LMFDB - Embedded newform 26.3.f.b.19.2

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			19.2
Root			$-3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.3.f.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(2.38787 - 4.13592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.88981 + 5.88981i) q^{5} +(6.52379 + 1.74804i) q^{6} +(0.0922225 - 0.344179i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(2.38787 - 4.13592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.88981 + 5.88981i) q^{5} +(6.52379 + 1.74804i) q^{6} +(0.0922225 - 0.344179i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +(-10.2015 - 5.88981i) q^{10} +(0.715507 - 0.191720i) q^{11} +9.55149i q^{12} +(11.4820 - 6.09614i) q^{13} +0.503913 q^{14} +(10.2956 + 38.4239i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-2.49470 + 1.44031i) q^{17} +(13.8077 - 13.8077i) q^{18} +(-10.4951 - 2.81216i) q^{19} +(4.31164 - 16.0913i) q^{20} +(-1.20328 - 1.20328i) q^{21} +(0.523787 + 0.907226i) q^{22} +(19.8278 + 11.4476i) q^{23} +(-13.0476 + 3.49609i) q^{24} -44.3798i q^{25} +(12.5302 + 13.4534i) q^{26} -22.9605 q^{27} +(0.184445 + 0.688358i) q^{28} +(-15.2092 + 26.3432i) q^{29} +(-48.7195 + 28.1282i) q^{30} +(14.8631 - 14.8631i) q^{31} +(5.46410 + 1.46410i) q^{32} +(0.915603 - 3.41708i) q^{33} +(-2.88063 - 2.88063i) q^{34} +(1.48398 + 2.57032i) q^{35} +(23.9157 + 13.8077i) q^{36} +(-40.2792 + 10.7928i) q^{37} -15.3659i q^{38} +(2.20453 - 62.0455i) q^{39} +23.5593 q^{40} +(-6.66907 - 24.8893i) q^{41} +(1.20328 - 2.08414i) q^{42} +(-25.3907 + 14.6593i) q^{43} +(-1.04757 + 1.04757i) q^{44} +(111.092 + 29.7670i) q^{45} +(-8.38019 + 31.2753i) q^{46} +(21.2000 + 21.2000i) q^{47} +(-9.55149 - 16.5437i) q^{48} +(42.3253 + 24.4365i) q^{49} +(60.6239 - 16.2441i) q^{50} +13.7571i q^{51} +(-13.7913 + 22.0409i) q^{52} -85.8410 q^{53} +(-8.40412 - 31.3646i) q^{54} +(-3.08501 + 5.34339i) q^{55} +(-0.872803 + 0.503913i) q^{56} +(-36.6919 + 36.6919i) q^{57} +(-41.5524 - 11.1339i) q^{58} +(25.9010 - 96.6638i) q^{59} +(-56.2565 - 56.2565i) q^{60} +(-7.73202 - 13.3923i) q^{61} +(25.7437 + 14.8631i) q^{62} +(-4.75233 + 1.27338i) q^{63} +8.00000i q^{64} +(-31.7219 + 103.532i) q^{65} +5.00295 q^{66} +(18.0146 + 67.2315i) q^{67} +(2.88063 - 4.98939i) q^{68} +(94.6923 - 54.6706i) q^{69} +(-2.96795 + 2.96795i) q^{70} +(-94.2060 - 25.2424i) q^{71} +(-10.1080 + 37.7234i) q^{72} +(50.9541 + 50.9541i) q^{73} +(-29.4864 - 51.0720i) q^{74} +(-183.551 - 105.973i) q^{75} +(20.9903 - 5.62432i) q^{76} -0.263943i q^{77} +(85.5627 - 19.6988i) q^{78} +105.981 q^{79} +(8.62328 + 32.1825i) q^{80} +(7.30809 - 12.6580i) q^{81} +(31.5584 - 18.2202i) q^{82} +(-27.2221 + 27.2221i) q^{83} +(3.28742 + 0.880862i) q^{84} +(6.21012 - 23.1765i) q^{85} +(-29.3186 - 29.3186i) q^{86} +(72.6355 + 125.808i) q^{87} +(-1.81445 - 1.04757i) q^{88} +(82.1525 - 22.0127i) q^{89} +162.650i q^{90} +(-1.03926 - 4.51407i) q^{91} -45.7902 q^{92} +(-25.9814 - 96.9639i) q^{93} +(-21.2000 + 36.7195i) q^{94} +(78.3775 - 45.2513i) q^{95} +(19.1030 - 19.1030i) q^{96} +(-19.6341 - 5.26095i) q^{97} +(-17.8888 + 66.7618i) q^{98} +(-7.23232 - 7.23232i) 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
$3$	2.38787	−	4.13592i	0.795957	−	1.37864i	−0.126272	−	0.991996i	$-0.540301\pi$
$3$	2.38787	−	4.13592i	0.795957	−	1.37864i	0.922230	−	0.386643i	$-0.126365\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−5.88981	+	5.88981i	−1.17796	+	1.17796i	−0.197700	+	0.980263i	$0.563347\pi$
$5$	−5.88981	+	5.88981i	−1.17796	+	1.17796i	−0.980263	+	0.197700i	$0.936653\pi$
$6$	6.52379	+	1.74804i	1.08730	+	0.291341i
$7$	0.0922225	−	0.344179i	0.0131746	−	0.0491684i	−0.959026	−	0.283319i	$-0.908564\pi$
$7$	0.0922225	−	0.344179i	0.0131746	−	0.0491684i	0.972200	+	0.234151i	$0.0752310\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−6.90386	−	11.9578i	−0.767096	−	1.32865i
$10$	−10.2015	−	5.88981i	−1.02015	−	0.588981i
$11$	0.715507	−	0.191720i	0.0650461	−	0.0174290i	−0.226149	−	0.974093i	$-0.572614\pi$
$11$	0.715507	−	0.191720i	0.0650461	−	0.0174290i	0.291195	+	0.956664i	$0.405947\pi$
$12$			9.55149i			0.795957i
$13$	11.4820	−	6.09614i	0.883233	−	0.468933i
$13$	11.4820	−	6.09614i	0.883233	−	0.468933i
$14$	0.503913			0.0359938
$15$	10.2956	+	38.4239i	0.686377	+	2.56159i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−2.49470	+	1.44031i	−0.146747	+	0.0847244i	−0.571576	−	0.820549i	$-0.693668\pi$
$17$	−2.49470	+	1.44031i	−0.146747	+	0.0847244i	0.424829	+	0.905274i	$0.360334\pi$
$18$	13.8077	−	13.8077i	0.767096	−	0.767096i
$19$	−10.4951	−	2.81216i	−0.552375	−	0.148009i	−0.0281743	−	0.999603i	$-0.508969\pi$
$19$	−10.4951	−	2.81216i	−0.552375	−	0.148009i	−0.524201	+	0.851594i	$0.675636\pi$
$20$	4.31164	−	16.0913i	0.215582	−	0.804563i
$21$	−1.20328	−	1.20328i	−0.0572990	−	0.0572990i
$22$	0.523787	+	0.907226i	0.0238085	+	0.0412376i
$23$	19.8278	+	11.4476i	0.862076	+	0.497720i	0.864707	−	0.502277i	$-0.167504\pi$
$23$	19.8278	+	11.4476i	0.862076	+	0.497720i	−0.00263083	+	0.999997i	$0.500837\pi$
$24$	−13.0476	+	3.49609i	−0.543649	+	0.145670i
$25$		−	44.3798i		−	1.77519i
$26$	12.5302	+	13.4534i	0.481930	+	0.517439i
$27$	−22.9605			−0.850388
$28$	0.184445	+	0.688358i	0.00658732	+	0.0245842i
$29$	−15.2092	+	26.3432i	−0.524457	+	0.908386i	0.475138	+	0.879911i	$0.342398\pi$
$29$	−15.2092	+	26.3432i	−0.524457	+	0.908386i	−0.999595	+	0.0284745i	$0.990935\pi$
$30$	−48.7195	+	28.1282i	−1.62398	+	0.937608i
$31$	14.8631	−	14.8631i	0.479456	−	0.479456i	−0.425502	−	0.904958i	$-0.639902\pi$
$31$	14.8631	−	14.8631i	0.479456	−	0.479456i	0.904958	+	0.425502i	$0.139902\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	0.915603	−	3.41708i	0.0277456	−	0.103548i
$34$	−2.88063	−	2.88063i	−0.0847244	−	0.0847244i
$35$	1.48398	+	2.57032i	0.0423993	+	0.0734378i
$36$	23.9157	+	13.8077i	0.664325	+	0.383548i
$37$	−40.2792	+	10.7928i	−1.08863	+	0.291697i	−0.758126	−	0.652108i	$-0.773885\pi$
$37$	−40.2792	+	10.7928i	−1.08863	+	0.291697i	−0.330502	+	0.943805i	$0.607218\pi$
$38$		−	15.3659i		−	0.404367i
$39$	2.20453	−	62.0455i	0.0565264	−	1.59091i
$40$	23.5593			0.588981
$41$	−6.66907	−	24.8893i	−0.162660	−	0.607056i	−0.998327	−	0.0578194i	$-0.981585\pi$
$41$	−6.66907	−	24.8893i	−0.162660	−	0.607056i	0.835667	−	0.549237i	$-0.185081\pi$
$42$	1.20328	−	2.08414i	0.0286495	−	0.0496224i
$43$	−25.3907	+	14.6593i	−0.590480	+	0.340914i	−0.765287	−	0.643689i	$-0.777403\pi$
$43$	−25.3907	+	14.6593i	−0.590480	+	0.340914i	0.174807	+	0.984603i	$0.444070\pi$
$44$	−1.04757	+	1.04757i	−0.0238085	+	0.0238085i
$45$	111.092	+	29.7670i	2.46871	+	0.661489i
$46$	−8.38019	+	31.2753i	−0.182178	+	0.679898i
$47$	21.2000	+	21.2000i	0.451065	+	0.451065i	0.895708	−	0.444643i	$-0.146670\pi$
$47$	21.2000	+	21.2000i	0.451065	+	0.451065i	−0.444643	+	0.895708i	$0.646670\pi$
$48$	−9.55149	−	16.5437i	−0.198989	−	0.344660i
$49$	42.3253	+	24.4365i	0.863781	+	0.498704i
$50$	60.6239	−	16.2441i	1.21248	−	0.324883i
$51$			13.7571i			0.269748i
$52$	−13.7913	+	22.0409i	−0.265218	+	0.423863i
