LMFDB - Embedded newform 456.2.bu.c.131.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(35,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 9, 4]))

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

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

chi := DirichletCharacter("456.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bu (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			131.15
Character	$\chi$	$=$	456.131
Dual form			456.2.bu.c.275.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06720 - 0.927949i) q^{2} +(1.45315 - 0.942522i) q^{3} +(0.277823 + 1.98061i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-2.42541 - 0.342592i) q^{6} +(-3.92214 + 2.26445i) q^{7} +(1.54141 - 2.37151i) q^{8} +(1.22330 - 2.73926i) q^{9} +O(q^{10})$	\(q+(-1.06720 - 0.927949i) q^{2} +(1.45315 - 0.942522i) q^{3} +(0.277823 + 1.98061i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-2.42541 - 0.342592i) q^{6} +(-3.92214 + 2.26445i) q^{7} +(1.54141 - 2.37151i) q^{8} +(1.22330 - 2.73926i) q^{9} +(1.94343 + 0.746306i) q^{10} +(-0.674933 - 0.389673i) q^{11} +(2.27049 + 2.61627i) q^{12} +(-1.93582 - 2.30702i) q^{13} +(6.28700 + 1.22293i) q^{14} +(-1.53558 + 2.03539i) q^{15} +(-3.84563 + 1.10052i) q^{16} +(-6.89185 - 1.21522i) q^{17} +(-3.84740 + 1.78817i) q^{18} +(-1.66915 + 4.02665i) q^{19} +(-1.38149 - 2.59986i) q^{20} +(-3.56518 + 6.98730i) q^{21} +(0.358691 + 1.04216i) q^{22} +(-2.25555 - 0.820955i) q^{23} +(0.00470611 - 4.89898i) q^{24} +(-2.17025 + 1.82106i) q^{25} +(-0.0748931 + 4.25839i) q^{26} +(-0.804166 - 5.13355i) q^{27} +(-5.57465 - 7.13912i) q^{28} +(-0.354954 - 2.01304i) q^{29} +(3.52750 - 0.747227i) q^{30} +(5.63852 - 3.25540i) q^{31} +(5.12527 + 2.39407i) q^{32} +(-1.34806 + 0.0698856i) q^{33} +(6.22730 + 7.69216i) q^{34} +(4.28532 - 5.10705i) q^{35} +(5.76526 + 1.66186i) q^{36} +5.12134i q^{37} +(5.51784 - 2.74835i) q^{38} +(-4.98746 - 1.52790i) q^{39} +(-0.938212 + 4.05651i) q^{40} +(-1.68681 + 2.01026i) q^{41} +(10.2886 - 4.14853i) q^{42} +(-0.343217 + 0.124921i) q^{43} +(0.584277 - 1.44504i) q^{44} +(-0.313029 + 4.40505i) q^{45} +(1.64532 + 2.96916i) q^{46} +(-0.490410 - 2.78126i) q^{47} +(-4.55102 + 5.22381i) q^{48} +(6.75547 - 11.7008i) q^{49} +(4.00593 + 0.0704530i) q^{50} +(-11.1603 + 4.72982i) q^{51} +(4.03150 - 4.47505i) q^{52} +(-6.24605 - 2.27338i) q^{53} +(-3.90546 + 6.22474i) q^{54} +(1.12981 + 0.199216i) q^{55} +(-0.675474 + 12.7918i) q^{56} +(1.36969 + 7.42455i) q^{57} +(-1.48919 + 2.47769i) q^{58} +(14.3723 + 2.53423i) q^{59} +(-4.45793 - 2.47590i) q^{60} +(-2.28545 + 6.27923i) q^{61} +(-9.03826 - 1.75810i) q^{62} +(1.40494 + 13.5139i) q^{63} +(-3.24810 - 7.31094i) q^{64} +(3.83930 + 2.21662i) q^{65} +(1.50349 + 1.17634i) q^{66} +(1.30535 + 7.40302i) q^{67} +(0.492159 - 13.9877i) q^{68} +(-4.05143 + 0.932938i) q^{69} +(-9.31237 + 1.47367i) q^{70} +(-5.55190 + 2.02073i) q^{71} +(-4.61056 - 7.12340i) q^{72} +(1.02524 + 0.860276i) q^{73} +(4.75234 - 5.46548i) q^{74} +(-1.43732 + 4.69178i) q^{75} +(-8.43896 - 2.18723i) q^{76} +3.52958 q^{77} +(3.90480 + 6.25868i) q^{78} +(10.0657 - 11.9958i) q^{79} +(4.76549 - 3.45849i) q^{80} +(-6.00706 - 6.70188i) q^{81} +(3.66558 - 0.580075i) q^{82} +(-2.94697 + 1.70143i) q^{83} +(-14.8296 - 5.11999i) q^{84} +(10.1452 - 1.78887i) q^{85} +(0.482200 + 0.185172i) q^{86} +(-2.41314 - 2.59070i) q^{87} +(-1.96446 + 0.999963i) q^{88} +(-10.1930 - 12.1475i) q^{89} +(4.42172 - 4.41059i) q^{90} +(12.8167 + 4.66490i) q^{91} +(0.999346 - 4.69545i) q^{92} +(5.12534 - 10.0450i) q^{93} +(-2.05750 + 3.42323i) q^{94} +(0.281587 - 6.41035i) q^{95} +(9.70427 - 1.35173i) q^{96} +(0.436566 - 2.47589i) q^{97} +(-18.0672 + 6.21836i) q^{98} +(-1.89306 + 1.37213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 432 * q - 18 * q^3 - 6 * q^4 + 6 * q^6 - 18 * q^9	$ 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 6 q^{16} - 12 q^{18} - 24 q^{19} + 24 q^{22} - 18 q^{24} - 24 q^{25} - 36 q^{27} - 36 q^{28} - 48 q^{30} - 54 q^{34} + 66 q^{36} + 18 q^{40} - 51 q^{42} - 24 q^{43} - 6 q^{46} + 117 q^{48} + 228 q^{49} + 66 q^{51} + 12 q^{52} + 21 q^{54} - 12 q^{57} - 96 q^{58} + 48 q^{60} - 144 q^{64} - 78 q^{66} + 60 q^{67} - 162 q^{70} - 84 q^{72} - 72 q^{73} - 192 q^{75} - 132 q^{76} + 3 q^{78} - 42 q^{81} - 252 q^{82} - 45 q^{84} - 126 q^{88} + 24 q^{90} - 108 q^{91} - 48 q^{94} + 138 q^{96} - 84 q^{97} + 18 q^{99}+O(q^{100}) $ 432 * q - 18 * q^3 - 6 * q^4 + 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 6 * q^16 - 12 * q^18 - 24 * q^19 + 24 * q^22 - 18 * q^24 - 24 * q^25 - 36 * q^27 - 36 * q^28 - 48 * q^30 - 54 * q^34 + 66 * q^36 + 18 * q^40 - 51 * q^42 - 24 * q^43 - 6 * q^46 + 117 * q^48 + 228 * q^49 + 66 * q^51 + 12 * q^52 + 21 * q^54 - 12 * q^57 - 96 * q^58 + 48 * q^60 - 144 * q^64 - 78 * q^66 + 60 * q^67 - 162 * q^70 - 84 * q^72 - 72 * q^73 - 192 * q^75 - 132 * q^76 + 3 * q^78 - 42 * q^81 - 252 * q^82 - 45 * q^84 - 126 * q^88 + 24 * q^90 - 108 * q^91 - 48 * q^94 + 138 * q^96 - 84 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.06720	−	0.927949i	−0.754623	−	0.656159i
$2$	−1.06720	−	0.927949i	−0.754623	−	0.656159i
$3$	1.45315	−	0.942522i	0.838978	−	0.544166i
$3$	1.45315	−	0.942522i	0.838978	−	0.544166i
$4$	0.277823	+	1.98061i	0.138912	+	0.990305i
$5$	−1.38328	+	0.503472i	−0.618620	+	0.225159i	−0.632271	−	0.774747i	$-0.717877\pi$
$5$	−1.38328	+	0.503472i	−0.618620	+	0.225159i	0.0136505	+	0.999907i	$0.495655\pi$
$6$	−2.42541	−	0.342592i	−0.990171	−	0.139863i
$7$	−3.92214	+	2.26445i	−1.48243	+	0.855882i	−0.999801	−	0.0199427i	$-0.993652\pi$
$7$	−3.92214	+	2.26445i	−1.48243	+	0.855882i	−0.482630	+	0.875825i	$0.660318\pi$
$8$	1.54141	−	2.37151i	0.544971	−	0.838455i
$9$	1.22330	−	2.73926i	0.407768	−	0.913086i
$10$	1.94343	+	0.746306i	0.614565	+	0.236003i
$11$	−0.674933	−	0.389673i	−0.203500	−	0.117491i	0.394787	−	0.918773i	$-0.370818\pi$
$11$	−0.674933	−	0.389673i	−0.203500	−	0.117491i	−0.598287	+	0.801282i	$0.704152\pi$
$12$	2.27049	+	2.61627i	0.655433	+	0.755253i
$13$	−1.93582	−	2.30702i	−0.536900	−	0.639853i	0.427589	−	0.903973i	$-0.359363\pi$
$13$	−1.93582	−	2.30702i	−0.536900	−	0.639853i	−0.964490	+	0.264120i	$0.914918\pi$
$14$	6.28700	+	1.22293i	1.68027	+	0.326842i
$15$	−1.53558	+	2.03539i	−0.396485	+	0.525536i
$16$	−3.84563	+	1.10052i	−0.961407	+	0.275130i
$17$	−6.89185	−	1.21522i	−1.67152	−	0.294734i	−0.743908	−	0.668282i	$-0.767030\pi$
$17$	−6.89185	−	1.21522i	−1.67152	−	0.294734i	−0.927611	+	0.373549i	$0.878141\pi$
$18$	−3.84740	+	1.78817i	−0.906840	+	0.421475i
$19$	−1.66915	+	4.02665i	−0.382929	+	0.923778i
$19$	−1.66915	+	4.02665i	−0.382929	+	0.923778i
$20$	−1.38149	−	2.59986i	−0.308910	−	0.581345i
$21$	−3.56518	+	6.98730i	−0.777985	+	1.52475i
$22$	0.358691	+	1.04216i	0.0764731	+	0.222189i
$23$	−2.25555	−	0.820955i	−0.470316	−	0.171181i	0.0959797	−	0.995383i	$-0.469402\pi$
$23$	−2.25555	−	0.820955i	−0.470316	−	0.171181i	−0.566295	+	0.824202i	$0.691624\pi$
$24$	0.00470611	−	4.89898i	0.000960630	−	1.00000i
$25$	−2.17025	+	1.82106i	−0.434050	+	0.364211i
$26$	−0.0748931	+	4.25839i	−0.0146877	+	0.835140i
$27$	−0.804166	−	5.13355i	−0.154762	−	0.987952i
$28$	−5.57465	−	7.13912i	−1.05351	−	1.34917i
$29$	−0.354954	−	2.01304i	−0.0659132	−	0.373812i	−0.999865	−	0.0164141i	$-0.994775\pi$
$29$	−0.354954	−	2.01304i	−0.0659132	−	0.373812i	0.933952	−	0.357398i	$-0.116336\pi$
$30$	3.52750	−	0.747227i	0.644031	−	0.136424i
$31$	5.63852	−	3.25540i	1.01271	−	0.584687i	0.100725	−	0.994914i	$-0.467884\pi$
$31$	5.63852	−	3.25540i	1.01271	−	0.584687i	0.911983	+	0.410227i	$0.134551\pi$
$32$	5.12527	+	2.39407i	0.906029	+	0.423217i
$33$	−1.34806	+	0.0698856i	−0.234666	+	0.0121655i
$34$	6.22730	+	7.69216i	1.06797	+	1.31919i
$35$	4.28532	−	5.10705i	0.724352	−	0.863249i
$36$	5.76526	+	1.66186i	0.960877	+	0.276976i
$37$			5.12134i			0.841943i	0.907074	+	0.420972i	$0.138311\pi$
$37$			5.12134i			0.841943i	−0.907074	+	0.420972i	$0.861689\pi$
$38$	5.51784	−	2.74835i	0.895112	−	0.445842i
$39$	−4.98746	−	1.52790i	−0.798634	−	0.244660i
$40$	−0.938212	+	4.05651i	−0.148344	+	0.641390i
$41$	−1.68681	+	2.01026i	−0.263436	+	0.313951i	−0.881506	−	0.472172i	$-0.843470\pi$
$41$	−1.68681	+	2.01026i	−0.263436	+	0.313951i	0.618071	+	0.786123i	$0.287915\pi$
$42$	10.2886	−	4.14853i	1.58757	−	0.640132i
$43$	−0.343217	+	0.124921i	−0.0523401	+	0.0190502i	−0.368058	−	0.929803i	$-0.619977\pi$
$43$	−0.343217	+	0.124921i	−0.0523401	+	0.0190502i	0.315717	+	0.948853i	$0.397755\pi$
$44$	0.584277	−	1.44504i	0.0880831	−	0.217848i
$45$	−0.313029	+	4.40505i	−0.0466636	+	0.656666i
$46$	1.64532	+	2.96916i	0.242589	+	0.437779i
$47$	−0.490410	−	2.78126i	−0.0715337	−	0.405688i	−0.999458	−	0.0329192i	$-0.989520\pi$
$47$	−0.490410	−	2.78126i	−0.0715337	−	0.405688i	0.927924	−	0.372769i	$-0.121592\pi$
$48$	−4.55102	+	5.22381i	−0.656883	+	0.753992i
$49$	6.75547	−	11.7008i	0.965067	−	1.67155i
$50$	4.00593	+	0.0704530i	0.566525	+	0.00996356i
$51$	−11.1603	+	4.72982i	−1.56275	+	0.662308i
$52$	4.03150	−	4.47505i	0.559068	−	0.620578i
$53$	−6.24605	−	2.27338i	−0.857962	−	0.312272i	−0.124680	−	0.992197i	$-0.539790\pi$
$53$	−6.24605	−	2.27338i	−0.857962	−	0.312272i	−0.733282	+	0.679925i	$0.762013\pi$
$54$	−3.90546	+	6.22474i	−0.531466	+	0.847079i
$55$	1.12981	+	0.199216i	0.152343	+	0.0268622i
$56$	−0.675474	+	12.7918i	−0.0902640	+	1.70938i
$57$	1.36969	+	7.42455i	0.181419	+	0.983406i
$58$	−1.48919	+	2.47769i	−0.195541	+	0.325337i
$59$	14.3723	+	2.53423i	1.87112	+	0.329928i	0.989785	−	0.142569i	$-0.0455362\pi$
$59$	14.3723	+	2.53423i	1.87112	+	0.329928i	0.881332	+	0.472497i	$0.156647\pi$
$60$	−4.45793	−	2.47590i	−0.575517	−	0.319638i
