LMFDB - Embedded newform 966.2.r.b.113.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.15
Character	$\chi$	$=$	966.113
Dual form			966.2.r.b.701.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(-1.28014 - 1.16672i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.854693 + 0.250960i) q^{5} +(-1.67361 + 0.446142i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.277508 + 2.98714i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(-1.28014 - 1.16672i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.854693 + 0.250960i) q^{5} +(-1.67361 + 0.446142i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.277508 + 2.98714i) q^{9} +(0.673203 - 0.583334i) q^{10} +(5.04410 - 3.24164i) q^{11} +(-0.529501 + 1.64913i) q^{12} +(0.517786 + 0.597556i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-0.801323 - 1.31846i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.35581 - 5.15850i) q^{17} +(2.66297 + 1.38151i) q^{18} +(0.221397 - 0.101109i) q^{19} +(-0.126771 - 0.881709i) q^{20} +(0.203422 + 1.72006i) q^{21} -5.99593i q^{22} +(-1.23742 - 4.63344i) q^{23} +(1.10107 + 1.33703i) q^{24} +(-3.53875 - 2.27422i) q^{25} +(0.782632 - 0.112526i) q^{26} +(3.12992 - 4.14772i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(-9.65002 - 4.40701i) q^{29} +(-1.54238 - 0.0386946i) q^{30} +(-1.07812 + 7.49848i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-10.2392 - 1.73532i) q^{33} +(-3.06596 - 4.77073i) q^{34} +(-0.481590 - 0.749368i) q^{35} +(2.60191 - 1.49333i) q^{36} +(0.00514929 + 0.0175369i) q^{37} +(0.0346383 - 0.240915i) q^{38} +(0.0343465 - 1.36907i) q^{39} +(-0.810278 - 0.370042i) q^{40} +(-2.32563 + 7.92037i) q^{41} +(1.55699 + 0.758807i) q^{42} +(4.07764 - 0.586276i) q^{43} +(-5.04410 - 3.24164i) q^{44} +(-0.512469 + 2.62273i) q^{45} +(-4.56690 - 1.46404i) q^{46} +3.11302i q^{47} +(1.72006 - 0.203422i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-3.82638 + 1.74745i) q^{50} +(-9.03432 + 3.85502i) q^{51} +(0.328461 - 0.719228i) q^{52} +(3.73466 - 4.31002i) q^{53} +(-1.79713 - 4.87548i) q^{54} +(5.12468 - 1.50474i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-0.401385 - 0.128876i) q^{57} +(-8.92461 + 5.73550i) q^{58} +(6.98134 - 6.04937i) q^{59} +(-0.866427 + 1.27662i) q^{60} +(-11.0326 - 1.58624i) q^{61} +(5.72525 + 4.96095i) q^{62} +(1.74643 - 2.43926i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.292585 + 0.640671i) q^{65} +(-6.99559 + 7.67562i) q^{66} +(2.25890 - 3.51492i) q^{67} -5.67098 q^{68} +(-3.82188 + 7.37518i) q^{69} -0.890776 q^{70} +(2.07320 - 3.22596i) q^{71} +(0.150430 - 2.99623i) q^{72} +(-0.110554 - 0.242079i) q^{73} +(0.0175369 + 0.00514929i) q^{74} +(1.87670 + 7.04006i) q^{75} +(-0.183944 - 0.159388i) q^{76} +(-5.93490 - 0.853309i) q^{77} +(-1.13316 - 0.769068i) q^{78} +(0.654880 - 0.567456i) q^{79} +(-0.749368 + 0.481590i) q^{80} +(-8.84598 + 1.65791i) q^{81} +(5.40571 + 6.23852i) q^{82} +(6.06737 - 1.78154i) q^{83} +(1.48012 - 0.899579i) q^{84} +(3.30807 - 3.81772i) q^{85} +(1.71133 - 3.74729i) q^{86} +(7.21158 + 16.9005i) q^{87} +(-5.45409 + 2.49080i) q^{88} +(-1.88807 - 13.1318i) q^{89} +(1.92932 + 1.84907i) q^{90} -0.790680i q^{91} +(-3.70069 + 3.05040i) q^{92} +(10.1288 - 8.34122i) q^{93} +(2.61884 + 1.68302i) q^{94} +(0.214601 - 0.0308550i) q^{95} +(0.758807 - 1.55699i) q^{96} +(-1.96716 + 6.69953i) q^{97} +(0.909632 + 0.415415i) q^{98} +(11.0830 + 14.1678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−1.28014	−	1.16672i	−0.739088	−	0.673609i
$3$	−1.28014	−	1.16672i	−0.739088	−	0.673609i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	0.854693	+	0.250960i	0.382230	+	0.112233i	0.467202	−	0.884150i	$-0.345262\pi$
$5$	0.854693	+	0.250960i	0.382230	+	0.112233i	−0.0849721	+	0.996383i	$0.527080\pi$
$6$	−1.67361	+	0.446142i	−0.683247	+	0.182137i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	0.277508	+	2.98714i	0.0925027	+	0.995712i
$10$	0.673203	−	0.583334i	0.212886	−	0.184466i
$11$	5.04410	−	3.24164i	1.52085	−	0.977392i	0.529193	−	0.848501i	$-0.322495\pi$
$11$	5.04410	−	3.24164i	1.52085	−	0.977392i	0.991659	−	0.128891i	$-0.0411417\pi$
$12$	−0.529501	+	1.64913i	−0.152854	+	0.476063i
$13$	0.517786	+	0.597556i	0.143608	+	0.165732i	0.822997	−	0.568046i	$-0.192300\pi$
$13$	0.517786	+	0.597556i	0.143608	+	0.165732i	−0.679389	+	0.733778i	$0.737755\pi$
$14$	−0.959493	+	0.281733i	−0.256435	+	0.0752962i
$15$	−0.801323	−	1.31846i	−0.206901	−	0.340424i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	2.35581	−	5.15850i	0.571368	−	1.25112i	−0.374698	−	0.927147i	$-0.622254\pi$
$17$	2.35581	−	5.15850i	0.571368	−	1.25112i	0.946066	−	0.323974i	$-0.105019\pi$
$18$	2.66297	+	1.38151i	0.627669	+	0.325626i
$19$	0.221397	−	0.101109i	0.0507920	−	0.0231959i	−0.389857	−	0.920875i	$-0.627476\pi$
$19$	0.221397	−	0.101109i	0.0507920	−	0.0231959i	0.440649	+	0.897679i	$0.354748\pi$
$20$	−0.126771	−	0.881709i	−0.0283468	−	0.197156i
$21$	0.203422	+	1.72006i	0.0443903	+	0.375349i
$22$		−	5.99593i		−	1.27834i
$23$	−1.23742	−	4.63344i	−0.258020	−	0.966140i
$23$	−1.23742	−	4.63344i	−0.258020	−	0.966140i
$24$	1.10107	+	1.33703i	0.224754	+	0.272920i
$25$	−3.53875	−	2.27422i	−0.707750	−	0.454843i
$26$	0.782632	−	0.112526i	0.153487	−	0.0220681i
$27$	3.12992	−	4.14772i	0.602353	−	0.798230i
$28$	−0.281733	+	0.959493i	−0.0532424	+	0.181327i
$29$	−9.65002	−	4.40701i	−1.79196	−	0.818362i	−0.967679	−	0.252185i	$-0.918851\pi$
$29$	−9.65002	−	4.40701i	−1.79196	−	0.818362i	−0.824284	−	0.566177i	$-0.808422\pi$
$30$	−1.54238	−	0.0386946i	−0.281599	−	0.00706463i
$31$	−1.07812	+	7.49848i	−0.193636	+	1.34677i	0.628649	+	0.777689i	$0.283608\pi$
$31$	−1.07812	+	7.49848i	−0.193636	+	1.34677i	−0.822284	+	0.569077i	$0.807301\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−10.2392	−	1.73532i	−1.78242	−	0.302080i
$34$	−3.06596	−	4.77073i	−0.525808	−	0.818174i
$35$	−0.481590	−	0.749368i	−0.0814035	−	0.126666i
$36$	2.60191	−	1.49333i	0.433652	−	0.248889i
$37$	0.00514929	+	0.0175369i	0.000846538	+	0.00288304i	0.959915	−	0.280291i	$-0.0904309\pi$
$37$	0.00514929	+	0.0175369i	0.000846538	+	0.00288304i	−0.959069	+	0.283174i	$0.908613\pi$
$38$	0.0346383	−	0.240915i	0.00561908	−	0.0390815i
$39$	0.0343465	−	1.36907i	0.00549984	−	0.219226i
$40$	−0.810278	−	0.370042i	−0.128116	−	0.0585087i
$41$	−2.32563	+	7.92037i	−0.363203	+	1.23695i	0.551961	+	0.833870i	$0.313880\pi$
$41$	−2.32563	+	7.92037i	−0.363203	+	1.23695i	−0.915163	+	0.403084i	$0.867938\pi$
$42$	1.55699	+	0.758807i	0.240248	+	0.117087i
$43$	4.07764	−	0.586276i	0.621834	−	0.0894062i	0.175805	−	0.984425i	$-0.443747\pi$
$43$	4.07764	−	0.586276i	0.621834	−	0.0894062i	0.446029	+	0.895019i	$0.352838\pi$
$44$	−5.04410	−	3.24164i	−0.760426	−	0.488696i
$45$	−0.512469	+	2.62273i	−0.0763944	+	0.390973i
$46$	−4.56690	−	1.46404i	−0.673353	−	0.215862i
$47$			3.11302i			0.454080i	0.973885	+	0.227040i	$0.0729049\pi$
$47$			3.11302i			0.454080i	−0.973885	+	0.227040i	$0.927095\pi$
$48$	1.72006	−	0.203422i	0.248270	−	0.0293614i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−3.82638	+	1.74745i	−0.541132	+	0.247127i
$51$	−9.03432	+	3.85502i	−1.26506	+	0.539810i
$52$	0.328461	−	0.719228i	0.0455493	−	0.0997390i
$53$	3.73466	−	4.31002i	0.512994	−	0.592027i	−0.438868	−	0.898551i	$-0.644621\pi$
$53$	3.73466	−	4.31002i	0.512994	−	0.592027i	0.951863	+	0.306524i	$0.0991661\pi$
$54$	−1.79713	−	4.87548i	−0.244558	−	0.663469i
$55$	5.12468	−	1.50474i	0.691011	−	0.202899i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	−0.401385	−	0.128876i	−0.0531648	−	0.0170701i
$58$	−8.92461	+	5.73550i	−1.17186	+	0.753108i
$59$	6.98134	−	6.04937i	0.908894	−	0.787561i	−0.0687926	−	0.997631i	$-0.521915\pi$
$59$	6.98134	−	6.04937i	0.908894	−	0.787561i	0.977686	+	0.210070i	$0.0673692\pi$
$60$	−0.866427	+	1.27662i	−0.111855	+	0.164810i
$61$	−11.0326	−	1.58624i	−1.41257	−	0.203098i	−0.606581	−	0.795022i	$-0.707459\pi$
$61$	−11.0326	−	1.58624i	−1.41257	−	0.203098i	−0.805994	+	0.591924i	$0.798369\pi$
$62$	5.72525	+	4.96095i	0.727107	+	0.630042i
$63$	1.74643	−	2.43926i	0.220030	−	0.307317i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	0.292585	+	0.640671i	0.0362907	+	0.0794655i
$66$	−6.99559	+	7.67562i	−0.861098	+	0.944803i
$67$	2.25890	−	3.51492i	0.275969	−	0.429416i	−0.675408	−	0.737444i	$-0.736033\pi$
$67$	2.25890	−	3.51492i	0.275969	−	0.429416i	0.951377	+	0.308028i	$0.0996690\pi$
$68$	−5.67098			−0.687707
$69$	−3.82188	+	7.37518i	−0.460101	+	0.887867i
$70$	−0.890776			−0.106468
$71$	2.07320	−	3.22596i	0.246044	−	0.382851i	−0.696163	−	0.717884i	$-0.745111\pi$
$71$	2.07320	−	3.22596i	0.246044	−	0.382851i	0.942207	+	0.335032i	$0.108747\pi$
$72$	0.150430	−	2.99623i	0.0177284	−	0.353109i
$73$	−0.110554	−	0.242079i	−0.0129394	−	0.0283333i	0.903052	−	0.429531i	$-0.141321\pi$
$73$	−0.110554	−	0.242079i	−0.0129394	−	0.0283333i	−0.915991	+	0.401198i	$0.868594\pi$
$74$	0.0175369	+	0.00514929i	0.00203862	+	0.000598593i
$75$	1.87670	+	7.04006i	0.216703	+	0.812916i
$76$	−0.183944	−	0.159388i	−0.0210998	−	0.0182831i
$77$	−5.93490	−	0.853309i	−0.676344	−	0.0972436i
$78$	−1.13316	−	0.769068i	−0.128306	−	0.0870798i
$79$	0.654880	−	0.567456i	0.0736797	−	0.0638438i	−0.617242	−	0.786773i	$-0.711750\pi$
$79$	0.654880	−	0.567456i	0.0736797	−	0.0638438i	0.690922	+	0.722929i	$0.257205\pi$
