LMFDB - Embedded newform 525.2.bo.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	525.4
Dual form			525.2.bo.a.394.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408094 - 1.91993i) q^{2} +(-0.406737 - 0.913545i) q^{3} +(-1.69250 + 0.753548i) q^{4} +(1.10575 + 1.94353i) q^{5} +(-1.58796 + 1.15372i) q^{6} +(-2.49128 + 0.890806i) q^{7} +(-0.169980 - 0.233957i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.408094 - 1.91993i) q^{2} +(-0.406737 - 0.913545i) q^{3} +(-1.69250 + 0.753548i) q^{4} +(1.10575 + 1.94353i) q^{5} +(-1.58796 + 1.15372i) q^{6} +(-2.49128 + 0.890806i) q^{7} +(-0.169980 - 0.233957i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(3.28020 - 2.91610i) q^{10} +(-0.277019 - 0.307661i) q^{11} +(1.37680 + 1.23968i) q^{12} +(-3.84383 + 1.24894i) q^{13} +(2.72696 + 4.41954i) q^{14} +(1.32576 - 1.80066i) q^{15} +(-2.85917 + 3.17543i) q^{16} +(-6.70055 + 0.704256i) q^{17} +(1.69985 + 0.981411i) q^{18} +(-0.792166 - 0.352695i) q^{19} +(-3.33602 - 2.45619i) q^{20} +(1.82709 + 1.91357i) q^{21} +(-0.477637 + 0.657411i) q^{22} +(1.35705 + 6.38444i) q^{23} +(-0.144593 + 0.250443i) q^{24} +(-2.55464 + 4.29812i) q^{25} +(3.96651 + 6.87019i) q^{26} +(0.951057 + 0.309017i) q^{27} +(3.54521 - 3.38498i) q^{28} +(5.09755 + 3.70359i) q^{29} +(-3.99817 - 1.81052i) q^{30} +(-0.542308 - 5.15972i) q^{31} +(6.76251 + 3.90434i) q^{32} +(-0.168388 + 0.378206i) q^{33} +(4.08657 + 12.5772i) q^{34} +(-4.48604 - 3.85687i) q^{35} +(0.572506 - 1.76199i) q^{36} +(-5.62447 - 5.06429i) q^{37} +(-0.353872 + 1.66484i) q^{38} +(2.70438 + 3.00352i) q^{39} +(0.266748 - 0.589059i) q^{40} +(-2.24236 - 6.90127i) q^{41} +(2.92830 - 4.28879i) q^{42} -11.8634i q^{43} +(0.700691 + 0.311968i) q^{44} +(-2.18422 - 0.478745i) q^{45} +(11.7039 - 5.21089i) q^{46} +(-8.82158 - 0.927185i) q^{47} +(4.06382 + 1.32042i) q^{48} +(5.41293 - 4.43849i) q^{49} +(9.29461 + 3.15069i) q^{50} +(3.36873 + 5.83481i) q^{51} +(5.56453 - 5.01033i) q^{52} +(5.16775 + 11.6070i) q^{53} +(0.205171 - 1.95207i) q^{54} +(0.291635 - 0.878591i) q^{55} +(0.631877 + 0.431433i) q^{56} +0.867134i q^{57} +(5.03035 - 11.2983i) q^{58} +(9.81143 + 2.08548i) q^{59} +(-0.886956 + 4.04663i) q^{60} +(-10.4632 + 2.22402i) q^{61} +(-9.68498 + 3.14684i) q^{62} +(1.00499 - 2.44745i) q^{63} +(2.09548 - 6.44924i) q^{64} +(-6.67765 - 6.08959i) q^{65} +(0.794847 + 0.168950i) q^{66} +(4.55668 - 0.478926i) q^{67} +(10.8100 - 6.24114i) q^{68} +(5.28051 - 3.83651i) q^{69} +(-5.57420 + 10.1868i) q^{70} +(1.61710 + 1.17489i) q^{71} +(0.287602 + 0.0302282i) q^{72} +(4.27476 - 3.84901i) q^{73} +(-7.42777 + 12.8653i) q^{74} +(4.96559 + 0.585575i) q^{75} +1.60651 q^{76} +(0.964197 + 0.519698i) q^{77} +(4.66291 - 6.41794i) q^{78} +(-1.02063 + 9.71063i) q^{79} +(-9.33307 - 2.04566i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-12.3349 + 7.12154i) q^{82} +(0.0508112 + 0.0699356i) q^{83} +(-4.53430 - 1.86192i) q^{84} +(-8.77787 - 12.2440i) q^{85} +(-22.7768 + 4.84136i) q^{86} +(1.31003 - 6.16323i) q^{87} +(-0.0248918 + 0.117107i) q^{88} +(-6.88750 + 1.46398i) q^{89} +(-0.0277923 + 4.38891i) q^{90} +(8.46348 - 6.53555i) q^{91} +(-7.10779 - 9.78303i) q^{92} +(-4.49306 + 2.59407i) q^{93} +(1.81990 + 17.3152i) q^{94} +(-0.190463 - 1.92959i) q^{95} +(0.816229 - 7.76590i) q^{96} +(-1.91526 + 2.63613i) q^{97} +(-10.7306 - 8.58112i) q^{98} +0.413998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.408094	−	1.91993i	−0.288566	−	1.35759i	−0.848560	−	0.529099i	$-0.822530\pi$
$2$	−0.408094	−	1.91993i	−0.288566	−	1.35759i	0.559995	−	0.828496i	$-0.310803\pi$
$3$	−0.406737	−	0.913545i	−0.234830	−	0.527436i
$3$	−0.406737	−	0.913545i	−0.234830	−	0.527436i
$4$	−1.69250	+	0.753548i	−0.846248	+	0.376774i
$5$	1.10575	+	1.94353i	0.494506	+	0.869174i
$5$	1.10575	+	1.94353i	0.494506	+	0.869174i
$6$	−1.58796	+	1.15372i	−0.648280	+	0.471003i
$7$	−2.49128	+	0.890806i	−0.941615	+	0.336693i
$7$	−2.49128	+	0.890806i	−0.941615	+	0.336693i
$8$	−0.169980	−	0.233957i	−0.0600969	−	0.0827163i
$9$	−0.669131	+	0.743145i	−0.223044	+	0.247715i
$10$	3.28020	−	2.91610i	1.03729	−	0.922153i
$11$	−0.277019	−	0.307661i	−0.0835243	−	0.0927632i	0.699934	−	0.714208i	$-0.253213\pi$
$11$	−0.277019	−	0.307661i	−0.0835243	−	0.0927632i	−0.783458	+	0.621445i	$0.786546\pi$
$12$	1.37680	+	1.23968i	0.397448	+	0.357864i
$13$	−3.84383	+	1.24894i	−1.06609	+	0.346392i	−0.788962	−	0.614442i	$-0.789381\pi$
$13$	−3.84383	+	1.24894i	−1.06609	+	0.346392i	−0.277124	+	0.960834i	$0.589381\pi$
$14$	2.72696	+	4.41954i	0.728810	+	1.18117i
$15$	1.32576	−	1.80066i	0.342309	−	0.464928i
$16$	−2.85917	+	3.17543i	−0.714792	+	0.793857i
$17$	−6.70055	+	0.704256i	−1.62512	+	0.170807i	−0.872831	−	0.488023i	$-0.837718\pi$
$17$	−6.70055	+	0.704256i	−1.62512	+	0.170807i	−0.752291	+	0.658831i	$0.771051\pi$
$18$	1.69985	+	0.981411i	0.400659	+	0.231321i
$19$	−0.792166	−	0.352695i	−0.181735	−	0.0809138i	0.313852	−	0.949472i	$-0.398380\pi$
$19$	−0.792166	−	0.352695i	−0.181735	−	0.0809138i	−0.495587	+	0.868558i	$0.665047\pi$
$20$	−3.33602	−	2.45619i	−0.745957	−	0.549220i
$21$	1.82709	+	1.91357i	0.398703	+	0.417576i
$22$	−0.477637	+	0.657411i	−0.101833	+	0.140160i
$23$	1.35705	+	6.38444i	0.282965	+	1.33125i	0.858224	+	0.513275i	$0.171568\pi$
$23$	1.35705	+	6.38444i	0.282965	+	1.33125i	−0.575259	+	0.817972i	$0.695099\pi$
$24$	−0.144593	+	0.250443i	−0.0295150	+	0.0511215i
$25$	−2.55464	+	4.29812i	−0.510927	+	0.859624i
$26$	3.96651	+	6.87019i	0.777896	+	1.34736i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	3.54521	−	3.38498i	0.669982	−	0.639702i
$29$	5.09755	+	3.70359i	0.946591	+	0.687739i	0.949998	−	0.312255i	$-0.101084\pi$
$29$	5.09755	+	3.70359i	0.946591	+	0.687739i	−0.00340677	+	0.999994i	$0.501084\pi$
$30$	−3.99817	−	1.81052i	−0.729962	−	0.330555i
$31$	−0.542308	−	5.15972i	−0.0974014	−	0.926712i	−0.928686	−	0.370866i	$-0.879061\pi$
$31$	−0.542308	−	5.15972i	−0.0974014	−	0.926712i	0.831285	−	0.555846i	$-0.187606\pi$
$32$	6.76251	+	3.90434i	1.19545	+	0.690196i
$33$	−0.168388	+	0.378206i	−0.0293126	+	0.0658373i
$34$	4.08657	+	12.5772i	0.700841	+	2.15697i
$35$	−4.48604	−	3.85687i	−0.758279	−	0.651930i
$36$	0.572506	−	1.76199i	0.0954176	−	0.293665i
$37$	−5.62447	−	5.06429i	−0.924657	−	0.832564i	0.0615466	−	0.998104i	$-0.480397\pi$
$37$	−5.62447	−	5.06429i	−0.924657	−	0.832564i	−0.986203	+	0.165540i	$0.947063\pi$
$38$	−0.353872	+	1.66484i	−0.0574056	+	0.270072i
$39$	2.70438	+	3.00352i	0.433048	+	0.480949i
$40$	0.266748	−	0.589059i	0.0421766	−	0.0931384i
$41$	−2.24236	−	6.90127i	−0.350198	−	1.07780i	−0.958742	−	0.284278i	$-0.908246\pi$
$41$	−2.24236	−	6.90127i	−0.350198	−	1.07780i	0.608544	−	0.793520i	$-0.291754\pi$
$42$	2.92830	−	4.28879i	0.451847	−	0.661775i
$43$		−	11.8634i		−	1.80914i	−0.426320	−	0.904572i	$-0.640190\pi$
$43$		−	11.8634i		−	1.80914i	0.426320	−	0.904572i	$-0.359810\pi$
$44$	0.700691	+	0.311968i	0.105633	+	0.0470309i
$45$	−2.18422	−	0.478745i	−0.325604	−	0.0713671i
$46$	11.7039	−	5.21089i	1.72564	−	0.768304i
$47$	−8.82158	−	0.927185i	−1.28676	−	0.135244i	−0.563671	−	0.825999i	$-0.690611\pi$
$47$	−8.82158	−	0.927185i	−1.28676	−	0.135244i	−0.723088	+	0.690755i	$0.757278\pi$
$48$	4.06382	+	1.32042i	0.586562	+	0.190586i
$49$	5.41293	−	4.43849i	0.773276	−	0.634070i
$50$	9.29461	+	3.15069i	1.31446	+	0.445575i
$51$	3.36873	+	5.83481i	0.471716	+	0.817037i
$52$	5.56453	−	5.01033i	0.771662	−	0.694807i
$53$	5.16775	+	11.6070i	0.709846	+	1.59434i	0.801113	+	0.598513i	$0.204242\pi$
$53$	5.16775	+	11.6070i	0.709846	+	1.59434i	−0.0912674	+	0.995826i	$0.529092\pi$
$54$	0.205171	−	1.95207i	0.0279202	−	0.265643i
$55$	0.291635	−	0.878591i	0.0393241	−	0.118469i
$56$	0.631877	+	0.431433i	0.0844381	+	0.0576526i
$57$			0.867134i			0.114855i
$58$	5.03035	−	11.2983i	0.660517	−	1.48355i
$59$	9.81143	+	2.08548i	1.27734	+	0.271507i	0.796144	−	0.605107i	$-0.206870\pi$
$59$	9.81143	+	2.08548i	1.27734	+	0.271507i	0.481195	+	0.876614i	$0.340203\pi$
$60$	−0.886956	+	4.04663i	−0.114506	+	0.522417i
$61$	−10.4632	+	2.22402i	−1.33967	+	0.284756i	−0.821348	−	0.570428i	$-0.806777\pi$
$61$	−10.4632	+	2.22402i	−1.33967	+	0.284756i	−0.518324	+	0.855184i	$0.673444\pi$
$62$	−9.68498	+	3.14684i	−1.22999	+	0.399649i
$63$	1.00499	−	2.44745i	0.126617	−	0.308349i
$64$	2.09548	−	6.44924i	0.261935	−	0.806154i
$65$	−6.67765	−	6.08959i	−0.828261	−	0.755321i
$66$	0.794847	+	0.168950i	0.0978389	+	0.0207963i
$67$	4.55668	−	0.478926i	0.556687	−	0.0585101i	0.177992	−	0.984032i	$-0.443040\pi$
$67$	4.55668	−	0.478926i	0.556687	−	0.0585101i	0.378694	+	0.925522i	$0.376373\pi$
$68$	10.8100	−	6.24114i	1.31090	−	0.756849i
$69$	5.28051	−	3.83651i	0.635699	−	0.461862i
$70$	−5.57420	+	10.1868i	−0.666244	+	1.21756i
$71$	1.61710	+	1.17489i	0.191915	+	0.139434i	0.679593	−	0.733589i	$-0.262156\pi$
$71$	1.61710	+	1.17489i	0.191915	+	0.139434i	−0.487679	+	0.873023i	$0.662156\pi$
$72$	0.287602	+	0.0302282i	0.0338943	+	0.00356243i
$73$	4.27476	−	3.84901i	0.500323	−	0.450493i	−0.379918	−	0.925020i	$-0.624048\pi$
$73$	4.27476	−	3.84901i	0.500323	−	0.450493i	0.880241	+	0.474527i	$0.157381\pi$
$74$	−7.42777	+	12.8653i	−0.863461	+	1.49556i
$75$	4.96559	+	0.585575i	0.573377	+	0.0676164i
$76$	1.60651			0.184280
$77$	0.964197	+	0.519698i	0.109880	+	0.0592251i
$78$	4.66291	−	6.41794i	0.527971	−	0.726689i
