LMFDB - Embedded newform 77.2.n.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	77.17
Dual form			77.2.n.a.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33360 - 1.20078i) q^{2} +(-1.17499 - 2.63908i) q^{3} +(0.127565 + 1.21370i) q^{4} +(0.418270 + 1.96780i) q^{5} +(-1.60198 + 4.93040i) q^{6} +(-1.17364 - 2.37120i) q^{7} +(-0.822345 + 1.13186i) q^{8} +(-3.57672 + 3.97235i) q^{9} +O(q^{10})$	\(q+(-1.33360 - 1.20078i) q^{2} +(-1.17499 - 2.63908i) q^{3} +(0.127565 + 1.21370i) q^{4} +(0.418270 + 1.96780i) q^{5} +(-1.60198 + 4.93040i) q^{6} +(-1.17364 - 2.37120i) q^{7} +(-0.822345 + 1.13186i) q^{8} +(-3.57672 + 3.97235i) q^{9} +(1.80510 - 3.12652i) q^{10} +(2.87587 - 1.65208i) q^{11} +(3.05315 - 1.76274i) q^{12} +(-1.45177 - 4.46807i) q^{13} +(-1.28213 + 4.57152i) q^{14} +(4.70172 - 3.41600i) q^{15} +(4.84323 - 1.02946i) q^{16} +(-0.385539 - 0.428185i) q^{17} +(9.53987 - 1.00268i) q^{18} +(0.144087 - 1.37090i) q^{19} +(-2.33496 + 0.758675i) q^{20} +(-4.87876 + 5.88345i) q^{21} +(-5.81906 - 1.25008i) q^{22} +(0.408298 + 0.707192i) q^{23} +(3.95331 + 0.840303i) q^{24} +(0.870426 - 0.387539i) q^{25} +(-3.42911 + 7.70190i) q^{26} +(6.44364 + 2.09366i) q^{27} +(2.72820 - 1.72692i) q^{28} +(0.425221 + 0.585266i) q^{29} +(-10.3721 - 1.09015i) q^{30} +(0.746819 - 3.51351i) q^{31} +(-5.27188 - 3.04372i) q^{32} +(-7.73908 - 5.64847i) q^{33} +1.03398i q^{34} +(4.17515 - 3.30129i) q^{35} +(-5.27750 - 3.83433i) q^{36} +(8.86232 + 3.94576i) q^{37} +(-1.83831 + 1.65522i) q^{38} +(-10.0858 + 9.08127i) q^{39} +(-2.57124 - 1.14479i) q^{40} +(-2.23288 - 1.62228i) q^{41} +(13.5711 - 1.98787i) q^{42} +8.37074i q^{43} +(2.37198 + 3.27969i) q^{44} +(-9.31284 - 5.37677i) q^{45} +(0.304677 - 1.43339i) q^{46} +(3.52320 + 0.370304i) q^{47} +(-8.40758 - 11.5720i) q^{48} +(-4.24516 + 5.56585i) q^{49} +(-1.62615 - 0.528369i) q^{50} +(-0.677006 + 1.52058i) q^{51} +(5.23770 - 2.33197i) q^{52} +(6.25897 + 1.33038i) q^{53} +(-6.07923 - 10.5295i) q^{54} +(4.45385 + 4.96814i) q^{55} +(3.64900 + 0.621549i) q^{56} +(-3.78720 + 1.23054i) q^{57} +(0.135701 - 1.29111i) q^{58} +(-5.67532 + 0.596501i) q^{59} +(4.74576 + 5.27070i) q^{60} +(13.2611 - 2.81874i) q^{61} +(-5.21492 + 3.78886i) q^{62} +(13.6170 + 3.81902i) q^{63} +(0.315602 + 0.971325i) q^{64} +(8.18506 - 4.72565i) q^{65} +(3.53829 + 16.8258i) q^{66} +(-0.838413 + 1.45217i) q^{67} +(0.470505 - 0.522549i) q^{68} +(1.38659 - 1.90847i) q^{69} +(-9.53214 - 0.610845i) q^{70} +(2.10176 - 6.46855i) q^{71} +(-1.55485 - 7.31499i) q^{72} +(0.650590 + 6.18995i) q^{73} +(-7.08083 - 15.9038i) q^{74} +(-2.04549 - 1.84176i) q^{75} +1.68224 q^{76} +(-7.29263 - 4.88033i) q^{77} +24.3551 q^{78} +(-5.67714 - 5.11172i) q^{79} +(4.05155 + 9.09993i) q^{80} +(-0.369668 - 3.51716i) q^{81} +(1.02977 + 4.84469i) q^{82} +(0.369293 - 1.13657i) q^{83} +(-7.76309 - 5.17081i) q^{84} +(0.681324 - 0.937762i) q^{85} +(10.0514 - 11.1633i) q^{86} +(1.04493 - 1.80987i) q^{87} +(-0.495040 + 4.61366i) q^{88} +(-12.6666 + 7.31306i) q^{89} +(5.96331 + 18.3532i) q^{90} +(-8.89084 + 8.68632i) q^{91} +(-0.806233 + 0.585763i) q^{92} +(-10.1499 + 2.15743i) q^{93} +(-4.25391 - 4.72444i) q^{94} +(2.75792 - 0.289870i) q^{95} +(-1.83819 + 17.4892i) q^{96} +(-9.81655 + 3.18959i) q^{97} +(12.3447 - 2.32513i) q^{98} +(-3.72357 + 17.3330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.33360	−	1.20078i	−0.943001	−	0.849082i	0.0457041	−	0.998955i	$-0.485447\pi$
$2$	−1.33360	−	1.20078i	−0.943001	−	0.849082i	−0.988705	+	0.149873i	$0.952114\pi$
$3$	−1.17499	−	2.63908i	−0.678382	−	1.52367i	−0.843346	−	0.537371i	$-0.819417\pi$
$3$	−1.17499	−	2.63908i	−0.678382	−	1.52367i	0.164964	−	0.986300i	$-0.447249\pi$
$4$	0.127565	+	1.21370i	0.0637824	+	0.606849i
$5$	0.418270	+	1.96780i	0.187056	+	0.880029i	0.967118	+	0.254327i	$0.0818539\pi$
$5$	0.418270	+	1.96780i	0.187056	+	0.880029i	−0.780062	+	0.625702i	$0.784813\pi$
$6$	−1.60198	+	4.93040i	−0.654007	+	2.01283i
$7$	−1.17364	−	2.37120i	−0.443593	−	0.896228i
$7$	−1.17364	−	2.37120i	−0.443593	−	0.896228i
$8$	−0.822345	+	1.13186i	−0.290743	+	0.400173i
$9$	−3.57672	+	3.97235i	−1.19224	+	1.32412i
$10$	1.80510	−	3.12652i	0.570823	−	0.988694i
$11$	2.87587	−	1.65208i	0.867108	−	0.498120i
$11$	2.87587	−	1.65208i	0.867108	−	0.498120i
$12$	3.05315	−	1.76274i	0.881369	−	0.508859i
$13$	−1.45177	−	4.46807i	−0.402647	−	1.23922i	−0.922844	−	0.385174i	$-0.874141\pi$
$13$	−1.45177	−	4.46807i	−0.402647	−	1.23922i	0.520197	−	0.854046i	$-0.325859\pi$
$14$	−1.28213	+	4.57152i	−0.342663	+	1.22179i
$15$	4.70172	−	3.41600i	1.21398	−	0.882007i
$16$	4.84323	−	1.02946i	1.21081	−	0.257365i
$17$	−0.385539	−	0.428185i	−0.0935070	−	0.103850i	0.694575	−	0.719420i	$-0.255592\pi$
$17$	−0.385539	−	0.428185i	−0.0935070	−	0.103850i	−0.788082	+	0.615570i	$0.788926\pi$
$18$	9.53987	−	1.00268i	2.24857	−	0.236334i
$19$	0.144087	−	1.37090i	0.0330559	−	0.314505i	−0.965483	−	0.260466i	$-0.916124\pi$
$19$	0.144087	−	1.37090i	0.0330559	−	0.314505i	0.998539	−	0.0540392i	$-0.0172096\pi$
$20$	−2.33496	+	0.758675i	−0.522113	+	0.169645i
$21$	−4.87876	+	5.88345i	−1.06463	+	1.28387i
$22$	−5.81906	−	1.25008i	−1.24063	−	0.266519i
$23$	0.408298	+	0.707192i	0.0851360	+	0.147460i	0.905449	−	0.424455i	$-0.139534\pi$
$23$	0.408298	+	0.707192i	0.0851360	+	0.147460i	−0.820313	+	0.571915i	$0.806201\pi$
$24$	3.95331	+	0.840303i	0.806967	+	0.171526i
$25$	0.870426	−	0.387539i	0.174085	−	0.0775077i
$26$	−3.42911	+	7.70190i	−0.672503	+	1.51047i
$27$	6.44364	+	2.09366i	1.24008	+	0.402926i
$28$	2.72820	−	1.72692i	0.515582	−	0.326357i
$29$	0.425221	+	0.585266i	0.0789615	+	0.108681i	0.846671	−	0.532117i	$-0.178603\pi$
$29$	0.425221	+	0.585266i	0.0789615	+	0.108681i	−0.767709	+	0.640798i	$0.778603\pi$
$30$	−10.3721	−	1.09015i	−1.89368	−	0.199034i
$31$	0.746819	−	3.51351i	0.134133	−	0.631044i	−0.858795	−	0.512320i	$-0.828786\pi$
$31$	0.746819	−	3.51351i	0.134133	−	0.631044i	0.992927	−	0.118724i	$-0.0378805\pi$
$32$	−5.27188	−	3.04372i	−0.931945	−	0.538059i
$33$	−7.73908	−	5.64847i	−1.34720	−	0.983272i
$34$			1.03398i			0.177326i
$35$	4.17515	−	3.30129i	0.705730	−	0.558019i
$36$	−5.27750	−	3.83433i	−0.879583	−	0.639054i
$37$	8.86232	+	3.94576i	1.45696	+	0.648679i	0.973914	−	0.226918i	$-0.0728650\pi$
$37$	8.86232	+	3.94576i	1.45696	+	0.648679i	0.483042	+	0.875597i	$0.339532\pi$
$38$	−1.83831	+	1.65522i	−0.298213	+	0.268512i
$39$	−10.0858	+	9.08127i	−1.61502	+	1.45417i
$40$	−2.57124	−	1.14479i	−0.406549	−	0.181007i
$41$	−2.23288	−	1.62228i	−0.348717	−	0.253358i	0.399614	−	0.916684i	$-0.369144\pi$
$41$	−2.23288	−	1.62228i	−0.348717	−	0.253358i	−0.748331	+	0.663326i	$0.769144\pi$
$42$	13.5711	−	1.98787i	2.09406	−	0.306736i
$43$			8.37074i			1.27653i	0.769819	+	0.638263i	$0.220347\pi$
$43$			8.37074i			1.27653i	−0.769819	+	0.638263i	$0.779653\pi$
$44$	2.37198	+	3.27969i	0.357589	+	0.494432i
$45$	−9.31284	−	5.37677i	−1.38828	−	0.801522i
$46$	0.304677	−	1.43339i	0.0449222	−	0.211342i
$47$	3.52320	+	0.370304i	0.513912	+	0.0540143i	0.357935	−	0.933746i	$-0.383481\pi$
$47$	3.52320	+	0.370304i	0.513912	+	0.0540143i	0.155977	+	0.987761i	$0.450147\pi$
$48$	−8.40758	−	11.5720i	−1.21353	−	1.67028i
$49$	−4.24516	+	5.56585i	−0.606451	+	0.795121i
$50$	−1.62615	−	0.528369i	−0.229973	−	0.0747227i
$51$	−0.677006	+	1.52058i	−0.0947998	+	0.212924i
$52$	5.23770	−	2.33197i	0.726338	−	0.323386i
$53$	6.25897	+	1.33038i	0.859736	+	0.182742i	0.616626	−	0.787256i	$-0.288499\pi$
$53$	6.25897	+	1.33038i	0.859736	+	0.182742i	0.243110	+	0.969999i	$0.421832\pi$
$54$	−6.07923	−	10.5295i	−0.827278	−	1.43289i
$55$	4.45385	+	4.96814i	0.600557	+	0.669904i
$56$	3.64900	+	0.621549i	0.487618	+	0.0830580i
$57$	−3.78720	+	1.23054i	−0.501627	+	0.162989i
$58$	0.135701	−	1.29111i	0.0178185	−	0.169531i
$59$	−5.67532	+	0.596501i	−0.738864	+	0.0776578i	−0.466481	−	0.884531i	$-0.654478\pi$
$59$	−5.67532	+	0.596501i	−0.738864	+	0.0776578i	−0.272383	+	0.962189i	$0.587812\pi$
$60$	4.74576	+	5.27070i	0.612675	+	0.680445i
$61$	13.2611	−	2.81874i	1.69792	−	0.360903i	0.745689	−	0.666294i	$-0.232120\pi$
$61$	13.2611	−	2.81874i	1.69792	−	0.360903i	0.952227	+	0.305391i	$0.0987871\pi$
$62$	−5.21492	+	3.78886i	−0.662295	+	0.481186i
$63$	13.6170	+	3.81902i	1.71558	+	0.481151i
$64$	0.315602	+	0.971325i	0.0394503	+	0.121416i
$65$	8.18506	−	4.72565i	1.01523	−	0.586144i
$66$	3.53829	+	16.8258i	0.435533	+	2.07111i
$67$	−0.838413	+	1.45217i	−0.102428	+	0.177411i	−0.912685	−	0.408665i	$-0.865995\pi$
$67$	−0.838413	+	1.45217i	−0.102428	+	0.177411i	0.810256	+	0.586076i	$0.199328\pi$
$68$	0.470505	−	0.522549i	0.0570572	−	0.0633684i
$69$	1.38659	−	1.90847i	0.166926	−	0.229753i
$70$	−9.53214	−	0.610845i	−1.13931	−	0.0730100i
$71$	2.10176	−	6.46855i	0.249433	−	0.767676i	−0.745443	−	0.666570i	$-0.767762\pi$
$71$	2.10176	−	6.46855i	0.249433	−	0.767676i	0.994876	−	0.101106i	$-0.0322381\pi$
$72$	−1.55485	−	7.31499i	−0.183241	−	0.862080i
$73$	0.650590	+	6.18995i	0.0761458	+	0.724479i	0.964278	+	0.264891i	$0.0853360\pi$
$73$	0.650590	+	6.18995i	0.0761458	+	0.724479i	−0.888133	+	0.459587i	$0.847997\pi$
$74$	−7.08083	−	15.9038i	−0.823130	−	1.84878i
$75$	−2.04549	−	1.84176i	−0.236192	−	0.212669i
$76$	1.68224			0.192966
$77$	−7.29263	−	4.88033i	−0.831072	−	0.556165i
$78$	24.3551			2.75767
$79$	−5.67714	−	5.11172i	−0.638728	−	0.575113i	0.284827	−	0.958579i	$-0.408064\pi$
$79$	−5.67714	−	5.11172i	−0.638728	−	0.575113i	−0.923555	+	0.383466i	$0.874730\pi$
$80$	4.05155	+	9.09993i	0.452977	+	1.01740i
