LMFDB - Embedded newform 26.3.f.b.19.1

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			19.1
Root			$3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.3.f.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-1.52185 + 2.63592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.79174 - 4.79174i) q^{5} +(-4.15776 - 1.11407i) q^{6} +(1.13983 - 4.25390i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.52185 + 2.63592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.79174 - 4.79174i) q^{5} +(-4.15776 - 1.11407i) q^{6} +(1.13983 - 4.25390i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +(8.29953 + 4.79174i) q^{10} +(-13.8758 + 3.71800i) q^{11} -6.08739i q^{12} +(1.84809 - 12.8680i) q^{13} +6.22814 q^{14} +(5.33833 + 19.9229i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-20.9957 + 12.1219i) q^{17} +(0.264067 - 0.264067i) q^{18} +(25.4592 + 6.82178i) q^{19} +(-3.50779 + 13.0913i) q^{20} +(9.47827 + 9.47827i) q^{21} +(-10.1578 - 17.5938i) q^{22} +(-5.44507 - 3.14371i) q^{23} +(8.31552 - 2.22814i) q^{24} -20.9215i q^{25} +(18.2544 - 2.18546i) q^{26} -26.5895 q^{27} +(2.27966 + 8.50779i) q^{28} +(11.1112 - 19.2451i) q^{29} +(-25.2612 + 14.5846i) q^{30} +(-8.59518 + 8.59518i) q^{31} +(5.46410 + 1.46410i) q^{32} +(11.3164 - 42.2336i) q^{33} +(-24.2437 - 24.2437i) q^{34} +(-14.9218 - 25.8453i) q^{35} +(0.457378 + 0.264067i) q^{36} +(-6.13936 + 1.64504i) q^{37} +37.2749i q^{38} +(31.1064 + 24.4545i) q^{39} -19.1669 q^{40} +(18.8845 + 70.4778i) q^{41} +(-9.47827 + 16.4168i) q^{42} +(26.9695 - 15.5708i) q^{43} +(20.3155 - 20.3155i) q^{44} +(-1.72849 - 0.463147i) q^{45} +(2.30136 - 8.58878i) q^{46} +(7.65637 + 7.65637i) q^{47} +(6.08739 + 10.5437i) q^{48} +(25.6388 + 14.8026i) q^{49} +(28.5793 - 7.65779i) q^{50} -73.7905i q^{51} +(9.66698 + 24.1361i) q^{52} -33.7616 q^{53} +(-9.73243 - 36.3219i) q^{54} +(-48.6733 + 84.3047i) q^{55} +(-10.7875 + 6.22814i) q^{56} +(-56.7267 + 56.7267i) q^{57} +(30.3563 + 8.13394i) q^{58} +(9.77592 - 36.4842i) q^{59} +(-29.1692 - 29.1692i) q^{60} +(11.5359 + 19.9807i) q^{61} +(-14.8873 - 8.59518i) q^{62} +(-1.12332 + 0.300991i) q^{63} +8.00000i q^{64} +(-52.8043 - 70.5155i) q^{65} +61.8342 q^{66} +(-27.8544 - 103.954i) q^{67} +(24.2437 - 41.9914i) q^{68} +(16.5731 - 9.56849i) q^{69} +(29.8436 - 29.8436i) q^{70} +(2.20861 + 0.591796i) q^{71} +(-0.193311 + 0.721445i) q^{72} +(38.1773 + 38.1773i) q^{73} +(-4.49432 - 7.78440i) q^{74} +(55.1473 + 31.8393i) q^{75} +(-50.9185 + 13.6436i) q^{76} +63.2639i q^{77} +(-22.0197 + 51.4430i) q^{78} -19.1299 q^{79} +(-7.01559 - 26.1825i) q^{80} +(41.6534 - 72.1459i) q^{81} +(-89.3622 + 51.5933i) q^{82} +(34.7720 - 34.7720i) q^{83} +(-25.8951 - 6.93858i) q^{84} +(-42.5210 + 158.691i) q^{85} +(31.1417 + 31.1417i) q^{86} +(33.8190 + 58.5762i) q^{87} +(35.1875 + 20.3155i) q^{88} +(3.47190 - 0.930292i) q^{89} -2.53068i q^{90} +(-52.6325 - 22.5289i) q^{91} +12.5748 q^{92} +(-9.57562 - 35.7367i) q^{93} +(-7.65637 + 13.2612i) q^{94} +(154.682 - 89.3058i) q^{95} +(-12.1748 + 12.1748i) q^{96} +(-24.3107 - 6.51404i) q^{97} +(-10.8362 + 40.4414i) q^{98} +(2.68233 + 2.68233i) 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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$	−1.52185	+	2.63592i	−0.507282	+	0.878639i	0.492682	+	0.870209i	$0.336016\pi$
$3$	−1.52185	+	2.63592i	−0.507282	+	0.878639i	−0.999964	+	0.00842924i	$0.997317\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	4.79174	−	4.79174i	0.958347	−	0.958347i	−0.0408192	−	0.999167i	$-0.512997\pi$
$5$	4.79174	−	4.79174i	0.958347	−	0.958347i	0.999167	+	0.0408192i	$0.0129968\pi$
$6$	−4.15776	−	1.11407i	−0.692960	−	0.185678i
$7$	1.13983	−	4.25390i	0.162833	−	0.607700i	−0.835474	−	0.549530i	$-0.814807\pi$
$7$	1.13983	−	4.25390i	0.162833	−	0.607700i	0.998307	−	0.0581698i	$-0.0185265\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−0.132034	−	0.228689i	−0.0146704	−	0.0254099i
$10$	8.29953	+	4.79174i	0.829953	+	0.479174i
$11$	−13.8758	+	3.71800i	−1.26143	+	0.338000i	−0.826743	−	0.562580i	$-0.809809\pi$
$11$	−13.8758	+	3.71800i	−1.26143	+	0.338000i	−0.434690	+	0.900580i	$0.643142\pi$
$12$		−	6.08739i		−	0.507282i
$13$	1.84809	−	12.8680i	0.142161	−	0.989844i
$13$	1.84809	−	12.8680i	0.142161	−	0.989844i
$14$	6.22814			0.444867
$15$	5.33833	+	19.9229i	0.355888	+	1.32819i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−20.9957	+	12.1219i	−1.23504	+	0.713051i	−0.968076	−	0.250656i	$-0.919354\pi$
$17$	−20.9957	+	12.1219i	−1.23504	+	0.713051i	−0.266964	+	0.963707i	$0.586020\pi$
$18$	0.264067	−	0.264067i	0.0146704	−	0.0146704i
$19$	25.4592	+	6.82178i	1.33996	+	0.359041i	0.856419	−	0.516281i	$-0.172684\pi$
$19$	25.4592	+	6.82178i	1.33996	+	0.359041i	0.483540	+	0.875322i	$0.339351\pi$
$20$	−3.50779	+	13.0913i	−0.175390	+	0.654563i
$21$	9.47827	+	9.47827i	0.451346	+	0.451346i
$22$	−10.1578	−	17.5938i	−0.461716	−	0.799716i
$23$	−5.44507	−	3.14371i	−0.236742	−	0.136683i	0.376936	−	0.926239i	$-0.376978\pi$
$23$	−5.44507	−	3.14371i	−0.236742	−	0.136683i	−0.613678	+	0.789556i	$0.710311\pi$
$24$	8.31552	−	2.22814i	0.346480	−	0.0928391i
$25$		−	20.9215i		−	0.836859i
$26$	18.2544	−	2.18546i	0.702093	−	0.0840562i
$27$	−26.5895			−0.984796
$28$	2.27966	+	8.50779i	0.0814163	+	0.303850i
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	−0.608366	−	0.793657i	$-0.708175\pi$
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	0.991510	+	0.130032i	$0.0415080\pi$
$30$	−25.2612	+	14.5846i	−0.842041	+	0.486153i
$31$	−8.59518	+	8.59518i	−0.277264	+	0.277264i	−0.832016	−	0.554752i	$-0.812813\pi$
$31$	−8.59518	+	8.59518i	−0.277264	+	0.277264i	0.554752	+	0.832016i	$0.312813\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	11.3164	−	42.2336i	0.342923	−	1.27980i
$34$	−24.2437	−	24.2437i	−0.713051	−	0.713051i
$35$	−14.9218	−	25.8453i	−0.426337	−	0.738438i
$36$	0.457378	+	0.264067i	0.0127049	+	0.00733521i
$37$	−6.13936	+	1.64504i	−0.165929	+	0.0444605i	−0.340827	−	0.940126i	$-0.610707\pi$
$37$	−6.13936	+	1.64504i	−0.165929	+	0.0444605i	0.174898	+	0.984587i	$0.444040\pi$
$38$			37.2749i			0.980919i
$39$	31.1064	+	24.4545i	0.797599	+	0.627038i
$40$	−19.1669			−0.479174
$41$	18.8845	+	70.4778i	0.460596	+	1.71897i	0.671091	+	0.741375i	$0.265826\pi$
$41$	18.8845	+	70.4778i	0.460596	+	1.71897i	−0.210495	+	0.977595i	$0.567508\pi$
$42$	−9.47827	+	16.4168i	−0.225673	+	0.390877i
$43$	26.9695	−	15.5708i	0.627197	−	0.362113i	−0.152468	−	0.988308i	$-0.548722\pi$
$43$	26.9695	−	15.5708i	0.627197	−	0.362113i	0.779666	+	0.626196i	$0.215389\pi$
$44$	20.3155	−	20.3155i	0.461716	−	0.461716i
$45$	−1.72849	−	0.463147i	−0.0384109	−	0.0102922i
$46$	2.30136	−	8.58878i	0.0500295	−	0.186713i
$47$	7.65637	+	7.65637i	0.162902	+	0.162902i	0.783851	−	0.620949i	$-0.213253\pi$
$47$	7.65637	+	7.65637i	0.162902	+	0.162902i	−0.620949	+	0.783851i	$0.713253\pi$
$48$	6.08739	+	10.5437i	0.126821	+	0.219660i
$49$	25.6388	+	14.8026i	0.523241	+	0.302093i
$50$	28.5793	−	7.65779i	0.571585	−	0.153156i
$51$		−	73.7905i		−	1.44687i
$52$	9.66698	+	24.1361i	0.185903	+	0.464155i
