LMFDB - Embedded newform 224.2.bd.a.109.23

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			109.23
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.956234 - 1.04193i) q^{2} +(1.46089 + 1.90386i) q^{3} +(-0.171232 - 1.99266i) q^{4} +(2.38518 + 1.83021i) q^{5} +(3.38064 + 0.298400i) q^{6} +(-2.64555 - 0.0324859i) q^{7} +(-2.23994 - 1.72703i) q^{8} +(-0.714054 + 2.66488i) q^{9} +O(q^{10})$	\(q+(0.956234 - 1.04193i) q^{2} +(1.46089 + 1.90386i) q^{3} +(-0.171232 - 1.99266i) q^{4} +(2.38518 + 1.83021i) q^{5} +(3.38064 + 0.298400i) q^{6} +(-2.64555 - 0.0324859i) q^{7} +(-2.23994 - 1.72703i) q^{8} +(-0.714054 + 2.66488i) q^{9} +(4.18774 - 0.735076i) q^{10} +(-1.92231 - 0.253077i) q^{11} +(3.54360 - 3.23705i) q^{12} +(-3.09779 - 1.28315i) q^{13} +(-2.56362 + 2.72541i) q^{14} +7.21480i q^{15} +(-3.94136 + 0.682414i) q^{16} +(5.06039 + 2.92162i) q^{17} +(2.09382 + 3.29225i) q^{18} +(-0.998902 - 7.58742i) q^{19} +(3.23857 - 5.06624i) q^{20} +(-3.80300 - 5.08423i) q^{21} +(-2.10187 + 1.76091i) q^{22} +(1.60177 - 5.97789i) q^{23} +(0.0157347 - 6.78755i) q^{24} +(1.04531 + 3.90115i) q^{25} +(-4.29916 + 2.00069i) q^{26} +(0.534560 - 0.221422i) q^{27} +(0.388270 + 5.27724i) q^{28} +(-0.519720 + 1.25471i) q^{29} +(7.51730 + 6.89903i) q^{30} +(-3.29306 + 5.70375i) q^{31} +(-3.05784 + 4.75916i) q^{32} +(-2.32646 - 4.02954i) q^{33} +(7.88303 - 2.47882i) q^{34} +(-6.25066 - 4.91941i) q^{35} +(5.43247 + 0.966550i) q^{36} +(-0.278939 - 0.214037i) q^{37} +(-8.86073 - 6.21456i) q^{38} +(-2.08258 - 7.77230i) q^{39} +(-2.18183 - 8.21887i) q^{40} +(3.08076 + 3.08076i) q^{41} +(-8.93397 - 0.899257i) q^{42} +(1.50539 + 3.63434i) q^{43} +(-0.175134 + 3.87385i) q^{44} +(-6.58045 + 5.04936i) q^{45} +(-4.69687 - 7.38520i) q^{46} +(-3.75988 + 2.17077i) q^{47} +(-7.05710 - 6.50689i) q^{48} +(6.99789 + 0.171886i) q^{49} +(5.06428 + 2.64127i) q^{50} +(1.83029 + 13.9024i) q^{51} +(-2.02643 + 6.39254i) q^{52} +(-5.47403 - 0.720670i) q^{53} +(0.280459 - 0.768705i) q^{54} +(-4.12188 - 4.12188i) q^{55} +(5.86979 + 4.64173i) q^{56} +(12.9861 - 12.9861i) q^{57} +(0.810350 + 1.74131i) q^{58} +(-1.75939 + 13.3639i) q^{59} +(14.3766 - 1.23540i) q^{60} +(-0.248180 + 0.0326735i) q^{61} +(2.79396 + 8.88525i) q^{62} +(1.97564 - 7.02689i) q^{63} +(2.03470 + 7.73692i) q^{64} +(-5.04035 - 8.73014i) q^{65} +(-6.42314 - 1.42918i) q^{66} +(3.34929 + 4.36487i) q^{67} +(4.95528 - 10.5839i) q^{68} +(13.7211 - 5.68347i) q^{69} +(-11.1028 + 1.80864i) q^{70} +(-2.25231 + 2.25231i) q^{71} +(6.20179 - 4.73600i) q^{72} +(-2.14893 + 0.575804i) q^{73} +(-0.489742 + 0.0859646i) q^{74} +(-5.90018 + 7.68926i) q^{75} +(-14.9481 + 3.28968i) q^{76} +(5.07736 + 0.731978i) q^{77} +(-10.0896 - 5.26224i) q^{78} +(-5.61531 + 3.24200i) q^{79} +(-10.6498 - 5.58585i) q^{80} +(8.37030 + 4.83260i) q^{81} +(6.15586 - 0.264005i) q^{82} +(-10.7528 - 4.45397i) q^{83} +(-9.47993 + 8.44866i) q^{84} +(6.72276 + 16.2302i) q^{85} +(5.22624 + 1.90677i) q^{86} +(-3.14806 + 0.843520i) q^{87} +(3.86880 + 3.88678i) q^{88} +(4.34060 + 1.16306i) q^{89} +(-1.03138 + 11.6847i) q^{90} +(8.15367 + 3.49526i) q^{91} +(-12.1862 - 2.16817i) q^{92} +(-15.6700 + 2.06299i) q^{93} +(-1.33354 + 5.99329i) q^{94} +(11.5040 - 19.9256i) q^{95} +(-13.5280 + 1.13089i) q^{96} +8.30414 q^{97} +(6.87071 - 7.12694i) q^{98} +(2.04706 - 4.94203i) 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 $

$2$	0.956234	−	1.04193i	0.676160	−	0.736755i
$2$	0.956234	−	1.04193i	0.676160	−	0.736755i
$3$	1.46089	+	1.90386i	0.843443	+	1.09920i	0.993868	+	0.110575i	$0.0352694\pi$
$3$	1.46089	+	1.90386i	0.843443	+	1.09920i	−0.150424	+	0.988622i	$0.548064\pi$
$4$	−0.171232	−	1.99266i	−0.0856161	−	0.996328i
$5$	2.38518	+	1.83021i	1.06669	+	0.818496i	0.984016	−	0.178081i	$-0.0569888\pi$
$5$	2.38518	+	1.83021i	1.06669	+	0.818496i	0.0826692	+	0.996577i	$0.473656\pi$
$6$	3.38064	+	0.298400i	1.38014	+	0.121821i
$7$	−2.64555	−	0.0324859i	−0.999925	−	0.0122785i
$7$	−2.64555	−	0.0324859i	−0.999925	−	0.0122785i
$8$	−2.23994	−	1.72703i	−0.791940	−	0.610599i
$9$	−0.714054	+	2.66488i	−0.238018	+	0.888295i
$10$	4.18774	−	0.735076i	1.32428	−	0.232451i
$11$	−1.92231	−	0.253077i	−0.579600	−	0.0763057i	−0.164974	−	0.986298i	$-0.552754\pi$
$11$	−1.92231	−	0.253077i	−0.579600	−	0.0763057i	−0.414625	+	0.909992i	$0.636087\pi$
$12$	3.54360	−	3.23705i	1.02295	−	0.934455i
$13$	−3.09779	−	1.28315i	−0.859172	−	0.355880i	−0.0907881	−	0.995870i	$-0.528939\pi$
$13$	−3.09779	−	1.28315i	−0.859172	−	0.355880i	−0.768383	+	0.639990i	$0.778939\pi$
$14$	−2.56362	+	2.72541i	−0.685155	+	0.728397i
$15$			7.21480i			1.86285i
$16$	−3.94136	+	0.682414i	−0.985340	+	0.170603i
$17$	5.06039	+	2.92162i	1.22732	+	0.708596i	0.966469	−	0.256782i	$-0.0826623\pi$
$17$	5.06039	+	2.92162i	1.22732	+	0.708596i	0.260855	+	0.965378i	$0.415996\pi$
$18$	2.09382	+	3.29225i	0.493518	+	0.775990i
$19$	−0.998902	−	7.58742i	−0.229164	−	1.74067i	−0.589427	−	0.807822i	$-0.700646\pi$
$19$	−0.998902	−	7.58742i	−0.229164	−	1.74067i	0.360263	−	0.932851i	$-0.382687\pi$
$20$	3.23857	−	5.06624i	0.724166	−	1.13284i
$21$	−3.80300	−	5.08423i	−0.829883	−	1.10947i
$22$	−2.10187	+	1.76091i	−0.448120	+	0.375428i
$23$	1.60177	−	5.97789i	0.333992	−	1.24648i	−0.570965	−	0.820974i	$-0.693431\pi$
$23$	1.60177	−	5.97789i	0.333992	−	1.24648i	0.904957	−	0.425502i	$-0.139903\pi$
$24$	0.0157347	−	6.78755i	0.00321184	−	1.38550i
$25$	1.04531	+	3.90115i	0.209062	+	0.780230i
$26$	−4.29916	+	2.00069i	−0.843134	+	0.392367i
$27$	0.534560	−	0.221422i	0.102876	−	0.0426127i
$28$	0.388270	+	5.27724i	0.0733762	+	0.997304i
$29$	−0.519720	+	1.25471i	−0.0965095	+	0.232995i	−0.964760	−	0.263132i	$-0.915245\pi$
$29$	−0.519720	+	1.25471i	−0.0965095	+	0.232995i	0.868250	+	0.496126i	$0.165245\pi$
$30$	7.51730	+	6.89903i	1.37247	+	1.25959i
$31$	−3.29306	+	5.70375i	−0.591451	+	1.02442i	0.402586	+	0.915382i	$0.368111\pi$
$31$	−3.29306	+	5.70375i	−0.591451	+	1.02442i	−0.994037	+	0.109041i	$0.965222\pi$
$32$	−3.05784	+	4.75916i	−0.540554	+	0.841309i
$33$	−2.32646	−	4.02954i	−0.404984	−	0.701454i
$34$	7.88303	−	2.47882i	1.35193	−	0.425113i
$35$	−6.25066	−	4.91941i	−1.05655	−	0.831532i
$36$	5.43247	+	0.966550i	0.905411	+	0.161092i
$37$	−0.278939	−	0.214037i	−0.0458572	−	0.0351875i	0.585579	−	0.810616i	$-0.300867\pi$
$37$	−0.278939	−	0.214037i	−0.0458572	−	0.0351875i	−0.631436	+	0.775428i	$0.717534\pi$
$38$	−8.86073	−	6.21456i	−1.43740	−	1.00814i
$39$	−2.08258	−	7.77230i	−0.333480	−	1.24456i
$40$	−2.18183	−	8.21887i	−0.344978	−	1.29952i
$41$	3.08076	+	3.08076i	0.481133	+	0.481133i	0.905494	−	0.424360i	$-0.139501\pi$
$41$	3.08076	+	3.08076i	0.481133	+	0.481133i	−0.424360	+	0.905494i	$0.639501\pi$
$42$	−8.93397	−	0.899257i	−1.37854	−	0.138758i
$43$	1.50539	+	3.63434i	0.229571	+	0.554232i	0.996125	−	0.0879468i	$-0.0280306\pi$
$43$	1.50539	+	3.63434i	0.229571	+	0.554232i	−0.766555	+	0.642179i	$0.778031\pi$
$44$	−0.175134	+	3.87385i	−0.0264025	+	0.584004i
$45$	−6.58045	+	5.04936i	−0.980956	+	0.752714i
$46$	−4.69687	−	7.38520i	−0.692516	−	1.08889i
$47$	−3.75988	+	2.17077i	−0.548434	+	0.316639i	−0.748490	−	0.663146i	$-0.769221\pi$
$47$	−3.75988	+	2.17077i	−0.548434	+	0.316639i	0.200056	+	0.979784i	$0.435888\pi$
$48$	−7.05710	−	6.50689i	−1.01861	−	0.939188i
$49$	6.99789	+	0.171886i	0.999698	+	0.0245552i
$50$	5.06428	+	2.64127i	0.716197	+	0.373532i
$51$	1.83029	+	13.9024i	0.256292	+	1.94673i
$52$	−2.02643	+	6.39254i	−0.281015	+	0.886486i
$53$	−5.47403	−	0.720670i	−0.751916	−	0.0989916i	−0.255180	−	0.966893i	$-0.582135\pi$
$53$	−5.47403	−	0.720670i	−0.751916	−	0.0989916i	−0.496736	+	0.867902i	$0.665468\pi$
$54$	0.280459	−	0.768705i	0.0381656	−	0.104608i
$55$	−4.12188	−	4.12188i	−0.555794	−	0.555794i
$56$	5.86979	+	4.64173i	0.784383	+	0.620277i
$57$	12.9861	−	12.9861i	1.72006	−	1.72006i
$58$	0.810350	+	1.74131i	0.106404	+	0.228645i
$59$	−1.75939	+	13.3639i	−0.229053	+	1.73983i	0.361091	+	0.932531i	$0.382404\pi$
$59$	−1.75939	+	13.3639i	−0.229053	+	1.73983i	−0.590144	+	0.807298i	$0.700929\pi$
$60$	14.3766	−	1.23540i	1.85601	−	0.159490i
$61$	−0.248180	+	0.0326735i	−0.0317762	+	0.00418341i	−0.146398	−	0.989226i	$-0.546768\pi$
$61$	−0.248180	+	0.0326735i	−0.0317762	+	0.00418341i	0.114621	+	0.993409i	$0.463435\pi$
$62$	2.79396	+	8.88525i	0.354834	+	1.12843i
$63$	1.97564	−	7.02689i	0.248907	−	0.885306i
$64$	2.03470	+	7.73692i	0.254338	+	0.967115i
$65$	−5.04035	−	8.73014i	−0.625179	−	1.08284i
$66$	−6.42314	−	1.42918i	−0.790634	−	0.175920i
$67$	3.34929	+	4.36487i	0.409180	+	0.533254i	0.951798	−	0.306726i	$-0.0992334\pi$
$67$	3.34929	+	4.36487i	0.409180	+	0.533254i	−0.542618	+	0.839980i	$0.682567\pi$
$68$	4.95528	−	10.5839i	0.600915	−	1.28348i
$69$	13.7211	−	5.68347i	1.65183	−	0.684209i
$70$	−11.1028	+	1.80864i	−1.32704	+	0.216174i
$71$	−2.25231	+	2.25231i	−0.267300	+	0.267300i	−0.828011	−	0.560712i	$-0.810528\pi$
$71$	−2.25231	+	2.25231i	−0.267300	+	0.267300i	0.560712	+	0.828011i	$0.310528\pi$
$72$	6.20179	−	4.73600i	0.730888	−	0.558143i
$73$	−2.14893	+	0.575804i	−0.251513	+	0.0673928i	−0.382373	−	0.924008i	$-0.624893\pi$
$73$	−2.14893	+	0.575804i	−0.251513	+	0.0673928i	0.130860	+	0.991401i	$0.458226\pi$
$74$	−0.489742	+	0.0859646i	−0.0569313	+	0.00999318i
$75$	−5.90018	+	7.68926i	−0.681294	+	0.887880i
$76$	−14.9481	+	3.28968i	−1.71466	+	0.377352i