$79$	−1.02063	+	9.71063i	−0.114830	+	1.09253i	0.773649	+	0.633614i	$0.218429\pi$
$79$	−1.02063	+	9.71063i	−0.114830	+	1.09253i	−0.888479	+	0.458917i	$0.848237\pi$
$80$	−9.33307	−	2.04566i	−1.04347	−	0.228712i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−12.3349	+	7.12154i	−1.36216	+	0.786442i
$83$	0.0508112	+	0.0699356i	0.00557725	+	0.00767643i	0.811797	−	0.583940i	$-0.198490\pi$
$83$	0.0508112	+	0.0699356i	0.00557725	+	0.00767643i	−0.806219	+	0.591617i	$0.798490\pi$
$84$	−4.53430	−	1.86192i	−0.494733	−	0.203152i
$85$	−8.77787	−	12.2440i	−0.952094	−	1.32805i
$86$	−22.7768	+	4.84136i	−2.45609	+	0.522057i
$87$	1.31003	−	6.16323i	0.140450	−	0.660768i
$88$	−0.0248918	+	0.117107i	−0.00265347	+	0.0124836i
$89$	−6.88750	+	1.46398i	−0.730074	+	0.155182i	−0.557928	−	0.829889i	$-0.688403\pi$
$89$	−6.88750	+	1.46398i	−0.730074	+	0.155182i	−0.172146	+	0.985071i	$0.555070\pi$
$90$	−0.0277923	+	4.38891i	−0.00292957	+	0.462632i
$91$	8.46348	−	6.53555i	0.887214	−	0.685111i
$92$	−7.10779	−	9.78303i	−0.741038	−	1.01995i
$93$	−4.49306	+	2.59407i	−0.465908	+	0.268992i
$94$	1.81990	+	17.3152i	0.187708	+	1.78592i
$95$	−0.190463	−	1.92959i	−0.0195411	−	0.197972i
$96$	0.816229	−	7.76590i	0.0833060	−	0.792604i
$97$	−1.91526	+	2.63613i	−0.194465	+	0.267658i	−0.895104	−	0.445858i	$-0.852899\pi$
$97$	−1.91526	+	2.63613i	−0.194465	+	0.267658i	0.700638	+	0.713516i	$0.252899\pi$
$98$	−10.7306	−	8.58112i	−1.08395	−	0.866825i
$99$	0.413998			0.0416084
$100$	1.08488	−	9.19959i	0.108488	−	0.919959i
$101$	−4.40299	+	7.62620i	−0.438114	+	0.758836i	−0.997544	−	0.0700419i	$-0.977687\pi$
$101$	−4.40299	+	7.62620i	−0.438114	+	0.758836i	0.559430	+	0.828878i	$0.311020\pi$
$102$	9.82766	−	8.84887i	0.973084	−	0.876169i
$103$	2.48025	+	0.260685i	0.244387	+	0.0256861i	0.225930	−	0.974144i	$-0.427458\pi$
$103$	2.48025	+	0.260685i	0.244387	+	0.0256861i	0.0184569	+	0.999830i	$0.494125\pi$
$104$	0.945569	+	0.686996i	0.0927207	+	0.0673655i
$105$	−1.69879	+	5.66693i	−0.165785	+	0.553036i
$106$	20.1756	−	14.6584i	1.95963	−	1.42375i
$107$	12.2618	−	7.07934i	1.18539	−	0.684386i	0.228136	−	0.973629i	$-0.426737\pi$
$107$	12.2618	−	7.07934i	1.18539	−	0.684386i	0.957256	+	0.289243i	$0.0934036\pi$
$108$	−1.84252	+	0.193657i	−0.177296	+	0.0186346i
$109$	−19.5757	−	4.16095i	−1.87501	−	0.398547i	−0.878199	−	0.478295i	$-0.841255\pi$
$109$	−19.5757	−	4.16095i	−1.87501	−	0.398547i	−0.996815	+	0.0797479i	$0.974588\pi$
$110$	−1.80585	−	0.201371i	−0.172181	−	0.0192000i
$111$	−2.33878	+	7.19804i	−0.221988	+	0.683208i
$112$	4.29429	−	10.4578i	0.405772	−	0.988172i
$113$	−8.21325	+	2.66865i	−0.772638	+	0.251045i	−0.668694	−	0.743538i	$-0.733146\pi$
$113$	−8.21325	+	2.66865i	−0.772638	+	0.251045i	−0.103944	+	0.994583i	$0.533146\pi$
$114$	1.66484	−	0.353872i	0.155926	−	0.0331431i
$115$	−10.9078	+	9.69706i	−1.01716	+	0.904256i
$116$	−11.4184	−	2.42706i	−1.06017	−	0.225347i
$117$	1.64388	−	3.69222i	0.151977	−	0.341346i
$118$		−	19.6883i		−	1.81246i
$119$	16.0656	−	7.72338i	1.47273	−	0.708001i
$120$	−0.646628	−	0.00409470i	−0.0590288	−	0.000373793i
$121$	1.13190	−	10.7693i	0.102900	−	0.979026i
$122$	8.53991	+	19.1809i	0.773167	+	1.73656i
$123$	−5.39258	+	4.85550i	−0.486232	+	0.437806i
$124$	4.80595	+	8.32414i	0.431587	+	0.747530i
$125$	−11.1783	−	0.212379i	−0.999820	−	0.0189958i
$126$	−5.10905	−	0.930728i	−0.455151	−	0.0829158i
$127$	−8.97439	−	2.91596i	−0.796349	−	0.258749i	−0.117543	−	0.993068i	$-0.537502\pi$
$127$	−8.97439	−	2.91596i	−0.796349	−	0.258749i	−0.678805	+	0.734318i	$0.737502\pi$
$128$	2.29458	+	0.241170i	0.202814	+	0.0213166i
$129$	−10.8377	+	4.82526i	−0.954207	+	0.424840i
$130$	−8.96648	+	15.3057i	−0.786412	+	1.34240i
$131$	−5.74636	−	2.55845i	−0.502062	−	0.223532i	0.140048	−	0.990145i	$-0.455274\pi$
$131$	−5.74636	−	2.55845i	−0.502062	−	0.223532i	−0.642110	+	0.766612i	$0.721941\pi$
$132$		−	0.767001i		−	0.0667589i
$133$	2.28769	+	0.172996i	0.198368	+	0.0150006i
$134$	−2.77905	−	8.55305i	−0.240074	−	0.738871i
$135$	0.451045	+	2.19010i	0.0388198	+	0.188494i
$136$	1.30372	+	1.44793i	0.111793	+	0.124159i
$137$	−0.168652	+	0.793448i	−0.0144090	+	0.0677888i	−0.984765	−	0.173892i	$-0.944365\pi$
$137$	−0.168652	+	0.793448i	−0.0144090	+	0.0677888i	0.970356	+	0.241681i	$0.0776988\pi$
$138$	−9.52078	−	8.57255i	−0.810462	−	0.729744i
$139$	−2.41207	+	7.42360i	−0.204590	+	0.629662i	0.795140	+	0.606425i	$0.207397\pi$
$139$	−2.41207	+	7.42360i	−0.204590	+	0.629662i	−0.999730	+	0.0232365i	$0.992603\pi$
$140$	10.4989	+	3.14730i	0.887322	+	0.265995i
$141$	2.74103	+	8.43603i	0.230837	+	0.710442i
$142$	1.59578	−	3.58419i	0.133915	−	0.300778i
$143$	1.44906	+	0.836616i	0.121177	+	0.0699613i
$144$	−0.446646	−	4.24955i	−0.0372205	−	0.354129i
$145$	−1.56143	+	14.0025i	−0.129670	+	1.16284i
$146$	−9.13434	−	6.63648i	−0.755963	−	0.549239i
$147$	−6.25640	−	3.13966i	−0.516019	−	0.258955i
$148$	13.3356	+	4.33299i	1.09618	+	0.356170i
$149$	−4.43643	−	7.68413i	−0.363447	−	0.629508i	0.625079	−	0.780562i	$-0.285067\pi$
$149$	−4.43643	−	7.68413i	−0.363447	−	0.629508i	−0.988526	+	0.151053i	$0.951734\pi$
$150$	−0.902164	−	9.77255i	−0.0736613	−	0.797926i
$151$	−7.65334	+	13.2560i	−0.622820	+	1.07876i	0.366138	+	0.930561i	$0.380680\pi$
$151$	−7.65334	+	13.2560i	−0.622820	+	1.07876i	−0.988958	+	0.148196i	$0.952653\pi$
$152$	0.0521367	+	0.245284i	0.00422884	+	0.0198951i
$153$	3.96018	−	5.45072i	0.320161	−	0.440664i
$154$	0.604301	−	2.06328i	0.0486960	−	0.166263i
$155$	9.42842	−	6.75934i	0.757309	−	0.542924i
$156$	−6.84046	−	3.04557i	−0.547675	−	0.243841i
$157$	2.71542	+	1.56775i	0.216714	+	0.125120i	0.604428	−	0.796660i	$-0.293402\pi$
$157$	2.71542	+	1.56775i	0.216714	+	0.125120i	−0.387714	+	0.921780i	$0.626735\pi$
$158$	19.0602	−	2.00331i	1.51635	−	0.159375i
$159$	8.50158	−	9.44196i	0.674219	−	0.748796i
$160$	−0.110566	+	17.4604i	−0.00874101	+	1.38036i
$161$	−9.06809	−	14.6965i	−0.714666	−	1.15825i
$162$	−1.86675	+	0.606545i	−0.146666	+	0.0476547i
$163$	8.98178	+	8.08723i	0.703507	+	0.633441i	0.941180	−	0.337905i	$-0.109718\pi$
$163$	8.98178	+	8.08723i	0.703507	+	0.633441i	−0.237673	+	0.971345i	$0.576385\pi$
$164$	8.99563	+	9.99065i	0.702440	+	0.780139i
$165$	−0.921251	+	0.0909332i	−0.0717193	+	0.00707914i
$166$	0.113536	−	0.126094i	0.00881208	−	0.00978680i
$167$	−3.99267	−	5.49543i	−0.308962	−	0.425249i	0.626095	−	0.779747i	$-0.284652\pi$
$167$	−3.99267	−	5.49543i	−0.308962	−	0.425249i	−0.935057	+	0.354497i	$0.884652\pi$
$168$	0.137126	−	0.752728i	0.0105795	−	0.0580742i
$169$	2.69795	−	1.96017i	0.207534	−	0.150783i
$170$	−19.9254	+	21.8496i	−1.52821	+	1.67579i
$171$	0.792166	−	0.352695i	0.0605785	−	0.0269713i
$172$	8.93960	+	20.0787i	0.681638	+	1.53099i
$173$	0.994696	+	4.67968i	0.0756254	+	0.355789i	0.999647	−	0.0265496i	$-0.00845200\pi$
$173$	0.994696	+	4.67968i	0.0756254	+	0.355789i	−0.924022	+	0.382339i	$0.875119\pi$
$174$	−12.3676			−0.937584
$175$	2.53552	−	12.9835i	0.191668	−	0.981460i
$176$	1.76900			0.133343
$177$	−2.08548	−	9.81143i	−0.156755	−	0.737472i
$178$	5.62149	+	12.6261i	0.421349	+	0.946364i
$179$	18.1481	−	8.08004i	1.35645	−	0.603930i	0.405733	−	0.913992i	$-0.367016\pi$
$179$	18.1481	−	8.08004i	1.35645	−	0.603930i	0.950717	+	0.310061i	$0.100350\pi$
$180$	4.05754	−	0.835637i	0.302431	−	0.0622847i
$181$	−13.1195	+	9.53189i	−0.975166	+	0.708500i	−0.956623	−	0.291329i	$-0.905903\pi$
$181$	−13.1195	+	9.53189i	−0.975166	+	0.708500i	−0.0185429	+	0.999828i	$0.505903\pi$
$182$	−16.0017	−	13.5822i	−1.18612	−	1.00678i
$183$	6.28749	+	8.65399i	0.464785	+	0.639722i
$184$	1.26301	−	1.40272i	0.0931104	−	0.103410i
$185$	3.62337	−	16.5312i	0.266395	−	1.21540i
$186$	6.81402	+	7.56773i	0.499628	+	0.554893i
$187$	2.07285	+	1.86640i	0.151582	+	0.136485i
$188$	15.6292	−	5.07822i	1.13987	−	0.370368i
$189$	−2.64462	+	0.0773592i	−0.192368	+	0.00562706i
$190$	−3.62696	+	1.15313i	−0.263127	+	0.0836568i
$191$	3.61559	−	4.01552i	0.261615	−	0.290553i	−0.597999	−	0.801497i	$-0.704037\pi$
$191$	3.61559	−	4.01552i	0.261615	−	0.290553i	0.859614	+	0.510944i	$0.170704\pi$
$192$	−6.74398	+	0.708821i	−0.486705	+	0.0511547i
$193$	3.77200	+	2.17777i	0.271515	+	0.156759i	0.629576	−	0.776939i	$-0.283229\pi$
$193$	3.77200	+	2.17777i	0.271515	+	0.156759i	−0.358061	+	0.933698i	$0.616562\pi$
$194$	5.84279	+	2.60138i	0.419488	+	0.186768i
$195$	−2.84707	+	8.57720i	−0.203883	+	0.614226i
$196$	−5.81675	+	11.5910i	−0.415482	+	0.827931i
$197$	4.16589	−	5.73386i	0.296807	−	0.408520i	−0.634403	−	0.773003i	$-0.718754\pi$
$197$	4.16589	−	5.73386i	0.296807	−	0.408520i	0.931210	+	0.364482i	$0.118754\pi$
$198$	−0.168950	−	0.794847i	−0.0120068	−	0.0564873i
$199$	−4.27196	+	7.39925i	−0.302831	+	0.524519i	−0.976776	−	0.214263i	$-0.931265\pi$
$199$	−4.27196	+	7.39925i	−0.302831	+	0.524519i	0.673945	+	0.738782i	$0.264598\pi$
$200$	1.43981	−	0.132918i	0.101810	−	0.00939870i
$201$	−2.29089	−	3.96794i	−0.161587	−	0.279877i
$202$	16.4386	+	5.34123i	1.15662	+	0.375807i
$203$	−15.9986	−	4.68574i	−1.12288	−	0.328874i
$204$	−10.0984	−	7.33690i	−0.707027	−	0.513685i
$205$	10.9334	−	11.9892i	0.763619	−	0.837360i
$206$	−0.511679	−	4.86830i	−0.0356503	−	0.339190i
$207$	−5.65261	−	3.26353i	−0.392883	−	0.226831i
$208$	7.02424	−	15.7767i	0.487043	−	1.09392i
$209$	0.110935	+	0.341422i	0.00767351	+	0.0236166i
$210$	11.5734	+	0.948922i	0.798638	+	0.0654818i