$61$	−2.28545	+	6.27923i	−0.292622	+	0.803973i	0.703059	+	0.711132i	$0.251817\pi$
$61$	−2.28545	+	6.27923i	−0.292622	+	0.803973i	−0.995681	+	0.0928409i	$0.970405\pi$
$62$	−9.03826	−	1.75810i	−1.14786	−	0.223279i
$63$	1.40494	+	13.5139i	0.177006	+	1.70259i
$64$	−3.24810	−	7.31094i	−0.406013	−	0.913867i
$65$	3.83930	+	2.21662i	0.476206	+	0.274938i
$66$	1.50349	+	1.17634i	0.185067	+	0.144798i
$67$	1.30535	+	7.40302i	0.159474	+	0.904423i	0.954581	+	0.297953i	$0.0963039\pi$
$67$	1.30535	+	7.40302i	0.159474	+	0.904423i	−0.795106	+	0.606470i	$0.792585\pi$
$68$	0.492159	−	13.9877i	0.0596831	−	1.69625i
$69$	−4.05143	+	0.932938i	−0.487735	+	0.112313i
$70$	−9.31237	+	1.47367i	−1.11304	+	0.176138i
$71$	−5.55190	+	2.02073i	−0.658889	+	0.239816i	−0.649757	−	0.760142i	$-0.725129\pi$
$71$	−5.55190	+	2.02073i	−0.658889	+	0.239816i	−0.00913244	+	0.999958i	$0.502907\pi$
$72$	−4.61056	−	7.12340i	−0.543359	−	0.839500i
$73$	1.02524	+	0.860276i	0.119995	+	0.100688i	0.700811	−	0.713347i	$-0.252822\pi$
$73$	1.02524	+	0.860276i	0.119995	+	0.100688i	−0.580816	+	0.814035i	$0.697266\pi$
$74$	4.75234	−	5.46548i	0.552448	−	0.635350i
$75$	−1.43732	+	4.69178i	−0.165967	+	0.541760i
$76$	−8.43896	−	2.18723i	−0.968015	−	0.250893i
$77$	3.52958			0.402233
$78$	3.90480	+	6.25868i	0.442132	+	0.708656i
$79$	10.0657	−	11.9958i	1.13248	−	1.34964i	0.203686	−	0.979036i	$-0.434708\pi$
$79$	10.0657	−	11.9958i	1.13248	−	1.34964i	0.928793	−	0.370600i	$-0.120848\pi$
$80$	4.76549	−	3.45849i	0.532798	−	0.386671i
$81$	−6.00706	−	6.70188i	−0.667451	−	0.744654i
$82$	3.66558	−	0.580075i	0.404796	−	0.0640586i
$83$	−2.94697	+	1.70143i	−0.323472	+	0.186757i	−0.652939	−	0.757410i	$-0.726464\pi$
$83$	−2.94697	+	1.70143i	−0.323472	+	0.186757i	0.329467	+	0.944167i	$0.393131\pi$
$84$	−14.8296	−	5.11999i	−1.61804	−	0.558637i
$85$	10.1452	−	1.78887i	1.10040	−	0.194030i
$86$	0.482200	+	0.185172i	0.0519970	+	0.0199677i
$87$	−2.41314	−	2.59070i	−0.258716	−	0.277753i
$88$	−1.96446	+	0.999963i	−0.209412	+	0.106596i
$89$	−10.1930	−	12.1475i	−1.08046	−	1.28764i	−0.955344	−	0.295495i	$-0.904515\pi$
$89$	−10.1930	−	12.1475i	−1.08046	−	1.28764i	−0.125112	−	0.992143i	$-0.539929\pi$
$90$	4.42172	−	4.41059i	0.466091	−	0.464917i
$91$	12.8167	+	4.66490i	1.34356	+	0.489015i
$92$	0.999346	−	4.69545i	0.104189	−	0.489535i
$93$	5.12534	−	10.0450i	0.531473	−	1.04162i
$94$	−2.05750	+	3.42323i	−0.212215	+	0.353079i
$95$	0.281587	−	6.41035i	0.0288902	−	0.657688i
$96$	9.70427	−	1.35173i	0.990438	−	0.137960i
$97$	0.436566	−	2.47589i	0.0443266	−	0.251388i	−0.954590	−	0.297922i	$-0.903706\pi$
$97$	0.436566	−	2.47589i	0.0443266	−	0.251388i	0.998917	+	0.0465338i	$0.0148175\pi$
$98$	−18.0672	+	6.21836i	−1.82506	+	0.628149i
$99$	−1.89306	+	1.37213i	−0.190260	+	0.137904i
$100$	−4.20975	−	3.79249i	−0.420975	−	0.379249i
$101$	−7.68054	+	6.44474i	−0.764242	+	0.641276i	−0.939227	−	0.343296i	$-0.888457\pi$
$101$	−7.68054	+	6.44474i	−0.764242	+	0.641276i	0.174985	+	0.984571i	$0.444012\pi$
$102$	16.2993	+	5.30850i	1.61387	+	0.525620i
$103$	14.9501	+	8.63142i	1.47307	+	0.850479i	0.999541	−	0.0302978i	$-0.00964556\pi$
$103$	14.9501	+	8.63142i	1.47307	+	0.850479i	0.473532	+	0.880777i	$0.342979\pi$
$104$	−8.45502	+	1.03475i	−0.829083	+	0.101465i
$105$	1.41372	−	11.4603i	0.137965	−	1.11841i
$106$	4.55620	+	8.22216i	0.442537	+	0.798607i
$107$	−10.3723	+	5.98847i	−1.00273	+	0.578927i	−0.909055	−	0.416676i	$-0.863195\pi$
$107$	−10.3723	+	5.98847i	−1.00273	+	0.578927i	−0.0936759	+	0.995603i	$0.529862\pi$
$108$	9.94414	−	3.01896i	0.956875	−	0.290499i
$109$	−3.39045	−	9.31520i	−0.324747	−	0.892234i	−0.989417	−	0.145098i	$-0.953650\pi$
$109$	−3.39045	−	9.31520i	−0.324747	−	0.892234i	0.664671	−	0.747136i	$-0.268572\pi$
$110$	−1.02087	−	1.26101i	−0.0973359	−	0.120232i
$111$	4.82698	+	7.44209i	0.458156	+	0.706372i
$112$	12.5910	−	13.0246i	1.18974	−	1.23071i
$113$		−	7.14511i		−	0.672155i	−0.941834	−	0.336078i	$-0.890900\pi$
$113$		−	7.14511i		−	0.672155i	0.941834	−	0.336078i	$-0.109100\pi$
$114$	5.42787	−	9.19446i	0.508367	−	0.861141i
$115$	3.53338			0.329490
$116$	3.88844	−	1.26229i	0.361032	−	0.117201i
$117$	−8.68763	+	2.48053i	−0.803171	+	0.229325i
$118$	−12.9865	−	16.0413i	−1.19550	−	1.47672i
$119$	29.7826	−	10.8400i	2.73017	−	0.993700i
$120$	2.45999	+	6.77901i	0.224565	+	0.618836i
$121$	−5.19631	−	9.00027i	−0.472392	−	0.818207i
$122$	8.26583	−	4.58040i	0.748353	−	0.414690i
$123$	−0.556476	+	4.51108i	−0.0501757	+	0.406750i
$124$	8.01419	+	10.2633i	0.719695	+	0.921670i
$125$	5.76534	−	9.98586i	0.515668	−	0.893162i
$126$	11.0408	−	15.7257i	0.983595	−	1.40096i
$127$	−8.25889	−	9.84257i	−0.732858	−	0.873386i	0.262954	−	0.964808i	$-0.415303\pi$
$127$	−8.25889	−	9.84257i	−0.732858	−	0.873386i	−0.995812	+	0.0914219i	$0.970859\pi$
$128$	−3.31781	+	10.8163i	−0.293256	+	0.956034i
$129$	−0.381006	+	0.505018i	−0.0335457	+	0.0444644i
$130$	−2.04038	−	5.92824i	−0.178953	−	0.519941i
$131$	6.38338	+	1.12556i	0.557719	+	0.0983409i	0.445401	−	0.895331i	$-0.353061\pi$
$131$	6.38338	+	1.12556i	0.557719	+	0.0983409i	0.112318	+	0.993672i	$0.464172\pi$
$132$	−0.512937	−	2.65056i	−0.0446454	−	0.230701i
$133$	−2.57152	−	19.5728i	−0.222979	−	1.69718i
$134$	5.47655	−	9.11179i	0.473102	−	0.787139i
$135$	3.69698	+	6.69624i	0.318185	+	0.576321i
$136$	−13.5051	+	14.4709i	−1.15805	+	1.24087i
$137$	−2.01091	+	5.52493i	−0.171804	+	0.472027i	−0.995473	−	0.0950435i	$-0.969701\pi$
$137$	−2.01091	+	5.52493i	−0.171804	+	0.472027i	0.823669	+	0.567070i	$0.191923\pi$
$138$	5.18940	+	2.76389i	0.441751	+	0.235278i
$139$	−12.3615	+	10.3725i	−1.04849	+	0.879783i	−0.992933	−	0.118672i	$-0.962136\pi$
$139$	−12.3615	+	10.3725i	−1.04849	+	0.879783i	−0.0555516	+	0.998456i	$0.517692\pi$
$140$	11.3056	+	7.06870i	0.955500	+	0.597414i
$141$	−3.33404	−	3.57937i	−0.280777	−	0.301437i
$142$	7.80010	+	2.99536i	0.654570	+	0.251365i
$143$	0.407566	+	2.31142i	0.0340824	+	0.193291i
$144$	−1.68977	+	11.8804i	−0.140814	+	0.990036i
$145$	1.50451	+	2.60589i	0.124943	+	0.216407i
$146$	−0.295839	−	1.86945i	−0.0244838	−	0.154717i
$147$	−1.21156	−	23.3703i	−0.0999275	−	1.92755i
$148$	−10.1434	+	1.42283i	−0.833780	+	0.116956i
$149$	8.14449	+	6.83404i	0.667222	+	0.559866i	0.912242	−	0.409652i	$-0.134350\pi$
$149$	8.14449	+	6.83404i	0.667222	+	0.559866i	−0.245019	+	0.969518i	$0.578794\pi$
$150$	5.88764	−	3.67330i	0.480723	−	0.299924i
$151$			0.110330i			0.00897852i	0.999990	+	0.00448926i	$0.00142898\pi$
$151$			0.110330i			0.00897852i	−0.999990	+	0.00448926i	$0.998571\pi$
$152$	6.97640	+	10.1651i	0.565861	+	0.824501i
$153$	−11.7596	+	17.3920i	−0.950708	+	1.40606i
$154$	−3.76676	−	3.27527i	−0.303534	−	0.263928i
$155$	−6.16063	+	7.34196i	−0.494834	+	0.589720i
$156$	1.64054	−	10.3027i	0.131348	−	0.824877i
$157$	−4.26475	−	11.7173i	−0.340364	−	0.935142i	−0.985289	−	0.170896i	$-0.945334\pi$
$157$	−4.26475	−	11.7173i	−0.340364	−	0.935142i	0.644925	−	0.764246i	$-0.276888\pi$
$158$	−21.8736	+	3.46148i	−1.74017	+	0.275380i
$159$	−11.2192	+	2.58348i	−0.889739	+	0.204883i
$160$	−8.29502	−	0.731239i	−0.655779	−	0.0578096i
$161$	10.7056	−	1.88769i	0.843721	−	0.148771i
$162$	0.191719	+	12.7265i	0.0150628	+	0.999887i
$163$	−1.39649	+	2.41879i	−0.109381	+	0.189454i	−0.915520	−	0.402273i	$-0.868220\pi$
$163$	−1.39649	+	2.41879i	−0.109381	+	0.189454i	0.806138	+	0.591727i	$0.201554\pi$
$164$	−4.45018	−	2.78242i	−0.347501	−	0.217270i
$165$	1.82955	−	0.775379i	0.142430	−	0.0603632i
$166$	4.72384	+	0.918869i	0.366641	+	0.0713181i
$167$	−12.3186	−	4.48361i	−0.953244	−	0.346952i	−0.181861	−	0.983324i	$-0.558212\pi$
$167$	−12.3186	−	4.48361i	−0.953244	−	0.346952i	−0.771382	+	0.636372i	$0.780434\pi$
$168$	11.0750	+	19.2251i	0.854457	+	1.48325i
$169$	0.682479	−	3.87053i	0.0524984	−	0.297733i
$170$	−12.4869	−	7.50511i	−0.957699	−	0.575616i
$171$	8.98817	+	9.49804i	0.687342	+	0.726333i
$172$	−0.342773	−	0.645073i	−0.0261362	−	0.0491863i
$173$	−2.85482	+	16.1905i	−0.217048	+	1.23094i	0.660268	+	0.751030i	$0.270443\pi$
$173$	−2.85482	+	16.1905i	−0.217048	+	1.23094i	−0.877317	+	0.479912i	$0.840669\pi$
$174$	0.171256	+	5.00406i	0.0129829	+	0.379357i
$175$	4.38834	−	12.0569i	0.331727	−	0.911414i
$176$	3.02438	+	0.755760i	0.227971	+	0.0569676i
$177$	23.2737	−	9.86362i	1.74936	−	0.741395i
$178$	−0.394347	+	22.4224i	−0.0295575	+	1.68063i
$179$	10.6108	+	6.12613i	0.793086	+	0.457888i	0.841048	−	0.540961i	$-0.181939\pi$
$179$	10.6108	+	6.12613i	0.793086	+	0.457888i	−0.0479621	+	0.998849i	$0.515273\pi$
$180$	−8.81165	+	0.603837i	−0.656782	+	0.0450073i
$181$	−2.48360	+	0.437926i	−0.184605	+	0.0325508i	−0.265186	−	0.964197i	$-0.585433\pi$
$181$	−2.48360	+	0.437926i	−0.184605	+	0.0325508i	0.0805815	+	0.996748i	$0.474322\pi$
$182$	−9.34918	−	16.8716i	−0.693007	−	1.25061i
$183$	2.59720	+	11.2788i	0.191991	+	0.833750i
$184$	−5.42364	+	4.08364i	−0.399836	+	0.301050i
$185$	−2.57845	−	7.08423i	−0.189571	−	0.520843i
$186$	−14.7910	+	5.96398i	−1.08453	+	0.437300i
$187$	4.17800	+	3.50575i	0.305525	+	0.256366i
$188$	5.37233	−	1.74401i	0.391818	−	0.127195i
$189$	14.7787	+	18.3135i	1.07499	+	1.33211i
$190$	−6.24898	+	6.57981i	−0.453349	+	0.477350i
$191$	3.53097			0.255492			0.127746	−	0.991807i	$-0.459226\pi$
$191$	3.53097			0.255492			0.127746	+	0.991807i	$0.459226\pi$
$192$	−11.6107	−	7.56250i	−0.837931	−	0.545776i
$193$	−2.83709	−	2.38060i	−0.204218	−	0.171360i	0.534942	−	0.844888i	$-0.320333\pi$
$193$	−2.83709	−	2.38060i	−0.204218	−	0.171360i	−0.739161	+	0.673529i	$0.764778\pi$
$194$	−2.76340	+	2.23715i	−0.198401	+	0.160618i
$195$	7.66830	−	0.397538i	0.549138	−	0.0284683i
$196$	25.0516	+	10.1292i	1.78940	+	0.723514i
$197$	−3.59817	−	6.23221i	−0.256359	−	0.444026i	0.708905	−	0.705304i	$-0.249190\pi$
