LMFDB - Embedded newform 49.2.e.a.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	49.36
Dual form			49.2.e.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 2.19064i) q^{2} +(-0.500000 - 0.626980i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(0.153989 + 0.193096i) q^{5} +(-1.12349 + 1.40881i) q^{6} +(2.06853 + 1.64960i) q^{7} +(1.46950 + 1.84270i) q^{8} +(0.524459 - 2.29780i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 2.19064i) q^{2} +(-0.500000 - 0.626980i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(0.153989 + 0.193096i) q^{5} +(-1.12349 + 1.40881i) q^{6} +(2.06853 + 1.64960i) q^{7} +(1.46950 + 1.84270i) q^{8} +(0.524459 - 2.29780i) q^{9} +(0.346011 - 0.433884i) q^{10} +(-0.233406 - 1.02262i) q^{11} +(2.20291 + 1.06086i) q^{12} +(1.18933 + 5.21081i) q^{13} +(2.57942 - 5.35621i) q^{14} +(0.0440730 - 0.193096i) q^{15} +(-0.500000 + 0.626980i) q^{16} +(4.44989 + 2.14295i) q^{17} -5.29590 q^{18} -5.85086 q^{19} +(-0.678448 - 0.326723i) q^{20} -2.12173i q^{21} +(-2.12349 + 1.02262i) q^{22} +(-5.44989 + 2.62453i) q^{23} +(0.420583 - 1.84270i) q^{24} +(1.09903 - 4.81517i) q^{25} +(10.8204 - 5.21081i) q^{26} +(-3.87047 + 1.86392i) q^{27} +(-7.86443 - 1.79500i) q^{28} +(-2.04407 - 0.984374i) q^{29} -0.445042 q^{30} -0.198062 q^{31} +(5.87047 + 2.82707i) q^{32} +(-0.524459 + 0.657650i) q^{33} +(2.46950 - 10.8196i) q^{34} +0.653447i q^{35} +(1.59903 + 7.00581i) q^{36} +(5.29590 + 2.55037i) q^{37} +(2.92543 + 12.8171i) q^{38} +(2.67241 - 3.35109i) q^{39} +(-0.129531 + 0.567511i) q^{40} +(-3.04892 - 3.82322i) q^{41} +(-4.64795 + 1.06086i) q^{42} +(2.67845 - 3.35867i) q^{43} +(1.99396 + 2.50035i) q^{44} +(0.524459 - 0.252566i) q^{45} +(8.47434 + 10.6265i) q^{46} +(-1.82155 - 7.98074i) q^{47} +0.643104 q^{48} +(1.55765 + 6.82450i) q^{49} -11.0978 q^{50} +(-0.881355 - 3.86147i) q^{51} +(-10.1603 - 12.7406i) q^{52} +(-3.08815 + 1.48717i) q^{53} +(6.01842 + 7.54686i) q^{54} +(0.161522 - 0.202542i) q^{55} +6.23576i q^{56} +(2.92543 + 3.66837i) q^{57} +(-1.13437 + 4.97002i) q^{58} +(-2.96346 + 3.71606i) q^{59} +(0.134375 + 0.588735i) q^{60} +(-2.96950 - 1.43004i) q^{61} +(0.0990311 + 0.433884i) q^{62} +(4.87531 - 3.88793i) q^{63} +(2.90097 - 12.7100i) q^{64} +(-0.823044 + 1.03206i) q^{65} +(1.70291 + 0.820077i) q^{66} -3.35690 q^{67} -15.0586 q^{68} +(4.37047 + 2.10471i) q^{69} +(1.43147 - 0.326723i) q^{70} +(3.65883 - 1.76200i) q^{71} +(5.00484 - 2.41021i) q^{72} +(3.09299 - 13.5513i) q^{73} +(2.93900 - 12.8766i) q^{74} +(-3.56853 + 1.71851i) q^{75} +(16.0722 - 7.73995i) q^{76} +(1.20410 - 2.50035i) q^{77} +(-8.67725 - 4.17874i) q^{78} +8.64310 q^{79} -0.198062 q^{80} +(-3.26659 - 1.57311i) q^{81} +(-6.85086 + 8.59070i) q^{82} +(-2.62080 + 11.4825i) q^{83} +(2.80678 + 5.82834i) q^{84} +(0.271438 + 1.18925i) q^{85} +(-8.69687 - 4.18819i) q^{86} +(0.404854 + 1.77378i) q^{87} +(1.54138 - 1.93284i) q^{88} +(-3.70775 + 16.2447i) q^{89} +(-0.815511 - 1.02262i) q^{90} +(-6.13557 + 12.7406i) q^{91} +(11.4988 - 14.4190i) q^{92} +(0.0990311 + 0.124181i) q^{93} +(-16.5722 + 7.98074i) q^{94} +(-0.900969 - 1.12978i) q^{95} +(-1.16272 - 5.09420i) q^{96} -1.69202 q^{97} +(14.1712 - 6.82450i) q^{98} -2.47219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 7 q^{4} + 6 q^{5} - 2 q^{6} + 7 q^{7} - q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 7 * q^4 + 6 * q^5 - 2 * q^6 + 7 * q^7 - q^8 - 6 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 7 q^{4} + 6 q^{5} - 2 q^{6} + 7 q^{7} - q^{8} - 6 q^{9} - 3 q^{10} + 2 q^{11} + 7 q^{14} + 4 q^{15} - 3 q^{16} + 4 q^{17} - 4 q^{18} - 8 q^{19} - 8 q^{22} - 10 q^{23} + 11 q^{24} + 11 q^{25} + 28 q^{26} - 9 q^{27} - 14 q^{28} - 16 q^{29} - 2 q^{30} - 10 q^{31} + 21 q^{32} + 6 q^{33} + 5 q^{34} + 14 q^{36} + 4 q^{37} + 4 q^{38} - 7 q^{39} - 15 q^{40} - 14 q^{42} + 12 q^{43} - 7 q^{44} - 6 q^{45} + 19 q^{46} - 15 q^{47} + 12 q^{48} + 7 q^{49} - 30 q^{50} + 12 q^{51} - 26 q^{53} + 8 q^{54} - 19 q^{55} + 4 q^{57} + q^{58} + 11 q^{59} - 7 q^{60} - 8 q^{61} + 5 q^{62} - 7 q^{63} + 13 q^{64} + 35 q^{65} - 3 q^{66} - 12 q^{67} - 28 q^{68} + 12 q^{69} + 14 q^{70} + 5 q^{71} + 8 q^{72} + 4 q^{73} - 2 q^{74} - 16 q^{75} + 28 q^{76} + 35 q^{77} - 7 q^{78} + 60 q^{79} - 10 q^{80} - 23 q^{81} - 14 q^{82} - 14 q^{83} - 14 q^{84} - 17 q^{85} - 20 q^{86} + 36 q^{87} + 16 q^{88} + 13 q^{89} + 10 q^{90} - 70 q^{91} + 28 q^{92} + 5 q^{93} - 31 q^{94} - q^{95} - 28 q^{96} + 21 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 7 * q^4 + 6 * q^5 - 2 * q^6 + 7 * q^7 - q^8 - 6 * q^9 - 3 * q^10 + 2 * q^11 + 7 * q^14 + 4 * q^15 - 3 * q^16 + 4 * q^17 - 4 * q^18 - 8 * q^19 - 8 * q^22 - 10 * q^23 + 11 * q^24 + 11 * q^25 + 28 * q^26 - 9 * q^27 - 14 * q^28 - 16 * q^29 - 2 * q^30 - 10 * q^31 + 21 * q^32 + 6 * q^33 + 5 * q^34 + 14 * q^36 + 4 * q^37 + 4 * q^38 - 7 * q^39 - 15 * q^40 - 14 * q^42 + 12 * q^43 - 7 * q^44 - 6 * q^45 + 19 * q^46 - 15 * q^47 + 12 * q^48 + 7 * q^49 - 30 * q^50 + 12 * q^51 - 26 * q^53 + 8 * q^54 - 19 * q^55 + 4 * q^57 + q^58 + 11 * q^59 - 7 * q^60 - 8 * q^61 + 5 * q^62 - 7 * q^63 + 13 * q^64 + 35 * q^65 - 3 * q^66 - 12 * q^67 - 28 * q^68 + 12 * q^69 + 14 * q^70 + 5 * q^71 + 8 * q^72 + 4 * q^73 - 2 * q^74 - 16 * q^75 + 28 * q^76 + 35 * q^77 - 7 * q^78 + 60 * q^79 - 10 * q^80 - 23 * q^81 - 14 * q^82 - 14 * q^83 - 14 * q^84 - 17 * q^85 - 20 * q^86 + 36 * q^87 + 16 * q^88 + 13 * q^89 + 10 * q^90 - 70 * q^91 + 28 * q^92 + 5 * q^93 - 31 * q^94 - q^95 - 28 * q^96 + 21 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−0.500000	−	2.19064i	−0.353553	−	1.54902i	−0.768908	−	0.639359i	$-0.779200\pi$
$2$	−0.500000	−	2.19064i	−0.353553	−	1.54902i	0.415355	−	0.909659i	$-0.363657\pi$
$3$	−0.500000	−	0.626980i	−0.288675	−	0.361987i	0.616255	−	0.787546i	$-0.288649\pi$
$3$	−0.500000	−	0.626980i	−0.288675	−	0.361987i	−0.904931	+	0.425559i	$0.860077\pi$
$4$	−2.74698	+	1.32288i	−1.37349	+	0.661438i
$5$	0.153989	+	0.193096i	0.0688661	+	0.0863553i	0.815071	−	0.579361i	$-0.196698\pi$
$5$	0.153989	+	0.193096i	0.0688661	+	0.0863553i	−0.746205	+	0.665716i	$0.768126\pi$
$6$	−1.12349	+	1.40881i	−0.458663	+	0.575145i
$7$	2.06853	+	1.64960i	0.781831	+	0.623490i
$7$	2.06853	+	1.64960i	0.781831	+	0.623490i
$8$	1.46950	+	1.84270i	0.519547	+	0.651491i
$9$	0.524459	−	2.29780i	0.174820	−	0.765935i
$10$	0.346011	−	0.433884i	0.109418	−	0.137206i
$11$	−0.233406	−	1.02262i	−0.0703746	−	0.308331i	0.927474	−	0.373887i	$-0.121975\pi$
$11$	−0.233406	−	1.02262i	−0.0703746	−	0.308331i	−0.997849	+	0.0655557i	$0.979118\pi$
$12$	2.20291	+	1.06086i	0.635924	+	0.306245i
$13$	1.18933	+	5.21081i	0.329862	+	1.44522i	0.819393	+	0.573232i	$0.194311\pi$
$13$	1.18933	+	5.21081i	0.329862	+	1.44522i	−0.489531	+	0.871986i	$0.662832\pi$
$14$	2.57942	−	5.35621i	0.689378	−	1.43151i
$15$	0.0440730	−	0.193096i	0.0113796	−	0.0498573i
$16$	−0.500000	+	0.626980i	−0.125000	+	0.156745i
$17$	4.44989	+	2.14295i	1.07926	+	0.519742i	0.887079	−	0.461618i	$-0.152731\pi$
$17$	4.44989	+	2.14295i	1.07926	+	0.519742i	0.192177	+	0.981360i	$0.438445\pi$
$18$	−5.29590			−1.24825
$19$	−5.85086			−1.34228			−0.671139	−	0.741331i	$-0.734195\pi$
$19$	−5.85086			−1.34228			−0.671139	+	0.741331i	$0.734195\pi$
$20$	−0.678448	−	0.326723i	−0.151706	−	0.0730576i
$21$		−	2.12173i		−	0.462999i
$22$	−2.12349	+	1.02262i	−0.452730	+	0.218023i
$23$	−5.44989	+	2.62453i	−1.13638	+	0.547252i	−0.904915	−	0.425592i	$-0.860066\pi$
$23$	−5.44989	+	2.62453i	−1.13638	+	0.547252i	−0.231465	+	0.972843i	$0.574352\pi$
$24$	0.420583	−	1.84270i	0.0858512	−	0.376139i
$25$	1.09903	−	4.81517i	0.219806	−	0.963034i
$26$	10.8204	−	5.21081i	2.12205	−	1.02192i
$27$	−3.87047	+	1.86392i	−0.744872	+	0.358712i
$28$	−7.86443	−	1.79500i	−1.48624	−	0.339224i
$29$	−2.04407	−	0.984374i	−0.379575	−	0.182794i	0.234361	−	0.972150i	$-0.424700\pi$
$29$	−2.04407	−	0.984374i	−0.379575	−	0.182794i	−0.613936	+	0.789356i	$0.710415\pi$
$30$	−0.445042			−0.0812532
$31$	−0.198062			−0.0355730			−0.0177865	−	0.999842i	$-0.505662\pi$
$31$	−0.198062			−0.0355730			−0.0177865	+	0.999842i	$0.505662\pi$
$32$	5.87047	+	2.82707i	1.03776	+	0.499760i
$33$	−0.524459	+	0.657650i	−0.0912965	+	0.114482i
$34$	2.46950	−	10.8196i	0.423516	−	1.85554i
$35$			0.653447i			0.110453i
$36$	1.59903	+	7.00581i	0.266505	+	1.16764i
$37$	5.29590	+	2.55037i	0.870640	+	0.419278i	0.815197	−	0.579184i	$-0.196629\pi$
$37$	5.29590	+	2.55037i	0.870640	+	0.419278i	0.0554430	+	0.998462i	$0.482343\pi$
$38$	2.92543	+	12.8171i	0.474567	+	2.07921i
$39$	2.67241	−	3.35109i	0.427928	−	0.536604i
$40$	−0.129531	+	0.567511i	−0.0204806	+	0.0897313i
$41$	−3.04892	−	3.82322i	−0.476161	−	0.597087i	0.484507	−	0.874788i	$-0.338999\pi$
$41$	−3.04892	−	3.82322i	−0.476161	−	0.597087i	−0.960668	+	0.277701i	$0.910428\pi$
$42$	−4.64795	+	1.06086i	−0.717194	+	0.163695i
$43$	2.67845	−	3.35867i	0.408459	−	0.512192i	−0.534469	−	0.845188i	$-0.679488\pi$
$43$	2.67845	−	3.35867i	0.408459	−	0.512192i	0.942928	+	0.332996i	$0.108060\pi$
$44$	1.99396	+	2.50035i	0.300601	+	0.376941i
$45$	0.524459	−	0.252566i	0.0781817	−	0.0376503i
$46$	8.47434	+	10.6265i	1.24947	+	1.56679i
$47$	−1.82155	−	7.98074i	−0.265701	−	1.16411i	−0.914960	−	0.403544i	$-0.867778\pi$
$47$	−1.82155	−	7.98074i	−0.265701	−	1.16411i	0.649260	−	0.760567i	$-0.275079\pi$
$48$	0.643104			0.0928241
$49$	1.55765	+	6.82450i	0.222521	+	0.974928i
$50$	−11.0978			−1.56947
$51$	−0.881355	−	3.86147i	−0.123414	−	0.540713i
$52$	−10.1603	−	12.7406i	−1.40898	−	1.76681i
$53$	−3.08815	+	1.48717i	−0.424189	+	0.204279i	−0.633785	−	0.773509i	$-0.718500\pi$
$53$	−3.08815	+	1.48717i	−0.424189	+	0.204279i	0.209595	+	0.977788i	$0.432785\pi$