$53$	−33.7616			−0.637010			−0.318505	−	0.947921i	$-0.603181\pi$
$53$	−33.7616			−0.637010			−0.318505	+	0.947921i	$0.603181\pi$
$54$	−9.73243	−	36.3219i	−0.180230	−	0.672628i
$55$	−48.6733	+	84.3047i	−0.884969	+	1.53281i
$56$	−10.7875	+	6.22814i	−0.192633	+	0.111217i
$57$	−56.7267	+	56.7267i	−0.995205	+	0.995205i
$58$	30.3563	+	8.13394i	0.523384	+	0.140240i
$59$	9.77592	−	36.4842i	0.165694	−	0.618377i	−0.832257	−	0.554390i	$-0.812952\pi$
$59$	9.77592	−	36.4842i	0.165694	−	0.618377i	0.997951	−	0.0639871i	$-0.0203817\pi$
$60$	−29.1692	−	29.1692i	−0.486153	−	0.486153i
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	0.944955	−	0.327201i	$-0.106106\pi$
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	−0.755842	+	0.654754i	$0.772772\pi$
$62$	−14.8873	−	8.59518i	−0.240118	−	0.138632i
$63$	−1.12332	+	0.300991i	−0.0178304	+	0.00477764i
$64$			8.00000i			0.125000i
$65$	−52.8043	−	70.5155i	−0.812374	−	1.08485i
$66$	61.8342			0.936882
$67$	−27.8544	−	103.954i	−0.415737	−	1.55155i	−0.783355	−	0.621575i	$-0.786493\pi$
$67$	−27.8544	−	103.954i	−0.415737	−	1.55155i	0.367618	−	0.929977i	$-0.380173\pi$
$68$	24.2437	−	41.9914i	0.356525	−	0.617520i
$69$	16.5731	−	9.56849i	0.240190	−	0.138674i
$70$	29.8436	−	29.8436i	0.426337	−	0.426337i
$71$	2.20861	+	0.591796i	0.0311072	+	0.00833516i	0.274339	−	0.961633i	$-0.411541\pi$
$71$	2.20861	+	0.591796i	0.0311072	+	0.00833516i	−0.243232	+	0.969968i	$0.578208\pi$
$72$	−0.193311	+	0.721445i	−0.00268487	+	0.0100201i
$73$	38.1773	+	38.1773i	0.522977	+	0.522977i	0.918469	−	0.395492i	$-0.129426\pi$
$73$	38.1773	+	38.1773i	0.522977	+	0.522977i	−0.395492	+	0.918469i	$0.629426\pi$
$74$	−4.49432	−	7.78440i	−0.0607341	−	0.105195i
$75$	55.1473	+	31.8393i	0.735297	+	0.424524i
$76$	−50.9185	+	13.6436i	−0.669980	+	0.179521i
$77$			63.2639i			0.821610i
$78$	−22.0197	+	51.4430i	−0.282304	+	0.659526i
$79$	−19.1299			−0.242150			−0.121075	−	0.992643i	$-0.538634\pi$
$79$	−19.1299			−0.242150			−0.121075	+	0.992643i	$0.538634\pi$
$80$	−7.01559	−	26.1825i	−0.0876949	−	0.327282i
$81$	41.6534	−	72.1459i	0.514240	−	0.890690i
$82$	−89.3622	+	51.5933i	−1.08978	+	0.629187i
$83$	34.7720	−	34.7720i	0.418940	−	0.418940i	−0.465898	−	0.884838i	$-0.654269\pi$
$83$	34.7720	−	34.7720i	0.418940	−	0.418940i	0.884838	+	0.465898i	$0.154269\pi$
$84$	−25.8951	−	6.93858i	−0.308275	−	0.0826021i
$85$	−42.5210	+	158.691i	−0.500247	+	1.86695i
$86$	31.1417	+	31.1417i	0.362113	+	0.362113i
$87$	33.8190	+	58.5762i	0.388724	+	0.673290i
$88$	35.1875	+	20.3155i	0.399858	+	0.230858i
$89$	3.47190	−	0.930292i	0.0390101	−	0.0104527i	−0.239261	−	0.970955i	$-0.576905\pi$
$89$	3.47190	−	0.930292i	0.0390101	−	0.0104527i	0.278271	+	0.960503i	$0.410239\pi$
$90$		−	2.53068i		−	0.0281187i
$91$	−52.6325	−	22.5289i	−0.578379	−	0.247570i
$92$	12.5748			0.136683
$93$	−9.57562	−	35.7367i	−0.102964	−	0.384266i
$94$	−7.65637	+	13.2612i	−0.0814508	+	0.141077i
$95$	154.682	−	89.3058i	1.62823	−	0.940061i
$96$	−12.1748	+	12.1748i	−0.126821	+	0.126821i
$97$	−24.3107	−	6.51404i	−0.250626	−	0.0671551i	0.131319	−	0.991340i	$-0.458079\pi$
$97$	−24.3107	−	6.51404i	−0.250626	−	0.0671551i	−0.381945	+	0.924185i	$0.624746\pi$
$98$	−10.8362	+	40.4414i	−0.110574	+	0.412667i
$99$	2.68233	+	2.68233i	0.0270943	+	0.0270943i
$100$	20.9215	+	36.2371i	0.209215	+	0.362371i
$101$	−131.473	−	75.9060i	−1.30171	−	0.751545i	−0.321016	−	0.947074i	$-0.604024\pi$
$101$	−131.473	−	75.9060i	−1.30171	−	0.751545i	−0.980698	+	0.195529i	$0.937358\pi$
$102$	100.800	−	27.0092i	0.988232	−	0.264796i
$103$			17.3672i			0.168614i	0.996440	+	0.0843069i	$0.0268676\pi$
$103$			17.3672i			0.168614i	−0.996440	+	0.0843069i	$0.973132\pi$
$104$	−29.4321	+	22.0397i	−0.283001	+	0.211921i
$105$	90.8347			0.865093
$106$	−12.3576	−	46.1191i	−0.116581	−	0.435086i
$107$	−26.5964	+	46.0662i	−0.248564	+	0.430526i	−0.963128	−	0.269045i	$-0.913292\pi$
$107$	−26.5964	+	46.0662i	−0.248564	+	0.430526i	0.714564	+	0.699571i	$0.246625\pi$
$108$	46.0544	−	26.5895i	0.426429	−	0.246199i
$109$	53.3779	−	53.3779i	0.489705	−	0.489705i	−0.418508	−	0.908213i	$-0.637447\pi$
$109$	53.3779	−	53.3779i	0.489705	−	0.489705i	0.908213	+	0.418508i	$0.137447\pi$
$110$	−132.978	−	35.6313i	−1.20889	−	0.323921i
$111$	5.00699	−	18.6863i	0.0451080	−	0.168345i
$112$	−12.4563	−	12.4563i	−0.111217	−	0.111217i
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	0.774680	−	0.632354i	$-0.217911\pi$
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	−0.934974	+	0.354715i	$0.884578\pi$
$114$	−98.2535	−	56.7267i	−0.861873	−	0.497603i
$115$	−41.1552	+	11.0275i	−0.357871	+	0.0958912i
$116$			44.4447i			0.383144i
$117$	−3.18677	+	1.27637i	−0.0272374	+	0.0109091i
$118$	53.4166			0.452683
$119$	27.6337	+	103.130i	0.232216	+	0.866641i
$120$	29.1692	−	50.5225i	0.243076	−	0.421020i
$121$	73.9242	−	42.6801i	0.610943	−	0.352728i
$122$	−23.0717	+	23.0717i	−0.189113	+	0.189113i
$123$	−214.513	−	57.4785i	−1.74401	−	0.467305i
$124$	6.29211	−	23.4825i	0.0507428	−	0.189375i
$125$	19.5432	+	19.5432i	0.156346	+	0.156346i
$126$	−0.822324	−	1.42431i	−0.00652638	−	0.0113040i
$127$	−115.255	−	66.5425i	−0.907520	−	0.523957i	−0.0278874	−	0.999611i	$-0.508878\pi$
$127$	−115.255	−	66.5425i	−0.907520	−	0.523957i	−0.879632	+	0.475654i	$0.842211\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$			94.7857i			0.734773i
$130$	76.9982	−	97.9425i	0.592294	−	0.753404i
$131$	38.2739			0.292167			0.146083	−	0.989272i	$-0.453333\pi$
$131$	38.2739			0.292167			0.146083	+	0.989272i	$0.453333\pi$
$132$	22.6329	+	84.4671i	0.171461	+	0.639902i
$133$	58.0383	−	100.525i	0.436378	−	0.755829i
$134$	131.808	−	76.0996i	0.983644	−	0.567907i
$135$	−127.410	+	127.410i	−0.943777	+	0.943777i
$136$	66.2351	+	17.7476i	0.487023	+	0.130497i
$137$	2.07966	−	7.76140i	0.0151800	−	0.0566525i	−0.957920	−	0.287034i	$-0.907331\pi$
$137$	2.07966	−	7.76140i	0.0151800	−	0.0566525i	0.973100	+	0.230381i	$0.0739974\pi$
$138$	19.1370	+	19.1370i	0.138674	+	0.138674i
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.854012	+	0.520253i	$0.174162\pi$
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.0235463	+	0.999723i	$0.492504\pi$
$140$	51.6906	+	29.8436i	0.369219	+	0.213169i
$141$	−31.8334	+	8.52973i	−0.225769	+	0.0604945i
$142$			3.23364i			0.0227721i
$143$	22.1994	+	185.424i	0.155241	+	1.29667i
$144$	−1.05627			−0.00733521
$145$	−38.9757	−	145.459i	−0.268798	−	1.00317i
$146$	−38.1773	+	66.1251i	−0.261488	+	0.452911i
$147$	−78.0367	+	45.0545i	−0.530862	+	0.306493i
$148$	8.98865	−	8.98865i	0.0607341	−	0.0607341i
$149$	182.687	+	48.9509i	1.22609	+	0.328529i	0.813055	−	0.582187i	$-0.197803\pi$
$149$	182.687	+	48.9509i	1.22609	+	0.328529i	0.413033	+	0.910716i	$0.364469\pi$
$150$	−23.3080	+	86.9865i	−0.155386	+	0.579910i
$151$	−70.5995	−	70.5995i	−0.467546	−	0.467546i	0.433573	−	0.901119i	$-0.357253\pi$
$151$	−70.5995	−	70.5995i	−0.467546	−	0.467546i	−0.901119	+	0.433573i	$0.857253\pi$
$152$	−37.2749	−	64.5620i	−0.245230	−	0.424750i
$153$	5.54428	+	3.20099i	0.0362371	+	0.0209215i
$154$	−86.4202	+	23.1562i	−0.561170	+	0.150365i
