LMFDB - Embedded newform 98.2.e.b.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(15,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("98.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.e (of order $7$, degree $6$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + \cdots + 5103 $ x^18 + 37x^16 + 557x^14 + 4495x^12 + 21331x^10 + 60904x^8 + 101893x^6 + 91665x^4 + 36855x^2 + 5103
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.3
Root			$-0.691444i$ of defining polynomial
Character	$\chi$	$=$	98.43
Dual form			98.2.e.b.57.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 + 0.781831i) q^{2} +(1.93237 + 0.930578i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.21470 + 0.584969i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(-2.20984 - 1.45485i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.997592 + 1.25094i) q^{9} +O(q^{10})$	\(q+(-0.623490 + 0.781831i) q^{2} +(1.93237 + 0.930578i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.21470 + 0.584969i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(-2.20984 - 1.45485i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.997592 + 1.25094i) q^{9} +(-1.21470 + 0.584969i) q^{10} +(0.840599 - 1.05408i) q^{11} +(0.477255 - 2.09099i) q^{12} +(-3.94258 + 4.94384i) q^{13} +(2.51526 - 0.820642i) q^{14} +(1.80289 + 2.26075i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.988153 - 4.32938i) q^{17} -1.60001 q^{18} +1.39174 q^{19} +(0.300006 - 1.31441i) q^{20} +(-2.91638 - 4.86773i) q^{21} +(0.300006 + 1.31441i) q^{22} +(-1.24953 - 5.47455i) q^{23} +(1.33724 + 1.67684i) q^{24} +(-1.98414 - 2.48803i) q^{25} +(-1.40709 - 6.16487i) q^{26} +(-0.668151 - 2.92736i) q^{27} +(-0.926636 + 2.47817i) q^{28} +(-1.36054 + 5.96092i) q^{29} -2.89161 q^{30} +4.88865 q^{31} +(0.222521 - 0.974928i) q^{32} +(2.60525 - 1.25462i) q^{33} +(2.76874 + 3.47189i) q^{34} +(-1.83326 - 3.05990i) q^{35} +(0.997592 - 1.25094i) q^{36} +(-0.318780 + 1.39667i) q^{37} +(-0.867738 + 1.08811i) q^{38} +(-12.2191 + 5.88443i) q^{39} +(0.840599 + 1.05408i) q^{40} +(5.29397 + 2.54944i) q^{41} +(5.62408 + 0.754867i) q^{42} +(-7.44405 + 3.58487i) q^{43} +(-1.21470 - 0.584969i) q^{44} +(0.480014 + 2.10308i) q^{45} +(5.05924 + 2.43640i) q^{46} +(2.40436 - 3.01497i) q^{47} -2.14476 q^{48} +(2.76683 + 6.42998i) q^{49} +3.18231 q^{50} +(5.93830 - 7.44639i) q^{51} +(5.69719 + 2.74362i) q^{52} +(2.97310 + 13.0260i) q^{53} +(2.70529 + 1.30280i) q^{54} +(1.63768 - 0.788665i) q^{55} +(-1.35977 - 2.26959i) q^{56} +(2.68936 + 1.29513i) q^{57} +(-3.81215 - 4.78029i) q^{58} +(6.07405 - 2.92511i) q^{59} +(1.80289 - 2.26075i) q^{60} +(-2.30850 + 10.1142i) q^{61} +(-3.04802 + 3.82210i) q^{62} +(-0.384593 - 4.21573i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-7.68105 + 3.69900i) q^{65} +(-0.643443 + 2.81911i) q^{66} -10.3879 q^{67} -4.44072 q^{68} +(2.67995 - 11.7416i) q^{69} +(3.53534 + 0.474516i) q^{70} +(-1.29530 - 5.67509i) q^{71} +(0.356036 + 1.55990i) q^{72} +(-4.79069 - 6.00734i) q^{73} +(-0.893203 - 1.12004i) q^{74} +(-1.51877 - 6.65418i) q^{75} +(-0.309692 - 1.35685i) q^{76} +(-3.39112 + 1.10640i) q^{77} +(3.01788 - 13.2222i) q^{78} -5.78120 q^{79} -1.34822 q^{80} +(2.50113 - 10.9582i) q^{81} +(-5.29397 + 2.54944i) q^{82} +(4.84202 + 6.07170i) q^{83} +(-4.09673 + 3.92643i) q^{84} +(3.73287 - 4.68086i) q^{85} +(1.83853 - 8.05512i) q^{86} +(-8.17617 + 10.2526i) q^{87} +(1.21470 - 0.584969i) q^{88} +(6.48525 + 8.13225i) q^{89} +(-1.94354 - 0.935958i) q^{90} +(15.9050 - 5.18926i) q^{91} +(-5.05924 + 2.43640i) q^{92} +(9.44665 + 4.54927i) q^{93} +(0.858105 + 3.75960i) q^{94} +(1.69055 + 0.814127i) q^{95} +(1.33724 - 1.67684i) q^{96} +3.70350 q^{97} +(-6.75225 - 1.84584i) q^{98} +2.15716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9} + 7 q^{11} + 2 q^{12} - 10 q^{13} + q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 32 q^{18} - 44 q^{19} + 7 q^{20} - 5 q^{21} + 7 q^{22} + 21 q^{23} - 2 q^{24} + q^{25} + 3 q^{26} + 10 q^{27} - 8 q^{28} + 11 q^{29} - 24 q^{31} + 3 q^{32} - 14 q^{33} - q^{34} - 21 q^{35} - 10 q^{36} - 13 q^{37} - 19 q^{38} - 3 q^{39} + 7 q^{40} + 8 q^{41} + 61 q^{42} - 24 q^{43} + 98 q^{45} + 21 q^{46} + 40 q^{47} + 2 q^{48} - 43 q^{49} - 50 q^{50} + 36 q^{51} + 18 q^{52} + 10 q^{53} + 4 q^{54} + 49 q^{55} + q^{56} + 19 q^{57} + 24 q^{58} + 13 q^{59} + 7 q^{60} + 27 q^{61} - 11 q^{62} + 41 q^{63} - 3 q^{64} - 21 q^{66} - 86 q^{67} - 34 q^{68} - 91 q^{69} - 14 q^{70} + 3 q^{72} + 5 q^{73} + 13 q^{74} - 3 q^{75} - 2 q^{76} - 14 q^{77} + 38 q^{78} - 66 q^{79} - 2 q^{81} - 8 q^{82} + 55 q^{83} + 23 q^{84} - 49 q^{85} - 18 q^{86} - 110 q^{87} + 62 q^{89} + 21 q^{90} + 39 q^{91} - 21 q^{92} + 46 q^{93} + 23 q^{94} - 7 q^{95} - 2 q^{96} - 32 q^{97} - 48 q^{98} + 14 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9 + 7 * q^11 + 2 * q^12 - 10 * q^13 + q^14 + 7 * q^15 - 3 * q^16 + q^17 - 32 * q^18 - 44 * q^19 + 7 * q^20 - 5 * q^21 + 7 * q^22 + 21 * q^23 - 2 * q^24 + q^25 + 3 * q^26 + 10 * q^27 - 8 * q^28 + 11 * q^29 - 24 * q^31 + 3 * q^32 - 14 * q^33 - q^34 - 21 * q^35 - 10 * q^36 - 13 * q^37 - 19 * q^38 - 3 * q^39 + 7 * q^40 + 8 * q^41 + 61 * q^42 - 24 * q^43 + 98 * q^45 + 21 * q^46 + 40 * q^47 + 2 * q^48 - 43 * q^49 - 50 * q^50 + 36 * q^51 + 18 * q^52 + 10 * q^53 + 4 * q^54 + 49 * q^55 + q^56 + 19 * q^57 + 24 * q^58 + 13 * q^59 + 7 * q^60 + 27 * q^61 - 11 * q^62 + 41 * q^63 - 3 * q^64 - 21 * q^66 - 86 * q^67 - 34 * q^68 - 91 * q^69 - 14 * q^70 + 3 * q^72 + 5 * q^73 + 13 * q^74 - 3 * q^75 - 2 * q^76 - 14 * q^77 + 38 * q^78 - 66 * q^79 - 2 * q^81 - 8 * q^82 + 55 * q^83 + 23 * q^84 - 49 * q^85 - 18 * q^86 - 110 * q^87 + 62 * q^89 + 21 * q^90 + 39 * q^91 - 21 * q^92 + 46 * q^93 + 23 * q^94 - 7 * q^95 - 2 * q^96 - 32 * q^97 - 48 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

Coefficient data

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

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

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

$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$2$	−0.623490	+	0.781831i	−0.440874	+	0.552838i
$3$	1.93237	+	0.930578i	1.11565	+	0.537270i	0.898546	−	0.438879i	$-0.144624\pi$
$3$	1.93237	+	0.930578i	1.11565	+	0.537270i	0.217105	+	0.976148i	$0.430338\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	1.21470	+	0.584969i	0.543231	+	0.261606i	0.685313	−	0.728249i	$-0.259665\pi$
$5$	1.21470	+	0.584969i	0.543231	+	0.261606i	−0.142082	+	0.989855i	$0.545380\pi$
$6$	−1.93237	+	0.930578i	−0.788885	+	0.379907i
$7$	−2.20984	−	1.45485i	−0.835243	−	0.549881i
$7$	−2.20984	−	1.45485i	−0.835243	−	0.549881i
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	0.997592	+	1.25094i	0.332531	+	0.416980i
$10$	−1.21470	+	0.584969i	−0.384122	+	0.184984i
$11$	0.840599	−	1.05408i	0.253450	−	0.317816i	−0.638787	−	0.769384i	$-0.720563\pi$
$11$	0.840599	−	1.05408i	0.253450	−	0.317816i	0.892237	+	0.451567i	$0.149135\pi$
$12$	0.477255	−	2.09099i	0.137772	−	0.603617i
$13$	−3.94258	+	4.94384i	−1.09347	+	1.37117i	−0.170931	+	0.985283i	$0.554677\pi$
$13$	−3.94258	+	4.94384i	−1.09347	+	1.37117i	−0.922544	+	0.385891i	$0.873894\pi$
$14$	2.51526	−	0.820642i	0.672232	−	0.219326i
$15$	1.80289	+	2.26075i	0.465503	+	0.583723i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.988153	−	4.32938i	0.239662	−	1.05003i	−0.701658	−	0.712514i	$-0.747556\pi$
$17$	0.988153	−	4.32938i	0.239662	−	1.05003i	0.941320	−	0.337515i	$-0.109586\pi$
$18$	−1.60001			−0.377127
$19$	1.39174			0.319288			0.159644	−	0.987175i	$-0.448965\pi$
$19$	1.39174			0.319288			0.159644	+	0.987175i	$0.448965\pi$
$20$	0.300006	−	1.31441i	0.0670835	−	0.293912i
$21$	−2.91638	−	4.86773i	−0.636406	−	1.06223i
$22$	0.300006	+	1.31441i	0.0639616	+	0.280234i
$23$	−1.24953	−	5.47455i	−0.260545	−	1.14152i	−0.920663	−	0.390359i	$-0.872351\pi$
$23$	−1.24953	−	5.47455i	−0.260545	−	1.14152i	0.660118	−	0.751162i	$-0.270506\pi$
$24$	1.33724	+	1.67684i	0.272963	+	0.342284i
$25$	−1.98414	−	2.48803i	−0.396828	−	0.497606i
$26$	−1.40709	−	6.16487i	−0.275953	−	1.20903i
$27$	−0.668151	−	2.92736i	−0.128586	−	0.563371i
$28$	−0.926636	+	2.47817i	−0.175118	+	0.468331i
$29$	−1.36054	+	5.96092i	−0.252646	+	1.10692i	0.676278	+	0.736646i	$0.263592\pi$
$29$	−1.36054	+	5.96092i	−0.252646	+	1.10692i	−0.928925	+	0.370269i	$0.879265\pi$
$30$	−2.89161			−0.527933
$31$	4.88865			0.878027			0.439013	−	0.898481i	$-0.355328\pi$
$31$	4.88865			0.878027			0.439013	+	0.898481i	$0.355328\pi$
$32$	0.222521	−	0.974928i	0.0393365	−	0.172345i
$33$	2.60525	−	1.25462i	0.453515	−	0.218401i
$34$	2.76874	+	3.47189i	0.474836	+	0.595425i
$35$	−1.83326	−	3.05990i	−0.309877	−	0.517217i
$36$	0.997592	−	1.25094i	0.166265	−	0.208490i
$37$	−0.318780	+	1.39667i	−0.0524072	+	0.229611i	−0.994348	−	0.106167i	$-0.966142\pi$
$37$	−0.318780	+	1.39667i	−0.0524072	+	0.229611i	0.941941	+	0.335778i	$0.108999\pi$
$38$	−0.867738	+	1.08811i	−0.140766	+	0.176515i
$39$	−12.2191	+	5.88443i	−1.95663	+	0.942262i
$40$	0.840599	+	1.05408i	0.132910	+	0.166664i
$41$	5.29397	+	2.54944i	0.826779	+	0.398156i	0.798906	−	0.601456i	$-0.205412\pi$
$41$	5.29397	+	2.54944i	0.826779	+	0.398156i	0.0278726	+	0.999611i	$0.491127\pi$
$42$	5.62408	+	0.754867i	0.867814	+	0.116479i
$43$	−7.44405	+	3.58487i	−1.13521	+	0.546687i	−0.904558	−	0.426350i	$-0.859799\pi$
$43$	−7.44405	+	3.58487i	−1.13521	+	0.546687i	−0.230649	+	0.973037i	$0.574085\pi$
$44$	−1.21470	−	0.584969i	−0.183123	−	0.0881874i
$45$	0.480014	+	2.10308i	0.0715563	+	0.313508i
$46$	5.05924	+	2.43640i	0.745944	+	0.359228i
$47$	2.40436	−	3.01497i	0.350711	−	0.439778i	−0.574917	−	0.818212i	$-0.694966\pi$
$47$	2.40436	−	3.01497i	0.350711	−	0.439778i	0.925628	+	0.378433i	$0.123537\pi$
