LMFDB - Embedded newform 26.3.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,3,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.708448687337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.612074651904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$4.71318 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.7
Dual form			26.3.f.b.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(-2.78960 + 4.83174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(2.04213 - 7.62134i) q^{6} +(7.67890 + 2.05755i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 - 19.1630i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.78960 + 4.83174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(2.04213 - 7.62134i) q^{6} +(7.67890 + 2.05755i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 - 19.1630i) q^{9} +(-0.560999 - 0.323893i) q^{10} +(1.44868 + 5.40655i) q^{11} +11.1584i q^{12} +(12.8550 + 1.93621i) q^{13} -11.2427 q^{14} +(-2.46850 + 0.661433i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.74285 + 1.00623i) q^{17} +(22.1276 + 22.1276i) q^{18} +(1.19911 - 4.47512i) q^{19} +(0.884892 + 0.237106i) q^{20} +(-31.3626 + 31.3626i) q^{21} +(-3.95787 - 6.85523i) q^{22} +(-15.0976 - 8.71663i) q^{23} +(-4.08426 - 15.2427i) q^{24} -24.7902i q^{25} +(-18.2690 + 2.06034i) q^{26} +73.2415 q^{27} +(15.3578 - 4.11511i) q^{28} +(8.25026 - 14.2899i) q^{29} +(3.12993 - 1.80707i) q^{30} +(-9.27353 - 9.27353i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-30.1643 - 8.08249i) q^{33} +(2.01247 - 2.01247i) q^{34} +(1.82071 + 3.15357i) q^{35} +(-38.3261 - 22.1276i) q^{36} +(9.12370 + 34.0501i) q^{37} +6.55204i q^{38} +(-45.2156 + 56.7107i) q^{39} -1.29557 q^{40} +(58.6217 - 15.7076i) q^{41} +(31.3626 - 54.3217i) q^{42} +(-45.2101 + 26.1020i) q^{43} +(7.91574 + 7.91574i) q^{44} +(2.62329 - 9.79026i) q^{45} +(23.8143 + 6.38102i) q^{46} +(8.73527 - 8.73527i) q^{47} +(11.1584 + 19.3269i) q^{48} +(12.2967 + 7.09948i) q^{49} +(9.07384 + 33.8640i) q^{50} -11.2280i q^{51} +(24.2017 - 9.50138i) q^{52} -23.4425 q^{53} +(-100.050 + 26.8082i) q^{54} +(-1.28193 + 2.22036i) q^{55} +(-19.4729 + 11.2427i) q^{56} +(18.2776 + 18.2776i) q^{57} +(-6.03961 + 22.5401i) q^{58} +(34.0864 + 9.13343i) q^{59} +(-3.61413 + 3.61413i) q^{60} +(-13.9421 - 24.1483i) q^{61} +(16.0622 + 9.27353i) q^{62} +(-45.5287 - 169.915i) q^{63} -8.00000i q^{64} +(3.53652 + 4.79077i) q^{65} +44.1635 q^{66} +(-33.0643 + 8.85955i) q^{67} +(-2.01247 + 3.48570i) q^{68} +(84.2329 - 48.6319i) q^{69} +(-3.64143 - 3.64143i) q^{70} +(19.7955 - 73.8778i) q^{71} +(60.4537 + 16.1985i) q^{72} +(-18.9304 + 18.9304i) q^{73} +(-24.9264 - 43.1738i) q^{74} +(119.780 + 69.1548i) q^{75} +(-2.39821 - 8.95025i) q^{76} +44.4971i q^{77} +(41.0082 - 94.0184i) q^{78} -142.837 q^{79} +(1.76978 - 0.474212i) q^{80} +(-104.741 + 181.416i) q^{81} +(-74.3293 + 42.9141i) q^{82} +(-91.7157 - 91.7157i) q^{83} +(-22.9590 + 85.6843i) q^{84} +(-0.890409 - 0.238584i) q^{85} +(52.2041 - 52.2041i) q^{86} +(46.0299 + 79.7262i) q^{87} +(-13.7105 - 7.91574i) q^{88} +(40.4072 + 150.802i) q^{89} +14.3339i q^{90} +(94.7284 + 41.3178i) q^{91} -34.8665 q^{92} +(70.6767 - 18.9378i) q^{93} +(-8.73527 + 15.1299i) q^{94} +(1.83784 - 1.06108i) q^{95} +(-22.3168 - 22.3168i) q^{96} +(29.1440 - 108.767i) q^{97} +(-19.3961 - 5.19718i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9} - 18 q^{10} - 18 q^{11} + 36 q^{13} + 20 q^{14} + 66 q^{15} + 16 q^{16} - 42 q^{17} + 84 q^{18} + 46 q^{19} + 24 q^{20} - 102 q^{21} - 42 q^{22} - 36 q^{23} - 12 q^{24} + 40 q^{26} + 72 q^{27} - 4 q^{28} - 6 q^{29} - 192 q^{30} + 32 q^{31} + 16 q^{32} + 42 q^{33} - 60 q^{34} - 78 q^{35} - 48 q^{36} - 106 q^{37} + 12 q^{39} - 24 q^{40} + 132 q^{41} + 102 q^{42} - 108 q^{43} + 84 q^{44} + 240 q^{45} + 90 q^{46} + 60 q^{47} + 258 q^{49} + 194 q^{50} + 32 q^{52} - 132 q^{53} - 270 q^{54} - 162 q^{55} - 12 q^{56} - 294 q^{57} - 24 q^{58} + 18 q^{59} - 120 q^{60} + 36 q^{61} - 12 q^{62} - 72 q^{63} - 300 q^{65} + 108 q^{66} - 74 q^{67} + 60 q^{68} + 258 q^{69} + 156 q^{70} - 174 q^{71} + 132 q^{72} + 166 q^{73} - 32 q^{74} + 6 q^{75} - 92 q^{76} + 126 q^{78} - 96 q^{79} + 48 q^{80} - 12 q^{81} - 252 q^{82} - 240 q^{83} - 132 q^{84} - 24 q^{85} + 132 q^{86} + 360 q^{87} - 12 q^{88} + 294 q^{89} + 298 q^{91} - 216 q^{92} + 270 q^{93} - 60 q^{94} + 714 q^{95} - 58 q^{97} - 250 q^{98} + 252 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9 - 18 * q^10 - 18 * q^11 + 36 * q^13 + 20 * q^14 + 66 * q^15 + 16 * q^16 - 42 * q^17 + 84 * q^18 + 46 * q^19 + 24 * q^20 - 102 * q^21 - 42 * q^22 - 36 * q^23 - 12 * q^24 + 40 * q^26 + 72 * q^27 - 4 * q^28 - 6 * q^29 - 192 * q^30 + 32 * q^31 + 16 * q^32 + 42 * q^33 - 60 * q^34 - 78 * q^35 - 48 * q^36 - 106 * q^37 + 12 * q^39 - 24 * q^40 + 132 * q^41 + 102 * q^42 - 108 * q^43 + 84 * q^44 + 240 * q^45 + 90 * q^46 + 60 * q^47 + 258 * q^49 + 194 * q^50 + 32 * q^52 - 132 * q^53 - 270 * q^54 - 162 * q^55 - 12 * q^56 - 294 * q^57 - 24 * q^58 + 18 * q^59 - 120 * q^60 + 36 * q^61 - 12 * q^62 - 72 * q^63 - 300 * q^65 + 108 * q^66 - 74 * q^67 + 60 * q^68 + 258 * q^69 + 156 * q^70 - 174 * q^71 + 132 * q^72 + 166 * q^73 - 32 * q^74 + 6 * q^75 - 92 * q^76 + 126 * q^78 - 96 * q^79 + 48 * q^80 - 12 * q^81 - 252 * q^82 - 240 * q^83 - 132 * q^84 - 24 * q^85 + 132 * q^86 + 360 * q^87 - 12 * q^88 + 294 * q^89 + 298 * q^91 - 216 * q^92 + 270 * q^93 - 60 * q^94 + 714 * q^95 - 58 * q^97 - 250 * q^98 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$3$	−2.78960	+	4.83174i	−0.929868	+	1.61058i	−0.146330	+	0.989236i	$0.546746\pi$
$3$	−2.78960	+	4.83174i	−0.929868	+	1.61058i	−0.783539	+	0.621343i	$0.786587\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	0.738754	−	0.673975i	$-0.235415\pi$
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	−0.673975	+	0.738754i	$0.735415\pi$
$6$	2.04213	−	7.62134i	0.340355	−	1.27022i
$7$	7.67890	+	2.05755i	1.09699	+	0.293936i	0.761536	−	0.648122i	$-0.224445\pi$
$7$	7.67890	+	2.05755i	1.09699	+	0.293936i	0.335449	+	0.942058i	$0.391112\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−11.0638	−	19.1630i	−1.22931	−	2.12923i
$10$	−0.560999	−	0.323893i	−0.0560999	−	0.0323893i
$11$	1.44868	+	5.40655i	0.131698	+	0.491504i	0.999990	−	0.00455003i	$-0.00144833\pi$
$11$	1.44868	+	5.40655i	0.131698	+	0.491504i	−0.868291	+	0.496054i	$0.834782\pi$
$12$			11.1584i			0.929868i
$13$	12.8550	+	1.93621i	0.988846	+	0.148939i
$13$	12.8550	+	1.93621i	0.988846	+	0.148939i
$14$	−11.2427			−0.803049
$15$	−2.46850	+	0.661433i	−0.164567	+	0.0440955i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−1.74285	+	1.00623i	−0.102520	+	0.0591902i	−0.550384	−	0.834912i	$-0.685519\pi$
$17$	−1.74285	+	1.00623i	−0.102520	+	0.0591902i	0.447863	+	0.894102i	$0.352185\pi$
$18$	22.1276	+	22.1276i	1.22931	+	1.22931i
$19$	1.19911	−	4.47512i	0.0631108	−	0.235533i	−0.927164	−	0.374655i	$-0.877761\pi$
$19$	1.19911	−	4.47512i	0.0631108	−	0.235533i	0.990275	+	0.139122i	$0.0444279\pi$
$20$	0.884892	+	0.237106i	0.0442446	+	0.0118553i
$21$	−31.3626	+	31.3626i	−1.49346	+	1.49346i
$22$	−3.95787	−	6.85523i	−0.179903	−	0.311601i
$23$	−15.0976	−	8.71663i	−0.656419	−	0.378984i	0.134492	−	0.990915i	$-0.457060\pi$
$23$	−15.0976	−	8.71663i	−0.656419	−	0.378984i	−0.790911	+	0.611931i	$0.790393\pi$
$24$	−4.08426	−	15.2427i	−0.170178	−	0.635112i
$25$		−	24.7902i		−	0.991607i
$26$	−18.2690	+	2.06034i	−0.702652	+	0.0792439i
$27$	73.2415			2.71265
$28$	15.3578	−	4.11511i	0.548493	−	0.146968i
$29$	8.25026	−	14.2899i	0.284492	−	0.492754i	−0.687994	−	0.725716i	$-0.741508\pi$