$77$	5.07736	+	0.731978i	0.578619	+	0.0834166i
$78$	−10.0896	−	5.26224i	−1.14242	−	0.595831i
$79$	−5.61531	+	3.24200i	−0.631771	+	0.364753i	−0.781438	−	0.623983i	$-0.785513\pi$
$79$	−5.61531	+	3.24200i	−0.631771	+	0.364753i	0.149666	+	0.988737i	$0.452180\pi$
$80$	−10.6498	−	5.58585i	−1.19069	−	0.624517i
$81$	8.37030	+	4.83260i	0.930033	+	0.536955i
$82$	6.15586	−	0.264005i	0.679801	−	0.0291545i
$83$	−10.7528	−	4.45397i	−1.18028	−	0.488887i	−0.295700	−	0.955281i	$-0.595553\pi$
$83$	−10.7528	−	4.45397i	−1.18028	−	0.488887i	−0.884577	+	0.466394i	$0.845553\pi$
$84$	−9.47993	+	8.44866i	−1.03435	+	0.921825i
$85$	6.72276	+	16.2302i	0.729185	+	1.76041i
$86$	5.22624	+	1.90677i	0.563560	+	0.205612i
$87$	−3.14806	+	0.843520i	−0.337507	+	0.0904348i
$88$	3.86880	+	3.88678i	0.412416	+	0.414332i
$89$	4.34060	+	1.16306i	0.460103	+	0.123284i	0.481423	−	0.876489i	$-0.340120\pi$
$89$	4.34060	+	1.16306i	0.460103	+	0.123284i	−0.0213199	+	0.999773i	$0.506787\pi$
$90$	−1.03138	+	11.6847i	−0.108717	+	1.23168i
$91$	8.15367	+	3.49526i	0.854737	+	0.366403i
$92$	−12.1862	−	2.16817i	−1.27049	−	0.226048i
$93$	−15.6700	+	2.06299i	−1.62490	+	0.213922i
$94$	−1.33354	+	5.99329i	−0.137544	+	0.618160i
$95$	11.5040	−	19.9256i	1.18029	−	2.04432i
$96$	−13.5280	+	1.13089i	−1.38069	+	0.115421i
$97$	8.30414			0.843157			0.421579	−	0.906792i	$-0.361476\pi$
$97$	8.30414			0.843157			0.421579	+	0.906792i	$0.361476\pi$
$98$	6.87071	−	7.12694i	0.694047	−	0.719930i
$99$	2.04706	−	4.94203i	0.205737	−	0.496693i
$100$	7.59466	−	2.75094i	0.759466	−	0.275094i
$101$	2.46579	−	18.7296i	0.245355	−	1.86366i	−0.215931	−	0.976409i	$-0.569279\pi$
$101$	2.46579	−	18.7296i	0.245355	−	1.86366i	0.461286	−	0.887251i	$-0.347388\pi$
$102$	16.2355	+	11.3870i	1.60756	+	1.12748i
$103$	4.16565	+	1.11618i	0.410454	+	0.109981i	0.458137	−	0.888882i	$-0.348517\pi$
$103$	4.16565	+	1.11618i	0.410454	+	0.109981i	−0.0476829	+	0.998863i	$0.515184\pi$
$104$	4.72283	+	8.22416i	0.463112	+	0.806445i
$105$	0.234379	−	19.0871i	0.0228731	−	1.86271i
$106$	−5.98534	+	5.01442i	−0.581348	+	0.487044i
$107$	7.37151	−	9.60674i	0.712631	−	0.928718i	−0.286942	−	0.957948i	$-0.592639\pi$
$107$	7.37151	−	9.60674i	0.712631	−	0.928718i	0.999573	+	0.0292296i	$0.00930541\pi$
$108$	−0.532752	−	1.02728i	−0.0512641	−	0.0988501i
$109$	−9.45792	+	7.25732i	−0.905905	+	0.695125i	−0.952743	−	0.303777i	$-0.901752\pi$
$109$	−9.45792	+	7.25732i	−0.905905	+	0.695125i	0.0468385	+	0.998902i	$0.485085\pi$
$110$	−8.23619	+	0.353224i	−0.785290	+	0.0336785i
$111$		−	0.843745i		−	0.0800847i
$112$	10.4492	−	1.67732i	0.987360	−	0.158492i
$113$		−	7.37208i		−	0.693507i	−0.937956	−	0.346753i	$-0.887284\pi$
$113$		−	7.37208i		−	0.693507i	0.937956	−	0.346753i	$-0.112716\pi$
$114$	−1.11284	−	25.9484i	−0.104227	−	2.43029i
$115$	14.7613	−	11.3268i	1.37650	−	1.05623i
$116$	2.58921	+	0.820776i	0.240402	+	0.0762071i
$117$	5.63142	−	7.33901i	0.520625	−	0.678492i
$118$	12.2418	+	14.6122i	1.12695	+	1.34516i
$119$	−13.2926	−	7.89368i	−1.21853	−	0.723612i
$120$	12.4602	−	16.1607i	1.13746	−	1.47527i
$121$	−6.99394	−	1.87402i	−0.635813	−	0.170366i
$122$	−0.203275	+	0.289829i	−0.0184036	+	0.0262399i
$123$	−1.36471	+	10.3660i	−0.123052	+	0.934669i
$124$	11.9295	+	5.58527i	1.07130	+	0.501572i
$125$	1.10592	−	2.66992i	0.0989164	−	0.238805i
$126$	−5.43235	−	8.77783i	−0.483952	−	0.781991i
$127$	19.0540			1.69077			0.845385	−	0.534157i	$-0.179371\pi$
$127$	19.0540			1.69077			0.845385	+	0.534157i	$0.179371\pi$
$128$	10.0070	+	5.27829i	0.884500	+	0.466540i
$129$	−4.72009	+	8.17543i	−0.415581	+	0.719807i
$130$	−13.9159	−	3.09637i	−1.22051	−	0.271570i
$131$	7.08480	−	0.932731i	0.619002	−	0.0814931i	0.185498	−	0.982645i	$-0.440610\pi$
$131$	7.08480	−	0.932731i	0.619002	−	0.0814931i	0.433504	+	0.901152i	$0.357277\pi$
$132$	−7.63113	+	5.32582i	−0.664205	+	0.463553i
$133$	2.39616	+	20.1054i	0.207774	+	1.74336i
$134$	7.75059	+	0.684124i	0.669549	+	0.0590993i
$135$	1.68027	+	0.450228i	0.144615	+	0.0387494i
$136$	−6.28926	−	15.2837i	−0.539299	−	1.31057i
$137$	−3.25820	+	0.873031i	−0.278366	+	0.0745881i	−0.395301	−	0.918552i	$-0.629360\pi$
$137$	−3.25820	+	0.873031i	−0.278366	+	0.0745881i	0.116935	+	0.993140i	$0.462693\pi$
$138$	7.19882	−	19.7311i	0.612804	−	1.67963i
$139$	−0.885342	−	2.13740i	−0.0750937	−	0.181292i	0.881875	−	0.471483i	$-0.156281\pi$
$139$	−0.885342	−	2.13740i	−0.0750937	−	0.181292i	−0.956969	+	0.290191i	$0.906281\pi$
$140$	−8.73238	+	13.2978i	−0.738021	+	1.12387i
$141$	−9.62560	−	3.98705i	−0.810622	−	0.335771i
$142$	0.193011	+	4.50048i	0.0161971	+	0.377672i
$143$	5.63018	+	3.25059i	0.470820	+	0.271828i
$144$	0.995788	−	10.9905i	0.0829824	−	0.915879i
$145$	−3.53602	+	2.04152i	−0.293651	+	0.169539i
$146$	−1.45493	+	2.78964i	−0.120411	+	0.230872i
$147$	9.89588	+	13.5741i	0.816198	+	1.11958i
$148$	−0.378739	+	0.592479i	−0.0311322	+	0.0487014i
$149$	0.500386	−	0.652116i	0.0409932	−	0.0534234i	−0.772407	−	0.635128i	$-0.780947\pi$
$149$	0.500386	−	0.652116i	0.0409932	−	0.0534234i	0.813400	+	0.581705i	$0.197614\pi$
$150$	2.36971	+	13.5003i	0.193486	+	1.10230i
$151$	4.00602	−	1.07341i	0.326006	−	0.0873529i	−0.0921044	−	0.995749i	$-0.529359\pi$
$151$	4.00602	−	1.07341i	0.326006	−	0.0873529i	0.418110	+	0.908396i	$0.362693\pi$
$152$	−10.8662	+	18.7205i	−0.881369	+	1.51844i
$153$	−11.3992	+	11.3992i	−0.921567	+	0.921567i
$154$	5.61781	−	4.59031i	0.452696	−	0.369897i
$155$	−18.2936	+	7.57747i	−1.46938	+	0.608637i
$156$	−15.1309	+	5.48074i	−1.21144	+	0.438810i
$157$	5.19520	+	6.77052i	0.414622	+	0.540347i	0.953244	−	0.302201i	$-0.0977214\pi$
$157$	5.19520	+	6.77052i	0.414622	+	0.540347i	−0.538622	+	0.842548i	$0.681055\pi$
$158$	−1.99162	+	8.95086i	−0.158444	+	0.712092i
$159$	−6.62488	−	11.4746i	−0.525387	−	0.909997i
$160$	−16.0038	+	5.75497i	−1.26521	+	0.454970i
$161$	−4.43177	+	15.7628i	−0.349272	+	1.24228i
$162$	13.0392	−	4.10017i	1.02446	−	0.322139i
$163$	−6.54332	+	0.861445i	−0.512512	+	0.0674735i	−0.382347	−	0.924019i	$-0.624884\pi$
$163$	−6.54332	+	0.861445i	−0.512512	+	0.0674735i	−0.130165	+	0.991492i	$0.541551\pi$
$164$	5.61137	−	6.66642i	0.438174	−	0.520560i
$165$	1.82590	−	13.8691i	0.142146	−	1.07971i
$166$	−14.9229	+	6.94465i	−1.15825	+	0.539009i
$167$	14.7002	−	14.7002i	1.13753	−	1.13753i	0.148644	−	0.988891i	$-0.452509\pi$
$167$	14.7002	−	14.7002i	1.13753	−	1.13753i	0.988891	−	0.148644i	$-0.0474907\pi$
$168$	−0.262127	+	17.9563i	−0.0202235	+	1.38536i
$169$	−1.24257	−	1.24257i	−0.0955820	−	0.0955820i
$170$	23.3392	+	8.51521i	1.79004	+	0.653087i
$171$	20.9329	+	2.75586i	1.60078	+	0.210746i
$172$	6.98423	−	3.62205i	0.532542	−	0.276179i
$173$	−1.57985	−	12.0002i	−0.120114	−	0.912357i	−0.940321	−	0.340290i	$-0.889475\pi$
$173$	−1.57985	−	12.0002i	−0.120114	−	0.912357i	0.820207	−	0.572068i	$-0.193858\pi$
$174$	−2.13139	+	4.08666i	−0.161581	+	0.309809i
$175$	−2.63869	−	10.3546i	−0.199466	−	0.782738i
$176$	7.74923	−	0.314344i	0.584120	−	0.0236946i
$177$	−28.0133	+	16.1735i	−2.10561	+	1.21567i
$178$	5.36246	−	3.41044i	0.401933	−	0.255623i
$179$	−6.50486	+	4.99136i	−0.486196	+	0.373072i	−0.822576	−	0.568655i	$-0.807464\pi$
$179$	−6.50486	+	4.99136i	−0.486196	+	0.373072i	0.336380	+	0.941726i	$0.390797\pi$
$180$	11.1884	+	12.2480i	0.833936	+	0.912910i
$181$	5.13845	+	12.4053i	0.381938	+	0.922080i	0.991591	+	0.129412i	$0.0413088\pi$
$181$	5.13845	+	12.4053i	0.381938	+	0.922080i	−0.609653	+	0.792668i	$0.708691\pi$
$182$	11.4386	−	5.15326i	0.847888	−	0.381985i
$183$	−0.424769	−	0.424769i	−0.0313998	−	0.0313998i
$184$	−13.9119	+	10.6238i	−1.02560	+	0.783199i
$185$	−0.273585	−	1.02103i	−0.0201144	−	0.0750679i
$186$	−12.8347	+	18.2997i	−0.941083	+	1.34180i
$187$	−8.98826	−	6.89693i	−0.657287	−	0.504354i
$188$	4.96940	+	7.12044i	0.362431	+	0.519311i
$189$	−1.42140	+	0.568418i	−0.103392	+	0.0413463i
$190$	−9.76047	−	31.0399i	−0.708099	−	2.25187i
$191$	6.95030	+	12.0383i	0.502906	+	0.871059i	0.999994	+	0.00335879i	$0.00106914\pi$
$191$	6.95030	+	12.0383i	0.502906	+	0.871059i	−0.497088	+	0.867700i	$0.665598\pi$
$192$	−11.7576	+	15.1766i	−0.848531	+	1.09527i
$193$	1.61354	−	2.79474i	0.116145	−	0.201170i	−0.802092	−	0.597201i	$-0.796279\pi$
$193$	1.61354	−	2.79474i	0.116145	−	0.201170i	0.918237	+	0.396031i	$0.129613\pi$
$194$	7.94070	−	8.65232i	0.570109	−	0.621200i
$195$	9.25763	−	22.3499i	0.662953	−	1.60051i
$196$	−0.855753	−	13.9738i	−0.0611252	−	0.998130i
$197$	−17.7271	+	7.34279i	−1.26300	+	0.523152i	−0.910829	−	0.412783i	$-0.864557\pi$
$197$	−17.7271	+	7.34279i	−1.26300	+	0.523152i	−0.352171	+	0.935935i	$0.614557\pi$
$198$	−3.19178	−	6.85863i	−0.226830	−	0.487422i
$199$	−1.63675	−	6.10844i	−0.116026	−	0.433016i	0.883335	−	0.468742i	$-0.155292\pi$
$199$	−1.63675	−	6.10844i	−0.116026	−	0.433016i	−0.999362	+	0.0357255i	$0.988626\pi$
$200$	4.39598	−	10.5436i	0.310843	−	0.745548i
$201$	−3.41720	+	12.7532i	−0.241031	+	0.899540i
$202$	−17.1570	−	20.4790i	−1.20716	−	1.44090i
$203$	1.41571	−	3.30253i	0.0993631	−	0.231792i
$204$	27.3894	−	6.02769i	1.91764	−	0.422023i
$205$	1.70972	+	12.9866i	0.119412	+	0.907024i
$206$	5.14632	−	3.27298i	0.358561	−	0.228039i
$207$	14.7866	+	8.53707i	1.02774	+	0.593368i
$208$	13.0851	+	2.94336i	0.907290	+	0.204086i
$209$			14.8382i			1.02638i
$210$	−19.6633	−	18.4960i	−1.35690	−	1.27634i
$211$	−8.37528	−	3.46915i	−0.576578	−	0.238826i	0.0752865	−	0.997162i	$-0.476013\pi$