$53$	−85.8410			−1.61964			−0.809821	−	0.586678i	$-0.800436\pi$
$53$	−85.8410			−1.61964			−0.809821	+	0.586678i	$0.800436\pi$
$54$	−8.40412	−	31.3646i	−0.155632	−	0.580826i
$55$	−3.08501	+	5.34339i	−0.0560911	+	0.0971526i
$56$	−0.872803	+	0.503913i	−0.0155858	+	0.00899844i
$57$	−36.6919	+	36.6919i	−0.643718	+	0.643718i
$58$	−41.5524	−	11.1339i	−0.716421	−	0.191965i
$59$	25.9010	−	96.6638i	0.439000	−	1.63837i	−0.292309	−	0.956324i	$-0.594424\pi$
$59$	25.9010	−	96.6638i	0.439000	−	1.63837i	0.731309	−	0.682046i	$-0.238910\pi$
$60$	−56.2565	−	56.2565i	−0.937608	−	0.937608i
$61$	−7.73202	−	13.3923i	−0.126754	−	0.219545i	0.795663	−	0.605740i	$-0.207123\pi$
$61$	−7.73202	−	13.3923i	−0.126754	−	0.219545i	−0.922417	+	0.386195i	$0.873789\pi$
$62$	25.7437	+	14.8631i	0.415221	+	0.239728i
$63$	−4.75233	+	1.27338i	−0.0754338	+	0.0202124i
$64$			8.00000i			0.125000i
$65$	−31.7219	+	103.532i	−0.488030	+	1.59280i
$66$	5.00295			0.0758023
$67$	18.0146	+	67.2315i	0.268875	+	1.00346i	0.959836	+	0.280563i	$0.0905212\pi$
$67$	18.0146	+	67.2315i	0.268875	+	1.00346i	−0.690960	+	0.722893i	$0.742812\pi$
$68$	2.88063	−	4.98939i	0.0423622	−	0.0733735i
$69$	94.6923	−	54.6706i	1.37235	−	0.792328i
$70$	−2.96795	+	2.96795i	−0.0423993	+	0.0423993i
$71$	−94.2060	−	25.2424i	−1.32685	−	0.355527i	−0.475307	−	0.879820i	$-0.657663\pi$
$71$	−94.2060	−	25.2424i	−1.32685	−	0.355527i	−0.851538	+	0.524293i	$0.824330\pi$
$72$	−10.1080	+	37.7234i	−0.140388	+	0.523936i
$73$	50.9541	+	50.9541i	0.698001	+	0.698001i	0.963979	−	0.265978i	$-0.0856949\pi$
$73$	50.9541	+	50.9541i	0.698001	+	0.698001i	−0.265978	+	0.963979i	$0.585695\pi$
$74$	−29.4864	−	51.0720i	−0.398465	−	0.690162i
$75$	−183.551	−	105.973i	−2.44735	−	1.41298i
$76$	20.9903	−	5.62432i	0.276188	−	0.0740043i
$77$		−	0.263943i		−	0.00342783i
$78$	85.5627	−	19.6988i	1.09696	−	0.252549i
$79$	105.981			1.34153			0.670767	−	0.741669i	$-0.265965\pi$
$79$	105.981			1.34153			0.670767	+	0.741669i	$0.265965\pi$
$80$	8.62328	+	32.1825i	0.107791	+	0.402282i
$81$	7.30809	−	12.6580i	0.0902233	−	0.156271i
$82$	31.5584	−	18.2202i	0.384858	−	0.222198i
$83$	−27.2221	+	27.2221i	−0.327977	+	0.327977i	−0.851817	−	0.523840i	$-0.824499\pi$
$83$	−27.2221	+	27.2221i	−0.327977	+	0.327977i	0.523840	+	0.851817i	$0.324499\pi$
$84$	3.28742	+	0.880862i	0.0391360	+	0.0104864i
$85$	6.21012	−	23.1765i	0.0730602	−	0.272664i
$86$	−29.3186	−	29.3186i	−0.340914	−	0.340914i
$87$	72.6355	+	125.808i	0.834891	+	1.44607i
$88$	−1.81445	−	1.04757i	−0.0206188	−	0.0119043i
$89$	82.1525	−	22.0127i	0.923061	−	0.247334i	0.234168	−	0.972196i	$-0.424763\pi$
$89$	82.1525	−	22.0127i	0.923061	−	0.247334i	0.688893	+	0.724863i	$0.258097\pi$
$90$			162.650i			1.80722i
$91$	−1.03926	−	4.51407i	−0.0114204	−	0.0496052i
$92$	−45.7902			−0.497720
$93$	−25.9814	−	96.9639i	−0.279370	−	1.04262i
$94$	−21.2000	+	36.7195i	−0.225532	+	0.390633i
$95$	78.3775	−	45.2513i	0.825026	−	0.476329i
$96$	19.1030	−	19.1030i	0.198989	−	0.198989i
$97$	−19.6341	−	5.26095i	−0.202414	−	0.0542366i	0.156188	−	0.987727i	$-0.450080\pi$
$97$	−19.6341	−	5.26095i	−0.202414	−	0.0542366i	−0.358601	+	0.933491i	$0.616746\pi$
$98$	−17.8888	+	66.7618i	−0.182538	+	0.681243i
$99$	−7.23232	−	7.23232i	−0.0730537	−	0.0730537i
$100$	44.3798	+	76.8681i	0.443798	+	0.768681i
$101$	−24.0962	−	13.9119i	−0.238576	−	0.137742i	0.375946	−	0.926642i	$-0.377318\pi$
$101$	−24.0962	−	13.9119i	−0.238576	−	0.137742i	−0.614522	+	0.788900i	$0.710651\pi$
$102$	−18.7926	+	5.03546i	−0.184241	+	0.0493673i
$103$		−	68.0852i		−	0.661021i	−0.943802	−	0.330511i	$-0.892779\pi$
$103$		−	68.0852i		−	0.661021i	0.943802	−	0.330511i	$-0.107221\pi$
$104$	−35.1563	−	10.7718i	−0.338042	−	0.103575i
$105$	14.1742			0.134992
$106$	−31.4200	−	117.261i	−0.296415	−	1.10624i
$107$	64.2996	−	111.370i	0.600930	−	1.04084i	−0.391750	−	0.920072i	$-0.628130\pi$
$107$	64.2996	−	111.370i	0.600930	−	1.04084i	0.992680	−	0.120770i	$-0.0385365\pi$
$108$	39.7687	−	22.9605i	0.368229	−	0.212597i
$109$	−30.5407	+	30.5407i	−0.280190	+	0.280190i	−0.833185	−	0.552995i	$-0.813485\pi$
$109$	−30.5407	+	30.5407i	−0.280190	+	0.280190i	0.552995	+	0.833185i	$0.313485\pi$
$110$	−8.42840	−	2.25838i	−0.0766219	−	0.0205308i
$111$	−51.5436	+	192.363i	−0.464357	+	1.73300i
$112$	−1.00783	−	1.00783i	−0.00899844	−	0.00899844i
$113$	−23.0706	−	39.9595i	−0.204165	−	0.353624i	0.745701	−	0.666280i	$-0.232115\pi$
$113$	−23.0706	−	39.9595i	−0.204165	−	0.353624i	−0.949866	+	0.312656i	$0.898781\pi$
$114$	−63.5522	−	36.6919i	−0.557476	−	0.321859i
$115$	−184.206	+	49.3578i	−1.60179	+	0.429198i
$116$		−	60.8370i		−	0.524457i
$117$	−152.167	−	95.2135i	−1.30057	−	0.813791i
$118$	141.526			1.19937
$119$	0.265659	+	0.991451i	0.00223243	+	0.00833152i
$120$	56.2565	−	97.4391i	0.468804	−	0.811992i
$121$	−104.314	+	60.2256i	−0.862098	+	0.497733i
$122$	15.4640	−	15.4640i	0.126754	−	0.126754i
$123$	−118.865	−	31.8498i	−0.966381	−	0.258941i
$124$	−10.8806	+	40.6068i	−0.0877465	+	0.327474i
$125$	114.143	+	114.143i	0.913147	+	0.913147i
$126$	−3.47895	−	6.02571i	−0.0276107	−	0.0478231i
$127$	199.748	+	115.325i	1.57282	+	0.908067i	0.995822	+	0.0913210i	$0.0291089\pi$
$127$	199.748	+	115.325i	1.57282	+	0.908067i	0.576997	+	0.816746i	$0.304224\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$			140.018i			1.08541i
$130$	−153.039	−	5.43759i	−1.17722	−	0.0418276i
$131$	162.262			1.23864			0.619321	−	0.785138i	$-0.287408\pi$
$131$	162.262			1.23864			0.619321	+	0.785138i	$0.287408\pi$
$132$	1.83121	+	6.83416i	0.0138728	+	0.0517739i
$133$	−1.93577	+	3.35286i	−0.0145547	+	0.0252095i
$134$	−85.2462	+	49.2169i	−0.636165	+	0.367290i
$135$	135.233	−	135.233i	1.00173	−	1.00173i
$136$	7.87002	+	2.10877i	0.0578678	+	0.0155056i
$137$	−26.7470	+	99.8210i	−0.195233	+	0.728620i	0.796973	+	0.604015i	$0.206433\pi$
$137$	−26.7470	+	99.8210i	−0.195233	+	0.728620i	−0.992206	+	0.124606i	$0.960233\pi$
$138$	109.341	+	109.341i	0.792328	+	0.792328i
$139$	12.7892	+	22.1516i	0.0920087	+	0.159364i	0.908356	−	0.418197i	$-0.137338\pi$
$139$	12.7892	+	22.1516i	0.0920087	+	0.159364i	−0.816348	+	0.577561i	$0.804005\pi$
$140$	−5.14064	−	2.96795i	−0.0367189	−	0.0211997i
$141$	138.305	−	37.0586i	0.980883	−	0.262827i
$142$		−	137.927i		−	0.971318i
$143$	7.04673	−	6.56316i	0.0492778	−	0.0458962i
$144$	−55.2309			−0.383548
$145$	−65.5768	−	244.736i	−0.452254	−	1.68784i
$146$	−50.9541	+	88.2551i	−0.349001	+	0.604487i
$147$	202.135	−	116.703i	1.37507	−	0.793895i
$148$	58.9729	−	58.9729i	0.398465	−	0.398465i
$149$	−25.9865	−	6.96307i	−0.174406	−	0.0467320i	0.170559	−	0.985347i	$-0.445443\pi$
$149$	−25.9865	−	6.96307i	−0.174406	−	0.0467320i	−0.344965	+	0.938615i	$0.612109\pi$
$150$	77.5778	−	289.524i	0.517185	−	1.93016i
$151$	−109.697	−	109.697i	−0.726468	−	0.726468i	0.243446	−	0.969914i	$-0.421722\pi$
$151$	−109.697	−	109.697i	−0.726468	−	0.726468i	−0.969914	+	0.243446i	$0.921722\pi$
$152$	15.3659	+	26.6146i	0.101092	+	0.175096i
$153$	34.4461	+	19.8875i	0.225138	+	0.129983i
$154$	0.360553	−	0.0966099i	0.00234125	−	0.000627337i
$155$			175.082i			1.12956i