$197$	−3.59817	−	6.23221i	−0.256359	−	0.444026i	−0.965264	+	0.261278i	$0.915856\pi$
$198$	3.29353	+	0.292332i	0.234061	+	0.0207751i
$199$	−20.3950	+	3.59618i	−1.44576	+	0.254927i	−0.840808	−	0.541334i	$-0.817919\pi$
$199$	−20.3950	+	3.59618i	−1.44576	+	0.254927i	−0.604954	+	0.796261i	$0.706808\pi$
$200$	0.973401	+	7.95376i	0.0688298	+	0.562416i
$201$	8.87439	+	9.52740i	0.625951	+	0.672011i
$202$	14.1770	+	0.249334i	0.997493	+	0.0175431i
$203$	5.95061	+	7.09166i	0.417651	+	0.497737i
$204$	−12.4685	−	20.7901i	−0.872970	−	1.45560i
$205$	1.32122	−	3.63001i	0.0922778	−	0.253531i
$206$	−7.94516	−	23.0843i	−0.553565	−	1.60836i
$207$	−5.00803	+	5.17427i	−0.348082	+	0.359636i
$208$	9.98337	+	6.74155i	0.692222	+	0.467442i
$209$	2.69564	−	2.06730i	0.186461	−	0.142998i
$210$	−12.1433	+	10.9186i	−0.837969	+	0.753454i
$211$	3.42858	−	19.4445i	0.236033	−	1.33861i	−0.604393	−	0.796686i	$-0.706584\pi$
$211$	3.42858	−	19.4445i	0.236033	−	1.33861i	0.840426	−	0.541926i	$-0.182305\pi$
$212$	2.76738	−	13.0026i	0.190064	−	0.893022i
$213$	−6.16317	+	8.16921i	−0.422294	+	0.559745i
$214$	16.6263	+	3.23411i	1.13655	+	0.221079i
$215$	0.411870	−	0.345600i	0.0280893	−	0.0235697i
$216$	−13.4138	−	6.00583i	−0.912694	−	0.408645i
$217$	−14.7434	+	25.5363i	−1.00085	+	1.73352i
$218$	−5.02574	+	13.0873i	−0.340386	+	0.886386i
$219$	2.30066	+	0.283803i	0.155464	+	0.0191777i
$220$	−0.0806816	+	2.29306i	−0.00543956	+	0.154598i
$221$	10.5379	+	18.2521i	0.708853	+	1.22777i
$222$	1.75453	−	12.4214i	0.117757	−	0.833668i
$223$	−3.08611	−	8.47903i	−0.206662	−	0.567798i	0.792450	−	0.609937i	$-0.208805\pi$
$223$	−3.08611	−	8.47903i	−0.206662	−	0.567798i	−0.999112	+	0.0421387i	$0.986583\pi$
$224$	−25.5233	+	2.21602i	−1.70535	+	0.148064i
$225$	2.33347	+	8.17258i	0.155565	+	0.544839i
$226$	−6.63029	+	7.62525i	−0.441041	+	0.507224i
$227$		−	5.08237i		−	0.337329i	−0.985674	−	0.168664i	$-0.946055\pi$
$227$		−	5.08237i		−	0.337329i	0.985674	−	0.168664i	$-0.0539454\pi$
$228$	−14.3246	+	4.77553i	−0.948670	+	0.316267i
$229$			26.2190i			1.73260i	0.499524	+	0.866300i	$0.333508\pi$
$229$			26.2190i			1.73260i	−0.499524	+	0.866300i	$0.666492\pi$
$230$	−3.77082	−	3.27880i	−0.248641	−	0.216198i
$231$	5.12901	−	3.32671i	0.337464	−	0.218881i
$232$	−5.32107	−	2.26115i	−0.349346	−	0.148452i
$233$	2.18872	+	6.01346i	0.143388	+	0.393955i	0.990510	−	0.137444i	$-0.0438888\pi$
$233$	2.18872	+	6.01346i	0.143388	+	0.393955i	−0.847122	+	0.531399i	$0.821667\pi$
$234$	11.5732	+	5.41446i	0.756565	+	0.353954i
$235$	2.07866	+	3.60034i	0.135597	+	0.234860i
$236$	−1.02635	+	29.1700i	−0.0668099	+	1.89881i
$237$	3.32065	−	26.9189i	0.215699	−	1.74857i
$238$	−41.8429	−	16.0683i	−2.71227	−	1.04155i
$239$	1.28049	−	2.21787i	0.0828281	−	0.143462i	−0.821636	−	0.570013i	$-0.806938\pi$
$239$	1.28049	−	2.21787i	0.0828281	−	0.143462i	0.904464	+	0.426551i	$0.140271\pi$
$240$	3.66528	−	9.51729i	0.236593	−	0.614338i
$241$	7.18930	−	6.03254i	0.463104	−	0.388590i	−0.381168	−	0.924506i	$-0.624478\pi$
$241$	7.18930	−	6.03254i	0.463104	−	0.388590i	0.844271	+	0.535916i	$0.180034\pi$
$242$	−2.80630	+	14.4270i	−0.180396	+	0.927402i
$243$	−15.0458	−	4.07707i	−0.965192	−	0.261544i
$244$	−13.0716	−	2.78207i	−0.836826	−	0.178104i
$245$	−3.45366	+	19.5867i	−0.220646	+	1.25135i
$246$	4.77992	−	4.29783i	0.304756	−	0.274020i
$247$	12.5208	−	3.94413i	0.796677	−	0.250959i
$248$	0.971069	−	18.3897i	0.0616630	−	1.16775i
$249$	−2.67875	+	5.25002i	−0.169759	+	0.332707i
$250$	−15.4191	+	5.30695i	−0.975191	+	0.335641i
$251$	−6.57104	+	18.0538i	−0.414760	+	1.13954i	0.539870	+	0.841749i	$0.318474\pi$
$251$	−6.57104	+	18.0538i	−0.414760	+	1.13954i	−0.954630	+	0.297795i	$0.903749\pi$
$252$	−26.3754	+	6.53711i	−1.66149	+	0.411799i
$253$	1.20244	+	1.43302i	0.0755970	+	0.0900930i
$254$	−0.319520	+	18.1678i	−0.0200485	+	1.13995i
$255$	13.0564	−	12.1615i	0.817625	−	0.761585i
$256$	13.5777	−	8.46437i	0.848607	−	0.529023i
$257$	−26.8702	+	4.73795i	−1.67612	+	0.295545i	−0.929257	−	0.369434i	$-0.879552\pi$
$257$	−26.8702	+	4.73795i	−1.67612	+	0.295545i	−0.746862	+	0.664979i	$0.768441\pi$
$258$	0.875240	−	0.185401i	0.0544901	−	0.0115426i
$259$	−11.5970	−	20.0866i	−0.720604	−	1.24812i
$260$	−3.32361	+	8.21998i	−0.206122	+	0.509782i
$261$	−5.94845	−	1.49025i	−0.368200	−	0.0922442i
$262$	−5.76787	−	7.12465i	−0.356340	−	0.440162i
$263$	−6.72819	−	5.64563i	−0.414878	−	0.348124i	0.411332	−	0.911485i	$-0.365064\pi$
$263$	−6.72819	−	5.64563i	−0.414878	−	0.348124i	−0.826211	+	0.563361i	$0.809508\pi$
$264$	−1.91217	+	3.30465i	−0.117686	+	0.203387i
$265$	9.78461			0.601064
$266$	−15.4182	+	23.2743i	−0.945353	+	1.42704i
$267$	−26.2613	−	8.04510i	−1.60717	−	0.492352i
$268$	−14.2998	+	4.64213i	−0.873502	+	0.283563i
$269$	0.784327	+	0.658129i	0.0478213	+	0.0401268i	0.666385	−	0.745608i	$-0.267841\pi$
$269$	0.784327	+	0.658129i	0.0478213	+	0.0401268i	−0.618564	+	0.785735i	$0.712285\pi$
$270$	2.26836	−	10.5768i	0.138048	−	0.643685i
$271$	5.71464	+	15.7008i	0.347140	+	0.953759i	0.983266	+	0.182174i	$0.0583134\pi$
$271$	5.71464	+	15.7008i	0.347140	+	0.953759i	−0.636127	+	0.771585i	$0.719464\pi$
$272$	27.8409	−	2.91132i	1.68810	−	0.176525i
$273$	23.0214	−	5.30122i	1.39332	−	0.320845i
$274$	7.27289	−	4.03017i	0.439372	−	0.243472i
$275$	2.17439	−	0.383404i	0.131121	−	0.0231201i
$276$	−2.97337	−	7.76511i	−0.178976	−	0.467405i
$277$	−8.62052	−	4.97706i	−0.517957	−	0.299043i	0.218141	−	0.975917i	$-0.430001\pi$
$277$	−8.62052	−	4.97706i	−0.517957	−	0.299043i	−0.736098	+	0.676875i	$0.763334\pi$
$278$	22.8173	+	0.401291i	1.36849	+	0.0240678i
$279$	−2.01976	−	19.4277i	−0.120920	−	1.16311i
$280$	−5.50596	−	18.0347i	−0.329044	−	1.07778i
$281$	−2.58049	+	7.08984i	−0.153939	+	0.422945i	−0.992558	−	0.121775i	$-0.961141\pi$
$281$	−2.58049	+	7.08984i	−0.153939	+	0.422945i	0.838619	+	0.544719i	$0.183364\pi$
$282$	0.236611	+	6.91371i	0.0140900	+	0.411705i
$283$	−0.781735	+	4.43344i	−0.0464693	+	0.263540i	−0.999187	−	0.0403165i	$-0.987163\pi$
$283$	−0.781735	+	4.43344i	−0.0464693	+	0.263540i	0.952718	+	0.303857i	$0.0982745\pi$
$284$	−5.54471	−	10.4347i	−0.329018	−	0.619188i
$285$	−5.63271	−	9.58061i	−0.333653	−	0.567506i
$286$	1.70993	−	2.84495i	0.101110	−	0.168225i
$287$	2.06377	−	11.7042i	0.121821	−	0.690880i
$288$	12.8277	−	11.1108i	0.755882	−	0.654708i
$289$	30.0460	+	10.9359i	1.76741	+	0.643286i
$290$	0.812519	−	4.17710i	0.0477127	−	0.245288i
$291$	−1.69918	−	4.00932i	−0.0996079	−	0.235030i
$292$	−1.41904	+	2.26960i	−0.0830429	+	0.132818i
$293$	10.7771	−	18.6665i	0.629606	−	1.09051i	−0.358025	−	0.933712i	$-0.616550\pi$
$293$	10.7771	−	18.6665i	0.629606	−	1.09051i	0.987631	−	0.156797i	$-0.0501169\pi$
$294$	−20.3934	+	26.0650i	−1.18937	+	1.52014i
$295$	−21.1568	+	3.73052i	−1.23180	+	0.217199i
$296$	12.1453	+	7.89409i	0.705931	+	0.458835i
$297$	−1.45765	+	3.77816i	−0.0845812	+	0.219231i
$298$	−2.35015	−	14.8509i	−0.136140	−	0.860292i
$299$	2.47239	+	6.79284i	0.142982	+	0.392840i
$300$	−9.69191	−	1.54328i	−0.559563	−	0.0891013i
$301$	1.06327	−	1.26715i	0.0612858	−	0.0730376i
$302$	0.102381	−	0.117744i	0.00589134	−	0.00677540i
$303$	−5.08668	+	16.6043i	−0.292222	+	0.953890i
$304$	1.98751	−	17.3219i	0.113992	−	0.993482i
$305$		−	9.83657i		−	0.563240i
$306$	28.6887	−	7.64835i	1.64002	−	0.437227i
$307$	9.91892	+	8.32296i	0.566103	+	0.475017i	0.880350	−	0.474325i	$-0.157308\pi$
$307$	9.91892	+	8.32296i	0.566103	+	0.475017i	−0.314247	+	0.949341i	$0.601752\pi$
$308$	0.980598	+	6.99072i	0.0558748	+	0.398333i
$309$	29.8600	−	1.54800i	1.69868	−	0.0880624i
$310$	13.3876	−	2.11857i	0.760363	−	0.120327i
$311$	15.7772	+	27.3270i	0.894644	+	1.54957i	0.834244	+	0.551395i	$0.185904\pi$
$311$	15.7772	+	27.3270i	0.894644	+	1.54957i	0.0604003	+	0.998174i	$0.480762\pi$
$312$	−11.3112	+	9.47269i	−0.640368	+	0.536286i
$313$	3.25294	+	18.4484i	0.183867	+	1.04276i	0.927402	+	0.374066i	$0.122037\pi$
$313$	3.25294	+	18.4484i	0.183867	+	1.04276i	−0.743535	+	0.668697i	$0.766852\pi$
$314$	−6.32172	+	16.4621i	−0.356755	+	0.929012i
$315$	−8.74727	−	17.9861i	−0.492853	−	1.01340i
$316$	26.5555	+	16.6035i	1.49387	+	0.934019i
$317$	3.02944	−	2.54200i	0.170150	−	0.142773i	−0.553736	−	0.832692i	$-0.686798\pi$
$317$	3.02944	−	2.54200i	0.170150	−	0.142773i	0.723886	+	0.689919i	$0.242354\pi$
$318$	14.3704	+	7.65373i	0.805853	+	0.429200i
$319$	−0.544857	+	1.49698i	−0.0305062	+	0.0838150i
$320$	8.17387	+	8.47773i	0.456933	+	0.473919i
$321$	−9.42831	+	18.4783i	−0.526237	+	1.03136i
$322$	−13.1767	−	7.91973i	−0.734308	−	0.441349i
$323$	16.3968	−	25.7227i	0.912341	−	1.43125i
$324$	11.6049	−	13.7596i	0.644717	−	0.764421i
$325$	8.40244	+	1.48158i	0.466083	+	0.0821831i
$326$	3.73484	−	1.28546i	0.206854	−	0.0711949i
$327$	−13.7066	−	10.3408i	−0.757978	−	0.571849i
$328$	2.16729	+	7.09893i	0.119668	+	0.391973i
$329$	8.22148	+	9.79797i	0.453265	+	0.540180i
$330$	−2.67200	−	0.870244i	−0.147089	−	0.0479054i
$331$	10.7723	−	18.6581i	0.592098	−	1.02554i	−0.401851	−	0.915705i	$-0.631633\pi$
$331$	10.7723	−	18.6581i	0.592098	−	1.02554i	0.993949	−	0.109839i	$-0.0350336\pi$
$332$	−4.18861	−	5.36410i	−0.229880	−	0.294393i
$333$	14.0287	+	6.26495i	0.768766	+	0.343317i
$334$	8.98585	+	16.2159i	0.491684	+	0.887297i
$335$	−5.53288	−	9.58322i	−0.302293	−	0.523587i
$336$	6.02069	−	30.7941i	0.328456	−	1.67996i
$337$	−27.7675	+	10.1066i	−1.51259	+	0.550539i	−0.959286	−	0.282437i	$-0.908857\pi$
$337$	−27.7675	+	10.1066i	−1.51259	+	0.550539i	−0.553308	+	0.832977i	$0.686635\pi$
$338$	−4.31999	+	3.49732i	−0.234977	+	0.190229i
$339$	−6.73442	−	10.3829i	−0.365764	−	0.563923i
$340$	6.36160	+	19.5966i	0.345006	+	1.06278i
$341$	−5.07416			−0.274781
$342$	−0.778461	−	18.4769i	−0.0420944	−	0.999114i
$343$			29.4874i			1.59217i