$48$	−2.14476			−0.309570
$49$	2.76683	+	6.42998i	0.395261	+	0.918569i
$50$	3.18231			0.450047
$51$	5.93830	−	7.44639i	0.831528	−	1.04270i
$52$	5.69719	+	2.74362i	0.790059	+	0.380472i
$53$	2.97310	+	13.0260i	0.408386	+	1.78926i	0.591651	+	0.806194i	$0.298476\pi$
$53$	2.97310	+	13.0260i	0.408386	+	1.78926i	−0.183265	+	0.983064i	$0.558667\pi$
$54$	2.70529	+	1.30280i	0.368143	+	0.177288i
$55$	1.63768	−	0.788665i	0.220825	−	0.106344i
$56$	−1.35977	−	2.26959i	−0.181706	−	0.303287i
$57$	2.68936	+	1.29513i	0.356214	+	0.171544i
$58$	−3.81215	−	4.78029i	−0.500560	−	0.627683i
$59$	6.07405	−	2.92511i	0.790773	−	0.380816i	0.00551511	−	0.999985i	$-0.498244\pi$
$59$	6.07405	−	2.92511i	0.790773	−	0.380816i	0.785258	+	0.619168i	$0.212530\pi$
$60$	1.80289	−	2.26075i	0.232752	−	0.291861i
$61$	−2.30850	+	10.1142i	−0.295572	+	1.29499i	0.581073	+	0.813851i	$0.302633\pi$
$61$	−2.30850	+	10.1142i	−0.295572	+	1.29499i	−0.876646	+	0.481136i	$0.840224\pi$
$62$	−3.04802	+	3.82210i	−0.387099	+	0.485407i
$63$	−0.384593	−	4.21573i	−0.0484542	−	0.531132i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−7.68105	+	3.69900i	−0.952717	+	0.458804i
$66$	−0.643443	+	2.81911i	−0.0792023	+	0.347008i
$67$	−10.3879			−1.26908			−0.634539	−	0.772891i	$-0.718810\pi$
$67$	−10.3879			−1.26908			−0.634539	+	0.772891i	$0.718810\pi$
$68$	−4.44072			−0.538516
$69$	2.67995	−	11.7416i	0.322628	−	1.41352i
$70$	3.53534	+	0.474516i	0.422554	+	0.0567155i
$71$	−1.29530	−	5.67509i	−0.153724	−	0.673509i	−0.991783	−	0.127930i	$-0.959167\pi$
$71$	−1.29530	−	5.67509i	−0.153724	−	0.673509i	0.838059	−	0.545579i	$-0.183690\pi$
$72$	0.356036	+	1.55990i	0.0419593	+	0.183836i
$73$	−4.79069	−	6.00734i	−0.560708	−	0.703105i	0.417981	−	0.908456i	$-0.362738\pi$
$73$	−4.79069	−	6.00734i	−0.560708	−	0.703105i	−0.978688	+	0.205351i	$0.934167\pi$
$74$	−0.893203	−	1.12004i	−0.103833	−	0.130202i
$75$	−1.51877	−	6.65418i	−0.175373	−	0.768359i
$76$	−0.309692	−	1.35685i	−0.0355241	−	0.155641i
$77$	−3.39112	+	1.10640i	−0.386454	+	0.126086i
$78$	3.01788	−	13.2222i	0.341707	−	1.49712i
$79$	−5.78120			−0.650436			−0.325218	−	0.945639i	$-0.605438\pi$
$79$	−5.78120			−0.650436			−0.325218	+	0.945639i	$0.605438\pi$
$80$	−1.34822			−0.150735
$81$	2.50113	−	10.9582i	0.277904	−	1.21758i
$82$	−5.29397	+	2.54944i	−0.584621	+	0.281539i
$83$	4.84202	+	6.07170i	0.531480	+	0.666455i	0.973002	−	0.230795i	$-0.0741327\pi$
$83$	4.84202	+	6.07170i	0.531480	+	0.666455i	−0.441522	+	0.897250i	$0.645561\pi$
$84$	−4.09673	+	3.92643i	−0.446990	+	0.428409i
$85$	3.73287	−	4.68086i	0.404886	−	0.507711i
$86$	1.83853	−	8.05512i	0.198254	−	0.868606i
$87$	−8.17617	+	10.2526i	−0.876577	+	1.09919i
$88$	1.21470	−	0.584969i	0.129488	−	0.0623579i
$89$	6.48525	+	8.13225i	0.687436	+	0.862017i	0.996015	−	0.0891815i	$-0.0284251\pi$
$89$	6.48525	+	8.13225i	0.687436	+	0.862017i	−0.308580	+	0.951198i	$0.599854\pi$
$90$	−1.94354	−	0.935958i	−0.204867	−	0.0986587i
$91$	15.9050	−	5.18926i	1.66730	−	0.543982i
$92$	−5.05924	+	2.43640i	−0.527462	+	0.254012i
$93$	9.44665	+	4.54927i	0.979572	+	0.471737i
$94$	0.858105	+	3.75960i	0.0885068	+	0.387773i
$95$	1.69055	+	0.814127i	0.173447	+	0.0835277i
$96$	1.33724	−	1.67684i	0.136481	−	0.171142i
$97$	3.70350			0.376033			0.188017	−	0.982166i	$-0.439794\pi$
$97$	3.70350			0.376033			0.188017	+	0.982166i	$0.439794\pi$
$98$	−6.75225	−	1.84584i	−0.682080	−	0.186458i
$99$	2.15716			0.216803
$100$	−1.98414	+	2.48803i	−0.198414	+	0.248803i
$101$	−12.9698	−	6.24594i	−1.29055	−	0.621495i	−0.342468	−	0.939530i	$-0.611263\pi$
$101$	−12.9698	−	6.24594i	−1.29055	−	0.621495i	−0.948079	+	0.318035i	$0.896977\pi$
$102$	2.11936	+	9.28550i	0.209847	+	0.919402i
$103$	−1.50907	−	0.726731i	−0.148693	−	0.0716069i	0.358057	−	0.933700i	$-0.383439\pi$
$103$	−1.50907	−	0.726731i	−0.148693	−	0.0716069i	−0.506751	+	0.862093i	$0.669154\pi$
$104$	−5.69719	+	2.74362i	−0.558656	+	0.269034i
$105$	−0.695051	−	7.61883i	−0.0678301	−	0.743522i
$106$	−12.0378	−	5.79711i	−1.16922	−	0.563065i
$107$	9.00966	+	11.2978i	0.870997	+	1.09220i	0.994996	+	0.0999131i	$0.0318565\pi$
$107$	9.00966	+	11.2978i	0.870997	+	1.09220i	−0.123999	+	0.992282i	$0.539572\pi$
$108$	−2.70529	+	1.30280i	−0.260316	+	0.125362i
$109$	11.5675	−	14.5052i	1.10796	−	1.38934i	0.195246	−	0.980754i	$-0.437450\pi$
$109$	11.5675	−	14.5052i	1.10796	−	1.38934i	0.912719	−	0.408589i	$-0.133979\pi$
$110$	−0.404474	+	1.77211i	−0.0385650	+	0.168964i
$111$	−1.91571	+	2.40222i	−0.181831	+	0.228009i
$112$	2.62224	+	0.351958i	0.247778	+	0.0332569i
$113$	−0.715156	−	0.896778i	−0.0672763	−	0.0843618i	0.747055	−	0.664763i	$-0.231467\pi$
$113$	−0.715156	−	0.896778i	−0.0672763	−	0.0843618i	−0.814331	+	0.580401i	$0.802896\pi$
$114$	−2.68936	+	1.29513i	−0.251881	+	0.121300i
$115$	1.68464	−	7.38087i	0.157093	−	0.688270i
$116$	6.11422			0.567691
$117$	−10.1175			−0.935366
$118$	−1.50017	+	6.57265i	−0.138101	+	0.605062i
$119$	−8.48226	+	8.12965i	−0.777568	+	0.745243i
$120$	0.643443	+	2.81911i	0.0587380	+	0.257348i
$121$	2.04326	+	8.95209i	0.185751	+	0.813827i
$122$	−6.46826	−	8.11094i	−0.585609	−	0.734330i
$123$	7.85743	+	9.85290i	0.708480	+	0.888406i
$124$	−1.08783	−	4.76608i	−0.0976896	−	0.428006i
$125$	−2.45475	−	10.7549i	−0.219559	−	0.961952i
$126$	3.53578	+	2.32778i	0.314992	+	0.207375i
$127$	−2.98988	+	13.0995i	−0.265309	+	1.16240i	0.650093	+	0.759855i	$0.274730\pi$
$127$	−2.98988	+	13.0995i	−0.265309	+	1.16240i	−0.915402	+	0.402541i	$0.868127\pi$
$128$	−1.00000			−0.0883883
$129$	−17.7206			−1.56021
$130$	1.89706	−	8.31157i	0.166383	−	0.728973i
$131$	13.8012	−	6.64631i	1.20582	−	0.580691i	0.280489	−	0.959857i	$-0.409504\pi$
$131$	13.8012	−	6.64631i	1.20582	−	0.580691i	0.925328	+	0.379167i	$0.123789\pi$
$132$	−1.80289	−	2.26075i	−0.156921	−	0.196773i
$133$	−3.07554	−	2.02478i	−0.266683	−	0.175570i
$134$	6.47672	−	8.12155i	0.559504	−	0.701595i
$135$	0.900812	−	3.94671i	0.0775295	−	0.339679i
$136$	2.76874	−	3.47189i	0.237418	−	0.297712i
$137$	−1.57604	+	0.758980i	−0.134650	+	0.0648440i	−0.499996	−	0.866028i	$-0.666665\pi$
$137$	−1.57604	+	0.758980i	−0.134650	+	0.0648440i	0.365346	+	0.930872i	$0.380951\pi$
$138$	7.50904	+	9.41604i	0.639212	+	0.801546i
$139$	1.54942	+	0.746161i	0.131420	+	0.0632885i	0.498438	−	0.866925i	$-0.333907\pi$
$139$	1.54942	+	0.746161i	0.131420	+	0.0632885i	−0.367018	+	0.930214i	$0.619621\pi$
$140$	−2.57524	+	2.46819i	−0.217648	+	0.208600i
$141$	7.45176	−	3.58858i	0.627551	−	0.302213i
$142$	5.24457	+	2.52565i	0.440115	+	0.211948i
$143$	1.89706	+	8.31157i	0.158640	+	0.695049i
$144$	−1.44156	−	0.694220i	−0.120130	−	0.0578516i
$145$	−5.13961	+	6.44486i	−0.426821	+	0.535217i
$146$	7.68367			0.635905
$147$	−0.637080	+	14.9998i	−0.0525454	+	1.23716i
$148$	1.43259			0.117758
$149$	−3.55462	+	4.45735i	−0.291206	+	0.365161i	−0.905817	−	0.423670i	$-0.860742\pi$
$149$	−3.55462	+	4.45735i	−0.291206	+	0.365161i	0.614611	+	0.788830i	$0.289313\pi$
$150$	6.14939	+	2.96139i	0.502096	+	0.241797i
$151$	−4.26030	−	18.6656i	−0.346698	−	1.51898i	−0.784623	−	0.619973i	$-0.787144\pi$
$151$	−4.26030	−	18.6656i	−0.346698	−	1.51898i	0.437925	−	0.899012i	$-0.355714\pi$
$152$	1.25392	+	0.603855i	0.101706	+	0.0489791i
$153$	6.40157	−	3.08283i	0.517536	−	0.249232i
$154$	1.24931	−	3.34111i	0.100672	−	0.269235i
$155$	5.93824	+	2.85971i	0.476971	+	0.229697i
$156$	8.45590	+	10.6034i	0.677014	+	0.848949i
$157$	8.48490	−	4.08611i	0.677169	−	0.326107i	−0.0634958	−	0.997982i	$-0.520225\pi$
$157$	8.48490	−	4.08611i	0.677169	−	0.326107i	0.740665	+	0.671875i	$0.234511\pi$
$158$	3.60452	−	4.51992i	0.286760	−	0.359586i
$159$	−6.37659	+	27.9377i	−0.505697	+	2.21560i
$160$	0.840599	−	1.05408i	0.0664552	−	0.0833322i
$161$	−5.20337	+	13.9158i	−0.410083	+	1.09672i
$162$	7.00802	+	8.78778i	0.550602	+	0.690434i
$163$	5.78590	−	2.78634i	0.453187	−	0.218243i	−0.193344	−	0.981131i	$-0.561933\pi$
$163$	5.78590	−	2.78634i	0.453187	−	0.218243i	0.646531	+	0.762888i	$0.276219\pi$
$164$	1.30750	−	5.72854i	0.102099	−	0.447324i
$165$	3.89851			0.303499
$166$	−7.76599			−0.602758
$167$	2.52705	−	11.0717i	0.195549	−	0.856755i	−0.777998	−	0.628267i	$-0.783765\pi$
$167$	2.52705	−	11.0717i	0.195549	−	0.856755i	0.973547	−	0.228488i	$-0.0733782\pi$
$168$	−0.515534	−	5.65105i	−0.0397743	−	0.435988i
$169$	−6.00483	−	26.3089i	−0.461910	−	2.02376i
$170$	1.33224	+	5.83694i	0.102178	+	0.447673i
$171$	1.38839	+	1.74099i	0.106173	+	0.133137i
$172$	5.15145	+	6.45971i	0.392794	+	0.492548i
$173$	−3.47023	−	15.2041i	−0.263837	−	1.15594i	−0.917050	−	0.398771i	$-0.869437\pi$
$173$	−3.47023	−	15.2041i	−0.263837	−	1.15594i	0.653214	−	0.757174i	$-0.273420\pi$
$174$	−2.91804	−	12.7848i	−0.221216	−	0.969211i
$175$	0.764928	+	8.38479i	0.0578231	+	0.633830i
$176$	−0.300006	+	1.31441i	−0.0226138	+	0.0990777i
$177$	14.4593			1.08683
$178$	−10.4015			−0.779628
$179$	−1.26060	+	5.52304i	−0.0942215	+	0.412811i	−0.999939	−	0.0110711i	$-0.996476\pi$
$179$	−1.26060	+	5.52304i	−0.0942215	+	0.412811i	0.905717	+	0.423882i	$0.139333\pi$
$180$	1.94354	−	0.935958i	0.144863	−	0.0697622i
$181$	−3.98556	−	4.99774i	−0.296245	−	0.371479i	0.611326	−	0.791379i	$-0.290637\pi$
$181$	−3.98556	−	4.99774i	−0.296245	−	0.371479i	−0.907570	+	0.419900i	$0.862065\pi$
$182$	−5.85950	+	15.6705i	−0.434335	+	1.16157i
$183$	−13.8729	+	17.3961i	−1.02551	+	1.28595i
$184$	1.24953	−	5.47455i	0.0921165	−	0.403589i
$185$	−1.20423	+	1.51006i	−0.0885368	+	0.111022i
$186$	−9.44665	+	4.54927i	−0.692662	+	0.333568i
$187$	−3.73287	−	4.68086i	−0.272974	−	0.342299i
$188$	−3.47440	−	1.67318i	−0.253396	−	0.122029i
$189$	−2.78236	+	7.44107i	−0.202387	+	0.541258i
$190$	−1.69055	+	0.814127i	−0.122646	+	0.0590630i
$191$	−13.0416	−	6.28050i	−0.943657	−	0.454441i	−0.102199	−	0.994764i	$-0.532588\pi$