$155$			82.3717i			0.531430i
$156$	−78.3323	−	11.2500i	−0.502130	−	0.0721157i
$157$	176.794			1.12608			0.563038	−	0.826431i	$-0.309632\pi$
$157$	176.794			1.12608			0.563038	+	0.826431i	$0.309632\pi$
$158$	−7.00202	−	26.1319i	−0.0443166	−	0.165392i
$159$	51.3799	−	88.9926i	0.323144	−	0.559702i
$160$	33.1981	−	19.1669i	0.207488	−	0.119793i
$161$	−19.5795	+	19.5795i	−0.121612	+	0.121612i
$162$	113.799	+	30.4924i	0.702465	+	0.188225i
$163$	31.3812	−	117.116i	0.192523	−	0.718504i	−0.800372	−	0.599504i	$-0.795365\pi$
$163$	31.3812	−	117.116i	0.192523	−	0.718504i	0.992894	−	0.119000i	$-0.0379688\pi$
$164$	−103.187	−	103.187i	−0.629187	−	0.629187i
$165$	−148.147	−	256.598i	−0.897858	−	1.55514i
$166$	60.2269	+	34.7720i	0.362813	+	0.209470i
$167$	286.599	−	76.7939i	1.71616	−	0.459844i	0.739238	−	0.673444i	$-0.235186\pi$
$167$	286.599	−	76.7939i	1.71616	−	0.459844i	0.976921	+	0.213601i	$0.0685191\pi$
$168$		−	37.9131i		−	0.225673i
$169$	−162.169	−	47.5624i	−0.959581	−	0.281434i
$170$	−232.339			−1.36670
$171$	−1.80141	−	6.72295i	−0.0105346	−	0.0393155i
$172$	−31.1417	+	53.9390i	−0.181056	+	0.313599i
$173$	−241.179	+	139.245i	−1.39410	+	0.804884i	−0.993766	−	0.111485i	$-0.964439\pi$
$173$	−241.179	+	139.245i	−1.39410	+	0.804884i	−0.400334	+	0.916369i	$0.631106\pi$
$174$	−67.6380	+	67.6380i	−0.388724	+	0.388724i
$175$	−88.9978	−	23.8469i	−0.508559	−	0.136268i
$176$	−14.8720	+	55.5030i	−0.0845000	+	0.315358i
$177$	81.2919	+	81.2919i	0.459276	+	0.459276i
$178$	2.54160	+	4.40219i	0.0142787	+	0.0247314i
$179$	68.2036	+	39.3774i	0.381026	+	0.219985i	0.678264	−	0.734818i	$-0.262732\pi$
$179$	68.2036	+	39.3774i	0.381026	+	0.219985i	−0.297239	+	0.954803i	$0.596066\pi$
$180$	3.45698	−	0.926294i	0.0192054	−	0.00514608i
$181$		−	200.758i		−	1.10916i	−0.832130	−	0.554581i	$-0.812879\pi$
$181$		−	200.758i		−	1.10916i	0.832130	−	0.554581i	$-0.187121\pi$
$182$	11.5102	−	80.1435i	0.0632427	−	0.440349i
$183$	−70.2233			−0.383734
$184$	4.60271	+	17.1776i	0.0250147	+	0.0933563i
$185$	−21.5356	+	37.3008i	−0.116409	+	0.201626i
$186$	45.3123	−	26.1611i	0.243615	−	0.140651i
$187$	246.262	−	246.262i	1.31691	−	1.31691i
$188$	−20.9176	−	5.60485i	−0.111264	−	0.0298131i
$189$	−30.3075	+	113.109i	−0.160357	+	0.598460i
$190$	178.612	+	178.612i	0.940061	+	0.940061i
$191$	−20.2650	−	35.1001i	−0.106100	−	0.183770i	0.808087	−	0.589063i	$-0.200503\pi$
$191$	−20.2650	−	35.1001i	−0.106100	−	0.183770i	−0.914187	+	0.405293i	$0.867170\pi$
$192$	−21.0873	−	12.1748i	−0.109830	−	0.0634103i
$193$	−140.149	+	37.5529i	−0.726163	+	0.194575i	−0.602920	−	0.797802i	$-0.705996\pi$
$193$	−140.149	+	37.5529i	−0.726163	+	0.194575i	−0.123243	+	0.992377i	$0.539329\pi$
$194$		−	35.5934i		−	0.183471i
$195$	266.233	−	31.8740i	1.36530	−	0.163457i
$196$	−59.2103			−0.302093
$197$	−40.0731	−	149.555i	−0.203417	−	0.759161i	−0.989926	−	0.141583i	$-0.954781\pi$
$197$	−40.0731	−	149.555i	−0.203417	−	0.759161i	0.786510	−	0.617578i	$-0.211886\pi$
$198$	−2.68233	+	4.64594i	−0.0135471	+	0.0234643i
$199$	−225.470	+	130.175i	−1.13302	+	0.654147i	−0.944691	−	0.327960i	$-0.893639\pi$
$199$	−225.470	+	130.175i	−1.13302	+	0.654147i	−0.188324	+	0.982107i	$0.560305\pi$
$200$	−41.8430	+	41.8430i	−0.209215	+	0.209215i
$201$	316.404	+	84.7802i	1.57415	+	0.421792i
$202$	55.5671	−	207.379i	0.275084	−	1.02663i
$203$	−69.2019	−	69.2019i	−0.340896	−	0.340896i
$204$	73.7905	+	127.809i	0.361718	+	0.626514i
$205$	428.200	+	247.221i	2.08878	+	1.20596i
$206$	−23.7241	+	6.35684i	−0.115165	+	0.0308585i
$207$			1.66030i			0.00802079i
$208$	−40.8798	−	32.1379i	−0.196537	−	0.154509i
$209$	−378.630			−1.81162
$210$	33.2478	+	124.083i	0.158323	+	0.590869i
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.352831	+	0.935687i	$0.614781\pi$
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.633913	+	0.773404i	$0.718552\pi$
$212$	58.4767	−	33.7616i	0.275834	−	0.159253i
$213$	−4.92110	+	4.92110i	−0.0231037	+	0.0231037i
$214$	−72.6626	−	19.4699i	−0.339545	−	0.0909808i
$215$	54.6193	−	203.842i	0.254043	−	0.948103i
$216$	53.1790	+	53.1790i	0.246199	+	0.246199i
$217$	26.7660	+	46.3600i	0.123346	+	0.213641i
$218$	92.4532	+	53.3779i	0.424097	+	0.244853i
$219$	−158.732	+	42.5322i	−0.724805	+	0.194211i
$220$		−	194.693i		−	0.884969i
$221$	117.182	+	292.574i	0.530234	+	1.32386i
$222$	27.3587			0.123237
$223$	52.8772	+	197.340i	0.237118	+	0.884935i	0.977183	+	0.212400i	$0.0681279\pi$
$223$	52.8772	+	197.340i	0.237118	+	0.884935i	−0.740065	+	0.672535i	$0.765205\pi$
$224$	12.4563	−	21.5749i	0.0556084	−	0.0963165i
$225$	−4.78451	+	2.76234i	−0.0212645	+	0.0122771i
$226$	36.2266	−	36.2266i	0.160295	−	0.160295i
$227$	−107.452	−	28.7917i	−0.473358	−	0.126836i	0.0142503	−	0.999898i	$-0.495464\pi$
$227$	−107.452	−	28.7917i	−0.473358	−	0.126836i	−0.487608	+	0.873063i	$0.662130\pi$
$228$	41.5268	−	154.980i	0.182135	−	0.679738i
$229$	−212.309	−	212.309i	−0.927114	−	0.927114i	0.0704045	−	0.997519i	$-0.477571\pi$
$229$	−212.309	−	212.309i	−0.927114	−	0.927114i	−0.997519	+	0.0704045i	$0.977571\pi$
$230$	−30.1277	−	52.1826i	−0.130990	−	0.226881i
$231$	−166.758	−	96.2780i	−0.721898	−	0.416788i
$232$	−60.7126	+	16.2679i	−0.261692	+	0.0701202i
$233$		−	46.5826i		−	0.199925i	−0.994991	−	0.0999627i	$-0.968128\pi$
$233$		−	46.5826i		−	0.199925i	0.994991	−	0.0999627i	$-0.0318723\pi$
$234$	−2.90999	−	3.88603i	−0.0124359	−	0.0166070i
$235$	73.3746			0.312233
$236$	19.5518	+	72.9685i	0.0828468	+	0.309188i
$237$	29.1127	−	50.4247i	0.122839	−	0.212763i
$238$	−130.764	+	75.4966i	−0.549429	+	0.317213i
$239$	138.309	−	138.309i	0.578698	−	0.578698i	−0.355847	−	0.934544i	$-0.615808\pi$
$239$	138.309	−	138.309i	0.578698	−	0.578698i	0.934544	+	0.355847i	$0.115808\pi$
$240$	79.6916	+	21.3533i	0.332048	+	0.0889721i
$241$	−58.1972	+	217.195i	−0.241482	+	0.901223i	0.733637	+	0.679541i	$0.237821\pi$
$241$	−58.1972	+	217.195i	−0.241482	+	0.901223i	−0.975119	+	0.221682i	$0.928845\pi$
$242$	85.3603	+	85.3603i	0.352728	+	0.352728i
$243$	7.12754	+	12.3453i	0.0293314	+	0.0508035i
$244$	−39.9614	−	23.0717i	−0.163776	−	0.0945563i
$245$	193.784	−	51.9244i	0.790957	−	0.211936i
$246$		−	314.068i		−	1.27670i
$247$	134.833	−	315.001i	0.545884	−	1.27531i
$248$	34.3807			0.138632
$249$	38.7384	+	144.574i	0.155576	+	0.580618i
$250$	−19.5432	+	33.8498i	−0.0781728	+	0.135399i
$251$	3.02255	−	1.74507i	0.0120420	−	0.00695247i	−0.493967	−	0.869481i	$-0.664454\pi$
$251$	3.02255	−	1.74507i	0.0120420	−	0.00695247i	0.506009	+	0.862528i	$0.331120\pi$
$252$	1.64465	−	1.64465i	0.00652638	−	0.00652638i
$253$	87.2427	+	23.3766i	0.344833	+	0.0923977i
$254$	48.7125	−	181.798i	0.191781	−	0.715738i
$255$	−353.584	−	353.584i	−1.38661	−	1.38661i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−160.572	−	92.7065i	−0.624795	−	0.360726i	0.153938	−	0.988080i	$-0.450804\pi$
$257$	−160.572	−	92.7065i	−0.624795	−	0.360726i	−0.778734	+	0.627355i	$0.784138\pi$
$258$	−129.480	+	34.6940i	−0.501859	+	0.134473i
$259$			27.9913i			0.108074i
$260$	161.975	+	69.3320i	0.622982	+	0.266662i
$261$	−5.86820			−0.0224835