$156$	58.2272	+	109.671i	0.373251	+	0.703016i
$157$	−142.680			−0.908790			−0.454395	−	0.890800i	$-0.650145\pi$
$157$	−142.680			−0.908790			−0.454395	+	0.890800i	$0.650145\pi$
$158$	38.7918	+	144.773i	0.245518	+	0.916284i
$159$	−204.977	+	355.031i	−1.28917	+	2.23290i
$160$	−40.8058	+	23.5593i	−0.255036	+	0.147245i
$161$	5.76857	−	5.76857i	0.0358296	−	0.0358296i
$162$	19.9661	+	5.34989i	0.123247	+	0.0330240i
$163$	6.87526	−	25.6588i	0.0421795	−	0.157416i	−0.941624	−	0.336666i	$-0.890701\pi$
$163$	6.87526	−	25.6588i	0.0421795	−	0.157416i	0.983804	+	0.179250i	$0.0573672\pi$
$164$	36.4405	+	36.4405i	0.222198	+	0.222198i
$165$	14.7332	+	25.5187i	0.0892922	+	0.154659i
$166$	−47.1500	−	27.2221i	−0.284036	−	0.163988i
$167$	7.26931	−	1.94780i	0.0435288	−	0.0116635i	−0.236989	−	0.971512i	$-0.576161\pi$
$167$	7.26931	−	1.94780i	0.0435288	−	0.0116635i	0.280518	+	0.959849i	$0.409494\pi$
$168$			4.81312i			0.0286495i
$169$	94.6743	−	139.992i	0.560203	−	0.828356i
$170$	33.9327			0.199604
$171$	38.8296	+	144.914i	0.227074	+	0.847450i
$172$	29.3186	−	50.7813i	0.170457	−	0.295240i
$173$	−24.9669	+	14.4146i	−0.144317	+	0.0833216i	−0.570420	−	0.821353i	$-0.693220\pi$
$173$	−24.9669	+	14.4146i	−0.144317	+	0.0833216i	0.426103	+	0.904675i	$0.359886\pi$
$174$	−145.271	+	145.271i	−0.834891	+	0.834891i
$175$	−15.2746	−	4.09281i	−0.0872834	−	0.0233875i
$176$	0.766878	−	2.86203i	0.00435726	−	0.0162615i
$177$	−337.945	−	337.945i	−1.90929	−	1.90929i
$178$	60.1398	+	104.165i	0.337864	+	0.585197i
$179$	−183.682	−	106.049i	−1.02616	−	0.592453i	−0.110277	−	0.993901i	$-0.535174\pi$
$179$	−183.682	−	106.049i	−1.02616	−	0.592453i	−0.915882	+	0.401448i	$0.868507\pi$
$180$	−222.184	+	59.5340i	−1.23435	+	0.330744i
$181$		−	112.088i		−	0.619270i	−0.950856	−	0.309635i	$-0.899793\pi$
$181$		−	112.088i		−	0.619270i	0.950856	−	0.309635i	$-0.100207\pi$
$182$	5.78595	−	3.07192i	0.0317909	−	0.0168787i
$183$	−73.8523			−0.403564
$184$	−16.7604	−	62.5506i	−0.0910891	−	0.339949i
$185$	173.670	−	300.805i	0.938755	−	1.62597i
$186$	122.945	−	70.9825i	0.660996	−	0.381626i
$187$	−1.50884	+	1.50884i	−0.00806865	+	0.00806865i
$188$	−57.9196	−	15.5195i	−0.308083	−	0.0825505i
$189$	−2.11747	+	7.90251i	−0.0112036	+	0.0418122i
$190$	90.5025	+	90.5025i	0.476329	+	0.476329i
$191$	−132.524	−	229.538i	−0.693843	−	1.20177i	−0.970569	−	0.240823i	$-0.922583\pi$
$191$	−132.524	−	229.538i	−0.693843	−	1.20177i	0.276726	−	0.960949i	$-0.410751\pi$
$192$	33.0873	+	19.1030i	0.172330	+	0.0994947i
$193$	153.771	−	41.2029i	0.796742	−	0.213486i	0.162589	−	0.986694i	$-0.448016\pi$
$193$	153.771	−	41.2029i	0.796742	−	0.213486i	0.634153	+	0.773208i	$0.281349\pi$
$194$		−	28.7464i		−	0.148177i
$195$	352.452	+	378.421i	1.80745	+	1.94062i
$196$	−97.7461			−0.498704
$197$	77.8551	+	290.559i	0.395204	+	1.47492i	0.821433	+	0.570305i	$0.193175\pi$
$197$	77.8551	+	290.559i	0.395204	+	1.47492i	−0.426230	+	0.904615i	$0.640158\pi$
$198$	7.23232	−	12.5267i	0.0365268	−	0.0632663i
$199$	−162.223	+	93.6594i	−0.815190	+	0.470650i	−0.848755	−	0.528786i	$-0.822647\pi$
$199$	−162.223	+	93.6594i	−0.815190	+	0.470650i	0.0335648	+	0.999437i	$0.489314\pi$
$200$	−88.7596	+	88.7596i	−0.443798	+	0.443798i
$201$	321.081	+	86.0333i	1.59742	+	0.428026i
$202$	10.1842	−	38.0081i	0.0504170	−	0.188159i
$203$	7.66414	+	7.66414i	0.0377544	+	0.0377544i
$204$	−13.7571	−	23.8281i	−0.0674370	−	0.116804i
$205$	185.873	+	107.314i	0.906697	+	0.523482i
$206$	93.0061	−	24.9209i	0.451486	−	0.120975i
$207$		−	316.130i		−	1.52720i
$208$	1.84644	−	51.9672i	0.00887711	−	0.249842i
$209$	−8.04849			−0.0385095
$210$	5.18811	+	19.3623i	0.0247053	+	0.0922014i
$211$	−84.9065	+	147.062i	−0.402401	+	0.696978i	−0.994015	−	0.109243i	$-0.965157\pi$
$211$	−84.9065	+	147.062i	−0.402401	+	0.696978i	0.591614	+	0.806221i	$0.298491\pi$
$212$	148.681	−	85.8410i	0.701325	−	0.404910i
$213$	−329.353	+	329.353i	−1.54626	+	1.54626i
$214$	175.670	+	47.0705i	0.820886	+	0.219956i
$215$	63.2057	−	235.887i	0.293980	−	1.09715i
$216$	45.9210	+	45.9210i	0.212597	+	0.212597i
$217$	−3.74486	−	6.48629i	−0.0172574	−	0.0298907i
$218$	−52.8981	−	30.5407i	−0.242652	−	0.140095i
$219$	332.414	−	89.0700i	1.51787	−	0.406712i
$220$		−	12.3400i		−	0.0560911i
$221$	−19.8639	+	31.7458i	−0.0898817	+	0.143646i
$222$	−281.639			−1.26865
$223$	−62.2439	−	232.297i	−0.279121	−	1.04169i	−0.953029	−	0.302878i	$-0.902053\pi$
$223$	−62.2439	−	232.297i	−0.279121	−	1.04169i	0.673909	−	0.738815i	$-0.264614\pi$
$224$	1.00783	−	1.74561i	0.00449922	−	0.00779288i
$225$	−530.687	+	306.392i	−2.35861	+	1.36174i
$226$	46.1413	−	46.1413i	0.204165	−	0.204165i
$227$	87.3971	+	23.4180i	0.385009	+	0.103163i	0.446132	−	0.894967i	$-0.352801\pi$
$227$	87.3971	+	23.4180i	0.385009	+	0.103163i	−0.0611224	+	0.998130i	$0.519468\pi$
$228$	26.8603	−	100.244i	0.117808	−	0.439667i
$229$	248.887	+	248.887i	1.08684	+	1.08684i	0.995852	+	0.0909923i	$0.0290039\pi$
$229$	248.887	+	248.887i	1.08684	+	1.08684i	0.0909923	+	0.995852i	$0.470996\pi$
$230$	−134.848	−	233.563i	−0.586295	−	1.01549i
$231$	−1.09165	−	0.630263i	−0.00472574	−	0.00272841i
$232$	83.1049	−	22.2679i	0.358211	−	0.0959823i
$233$			384.870i			1.65180i	0.563815	+	0.825901i	$0.309333\pi$
$233$			384.870i			1.65180i	−0.563815	+	0.825901i	$0.690667\pi$
$234$	74.3670	−	242.715i	0.317808	−	1.03724i
$235$	−249.728			−1.06267
$236$	51.8020	+	193.328i	0.219500	+	0.819185i
$237$	253.069	−	438.329i	1.06780	−	1.84949i
$238$	−1.25711	+	0.725793i	−0.00528198	+	0.00304955i
$239$	210.628	−	210.628i	0.881290	−	0.881290i	−0.112375	−	0.993666i	$-0.535846\pi$
$239$	210.628	−	210.628i	0.881290	−	0.881290i	0.993666	+	0.112375i	$0.0358459\pi$
$240$	153.696	+	41.1826i	0.640398	+	0.171594i
$241$	−48.4880	+	180.960i	−0.201195	+	0.750870i	0.789381	+	0.613904i	$0.210402\pi$
$241$	−48.4880	+	180.960i	−0.201195	+	0.750870i	−0.990576	+	0.136966i	$0.956265\pi$
$242$	−120.451	−	120.451i	−0.497733	−	0.497733i
$243$	−138.224	−	239.411i	−0.568822	−	0.985228i
$244$	26.7845	+	15.4640i	0.109773	+	0.0633772i
$245$	−393.215	+	105.362i	−1.60496	+	0.430047i
$246$		−	174.030i		−	0.707440i
$247$	−137.649	+	31.6904i	−0.557283	+	0.128301i
$248$	−59.4525			−0.239728
$249$	47.5853	+	177.591i	0.191106	+	0.713216i
$250$	−114.143	+	197.702i	−0.456573	+	0.790808i
$251$	−87.0514	+	50.2592i	−0.346818	+	0.200236i	−0.663283	−	0.748369i	$-0.730837\pi$
$251$	−87.0514	+	50.2592i	−0.346818	+	0.200236i	0.316465	+	0.948604i	$0.397504\pi$
$252$	6.95789	−	6.95789i	0.0276107	−	0.0276107i
$253$	16.3816	+	4.38944i	0.0647495	+	0.0173496i
$254$	−84.4234	+	315.073i	−0.332376	+	1.24044i
$255$	−81.0270	−	81.0270i	−0.317753	−	0.317753i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−60.1930	−	34.7524i	−0.234214	−	0.135223i	0.378301	−	0.925683i	$-0.376509\pi$
$257$	−60.1930	−	34.7524i	−0.234214	−	0.135223i	−0.612515	+	0.790459i	$0.709842\pi$
$258$	−191.268	+	51.2502i	−0.741350	+	0.198644i
$259$			14.8586i			0.0573691i
$260$	−48.5881	−	211.045i	−0.186877	−	0.811711i
$261$	420.010			1.60924
$262$	59.3920	+	221.654i	0.226687	+	0.846008i