$29$	8.25026	−	14.2899i	0.284492	−	0.492754i	0.972486	+	0.232962i	$0.0748418\pi$
$30$	3.12993	−	1.80707i	0.104331	−	0.0602356i
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	0.541533	−	0.840679i	$-0.317844\pi$
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	−0.840679	+	0.541533i	$0.817844\pi$
$32$	−1.46410	+	5.46410i	−0.0457532	+	0.170753i
$33$	−30.1643	−	8.08249i	−0.914069	−	0.244924i
$34$	2.01247	−	2.01247i	0.0591902	−	0.0591902i
$35$	1.82071	+	3.15357i	0.0520204	+	0.0901020i
$36$	−38.3261	−	22.1276i	−1.06461	−	0.614655i
$37$	9.12370	+	34.0501i	0.246586	+	0.920273i	0.972579	+	0.232571i	$0.0747138\pi$
$37$	9.12370	+	34.0501i	0.246586	+	0.920273i	−0.725993	+	0.687702i	$0.758620\pi$
$38$			6.55204i			0.172422i
$39$	−45.2156	+	56.7107i	−1.15938	+	1.45412i
$40$	−1.29557			−0.0323893
$41$	58.6217	−	15.7076i	1.42980	−	0.383113i	0.540849	−	0.841120i	$-0.318103\pi$
$41$	58.6217	−	15.7076i	1.42980	−	0.383113i	0.888949	+	0.458007i	$0.151436\pi$
$42$	31.3626	−	54.3217i	0.746730	−	1.29337i
$43$	−45.2101	+	26.1020i	−1.05140	+	0.607024i	−0.923040	−	0.384704i	$-0.874304\pi$
$43$	−45.2101	+	26.1020i	−1.05140	+	0.607024i	−0.128357	+	0.991728i	$0.540970\pi$
$44$	7.91574	+	7.91574i	0.179903	+	0.179903i
$45$	2.62329	−	9.79026i	0.0582954	−	0.217561i
$46$	23.8143	+	6.38102i	0.517702	+	0.138718i
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	−0.608045	−	0.793902i	$-0.708046\pi$
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	0.793902	+	0.608045i	$0.208046\pi$
$48$	11.1584	+	19.3269i	0.232467	+	0.402645i
$49$	12.2967	+	7.09948i	0.250952	+	0.144887i
$50$	9.07384	+	33.8640i	0.181477	+	0.677280i
$51$		−	11.2280i		−	0.220156i
$52$	24.2017	−	9.50138i	0.465418	−	0.182719i
$53$	−23.4425			−0.442311			−0.221155	−	0.975239i	$-0.570983\pi$
$53$	−23.4425			−0.442311			−0.221155	+	0.975239i	$0.570983\pi$
$54$	−100.050	+	26.8082i	−1.85277	+	0.496449i
$55$	−1.28193	+	2.22036i	−0.0233077	+	0.0403702i
$56$	−19.4729	+	11.2427i	−0.347730	+	0.200762i
$57$	18.2776	+	18.2776i	0.320660	+	0.320660i
$58$	−6.03961	+	22.5401i	−0.104131	+	0.388623i
$59$	34.0864	+	9.13343i	0.577736	+	0.154804i	0.535842	−	0.844318i	$-0.319994\pi$
$59$	34.0864	+	9.13343i	0.577736	+	0.154804i	0.0418940	+	0.999122i	$0.486661\pi$
$60$	−3.61413	+	3.61413i	−0.0602356	+	0.0602356i
$61$	−13.9421	−	24.1483i	−0.228558	−	0.395875i	0.728823	−	0.684702i	$-0.240068\pi$
$61$	−13.9421	−	24.1483i	−0.228558	−	0.395875i	−0.957381	+	0.288828i	$0.906734\pi$
$62$	16.0622	+	9.27353i	0.259068	+	0.149573i
$63$	−45.5287	−	169.915i	−0.722677	−	2.69707i
$64$		−	8.00000i		−	0.125000i
$65$	3.53652	+	4.79077i	0.0544080	+	0.0737042i
$66$	44.1635			0.669145
$67$	−33.0643	+	8.85955i	−0.493497	+	0.132232i	−0.496980	−	0.867762i	$-0.665558\pi$
$67$	−33.0643	+	8.85955i	−0.493497	+	0.132232i	0.00348324	+	0.999994i	$0.498891\pi$
$68$	−2.01247	+	3.48570i	−0.0295951	+	0.0512602i
$69$	84.2329	−	48.6319i	1.22077	−	0.704810i
$70$	−3.64143	−	3.64143i	−0.0520204	−	0.0520204i
$71$	19.7955	−	73.8778i	0.278810	−	1.04053i	−0.674435	−	0.738334i	$-0.735613\pi$
$71$	19.7955	−	73.8778i	0.278810	−	1.04053i	0.953245	−	0.302198i	$-0.0977205\pi$
$72$	60.4537	+	16.1985i	0.839634	+	0.224979i
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	−0.824778	−	0.565457i	$-0.808700\pi$
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	0.565457	+	0.824778i	$0.308700\pi$
$74$	−24.9264	−	43.1738i	−0.336843	−	0.583430i
$75$	119.780	+	69.1548i	1.59706	+	0.922064i
$76$	−2.39821	−	8.95025i	−0.0315554	−	0.117766i
$77$			44.4971i			0.577884i
$78$	41.0082	−	94.0184i	0.525746	−	1.20536i
$79$	−142.837			−1.80806			−0.904029	−	0.427471i	$-0.859404\pi$
$79$	−142.837			−1.80806			−0.904029	+	0.427471i	$0.859404\pi$
$80$	1.76978	−	0.474212i	0.0221223	−	0.00592766i
$81$	−104.741	+	181.416i	−1.29310	+	2.23971i
$82$	−74.3293	+	42.9141i	−0.906455	+	0.523342i
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.993797	−	0.111212i	$-0.964527\pi$
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.111212	−	0.993797i	$-0.535473\pi$
$84$	−22.9590	+	85.6843i	−0.273322	+	1.02005i
$85$	−0.890409	−	0.238584i	−0.0104754	−	0.00280687i
$86$	52.2041	−	52.2041i	0.607024	−	0.607024i
$87$	46.0299	+	79.7262i	0.529080	+	0.916393i
$88$	−13.7105	−	7.91574i	−0.155801	−	0.0899515i
$89$	40.4072	+	150.802i	0.454014	+	1.69440i	0.690970	+	0.722883i	$0.257183\pi$
$89$	40.4072	+	150.802i	0.454014	+	1.69440i	−0.236956	+	0.971520i	$0.576150\pi$
$90$			14.3339i			0.159266i
$91$	94.7284	+	41.3178i	1.04097	+	0.454042i
$92$	−34.8665			−0.378984
$93$	70.6767	−	18.9378i	0.759965	−	0.203632i
$94$	−8.73527	+	15.1299i	−0.0929284	+	0.160957i
$95$	1.83784	−	1.06108i	0.0193457	−	0.0111693i
$96$	−22.3168	−	22.3168i	−0.232467	−	0.232467i
$97$	29.1440	−	108.767i	0.300454	−	1.12131i	−0.636335	−	0.771413i	$-0.719550\pi$
$97$	29.1440	−	108.767i	0.300454	−	1.12131i	0.936789	−	0.349896i	$-0.113783\pi$
$98$	−19.3961	−	5.19718i	−0.197920	−	0.0530325i
$99$	87.5780	−	87.5780i	0.884626	−	0.884626i
$100$	−24.7902	−	42.9379i	−0.247902	−	0.429379i
$101$	−84.6101	−	48.8497i	−0.837724	−	0.483660i	0.0187659	−	0.999824i	$-0.494026\pi$
$101$	−84.6101	−	48.8497i	−0.837724	−	0.483660i	−0.856490	+	0.516164i	$0.827360\pi$
$102$	4.10973	+	15.3377i	0.0402914	+	0.150370i
$103$			108.442i			1.05284i	0.850226	+	0.526418i	$0.176465\pi$
$103$			108.442i			1.05284i	−0.850226	+	0.526418i	$0.823535\pi$
$104$	−29.5824	+	21.8376i	−0.284446	+	0.209977i
$105$	−20.3163			−0.193488
$106$	32.0230	−	8.58054i	0.302104	−	0.0809485i
$107$	37.6493	−	65.2105i	0.351863	−	0.609444i	−0.634713	−	0.772748i	$-0.718882\pi$
$107$	37.6493	−	65.2105i	0.351863	−	0.609444i	0.986576	+	0.163304i	$0.0522151\pi$
$108$	126.858	−	73.2415i	1.17461	−	0.678162i
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	0.733373	−	0.679826i	$-0.237945\pi$
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	−0.679826	+	0.733373i	$0.737945\pi$
$110$	0.938435	−	3.50229i	0.00853123	−	0.0318390i
$111$	−189.973	−	50.9030i	−1.71147	−	0.458586i
$112$	22.4854	−	22.4854i	0.200762	−	0.200762i
$113$	57.2435	+	99.1486i	0.506580	+	0.877422i	0.999971	+	0.00761416i	$0.00242369\pi$
$113$	57.2435	+	99.1486i	0.506580	+	0.877422i	−0.493391	+	0.869807i	$0.664243\pi$
$114$	−31.6577	−	18.2776i	−0.277699	−	0.160330i
$115$	−2.06677	−	7.71328i	−0.0179719	−	0.0670720i
$116$		−	33.0010i		−	0.284492i
$117$	−105.121	−	267.763i	−0.898473	−	2.28857i
$118$	−49.9060			−0.422932
$119$	−15.4535	+	4.14076i	−0.129862	+	0.0347963i
$120$	3.61413	−	6.25986i	0.0301178	−	0.0521655i
$121$	77.6570	−	44.8353i	0.641793	−	0.370540i
$122$	27.8841	+	27.8841i	0.228558	+	0.228558i
$123$	−87.6362	+	327.063i	−0.712489	+	2.65905i
$124$	−25.3357	−	6.78869i	−0.204321	−	0.0547475i
$125$	16.1267	−	16.1267i	0.129014	−	0.129014i
$126$	124.387	+	215.444i	0.987196	+	1.70987i
$127$	83.8081	+	48.3866i	0.659906	+	0.380997i	0.792241	−	0.610208i	$-0.208914\pi$
$127$	83.8081	+	48.3866i	0.659906	+	0.380997i	−0.132335	+	0.991205i	$0.542247\pi$
$128$	2.92820	+	10.9282i	0.0228766	+	0.0853766i
$129$		−	291.258i		−	2.25781i
$130$	−6.58452	−	5.24986i	−0.0506502	−	0.0403835i
$131$	159.613			1.21842			0.609212	−	0.793008i	$-0.291486\pi$
$131$	159.613			1.21842			0.609212	+	0.793008i	$0.291486\pi$
$132$	−60.3285	+	16.1650i	−0.457034	+	0.122462i
$133$	18.4156	−	31.8968i	0.138463	−	0.239825i
$134$	41.9239	−	24.2048i	0.312865	−	0.180632i
$135$	23.7224	+	23.7224i	0.175722	+	0.175722i
$136$	1.47323	−	5.49816i	0.0108326	−	0.0404277i
$137$	−122.224	−	32.7498i	−0.892146	−	0.239050i	−0.216506	−	0.976281i	$-0.569466\pi$
$137$	−122.224	−	32.7498i	−0.892146	−	0.239050i	−0.675640	+	0.737232i	$0.736133\pi$