$191$	−13.0416	−	6.28050i	−0.943657	−	0.454441i	−0.841458	+	0.540323i	$0.818302\pi$
$192$	0.477255	+	2.09099i	0.0344429	+	0.150904i
$193$	3.53355	+	1.70167i	0.254351	+	0.122489i	0.556715	−	0.830704i	$-0.312062\pi$
$193$	3.53355	+	1.70167i	0.254351	+	0.122489i	−0.302364	+	0.953192i	$0.597776\pi$
$194$	−2.30909	+	2.89551i	−0.165783	+	0.207886i
$195$	−18.2848			−1.30940
$196$	5.65309	−	4.12826i	0.403792	−	0.294876i
$197$	−9.22994			−0.657606			−0.328803	−	0.944399i	$-0.606645\pi$
$197$	−9.22994			−0.657606			−0.328803	+	0.944399i	$0.606645\pi$
$198$	−1.34497	+	1.68654i	−0.0955828	+	0.119857i
$199$	14.7371	+	7.09699i	1.04468	+	0.503093i	0.875866	−	0.482555i	$-0.160291\pi$
$199$	14.7371	+	7.09699i	1.04468	+	0.503093i	0.168817	+	0.985647i	$0.446005\pi$
$200$	−0.708131	−	3.10253i	−0.0500724	−	0.219382i
$201$	−20.0731	−	9.66671i	−1.41585	−	0.681837i
$202$	12.9698	−	6.24594i	0.912554	−	0.439463i
$203$	11.6788	−	11.1933i	0.819693	−	0.785618i
$204$	−8.58109	−	4.13244i	−0.600797	−	0.289328i
$205$	4.93924	+	6.19361i	0.344972	+	0.432581i
$206$	1.50907	−	0.726731i	0.105142	−	0.0506337i
$207$	5.60181	−	7.02445i	0.389353	−	0.488233i
$208$	1.40709	−	6.16487i	0.0975642	−	0.427457i
$209$	1.16990	−	1.46701i	0.0809236	−	0.101475i
$210$	6.39000	+	4.20685i	0.440952	+	0.290300i
$211$	−14.2940	−	17.9241i	−0.984040	−	1.23395i	−0.972233	−	0.234017i	$-0.924813\pi$
$211$	−14.2940	−	17.9241i	−0.984040	−	1.23395i	−0.0118073	−	0.999930i	$-0.503758\pi$
$212$	12.0378	−	5.79711i	0.826761	−	0.398147i
$213$	2.77812	−	12.1717i	0.190353	−	0.833993i
$214$	−14.4504			−0.987807
$215$	−11.1393			−0.759697
$216$	0.668151	−	2.92736i	0.0454619	−	0.199182i
$217$	−10.8031	−	7.11224i	−0.733365	−	0.482810i
$218$	4.12839	+	18.0877i	0.279610	+	1.22505i
$219$	−3.66707	−	16.0665i	−0.247798	−	1.08567i
$220$	−1.13331	−	1.42113i	−0.0764077	−	0.0958123i
$221$	17.5079	+	21.9542i	1.17771	+	1.47680i
$222$	−0.683709	−	2.99552i	−0.0458875	−	0.201046i
$223$	3.82009	+	16.7369i	0.255812	+	1.12079i	0.925680	+	0.378306i	$0.123493\pi$
$223$	3.82009	+	16.7369i	0.255812	+	1.12079i	−0.669868	+	0.742480i	$0.733649\pi$
$224$	−1.91011	+	1.83070i	−0.127625	+	0.122319i
$225$	1.13302	−	4.96408i	0.0755346	−	0.330939i
$226$	1.14702			0.0762988
$227$	−4.63731			−0.307789			−0.153895	−	0.988087i	$-0.549182\pi$
$227$	−4.63731			−0.307789			−0.153895	+	0.988087i	$0.549182\pi$
$228$	0.664216	−	2.91012i	0.0439888	−	0.192728i
$229$	4.57302	−	2.20225i	0.302194	−	0.145529i	−0.276642	−	0.960973i	$-0.589222\pi$
$229$	4.57302	−	2.20225i	0.302194	−	0.145529i	0.578836	+	0.815444i	$0.303507\pi$
$230$	4.72025	+	5.91900i	0.311244	+	0.390287i
$231$	−7.58248	−	1.01772i	−0.498890	−	0.0669614i
$232$	−3.81215	+	4.78029i	−0.250280	+	0.313841i
$233$	2.39584	−	10.4969i	0.156957	−	0.687674i	−0.833805	−	0.552059i	$-0.813842\pi$
$233$	2.39584	−	10.4969i	0.156957	−	0.687674i	0.990762	−	0.135614i	$-0.0433007\pi$
$234$	6.30818	−	7.91021i	0.412379	−	0.517106i
$235$	4.68424	−	2.25581i	0.305566	−	0.147153i
$236$	−4.20337	−	5.27086i	−0.273616	−	0.343104i
$237$	−11.1714	−	5.37986i	−0.725660	−	0.349459i
$238$	−1.06741	−	11.7005i	−0.0691899	−	0.758428i
$239$	23.8771	−	11.4986i	1.54448	−	0.743784i	0.548743	−	0.835991i	$-0.315107\pi$
$239$	23.8771	−	11.4986i	1.54448	−	0.743784i	0.995740	+	0.0922073i	$0.0293922\pi$
$240$	−2.60525	−	1.25462i	−0.168168	−	0.0809854i
$241$	2.25719	+	9.88941i	0.145399	+	0.637033i	0.994128	+	0.108206i	$0.0345107\pi$
$241$	2.25719	+	9.88941i	0.145399	+	0.637033i	−0.848730	+	0.528827i	$0.822632\pi$
$242$	−8.27298	−	3.98406i	−0.531807	−	0.256105i
$243$	9.41421	−	11.8050i	0.603922	−	0.757294i
$244$	10.3743			0.664145
$245$	−0.400474	+	9.42901i	−0.0255853	+	0.602398i
$246$	−12.6023			−0.803495
$247$	−5.48706	+	6.88056i	−0.349133	+	0.437799i
$248$	4.40452	+	2.12110i	0.279687	+	0.134690i
$249$	3.70636	+	16.2386i	0.234881	+	1.02908i
$250$	9.93906	+	4.78640i	0.628602	+	0.302719i
$251$	−5.07195	+	2.44252i	−0.320138	+	0.154171i	−0.587050	−	0.809550i	$-0.699711\pi$
$251$	−5.07195	+	2.44252i	−0.320138	+	0.154171i	0.266912	+	0.963721i	$0.413997\pi$
$252$	−4.02445	+	1.31304i	−0.253517	+	0.0827136i
$253$	−6.82095	−	3.28480i	−0.428830	−	0.206513i
$254$	−8.37747	−	10.5050i	−0.525649	−	0.659143i
$255$	11.5692	−	5.57142i	0.724490	−	0.348896i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−0.931692	+	4.08201i	−0.0581173	+	0.254629i	−0.995638	−	0.0933010i	$-0.970258\pi$
$257$	−0.931692	+	4.08201i	−0.0581173	+	0.254629i	0.937521	+	0.347930i	$0.113115\pi$
$258$	11.0486	−	13.8546i	0.687858	−	0.862547i
$259$	2.73640	−	2.62264i	0.170031	−	0.162963i
$260$	5.31545	+	6.66536i	0.329650	+	0.413368i
$261$	−8.81402	+	4.24461i	−0.545574	+	0.262735i
$262$	−3.40862	+	14.9341i	−0.210585	+	0.922633i
$263$	−21.0019			−1.29503			−0.647516	−	0.762052i	$-0.724192\pi$
$263$	−21.0019			−1.29503			−0.647516	+	0.762052i	$0.724192\pi$
$264$	2.89161			0.177966
$265$	−4.00838	+	17.5619i	−0.246233	+	1.07882i
$266$	3.50060	−	1.14212i	0.214636	−	0.0700281i
$267$	4.96419	+	21.7495i	0.303803	+	1.33105i
$268$	2.31152	+	10.1274i	0.141198	+	0.618630i
$269$	7.01902	+	8.80157i	0.427957	+	0.536641i	0.948325	−	0.317301i	$-0.102777\pi$
$269$	7.01902	+	8.80157i	0.427957	+	0.536641i	−0.520368	+	0.853942i	$0.674205\pi$
$270$	2.52402	+	3.16502i	0.153607	+	0.192617i
$271$	−1.46018	−	6.39745i	−0.0886993	−	0.388617i	0.911019	−	0.412365i	$-0.135297\pi$
$271$	−1.46018	−	6.39745i	−0.0886993	−	0.388617i	−0.999718	+	0.0237480i	$0.992440\pi$
$272$	0.988153	+	4.32938i	0.0599156	+	0.262507i
$273$	35.5633	+	4.77333i	2.15239	+	0.288895i
$274$	0.389249	−	1.70541i	0.0235154	−	0.103028i
$275$	−4.29045			−0.258724
$276$	−12.0436			−0.724937
$277$	5.45364	−	23.8940i	0.327677	−	1.43565i	−0.495868	−	0.868398i	$-0.665150\pi$
$277$	5.45364	−	23.8940i	0.327677	−	1.43565i	0.823545	−	0.567250i	$-0.191993\pi$
$278$	−1.54942	+	0.746161i	−0.0929280	+	0.0447518i
$279$	4.87687	+	6.11540i	0.291971	+	0.366120i
$280$	−0.324069	−	3.55229i	−0.0193668	−	0.212290i
$281$	2.25301	−	2.82518i	0.134403	−	0.168536i	−0.710075	−	0.704126i	$-0.751339\pi$
$281$	2.25301	−	2.82518i	0.134403	−	0.168536i	0.844478	+	0.535589i	$0.179911\pi$
$282$	−1.84043	+	8.06346i	−0.109596	+	0.480172i
$283$	−8.89801	+	11.1578i	−0.528932	+	0.663260i	−0.972479	−	0.232992i	$-0.925149\pi$
$283$	−8.89801	+	11.1578i	−0.528932	+	0.663260i	0.443547	+	0.896251i	$0.353720\pi$
$284$	−5.24457	+	2.52565i	−0.311208	+	0.149870i
$285$	2.50916	+	3.14638i	0.148630	+	0.186376i
$286$	−7.68105	−	3.69900i	−0.454190	−	0.218726i
$287$	−7.98979	−	13.3358i	−0.471623	−	0.787187i
$288$	1.44156	−	0.694220i	0.0849448	−	0.0409073i
$289$	−2.45062	−	1.18016i	−0.144154	−	0.0694211i
$290$	−1.83430	−	8.03661i	−0.107714	−	0.471926i
$291$	7.15651	+	3.44640i	0.419522	+	0.202031i
$292$	−4.79069	+	6.00734i	−0.280354	+	0.351553i
$293$	12.5071			0.730675			0.365338	−	0.930875i	$-0.380954\pi$
$293$	12.5071			0.730675			0.365338	+	0.930875i	$0.380954\pi$
$294$	−11.3301	−	9.85033i	−0.660786	−	0.574483i
$295$	9.08925			0.529196
$296$	−0.893203	+	1.12004i	−0.0519164	+	0.0651011i
$297$	−3.64731	−	1.75645i	−0.211639	−	0.101920i
$298$	−1.26863	−	5.55823i	−0.0734897	−	0.321979i
$299$	31.9916	+	15.4064i	1.85012	+	0.890973i
$300$	−6.14939	+	2.96139i	−0.355035	+	0.170976i
$301$	21.6656	+	2.90798i	1.24879	+	0.167613i
$302$	17.2496	+	8.30697i	0.992603	+	0.478012i
$303$	−19.2501	−	24.1389i	−1.10589	−	1.38674i
$304$	−1.25392	+	0.603855i	−0.0719171	+	0.0346335i
$305$	−8.72061	+	10.9353i	−0.499341	+	0.626154i
$306$	−1.58106	+	6.92707i	−0.0903830	+	0.395994i
$307$	−13.5861	+	17.0364i	−0.775400	+	0.972321i	−0.999998	−	0.00213071i	$-0.999322\pi$
$307$	−13.5861	+	17.0364i	−0.775400	+	0.972321i	0.224598	+	0.974452i	$0.427893\pi$
$308$	1.83326	+	3.05990i	0.104460	+	0.174354i
$309$	−2.23980	−	2.80862i	−0.127418	−	0.159777i
$310$	−5.93824	+	2.85971i	−0.337270	+	0.162420i
$311$	−1.42989	+	6.26476i	−0.0810816	+	0.355242i	−0.999152	−	0.0411758i	$-0.986890\pi$
$311$	−1.42989	+	6.26476i	−0.0810816	+	0.355242i	0.918070	+	0.396418i	$0.129747\pi$
$312$	−13.5622			−0.767809
$313$	−17.6262			−0.996290			−0.498145	−	0.867094i	$-0.665985\pi$
$313$	−17.6262			−0.996290			−0.498145	+	0.867094i	$0.665985\pi$
$314$	−2.09560	+	9.18142i	−0.118261	+	0.518137i
$315$	1.99891	−	5.34583i	0.112626	−	0.301203i
$316$	1.28644	+	5.63625i	0.0723678	+	0.317064i
$317$	0.481112	+	2.10789i	0.0270219	+	0.118391i	0.986640	−	0.162915i	$-0.0520896\pi$
$317$	0.481112	+	2.10789i	0.0270219	+	0.118391i	−0.959618	+	0.281306i	$0.909232\pi$
$318$	−17.8668	−	22.4043i	−1.00192	−	1.25637i
$319$	5.13961	+	6.44486i	0.287763	+	0.360843i
$320$	0.300006	+	1.31441i	0.0167709	+	0.0734780i
$321$	6.89651	+	30.2156i	0.384926	+	1.68647i
$322$	−7.63554	−	12.7445i	−0.425512	−	0.710223i
$323$	1.37526	−	6.02539i	0.0765213	−	0.335262i
$324$	−11.2400			−0.624444
$325$	20.1231			1.11623
$326$	−1.42900	+	6.26086i	−0.0791450	+	0.346757i
$327$	35.8508	−	17.2648i	1.98255	−	0.954748i
$328$	3.66354	+	4.59393i	0.202285	+	0.253657i
$329$	−9.69958	+	3.16463i	−0.534755	+	0.174472i
$330$	−2.43068	+	3.04798i	−0.133805	+	0.167786i
$331$	−4.18421	+	18.3322i	−0.229985	+	1.00763i	0.719666	+	0.694320i	$0.244295\pi$
$331$	−4.18421	+	18.3322i	−0.229985	+	1.00763i	−0.949651	+	0.313309i	$0.898562\pi$
$332$	4.84202	−	6.07170i	0.265740	−	0.333228i
$333$	−2.06516	+	0.994529i	−0.113170	+	0.0544999i
$334$	7.08063	+	8.87882i	0.387435	+	0.485828i
$335$	−12.6181	−	6.07658i	−0.689403	−	0.331999i
$336$	4.73960	+	3.12031i	0.258566	+	0.170227i
$337$	6.56597	−	3.16200i	0.357671	−	0.172245i	−0.246415	−	0.969164i	$-0.579253\pi$
$337$	6.56597	−	3.16200i	0.357671	−	0.172245i	0.604086	+	0.796919i	$0.293538\pi$
$338$	24.3131	+	11.7086i	1.32246	+	0.636862i
