i
$471$	38.7826	+	38.7826i	1.78701	+	1.78701i
$472$	−3.96555	−	9.71157i	−0.182529	−	0.447011i
$473$	−16.9158	+	16.9158i	−0.777791	+	0.777791i
$474$	−74.3692	+	9.66405i	−3.41589	+	0.443884i
$475$	−14.1715	−	34.2130i	−0.650232	−	1.56980i
$476$	16.2455	−	4.29462i	0.744609	−	0.196843i
$477$	54.6539	+	22.6384i	2.50243	+	1.03654i
$478$	34.7328	−	19.9754i	1.58864	−	0.913654i
$479$	−34.2697			−1.56582			−0.782911	−	0.622134i	$-0.786266\pi$
$479$	−34.2697			−1.56582			−0.782911	+	0.622134i	$0.786266\pi$
$480$	−4.77077	−	2.80800i	−0.217755	−	0.128167i
$481$	−5.05713			−0.230585
$482$	37.0710	−	21.3201i	1.68854	−	0.971106i
$483$	−16.1158	−	6.67536i	−0.733292	−	0.303740i
$484$	−2.96649	−	11.2215i	−0.134841	−	0.510068i
$485$	−0.602729	−	1.45512i	−0.0273685	−	0.0660735i
$486$	74.9319	−	9.73717i	3.39898	−	0.441687i
$487$	−19.0180	+	19.0180i	−0.861786	+	0.861786i	−0.991545	−	0.129760i	$-0.958579\pi$
$487$	−19.0180	+	19.0180i	−0.861786	+	0.861786i	0.129760	+	0.991545i	$0.458579\pi$
$488$	−8.76836	−	3.68376i	−0.396925	−	0.166756i
$489$	−16.0328	−	16.0328i	−0.725029	−	0.725029i
$490$	0.151406	+	0.116582i	0.00683984	+	0.00526664i
$491$	0.560176	−	0.232033i	0.0252804	−	0.0104715i	−0.370007	−	0.929029i	$-0.620645\pi$
$491$	0.560176	−	0.232033i	0.0252804	−	0.0104715i	0.395288	+	0.918557i	$0.370645\pi$
$492$	17.6612	+	2.38543i	0.796229	+	0.107543i
$493$	9.78989	−	23.6349i	0.440914	−	1.06446i
$494$	2.77618	−	10.2918i	0.124906	−	0.463049i
$495$		−	5.38528i		−	0.242050i
$496$	−2.31259	−	4.06831i	−0.103838	−	0.182672i
$497$			11.2905i			0.506448i
$498$	−12.1605	−	3.28027i	−0.544927	−	0.146993i
$499$	−8.71194	+	21.0325i	−0.390000	+	0.941544i	0.599938	+	0.800046i	$0.295192\pi$
$499$	−8.71194	+	21.0325i	−0.390000	+	0.941544i	−0.989939	+	0.141498i	$0.954808\pi$
$500$	−4.65076	+	3.54394i	−0.207988	+	0.158490i
$501$	−55.6652	+	23.0573i	−2.48694	+	1.03012i
$502$	10.6246	−	13.7983i	0.474200	−	0.615848i
$503$	−23.1030	−	23.1030i	−1.03011	−	1.03011i	−0.999532	−	0.0305798i	$-0.990265\pi$
$503$	−23.1030	−	23.1030i	−1.03011	−	1.03011i	−0.0305798	−	0.999532i	$-0.509735\pi$
$504$	−57.9474	−	0.291511i	−2.58118	−	0.0129849i
$505$	−1.44373	+	1.44373i	−0.0642452	+	0.0642452i
$506$	0.853862	+	6.57085i	0.0379588	+	0.292110i
$507$	−1.26981	−	3.06559i	−0.0563941	−	0.136147i
$508$	3.15892	−	5.42928i	0.140154	−	0.240885i
$509$	−0.582331	−	0.241209i	−0.0258114	−	0.0106914i	0.369740	−	0.929135i	$-0.379447\pi$
$509$	−0.582331	−	0.241209i	−0.0258114	−	0.0106914i	−0.395552	+	0.918444i	$0.629447\pi$
$510$	2.26646	+	3.94086i	0.100360	+	0.174504i
$511$	−5.73986			−0.253917
$512$	22.6248	+	0.341473i	0.999886	+	0.0150911i
$513$	125.309			5.53253
$514$	11.9057	+	20.7013i	0.525137	+	0.913097i
$515$	−3.12705	−	1.29527i	−0.137794	−	0.0570763i
