LMFDB - Embedded newform 224.2.bd.a.109.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.22
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.954861 - 1.04319i) q^{2} +(-2.06202 - 2.68727i) q^{3} +(-0.176481 - 1.99220i) q^{4} +(-0.668458 - 0.512926i) q^{5} +(-4.77227 - 0.414901i) q^{6} +(2.64566 - 0.0215710i) q^{7} +(-2.24675 - 1.71817i) q^{8} +(-2.19306 + 8.18461i) q^{9} +O(q^{10})$	\(q+(0.954861 - 1.04319i) q^{2} +(-2.06202 - 2.68727i) q^{3} +(-0.176481 - 1.99220i) q^{4} +(-0.668458 - 0.512926i) q^{5} +(-4.77227 - 0.414901i) q^{6} +(2.64566 - 0.0215710i) q^{7} +(-2.24675 - 1.71817i) q^{8} +(-2.19306 + 8.18461i) q^{9} +(-1.17336 + 0.207554i) q^{10} +(3.45859 + 0.455332i) q^{11} +(-4.98967 + 4.58220i) q^{12} +(-2.36539 - 0.979776i) q^{13} +(2.50374 - 2.78052i) q^{14} +2.85399i q^{15} +(-3.93771 + 0.703170i) q^{16} +(1.09903 + 0.634523i) q^{17} +(6.44401 + 10.1029i) q^{18} +(-0.514576 - 3.90859i) q^{19} +(-0.903880 + 1.42222i) q^{20} +(-5.51336 - 7.06513i) q^{21} +(3.77747 - 3.17318i) q^{22} +(0.535059 - 1.99687i) q^{23} +(0.0156490 + 9.58052i) q^{24} +(-1.11035 - 4.14389i) q^{25} +(-3.28071 + 1.53199i) q^{26} +(17.1282 - 7.09473i) q^{27} +(-0.509883 - 5.26688i) q^{28} +(-1.54411 + 3.72780i) q^{29} +(2.97725 + 2.72516i) q^{30} +(-0.504081 + 0.873093i) q^{31} +(-3.02643 + 4.77920i) q^{32} +(-5.90807 - 10.2331i) q^{33} +(1.71134 - 0.540609i) q^{34} +(-1.77958 - 1.34261i) q^{35} +(16.6924 + 2.92458i) q^{36} +(3.71686 + 2.85205i) q^{37} +(-4.56874 - 3.19536i) q^{38} +(2.24454 + 8.37676i) q^{39} +(0.620566 + 2.30094i) q^{40} +(2.73619 + 2.73619i) q^{41} +(-12.6348 - 0.994746i) q^{42} +(-3.86947 - 9.34172i) q^{43} +(0.296736 - 6.97056i) q^{44} +(5.66407 - 4.34619i) q^{45} +(-1.57220 - 2.46490i) q^{46} +(0.618350 - 0.357005i) q^{47} +(10.0092 + 9.13174i) q^{48} +(6.99907 - 0.114139i) q^{49} +(-5.38309 - 2.79853i) q^{50} +(-0.561074 - 4.26178i) q^{51} +(-1.53446 + 4.88524i) q^{52} +(12.8920 + 1.69727i) q^{53} +(8.95391 - 24.6424i) q^{54} +(-2.07837 - 2.07837i) q^{55} +(-5.98121 - 4.49723i) q^{56} +(-9.44238 + 9.44238i) q^{57} +(2.41439 + 5.17032i) q^{58} +(-0.487469 + 3.70269i) q^{59} +(5.68571 - 0.503675i) q^{60} +(-10.4200 + 1.37182i) q^{61} +(0.429473 + 1.35953i) q^{62} +(-5.62554 + 21.7010i) q^{63} +(2.09579 + 7.72060i) q^{64} +(1.07861 + 1.86821i) q^{65} +(-16.3164 - 3.60794i) q^{66} +(2.82630 + 3.68330i) q^{67} +(1.07014 - 2.30146i) q^{68} +(-6.46942 + 2.67972i) q^{69} +(-3.09985 + 0.574430i) q^{70} +(4.29918 - 4.29918i) q^{71} +(18.9898 - 14.6207i) q^{72} +(6.39177 - 1.71267i) q^{73} +(6.52431 - 1.15407i) q^{74} +(-8.84619 + 11.5286i) q^{75} +(-7.69588 + 1.71493i) q^{76} +(9.16009 + 1.13005i) q^{77} +(10.8818 + 5.65716i) q^{78} +(-6.60200 + 3.81167i) q^{79} +(2.99287 + 1.54971i) q^{80} +(-32.3697 - 18.6887i) q^{81} +(5.46704 - 0.241679i) q^{82} +(-1.04622 - 0.433358i) q^{83} +(-13.1021 + 12.2306i) q^{84} +(-0.409190 - 0.987871i) q^{85} +(-13.4400 - 4.88346i) q^{86} +(13.2016 - 3.53735i) q^{87} +(-6.98826 - 6.96546i) q^{88} +(9.58137 + 2.56732i) q^{89} +(0.874503 - 10.0587i) q^{90} +(-6.27916 - 2.54113i) q^{91} +(-4.07258 - 0.713534i) q^{92} +(3.38566 - 0.445731i) q^{93} +(0.218016 - 0.985945i) q^{94} +(-1.66085 + 2.87667i) q^{95} +(19.0835 - 1.72196i) q^{96} -0.768699 q^{97} +(6.56407 - 7.41033i) q^{98} +(-11.3116 + 27.3086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.954861	−	1.04319i	0.675189	−	0.737645i
$2$	0.954861	−	1.04319i	0.675189	−	0.737645i
$3$	−2.06202	−	2.68727i	−1.19050	−	1.55150i	−0.761458	−	0.648214i	$-0.775516\pi$
$3$	−2.06202	−	2.68727i	−1.19050	−	1.55150i	−0.429047	−	0.903282i	$-0.641150\pi$
$4$	−0.176481	−	1.99220i	−0.0882405	−	0.996099i
$5$	−0.668458	−	0.512926i	−0.298944	−	0.229388i	0.448388	−	0.893839i	$-0.351998\pi$
$5$	−0.668458	−	0.512926i	−0.298944	−	0.229388i	−0.747331	+	0.664452i	$0.768665\pi$
$6$	−4.77227	−	0.414901i	−1.94827	−	0.169383i
$7$	2.64566	−	0.0215710i	0.999967	−	0.00815308i
$7$	2.64566	−	0.0215710i	0.999967	−	0.00815308i
$8$	−2.24675	−	1.71817i	−0.794347	−	0.607465i
$9$	−2.19306	+	8.18461i	−0.731020	+	2.72820i
$10$	−1.17336	+	0.207554i	−0.371050	+	0.0656344i
$11$	3.45859	+	0.455332i	1.04280	+	0.137288i	0.632421	−	0.774625i	$-0.282061\pi$
$11$	3.45859	+	0.455332i	1.04280	+	0.137288i	0.410384	+	0.911913i	$0.365395\pi$
$12$	−4.98967	+	4.58220i	−1.44039	+	1.32277i
$13$	−2.36539	−	0.979776i	−0.656041	−	0.271741i	0.0297305	−	0.999558i	$-0.490535\pi$
$13$	−2.36539	−	0.979776i	−0.656041	−	0.271741i	−0.685772	+	0.727817i	$0.740535\pi$
$14$	2.50374	−	2.78052i	0.669152	−	0.743125i
$15$			2.85399i			0.736897i
$16$	−3.93771	+	0.703170i	−0.984427	+	0.175793i
$17$	1.09903	+	0.634523i	0.266553	+	0.153894i	0.627320	−	0.778761i	$-0.284152\pi$
$17$	1.09903	+	0.634523i	0.266553	+	0.153894i	−0.360767	+	0.932656i	$0.617485\pi$
$18$	6.44401	+	10.1029i	1.51887	+	2.38128i
$19$	−0.514576	−	3.90859i	−0.118052	−	0.896693i	−0.943304	−	0.331929i	$-0.892301\pi$
$19$	−0.514576	−	3.90859i	−0.118052	−	0.896693i	0.825253	−	0.564764i	$-0.191033\pi$
$20$	−0.903880	+	1.42222i	−0.202114	+	0.318019i
$21$	−5.51336	−	7.06513i	−1.20311	−	1.54174i
$22$	3.77747	−	3.17318i	0.805359	−	0.676524i
$23$	0.535059	−	1.99687i	0.111567	−	0.416375i	−0.887440	−	0.460924i	$-0.847518\pi$
$23$	0.535059	−	1.99687i	0.111567	−	0.416375i	0.999007	+	0.0445482i	$0.0141848\pi$
$24$	0.0156490	+	9.58052i	0.00319433	+	1.95562i
$25$	−1.11035	−	4.14389i	−0.222070	−	0.828778i
$26$	−3.28071	+	1.53199i	−0.643400	+	0.300449i
$27$	17.1282	−	7.09473i	3.29632	−	1.36538i
$28$	−0.509883	−	5.26688i	−0.0963588	−	0.995347i
$29$	−1.54411	+	3.72780i	−0.286733	+	0.692235i	−0.999962	−	0.00869603i	$-0.997232\pi$
$29$	−1.54411	+	3.72780i	−0.286733	+	0.692235i	0.713229	+	0.700931i	$0.247232\pi$
$30$	2.97725	+	2.72516i	0.543568	+	0.497544i
$31$	−0.504081	+	0.873093i	−0.0905356	+	0.156812i	−0.907737	−	0.419541i	$-0.862191\pi$
$31$	−0.504081	+	0.873093i	−0.0905356	+	0.156812i	0.817201	+	0.576353i	$0.195525\pi$
$32$	−3.02643	+	4.77920i	−0.535002	+	0.844851i
$33$	−5.90807	−	10.2331i	−1.02846	−	1.78135i
$34$	1.71134	−	0.540609i	0.293493	−	0.0927137i
$35$	−1.77958	−	1.34261i	−0.300804	−	0.226943i
$36$	16.6924	+	2.92458i	2.78207	+	0.487430i
$37$	3.71686	+	2.85205i	0.611048	+	0.468874i	0.867334	−	0.497727i	$-0.165832\pi$
$37$	3.71686	+	2.85205i	0.611048	+	0.468874i	−0.256285	+	0.966601i	$0.582499\pi$
$38$	−4.56874	−	3.19536i	−0.741148	−	0.518356i
$39$	2.24454	+	8.37676i	0.359415	+	1.34135i
$40$	0.620566	+	2.30094i	0.0981200	+	0.363811i
$41$	2.73619	+	2.73619i	0.427321	+	0.427321i	0.887715	−	0.460394i	$-0.152292\pi$
$41$	2.73619	+	2.73619i	0.427321	+	0.427321i	−0.460394	+	0.887715i	$0.652292\pi$
$42$	−12.6348	−	0.994746i	−1.94959	−	0.153493i
$43$	−3.86947	−	9.34172i	−0.590088	−	1.42460i	−0.883417	−	0.468587i	$-0.844763\pi$
$43$	−3.86947	−	9.34172i	−0.590088	−	1.42460i	0.293329	−	0.956012i	$-0.405237\pi$
$44$	0.296736	−	6.97056i	0.0447347	−	1.05085i
$45$	5.66407	−	4.34619i	0.844349	−	0.647892i
$46$	−1.57220	−	2.46490i	−0.231808	−	0.363429i
$47$	0.618350	−	0.357005i	0.0901956	−	0.0520745i	−0.454224	−	0.890888i	$-0.650083\pi$
$47$	0.618350	−	0.357005i	0.0901956	−	0.0520745i	0.544419	+	0.838813i	$0.316750\pi$
$48$	10.0092	+	9.13174i	1.44471	+	1.31805i
$49$	6.99907	−	0.114139i	0.999867	−	0.0163056i
$50$	−5.38309	−	2.79853i	−0.761283	−	0.395772i
$51$	−0.561074	−	4.26178i	−0.0785660	−	0.596768i
$52$	−1.53446	+	4.88524i	−0.212792	+	0.677461i
$53$	12.8920	+	1.69727i	1.77086	+	0.233138i	0.944155	−	0.329501i	$-0.106881\pi$
$53$	12.8920	+	1.69727i	1.77086	+	0.233138i	0.826702	+	0.562639i	$0.190214\pi$
$54$	8.95391	−	24.6424i	1.21847	−	3.35341i
$55$	−2.07837	−	2.07837i	−0.280248	−	0.280248i
$56$	−5.98121	−	4.49723i	−0.799273	−	0.600968i
$57$	−9.44238	+	9.44238i	−1.25067	+	1.25067i
$58$	2.41439	+	5.17032i	0.317025	+	0.678897i
$59$	−0.487469	+	3.70269i	−0.0634631	+	0.482050i	0.929970	+	0.367635i	$0.119833\pi$
$59$	−0.487469	+	3.70269i	−0.0634631	+	0.482050i	−0.993433	+	0.114414i	$0.963501\pi$
$60$	5.68571	−	0.503675i	0.734022	−	0.0650241i
$61$	−10.4200	+	1.37182i	−1.33415	+	0.175644i	−0.763638	−	0.645645i	$-0.776589\pi$
$61$	−10.4200	+	1.37182i	−1.33415	+	0.175644i	−0.570512	+	0.821289i	$0.693255\pi$
$62$	0.429473	+	1.35953i	0.0545431	+	0.172661i
$63$	−5.62554	+	21.7010i	−0.708752	+	2.73407i
$64$	2.09579	+	7.72060i	0.261973	+	0.965075i
$65$	1.07861	+	1.86821i	0.133785	+	0.231723i
$66$	−16.3164	−	3.60794i	−2.00841	−	0.444107i
$67$	2.82630	+	3.68330i	0.345287	+	0.449987i	0.933424	−	0.358774i	$-0.116805\pi$
$67$	2.82630	+	3.68330i	0.345287	+	0.449987i	−0.588137	+	0.808761i	$0.700138\pi$
$68$	1.07014	−	2.30146i	0.129773	−	0.279093i
$69$	−6.46942	+	2.67972i	−0.778827	+	0.322601i
$70$	−3.09985	+	0.574430i	−0.370502	+	0.0686575i
$71$	4.29918	−	4.29918i	0.510219	−	0.510219i	−0.404374	−	0.914593i	$-0.632511\pi$
$71$	4.29918	−	4.29918i	0.510219	−	0.510219i	0.914593	+	0.404374i	$0.132511\pi$
$72$	18.9898	−	14.6207i	2.23797	−	1.72307i
$73$	6.39177	−	1.71267i	0.748101	−	0.200453i	0.135425	−	0.990788i	$-0.456760\pi$
$73$	6.39177	−	1.71267i	0.748101	−	0.200453i	0.612675	+	0.790335i	$0.290093\pi$
$74$	6.52431	−	1.15407i	0.758436	−	0.134158i
$75$	−8.84619	+	11.5286i	−1.02147	+	1.33121i
$76$	−7.69588	+	1.71493i	−0.882778	+	0.196716i
$77$	9.16009	+	1.13005i	1.04389	+	0.128781i
