LMFDB - Embedded newform 90.2.l.b.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.l (of order $12$, degree $4$, 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:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.1
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	90.47
Dual form			90.2.l.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.661570 + 2.13596i) q^{5} +(1.69185 - 0.370982i) q^{6} +(3.75574 - 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.661570 + 2.13596i) q^{5} +(1.69185 - 0.370982i) q^{6} +(3.75574 - 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +(1.89195 - 1.19185i) q^{10} +(-3.44125 - 1.98681i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(0.956351 + 0.256253i) q^{13} +(-1.94411 - 3.36730i) q^{14} +(-3.74831 + 0.974763i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.120239 + 0.120239i) q^{17} +(0.507306 + 2.95680i) q^{18} -1.88492i q^{19} +(-1.64092 - 1.51901i) q^{20} +(1.44246 + 6.57832i) q^{21} +(-1.02845 + 3.83821i) q^{22} +(1.36362 - 5.08911i) q^{23} +(-1.27970 + 1.16721i) q^{24} +(-4.12465 + 2.82617i) q^{25} -0.990087i q^{26} +(0.713876 - 5.14688i) q^{27} +(-2.74939 + 2.74939i) q^{28} +(-2.15618 + 3.73461i) q^{29} +(1.91168 + 3.36830i) q^{30} +(-4.70172 - 8.14362i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.71134 - 5.79609i) q^{33} +(0.147262 + 0.0850217i) q^{34} +(4.63420 + 7.35634i) q^{35} +(2.72474 - 1.25529i) q^{36} +(3.26863 + 3.26863i) q^{37} +(-1.82070 + 0.487854i) q^{38} +(-0.519447 + 1.63432i) q^{39} +(-1.04255 + 1.97815i) q^{40} +(7.15775 - 4.13253i) q^{41} +(5.98083 - 3.09591i) q^{42} +(0.533983 + 1.99285i) q^{43} +3.97361 q^{44} +(-1.38840 - 6.56295i) q^{45} -5.26863 q^{46} +(0.897060 + 3.34787i) q^{47} +(1.45865 + 0.933998i) q^{48} +(7.03067 - 4.05916i) q^{49} +(3.79741 + 3.25264i) q^{50} +(-0.198476 - 0.217604i) q^{51} +(-0.956351 + 0.256253i) q^{52} +(-3.66571 - 3.66571i) q^{53} +(-5.15627 + 0.642559i) q^{54} +(1.96711 - 8.66478i) q^{55} +(3.36730 + 1.94411i) q^{56} +(3.26134 + 0.149933i) q^{57} +(4.16541 + 1.11612i) q^{58} +(2.72877 + 4.72637i) q^{59} +(2.75875 - 2.71832i) q^{60} +(-4.35623 + 7.54520i) q^{61} +(-6.64923 + 6.64923i) q^{62} +(-11.4967 + 1.97252i) q^{63} +1.00000i q^{64} +(0.0853460 + 2.21226i) q^{65} +(-6.55916 - 2.08475i) q^{66} +(-2.10759 + 7.86563i) q^{67} +(0.0440105 - 0.164249i) q^{68} +(8.69683 + 2.76418i) q^{69} +(5.90626 - 6.38026i) q^{70} +6.94911i q^{71} +(-1.91774 - 2.30701i) q^{72} +(-8.27728 + 8.27728i) q^{73} +(2.31127 - 4.00324i) q^{74} +(-4.56182 - 7.36137i) q^{75} +(0.942462 + 1.63239i) q^{76} +(-14.9238 - 3.99883i) q^{77} +(1.71307 + 0.0787547i) q^{78} +(-11.7529 - 6.78553i) q^{79} +(2.18058 + 0.495044i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-5.84428 - 5.84428i) q^{82} +(6.75913 - 1.81110i) q^{83} +(-4.53837 - 4.97576i) q^{84} +(-0.336372 - 0.177279i) q^{85} +(1.78674 - 1.03157i) q^{86} +(-6.29020 - 4.02773i) q^{87} +(-1.02845 - 3.83821i) q^{88} +4.87832 q^{89} +(-5.97998 + 3.03971i) q^{90} +3.84968 q^{91} +(1.36362 + 5.08911i) q^{92} +(14.4643 - 7.48725i) q^{93} +(3.00162 - 1.73299i) q^{94} +(4.02612 - 1.24701i) q^{95} +(0.524648 - 1.65068i) q^{96} +(1.44518 - 0.387234i) q^{97} +(-5.74052 - 5.74052i) q^{98} +(9.73332 + 6.88249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 + 8 * q^7	$ 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.661570	+	2.13596i	0.295863	+	0.955230i
$5$	0.661570	+	2.13596i	0.295863	+	0.955230i
$6$	1.69185	−	0.370982i	0.690697	−	0.151453i
$7$	3.75574	−	1.00635i	1.41954	−	0.380364i	0.534217	−	0.845347i	$-0.320606\pi$
$7$	3.75574	−	1.00635i	1.41954	−	0.380364i	0.885319	+	0.464984i	$0.153940\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.98735	−	0.275255i	−0.995782	−	0.0917517i
$10$	1.89195	−	1.19185i	0.598288	−	0.376898i
$11$	−3.44125	−	1.98681i	−1.03758	−	0.599044i	−0.118430	−	0.992962i	$-0.537786\pi$
$11$	−3.44125	−	1.98681i	−1.03758	−	0.599044i	−0.919145	+	0.393918i	$0.871119\pi$
$12$	−0.796225	−	1.53819i	−0.229850	−	0.444037i