$516$	−35.0239	+	60.1960i	−1.54184	+	2.64998i
$517$	9.48586	+	22.9009i	0.417188	+	1.00718i
$518$	2.35722	+	18.1398i	0.103570	+	0.797018i
$519$	36.0344	−	36.0344i	1.58173	−	1.58173i
$520$	−0.834155	−	0.00419631i	−0.0365801	−	0.000184020i
$521$	−17.3865	−	17.3865i	−0.761717	−	0.761717i	0.214916	−	0.976633i	$-0.431052\pi$
$521$	−17.3865	−	17.3865i	−0.761717	−	0.761717i	−0.976633	+	0.214916i	$0.931052\pi$
$522$	−53.8235	+	69.9011i	−2.35579	+	3.05949i
$523$	−18.5566	+	7.68639i	−0.811423	+	0.336102i	−0.749522	−	0.661980i	$-0.769716\pi$
$523$	−18.5566	+	7.68639i	−0.811423	+	0.336102i	−0.0619014	+	0.998082i	$0.519716\pi$
$524$	15.2283	−	11.6041i	0.665250	−	0.506928i
$525$	−15.9565	+	38.5223i	−0.696397	+	1.68125i
$526$	−10.8925	−	2.93822i	−0.474935	−	0.128112i
$527$			3.84304i			0.167405i
$528$	14.9520	+	26.3035i	0.650702	+	1.14471i
$529$		−	18.7755i		−	0.816327i
$530$	0.802212	−	2.97394i	0.0348458	−	0.129180i
$531$	11.3688	−	27.4467i	0.493364	−	1.19109i
$532$	−38.2104	−	5.16092i	−1.65663	−	0.223754i
$533$	2.48104	−	1.02768i	0.107466	−	0.0445137i
$534$	27.5604	+	21.2214i	1.19266	+	0.918338i
$535$	−4.20447	−	4.20447i	−0.181775	−	0.181775i
$536$	−6.58450	−	2.76628i	−0.284407	−	0.119485i
$537$	44.1001	−	44.1001i	1.90306	−	1.90306i
$538$	−6.34860	+	0.824982i	−0.273708	+	0.0355675i
$539$	−0.399678	−	0.964907i	−0.0172153	−	0.0415615i
$540$	−2.50621	−	9.48035i	−0.107850	−	0.407969i
$541$	−22.6470	−	9.38069i	−0.973670	−	0.403307i	−0.161593	−	0.986858i	$-0.551663\pi$
$541$	−22.6470	−	9.38069i	−0.973670	−	0.403307i	−0.812077	+	0.583550i	$0.801663\pi$
$542$	−36.0048	+	20.7069i	−1.54654	+	0.889439i
$543$	−17.2296			−0.739394
$544$	−16.0141	−	9.42566i	−0.686600	−	0.404122i
$545$	0.153374			0.00656980
$546$	−10.4043	+	5.98369i	−0.445264	+	0.256078i
$547$	−19.1087	−	7.91509i	−0.817030	−	0.338425i	−0.0652750	−	0.997867i	$-0.520792\pi$
$547$	−19.1087	−	7.91509i	−0.817030	−	0.338425i	−0.751755	+	0.659442i	$0.770792\pi$
$548$	−15.3907	+	4.06865i	−0.657458	+	0.173804i
$549$	−10.3075	−	24.8845i	−0.439914	−	1.06205i
$550$	15.7066	−	2.04103i	0.669733	−	0.0870298i
$551$	−41.5078	+	41.5078i	−1.76829	+	1.76829i
$552$	7.29218	+	17.8585i	0.310376	+	0.760107i
$553$	28.9035	+	28.9035i	1.22910	+	1.22910i
$554$	−5.39725	−	4.15586i	−0.229307	−	0.176565i
$555$	−4.57220	+	1.89387i	−0.194079	+	0.0803902i
$556$	−3.12366	+	23.1270i	−0.132473	+	0.980802i
$557$	−6.63612	+	16.0210i	−0.281182	+	0.678832i	−0.999864	−	0.0165063i	$-0.994746\pi$
$557$	−6.63612	+	16.0210i	−0.281182	+	0.678832i	0.718682	+	0.695339i	$0.244746\pi$
$558$	3.45159	−	12.7956i	0.146117	−	0.541682i
$559$			10.4943i			0.443861i
$560$	0.373762	+	2.99405i	0.0157943	+	0.126522i
$561$		−	24.8470i		−	1.04904i
$562$	8.20106	+	2.21221i	0.345941	+	0.0933166i