$263$	−129.589	+	224.455i	−0.492735	+	0.853441i	−0.999965	−	0.00836922i	$-0.997336\pi$
$263$	−129.589	+	224.455i	−0.492735	+	0.853441i	0.507230	+	0.861810i	$0.330669\pi$
$264$	−8.66536	+	5.00295i	−0.0328233	+	0.0189506i
$265$	505.587	−	505.587i	1.90788	−	1.90788i
$266$	−5.28863	−	1.41708i	−0.0198821	−	0.00532739i
$267$	105.127	−	392.339i	0.393734	−	1.46943i
$268$	−98.4338	−	98.4338i	−0.367290	−	0.367290i
$269$	−21.0056	−	36.3828i	−0.0780878	−	0.135252i	0.824337	−	0.566099i	$-0.191548\pi$
$269$	−21.0056	−	36.3828i	−0.0780878	−	0.135252i	−0.902425	+	0.430847i	$0.858215\pi$
$270$	234.230	+	135.233i	0.867520	+	0.500863i
$271$	−304.350	+	81.5504i	−1.12306	+	0.300924i	−0.772122	−	0.635474i	$-0.780805\pi$
$271$	−304.350	+	81.5504i	−1.12306	+	0.300924i	−0.350941	+	0.936398i	$0.614138\pi$
$272$			11.5225i			0.0423622i
$273$	−21.1514	−	6.48074i	−0.0774778	−	0.0237390i
$274$	−146.148			−0.533387
$275$	−8.50847	−	31.7540i	−0.0309399	−	0.115469i
$276$	−109.341	+	189.385i	−0.396164	+	0.686176i
$277$	−164.261	+	94.8364i	−0.593001	+	0.342370i	−0.766283	−	0.642503i	$-0.777896\pi$
$277$	−164.261	+	94.8364i	−0.593001	+	0.342370i	0.173282	+	0.984872i	$0.444563\pi$
$278$	−25.5784	+	25.5784i	−0.0920087	+	0.0920087i
$279$	−280.344	−	75.1180i	−1.00482	−	0.269240i
$280$	2.17269	−	8.10860i	0.00775961	−	0.0289593i
$281$	−32.8661	−	32.8661i	−0.116961	−	0.116961i	0.646204	−	0.763165i	$-0.276356\pi$
$281$	−32.8661	−	32.8661i	−0.116961	−	0.116961i	−0.763165	+	0.646204i	$0.776356\pi$
$282$	101.246	+	175.363i	0.359028	+	0.621855i
$283$	456.365	+	263.482i	1.61260	+	0.931033i	0.988766	+	0.149474i	$0.0477582\pi$
$283$	456.365	+	263.482i	1.61260	+	0.931033i	0.623831	+	0.781559i	$0.285575\pi$
$284$	188.412	−	50.4849i	0.663423	−	0.177764i
$285$		−	432.217i		−	1.51655i
$286$	11.5447	+	7.22373i	0.0403662	+	0.0252578i
$287$	−9.18141			−0.0319910
$288$	−20.2159	−	75.4468i	−0.0701942	−	0.261968i
$289$	−140.351	+	243.095i	−0.485644	+	0.841159i
$290$	310.313	−	179.159i	1.07004	−	0.617791i
$291$	−68.6426	+	68.6426i	−0.235885	+	0.235885i
$292$	−139.209	−	37.3010i	−0.476744	−	0.127743i
$293$	35.4435	−	132.277i	0.120968	−	0.451457i	−0.878696	−	0.477381i	$-0.841586\pi$
$293$	35.4435	−	132.277i	0.120968	−	0.451457i	0.999664	+	0.0259239i	$0.00825274\pi$
$294$	233.405	+	233.405i	0.793895	+	0.793895i
$295$	416.780	+	721.884i	1.41281	+	2.44706i
$296$	102.144	+	58.9729i	0.345081	+	0.199233i
$297$	−16.4284	+	4.40197i	−0.0553144	+	0.0148215i
$298$		−	38.0469i		−	0.127674i
$299$	297.449	+	10.5686i	0.994812	+	0.0353465i
$300$	423.893			1.41298
$301$	2.70383	+	10.0908i	0.00898283	+	0.0335244i
$302$	109.697	−	190.000i	0.363234	−	0.629140i
$303$	−115.077	+	66.4398i	−0.379792	+	0.219273i
$304$	−30.7319	+	30.7319i	−0.101092	+	0.101092i
$305$	124.418	+	33.3377i	0.407928	+	0.109304i
$306$	−14.5586	+	54.3336i	−0.0475772	+	0.177561i
$307$	−306.038	−	306.038i	−0.996866	−	0.996866i	0.00312957	−	0.999995i	$-0.499004\pi$
$307$	−306.038	−	306.038i	−0.996866	−	0.996866i	−0.999995	+	0.00312957i	$0.999004\pi$
$308$	0.263943	+	0.457163i	0.000856959	+	0.00148430i
$309$	−281.595	−	162.579i	−0.911309	−	0.526145i
$310$	−239.167	+	64.0845i	−0.771505	+	0.206724i
$311$		−	138.274i		−	0.444611i	−0.974977	−	0.222305i	$-0.928642\pi$
$311$		−	138.274i		−	0.444611i	0.974977	−	0.222305i	$-0.0713582\pi$
$312$	−128.500	+	119.682i	−0.411859	+	0.383596i
$313$	525.434			1.67870			0.839352	−	0.543589i	$-0.182935\pi$
$313$	525.434			1.67870			0.839352	+	0.543589i	$0.182935\pi$
$314$	−52.2245	−	194.905i	−0.166320	−	0.620715i
$315$	20.4903	−	35.4903i	0.0650487	−	0.112668i
$316$	−183.565	+	105.981i	−0.580901	+	0.335383i
$317$	24.3899	−	24.3899i	0.0769397	−	0.0769397i	−0.667590	−	0.744529i	$-0.732674\pi$
$317$	24.3899	−	24.3899i	0.0769397	−	0.0769397i	0.744529	+	0.667590i	$0.232674\pi$
$318$	−560.008	−	150.054i	−1.76103	−	0.471867i
$319$	−5.83182	+	21.7646i	−0.0182816	+	0.0682277i
$320$	−47.1185	−	47.1185i	−0.147245	−	0.147245i
$321$	−307.078	−	531.875i	−0.956630	−	1.65693i
$322$	9.99146	+	5.76857i	0.0310294	+	0.0179148i
$323$	30.2326	−	8.10079i	0.0935993	−	0.0250799i
$324$			29.2323i			0.0902233i
$325$	−270.545	−	509.570i	−0.832447	−	1.56791i
$326$	37.5671			0.115237
$327$	53.3865	+	199.241i	0.163261	+	0.609300i
$328$	−36.4405	+	63.1167i	−0.111099	+	0.192429i
$329$	9.25172	−	5.34148i	0.0281207	−	0.0162355i
$330$	−29.4664	+	29.4664i	−0.0892922	+	0.0892922i
$331$	−21.4194	−	5.73931i	−0.0647111	−	0.0173393i	0.226318	−	0.974053i	$-0.427331\pi$
$331$	−21.4194	−	5.73931i	−0.0647111	−	0.0173393i	−0.291029	+	0.956714i	$0.593998\pi$
$332$	19.9279	−	74.3720i	0.0600239	−	0.224012i
$333$	407.141	+	407.141i	1.22264	+	1.22264i
$334$	5.32150	+	9.21711i	0.0159326	+	0.0275961i
$335$	−502.084	−	289.878i	−1.49876	−	0.865308i
$336$	−6.57484	+	1.76172i	−0.0195680	+	0.00524322i
$337$			544.688i			1.61629i	0.588987	+	0.808143i	$0.299527\pi$
$337$			544.688i			1.61629i	−0.588987	+	0.808143i	$0.700473\pi$
$338$	225.886	+	78.0868i	0.668302	+	0.231026i
$339$	−220.359			−0.650026
$340$	12.4202	+	46.3530i	0.0365301	+	0.136332i
$341$	7.78512	−	13.4842i	0.0228303	−	0.0395432i
$342$	−183.744	+	106.084i	−0.537262	+	0.310188i
$343$	24.6597	−	24.6597i	0.0718943	−	0.0718943i
$344$	80.0999	+	21.4627i	0.232849	+	0.0623916i
$345$	−235.720	+	879.719i	−0.683247	+	2.54991i
$346$	−28.8293	−	28.8293i	−0.0833216	−	0.0833216i
$347$	320.301	+	554.777i	0.923057	+	1.59878i	0.794657	+	0.607059i	$0.207651\pi$
$347$	320.301	+	554.777i	0.923057	+	1.59878i	0.128400	+	0.991722i	$0.459016\pi$
$348$	−251.617	−	145.271i	−0.723036	−	0.417445i
$349$	−58.4257	+	15.6551i	−0.167409	+	0.0448571i	−0.341550	−	0.939864i	$-0.610952\pi$
$349$	−58.4257	+	15.6551i	−0.167409	+	0.0448571i	0.174141	+	0.984721i	$0.444285\pi$
$350$		−	22.3635i		−	0.0638958i
$351$	−263.633	+	139.970i	−0.751091	+	0.398776i
$352$	4.19030			0.0119043
$353$	−75.9253	−	283.357i	−0.215086	−	0.802711i	−0.986136	−	0.165937i	$-0.946935\pi$
$353$	−75.9253	−	283.357i	−0.215086	−	0.802711i	0.771051	−	0.636774i	$-0.219732\pi$
$354$	337.945	−	585.338i	0.954647	−	1.65350i
$355$	703.529	−	406.183i	1.98177	−	1.14418i
$356$	−120.280	+	120.280i	−0.337864	+	0.337864i
$357$	4.73492	+	1.26872i	0.0132631	+	0.00355383i
$358$	77.6333	−	289.732i	0.216853	−	0.809306i
$359$	−118.752	−	118.752i	−0.330785	−	0.330785i	0.522099	−	0.852885i	$-0.325149\pi$
$359$	−118.752	−	118.752i	−0.330785	−	0.330785i	−0.852885	+	0.522099i	$0.825149\pi$
$360$	−162.650	−	281.718i	−0.451805	−	0.782550i
$361$	−210.396	−	121.472i	−0.582813	−	0.336487i
$362$	153.115	−	41.0270i	0.422969	−	0.113334i
$363$			575.245i			1.58470i
$364$	6.31412	+	6.77935i	0.0173465	+	0.0186246i
$365$	−600.220			−1.64444
$366$	−27.0318	−	100.884i	−0.0738574	−	0.275640i
$367$	51.1578	−	88.6080i	0.139395	−	0.241439i	−0.787873	−	0.615838i	$-0.788818\pi$
$367$	51.1578	−	88.6080i	0.139395	−	0.241439i	0.927268	+	0.374399i	$0.122151\pi$
$368$	79.3110	−	45.7902i	0.215519	−	0.124430i
$369$	−251.580	+	251.580i	−0.681789	+	0.681789i
$370$	474.474	+	127.135i	1.28236	+	0.343608i
$371$	−7.91647	+	29.5447i	−0.0213382	+	0.0796352i