$211$	−8.37528	−	3.46915i	−0.576578	−	0.238826i	−0.651864	+	0.758336i	$0.726013\pi$
$212$	−0.498717	+	11.0313i	−0.0342520	+	0.757630i
$213$	−7.57845	−	0.997722i	−0.519267	−	0.0683628i
$214$	−2.96065	−	16.8669i	−0.202386	−	1.15300i
$215$	−3.06099	+	11.4238i	−0.208758	+	0.779094i
$216$	−1.57979	−	0.427231i	−0.107491	−	0.0290694i
$217$	8.89725	−	14.9826i	0.603985	−	1.01708i
$218$	−1.48238	+	16.7942i	−0.100399	+	1.13745i
$219$	−4.23560	−	3.25009i	−0.286215	−	0.219621i
$220$	−7.50769	+	8.91929i	−0.506169	+	0.601338i
$221$	−11.9271	−	15.5438i	−0.802307	−	1.04559i
$222$	−0.879123	−	0.806818i	−0.0590028	−	0.0541501i
$223$	0.798307			0.0534586			0.0267293	−	0.999643i	$-0.491491\pi$
$223$	0.798307			0.0534586			0.0267293	+	0.999643i	$0.491491\pi$
$224$	8.24427	−	12.4913i	0.550843	−	0.834609i
$225$	−11.1425			−0.742835
$226$	−7.68118	−	7.04943i	−0.510945	−	0.468921i
$227$	−6.26430	−	8.16379i	−0.415776	−	0.541850i	0.537772	−	0.843090i	$-0.319266\pi$
$227$	−6.26430	−	8.16379i	−0.415776	−	0.541850i	−0.953548	+	0.301240i	$0.902599\pi$
$228$	−28.1005	−	23.6533i	−1.86100	−	1.56648i
$229$	5.42987	+	4.16649i	0.358816	+	0.275329i	0.772399	−	0.635137i	$-0.219056\pi$
$229$	5.42987	+	4.16649i	0.358816	+	0.275329i	−0.413584	+	0.910466i	$0.635723\pi$
$230$	2.31360	−	26.2113i	0.152554	−	1.72832i
$231$	6.02386	+	10.7359i	0.396341	+	0.706373i
$232$	3.33108	−	1.91292i	0.218696	−	0.125589i
$233$	5.56740	−	20.7778i	0.364732	−	1.36120i	−0.503051	−	0.864257i	$-0.667789\pi$
$233$	5.56740	−	20.7778i	0.364732	−	1.36120i	0.867783	−	0.496943i	$-0.165544\pi$
$234$	−2.26177	−	12.8854i	−0.147857	−	0.842342i
$235$	−12.9410	−	1.70371i	−0.844175	−	0.111138i
$236$	26.9309	+	1.21753i	1.75305	+	0.0792545i
$237$	−14.3757	−	5.95459i	−0.933799	−	0.386792i
$238$	−20.9355	+	6.30175i	−1.35705	+	0.408482i
$239$			2.32832i			0.150607i	0.997161	+	0.0753033i	$0.0239925\pi$
$239$			2.32832i			0.150607i	−0.997161	+	0.0753033i	$0.976007\pi$
$240$	−4.92348	−	28.4361i	−0.317809	−	1.83554i
$241$	18.9389	+	10.9344i	1.21996	+	0.704347i	0.964910	−	0.262580i	$-0.0845734\pi$
$241$	18.9389	+	10.9344i	1.21996	+	0.704347i	0.255054	+	0.966927i	$0.417907\pi$
$242$	−8.64044	+	5.49519i	−0.555429	+	0.353244i
$243$	2.80089	+	21.2748i	0.179677	+	1.36478i
$244$	0.107603	+	0.488942i	0.00688860	+	0.0313013i
$245$	16.3766	+	13.2176i	1.04627	+	0.844442i
$246$	9.49564	+	11.3342i	0.605420	+	0.722645i
$247$	−6.64137	+	24.7859i	−0.422580	+	1.57709i
$248$	17.2268	−	7.08885i	1.09391	−	0.450142i
$249$	−7.22892	−	26.9787i	−0.458114	−	1.70970i
$250$	−1.72435	−	3.70536i	−0.109058	−	0.234348i
$251$	−16.1399	+	6.68535i	−1.01874	+	0.421975i	−0.828635	−	0.559789i	$-0.810882\pi$
$251$	−16.1399	+	6.68535i	−1.01874	+	0.421975i	−0.190103	+	0.981764i	$0.560882\pi$
$252$	−14.3405	−	2.73354i	−0.903365	−	0.172197i
$253$	−4.59198	+	11.0860i	−0.288695	+	0.696972i
$254$	18.2201	−	19.8529i	1.14323	−	1.24568i
$255$	−21.0789	+	36.5097i	−1.32001	+	2.28632i
$256$	15.0686	−	5.37927i	0.941789	−	0.336205i
$257$	−4.35584	−	7.54453i	−0.271710	−	0.470615i	0.697590	−	0.716497i	$-0.254256\pi$
$257$	−4.35584	−	7.54453i	−0.271710	−	0.470615i	−0.969300	+	0.245882i	$0.920922\pi$
$258$	4.00471	+	12.7356i	0.249322	+	0.792885i
$259$	0.730993	+	0.575308i	0.0454217	+	0.0357479i
$260$	−16.5331	+	11.5386i	−1.02534	+	0.715592i
$261$	−2.97256	−	2.28093i	−0.183997	−	0.141186i
$262$	5.80289	−	8.27377i	0.358504	−	0.511155i
$263$	4.03528	+	15.0599i	0.248826	+	0.928632i	0.971422	+	0.237361i	$0.0762824\pi$
$263$	4.03528	+	15.0599i	0.248826	+	0.928632i	−0.722595	+	0.691271i	$0.757051\pi$
$264$	−1.74802	+	13.0438i	−0.107583	+	0.802792i
$265$	−11.7376	−	11.7376i	−0.721033	−	0.721033i
$266$	23.2396	+	16.7288i	1.42491	+	1.02571i
$267$	4.12682	+	9.96302i	0.252557	+	0.609727i
$268$	8.12419	−	7.42138i	0.496264	−	0.453333i
$269$	13.4278	−	10.3035i	0.818710	−	0.628218i	−0.112110	−	0.993696i	$-0.535761\pi$
$269$	13.4278	−	10.3035i	0.818710	−	0.628218i	0.930820	+	0.365478i	$0.119094\pi$
$270$	2.07584	−	1.32020i	0.126332	−	0.0803449i
$271$	2.32687	−	1.34342i	0.141347	−	0.0816069i	−0.427659	−	0.903940i	$-0.640661\pi$
$271$	2.32687	−	1.34342i	0.141347	−	0.0816069i	0.569006	+	0.822333i	$0.307328\pi$
$272$	−21.9386	−	8.06186i	−1.33022	−	0.488822i
$273$	5.25709	+	20.6297i	0.318173	+	1.24856i
$274$	−2.20596	+	4.22963i	−0.133267	+	0.255521i
$275$	−1.02212	−	7.76378i	−0.0616362	−	0.468173i
$276$	−13.6747	−	26.3683i	−0.823120	−	1.58718i
$277$	−26.1045	−	3.43673i	−1.56847	−	0.206493i	−0.704377	−	0.709826i	$-0.748773\pi$
$277$	−26.1045	−	3.43673i	−1.56847	−	0.206493i	−0.864092	+	0.503333i	$0.832107\pi$
$278$	−3.07362	−	1.12140i	−0.184343	−	0.0672569i
$279$	−12.8484	−	12.8484i	−0.769214	−	0.769214i
$280$	5.50515	+	21.8143i	0.328996	+	1.30365i
$281$	−10.3635	+	10.3635i	−0.618234	+	0.618234i	−0.945078	−	0.326844i	$-0.894015\pi$
$281$	−10.3635	+	10.3635i	−0.618234	+	0.618234i	0.326844	+	0.945078i	$0.394015\pi$
$282$	−13.3586	+	6.21663i	−0.795490	+	0.370195i
$283$	2.10622	−	15.9983i	0.125202	−	0.951000i	−0.807378	−	0.590035i	$-0.799114\pi$
$283$	2.10622	−	15.9983i	0.125202	−	0.951000i	0.932579	−	0.360965i	$-0.117553\pi$
$284$	4.87374	+	4.10241i	0.289203	+	0.243433i
$285$	54.7417	−	7.20688i	3.24262	−	0.426898i
$286$	8.77066	−	2.75793i	0.518620	−	0.163080i
$287$	−8.05022	−	8.25038i	−0.475190	−	0.487005i
$288$	−10.4992	−	11.5471i	−0.618669	−	0.680418i
$289$	8.57168	+	14.8466i	0.504216	+	0.873328i
$290$	−1.25414	+	5.63646i	−0.0736458	+	0.330984i
$291$	12.1314	+	15.8100i	0.711156	+	0.926796i
$292$	1.51535	+	4.18348i	0.0886789	+	0.244820i
$293$	−14.4660	+	5.99200i	−0.845110	+	0.350056i	−0.762867	−	0.646556i	$-0.776209\pi$
$293$	−14.4660	+	5.99200i	−0.845110	+	0.350056i	−0.0822440	+	0.996612i	$0.526209\pi$
$294$	23.6061	+	2.66926i	1.37673	+	0.155674i
$295$	−28.6552	+	28.6552i	−1.66837	+	1.66837i
$296$	0.255157	+	0.961168i	0.0148307	+	0.0558667i
$297$	−1.08363	+	0.290358i	−0.0628786	+	0.0168483i
$298$	−0.200972	−	1.14494i	−0.0116420	−	0.0663247i
$299$	−12.6325	+	16.4629i	−0.730553	+	0.952076i
$300$	16.3324	+	10.4404i	0.942949	+	0.602776i
$301$	−3.86453	−	9.66375i	−0.222748	−	0.557009i
$302$	2.71228	−	5.20042i	0.156074	−	0.299251i
$303$	39.2608	−	22.6672i	2.25547	−	1.30220i
$304$	9.11479	+	29.2231i	0.522769	+	1.67606i
$305$	−0.651753	−	0.376290i	−0.0373193	−	0.0215463i
$306$	0.976848	+	22.7774i	0.0558427	+	1.30210i
$307$	12.2540	+	5.07576i	0.699370	+	0.289689i	0.703898	−	0.710301i	$-0.251441\pi$
$307$	12.2540	+	5.07576i	0.699370	+	0.289689i	−0.00452769	+	0.999990i	$0.501441\pi$
$308$	0.589173	−	10.2428i	0.0335712	−	0.583636i
$309$	3.96048	+	9.56145i	0.225304	+	0.543932i
$310$	−9.59780	+	26.3065i	−0.545119	+	1.49411i
$311$	16.7427	−	4.48620i	0.949393	−	0.254389i	0.249288	−	0.968429i	$-0.419803\pi$
$311$	16.7427	−	4.48620i	0.949393	−	0.254389i	0.700105	+	0.714040i	$0.253137\pi$
$312$	−8.75816	+	21.0062i	−0.495833	+	1.18924i
$313$	−27.9640	−	7.49292i	−1.58062	−	0.423525i	−0.641500	−	0.767123i	$-0.721687\pi$
$313$	−27.9640	−	7.49292i	−1.58062	−	0.423525i	−0.939117	+	0.343598i	$0.888354\pi$
$314$	12.0222	+	1.06117i	0.678454	+	0.0598853i
$315$	17.5730	−	13.1446i	0.990125	−	0.740613i
$316$	7.42171	+	10.6342i	0.417504	+	0.598223i
$317$	−13.3459	+	1.75702i	−0.749582	+	0.0986843i	−0.495632	−	0.868533i	$-0.665063\pi$
$317$	−13.3459	+	1.75702i	−0.749582	+	0.0986843i	−0.253950	+	0.967217i	$0.581730\pi$
$318$	−18.2907	−	4.06978i	−1.02569	−	0.228222i
$319$	1.31660	−	2.28043i	0.0737157	−	0.127679i
$320$	−9.30709	+	22.1779i	−0.520282	+	1.23978i
$321$	29.0589			1.62191
$322$	12.1859	+	19.6905i	0.679094	+	1.09731i
$323$	17.1127	−	41.3137i	0.952175	−	2.29875i
$324$	8.19644	−	17.5066i	0.455358	−	0.972591i
$325$	1.76759	−	13.4262i	0.0980485	−	0.744752i
$326$	−5.35938	+	7.64142i	−0.296829	+	0.423219i
$327$	−27.6339	−	7.40448i	−1.52816	−	0.409469i
$328$	−1.58015	−	12.2213i	−0.0872493	−	0.674808i
$329$	10.0175	−	5.62073i	0.552281	−	0.309881i
$330$	−12.7046	−	15.1646i	−0.699367	−	0.834782i
$331$	12.7338	−	16.5950i	0.699912	−	0.912143i	−0.299204	−	0.954189i	$-0.596721\pi$
$331$	12.7338	−	16.5950i	0.699912	−	0.912143i	0.999116	+	0.0420461i	$0.0133876\pi$
$332$	−7.03400	+	22.1894i	−0.386041	+	1.21780i
$333$	0.769561	−	0.590505i	0.0421717	−	0.0323595i
$334$	−1.25973	−	29.3734i	−0.0689293	−	1.60724i
$335$			16.5409i			0.903727i
$336$	18.4586	+	17.4436i	1.00700	+	0.951624i
$337$		−	32.6300i		−	1.77747i	−0.458423	−	0.888734i	$-0.651586\pi$
$337$		−	32.6300i		−	1.77747i	0.458423	−	0.888734i	$-0.348414\pi$
$338$	−2.48285	+	0.106481i	−0.135049	+	0.00579182i
$339$	14.0354	−	10.7698i	0.762301	−	0.584934i
$340$	31.1900	−	16.1753i	1.69152	−	0.877227i
$341$	7.77379	−	10.1310i	0.420974	−	0.548624i
$342$	22.8881	−	19.1753i	1.23765	−	1.03688i
$343$	−18.5077	−	0.682067i	−0.999322	−	0.0368282i
$344$	2.90464	−	10.7406i	0.156608	−	0.579094i
$345$	43.1293	+	11.5565i	2.32200	+	0.622179i
$346$	−14.0141	−	9.82889i	−0.753400	−	0.528405i
$347$	−0.185553	+	1.40941i	−0.00996098	+	0.0756612i	−0.995703	−	0.0926005i	$-0.970482\pi$
$347$	−0.185553	+	1.40941i	−0.00996098	+	0.0756612i	0.985742	+	0.168262i	$0.0538154\pi$
$348$	2.21989	+	6.12856i	0.118999	+	0.328525i
$349$	−2.42934	+	5.86494i	−0.130040	+	0.313943i	−0.975467	−	0.220148i	$-0.929346\pi$
$349$	−2.42934	+	5.86494i	−0.130040	+	0.313943i	0.845427	+	0.534091i	$0.179346\pi$