$80$	−0.749368	+	0.481590i	−0.0837819	+	0.0538434i
$81$	−8.84598	+	1.65791i	−0.982886	+	0.184212i
$82$	5.40571	+	6.23852i	0.596961	+	0.688929i
$83$	6.06737	−	1.78154i	0.665980	−	0.195550i	0.0687681	−	0.997633i	$-0.478093\pi$
$83$	6.06737	−	1.78154i	0.665980	−	0.195550i	0.597212	+	0.802083i	$0.296275\pi$
$84$	1.48012	−	0.899579i	0.161494	−	0.0981522i
$85$	3.30807	−	3.81772i	0.358811	−	0.414090i
$86$	1.71133	−	3.74729i	0.184538	−	0.404081i
$87$	7.21158	+	16.9005i	0.773163	+	1.81192i
$88$	−5.45409	+	2.49080i	−0.581408	+	0.265520i
$89$	−1.88807	−	13.1318i	−0.200135	−	1.39197i	−0.803880	−	0.594792i	$-0.797235\pi$
$89$	−1.88807	−	13.1318i	−0.200135	−	1.39197i	0.603745	−	0.797178i	$-0.293675\pi$
$90$	1.92932	+	1.84907i	0.203368	+	0.194909i
$91$		−	0.790680i		−	0.0828858i
$92$	−3.70069	+	3.05040i	−0.385823	+	0.318026i
$93$	10.1288	−	8.34122i	1.05031	−	0.864944i
$94$	2.61884	+	1.68302i	0.270112	+	0.173591i
$95$	0.214601	−	0.0308550i	0.0220176	−	0.00316565i
$96$	0.758807	−	1.55699i	0.0774454	−	0.158909i
$97$	−1.96716	+	6.69953i	−0.199735	+	0.680234i	0.797321	+	0.603555i	$0.206250\pi$
$97$	−1.96716	+	6.69953i	−0.199735	+	0.680234i	−0.997056	+	0.0766787i	$0.975568\pi$
$98$	0.909632	+	0.415415i	0.0918867	+	0.0419633i
$99$	11.0830	+	14.1678i	1.11388	+	1.42392i
$100$	−0.598650	+	4.16370i	−0.0598650	+	0.416370i
$101$	5.23646	+	17.8337i	0.521047	+	1.77452i	0.625754	+	0.780020i	$0.284791\pi$
$101$	5.23646	+	17.8337i	0.521047	+	1.77452i	−0.104707	+	0.994503i	$0.533391\pi$
$102$	−1.64127	+	9.68433i	−0.162510	+	0.958892i
$103$	−4.11874	−	6.40888i	−0.405831	−	0.631486i	0.576837	−	0.816860i	$-0.304287\pi$
$103$	−4.11874	−	6.40888i	−0.405831	−	0.631486i	−0.982668	+	0.185373i	$0.940651\pi$
$104$	−0.427474	−	0.665163i	−0.0419173	−	0.0652246i
$105$	−0.257805	+	1.52118i	−0.0251592	+	0.148452i
$106$	−1.60671	−	5.47197i	−0.156058	−	0.531484i
$107$	1.81502	−	12.6238i	0.175465	−	1.22039i	−0.691634	−	0.722249i	$-0.743109\pi$
$107$	1.81502	−	12.6238i	0.175465	−	1.22039i	0.867098	−	0.498137i	$-0.165982\pi$
$108$	−5.07312	−	1.12405i	−0.488161	−	0.108161i
$109$	−15.8580	−	7.24210i	−1.51892	−	0.693668i	−0.530821	−	0.847484i	$-0.678116\pi$
$109$	−15.8580	−	7.24210i	−1.51892	−	0.693668i	−0.988099	+	0.153817i	$0.950844\pi$
$110$	1.50474	−	5.12468i	0.143471	−	0.488619i
$111$	0.0138689	−	0.0284574i	0.00131638	−	0.00270106i
$112$	0.989821	−	0.142315i	0.0935293	−	0.0134475i
$113$	10.9534	+	7.03934i	1.03041	+	0.662205i	0.942597	−	0.333932i	$-0.108375\pi$
$113$	10.9534	+	7.03934i	1.03041	+	0.662205i	0.0878142	+	0.996137i	$0.472012\pi$
$114$	−0.325423	+	0.267991i	−0.0304787	+	0.0250997i
$115$	0.105197	−	4.27071i	0.00980970	−	0.398246i
$116$			10.6087i			0.984993i
$117$	−1.64129	+	1.71252i	−0.151738	+	0.158323i
$118$	−1.31465	−	9.14362i	−0.121024	−	0.841738i
$119$	−5.15850	+	2.35581i	−0.472879	+	0.215957i
$120$	0.605531	+	1.41908i	0.0552772	+	0.129543i
$121$	10.3651	−	22.6964i	0.942280	−	2.06331i
$122$	−7.29909	+	8.42359i	−0.660828	+	0.762636i
$123$	12.2180	−	7.42580i	1.10166	−	0.669562i
$124$	7.26872	−	2.13429i	0.652750	−	0.191665i
$125$	−5.37047	−	6.19786i	−0.480350	−	0.554353i
$126$	−1.10784	−	2.78795i	−0.0986943	−	0.248371i
$127$	−13.9758	+	8.98168i	−1.24015	+	0.796995i	−0.985440	−	0.170023i	$-0.945616\pi$
$127$	−13.9758	+	8.98168i	−1.24015	+	0.796995i	−0.254709	+	0.967018i	$0.581980\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−5.90396	−	4.00697i	−0.519815	−	0.352794i
$130$	0.697150	+	0.100235i	0.0611441	+	0.00879119i
$131$	−2.35319	−	2.03905i	−0.205599	−	0.178153i	0.545975	−	0.837802i	$-0.316160\pi$
$131$	−2.35319	−	2.03905i	−0.205599	−	0.178153i	−0.751574	+	0.659649i	$0.770705\pi$
$132$	2.67504	+	10.0348i	0.232832	+	0.873419i
$133$	−0.233533	−	0.0685715i	−0.0202499	−	0.00594590i
$134$	−1.73569	−	3.80062i	−0.149940	−	0.328324i
$135$	3.71603	−	2.75955i	0.319825	−	0.237504i
$136$	−3.06596	+	4.77073i	−0.262904	+	0.409087i
$137$	13.7355			1.17350			0.586751	−	0.809768i	$-0.300407\pi$
$137$	13.7355			1.17350			0.586751	+	0.809768i	$0.300407\pi$
$138$	4.13813	+	7.20249i	0.352261	+	0.613117i
$139$	−2.42279			−0.205499			−0.102749	−	0.994707i	$-0.532764\pi$
$139$	−2.42279			−0.205499			−0.102749	+	0.994707i	$0.532764\pi$
$140$	−0.481590	+	0.749368i	−0.0407018	+	0.0633332i
$141$	3.63203	−	3.98509i	0.305872	−	0.335605i
$142$	−1.59300	−	3.48817i	−0.133681	−	0.292721i
$143$	4.54882	+	1.33566i	0.380392	+	0.111693i
$144$	−2.43926	−	1.74643i	−0.203271	−	0.145536i
$145$	−7.14181	−	6.18842i	−0.593095	−	0.513920i
$146$	−0.263420	−	0.0378741i	−0.0218008	−	0.00313448i
$147$	0.972666	−	1.43315i	0.0802242	−	0.118204i
$148$	0.0138130	−	0.0119690i	0.00113542	−	0.000983849i
$149$	9.10415	−	5.85088i	0.745841	−	0.479323i	−0.111698	−	0.993742i	$-0.535629\pi$
$149$	9.10415	−	5.85088i	0.745841	−	0.479323i	0.857539	+	0.514419i	$0.171992\pi$
$150$	6.93709	+	2.22736i	0.566411	+	0.181863i
$151$	3.95496	+	4.56427i	0.321850	+	0.371435i	0.893500	−	0.449063i	$-0.148242\pi$
$151$	3.95496	+	4.56427i	0.321850	+	0.371435i	−0.571650	+	0.820497i	$0.693697\pi$
$152$	−0.233533	+	0.0685715i	−0.0189420	+	0.00556188i
$153$	16.0629	+	5.60560i	1.29861	+	0.453186i
$154$	−3.92650	+	4.53142i	−0.316406	+	0.365152i
$155$	−2.80328	+	6.13833i	−0.225165	+	0.493043i
$156$	−1.25962	+	0.537489i	−0.100850	+	0.0430335i
$157$	−1.14177	+	0.521429i	−0.0911231	+	0.0416145i	−0.460455	−	0.887683i	$-0.652314\pi$
$157$	−1.14177	+	0.521429i	−0.0911231	+	0.0416145i	0.369332	+	0.929298i	$0.379587\pi$
$158$	−0.123320	−	0.857710i	−0.00981082	−	0.0682357i
$159$	−9.80948	+	1.16011i	−0.777943	+	0.0920028i
$160$			0.890776i			0.0704220i
$161$	−2.09908	+	4.31206i	−0.165431	+	0.339838i
$162$	−3.38777	+	8.33804i	−0.266169	+	0.655099i
$163$	15.1833	+	9.75770i	1.18925	+	0.764282i	0.977064	−	0.212948i	$-0.0683065\pi$
$163$	15.1833	+	9.75770i	1.18925	+	0.764282i	0.212183	+	0.977230i	$0.431943\pi$
$164$	8.17072	−	1.17477i	0.638026	−	0.0917343i
$165$	−8.31591	−	4.05281i	−0.647393	−	0.315511i
$166$	1.78154	−	6.06737i	0.138274	−	0.470919i
$167$	10.9453	+	4.99857i	0.846975	+	0.386801i	0.791137	−	0.611639i	$-0.209490\pi$
$167$	10.9453	+	4.99857i	0.846975	+	0.386801i	0.0558384	+	0.998440i	$0.482217\pi$
$168$	0.0434392	−	1.73151i	0.00335140	−	0.133589i
$169$	1.76112	−	12.2489i	0.135471	−	0.942221i
$170$	−1.42319	−	4.84695i	−0.109154	−	0.371744i
$171$	0.363465	+	0.633286i	0.0277949	+	0.0484286i
$172$	−2.22721	−	3.46560i	−0.169823	−	0.264250i
$173$	9.35504	+	14.5567i	0.711250	+	1.10673i	0.989263	+	0.146150i	$0.0466881\pi$
$173$	9.35504	+	14.5567i	0.711250	+	1.10673i	−0.278012	+	0.960578i	$0.589676\pi$
$174$	18.1165	+	3.07033i	1.37341	+	0.232761i
$175$	1.18511	+	4.03613i	0.0895861	+	0.305102i
$176$	−0.853309	+	5.93490i	−0.0643206	+	0.447360i
$177$	−15.9950	−	0.401276i	−1.20226	−	0.0301617i
$178$	−12.0680	−	5.51125i	−0.904531	−	0.413086i
$179$	−0.665674	+	2.26708i	−0.0497548	+	0.169449i	−0.980622	−	0.195907i	$-0.937235\pi$
$179$	−0.665674	+	2.26708i	−0.0497548	+	0.169449i	0.930868	+	0.365357i	$0.119053\pi$
$180$	2.59861	−	0.623363i	0.193689	−	0.0464627i
$181$	13.2186	−	1.90055i	0.982531	−	0.141267i	0.367716	−	0.929938i	$-0.380140\pi$
$181$	13.2186	−	1.90055i	0.982531	−	0.141267i	0.614815	+	0.788672i	$0.289231\pi$
$182$	−0.665163	−	0.427474i	−0.0493051	−	0.0316865i
$183$	12.2725	+	14.9026i	0.907209	+	1.10163i
$184$	0.565417	+	4.76238i	0.0416831	+	0.351088i
$185$			0.0162809i			0.00119700i
$186$	−1.54104	−	13.0305i	−0.112995	−	0.955442i
$187$	−4.83910	−	33.6567i	−0.353870	−	2.46122i
$188$	2.83170	−	1.29319i	0.206523	−	0.0943159i
$189$	−5.08162	+	1.08498i	−0.369633	+	0.0789208i
$190$	0.0900652	−	0.197215i	0.00653402	−	0.0143075i
$191$	0.335754	−	0.387480i	0.0242943	−	0.0280371i	−0.743472	−	0.668767i	$-0.766823\pi$
$191$	0.335754	−	0.387480i	0.0242943	−	0.0280371i	0.767767	+	0.640730i	$0.221368\pi$
$192$	−0.899579	−	1.48012i	−0.0649216	−	0.106818i
$193$	4.49793	−	1.32071i	0.323768	−	0.0950669i	−0.115810	−	0.993271i	$-0.536946\pi$
$193$	4.49793	−	1.32071i	0.323768	−	0.0950669i	0.439578	+	0.898205i	$0.355128\pi$
$194$	4.57248	+	5.27692i	0.328285	+	0.378861i
$195$	0.372938	−	1.16151i	0.0267066	−	0.0831777i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	5.44578	−	4.71879i	0.387996	−	0.336200i	−0.438920	−	0.898526i	$-0.644639\pi$
$197$	5.44578	−	4.71879i	0.387996	−	0.336200i	0.826916	+	0.562326i	$0.190093\pi$
$198$	17.9107	−	1.66392i	1.27286	−	0.118250i
$199$	26.5772	+	3.82123i	1.88401	+	0.270880i	0.985704	−	0.168488i	$-0.0538883\pi$
$199$	26.5772	+	3.82123i	1.88401	+	0.270880i	0.898307	+	0.439368i	$0.144797\pi$
$200$	3.17907	+	2.75468i	0.224795	+	0.194786i
$201$	−6.99266	+	1.86407i	−0.493224	+	0.131481i
$202$	17.8337	+	5.23646i	1.25478	+	0.368436i
$203$	4.40701	+	9.65002i	0.309312	+	0.677298i
$204$	7.25964	+	6.61647i	0.508276	+	0.463246i
$205$	−3.97540	+	6.18584i	−0.277654	+	0.432038i
$206$	−7.61826			−0.530789
$207$	13.4973	−	4.98216i	0.938130	−	0.346284i
$208$	−0.790680			−0.0548238
$209$	0.788991	−	1.22769i	0.0545756	−	0.0849213i
$210$	1.14032	+	1.03929i	0.0786893	+	0.0717178i
$211$	11.0458	+	24.1869i	0.760423	+	1.66509i	0.746675	+	0.665189i	$0.231649\pi$
$211$	11.0458	+	24.1869i	0.760423	+	1.66509i	0.0137477	+	0.999905i	$0.495624\pi$
$212$	−5.47197	−	1.60671i	−0.375816	−	0.110350i