$54$	6.01842	+	7.54686i	0.819003	+	1.02700i
$55$	0.161522	−	0.202542i	0.0217796	−	0.0273108i
$56$			6.23576i			0.833289i
$57$	2.92543	+	3.66837i	0.387482	+	0.485887i
$58$	−1.13437	+	4.97002i	−0.148951	+	0.652596i
$59$	−2.96346	+	3.71606i	−0.385810	+	0.483790i	−0.936375	−	0.351002i	$-0.885841\pi$
$59$	−2.96346	+	3.71606i	−0.385810	+	0.483790i	0.550565	+	0.834792i	$0.314412\pi$
$60$	0.134375	+	0.588735i	0.0173477	+	0.0760054i
$61$	−2.96950	−	1.43004i	−0.380206	−	0.183097i	0.234013	−	0.972234i	$-0.424814\pi$
$61$	−2.96950	−	1.43004i	−0.380206	−	0.183097i	−0.614218	+	0.789136i	$0.710529\pi$
$62$	0.0990311	+	0.433884i	0.0125770	+	0.0551033i
$63$	4.87531	−	3.88793i	0.614232	−	0.489834i
$64$	2.90097	−	12.7100i	0.362621	−	1.58875i
$65$	−0.823044	+	1.03206i	−0.102086	+	0.128012i
$66$	1.70291	+	0.820077i	0.209613	+	0.100944i
$67$	−3.35690			−0.410110			−0.205055	−	0.978750i	$-0.565737\pi$
$67$	−3.35690			−0.410110			−0.205055	+	0.978750i	$0.565737\pi$
$68$	−15.0586			−1.82612
$69$	4.37047	+	2.10471i	0.526143	+	0.253377i
$70$	1.43147	−	0.326723i	0.171093	−	0.0390509i
$71$	3.65883	−	1.76200i	0.434224	−	0.209111i	−0.203986	−	0.978974i	$-0.565390\pi$
$71$	3.65883	−	1.76200i	0.434224	−	0.209111i	0.638209	+	0.769863i	$0.279675\pi$
$72$	5.00484	−	2.41021i	0.589827	−	0.284046i
$73$	3.09299	−	13.5513i	0.362007	−	1.58606i	−0.386086	−	0.922463i	$-0.626173\pi$
$73$	3.09299	−	13.5513i	0.362007	−	1.58606i	0.748093	−	0.663594i	$-0.230970\pi$
$74$	2.93900	−	12.8766i	0.341652	−	1.49687i
$75$	−3.56853	+	1.71851i	−0.412059	+	0.198437i
$76$	16.0722	−	7.73995i	1.84361	−	0.887834i
$77$	1.20410	−	2.50035i	0.137220	−	0.284941i
$78$	−8.67725	−	4.17874i	−0.982505	−	0.473150i
$79$	8.64310			0.972425			0.486213	−	0.873841i	$-0.338378\pi$
$79$	8.64310			0.972425			0.486213	+	0.873841i	$0.338378\pi$
$80$	−0.198062			−0.0221440
$81$	−3.26659	−	1.57311i	−0.362955	−	0.174790i
$82$	−6.85086	+	8.59070i	−0.756550	+	0.948684i
$83$	−2.62080	+	11.4825i	−0.287670	+	1.26037i	0.600042	+	0.799968i	$0.295150\pi$
$83$	−2.62080	+	11.4825i	−0.287670	+	1.26037i	−0.887713	+	0.460398i	$0.847707\pi$
$84$	2.80678	+	5.82834i	0.306245	+	0.635924i
$85$	0.271438	+	1.18925i	0.0294416	+	0.128992i
$86$	−8.69687	−	4.18819i	−0.937807	−	0.451624i
$87$	0.404854	+	1.77378i	0.0434049	+	0.190169i
$88$	1.54138	−	1.93284i	0.164312	−	0.206041i
$89$	−3.70775	+	16.2447i	−0.393021	+	1.72194i	0.260893	+	0.965368i	$0.415983\pi$
$89$	−3.70775	+	16.2447i	−0.393021	+	1.72194i	−0.653914	+	0.756569i	$0.726874\pi$
$90$	−0.815511	−	1.02262i	−0.0859624	−	0.107793i
$91$	−6.13557	+	12.7406i	−0.643183	+	1.33558i
$92$	11.4988	−	14.4190i	1.19883	−	1.50329i
$93$	0.0990311	+	0.124181i	0.0102691	+	0.0128770i
$94$	−16.5722	+	7.98074i	−1.70929	+	0.823151i
$95$	−0.900969	−	1.12978i	−0.0924375	−	0.115913i
$96$	−1.16272	−	5.09420i	−0.118669	−	0.519925i
$97$	−1.69202			−0.171799			−0.0858994	−	0.996304i	$-0.527376\pi$
$97$	−1.69202			−0.171799			−0.0858994	+	0.996304i	$0.527376\pi$
$98$	14.1712	−	6.82450i	1.43151	−	0.689378i
$99$	−2.47219			−0.248464
$100$	3.35086	+	14.6811i	0.335086	+	1.46811i
$101$	−6.03534	−	7.56808i	−0.600539	−	0.753052i	0.384923	−	0.922949i	$-0.374228\pi$
$101$	−6.03534	−	7.56808i	−0.600539	−	0.753052i	−0.985462	+	0.169897i	$0.945657\pi$
$102$	−8.01842	+	3.86147i	−0.793942	+	0.382342i
$103$	1.96197	+	2.46023i	0.193318	+	0.242414i	0.869038	−	0.494745i	$-0.164739\pi$
$103$	1.96197	+	2.46023i	0.193318	+	0.242414i	−0.675720	+	0.737159i	$0.736167\pi$
$104$	−7.85421	+	9.84886i	−0.770168	+	0.965761i
$105$	0.409698	−	0.326723i	0.0399824	−	0.0318849i
$106$	4.80194	+	6.02144i	0.466405	+	0.584854i
$107$	1.17725	−	5.15788i	0.113809	−	0.498631i	−0.885606	−	0.464437i	$-0.846257\pi$
$107$	1.17725	−	5.15788i	0.113809	−	0.498631i	0.999415	−	0.0341934i	$-0.0108862\pi$
$108$	8.16637	−	10.2403i	0.785809	−	0.985373i
$109$	1.29925	+	5.69238i	0.124446	+	0.545231i	0.998260	+	0.0589714i	$0.0187821\pi$
$109$	1.29925	+	5.69238i	0.124446	+	0.545231i	−0.873814	+	0.486260i	$0.838361\pi$
$110$	−0.524459	−	0.252566i	−0.0500052	−	0.0240812i
$111$	−1.04892	−	4.59561i	−0.0995588	−	0.436196i
$112$	−2.06853	+	0.472129i	−0.195458	+	0.0446120i
$113$	−0.292249	+	1.28043i	−0.0274925	+	0.120452i	−0.986812	−	0.161870i	$-0.948248\pi$
$113$	−0.292249	+	1.28043i	−0.0274925	+	0.120452i	0.959320	+	0.282322i	$0.0911047\pi$
$114$	6.57338	−	8.24275i	0.615653	−	0.772005i
$115$	−1.34601	−	0.648205i	−0.125516	−	0.0604454i
$116$	6.91723			0.642249
$117$	12.5972			1.16461
$118$	9.62229	+	4.63385i	0.885804	+	0.426581i
$119$	5.66972	+	11.7733i	0.519742	+	1.07926i
$120$	0.420583	−	0.202542i	0.0383938	−	0.0184895i
$121$	8.91939	−	4.29535i	0.810853	−	0.390486i
$122$	−1.64795	+	7.22013i	−0.149198	+	0.653680i
$123$	−0.872625	+	3.82322i	−0.0786820	+	0.344728i
$124$	0.544073	−	0.262012i	0.0488592	−	0.0235293i
$125$	2.21164	−	1.06507i	0.197815	−	0.0952625i
$126$	−10.9547	−	8.73611i	−0.975925	−	0.778274i
$127$	10.1066	+	4.86706i	0.896813	+	0.431882i	0.824737	−	0.565517i	$-0.191323\pi$
$127$	10.1066	+	4.86706i	0.896813	+	0.431882i	0.0720759	+	0.997399i	$0.477038\pi$
$128$	−16.2620			−1.43738
$129$	−3.44504			−0.303319
$130$	2.67241	+	1.28696i	0.234386	+	0.112874i
$131$	12.1453	−	15.2297i	1.06114	−	1.33062i	0.119933	−	0.992782i	$-0.461732\pi$
$131$	12.1453	−	15.2297i	1.06114	−	1.33062i	0.941203	−	0.337841i	$-0.109697\pi$
$132$	0.570688	−	2.50035i	0.0496720	−	0.217627i
$133$	−12.1027	−	9.65156i	−1.04944	−	0.836897i
$134$	1.67845	+	7.35376i	0.144996	+	0.635268i
$135$	−0.955927	−	0.460350i	−0.0822731	−	0.0396206i
$136$	2.59030	+	11.3489i	0.222117	+	0.973156i
$137$	−5.72737	+	7.18189i	−0.489322	+	0.613590i	−0.963783	−	0.266686i	$-0.914071\pi$
$137$	−5.72737	+	7.18189i	−0.489322	+	0.613590i	0.474462	+	0.880276i	$0.342643\pi$
$138$	2.42543	−	10.6265i	0.206466	−	0.904587i
$139$	−9.23155	−	11.5760i	−0.783009	−	0.981863i	−0.999984	−	0.00568553i	$-0.998190\pi$
$139$	−9.23155	−	11.5760i	−0.783009	−	0.981863i	0.216974	−	0.976177i	$-0.430381\pi$
$140$	−0.864429	−	1.79500i	−0.0730576	−	0.151706i
$141$	−4.09299	+	5.13245i	−0.344692	+	0.432230i
$142$	−5.68933	−	7.13420i	−0.477438	−	0.598689i
$143$	5.05107	−	2.43247i	0.422392	−	0.203413i
$144$	1.17845	+	1.47773i	0.0982040	+	0.123144i
$145$	−0.124686	−	0.546286i	−0.0103546	−	0.0453666i
$146$	−31.2325			−2.58482
$147$	3.50000	−	4.38886i	0.288675	−	0.361987i
$148$	−17.9215			−1.47314
$149$	−0.0304995	−	0.133627i	−0.00249861	−	0.0109471i	0.973663	−	0.227991i	$-0.0732157\pi$
$149$	−0.0304995	−	0.133627i	−0.00249861	−	0.0109471i	−0.976162	+	0.217044i	$0.930359\pi$
$150$	5.54892	+	6.95812i	0.453067	+	0.568128i
$151$	8.89493	−	4.28357i	0.723859	−	0.348592i	−0.0354066	−	0.999373i	$-0.511273\pi$
$151$	8.89493	−	4.28357i	0.723859	−	0.348592i	0.759266	+	0.650781i	$0.225558\pi$
$152$	−8.59783	−	10.7813i	−0.697376	−	0.874482i
$153$	7.25786	−	9.10107i	0.586764	−	0.735778i
$154$	−6.07942	−	1.38759i	−0.489893	−	0.111815i
$155$	−0.0304995	−	0.0382451i	−0.00244978	−	0.00307192i
$156$	−2.90797	+	12.7406i	−0.232824	+	1.02007i
$157$	4.52446	−	5.67349i	0.361091	−	0.452794i	−0.567789	−	0.823174i	$-0.692201\pi$
$157$	4.52446	−	5.67349i	0.361091	−	0.452794i	0.928880	+	0.370380i	$0.120773\pi$
$158$	−4.32155	−	18.9340i	−0.343804	−	1.50630i
$159$	2.47650	+	1.19262i	0.196399	+	0.0945809i
$160$	0.358092	+	1.56890i	0.0283097	+	0.124033i
$161$	−15.6027	−	3.56121i	−1.22966	−	0.280663i
$162$	−1.81282	+	7.94250i	−0.142429	+	0.624021i
$163$	−7.93631	+	9.95182i	−0.621620	+	0.779487i	−0.988571	−	0.150753i	$-0.951830\pi$
$163$	−7.93631	+	9.95182i	−0.621620	+	0.779487i	0.366951	+	0.930240i	$0.380402\pi$
$164$	13.4330	+	6.46897i	1.04894	+	0.505142i
$165$	−0.207751			−0.0161734
$166$	26.4644			2.05404
$167$	7.21260	+	3.47340i	0.558127	+	0.268780i	0.691610	−	0.722271i	$-0.256902\pi$
$167$	7.21260	+	3.47340i	0.558127	+	0.268780i	−0.133483	+	0.991051i	$0.542616\pi$
$168$	3.90970	−	3.11788i	0.301640	−	0.240550i
$169$	−14.0254	+	6.75429i	−1.07888	+	0.519560i
$170$	2.46950	−	1.18925i	0.189402	−	0.0912112i
$171$	−3.06853	+	13.4441i	−0.234656	+	1.02810i
$172$	−2.91454	+	12.7694i	−0.222232	+	0.973661i
$173$	−11.0281	+	5.31086i	−0.838451	+	0.403777i	−0.803278	−	0.595604i	$-0.796913\pi$
$173$	−11.0281	+	5.31086i	−0.838451	+	0.403777i	−0.0351734	+	0.999381i	$0.511198\pi$
$174$	3.68329	−	1.77378i	0.279230	−	0.134470i
$175$	10.2165	−	8.14737i	0.772293	−	0.615883i
$176$	0.757865	+	0.364968i	0.0571262	+	0.0275105i
$177$	3.81163			0.286499
$178$	37.4403			2.80627
$179$	0.411854	+	0.198338i	0.0307834	+	0.0148245i	0.449212	−	0.893425i	$-0.351705\pi$
$179$	0.411854	+	0.198338i	0.0307834	+	0.0148245i	−0.418429	+	0.908250i	$0.637419\pi$
$180$	−1.10656	+	1.38759i	−0.0824784	+	0.103425i
$181$	2.08695	−	9.14352i	0.155122	−	0.679633i	−0.836228	−	0.548383i	$-0.815244\pi$
$181$	2.08695	−	9.14352i	0.155122	−	0.679633i	0.991349	−	0.131250i	$-0.0418991\pi$
$182$	30.9780	+	7.07052i	2.29624	+	0.524102i
$183$	0.588146	+	2.57684i	0.0434770	+	0.190485i
$184$	−12.8448	−	6.18574i	−0.946932	−	0.456019i
$185$	0.323044	+	1.41535i	0.0237507	+	0.104058i
$186$	0.222521	−	0.279032i	0.0163160	−	0.0204597i
$187$	1.15279	−	5.05072i	0.0843006	−	0.369345i
$188$	15.5613	+	19.5132i	1.13492	+	1.42315i
$189$	−11.0809	−	2.52915i	−0.806018	−	0.183968i
$190$	−2.02446	+	2.53859i	−0.146870	+	0.184169i
$191$	−3.36294	−	4.21699i	−0.243334	−	0.305131i	0.645135	−	0.764069i	$-0.276801\pi$
$191$	−3.36294	−	4.21699i	−0.243334	−	0.305131i	−0.888468	+	0.458938i	$0.848230\pi$
$192$	−9.41939	+	4.53614i	−0.679786	+	0.327368i
$193$	−14.0097	−	17.5676i	−1.00844	−	1.26454i	−0.964104	−	0.265526i	$-0.914454\pi$
$193$	−14.0097	−	17.5676i	−1.00844	−	1.26454i	−0.0443359	−	0.999017i	$-0.514117\pi$