$372$	141.965	+	141.965i	0.381626	+	0.381626i
$373$	−302.308	−	523.613i	−0.810477	−	1.40379i	−0.912530	−	0.409009i	$-0.865875\pi$
$373$	−302.308	−	523.613i	−0.810477	−	1.40379i	0.102053	−	0.994779i	$-0.467459\pi$
$374$	−2.61338	−	1.50884i	−0.00698765	−	0.00403432i
$375$	744.647	−	199.528i	1.98573	−	0.532073i
$376$		−	84.8001i		−	0.225532i
$377$	−14.0415	+	395.191i	−0.0372453	+	1.04825i
$378$	−11.5701			−0.0306087
$379$	−99.3166	−	370.655i	−0.262049	−	0.977980i	−0.964032	−	0.265787i	$-0.914368\pi$
$379$	−99.3166	−	370.655i	−0.262049	−	0.977980i	0.701983	−	0.712194i	$-0.252298\pi$
$380$	−90.5025	+	156.755i	−0.238165	+	0.412513i
$381$	953.945	−	550.760i	2.50379	−	1.44557i
$382$	265.048	−	265.048i	0.693843	−	0.693843i
$383$	395.727	+	106.035i	1.03323	+	0.276853i	0.735305	−	0.677736i	$-0.237039\pi$
$383$	395.727	+	106.035i	1.03323	+	0.276853i	0.297925	+	0.954589i	$0.403706\pi$
$384$	−13.9843	+	52.1903i	−0.0364176	+	0.135912i
$385$	1.55458	+	1.55458i	0.00403786	+	0.00403786i
$386$	112.568	+	194.974i	0.291628	+	0.505114i
$387$	350.587	+	202.412i	0.905910	+	0.523027i
$388$	39.2682	−	10.5219i	0.101207	−	0.0271183i
$389$			43.6909i			0.112316i	0.998422	+	0.0561579i	$0.0178850\pi$
$389$			43.6909i			0.112316i	−0.998422	+	0.0561579i	$0.982115\pi$
$390$	−387.926	+	619.970i	−0.994682	+	1.58967i
$391$	−65.9523			−0.168676
$392$	−35.7775	−	133.524i	−0.0912692	−	0.340621i
$393$	387.461	−	671.102i	0.985906	−	1.70764i
$394$	−368.414	+	212.704i	−0.935062	+	0.539858i
$395$	−624.209	+	624.209i	−1.58028	+	1.58028i
$396$	19.7591	+	5.29442i	0.0498966	+	0.0133698i
$397$	−70.9301	+	264.715i	−0.178665	+	0.666788i	0.817233	+	0.576307i	$0.195507\pi$
$397$	−70.9301	+	264.715i	−0.178665	+	0.666788i	−0.995898	+	0.0904803i	$0.971160\pi$
$398$	−187.319	−	187.319i	−0.470650	−	0.470650i
$399$	9.24476	+	16.0124i	0.0231698	+	0.0401313i
$400$	−153.736	−	88.7596i	−0.384340	−	0.221899i
$401$	86.0849	−	23.0664i	0.214676	−	0.0575222i	−0.149878	−	0.988704i	$-0.547888\pi$
$401$	86.0849	−	23.0664i	0.214676	−	0.0575222i	0.364554	+	0.931182i	$0.381221\pi$
$402$			470.095i			1.16939i
$403$	80.0513	−	261.267i	0.198639	−	0.648304i
$404$	55.6477			0.137742
$405$	31.5099	+	117.596i	0.0778021	+	0.290361i
$406$	−7.66414	+	13.2747i	−0.0188772	+	0.0326962i
$407$	−26.7509	+	15.4446i	−0.0657270	+	0.0379475i
$408$	27.5143	−	27.5143i	0.0674370	−	0.0674370i
$409$	−705.246	−	188.970i	−1.72432	−	0.462030i	−0.745456	−	0.666554i	$-0.767768\pi$
$409$	−705.246	−	188.970i	−1.72432	−	0.462030i	−0.978861	+	0.204525i	$0.934435\pi$
$410$	−78.5591	+	293.187i	−0.191608	+	0.715089i
$411$	348.983	+	348.983i	0.849107	+	0.849107i
$412$	68.0852	+	117.927i	0.165255	+	0.286231i
$413$	−30.8810	−	17.8291i	−0.0747724	−	0.0431699i
$414$	431.841	−	115.711i	1.04309	−	0.279496i
$415$		−	320.666i		−	0.772688i
$416$	71.6644	−	16.4990i	0.172270	−	0.0396611i
$417$	122.156			0.292940
$418$	−2.94595	−	10.9944i	−0.00704773	−	0.0263025i
$419$	−130.487	+	226.011i	−0.311426	+	0.539405i	−0.978671	−	0.205433i	$-0.934140\pi$
$419$	−130.487	+	226.011i	−0.311426	+	0.539405i	0.667246	+	0.744838i	$0.267473\pi$
$420$	−24.5504	+	14.1742i	−0.0584533	+	0.0337480i
$421$	−103.038	+	103.038i	−0.244745	+	0.244745i	−0.818810	−	0.574065i	$-0.805366\pi$
$421$	−103.038	+	103.038i	−0.244745	+	0.244745i	0.574065	+	0.818810i	$0.305366\pi$
$422$	−231.969	−	62.1559i	−0.549690	−	0.147289i
$423$	107.145	−	399.869i	0.253297	−	0.945316i
$424$	171.682	+	171.682i	0.404910	+	0.404910i
$425$	63.9208	+	110.714i	0.150402	+	0.260504i
$426$	−570.455	−	329.353i	−1.33910	−	0.773128i
$427$	−5.32240	+	1.42613i	−0.0124646	+	0.00333989i
$428$			257.198i			0.600930i
$429$	−10.3180	−	44.8166i	−0.0240512	−	0.104468i
$430$	345.362			0.803168
$431$	−35.2588	−	131.588i	−0.0818069	−	0.305308i	0.912883	−	0.408220i	$-0.133850\pi$
$431$	−35.2588	−	131.588i	−0.0818069	−	0.305308i	−0.994690	+	0.102913i	$0.967184\pi$
$432$	−45.9210	+	79.5375i	−0.106299	+	0.184114i
$433$	174.382	−	100.679i	0.402729	−	0.232516i	−0.284932	−	0.958548i	$-0.591971\pi$
$433$	174.382	−	100.679i	0.402729	−	0.232516i	0.687661	+	0.726032i	$0.258638\pi$
$434$	7.48972	−	7.48972i	0.0172574	−	0.0172574i
$435$	−1168.80	−	313.178i	−2.68689	−	0.719950i
$436$	22.3574	−	83.4388i	0.0512783	−	0.191373i
$437$	−175.902	−	175.902i	−0.402523	−	0.402523i
$438$	243.344	+	421.484i	0.555579	+	0.962291i
$439$	−64.3905	−	37.1759i	−0.146675	−	0.0846830i	0.424866	−	0.905256i	$-0.360321\pi$
$439$	−64.3905	−	37.1759i	−0.146675	−	0.0846830i	−0.571542	+	0.820573i	$0.693654\pi$
$440$	16.8568	−	4.51677i	0.0383109	−	0.0102654i
$441$		−	674.826i		−	1.53022i
$442$	−50.6362	−	15.5148i	−0.114561	−	0.0351013i
$443$	130.644			0.294908			0.147454	−	0.989069i	$-0.452892\pi$
$443$	130.644			0.294908			0.147454	+	0.989069i	$0.452892\pi$
$444$	−103.087	−	384.726i	−0.232178	−	0.866501i
$445$	−354.212	+	613.513i	−0.795982	+	1.37868i
$446$	294.541	−	170.054i	0.660407	−	0.381286i
$447$	−90.8512	+	90.8512i	−0.203246	+	0.203246i
$448$	2.75343	+	0.737780i	0.00614605	+	0.00164683i
$449$	186.560	−	696.251i	0.415501	−	1.55067i	−0.368330	−	0.929695i	$-0.620070\pi$
$449$	186.560	−	696.251i	0.415501	−	1.55067i	0.783831	−	0.620975i	$-0.213263\pi$
$450$	−612.784	−	612.784i	−1.36174	−	1.36174i
$451$	−9.54353	−	16.5299i	−0.0211608	−	0.0366516i
$452$	79.9190	+	46.1413i	0.176812	+	0.102082i
$453$	−715.638	+	191.755i	−1.57977	+	0.423299i
$454$			127.958i			0.281846i
$455$	32.7081	+	20.4660i	0.0718859	+	0.0449802i
$456$	146.768			0.321859
$457$	−93.8520	−	350.261i	−0.205365	−	0.766434i	−0.989338	−	0.145639i	$-0.953476\pi$
$457$	−93.8520	−	350.261i	−0.205365	−	0.766434i	0.783972	−	0.620796i	$-0.213190\pi$
$458$	−248.887	+	431.085i	−0.543422	+	0.941234i
$459$	57.2795	−	33.0703i	0.124792	−	0.0720486i
$460$	269.696	−	269.696i	0.586295	−	0.586295i
$461$	835.746	+	223.937i	1.81290	+	0.485765i	0.995867	−	0.0908282i	$-0.0289514\pi$
$461$	835.746	+	223.937i	1.81290	+	0.485765i	0.817032	+	0.576593i	$0.195618\pi$
$462$	0.461384	−	1.72191i	0.000998667	−	0.00372708i
$463$	163.492	+	163.492i	0.353114	+	0.353114i	0.861267	−	0.508153i	$-0.169672\pi$
$463$	163.492	+	163.492i	0.353114	+	0.353114i	−0.508153	+	0.861267i	$0.669672\pi$
$464$	60.8370	+	105.373i	0.131114	+	0.227096i
$465$	724.125	+	418.074i	1.55726	+	0.899083i
$466$	−525.742	+	140.872i	−1.12820	+	0.302301i
$467$		−	242.866i		−	0.520056i	−0.965601	−	0.260028i	$-0.916268\pi$
$467$		−	242.866i		−	0.520056i	0.965601	−	0.260028i	$-0.0837318\pi$
$468$	358.775	+	12.7476i	0.766612	+	0.0272384i
$469$	24.8010			0.0528807
$470$	−91.4070	−	341.135i	−0.194483	−	0.725820i
$471$	−340.702	+	590.113i	−0.723358	+	1.25289i
$472$	−245.130	+	141.526i	−0.519342	+	0.299842i
$473$	−15.3567	+	15.3567i	−0.0324666	+	0.0324666i
$474$	691.398	+	185.260i	1.45865	+	0.390843i
$475$	−124.803	+	465.772i	−0.262744	+	0.980572i
$476$	−1.45159	−	1.45159i	−0.00304955	−	0.00304955i
$477$	592.635	+	1026.47i	1.24242	+	2.15194i
$478$	364.819	+	210.628i	0.763220	+	0.440645i
$479$	215.917	−	57.8547i	0.450766	−	0.120782i	−0.0262919	−	0.999654i	$-0.508370\pi$