$339$	−0.547422	−	2.39841i	−0.0297319	−	0.130264i
$340$	−5.39415	−	2.59768i	−0.292539	−	0.140879i
$341$	4.10939	−	5.15301i	0.222536	−	0.279051i
$342$	−2.22681			−0.120412
$343$	3.24040	−	18.2346i	0.174965	−	0.984575i
$344$	−8.26228			−0.445472
$345$	10.1238	−	12.6949i	0.545048	−	0.683468i
$346$	14.0507	+	6.76645i	0.755369	+	0.363767i
$347$	−3.32033	−	14.5473i	−0.178245	−	0.780941i	−0.982440	−	0.186576i	$-0.940261\pi$
$347$	−3.32033	−	14.5473i	−0.178245	−	0.780941i	0.804196	−	0.594364i	$-0.202596\pi$
$348$	11.8149	+	5.68976i	0.633345	+	0.305003i
$349$	22.6289	−	10.8975i	1.21130	−	0.583329i	0.284420	−	0.958700i	$-0.408199\pi$
$349$	22.6289	−	10.8975i	1.21130	−	0.583329i	0.926875	+	0.375371i	$0.122485\pi$
$350$	−7.03242	−	4.62978i	−0.375898	−	0.247472i
$351$	17.1066	+	8.23812i	0.913084	+	0.439718i
$352$	−0.840599	−	1.05408i	−0.0448041	−	0.0561825i
$353$	−6.67348	+	3.21378i	−0.355193	+	0.171052i	−0.602968	−	0.797766i	$-0.706015\pi$
$353$	−6.67348	+	3.21378i	−0.355193	+	0.171052i	0.247774	+	0.968818i	$0.420301\pi$
$354$	−9.01524	+	11.3047i	−0.479154	+	0.600841i
$355$	1.74635	−	7.65125i	0.0926865	−	0.406086i
$356$	6.48525	−	8.13225i	0.343718	−	0.431008i
$357$	−23.9561	+	7.81604i	−1.26789	+	0.413669i
$358$	−3.53212	−	4.42913i	−0.186678	−	0.234087i
$359$	−12.5648	+	6.05088i	−0.663143	+	0.319353i	−0.735005	−	0.678062i	$-0.762820\pi$
$359$	−12.5648	+	6.05088i	−0.663143	+	0.319353i	0.0718617	+	0.997415i	$0.477106\pi$
$360$	−0.480014	+	2.10308i	−0.0252990	+	0.110842i
$361$	−17.0630			−0.898055
$362$	6.39235			0.335974
$363$	−4.38230	+	19.2001i	−0.230011	+	1.00775i
$364$	−8.59835	−	14.3515i	−0.450676	−	0.752225i
$365$	−2.30515	−	10.0995i	−0.120657	−	0.528633i
$366$	−4.95118	−	21.6925i	−0.258802	−	1.13389i
$367$	−0.429818	−	0.538974i	−0.0224363	−	0.0281342i	0.770487	−	0.637456i	$-0.220013\pi$
$367$	−0.429818	−	0.538974i	−0.0224363	−	0.0281342i	−0.792923	+	0.609322i	$0.791442\pi$
$368$	3.50110	+	4.39024i	0.182508	+	0.228857i
$369$	2.09202	+	9.16574i	0.108906	+	0.477149i
$370$	−0.429785	−	1.88301i	−0.0223435	−	0.0978931i
$371$	12.3808	−	33.1108i	0.642778	−	1.71903i
$372$	2.33313	−	10.2221i	0.120967	−	0.529992i
$373$	−24.2264			−1.25439			−0.627197	−	0.778860i	$-0.715798\pi$
$373$	−24.2264			−1.25439			−0.627197	+	0.778860i	$0.715798\pi$
$374$	5.98705			0.309583
$375$	5.26485	−	23.0668i	0.271876	−	1.19117i
$376$	3.47440	−	1.67318i	0.179178	−	0.0862877i
$377$	−24.1058	−	30.2277i	−1.24151	−	1.55681i
$378$	−4.08289	−	6.81477i	−0.210001	−	0.350514i
$379$	−2.46956	+	3.09673i	−0.126853	+	0.159069i	−0.841202	−	0.540721i	$-0.818151\pi$
$379$	−2.46956	+	3.09673i	−0.126853	+	0.159069i	0.714349	+	0.699790i	$0.246723\pi$
$380$	0.417532	−	1.82933i	0.0214189	−	0.0938425i
$381$	−17.9677	+	22.5308i	−0.920513	+	1.15429i
$382$	13.0416	−	6.28050i	0.667266	−	0.321339i
$383$	−0.678704	−	0.851068i	−0.0346802	−	0.0434876i	0.764189	−	0.644992i	$-0.223139\pi$
$383$	−0.678704	−	0.851068i	−0.0346802	−	0.0434876i	−0.798869	+	0.601505i	$0.794568\pi$
$384$	−1.93237	−	0.930578i	−0.0986106	−	0.0474884i
$385$	−4.76641	−	0.639750i	−0.242919	−	0.0326047i
$386$	−3.53355	+	1.70167i	−0.179853	+	0.0866127i
$387$	−11.9106	−	5.73583i	−0.605449	−	0.291569i
$388$	−0.824106	−	3.61064i	−0.0418376	−	0.183303i
$389$	−15.2951	−	7.36573i	−0.775492	−	0.373457i	0.00390128	−	0.999992i	$-0.498758\pi$
$389$	−15.2951	−	7.36573i	−0.775492	−	0.373457i	−0.779393	+	0.626535i	$0.784472\pi$
$390$	11.4004	−	14.2956i	0.577281	−	0.723888i
$391$	−24.9361			−1.26107
$392$	−0.297040	+	6.99369i	−0.0150028	+	0.353235i
$393$	32.8539			1.65726
$394$	5.75477	−	7.21626i	0.289921	−	0.363550i
$395$	−7.02243	−	3.38182i	−0.353337	−	0.170158i
$396$	−0.480014	−	2.10308i	−0.0241216	−	0.105684i
$397$	−8.60578	−	4.14433i	−0.431912	−	0.207998i	0.205280	−	0.978703i	$-0.434190\pi$
$397$	−8.60578	−	4.14433i	−0.431912	−	0.207998i	−0.637191	+	0.770706i	$0.719904\pi$
$398$	−14.7371	+	7.09699i	−0.738702	+	0.355740i
$399$	−4.05885	−	6.77464i	−0.203197	−	0.339156i
$400$	2.86716	+	1.38075i	0.143358	+	0.0690377i
$401$	−10.7660	−	13.5001i	−0.537626	−	0.674162i	0.436621	−	0.899646i	$-0.356175\pi$
$401$	−10.7660	−	13.5001i	−0.537626	−	0.674162i	−0.974247	+	0.225484i	$0.927604\pi$
$402$	20.0731	−	9.66671i	1.00116	−	0.482132i
$403$	−19.2739	+	24.1687i	−0.960100	+	1.20393i
$404$	−3.20328	+	14.0345i	−0.159369	+	0.698243i
$405$	9.44833	−	11.8478i	0.469491	−	0.588724i
$406$	1.46967	+	16.1098i	0.0729383	+	0.799516i
$407$	1.20423	+	1.51006i	0.0596915	+	0.0748508i
$408$	8.58109	−	4.13244i	0.424827	−	0.204586i
$409$	0.983605	−	4.30945i	0.0486361	−	0.213089i	−0.944771	−	0.327733i	$-0.893716\pi$
$409$	0.983605	−	4.30945i	0.0486361	−	0.213089i	0.993407	+	0.114644i	$0.0365727\pi$
$410$	−7.92193			−0.391236
$411$	−3.75177			−0.185061
$412$	−0.372710	+	1.63295i	−0.0183621	+	0.0804496i
$413$	−17.6783	−	2.37279i	−0.869892	−	0.116757i
$414$	1.99926	+	8.75934i	0.0982584	+	0.430498i
$415$	2.32985	+	10.2077i	0.114368	+	0.501078i
$416$	3.94258	+	4.94384i	0.193301	+	0.242392i
$417$	2.29968	+	2.88371i	0.112616	+	0.141216i
$418$	0.417532	+	1.82933i	0.0204222	+	0.0894753i
$419$	1.06671	+	4.67354i	0.0521120	+	0.228317i	0.994277	−	0.106831i	$-0.0340705\pi$
$419$	1.06671	+	4.67354i	0.0521120	+	0.228317i	−0.942165	+	0.335149i	$0.891213\pi$
$420$	−7.27315	+	2.37297i	−0.354893	+	0.115789i
$421$	−6.49465	+	28.4549i	−0.316530	+	1.38681i	0.527064	+	0.849826i	$0.323293\pi$
$421$	−6.49465	+	28.4549i	−0.316530	+	1.38681i	−0.843593	+	0.536982i	$0.819564\pi$
$422$	22.9258			1.11601
$423$	6.17011			0.300001
$424$	−2.97310	+	13.0260i	−0.144386	+	0.632598i
$425$	−12.7323	+	6.13154i	−0.617606	+	0.297423i
$426$	7.78411	+	9.76097i	0.377141	+	0.472920i
$427$	19.8160	−	18.9922i	0.958964	−	0.919099i
$428$	9.00966	−	11.2978i	0.435498	−	0.546098i
$429$	−4.06875	+	17.8264i	−0.196441	+	0.860665i
$430$	6.94526	−	8.70909i	0.334930	−	0.419989i
$431$	16.4961	−	7.94411i	0.794590	−	0.382655i	0.00787381	−	0.999969i	$-0.497494\pi$
$431$	16.4961	−	7.94411i	0.794590	−	0.382655i	0.786716	+	0.617314i	$0.211779\pi$
$432$	1.87212	+	2.34756i	0.0900723	+	0.112947i
$433$	23.2031	+	11.1740i	1.11507	+	0.536989i	0.898366	−	0.439248i	$-0.144755\pi$
$433$	23.2031	+	11.1740i	1.11507	+	0.536989i	0.216704	+	0.976237i	$0.430469\pi$
$434$	12.2962	−	4.01183i	0.590238	−	0.192574i
$435$	−15.9290	+	7.67103i	−0.763739	+	0.367798i
$436$	−16.7155	−	8.04976i	−0.800527	−	0.385514i
$437$	−1.73902	−	7.61916i	−0.0831888	−	0.364474i
$438$	14.8477	+	7.15026i	0.709449	+	0.341652i
$439$	−11.6792	+	14.6453i	−0.557420	+	0.698982i	−0.978078	−	0.208237i	$-0.933228\pi$
$439$	−11.6792	+	14.6453i	−0.557420	+	0.698982i	0.420659	+	0.907219i	$0.361799\pi$
$440$	1.81769			0.0866549
$441$	−5.28336	+	9.87563i	−0.251589	+	0.470268i
$442$	−28.0805			−1.33565
$443$	−1.41046	+	1.76867i	−0.0670131	+	0.0840318i	−0.814208	−	0.580573i	$-0.802829\pi$
$443$	−1.41046	+	1.76867i	−0.0670131	+	0.0840318i	0.747195	+	0.664605i	$0.231400\pi$
$444$	2.76828	+	1.33313i	0.131377	+	0.0632677i
$445$	3.12053	+	13.6719i	0.147927	+	0.648112i
$446$	−15.4672	−	7.44863i	−0.732395	−	0.352703i
$447$	−11.0167	+	5.30538i	−0.521074	+	0.250936i
$448$	−0.240369	−	2.63481i	−0.0113564	−	0.124483i
$449$	−0.220557	−	0.106215i	−0.0104087	−	0.00501258i	0.428672	−	0.903460i	$-0.358982\pi$
$449$	−0.220557	−	0.106215i	−0.0104087	−	0.00501258i	−0.439081	+	0.898448i	$0.644696\pi$
$450$	3.17465	+	3.98088i	0.149654	+	0.187661i
$451$	7.13741	−	3.43720i	0.336088	−	0.161851i
$452$	−0.715156	+	0.896778i	−0.0336381	+	0.0421809i
$453$	9.13734	−	40.0333i	0.429310	−	1.88093i
$454$	2.89132	−	3.62560i	0.135696	−	0.170158i
$455$	22.3554	+	3.00056i	1.04804	+	0.140668i
$456$	1.86109	+	2.33374i	0.0871537	+	0.109287i
$457$	27.2101	−	13.1037i	1.27283	−	0.612965i	0.329296	−	0.944227i	$-0.393189\pi$
$457$	27.2101	−	13.1037i	1.27283	−	0.612965i	0.943539	+	0.331262i	$0.107474\pi$
$458$	−1.12944	+	4.94841i	−0.0527754	+	0.231224i
$459$	−13.3339			−0.622373
$460$	−7.57069			−0.352985
$461$	−5.36722	+	23.5153i	−0.249977	+	1.09522i	0.681615	+	0.731711i	$0.261278\pi$
$461$	−5.36722	+	23.5153i	−0.249977	+	1.09522i	−0.931591	+	0.363508i	$0.881579\pi$
$462$	5.52329	−	5.29368i	0.256966	−	0.246284i
$463$	4.43486	+	19.4304i	0.206105	+	0.903006i	0.967130	+	0.254283i	$0.0818395\pi$
$463$	4.43486	+	19.4304i	0.206105	+	0.903006i	−0.761024	+	0.648723i	$0.775303\pi$
$464$	−1.36054	−	5.96092i	−0.0631615	−	0.276729i
$465$	8.81367	+	11.0520i	0.408724	+	0.512524i
$466$	6.71301	+	8.41784i	0.310974	+	0.389949i
$467$	−8.24315	−	36.1156i	−0.381447	−	1.67123i	−0.692951	−	0.720985i	$-0.743690\pi$
$467$	−8.24315	−	36.1156i	−0.381447	−	1.67123i	0.311503	−	0.950245i	$-0.399167\pi$
$468$	2.25136	+	9.86386i	0.104069	+	0.455957i
$469$	22.9555	+	15.1128i	1.05999	+	0.697843i
$470$	−1.15691	+	5.06876i	−0.0533643	+	0.233804i
$471$	20.1984			0.930692
$472$	6.74168			0.310311
$473$	−2.47874	+	10.8601i	−0.113972	+	0.499346i
$474$	11.1714	−	5.37986i	0.513119	−	0.247105i
$475$	−2.76141	−	3.46270i	−0.126702	−	0.158880i
$476$	9.81330	+	6.46058i	0.449792	+	0.296120i
$477$	−13.3288	+	16.7138i	−0.610284	+	0.765272i
$478$	−5.89716	+	25.8372i	−0.269730	+	1.18176i
$479$	−10.0862	+	12.6478i	−0.460852	+	0.577890i	−0.956905	−	0.290402i	$-0.906211\pi$
$479$	−10.0862	+	12.6478i	−0.460852	+	0.577890i	0.496052	+	0.868293i	$0.334782\pi$
$480$	2.60525	−	1.25462i	0.118913	−	0.0572653i
$481$	−5.64809	−	7.08248i	−0.257531	−	0.322933i
$482$	−9.13919	−	4.40120i	−0.416279	−	0.200469i
$483$	−23.0045	+	22.0482i	−1.04674	+	1.00323i
$484$	8.27298	−	3.98406i	0.376044	−	0.181093i
$485$	4.49864	+	2.16643i	0.204273	+	0.0983726i
$486$	3.35989	+	14.7206i	0.152408	+	0.667742i
$487$	0.969150	+	0.466718i	0.0439164	+	0.0211490i	0.455713	−	0.890127i	$-0.349384\pi$