$13$	0.956351	+	0.256253i	0.265244	+	0.0710719i	0.388990	−	0.921242i	$-0.372824\pi$
$13$	0.956351	+	0.256253i	0.265244	+	0.0710719i	−0.123746	+	0.992314i	$0.539491\pi$
$14$	−1.94411	−	3.36730i	−0.519586	−	0.899950i
$15$	−3.74831	+	0.974763i	−0.967810	+	0.251683i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	−0.721538	−	0.692375i	$-0.756564\pi$
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	0.692375	+	0.721538i	$0.256564\pi$
$18$	0.507306	+	2.95680i	0.119573	+	0.696923i
$19$		−	1.88492i		−	0.432431i	−0.976346	−	0.216216i	$-0.930629\pi$
$19$		−	1.88492i		−	0.432431i	0.976346	−	0.216216i	$-0.0693714\pi$
$20$	−1.64092	−	1.51901i	−0.366920	−	0.339661i
$21$	1.44246	+	6.57832i	0.314771	+	1.43551i
$22$	−1.02845	+	3.83821i	−0.219265	+	0.818310i
$23$	1.36362	−	5.08911i	0.284335	−	1.06115i	−0.664989	−	0.746853i	$-0.731564\pi$
$23$	1.36362	−	5.08911i	0.284335	−	1.06115i	0.949324	−	0.314299i	$-0.101770\pi$
$24$	−1.27970	+	1.16721i	−0.261217	+	0.238255i
$25$	−4.12465	+	2.82617i	−0.824930	+	0.565235i
$26$		−	0.990087i		−	0.194172i
$27$	0.713876	−	5.14688i	0.137386	−	0.990518i
$28$	−2.74939	+	2.74939i	−0.519586	+	0.519586i
$29$	−2.15618	+	3.73461i	−0.400392	+	0.693499i	−0.993773	−	0.111422i	$-0.964459\pi$
$29$	−2.15618	+	3.73461i	−0.400392	+	0.693499i	0.593381	+	0.804922i	$0.297793\pi$
$30$	1.91168	+	3.36830i	0.349024	+	0.614965i
$31$	−4.70172	−	8.14362i	−0.844454	−	1.46264i	−0.886095	−	0.463504i	$-0.846592\pi$
$31$	−4.70172	−	8.14362i	−0.844454	−	1.46264i	0.0416413	−	0.999133i	$-0.486741\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.71134	−	5.79609i	0.646062	−	1.00897i
$34$	0.147262	+	0.0850217i	0.0252552	+	0.0145811i
$35$	4.63420	+	7.35634i	0.783323	+	1.24345i
$36$	2.72474	−	1.25529i	0.454124	−	0.209216i
$37$	3.26863	+	3.26863i	0.537360	+	0.537360i	0.922753	−	0.385393i	$-0.125934\pi$
$37$	3.26863	+	3.26863i	0.537360	+	0.537360i	−0.385393	+	0.922753i	$0.625934\pi$
$38$	−1.82070	+	0.487854i	−0.295356	+	0.0791404i
$39$	−0.519447	+	1.63432i	−0.0831781	+	0.261700i
$40$	−1.04255	+	1.97815i	−0.164842	+	0.312773i
$41$	7.15775	−	4.13253i	1.11785	−	0.645393i	0.177001	−	0.984211i	$-0.443360\pi$
$41$	7.15775	−	4.13253i	1.11785	−	0.645393i	0.940852	+	0.338818i	$0.110027\pi$
$42$	5.98083	−	3.09591i	0.922862	−	0.477709i
$43$	0.533983	+	1.99285i	0.0814316	+	0.303907i	0.994615	−	0.103643i	$-0.0330500\pi$
$43$	0.533983	+	1.99285i	0.0814316	+	0.303907i	−0.913183	+	0.407550i	$0.866383\pi$
$44$	3.97361			0.599044
$45$	−1.38840	−	6.56295i	−0.206971	−	0.978347i
$46$	−5.26863			−0.776818
$47$	0.897060	+	3.34787i	0.130850	+	0.488338i	0.999981	−	0.00624459i	$-0.00198773\pi$
$47$	0.897060	+	3.34787i	0.130850	+	0.488338i	−0.869131	+	0.494582i	$0.835321\pi$
$48$	1.45865	+	0.933998i	0.210537	+	0.134811i
$49$	7.03067	−	4.05916i	1.00438	−	0.579880i
$50$	3.79741	+	3.25264i	0.537035	+	0.459993i
$51$	−0.198476	−	0.217604i	−0.0277922	−	0.0304707i
$52$	−0.956351	+	0.256253i	−0.132622	+	0.0355359i
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	0.409007	−	0.912531i	$-0.365875\pi$
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	−0.912531	+	0.409007i	$0.865875\pi$
$54$	−5.15627	+	0.642559i	−0.701679	+	0.0874413i
$55$	1.96711	−	8.66478i	0.265245	−	1.16836i
$56$	3.36730	+	1.94411i	0.449975	+	0.259793i
$57$	3.26134	+	0.149933i	0.431975	+	0.0198591i
$58$	4.16541	+	1.11612i	0.546946	+	0.146554i
$59$	2.72877	+	4.72637i	0.355255	+	0.615320i	0.987162	−	0.159724i	$-0.0510606\pi$
$59$	2.72877	+	4.72637i	0.355255	+	0.615320i	−0.631906	+	0.775045i	$0.717727\pi$
$60$	2.75875	−	2.71832i	0.356153	−	0.350934i
$61$	−4.35623	+	7.54520i	−0.557758	+	0.966064i	0.439926	+	0.898034i	$0.355005\pi$
$61$	−4.35623	+	7.54520i	−0.557758	+	0.966064i	−0.997683	+	0.0680302i	$0.978329\pi$
$62$	−6.64923	+	6.64923i	−0.844454	+	0.844454i
$63$	−11.4967	+	1.97252i	−1.44845	+	0.248514i
$64$			1.00000i			0.125000i
$65$	0.0853460	+	2.21226i	0.0105859	+	0.274397i
$66$	−6.55916	−	2.08475i	−0.807377	−	0.256614i
$67$	−2.10759	+	7.86563i	−0.257483	+	0.960940i	0.709209	+	0.704998i	$0.249052\pi$