$78$	10.8818	+	5.65716i	1.23212	+	0.640547i
$79$	−6.60200	+	3.81167i	−0.742783	+	0.428846i	−0.823080	−	0.567925i	$-0.807746\pi$
$79$	−6.60200	+	3.81167i	−0.742783	+	0.428846i	0.0802971	+	0.996771i	$0.474413\pi$
$80$	2.99287	+	1.54971i	0.334613	+	0.173263i
$81$	−32.3697	−	18.6887i	−3.59663	−	2.07652i
$82$	5.46704	−	0.241679i	0.603734	−	0.0266889i
$83$	−1.04622	−	0.433358i	−0.114838	−	0.0475673i	0.324525	−	0.945877i	$-0.394796\pi$
$83$	−1.04622	−	0.433358i	−0.114838	−	0.0475673i	−0.439362	+	0.898310i	$0.644796\pi$
$84$	−13.1021	+	12.2306i	−1.42956	+	1.33447i
$85$	−0.409190	−	0.987871i	−0.0443829	−	0.107150i
$86$	−13.4400	−	4.88346i	−1.44927	−	0.526597i
$87$	13.2016	−	3.53735i	1.41536	−	0.379244i
$88$	−6.98826	−	6.96546i	−0.744951	−	0.742521i
$89$	9.58137	+	2.56732i	1.01562	+	0.272135i	0.727977	−	0.685602i	$-0.240461\pi$
$89$	9.58137	+	2.56732i	1.01562	+	0.272135i	0.287646	+	0.957737i	$0.407127\pi$
$90$	0.874503	−	10.0587i	0.0921807	−	1.06028i
$91$	−6.27916	−	2.54113i	−0.658235	−	0.266383i
$92$	−4.07258	−	0.713534i	−0.424596	−	0.0743911i
$93$	3.38566	−	0.445731i	0.351077	−	0.0462201i
$94$	0.218016	−	0.985945i	0.0224866	−	0.101692i
$95$	−1.66085	+	2.87667i	−0.170399	+	0.295140i
$96$	19.0835	−	1.72196i	1.94771	−	0.175746i
$97$	−0.768699			−0.0780496			−0.0390248	−	0.999238i	$-0.512425\pi$
$97$	−0.768699			−0.0780496			−0.0390248	+	0.999238i	$0.512425\pi$
$98$	6.56407	−	7.41033i	0.663071	−	0.748556i
$99$	−11.3116	+	27.3086i	−1.13686	+	2.74462i
$100$	−8.05949	+	2.94336i	−0.805949	+	0.294336i
$101$	−1.81509	+	13.7870i	−0.180608	+	1.37185i	0.625564	+	0.780173i	$0.284869\pi$
$101$	−1.81509	+	13.7870i	−0.180608	+	1.37185i	−0.806172	+	0.591682i	$0.798464\pi$
$102$	−4.98158	−	3.48410i	−0.493250	−	0.344977i
$103$	10.5120	+	2.81668i	1.03578	+	0.277536i	0.736362	−	0.676587i	$-0.236542\pi$
$103$	10.5120	+	2.81668i	1.03578	+	0.277536i	0.299415	+	0.954123i	$0.403208\pi$
$104$	3.63102	+	6.26546i	0.356051	+	0.614378i
$105$	0.0615635	+	7.55070i	0.00600798	+	0.736872i
$106$	14.0807	−	11.8282i	1.36764	−	1.14885i
$107$	−2.06278	+	2.68827i	−0.199416	+	0.259885i	−0.882348	−	0.470598i	$-0.844038\pi$
$107$	−2.06278	+	2.68827i	−0.199416	+	0.259885i	0.682931	+	0.730483i	$0.260705\pi$
$108$	−17.1569	−	32.8707i	−1.65092	−	3.16298i
$109$	10.4648	−	8.02989i	1.00234	−	0.769124i	0.0292573	−	0.999572i	$-0.490686\pi$
$109$	10.4648	−	8.02989i	1.00234	−	0.769124i	0.973085	+	0.230448i	$0.0740191\pi$
$110$	−4.15269	+	0.183576i	−0.395943	+	0.0175033i
$111$		−	15.8692i		−	1.50624i
$112$	−10.4027	+	1.94529i	−0.982961	+	0.183813i
$113$		−	4.79063i		−	0.450665i	−0.974282	−	0.225332i	$-0.927653\pi$
$113$		−	4.79063i		−	0.450665i	0.974282	−	0.225332i	$-0.0723468\pi$
$114$	0.834014	+	18.8663i	0.0781126	+	1.76699i
$115$	−1.38191	+	1.06038i	−0.128864	+	0.0988806i
$116$	7.69902	+	2.41828i	0.714836	+	0.224531i
$117$	13.2065	−	17.2111i	1.22094	−	1.59116i
$118$	3.39714	+	4.04408i	0.312732	+	0.372288i
$119$	2.92134	+	1.65503i	0.267799	+	0.151716i
$120$	4.90364	−	6.41221i	0.447639	−	0.585352i
$121$	1.12934	+	0.302606i	0.102667	+	0.0275096i
$122$	−8.51862	+	12.1800i	−0.771240	+	1.10272i
$123$	1.71082	−	12.9949i	0.154259	−	1.17171i
$124$	1.82834	+	0.850144i	0.164189	+	0.0763452i
$125$	−2.99548	+	7.23173i	−0.267924	+	0.646825i
$126$	17.2666	+	26.5900i	1.53823	+	2.36882i
$127$	12.5453			1.11322			0.556608	−	0.830775i	$-0.312103\pi$
$127$	12.5453			1.11322			0.556608	+	0.830775i	$0.312103\pi$
$128$	10.0552	+	5.18580i	0.888764	+	0.458365i
$129$	−17.1248	+	29.6611i	−1.50776	+	2.61151i
$130$	2.97882	+	0.658687i	0.261260	+	0.0577706i
$131$	6.38252	−	0.840275i	0.557644	−	0.0734152i	0.153564	−	0.988139i	$-0.450925\pi$
$131$	6.38252	−	0.840275i	0.557644	−	0.0734152i	0.404080	+	0.914724i	$0.367592\pi$
$132$	−19.3436	+	13.5760i	−1.68365	+	1.18164i
$133$	−1.44571	−	10.3297i	−0.125359	−	0.895700i
$134$	6.54110	+	0.568683i	0.565065	+	0.0491268i
$135$	−15.0886	−	4.04297i	−1.29862	−	0.347963i
$136$	−1.37902	−	3.31393i	−0.118250	−	0.284167i
$137$	−10.6574	+	2.85563i	−0.910520	+	0.243973i	−0.683529	−	0.729924i	$-0.739556\pi$
$137$	−10.6574	+	2.85563i	−0.910520	+	0.243973i	−0.226992	+	0.973897i	$0.572889\pi$
$138$	−3.38194	+	9.30758i	−0.287890	+	0.792314i
$139$	−5.46203	−	13.1865i	−0.463283	−	1.11846i	−0.967041	−	0.254620i	$-0.918050\pi$
$139$	−5.46203	−	13.1865i	−0.463283	−	1.11846i	0.503758	−	0.863845i	$-0.331950\pi$
$140$	−2.36068	+	3.78222i	−0.199514	+	0.319656i
$141$	−2.23441	−	0.925525i	−0.188172	−	0.0779433i
$142$	−0.379732	−	8.58997i	−0.0318664	−	0.720855i
$143$	−7.73479	−	4.46568i	−0.646816	−	0.373439i
$144$	2.88046	−	33.7707i	0.240038	−	2.81422i
$145$	2.94426	−	1.69987i	0.244507	−	0.141166i
$146$	4.31662	−	8.30318i	0.357246	−	0.687176i
$147$	−14.7389	−	18.5730i	−1.21564	−	1.53188i
$148$	5.02589	−	7.90806i	0.413126	−	0.650038i
$149$	−9.88879	+	12.8873i	−0.810121	+	1.05577i	0.187178	+	0.982326i	$0.440066\pi$
$149$	−9.88879	+	12.8873i	−0.810121	+	1.05577i	−0.997299	+	0.0734443i	$0.976601\pi$
$150$	3.57959	+	20.2364i	0.292272	+	1.65230i
$151$	−12.6689	+	3.39462i	−1.03098	+	0.276250i	−0.734370	−	0.678749i	$-0.762522\pi$
$151$	−12.6689	+	3.39462i	−1.03098	+	0.276250i	−0.296609	+	0.954999i	$0.595856\pi$
$152$	−5.55950	+	9.66576i	−0.450935	+	0.783997i
$153$	−7.60355	+	7.60355i	−0.614711	+	0.614711i
$154$	9.92547	−	8.47665i	0.799817	−	0.683068i
$155$	0.784789	−	0.325070i	0.0630358	−	0.0261103i
$156$	16.2920	−	5.94992i	1.30441	−	0.476375i
$157$	−1.33154	−	1.73529i	−0.106268	−	0.138491i	0.737192	−	0.675684i	$-0.236152\pi$
$157$	−1.33154	−	1.73529i	−0.106268	−	0.138491i	−0.843460	+	0.537192i	$0.819485\pi$
$158$	−2.32771	+	10.5267i	−0.185183	+	0.837462i
$159$	−22.0226	−	38.1442i	−1.74650	−	3.02503i
$160$	4.47442	−	1.64236i	0.353734	−	0.129840i
$161$	1.37251	−	5.29458i	0.108169	−	0.417271i
$162$	−50.4043	+	15.9226i	−3.96014	+	1.25100i
$163$	−8.05104	+	1.05994i	−0.630606	+	0.0830208i	−0.439053	−	0.898461i	$-0.644686\pi$
$163$	−8.05104	+	1.05994i	−0.630606	+	0.0830208i	−0.191553	+	0.981482i	$0.561352\pi$
$164$	4.96815	−	5.93392i	0.387947	−	0.463361i
$165$	−1.29951	+	9.87078i	−0.101167	+	0.768439i
$166$	−1.45107	+	0.677606i	−0.112625	+	0.0525924i
$167$	−1.71372	+	1.71372i	−0.132611	+	0.132611i	−0.770297	−	0.637685i	$-0.779892\pi$
$167$	−1.71372	+	1.71372i	−0.132611	+	0.132611i	0.637685	+	0.770297i	$0.279892\pi$
$168$	0.248063	+	25.3465i	0.0191385	+	1.95552i
$169$	−4.55728	−	4.55728i	−0.350560	−	0.350560i
$170$	−1.42125	−	0.516418i	−0.109005	−	0.0396075i
$171$	33.1188	+	4.36017i	2.53266	+	0.333431i
$172$	−17.9277	+	9.35738i	−1.36697	+	0.713494i
$173$	2.94256	+	22.3510i	0.223719	+	1.69931i	0.622786	+	0.782392i	$0.286001\pi$
$173$	2.94256	+	22.3510i	0.223719	+	1.69931i	−0.399067	+	0.916922i	$0.630666\pi$
$174$	8.91555	−	17.1494i	0.675886	−	1.30009i
$175$	−3.02701	−	10.9394i	−0.228820	−	0.826940i
$176$	−13.9391	+	0.639013i	−1.05070	+	0.0481674i
$177$	10.9553	−	6.32505i	0.823452	−	0.475420i
$178$	11.8271	−	7.54373i	0.886476	−	0.565426i
$179$	3.58823	−	2.75335i	0.268197	−	0.205795i	−0.465904	−	0.884836i	$-0.654271\pi$
$179$	3.58823	−	2.75335i	0.268197	−	0.205795i	0.734101	+	0.679041i	$0.237604\pi$
$180$	−9.65808	−	10.5169i	−0.719870	−	0.783885i
$181$	6.91135	+	16.6855i	0.513716	+	1.24022i	0.941706	+	0.336437i	$0.109222\pi$
$181$	6.91135	+	16.6855i	0.513716	+	1.24022i	−0.427989	+	0.903784i	$0.640778\pi$
$182$	−8.64660	+	4.12391i	−0.640929	+	0.305685i
$183$	25.1727	+	25.1727i	1.86082	+	1.86082i
$184$	−4.63310	+	3.56714i	−0.341557	+	0.262973i
$185$	−1.02168	−	3.81295i	−0.0751152	−	0.280334i
$186$	2.76785	−	3.95749i	0.202949	−	0.290177i
$187$	3.51216	+	2.69498i	0.256835	+	0.197076i
$188$	−0.820351	−	1.16887i	−0.0598302	−	0.0852487i
$189$	45.1624	−	19.1397i	3.28508	−	1.39221i
$190$	1.41503	+	4.47939i	0.102657	+	0.324969i
$191$	1.84604	+	3.19743i	0.133575	+	0.231358i	0.925052	−	0.379840i	$-0.124021\pi$
$191$	1.84604	+	3.19743i	0.133575	+	0.231358i	−0.791477	+	0.611198i	$0.790688\pi$
$192$	16.4258	−	21.5519i	1.18543	−	1.55538i
$193$	11.0805	−	19.1920i	0.797592	−	1.38147i	−0.123588	−	0.992334i	$-0.539440\pi$
$193$	11.0805	−	19.1920i	0.797592	−	1.38147i	0.921180	−	0.389137i	$-0.127227\pi$
$194$	−0.734001	+	0.801898i	−0.0526982	+	0.0575729i
$195$	2.79627	−	6.75080i	0.200245	−	0.483435i
$196$	−1.46259	−	13.9234i	−0.104471	−	0.994528i
$197$	10.1582	−	4.20764i	0.723738	−	0.299782i	0.00976224	−	0.999952i	$-0.496893\pi$
$197$	10.1582	−	4.20764i	0.723738	−	0.299782i	0.713976	+	0.700170i	$0.246893\pi$
$198$	17.6870	+	37.8761i	1.25696	+	2.69174i
$199$	5.72251	+	21.3567i	0.405658	+	1.51394i	0.802839	+	0.596195i	$0.203322\pi$
$199$	5.72251	+	21.3567i	0.405658	+	1.51394i	−0.397182	+	0.917740i	$0.630012\pi$
$200$	−4.62522	+	11.2181i	−0.327053	+	0.793237i
$201$	4.07016	−	15.1901i	0.287087	−	1.07142i
$202$	12.6492	+	15.0581i	0.889997	+	1.05949i
$203$	−4.00477	+	9.89581i	−0.281080	+	0.694550i
$204$	−8.39129	+	1.86989i	−0.587507	+	0.130919i
$205$	−0.425566	−	3.23249i	−0.0297228	−	0.225767i
$206$	12.9758	−	8.27644i	0.904068	−	0.576647i
$207$	15.1702	+	8.75849i	1.05440	+	0.608757i
$208$	10.0032	+	2.19480i	0.693595	+	0.152182i
$209$		−	13.7525i		−	0.951282i
$210$	7.93558	+	7.14564i	0.547607	+	0.493096i
$211$	4.48972	+	1.85970i	0.309085	+	0.128027i	0.531834	−	0.846849i	$-0.321503\pi$