$213$	−6.41779	+	1.71082i	−0.439740	+	0.117224i
$214$	−9.63851	−	8.35182i	−0.658875	−	0.570918i
$215$	3.63226	+	0.522240i	0.247718	+	0.0356165i
$216$	−3.68834	+	3.66007i	−0.250960	+	0.249036i
$217$	5.72525	−	4.96095i	0.388655	−	0.336771i
$218$	−14.6659	+	9.42522i	−0.993302	+	0.638356i
$219$	−0.140916	+	0.438881i	−0.00952219	+	0.0296568i
$220$	−3.49763	−	4.03648i	−0.235810	−	0.272139i
$221$	4.30230	−	1.26327i	0.289404	−	0.0849767i
$222$	−0.0164418	−	0.0270525i	−0.00110350	−	0.00181564i
$223$	6.12882	−	7.07304i	0.410416	−	0.473646i	−0.512477	−	0.858701i	$-0.671272\pi$
$223$	6.12882	−	7.07304i	0.410416	−	0.473646i	0.922894	+	0.385055i	$0.125818\pi$
$224$	0.415415	−	0.909632i	0.0277561	−	0.0607773i
$225$	5.81136	−	11.2018i	0.387424	−	0.746789i
$226$	11.8437	−	5.40885i	0.787834	−	0.359792i
$227$	3.10719	+	21.6110i	0.206232	+	1.43437i	0.785311	+	0.619102i	$0.212503\pi$
$227$	3.10719	+	21.6110i	0.206232	+	1.43437i	−0.579079	+	0.815271i	$0.696588\pi$
$228$	0.0495113	+	0.418650i	0.00327897	+	0.0277258i
$229$			3.76322i			0.248681i	0.992240	+	0.124340i	$0.0396815\pi$
$229$			3.76322i			0.248681i	−0.992240	+	0.124340i	$0.960319\pi$
$230$	−3.53588	−	2.39742i	−0.233149	−	0.158081i
$231$	6.60191	+	8.01674i	0.434374	+	0.527463i
$232$	8.92461	+	5.73550i	0.585929	+	0.376554i
$233$	−8.80650	+	1.26618i	−0.576933	+	0.0829504i	−0.424604	−	0.905379i	$-0.639587\pi$
$233$	−8.80650	+	1.26618i	−0.576933	+	0.0829504i	−0.152329	+	0.988330i	$0.548677\pi$
$234$	0.553316	+	2.30660i	0.0361714	+	0.150787i
$235$	−0.781245	+	2.66067i	−0.0509628	+	0.173563i
$236$	−8.40286	−	3.83746i	−0.546979	−	0.249797i
$237$	−1.50040	−	0.0376413i	−0.0974616	−	0.00244507i
$238$	−0.807065	+	5.61326i	−0.0523142	+	0.363853i
$239$	−4.93729	−	16.8149i	−0.319367	−	1.08766i	−0.950173	−	0.311723i	$-0.899094\pi$
$239$	−4.93729	−	16.8149i	−0.319367	−	1.08766i	0.630807	−	0.775940i	$-0.282724\pi$
$240$	1.52118	+	0.257805i	0.0981916	+	0.0166412i
$241$	2.99619	+	4.66216i	0.193001	+	0.300316i	0.924245	−	0.381801i	$-0.124696\pi$
$241$	2.99619	+	4.66216i	0.193001	+	0.300316i	−0.731243	+	0.682117i	$0.761060\pi$
$242$	−13.4896	−	20.9902i	−0.867145	−	1.34930i
$243$	13.2584	+	8.19846i	0.850527	+	0.525932i
$244$	3.14019	+	10.6945i	0.201030	+	0.684646i
$245$	−0.126771	+	0.881709i	−0.00809908	+	0.0563303i
$246$	0.358579	−	14.2931i	0.0228622	−	0.911297i
$247$	0.175055	+	0.0799447i	0.0111385	+	0.00508676i
$248$	2.13429	−	7.26872i	0.135527	−	0.461564i
$249$	−9.84564	−	4.79833i	−0.623942	−	0.304082i
$250$	−8.11747	+	1.16712i	−0.513394	+	0.0738149i
$251$	15.7065	+	10.0940i	0.991386	+	0.637125i	0.932512	−	0.361140i	$-0.117612\pi$
$251$	15.7065	+	10.0940i	0.991386	+	0.637125i	0.0588746	+	0.998265i	$0.481249\pi$
$252$	−2.94432	−	0.575307i	−0.185475	−	0.0362409i
$253$	−21.2616	−	19.3603i	−1.33671	−	1.21717i
$254$			16.6130i			1.04239i
$255$	−8.68902	+	1.02760i	−0.544128	+	0.0643508i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−24.0641	+	10.9897i	−1.50108	+	0.685520i	−0.985242	−	0.171167i	$-0.945246\pi$
$257$	−24.0641	+	10.9897i	−1.50108	+	0.685520i	−0.515837	+	0.856687i	$0.672519\pi$
$258$	−6.56280	+	2.80040i	−0.408582	+	0.174345i
$259$	0.00759263	−	0.0166255i	0.000471783	−	0.00103306i
$260$	0.461231	−	0.532289i	0.0286043	−	0.0330111i
$261$	10.4864	−	30.0489i	0.649092	−	1.85998i
$262$	−2.98759	+	0.877236i	−0.184574	+	0.0541958i
$263$	−11.9013	−	13.7348i	−0.733865	−	0.846925i	0.259036	−	0.965868i	$-0.416595\pi$
$263$	−11.9013	−	13.7348i	−0.733865	−	0.846925i	−0.992901	+	0.118942i	$0.962050\pi$
$264$	9.88806	+	3.17485i	0.608568	+	0.195399i
$265$	4.27363	−	2.74649i	0.262527	−	0.168716i
$266$	−0.183944	+	0.159388i	−0.0112783	+	0.00977271i
$267$	−12.9042	+	19.0134i	−0.789725	+	1.16360i
$268$	−4.13567	−	0.594620i	−0.252626	−	0.0363222i
$269$	−7.13791	−	6.18503i	−0.435206	−	0.377108i	0.409525	−	0.912299i	$-0.365694\pi$
$269$	−7.13791	−	6.18503i	−0.435206	−	0.377108i	−0.844731	+	0.535191i	$0.820240\pi$
$270$	−0.312438	−	4.61805i	−0.0190144	−	0.281045i
$271$	−10.1782	−	2.98858i	−0.618280	−	0.181543i	−0.0424308	−	0.999099i	$-0.513510\pi$
$271$	−10.1782	−	2.98858i	−0.618280	−	0.181543i	−0.575849	+	0.817556i	$0.695328\pi$
$272$	2.35581	+	5.15850i	0.142842	+	0.312780i
$273$	−0.922506	+	1.01218i	−0.0558326	+	0.0612599i
$274$	7.42596	−	11.5550i	0.448619	−	0.698065i
$275$	−25.2220			−1.52094
$276$	8.29636	+	0.412748i	0.499382	+	0.0248445i
$277$	19.7452			1.18638			0.593188	−	0.805064i	$-0.297869\pi$
$277$	19.7452			1.18638			0.593188	+	0.805064i	$0.297869\pi$
$278$	−1.30986	+	2.03818i	−0.0785602	+	0.122242i
$279$	−22.6982	−	1.13960i	−1.35890	−	0.0682260i
$280$	0.370042	+	0.810278i	0.0221142	+	0.0484234i
$281$	−3.01320	−	0.884754i	−0.179752	−	0.0527800i	0.190618	−	0.981664i	$-0.438951\pi$
$281$	−3.01320	−	0.884754i	−0.179752	−	0.0527800i	−0.370370	+	0.928884i	$0.620769\pi$
$282$	−1.38885	−	5.20997i	−0.0827047	−	0.310249i
$283$	10.4544	+	9.05883i	0.621452	+	0.538492i	0.907676	−	0.419671i	$-0.137855\pi$
$283$	10.4544	+	9.05883i	0.621452	+	0.538492i	−0.286224	+	0.958163i	$0.592400\pi$
$284$	−3.79568	−	0.545736i	−0.225232	−	0.0323835i
$285$	−0.310718	−	0.210882i	−0.0184054	−	0.0124916i
$286$	3.58291	−	3.10460i	0.211862	−	0.183579i
$287$	6.94433	−	4.46285i	0.409911	−	0.263434i
$288$	−2.78795	+	1.10784i	−0.164282	+	0.0652802i
$289$	−9.92769	−	11.4572i	−0.583982	−	0.673951i
$290$	−9.06718	+	2.66237i	−0.532443	+	0.156339i
$291$	10.3347	−	6.28119i	0.605833	−	0.368210i
$292$	−0.174277	+	0.201127i	−0.0101988	+	0.0117701i
$293$	−11.1384	+	24.3898i	−0.650714	+	1.42487i	0.240213	+	0.970720i	$0.422783\pi$
$293$	−11.1384	+	24.3898i	−0.650714	+	1.42487i	−0.890927	+	0.454146i	$0.849945\pi$
$294$	−0.679780	−	1.59308i	−0.0396456	−	0.0929102i
$295$	7.48506	−	3.41831i	0.435797	−	0.199022i
$296$	−0.00260112	−	0.0180912i	−0.000151187	−	0.00105153i
$297$	2.34216	−	31.0676i	0.135906	−	1.80272i
$298$		−	10.8221i		−	0.626909i
$299$	2.12803	−	3.13856i	0.123067	−	0.181507i
$300$	5.62425	−	4.63166i	0.324716	−	0.267409i
$301$	−3.46560	−	2.22721i	−0.199754	−	0.128374i
$302$	5.97792	−	0.859495i	0.343991	−	0.0494584i
$303$	14.1037	−	28.9392i	0.810235	−	1.66251i
$304$	−0.0685715	+	0.233533i	−0.00393285	+	0.0133940i
$305$	−9.03137	−	4.12449i	−0.517135	−	0.236167i
$306$	13.4000	−	10.4824i	0.766027	−	0.599237i
$307$	−1.00765	+	7.00839i	−0.0575099	+	0.399990i	0.940651	+	0.339375i	$0.110215\pi$
$307$	−1.00765	+	7.00839i	−0.0575099	+	0.399990i	−0.998161	+	0.0606155i	$0.980694\pi$
$308$	1.68925	+	5.75305i	0.0962538	+	0.327810i
$309$	−2.20485	+	13.0097i	−0.125429	+	0.740096i
$310$	3.64832	+	5.67690i	0.207211	+	0.322426i
$311$	7.63465	+	11.8797i	0.432921	+	0.673639i	0.987343	−	0.158597i	$-0.0506971\pi$
$311$	7.63465	+	11.8797i	0.432921	+	0.673639i	−0.554422	+	0.832236i	$0.687061\pi$
$312$	−0.228836	+	1.35024i	−0.0129553	+	0.0764426i
$313$	5.99213	+	20.4073i	0.338695	+	1.15349i	0.936154	+	0.351591i	$0.114359\pi$
$313$	5.99213	+	20.4073i	0.338695	+	1.15349i	−0.597459	+	0.801900i	$0.703823\pi$
$314$	−0.178633	+	1.24242i	−0.0100809	+	0.0701140i
$315$	2.10482	−	1.64653i	0.118593	−	0.0927715i
$316$	−0.788223	−	0.359970i	−0.0443410	−	0.0202499i
$317$	−6.57891	+	22.4057i	−0.369508	+	1.25843i	0.539618	+	0.841910i	$0.318569\pi$
$317$	−6.57891	+	22.4057i	−0.369508	+	1.25843i	−0.909127	+	0.416520i	$0.863250\pi$
$318$	−4.32746	+	8.87947i	−0.242672	+	0.497936i
$319$	−62.9616	+	9.05251i	−3.52517	+	0.506843i
$320$	0.749368	+	0.481590i	0.0418910	+	0.0269217i
$321$	−17.0519	+	14.0425i	−0.951746	+	0.783778i
$322$	2.49269	+	4.09713i	0.138912	+	0.228324i
$323$		−	1.38027i		−	0.0768004i
$324$	5.18284	+	7.35786i	0.287936	+	0.408770i
$325$	−0.473341	−	3.29216i	−0.0262562	−	0.182616i
$326$	16.4174	−	7.49757i	0.909276	−	0.415252i
$327$	11.8509	+	27.7728i	0.655355	+	1.53584i
$328$	3.42915	−	7.50878i	0.189343	−	0.414603i
$329$	2.03859	−	2.35266i	0.112391	−	0.129706i
$330$	−7.90536	+	4.80468i	−0.435176	+	0.264489i
$331$	−21.3216	+	6.26058i	−1.17194	+	0.344113i	−0.809061	−	0.587724i	$-0.800024\pi$
$331$	−21.3216	+	6.26058i	−1.17194	+	0.344113i	−0.362878	+	0.931837i	$0.618206\pi$
$332$	−4.14102	−	4.77900i	−0.227268	−	0.262281i
$333$	−0.0509561	+	0.0202483i	−0.00279238	+	0.00110960i
$334$	10.1226	−	6.50537i	0.553882	−	0.355958i
$335$	2.81278	−	2.43728i	0.153678	−	0.133163i
$336$	−1.43315	−	0.972666i	−0.0781848	−	0.0530633i
$337$	31.9595	+	4.59508i	1.74095	+	0.250310i	0.938220	−	0.346039i	$-0.112473\pi$
$337$	31.9595	+	4.59508i	1.74095	+	0.250310i	0.802725	+	0.596349i	$0.203382\pi$
$338$	−9.35227	−	8.10379i	−0.508696	−	0.440788i
$339$	−5.80893	−	21.7910i	−0.315498	−	1.18352i
$340$	−4.84695	−	1.42319i	−0.262863	−	0.0771834i
$341$	18.8693	+	41.3179i	1.02183	+	2.23749i
$342$	0.729258	+	0.0366136i	0.0394338	+	0.00197984i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−4.11957			−0.222112
$345$	−5.11741	+	5.34437i	−0.275512	+	0.287731i
$346$	17.3036			0.930248
$347$	14.9645	−	23.2852i	0.803336	−	1.25002i	−0.161424	−	0.986885i	$-0.551609\pi$
$347$	14.9645	−	23.2852i	0.803336	−	1.25002i	0.964760	−	0.263131i	$-0.0847551\pi$
$348$	12.3774	−	13.5806i	0.663500	−	0.727997i
$349$	1.73501	+	3.79913i	0.0928727	+	0.203363i	0.950367	−	0.311130i	$-0.100707\pi$
$349$	1.73501	+	3.79913i	0.0928727	+	0.203363i	−0.857495	+	0.514493i	$0.827980\pi$
$350$	4.03613	+	1.18511i	0.215740	+	0.0633470i