$479$	215.917	−	57.8547i	0.450766	−	0.120782i	0.477058	+	0.878872i	$0.341703\pi$
$480$			225.026i			0.468804i
$481$	−396.693	+	369.471i	−0.824726	+	0.768130i
$482$	−264.943			−0.549675
$483$	−10.0837	−	37.6329i	−0.0208773	−	0.0779150i
$484$	120.451	−	208.628i	0.248866	−	0.431049i
$485$	146.627	−	84.6553i	0.302324	−	0.174547i
$486$	276.447	−	276.447i	0.568822	−	0.568822i
$487$	20.8396	+	5.58396i	0.0427918	+	0.0114660i	0.280151	−	0.959956i	$-0.409615\pi$
$487$	20.8396	+	5.58396i	0.0427918	+	0.0114660i	−0.237360	+	0.971422i	$0.576282\pi$
$488$	−11.3205	+	42.2485i	−0.0231977	+	0.0865749i
$489$	−89.7055	−	89.7055i	−0.183447	−	0.183447i
$490$	−287.853	−	498.576i	−0.587455	−	1.01750i
$491$	−50.4972	−	29.1546i	−0.102846	−	0.0593780i	0.447695	−	0.894186i	$-0.352245\pi$
$491$	−50.4972	−	29.1546i	−0.102846	−	0.0593780i	−0.550541	+	0.834808i	$0.685578\pi$
$492$	237.730	−	63.6995i	0.483191	−	0.129471i
$493$		−	87.6244i		−	0.177737i
$494$	−93.6729	−	176.432i	−0.189621	−	0.357150i
$495$	85.1940			0.172109
$496$	−21.7611	−	81.2137i	−0.0438733	−	0.163737i
$497$	−17.3758	+	30.0958i	−0.0349614	+	0.0605549i
$498$	−225.176	+	130.006i	−0.452161	+	0.261055i
$499$	625.494	−	625.494i	1.25350	−	1.25350i	0.299353	−	0.954142i	$-0.403229\pi$
$499$	625.494	−	625.494i	1.25350	−	1.25350i	0.954142	−	0.299353i	$-0.0967709\pi$
$500$	−311.845	−	83.5587i	−0.623691	−	0.167117i
$501$	9.30221	−	34.7163i	0.0185673	−	0.0692941i
$502$	−100.518	−	100.518i	−0.200236	−	0.200236i
$503$	5.25707	+	9.10551i	0.0104514	+	0.0181024i	0.871204	−	0.490921i	$-0.163340\pi$
$503$	5.25707	+	9.10551i	0.0104514	+	0.0181024i	−0.860752	+	0.509024i	$0.830006\pi$
$504$	12.0514	+	6.95789i	0.0239116	+	0.0138053i
$505$	223.860	−	59.9832i	0.443288	−	0.118779i
$506$			23.9843i			0.0473999i
$507$	−352.925	−	725.848i	−0.696105	−	1.43165i
$508$	−461.298			−0.908067
$509$	26.3711	+	98.4183i	0.0518097	+	0.193356i	0.986980	−	0.160841i	$-0.0514207\pi$
$509$	26.3711	+	98.4183i	0.0518097	+	0.193356i	−0.935171	+	0.354198i	$0.884754\pi$
$510$	81.0270	−	140.343i	0.158876	−	0.275182i
$511$	22.2364	−	12.8382i	0.0435155	−	0.0251237i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	240.973	+	64.5686i	0.469734	+	0.125865i
$514$	25.4405	−	94.9454i	0.0494952	−	0.184719i
$515$	401.009	+	401.009i	0.778658	+	0.778658i
$516$	−140.018	−	242.518i	−0.271353	−	0.469997i
$517$	19.2332	+	11.1043i	0.0372016	+	0.0214784i
$518$	−20.2972	+	5.43862i	−0.0391838	+	0.0104993i
$519$			137.681i			0.265282i
$520$	270.508	−	143.620i	0.520208	−	0.276193i
$521$	170.985			0.328185			0.164093	−	0.986445i	$-0.447530\pi$
$521$	170.985			0.328185			0.164093	+	0.986445i	$0.447530\pi$
$522$	153.734	+	573.745i	0.294510	+	1.09913i
$523$	417.695	−	723.469i	0.798652	−	1.38331i	−0.121842	−	0.992549i	$-0.538880\pi$
$523$	417.695	−	723.469i	0.798652	−	1.38331i	0.920494	−	0.390756i	$-0.127786\pi$
$524$	−281.046	+	162.262i	−0.536347	+	0.309660i
$525$	−53.4013	+	53.4013i	−0.101717	+	0.101717i
$526$	−354.044	−	94.8659i	−0.673088	−	0.180353i
$527$	−15.6714	+	58.4866i	−0.0297371	+	0.110980i
$528$	−10.0059	−	10.0059i	−0.0189506	−	0.0189506i
$529$	−2.40684	−	4.16878i	−0.00454980	−	0.00788048i
$530$	875.703	+	505.587i	1.65227	+	0.953938i
$531$	−1334.71	+	357.634i	−2.51357	+	0.673510i
$532$		−	7.74309i		−	0.0145547i
$533$	−228.303	−	245.124i	−0.428336	−	0.459895i
$534$	574.424			1.07570
$535$	277.237	+	1034.66i	0.518199	+	1.93395i
$536$	98.4338	−	170.492i	0.183645	−	0.318083i
$537$	−877.220	+	506.463i	−1.63356	+	0.943135i
$538$	42.0112	−	42.0112i	0.0780878	−	0.0780878i
$539$	34.9690	+	9.36991i	0.0648775	+	0.0173839i
$540$	−98.9974	+	369.463i	−0.183329	+	0.684191i
$541$	503.966	+	503.966i	0.931545	+	0.931545i	0.997803	−	0.0662572i	$-0.0211058\pi$
$541$	503.966	+	503.966i	0.931545	+	0.931545i	−0.0662572	+	0.997803i	$0.521106\pi$
$542$	−222.800	−	385.900i	−0.411070	−	0.711993i
$543$	−463.586	−	267.651i	−0.853749	−	0.492912i
$544$	−15.7400	+	4.21753i	−0.0289339	+	0.00775282i
$545$		−	359.758i		−	0.660107i
$546$	1.11089	−	31.2655i	0.00203460	−	0.0572629i
$547$	−249.081			−0.455359			−0.227680	−	0.973736i	$-0.573114\pi$
$547$	−249.081			−0.455359			−0.227680	+	0.973736i	$0.573114\pi$
$548$	−53.4939	−	199.642i	−0.0976166	−	0.364310i
$549$	−106.762	+	184.917i	−0.194466	+	0.336824i
$550$	40.2625	−	23.2456i	0.0732046	−	0.0422647i
$551$	233.704	−	233.704i	0.424146	−	0.424146i
$552$	−298.726	−	80.0433i	−0.541170	−	0.145006i
$553$	9.77384	−	36.4765i	0.0176742	−	0.0659611i
$554$	−189.673	−	189.673i	−0.342370	−	0.342370i
$555$	−829.402	−	1436.57i	−1.49442	−	2.58841i
$556$	−44.3031	−	25.5784i	−0.0796819	−	0.0460044i
$557$	632.239	−	169.408i	1.13508	−	0.304144i	0.358109	−	0.933680i	$-0.383422\pi$
$557$	632.239	−	169.408i	1.13508	−	0.304144i	0.776971	+	0.629536i	$0.216755\pi$
$558$		−	410.452i		−	0.735577i
$559$	−202.171	+	323.103i	−0.361666	+	0.578003i
$560$	11.8718			0.0211997
$561$	2.63751	+	9.84333i	0.00470145	+	0.0175460i
$562$	32.8661	−	56.9258i	0.0584806	−	0.101291i
$563$	−828.273	+	478.204i	−1.47118	+	0.849385i	−0.999476	−	0.0323732i	$-0.989694\pi$
$563$	−828.273	+	478.204i	−1.47118	+	0.849385i	−0.471702	+	0.881758i	$0.656360\pi$
$564$	−202.492	+	202.492i	−0.359028	+	0.359028i
$565$	371.236	+	99.4723i	0.657055	+	0.176057i
$566$	−192.883	+	719.847i	−0.340782	+	1.27182i
$567$	−3.68264	−	3.68264i	−0.00649495	−	0.00649495i
$568$	137.927	+	238.897i	0.242830	+	0.420593i
$569$	−281.681	−	162.629i	−0.495046	−	0.285815i	0.231619	−	0.972807i	$-0.425598\pi$
$569$	−281.681	−	162.629i	−0.495046	−	0.285815i	−0.726666	+	0.686991i	$0.758931\pi$
$570$	590.419	−	158.202i	1.03582	−	0.277548i
$571$		−	218.946i		−	0.383442i	−0.981449	−	0.191721i	$-0.938593\pi$
$571$		−	218.946i		−	0.383442i	0.981449	−	0.191721i	$-0.0614069\pi$
$572$	−5.64213	+	18.4144i	−0.00986387	+	0.0321931i
$573$	−1265.80			−2.20908
$574$	−3.36063	−	12.5420i	−0.00585475	−	0.0218502i
$575$	508.040	−	879.951i	0.883548	−	1.53035i
$576$	95.6628	−	55.2309i	0.166081	−	0.0958870i
$577$	−478.578	+	478.578i	−0.829425	+	0.829425i	−0.987437	−	0.158012i	$-0.949492\pi$
$577$	−478.578	+	478.578i	−0.829425	+	0.829425i	0.158012	+	0.987437i	$0.449492\pi$
$578$	−383.446	−	102.744i	−0.663401	−	0.177758i
$579$	196.774	−	734.372i	0.339852	−	1.26834i
$580$	358.319	+	358.319i	0.617791	+	0.617791i
$581$	6.85877	+	11.8797i	0.0118051	+	0.0204471i
$582$	−118.892	−	68.6426i	−0.204283	−	0.117943i
$583$	−61.4198	+	16.4574i	−0.105351	+	0.0282288i
$584$		−	203.816i		−	0.349001i
$585$	1457.03	−	335.446i	2.49064	−	0.573412i
$586$	193.667			0.330490
$587$	64.1765	+	239.510i	0.109330	+	0.408024i	0.998800	−	0.0489685i	$-0.0155934\pi$
$587$	64.1765	+	239.510i	0.109330	+	0.408024i	−0.889471	+	0.456992i	$0.848927\pi$
$588$	−233.405	+	404.269i	−0.396947	+	0.687533i
$589$	−197.788	+	114.193i	−0.335803	+	0.193876i
$590$	−833.560	+	833.560i	−1.41281	+	1.41281i
$591$	1387.64	+	371.816i	2.34795	+	0.629130i
$592$	−43.1711	+	161.117i	−0.0729242	+	0.272157i
$593$	−107.905	−	107.905i	−0.181964	−	0.181964i	0.610247	−	0.792211i	$-0.291070\pi$