$211$	−1.81044	+	5.57196i	−0.124636	+	0.383589i	−0.993835	−	0.110873i	$-0.964635\pi$
$211$	−1.81044	+	5.57196i	−0.124636	+	0.383589i	0.869199	+	0.494463i	$0.164635\pi$
$212$	−17.4928	−	15.7506i	−1.20141	−	1.08176i
$213$	0.415584	−	1.95517i	0.0284753	−	0.133966i
$214$	−18.5958	−	20.6527i	−1.27118	−	1.41179i
$215$	23.0568	−	13.1179i	1.57246	−	0.894633i
$216$	−0.0893636	−	0.275033i	−0.00608042	−	0.0187136i
$217$	5.94734	+	12.3712i	0.403732	+	0.839811i
$218$			39.2821i			2.66052i
$219$	−5.25495	−	2.33966i	−0.355097	−	0.158099i
$220$	0.168469	+	1.70677i	0.0113582	+	0.115071i
$221$	24.8762	−	11.0756i	1.67335	−	0.745025i
$222$	14.7742	+	1.55283i	0.991577	+	0.104219i
$223$	0.186641	+	0.0606433i	0.0124984	+	0.00406098i	0.315260	−	0.949005i	$-0.397908\pi$
$223$	0.186641	+	0.0606433i	0.0124984	+	0.00406098i	−0.302761	+	0.953066i	$0.597908\pi$
$224$	−20.3253	−	3.70271i	−1.35804	−	0.247398i
$225$	−1.48474	−	4.77447i	−0.0989826	−	0.318298i
$226$	8.47539	+	14.6798i	0.563774	+	0.976486i
$227$	9.49133	−	8.54604i	0.629962	−	0.567220i	−0.291073	−	0.956701i	$-0.594012\pi$
$227$	9.49133	−	8.54604i	0.629962	−	0.567220i	0.921035	+	0.389481i	$0.127345\pi$
$228$	−0.653427	−	1.46762i	−0.0432743	−	0.0971956i
$229$	0.294063	−	2.79782i	0.0194322	−	0.184885i	−0.980500	−	0.196519i	$-0.937036\pi$
$229$	0.294063	−	2.79782i	0.0194322	−	0.184885i	0.999932	+	0.0116332i	$0.00370305\pi$
$230$	23.0691	+	16.9849i	1.52113	+	1.11995i
$231$	0.0825937	−	1.09222i	0.00543427	−	0.0718627i
$232$		−	1.82214i		−	0.119629i
$233$	−7.55830	+	16.9762i	−0.495161	+	1.11215i	0.477228	+	0.878780i	$0.341642\pi$
$233$	−7.55830	+	16.9762i	−0.495161	+	1.11215i	−0.972388	+	0.233369i	$0.925025\pi$
$234$	−7.75966	−	1.64937i	−0.507265	−	0.107822i
$235$	−7.95244	−	18.1703i	−0.518760	−	1.18530i
$236$	−18.1773	+	3.86371i	−1.18324	+	0.251506i
$237$	9.28623	−	3.01728i	0.603205	−	0.195993i
$238$	−21.3846	−	27.6929i	−1.38616	−	1.79506i
$239$	4.09325	−	12.5977i	0.264771	−	0.814880i	−0.726976	−	0.686663i	$-0.759075\pi$
$239$	4.09325	−	12.5977i	0.264771	−	0.814880i	0.991746	−	0.128217i	$-0.0409254\pi$
$240$	1.92730	+	9.35822i	0.124407	+	0.604071i
$241$	12.4963	+	2.65618i	0.804959	+	0.171099i	0.591975	−	0.805956i	$-0.298348\pi$
$241$	12.4963	+	2.65618i	0.804959	+	0.171099i	0.212984	+	0.977056i	$0.431682\pi$
$242$	−21.1382	+	2.22171i	−1.35881	+	0.142817i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	16.0330	−	11.6486i	1.02641	−	0.745728i
$245$	14.6117	+	5.61235i	0.933507	+	0.358560i
$246$	11.5229	+	8.37187i	0.734673	+	0.533771i
$247$	3.48544	+	0.366335i	0.221774	+	0.0233093i
$248$	−1.11497	+	1.00392i	−0.0708007	+	0.0637492i
$249$	0.0432226	−	0.0748637i	0.00273912	−	0.00474429i
$250$	4.15405	+	21.5483i	0.262725	+	1.36283i
$251$	−24.4953			−1.54613			−0.773065	−	0.634327i	$-0.781277\pi$
$251$	−24.4953			−1.54613			−0.773065	+	0.634327i	$0.781277\pi$
$252$	0.143321	+	4.89960i	0.00902837	+	0.308646i
$253$	1.58831	−	2.18612i	0.0998562	−	0.137440i
$254$	−1.93604	+	18.4202i	−0.121478	+	1.15579i
$255$	−7.61517	+	12.9991i	−0.476881	+	0.814033i
$256$	−1.89101	−	17.9918i	−0.118188	−	1.12449i
$257$	−12.3376	+	7.12310i	−0.769597	+	0.444327i	−0.832731	−	0.553678i	$-0.813224\pi$
$257$	−12.3376	+	7.12310i	−0.769597	+	0.444327i	0.0631339	+	0.998005i	$0.479890\pi$
$258$	13.6870	+	18.8385i	0.852113	+	1.17283i
$259$	18.5234	+	7.60625i	1.15099	+	0.472630i
$260$	15.8907	+	5.27468i	0.985500	+	0.327122i
$261$	−6.16323	+	1.31003i	−0.381494	+	0.0810891i
$262$	−2.56698	+	12.0767i	−0.158589	+	0.746101i
$263$	−1.37034	+	6.44694i	−0.0844988	+	0.397536i	−0.999988	−	0.00480595i	$-0.998470\pi$
$263$	−1.37034	+	6.44694i	−0.0844988	+	0.397536i	0.915490	+	0.402341i	$0.131804\pi$
$264$	0.117107	−	0.0248918i	0.00720741	−	0.00153198i
$265$	−16.8443	+	22.8781i	−1.03474	+	1.40539i
$266$	−0.601452	−	4.46280i	−0.0368774	−	0.273632i
$267$	4.13882	+	5.69659i	0.253291	+	0.348626i
$268$	−7.35127	+	4.24426i	−0.449050	+	0.259259i
$269$	1.21989	+	11.6065i	0.0743779	+	0.707658i	0.966640	+	0.256140i	$0.0824508\pi$
$269$	1.21989	+	11.6065i	0.0743779	+	0.707658i	−0.892262	+	0.451518i	$0.850883\pi$
$270$	4.02078	−	1.75974i	0.244697	−	0.107095i
$271$	−0.00886435	+	0.0843387i	−0.000538471	+	0.00512321i	−0.994788	−	0.101967i	$-0.967487\pi$
$271$	−0.00886435	+	0.0843387i	−0.000538471	+	0.00512321i	0.994249	+	0.107090i	$0.0341532\pi$
$272$	16.9217	−	23.2907i	1.02603	−	1.41221i
$273$	−9.41293	−	5.07353i	−0.569696	−	0.307064i
$274$	1.59219			0.0961877
$275$	2.03004	−	0.404699i	0.122416	−	0.0244043i
$276$	−6.04625	+	10.4724i	−0.363941	+	0.630365i
$277$	13.5797	−	12.2272i	0.815923	−	0.734660i	−0.151328	−	0.988484i	$-0.548355\pi$
$277$	13.5797	−	12.2272i	0.815923	−	0.734660i	0.967251	+	0.253824i	$0.0816882\pi$
$278$	15.2371	+	1.60149i	0.913863	+	0.0960509i
$279$	4.19729	+	3.04951i	0.251285	+	0.182569i
$280$	−0.139807	+	1.70513i	−0.00835505	+	0.101901i
$281$	2.95288	−	2.14539i	0.176154	−	0.127983i	−0.496215	−	0.868200i	$-0.665277\pi$
$281$	2.95288	−	2.14539i	0.176154	−	0.127983i	0.672369	+	0.740217i	$0.265277\pi$
$282$	15.0780	−	8.70528i	0.897881	−	0.518392i
$283$	−6.95745	+	0.731257i	−0.413577	+	0.0434687i	−0.309033	−	0.951051i	$-0.600005\pi$
$283$	−6.95745	+	0.731257i	−0.413577	+	0.0434687i	−0.104545	+	0.994520i	$0.533339\pi$
$284$	−3.62228	−	0.769939i	−0.214943	−	0.0456874i
$285$	−1.68530	+	0.958833i	−0.0998288	+	0.0567964i
$286$	1.01489	−	3.12351i	0.0600117	−	0.184697i
$287$	11.7340	+	15.1955i	0.692638	+	0.896961i
$288$	−7.42650	+	2.41301i	−0.437610	+	0.142188i
$289$	27.7729	−	5.90331i	1.63370	−	0.347253i
$290$	27.5210	−	2.71649i	1.61609	−	0.159518i
$291$	3.18723	+	0.677467i	0.186839	+	0.0397138i
$292$	−4.33460	+	9.73568i	−0.253664	+	0.569738i
$293$			13.4383i			0.785076i	0.919736	+	0.392538i	$0.128403\pi$
$293$			13.4383i			0.785076i	−0.919736	+	0.392538i	$0.871597\pi$
$294$	−3.47473	+	13.2931i	−0.202651	+	0.775270i
$295$	6.79577	+	21.3749i	0.395665	+	1.24449i
$296$	−0.228781	+	2.17671i	−0.0132976	+	0.126519i
$297$	−0.168388	−	0.378206i	−0.00977088	−	0.0219458i
$298$	−12.9425	+	11.6535i	−0.749739	+	0.675068i
$299$	−13.1900	−	22.8458i	−0.762799	−	1.32121i
$300$	−8.84550	+	2.75073i	−0.510695	+	0.158813i
$301$	10.5679	+	29.5549i	0.609126	+	1.70352i
$302$	28.5738	+	9.28420i	1.64424	+	0.534246i
$303$	8.75774	+	0.920476i	0.503119	+	0.0528799i
$304$	3.38489	−	1.50705i	0.194137	−	0.0864353i
$305$	−15.8921	−	17.8763i	−0.909978	−	1.02359i
$306$	−12.0811	−	5.37886i	−0.690631	−	0.307489i
$307$		−	10.7355i		−	0.612710i	−0.951917	−	0.306355i	$-0.900891\pi$
$307$		−	10.7355i		−	0.612710i	0.951917	−	0.306355i	$-0.0991094\pi$
$308$	−2.02352	−	0.153019i	−0.115301	−	0.00871905i
$309$	−0.770663	−	2.37186i	−0.0438415	−	0.134930i
$310$	−16.8251	−	15.3434i	−0.955604	−	0.871449i
$311$	17.6599	+	19.6133i	1.00140	+	1.11217i	0.993686	+	0.112200i	$0.0357897\pi$
$311$	17.6599	+	19.6133i	1.00140	+	1.11217i	0.00771691	+	0.999970i	$0.497544\pi$
$312$	0.243005	−	1.14325i	0.0137574	−	0.0647236i
$313$	−9.81534	−	8.83777i	−0.554796	−	0.499540i	0.343368	−	0.939201i	$-0.388432\pi$
$313$	−9.81534	−	8.83777i	−0.554796	−	0.499540i	−0.898164	+	0.439660i	$0.855099\pi$
$314$	1.90182	−	5.85320i	0.107326	−	0.330315i
$315$	5.86796	−	0.753025i	0.330622	−	0.0424281i
$316$	−5.59001	−	17.2043i	−0.314463	−	0.967817i
$317$	1.96084	−	4.40412i	0.110132	−	0.247360i	−0.850069	−	0.526672i	$-0.823440\pi$
$317$	1.96084	−	4.40412i	0.110132	−	0.247360i	0.960200	+	0.279312i	$0.0901064\pi$
$318$	−21.5973	−	12.4692i	−1.21112	−	0.699239i
$319$	−0.272670	−	2.59428i	−0.0152666	−	0.145252i
$320$	14.8514	−	3.05860i	0.830217	−	0.170981i
$321$	−11.4546	−	8.32227i	−0.639335	−	0.464504i
$322$	−24.5157	+	23.4076i	−1.36621	+	1.30446i
$323$	5.55634	+	1.80536i	0.309163	+	0.100453i
$324$	0.926334	+	1.60446i	0.0514630	+	0.0891365i
$325$	4.45151	−	19.7118i	0.246925	−	1.09341i
$326$	11.8615	−	20.5447i	0.656948	−	1.13787i
$327$	4.16095	+	19.5757i	0.230101	+	1.08254i
$328$	−1.23345	+	1.69769i	−0.0681056	+	0.0937393i
$329$	22.8029	−	5.54844i	1.25717	−	0.305895i
$330$	0.550542	+	1.73163i	0.0303063	+	0.0953230i
$331$	−29.5911	−	13.1748i	−1.62647	−	0.724152i	−0.627937	−	0.778264i	$-0.716101\pi$
$331$	−29.5911	−	13.1748i	−1.62647	−	0.724152i	−0.998535	+	0.0541117i	$0.982767\pi$
$332$	−0.138698	−	0.0800771i	−0.00761202	−	0.00439480i
$333$	7.52700	−	0.791120i	0.412477	−	0.0433531i
$334$	−8.92146	+	9.90829i	−0.488161	+	0.542157i
$335$	5.96935	+	8.32648i	0.326141	+	0.454924i
$336$	−11.3003	+	0.330553i	−0.616485	+	0.0180331i
$337$	−3.19342	+	1.03761i	−0.173957	+	0.0565220i	−0.394700	−	0.918810i	$-0.629152\pi$
$337$	−3.19342	+	1.03761i	−0.173957	+	0.0565220i	0.220744	+	0.975332i	$0.429152\pi$
$338$	−4.86441	−	4.37993i	−0.264589	−	0.238237i
$339$	5.77856	+	6.41774i	0.313848	+	0.348564i
$340$	24.0830	+	14.1084i	1.30608	+	0.765135i
$341$	−1.43721	+	1.59619i	−0.0778294	+	0.0864383i
$342$	−1.00043	−	1.37697i	−0.0540969	−	0.0744580i
$343$	−9.53128	+	15.8794i	−0.514641	+	0.857406i
$344$	−2.77551	+	2.01653i	−0.149646	+	0.108724i
$345$	13.2953	+	6.02062i	0.715795	+	0.324139i
$346$	8.57872	−	3.81949i	0.461195	−	0.205337i
$347$	5.48265	+	12.3142i	0.294324	+	0.661062i	0.998816	−	0.0486495i	$-0.0154917\pi$
$347$	5.48265	+	12.3142i	0.294324	+	0.661062i	−0.704492	+	0.709712i	$0.748825\pi$
$348$	2.42706	+	11.4184i	0.130104	+	0.612091i