$194$	0.846011	+	3.70662i	0.0607400	+	0.266119i
$195$	1.05861			0.0758084
$196$	−13.3068	−	16.6862i	−0.950484	−	1.19187i
$197$	2.81940			0.200874			0.100437	−	0.994943i	$-0.467976\pi$
$197$	2.81940			0.200874			0.100437	+	0.994943i	$0.467976\pi$
$198$	1.23609	+	5.41568i	0.0878454	+	0.384876i
$199$	1.66152	+	2.08348i	0.117782	+	0.147694i	0.837227	−	0.546855i	$-0.184175\pi$
$199$	1.66152	+	2.08348i	0.117782	+	0.147694i	−0.719445	+	0.694549i	$0.755604\pi$
$200$	10.4879	−	5.05072i	0.741608	−	0.357140i
$201$	1.67845	+	2.10471i	0.118389	+	0.148455i
$202$	−13.5613	+	17.0053i	−0.954169	+	1.19649i
$203$	−2.60441	−	5.40811i	−0.182794	−	0.379575i
$204$	7.52930	+	9.44145i	0.527157	+	0.661034i
$205$	0.268750	−	1.17747i	0.0187703	−	0.0822381i
$206$	4.40850	−	5.52809i	0.307155	−	0.385160i
$207$	3.17241	+	13.8992i	0.220498	+	0.966063i
$208$	−3.86174	−	1.85972i	−0.267764	−	0.128948i
$209$	1.36563	+	5.98319i	0.0944623	+	0.413866i
$210$	−0.920583	−	0.734141i	−0.0635263	−	0.0506605i
$211$	−0.538032	+	2.35727i	−0.0370397	+	0.162281i	−0.990065	−	0.140608i	$-0.955094\pi$
$211$	−0.538032	+	2.35727i	−0.0370397	+	0.162281i	0.953026	+	0.302890i	$0.0979513\pi$
$212$	6.51573	−	8.17047i	0.447502	−	0.561150i
$213$	−2.93416	−	1.41302i	−0.201045	−	0.0968182i
$214$	−11.8877			−0.812626
$215$	1.06100			0.0723595
$216$	−9.12229	−	4.39306i	−0.620693	−	0.298910i
$217$	−0.409698	−	0.326723i	−0.0278121	−	0.0221794i
$218$	11.8204	−	5.69238i	0.800576	−	0.385537i
$219$	−10.0429	+	4.83639i	−0.678635	+	0.326813i
$220$	−0.175760	+	0.770053i	−0.0118497	+	0.0519169i
$221$	−5.87412	+	25.7362i	−0.395136	+	1.73120i
$222$	−9.54288	+	4.59561i	−0.640476	+	0.308437i
$223$	−12.7397	+	6.13514i	−0.853116	+	0.410839i	−0.808733	−	0.588175i	$-0.799846\pi$
$223$	−12.7397	+	6.13514i	−0.853116	+	0.410839i	−0.0443829	+	0.999015i	$0.514132\pi$
$224$	7.47972	+	15.5318i	0.499760	+	1.03776i
$225$	−10.4879	−	5.05072i	−0.699195	−	0.336714i
$226$	2.95108			0.196303
$227$	−11.1564			−0.740479			−0.370239	−	0.928936i	$-0.620724\pi$
$227$	−11.1564			−0.740479			−0.370239	+	0.928936i	$0.620724\pi$
$228$	−12.8889	−	6.20696i	−0.853587	−	0.411066i
$229$	4.94653	−	6.20276i	0.326876	−	0.409890i	−0.591054	−	0.806632i	$-0.701288\pi$
$229$	4.94653	−	6.20276i	0.326876	−	0.409890i	0.917930	+	0.396742i	$0.129859\pi$
$230$	−0.746980	+	3.27273i	−0.0492544	+	0.215798i
$231$	−2.16972	+	0.495224i	−0.142757	+	0.0325834i
$232$	−1.18987	−	5.21314i	−0.0781185	−	0.342260i
$233$	15.9487	+	7.68048i	1.04483	+	0.503165i	0.875915	−	0.482465i	$-0.160258\pi$
$233$	15.9487	+	7.68048i	1.04483	+	0.503165i	0.168918	+	0.985630i	$0.445973\pi$
$234$	−6.29859	−	27.5959i	−0.411751	−	1.80400i
$235$	1.26055	−	1.58068i	0.0822294	−	0.103112i
$236$	3.22468	−	14.1282i	0.209909	−	0.919670i
$237$	−4.32155	−	5.41905i	−0.280715	−	0.352005i
$238$	22.9562	−	18.3070i	1.48803	−	1.18667i
$239$	10.3110	−	12.9295i	0.666961	−	0.836342i	−0.327120	−	0.944983i	$-0.606078\pi$
$239$	10.3110	−	12.9295i	0.666961	−	0.836342i	0.994081	+	0.108640i	$0.0346497\pi$
$240$	0.0990311	+	0.124181i	0.00639243	+	0.00801586i
$241$	−9.85570	+	4.74625i	−0.634861	+	0.305733i	−0.723493	−	0.690331i	$-0.757465\pi$
$241$	−9.85570	+	4.74625i	−0.634861	+	0.305733i	0.0886320	+	0.996064i	$0.471750\pi$
$242$	−13.8693	−	17.3915i	−0.891551	−	1.11797i
$243$	3.51477	+	15.3992i	0.225473	+	0.987860i
$244$	10.0489			0.643316
$245$	−1.07792	+	1.35168i	−0.0688661	+	0.0863553i
$246$	8.81163			0.561809
$247$	−6.95862	−	30.4877i	−0.442766	−	1.93989i
$248$	−0.291053	−	0.364968i	−0.0184819	−	0.0231755i
$249$	8.50969	−	4.09805i	0.539280	−	0.259703i
$250$	−3.43900	−	4.31237i	−0.217502	−	0.272738i
$251$	8.49127	−	10.6477i	0.535964	−	0.672078i	−0.437949	−	0.899000i	$-0.644295\pi$
$251$	8.49127	−	10.6477i	0.535964	−	0.672078i	0.973913	+	0.226922i	$0.0728663\pi$
$252$	−8.24914	+	17.1295i	−0.519647	+	1.07906i
$253$	3.95593	+	4.96058i	0.248707	+	0.311869i
$254$	5.60872	−	24.5734i	0.351922	−	1.54187i
$255$	0.609916	−	0.764811i	0.0381944	−	0.0478943i
$256$	2.32908	+	10.2044i	0.145568	+	0.637774i
$257$	14.5075	+	6.98646i	0.904955	+	0.435803i	0.827676	−	0.561206i	$-0.189663\pi$
$257$	14.5075	+	6.98646i	0.904955	+	0.435803i	0.0772790	+	0.997010i	$0.475377\pi$
$258$	1.72252	+	7.54686i	0.107239	+	0.469847i
$259$	6.74764	+	14.0116i	0.419278	+	0.870640i
$260$	0.895592	−	3.92385i	0.0555423	−	0.243347i
$261$	−3.33393	+	4.18061i	−0.206365	+	0.258774i
$262$	−39.4354	−	18.9911i	−2.43633	−	1.17327i
$263$	31.5013			1.94245			0.971225	−	0.238163i	$-0.0765451\pi$
$263$	31.5013			1.94245			0.971225	+	0.238163i	$0.0765451\pi$
$264$	−1.98254			−0.122017
$265$	−0.762709	−	0.367301i	−0.0468528	−	0.0225631i
$266$	−15.0918	+	31.3384i	−0.925337	+	1.92148i
$267$	12.0390	−	5.79767i	0.736774	−	0.354812i
$268$	9.22132	−	4.44076i	0.563282	−	0.271262i
$269$	0.730718	−	3.20148i	0.0445526	−	0.195198i	−0.947754	−	0.319002i	$-0.896652\pi$
$269$	0.730718	−	3.20148i	0.0445526	−	0.195198i	0.992307	+	0.123804i	$0.0395095\pi$
$270$	−0.530499	+	2.32427i	−0.0322852	+	0.141451i
$271$	−9.42543	+	4.53905i	−0.572554	+	0.275727i	−0.697675	−	0.716414i	$-0.745782\pi$
$271$	−9.42543	+	4.53905i	−0.572554	+	0.275727i	0.125121	+	0.992141i	$0.460068\pi$
$272$	−3.56853	+	1.71851i	−0.216374	+	0.104200i
$273$	11.0559	−	2.52344i	0.669135	−	0.152726i
$274$	18.5966	+	8.95567i	1.12346	+	0.541032i
$275$	−5.18060			−0.312402
$276$	−14.7899			−0.890245
$277$	−21.8925	−	10.5429i	−1.31539	−	0.633461i	−0.361156	−	0.932505i	$-0.617618\pi$
$277$	−21.8925	−	10.5429i	−1.31539	−	0.633461i	−0.954239	+	0.299045i	$0.903332\pi$
$278$	−20.7431	+	26.0110i	−1.24409	+	1.56004i
$279$	−0.103875	+	0.455108i	−0.00621886	+	0.0272466i
$280$	−1.20410	+	0.960240i	−0.0719589	+	0.0573853i
$281$	−0.955927	−	4.18819i	−0.0570258	−	0.249846i	0.938378	−	0.345610i	$-0.112328\pi$
$281$	−0.955927	−	4.18819i	−0.0570258	−	0.249846i	−0.995404	+	0.0957634i	$0.969471\pi$
$282$	13.2899	+	6.40006i	0.791399	+	0.381118i
$283$	4.36347	+	19.1176i	0.259381	+	1.13642i	0.921915	+	0.387392i	$0.126624\pi$
$283$	4.36347	+	19.1176i	0.259381	+	1.13642i	−0.662534	+	0.749032i	$0.730519\pi$
$284$	−7.71983	+	9.68036i	−0.458088	+	0.574424i
$285$	−0.257865	+	1.12978i	−0.0152746	+	0.0669223i
$286$	−7.85421	−	9.84886i	−0.464429	−	0.582376i
$287$		−	12.9379i		−	0.763703i
$288$	9.57487	−	12.0065i	0.564205	−	0.707490i
$289$	4.60992	+	5.78065i	0.271172	+	0.340038i
$290$	−1.13437	+	0.546286i	−0.0666128	+	0.0320790i
$291$	0.846011	+	1.06086i	0.0495940	+	0.0621889i
$292$	9.43027	+	41.3167i	0.551865	+	2.41788i
$293$	32.1280			1.87694			0.938468	−	0.345366i	$-0.112245\pi$
$293$	32.1280			1.87694			0.938468	+	0.345366i	$0.112245\pi$
$294$	−11.3644	−	5.47282i	−0.662787	−	0.319181i
$295$	−1.17390			−0.0683470
$296$	3.08277	+	13.5065i	0.179182	+	0.785049i
$297$	2.80947	+	3.52296i	0.163022	+	0.204423i
$298$	−0.277479	+	0.133627i	−0.0160739	+	0.00774080i
$299$	−20.1576	−	25.2769i	−1.16575	−	1.46180i
$300$	7.52930	−	9.44145i	0.434705	−	0.545102i
$301$	11.0809	−	2.52915i	0.638693	−	0.145778i
$302$	−13.8312	−	17.3438i	−0.795898	−	0.998025i
$303$	−1.72737	+	7.56808i	−0.0992345	+	0.434775i
$304$	2.92543	−	3.66837i	0.167785	−	0.210395i
$305$	−0.181136	−	0.793610i	−0.0103718	−	0.0454420i
$306$	−23.5661	−	11.3489i	−1.34719	−	0.648771i
$307$	5.39642	+	23.6433i	0.307990	+	1.34939i	0.857749	+	0.514069i	$0.171862\pi$
$307$	5.39642	+	23.6433i	0.307990	+	1.34939i	−0.549759	+	0.835323i	$0.685280\pi$
$308$			8.46128i			0.482126i
$309$	0.561531	−	2.46023i	0.0319444	−	0.139958i
$310$	−0.0685317	+	0.0859360i	−0.00389234	+	0.00488084i
$311$	9.81767	+	4.72794i	0.556709	+	0.268097i	0.691012	−	0.722843i	$-0.257165\pi$
$311$	9.81767	+	4.72794i	0.556709	+	0.268097i	−0.134303	+	0.990940i	$0.542880\pi$
$312$	10.1021			0.571921
$313$	8.42519			0.476220			0.238110	−	0.971238i	$-0.423472\pi$
$313$	8.42519			0.476220			0.238110	+	0.971238i	$0.423472\pi$
$314$	−14.6908	−	7.07473i	−0.829051	−	0.399250i
$315$	1.50149	+	0.342706i	0.0845995	+	0.0193093i
$316$	−23.7424	+	11.4338i	−1.33562	+	0.643199i
$317$	−30.8364	+	14.8500i	−1.73194	+	0.834060i	−0.746218	+	0.665702i	$0.768132\pi$
$317$	−30.8364	+	14.8500i	−1.73194	+	0.834060i	−0.985726	+	0.168358i	$0.946153\pi$
$318$	1.37435	−	6.02144i	0.0770700	−	0.337666i
$319$	−0.529540	+	2.32007i	−0.0296485	+	0.129899i
$320$	2.90097	−	1.39703i	0.162169	−	0.0780965i
$321$	−3.82251	+	1.84082i	−0.213352	+	0.102745i
$322$			35.9605i			2.00400i
$323$	−26.0356	−	12.5381i	−1.44866	−	0.697639i
$324$	11.0543			0.614127
$325$	26.3980			1.46430
$326$	25.7690	+	12.4097i	1.42722	+	0.687311i
$327$	2.91939	−	3.66080i	0.161442	−	0.202442i
$328$	2.56465	−	11.2365i	0.141609	−	0.620429i
$329$	9.39708	−	19.5132i	0.518078	−	1.07580i
$330$	0.103875	+	0.455108i	0.00571816	+	0.0250529i
$331$	8.97823	+	4.32369i	0.493488	+	0.237651i	0.664040	−	0.747697i	$-0.268841\pi$
$331$	8.97823	+	4.32369i	0.493488	+	0.237651i	−0.170551	+	0.985349i	$0.554555\pi$
$332$	−7.99061	−	35.0091i	−0.438542	−	1.92138i
$333$	8.63773	−	10.8314i	0.473345	−	0.593555i
$334$	4.00269	−	17.5369i	0.219017	−	0.959578i
$335$	−0.516926	−	0.648205i	−0.0282427	−	0.0354152i
$336$	1.33028	+	1.06086i	0.0725728	+	0.0578749i
$337$	−13.7473	+	17.2385i	−0.748862	+	0.939043i	−0.999579	−	0.0290174i	$-0.990762\pi$
$337$	−13.7473	+	17.2385i	−0.748862	+	0.939043i	0.250717	+	0.968060i	$0.419334\pi$
$338$	21.8089	+	27.3475i	1.18625	+	1.48751i
$339$	0.948927	−	0.456979i	0.0515386	−	0.0248197i
$340$	−2.31886	−	2.90776i	−0.125758	−	0.157696i
$341$	0.0462289	+	0.202542i	0.00250344	+	0.0109683i
$342$	30.9855			1.67551
$343$	−8.03564	+	16.6862i	−0.433884	+	0.900969i
$344$	10.1250			0.545902
$345$	0.266594	+	1.16802i	0.0143529	+	0.0628843i