$211$	4.48972	+	1.85970i	0.309085	+	0.128027i	−0.222749	+	0.974876i	$0.571503\pi$
$212$	1.10610	−	25.9830i	0.0759671	−	1.78452i
$213$	−20.4180	−	2.68809i	−1.39902	−	0.184185i
$214$	0.834699	+	4.71879i	0.0570588	+	0.322570i
$215$	−2.20503	+	8.22930i	−0.150382	+	0.561234i
$216$	−50.6727	−	13.4890i	−3.44784	−	0.917813i
$217$	−1.31479	+	2.32078i	−0.0892540	+	0.157545i
$218$	1.61571	−	18.5841i	0.109429	−	1.25868i
$219$	−17.7823	−	13.6449i	−1.20162	−	0.922035i
$220$	−3.77374	+	4.50732i	−0.254425	+	0.303884i
$221$	−1.97793	−	2.57769i	−0.133050	−	0.173394i
$222$	−16.5545	−	15.1529i	−1.11107	−	1.01699i
$223$	−1.17828			−0.0789035			−0.0394517	−	0.999221i	$-0.512561\pi$
$223$	−1.17828			−0.0789035			−0.0394517	+	0.999221i	$0.512561\pi$
$224$	−7.90381	+	12.7094i	−0.528096	+	0.849185i
$225$	36.3512			2.42341
$226$	−4.99753	−	4.57439i	−0.332431	−	0.304284i
$227$	−9.53100	−	12.4210i	−0.632595	−	0.824414i	0.361563	−	0.932348i	$-0.382243\pi$
$227$	−9.53100	−	12.4210i	−0.632595	−	0.824414i	−0.994158	+	0.107934i	$0.965577\pi$
$228$	20.4775	+	17.1447i	1.35616	+	1.13544i
$229$	0.908605	+	0.697197i	0.0600423	+	0.0460721i	0.638347	−	0.769749i	$-0.279619\pi$
$229$	0.908605	+	0.697197i	0.0600423	+	0.0460721i	−0.578304	+	0.815821i	$0.696285\pi$
$230$	−0.213360	+	2.45410i	−0.0140685	+	0.161819i
$231$	−15.8515	−	26.9458i	−1.04295	−	1.77290i
$232$	9.87421	−	5.72240i	0.648274	−	0.375694i
$233$	−2.00835	+	7.49525i	−0.131571	+	0.491030i	−0.999988	−	0.00480371i	$-0.998471\pi$
$233$	−2.00835	+	7.49525i	−0.131571	+	0.491030i	0.868417	+	0.495834i	$0.165138\pi$
$234$	−5.34399	−	30.2111i	−0.349347	−	1.97496i
$235$	−0.596458	−	0.0785252i	−0.0389086	−	0.00512242i
$236$	7.46253	+	0.317680i	0.485769	+	0.0206792i
$237$	23.8564	+	9.88165i	1.54964	+	0.641882i
$238$	4.51598	−	1.46719i	0.292727	−	0.0951035i
$239$		−	7.07538i		−	0.457668i	−0.973465	−	0.228834i	$-0.926509\pi$
$239$		−	7.07538i		−	0.457668i	0.973465	−	0.228834i	$-0.0734913\pi$
$240$	−2.00684	−	11.2382i	−0.129541	−	0.725421i
$241$	3.24154	+	1.87151i	0.208806	+	0.120554i	0.600756	−	0.799432i	$-0.294866\pi$
$241$	3.24154	+	1.87151i	0.208806	+	0.120554i	−0.391950	+	0.919986i	$0.628199\pi$
$242$	1.39404	−	0.889168i	0.0896122	−	0.0571579i
$243$	9.26570	+	70.3800i	0.594395	+	4.51488i
$244$	4.57189	+	20.5167i	0.292685	+	1.31345i
$245$	−4.73713	−	3.51371i	−0.302644	−	0.224483i
$246$	−11.9226	−	14.1931i	−0.760156	−	0.904917i
$247$	−2.61237	+	9.74951i	−0.166221	+	0.620347i
$248$	2.63267	−	1.09553i	0.167174	−	0.0695661i
$249$	0.992769	+	3.70507i	0.0629142	+	0.234799i
$250$	4.68378	+	10.0301i	0.296228	+	0.634362i
$251$	−5.06706	+	2.09885i	−0.319830	+	0.132478i	−0.536822	−	0.843695i	$-0.680375\pi$
$251$	−5.06706	+	2.09885i	−0.319830	+	0.132478i	0.216992	+	0.976173i	$0.430375\pi$
$252$	44.2255	+	7.37738i	2.78595	+	0.464732i
$253$	2.75979	−	6.66272i	0.173506	−	0.418881i
$254$	11.9790	−	13.0871i	0.751630	−	0.821158i
$255$	−1.81092	+	3.13661i	−0.113404	+	0.196422i
$256$	15.0111	−	5.53776i	0.938194	−	0.346110i
$257$	12.1839	+	21.1031i	0.760009	+	1.31637i	0.942845	+	0.333230i	$0.108139\pi$
$257$	12.1839	+	21.1031i	0.760009	+	1.31637i	−0.182837	+	0.983143i	$0.558528\pi$
$258$	14.5902	+	46.1866i	0.908348	+	2.87545i
$259$	9.89509	+	7.46538i	0.614851	+	0.463876i
$260$	3.53149	−	2.47851i	0.219014	−	0.153711i
$261$	−27.1243	−	20.8132i	−1.67895	−	1.28830i
$262$	5.21786	−	7.46052i	0.322360	−	0.460912i
$263$	2.74101	+	10.2296i	0.169018	+	0.630783i	0.997494	+	0.0707580i	$0.0225418\pi$
$263$	2.74101	+	10.2296i	0.169018	+	0.630783i	−0.828476	+	0.560025i	$0.810792\pi$
$264$	−4.30820	+	33.1422i	−0.265151	+	2.03976i
$265$	−7.74722	−	7.74722i	−0.475908	−	0.475908i
$266$	−12.1563	−	8.35530i	−0.745350	−	0.512296i
$267$	−12.8578	−	31.0416i	−0.786887	−	1.89971i
$268$	6.83908	−	6.28058i	0.417763	−	0.383647i
$269$	7.90657	−	6.06693i	0.482072	−	0.369907i	−0.338949	−	0.940805i	$-0.610071\pi$
$269$	7.90657	−	6.06693i	0.482072	−	0.369907i	0.821021	+	0.570898i	$0.193405\pi$
$270$	−18.6250	+	11.8797i	−1.13348	+	0.722977i
$271$	−7.46102	+	4.30762i	−0.453225	+	0.261669i	−0.709191	−	0.705016i	$-0.750940\pi$
$271$	−7.46102	+	4.30762i	−0.453225	+	0.261669i	0.255966	+	0.966686i	$0.417606\pi$
$272$	−4.77382	−	1.72576i	−0.289456	−	0.104640i
$273$	6.11901	+	22.1137i	0.370339	+	1.33838i
$274$	−7.19734	+	13.8444i	−0.434807	+	0.836369i
$275$	−1.95341	−	14.8376i	−0.117795	−	0.894741i
$276$	6.48027	+	12.4154i	0.390066	+	0.747322i
$277$	−8.59483	−	1.13153i	−0.516413	−	0.0679871i	−0.132185	−	0.991225i	$-0.542199\pi$
$277$	−8.59483	−	1.13153i	−0.516413	−	0.0679871i	−0.384228	+	0.923238i	$0.625532\pi$
$278$	−18.9715	−	6.89336i	−1.13783	−	0.413436i
$279$	−6.04045	−	6.04045i	−0.361632	−	0.361632i
$280$	1.69144	+	6.07413i	0.101083	+	0.362999i
$281$	2.38235	−	2.38235i	0.142119	−	0.142119i	−0.632468	−	0.774587i	$-0.717958\pi$
$281$	2.38235	−	2.38235i	0.142119	−	0.142119i	0.774587	+	0.632468i	$0.217958\pi$
$282$	−3.09905	+	1.44717i	−0.184546	+	0.0861775i
$283$	−0.879378	+	6.67954i	−0.0522736	+	0.397058i	0.945228	+	0.326411i	$0.105839\pi$
$283$	−0.879378	+	6.67954i	−0.0522736	+	0.397058i	−0.997501	+	0.0706462i	$0.977494\pi$
$284$	−9.32355	−	7.80610i	−0.553251	−	0.463207i
$285$	11.1551	−	1.46859i	0.660770	−	0.0869920i
$286$	−12.0442	+	3.80473i	−0.712188	+	0.224979i
$287$	7.29806	+	7.18001i	0.430791	+	0.423823i
$288$	−32.4787	−	35.2512i	−1.91383	−	2.07720i
$289$	−7.69476	−	13.3277i	−0.452633	−	0.783983i
$290$	1.03807	−	4.69455i	0.0609579	−	0.275673i
$291$	1.58507	+	2.06570i	0.0929184	+	0.121094i
$292$	−4.54001	−	12.4314i	−0.265684	−	0.727494i
$293$	−28.9756	+	12.0021i	−1.69277	+	0.701170i	−0.999804	−	0.0197953i	$-0.993699\pi$
$293$	−28.9756	+	12.0021i	−1.69277	+	0.701170i	−0.692971	+	0.720966i	$0.743699\pi$
$294$	−33.4488	−	2.35922i	−1.95077	−	0.137592i
$295$	2.22506	−	2.22506i	0.129548	−	0.129548i
$296$	−3.45056	−	12.7940i	−0.200560	−	0.743639i
$297$	62.4699	−	16.7388i	3.62487	−	0.971281i
$298$	4.00147	+	22.6215i	0.231799	+	1.31043i
$299$	−3.22211	+	4.19913i	−0.186339	+	0.242842i
$300$	24.5284	+	15.5888i	1.41615	+	0.900019i
$301$	−10.4388	−	24.6316i	−0.601683	−	1.41974i
$302$	−8.55580	+	16.4574i	−0.492331	+	0.947017i
$303$	40.7921	−	23.5513i	2.34344	−	1.35299i
$304$	4.77466	+	15.0291i	0.273845	+	0.861976i
$305$	7.66901	+	4.42770i	0.439126	+	0.253530i
$306$	0.671596	+	15.1923i	0.0383926	+	0.868484i
$307$	−13.2158	−	5.47415i	−0.754263	−	0.312426i	−0.0277837	−	0.999614i	$-0.508845\pi$
$307$	−13.2158	−	5.47415i	−0.754263	−	0.312426i	−0.726480	+	0.687188i	$0.758845\pi$
$308$	0.634703	−	18.4481i	0.0361655	−	1.05118i
$309$	−14.1067	−	34.0566i	−0.802503	−	1.93741i
$310$	0.410255	−	1.12908i	0.0233009	−	0.0641274i
$311$	−12.2887	+	3.29275i	−0.696830	+	0.186715i	−0.589810	−	0.807542i	$-0.700797\pi$
$311$	−12.2887	+	3.29275i	−0.696830	+	0.186715i	−0.107020	+	0.994257i	$0.534131\pi$
$312$	9.34975	−	22.6770i	0.529326	−	1.28383i
$313$	−10.7757	−	2.88734i	−0.609078	−	0.163202i	−0.0589203	−	0.998263i	$-0.518766\pi$
$313$	−10.7757	−	2.88734i	−0.609078	−	0.163202i	−0.550158	+	0.835061i	$0.685432\pi$
$314$	−3.08167	−	0.267920i	−0.173909	−	0.0151196i
$315$	14.8915	−	11.6207i	0.839039	−	0.654754i
$316$	8.75873	+	12.4798i	0.492717	+	0.702044i
$317$	−22.8380	+	3.00668i	−1.28271	+	0.168872i	−0.740891	−	0.671625i	$-0.765597\pi$
$317$	−22.8380	+	3.00668i	−1.28271	+	0.168872i	−0.541817	+	0.840497i	$0.682263\pi$
$318$	−60.8200	−	13.4487i	−3.41062	−	0.754168i
$319$	−7.03782	+	12.1899i	−0.394042	+	0.682501i
$320$	2.55915	−	6.23588i	0.143061	−	0.348596i
$321$	11.4776			0.640616
$322$	−4.21268	−	6.48737i	−0.234764	−	0.361527i
$323$	1.91456	−	4.62216i	0.106529	−	0.257184i
$324$	−31.5189	+	67.7851i	−1.75105	+	3.76584i
$325$	−1.43367	+	10.8898i	−0.0795257	+	0.604058i
$326$	−6.58190	+	9.41084i	−0.364538	+	0.521218i
$327$	−43.1570	−	11.5639i	−2.38659	−	0.639484i
$328$	−1.44630	−	10.8488i	−0.0798586	−	0.599023i
$329$	1.62825	−	0.957852i	0.0897681	−	0.0528081i
$330$	9.05622	+	10.7809i	0.498529	+	0.593467i
$331$	−11.7436	+	15.3046i	−0.645488	+	0.841216i	−0.995424	−	0.0955578i	$-0.969537\pi$
$331$	−11.7436	+	15.3046i	−0.645488	+	0.841216i	0.349936	+	0.936773i	$0.386203\pi$
$332$	−0.678698	+	2.16076i	−0.0372484	+	0.118587i
$333$	−31.4942	+	24.1663i	−1.72587	+	1.32431i
$334$	0.151367	+	3.42409i	0.00828243	+	0.187358i
$335$		−	3.91182i		−	0.213725i
$336$	26.6780	+	23.9436i	1.45541	+	1.30623i
$337$			11.9312i			0.649935i	0.945725	+	0.324968i	$0.105353\pi$
$337$			11.9312i			0.649935i	−0.945725	+	0.324968i	$0.894647\pi$
$338$	−9.10567	+	0.402530i	−0.495283	+	0.0218947i
$339$	−12.8737	+	9.87836i	−0.699205	+	0.536519i
$340$	−1.89582	+	0.989528i	−0.102815	+	0.0536647i
$341$	−2.14096	+	2.79015i	−0.115939	+	0.151095i
$342$	36.1723	−	30.3858i	1.95597	−	1.64307i
$343$	18.5147	−	0.452951i	0.999701	−	0.0244571i
$344$	−7.35693	+	27.6369i	−0.396659	+	1.49008i
$345$	5.69904	+	1.52705i	0.306826	+	0.0822137i
$346$	26.1260	+	18.2724i	1.40454	+	0.982332i
$347$	2.30266	−	17.4904i	0.123613	−	0.938935i	−0.811442	−	0.584433i	$-0.801317\pi$
$347$	2.30266	−	17.4904i	0.123613	−	0.938935i	0.935055	−	0.354502i	$-0.115350\pi$
$348$	−9.37693	−	25.6759i	−0.502656	−	1.37637i
$349$	8.57128	−	20.6929i	0.458810	−	1.10767i	−0.510070	−	0.860133i	$-0.670380\pi$
$349$	8.57128	−	20.6929i	0.458810	−	1.10767i	0.968880	−	0.247532i	$-0.0796196\pi$