$67$	−2.10759	+	7.86563i	−0.257483	+	0.960940i	−0.966692	+	0.255942i	$0.917615\pi$
$68$	0.0440105	−	0.164249i	0.00533705	−	0.0199182i
$69$	8.69683	+	2.76418i	1.04698	+	0.332768i
$70$	5.90626	−	6.38026i	0.705933	−	0.762587i
$71$			6.94911i			0.824708i	0.911024	+	0.412354i	$0.135293\pi$
$71$			6.94911i			0.824708i	−0.911024	+	0.412354i	$0.864707\pi$
$72$	−1.91774	−	2.30701i	−0.226008	−	0.271883i
$73$	−8.27728	+	8.27728i	−0.968783	+	0.968783i	−0.999527	−	0.0307446i	$-0.990212\pi$
$73$	−8.27728	+	8.27728i	−0.968783	+	0.968783i	0.0307446	+	0.999527i	$0.490212\pi$
$74$	2.31127	−	4.00324i	0.268680	−	0.465368i
$75$	−4.56182	−	7.36137i	−0.526754	−	0.850018i
$76$	0.942462	+	1.63239i	0.108108	+	0.187248i
$77$	−14.9238	−	3.99883i	−1.70073	−	0.455709i
$78$	1.71307	+	0.0787547i	0.193967	+	0.00891722i
$79$	−11.7529	−	6.78553i	−1.32230	−	0.763431i	−0.338206	−	0.941072i	$-0.609820\pi$
$79$	−11.7529	−	6.78553i	−1.32230	−	0.763431i	−0.984095	+	0.177641i	$0.943153\pi$
$80$	2.18058	+	0.495044i	0.243796	+	0.0553475i
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$	−5.84428	−	5.84428i	−0.645393	−	0.645393i
$83$	6.75913	−	1.81110i	0.741911	−	0.198795i	0.131984	−	0.991252i	$-0.457865\pi$
$83$	6.75913	−	1.81110i	0.741911	−	0.198795i	0.609927	+	0.792457i	$0.291199\pi$
$84$	−4.53837	−	4.97576i	−0.495176	−	0.542900i
$85$	−0.336372	−	0.177279i	−0.0364847	−	0.0192286i
$86$	1.78674	−	1.03157i	0.192669	−	0.111238i
$87$	−6.29020	−	4.02773i	−0.674380	−	0.431818i
$88$	−1.02845	−	3.83821i	−0.109633	−	0.409155i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$	−5.97998	+	3.03971i	−0.630345	+	0.320414i
$91$	3.84968			0.403557
$92$	1.36362	+	5.08911i	0.142168	+	0.530576i
$93$	14.4643	−	7.48725i	1.49987	−	0.776392i
$94$	3.00162	−	1.73299i	0.309594	−	0.178744i
$95$	4.02612	−	1.24701i	0.413072	−	0.127940i
$96$	0.524648	−	1.65068i	0.0535466	−	0.168472i
$97$	1.44518	−	0.387234i	0.146736	−	0.0393177i	−0.184704	−	0.982794i	$-0.559132\pi$
$97$	1.44518	−	0.387234i	0.146736	−	0.0393177i	0.331439	+	0.943477i	$0.392466\pi$
$98$	−5.74052	−	5.74052i	−0.579880	−	0.579880i
$99$	9.73332	+	6.88249i	0.978235	+	0.691717i
$100$	2.15896	−	4.50986i	0.215896	−	0.450986i
$101$	−8.91944	−	5.14964i	−0.887517	−	0.512408i	−0.0143875	−	0.999896i	$-0.504580\pi$
$101$	−8.91944	−	5.14964i	−0.887517	−	0.512408i	−0.873130	+	0.487488i	$0.837913\pi$
$102$	−0.158820	+	0.248033i	−0.0157255	+	0.0245589i
$103$	−6.26326	−	1.67823i	−0.617137	−	0.165361i	−0.0633111	−	0.997994i	$-0.520166\pi$
$103$	−6.26326	−	1.67823i	−0.617137	−	0.165361i	−0.553826	+	0.832632i	$0.686833\pi$
$104$	0.495044	+	0.857441i	0.0485430	+	0.0840790i
$105$	−13.0967	+	7.43306i	−1.27811	+	0.725392i
$106$	−2.59205	+	4.48956i	−0.251762	+	0.436065i
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	−0.505235	−	0.862982i	$-0.668594\pi$
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	0.862982	+	0.505235i	$0.168594\pi$
$108$	1.95521	+	4.81427i	0.188140	+	0.463253i
$109$			7.30160i			0.699367i	0.936868	+	0.349683i	$0.113711\pi$
$109$			7.30160i			0.699367i	−0.936868	+	0.349683i	$0.886289\pi$
$110$	−8.87866	+	0.342527i	−0.846547	+	0.0326587i
$111$	−5.91546	+	5.39547i	−0.561471	+	0.512115i
$112$	1.00635	−	3.75574i	0.0950909	−	0.354884i
$113$	−1.09205	+	4.07557i	−0.102731	+	0.383397i	−0.998078	−	0.0619722i	$-0.980261\pi$
$113$	−1.09205	+	4.07557i	−0.102731	+	0.383397i	0.895347	+	0.445369i	$0.146928\pi$
$114$	−0.699273	−	3.18902i	−0.0654929	−	0.298679i
$115$	11.7723	−	0.454159i	1.09777	−	0.0423505i
$116$		−	4.31235i		−	0.400392i
$117$	−2.78641	−	1.02876i	−0.257604	−	0.0951087i
$118$	3.85906	−	3.85906i	0.355255	−	0.355255i
$119$	−0.330584	+	0.572588i	−0.0303046	+	0.0524891i
$120$	−3.33972	−	1.96119i	−0.304873	−	0.179032i
$121$	2.39479	+	4.14790i	0.217708	+	0.377081i
$122$	8.41558	+	2.25495i	0.761911	+	0.204153i
$123$	6.58085	+	12.7132i	0.593375	+	1.14631i
$124$	8.14362	+	4.70172i	0.731318	+	0.422227i
$125$	−8.76534	−	6.94038i	−0.783996	−	0.620766i
$126$	4.88087	+	10.5944i	0.434823	+	0.943827i