$138$	−97.2638	+	97.2638i	−0.704810	+	0.704810i
$139$	−30.2234	−	52.3485i	−0.217435	−	0.376608i	0.736588	−	0.676341i	$-0.236436\pi$
$139$	−30.2234	−	52.3485i	−0.217435	−	0.376608i	−0.954023	+	0.299733i	$0.903102\pi$
$140$	6.30714	+	3.64143i	0.0450510	+	0.0260102i
$141$	17.8386	+	66.5745i	0.126515	+	0.472159i
$142$			108.165i			0.761723i
$143$	8.15456	+	72.3061i	0.0570249	+	0.505637i
$144$	−88.5103			−0.614655
$145$	7.30059	−	1.95619i	0.0503489	−	0.0134910i
$146$	18.9304	−	32.7884i	0.129660	−	0.224578i
$147$	−68.6056	+	39.6095i	−0.466705	+	0.269452i
$148$	49.8528	+	49.8528i	0.336843	+	0.336843i
$149$	−56.5047	+	210.878i	−0.379226	+	1.41529i	0.467844	+	0.883811i	$0.345031\pi$
$149$	−56.5047	+	210.878i	−0.379226	+	1.41529i	−0.847070	+	0.531481i	$0.821636\pi$
$150$	−188.934	−	50.6248i	−1.25956	−	0.337499i
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	−0.419557	−	0.907729i	$-0.637815\pi$
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	0.907729	+	0.419557i	$0.137815\pi$
$152$	6.55204	+	11.3485i	0.0431055	+	0.0746609i
$153$	38.5650	+	22.2655i	0.252059	+	0.145526i
$154$	−16.2871	−	60.7841i	−0.105760	−	0.394702i
$155$		−	6.00726i		−	0.0387565i
$156$	−21.6051	+	143.441i	−0.138494	+	0.919497i
$157$	−127.109			−0.809611			−0.404805	−	0.914403i	$-0.632661\pi$
$157$	−127.109			−0.809611			−0.404805	+	0.914403i	$0.632661\pi$
$158$	195.118	−	52.2818i	1.23493	−	0.330898i
$159$	65.3952	−	113.268i	0.411291	−	0.712376i
$160$	−2.24400	+	1.29557i	−0.0140250	+	0.00809733i
$161$	−97.9983	−	97.9983i	−0.608685	−	0.608685i
$162$	76.6755	−	286.157i	0.473306	−	1.76640i
$163$	163.306	+	43.7578i	1.00188	+	0.268453i	0.722232	−	0.691650i	$-0.243116\pi$
$163$	163.306	+	43.7578i	1.00188	+	0.268453i	0.279646	+	0.960103i	$0.409783\pi$
$164$	85.8281	−	85.8281i	0.523342	−	0.523342i
$165$	−7.15213	−	12.3879i	−0.0433463	−	0.0750779i
$166$	158.856	+	91.7157i	0.956965	+	0.552504i
$167$	43.1534	+	161.051i	0.258403	+	0.964375i	0.966165	+	0.257924i	$0.0830383\pi$
$167$	43.1534	+	161.051i	0.258403	+	0.964375i	−0.707762	+	0.706451i	$0.750295\pi$
$168$		−	125.451i		−	0.746730i
$169$	161.502	+	49.7800i	0.955634	+	0.294556i
$170$	1.30365			0.00766852
$171$	−99.0237	+	26.5333i	−0.579086	+	0.155166i
$172$	−52.2041	+	90.4201i	−0.303512	+	0.525698i
$173$	−121.663	+	70.2419i	−0.703252	+	0.406023i	−0.808557	−	0.588417i	$-0.799751\pi$
$173$	−121.663	+	70.2419i	−0.703252	+	0.406023i	0.105305	+	0.994440i	$0.466418\pi$
$174$	−92.0599	−	92.0599i	−0.529080	−	0.529080i
$175$	51.0071	−	190.361i	0.291469	−	1.08778i
$176$	21.6262	+	5.79472i	0.122876	+	0.0329245i
$177$	−139.218	+	139.218i	−0.786543	+	0.786543i
$178$	−110.395	−	191.209i	−0.620195	−	1.07421i
$179$	−273.667	−	158.002i	−1.52886	−	0.882691i	−0.999410	−	0.0343526i	$-0.989063\pi$
$179$	−273.667	−	158.002i	−1.52886	−	0.882691i	−0.529455	−	0.848338i	$-0.677604\pi$
$180$	−5.24659	−	19.5805i	−0.0291477	−	0.108781i
$181$			83.6580i			0.462199i	0.972930	+	0.231099i	$0.0742323\pi$
$181$			83.6580i			0.462199i	−0.972930	+	0.231099i	$0.925768\pi$
$182$	−144.525	−	21.7682i	−0.794092	−	0.119606i
$183$	155.571			0.850116
$184$	47.6285	−	12.7620i	0.258851	−	0.0693589i
$185$	−8.07349	+	13.9837i	−0.0436405	+	0.0755876i
$186$	−89.6145	+	51.7389i	−0.481798	+	0.278166i
$187$	−7.96508	−	7.96508i	−0.0425940	−	0.0425940i
$188$	6.39466	−	23.8652i	0.0340142	−	0.126943i
$189$	562.414	+	150.698i	2.97573	+	0.797346i
$190$	−2.12216	+	2.12216i	−0.0111693	+	0.0111693i
$191$	−34.5567	−	59.8539i	−0.180925	−	0.313371i	0.761271	−	0.648434i	$-0.224576\pi$
$191$	−34.5567	−	59.8539i	−0.180925	−	0.313371i	−0.942196	+	0.335063i	$0.891242\pi$
$192$	38.6539	+	22.3168i	0.201322	+	0.116234i
$193$	−84.0297	−	313.603i	−0.435387	−	1.62489i	−0.740139	−	0.672454i	$-0.765240\pi$
$193$	−84.0297	−	313.603i	−0.435387	−	1.62489i	0.304752	−	0.952432i	$-0.401426\pi$
$194$			159.246i			0.820855i
$195$	−33.0132	+	3.72318i	−0.169299	+	0.0190932i
$196$	28.3979			0.144887
$197$	−309.232	+	82.8586i	−1.56971	+	0.420602i	−0.935721	−	0.352742i	$-0.885249\pi$
$197$	−309.232	+	82.8586i	−1.56971	+	0.420602i	−0.633987	+	0.773344i	$0.718583\pi$
$198$	−87.5780	+	151.690i	−0.442313	+	0.766109i
$199$	149.667	−	86.4100i	0.752093	−	0.434221i	−0.0743564	−	0.997232i	$-0.523690\pi$
$199$	149.667	−	86.4100i	0.752093	−	0.434221i	0.826450	+	0.563010i	$0.190357\pi$
$200$	49.5804	+	49.5804i	0.247902	+	0.247902i
$201$	49.4293	−	184.473i	0.245917	−	0.917775i
$202$	133.460	+	35.7604i	0.660692	+	0.177032i
$203$	92.7551	−	92.7551i	0.456922	−	0.456922i
$204$	−11.2280	−	19.4474i	−0.0550391	−	0.0953305i
$205$	24.0748	+	13.8996i	0.117438	+	0.0678028i
$206$	−39.6926	−	148.135i	−0.192682	−	0.719101i
$207$			385.756i			1.86355i
$208$	32.4172	−	40.6586i	0.155852	−	0.195474i
$209$	25.9321			0.124077
$210$	27.7526	−	7.43628i	0.132155	−	0.0354108i
$211$	−115.089	+	199.341i	−0.545447	+	0.944743i	0.453131	+	0.891444i	$0.350307\pi$
$211$	−115.089	+	199.341i	−0.545447	+	0.944743i	−0.998579	+	0.0532988i	$0.983026\pi$
$212$	−40.6035	+	23.4425i	−0.191526	+	0.110578i
$213$	301.736	+	301.736i	1.41660	+	1.41660i
$214$	−27.5612	+	102.860i	−0.128791	+	0.480653i
$215$	−23.0975	−	6.18896i	−0.107430	−	0.0287858i
$216$	−146.483	+	146.483i	−0.678162	+	0.678162i
$217$	−52.1297	−	90.2912i	−0.240229	−	0.416089i
$218$	−10.1093	−	5.83660i	−0.0463728	−	0.0267734i
$219$	−38.6584	−	144.275i	−0.176522	−	0.658790i
$220$			5.12770i			0.0233077i
$221$	−24.3526	+	9.56062i	−0.110193	+	0.0432607i
$222$	278.139			1.25288
$223$	−254.206	+	68.1143i	−1.13994	+	0.305445i	−0.778926	−	0.627116i	$-0.784235\pi$
$223$	−254.206	+	68.1143i	−1.13994	+	0.305445i	−0.361012	+	0.932561i	$0.617569\pi$
$224$	−22.4854	+	38.9458i	−0.100381	+	0.173865i
$225$	−475.055	+	274.273i	−2.11136	+	1.21899i
$226$	−114.487	−	114.487i	−0.506580	−	0.506580i
$227$	30.8416	−	115.102i	0.135866	−	0.507059i	−0.864127	−	0.503274i	$-0.832129\pi$
$227$	30.8416	−	115.102i	0.135866	−	0.507059i	0.999993	−	0.00378487i	$-0.00120476\pi$
$228$	49.9353	+	13.3801i	0.219015	+	0.0586848i
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	−0.999800	−	0.0200093i	$-0.993630\pi$
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	0.0200093	+	0.999800i	$0.493630\pi$
$230$	5.64651	+	9.78005i	0.0245501	+	0.0425219i
$231$	−214.998	−	124.129i	−0.930727	−	0.537356i
$232$	12.0792	+	45.0803i	0.0520656	+	0.194311i
$233$		−	230.683i		−	0.990054i	−0.868878	−	0.495027i	$-0.835158\pi$
$233$		−	230.683i		−	0.990054i	0.868878	−	0.495027i	$-0.164842\pi$
$234$	241.606	+	327.294i	1.03251	+	1.39869i
$235$	5.65859			0.0240791
$236$	68.1729	−	18.2669i	0.288868	−	0.0774020i
$237$	398.458	−	690.149i	1.68126	−	2.91202i
$238$	19.5943	−	11.3128i	0.0823290	−	0.0475326i
$239$	184.518	+	184.518i	0.772041	+	0.772041i	0.978463	−	0.206422i	$-0.0661820\pi$
$239$	184.518	+	184.518i	0.772041	+	0.772041i	−0.206422	+	0.978463i	$0.566182\pi$
$240$	−2.64573	+	9.87400i	−0.0110239	+	0.0411417i
$241$	214.865	+	57.5730i	0.891557	+	0.238892i	0.675387	−	0.737464i	$-0.263977\pi$
$241$	214.865	+	57.5730i	0.891557	+	0.238892i	0.216170	+	0.976356i	$0.430643\pi$
$242$	−89.6706	+	89.6706i	−0.370540	+	0.370540i
$243$	−254.784	−	441.298i	−1.04849	−	1.81604i
$244$	−48.2967	−	27.8841i	−0.197937	−	0.114279i
$245$	1.68333	+	6.28228i	0.00687074	+	0.0256419i
$246$		−	478.853i		−	1.94656i
$247$	24.0793	−	55.2060i	0.0974871	−	0.223506i
$248$	37.0941			0.149573
$249$	698.997	−	187.296i	2.80722	−	0.752191i
$250$	−16.1267	+	27.9323i	−0.0645068	+	0.111729i
$251$	218.211	−	125.984i	0.869366	−	0.501929i	0.00222866	−	0.999998i	$-0.499291\pi$
$251$	218.211	−	125.984i	0.869366	−	0.501929i	0.867138	+	0.498069i	$0.165957\pi$