$487$	0.969150	+	0.466718i	0.0439164	+	0.0211490i	−0.411797	+	0.911276i	$0.635099\pi$
$488$	−6.46826	+	8.11094i	−0.292804	+	0.367165i
$489$	13.7734			0.622854
$490$	−7.12221	−	6.19200i	−0.321749	−	0.279726i
$491$	−2.32348			−0.104857			−0.0524286	−	0.998625i	$-0.516696\pi$
$491$	−2.32348			−0.104857			−0.0524286	+	0.998625i	$0.516696\pi$
$492$	7.85743	−	9.85290i	0.354240	−	0.444203i
$493$	24.4627	+	11.7806i	1.10174	+	0.530572i
$494$	−1.95831	−	8.57991i	−0.0881085	−	0.386029i
$495$	2.62031	+	1.26187i	0.117774	+	0.0567170i
$496$	−4.40452	+	2.12110i	−0.197769	+	0.0952404i
$497$	−5.39398	+	14.4255i	−0.241953	+	0.647074i
$498$	−15.0067	−	7.22686i	−0.672468	−	0.323843i
$499$	0.837465	+	1.05015i	0.0374901	+	0.0470111i	0.800223	−	0.599702i	$-0.204714\pi$
$499$	0.837465	+	1.05015i	0.0374901	+	0.0470111i	−0.762733	+	0.646714i	$0.776143\pi$
$500$	−9.93906	+	4.78640i	−0.444488	+	0.214054i
$501$	15.1863	−	19.0430i	0.678473	−	0.850778i
$502$	1.25267	−	5.48829i	0.0559093	−	0.244955i
$503$	20.9686	−	26.2938i	0.934943	−	1.17238i	−0.0498682	−	0.998756i	$-0.515880\pi$
$503$	20.9686	−	26.2938i	0.934943	−	1.17238i	0.984812	−	0.173626i	$-0.0555484\pi$
$504$	1.48263	−	3.96511i	0.0660416	−	0.176620i
$505$	−12.1008	−	15.1739i	−0.538478	−	0.675230i
$506$	6.82095	−	3.28480i	0.303228	−	0.146027i
$507$	12.8790	−	56.4264i	0.571974	−	2.50598i
$508$	13.4364			0.596145
$509$	12.7052			0.563149			0.281574	−	0.959539i	$-0.409143\pi$
$509$	12.7052			0.563149			0.281574	+	0.959539i	$0.409143\pi$
$510$	−2.85735	+	12.5189i	−0.126526	+	0.554345i
$511$	1.84691	+	20.2450i	0.0817026	+	0.895587i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	−0.929895	−	4.07413i	−0.0410558	−	0.179877i
$514$	−2.61054	−	3.27352i	−0.115146	−	0.144389i
$515$	−1.40796	−	1.76552i	−0.0620419	−	0.0777981i
$516$	3.94321	+	17.2763i	0.173590	+	0.760549i
$517$	−1.15691	−	5.06876i	−0.0508809	−	0.222924i
$518$	0.344349	+	3.77459i	0.0151298	+	0.165846i
$519$	7.44283	−	32.6092i	0.326704	−	1.43138i
$520$	−8.52532			−0.373860
$521$	−1.89668			−0.0830952			−0.0415476	−	0.999137i	$-0.513229\pi$
$521$	−1.89668			−0.0830952			−0.0415476	+	0.999137i	$0.513229\pi$
$522$	2.17688	−	9.53755i	0.0952796	−	0.417447i
$523$	−32.8133	+	15.8021i	−1.43483	+	0.690976i	−0.979888	−	0.199547i	$-0.936053\pi$
$523$	−32.8133	+	15.8021i	−1.43483	+	0.690976i	−0.454938	+	0.890523i	$0.650339\pi$
$524$	−9.55073	−	11.9762i	−0.417226	−	0.523184i
$525$	−6.32458	+	16.9143i	−0.276027	+	0.738201i
$526$	13.0945	−	16.4199i	0.570946	−	0.715943i
$527$	4.83073	−	21.1648i	0.210430	−	0.921954i
$528$	−1.80289	+	2.26075i	−0.0784606	+	0.0983865i
$529$	−7.68704	+	3.70188i	−0.334219	+	0.160952i
$530$	−11.2312	−	14.0835i	−0.487853	−	0.611749i
$531$	9.71855	+	4.68021i	0.421749	+	0.203104i
$532$	−1.28964	+	3.44898i	−0.0559130	+	0.149532i
$533$	−33.4759	+	16.1211i	−1.45000	+	0.698284i
$534$	−20.0996	−	9.67945i	−0.869794	−	0.418871i
$535$	4.33520	+	18.9938i	0.187427	+	0.821172i
$536$	−9.35914	−	4.50712i	−0.404253	−	0.194678i
$537$	−7.57556	+	9.49945i	−0.326909	+	0.409931i
$538$	−11.2576			−0.485351
$539$	9.10350	+	2.48859i	0.392115	+	0.107191i
$540$	−4.04821			−0.174207
$541$	−15.9773	+	20.0349i	−0.686919	+	0.861369i	−0.995971	−	0.0896759i	$-0.971417\pi$
$541$	−15.9773	+	20.0349i	−0.686919	+	0.861369i	0.309052	+	0.951045i	$0.399988\pi$
$542$	5.91213	+	2.84713i	0.253948	+	0.122295i
$543$	−3.05078	−	13.3663i	−0.130922	−	0.573605i
$544$	−4.00095	−	1.92676i	−0.171539	−	0.0826090i
$545$	22.5361	−	10.8528i	0.965341	−	0.464884i
$546$	−25.9053	+	24.8284i	−1.10865	+	1.06256i
$547$	15.0226	+	7.23448i	0.642318	+	0.309324i	0.726541	−	0.687123i	$-0.241127\pi$
$547$	15.0226	+	7.23448i	0.642318	+	0.309324i	−0.0842232	+	0.996447i	$0.526841\pi$
$548$	1.09065	+	1.36763i	0.0465903	+	0.0584224i
$549$	−14.9552	+	7.20203i	−0.638271	+	0.307375i
$550$	2.67505	−	3.35441i	0.114064	−	0.143032i
$551$	−1.89352	+	8.29607i	−0.0806669	+	0.353425i
$552$	7.50904	−	9.41604i	0.319606	−	0.400773i
$553$	12.7756	+	8.41077i	0.543272	+	0.357662i
$554$	15.2808	+	19.1615i	0.649217	+	0.814093i
$555$	−3.73224	+	1.79735i	−0.158425	+	0.0762934i
$556$	0.382675	−	1.67661i	0.0162290	−	0.0711040i
$557$	33.3889			1.41473			0.707367	−	0.706846i	$-0.249883\pi$
$557$	33.3889			1.41473			0.707367	+	0.706846i	$0.249883\pi$
$558$	−7.82189			−0.331127
$559$	11.6258	−	50.9358i	0.491718	−	2.15436i
$560$	2.97935	+	1.96145i	0.125900	+	0.0828865i
$561$	−2.85735	−	12.5189i	−0.120637	−	0.528547i
$562$	0.804089	+	3.52295i	0.0339185	+	0.148607i
$563$	11.4558	+	14.3651i	0.482804	+	0.605418i	0.962254	−	0.272152i	$-0.0877352\pi$
$563$	11.4558	+	14.3651i	0.482804	+	0.605418i	−0.479450	+	0.877569i	$0.659164\pi$
$564$	−5.15678	−	6.46639i	−0.217139	−	0.272284i
$565$	−0.344114	−	1.50766i	−0.0144770	−	0.0634278i
$566$	−3.17566	−	13.9135i	−0.133483	−	0.584828i
$567$	−21.4696	+	20.5771i	−0.901640	+	0.864158i
$568$	1.29530	−	5.67509i	0.0543497	−	0.238121i
$569$	5.85600			0.245496			0.122748	−	0.992438i	$-0.460829\pi$
$569$	5.85600			0.245496			0.122748	+	0.992438i	$0.460829\pi$
$570$	−4.02437			−0.168562
$571$	−0.742150	+	3.25157i	−0.0310580	+	0.136074i	−0.988080	−	0.153941i	$-0.950803\pi$
$571$	−0.742150	+	3.25157i	−0.0310580	+	0.136074i	0.957022	+	0.290015i	$0.0936604\pi$
$572$	7.68105	−	3.69900i	0.321161	−	0.154663i
$573$	−19.3566	−	24.2725i	−0.808635	−	1.01400i
$574$	15.4079	+	2.06806i	0.643113	+	0.0863190i
$575$	−11.1416	+	13.9711i	−0.464637	+	0.582636i
$576$	−0.356036	+	1.55990i	−0.0148348	+	0.0649957i
$577$	18.0909	−	22.6853i	0.753134	−	0.944400i	−0.246560	−	0.969127i	$-0.579300\pi$
$577$	18.0909	−	22.6853i	0.753134	−	0.944400i	0.999694	+	0.0247274i	$0.00787177\pi$
$578$	2.45062	−	1.18016i	0.101933	−	0.0490881i
$579$	5.24458	+	6.57649i	0.217957	+	0.273310i
$580$	7.42695	+	3.57663i	0.308387	+	0.148511i
$581$	−1.86670	−	20.4619i	−0.0774438	−	0.848903i
$582$	−7.15651	+	3.44640i	−0.296647	+	0.142858i
$583$	16.2296	+	7.81576i	0.672161	+	0.323696i
$584$	−1.70978	−	7.49102i	−0.0707511	−	0.309981i
$585$	−12.2898	−	5.91844i	−0.508120	−	0.244698i
$586$	−7.79808	+	9.77848i	−0.322136	+	0.403945i
$587$	−22.5431			−0.930453			−0.465226	−	0.885192i	$-0.654027\pi$
$587$	−22.5431			−0.930453			−0.465226	+	0.885192i	$0.654027\pi$
$588$	14.7655	−	2.71667i	0.608919	−	0.112034i
$589$	6.80374			0.280343
$590$	−5.66705	+	7.10626i	−0.233309	+	0.292560i
$591$	−17.8356	−	8.58918i	−0.733659	−	0.353312i
$592$	−0.318780	−	1.39667i	−0.0131018	−	0.0574027i
$593$	37.8671	+	18.2358i	1.55502	+	0.748856i	0.996731	−	0.0807937i	$-0.0257455\pi$
$593$	37.8671	+	18.2358i	1.55502	+	0.748856i	0.558284	+	0.829650i	$0.311460\pi$
$594$	3.64731	−	1.75645i	0.149651	−	0.0720681i
$595$	−15.0590	+	4.91323i	−0.617359	+	0.201423i
$596$	5.13657	+	2.47364i	0.210402	+	0.101324i
$597$	21.8731	+	27.4280i	0.895206	+	1.12255i
$598$	−31.9916	+	15.4064i	−1.30824	+	0.630013i
$599$	3.21155	−	4.02715i	0.131220	−	0.164545i	−0.711881	−	0.702301i	$-0.752156\pi$
$599$	3.21155	−	4.02715i	0.131220	−	0.164545i	0.843101	+	0.537756i	$0.180728\pi$
$600$	1.51877	−	6.65418i	0.0620037	−	0.271656i
$601$	−13.1096	+	16.4389i	−0.534753	+	0.670559i	−0.973668	−	0.227970i	$-0.926791\pi$
$601$	−13.1096	+	16.4389i	−0.534753	+	0.670559i	0.438916	+	0.898528i	$0.355363\pi$
$602$	−15.7819	+	15.1258i	−0.643220	+	0.616481i
$603$	−10.3628	−	12.9946i	−0.422007	−	0.529181i
$604$	−17.2496	+	8.30697i	−0.701876	+	0.338006i
$605$	−2.75475	+	12.0694i	−0.111997	+	0.490689i
$606$	30.8748			1.25420
$607$	−5.05431			−0.205148			−0.102574	−	0.994725i	$-0.532708\pi$
$607$	−5.05431			−0.205148			−0.102574	+	0.994725i	$0.532708\pi$
$608$	0.309692	−	1.35685i	0.0125597	−	0.0550275i
$609$	32.9840	−	10.7615i	1.33658	−	0.436080i
$610$	−3.11235	−	13.6361i	−0.126015	−	0.552110i
$611$	5.42615	+	23.7735i	0.219518	+	0.961773i
$612$	−4.43002	−	5.55507i	−0.179073	−	0.224551i
$613$	−13.1223	−	16.4549i	−0.530005	−	0.664605i	0.442695	−	0.896672i	$-0.354023\pi$
$613$	−13.1223	−	16.4549i	−0.530005	−	0.664605i	−0.972700	+	0.232067i	$0.925451\pi$
$614$	−4.84883	−	21.2441i	−0.195683	−	0.857342i
$615$	3.78078	+	16.5647i	0.152456	+	0.667952i
$616$	−3.53534	−	0.474516i	−0.142443	−	0.0191188i
$617$	1.12264	−	4.91861i	0.0451958	−	0.198016i	−0.947290	−	0.320378i	$-0.896190\pi$
$617$	1.12264	−	4.91861i	0.0451958	−	0.198016i	0.992485	+	0.122363i	$0.0390471\pi$
$618$	3.59236			0.144506
$619$	−36.8766			−1.48220			−0.741098	−	0.671397i	$-0.765695\pi$
$619$	−36.8766			−1.48220			−0.741098	+	0.671397i	$0.765695\pi$
$620$	1.46662	−	6.42570i	0.0589011	−	0.258062i
$621$	−15.1911	+	7.31564i	−0.609597	+	0.293567i
$622$	−4.00646	−	5.02394i	−0.160645	−	0.201442i
$623$	−2.50020	−	27.4061i	−0.100169	−	1.09800i
$624$	8.45590	−	10.6034i	0.338507	−	0.424474i
$625$	−0.231127	+	1.01263i	−0.00924507	+	0.0405053i
$626$	10.9897	−	13.7807i	0.439238	−	0.550788i
$627$	3.62584	−	1.74611i	0.144802	−	0.0697329i
$628$	−5.87174	−	7.36292i	−0.234308	−	0.293813i
$629$	5.73171	+	2.76024i	0.228538	+	0.110058i
$630$	2.93324	+	4.89588i	0.116863	+	0.195056i
$631$	24.6596	−	11.8754i	0.981682	−	0.472753i	0.126999	−	0.991903i	$-0.459466\pi$
$631$	24.6596	−	11.8754i	0.981682	−	0.472753i	0.854683	+	0.519149i	$0.173751\pi$
$632$	−5.20868	−	2.50837i	−0.207190	−	0.0997775i
$633$	−10.9415	−	47.9376i	−0.434884	−	1.90535i
$634$	−1.94798	−	0.938099i	−0.0773643	−	0.0372567i
$635$	−11.2946	+	14.1630i	−0.448214	+	0.562043i
$636$	28.6561			1.13629
$637$	−42.6972	−	11.6720i	−1.69173	−	0.462460i
$638$	−8.24329			−0.326355
$639$	5.80701	−	7.28177i	0.229722	−	0.288062i
$640$	−1.21470	−	0.584969i	−0.0480153	−	0.0231229i
$641$	4.85447	+	21.2688i	0.191740	+	0.840068i	0.975674	+	0.219224i	$0.0703527\pi$
