LMFDB - Embedded newform 416.2.bf.a.53.18

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			53.18
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.18

$q$-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 $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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	0.775053	−	0.631896i	$-0.217723\pi$
$3$	3.06559	−	1.26981i	1.76992	−	0.733124i	0.994863	−	0.101228i	$-0.0322771\pi$
$4$	−1.00580	−	1.72869i	−0.502902	−	0.864344i
$5$	0.112862	−	0.272473i	0.0504734	−	0.121853i	−0.896632	−	0.442777i	$-0.853993\pi$
$5$	0.112862	−	0.272473i	0.0504734	−	0.121853i	0.947105	+	0.320924i	$0.103993\pi$
$6$	−0.604704	+	4.65347i	−0.246869	+	1.89977i
$7$	−1.80857	−	1.80857i	−0.683575	−	0.683575i	0.277229	−	0.960804i	$-0.410584\pi$
$7$	−1.80857	−	1.80857i	−0.683575	−	0.683575i	−0.960804	+	0.277229i	$0.910584\pi$
$8$	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	0.0418749	−	0.999123i	$-0.486667\pi$
$11$	−2.10606	−	0.872359i	−0.635002	−	0.263026i	−0.676877	+	0.736097i	$0.736667\pi$
$12$	−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	$-0.869583\pi$
$17$		−	3.28489i		−	0.796702i	0.917233	−	0.398351i	$-0.130417\pi$
$18$	2.95029	+	10.9372i	0.695390	+	2.57793i
$19$	2.88448	+	6.96374i	0.661744	+	1.59759i	0.795069	+	0.606519i	$0.207435\pi$
$19$	2.88448	+	6.96374i	0.661744	+	1.59759i	−0.133325	+	0.991072i	$0.542565\pi$
$20$	−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	−0.539159	−	0.842204i	$-0.681258\pi$
$23$	1.45336	−	1.45336i	0.303046	−	0.303046i	0.842204	+	0.539159i	$0.181258\pi$
$24$	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	−0.932385	−	0.361467i	$-0.882276\pi$
$29$	−7.19503	+	2.98028i	−1.33608	+	0.553424i	−0.403700	+	0.914892i	$0.632276\pi$
$30$	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	−0.681194	−	0.732103i	$-0.738539\pi$
$37$	1.93528	−	4.67218i	0.318158	−	0.768102i	0.999352	−	0.0359985i	$-0.0114612\pi$
$38$	−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	−0.839664	−	0.543106i	$-0.817248\pi$
$41$	−1.89890	+	1.89890i	−0.296559	+	0.296559i	0.543106	+	0.839664i	$0.317248\pi$
$42$	9.50977	−	7.32247i	1.46739	−	1.12988i
$43$	9.69546	+	4.01599i	1.47854	+	0.612433i	0.968789	−	0.247887i	$-0.0797363\pi$
$43$	9.69546	+	4.01599i	1.47854	+	0.612433i	0.509754	+	0.860320i	$0.329736\pi$
$44$	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	$0.291510\pi$
$47$			10.8738i			1.58611i	−0.609152	+	0.793054i	$0.708490\pi$
$48$	−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	0.798411	−	0.602113i	$-0.205674\pi$
$53$	6.82302	+	2.82619i	0.937214	+	0.388207i	0.138803	+	0.990320i	$0.455674\pi$
$54$	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	−0.988939	−	0.148320i	$-0.952613\pi$
$59$	−1.41929	+	3.42646i	−0.184775	+	0.446087i	0.804164	+	0.594408i	$0.202613\pi$
$60$	−1.69170	+	0.984280i	−0.218397	+	0.127070i
$61$	−3.10660	+	1.28679i	−0.397759	+	0.164757i	−0.572591	−	0.819841i	$-0.694062\pi$
$61$	−3.10660	+	1.28679i	−0.397759	+	0.164757i	0.174832	+	0.984598i	$0.444062\pi$
$62$	−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	−0.520606	−	0.853797i	$-0.674294\pi$