$127$	13.7871	+	13.7871i	1.22341	+	1.22341i	0.966411	+	0.257000i	$0.0827341\pi$
$127$	13.7871	+	13.7871i	1.22341	+	1.22341i	0.257000	+	0.966411i	$0.417266\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−3.49055	+	0.765391i	−0.307326	+	0.0673889i
$130$	2.11479	−	0.655012i	0.185479	−	0.0574483i
$131$	−3.88249	+	2.24156i	−0.339215	+	0.195846i	−0.659925	−	0.751332i	$-0.729412\pi$
$131$	−3.88249	+	2.24156i	−0.339215	+	0.195846i	0.320710	+	0.947178i	$0.396079\pi$
$132$	−0.316074	+	6.87523i	−0.0275107	+	0.598412i
$133$	−1.89689	−	7.07929i	−0.164481	−	0.613852i
$134$	8.14310			0.703457
$135$	11.4658	−	1.88021i	0.986820	−	0.161823i
$136$	−0.170043			−0.0145811
$137$	−3.23492	−	12.0729i	−0.276378	−	1.03146i	−0.954912	−	0.296888i	$-0.904051\pi$
$137$	−3.23492	−	12.0729i	−0.276378	−	1.03146i	0.678534	−	0.734569i	$-0.262616\pi$
$138$	0.419084	−	9.11591i	0.0356748	−	0.775998i
$139$	3.60435	−	2.08097i	0.305717	−	0.176506i	−0.339291	−	0.940681i	$-0.610187\pi$
$139$	3.60435	−	2.08097i	0.305717	−	0.176506i	0.645008	+	0.764176i	$0.276854\pi$
$140$	−7.69151	−	4.05368i	−0.650051	−	0.342598i
$141$	−5.86393	+	1.28581i	−0.493832	+	0.108285i
$142$	6.71233	−	1.79856i	0.563286	−	0.150932i
$143$	−2.78191	−	2.78191i	−0.232635	−	0.232635i
$144$	−1.73205	+	2.44949i	−0.144338	+	0.204124i
$145$	−9.40344	−	2.13480i	−0.780913	−	0.177286i
$146$	10.1376	+	5.85292i	0.838990	+	0.484391i
$147$	6.46401	+	12.4875i	0.533143	+	1.02995i
$148$	−4.46504	−	1.19640i	−0.367024	−	0.0983437i
$149$	0.518244	+	0.897625i	0.0424562	+	0.0735363i	0.886473	−	0.462781i	$-0.153148\pi$
$149$	0.518244	+	0.897625i	0.0424562	+	0.0735363i	−0.844016	+	0.536317i	$0.819815\pi$
$150$	−5.92985	+	6.31165i	−0.484170	+	0.515344i
$151$	−2.03451	+	3.52388i	−0.165566	+	0.286769i	−0.936856	−	0.349715i	$-0.886278\pi$
$151$	−2.03451	+	3.52388i	−0.165566	+	0.286769i	0.771290	+	0.636484i	$0.219612\pi$
$152$	1.33284	−	1.33284i	0.108108	−	0.108108i
$153$	0.392291	−	0.326099i	0.0317149	−	0.0263635i
$154$			15.4503i			1.24502i
$155$	14.2839	−	15.4303i	1.14731	−	1.23939i
$156$	−0.367304	−	1.67508i	−0.0294079	−	0.134114i
$157$	2.36186	−	8.81460i	0.188497	−	0.703481i	−0.805357	−	0.592789i	$-0.798027\pi$
$157$	2.36186	−	8.81460i	0.188497	−	0.703481i	0.993855	−	0.110692i	$-0.0353067\pi$
$158$	−3.51245	+	13.1086i	−0.279435	+	1.04287i
$159$	6.63408	−	6.05092i	0.526117	−	0.479869i
$160$	−0.0862005	−	2.23441i	−0.00681475	−	0.176645i
$161$		−	20.4857i		−	1.61450i
$162$	−0.701625	−	8.97261i	−0.0551249	−	0.704955i
$163$	5.03848	−	5.03848i	0.394644	−	0.394644i	−0.481695	−	0.876339i	$-0.659979\pi$
$163$	5.03848	−	5.03848i	0.394644	−	0.394644i	0.876339	+	0.481695i	$0.159979\pi$
$164$	−4.13253	+	7.15775i	−0.322696	+	0.558926i
$165$	14.8355	+	4.09276i	1.15494	+	0.318621i
$166$	−3.49878	−	6.06007i	−0.271558	−	0.470353i
$167$	−10.4641	−	2.80384i	−0.809734	−	0.216968i	−0.169881	−	0.985465i	$-0.554338\pi$
$167$	−10.4641	−	2.80384i	−0.809734	−	0.216968i	−0.639853	+	0.768497i	$0.721005\pi$
$168$	−3.63160	+	5.67155i	−0.280184	+	0.437569i
$169$	−10.4094	−	6.00986i	−0.800722	−	0.462297i
$170$	−0.0841789	+	0.370793i	−0.00645623	+	0.0284386i
$171$	−0.518835	+	5.63092i	−0.0396763	+	0.430607i
$172$	−1.45887	−	1.45887i	−0.111238	−	0.111238i
$173$	3.64139	−	0.975709i	0.276850	−	0.0741818i	−0.117722	−	0.993047i	$-0.537559\pi$
$173$	3.64139	−	0.975709i	0.276850	−	0.0741818i	0.394573	+	0.918865i	$0.370893\pi$
$174$	−2.26247	+	7.11832i	−0.171517	+	0.539638i
$175$	−12.6470	+	14.7652i	−0.956023	+	1.11614i
$176$	−3.44125	+	1.98681i	−0.259394	+	0.149761i
$177$	−8.39472	+	4.34543i	−0.630986	+	0.326622i
$178$	−1.26260	−	4.71209i	−0.0946359	−	0.353186i
$179$	−12.8952			−0.963836			−0.481918	−	0.876216i	$-0.660060\pi$
$179$	−12.8952			−0.963836			−0.481918	+	0.876216i	$0.660060\pi$
$180$	4.48387	+	4.98948i	0.334208	+	0.371894i
$181$	24.3197			1.80767			0.903835	−	0.427881i	$-0.140740\pi$
$181$	24.3197			1.80767			0.903835	+	0.427881i	$0.140740\pi$
$182$	−0.996372	−	3.71851i	−0.0738560	−	0.275634i
$183$	−12.7084	−	8.13741i	−0.939430	−	0.601535i