$349$	19.4973			1.04366			0.521832	−	0.853048i	$-0.325249\pi$
$349$	19.4973			1.04366			0.521832	+	0.853048i	$0.325249\pi$
$350$	−25.9621	+	0.430455i	−1.38773	+	0.0230088i
$351$	−4.04164			−0.215727
$352$	−0.672133	−	3.16214i	−0.0358248	−	0.168542i
$353$	11.8519	+	26.6199i	0.630814	+	1.41683i	0.892219	+	0.451603i	$0.149148\pi$
$353$	11.8519	+	26.6199i	0.630814	+	1.41683i	−0.261405	+	0.965229i	$0.584186\pi$
$354$	−17.9862	+	8.00796i	−0.955954	+	0.425618i
$355$	−0.495334	+	4.44203i	−0.0262896	+	0.235758i
$356$	10.5539	−	7.66785i	0.559355	−	0.406395i
$357$	−13.5901	−	11.5352i	−0.719265	−	0.610510i
$358$	−22.9192	−	31.5456i	−1.21132	−	1.66724i
$359$	1.21328	−	1.34749i	0.0640347	−	0.0711178i	−0.710276	−	0.703923i	$-0.751430\pi$
$359$	1.21328	−	1.34749i	0.0640347	−	0.0711178i	0.774311	+	0.632805i	$0.218097\pi$
$360$	0.259267	+	0.592390i	0.0136646	+	0.0312217i
$361$	−12.2103	−	13.5610i	−0.642650	−	0.713735i
$362$	23.6545	+	21.2986i	1.24325	+	1.11943i
$363$	−10.2986	+	3.34622i	−0.540537	+	0.175631i
$364$	−9.39957	+	17.4390i	−0.492671	+	0.914053i
$365$	12.2075	+	4.05210i	0.638970	+	0.212096i
$366$	14.0492	−	15.6032i	0.734362	−	0.815591i
$367$	5.88340	−	0.618370i	0.307111	−	0.0322787i	0.0502806	−	0.998735i	$-0.483988\pi$
$367$	5.88340	−	0.618370i	0.307111	−	0.0322787i	0.256831	+	0.966456i	$0.417322\pi$
$368$	−24.1534	−	13.9449i	−1.25908	−	0.726930i
$369$	6.62908	+	2.95146i	0.345096	+	0.153647i
$370$	−33.2173	−	0.210345i	−1.72689	−	0.0109353i
$371$	−23.2139	−	24.3127i	−1.20520	−	1.26225i
$372$	5.64973	−	7.77619i	0.292925	−	0.403176i
$373$	5.12965	+	24.1331i	0.265603	+	1.24957i	0.885410	+	0.464811i	$0.153878\pi$
$373$	5.12965	+	24.1331i	0.265603	+	1.24957i	−0.619807	+	0.784754i	$0.712789\pi$
$374$	2.73744	−	4.74139i	0.141550	−	0.245172i
$375$	4.35262	+	10.2983i	0.224768	+	0.531801i
$376$	1.28257	+	2.22147i	0.0661434	+	0.114564i
$377$	−24.2196	−	7.86944i	−1.24738	−	0.405297i
$378$	1.22778	+	5.04591i	0.0631500	+	0.259534i
$379$	−2.94724	−	2.14129i	−0.151390	−	0.109991i	0.509512	−	0.860464i	$-0.329826\pi$
$379$	−2.94724	−	2.14129i	−0.151390	−	0.109991i	−0.660902	+	0.750473i	$0.729826\pi$
$380$	1.77640	+	3.12231i	0.0911273	+	0.160171i
$381$	0.986355	+	9.38454i	0.0505325	+	0.480785i
$382$	−9.18502	−	5.30297i	−0.469946	−	0.271324i
$383$	5.74450	−	12.9023i	0.293530	−	0.659279i	−0.705234	−	0.708974i	$-0.749158\pi$
$383$	5.74450	−	12.9023i	0.293530	−	0.659279i	0.998764	+	0.0496950i	$0.0158249\pi$
$384$	−0.712969	−	2.19429i	−0.0363835	−	0.111977i
$385$	0.0561095	+	2.44860i	0.00285961	+	0.124792i
$386$	2.64183	−	8.13071i	0.134465	−	0.413842i
$387$	8.81619	+	7.93813i	0.448152	+	0.403518i
$388$	1.25512	−	5.90488i	0.0637191	−	0.299775i
$389$	−12.7620	−	14.1736i	−0.647057	−	0.718629i	0.326977	−	0.945032i	$-0.393970\pi$
$389$	−12.7620	−	14.1736i	−0.647057	−	0.718629i	−0.974034	+	0.226403i	$0.927303\pi$
$390$	17.6295	+	1.96588i	0.892704	+	0.0995462i
$391$	−13.5893	−	41.8235i	−0.687240	−	2.11511i
$392$	−1.95850	−	0.511940i	−0.0989193	−	0.0258569i
$393$			6.29018i			0.317297i
$394$	−12.7087	−	5.65827i	−0.640254	−	0.285059i
$395$	−20.0015	+	8.75390i	−1.00638	+	0.440456i
$396$	−0.700691	+	0.311968i	−0.0352110	+	0.0156770i
$397$	−12.1002	−	1.27178i	−0.607292	−	0.0638289i	−0.204109	−	0.978948i	$-0.565430\pi$
$397$	−12.1002	−	1.27178i	−0.607292	−	0.0638289i	−0.403183	+	0.915119i	$0.632096\pi$
$398$	15.9494	+	5.18227i	0.799471	+	0.259764i
$399$	−0.772448	−	2.16027i	−0.0386708	−	0.108149i
$400$	−6.34423	−	20.4011i	−0.317211	−	1.02006i
$401$	9.45656	+	16.3792i	0.472238	+	0.817940i	0.999495	−	0.0317656i	$-0.0101130\pi$
$401$	9.45656	+	16.3792i	0.472238	+	0.817940i	−0.527258	+	0.849706i	$0.676780\pi$
$402$	−6.68326	+	6.01763i	−0.333331	+	0.300132i
$403$	8.52869	+	19.1557i	0.424844	+	0.954216i
$404$	1.70534	−	16.2252i	0.0848436	−	0.807233i
$405$	1.81730	−	1.30285i	0.0903025	−	0.0647390i
$406$	−2.46736	+	32.6284i	−0.122453	+	1.61932i
$407$			3.13333i			0.155313i
$408$	0.792479	−	1.77994i	0.0392335	−	0.0881200i
$409$	−2.10283	−	0.446970i	−0.103978	−	0.0221013i	0.155629	−	0.987816i	$-0.450260\pi$
$409$	−2.10283	−	0.446970i	−0.103978	−	0.0221013i	−0.259607	+	0.965714i	$0.583593\pi$
$410$	−27.4802	−	16.0986i	−1.35715	−	0.795052i
$411$	0.793448	−	0.168652i	0.0391379	−	0.00831901i
$412$	−4.39426	+	1.42778i	−0.216490	+	0.0703418i
$413$	−26.3008	+	3.54456i	−1.29418	+	0.174416i
$414$	−3.95896	+	12.1844i	−0.194572	+	0.598832i
$415$	−0.0797377	+	0.176084i	−0.00391417	+	0.00864364i
$416$	−30.8702	−	6.56166i	−1.51354	−	0.321712i
$417$	7.76288	−	0.815911i	0.380150	−	0.0399553i
$418$	0.610234	−	0.352319i	0.0298475	−	0.0172325i
$419$	2.73721	−	1.98870i	0.133722	−	0.0971544i	−0.518914	−	0.854827i	$-0.673663\pi$
$419$	2.73721	−	1.98870i	0.133722	−	0.0971544i	0.652635	+	0.757672i	$0.273663\pi$
$420$	−1.39510	−	10.8714i	−0.0680742	−	0.530469i
$421$	13.2347	+	9.61558i	0.645020	+	0.468635i	0.861571	−	0.507637i	$-0.169481\pi$
$421$	13.2347	+	9.61558i	0.645020	+	0.468635i	−0.216551	+	0.976271i	$0.569481\pi$
$422$	11.4366	+	1.20203i	0.556725	+	0.0585141i
$423$	6.59182	−	5.93530i	0.320505	−	0.288584i
$424$	1.83712	−	3.18198i	0.0892183	−	0.154531i
$425$	14.0905	−	30.5989i	0.683490	−	1.48426i
$426$	−3.92338			−0.190088
$427$	24.0855	−	14.8613i	1.16558	−	0.719188i
$428$	−15.4184	+	21.2216i	−0.745276	+	1.02579i
$429$	0.174900	−	1.66407i	0.00844427	−	0.0803418i
$430$	−34.5948	−	38.9141i	−1.66831	−	1.87661i
$431$	0.00767857	+	0.0730567i	0.000369864	+	0.00351902i	0.994705	−	0.102769i	$-0.0327702\pi$
$431$	0.00767857	+	0.0730567i	0.000369864	+	0.00351902i	−0.994335	+	0.106288i	$0.966104\pi$
$432$	−3.70049	+	2.13648i	−0.178040	+	0.102791i
$433$	−12.3480	−	16.9956i	−0.593408	−	0.816756i	0.401677	−	0.915781i	$-0.368427\pi$
$433$	−12.3480	−	16.9956i	−0.593408	−	0.816756i	−0.995085	+	0.0990255i	$0.968427\pi$
$434$	21.3247	−	16.4671i	1.02362	−	0.790445i
$435$	13.4270	−	4.26889i	0.643776	−	0.204678i
$436$	36.2673	−	7.70886i	1.73689	−	0.369187i
$437$	1.17675	−	5.53616i	0.0562915	−	0.264831i
$438$	−2.34746	+	11.0439i	−0.112166	+	0.527700i
$439$	28.6085	−	6.08092i	1.36541	−	0.290226i	0.533810	−	0.845605i	$-0.320760\pi$
$439$	28.6085	−	6.08092i	1.36541	−	0.290226i	0.831598	+	0.555378i	$0.187427\pi$
$440$	−0.255124	+	0.0811125i	−0.0121626	+	0.00386689i
$441$	−0.323518	+	6.99252i	−0.0154056	+	0.332977i
$442$	−31.4162	−	43.2406i	−1.49431	−	2.05675i
$443$	−1.24540	+	0.719030i	−0.0591705	+	0.0341621i	−0.529293	−	0.848439i	$-0.677543\pi$
$443$	−1.24540	+	0.719030i	−0.0591705	+	0.0341621i	0.470123	+	0.882601i	$0.344210\pi$
$444$	−1.46568	−	13.9450i	−0.0695582	−	0.661802i
$445$	−10.4612	−	11.7673i	−0.495906	−	0.557823i
$446$	0.0402639	−	0.383085i	0.00190655	−	0.0181396i
$447$	−5.21534	+	7.17830i	−0.246677	+	0.339522i
$448$	0.524583	+	17.9335i	0.0247842	+	0.847279i
$449$	1.84509			0.0870753			0.0435377	−	0.999052i	$-0.486137\pi$
$449$	1.84509			0.0870753			0.0435377	+	0.999052i	$0.486137\pi$
$450$	−8.56073	+	4.79902i	−0.403557	+	0.226228i
$451$	−1.50207	+	2.60167i	−0.0707299	+	0.122508i
$452$	11.8899	−	10.7058i	0.559256	−	0.503556i
$453$	15.2228	+	1.59998i	0.715231	+	0.0751738i
$454$	−20.2811	−	14.7351i	−0.951841	−	0.691553i
$455$	22.0605	+	9.22238i	1.03421	+	0.432352i
$456$	0.202872	−	0.147395i	0.00950035	−	0.00690241i
$457$	−10.6480	+	6.14760i	−0.498090	+	0.287572i	−0.727924	−	0.685657i	$-0.759515\pi$
$457$	−10.6480	+	6.14760i	−0.498090	+	0.287572i	0.229834	+	0.973230i	$0.426182\pi$
$458$	−5.49163	+	0.577193i	−0.256607	+	0.0269705i
$459$	−6.59023	−	1.40080i	−0.307606	−	0.0653836i
$460$	11.1542	−	24.6318i	0.520068	−	1.14846i
$461$	−6.96579	+	21.4385i	−0.324429	+	0.998490i	0.647269	+	0.762262i	$0.275911\pi$
$461$	−6.96579	+	21.4385i	−0.324429	+	0.998490i	−0.971698	+	0.236228i	$0.924089\pi$
$462$	−2.13069	+	0.287153i	−0.0991285	+	0.0133596i
$463$	−0.693566	+	0.225353i	−0.0322327	+	0.0104730i	−0.325089	−	0.945683i	$-0.605394\pi$
$463$	−0.693566	+	0.225353i	−0.0322327	+	0.0104730i	0.292856	+	0.956156i	$0.405394\pi$
$464$	−26.3352	+	5.59772i	−1.22258	+	0.259868i
$465$	−10.0099	−	5.86402i	−0.464196	−	0.271937i
$466$	35.6776	+	7.58351i	1.65273	+	0.351299i
$467$	−2.74092	+	6.15620i	−0.126835	+	0.284875i	−0.965790	−	0.259325i	$-0.916500\pi$
$467$	−2.74092	+	6.15620i	−0.126835	+	0.284875i	0.838956	+	0.544200i	$0.183167\pi$
$468$			7.48781i			0.346124i
$469$	−10.9253	+	5.25225i	−0.504484	+	0.242526i
$470$	−31.6403	+	22.6833i	−1.45946	+	1.04630i
$471$	0.327748	−	3.11832i	0.0151018	−	0.143684i
$472$	−1.17983	−	2.64994i	−0.0543061	−	0.121973i
$473$	−3.64989	+	3.28637i	−0.167822	+	0.151108i
$474$	−9.58261	−	16.5976i	−0.440144	−	0.762351i
$475$	3.53962	−	2.50382i	0.162409	−	0.114883i
$476$	−21.3710	+	25.1780i	−0.979538	+	1.15403i
$477$	−12.0836	−	3.92619i	−0.553268	−	0.179768i
$478$	−25.8572	−	2.71770i	−1.18268	−	0.124305i
$479$	−2.95827	+	1.31711i	−0.135167	+	0.0601801i	−0.473205	−	0.880952i	$-0.656903\pi$
$479$	−2.95827	+	1.31711i	−0.135167	+	0.0601801i	0.338039	+	0.941132i	$0.390237\pi$
$480$	15.9958	−	7.00077i	0.730106	−	0.319540i
$481$	27.9444	+	12.4417i	1.27416	+	0.567291i
$482$		−	25.0760i		−	1.14218i
$483$	−9.73763	+	14.2617i	−0.443077	+	0.648931i
$484$	6.19944	+	19.0799i	0.281793	+	0.867269i
$485$	−7.24120	−	0.807472i	−0.328806	−	0.0366654i
$486$	1.31338	+	1.45866i	0.0595763	+	0.0661662i