$344$	−0.232788	+	1.00650i	−0.0125511	+	0.0542666i
$345$	5.13455	−	3.33029i	0.276435	−	0.179297i
$346$	18.0706	−	14.6294i	0.971483	−	0.786479i
$347$	1.35785	+	3.73066i	0.0728932	+	0.200272i	0.970789	−	0.239936i	$-0.0771266\pi$
$347$	1.35785	+	3.73066i	0.0728932	+	0.200272i	−0.897895	+	0.440209i	$0.854904\pi$
$348$	4.46075	−	5.49924i	0.239121	−	0.294790i
$349$	−9.78332	+	5.64840i	−0.523689	+	0.302352i	−0.738443	−	0.674316i	$-0.764438\pi$
$349$	−9.78332	+	5.64840i	−0.523689	+	0.302352i	0.214754	+	0.976668i	$0.431105\pi$
$350$	−15.8714	+	8.79491i	−0.848361	+	0.470108i
$351$	−10.2865	+	11.7929i	−0.549052	+	0.629457i
$352$	−2.52631	−	3.61302i	−0.134653	−	0.192574i
$353$	−15.3609	−	8.86865i	−0.817581	−	0.472030i	0.0320008	−	0.999488i	$-0.489812\pi$
$353$	−15.3609	−	8.86865i	−0.817581	−	0.472030i	−0.849581	+	0.527457i	$0.823145\pi$
$354$	−33.9906	−	11.0704i	−1.80658	−	0.588385i
$355$	6.66243	−	5.59045i	0.353605	−	0.296710i
$356$	21.2277	−	23.5632i	1.12507	−	1.24885i
$357$	33.0617	−	43.8229i	1.74981	−	2.31936i
$358$	−5.63905	−	16.3840i	−0.298033	−	0.865923i
$359$	−4.54098	+	25.7532i	−0.239664	+	1.35920i	0.592902	+	0.805274i	$0.297982\pi$
$359$	−4.54098	+	25.7532i	−0.239664	+	1.35920i	−0.832566	+	0.553926i	$0.813129\pi$
$360$	9.96411	+	7.53234i	0.525154	+	0.396989i
$361$	−13.4279	−	13.4422i	−0.706731	−	0.707482i
$362$	3.05686	+	1.83730i	0.160665	+	0.0965663i
$363$	−16.0340	−	8.18113i	−0.841566	−	0.429398i
$364$	−5.67857	+	26.6809i	−0.297638	+	1.39846i
$365$	−1.85131	−	0.673823i	−0.0969021	−	0.0352695i
$366$	7.69438	−	14.4467i	0.402192	−	0.755143i
$367$	−1.06048	−	1.26384i	−0.0553568	−	0.0659717i	0.737656	−	0.675177i	$-0.235933\pi$
$367$	−1.06048	−	1.26384i	−0.0553568	−	0.0659717i	−0.793012	+	0.609206i	$0.791488\pi$
$368$	9.57750	+	0.674808i	0.499262	+	0.0351768i
$369$	3.44315	+	7.07977i	0.179243	+	0.368558i
$370$	−3.82209	+	9.95295i	−0.198701	+	0.517429i
$371$	29.6459	−	5.22737i	1.53914	−	0.271391i
$372$	21.3192	+	7.36056i	1.10535	+	0.381627i
$373$	29.8409	−	17.2287i	1.54510	−	0.892066i	0.546599	−	0.837394i	$-0.315922\pi$
$373$	29.8409	−	17.2287i	1.54510	−	0.892066i	0.998504	−	0.0546719i	$-0.0174113\pi$
$374$	−1.20559	−	7.61830i	−0.0623395	−	0.393933i
$375$	−1.03398	−	19.9449i	−0.0533946	−	1.02995i
$376$	−7.35170	−	3.12405i	−0.379135	−	0.161110i
$377$	−3.95701	+	4.71578i	−0.203796	+	0.242875i
$378$	1.22218	−	33.2580i	0.0628624	−	1.71061i
$379$	1.76237			0.0905271			0.0452636	−	0.998975i	$-0.485587\pi$
$379$	1.76237			0.0905271			0.0452636	+	0.998975i	$0.485587\pi$
$380$	12.7746	−	1.22323i	0.655324	−	0.0627503i
$381$	−21.2783	−	6.51856i	−1.09012	−	0.333956i
$382$	−3.76824	−	3.27656i	−0.192800	−	0.167643i
$383$	12.3911	+	10.3974i	0.633156	+	0.531281i	0.901908	−	0.431928i	$-0.142167\pi$
$383$	12.3911	+	10.3974i	0.633156	+	0.531281i	−0.268752	+	0.963210i	$0.586611\pi$
$384$	5.37332	+	18.8448i	0.274206	+	0.961671i
$385$	−4.88238	+	1.77704i	−0.248829	+	0.0905665i
$386$	0.818662	+	5.17325i	0.0416688	+	0.263312i
$387$	−0.0776683	+	1.09298i	−0.00394810	+	0.0555591i
$388$	5.02506	+	0.176808i	0.255109	+	0.00897605i
$389$	−4.78738	−	27.1506i	−0.242730	−	1.37659i	−0.825706	−	0.564101i	$-0.809223\pi$
$389$	−4.78738	−	27.1506i	−0.242730	−	1.37659i	0.582976	−	0.812489i	$-0.301888\pi$
$390$	−8.55249	−	6.69154i	−0.433072	−	0.338839i
$391$	14.5473	+	8.39889i	0.735688	+	0.424750i
$392$	−17.3356	−	34.0564i	−0.875581	−	1.72011i
$393$	10.3369	−	4.38087i	0.521427	−	0.220986i
$394$	−1.94321	+	9.98991i	−0.0978976	+	0.503285i
$395$	−7.88408	+	21.6613i	−0.396691	+	1.08990i
$396$	−3.24358	−	3.36821i	−0.162996	−	0.169259i
$397$	35.2581	+	6.21695i	1.76955	+	0.312020i	0.961029	−	0.276446i	$-0.0891567\pi$
$397$	35.2581	+	6.21695i	1.76955	+	0.312020i	0.808522	+	0.588466i	$0.200268\pi$
$398$	25.1025	+	15.0876i	1.25828	+	0.756275i
$399$	−22.1846	−	26.0186i	−1.11062	−	1.30256i
$400$	6.34187	−	9.39151i	0.317094	−	0.469575i
$401$	−16.0877	−	2.83669i	−0.803379	−	0.141657i	−0.243143	−	0.969990i	$-0.578178\pi$
$401$	−16.0877	−	2.83669i	−0.803379	−	0.141657i	−0.560236	+	0.828333i	$0.689290\pi$
$402$	−0.629800	−	18.4026i	−0.0314116	−	0.917838i
$403$	−18.4255	−	6.70632i	−0.917837	−	0.334065i
$404$	−14.8983	−	13.4217i	−0.741220	−	0.667752i
$405$	11.6836	+	6.24618i	0.580564	+	0.310375i
$406$	0.230217	−	13.0901i	0.0114255	−	0.649649i
$407$	1.99565	−	3.45656i	0.0989205	−	0.171335i
$408$	−5.98576	+	33.7573i	−0.296339	+	1.67123i
$409$	2.50225	+	14.1909i	0.123728	+	0.701697i	0.982055	+	0.188594i	$0.0603930\pi$
$409$	2.50225	+	14.1909i	0.123728	+	0.701697i	−0.858327	+	0.513103i	$0.828496\pi$
$410$	−4.77847	+	2.64792i	−0.235992	+	0.130772i
$411$	2.28521	+	9.92390i	0.112721	+	0.489510i
$412$	−12.9420	+	32.0082i	−0.637607	+	1.57693i
$413$	−62.1089	+	22.6058i	−3.05618	+	1.11236i
$414$	10.1460	−	0.874771i	0.498650	−	0.0429927i
$415$	3.21985	−	3.83727i	0.158056	−	0.188364i
$416$	−4.39843	−	16.4586i	−0.215651	−	0.806950i
$417$	−8.18677	+	26.7238i	−0.400908	+	1.30867i
$418$	−4.79513	−	0.295196i	−0.234537	−	0.0144385i
$419$		−	33.5961i		−	1.64128i	−0.571447	−	0.820639i	$-0.693618\pi$
$419$		−	33.5961i		−	1.64128i	0.571447	−	0.820639i	$-0.306382\pi$
$420$	23.0912	−	0.383920i	1.12674	−	0.0187334i
$421$	−17.1058	+	20.3858i	−0.833684	+	0.993545i	0.166289	+	0.986077i	$0.446822\pi$
$421$	−17.1058	+	20.3858i	−0.833684	+	0.993545i	−0.999972	+	0.00746828i	$0.997623\pi$
$422$	−21.7024	+	17.5695i	−1.05646	+	0.855272i
$423$	−8.21850	−	2.05896i	−0.399597	−	0.100110i
$424$	−15.0191	+	11.3084i	−0.729391	+	0.549182i
$425$	17.1700	−	9.91311i	0.832868	−	0.480857i
$426$	14.1579	−	2.99906i	0.685954	−	0.145305i
$427$	−5.25513	−	29.8033i	−0.254314	−	1.44228i
$428$	−14.7425	−	18.8798i	−0.712605	−	0.912590i
$429$	2.77082	+	2.97471i	0.133777	+	0.143620i
$430$	−0.760246	−	0.0133706i	−0.0366623	−	0.000644786i
$431$	−19.5027	+	16.3647i	−0.939410	+	0.788259i	−0.977483	−	0.211016i	$-0.932323\pi$
$431$	−19.5027	+	16.3647i	−0.939410	+	0.788259i	0.0380726	+	0.999275i	$0.487878\pi$
$432$	8.74209	+	18.8567i	0.420604	+	0.907244i
$433$	6.48946	+	2.36197i	0.311863	+	0.113509i	0.493210	−	0.869910i	$-0.335823\pi$
$433$	6.48946	+	2.36197i	0.311863	+	0.113509i	−0.181347	+	0.983419i	$0.558046\pi$
$434$	39.4305	−	13.5712i	1.89272	−	0.651437i
$435$	4.64239	+	2.36871i	0.222585	+	0.113571i
$436$	17.5078	−	9.30314i	0.838473	−	0.445540i
$437$	7.07055	−	7.71204i	0.338230	−	0.368917i
$438$	−2.19190	−	2.43776i	−0.104733	−	0.116481i
$439$	−30.5507	−	5.38691i	−1.45810	−	0.257103i	−0.612312	−	0.790616i	$-0.709760\pi$
$439$	−30.5507	−	5.38691i	−1.45810	−	0.257103i	−0.845792	+	0.533513i	$0.820872\pi$
$440$	2.21394	−	2.37228i	0.105545	−	0.113094i
$441$	−23.7876	−	32.8186i	−1.13274	−	1.56279i
$442$	5.69103	−	29.2572i	0.270695	−	1.39162i
$443$	−16.4763	−	19.6356i	−0.782810	−	0.932917i	0.216246	−	0.976339i	$-0.430619\pi$
$443$	−16.4763	−	19.6356i	−0.782810	−	0.932917i	−0.999057	+	0.0434217i	$0.986174\pi$
$444$	−13.3988	+	11.6279i	−0.635880	+	0.551838i
$445$	20.2157	+	11.6715i	0.958316	+	0.553284i
$446$	−4.57461	+	11.9126i	−0.216614	+	0.564076i
$447$	18.2764	+	2.25453i	0.864445	+	0.106636i
$448$	29.2948	+	21.3194i	1.38405	+	1.00725i
$449$	3.93240	−	2.27037i	0.185581	−	0.107145i	−0.404331	−	0.914613i	$-0.632496\pi$
$449$	3.93240	−	2.27037i	0.185581	−	0.107145i	0.589912	+	0.807467i	$0.299162\pi$
$450$	5.09346	−	10.8871i	0.240108	−	0.513223i
$451$	1.92183	−	0.699489i	0.0904954	−	0.0329376i
$452$	14.1517	−	1.98508i	0.665639	−	0.0933701i
$453$	0.103988	+	0.160326i	0.00488580	+	0.00753278i
$454$	−4.71618	+	5.42390i	−0.221341	+	0.254556i
$455$	−20.0777			−0.941257
$456$	19.7186	+	8.19606i	0.923410	+	0.383816i
$457$	11.4634			0.536234			0.268117	−	0.963386i	$-0.413599\pi$
$457$	11.4634			0.536234			0.268117	+	0.963386i	$0.413599\pi$
$458$	24.3299	−	27.9809i	1.13686	−	1.30746i
$459$	−0.696197	+	36.3569i	−0.0324957	+	1.69699i
$460$	0.981656	+	6.99825i	0.0457699	+	0.326295i
$461$	−28.7645	+	10.4694i	−1.33970	+	0.487610i	−0.909717	−	0.415228i	$-0.863702\pi$
$461$	−28.7645	+	10.4694i	−1.33970	+	0.487610i	−0.429981	+	0.902838i	$0.641480\pi$
$462$	−8.56069	−	1.20921i	−0.398279	−	0.0562574i
$463$	−26.6080	+	15.3622i	−1.23658	+	0.713940i	−0.968394	−	0.249427i	$-0.919758\pi$
$463$	−26.6080	+	15.3622i	−1.23658	+	0.713940i	−0.268186	+	0.963367i	$0.586424\pi$
$464$	3.58041	+	7.35078i	0.166216	+	0.341251i
$465$	−2.03238	+	16.4755i	−0.0942493	+	0.764034i
$466$	3.24438	−	8.44857i	0.150293	−	0.391372i
$467$	17.5349	+	10.1238i	0.811419	+	0.468473i	0.847448	−	0.530878i	$-0.178138\pi$
$467$	17.5349	+	10.1238i	0.811419	+	0.468473i	−0.0360293	+	0.999351i	$0.511471\pi$
$468$	−7.32658	−	16.5176i	−0.338671	−	0.763529i
$469$	−21.8836	−	26.0798i	−1.01049	−	1.20425i
$470$	1.12259	−	5.77116i	0.0517813	−	0.266204i
$471$	−17.2411	−	13.0074i	−0.794429	−	0.599349i
$472$	28.1636	−	30.1778i	1.29634	−	1.38905i
$473$	0.280327	+	0.0494291i	0.0128894	+	0.00227275i
$474$	−28.5231	+	25.6464i	−1.31011	+	1.17798i
$475$	−3.71030	−	11.7785i	−0.170240	−	0.540433i
$476$	29.7441	+	55.9761i	1.36332	+	2.56566i
$477$	−13.8682	+	14.3285i	−0.634981	+	0.656058i
$478$	−3.42461	+	1.17868i	−0.156638	+	0.0539117i
$479$	25.6004	+	9.31777i	1.16971	+	0.425740i	0.852557	−	0.522634i	$-0.175051\pi$
$479$	25.6004	+	9.31777i	1.16971	+	0.425740i	0.317154	+	0.948374i	$0.397273\pi$
$480$	−12.7431	+	6.75564i	−0.581642	+	0.308351i
$481$	11.8150	−	9.91400i	0.538720	−	0.452040i
$482$	−13.2703	−	0.233387i	−0.604446	−	0.0106305i
$483$	13.7777	−	12.8334i	0.626907	−	0.583939i
$484$	16.3824	−	12.7923i	0.744653	−	0.581470i
$485$	0.642648	+	3.64464i	0.0291811	+	0.165495i
$486$	12.2736	+	18.3128i	0.556741	+	0.830686i
$487$	8.82502	−	5.09513i	0.399900	−	0.230882i	−0.286541	−	0.958068i	$-0.592505\pi$