$252$	−248.773	−	248.773i	−0.987196	−	0.987196i
$253$	25.2552	−	94.2537i	0.0998230	−	0.372544i
$254$	−132.195	−	35.4215i	−0.520452	−	0.139455i
$255$	3.63666	−	3.63666i	0.0142614	−	0.0142614i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	251.399	+	145.145i	0.978204	+	0.564767i	0.901728	−	0.432305i	$-0.142300\pi$
$257$	251.399	+	145.145i	0.978204	+	0.564767i	0.0764769	+	0.997071i	$0.475633\pi$
$258$	106.608	+	397.865i	0.413208	+	1.54211i
$259$			280.240i			1.08201i
$260$	10.9162	+	4.76134i	0.0419854	+	0.0183128i
$261$	−365.117			−1.39891
$262$	−218.036	+	58.4226i	−0.832199	+	0.222987i
$263$	53.9337	−	93.4160i	0.205071	−	0.355194i	−0.745084	−	0.666970i	$-0.767591\pi$
$263$	53.9337	−	93.4160i	0.205071	−	0.355194i	0.950155	+	0.311777i	$0.100924\pi$
$264$	76.4935	−	44.1635i	0.289748	−	0.167286i
$265$	−7.59285	−	7.59285i	−0.0286523	−	0.0286523i
$266$	−13.4812	+	50.3124i	−0.0506811	+	0.189144i
$267$	−841.355	−	225.440i	−3.15114	−	0.844346i
$268$	−48.4095	+	48.4095i	−0.180632	+	0.180632i
$269$	217.712	+	377.087i	0.809337	+	1.40181i	0.913324	+	0.407234i	$0.133507\pi$
$269$	217.712	+	377.087i	0.809337	+	1.40181i	−0.103987	+	0.994579i	$0.533160\pi$
$270$	−41.0884	−	23.7224i	−0.152179	−	0.0878608i
$271$	21.7703	+	81.2480i	0.0803333	+	0.299808i	0.994390	−	0.105779i	$-0.0337337\pi$
$271$	21.7703	+	81.2480i	0.0803333	+	0.299808i	−0.914056	+	0.405587i	$0.867067\pi$
$272$			8.04987i			0.0295951i
$273$	−463.892	+	342.442i	−1.69924	+	1.25437i
$274$	178.948			0.653096
$275$	134.029	−	35.9131i	0.487379	−	0.130593i
$276$	97.2638	−	168.466i	0.352405	−	0.610383i
$277$	−31.8797	+	18.4057i	−0.115089	+	0.0664467i	−0.556439	−	0.830888i	$-0.687833\pi$
$277$	−31.8797	+	18.4057i	−0.115089	+	0.0664467i	0.441350	+	0.897335i	$0.354500\pi$
$278$	60.4469	+	60.4469i	0.217435	+	0.217435i
$279$	−75.1086	+	280.309i	−0.269207	+	1.00469i
$280$	−9.94856	−	2.66571i	−0.0355306	−	0.00952039i
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	−0.758647	−	0.651501i	$-0.774139\pi$
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	0.651501	+	0.758647i	$0.274139\pi$
$282$	−48.7359	−	84.4131i	−0.172822	−	0.299337i
$283$	−90.8978	−	52.4799i	−0.321194	−	0.185441i	0.330731	−	0.943725i	$-0.392705\pi$
$283$	−90.8978	−	52.4799i	−0.321194	−	0.185441i	−0.651924	+	0.758284i	$0.726038\pi$
$284$	−39.5910	−	147.756i	−0.139405	−	0.520266i
$285$			11.8400i			0.0415438i
$286$	−37.6052	−	95.7872i	−0.131487	−	0.334920i
$287$	482.469			1.68108
$288$	120.907	−	32.3970i	0.419817	−	0.112490i
$289$	−142.475	+	246.774i	−0.492993	+	0.853889i
$290$	−9.25678	+	5.34441i	−0.0319199	+	0.0184290i
$291$	444.233	+	444.233i	1.52657	+	1.52657i
$292$	−13.8580	+	51.7188i	−0.0474589	+	0.177119i
$293$	121.399	+	32.5289i	0.414333	+	0.111020i	0.459963	−	0.887938i	$-0.347863\pi$
$293$	121.399	+	32.5289i	0.414333	+	0.111020i	−0.0456298	+	0.998958i	$0.514529\pi$
$294$	79.2190	−	79.2190i	0.269452	−	0.269452i
$295$	8.08211	+	13.9986i	0.0273970	+	0.0474529i
$296$	−86.3476	−	49.8528i	−0.291715	−	0.168422i
$297$	106.103	+	395.984i	0.357251	+	1.33328i
$298$		−	308.748i		−	1.03607i
$299$	−177.203	−	141.285i	−0.592652	−	0.472524i
$300$	276.619			0.922064
$301$	−400.870	+	107.413i	−1.33179	+	0.356853i
$302$	−73.7140	+	127.676i	−0.244086	+	0.422769i
$303$	472.058	−	272.543i	1.55795	−	0.899480i
$304$	−13.1041	−	13.1041i	−0.0431055	−	0.0431055i
$305$	3.30575	−	12.3372i	0.0108385	−	0.0404499i
$306$	−60.8305	−	16.2995i	−0.198793	−	0.0532663i
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	−0.917342	−	0.398100i	$-0.869670\pi$
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	0.398100	+	0.917342i	$0.369670\pi$
$308$	44.4971	+	77.0712i	0.144471	+	0.250231i
$309$	−523.964	−	302.511i	−1.69568	−	0.978999i
$310$	2.19881	+	8.20607i	0.00709294	+	0.0264712i
$311$		−	461.756i		−	1.48475i	−0.669986	−	0.742374i	$-0.733700\pi$
$311$		−	461.756i		−	1.48475i	0.669986	−	0.742374i	$-0.266300\pi$
$312$	−22.9902	−	203.853i	−0.0736864	−	0.653374i
$313$	8.16759			0.0260945			0.0130473	−	0.999915i	$-0.495847\pi$
$313$	8.16759			0.0260945			0.0130473	+	0.999915i	$0.495847\pi$
$314$	173.634	−	46.5251i	0.552974	−	0.148169i
$315$	40.2880	−	69.7808i	0.127898	−	0.221526i
$316$	−247.400	+	142.837i	−0.782912	+	0.452014i
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	0.547685	−	0.836684i	$-0.315509\pi$
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	−0.836684	+	0.547685i	$0.815509\pi$
$318$	−47.8726	+	178.663i	−0.150543	+	0.561833i
$319$	89.2109	+	23.9040i	0.279658	+	0.0749341i
$320$	2.59114	−	2.59114i	0.00809733	−	0.00809733i
$321$	210.053	+	363.823i	0.654372	+	1.13341i
$322$	169.738	+	97.9983i	0.527137	+	0.304343i
$323$	2.41316	+	9.00604i	0.00747109	+	0.0278825i
$324$			418.963i			1.29310i
$325$	47.9991	−	318.678i	0.147689	−	0.980547i
$326$	−239.097			−0.733426
$327$	−44.4827	+	11.9191i	−0.136033	+	0.0364499i
$328$	−85.8281	+	148.659i	−0.261671	+	0.453228i
$329$	85.0505	−	49.1039i	0.258512	−	0.149252i
$330$	14.3043	+	14.3043i	0.0433463	+	0.0433463i
$331$	38.7033	−	144.443i	0.116928	−	0.436382i	−0.882496	−	0.470321i	$-0.844138\pi$
$331$	38.7033	−	144.443i	0.116928	−	0.436382i	0.999424	+	0.0339382i	$0.0108049\pi$
$332$	−250.572	−	67.1406i	−0.754735	−	0.202231i
$333$	551.561	−	551.561i	1.65634	−	1.65634i
$334$	−117.897	−	204.204i	−0.352986	−	0.611389i
$335$	−13.5789	−	7.83975i	−0.0405339	−	0.0234022i
$336$	45.9181	+	171.369i	0.136661	+	0.510026i
$337$			61.7332i			0.183185i	0.995797	+	0.0915923i	$0.0291956\pi$
$337$			61.7332i			0.183185i	−0.995797	+	0.0915923i	$0.970804\pi$
$338$	−238.837	−	8.88689i	−0.706618	−	0.0262926i
$339$	−638.747			−1.88421
$340$	−1.78082	+	0.477169i	−0.00523770	+	0.00140344i
$341$	36.7034	−	63.5721i	0.107635	−	0.186429i
$342$	125.557	−	72.4904i	0.367126	−	0.211960i
$343$	−195.629	−	195.629i	−0.570346	−	0.570346i
$344$	38.2160	−	142.624i	0.111093	−	0.414605i
$345$	43.0340	+	11.5309i	0.124736	+	0.0334230i
$346$	140.484	−	140.484i	0.406023	−	0.406023i
$347$	−110.431	−	191.272i	−0.318245	−	0.551216i	0.661877	−	0.749612i	$-0.269760\pi$
$347$	−110.431	−	191.272i	−0.318245	−	0.551216i	−0.980122	+	0.198396i	$0.936427\pi$
$348$	159.452	+	92.0599i	0.458196	+	0.264540i
$349$	−75.3230	−	281.109i	−0.215825	−	0.805470i	−0.985874	−	0.167486i	$-0.946435\pi$
$349$	−75.3230	−	281.109i	−0.215825	−	0.805470i	0.770049	−	0.637984i	$-0.220232\pi$
$350$			278.708i			0.796309i
$351$	941.520	+	141.811i	2.68239	+	0.404020i
$352$	−31.6629			−0.0899515
$353$	19.0412	−	5.10208i	0.0539412	−	0.0144535i	−0.231748	−	0.972776i	$-0.574444\pi$
$353$	19.0412	−	5.10208i	0.0539412	−	0.0144535i	0.285689	+	0.958322i	$0.407778\pi$
$354$	139.218	−	241.133i	0.393271	−	0.681166i
$355$	30.3401	−	17.5169i	0.0854652	−	0.0493433i
$356$	220.789	+	220.789i	0.620195	+	0.620195i
$357$	23.1022	−	86.2185i	0.0647120	−	0.241508i
$358$	431.668	+	115.665i	1.20578	+	0.323087i
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	−0.977708	−	0.209970i	$-0.932663\pi$
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	0.209970	+	0.977708i	$0.432663\pi$
$360$	14.3339	+	24.8271i	0.0398165	+	0.0689642i
$361$	294.046	+	169.768i	0.814533	+	0.470271i
$362$	−30.6210	−	114.279i	−0.0845883	−	0.315688i
$363$			500.291i			1.37821i
$364$	205.392	−	23.1638i	0.564264	−	0.0636367i
$365$	−12.2628			−0.0335968
$366$	−212.514	+	56.9430i	−0.580640	+	0.155582i
$367$	−234.367	+	405.936i	−0.638603	+	1.10609i	0.347136	+	0.937815i	$0.387154\pi$
$367$	−234.367	+	405.936i	−0.638603	+	1.10609i	−0.985739	+	0.168278i	$0.946179\pi$
$368$	−60.3906	+	34.8665i	−0.164105	+	0.0947460i
$369$	−949.584	−	949.584i	−2.57340	−	2.57340i