$184$	4.56277	−	2.63432i	0.336372	−	0.194204i
$185$	−4.81924	+	9.14410i	−0.354318	+	0.672288i
$186$	−10.9758	−	12.0336i	−0.804782	−	0.882344i
$187$	0.652663	−	0.174880i	0.0477274	−	0.0127885i
$188$	−2.45081	−	2.45081i	−0.178744	−	0.178744i
$189$	−2.49842	−	20.0488i	−0.181733	−	1.45833i
$190$	−2.24656	−	3.56619i	−0.162982	−	0.258718i
$191$	11.8036	+	6.81478i	0.854075	+	0.493100i	0.862024	−	0.506868i	$-0.169197\pi$
$191$	11.8036	+	6.81478i	0.854075	+	0.493100i	−0.00794868	+	0.999968i	$0.502530\pi$
$192$	−1.73022	−	0.0795432i	−0.124868	−	0.00574054i
$193$	15.6521	+	4.19397i	1.12666	+	0.301889i	0.773577	−	0.633702i	$-0.218466\pi$
$193$	15.6521	+	4.19397i	1.12666	+	0.301889i	0.353086	+	0.935591i	$0.385132\pi$
$194$	−0.748079	−	1.29571i	−0.0537090	−	0.0930267i
$195$	−3.83449	−	0.0283024i	−0.274593	−	0.00202678i
$196$	−4.05916	+	7.03067i	−0.289940	+	0.502191i
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	−0.664543	−	0.747250i	$-0.731374\pi$
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	0.747250	+	0.664543i	$0.231374\pi$
$198$	4.12881	−	11.1830i	0.293422	−	0.794740i
$199$		−	17.1733i		−	1.21738i	−0.793407	−	0.608691i	$-0.791695\pi$
$199$		−	17.1733i		−	1.21738i	0.793407	−	0.608691i	$-0.208305\pi$
$200$	−4.91498	−	0.918161i	−0.347541	−	0.0649238i
$201$	−13.4417	−	4.27226i	−0.948101	−	0.301342i
$202$	−2.66565	+	9.94834i	−0.187554	+	0.699963i
$203$	−4.33973	+	16.1961i	−0.304589	+	1.13674i
$204$	0.280687	+	0.0892129i	0.0196520	+	0.00624615i
$205$	13.5623	+	12.5547i	0.947230	+	0.876859i
$206$			6.48420i			0.451776i
$207$	−5.47442	+	14.8276i	−0.380498	+	1.03059i
$208$	0.700097	−	0.700097i	0.0485430	−	0.0485430i
$209$	−3.74498	+	6.48649i	−0.259046	+	0.448680i
$210$	10.5695	+	10.7267i	0.729363	+	0.740210i
$211$	−9.10894	−	15.7771i	−0.627085	−	1.08614i	−0.988134	−	0.153597i	$-0.950914\pi$
$211$	−9.10894	−	15.7771i	−0.627085	−	1.08614i	0.361048	−	0.932547i	$-0.382419\pi$
$212$	5.00745	+	1.34174i	0.343913	+	0.0921513i
$213$	−12.0235	−	0.552755i	−0.823838	−	0.0378741i
$214$	−4.53225	−	2.61670i	−0.309818	−	0.178874i
$215$	−3.90338	+	2.45898i	−0.266208	+	0.167701i
$216$	4.14418	−	3.13461i	0.281976	−	0.213283i
$217$	−25.8537	−	25.8537i	−1.75507	−	1.75507i
$218$	7.05281	−	1.88979i	0.477676	−	0.127993i
$219$	−13.6631	−	14.9799i	−0.923270	−	1.01225i
$220$	2.62882	+	8.48747i	0.177235	+	0.572225i
$221$	−0.145802	+	0.0841789i	−0.00980771	+	0.00566249i
$222$	6.74266	+	4.31745i	0.452538	+	0.289768i
$223$	1.21534	+	4.53570i	0.0813849	+	0.303733i	0.994605	−	0.103734i	$-0.0330790\pi$
$223$	1.21534	+	4.53570i	0.0813849	+	0.303733i	−0.913220	+	0.407466i	$0.866412\pi$
$224$	−3.88823			−0.259793
$225$	13.0997	−	7.30743i	0.873312	−	0.487162i
$226$	4.21934			0.280666
$227$	6.47859	+	24.1784i	0.429999	+	1.60478i	0.752758	+	0.658297i	$0.228723\pi$
$227$	6.47859	+	24.1784i	0.429999	+	1.60478i	−0.322759	+	0.946481i	$0.604610\pi$
$228$	−2.89937	+	1.50082i	−0.192015	+	0.0993945i
$229$	−19.7350	+	11.3940i	−1.30412	+	0.752935i	−0.981108	−	0.193459i	$-0.938029\pi$
$229$	−19.7350	+	11.3940i	−1.30412	+	0.752935i	−0.323014	+	0.946394i	$0.604696\pi$
$230$	−3.48557	−	11.2536i	−0.229832	−	0.742040i
$231$	8.10596	−	25.5035i	0.533333	−	1.67801i
$232$	−4.16541	+	1.11612i	−0.273473	+	0.0732768i
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.882553	+	0.470214i	$0.155823\pi$
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.470214	+	0.882553i	$0.344177\pi$
$234$	−0.272527	+	2.95773i	−0.0178156	+	0.193353i
$235$	−6.55746	+	4.13094i	−0.427761	+	0.269473i
$236$	−4.72637	−	2.72877i	−0.307660	−	0.177628i
$237$	12.6753	−	19.7954i	0.823352	−	1.28585i
$238$	0.638639	+	0.171123i	0.0413968	+	0.0110922i
$239$	−4.56277	−	7.90295i	−0.295141	−	0.511199i	0.679877	−	0.733327i	$-0.262033\pi$
$239$	−4.56277	−	7.90295i	−0.295141	−	0.511199i	−0.975018	+	0.222127i	$0.928700\pi$
$240$	−1.02999	+	3.73351i	−0.0664853	+	0.240997i
$241$	0.869654	−	1.50629i	0.0560194	−	0.0970284i	−0.836656	−	0.547729i	$-0.815492\pi$