$350$	−14.3022	−	7.28786i	−0.764485	−	0.389552i
$351$	−47.4661			−2.53355
$352$	−12.6433	+	15.1513i	−0.673890	+	0.807565i
$353$	1.74631	−	3.02470i	0.0929467	−	0.160988i	−0.815803	−	0.578330i	$-0.803705\pi$
$353$	1.74631	−	3.02470i	0.0929467	−	0.160988i	0.908750	+	0.417341i	$0.137038\pi$
$354$	3.86258	−	17.4680i	0.205294	−	0.928413i
$355$	−5.07899	+	0.668661i	−0.269565	+	0.0354889i
$356$	3.42368	−	19.5411i	0.181455	−	1.03567i
$357$	−1.57634	−	11.2631i	−0.0834289	−	0.596108i
$358$	0.554005	−	6.37227i	0.0292801	−	0.336785i
$359$	−5.47199	−	1.46621i	−0.288800	−	0.0773838i	0.111510	−	0.993763i	$-0.464431\pi$
$359$	−5.47199	−	1.46621i	−0.288800	−	0.0773838i	−0.400311	+	0.916379i	$0.631098\pi$
$360$	−20.1932	+	0.0329840i	−1.06428	+	0.00173841i
$361$	3.34029	−	0.895027i	0.175805	−	0.0471067i
$362$	24.0055	+	8.72247i	1.26170	+	0.458443i
$363$	−1.51553	−	3.65882i	−0.0795449	−	0.192038i
$364$	−3.95429	+	12.9578i	−0.207261	+	0.679173i
$365$	−5.15111	−	2.13366i	−0.269621	−	0.111681i
$366$	50.2964	−	2.22342i	2.62903	−	0.116220i
$367$	−11.5797	−	6.68554i	−0.604455	−	0.348982i	0.166337	−	0.986069i	$-0.446806\pi$
$367$	−11.5797	−	6.68554i	−0.604455	−	0.348982i	−0.770792	+	0.637086i	$0.780139\pi$
$368$	−0.702769	+	8.23932i	−0.0366343	+	0.429504i
$369$	−28.3953	+	16.3940i	−1.47820	+	0.853438i
$370$	−4.95318	−	2.57504i	−0.257504	−	0.133870i
$371$	34.1446	+	4.21231i	1.77270	+	0.218692i
$372$	−1.48549	−	6.66624i	−0.0770190	−	0.345629i
$373$	−17.5020	+	22.8091i	−0.906220	+	1.18101i	0.0767150	+	0.997053i	$0.475557\pi$
$373$	−17.5020	+	22.8091i	−0.906220	+	1.18101i	−0.982935	+	0.183955i	$0.941110\pi$
$374$	6.16500	−	1.09052i	0.318784	−	0.0563893i
$375$	25.6103	−	6.86227i	1.32251	−	0.354366i
$376$	−2.00267	−	0.260330i	−0.103280	−	0.0134255i
$377$	7.30482	−	7.30482i	0.376217	−	0.376217i
$378$	23.1575	−	65.3886i	1.19109	−	3.36323i
$379$	−22.5376	+	9.33539i	−1.15768	+	0.479527i	−0.877102	−	0.480304i	$-0.840526\pi$
$379$	−22.5376	+	9.33539i	−1.15768	+	0.479527i	−0.280578	+	0.959831i	$0.590526\pi$
$380$	6.02401	+	2.80106i	0.309025	+	0.143691i
$381$	−25.8686	−	33.7126i	−1.32529	−	1.72715i
$382$	5.09824	+	1.12734i	0.260848	+	0.0576797i
$383$	−2.26214	−	3.91814i	−0.115590	−	0.200208i	0.802425	−	0.596752i	$-0.203543\pi$
$383$	−2.26214	−	3.91814i	−0.115590	−	0.200208i	−0.918015	+	0.396545i	$0.870209\pi$
$384$	−6.79836	−	37.7143i	−0.346927	−	1.92460i
$385$	−5.54351	−	5.45384i	−0.282523	−	0.277953i
$386$	−9.44051	−	29.8847i	−0.480510	−	1.52109i
$387$	84.9443	−	11.1831i	4.31796	−	0.568470i
$388$	0.135661	+	1.53140i	0.00688713	+	0.0777451i
$389$	−2.54308	+	19.3166i	−0.128939	+	0.979392i	0.797598	+	0.603189i	$0.206104\pi$
$389$	−2.54308	+	19.3166i	−0.128939	+	0.979392i	−0.926537	+	0.376203i	$0.877230\pi$
$390$	−4.37230	−	9.36311i	−0.221400	−	0.474119i
$391$	1.85510	−	1.85510i	0.0938165	−	0.0938165i
$392$	−15.9213	−	11.7691i	−0.804146	−	0.594432i
$393$	−15.4189	−	15.4189i	−0.777781	−	0.777781i
$394$	5.31026	−	14.6146i	0.267527	−	0.736272i
$395$	6.36827	+	0.838398i	0.320422	+	0.0421844i
$396$	56.4005	+	17.7155i	2.83423	+	0.890238i
$397$	−2.81950	−	21.4162i	−0.141506	−	1.07485i	−0.903903	−	0.427738i	$-0.859311\pi$
$397$	−2.81950	−	21.4162i	−0.141506	−	1.07485i	0.762396	−	0.647110i	$-0.224023\pi$
$398$	27.7432	+	14.4230i	1.39064	+	0.722961i
$399$	−24.7777	+	25.1850i	−1.24044	+	1.26083i
$400$	7.28610	+	15.5367i	0.364305	+	0.776833i
$401$	11.5116	−	6.64625i	0.574864	−	0.331898i	−0.184226	−	0.982884i	$-0.558978\pi$
$401$	11.5116	−	6.64625i	0.574864	−	0.331898i	0.759090	+	0.650986i	$0.225644\pi$
$402$	−11.9596	−	18.7503i	−0.596493	−	0.935182i
$403$	2.04778	−	1.57132i	0.102007	−	0.0782730i
$404$	27.7867	+	1.18288i	1.38244	+	0.0588504i
$405$	12.0519	+	29.0959i	0.598864	+	1.44578i
$406$	6.49919	+	13.6269i	0.322549	+	0.676289i
$407$	11.5565	+	11.5565i	0.572833	+	0.572833i
$408$	−6.06186	+	10.5392i	−0.300107	+	0.521767i
$409$	2.88279	+	10.7587i	0.142545	+	0.531985i	0.999852	+	0.0171800i	$0.00546884\pi$
$409$	2.88279	+	10.7587i	0.142545	+	0.531985i	−0.857308	+	0.514805i	$0.827864\pi$
$410$	−3.77845	−	2.64264i	−0.186604	−	0.130510i
$411$	29.6495	+	22.7509i	1.46250	+	1.12222i
$412$	3.75622	−	21.4391i	0.185056	−	1.05623i
$413$	−1.20981	+	9.80660i	−0.0595308	+	0.482551i
$414$	23.6221	−	7.46217i	1.16096	−	0.366746i
$415$	0.477073	+	0.826315i	0.0234186	+	0.0405622i
$416$	11.8412	−	8.33945i	0.580564	−	0.408875i
$417$	−24.1729	+	41.8687i	−1.18375	+	2.05032i
$418$	−14.3465	−	13.1317i	−0.701709	−	0.642295i
$419$	−6.37578	+	15.3925i	−0.311477	+	0.751972i	0.688174	+	0.725546i	$0.258413\pi$
$419$	−6.37578	+	15.3925i	−0.311477	+	0.751972i	−0.999651	+	0.0264264i	$0.991587\pi$
$420$	15.0316	−	1.45520i	0.733468	−	0.0710065i
$421$	5.65256	−	2.34137i	0.275489	−	0.114111i	−0.240662	−	0.970609i	$-0.577364\pi$
$421$	5.65256	−	2.34137i	0.275489	−	0.114111i	0.516151	+	0.856498i	$0.327364\pi$
$422$	6.22708	−	2.90786i	0.303130	−	0.141553i
$423$	1.56586	+	5.84388i	0.0761349	+	0.284139i
$424$	−26.0490	−	25.9641i	−1.26505	−	1.26093i
$425$	1.40909	−	5.25879i	0.0683508	−	0.255089i
$426$	−22.3006	+	18.7331i	−1.08047	+	0.907622i
$427$	−27.5383	+	3.85416i	−1.33267	+	0.186516i
$428$	5.71960	+	3.63504i	0.276467	+	0.175706i
$429$	3.94876	+	29.9938i	0.190648	+	1.44811i
$430$	6.47920	+	10.1581i	0.312455	+	0.489867i
$431$	−15.9358	−	9.20055i	−0.767602	−	0.443175i	0.0644168	−	0.997923i	$-0.479481\pi$
$431$	−15.9358	−	9.20055i	−0.767602	−	0.443175i	−0.832018	+	0.554748i	$0.812815\pi$
$432$	−62.4570	+	39.9810i	−3.00497	+	1.92359i
$433$		−	4.54880i		−	0.218601i	−0.994009	−	0.109301i	$-0.965139\pi$
$433$		−	4.54880i		−	0.218601i	0.994009	−	0.109301i	$-0.0348611\pi$
$434$	1.16557	+	3.58760i	0.0559491	+	0.172210i
$435$	−10.6391	−	4.40686i	−0.510106	−	0.211293i
$436$	−17.8440	−	19.4307i	−0.854571	−	0.930564i
$437$	−8.08027	−	1.06379i	−0.386532	−	0.0508878i
$438$	−31.2138	+	5.52137i	−1.49145	+	0.263821i
$439$	7.84225	−	29.2677i	0.374290	−	1.39687i	−0.480089	−	0.877220i	$-0.659396\pi$
$439$	7.84225	−	29.2677i	0.374290	−	1.39687i	0.854379	−	0.519650i	$-0.173938\pi$
$440$	1.09859	+	8.24058i	0.0523732	+	0.392854i
$441$	−14.4152	+	57.5349i	−0.686437	+	2.73976i
$442$	−4.57767	−	0.397983i	−0.217738	−	0.0189301i
$443$	16.9754	+	13.0257i	0.806527	+	0.618870i	0.927516	−	0.373784i	$-0.121940\pi$
$443$	16.9754	+	13.0257i	0.806527	+	0.618870i	−0.120989	+	0.992654i	$0.538606\pi$
$444$	−31.6146	+	2.80061i	−1.50036	+	0.132911i
$445$	−5.08790	−	6.63068i	−0.241190	−	0.314324i
$446$	−1.12509	+	1.22917i	−0.0532747	+	0.0582027i
$447$	55.0225			2.60248
$448$	5.71128	+	20.3809i	0.269833	+	0.962907i
$449$	−6.34144			−0.299271			−0.149635	−	0.988741i	$-0.547810\pi$
$449$	−6.34144			−0.299271			−0.149635	+	0.988741i	$0.547810\pi$
$450$	34.7103	−	37.9211i	1.63626	−	1.78762i
$451$	8.21749	+	10.7092i	0.386946	+	0.504278i
$452$	−9.54389	+	0.845455i	−0.448907	+	0.0397669i
$453$	35.2457	+	27.0450i	1.65599	+	1.27068i
$454$	−22.0583	−	1.91775i	−1.03525	−	0.0900043i
$455$	2.89394	+	4.91939i	0.135670	+	0.230624i
$456$	37.4383	−	4.99107i	1.75321	−	0.233728i
$457$	−3.07329	+	11.4697i	−0.143763	+	0.536529i	0.856045	+	0.516902i	$0.172915\pi$
$457$	−3.07329	+	11.4697i	−0.143763	+	0.536529i	−0.999807	+	0.0196275i	$0.993752\pi$
$458$	1.59490	−	0.282119i	0.0745247	−	0.0131826i
$459$	23.3261	+	3.07094i	1.08877	+	0.143339i
$460$	2.35636	+	2.56590i	0.109866	+	0.119636i
$461$	−5.10188	−	2.11327i	−0.237618	−	0.0984247i	0.260697	−	0.965421i	$-0.416048\pi$
$461$	−5.10188	−	2.11327i	−0.237618	−	0.0984247i	−0.498315	+	0.866996i	$0.666048\pi$
$462$	−43.2455	−	9.19343i	−2.01196	−	0.427717i
$463$			31.8265i			1.47910i	0.673100	+	0.739552i	$0.264963\pi$
$463$			31.8265i			1.47910i	−0.673100	+	0.739552i	$0.735037\pi$
$464$	3.45896	−	15.7648i	0.160578	−	0.731861i
$465$	−2.49180	−	1.43864i	−0.115554	−	0.0667154i
$466$	5.90126	+	9.25201i	0.273371	+	0.428591i
$467$	−4.81631	−	36.5835i	−0.222872	−	1.69288i	−0.627672	−	0.778478i	$-0.715992\pi$
$467$	−4.81631	−	36.5835i	−0.222872	−	1.69288i	0.404800	−	0.914405i	$-0.367341\pi$
$468$	−36.6186	−	23.2726i	−1.69269	−	1.07578i
$469$	7.55689	+	9.68381i	0.348945	+	0.447157i
$470$	−0.651451	+	0.547237i	−0.0300492	+	0.0252422i
$471$	−1.91755	+	7.15640i	−0.0883561	+	0.329749i
$472$	7.45708	−	7.48148i	0.343240	−	0.344363i
$473$	−9.12932	−	34.0711i	−0.419767	−	1.56659i
$474$	33.0880	−	15.4511i	1.51978	−	0.709693i
$475$	−15.6254	+	6.47226i	−0.716943	+	0.296968i
$476$	2.78158	−	6.11197i	0.127494	−	0.280142i
$477$	−42.1645	+	101.794i	−1.93058	+	4.66083i
$478$	−7.38094	−	6.75600i	−0.337597	−	0.309012i
$479$	10.6747	−	18.4891i	0.487738	−	0.844788i	−0.512162	−	0.858889i	$-0.671155\pi$
$479$	10.6747	−	18.4891i	0.487738	−	0.844788i	0.999901	+	0.0141011i	$0.00448865\pi$
$480$	−13.6398	−	8.63739i	−0.622568	−	0.394241i
$481$	−5.99746	−	10.3879i	−0.273461	−	0.473648i
$482$	5.04756	−	1.59451i	0.229910	−	0.0726280i
$483$	−17.0581	+	7.22919i	−0.776171	+	0.328940i
$484$	0.403544	−	2.30328i	0.0183429	−	0.104694i
$485$	0.513843	+	0.394286i	0.0233324	+	0.0179036i
$486$	82.2670	+	57.5372i	3.73171	+	2.60994i
$487$	0.885191	+	3.30358i	0.0401119	+	0.149699i	0.983077	−	0.183191i	$-0.0586427\pi$
$487$	0.885191	+	3.30358i	0.0401119	+	0.149699i	−0.942965	+	0.332891i	$0.891976\pi$
