LMFDB - Embedded newform 390.2.bn.b.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.3
Root			$0.117630 - 0.893490i$ of defining polynomial
Character	$\chi$	$=$	390.97
Dual form			390.2.bn.b.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.23607 + 0.00342112i) q^{5} +(0.965926 + 0.258819i) q^{6} +(3.25724 - 1.88057i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.23607 + 0.00342112i) q^{5} +(0.965926 + 0.258819i) q^{6} +(3.25724 - 1.88057i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.11507 + 1.93820i) q^{10} +(4.81242 - 1.28948i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.57858 + 0.440224i) q^{13} -3.76113i q^{14} +(-0.582041 - 2.15899i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.59335 - 1.49873i) q^{17} +1.00000i q^{18} +(0.910792 - 3.39912i) q^{19} +(1.12100 + 1.93478i) q^{20} +(2.65952 + 2.65952i) q^{21} +(1.28948 - 4.81242i) q^{22} +(5.57258 - 1.49317i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(4.99998 - 0.0152997i) q^{25} +(2.17053 - 2.87903i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.25724 - 1.88057i) q^{28} +(-3.67601 - 2.12235i) q^{29} +(-2.16076 - 0.575432i) q^{30} +(-2.51448 + 2.51448i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.49109 + 4.31470i) q^{33} +(-4.09462 + 4.09462i) q^{34} +(-7.27696 + 4.21621i) q^{35} +(0.866025 + 0.500000i) q^{36} +(1.47447 + 0.851284i) q^{37} +(-2.48833 - 2.48833i) q^{38} +(0.500979 + 3.57058i) q^{39} +(2.23607 - 0.00342112i) q^{40} +(2.10480 + 7.85522i) q^{41} +(3.63298 - 0.973453i) q^{42} +(0.161303 - 0.601992i) q^{43} +(-3.52294 - 3.52294i) q^{44} +(1.93478 - 1.12100i) q^{45} +(1.49317 - 5.57258i) q^{46} +9.18458i q^{47} +(-0.965926 - 0.258819i) q^{48} +(3.57307 - 6.18873i) q^{49} +(2.48674 - 4.33776i) q^{50} -5.79066i q^{51} +(-1.40804 - 3.31925i) q^{52} +(-6.03244 + 6.03244i) q^{53} +(-0.965926 + 0.258819i) q^{54} +(-10.7565 + 2.89983i) q^{55} +(-3.25724 + 1.88057i) q^{56} +3.51903 q^{57} +(-3.67601 + 2.12235i) q^{58} +(-5.50190 - 1.47423i) q^{59} +(-1.57872 + 1.58356i) q^{60} +(-2.64801 - 4.58649i) q^{61} +(0.920362 + 3.43484i) q^{62} +(-1.88057 + 3.25724i) q^{63} +1.00000 q^{64} +(-8.00343 - 0.972128i) q^{65} +4.98218 q^{66} +(-2.69190 + 4.66250i) q^{67} +(1.49873 + 5.59335i) q^{68} +(2.88458 + 4.99624i) q^{69} +(0.0128673 + 8.41014i) q^{70} +(-11.0111 - 2.95042i) q^{71} +(0.866025 - 0.500000i) q^{72} -5.27482 q^{73} +(1.47447 - 0.851284i) q^{74} +(1.30887 + 4.82565i) q^{75} +(-3.39912 + 0.910792i) q^{76} +(13.2502 - 13.2502i) q^{77} +(3.34270 + 1.35143i) q^{78} +4.66690i q^{79} +(1.11507 - 1.93820i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.85522 + 2.10480i) q^{82} -0.863680i q^{83} +(0.973453 - 3.63298i) q^{84} +(12.5122 + 3.33213i) q^{85} +(-0.440689 - 0.440689i) q^{86} +(1.09861 - 4.10006i) q^{87} +(-4.81242 + 1.28948i) q^{88} +(-3.59112 - 13.4022i) q^{89} +(-0.00342112 - 2.23607i) q^{90} +(12.4841 - 5.29584i) q^{91} +(-4.07941 - 4.07941i) q^{92} +(-3.07959 - 1.77800i) q^{93} +(7.95408 + 4.59229i) q^{94} +(-2.02496 + 7.60378i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(8.93684 + 15.4791i) q^{97} +(-3.57307 - 6.18873i) q^{98} +(-3.52294 + 3.52294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.23607	+	0.00342112i	−0.999999	+	0.00152997i
$5$	−2.23607	+	0.00342112i	−0.999999	+	0.00152997i
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	3.25724	−	1.88057i	1.23112	−	0.710788i	0.263857	−	0.964562i	$-0.415005\pi$
$7$	3.25724	−	1.88057i	1.23112	−	0.710788i	0.967263	+	0.253774i	$0.0816720\pi$
$8$	−1.00000			−0.353553
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−1.11507	+	1.93820i	−0.352616	+	0.612913i
$11$	4.81242	−	1.28948i	1.45100	−	0.388794i	0.554628	−	0.832099i	$-0.312861\pi$
$11$	4.81242	−	1.28948i	1.45100	−	0.388794i	0.896371	+	0.443305i	$0.146194\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.57858	+	0.440224i	0.992518	+	0.122096i
$13$	3.57858	+	0.440224i	0.992518	+	0.122096i
$14$		−	3.76113i		−	1.00521i
$15$	−0.582041	−	2.15899i	−0.150282	−	0.557448i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.59335	−	1.49873i	−1.35659	−	0.363496i	−0.494025	−	0.869448i	$-0.664475\pi$
$17$	−5.59335	−	1.49873i	−1.35659	−	0.363496i	−0.862562	+	0.505952i	$0.831141\pi$
$18$			1.00000i			0.235702i
$19$	0.910792	−	3.39912i	0.208950	−	0.779812i	−0.779259	−	0.626702i	$-0.784404\pi$
$19$	0.910792	−	3.39912i	0.208950	−	0.779812i	0.988209	−	0.153110i	$-0.0489290\pi$
$20$	1.12100	+	1.93478i	0.250662	+	0.432630i
$21$	2.65952	+	2.65952i	0.580356	+	0.580356i
$22$	1.28948	−	4.81242i	0.274919	−	1.02601i
$23$	5.57258	−	1.49317i	1.16196	−	0.311347i	0.374214	−	0.927342i	$-0.377913\pi$
$23$	5.57258	−	1.49317i	1.16196	−	0.311347i	0.787750	+	0.615995i	$0.211246\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	4.99998	−	0.0152997i	0.999995	−	0.00305994i
$26$	2.17053	−	2.87903i	0.425677	−	0.564623i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−3.25724	−	1.88057i	−0.615560	−	0.355394i
$29$	−3.67601	−	2.12235i	−0.682618	−	0.394110i	0.118223	−	0.992987i	$-0.462280\pi$
$29$	−3.67601	−	2.12235i	−0.682618	−	0.394110i	−0.800841	+	0.598877i	$0.795614\pi$
$30$	−2.16076	−	0.575432i	−0.394499	−	0.105059i
$31$	−2.51448	+	2.51448i	−0.451613	+	0.451613i	−0.895890	−	0.444276i	$-0.853461\pi$
$31$	−2.51448	+	2.51448i	−0.451613	+	0.451613i	0.444276	+	0.895890i	$0.353461\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.49109	+	4.31470i	0.433643	+	0.751092i
$34$	−4.09462	+	4.09462i	−0.702221	+	0.702221i
$35$	−7.27696	+	4.21621i	−1.23003	+	0.712670i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	1.47447	+	0.851284i	0.242401	+	0.139950i	0.616280	−	0.787527i	$-0.288639\pi$
$37$	1.47447	+	0.851284i	0.242401	+	0.139950i	−0.373879	+	0.927478i	$0.621972\pi$
$38$	−2.48833	−	2.48833i	−0.403661	−	0.403661i
$39$	0.500979	+	3.57058i	0.0802209	+	0.571750i
$40$	2.23607	−	0.00342112i	0.353553	−	0.000540927i
$41$	2.10480	+	7.85522i	0.328715	+	1.22678i	0.910525	+	0.413455i	$0.135678\pi$
$41$	2.10480	+	7.85522i	0.328715	+	1.22678i	−0.581810	+	0.813325i	$0.697655\pi$
$42$	3.63298	−	0.973453i	0.560581	−	0.150207i
$43$	0.161303	−	0.601992i	0.0245985	−	0.0918029i	−0.952535	−	0.304428i	$-0.901535\pi$
$43$	0.161303	−	0.601992i	0.0245985	−	0.0918029i	0.977134	+	0.212625i	$0.0682013\pi$
$44$	−3.52294	−	3.52294i	−0.531102	−	0.531102i
$45$	1.93478	−	1.12100i	0.288420	−	0.167108i
$46$	1.49317	−	5.57258i	0.220156	−	0.821633i
$47$			9.18458i			1.33971i	0.742493	+	0.669854i	$0.233643\pi$
$47$			9.18458i			1.33971i	−0.742493	+	0.669854i	$0.766357\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$	3.57307	−	6.18873i	0.510438	−	0.884105i
$50$	2.48674	−	4.33776i	0.351678	−	0.613451i
$51$		−	5.79066i		−	0.810855i
$52$	−1.40804	−	3.31925i	−0.195260	−	0.460297i
$53$	−6.03244	+	6.03244i	−0.828619	+	0.828619i	−0.987326	−	0.158707i	$-0.949268\pi$
$53$	−6.03244	+	6.03244i	−0.828619	+	0.828619i	0.158707	+	0.987326i	$0.449268\pi$
$54$	−0.965926	+	0.258819i	−0.131446	+	0.0352208i
$55$	−10.7565	+	2.89983i	−1.45040	+	0.391014i
$56$	−3.25724	+	1.88057i	−0.435267	+	0.251301i
$57$	3.51903			0.466107
$58$	−3.67601	+	2.12235i	−0.482684	+	0.278678i
$59$	−5.50190	−	1.47423i	−0.716287	−	0.191928i	−0.117773	−	0.993041i	$-0.537575\pi$
$59$	−5.50190	−	1.47423i	−0.716287	−	0.191928i	−0.598514	+	0.801112i	$0.704242\pi$
$60$	−1.57872	+	1.58356i	−0.203812	+	0.204436i
$61$	−2.64801	−	4.58649i	−0.339043	−	0.587240i	0.645210	−	0.764005i	$-0.276770\pi$
$61$	−2.64801	−	4.58649i	−0.339043	−	0.587240i	−0.984253	+	0.176765i	$0.943437\pi$
$62$	0.920362	+	3.43484i	0.116886	+	0.436225i
$63$	−1.88057	+	3.25724i	−0.236929	+	0.410373i
$64$	1.00000			0.125000
$65$	−8.00343	−	0.972128i	−0.992704	−	0.120578i
$66$	4.98218			0.613264
$67$	−2.69190	+	4.66250i	−0.328868	+	0.569616i	−0.982287	−	0.187380i	$-0.940000\pi$
$67$	−2.69190	+	4.66250i	−0.328868	+	0.569616i	0.653420	+	0.756996i	$0.273334\pi$
$68$	1.49873	+	5.59335i	0.181748	+	0.678293i
$69$	2.88458	+	4.99624i	0.347263	+	0.601477i
$70$	0.0128673	+	8.41014i	0.00153794	+	1.00520i
$71$	−11.0111	−	2.95042i	−1.30678	−	0.350150i	−0.462770	−	0.886479i	$-0.653144\pi$
$71$	−11.0111	−	2.95042i	−1.30678	−	0.350150i	−0.844010	+	0.536328i	$0.819811\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−5.27482			−0.617371			−0.308686	−	0.951164i	$-0.599889\pi$
$73$	−5.27482			−0.617371			−0.308686	+	0.951164i	$0.599889\pi$
$74$	1.47447	−	0.851284i	0.171403	−	0.0989597i
$75$	1.30887	+	4.82565i	0.151135	+	0.557218i
$76$	−3.39912	+	0.910792i	−0.389906	+	0.104475i
$77$	13.2502	−	13.2502i	1.51000	−	1.51000i
$78$	3.34270	+	1.35143i	0.378486	+	0.153019i
$79$			4.66690i			0.525068i	0.964923	+	0.262534i	$0.0845582\pi$
$79$			4.66690i			0.525068i	−0.964923	+	0.262534i	$0.915442\pi$
$80$	1.11507	−	1.93820i	0.124669	−	0.216697i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	7.85522	+	2.10480i	0.867464	+	0.232436i
$83$		−	0.863680i		−	0.0948012i	−0.998876	−	0.0474006i	$-0.984906\pi$