$350$	−13.3120	−	7.15214i	−0.711557	−	0.382298i
$351$	−1.94007			−0.103553
$352$	7.08256	−	8.37474i	0.377502	−	0.446375i
$353$	11.9957	−	20.7772i	0.638468	−	1.10586i	−0.347301	−	0.937754i	$-0.612902\pi$
$353$	11.9957	−	20.7772i	0.638468	−	1.10586i	0.985769	−	0.168105i	$-0.0537648\pi$
$354$	−9.93565	+	44.6535i	−0.528074	+	2.37331i
$355$	−9.49436	+	1.24996i	−0.503908	+	0.0663408i
$356$	1.57433	−	8.84848i	0.0834393	−	0.468969i
$357$	−4.39050	−	36.8391i	−0.232370	−	1.94973i
$358$	−1.01953	+	11.5505i	−0.0538840	+	0.610463i
$359$	−4.19371	−	1.12370i	−0.221336	−	0.0593067i	0.146447	−	0.989219i	$-0.453216\pi$
$359$	−4.19371	−	1.12370i	−0.221336	−	0.0593067i	−0.367783	+	0.929912i	$0.619883\pi$
$360$	23.4603	+	0.0543850i	1.23647	+	0.00286634i
$361$	−38.2185	+	10.2406i	−2.01150	+	0.538980i
$362$	17.8390	+	6.50849i	0.937598	+	0.342079i
$363$	−6.64947	−	16.0533i	−0.349007	−	0.842577i
$364$	5.56869	−	16.8460i	0.291878	−	0.882969i
$365$	−6.17943	−	2.55960i	−0.323446	−	0.133976i
$366$	−0.848757	+	0.0364004i	−0.0443652	+	0.00190268i
$367$	−2.07087	−	1.19562i	−0.108098	−	0.0624106i	0.444976	−	0.895542i	$-0.353212\pi$
$367$	−2.07087	−	1.19562i	−0.108098	−	0.0624106i	−0.553074	+	0.833132i	$0.686546\pi$
$368$	−2.23376	+	24.6541i	−0.116443	+	1.28518i
$369$	−10.4097	+	6.01004i	−0.541907	+	0.312870i
$370$	−1.32546	−	0.691291i	−0.0689072	−	0.0359385i
$371$	14.4584	+	2.08440i	0.750644	+	0.108217i
$372$	6.79403	+	30.8716i	0.352254	+	1.60062i
$373$	22.2834	−	29.0403i	1.15379	−	1.50365i	0.323582	−	0.946200i	$-0.395113\pi$
$373$	22.2834	−	29.0403i	1.15379	−	1.50365i	0.830210	−	0.557451i	$-0.188220\pi$
$374$	−15.7810	+	2.77004i	−0.816016	+	0.143236i
$375$	6.69880	−	1.79494i	0.345924	−	0.0926902i
$376$	12.1709	+	1.63104i	0.627667	+	0.0841146i
$377$	3.21996	−	3.21996i	0.165837	−	0.165837i
$378$	−0.766940	+	2.02454i	−0.0394471	+	0.104131i
$379$	5.45923	−	2.26129i	0.280422	−	0.116154i	−0.238040	−	0.971255i	$-0.576505\pi$
$379$	5.45923	−	2.26129i	0.280422	−	0.116154i	0.518462	+	0.855101i	$0.326505\pi$
$380$	−41.6747	−	19.5117i	−2.13786	−	1.00093i
$381$	27.8358	+	36.2763i	1.42607	+	1.85849i
$382$	19.1891	+	4.26969i	0.981802	+	0.218456i
$383$	15.9043	+	27.5470i	0.812670	+	1.40759i	0.910989	+	0.412431i	$0.135320\pi$
$383$	15.9043	+	27.5470i	0.812670	+	1.40759i	−0.0983185	+	0.995155i	$0.531346\pi$
$384$	4.56990	+	26.7629i	0.233207	+	1.36574i
$385$	10.7707	+	11.0386i	0.548928	+	0.562577i
$386$	−1.36899	−	4.35362i	−0.0696800	−	0.221594i
$387$	−10.7600	+	1.41659i	−0.546964	+	0.0720091i
$388$	−1.42194	−	16.5473i	−0.0721878	−	0.840061i
$389$	−1.72034	+	13.0673i	−0.0872246	+	0.662537i	0.890852	+	0.454293i	$0.150108\pi$
$389$	−1.72034	+	13.0673i	−0.0872246	+	0.662537i	−0.978077	+	0.208244i	$0.933225\pi$
$390$	−14.4345	−	31.0175i	−0.730922	−	1.57063i
$391$	25.5707	−	25.5707i	1.29317	−	1.29317i
$392$	−15.3780	−	12.4706i	−0.776708	−	0.629861i
$393$	12.1259	+	12.1259i	0.611670	+	0.611670i
$394$	−9.30056	+	25.4918i	−0.468555	+	1.28426i
$395$	−19.3271	−	2.54446i	−0.972450	−	0.128025i
$396$	−10.1983	−	3.23285i	−0.512484	−	0.162457i
$397$	1.47057	+	11.1701i	0.0738058	+	0.560611i	0.987898	+	0.155104i	$0.0495714\pi$
$397$	1.47057	+	11.1701i	0.0738058	+	0.560611i	−0.914092	+	0.405506i	$0.867095\pi$
$398$	−7.92968	−	4.13572i	−0.397479	−	0.207305i
$399$	−34.7774	+	33.9336i	−1.74105	+	1.69881i
$400$	−6.78214	−	14.6625i	−0.339107	−	0.733125i
$401$	11.0143	−	6.35910i	0.550027	−	0.317558i	−0.199106	−	0.979978i	$-0.563804\pi$
$401$	11.0143	−	6.35910i	0.550027	−	0.317558i	0.749133	+	0.662420i	$0.230470\pi$
$402$	10.0203	+	15.7555i	0.499765	+	0.785813i
$403$	17.5199	−	13.4435i	0.872730	−	0.669670i
$404$	−37.7438	−	1.70638i	−1.87782	−	0.0848953i
$405$	11.1200	+	26.8460i	0.552557	+	1.33399i
$406$	−2.08725	−	4.63306i	−0.103589	−	0.229935i
$407$	0.482039	+	0.482039i	0.0238938	+	0.0238938i
$408$	19.9102	−	34.3017i	0.985704	−	1.69819i
$409$	6.47809	+	24.1766i	0.320321	+	1.19545i	0.918933	+	0.394415i	$0.129053\pi$
$409$	6.47809	+	24.1766i	0.320321	+	1.19545i	−0.598612	+	0.801039i	$0.704281\pi$
$410$	15.1660	+	10.6368i	0.748996	+	0.525316i
$411$	−6.42199	−	4.92777i	−0.316773	−	0.243069i
$412$	1.51088	−	8.49184i	0.0744355	−	0.418363i
$413$	5.08869	−	35.2977i	0.250398	−	1.73689i
$414$	23.0345	−	7.24319i	1.13208	−	0.355983i
$415$	−17.4957	−	30.3035i	−0.858832	−	1.48754i
$416$	15.5792	−	10.8192i	0.763834	−	0.530456i
$417$	2.77595	−	4.80808i	0.135939	−	0.235453i
$418$	15.4603	+	14.1888i	0.756190	+	0.693996i
$419$	−8.46801	+	20.4436i	−0.413689	+	0.998734i	0.570449	+	0.821333i	$0.306769\pi$
$419$	−8.46801	+	20.4436i	−0.413689	+	0.998734i	−0.984139	+	0.177401i	$0.943231\pi$
$420$	−38.0742	+	2.80129i	−1.85783	+	0.136689i
$421$	8.20981	−	3.40062i	0.400122	−	0.165736i	−0.173543	−	0.984826i	$-0.555521\pi$
$421$	8.20981	−	3.40062i	0.400122	−	0.165736i	0.573664	+	0.819090i	$0.305521\pi$
$422$	−11.6233	+	5.40912i	−0.565815	+	0.263312i
$423$	−3.10009	−	11.5697i	−0.150731	−	0.562537i
$424$	11.0169	+	11.0681i	0.535028	+	0.537514i
$425$	−6.10799	+	22.7953i	−0.296281	+	1.10574i
$426$	−8.28633	+	6.94215i	−0.401474	+	0.336348i
$427$	0.657634	−	0.0783771i	0.0318251	−	0.00379293i
$428$	−20.4052	−	13.0439i	−0.986321	−	0.630501i
$429$	2.03638	+	15.4679i	0.0983174	+	0.746795i
$430$	8.97573	+	14.1131i	0.432848	+	0.680595i
$431$	5.49390	+	3.17191i	0.264632	+	0.152785i	0.626446	−	0.779465i	$-0.284509\pi$
$431$	5.49390	+	3.17191i	0.264632	+	0.152785i	−0.361814	+	0.932250i	$0.617842\pi$
$432$	−1.95579	+	1.23750i	−0.0940981	+	0.0595390i
$433$		−	0.00144983i		−	6.96741e-5i	−1.00000		3.48371e-5i	$-0.999989\pi$
$433$		−	0.00144983i		−	6.96741e-5i	1.00000		3.48371e-5i	$-1.10890e-5\pi$
$434$	−7.10293	−	23.5972i	−0.340952	−	1.13270i
$435$	−9.05251	−	3.74967i	−0.434035	−	0.179783i
$436$	16.0808	+	17.6037i	0.770133	+	0.843064i
$437$	−46.9568	−	6.18198i	−2.24625	−	0.295724i
$438$	−7.43658	+	1.30535i	−0.355334	+	0.0623719i
$439$	4.31946	−	16.1204i	0.206156	−	0.769386i	−0.782937	−	0.622100i	$-0.786280\pi$
$439$	4.31946	−	16.1204i	0.206156	−	0.769386i	0.989094	−	0.147286i	$-0.0470538\pi$
$440$	2.11415	+	16.3514i	0.100788	+	0.779523i
$441$	−5.45493	+	18.5258i	−0.259758	+	0.882183i
$442$	−27.6006	−	2.43623i	−1.31283	−	0.115880i
$443$	−27.3001	−	20.9481i	−1.29707	−	0.995274i	−0.999172	−	0.0406756i	$-0.987049\pi$
$443$	−27.3001	−	20.9481i	−1.29707	−	0.995274i	−0.297894	−	0.954599i	$-0.596284\pi$
$444$	−1.68129	+	0.144476i	−0.0797907	+	0.00685654i
$445$	8.22447	+	10.7183i	0.389877	+	0.508098i
$446$	0.763369	−	0.831780i	0.0361466	−	0.0393859i
$447$	1.97255			0.0932983
$448$	−5.13157	−	20.5345i	−0.242444	−	0.970165i
$449$	−21.4287			−1.01128			−0.505642	−	0.862743i	$-0.668744\pi$
$449$	−21.4287			−1.01128			−0.505642	+	0.862743i	$0.668744\pi$
$450$	−10.6549	+	11.6097i	−0.502275	+	0.547287i
$451$	−5.14251	−	6.70185i	−0.242151	−	0.315578i
$452$	−14.6900	+	1.26234i	−0.690960	+	0.0593753i
$453$	7.89598	+	6.05880i	0.370985	+	0.284667i
$454$	−14.4962	−	1.27954i	−0.680341	−	0.0600519i
$455$	13.0509	+	23.2598i	0.611836	+	1.09044i
$456$	−51.5157	+	6.66072i	−2.41244	+	0.311917i
$457$	−9.47018	+	35.3432i	−0.442996	+	1.65328i	0.278177	+	0.960530i	$0.410270\pi$
$457$	−9.47018	+	35.3432i	−0.442996	+	1.65328i	−0.721173	+	0.692755i	$0.756397\pi$
$458$	9.53341	−	1.67340i	0.445467	−	0.0781930i
$459$	3.35199	+	0.441298i	0.156458	+	0.0205980i
$460$	−25.0980	−	27.4748i	−1.17020	−	1.28102i
$461$	6.98114	+	2.89168i	0.325144	+	0.134679i	0.539284	−	0.842124i	$-0.318695\pi$
$461$	6.98114	+	2.89168i	0.325144	+	0.134679i	−0.214140	+	0.976803i	$0.568695\pi$
$462$	16.9463	+	3.98964i	0.788414	+	0.185615i
$463$		−	30.6456i		−	1.42422i	−0.702068	−	0.712110i	$-0.747740\pi$
$463$		−	30.6456i		−	1.42422i	0.702068	−	0.712110i	$-0.252260\pi$
$464$	1.19217	−	5.29994i	0.0553450	−	0.246044i
$465$	−41.1514	−	23.7588i	−1.90835	−	1.10179i
$466$	−16.3253	−	25.6693i	−0.756254	−	1.18911i
$467$	−0.659844	−	5.01201i	−0.0305339	−	0.231928i	0.969373	−	0.245594i	$-0.0789831\pi$
$467$	−0.659844	−	5.01201i	−0.0305339	−	0.231928i	−0.999907	+	0.0136662i	$0.995650\pi$
$468$	−15.5884	−	9.96481i	−0.720574	−	0.460624i
$469$	−8.71891	−	11.6563i	−0.402602	−	0.538238i
$470$	−14.1497	+	11.8544i	−0.652678	+	0.546803i
$471$	−5.30055	+	19.7819i	−0.244237	+	0.911503i
$472$	27.0208	−	26.8958i	1.24373	−	1.23798i
$473$	−1.97407	−	7.36733i	−0.0907679	−	0.338750i
$474$	−19.9508	+	9.28443i	−0.916368	+	0.426448i
$475$	28.5555	−	11.8281i	1.31022	−	0.542709i
$476$	−13.4533	+	27.8392i	−0.616629	+	1.27601i
$477$	5.82925	−	14.0731i	0.266903	−	0.644361i
$478$	2.42595	+	2.22642i	0.110960	+	0.101834i
$479$	−2.82884	+	4.89969i	−0.129253	+	0.223872i	−0.923387	−	0.383870i	$-0.874591\pi$
$479$	−2.82884	+	4.89969i	−0.129253	+	0.223872i	0.794135	+	0.607742i	$0.207925\pi$
$480$	−34.3364	−	22.0617i	−1.56723	−	1.00697i
$481$	0.589451	+	1.02096i	0.0268767	+	0.0465518i
$482$	29.5029	−	9.27718i	1.34382	−	0.422564i
$483$	−36.4845	+	14.5902i	−1.66010	+	0.663876i
$484$	−2.53669	+	14.2574i	−0.115304	+	0.648064i
$485$	19.8069	+	15.1983i	0.899383	+	0.690121i
$486$	24.8452	+	17.4254i	1.12700	+	0.790432i
$487$	2.75087	+	10.2664i	0.124654	+	0.465215i	0.999827	−	0.0185949i	$-0.00591929\pi$
$487$	2.75087	+	10.2664i	0.124654	+	0.465215i	−0.875173	+	0.483810i	$0.839253\pi$