$262$	14.0092	+	52.2831i	0.0534703	+	0.199554i
$263$	93.6758	−	162.251i	0.356182	−	0.616925i	−0.631138	−	0.775671i	$-0.717412\pi$
$263$	93.6758	−	162.251i	0.356182	−	0.616925i	0.987319	+	0.158746i	$0.0507451\pi$
$264$	−107.100	+	61.8342i	−0.405682	+	0.234221i
$265$	−161.776	+	161.776i	−0.610477	+	0.610477i
$266$	158.564	+	42.4870i	0.596104	+	0.159726i
$267$	−2.83152	+	10.5674i	−0.0106050	+	0.0395782i
$268$	152.199	+	152.199i	0.567907	+	0.567907i
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	−0.985559	−	0.169334i	$-0.945838\pi$
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	0.346132	−	0.938186i	$-0.387495\pi$
$270$	−220.680	−	127.410i	−0.817335	−	0.471888i
$271$	23.4296	−	6.27795i	0.0864562	−	0.0231659i	−0.215332	−	0.976541i	$-0.569083\pi$
$271$	23.4296	−	6.27795i	0.0864562	−	0.0231659i	0.301788	+	0.953375i	$0.402417\pi$
$272$			96.9749i			0.356525i
$273$	139.483	−	104.449i	0.510926	−	0.382598i
$274$	11.3635			0.0414725
$275$	77.7860	+	290.301i	0.282858	+	1.05564i
$276$	−19.1370	+	33.1462i	−0.0693369	+	0.120095i
$277$	−428.588	+	247.446i	−1.54725	+	0.893306i	−0.548901	+	0.835888i	$0.684953\pi$
$277$	−428.588	+	247.446i	−1.54725	+	0.893306i	−0.998350	+	0.0574180i	$0.981713\pi$
$278$	−243.961	+	243.961i	−0.877558	+	0.877558i
$279$	3.10048	+	0.830770i	0.0111128	+	0.00297767i
$280$	−21.8470	+	81.5342i	−0.0780251	+	0.291194i
$281$	145.653	+	145.653i	0.518337	+	0.518337i	0.917068	−	0.398731i	$-0.130549\pi$
$281$	145.653	+	145.653i	0.518337	+	0.518337i	−0.398731	+	0.917068i	$0.630549\pi$
$282$	−23.3036	−	40.3631i	−0.0826370	−	0.143132i
$283$	372.577	+	215.107i	1.31653	+	0.760096i	0.983168	−	0.182704i	$-0.0584851\pi$
$283$	372.577	+	215.107i	1.31653	+	0.760096i	0.333357	+	0.942801i	$0.391818\pi$
$284$	−4.41723	+	1.18359i	−0.0155536	+	0.00416758i
$285$			543.639i			1.90750i
$286$	−245.168	+	98.1949i	−0.857232	+	0.343339i
$287$	321.330			1.11962
$288$	−0.386621	−	1.44289i	−0.00134244	−	0.00501004i
$289$	149.379	−	258.732i	0.516883	−	0.895267i
$290$	184.435	−	106.484i	0.635983	−	0.367185i
$291$	54.1677	−	54.1677i	0.186143	−	0.186143i
$292$	−104.302	−	27.9477i	−0.357200	−	0.0957114i
$293$	24.5565	−	91.6460i	0.0838105	−	0.312785i	−0.911276	−	0.411797i	$-0.864901\pi$
$293$	24.5565	−	91.6460i	0.0838105	−	0.312785i	0.995086	+	0.0990115i	$0.0315681\pi$
$294$	−90.1090	−	90.1090i	−0.306493	−	0.306493i
$295$	−127.979	−	221.667i	−0.433828	−	0.751412i
$296$	15.5688	+	8.98865i	0.0525973	+	0.0303671i
$297$	368.950	−	98.8597i	1.24225	−	0.332861i
$298$			267.473i			0.897559i
$299$	−50.5161	+	64.2571i	−0.168950	+	0.214907i
$300$	−127.357			−0.424524
$301$	−35.4962	−	132.474i	−0.117927	−	0.440111i
$302$	70.5995	−	122.282i	0.233773	−	0.404907i
$303$	400.164	−	231.035i	1.32067	−	0.762490i
$304$	74.5498	−	74.5498i	0.245230	−	0.245230i
$305$	151.019	+	40.4655i	0.495145	+	0.132674i
$306$	−2.34329	+	8.74526i	−0.00765780	+	0.0285793i
$307$	210.306	+	210.306i	0.685035	+	0.685035i	0.961130	−	0.276095i	$-0.0890406\pi$
$307$	210.306	+	210.306i	0.685035	+	0.685035i	−0.276095	+	0.961130i	$0.589041\pi$
$308$	−63.2639	−	109.576i	−0.205402	−	0.355767i
$309$	−45.7785	−	26.4302i	−0.148151	−	0.0855347i
$310$	−112.522	+	30.1501i	−0.362974	+	0.0972585i
$311$		−	246.623i		−	0.793001i	−0.918035	−	0.396500i	$-0.870225\pi$
$311$		−	246.623i		−	0.793001i	0.918035	−	0.396500i	$-0.129775\pi$
$312$	−13.3038	−	111.122i	−0.0426402	−	0.356159i
$313$	−118.526			−0.378679			−0.189339	−	0.981912i	$-0.560635\pi$
$313$	−118.526			−0.378679			−0.189339	+	0.981912i	$0.560635\pi$
$314$	64.7111	+	241.505i	0.206086	+	0.769125i
$315$	−3.94036	+	6.82490i	−0.0125091	+	0.0216664i
$316$	33.1339	−	19.1299i	0.104854	−	0.0605376i
$317$	−284.814	+	284.814i	−0.898466	+	0.898466i	−0.995300	−	0.0968348i	$-0.969128\pi$
$317$	−284.814	+	284.814i	−0.898466	+	0.898466i	0.0968348	+	0.995300i	$0.469128\pi$
$318$	140.372	+	37.6127i	0.441423	+	0.118279i
$319$	−82.6227	+	308.352i	−0.259005	+	0.966621i
$320$	38.3339	+	38.3339i	0.119793	+	0.119793i
$321$	−80.9512	−	140.212i	−0.252184	−	0.436796i
$322$	−33.9126	−	19.5795i	−0.105319	−	0.0608058i
$323$	−617.227	+	165.385i	−1.91092	+	0.512029i
$324$			166.614i			0.514240i
$325$	−269.217	−	38.6648i	−0.828360	−	0.118969i
$326$	171.470			0.525981
$327$	59.4666	+	221.933i	0.181855	+	0.678693i
$328$	103.187	−	178.724i	0.314593	−	0.544892i
$329$	41.2964	−	23.8425i	0.125521	−	0.0724695i
$330$	296.293	−	296.293i	0.897858	−	0.897858i
$331$	−433.118	−	116.054i	−1.30851	−	0.350615i	−0.463850	−	0.885914i	$-0.653532\pi$
$331$	−433.118	−	116.054i	−1.30851	−	0.350615i	−0.844663	+	0.535299i	$0.820199\pi$
$332$	−25.4549	+	94.9990i	−0.0766714	+	0.286141i
$333$	1.18680	+	1.18680i	0.00356398	+	0.00356398i
$334$	209.805	+	363.392i	0.628158	+	1.08800i
$335$	−631.591	−	364.649i	−1.88535	−	1.08850i
$336$	51.7902	−	13.8772i	0.154138	−	0.0413010i
$337$		−	474.455i		−	1.40788i	−0.710260	−	0.703939i	$-0.751423\pi$
$337$		−	474.455i		−	1.40788i	0.710260	−	0.703939i	$-0.248577\pi$
$338$	5.61338	−	238.936i	0.0166076	−	0.706912i
$339$	110.263			0.325259
$340$	−85.0420	−	317.381i	−0.250124	−	0.933474i
$341$	87.3078	−	151.222i	0.256035	−	0.443465i
$342$	8.52436	−	4.92154i	0.0249250	−	0.0143905i
$343$	244.782	−	244.782i	0.713650	−	0.713650i
$344$	−85.0807	−	22.7973i	−0.247328	−	0.0662712i
$345$	33.5643	−	125.264i	0.0972878	−	0.363083i
$346$	−278.490	−	278.490i	−0.804884	−	0.804884i
$347$	266.818	+	462.142i	0.768927	+	1.33182i	0.938145	+	0.346242i	$0.112543\pi$
$347$	266.818	+	462.142i	0.768927	+	1.33182i	−0.169218	+	0.985579i	$0.554124\pi$
$348$	−117.152	−	67.6380i	−0.336645	−	0.194362i
$349$	260.973	−	69.9275i	0.747774	−	0.200365i	0.135244	−	0.990812i	$-0.456818\pi$
$349$	260.973	−	69.9275i	0.747774	−	0.200365i	0.612531	+	0.790447i	$0.290152\pi$
$350$		−	130.302i		−	0.372291i
$351$	−49.1398	+	342.153i	−0.140000	+	0.974794i
$352$	−81.2621			−0.230858
$353$	−91.3587	−	340.955i	−0.258806	−	0.965879i	−0.965933	−	0.258792i	$-0.916676\pi$
$353$	−91.3587	−	340.955i	−0.258806	−	0.965879i	0.707127	−	0.707087i	$-0.249991\pi$
$354$	−81.2919	+	140.802i	−0.229638	+	0.397745i
$355$	13.4188	−	7.74736i	0.0377995	−	0.0218236i
$356$	−5.08321	+	5.08321i	−0.0142787	+	0.0142787i
$357$	−313.897	−	84.1085i	−0.879263	−	0.235598i
$358$	−28.8262	+	107.581i	−0.0805202	+	0.300505i
$359$	116.092	+	116.092i	0.323375	+	0.323375i	0.850060	−	0.526685i	$-0.176565\pi$
$359$	116.092	+	116.092i	0.323375	+	0.323375i	−0.526685	+	0.850060i	$0.676565\pi$
$360$	2.53068	+	4.38327i	0.00702967	+	0.0121758i
$361$	289.001	+	166.855i	0.800556	+	0.462201i
$362$	274.241	−	73.4826i	0.757572	−	0.202991i
$363$			259.810i			0.715731i
$364$	113.691	−	13.6114i	0.312338	−	0.0373938i
$365$	365.871			1.00239
$366$	−25.7035	−	95.9268i	−0.0702282	−	0.262095i
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.160497	+	0.987036i	$0.551310\pi$
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.774550	+	0.632513i	$0.782024\pi$
$368$	−21.7803	+	12.5748i	−0.0591855	+	0.0341708i
$369$	13.6241	−	13.6241i	0.0369217	−	0.0369217i
$370$	−58.8364	−	15.7652i	−0.159017	−	0.0426086i