$351$	4.09913	−	0.277330i	0.218795	−	0.0148028i
$352$	4.53142	+	3.92650i	0.241525	+	0.209283i
$353$	−12.2533	−	1.76176i	−0.652176	−	0.0937688i	−0.191718	−	0.981450i	$-0.561406\pi$
$353$	−12.2533	−	1.76176i	−0.652176	−	0.0937688i	−0.460458	+	0.887681i	$0.652315\pi$
$354$	−8.98514	+	13.2389i	−0.477555	+	0.703641i
$355$	2.58154	−	2.23692i	0.137014	−	0.118723i
$356$	−11.1608	+	7.17260i	−0.591520	+	0.380147i
$357$	9.35218	+	3.00279i	0.494970	+	0.158925i
$358$	1.54730	+	1.78568i	0.0817772	+	0.0943759i
$359$	6.04088	−	1.77376i	0.318825	−	0.0936156i	−0.118404	−	0.992965i	$-0.537778\pi$
$359$	6.04088	−	1.77376i	0.318825	−	0.0936156i	0.437230	+	0.899350i	$0.355960\pi$
$360$	0.880506	−	2.52310i	0.0464067	−	0.132979i
$361$	−12.4036	+	14.3145i	−0.652819	+	0.753393i
$362$	5.54767	−	12.1477i	0.291579	−	0.638469i
$363$	−39.7491	+	16.9613i	−2.08629	+	0.890237i
$364$	−0.719228	+	0.328461i	−0.0376978	+	0.0172160i
$365$	−0.0337373	−	0.234648i	−0.00176589	−	0.0122820i
$366$	19.1719	−	2.26734i	1.00213	−	0.118516i
$367$		−	19.0668i		−	0.995277i	−0.867385	−	0.497638i	$-0.834201\pi$
$367$		−	19.0668i		−	0.995277i	0.867385	−	0.497638i	$-0.165799\pi$
$368$	4.31206	+	2.09908i	0.224782	+	0.109422i
$369$	−24.3046	−	4.74901i	−1.26525	−	0.247224i
$370$	0.0136964	+	0.00880212i	0.000712040	+	0.000457601i
$371$	−5.64493	+	0.811618i	−0.293070	+	0.0421371i
$372$	−11.7951	−	5.74841i	−0.611547	−	0.298041i
$373$	−4.61298	+	15.7104i	−0.238851	+	0.813452i	0.749597	+	0.661894i	$0.230247\pi$
$373$	−4.61298	+	15.7104i	−0.238851	+	0.813452i	−0.988448	+	0.151558i	$0.951571\pi$
$374$	−30.9300	−	14.1253i	−1.59935	−	0.730400i
$375$	−0.356242	+	14.2000i	−0.0183963	+	0.733284i
$376$	0.443029	−	3.08133i	0.0228475	−	0.158908i
$377$	−2.36320	−	8.04832i	−0.121711	−	0.414509i
$378$	−1.83458	+	4.86151i	−0.0943608	+	0.250049i
$379$	7.26422	+	11.3033i	0.373138	+	0.580614i	0.976144	−	0.217122i	$-0.0696671\pi$
$379$	7.26422	+	11.3033i	0.373138	+	0.580614i	−0.603007	+	0.797736i	$0.706031\pi$
$380$	−0.117215	−	0.182390i	−0.00601301	−	0.00935643i
$381$	28.3701	+	4.80808i	1.45344	+	0.246325i
$382$	−0.144447	−	0.491942i	−0.00739056	−	0.0251699i
$383$	1.90657	−	13.2605i	0.0974213	−	0.677580i	−0.881326	−	0.472509i	$-0.843348\pi$
$383$	1.90657	−	13.2605i	0.0974213	−	0.677580i	0.978747	−	0.205071i	$-0.0657425\pi$
$384$	−1.73151	−	0.0434392i	−0.0883605	−	0.00221675i
$385$	−4.85837	−	2.21874i	−0.247605	−	0.113078i
$386$	1.32071	−	4.49793i	0.0672224	−	0.228939i
$387$	2.88286	+	12.0178i	0.146544	+	0.610897i
$388$	6.91129	−	0.993694i	0.350868	−	0.0504472i
$389$	7.22987	+	4.64635i	0.366569	+	0.235580i	0.710938	−	0.703255i	$-0.248271\pi$
$389$	7.22987	+	4.64635i	0.366569	+	0.235580i	−0.344369	+	0.938834i	$0.611907\pi$
$390$	−0.775502	−	0.941697i	−0.0392691	−	0.0476847i
$391$	−26.8168	−	4.53228i	−1.35618	−	0.229207i
$392$		−	1.00000i		−	0.0505076i
$393$	0.633399	+	5.35579i	0.0319507	+	0.270164i
$394$	−1.02549	−	7.13245i	−0.0516635	−	0.359328i
$395$	0.702130	−	0.320652i	0.0353280	−	0.0161338i
$396$	8.28346	−	15.9670i	0.416259	−	0.802371i
$397$	7.89735	−	17.2928i	0.396357	−	0.867900i	−0.601270	−	0.799046i	$-0.705338\pi$
$397$	7.89735	−	17.2928i	0.396357	−	0.867900i	0.997627	−	0.0688543i	$-0.0219343\pi$
$398$	17.5834	−	20.2923i	0.881375	−	1.01716i
$399$	0.218951	+	0.360250i	0.0109612	+	0.0180351i
$400$	4.03613	−	1.18511i	0.201806	−	0.0592557i
$401$	−6.67068	−	7.69837i	−0.333118	−	0.384438i	0.564337	−	0.825544i	$-0.309132\pi$
$401$	−6.67068	−	7.69837i	−0.333118	−	0.384438i	−0.897455	+	0.441106i	$0.854586\pi$
$402$	−2.21236	+	6.89039i	−0.110343	+	0.343661i
$403$	−5.03900	+	3.23837i	−0.251010	+	0.161315i
$404$	14.0468	−	12.1717i	0.698856	−	0.605562i
$405$	−7.97666	−	0.802987i	−0.396364	−	0.0399007i
$406$	10.5007	+	1.50978i	0.521142	+	0.0749289i
$407$	0.0828218	+	0.0717655i	0.00410532	+	0.00355728i
$408$	9.49099	−	2.53006i	0.469874	−	0.125257i
$409$	9.73183	+	2.85752i	0.481208	+	0.141295i	0.513335	−	0.858188i	$-0.328410\pi$
$409$	9.73183	+	2.85752i	0.481208	+	0.141295i	−0.0321268	+	0.999484i	$0.510228\pi$
$410$	3.05460	+	6.68864i	0.150856	+	0.330328i
$411$	−17.5833	−	16.0255i	−0.867321	−	0.790481i
$412$	−4.11874	+	6.40888i	−0.202916	+	0.315743i
$413$	−9.23764			−0.454555
$414$	3.10595	−	14.0482i	0.152649	−	0.690433i
$415$	5.63284			0.276505
$416$	−0.427474	+	0.665163i	−0.0209586	+	0.0326123i
$417$	3.10151	+	2.82673i	0.151882	+	0.138426i
$418$	−0.606241	−	1.32748i	−0.0296522	−	0.0649293i
$419$	2.52710	+	0.742024i	0.123457	+	0.0362502i	0.342877	−	0.939380i	$-0.388598\pi$
$419$	2.52710	+	0.742024i	0.123457	+	0.0362502i	−0.219420	+	0.975630i	$0.570417\pi$
$420$	1.49081	−	0.397412i	0.0727440	−	0.0193917i
$421$	−8.31487	−	7.20488i	−0.405242	−	0.351144i	0.428265	−	0.903653i	$-0.359125\pi$
$421$	−8.31487	−	7.20488i	−0.405242	−	0.351144i	−0.833507	+	0.552509i	$0.813670\pi$
$422$	26.3191	+	3.78412i	1.28119	+	0.184208i
$423$	−9.29901	+	0.863888i	−0.452134	+	0.0420037i
$424$	−4.31002	+	3.73466i	−0.209313	+	0.181371i
$425$	−20.0682	+	12.8970i	−0.973449	+	0.625598i
$426$	−2.03048	+	6.32393i	−0.0983772	+	0.306396i
$427$	7.29909	+	8.42359i	0.353228	+	0.407646i
$428$	−12.2370	+	3.59310i	−0.591496	+	0.173679i
$429$	−4.26478	−	7.01705i	−0.205906	−	0.338786i
$430$	2.40308	−	2.77331i	0.115887	−	0.133741i
$431$	2.11178	−	4.62415i	0.101721	−	0.222738i	−0.851928	−	0.523659i	$-0.824567\pi$
$431$	2.11178	−	4.62415i	0.101721	−	0.222738i	0.953649	+	0.300921i	$0.0972940\pi$
$432$	1.08498	+	5.08162i	0.0522012	+	0.244489i
$433$	10.7758	−	4.92116i	0.517854	−	0.236496i	−0.139303	−	0.990250i	$-0.544486\pi$
$433$	10.7758	−	4.92116i	0.517854	−	0.236496i	0.657157	+	0.753754i	$0.271759\pi$
$434$	−1.07812	−	7.49848i	−0.0517513	−	0.359938i
$435$	1.92233	+	16.2546i	0.0921688	+	0.779346i
$436$			17.4334i			0.834909i
$437$	−0.742443	−	0.900718i	−0.0355159	−	0.0430872i
$438$	0.293026	+	0.355823i	0.0140013	+	0.0170019i
$439$	−27.8493	−	17.8977i	−1.32918	−	0.854210i	−0.333116	−	0.942886i	$-0.608100\pi$
$439$	−27.8493	−	17.8977i	−1.32918	−	0.854210i	−0.996060	+	0.0886764i	$0.971736\pi$
$440$	−5.28666	+	0.760107i	−0.252032	+	0.0362367i
$441$	−2.91724	+	0.699798i	−0.138916	+	0.0333237i
$442$	1.26327	−	4.30230i	0.0600876	−	0.204640i
$443$	7.70507	+	3.51879i	0.366079	+	0.167183i	0.589957	−	0.807435i	$-0.299145\pi$
$443$	7.70507	+	3.51879i	0.366079	+	0.167183i	−0.223878	+	0.974617i	$0.571872\pi$
$444$	−0.0316471		0.000793948i	−0.00150191		3.76791e-5i
$445$	1.68185	−	11.6975i	0.0797272	−	0.554515i
$446$	−2.63673	−	8.97987i	−0.124853	−	0.425209i
$447$	−18.4809	−	3.13210i	−0.874119	−	0.148143i
$448$	−0.540641	−	0.841254i	−0.0255429	−	0.0397455i
$449$	5.08053	+	7.90546i	0.239765	+	0.373082i	0.940193	−	0.340641i	$-0.110644\pi$
$449$	5.08053	+	7.90546i	0.239765	+	0.373082i	−0.700428	+	0.713723i	$0.747008\pi$
$450$	−6.28173	−	10.9450i	−0.296124	−	0.515952i
$451$	13.9443	+	47.4900i	0.656612	+	2.23622i
$452$	1.85299	−	12.8878i	0.0871573	−	0.606193i
$453$	0.262346	−	10.4572i	0.0123261	−	0.491324i
$454$	19.8602	+	9.06986i	0.932086	+	0.425669i
$455$	0.198430	−	0.675789i	0.00930252	−	0.0316815i
$456$	0.378959	+	0.184688i	0.0177464	+	0.00864880i
$457$	9.24807	−	1.32967i	0.432606	−	0.0621994i	0.0774280	−	0.996998i	$-0.475329\pi$
$457$	9.24807	−	1.32967i	0.432606	−	0.0621994i	0.355178	+	0.934799i	$0.384420\pi$
$458$	3.16583	+	2.03455i	0.147929	+	0.0950684i
$459$	−14.0226	−	25.9169i	−0.654517	−	1.20970i
$460$	−3.92848	+	1.67843i	−0.183166	+	0.0782571i
$461$		−	18.4418i		−	0.858920i	−0.903086	−	0.429460i	$-0.858704\pi$
$461$		−	18.4418i		−	0.858920i	0.903086	−	0.429460i	$-0.141296\pi$
$462$	10.3134	−	1.21970i	0.479822	−	0.0567457i
$463$	−0.549340	−	3.82074i	−0.0255300	−	0.177565i	0.973067	−	0.230524i	$-0.0740439\pi$
$463$	−0.549340	−	3.82074i	−0.0255300	−	0.177565i	−0.998597	+	0.0529587i	$0.983135\pi$
$464$	9.65002	−	4.40701i	0.447991	−	0.204591i
$465$	10.7503	−	4.58725i	0.498535	−	0.212729i
$466$	−3.69597	+	8.09305i	−0.171213	+	0.374903i
$467$	14.0939	−	16.2652i	0.652187	−	0.752663i	−0.329294	−	0.944228i	$-0.606811\pi$
$467$	14.0939	−	16.2652i	0.652187	−	0.752663i	0.981480	+	0.191564i	$0.0613560\pi$
$468$	2.23958	+	0.781565i	0.103525	+	0.0361279i
$469$	−4.00895	+	1.17713i	−0.185116	+	0.0543550i
$470$	1.81593	+	2.09569i	0.0837626	+	0.0966672i
$471$	2.06999	+	0.664629i	0.0953799	+	0.0306245i
$472$	−7.77120	+	4.99425i	−0.357698	+	0.229879i
$473$	18.6675	−	16.1755i	0.858332	−	0.743749i
$474$	−0.842844	+	1.24187i	−0.0387131	+	0.0570409i
$475$	−1.01341	−	0.145707i	−0.0464986	−	0.00668549i
$476$	4.28584	+	3.71370i	0.196441	+	0.170217i
$477$	13.9110	+	9.95986i	0.636942	+	0.456031i
$478$	−16.8149	−	4.93729i	−0.769094	−	0.225826i
$479$	−2.31278	−	5.06428i	−0.105673	−	0.231393i	0.849408	−	0.527737i	$-0.176960\pi$
$479$	−2.31278	−	5.06428i	−0.105673	−	0.231393i	−0.955081	+	0.296345i	$0.904232\pi$
$480$	1.03929	−	1.14032i	0.0474369	−	0.0520481i
$481$	−0.00781304	+	0.0121573i	−0.000356244	+	0.000554327i
$482$	5.54192			0.252427
$483$	7.71810	−	3.07098i	0.351186	−	0.139735i
$484$	−24.9511			−1.13414
$485$	−3.36263	+	5.23236i	−0.152689	+	0.237589i
$486$	14.0650	−	6.72125i	0.638002	−	0.304882i
$487$	−10.0509	−	22.0083i	−0.455448	−	0.997292i	−0.988502	−	0.151211i	$-0.951683\pi$
$487$	−10.0509	−	22.0083i	−0.455448	−	0.997292i	0.533053	−	0.846082i	$-0.321044\pi$