$488$	0.612337	+	0.355428i	0.0277192	+	0.0160895i
$489$	−11.1991	−	11.1991i	−0.506442	−	0.506442i
$490$	29.4317	−	4.42416i	1.32959	−	0.199863i
$491$	9.91313	+	23.9324i	0.447373	+	1.08006i	0.973302	+	0.229527i	$0.0737178\pi$
$491$	9.91313	+	23.9324i	0.447373	+	1.08006i	−0.525929	+	0.850529i	$0.676282\pi$
$492$	20.8895	+	0.944404i	0.941773	+	0.0425770i
$493$	−6.29578	+	4.83092i	−0.283548	+	0.217574i
$494$	19.4745	+	30.6210i	0.876198	+	1.37770i
$495$	13.9276	−	8.04109i	0.625998	−	0.361420i
$496$	9.08682	−	24.7277i	0.408010	−	1.11031i
$497$	6.03176	−	5.88542i	0.270561	−	0.263997i
$498$	−35.0224	−	18.2659i	−1.56939	−	0.818516i
$499$	−3.50442	−	26.6187i	−0.156880	−	1.19162i	−0.870888	−	0.491481i	$-0.836456\pi$
$499$	−3.50442	−	26.6187i	−0.156880	−	1.19162i	0.714008	−	0.700137i	$-0.246878\pi$
$500$	−5.50961	−	1.74654i	−0.246397	−	0.0781076i
$501$	49.4625	+	6.51186i	2.20982	+	0.290928i
$502$	−8.46782	+	23.2093i	−0.377937	+	1.03588i
$503$	21.0632	+	21.0632i	0.939162	+	0.939162i	0.998253	−	0.0590910i	$-0.0188202\pi$
$503$	21.0632	+	21.0632i	0.939162	+	0.939162i	−0.0590910	+	0.998253i	$0.518820\pi$
$504$	−16.5610	+	12.3279i	−0.737686	+	0.549127i
$505$	40.1604	−	40.1604i	1.78712	−	1.78712i
$506$	7.15983	+	15.3853i	0.318293	+	0.683962i
$507$	0.550429	−	4.18093i	0.0244454	−	0.185681i
$508$	−3.26266	−	37.9681i	−0.144757	−	1.68456i
$509$	5.98922	−	0.788496i	0.265468	−	0.0349495i	0.00338268	−	0.999994i	$-0.498923\pi$
$509$	5.98922	−	0.788496i	0.265468	−	0.0349495i	0.262085	+	0.965045i	$0.415590\pi$
$510$	17.8841	+	56.8745i	0.791923	+	2.51844i
$511$	5.70381	−	1.45351i	0.252322	−	0.0642995i
$512$	8.80431	−	20.8443i	0.389099	−	0.921196i
$513$	−2.21399	−	3.83475i	−0.0977503	−	0.169308i
$514$	−12.0261	−	2.67587i	−0.530447	−	0.118027i
$515$	7.89298	+	10.2863i	0.347806	+	0.453270i
$516$	17.0991	+	8.00562i	0.752744	+	0.352428i
$517$	7.77704	−	3.22135i	0.342034	−	0.141675i
$518$	1.29843	−	0.211514i	0.0570498	−	0.00929339i
$519$	20.5387	−	20.5387i	0.901551	−	0.901551i
$520$	−3.78715	+	28.2599i	−0.166078	+	1.23928i
$521$	−3.74368	+	1.00312i	−0.164014	+	0.0439473i	−0.339891	−	0.940465i	$-0.610390\pi$
$521$	−3.74368	+	1.00312i	−0.164014	+	0.0439473i	0.175878	+	0.984412i	$0.443724\pi$
$522$	−5.21903	+	0.916098i	−0.228431	+	0.0400965i
$523$	−20.8017	+	27.1092i	−0.909593	+	1.18540i	0.0725685	+	0.997363i	$0.476880\pi$
$523$	−20.8017	+	27.1092i	−0.909593	+	1.18540i	−0.982161	+	0.188041i	$0.939786\pi$
$524$	−3.07176	−	13.9579i	−0.134190	−	0.609752i
$525$	15.8590	−	20.1507i	0.692145	−	0.879448i
$526$	19.5500	+	10.1963i	0.852421	+	0.444580i
$527$	−33.3283	+	19.2421i	−1.45180	+	0.838200i
$528$	11.9192	+	14.2943i	0.518718	+	0.622078i
$529$	−13.2509	−	7.65043i	−0.576128	−	0.332627i
$530$	−23.4536	+	1.00585i	−1.01876	+	0.0436913i
$531$	−34.3569	−	14.2311i	−1.49096	−	0.617577i
$532$	39.6528	−	8.21741i	1.71917	−	0.356270i
$533$	−5.59047	−	13.4966i	−0.242150	−	0.584602i
$534$	14.3270	+	5.22713i	0.619988	+	0.226200i
$535$	35.1648	−	9.42237i	1.52030	−	0.407364i
$536$	0.0360741	−	15.5614i	0.00155816	−	0.672151i
$537$	−19.0057	−	5.09257i	−0.820158	−	0.219761i
$538$	2.10460	−	23.8435i	0.0907357	−	1.02796i
$539$	−13.4086	−	2.10143i	−0.577551	−	0.0905149i
$540$	0.609432	−	3.42530i	0.0262258	−	0.147401i
$541$	−26.9919	+	3.55355i	−1.16047	+	0.152779i	−0.686074	−	0.727531i	$-0.740668\pi$
$541$	−26.9919	+	3.55355i	−1.16047	+	0.152779i	−0.474398	+	0.880310i	$0.657334\pi$
$542$	0.825286	−	3.70906i	0.0354491	−	0.159318i
$543$	−16.1114	+	27.9057i	−0.691404	+	1.19755i
$544$	−29.3783	+	15.1494i	−1.25958	+	0.649525i
$545$	−35.8413			−1.53527
$546$	26.5217	+	14.2493i	1.13502	+	0.609813i
$547$	−14.4444	+	34.8719i	−0.617598	+	1.49101i	0.236887	+	0.971537i	$0.423873\pi$
$547$	−14.4444	+	34.8719i	−0.617598	+	1.49101i	−0.854485	+	0.519476i	$0.826127\pi$
$548$	2.29756	+	6.34297i	0.0981468	+	0.270958i
$549$	0.0901426	−	0.684701i	0.00384719	−	0.0292223i
$550$	−9.06669	−	6.35901i	−0.386605	−	0.271149i
$551$	10.0392	+	2.68999i	0.427684	+	0.114598i
$552$	−40.5501	−	10.9662i	−1.72593	−	0.466751i
$553$	14.9609	−	8.39446i	0.636202	−	0.356969i
$554$	−28.5429	+	23.9127i	−1.21267	+	1.01596i
$555$	1.54423	−	2.01248i	0.0655491	−	0.0854252i
$556$	−4.10751	+	2.13018i	−0.174197	+	0.0903395i
$557$	25.9786	−	19.9340i	1.10075	−	0.844633i	0.111922	−	0.993717i	$-0.464299\pi$
$557$	25.9786	−	19.9340i	1.10075	−	0.844633i	0.988824	+	0.149084i	$0.0476326\pi$
$558$	−25.6732	+	1.10104i	−1.08683	+	0.0466108i
$559$		−	13.1901i		−	0.557880i
$560$	27.9932	+	15.1236i	1.18293	+	0.639090i
$561$		−	27.1881i		−	1.14788i
$562$	0.888098	+	20.7080i	0.0374621	+	0.873513i
$563$	−4.16080	+	3.19269i	−0.175357	+	0.134556i	−0.692711	−	0.721216i	$-0.743584\pi$
$563$	−4.16080	+	3.19269i	−0.175357	+	0.134556i	0.517354	+	0.855772i	$0.326917\pi$
$564$	−6.29662	+	19.8632i	−0.265135	+	0.836393i
$565$	13.4925	−	17.5837i	0.567633	−	0.739753i
$566$	−14.6551	−	17.4926i	−0.615998	−	0.735271i
$567$	−21.9871	−	13.0568i	−0.923370	−	0.548334i
$568$	8.93485	−	1.15523i	0.374898	−	0.0484724i
$569$	−3.55406	−	0.952308i	−0.148994	−	0.0399228i	0.183551	−	0.983010i	$-0.441241\pi$
$569$	−3.55406	−	0.952308i	−0.148994	−	0.0399228i	−0.332545	+	0.943087i	$0.607907\pi$
$570$	44.8368	−	63.9284i	1.87801	−	2.67767i
$571$	−1.50399	+	11.4239i	−0.0629399	+	0.478076i	0.930727	+	0.365714i	$0.119175\pi$
$571$	−1.50399	+	11.4239i	−0.0629399	+	0.478076i	−0.993667	+	0.112362i	$0.964158\pi$
$572$	5.51324	−	11.7756i	0.230520	−	0.492364i
$573$	−12.7656	+	30.8190i	−0.533292	+	1.28748i
$574$	−16.2942	+	0.498460i	−0.680107	+	0.0208053i
$575$	24.9950			1.04236
$576$	−22.0709	−	0.102329i	−0.919621	−	0.00426371i
$577$	−18.3845	+	31.8429i	−0.765358	+	1.32564i	0.174700	+	0.984622i	$0.444105\pi$
$577$	−18.3845	+	31.8429i	−0.765358	+	1.32564i	−0.940057	+	0.341017i	$0.889229\pi$
$578$	23.6656	+	5.26573i	0.984360	+	0.219026i
$579$	7.67801	−	1.01083i	0.319087	−	0.0420086i
$580$	4.67353	+	6.69650i	0.194058	+	0.278057i
$581$	28.3025	+	12.1325i	1.17418	+	0.503342i
$582$	28.0733	+	2.47796i	1.16368	+	0.102715i
$583$	10.3404	+	2.77071i	0.428256	+	0.114751i
$584$	5.80792	+	2.42151i	0.240333	+	0.100203i
$585$	26.8639	−	7.19816i	1.11069	−	0.297607i
$586$	−7.58961	+	20.8023i	−0.313524	+	0.859333i
$587$	−11.3171	−	27.3220i	−0.467108	−	1.12770i	−0.965420	−	0.260701i	$-0.916046\pi$
$587$	−11.3171	−	27.3220i	−0.467108	−	1.12770i	0.498311	−	0.866998i	$-0.333954\pi$
$588$	25.3541	−	22.0434i	1.04559	−	0.909055i
$589$	46.5662	+	19.2883i	1.91873	+	0.794762i
$590$	2.45560	+	57.2578i	0.101096	+	2.35727i
$591$	−39.8769	−	23.0229i	−1.64032	−	0.947037i
$592$	1.24546	+	0.653245i	0.0511880	+	0.0268482i
$593$	−3.60855	+	2.08339i	−0.148185	+	0.0855548i	−0.572259	−	0.820073i	$-0.693933\pi$
$593$	−3.60855	+	2.08339i	−0.148185	+	0.0855548i	0.424074	+	0.905627i	$0.360600\pi$
$594$	−0.733672	+	1.40672i	−0.0301029	+	0.0577182i
$595$	−17.2581	−	43.1561i	−0.707515	−	1.76923i
$596$	−1.38512	−	0.885434i	−0.0567369	−	0.0362688i
$597$	9.23854	−	12.0399i	0.378108	−	0.492760i
$598$	5.07362	+	28.9045i	0.207476	+	1.18199i
$599$	−15.7535	+	4.22113i	−0.643669	+	0.172471i	−0.565865	−	0.824498i	$-0.691458\pi$
$599$	−15.7535	+	4.22113i	−0.643669	+	0.172471i	−0.0778041	+	0.996969i	$0.524791\pi$
$600$	26.4957	−	7.03371i	1.08168	−	0.287150i
$601$	−22.2825	+	22.2825i	−0.908921	+	0.908921i	−0.996185	−	0.0872643i	$-0.972188\pi$
$601$	−22.2825	+	22.2825i	−0.908921	+	0.908921i	0.0872643	+	0.996185i	$0.472188\pi$
$602$	−13.7643	−	5.21424i	−0.560993	−	0.212516i
$603$	−14.0235	+	5.80871i	−0.571079	+	0.236549i
$604$	−2.82490	−	7.79883i	−0.114943	−	0.317330i
$605$	−13.2520	−	17.2703i	−0.538768	−	0.702137i
$606$	13.9249	−	62.5821i	0.565659	−	2.54222i
$607$	−8.75521	−	15.1645i	−0.355363	−	0.615507i	0.631817	−	0.775118i	$-0.282309\pi$
$607$	−8.75521	−	15.1645i	−0.355363	−	0.615507i	−0.987180	+	0.159611i	$0.948976\pi$
$608$	39.1642	+	18.4471i	1.58832	+	0.748130i
$609$	8.35576	−	2.12931i	0.338592	−	0.0862839i
$610$	−1.01530	+	0.319259i	−0.0411081	+	0.0129264i
$611$	14.4327	−	1.90010i	0.583885	−	0.0768699i
$612$	24.6665	+	20.7627i	0.997085	+	0.839283i
$613$	−5.59493	+	42.4977i	−0.225977	+	1.71647i	0.383396	+	0.923584i	$0.374755\pi$
$613$	−5.59493	+	42.4977i	−0.225977	+	1.71647i	−0.609373	+	0.792884i	$0.708579\pi$
$614$	17.0062	−	7.91414i	0.686316	−	0.319389i
$615$	−22.2270	+	22.2270i	−0.896281	+	0.896281i
$616$	−10.1089	−	10.4084i	−0.407297	−	0.419365i
$617$	18.6358	+	18.6358i	0.750248	+	0.750248i	0.974525	−	0.224277i	$-0.0720021\pi$
$617$	18.6358	+	18.6358i	0.750248	+	0.750248i	−0.224277	+	0.974525i	$0.572002\pi$
$618$	13.7495	+	5.01645i	0.553086	+	0.201791i
$619$	0.605111	+	0.0796643i	0.0243214	+	0.00320198i	0.142677	−	0.989769i	$-0.454429\pi$
$619$	0.605111	+	0.0796643i	0.0243214	+	0.00320198i	−0.118356	+	0.992971i	$0.537762\pi$
$620$	18.2317	+	35.1554i	0.732204	+	1.41187i
$621$	−0.467394	−	3.55021i	−0.0187559	−	0.142465i
$622$	11.3357	−	21.7346i	0.454519	−	0.871478i
$623$	−11.4455	−	3.21795i	−0.458554	−	0.128924i
$624$	13.5121	+	29.2122i	0.540918	+	1.16943i
$625$	25.0127	−	14.4411i	1.00051	−	0.577644i
$626$	−34.5472	+	21.9715i	−1.38078	+	0.878157i
$627$	−28.2499	+	21.6769i	−1.12819	+	0.865693i
$628$	12.6017	−	11.5116i	0.502864	−	0.459362i
$629$	−0.786203	−	1.89806i	−0.0313480	−	0.0756807i
$630$	3.10816	−	30.8791i	0.123832	−	1.23025i