$67$	−2.33286	+	0.966304i	−0.285005	+	0.118053i	0.235601	+	0.971850i	$0.424294\pi$
$68$	−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	0.867638	−	0.497197i	$-0.165637\pi$
$71$	3.12139	+	3.12139i	0.370441	+	0.370441i	−0.497197	+	0.867638i	$0.665637\pi$
$72$	15.9397	−	16.1008i	1.87851	−	1.89750i
$73$	1.58685	−	1.58685i	0.185727	−	0.185727i	−0.608119	−	0.793846i	$-0.708076\pi$
$73$	1.58685	−	1.58685i	0.185727	−	0.185727i	0.793846	+	0.608119i	$0.208076\pi$
$74$	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	$0.355724\pi$
$79$			15.9814i			1.79805i	−0.437894	+	0.899026i	$0.644276\pi$
$80$	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	0.970173	−	0.242415i	$-0.0779395\pi$
$83$	1.02714	+	2.47975i	0.112744	+	0.272187i	−0.857429	+	0.514602i	$0.827940\pi$
$84$	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	0.372458	−	0.928049i	$-0.378515\pi$
$89$	−5.24144	−	5.24144i	−0.555591	−	0.555591i	−0.928049	+	0.372458i	$0.878515\pi$
$90$	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	−0.735540	−	0.677481i	$-0.763072\pi$
$101$	2.64931	−	6.39601i	0.263617	−	0.636427i	0.999157	+	0.0410541i	$0.0130716\pi$
$102$	15.2861	+	1.98639i	1.51355	+	0.196681i
$103$	−8.11516	−	8.11516i	−0.799611	−	0.799611i	0.183423	−	0.983034i	$-0.441282\pi$
$103$	−8.11516	−	8.11516i	−0.799611	−	0.799611i	−0.983034	+	0.183423i	$0.941282\pi$
$104$	−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	−0.986165	−	0.165765i	$-0.946991\pi$
$107$	−18.6266	−	7.71540i	−1.80070	−	0.745876i	−0.814538	−	0.580111i	$-0.803009\pi$
$108$	−32.9503	+	4.45046i	−3.17065	+	0.428246i
$109$	0.199014	+	0.480461i	0.0190620	+	0.0460198i	0.933124	−	0.359555i	$-0.117071\pi$
$109$	0.199014	+	0.480461i	0.0190620	+	0.0460198i	−0.914062	+	0.405575i	$0.867071\pi$
$110$	−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	$0.0181303\pi$
$113$			1.21029i			0.113854i	−0.998378	+	0.0569272i	$0.981870\pi$
$114$	−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	−0.733972	−	0.679180i	$-0.762336\pi$
$131$	−8.84413	+	3.66336i	−0.772715	+	0.320069i	−0.0387436	+	0.999249i	$0.512336\pi$
$132$	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	−0.424544	−	0.905407i	$-0.639566\pi$
$137$	5.62836	−	5.62836i	0.480864	−	0.480864i	0.905407	+	0.424544i	$0.139566\pi$
$138$	5.88430	+	7.64200i	0.500905	+	0.650530i
$139$	10.7803	+	4.46534i	0.914371	+	0.378745i	0.789728	−	0.613457i	$-0.210222\pi$
$139$	10.7803	+	4.46534i	0.914371	+	0.378745i	0.124643	+	0.992202i	$0.460222\pi$
$140$	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	0.0640003	−	0.997950i	$-0.479614\pi$
$149$	−7.28001	−	3.01548i	−0.596402	−	0.247038i	−0.660402	+	0.750912i	$0.729614\pi$
$150$	−18.2671	+	14.0655i	−1.49150	+	1.14845i
$151$	9.17952	−	9.17952i	0.747019	−	0.747019i	−0.226899	−	0.973918i	$-0.572859\pi$
$151$	9.17952	−	9.17952i	0.747019	−	0.747019i	0.973918	+	0.226899i	$0.0728588\pi$
$152$	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	0.321748	−	0.946825i	$-0.395730\pi$
$157$	15.2711	−	6.32549i	1.21876	−	0.504829i	0.897017	+	0.441997i	$0.145730\pi$
$158$	−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	−0.615966	−	0.787773i	$-0.711234\pi$