$641$	4.85447	+	21.2688i	0.191740	+	0.840068i	−0.783934	+	0.620844i	$0.786790\pi$
$642$	−27.9234	−	13.4472i	−1.10205	−	0.530719i
$643$	−22.0770	+	10.6317i	−0.870634	+	0.419275i	−0.815195	−	0.579187i	$-0.803370\pi$
$643$	−22.0770	+	10.6317i	−0.870634	+	0.419275i	−0.0554389	+	0.998462i	$0.517656\pi$
$644$	14.7247	+	1.97636i	0.580236	+	0.0778796i
$645$	−21.5253	−	10.3660i	−0.847557	−	0.408162i
$646$	3.85338	+	4.83199i	0.151609	+	0.190112i
$647$	9.12076	−	4.39233i	0.358574	−	0.172680i	−0.245919	−	0.969290i	$-0.579090\pi$
$647$	9.12076	−	4.39233i	0.358574	−	0.172680i	0.604493	+	0.796610i	$0.293376\pi$
$648$	7.00802	−	8.78778i	0.275301	−	0.345217i
$649$	2.02255	−	8.86136i	0.0793919	−	0.347839i
$650$	−12.5465	+	15.7328i	−0.492115	+	0.617093i
$651$	−14.2571	−	23.7966i	−0.558781	−	0.932663i
$652$	−4.00397	−	5.02082i	−0.156808	−	0.196630i
$653$	40.9135	−	19.7029i	1.60107	−	0.771034i	0.601457	−	0.798905i	$-0.294587\pi$
$653$	40.9135	−	19.7029i	1.60107	−	0.771034i	0.999612	+	0.0278715i	$0.00887291\pi$
$654$	−8.85442	+	38.7937i	−0.346235	+	1.51696i
$655$	20.6522			0.806949
$656$	−5.87586			−0.229414
$657$	2.73567	−	11.9857i	0.106728	−	0.467608i
$658$	3.57338	−	9.55655i	0.139305	−	0.372553i
$659$	−4.55935	−	19.9758i	−0.177607	−	0.778148i	−0.982731	−	0.185041i	$-0.940758\pi$
$659$	−4.55935	−	19.9758i	−0.177607	−	0.778148i	0.805124	−	0.593107i	$-0.202099\pi$
$660$	−0.867500	−	3.80077i	−0.0337674	−	0.147945i
$661$	−12.7555	−	15.9949i	−0.496132	−	0.622130i	0.469220	−	0.883081i	$-0.344535\pi$
$661$	−12.7555	−	15.9949i	−0.496132	−	0.622130i	−0.965352	+	0.260951i	$0.915964\pi$
$662$	−11.7239	−	14.7013i	−0.455662	−	0.571382i
$663$	13.4015	+	58.7160i	0.520473	+	2.28034i
$664$	1.72810	+	7.57128i	0.0670631	+	0.293823i
$665$	−2.55143	−	4.25859i	−0.0989401	−	0.165141i
$666$	0.510053	−	2.23469i	0.0197641	−	0.0865924i
$667$	34.3334			1.32939
$668$	−11.3564			−0.439394
$669$	−8.19319	+	35.8967i	−0.316767	+	1.38785i
$670$	12.6181	−	6.07658i	0.487481	−	0.234759i
$671$	8.72061	+	10.9353i	0.336656	+	0.422153i
$672$	−5.39464	+	1.76008i	−0.208103	+	0.0678967i
$673$	6.76513	−	8.48320i	0.260776	−	0.327003i	−0.634156	−	0.773205i	$-0.718652\pi$
$673$	6.76513	−	8.48320i	0.260776	−	0.327003i	0.894932	+	0.446202i	$0.147224\pi$
$674$	−1.62166	+	7.10496i	−0.0624640	+	0.273673i
$675$	−5.95766	+	7.47067i	−0.229310	+	0.287546i
$676$	−24.3131	+	11.7086i	−0.935118	+	0.450329i
$677$	10.8832	+	13.6470i	0.418274	+	0.524499i	0.945673	−	0.325119i	$-0.105404\pi$
$677$	10.8832	+	13.6470i	0.418274	+	0.524499i	−0.527399	+	0.849617i	$0.676833\pi$
$678$	2.21647	+	1.06739i	0.0851228	+	0.0409930i
$679$	−8.18416	−	5.38803i	−0.314079	−	0.206774i
$680$	5.39415	−	2.59768i	0.206856	−	0.0996166i
$681$	−8.96098	−	4.31538i	−0.343386	−	0.165366i
$682$	1.46662	+	6.42570i	0.0561600	+	0.246053i
$683$	28.5306	+	13.7396i	1.09169	+	0.525731i	0.891037	−	0.453930i	$-0.149979\pi$
$683$	28.5306	+	13.7396i	1.09169	+	0.525731i	0.200655	+	0.979662i	$0.435693\pi$
$684$	1.38839	−	1.74099i	0.0530865	−	0.0665684i
$685$	−2.35839			−0.0901096
$686$	12.2360	+	13.9025i	0.467173	+	0.530801i
$687$	10.8861			0.415331
$688$	5.15145	−	6.45971i	0.196397	−	0.246274i
$689$	−76.1201	−	36.6575i	−2.89994	−	1.39654i
$690$	3.61315	+	15.8302i	0.137550	+	0.602647i
$691$	20.9395	+	10.0839i	0.796575	+	0.383610i	0.787474	−	0.616348i	$-0.211389\pi$
$691$	20.9395	+	10.0839i	0.796575	+	0.383610i	0.00910140	+	0.999959i	$0.497103\pi$
$692$	−14.0507	+	6.76645i	−0.534127	+	0.257222i
$693$	−4.76700	−	3.13835i	−0.181083	−	0.119216i
$694$	13.4437	+	6.47416i	0.510317	+	0.245756i
$695$	1.44560	+	1.81273i	0.0548347	+	0.0687606i
$696$	−11.8149	+	5.68976i	−0.447843	+	0.215670i
$697$	16.2687	−	20.4004i	0.616223	−	0.772719i
$698$	−5.58887	+	24.4864i	−0.211542	+	0.926825i
$699$	14.3978	−	18.0543i	0.544575	−	0.682876i
$700$	8.00435	−	2.61154i	0.302536	−	0.0987070i
$701$	1.95508	+	2.45159i	0.0738424	+	0.0925954i	0.817381	−	0.576098i	$-0.195425\pi$
$701$	1.95508	+	2.45159i	0.0738424	+	0.0925954i	−0.743538	+	0.668693i	$0.766854\pi$
$702$	−17.1066	+	8.23812i	−0.645648	+	0.310928i
$703$	−0.443661	+	1.94380i	−0.0167330	+	0.0733120i
$704$	1.34822			0.0508128
$705$	11.1509			0.419966
$706$	1.64821	−	7.22129i	0.0620313	−	0.271777i
$707$	19.5744	+	32.6717i	0.736172	+	1.22875i
$708$	−3.21750	−	14.0968i	−0.120921	−	0.529790i
$709$	−0.483517	−	2.11843i	−0.0181589	−	0.0795592i	0.965037	−	0.262115i	$-0.0844201\pi$
$709$	−0.483517	−	2.11843i	−0.0181589	−	0.0795592i	−0.983195	+	0.182556i	$0.941563\pi$
$710$	4.89316	+	6.13582i	0.183637	+	0.230273i
$711$	−5.76728	−	7.23193i	−0.216290	−	0.271219i
$712$	2.31456	+	10.1408i	0.0867418	+	0.380041i
$713$	−6.10851	−	26.7631i	−0.228765	−	1.00229i
$714$	8.82556	−	23.6029i	0.330288	−	0.883315i
$715$	−2.55765	+	11.2058i	−0.0956507	+	0.419073i
$716$	5.66507			0.211714
$717$	56.8397			2.12272
$718$	3.10324	−	13.5962i	0.115812	−	0.507406i
$719$	−14.6066	+	7.03416i	−0.544734	+	0.262330i	−0.685950	−	0.727649i	$-0.740613\pi$
$719$	−14.6066	+	7.03416i	−0.544734	+	0.262330i	0.141216	+	0.989979i	$0.454899\pi$
$720$	−1.34497	−	1.68654i	−0.0501241	−	0.0628536i
$721$	2.27753	+	3.80143i	0.0848197	+	0.141573i
$722$	10.6386	−	13.3404i	0.395929	−	0.496479i
$723$	−4.84115	+	21.2105i	−0.180044	+	0.788826i
$724$	−3.98556	+	4.99774i	−0.148122	+	0.185740i
$725$	17.5305	−	8.44223i	0.651065	−	0.313536i
$726$	−12.2789	−	15.3973i	−0.455714	−	0.571448i
$727$	46.2682	+	22.2816i	1.71599	+	0.826379i	0.990396	+	0.138260i	$0.0441510\pi$
$727$	46.2682	+	22.2816i	1.71599	+	0.826379i	0.725598	+	0.688119i	$0.241563\pi$
$728$	16.5815	+	2.22558i	0.614550	+	0.0824853i
$729$	−1.20346	+	0.579555i	−0.0445725	+	0.0214650i
$730$	9.33336	+	4.49471i	0.345443	+	0.166357i
$731$	8.16439	+	35.7705i	0.301971	+	1.32302i
$732$	20.0469	+	9.65408i	0.740955	+	0.356825i
$733$	−10.9061	+	13.6758i	−0.402824	+	0.505126i	−0.941326	−	0.337499i	$-0.890419\pi$
$733$	−10.9061	+	13.6758i	−0.402824	+	0.505126i	0.538502	+	0.842624i	$0.318991\pi$
$734$	0.689374			0.0254453
$735$	−9.54830	+	17.8476i	−0.352194	+	0.658320i
$736$	−5.61533			−0.206984
$737$	−8.73202	+	10.9496i	−0.321648	+	0.403334i
$738$	−8.47041	−	4.07914i	−0.311800	−	0.150155i
$739$	−1.87038	−	8.19468i	−0.0688031	−	0.301446i	0.928805	−	0.370569i	$-0.120837\pi$
$739$	−1.87038	−	8.19468i	−0.0688031	−	0.301446i	−0.997608	+	0.0691226i	$0.977980\pi$
$740$	1.74016	+	0.838019i	0.0639697	+	0.0308062i
$741$	−17.0059	+	8.18961i	−0.624727	+	0.300853i
$742$	18.1678	+	30.3239i	0.666961	+	1.11323i
$743$	−21.3935	−	10.3026i	−0.784851	−	0.377964i	−0.00186062	−	0.999998i	$-0.500592\pi$
$743$	−21.3935	−	10.3026i	−0.784851	−	0.377964i	−0.782990	+	0.622034i	$0.786307\pi$
$744$	6.53728	+	8.19750i	0.239668	+	0.300535i
$745$	−6.92521	+	3.33501i	−0.253720	+	0.122185i
$746$	15.1049	−	18.9409i	0.553030	−	0.693477i
$747$	−2.76498	+	12.1141i	−0.101165	+	0.443234i
$748$	−3.73287	+	4.68086i	−0.136487	+	0.171149i
$749$	−3.47342	−	38.0740i	−0.126916	−	1.39119i
$750$	14.7518	+	18.4982i	0.538659	+	0.675457i
$751$	9.97387	−	4.80316i	0.363952	−	0.175270i	−0.242966	−	0.970035i	$-0.578120\pi$
$751$	9.97387	−	4.80316i	0.363952	−	0.175270i	0.606917	+	0.794765i	$0.292406\pi$
$752$	−0.858105	+	3.75960i	−0.0312919	+	0.137099i
$753$	−12.0738			−0.439994
$754$	38.6627			1.40801
$755$	5.74381	−	25.1653i	0.209039	−	0.915858i
$756$	7.87364	+	1.05680i	0.286361	+	0.0384356i
$757$	0.100651	+	0.440980i	0.00365821	+	0.0160277i	0.976724	−	0.214500i	$-0.0688121\pi$
$757$	0.100651	+	0.440980i	0.00365821	+	0.0160277i	−0.973066	+	0.230527i	$0.925955\pi$
$758$	−0.881377	−	3.86156i	−0.0320130	−	0.140258i
$759$	−10.1238	−	12.6949i	−0.367471	−	0.460794i
$760$	1.16990	+	1.46701i	0.0424367	+	0.0532139i
$761$	11.1571	+	48.8827i	0.404446	+	1.77199i	0.609031	+	0.793146i	$0.291558\pi$
$761$	11.1571	+	48.8827i	0.404446	+	1.77199i	−0.204585	+	0.978849i	$0.565585\pi$
$762$	−6.41260	−	28.0954i	−0.232304	−	1.01779i
$763$	−46.6652	+	15.2252i	−1.68939	+	0.551190i
$764$	−3.22101	+	14.1122i	−0.116532	+	0.510560i
$765$	9.57936			0.346342
$766$	1.08856			0.0393312
$767$	−9.48616	+	41.5616i	−0.342525	+	1.50070i
$768$	1.93237	−	0.930578i	0.0697282	−	0.0335793i
$769$	19.6850	+	24.6842i	0.709860	+	0.890136i	0.997717	−	0.0675370i	$-0.0215141\pi$
$769$	19.6850	+	24.6842i	0.709860	+	0.890136i	−0.287857	+	0.957674i	$0.592943\pi$
$770$	3.47198	−	3.32765i	0.125122	−	0.119920i
$771$	−5.59900	+	7.02092i	−0.201643	+	0.252852i
$772$	0.872715	−	3.82362i	0.0314097	−	0.137615i
$773$	−11.8866	+	14.9053i	−0.427530	+	0.536105i	−0.948209	−	0.317647i	$-0.897107\pi$
$773$	−11.8866	+	14.9053i	−0.427530	+	0.536105i	0.520679	+	0.853752i	$0.325679\pi$
$774$	11.9106	−	5.73583i	0.428117	−	0.206170i
$775$	−9.69975	−	12.1631i	−0.348425	−	0.436912i
$776$	3.33674	+	1.60689i	0.119782	+	0.0576839i
$777$	7.72829	−	2.52147i	0.277251	−	0.0904573i
$778$	15.2951	−	7.36573i	0.548356	−	0.264074i
$779$	7.36784	+	3.54817i	0.263980	+	0.127126i
$780$	4.06875	+	17.8264i	0.145685	+	0.638286i
$781$	−7.07082	−	3.40513i	−0.253014	−	0.121845i
$782$	15.5474	−	19.4958i	0.555975	−	0.697170i
$783$	18.3588			0.656090
$784$	−5.28269	−	4.59273i	−0.188667	−	0.164026i
$785$	12.6969			0.453171
$786$	−20.4841	+	25.6862i	−0.730642	+	0.916197i
$787$	−18.3036	−	8.81453i	−0.652452	−	0.314204i	0.0782170	−	0.996936i	$-0.475077\pi$
$787$	−18.3036	−	8.81453i	−0.652452	−	0.314204i	−0.730669	+	0.682732i	$0.760792\pi$
$788$	2.05385	+	8.99853i	0.0731655	+	0.320559i
$789$	−40.5833	−	19.5439i	−1.44480	−	0.695781i
$790$	7.02243	−	3.38182i	0.249847	−	0.120320i
$791$	0.275708	+	3.02218i	0.00980305	+	0.107457i
$792$	1.94354	+	0.935958i	0.0690606	+	0.0332578i
$793$	−40.9014	−	51.2888i	−1.45245	−	1.82132i
$794$	8.60578	−	4.14433i	0.305408	−	0.147077i
$795$	−24.0883	+	30.2058i	−0.854325	+	1.07129i