$631$	14.5492	+	14.5492i	0.579193	+	0.579193i	0.934681	−	0.355488i	$-0.115685\pi$
$631$	14.5492	+	14.5492i	0.579193	+	0.579193i	−0.355488	+	0.934681i	$0.615685\pi$
$632$	18.1770	+	2.43593i	0.723043	+	0.0968961i
$633$	−5.63053	−	21.0134i	−0.223794	−	0.835209i
$634$	−10.9311	+	15.5856i	−0.434131	+	0.618985i
$635$	45.4473	+	34.8729i	1.80352	+	1.38389i
$636$	−21.7306	+	15.1659i	−0.861675	+	0.601369i
$637$	−21.4574	−	9.51178i	−0.850174	−	0.376870i
$638$	−1.11706	−	3.55243i	−0.0442248	−	0.140642i
$639$	−4.39387	−	7.61041i	−0.173819	−	0.301063i
$640$	14.2080	+	30.9046i	0.561622	+	1.22161i
$641$	4.03070	−	6.98137i	0.159203	−	0.275748i	−0.775379	−	0.631497i	$-0.782441\pi$
$641$	4.03070	−	6.98137i	0.159203	−	0.275748i	0.934581	+	0.355749i	$0.115774\pi$
$642$	27.7871	−	30.2773i	1.09667	−	1.19495i
$643$	−10.4766	+	25.2927i	−0.413156	+	0.997446i	0.571129	+	0.820860i	$0.306505\pi$
$643$	−10.4766	+	25.2927i	−0.413156	+	0.997446i	−0.984285	+	0.176586i	$0.943495\pi$
$644$	32.1687	+	6.13189i	1.26762	+	0.241630i
$645$	−26.2210	+	10.8611i	−1.03245	+	0.427656i
$646$	−26.6822	−	57.3357i	−1.04980	−	2.25584i
$647$	6.34141	+	23.6664i	0.249306	+	0.930424i	0.971170	+	0.238389i	$0.0766192\pi$
$647$	6.34141	+	23.6664i	0.249306	+	0.930424i	−0.721863	+	0.692035i	$0.756714\pi$
$648$	−10.4030	−	25.2805i	−0.408667	−	0.993114i
$649$	6.76419	−	25.2443i	0.265518	−	0.990926i
$650$	−12.2989	−	14.6803i	−0.482404	−	0.575809i
$651$	41.5227	−	4.94869i	1.62740	−	0.193954i
$652$	2.83699	+	12.8911i	0.111105	+	0.504854i
$653$	−1.74866	−	13.2824i	−0.0684303	−	0.519780i	−0.990991	−	0.133928i	$-0.957241\pi$
$653$	−1.74866	−	13.2824i	−0.0684303	−	0.519780i	0.922561	−	0.385852i	$-0.126092\pi$
$654$	−34.1394	+	21.7121i	−1.33496	+	0.849012i
$655$	18.6056	+	10.7420i	0.726982	+	0.419723i
$656$	−14.2447	−	10.0400i	−0.556163	−	0.391997i
$657$		−	6.13781i		−	0.239459i
$658$	3.72264	−	15.8122i	0.145124	−	0.616425i
$659$	−18.8514	−	7.80851i	−0.734347	−	0.304176i	−0.0160098	−	0.999872i	$-0.505096\pi$
$659$	−18.8514	−	7.80851i	−0.734347	−	0.304176i	−0.718337	+	0.695696i	$0.755096\pi$
$660$	−27.9490	−	1.26356i	−1.08791	−	0.0491840i
$661$	17.2530	+	2.27140i	0.671063	+	0.0883471i	0.458356	−	0.888769i	$-0.348439\pi$
$661$	17.2530	+	2.27140i	0.671063	+	0.0883471i	0.212707	+	0.977116i	$0.431772\pi$
$662$	−5.11432	−	29.1364i	−0.198774	−	1.13242i
$663$	12.1690	−	45.4153i	0.472605	−	1.76379i
$664$	16.3936	+	28.5472i	0.636195	+	1.10784i
$665$	−31.0818	+	52.3404i	−1.20530	+	2.02967i
$666$	0.120616	−	1.36649i	0.00467379	−	0.0529504i
$667$	6.66808	+	5.11659i	0.258189	+	0.198115i
$668$	−31.8096	−	26.7753i	−1.23075	−	1.03597i
$669$	1.16624	+	1.51987i	0.0450893	+	0.0587616i
$670$	17.2345	+	15.8170i	0.665826	+	0.611064i
$671$	0.485348			0.0187367
$672$	35.8256	−	2.55237i	1.38200	−	0.0984598i
$673$	−15.5979			−0.601255			−0.300628	−	0.953742i	$-0.597196\pi$
$673$	−15.5979			−0.601255			−0.300628	+	0.953742i	$0.597196\pi$
$674$	−33.9981	−	31.2019i	−1.30956	−	1.20185i
$675$	1.42258	+	1.85394i	0.0547552	+	0.0713583i
$676$	−2.26324	+	2.68877i	−0.0870477	+	0.103414i
$677$	10.8073	+	8.29270i	0.415357	+	0.318714i	0.795212	−	0.606331i	$-0.207360\pi$
$677$	10.8073	+	8.29270i	0.415357	+	0.318714i	−0.379855	+	0.925046i	$0.624026\pi$
$678$	2.19983	−	24.9224i	0.0844840	−	0.957138i
$679$	−21.9690	−	0.269768i	−0.843094	−	0.0103527i
$680$	12.9715	−	47.9651i	0.497433	−	1.83938i
$681$	6.39132	−	23.8527i	0.244916	−	0.914039i
$682$	−3.12222	−	17.7873i	−0.119556	−	0.681112i
$683$	−15.7751	−	2.07684i	−0.603619	−	0.0794679i	−0.177478	−	0.984125i	$-0.556794\pi$
$683$	−15.7751	−	2.07684i	−0.603619	−	0.0794679i	−0.426141	+	0.904657i	$0.640127\pi$
$684$	1.90711	−	42.1839i	0.0729202	−	1.61294i
$685$	−9.36922	−	3.88086i	−0.357979	−	0.148280i
$686$	−18.4084	+	18.6315i	−0.702834	+	0.711354i
$687$			16.4245i			0.626634i
$688$	−8.41343	−	13.2970i	−0.320759	−	0.506942i
$689$	16.0327	+	9.25646i	0.610796	+	0.352643i
$690$	53.2827	−	33.8870i	2.02844	−	1.29005i
$691$	5.42552	+	41.2109i	0.206397	+	1.56774i	0.710251	+	0.703949i	$0.248581\pi$
$691$	5.42552	+	41.2109i	0.206397	+	1.56774i	−0.503854	+	0.863789i	$0.668085\pi$
$692$	−23.6417	+	5.20292i	−0.898724	+	0.197786i
$693$	−5.57614	+	13.0079i	−0.211820	+	0.494130i
$694$	1.29108	+	1.54106i	0.0490085	+	0.0584979i
$695$	1.80021	−	6.71846i	0.0682857	−	0.254846i
$696$	8.50827	+	3.54737i	0.322505	+	0.134463i
$697$	6.58904	+	24.5906i	0.249578	+	0.931436i
$698$	3.78784	+	8.13946i	0.143372	+	0.308083i
$699$	47.6915	−	19.7545i	1.80386	−	0.747182i
$700$	−20.1814	+	7.03105i	−0.762786	+	0.265749i
$701$	4.30717	−	10.3984i	0.162680	−	0.392744i	−0.821429	−	0.570311i	$-0.806823\pi$
$701$	4.30717	−	10.3984i	0.162680	−	0.392744i	0.984109	+	0.177567i	$0.0568228\pi$
$702$	−1.85516	+	2.02142i	−0.0700186	+	0.0762934i
$703$	−1.34536	+	2.33022i	−0.0507411	+	0.0878861i
$704$	−1.95330	−	15.3877i	−0.0736177	−	0.579947i
$705$	−15.6616	−	27.1267i	−0.589851	−	1.02165i
$706$	−10.1776	−	32.3666i	−0.383041	−	1.21813i
$707$	−7.13183	+	49.4699i	−0.268220	+	1.86051i
$708$	37.0250	+	53.0514i	1.39148	+	1.99379i
$709$	−8.06618	−	6.18940i	−0.302932	−	0.232448i	0.446098	−	0.894984i	$-0.352813\pi$
$709$	−8.06618	−	6.18940i	−0.302932	−	0.232448i	−0.749030	+	0.662536i	$0.769480\pi$
$710$	−7.77646	+	11.0877i	−0.291846	+	0.416114i
$711$	−4.62992	−	17.2791i	−0.173636	−	0.648017i
$712$	−7.71406	−	10.1016i	−0.289097	−	0.378572i
$713$	28.8217	+	28.8217i	1.07938	+	1.07938i
$714$	−42.5821	−	30.6522i	−1.59359	−	1.14713i
$715$	7.47974	+	18.0577i	0.279726	+	0.675319i
$716$	11.0599	+	12.1073i	0.413328	+	0.452470i
$717$	−4.43281	+	3.40142i	−0.165546	+	0.127028i
$718$	−5.18099	+	3.29503i	−0.193353	+	0.122969i
$719$	12.0147	−	6.93668i	0.448072	−	0.258695i	−0.258943	−	0.965892i	$-0.583374\pi$
$719$	12.0147	−	6.93668i	0.448072	−	0.258695i	0.707016	+	0.707198i	$0.250041\pi$
$720$	22.4902	−	24.3919i	0.838160	−	0.909034i
$721$	−10.9842	−	3.08824i	−0.409072	−	0.115012i
$722$	−25.8758	+	49.6134i	−0.962999	+	1.84642i
$723$	6.85003	+	52.0311i	0.254755	+	1.93506i
$724$	23.8397	−	12.3634i	0.885994	−	0.459480i
$725$	−5.43810	−	0.715939i	−0.201966	−	0.0265893i
$726$	−23.0848	−	8.42239i	−0.856757	−	0.312584i
$727$	1.75167	+	1.75167i	0.0649657	+	0.0649657i	0.738843	−	0.673877i	$-0.235372\pi$
$727$	1.75167	+	1.75167i	0.0649657	+	0.0649657i	−0.673877	+	0.738843i	$0.735372\pi$
$728$	−12.2273	−	21.9109i	−0.453175	−	0.812071i
$729$	−15.9097	+	15.9097i	−0.589247	+	0.589247i
$730$	−8.57591	+	3.99095i	−0.317409	+	0.147712i
$731$	−3.00028	+	22.7894i	−0.110969	+	0.842895i
$732$	−0.773684	+	0.919152i	−0.0285962	+	0.0339728i
$733$	−37.8903	+	4.98836i	−1.39951	+	0.184249i	−0.792223	−	0.610232i	$-0.791076\pi$
$733$	−37.8903	+	4.98836i	−1.39951	+	0.184249i	−0.607288	+	0.794481i	$0.707743\pi$
$734$	−3.22598	+	1.01441i	−0.119073	+	0.0374425i
$735$	−1.24013	+	50.4883i	−0.0457427	+	1.86229i
$736$	23.5518	+	25.9025i	0.868131	+	0.954779i
$737$	−5.33373	−	9.23829i	−0.196470	−	0.340297i
$738$	−3.69207	+	16.5932i	−0.135907	+	0.610803i
$739$	−24.7104	−	32.2032i	−0.908988	−	1.18462i	−0.982301	−	0.187307i	$-0.940024\pi$
$739$	−24.7104	−	32.2032i	−0.908988	−	1.18462i	0.0733140	−	0.997309i	$-0.476642\pi$
$740$	−1.98772	+	0.719995i	−0.0730702	+	0.0264675i
$741$	−56.8914	+	23.5652i	−2.08996	+	0.865688i
$742$	15.9974	−	13.0715i	0.587284	−	0.479869i
$743$	33.7661	−	33.7661i	1.23876	−	1.23876i	0.278247	−	0.960510i	$-0.410247\pi$
$743$	33.7661	−	33.7661i	1.23876	−	1.23876i	0.960510	−	0.278247i	$-0.0897533\pi$
$744$	38.6627	+	22.4416i	1.41744	+	0.822748i
$745$	2.38702	−	0.639600i	0.0874537	−	0.0234331i
$746$	−8.94978	−	50.9871i	−0.327675	−	1.86677i
$747$	19.5474	−	25.4747i	0.715203	−	0.932070i
$748$	−12.2041	+	19.0915i	−0.446228	+	0.698054i
$749$	−19.8138	+	25.1756i	−0.723980	+	0.919898i
$750$	4.53542	−	8.69605i	0.165610	−	0.317535i
$751$	4.67779	−	2.70073i	0.170695	−	0.0985509i	−0.412218	−	0.911085i	$-0.635246\pi$
$751$	4.67779	−	2.70073i	0.170695	−	0.0985509i	0.582914	+	0.812534i	$0.301913\pi$
$752$	13.3377	−	11.1216i	0.486375	−	0.405562i
$753$	−36.3065	−	20.9616i	−1.32308	−	0.763882i
$754$	−0.275934	−	6.43401i	−0.0100489	−	0.234313i
$755$	11.5197	+	4.77160i	0.419243	+	0.173656i
$756$	1.37605	+	2.73503i	0.0500465	+	0.0994721i
$757$	−9.64375	−	23.2821i	−0.350508	−	0.846201i	−0.996557	−	0.0829054i	$-0.973580\pi$
$757$	−9.64375	−	23.2821i	−0.350508	−	0.846201i	0.646050	−	0.763295i	$-0.276420\pi$
$758$	2.86420	−	7.85045i	0.104032	−	0.285141i
$759$	−27.8146	+	7.45291i	−1.00961	+	0.270523i
$760$	−60.1805	+	24.7643i	−2.18298	+	0.898295i
$761$	49.0082	+	13.1317i	1.77654	+	0.476024i	0.989947	−	0.141442i	$-0.0451739\pi$
$761$	49.0082	+	13.1317i	1.77654	+	0.476024i	0.786598	+	0.617466i	$0.211841\pi$
$762$	64.4148	+	5.68572i	2.33350	+	0.205972i
$763$	25.2572	−	18.8924i	0.914371	−	0.683949i
$764$	22.7980	−	15.9109i	0.824804	−	0.575636i
$765$	−48.0519	+	6.32616i	−1.73732	+	0.228723i
$766$	43.9102	+	9.77027i	1.58654	+	0.353014i
$767$	22.5980	−	39.1409i	0.815967	−	1.41330i
$768$	32.2550	+	20.8301i	1.16390	+	0.751642i
$769$	43.1639			1.55653			0.778266	−	0.627935i	$-0.216100\pi$
$769$	43.1639			1.55653			0.778266	+	0.627935i	$0.216100\pi$
$770$	21.8007	−	0.666911i	0.785644	−	0.0240338i
$771$	8.00038	−	19.3146i	0.288127	−	0.695600i
$772$	−5.84525	−	2.73669i	−0.210375	−	0.0984956i