$563$	−7.00306	+	16.9069i	−0.295144	+	0.712540i	0.704851	+	0.709355i	$0.251014\pi$
$563$	−7.00306	+	16.9069i	−0.295144	+	0.712540i	−0.999995	+	0.00318479i	$0.998986\pi$
$564$	43.7373	+	57.3971i	1.84167	+	2.41685i
$565$	0.329771	−	0.136596i	0.0138736	−	0.00574662i
$566$	−1.34323	+	1.74446i	−0.0564600	+	0.0733251i
$567$	−56.3062	−	56.3062i	−2.36464	−	2.36464i
$568$	8.87292	−	8.78410i	0.372300	−	0.368573i
$569$	10.0101	−	10.0101i	0.419644	−	0.419644i	−0.465437	−	0.885081i	$-0.654103\pi$
$569$	10.0101	−	10.0101i	0.419644	−	0.419644i	0.885081	+	0.465437i	$0.154103\pi$
$570$	−1.34424	−	10.3445i	−0.0563041	−	0.433285i
$571$	−5.55506	−	13.4111i	−0.232472	−	0.561237i	0.763995	−	0.645222i	$-0.223235\pi$
$571$	−5.55506	−	13.4111i	−0.232472	−	0.561237i	−0.996467	+	0.0839853i	$0.973235\pi$
$572$	3.94069	+	2.29281i	0.164769	+	0.0958674i
$573$	−71.2018	−	29.4928i	−2.97450	−	1.23208i
$574$	−4.84272	−	8.42041i	−0.202131	−	0.351461i
$575$	10.0980			0.421116
$576$	44.8545	+	45.7663i	1.86894	+	1.90693i
$577$	−6.67199			−0.277759			−0.138879	−	0.990309i	$-0.544350\pi$
$577$	−6.67199			−0.277759			−0.138879	+	0.990309i	$0.544350\pi$
$578$	−4.37803	−	7.61242i	−0.182102	−	0.316635i
$579$	−8.97186	−	3.71626i	−0.372858	−	0.154443i
$580$	3.97047	+	2.31014i	0.164865	+	0.0959233i
$581$	2.62713	+	6.34245i	0.108992	+	0.263129i
$582$	3.22937	+	24.8515i	0.133862	+	1.03013i
$583$	−11.9043	+	11.9043i	−0.493024	+	0.493024i
$584$	4.46566	+	4.51082i	0.184790	+	0.186659i
$585$	−1.67046	−	1.67046i	−0.0690652	−	0.0690652i
$586$	−11.4547	+	14.8763i	−0.473189	+	0.614535i
$587$	40.7785	−	16.8910i	1.68311	−	0.697166i	0.683642	−	0.729818i	$-0.260395\pi$
$587$	40.7785	−	16.8910i	1.68311	−	0.697166i	0.999467	+	0.0326515i	$0.0103951\pi$
$588$	−1.84283	−	2.41837i	−0.0759969	−	0.0997319i
$589$	3.37459	−	8.14698i	0.139048	−	0.335690i
$590$	−1.49349	−	0.402864i	−0.0614858	−	0.0165856i
$591$		−	21.5660i		−	0.887106i
$592$	12.4217	−	15.9654i	0.510529	−	0.656174i
$593$		−	11.0235i		−	0.452682i	−0.974048	−	0.226341i	$-0.927324\pi$
$593$		−	11.0235i		−	0.452682i	0.974048	−	0.226341i	$-0.0726763\pi$
$594$	−13.9583	+	51.7457i	−0.572714	+	2.12315i
$595$	0.948239	−	2.28925i	0.0388740	−	0.0938501i
$596$	2.10944	−	15.6178i	0.0864059	−	0.639732i
$597$	5.44834	−	2.25678i	0.222986	−	0.0923637i
$598$	2.30308	+	1.77336i	0.0941799	+	0.0725180i
$599$	−1.21441	−	1.21441i	−0.0496196	−	0.0496196i	0.681862	−	0.731481i	$-0.261171\pi$
$599$	−1.21441	−	1.21441i	−0.0496196	−	0.0496196i	−0.731481	+	0.681862i	$0.761171\pi$
$600$	42.6880	−	17.4309i	1.74273	−	0.711612i
$601$	−28.6674	+	28.6674i	−1.16937	+	1.16937i	−0.187010	+	0.982358i	$0.559880\pi$
$601$	−28.6674	+	28.6674i	−1.16937	+	1.16937i	−0.982358	+	0.187010i	$0.940120\pi$
$602$	37.6428	−	4.89157i	1.53421	−	0.199365i