$370$	5.91021	−	22.0572i	0.0159735	−	0.0596140i
$371$	−180.012	−	48.2341i	−0.485208	−	0.130011i
$372$	103.478	−	103.478i	0.278166	−	0.278166i
$373$	−130.407	−	225.872i	−0.349617	−	0.605555i	0.636564	−	0.771224i	$-0.280355\pi$
$373$	−130.407	−	225.872i	−0.349617	−	0.605555i	−0.986181	+	0.165669i	$0.947022\pi$
$374$	13.7959	+	7.96508i	0.0368875	+	0.0212970i
$375$	32.9329	+	122.907i	0.0878209	+	0.327752i
$376$			34.9411i			0.0929284i
$377$	133.725	−	167.722i	0.354709	−	0.444886i
$378$	−823.431			−2.17839
$379$	206.894	−	55.4370i	0.545893	−	0.146272i	0.0246758	−	0.999696i	$-0.492145\pi$
$379$	206.894	−	55.4370i	0.545893	−	0.146272i	0.521218	+	0.853424i	$0.325478\pi$
$380$	2.12216	−	3.67569i	0.00558463	−	0.00967286i
$381$	−467.583	+	269.959i	−1.22725	+	0.708554i
$382$	69.1133	+	69.1133i	0.180925	+	0.180925i
$383$	−177.535	+	662.570i	−0.463538	+	1.72995i	0.198151	+	0.980171i	$0.436506\pi$
$383$	−177.535	+	662.570i	−0.463538	+	1.72995i	−0.661690	+	0.749778i	$0.730160\pi$
$384$	−60.9707	−	16.3371i	−0.158778	−	0.0425444i
$385$	−14.4123	+	14.4123i	−0.0374345	+	0.0374345i
$386$	229.573	+	397.633i	0.594750	+	1.03014i
$387$	1000.39	+	577.575i	2.58498	+	1.49244i
$388$	−58.2880	−	217.534i	−0.150227	−	0.560654i
$389$		−	374.691i		−	0.963216i	−0.876387	−	0.481608i	$-0.840053\pi$
$389$		−	374.691i		−	0.963216i	0.876387	−	0.481608i	$-0.159947\pi$
$390$	43.7342	−	17.1696i	0.112139	−	0.0440247i
$391$	35.0839			0.0897286
$392$	−38.7923	+	10.3944i	−0.0989599	+	0.0265162i
$393$	−445.258	+	771.210i	−1.13297	+	1.96237i
$394$	392.091	−	226.374i	0.995155	−	0.574553i
$395$	−46.2638	−	46.2638i	−0.117123	−	0.117123i
$396$	64.1116	−	239.268i	0.161898	−	0.604211i
$397$	630.268	+	168.880i	1.58758	+	0.425390i	0.941261	−	0.337680i	$-0.109642\pi$
$397$	630.268	+	168.880i	1.58758	+	0.425390i	0.646316	+	0.763070i	$0.276309\pi$
$398$	−172.820	+	172.820i	−0.434221	+	0.434221i
$399$	102.745	+	177.959i	0.257505	+	0.446012i
$400$	−85.8757	−	49.5804i	−0.214689	−	0.123951i
$401$	−111.879	−	417.539i	−0.279001	−	1.04125i	−0.953113	−	0.302616i	$-0.902140\pi$
$401$	−111.879	−	417.539i	−0.279001	−	1.04125i	0.674112	−	0.738629i	$-0.264527\pi$
$402$			270.087i			0.671858i
$403$	−101.256	−	137.167i	−0.251255	−	0.340364i
$404$	−195.399			−0.483660
$405$	−92.6843	+	24.8347i	−0.228850	+	0.0613202i
$406$	−92.7551	+	160.656i	−0.228461	+	0.395706i
$407$	−170.876	+	98.6554i	−0.419843	+	0.242397i
$408$	22.4560	+	22.4560i	0.0550391	+	0.0550391i
$409$	72.2456	−	269.624i	0.176640	−	0.659228i	−0.819627	−	0.572897i	$-0.805819\pi$
$409$	72.2456	−	269.624i	0.176640	−	0.659228i	0.996267	−	0.0863302i	$-0.0275140\pi$
$410$	−37.9743	−	10.1752i	−0.0926203	−	0.0248175i
$411$	499.195	−	499.195i	1.21459	−	1.21459i
$412$	108.442	+	187.827i	0.263209	+	0.455892i
$413$	242.954	+	140.269i	0.588265	+	0.339635i
$414$	−141.196	−	526.952i	−0.341054	−	1.27283i
$415$		−	59.4122i		−	0.143162i
$416$	−29.4007	+	67.4062i	−0.0706747	+	0.162034i
$417$	337.246			0.808743
$418$	−35.4239	+	9.49181i	−0.0847462	+	0.0227077i
$419$	−93.7951	+	162.458i	−0.223855	+	0.387728i	−0.955975	−	0.293447i	$-0.905197\pi$
$419$	−93.7951	+	162.458i	−0.223855	+	0.387728i	0.732121	+	0.681175i	$0.238531\pi$
$420$	−35.1888	+	20.3163i	−0.0837829	+	0.0483721i
$421$	410.480	+	410.480i	0.975013	+	0.975013i	0.999695	−	0.0246826i	$-0.00785752\pi$
$421$	410.480	+	410.480i	0.975013	+	0.975013i	−0.0246826	+	0.999695i	$0.507858\pi$
$422$	84.2513	−	314.430i	0.199648	−	0.745095i
$423$	−264.040	−	70.7492i	−0.624207	−	0.167256i
$424$	46.8849	−	46.8849i	0.110578	−	0.110578i
$425$	24.9447	+	43.2055i	0.0586935	+	0.101660i
$426$	−522.623	−	301.736i	−1.22681	−	0.708302i
$427$	−57.3731	−	214.119i	−0.134363	−	0.501450i
$428$		−	150.597i		−	0.351863i
$429$	−372.112	−	162.305i	−0.867394	−	0.378333i
$430$	33.8171			0.0786444
$431$	−516.808	+	138.478i	−1.19909	+	0.321295i	−0.802473	−	0.596689i	$-0.796483\pi$
$431$	−516.808	+	138.478i	−1.19909	+	0.321295i	−0.396617	+	0.917984i	$0.629816\pi$
$432$	146.483	−	253.716i	0.339081	−	0.587305i
$433$	140.192	−	80.9400i	0.323769	−	0.186928i	−0.329302	−	0.944225i	$-0.606813\pi$
$433$	140.192	−	80.9400i	0.323769	−	0.186928i	0.653071	+	0.757296i	$0.273480\pi$
$434$	104.259	+	104.259i	0.240229	+	0.240229i
$435$	−10.9140	+	40.7315i	−0.0250896	+	0.0936357i
$436$	15.9459	+	4.27268i	0.0365731	+	0.00979974i
$437$	−57.1117	+	57.1117i	−0.130690	+	0.130690i
$438$	105.617	+	182.933i	0.241134	+	0.417656i
$439$	−142.255	−	82.1308i	−0.324043	−	0.187086i	0.329150	−	0.944277i	$-0.393238\pi$
$439$	−142.255	−	82.1308i	−0.324043	−	0.187086i	−0.653193	+	0.757191i	$0.726571\pi$
$440$	−1.87687	−	7.00457i	−0.00426561	−	0.0159195i
$441$		−	314.189i		−	0.712446i
$442$	29.7668	−	21.9737i	0.0673458	−	0.0497143i
$443$	309.912			0.699575			0.349788	−	0.936829i	$-0.386254\pi$
$443$	309.912			0.699575			0.349788	+	0.936829i	$0.386254\pi$
$444$	−379.945	+	101.806i	−0.855733	+	0.229293i
$445$	−35.7561	+	61.9313i	−0.0803507	+	0.139172i
$446$	322.321	−	186.092i	0.722692	−	0.417246i
$447$	−861.284	−	861.284i	−1.92681	−	1.92681i
$448$	16.4604	−	61.4312i	0.0367420	−	0.137123i
$449$	−131.440	−	35.2192i	−0.292739	−	0.0784392i	0.109461	−	0.993991i	$-0.465088\pi$
$449$	−131.440	−	35.2192i	−0.292739	−	0.0784392i	−0.402200	+	0.915552i	$0.631754\pi$
$450$	548.547	−	548.547i	1.21899	−	1.21899i
$451$	169.848	+	294.186i	0.376603	+	0.652296i
$452$	198.297	+	114.487i	0.438711	+	0.253290i
$453$	150.534	+	561.799i	0.332304	+	1.24018i
$454$			168.522i			0.371193i
$455$	17.2993	+	44.0644i	0.0380204	+	0.0968449i
$456$	−73.1104			−0.160330
$457$	219.352	−	58.7751i	0.479981	−	0.128611i	−0.0107126	−	0.999943i	$-0.503410\pi$
$457$	219.352	−	58.7751i	0.479981	−	0.128611i	0.490694	+	0.871332i	$0.336743\pi$
$458$	224.372	−	388.624i	0.489895	−	0.848523i
$459$	−127.649	+	73.6981i	−0.278102	+	0.160562i
$460$	−11.2930	−	11.2930i	−0.0245501	−	0.0245501i
$461$	−177.023	+	660.658i	−0.383998	+	1.43310i	0.455743	+	0.890111i	$0.349373\pi$
$461$	−177.023	+	660.658i	−0.383998	+	1.43310i	−0.839741	+	0.542987i	$0.817293\pi$
$462$	339.127	+	90.8689i	0.734042	+	0.196686i
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.230575	−	0.973055i	$-0.425939\pi$
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.973055	−	0.230575i	$-0.0740607\pi$
$464$	−33.0010	−	57.1595i	−0.0711229	−	0.123189i
$465$	29.0255	+	16.7579i	0.0624205	+	0.0360385i
$466$	84.4357	+	315.118i	0.181192	+	0.676219i
$467$		−	91.0355i		−	0.194937i	−0.995239	−	0.0974684i	$-0.968926\pi$
$467$		−	91.0355i		−	0.194937i	0.995239	−	0.0974684i	$-0.0310745\pi$
$468$	−449.838	−	358.657i	−0.961193	−	0.766362i
$469$	−272.126			−0.580227
$470$	−7.72977	+	2.07119i	−0.0164463	+	0.00440678i
$471$	354.583	−	614.157i	0.752831	−	1.30394i
$472$	−86.4397	+	49.9060i	−0.183135	+	0.105733i
$473$	−206.617	−	206.617i	−0.436822	−	0.436822i
$474$	−291.691	+	1088.61i	−0.615382	+	2.29664i
$475$	−110.939	−	29.7261i	−0.233556	−	0.0625812i
$476$	−22.6255	+	22.6255i	−0.0475326	+	0.0475326i
$477$	259.362	+	449.229i	0.543737	+	0.941780i
$478$	−319.594	−	184.518i	−0.668607	−	0.386021i
$479$	191.280	+	713.865i	0.399331	+	1.49032i	0.814276	+	0.580477i	$0.197134\pi$
$479$	191.280	+	713.865i	0.399331	+	1.49032i	−0.414945	+	0.909846i	$0.636199\pi$
$480$		−	14.4565i		−	0.0301178i
$481$	51.3569	+	455.380i	0.106771	+	0.946735i
$482$	−314.584			−0.652665
$483$	746.879	−	200.125i	1.54633	−	0.414338i
$484$	89.6706	−	155.314i	0.185270	−	0.320897i
$485$	44.6684	−	25.7893i	0.0920998	−	0.0531738i
$486$	509.567	+	509.567i	1.04849	+	1.04849i
$487$	155.484	−	580.273i	0.319268	−	1.19153i	−0.600681	−	0.799489i	$-0.705104\pi$