$83$		−	0.863680i		−	0.0948012i	0.998876	−	0.0474006i	$-0.0150937\pi$
$84$	0.973453	−	3.63298i	0.106212	−	0.396390i
$85$	12.5122	+	3.33213i	1.35714	+	0.361420i
$86$	−0.440689	−	0.440689i	−0.0475207	−	0.0475207i
$87$	1.09861	−	4.10006i	0.117783	−	0.439572i
$88$	−4.81242	+	1.28948i	−0.513006	+	0.137459i
$89$	−3.59112	−	13.4022i	−0.380658	−	1.42063i	−0.844899	−	0.534925i	$-0.820340\pi$
$89$	−3.59112	−	13.4022i	−0.380658	−	1.42063i	0.464242	−	0.885709i	$-0.346327\pi$
$90$	−0.00342112	−	2.23607i	−0.000360618	−	0.235702i
$91$	12.4841	−	5.29584i	1.30869	−	0.555154i
$92$	−4.07941	−	4.07941i	−0.425308	−	0.425308i
$93$	−3.07959	−	1.77800i	−0.319339	−	0.184370i
$94$	7.95408	+	4.59229i	0.820401	+	0.473658i
$95$	−2.02496	+	7.60378i	−0.207757	+	0.780131i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	8.93684	+	15.4791i	0.907399	+	1.57166i	0.817664	+	0.575696i	$0.195269\pi$
$97$	8.93684	+	15.4791i	0.907399	+	1.57166i	0.0897349	+	0.995966i	$0.471398\pi$
$98$	−3.57307	−	6.18873i	−0.360934	−	0.625156i
$99$	−3.52294	+	3.52294i	−0.354068	+	0.354068i
$100$	−2.51324	−	4.32246i	−0.251324	−	0.432246i
$101$	−3.70757	−	2.14057i	−0.368917	−	0.212994i	0.304068	−	0.952650i	$-0.401655\pi$
$101$	−3.70757	−	2.14057i	−0.368917	−	0.212994i	−0.672985	+	0.739656i	$0.734988\pi$
$102$	−5.01486	−	2.89533i	−0.496545	−	0.286680i
$103$	5.75774	+	5.75774i	0.567327	+	0.567327i	0.931379	−	0.364052i	$-0.118607\pi$
$103$	5.75774	+	5.75774i	0.567327	+	0.567327i	−0.364052	+	0.931379i	$0.618607\pi$
$104$	−3.57858	−	0.440224i	−0.350908	−	0.0431676i
$105$	−5.95597	−	5.93777i	−0.581243	−	0.579467i
$106$	2.20803	+	8.24046i	0.214462	+	0.800384i
$107$	4.02443	−	1.07834i	0.389056	−	0.104247i	−0.0589882	−	0.998259i	$-0.518787\pi$
$107$	4.02443	−	1.07834i	0.389056	−	0.104247i	0.448044	+	0.894011i	$0.352121\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−4.69157	−	4.69157i	−0.449371	−	0.449371i	0.445774	−	0.895145i	$-0.352928\pi$
$109$	−4.69157	−	4.69157i	−0.449371	−	0.449371i	−0.895145	+	0.445774i	$0.852928\pi$
$110$	−2.86691	+	10.7653i	−0.273349	+	1.02643i
$111$	−0.440657	+	1.64455i	−0.0418253	+	0.156094i
$112$			3.76113i			0.355394i
$113$	19.6989	+	5.27831i	1.85312	+	0.496542i	0.999695	−	0.0246772i	$-0.00785579\pi$
$113$	19.6989	+	5.27831i	1.85312	+	0.496542i	0.853423	+	0.521219i	$0.174522\pi$
$114$	1.75952	−	3.04757i	0.164794	−	0.285431i
$115$	−12.4556	+	3.35789i	−1.16149	+	0.313125i
$116$			4.24469i			0.394110i
$117$	−3.31925	+	1.40804i	−0.306865	+	0.130174i
$118$	−4.02767	+	4.02767i	−0.370777	+	0.370777i
$119$	−21.0373	+	5.63694i	−1.92849	+	0.516737i
$120$	0.582041	+	2.15899i	0.0531328	+	0.197088i
$121$	11.9703	−	6.91107i	1.08821	−	0.628279i
$122$	−5.29602			−0.479480
$123$	−7.04280	+	4.06616i	−0.635028	+	0.366633i
$124$	3.43484	+	0.920362i	0.308458	+	0.0826510i
$125$	−11.1802	+	0.0513167i	−0.999989	+	0.00458990i
$126$	1.88057	+	3.25724i	0.167534	+	0.290178i
$127$	3.03693	+	11.3340i	0.269484	+	1.00573i	0.959448	+	0.281884i	$0.0909595\pi$
$127$	3.03693	+	11.3340i	0.269484	+	1.00573i	−0.689964	+	0.723843i	$0.742374\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.623228			0.0548722
$130$	−4.84360	+	6.44511i	−0.424812	+	0.565274i
$131$	−8.55747			−0.747669			−0.373835	−	0.927495i	$-0.621957\pi$
$131$	−8.55747			−0.747669			−0.373835	+	0.927495i	$0.621957\pi$
$132$	2.49109	−	4.31470i	0.216822	−	0.375546i
$133$	−3.42561	−	12.7846i	−0.297038	−	1.10856i
$134$	2.69190	+	4.66250i	0.232545	+	0.402779i
$135$	1.58356	+	1.57872i	0.136291	+	0.135874i
$136$	5.59335	+	1.49873i	0.479626	+	0.128515i
$137$	15.6758	−	9.05042i	1.33927	−	0.773230i	0.352574	−	0.935784i	$-0.385307\pi$
$137$	15.6758	−	9.05042i	1.33927	−	0.773230i	0.986700	+	0.162554i	$0.0519733\pi$
$138$	5.76916			0.491104
$139$	−5.27198	+	3.04378i	−0.447164	+	0.258170i	−0.706632	−	0.707582i	$-0.749786\pi$
$139$	−5.27198	+	3.04378i	−0.447164	+	0.258170i	0.259468	+	0.965752i	$0.416453\pi$
$140$	7.28983	+	4.19393i	0.616103	+	0.354452i
$141$	−8.87162	+	2.37714i	−0.747125	+	0.200192i
$142$	−8.06070	+	8.06070i	−0.676439	+	0.676439i
$143$	17.7893	−	2.49597i	1.48761	−	0.208724i
$144$		−	1.00000i		−	0.0833333i
$145$	8.22706	+	4.73313i	0.683220	+	0.393065i
$146$	−2.63741	+	4.56813i	−0.218274	+	0.378061i
$147$	6.90263	+	1.84956i	0.569320	+	0.152549i
$148$		−	1.70257i		−	0.139950i
$149$	−3.21271	+	11.9900i	−0.263195	+	0.982259i	0.700150	+	0.713996i	$0.253116\pi$
$149$	−3.21271	+	11.9900i	−0.263195	+	0.982259i	−0.963346	+	0.268263i	$0.913550\pi$
$150$	4.83357	+	1.27931i	0.394659	+	0.104455i
$151$	−10.5457	−	10.5457i	−0.858194	−	0.858194i	0.132931	−	0.991125i	$-0.457561\pi$
$151$	−10.5457	−	10.5457i	−0.858194	−	0.858194i	−0.991125	+	0.132931i	$0.957561\pi$
$152$	−0.910792	+	3.39912i	−0.0738750	+	0.275705i
$153$	5.59335	−	1.49873i	0.452195	−	0.121165i
$154$	−4.84992	−	18.1002i	−0.390818	−	1.45855i
$155$	5.61393	−	5.63114i	0.450922	−	0.452304i
$156$	2.84172	−	2.21915i	0.227520	−	0.177674i
$157$	−14.4314	−	14.4314i	−1.15175	−	1.15175i	−0.986202	−	0.165545i	$-0.947062\pi$
$157$	−14.4314	−	14.4314i	−1.15175	−	1.15175i	−0.165545	−	0.986202i	$-0.552938\pi$
$158$	4.04166	+	2.33345i	0.321537	+	0.185640i
$159$	−7.38820	−	4.26558i	−0.585922	−	0.338282i
$160$	−1.12100	−	1.93478i	−0.0886225	−	0.152958i
$161$	15.3432	−	15.3432i	1.20922	−	1.20922i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	3.60932	+	6.25152i	0.282704	+	0.489657i	0.972050	−	0.234775i	$-0.0754354\pi$
$163$	3.60932	+	6.25152i	0.282704	+	0.489657i	−0.689346	+	0.724432i	$0.742102\pi$
$164$	5.75042	−	5.75042i	0.449032	−	0.449032i
$165$	−5.58500	−	9.63942i	−0.434792	−	0.750428i
$166$	−0.747969	−	0.431840i	−0.0580536	−	0.0335173i
$167$	10.6044	+	6.12243i	0.820590	+	0.473768i	0.850620	−	0.525781i	$-0.176227\pi$
$167$	10.6044	+	6.12243i	0.820590	+	0.473768i	−0.0300300	+	0.999549i	$0.509560\pi$
$168$	−2.65952	−	2.65952i	−0.205187	−	0.205187i
$169$	12.6124	+	3.15075i	0.970185	+	0.242366i
$170$	9.14182	−	9.16984i	0.701146	−	0.703294i
$171$	0.910792	+	3.39912i	0.0696500	+	0.259937i
$172$	−0.601992	+	0.161303i	−0.0459015	+	0.0122993i
$173$	−0.704267	+	2.62836i	−0.0535444	+	0.199831i	−0.987517	−	0.157515i	$-0.949652\pi$
$173$	−0.704267	+	2.62836i	−0.0535444	+	0.199831i	0.933972	+	0.357346i	$0.116318\pi$
$174$	−3.00145	−	3.00145i	−0.227539	−	0.227539i
$175$	16.2573	−	9.45263i	1.22894	−	0.714551i
$176$	−1.28948	+	4.81242i	−0.0971985	+	0.362750i
$177$		−	5.69599i		−	0.428137i
$178$	−13.4022	−	3.59112i	−1.00454	−	0.269166i
$179$	5.19092	−	8.99094i	0.387988	−	0.672015i	−0.604191	−	0.796840i	$-0.706504\pi$
$179$	5.19092	−	8.99094i	0.387988	−	0.672015i	0.992179	+	0.124825i	$0.0398369\pi$
$180$	−1.93820	−	1.11507i	−0.144465	−	0.0831124i
$181$		−	0.00298723i		−	0.000222039i	−1.00000		0.000111020i	$-0.999965\pi$
$181$		−	0.00298723i		−	0.000222039i	1.00000		0.000111020i	$-3.53386e-5\pi$
$182$	1.65574	−	13.4595i	0.122732	−	0.997685i
$183$	3.74485	−	3.74485i	0.276828	−	0.276828i
$184$	−5.57258	+	1.49317i	−0.410816	+	0.110078i
$185$	−3.29992	−	1.89848i	−0.242615	−	0.139579i
$186$	−3.07959	+	1.77800i	−0.225807	+	0.130370i
$187$	−28.8501			−2.10973
$188$	7.95408	−	4.59229i	0.580111	−	0.334927i
$189$	−3.63298	−	0.973453i	−0.264260	−	0.0708083i
$190$	5.57258	+	5.55556i	0.404278	+	0.403043i
$191$	1.39117	+	2.40958i	0.100662	+	0.174351i	0.911957	−	0.410285i	$-0.134571\pi$
$191$	1.39117	+	2.40958i	0.100662	+	0.174351i	−0.811296	+	0.584636i	$0.801237\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	7.58514	−	13.1378i	0.545990	−	0.945683i	−0.452554	−	0.891737i	$-0.649487\pi$
$193$	7.58514	−	13.1378i	0.545990	−	0.945683i	0.998544	−	0.0539455i	$-0.0171797\pi$
$194$	17.8737			1.28326
$195$	−1.13244	−	7.98233i	−0.0810956	−	0.571626i
$196$	−7.14613			−0.510438
$197$	−10.6561	+	18.4569i	−0.759215	+	1.31500i	0.184036	+	0.982919i	$0.441084\pi$
$197$	−10.6561	+	18.4569i	−0.759215	+	1.31500i	−0.943251	+	0.332080i	$0.892250\pi$
$198$	1.28948	+	4.81242i	0.0916396	+	0.342004i
$199$	4.07958	+	7.06604i	0.289194	+	0.500899i	0.973618	−	0.228186i	$-0.0732794\pi$
$199$	4.07958	+	7.06604i	0.289194	+	0.500899i	−0.684424	+	0.729085i	$0.739946\pi$
$200$	−4.99998	+	0.0152997i	−0.353552	+	0.00108185i
$201$	−5.20035	−	1.39343i	−0.366804	−	0.0982849i
$202$	−3.70757	+	2.14057i	−0.260864	+	0.150610i
$203$	−15.9649			−1.12051
$204$	−5.01486	+	2.89533i	−0.351110	+	0.202714i
$205$	−4.73334	−	17.5576i	−0.330591	−	1.22628i
$206$	7.86522	−	2.10748i	0.547996	−	0.146835i
$207$	−4.07941	+	4.07941i	−0.283539	+	0.283539i
$208$	−2.17053	+	2.87903i	−0.150499	+	0.199624i
$209$		−	17.5325i		−	1.21275i
$210$	−8.12024	+	2.18913i	−0.560350	+	0.151065i
$211$	13.4348	−	23.2697i	0.924887	−	1.60195i	0.133144	−	0.991097i	$-0.457493\pi$
$211$	13.4348	−	23.2697i	0.924887	−	1.60195i	0.791743	−	0.610854i	$-0.209174\pi$
$212$	8.24046	+	2.20803i	0.565957	+	0.151648i
$213$		−	11.3995i		−	0.781084i
$214$	1.07834	−	4.02443i	0.0737139	−	0.275104i