$487$	−0.319217	+	1.50180i	−0.0144651	+	0.0680530i	−0.984788	−	0.173759i	$-0.944409\pi$
$487$	−0.319217	+	1.50180i	−0.0144651	+	0.0680530i	0.970323	+	0.241812i	$0.0777418\pi$
$488$	2.29885	+	2.06989i	0.104064	+	0.0936997i
$489$	3.73483	−	11.4946i	0.168895	−	0.519805i
$490$	4.81238	−	30.3438i	0.217401	−	1.37079i
$491$	7.41184	+	22.8113i	0.334492	+	1.02946i	0.966972	+	0.254883i	$0.0820369\pi$
$491$	7.41184	+	22.8113i	0.334492	+	1.02946i	−0.632480	+	0.774576i	$0.717963\pi$
$492$	5.46807	−	12.2815i	0.246519	−	0.553692i
$493$	−36.7647	−	21.2261i	−1.65580	−	0.955975i
$494$	−0.719050	−	6.84130i	−0.0323516	−	0.307805i
$495$	0.457778	+	0.804619i	0.0205756	+	0.0361649i
$496$	17.9348	+	13.0304i	0.805298	+	0.585083i
$497$	−5.07525	−	1.48646i	−0.227656	−	0.0666769i
$498$	−0.161372	−	0.0524329i	−0.00723124	−	0.00234957i
$499$	14.5497	+	25.2007i	0.651332	+	1.12814i	0.982800	+	0.184674i	$0.0591228\pi$
$499$	14.5497	+	25.2007i	0.651332	+	1.12814i	−0.331468	+	0.943467i	$0.607544\pi$
$500$	19.0793	−	8.06395i	0.853253	−	0.360631i
$501$	−3.39636	+	5.88268i	−0.151738	+	0.262819i
$502$	9.99638	+	47.0293i	0.446160	+	2.09902i
$503$	24.6343	−	33.9062i	1.09839	−	1.51180i	0.260886	−	0.965370i	$-0.415985\pi$
$503$	24.6343	−	33.9062i	1.09839	−	1.51180i	0.837503	−	0.546433i	$-0.184015\pi$
$504$	−0.743425	+	0.180891i	−0.0331148	+	0.00805752i
$505$	−19.6904	−	0.124687i	−0.876210	−	0.00554851i
$506$	−4.84538	−	2.15730i	−0.215403	−	0.0959037i
$507$	−2.88806	−	1.66742i	−0.128263	−	0.0740528i
$508$	17.3864	−	1.82739i	0.771399	−	0.0810773i
$509$	−10.6794	+	11.8607i	−0.473356	+	0.525715i	−0.931782	−	0.363018i	$-0.881746\pi$
$509$	−10.6794	+	11.8607i	−0.473356	+	0.525715i	0.458427	+	0.888732i	$0.348413\pi$
$510$	28.0650	+	9.31576i	1.24274	+	0.412509i
$511$	−7.22090	+	13.3969i	−0.319434	+	0.592646i
$512$	−29.3827	+	9.54702i	−1.29854	+	0.421922i
$513$	−0.644406	−	0.580226i	−0.0284512	−	0.0256176i
$514$	18.7107	+	20.7804i	0.825295	+	0.916583i
$515$	2.23589	+	5.10871i	0.0985250	+	0.225117i
$516$	14.7067	−	16.3335i	0.647427	−	0.719041i
$517$	2.15849	+	2.97090i	0.0949301	+	0.130660i
$518$	7.04418	−	38.6677i	0.309504	−	1.69896i
$519$	3.87052	−	2.81210i	0.169897	−	0.123437i
$520$	−0.289637	+	2.59739i	−0.0127014	+	0.113903i
$521$	37.8996	−	16.8740i	1.66041	−	0.739263i	0.660479	−	0.750844i	$-0.270353\pi$
$521$	37.8996	−	16.8740i	1.66041	−	0.739263i	0.999933	+	0.0115809i	$0.00368639\pi$
$522$	5.03035	+	11.2983i	0.220172	+	0.494515i
$523$	−1.91348	−	9.00222i	−0.0836707	−	0.393640i	0.916306	−	0.400479i	$-0.131156\pi$
$523$	−1.91348	−	9.00222i	−0.0836707	−	0.393640i	−0.999977	+	0.00683943i	$0.997823\pi$
$524$	11.6536			0.509090
$525$	−12.8923	+	2.96455i	−0.562666	+	0.129383i
$526$	12.9369			0.564076
$527$	7.26752	+	34.1910i	0.316578	+	1.48938i
$528$	−0.719516	−	1.61606i	−0.0313129	−	0.0703299i
$529$	−17.9079	+	7.97311i	−0.778604	+	0.346657i
$530$	50.7984	+	23.0034i	2.20654	+	0.999205i
$531$	−8.11494	+	5.89585i	−0.352159	+	0.255858i
$532$	−4.00227	+	1.43109i	−0.173520	+	0.0620456i
$533$	17.2385	+	23.7267i	0.746682	+	1.02772i
$534$	9.24803	−	10.2710i	0.400201	−	0.444469i
$535$	27.3174	+	16.0032i	1.18103	+	0.691879i
$536$	−0.886591	−	0.984659i	−0.0382949	−	0.0425308i
$537$	−14.7630	−	13.2926i	−0.637069	−	0.573619i
$538$	21.7857	−	7.07862i	0.939250	−	0.305181i
$539$	−2.86503	−	0.435801i	−0.123406	−	0.0187713i
$540$	−2.41374	−	3.36686i	−0.103871	−	0.144887i
$541$	4.65973	−	5.17516i	0.200338	−	0.222497i	−0.634602	−	0.772839i	$-0.718836\pi$
$541$	4.65973	−	5.17516i	0.200338	−	0.222497i	0.834939	+	0.550342i	$0.185503\pi$
$542$	0.165542	−	0.0173991i	0.00711063	−	0.000747357i
$543$	14.0440	+	8.10831i	0.602686	+	0.347961i
$544$	−48.0622	−	21.3987i	−2.06065	−	0.917461i
$545$	−13.5589	−	42.6470i	−0.580800	−	1.82680i
$546$	−5.89946	+	20.1426i	−0.252474	+	0.862025i
$547$	−23.8261	+	32.7939i	−1.01873	+	1.40216i	−0.105643	+	0.994404i	$0.533690\pi$
$547$	−23.8261	+	32.7939i	−1.01873	+	1.40216i	−0.913089	+	0.407760i	$0.866310\pi$
$548$	−0.312457	−	1.46999i	−0.0133475	−	0.0627951i
$549$	5.34846	−	9.26381i	0.228267	−	0.395370i
$550$	−1.60544	−	3.73239i	−0.0684562	−	0.159150i
$551$	−2.73187	−	4.73174i	−0.116382	−	0.201579i
$552$	−1.79516	−	0.583282i	−0.0764070	−	0.0248261i
$553$	−6.10761	−	25.1011i	−0.259722	−	1.06741i
$554$	−29.0171	−	21.0822i	−1.23282	−	0.895695i
$555$	−16.5757	+	3.41372i	−0.703601	+	0.144904i
$556$	−1.51161	−	14.3820i	−0.0641067	−	0.609934i
$557$	−0.157615	−	0.0909993i	−0.00667838	−	0.00385577i	0.496657	−	0.867947i	$-0.334561\pi$
$557$	−0.157615	−	0.0909993i	−0.00667838	−	0.00385577i	−0.503335	+	0.864091i	$0.667894\pi$
$558$	4.14196	−	9.30299i	0.175343	−	0.393827i
$559$	14.8166	+	45.6007i	0.626674	+	1.92870i
$560$	25.0735	−	3.21764i	1.05955	−	0.135970i
$561$	0.861940	−	2.65278i	0.0363911	−	0.112000i
$562$	−5.32405	−	4.79380i	−0.224582	−	0.202214i
$563$	5.37830	−	25.3029i	0.226668	−	1.06639i	−0.706712	−	0.707502i	$-0.749822\pi$
$563$	5.37830	−	25.3029i	0.226668	−	1.06639i	0.933380	−	0.358889i	$-0.116844\pi$
$564$	−10.9961	−	12.2125i	−0.463021	−	0.514237i
$565$	−14.2684	−	13.0119i	−0.600276	−	0.547413i
$566$	4.24325	+	13.0594i	0.178357	+	0.548927i
$567$	1.14634	+	2.38452i	0.0481415	+	0.100140i
$568$		−	0.578040i		−	0.0242540i
$569$	−34.2351	−	15.2424i	−1.43521	−	0.638996i	−0.465899	−	0.884838i	$-0.654269\pi$
$569$	−34.2351	−	15.2424i	−1.43521	−	0.638996i	−0.969310	+	0.245841i	$0.920936\pi$
$570$	2.52865	+	2.84437i	0.105914	+	0.119138i
$571$	−20.0957	+	8.94720i	−0.840981	+	0.374429i	−0.781580	−	0.623805i	$-0.785586\pi$
$571$	−20.0957	+	8.94720i	−0.840981	+	0.374429i	−0.0594011	+	0.998234i	$0.518919\pi$
$572$	−3.08296	−	0.324032i	−0.128905	−	0.0135485i
$573$	−5.13896	−	1.66975i	−0.214683	−	0.0697547i
$574$	24.3857	−	28.7297i	1.01784	−	1.19915i
$575$	−30.9078	−	10.4771i	−1.28895	−	0.436927i
$576$	3.39056	+	5.87263i	0.141273	+	0.244693i
$577$	15.7918	−	14.2190i	0.657420	−	0.591944i	−0.271404	−	0.962466i	$-0.587488\pi$
$577$	15.7918	−	14.2190i	0.657420	−	0.591944i	0.928824	+	0.370522i	$0.120821\pi$
$578$	−22.6679	−	50.9128i	−0.942859	−	2.11770i
$579$	0.455277	−	4.33167i	0.0189207	−	0.180018i
$580$	−7.90884	−	24.8758i	−0.328397	−	1.03291i
$581$	−0.188884	−	0.128966i	−0.00783622	−	0.00535042i
$582$		−	6.39572i		−	0.265111i
$583$	2.13944	−	4.80526i	0.0886066	−	0.199014i
$584$	−1.62713	−	0.345856i	−0.0673310	−	0.0143116i
$585$	8.99367	−	0.887731i	0.371843	−	0.0367032i
$586$	25.8007	−	5.48410i	1.06582	−	0.226546i
$587$	19.2001	−	6.23851i	0.792475	−	0.257491i	0.115317	−	0.993329i	$-0.463212\pi$
$587$	19.2001	−	6.23851i	0.792475	−	0.257491i	0.677158	+	0.735838i	$0.263212\pi$
$588$	12.9548	+	0.599371i	0.534248	+	0.0247177i
$589$	−1.39021	+	4.27862i	−0.0572826	+	0.176298i
$590$	38.2649	−	21.7703i	1.57534	−	0.896271i
$591$	−6.93256	−	1.47356i	−0.285167	−	0.0606142i
$592$	32.1626	−	3.38042i	1.32187	−	0.138935i
$593$	−29.4901	+	17.0261i	−1.21101	+	0.699180i	−0.962980	−	0.269572i	$-0.913118\pi$
$593$	−29.4901	+	17.0261i	−1.21101	+	0.699180i	−0.248034	+	0.968751i	$0.579785\pi$
$594$	−0.657411	+	0.477637i	−0.0269739	+	0.0195977i
$595$	32.7751	+	22.6838i	1.34365	+	0.929947i
$596$	13.2990	+	9.66230i	0.544749	+	0.395783i
$597$	8.49711	+	0.893083i	0.347764	+	0.0365514i
$598$	−38.4795	+	34.6471i	−1.57355	+	1.41683i
$599$	−21.6136	+	37.4359i	−0.883108	+	1.52959i	−0.0352419	+	0.999379i	$0.511220\pi$
$599$	−21.6136	+	37.4359i	−0.883108	+	1.52959i	−0.847866	+	0.530210i	$0.822113\pi$
$600$	−0.707050	−	1.26127i	−0.0288652	−	0.0514911i
$601$	3.24837			0.132504			0.0662520	−	0.997803i	$-0.478896\pi$
$601$	3.24837			0.132504			0.0662520	+	0.997803i	$0.478896\pi$
$602$	52.4306	−	32.3509i	2.13691	−	1.31852i
$603$	−2.69310	+	3.70674i	−0.109672	+	0.150950i
$604$	2.96424	−	28.2029i	0.120613	−	1.14756i
$605$	22.1821	−	9.70825i	0.901829	−	0.394696i
$606$	−1.80673	−	17.1899i	−0.0733934	−	0.698291i
$607$	−11.9769	+	6.91486i	−0.486127	+	0.280665i	−0.722966	−	0.690883i	$-0.757222\pi$
$607$	−11.9769	+	6.91486i	−0.486127	+	0.280665i	0.236840	+	0.971549i	$0.423888\pi$
$608$	−3.98000	−	5.47799i	−0.161410	−	0.222162i
$609$	2.22658	+	16.5213i	0.0902255	+	0.669477i
$610$	−27.8358	+	37.8069i	−1.12704	+	1.53076i
$611$	35.0666	−	7.45364i	1.41864	−	0.301542i
$612$	−2.59521	+	12.2095i	−0.104905	+	0.493540i
$613$	2.55603	−	12.0252i	0.103237	−	0.485692i	−0.895904	−	0.444248i	$-0.853471\pi$
$613$	2.55603	−	12.0252i	0.103237	−	0.485692i	0.999141	−	0.0414441i	$-0.0131959\pi$
$614$	−20.6115	+	4.38110i	−0.831811	+	0.176807i
$615$	−15.3997	−	5.11169i	−0.620974	−	0.206123i
$616$	−0.0423069	−	0.313919i	−0.00170459	−	0.0126481i
$617$	16.7839	+	23.1011i	0.675696	+	0.930015i	0.999872	−	0.0159811i	$-0.00508717\pi$
$617$	16.7839	+	23.1011i	0.675696	+	0.930015i	−0.324176	+	0.945997i	$0.605087\pi$
$618$	−4.23929	+	2.44756i	−0.170529	+	0.0984551i
$619$	0.394225	+	3.75080i	0.0158453	+	0.150758i	0.999584	−	0.0288490i	$-0.00918420\pi$
$619$	0.394225	+	3.75080i	0.0158453	+	0.150758i	−0.983739	+	0.179607i	$0.942518\pi$
$620$	−10.8641	+	18.5449i	−0.436312	+	0.744782i
$621$	−0.682264	+	6.49131i	−0.0273783	+	0.260487i
$622$	30.4493	−	41.9099i	1.22091	−	1.68043i
$623$	15.8546	−	9.78262i	0.635199	−	0.391932i
$624$	−17.2698			−0.691343
$625$	−11.9477	−	21.9603i	−0.477906	−	0.878411i
$626$	−12.9623	+	22.4514i	−0.518078	+	0.897338i
