LMFDB - Embedded newform 26.3.f.b.15.1

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			15.1
Root			$4.71318 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.15
Dual form			26.3.f.b.7.1

$q$-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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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	−0.783539	−	0.621343i	$-0.786587\pi$
$3$	−2.78960	−	4.83174i	−0.929868	−	1.61058i	−0.146330	−	0.989236i	$-0.546746\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	0.323893	−	0.323893i	0.0647786	−	0.0647786i	−0.673975	−	0.738754i	$-0.735415\pi$
$5$	0.323893	−	0.323893i	0.0647786	−	0.0647786i	0.738754	+	0.673975i	$0.235415\pi$
$6$	2.04213	+	7.62134i	0.340355	+	1.27022i
$7$	7.67890	−	2.05755i	1.09699	−	0.293936i	0.335449	−	0.942058i	$-0.391112\pi$
$7$	7.67890	−	2.05755i	1.09699	−	0.293936i	0.761536	+	0.648122i	$0.224445\pi$
$8$	−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	−0.868291	−	0.496054i	$-0.834782\pi$
$11$	1.44868	−	5.40655i	0.131698	−	0.491504i	0.999990	+	0.00455003i	$0.00144833\pi$
$12$		−	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	0.447863	−	0.894102i	$-0.352185\pi$
$17$	−1.74285	−	1.00623i	−0.102520	−	0.0591902i	−0.550384	+	0.834912i	$0.685519\pi$
$18$	22.1276	−	22.1276i	1.22931	−	1.22931i
$19$	1.19911	+	4.47512i	0.0631108	+	0.235533i	0.990275	−	0.139122i	$-0.0444279\pi$
$19$	1.19911	+	4.47512i	0.0631108	+	0.235533i	−0.927164	+	0.374655i	$0.877761\pi$
$20$	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	−0.790911	−	0.611931i	$-0.790393\pi$
$23$	−15.0976	+	8.71663i	−0.656419	+	0.378984i	0.134492	+	0.990915i	$0.457060\pi$
$24$	−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	0.972486	−	0.232962i	$-0.0748418\pi$
$29$	8.25026	+	14.2899i	0.284492	+	0.492754i	−0.687994	+	0.725716i	$0.741508\pi$
$30$	3.12993	+	1.80707i	0.104331	+	0.0602356i
$31$	−9.27353	+	9.27353i	−0.299146	+	0.299146i	−0.840679	−	0.541533i	$-0.817844\pi$
$31$	−9.27353	+	9.27353i	−0.299146	+	0.299146i	0.541533	+	0.840679i	$0.317844\pi$
$32$	−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	−0.725993	−	0.687702i	$-0.758620\pi$
$37$	9.12370	−	34.0501i	0.246586	−	0.920273i	0.972579	−	0.232571i	$-0.0747138\pi$
$38$		−	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	0.888949	−	0.458007i	$-0.151436\pi$
$41$	58.6217	+	15.7076i	1.42980	+	0.383113i	0.540849	+	0.841120i	$0.318103\pi$
$42$	31.3626	+	54.3217i	0.746730	+	1.29337i
$43$	−45.2101	−	26.1020i	−1.05140	−	0.607024i	−0.128357	−	0.991728i	$-0.540970\pi$
$43$	−45.2101	−	26.1020i	−1.05140	−	0.607024i	−0.923040	+	0.384704i	$0.874304\pi$
$44$	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	0.793902	−	0.608045i	$-0.208046\pi$
$47$	8.73527	+	8.73527i	0.185857	+	0.185857i	−0.608045	+	0.793902i	$0.708046\pi$
$48$	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	0.0418940	−	0.999122i	$-0.486661\pi$
$59$	34.0864	−	9.13343i	0.577736	−	0.154804i	0.535842	+	0.844318i	$0.319994\pi$
$60$	−3.61413	−	3.61413i	−0.0602356	−	0.0602356i
$61$	−13.9421	+	24.1483i	−0.228558	+	0.395875i	−0.957381	−	0.288828i	$-0.906734\pi$
$61$	−13.9421	+	24.1483i	−0.228558	+	0.395875i	0.728823	+	0.684702i	$0.240068\pi$
$62$	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	0.00348324	−	0.999994i	$-0.498891\pi$