$346$	17.1482	+	21.5032i	0.921895	+	1.15602i
$347$	22.4807	−	10.8261i	1.20683	−	0.581177i	0.281212	−	0.959646i	$-0.409264\pi$
$347$	22.4807	−	10.8261i	1.20683	−	0.581177i	0.925614	+	0.378469i	$0.123549\pi$
$348$	−3.45862	−	4.33697i	−0.185401	−	0.232486i
$349$	−1.97554	+	2.47725i	−0.105748	+	0.132604i	−0.831889	−	0.554942i	$-0.812741\pi$
$349$	−1.97554	+	2.47725i	−0.105748	+	0.132604i	0.726141	+	0.687546i	$0.241312\pi$
$350$	−22.9562	−	18.3070i	−1.22706	−	0.978549i
$351$	−14.3158	−	17.9515i	−0.764121	−	0.958178i
$352$	1.52081	−	6.66311i	0.0810595	−	0.355145i
$353$	−14.9547	+	18.7526i	−0.795960	+	0.998102i	0.203858	+	0.979001i	$0.434652\pi$
$353$	−14.9547	+	18.7526i	−0.795960	+	0.998102i	−0.999818	+	0.0191017i	$0.993919\pi$
$354$	−1.90581	−	8.34991i	−0.101293	−	0.443793i
$355$	0.903657	+	0.435178i	0.0479611	+	0.0230969i
$356$	−11.3046	−	49.5288i	−0.599144	−	2.62502i
$357$	4.54676	−	9.44145i	0.240640	−	0.499694i
$358$	0.228562	−	1.00139i	0.0120799	−	0.0529253i
$359$	−19.4249	+	24.3580i	−1.02521	+	1.28557i	−0.0675317	+	0.997717i	$0.521512\pi$
$359$	−19.4249	+	24.3580i	−1.02521	+	1.28557i	−0.957675	+	0.287851i	$0.907059\pi$
$360$	1.23609	+	0.595272i	0.0651479	+	0.0313736i
$361$	15.2325			0.801711
$362$	−21.0737			−1.10761
$363$	−7.15279	−	3.44460i	−0.375424	−	0.180795i
$364$		−	43.1149i		−	2.25983i
$365$	3.09299	−	1.48951i	0.161895	−	0.0779643i
$366$	5.35086	−	2.57684i	0.279694	−	0.134693i
$367$	−2.13587	+	9.35784i	−0.111491	+	0.488475i	0.888093	+	0.459663i	$0.152030\pi$
$367$	−2.13587	+	9.35784i	−0.111491	+	0.488475i	−0.999585	+	0.0288126i	$0.990827\pi$
$368$	1.07942	−	4.72923i	0.0562685	−	0.246528i
$369$	−10.3840	+	5.00069i	−0.540572	+	0.260326i
$370$	2.93900	−	1.41535i	0.152791	−	0.0735805i
$371$	−8.84117	−	2.01794i	−0.459010	−	0.104766i
$372$	−0.436313	−	0.210117i	−0.0226218	−	0.0108941i
$373$	1.69633			0.0878328			0.0439164	−	0.999035i	$-0.486016\pi$
$373$	1.69633			0.0878328			0.0439164	+	0.999035i	$0.486016\pi$
$374$	−11.6407			−0.601927
$375$	−1.77359	−	0.854118i	−0.0915880	−	0.0441065i
$376$	12.0293	−	15.0843i	0.620364	−	0.777912i
$377$	2.69830	−	11.8220i	0.138969	−	0.608865i
$378$			25.5389i			1.31358i
$379$	−4.66487	−	20.4382i	−0.239619	−	1.04984i	−0.941360	−	0.337405i	$-0.890451\pi$
$379$	−4.66487	−	20.4382i	−0.239619	−	1.04984i	0.701741	−	0.712432i	$-0.252406\pi$
$380$	3.96950	+	1.91161i	0.203631	+	0.0980636i
$381$	−2.00173	−	8.77015i	−0.102552	−	0.449308i
$382$	−7.55645	+	9.47549i	−0.386622	+	0.484808i
$383$	−0.714988	+	3.13257i	−0.0365342	+	0.160067i	−0.989904	−	0.141737i	$-0.954731\pi$
$383$	−0.714988	+	3.13257i	−0.0365342	+	0.160067i	0.953370	+	0.301803i	$0.0975886\pi$
$384$	8.13102	+	10.1960i	0.414935	+	0.520311i
$385$	0.668227	−	0.152518i	0.0340560	−	0.00777306i
$386$	−31.4795	+	39.4740i	−1.60226	+	2.00917i
$387$	−6.31282	−	7.91603i	−0.320899	−	0.402394i
$388$	4.64795	−	2.23833i	0.235964	−	0.113634i
$389$	8.08008	+	10.1321i	0.409676	+	0.513718i	0.943272	−	0.332022i	$-0.107731\pi$
$389$	8.08008	+	10.1321i	0.409676	+	0.513718i	−0.533595	+	0.845740i	$0.679159\pi$
$390$	−0.529303	−	2.31903i	−0.0268023	−	0.117429i
$391$	−29.8756			−1.51087
$392$	−10.2865	+	12.8989i	−0.519547	+	0.651491i
$393$	−15.6213			−0.787992
$394$	−1.40970	−	6.17629i	−0.0710196	−	0.311157i
$395$	1.33095	+	1.66895i	0.0669671	+	0.0839741i
$396$	6.79105	−	3.27040i	0.341263	−	0.164344i
$397$	1.85623	+	2.32764i	0.0931616	+	0.116821i	0.826227	−	0.563337i	$-0.190483\pi$
$397$	1.85623	+	2.32764i	0.0931616	+	0.116821i	−0.733066	+	0.680158i	$0.761911\pi$
$398$	3.73341	−	4.68154i	0.187139	−	0.234665i
$399$			12.4139i			0.621473i
$400$	2.46950	+	3.09666i	0.123475	+	0.154833i
$401$	−1.94989	+	8.54301i	−0.0973727	+	0.426618i	−0.999993	−	0.00382070i	$-0.998784\pi$
$401$	−1.94989	+	8.54301i	−0.0973727	+	0.426618i	0.902620	+	0.430438i	$0.141641\pi$
$402$	3.77144	−	4.72923i	0.188102	−	0.235873i
$403$	−0.235562	−	1.03206i	−0.0117342	−	0.0514108i
$404$	26.5906	+	12.8054i	1.32293	+	0.637090i
$405$	−0.199259	−	0.873009i	−0.00990125	−	0.0433802i
$406$	−10.5450	+	8.40938i	−0.523341	+	0.417351i
$407$	1.37196	−	6.01096i	0.0680056	−	0.297952i
$408$	5.82036	−	7.29850i	0.288151	−	0.361329i
$409$	0.226406	+	0.109031i	0.0111950	+	0.00539125i	0.439473	−	0.898256i	$-0.355165\pi$
$409$	0.226406	+	0.109031i	0.0111950	+	0.00539125i	−0.428278	+	0.903647i	$0.640880\pi$
$410$	−2.71379			−0.134025
$411$	7.36658			0.363367
$412$	−8.64406	−	4.16276i	−0.425862	−	0.205085i
$413$	−12.2600	+	2.79827i	−0.603276	+	0.137694i
$414$	28.8620	−	13.8992i	1.41849	−	0.683110i
$415$	−2.62080	+	1.26211i	−0.128650	+	0.0619546i
$416$	−7.74937	+	33.9522i	−0.379944	+	1.66464i
$417$	−2.64214	+	11.5760i	−0.129386	+	0.566879i
$418$	12.4242	−	5.98319i	0.607689	−	0.292648i
$419$	4.63318	−	2.23122i	0.226346	−	0.109002i	−0.317274	−	0.948334i	$-0.602768\pi$
$419$	4.63318	−	2.23122i	0.226346	−	0.109002i	0.543620	+	0.839332i	$0.317053\pi$
$420$	−0.693218	+	1.43948i	−0.0338256	+	0.0702395i
$421$	28.9376	+	13.9356i	1.41033	+	0.679179i	0.975228	−	0.221201i	$-0.0709978\pi$
$421$	28.9376	+	13.9356i	1.41033	+	0.679179i	0.435103	+	0.900381i	$0.356712\pi$
$422$	5.43296			0.264472
$423$	−19.2935			−0.938082
$424$	−7.27844	−	3.50511i	−0.353472	−	0.170223i
$425$	15.2092	−	19.0718i	0.737757	−	0.925118i
$426$	−1.62833	+	7.13420i	−0.0788930	+	0.345653i
$427$	−3.78352	−	7.85656i	−0.183097	−	0.380206i
$428$	3.58934	+	15.7259i	0.173497	+	0.760142i
$429$	−4.05065	−	1.95069i	−0.195567	−	0.0941801i
$430$	−0.530499	−	2.32427i	−0.0255830	−	0.112086i
$431$	−7.10723	+	8.91218i	−0.342343	+	0.429285i	−0.922962	−	0.384891i	$-0.874239\pi$
$431$	−7.10723	+	8.91218i	−0.342343	+	0.429285i	0.580619	+	0.814175i	$0.302811\pi$
$432$	0.766594	−	3.35867i	0.0368828	−	0.161594i
$433$	−5.26205	−	6.59840i	−0.252878	−	0.317099i	0.639148	−	0.769084i	$-0.279287\pi$
$433$	−5.26205	−	6.59840i	−0.252878	−	0.317099i	−0.892025	+	0.451985i	$0.850716\pi$
$434$	−0.510885	+	1.06086i	−0.0245233	+	0.0509231i
$435$	−0.280167	+	0.351319i	−0.0134330	+	0.0168445i
$436$	−11.0993	−	13.9181i	−0.531561	−	0.666557i
$437$	31.8865	−	15.3557i	1.52534	−	0.734564i
$438$	15.6163	+	19.5822i	0.746173	+	0.935672i
$439$	−3.88716	−	17.0308i	−0.185524	−	0.812834i	−0.978939	−	0.204153i	$-0.934556\pi$
$439$	−3.88716	−	17.0308i	−0.185524	−	0.812834i	0.793415	−	0.608681i	$-0.208301\pi$
$440$	0.610580			0.0291083
$441$	16.4983			0.785632
$442$	59.3159			2.82137
$443$	−1.94331	−	8.51421i	−0.0923296	−	0.404522i	0.907552	−	0.419941i	$-0.137949\pi$
$443$	−1.94331	−	8.51421i	−0.0923296	−	0.404522i	−0.999881	+	0.0154184i	$0.995092\pi$
$444$	8.96077	+	11.2365i	0.425259	+	0.533258i
$445$	−3.70775	+	1.78556i	−0.175764	+	0.0846436i
$446$	19.8098	+	24.8407i	0.938020	+	1.17624i
$447$	−0.0685317	+	0.0859360i	−0.00324144	+	0.00406463i
$448$	26.9671	−	21.5056i	1.27408	−	1.01604i
$449$	−5.73005	−	7.18526i	−0.270418	−	0.339093i	0.628017	−	0.778199i	$-0.283867\pi$
$449$	−5.73005	−	7.18526i	−0.270418	−	0.339093i	−0.898435	+	0.439106i	$0.855295\pi$
$450$	−5.82036	+	25.5006i	−0.274374	+	1.20211i
$451$	−3.19806	+	4.01024i	−0.150591	+	0.188835i
$452$	−0.891043	−	3.90392i	−0.0419111	−	0.183625i
$453$	−7.13318	−	3.43516i	−0.335146	−	0.161398i
$454$	5.57822	+	24.4398i	0.261799	+	1.14702i
$455$	−3.40499	+	0.777166i	−0.159628	+	0.0364341i
$456$	−2.46077	+	10.7813i	−0.115236	+	0.504883i
$457$	20.4163	−	25.6013i	0.955036	−	1.19758i	−0.0251878	−	0.999683i	$-0.508018\pi$
$457$	20.4163	−	25.6013i	0.955036	−	1.19758i	0.980223	−	0.197894i	$-0.0634102\pi$
$458$	−16.0613	−	7.73471i	−0.750495	−	0.361419i
$459$	−21.2174			−0.990345
$460$	4.55496			0.212376
$461$	12.5804	+	6.05839i	0.585927	+	0.282167i	0.703269	−	0.710924i	$-0.251723\pi$
$461$	12.5804	+	6.05839i	0.585927	+	0.282167i	−0.117342	+	0.993092i	$0.537437\pi$
$462$	2.16972	+	4.50547i	0.100944	+	0.209613i
$463$	−15.4025	+	7.41743i	−0.715813	+	0.344717i	−0.756087	−	0.654471i	$-0.772891\pi$
$463$	−15.4025	+	7.41743i	−0.715813	+	0.344717i	0.0402738	+	0.999189i	$0.487177\pi$
$464$	1.63922	−	0.789406i	0.0760988	−	0.0366473i
$465$	−0.00872920	+	0.0382451i	−0.000404807	+	0.00177357i
$466$	8.85086	−	38.7781i	0.410008	−	1.79636i
$467$	7.71648	−	3.71606i	0.357076	−	0.171959i	−0.246741	−	0.969081i	$-0.579360\pi$
$467$	7.71648	−	3.71606i	0.357076	−	0.171959i	0.603818	+	0.797123i	$0.293646\pi$
$468$	−34.6042	+	16.6645i	−1.59958	+	0.770316i
$469$	−6.94385	−	5.53753i	−0.320637	−	0.255699i
$470$	−4.09299	−	1.97108i	−0.188796	−	0.0909192i
$471$	−5.81940			−0.268144
$472$	−11.2024			−0.515631
$473$	−4.05980	−	1.95510i	−0.186670	−	0.0898955i
$474$	−9.71044	+	12.1765i	−0.446015	+	0.559285i
$475$	−6.43027	+	28.1729i	−0.295041	+	1.29266i
$476$	−31.1492	−	24.8407i	−1.42772	−	1.13857i
$477$	1.79763	+	7.87591i	0.0823076	+	0.360613i
$478$	−33.4795	−	16.1229i	−1.53132	−	0.737443i
$479$	−0.202611	−	0.887697i	−0.00925754	−	0.0405599i	0.970088	−	0.242753i	$-0.0780504\pi$
$479$	−0.202611	−	0.887697i	−0.00925754	−	0.0405599i	−0.979346	+	0.202193i	$0.935193\pi$
$480$	0.804626	−	1.00897i	0.0367260	−	0.0460529i
$481$	−6.99090	+	30.6291i	−0.318758	+	1.39657i
$482$	15.3252	+	19.2172i	0.698044	+	0.875319i
$483$	5.56853	+	11.5632i	0.253377	+	0.526143i
$484$	−18.8192	+	23.5985i	−0.855416	+	1.07266i
$485$	−0.260553	−	0.326723i	−0.0118311	−	0.0148357i
$486$	31.9768	−	15.3992i	1.45050	−	0.698523i
$487$	−10.6875	−	13.4017i	−0.484296	−	0.607287i	0.478311	−	0.878190i	$-0.341249\pi$
$487$	−10.6875	−	13.4017i	−0.484296	−	0.607287i	−0.962607	+	0.270903i	$0.912678\pi$
$488$	−1.72856	−	7.57332i	−0.0782483	−	0.342828i
$489$	10.2078			0.461610
$490$	3.50000	+	1.68551i	0.158114	+	0.0761436i