$81$	−0.369668	−	3.51716i	−0.0410742	−	0.390795i
$82$	1.02977	+	4.84469i	0.113719	+	0.535006i
$83$	0.369293	−	1.13657i	0.0405351	−	0.124754i	−0.928741	−	0.370729i	$-0.879108\pi$
$83$	0.369293	−	1.13657i	0.0405351	−	0.124754i	0.969276	+	0.245974i	$0.0791079\pi$
$84$	−7.76309	−	5.17081i	−0.847023	−	0.564182i
$85$	0.681324	−	0.937762i	0.0739000	−	0.101715i
$86$	10.0514	−	11.1633i	1.08387	−	1.20376i
$87$	1.04493	−	1.80987i	0.112028	−	0.194039i
$88$	−0.495040	+	4.61366i	−0.0527714	+	0.491818i
$89$	−12.6666	+	7.31306i	−1.34266	+	0.775183i	−0.987197	−	0.159508i	$-0.949009\pi$
$89$	−12.6666	+	7.31306i	−1.34266	+	0.775183i	−0.355460	+	0.934691i	$0.615676\pi$
$90$	5.96331	+	18.3532i	0.628588	+	1.93460i
$91$	−8.89084	+	8.68632i	−0.932013	+	0.910573i
$92$	−0.806233	+	0.585763i	−0.0840556	+	0.0610700i
$93$	−10.1499	+	2.15743i	−1.05250	+	0.223715i
$94$	−4.25391	−	4.72444i	−0.438757	−	0.487289i
$95$	2.75792	−	0.289870i	0.282957	−	0.0297400i
$96$	−1.83819	+	17.4892i	−0.187610	+	1.78499i
$97$	−9.81655	+	3.18959i	−0.996720	+	0.323854i	−0.761554	−	0.648101i	$-0.775563\pi$
$97$	−9.81655	+	3.18959i	−0.996720	+	0.323854i	−0.235166	+	0.971955i	$0.575563\pi$
$98$	12.3447	−	2.32513i	1.24701	−	0.234874i
$99$	−3.72357	+	17.3330i	−0.374233	+	1.74203i
$100$	0.581390	+	1.00700i	0.0581390	+	0.100700i
$101$	5.24708	+	1.11530i	0.522104	+	0.110977i	0.461423	−	0.887180i	$-0.347339\pi$
$101$	5.24708	+	1.11530i	0.522104	+	0.110977i	0.0606817	+	0.998157i	$0.480673\pi$
$102$	2.72875	−	1.21492i	0.270186	−	0.120295i
$103$	3.87602	−	8.70567i	0.381915	−	0.857796i	−0.615648	−	0.788022i	$-0.711106\pi$
$103$	3.87602	−	8.70567i	0.381915	−	0.857796i	0.997563	−	0.0697740i	$-0.0222278\pi$
$104$	6.25109	+	2.03110i	0.612969	+	0.199166i
$105$	−13.6181	−	7.13956i	−1.32899	−	0.696750i
$106$	−6.74949	−	9.28987i	−0.655568	−	0.902312i
$107$	−1.44193	−	0.151553i	−0.139397	−	0.0146512i	0.0345729	−	0.999402i	$-0.488993\pi$
$107$	−1.44193	−	0.151553i	−0.139397	−	0.0146512i	−0.173970	+	0.984751i	$0.555660\pi$
$108$	−1.71909	+	8.08770i	−0.165420	+	0.778240i
$109$	−6.50025	−	3.75292i	−0.622611	−	0.359465i	0.155274	−	0.987871i	$-0.450374\pi$
$109$	−6.50025	−	3.75292i	−0.622611	−	0.359465i	−0.777885	+	0.628407i	$0.783707\pi$
$110$	0.0259823	−	11.9736i	0.00247731	−	1.14164i
$111$		−	28.0246i		−	2.65997i
$112$	−8.12525	−	10.2760i	−0.767764	−	0.970995i
$113$	−7.45715	−	5.41794i	−0.701509	−	0.509676i	0.178914	−	0.983865i	$-0.442742\pi$
$113$	−7.45715	−	5.41794i	−0.701509	−	0.509676i	−0.880423	+	0.474188i	$0.842742\pi$
$114$	6.52824	+	2.90656i	0.611426	+	0.272224i
$115$	−1.22084	+	1.09925i	−0.113844	+	0.102505i
$116$	−0.656093	+	0.590749i	−0.0609167	+	0.0548497i
$117$	22.9413	+	10.2141i	2.12093	+	0.944297i
$118$	8.28491	+	6.01934i	0.762688	+	0.554125i
$119$	−0.562828	+	1.41672i	−0.0515943	+	0.129871i
$120$			8.13082i			0.742239i
$121$	5.54129	−	9.50232i	0.503754	−	0.863847i
$122$	−21.0698	−	12.1647i	−1.90757	−	1.10134i
$123$	−1.65771	+	7.79890i	−0.149471	+	0.703203i
$124$	4.35960	+	0.458212i	0.391504	+	0.0411487i
$125$	7.03910	+	9.68849i	0.629596	+	0.866565i
$126$	−13.5739	−	21.4441i	−1.20926	−	1.91039i
$127$	9.48419	+	3.08160i	0.841586	+	0.273448i	0.697918	−	0.716178i	$-0.254110\pi$
$127$	9.48419	+	3.08160i	0.841586	+	0.273448i	0.143668	+	0.989626i	$0.454110\pi$
$128$	−4.20651	+	9.44798i	−0.371806	+	0.835091i
$129$	22.0910	−	9.83555i	1.94500	−	0.865972i
$130$	−16.5901	−	3.52634i	−1.45505	−	0.309280i
$131$	6.87588	+	11.9094i	0.600749	+	1.04053i	0.992708	+	0.120545i	$0.0384641\pi$
$131$	6.87588	+	11.9094i	0.600749	+	1.04053i	−0.391959	+	0.919983i	$0.628203\pi$
$132$	5.86830	−	10.1134i	0.510770	−	0.880263i
$133$	−3.41977	+	1.26728i	−0.296532	+	0.109887i
$134$	2.86186	−	0.929874i	0.247227	−	0.0803289i
$135$	−1.42474	+	13.5555i	−0.122622	+	1.16667i
$136$	0.801691	−	0.0842611i	0.0687444	−	0.00722533i
$137$	−11.3225	−	12.5750i	−0.967350	−	1.07435i	−0.997199	−	0.0747963i	$-0.976169\pi$
$137$	−11.3225	−	12.5750i	−0.967350	−	1.07435i	0.0298491	−	0.999554i	$-0.490497\pi$
$138$	−4.14082	+	0.880159i	−0.352490	+	0.0749241i
$139$	0.206041	−	0.149697i	0.0174762	−	0.0126972i	−0.579013	−	0.815318i	$-0.696562\pi$
$139$	0.206041	−	0.149697i	0.0174762	−	0.0126972i	0.596489	+	0.802621i	$0.296562\pi$
$140$	4.53936	+	4.64625i	0.383646	+	0.392680i
$141$	−3.16248	−	9.73310i	−0.266329	−	0.819675i
$142$	−10.5702	+	6.10273i	−0.887035	+	0.512130i
$143$	−11.5567	−	10.4512i	−0.966419	−	0.873972i
$144$	−13.2335	+	22.9211i	−1.10279	+	1.91009i
$145$	−0.973832	+	1.08155i	−0.0808724	+	0.0898179i
$146$	6.56516	−	9.03616i	0.543336	−	0.747838i
$147$	19.6767	+	4.66346i	1.62291	+	0.384636i
$148$	−3.65844	+	11.2595i	−0.300722	+	0.925526i
$149$	2.55139	+	12.0034i	0.209018	+	0.983353i	0.950102	+	0.311940i	$0.100979\pi$
$149$	2.55139	+	12.0034i	0.209018	+	0.983353i	−0.741083	+	0.671413i	$0.765688\pi$
$150$	0.516311	+	4.91237i	0.0421566	+	0.401094i
$151$	2.31570	+	5.20115i	0.188449	+	0.423263i	0.982919	−	0.184041i	$-0.0589178\pi$
$151$	2.31570	+	5.20115i	0.188449	+	0.423263i	−0.794470	+	0.607304i	$0.792251\pi$
$152$	1.43317	+	1.29044i	0.116246	+	0.104668i
$153$	3.07987			0.248992
$154$	3.86527	+	15.2653i	0.311472	+	1.23011i
$155$	7.22626			0.580427
$156$	−12.3085	−	11.0826i	−0.985469	−	0.887320i
$157$	3.01868	+	6.78006i	0.240917	+	0.541108i	0.993021	−	0.117936i	$-0.0376278\pi$
$157$	3.01868	+	6.78006i	0.240917	+	0.541108i	−0.752104	+	0.659044i	$0.770961\pi$
$158$	1.43299	+	13.6340i	0.114003	+	1.08466i
$159$	−3.84325	−	18.0811i	−0.304790	−	1.43392i
$160$	3.78438	−	11.6471i	0.299181	−	0.920786i
$161$	1.19770	−	1.79814i	0.0943920	−	0.141713i
$162$	−3.73035	+	5.13439i	−0.293084	+	0.403396i
$163$	−7.32402	+	8.13415i	−0.573661	+	0.637116i	−0.958236	−	0.285978i	$-0.907681\pi$
$163$	−7.32402	+	8.13415i	−0.573661	+	0.637116i	0.384575	+	0.923094i	$0.374348\pi$
$164$	1.68412	−	2.91699i	0.131508	−	0.227778i
$165$	7.87806	−	17.5916i	0.613306	−	1.36950i
$166$	−1.85726	+	1.07229i	−0.144151	+	0.0832258i
$167$	1.48944	+	4.58403i	0.115256	+	0.354723i	0.992000	−	0.126234i	$-0.0402892\pi$
$167$	1.48944	+	4.58403i	0.115256	+	0.354723i	−0.876744	+	0.480957i	$0.840289\pi$
$168$	−2.64723	−	10.3603i	−0.204238	−	0.799314i
$169$	−7.33884	+	5.33198i	−0.564526	+	0.410152i
$170$	−2.03467	+	0.432482i	−0.156052	+	0.0331698i
$171$	4.93033	+	5.47568i	0.377032	+	0.418736i
$172$	−10.1595	+	1.06781i	−0.774658	+	0.0814198i
$173$	−1.77904	+	16.9264i	−0.135258	+	1.28689i	0.690692	+	0.723149i	$0.257306\pi$
$173$	−1.77904	+	16.9264i	−0.135258	+	1.28689i	−0.825950	+	0.563744i	$0.809361\pi$
$174$	−3.56679	+	1.15892i	−0.270398	+	0.0878576i
$175$	−1.94049	−	1.60912i	−0.146688	−	0.121638i
$176$	12.2278	−	10.9620i	0.921703	−	0.826290i
$177$	8.24267	+	14.2767i	0.619557	+	1.07310i
$178$	25.6736	+	5.45710i	1.92432	+	0.409027i
$179$	18.2082	−	8.10681i	1.36094	−	0.605931i	0.409093	−	0.912493i	$-0.365845\pi$
$179$	18.2082	−	8.10681i	1.36094	−	0.605931i	0.951851	+	0.306561i	$0.0991785\pi$
$180$	5.33778	−	11.9889i	0.397855	−	0.893597i
$181$	17.1058	+	5.55801i	1.27146	+	0.413124i	0.865566	−	0.500795i	$-0.166959\pi$
$181$	17.1058	+	5.55801i	1.27146	+	0.413124i	0.405898	+	0.913919i	$0.366959\pi$
$182$	22.2873	−	0.908140i	1.65204	−	0.0673158i
$183$	−23.0206	−	31.6852i	−1.70173	−	2.34224i
$184$	−1.13620	−	0.119420i	−0.0837621	−	0.00880375i
$185$	−4.05764	+	19.0897i	−0.298324	+	1.40350i
$186$	16.1266	+	9.31069i	1.18246	+	0.682693i
$187$	−1.81616	−	0.594465i	−0.132810	−	0.0434716i
$188$			4.32334i			0.315312i
$189$	−2.59799	−	17.7363i	−0.188976	−	1.29013i
$190$	−4.02605	−	2.92510i	−0.292081	−	0.212209i
$191$	−22.2311	−	9.89792i	−1.60859	−	0.716188i	−0.611411	−	0.791313i	$-0.709398\pi$
$191$	−22.2311	−	9.89792i	−1.60859	−	0.716188i	−0.997174	+	0.0751244i	$0.976065\pi$
$192$	2.19257	−	1.97420i	0.158235	−	0.142475i
$193$	13.8200	−	12.4436i	0.994786	−	0.895709i	0.000238995	−	1.00000i	$-0.499924\pi$
$193$	13.8200	−	12.4436i	0.994786	−	0.895709i	0.994547	+	0.104291i	$0.0332573\pi$
$194$	16.9214	+	7.53390i	1.21489	+	0.540902i
$195$	−22.0887	−	16.0484i	−1.58181	−	1.14925i
$196$	−7.29679	−	4.44233i	−0.521199	−	0.317309i
$197$		−	3.97471i		−	0.283187i	−0.989925	−	0.141593i	$-0.954777\pi$
$197$		−	3.97471i		−	0.283187i	0.989925	−	0.141593i	$-0.0452225\pi$
$198$	25.7789	−	18.6442i	1.83203	−	1.32498i
$199$	13.4921	+	7.78964i	0.956427	+	0.552193i	0.895071	−	0.445923i	$-0.147124\pi$
$199$	13.4921	+	7.78964i	0.956427	+	0.552193i	0.0613554	+	0.998116i	$0.480458\pi$
$200$	−0.277150	+	1.30389i	−0.0195975	+	0.0921990i
$201$	4.81753	+	0.506342i	0.339802	+	0.0357146i
$202$	−5.65830	−	7.78798i	−0.398117	−	0.547961i
$203$	0.888728	−	1.69517i	0.0623764	−	0.118978i
$204$	−1.93189	−	0.627708i	−0.135259	−	0.0439484i
$205$	2.25839	−	5.07242i	0.157733	−	0.354273i
$206$	−15.6227	+	6.95568i	−1.08849	+	0.484625i
$207$	−4.26958	−	0.907528i	−0.296757	−	0.0630776i
$208$	−11.6309	−	20.1454i	−0.806460	−	1.39683i
$209$	−1.85045	−	4.18057i	−0.127998	−	0.289176i
$210$	9.58812	+	25.8738i	0.661643	+	1.78546i
$211$	−12.3212	+	4.00339i	−0.848223	+	0.275604i	−0.700702	−	0.713454i	$-0.747130\pi$
$211$	−12.3212	+	4.00339i	−0.848223	+	0.275604i	−0.147522	+	0.989059i	$0.547130\pi$
$212$	−0.816261	+	7.76621i	−0.0560610	+	0.533385i
$213$	−19.5405	+	2.05379i	−1.33890	+	0.140724i
$214$	1.74099	+	1.93356i	0.119011	+	0.132176i
$215$	−16.4720	+	3.50122i	−1.12338	+	0.238782i
$216$	−7.66863	+	5.57158i	−0.521784	+	0.379098i
$217$	−9.20771	+	2.35272i	−0.625060	+	0.159713i