$215$	−0.358625	+	1.34665i	−0.0244580	+	0.0918405i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−3.46161	+	12.9189i	−0.234989	+	0.876991i
$218$	−6.40881	+	1.71723i	−0.434059	+	0.116306i
$219$	−1.36522	−	5.09509i	−0.0922533	−	0.344294i
$220$	7.88957	+	7.86546i	0.531914	+	0.530289i
$221$	−19.3564	−	7.82566i	−1.30206	−	0.526411i
$222$	1.20390	+	1.20390i	0.0808003	+	0.0808003i
$223$	−14.0273	−	8.09867i	−0.939338	−	0.542327i	−0.0495855	−	0.998770i	$-0.515790\pi$
$223$	−14.0273	−	8.09867i	−0.939338	−	0.542327i	−0.889753	+	0.456443i	$0.849123\pi$
$224$	3.25724	+	1.88057i	0.217633	+	0.125651i
$225$	−4.32246	+	2.51324i	−0.288164	+	0.167549i
$226$	14.4206	−	14.4206i	0.959245	−	0.959245i
$227$	10.7902	+	18.6891i	0.716169	+	1.24044i	0.962507	+	0.271257i	$0.0874394\pi$
$227$	10.7902	+	18.6891i	0.716169	+	1.24044i	−0.246338	+	0.969184i	$0.579227\pi$
$228$	−1.75952	−	3.04757i	−0.116527	−	0.201830i
$229$	−9.43282	+	9.43282i	−0.623338	+	0.623338i	−0.946384	−	0.323045i	$-0.895293\pi$
$229$	−9.43282	+	9.43282i	−0.623338	+	0.623338i	0.323045	+	0.946384i	$0.395293\pi$
$230$	−3.31976	+	12.4658i	−0.218898	+	0.821969i
$231$	16.2282	+	9.36933i	1.06773	+	0.616457i
$232$	3.67601	+	2.12235i	0.241342	+	0.139339i
$233$	−8.62757	−	8.62757i	−0.565211	−	0.565211i	0.365572	−	0.930783i	$-0.380873\pi$
$233$	−8.62757	−	8.62757i	−0.565211	−	0.565211i	−0.930783	+	0.365572i	$0.880873\pi$
$234$	−0.440224	+	3.57858i	−0.0287784	+	0.233939i
$235$	−0.0314216	−	20.5373i	−0.00204972	−	1.33971i
$236$	1.47423	+	5.50190i	0.0959642	+	0.358143i
$237$	−4.50788	+	1.20788i	−0.292819	+	0.0784605i
$238$	−5.63694	+	21.0373i	−0.365388	+	1.36365i
$239$	4.17052	+	4.17052i	0.269768	+	0.269768i	0.829007	−	0.559238i	$-0.188906\pi$
$239$	4.17052	+	4.17052i	0.269768	+	0.269768i	−0.559238	+	0.829007i	$0.688906\pi$
$240$	2.16076	+	0.575432i	0.139476	+	0.0371440i
$241$	−5.18377	+	19.3461i	−0.333916	+	1.24619i	0.571124	+	0.820864i	$0.306508\pi$
$241$	−5.18377	+	19.3461i	−0.333916	+	1.24619i	−0.905040	+	0.425327i	$0.860159\pi$
$242$		−	13.8221i		−	0.888521i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−2.64801	+	4.58649i	−0.169522	+	0.293620i
$245$	−7.96844	+	13.8506i	−0.509085	+	0.884885i
$246$			8.13232i			0.518498i
$247$	4.75572	−	11.7631i	0.302599	−	0.748466i
$248$	2.51448	−	2.51448i	0.159669	−	0.159669i
$249$	0.834251	−	0.223537i	0.0528685	−	0.0141661i
$250$	−5.54567	+	9.70801i	−0.350739	+	0.613989i
$251$	2.57154	−	1.48468i	0.162314	−	0.0937120i	−0.416643	−	0.909070i	$-0.636793\pi$
$251$	2.57154	−	1.48468i	0.162314	−	0.0937120i	0.578957	+	0.815358i	$0.303460\pi$
$252$	3.76113			0.236929
$253$	24.8922	−	14.3715i	1.56496	−	0.903529i
$254$	11.3340	+	3.03693i	0.711157	+	0.190554i
$255$	0.0198106	+	12.9483i	0.00124059	+	0.810854i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.56761	−	20.7786i	−0.347298	−	1.29613i	−0.889905	−	0.456147i	$-0.849229\pi$
$257$	−5.56761	−	20.7786i	−0.347298	−	1.29613i	0.542606	−	0.839987i	$-0.317438\pi$
$258$	0.311614	−	0.539731i	0.0194002	−	0.0336022i
$259$	6.40359			0.397899
$260$	3.15983	+	7.41724i	0.195964	+	0.459998i
$261$	4.24469			0.262740
$262$	−4.27873	+	7.41098i	−0.264341	+	0.457852i
$263$	−0.585863	−	2.18647i	−0.0361259	−	0.134824i	0.945508	−	0.325600i	$-0.105566\pi$
$263$	−0.585863	−	2.18647i	−0.0361259	−	0.134824i	−0.981634	+	0.190776i	$0.938900\pi$
$264$	−2.49109	−	4.31470i	−0.153316	−	0.265551i
$265$	13.4683	−	13.5096i	0.827350	−	0.829886i
$266$	−12.7846	−	3.42561i	−0.783872	−	0.210038i
$267$	12.0161	−	6.93751i	0.735374	−	0.424568i
$268$	5.38380			0.328868
$269$	15.4313	−	8.90928i	0.940864	−	0.543208i	0.0506331	−	0.998717i	$-0.483876\pi$
$269$	15.4313	−	8.90928i	0.940864	−	0.543208i	0.890231	+	0.455509i	$0.150543\pi$
$270$	2.15899	−	0.582041i	0.131392	−	0.0354219i
$271$	−17.8068	+	4.77131i	−1.08168	+	0.289837i	−0.755286	−	0.655395i	$-0.772502\pi$
$271$	−17.8068	+	4.77131i	−1.08168	+	0.289837i	−0.326399	+	0.945232i	$0.605835\pi$
$272$	4.09462	−	4.09462i	0.248273	−	0.248273i
$273$	8.34652	+	10.6881i	0.505154	+	0.646873i
$274$		−	18.1008i		−	1.09351i
$275$	24.0423	−	6.52102i	1.44980	−	0.393232i
$276$	2.88458	−	4.99624i	0.173631	−	0.300738i
$277$	−10.1048	−	2.70758i	−0.607139	−	0.162683i	−0.0578648	−	0.998324i	$-0.518429\pi$
$277$	−10.1048	−	2.70758i	−0.607139	−	0.162683i	−0.549275	+	0.835642i	$0.685096\pi$
$278$			6.08756i			0.365107i
$279$	0.920362	−	3.43484i	0.0551006	−	0.205638i
$280$	7.27696	−	4.21621i	0.434882	−	0.251967i
$281$	16.2537	+	16.2537i	0.969616	+	0.969616i	0.999552	−	0.0299357i	$-0.00953025\pi$
$281$	16.2537	+	16.2537i	0.969616	+	0.969616i	−0.0299357	+	0.999552i	$0.509530\pi$
$282$	−2.37714	+	8.87162i	−0.141557	+	0.528297i
$283$	−30.0638	+	8.05557i	−1.78711	+	0.478854i	−0.991849	−	0.127418i	$-0.959331\pi$
$283$	−30.0638	+	8.05557i	−1.78711	+	0.478854i	−0.795258	+	0.606272i	$0.792664\pi$
$284$	2.95042	+	11.0111i	0.175075	+	0.653390i
$285$	−7.86879	+	0.0120390i	−0.466107	+	0.000713131i
$286$	6.73306	−	16.6539i	0.398134	−	0.984768i
$287$	21.6281	+	21.6281i	1.27667	+	1.27667i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	14.3169	+	8.26588i	0.842172	+	0.486228i
$290$	8.21254	−	4.75828i	0.482257	−	0.279416i
$291$	−12.6386	+	12.6386i	−0.740888	+	0.740888i
$292$	2.63741	+	4.56813i	0.154343	+	0.267330i
$293$	0.136000	+	0.235560i	0.00794523	+	0.0137615i	0.869971	−	0.493103i	$-0.164138\pi$
$293$	0.136000	+	0.235560i	0.00794523	+	0.0137615i	−0.862025	+	0.506865i	$0.830804\pi$
$294$	5.05308	−	5.05308i	0.294702	−	0.294702i
$295$	12.3077	+	3.27765i	0.716580	+	0.190832i
$296$	−1.47447	−	0.851284i	−0.0857016	−	0.0494799i
$297$	−4.31470	−	2.49109i	−0.250364	−	0.144548i
$298$	8.77729	+	8.77729i	0.508455	+	0.508455i
$299$	20.5992	−	2.89023i	1.19128	−	0.167146i
$300$	3.52470	−	3.54634i	0.203499	−	0.204748i
$301$	−0.606683	−	2.26417i	−0.0349687	−	0.130505i
$302$	−14.4056	+	3.85998i	−0.828952	+	0.222117i
$303$	1.10804	−	4.13526i	0.0636552	−	0.237564i
$304$	2.48833	+	2.48833i	0.142716	+	0.142716i
$305$	5.93682	+	10.2466i	0.339941	+	0.586721i
$306$	1.49873	−	5.59335i	0.0856769	−	0.319750i
$307$			19.6291i			1.12029i	0.828395	+	0.560145i	$0.189255\pi$
$307$			19.6291i			1.12029i	−0.828395	+	0.560145i	$0.810745\pi$
$308$	−18.1002	−	4.84992i	−1.03135	−	0.276350i
$309$	−4.07134	+	7.05177i	−0.231610	+	0.401161i
$310$	−2.06974	−	7.67737i	−0.117553	−	0.436046i
$311$		−	7.66916i		−	0.434878i	−0.976074	−	0.217439i	$-0.930230\pi$
$311$		−	7.66916i		−	0.434878i	0.976074	−	0.217439i	$-0.0697704\pi$
$312$	−0.500979	−	3.57058i	−0.0283624	−	0.202144i
$313$	−7.66815	+	7.66815i	−0.433429	+	0.433429i	−0.889793	−	0.456364i	$-0.849152\pi$
$313$	−7.66815	+	7.66815i	−0.433429	+	0.433429i	0.456364	+	0.889793i	$0.349152\pi$
$314$	−19.7136	+	5.28224i	−1.11250	+	0.298094i
$315$	4.19393	−	7.28983i	0.236301	−	0.410735i
$316$	4.04166	−	2.33345i	0.227361	−	0.131267i
$317$	−16.1221			−0.905509			−0.452755	−	0.891635i	$-0.649559\pi$
$317$	−16.1221			−0.905509			−0.452755	+	0.891635i	$0.649559\pi$
$318$	−7.38820	+	4.26558i	−0.414309	+	0.239202i
$319$	−20.4272	−	5.47346i	−1.14371	−	0.306455i
$320$	−2.23607	+	0.00342112i	−0.125000	+	0.000191247i
$321$	2.08320	+	3.60820i	0.116273	+	0.201390i
$322$	−5.61601	−	20.9592i	−0.312968	−	1.16801i
$323$	−10.1888	+	17.6475i	−0.566918	+	0.981930i
$324$	−1.00000			−0.0555556
$325$	17.8995	+	2.14636i	0.992887	+	0.119059i
$326$	7.21863			0.399803
$327$	3.31744	−	5.74598i	0.183455	−	0.317753i
$328$	−2.10480	−	7.85522i	−0.116218	−	0.433732i
$329$	17.2722	+	29.9164i	0.952248	+	1.64934i
$330$	−11.1405	+	0.0170447i	−0.613264	+	0.000938278i
$331$	−32.8247	−	8.79534i	−1.80421	−	0.483436i	−0.809584	−	0.587004i	$-0.800307\pi$
$331$	−32.8247	−	8.79534i	−1.80421	−	0.483436i	−0.994622	+	0.103568i	$0.966974\pi$
$332$	−0.747969	+	0.431840i	−0.0410501	+	0.0237003i
$333$	−1.70257			−0.0933001
$334$	10.6044	−	6.12243i	0.580245	−	0.335004i
$335$	6.00331	−	10.4349i	0.327996	−	0.570118i
$336$	−3.63298	+	0.973453i	−0.198195	+	0.0531062i
$337$	−20.5522	+	20.5522i	−1.11955	+	1.11955i	−0.127743	+	0.991807i	$0.540773\pi$
$337$	−20.5522	+	20.5522i	−1.11955	+	1.11955i	−0.991807	+	0.127743i	$0.959227\pi$
$338$	9.03483	−	9.34729i	0.491430	−	0.508425i
$339$			20.3938i			1.10764i
$340$	−3.37040	−	12.5020i	−0.182786	−	0.678014i
$341$	−8.85834	+	15.3431i	−0.479706	+	0.830875i
$342$	3.39912	+	0.910792i	0.183804	+	0.0492500i
$343$		−	0.549625i		−	0.0296770i
$344$	−0.161303	+	0.601992i	−0.00869689	+	0.0324572i
$345$	−6.46721	−	11.1621i	−0.348183	−	0.600945i
$346$	1.92409	+	1.92409i	0.103440	+	0.103440i
$347$	1.75339	−	6.54372i	0.0941267	−	0.351285i	−0.902759	−	0.430147i	$-0.858462\pi$
$347$	1.75339	−	6.54372i	0.0941267	−	0.351285i	0.996886	+	0.0788614i	$0.0251284\pi$
$348$	−4.10006	+	1.09861i	−0.219786	+	0.0588915i
$349$	2.76578	+	10.3220i	0.148049	+	0.552526i	0.999601	+	0.0282557i	$0.00899528\pi$
$349$	2.76578	+	10.3220i	0.148049	+	0.552526i	−0.851552	+	0.524271i	$0.824338\pi$
$350$	−0.0575443	−	18.8056i	−0.00307587	−	1.00520i