$488$	25.7683	+	14.8212i	1.16647	+	0.670926i
$489$	19.4497	+	19.4497i	0.879546	+	0.879546i
$490$	−8.18876	+	1.58661i	−0.369930	+	0.0716759i
$491$	−3.00242	−	7.24848i	−0.135497	−	0.327119i	0.841538	−	0.540198i	$-0.181651\pi$
$491$	−3.00242	−	7.24848i	−0.135497	−	0.327119i	−0.977035	+	0.213079i	$0.931651\pi$
$492$	−26.1904	−	1.11493i	−1.18076	−	0.0502648i
$493$	−4.06239	+	3.11718i	−0.182961	+	0.140391i
$494$	7.67612	+	12.0346i	0.345365	+	0.541463i
$495$	21.5687	−	12.4527i	0.969439	−	0.559706i
$496$	1.37099	−	3.79244i	0.0615592	−	0.170286i
$497$	11.2815	−	11.4669i	0.506042	−	0.514362i
$498$	4.81304	+	2.50218i	0.215677	+	0.112125i
$499$	2.16088	+	16.4135i	0.0967341	+	0.734768i	0.969232	+	0.246150i	$0.0791656\pi$
$499$	2.16088	+	16.4135i	0.0967341	+	0.734768i	−0.872498	+	0.488618i	$0.837501\pi$
$500$	14.9357	+	4.69133i	0.667944	+	0.209803i
$501$	8.13893	+	1.07151i	0.363621	+	0.0478716i
$502$	−2.64885	+	7.29000i	−0.118224	+	0.325369i
$503$	−28.2978	−	28.2978i	−1.26174	−	1.26174i	−0.950250	−	0.311488i	$-0.899173\pi$
$503$	−28.2978	−	28.2978i	−1.26174	−	1.26174i	−0.311488	−	0.950250i	$-0.600827\pi$
$504$	49.9252	−	39.0912i	2.22385	−	1.74126i
$505$	8.28501	−	8.28501i	0.368678	−	0.368678i
$506$	−4.31525	−	9.24094i	−0.191836	−	0.410810i
$507$	−2.84946	+	21.6438i	−0.126549	+	0.961236i
$508$	−2.21401	−	24.9927i	−0.0982307	−	1.10887i
$509$	11.4150	−	1.50281i	0.505962	−	0.0666111i	0.126775	−	0.991931i	$-0.459537\pi$
$509$	11.4150	−	1.50281i	0.505962	−	0.0666111i	0.379186	+	0.925320i	$0.376204\pi$
$510$	1.54289	+	4.88416i	0.0683205	+	0.216274i
$511$	16.8735	−	4.66903i	0.746441	−	0.206546i
$512$	8.55659	−	20.9472i	0.378152	−	0.925744i
$513$	−36.5442	−	63.2963i	−1.61346	−	2.79460i
$514$	33.6484	+	7.44044i	1.48417	+	0.328184i
$515$	−5.58208	−	7.27471i	−0.245976	−	0.320562i
$516$	62.1129	+	28.8814i	2.73437	+	1.27143i
$517$	2.30118	−	0.953178i	0.101206	−	0.0419207i
$518$	17.2362	−	3.19403i	0.757316	−	0.140338i
$519$	53.9955	−	53.9955i	2.37014	−	2.37014i
$520$	0.786530	−	6.05064i	0.0344916	−	0.265338i
$521$	−22.2964	+	5.97431i	−0.976825	+	0.261739i	−0.711707	−	0.702477i	$-0.752078\pi$
$521$	−22.2964	+	5.97431i	−0.976825	+	0.261739i	−0.265118	+	0.964216i	$0.585411\pi$
$522$	−47.6119	+	8.42200i	−2.08392	+	0.368621i
$523$	18.0178	−	23.4812i	0.787862	−	1.02676i	−0.210924	−	0.977503i	$-0.567647\pi$
$523$	18.0178	−	23.4812i	0.787862	−	1.02676i	0.998786	−	0.0492598i	$-0.0156862\pi$
$524$	−2.80039	−	12.5670i	−0.122336	−	0.548990i
$525$	−23.1554	+	30.6916i	−1.01058	+	1.33949i
$526$	13.2887	+	6.90844i	0.579413	+	0.301222i
$527$	−1.10800	+	0.639702i	−0.0482650	+	0.0278658i
$528$	30.4598	+	36.1405i	1.32559	+	1.57281i
$529$	16.2174	+	9.36312i	0.705104	+	0.407092i
$530$	−15.4793	+	0.684286i	−0.672378	+	0.0297235i
$531$	−29.2361	−	12.1100i	−1.26874	−	0.525528i
$532$	−20.3237	+	4.70313i	−0.881145	+	0.203907i
$533$	−3.79130	−	9.15301i	−0.164219	−	0.396461i
$534$	−44.6596	−	16.2272i	−1.93261	−	0.702222i
$535$	2.75776	−	0.738941i	0.119229	−	0.0319472i
$536$	−0.0214492	−	13.1315i	−0.000926466	−	0.567196i
$537$	−14.7980	−	3.96511i	−0.638580	−	0.171107i
$538$	1.22073	−	14.0411i	0.0526296	−	0.605355i
$539$	24.2589	+	2.79214i	1.04490	+	0.120266i
$540$	−5.39155	+	30.7729i	−0.232015	+	1.32425i
$541$	−0.775610	+	0.102111i	−0.0333461	+	0.00439009i	−0.147181	−	0.989110i	$-0.547020\pi$
$541$	−0.775610	+	0.102111i	−0.0333461	+	0.00439009i	0.113835	+	0.993500i	$0.463687\pi$
$542$	−2.63058	+	11.8964i	−0.112993	+	0.510995i
$543$	30.5871	−	52.9783i	1.31262	−	2.27352i
$544$	−6.35863	+	3.33213i	−0.272624	+	0.142864i
$545$	−11.1140			−0.476071
$546$	28.9115	+	14.7322i	1.23730	+	0.630480i
$547$	−6.53974	+	15.7883i	−0.279619	+	0.675060i	−0.999825	−	0.0187003i	$-0.994047\pi$
$547$	−6.53974	+	15.7883i	−0.279619	+	0.675060i	0.720206	+	0.693760i	$0.244047\pi$
$548$	7.56981	+	20.7276i	0.323366	+	0.885440i
$549$	11.6239	−	88.2924i	0.496097	−	3.76823i
$550$	−17.3436	−	12.1301i	−0.739535	−	0.517228i
$551$	15.3650	+	4.11704i	0.654571	+	0.175392i
$552$	19.1394	+	5.09489i	0.814627	+	0.216853i
$553$	−17.3845	+	10.2268i	−0.739262	+	0.434888i
$554$	−9.38726	+	7.88556i	−0.398827	+	0.335025i
$555$	−8.13972	+	10.6079i	−0.345512	+	0.450280i
$556$	−25.3062	+	13.2086i	−1.07322	+	0.560170i
$557$	12.5848	−	9.65663i	0.533234	−	0.409165i	−0.306739	−	0.951794i	$-0.599238\pi$
$557$	12.5848	−	9.65663i	0.533234	−	0.409165i	0.839972	+	0.542629i	$0.182571\pi$
$558$	−12.0691	+	0.533533i	−0.510926	+	0.0225862i
$559$			25.8880i			1.09495i
$560$	7.95155	+	4.03546i	0.336014	+	0.170529i
$561$		−	14.9952i		−	0.633099i
$562$	−0.210425	−	4.76005i	−0.00887625	−	0.200791i
$563$	33.9464	−	26.0480i	1.43067	−	1.09779i	0.452077	−	0.891979i	$-0.350683\pi$
$563$	33.9464	−	26.0480i	1.43067	−	1.09779i	0.978592	−	0.205812i	$-0.0659835\pi$
$564$	−1.44950	+	4.61474i	−0.0610349	+	0.194315i
$565$	−2.45724	+	3.20234i	−0.103377	+	0.134723i
$566$	6.12833	+	7.29539i	0.257593	+	0.306648i
$567$	−86.0425	−	48.7456i	−3.61344	−	2.04712i
$568$	−17.0459	+	2.27247i	−0.715231	+	0.0953507i
$569$	17.3665	+	4.65335i	0.728042	+	0.195078i	0.603757	−	0.797168i	$-0.293670\pi$
$569$	17.3665	+	4.65335i	0.728042	+	0.195078i	0.124285	+	0.992247i	$0.460336\pi$
$570$	9.11953	−	13.0391i	0.381975	−	0.546150i
$571$	−5.76086	+	43.7580i	−0.241084	+	1.83122i	0.259752	+	0.965675i	$0.416359\pi$
$571$	−5.76086	+	43.7580i	−0.241084	+	1.83122i	−0.500837	+	0.865542i	$0.666974\pi$
$572$	−7.53149	+	16.1973i	−0.314907	+	0.677245i
$573$	4.78581	−	11.5540i	0.199930	−	0.482674i
$574$	14.4587	−	0.757330i	0.603496	−	0.0316103i
$575$	−8.86890			−0.369859
$576$	−67.7863	+	0.221447i	−2.82443	+	0.00922695i
$577$	−4.54882	+	7.87878i	−0.189370	+	0.327998i	−0.945040	−	0.326954i	$-0.893978\pi$
$577$	−4.54882	+	7.87878i	−0.189370	+	0.327998i	0.755671	+	0.654952i	$0.227311\pi$
$578$	−21.2507	−	4.69904i	−0.883914	−	0.195454i
$579$	−74.4223	+	9.79788i	−3.09288	+	0.407186i
$580$	−3.90608	−	5.56555i	−0.162191	−	0.231097i
$581$	−2.77729	−	1.12395i	−0.115222	−	0.0466294i
$582$	3.66844	+	0.318934i	0.152062	+	0.0132202i
$583$	43.8155	+	11.7403i	1.81465	+	0.486234i
$584$	−17.3034	−	7.13421i	−0.716019	−	0.295216i
$585$	−17.6560	+	4.73092i	−0.729987	+	0.195599i
$586$	−15.1473	+	41.6874i	−0.625728	+	1.72209i
$587$	15.3061	+	36.9523i	0.631752	+	1.52518i	0.837419	+	0.546562i	$0.184064\pi$
$587$	15.3061	+	36.9523i	0.631752	+	1.52518i	−0.205667	+	0.978622i	$0.565936\pi$
$588$	−34.4000	+	32.6406i	−1.41863	+	1.34608i
$589$	3.67195	+	1.52097i	0.151300	+	0.0626706i
$590$	−0.196532	−	4.44578i	−0.00809111	−	0.183030i
$591$	−32.2533	−	18.6215i	−1.32673	−	0.765985i
$592$	−16.6414	−	8.61695i	−0.683957	−	0.354155i
$593$	35.7232	−	20.6248i	1.46697	−	0.846958i	0.467657	−	0.883910i	$-0.345098\pi$
$593$	35.7232	−	20.6248i	1.46697	−	0.846958i	0.999317	+	0.0369517i	$0.0117648\pi$
$594$	42.1884	−	81.1510i	1.73101	−	3.32967i
$595$	−1.10389	−	2.60475i	−0.0452550	−	0.106784i
$596$	27.4193	+	17.4261i	1.12314	+	0.713799i
$597$	45.5913	−	59.4157i	1.86593	−	2.43172i
$598$	1.30382	+	7.37085i	0.0533171	+	0.301416i
$599$	4.55044	−	1.21929i	0.185926	−	0.0498187i	−0.164655	−	0.986351i	$-0.552651\pi$
$599$	4.55044	−	1.21929i	0.185926	−	0.0498187i	0.350581	+	0.936533i	$0.385984\pi$
$600$	39.6832	−	10.7026i	1.62006	−	0.436932i
$601$	17.8077	−	17.8077i	0.726392	−	0.726392i	−0.243507	−	0.969899i	$-0.578298\pi$
$601$	17.8077	−	17.8077i	0.726392	−	0.726392i	0.969899	+	0.243507i	$0.0782979\pi$
$602$	−35.6630	−	12.6301i	−1.45351	−	0.514764i
$603$	−36.3446	+	15.0544i	−1.48007	+	0.613064i
$604$	8.99856	+	24.6398i	0.366146	+	1.00258i
$605$	−0.599703	−	0.781548i	−0.0243814	−	0.0317744i
$606$	14.3823	−	65.0420i	0.584241	−	2.64215i
$607$	7.93255	+	13.7396i	0.321972	+	0.557672i	0.980895	−	0.194538i	$-0.0623209\pi$
$607$	7.93255	+	13.7396i	0.321972	+	0.557672i	−0.658923	+	0.752211i	$0.728988\pi$
$608$	20.2373	+	9.36980i	0.820730	+	0.379996i
$609$	34.8506	−	9.64341i	1.41222	−	0.390771i
$610$	11.9418	−	3.77237i	0.483508	−	0.152739i
$611$	−1.81242	+	0.238610i	−0.0733228	+	0.00965313i
$612$	16.4897	+	13.8059i	0.666555	+	0.558070i
$613$	1.97019	−	14.9651i	0.0795754	−	0.604435i	−0.904473	−	0.426532i	$-0.859735\pi$
$613$	1.97019	−	14.9651i	0.0795754	−	0.604435i	0.984048	−	0.177903i	$-0.0569314\pi$
$614$	−18.3298	+	8.55947i	−0.739730	+	0.345432i
$615$	−7.80906	+	7.80906i	−0.314892	+	0.314892i
$616$	−18.6388	−	18.2775i	−0.750980	−	0.736423i
$617$	−23.1949	−	23.1949i	−0.933792	−	0.933792i	0.0641486	−	0.997940i	$-0.479567\pi$
$617$	−23.1949	−	23.1949i	−0.933792	−	0.933792i	−0.997940	+	0.0641486i	$0.979567\pi$
$618$	−48.9974	−	17.8034i	−1.97096	−	0.716157i
$619$	15.7699	+	2.07615i	0.633846	+	0.0834474i	0.440601	−	0.897703i	$-0.354765\pi$
$619$	15.7699	+	2.07615i	0.633846	+	0.0834474i	0.193245	+	0.981150i	$0.438099\pi$
$620$	−0.786105	−	1.50609i	−0.0315707	−	0.0604859i
$621$	−5.00264	−	37.9988i	−0.200749	−	1.52484i
$622$	−8.29907	+	15.9636i	−0.332762	+	0.640081i
$623$	25.4044	+	6.58558i	1.01781	+	0.263846i
$624$	−14.7286	−	31.4069i	−0.589618	−	1.25728i
$625$	−12.8649	+	7.42753i	−0.514594	+	0.297101i
$626$	−13.3013	+	8.48406i	−0.531628	+	0.339091i
$627$	−36.9568	+	28.3579i	−1.47591	+	1.13251i
$628$	−3.22206	+	2.95893i	−0.128574	+	0.118074i
$629$	2.27524	+	5.49291i	0.0907197	+	0.219017i
$630$	2.09667	−	26.6308i	0.0835331	−	1.06100i