$163$	−6.31309	+	2.61497i	−0.494480	+	0.204820i	0.121486	+	0.992593i	$0.461234\pi$
$164$	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	0.00641173	−	0.999979i	$-0.497959\pi$
$167$	−12.8397	−	12.8397i	−0.993568	−	0.993568i	−0.999979	+	0.00641173i	$0.997959\pi$
$168$	−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	0.973500	+	0.228689i	$0.0734438\pi$
$173$	5.87725	+	14.1889i	0.446839	+	1.07876i	−0.526661	+	0.850075i	$0.676556\pi$
$174$	−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	0.926385	+	0.376578i	$0.122899\pi$
$179$	7.19276	+	17.3649i	0.537612	+	1.29791i	−0.388773	+	0.921334i	$0.627101\pi$
$180$	−2.86368	+	3.75805i	−0.213446	+	0.280109i
$181$	−4.79726	−	1.98709i	−0.356577	−	0.147699i	0.197202	−	0.980363i	$-0.436815\pi$
$181$	−4.79726	−	1.98709i	−0.356577	−	0.147699i	−0.553779	+	0.832664i	$0.686815\pi$
$182$	−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	−0.987378	−	0.158379i	$-0.949373\pi$
$197$	−2.48720	+	6.00463i	−0.177206	+	0.427812i	0.810173	+	0.586191i	$0.199373\pi$
$198$	3.32771	−	25.6082i	0.236490	−	1.81990i
$199$	1.25671	+	1.25671i	0.0890859	+	0.0890859i	0.750245	−	0.661159i	$-0.229935\pi$
$199$	1.25671	+	1.25671i	0.0890859	+	0.0890859i	−0.661159	+	0.750245i	$0.729935\pi$
$200$	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	0.970143	+	0.242533i	$0.0779784\pi$
$211$	6.61863	+	15.9788i	0.455645	+	1.10003i	−0.514498	+	0.857492i	$0.672022\pi$
$212$	−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	−0.762722	−	0.646726i	$-0.776138\pi$
$227$	−12.7273	+	5.27184i	−0.844743	+	0.349904i	−0.0820213	+	0.996631i	$0.526138\pi$
$228$	12.7844	−	48.3600i	0.846665	−	3.20272i
$229$	3.11942	−	7.53094i	0.206137	−	0.497658i	−0.786672	−	0.617372i	$-0.788197\pi$
$229$	3.11942	−	7.53094i	0.206137	−	0.497658i	0.992809	+	0.119713i	$0.0381975\pi$
$230$	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	−0.891658	−	0.452709i	$-0.850458\pi$
$233$	−6.70028	+	6.70028i	−0.438950	+	0.438950i	0.452709	+	0.891658i	$0.350458\pi$
$234$	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	$-0.631147\pi$
$239$		−	28.3318i		−	1.83263i	0.400454	−	0.916317i	$-0.368853\pi$
$240$	3.40302	+	1.93442i	0.219664	+	0.124866i
$241$		−	30.2391i		−	1.94787i	−0.226825	−	0.973936i	$-0.572834\pi$
$241$		−	30.2391i		−	1.94787i	0.226825	−	0.973936i	$-0.427166\pi$
$242$	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	−0.702534	−	0.711650i	$-0.747948\pi$
$251$	4.71241	−	11.3768i	0.297445	−	0.718095i	0.999979	−	0.00644558i	$-0.00205171\pi$
$252$	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	0.859302	−	0.511469i	$-0.170898\pi$
$263$	5.64090	+	5.64090i	0.347833	+	0.347833i	−0.511469	+	0.859302i	$0.670898\pi$
$264$	−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	0.967852	−	0.251522i	$-0.0809312\pi$
$269$	1.73236	+	4.18230i	0.105624	+	0.254999i	−0.862227	+	0.506521i	$0.830931\pi$
$270$	6.69462	−	1.80586i	0.407422	−	0.109901i
$271$			29.3694i			1.78406i	0.451974	+	0.892031i	$0.350720\pi$
$271$			29.3694i			1.78406i	−0.451974	+	0.892031i	$0.649280\pi$
$272$	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	0.512345	−	0.858780i	$-0.328777\pi$
$277$	4.45007	+	1.84328i	0.267378	+	0.110752i	−0.244966	+	0.969532i	$0.578777\pi$