$241$	0.869654	−	1.50629i	0.0560194	−	0.0970284i	0.892675	+	0.450701i	$0.148826\pi$
$242$	3.38674	−	3.38674i	0.217708	−	0.217708i
$243$	−3.54930	+	15.1790i	−0.227688	+	0.973734i
$244$		−	8.71245i		−	0.557758i
$245$	13.3215	+	12.3318i	0.851078	+	0.787851i
$246$	10.5768	−	9.64703i	0.674351	−	0.615072i
$247$	0.483018	−	1.80265i	0.0307337	−	0.114700i
$248$	2.43379	−	9.08302i	0.154546	−	0.576773i
$249$	2.59597	+	11.8389i	0.164513	+	0.750258i
$250$	−4.43525	+	10.2630i	−0.280510	+	0.649087i
$251$			6.16751i			0.389290i	0.980874	+	0.194645i	$0.0623555\pi$
$251$			6.16751i			0.389290i	−0.980874	+	0.194645i	$0.937645\pi$
$252$	8.97017	−	7.45660i	0.565068	−	0.469722i
$253$	−14.8036	+	14.8036i	−0.930696	+	0.930696i
$254$	9.74898	−	16.8857i	0.611706	−	1.05951i
$255$	0.333488	−	0.567897i	0.0208839	−	0.0355631i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	28.0634	+	7.51956i	1.75055	+	0.469057i	0.984743	−	0.174018i	$-0.0556750\pi$
$257$	28.0634	+	7.51956i	1.75055	+	0.469057i	0.765803	+	0.643075i	$0.222342\pi$
$258$	1.64273	+	3.17351i	0.102272	+	0.197574i
$259$	15.5655	+	8.98676i	0.967194	+	0.558410i
$260$	−1.18004	−	1.87320i	−0.0731830	−	0.116171i
$261$	7.46922	−	10.5631i	0.462333	−	0.653838i
$262$	3.17004	+	3.17004i	0.195846	+	0.195846i
$263$	−18.0249	+	4.82975i	−1.11146	+	0.297815i	−0.767424	−	0.641141i	$-0.778462\pi$
$263$	−18.0249	+	4.82975i	−1.11146	+	0.297815i	−0.344038	+	0.938956i	$0.611795\pi$
$264$	6.72277	−	1.47414i	0.413758	−	0.0907269i
$265$	5.40469	−	10.2549i	0.332007	−	0.629956i
$266$	−6.34711	+	3.66451i	−0.389167	+	0.224685i
$267$	−0.388037	+	8.44057i	−0.0237475	+	0.516555i
$268$	−2.10759	−	7.86563i	−0.128742	−	0.480470i
$269$	−15.5553			−0.948425			−0.474212	−	0.880411i	$-0.657267\pi$
$269$	−15.5553			−0.948425			−0.474212	+	0.880411i	$0.657267\pi$
$270$	−4.78372	−	10.5885i	−0.291128	−	0.644395i
$271$	−1.87184			−0.113706			−0.0568532	−	0.998383i	$-0.518107\pi$
$271$	−1.87184			−0.113706			−0.0568532	+	0.998383i	$0.518107\pi$
$272$	0.0440105	+	0.164249i	0.00266853	+	0.00995908i
$273$	−0.306216	+	6.66081i	−0.0185331	+	0.403131i
$274$	−10.8243	+	6.24939i	−0.653918	+	0.377540i
$275$	19.8090	−	1.53069i	1.19453	−	0.0923040i
$276$	−8.91376	+	1.95457i	−0.536545	+	0.117651i
$277$	3.99035	−	1.06921i	0.239757	−	0.0642426i	−0.136940	−	0.990579i	$-0.543727\pi$
$277$	3.99035	−	1.06921i	0.239757	−	0.0642426i	0.376696	+	0.926337i	$0.377060\pi$
$278$	−2.94294	−	2.94294i	−0.176506	−	0.176506i
$279$	11.8041	+	25.6220i	0.706692	+	1.53395i
$280$	−1.92484	+	8.47860i	−0.115031	+	0.506693i
$281$	0.248640	+	0.143552i	0.0148326	+	0.00856361i	0.507398	−	0.861712i	$-0.330607\pi$
$281$	0.248640	+	0.143552i	0.0148326	+	0.00856361i	−0.492565	+	0.870275i	$0.663941\pi$
$282$	2.75970	+	5.33132i	0.164338	+	0.317476i
$283$	17.4857	+	4.68527i	1.03941	+	0.278510i	0.737871	−	0.674942i	$-0.235831\pi$
$283$	17.4857	+	4.68527i	1.03941	+	0.278510i	0.301544	+	0.953452i	$0.402498\pi$
$284$	−3.47456	−	6.01811i	−0.206177	−	0.357109i
$285$	1.83735	+	7.06528i	0.108835	+	0.418511i
$286$	−1.96711	+	3.40713i	−0.116318	+	0.201468i
$287$	22.7239	−	22.7239i	1.34135	−	1.34135i
$288$	2.81431	+	1.03906i	0.165835	+	0.0612271i
$289$			16.9711i			0.998299i
$290$	0.371727	+	9.63555i	0.0218286	+	0.565819i
$291$	0.555048	+	2.53128i	0.0325375	+	0.148386i
$292$	3.02970	−	11.3070i	0.177300	−	0.661691i
$293$	5.53752	−	20.6663i	0.323505	−	1.20734i	−0.592300	−	0.805717i	$-0.701780\pi$
$293$	5.53752	−	20.6663i	0.323505	−	1.20734i	0.915806	−	0.401621i	$-0.131553\pi$
$294$	10.3890	−	9.47576i	0.605899	−	0.552637i
$295$	−8.29006	+	8.95536i	−0.482666	+	0.521401i
$296$			4.62255i			0.268680i
$297$	−12.6825	+	16.2934i	−0.735912	+	0.945436i
$298$	0.732907	−	0.732907i	0.0424562	−	0.0424562i
$299$	2.60820	−	4.51754i	0.150836	−	0.261256i
$300$	7.63134	+	4.09422i	0.440596	+	0.236380i
$301$	4.01100	+	6.94725i	0.231190	+	0.400433i
$302$	3.93037	+	1.05314i	0.226168	+	0.0606014i
$303$	9.61951	−	15.0230i	0.552626	−	0.863049i
$304$	−1.63239	−	0.942462i	−0.0936241	−	0.0540539i
$305$	−18.9982	−	4.31304i	−1.08783	−	0.246964i