$487$	8.82502	−	5.09513i	0.399900	−	0.230882i	0.686441	+	0.727186i	$0.259172\pi$
$488$	11.3684	+	15.0988i	0.514624	+	0.683492i
$489$	0.250452	+	4.83109i	0.0113258	+	0.218469i
$490$	21.8612	−	17.6980i	0.987586	−	0.799516i
$491$	−13.2079	+	15.7406i	−0.596064	+	0.710361i	−0.976759	−	0.214339i	$-0.931240\pi$
$491$	−13.2079	+	15.7406i	−0.596064	+	0.710361i	0.380695	+	0.924700i	$0.375685\pi$
$492$	−9.08929	+	0.151121i	−0.409777	+	0.00681305i
$493$			14.3049i			0.644261i
$494$	−17.0221	−	7.40945i	−0.765859	−	0.333367i
$495$	1.92780	−	2.85113i	0.0866482	−	0.128149i
$496$	−18.1010	+	18.7244i	−0.812760	+	0.840748i
$497$	17.1995	−	20.4976i	0.771503	−	0.919442i
$498$	7.73051	−	3.11707i	0.346413	−	0.139679i
$499$	−16.4401	+	5.98371i	−0.735960	+	0.267868i	−0.682686	−	0.730712i	$-0.739188\pi$
$499$	−16.4401	+	5.98371i	−0.735960	+	0.267868i	−0.0532747	+	0.998580i	$0.516966\pi$
$500$	21.3798	+	8.64458i	0.956135	+	0.386598i
$501$	−22.1267	+	5.09521i	−0.988550	+	0.227637i
$502$	23.7656	−	13.1694i	1.06071	−	0.587778i
$503$	−7.31597	−	41.4909i	−0.326203	−	1.84999i	−0.501082	−	0.865400i	$-0.667064\pi$
$503$	−7.31597	−	41.4909i	−0.326203	−	1.84999i	0.174879	−	0.984590i	$-0.444047\pi$
$504$	34.2138	+	17.4986i	1.52401	+	0.779450i
$505$	7.37957	−	12.7818i	0.328387	−	0.568782i
$506$	0.0465202	−	2.64512i	0.00206807	−	0.117590i
$507$	−2.65632	−	6.26772i	−0.117971	−	0.278359i
$508$	17.1998	−	19.0921i	0.763116	−	0.847077i
$509$	5.18539	+	1.88733i	0.229838	+	0.0836544i	0.454372	−	0.890812i	$-0.349864\pi$
$509$	5.18539	+	1.88733i	0.229838	+	0.0836544i	−0.224534	+	0.974466i	$0.572086\pi$
$510$	−25.2191	+	0.863083i	−1.11672	+	0.0382179i
$511$	−5.96918	−	1.05253i	−0.264061	−	0.0465611i
$512$	−22.3446	−	3.56627i	−0.987502	−	0.157608i
$513$	22.0133	+	5.33055i	0.971911	+	0.235350i
$514$	33.0724	+	19.8779i	1.45876	+	0.876775i
$515$	−25.0257	−	4.41271i	−1.10277	−	0.194447i
$516$	−1.10610	−	0.614318i	−0.0486932	−	0.0270438i
$517$	−0.752785	+	2.06826i	−0.0331075	+	0.0909620i
$518$	−6.26304	+	32.1978i	−0.275182	+	1.41469i
$519$	11.1114	+	26.2180i	0.487737	+	1.15084i
$520$	11.1747	−	5.68820i	0.490042	−	0.249444i
$521$	−31.8798	−	18.4058i	−1.39668	−	0.806373i	−0.402635	−	0.915360i	$-0.631906\pi$
$521$	−31.8798	−	18.4058i	−1.39668	−	0.806373i	−0.994043	+	0.108988i	$0.965239\pi$
$522$	4.96530	+	7.11025i	0.217325	+	0.311207i
$523$	−0.151153	−	0.857230i	−0.00660945	−	0.0374840i	0.981325	−	0.192359i	$-0.0616137\pi$
$523$	−0.151153	−	0.857230i	−0.00660945	−	0.0374840i	−0.987934	+	0.154875i	$0.950503\pi$
$524$	−0.455849	+	12.9557i	−0.0199138	+	0.565972i
$525$	−4.98694	−	21.6566i	−0.217648	−	0.945171i
$526$	1.94147	+	12.2684i	0.0846519	+	0.534928i
$527$	−42.8158	+	15.5837i	−1.86509	+	0.678836i
$528$	5.10721	−	1.75231i	0.222263	−	0.0762597i
$529$	−13.2055	−	11.0807i	−0.574151	−	0.481769i
$530$	−10.4421	−	9.07961i	−0.453576	−	0.394393i
$531$	24.5236	−	36.2694i	1.06423	−	1.57396i
$532$	38.0517	−	10.5310i	1.64975	−	0.456575i
$533$	7.90309			0.342321
$534$	20.5606	+	32.9549i	0.889744	+	1.42610i
$535$	11.3328	−	13.5059i	0.489959	−	0.583910i
$536$	19.5684	+	8.31545i	0.845227	+	0.359173i
$537$	21.1931	−	1.09869i	0.914548	−	0.0474118i
$538$	−0.226323	−	1.43017i	−0.00975747	−	0.0616590i
$539$	−9.11898	+	5.26485i	−0.392782	+	0.226773i
$540$	−12.2355	+	9.18264i	−0.526534	+	0.395158i
$541$	−10.2859	+	1.81368i	−0.442225	+	0.0779763i	−0.390327	−	0.920676i	$-0.627638\pi$
$541$	−10.2859	+	1.81368i	−0.442225	+	0.0779763i	−0.0518980	+	0.998652i	$0.516527\pi$
$542$	8.47093	−	22.0588i	0.363857	−	0.947507i
$543$	−3.19629	+	2.97722i	−0.137166	+	0.127765i
$544$	−32.4133	−	22.7279i	−1.38971	−	0.974451i
$545$	9.37987	+	11.1785i	0.401790	+	0.478834i
$546$	−29.4877	−	15.7052i	−1.26196	−	0.672121i
$547$	−6.24777	−	2.27400i	−0.267135	−	0.0972293i	0.204980	−	0.978766i	$-0.434287\pi$
$547$	−6.24777	−	2.27400i	−0.267135	−	0.0972293i	−0.472115	+	0.881537i	$0.656509\pi$
$548$	−11.5014	−	2.44788i	−0.491316	−	0.104568i
$549$	14.4046	+	13.9418i	0.614774	+	0.595023i
$550$	−2.67628	−	1.60855i	−0.114117	−	0.0685890i
$551$	8.69829	+	1.93079i	0.370560	+	0.0822543i
$552$	−4.03245	+	11.0460i	−0.171633	+	0.470151i
$553$	−12.3151	+	69.8426i	−0.523693	+	2.97001i
$554$	4.58135	+	13.3109i	0.194643	+	0.565526i
$555$	−10.4239	−	7.86422i	−0.442471	−	0.333818i
$556$	−23.9782	−	21.6015i	−1.01690	−	0.916108i
$557$	5.48953	−	4.60626i	0.232599	−	0.195173i	−0.519037	−	0.854752i	$-0.673709\pi$
$557$	5.48953	−	4.60626i	0.232599	−	0.195173i	0.751636	+	0.659578i	$0.229265\pi$
$558$	−15.8724	+	22.6074i	−0.671933	+	0.957049i
$559$	0.952602	+	0.549985i	0.0402908	+	0.0232619i
$560$	−10.8594	+	24.3559i	−0.458892	+	1.02922i
$561$	9.37552	+	1.15654i	0.395835	+	0.0488292i
$562$	9.33290	−	5.17170i	0.393685	−	0.218155i
$563$	−17.6840	+	10.2099i	−0.745292	+	0.430294i	−0.823990	−	0.566604i	$-0.808257\pi$
$563$	−17.6840	+	10.2099i	−0.745292	+	0.430294i	0.0786984	+	0.996898i	$0.474924\pi$
$564$	6.16305	−	7.59786i	0.259511	−	0.319927i
$565$	3.59736	+	9.88366i	0.151342	+	0.415809i
$566$	4.94827	−	4.00595i	0.207991	−	0.168382i
$567$	38.7366	+	12.6831i	1.62679	+	0.532638i
$568$	−3.76559	+	16.2811i	−0.158001	+	0.683142i
$569$			21.4277i			0.898297i	0.893457	+	0.449148i	$0.148273\pi$
$569$			21.4277i			0.898297i	−0.893457	+	0.449148i	$0.851727\pi$
$570$	−2.87910	+	15.4513i	−0.120592	+	0.647183i
$571$	17.1460			0.717539			0.358769	−	0.933426i	$-0.383196\pi$
$571$	17.1460			0.717539			0.358769	+	0.933426i	$0.383196\pi$
$572$	−4.46479	+	1.44940i	−0.186682	+	0.0606023i
$573$	5.13104	−	3.32802i	0.214352	−	0.139030i
$574$	−13.0634	+	10.5757i	−0.545255	+	0.441420i
$575$	6.39012	−	2.32581i	0.266487	−	0.0969932i
$576$	−24.0000	−	0.0461102i	−0.999998	−	0.00192126i
$577$	−12.7105	−	22.0152i	−0.529143	−	0.916503i	−0.999422	−	0.0339852i	$-0.989180\pi$
$577$	−12.7105	−	22.0152i	−0.529143	−	0.916503i	0.470279	−	0.882518i	$-0.344153\pi$
$578$	−21.9171	−	39.5519i	−0.911633	−	1.64514i
$579$	−6.36650	−	0.785356i	−0.264583	−	0.0326383i
$580$	−4.74325	+	3.70382i	−0.196953	+	0.153793i
$581$	7.70562	−	13.3465i	0.319683	−	0.553707i
$582$	−1.90707	+	5.85549i	−0.0790508	+	0.242718i
$583$	3.32979	+	3.96829i	0.137906	+	0.164350i
$584$	3.62047	−	1.10532i	0.149816	−	0.0457384i
$585$	10.7685	−	7.80523i	0.445223	−	0.322706i
$586$	−28.8229	+	9.92025i	−1.19066	+	0.409802i
$587$	2.07858	+	0.366509i	0.0857920	+	0.0151274i	0.216379	−	0.976309i	$-0.430575\pi$
$587$	2.07858	+	0.366509i	0.0857920	+	0.0151274i	−0.130587	+	0.991437i	$0.541686\pi$
$588$	45.9508	−	8.89242i	1.89498	−	0.366717i
$589$	3.69685	+	28.1381i	0.152326	+	1.15941i
$590$	26.0402	+	15.6512i	1.07206	+	0.644351i
$591$	−11.1027	−	5.66499i	−0.456703	−	0.233027i
$592$	−5.63613	−	19.6948i	−0.231643	−	0.809450i
$593$	11.0522	−	30.3658i	0.453861	−	1.24697i	−0.476125	−	0.879378i	$-0.657959\pi$
$593$	11.0522	−	30.3658i	0.453861	−	1.24697i	0.929986	−	0.367595i	$-0.119819\pi$
$594$	5.06154	−	2.67943i	0.207677	−	0.109938i
$595$	−35.7400	+	29.9894i	−1.46520	+	1.22945i
$596$	−11.2728	+	18.0297i	−0.461753	+	0.738525i
$597$	−26.2475	+	24.4485i	−1.07424	+	1.00061i
$598$	3.66487	−	9.54356i	0.149868	−	0.390265i
$599$	−5.13441	−	29.1187i	−0.209786	−	1.18976i	−0.889728	−	0.456492i	$-0.849106\pi$
$599$	−5.13441	−	29.1187i	−0.209786	−	1.18976i	0.679941	−	0.733267i	$-0.262005\pi$
$600$	8.91110	+	10.6406i	0.363794	+	0.434400i
$601$	−6.55642	−	11.3561i	−0.267442	−	0.463223i	0.700759	−	0.713398i	$-0.252845\pi$
$601$	−6.55642	−	11.3561i	−0.267442	−	0.463223i	−0.968201	+	0.250176i	$0.919512\pi$
$602$	−2.31057	+	0.365646i	−0.0941719	+	0.0149026i
$603$	21.8756	+	5.48044i	0.890844	+	0.223181i
$604$	−0.218521	+	0.0306522i	−0.00889147	+	0.00124722i
$605$	11.7193	+	9.83368i	0.476458	+	0.399796i
$606$	20.8364	−	12.9999i	0.846421	−	0.528083i
$607$		−	8.94495i		−	0.363064i	−0.983385	−	0.181532i	$-0.941894\pi$
$607$		−	8.94495i		−	0.363064i	0.983385	−	0.181532i	$-0.0581057\pi$
$608$	−18.1949	+	16.6416i	−0.737902	+	0.674907i
$609$	15.3312	+	4.69668i	0.621251	+	0.190319i
$610$	−9.12783	+	10.4976i	−0.369575	+	0.425034i
$611$	−5.46707	+	6.51540i	−0.221174	+	0.263585i
$612$	−37.7138	−	18.4593i	−1.52449	−	0.746174i
$613$	7.25811	+	19.9415i	0.293152	+	0.805429i	0.995601	+	0.0936946i	$0.0298677\pi$
$613$	7.25811	+	19.9415i	0.293152	+	0.805429i	−0.702449	+	0.711734i	$0.747910\pi$
$614$	−2.86217	−	18.0865i	−0.115508	−	0.729912i
$615$	−1.50144	−	6.52024i	−0.0605439	−	0.262921i
$616$	5.44053	−	8.37042i	0.219205	−	0.337254i
$617$	31.6906	−	5.58791i	1.27582	−	0.224961i	0.505614	−	0.862760i	$-0.331266\pi$
$617$	31.6906	−	5.58791i	1.27582	−	0.224961i	0.770203	+	0.637799i	$0.220155\pi$
$618$	−33.3030	−	26.0565i	−1.33964	−	1.04815i
$619$	−11.3746	+	19.7014i	−0.457184	+	0.791866i	−0.998811	−	0.0487529i	$-0.984475\pi$
$619$	−11.3746	+	19.7014i	−0.457184	+	0.791866i	0.541627	+	0.840619i	$0.317809\pi$
$620$	−16.2531	−	10.1620i	−0.652741	−	0.408117i
$621$	−2.40057	+	12.2392i	−0.0963316	+	0.491141i
$622$	8.52059	−	43.8037i	0.341644	−	1.75637i
$623$	67.4859	+	24.5629i	2.70377	+	0.984091i
$624$	20.8614	+	0.386940i	0.835125	+	0.0154900i
$625$	−0.487684	+	2.76579i	−0.0195074	+	0.110632i
$626$	13.6476	−	22.7066i	0.545468	−	0.907539i
$627$	1.96870	−	5.54480i	0.0786222	−	0.221438i
$628$	22.0225	−	11.7021i	0.878795	−	0.466966i
$629$	6.22355	−	35.2955i	0.248149	−	1.40732i
$630$	−7.35508	+	27.3117i	−0.293033	+	1.08813i
$631$	1.86340	−	5.11965i	0.0741808	−	0.203810i	−0.897060	−	0.441908i	$-0.854302\pi$
$631$	1.86340	−	5.11965i	0.0741808	−	0.203810i	0.971241	+	0.238098i	$0.0765239\pi$
$632$	−12.9328	−	42.3614i	−0.514440	−	1.68505i
$633$	−13.3446	−	31.4873i	−0.530400	−	1.25151i
$634$	−5.59186	−	0.0983449i	−0.222081	−	0.00390577i