$67$	−33.0643	−	8.85955i	−0.493497	−	0.132232i	−0.496980	+	0.867762i	$0.665558\pi$
$68$	−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	0.953245	+	0.302198i	$0.0977205\pi$
$71$	19.7955	+	73.8778i	0.278810	+	1.04053i	−0.674435	+	0.738334i	$0.735613\pi$
$72$	60.4537	−	16.1985i	0.839634	−	0.224979i
$73$	−18.9304	−	18.9304i	−0.259320	−	0.259320i	0.565457	−	0.824778i	$-0.308700\pi$
$73$	−18.9304	−	18.9304i	−0.259320	−	0.259320i	−0.824778	+	0.565457i	$0.808700\pi$
$74$	−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	−0.111212	+	0.993797i	$0.535473\pi$
$83$	−91.7157	+	91.7157i	−1.10501	+	1.10501i	−0.993797	+	0.111212i	$0.964527\pi$
$84$	−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	−0.236956	−	0.971520i	$-0.576150\pi$
$89$	40.4072	−	150.802i	0.454014	−	1.69440i	0.690970	−	0.722883i	$-0.257183\pi$
$90$		−	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	0.936789	+	0.349896i	$0.113783\pi$
$97$	29.1440	+	108.767i	0.300454	+	1.12131i	−0.636335	+	0.771413i	$0.719550\pi$
$98$	−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	−0.856490	−	0.516164i	$-0.827360\pi$
$101$	−84.6101	+	48.8497i	−0.837724	+	0.483660i	0.0187659	+	0.999824i	$0.494026\pi$
$102$	4.10973	−	15.3377i	0.0402914	−	0.150370i
$103$		−	108.442i		−	1.05284i	−0.850226	−	0.526418i	$-0.823535\pi$
$103$		−	108.442i		−	1.05284i	0.850226	−	0.526418i	$-0.176465\pi$
$104$	−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	0.986576	−	0.163304i	$-0.0522151\pi$
$107$	37.6493	+	65.2105i	0.351863	+	0.609444i	−0.634713	+	0.772748i	$0.718882\pi$
$108$	126.858	+	73.2415i	1.17461	+	0.678162i
$109$	5.83660	−	5.83660i	0.0535468	−	0.0535468i	−0.679826	−	0.733373i	$-0.737945\pi$
$109$	5.83660	−	5.83660i	0.0535468	−	0.0535468i	0.733373	+	0.679826i	$0.237945\pi$
$110$	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	−0.493391	−	0.869807i	$-0.664243\pi$
$113$	57.2435	−	99.1486i	0.506580	−	0.877422i	0.999971	−	0.00761416i	$-0.00242369\pi$
$114$	−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	−0.132335	−	0.991205i	$-0.542247\pi$
$127$	83.8081	−	48.3866i	0.659906	−	0.380997i	0.792241	+	0.610208i	$0.208914\pi$
$128$	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	−0.675640	−	0.737232i	$-0.736133\pi$
$137$	−122.224	+	32.7498i	−0.892146	+	0.239050i	−0.216506	+	0.976281i	$0.569466\pi$
$138$	−97.2638	−	97.2638i	−0.704810	−	0.704810i
$139$	−30.2234	+	52.3485i	−0.217435	+	0.376608i	−0.954023	−	0.299733i	$-0.903102\pi$
$139$	−30.2234	+	52.3485i	−0.217435	+	0.376608i	0.736588	+	0.676341i	$0.236436\pi$
$140$	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	−0.847070	−	0.531481i	$-0.821636\pi$
$149$	−56.5047	−	210.878i	−0.379226	−	1.41529i	0.467844	−	0.883811i	$-0.345031\pi$
$150$	−188.934	+	50.6248i	−1.25956	+	0.337499i
$151$	73.7140	+	73.7140i	0.488172	+	0.488172i	0.907729	−	0.419557i	$-0.137815\pi$
$151$	73.7140	+	73.7140i	0.488172	+	0.488172i	−0.419557	+	0.907729i	$0.637815\pi$
$152$	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	0.279646	−	0.960103i	$-0.409783\pi$
$163$	163.306	−	43.7578i	1.00188	−	0.268453i	0.722232	+	0.691650i	$0.243116\pi$
$164$	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	−0.707762	−	0.706451i	$-0.750295\pi$
$167$	43.1534	−	161.051i	0.258403	−	0.964375i	0.966165	−	0.257924i	$-0.0830383\pi$
$168$			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	0.105305	−	0.994440i	$-0.466418\pi$