$351$	−2.21915	−	2.84172i	−0.118449	−	0.151680i
$352$	3.52294	+	3.52294i	0.187773	+	0.187773i
$353$	16.7759	+	9.68559i	0.892893	+	0.515512i	0.874888	−	0.484326i	$-0.160935\pi$
$353$	16.7759	+	9.68559i	0.892893	+	0.515512i	0.0180051	+	0.999838i	$0.494268\pi$
$354$	−4.93287	−	2.84800i	−0.262179	−	0.151369i
$355$	24.6317	+	6.55966i	1.30731	+	0.348151i
$356$	−9.81111	+	9.81111i	−0.519988	+	0.519988i
$357$	−10.8897	−	18.8616i	−0.576346	−	0.998260i
$358$	−5.19092	−	8.99094i	−0.274349	−	0.475186i
$359$	−22.5724	+	22.5724i	−1.19133	+	1.19133i	−0.214632	+	0.976695i	$0.568855\pi$
$359$	−22.5724	+	22.5724i	−1.19133	+	1.19133i	−0.976695	+	0.214632i	$0.931145\pi$
$360$	−1.93478	+	1.12100i	−0.101972	+	0.0590816i
$361$	5.72998	+	3.30821i	0.301578	+	0.174116i
$362$	−0.00258702	−	0.00149362i	−0.000135971	−	7.85027e-5i
$363$	9.77373	+	9.77373i	0.512988	+	0.512988i
$364$	−10.8284	−	8.16367i	−0.567562	−	0.427892i
$365$	11.7948	−	0.0180458i	0.617371	−	0.000944561i
$366$	−1.37071	−	5.11557i	−0.0716483	−	0.267395i
$367$	−15.2447	+	4.08480i	−0.795766	+	0.213225i	−0.633724	−	0.773559i	$-0.718475\pi$
$367$	−15.2447	+	4.08480i	−0.795766	+	0.213225i	−0.162042	+	0.986784i	$0.551808\pi$
$368$	−1.49317	+	5.57258i	−0.0778368	+	0.290491i
$369$	−5.75042	−	5.75042i	−0.299355	−	0.299355i
$370$	−3.29409	+	1.90857i	−0.171252	+	0.0992219i
$371$	−8.30468	+	30.9935i	−0.431157	+	1.60910i
$372$			3.55601i			0.184370i
$373$	−12.0416	−	3.22653i	−0.623490	−	0.167064i	−0.0667760	−	0.997768i	$-0.521271\pi$
$373$	−12.0416	−	3.22653i	−0.623490	−	0.167064i	−0.556714	+	0.830704i	$0.687938\pi$
$374$	−14.4251	+	24.9849i	−0.745902	+	1.29194i
$375$	−2.94322	−	10.7860i	−0.151987	−	0.556986i
$376$		−	9.18458i		−	0.473658i
$377$	−12.2206	−	9.21324i	−0.629391	−	0.474506i
$378$	−2.65952	+	2.65952i	−0.136791	+	0.136791i
$379$	31.0709	−	8.32543i	1.59601	−	0.427649i	0.652173	−	0.758070i	$-0.273858\pi$
$379$	31.0709	−	8.32543i	1.59601	−	0.427649i	0.943833	+	0.330422i	$0.107191\pi$
$380$	7.59755	−	2.04822i	0.389746	−	0.105071i
$381$	−10.1618	+	5.86690i	−0.520603	+	0.300570i
$382$	2.78234			0.142357
$383$	0.837053	−	0.483273i	0.0427714	−	0.0246941i	−0.478462	−	0.878108i	$-0.658805\pi$
$383$	0.837053	−	0.483273i	0.0427714	−	0.0246941i	0.521233	+	0.853414i	$0.325472\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	−29.5831	+	29.6737i	−1.50769	+	1.51231i
$386$	−7.58514	−	13.1378i	−0.386073	−	0.668699i
$387$	0.161303	+	0.601992i	0.00819951	+	0.0306010i
$388$	8.93684	−	15.4791i	0.453700	−	0.785831i
$389$	12.4738			0.632446			0.316223	−	0.948685i	$-0.397585\pi$
$389$	12.4738			0.632446			0.316223	+	0.948685i	$0.397585\pi$
$390$	−7.47912	−	3.01044i	−0.378720	−	0.152440i
$391$	−33.4073			−1.68948
$392$	−3.57307	+	6.18873i	−0.180467	+	0.312578i
$393$	−2.21484	−	8.26588i	−0.111724	−	0.416958i
$394$	10.6561	+	18.4569i	0.536846	+	0.929845i
$395$	−0.0159661	−	10.4355i	−0.000803340	−	0.525067i
$396$	4.81242	+	1.28948i	0.241833	+	0.0647990i
$397$	24.9257	−	14.3909i	1.25099	−	0.722258i	0.279682	−	0.960093i	$-0.409771\pi$
$397$	24.9257	−	14.3909i	1.25099	−	0.722258i	0.971306	+	0.237835i	$0.0764377\pi$
$398$	8.15916			0.408982
$399$	11.4623	−	6.61778i	0.573834	−	0.331303i
$400$	−2.48674	+	4.33776i	−0.124337	+	0.216888i
$401$	29.8455	−	7.99709i	1.49042	−	0.399356i	0.580538	−	0.814233i	$-0.302842\pi$
$401$	29.8455	−	7.99709i	1.49042	−	0.399356i	0.909877	+	0.414877i	$0.136176\pi$
$402$	−3.80692	+	3.80692i	−0.189872	+	0.189872i
$403$	−10.1052	+	7.89131i	−0.503375	+	0.393094i
$404$			4.28113i			0.212994i
$405$	−1.11507	+	1.93820i	−0.0554083	+	0.0963099i
$406$	−7.98243	+	13.8260i	−0.396161	+	0.686171i
$407$	8.19347	+	2.19543i	0.406135	+	0.108824i
$408$			5.79066i			0.286680i
$409$	−5.05270	+	18.8569i	−0.249840	+	0.932416i	0.721049	+	0.692884i	$0.243660\pi$
$409$	−5.05270	+	18.8569i	−0.249840	+	0.932416i	−0.970889	+	0.239531i	$0.923006\pi$
$410$	−17.5720	−	4.67960i	−0.867819	−	0.231109i
$411$	12.7992	+	12.7992i	0.631339	+	0.631339i
$412$	2.10748	−	7.86522i	0.103828	−	0.387492i
$413$	−20.6934	+	5.54478i	−1.01826	+	0.272841i
$414$	1.49317	+	5.57258i	0.0733853	+	0.273878i
$415$	0.00295476	+	1.93124i	0.000145043	+	0.0948011i
$416$	1.40804	+	3.31925i	0.0690349	+	0.162740i
$417$	−4.30455	−	4.30455i	−0.210795	−	0.210795i
$418$	−15.1836	−	8.76623i	−0.742652	−	0.428770i
$419$	−22.8482	−	13.1914i	−1.11621	−	0.644442i	−0.175777	−	0.984430i	$-0.556244\pi$
$419$	−22.8482	−	13.1914i	−1.11621	−	0.644442i	−0.940430	+	0.339988i	$0.889577\pi$
$420$	−2.16428	+	8.12690i	−0.105606	+	0.396552i
$421$	3.11591	−	3.11591i	0.151860	−	0.151860i	−0.627088	−	0.778948i	$-0.715753\pi$
$421$	3.11591	−	3.11591i	0.151860	−	0.151860i	0.778948	+	0.627088i	$0.215753\pi$
$422$	−13.4348	−	23.2697i	−0.653994	−	1.13275i
$423$	−4.59229	−	7.95408i	−0.223285	−	0.386741i
$424$	6.03244	−	6.03244i	0.292961	−	0.292961i
$425$	−27.9895	−	7.40806i	−1.35769	−	0.359343i
$426$	−9.87230	−	5.69977i	−0.478314	−	0.276155i
$427$	−17.2504	−	9.95953i	−0.834806	−	0.481975i
$428$	−2.94608	−	2.94608i	−0.142404	−	0.142404i
$429$	7.01512	+	16.5371i	0.338693	+	0.798419i
$430$	0.986917	+	0.983901i	0.0475933	+	0.0474479i
$431$	−4.64056	−	17.3188i	−0.223528	−	0.834217i	−0.982989	−	0.183664i	$-0.941204\pi$
$431$	−4.64056	−	17.3188i	−0.223528	−	0.834217i	0.759461	−	0.650552i	$-0.225463\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	6.90240	−	25.7601i	0.331708	−	1.23795i	−0.575686	−	0.817671i	$-0.695265\pi$
$433$	6.90240	−	25.7601i	0.331708	−	1.23795i	0.907394	−	0.420281i	$-0.138069\pi$
$434$	9.45728	+	9.45728i	0.453964	+	0.453964i
$435$	−2.44253	+	9.17175i	−0.117110	+	0.439752i
$436$	−1.71723	+	6.40881i	−0.0822406	+	0.306926i
$437$		−	20.3019i		−	0.971170i
$438$	−5.09509	−	1.36522i	−0.243453	−	0.0652330i
$439$	1.66483	−	2.88358i	0.0794582	−	0.137626i	−0.823558	−	0.567232i	$-0.808014\pi$
$439$	1.66483	−	2.88358i	0.0794582	−	0.137626i	0.903016	+	0.429606i	$0.141348\pi$
$440$	10.7565	−	2.89983i	0.512795	−	0.138244i
$441$			7.14613i			0.340292i
$442$	−16.4554	+	12.8503i	−0.782706	+	0.611228i
$443$	17.4398	−	17.4398i	0.828592	−	0.828592i	−0.158730	−	0.987322i	$-0.550740\pi$
$443$	17.4398	−	17.4398i	0.828592	−	0.828592i	0.987322	+	0.158730i	$0.0507399\pi$
$444$	1.64455	−	0.440657i	0.0780471	−	0.0209127i
$445$	8.07582	+	29.9560i	0.382831	+	1.42005i
$446$	−14.0273	+	8.09867i	−0.664212	+	0.383483i
$447$	−12.4130			−0.587113
$448$	3.25724	−	1.88057i	0.153890	−	0.0888485i
$449$	−19.0521	−	5.10499i	−0.899123	−	0.240919i	−0.220483	−	0.975391i	$-0.570763\pi$
$449$	−19.0521	−	5.10499i	−0.899123	−	0.240919i	−0.678640	+	0.734471i	$0.737430\pi$
$450$	0.0152997	+	4.99998i	0.000721235	+	0.235701i
$451$	20.2584	+	35.0885i	0.953929	+	1.65225i
$452$	−5.27831	−	19.6989i	−0.248271	−	0.926559i
$453$	7.45691	−	12.9157i	0.350356	−	0.606835i
$454$	21.5804			1.01282
$455$	−27.8972	+	11.8845i	−1.30784	+	0.557156i
$456$	−3.51903			−0.164794
$457$	0.994792	−	1.72303i	0.0465344	−	0.0806000i	−0.841820	−	0.539758i	$-0.818516\pi$
$457$	0.994792	−	1.72303i	0.0465344	−	0.0806000i	0.888354	+	0.459158i	$0.151849\pi$
$458$	3.45265	+	12.8855i	0.161332	+	0.602099i
$459$	2.89533	+	5.01486i	0.135142	+	0.234074i
$460$	9.13579	+	9.10788i	0.425959	+	0.424657i
$461$	26.2500	+	7.03368i	1.22259	+	0.327591i	0.811689	−	0.584090i	$-0.198549\pi$
$461$	26.2500	+	7.03368i	1.22259	+	0.327591i	0.410898	+	0.911681i	$0.365215\pi$
$462$	16.2282	−	9.36933i	0.755002	−	0.435901i
$463$	24.4623			1.13686			0.568430	−	0.822731i	$-0.307551\pi$
$463$	24.4623			1.13686			0.568430	+	0.822731i	$0.307551\pi$
$464$	3.67601	−	2.12235i	0.170654	−	0.0985274i
$465$	6.89225	+	3.96520i	0.319620	+	0.183882i
$466$	−11.7855	+	3.15791i	−0.545952	+	0.146287i
$467$	19.8875	−	19.8875i	0.920284	−	0.920284i	−0.0767650	−	0.997049i	$-0.524459\pi$
$467$	19.8875	−	19.8875i	0.920284	−	0.920284i	0.997049	+	0.0767650i	$0.0244591\pi$
$468$	2.87903	+	2.17053i	0.133083	+	0.100333i
$469$			20.2492i			0.935020i
$470$	−17.8015	−	10.2414i	−0.821124	−	0.472403i
$471$	10.2045	−	17.6747i	0.470199	−	0.814408i
$472$	5.50190	+	1.47423i	0.253246	+	0.0678570i
$473$		−	3.10504i		−	0.142770i
$474$	−1.20788	+	4.50788i	−0.0554799	+	0.207054i
$475$	4.50194	−	17.0095i	0.206563	−	0.780448i
$476$	15.4004	+	15.4004i	0.705876	+	0.705876i
$477$	2.20803	−	8.24046i	0.101099	−	0.377305i
$478$	5.69703	−	1.52652i	0.260576	−	0.0698212i
$479$	0.684672	+	2.55523i	0.0312834	+	0.116751i	0.979802	−	0.199970i	$-0.0640846\pi$
$479$	0.684672	+	2.55523i	0.0312834	+	0.116751i	−0.948519	+	0.316722i	$0.897418\pi$
$480$	1.57872	−	1.58356i	0.0720583	−	0.0722791i
$481$	4.90173	+	3.69548i	0.223500	+	0.168499i
$482$	14.1623	+	14.1623i	0.645076	+	0.645076i
$483$	18.7915	+	10.8493i	0.855045	+	0.493660i
$484$	−11.9703	−	6.91107i	−0.544106	−	0.314140i
$485$	−20.0363	−	34.5816i	−0.909803	−	1.57027i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−11.7279	−	20.3134i	−0.531443	−	0.920487i	−0.999326	−	0.0366965i	$-0.988317\pi$