$593$	−107.905	−	107.905i	−0.181964	−	0.181964i	−0.792211	+	0.610247i	$0.791070\pi$
$594$	−12.0264	−	20.8304i	−0.0202465	−	0.0350679i
$595$	−7.40414	−	4.27478i	−0.0124439	−	0.00718451i
$596$	51.9730	−	13.9261i	0.0872031	−	0.0233660i
$597$			894.587i			1.49847i
$598$	94.4368	+	410.191i	0.157921	+	0.685938i
$599$	788.030			1.31558			0.657788	−	0.753203i	$-0.271492\pi$
$599$	788.030			1.31558			0.657788	+	0.753203i	$0.271492\pi$
$600$	155.156	+	579.049i	0.258593	+	0.965081i
$601$	−191.526	+	331.733i	−0.318679	+	0.551968i	−0.980213	−	0.197947i	$-0.936573\pi$
$601$	−191.526	+	331.733i	−0.318679	+	0.551968i	0.661534	+	0.749915i	$0.269906\pi$
$602$	−12.7947	+	7.38701i	−0.0212536	+	0.0122708i
$603$	679.574	−	679.574i	1.12699	−	1.12699i
$604$	299.697	+	80.3035i	0.496187	+	0.132953i
$605$	259.671	−	969.107i	0.429209	−	1.60183i
$606$	−132.880	−	132.880i	−0.219273	−	0.219273i
$607$	−118.890	−	205.923i	−0.195865	−	0.339248i	0.751319	−	0.659939i	$-0.229418\pi$
$607$	−118.890	−	205.923i	−0.195865	−	0.339248i	−0.947184	+	0.320692i	$0.896085\pi$
$608$	−53.2292	−	30.7319i	−0.0875480	−	0.0505459i
$609$	49.9992	−	13.3972i	0.0821005	−	0.0219988i
$610$			182.161i			0.298624i
$611$	372.658	+	114.181i	0.609915	+	0.186876i
$612$	−79.5499			−0.129983
$613$	113.399	+	423.210i	0.184990	+	0.690391i	0.994633	+	0.103468i	$0.0329940\pi$
$613$	113.399	+	423.210i	0.184990	+	0.690391i	−0.809643	+	0.586923i	$0.800339\pi$
$614$	306.038	−	530.073i	0.498433	−	0.863311i
$615$	887.681	−	512.503i	1.44338	−	0.833338i
$616$	−0.527886	+	0.527886i	−0.000856959	+	0.000856959i
$617$	−111.769	−	29.9483i	−0.181149	−	0.0485386i	0.167104	−	0.985939i	$-0.446558\pi$
$617$	−111.769	−	29.9483i	−0.181149	−	0.0485386i	−0.348253	+	0.937401i	$0.613225\pi$
$618$	119.016	−	444.173i	0.192582	−	0.718727i
$619$	−471.622	−	471.622i	−0.761910	−	0.761910i	0.214757	−	0.976667i	$-0.431104\pi$
$619$	−471.622	−	471.622i	−0.761910	−	0.761910i	−0.976667	+	0.214757i	$0.931104\pi$
$620$	−175.082	−	303.251i	−0.282390	−	0.489115i
$621$	−455.255	−	262.841i	−0.733099	−	0.423255i
$622$	188.886	−	50.6118i	0.303675	−	0.0813694i
$623$		−	30.3052i		−	0.0486440i
$624$	−210.523	−	131.728i	−0.337376	−	0.211102i
$625$	−235.071			−0.376114
$626$	192.322	+	717.756i	0.307224	+	1.14658i
$627$	−19.2188	+	33.2879i	−0.0306519	+	0.0530907i
$628$	247.129	−	142.680i	0.393518	−	0.227197i
$629$	84.9395	−	84.9395i	0.135039	−	0.135039i
$630$	55.9807	+	15.0000i	0.0888582	+	0.0238095i
$631$	−220.328	+	822.277i	−0.349173	+	1.30313i	0.538487	+	0.842634i	$0.318996\pi$
$631$	−220.328	+	822.277i	−0.349173	+	1.30313i	−0.887660	+	0.460499i	$0.847670\pi$
$632$	−211.962	−	211.962i	−0.335383	−	0.335383i
$633$	405.492	+	702.333i	0.640588	+	1.10953i
$634$	42.2445	+	24.3899i	0.0666318	+	0.0384699i
$635$	−1855.72	+	497.238i	−2.92239	+	0.783052i
$636$		−	819.909i		−	1.28917i
$637$	634.949	+	22.5603i	0.996780	+	0.0354164i
$638$	−31.8657			−0.0499462
$639$	348.541	+	1300.77i	0.545447	+	2.03564i
$640$	47.1185	−	81.6116i	0.0736227	−	0.127518i
$641$	25.2926	−	14.6027i	0.0394580	−	0.0227811i	−0.480141	−	0.877191i	$-0.659415\pi$
$641$	25.2926	−	14.6027i	0.0394580	−	0.0227811i	0.519599	+	0.854410i	$0.326081\pi$
$642$	614.156	−	614.156i	0.956630	−	0.956630i
$643$	197.411	+	52.8962i	0.307016	+	0.0822648i	0.409038	−	0.912517i	$-0.365864\pi$
$643$	197.411	+	52.8962i	0.307016	+	0.0822648i	−0.102022	+	0.994782i	$0.532531\pi$
$644$	−4.22289	+	15.7600i	−0.00655728	+	0.0244721i
$645$	−824.681	−	824.681i	−1.27857	−	1.27857i
$646$	22.1318	+	38.3334i	0.0342597	+	0.0593396i
$647$	−915.647	−	528.649i	−1.41522	−	0.817077i	−0.419345	−	0.907827i	$-0.637740\pi$
$647$	−915.647	−	528.649i	−1.41522	−	0.817077i	−0.995874	+	0.0907495i	$0.971074\pi$
$648$	−39.9321	+	10.6998i	−0.0616237	+	0.0165120i
$649$		−	74.1294i		−	0.114221i
$650$	597.060	−	556.087i	0.918553	−	0.855519i
$651$	−35.7690			−0.0549447
$652$	13.7505	+	51.3177i	0.0210898	+	0.0787081i
$653$	−38.0505	+	65.9054i	−0.0582703	+	0.100927i	−0.893689	−	0.448687i	$-0.851892\pi$
$653$	−38.0505	+	65.9054i	−0.0582703	+	0.100927i	0.835419	+	0.549614i	$0.185225\pi$
$654$	−252.628	+	145.855i	−0.386281	+	0.223019i
$655$	−955.693	+	955.693i	−1.45907	+	1.45907i
$656$	−99.5572	−	26.6763i	−0.151764	−	0.0406650i
$657$	257.521	−	961.081i	0.391965	−	1.46283i
$658$	10.6830	+	10.6830i	0.0162355	+	0.0162355i
$659$	421.818	+	730.610i	0.640087	+	1.10866i	0.985413	+	0.170181i	$0.0544352\pi$
$659$	421.818	+	730.610i	0.640087	+	1.10866i	−0.345325	+	0.938483i	$0.612231\pi$
$660$	−51.0374	−	29.4664i	−0.0773293	−	0.0446461i
$661$	809.079	−	216.792i	1.22402	−	0.327976i	0.411773	−	0.911286i	$-0.364910\pi$
$661$	809.079	−	216.792i	1.22402	−	0.327976i	0.812249	+	0.583311i	$0.198243\pi$
$662$		−	31.3602i		−	0.0473718i
$663$	83.8654	+	157.960i	0.126494	+	0.238250i
$664$	108.888			0.163988
$665$	−8.34636	−	31.1491i	−0.0125509	−	0.0468407i
$666$	−407.141	+	705.188i	−0.611322	+	1.05884i
$667$	−603.130	+	348.218i	−0.904244	+	0.522065i
$668$	−10.6430	+	10.6430i	−0.0159326	+	0.0159326i
$669$	−1109.39	−	297.261i	−1.65829	−	0.444336i
$670$	212.206	−	791.962i	0.316725	−	1.18203i
$671$	−8.09987	−	8.09987i	−0.0120713	−	0.0120713i
$672$	−4.81312	−	8.33656i	−0.00716238	−	0.0124056i
$673$	334.718	+	193.250i	0.497353	+	0.287147i	0.727620	−	0.685981i	$-0.240627\pi$
$673$	334.718	+	193.250i	0.497353	+	0.287147i	−0.230267	+	0.973128i	$0.573960\pi$
$674$	−744.058	+	199.370i	−1.10394	+	0.295801i
$675$			1018.98i			1.50960i
$676$	−23.9886	+	337.148i	−0.0354860	+	0.498739i
$677$	328.683			0.485500			0.242750	−	0.970089i	$-0.421951\pi$
$677$	328.683			0.485500			0.242750	+	0.970089i	$0.421951\pi$
$678$	−80.6570	−	301.016i	−0.118963	−	0.443976i
$679$	−3.62141	+	6.27247i	−0.00533345	+	0.00923781i
$680$	−58.7732	+	33.9327i	−0.0864312	+	0.0499011i
$681$	305.548	−	305.548i	0.448675	−	0.448675i
$682$	21.2693	+	5.69910i	0.0311867	+	0.00835646i
$683$	−209.208	+	780.775i	−0.306308	+	1.14316i	0.625506	+	0.780219i	$0.284892\pi$
$683$	−209.208	+	780.775i	−0.306308	+	1.14316i	−0.931814	+	0.362936i	$0.881774\pi$
$684$	−212.169	−	212.169i	−0.310188	−	0.310188i
$685$	−430.392	−	745.462i	−0.628310	−	1.08827i
$686$	42.7119	+	24.6597i	0.0622623	+	0.0359471i
$687$	1623.69	−	435.066i	2.36345	−	0.633283i
$688$			117.274i			0.170457i
$689$	−985.629	+	523.298i	−1.43052	+	0.759504i
$690$	−1288.00			−1.86666
$691$	−208.788	−	779.206i	−0.302153	−	1.12765i	−0.935369	−	0.353674i	$-0.884932\pi$
$691$	−208.788	−	779.206i	−0.302153	−	1.12765i	0.633216	−	0.773975i	$-0.281735\pi$
$692$	28.8293	−	49.9338i	0.0416608	−	0.0721586i
$693$	−3.15619	+	1.82223i	−0.00455439	+	0.00262948i
$694$	−640.601	+	640.601i	−0.923057	+	0.923057i
$695$	−205.795	−	55.1425i	−0.296107	−	0.0793417i
$696$	106.346	−	396.888i	0.152796	−	0.570241i
$697$	52.4857	+	52.4857i	0.0753023	+	0.0753023i
$698$	−42.7706	−	74.0809i	−0.0612759	−	0.106133i
$699$	1591.79	+	919.020i	2.27724	+	1.31476i
$700$	30.5492	−	8.18563i	0.0436417	−	0.0116938i
$701$		−	1080.31i		−	1.54110i	−0.637378	−	0.770552i	$-0.719981\pi$
$701$		−	1080.31i		−	1.54110i	0.637378	−	0.770552i	$-0.280019\pi$