$278$	−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	0.568986	−	0.822347i	$-0.307336\pi$
$281$	−4.24709	−	4.24709i	−0.253360	−	0.253360i	−0.822347	+	0.568986i	$0.807336\pi$
$282$	−50.6009	−	6.57543i	−3.01324	−	0.391561i
$283$	−0.595770	+	1.43832i	−0.0354149	+	0.0854991i	−0.940597	−	0.339524i	$-0.889734\pi$
$283$	−0.595770	+	1.43832i	−0.0354149	+	0.0854991i	0.905183	+	0.425023i	$0.139734\pi$
$284$	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	0.703174	+	0.711018i	$0.251766\pi$
$293$	−5.08058	+	12.2656i	−0.296811	+	0.716564i	−0.999985	+	0.00554657i	$0.998234\pi$
$294$	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	0.864031	+	0.503439i	$0.167932\pi$
$307$	10.6715	+	25.7633i	0.609054	+	1.47039i	−0.254976	+	0.966947i	$0.582068\pi$
$308$	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	−0.227638	−	0.973746i	$-0.573100\pi$
$311$	13.1578	−	13.1578i	0.746108	−	0.746108i	0.973746	+	0.227638i	$0.0731003\pi$
$312$	−6.66963	−	6.60286i	−0.377594	−	0.373814i
$313$	−5.55875	−	5.55875i	−0.314199	−	0.314199i	0.532335	−	0.846534i	$-0.321315\pi$
$313$	−5.55875	−	5.55875i	−0.314199	−	0.314199i	−0.846534	+	0.532335i	$0.821315\pi$
$314$	−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	0.193431	−	0.981114i	$-0.438038\pi$
$317$	18.2311	−	7.55156i	1.02396	−	0.424138i	0.830529	+	0.556976i	$0.188038\pi$
$318$	−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	0.0399972	−	0.999200i	$-0.487265\pi$
$331$	−11.6121	−	4.80991i	−0.638261	−	0.264377i	−0.678259	+	0.734823i	$0.737265\pi$
$332$	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	$0.179438\pi$
$337$			19.6182i			1.06867i	−0.845272	+	0.534336i	$0.820562\pi$
$338$	−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	−0.921321	−	0.388802i	$-0.872889\pi$
$347$	0.0945569	−	0.228280i	0.00507608	−	0.0122547i	0.926397	+	0.376548i	$0.122889\pi$
$348$	49.9663	+	13.2090i	2.67847	+	0.708076i
$349$	32.9217	−	13.6366i	1.76226	−	0.729952i	0.766068	−	0.642759i	$-0.222210\pi$
$349$	32.9217	−	13.6366i	1.76226	−	0.729952i	0.996191	−	0.0871930i	$-0.0277897\pi$
$350$	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	0.806808	−	0.590813i	$-0.201193\pi$
$359$	4.09252	+	4.09252i	0.215995	+	0.215995i	−0.590813	+	0.806808i	$0.701193\pi$
$360$	−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	$0.0933296\pi$
$367$			11.0737i			0.578041i	−0.957323	+	0.289021i	$0.906670\pi$
$368$	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	0.822460	−	0.568822i	$-0.192601\pi$
$373$	19.3482	+	8.01427i	1.00181	+	0.414963i	0.179349	+	0.983785i	$0.442601\pi$
$374$	−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	−0.547523	−	0.836791i	$-0.684429\pi$
$379$	8.39719	−	20.2726i	0.431335	−	1.04133i	0.978858	−	0.204543i	$-0.0655709\pi$
$380$	−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	−0.500314	−	0.865844i	$-0.666782\pi$
$389$	9.18515	−	22.1749i	0.465706	−	1.12431i	0.966020	−	0.258469i	$-0.0832179\pi$
$390$	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	0.754439	−	0.656370i	$-0.227909\pi$
$397$	−4.84479	−	11.6964i	−0.243153	−	0.587024i	−0.997593	+	0.0693458i	$0.977909\pi$