$488$	10.6945	+	3.14019i	0.484118	+	0.142150i
$489$	−8.05215	−	30.2059i	−0.364131	−	1.36596i
$490$	0.673203	+	0.583334i	0.0304122	+	0.0263523i
$491$	37.6086	+	5.40730i	1.69725	+	0.244028i	0.921880	−	0.387475i	$-0.126653\pi$
$491$	37.6086	+	5.40730i	1.69725	+	0.244028i	0.775373	+	0.631504i	$0.217562\pi$
$492$	−11.8303	−	8.02911i	−0.533351	−	0.361980i
$493$	−45.4672	+	39.3976i	−2.04774	+	1.77438i
$494$	0.161895	−	0.104044i	0.00728402	−	0.00468116i
$495$	5.91701	+	14.8905i	0.265950	+	0.669280i
$496$	−4.96095	−	5.72525i	−0.222753	−	0.257071i
$497$	−3.67938	+	1.08036i	−0.165043	+	0.0484609i
$498$	−9.35957	+	5.68851i	−0.419412	+	0.254908i
$499$	−7.72820	+	8.91882i	−0.345962	+	0.399261i	−0.901888	−	0.431971i	$-0.857818\pi$
$499$	−7.72820	+	8.91882i	−0.345962	+	0.399261i	0.555926	+	0.831232i	$0.312364\pi$
$500$	−3.40679	+	7.45984i	−0.152356	+	0.333614i
$501$	−8.17959	−	19.1690i	−0.365437	−	0.856410i
$502$	16.9832	−	7.75595i	0.757996	−	0.346165i
$503$	2.43043	+	16.9040i	0.108367	+	0.753711i	0.969458	+	0.245259i	$0.0788730\pi$
$503$	2.43043	+	16.9040i	0.108367	+	0.753711i	−0.861090	+	0.508452i	$0.830218\pi$
$504$	−2.07580	+	2.16589i	−0.0924634	+	0.0964762i
$505$			16.5565i			0.736755i
$506$	−27.7818	+	7.41948i	−1.23505	+	0.329836i
$507$	−16.5455	+	13.6255i	−0.734813	+	0.605130i
$508$	13.9758	+	8.98168i	0.620074	+	0.398498i
$509$	−5.79123	+	0.832653i	−0.256692	+	0.0369067i	−0.269459	−	0.963012i	$-0.586845\pi$
$509$	−5.79123	+	0.832653i	−0.256692	+	0.0369067i	0.0127676	+	0.999918i	$0.495936\pi$
$510$	−3.83317	+	7.86523i	−0.169736	+	0.348278i
$511$	−0.0749772	+	0.255349i	−0.00331680	+	0.0112960i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	0.273584	−	1.23476i	0.0120790	−	0.0545159i
$514$	−3.76491	+	26.1855i	−0.166063	+	1.15499i
$515$	−1.91188	−	6.51127i	−0.0842475	−	0.286921i
$516$	−1.19227	+	7.03499i	−0.0524867	+	0.309698i
$517$	10.0913	+	15.7024i	0.443815	+	0.690589i
$518$	−0.00988141	−	0.0153758i	−0.000434164	−	0.000675573i
$519$	5.00794	−	29.5494i	0.219824	−	1.29707i
$520$	−0.198430	−	0.675789i	−0.00870171	−	0.0296353i
$521$	−4.92543	+	34.2571i	−0.215787	+	1.50083i	0.537570	+	0.843219i	$0.319342\pi$
$521$	−4.92543	+	34.2571i	−0.215787	+	1.50083i	−0.753357	+	0.657612i	$0.771567\pi$
$522$	−19.6094	−	25.0674i	−0.858279	−	1.09717i
$523$	8.77901	+	4.00924i	0.383879	+	0.175312i	0.598001	−	0.801495i	$-0.295962\pi$
$523$	8.77901	+	4.00924i	0.383879	+	0.175312i	−0.214122	+	0.976807i	$0.568689\pi$
$524$	−0.877236	+	2.98759i	−0.0383222	+	0.130513i
$525$	3.19194	−	6.54950i	0.139308	−	0.285844i
$526$	−17.9888	+	2.58640i	−0.784348	+	0.112772i
$527$	36.1411	+	23.2265i	1.57433	+	1.01176i
$528$	8.01674	−	6.60191i	0.348884	−	0.287311i
$529$	−19.9376	+	11.4670i	−0.866852	+	0.498566i
$530$		−	5.08007i		−	0.220664i
$531$	20.0077	+	19.1755i	0.868259	+	0.832145i
$532$	0.0346383	+	0.240915i	0.00150176	+	0.0104450i
$533$	−5.93705	+	2.71136i	−0.257162	+	0.117442i
$534$	9.01854	+	21.1351i	0.390270	+	0.914607i
$535$	4.71935	−	10.3339i	0.204035	−	0.446775i
$536$	−2.73614	+	3.15767i	−0.118183	+	0.136391i
$537$	3.49721	−	2.12552i	0.150916	−	0.0917228i
$538$	−9.06223	+	2.66091i	−0.390700	+	0.114720i
$539$	3.92650	+	4.53142i	0.169126	+	0.195182i
$540$	−4.05387	−	2.23387i	−0.174451	−	0.0961303i
$541$	−26.1619	+	16.8133i	−1.12479	+	0.722858i	−0.964466	−	0.264206i	$-0.914890\pi$
$541$	−26.1619	+	16.8133i	−1.12479	+	0.722858i	−0.160323	+	0.987065i	$0.551254\pi$
$542$	−8.01689	+	6.94667i	−0.344355	+	0.298385i
$543$	−19.1390	−	12.9895i	−0.821335	−	0.557433i
$544$	5.61326	+	0.807065i	0.240666	+	0.0346026i
$545$	−11.7362	−	10.1695i	−0.502725	−	0.435614i
$546$	0.352756	+	1.32329i	0.0150966	+	0.0566315i
$547$	0.327239	+	0.0960860i	0.0139917	+	0.00410834i	0.288721	−	0.957413i	$-0.406770\pi$
$547$	0.327239	+	0.0960860i	0.0139917	+	0.00410834i	−0.274729	+	0.961522i	$0.588588\pi$
$548$	−5.70593	−	12.4942i	−0.243745	−	0.533727i
$549$	1.67670	−	33.3960i	0.0715598	−	1.42531i
$550$	−13.6360	+	21.2181i	−0.581442	+	0.904742i
$551$	−2.58208			−0.110000
$552$	4.83258	−	6.75620i	0.205688	−	0.287563i
$553$	−0.866530			−0.0368486
$554$	10.6751	−	16.6108i	0.453541	−	0.705724i
$555$	0.0189953	−	0.0208418i	0.000806307	−	0.000884686i
$556$	1.00646	+	2.20385i	0.0426836	+	0.0934641i
$557$	19.2136	+	5.64164i	0.814108	+	0.239044i	0.662177	−	0.749347i	$-0.269633\pi$
$557$	19.2136	+	5.64164i	0.814108	+	0.239044i	0.151931	+	0.988391i	$0.451451\pi$
$558$	−13.2302	+	18.4788i	−0.560081	+	0.782270i
$559$	2.46168	+	2.13305i	0.104118	+	0.0902186i
$560$	0.881709	+	0.126771i	0.0372590	+	0.00535703i
$561$	−33.0734	+	48.7311i	−1.39636	+	2.05743i
$562$	−2.37336	+	2.05653i	−0.100114	+	0.0867494i
$563$	14.2673	−	9.16903i	0.601295	−	0.386429i	−0.204289	−	0.978911i	$-0.565488\pi$
$563$	14.2673	−	9.16903i	0.601295	−	0.386429i	0.805584	+	0.592482i	$0.201852\pi$
$564$	−5.13377	−	1.64835i	−0.216171	−	0.0694079i
$565$	7.59522	+	8.76535i	0.319533	+	0.368761i
$566$	13.2729	−	3.89727i	0.557900	−	0.163814i
$567$	7.77104	+	4.53992i	0.326353	+	0.190659i
$568$	−2.51120	+	2.89808i	−0.105368	+	0.121601i
$569$	−19.4174	+	42.5181i	−0.814018	+	1.78245i	−0.224945	+	0.974372i	$0.572220\pi$
$569$	−19.4174	+	42.5181i	−0.814018	+	1.78245i	−0.589073	+	0.808080i	$0.700507\pi$
$570$	−0.345392	+	0.147382i	−0.0144669	+	0.00617314i
$571$	−1.94581	+	0.888623i	−0.0814297	+	0.0371877i	−0.455714	−	0.890126i	$-0.650616\pi$
$571$	−1.94581	+	0.888623i	−0.0814297	+	0.0371877i	0.374284	+	0.927314i	$0.377889\pi$
$572$	−0.674695	−	4.69261i	−0.0282104	−	0.196208i
$573$	−0.881894	+	0.104297i	−0.0368417	+	0.00435705i
$574$		−	8.25475i		−	0.344546i
$575$	−6.15853	+	19.2107i	−0.256829	+	0.801144i
$576$	−0.575307	+	2.94432i	−0.0239711	+	0.122680i
$577$	1.76085	+	1.13163i	0.0733051	+	0.0471103i	0.576780	−	0.816900i	$-0.304309\pi$
$577$	1.76085	+	1.13163i	0.0733051	+	0.0471103i	−0.503475	+	0.864010i	$0.667945\pi$
$578$	−15.0057	+	2.15749i	−0.624155	+	0.0897399i
$579$	−7.29888	−	3.55715i	−0.303331	−	0.147830i
$580$	−2.66237	+	9.06718i	−0.110549	+	0.376494i
$581$	−5.75207	−	2.62688i	−0.238636	−	0.108982i
$582$	0.303308	−	12.0900i	0.0125725	−	0.501147i
$583$	4.86640	−	33.8466i	0.201546	−	1.40178i
$584$	0.0749772	+	0.255349i	0.00310258	+	0.0105664i
$585$	−1.83258	+	1.05178i	−0.0757678	+	0.0434858i
$586$	14.4961	+	22.5564i	0.598828	+	0.931795i
$587$	−24.4870	−	38.1025i	−1.01069	−	1.57266i	−0.804331	−	0.594182i	$-0.797476\pi$
$587$	−24.4870	−	38.1025i	−1.01069	−	1.57266i	−0.206356	−	0.978477i	$-0.566160\pi$
$588$	−1.70770	−	0.289416i	−0.0704243	−	0.0119353i
$589$	0.519469	+	1.76915i	0.0214044	+	0.0728966i
$590$	1.17106	−	8.14491i	0.0482118	−	0.335321i
$591$	−12.4769	−	0.313014i	−0.513230	−	0.0128757i
$592$	−0.0166255	−	0.00759263i	−0.000683306	−	0.000312055i
$593$	10.1131	−	34.4420i	0.415294	−	1.41436i	−0.440829	−	0.897591i	$-0.645315\pi$
$593$	10.1131	−	34.4420i	0.415294	−	1.41436i	0.856123	−	0.516772i	$-0.172866\pi$
$594$	−24.8695	−	18.7668i	−1.02041	−	0.770009i
$595$	−5.00015	+	0.718913i	−0.204986	+	0.0294726i
$596$	−9.10415	−	5.85088i	−0.372921	−	0.239662i
$597$	−29.5642	−	35.9000i	−1.20998	−	1.46929i
$598$	−1.48983	−	3.48704i	−0.0609235	−	0.142596i
$599$		−	7.74052i		−	0.316269i	−0.987418	−	0.158134i	$-0.949452\pi$
$599$		−	7.74052i		−	0.316269i	0.987418	−	0.158134i	$-0.0505479\pi$
$600$	−0.855698	−	7.23548i	−0.0349337	−	0.295387i
$601$	−4.34620	−	30.2285i	−0.177285	−	1.23304i	−0.863011	−	0.505185i	$-0.831424\pi$
$601$	−4.34620	−	30.2285i	−0.177285	−	1.23304i	0.685726	−	0.727860i	$-0.259485\pi$
$602$	−3.74729	+	1.71133i	−0.152728	+	0.0697486i
$603$	11.1264	+	5.77224i	0.453103	+	0.235064i
$604$	2.50885	−	5.49362i	0.102084	−	0.223532i
$605$	14.5549	−	16.7972i	0.591739	−	0.682903i
$606$	−16.7201	−	27.5104i	−0.679210	−	1.11754i
$607$	43.1931	−	12.6826i	1.75315	−	0.514772i	0.762010	−	0.647565i	$-0.224213\pi$
$607$	43.1931	−	12.6826i	1.75315	−	0.514772i	0.991144	+	0.132793i	$0.0423945\pi$
$608$	0.159388	+	0.183944i	0.00646404	+	0.00745990i
$609$	5.61732	−	17.4951i	0.227625	−	0.708938i
$610$	−8.35247	+	5.36780i	−0.338181	+	0.217336i
$611$	−1.86020	+	1.61188i	−0.0752558	+	0.0652095i
$612$	−1.57374	−	16.9400i	−0.0636148	−	0.684759i
$613$	11.5159	+	1.65574i	0.465124	+	0.0668747i	0.370893	−	0.928676i	$-0.379052\pi$
$613$	11.5159	+	1.65574i	0.465124	+	0.0668747i	0.0942309	+	0.995550i	$0.469961\pi$
$614$	5.35106	+	4.63672i	0.215951	+	0.187123i
$615$	12.3062	−	3.28054i	0.496235	−	0.132284i
$616$	5.75305	+	1.68925i	0.231797	+	0.0680617i
$617$	−11.2497	−	24.6333i	−0.452894	−	0.991700i	−0.989050	−	0.147581i	$-0.952851\pi$
$617$	−11.2497	−	24.6333i	−0.452894	−	0.991700i	0.536156	−	0.844119i	$-0.319876\pi$
$618$	9.75242	+	8.88840i	0.392300	+	0.357544i
$619$	−8.76526	+	13.6390i	−0.352305	+	0.548198i	−0.971500	−	0.237040i	$-0.923823\pi$
$619$	−8.76526	+	13.6390i	−0.352305	+	0.548198i	0.619195	+	0.785238i	$0.287459\pi$
$620$	6.74815			0.271012
$621$	−23.0913	−	9.36982i	−0.926621	−	0.375998i
$622$	14.1215			0.566220
$623$	−7.17260	+	11.1608i	−0.287364	+	0.447147i
$624$	1.01218	+	0.922506i	0.0405196	+	0.0369298i
$625$	5.70257	+	12.4869i	0.228103	+	0.499475i
$626$	20.4073	+	5.99213i	0.815641	+	0.239494i
$627$	−2.44240	+	0.651083i	−0.0975400	+	0.0260017i
$628$	0.948616	+	0.821981i	0.0378539	+	0.0328006i
$629$	0.102595	+	0.0147509i	0.00409072	+	0.000588157i