$173$	−121.663	−	70.2419i	−0.703252	−	0.406023i	−0.808557	+	0.588417i	$0.799751\pi$
$174$	−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	−0.529455	+	0.848338i	$0.677604\pi$
$179$	−273.667	+	158.002i	−1.52886	+	0.882691i	−0.999410	+	0.0343526i	$0.989063\pi$
$180$	−5.24659	+	19.5805i	−0.0291477	+	0.108781i
$181$		−	83.6580i		−	0.462199i	−0.972930	−	0.231099i	$-0.925768\pi$
$181$		−	83.6580i		−	0.462199i	0.972930	−	0.231099i	$-0.0742323\pi$
$182$	−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	−0.942196	−	0.335063i	$-0.891242\pi$
$191$	−34.5567	+	59.8539i	−0.180925	+	0.313371i	0.761271	+	0.648434i	$0.224576\pi$
$192$	38.6539	−	22.3168i	0.201322	−	0.116234i
$193$	−84.0297	+	313.603i	−0.435387	+	1.62489i	0.304752	+	0.952432i	$0.401426\pi$
$193$	−84.0297	+	313.603i	−0.435387	+	1.62489i	−0.740139	+	0.672454i	$0.765240\pi$
$194$		−	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	−0.633987	−	0.773344i	$-0.718583\pi$
$197$	−309.232	−	82.8586i	−1.56971	−	0.420602i	−0.935721	+	0.352742i	$0.885249\pi$
$198$	−87.5780	−	151.690i	−0.442313	−	0.766109i
$199$	149.667	+	86.4100i	0.752093	+	0.434221i	0.826450	−	0.563010i	$-0.190357\pi$
$199$	149.667	+	86.4100i	0.752093	+	0.434221i	−0.0743564	+	0.997232i	$0.523690\pi$
$200$	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	−0.998579	−	0.0532988i	$-0.983026\pi$
$211$	−115.089	−	199.341i	−0.545447	−	0.944743i	0.453131	−	0.891444i	$-0.350307\pi$
$212$	−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	−0.361012	−	0.932561i	$-0.617569\pi$
$223$	−254.206	−	68.1143i	−1.13994	−	0.305445i	−0.778926	+	0.627116i	$0.784235\pi$
$224$	−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	0.999993	+	0.00378487i	$0.00120476\pi$
$227$	30.8416	+	115.102i	0.135866	+	0.507059i	−0.864127	+	0.503274i	$0.832129\pi$
$228$	49.9353	−	13.3801i	0.219015	−	0.0586848i
$229$	−224.372	−	224.372i	−0.979791	−	0.979791i	0.0200093	−	0.999800i	$-0.493630\pi$
$229$	−224.372	−	224.372i	−0.979791	−	0.979791i	−0.999800	+	0.0200093i	$0.993630\pi$
$230$	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	$0.164842\pi$
$233$			230.683i			0.990054i	−0.868878	+	0.495027i	$0.835158\pi$
$234$	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	−0.206422	−	0.978463i	$-0.566182\pi$
$239$	184.518	−	184.518i	0.772041	−	0.772041i	0.978463	+	0.206422i	$0.0661820\pi$
$240$	−2.64573	−	9.87400i	−0.0110239	−	0.0411417i
$241$	214.865	−	57.5730i	0.891557	−	0.238892i	0.216170	−	0.976356i	$-0.430643\pi$
$241$	214.865	−	57.5730i	0.891557	−	0.238892i	0.675387	+	0.737464i	$0.263977\pi$
$242$	−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	0.867138	−	0.498069i	$-0.165957\pi$
$251$	218.211	+	125.984i	0.869366	+	0.501929i	0.00222866	+	0.999998i	$0.499291\pi$
$252$	−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	0.0764769	−	0.997071i	$-0.475633\pi$
$257$	251.399	−	145.145i	0.978204	−	0.564767i	0.901728	+	0.432305i	$0.142300\pi$
$258$	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	0.950155	−	0.311777i	$-0.100924\pi$
$263$	53.9337	+	93.4160i	0.205071	+	0.355194i	−0.745084	+	0.666970i	$0.767591\pi$
$264$	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	−0.103987	−	0.994579i	$-0.533160\pi$
$269$	217.712	−	377.087i	0.809337	−	1.40181i	0.913324	−	0.407234i	$-0.133507\pi$
$270$	−41.0884	+	23.7224i	−0.152179	+	0.0878608i