$796$	3.63975	−	15.9468i	0.129008	−	0.565219i
$797$	−18.1712	+	22.7860i	−0.643658	+	0.807122i	−0.991455	−	0.130448i	$-0.958358\pi$
$797$	−18.1712	+	22.7860i	−0.643658	+	0.807122i	0.347797	+	0.937570i	$0.386930\pi$
$798$	7.82728	+	1.05058i	0.277083	+	0.0371902i
$799$	−10.6771	−	13.3886i	−0.377728	−	0.473655i
$800$	−2.86716	+	1.38075i	−0.101370	+	0.0488170i
$801$	−3.70333	+	16.2253i	−0.130851	+	0.573294i
$802$	17.2673			0.609728
$803$	−10.3593			−0.365570
$804$	−4.95766	+	21.7209i	−0.174843	+	0.766037i
$805$	−14.4608	+	13.8597i	−0.509678	+	0.488490i
$806$	−6.87877	−	30.1378i	−0.242294	−	1.06156i
$807$	5.37276	+	23.5396i	0.189130	+	0.828633i
$808$	−8.97540	−	11.2548i	−0.315754	−	0.395942i
$809$	−24.7983	−	31.0960i	−0.871860	−	1.09328i	−0.994899	−	0.100877i	$-0.967835\pi$
$809$	−24.7983	−	31.0960i	−0.871860	−	1.09328i	0.123038	−	0.992402i	$-0.460736\pi$
$810$	3.37207	+	14.7740i	0.118482	+	0.519106i
$811$	−4.53521	−	19.8701i	−0.159253	−	0.697732i	−0.989998	−	0.141080i	$-0.954943\pi$
$811$	−4.53521	−	19.8701i	−0.159253	−	0.697732i	0.830745	−	0.556652i	$-0.187914\pi$
$812$	−13.5115	−	8.89527i	−0.474160	−	0.312163i
$813$	3.13173	−	13.7210i	0.109835	−	0.481217i
$814$	−1.93144			−0.0676968
$815$	8.65807			0.303279
$816$	−2.11936	+	9.28550i	−0.0741923	+	0.325058i
$817$	−10.3602	+	4.98922i	−0.362458	+	0.174551i
$818$	2.75600	+	3.45591i	0.0963613	+	0.120833i
$819$	22.3582	+	14.7195i	0.781258	+	0.514340i
$820$	4.93924	−	6.19361i	0.172486	−	0.216290i
$821$	2.66410	−	11.6722i	0.0929777	−	0.407362i	−0.906925	−	0.421292i	$-0.861577\pi$
$821$	2.66410	−	11.6722i	0.0929777	−	0.407362i	0.999903	+	0.0139295i	$0.00443404\pi$
$822$	2.33919	−	2.93325i	0.0815887	−	0.102309i
$823$	−25.7315	+	12.3916i	−0.896942	+	0.431945i	−0.824784	−	0.565449i	$-0.808703\pi$
$823$	−25.7315	+	12.3916i	−0.896942	+	0.431945i	−0.0721586	+	0.997393i	$0.522989\pi$
$824$	−1.04431	−	1.30952i	−0.0363803	−	0.0456194i
$825$	−8.29071	−	3.99260i	−0.288645	−	0.139004i
$826$	12.8774	−	12.3420i	0.448060	−	0.429434i
$827$	−45.3777	+	21.8527i	−1.57794	+	0.759895i	−0.998480	−	0.0551083i	$-0.982450\pi$
$827$	−45.3777	+	21.8527i	−1.57794	+	0.759895i	−0.579457	+	0.815003i	$0.696735\pi$
$828$	−8.09485	−	3.89827i	−0.281315	−	0.135474i
$829$	−3.50613	−	15.3614i	−0.121773	−	0.533522i	−0.998609	−	0.0527322i	$-0.983207\pi$
$829$	−3.50613	−	15.3614i	−0.121773	−	0.533522i	0.876836	−	0.480790i	$-0.159650\pi$
$830$	−9.43336	−	4.54287i	−0.327437	−	0.157685i
$831$	32.7736	−	41.0968i	1.13690	−	1.42563i
$832$	−6.32341			−0.219225
$833$	30.5719	−	5.62484i	1.05925	−	0.194889i
$834$	−3.68841			−0.127719
$835$	9.54622	−	11.9706i	0.330360	−	0.414259i
$836$	−1.69055	−	0.814127i	−0.0584690	−	0.0281572i
$837$	−3.26635	−	14.3108i	−0.112902	−	0.494654i
$838$	−4.31900	−	2.07992i	−0.149197	−	0.0718497i
$839$	11.6905	−	5.62986i	0.403602	−	0.194365i	−0.221059	−	0.975260i	$-0.570951\pi$
$839$	11.6905	−	5.62986i	0.403602	−	0.194365i	0.624661	+	0.780896i	$0.285237\pi$
$840$	2.67947	−	7.16590i	0.0924504	−	0.247247i
$841$	−7.55341	−	3.63753i	−0.260463	−	0.125432i
$842$	−18.1976	−	22.8191i	−0.627131	−	0.786397i
$843$	6.98269	−	3.36269i	0.240497	−	0.115817i
$844$	−14.2940	+	17.9241i	−0.492020	+	0.616974i
$845$	8.09582	−	35.4701i	0.278505	−	1.22021i
$846$	−3.84700	+	4.82399i	−0.132263	+	0.165852i
$847$	8.50867	−	22.7554i	0.292361	−	0.781884i
$848$	−8.33043	−	10.4460i	−0.286068	−	0.358718i
$849$	−27.5774	+	13.2806i	−0.946453	+	0.455788i
$850$	3.14461	−	13.7774i	0.107859	−	0.472562i
$851$	8.04445			0.275760
$852$	−12.4847			−0.427720
$853$	6.72523	−	29.4652i	0.230268	−	1.00887i	−0.719151	−	0.694854i	$-0.755469\pi$
$853$	6.72523	−	29.4652i	0.230268	−	1.00887i	0.949418	−	0.314014i	$-0.101674\pi$
$854$	2.49365	+	27.3343i	0.0853310	+	0.935359i
$855$	0.668056	+	2.92695i	0.0228471	+	0.100099i
$856$	3.21551	+	14.0881i	0.109904	+	0.481520i
$857$	27.6363	+	34.6549i	0.944040	+	1.18379i	0.982825	+	0.184541i	$0.0590798\pi$
$857$	27.6363	+	34.6549i	0.944040	+	1.18379i	−0.0387851	+	0.999248i	$0.512349\pi$
$858$	−11.4004	−	14.2956i	−0.389203	−	0.488045i
$859$	−4.52677	−	19.8331i	−0.154452	−	0.676696i	−0.991559	−	0.129658i	$-0.958612\pi$
$859$	−4.52677	−	19.8331i	−0.154452	−	0.676696i	0.837107	−	0.547039i	$-0.184245\pi$
$860$	2.47874	+	10.8601i	0.0845242	+	0.370325i
$861$	−3.02921	−	33.2047i	−0.103235	−	1.13161i
$862$	−4.07421	+	17.8503i	−0.138768	+	0.607982i
$863$	−43.2013			−1.47059			−0.735295	−	0.677747i	$-0.762957\pi$
$863$	−43.2013			−1.47059			−0.735295	+	0.677747i	$0.762957\pi$
$864$	−3.00264			−0.102152
$865$	4.67862	−	20.4984i	0.159078	−	0.696966i
$866$	−23.2031	+	11.1740i	−0.788473	+	0.379709i
$867$	−3.63727	−	4.56100i	−0.123528	−	0.154900i
$868$	−4.53000	+	12.1149i	−0.153758	+	0.411207i
$869$	−4.85967	+	6.09383i	−0.164853	+	0.206719i
$870$	3.93415	−	17.2366i	0.133380	−	0.584377i
$871$	40.9550	−	51.3559i	1.38771	−	1.74013i
$872$	16.7155	−	8.04976i	0.566058	−	0.272599i
$873$	3.69458	+	4.63286i	0.125043	+	0.156798i
$874$	7.04117	+	3.39085i	0.238171	+	0.114697i
$875$	−10.2222	+	27.3380i	−0.345574	+	0.924195i
$876$	−14.8477	+	7.15026i	−0.501656	+	0.241585i
$877$	1.86693	+	0.899068i	0.0630419	+	0.0303594i	0.465139	−	0.885238i	$-0.346004\pi$
$877$	1.86693	+	0.899068i	0.0630419	+	0.0303594i	−0.402097	+	0.915597i	$0.631719\pi$
$878$	−4.16827	−	18.2624i	−0.140672	−	0.616326i
$879$	24.1684	+	11.6389i	0.815179	+	0.392570i
$880$	−1.13331	+	1.42113i	−0.0382039	+	0.0479061i
$881$	16.2998			0.549154			0.274577	−	0.961565i	$-0.411462\pi$
$881$	16.2998			0.549154			0.274577	+	0.961565i	$0.411462\pi$
$882$	−4.42696	−	10.2881i	−0.149063	−	0.346417i
$883$	27.6453			0.930337			0.465168	−	0.885222i	$-0.345994\pi$
$883$	27.6453			0.930337			0.465168	+	0.885222i	$0.345994\pi$
$884$	17.5079	−	21.9542i	0.588854	−	0.738400i
$885$	17.5637	+	8.45825i	0.590399	+	0.284321i
$886$	−0.503389	−	2.20549i	−0.0169117	−	0.0740949i
$887$	−13.8567	−	6.67302i	−0.465262	−	0.224058i	0.186540	−	0.982447i	$-0.440272\pi$
$887$	−13.8567	−	6.67302i	−0.465262	−	0.224058i	−0.651802	+	0.758389i	$0.725987\pi$
$888$	−2.76828	+	1.33313i	−0.0928974	+	0.0447370i
$889$	25.6650	−	24.5981i	0.860778	−	0.824994i
$890$	−12.6348	−	6.08458i	−0.423518	−	0.203956i
$891$	−9.44833	−	11.8478i	−0.316531	−	0.396917i
$892$	15.4672	−	7.44863i	0.517881	−	0.249398i
$893$	3.34625	−	4.19606i	0.111978	−	0.140416i
$894$	2.72091	−	11.9211i	0.0910009	−	0.398701i
$895$	−4.76206	+	5.97143i	−0.159178	+	0.199603i
$896$	2.20984	+	1.45485i	0.0738257	+	0.0486031i
$897$	47.4827	+	59.5414i	1.58540	+	1.98803i
$898$	0.220557	−	0.106215i	0.00736009	−	0.00354443i
$899$	−6.65120	+	29.1408i	−0.221830	+	0.971901i
$900$	−5.09174			−0.169725
$901$	59.3324			1.97665
$902$	−1.76280	+	7.72331i	−0.0586947	+	0.257158i
$903$	39.1599	+	25.7809i	1.30316	+	0.857933i
$904$	−0.255236	−	1.11826i	−0.00848903	−	0.0371929i
$905$	−1.91775	−	8.40219i	−0.0637480	−	0.279298i
$906$	25.6023	+	32.1042i	0.850578	+	1.06659i
$907$	−18.9865	−	23.8083i	−0.630436	−	0.790542i	0.359335	−	0.933209i	$-0.383004\pi$
$907$	−18.9865	−	23.8083i	−0.630436	−	0.790542i	−0.989771	+	0.142667i	$0.954432\pi$
$908$	1.03190	+	4.52104i	0.0342448	+	0.150036i
$909$	−5.12530	−	22.4554i	−0.169995	−	0.744798i
$910$	−16.2843	+	15.6073i	−0.539819	+	0.517379i
$911$	0.600845	−	2.63247i	0.0199069	−	0.0872178i	−0.963999	−	0.265907i	$-0.914329\pi$
$911$	0.600845	−	2.63247i	0.0199069	−	0.0872178i	0.983906	+	0.178689i	$0.0571857\pi$
$912$	−2.98496			−0.0988420
$913$	10.4702			0.346514
$914$	−6.72034	+	29.4437i	−0.222289	+	0.973912i
$915$	−27.0276	+	13.0158i	−0.893504	+	0.430289i
$916$	−3.16463	−	3.96832i	−0.104562	−	0.131117i
$917$	−40.1679	−	5.39136i	−1.32646	−	0.178038i
$918$	8.31355	−	10.4249i	0.274388	−	0.344072i
$919$	9.74185	−	42.6818i	0.321354	−	1.40794i	−0.513792	−	0.857915i	$-0.671760\pi$
$919$	9.74185	−	42.6818i	0.321354	−	1.40794i	0.835146	−	0.550029i	$-0.185383\pi$
$920$	4.72025	−	5.91900i	0.155622	−	0.195144i
$921$	−42.1071	+	20.2777i	−1.38747	+	0.668173i
$922$	−15.0386	−	18.8578i	−0.495271	−	0.621050i
$923$	33.1636	+	15.9707i	1.09159	+	0.525683i
$924$	0.695051	+	7.61883i	0.0228655	+	0.250641i
$925$	4.10746	−	1.97805i	0.135052	−	0.0650378i
$926$	−17.9564	−	8.64733i	−0.590083	−	0.284169i
$927$	−0.596341	−	2.61274i	−0.0195864	−	0.0858136i
$928$	5.50872	+	2.65286i	0.180833	+	0.0870844i
$929$	−13.3108	+	16.6913i	−0.436714	+	0.547622i	−0.950674	−	0.310192i	$-0.899607\pi$
$929$	−13.3108	+	16.6913i	−0.436714	+	0.547622i	0.513960	+	0.857814i	$0.328178\pi$
$930$	−14.1360			−0.463539
$931$	3.85071	+	8.94889i	0.126202	+	0.293288i
$932$	−10.7668			−0.352679
$933$	−8.59292	+	10.7752i	−0.281319	+	0.352763i
$934$	33.3758	+	16.0729i	1.09209	+	0.525923i
$935$	−1.79615	−	7.86946i	−0.0587405	−	0.257359i
$936$	−9.11558	−	4.38983i	−0.297952	−	0.143486i
$937$	−29.6876	+	14.2968i	−0.969851	+	0.467056i	−0.850603	−	0.525809i	$-0.823763\pi$
$937$	−29.6876	+	14.2968i	−0.969851	+	0.467056i	−0.119248	+	0.992864i	$0.538048\pi$
$938$	−26.1282	+	8.52472i	−0.853116	+	0.278342i
$939$	−34.0602	−	16.4025i	−1.11151	−	0.535277i
$940$	−3.24159	−	4.06483i	−0.105729	−	0.132580i
$941$	11.9104	−	5.73573i	0.388267	−	0.186979i	−0.229558	−	0.973295i	$-0.573728\pi$
$941$	11.9104	−	5.73573i	0.388267	−	0.186979i	0.617825	+	0.786315i	$0.288014\pi$
$942$	−12.5935	+	15.7917i	−0.410318	+	0.514522i
$943$	7.34206	−	32.1677i	0.239090	−	1.04752i
$944$	−4.20337	+	5.27086i	−0.136808	+	0.171552i
$945$	−7.73253	+	7.41108i	−0.251539	+	0.241082i
$946$	−6.94526	−	8.70909i	−0.225810	−	0.283157i
$947$	1.79388	−	0.863886i	0.0582932	−	0.0280725i	−0.404510	−	0.914534i	$-0.632558\pi$
$947$	1.79388	−	0.863886i	0.0582932	−	0.0280725i	0.462803	+	0.886461i	$0.346844\pi$
$948$	−2.75911	+	12.0884i	−0.0896116	+	0.392614i