$487$	155.484	−	580.273i	0.319268	−	1.19153i	0.919949	−	0.392037i	$-0.128230\pi$
$488$	76.1808	+	20.4126i	0.156108	+	0.0418291i
$489$	−666.986	+	666.986i	−1.36398	+	1.36398i
$490$	−4.59895	−	7.96561i	−0.00938560	−	0.0162563i
$491$	−482.376	−	278.500i	−0.982436	−	0.567210i	−0.0794313	−	0.996840i	$-0.525310\pi$
$491$	−482.376	−	278.500i	−0.982436	−	0.567210i	−0.903005	+	0.429631i	$0.858644\pi$
$492$	175.272	+	654.125i	0.356245	+	1.32952i
$493$			33.2068i			0.0673565i
$494$	−12.6861	+	84.2265i	−0.0256804	+	0.170499i
$495$	56.7318			0.114610
$496$	−50.6715	+	13.5774i	−0.102160	+	0.0273738i
$497$	304.015	−	526.570i	0.611700	−	1.05950i
$498$	−886.292	+	511.701i	−1.77970	+	1.02751i
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	0.793898	−	0.608051i	$-0.208048\pi$
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	−0.608051	+	0.793898i	$0.708048\pi$
$500$	11.8056	−	44.0590i	0.0236111	−	0.0881179i
$501$	−898.535	−	240.762i	−1.79348	−	0.480562i
$502$	−251.968	+	251.968i	−0.501929	+	0.501929i
$503$	68.4278	+	118.520i	0.136039	+	0.235627i	0.925994	−	0.377538i	$-0.123229\pi$
$503$	68.4278	+	118.520i	0.136039	+	0.235627i	−0.789955	+	0.613165i	$0.789896\pi$
$504$	430.888	+	248.773i	0.854937	+	0.493598i
$505$	−11.5826	−	43.2267i	−0.0229358	−	0.0855974i
$506$			137.997i			0.272721i
$507$	−691.051	+	641.469i	−1.36302	+	1.26523i
$508$	193.547			0.380997
$509$	163.752	−	43.8773i	0.321713	−	0.0862029i	−0.0943482	−	0.995539i	$-0.530077\pi$
$509$	163.752	−	43.8773i	0.321713	−	0.0862029i	0.416062	+	0.909336i	$0.363410\pi$
$510$	−3.63666	+	6.29889i	−0.00713072	+	0.0123508i
$511$	−184.315	+	106.414i	−0.360694	+	0.208247i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	87.8243	−	327.765i	0.171197	−	0.638918i
$514$	−396.544	−	106.254i	−0.771486	−	0.206719i
$515$	−35.1237	+	35.1237i	−0.0682013	+	0.0682013i
$516$	−291.258	−	504.473i	−0.564453	−	0.977661i
$517$	59.8823	+	34.5730i	0.115826	+	0.0668724i
$518$	−102.575	−	382.815i	−0.198021	−	0.739024i
$519$		−	783.789i		−	1.51019i
$520$	−16.6546	−	2.50850i	−0.0320281	−	0.00482404i
$521$	161.073			0.309161			0.154580	−	0.987980i	$-0.450597\pi$
$521$	161.073			0.309161			0.154580	+	0.987980i	$0.450597\pi$
$522$	498.758	−	133.642i	0.955476	−	0.256019i
$523$	−67.7062	+	117.271i	−0.129457	+	0.224227i	−0.923466	−	0.383679i	$-0.874657\pi$
$523$	−67.7062	+	117.271i	−0.129457	+	0.224227i	0.794009	+	0.607906i	$0.207990\pi$
$524$	276.459	−	159.613i	0.527593	−	0.304606i
$525$	777.486	+	777.486i	1.48093	+	1.48093i
$526$	−39.4822	+	147.350i	−0.0750613	+	0.280133i
$527$	25.4937	+	6.83101i	0.0483751	+	0.0129621i
$528$	−88.3271	+	88.3271i	−0.167286	+	0.167286i
$529$	−112.541	−	194.926i	−0.212742	−	0.368481i
$530$	13.1512	+	7.59285i	0.0248136	+	0.0143261i
$531$	−202.101	−	754.250i	−0.380604	−	1.42043i
$532$		−	73.6625i		−	0.138463i
$533$	783.995	−	88.4177i	1.47091	−	0.165887i
$534$	1231.83			2.30680
$535$	33.3156	−	8.92689i	0.0622721	−	0.0166858i
$536$	48.4095	−	83.8477i	0.0903162	−	0.156432i
$537$	1526.84	−	881.524i	2.84329	−	1.64157i
$538$	−435.423	−	435.423i	−0.809337	−	0.809337i
$539$	−20.5698	+	76.7674i	−0.0381628	+	0.142426i
$540$	64.8108	+	17.3660i	0.120020	+	0.0321593i
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	−0.815288	−	0.579055i	$-0.803422\pi$
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	0.579055	+	0.815288i	$0.303422\pi$
$542$	−59.4776	−	103.018i	−0.109737	−	0.190071i
$543$	−404.213	−	233.373i	−0.744408	−	0.429784i
$544$	−2.94646	−	10.9963i	−0.00541628	−	0.0202138i
$545$			3.78087i			0.00693737i
$546$	508.345	−	637.581i	0.931035	−	1.16773i
$547$	−161.504			−0.295254			−0.147627	−	0.989043i	$-0.547163\pi$
$547$	−161.504			−0.295254			−0.147627	+	0.989043i	$0.547163\pi$
$548$	−244.448	+	65.4996i	−0.446073	+	0.119525i
$549$	−308.504	+	534.344i	−0.561938	+	0.973305i
$550$	−169.942	+	98.1163i	−0.308986	+	0.178393i
$551$	−54.0560	−	54.0560i	−0.0981053	−	0.0981053i
$552$	−71.2020	+	265.730i	−0.128989	+	0.481394i
$553$	−1096.83	−	293.894i	−1.98341	−	0.531454i
$554$	36.8115	−	36.8115i	0.0664467	−	0.0664467i
$555$	−45.0437	−	78.0180i	−0.0811598	−	0.140573i
$556$	−104.697	−	60.4469i	−0.188304	−	0.108717i
$557$	−154.013	−	574.784i	−0.276504	−	1.03193i	−0.954827	−	0.297163i	$-0.903959\pi$
$557$	−154.013	−	574.784i	−0.276504	−	1.03193i	0.678323	−	0.734764i	$-0.262707\pi$
$558$		−	410.401i		−	0.735486i
$559$	−631.715	+	248.006i	−1.13008	+	0.443659i
$560$	14.5657			0.0260102
$561$	60.7046	−	16.2658i	0.108208	−	0.0289942i
$562$	30.1080	−	52.1486i	0.0535730	−	0.0927912i
$563$	−538.929	+	311.151i	−0.957244	+	0.552665i	−0.895324	−	0.445416i	$-0.853056\pi$
$563$	−538.929	+	311.151i	−0.957244	+	0.552665i	−0.0619205	+	0.998081i	$0.519723\pi$
$564$	97.4718	+	97.4718i	0.172822	+	0.172822i
$565$	−13.5728	+	50.6543i	−0.0240226	+	0.0896537i
$566$	143.378	+	38.4179i	0.253317	+	0.0678762i
$567$	−1177.57	+	1177.57i	−2.07684	+	2.07684i
$568$	108.165	+	187.347i	0.190431	+	0.329836i
$569$	675.493	+	389.996i	1.18716	+	0.685406i	0.957660	−	0.287903i	$-0.0929580\pi$
$569$	675.493	+	389.996i	1.18716	+	0.685406i	0.229499	+	0.973309i	$0.426291\pi$
$570$	−4.33373	−	16.1737i	−0.00760304	−	0.0283749i
$571$			556.142i			0.973980i	0.873408	+	0.486990i	$0.161905\pi$
$571$			556.142i			0.973980i	−0.873408	+	0.486990i	$0.838095\pi$
$572$	86.4303	+	117.083i	0.151102	+	0.204691i
$573$	385.598			0.672945
$574$	−659.065	+	176.596i	−1.14820	+	0.307659i
$575$	−216.087	+	374.273i	−0.375803	+	0.650910i
$576$	−153.304	+	88.5103i	−0.266153	+	0.153664i
$577$	401.975	+	401.975i	0.696663	+	0.696663i	0.963689	−	0.267026i	$-0.0860409\pi$
$577$	401.975	+	401.975i	0.696663	+	0.696663i	−0.267026	+	0.963689i	$0.586041\pi$
$578$	104.299	−	389.249i	0.180448	−	0.673441i
$579$	1749.66	+	468.819i	3.02186	+	0.809705i
$580$	10.6888	−	10.6888i	0.0184290	−	0.0184290i
$581$	−515.565	−	892.985i	−0.887376	−	1.53698i
$582$	−769.434	−	444.233i	−1.32205	−	0.763287i
$583$	−33.9606	−	126.743i	−0.0582515	−	0.217398i
$584$		−	75.7216i		−	0.129660i
$585$	52.6785	−	120.775i	0.0900486	−	0.206452i
$586$	−177.741			−0.303313
$587$	647.776	−	173.571i	1.10354	−	0.295692i	0.339333	−	0.940666i	$-0.389799\pi$
$587$	647.776	−	173.571i	1.10354	−	0.295692i	0.764204	+	0.644974i	$0.223132\pi$
$588$	−79.2190	+	137.211i	−0.134726	+	0.233353i
$589$	−52.6201	+	30.3802i	−0.0893381	+	0.0515794i
$590$	−16.1642	−	16.1642i	−0.0273970	−	0.0273970i
$591$	462.285	−	1725.27i	0.782209	−	2.91924i
$592$	136.200	+	36.4948i	0.230068	+	0.0616466i
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	−0.845962	−	0.533243i	$-0.820973\pi$
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	0.533243	+	0.845962i	$0.320973\pi$
$594$	−289.880	−	502.087i	−0.488014	−	0.845264i
$595$	−6.34646	−	3.66413i	−0.0106663	−	0.00615820i
$596$	113.009	+	421.757i	0.189613	+	0.707646i
$597$			964.199i			1.61507i
$598$	293.778	+	128.137i	0.491267	+	0.214277i
$599$	−171.466			−0.286254			−0.143127	−	0.989704i	$-0.545716\pi$
$599$	−171.466			−0.286254			−0.143127	+	0.989704i	$0.545716\pi$
$600$	−377.869	+	101.250i	−0.629782	+	0.168749i
$601$	−53.8259	+	93.2293i	−0.0895606	+	0.155124i	−0.907325	−	0.420429i	$-0.861880\pi$
$601$	−53.8259	+	93.2293i	−0.0895606	+	0.155124i	0.817765	+	0.575552i	$0.195213\pi$
$602$	508.282	−	293.457i	0.844323	−	0.487470i
$603$	535.593	+	535.593i	0.888213	+	0.888213i
$604$	53.9624	−	201.390i	0.0893417	−	0.333428i
$605$	39.6744	+	10.6307i	0.0655775	+	0.0175714i
$606$	−545.085	+	545.085i	−0.899480	+	0.899480i
$607$	−216.797	−	375.504i	−0.357162	−	0.618623i	0.630323	−	0.776333i	$-0.282922\pi$
$607$	−216.797	−	375.504i	−0.357162	−	0.618623i	−0.987486	+	0.157710i	$0.949589\pi$