$491$	24.2078			1.09248			0.546240	−	0.837629i	$-0.316059\pi$
$491$	24.2078			1.09248			0.546240	+	0.837629i	$0.316059\pi$
$492$	−2.66056	−	11.6567i	−0.119947	−	0.525524i
$493$	−6.98643	−	8.76070i	−0.314653	−	0.394562i
$494$	−63.3083	+	30.4877i	−2.84838	+	1.37171i
$495$	−0.380691	−	0.477371i	−0.0171108	−	0.0214562i
$496$	0.0990311	−	0.124181i	0.00444663	−	0.00557590i
$497$	10.4750	+	2.39085i	0.469868	+	0.107244i
$498$	−13.2322	−	16.5927i	−0.592949	−	0.743535i
$499$	2.34159	−	10.2592i	0.104824	−	0.459264i	−0.895086	−	0.445893i	$-0.852886\pi$
$499$	2.34159	−	10.2592i	0.104824	−	0.459264i	0.999911	−	0.0133719i	$-0.00425653\pi$
$500$	−4.66637	+	5.85144i	−0.208686	+	0.261684i
$501$	−1.42854	−	6.25886i	−0.0638226	−	0.279625i
$502$	−27.5710	−	13.2775i	−1.23055	−	0.592603i
$503$	−6.45593	−	28.2853i	−0.287856	−	1.26118i	−0.887461	−	0.460882i	$-0.847533\pi$
$503$	−6.45593	−	28.2853i	−0.287856	−	1.26118i	0.599606	−	0.800295i	$-0.295324\pi$
$504$	14.3286	+	3.27040i	0.638244	+	0.145675i
$505$	0.531991	−	2.33081i	0.0236733	−	0.103720i
$506$	8.88889	−	11.1463i	0.395159	−	0.495514i
$507$	11.2475	+	5.41652i	0.499520	+	0.240556i
$508$	−34.2010			−1.51743
$509$	−22.7178			−1.00695			−0.503475	−	0.864010i	$-0.667946\pi$
$509$	−22.7178			−1.00695			−0.503475	+	0.864010i	$0.667946\pi$
$510$	−1.98039	−	0.953703i	−0.0876930	−	0.0422307i
$511$	28.7521	−	22.9291i	1.27192	−	1.01432i
$512$	−8.11356	+	3.90729i	−0.358572	+	0.172679i
$513$	22.6456	−	10.9055i	0.999826	−	0.481491i
$514$	8.05107	−	35.2741i	0.355118	−	1.55587i
$515$	−0.172940	+	0.757698i	−0.00762063	+	0.0333882i
$516$	9.46346	−	4.55736i	0.416606	−	0.200627i
$517$	−7.73609	+	3.72551i	−0.340233	+	0.163848i
$518$	27.3207	−	21.7875i	1.20040	−	0.957287i
$519$	8.84385	+	4.25898i	0.388202	+	0.186948i
$520$	−3.11124			−0.136437
$521$	−31.9573			−1.40008			−0.700038	−	0.714106i	$-0.746833\pi$
$521$	−31.9573			−1.40008			−0.700038	+	0.714106i	$0.746833\pi$
$522$	10.8252	+	5.21314i	0.473806	+	0.228173i
$523$	−0.348699	+	0.437255i	−0.0152475	+	0.0191198i	−0.789397	−	0.613883i	$-0.789607\pi$
$523$	−0.348699	+	0.437255i	−0.0152475	+	0.0191198i	0.774149	+	0.633003i	$0.218178\pi$
$524$	−13.2158	+	57.9023i	−0.577336	+	2.52947i
$525$	−10.2165	−	2.33184i	−0.445884	−	0.101770i
$526$	−15.7506	−	69.0080i	−0.686760	−	3.00889i
$527$	−0.881355	−	0.424438i	−0.0383924	−	0.0184888i
$528$	−0.150104	−	0.657650i	−0.00653246	−	0.0286206i
$529$	8.47285	−	10.6246i	0.368385	−	0.461940i
$530$	−0.423272	+	1.85447i	−0.0183857	+	0.0805532i
$531$	6.98457	+	8.75837i	0.303104	+	0.380081i
$532$	46.0136	+	10.5023i	1.99494	+	0.455333i
$533$	16.2959	−	20.4344i	0.705854	−	0.885112i
$534$	−18.7201	−	23.4743i	−0.810099	−	1.01583i
$535$	1.17725	−	0.566934i	0.0508970	−	0.0245107i
$536$	−4.93296	−	6.18574i	−0.213071	−	0.267183i
$537$	−0.0815727	−	0.357394i	−0.00352012	−	0.0154227i
$538$	−7.37867			−0.318117
$539$	6.61529	−	3.18576i	0.284941	−	0.137220i
$540$	3.23490			0.139208
$541$	10.2008	+	44.6924i	0.438565	+	1.92148i	0.385012	+	0.922912i	$0.374197\pi$
$541$	10.2008	+	44.6924i	0.438565	+	1.92148i	0.0535529	+	0.998565i	$0.482945\pi$
$542$	14.6561	+	18.3782i	0.629535	+	0.789412i
$543$	−6.77628	+	3.26329i	−0.290798	+	0.140041i
$544$	20.0646	+	25.1603i	0.860265	+	1.07874i
$545$	−0.899108	+	1.12745i	−0.0385136	+	0.0482945i
$546$	−11.0559	−	22.9578i	−0.473150	−	0.982505i
$547$	10.6047	+	13.2979i	0.453424	+	0.568576i	0.955026	−	0.296523i	$-0.0958270\pi$
$547$	10.6047	+	13.2979i	0.453424	+	0.568576i	−0.501601	+	0.865099i	$0.667256\pi$
$548$	6.23221	−	27.3051i	0.266227	−	1.16642i
$549$	−4.84332	+	6.07333i	−0.206708	+	0.259204i
$550$	2.59030	+	11.3489i	0.110451	+	0.483917i
$551$	11.9596	+	5.75943i	0.509495	+	0.245360i
$552$	2.54407	+	11.1463i	0.108283	+	0.474419i
$553$	17.8785	+	14.2577i	0.760273	+	0.606297i
$554$	−12.1494	+	53.2302i	−0.516180	+	2.26153i
$555$	0.725873	−	0.910216i	0.0308116	−	0.0386365i
$556$	40.6725	+	19.5868i	1.72490	+	0.830666i
$557$	−30.7071			−1.30110			−0.650551	−	0.759463i	$-0.725462\pi$
$557$	−30.7071			−1.30110			−0.650551	+	0.759463i	$0.725462\pi$
$558$	1.04892			0.0444042
$559$	20.6869	+	9.96231i	0.874964	+	0.421361i
$560$	−0.409698	−	0.326723i	−0.0173129	−	0.0138066i
$561$	−3.74309	+	1.80258i	−0.158034	+	0.0761050i
$562$	−8.69687	+	4.18819i	−0.366855	+	0.176668i
$563$	9.61237	−	42.1145i	0.405113	−	1.77492i	−0.201056	−	0.979580i	$-0.564437\pi$
$563$	9.61237	−	42.1145i	0.405113	−	1.77492i	0.606169	−	0.795336i	$-0.292706\pi$
$564$	4.45377	−	19.5132i	0.187538	−	0.821656i
$565$	−0.292249	+	0.140740i	−0.0122950	+	0.00592096i
$566$	39.6981	−	19.1176i	1.66864	−	0.803573i
$567$	−4.16205	−	8.64260i	−0.174790	−	0.362955i
$568$	8.62349	+	4.15285i	0.361834	+	0.174250i
$569$	−10.3002			−0.431807			−0.215904	−	0.976415i	$-0.569270\pi$
$569$	−10.3002			−0.431807			−0.215904	+	0.976415i	$0.569270\pi$
$570$	2.60388			0.109064
$571$	5.86443	+	2.82416i	0.245419	+	0.118187i	0.552550	−	0.833480i	$-0.313655\pi$
$571$	5.86443	+	2.82416i	0.245419	+	0.118187i	−0.307131	+	0.951667i	$0.599369\pi$
$572$	−10.6573	+	13.3639i	−0.445606	+	0.558772i
$573$	−0.962500	+	4.21699i	−0.0402090	+	0.176167i
$574$	−28.3424	+	6.46897i	−1.18299	+	0.270010i
$575$	6.64795	+	29.1266i	0.277239	+	1.21466i
$576$	−27.6836	−	13.3317i	−1.15348	−	0.555488i
$577$	1.61811	+	7.08942i	0.0673629	+	0.295136i	0.997376	−	0.0723890i	$-0.0230623\pi$
$577$	1.61811	+	7.08942i	0.0673629	+	0.295136i	−0.930014	+	0.367525i	$0.880205\pi$
$578$	10.3584	−	12.9890i	0.430852	−	0.540271i
$579$	−4.00969	+	17.5676i	−0.166637	+	0.730084i
$580$	1.06518	+	1.33569i	0.0442292	+	0.0554616i
$581$	−24.3627	+	19.4286i	−1.01074	+	0.806034i
$582$	1.90097	−	2.38374i	0.0787977	−	0.0988092i
$583$	2.24160	+	2.81088i	0.0928377	+	0.116415i
$584$	29.5160	−	14.2142i	1.22138	−	0.588186i
$585$	1.93983	+	2.43247i	0.0802021	+	0.100570i
$586$	−16.0640	−	70.3809i	−0.663597	−	2.90741i
$587$	−23.8006			−0.982356			−0.491178	−	0.871059i	$-0.663434\pi$
$587$	−23.8006			−0.982356			−0.491178	+	0.871059i	$0.663434\pi$
$588$	−3.80851	+	16.6862i	−0.157060	+	0.688126i
$589$	1.15883			0.0477489
$590$	0.586950	+	2.57159i	0.0241643	+	0.105871i
$591$	−1.40970	−	1.76771i	−0.0579872	−	0.0727137i
$592$	−4.24698	+	2.04524i	−0.174550	+	0.0840587i
$593$	12.5274	+	15.7089i	0.514440	+	0.645088i	0.969418	−	0.245415i	$-0.0789242\pi$
$593$	12.5274	+	15.7089i	0.514440	+	0.645088i	−0.454978	+	0.890503i	$0.650353\pi$
$594$	6.31282	−	7.91603i	0.259018	−	0.324799i
$595$	−1.40030	+	2.90776i	−0.0574069	+	0.119207i
$596$	0.260553	+	0.326723i	0.0106727	+	0.0133831i
$597$	0.475541	−	2.08348i	0.0194626	−	0.0852713i
$598$	−45.2938	+	56.7966i	−1.85220	+	2.32259i
$599$	3.33004	+	14.5899i	0.136062	+	0.596126i	0.996278	+	0.0861968i	$0.0274714\pi$
$599$	3.33004	+	14.5899i	0.136062	+	0.596126i	−0.860216	+	0.509929i	$0.829671\pi$
$600$	−8.41066	−	4.05036i	−0.343364	−	0.165355i
$601$	−4.50700	−	19.7465i	−0.183844	−	0.805475i	−0.979777	−	0.200090i	$-0.935876\pi$
$601$	−4.50700	−	19.7465i	−0.183844	−	0.805475i	0.795933	−	0.605385i	$-0.206981\pi$
$602$	−11.0809	−	23.0097i	−0.451624	−	0.937807i
$603$	−1.76055	+	7.71349i	−0.0716953	+	0.314117i
$604$	−18.7676	+	23.5338i	−0.763641	+	0.957575i
$605$	2.20291	+	1.06086i	0.0895609	+	0.0431303i
$606$	17.4426			0.708559
$607$	−17.0411			−0.691679			−0.345839	−	0.938294i	$-0.612406\pi$
$607$	−17.0411			−0.691679			−0.345839	+	0.938294i	$0.612406\pi$
$608$	−34.3473	−	16.5408i	−1.39297	−	0.670817i
$609$	−2.08857	+	4.33697i	−0.0846332	+	0.175743i
$610$	−1.64795	+	0.793610i	−0.0667235	+	0.0321323i
$611$	39.4197	−	18.9835i	1.59475	−	0.767991i
$612$	−7.89762	+	34.6017i	−0.319242	+	1.39869i
$613$	−3.16434	+	13.8639i	−0.127807	+	0.559957i	0.869958	+	0.493126i	$0.164146\pi$
$613$	−3.16434	+	13.8639i	−0.127807	+	0.559957i	−0.997764	+	0.0668309i	$0.978711\pi$
$614$	49.0957	−	23.6433i	1.98134	−	0.954164i
$615$	−0.872625	+	0.420234i	−0.0351876	+	0.0169455i
$616$	6.37681	−	1.45546i	0.256929	−	0.0586423i
$617$	−1.27263	−	0.612869i	−0.0512343	−	0.0246732i	0.408091	−	0.912941i	$-0.366195\pi$
$617$	−1.27263	−	0.612869i	−0.0512343	−	0.0246732i	−0.459325	+	0.888268i	$0.651909\pi$
$618$	−5.67025			−0.228091
$619$	9.00192			0.361818			0.180909	−	0.983500i	$-0.442096\pi$
$619$	9.00192			0.361818			0.180909	+	0.983500i	$0.442096\pi$
$620$	0.134375	+	0.0647116i	0.00539663	+	0.00259888i
$621$	16.2017	−	20.3163i	0.650152	−	0.815265i
$622$	5.44839	−	23.8710i	0.218461	−	0.957139i
$623$	−34.4669	+	27.4864i	−1.38089	+	1.10122i
$624$	0.764865	+	3.35109i	0.0306191	+	0.134151i
$625$	−21.7032	−	10.4517i	−0.868128	−	0.418068i
$626$	−4.21260	−	18.4566i	−0.168369	−	0.737674i
$627$	3.06853	−	3.84782i	0.122545	−	0.153667i
$628$	−4.92327	+	21.5703i	−0.196460	+	0.860747i
$629$	18.1008	+	22.6977i	0.721727	+	0.905017i
$630$		−	3.46059i		−	0.137873i
$631$	−18.6833	+	23.4281i	−0.743770	+	0.932658i	−0.999418	−	0.0341117i	$-0.989140\pi$
$631$	−18.6833	+	23.4281i	−0.743770	+	0.932658i	0.255648	+	0.966770i	$0.417711\pi$
$632$	12.7010	+	15.9266i	0.505220	+	0.633526i
$633$	1.74698	−	0.841301i	0.0694362	−	0.0334387i
$634$	47.9493	+	60.1265i	1.90431	+	2.38793i
$635$	0.616490	+	2.70102i	0.0244646	+	0.107187i
$636$	−8.38059			−0.332312
$637$	−33.7086	+	16.2332i	−1.33558	+	0.643183i
$638$	5.34721			0.211698
$639$	−2.12983	−	9.33138i	−0.0842546	−	0.369144i
$640$	−2.50418	−	3.14014i	−0.0989864	−	0.124125i
$641$	−1.97046	+	0.948924i	−0.0778285	+	0.0374802i	−0.472393	−	0.881388i	$-0.656610\pi$
$641$	−1.97046	+	0.948924i	−0.0778285	+	0.0374802i	0.394565	+	0.918868i	$0.370895\pi$
$642$	5.94385	+	7.45335i	0.234585	+	0.294160i
$643$	16.0538	−	20.1308i	0.633099	−	0.793880i	−0.357022	−	0.934096i	$-0.616208\pi$