$398$	−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	$-0.885000\pi$
$401$		−	14.1566i		−	0.706948i	0.935444	−	0.353474i	$-0.115000\pi$
$402$	−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	0.355978	−	0.934494i	$-0.384148\pi$
$409$	−11.6998	−	11.6998i	−0.578516	−	0.578516i	−0.934494	+	0.355978i	$0.884148\pi$
$410$	−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	−0.413207	−	0.910637i	$-0.635591\pi$
$419$	−1.25827	+	0.521191i	−0.0614703	+	0.0254618i	0.351736	+	0.936099i	$0.385591\pi$
$420$	4.83969	+	1.27941i	0.236152	+	0.0624288i
$421$	−7.05827	+	17.0402i	−0.343999	+	0.830487i	0.653304	+	0.757095i	$0.273382\pi$
$421$	−7.05827	+	17.0402i	−0.343999	+	0.830487i	−0.997303	+	0.0733914i	$0.976618\pi$
$422$	−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	$-0.786979\pi$
$431$		−	25.7588i		−	1.24076i	0.784302	−	0.620379i	$-0.213021\pi$
$432$	40.8350	+	52.4845i	1.96468	+	2.52516i
$433$		−	8.12124i		−	0.390282i	−0.980775	−	0.195141i	$-0.937484\pi$
$433$		−	8.12124i		−	0.390282i	0.980775	−	0.195141i	$-0.0625164\pi$
$434$	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	−0.860511	−	0.509431i	$-0.829856\pi$
$439$	−7.35595	+	7.35595i	−0.351080	+	0.351080i	0.509431	+	0.860511i	$0.329856\pi$
$440$	−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	−0.735122	−	0.677934i	$-0.762875\pi$
$443$	5.55781	−	13.4177i	0.264060	−	0.637496i	0.999182	+	0.0404380i	$0.0128753\pi$
$444$	−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	0.112429	−	0.993660i	$-0.464137\pi$
$457$	23.6455	−	23.6455i	1.10609	−	1.10609i	0.993660	−	0.112429i	$-0.0358632\pi$
$458$	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	0.910638	−	0.413206i	$-0.135591\pi$
$461$	−0.546667	−	1.31977i	−0.0254608	−	0.0614679i	−0.936099	+	0.351738i	$0.885591\pi$
$462$	−26.4160	+	7.12564i	−1.22898	+	0.331515i
$463$		−	5.59612i		−	0.260074i	−0.991509	−	0.130037i	$-0.958490\pi$
$463$		−	5.59612i		−	0.260074i	0.991509	−	0.130037i	$-0.0415096\pi$
$464$	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	0.987398	+	0.158254i	$0.0505864\pi$
$467$	8.66794	+	20.9263i	0.401105	+	0.968352i	−0.586294	+	0.810098i	$0.699414\pi$
$468$	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	0.129760	−	0.991545i	$-0.458579\pi$
$487$	−19.0180	−	19.0180i	−0.861786	−	0.861786i	−0.991545	+	0.129760i	$0.958579\pi$
$488$	−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	0.395288	−	0.918557i	$-0.370645\pi$
$491$	0.560176	+	0.232033i	0.0252804	+	0.0104715i	−0.370007	+	0.929029i	$0.620645\pi$
$492$	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	−0.989939	−	0.141498i	$-0.954808\pi$
$499$	−8.71194	−	21.0325i	−0.390000	−	0.941544i	0.599938	−	0.800046i	$-0.295192\pi$
$500$	−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	−0.0305798	+	0.999532i	$0.509735\pi$
$503$	−23.1030	+	23.1030i	−1.03011	+	1.03011i	−0.999532	+	0.0305798i	$0.990265\pi$
$504$	−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	−0.395552	−	0.918444i	$-0.629447\pi$
$509$	−0.582331	+	0.241209i	−0.0258114	+	0.0106914i	0.369740	+	0.929135i	$0.379447\pi$
$510$	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	−0.976633	−	0.214916i	$-0.931052\pi$