$702$	−287.699	−	308.897i	−0.409828	−	0.440024i
$703$	453.087			0.644505
$704$	1.53376	+	5.72406i	0.00217863	+	0.00813076i
$705$	−596.320	+	1032.86i	−0.845843	+	1.46504i
$706$	359.282	−	207.432i	0.508898	−	0.293813i
$707$	−7.01040	+	7.01040i	−0.00991570	+	0.00991570i
$708$	923.283	+	247.393i	1.30407	+	0.349425i
$709$	204.436	−	762.964i	0.288343	−	1.07611i	−0.658018	−	0.753002i	$-0.728605\pi$
$709$	204.436	−	762.964i	0.288343	−	1.07611i	0.946361	−	0.323110i	$-0.104728\pi$
$710$	812.365	+	812.365i	1.14418	+	1.14418i
$711$	−731.679	−	1267.31i	−1.02908	−	1.78243i
$712$	−208.330	−	120.280i	−0.292599	−	0.168932i
$713$	464.849	−	124.556i	0.651962	−	0.174693i
$714$			6.93240i			0.00970925i
$715$	−2.84814	+	80.1597i	−0.00398341	+	0.112111i
$716$	424.196			0.592453
$717$	−368.188	−	1374.10i	−0.513511	−	1.91645i
$718$	118.752	−	205.684i	0.165393	−	0.286469i
$719$	−700.700	+	404.550i	−0.974548	+	0.562656i	−0.900620	−	0.434608i	$-0.856887\pi$
$719$	−700.700	+	404.550i	−0.974548	+	0.562656i	−0.0739286	+	0.997264i	$0.523554\pi$
$720$	325.300	−	325.300i	0.451805	−	0.451805i
$721$	−23.4335	−	6.27898i	−0.0325014	−	0.00870871i
$722$	88.9237	−	331.868i	0.123163	−	0.459650i
$723$	632.651	+	632.651i	0.875036	+	0.875036i
$724$	112.088	+	194.142i	0.154817	+	0.268152i
$725$	1169.11	+	674.983i	1.61256	+	0.931011i
$726$	−785.799	+	210.554i	−1.08237	+	0.290019i
$727$		−	1368.53i		−	1.88243i	−0.337808	−	0.941215i	$-0.609685\pi$
$727$		−	1368.53i		−	1.88243i	0.337808	−	0.941215i	$-0.390315\pi$
$728$	−6.94963	+	11.1067i	−0.00954620	+	0.0152564i
$729$	−1188.70			−1.63059
$730$	−219.696	−	819.916i	−0.300953	−	1.12317i
$731$	42.2280	−	73.1410i	0.0577674	−	0.100056i
$732$	127.916	−	73.8523i	0.174749	−	0.100891i
$733$	204.408	−	204.408i	0.278865	−	0.278865i	−0.553791	−	0.832656i	$-0.686819\pi$
$733$	204.408	−	204.408i	0.278865	−	0.278865i	0.832656	+	0.553791i	$0.186819\pi$
$734$	139.766	+	37.4501i	0.190417	+	0.0510220i
$735$	−503.180	+	1877.89i	−0.684598	+	2.55496i
$736$	91.5805	+	91.5805i	0.124430	+	0.124430i
$737$	25.7792	+	44.6509i	0.0349786	+	0.0605846i
$738$	−435.749	−	251.580i	−0.590446	−	0.340894i
$739$	234.406	−	62.8090i	0.317194	−	0.0849918i	−0.0967096	−	0.995313i	$-0.530832\pi$
$739$	234.406	−	62.8090i	0.317194	−	0.0849918i	0.413903	+	0.910321i	$0.364165\pi$
$740$			694.678i			0.938755i
$741$	−197.619	+	644.976i	−0.266692	+	0.870414i
$742$	−43.2564			−0.0582970
$743$	23.3630	+	87.1920i	0.0314442	+	0.117351i	0.979864	−	0.199665i	$-0.0639855\pi$
$743$	23.3630	+	87.1920i	0.0314442	+	0.117351i	−0.948420	+	0.317017i	$0.897319\pi$
$744$	−141.965	+	245.891i	−0.190813	+	0.330498i
$745$	194.067	−	112.045i	0.260493	−	0.150395i
$746$	604.616	−	604.616i	0.810477	−	0.810477i
$747$	513.454	+	137.580i	0.687355	+	0.184176i
$748$	1.10455	−	4.12222i	0.00147666	−	0.00551099i
$749$	−32.4014	−	32.4014i	−0.0432595	−	0.0432595i
$750$	545.119	+	944.174i	0.726826	+	1.25890i
$751$	339.714	+	196.134i	0.452349	+	0.261164i	0.708822	−	0.705387i	$-0.249227\pi$
$751$	339.714	+	196.134i	0.452349	+	0.261164i	−0.256473	+	0.966552i	$0.582560\pi$
$752$	115.839	−	31.0390i	0.154041	−	0.0412753i
$753$			480.050i			0.637516i
$754$	−544.981	+	125.469i	−0.722786	+	0.166404i
$755$	1292.19			1.71150
$756$	−4.23494	−	15.8050i	−0.00560178	−	0.0209061i
$757$	178.827	−	309.738i	0.236232	−	0.409165i	−0.723398	−	0.690431i	$-0.757421\pi$
$757$	178.827	−	309.738i	0.236232	−	0.409165i	0.959630	+	0.281266i	$0.0907542\pi$
$758$	469.971	−	271.338i	0.620015	−	0.357966i
$759$	57.2715	−	57.2715i	0.0754566	−	0.0754566i
$760$	−247.257	−	66.2524i	−0.325339	−	0.0871743i
$761$	−215.873	+	805.649i	−0.283670	+	1.05867i	0.666135	+	0.745831i	$0.267947\pi$
$761$	−215.873	+	805.649i	−0.283670	+	1.05867i	−0.949806	+	0.312841i	$0.898719\pi$
$762$	1101.52	+	1101.52i	1.44557	+	1.44557i
$763$	7.69493	+	13.3280i	0.0100851	+	0.0174679i
$764$

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)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(2.38787 - 4.13592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.88981 + 5.88981i) q^{5} +(6.52379 + 1.74804i) q^{6} +(0.0922225 - 0.344179i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(2.38787 - 4.13592i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-5.88981 + 5.88981i) q^{5} +(6.52379 + 1.74804i) q^{6} +(0.0922225 - 0.344179i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-6.90386 - 11.9578i) q^{9} +(-10.2015 - 5.88981i) q^{10} +(0.715507 - 0.191720i) q^{11} +9.55149i q^{12} +(11.4820 - 6.09614i) q^{13} +0.503913 q^{14} +(10.2956 + 38.4239i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-2.49470 + 1.44031i) q^{17} +(13.8077 - 13.8077i) q^{18} +(-10.4951 - 2.81216i) q^{19} +(4.31164 - 16.0913i) q^{20} +(-1.20328 - 1.20328i) q^{21} +(0.523787 + 0.907226i) q^{22} +(19.8278 + 11.4476i) q^{23} +(-13.0476 + 3.49609i) q^{24} -44.3798i q^{25} +(12.5302 + 13.4534i) q^{26} -22.9605 q^{27} +(0.184445 + 0.688358i) q^{28} +(-15.2092 + 26.3432i) q^{29} +(-48.7195 + 28.1282i) q^{30} +(14.8631 - 14.8631i) q^{31} +(5.46410 + 1.46410i) q^{32} +(0.915603 - 3.41708i) q^{33} +(-2.88063 - 2.88063i) q^{34} +(1.48398 + 2.57032i) q^{35} +(23.9157 + 13.8077i) q^{36} +(-40.2792 + 10.7928i) q^{37} -15.3659i q^{38} +(2.20453 - 62.0455i) q^{39} +23.5593 q^{40} +(-6.66907 - 24.8893i) q^{41} +(1.20328 - 2.08414i) q^{42} +(-25.3907 + 14.6593i) q^{43} +(-1.04757 + 1.04757i) q^{44} +(111.092 + 29.7670i) q^{45} +(-8.38019 + 31.2753i) q^{46} +(21.2000 + 21.2000i) q^{47} +(-9.55149 - 16.5437i) q^{48} +(42.3253 + 24.4365i) q^{49} +(60.6239 - 16.2441i) q^{50} +13.7571i q^{51} +(-13.7913 + 22.0409i) q^{52} -85.8410 q^{53} +(-8.40412 - 31.3646i) q^{54} +(-3.08501 + 5.34339i) q^{55} +(-0.872803 + 0.503913i) q^{56} +(-36.6919 + 36.6919i) q^{57} +(-41.5524 - 11.1339i) q^{58} +(25.9010 - 96.6638i) q^{59} +(-56.2565 - 56.2565i) q^{60} +(-7.73202 - 13.3923i) q^{61} +(25.7437 + 14.8631i) q^{62} +(-4.75233 + 1.27338i) q^{63} +8.00000i q^{64} +(-31.7219 + 103.532i) q^{65} +5.00295 q^{66} +(18.0146 + 67.2315i) q^{67} +(2.88063 - 4.98939i) q^{68} +(94.6923 - 54.6706i) q^{69} +(-2.96795 + 2.96795i) q^{70} +(-94.2060 - 25.2424i) q^{71} +(-10.1080 + 37.7234i) q^{72} +(50.9541 + 50.9541i) q^{73} +(-29.4864 - 51.0720i) q^{74} +(-183.551 - 105.973i) q^{75} +(20.9903 - 5.62432i) q^{76} -0.263943i q^{77} +(85.5627 - 19.6988i) q^{78} +105.981 q^{79} +(8.62328 + 32.1825i) q^{80} +(7.30809 - 12.6580i) q^{81} +(31.5584 - 18.2202i) q^{82} +(-27.2221 + 27.2221i) q^{83} +(3.28742 + 0.880862i) q^{84} +(6.21012 - 23.1765i) q^{85} +(-29.3186 - 29.3186i) q^{86} +(72.6355 + 125.808i) q^{87} +(-1.81445 - 1.04757i) q^{88} +(82.1525 - 22.0127i) q^{89} +162.650i q^{90} +(-1.03926 - 4.51407i) q^{91} -45.7902 q^{92} +(-25.9814 - 96.9639i) q^{93} +(-21.2000 + 36.7195i) q^{94} +(78.3775 - 45.2513i) q^{95} +(19.1030 - 19.1030i) q^{96} +(-19.6341 - 5.26095i) q^{97} +(-17.8888 + 66.7618i) q^{98} +(-7.23232 - 7.23232i) 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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