$487$	−11.7279	−	20.3134i	−0.531443	−	0.920487i	0.467883	−	0.883790i	$-0.345017\pi$
$488$	2.64801	+	4.58649i	0.119870	+	0.207621i
$489$	−5.10434	+	5.10434i	−0.230826	+	0.230826i
$490$	8.01078	+	13.8262i	0.361890	+	0.624603i
$491$	5.36184	+	3.09566i	0.241976	+	0.139705i	0.616085	−	0.787680i	$-0.288718\pi$
$491$	5.36184	+	3.09566i	0.241976	+	0.139705i	−0.374108	+	0.927385i	$0.622051\pi$
$492$	7.04280	+	4.06616i	0.317514	+	0.183317i
$493$	17.3804	+	17.3804i	0.782773	+	0.782773i
$494$	−7.80926	−	10.0001i	−0.351355	−	0.449926i
$495$	7.86546	−	7.88957i	0.353526	−	0.354610i
$496$	−0.920362	−	3.43484i	−0.0413255	−	0.154229i
$497$	−41.4143	+	11.0969i	−1.85769	+	0.497765i
$498$	0.223537	−	0.834251i	0.0100169	−	0.0373837i
$499$	−22.7471	−	22.7471i	−1.01830	−	1.01830i	−0.999829	−	0.0184704i	$-0.994120\pi$
$499$	−22.7471	−	22.7471i	−1.01830	−	1.01830i	−0.0184704	−	0.999829i	$-0.505880\pi$
$500$	5.63455	+	9.65670i	0.251985	+	0.431861i
$501$	−3.16920	+	11.8276i	−0.141590	+	0.528419i
$502$		−	2.96935i		−	0.132529i
$503$	20.8211	+	5.57901i	0.928369	+	0.248756i	0.691159	−	0.722703i	$-0.257100\pi$
$503$	20.8211	+	5.57901i	0.928369	+	0.248756i	0.237210	+	0.971458i	$0.423767\pi$
$504$	1.88057	−	3.25724i	0.0837671	−	0.145089i
$505$	8.29769	+	4.77376i	0.369242	+	0.212430i
$506$		−	28.7430i		−	1.27778i
$507$	0.220937	+	12.9981i	0.00981216	+	0.577267i
$508$	8.29705	−	8.29705i	0.368122	−	0.368122i
$509$	7.66864	−	2.05481i	0.339907	−	0.0910777i	−0.0848280	−	0.996396i	$-0.527034\pi$
$509$	7.66864	−	2.05481i	0.339907	−	0.0910777i	0.424735	+	0.905318i	$0.360367\pi$
$510$	11.2235	+	6.45699i	0.496983	+	0.285920i
$511$	−17.1814	+	9.91966i	−0.760058	+	0.438820i
$512$	−1.00000			−0.0441942
$513$	−3.04757	+	1.75952i	−0.134554	+	0.0776845i
$514$	−20.7786	−	5.56761i	−0.916505	−	0.245577i
$515$	−12.8944	−	12.8550i	−0.568195	−	0.566459i
$516$	−0.311614	−	0.539731i	−0.0137180	−	0.0237603i
$517$	11.8434	+	44.2000i	0.520871	+	1.94392i
$518$	3.20179	−	5.54567i	0.140679	−	0.243663i
$519$	−2.72108			−0.119442
$520$	8.00343	+	0.972128i	0.350974	+	0.0426306i
$521$	−5.20619			−0.228087			−0.114044	−	0.993476i	$-0.536380\pi$
$521$	−5.20619			−0.228087			−0.114044	+	0.993476i	$0.536380\pi$
$522$	2.12235	−	3.67601i	0.0928925	−	0.160895i
$523$	−6.83174	−	25.4964i	−0.298731	−	1.11488i	−0.938209	−	0.346070i	$-0.887516\pi$
$523$	−6.83174	−	25.4964i	−0.298731	−	1.11488i	0.639478	−	0.768809i	$-0.279151\pi$
$524$	4.27873	+	7.41098i	0.186917	+	0.323750i
$525$	13.3382	+	13.2569i	0.582129	+	0.578577i
$526$	−2.18647	−	0.585863i	−0.0953346	−	0.0255448i
$527$	17.8329	−	10.2958i	0.776812	−	0.448493i
$528$	−4.98218			−0.216822
$529$	8.90555	−	5.14162i	0.387198	−	0.223549i
$530$	−4.96548	−	18.4187i	−0.215687	−	0.800055i
$531$	5.50190	−	1.47423i	0.238762	−	0.0639762i
$532$	−9.35895	+	9.35895i	−0.405762	+	0.405762i
$533$	4.07413	+	29.0371i	0.176470	+	1.25774i
$534$		−	13.8750i		−	0.600430i
$535$	−8.99519	+	2.42501i	−0.388896	+	0.104842i
$536$	2.69190	−	4.66250i	0.116272	−	0.201390i
$537$	10.0281	+	2.68702i	0.432744	+	0.115953i
$538$		−	17.8186i		−	0.768212i
$539$	9.21482	−	34.3902i	0.396910	−	1.48129i
$540$	0.575432	−	2.16076i	0.0247626	−	0.0929843i
$541$	−11.8712	−	11.8712i	−0.510382	−	0.510382i	0.404261	−	0.914644i	$-0.367529\pi$
$541$	−11.8712	−	11.8712i	−0.510382	−	0.510382i	−0.914644	+	0.404261i	$0.867529\pi$
$542$	−4.77131	+	17.8068i	−0.204945	+	0.764867i
$543$	0.00288545		0.000773153i	0.000123826		3.31792e-5i
$544$	−1.49873	−	5.59335i	−0.0642577	−	0.239813i
$545$	10.5067	+	10.4746i	0.450058	+	0.448683i
$546$	13.4294	−	1.88425i	0.574726	−	0.0806385i
$547$	21.6851	+	21.6851i	0.927187	+	0.927187i	0.997523	−	0.0703361i	$-0.0224072\pi$
$547$	21.6851	+	21.6851i	0.927187	+	0.927187i	−0.0703361	+	0.997523i	$0.522407\pi$
$548$	−15.6758	−	9.05042i	−0.669637	−	0.386615i
$549$	4.58649	+	2.64801i	0.195747	+	0.113014i
$550$	6.37376	−	24.0817i	0.271778	−	1.02685i
$551$	−10.5622	+	10.5622i	−0.449965	+	0.449965i
$552$	−2.88458	−	4.99624i	−0.122776	−	0.212654i
$553$	8.77643	+	15.2012i	0.373212	+	0.646422i
$554$	−7.39724	+	7.39724i	−0.314278	+	0.314278i
$555$	0.979711	−	3.67884i	0.0415864	−	0.156158i
$556$	5.27198	+	3.04378i	0.223582	+	0.129085i
$557$	3.30540	+	1.90837i	0.140054	+	0.0808603i	0.568390	−	0.822759i	$-0.307567\pi$
$557$	3.30540	+	1.90837i	0.140054	+	0.0808603i	−0.428336	+	0.903620i	$0.640900\pi$
$558$	−2.51448	−	2.51448i	−0.106446	−	0.106446i
$559$	0.842248	−	2.08326i	0.0356233	−	0.0881127i
$560$	−0.0128673	−	8.41014i	−0.000543743	−	0.355393i
$561$	−7.46696	−	27.8671i	−0.315255	−	1.17655i
$562$	22.2030	−	5.94928i	0.936577	−	0.250955i
$563$	1.09024	−	4.06884i	0.0459482	−	0.171481i	−0.939139	−	0.343538i	$-0.888375\pi$
$563$	1.09024	−	4.06884i	0.0459482	−	0.171481i	0.985087	+	0.172057i	$0.0550413\pi$
$564$	6.49448	+	6.49448i	0.273467	+	0.273467i
$565$	−44.0661	−	11.7353i	−1.85388	−	0.493706i
$566$	−8.05557	+	30.0638i	−0.338601	+	1.26368i
$567$		−	3.76113i		−	0.157953i
$568$	11.0111	+	2.95042i	0.462016	+	0.123797i
$569$	10.2866	−	17.8168i	0.431235	−	0.746921i	−0.565745	−	0.824580i	$-0.691411\pi$
$569$	10.2866	−	17.8168i	0.431235	−	0.746921i	0.996980	+	0.0776595i	$0.0247447\pi$
$570$	−3.92397	+	6.82059i	−0.164357	+	0.285683i
$571$			0.531359i			0.0222367i	0.999938	+	0.0111183i	$0.00353915\pi$
$571$			0.531359i			0.0222367i	−0.999938	+	0.0111183i	$0.996461\pi$
$572$	−11.0562	−	14.1580i	−0.462283	−	0.591975i
$573$	−1.96741	+	1.96741i	−0.0821898	+	0.0821898i
$574$	29.5445	−	7.91644i	1.23317	−	0.330426i
$575$	27.8399	−	7.55107i	1.16101	−	0.314901i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	10.8877			0.453261			0.226630	−	0.973981i	$-0.427229\pi$
$577$	10.8877			0.453261			0.226630	+	0.973981i	$0.427229\pi$
$578$	14.3169	−	8.26588i	0.595505	−	0.343815i
$579$	14.6534	+	3.92636i	0.608973	+	0.163174i
$580$	−0.0145216	−	9.49140i	−0.000602977	−	0.394109i
$581$	−1.62421	−	2.81321i	−0.0673835	−	0.116712i
$582$	4.62605	+	17.2647i	0.191756	+	0.715643i
$583$	−21.2519	+	36.8093i	−0.880163	+	1.52449i
$584$	5.27482			0.218274
$585$	7.41724	−	3.15983i	0.306665	−	0.130643i
$586$	0.272001			0.0112363
$587$	−4.94658	+	8.56772i	−0.204167	+	0.353628i	−0.949867	−	0.312654i	$-0.898782\pi$
$587$	−4.94658	+	8.56772i	−0.204167	+	0.353628i	0.745700	+	0.666282i	$0.232115\pi$
$588$	−1.84956	−	6.90263i	−0.0762744	−	0.284660i
$589$	6.25685	+	10.8372i	0.257809	+	0.446538i
$590$	8.99236	−	9.01992i	0.370210	−	0.371344i
$591$	−20.5860	−	5.51600i	−0.846795	−	0.226898i
$592$	−1.47447	+	0.851284i	−0.0606002	+	0.0349875i
$593$	16.3568			0.671694			0.335847	−	0.941916i	$-0.390977\pi$
$593$	16.3568			0.671694			0.335847	+	0.941916i	$0.390977\pi$
$594$	−4.31470	+	2.49109i	−0.177034	+	0.102211i
$595$	47.0216	−	12.6765i	1.92770	−	0.519687i
$596$	11.9900	−	3.21271i	0.491129	−	0.131598i
$597$	−5.76940	+	5.76940i	−0.236126	+	0.236126i
$598$	7.79661	−	19.2846i	0.318827	−	0.788605i
$599$			4.71267i			0.192554i	0.995355	+	0.0962772i	$0.0306935\pi$
$599$			4.71267i			0.192554i	−0.995355	+	0.0962772i	$0.969306\pi$
$600$	−1.30887	−	4.82565i	−0.0534343	−	0.197006i
$601$	7.92625	−	13.7287i	0.323318	−	0.560004i	−0.657852	−	0.753147i	$-0.728535\pi$
$601$	7.92625	−	13.7287i	0.323318	−	0.560004i	0.981171	+	0.193143i	$0.0618682\pi$
$602$	−2.26417	−	0.606683i	−0.0922808	−	0.0247266i
$603$		−	5.38380i		−	0.219245i
$604$	−3.85998	+	14.4056i	−0.157060	+	0.586157i
$605$	−26.7428	+	15.4946i	−1.08725	+	0.629943i
$606$	−3.02722	−	3.02722i	−0.122972	−	0.122972i
$607$	1.00645	−	3.75611i	0.0408504	−	0.152456i	−0.942488	−	0.334240i	$-0.891520\pi$
$607$	1.00645	−	3.75611i	0.0408504	−	0.152456i	0.983338	+	0.181784i	$0.0581872\pi$
$608$	3.39912	−	0.910792i	0.137853	−	0.0369375i
$609$	−4.13201	−	15.4209i	−0.167437	−	0.624885i
$610$	11.8423	−	0.0181184i	0.479479	−	0.000733591i
$611$	−4.04328	+	32.8677i	−0.163573	+	1.32969i
$612$	−4.09462	−	4.09462i	−0.165515	−	0.165515i
$613$	−25.1148	−	14.5000i	−1.01438	−	0.585651i	−0.101906	−	0.994794i	$-0.532494\pi$
$613$	−25.1148	−	14.5000i	−1.01438	−	0.585651i	−0.912470	+	0.409143i	$0.865828\pi$
$614$	16.9993	+	9.81453i	0.686035	+	0.396082i
$615$	15.7342	−	9.11630i	0.634466	−	0.367605i
$616$	−13.2502	+	13.2502i	−0.533867	+	0.533867i
$617$	−0.289643	−	0.501676i	−0.0116606	−	0.0201967i	0.860136	−	0.510064i	$-0.170378\pi$
$617$	−0.289643	−	0.501676i	−0.0116606	−	0.0201967i	−0.871797	+	0.489868i	$0.837045\pi$
$618$	4.07134	+	7.05177i	0.163773	+	0.283664i
$619$	0.846805	−	0.846805i	0.0340360	−	0.0340360i	−0.689884	−	0.723920i	$-0.742338\pi$
$619$	0.846805	−	0.846805i	0.0340360	−	0.0340360i	0.723920	+	0.689884i	$0.242338\pi$
$620$	−7.68367	−	2.04624i	−0.308584	−	0.0821789i
$621$	−4.99624	−	2.88458i	−0.200492	−	0.115754i
$622$	−6.64169	−	3.83458i	−0.266307	−	0.153753i
$623$	−36.9009	−	36.9009i	−1.47840	−	1.47840i
$624$	−3.34270	−	1.35143i	−0.133815	−	0.0541004i
$625$	24.9995	−	0.152996i	0.999981	−	0.00611986i
$626$	2.80674	+	10.4749i	0.112180	+	0.418660i
$627$	16.9351	−	4.53773i	0.676321	−	0.181220i