$608$	22.6969	+	13.1041i	0.0373305	+	0.0215528i
$609$	189.418	+	706.918i	0.311031	+	1.16078i
$610$			18.0629i			0.0296114i
$611$	129.205	−	95.3786i	0.211465	−	0.156102i
$612$	89.0621			0.145526
$613$	620.451	−	166.249i	1.01216	−	0.271206i	0.285626	−	0.958341i	$-0.407799\pi$
$613$	620.451	−	166.249i	1.01216	−	0.271206i	0.726530	+	0.687135i	$0.241132\pi$
$614$	159.407	−	276.102i	0.259621	−	0.449677i
$615$	−134.318	+	77.5486i	−0.218403	+	0.126095i
$616$	−88.9941	−	88.9941i	−0.144471	−	0.144471i
$617$	−107.181	+	400.004i	−0.173713	+	0.648304i	0.823055	+	0.567962i	$0.192268\pi$
$617$	−107.181	+	400.004i	−0.173713	+	0.648304i	−0.996767	+	0.0803421i	$0.974399\pi$
$618$	826.475	+	221.453i	1.33734	+	0.358339i
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.128120	−	0.991759i	$-0.459106\pi$
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.991759	−	0.128120i	$-0.0408943\pi$
$620$	−6.00726	−	10.4049i	−0.00968913	−	0.0167821i
$621$	−1105.77	−	638.419i	−1.78063	−	1.02805i
$622$	169.015	+	630.771i	0.271728	+	1.01410i
$623$			1241.13i			1.99219i
$624$	106.020	+	270.053i	0.169905	+	0.432777i
$625$	−609.308			−0.974893
$626$	−11.1571	+	2.98955i	−0.0178229	+	0.00477563i
$627$	−72.3403	+	125.297i	−0.115375	+	0.199836i
$628$	−220.159	+	127.109i	−0.350572	+	0.202403i
$629$	−50.1636	−	50.1636i	−0.0797513	−	0.0797513i
$630$	−29.4928	+	110.069i	−0.0468140	+	0.174712i
$631$	507.808	+	136.067i	0.804767	+	0.215637i	0.637676	−	0.770305i	$-0.279896\pi$
$631$	507.808	+	136.067i	0.804767	+	0.215637i	0.167091	+	0.985941i	$0.446563\pi$
$632$	285.673	−	285.673i	0.452014	−	0.452014i
$633$	−642.108	−	1112.16i	−1.01439	−	1.75697i
$634$	158.678	+	91.6127i	0.250281	+	0.144500i
$635$	11.4728	+	42.8170i	0.0180674	+	0.0674283i
$636$		−	261.581i		−	0.411291i
$637$	144.328	+	115.073i	0.226574	+	0.180648i
$638$	−130.614			−0.204724
$639$	−1634.74	+	438.026i	−2.55827	+	0.685487i
$640$	−2.59114	+	4.48799i	−0.00404866	+	0.00701249i
$641$	−936.399	+	540.630i	−1.46084	+	0.843416i	−0.999050	−	0.0435728i	$-0.986126\pi$
$641$	−936.399	+	540.630i	−1.46084	+	0.843416i	−0.461790	+	0.886989i	$0.652793\pi$
$642$	−420.107	−	420.107i	−0.654372	−	0.654372i
$643$	−102.193	+	381.388i	−0.158931	+	0.593138i	0.839806	+	0.542887i	$0.182669\pi$
$643$	−102.193	+	381.388i	−0.158931	+	0.593138i	−0.998737	+	0.0502511i	$0.983998\pi$
$644$	−267.736	−	71.7397i	−0.415740	−	0.111397i
$645$	94.3363	−	94.3363i	0.146258	−	0.146258i
$646$	−6.59288	−	11.4192i	−0.0102057	−	0.0176768i
$647$	275.454	+	159.033i	0.425740	+	0.245801i	0.697530	−	0.716555i	$-0.254282\pi$
$647$	275.454	+	159.033i	0.425740	+	0.245801i	−0.271790	+	0.962357i	$0.587616\pi$
$648$	−153.351	−	572.314i	−0.236653	−	0.883200i
$649$			197.521i			0.304347i
$650$	51.0763	+	452.891i	0.0785789	+	0.696755i
$651$	581.685			0.893525
$652$	326.613	−	87.5156i	0.500939	−	0.134226i
$653$	201.115	−	348.341i	0.307986	−	0.533447i	−0.669936	−	0.742419i	$-0.733678\pi$
$653$	201.115	−	348.341i	0.307986	−	0.533447i	0.977922	+	0.208972i	$0.0670117\pi$
$654$	56.4018	−	32.5636i	0.0862413	−	0.0497914i
$655$	51.6977	+	51.6977i	0.0789278	+	0.0789278i
$656$	62.8305	−	234.487i	0.0957783	−	0.357449i
$657$	572.206	+	153.322i	0.870937	+	0.233367i
$658$	−98.2079	+	98.2079i	−0.149252	+	0.149252i
$659$	−292.874	−	507.272i	−0.444421	−	0.769760i	0.553591	−	0.832789i	$-0.313257\pi$
$659$	−292.874	−	507.272i	−0.444421	−	0.769760i	−0.998012	+	0.0630290i	$0.979924\pi$
$660$	−24.7757	−	14.3043i	−0.0375390	−	0.0216731i
$661$	209.306	+	781.140i	0.316650	+	1.18176i	0.922443	+	0.386133i	$0.126189\pi$
$661$	209.306	+	781.140i	0.316650	+	1.18176i	−0.605793	+	0.795623i	$0.707144\pi$
$662$			211.479i			0.319454i
$663$	21.7398	−	144.336i	0.0327900	−	0.217701i
$664$	366.863			0.552504
$665$	16.2958	−	4.36646i	0.0245050	−	0.00656610i
$666$	−551.561	+	955.332i	−0.828170	+	1.43443i
$667$	−249.119	+	143.829i	−0.373492	+	0.215636i
$668$	235.794	+	235.794i	0.352986	+	0.352986i
$669$	380.024	−	1418.27i	0.568048	−	2.11998i
$670$	21.4186	+	5.73910i	0.0319681	+	0.00856582i
$671$	110.362	−	110.362i	0.164473	−	0.164473i
$672$	−125.451	−	217.287i	−0.186682	−	0.323343i
$673$	−373.474	−	215.625i	−0.554939	−	0.320394i	0.196173	−	0.980569i	$-0.437149\pi$
$673$	−373.474	−	215.625i	−0.554939	−	0.320394i	−0.751112	+	0.660175i	$0.770482\pi$
$674$	−22.5959	−	84.3291i	−0.0335251	−	0.125117i
$675$		−	1815.67i		−	2.68988i
$676$	329.510	−	75.2806i	0.487441	−	0.111362i
$677$	6.72056			0.00992697			0.00496348	−	0.999988i	$-0.498420\pi$
$677$	6.72056			0.00992697			0.00496348	+	0.999988i	$0.498420\pi$
$678$	872.544	−	233.798i	1.28694	−	0.344834i
$679$	447.588	−	775.244i	0.659186	−	1.14174i
$680$	2.25799	−	1.30365i	0.00332057	−	0.00191713i
$681$	470.109	+	470.109i	0.690321	+	0.690321i
$682$	−26.8687	+	100.276i	−0.0393970	+	0.147032i
$683$	118.413	+	31.7287i	0.173372	+	0.0464549i	0.344461	−	0.938801i	$-0.388062\pi$
$683$	118.413	+	31.7287i	0.173372	+	0.0464549i	−0.171089	+	0.985256i	$0.554728\pi$
$684$	−144.981	+	144.981i	−0.211960	+	0.211960i
$685$	−28.9801	−	50.1949i	−0.0423067	−	0.0732773i
$686$	338.839	+	195.629i	0.493934	+	0.285173i
$687$	−458.197	−	1710.02i	−0.666954	−	2.48911i
$688$			208.816i			0.303512i
$689$	−301.353	−	45.3896i	−0.437377	−	0.0658775i
$690$	−63.0061			−0.0913133
$691$	90.8900	−	24.3539i	0.131534	−	0.0352444i	−0.192451	−	0.981307i	$-0.561644\pi$
$691$	90.8900	−	24.3539i	0.131534	−	0.0352444i	0.323985	+	0.946062i	$0.394977\pi$
$692$	−140.484	+	243.325i	−0.203011	+	0.351626i
$693$	852.699	−	492.306i	1.23045	−	0.710398i
$694$	220.862	+	220.862i	0.318245	+	0.318245i
$695$	7.16616	−	26.7445i	0.0103110	−	0.0384813i
$696$	−251.512	−	67.3925i	−0.361368	−	0.0968283i
$697$	−86.3632	+	86.3632i	−0.123907	+	0.123907i
$698$	205.786	+	356.432i	0.294823	+	0.510648i
$699$	1114.60	+	643.513i	1.59456	+	0.920620i
$700$	−102.014	−	380.722i	−0.145735	−	0.543889i
$701$		−	716.506i		−	1.02212i	−0.859545	−	0.511060i	$-0.829253\pi$
$701$		−	716.506i		−	1.02212i	0.859545	−	0.511060i	$-0.170747\pi$
$702$	−1338.05	+	150.903i	−1.90605	+	0.214961i
$703$	163.319			0.232317
$704$	43.2524	−	11.5894i	0.0614380	−	0.0164623i
$705$	−15.7852	+	27.3408i	−0.0223904	+	0.0387813i
$706$	−24.1433	+	13.9392i	−0.0341973	+	0.0197438i
$707$	−549.201	−	549.201i	−0.776805	−	0.776805i
$708$	−101.915	+	380.351i	−0.143947	+	0.537219i
$709$	−957.045	−	256.439i	−1.34985	−	0.361692i	−0.489772	−	0.871851i	$-0.662920\pi$
$709$	−957.045	−	256.439i	−1.34985	−	0.361692i	−0.860080	+	0.510159i	$0.829587\pi$
$710$	−35.0338	+	35.0338i	−0.0493433	+	0.0493433i
$711$	1580.31	+	2737.18i	2.22266	+	3.84977i
$712$	−382.418	−	220.789i	−0.537104	−	0.310097i
$713$	59.1745	+	220.842i	0.0829937	+	0.309737i
$714$			126.233i			0.176796i
$715$	−20.7783	+	26.0607i	−0.0290605	+	0.0364485i
$716$	−632.006			−0.882691
$717$	−1406.27	+	376.810i	−1.96133	+	0.525537i
$718$	275.618	−	477.384i	0.383869	−	0.664881i
$719$	150.591	−	86.9435i	0.209445	−	0.120923i	−0.391609	−	0.920132i	$-0.628081\pi$
$719$	150.591	−	86.9435i	0.209445	−	0.120923i	0.601053	+	0.799209i	$0.294748\pi$
$720$	−28.6679	−	28.6679i	−0.0398165	−	0.0398165i
$721$	−223.126	+	832.716i	−0.309467	+	1.15495i
$722$	−463.814	−	124.279i	−0.642402	−	0.172131i
$723$	−877.566	+	877.566i	−1.21378	+	1.21378i
$724$	83.6580	+	144.900i	0.115550	+	0.200138i
$725$	−354.249	−	204.526i	−0.488619	−	0.282104i
$726$	−183.119	−	683.410i	−0.252230	−	0.941336i
$727$		−	729.011i		−	1.00277i	−0.865225	−	0.501383i	$-0.832825\pi$
$727$		−	729.011i		−	1.00277i	0.865225	−	0.501383i	$-0.167175\pi$
$728$	−272.092	+	106.821i	−0.373753	+	0.146732i
$729$	957.649			1.31365