$635$	16.3798	+	9.45688i	0.650012	+	0.375285i
$636$	−8.23382	−	21.5031i	−0.326492	−	0.852652i
$637$	−40.0715	+	7.06568i	−1.58769	+	0.279952i
$638$	1.97059	−	1.09198i	0.0780166	−	0.0432318i
$639$	−1.25637	+	17.6800i	−0.0497011	+	0.699411i
$640$	−0.856248	−	16.6323i	−0.0338462	−	0.657451i
$641$	−3.10143	−	8.52111i	−0.122499	−	0.336564i	0.863252	−	0.504773i	$-0.168424\pi$
$641$	−3.10143	−	8.52111i	−0.122499	−	0.336564i	−0.985751	+	0.168209i	$0.946202\pi$
$642$	27.2088	−	10.9710i	1.07385	−	0.432992i
$643$	0.680574	+	0.571069i	0.0268392	+	0.0225208i	0.656109	−	0.754667i	$-0.272201\pi$
$643$	0.680574	+	0.571069i	0.0268392	+	0.0225208i	−0.629269	+	0.777187i	$0.716646\pi$
$644$	6.71304	+	20.6792i	0.264531	+	0.814875i
$645$	0.272774	−	0.890406i	0.0107405	−	0.0350597i
$646$	−41.3679	+	12.2359i	−1.62760	+	0.481413i
$647$	−24.7385			−0.972571			−0.486285	−	0.873800i	$-0.661648\pi$
$647$	−24.7385			−0.972571			−0.486285	+	0.873800i	$0.661648\pi$
$648$	−25.1529	+	3.91543i	−0.988100	+	0.153813i
$649$	−8.71283	−	7.31094i	−0.342009	−	0.286979i
$650$	−7.59224	−	9.37817i	−0.297792	−	0.367842i
$651$	2.64414	+	51.0041i	0.103632	+	1.99901i
$652$	−5.17865	−	2.09390i	−0.202812	−	0.0820035i
$653$	1.58553	+	2.74622i	0.0620466	+	0.107468i	0.895380	−	0.445303i	$-0.146904\pi$
$653$	1.58553	+	2.74622i	0.0620466	+	0.107468i	−0.833334	+	0.552771i	$0.813571\pi$
$654$	5.03194	+	23.7547i	0.196764	+	0.928884i
$655$	−9.39667	+	1.65689i	−0.367158	+	0.0647399i
$656$	4.27452	−	9.58710i	0.166892	−	0.374313i
$657$	3.61069	−	1.75601i	0.140867	−	0.0685085i
$658$	0.318072	−	18.0855i	0.0123998	−	0.705046i
$659$	−2.03309	−	2.42294i	−0.0791980	−	0.0943845i	0.724990	−	0.688759i	$-0.241844\pi$
$659$	−2.03309	−	2.42294i	−0.0791980	−	0.0943845i	−0.804188	+	0.594374i	$0.797400\pi$
$660$	2.04401	+	3.40820i	0.0795631	+	0.132664i
$661$	0.186308	−	0.511876i	0.00724653	−	0.0199097i	−0.936017	−	0.351956i	$-0.885517\pi$
$661$	0.186308	−	0.511876i	0.00724653	−	0.0199097i	0.943263	+	0.332046i	$0.107739\pi$
$662$	−28.8099	+	9.91581i	−1.11973	+	0.385389i
$663$	32.5161	+	16.5909i	1.26282	+	0.644338i
$664$	−0.507529	+	9.61137i	−0.0196959	+	0.372993i
$665$	13.4115	+	25.7799i	0.520075	+	0.999703i
$666$	−9.15781	−	19.7038i	−0.354858	−	0.763508i
$667$	−0.851999	+	4.83193i	−0.0329895	+	0.187093i
$668$	5.45789	−	25.6440i	0.211172	−	0.992197i
$669$	−12.4763	−	9.41259i	−0.482361	−	0.363912i
$670$	−2.98806	+	15.3614i	−0.115439	+	0.593463i
$671$	3.98937	−	3.34748i	0.154008	−	0.129228i
$672$	−35.0006	+	27.2765i	−1.35018	+	1.05221i
$673$	14.9014	−	25.8101i	0.574408	−	0.994905i	−0.421697	−	0.906737i	$-0.638565\pi$
$673$	14.9014	−	25.8101i	0.574408	−	0.994905i	0.996106	−	0.0881678i	$-0.0281012\pi$
$674$	39.0118	+	14.9811i	1.50268	+	0.577052i
$675$	11.0937	+	9.67666i	0.426998	+	0.372455i
$676$	7.85562	+	0.276401i	0.302139	+	0.0106308i
$677$	17.9769	+	31.1369i	0.690907	+	1.19669i	0.971541	+	0.236872i	$0.0761222\pi$
$677$	17.9769	+	31.1369i	0.690907	+	1.19669i	−0.280633	+	0.959815i	$0.590545\pi$
$678$	−2.44786	+	17.3298i	−0.0940095	+	0.665549i
$679$	3.89425	+	10.6994i	0.149448	+	0.410604i
$680$	11.3956	−	26.8167i	0.437000	−	1.02837i
$681$	−4.79025	−	7.38546i	−0.183563	−	0.283011i
$682$	5.41514	+	4.70856i	0.207356	+	0.180300i
$683$			18.4184i			0.704761i	0.935857	+	0.352380i	$0.114628\pi$
$683$			18.4184i			0.704761i	−0.935857	+	0.352380i	$0.885372\pi$
$684$	−16.3148	+	20.4408i	−0.623812	+	0.781575i
$685$		−	8.65495i		−	0.330689i
$686$	27.3628	−	31.4689i	1.04472	−	1.20149i
$687$	24.7120	+	38.1002i	0.942821	+	1.45361i
$688$	1.18241	−	0.858115i	0.0450789	−	0.0327153i
$689$	6.84652	+	18.8106i	0.260831	+	0.716629i
$690$	−8.56992	−	1.21051i	−0.326251	−	0.0460834i
$691$	1.20204	+	2.08199i	0.0457276	+	0.0792025i	0.887983	−	0.459876i	$-0.152106\pi$
$691$	1.20204	+	2.08199i	0.0457276	+	0.0792025i	−0.842256	+	0.539078i	$0.818773\pi$
$692$	−32.8602	−	1.15619i	−1.24916	−	0.0439519i
$693$	4.31774	−	9.66842i	0.164018	−	0.367273i
$694$	2.01277	−	5.24137i	0.0764036	−	0.198960i
$695$	11.8771	−	20.5717i	0.450523	−	0.780328i
$696$	−9.86352	+	1.72944i	−0.373876	+	0.0655541i
$697$	14.0682	−	11.8046i	0.532869	−	0.447131i
$698$	15.6822	+	3.05045i	0.593579	+	0.115461i
$699$	8.84836	+	6.67555i	0.334676	+	0.252493i
$700$	25.0991	+	5.34191i	0.948658	+	0.201905i
$701$	0.496434	−	2.81541i	0.0187500	−	0.106337i	−0.973996	−	0.226563i	$-0.927251\pi$
$701$	0.496434	−	2.81541i	0.0187500	−	0.106337i	0.992746	+	0.120227i	$0.0383621\pi$
$702$	21.9209	−	3.03999i	0.827351	−	0.114737i
$703$	−20.6219	−	8.54827i	−0.777768	−	0.322404i
$704$	−0.656623	+	6.20009i	−0.0247474	+	0.233675i
$705$	6.41401	+	3.27266i	0.241565	+	0.123256i
$706$	8.16352	+	23.7188i	0.307238	+	0.892668i
$707$	15.5304	−	42.6694i	0.584080	−	1.60475i
$708$	26.0020	+	43.3559i	0.977213	+	1.62941i
$709$	−14.8741	−	17.7263i	−0.558609	−	0.665724i	0.410642	−	0.911796i	$-0.365304\pi$
$709$	−14.8741	−	17.7263i	−0.558609	−	0.665724i	−0.969252	+	0.246072i	$0.920860\pi$
$710$	−12.2978	−	0.216283i	−0.461528	−	0.00811696i
$711$	−20.5463	−	42.2471i	−0.770545	−	1.58439i
$712$	−44.5196	+	5.44842i	−1.66844	+	0.204188i
$713$	−15.3905	+	2.71376i	−0.576380	+	0.101631i
$714$	−75.9488	+	16.0881i	−2.84231	+	0.602084i
$715$	−1.72751	−	2.99214i	−0.0646053	−	0.111900i
$716$	−9.18555	+	22.7178i	−0.343280	+	0.849002i
$717$	−0.229649	−	4.42980i	−0.00857639	−	0.165434i
$718$	28.7437	−	23.2699i	1.07271	−	0.868426i
$719$	−31.3315	−	26.2902i	−1.16847	−	0.980460i	−0.168480	−	0.985705i	$-0.553886\pi$
$719$	−31.3315	−	26.2902i	−1.16847	−	0.980460i	−0.999986	+	0.00524549i	$0.998330\pi$
$720$	−3.64405	−	17.2847i	−0.135806	−	0.644162i
$721$	−78.1817			−2.91164
$722$	1.85659	+	26.8058i	0.0690951	+	0.997610i
$723$	4.76135	−	15.5423i	0.177076	−	0.578024i
$724$	−1.55736	−	4.79738i	−0.0578789	−	0.178293i
$725$	4.43620	+	3.72241i	0.164756	+	0.138247i
$726$	9.51977	+	23.6096i	0.353312	+	0.876235i
$727$	−0.992714	−	2.72746i	−0.0368177	−	0.101156i	0.919922	−	0.392102i	$-0.128252\pi$
$727$	−0.992714	−	2.72746i	−0.0368177	−	0.101156i	−0.956739	+	0.290946i	$0.906030\pi$
$728$	30.8187	−	23.2044i	1.14222	−	0.860012i
$729$	−25.7066	+	8.25644i	−0.952098	+	0.305794i
$730$	1.35044	+	2.43702i	0.0499822	+	0.0901983i
$731$	2.51720	−	0.443851i	0.0931022	−	0.0164164i
$732$	−21.6173	+	8.27754i	−0.798997	+	0.305947i
$733$	−7.80127	−	4.50407i	−0.288147	−	0.166362i	0.348959	−	0.937138i	$-0.386535\pi$
$733$	−7.80127	−	4.50407i	−0.288147	−	0.166362i	−0.637106	+	0.770776i	$0.719869\pi$
$734$	−0.0410280	+	2.33284i	−0.00151437	+	0.0861066i
$735$	13.4422	+	31.7176i	0.495822	+	1.16992i
$736$	−9.59490	−	9.60758i	−0.353673	−	0.354140i
$737$	2.00373	−	5.50520i	0.0738084	−	0.202787i
$738$	2.89514	−	10.7506i	0.106572	−	0.395734i
$739$	7.66528	−	43.4719i	0.281972	−	1.59914i	−0.433934	−	0.900945i	$-0.642875\pi$
$739$	7.66528	−	43.4719i	0.281972	−	1.59914i	0.715906	−	0.698197i	$-0.246014\pi$
$740$	13.3147	−	7.07506i	0.489460	−	0.260085i
$741$	14.4771	−	17.5325i	0.531831	−	0.644073i
$742$	−36.4887	−	21.9312i	−1.33954	−	0.805120i
$743$	0.0629646	−	0.357090i	0.00230995	−	0.0131004i	−0.983631	−	0.180195i	$-0.942327\pi$
$743$	0.0629646	−	0.357090i	0.00230995	−	0.0131004i	0.985941	+	0.167094i	$0.0534384\pi$
$744$	−15.9216	−	27.6383i	−0.583714	−	1.01327i
$745$	−14.7068	−	5.35285i	−0.538816	−	0.196113i
$746$	−47.8335	−	9.30444i	−1.75131	−	0.340660i
$747$	1.05563	+	10.1539i	0.0386234	+	0.371511i
$748$	−5.78279	+	9.24896i	−0.211440	+	0.338175i
$749$	27.1212	−	46.9753i	0.990986	−	1.71644i
$750$	−17.4044	+	22.2447i	−0.635519	+	0.812261i
$751$	−4.56350	+	0.804668i	−0.166524	+	0.0293628i	−0.256289	−	0.966600i	$-0.582500\pi$
$751$	−4.56350	+	0.804668i	−0.166524	+	0.0293628i	0.0897642	+	0.995963i	$0.471389\pi$
$752$	4.94676	+	10.1560i	0.180390	+	0.370350i
$753$	7.46737	+	32.4282i	0.272126	+	1.18175i
$754$	8.59891	−	1.36077i	0.313154	−	0.0495563i
$755$	−0.0555480	−	0.152617i	−0.00202160	−	0.00555430i
$756$	−32.1661	+	34.3588i	−1.16987	+	1.24962i
$757$	4.28010	−	5.10082i	0.155563	−	0.185393i	−0.682634	−	0.730760i	$-0.739166\pi$
$757$	4.28010	−	5.10082i	0.155563	−	0.185393i	0.838197	+	0.545368i	$0.183610\pi$
$758$	−1.88080	−	1.63539i	−0.0683138	−	0.0594001i
$759$	3.09799	+	0.949062i	0.112450	+	0.0344488i
$760$	−14.7681	−	10.5488i	−0.535697	−	0.382644i
$761$		−	33.1635i		−	1.20217i	−0.799184	−	0.601087i	$-0.794734\pi$
$761$		−	33.1635i		−	1.20217i	0.799184	−	0.601087i	$-0.205266\pi$
$762$	16.6592	+	26.7017i	0.603501	+	0.967301i
$763$	34.3916	+	28.8580i	1.24506	+	1.04473i
$764$	0.980985	+	6.99347i	0.0354908	+	0.253015i
$765$	7.51044	−	29.9785i	0.271541	−	1.08388i
$766$	−3.57554	−	22.5944i	−0.129190	−	0.816368i
$767$	−21.9757	−	38.0631i	−0.793498	−	1.37438i
$768$	11.7526	−	25.0973i	0.424087	−	0.905622i
$769$	−0.936070	−	5.30871i	−0.0337555	−	0.191437i	0.963267	−	0.268545i	$-0.0865427\pi$
$769$	−0.936070	−	5.30871i	−0.0337555	−	0.191437i	−0.997023	+	0.0771074i	$0.975432\pi$
$770$	6.85947	+	2.63414i	0.247198	+	0.0949280i
$771$	−34.5809	+	32.2108i	−1.24540	+	1.16004i
$772$	3.92684	−	6.28056i	0.141330	−	0.226042i
$773$	−7.89932	+	6.62832i	−0.284119	+	0.238404i	−0.773698	−	0.633555i	$-0.781595\pi$
$773$	−7.89932	+	6.62832i	−0.284119	+	0.238404i	0.489579	+	0.871959i	$0.337151\pi$
$774$	1.09711	−	1.09435i	0.0394349	−	0.0393356i
$775$	−6.30873	+	17.3331i	−0.226616	+	0.622623i
$776$	−5.19866	−	4.85168i	−0.186621	−	0.174165i
$777$	−35.7843	−	18.2585i	−1.28376	−	0.655019i
$778$	−20.0853	+	33.4175i	−0.720092	+	1.19808i
$779$	−5.27910	−	10.1476i	−0.189143	−	0.363577i
$780$	2.91780	+	15.0775i	0.104474	+	0.539860i
$781$	4.53458	+	0.799569i	0.162260	+	0.0286108i
$782$	−7.73111	−	22.4624i	−0.276464	−	0.803254i