$218$	4.16232	+	12.8103i	0.281908	+	0.867623i
$219$	15.5713	−	8.99010i	1.05221	−	0.607494i
$220$	−5.46167	+	6.03939i	−0.368225	+	0.407175i
$221$	−1.35345	+	2.34424i	−0.0910428	+	0.157691i
$222$	−33.6514	+	37.3737i	−2.25854	+	2.50836i
$223$	−0.691406	+	0.951639i	−0.0463000	+	0.0637265i	−0.831539	−	0.555466i	$-0.812540\pi$
$223$	−0.691406	+	0.951639i	−0.0463000	+	0.0637265i	0.785239	+	0.619192i	$0.212540\pi$
$224$	−1.02999	+	16.0729i	−0.0688194	+	1.07392i
$225$	−1.57383	+	4.84375i	−0.104922	+	0.322917i
$226$	3.43912	+	16.1798i	0.228767	+	1.07626i
$227$	−1.76263	−	16.7703i	−0.116990	−	1.11308i	−0.882713	−	0.469912i	$-0.844286\pi$
$227$	−1.76263	−	16.7703i	−0.116990	−	1.11308i	0.765724	−	0.643170i	$-0.222381\pi$
$228$	−1.97661	−	4.43955i	−0.130904	−	0.294016i
$229$	−4.38287	−	3.94635i	−0.289628	−	0.260782i	0.511489	−	0.859290i	$-0.329094\pi$
$229$	−4.38287	−	3.94635i	−0.289628	−	0.260782i	−0.801117	+	0.598508i	$0.795761\pi$
$230$	2.94807			0.194390
$231$	−4.31077	+	24.9801i	−0.283628	+	1.64357i
$232$	−1.01212			−0.0664488
$233$	9.54553	+	8.59483i	0.625348	+	0.563066i	0.919696	−	0.392632i	$-0.128436\pi$
$233$	9.54553	+	8.59483i	0.625348	+	0.563066i	−0.294347	+	0.955699i	$0.595102\pi$
$234$	−18.3297	−	41.1692i	−1.19825	−	2.69131i
$235$	0.744964	+	7.08786i	0.0485961	+	0.462361i
$236$	−1.44794	−	6.81203i	−0.0942530	−	0.443426i
$237$	−6.81962	+	20.9886i	−0.442982	+	1.36336i
$238$	2.45177	−	1.21351i	0.158924	−	0.0786604i
$239$	2.69800	−	3.71348i	0.174519	−	0.240205i	−0.712793	−	0.701375i	$-0.752570\pi$
$239$	2.69800	−	3.71348i	0.174519	−	0.240205i	0.887312	+	0.461170i	$0.152570\pi$
$240$	19.2549	−	21.3847i	1.24290	−	1.38038i
$241$	−3.85526	+	6.67751i	−0.248339	+	0.430136i	−0.963065	−	0.269268i	$-0.913218\pi$
$241$	−3.85526	+	6.67751i	−0.248339	+	0.430136i	0.714726	+	0.699405i	$0.246551\pi$
$242$	−18.8001	+	6.01845i	−1.20852	+	0.386881i
$243$	8.75491	−	5.05465i	0.561628	−	0.324256i
$244$	5.11276	+	15.7355i	0.327311	+	1.00736i
$245$	−12.7281	−	6.02561i	−0.813169	−	0.384962i
$246$	11.5755	−	8.41011i	0.738028	−	0.536209i
$247$	−6.33445	+	1.34643i	−0.403052	+	0.0856712i
$248$	3.36265	+	3.73461i	0.213529	+	0.237148i
$249$	−3.43340	+	0.360865i	−0.217583	+	0.0228689i
$250$	2.24640	−	21.3731i	0.142075	−	1.35175i
$251$	−17.6741	+	5.74265i	−1.11558	+	0.362473i	−0.808078	−	0.589076i	$-0.799492\pi$
$251$	−17.6741	+	5.74265i	−1.11558	+	0.362473i	−0.307499	+	0.951549i	$0.599492\pi$
$252$	−2.89808	+	17.0141i	−0.182562	+	1.07179i
$253$	2.34255	+	1.35926i	0.147275	+	0.0854557i
$254$	−8.94783	−	15.4981i	−0.561437	−	0.972437i
$255$	−3.27537	−	0.696202i	−0.205112	−	0.0435979i
$256$	18.8208	−	8.37957i	1.17630	−	0.523723i
$257$	7.84522	−	17.6206i	0.489371	−	1.09915i	−0.485064	−	0.874478i	$-0.661204\pi$
$257$	7.84522	−	17.6206i	0.489371	−	1.09915i	0.974436	−	0.224667i	$-0.0721295\pi$
$258$	−41.2710	−	13.4098i	−2.56942	−	0.834856i
$259$	−1.04497	−	25.6452i	−0.0649311	−	1.59351i
$260$	6.77963	+	9.33136i	0.420455	+	0.578707i
$261$	−3.84578	−	0.404208i	−0.238048	−	0.0250198i
$262$	5.13087	−	24.1389i	0.316986	−	1.49130i
$263$	−11.3727	−	6.56600i	−0.701268	−	0.404877i	0.106552	−	0.994307i	$-0.466019\pi$
$263$	−11.3727	−	6.56600i	−0.701268	−	0.404877i	−0.807819	+	0.589430i	$0.799352\pi$
$264$	12.7575	−	4.11457i	0.785168	−	0.253234i
$265$			12.8729i			0.790775i
$266$	6.08235	+	2.41636i	0.372933	+	0.148157i
$267$	34.1829	+	24.8353i	2.09196	+	1.51990i
$268$	−1.86945	−	0.832334i	−0.114195	−	0.0508429i
$269$	17.6571	−	15.8985i	1.07657	−	0.969350i	0.0769556	−	0.997035i	$-0.475480\pi$
$269$	17.6571	−	15.8985i	1.07657	−	0.969350i	0.999617	+	0.0276845i	$0.00881338\pi$
$270$	18.1773	−	16.3669i	1.10624	−	0.996059i
$271$	−12.6913	−	5.65053i	−0.770941	−	0.343245i	−0.0167156	−	0.999860i	$-0.505321\pi$
$271$	−12.6913	−	5.65053i	−0.770941	−	0.343245i	−0.754226	+	0.656615i	$0.771988\pi$
$272$	−2.30805	−	1.67690i	−0.139946	−	0.101677i
$273$	33.3705	+	13.2572i	2.01968	+	0.802365i
$274$			30.3659i			1.83447i
$275$	1.86299	−	2.55252i	0.112343	−	0.153923i
$276$	2.49319	+	1.43944i	0.150072	+	0.0866443i
$277$	0.0415710	−	0.195576i	0.00249776	−	0.0117510i	−0.976881	−	0.213783i	$-0.931421\pi$
$277$	0.0415710	−	0.195576i	0.00249776	−	0.0117510i	0.979379	+	0.202032i	$0.0647546\pi$
$278$	−0.454531	−	0.0477731i	−0.0272610	−	0.00286524i
$279$	11.2857	+	15.5335i	0.675658	+	0.929964i
$280$	0.303178	+	7.44049i	0.0181184	+	0.444654i
$281$	1.00492	+	0.326519i	0.0599486	+	0.0194785i	0.338838	−	0.940845i	$-0.389966\pi$
$281$	1.00492	+	0.326519i	0.0599486	+	0.0194785i	−0.278889	+	0.960323i	$0.589966\pi$
$282$	−7.46985	+	16.7776i	−0.444823	+	0.999090i
$283$	−14.2947	+	6.36439i	−0.849729	+	0.378324i	−0.784937	−	0.619575i	$-0.787305\pi$
$283$	−14.2947	+	6.36439i	−0.849729	+	0.378324i	−0.0647917	+	0.997899i	$0.520638\pi$
$284$	8.11898	+	1.72574i	0.481773	+	0.102404i
$285$	−4.00553	−	6.93778i	−0.237267	−	0.410958i
$286$	2.86245	+	27.8148i	0.169260	+	1.64473i
$287$	−1.22616	+	7.19857i	−0.0723781	+	0.424918i
$288$	30.9468	−	10.0552i	1.82356	−	0.592509i
$289$	1.74228	−	16.5767i	0.102487	−	0.975100i
$290$	2.59742	−	0.272999i	0.152525	−	0.0160311i
$291$	19.9519	+	22.1589i	1.16960	+	1.29898i
$292$	−7.42973	+	1.57924i	−0.434792	+	0.0924179i
$293$	−2.16413	+	1.57233i	−0.126430	+	0.0918565i	−0.649203	−	0.760615i	$-0.724897\pi$
$293$	−2.16413	+	1.57233i	−0.126430	+	0.0918565i	0.522773	+	0.852472i	$0.324897\pi$
$294$	−20.6412	−	29.8467i	−1.20382	−	1.74069i
$295$	−3.54761	−	10.9184i	−0.206550	−	0.635695i
$296$	−11.7539	+	6.78613i	−0.683183	+	0.394436i
$297$	21.9900	−	4.62426i	1.27599	−	0.268327i
$298$	11.0109	−	19.0714i	0.637843	−	1.10478i
$299$	2.56704	−	2.85098i	0.148455	−	0.164877i
$300$	1.97441	−	2.71755i	0.113993	−	0.156898i
$301$	19.8487	−	9.82420i	1.14406	−	0.566257i
$302$	3.15722	−	9.71693i	0.181678	−	0.559146i
$303$	−3.22192	−	15.1579i	−0.185094	−	0.870800i
$304$	−0.713438	−	6.78791i	−0.0409185	−	0.389313i
$305$	11.0935	+	24.9163i	0.635210	+	1.42671i
$306$	−4.10732	−	3.69825i	−0.234800	−	0.211415i
$307$	1.94883			0.111226			0.0556129	−	0.998452i	$-0.482289\pi$
$307$	1.94883			0.111226			0.0556129	+	0.998452i	$0.482289\pi$
$308$	4.99296	−	9.47360i	0.284500	−	0.539809i
$309$	−27.5292			−1.56608
$310$	−9.63698	−	8.67717i	−0.547343	−	0.492830i
$311$	1.01981	+	2.29054i	0.0578283	+	0.129885i	0.940148	−	0.340765i	$-0.110686\pi$
$311$	1.01981	+	2.29054i	0.0578283	+	0.129885i	−0.882320	+	0.470650i	$0.844019\pi$
$312$	−1.98475	−	18.8836i	−0.112364	−	1.06907i
$313$	2.59421	+	12.2048i	0.146633	+	0.689856i	0.988629	+	0.150372i	$0.0480471\pi$
$313$	2.59421	+	12.2048i	0.146633	+	0.689856i	−0.841996	+	0.539483i	$0.818620\pi$
$314$	4.11566	−	12.6667i	0.232260	−	0.714823i
$315$	−1.81950	+	28.3930i	−0.102517	+	1.59976i
$316$	5.47988	−	7.54240i	0.308267	−	0.424293i
$317$	5.35008	−	5.94187i	0.300491	−	0.333729i	−0.573924	−	0.818909i	$-0.694579\pi$
$317$	5.35008	−	5.94187i	0.300491	−	0.333729i	0.874414	+	0.485180i	$0.161246\pi$
$318$	−16.5861	+	28.7279i	−0.930101	+	1.61098i
$319$	2.18979	+	0.980655i	0.122604	+	0.0549061i
$320$	−1.77937	+	1.02732i	−0.0994698	+	0.0574289i
$321$	1.29430	+	3.98345i	0.0722408	+	0.222334i
$322$	−3.75644	+	0.959832i	−0.209338	+	0.0534894i
$323$	−0.642548	+	0.466839i	−0.0357524	+	0.0259756i
$324$	4.22161	−	0.897330i	0.234534	−	0.0498517i
$325$	−2.99520	−	3.32651i	−0.166144	−	0.184522i
$326$	19.5347	−	2.05318i	1.08193	−	0.113715i
$327$	−2.26650	+	21.5643i	−0.125338	+	1.19251i
$328$	3.67239	−	1.19323i	0.202774	−	0.0658852i
$329$	−3.25690	−	8.78881i	−0.179559	−	0.484543i
$330$	−31.6299	+	14.0004i	−1.74117	+	0.770695i
$331$	7.04778	+	12.2071i	0.387381	+	0.670964i	0.992096	−	0.125478i	$-0.0400464\pi$
$331$	7.04778	+	12.2071i	0.387381	+	0.670964i	−0.604715	+	0.796442i	$0.706713\pi$
$332$	1.42656	+	0.303224i	0.0782925	+	0.0166416i
$333$	−47.3720	+	21.0914i	−2.59597	+	1.15580i
$334$	3.51810	−	7.90178i	0.192502	−	0.432366i
$335$	−3.20828	−	1.04243i	−0.175287	−	0.0569541i
$336$	−17.5722	+	33.5174i	−0.958640	+	1.82852i
$337$	10.1848	+	14.0182i	0.554802	+	0.763620i	0.990654	−	0.136399i	$-0.0435528\pi$
$337$	10.1848	+	14.0182i	0.554802	+	0.763620i	−0.435852	+	0.900019i	$0.643553\pi$
$338$	16.1897	+	1.70160i	0.880601	+	0.0925549i
$339$	−5.53625	+	26.0460i	−0.300688	+	1.41462i
$340$	1.22507	+	0.707296i	0.0664389	+	0.0383585i
$341$	−3.65682	−	11.3382i	−0.198028	−	0.613998i
$342$		−	13.2227i		−	0.714999i
$343$	18.1800	+	3.53382i	0.981627	+	0.190808i
$344$	−9.47450	−	6.88363i	−0.510831	−	0.371140i
$345$	4.33547	+	1.93028i	0.233414	+	0.103923i
$346$	22.6975	−	20.4369i	1.22023	−	1.09870i
$347$	−8.02516	+	7.22589i	−0.430813	+	0.387906i	−0.855811	−	0.517288i	$-0.826942\pi$
$347$	−8.02516	+	7.22589i	−0.430813	+	0.387906i	0.424998	+	0.905194i	$0.360275\pi$
$348$	2.32994	+	1.03735i	0.124898	+	0.0556080i
$349$	9.73410	+	7.07224i	0.521054	+	0.378568i	0.817001	−	0.576636i	$-0.195635\pi$
$349$	9.73410	+	7.07224i	0.521054	+	0.378568i	−0.295947	+	0.955204i	$0.595635\pi$
$350$	0.655645	+	4.47605i	0.0350457	+	0.239255i
$351$		−	31.8302i		−	1.69897i
$352$	−20.1897	−	0.0438108i	−1.07612	−	0.00233512i
$353$	−0.0402959	−	0.0232648i	−0.00214473	−	0.00123826i	0.498927	−	0.866644i	$-0.333727\pi$
$353$	−0.0402959	−	0.0232648i	−0.00214473	−	0.00123826i	−0.501072	+	0.865406i	$0.667061\pi$
$354$	6.15079	−	28.9372i	0.326911	−	1.53799i
$355$	13.6079	+	1.43025i	0.722234	+	0.0759099i
$356$	−10.4917	−	14.4405i	−0.556057	−	0.765347i
$357$	4.40016	−	0.179293i	0.232881	−	0.00948922i