$628$	−5.28224	+	19.7136i	−0.210784	+	0.786658i
$629$	−6.97136	−	6.97136i	−0.277966	−	0.277966i
$630$	−4.21621	−	7.27696i	−0.167978	−	0.289921i
$631$	5.89718	−	22.0086i	0.234763	−	0.876147i	−0.743493	−	0.668744i	$-0.766832\pi$
$631$	5.89718	−	22.0086i	0.234763	−	0.876147i	0.978256	−	0.207403i	$-0.0665012\pi$
$632$		−	4.66690i		−	0.185640i
$633$	25.9540	+	6.95434i	1.03158	+	0.276410i
$634$	−8.06107	+	13.9622i	−0.320146	+	0.554509i
$635$	−6.82955	−	25.3331i	−0.271022	−	1.00531i
$636$			8.53115i			0.338282i
$637$	15.5109	−	20.5739i	0.614565	−	0.815167i
$638$	−14.9538	+	14.9538i	−0.592025	+	0.592025i
$639$	11.0111	−	2.95042i	0.435593	−	0.116717i
$640$	−1.11507	+	1.93820i	−0.0440770	+	0.0766141i
$641$	27.3666	−	15.8001i	1.08092	−	0.624067i	0.149773	−	0.988720i	$-0.452146\pi$
$641$	27.3666	−	15.8001i	1.08092	−	0.624067i	0.931144	+	0.364653i	$0.118812\pi$
$642$	4.16639			0.164434
$643$	18.2698	−	10.5481i	0.720491	−	0.415976i	−0.0944423	−	0.995530i	$-0.530107\pi$
$643$	18.2698	−	10.5481i	0.720491	−	0.415976i	0.814933	+	0.579555i	$0.196773\pi$
$644$	−20.9592	−	5.61601i	−0.825910	−	0.221302i
$645$	−1.39358	+	0.00213214i	−0.0548721	+	8.39529e-5i
$646$	10.1888	+	17.6475i	0.400871	+	0.694330i
$647$	−3.53543	−	13.1944i	−0.138992	−	0.518726i	−0.999950	−	0.0100486i	$-0.996801\pi$
$647$	−3.53543	−	13.1944i	−0.138992	−	0.518726i	0.860957	−	0.508677i	$-0.169865\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−28.3785			−1.11395
$650$	10.8086	−	14.4283i	0.423947	−	0.565923i
$651$	−13.3746			−0.524193
$652$	3.60932	−	6.25152i	0.141352	−	0.244828i
$653$	−13.0687	−	48.7729i	−0.511416	−	1.90863i	−0.405024	−	0.914306i	$-0.632737\pi$
$653$	−13.0687	−	48.7729i	−0.511416	−	1.90863i	−0.106392	−	0.994324i	$-0.533930\pi$
$654$	−3.31744	−	5.74598i	−0.129722	−	0.224686i
$655$	19.1351	−	0.0292761i	0.747668	−	0.00114391i
$656$	−7.85522	−	2.10480i	−0.306695	−	0.0821786i
$657$	4.56813	−	2.63741i	0.178220	−	0.102895i
$658$	34.5444			1.34668
$659$	−24.7744	+	14.3035i	−0.965072	+	0.557184i	−0.897730	−	0.440546i	$-0.854785\pi$
$659$	−24.7744	+	14.3035i	−0.965072	+	0.557184i	−0.0673415	+	0.997730i	$0.521452\pi$
$660$	−5.55548	+	9.65647i	−0.216247	+	0.375877i
$661$	14.3142	−	3.83548i	0.556758	−	0.149183i	0.0305416	−	0.999533i	$-0.490277\pi$
$661$	14.3142	−	3.83548i	0.556758	−	0.149183i	0.526217	+	0.850351i	$0.323610\pi$
$662$	−24.0293	+	24.0293i	−0.933926	+	0.933926i
$663$	2.54919	−	20.7223i	0.0990024	−	0.804788i
$664$			0.863680i			0.0335173i
$665$	7.70363	+	28.5754i	0.298734	+	1.10811i
$666$	−0.851284	+	1.47447i	−0.0329866	+	0.0571344i
$667$	−23.6539	−	6.33804i	−0.915882	−	0.245410i
$668$		−	12.2449i		−	0.473768i
$669$	4.19218	−	15.6454i	0.162079	−	0.604887i
$670$	−6.03521	−	10.4165i	−0.233161	−	0.402423i
$671$	−18.6576	−	18.6576i	−0.720267	−	0.720267i
$672$	−0.973453	+	3.63298i	−0.0375518	+	0.140145i
$673$	3.67407	−	0.984464i	0.141625	−	0.0379483i	−0.187310	−	0.982301i	$-0.559977\pi$
$673$	3.67407	−	0.984464i	0.141625	−	0.0379483i	0.328935	+	0.944353i	$0.393310\pi$
$674$	7.52263	+	28.0748i	0.289761	+	1.08140i
$675$	−3.54634	−	3.52470i	−0.136499	−	0.135666i
$676$	−3.57757	−	12.4980i	−0.137599	−	0.480694i
$677$	−10.7203	−	10.7203i	−0.412015	−	0.412015i	0.470425	−	0.882440i	$-0.344101\pi$
$677$	−10.7203	−	10.7203i	−0.412015	−	0.412015i	−0.882440	+	0.470425i	$0.844101\pi$
$678$	17.6616	+	10.1969i	0.678288	+	0.391610i
$679$	58.2189	+	33.6127i	2.23423	+	1.28994i
$680$	−12.5122	−	3.33213i	−0.479822	−	0.127781i
$681$	−15.2596	+	15.2596i	−0.584750	+	0.584750i
$682$	8.85834	+	15.3431i	0.339203	+	0.587517i
$683$	7.89765	+	13.6791i	0.302195	+	0.523417i	0.976633	−	0.214914i	$-0.0689472\pi$
$683$	7.89765	+	13.6791i	0.302195	+	0.523417i	−0.674438	+	0.738332i	$0.735614\pi$
$684$	2.48833	−	2.48833i	0.0951437	−	0.0951437i
$685$	−35.0211	+	20.2910i	−1.33809	+	0.775278i
$686$	−0.475989	−	0.274813i	−0.0181734	−	0.0104924i
$687$	−11.5528	−	6.67001i	−0.440767	−	0.254477i
$688$	0.440689	+	0.440689i	0.0168011	+	0.0168011i
$689$	−24.2432	+	18.9319i	−0.923591	+	0.721248i
$690$	−12.9002	+	0.0197370i	−0.491103	+	0.000751375i
$691$	−3.09521	−	11.5515i	−0.117747	−	0.439439i	0.881731	−	0.471753i	$-0.156379\pi$
$691$	−3.09521	−	11.5515i	−0.117747	−	0.439439i	−0.999478	+	0.0323148i	$0.989712\pi$
$692$	2.62836	−	0.704267i	0.0999153	−	0.0267722i
$693$	−4.84992	+	18.1002i	−0.184233	+	0.687568i
$694$	−4.79034	−	4.79034i	−0.181839	−	0.181839i
$695$	11.7781	−	6.82413i	0.446768	−	0.258854i
$696$	−1.09861	+	4.10006i	−0.0416426	+	0.155412i
$697$		−	47.0915i		−	1.78372i
$698$	10.3220	+	2.76578i	0.390695	+	0.104686i
$699$	6.10061	−	10.5666i	0.230746	−	0.399664i
$700$	−16.3149	−	9.35296i	−0.616645	−	0.353509i
$701$		−	22.5243i		−	0.850729i	−0.905022	−	0.425365i	$-0.860146\pi$
$701$		−	22.5243i		−	0.850729i	0.905022	−	0.425365i	$-0.139854\pi$
$702$	−3.57058	+	0.500979i	−0.134763	+	0.0189082i
$703$	4.23655	−	4.23655i	0.159785	−	0.159785i
$704$	4.81242	−	1.28948i	0.181375	−	0.0485992i
$705$	19.8294	−	5.34580i	0.746818	−	0.201334i
$706$	16.7759	−	9.68559i	0.631370	−	0.364522i
$707$	−16.1019			−0.605575
$708$	−4.93287	+	2.84800i	−0.185389	+	0.107034i
$709$	4.86426	+	1.30338i	0.182681	+	0.0489493i	0.349000	−	0.937123i	$-0.386521\pi$
$709$	4.86426	+	1.30338i	0.182681	+	0.0489493i	−0.166319	+	0.986072i	$0.553188\pi$
$710$	17.9967	−	18.0518i	0.675403	−	0.677473i
$711$	−2.33345	−	4.04166i	−0.0875113	−	0.151574i
$712$	3.59112	+	13.4022i	0.134583	+	0.502270i
$713$	−10.2576	+	17.7667i	−0.384150	+	0.665367i
$714$	−21.7795			−0.815076
$715$	−39.7694	+	5.64201i	−1.48729	+	0.210999i
$716$	−10.3818			−0.387988
$717$	−2.94900	+	5.10782i	−0.110132	+	0.190755i
$718$	8.26208	+	30.8345i	0.308338	+	1.15073i
$719$	−17.5027	−	30.3156i	−0.652741	−	1.13058i	−0.982455	−	0.186500i	$-0.940286\pi$
$719$	−17.5027	−	30.3156i	−0.652741	−	1.13058i	0.329714	−	0.944081i	$-0.393048\pi$
$720$	0.00342112	+	2.23607i	0.000127498	+	0.0833332i
$721$	29.5822	+	7.92652i	1.10170	+	0.295199i
$722$	5.72998	−	3.30821i	0.213248	−	0.123119i
$723$	−20.0285			−0.744870
$724$	−0.00258702	+	0.00149362i	−9.61458e−5	+	5.55098e-5i
$725$	−18.4124	−	10.5554i	−0.683821	−	0.392019i
$726$	13.3512	−	3.57743i	0.495508	−	0.132771i
$727$	−23.3980	+	23.3980i	−0.867783	+	0.867783i	−0.992227	−	0.124444i	$-0.960285\pi$
$727$	−23.3980	+	23.3980i	−0.867783	+	0.867783i	0.124444	+	0.992227i	$0.460285\pi$
$728$	−12.4841	+	5.29584i	−0.462693	+	0.196277i
$729$			1.00000i			0.0370370i
$730$	5.88180	−	10.2237i	0.217695	−	0.378395i
$731$	−1.80445	+	3.12540i	−0.0667400	+	0.115597i
$732$	−5.11557	−	1.37071i	−0.189077	−	0.0506630i
$733$		−	4.64195i		−	0.171454i	−0.996319	−	0.0857271i	$-0.972679\pi$
$733$		−	4.64195i		−	0.171454i	0.996319	−	0.0857271i	$-0.0273213\pi$
$734$	−4.08480	+	15.2447i	−0.150773	+	0.562692i
$735$	−15.4411	−	4.11211i	−0.569552	−	0.151678i
$736$	4.07941	+	4.07941i	0.150369	+	0.150369i
$737$	−6.94232	+	25.9091i	−0.255724	+	0.954373i
$738$	−7.85522	+	2.10480i	−0.289155	+	0.0774788i
$739$	10.1270	+	37.7945i	0.372528	+	1.39029i	0.856923	+	0.515444i	$0.172373\pi$
$739$	10.1270	+	37.7945i	0.372528	+	1.39029i	−0.484396	+	0.874849i	$0.660960\pi$
$740$	0.00582469	+	3.80705i	0.000214120	+	0.139950i
$741$	12.5931	+	1.54916i	0.462620	+	0.0569100i
$742$	22.6888	+	22.6888i	0.832932	+	0.832932i
$743$	−3.38967	−	1.95703i	−0.124355	−	0.0717964i	0.436532	−	0.899689i	$-0.356207\pi$
$743$	−3.38967	−	1.95703i	−0.124355	−	0.0717964i	−0.560887	+	0.827892i	$0.689540\pi$
$744$	3.07959	+	1.77800i	0.112903	+	0.0651848i
$745$	7.14281	−	26.8214i	0.261692	−	0.982660i
$746$	−8.81505	+	8.81505i	−0.322742	+	0.322742i
$747$	0.431840	+	0.747969i	0.0158002	+	0.0273667i
$748$	14.4251	+	24.9849i	0.527433	+	0.913540i
$749$	11.0806	−	11.0806i	0.404877	−	0.404877i
$750$	−10.8125	−	2.84409i	−0.394818	−	0.103851i
$751$	27.1308	+	15.6640i	0.990018	+	0.571587i	0.905280	−	0.424816i	$-0.139661\pi$
$751$	27.1308	+	15.6640i	0.990018	+	0.571587i	0.0847385	+	0.996403i	$0.472995\pi$
$752$	−7.95408	−	4.59229i	−0.290055	−	0.167464i
$753$	2.09965	+	2.09965i	0.0765155	+	0.0765155i
$754$	−14.0892	+	5.97670i	−0.513098	+	0.217659i
$755$	23.6169	+	23.5447i	0.859506	+	0.856880i
$756$	0.973453	+	3.63298i	0.0354042	+	0.132130i
$757$	−19.6990	+	5.27833i	−0.715973	+	0.191844i	−0.598374	−	0.801217i	$-0.704186\pi$
$757$	−19.6990	+	5.27833i	−0.715973	+	0.191844i	−0.117599	+	0.993061i	$0.537520\pi$
$758$	8.32543	−	31.0709i	0.302393	−	1.12855i
$759$	20.3244	+	20.3244i	0.737729	+	0.737729i
$760$	2.02496	−	7.60378i	0.0734531	−	0.275818i
$761$	−3.01185	+	11.2404i	−0.109180	+	0.407464i	−0.998786	−	0.0492648i	$-0.984312\pi$
$761$	−3.01185	+	11.2404i	−0.109180	+	0.407464i	0.889606	+	0.456728i	$0.150979\pi$
$762$			11.7338i			0.425071i
$763$	−24.1044	−	6.45875i	−0.872637	−	0.233822i
$764$	1.39117	−	2.40958i	0.0503308	−	0.0871755i
$765$	−12.5020	+	3.37040i	−0.452010	+	0.121857i
$766$		−	0.966546i		−	0.0349227i