$773$	4.26653	−	32.4075i	0.153456	−	1.16562i	−0.725330	−	0.688401i	$-0.758313\pi$
$773$	4.26653	−	32.4075i	0.153456	−	1.16562i	0.878787	−	0.477215i	$-0.158354\pi$
$774$	−8.81314	+	12.5658i	−0.316782	+	0.451668i
$775$	−25.6934	−	6.88454i	−0.922936	−	0.247300i
$776$	−18.6008	−	14.3415i	−0.667730	−	0.514831i
$777$	−0.0274098	+	2.23217i	−0.000983323	+	0.0800787i
$778$	11.9701	+	14.2878i	0.429150	+	0.512244i
$779$	20.2976	−	26.4524i	0.727237	−	0.947754i
$780$	−46.1209	−	14.6203i	−1.65139	−	0.523489i
$781$	4.89965	−	3.75963i	0.175323	−	0.134530i
$782$	−2.19127	−	51.0944i	−0.0783598	−	1.82713i
$783$			0.785798i			0.0280821i
$784$	−27.6985	+	4.09799i	−0.989232	+	0.146357i
$785$			25.6573i			0.915747i
$786$	24.2295	−	1.03912i	0.864237	−	0.0370644i
$787$	10.2607	−	7.87329i	0.365754	−	0.280653i	−0.409491	−	0.912314i	$-0.634294\pi$
$787$	10.2607	−	7.87329i	0.365754	−	0.280653i	0.775244	+	0.631662i	$0.217627\pi$
$788$	17.6671	+	34.0666i	0.629364	+	1.21357i
$789$	−22.7769	+	29.6834i	−0.810879	+	1.05676i
$790$	−21.1323	+	17.7043i	−0.751855	+	0.629892i
$791$	−0.239489	+	19.5032i	−0.00851524	+	0.693455i
$792$	−13.1204	+	7.53454i	−0.466212	+	0.267728i
$793$	0.810733	+	0.217235i	0.0287900	+	0.00771425i
$794$	13.0446	+	9.14899i	0.462937	+	0.324685i
$795$	5.19949	−	39.4940i	0.184407	−	1.40071i
$796$	−11.8918	+	4.30745i	−0.421492	+	0.152673i
$797$	5.45864	−	13.1783i	0.193355	−	0.466801i	−0.797234	−	0.603671i	$-0.793704\pi$
$797$	5.45864	−	13.1783i	0.193355	−	0.466801i	0.990589	+	0.136870i	$0.0437043\pi$
$798$	2.10113	+	68.6840i	0.0743791	+	2.43139i
$799$	−25.3686			−0.897476
$800$	−21.7626	−	6.95427i	−0.769424	−	0.245871i
$801$	−6.19885	+	10.7367i	−0.219025	+	0.379363i
$802$	3.90651	−	17.5569i	0.137944	−	0.619956i
$803$	4.27664	−	0.563031i	0.150919	−	0.0198689i
$804$	25.9978	+	4.62556i	0.916873	+	0.163131i
$805$	−39.4198	+	29.4860i	−1.38937	+	1.03925i
$806$	2.74597	−	31.1097i	0.0967227	−	1.09579i
$807$	39.2331	+	10.5125i	1.38107	+	0.370057i
$808$	−37.8698	+	37.6946i	−1.33226	+	1.32609i
$809$	−11.6349	+	3.11756i	−0.409061	+	0.109608i	−0.457481	−	0.889219i	$-0.651248\pi$
$809$	−11.6349	+	3.11756i	−0.409061	+	0.109608i	0.0484197	+	0.998827i	$0.484582\pi$
$810$	38.6050	+	14.0849i	1.35644	+	0.494892i
$811$	2.64598	+	6.38796i	0.0929129	+	0.224312i	0.963503	−	0.267697i	$-0.0862627\pi$
$811$	2.64598	+	6.38796i	0.0929129	+	0.224312i	−0.870590	+	0.492009i	$0.836263\pi$
$812$	−6.82322	−	2.25552i	−0.239448	−	0.0791531i
$813$	5.95698	+	2.46746i	0.208921	+	0.0865377i
$814$	0.963194	−	0.0413083i	0.0337599	−	0.00144785i
$815$	−17.1836	−	9.92097i	−0.601916	−	0.347517i
$816$	−16.7011	−	53.5455i	−0.584654	−	1.87447i
$817$	26.0715	−	15.0524i	0.912128	−	0.526617i
$818$	31.3848	+	16.3687i	1.09735	+	0.572320i
$819$	−15.1366	+	19.2328i	−0.528917	+	0.672048i
$820$	25.5851	−	5.63061i	0.893470	−	0.196629i
$821$	−6.86083	+	8.94120i	−0.239444	+	0.312050i	−0.897582	−	0.440848i	$-0.854678\pi$
$821$	−6.86083	+	8.94120i	−0.239444	+	0.312050i	0.658137	+	0.752898i	$0.271345\pi$
$822$	−11.2753	+	1.97916i	−0.393272	+	0.0690311i
$823$	39.0017	−	10.4505i	1.35952	−	0.364281i	0.495877	−	0.868393i	$-0.334847\pi$
$823$	39.0017	−	10.4505i	1.35952	−	0.364281i	0.863638	+	0.504112i	$0.168180\pi$
$824$	−7.40314	−	9.69441i	−0.257901	−	0.337721i
$825$	13.2880	−	13.2880i	0.462628	−	0.462628i
$826$	−31.9117	−	39.0549i	−1.11035	−	1.35889i
$827$	−1.02367	+	0.424018i	−0.0355965	+	0.0147445i	−0.400411	−	0.916336i	$-0.631133\pi$
$827$	−1.02367	+	0.424018i	−0.0355965	+	0.0147445i	0.364814	+	0.931080i	$0.381133\pi$
$828$	14.4795	−	30.9265i	0.503198	−	1.07477i
$829$	0.530532	+	0.691402i	0.0184261	+	0.0240134i	0.802476	−	0.596685i	$-0.203516\pi$
$829$	0.530532	+	0.691402i	0.0184261	+	0.0240134i	−0.784049	+	0.620698i	$0.786849\pi$
$830$	−48.3041	−	10.7479i	−1.67666	−	0.373066i
$831$	−31.5927	−	54.7202i	−1.09594	−	1.89822i
$832$	3.62452	−	26.5782i	0.125658	−	0.921432i
$833$	34.9098	+	21.3150i	1.20955	+	0.738519i
$834$	−2.35522	−	7.48999i	−0.0815547	−	0.259357i
$835$	61.9671	−	8.15812i	2.14446	−	0.282323i
$836$	29.5674	−	2.54078i	1.02261	−	0.0878746i
$837$	−0.497403	+	3.77815i	−0.0171928	+	0.130592i
$838$	13.2034	+	28.3719i	0.456102	+	0.980091i
$839$	−32.0111	+	32.0111i	−1.10515	+	1.10515i	−0.111367	+	0.993779i	$0.535523\pi$
$839$	−32.0111	+	32.0111i	−1.10515	+	1.10515i	−0.993779	+	0.111367i	$0.964477\pi$
$840$	−33.4891	+	42.3493i	−1.15548	+	1.46119i
$841$	19.2019	+	19.2019i	0.662134	+	0.662134i
$842$	4.30730	−	11.8058i	0.148440	−	0.406856i
$843$	−34.8706	−	4.59080i	−1.20101	−	0.158116i
$844$	−5.47871	+	17.2831i	−0.188585	+	0.594908i
$845$	−0.689583	−	5.23790i	−0.0237224	−	0.180189i
$846$	−15.0192	−	7.83326i	−0.516371	−	0.269313i
$847$	18.4420	+	5.18502i	0.633673	+	0.178160i
$848$	22.0669	−	0.895135i	0.757781	−	0.0307391i
$849$	33.5355	−	19.3617i	1.15094	−	0.664493i
$850$	17.9104	+	28.1617i	0.614323	+	0.965940i
$851$	−1.72629	+	1.32463i	−0.0591763	+	0.0454076i
$852$	−0.690443	+	15.2721i	−0.0236542	+	0.523213i
$853$	−6.53849	−	15.7853i	−0.223874	−	0.540479i	0.771536	−	0.636186i	$-0.219489\pi$
$853$	−6.53849	−	15.7853i	−0.223874	−	0.540479i	−0.995410	+	0.0957069i	$0.969489\pi$
$854$	0.547189	−	0.760155i	0.0187244	−	0.0260120i
$855$	44.8848	+	44.8848i	1.53503	+	1.53503i
$856$	−33.1029	+	8.78771i	−1.13144	+	0.300358i
$857$	−10.1455	−	37.8634i	−0.346563	−	1.29339i	−0.890776	−	0.454443i	$-0.849838\pi$
$857$	−10.1455	−	37.8634i	−0.346563	−	1.29339i	0.544213	−	0.838947i	$-0.316828\pi$
$858$	18.0637	+	12.6691i	0.616683	+	0.432517i
$859$	42.5354	+	32.6386i	1.45129	+	1.11361i	0.971728	+	0.236105i	$0.0758708\pi$
$859$	42.5354	+	32.6386i	1.45129	+	1.11361i	0.479561	+	0.877509i	$0.340796\pi$
$860$	23.2878	+	4.14338i	0.794106	+	0.141288i
$861$	3.94715	−	27.3794i	0.134519	−	0.933088i
$862$	8.55836	−	2.69117i	0.291499	−	0.0916617i
$863$	−4.92802	−	8.53559i	−0.167752	−	0.290555i	0.769877	−	0.638192i	$-0.220317\pi$
$863$	−4.92802	−	8.53559i	−0.167752	−	0.290555i	−0.937629	+	0.347637i	$0.886984\pi$
$864$	−0.580813	+	3.22113i	−0.0197597	+	0.109585i
$865$	18.1947	−	31.5141i	0.618637	−	1.07151i
$866$	−0.00151061	−	0.00138637i	−5.13328e−5	−	4.71108e-5i
$867$	−15.7436	+	38.0085i	−0.534682	+	1.29084i
$868$	−31.3786	−	15.1637i	−1.06506	−	0.514689i
$869$	11.6149	−	4.81103i	0.394007	−	0.163203i
$870$	−12.5632	+	5.84651i	−0.425933	+	0.198215i
$871$	−4.77461	−	17.8191i	−0.161781	−	0.603776i
$872$	33.7189	+	0.0781662i	1.14186	+	0.00264704i
$873$	−5.92960	+	22.1296i	−0.200687	+	0.748972i
$874$	−51.3428	+	43.0142i	−1.73670	+	1.45498i
$875$	−3.01250	+	7.02750i	−0.101841	+	0.237573i
$876$	−5.75104	+	8.99661i	−0.194310	+	0.303967i
$877$	−2.43028	−	18.4598i	−0.0820647	−	0.623344i	−0.982214	−	0.187763i	$-0.939876\pi$
$877$	−2.43028	−	18.4598i	−0.0820647	−	0.623344i	0.900150	−	0.435581i	$-0.143457\pi$
$878$	−12.6659	−	19.9155i	−0.427455	−	0.672115i
$879$	−32.5411	−	18.7876i	−1.09758	−	0.633690i
$880$	19.0586	+	13.4330i	0.642467	+	0.452826i
$881$			19.1142i			0.643974i	0.946744	+	0.321987i	$0.104351\pi$
$881$			19.1142i			0.643974i	−0.946744	+	0.321987i	$0.895649\pi$
$882$	14.0864	+	23.3987i	0.474314	+	0.787875i
$883$	−23.7624	−	9.84269i	−0.799667	−	0.331233i	−0.0548441	−	0.998495i	$-0.517466\pi$
$883$	−23.7624	−	9.84269i	−0.799667	−	0.331233i	−0.744823	+	0.667262i	$0.767466\pi$
$884$	−28.9311	+	26.4283i	−0.973057	+	0.888880i
$885$	−96.4176	−	12.6936i	−3.24104	−	0.426692i
$886$	−47.9317	+	8.41347i	−1.61030	+	0.282656i
$887$	7.92433	−	29.5740i	0.266073	−	0.992998i	−0.695517	−	0.718509i	$-0.744825\pi$
$887$	7.92433	−	29.5740i	0.266073	−	0.992998i	0.961590	−	0.274489i	$-0.0885087\pi$
$888$	−1.45718	+	1.88994i	−0.0488997	+	0.0634223i
$889$	−50.4084	−	0.618987i	−1.69064	−	0.0207602i
$890$	19.0323	+	1.67993i	0.637963	+	0.0563113i
$891$	−14.8673	−	11.4081i	−0.498074	−	0.382186i
$892$	−0.136696	−	1.59075i	−0.00457692	−	0.0532623i
$893$	20.2263	+	26.3594i	0.676846	+	0.882083i
$894$	1.88622	−	2.05525i	0.0630845	−	0.0687380i
$895$	−24.6505			−0.823976
$896$	−26.3025	−	14.2891i	−0.878705	−	0.477365i
$897$	−49.7978			−1.66270
$898$	−20.4909	+	22.3272i	−0.683790	+	0.745069i
$899$	−5.44511	−	7.09620i	−0.181604	−	0.236672i
$900$	1.90796	+	22.2032i	0.0635986	+	0.740107i
$901$	−25.5952	−	19.6399i	−0.852700	−	0.654299i
$902$	−11.9003	−	1.05041i	−0.396237	−	0.0349748i
$903$	12.7528	−	21.4752i	0.424387	−	0.714650i
$904$	−12.7318	+	16.5130i	−0.423455	+	0.549216i
$905$	−10.4482	+	38.9934i	−0.347311	+	1.29618i
$906$	13.8632	−	2.43342i	0.460575	−	0.0808449i
$907$	26.7458	+	3.52115i	0.888078	+	0.116918i	0.560742	−	0.827990i	$-0.310516\pi$
$907$	26.7458	+	3.52115i	0.888078	+	0.116918i	0.327336	+	0.944908i	$0.393849\pi$
$908$	−15.1950	+	13.8805i	−0.504263	+	0.460640i
$909$	48.1514	+	19.9450i	1.59708	+	0.661533i
$910$	36.7148	+	8.64369i	1.21708	+	0.286536i
$911$		−	25.3414i		−	0.839599i	−0.907617	−	0.419799i	$-0.862100\pi$
$911$		−	25.3414i		−	0.839599i	0.907617	−	0.419799i	$-0.137900\pi$
$912$	−42.3211	+	60.0449i	−1.40139	+	1.98829i
$913$	19.5431	+	11.2832i	0.646783	+	0.373420i
$914$	27.7694	+	43.6636i	0.918530	+	1.44426i
$915$	−0.235733	−	1.79057i	−0.00779308	−	0.0591943i
$916$	7.37260	−	11.5333i	0.243598	−	0.381071i
$917$	−18.7735	+	2.23743i	−0.619956	+	0.0738865i
$918$	3.66509	−	3.07055i	0.120966	−	0.101343i
$919$	−8.63055	+	32.2097i	−0.284696	+	1.06250i	0.664366	+	0.747408i	$0.268702\pi$