$358$	−34.0171	−	11.0528i	−1.79786	−	0.584159i
$359$	−8.90985	+	20.0119i	−0.470244	+	1.05619i	0.510320	+	0.859985i	$0.329527\pi$
$359$	−8.90985	+	20.0119i	−0.470244	+	1.05619i	−0.980564	+	0.196201i	$0.937140\pi$
$360$	13.7441	−	6.11927i	0.724378	−	0.322514i
$361$	16.7262	+	3.55526i	0.880327	+	0.187119i
$362$	−16.1384	−	27.9525i	−0.848216	−	1.46915i
$363$	−31.5883	−	3.45873i	−1.65796	−	0.181536i
$364$	−11.6767	−	9.68272i	−0.612026	−	0.507513i
$365$	−11.9085	+	3.86930i	−0.623318	+	0.202528i
$366$	−7.34661	+	69.8983i	−0.384013	+	3.65364i
$367$	−24.0449	+	2.52722i	−1.25513	+	0.131920i	−0.708657	−	0.705554i	$-0.750698\pi$
$367$	−24.0449	+	2.52722i	−1.25513	+	0.131920i	−0.546478	+	0.837473i	$0.684032\pi$
$368$	2.70551	+	3.00477i	0.141034	+	0.156634i
$369$	14.4307	−	3.06733i	0.751230	−	0.159679i
$370$	28.3339	−	20.5858i	1.47301	−	1.07020i
$371$	−4.19115	−	16.4026i	−0.217594	−	0.851583i
$372$	−3.91324	−	12.0437i	−0.202892	−	0.624437i
$373$	32.4952	−	18.7611i	1.68254	−	0.971414i	0.722574	−	0.691293i	$-0.242959\pi$
$373$	32.4952	−	18.7611i	1.68254	−	0.971414i	0.959965	−	0.280121i	$-0.0903747\pi$
$374$	1.70821	+	2.97359i	0.0883294	+	0.153761i
$375$	17.2978	−	29.9606i	0.893253	−	1.54716i
$376$	−3.31642	+	3.68326i	−0.171031	+	0.189949i
$377$	1.99769	−	2.74959i	0.102886	−	0.141611i
$378$	−17.8328	+	26.7729i	−0.917220	+	1.37705i
$379$	−4.13051	+	12.7124i	−0.212170	+	0.652992i	0.787173	+	0.616733i	$0.211544\pi$
$379$	−4.13051	+	12.7124i	−0.212170	+	0.652992i	−0.999342	+	0.0362589i	$0.988456\pi$
$380$	0.703628	+	3.31031i	0.0360953	+	0.169815i
$381$	−3.01127	−	28.6504i	−0.154272	−	1.46780i
$382$	17.7622	+	39.8946i	0.908795	+	2.04119i
$383$	−0.247526	−	0.222874i	−0.0126480	−	0.0113883i	0.662782	−	0.748812i	$-0.269375\pi$
$383$	−0.247526	−	0.222874i	−0.0126480	−	0.0113883i	−0.675430	+	0.737424i	$0.736042\pi$
$384$	29.8765			1.52463
$385$	6.55324	−	16.3917i	0.333984	−	0.835401i
$386$	−33.3725			−1.69861
$387$	−33.2515	−	29.9398i	−1.69027	−	1.52192i
$388$	−5.12344	−	11.5074i	−0.260103	−	0.584202i
$389$	0.586452	+	5.57972i	0.0297343	+	0.282903i	0.999278	+	0.0379857i	$0.0120941\pi$
$389$	0.586452	+	5.57972i	0.0297343	+	0.282903i	−0.969544	+	0.244917i	$0.921239\pi$
$390$	10.1870	+	47.9260i	0.515838	+	2.42683i
$391$	0.145394	−	0.447477i	0.00735290	−	0.0226299i
$392$	−2.80878	−	9.38197i	−0.141865	−	0.473861i
$393$	23.3506	−	32.1394i	1.17788	−	1.62122i
$394$	−4.77277	+	5.30070i	−0.240449	+	0.267045i
$395$	7.68428	−	13.3096i	0.386638	−	0.669677i
$396$	−21.5120	−	2.30821i	−1.08102	−	0.115992i
$397$	−0.206595	+	0.119278i	−0.0103687	+	0.00598639i	−0.505175	−	0.863017i	$-0.668572\pi$
$397$	−0.206595	+	0.119278i	−0.0103687	+	0.00598639i	0.494807	+	0.869003i	$0.335239\pi$
$398$	−8.63940	−	26.5894i	−0.433054	−	1.33280i
$399$	7.36265	+	7.53600i	0.368593	+	0.377272i
$400$	3.81672	−	2.77301i	0.190836	−	0.138650i
$401$	−29.2257	+	6.21212i	−1.45946	+	0.310218i	−0.868181	−	0.496247i	$-0.834711\pi$
$401$	−29.2257	+	6.21212i	−1.45946	+	0.310218i	−0.591281	+	0.806466i	$0.701378\pi$
$402$	−5.81667	−	6.46006i	−0.290109	−	0.322199i
$403$	−16.7828	+	1.76394i	−0.836011	+	0.0878683i
$404$	−0.684296	+	6.51065i	−0.0340450	+	0.323917i
$405$	6.76645	−	2.19855i	0.336228	−	0.109247i
$406$	−3.22075	+	1.19352i	−0.159843	+	0.0592335i
$407$	32.0056	−	3.29372i	1.58646	−	0.163264i
$408$	−1.16435	−	2.01672i	−0.0576440	−	0.0998424i
$409$	2.79087	+	0.593217i	0.137999	+	0.0293327i	0.276393	−	0.961045i	$-0.410861\pi$
$409$	2.79087	+	0.593217i	0.137999	+	0.0293327i	−0.138394	+	0.990377i	$0.544194\pi$
$410$	−9.10267	+	4.05277i	−0.449549	+	0.200152i
$411$	−19.8824	+	44.6565i	−0.980724	+	2.20274i
$412$	11.0605	+	3.59377i	0.544912	+	0.177053i
$413$	8.07519	+	12.7572i	0.397354	+	0.627743i
$414$	4.60419	+	6.33713i	0.226284	+	0.311453i
$415$	2.39100	+	0.251305i	0.117370	+	0.0123361i
$416$	−5.94604	+	27.9739i	−0.291529	+	1.37153i
$417$	−0.637159	−	0.367864i	−0.0312018	−	0.0180144i
$418$	−2.55219	+	7.79722i	−0.124832	+	0.381374i
$419$		−	12.7923i		−	0.624946i	−0.949927	−	0.312473i	$-0.898843\pi$
$419$		−	12.7923i		−	0.624946i	0.949927	−	0.312473i	$-0.101157\pi$
$420$	6.92808	−	17.4390i	0.338056	−	0.850938i
$421$	−12.9084	−	9.37849i	−0.629116	−	0.457079i	0.226978	−	0.973900i	$-0.427115\pi$
$421$	−12.9084	−	9.37849i	−0.629116	−	0.457079i	−0.856094	+	0.516820i	$0.827115\pi$
$422$	21.2388	+	9.45610i	1.03389	+	0.460316i
$423$	−14.0725	+	12.6709i	−0.684228	+	0.616082i
$424$	−6.65284	+	5.99024i	−0.323090	+	0.290912i
$425$	−0.501521	−	0.223292i	−0.0243274	−	0.0108312i
$426$	28.5255	+	20.7250i	1.38207	+	1.00413i
$427$	−22.2476	−	28.1366i	−1.07664	−	1.36163i
$428$		−	1.76940i		−	0.0855274i
$429$	−14.0025	+	42.7790i	−0.676045	+	2.06539i
$430$	26.1713	+	15.1100i	1.26209	+	0.728669i
$431$	−3.31196	+	15.5815i	−0.159531	+	0.750536i	0.823532	+	0.567270i	$0.192000\pi$
$431$	−3.31196	+	15.5815i	−0.159531	+	0.750536i	−0.983063	+	0.183266i	$0.941333\pi$
$432$	33.3634	+	3.50663i	1.60520	+	0.168713i
$433$	−7.87012	−	10.8323i	−0.378214	−	0.520567i	0.576896	−	0.816817i	$-0.304264\pi$
$433$	−7.87012	−	10.8323i	−0.378214	−	0.520567i	−0.955110	+	0.296251i	$0.904264\pi$
$434$	15.1046	+	7.91886i	0.725042	+	0.380117i
$435$	3.99854	+	1.29920i	0.191715	+	0.0622921i
$436$	3.72571	−	8.36808i	0.178429	−	0.400758i
$437$	1.02832	−	0.457837i	0.0491912	−	0.0219013i
$438$	−31.5611	−	6.70852i	−1.50805	−	0.320546i
$439$	6.51975	+	11.2925i	0.311171	+	0.538963i	0.978616	−	0.205695i	$-0.0659456\pi$
$439$	6.51975	+	11.2925i	0.311171	+	0.538963i	−0.667446	+	0.744659i	$0.732612\pi$
$440$	−9.28584	+	0.955613i	−0.442685	+	0.0455571i
$441$	−6.92576	−	36.7707i	−0.329798	−	1.75099i
$442$	4.61989	−	1.50109i	0.219746	−	0.0713997i
$443$	1.99984	−	19.0272i	0.0950153	−	0.904010i	−0.838362	−	0.545114i	$-0.816486\pi$
$443$	1.99984	−	19.0272i	0.0950153	−	0.904010i	0.933377	−	0.358896i	$-0.116847\pi$
$444$	34.0133	−	3.57495i	1.61420	−	0.169659i
$445$	−19.6887	−	21.8665i	−0.933335	−	1.03657i
$446$	2.06477	−	0.438881i	0.0977699	−	0.0207816i
$447$	28.6799	−	20.8372i	1.35651	−	0.985564i
$448$	1.93280	−	1.88834i	0.0913162	−	0.0892156i
$449$	8.51490	+	26.2062i	0.401843	+	1.23674i	0.923503	+	0.383591i	$0.125313\pi$
$449$	8.51490	+	26.2062i	0.401843	+	1.23674i	−0.521660	+	0.853153i	$0.674687\pi$
$450$	7.91517	−	4.56982i	0.373125	−	0.215424i
$451$	−9.10161	−	0.976590i	−0.428578	−	0.0459858i
$452$	5.62447	−	9.74186i	0.264553	−	0.458219i
$453$	11.0053	−	12.2226i	0.517073	−	0.574268i
$454$	−17.7868	+	24.4814i	−0.834776	+	1.14897i
$455$	−20.8117	−	13.8622i	−0.975669	−	0.649870i
$456$	1.72159	−	5.29851i	0.0806208	−	0.248125i
$457$	2.17193	+	10.2181i	0.101598	+	0.477983i	0.999301	+	0.0373811i	$0.0119016\pi$
$457$	2.17193	+	10.2181i	0.101598	+	0.477983i	−0.897703	+	0.440602i	$0.854765\pi$
$458$	1.10630	+	10.5257i	0.0516940	+	0.491836i
$459$	−1.58780	−	3.56626i	−0.0741121	−	0.166459i
$460$	−1.48989	−	1.34150i	−0.0694664	−	0.0625479i
$461$	−37.8146			−1.76120			−0.880601	−	0.473858i	$-0.842861\pi$
$461$	−37.8146			−1.76120			−0.880601	+	0.473858i	$0.842861\pi$
$462$	35.7446	−	28.1373i	1.66299	−	1.30907i
$463$	10.3030			0.478821			0.239410	−	0.970918i	$-0.423046\pi$
$463$	10.3030			0.478821			0.239410	+	0.970918i	$0.423046\pi$
$464$	2.66195	+	2.39683i	0.123578	+	0.111270i
$465$	−8.49080	−	19.0706i	−0.393751	−	0.884380i
$466$	−2.40943	−	22.9242i	−0.111615	−	1.06194i
$467$	0.766746	+	3.60726i	0.0354808	+	0.166924i	0.992321	−	0.123691i	$-0.0394733\pi$
$467$	0.766746	+	3.60726i	0.0354808	+	0.166924i	−0.956840	+	0.290615i	$0.906140\pi$
$468$	−9.47036	+	29.1468i	−0.437768	+	1.34731i
$469$	4.42738	+	0.283719i	0.204438	+	0.0131009i
$470$	7.51750	−	10.3469i	0.346756	−	0.477269i
$471$	14.3462	−	15.9330i	0.661037	−	0.734156i
$472$	3.99192	−	6.91420i	0.183743	−	0.318252i
$473$	13.8291	+	24.0732i	0.635862	+	1.10689i
$474$	34.2975	−	19.8016i	1.57533	−	0.909520i
$475$	−0.405858	−	1.24910i	−0.0186221	−	0.0573128i
$476$	−1.79127	−	0.502379i	−0.0821027	−	0.0230265i
$477$	−27.6713	+	20.1044i	−1.26698	+	0.920518i
$478$	−8.05715	+	1.71260i	−0.368525	+	0.0783325i
$479$	14.2597	+	15.8370i	0.651543	+	0.723611i	0.974894	−	0.222667i	$-0.0714764\pi$
$479$	14.2597	+	15.8370i	0.651543	+	0.723611i	−0.323352	+	0.946279i	$0.604810\pi$
$480$	−35.1842	+	3.69801i	−1.60593	+	0.168790i
$481$	4.76393	−	45.3258i	0.217217	−	2.06668i
$482$	13.1596	−	4.27583i	0.599405	−	0.194759i
$483$	−6.15272	−	1.04802i	−0.279958	−	0.0476865i
$484$	12.2398	+	5.51329i	0.556355	+	0.250604i
$485$	−10.3825	−	17.9829i	−0.471443	−	0.816563i
$486$	−17.7451	−	3.77184i	−0.804936	−	0.171094i
$487$	−29.2244	+	13.0115i	−1.32428	+	0.589609i	−0.942365	−	0.334587i	$-0.891403\pi$
$487$	−29.2244	+	13.0115i	−1.32428	+	0.589609i	−0.381918	+	0.924196i	$0.624736\pi$
$488$	−7.71481	+	17.3277i	−0.349233	+	0.784390i
$489$	30.0723	+	9.77108i	1.35992	+	0.441864i
$490$	9.73883	+	23.3195i	0.439955	+	1.05347i
$491$	18.9744	+	26.1160i	0.856303	+	1.17860i	0.982438	+	0.186587i	$0.0597428\pi$
$491$	18.9744	+	26.1160i	0.856303	+	1.17860i	−0.126135	+	0.992013i	$0.540257\pi$
$492$	−9.67698	−	1.01709i	−0.436272	−	0.0458540i
$493$	0.0866628	−	0.407716i	0.00390309	−	0.0183626i
$494$	10.0644	+	5.81070i	0.452820	+	0.261436i
$495$	−35.6654	−	0.0773923i	−1.60304	−	0.00347853i
$496$		−	17.7855i		−	0.798594i
$497$	−17.8049	+	2.60804i	−0.798660	+	0.116987i
$498$	5.01212	+	3.64152i	0.224598	+	0.163180i
$499$	37.2170	+	16.5701i	1.66606	+	0.741778i	0.999992	−	0.00411242i	$-0.00130903\pi$