$643$	16.0538	−	20.1308i	0.633099	−	0.793880i	0.990121	+	0.140215i	$0.0447795\pi$
$644$	47.5713	−	10.8578i	1.87457	−	0.427859i
$645$	−0.530499	−	0.665225i	−0.0208884	−	0.0261932i
$646$	−14.4487	+	63.3038i	−0.568476	+	2.49066i
$647$	5.04809	−	6.33010i	0.198461	−	0.248862i	−0.672636	−	0.739974i	$-0.734838\pi$
$647$	5.04809	−	6.33010i	0.198461	−	0.248862i	0.871097	+	0.491112i	$0.163409\pi$
$648$	−1.90150	−	8.33102i	−0.0746980	−	0.327273i
$649$	4.49180	+	2.16314i	0.176319	+	0.0849106i
$650$	−13.1990	−	57.8287i	−0.517708	−	2.26823i
$651$			0.420234i			0.0164703i
$652$	8.63587	−	37.8362i	0.338207	−	1.48178i
$653$	21.5127	−	26.9760i	0.841856	−	1.05565i	−0.155838	−	0.987783i	$-0.549808\pi$
$653$	21.5127	−	26.9760i	0.841856	−	1.05565i	0.997694	−	0.0678713i	$-0.0216207\pi$
$654$	−9.47919	−	4.56494i	−0.370666	−	0.178503i
$655$	4.81104			0.187983
$656$	3.92154			0.153111
$657$	−29.5160	−	14.2142i	−1.15153	−	0.554548i
$658$	−47.4451	−	10.8290i	−1.84960	−	0.422160i
$659$	17.3044	−	8.33335i	0.674083	−	0.324621i	−0.0653392	−	0.997863i	$-0.520813\pi$
$659$	17.3044	−	8.33335i	0.674083	−	0.324621i	0.739422	+	0.673242i	$0.235099\pi$
$660$	0.570688	−	0.274829i	0.0222140	−	0.0106977i
$661$	2.72760	−	11.9504i	0.106091	−	0.464817i	−0.893776	−	0.448514i	$-0.851953\pi$
$661$	2.72760	−	11.9504i	0.106091	−	0.464817i	0.999867	−	0.0163027i	$-0.00518953\pi$
$662$	4.98254	−	21.8299i	0.193652	−	0.848445i
$663$	19.0731	−	9.18514i	0.740739	−	0.356721i
$664$	−25.0100	+	12.0442i	−0.970576	+	0.467405i
$665$		−	3.82322i		−	0.148258i
$666$	−28.0465	−	13.5065i	−1.08678	−	0.523366i
$667$	13.7235			0.531375
$668$	−24.4077			−0.944364
$669$	10.2165	+	4.92000i	0.394992	+	0.190218i
$670$	−1.16152	+	1.45650i	−0.0448735	+	0.0562696i
$671$	−0.769282	+	3.37045i	−0.0296978	+	0.130115i
$672$	5.99827	−	12.4555i	0.231388	−	0.480483i
$673$	1.09946	+	4.81704i	0.0423810	+	0.185683i	0.991688	−	0.128668i	$-0.0410702\pi$
$673$	1.09946	+	4.81704i	0.0423810	+	0.185683i	−0.949307	+	0.314351i	$0.898213\pi$
$674$	44.6371	+	21.4961i	1.71936	+	0.827999i
$675$	4.72132	+	20.6855i	0.181724	+	0.796184i
$676$	29.5925	−	37.1078i	1.13817	−	1.42722i
$677$	4.14848	−	18.1757i	0.159439	−	0.698548i	−0.830496	−	0.557025i	$-0.811943\pi$
$677$	4.14848	−	18.1757i	0.159439	−	0.698548i	0.989935	−	0.141523i	$-0.0452000\pi$
$678$	−1.47554	−	1.85027i	−0.0566678	−	0.0710592i
$679$	−3.50000	−	2.79116i	−0.134318	−	0.107115i
$680$	−1.79254	+	2.24778i	−0.0687409	+	0.0861984i
$681$	5.57822	+	6.99487i	0.213758	+	0.268044i
$682$	0.420583	−	0.202542i	0.0161050	−	0.00775574i
$683$	6.80798	+	8.53694i	0.260500	+	0.326657i	0.894831	−	0.446405i	$-0.147296\pi$
$683$	6.80798	+	8.53694i	0.260500	+	0.326657i	−0.634331	+	0.773061i	$0.718724\pi$
$684$	−9.35570	−	40.9900i	−0.357724	−	1.56729i
$685$	−2.26875			−0.0866845
$686$	40.5713	+	9.26013i	1.54902	+	0.353553i
$687$	−6.36227			−0.242736
$688$	0.766594	+	3.35867i	0.0292261	+	0.128048i
$689$	−11.4222	−	14.3230i	−0.435151	−	0.545663i
$690$	2.42543	−	1.16802i	0.0923344	−	0.0444659i
$691$	1.62229	+	2.03429i	0.0617149	+	0.0773881i	0.811731	−	0.584032i	$-0.198526\pi$
$691$	1.62229	+	2.03429i	0.0617149	+	0.0773881i	−0.750016	+	0.661420i	$0.769954\pi$
$692$	23.2684	−	29.1776i	0.884531	−	1.10917i
$693$	−5.11380	−	4.07812i	−0.194257	−	0.154915i
$694$	−34.9565	−	43.8341i	−1.32693	−	1.66392i
$695$	0.813724	−	3.56516i	0.0308663	−	0.135234i
$696$	−2.67360	+	3.35259i	−0.101343	+	0.127080i
$697$	−5.37435	−	23.5466i	−0.203568	−	0.891890i
$698$	6.41454	+	3.08908i	0.242794	+	0.116923i
$699$	−3.15883	−	13.8398i	−0.119478	−	0.523468i
$700$	−17.2865	+	35.8958i	−0.653368	+	1.35673i
$701$	−5.79643	+	25.3958i	−0.218928	+	0.959187i	0.739344	+	0.673328i	$0.235136\pi$
$701$	−5.79643	+	25.3958i	−0.218928	+	0.959187i	−0.958272	+	0.285859i	$0.907721\pi$
$702$	−32.1673	+	40.3366i	−1.21408	+	1.52241i
$703$	−30.9855	−	14.9218i	−1.16864	−	0.562788i
$704$	−13.6746			−0.515379
$705$	−1.62133			−0.0610630
$706$	48.5577	+	23.3842i	1.82749	+	0.880074i
$707$		−	25.6107i		−	0.963190i
$708$	−10.4705	+	5.04231i	−0.393504	+	0.189502i
$709$	−4.83124	+	2.32660i	−0.181441	+	0.0873774i	−0.522399	−	0.852701i	$-0.674963\pi$
$709$	−4.83124	+	2.32660i	−0.181441	+	0.0873774i	0.340958	+	0.940079i	$0.389249\pi$
$710$	0.501492	−	2.19718i	0.0188207	−	0.0824587i
$711$	4.53295	−	19.8602i	0.169999	−	0.744814i
$712$	−35.3826	+	17.0394i	−1.32602	+	0.638577i
$713$	1.07942	−	0.519820i	0.0404245	−	0.0194674i
$714$	−22.9562	−	5.23961i	−0.859115	−	0.196087i
$715$	1.24751	+	0.600770i	0.0466543	+	0.0224675i
$716$	−1.39373			−0.0520862
$717$	−13.2620			−0.495280
$718$	63.0722	+	30.3740i	2.35384	+	1.13355i
$719$	−28.8567	+	36.1851i	−1.07617	+	1.34948i	−0.143132	+	0.989704i	$0.545717\pi$
$719$	−28.8567	+	36.1851i	−1.07617	+	1.34948i	−0.933040	+	0.359773i	$0.882854\pi$
$720$	−0.103875	+	0.455108i	−0.00387121	+	0.0169609i
$721$			8.32552i			0.310059i
$722$	−7.61625	−	33.3690i	−0.283448	−	1.24186i
$723$	7.90366	+	3.80620i	0.293940	+	0.141554i
$724$	6.36294	+	27.8778i	0.236477	+	1.03607i
$725$	−6.98643	+	8.76070i	−0.259469	+	0.325364i
$726$	−3.96950	+	17.3915i	−0.147322	+	0.645460i
$727$	−0.933329	−	1.17036i	−0.0346152	−	0.0434061i	0.764223	−	0.644953i	$-0.223123\pi$
$727$	−0.933329	−	1.17036i	−0.0346152	−	0.0434061i	−0.798838	+	0.601546i	$0.794551\pi$
$728$	−32.4934	+	7.41640i	−1.20428	+	0.274870i
$729$	1.11596	−	1.39937i	0.0413317	−	0.0518284i
$730$	−4.80947	−	6.03089i	−0.178006	−	0.223213i
$731$	19.1163	−	9.20590i	0.707040	−	0.340493i
$732$	−5.02446	−	6.30047i	−0.185709	−	0.232872i
$733$	−6.21624	−	27.2351i	−0.229602	−	1.00595i	−0.949965	−	0.312356i	$-0.898882\pi$
$733$	−6.21624	−	27.2351i	−0.229602	−	1.00595i	0.720363	−	0.693597i	$-0.243975\pi$
$734$	21.5676			0.796076
$735$	1.38644			0.0511395
$736$	−39.4131			−1.45279
$737$	0.783520	+	3.43282i	0.0288613	+	0.126450i
$738$	16.1468	+	20.2474i	0.594370	+	0.745317i
$739$	17.0679	−	8.21945i	0.627852	−	0.302357i	−0.0927683	−	0.995688i	$-0.529572\pi$
$739$	17.0679	−	8.21945i	0.627852	−	0.302357i	0.720620	+	0.693330i	$0.243857\pi$
$740$	−2.75973	−	3.46059i	−0.101450	−	0.127214i
$741$	−15.6359	+	19.6068i	−0.574398	+	0.720272i
$742$			20.3768i			0.748056i
$743$	19.9813	+	25.0558i	0.733044	+	0.919209i	0.998997	−	0.0447775i	$-0.0142579\pi$
$743$	19.9813	+	25.0558i	0.733044	+	0.919209i	−0.265953	+	0.963986i	$0.585686\pi$
$744$	−0.0833017	+	0.364968i	−0.00305399	+	0.0133804i
$745$	0.0211063	−	0.0264664i	0.000773274	−	0.000969655i
$746$	−0.848167	−	3.71606i	−0.0310536	−	0.136055i
$747$	25.0100	+	12.0442i	0.915067	+	0.440673i
$748$	3.51477	+	15.3992i	0.128513	+	0.563051i
$749$	10.9436	−	8.72724i	0.399871	−	0.318886i
$750$	−0.984271	+	4.31237i	−0.0359405	+	0.157466i
$751$	0.0752364	−	0.0943435i	0.00274542	−	0.00344264i	−0.780457	−	0.625210i	$-0.785013\pi$
$751$	0.0752364	−	0.0943435i	0.00274542	−	0.00344264i	0.783202	+	0.621767i	$0.213585\pi$
$752$	5.91454	+	2.84829i	0.215681	+	0.103867i
$753$	−10.9215			−0.398003
$754$	−27.2470			−0.992276
$755$	2.19687	+	1.05795i	0.0799521	+	0.0385029i
$756$	33.7848	−	7.71115i	1.22874	−	0.280452i
$757$	19.6114	−	9.44436i	0.712789	−	0.343261i	−0.0421004	−	0.999113i	$-0.513405\pi$
$757$	19.6114	−	9.44436i	0.712789	−	0.343261i	0.754889	+	0.655852i	$0.227691\pi$
$758$	−42.4403	+	20.4382i	−1.54150	+	0.742347i
$759$	1.13222	−	4.96058i	0.0410969	−	0.180057i
$760$	0.757865	−	3.32042i	0.0274906	−	0.120444i
$761$	−24.4943	+	11.7958i	−0.887916	+	0.427598i	−0.821510	−	0.570195i	$-0.806868\pi$
$761$	−24.4943	+	11.7958i	−0.887916	+	0.427598i	−0.0664065	+	0.997793i	$0.521153\pi$
$762$	−18.2114	+	8.77015i	−0.659729	+	0.317709i
$763$	−6.70261	+	13.9181i	−0.242651	+	0.503870i
$764$	14.8165	+	7.13524i	0.536041	+	0.258144i
$765$	2.87502			0.103947
$766$	7.21983			0.260863
$767$	−22.8882	−	11.0224i	−0.826446	−	0.397995i
$768$	5.23341	−	6.56248i	0.188844	−	0.236803i
$769$	9.52691	−	41.7401i	0.343549	−	1.50519i	−0.447973	−	0.894047i	$-0.647854\pi$
$769$	9.52691	−	41.7401i	0.343549	−	1.50519i	0.791522	−	0.611140i	$-0.209289\pi$
$770$	−0.668227	−	1.38759i	−0.0240812	−	0.0500052i
$771$	−2.87339	−	12.5892i	−0.103483	−	0.453388i
$772$	61.7241	+	29.7247i	2.22150	+	1.06982i
$773$	−6.44707	−	28.2464i	−0.231885	−	1.01595i	−0.948075	−	0.318048i	$-0.896973\pi$
$773$	−6.44707	−	28.2464i	−0.231885	−	1.01595i	0.716190	−	0.697906i	$-0.245885\pi$
$774$	−14.1848	+	17.7872i	−0.509862	+	0.639346i
$775$	−0.217677	+	0.953703i	−0.00781917	+	0.0342580i
$776$	−2.48643	−	3.11788i	−0.0892575	−	0.111925i
$777$	5.41119	−	11.2365i	0.194125	−	0.403105i
$778$	18.1558	−	22.7666i	0.650916	−	0.816223i
$779$	17.8388	+	22.3691i	0.639140	+	0.801457i
$780$	−2.90797	+	1.40040i	−0.104122	+	0.0501425i
$781$	−2.65585	−	3.33033i	−0.0950338	−	0.119169i
$782$	14.9378	+	65.4468i	0.534175	+	2.34037i
$783$	9.74632			0.348305
$784$	−5.05765	−	2.43563i	−0.180630	−	0.0869869i
$785$	1.79225			0.0639681
$786$	7.81067	+	34.2208i	0.278597	+	1.22061i
$787$	−16.3448	−	20.4957i	−0.582630	−	0.730595i	0.399929	−	0.916546i	$-0.369035\pi$
$787$	−16.3448	−	20.4957i	−0.582630	−	0.730595i	−0.982559	+	0.185951i	$0.940463\pi$
$788$	−7.74482	+	3.72971i	−0.275898	+	0.132865i
$789$	−15.7506	−	19.7507i	−0.560737	−	0.703142i
$790$	2.99061	−	3.75010i	0.106401	−	0.133423i
$791$	−2.71672	+	2.16651i	−0.0965953	+	0.0770322i
$792$	−3.63288	−	4.55549i	−0.129089	−	0.161872i
$793$	3.91992	−	17.1743i	0.139200	−	0.609877i
$794$	4.17092	−	5.23016i	0.148020	−	0.185612i
$795$	0.151064	+	0.661854i	0.00535768	+	0.0234735i
$796$	−7.32036	−	3.52530i	−0.259463	−	0.124951i
$797$	12.2068	+	53.4814i	0.432387	+	1.89441i	0.447033	+	0.894517i	$0.352481\pi$
$797$	12.2068	+	53.4814i	0.432387	+	1.89441i	−0.0146465	+	0.999893i	$0.504662\pi$