$949$	48.5870			1.57720
$950$	4.42896			0.143695
$951$	−1.03187	+	4.52092i	−0.0334607	+	0.146601i
$952$	−11.1696	+	3.64424i	−0.362008	+	0.118111i
$953$	5.19823	+	22.7749i	0.168387	+	0.737752i	0.986643	+	0.162898i	$0.0520841\pi$
$953$	5.19823	+	22.7749i	0.168387	+	0.737752i	−0.818256	+	0.574854i	$0.805059\pi$
$954$	−4.75699	−	20.8418i	−0.154013	−	0.674777i
$955$	−12.1677	−	15.2579i	−0.393739	−	0.493733i
$956$	−16.5235	−	20.7198i	−0.534408	−	0.670126i
$957$	3.93415	+	17.2366i	0.127173	+	0.557181i
$958$	−3.59974	−	15.7715i	−0.116302	−	0.509554i
$959$	4.58700	+	0.615670i	0.148122	+	0.0198810i
$960$	−0.643443	+	2.81911i	−0.0207670	+	0.0909863i
$961$	−7.10115			−0.229069
$962$	9.05883			0.292068
$963$	−5.14486	+	22.5411i	−0.165791	+	0.726377i
$964$	9.13919	−	4.40120i	0.294354	−	0.141753i
$965$	3.29679	+	4.13404i	0.106127	+	0.133079i
$966$	−2.89490	−	31.7325i	−0.0931417	−	1.02098i
$967$	−12.2152	+	15.3173i	−0.392813	+	0.492572i	−0.938433	−	0.345461i	$-0.887723\pi$
$967$	−12.2152	+	15.3173i	−0.392813	+	0.492572i	0.545620	+	0.838033i	$0.316294\pi$
$968$	−2.04326	+	8.95209i	−0.0656728	+	0.287731i
$969$	8.26459	−	10.3635i	0.265497	−	0.332923i
$970$	−4.49864	+	2.16643i	−0.144443	+	0.0695600i
$971$	−9.62300	−	12.0669i	−0.308817	−	0.387244i	0.603068	−	0.797690i	$-0.293945\pi$
$971$	−9.62300	−	12.0669i	−0.308817	−	0.387244i	−0.911885	+	0.410445i	$0.865373\pi$
$972$	−13.6039	−	6.55130i	−0.436346	−	0.210133i
$973$	−2.33842	−	3.90307i	−0.0749664	−	0.125127i
$974$	−0.969150	+	0.466718i	−0.0310536	+	0.0149546i
$975$	38.8851	+	18.7261i	1.24532	+	0.599714i
$976$	−2.30850	−	10.1142i	−0.0738931	−	0.323747i
$977$	−55.0877	−	26.5288i	−1.76241	−	0.848732i	−0.971585	−	0.236691i	$-0.923937\pi$
$977$	−55.0877	−	26.5288i	−1.76241	−	0.848732i	−0.790826	−	0.612041i	$-0.790349\pi$
$978$	−8.58757	+	10.7685i	−0.274600	+	0.344338i
$979$	14.0235			0.448194
$980$	9.28172	−	1.70772i	0.296494	−	0.0545511i
$981$	29.6847			0.947760
$982$	1.44867	−	1.81657i	0.0462288	−	0.0579691i
$983$	19.4938	+	9.38774i	0.621757	+	0.299422i	0.718115	−	0.695924i	$-0.245005\pi$
$983$	19.4938	+	9.38774i	0.621757	+	0.299422i	−0.0963580	+	0.995347i	$0.530719\pi$
$984$	2.80428	+	12.2864i	0.0893973	+	0.391675i
$985$	−11.2116	−	5.39923i	−0.357232	−	0.172034i
$986$	−24.4627	+	11.7806i	−0.779050	+	0.375171i
$987$	−21.6881	−	2.91099i	−0.690339	−	0.0926577i
$988$	7.92903	+	3.81842i	0.252256	+	0.121480i
$989$	28.9271	+	36.2734i	0.919828	+	1.15343i
$990$	−2.62031	+	1.26187i	−0.0832789	+	0.0401050i
$991$	−21.3936	+	26.8267i	−0.679590	+	0.852179i	−0.995316	−	0.0966713i	$-0.969180\pi$
$991$	−21.3936	+	26.8267i	−0.679590	+	0.852179i	0.315726	+	0.948850i	$0.397752\pi$
$992$	1.08783	−	4.76608i	0.0345385	−	0.151323i
$993$	−25.1450	+	31.5308i	−0.797952	+	1.00060i
$994$	−7.91524	−	13.2114i	−0.251056	−	0.419039i
$995$	13.7496	+	17.2415i	0.435892	+	0.546591i
$996$	15.0067	−	7.22686i	0.475507	−	0.228992i
$997$	−6.99611	+	30.6520i	−0.221569	+	0.970758i	0.734728	+	0.678362i	$0.237310\pi$
$997$	−6.99611	+	30.6520i	−0.221569	+	0.970758i	−0.956297	+	0.292396i	$0.905547\pi$
$998$	−1.34319			−0.0425179
$999$	4.30154			0.136095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.e.b.43.3	✓	18
3.2	odd	2		882.2.u.g.631.2		18
4.3	odd	2		784.2.u.d.337.1		18
7.2	even	3		686.2.g.h.165.1		36
7.3	odd	6		686.2.g.g.569.3		36
7.4	even	3		686.2.g.h.569.1		36
7.5	odd	6		686.2.g.g.165.3		36
7.6	odd	2		686.2.e.b.295.1		18
49.3	odd	42		686.2.g.g.79.3		36
49.5	odd	42		686.2.g.g.557.3		36
49.8	even	7	inner	98.2.e.b.57.3	yes	18
49.20	odd	14		4802.2.a.c.1.7		9
49.29	even	7		4802.2.a.d.1.3		9
49.41	odd	14		686.2.e.b.393.1		18
49.44	even	21		686.2.g.h.557.1		36
49.46	even	21		686.2.g.h.79.1		36
147.8	odd	14		882.2.u.g.253.2		18
196.155	odd	14		784.2.u.d.449.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.43.3	✓	18	1.1	even	1	trivial
98.2.e.b.57.3	yes	18	49.8	even	7	inner
686.2.e.b.295.1		18	7.6	odd	2
686.2.e.b.393.1		18	49.41	odd	14
686.2.g.g.79.3		36	49.3	odd	42
686.2.g.g.165.3		36	7.5	odd	6
686.2.g.g.557.3		36	49.5	odd	42
686.2.g.g.569.3		36	7.3	odd	6
686.2.g.h.79.1		36	49.46	even	21
686.2.g.h.165.1		36	7.2	even	3
686.2.g.h.557.1		36	49.44	even	21
686.2.g.h.569.1		36	7.4	even	3
784.2.u.d.337.1		18	4.3	odd	2
784.2.u.d.449.1		18	196.155	odd	14
882.2.u.g.253.2		18	147.8	odd	14
882.2.u.g.631.2		18	3.2	odd	2
4802.2.a.c.1.7		9	49.20	odd	14
4802.2.a.d.1.3		9	49.29	even	7

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 + 0.781831i) q^{2} +(1.93237 + 0.930578i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.21470 + 0.584969i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(-2.20984 - 1.45485i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.997592 + 1.25094i) q^{9} +O(q^{10})\)	\(q+(-0.623490 + 0.781831i) q^{2} +(1.93237 + 0.930578i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.21470 + 0.584969i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(-2.20984 - 1.45485i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.997592 + 1.25094i) q^{9} +(-1.21470 + 0.584969i) q^{10} +(0.840599 - 1.05408i) q^{11} +(0.477255 - 2.09099i) q^{12} +(-3.94258 + 4.94384i) q^{13} +(2.51526 - 0.820642i) q^{14} +(1.80289 + 2.26075i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.988153 - 4.32938i) q^{17} -1.60001 q^{18} +1.39174 q^{19} +(0.300006 - 1.31441i) q^{20} +(-2.91638 - 4.86773i) q^{21} +(0.300006 + 1.31441i) q^{22} +(-1.24953 - 5.47455i) q^{23} +(1.33724 + 1.67684i) q^{24} +(-1.98414 - 2.48803i) q^{25} +(-1.40709 - 6.16487i) q^{26} +(-0.668151 - 2.92736i) q^{27} +(-0.926636 + 2.47817i) q^{28} +(-1.36054 + 5.96092i) q^{29} -2.89161 q^{30} +4.88865 q^{31} +(0.222521 - 0.974928i) q^{32} +(2.60525 - 1.25462i) q^{33} +(2.76874 + 3.47189i) q^{34} +(-1.83326 - 3.05990i) q^{35} +(0.997592 - 1.25094i) q^{36} +(-0.318780 + 1.39667i) q^{37} +(-0.867738 + 1.08811i) q^{38} +(-12.2191 + 5.88443i) q^{39} +(0.840599 + 1.05408i) q^{40} +(5.29397 + 2.54944i) q^{41} +(5.62408 + 0.754867i) q^{42} +(-7.44405 + 3.58487i) q^{43} +(-1.21470 - 0.584969i) q^{44} +(0.480014 + 2.10308i) q^{45} +(5.05924 + 2.43640i) q^{46} +(2.40436 - 3.01497i) q^{47} -2.14476 q^{48} +(2.76683 + 6.42998i) q^{49} +3.18231 q^{50} +(5.93830 - 7.44639i) q^{51} +(5.69719 + 2.74362i) q^{52} +(2.97310 + 13.0260i) q^{53} +(2.70529 + 1.30280i) q^{54} +(1.63768 - 0.788665i) q^{55} +(-1.35977 - 2.26959i) q^{56} +(2.68936 + 1.29513i) q^{57} +(-3.81215 - 4.78029i) q^{58} +(6.07405 - 2.92511i) q^{59} +(1.80289 - 2.26075i) q^{60} +(-2.30850 + 10.1142i) q^{61} +(-3.04802 + 3.82210i) q^{62} +(-0.384593 - 4.21573i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-7.68105 + 3.69900i) q^{65} +(-0.643443 + 2.81911i) q^{66} -10.3879 q^{67} -4.44072 q^{68} +(2.67995 - 11.7416i) q^{69} +(3.53534 + 0.474516i) q^{70} +(-1.29530 - 5.67509i) q^{71} +(0.356036 + 1.55990i) q^{72} +(-4.79069 - 6.00734i) q^{73} +(-0.893203 - 1.12004i) q^{74} +(-1.51877 - 6.65418i) q^{75} +(-0.309692 - 1.35685i) q^{76} +(-3.39112 + 1.10640i) q^{77} +(3.01788 - 13.2222i) q^{78} -5.78120 q^{79} -1.34822 q^{80} +(2.50113 - 10.9582i) q^{81} +(-5.29397 + 2.54944i) q^{82} +(4.84202 + 6.07170i) q^{83} +(-4.09673 + 3.92643i) q^{84} +(3.73287 - 4.68086i) q^{85} +(1.83853 - 8.05512i) q^{86} +(-8.17617 + 10.2526i) q^{87} +(1.21470 - 0.584969i) q^{88} +(6.48525 + 8.13225i) q^{89} +(-1.94354 - 0.935958i) q^{90} +(15.9050 - 5.18926i) q^{91} +(-5.05924 + 2.43640i) q^{92} +(9.44665 + 4.54927i) q^{93} +(0.858105 + 3.75960i) q^{94} +(1.69055 + 0.814127i) q^{95} +(1.33724 - 1.67684i) q^{96} +3.70350 q^{97} +(-6.75225 - 1.84584i) q^{98} +2.15716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9} + 7 q^{11} + 2 q^{12} - 10 q^{13} + q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 32 q^{18} - 44 q^{19} + 7 q^{20} - 5 q^{21} + 7 q^{22} + 21 q^{23} - 2 q^{24} + q^{25} + 3 q^{26} + 10 q^{27} - 8 q^{28} + 11 q^{29} - 24 q^{31} + 3 q^{32} - 14 q^{33} - q^{34} - 21 q^{35} - 10 q^{36} - 13 q^{37} - 19 q^{38} - 3 q^{39} + 7 q^{40} + 8 q^{41} + 61 q^{42} - 24 q^{43} + 98 q^{45} + 21 q^{46} + 40 q^{47} + 2 q^{48} - 43 q^{49} - 50 q^{50} + 36 q^{51} + 18 q^{52} + 10 q^{53} + 4 q^{54} + 49 q^{55} + q^{56} + 19 q^{57} + 24 q^{58} + 13 q^{59} + 7 q^{60} + 27 q^{61} - 11 q^{62} + 41 q^{63} - 3 q^{64} - 21 q^{66} - 86 q^{67} - 34 q^{68} - 91 q^{69} - 14 q^{70} + 3 q^{72} + 5 q^{73} + 13 q^{74} - 3 q^{75} - 2 q^{76} - 14 q^{77} + 38 q^{78} - 66 q^{79} - 2 q^{81} - 8 q^{82} + 55 q^{83} + 23 q^{84} - 49 q^{85} - 18 q^{86} - 110 q^{87} + 62 q^{89} + 21 q^{90} + 39 q^{91} - 21 q^{92} + 46 q^{93} + 23 q^{94} - 7 q^{95} - 2 q^{96} - 32 q^{97} - 48 q^{98} + 14 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9 + 7 * q^11 + 2 * q^12 - 10 * q^13 + q^14 + 7 * q^15 - 3 * q^16 + q^17 - 32 * q^18 - 44 * q^19 + 7 * q^20 - 5 * q^21 + 7 * q^22 + 21 * q^23 - 2 * q^24 + q^25 + 3 * q^26 + 10 * q^27 - 8 * q^28 + 11 * q^29 - 24 * q^31 + 3 * q^32 - 14 * q^33 - q^34 - 21 * q^35 - 10 * q^36 - 13 * q^37 - 19 * q^38 - 3 * q^39 + 7 * q^40 + 8 * q^41 + 61 * q^42 - 24 * q^43 + 98 * q^45 + 21 * q^46 + 40 * q^47 + 2 * q^48 - 43 * q^49 - 50 * q^50 + 36 * q^51 + 18 * q^52 + 10 * q^53 + 4 * q^54 + 49 * q^55 + q^56 + 19 * q^57 + 24 * q^58 + 13 * q^59 + 7 * q^60 + 27 * q^61 - 11 * q^62 + 41 * q^63 - 3 * q^64 - 21 * q^66 - 86 * q^67 - 34 * q^68 - 91 * q^69 - 14 * q^70 + 3 * q^72 + 5 * q^73 + 13 * q^74 - 3 * q^75 - 2 * q^76 - 14 * q^77 + 38 * q^78 - 66 * q^79 - 2 * q^81 - 8 * q^82 + 55 * q^83 + 23 * q^84 - 49 * q^85 - 18 * q^86 - 110 * q^87 + 62 * q^89 + 21 * q^90 + 39 * q^91 - 21 * q^92 + 46 * q^93 + 23 * q^94 - 7 * q^95 - 2 * q^96 - 32 * q^97 - 48 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more