$499$	37.2170	+	16.5701i	1.66606	+	0.741778i	0.666069	+	0.745890i	$0.267976\pi$
$500$	−10.8610	+	9.77925i	−0.485717	+	0.437341i
$501$	10.3475	−	9.31695i	0.462293	−	0.416251i
$502$	30.4659	+	13.5643i	1.35976	+	0.605404i
$503$	11.2045	+	8.14051i	0.499582	+	0.362967i	0.808857	−	0.588005i	$-0.200086\pi$
$503$	11.2045	+	8.14051i	0.499582	+	0.362967i	−0.309275	+	0.950973i	$0.600086\pi$
$504$	−15.5205	+	12.2720i	−0.691336	+	0.546638i
$505$			10.7917i			0.480226i
$506$	−1.49186	−	4.62560i	−0.0663213	−	0.205633i
$507$	22.6946	+	13.1027i	1.00790	+	0.581912i
$508$	−2.53028	+	11.9040i	−0.112263	+	0.528157i
$509$	−6.15867	−	0.647302i	−0.272978	−	0.0286912i	−0.0329497	−	0.999457i	$-0.510490\pi$
$509$	−6.15867	−	0.647302i	−0.272978	−	0.0286912i	−0.240028	+	0.970766i	$0.577157\pi$
$510$	3.53207	+	4.86147i	0.156403	+	0.215270i
$511$	13.9140	−	8.80743i	0.615521	−	0.389618i
$512$	−15.4898	−	5.03293i	−0.684557	−	0.222426i
$513$	3.79865	−	8.53190i	0.167714	−	0.376692i
$514$	−31.6210	+	14.0786i	−1.39474	+	0.620979i
$515$	18.7523	+	3.98592i	0.826324	+	0.175641i
$516$	14.7554	+	25.5571i	0.649571	+	1.12509i
$517$	10.7441	−	4.75565i	0.472523	−	0.209153i
$518$	−29.4007	+	35.4553i	−1.29179	+	1.55782i
$519$	46.7605	−	15.1934i	2.05256	−	0.666916i
$520$	−1.38217	+	13.1505i	−0.0606121	+	0.576686i
$521$	29.0973	−	3.05825i	1.27478	−	0.133984i	0.557149	−	0.830413i	$-0.311895\pi$
$521$	29.0973	−	3.05825i	1.27478	−	0.133984i	0.717626	+	0.696428i	$0.245229\pi$
$522$	4.64339	+	5.15700i	0.203235	+	0.225716i
$523$	−19.1831	+	4.07750i	−0.838819	+	0.178297i	−0.607239	−	0.794519i	$-0.707723\pi$
$523$	−19.1831	+	4.07750i	−0.838819	+	0.178297i	−0.231580	+	0.972816i	$0.574390\pi$
$524$	−13.5773	+	9.86446i	−0.593126	+	0.430931i
$525$	−1.96653	+	7.01182i	−0.0858264	+	0.306021i
$526$	7.28228	+	22.4126i	0.317522	+	0.977234i
$527$	−1.79236	+	1.03482i	−0.0780763	+	0.0450774i
$528$	−43.2970	−	19.3898i	−1.88426	−	0.843831i
$529$	11.1666	−	19.3411i	0.485504	−	0.840917i
$530$	15.4575	−	17.1673i	0.671433	−	0.745702i
$531$	17.9295	−	24.6779i	0.778076	−	1.07093i
$532$	−1.97433	−	3.98891i	−0.0855982	−	0.172941i
$533$	−4.00686	+	12.3318i	−0.173556	+	0.534151i
$534$	−15.7646	−	74.1667i	−0.682202	−	3.20951i
$535$	−0.304890	−	2.90083i	−0.0131815	−	0.125414i
$536$	−0.954193	−	2.14315i	−0.0412149	−	0.0925701i
$537$	−42.7890	−	38.5273i	−1.84648	−	1.66258i
$538$	−42.6383			−1.83827
$539$	−3.01333	+	23.0200i	−0.129793	+	0.991541i
$540$	−16.6341			−0.715816
$541$	−22.4251	−	20.1916i	−0.964129	−	0.868106i	0.0271839	−	0.999630i	$-0.491346\pi$
$541$	−22.4251	−	20.1916i	−0.964129	−	0.868106i	−0.991313	+	0.131525i	$0.958013\pi$
$542$	10.1401	+	22.7751i	0.435555	+	0.978273i
$543$	−5.43117	−	51.6741i	−0.233074	−	2.21755i
$544$	0.729241	+	3.43081i	0.0312660	+	0.147095i
$545$	4.66615	−	14.3609i	0.199876	−	0.615155i
$546$	−28.5840	−	57.7507i	−1.22328	−	2.47150i
$547$	−11.1154	+	15.2991i	−0.475261	+	0.654141i	−0.977586	−	0.210538i	$-0.932478\pi$
$547$	−11.1154	+	15.2991i	−0.475261	+	0.654141i	0.502324	+	0.864679i	$0.332478\pi$
$548$	13.8178	−	15.3463i	0.590269	−	0.655560i
$549$	−36.2344	+	62.7598i	−1.54645	+	2.67852i
$550$	−5.54952	+	1.16701i	−0.236632	+	0.0497613i
$551$	0.863609	−	0.498605i	0.0367910	−	0.0212413i
$552$	1.01987	+	3.13885i	0.0434087	+	0.133598i
$553$	−5.45800	+	19.4609i	−0.232098	+	0.827562i
$554$	−0.290284	+	0.210903i	−0.0123330	+	0.00896043i
$555$	55.1468	−	11.7218i	2.34085	−	0.497564i
$556$	0.207971	+	0.230975i	0.00881993	+	0.00979552i
$557$	33.7436	−	3.54659i	1.42976	−	0.150274i	0.642213	−	0.766526i	$-0.278016\pi$
$557$	33.7436	−	3.54659i	1.42976	−	0.150274i	0.787549	+	0.616252i	$0.211350\pi$
$558$	3.60163	−	34.2672i	0.152469	−	1.45065i
$559$	37.4011	−	12.1523i	1.58190	−	0.513989i
$560$	16.8227	−	20.2870i	0.710889	−	0.857284i
$561$	0.565131	+	5.49146i	0.0238598	+	0.231850i
$562$	−0.948090	−	1.64214i	−0.0399928	−	0.0692695i
$563$	34.2474	+	7.27952i	1.44336	+	0.306795i	0.862023	−	0.506870i	$-0.169198\pi$
$563$	34.2474	+	7.27952i	1.44336	+	0.306795i	0.581334	+	0.813665i	$0.302531\pi$
$564$	11.4096	−	5.07989i	0.480432	−	0.213902i
$565$	7.54233	−	16.9404i	0.317308	−	0.712686i
$566$	26.7057	+	8.67720i	1.12252	+	0.364730i
$567$	−7.90601	+	5.00442i	−0.332021	+	0.210166i
$568$	5.59312	+	7.69828i	0.234682	+	0.323012i
$569$	−29.0841	−	3.05686i	−1.21927	−	0.128150i	−0.527048	−	0.849836i	$-0.676701\pi$
$569$	−29.0841	−	3.05686i	−1.21927	−	0.128150i	−0.692221	+	0.721685i	$0.743368\pi$
$570$	−2.98898	+	14.0620i	−0.125194	+	0.588993i
$571$	−13.0386	−	7.52785i	−0.545649	−	0.315031i	0.201716	−	0.979444i	$-0.435348\pi$
$571$	−13.0386	−	7.52785i	−0.545649	−	0.315031i	−0.747365	+	0.664413i	$0.768681\pi$
$572$	11.2104	−	15.3595i	0.468728	−	0.642214i
$573$			70.2995i			2.93680i
$574$	10.2791	−	8.12769i	0.429043	−	0.339243i
$575$	0.629457	+	0.457327i	0.0262502	+	0.0190719i
$576$	−4.98726	−	2.22047i	−0.207803	−	0.0925197i
$577$	−16.7491	+	15.0810i	−0.697275	+	0.627829i	−0.939563	−	0.342375i	$-0.888769\pi$
$577$	−16.7491	+	15.0810i	−0.697275	+	0.627829i	0.242289	+	0.970204i	$0.422102\pi$
$578$	−22.2286	+	20.0147i	−0.924586	+	0.832501i
$579$	−49.0780	−	21.8509i	−2.03961	−	0.908093i
$580$	−1.43690	−	1.04397i	−0.0596641	−	0.0433485i
$581$	−3.12844	+	0.458249i	−0.129789	+	0.0190114i
$582$		−	53.5091i		−	2.21803i
$583$	20.1979	−	6.51427i	0.836511	−	0.269794i
$584$	−7.54116	−	4.35389i	−0.312056	−	0.180165i
$585$	−10.5038	+	49.4163i	−0.434277	+	2.04311i
$586$	4.77412	+	0.501780i	0.197217	+	0.0207283i
$587$	3.78610	+	5.21112i	0.156269	+	0.215086i	0.879972	−	0.475026i	$-0.157561\pi$
$587$	3.78610	+	5.21112i	0.156269	+	0.215086i	−0.723703	+	0.690112i	$0.757561\pi$
$588$	−3.14997	+	24.4765i	−0.129903	+	1.00939i
$589$	−4.70905	−	1.53006i	−0.194033	−	0.0630451i
$590$	−8.37955	+	18.8208i	−0.344981	+	0.774839i
$591$	−10.4896	+	4.67026i	−0.431483	+	0.192109i
$592$	46.9843	+	9.98681i	1.93104	+	0.410455i
$593$	20.6673	+	35.7968i	0.848704	+	1.47000i	0.882365	+	0.470565i	$0.155950\pi$
$593$	20.6673	+	35.7968i	0.848704	+	1.47000i	−0.0336616	+	0.999433i	$0.510717\pi$
$594$	−34.8787	−	20.2383i	−1.43109	−	0.830386i
$595$	−3.02325	−	0.514962i	−0.123941	−	0.0211114i
$596$	−14.2430	+	4.62782i	−0.583415	+	0.189563i
$597$	4.70440	−	44.7593i	0.192538	−	1.83188i
$598$	−6.84682	+	0.719630i	−0.279987	+	0.0294279i
$599$	−25.5028	−	28.3237i	−1.04201	−	1.15727i	−0.987315	−	0.158772i	$-0.949247\pi$
$599$	−25.5028	−	28.3237i	−1.04201	−	1.15727i	−0.0546996	−	0.998503i	$-0.517420\pi$
$600$	3.76671	−	0.800640i	0.153775	−	0.0326860i
$601$	−36.9913	+	26.8757i	−1.50891	+	1.09628i	−0.542245	+	0.840220i	$0.682426\pi$
$601$	−36.9913	+	26.8757i	−1.50891	+	1.09628i	−0.966660	+	0.256064i	$0.917574\pi$
$602$	−38.2670	−	10.7323i	−1.55965	−	0.437418i
$603$	−2.76978	−	8.52449i	−0.112794	−	0.347144i
$604$	−6.01722	+	3.47404i	−0.244837	+	0.141357i
$605$	21.0165	+	6.92964i	0.854440	+	0.281730i
$606$	−13.9046	+	24.0835i	−0.564836	+	0.978325i
$607$	−28.2704	+	31.3975i	−1.14746	+	1.27438i	−0.191303	+	0.981531i	$0.561271\pi$
$607$	−28.2704	+	31.3975i	−1.14746	+	1.27438i	−0.956158	+	0.292853i	$0.905395\pi$
$608$	−4.93224	+	6.78865i	−0.200029	+	0.275316i
$609$	−5.51794	−	0.353604i	−0.223598	−	0.0143288i
$610$	15.1248	−	46.5494i	0.612386	−	1.88473i
$611$	−3.46032	−	16.2795i	−0.139990	−	0.658599i
$612$	0.392882	+	3.73803i	0.0158813	+	0.151101i
$613$	−14.6818	−	32.9758i	−0.592991	−	1.33188i	−0.921867	−	0.387507i	$-0.873336\pi$
$613$	−14.6818	−	32.9758i	−0.592991	−	1.33188i	0.328876	−	0.944373i	$-0.393330\pi$
$614$	−2.59897	−	2.34013i	−0.104886	−	0.0944398i
$615$	−16.0401			−0.646798
$616$	11.5209	−	4.24092i	0.464190	−	0.170872i
$617$	−13.7471			−0.553439			−0.276720	−	0.960951i	$-0.589247\pi$
$617$	−13.7471			−0.553439			−0.276720	+	0.960951i	$0.589247\pi$
$618$	36.7131	+	33.0566i	1.47682	+	1.32973i
$619$	−9.69363	−	21.7722i	−0.389620	−	0.875101i	−0.996754	−	0.0805016i	$-0.974348\pi$
$619$	−9.69363	−	21.7722i	−0.389620	−	0.875101i	0.607135	−	0.794599i	$-0.292319\pi$
$620$	0.921816	+	8.77049i	0.0370210	+	0.352232i
$621$	1.15030	+	5.41173i	0.0461599	+	0.217165i
$622$	1.39041	−	4.27925i	0.0557505	−	0.171582i
$623$	32.2067	+	21.4521i	1.29033	+	0.859461i
$624$	−39.4989	+	54.3656i	−1.58122	+	2.17637i
$625$	−12.9331	+	14.3636i	−0.517323	+	0.574545i
$626$	11.1957	−	19.3915i	0.447469	−	0.775038i
$627$	−8.85858	+	9.79561i	−0.353777	+	0.391199i
$628$	−7.84387	+	4.52866i	−0.313004	+	0.180713i
$629$	−1.72726	−	5.31595i	−0.0688703	−	0.211961i
$630$	36.5203	−	35.6802i	1.45500	−	1.42153i
$631$	−9.02470	+	6.55683i	−0.359267	+	0.261023i	−0.752747	−	0.658310i	$-0.771271\pi$
$631$	−9.02470	+	6.55683i	−0.359267	+	0.261023i	0.393479	+	0.919334i	$0.371271\pi$
$632$	10.4543	−	2.22213i	0.415850	−	0.0883917i
$633$	25.0425	+	27.8125i	0.995350	+	1.10545i
$634$	−14.2698	+	1.49982i	−0.566726	+	0.0595653i
$635$	−2.09704	+	19.9520i	−0.0832183	+	0.791770i
$636$	21.4547	−	6.97106i	0.850734	−	0.276420i
$637$	31.0316	+	10.8874i	1.22952	+	0.431373i
$638$	−1.74276	−	3.93726i	−0.0689964	−	0.155878i
$639$	18.1779	+	31.4851i	0.719109	+	1.24553i
$640$	−20.3512	−	4.32578i	−0.804453	−	0.170992i
$641$	−13.4121	+	5.97145i	−0.529746	+	0.235858i	−0.654138	−	0.756375i	$-0.726969\pi$
$641$	−13.4121	+	5.97145i	−0.529746	+	0.235858i	0.124392	+	0.992233i	$0.460302\pi$
$642$	3.05717	−	6.86652i	0.120657	−	0.271000i
$643$	−41.6038	−	13.5179i	−1.64069	−	0.533094i	−0.664000	−	0.747733i	$-0.731142\pi$
$643$	−41.6038	−	13.5179i	−1.64069	−	0.533094i	−0.976693	+	0.214639i	$0.931142\pi$