$371$	−38.4824	+	143.618i	−0.103726	+	0.387111i
$372$	52.3222	+	52.3222i	0.140651	+	0.140651i
$373$	308.636	+	534.572i	0.827441	+	1.43317i	0.900039	+	0.435809i	$0.143538\pi$
$373$	308.636	+	534.572i	0.827441	+	1.43317i	−0.0725981	+	0.997361i	$0.523129\pi$
$374$	426.538	+	246.262i	1.14048	+	0.658455i
$375$	−81.2560	+	21.7725i	−0.216683	+	0.0580599i
$376$		−	30.6255i		−	0.0814508i
$377$	−227.111	−	178.545i	−0.602417	−	0.473594i
$378$	−165.603			−0.438103
$379$	−138.900	−	518.382i	−0.366491	−	1.36776i	−0.865389	−	0.501101i	$-0.832928\pi$
$379$	−138.900	−	518.382i	−0.366491	−	1.36776i	0.498898	−	0.866661i	$-0.333738\pi$
$380$	−178.612	+	309.364i	−0.470030	+	0.814116i
$381$	350.801	−	202.535i	0.920737	−	0.531588i
$382$	40.5301	−	40.5301i	0.106100	−	0.106100i
$383$	−253.061	−	67.8074i	−0.660732	−	0.177043i	−0.0871559	−	0.996195i	$-0.527778\pi$
$383$	−253.061	−	67.8074i	−0.660732	−	0.177043i	−0.573577	+	0.819152i	$0.694444\pi$
$384$	8.91255	−	33.2621i	0.0232098	−	0.0866200i
$385$	303.144	+	303.144i	0.787387	+	0.787387i
$386$	−102.596	−	177.702i	−0.265794	−	0.460369i
$387$	−7.12176	−	4.11175i	−0.0184025	−	0.0106247i
$388$	48.6215	−	13.0281i	0.125313	−	0.0335775i
$389$			184.591i			0.474527i	0.971445	+	0.237264i	$0.0762505\pi$
$389$			184.591i			0.474527i	−0.971445	+	0.237264i	$0.923749\pi$
$390$	140.989	+	352.014i	0.361510	+	0.902601i
$391$	152.431			0.389848
$392$	−21.6725	−	80.8828i	−0.0552869	−	0.206334i
$393$	−58.2469	+	100.887i	−0.148211	+	0.256709i
$394$	189.628	−	109.482i	0.481289	−	0.277872i
$395$	−91.6653	+	91.6653i	−0.232064	+	0.232064i
$396$	−7.32827	−	1.96360i	−0.0185057	−	0.00495860i
$397$	65.7046	−	245.213i	0.165503	−	0.617664i	−0.832473	−	0.554066i	$-0.813076\pi$
$397$	65.7046	−	245.213i	0.165503	−	0.617664i	0.997976	−	0.0635986i	$-0.0202578\pi$
$398$	−260.350	−	260.350i	−0.654147	−	0.654147i
$399$	176.651	+	305.968i	0.442734	+	0.766838i
$400$	−72.4741	−	41.8430i	−0.181185	−	0.104607i
$401$	−261.805	+	70.1504i	−0.652880	+	0.174939i	−0.570031	−	0.821623i	$-0.693069\pi$
$401$	−261.805	+	70.1504i	−0.652880	+	0.174939i	−0.0828492	+	0.996562i	$0.526402\pi$
$402$			463.248i			1.15236i
$403$	94.7178	+	126.487i	0.235032	+	0.313864i
$404$	303.624			0.751545
$405$	−146.112	−	545.296i	−0.360770	−	1.34641i
$406$	69.2019	−	119.861i	0.170448	−	0.295225i
$407$	79.0721	−	45.6523i	0.194280	−	0.112168i
$408$	−147.581	+	147.581i	−0.361718	+	0.361718i
$409$	152.496	+	40.8612i	0.372851	+	0.0999051i	0.440378	−	0.897812i	$-0.354844\pi$
$409$	152.496	+	40.8612i	0.372851	+	0.0999051i	−0.0675274	+	0.997717i	$0.521511\pi$
$410$	−180.979	+	675.422i	−0.441411	+	1.64737i
$411$	17.2935	+	17.2935i	0.0420766	+	0.0420766i
$412$	−17.3672	−	30.0809i	−0.0421534	−	0.0730119i
$413$	−144.057	−	83.1715i	−0.348807	−	0.201384i
$414$	−2.26802	+	0.607713i	−0.00547830	+	0.00146791i
$415$		−	333.237i		−	0.802980i
$416$	28.9382	−	67.6061i	0.0695629	−	0.162515i
$417$	−742.543			−1.78068
$418$	−138.588	−	517.218i	−0.331550	−	1.23736i
$419$	326.238	−	565.061i	0.778611	−	1.34859i	−0.154132	−	0.988050i	$-0.549258\pi$
$419$	326.238	−	565.061i	0.778611	−	1.34859i	0.932743	−	0.360543i	$-0.117409\pi$
$420$	−157.330	+	90.8347i	−0.374596	+	0.216273i
$421$	294.576	−	294.576i	0.699704	−	0.699704i	−0.264642	−	0.964347i	$-0.585254\pi$
$421$	294.576	−	294.576i	0.699704	−	0.699704i	0.964347	+	0.264642i	$0.0852538\pi$
$422$	−568.821	−	152.415i	−1.34792	−	0.361173i
$423$	0.740029	−	2.76183i	0.00174948	−	0.00652914i
$424$	67.5231	+	67.5231i	0.159253	+	0.159253i
$425$	253.607	+	439.261i	0.596723	+	1.03355i
$426$	−8.52359	−	4.92110i	−0.0200084	−	0.0115519i
$427$	98.1448	−	26.2978i	0.229847	−	0.0615874i
$428$		−	106.385i		−	0.248564i
$429$	−522.546	−	223.671i	−1.21806	−	0.521378i
$430$	298.445			0.694059
$431$	18.2792	+	68.2190i	0.0424112	+	0.158281i	0.983884	−	0.178808i	$-0.0572243\pi$
$431$	18.2792	+	68.2190i	0.0424112	+	0.158281i	−0.941473	+	0.337089i	$0.890558\pi$
$432$	−53.1790	+	92.1087i	−0.123100	+	0.213215i
$433$	404.363	−	233.459i	0.933864	−	0.539167i	0.0458326	−	0.998949i	$-0.485406\pi$
$433$	404.363	−	233.459i	0.933864	−	0.539167i	0.888032	+	0.459782i	$0.152073\pi$
$434$	−53.5320	+	53.5320i	−0.123346	+	0.123346i
$435$	442.734	+	118.630i	1.01778	+	0.272713i
$436$	−39.0753	+	145.831i	−0.0896223	+	0.334475i
$437$	−117.182	−	117.182i	−0.268150	−	0.268150i
$438$	−116.200	−	201.264i	−0.265297	−	0.459508i
$439$	103.577	+	59.8002i	0.235938	+	0.136219i	0.613309	−	0.789843i	$-0.289838\pi$
$439$	103.577	+	59.8002i	0.235938	+	0.136219i	−0.377370	+	0.926063i	$0.623172\pi$
$440$	265.956	−	71.2627i	0.604445	−	0.161961i
$441$		−	7.81775i		−	0.0177273i
$442$	−356.772	+	267.163i	−0.807177	+	0.604441i
$443$	−56.7213			−0.128039			−0.0640195	−	0.997949i	$-0.520392\pi$
$443$	−56.7213			−0.128039			−0.0640195	+	0.997949i	$0.520392\pi$
$444$	10.0140	+	37.3727i	0.0225540	+	0.0841727i
$445$	12.1787	−	21.0941i	0.0273679	−	0.0474025i
$446$	−250.218	+	144.463i	−0.561026	+	0.323909i
$447$	−407.052	+	407.052i	−0.910631	+	0.910631i
$448$	34.0312	+	9.11863i	0.0759625	+	0.0203541i
$449$	47.8299	−	178.504i	0.106525	−	0.397558i	−0.891988	−	0.452058i	$-0.850690\pi$
$449$	47.8299	−	178.504i	0.106525	−	0.397558i	0.998514	+	0.0545000i	$0.0173565\pi$
$450$	−5.52468	−	5.52468i	−0.0122771	−	0.0122771i
$451$	−524.072	−	907.720i	−1.16202	−	2.01268i
$452$	62.7464	+	36.2266i	0.138819	+	0.0801474i
$453$	293.536	−	78.6527i	0.647982	−	0.173626i
$454$		−	157.321i		−	0.346522i
$455$	−360.153	+	144.249i	−0.791546	+	0.317030i
$456$	226.907			0.497603
$457$	76.6418	+	286.031i	0.167706	+	0.625889i	0.997680	+	0.0680852i	$0.0216890\pi$
$457$	76.6418	+	286.031i	0.167706	+	0.625889i	−0.829973	+	0.557803i	$0.811644\pi$
$458$	212.309	−	367.730i	0.463557	−	0.802904i
$459$	558.265	−	322.314i	1.21626	−	0.702210i
$460$	60.2553	−	60.2553i	0.130990	−	0.130990i
$461$	596.206	+	159.753i	1.29329	+	0.346535i	0.838908	−	0.544273i	$-0.183194\pi$
$461$	596.206	+	159.753i	1.29329	+	0.346535i	0.454379	+	0.890808i	$0.349861\pi$
$462$	70.4804	−	263.036i	0.152555	−	0.569343i
$463$	198.699	+	198.699i	0.429156	+	0.429156i	0.888341	−	0.459185i	$-0.151858\pi$
$463$	198.699	+	198.699i	0.429156	+	0.429156i	−0.459185	+	0.888341i	$0.651858\pi$
$464$	−44.4447	−	76.9805i	−0.0957860	−	0.165906i
$465$	−217.125	−	125.357i	−0.466935	−	0.269585i
$466$	63.6330	−	17.0504i	0.136552	−	0.0365889i
$467$			522.015i			1.11781i	0.829233	+	0.558903i	$0.188777\pi$
$467$			522.015i			1.11781i	−0.829233	+	0.558903i	$0.811223\pi$
$468$	4.24329	−	5.39751i	0.00906685	−	0.0115331i
$469$	−473.959			−1.01057
$470$	26.8570	+	100.232i	0.0571425	+	0.213259i
$471$	−269.053	+	466.014i	−0.571239	+	0.989414i
$472$	−92.5203	+	53.4166i	−0.196018	+	0.113171i
$473$	−316.330	+	316.330i	−0.668773	+	0.668773i
$474$	79.5374	+	21.3120i	0.167801	+	0.0449620i
$475$	142.722	−	532.645i	0.300467	−	1.12136i
$476$	−150.993	−	150.993i	−0.317213	−	0.317213i
$477$	4.45766	+	7.72090i	0.00934520	+	0.0161864i
$478$	239.558	+	138.309i	0.501167	+	0.289349i
$479$	327.970	−	87.8794i	0.684698	−	0.183464i	0.100331	−	0.994954i	$-0.468010\pi$