$603$	−7.74031	−	18.6868i	−0.315210	−	0.760984i
$604$	−25.1013	+	6.63573i	−1.02136	+	0.270004i
$605$	−1.58129	−	0.654993i	−0.0642887	−	0.0266292i
$606$	28.1616	−	16.1962i	1.14399	−	0.657926i
$607$	15.5590			0.631520			0.315760	−	0.948839i	$-0.397741\pi$
$607$	15.5590			0.631520			0.315760	+	0.948839i	$0.397741\pi$
$608$	25.6722	+	34.0438i	1.04114	+	1.38066i
$609$	66.0946			2.67829
$610$	−1.21574	+	0.699195i	−0.0492240	+	0.0283096i
$611$	10.0461	+	4.16122i	0.406421	+	0.168345i
$612$	−13.4499	−	50.8776i	−0.543680	−	2.05661i
$613$	5.26764	+	12.7172i	0.212758	+	0.513644i	0.993845	−	0.110779i	$-0.0353345\pi$
$613$	5.26764	+	12.7172i	0.212758	+	0.513644i	−0.781087	+	0.624422i	$0.785334\pi$
$614$	−39.1079	+	5.08195i	−1.57827	+	0.205091i
$615$	1.85827	−	1.85827i	0.0749326	−	0.0749326i
$616$	6.38745	−	15.2039i	0.257358	−	0.612582i
$617$	−25.0060	−	25.0060i	−1.00670	−	1.00670i	−0.999977	−	0.00672483i	$-0.997859\pi$
$617$	−25.0060	−	25.0060i	−1.00670	−	1.00670i	−0.00672483	−	0.999977i	$-0.502141\pi$
$618$	42.6709	+	32.8564i	1.71648	+	1.32168i
$619$	−14.5881	+	6.04260i	−0.586346	+	0.242873i	−0.656078	−	0.754693i	$-0.727786\pi$
$619$	−14.5881	+	6.04260i	−0.586346	+	0.242873i	0.0697316	+	0.997566i	$0.477786\pi$
$620$	−0.683858	−	0.0923659i	−0.0274644	−	0.00370950i
$621$	−13.0762	+	31.5688i	−0.524730	+	1.26681i
$622$	6.85357	−	25.4074i	0.274803	−	1.01874i
$623$		−	18.9590i		−	0.759577i
$624$	12.7971	+	3.52113i	0.512293	+	0.140958i
$625$		−	23.7029i		−	0.948115i
$626$	10.7338	+	2.89542i	0.429010	+	0.115724i
$627$	−21.8183	+	52.6740i	−0.871339	+	2.10360i
$628$	−26.2945	+	20.0367i	−1.04926	+	0.799552i
$629$	−15.3476	+	6.35718i	−0.611948	+	0.253477i
$630$	−5.21329	+	6.77055i	−0.207702	+	0.269745i
$631$	−20.5327	−	20.5327i	−0.817396	−	0.817396i	0.168334	−	0.985730i	$-0.446161\pi$
$631$	−20.5327	−	20.5327i	−0.817396	−	0.817396i	−0.985730	+	0.168334i	$0.946161\pi$
$632$	0.227393	−	45.2018i	0.00904519	−	1.79803i
$633$	40.5800	−	40.5800i	1.61291	−	1.61291i
$634$	−3.59618	−	27.6743i	−0.142823	−	1.09908i
$635$	−0.354464	−	0.855753i	−0.0140665	−	0.0339595i
$636$	−24.6475	+	42.3619i	−0.977336	+	1.67976i
$637$	−0.423282	−	0.175329i	−0.0167710	−	0.00694679i
$638$	−12.5168	−	21.7640i	−0.495546	−	0.861645i
$639$	35.3596			1.39881
$640$	2.06216	−	2.62313i	0.0815142	−	0.103688i
$641$	−15.5494			−0.614163			−0.307081	−	0.951683i	$-0.599352\pi$
$641$	−15.5494			−0.614163			−0.307081	+	0.951683i	$0.599352\pi$
$642$	47.1670	+	82.0129i	1.86153	+	3.23679i
$643$	10.4823	+	4.34189i	0.413380	+	0.171227i	0.579674	−	0.814849i	$-0.303180\pi$
$643$	10.4823	+	4.34189i	0.413380	+	0.171227i	−0.166294	+	0.986076i	$0.553180\pi$
$644$	5.28750	−	9.08769i	0.208357	−	0.358105i
$645$	3.93005	+	9.48798i	0.154746	+	0.373589i