$521$	−17.3865	+	17.3865i	−0.761717	+	0.761717i	0.214916	+	0.976633i	$0.431052\pi$
$522$	−53.8235	−	69.9011i	−2.35579	−	3.05949i
$523$	−18.5566	−	7.68639i	−0.811423	−	0.336102i	−0.0619014	−	0.998082i	$-0.519716\pi$
$523$	−18.5566	−	7.68639i	−0.811423	−	0.336102i	−0.749522	+	0.661980i	$0.769716\pi$
$524$	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	−0.812077	−	0.583550i	$-0.801663\pi$
$541$	−22.6470	+	9.38069i	−0.973670	+	0.403307i	−0.161593	+	0.986858i	$0.551663\pi$
$542$	−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	−0.751755	−	0.659442i	$-0.770792\pi$
$547$	−19.1087	+	7.91509i	−0.817030	+	0.338425i	−0.0652750	+	0.997867i	$0.520792\pi$
$548$	−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	0.718682	−	0.695339i	$-0.244746\pi$
$557$	−6.63612	−	16.0210i	−0.281182	−	0.678832i	−0.999864	+	0.0165063i	$0.994746\pi$
$558$	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	−0.999995	−	0.00318479i	$-0.998986\pi$
$563$	−7.00306	−	16.9069i	−0.295144	−	0.712540i	0.704851	−	0.709355i	$-0.251014\pi$
$564$	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	0.885081	−	0.465437i	$-0.154103\pi$
$569$	10.0101	+	10.0101i	0.419644	+	0.419644i	−0.465437	+	0.885081i	$0.654103\pi$
$570$	−1.34424	+	10.3445i	−0.0563041	+	0.433285i
$571$	−5.55506	+	13.4111i	−0.232472	+	0.561237i	−0.996467	−	0.0839853i	$-0.973235\pi$
$571$	−5.55506	+	13.4111i	−0.232472	+	0.561237i	0.763995	+	0.645222i	$0.223235\pi$
$572$	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	0.999467	−	0.0326515i	$-0.0103951\pi$
$587$	40.7785	+	16.8910i	1.68311	+	0.697166i	0.683642	+	0.729818i	$0.260395\pi$
$588$	−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	$0.0726763\pi$
$593$			11.0235i			0.452682i	−0.974048	+	0.226341i	$0.927324\pi$
$594$	−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	−0.731481	−	0.681862i	$-0.761171\pi$
$599$	−1.21441	+	1.21441i	−0.0496196	+	0.0496196i	0.681862	+	0.731481i	$0.261171\pi$
$600$	42.6880	+	17.4309i	1.74273	+	0.711612i
$601$	−28.6674	−	28.6674i	−1.16937	−	1.16937i	−0.982358	−	0.187010i	$-0.940120\pi$
$601$	−28.6674	−	28.6674i	−1.16937	−	1.16937i	−0.187010	−	0.982358i	$-0.559880\pi$
$602$	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	−0.781087	−	0.624422i	$-0.785334\pi$
$613$	5.26764	−	12.7172i	0.212758	−	0.513644i	0.993845	+	0.110779i	$0.0353345\pi$
$614$	−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	−0.00672483	+	0.999977i	$0.502141\pi$
$617$	−25.0060	+	25.0060i	−1.00670	+	1.00670i	−0.999977	+	0.00672483i	$0.997859\pi$
$618$	42.6709	−	32.8564i	1.71648	−	1.32168i
$619$	−14.5881	−	6.04260i	−0.586346	−	0.242873i	0.0697316	−	0.997566i	$-0.477786\pi$
$619$	−14.5881	−	6.04260i	−0.586346	−	0.242873i	−0.656078	+	0.754693i	$0.727786\pi$
$620$	−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	−0.985730	−	0.168334i	$-0.946161\pi$
$631$	−20.5327	+	20.5327i	−0.817396	+	0.817396i	0.168334	+	0.985730i	$0.446161\pi$
$632$	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	−0.166294	−	0.986076i	$-0.553180\pi$
$643$	10.4823	−	4.34189i	0.413380	−	0.171227i	0.579674	+	0.814849i	$0.303180\pi$
$644$	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	0.936165	−	0.351560i	$-0.114349\pi$