$767$	−19.0400	−	7.69772i	−0.687494	−	0.277949i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−25.8288	+	6.92080i	−0.931409	+	0.249570i	−0.692455	−	0.721461i	$-0.743471\pi$
$769$	−25.8288	+	6.92080i	−0.931409	+	0.249570i	−0.238954	+	0.971031i	$0.576804\pi$
$770$	10.9067	+	40.4565i	0.393049	+	1.45795i
$771$	18.6296	−	10.7558i	0.670928	−	0.387361i
$772$	−15.1703			−0.545990
$773$	−28.0174	+	16.1759i	−1.00772	+	0.581805i	−0.910522	−	0.413460i	$-0.864320\pi$
$773$	−28.0174	+	16.1759i	−1.00772	+	0.581805i	−0.0971942	+	0.995265i	$0.530987\pi$
$774$	0.601992	+	0.161303i	0.0216382	+	0.00579793i
$775$	−12.5339	+	12.6108i	−0.450229	+	0.452993i
$776$	−8.93684	−	15.4791i	−0.320814	−	0.555666i
$777$	1.65737	+	6.18539i	0.0594578	+	0.221900i
$778$	6.23689	−	10.8026i	0.223603	−	0.387292i
$779$	28.6179			1.02534
$780$	−6.34668	+	4.97188i	−0.227248	+	0.178022i
$781$	−56.7946			−2.03227
$782$	−16.7036	+	28.9315i	−0.597321	+	1.03459i
$783$	1.09861	+	4.10006i	0.0392610	+	0.146524i
$784$	3.57307	+	6.18873i	0.127610	+	0.221026i
$785$	32.3188	+	32.2201i	1.15351	+	1.14998i
$786$	−8.26588	−	2.21484i	−0.294834	−	0.0790006i
$787$	34.3166	−	19.8127i	1.22325	−	0.706246i	0.257643	−	0.966240i	$-0.417054\pi$
$787$	34.3166	−	19.8127i	1.22325	−	0.706246i	0.965610	+	0.259994i	$0.0837207\pi$
$788$	21.3122			0.759215
$789$	1.96034	−	1.13180i	0.0697898	−	0.0402932i
$790$	−9.04540	−	5.20393i	−0.321821	−	0.185147i
$791$	74.0903	−	19.8524i	2.63435	−	0.705871i
$792$	3.52294	−	3.52294i	0.125182	−	0.125182i
$793$	−7.45703	−	17.5788i	−0.264807	−	0.624242i
$794$		−	28.7818i		−	1.02143i
$795$	16.5351	+	9.51283i	0.586439	+	0.337385i
$796$	4.07958	−	7.06604i	0.144597	−	0.250449i
$797$	38.2764	+	10.2561i	1.35582	+	0.363291i	0.862280	−	0.506432i	$-0.169036\pi$
$797$	38.2764	+	10.2561i	1.35582	+	0.363291i	0.493541	+	0.869723i	$0.335702\pi$
$798$		−	13.2356i		−	0.468533i
$799$	13.7652	−	51.3726i	0.486979	−	1.81743i
$800$	2.51324	+	4.32246i	0.0888564	+	0.152822i
$801$	9.81111	+	9.81111i	0.346659	+	0.346659i
$802$	7.99709	−	29.8455i	0.282387	−	1.05388i
$803$	−25.3847	+	6.80180i	−0.895805	+	0.240030i
$804$	1.39343	+	5.20035i	0.0491425	+	0.183402i
$805$	−34.2560	+	34.3610i	−1.20736	+	1.21106i
$806$	1.78149	+	12.6970i	0.0627502	+	0.447233i
$807$	12.5996	+	12.5996i	0.443528	+	0.443528i
$808$	3.70757	+	2.14057i	0.130432	+	0.0753049i
$809$	−34.6702	−	20.0168i	−1.21894	−	0.703754i	−0.254247	−	0.967139i	$-0.581828\pi$
$809$	−34.6702	−	20.0168i	−1.21894	−	0.703754i	−0.964691	+	0.263385i	$0.915161\pi$
$810$	1.12100	+	1.93478i	0.0393878	+	0.0679812i
$811$	0.134654	−	0.134654i	0.00472836	−	0.00472836i	−0.704739	−	0.709467i	$-0.748936\pi$
$811$	0.134654	−	0.134654i	0.00472836	−	0.00472836i	0.709467	+	0.704739i	$0.248936\pi$
$812$	7.98243	+	13.8260i	0.280128	+	0.485196i
$813$	−9.21747	−	15.9651i	−0.323271	−	0.559921i
$814$	5.99804	−	5.99804i	0.210231	−	0.210231i
$815$	−8.09206	−	13.9665i	−0.283452	−	0.489224i
$816$	5.01486	+	2.89533i	0.175555	+	0.101357i
$817$	−1.89933	−	1.09658i	−0.0664492	−	0.0383645i
$818$	13.8042	+	13.8042i	0.482654	+	0.482654i
$819$	−8.16367	+	10.8284i	−0.285262	+	0.378375i
$820$	−12.8386	+	12.8780i	−0.448345	+	0.449719i
$821$	−1.46544	−	5.46909i	−0.0511441	−	0.190872i	0.935628	−	0.352989i	$-0.114835\pi$
$821$	−1.46544	−	5.46909i	−0.0511441	−	0.190872i	−0.986772	+	0.162116i	$0.948168\pi$
$822$	17.4841	−	4.68484i	0.609827	−	0.163403i
$823$	−12.9670	+	48.3934i	−0.452000	+	1.68689i	0.244762	+	0.969583i	$0.421290\pi$
$823$	−12.9670	+	48.3934i	−0.452000	+	1.68689i	−0.696761	+	0.717303i	$0.745376\pi$
$824$	−5.75774	−	5.75774i	−0.200580	−	0.200580i
$825$	12.5214	+	21.5353i	0.435940	+	0.749762i
$826$	−5.54478	+	20.6934i	−0.192928	+	0.720015i
$827$		−	30.5662i		−	1.06289i	−0.847093	−	0.531445i	$-0.821649\pi$
$827$		−	30.5662i		−	1.06289i	0.847093	−	0.531445i	$-0.178351\pi$
$828$	5.57258	+	1.49317i	0.193661	+	0.0518912i
$829$	−5.90667	+	10.2307i	−0.205147	+	0.355325i	−0.950180	−	0.311703i	$-0.899101\pi$
$829$	−5.90667	+	10.2307i	−0.205147	+	0.355325i	0.745032	+	0.667028i	$0.232434\pi$
$830$	1.67398	+	0.963064i	0.0581049	+	0.0334284i
$831$		−	10.4613i		−	0.362898i
$832$	3.57858	+	0.440224i	0.124065	+	0.0152620i
$833$	−29.2607	+	29.2607i	−1.01382	+	1.01382i
$834$	−5.88013	+	1.57558i	−0.203612	+	0.0545577i
$835$	−23.7330	−	13.6539i	−0.821314	−	0.472512i
$836$	−15.1836	+	8.76623i	−0.525134	+	0.303186i
$837$	3.55601			0.122914
$838$	−22.8482	+	13.1914i	−0.789277	+	0.455690i
$839$	−13.8724	−	3.71711i	−0.478929	−	0.128329i	0.0112747	−	0.999936i	$-0.496411\pi$
$839$	−13.8724	−	3.71711i	−0.478929	−	0.128329i	−0.490204	+	0.871608i	$0.663078\pi$
$840$	5.95597	+	5.93777i	0.205500	+	0.204873i
$841$	−5.49130	−	9.51121i	−0.189355	−	0.327973i
$842$	−1.14050	−	4.25641i	−0.0393043	−	0.146686i
$843$	−11.4931	+	19.9067i	−0.395844	+	0.685622i
$844$	−26.8695			−0.924887
$845$	−28.2129	−	7.00214i	−0.970555	−	0.240881i
$846$	−9.18458			−0.315772
$847$	25.9935	−	45.0220i	0.893146	−	1.54697i
$848$	−2.20803	−	8.24046i	−0.0758239	−	0.282979i
$849$	−15.5622	−	26.9545i	−0.534092	−	0.925074i
$850$	−20.4103	+	20.5356i	−0.700069	+	0.704366i
$851$	9.48770	+	2.54222i	0.325234	+	0.0871462i
$852$	−9.87230	+	5.69977i	−0.338219	+	0.195271i
$853$	−14.5823			−0.499290			−0.249645	−	0.968337i	$-0.580314\pi$
$853$	−14.5823			−0.499290			−0.249645	+	0.968337i	$0.580314\pi$
$854$	−17.2504	+	9.95953i	−0.590297	+	0.340808i
$855$	−2.04822	−	7.59755i	−0.0700477	−	0.259831i
$856$	−4.02443	+	1.07834i	−0.137552	+	0.0368570i
$857$	−14.3338	+	14.3338i	−0.489634	+	0.489634i	−0.908191	−	0.418557i	$-0.862536\pi$
$857$	−14.3338	+	14.3338i	−0.489634	+	0.489634i	0.418557	+	0.908191i	$0.362536\pi$
$858$	17.8291	+	2.19328i	0.608676	+	0.0748773i
$859$		−	29.5931i		−	1.00970i	−0.863206	−	0.504851i	$-0.831547\pi$
$859$		−	29.5931i		−	1.00970i	0.863206	−	0.504851i	$-0.168453\pi$
$860$	1.34554	−	0.362744i	0.0458826	−	0.0123695i
$861$	−15.2934	+	26.4889i	−0.521197	+	0.902740i
$862$	−17.3188	−	4.64056i	−0.589880	−	0.158058i
$863$			35.3652i			1.20385i	0.798554	+	0.601923i	$0.205599\pi$
$863$			35.3652i			1.20385i	−0.798554	+	0.601923i	$0.794401\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	1.56579	−	5.87959i	0.0532386	−	0.199912i
$866$	−18.8577	−	18.8577i	−0.640811	−	0.640811i
$867$	−4.27873	+	15.9685i	−0.145313	+	0.542317i
$868$	12.9189	−	3.46161i	0.438496	−	0.117495i
$869$	6.01790	+	22.4591i	0.204143	+	0.761873i
$870$	6.72171	+	6.70117i	0.227887	+	0.227191i
$871$	−11.6857	+	15.5001i	−0.395955	+	0.525200i
$872$	4.69157	+	4.69157i	0.158877	+	0.158877i
$873$	−15.4791	−	8.93684i	−0.523887	−	0.302466i
$874$	−17.5819	−	10.1509i	−0.594718	−	0.343360i
$875$	−36.3201	+	21.1923i	−1.22784	+	0.716431i
$876$	−3.72986	+	3.72986i	−0.126020	+	0.126020i
$877$	13.0323	+	22.5726i	0.440069	+	0.762222i	0.997694	−	0.0678711i	$-0.0216207\pi$
$877$	13.0323	+	22.5726i	0.440069	+	0.762222i	−0.557625	+	0.830093i	$0.688287\pi$
$878$	−1.66483	−	2.88358i	−0.0561854	−	0.0973160i
$879$	−0.192334	+	0.192334i	−0.00648725	+	0.00648725i
$880$	2.86691	−	10.7653i	0.0966434	−	0.362898i
$881$	−5.95223	−	3.43652i	−0.200536	−	0.115779i	0.396370	−	0.918091i	$-0.370270\pi$
$881$	−5.95223	−	3.43652i	−0.200536	−	0.115779i	−0.596905	+	0.802312i	$0.703603\pi$
$882$	6.18873	+	3.57307i	0.208385	+	0.120311i
$883$	−33.6939	−	33.6939i	−1.13389	−	1.13389i	−0.989524	−	0.144366i	$-0.953886\pi$
$883$	−33.6939	−	33.6939i	−1.13389	−	1.13389i	−0.144366	−	0.989524i	$-0.546114\pi$
$884$	2.90100	+	20.6760i	0.0975712	+	0.695409i
$885$	0.0194867	+	12.7366i	0.000655038	+	0.428136i
$886$	−6.38343	−	23.8233i	−0.214455	−	0.800358i
$887$	6.09194	−	1.63233i	0.204547	−	0.0548083i	−0.155090	−	0.987900i	$-0.549567\pi$
$887$	6.09194	−	1.63233i	0.204547	−	0.0548083i	0.359638	+	0.933092i	$0.382900\pi$
$888$	0.440657	−	1.64455i	0.0147875	−	0.0551876i
$889$	31.2063	+	31.2063i	1.04663	+	1.04663i
$890$	29.9806	+	7.98412i	1.00495	+	0.267628i
$891$	1.28948	−	4.81242i	0.0431993	−	0.161222i
$892$			16.1973i			0.542327i
$893$	31.2195	+	8.36524i	1.04472	+	0.279932i
$894$	−6.20648	+	10.7499i	−0.207576	+	0.359532i
$895$	−11.5765	+	20.1221i	−0.386959	+	0.672608i
$896$		−	3.76113i		−	0.125651i
$897$	8.12323	+	19.1493i	0.271227	+	0.639376i
$898$	−13.9471	+	13.9471i	−0.465420	+	0.465420i
$899$	14.5798	−	3.90665i	0.486264	−	0.130294i
$900$	4.33776	+	2.48674i	0.144592	+	0.0828913i
$901$	42.7825	−	24.7005i	1.42529	−	0.822893i
$902$	40.5167			1.34906
$903$	2.03000	−	1.17202i	0.0675542	−	0.0390025i
$904$	−19.6989	−	5.27831i	−0.655176	−	0.175554i
$905$	1.02197e−5		0.00667965i	3.39714e−7		0.000222039i
$906$	−7.45691	−	12.9157i	−0.247739	−	0.429097i
$907$	−5.22227	−	19.4898i	−0.173403	−	0.647148i	−0.996818	−	0.0797087i	$-0.974601\pi$
$907$	−5.22227	−	19.4898i	−0.173403	−	0.647148i	0.823416	−	0.567439i	$-0.192066\pi$
$908$	10.7902	−	18.6891i	0.358085	−	0.620221i
$909$	4.28113			0.141996
$910$	−3.65630	+	30.1020i	−0.121205	+	0.997871i
$911$	−20.6188			−0.683131			−0.341565	−	0.939858i	$-0.610957\pi$