$271$	21.7703	−	81.2480i	0.0803333	−	0.299808i	−0.914056	−	0.405587i	$-0.867067\pi$
$271$	21.7703	−	81.2480i	0.0803333	−	0.299808i	0.994390	+	0.105779i	$0.0337337\pi$
$272$		−	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	0.441350	−	0.897335i	$-0.354500\pi$
$277$	−31.8797	−	18.4057i	−0.115089	−	0.0664467i	−0.556439	+	0.830888i	$0.687833\pi$
$278$	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	0.651501	−	0.758647i	$-0.274139\pi$
$281$	−30.1080	−	30.1080i	−0.107146	−	0.107146i	−0.758647	+	0.651501i	$0.774139\pi$
$282$	−48.7359	+	84.4131i	−0.172822	+	0.299337i
$283$	−90.8978	+	52.4799i	−0.321194	+	0.185441i	−0.651924	−	0.758284i	$-0.726038\pi$
$283$	−90.8978	+	52.4799i	−0.321194	+	0.185441i	0.330731	+	0.943725i	$0.392705\pi$
$284$	−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	−0.0456298	−	0.998958i	$-0.514529\pi$
$293$	121.399	−	32.5289i	0.414333	−	0.111020i	0.459963	+	0.887938i	$0.347863\pi$
$294$	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	0.398100	−	0.917342i	$-0.369670\pi$
$307$	−159.407	−	159.407i	−0.519242	−	0.519242i	−0.917342	+	0.398100i	$0.869670\pi$
$308$	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	$0.266300\pi$
$311$			461.756i			1.48475i	−0.669986	+	0.742374i	$0.733700\pi$
$312$	−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	−0.836684	−	0.547685i	$-0.815509\pi$
$317$	−91.6127	+	91.6127i	−0.288999	+	0.288999i	0.547685	+	0.836684i	$0.315509\pi$
$318$	−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	0.999424	−	0.0339382i	$-0.0108049\pi$
$331$	38.7033	+	144.443i	0.116928	+	0.436382i	−0.882496	+	0.470321i	$0.844138\pi$
$332$	−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	$-0.970804\pi$
$337$		−	61.7332i		−	0.183185i	0.995797	−	0.0915923i	$-0.0291956\pi$
$338$	−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	−0.980122	−	0.198396i	$-0.936427\pi$
$347$	−110.431	+	191.272i	−0.318245	+	0.551216i	0.661877	+	0.749612i	$0.269760\pi$
$348$	159.452	−	92.0599i	0.458196	−	0.264540i
$349$	−75.3230	+	281.109i	−0.215825	+	0.805470i	0.770049	+	0.637984i	$0.220232\pi$
$349$	−75.3230	+	281.109i	−0.215825	+	0.805470i	−0.985874	+	0.167486i	$0.946435\pi$
$350$		−	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	0.285689	−	0.958322i	$-0.407778\pi$
$353$	19.0412	+	5.10208i	0.0539412	+	0.0144535i	−0.231748	+	0.972776i	$0.574444\pi$
$354$	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	0.209970	−	0.977708i	$-0.432663\pi$
$359$	−275.618	−	275.618i	−0.767738	−	0.767738i	−0.977708	+	0.209970i	$0.932663\pi$
$360$	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	−0.985739	−	0.168278i	$-0.946179\pi$
$367$	−234.367	−	405.936i	−0.638603	−	1.10609i	0.347136	−	0.937815i	$-0.387154\pi$
$368$	−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	−0.986181	−	0.165669i	$-0.947022\pi$
$373$	−130.407	+	225.872i	−0.349617	+	0.605555i	0.636564	+	0.771224i	$0.280355\pi$
$374$	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	0.521218	−	0.853424i	$-0.325478\pi$
$379$	206.894	+	55.4370i	0.545893	+	0.146272i	0.0246758	+	0.999696i	$0.492145\pi$
$380$	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	−0.661690	−	0.749778i	$-0.730160\pi$
$383$	−177.535	−	662.570i	−0.463538	−	1.72995i	0.198151	−	0.980171i	$-0.436506\pi$
$384$	−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	$0.159947\pi$