$730$	16.7514	−	4.48851i	0.0229471	−	0.00614865i
$731$	52.5295	−	90.9838i	0.0718598	−	0.124465i
$732$	269.457	−	155.571i	0.368111	−	0.212529i
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.999157	−	0.0410404i	$-0.986933\pi$
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.0410404	−	0.999157i	$-0.513067\pi$
$734$	171.569	−	640.304i	0.233745	−	0.872348i
$735$	−35.0501	−	9.39166i	−0.0476873	−	0.0127778i
$736$	69.7330	−	69.7330i	0.0947460	−	0.0947460i
$737$	−95.7992	−	165.929i	−0.129985	−	0.225141i
$738$	1644.73	+	949.584i	2.22863	+	1.28670i
$739$	158.814	+	592.703i	0.214904	+	0.802033i	0.986200	+	0.165557i	$0.0529421\pi$
$739$	158.814	+	592.703i	0.214904	+	0.802033i	−0.771296	+	0.636476i	$0.780391\pi$
$740$			32.2940i			0.0436405i
$741$	199.569	+	270.348i	0.269324	+	0.364842i
$742$	263.556			0.355197
$743$	160.852	−	43.1002i	0.216490	−	0.0580084i	−0.148944	−	0.988846i	$-0.547587\pi$
$743$	160.852	−	43.1002i	0.216490	−	0.0580084i	0.365434	+	0.930837i	$0.380921\pi$
$744$	−103.478	+	179.229i	−0.139083	+	0.240899i
$745$	−86.6036	+	50.0006i	−0.116246	+	0.0671149i
$746$	260.814	+	260.814i	0.349617	+	0.349617i
$747$	−742.829	+	2772.27i	−0.994416	+	3.71121i
$748$	−21.7610	−	5.83084i	−0.0290923	−	0.00779525i
$749$	423.279	−	423.279i	0.565126	−	0.565126i
$750$	−89.9742	−	155.840i	−0.119966	−	0.207787i
$751$	−116.272	−	67.1297i	−0.154823	−	0.0893871i	0.420587	−	0.907252i	$-0.361824\pi$
$751$	−116.272	−	67.1297i	−0.154823	−	0.0893871i	−0.575410	+	0.817865i	$0.695158\pi$
$752$	−12.7893	−	47.7304i	−0.0170071	−	0.0634713i
$753$			1405.78i			1.86691i
$754$	−121.282	+	278.059i	−0.160851	+	0.368779i
$755$	47.7509			0.0632462
$756$	1124.83	−	301.397i	1.48787	−	0.398673i
$757$	598.217	−	1036.14i	0.790247	−	1.36875i	−0.135567	−	0.990768i	$-0.543285\pi$
$757$	598.217	−	1036.14i	0.790247	−	1.36875i	0.925814	−	0.377980i	$-0.123381\pi$
$758$	−262.331	+	151.457i	−0.346083	+	0.199811i
$759$	384.957	+	384.957i	0.507190	+	0.507190i
$760$	−1.55353	+	5.79785i	−0.00204412	+	0.00762875i
$761$	−33.7907	−	9.05420i	−0.0444031	−	0.0118978i	0.236549	−	0.971620i	$-0.423984\pi$
$761$	−33.7907	−	9.05420i	−0.0444031	−	0.0118978i	−0.280952	+	0.959722i	$0.590650\pi$
$762$	539.918	−	539.918i	0.708554	−	0.708554i
$763$	32.8095	+	56.8277i	0.0430007	+	0.0744793i
$764$	−119.708	−	69.1133i	−0.156686

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.78960 + 4.83174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(2.04213 - 7.62134i) q^{6} +(7.67890 + 2.05755i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 - 19.1630i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.78960 + 4.83174i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(2.04213 - 7.62134i) q^{6} +(7.67890 + 2.05755i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 - 19.1630i) q^{9} +(-0.560999 - 0.323893i) q^{10} +(1.44868 + 5.40655i) q^{11} +11.1584i q^{12} +(12.8550 + 1.93621i) q^{13} -11.2427 q^{14} +(-2.46850 + 0.661433i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.74285 + 1.00623i) q^{17} +(22.1276 + 22.1276i) q^{18} +(1.19911 - 4.47512i) q^{19} +(0.884892 + 0.237106i) q^{20} +(-31.3626 + 31.3626i) q^{21} +(-3.95787 - 6.85523i) q^{22} +(-15.0976 - 8.71663i) q^{23} +(-4.08426 - 15.2427i) q^{24} -24.7902i q^{25} +(-18.2690 + 2.06034i) q^{26} +73.2415 q^{27} +(15.3578 - 4.11511i) q^{28} +(8.25026 - 14.2899i) q^{29} +(3.12993 - 1.80707i) q^{30} +(-9.27353 - 9.27353i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-30.1643 - 8.08249i) q^{33} +(2.01247 - 2.01247i) q^{34} +(1.82071 + 3.15357i) q^{35} +(-38.3261 - 22.1276i) q^{36} +(9.12370 + 34.0501i) q^{37} +6.55204i q^{38} +(-45.2156 + 56.7107i) q^{39} -1.29557 q^{40} +(58.6217 - 15.7076i) q^{41} +(31.3626 - 54.3217i) q^{42} +(-45.2101 + 26.1020i) q^{43} +(7.91574 + 7.91574i) q^{44} +(2.62329 - 9.79026i) q^{45} +(23.8143 + 6.38102i) q^{46} +(8.73527 - 8.73527i) q^{47} +(11.1584 + 19.3269i) q^{48} +(12.2967 + 7.09948i) q^{49} +(9.07384 + 33.8640i) q^{50} -11.2280i q^{51} +(24.2017 - 9.50138i) q^{52} -23.4425 q^{53} +(-100.050 + 26.8082i) q^{54} +(-1.28193 + 2.22036i) q^{55} +(-19.4729 + 11.2427i) q^{56} +(18.2776 + 18.2776i) q^{57} +(-6.03961 + 22.5401i) q^{58} +(34.0864 + 9.13343i) q^{59} +(-3.61413 + 3.61413i) q^{60} +(-13.9421 - 24.1483i) q^{61} +(16.0622 + 9.27353i) q^{62} +(-45.5287 - 169.915i) q^{63} -8.00000i q^{64} +(3.53652 + 4.79077i) q^{65} +44.1635 q^{66} +(-33.0643 + 8.85955i) q^{67} +(-2.01247 + 3.48570i) q^{68} +(84.2329 - 48.6319i) q^{69} +(-3.64143 - 3.64143i) q^{70} +(19.7955 - 73.8778i) q^{71} +(60.4537 + 16.1985i) q^{72} +(-18.9304 + 18.9304i) q^{73} +(-24.9264 - 43.1738i) q^{74} +(119.780 + 69.1548i) q^{75} +(-2.39821 - 8.95025i) q^{76} +44.4971i q^{77} +(41.0082 - 94.0184i) q^{78} -142.837 q^{79} +(1.76978 - 0.474212i) q^{80} +(-104.741 + 181.416i) q^{81} +(-74.3293 + 42.9141i) q^{82} +(-91.7157 - 91.7157i) q^{83} +(-22.9590 + 85.6843i) q^{84} +(-0.890409 - 0.238584i) q^{85} +(52.2041 - 52.2041i) q^{86} +(46.0299 + 79.7262i) q^{87} +(-13.7105 - 7.91574i) q^{88} +(40.4072 + 150.802i) q^{89} +14.3339i q^{90} +(94.7284 + 41.3178i) q^{91} -34.8665 q^{92} +(70.6767 - 18.9378i) q^{93} +(-8.73527 + 15.1299i) q^{94} +(1.83784 - 1.06108i) q^{95} +(-22.3168 - 22.3168i) q^{96} +(29.1440 - 108.767i) q^{97} +(-19.3961 - 5.19718i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9	\( 8 q - 4 q^{2} + 6 q^{5} + 6 q^{6} - 2 q^{7} - 16 q^{8} - 42 q^{9} - 18 q^{10} - 18 q^{11} + 36 q^{13} + 20 q^{14} + 66 q^{15} + 16 q^{16} - 42 q^{17} + 84 q^{18} + 46 q^{19} + 24 q^{20} - 102 q^{21} - 42 q^{22} - 36 q^{23} - 12 q^{24} + 40 q^{26} + 72 q^{27} - 4 q^{28} - 6 q^{29} - 192 q^{30} + 32 q^{31} + 16 q^{32} + 42 q^{33} - 60 q^{34} - 78 q^{35} - 48 q^{36} - 106 q^{37} + 12 q^{39} - 24 q^{40} + 132 q^{41} + 102 q^{42} - 108 q^{43} + 84 q^{44} + 240 q^{45} + 90 q^{46} + 60 q^{47} + 258 q^{49} + 194 q^{50} + 32 q^{52} - 132 q^{53} - 270 q^{54} - 162 q^{55} - 12 q^{56} - 294 q^{57} - 24 q^{58} + 18 q^{59} - 120 q^{60} + 36 q^{61} - 12 q^{62} - 72 q^{63} - 300 q^{65} + 108 q^{66} - 74 q^{67} + 60 q^{68} + 258 q^{69} + 156 q^{70} - 174 q^{71} + 132 q^{72} + 166 q^{73} - 32 q^{74} + 6 q^{75} - 92 q^{76} + 126 q^{78} - 96 q^{79} + 48 q^{80} - 12 q^{81} - 252 q^{82} - 240 q^{83} - 132 q^{84} - 24 q^{85} + 132 q^{86} + 360 q^{87} - 12 q^{88} + 294 q^{89} + 298 q^{91} - 216 q^{92} + 270 q^{93} - 60 q^{94} + 714 q^{95} - 58 q^{97} - 250 q^{98} + 252 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 + 6 * q^6 - 2 * q^7 - 16 * q^8 - 42 * q^9 - 18 * q^10 - 18 * q^11 + 36 * q^13 + 20 * q^14 + 66 * q^15 + 16 * q^16 - 42 * q^17 + 84 * q^18 + 46 * q^19 + 24 * q^20 - 102 * q^21 - 42 * q^22 - 36 * q^23 - 12 * q^24 + 40 * q^26 + 72 * q^27 - 4 * q^28 - 6 * q^29 - 192 * q^30 + 32 * q^31 + 16 * q^32 + 42 * q^33 - 60 * q^34 - 78 * q^35 - 48 * q^36 - 106 * q^37 + 12 * q^39 - 24 * q^40 + 132 * q^41 + 102 * q^42 - 108 * q^43 + 84 * q^44 + 240 * q^45 + 90 * q^46 + 60 * q^47 + 258 * q^49 + 194 * q^50 + 32 * q^52 - 132 * q^53 - 270 * q^54 - 162 * q^55 - 12 * q^56 - 294 * q^57 - 24 * q^58 + 18 * q^59 - 120 * q^60 + 36 * q^61 - 12 * q^62 - 72 * q^63 - 300 * q^65 + 108 * q^66 - 74 * q^67 + 60 * q^68 + 258 * q^69 + 156 * q^70 - 174 * q^71 + 132 * q^72 + 166 * q^73 - 32 * q^74 + 6 * q^75 - 92 * q^76 + 126 * q^78 - 96 * q^79 + 48 * q^80 - 12 * q^81 - 252 * q^82 - 240 * q^83 - 132 * q^84 - 24 * q^85 + 132 * q^86 + 360 * q^87 - 12 * q^88 + 294 * q^89 + 298 * q^91 - 216 * q^92 + 270 * q^93 - 60 * q^94 + 714 * q^95 - 58 * q^97 - 250 * q^98 + 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more