$911$	−20.6188			−0.683131			−0.341565	+	0.939858i	$0.610957\pi$
$912$	−1.75952	+	3.04757i	−0.0582634	+	0.100915i
$913$	−1.11370	−	4.15639i	−0.0368581	−	0.137556i
$914$	−0.994792	−	1.72303i	−0.0329048	−	0.0569928i
$915$	−8.36093	+	8.38655i	−0.276404	+	0.277251i
$916$	12.8855	+	3.45265i	0.425748	+	0.114079i
$917$	−27.8737	+	16.0929i	−0.920471	+	0.531434i
$918$	5.79066			0.191120
$919$	27.9054	−	16.1112i	0.920515	−	0.531460i	0.0367158	−	0.999326i	$-0.488310\pi$
$919$	27.9054	−	16.1112i	0.920515	−	0.531460i	0.883799	+	0.467866i	$0.154977\pi$
$920$	12.4556	−	3.35789i	0.410647	−	0.110706i
$921$	−18.9602	+	5.08038i	−0.624761	+	0.167404i
$922$	19.2164	−	19.2164i	0.632857	−	0.632857i
$923$	−38.1053	−	15.4057i	−1.25425	−	0.507084i
$924$		−	18.7387i		−	0.616457i
$925$	7.38532	+	4.23384i	0.242828	+	0.139208i
$926$	12.2312	−	21.1850i	0.401941	−	0.696182i
$927$	−7.86522	−	2.10748i	−0.258328	−	0.0692187i
$928$		−	4.24469i		−	0.139339i
$929$	−8.81881	+	32.9123i	−0.289336	+	1.07982i	0.656276	+	0.754521i	$0.272131\pi$
$929$	−8.81881	+	32.9123i	−0.289336	+	1.07982i	−0.945612	+	0.325296i	$0.894536\pi$
$930$	6.88009	−	3.98627i	0.225607	−	0.130715i
$931$	−17.7819	−	17.7819i	−0.582780	−	0.582780i
$932$	−3.15791	+	11.7855i	−0.103441	+	0.386046i
$933$	7.40784	−	1.98492i	0.242522	−	0.0649835i
$934$	−7.27933	−	27.1668i	−0.238187	−	0.888926i
$935$	64.5108	−	0.0986999i	2.10973	−	0.00322783i
$936$	3.31925	−	1.40804i	0.108493	−	0.0460233i
$937$	9.87270	+	9.87270i	0.322527	+	0.322527i	0.849736	−	0.527209i	$-0.176761\pi$
$937$	9.87270	+	9.87270i	0.322527	+	0.322527i	−0.527209	+	0.849736i	$0.676761\pi$
$938$	17.5363	+	10.1246i	0.572581	+	0.330580i
$939$	−9.39152	−	5.42220i	−0.306481	−	0.176947i
$940$	−17.7701	+	10.2959i	−0.579598	+	0.335814i
$941$	23.0680	−	23.0680i	0.751996	−	0.751996i	−0.222856	−	0.974851i	$-0.571538\pi$
$941$	23.0680	−	23.0680i	0.751996	−	0.751996i	0.974851	+	0.222856i	$0.0715379\pi$
$942$	−10.2045	−	17.6747i	−0.332481	−	0.575874i
$943$	23.4584	+	40.6311i	0.763909	+	1.32313i
$944$	4.02767	−	4.02767i	0.131090	−	0.131090i
$945$	8.12690	+	2.16428i	0.264368	+	0.0704039i
$946$	−2.68904	−	1.55252i	−0.0874282	−	0.0504767i
$947$	28.2096	+	16.2868i	0.916688	+	0.529250i	0.882577	−	0.470168i	$-0.155807\pi$
$947$	28.2096	+	16.2868i	0.916688	+	0.529250i	0.0341110	+	0.999418i	$0.489140\pi$
$948$	3.30000	+	3.30000i	0.107179	+	0.107179i
$949$	−18.8764	−	2.32211i	−0.612752	−	0.0753788i
$950$	−12.4797	−	12.4035i	−0.404894	−	0.402424i
$951$	−4.17272	−	15.5728i	−0.135310	−	0.504982i
$952$	21.0373	−	5.63694i	0.681824	−	0.182694i
$953$	−1.76540	+	6.58856i	−0.0571869	+	0.213424i	−0.988607	−	0.150523i	$-0.951904\pi$
$953$	−1.76540	+	6.58856i	−0.0571869	+	0.213424i	0.931420	+	0.363947i	$0.118571\pi$
$954$	−6.03244	−	6.03244i	−0.195307	−	0.195307i
$955$	−3.11899	−	5.38322i	−0.100928	−	0.174197i
$956$	1.52652	−	5.69703i	0.0493710	−	0.184255i
$957$		−	21.1478i		−	0.683612i
$958$	2.55523	+	0.684672i	0.0825557	+	0.0221207i
$959$	34.0399	−	58.9588i	1.09920	−	1.90388i
$960$	−0.582041	−	2.15899i	−0.0187853	−	0.0696810i
$961$			18.3548i			0.592091i
$962$	5.65125	−	2.39729i	0.182204	−	0.0772916i
$963$	−2.94608	+	2.94608i	−0.0949362	+	0.0949362i
$964$	19.3461	−	5.18377i	0.623096	−	0.166958i
$965$	−16.9159	+	29.4030i	−0.544543	+	0.946517i
$966$	18.7915	−	10.8493i	0.604608	−	0.349071i
$967$	39.2212			1.26127			0.630634	−	0.776080i	$-0.282795\pi$
$967$	39.2212			1.26127			0.630634	+	0.776080i	$0.282795\pi$
$968$	−11.9703	+	6.91107i	−0.384741	+	0.222130i
$969$	−19.6832	−	5.27409i	−0.632315	−	0.169428i
$970$	−39.9667	+	0.0611481i	−1.28325	+	0.00196335i
$971$	9.50097	+	16.4562i	0.304901	+	0.528104i	0.977239	−	0.212140i	$-0.0680434\pi$
$971$	9.50097	+	16.4562i	0.304901	+	0.528104i	−0.672338	+	0.740244i	$0.734710\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−11.4481	+	19.8286i	−0.367008	+	0.635677i
$974$	−23.4559			−0.751574
$975$	2.55951	+	17.8451i	0.0819700	+	0.571502i
$976$	5.29602			0.169522
$977$	18.8717	−	32.6867i	0.603758	−	1.04574i	−0.388488	−	0.921454i	$-0.627002\pi$
$977$	18.8717	−	32.6867i	0.603758	−	1.04574i	0.992246	−	0.124286i	$-0.0396642\pi$
$978$	1.86832	+	6.97266i	0.0597423	+	0.222961i
$979$	−34.5639	−	59.8665i	−1.10467	−	1.91334i
$980$	15.9792	−	0.0244478i	0.510437	−	0.000780956i
$981$	6.40881	+	1.71723i	0.204617	+	0.0548271i
$982$	5.36184	−	3.09566i	0.171103	−	0.0987864i
$983$	37.0716			1.18240			0.591201	−	0.806524i	$-0.298654\pi$
$983$	37.0716			1.18240			0.591201	+	0.806524i	$0.298654\pi$
$984$	7.04280	−	4.06616i	0.224516	−	0.129624i
$985$	23.7646	−	41.3073i	0.757202	−	1.31616i
$986$	23.7420	−	6.36166i	0.756100	−	0.202596i
$987$	−24.4266	+	24.4266i	−0.777507	+	0.777507i
$988$	−12.5650	+	1.76296i	−0.399745	+	0.0560873i
$989$		−	3.59550i		−	0.114330i
$990$	−2.89983	−	10.7565i	−0.0921628	−	0.341863i
$991$	−11.5529	+	20.0103i	−0.366991	+	0.635647i	−0.989094	−	0.147289i	$-0.952945\pi$
$991$	−11.5529	+	20.0103i	−0.366991	+	0.635647i	0.622103	+	0.782936i	$0.286279\pi$
$992$	−3.43484	−	0.920362i	−0.109056	−	0.0292215i
$993$		−	33.9826i		−	1.07840i
$994$	−11.0969	+	41.4143i	−0.351973	+	1.31358i
$995$	−9.14639	−	15.7862i	−0.289960	−	0.500456i
$996$	−0.610714	−	0.610714i	−0.0193512	−	0.0193512i
$997$	16.0641	−	59.9519i	0.508754	−	1.89870i	0.0761863	−	0.997094i	$-0.475726\pi$
$997$	16.0641	−	59.9519i	0.508754	−	1.89870i	0.432568	−	0.901602i	$-0.357608\pi$
$998$	−31.0731	+	8.32601i	−0.983602	+	0.263555i
$999$	−0.440657	−	1.64455i	−0.0139418	−	0.0520314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.b.97.3	yes	16
5.3	odd	4		390.2.bd.b.253.2	yes	16
13.11	odd	12		390.2.bd.b.37.2	✓	16
65.63	even	12	inner	390.2.bn.b.193.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.37.2	✓	16	13.11	odd	12
390.2.bd.b.253.2	yes	16	5.3	odd	4
390.2.bn.b.97.3	yes	16	1.1	even	1	trivial
390.2.bn.b.193.3	yes	16	65.63	even	12	inner

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.23607 + 0.00342112i) q^{5} +(0.965926 + 0.258819i) q^{6} +(3.25724 - 1.88057i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.23607 + 0.00342112i) q^{5} +(0.965926 + 0.258819i) q^{6} +(3.25724 - 1.88057i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.11507 + 1.93820i) q^{10} +(4.81242 - 1.28948i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.57858 + 0.440224i) q^{13} -3.76113i q^{14} +(-0.582041 - 2.15899i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.59335 - 1.49873i) q^{17} +1.00000i q^{18} +(0.910792 - 3.39912i) q^{19} +(1.12100 + 1.93478i) q^{20} +(2.65952 + 2.65952i) q^{21} +(1.28948 - 4.81242i) q^{22} +(5.57258 - 1.49317i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(4.99998 - 0.0152997i) q^{25} +(2.17053 - 2.87903i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.25724 - 1.88057i) q^{28} +(-3.67601 - 2.12235i) q^{29} +(-2.16076 - 0.575432i) q^{30} +(-2.51448 + 2.51448i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.49109 + 4.31470i) q^{33} +(-4.09462 + 4.09462i) q^{34} +(-7.27696 + 4.21621i) q^{35} +(0.866025 + 0.500000i) q^{36} +(1.47447 + 0.851284i) q^{37} +(-2.48833 - 2.48833i) q^{38} +(0.500979 + 3.57058i) q^{39} +(2.23607 - 0.00342112i) q^{40} +(2.10480 + 7.85522i) q^{41} +(3.63298 - 0.973453i) q^{42} +(0.161303 - 0.601992i) q^{43} +(-3.52294 - 3.52294i) q^{44} +(1.93478 - 1.12100i) q^{45} +(1.49317 - 5.57258i) q^{46} +9.18458i q^{47} +(-0.965926 - 0.258819i) q^{48} +(3.57307 - 6.18873i) q^{49} +(2.48674 - 4.33776i) q^{50} -5.79066i q^{51} +(-1.40804 - 3.31925i) q^{52} +(-6.03244 + 6.03244i) q^{53} +(-0.965926 + 0.258819i) q^{54} +(-10.7565 + 2.89983i) q^{55} +(-3.25724 + 1.88057i) q^{56} +3.51903 q^{57} +(-3.67601 + 2.12235i) q^{58} +(-5.50190 - 1.47423i) q^{59} +(-1.57872 + 1.58356i) q^{60} +(-2.64801 - 4.58649i) q^{61} +(0.920362 + 3.43484i) q^{62} +(-1.88057 + 3.25724i) q^{63} +1.00000 q^{64} +(-8.00343 - 0.972128i) q^{65} +4.98218 q^{66} +(-2.69190 + 4.66250i) q^{67} +(1.49873 + 5.59335i) q^{68} +(2.88458 + 4.99624i) q^{69} +(0.0128673 + 8.41014i) q^{70} +(-11.0111 - 2.95042i) q^{71} +(0.866025 - 0.500000i) q^{72} -5.27482 q^{73} +(1.47447 - 0.851284i) q^{74} +(1.30887 + 4.82565i) q^{75} +(-3.39912 + 0.910792i) q^{76} +(13.2502 - 13.2502i) q^{77} +(3.34270 + 1.35143i) q^{78} +4.66690i q^{79} +(1.11507 - 1.93820i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.85522 + 2.10480i) q^{82} -0.863680i q^{83} +(0.973453 - 3.63298i) q^{84} +(12.5122 + 3.33213i) q^{85} +(-0.440689 - 0.440689i) q^{86} +(1.09861 - 4.10006i) q^{87} +(-4.81242 + 1.28948i) q^{88} +(-3.59112 - 13.4022i) q^{89} +(-0.00342112 - 2.23607i) q^{90} +(12.4841 - 5.29584i) q^{91} +(-4.07941 - 4.07941i) q^{92} +(-3.07959 - 1.77800i) q^{93} +(7.95408 + 4.59229i) q^{94} +(-2.02496 + 7.60378i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(8.93684 + 15.4791i) q^{97} +(-3.57307 - 6.18873i) q^{98} +(-3.52294 + 3.52294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

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