$479$	327.970	−	87.8794i	0.684698	−	0.183464i	0.584367	+	0.811490i	$0.301343\pi$
$480$			116.677i			0.243076i
$481$	9.82218	+	82.0413i	0.0204203	+	0.170564i
$482$	−317.995			−0.659741
$483$	−21.8129	−	81.4067i	−0.0451612	−	0.168544i
$484$	−85.3603	+	147.848i	−0.176364	+	0.305472i
$485$	−147.704	+	85.2771i	−0.304545	+	0.175829i
$486$	−14.2551	+	14.2551i	−0.0293314	+	0.0293314i
$487$	208.431	+	55.8489i	0.427990	+	0.114679i	0.466382	−	0.884583i	$-0.345557\pi$
$487$	208.431	+	55.8489i	0.427990	+	0.114679i	−0.0383927	+	0.999263i	$0.512224\pi$
$488$	16.8897	−	63.0332i	0.0346100	−	0.129166i
$489$	260.951	+	260.951i	0.533642	+	0.533642i
$490$	141.860	+	245.709i	0.289510	+	0.501447i
$491$	−480.847	−	277.617i	−0.979322	−	0.565412i	−0.0772564	−	0.997011i	$-0.524616\pi$
$491$	−480.847	−	277.617i	−0.979322	−	0.565412i	−0.902065	+	0.431600i	$0.857949\pi$
$492$	429.025	−	114.957i	0.872003	−	0.233652i
$493$			538.753i			1.09280i
$494$	479.652	+	68.8874i	0.970956	+	0.139448i
$495$	25.7061			0.0519315
$496$	12.5842	+	46.9649i	0.0253714	+	0.0946874i
$497$	5.03488	−	8.72067i	0.0101305	−	0.0175466i
$498$	−183.312	+	105.835i	−0.368097	+	0.212521i
$499$	−401.619	+	401.619i	−0.804847	+	0.804847i	−0.983849	−	0.179002i	$-0.942713\pi$
$499$	−401.619	+	401.619i	−0.804847	+	0.804847i	0.179002	+	0.983849i	$0.442713\pi$
$500$	−53.3930	−	14.3066i	−0.106786	−	0.0286132i
$501$	−233.737	+	872.318i	−0.466541	+	1.74115i
$502$	3.49014	+	3.49014i	0.00695247	+	0.00695247i
$503$	196.833	+	340.925i	0.391319	+	0.677784i	0.992624	−	0.121236i	$-0.0386857\pi$
$503$	196.833	+	340.925i	0.391319	+	0.677784i	−0.601305	+	0.799020i	$0.705352\pi$
$504$	2.84861	+	1.64465i	0.00565201	+	0.00326319i
$505$	−993.706	+	266.263i	−1.96773	+	0.527253i
$506$			127.732i			0.252435i
$507$	372.167	−	355.081i	0.734057	−	0.700358i
$508$	266.170			0.523957
$509$	113.097	+	422.083i	0.222194	+	0.829239i	0.983509	+	0.180858i	$0.0578873\pi$
$509$	113.097	+	422.083i	0.222194	+	0.829239i	−0.761315	+	0.648382i	$0.775446\pi$
$510$	353.584	−	612.426i	0.693303	−	1.20084i
$511$	205.918	−	118.887i	0.402971	−	0.232655i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−676.948	−	181.388i	−1.31959	−	0.353582i
$514$	67.8659	−	253.279i	0.132035	−	0.492761i
$515$	83.2191	+	83.2191i	0.161591	+	0.161591i
$516$	−94.7857	−	164.174i	−0.183693	−	0.318166i
$517$	−134.704	−	77.7716i	−0.260550	−	0.150429i
$518$	−38.2368	+	10.2455i	−0.0738162	+	0.0197790i
$519$		−	847.638i		−	1.63321i
$520$	−35.4223	+	246.640i	−0.0681198	+	0.474307i
$521$	947.876			1.81934			0.909669	−	0.415333i	$-0.136335\pi$
$521$	947.876			1.81934			0.909669	+	0.415333i	$0.136335\pi$
$522$	−2.14791	−	8.01611i	−0.00411477	−	0.0153565i
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	−0.793258	−	0.608886i	$-0.791617\pi$
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	0.923940	+	0.382538i	$0.124950\pi$
$524$	−66.2923	+	38.2739i	−0.126512	+	0.0730417i
$525$	198.299	−	198.299i	0.377713	−	0.377713i
$526$	255.927	+	68.5754i	0.486553	+	0.130372i
$527$	76.2721	−	284.651i	0.144729	−	0.540135i
$528$	−123.668	−	123.668i	−0.234221	−	0.234221i
$529$	−244.734	−	423.892i	−0.462635	−	0.801308i
$530$	−280.205	−	161.776i	−0.528689	−	0.305239i
$531$	−9.63430	+	2.58150i	−0.0181437	+	0.00486159i
$532$			232.153i			0.436378i
$533$	941.806	−	112.755i	1.76699	−	0.211548i
$534$	−15.4717			−0.0289733
$535$	93.2946	+	348.180i	0.174382	+	0.650804i
$536$	−152.199	+	263.617i	−0.283954	+	0.491822i
$537$	−207.591	+	119.853i	−0.386575	+	0.223189i
$538$	344.012	−	344.012i	0.639427	−	0.639427i
$539$	−410.794	−	110.072i	−0.762141	−	0.204215i
$540$	93.2705	−	348.090i	0.172723	−	0.644612i
$541$	−394.763	−	394.763i	−0.729691	−	0.729691i	0.240867	−	0.970558i	$-0.422568\pi$
$541$	−394.763	−	394.763i	−0.729691	−	0.729691i	−0.970558	+	0.240867i	$0.922568\pi$
$542$	17.1517	+	29.7076i	0.0316452	+	0.0548110i
$543$	529.182	+	305.523i	0.974552	+	0.562658i
$544$	−132.470	+	35.4953i	−0.243511	+	0.0652487i
$545$		−	511.545i		−	0.938616i
$546$	193.735	+	152.306i	0.354825	+	0.278949i
$547$	−716.303			−1.30951			−0.654756	−	0.755840i	$-0.727229\pi$
$547$	−716.303			−1.30951			−0.654756	+	0.755840i	$0.727229\pi$
$548$	4.15932	+	15.5228i	0.00759000	+	0.0283263i
$549$	3.04625	−	5.27625i	0.00554872	−	0.00961066i
$550$	−368.087	+	212.515i	−0.669250	+	0.386392i
$551$	414.168	−	414.168i	0.751666	−	0.751666i
$552$	−52.2832	−	14.0092i	−0.0947159	−	0.0253791i
$553$	−21.8048	+	81.3765i	−0.0394300	+	0.147155i
$554$	−494.891	−	494.891i	−0.893306	−	0.893306i
$555$	−65.5478	−	113.532i	−0.118104	−	0.204562i
$556$	−422.553	−	243.961i	−0.759988	−	0.438779i
$557$	−58.2268	+	15.6018i	−0.104536	+	0.0280104i	−0.310708	−	0.950505i	$-0.600566\pi$
$557$	−58.2268	+	15.6018i	−0.104536	+	0.0280104i	0.206172	+	0.978516i	$0.433899\pi$
$558$			4.53941i			0.00813515i
$559$	−150.523	−	375.819i	−0.269272	−	0.672306i
$560$	−119.374			−0.213169
$561$	274.353	+	1023.90i	0.489043	+	1.82513i
$562$	−145.653	+	252.278i	−0.259168	+	0.448893i
$563$	−233.194	+	134.635i	−0.414199	+	0.239138i	−0.692592	−	0.721329i	$-0.743531\pi$
$563$	−233.194	+	134.635i	−0.414199	+	0.239138i	0.278393	+	0.960467i	$0.410198\pi$
$564$	46.6073	−	46.6073i	0.0826370	−	0.0826370i
$565$	−237.126	−	63.5378i	−0.419693	−	0.112456i
$566$	−157.469	+	587.684i	−0.278215	+	1.03831i
$567$	−259.423	−	259.423i	−0.457537	−	0.457537i
$568$	−3.23364	−	5.60082i	−0.00569302	−	0.00986060i
$569$	232.943	+	134.490i	0.409390	+	0.236361i	0.690528	−	0.723306i	$-0.257378\pi$
$569$	232.943	+	134.490i	0.409390	+	0.236361i	−0.281138	+	0.959667i	$0.590712\pi$
$570$	−742.624	+	198.986i	−1.30285	+	0.349097i
$571$		−	328.719i		−	0.575689i	−0.957677	−	0.287845i	$-0.907061\pi$
$571$		−	328.719i		−	0.575689i	0.957677	−	0.287845i	$-0.0929387\pi$
$572$	−223.875	−	298.964i	−0.391389	−	0.522665i
$573$	123.361			0.215290
$574$	117.615	+	438.945i	0.204904	+	0.764713i
$575$	−65.7711	+	113.919i	−0.114384	+	0.198120i
$576$	1.82951	−	1.05627i	0.00317624	−	0.00183380i
$577$	−18.1490	+	18.1490i	−0.0314540	+	0.0314540i	−0.722659	−	0.691205i	$-0.757080\pi$
$577$	−18.1490	+	18.1490i	−0.0314540	+	0.0314540i	0.691205	+	0.722659i	$0.257080\pi$
$578$	408.111	+	109.353i	0.706075	+	0.189192i
$579$	114.300	−	426.572i	0.197409	−	0.736739i
$580$	212.967	+	212.967i	0.367185	+	0.367185i
$581$	−108.283	−	187.551i	−0.186373	−	0.322807i
$582$	93.8212	+	54.1677i	0.161205	+	0.0930716i
$583$	468.467	−	125.525i	0.803546	−	0.215309i
$584$		−	152.709i		−	0.261488i
$585$	−9.15417	+	21.3862i	−0.0156481	+	0.0365576i
$586$	134.179			0.228975
$587$	−30.1430	−	112.495i	−0.0513509	−	0.191644i	0.935486	−	0.353364i	$-0.114962\pi$
$587$	−30.1430	−	112.495i	−0.0513509	−	0.191644i	−0.986837	+	0.161720i	$0.948296\pi$
$588$	90.1090	−	156.073i	0.153247	−	0.265431i
$589$	−277.461	+	160.192i	−0.471072	+	0.271973i
$590$	255.958	−	255.958i	0.433828	−	0.433828i
$591$	455.199	+	121.970i	0.770218	+	0.206379i
$592$	−6.58015	+	24.5574i	−0.0111151	+	0.0414822i
$593$	215.404	+	215.404i	0.363244	+	0.363244i	0.865006	−	0.501762i	$-0.167315\pi$