$631$	26.5228	+	26.5228i	1.05585	+	1.05585i	0.998345	+	0.0575098i	$0.0183160\pi$
$631$	26.5228	+	26.5228i	1.05585	+	1.05585i	0.0575098	+	0.998345i	$0.481684\pi$
$632$	21.3822	+	2.77949i	0.850536	+	0.110562i
$633$	−4.26035	−	15.8998i	−0.169334	−	0.631962i
$634$	−18.6706	+	26.6952i	−0.741503	+	1.06020i
$635$	−8.38601	−	6.43481i	−0.332789	−	0.255358i
$636$	−72.1042	+	50.6050i	−2.85912	+	2.00662i
$637$	−16.6674	−	6.58754i	−0.660385	−	0.261008i
$638$	5.99617	+	18.9814i	0.237391	+	0.751480i
$639$	25.7588	+	44.6155i	1.01900	+	1.76496i
$640$	−4.06156	−	8.62408i	−0.160547	−	0.340897i
$641$	17.5308	−	30.3642i	0.692425	−	1.19931i	−0.278616	−	0.960402i	$-0.589876\pi$
$641$	17.5308	−	30.3642i	0.692425	−	1.19931i	0.971041	−	0.238912i	$-0.0767908\pi$
$642$	10.9595	−	11.9733i	0.432537	−	0.472547i
$643$	16.8327	−	40.6378i	0.663818	−	1.60260i	−0.127953	−	0.991780i	$-0.540841\pi$
$643$	16.8327	−	40.6378i	0.663818	−	1.60260i	0.791771	−	0.610818i	$-0.209159\pi$
$644$	−10.7901	−	1.79992i	−0.425188	−	0.0709269i
$645$	26.6612	−	11.0434i	1.04978	−	0.434834i
$646$	−2.99364	−	6.41076i	−0.117783	−	0.252228i
$647$	8.17740	+	30.5185i	0.321487	+	1.19981i	0.917797	+	0.397051i	$0.129966\pi$
$647$	8.17740	+	30.5185i	0.321487	+	1.19981i	−0.596310	+	0.802754i	$0.703367\pi$
$648$	40.6164	+	97.6054i	1.59556	+	3.83430i
$649$	−3.37191	+	12.5841i	−0.132359	+	0.493971i
$650$	9.99116	+	11.8938i	0.391886	+	0.466515i
$651$	8.94770	−	1.25229i	0.350688	−	0.0490809i
$652$	3.53246	+	15.8522i	0.138342	+	0.620820i
$653$	−3.18977	−	24.2287i	−0.124825	−	0.948144i	−0.933170	−	0.359434i	$-0.882970\pi$
$653$	−3.18977	−	24.2287i	−0.124825	−	0.948144i	0.808345	−	0.588709i	$-0.200364\pi$
$654$	−53.2722	+	33.9789i	−2.08311	+	1.32868i
$655$	−4.69745	−	2.71207i	−0.183545	−	0.105970i
$656$	−12.6983	−	8.85031i	−0.495786	−	0.345547i
$657$			56.0701i			2.18750i
$658$	0.555528	−	2.61318i	0.0216567	−	0.101872i
$659$	6.33383	+	2.62356i	0.246731	+	0.102199i	0.502622	−	0.864506i	$-0.332369\pi$
$659$	6.33383	+	2.62356i	0.246731	+	0.102199i	−0.255891	+	0.966706i	$0.582369\pi$
$660$	19.8939	+	0.846883i	0.774369	+	0.0329649i
$661$	19.4254	+	2.55740i	0.755560	+	0.0994714i	0.498459	−	0.866913i	$-0.333899\pi$
$661$	19.4254	+	2.55740i	0.755560	+	0.0994714i	0.257101	+	0.966385i	$0.417233\pi$
$662$	4.75203	+	26.8645i	0.184693	+	1.04412i
$663$	−2.84843	+	10.6305i	−0.110624	+	0.412854i
$664$	1.60601	+	2.77123i	0.0623254	+	0.107545i
$665$	−4.33199	+	7.64653i	−0.167987	+	0.296520i
$666$	−4.86254	+	55.9299i	−0.188420	+	2.16724i
$667$	6.61773	+	5.07796i	0.256240	+	0.196620i
$668$	3.71650	+	3.11163i	0.143796	+	0.120392i
$669$	2.42963	+	3.16636i	0.0939350	+	0.122418i
$670$	−4.08076	−	3.73524i	−0.157653	−	0.144305i
$671$	−36.6633			−1.41537
$672$	50.4515	−	4.96737i	1.94621	−	0.191620i
$673$	−40.6944			−1.56865			−0.784327	−	0.620348i	$-0.786991\pi$
$673$	−40.6944			−1.56865			−0.784327	+	0.620348i	$0.786991\pi$
$674$	12.4465	+	11.3927i	0.479422	+	0.438829i
$675$	−48.4181	−	63.0997i	−1.86361	−	2.42871i
$676$	−8.27474	+	9.88328i	−0.318259	+	0.380126i
$677$	26.2433	+	20.1372i	1.00861	+	0.773935i	0.974249	−	0.225474i	$-0.0723931\pi$
$677$	26.2433	+	20.1372i	1.00861	+	0.773935i	0.0343629	+	0.999409i	$0.489060\pi$
$678$	−1.98764	+	22.8622i	−0.0763348	+	0.878016i
$679$	−2.03372	+	0.0165816i	−0.0780470	+	0.000636344i
$680$	−0.777983	+	2.92256i	−0.0298343	+	0.112075i
$681$	−13.7256	+	51.2248i	−0.525967	+	1.96294i
$682$	0.866333	+	4.89762i	0.0331736	+	0.187540i
$683$	−16.5761	−	2.18228i	−0.634266	−	0.0835027i	−0.193465	−	0.981107i	$-0.561972\pi$
$683$	−16.5761	−	2.18228i	−0.634266	−	0.0835027i	−0.440802	+	0.897605i	$0.645306\pi$
$684$	2.84149	−	66.7487i	0.108647	−	2.55220i
$685$	8.58873	+	3.55757i	0.328159	+	0.135928i
$686$	17.2065	−	19.7468i	0.656946	−	0.753938i
$687$		−	3.87930i		−	0.148004i
$688$	21.8057	+	34.0641i	0.831333	+	1.29868i
$689$	−28.8317	−	16.6460i	−1.09840	−	0.634163i
$690$	7.03479	−	4.48704i	0.267810	−	0.170819i
$691$	3.55207	+	26.9807i	0.135127	+	1.02639i	0.915851	+	0.401517i	$0.131517\pi$
$691$	3.55207	+	26.9807i	0.135127	+	1.02639i	−0.780724	+	0.624876i	$0.785150\pi$
$692$	44.0083	−	9.80669i	1.67294	−	0.372795i
$693$	−29.3376	+	72.4935i	−1.11444	+	2.75380i
$694$	−16.0471	−	19.1030i	−0.609138	−	0.725141i
$695$	−3.11256	+	11.6162i	−0.118066	+	0.440629i
$696$	−35.7384	−	14.7350i	−1.35466	−	0.558529i
$697$	1.27097	+	4.74332i	0.0481414	+	0.179666i
$698$	−13.4022	−	28.7003i	−0.507281	−	1.08632i
$699$	24.2830	−	10.0584i	0.918468	−	0.380442i
$700$	−21.2592	+	7.96099i	−0.803523	+	0.300897i
$701$	−5.16771	+	12.4760i	−0.195182	+	0.471211i	−0.990924	−	0.134425i	$-0.957081\pi$
$701$	−5.16771	+	12.4760i	−0.195182	+	0.471211i	0.795742	+	0.605636i	$0.207081\pi$
$702$	−45.3235	+	49.5161i	−1.71063	+	1.86886i
$703$	9.23489	−	15.9953i	0.348300	−	0.603274i
$704$	3.73303	+	27.6567i	0.140694	+	1.04235i
$705$	1.01889	+	1.76476i	0.0383735	+	0.0664649i
$706$	−1.48784	−	4.70989i	−0.0559957	−	0.177259i
$707$	−4.50471	+	36.5148i	−0.169417	+	1.37328i
$708$	−14.5342	−	20.7089i	−0.546227	−	0.778288i
$709$	11.4945	+	8.82005i	0.431685	+	0.331244i	0.801641	−	0.597806i	$-0.203961\pi$
$709$	11.4945	+	8.82005i	0.431685	+	0.331244i	−0.369956	+	0.929049i	$0.620627\pi$
$710$	−4.15219	+	5.93681i	−0.155829	+	0.222805i
$711$	−16.7184	−	62.3940i	−0.626990	−	2.33996i
$712$	−17.1159	−	22.2305i	−0.641444	−	0.833125i
$713$	1.47374	+	1.47374i	0.0551919	+	0.0551919i
$714$	−13.2547	−	9.11030i	−0.496046	−	0.340944i
$715$	2.87982	+	6.95250i	0.107699	+	0.260009i
$716$	−6.11847	−	6.66256i	−0.228658	−	0.248992i
$717$	−19.0134	+	14.5895i	−0.710070	+	0.544856i
$718$	−6.75452	+	4.30828i	−0.252077	+	0.160783i
$719$	−23.3870	+	13.5025i	−0.872187	+	0.503558i	−0.868075	−	0.496434i	$-0.834642\pi$
$719$	−23.3870	+	13.5025i	−0.872187	+	0.503558i	−0.00411285	+	0.999992i	$0.501309\pi$
$720$	−19.2473	+	21.0968i	−0.717306	+	0.786233i
$721$	27.8720	+	7.22523i	1.03801	+	0.269082i
$722$	2.25583	−	4.33917i	0.0839532	−	0.161487i
$723$	−1.65487	−	12.5700i	−0.0615453	−	0.467483i
$724$	32.0210	−	16.7134i	1.19005	−	0.621150i
$725$	17.1621	+	2.25943i	0.637384	+	0.0839132i
$726$	−5.26396	−	1.91268i	−0.195364	−	0.0709862i
$727$	−21.2433	−	21.2433i	−0.787871	−	0.787871i	0.193274	−	0.981145i	$-0.438089\pi$
$727$	−21.2433	−	21.2433i	−0.787871	−	0.787871i	−0.981145	+	0.193274i	$0.938089\pi$
$728$	9.74161	+	16.4980i	0.361048	+	0.611455i
$729$	90.7348	−	90.7348i	3.36055	−	3.36055i
$730$	−7.14440	+	3.33622i	−0.264426	+	0.123479i
$731$	1.67489	−	12.7221i	0.0619481	−	0.470542i
$732$	45.7066	−	54.5916i	1.68936	−	2.01776i
$733$	−1.58425	+	0.208570i	−0.0585155	+	0.00770371i	−0.159727	−	0.987161i	$-0.551061\pi$
$733$	−1.58425	+	0.208570i	−0.0585155	+	0.00770371i	0.101212	+	0.994865i	$0.467728\pi$
$734$	−18.0313	+	5.69604i	−0.665547	+	0.210245i
$735$	0.325752	+	19.9753i	0.0120156	+	0.736799i
$736$	7.92411	+	8.60052i	0.292086	+	0.317019i
$737$	8.09788	+	14.0259i	0.298289	+	0.516652i
$738$	−10.0115	+	45.2756i	−0.368528	+	1.66662i
$739$	16.1292	+	21.0200i	0.593324	+	0.773235i	0.989436	−	0.144967i	$-0.0463076\pi$
$739$	16.1292	+	21.0200i	0.593324	+	0.773235i	−0.396112	+	0.918202i	$0.629641\pi$
$740$	−7.41585	+	2.70830i	−0.272612	+	0.0995590i
$741$	31.5863	−	13.0835i	1.16035	−	0.480634i
$742$	36.9976	−	31.5971i	1.35822	−	1.15996i
$743$	−21.3093	+	21.3093i	−0.781762	+	0.781762i	−0.980128	−	0.198366i	$-0.936437\pi$
$743$	−21.3093	+	21.3093i	−0.781762	+	0.781762i	0.198366	+	0.980128i	$0.436437\pi$
$744$	−8.37258	−	4.81569i	−0.306954	−	0.176552i
$745$	13.2205	−	3.54242i	0.484361	−	0.129784i
$746$	7.08215	+	40.0374i	0.259296	+	1.46587i
$747$	5.84129	−	7.61251i	0.213722	−	0.278527i
$748$	4.74910	−	7.47254i	0.173644	−	0.273223i
$749$	−5.39943	+	7.15675i	−0.197291	+	0.261502i
$750$	17.2957	−	33.2689i	0.631549	−	1.21481i
$751$	−31.8497	+	18.3884i	−1.16221	+	0.671003i	−0.951833	−	0.306617i	$-0.900803\pi$
$751$	−31.8497	+	18.3884i	−1.16221	+	0.671003i	−0.210379	+	0.977620i	$0.567470\pi$
$752$	−2.18385	+	1.84059i	−0.0796367	+	0.0671192i
$753$	16.0885	+	9.28871i	0.586298	+	0.338499i
$754$	−0.645210	−	14.5954i	−0.0234972	−	0.531533i
$755$	10.2098	+	4.22904i	0.371573	+	0.153910i
$756$	−46.1005	−	86.5947i	−1.67666	−	3.14942i
$757$	−6.87840	−	16.6059i	−0.250000	−	0.603553i	0.748204	−	0.663469i	$-0.230917\pi$
$757$	−6.87840	−	16.6059i	−0.250000	−	0.603553i	−0.998203	+	0.0599165i	$0.980917\pi$
$758$	−11.7817	+	32.4250i	−0.427932	+	1.17773i
$759$	−23.5952	+	6.32233i	−0.856453	+	0.229486i
$760$	8.67412	−	3.60955i	0.314643	−	0.130932i
$761$	−48.7791	−	13.0703i	−1.76824	−	0.473799i	−0.779880	−	0.625929i	$-0.784720\pi$
$761$	−48.7791	−	13.0703i	−1.76824	−	0.473799i	−0.988360	+	0.152131i	$0.951387\pi$
$762$	−59.8695	−	5.20506i	−2.16884	−	0.188559i
$763$	27.5130	−	21.4701i	0.996038	−	0.777271i
$764$	6.04413	−	4.24196i	0.218669	−	0.153469i
$765$	8.98272	−	1.18260i	0.324771	−	0.0427569i
$766$	−6.24739	−	1.38144i	−0.225727	−	0.0499136i
$767$	4.78087	−	8.28071i	0.172627	−	0.298999i
$768$	−45.8346	−	28.9199i	−1.65391	−	1.04356i
$769$	5.47842			0.197557			0.0987784	−	0.995109i	$-0.468507\pi$
$769$	5.47842			0.197557			0.0987784	+	0.995109i	$0.468507\pi$
$770$	−10.9827	+	0.575257i	−0.395787	+	0.0207308i
$771$	31.5864	−	76.2562i	1.13755	−	2.74630i
$772$	−40.1898	−	18.6875i	−1.44646	−	0.672579i