$644$	2.33518	+	1.22427i	0.0920191	+	0.0482428i
$645$	28.5944	+	39.3568i	1.12590	+	1.54967i
$646$	1.41748	+	0.148983i	0.0557699	+	0.00586166i
$647$	7.60183	−	35.7638i	0.298859	−	1.40602i	−0.530681	−	0.847572i	$-0.678064\pi$
$647$	7.60183	−	35.7638i	0.298859	−	1.40602i	0.829540	−	0.558448i	$-0.188603\pi$
$648$	4.28492	+	2.47390i	0.168328	+	0.0971840i
$649$	−15.3360	+	11.0915i	−0.601992	+	0.435380i
$650$			8.03284i			0.315074i
$651$	17.0280	+	21.5354i	0.667380	+	0.844039i
$652$	−10.8067	−	7.85151i	−0.423222	−	0.307489i
$653$	−7.03352	−	3.13153i	−0.275243	−	0.122546i	0.264473	−	0.964393i	$-0.414802\pi$
$653$	−7.03352	−	3.13153i	−0.275243	−	0.122546i	−0.539716	+	0.841847i	$0.681469\pi$
$654$	28.9167	−	26.0367i	1.13073	−	1.01811i
$655$	−20.5593	+	18.5117i	−0.803320	+	0.723313i
$656$	−12.4844	−	5.55842i	−0.487435	−	0.217020i
$657$	−26.9156	−	19.5553i	−1.05008	−	0.762927i
$658$	−6.21005	+	15.6316i	−0.242093	+	0.609385i
$659$		−	49.2350i		−	1.91793i	−0.283533	−	0.958963i	$-0.591506\pi$
$659$		−	49.2350i		−	1.91793i	0.283533	−	0.958963i	$-0.408494\pi$
$660$	22.3558	+	7.31751i	0.870199	+	0.284834i
$661$	9.22894	+	5.32833i	0.358964	+	0.207248i	0.668626	−	0.743599i	$-0.266883\pi$
$661$	9.22894	+	5.32833i	0.358964	+	0.207248i	−0.309662	+	0.950847i	$0.600216\pi$
$662$	5.25915	−	24.7423i	0.204403	−	0.961638i
$663$	7.77692	+	0.817387i	0.302031	+	0.0317447i
$664$	0.982748	+	1.35264i	0.0381380	+	0.0524925i
$665$	−3.92414	−	6.19938i	−0.152172	−	0.240402i
$666$	88.5017	+	28.7559i	3.42937	+	1.11427i
$667$	−0.240279	+	0.539676i	−0.00930365	+	0.0208963i
$668$	−5.37363	+	2.39249i	−0.207912	+	0.0925683i
$669$	3.32384	+	0.706505i	0.128507	+	0.0273151i
$670$	3.02684	+	5.24264i	0.116937	+	0.202541i
$671$	33.4806	−	30.0148i	1.29250	−	1.15871i
$672$	43.6278	−	16.1673i	1.68298	−	0.623667i
$673$	−15.7291	+	5.11069i	−0.606312	+	0.197003i	−0.596053	−	0.802945i	$-0.703265\pi$
$673$	−15.7291	+	5.11069i	−0.606312	+	0.197003i	−0.0102583	+	0.999947i	$0.503265\pi$
$674$	3.25030	−	30.9245i	0.125197	−	1.19117i
$675$	6.42008	−	0.674778i	0.247109	−	0.0259722i
$676$	−7.40759	−	8.22696i	−0.284907	−	0.316421i
$677$	12.7560	−	2.71137i	0.490253	−	0.104206i	0.0438492	−	0.999038i	$-0.486038\pi$
$677$	12.7560	−	2.71137i	0.490253	−	0.104206i	0.446404	+	0.894832i	$0.352705\pi$
$678$	38.6588	−	28.0872i	1.48468	−	1.07868i
$679$	19.0842	+	19.5336i	0.732385	+	0.749629i
$680$	0.501132	+	1.54233i	0.0192175	+	0.0591455i
$681$	−42.1869	+	24.3566i	−1.61661	+	0.933348i
$682$	−8.73796	+	19.5117i	−0.334594	+	0.747143i
$683$	−7.73841	+	13.4033i	−0.296102	+	0.512864i	−0.975241	−	0.221146i	$-0.929020\pi$
$683$	−7.73841	+	13.4033i	−0.296102	+	0.512864i	0.679139	+	0.734010i	$0.262354\pi$
$684$	−6.01689	+	6.68243i	−0.230061	+	0.255509i
$685$	20.0092	−	27.5403i	0.764511	−	1.05226i
$686$	−20.0016	−	26.5430i	−0.763664	−	1.01341i
$687$	−5.26488	+	16.2036i	−0.200868	+	0.618207i
$688$	8.61734	+	40.5414i	0.328533	+	1.54563i
$689$	−3.14230	−	29.8969i	−0.119712	−	1.13898i
$690$	−3.46396	−	7.78018i	−0.131871	−	0.296187i
$691$	32.7311	+	29.4712i	1.24515	+	1.12114i	0.987949	+	0.154778i	$0.0494662\pi$
$691$	32.7311	+	29.4712i	1.24515	+	1.12114i	0.257199	+	0.966359i	$0.417201\pi$
$692$	−20.7705			−0.789576
$693$	45.4701	−	11.5133i	1.72726	−	0.437354i
$694$	19.3791			0.735622
$695$	0.380756	+	0.342834i	0.0144429	+	0.0130044i
$696$	1.18923	+	2.67106i	0.0450777	+	0.101246i
$697$	0.166226	+	1.58154i	0.00629627	+	0.0599050i
$698$	−4.48922	−	21.1201i	−0.169919	−	0.799408i
$699$	11.4665	−	35.2902i	0.433703	−	1.33480i
$700$	1.70545	−	2.56044i	0.0644599	−	0.0967755i
$701$	14.2779	−	19.6518i	0.539269	−	0.742240i	−0.449239	−	0.893412i	$-0.648305\pi$
$701$	14.2779	−	19.6518i	0.539269	−	0.742240i	0.988507	+	0.151172i	$0.0483048\pi$
$702$	−38.2211	+	42.4489i	−1.44256	+	1.60213i
$703$	6.68618	−	11.5808i	0.252174	−	0.436778i
$704$	2.51233	+	2.27201i	0.0946872	+	0.0856295i
$705$	17.8301	−	10.2942i	0.671519	−	0.387702i
$706$	0.0258028	+	0.0794127i	0.000971100	+	0.00298874i
$707$	−3.51357	−	13.7508i	−0.132141	−	0.517153i
$708$	−16.2761	+	11.8253i	−0.611695	+	0.444423i
$709$	−22.4007	+	4.76143i	−0.841278	+	0.178819i	−0.608344	−	0.793674i	$-0.708166\pi$
$709$	−22.4007	+	4.76143i	−0.841278	+	0.178819i	−0.232934	+	0.972493i	$0.574833\pi$
$710$	−16.4302	−	18.2476i	−0.616614	−	0.684819i
$711$	40.6111	−	4.26839i	1.52303	−	0.160077i
$712$	2.13894	−	20.3507i	0.0801602	−	0.762674i
$713$	2.78965	−	0.906412i	0.104473	−	0.0339454i
$714$	−6.08336	−	5.04453i	−0.227664	−	0.188787i
$715$	15.7321	−	27.1127i	0.588346	−	1.01396i
$716$	12.1619	+	21.0651i	0.454513	+	0.787239i
$717$	−12.9703	−	2.75692i	−0.484384	−	0.102959i
$718$	35.9121	−	15.9891i	1.34023	−	0.596708i
$719$	15.8555	−	35.6121i	0.591311	−	1.32811i	−0.331719	−	0.943378i	$-0.607629\pi$
$719$	15.8555	−	35.6121i	0.591311	−	1.32811i	0.923030	−	0.384728i	$-0.125705\pi$
$720$	−50.6394	−	16.4537i	−1.88722	−	0.613195i
$721$	−25.1919	+	1.02650i	−0.938196	+	0.0382287i
$722$	−18.0370	−	24.8259i	−0.671269	−	0.923923i
$723$	22.1524	+	2.32831i	0.823855	+	0.0865907i
$724$	−4.56365	+	21.4703i	−0.169607	+	0.797936i
$725$	0.596937	+	0.344641i	0.0221697	+	0.0127997i
$726$	37.9731	+	42.5433i	1.40932	+	1.57893i
$727$			46.1620i			1.71205i	0.516933	+	0.856026i	$0.327074\pi$
$727$			46.1620i			1.71205i	−0.516933	+	0.856026i	$0.672926\pi$
$728$	−2.52036	−	17.2063i	−0.0934108	−	0.637709i
$729$	−32.2099	−	23.4019i	−1.19296	−	0.866735i
$730$	20.5274	+	9.13939i	0.759753	+	0.338264i
$731$	3.58422	−	3.22725i	0.132567	−	0.119364i
$732$	35.5196	−	31.9820i	1.31284	−	1.18209i
$733$	−19.2319	−	8.56258i	−0.710345	−	0.316266i	0.0195653	−	0.999809i	$-0.493772\pi$
$733$	−19.2319	−	8.56258i	−0.710345	−	0.316266i	−0.729911	+	0.683542i	$0.760438\pi$
$734$	35.1011	+	25.5024i	1.29560	+	0.941312i
$735$	−0.946600	+	40.6705i	−0.0349159	+	1.50015i
$736$		−	4.97098i		−	0.183233i
$737$	−0.0120680	+	5.56139i	−0.000444530	+	0.204856i
$738$	−22.9280	−	13.2375i	−0.843991	−	0.487279i
$739$	5.00674	−	23.5549i	0.184176	−	0.866480i	−0.784882	−	0.619645i	$-0.787276\pi$
$739$	5.00674	−	23.5549i	0.184176	−	0.866480i	0.969058	−	0.246834i	$-0.0793903\pi$
$740$	−23.6867	−	2.48958i	−0.870741	−	0.0915186i
$741$	10.9963	+	15.1351i	0.403958	+	0.556000i
$742$	−14.1067	+	26.9073i	−0.517873	+	0.987798i
$743$	−21.1622	−	6.87601i	−0.776365	−	0.252256i	−0.106078	−	0.994358i	$-0.533829\pi$
$743$	−21.1622	−	6.87601i	−0.776365	−	0.252256i	−0.670287	+	0.742102i	$0.733829\pi$
$744$	5.90482	−	13.2624i	0.216481	−	0.486224i
$745$	−22.5531	+	10.0413i	−0.826281	+	0.367884i
$746$	−65.8638	−	13.9998i	−2.41145	−	0.512569i
$747$	3.19398	+	5.53214i	0.116862	+	0.202410i
$748$	0.489823	−	2.28010i	0.0179097	−	0.0833686i
$749$	1.33294	+	3.59698i	0.0487047	+	0.131431i
$750$	−59.0446	+	19.1848i	−2.15600	+	0.700528i
$751$	−3.56235	+	33.8935i	−0.129992	+	1.23679i	0.713889	+	0.700259i	$0.246932\pi$
$751$	−3.56235	+	33.8935i	−0.129992	+	1.23679i	−0.843881	+	0.536531i	$0.819734\pi$
$752$	17.4449	−	1.83353i	0.636150	−	0.0668621i
$753$	35.9222	+	39.8956i	1.30908	+	1.45388i
$754$	−5.96579	+	1.26807i	−0.217261	+	0.0461803i
$755$	−9.26625	+	6.73232i	−0.337233	+	0.245014i
$756$	21.1951	−	5.41571i	0.770860	−	0.196968i
$757$	−3.02432	−	9.30790i	−0.109921	−	0.338301i	0.880933	−	0.473241i	$-0.156916\pi$
$757$	−3.02432	−	9.30790i	−0.109921	−	0.338301i	−0.990854	+	0.134940i	$0.956916\pi$
$758$	20.7733	−	11.9935i	0.754520	−	0.435622i
$759$	0.834706	−	7.77928i	0.0302979	−	0.282370i
$760$	−1.93987	+	3.35996i	−0.0703666	+	0.121878i
$761$	1.96626	−	2.18375i	0.0712768	−	0.0791609i	−0.706452	−	0.707761i	$-0.749705\pi$
$761$	1.96626	−	2.18375i	0.0712768	−	0.0791609i	0.777728	+	0.628600i	$0.216372\pi$
$762$	−30.3870	+	41.8241i	−1.10081	+	1.51513i
$763$	−1.26999	+	19.8179i	−0.0459766	+	0.717457i
$764$	9.17718	−	28.2445i	0.332019	−	1.02185i
$765$	1.28821	+	6.06057i	0.0465755	+	0.219120i
$766$	0.0624793	+	0.594451i	0.00225747	+	0.0214784i
$767$	10.9044	+	24.4918i	0.393737	+	0.884347i
$768$	−44.2286	−	39.8236i	−1.59596	−	1.43701i
$769$	33.5697			1.21055			0.605277	−	0.796015i	$-0.293062\pi$
$769$	33.5697			1.21055			0.605277	+	0.796015i	$0.293062\pi$
$770$	−28.4224	+	13.9911i	−1.02427	+	0.504204i
$771$	−55.7203			−2.00672
$772$	16.8657	+	15.1859i	0.607010	+	0.546554i
$773$	14.8196	+	33.2854i	0.533024	+	1.19719i	0.956619	+	0.291341i	$0.0941013\pi$
$773$	14.8196	+	33.2854i	0.533024	+	1.19719i	−0.423595	+	0.905852i	$0.639232\pi$
$774$	8.39317	+	79.8557i	0.301686	+	2.87035i
$775$	−0.711569	−	3.34767i	−0.0255603	−	0.120252i
$776$	4.46242	−	13.7339i	0.160191	−	0.493018i
$777$	−66.4518	+	32.8906i	−2.38394	+	1.17995i
$778$	5.91794	−	8.14534i	0.212168	−	0.292025i
$779$	−2.54571	+	2.82730i	−0.0912096	+	0.101298i
$780$	16.6602	−	28.8562i	0.596529	−	1.03322i
$781$	−4.64214	−	22.0750i	−0.166109	−	0.789906i
$782$	−0.731222	+	0.422171i	−0.0261484	+	0.0150968i
$783$	1.51462	+	4.66152i	0.0541280	+	0.166589i
$784$	−14.8304	+	31.3269i	−0.529659	+	1.11882i
$785$	−12.0792	+	8.77606i	−0.431125	+	0.313231i
$786$	−69.7330	+	14.8222i	−2.48729	+	0.528691i
$787$	−1.97010	−	2.18802i	−0.0702266	−	0.0779946i	0.707008	−	0.707206i	$-0.250045\pi$
$787$	−1.97010	−	2.18802i	−0.0702266	−	0.0779946i	−0.777234	+	0.629211i	$0.783378\pi$
$788$	4.82410	−	0.507033i	0.171851	−	0.0180623i
$789$	−3.96540	+	37.7283i	−0.141172	+	1.34316i
$790$	−26.2297	+	8.52255i	−0.933211	+	0.303219i
$791$	−4.09501	+	24.0411i	−0.145602	+	0.854802i