$593$	215.404	+	215.404i	0.363244	+	0.363244i	−0.501762	+	0.865006i	$0.667315\pi$
$594$	270.090	+	467.809i	0.454697	+	0.787558i
$595$	626.587	+	361.760i	1.05309	+	0.608000i
$596$	−365.374	+	97.9017i	−0.613044	+	0.164265i
$597$		−	792.427i		−	1.32735i
$598$	−106.267	−	45.4866i	−0.177704	−	0.0760646i
$599$	−657.704			−1.09800			−0.549002	−	0.835821i	$-0.684992\pi$
$599$	−657.704			−1.09800			−0.549002	+	0.835821i	$0.684992\pi$
$600$	−46.6159	−	173.973i	−0.0776932	−	0.289955i
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	−0.963211	−	0.268747i	$-0.913390\pi$
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	0.714347	+	0.699791i	$0.246724\pi$
$602$	167.970	−	96.9774i	0.279019	−	0.161092i
$603$	−20.0954	+	20.0954i	−0.0333257	+	0.0333257i
$604$	192.881	+	51.6824i	0.319340	+	0.0855669i
$605$	149.713	−	558.737i	0.247460	−	0.923532i
$606$	462.069	+	462.069i	0.762490	+	0.762490i
$607$	355.980	+	616.576i	0.586459	+	1.01578i	0.994692	+	0.102898i	$0.0328116\pi$
$607$	355.980	+	616.576i	0.586459	+	1.01578i	−0.408233	+	0.912878i	$0.633855\pi$
$608$	129.124	+	74.5498i	0.212375	+	0.122615i
$609$	287.725	−	77.0957i	0.472455	−	0.126594i
$610$			221.107i			0.362471i
$611$	112.672	−	84.3723i	0.184405	−	0.138089i
$612$	−12.8040			−0.0209215
$613$	189.142	+	705.887i	0.308551	+	1.15153i	0.929845	+	0.367951i	$0.119941\pi$
$613$	189.142	+	705.887i	0.308551	+	1.15153i	−0.621294	+	0.783578i	$0.713393\pi$
$614$	−210.306	+	364.260i	−0.342517	+	0.593257i
$615$	−1303.31	+	752.466i	−2.11920	+	1.22352i
$616$	126.528	−	126.528i	0.205402	−	0.205402i
$617$	338.746	+	90.7668i	0.549021	+	0.147110i	0.522658	−	0.852543i	$-0.324941\pi$
$617$	338.746	+	90.7668i	0.549021	+	0.147110i	0.0263636	+	0.999652i	$0.491607\pi$
$618$	19.3483	−	72.2087i	0.0313079	−	0.116843i
$619$	283.795	+	283.795i	0.458474	+	0.458474i	0.898154	−	0.439680i	$-0.144908\pi$
$619$	283.795	+	283.795i	0.458474	+	0.458474i	−0.439680	+	0.898154i	$0.644908\pi$
$620$	−82.3717	−	142.672i	−0.132858	−	0.230116i
$621$	144.782	+	83.5897i	0.233143	+	0.134605i
$622$	336.894	−	90.2704i	0.541630	−	0.145129i
$623$		−	15.8295i		−	0.0254084i
$624$	146.926	−	58.8466i	0.235458	−	0.0943055i
$625$	710.329			1.13653
$626$	−43.3837	−	161.910i	−0.0693030	−	0.258642i
$627$	576.216	−	998.036i	0.919005	−	1.59176i
$628$	−306.216	+	176.794i	−0.487606	+	0.281519i
$629$	108.959	−	108.959i	0.173226	−	0.173226i
$630$	−10.7653	−	2.88454i	−0.0170877	−	0.00457864i
$631$	−298.859	+	1115.36i	−0.473627	+	1.76760i	0.152944	+	0.988235i	$0.451125\pi$
$631$	−298.859	+	1115.36i	−0.473627	+	1.76760i	−0.626570	+	0.779365i	$0.715542\pi$
$632$	38.2597	+	38.2597i	0.0605376	+	0.0605376i
$633$	−633.706	−	1097.61i	−1.00112	−	1.73398i
$634$	−493.312	−	284.814i	−0.778094	−	0.449233i
$635$	−871.126	+	233.417i	−1.37185	+	0.367587i
$636$			205.520i			0.323144i
$637$	237.862	−	302.563i	0.373410	−	0.474981i
$638$	−451.459			−0.707615
$639$	−0.156274	−	0.583223i	−0.000244560	−	0.000912712i
$640$	−38.3339	+	66.3963i	−0.0598967	+	0.103744i
$641$	225.174	−	130.005i	0.351286	−	0.202815i	−0.313965	−	0.949434i	$-0.601658\pi$
$641$	225.174	−	130.005i	0.351286	−	0.202815i	0.665252	+	0.746619i	$0.268324\pi$
$642$	161.902	−	161.902i	0.252184	−	0.252184i
$643$	11.9154	+	3.19272i	0.0185309	+	0.00496535i	0.268073	−	0.963399i	$-0.413613\pi$
$643$	11.9154	+	3.19272i	0.0185309	+	0.00496535i	−0.249542	+	0.968364i	$0.580280\pi$
$644$	14.3332	−	53.4921i	0.0222565	−	0.0830622i
$645$	454.188	+	454.188i	0.704168	+	0.704168i
$646$	−451.841	−	782.612i	−0.699445	−	1.21147i
$647$	822.864	+	475.081i	1.27182	+	0.734283i	0.975329	−	0.220755i	$-0.0708520\pi$
$647$	822.864	+	475.081i	1.27182	+	0.734283i	0.296486	+	0.955037i	$0.404185\pi$
$648$	−227.599	+	60.9849i	−0.351232	+	0.0941124i
$649$			542.593i			0.836045i
$650$	−45.7231	−	381.909i	−0.0703432	−	0.587553i
$651$	−162.935			−0.250284
$652$	62.7624	+	234.232i	0.0962613	+	0.359252i
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	−0.997147	−	0.0754792i	$-0.975951\pi$
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	0.563941	+	0.825815i	$0.309285\pi$
$654$	−281.399	+	162.466i	−0.430274	+	0.248419i
$655$	183.398	−	183.398i	0.279997	−	0.279997i
$656$	281.911	+	75.5378i	0.429742	+	0.115149i
$657$	3.69004	−	13.7714i	0.00561650	−	0.0209611i
$658$	47.6849	+	47.6849i	0.0724695	+	0.0724695i
$659$	−190.174	−	329.390i	−0.288579	−	0.499833i	0.684892	−	0.728645i	$-0.259849\pi$
$659$	−190.174	−	329.390i	−0.288579	−	0.499833i	−0.973471	+	0.228811i	$0.926516\pi$
$660$	513.195	+	296.293i	0.777568	+	0.448929i
$661$	−960.224	+	257.291i	−1.45268	+	0.389245i	−0.896956	−	0.442119i	$-0.854227\pi$
$661$	−960.224	+	257.291i	−1.45268	+	0.389245i	−0.555728	+	0.831364i	$0.687560\pi$
$662$		−	634.128i		−	0.957898i
$663$	−949.533	−	136.372i	−1.43218	−	0.205689i
$664$	−139.088			−0.209470
$665$	−203.586	−	759.795i	−0.306145	−	1.14255i
$666$	−1.18680	+	2.05561i	−0.00178199	+	0.00308650i
$667$	−121.002	+	69.8606i	−0.181413	+	0.104739i
$668$	−419.609	+	419.609i	−0.628158	+	0.628158i
$669$	−600.644	−	160.942i	−0.897823	−	0.240571i
$670$	266.942	−	996.240i	0.398420	−	1.48693i
$671$	−234.357	−	234.357i	−0.349266	−	0.349266i
$672$	37.9131	+	65.6674i	0.0564183	+	0.0977193i
$673$	−548.632	−	316.753i	−0.815204	−	0.470658i	0.0335560	−	0.999437i	$-0.489317\pi$
$673$	−548.632	−	316.753i	−0.815204	−	0.470658i	−0.848760	+	0.528779i	$0.822650\pi$
$674$	648.117	−	173.663i	0.961599	−	0.257660i
$675$			556.292i			0.824136i
$676$	328.448	−	79.7887i	0.485869	−	0.118031i
$677$	−221.745			−0.327540			−0.163770	−	0.986499i	$-0.552366\pi$
$677$	−221.745			−0.327540			−0.163770	+	0.986499i	$0.552366\pi$
$678$	40.3590	+	150.622i	0.0595265	+	0.222156i
$679$	−55.4201	+	95.9905i	−0.0816202	+	0.141370i
$680$	402.423	−	232.339i	0.591799	−	0.341675i
$681$	239.418	−	239.418i	0.351569	−	0.351569i
$682$	238.529	+	63.9137i	0.349750	+	0.0937152i
$683$	173.007	−	645.671i	0.253304	−	0.945345i	−0.715722	−	0.698386i	$-0.753902\pi$
$683$	173.007	−	645.671i	0.253304	−	0.945345i	0.969026	−	0.246959i	$-0.0794313\pi$
$684$	9.84309	+	9.84309i	0.0143905	+	0.0143905i
$685$	−27.2254	−	47.1558i	−0.0397451	−	0.0688405i
$686$	423.975	+	244.782i	0.618039	+	0.356825i
$687$	882.731	−	236.527i	1.28491	−	0.344290i
$688$		−	124.567i		−	0.181056i
$689$	−62.3944	+	434.443i	−0.0905580	+	0.630541i
$690$	183.399			0.265795
$691$	−146.869	−	548.121i	−0.212545	−	0.793229i	−0.987016	−	0.160620i	$-0.948651\pi$
$691$	−146.869	−	548.121i	−0.212545	−	0.793229i	0.774471	−	0.632609i	$-0.218016\pi$
$692$	278.490	−	482.359i	0.402442	−	0.697050i
$693$	14.4678	−	8.35297i	0.0208770	−	0.0120534i
$694$	−533.636	+	533.636i	−0.768927	+	0.768927i
$695$	1596.88	+	427.883i	2.29767	+	0.615659i
$696$	49.5145	−	184.790i	0.0711415	−	0.265504i
$697$	−1250.81	−	1250.81i	−1.79457	−	1.79457i
$698$	191.046	+	330.901i	0.273704	+	0.474070i
$699$	122.788	+	70.8916i	0.175662	+	0.101419i
$700$	177.996	−	47.6938i	0.254280	−	0.0681340i
$701$		−	597.453i		−	0.852287i	−0.904656	−	0.426143i	$-0.859872\pi$
$701$		−	597.453i		−	0.852287i	0.904656	−	0.426143i	$-0.140128\pi$