$646$	−4.51224	−	34.7237i	−0.177532	−	1.36619i
$647$	14.8701	−	14.8701i	0.584605	−	0.584605i	−0.351560	−	0.936165i	$-0.614349\pi$
$647$	14.8701	−	14.8701i	0.584605	−	0.584605i	0.936165	+	0.351560i	$0.114349\pi$
$648$	−0.442978	+	88.0564i	−0.0174018	+	3.45918i
$649$	5.97821	+	5.97821i	0.234665	+	0.234665i
$650$	4.23895	−	5.50517i	0.166265	−	0.215930i
$651$	−9.17313	+	3.79964i	−0.359523	+	0.148919i
$652$	10.8702	−	8.28322i	0.425710	−	0.324396i
$653$	9.07895	−	21.9185i	0.355287	−	0.857738i	−0.640663	−	0.767822i	$-0.721340\pi$
$653$	9.07895	−	21.9185i	0.355287	−	0.857738i	0.995949	−	0.0899154i	$-0.0286597\pi$
$654$	−2.35616	−	0.635567i	−0.0921330	−	0.0248526i
$655$		−	2.82324i		−	0.110313i
$656$	−2.84972	+	10.3569i	−0.111263	+	0.404370i
$657$			17.9761i			0.701316i
$658$	10.2436	−	37.9747i	0.399336	−	1.48041i
$659$	−4.33631	+	10.4688i	−0.168919	+	0.407806i	−0.985557	−	0.169344i	$-0.945835\pi$
$659$	−4.33631	+	10.4688i	−0.168919	+	0.407806i	0.816638	+	0.577150i	$0.195835\pi$
$660$	4.42146	+	0.597188i	0.172105	+	0.0232455i
$661$	−27.7462	+	11.4929i	−1.07920	+	0.447020i	−0.850229	−	0.526412i	$-0.823537\pi$
$661$	−27.7462	+	11.4929i	−1.07920	+	0.447020i	−0.228973	+	0.973433i	$0.573537\pi$
$662$	14.0838	+	10.8444i	0.547381	+	0.421481i
$663$	−7.70732	−	7.70732i	−0.299328	−	0.299328i
$664$	2.94045	−	6.99908i	0.114112	−	0.271617i
$665$	−4.02040	+	4.02040i	−0.155905	+	0.155905i
$666$	56.8104	−	7.38234i	2.20136	−	0.286060i
$667$	−6.12554	−	14.7884i	−0.237182	−	0.572607i
$668$	−9.28163	−	35.1101i	−0.359117	−	1.35845i
$669$	79.5345	+	32.9443i	3.07498	+	1.27370i
$670$	−0.912950	+	0.525052i	−0.0352703	+	0.0202845i
$671$	7.66523			0.295913
$672$	6.66529	−	47.5441i	0.257119	−	1.83405i
$673$	−7.56019			−0.291424			−0.145712	−	0.989327i	$-0.546547\pi$
$673$	−7.56019			−0.291424			−0.145712	+	0.989327i	$0.546547\pi$
$674$	−24.0505	+	13.8318i	−0.926391	+	0.532783i
$675$	75.4604	+	31.2567i	2.90447	+	1.20307i
$676$	1.93358	−	0.511156i	0.0743683	−	0.0196599i
$677$	9.47895	+	22.8842i	0.364306	+	0.879512i	0.994660	+	0.103204i	$0.0329095\pi$
$677$	9.47895	+	22.8842i	0.364306	+	0.879512i	−0.630355	+	0.776307i	$0.717090\pi$
$678$	−5.63205	+	0.731867i	−0.216297	+	0.0281072i
$679$	9.65851	−	9.65851i	0.370660	−	0.370660i
$680$	−2.53680	+	1.03586i	−0.0972820	+	0.0397234i
$681$	−32.3225	−	32.3225i	−1.23860	−	1.23860i
$682$	2.98835	+	2.30101i	0.114430	+	0.0881104i
$683$	19.5599	−	8.10196i	0.748437	−	0.310013i	0.0243334	−	0.999704i	$-0.492254\pi$
$683$	19.5599	−	8.10196i	0.748437	−	0.310013i	0.724104	+	0.689691i	$0.242254\pi$
$684$	−16.1630	+	119.667i	−0.618007	+	4.57560i
$685$	−0.898347	+	2.16880i	−0.0343241	+	0.0828657i
$686$	−7.02589	+	26.0462i	−0.268250	+	0.994449i
$687$			27.0478i			1.03194i
$688$	−33.1306	−	25.7769i	−1.26309	−	0.982734i