$630$	−0.247198	−	2.66087i	−0.00984859	−	0.106012i
$631$	1.46770	−	1.27177i	0.0584280	−	0.0506282i	−0.625157	−	0.780499i	$-0.714965\pi$
$631$	1.46770	−	1.27177i	0.0584280	−	0.0506282i	0.683585	+	0.729871i	$0.260420\pi$
$632$	−0.728971	+	0.468481i	−0.0289969	+	0.0186352i
$633$	14.0793	−	43.8499i	0.559602	−	1.74288i
$634$	15.2921	+	17.6480i	0.607325	+	0.700890i
$635$	−14.1990	+	4.16921i	−0.563471	+	0.165450i
$636$	5.13028	+	8.44109i	0.203429	+	0.334711i
$637$	−0.517786	+	0.597556i	−0.0205154	+	0.0236760i
$638$	−26.4241	+	57.8608i	−1.04614	+	2.29073i
$639$	10.2117	+	5.29770i	0.403970	+	0.209574i
$640$	0.810278	−	0.370042i	0.0320290	−	0.0146272i
$641$	−5.15624	−	35.8624i	−0.203659	−	1.41648i	−0.793308	−	0.608821i	$-0.791643\pi$
$641$	−5.15624	−	35.8624i	−0.203659	−	1.41648i	0.589648	−	0.807660i	$-0.299266\pi$
$642$	2.59436	+	21.9370i	0.102391	+	0.865783i
$643$		−	3.70531i		−	0.146123i	−0.997327	−	0.0730616i	$-0.976723\pi$
$643$		−	3.70531i		−	0.146123i	0.997327	−	0.0730616i	$-0.0232770\pi$
$644$	4.79438	+	0.118096i	0.188925	+	0.00465365i
$645$	−4.04049	−	4.90639i	−0.159094	−	0.193189i
$646$	−1.16116	−	0.746232i	−0.0456852	−	0.0293601i
$647$	−25.1978	+	3.62290i	−0.990629	+	0.142431i	−0.618529	−	0.785762i	$-0.712271\pi$
$647$	−25.1978	+	3.62290i	−0.990629	+	0.142431i	−0.372100	+	0.928193i	$0.621362\pi$
$648$	8.99188	−	0.382121i	0.353235	−	0.0150111i
$649$	15.6047	−	53.1446i	0.612537	−	2.08611i
$650$	−3.02545	−	1.38168i	−0.118668	−	0.0541938i
$651$	−13.1172	−	0.329077i	−0.514103	−	0.0128976i
$652$	2.56855	−	17.8647i	0.100592	−	0.699635i
$653$	7.09656	+	24.1687i	0.277710	+	0.945793i	0.973718	+	0.227759i	$0.0731397\pi$
$653$	7.09656	+	24.1687i	0.277710	+	0.945793i	−0.696008	+	0.718034i	$0.745042\pi$
$654$	29.7710	+	5.04551i	1.16414	+	0.197295i
$655$	−1.49953	−	2.33332i	−0.0585917	−	0.0911704i
$656$	−4.46285	−	6.94433i	−0.174245	−	0.271131i
$657$	0.692445	−	0.397419i	0.0270148	−	0.0155048i
$658$	−0.877039	−	2.98692i	−0.0341905	−	0.116442i
$659$	−1.81529	+	12.6256i	−0.0707136	+	0.491824i	0.923431	+	0.383765i	$0.125373\pi$
$659$	−1.81529	+	12.6256i	−0.0707136	+	0.491824i	−0.994144	+	0.108059i	$0.965536\pi$
$660$	−0.232010	+	9.24802i	−0.00903097	+	0.359979i
$661$	−21.1325	−	9.65091i	−0.821960	−	0.375377i	−0.0403824	−	0.999184i	$-0.512858\pi$
$661$	−21.1325	−	9.65091i	−0.821960	−	0.375377i	−0.781578	+	0.623808i	$0.785585\pi$
$662$	−6.26058	+	21.3216i	−0.243324	+	0.828686i
$663$	−6.98143	−	3.40244i	−0.271136	−	0.132140i
$664$	−6.25915	+	0.899930i	−0.242902	+	0.0349241i
$665$	−0.182390	−	0.117215i	−0.00707280	−	0.00454541i
$666$	−0.0105150	+	0.0538140i	−0.000407448	+	0.00208525i
$667$	−8.47853	+	50.1661i	−0.328290	+	1.94244i
$668$		−	12.0327i		−	0.465559i
$669$	−16.0980	+	1.90382i	−0.622386	+	0.0736060i
$670$	−0.529673	−	3.68395i	−0.0204630	−	0.142324i
$671$	−60.7913	+	27.7625i	−2.34682	+	1.07176i
$672$	−1.59308	+	0.679780i	−0.0614543	+	0.0262231i
$673$	14.6246	−	32.0234i	0.563736	−	1.23441i	−0.386330	−	0.922361i	$-0.626257\pi$
$673$	14.6246	−	32.0234i	0.563736	−	1.23441i	0.950066	−	0.312049i	$-0.101015\pi$
$674$	21.1442	−	24.4018i	0.814446	−	0.939921i
$675$	−20.5088	+	7.55965i	−0.789385	+	0.290971i
$676$	−11.8736	+	3.48639i	−0.456675	+	0.134092i
$677$	−23.8289	−	27.5000i	−0.915818	−	1.05691i	−0.998180	−	0.0603078i	$-0.980792\pi$
$677$	−23.8289	−	27.5000i	−0.915818	−	1.05691i	0.0823618	−	0.996602i	$-0.473754\pi$
$678$	−21.4723	−	6.89430i	−0.824637	−	0.264774i
$679$	5.87394	−	3.77495i	0.225421	−	0.144869i
$680$	−3.81772	+	3.30807i	−0.146403	+	0.126859i
$681$	21.2365	−	31.2903i	0.813783	−	1.19905i
$682$	44.9603	+	6.46432i	1.72162	+	0.247532i
$683$	−13.5292	−	11.7231i	−0.517681	−	0.448573i	0.356414	−	0.934328i	$-0.383999\pi$
$683$	−13.5292	−	11.7231i	−0.517681	−	0.448573i	−0.874095	+	0.485755i	$0.838545\pi$
$684$	0.425068	−	0.593696i	0.0162529	−	0.0227005i
$685$	11.7396	+	3.44706i	0.448548	+	0.131706i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	4.39065	−	4.81745i	0.167514	−	0.183797i
$688$	−2.22721	+	3.46560i	−0.0849115	+	0.132125i
$689$	4.50923			0.171788
$690$	1.72929	+	7.19443i	0.0658328	+	0.273887i
$691$	−24.8279			−0.944498			−0.472249	−	0.881465i	$-0.656558\pi$
$691$	−24.8279			−0.944498			−0.472249	+	0.881465i	$0.656558\pi$
$692$	9.35504	−	14.5567i	0.355625	−	0.553364i
$693$	0.901970	−	17.9652i	0.0342630	−	0.682440i
$694$	−11.4984	−	25.1779i	−0.436471	−	0.955739i
$695$	−2.07074	−	0.608025i	−0.0785478	−	0.0230637i
$696$	−4.73299	−	17.7548i	−0.179403	−	0.672994i
$697$	35.3785	+	30.6557i	1.34006	+	1.16117i
$698$	4.13405	+	0.594386i	0.156476	+	0.0224979i
$699$	12.7508	+	8.65387i	0.482280	+	0.327319i
$700$	3.17907	−	2.75468i	0.120158	−	0.104117i
$701$	12.7446	−	8.19043i	0.481355	−	0.309348i	−0.277365	−	0.960765i	$-0.589461\pi$
$701$	12.7446	−	8.19043i	0.481355	−	0.309348i	0.758720	+	0.651416i	$0.225825\pi$
$702$	1.98285	−	3.59834i	0.0748378	−	0.135811i
$703$	0.00291317	+	0.00336198i	0.000109872	+	0.000126799i
$704$	5.75305	−	1.68925i	0.216826	−	0.0636659i
$705$	4.10438	−	2.49453i	0.154580	−	0.0939496i
$706$	−8.10671	+	9.35564i	−0.305100	+	0.352104i
$707$	7.72116	−	16.9070i	0.290384	−	0.635853i
$708$	6.27956	+	14.7163i	0.236000	+	0.553072i
$709$	−31.7576	+	14.5032i	−1.19268	+	0.544680i	−0.910030	−	0.414543i	$-0.863942\pi$
$709$	−31.7576	+	14.5032i	−1.19268	+	0.544680i	−0.282652	+	0.959222i	$0.591214\pi$
$710$	−0.486128	−	3.38110i	−0.0182441	−	0.126890i
$711$	1.87680	+	1.79874i	0.0703857	+	0.0674581i
$712$			13.2669i			0.497196i
$713$	36.0779	−	4.28336i	1.35113	−	0.160413i
$714$	7.58228	−	6.24412i	0.283760	−	0.233680i
$715$	3.55265	+	2.28315i	0.132862	+	0.0853850i
$716$	2.33874	−	0.336260i	0.0874028	−	0.0125666i
$717$	−13.2979	+	27.2858i	−0.496619	+	1.01901i
$718$	1.77376	−	6.04088i	0.0661962	−	0.225444i
$719$	−11.8695	−	5.42062i	−0.442657	−	0.202155i	0.181602	−	0.983372i	$-0.441872\pi$
$719$	−11.8695	−	5.42062i	−0.442657	−	0.202155i	−0.624259	+	0.781217i	$0.714599\pi$
$720$	−1.64653	−	2.10482i	−0.0613626	−	0.0784420i
$721$	−1.08419	+	7.54071i	−0.0403774	+	0.280831i
$722$	5.33623	+	18.1735i	0.198594	+	0.676349i
$723$	1.60392	−	9.46393i	0.0596504	−	0.351967i
$724$	−7.22000	−	11.2345i	−0.268329	−	0.417529i
$725$	24.1265	+	37.5415i	0.896035	+	1.39426i
$726$	−7.22126	+	42.6091i	−0.268006	+	1.58137i
$727$	−1.06200	−	3.61685i	−0.0393875	−	0.134142i	0.937452	−	0.348114i	$-0.113178\pi$
$727$	−1.06200	−	3.61685i	−0.0393875	−	0.134142i	−0.976840	+	0.213973i	$0.931360\pi$
$728$	−0.112526	+	0.782632i	−0.00417047	+	0.0290063i
$729$	−7.40724	−	25.9641i	−0.274342	−	0.961632i
$730$	−0.215638	−	0.0984788i	−0.00798114	−	0.00364486i
$731$	6.58183	−	22.4157i	0.243438	−	0.829073i
$732$	8.45767	−	17.3542i	0.312605	−	0.641430i
$733$	−24.6926	+	3.55026i	−0.912043	+	0.131132i	−0.582333	−	0.812950i	$-0.697860\pi$
$733$	−24.6926	+	3.55026i	−0.912043	+	0.131132i	−0.329710	+	0.944082i	$0.606951\pi$
$734$	−16.0400	−	10.3083i	−0.592046	−	0.380485i
$735$	1.19100	−	0.980803i	0.0439305	−	0.0361775i
$736$	4.09713	−	2.49269i	0.151022	−	0.0918817i
$737$		−	25.0522i		−	0.922809i
$738$	−17.1352	+	17.8788i	−0.630755	+	0.658129i
$739$	6.20707	+	43.1711i	0.228331	+	1.58808i	0.705139	+	0.709069i	$0.250885\pi$
$739$	6.20707	+	43.1711i	0.228331	+	1.58808i	−0.476808	+	0.879007i	$0.658206\pi$
$740$	0.0148096	−	0.00676333i	0.000544413	−	0.000248625i
$741$	−0.130821	−	0.306581i	−0.00480581	−	0.0112625i
$742$	−2.36910	+	5.18761i	−0.0869725	+	0.190443i
$743$	28.7927	−	33.2285i	1.05630	−	1.21904i	0.0813328	−	0.996687i	$-0.474082\pi$
$743$	28.7927	−	33.2285i	1.05630	−	1.21904i	0.974967	−	0.222348i	$-0.0713722\pi$
$744$	−11.2128	+	6.81484i	−0.411080	+	0.249844i
$745$	9.24960	−	2.71593i	0.338879	−	0.0995038i
$746$	10.7224	+	12.3743i	0.392576	+	0.453057i
$747$	7.00545	+	17.6297i	0.256316	+	0.645036i
$748$	−28.6050	+	18.3833i	−1.04590	+	0.672160i
$749$	−9.63851	+	8.35182i	−0.352184	+	0.305169i
$750$	11.7532	+	7.97678i	0.429166	+	0.291271i
$751$	26.6864	+	3.83692i	0.973799	+	0.140011i	0.610806	−	0.791780i	$-0.290846\pi$
$751$	26.6864	+	3.83692i	0.973799	+	0.140011i	0.362994	+	0.931792i	$0.381755\pi$
$752$	−2.35266	−	2.03859i	−0.0857928	−	0.0743399i
$753$	−8.32963	−	31.2468i	−0.303549	−	1.13870i
$754$	−8.04832	−	2.36320i	−0.293102	−	0.0860626i
$755$	2.23483	+	4.89359i	0.0813337	+	0.178096i
$756$	3.09791	+	4.17168i	0.112670	+	0.151723i
$757$	7.15123	−	11.1275i	0.259916	−	0.404437i	−0.686630	−	0.727007i	$-0.740911\pi$
$757$	7.15123	−	11.1275i	0.259916	−	0.404437i	0.946545	+	0.322570i	$0.104547\pi$
$758$	13.4363			0.488029
$759$	4.62975	+	49.5903i	0.168049	+	1.80001i
$760$	−0.216808			−0.00786445
$761$	22.3743	−	34.8151i	0.811069	−	1.26205i	−0.150808	−	0.988563i	$-0.548187\pi$
$761$	22.3743	−	34.8151i	0.811069	−	1.26205i	0.961876	−	0.273484i	$-0.0881762\pi$
$762$	19.3828	−	21.2670i	0.702166	−	0.770421i
$763$	7.24210	+	15.8580i	0.262182	+	0.574098i
$764$	−0.491942	−	0.144447i	−0.0177978	−	0.00522591i
$765$	12.3221	+	8.82222i	0.445506	+	0.318968i
$766$	−10.1247	−	8.77308i	−0.365819	−	0.316984i
$767$	7.22968	+	1.03947i	0.261049	+	0.0375331i
$768$	−0.972666	+	1.43315i	−0.0350981	+	0.0517144i
$769$	17.9928	−	15.5908i	0.648836	−	0.562219i	−0.267038	−	0.963686i	$-0.586045\pi$
$769$	17.9928	−	15.5908i	0.648836	−	0.562219i	0.915874	+	0.401467i	$0.131499\pi$