$773$	−5.25490	+	39.9149i	−0.189006	+	1.43564i	0.589381	+	0.807855i	$0.299372\pi$
$773$	−5.25490	+	39.9149i	−0.189006	+	1.43564i	−0.778387	+	0.627785i	$0.783962\pi$
$774$	69.4439	−	99.2911i	2.49611	−	3.56895i
$775$	4.17771	+	1.11941i	0.150068	+	0.0402105i
$776$	1.72708	+	1.32076i	0.0619984	+	0.0474124i
$777$	−0.342314	−	41.9845i	−0.0122805	−	1.50619i
$778$	17.7226	+	21.0976i	0.635385	+	0.756386i
$779$	9.28667	−	12.1026i	0.332730	−	0.433622i
$780$	−13.9424	−	4.37934i	−0.499219	−	0.156806i
$781$	16.8267	−	12.9116i	0.602106	−	0.462012i
$782$	−0.163855	−	3.70658i	−0.00585944	−	0.132547i
$783$			74.8055i			2.67333i
$784$	−27.4800	+	5.37098i	−0.981430	+	0.191821i
$785$			1.84295i			0.0657777i
$786$	−30.8077	+	1.36190i	−1.09888	+	0.0485774i
$787$	11.9620	−	9.17875i	0.426399	−	0.327187i	−0.373169	−	0.927763i	$-0.621729\pi$
$787$	11.9620	−	9.17875i	0.426399	−	0.327187i	0.799567	+	0.600576i	$0.205062\pi$
$788$	−10.1752	−	19.4945i	−0.362476	−	0.694462i
$789$	21.8376	−	28.4594i	0.777441	−	1.01318i
$790$	6.95542	−	5.84274i	0.247463	−	0.207875i
$791$	−0.103339	−	12.6744i	−0.00367430	−	0.450650i
$792$	72.3352	−	41.9205i	2.57032	−	1.48958i
$793$	25.9915	+	6.96441i	0.922987	+	0.247313i
$794$	−25.0333	−	17.5082i	−0.888400	−	0.621344i
$795$	−4.84399	+	36.7937i	−0.171799	+	1.30494i
$796$	41.5368	−	15.1694i	1.47223	−	0.537666i
$797$	−6.23077	+	15.0424i	−0.220705	+	0.532830i	−0.994986	−	0.100012i	$-0.968112\pi$
$797$	−6.23077	+	15.0424i	−0.220705	+	0.532830i	0.774281	+	0.632842i	$0.218112\pi$
$798$	2.61349	+	49.8960i	0.0925164	+	1.76630i
$799$	0.906110			0.0320559
$800$	23.1649	+	7.23458i	0.819002	+	0.255781i
$801$	−42.0250	+	72.7894i	−1.48488	+	2.57189i
$802$	4.05873	−	18.3550i	0.143319	−	0.648139i
$803$	22.8864	−	3.01305i	0.807642	−	0.106328i
$804$	−30.9799	−	5.42782i	−1.09258	−	0.191424i
$805$	−3.63319	+	2.83521i	−0.128053	+	0.0999280i
$806$	0.316167	−	3.63661i	0.0111365	−	0.128094i
$807$	−32.6069	−	8.73700i	−1.14782	−	0.307557i
$808$	27.7664	−	27.8573i	0.976819	−	0.980015i
$809$	−1.15967	+	0.310733i	−0.0407719	+	0.0109248i	−0.279147	−	0.960248i	$-0.590052\pi$
$809$	−1.15967	+	0.310733i	−0.0407719	+	0.0109248i	0.238375	+	0.971173i	$0.423385\pi$
$810$	41.8603	+	15.2101i	1.47082	+	0.534429i
$811$	−3.21746	−	7.76763i	−0.112980	−	0.272758i	0.857268	−	0.514870i	$-0.172160\pi$
$811$	−3.21746	−	7.76763i	−0.112980	−	0.272758i	−0.970248	+	0.242112i	$0.922160\pi$
$812$	20.4212	+	6.23187i	0.716643	+	0.218696i
$813$	26.9605	+	11.1674i	0.945545	+	0.391658i
$814$	23.0904	−	1.02075i	0.809318	−	0.0357771i
$815$	5.92545	+	3.42106i	0.207560	+	0.119835i
$816$	5.20610	+	16.3871i	0.182250	+	0.573663i
$817$	−34.5218	+	19.9312i	−1.20777	+	0.697304i
$818$	13.9760	+	7.26579i	0.488660	+	0.254042i
$819$	34.5688	−	45.8196i	1.20793	−	1.60107i
$820$	−6.36466	+	1.41828i	−0.222264	+	0.0495286i
$821$	13.2808	−	17.3079i	0.463504	−	0.604050i	−0.501863	−	0.864947i	$-0.667352\pi$
$821$	13.2808	−	17.3079i	0.463504	−	0.604050i	0.965367	+	0.260897i	$0.0840183\pi$
$822$	52.0446	−	9.20609i	1.81526	−	0.321099i
$823$	19.7357	−	5.28816i	0.687943	−	0.184334i	0.102119	−	0.994772i	$-0.467438\pi$
$823$	19.7357	−	5.28816i	0.687943	−	0.184334i	0.585824	+	0.810439i	$0.300771\pi$
$824$	−18.7783	−	24.3898i	−0.654173	−	0.849658i
$825$	−35.8447	+	35.8447i	−1.24795	+	1.24795i
$826$	9.07492	+	10.6260i	0.315757	+	0.369726i
$827$	32.7442	−	13.5631i	1.13863	−	0.471635i	0.267923	−	0.963440i	$-0.413663\pi$
$827$	32.7442	−	13.5631i	1.13863	−	0.471635i	0.870705	+	0.491805i	$0.163663\pi$
$828$	14.7714	−	31.7677i	0.513342	−	1.10400i
$829$	4.54041	+	5.91718i	0.157695	+	0.205512i	0.865518	−	0.500878i	$-0.166989\pi$
$829$	4.54041	+	5.91718i	0.157695	+	0.205512i	−0.707823	+	0.706390i	$0.750323\pi$
$830$	1.31754	+	0.291339i	0.0457325	+	0.0101125i
$831$	14.6819	+	25.4299i	0.509311	+	0.882152i
$832$	2.60711	−	20.3156i	0.0903854	−	0.704318i
$833$	7.76458	+	4.31563i	0.269027	+	0.149528i
$834$	20.5952	+	65.1957i	0.713152	+	2.25754i
$835$	2.02456	−	0.266538i	0.0700627	−	0.00922394i
$836$	−27.3978	+	2.42706i	−0.947571	+	0.0839416i
$837$	−2.43963	+	18.5308i	−0.0843259	+	0.640519i
$838$	9.96928	+	21.3488i	0.344383	+	0.737483i
$839$	−20.5269	+	20.5269i	−0.708666	+	0.708666i	−0.966255	−	0.257589i	$-0.917072\pi$
$839$	−20.5269	+	20.5269i	−0.708666	+	0.708666i	0.257589	+	0.966255i	$0.417072\pi$
$840$	12.8351	−	17.0703i	0.442852	−	0.588982i
$841$	8.99387	+	8.99387i	0.310133	+	0.310133i
$842$	2.95492	−	8.13236i	0.101833	−	0.280260i
$843$	−11.3145	−	1.48958i	−0.389691	−	0.0513038i
$844$	2.91255	−	9.27262i	0.100254	−	0.319177i
$845$	0.708804	+	5.38390i	0.0243836	+	0.185212i
$846$	7.59145	+	3.94661i	0.260999	+	0.135687i
$847$	2.99438	+	0.776233i	0.102888	+	0.0266717i
$848$	−51.9586	+	2.38195i	−1.78426	+	0.0817964i
$849$	19.7630	−	11.4102i	0.678265	−	0.391597i
$850$	−4.14042	−	6.49135i	−0.142015	−	0.222652i
$851$	7.68390	−	5.89606i	0.263401	−	0.202114i
$852$	−1.75181	+	41.1512i	−0.0600159	+	1.40982i
$853$	−17.9394	−	43.3095i	−0.614232	−	1.48289i	−0.858310	−	0.513132i	$-0.828485\pi$
$853$	−17.9394	−	43.3095i	−0.614232	−	1.48289i	0.244077	−	0.969756i	$-0.421515\pi$
$854$	−22.2747	+	32.4078i	−0.762223	+	1.10897i
$855$	−19.9021	−	19.9021i	−0.680637	−	0.680637i
$856$	9.25345	−	2.49566i	0.316276	−	0.0853000i
$857$	−11.5700	−	43.1800i	−0.395225	−	1.47500i	−0.821397	−	0.570357i	$-0.806805\pi$
$857$	−11.5700	−	43.1800i	−0.395225	−	1.47500i	0.426172	−	0.904642i	$-0.359862\pi$
$858$	35.0597	+	24.5206i	1.19692	+	0.837120i
$859$	−36.2510	−	27.8164i	−1.23687	−	0.949083i	−0.237120	−	0.971480i	$-0.576203\pi$
$859$	−36.2510	−	27.8164i	−1.23687	−	0.949083i	−0.999749	+	0.0223972i	$0.992870\pi$
$860$	16.7835	+	2.94055i	0.572314	+	0.100272i
$861$	4.24593	−	34.4172i	0.144701	−	1.17293i
$862$	−24.8144	+	7.83881i	−0.845182	+	0.266991i
$863$	−21.4162	−	37.0939i	−0.729014	−	1.26269i	−0.957300	−	0.289096i	$-0.906645\pi$
$863$	−21.4162	−	37.0939i	−0.729014	−	1.26269i	0.228286	−	0.973594i	$-0.426688\pi$
$864$	−17.9301	+	103.331i	−0.609994	+	3.51538i
$865$	9.49742	−	16.4500i	0.322922	−	0.559317i
$866$	−4.74525	−	4.34347i	−0.161250	−	0.147597i
$867$	−19.9485	+	48.1599i	−0.677485	+	1.63559i
$868$	4.85550	+	2.20976i	0.164806	+	0.0750040i
$869$	−24.5692	+	10.1769i	−0.833453	+	0.345228i
$870$	−14.7560	+	6.89064i	−0.500277	+	0.233615i
$871$	−3.07648	−	11.4816i	−0.104243	−	0.389039i
$872$	−37.3084	+	0.0609401i	−1.26342	+	0.00206369i
$873$	1.68580	−	6.29150i	0.0570558	−	0.212935i
$874$	−8.82526	+	7.41346i	−0.298519	+	0.250764i
$875$	−7.76903	+	19.1973i	−0.262641	+	0.648988i
$876$	−24.0450	+	37.8340i	−0.812407	+	1.27829i
$877$	0.758790	+	5.76358i	0.0256225	+	0.194622i	0.999469	−	0.0325848i	$-0.0103739\pi$
$877$	0.758790	+	5.76358i	0.0256225	+	0.194622i	−0.973846	+	0.227207i	$0.927041\pi$
$878$	−23.0434	−	36.1275i	−0.777678	−	1.21924i
$879$	92.0011	+	53.1169i	3.10312	+	1.79159i
$880$	9.64547	+	6.72258i	0.325149	+	0.226618i
$881$			2.16222i			0.0728469i	0.999336	+	0.0364235i	$0.0115965\pi$
$881$			2.16222i			0.0728469i	−0.999336	+	0.0364235i	$0.988403\pi$
$882$	46.2552	+	69.9756i	1.55750	+	2.35620i
$883$	2.05737	+	0.852192i	0.0692362	+	0.0286786i	0.417033	−	0.908891i	$-0.363070\pi$
$883$	2.05737	+	0.852192i	0.0692362	+	0.0286786i	−0.347797	+	0.937570i	$0.613070\pi$
$884$	−4.78621	+	4.39535i	−0.160978	+	0.147832i
$885$	−10.5675	−	1.39123i	−0.355221	−	0.0467657i
$886$	29.7974	−	5.27082i	1.00106	−	0.177077i
$887$	12.1785	−	45.4508i	0.408914	−	1.52609i	−0.387806	−	0.921741i	$-0.626767\pi$
$887$	12.1785	−	45.4508i	0.408914	−	1.52609i	0.796721	−	0.604348i	$-0.206566\pi$
$888$	−27.2659	+	35.6541i	−0.914985	+	1.19647i
$889$	33.1906	−	0.270615i	1.11318	−	0.00907613i
$890$	−11.7753	−	1.02374i	−0.394708	−	0.0343160i
$891$	−103.444	−	79.3754i	−3.46550	−	2.65918i
$892$	0.207944	+	2.34737i	0.00696248	+	0.0785957i
$893$	−1.71357	−	2.23317i	−0.0573425	−	0.0747303i
$894$	52.5389	−	57.3988i	1.75716	−	1.91970i
$895$	−3.81085			−0.127383
$896$	26.7146	+	13.5030i	0.892472	+	0.451103i
$897$	17.9282			0.598606
$898$	−6.05519	+	6.61531i	−0.202064	+	0.220756i
$899$	−2.47636	−	3.22726i	−0.0825913	−	0.107635i
$900$	−6.41529	−	72.4188i	−0.213843	−	2.41396i
$901$	13.0917	+	10.0456i	0.436149	+	0.334669i
$902$	19.0183	+	1.65345i	0.633240	+	0.0550539i
$903$	−44.6667	+	78.8426i	−1.48642	+	2.62372i
$904$	−8.23112	+	10.7634i	−0.273763	+	0.357984i
$905$	3.93846	−	14.6986i	0.130919	−	0.488596i
$906$	61.8677	−	10.9437i	2.05542	−	0.363579i
$907$	−18.7071	−	2.46284i	−0.621160	−	0.0817773i	−0.186624	−	0.982431i	$-0.559755\pi$
$907$	−18.7071	−	2.46284i	−0.621160	−	0.0817773i	−0.434537	+	0.900654i	$0.643088\pi$
$908$	−23.0631	+	21.1797i	−0.765377	+	0.702874i
$909$	−108.860	−	45.0914i	−3.61067	−	1.49559i
$910$	7.89516	+	1.67841i	0.261722	+	0.0556386i
$911$		−	17.1697i		−	0.568858i	−0.958697	−	0.284429i	$-0.908196\pi$
$911$		−	17.1697i		−	0.568858i	0.958697	−	0.284429i	$-0.0918040\pi$
$912$	30.5417	−	43.8209i	1.01134	−	1.45106i
$913$	−3.42112	−	1.97519i	−0.113223	−	0.0653691i
$914$	9.03046	+	14.1580i	0.298701	+	0.468304i
$915$	−3.91517	−	29.7387i	−0.129432	−	0.983131i
$916$	1.22860	−	1.93316i	0.0405942	−	0.0638735i
$917$	16.8679	−	2.36076i	0.557027	−	0.0779593i
$918$	25.4768	−	21.4012i	0.840858	−	0.706344i
$919$	5.77324	−	21.5460i	0.190442	−	0.710738i	−0.802958	−	0.596035i	$-0.796742\pi$