$689$			7.38518i			0.281353i
$690$	2.74635	+	0.740820i	0.104552	+	0.0282025i
$691$	16.8125	−	40.5889i	0.639577	−	1.54408i	−0.187666	−	0.982233i	$-0.560092\pi$
$691$	16.8125	−	40.5889i	0.639577	−	1.54408i	0.827244	−	0.561843i	$-0.189908\pi$
$692$	18.6169	+	24.4312i	0.707707	+	0.928734i
$693$	43.1485	−	17.8727i	1.63908	−	0.678928i
$694$	0.213188	−	0.276870i	0.00809251	−	0.0105098i
$695$	2.43336	+	2.43336i	0.0923027	+	0.0923027i
$696$	−51.4221	−	51.9421i	−1.94915	−	1.96886i
$697$	6.23769	−	6.23769i	0.236269	−	0.236269i
$698$	−6.49400	−	49.9742i	−0.245802	−	1.89155i
$699$	−12.0322	−	29.0483i	−0.455100	−	1.09871i
$700$	−21.7228	−	12.6390i	−0.821043	−	0.477708i
$701$	32.9014	+	13.6282i	1.24267	+	0.514730i	0.904548	−	0.426373i	$-0.140209\pi$
$701$	32.9014	+	13.6282i	1.24267	+	0.514730i	0.338121	+	0.941103i	$0.390209\pi$
$702$	11.7213	+	20.3808i	0.442393	+	0.769223i
$703$	38.1181			1.43765
$704$	−16.9179	+	6.80901i	−0.637616	+	0.256624i
$705$	10.6411			0.400768
$706$	5.05085	+	8.78231i	0.190091	+	0.330527i
$707$	−16.3591	−	6.77616i	−0.615247	−	0.254844i
$708$	21.2738	+	12.3777i	0.799518	+	0.465184i
$709$	−7.14571	−	17.2513i	−0.268363	−	0.647885i	0.731044	−	0.682331i	$-0.239034\pi$
$709$	−7.14571	−	17.2513i	−0.268363	−	0.647885i	−0.999407	+	0.0344454i	$0.989034\pi$
$710$	−0.237255	−	1.82578i	−0.00890402	−	0.0685204i
$711$	90.5202	−	90.5202i	3.39477	−	3.39477i
$712$	−14.8994	+	14.7503i	−0.558379	+	0.552789i
$713$	1.70030	+	1.70030i	0.0636768	+	0.0636768i
$714$	−24.0535	+	31.2385i	−0.900180	+	1.16907i
$715$	0.621124	−	0.257278i	0.0232287	−	0.00962166i
$716$	22.7839	+	29.8997i	0.851475	+	1.11740i
$717$	−35.9760	+	86.8537i	−1.34355	+	3.24361i
$718$	−7.90258	−	2.13170i	−0.294922	−	0.0795544i
$719$			37.5386i			1.39995i	0.714166	+	0.699977i	$0.246806\pi$
$719$			37.5386i			1.39995i	−0.714166	+	0.699977i	$0.753194\pi$
$720$	9.37679	−	1.17055i	0.349452	−	0.0436238i
$721$		−	29.3537i		−	1.09319i
$722$	−13.9274	+	51.6314i	−0.518325	+	1.92152i
$723$	−38.3978	+	92.7005i	−1.42803	+	3.44757i
$724$	1.39004	−	10.2916i	0.0516604	−	0.382483i
$725$	−35.3494	+	14.6422i	−1.31284	+	0.543797i
$726$	21.5779	+	16.6149i	0.800831	+	0.616636i
$727$	−4.84821	−	4.84821i	−0.179810	−	0.179810i	0.611463	−	0.791273i	$-0.290581\pi$
$727$	−4.84821	−	4.84821i	−0.179810	−	0.179810i	−0.791273	+	0.611463i	$0.790581\pi$
$728$	−2.73478	−	6.69744i	−0.101358	−	0.248224i
$729$	−59.3203	+	59.3203i	−2.19705	+	2.19705i
$730$	0.928192	−	0.120616i	0.0343539	−	0.00446419i
$731$	13.1921	+	31.8485i	0.487927	+	1.17796i
$732$	21.5739	−	5.70323i	0.797395	−	0.210798i
$733$	−7.51757	−	3.11388i	−0.277668	−	0.115014i	0.239504	−	0.970895i	$-0.423015\pi$
$733$	−7.51757	−	3.11388i	−0.277668	−	0.115014i	−0.517172	+	0.855882i	$0.673015\pi$