$792$	−16.5565	−	18.4683i	−0.588308	−	0.656241i
$793$	−31.8464	−	55.1596i	−1.13090	−	1.95878i
$794$	0.418744	+	0.0890067i	0.0148607	+	0.00315873i
$795$	33.9725	−	15.1255i	1.20488	−	0.536447i
$796$	−7.73316	+	17.3690i	−0.274095	+	0.615627i
$797$	14.6246	+	4.75183i	0.518031	+	0.168318i	0.556352	−	0.830947i	$-0.312201\pi$
$797$	14.6246	+	4.75183i	0.518031	+	0.168318i	−0.0383206	+	0.999265i	$0.512201\pi$
$798$	−0.769753	−	18.8910i	−0.0272490	−	0.668734i
$799$	−1.19977	−	1.65135i	−0.0424450	−	0.0584205i
$800$	−5.76834	−	0.606277i	−0.203942	−	0.0214351i
$801$	16.2548	−	76.4730i	0.574336	−	2.70204i
$802$	46.4350	+	26.8092i	1.63968	+	0.946667i
$803$	12.0973	+	16.7267i	0.426904	+	0.590272i
$804$			5.91161i			0.208486i
$805$	4.03935	+	1.60473i	0.142368	+	0.0565593i
$806$	24.4997	+	17.8001i	0.862967	+	0.626982i
$807$	−62.7044	−	27.9178i	−2.20730	−	0.982752i
$808$	−5.57728	+	5.02180i	−0.196208	+	0.176666i
$809$	3.76055	−	3.38602i	0.132214	−	0.119046i	−0.600371	−	0.799722i	$-0.704980\pi$
$809$	3.76055	−	3.38602i	0.132214	−	0.119046i	0.732585	+	0.680676i	$0.238314\pi$
$810$	−11.6638	−	5.19304i	−0.409823	−	0.182465i
$811$	−23.4051	−	17.0048i	−0.821865	−	0.597120i	0.0953814	−	0.995441i	$-0.469593\pi$
$811$	−23.4051	−	17.0048i	−0.821865	−	0.597120i	−0.917246	+	0.398321i	$0.869593\pi$
$812$	2.17080	+	0.862402i	0.0761801	+	0.0302644i
$813$			40.1326i			1.40751i
$814$	−46.6379	−	34.0393i	−1.63466	−	1.19308i
$815$	−19.0698	−	11.0100i	−0.667987	−	0.385662i
$816$	−1.71352	+	8.06147i	−0.0599852	+	0.282208i
$817$	11.4754	+	1.20612i	0.401474	+	0.0421966i
$818$	−3.00959	−	4.14234i	−0.105228	−	0.144834i
$819$	−2.70504	−	66.3861i	−0.0945217	−	2.31972i
$820$	6.44447	+	2.09394i	0.225051	+	0.0731234i
$821$	13.4292	−	30.1625i	0.468683	−	1.05268i	−0.512339	−	0.858783i	$-0.671221\pi$
$821$	13.4292	−	30.1625i	0.468683	−	1.05268i	0.981022	−	0.193896i	$-0.0621125\pi$
$822$	80.1380	−	35.6797i	2.79513	−	1.24447i
$823$	4.61509	+	0.980967i	0.160872	+	0.0341943i	0.287643	−	0.957738i	$-0.407128\pi$
$823$	4.61509	+	0.980967i	0.160872	+	0.0341943i	−0.126772	+	0.991932i	$0.540462\pi$
$824$	6.66618	+	11.5462i	0.232228	+	0.402230i
$825$	−8.92530	−	1.91738i	−0.310739	−	0.0667547i
$826$	4.54957	−	26.7097i	0.158300	−	0.929348i
$827$	30.7669	−	9.99677i	1.06987	−	0.347622i	0.279433	−	0.960165i	$-0.409854\pi$
$827$	30.7669	−	9.99677i	1.06987	−	0.347622i	0.790437	+	0.612544i	$0.209854\pi$
$828$	0.556816	−	5.29775i	0.0193507	−	0.184110i
$829$	−5.32384	+	0.559559i	−0.184905	+	0.0194343i	−0.196528	−	0.980498i	$-0.562967\pi$
$829$	−5.32384	+	0.559559i	−0.184905	+	0.0194343i	0.0116235	+	0.999932i	$0.496300\pi$
$830$	−2.88689	−	3.20622i	−0.100205	−	0.111289i
$831$	−0.564985	+	0.120091i	−0.0195991	+	0.00416592i
$832$	3.88177	−	2.82027i	0.134576	−	0.0977753i
$833$	4.01988	−	0.328142i	0.139281	−	0.0113694i
$834$	0.407994	+	1.25568i	0.0141277	+	0.0434805i
$835$	−8.39748	+	4.84829i	−0.290607	+	0.167782i
$836$	4.83790	−	2.77918i	0.167322	−	0.0961200i
$837$	12.1683	−	21.0762i	0.420599	−	0.728499i
$838$	−15.3608	+	17.0599i	−0.530631	+	0.589325i
$839$	−15.9054	+	21.8918i	−0.549114	+	0.755790i	−0.989892	−	0.141826i	$-0.954703\pi$
$839$	−15.9054	+	21.8918i	−0.549114	+	0.755790i	0.440778	+	0.897616i	$0.354703\pi$
$840$	19.2798	−	9.54262i	0.665215	−	0.329252i
$841$	8.79977	−	27.0829i	0.303440	−	0.933893i
$842$	5.95315	+	28.0074i	0.205159	+	0.965197i
$843$	−0.319067	−	3.03572i	−0.0109893	−	0.104556i
$844$	−6.43064	−	14.4435i	−0.221352	−	0.497165i
$845$	−13.5619	−	12.2112i	−0.466543	−	0.420078i
$846$	33.9822			1.16833
$847$	−29.0353	−	1.98723i	−0.997666	−	0.0682819i
$848$	31.6832			1.08801
$849$	33.5922	+	30.2466i	1.15288	+	1.03806i
$850$	0.400706	+	0.900001i	0.0137441	+	0.0308698i
$851$	0.828054	+	7.87841i	0.0283853	+	0.270068i
$852$	−4.98537	−	23.4543i	−0.170796	−	0.803532i
$853$	7.86547	−	24.2074i	0.269308	−	0.828846i	−0.721361	−	0.692559i	$-0.756483\pi$
$853$	7.86547	−	24.2074i	0.269308	−	0.828846i	0.990669	−	0.136287i	$-0.0435169\pi$
$854$	−4.11652	+	64.2377i	−0.140865	+	2.19817i
$855$	−8.71286	+	11.9922i	−0.297974	+	0.410125i
$856$	1.35730	−	1.50744i	0.0463917	−	0.0515232i
$857$	1.85885	−	3.21962i	0.0634971	−	0.109980i	−0.832529	−	0.553981i	$-0.813108\pi$
$857$	1.85885	−	3.21962i	0.0634971	−	0.109980i	0.896026	+	0.444001i	$0.146441\pi$
$858$	70.0421	−	40.2364i	2.39120	−	1.37365i
$859$	−3.89561	+	2.24913i	−0.132916	+	0.0767394i	−0.564984	−	0.825102i	$-0.691118\pi$
$859$	−3.89561	+	2.24913i	−0.132916	+	0.0767394i	0.432067	+	0.901841i	$0.357784\pi$
$860$	−6.35067	−	19.5453i	−0.216556	−	0.666491i
$861$	20.4383	−	5.22232i	0.696535	−	0.177976i
$862$	23.1269	−	16.8027i	0.787705	−	0.572301i
$863$	14.8065	−	3.14722i	0.504019	−	0.107132i	0.0511165	−	0.998693i	$-0.483722\pi$
$863$	14.8065	−	3.14722i	0.504019	−	0.107132i	0.452902	+	0.891560i	$0.350389\pi$
$864$	−27.5976	−	30.6502i	−0.938888	−	1.04274i
$865$	−34.0520	+	3.57901i	−1.15780	+	0.121690i
$866$	−2.51160	+	23.8963i	−0.0853478	+	0.812030i
$867$	−45.7944	+	14.8795i	−1.55526	+	0.505334i
$868$	−4.03007	−	10.8752i	−0.136790	−	0.369130i
$869$	−24.7717	−	5.32159i	−0.840321	−	0.180523i
$870$	−3.77241	−	6.53400i	−0.127897	−	0.221523i
$871$	7.70560	+	1.63788i	0.261094	+	0.0554973i
$872$	9.59322	−	4.27118i	0.324868	−	0.144640i
$873$	22.4409	−	50.4031i	0.759509	−	1.70588i
$874$	−1.92113	−	0.624214i	−0.0649833	−	0.0211144i
$875$	14.7120	−	28.0619i	0.497356	−	0.948664i
$876$	12.8976	+	17.7520i	0.435770	+	0.599786i
$877$	22.7318	+	2.38921i	0.767599	+	0.0806779i	0.480231	−	0.877142i	$-0.340553\pi$
$877$	22.7318	+	2.38921i	0.767599	+	0.0806779i	0.287368	+	0.957820i	$0.407220\pi$
$878$	4.86512	−	22.8886i	0.164190	−	0.772452i
$879$	6.69233	+	3.86382i	0.225727	+	0.130323i
$880$	26.6855	+	19.4768i	0.899569	+	0.656562i
$881$			29.6337i			0.998385i	0.866491	+	0.499193i	$0.166370\pi$
$881$			29.6337i			0.998385i	−0.866491	+	0.499193i	$0.833630\pi$
$882$	−34.9174	+	57.3540i	−1.17573	+	1.93121i
$883$	41.3114	+	30.0145i	1.39024	+	1.01007i	0.995839	+	0.0911305i	$0.0290480\pi$
$883$	41.3114	+	30.0145i	1.39024	+	1.01007i	0.394401	+	0.918938i	$0.370952\pi$
$884$	−3.01785	−	1.34363i	−0.101501	−	0.0451913i
$885$	−24.6461	+	22.1915i	−0.828471	+	0.745958i
$886$	−25.5146	+	22.9734i	−0.857178	+	0.771807i
$887$	24.0500	+	10.7077i	0.807519	+	0.359530i	0.768614	−	0.639713i	$-0.220947\pi$
$887$	24.0500	+	10.7077i	0.807519	+	0.359530i	0.0389043	+	0.999243i	$0.487613\pi$
$888$	31.7199	+	23.0458i	1.06445	+	0.773368i
$889$	−3.82391	−	26.1056i	−0.128250	−	0.875553i
$890$			52.8032i			1.76997i
$891$	−6.87373	−	9.50417i	−0.230278	−	0.318402i
$892$	−1.24320	−	0.717762i	−0.0416254	−	0.0240325i
$893$	1.01530	−	4.77660i	0.0339756	−	0.159843i
$894$	−63.2686	−	6.64980i	−2.11602	−	0.222402i
$895$	23.5685	+	32.4393i	0.787809	+	1.08433i
$896$	27.3399	−	1.11402i	0.913363	−	0.0372169i
$897$	−10.5402	−	3.42472i	−0.351927	−	0.114348i
$898$	20.1124	−	45.1732i	0.671160	−	1.50745i
$899$	2.37390	−	1.05693i	0.0791740	−	0.0352505i
$900$	−6.07962	−	1.29226i	−0.202654	−	0.0430754i
$901$	−1.84343	−	3.19291i	−0.0614135	−	0.106371i
$902$	10.9653	+	12.2314i	0.365104	+	0.407263i
$903$	−49.2488	−	40.8388i	−1.63890	−	1.35903i
$904$	12.2647	−	3.98504i	0.407918	−	0.132540i
$905$	−3.78224	+	35.9856i	−0.125726	+	1.19620i
$906$	−29.3534	+	3.08517i	−0.975202	+	0.102498i
$907$	−7.23884	−	8.03954i	−0.240362	−	0.266949i	0.610879	−	0.791724i	$-0.290816\pi$
$907$	−7.23884	−	8.03954i	−0.240362	−	0.266949i	−0.851241	+	0.524775i	$0.824149\pi$
$908$	20.1292	−	4.27859i	0.668010	−	0.141990i
$909$	−23.1977	+	16.8541i	−0.769420	+	0.559016i
$910$	11.1091	+	43.4771i	0.368264	+	1.44125i
$911$	11.0015	+	33.8591i	0.364496	+	1.12180i	0.950296	+	0.311347i	$0.100780\pi$
$911$	11.0015	+	33.8591i	0.364496	+	1.12180i	−0.585801	+	0.810455i	$0.699220\pi$
$912$	−17.0755	+	9.85855i	−0.565427	+	0.326449i
$913$	−0.815654	−	3.87872i	−0.0269942	−	0.128367i
$914$	9.37324	−	16.2349i	0.310039	−	0.537004i
$915$	52.7214	−	58.5530i	1.74291	−	1.93570i
$916$	4.23058	−	5.82289i	0.139782	−	0.192394i
$917$	20.1697	−	30.2814i	0.666062	−	0.999979i
$918$	−2.16480	+	6.66258i	−0.0714492	+	0.219898i
$919$	6.39801	+	30.1003i	0.211051	+	0.992917i	0.948320	+	0.317317i	$0.102782\pi$
$919$	6.39801	+	30.1003i	0.211051	+	0.992917i	−0.737269	+	0.675600i	$0.763885\pi$
$920$	−0.240245	−	2.28578i	−0.00792064	−	0.0753598i
$921$	−2.28986	−	5.14312i	−0.0754536	−	0.169471i
$922$	50.4298	+	45.4072i	1.66082	+	1.49541i
$923$	−31.9532			−1.05175
$924$	−30.8682	−	2.04539i	−1.01549	−	0.0672883i
$925$	9.24312			0.303912
$926$	−13.7401	−	12.3717i	−0.451529	−	0.406558i
$927$	20.7186	+	46.5347i	0.680487	+	1.52840i
$928$	−0.460326	−	4.37971i	−0.0151109	−	0.143771i
$929$	2.89553	+	13.6224i	0.0949993	+	0.446937i	0.999778	+	0.0210552i	$0.00670257\pi$
$929$	2.89553	+	13.6224i	0.0949993	+	0.446937i	−0.904779	+	0.425881i	$0.859964\pi$
$930$	−11.5763	+	35.6283i	−0.379603	+	1.16830i
$931$	7.01853	+	6.62164i	0.230023	+	0.217015i
$932$	−9.21385	+	12.6818i	−0.301810	+	0.415406i
$933$	4.84663	−	5.38273i	0.158672	−	0.176223i
$934$	3.30900	−	5.73135i	0.108274	−	0.187536i
$935$	0.410147	−	3.82248i	0.0134133	−	0.125009i
$936$	−30.4266	+	17.5668i	−0.994526	+	0.574190i
$937$	−11.9520	−	36.7843i	−0.390453	−	1.20169i	−0.932446	−	0.361309i	$-0.882330\pi$
$937$	−11.9520	−	36.7843i	−0.390453	−	1.20169i	0.541993	−	0.840383i	$-0.317670\pi$
$938$	−5.56370	−	5.69470i	−0.181661	−	0.185938i
$939$	29.1612	−	21.1868i	0.951639	−	0.691406i