$783$	−10.0486	+	3.44099i	−0.359108	+	0.122971i
$784$	−13.1021	+	52.4315i	−0.467931	+	1.87255i
$785$	11.7986	+	14.0611i	0.421112	+	0.501861i
$786$	−15.0967	−	4.91685i	−0.538483	−	0.175378i
$787$	−15.3667	+	26.6159i	−0.547764	+	0.948754i	0.450664	+	0.892694i	$0.351187\pi$
$787$	−15.3667	+	26.6159i	−0.547764	+	0.948754i	−0.998427	+	0.0560605i	$0.982146\pi$
$788$	11.3439	−	8.85802i	0.404110	−	0.315554i
$789$	−15.0982	−	1.86248i	−0.537511	−	0.0663060i
$790$	28.5145	−	15.8009i	1.01450	−	0.562171i
$791$	16.1797	+	28.0241i	0.575285	+	0.996424i
$792$	0.336024	+	6.60442i	0.0119401	+	0.234678i
$793$	18.9105	−	6.88288i	0.671533	−	0.244418i
$794$	−31.8583	−	39.3524i	−1.13061	−	1.39656i
$795$	14.2185	−	9.22221i	0.504279	−	0.327078i
$796$	−12.7888	−	39.3954i	−0.453288	−	1.39633i
$797$	33.0971			1.17236			0.586180	−	0.810181i	$-0.300631\pi$
$797$	33.0971			1.17236			0.586180	+	0.810181i	$0.300631\pi$
$798$	−0.468489	+	48.3532i	−0.0165843	+	1.71168i
$799$			19.7639i			0.699198i
$800$	−15.4829	+	4.13767i	−0.547402	+	0.146289i
$801$	−45.7444	+	13.0611i	−1.61630	+	0.461492i
$802$	14.5364	+	17.9558i	0.513299	+	0.634042i
$803$	−0.356740	−	0.980136i	−0.0125891	−	0.0345882i
$804$	−16.4045	+	20.2236i	−0.578544	+	0.713233i
$805$	−13.8584	+	8.00117i	−0.488446	+	0.282004i
$806$	13.4405	+	24.2548i	0.473421	+	0.854340i
$807$	1.76005	+	0.217115i	0.0619566	+	0.00764282i
$808$	3.44488	+	28.1485i	0.121190	+	0.990259i
$809$	24.4496	+	14.1160i	0.859600	+	0.496291i	0.863878	−	0.503700i	$-0.168028\pi$
$809$	24.4496	+	14.1160i	0.859600	+	0.496291i	−0.00427805	+	0.999991i	$0.501362\pi$
$810$	−6.67262	−	17.5077i	−0.234452	−	0.615159i
$811$	−13.3614	+	11.2115i	−0.469182	+	0.393690i	−0.846496	−	0.532395i	$-0.821292\pi$
$811$	−13.3614	+	11.2115i	−0.469182	+	0.393690i	0.377314	+	0.926085i	$0.376848\pi$
$812$	−12.3926	+	13.7561i	−0.434895	+	0.482743i
$813$	23.1026	+	17.4295i	0.810245	+	0.611281i
$814$	−5.33726	+	1.83698i	−0.187071	+	0.0643860i
$815$	0.713938	−	4.04895i	0.0250082	−	0.141828i
$816$	37.7130	−	30.4712i	1.32022	−	1.06671i
$817$	0.0698669	−	1.59053i	0.00244433	−	0.0556455i
$818$	10.4981	−	17.4665i	0.367056	−	0.610702i
$819$	28.4571	−	29.4017i	0.994371	−	1.02738i
$820$	7.55671	+	1.60831i	0.263892	+	0.0561647i
$821$	2.51028	+	0.913666i	0.0876093	+	0.0318872i	0.385453	−	0.922727i	$-0.374045\pi$
$821$	2.51028	+	0.913666i	0.0876093	+	0.0318872i	−0.297844	+	0.954615i	$0.596267\pi$
$822$	6.77009	−	12.7113i	0.236134	−	0.443358i
$823$	7.38961	+	8.80660i	0.257586	+	0.306979i	0.879303	−	0.476263i	$-0.158009\pi$
$823$	7.38961	+	8.80660i	0.257586	+	0.306979i	−0.621717	+	0.783242i	$0.713565\pi$
$824$	43.5137	−	22.1496i	1.51587	−	0.771618i
$825$	2.79835	−	2.60655i	0.0974261	−	0.0907486i
$826$	87.2596	+	33.5090i	3.03615	+	1.16593i
$827$	−33.9701	+	5.98985i	−1.18126	+	0.208287i	−0.729581	−	0.683895i	$-0.760285\pi$
$827$	−33.9701	+	5.98985i	−1.18126	+	0.208287i	−0.451676	+	0.892182i	$0.649174\pi$
$828$	−11.6396	−	8.48143i	−0.404502	−	0.294750i
$829$	−8.50873	+	4.91252i	−0.295520	+	0.170619i	−0.640429	−	0.768018i	$-0.721243\pi$
$829$	−8.50873	+	4.91252i	−0.295520	+	0.170619i	0.344908	+	0.938636i	$0.387910\pi$
$830$	−6.99700	+	1.10727i	−0.242870	+	0.0384339i
$831$	−17.2179	+	0.892608i	−0.597283	+	0.0309642i
$832$	−10.5788	+	21.6461i	−0.366752	+	0.750444i
$833$	−60.7767	+	72.4309i	−2.10579	+	2.50958i
$834$	33.5352	−	20.9226i	1.16123	−	0.724492i
$835$	19.2974			0.667815
$836$	4.84343	+	4.76467i	0.167513	+	0.164789i
$837$	−21.2461	−	26.3277i	−0.734371	−	0.910020i
$838$	−31.1755	+	35.8537i	−1.07694	+	1.23855i
$839$	26.9731	+	22.6331i	0.931214	+	0.781381i	0.976035	−	0.217614i	$-0.0698274\pi$
$839$	26.9731	+	22.6331i	0.931214	+	0.781381i	−0.0448212	+	0.998995i	$0.514272\pi$
$840$	−24.9992	−	21.0177i	−0.862553	−	0.725181i
$841$	23.3247	−	8.48951i	0.804301	−	0.292742i
$842$	37.1722	−	5.88247i	1.28104	−	0.202723i
$843$	2.93249	+	12.7348i	0.101000	+	0.438609i
$844$	39.4644	+	1.38856i	1.35842	+	0.0477964i
$845$	1.00464	+	5.69762i	0.0345608	+	0.196004i
$846$	6.86015	+	9.82366i	0.235857	+	0.337744i
$847$	40.7613	+	23.5336i	1.40058	+	0.808623i
$848$	26.5219	+	1.86867i	0.910766	+	0.0641704i
$849$	3.04263	+	7.17926i	0.104423	+	0.246392i
$850$	−27.5227	−	5.35364i	−0.944020	−	0.183628i
$851$	4.20439	−	11.5515i	0.144125	−	0.395979i
$852$	−17.8923	−	9.93725i	−0.612980	−	0.340444i
$853$	−33.7848	−	5.95717i	−1.15677	−	0.203969i	−0.437840	−	0.899053i	$-0.644256\pi$
$853$	−33.7848	−	5.95717i	−1.15677	−	0.203969i	−0.718929	+	0.695084i	$0.755367\pi$
$854$	−22.0477	+	36.6825i	−0.754456	+	1.25525i
$855$	−17.2151	−	8.61314i	−0.588745	−	0.294563i
$856$	−1.78633	+	33.8288i	−0.0610555	+	1.15624i
$857$	−11.8672	−	2.09250i	−0.405375	−	0.0714786i	−0.0327571	−	0.999463i	$-0.510429\pi$
$857$	−11.8672	−	2.09250i	−0.405375	−	0.0714786i	−0.372618	+	0.927985i	$0.621540\pi$
$858$	−0.196640	−	5.74578i	−0.00671319	−	0.196158i
$859$	44.7691	+	16.2946i	1.52750	+	0.555966i	0.963008	−	0.269471i	$-0.0868489\pi$
$859$	44.7691	+	16.2946i	1.52750	+	0.555966i	0.564494	+	0.825437i	$0.309071\pi$
$860$	0.798926	+	0.719738i	0.0272431	+	0.0245429i
$861$	−8.03254	−	18.9532i	−0.273748	−	0.645923i
$862$	35.9988	+	0.633116i	1.22612	+	0.0215640i
$863$	−7.57109	+	13.1135i	−0.257723	+	0.446389i	−0.965632	−	0.259915i	$-0.916306\pi$
$863$	−7.57109	+	13.1135i	−0.257723	+	0.446389i	0.707909	+	0.706304i	$0.249639\pi$
$864$	8.16853	−	28.2361i	0.277899	−	0.960610i
$865$	−4.20245	−	23.8333i	−0.142888	−	0.810356i
$866$	−4.73375	−	8.54257i	−0.160859	−	0.290288i
$867$	53.9687	−	12.4276i	1.83287	−	0.422063i
$868$	−54.6735	−	22.1063i	−1.85574	−	0.750337i
$869$	−11.4681	+	4.17405i	−0.389029	+	0.141595i
$870$	−2.75630	−	6.83578i	−0.0934473	−	0.231755i
$871$	14.5520	−	17.3424i	0.493076	−	0.587625i
$872$	−27.3171	−	6.31806i	−0.925075	−	0.213957i
$873$	−6.24804	−	4.22463i	−0.211464	−	0.142982i
$874$	−14.7021	+	1.66917i	−0.497305	+	0.0564605i
$875$			52.2213i			1.76540i
$876$	0.0770718	+	4.63555i	0.00260401	+	0.156621i
$877$	16.5145	−	19.6812i	0.557654	−	0.664586i	−0.411394	−	0.911457i	$-0.634958\pi$
$877$	16.5145	−	19.6812i	0.557654	−	0.664586i	0.969048	+	0.246872i	$0.0794026\pi$
$878$	27.6048	+	34.0983i	0.931618	+	1.15076i
$879$	−1.93281	−	37.2829i	−0.0651922	−	1.25752i
$880$	−4.56406	+	0.477265i	−0.153855	+	0.0160886i
$881$	12.0939	−	6.98240i	0.407453	−	0.235243i	−0.282242	−	0.959343i	$-0.591078\pi$
$881$	12.0939	−	6.98240i	0.407453	−	0.235243i	0.689695	+	0.724100i	$0.257745\pi$
$882$	−5.06795	+	57.0976i	−0.170647	+	1.92258i
$883$	−9.54729	−	54.1454i	−0.321292	−	1.82214i	−0.534546	−	0.845140i	$-0.679517\pi$
$883$	−9.54729	−	54.1454i	−0.321292	−	1.82214i	0.213254	−	0.976997i	$-0.431594\pi$
$884$	−33.2226	+	25.9422i	−1.11740	+	0.872531i
$885$	−27.2280	+	25.3618i	−0.915259	+	0.852527i
$886$	−0.637433	+	36.2442i	−0.0214150	+	1.21765i
$887$	20.7612	−	17.4207i	0.697092	−	0.584930i	−0.223852	−	0.974623i	$-0.571863\pi$
$887$	20.7612	−	17.4207i	0.697092	−	0.584930i	0.920945	+	0.389693i	$0.127419\pi$
$888$	25.0893	+	0.0241016i	0.841943	+	0.000808796i
$889$	54.6806	+	19.9021i	1.83393	+	0.667495i
$890$	−10.7436	−	31.2150i	−0.360125	−	1.04633i
$891$	1.44282	+	6.86411i	0.0483363	+	0.229956i
$892$	15.9363	−	8.46806i	0.533585	−	0.283532i
$893$	12.0177	+	2.66761i	0.402158	+	0.0892682i
$894$	−17.4125	−	19.3656i	−0.582360	−	0.647683i
$895$	−17.7620	−	3.13191i	−0.593717	−	0.104688i
$896$	−11.4800	−	49.9361i	−0.383521	−	1.66825i
$897$	9.99516	+	7.54074i	0.333729	+	0.251778i
$898$	−6.30343	−	1.22613i	−0.210348	−	0.0409164i
$899$	−8.55467	−	10.1951i	−0.285314	−	0.340024i
$900$	−15.5384	+	6.89222i	−0.517947	+	0.229741i
$901$	40.2842	+	23.2581i	1.34206	+	0.774839i
$902$	−2.70006	−	1.03687i	−0.0899022	−	0.0345239i
$903$	0.350770	−	2.84352i	0.0116729	−	0.0946265i
$904$	−16.9447	−	11.0136i	−0.563572	−	0.366305i
$905$	3.21502	−	1.85619i	0.106871	−	0.0617020i
$906$	0.0377982	−	0.267596i	0.00125576	−	0.00889027i
$907$	6.93582	−	2.52443i	0.230300	−	0.0838224i	−0.224292	−	0.974522i	$-0.572007\pi$
$907$	6.93582	−	2.52443i	0.230300	−	0.0838224i	0.454593	+	0.890699i	$0.349785\pi$
$908$	10.0662	−	1.41200i	0.334058	−	0.0468589i
$909$	8.25817	+	28.9228i	0.273906	+	0.959310i
$910$	21.4269	+	18.6311i	0.710294	+	0.617614i
$911$	7.56349			0.250590			0.125295	−	0.992120i	$-0.460012\pi$
$911$	7.56349			0.250590			0.125295	+	0.992120i	$0.460012\pi$
$912$	−13.4382	−	27.0447i	−0.444982	−	0.895540i
$913$	2.65201			0.0877686
$914$	−12.2337	−	10.6374i	−0.404655	−	0.351855i
$915$	−9.27119	−	14.2940i	−0.306496	−	0.472546i
$916$	−51.9296	+	7.28424i	−1.71580	+	0.240678i
$917$	−27.5853	+	10.0402i	−0.910948	+	0.331558i
$918$	34.4803	−	38.1539i	1.13802	−	1.25927i
$919$	10.5977	−	6.11856i	0.349584	−	0.201833i	−0.314918	−	0.949119i	$-0.601977\pi$
$919$	10.5977	−	6.11856i	0.349584	−	0.201833i	0.664502	+	0.747286i	$0.268644\pi$
$920$	5.44640	−	8.37945i	0.179562	−	0.276262i
$921$	22.2583	+	2.74573i	0.733435	+	0.0904748i
$922$	40.4126	+	15.5190i	1.33092	+	0.511093i
$923$	15.4093	+	8.89659i	0.507205	+	0.292835i
$924$	8.01386	+	9.23434i	0.263637	+	0.303787i
$925$	−9.32625	−	11.1146i	−0.306645	−	0.365445i
$926$	42.6513	+	8.29642i	1.40161	+	0.272637i
$927$	41.9321	−	30.3932i	1.37723	−	0.998244i
$928$	3.00014	−	11.1672i	0.0984844	−	0.366580i
$929$	−3.23037	−	0.569602i	−0.105985	−	0.0186880i	0.120404	−	0.992725i	$-0.461581\pi$
$929$	−3.23037	−	0.569602i	−0.105985	−	0.0186880i	−0.226389	+	0.974037i	$0.572692\pi$
$930$	17.4574	−	15.6967i	0.572450	−	0.514715i
$931$	35.8393	+	46.7323i	1.17459	+	1.53159i
$932$	−11.3022	+	6.00568i	−0.370217	+	0.196722i
$933$	48.6830	+	24.8398i	1.59381	+	0.813220i
$934$	−9.31887	−	27.0756i	−0.304923	−	0.885940i
$935$	−7.54437	−	2.74593i	−0.246727	−	0.0898014i