$919$	5.77324	−	21.5460i	0.190442	−	0.710738i	0.993400	−	0.114703i	$-0.0365916\pi$
$920$	4.92671	−	0.00804737i	0.162429	−	0.000265314i
$921$	12.5406	+	46.8021i	0.413226	+	1.54218i
$922$	−7.07612	+	3.30434i	−0.233040	+	0.108823i
$923$	−14.3815	+	5.95700i	−0.473372	+	0.196077i
$924$	−50.8839	+	36.3347i	−1.67396	+	1.19533i
$925$	7.69155	−	18.5690i	0.252897	−	0.610546i
$926$	33.2010	+	30.3899i	1.09105	+	0.998674i
$927$	−46.1068	+	79.8594i	−1.51435	+	2.62293i
$928$	−13.1428	−	18.6615i	−0.431433	−	0.612594i
$929$	13.5571	+	23.4815i	0.444793	+	0.770404i	0.998038	−	0.0626144i	$-0.0199438\pi$
$929$	13.5571	+	23.4815i	0.444793	+	0.770404i	−0.553245	+	0.833019i	$0.686611\pi$
$930$	−3.88009	+	1.22571i	−0.127233	+	0.0401927i
$931$	−4.04768	−	27.2978i	−0.132657	−	0.894648i
$932$	15.2865	+	2.67826i	0.500725	+	0.0877292i
$933$	34.1881	+	26.2334i	1.11927	+	0.858844i
$934$	−42.7624	−	29.9078i	−1.39923	−	0.978615i
$935$	−0.965410	−	3.60296i	−0.0315723	−	0.117829i
$936$	−59.2433	+	15.9780i	−1.93643	+	0.522256i
$937$	13.3258	+	13.3258i	0.435334	+	0.435334i	0.890438	−	0.455104i	$-0.150398\pi$
$937$	13.3258	+	13.3258i	0.435334	+	0.435334i	−0.455104	+	0.890438i	$0.650398\pi$
$938$	17.3178	+	1.36345i	0.565447	+	0.0445181i
$939$	14.4606	+	34.9109i	0.471903	+	1.13928i
$940$	−0.0511743	+	1.20212i	−0.00166912	+	0.0392089i
$941$	−8.79465	+	6.74837i	−0.286697	+	0.219991i	−0.742090	−	0.670300i	$-0.766165\pi$
$941$	−8.79465	+	6.74837i	−0.286697	+	0.219991i	0.455393	+	0.890291i	$0.349499\pi$
$942$	5.63447	+	8.83373i	0.183581	+	0.287818i
$943$	6.92783	−	3.99978i	0.225601	−	0.130251i
$944$	−0.684114	−	14.9229i	−0.0222660	−	0.485699i
$945$	−40.0065	−	10.3709i	−1.30141	−	0.337364i
$946$	−44.2598	−	23.0096i	−1.43901	−	0.748105i
$947$	−0.993779	−	7.54850i	−0.0322935	−	0.245293i	0.967683	−	0.252170i	$-0.0811443\pi$
$947$	−0.993779	−	7.54850i	−0.0322935	−	0.245293i	−0.999976	+	0.00687699i	$0.997811\pi$
$948$	15.4760	−	49.2706i	0.502637	−	1.60024i
$949$	−16.7971	−	2.21138i	−0.545256	−	0.0717843i
$950$	−8.16832	+	22.4803i	−0.265015	+	0.729359i
$951$	55.1720	+	55.1720i	1.78907	+	1.78907i
$952$	−3.71991	−	8.73779i	−0.120563	−	0.283194i
$953$	−16.2057	+	16.2057i	−0.524953	+	0.524953i	−0.919063	−	0.394111i	$-0.871053\pi$
$953$	−16.2057	+	16.2057i	−0.524953	+	0.524953i	0.394111	+	0.919063i	$0.371053\pi$
$954$	65.9291	+	141.185i	2.13453	+	4.57102i
$955$	0.406047	−	3.08423i	0.0131394	−	0.0998034i
$956$	−14.0956	+	1.24867i	−0.455883	+	0.0403848i
$957$	47.2695	−	6.22315i	1.52801	−	0.201166i
$958$	−9.09475	−	28.7902i	−0.293838	−	0.930169i
$959$	−28.1342	+	7.78493i	−0.908501	+	0.251389i
$960$	−22.0345	+	5.98135i	−0.711161	+	0.193047i
$961$	14.9918	+	25.9666i	0.483607	+	0.837631i
$962$	−16.5633	−	3.66253i	−0.534021	−	0.118085i
$963$	−17.4786	−	22.7786i	−0.563240	−	0.734029i
$964$	3.15634	−	6.78809i	0.101659	−	0.218630i
$965$	−17.2509	+	7.14557i	−0.555327	+	0.230024i
$966$	−8.74671	+	24.6977i	−0.281421	+	0.794635i
$967$	−2.31392	+	2.31392i	−0.0744106	+	0.0744106i	−0.743333	−	0.668922i	$-0.766756\pi$
$967$	−2.31392	+	2.31392i	−0.0744106	+	0.0744106i	0.668922	+	0.743333i	$0.266756\pi$
$968$	−2.01742	−	2.62028i	−0.0648423	−	0.0842190i
$969$	−16.3688	+	4.38602i	−0.525843	+	0.140899i
$970$	0.901963	−	0.159547i	0.0289603	−	0.00512274i
$971$	−1.30632	+	1.70242i	−0.0419217	+	0.0546334i	−0.813844	−	0.581084i	$-0.802629\pi$
$971$	−1.30632	+	1.70242i	−0.0419217	+	0.0546334i	0.771922	+	0.635717i	$0.219296\pi$
$972$	138.576	−	30.8798i	4.44482	−	0.990471i
$973$	−14.7351	−	34.7692i	−0.472387	−	1.11465i
$974$	4.29149	+	2.23104i	0.137508	+	0.0714871i
$975$	32.2201	−	18.6023i	1.03187	−	0.595750i
$976$	40.0665	−	12.7289i	1.28250	−	0.407442i
$977$	10.2482	+	5.91679i	0.327869	+	0.189295i	0.654894	−	0.755720i	$-0.272713\pi$
$977$	10.2482	+	5.91679i	0.327869	+	0.189295i	−0.327026	+	0.945015i	$0.606046\pi$
$978$	38.8614	−	1.71793i	1.24265	−	0.0549333i
$979$	31.9690	+	13.2420i	1.02174	+	0.423217i
$980$	−6.16399	+	10.0574i	−0.196901	+	0.321272i
$981$	42.7717	+	103.260i	1.36559	+	3.29684i
$982$	−10.4284	−	3.78920i	−0.332784	−	0.120918i
$983$	−32.0590	+	8.59018i	−1.02252	+	0.273984i	−0.730853	−	0.682535i	$-0.760878\pi$
$983$	−32.0590	+	8.59018i	−1.02252	+	0.273984i	−0.291670	+	0.956519i	$0.594211\pi$
$984$	−26.1713	+	26.2569i	−0.834311	+	0.837041i
$985$	−8.94851	−	2.39775i	−0.285123	−	0.0763985i
$986$	−0.627212	+	7.21430i	−0.0199745	+	0.229750i
$987$	−5.93147	−	2.40043i	−0.188801	−	0.0764065i
$988$	19.8840	+	3.48376i	0.632594	+	0.110833i
$989$	−20.7246	+	2.72844i	−0.659003	+	0.0867594i
$990$	7.60460	−	34.3907i	0.241690	−	1.09301i
$991$	−3.65274	+	6.32673i	−0.116033	+	0.200975i	−0.918192	−	0.396135i	$-0.870351\pi$
$991$	−3.65274	+	6.32673i	−0.116033	+	0.200975i	0.802159	+	0.597110i	$0.203685\pi$
$992$	−2.64712	−	5.05145i	−0.0840463	−	0.160384i
$993$	65.3431			2.07360
$994$	−1.18994	−	22.7180i	−0.0377426	−	0.720571i
$995$	7.12915	−	17.2113i	0.226009	−	0.545634i
$996$	7.20602	−	2.63167i	0.228332	−	0.0833876i
$997$	−0.817569	+	6.21005i	−0.0258927	+	0.196674i	−0.999502	−	0.0315454i	$-0.989957\pi$
$997$	−0.817569	+	6.21005i	−0.0258927	+	0.196674i	0.973610	+	0.228220i	$0.0732905\pi$
$998$	19.1857	+	13.4184i	0.607312	+	0.424752i
$999$	83.8977	+	22.4803i	2.65440	+	0.711246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.22	yes	240
4.3	odd	2		896.2.bh.a.529.30		240
7.2	even	3	inner	224.2.bd.a.205.2	yes	240
28.23	odd	6		896.2.bh.a.401.1		240
32.5	even	8	inner	224.2.bd.a.165.2	yes	240
32.27	odd	8		896.2.bh.a.753.1		240
224.37	even	24	inner	224.2.bd.a.37.22	✓	240
224.219	odd	24		896.2.bh.a.625.30		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.22	✓	240	224.37	even	24	inner
224.2.bd.a.109.22	yes	240	1.1	even	1	trivial
224.2.bd.a.165.2	yes	240	32.5	even	8	inner
224.2.bd.a.205.2	yes	240	7.2	even	3	inner
896.2.bh.a.401.1		240	28.23	odd	6
896.2.bh.a.529.30		240	4.3	odd	2
896.2.bh.a.625.30		240	224.219	odd	24
896.2.bh.a.753.1		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.954861 - 1.04319i) q^{2} +(-2.06202 - 2.68727i) q^{3} +(-0.176481 - 1.99220i) q^{4} +(-0.668458 - 0.512926i) q^{5} +(-4.77227 - 0.414901i) q^{6} +(2.64566 - 0.0215710i) q^{7} +(-2.24675 - 1.71817i) q^{8} +(-2.19306 + 8.18461i) q^{9} +O(q^{10})\)	\(q+(0.954861 - 1.04319i) q^{2} +(-2.06202 - 2.68727i) q^{3} +(-0.176481 - 1.99220i) q^{4} +(-0.668458 - 0.512926i) q^{5} +(-4.77227 - 0.414901i) q^{6} +(2.64566 - 0.0215710i) q^{7} +(-2.24675 - 1.71817i) q^{8} +(-2.19306 + 8.18461i) q^{9} +(-1.17336 + 0.207554i) q^{10} +(3.45859 + 0.455332i) q^{11} +(-4.98967 + 4.58220i) q^{12} +(-2.36539 - 0.979776i) q^{13} +(2.50374 - 2.78052i) q^{14} +2.85399i q^{15} +(-3.93771 + 0.703170i) q^{16} +(1.09903 + 0.634523i) q^{17} +(6.44401 + 10.1029i) q^{18} +(-0.514576 - 3.90859i) q^{19} +(-0.903880 + 1.42222i) q^{20} +(-5.51336 - 7.06513i) q^{21} +(3.77747 - 3.17318i) q^{22} +(0.535059 - 1.99687i) q^{23} +(0.0156490 + 9.58052i) q^{24} +(-1.11035 - 4.14389i) q^{25} +(-3.28071 + 1.53199i) q^{26} +(17.1282 - 7.09473i) q^{27} +(-0.509883 - 5.26688i) q^{28} +(-1.54411 + 3.72780i) q^{29} +(2.97725 + 2.72516i) q^{30} +(-0.504081 + 0.873093i) q^{31} +(-3.02643 + 4.77920i) q^{32} +(-5.90807 - 10.2331i) q^{33} +(1.71134 - 0.540609i) q^{34} +(-1.77958 - 1.34261i) q^{35} +(16.6924 + 2.92458i) q^{36} +(3.71686 + 2.85205i) q^{37} +(-4.56874 - 3.19536i) q^{38} +(2.24454 + 8.37676i) q^{39} +(0.620566 + 2.30094i) q^{40} +(2.73619 + 2.73619i) q^{41} +(-12.6348 - 0.994746i) q^{42} +(-3.86947 - 9.34172i) q^{43} +(0.296736 - 6.97056i) q^{44} +(5.66407 - 4.34619i) q^{45} +(-1.57220 - 2.46490i) q^{46} +(0.618350 - 0.357005i) q^{47} +(10.0092 + 9.13174i) q^{48} +(6.99907 - 0.114139i) q^{49} +(-5.38309 - 2.79853i) q^{50} +(-0.561074 - 4.26178i) q^{51} +(-1.53446 + 4.88524i) q^{52} +(12.8920 + 1.69727i) q^{53} +(8.95391 - 24.6424i) q^{54} +(-2.07837 - 2.07837i) q^{55} +(-5.98121 - 4.49723i) q^{56} +(-9.44238 + 9.44238i) q^{57} +(2.41439 + 5.17032i) q^{58} +(-0.487469 + 3.70269i) q^{59} +(5.68571 - 0.503675i) q^{60} +(-10.4200 + 1.37182i) q^{61} +(0.429473 + 1.35953i) q^{62} +(-5.62554 + 21.7010i) q^{63} +(2.09579 + 7.72060i) q^{64} +(1.07861 + 1.86821i) q^{65} +(-16.3164 - 3.60794i) q^{66} +(2.82630 + 3.68330i) q^{67} +(1.07014 - 2.30146i) q^{68} +(-6.46942 + 2.67972i) q^{69} +(-3.09985 + 0.574430i) q^{70} +(4.29918 - 4.29918i) q^{71} +(18.9898 - 14.6207i) q^{72} +(6.39177 - 1.71267i) q^{73} +(6.52431 - 1.15407i) q^{74} +(-8.84619 + 11.5286i) q^{75} +(-7.69588 + 1.71493i) q^{76} +(9.16009 + 1.13005i) q^{77} +(10.8818 + 5.65716i) q^{78} +(-6.60200 + 3.81167i) q^{79} +(2.99287 + 1.54971i) q^{80} +(-32.3697 - 18.6887i) q^{81} +(5.46704 - 0.241679i) q^{82} +(-1.04622 - 0.433358i) q^{83} +(-13.1021 + 12.2306i) q^{84} +(-0.409190 - 0.987871i) q^{85} +(-13.4400 - 4.88346i) q^{86} +(13.2016 - 3.53735i) q^{87} +(-6.98826 - 6.96546i) q^{88} +(9.58137 + 2.56732i) q^{89} +(0.874503 - 10.0587i) q^{90} +(-6.27916 - 2.54113i) q^{91} +(-4.07258 - 0.713534i) q^{92} +(3.38566 - 0.445731i) q^{93} +(0.218016 - 0.985945i) q^{94} +(-1.66085 + 2.87667i) q^{95} +(19.0835 - 1.72196i) q^{96} -0.768699 q^{97} +(6.56407 - 7.41033i) q^{98} +(-11.3116 + 27.3086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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