$702$	−485.376	+	58.1103i	−0.691418	+	0.0827783i
$703$	−167.526			−0.238301
$704$	−29.7440	−	111.006i	−0.0422500	−	0.157679i
$705$	−111.665	+	193.409i	−0.158390	+	0.274339i
$706$	432.314	−	249.596i	0.612342	−	0.353536i
$707$	−472.753	+	472.753i	−0.668675	+	0.668675i
$708$	−222.094	−	59.5098i	−0.313692	−	0.0840534i
$709$	−10.2632	+	38.3029i	−0.0144757	+	0.0540239i	−0.972786	−	0.231706i	$-0.925569\pi$
$709$	−10.2632	+	38.3029i	−0.0144757	+	0.0540239i	0.958310	+	0.285730i	$0.0922360\pi$
$710$	15.4947	+	15.4947i	0.0218236	+	0.0218236i
$711$	2.52579	+	4.37479i	0.00355244	+	0.00615301i
$712$	−8.80437	−	5.08321i	−0.0123657	−	0.00713934i
$713$	73.8221	−	19.7806i	0.103537	−	0.0277427i
$714$		−	459.577i		−	0.643666i
$715$	994.877	+	782.129i	1.39144	+	1.09389i
$716$	−157.509			−0.219985
$717$	154.085	+	575.055i	0.214903	+	0.802029i
$718$	−116.092	+	201.077i	−0.161688	+	0.280051i
$719$	−864.778	+	499.280i	−1.20275	+	0.694409i	−0.961166	−	0.275971i	$-0.911001\pi$
$719$	−864.778	+	499.280i	−1.20275	+	0.694409i	−0.241585	+	0.970380i	$0.577667\pi$
$720$	−5.06137	+	5.06137i	−0.00702967	+	0.00702967i
$721$	73.8783	+	19.7956i	0.102466	+	0.0274558i
$722$	−122.146	+	455.855i	−0.169177	+	0.631379i
$723$	−483.940	−	483.940i	−0.669350	−	0.669350i
$724$	200.758	+	347.724i	0.277290	+	0.480281i
$725$	−402.636	−	232.462i	−0.555360	−	0.320638i
$726$	−354.908	+	95.0972i	−0.488854	+	0.130988i
$727$			685.178i			0.942473i	0.882007	+	0.471237i	$0.156192\pi$
$727$			685.178i			0.942473i	−0.882007	+	0.471237i	$0.843808\pi$
$728$	60.2073	+	150.323i	0.0827023	+	0.206487i
$729$	706.374			0.968963
$730$	133.918	+	499.789i	0.183450	+	0.684643i
$731$	−377.495	+	653.841i	−0.516409	+	0.894447i
$732$	121.630	−	70.2233i	0.166162	−	0.0959334i
$733$	176.253	−	176.253i	0.240454	−	0.240454i	−0.576584	−	0.817038i	$-0.695615\pi$
$733$	176.253	−	176.253i	0.240454	−	0.240454i	0.817038	+	0.576584i	$0.195615\pi$
$734$	−937.537	−	251.212i	−1.27730	−	0.342251i
$735$	−158.042	+	589.820i	−0.215023	+	0.802477i
$736$	−25.1497	−	25.1497i	−0.0341708	−	0.0341708i
$737$	773.001	+	1338.88i	1.04885	+	1.81666i
$738$	23.5976	+	13.6241i	0.0319751	+	0.0184608i
$739$	1337.69	−	358.434i	1.81014	−	0.485026i	0.814655	−	0.579946i	$-0.196926\pi$
$739$	1337.69	−	358.434i	1.81014	−	0.485026i	0.995485	+	0.0949200i	$0.0302595\pi$
$740$		−	86.1425i		−	0.116409i
$741$	625.121	+	834.793i	0.843618	+	1.12658i
$742$	−210.272			−0.283385
$743$	−150.945	−	563.335i	−0.203156	−	0.758190i	−0.990004	−	0.141042i	$-0.954955\pi$
$743$	−150.945	−	563.335i	−0.203156	−	0.758190i	0.786847	−	0.617148i	$-0.211712\pi$
$744$	−52.3222	+	90.6247i	−0.0703255	+	0.121807i
$745$	1109.95	−	640.829i	1.48986	−	0.860173i
$746$	−617.271	+	617.271i	−0.827441	+	0.827441i
$747$	−12.5431	−	3.36090i	−0.0167912	−	0.00449920i
$748$	−180.276	+	672.800i	−0.241011	+	0.899466i
$749$	165.646	+	165.646i	0.221156	+	0.221156i
$750$	−59.4835	−	103.028i	−0.0793113	−	0.137371i
$751$	−1012.32	−	584.461i	−1.34796	−	0.778244i	−0.359998	−	0.932953i	$-0.617223\pi$
$751$	−1012.32	−	584.461i	−1.34796	−	0.778244i	−0.987960	+	0.154709i	$0.950556\pi$
$752$	41.8352	−	11.2097i	0.0556319	−	0.0149065i
$753$			10.6229i			0.0141075i
$754$	160.769	−	375.591i	0.213221	−	0.498132i
$755$	−676.588			−0.896143
$756$	−60.6149	−	226.218i	−0.0801785	−	0.299230i
$757$	561.343	−	972.275i	0.741537	−	1.28438i	−0.210259	−	0.977646i	$-0.567431\pi$
$757$	561.343	−	972.275i	0.741537	−	1.28438i	0.951796	−	0.306733i	$-0.0992360\pi$
$758$	657.282	−	379.482i	0.867126	−	0.500636i
$759$	−194.389	+	194.389i	−0.256112	+	0.256112i
$760$	−487.976	−	130.753i	−0.642073	−	0.172043i
$761$	246.221	−	918.907i	0.323549	−	1.20750i	−0.592214	−	0.805781i	$-0.701746\pi$
$761$	246.221	−	918.907i	0.323549	−	1.20750i	0.915763	−	0.401719i	$-0.131587\pi$
$762$	405.070	+	405.070i	0.531588	+	0.531588i
$763$	−166.222	−	287.906i	−0.217854	−	0.377334i
$764$	70.2001	+

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)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.52185 + 2.63592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.79174 - 4.79174i) q^{5} +(-4.15776 - 1.11407i) q^{6} +(1.13983 - 4.25390i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.52185 + 2.63592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.79174 - 4.79174i) q^{5} +(-4.15776 - 1.11407i) q^{6} +(1.13983 - 4.25390i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.132034 - 0.228689i) q^{9} +(8.29953 + 4.79174i) q^{10} +(-13.8758 + 3.71800i) q^{11} -6.08739i q^{12} +(1.84809 - 12.8680i) q^{13} +6.22814 q^{14} +(5.33833 + 19.9229i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-20.9957 + 12.1219i) q^{17} +(0.264067 - 0.264067i) q^{18} +(25.4592 + 6.82178i) q^{19} +(-3.50779 + 13.0913i) q^{20} +(9.47827 + 9.47827i) q^{21} +(-10.1578 - 17.5938i) q^{22} +(-5.44507 - 3.14371i) q^{23} +(8.31552 - 2.22814i) q^{24} -20.9215i q^{25} +(18.2544 - 2.18546i) q^{26} -26.5895 q^{27} +(2.27966 + 8.50779i) q^{28} +(11.1112 - 19.2451i) q^{29} +(-25.2612 + 14.5846i) q^{30} +(-8.59518 + 8.59518i) q^{31} +(5.46410 + 1.46410i) q^{32} +(11.3164 - 42.2336i) q^{33} +(-24.2437 - 24.2437i) q^{34} +(-14.9218 - 25.8453i) q^{35} +(0.457378 + 0.264067i) q^{36} +(-6.13936 + 1.64504i) q^{37} +37.2749i q^{38} +(31.1064 + 24.4545i) q^{39} -19.1669 q^{40} +(18.8845 + 70.4778i) q^{41} +(-9.47827 + 16.4168i) q^{42} +(26.9695 - 15.5708i) q^{43} +(20.3155 - 20.3155i) q^{44} +(-1.72849 - 0.463147i) q^{45} +(2.30136 - 8.58878i) q^{46} +(7.65637 + 7.65637i) q^{47} +(6.08739 + 10.5437i) q^{48} +(25.6388 + 14.8026i) q^{49} +(28.5793 - 7.65779i) q^{50} -73.7905i q^{51} +(9.66698 + 24.1361i) q^{52} -33.7616 q^{53} +(-9.73243 - 36.3219i) q^{54} +(-48.6733 + 84.3047i) q^{55} +(-10.7875 + 6.22814i) q^{56} +(-56.7267 + 56.7267i) q^{57} +(30.3563 + 8.13394i) q^{58} +(9.77592 - 36.4842i) q^{59} +(-29.1692 - 29.1692i) q^{60} +(11.5359 + 19.9807i) q^{61} +(-14.8873 - 8.59518i) q^{62} +(-1.12332 + 0.300991i) q^{63} +8.00000i q^{64} +(-52.8043 - 70.5155i) q^{65} +61.8342 q^{66} +(-27.8544 - 103.954i) q^{67} +(24.2437 - 41.9914i) q^{68} +(16.5731 - 9.56849i) q^{69} +(29.8436 - 29.8436i) q^{70} +(2.20861 + 0.591796i) q^{71} +(-0.193311 + 0.721445i) q^{72} +(38.1773 + 38.1773i) q^{73} +(-4.49432 - 7.78440i) q^{74} +(55.1473 + 31.8393i) q^{75} +(-50.9185 + 13.6436i) q^{76} +63.2639i q^{77} +(-22.0197 + 51.4430i) q^{78} -19.1299 q^{79} +(-7.01559 - 26.1825i) q^{80} +(41.6534 - 72.1459i) q^{81} +(-89.3622 + 51.5933i) q^{82} +(34.7720 - 34.7720i) q^{83} +(-25.8951 - 6.93858i) q^{84} +(-42.5210 + 158.691i) q^{85} +(31.1417 + 31.1417i) q^{86} +(33.8190 + 58.5762i) q^{87} +(35.1875 + 20.3155i) q^{88} +(3.47190 - 0.930292i) q^{89} -2.53068i q^{90} +(-52.6325 - 22.5289i) q^{91} +12.5748 q^{92} +(-9.57562 - 35.7367i) q^{93} +(-7.65637 + 13.2612i) q^{94} +(154.682 - 89.3058i) q^{95} +(-12.1748 + 12.1748i) q^{96} +(-24.3107 - 6.51404i) q^{97} +(-10.8362 + 40.4414i) q^{98} +(2.68233 + 2.68233i) 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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