$798$	27.1945	−	6.20696i	0.962674	−	0.219724i
$799$	8.99665	−	39.4169i	0.318279	−	1.39447i
$800$	20.0646	−	25.1603i	0.709392	−	0.889550i
$801$	35.3826	+	17.0394i	1.25018	+	0.602056i
$802$	19.6896			0.695265
$803$	−14.5797			−0.514507
$804$	−7.39493	−	3.56121i	−0.260799	−	0.125594i
$805$	−1.71499	−	3.56121i	−0.0604454	−	0.125516i
$806$	−2.14310	+	1.03206i	−0.0754876	+	0.0363529i
$807$	−2.37263	+	1.14260i	−0.0835204	+	0.0402213i
$808$	5.07673	−	22.2426i	0.178599	−	0.782492i
$809$	8.74376	−	38.3089i	0.307414	−	1.34687i	−0.551254	−	0.834338i	$-0.685850\pi$
$809$	8.74376	−	38.3089i	0.307414	−	1.34687i	0.858668	−	0.512532i	$-0.171292\pi$
$810$	−1.81282	+	0.873009i	−0.0636961	+	0.0306744i
$811$	33.6754	−	16.2172i	1.18250	−	0.569463i	0.263863	−	0.964560i	$-0.415003\pi$
$811$	33.6754	−	16.2172i	1.18250	−	0.569463i	0.918640	+	0.395097i	$0.129289\pi$
$812$	14.3085	+	11.4107i	0.502130	+	0.400436i
$813$	7.55861	+	3.64003i	0.265092	+	0.127662i
$814$	−13.8538			−0.485577
$815$	−3.14377			−0.110121
$816$	2.86174	+	1.37814i	0.100181	+	0.0482446i
$817$	−15.6712	+	19.6511i	−0.548266	+	0.687504i
$818$	0.125646	−	0.550490i	0.00439310	−	0.0192474i
$819$	26.0576	+	20.7803i	0.910528	+	0.726122i
$820$	0.819396	+	3.59001i	0.0286146	+	0.125369i
$821$	−40.6432	−	19.5727i	−1.41846	−	0.683092i	−0.441644	−	0.897190i	$-0.645605\pi$
$821$	−40.6432	−	19.5727i	−1.41846	−	0.683092i	−0.976812	+	0.214098i	$0.931319\pi$
$822$	−3.68329	−	16.1376i	−0.128470	−	0.562862i
$823$	−24.8428	+	31.1519i	−0.865965	+	1.08589i	0.129577	+	0.991569i	$0.458638\pi$
$823$	−24.8428	+	31.1519i	−0.865965	+	1.08589i	−0.995542	+	0.0943167i	$0.969933\pi$
$824$	−1.65034	+	7.23062i	−0.0574924	+	0.251891i
$825$	2.59030	+	3.24814i	0.0901827	+	0.113086i
$826$	12.2600	+	25.4582i	0.426581	+	0.885804i
$827$	−17.2989	+	21.6921i	−0.601541	+	0.754309i	−0.985617	−	0.168993i	$-0.945949\pi$
$827$	−17.2989	+	21.6921i	−0.601541	+	0.754309i	0.384076	+	0.923301i	$0.374520\pi$
$828$	−27.1015	−	33.9842i	−0.941842	−	1.18103i
$829$	−20.2848	+	9.76863i	−0.704519	+	0.339279i	−0.751606	−	0.659612i	$-0.770721\pi$
$829$	−20.2848	+	9.76863i	−0.704519	+	0.339279i	0.0470868	+	0.998891i	$0.485006\pi$
$830$	4.07524	+	5.11018i	0.141454	+	0.177377i
$831$	4.33609	+	18.9976i	0.150417	+	0.659020i
$832$	69.6795			2.41570
$833$	−7.69322	+	33.7062i	−0.266554	+	1.16785i
$834$	26.6799			0.923851
$835$	0.439961	+	1.92759i	0.0152255	+	0.0667071i
$836$	−11.6664	−	14.6292i	−0.403490	−	0.505960i
$837$	0.766594	−	0.369172i	0.0264974	−	0.0127605i
$838$	−7.20440	−	9.03403i	−0.248872	−	0.312075i
$839$	−19.6377	+	24.6248i	−0.677967	+	0.850144i	−0.995165	−	0.0982154i	$-0.968687\pi$
$839$	−19.6377	+	24.6248i	−0.677967	+	0.850144i	0.317198	+	0.948359i	$0.397258\pi$
$840$	1.20410	+	0.274829i	0.0415455	+	0.00948249i
$841$	−14.8720	−	18.6488i	−0.512826	−	0.643064i
$842$	16.0591	−	70.3597i	0.553434	−	2.42475i
$843$	−2.14795	+	2.69344i	−0.0739793	+	0.0927671i
$844$	−1.64042	−	7.18713i	−0.0564654	−	0.247391i
$845$	−3.46399	−	1.66817i	−0.119165	−	0.0573868i
$846$	9.64675	+	42.2652i	0.331662	+	1.45311i
$847$	25.5356	+	5.82834i	0.877415	+	0.200264i
$848$	0.611645	−	2.67979i	0.0210040	−	0.0920245i
$849$	9.80463	−	12.2946i	0.336494	−	0.421950i
$850$	−49.3841	−	23.7821i	−1.69386	−	0.815720i
$851$	−35.5555			−1.21883
$852$	9.92931			0.340173
$853$	−40.2657	−	19.3909i	−1.37867	−	0.663933i	−0.409955	−	0.912106i	$-0.634456\pi$
$853$	−40.2657	−	19.3909i	−1.37867	−	0.663933i	−0.968716	+	0.248173i	$0.920170\pi$
$854$	−15.3192	+	12.2166i	−0.524211	+	0.418044i
$855$	−3.06853	+	1.47773i	−0.104942	+	0.0505372i
$856$	11.2344	−	5.41019i	0.383983	−	0.184916i
$857$	−6.74698	+	29.5604i	−0.230472	+	1.00977i	0.718777	+	0.695241i	$0.244702\pi$
$857$	−6.74698	+	29.5604i	−0.230472	+	1.00977i	−0.949249	+	0.314525i	$0.898155\pi$
$858$	−2.24794	+	9.84886i	−0.0767434	+	0.336235i
$859$	17.2213	−	8.29335i	0.587584	−	0.282966i	−0.116376	−	0.993205i	$-0.537128\pi$
$859$	17.2213	−	8.29335i	0.587584	−	0.282966i	0.703960	+	0.710240i	$0.251413\pi$
$860$	−2.91454	+	1.40357i	−0.0993851	+	0.0478613i
$861$	−8.11184	+	6.46897i	−0.276451	+	0.220462i
$862$	23.0770	+	11.1133i	0.786007	+	0.378521i
$863$	25.1987			0.857772			0.428886	−	0.903359i	$-0.358906\pi$
$863$	25.1987			0.857772			0.428886	+	0.903359i	$0.358906\pi$
$864$	−27.9909			−0.952270
$865$	−2.72372	−	1.31167i	−0.0926092	−	0.0445982i
$866$	−11.8237	+	14.8265i	−0.401786	+	0.503824i
$867$	1.31940	−	5.78065i	0.0448090	−	0.196321i
$868$	1.55765	+	0.355523i	0.0528700	+	0.0120672i
$869$	−2.01735	−	8.83860i	−0.0684340	−	0.299829i
$870$	0.909698	+	0.438087i	0.0308417	+	0.0148526i
$871$	−3.99247	−	17.4921i	−0.135280	−	0.592699i
$872$	−8.58008	+	10.7591i	−0.290558	+	0.364348i
$873$	−0.887395	+	3.88793i	−0.0300338	+	0.131587i
$874$	−49.5822	−	62.1741i	−1.67714	−	2.10307i
$875$	6.33177	+	1.44519i	0.214053	+	0.0488562i
$876$	21.1896	−	26.5710i	0.715931	−	0.897749i
$877$	−6.04102	−	7.57519i	−0.203991	−	0.255796i	0.669304	−	0.742989i	$-0.266592\pi$
$877$	−6.04102	−	7.57519i	−0.203991	−	0.255796i	−0.873295	+	0.487193i	$0.838021\pi$
$878$	−35.3647	+	17.0308i	−1.19350	+	0.574760i
$879$	−16.0640	−	20.1436i	−0.541825	−	0.679427i
$880$	0.0462289	+	0.202542i	0.00155838	+	0.00682770i
$881$	−18.1371			−0.611053			−0.305527	−	0.952184i	$-0.598832\pi$
$881$	−18.1371			−0.611053			−0.305527	+	0.952184i	$0.598832\pi$
$882$	−8.24914	−	36.1418i	−0.277763	−	1.21696i
$883$	17.4397			0.586891			0.293446	−	0.955976i	$-0.405198\pi$
$883$	17.4397			0.586891			0.293446	+	0.955976i	$0.405198\pi$
$884$	−17.9097	−	78.4675i	−0.602368	−	2.63915i
$885$	0.586950	+	0.736011i	0.0197301	+	0.0247408i
$886$	−17.6799	+	8.51421i	−0.593969	+	0.286040i
$887$	−33.6512	−	42.1973i	−1.12990	−	1.41685i	−0.895701	−	0.444658i	$-0.853325\pi$
$887$	−33.6512	−	42.1973i	−1.12990	−	1.41685i	−0.234197	−	0.972189i	$-0.575246\pi$
$888$	6.92692	−	8.68608i	0.232452	−	0.291486i
$889$	12.8770	+	26.7395i	0.431882	+	0.896813i
$890$	5.76540	+	7.22958i	0.193257	+	0.242336i
$891$	−0.846248	+	3.70765i	−0.0283504	+	0.124211i
$892$	26.8798	−	33.7062i	0.900002	−	1.12857i
$893$	10.6576	+	46.6942i	0.356644	+	1.56256i
$894$	0.222521	+	0.107160i	0.00744221	+	0.00358398i
$895$	0.0251227	+	0.110070i	0.000839758	+	0.00367922i
$896$	−33.6386	−	26.8259i	−1.12379	−	0.896189i
$897$	−5.76928	+	25.2769i	−0.192631	+	0.843970i
$898$	−12.8753	+	16.1451i	−0.429655	+	0.538770i
$899$	0.404854	+	0.194967i	0.0135026	+	0.00650252i
$900$	35.4916			1.18305
$901$	−16.9288			−0.563981
$902$	10.3840	+	5.00069i	0.345751	+	0.166505i
$903$	−7.12618	−	5.68294i	−0.237144	−	0.189116i
$904$	−2.78890	+	1.34306i	−0.0927573	+	0.0446696i
$905$	2.08695	−	1.00502i	0.0693726	−	0.0334081i
$906$	−3.95862	+	17.3438i	−0.131516	+	0.576210i
$907$	−7.45785	+	32.6750i	−0.247634	+	1.08495i	0.686247	+	0.727369i	$0.259257\pi$
$907$	−7.45785	+	32.6750i	−0.247634	+	1.08495i	−0.933880	+	0.357585i	$0.883600\pi$
$908$	30.6465	−	14.7586i	1.01704	−	0.489781i
$909$	−20.5553	+	9.89889i	−0.681775	+	0.328325i
$910$	3.40499	+	7.07052i	0.112874	+	0.234386i
$911$	13.5402	+	6.52061i	0.448606	+	0.216037i	0.644526	−	0.764583i	$-0.277055\pi$
$911$	13.5402	+	6.52061i	0.448606	+	0.216037i	−0.195919	+	0.980620i	$0.562769\pi$
$912$	−3.76271			−0.124596
$913$	12.3539			0.408855
$914$	−66.2914	−	31.9243i	−2.19272	−	1.05596i
$915$	−0.407010	+	0.510374i	−0.0134553	+	0.0168724i
$916$	−5.38255	+	23.5825i	−0.177844	+	0.779188i
$917$	50.2457	−	11.4683i	1.65926	−	0.378715i
$918$	10.6087	+	46.4798i	0.350140	+	1.53406i
$919$	19.0095	+	9.15447i	0.627064	+	0.301978i	0.720297	−	0.693666i	$-0.244006\pi$
$919$	19.0095	+	9.15447i	0.627064	+	0.301978i	−0.0932326	+	0.995644i	$0.529720\pi$
$920$	−0.783520	−	3.43282i	−0.0258319	−	0.113177i
$921$	12.1256	−	15.2051i	0.399554	−	0.501024i
$922$	6.98158	−	30.5883i	0.229926	−	1.00737i
$923$	13.5330	+	16.9699i	0.445445	+	0.558570i
$924$	5.30505	−	4.23064i	0.174523	−	0.139178i
$925$	18.1008	−	22.6977i	0.595151	−	0.746296i
$926$	23.9502	+	30.0326i	0.787052	+	0.986932i
$927$	6.68210	−	3.21793i	0.219469	−	0.105691i
$928$	−9.21678	−	11.5575i	−0.302555	−	0.379393i
$929$	6.46807	+	28.3385i	0.212210	+	0.929755i	0.963061	+	0.269283i	$0.0867866\pi$
$929$	6.46807	+	28.3385i	0.212210	+	0.929755i	−0.750851	+	0.660472i	$0.770356\pi$
$930$	0.0881460			0.00289042
$931$	−9.11356	−	39.9291i	−0.298685	−	1.30862i
$932$	−53.9711			−1.76788
$933$	−1.94451	−	8.51945i	−0.0636604	−	0.278914i
$934$	−11.9988	−	15.0460i	−0.392613	−	0.492321i
$935$	1.15279	−	0.555156i	0.0377004	−	0.0181555i
$936$	18.5115	+	23.2127i	0.605069	+	0.758732i
$937$	−33.3014	+	41.7586i	−1.08791	+	1.36420i	−0.161851	+	0.986815i	$0.551746\pi$
$937$	−33.3014	+	41.7586i	−1.08791	+	1.36420i	−0.926058	+	0.377380i	$0.876825\pi$
$938$	−8.65883	+	17.9803i	−0.282721	+	0.587076i
$939$	−4.21260	−	5.28243i	−0.137473	−	0.172386i
$940$	−1.37167	+	6.00966i	−0.0447388	+	0.196014i
$941$	10.4925	−	13.1571i	0.342045	−	0.428910i	−0.580822	−	0.814031i	$-0.697269\pi$
$941$	10.4925	−	13.1571i	0.342045	−	0.428910i	0.922866	+	0.385120i	$0.125840\pi$
$942$	2.90970	+	12.7482i	0.0948031	+	0.415359i
$943$	26.6504	+	12.8342i	0.867856	+	0.417938i
$944$	−0.848167	−	3.71606i	−0.0276055	−	0.120947i
$945$	−1.21797	−	2.52915i	−0.0396206	−	0.0822731i
$946$	−2.25302	+	9.87113i	−0.0732520	+	0.320938i
$947$	−25.2928	+	31.7162i	−0.821907	+	1.03064i	0.177015	+	0.984208i	$0.443356\pi$
$947$	−25.2928	+	31.7162i	−0.821907	+	1.03064i	−0.998922	+	0.0464304i	$0.985215\pi$
$948$	19.0400	+	9.16916i	0.618389	+	0.297800i
$949$	74.2917			2.41161
$950$	64.9318			2.10667
$951$	24.7289	+	11.9088i	0.801888	+	0.386169i
$952$	−13.3629	+	27.7484i	−0.433095	+	0.899332i