$306$	−0.416520	−	0.294524i	−0.0238108	−	0.0168368i
$307$	−20.2953	−	20.2953i	−1.15831	−	1.15831i	−0.984838	−	0.173476i	$-0.944500\pi$
$307$	−20.2953	−	20.2953i	−1.15831	−	1.15831i	−0.173476	−	0.984838i	$-0.555500\pi$
$308$	14.9238	−	3.99883i	0.850365	−	0.227855i
$309$	3.40192	−	10.7033i	0.193528	−	0.608892i
$310$	−18.6014	−	9.80356i	−1.05649	−	0.556805i
$311$	−11.9868	+	6.92056i	−0.679707	+	0.392429i	−0.799745	−	0.600340i	$-0.795032\pi$
$311$	−11.9868	+	6.92056i	−0.679707	+	0.392429i	0.120038	+	0.992769i	$0.461698\pi$
$312$	−1.52294	+	0.788332i	−0.0862196	+	0.0446305i
$313$	−4.79847	−	17.9081i	−0.271226	−	1.01223i	−0.958329	−	0.285668i	$-0.907785\pi$
$313$	−4.79847	−	17.9081i	−0.271226	−	1.01223i	0.687103	−	0.726560i	$-0.258882\pi$
$314$	−9.12554			−0.514984
$315$	−11.8191	−	23.2515i	−0.665931	−	1.31007i
$316$	13.5711			0.763431
$317$	0.217566	+	0.811966i	0.0122197	+	0.0456046i	0.971766	−	0.235945i	$-0.0758184\pi$
$317$	0.217566	+	0.811966i	0.0122197	+	0.0456046i	−0.959547	+	0.281549i	$0.909152\pi$
$318$	−7.56176	−	4.84194i	−0.424043	−	0.271522i
$319$	14.8399	−	8.56781i	0.830874	−	0.479705i
$320$	−2.13596	+	0.661570i	−0.119404	+	0.0369829i
$321$	6.10845	+	6.69716i	0.340941	+	0.373799i
$322$	−19.7876	+	5.30208i	−1.10272	+	0.295473i
$323$	0.226641	+	0.226641i	0.0126107	+	0.0126107i
$324$	−8.48528	+	3.00000i	−0.471405	+	0.166667i
$325$	−4.66883	+	1.64586i	−0.258980	+	0.0912958i
$326$	−6.17086	−	3.56275i	−0.341772	−	0.197322i
$327$	−12.6334	−	0.580793i	−0.698629	−	0.0321179i
$328$	7.98343	+	2.13915i	0.440811	+	0.118115i
$329$	6.73825	+	11.6710i	0.371492	+	0.643443i
$330$	0.113589	−	15.3893i	0.00625285	−	0.847153i
$331$	2.08211	−	3.60631i	0.114443	−	0.198221i	−0.803114	−	0.595825i	$-0.796825\pi$
$331$	2.08211	−	3.60631i	0.114443	−	0.198221i	0.917557	+	0.397604i	$0.130158\pi$
$332$	−4.94803	+	4.94803i	−0.271558	+	0.271558i
$333$	−8.86483	−	10.6642i	−0.485790	−	0.584397i
$334$			10.8332i			0.592766i
$335$	−18.1950	+	0.701939i	−0.994099	+	0.0383510i
$336$	6.41822	+	2.03995i	0.350143	+	0.111288i
$337$	−0.840764	+	3.13777i	−0.0457993	+	0.170925i	−0.985037	−	0.172341i	$-0.944867\pi$
$337$	−0.840764	+	3.13777i	−0.0457993	+	0.170925i	0.939238	+	0.343267i	$0.111533\pi$
$338$	−3.11093	+	11.6102i	−0.169213	+	0.631510i
$339$	−6.96478	−	2.21367i	−0.378275	−	0.120230i
$340$	0.379946	−	0.0146578i	0.0206055	−	0.000794932i
$341$			37.3656i			2.02346i
$342$	5.57334	−	0.956233i	0.301372	−	0.0517072i
$343$	3.07470	−	3.07470i	0.166018	−	0.166018i
$344$	−1.03157	+	1.78674i	−0.0556188	+	0.0963346i
$345$	−0.150608	+	20.4048i	−0.00810846	+	1.09856i
$346$	−1.88492	−	3.26478i	−0.101334	−	0.175516i
$347$	4.53334	+	1.21470i	0.243362	+	0.0652087i	0.378438	−	0.925627i	$-0.376461\pi$
$347$	4.53334	+	1.21470i	0.243362	+	0.0652087i	−0.135076	+	0.990835i	$0.543128\pi$
$348$	7.46134	+	0.343019i	0.399970	+	0.0183877i
$349$	−8.42818	−	4.86601i	−0.451150	−	0.260472i	0.257166	−	0.966367i	$-0.417211\pi$
$349$	−8.42818	−	4.86601i	−0.451150	−	0.260472i	−0.708316	+	0.705896i	$0.750545\pi$
$350$	17.5354	+	8.39455i	0.937305	+	0.448707i
$351$	2.00162	−	4.73929i	0.106839	−	0.252965i
$352$	2.80977	+	2.80977i	0.149761	+	0.149761i
$353$	−4.92815	+	1.32049i	−0.262299	+	0.0702827i	−0.387572	−	0.921840i	$-0.626686\pi$
$353$	−4.92815	+	1.32049i	−0.262299	+	0.0702827i	0.125273	+	0.992122i	$0.460019\pi$
$354$	6.37008	+	6.98400i	0.338566	+	0.371195i
$355$	−14.8430	+	4.59732i	−0.787786	+	0.244001i
$356$	−4.22474	+	2.43916i	−0.223911	+	0.129275i
$357$	−0.964409	−	0.617529i	−0.0510420	−	0.0326831i
$358$	3.33754	+	12.4559i	0.176394	+	0.658312i
$359$	−1.27697			−0.0673957			−0.0336978	−	0.999432i	$-0.510728\pi$
$359$	−1.27697			−0.0673957			−0.0336978	+	0.999432i	$0.510728\pi$
$360$	3.65896	−	5.62246i	0.192844	−	0.296330i
$361$	15.4471			0.813003
$362$	−6.29441	−	23.4910i	−0.330827	−	1.23466i
$363$	−7.36727	+	3.81358i	−0.386682	+	0.200161i
$364$	−3.33392	+	1.92484i	−0.174745	+	0.100889i
$365$	−23.1559	−	12.2039i	−1.21204	−	0.638784i
$366$	−4.57097	+	14.3815i	−0.238928	+	0.751731i