$627$	0.266783	−	0.240213i	0.0106543	−	0.00959316i
$628$	−5.77721	−	0.607209i	−0.230536	−	0.0242303i
$629$	41.2536	+	29.9725i	1.64489	+	1.19508i
$630$	−3.84043	−	10.9588i	−0.153006	−	0.436608i
$631$	33.6598	−	24.4552i	1.33997	−	0.973548i	0.340529	−	0.940234i	$-0.389394\pi$
$631$	33.6598	−	24.4552i	1.33997	−	0.973548i	0.999445	−	0.0333142i	$-0.0106062\pi$
$632$	2.44535	−	1.41183i	0.0972710	−	0.0561594i
$633$	5.82661	−	0.612401i	0.231587	−	0.0243408i
$634$	−9.25580	−	1.96738i	−0.367595	−	0.0781347i
$635$	−4.25617	−	20.6663i	−0.168901	−	0.820119i
$636$	−7.27392	+	22.3868i	−0.288430	+	0.887695i
$637$	−15.2630	+	23.8212i	−0.604742	+	0.943830i
$638$	−4.86956	+	1.58222i	−0.192788	+	0.0626405i
$639$	−1.95517	+	0.415584i	−0.0773452	+	0.0164402i
$640$	2.06851	+	4.72626i	0.0817648	+	0.186822i
$641$	22.6421	+	4.81274i	0.894311	+	0.190092i	0.632070	−	0.774911i	$-0.282205\pi$
$641$	22.6421	+	4.81274i	0.894311	+	0.190092i	0.262240	+	0.965003i	$0.415539\pi$
$642$	−11.3036	+	25.3883i	−0.446118	+	1.00200i
$643$			36.1493i			1.42559i	0.701373	+	0.712795i	$0.252571\pi$
$643$			36.1493i			1.42559i	−0.701373	+	0.712795i	$0.747429\pi$
$644$	26.4223	+	18.0406i	1.04118	+	0.710899i
$645$	−21.3618	−	15.7279i	−0.841122	−	0.619286i
$646$	1.19866	−	11.4045i	0.0471608	−	0.448705i
$647$	−2.12310	−	4.76856i	−0.0834677	−	0.187472i	0.866990	−	0.498326i	$-0.166052\pi$
$647$	−2.12310	−	4.76856i	−0.0834677	−	0.187472i	−0.950458	+	0.310854i	$0.899385\pi$
$648$	−0.214908	+	0.193504i	−0.00844237	+	0.00760154i
$649$	−2.07633	−	3.59631i	−0.0815031	−	0.141167i
$650$	−39.6619	−	0.502329i	−1.55567	−	0.0197030i
$651$	8.88265	−	10.4650i	0.348138	−	0.410155i
$652$	−21.2957	−	6.91940i	−0.834005	−	0.270985i
$653$	5.84746	+	0.614592i	0.228829	+	0.0240509i	0.218249	−	0.975893i	$-0.429966\pi$
$653$	5.84746	+	0.614592i	0.228829	+	0.0240509i	0.0105799	+	0.999944i	$0.496632\pi$
$654$	35.8859	−	15.9775i	1.40325	−	0.624768i
$655$	−1.38161	−	13.9972i	−0.0539841	−	0.546918i
$656$	28.3258	+	12.6114i	1.10594	+	0.492394i
$657$			5.75226i			0.224417i
$658$	−19.9583	−	41.5158i	−0.778057	−	1.61845i
$659$	−11.2893	−	34.7449i	−0.439769	−	1.35347i	−0.888120	−	0.459611i	$-0.847989\pi$
$659$	−11.2893	−	34.7449i	−0.439769	−	1.35347i	0.448352	−	0.893857i	$-0.352011\pi$
$660$	1.49069	−	0.848111i	0.0580251	−	0.0330127i
$661$	−12.9786	−	14.4142i	−0.504809	−	0.560648i	0.435842	−	0.900023i	$-0.356451\pi$
$661$	−12.9786	−	14.4142i	−0.504809	−	0.560648i	−0.940651	+	0.339376i	$0.889784\pi$
$662$	−13.2187	+	62.1893i	−0.513761	+	2.41706i
$663$	−20.2361	−	18.2207i	−0.785905	−	0.707632i
$664$	0.00772505	−	0.0237753i	0.000299790	−	0.000922659i
$665$	2.19339	+	4.63749i	0.0850560	+	0.179834i
$666$	−4.59062	−	14.1285i	−0.177883	−	0.547467i
$667$	−16.7277	+	37.5710i	−0.647698	+	1.45475i
$668$	10.8986	+	6.29234i	0.421681	+	0.243458i
$669$	−0.0205133	−	0.195171i	−0.000793089	−	0.00754574i
$670$	13.5502	−	14.8587i	0.523490	−	0.574042i
$671$	3.58274	+	2.60301i	0.138310	+	0.100488i
$672$	4.88446	+	20.0741i	0.188422	+	0.774376i
$673$	29.9868	+	9.74329i	1.15591	+	0.375576i	0.823365	−	0.567513i	$-0.192094\pi$
$673$	29.9868	+	9.74329i	1.15591	+	0.375576i	0.332541	+	0.943089i	$0.392094\pi$
$674$	3.29535	+	5.70771i	0.126932	+	0.219853i
$675$	−3.75780	+	3.29833i	−0.144638	+	0.126953i
$676$	−3.08918	+	5.35062i	−0.118815	+	0.205793i
$677$	−3.07276	−	14.4562i	−0.118096	−	0.555596i	−0.996918	−	0.0784475i	$-0.975004\pi$
$677$	−3.07276	−	14.4562i	−0.118096	−	0.555596i	0.878823	−	0.477149i	$-0.158330\pi$
$678$	9.96341	−	13.7135i	0.382643	−	0.526662i
$679$	2.42317	−	8.27345i	0.0929926	−	0.317506i
$680$	−1.37251	+	4.13488i	−0.0526334	+	0.158565i
$681$	−11.6677	−	5.19478i	−0.447106	−	0.199064i
$682$	3.65108	+	2.10795i	0.139807	+	0.0807177i
$683$	−29.4510	+	3.09543i	−1.12691	+	0.118443i	−0.649589	−	0.760285i	$-0.725059\pi$
$683$	−29.4510	+	3.09543i	−1.12691	+	0.118443i	−0.477322	+	0.878728i	$0.658393\pi$
$684$	−1.07497	+	1.19387i	−0.0411024	+	0.0456488i
$685$	−1.72858	+	0.549572i	−0.0660456	+	0.0209981i
$686$	34.3769	+	11.8191i	1.31252	+	0.451256i
$687$	−2.67555	+	0.869337i	−0.102078	+	0.0331673i
$688$	37.6712	+	33.9193i	1.43620	+	1.29316i
$689$	−34.3603	−	38.1610i	−1.30902	−	1.45382i
$690$	6.13343	−	27.9830i	0.233496	−	1.06530i
$691$	−6.82543	+	7.58040i	−0.259651	+	0.288372i	−0.858849	−	0.512229i	$-0.828820\pi$
$691$	−6.82543	+	7.58040i	−0.259651	+	0.288372i	0.599197	+	0.800601i	$0.295486\pi$
$692$	−5.20988	−	7.17079i	−0.198050	−	0.272592i
$693$	−1.03138	+	0.368792i	−0.0391791	+	0.0140092i
$694$	21.4050	−	15.5517i	0.812523	−	0.590333i
$695$	−17.0952	+	3.52070i	−0.648457	+	0.133548i
$696$	−1.66461	+	0.741132i	−0.0630969	+	0.0280925i
$697$	19.8853	+	44.6631i	0.753210	+	1.69174i
$698$	−7.95670	−	37.4333i	−0.301166	−	1.41687i
$699$	18.5828			0.702865
$700$	5.49232	+	23.8852i	0.207590	+	0.902774i
$701$	−19.7045			−0.744231			−0.372115	−	0.928187i	$-0.621367\pi$
$701$	−19.7045			−0.744231			−0.372115	+	0.928187i	$0.621367\pi$
$702$	1.64937	+	7.75966i	0.0622513	+	0.292869i
$703$	2.66936	+	5.99548i	0.100677	+	0.226124i
$704$	−2.56466	+	1.14186i	−0.0966594	+	0.0430356i
$705$	−13.3648	+	14.6554i	−0.503348	+	0.551955i
$706$	46.2715	−	33.6182i	1.74145	−	1.26524i
$707$	4.17561	−	22.9212i	0.157040	−	0.862040i
$708$	10.9231	+	15.0343i	0.410513	+	0.565023i
$709$	2.45147	−	2.72263i	0.0920669	−	0.102251i	−0.695351	−	0.718671i	$-0.744751\pi$
$709$	2.45147	−	2.72263i	0.0920669	−	0.102251i	0.787418	+	0.616420i	$0.211418\pi$
$710$	8.73052	−	0.861756i	0.327650	−	0.0323411i
$711$	−6.53347	−	7.25615i	−0.245024	−	0.272127i
$712$	1.51324	+	1.36253i	0.0567112	+	0.0510630i
$713$	32.2059	−	10.4643i	1.20612	−	0.391893i
$714$	−16.6008	+	30.7995i	−0.621270	+	1.15264i
$715$	−0.0236919	+	3.74138i	−0.000886027	+	0.139920i
$716$	−24.6268	+	27.3509i	−0.920348	+	1.02215i
$717$	−13.1735	+	1.38459i	−0.491973	+	0.0517084i
$718$	−3.08222	−	1.77952i	−0.115027	−	0.0664111i
$719$	−35.9484	−	16.0053i	−1.34065	−	0.596896i	−0.393985	−	0.919117i	$-0.628904\pi$
$719$	−35.9484	−	16.0053i	−1.34065	−	0.596896i	−0.946664	+	0.322221i	$0.895571\pi$
$720$	7.76526	−	5.56701i	0.289394	−	0.207470i
$721$	−6.41122	+	1.55999i	−0.238766	+	0.0580969i
$722$	−21.0531	+	28.9771i	−0.783516	+	1.07842i
$723$	−2.65618	−	12.4963i	−0.0987843	−	0.464743i
$724$	15.0220	−	26.0189i	0.558288	−	0.966984i
$725$	−28.9409	+	12.4486i	−1.07484	+	0.462328i
$726$	10.6273	+	18.4070i	0.394416	+	0.683149i
$727$	−48.0642	−	15.6170i	−1.78260	−	0.579202i	−0.783492	−	0.621402i	$-0.786563\pi$
$727$	−48.0642	−	15.6170i	−1.78260	−	0.579202i	−0.999109	+	0.0422003i	$0.986563\pi$
$728$	−2.96766	−	0.869180i	−0.109989	−	0.0322140i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	2.79794	−	25.0912i	0.103556	−	0.928666i
$731$	8.35484	+	79.4910i	0.309015	+	2.94008i
$732$	−17.1628	−	9.90893i	−0.634354	−	0.366244i
$733$	6.71374	−	15.0793i	0.247978	−	0.556967i	−0.746076	−	0.665861i	$-0.768064\pi$
$733$	6.71374	−	15.0793i	0.247978	−	0.556967i	0.994053	+	0.108894i	$0.0347309\pi$
$734$	−3.58821	−	11.0434i	−0.132443	−	0.407618i
$735$	−0.815971	−	15.6312i	−0.0300975	−	0.576565i
$736$	−15.7499	+	48.4732i	−0.580549	+	1.78675i
$737$	−1.40963	−	1.26924i	−0.0519245	−	0.0467530i
$738$	2.96130	−	13.9318i	0.109007	−	0.512838i
$739$	−3.56715	−	3.96172i	−0.131220	−	0.145734i	0.673954	−	0.738773i	$-0.264595\pi$
$739$	−3.56715	−	3.96172i	−0.131220	−	0.145734i	−0.805174	+	0.593039i	$0.797928\pi$
$740$	6.32449	+	30.7093i	0.232493	+	1.12890i
$741$	−1.08299	−	3.33311i	−0.0397848	−	0.122445i
$742$	−37.2053	+	54.4908i	−1.36585	+	2.00042i
$743$			4.71378i			0.172932i	0.996255	+	0.0864659i	$0.0275574\pi$
$743$			4.71378i			0.172932i	−0.996255	+	0.0864659i	$0.972443\pi$
$744$	1.37063	+	0.610243i	0.0502497	+	0.0223726i
$745$	10.0288	−	17.1191i	0.367426	−	0.627194i
$746$	44.2405	−	19.6971i	1.61976	−	0.721163i
$747$	−0.0859716	−	0.00903598i	−0.00314554	−	0.000330609i
$748$	−4.91472	−	1.59689i	−0.179700	−	0.0583880i
$749$	−24.2412	+	28.5595i	−0.885754	+	1.04354i
$750$	17.9957	−	12.5594i	0.657110	−	0.458604i
$751$	17.0799	+	29.5832i	0.623253	+	1.07951i	0.988876	+	0.148743i	$0.0475227\pi$
$751$	17.0799	+	29.5832i	0.623253	+	1.07951i	−0.365623	+	0.930763i	$0.619144\pi$
$752$	28.1666	−	25.3613i	1.02713	−	0.924831i
$753$	9.96314	+	22.3776i	0.363077	+	0.815484i
$754$	−5.22489	+	49.7115i	−0.190279	+	1.81038i
$755$	−34.2261	−	0.216733i	−1.24562	−	0.00788773i
$756$	4.41772	−	2.12378i	0.160671	−	0.0772411i
$757$		−	12.3569i		−	0.449119i	−0.974460	−	0.224560i	$-0.927906\pi$
$757$		−	12.3569i		−	0.449119i	0.974460	−	0.224560i	$-0.0720944\pi$
$758$	−2.90838	+	6.53234i	−0.105637	+	0.237265i
$759$	−2.64315	−	0.561818i	−0.0959401	−	0.0203927i
$760$	−0.419067	+	0.372552i	−0.0152012	+	0.0135139i
$761$	−30.6932	+	6.52404i	−1.11263	+	0.236496i	−0.727324	−	0.686294i	$-0.759236\pi$
$761$	−30.6932	+	6.52404i	−1.11263	+	0.236496i	−0.385303	+	0.922790i	$0.625903\pi$
$762$	17.6151	−	5.72350i	0.638129	−	0.207341i
$763$	52.4752	−	7.07209i	1.89973	−	0.256027i
$764$	−3.09349	+	9.52078i	−0.111919	+	0.344450i
$765$	14.9726	+	1.66961i	0.541336	+	0.0603648i
$766$	−27.1159	−	5.76366i	−0.979737	−	0.208249i
$767$	−40.3181	+	4.23760i	−1.45580	+	0.153011i
$768$	−15.6672	+	9.04545i	−0.565341	+	0.326400i
$769$	−24.1241	+	17.5272i	−0.869936	+	0.632046i	−0.930570	−	0.366114i	$-0.880688\pi$