$389$			374.691i			0.963216i	−0.876387	+	0.481608i	$0.840053\pi$
$390$	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	0.646316	−	0.763070i	$-0.276309\pi$
$397$	630.268	−	168.880i	1.58758	−	0.425390i	0.941261	+	0.337680i	$0.109642\pi$
$398$	−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	0.674112	+	0.738629i	$0.264527\pi$
$401$	−111.879	+	417.539i	−0.279001	+	1.04125i	−0.953113	+	0.302616i	$0.902140\pi$
$402$		−	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	0.996267	+	0.0863302i	$0.0275140\pi$
$409$	72.2456	+	269.624i	0.176640	+	0.659228i	−0.819627	+	0.572897i	$0.805819\pi$
$410$	−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	0.732121	−	0.681175i	$-0.238531\pi$
$419$	−93.7951	−	162.458i	−0.223855	−	0.387728i	−0.955975	+	0.293447i	$0.905197\pi$
$420$	−35.1888	−	20.3163i	−0.0837829	−	0.0483721i
$421$	410.480	−	410.480i	0.975013	−	0.975013i	−0.0246826	−	0.999695i	$-0.507858\pi$
$421$	410.480	−	410.480i	0.975013	−	0.975013i	0.999695	+	0.0246826i	$0.00785752\pi$
$422$	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	−0.396617	−	0.917984i	$-0.629816\pi$
$431$	−516.808	−	138.478i	−1.19909	−	0.321295i	−0.802473	+	0.596689i	$0.796483\pi$
$432$	146.483	+	253.716i	0.339081	+	0.587305i
$433$	140.192	+	80.9400i	0.323769	+	0.186928i	0.653071	−	0.757296i	$-0.273480\pi$
$433$	140.192	+	80.9400i	0.323769	+	0.186928i	−0.329302	+	0.944225i	$0.606813\pi$
$434$	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	−0.653193	−	0.757191i	$-0.726571\pi$
$439$	−142.255	+	82.1308i	−0.324043	+	0.187086i	0.329150	+	0.944277i	$0.393238\pi$
$440$	−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	−0.402200	−	0.915552i	$-0.631754\pi$
$449$	−131.440	+	35.2192i	−0.292739	+	0.0784392i	0.109461	+	0.993991i	$0.465088\pi$
$450$	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	0.490694	−	0.871332i	$-0.336743\pi$
$457$	219.352	+	58.7751i	0.479981	+	0.128611i	−0.0107126	+	0.999943i	$0.503410\pi$
$458$	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	−0.839741	−	0.542987i	$-0.817293\pi$
$461$	−177.023	−	660.658i	−0.383998	−	1.43310i	0.455743	−	0.890111i	$-0.349373\pi$
$462$	339.127	−	90.8689i	0.734042	−	0.196686i
$463$	557.281	+	557.281i	1.20363	+	1.20363i	0.973055	+	0.230575i	$0.0740607\pi$
$463$	557.281	+	557.281i	1.20363	+	1.20363i	0.230575	+	0.973055i	$0.425939\pi$
$464$	−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	$0.0310745\pi$
$467$			91.0355i			0.194937i	−0.995239	+	0.0974684i	$0.968926\pi$
$468$	−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	−0.414945	−	0.909846i	$-0.636199\pi$
$479$	191.280	−	713.865i	0.399331	−	1.49032i	0.814276	−	0.580477i	$-0.197134\pi$
$480$			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	0.919949	+	0.392037i	$0.128230\pi$
$487$	155.484	+	580.273i	0.319268	+	1.19153i	−0.600681	+	0.799489i	$0.705104\pi$
$488$	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	−0.903005	−	0.429631i	$-0.858644\pi$
$491$	−482.376	+	278.500i	−0.982436	+	0.567210i	−0.0794313	+	0.996840i	$0.525310\pi$
$492$	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	−0.608051	−	0.793898i	$-0.708048\pi$
$499$	92.7376	−	92.7376i	0.185847	−	0.185847i	0.793898	+	0.608051i	$0.208048\pi$
$500$	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	−0.789955	−	0.613165i	$-0.789896\pi$