$770$	−4.49316	+	2.88758i	−0.161922	+	0.104061i
$771$	43.6274	+	14.0078i	1.57120	+	0.504480i
$772$	−3.06987	−	3.54282i	−0.110487	−	0.127509i
$773$	−13.2591	+	3.89322i	−0.476896	+	0.140029i	−0.511342	−	0.859377i	$-0.670851\pi$
$773$	−13.2591	+	3.89322i	−0.476896	+	0.140029i	0.0344461	+	0.999407i	$0.489033\pi$
$774$	11.6686	+	4.07208i	0.419419	+	0.146368i
$775$	20.8683	−	24.0834i	0.749613	−	0.865100i
$776$	2.90058	−	6.35138i	0.104125	−	0.228001i
$777$	−0.0291171	+	0.0124245i	−0.00104457	+	0.000445726i
$778$	7.81752	−	3.57014i	0.280272	−	0.127996i
$779$	0.285931	+	1.98869i	0.0102445	+	0.0712522i
$780$	−1.21147	+	0.143274i	−0.0433777	+	0.00513003i
$781$		−	22.9926i		−	0.822741i
$782$	−18.3110	+	20.1094i	−0.654801	+	0.719109i
$783$	−48.4828	+	26.2320i	−1.73263	+	0.937456i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	−1.10672	+	0.159122i	−0.0395005	+	0.00567932i
$786$	4.84802	+	2.36271i	0.172923	+	0.0842751i
$787$	0.0616191	−	0.209855i	0.00219648	−	0.00748054i	−0.958387	−	0.285471i	$-0.907850\pi$
$787$	0.0616191	−	0.209855i	0.00219648	−	0.00748054i	0.960584	+	0.277990i	$0.0896683\pi$
$788$	−6.55462	−	2.99340i	−0.233499	−	0.106635i
$789$	−0.789453	+	31.4680i	−0.0281053	+	1.12029i
$790$	0.109850	−	0.764027i	0.00390831	−	0.0271829i
$791$	−3.66826	−	12.4929i	−0.130428	−	0.444198i
$792$	−8.95391	−	15.6009i	−0.318163	−	0.554354i
$793$	−4.76463	−	7.41391i	−0.169197	−	0.263276i
$794$	−10.2780	−	15.9929i	−0.364752	−	0.567565i
$795$	−8.67524	−	1.47025i	−0.307679	−	0.0521445i
$796$	−7.56467	−	25.7629i	−0.268123	−	0.913142i
$797$	−2.10732	+	14.6568i	−0.0746453	+	0.519169i	0.917854	+	0.396918i	$0.129920\pi$
$797$	−2.10732	+	14.6568i	−0.0746453	+	0.519169i	−0.992499	+	0.122251i	$0.960989\pi$
$798$	0.421435	+	0.0105728i	0.0149186	+	0.000374272i
$799$	16.0585	+	7.33368i	0.568110	+	0.259447i
$800$	1.18511	−	4.03613i	0.0419001	−	0.142699i
$801$	38.7026	−	9.28411i	1.36749	−	0.328038i
$802$	−10.0827	+	1.44968i	−0.356033	+	0.0511899i
$803$	−1.34238	−	0.862695i	−0.0473716	−	0.0304438i
$804$	4.60047	+	5.58638i	0.162246	+	0.197017i
$805$	−2.87623	+	3.15870i	−0.101374	+	0.111330i
$806$			5.98987i			0.210984i
$807$	1.92128	+	16.2457i	0.0676323	+	0.571875i
$808$	−2.64515	−	18.3974i	−0.0930562	−	0.647220i
$809$	−42.3897	+	19.3587i	−1.49034	+	0.680616i	−0.983414	−	0.181372i	$-0.941946\pi$
$809$	−42.3897	+	19.3587i	−1.49034	+	0.680616i	−0.506927	+	0.861989i	$0.669219\pi$
$810$	−4.98803	+	6.27627i	−0.175261	+	0.220526i
$811$	−6.52545	+	14.2888i	−0.229140	+	0.501746i	−0.988923	−	0.148431i	$-0.952578\pi$
$811$	−6.52545	+	14.2888i	−0.229140	+	0.501746i	0.759783	+	0.650177i	$0.225305\pi$
$812$	6.94722	−	8.01752i	0.243800	−	0.281360i
$813$	9.54262	+	15.7009i	0.334674	+	0.550655i
$814$	0.105150	−	0.0308748i	0.00368550	−	0.00108216i
$815$	10.5282	+	12.1502i	0.368788	+	0.425604i
$816$	3.00279	−	9.35218i	0.105119	−	0.327392i
$817$	0.843501	−	0.542085i	0.0295104	−	0.0189652i
$818$	7.66533	−	6.64204i	0.268012	−	0.232234i
$819$	2.36187	−	0.219420i	0.0825305	−	0.00766717i
$820$	7.27828	+	1.04646i	0.254169	+	0.0365439i
$821$	13.2292	+	11.4632i	0.461702	+	0.400067i	0.854413	−	0.519595i	$-0.173917\pi$
$821$	13.2292	+	11.4632i	0.461702	+	0.400067i	−0.392711	+	0.919662i	$0.628463\pi$
$822$	−22.9878	+	6.12798i	−0.801791	+	0.213738i
$823$	33.2585	+	9.76558i	1.15932	+	0.340407i	0.804168	−	0.594402i	$-0.202611\pi$
$823$	33.2585	+	9.76558i	1.15932	+	0.340407i	0.355151	+	0.934809i	$0.384429\pi$
$824$	3.16474	+	6.92981i	0.110249	+	0.241411i
$825$	32.2876	+	29.4271i	1.12411	+	1.02452i
$826$	−4.99425	+	7.77120i	−0.173772	+	0.270395i
$827$	−46.6353			−1.62167			−0.810834	−	0.585277i	$-0.800986\pi$
$827$	−46.6353			−1.62167			−0.810834	+	0.585277i	$0.800986\pi$
$828$	−10.1389	−	10.2079i	−0.352352	−	0.354751i
$829$	13.3102			0.462284			0.231142	−	0.972920i	$-0.425754\pi$
$829$	13.3102			0.462284			0.231142	+	0.972920i	$0.425754\pi$
$830$	3.04534	−	4.73864i	0.105705	−	0.164481i
$831$	−25.2766	−	23.0373i	−0.876837	−	0.799154i
$832$	0.328461	+	0.719228i	0.0113873	+	0.0249348i
$833$	5.44126	+	1.59770i	0.188529	+	0.0553570i
$834$	4.05480	−	1.08091i	0.140406	−	0.0374288i
$835$	8.10046	+	7.01908i	0.280328	+	0.242905i
$836$	−1.44451	−	0.207689i	−0.0499594	−	0.00718307i
$837$	27.7272	+	27.9414i	0.958392	+	0.965794i
$838$	1.99048	−	1.72476i	0.0687602	−	0.0595810i
$839$	30.7296	−	19.7487i	1.06090	−	0.681801i	0.110833	−	0.993839i	$-0.464648\pi$
$839$	30.7296	−	19.7487i	1.06090	−	0.681801i	0.950069	+	0.312039i	$0.101012\pi$
$840$	0.471667	−	1.46900i	0.0162740	−	0.0506855i
$841$	54.7101	+	63.1388i	1.88655	+	2.17720i
$842$	−10.5565	+	3.09966i	−0.363801	+	0.106822i
$843$	2.82504	+	4.64818i	0.0972997	+	0.160092i
$844$	17.4126	−	20.0952i	0.599366	−	0.691705i
$845$	4.57920	−	10.0270i	0.157529	−	0.344941i
$846$	−4.30068	+	8.28988i	−0.147860	+	0.285012i
$847$	−22.6964	+	10.3651i	−0.779856	+	0.356148i
$848$	0.811618	+	5.64493i	0.0278711	+	0.193848i
$849$	−2.81398	−	23.7940i	−0.0965755	−	0.816608i
$850$			23.8551i			0.818223i
$851$	0.0748842	−	0.0455594i	0.00256700	−	0.00156176i
$852$	4.22227	+	5.12713i	0.144653	+	0.175652i
$853$	−1.35658	−	0.871821i	−0.0464484	−	0.0298506i	0.517211	−	0.855858i	$-0.326970\pi$
$853$	−1.35658	−	0.871821i	−0.0464484	−	0.0298506i	−0.563659	+	0.826008i	$0.690607\pi$
$854$	11.0326	−	1.58624i	0.377526	−	0.0542801i
$855$	0.151722	+	0.632480i	0.00518877	+	0.0216304i
$856$	−3.59310	+	12.2370i	−0.122810	+	0.418251i
$857$	26.0739	+	11.9075i	0.890666	+	0.406754i	0.807559	−	0.589787i	$-0.200788\pi$
$857$	26.0739	+	11.9075i	0.890666	+	0.406754i	0.0831072	+	0.996541i	$0.473516\pi$
$858$	−8.20883	−	0.205939i	−0.280245	−	0.00703065i
$859$	−0.685691	+	4.76909i	−0.0233955	+	0.162719i	−0.998170	−	0.0604737i	$-0.980739\pi$
$859$	−0.685691	+	4.76909i	−0.0233955	+	0.162719i	0.974774	+	0.223193i	$0.0716480\pi$
$860$	−1.03385	−	3.52097i	−0.0352540	−	0.120064i
$861$	−14.0966	−	2.38906i	−0.480412	−	0.0814188i
$862$	−2.74837	−	4.27655i	−0.0936099	−	0.145660i
$863$	−14.8912	−	23.1711i	−0.506901	−	0.788753i	0.489634	−	0.871928i	$-0.337130\pi$
$863$	−14.8912	−	23.1711i	−0.506901	−	0.788753i	−0.996535	+	0.0831748i	$0.973494\pi$
$864$	4.86151	+	1.83458i	0.165392	+	0.0624138i
$865$	4.34252	+	14.7893i	0.147650	+	0.502850i
$866$	1.68592	−	11.7258i	0.0572897	−	0.398459i
$867$	−0.658538	+	26.2496i	−0.0223651	+	0.891485i
$868$	−6.89100	−	3.14701i	−0.233896	−	0.106817i
$869$	1.46378	−	4.98519i	0.0496555	−	0.169111i
$870$	14.7135	+	7.17071i	0.498834	+	0.243110i
$871$	3.26999	−	0.470154i	0.110799	−	0.0159306i
$872$	14.6659	+	9.42522i	0.496651	+	0.319178i
$873$	−20.5583	−	4.01700i	−0.695794	−	0.135955i
$874$	−1.15913	+	0.137618i	−0.0392081	+	0.00465500i
$875$			8.20094i			0.277242i
$876$	0.457759	−	0.0541365i	0.0154662	−	0.00182910i
$877$	5.03811	+	35.0408i	0.170125	+	1.18325i	0.878617	+	0.477527i	$0.158467\pi$
$877$	5.03811	+	35.0408i	0.170125	+	1.18325i	−0.708492	+	0.705719i	$0.750624\pi$
$878$	−30.1130	+	13.7521i	−1.01626	+	0.464112i
$879$	42.7149	−	18.2268i	1.44074	−	0.614775i
$880$	−2.21874	+	4.85837i	−0.0747938	+	0.163776i
$881$	−12.4679	+	14.3887i	−0.420053	+	0.484767i	−0.925853	−	0.377884i	$-0.876652\pi$
$881$	−12.4679	+	14.3887i	−0.420053	+	0.484767i	0.505800	+	0.862651i	$0.331197\pi$
$882$	−0.988471	+	2.83248i	−0.0332836	+	0.0953745i
$883$	18.8008	−	5.52043i	0.632699	−	0.185777i	0.0503702	−	0.998731i	$-0.483960\pi$
$883$	18.8008	−	5.52043i	0.632699	−	0.185777i	0.582329	+	0.812953i	$0.302142\pi$
$884$	−2.93635	−	3.38873i	−0.0987602	−	0.113975i
$885$	−13.5701	−	4.35709i	−0.456155	−	0.146462i
$886$	7.12586	−	4.57951i	0.239398	−	0.153852i
$887$	−26.3852	+	22.8629i	−0.885929	+	0.767662i	−0.973546	−	0.228493i	$-0.926620\pi$
$887$	−26.3852	+	22.8629i	−0.885929	+	0.767662i	0.0876169	+	0.996154i	$0.472075\pi$
$888$	−0.0177776	+	0.0261940i	−0.000596578	+	0.000879014i
$889$	16.4439	+	2.36428i	0.551512	+	0.0792954i
$890$	−8.93129	−	7.73900i	−0.299377	−	0.259412i
$891$	−39.2456	+	37.0382i	−1.31478	+	1.24083i
$892$	−8.97987	−	2.63673i	−0.300668	−	0.0882842i
$893$	0.314754	+	0.689214i	0.0105328	+	0.0230637i
$894$	−12.6264	+	13.8538i	−0.422291	+	0.463341i
$895$	−1.13789	+	1.77060i	−0.0380356	+	0.0591846i
$896$	−1.00000			−0.0334077
$897$	−6.38600	+	1.53497i	−0.213222	+	0.0512511i
$898$	9.39724			0.313590
$899$	43.4498	−	67.6091i	1.44913	−	2.25489i
$900$	−12.6037	−	0.632788i	−0.420123	−	0.0210929i
$901$	−13.4351	−	29.4188i	−0.447589	−	0.980083i
$902$	47.4900	+	13.9443i	1.58124	+	0.464295i
$903$	1.83791	+	6.89454i	0.0611619	+	0.229436i
$904$	−9.84013	−	8.52652i	−0.327278	−	0.283588i
$905$	11.7748	+	1.69296i	0.391408	+	0.0562759i
$906$	−8.65536	−	5.87431i	−0.287555	−	0.195161i
$907$	18.3914	−	15.9362i	0.610675	−	0.529153i	−0.293697	−	0.955899i	$-0.594886\pi$
$907$	18.3914	−	15.9362i	0.610675	−	0.529153i	0.904372	+	0.426746i	$0.140340\pi$
$908$	18.3673	−	11.8039i	0.609540	−	0.391728i
$909$	−51.8187	+	20.5910i	−1.71872	+	0.682961i
$910$	−0.461231	−	0.532289i	−0.0152897	−	0.0176452i
$911$	25.3683	−	7.44882i	0.840491	−	0.246790i	0.166973	−	0.985961i	$-0.446601\pi$
$911$	25.3683	−	7.44882i	0.840491	−	0.246790i	0.673518	+	0.739171i	$0.264783\pi$
$912$	0.360250	−	0.218951i	0.0119291	−	0.00725018i
$913$	24.8293	−	28.6545i	0.821729	−	0.948326i
$914$	3.88129	−	8.49885i	0.128382	−	0.281117i