$940$	−8.50749	+	1.80832i	−0.277484	+	0.0589810i
$941$	−30.1686	−	33.5056i	−0.983467	−	1.09225i	−0.995729	−	0.0923265i	$-0.970570\pi$
$941$	−30.1686	−	33.5056i	−0.983467	−	1.09225i	0.0122613	−	0.999925i	$-0.496097\pi$
$942$	−38.2643	+	4.02173i	−1.24672	+	0.131035i
$943$	0.235586	−	2.24145i	0.00767173	−	0.0729916i
$944$	−26.8728	+	8.73151i	−0.874636	+	0.284186i
$945$	33.8150	−	12.5309i	1.10000	−	0.407631i
$946$	10.4641	−	48.7098i	0.340218	−	1.58369i
$947$	18.1857	+	31.4985i	0.590956	+	1.02357i	0.994104	+	0.108431i	$0.0345825\pi$
$947$	18.1857	+	31.4985i	0.590956	+	1.02357i	−0.403148	+	0.915135i	$0.632084\pi$
$948$	−26.3438	−	5.59954i	−0.855606	−	0.181865i
$949$	26.7126	−	11.8932i	0.867129	−	0.386071i
$950$	−0.958648	+	2.15316i	−0.0311027	+	0.0698577i
$951$	−21.9673	−	7.13762i	−0.712340	−	0.231453i
$952$	−1.14069	−	1.80208i	−0.0369701	−	0.0584056i
$953$	−17.2576	−	23.7531i	−0.559030	−	0.769439i	0.432173	−	0.901791i	$-0.357747\pi$
$953$	−17.2576	−	23.7531i	−0.559030	−	0.769439i	−0.991203	+	0.132352i	$0.957747\pi$
$954$	61.0437	+	6.41595i	1.97636	+	0.207724i
$955$	10.1786	−	47.8864i	0.329371	−	1.54957i
$956$	4.85121	+	2.80085i	0.156899	+	0.0905859i
$957$	0.0150406	−	6.93127i	0.000486192	−	0.224056i
$958$		−	38.2431i		−	1.23558i
$959$	−16.5292	+	41.6064i	−0.533754	+	1.34354i
$960$	4.80192	+	3.48880i	0.154981	+	0.112600i
$961$	16.5329	+	7.36093i	0.533320	+	0.237449i
$962$	−60.7797	+	54.7263i	−1.95962	+	1.76445i
$963$	5.75942	−	5.18580i	0.185595	−	0.167110i
$964$	−8.59628	−	3.82731i	−0.276867	−	0.123269i
$965$	30.2670	+	21.9903i	0.974330	+	0.707892i
$966$	6.94685	+	8.78572i	0.223511	+	0.282676i
$967$		−	10.3829i		−	0.333892i	−0.985966	−	0.166946i	$-0.946609\pi$
$967$		−	10.3829i		−	0.333892i	0.985966	−	0.166946i	$-0.0533906\pi$
$968$	6.19845	+	14.0861i	0.199226	+	0.452746i
$969$	1.98701	+	1.14720i	0.0638320	+	0.0368534i
$970$	−7.74752	+	36.4492i	−0.248758	+	1.17031i
$971$	−35.6003	−	3.74174i	−1.14247	−	0.120078i	−0.485668	−	0.874143i	$-0.661424\pi$
$971$	−35.6003	−	3.74174i	−1.14247	−	0.120078i	−0.656800	+	0.754065i	$0.728090\pi$
$972$	7.25164	+	9.98102i	0.232596	+	0.320141i
$973$	−0.596779	−	0.312873i	−0.0191319	−	0.0100303i
$974$	54.5978	+	17.7399i	1.74943	+	0.568423i
$975$	−5.25957	+	11.8132i	−0.168441	+	0.378325i
$976$	61.3250	−	27.3037i	1.96297	−	0.873969i
$977$	−27.1641	−	5.77390i	−0.869055	−	0.184723i	−0.248258	−	0.968694i	$-0.579858\pi$
$977$	−27.1641	−	5.77390i	−0.869055	−	0.184723i	−0.620798	+	0.783971i	$0.713191\pi$
$978$	−28.3716	−	49.1411i	−0.907224	−	1.57136i
$979$	−24.3458	+	41.9576i	−0.778095	+	1.34097i
$980$	5.68961	−	16.2167i	0.181748	−	0.518025i
$981$	38.1575	−	12.3981i	1.21827	−	0.395842i
$982$	6.05533	−	57.6126i	0.193233	−	1.83849i
$983$	−45.4929	+	4.78150i	−1.45100	+	0.152506i	−0.796995	−	0.603986i	$-0.793578\pi$
$983$	−45.4929	+	4.78150i	−1.45100	+	0.152506i	−0.654003	+	0.756492i	$0.726912\pi$
$984$	−7.46406	−	8.28968i	−0.237946	−	0.264265i
$985$	7.82145	−	1.66250i	0.249212	−	0.0529717i
$986$	−0.605153	+	0.439669i	−0.0192720	+	0.0140019i
$987$	−19.3675	+	18.9220i	−0.616475	+	0.602293i
$988$	−2.44221	−	7.51635i	−0.0776971	−	0.239127i
$989$	−5.91972	+	3.41775i	−0.188236	+	0.108678i
$990$	47.4706	+	42.9296i	1.50871	+	1.36439i
$991$	−23.2826	+	40.3267i	−0.739597	+	1.28102i	0.213079	+	0.977035i	$0.431651\pi$
$991$	−23.2826	+	40.3267i	−0.739597	+	1.28102i	−0.952677	+	0.303985i	$0.901683\pi$
$992$	−14.6313	+	16.2497i	−0.464543	+	0.515928i
$993$	23.9344	−	32.9429i	0.759536	−	1.04541i
$994$	26.8764	+	17.9018i	0.852468	+	0.567809i
$995$	−9.68517	+	29.8079i	−0.307041	+	0.944974i
$996$	−0.875962	−	4.12108i	−0.0277559	−	0.130581i
$997$	5.94820	+	56.5933i	0.188381	+	1.79233i	0.525426	+	0.850839i	$0.323906\pi$
$997$	5.94820	+	56.5933i	0.188381	+	1.79233i	−0.337045	+	0.941489i	$0.609427\pi$
$998$	−29.7357	−	66.7874i	−0.941267	−	2.11412i
$999$	48.8445	+	43.9798i	1.54537	+	1.39146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.17.2	✓	48
3.2	odd	2		693.2.cg.a.325.5		48
7.2	even	3		539.2.s.d.215.2		48
7.3	odd	6		539.2.m.a.391.10		48
7.4	even	3		539.2.m.a.391.9		48
7.5	odd	6	inner	77.2.n.a.61.2	yes	48
7.6	odd	2		539.2.s.d.325.2		48
11.2	odd	10	inner	77.2.n.a.24.2	yes	48
11.3	even	5		847.2.i.b.241.5		48
11.4	even	5		847.2.r.a.360.5		48
11.5	even	5		847.2.r.d.766.5		48
11.6	odd	10		847.2.r.a.766.2		48
11.7	odd	10		847.2.r.d.360.2		48
11.8	odd	10		847.2.i.b.241.20		48
11.9	even	5		847.2.r.c.717.5		48
11.10	odd	2		847.2.r.c.94.5		48
21.5	even	6		693.2.cg.a.523.5		48
33.2	even	10		693.2.cg.a.640.5		48
77.2	odd	30		539.2.s.d.68.2		48
77.5	odd	30		847.2.r.d.40.2		48
77.13	even	10		539.2.s.d.178.2		48
77.19	even	30		847.2.i.b.362.5		48
77.24	even	30		539.2.m.a.244.9		48
77.26	odd	30		847.2.r.a.481.2		48
77.40	even	30		847.2.r.d.481.5		48
77.46	odd	30		539.2.m.a.244.10		48
77.47	odd	30		847.2.i.b.362.20		48
77.54	even	6		847.2.r.c.215.5		48
77.61	even	30		847.2.r.a.40.5		48
77.68	even	30	inner	77.2.n.a.68.2	yes	48
77.75	odd	30		847.2.r.c.838.5		48
231.68	odd	30		693.2.cg.a.145.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.2	✓	48	1.1	even	1	trivial
77.2.n.a.24.2	yes	48	11.2	odd	10	inner
77.2.n.a.61.2	yes	48	7.5	odd	6	inner
77.2.n.a.68.2	yes	48	77.68	even	30	inner
539.2.m.a.244.9		48	77.24	even	30
539.2.m.a.244.10		48	77.46	odd	30
539.2.m.a.391.9		48	7.4	even	3
539.2.m.a.391.10		48	7.3	odd	6
539.2.s.d.68.2		48	77.2	odd	30
539.2.s.d.178.2		48	77.13	even	10
539.2.s.d.215.2		48	7.2	even	3
539.2.s.d.325.2		48	7.6	odd	2
693.2.cg.a.145.5		48	231.68	odd	30
693.2.cg.a.325.5		48	3.2	odd	2
693.2.cg.a.523.5		48	21.5	even	6
693.2.cg.a.640.5		48	33.2	even	10
847.2.i.b.241.5		48	11.3	even	5
847.2.i.b.241.20		48	11.8	odd	10
847.2.i.b.362.5		48	77.19	even	30
847.2.i.b.362.20		48	77.47	odd	30
847.2.r.a.40.5		48	77.61	even	30
847.2.r.a.360.5		48	11.4	even	5
847.2.r.a.481.2		48	77.26	odd	30
847.2.r.a.766.2		48	11.6	odd	10
847.2.r.c.94.5		48	11.10	odd	2
847.2.r.c.215.5		48	77.54	even	6
847.2.r.c.717.5		48	11.9	even	5
847.2.r.c.838.5		48	77.75	odd	30
847.2.r.d.40.2		48	77.5	odd	30
847.2.r.d.360.2		48	11.7	odd	10
847.2.r.d.481.5		48	77.40	even	30
847.2.r.d.766.5		48	11.5	even	5

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33360 - 1.20078i) q^{2} +(-1.17499 - 2.63908i) q^{3} +(0.127565 + 1.21370i) q^{4} +(0.418270 + 1.96780i) q^{5} +(-1.60198 + 4.93040i) q^{6} +(-1.17364 - 2.37120i) q^{7} +(-0.822345 + 1.13186i) q^{8} +(-3.57672 + 3.97235i) q^{9} +O(q^{10})\)	\(q+(-1.33360 - 1.20078i) q^{2} +(-1.17499 - 2.63908i) q^{3} +(0.127565 + 1.21370i) q^{4} +(0.418270 + 1.96780i) q^{5} +(-1.60198 + 4.93040i) q^{6} +(-1.17364 - 2.37120i) q^{7} +(-0.822345 + 1.13186i) q^{8} +(-3.57672 + 3.97235i) q^{9} +(1.80510 - 3.12652i) q^{10} +(2.87587 - 1.65208i) q^{11} +(3.05315 - 1.76274i) q^{12} +(-1.45177 - 4.46807i) q^{13} +(-1.28213 + 4.57152i) q^{14} +(4.70172 - 3.41600i) q^{15} +(4.84323 - 1.02946i) q^{16} +(-0.385539 - 0.428185i) q^{17} +(9.53987 - 1.00268i) q^{18} +(0.144087 - 1.37090i) q^{19} +(-2.33496 + 0.758675i) q^{20} +(-4.87876 + 5.88345i) q^{21} +(-5.81906 - 1.25008i) q^{22} +(0.408298 + 0.707192i) q^{23} +(3.95331 + 0.840303i) q^{24} +(0.870426 - 0.387539i) q^{25} +(-3.42911 + 7.70190i) q^{26} +(6.44364 + 2.09366i) q^{27} +(2.72820 - 1.72692i) q^{28} +(0.425221 + 0.585266i) q^{29} +(-10.3721 - 1.09015i) q^{30} +(0.746819 - 3.51351i) q^{31} +(-5.27188 - 3.04372i) q^{32} +(-7.73908 - 5.64847i) q^{33} +1.03398i q^{34} +(4.17515 - 3.30129i) q^{35} +(-5.27750 - 3.83433i) q^{36} +(8.86232 + 3.94576i) q^{37} +(-1.83831 + 1.65522i) q^{38} +(-10.0858 + 9.08127i) q^{39} +(-2.57124 - 1.14479i) q^{40} +(-2.23288 - 1.62228i) q^{41} +(13.5711 - 1.98787i) q^{42} +8.37074i q^{43} +(2.37198 + 3.27969i) q^{44} +(-9.31284 - 5.37677i) q^{45} +(0.304677 - 1.43339i) q^{46} +(3.52320 + 0.370304i) q^{47} +(-8.40758 - 11.5720i) q^{48} +(-4.24516 + 5.56585i) q^{49} +(-1.62615 - 0.528369i) q^{50} +(-0.677006 + 1.52058i) q^{51} +(5.23770 - 2.33197i) q^{52} +(6.25897 + 1.33038i) q^{53} +(-6.07923 - 10.5295i) q^{54} +(4.45385 + 4.96814i) q^{55} +(3.64900 + 0.621549i) q^{56} +(-3.78720 + 1.23054i) q^{57} +(0.135701 - 1.29111i) q^{58} +(-5.67532 + 0.596501i) q^{59} +(4.74576 + 5.27070i) q^{60} +(13.2611 - 2.81874i) q^{61} +(-5.21492 + 3.78886i) q^{62} +(13.6170 + 3.81902i) q^{63} +(0.315602 + 0.971325i) q^{64} +(8.18506 - 4.72565i) q^{65} +(3.53829 + 16.8258i) q^{66} +(-0.838413 + 1.45217i) q^{67} +(0.470505 - 0.522549i) q^{68} +(1.38659 - 1.90847i) q^{69} +(-9.53214 - 0.610845i) q^{70} +(2.10176 - 6.46855i) q^{71} +(-1.55485 - 7.31499i) q^{72} +(0.650590 + 6.18995i) q^{73} +(-7.08083 - 15.9038i) q^{74} +(-2.04549 - 1.84176i) q^{75} +1.68224 q^{76} +(-7.29263 - 4.88033i) q^{77} +24.3551 q^{78} +(-5.67714 - 5.11172i) q^{79} +(4.05155 + 9.09993i) q^{80} +(-0.369668 - 3.51716i) q^{81} +(1.02977 + 4.84469i) q^{82} +(0.369293 - 1.13657i) q^{83} +(-7.76309 - 5.17081i) q^{84} +(0.681324 - 0.937762i) q^{85} +(10.0514 - 11.1633i) q^{86} +(1.04493 - 1.80987i) q^{87} +(-0.495040 + 4.61366i) q^{88} +(-12.6666 + 7.31306i) q^{89} +(5.96331 + 18.3532i) q^{90} +(-8.89084 + 8.68632i) q^{91} +(-0.806233 + 0.585763i) q^{92} +(-10.1499 + 2.15743i) q^{93} +(-4.25391 - 4.72444i) q^{94} +(2.75792 - 0.289870i) q^{95} +(-1.83819 + 17.4892i) q^{96} +(-9.81655 + 3.18959i) q^{97} +(12.3447 - 2.32513i) q^{98} +(-3.72357 + 17.3330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

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