$503$	68.4278	−	118.520i	0.136039	−	0.235627i	0.925994	+	0.377538i	$0.123229\pi$
$504$	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	0.416062	−	0.909336i	$-0.363410\pi$
$509$	163.752	+	43.8773i	0.321713	+	0.0862029i	−0.0943482	+	0.995539i	$0.530077\pi$
$510$	−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	0.794009	−	0.607906i	$-0.207990\pi$
$523$	−67.7062	−	117.271i	−0.129457	−	0.224227i	−0.923466	+	0.383679i	$0.874657\pi$
$524$	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	0.579055	−	0.815288i	$-0.303422\pi$
$541$	−127.802	−	127.802i	−0.236233	−	0.236233i	−0.815288	+	0.579055i	$0.803422\pi$
$542$	−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	0.678323	+	0.734764i	$0.262707\pi$
$557$	−154.013	+	574.784i	−0.276504	+	1.03193i	−0.954827	+	0.297163i	$0.903959\pi$
$558$			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	−0.0619205	−	0.998081i	$-0.519723\pi$
$563$	−538.929	−	311.151i	−0.957244	−	0.552665i	−0.895324	+	0.445416i	$0.853056\pi$
$564$	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	0.229499	−	0.973309i	$-0.426291\pi$
$569$	675.493	−	389.996i	1.18716	−	0.685406i	0.957660	+	0.287903i	$0.0929580\pi$
$570$	−4.33373	+	16.1737i	−0.00760304	+	0.0283749i
$571$		−	556.142i		−	0.973980i	−0.873408	−	0.486990i	$-0.838095\pi$
$571$		−	556.142i		−	0.973980i	0.873408	−	0.486990i	$-0.161905\pi$
$572$	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	−0.267026	−	0.963689i	$-0.586041\pi$
$577$	401.975	−	401.975i	0.696663	−	0.696663i	0.963689	+	0.267026i	$0.0860409\pi$
$578$	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	0.764204	−	0.644974i	$-0.223132\pi$
$587$	647.776	+	173.571i	1.10354	+	0.295692i	0.339333	+	0.940666i	$0.389799\pi$
$588$	−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	0.533243	−	0.845962i	$-0.320973\pi$
$593$	−185.442	−	185.442i	−0.312719	−	0.312719i	−0.845962	+	0.533243i	$0.820973\pi$
$594$	−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	0.817765	−	0.575552i	$-0.195213\pi$
$601$	−53.8259	−	93.2293i	−0.0895606	−	0.155124i	−0.907325	+	0.420429i	$0.861880\pi$
$602$	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	−0.987486	−	0.157710i	$-0.949589\pi$
$607$	−216.797	+	375.504i	−0.357162	+	0.618623i	0.630323	+	0.776333i	$0.282922\pi$
$608$	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	0.726530	−	0.687135i	$-0.241132\pi$
$613$	620.451	+	166.249i	1.01216	+	0.271206i	0.285626	+	0.958341i	$0.407799\pi$
$614$	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	−0.996767	−	0.0803421i	$-0.974399\pi$
$617$	−107.181	−	400.004i	−0.173713	−	0.648304i	0.823055	−	0.567962i	$-0.192268\pi$
$618$	826.475	−	221.453i	1.33734	−	0.358339i
$619$	693.205	+	693.205i	1.11988	+	1.11988i	0.991759	+	0.128120i	$0.0408943\pi$
$619$	693.205	+	693.205i	1.11988	+	1.11988i	0.128120	+	0.991759i	$0.459106\pi$
$620$	−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	0.167091	−	0.985941i	$-0.446563\pi$
$631$	507.808	−	136.067i	0.804767	−	0.215637i	0.637676	+	0.770305i	$0.279896\pi$
$632$	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	−0.461790	−	0.886989i	$-0.652793\pi$
$641$	−936.399	−	540.630i	−1.46084	−	0.843416i	−0.999050	+	0.0435728i	$0.986126\pi$
$642$	−420.107	+	420.107i	−0.654372	+	0.654372i
$643$	−102.193	−	381.388i	−0.158931	−	0.593138i	−0.998737	−	0.0502511i	$-0.983998\pi$