$936$	−7.50862	+	24.4263i	−0.245427	+	0.798398i
$937$	23.7387	−	19.9191i	0.775509	−	0.650729i	−0.166605	−	0.986024i	$-0.553280\pi$
$937$	23.7387	−	19.9191i	0.775509	−	0.650729i	0.942113	+	0.335295i	$0.108836\pi$
$938$	−0.846631	+	48.1391i	−0.0276435	+	1.57180i
$939$	22.1150	+	23.7423i	0.721696	+	0.774801i
$940$	−6.55337	+	5.11727i	−0.213747	+	0.166907i
$941$	4.41289	+	25.0268i	0.143856	+	0.815849i	0.968278	+	0.249874i	$0.0803892\pi$
$941$	4.41289	+	25.0268i	0.143856	+	0.815849i	−0.824422	+	0.565975i	$0.808500\pi$
$942$	6.32951	+	29.8803i	0.206227	+	0.973554i
$943$	5.45503	−	3.14946i	0.177640	−	0.102561i
$944$	−58.0596	+	6.07130i	−1.88968	+	0.197604i
$945$	−29.6634	−	17.8920i	−0.964950	−	0.582027i
$946$	−0.253296	−	0.312879i	−0.00823537	−	0.0101726i
$947$	24.4309	−	29.1156i	0.793898	−	0.946131i	−0.205573	−	0.978642i	$-0.565906\pi$
$947$	24.4309	−	29.1156i	0.793898	−	0.946131i	0.999471	+	0.0325108i	$0.0103503\pi$
$948$	54.2384	−	0.901781i	1.76158	−	0.0292885i
$949$		−	4.03059i		−	0.130838i
$950$	−6.97018	+	16.0129i	−0.226143	+	0.519528i
$951$	2.00634	−	6.54923i	0.0650601	−	0.212373i
$952$	20.2001	−	87.3386i	0.654691	−	2.83066i
$953$	−0.998729	+	1.19024i	−0.0323520	+	0.0385556i	−0.781978	−	0.623306i	$-0.785789\pi$
$953$	−0.998729	+	1.19024i	−0.0323520	+	0.0385556i	0.749626	+	0.661862i	$0.230233\pi$
$954$	28.0962	−	2.42241i	0.909649	−	0.0784283i
$955$	−4.88431	+	1.77774i	−0.158053	+	0.0575264i
$956$	4.74849	+	1.91998i	0.153577	+	0.0620964i
$957$	0.619180	+	2.68889i	0.0200152	+	0.0869193i
$958$	−18.6742	−	33.6997i	−0.603338	−	1.08879i
$959$	−4.62385	−	26.2232i	−0.149312	−	0.846791i
$960$	19.8683	+	4.61537i	0.641248	+	0.148960i
$961$	5.69527	−	9.86449i	0.183718	−	0.318209i
$962$	−21.8087	−	0.383553i	−0.703140	−	0.0123662i
$963$	3.71545	+	35.7382i	0.119729	+	1.15165i
$964$	13.9455	+	12.5632i	0.449153	+	0.404634i
$965$	5.12305	+	1.86464i	0.164917	+	0.0600248i
$966$	−26.6123	+	0.910763i	−0.856236	+	0.0293033i
$967$	13.8409	+	2.44053i	0.445094	+	0.0784821i	0.391703	−	0.920092i	$-0.371886\pi$
$967$	13.8409	+	2.44053i	0.445094	+	0.0784821i	0.0533909	+	0.998574i	$0.482997\pi$
$968$	−29.3539	−	1.55003i	−0.943469	−	0.0498199i
$969$	−0.417220	−	52.8333i	−0.0134030	−	1.69725i
$970$	2.69620	−	4.48590i	0.0865699	−	0.144033i
$971$	6.27762	+	1.10691i	0.201458	+	0.0355226i	0.273467	−	0.961881i	$-0.411830\pi$
$971$	6.27762	+	1.10691i	0.201458	+	0.0355226i	−0.0720082	+	0.997404i	$0.522941\pi$
$972$	3.89500	−	30.9327i	0.124932	−	0.992165i
$973$	24.9954	−	68.6743i	0.801316	−	2.20160i
$974$	−14.1461	−	2.75165i	−0.453269	−	0.0881687i
$975$	13.6064	−	5.76653i	0.435755	−	0.184677i
$976$	1.87859	−	26.6628i	0.0601324	−	0.853454i
$977$	38.9574	+	22.4921i	1.24636	+	0.719585i	0.970381	−	0.241579i	$-0.0776653\pi$
$977$	38.9574	+	22.4921i	1.24636	+	0.719585i	0.275977	+	0.961164i	$0.410999\pi$
$978$	4.21572	−	5.38813i	0.134804	−	0.172294i
$979$	2.14603	+	12.1707i	0.0685873	+	0.388978i
$980$	−39.7530	−	1.39872i	−1.26986	−	0.0446804i
$981$	−29.6643	−	2.10798i	−0.947107	−	0.0673027i
$982$	28.7019	−	4.54204i	0.915913	−	0.144942i
$983$	−48.5128	+	17.6572i	−1.54732	+	0.563178i	−0.967787	−	0.251772i	$-0.918987\pi$
$983$	−48.5128	+	17.6572i	−1.54732	+	0.563178i	−0.579532	+	0.814950i	$0.696764\pi$
$984$	9.84030	+	8.27311i	0.313697	+	0.263737i
$985$	8.11500	+	6.80929i	0.258565	+	0.216962i
$986$	13.2742	−	15.2662i	0.422738	−	0.486174i
$987$	21.1819	+	6.48902i	0.674226	+	0.206548i
$988$	11.2903	+	23.7030i	0.359193	+	0.754092i
$989$	0.876699			0.0278774
$990$	−4.70305	+	1.25382i	−0.149473	+	0.0398492i
$991$	22.3860	−	26.6785i	0.711113	−	0.847472i	−0.282622	−	0.959231i	$-0.591204\pi$
$991$	22.3860	−	26.6785i	0.711113	−	0.847472i	0.993735	+	0.111759i	$0.0356486\pi$
$992$	36.6926	−	3.18578i	1.16499	−	0.101148i
$993$	−1.93195	−	37.2662i	−0.0613085	−	1.18261i
$994$	−37.3760	+	5.91471i	−1.18549	+	0.187603i
$995$	26.4013	−	15.2428i	0.836978	−	0.483230i
$996$	−11.1425	−	3.84699i	−0.353063	−	0.121897i
$997$	−31.1768	+	5.49731i	−0.987380	+	0.174102i	−0.643942	−	0.765074i	$-0.722702\pi$
$997$	−31.1768	+	5.49731i	−0.987380	+	0.174102i	−0.343437	+	0.939176i	$0.611591\pi$
$998$	23.0974	+	8.86977i	0.731136	+	0.280768i
$999$	26.2906	−	4.11840i	0.831799	−	0.130301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bu.c.131.15	yes	432
3.2	odd	2	inner	456.2.bu.c.131.58	yes	432
8.3	odd	2	inner	456.2.bu.c.131.8	✓	432
19.9	even	9	inner	456.2.bu.c.275.65	yes	432
24.11	even	2	inner	456.2.bu.c.131.65	yes	432
57.47	odd	18	inner	456.2.bu.c.275.8	yes	432
152.123	odd	18	inner	456.2.bu.c.275.58	yes	432
456.275	even	18	inner	456.2.bu.c.275.15	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bu.c.131.8	✓	432	8.3	odd	2	inner
456.2.bu.c.131.15	yes	432	1.1	even	1	trivial
456.2.bu.c.131.58	yes	432	3.2	odd	2	inner
456.2.bu.c.131.65	yes	432	24.11	even	2	inner
456.2.bu.c.275.8	yes	432	57.47	odd	18	inner
456.2.bu.c.275.15	yes	432	456.275	even	18	inner
456.2.bu.c.275.58	yes	432	152.123	odd	18	inner
456.2.bu.c.275.65	yes	432	19.9	even	9	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06720 - 0.927949i) q^{2} +(1.45315 - 0.942522i) q^{3} +(0.277823 + 1.98061i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-2.42541 - 0.342592i) q^{6} +(-3.92214 + 2.26445i) q^{7} +(1.54141 - 2.37151i) q^{8} +(1.22330 - 2.73926i) q^{9} +O(q^{10})\)	\(q+(-1.06720 - 0.927949i) q^{2} +(1.45315 - 0.942522i) q^{3} +(0.277823 + 1.98061i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-2.42541 - 0.342592i) q^{6} +(-3.92214 + 2.26445i) q^{7} +(1.54141 - 2.37151i) q^{8} +(1.22330 - 2.73926i) q^{9} +(1.94343 + 0.746306i) q^{10} +(-0.674933 - 0.389673i) q^{11} +(2.27049 + 2.61627i) q^{12} +(-1.93582 - 2.30702i) q^{13} +(6.28700 + 1.22293i) q^{14} +(-1.53558 + 2.03539i) q^{15} +(-3.84563 + 1.10052i) q^{16} +(-6.89185 - 1.21522i) q^{17} +(-3.84740 + 1.78817i) q^{18} +(-1.66915 + 4.02665i) q^{19} +(-1.38149 - 2.59986i) q^{20} +(-3.56518 + 6.98730i) q^{21} +(0.358691 + 1.04216i) q^{22} +(-2.25555 - 0.820955i) q^{23} +(0.00470611 - 4.89898i) q^{24} +(-2.17025 + 1.82106i) q^{25} +(-0.0748931 + 4.25839i) q^{26} +(-0.804166 - 5.13355i) q^{27} +(-5.57465 - 7.13912i) q^{28} +(-0.354954 - 2.01304i) q^{29} +(3.52750 - 0.747227i) q^{30} +(5.63852 - 3.25540i) q^{31} +(5.12527 + 2.39407i) q^{32} +(-1.34806 + 0.0698856i) q^{33} +(6.22730 + 7.69216i) q^{34} +(4.28532 - 5.10705i) q^{35} +(5.76526 + 1.66186i) q^{36} +5.12134i q^{37} +(5.51784 - 2.74835i) q^{38} +(-4.98746 - 1.52790i) q^{39} +(-0.938212 + 4.05651i) q^{40} +(-1.68681 + 2.01026i) q^{41} +(10.2886 - 4.14853i) q^{42} +(-0.343217 + 0.124921i) q^{43} +(0.584277 - 1.44504i) q^{44} +(-0.313029 + 4.40505i) q^{45} +(1.64532 + 2.96916i) q^{46} +(-0.490410 - 2.78126i) q^{47} +(-4.55102 + 5.22381i) q^{48} +(6.75547 - 11.7008i) q^{49} +(4.00593 + 0.0704530i) q^{50} +(-11.1603 + 4.72982i) q^{51} +(4.03150 - 4.47505i) q^{52} +(-6.24605 - 2.27338i) q^{53} +(-3.90546 + 6.22474i) q^{54} +(1.12981 + 0.199216i) q^{55} +(-0.675474 + 12.7918i) q^{56} +(1.36969 + 7.42455i) q^{57} +(-1.48919 + 2.47769i) q^{58} +(14.3723 + 2.53423i) q^{59} +(-4.45793 - 2.47590i) q^{60} +(-2.28545 + 6.27923i) q^{61} +(-9.03826 - 1.75810i) q^{62} +(1.40494 + 13.5139i) q^{63} +(-3.24810 - 7.31094i) q^{64} +(3.83930 + 2.21662i) q^{65} +(1.50349 + 1.17634i) q^{66} +(1.30535 + 7.40302i) q^{67} +(0.492159 - 13.9877i) q^{68} +(-4.05143 + 0.932938i) q^{69} +(-9.31237 + 1.47367i) q^{70} +(-5.55190 + 2.02073i) q^{71} +(-4.61056 - 7.12340i) q^{72} +(1.02524 + 0.860276i) q^{73} +(4.75234 - 5.46548i) q^{74} +(-1.43732 + 4.69178i) q^{75} +(-8.43896 - 2.18723i) q^{76} +3.52958 q^{77} +(3.90480 + 6.25868i) q^{78} +(10.0657 - 11.9958i) q^{79} +(4.76549 - 3.45849i) q^{80} +(-6.00706 - 6.70188i) q^{81} +(3.66558 - 0.580075i) q^{82} +(-2.94697 + 1.70143i) q^{83} +(-14.8296 - 5.11999i) q^{84} +(10.1452 - 1.78887i) q^{85} +(0.482200 + 0.185172i) q^{86} +(-2.41314 - 2.59070i) q^{87} +(-1.96446 + 0.999963i) q^{88} +(-10.1930 - 12.1475i) q^{89} +(4.42172 - 4.41059i) q^{90} +(12.8167 + 4.66490i) q^{91} +(0.999346 - 4.69545i) q^{92} +(5.12534 - 10.0450i) q^{93} +(-2.05750 + 3.42323i) q^{94} +(0.281587 - 6.41035i) q^{95} +(9.70427 - 1.35173i) q^{96} +(0.436566 - 2.47589i) q^{97} +(-18.0672 + 6.21836i) q^{98} +(-1.89306 + 1.37213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 432 * q - 18 * q^3 - 6 * q^4 + 6 * q^6 - 18 * q^9	\( 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 6 q^{16} - 12 q^{18} - 24 q^{19} + 24 q^{22} - 18 q^{24} - 24 q^{25} - 36 q^{27} - 36 q^{28} - 48 q^{30} - 54 q^{34} + 66 q^{36} + 18 q^{40} - 51 q^{42} - 24 q^{43} - 6 q^{46} + 117 q^{48} + 228 q^{49} + 66 q^{51} + 12 q^{52} + 21 q^{54} - 12 q^{57} - 96 q^{58} + 48 q^{60} - 144 q^{64} - 78 q^{66} + 60 q^{67} - 162 q^{70} - 84 q^{72} - 72 q^{73} - 192 q^{75} - 132 q^{76} + 3 q^{78} - 42 q^{81} - 252 q^{82} - 45 q^{84} - 126 q^{88} + 24 q^{90} - 108 q^{91} - 48 q^{94} + 138 q^{96} - 84 q^{97} + 18 q^{99}+O(q^{100}) \) 432 * q - 18 * q^3 - 6 * q^4 + 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 6 * q^16 - 12 * q^18 - 24 * q^19 + 24 * q^22 - 18 * q^24 - 24 * q^25 - 36 * q^27 - 36 * q^28 - 48 * q^30 - 54 * q^34 + 66 * q^36 + 18 * q^40 - 51 * q^42 - 24 * q^43 - 6 * q^46 + 117 * q^48 + 228 * q^49 + 66 * q^51 + 12 * q^52 + 21 * q^54 - 12 * q^57 - 96 * q^58 + 48 * q^60 - 144 * q^64 - 78 * q^66 + 60 * q^67 - 162 * q^70 - 84 * q^72 - 72 * q^73 - 192 * q^75 - 132 * q^76 + 3 * q^78 - 42 * q^81 - 252 * q^82 - 45 * q^84 - 126 * q^88 + 24 * q^90 - 108 * q^91 - 48 * q^94 + 138 * q^96 - 84 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

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