$953$	17.8632	−	8.60248i	0.578647	−	0.278662i	−0.121580	−	0.992582i	$-0.538796\pi$
$953$	17.8632	−	8.60248i	0.578647	−	0.278662i	0.700227	+	0.713920i	$0.253082\pi$
$954$	16.3545	−	7.87591i	0.529497	−	0.254992i
$955$	0.296429	−	1.29874i	0.00959223	−	0.0420263i
$956$	−11.2198	+	49.1573i	−0.362875	+	1.58986i
$957$	1.71941	−	0.828022i	0.0555805	−	0.0267662i
$958$	−1.84332	+	0.887697i	−0.0595550	+	0.0286802i
$959$	−23.6945	+	5.40811i	−0.765134	+	0.174637i
$960$	−2.32640	−	1.12033i	−0.0750841	−	0.0361586i
$961$	−30.9608			−0.998735
$962$	70.5930			2.27601
$963$	−11.2344	−	5.41019i	−0.362022	−	0.174341i
$964$	20.7947	−	26.0757i	0.669752	−	0.839843i
$965$	1.23490	−	5.41044i	0.0397528	−	0.174168i
$966$	22.5465	−	17.9803i	0.725423	−	0.578505i
$967$	−3.43416	−	15.0460i	−0.110435	−	0.483848i	−0.999652	−	0.0263626i	$-0.991608\pi$
$967$	−3.43416	−	15.0460i	−0.110435	−	0.483848i	0.889217	−	0.457485i	$-0.151250\pi$
$968$	21.0221	+	10.1237i	0.675675	+	0.325388i
$969$	5.15668	+	22.5929i	0.165656	+	0.725788i
$970$	−0.585458	+	0.734141i	−0.0187979	+	0.0235718i
$971$	10.6974	−	46.8684i	0.343296	−	1.50408i	−0.448773	−	0.893646i	$-0.648139\pi$
$971$	10.6974	−	46.8684i	0.343296	−	1.50408i	0.792069	−	0.610432i	$-0.209004\pi$
$972$	−30.0262	−	37.6517i	−0.963092	−	1.20768i
$973$		−	39.1737i		−	1.25585i
$974$	−24.0145	+	30.1133i	−0.769475	+	0.964891i
$975$	−13.1990	−	16.5510i	−0.422707	−	0.530058i
$976$	2.38135	−	1.14680i	0.0762253	−	0.0367082i
$977$	2.78687	+	3.49463i	0.0891599	+	0.111803i	0.824410	−	0.565992i	$-0.191507\pi$
$977$	2.78687	+	3.49463i	0.0891599	+	0.111803i	−0.735250	+	0.677796i	$0.762935\pi$
$978$	−5.10388	−	22.3615i	−0.163204	−	0.715043i
$979$	17.4776			0.558585
$980$	1.17294	−	5.13898i	0.0374682	−	0.164159i
$981$	13.7614			0.439367
$982$	−12.1039	−	53.0305i	−0.386250	−	1.69227i
$983$	24.9943	+	31.3418i	0.797193	+	0.999648i	0.999792	+	0.0203866i	$0.00648970\pi$
$983$	24.9943	+	31.3418i	0.797193	+	0.999648i	−0.202599	+	0.979262i	$0.564939\pi$
$984$	−8.32736	+	4.01024i	−0.265466	+	0.127842i
$985$	0.434157	+	0.544415i	0.0138334	+	0.0173465i
$986$	−15.6984	+	19.6851i	−0.499938	+	0.626902i
$987$	−16.9330	+	3.86484i	−0.538982	+	0.123019i
$988$	59.4466	+	74.5437i	1.89125	+	2.37155i
$989$	−5.78232	+	25.3340i	−0.183867	+	0.805575i
$990$	−0.855404	+	1.07264i	−0.0271865	+	0.0340908i
$991$	−6.95718	−	30.4814i	−0.221002	−	0.968274i	−0.956726	−	0.290992i	$-0.906015\pi$
$991$	−6.95718	−	30.4814i	−0.221002	−	0.968274i	0.735723	−	0.677282i	$-0.236842\pi$
$992$	−1.16272	−	0.559936i	−0.0369163	−	0.0177780i
$993$	−1.77825	−	7.79102i	−0.0564310	−	0.247240i
$994$		−	24.1424i		−	0.765751i
$995$	−0.146457	+	0.641668i	−0.00464298	+	0.0203422i
$996$	−17.9547	+	22.5145i	−0.568917	+	0.713400i
$997$	31.4804	+	15.1602i	0.996996	+	0.480128i	0.859918	−	0.510432i	$-0.170515\pi$
$997$	31.4804	+	15.1602i	0.996996	+	0.480128i	0.137078	+	0.990560i	$0.456229\pi$
$998$	−23.6450			−0.748470
$999$	−25.2513			−0.798916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.a.36.1	yes	6
3.2	odd	2		441.2.u.a.379.1		6
4.3	odd	2		784.2.u.a.673.1		6
7.2	even	3		343.2.g.f.312.1		12
7.3	odd	6		343.2.g.e.128.1		12
7.4	even	3		343.2.g.f.128.1		12
7.5	odd	6		343.2.g.e.312.1		12
7.6	odd	2		343.2.e.a.246.1		6
49.8	even	7		2401.2.a.b.1.3		3
49.9	even	21		343.2.g.f.67.1		12
49.15	even	7	inner	49.2.e.a.15.1	✓	6
49.24	odd	42		343.2.g.e.177.1		12
49.25	even	21		343.2.g.f.177.1		12
49.34	odd	14		343.2.e.a.99.1		6
49.40	odd	42		343.2.g.e.67.1		12
49.41	odd	14		2401.2.a.a.1.3		3
147.113	odd	14		441.2.u.a.64.1		6
196.15	odd	14		784.2.u.a.113.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.a.15.1	✓	6	49.15	even	7	inner
49.2.e.a.36.1	yes	6	1.1	even	1	trivial
343.2.e.a.99.1		6	49.34	odd	14
343.2.e.a.246.1		6	7.6	odd	2
343.2.g.e.67.1		12	49.40	odd	42
343.2.g.e.128.1		12	7.3	odd	6
343.2.g.e.177.1		12	49.24	odd	42
343.2.g.e.312.1		12	7.5	odd	6
343.2.g.f.67.1		12	49.9	even	21
343.2.g.f.128.1		12	7.4	even	3
343.2.g.f.177.1		12	49.25	even	21
343.2.g.f.312.1		12	7.2	even	3
441.2.u.a.64.1		6	147.113	odd	14
441.2.u.a.379.1		6	3.2	odd	2
784.2.u.a.113.1		6	196.15	odd	14
784.2.u.a.673.1		6	4.3	odd	2
2401.2.a.a.1.3		3	49.41	odd	14
2401.2.a.b.1.3		3	49.8	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 2.19064i) q^{2} +(-0.500000 - 0.626980i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(0.153989 + 0.193096i) q^{5} +(-1.12349 + 1.40881i) q^{6} +(2.06853 + 1.64960i) q^{7} +(1.46950 + 1.84270i) q^{8} +(0.524459 - 2.29780i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 2.19064i) q^{2} +(-0.500000 - 0.626980i) q^{3} +(-2.74698 + 1.32288i) q^{4} +(0.153989 + 0.193096i) q^{5} +(-1.12349 + 1.40881i) q^{6} +(2.06853 + 1.64960i) q^{7} +(1.46950 + 1.84270i) q^{8} +(0.524459 - 2.29780i) q^{9} +(0.346011 - 0.433884i) q^{10} +(-0.233406 - 1.02262i) q^{11} +(2.20291 + 1.06086i) q^{12} +(1.18933 + 5.21081i) q^{13} +(2.57942 - 5.35621i) q^{14} +(0.0440730 - 0.193096i) q^{15} +(-0.500000 + 0.626980i) q^{16} +(4.44989 + 2.14295i) q^{17} -5.29590 q^{18} -5.85086 q^{19} +(-0.678448 - 0.326723i) q^{20} -2.12173i q^{21} +(-2.12349 + 1.02262i) q^{22} +(-5.44989 + 2.62453i) q^{23} +(0.420583 - 1.84270i) q^{24} +(1.09903 - 4.81517i) q^{25} +(10.8204 - 5.21081i) q^{26} +(-3.87047 + 1.86392i) q^{27} +(-7.86443 - 1.79500i) q^{28} +(-2.04407 - 0.984374i) q^{29} -0.445042 q^{30} -0.198062 q^{31} +(5.87047 + 2.82707i) q^{32} +(-0.524459 + 0.657650i) q^{33} +(2.46950 - 10.8196i) q^{34} +0.653447i q^{35} +(1.59903 + 7.00581i) q^{36} +(5.29590 + 2.55037i) q^{37} +(2.92543 + 12.8171i) q^{38} +(2.67241 - 3.35109i) q^{39} +(-0.129531 + 0.567511i) q^{40} +(-3.04892 - 3.82322i) q^{41} +(-4.64795 + 1.06086i) q^{42} +(2.67845 - 3.35867i) q^{43} +(1.99396 + 2.50035i) q^{44} +(0.524459 - 0.252566i) q^{45} +(8.47434 + 10.6265i) q^{46} +(-1.82155 - 7.98074i) q^{47} +0.643104 q^{48} +(1.55765 + 6.82450i) q^{49} -11.0978 q^{50} +(-0.881355 - 3.86147i) q^{51} +(-10.1603 - 12.7406i) q^{52} +(-3.08815 + 1.48717i) q^{53} +(6.01842 + 7.54686i) q^{54} +(0.161522 - 0.202542i) q^{55} +6.23576i q^{56} +(2.92543 + 3.66837i) q^{57} +(-1.13437 + 4.97002i) q^{58} +(-2.96346 + 3.71606i) q^{59} +(0.134375 + 0.588735i) q^{60} +(-2.96950 - 1.43004i) q^{61} +(0.0990311 + 0.433884i) q^{62} +(4.87531 - 3.88793i) q^{63} +(2.90097 - 12.7100i) q^{64} +(-0.823044 + 1.03206i) q^{65} +(1.70291 + 0.820077i) q^{66} -3.35690 q^{67} -15.0586 q^{68} +(4.37047 + 2.10471i) q^{69} +(1.43147 - 0.326723i) q^{70} +(3.65883 - 1.76200i) q^{71} +(5.00484 - 2.41021i) q^{72} +(3.09299 - 13.5513i) q^{73} +(2.93900 - 12.8766i) q^{74} +(-3.56853 + 1.71851i) q^{75} +(16.0722 - 7.73995i) q^{76} +(1.20410 - 2.50035i) q^{77} +(-8.67725 - 4.17874i) q^{78} +8.64310 q^{79} -0.198062 q^{80} +(-3.26659 - 1.57311i) q^{81} +(-6.85086 + 8.59070i) q^{82} +(-2.62080 + 11.4825i) q^{83} +(2.80678 + 5.82834i) q^{84} +(0.271438 + 1.18925i) q^{85} +(-8.69687 - 4.18819i) q^{86} +(0.404854 + 1.77378i) q^{87} +(1.54138 - 1.93284i) q^{88} +(-3.70775 + 16.2447i) q^{89} +(-0.815511 - 1.02262i) q^{90} +(-6.13557 + 12.7406i) q^{91} +(11.4988 - 14.4190i) q^{92} +(0.0990311 + 0.124181i) q^{93} +(-16.5722 + 7.98074i) q^{94} +(-0.900969 - 1.12978i) q^{95} +(-1.16272 - 5.09420i) q^{96} -1.69202 q^{97} +(14.1712 - 6.82450i) q^{98} -2.47219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 7 q^{4} + 6 q^{5} - 2 q^{6} + 7 q^{7} - q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 7 * q^4 + 6 * q^5 - 2 * q^6 + 7 * q^7 - q^8 - 6 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 7 q^{4} + 6 q^{5} - 2 q^{6} + 7 q^{7} - q^{8} - 6 q^{9} - 3 q^{10} + 2 q^{11} + 7 q^{14} + 4 q^{15} - 3 q^{16} + 4 q^{17} - 4 q^{18} - 8 q^{19} - 8 q^{22} - 10 q^{23} + 11 q^{24} + 11 q^{25} + 28 q^{26} - 9 q^{27} - 14 q^{28} - 16 q^{29} - 2 q^{30} - 10 q^{31} + 21 q^{32} + 6 q^{33} + 5 q^{34} + 14 q^{36} + 4 q^{37} + 4 q^{38} - 7 q^{39} - 15 q^{40} - 14 q^{42} + 12 q^{43} - 7 q^{44} - 6 q^{45} + 19 q^{46} - 15 q^{47} + 12 q^{48} + 7 q^{49} - 30 q^{50} + 12 q^{51} - 26 q^{53} + 8 q^{54} - 19 q^{55} + 4 q^{57} + q^{58} + 11 q^{59} - 7 q^{60} - 8 q^{61} + 5 q^{62} - 7 q^{63} + 13 q^{64} + 35 q^{65} - 3 q^{66} - 12 q^{67} - 28 q^{68} + 12 q^{69} + 14 q^{70} + 5 q^{71} + 8 q^{72} + 4 q^{73} - 2 q^{74} - 16 q^{75} + 28 q^{76} + 35 q^{77} - 7 q^{78} + 60 q^{79} - 10 q^{80} - 23 q^{81} - 14 q^{82} - 14 q^{83} - 14 q^{84} - 17 q^{85} - 20 q^{86} + 36 q^{87} + 16 q^{88} + 13 q^{89} + 10 q^{90} - 70 q^{91} + 28 q^{92} + 5 q^{93} - 31 q^{94} - q^{95} - 28 q^{96} + 21 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 7 * q^4 + 6 * q^5 - 2 * q^6 + 7 * q^7 - q^8 - 6 * q^9 - 3 * q^10 + 2 * q^11 + 7 * q^14 + 4 * q^15 - 3 * q^16 + 4 * q^17 - 4 * q^18 - 8 * q^19 - 8 * q^22 - 10 * q^23 + 11 * q^24 + 11 * q^25 + 28 * q^26 - 9 * q^27 - 14 * q^28 - 16 * q^29 - 2 * q^30 - 10 * q^31 + 21 * q^32 + 6 * q^33 + 5 * q^34 + 14 * q^36 + 4 * q^37 + 4 * q^38 - 7 * q^39 - 15 * q^40 - 14 * q^42 + 12 * q^43 - 7 * q^44 - 6 * q^45 + 19 * q^46 - 15 * q^47 + 12 * q^48 + 7 * q^49 - 30 * q^50 + 12 * q^51 - 26 * q^53 + 8 * q^54 - 19 * q^55 + 4 * q^57 + q^58 + 11 * q^59 - 7 * q^60 - 8 * q^61 + 5 * q^62 - 7 * q^63 + 13 * q^64 + 35 * q^65 - 3 * q^66 - 12 * q^67 - 28 * q^68 + 12 * q^69 + 14 * q^70 + 5 * q^71 + 8 * q^72 + 4 * q^73 - 2 * q^74 - 16 * q^75 + 28 * q^76 + 35 * q^77 - 7 * q^78 + 60 * q^79 - 10 * q^80 - 23 * q^81 - 14 * q^82 - 14 * q^83 - 14 * q^84 - 17 * q^85 - 20 * q^86 + 36 * q^87 + 16 * q^88 + 13 * q^89 + 10 * q^90 - 70 * q^91 + 28 * q^92 + 5 * q^93 - 31 * q^94 - q^95 - 28 * q^96 + 21 * q^98 - 2 * q^99

Introduction

L-functions

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