$643$	−102.193	−	381.388i	−0.158931	−	0.593138i	0.839806	−	0.542887i	$-0.182669\pi$
$644$	−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	−0.271790	−	0.962357i	$-0.587616\pi$
$647$	275.454	−	159.033i	0.425740	−	0.245801i	0.697530	+	0.716555i	$0.254282\pi$
$648$	−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	0.977922	−	0.208972i	$-0.0670117\pi$
$653$	201.115	+	348.341i	0.307986	+	0.533447i	−0.669936	+	0.742419i	$0.733678\pi$
$654$	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	−0.998012	−	0.0630290i	$-0.979924\pi$
$659$	−292.874	+	507.272i	−0.444421	+	0.769760i	0.553591	+	0.832789i	$0.313257\pi$
$660$	−24.7757	+	14.3043i	−0.0375390	+	0.0216731i
$661$	209.306	−	781.140i	0.316650	−	1.18176i	−0.605793	−	0.795623i	$-0.707144\pi$
$661$	209.306	−	781.140i	0.316650	−	1.18176i	0.922443	−	0.386133i	$-0.126189\pi$
$662$		−	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	−0.751112	−	0.660175i	$-0.770482\pi$
$673$	−373.474	+	215.625i	−0.554939	+	0.320394i	0.196173	+	0.980569i	$0.437149\pi$
$674$	−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	−0.171089	−	0.985256i	$-0.554728\pi$
$683$	118.413	−	31.7287i	0.173372	−	0.0464549i	0.344461	+	0.938801i	$0.388062\pi$
$684$	−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	0.323985	−	0.946062i	$-0.394977\pi$
$691$	90.8900	+	24.3539i	0.131534	+	0.0352444i	−0.192451	+	0.981307i	$0.561644\pi$
$692$	−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	$0.170747\pi$
$701$			716.506i			1.02212i	−0.859545	+	0.511060i	$0.829253\pi$
$702$	−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	−0.860080	−	0.510159i	$-0.829587\pi$
$709$	−957.045	+	256.439i	−1.34985	+	0.361692i	−0.489772	+	0.871851i	$0.662920\pi$
$710$	−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	0.601053	−	0.799209i	$-0.294748\pi$
$719$	150.591	+	86.9435i	0.209445	+	0.120923i	−0.391609	+	0.920132i	$0.628081\pi$
$720$	−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	$0.167175\pi$
$727$			729.011i			1.00277i	−0.865225	+	0.501383i	$0.832825\pi$
$728$	−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	−0.0410404	+	0.999157i	$0.513067\pi$
$733$	−762.465	+	762.465i	−1.04020	+	1.04020i	−0.999157	+	0.0410404i	$0.986933\pi$
$734$	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	−0.771296	−	0.636476i	$-0.780391\pi$
$739$	158.814	−	592.703i	0.214904	−	0.802033i	0.986200	−	0.165557i	$-0.0529421\pi$
$740$		−	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	0.365434	−	0.930837i	$-0.380921\pi$
$743$	160.852	+	43.1002i	0.216490	+	0.0580084i	−0.148944	+	0.988846i	$0.547587\pi$
$744$	−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	−0.575410	−	0.817865i	$-0.695158\pi$
$751$	−116.272	+	67.1297i	−0.154823	+	0.0893871i	0.420587	+	0.907252i	$0.361824\pi$
$752$	−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	0.925814	+	0.377980i	$0.123381\pi$
$757$	598.217	+	1036.14i	0.790247	+	1.36875i	−0.135567	+	0.990768i	$0.543285\pi$
$758$	−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	−0.280952	−	0.959722i	$-0.590650\pi$
$761$	−33.7907	+	9.05420i	−0.0444031	+	0.0118978i	0.236549	+	0.971620i	$0.423984\pi$
$762$	539.918	+	539.918i	0.708554	+	0.708554i
$763$	32.8095	−	56.8277i	0.0430007	−	0.0744793i
$764$	−119.708	+

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

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