$915$	6.74926	+	15.8170i	0.223124	+	0.522895i
$916$	3.42315	−	1.56330i	0.113104	−	0.0516529i
$917$	0.443128	+	3.08202i	0.0146334	+	0.101777i
$918$	−29.3839	−	2.21522i	−0.969813	−	0.0731133i
$919$			29.5346i			0.974258i	0.873330	+	0.487129i	$0.161956\pi$
$919$			29.5346i			0.974258i	−0.873330	+	0.487129i	$0.838044\pi$
$920$	−0.711913	+	4.21227i	−0.0234711	+	0.138875i
$921$	9.46680	−	7.79606i	0.311942	−	0.256889i
$922$	−15.5142	−	9.97039i	−0.510934	−	0.328357i
$923$	3.00117	−	0.431503i	0.0987846	−	0.0142031i
$924$	4.54975	−	9.33559i	0.149676	−	0.307118i
$925$	0.0216606	−	0.0737692i	0.000712196	−	0.00242552i
$926$	−3.51121	−	1.60352i	−0.115385	−	0.0526948i
$927$	18.0012	−	14.0818i	0.591238	−	0.462506i
$928$	1.50978	−	10.5007i	0.0495608	−	0.344703i
$929$	8.21178	+	27.9668i	0.269420	+	0.917559i	0.977413	+	0.211340i	$0.0677827\pi$
$929$	8.21178	+	27.9668i	0.269420	+	0.917559i	−0.707993	+	0.706220i	$0.750399\pi$
$930$	1.95302	−	11.5238i	0.0640421	−	0.377881i
$931$	0.131588	+	0.204755i	0.00431262	+	0.00671056i
$932$	4.81011	+	7.48468i	0.157560	+	0.245169i
$933$	4.08698	−	24.1152i	0.133802	−	0.789498i
$934$	−6.06343	−	20.6501i	−0.198401	−	0.675693i
$935$	4.31055	−	29.9806i	0.140970	−	0.980469i
$936$	1.86830	−	1.46151i	0.0610675	−	0.0477710i
$937$	9.03142	+	4.12451i	0.295044	+	0.134742i	0.557437	−	0.830219i	$-0.311785\pi$
$937$	9.03142	+	4.12451i	0.295044	+	0.134742i	−0.262394	+	0.964961i	$0.584512\pi$
$938$	−1.17713	+	4.00895i	−0.0384348	+	0.130897i
$939$	16.1390	−	33.1154i	0.526675	−	1.08068i
$940$	2.74478	−	0.394639i	0.0895247	−	0.0128717i
$941$	45.2185	+	29.0601i	1.47408	+	0.947334i	0.997678	+	0.0681058i	$0.0216955\pi$
$941$	45.2185	+	29.0601i	1.47408	+	0.947334i	0.476402	+	0.879228i	$0.341941\pi$
$942$	1.67824	−	1.38206i	0.0546800	−	0.0450299i
$943$	39.5764	+	0.974855i	1.28878	+	0.0317456i
$944$			9.23764i			0.300660i
$945$	−4.61551	−	0.347959i	−0.150142	−	0.0113191i
$946$	−3.51527	−	24.4492i	−0.114291	−	0.794913i
$947$	−3.01305	+	1.37602i	−0.0979111	+	0.0447145i	−0.463768	−	0.885956i	$-0.653503\pi$
$947$	−3.01305	+	1.37602i	−0.0979111	+	0.0447145i	0.365857	+	0.930671i	$0.380776\pi$
$948$	0.589050	+	1.38045i	0.0191314	+	0.0448349i
$949$	0.0874129	−	0.191407i	0.00283754	−	0.00621335i
$950$	−0.670469	+	0.773762i	−0.0217529	+	0.0251042i
$951$	34.5632	−	21.0066i	1.12079	−	0.681187i
$952$	5.44126	−	1.59770i	0.176352	−	0.0517817i
$953$	−17.0014	−	19.6206i	−0.550728	−	0.635574i	0.410324	−	0.911940i	$-0.365416\pi$
$953$	−17.0014	−	19.6206i	−0.550728	−	0.635574i	−0.961053	+	0.276365i	$0.910870\pi$
$954$	15.8996	−	6.31799i	0.514770	−	0.204553i
$955$	0.384209	−	0.246916i	0.0124327	−	0.00799001i
$956$	−13.2443	+	11.4763i	−0.428352	+	0.371169i
$957$	91.1613	+	61.8703i	2.94683	+	1.99998i
$958$	−5.51072	−	0.792322i	−0.178043	−	0.0255988i
$959$	−10.3806	−	8.99483i	−0.335207	−	0.290458i
$960$	−0.397412	−	1.49081i	−0.0128264	−	0.0481156i
$961$	−25.3205	−	7.43478i	−0.816792	−	0.239832i
$962$	0.00600335	+	0.0131455i	0.000193556	+	0.000423828i
$963$	38.2126	+	1.91853i	1.23138	+	0.0618236i
$964$	2.99619	−	4.66216i	0.0965007	−	0.150158i
$965$	4.17579			0.134424
$966$	1.58924	−	8.15318i	0.0511330	−	0.262324i
$967$	−23.6986			−0.762094			−0.381047	−	0.924556i	$-0.624436\pi$
$967$	−23.6986			−0.762094			−0.381047	+	0.924556i	$0.624436\pi$
$968$	−13.4896	+	20.9902i	−0.433572	+	0.674652i
$969$	−1.61040	+	1.76694i	−0.0517334	+	0.0567623i
$970$	2.58376	+	5.65766i	0.0829597	+	0.181656i
$971$	−8.29333	−	2.43514i	−0.266145	−	0.0781474i	0.145937	−	0.989294i	$-0.453380\pi$
$971$	−8.29333	−	2.43514i	−0.266145	−	0.0781474i	−0.412083	+	0.911147i	$0.635198\pi$
$972$	1.94985	−	15.4660i	0.0625414	−	0.496073i
$973$	1.83102	+	1.58659i	0.0587000	+	0.0508638i
$974$	−23.9485	−	3.44327i	−0.767359	−	0.110330i
$975$	−3.23510	+	4.76668i	−0.103606	+	0.152656i
$976$	8.42359	−	7.29909i	0.269633	−	0.233638i
$977$	−49.4159	+	31.7577i	−1.58096	+	1.01602i	−0.605494	+	0.795850i	$0.707025\pi$
$977$	−49.4159	+	31.7577i	−1.58096	+	1.01602i	−0.975462	+	0.220169i	$0.929339\pi$
$978$	−29.7641	−	9.55665i	−0.951752	−	0.305588i
$979$	−52.0923	−	60.1177i	−1.66488	−	1.92137i
$980$	0.854693	−	0.250960i	0.0273022	−	0.00801664i
$981$	17.2324	−	49.3797i	0.550189	−	1.57657i
$982$	24.8817	−	28.7150i	0.794006	−	0.916332i
$983$	6.76668	−	14.8170i	0.215824	−	0.472588i	−0.770493	−	0.637448i	$-0.779990\pi$
$983$	6.76668	−	14.8170i	0.215824	−	0.472588i	0.986317	+	0.164860i	$0.0527173\pi$
$984$	−13.1505	+	5.61141i	−0.419221	+	0.178885i
$985$	5.83870	−	2.66644i	0.186036	−	0.0849600i
$986$	8.56191	+	59.5494i	0.272667	+	1.89644i
$987$	−5.35459	+	0.633256i	−0.170438	+	0.0201568i
$988$		−	0.192445i		−	0.00612251i
$989$	−7.76222	−	18.1680i	−0.246824	−	0.577710i
$990$	15.7257	+	3.07273i	0.499795	+	0.0976577i
$991$	−12.9006	−	8.29069i	−0.409800	−	0.263362i	0.319459	−	0.947600i	$-0.396499\pi$
$991$	−12.9006	−	8.29069i	−0.409800	−	0.263362i	−0.729259	+	0.684238i	$0.760135\pi$
$992$	−7.49848	+	1.07812i	−0.238077	+	0.0342303i
$993$	34.5989	+	16.8620i	1.09796	+	0.535099i
$994$	−1.08036	+	3.67938i	−0.0342670	+	0.116703i
$995$	21.7564	+	9.93582i	0.689724	+	0.314987i
$996$	−0.274688	+	10.9492i	−0.00870383	+	0.346939i
$997$	−6.73584	+	46.8488i	−0.213326	+	1.48372i	0.548618	+	0.836073i	$0.315154\pi$
$997$	−6.73584	+	46.8488i	−0.213326	+	1.48372i	−0.761944	+	0.647643i	$0.775755\pi$
$998$	3.32481	+	11.3233i	0.105245	+	0.358431i
$999$	0.0888550	+	0.0335311i	0.00281125	+	0.00106088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.b.113.15	yes	240
3.2	odd	2		966.2.r.a.113.9	✓	240
23.11	odd	22		966.2.r.a.701.9	yes	240
69.11	even	22	inner	966.2.r.b.701.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.9	✓	240	3.2	odd	2
966.2.r.a.701.9	yes	240	23.11	odd	22
966.2.r.b.113.15	yes	240	1.1	even	1	trivial
966.2.r.b.701.15	yes	240	69.11	even	22	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.28014 - 1.16672i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.854693 + 0.250960i) q^{5} +(-1.67361 + 0.446142i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.277508 + 2.98714i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.28014 - 1.16672i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.854693 + 0.250960i) q^{5} +(-1.67361 + 0.446142i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.277508 + 2.98714i) q^{9} +(0.673203 - 0.583334i) q^{10} +(5.04410 - 3.24164i) q^{11} +(-0.529501 + 1.64913i) q^{12} +(0.517786 + 0.597556i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-0.801323 - 1.31846i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.35581 - 5.15850i) q^{17} +(2.66297 + 1.38151i) q^{18} +(0.221397 - 0.101109i) q^{19} +(-0.126771 - 0.881709i) q^{20} +(0.203422 + 1.72006i) q^{21} -5.99593i q^{22} +(-1.23742 - 4.63344i) q^{23} +(1.10107 + 1.33703i) q^{24} +(-3.53875 - 2.27422i) q^{25} +(0.782632 - 0.112526i) q^{26} +(3.12992 - 4.14772i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(-9.65002 - 4.40701i) q^{29} +(-1.54238 - 0.0386946i) q^{30} +(-1.07812 + 7.49848i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-10.2392 - 1.73532i) q^{33} +(-3.06596 - 4.77073i) q^{34} +(-0.481590 - 0.749368i) q^{35} +(2.60191 - 1.49333i) q^{36} +(0.00514929 + 0.0175369i) q^{37} +(0.0346383 - 0.240915i) q^{38} +(0.0343465 - 1.36907i) q^{39} +(-0.810278 - 0.370042i) q^{40} +(-2.32563 + 7.92037i) q^{41} +(1.55699 + 0.758807i) q^{42} +(4.07764 - 0.586276i) q^{43} +(-5.04410 - 3.24164i) q^{44} +(-0.512469 + 2.62273i) q^{45} +(-4.56690 - 1.46404i) q^{46} +3.11302i q^{47} +(1.72006 - 0.203422i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-3.82638 + 1.74745i) q^{50} +(-9.03432 + 3.85502i) q^{51} +(0.328461 - 0.719228i) q^{52} +(3.73466 - 4.31002i) q^{53} +(-1.79713 - 4.87548i) q^{54} +(5.12468 - 1.50474i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-0.401385 - 0.128876i) q^{57} +(-8.92461 + 5.73550i) q^{58} +(6.98134 - 6.04937i) q^{59} +(-0.866427 + 1.27662i) q^{60} +(-11.0326 - 1.58624i) q^{61} +(5.72525 + 4.96095i) q^{62} +(1.74643 - 2.43926i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.292585 + 0.640671i) q^{65} +(-6.99559 + 7.67562i) q^{66} +(2.25890 - 3.51492i) q^{67} -5.67098 q^{68} +(-3.82188 + 7.37518i) q^{69} -0.890776 q^{70} +(2.07320 - 3.22596i) q^{71} +(0.150430 - 2.99623i) q^{72} +(-0.110554 - 0.242079i) q^{73} +(0.0175369 + 0.00514929i) q^{74} +(1.87670 + 7.04006i) q^{75} +(-0.183944 - 0.159388i) q^{76} +(-5.93490 - 0.853309i) q^{77} +(-1.13316 - 0.769068i) q^{78} +(0.654880 - 0.567456i) q^{79} +(-0.749368 + 0.481590i) q^{80} +(-8.84598 + 1.65791i) q^{81} +(5.40571 + 6.23852i) q^{82} +(6.06737 - 1.78154i) q^{83} +(1.48012 - 0.899579i) q^{84} +(3.30807 - 3.81772i) q^{85} +(1.71133 - 3.74729i) q^{86} +(7.21158 + 16.9005i) q^{87} +(-5.45409 + 2.49080i) q^{88} +(-1.88807 - 13.1318i) q^{89} +(1.92932 + 1.84907i) q^{90} -0.790680i q^{91} +(-3.70069 + 3.05040i) q^{92} +(10.1288 - 8.34122i) q^{93} +(2.61884 + 1.68302i) q^{94} +(0.214601 - 0.0308550i) q^{95} +(0.758807 - 1.55699i) q^{96} +(-1.96716 + 6.69953i) q^{97} +(0.909632 + 0.415415i) q^{98} +(11.0830 + 14.1678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Introduction

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Modular forms

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