$769$	−24.1241	+	17.5272i	−0.869936	+	0.632046i	0.0606336	+	0.998160i	$0.480688\pi$
$770$	4.67825	−	1.10699i	0.168592	−	0.0398930i
$771$	11.5254	+	8.37371i	0.415078	+	0.301572i
$772$	−8.02515	−	0.843477i	−0.288832	−	0.0303574i
$773$	−20.4450	+	18.4088i	−0.735356	+	0.662118i	−0.949173	−	0.314756i	$-0.898077\pi$
$773$	−20.4450	+	18.4088i	−0.735356	+	0.662118i	0.213816	+	0.976874i	$0.431411\pi$
$774$	11.6428	−	20.1660i	0.418493	−	0.724850i
$775$	23.5625	+	10.8503i	0.846389	+	0.389754i
$776$	0.942296			0.0338264
$777$	−0.585491	−	20.0157i	−0.0210044	−	0.718060i
$778$	−22.0042	+	30.2862i	−0.788889	+	1.08581i
$779$	−0.657724	+	6.25783i	−0.0235654	+	0.224210i
$780$	−1.64467	−	16.6623i	−0.0588886	−	0.596606i
$781$	−0.0864993	−	0.822986i	−0.00309519	−	0.0294488i
$782$	−74.7525	+	43.1584i	−2.67314	+	1.54334i
$783$	3.70359	+	5.09755i	0.132355	+	0.182172i
$784$	−1.38238	+	29.8787i	−0.0493707	+	1.06710i
$785$	−0.0443966	+	7.01104i	−0.00158458	+	0.250235i
$786$	12.0767	−	2.56698i	0.430761	−	0.0915612i
$787$	2.00943	−	9.45362i	0.0716284	−	0.336985i	−0.927712	−	0.373296i	$-0.878227\pi$
$787$	2.00943	−	9.45362i	0.0716284	−	0.336985i	0.999341	+	0.0363113i	$0.0115608\pi$
$788$	−2.73002	+	12.8437i	−0.0972529	+	0.457539i
$789$	6.44694	−	1.37034i	0.229517	−	0.0487854i
$790$	24.9693	+	34.8290i	0.888369	+	1.23916i
$791$	18.0842	−	13.9647i	0.643002	−	0.496529i
$792$	−0.0703713	−	0.0968578i	−0.00250053	−	0.00344169i
$793$	37.4410	−	21.6166i	1.32957	−	0.767626i
$794$	2.49628	+	23.7505i	0.0885897	+	0.842875i
$795$	27.7514	+	6.08265i	0.984239	+	0.215730i
$796$	1.65459	−	15.7423i	0.0586452	−	0.557972i
$797$	−30.7106	+	42.2696i	−1.08783	+	1.49727i	−0.237225	+	0.971455i	$0.576238\pi$
$797$	−30.7106	+	42.2696i	−1.08783	+	1.49727i	−0.850602	+	0.525811i	$0.823762\pi$
$798$	−3.83234	+	2.36464i	−0.135663	+	0.0837073i
$799$	59.7624			2.11424
$800$	−34.0571	+	19.0919i	−1.20410	+	0.675001i
$801$	3.52069	−	6.09801i	0.124397	−	0.215463i
$802$	27.5878	−	24.8402i	0.974159	−	0.877137i
$803$	−2.36838	−	0.248927i	−0.0835783	−	0.00878444i
$804$	6.86735	+	4.98942i	0.242193	+	0.175963i
$805$	18.5362	−	33.8748i	0.653314	−	1.19393i
$806$	33.2972	−	24.1918i	1.17284	−	0.852120i
$807$	10.1069	−	5.83519i	0.355778	−	0.205409i
$808$	2.53262	−	0.266189i	0.0890973	−	0.00936451i
$809$	6.52185	+	1.38626i	0.229296	+	0.0487384i	0.321127	−	0.947036i	$-0.395938\pi$
$809$	6.52185	+	1.38626i	0.229296	+	0.0487384i	−0.0918306	+	0.995775i	$0.529272\pi$
$810$	−3.24300	−	2.95741i	−0.113947	−	0.103913i
$811$	8.34654	−	25.6880i	0.293087	−	0.902028i	−0.690771	−	0.723074i	$-0.742729\pi$
$811$	8.34654	−	25.6880i	0.293087	−	0.902028i	0.983857	−	0.178954i	$-0.0572714\pi$
$812$	30.6085	−	4.12511i	1.07415	−	0.144763i
$813$	0.0806527	−	0.0262056i	0.00282861	−	0.000919072i
$814$	6.01577	−	1.27869i	0.210853	−	0.0448181i
$815$	−5.78620	+	26.3988i	−0.202682	+	0.924710i
$816$	−28.1598	−	5.98554i	−0.985789	−	0.209536i
$817$	−4.18415	+	9.39775i	−0.146385	+	0.328786i
$818$			4.21969i			0.147538i
$819$	−0.806318	+	10.6627i	−0.0281750	+	0.372586i
$820$	−9.47026	+	28.5304i	−0.330716	+	0.996327i
$821$	2.23679	−	21.2817i	0.0780646	−	0.742735i	−0.883551	−	0.468335i	$-0.844854\pi$
$821$	2.23679	−	21.2817i	0.0780646	−	0.742735i	0.961616	−	0.274400i	$-0.0884793\pi$
$822$	−0.647602	−	1.45454i	−0.0225877	−	0.0507328i
$823$	26.0192	−	23.4278i	0.906971	−	0.816641i	−0.0766182	−	0.997061i	$-0.524412\pi$
$823$	26.0192	−	23.4278i	0.906971	−	0.816641i	0.983590	+	0.180420i	$0.0577456\pi$
$824$	−0.360604	−	0.624584i	−0.0125622	−	0.0217584i
$825$	−1.19540	−	1.68993i	−0.0416186	−	0.0588359i
$826$	17.5385	+	49.0491i	0.610241	+	1.70664i
$827$	−25.4175	−	8.25863i	−0.883852	−	0.287181i	−0.168296	−	0.985736i	$-0.553826\pi$
$827$	−25.4175	−	8.25863i	−0.883852	−	0.287181i	−0.715556	+	0.698556i	$0.753826\pi$
$828$	12.0262	+	1.26401i	0.417941	+	0.0439274i
$829$	−19.0491	+	8.48122i	−0.661603	+	0.294565i	−0.709936	−	0.704267i	$-0.751276\pi$
$829$	−19.0491	+	8.48122i	−0.661603	+	0.294565i	0.0483323	+	0.998831i	$0.484609\pi$
$830$	0.370610	+	0.0812318i	0.0128641	+	0.00281960i
$831$	−16.6934	−	7.43239i	−0.579089	−	0.257827i
$832$			27.4069i			0.950162i
$833$	−33.1438	+	33.5524i	−1.14836	+	1.16252i
$834$	−4.73447	−	14.5712i	−0.163941	−	0.504560i
$835$	6.26567	−	13.8364i	0.216832	−	0.478830i
$836$	−0.445034	−	0.494260i	−0.0153918	−	0.0170944i
$837$	1.07867	−	5.07476i	0.0372844	−	0.175409i
$838$	−4.93520	−	4.44368i	−0.170484	−	0.153504i
$839$	0.916759	−	2.82149i	0.0316500	−	0.0974088i	−0.933984	−	0.357316i	$-0.883692\pi$
$839$	0.916759	−	2.82149i	0.0316500	−	0.0974088i	0.965634	+	0.259907i	$0.0836919\pi$
$840$	1.61458	−	0.565819i	0.0557082	−	0.0195226i
$841$	3.30697	+	10.1778i	0.114034	+	0.350959i
$842$	13.0602	−	29.3338i	0.450085	−	1.01091i
$843$	−3.16096	−	1.82498i	−0.108869	−	0.0628556i
$844$	−1.13458	−	10.7948i	−0.0390537	−	0.371571i
$845$	6.79291	+	3.07609i	0.233683	+	0.105821i
$846$	−14.0854	−	10.2337i	−0.484267	−	0.351841i
$847$	6.77347	+	27.8376i	0.232739	+	0.956511i
$848$	−51.6325	−	16.7764i	−1.77307	−	0.576105i
$849$	3.49789	+	6.05852i	0.120047	+	0.207928i
$850$	−64.4979	−	14.5656i	−2.21226	−	0.499594i
$851$	24.6999	−	42.7816i	0.846703	−	1.46653i
$852$	0.769939	+	3.62228i	0.0263777	+	0.124097i
$853$	−33.7399	+	46.4390i	−1.15523	+	1.59004i	−0.427778	+	0.903884i	$0.640703\pi$
$853$	−33.7399	+	46.4390i	−1.15523	+	1.59004i	−0.727454	+	0.686156i	$0.759297\pi$
$854$	−38.3618	−	40.1777i	−1.31271	−	1.37485i
$855$	1.56141	+	1.14961i	0.0533992	+	0.0393158i
$856$	−3.74052	−	1.66538i	−0.127848	−	0.0569217i
$857$	39.4335	+	22.7669i	1.34702	+	0.777704i	0.987827	−	0.155558i	$-0.0497175\pi$
$857$	39.4335	+	22.7669i	1.34702	+	0.777704i	0.359196	+	0.933262i	$0.383051\pi$
$858$	−3.26626	+	0.343298i	−0.111508	+	0.0117200i
$859$	−2.77860	+	3.08595i	−0.0948046	+	0.105291i	−0.788680	−	0.614804i	$-0.789235\pi$
$859$	−2.77860	+	3.08595i	−0.0948046	+	0.105291i	0.693875	+	0.720095i	$0.255902\pi$
$860$	−29.1386	+	39.5764i	−0.993618	+	1.34954i
$861$	9.10910	−	16.9001i	0.310437	−	0.575955i
$862$	0.137130	−	0.0445563i	0.00467067	−	0.00151759i
$863$	32.3133	+	29.0950i	1.09996	+	0.990406i	0.999989	−	0.00458489i	$-0.00145942\pi$
$863$	32.3133	+	29.0950i	1.09996	+	0.990406i	0.0999676	+	0.994991i	$0.468126\pi$
$864$	5.22503	+	5.80298i	0.177759	+	0.197421i
$865$	−7.99522	+	7.10778i	−0.271846	+	0.241672i
$866$	−27.5912	+	30.6431i	−0.937586	+	1.04130i
$867$	−16.6892	−	22.9707i	−0.566794	−	0.780126i
$868$	−19.3881	−	16.4566i	−0.658076	−	0.558573i
$869$	3.27031	−	2.37602i	0.110938	−	0.0806010i
$870$	−13.6754	−	24.0368i	−0.463641	−	0.814924i
$871$	−16.9169	+	7.53190i	−0.573208	+	0.255209i
$872$	2.35399	+	5.28715i	0.0797162	+	0.179046i
$873$	−0.677467	−	3.18723i	−0.0229288	−	0.107871i
$874$	−11.1093			−0.375776
$875$	28.0375	−	9.42862i	0.947840	−	0.318745i
$876$	10.6570			0.360068
$877$	11.9453	+	56.1982i	0.403364	+	1.89768i	0.439329	+	0.898326i	$0.355216\pi$
$877$	11.9453	+	56.1982i	0.403364	+	1.89768i	−0.0359648	+	0.999353i	$0.511450\pi$
$878$	−23.3499	−	52.4446i	−0.788019	−	1.76992i
$879$	12.2765	−	5.46587i	0.414077	−	0.184359i
$880$	1.95607	+	3.43810i	0.0659390	+	0.115898i
$881$	33.5774	−	24.3954i	1.13125	−	0.821903i	0.145375	−	0.989377i	$-0.453561\pi$
$881$	33.5774	−	24.3954i	1.13125	−	0.821903i	0.985876	+	0.167474i	$0.0535610\pi$
$882$	13.5572	−	2.23247i	0.456494	−	0.0751712i
$883$	−18.7203	−	25.7663i	−0.629988	−	0.867105i	0.368044	−	0.929808i	$-0.380028\pi$
$883$	−18.7203	−	25.7663i	−0.629988	−	0.867105i	−0.998032	+	0.0627037i	$0.980028\pi$
$884$	−33.7569	+	37.4908i	−1.13537	+	1.26095i
$885$	16.7628	−	14.9022i	0.563476	−	0.500931i
$886$	1.88872	+	2.09764i	0.0634529	+	0.0704716i
$887$	−15.3578	−	13.8282i	−0.515663	−	0.464305i	0.369736	−	0.929137i	$-0.379448\pi$
$887$	−15.3578	−	13.8282i	−0.515663	−	0.464305i	−0.885399	+	0.464832i	$0.846115\pi$
$888$	2.08158	−	0.676345i	0.0698531	−	0.0226967i
$889$	24.9553	−	0.729980i	0.836973	−	0.0244827i
$890$	−18.3232	+	24.8868i	−0.614196	+	0.834208i
$891$	−0.277019	+	0.307661i	−0.00928048	+	0.0103070i
$892$	−0.361587	+	0.0380043i	−0.0121068	+	0.00127248i
$893$	6.66114	+	3.84581i	0.222907	+	0.128695i
$894$	15.9102	+	7.08367i	0.532116	+	0.236913i
$895$	35.7710	+	26.3369i	1.19569	+	0.880344i
$896$	−5.93126	+	1.44320i	−0.198150	+	0.0482140i
$897$	−15.5058	+	21.3419i	−0.517724	+	0.712586i
$898$	−0.752970	−	3.54245i	−0.0251269	−	0.118213i
$899$	16.3450	−	28.3104i	0.545137	−	0.944205i
$900$	6.11071	+	6.96195i	0.203690	+	0.232065i
$901$	−42.8011	−	74.1336i	−1.42591	−	2.46975i
$902$	5.60801	+	1.82215i	0.186726	+	0.0606710i
$903$	22.7014	−	21.6754i	0.755455	−	0.721311i
$904$	2.02043	+	1.46793i	0.0671986	+	0.0488227i
$905$	−33.0324	−	14.9583i	−1.09804	−	0.497232i
$906$	−3.14048	−	29.8797i	−0.104336	−	0.992687i
$907$	−33.9939	−	19.6264i	−1.12875	−	0.651683i	−0.185129	−	0.982714i	$-0.559270\pi$
$907$	−33.9939	−	19.6264i	−1.12875	−	0.651683i	−0.943620	+	0.331031i	$0.892604\pi$
$908$	−9.62420	+	21.6163i	−0.319390	+	0.717362i
$909$	−2.72120	−	8.37499i	−0.0902564	−	0.277781i
$910$	8.70355	−	46.1183i	0.288520	−	1.52881i
$911$	10.6987	−	32.9273i	0.354464	−	1.09093i	−0.601855	−	0.798605i	$-0.705572\pi$
$911$	10.6987	−	32.9273i	0.354464	−	1.09093i	0.956319	−	0.292324i	$-0.0944285\pi$
$912$	−2.75352	−	2.47928i	−0.0911782	−	0.0820972i