$647$	14.8701	+	14.8701i	0.584605	+	0.584605i	−0.351560	+	0.936165i	$0.614349\pi$
$648$	−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	0.995949	+	0.0899154i	$0.0286597\pi$
$653$	9.07895	+	21.9185i	0.355287	+	0.857738i	−0.640663	+	0.767822i	$0.721340\pi$
$654$	−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	0.816638	−	0.577150i	$-0.195835\pi$
$659$	−4.33631	−	10.4688i	−0.168919	−	0.407806i	−0.985557	+	0.169344i	$0.945835\pi$
$660$	4.42146	−	0.597188i	0.172105	−	0.0232455i
$661$	−27.7462	−	11.4929i	−1.07920	−	0.447020i	−0.228973	−	0.973433i	$-0.573537\pi$
$661$	−27.7462	−	11.4929i	−1.07920	−	0.447020i	−0.850229	+	0.526412i	$0.823537\pi$
$662$	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	−0.630355	−	0.776307i	$-0.717090\pi$
$677$	9.47895	−	22.8842i	0.364306	−	0.879512i	0.994660	−	0.103204i	$-0.0329095\pi$
$678$	−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	0.724104	−	0.689691i	$-0.242254\pi$
$683$	19.5599	+	8.10196i	0.748437	+	0.310013i	0.0243334	+	0.999704i	$0.492254\pi$
$684$	−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	0.827244	+	0.561843i	$0.189908\pi$
$691$	16.8125	+	40.5889i	0.639577	+	1.54408i	−0.187666	+	0.982233i	$0.560092\pi$
$692$	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	0.338121	−	0.941103i	$-0.390209\pi$
$701$	32.9014	−	13.6282i	1.24267	−	0.514730i	0.904548	+	0.426373i	$0.140209\pi$
$702$	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	−0.999407	−	0.0344454i	$-0.989034\pi$
$709$	−7.14571	+	17.2513i	−0.268363	+	0.647885i	0.731044	+	0.682331i	$0.239034\pi$
$710$	−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	$-0.753194\pi$
$719$		−	37.5386i		−	1.39995i	0.714166	−	0.699977i	$-0.246806\pi$
$720$	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	−0.791273	−	0.611463i	$-0.790581\pi$
$727$	−4.84821	+	4.84821i	−0.179810	+	0.179810i	0.611463	+	0.791273i	$0.290581\pi$
$728$	−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	−0.517172	−	0.855882i	$-0.673015\pi$
$733$	−7.51757	+	3.11388i	−0.277668	+	0.115014i	0.239504	+	0.970895i	$0.423015\pi$
$734$	−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	−0.918820	−	0.394678i	$-0.870856\pi$
$739$	−35.0529	+	14.5194i	−1.28944	+	0.534105i	−0.370624	+	0.928783i	$0.620856\pi$
$740$	−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	0.0301185	−	0.999546i	$-0.490412\pi$
$743$	−26.4247	−	26.4247i	−0.969428	−	0.969428i	−0.999546	+	0.0301185i	$0.990412\pi$
$744$	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	$-0.957932\pi$
$751$		−	7.22251i		−	0.263553i	0.991279	−	0.131777i	$-0.0420681\pi$
$752$	−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	−0.585924	−	0.810366i	$-0.699268\pi$
$757$	−43.2858	−	17.9296i	−1.57325	−	0.651662i	−0.987326	+	0.158704i	$0.949268\pi$
$758$	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	0.855171	−	0.518347i	$-0.173452\pi$
$761$	9.29170	+	9.29170i	0.336824	+	0.336824i	−0.518347	+	0.855171i	$0.673452\pi$
$762$	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	$0.539587\pi$

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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