$919$	−8.63055	+	32.2097i	−0.284696	+	1.06250i	−0.949061	+	0.315091i	$0.897965\pi$
$920$	−52.6263	−	0.121997i	−1.73504	−	0.00402212i
$921$	8.23809	+	30.7450i	0.271454	+	1.01308i
$922$	9.68853	−	4.50873i	0.319075	−	0.148487i
$923$	9.86720	−	4.08713i	0.324783	−	0.134529i
$924$	20.3616	−	13.8418i	0.669846	−	0.455363i
$925$	0.543413	−	1.31192i	0.0178673	−	0.0431355i
$926$	−31.9305	−	29.3044i	−1.04930	−	0.963001i
$927$	−5.94900	+	10.3040i	−0.195391	+	0.338427i
$928$	−4.38217	−	6.31014i	−0.143852	−	0.207141i
$929$	−10.6709	−	18.4825i	−0.350101	−	0.606392i	0.636166	−	0.771552i	$-0.280519\pi$
$929$	−10.6709	−	18.4825i	−0.350101	−	0.606392i	−0.986267	+	0.165160i	$0.947186\pi$
$930$	−64.1053	+	20.1579i	−2.10210	+	0.661003i
$931$	−5.68603	−	53.2676i	−0.186352	−	1.74577i
$932$	−42.3564	−	7.53608i	−1.38743	−	0.246853i
$933$	33.0004	+	25.3221i	1.08038	+	0.829007i
$934$	−5.85312	−	4.10515i	−0.191520	−	0.134324i
$935$	−8.81576	−	32.9009i	−0.288306	−	1.07597i
$936$	−25.2888	+	6.71332i	−0.826590	+	0.219432i
$937$	−40.2585	−	40.2585i	−1.31519	−	1.31519i	−0.917536	−	0.397654i	$-0.869825\pi$
$937$	−40.2585	−	40.2585i	−1.31519	−	1.31519i	−0.397654	−	0.917536i	$-0.630175\pi$
$938$	−20.4824	−	2.06167i	−0.668773	−	0.0673160i
$939$	−26.5867	−	64.1859i	−0.867623	−	2.09463i
$940$	−1.17900	+	26.0786i	−0.0384547	+	0.850590i
$941$	−11.8476	+	9.09100i	−0.386222	+	0.296358i	−0.783563	−	0.621313i	$-0.786600\pi$
$941$	−11.8476	+	9.09100i	−0.386222	+	0.296358i	0.397341	+	0.917671i	$0.369933\pi$
$942$	15.5428	+	24.4390i	0.506412	+	0.796264i
$943$	23.3511	−	13.4818i	0.760417	−	0.439027i
$944$	−2.18531	−	53.8725i	−0.0711259	−	1.75340i
$945$	−4.43062	−	1.24569i	−0.144128	−	0.0405222i
$946$	−9.56391	−	4.98805i	−0.310950	−	0.162176i
$947$	0.600630	+	4.56224i	0.0195178	+	0.148253i	0.998429	−	0.0560345i	$-0.0178457\pi$
$947$	0.600630	+	4.56224i	0.0195178	+	0.148253i	−0.978911	+	0.204287i	$0.934512\pi$
$948$	−9.40388	+	29.6654i	−0.305424	+	0.963486i
$949$	7.39577	+	0.973671i	0.240077	+	0.0316067i
$950$	14.9817	−	41.0632i	0.486071	−	1.33227i
$951$	−22.8420	−	22.8420i	−0.740704	−	0.740704i
$952$	16.1420	+	40.6382i	0.523167	+	1.31709i
$953$	11.7002	−	11.7002i	0.379008	−	0.379008i	−0.491736	−	0.870744i	$-0.663638\pi$
$953$	11.7002	−	11.7002i	0.379008	−	0.379008i	0.870744	+	0.491736i	$0.163638\pi$
$954$	−9.08900	−	19.5308i	−0.294267	−	0.632333i
$955$	−5.45489	+	41.4340i	−0.176516	+	1.34077i
$956$	4.63955	−	0.398684i	0.150054	−	0.0128943i
$957$	6.26503	−	0.824807i	0.202520	−	0.0266622i
$958$	2.40010	+	7.63269i	0.0775436	+	0.246601i
$959$	8.64809	−	2.20380i	0.279261	−	0.0711645i
$960$	−55.8203	+	14.6800i	−1.80159	+	0.473794i
$961$	−6.18850	−	10.7188i	−0.199629	−	0.345767i
$962$	1.62742	+	0.362110i	0.0524702	+	0.0116749i
$963$	20.3372	+	26.5039i	0.655357	+	0.854078i
$964$	18.5456	−	39.6111i	0.597312	−	1.27579i
$965$	8.96356	−	3.71283i	0.288547	−	0.119520i
$966$	−19.6858	+	51.9659i	−0.633381	+	1.67198i
$967$	−27.6128	+	27.6128i	−0.887968	+	0.887968i	−0.994328	−	0.106360i	$-0.966080\pi$
$967$	−27.6128	+	27.6128i	−0.887968	+	0.887968i	0.106360	+	0.994328i	$0.466080\pi$
$968$	12.4295	+	16.2765i	0.399501	+	0.523146i
$969$	103.655	−	27.7744i	3.32989	−	0.892241i
$970$	34.7756	−	6.10417i	1.11658	−	0.195993i
$971$	1.48777	−	1.93890i	0.0477448	−	0.0622223i	−0.768871	−	0.639404i	$-0.779181\pi$
$971$	1.48777	−	1.93890i	0.0477448	−	0.0622223i	0.816616	+	0.577182i	$0.195848\pi$
$972$	41.9138	−	9.22414i	1.34439	−	0.295864i
$973$	2.27278	+	5.68338i	0.0728621	+	0.182201i
$974$	13.3273	+	6.95087i	0.427035	+	0.222720i
$975$	28.1439	−	16.2489i	0.901328	−	0.520382i
$976$	0.955869	−	0.298139i	0.0305966	−	0.00954320i
$977$	−9.06427	−	5.23326i	−0.289992	−	0.167427i	0.347946	−	0.937514i	$-0.386879\pi$
$977$	−9.06427	−	5.23326i	−0.289992	−	0.167427i	−0.637938	+	0.770088i	$0.720212\pi$
$978$	−22.3777	+	0.959707i	−0.715559	+	0.0306880i
$979$	−8.04966	−	3.33428i	−0.257268	−	0.106564i
$980$	23.5339	−	34.8963i	0.751764	−	1.11472i
$981$	−12.5865	−	30.3864i	−0.401855	−	0.970163i
$982$	34.4152	+	12.5562i	1.09823	+	0.400685i
$983$	52.9842	−	14.1971i	1.68993	−	0.452817i	0.719562	−	0.694428i	$-0.244343\pi$
$983$	52.9842	−	14.1971i	1.68993	−	0.452817i	0.970373	+	0.241612i	$0.0776760\pi$
$984$	20.9593	−	20.8623i	0.668157	−	0.665067i
$985$	−55.7211	−	14.9304i	−1.77542	−	0.475723i
$986$	−0.986762	+	11.1792i	−0.0314249	+	0.356020i
$987$	25.3355	+	10.8607i	0.806438	+	0.345698i
$988$	50.5271	+	8.98982i	1.60748	+	0.286004i
$989$	24.1370	−	3.17770i	0.767512	−	0.101045i
$990$	4.93978	−	22.2007i	0.156997	−	0.705585i
$991$	−16.9237	+	29.3127i	−0.537600	+	0.931150i	0.461433	+	0.887175i	$0.347335\pi$
$991$	−16.9237	+	29.3127i	−0.537600	+	0.931150i	−0.999033	+	0.0439749i	$0.985998\pi$
$992$	−17.0754	−	33.1133i	−0.542146	−	1.05135i
$993$	50.1972			1.59296
$994$	−0.364418	−	11.9125i	−0.0115586	−	0.377842i
$995$	7.27581	−	17.5653i	0.230659	−	0.556859i
$996$	−52.5214	+	19.0244i	−1.66421	+	0.602810i
$997$	1.29528	−	9.83862i	0.0410219	−	0.311592i	−0.958616	−	0.284701i	$-0.908106\pi$
$997$	1.29528	−	9.83862i	0.0410219	−	0.311592i	0.999638	−	0.0268915i	$-0.00856085\pi$
$998$	−31.0859	−	21.8024i	−0.984007	−	0.690143i
$999$	−0.196502	−	0.0526525i	−0.00621705	−	0.00166585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.23	yes	240
4.3	odd	2		896.2.bh.a.529.7		240
7.2	even	3	inner	224.2.bd.a.205.3	yes	240
28.23	odd	6		896.2.bh.a.401.24		240
32.5	even	8	inner	224.2.bd.a.165.3	yes	240
32.27	odd	8		896.2.bh.a.753.24		240
224.37	even	24	inner	224.2.bd.a.37.23	✓	240
224.219	odd	24		896.2.bh.a.625.7		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.23	✓	240	224.37	even	24	inner
224.2.bd.a.109.23	yes	240	1.1	even	1	trivial
224.2.bd.a.165.3	yes	240	32.5	even	8	inner
224.2.bd.a.205.3	yes	240	7.2	even	3	inner
896.2.bh.a.401.24		240	28.23	odd	6
896.2.bh.a.529.7		240	4.3	odd	2
896.2.bh.a.625.7		240	224.219	odd	24
896.2.bh.a.753.24		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)

\(f(q)\)	\(=\)	\(q+(0.956234 - 1.04193i) q^{2} +(1.46089 + 1.90386i) q^{3} +(-0.171232 - 1.99266i) q^{4} +(2.38518 + 1.83021i) q^{5} +(3.38064 + 0.298400i) q^{6} +(-2.64555 - 0.0324859i) q^{7} +(-2.23994 - 1.72703i) q^{8} +(-0.714054 + 2.66488i) q^{9} +O(q^{10})\)	\(q+(0.956234 - 1.04193i) q^{2} +(1.46089 + 1.90386i) q^{3} +(-0.171232 - 1.99266i) q^{4} +(2.38518 + 1.83021i) q^{5} +(3.38064 + 0.298400i) q^{6} +(-2.64555 - 0.0324859i) q^{7} +(-2.23994 - 1.72703i) q^{8} +(-0.714054 + 2.66488i) q^{9} +(4.18774 - 0.735076i) q^{10} +(-1.92231 - 0.253077i) q^{11} +(3.54360 - 3.23705i) q^{12} +(-3.09779 - 1.28315i) q^{13} +(-2.56362 + 2.72541i) q^{14} +7.21480i q^{15} +(-3.94136 + 0.682414i) q^{16} +(5.06039 + 2.92162i) q^{17} +(2.09382 + 3.29225i) q^{18} +(-0.998902 - 7.58742i) q^{19} +(3.23857 - 5.06624i) q^{20} +(-3.80300 - 5.08423i) q^{21} +(-2.10187 + 1.76091i) q^{22} +(1.60177 - 5.97789i) q^{23} +(0.0157347 - 6.78755i) q^{24} +(1.04531 + 3.90115i) q^{25} +(-4.29916 + 2.00069i) q^{26} +(0.534560 - 0.221422i) q^{27} +(0.388270 + 5.27724i) q^{28} +(-0.519720 + 1.25471i) q^{29} +(7.51730 + 6.89903i) q^{30} +(-3.29306 + 5.70375i) q^{31} +(-3.05784 + 4.75916i) q^{32} +(-2.32646 - 4.02954i) q^{33} +(7.88303 - 2.47882i) q^{34} +(-6.25066 - 4.91941i) q^{35} +(5.43247 + 0.966550i) q^{36} +(-0.278939 - 0.214037i) q^{37} +(-8.86073 - 6.21456i) q^{38} +(-2.08258 - 7.77230i) q^{39} +(-2.18183 - 8.21887i) q^{40} +(3.08076 + 3.08076i) q^{41} +(-8.93397 - 0.899257i) q^{42} +(1.50539 + 3.63434i) q^{43} +(-0.175134 + 3.87385i) q^{44} +(-6.58045 + 5.04936i) q^{45} +(-4.69687 - 7.38520i) q^{46} +(-3.75988 + 2.17077i) q^{47} +(-7.05710 - 6.50689i) q^{48} +(6.99789 + 0.171886i) q^{49} +(5.06428 + 2.64127i) q^{50} +(1.83029 + 13.9024i) q^{51} +(-2.02643 + 6.39254i) q^{52} +(-5.47403 - 0.720670i) q^{53} +(0.280459 - 0.768705i) q^{54} +(-4.12188 - 4.12188i) q^{55} +(5.86979 + 4.64173i) q^{56} +(12.9861 - 12.9861i) q^{57} +(0.810350 + 1.74131i) q^{58} +(-1.75939 + 13.3639i) q^{59} +(14.3766 - 1.23540i) q^{60} +(-0.248180 + 0.0326735i) q^{61} +(2.79396 + 8.88525i) q^{62} +(1.97564 - 7.02689i) q^{63} +(2.03470 + 7.73692i) q^{64} +(-5.04035 - 8.73014i) q^{65} +(-6.42314 - 1.42918i) q^{66} +(3.34929 + 4.36487i) q^{67} +(4.95528 - 10.5839i) q^{68} +(13.7211 - 5.68347i) q^{69} +(-11.1028 + 1.80864i) q^{70} +(-2.25231 + 2.25231i) q^{71} +(6.20179 - 4.73600i) q^{72} +(-2.14893 + 0.575804i) q^{73} +(-0.489742 + 0.0859646i) q^{74} +(-5.90018 + 7.68926i) q^{75} +(-14.9481 + 3.28968i) q^{76} +(5.07736 + 0.731978i) q^{77} +(-10.0896 - 5.26224i) q^{78} +(-5.61531 + 3.24200i) q^{79} +(-10.6498 - 5.58585i) q^{80} +(8.37030 + 4.83260i) q^{81} +(6.15586 - 0.264005i) q^{82} +(-10.7528 - 4.45397i) q^{83} +(-9.47993 + 8.44866i) q^{84} +(6.72276 + 16.2302i) q^{85} +(5.22624 + 1.90677i) q^{86} +(-3.14806 + 0.843520i) q^{87} +(3.86880 + 3.88678i) q^{88} +(4.34060 + 1.16306i) q^{89} +(-1.03138 + 11.6847i) q^{90} +(8.15367 + 3.49526i) q^{91} +(-12.1862 - 2.16817i) q^{92} +(-15.6700 + 2.06299i) q^{93} +(-1.33354 + 5.99329i) q^{94} +(11.5040 - 19.9256i) q^{95} +(-13.5280 + 1.13089i) q^{96} +8.30414 q^{97} +(6.87071 - 7.12694i) q^{98} +(2.04706 - 4.94203i) 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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