$734$	−13.5755	+	7.80752i	−0.501082	+	0.288181i
$735$	−0.448353			−0.0165377
$736$	−11.2555	+	2.91498i	−0.414884	+	0.107448i
$737$	5.75612			0.212029
$738$	−26.3711	+	15.1664i	−0.970733	+	0.558285i
$739$	−35.0529	−	14.5194i	−1.28944	−	0.534105i	−0.370624	−	0.928783i	$-0.620856\pi$
$739$	−35.0529	−	14.5194i	−1.28944	−	0.534105i	−0.918820	+	0.394678i	$0.870856\pi$
$740$	−0.762370	−	2.88385i	−0.0280253	−	0.106013i
$741$	9.57117	+	23.1068i	0.351606	+	0.848851i
$742$	26.4905	−	3.44236i	0.972497	−	0.126373i
$743$	−26.4247	+	26.4247i	−0.969428	+	0.969428i	−0.999546	−	0.0301185i	$-0.990412\pi$
$743$	−26.4247	+	26.4247i	−0.969428	+	0.969428i	0.0301185	+	0.999546i	$0.490412\pi$
$744$	10.1228	+	4.25279i	0.371120	+	0.155915i
$745$	−1.64327	−	1.64327i	−0.0602048	−	0.0602048i
$746$	−23.4664	−	18.0690i	−0.859165	−	0.661553i
$747$	19.8633	−	8.22766i	0.726761	−	0.301034i
$748$	14.8416	+	2.00459i	0.542663	+	0.0732952i
$749$	19.7337	−	47.6413i	0.721053	−	1.74078i
$750$	3.57299	−	13.2457i	0.130467	−	0.483664i
$751$			7.22251i			0.263553i	0.991279	+	0.131777i	$0.0420681\pi$
$751$			7.22251i			0.263553i	−0.991279	+	0.131777i	$0.957932\pi$
$752$	−37.8130	+	21.4945i	−1.37890	+	0.783822i
$753$			40.8603i			1.48903i
$754$	−10.6336	−	2.86839i	−0.387253	−	0.104460i
$755$	−1.46515	+	3.53719i	−0.0533223	+	0.128731i
$756$	67.6419	−	51.5440i	2.46011	−	1.87464i
$757$	−43.2858	+	17.9296i	−1.57325	+	0.651662i	−0.987326	−	0.158704i	$-0.949268\pi$
$757$	−43.2858	+	17.9296i	−1.57325	+	0.651662i	−0.585924	+	0.810366i	$0.699268\pi$
$758$	18.9323	−	24.5876i	0.687653	−	0.893062i
$759$	−10.9932	−	10.9932i	−0.399030	−	0.399030i
$760$	6.28744	+	0.0316297i	0.228070	+	0.00114733i
$761$	9.29170	−	9.29170i	0.336824	−	0.336824i	−0.518347	−	0.855171i	$-0.673452\pi$
$761$	9.29170	−	9.29170i	0.336824	−	0.336824i	0.855171	+	0.518347i	$0.173452\pi$
$762$	1.89919	+	14.6151i	0.0688004	+	0.529450i
$763$	0.509017	+	1.22888i	0.0184277	+	0.0444883i
$764$	23.3610	−	40.1508i	0.845170	−	1.45261i
$765$	−7.16949	−	2.96970i	−0.259213	−	0.107370i
$766$	0.646191	+	1.12358i	0.0233478	+	0.0405967i
$767$	3.70878			0.133916
$768$	−42.5494	+	31.7516i	−1.53537	+	1.14574i
$769$	−6.87981			−0.248092			−0.124046	−	0.992276i	$-0.539587\pi$
$769$	−6.87981			−0.248092			−0.124046	+	0.992276i	\(0.539587\

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.705052 - 1.22593i) q^{2} +(3.06559 + 1.26981i) q^{3} +(-1.00580 + 1.72869i) q^{4} +(0.112862 + 0.272473i) q^{5} +(-0.604704 - 4.65347i) q^{6} +(-1.80857 + 1.80857i) q^{7} +(2.82839 + 0.0142285i) q^{8} +(5.66408 + 5.66408i) q^{9} +O(q^{10})\)	\(q+(-0.705052 - 1.22593i) q^{2} +(3.06559 + 1.26981i) q^{3} +(-1.00580 + 1.72869i) q^{4} +(0.112862 + 0.272473i) q^{5} +(-0.604704 - 4.65347i) q^{6} +(-1.80857 + 1.80857i) q^{7} +(2.82839 + 0.0142285i) q^{8} +(5.66408 + 5.66408i) q^{9} +(0.254459 - 0.330468i) q^{10} +(-2.10606 + 0.872359i) q^{11} +(-5.27848 + 4.02226i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(3.49231 + 0.942042i) q^{14} +0.978601i q^{15} +(-1.97672 - 3.47744i) q^{16} +3.28489i q^{17} +(2.95029 - 10.9372i) q^{18} +(2.88448 - 6.96374i) q^{19} +(-0.584537 - 0.0789510i) q^{20} +(-7.84086 + 3.24779i) q^{21} +(2.55433 + 1.96682i) q^{22} +(1.45336 + 1.45336i) q^{23} +(8.65261 + 3.63513i) q^{24} +(3.47403 - 3.47403i) q^{25} +(1.40242 - 0.182241i) q^{26} +(6.36202 + 15.3593i) q^{27} +(-1.30739 - 4.94551i) q^{28} +(-7.19503 - 2.98028i) q^{29} +(1.19970 - 0.689965i) q^{30} +1.16991 q^{31} +(-2.86940 + 4.87509i) q^{32} -7.56404 q^{33} +(4.02704 - 2.31602i) q^{34} +(-0.696904 - 0.288667i) q^{35} +(-15.4884 + 4.09448i) q^{36} +(1.93528 + 4.67218i) q^{37} +(-10.5708 + 1.37364i) q^{38} +(-2.34630 + 2.34630i) q^{39} +(0.315341 + 0.772265i) q^{40} +(-1.89890 - 1.89890i) q^{41} +(9.50977 + 7.32247i) q^{42} +(9.69546 - 4.01599i) q^{43} +(0.610247 - 4.51814i) q^{44} +(-0.904049 + 2.18257i) q^{45} +(0.757019 - 2.80640i) q^{46} -10.8738i q^{47} +(-1.64413 - 13.1704i) q^{48} +0.458157i q^{49} +(-6.70829 - 1.80954i) q^{50} +(-4.17117 + 10.0701i) q^{51} +(-1.21219 - 1.59078i) q^{52} +(6.82302 - 2.82619i) q^{53} +(14.3438 - 18.6285i) q^{54} +(-0.475388 - 0.475388i) q^{55} +(-5.14107 + 5.08961i) q^{56} +(17.6852 - 17.6852i) q^{57} +(1.41926 + 10.9219i) q^{58} +(-1.41929 - 3.42646i) q^{59} +(-1.69170 - 0.984280i) q^{60} +(-3.10660 - 1.28679i) q^{61} +(-0.824851 - 1.43423i) q^{62} -20.4878 q^{63} +(7.99960 + 0.0804878i) q^{64} -0.294922 q^{65} +(5.33304 + 9.27298i) q^{66} +(-2.33286 - 0.966304i) q^{67} +(-5.67854 - 3.30395i) q^{68} +(2.60991 + 6.30087i) q^{69} +(0.137468 + 1.05788i) q^{70} +(3.12139 - 3.12139i) q^{71} +(15.9397 + 16.1008i) q^{72} +(1.58685 + 1.58685i) q^{73} +(4.36329 - 5.66665i) q^{74} +(15.0613 - 6.23859i) q^{75} +(9.13691 + 11.9905i) q^{76} +(2.23124 - 5.38668i) q^{77} +(4.53066 + 1.22213i) q^{78} -15.9814i q^{79} +(0.724410 - 0.931072i) q^{80} +31.1330i q^{81} +(-0.989095 + 3.66675i) q^{82} +(1.02714 - 2.47975i) q^{83} +(2.27195 - 16.8210i) q^{84} +(-0.895042 + 0.370739i) q^{85} +(-11.7591 - 9.05446i) q^{86} +(-18.2726 - 18.2726i) q^{87} +(-5.96918 + 2.43741i) q^{88} +(-5.24144 + 5.24144i) q^{89} +(3.31307 - 0.430524i) q^{90} +(-0.978790 - 2.36301i) q^{91} +(-3.97419 + 1.05061i) q^{92} +(3.58647 + 1.48557i) q^{93} +(-13.3305 + 7.66660i) q^{94} +2.22298 q^{95} +(-14.9868 + 11.3014i) q^{96} -5.34042 q^{97} +(0.561668 - 0.323025i) q^{98} +(-16.8700 - 6.98780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

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