$913$	0.00744077	−	0.0350061i	0.000246254	−	0.00115853i
$914$	16.1483	+	17.9345i	0.534139	+	0.593221i
$915$	−9.86693	+	21.7891i	−0.326191	+	0.720325i
$916$	1.61059	+	4.95690i	0.0532155	+	0.163780i
$917$	16.5949	+	1.25491i	0.548011	+	0.0414407i
$918$			13.2244i			0.436471i
$919$	−8.40280	−	3.74117i	−0.277183	−	0.123410i	0.263437	−	0.964676i	$-0.415144\pi$
$919$	−8.40280	−	3.74117i	−0.277183	−	0.123410i	−0.540620	+	0.841267i	$0.681810\pi$
$920$	4.12280	+	0.903651i	0.135925	+	0.0297925i
$921$	−9.80740	+	4.36654i	−0.323165	+	0.143882i
$922$	44.0031	+	4.62491i	1.44916	+	0.152313i
$923$	−7.68322	−	2.49643i	−0.252896	−	0.0821710i
$924$	0.683249	+	1.91081i	0.0224772	+	0.0628611i
$925$	36.1354	−	11.2372i	1.18812	−	0.369477i
$926$	0.715702	+	1.23963i	0.0235194	+	0.0407368i
$927$	−1.85334	+	1.66876i	−0.0608717	+	0.0548091i
$928$	20.0122	+	44.9481i	0.656933	+	1.47549i
$929$	−4.81329	+	45.7954i	−0.157919	+	1.50250i	0.572729	+	0.819745i	$0.305885\pi$
$929$	−4.81329	+	45.7954i	−0.157919	+	1.50250i	−0.730648	+	0.682755i	$0.760782\pi$
$930$	−7.17354	+	21.6113i	−0.235230	+	0.708662i
$931$	−5.85338	+	1.60691i	−0.191837	+	0.0526642i
$932$		−	34.4277i		−	1.12772i
$933$	10.7347	−	24.1106i	0.351439	−	0.789346i
$934$	12.9380	+	2.75006i	0.423345	+	0.0899848i
$935$	−1.33536	+	6.09243i	−0.0436710	+	0.199244i
$936$	−1.14325	+	0.243005i	−0.0373682	+	0.00794286i
$937$	−7.03197	+	2.28482i	−0.229724	+	0.0746420i	−0.421617	−	0.906774i	$-0.638537\pi$
$937$	−7.03197	+	2.28482i	−0.229724	+	0.0746420i	0.191893	+	0.981416i	$0.438537\pi$
$938$	14.5425	+	18.8324i	0.474830	+	0.614901i
$939$	−4.08145	+	12.5614i	−0.133193	+	0.409926i
$940$	27.1516	+	24.7606i	0.885589	+	0.807600i
$941$	−41.5635	−	8.83459i	−1.35493	−	0.287999i	−0.527494	−	0.849559i	$-0.676868\pi$
$941$	−41.5635	−	8.83459i	−1.35493	−	0.287999i	−0.827436	+	0.561560i	$0.810202\pi$
$942$	−6.12070	+	0.643312i	−0.199423	+	0.0209602i
$943$	41.0177	−	23.6816i	1.33572	−	0.771179i
$944$	−34.6748	+	25.1927i	−1.12857	+	0.819953i
$945$	−3.07464	−	5.05437i	−0.100018	−	0.164419i
$946$	7.79910	+	5.66638i	0.253571	+	0.184230i
$947$	−23.3772	−	2.45704i	−0.759657	−	0.0798432i	−0.283224	−	0.959054i	$-0.591404\pi$
$947$	−23.3772	−	2.45704i	−0.759657	−	0.0798432i	−0.476433	+	0.879211i	$0.658071\pi$
$948$	−13.4432	+	12.1043i	−0.436616	+	0.393131i
$949$	−11.6243	+	20.1338i	−0.377340	+	0.653572i
$950$	−6.25165	−	5.77404i	−0.202830	−	0.187334i
$951$	−4.82091			−0.156329
$952$	−4.53776	−	2.44583i	−0.147070	−	0.0792699i
$953$	15.5795	−	21.4433i	0.504669	−	0.694618i	−0.478340	−	0.878175i	$-0.658761\pi$
$953$	15.5795	−	21.4433i	0.504669	−	0.694618i	0.983009	+	0.183557i	$0.0587613\pi$
$954$	−2.60678	+	24.8018i	−0.0843975	+	0.802989i
$955$	11.8022	+	2.58686i	0.381911	+	0.0837089i
$956$	2.56518	+	24.4061i	0.0829640	+	0.789350i
$957$	−2.25909	+	1.30428i	−0.0730259	+	0.0421615i
$958$	3.73600	+	5.14217i	0.120705	+	0.166136i
$959$	−0.286647	−	2.12693i	−0.00925632	−	0.0686823i
$960$	−8.83477	−	12.3234i	−0.285141	−	0.397735i
$961$	3.99401	−	0.848953i	0.128839	−	0.0273856i
$962$	12.4832	−	58.7287i	0.402474	−	1.89349i
$963$	−2.94376	+	13.8493i	−0.0948612	+	0.446287i
$964$	−23.1515	+	4.92101i	−0.745661	+	0.158495i
$965$	−0.0616716	+	9.73907i	−0.00198528	+	0.313512i
$966$	31.3554	+	12.8754i	1.00884	+	0.414260i
$967$	10.0180	+	13.7886i	0.322157	+	0.443411i	0.939124	−	0.343578i	$-0.111639\pi$
$967$	10.0180	+	13.7886i	0.322157	+	0.443411i	−0.616967	+	0.786989i	$0.711639\pi$
$968$	−2.71195	+	1.56574i	−0.0871653	+	0.0503249i
$969$	−0.610684	−	5.81027i	−0.0196180	−	0.186653i
$970$	1.40480	+	14.2321i	0.0451053	+	0.456966i
$971$	1.68072	−	15.9910i	0.0539369	−	0.513175i	−0.933884	−	0.357577i	$-0.883603\pi$
$971$	1.68072	−	15.9910i	0.0539369	−	0.513175i	0.987820	−	0.155598i	$-0.0497304\pi$
$972$	1.08897	−	1.49884i	0.0349288	−	0.0480753i
$973$	−0.603838	−	20.6429i	−0.0193582	−	0.661782i
$974$	3.01362			0.0965626
$975$	−19.8182	+	3.95085i	−0.634691	+	0.126529i
$976$	22.8538	−	39.5839i	0.731531	−	1.26705i
$977$	−14.7234	+	13.2570i	−0.471045	+	0.424130i	−0.870159	−	0.492771i	$-0.835984\pi$
$977$	−14.7234	+	13.2570i	−0.471045	+	0.424130i	0.399115	+	0.916901i	$0.369318\pi$
$978$	−23.5930	−	2.47973i	−0.754422	−	0.0792930i
$979$	2.35838	+	1.71346i	0.0753741	+	0.0547625i
$980$	−28.9594	+	1.51172i	−0.925074	+	0.0482902i
$981$	16.1909	−	11.7634i	0.516936	−	0.375576i
$982$	40.7713	−	23.5393i	1.30107	−	0.751171i
$983$	2.56164	−	0.269239i	0.0817035	−	0.00858738i	−0.0635885	−	0.997976i	$-0.520255\pi$
$983$	2.56164	−	0.269239i	0.0817035	−	0.00858738i	0.145292	+	0.989389i	$0.453588\pi$
$984$	2.05261	+	0.436295i	0.0654347	+	0.0139086i
$985$	15.7504	+	1.75634i	0.501849	+	0.0559616i
$986$	−25.7492	+	79.2478i	−0.820020	+	2.52376i
$987$	−14.3435	−	18.5748i	−0.456560	−	0.591242i
$988$	−6.17515	+	2.00643i	−0.196458	+	0.0638330i
$989$	75.7408	−	16.0992i	2.40842	−	0.511925i
$990$	1.35800	−	1.20726i	0.0431599	−	0.0383693i
$991$	−19.8832	−	4.22631i	−0.631611	−	0.134253i	−0.119028	−	0.992891i	$-0.537978\pi$
$991$	−19.8832	−	4.22631i	−0.631611	−	0.134253i	−0.512583	+	0.858638i	$0.671311\pi$
$992$	16.4779	−	37.0100i	0.523174	−	1.17507i
$993$			32.3915i			1.02791i
$994$	−0.782725	+	10.3507i	−0.0248265	+	0.328305i
$995$	−19.1044	−	0.120977i	−0.605650	−	0.00383521i
$996$	−0.0167407	+	0.159277i	−0.000530448	+	0.00504688i
$997$	−3.25405	−	7.30872i	−0.103057	−	0.231470i	0.854656	−	0.519194i	$-0.173768\pi$
$997$	−3.25405	−	7.30872i	−0.103057	−	0.231470i	−0.957713	+	0.287725i	$0.907101\pi$
$998$	42.4460	−	38.2186i	1.34361	−	1.20979i
$999$	−3.78423	−	6.55448i	−0.119728	−	0.207375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.4.7	✓	320
7.2	even	3	inner	525.2.bo.a.79.7	yes	320
25.19	even	10	inner	525.2.bo.a.319.7	yes	320
175.44	even	30	inner	525.2.bo.a.394.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.7	✓	320	1.1	even	1	trivial
525.2.bo.a.79.7	yes	320	7.2	even	3	inner
525.2.bo.a.319.7	yes	320	25.19	even	10	inner
525.2.bo.a.394.7	yes	320	175.44	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.408094 - 1.91993i) q^{2} +(-0.406737 - 0.913545i) q^{3} +(-1.69250 + 0.753548i) q^{4} +(1.10575 + 1.94353i) q^{5} +(-1.58796 + 1.15372i) q^{6} +(-2.49128 + 0.890806i) q^{7} +(-0.169980 - 0.233957i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.408094 - 1.91993i) q^{2} +(-0.406737 - 0.913545i) q^{3} +(-1.69250 + 0.753548i) q^{4} +(1.10575 + 1.94353i) q^{5} +(-1.58796 + 1.15372i) q^{6} +(-2.49128 + 0.890806i) q^{7} +(-0.169980 - 0.233957i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(3.28020 - 2.91610i) q^{10} +(-0.277019 - 0.307661i) q^{11} +(1.37680 + 1.23968i) q^{12} +(-3.84383 + 1.24894i) q^{13} +(2.72696 + 4.41954i) q^{14} +(1.32576 - 1.80066i) q^{15} +(-2.85917 + 3.17543i) q^{16} +(-6.70055 + 0.704256i) q^{17} +(1.69985 + 0.981411i) q^{18} +(-0.792166 - 0.352695i) q^{19} +(-3.33602 - 2.45619i) q^{20} +(1.82709 + 1.91357i) q^{21} +(-0.477637 + 0.657411i) q^{22} +(1.35705 + 6.38444i) q^{23} +(-0.144593 + 0.250443i) q^{24} +(-2.55464 + 4.29812i) q^{25} +(3.96651 + 6.87019i) q^{26} +(0.951057 + 0.309017i) q^{27} +(3.54521 - 3.38498i) q^{28} +(5.09755 + 3.70359i) q^{29} +(-3.99817 - 1.81052i) q^{30} +(-0.542308 - 5.15972i) q^{31} +(6.76251 + 3.90434i) q^{32} +(-0.168388 + 0.378206i) q^{33} +(4.08657 + 12.5772i) q^{34} +(-4.48604 - 3.85687i) q^{35} +(0.572506 - 1.76199i) q^{36} +(-5.62447 - 5.06429i) q^{37} +(-0.353872 + 1.66484i) q^{38} +(2.70438 + 3.00352i) q^{39} +(0.266748 - 0.589059i) q^{40} +(-2.24236 - 6.90127i) q^{41} +(2.92830 - 4.28879i) q^{42} -11.8634i q^{43} +(0.700691 + 0.311968i) q^{44} +(-2.18422 - 0.478745i) q^{45} +(11.7039 - 5.21089i) q^{46} +(-8.82158 - 0.927185i) q^{47} +(4.06382 + 1.32042i) q^{48} +(5.41293 - 4.43849i) q^{49} +(9.29461 + 3.15069i) q^{50} +(3.36873 + 5.83481i) q^{51} +(5.56453 - 5.01033i) q^{52} +(5.16775 + 11.6070i) q^{53} +(0.205171 - 1.95207i) q^{54} +(0.291635 - 0.878591i) q^{55} +(0.631877 + 0.431433i) q^{56} +0.867134i q^{57} +(5.03035 - 11.2983i) q^{58} +(9.81143 + 2.08548i) q^{59} +(-0.886956 + 4.04663i) q^{60} +(-10.4632 + 2.22402i) q^{61} +(-9.68498 + 3.14684i) q^{62} +(1.00499 - 2.44745i) q^{63} +(2.09548 - 6.44924i) q^{64} +(-6.67765 - 6.08959i) q^{65} +(0.794847 + 0.168950i) q^{66} +(4.55668 - 0.478926i) q^{67} +(10.8100 - 6.24114i) q^{68} +(5.28051 - 3.83651i) q^{69} +(-5.57420 + 10.1868i) q^{70} +(1.61710 + 1.17489i) q^{71} +(0.287602 + 0.0302282i) q^{72} +(4.27476 - 3.84901i) q^{73} +(-7.42777 + 12.8653i) q^{74} +(4.96559 + 0.585575i) q^{75} +1.60651 q^{76} +(0.964197 + 0.519698i) q^{77} +(4.66291 - 6.41794i) q^{78} +(-1.02063 + 9.71063i) q^{79} +(-9.33307 - 2.04566i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-12.3349 + 7.12154i) q^{82} +(0.0508112 + 0.0699356i) q^{83} +(-4.53430 - 1.86192i) q^{84} +(-8.77787 - 12.2440i) q^{85} +(-22.7768 + 4.84136i) q^{86} +(1.31003 - 6.16323i) q^{87} +(-0.0248918 + 0.117107i) q^{88} +(-6.88750 + 1.46398i) q^{89} +(-0.0277923 + 4.38891i) q^{90} +(8.46348 - 6.53555i) q^{91} +(-7.10779 - 9.78303i) q^{92} +(-4.49306 + 2.59407i) q^{93} +(1.81990 + 17.3152i) q^{94} +(-0.190463 - 1.92959i) q^{95} +(0.816229 - 7.76590i) q^{96} +(-1.91526 + 2.63613i) q^{97} +(-10.7306 - 8.58112i) q^{98} +0.413998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more