$367$	9.74300	−	2.61063i	0.508581	−	0.136274i	0.00460117	−	0.999989i	$-0.498535\pi$
$367$	9.74300	−	2.61063i	0.508581	−	0.136274i	0.503979	+	0.863716i	$0.331869\pi$
$368$	−3.72549	−	3.72549i	−0.194204	−	0.194204i
$369$	−22.5202	+	10.3751i	−1.17235	+	0.540105i
$370$	10.0798	+	2.28836i	0.524026	+	0.118966i
$371$	−17.4564	−	10.0785i	−0.906293	−	0.523249i
$372$	−8.78279	+	13.7163i	−0.455367	+	0.711156i
$373$	12.6656	+	3.39374i	0.655801	+	0.175721i	0.571350	−	0.820706i	$-0.306420\pi$
$373$	12.6656	+	3.39374i	0.655801	+	0.175721i	0.0844507	+	0.996428i	$0.473086\pi$
$374$	−0.337843	−	0.585162i	−0.0174695	−	0.0302580i
$375$	12.7056	−	14.6139i	0.656116	−	0.754660i
$376$	−1.73299	+	3.00162i	−0.0893720	+	0.154797i
$377$	−3.01907	+	3.01907i	−0.155490	+	0.155490i
$378$	−18.7190	+	7.60229i	−0.962800	+	0.391019i
$379$			0.587648i			0.0301854i	0.999886	+	0.0150927i	$0.00480434\pi$
$379$			0.587648i			0.0301854i	−0.999886	+	0.0150927i	$0.995196\pi$
$380$	−2.86322	+	3.09300i	−0.146880	+	0.158668i
$381$	−24.9515	+	22.7582i	−1.27830	+	1.16594i
$382$	3.52759	−	13.1652i	0.180487	−	0.673588i
$383$	3.75319	−	14.0071i	0.191779	−	0.715729i	−0.801298	−	0.598265i	$-0.795857\pi$
$383$	3.75319	−	14.0071i	0.191779	−	0.715729i	0.993077	−	0.117464i	$-0.0374765\pi$
$384$	0.370982	+	1.69185i	0.0189316	+	0.0863371i
$385$	−1.33182	−	34.5222i	−0.0678760	−	1.75942i
$386$		−	16.2043i		−	0.824775i
$387$	−1.04665	−	6.10031i	−0.0532041	−	0.310096i
$388$	−1.05794	+	1.05794i	−0.0537090	+	0.0537090i
$389$	10.3789	−	17.9767i	0.526230	−	0.911456i	−0.473303	−	0.880899i	$-0.656939\pi$
$389$	10.3789	−	17.9767i	0.526230	−	0.911456i	0.999533	−	0.0305570i	$-0.00972810\pi$
$390$	0.965100	+	3.71115i	0.0488697	+	0.187922i
$391$	0.447948	+	0.775869i	0.0226537	+	0.0392374i
$392$	7.84169	+	2.10118i	0.396065	+	0.106125i
$393$	−3.56957	−	6.89588i	−0.180061	−	0.347851i
$394$	−1.42175	−	0.820845i	−0.0716265	−	0.0413536i
$395$	6.71826	−	29.5928i	0.338032	−	1.48897i
$396$	−11.8705	−	1.09376i	−0.596517	−	0.0549633i
$397$	15.7430	+	15.7430i	0.790118	+	0.790118i	0.981513	−	0.191395i	$-0.0613012\pi$
$397$	15.7430	+	15.7430i	0.790118	+	0.790118i	−0.191395	+	0.981513i	$0.561301\pi$
$398$	−16.5881	+	4.44477i	−0.831487	+	0.222796i
$399$	12.3996	−	2.71893i	0.620758	−	0.136117i
$400$	0.385214	+	4.98514i	0.0192607	+	0.249257i
$401$	4.11737	−	2.37716i	0.205612	−	0.118710i	−0.393659	−	0.919257i	$-0.628791\pi$
$401$	4.11737	−	2.37716i	0.205612	−	0.118710i	0.599270	+	0.800547i	$0.295457\pi$
$402$	−0.647729	+	14.0894i	−0.0323058	+	0.702715i
$403$	−2.40966	−	8.99298i	−0.120034	−	0.447972i
$404$	10.2993			0.512408
$405$	2.34116	+	19.9880i	0.116333	+	0.993210i
$406$	16.7674			0.832153
$407$	−4.75404	−	17.7423i	−0.235649	−	0.879454i
$408$	0.0135258	−	0.294213i	0.000669627	−	0.0145657i
$409$	25.8797	−	14.9417i	1.27967	−	0.738817i	0.302882	−	0.953028i	$-0.402051\pi$
$409$	25.8797	−	14.9417i	1.27967	−	0.738817i	0.976787	+	0.214211i	$0.0687180\pi$
$410$	8.61674	−	16.3495i	0.425551	−	0.807446i
$411$	21.1461	−	4.63682i	1.04306	−	0.228718i
$412$	6.26326	−	1.67823i	0.308568	−	0.0826807i
$413$	15.0049	+	15.0049i	0.738343	+	0.738343i
$414$	15.7392	+	1.45022i	0.773541	+	0.0712744i
$415$	8.34009	+	13.2391i	0.409399	+	0.649880i
$416$	−0.857441	−	0.495044i	−0.0420395	−	0.0242715i
$417$	3.31384	+	6.40185i	0.162280	+	0.313500i
$418$	7.23474	+	1.93854i	0.353863	+	0.0948172i
$419$	−8.81638	−	15.2704i	−0.430708	−	0.746009i	0.566226	−	0.824250i	$-0.308403\pi$
$419$	−8.81638	−	15.2704i	−0.430708	−	0.746009i	−0.996934	+	0.0782412i	$0.975070\pi$
$420$	7.62557	−	12.9856i	0.372090	−	0.633632i
$421$	13.9462	−	24.1555i	0.679696	−	1.17727i	−0.295377	−	0.955381i	$-0.595445\pi$
$421$	13.9462	−	24.1555i	0.679696	−	1.17727i	0.975072	−	0.221887i	$-0.0712215\pi$
$422$	−12.8820	+	12.8820i	−0.627085	+	0.627085i
$423$	−1.75831	−	10.2482i	−0.0854919	−	0.498284i
$424$		−	5.18410i		−	0.251762i
$425$	0.156127	−	0.835759i	0.00757328	−	0.0405403i
$426$	2.57799	+	11.7569i	0.124904	+	0.569623i
$427$	−8.76775	+	32.7217i	−0.424301	+	1.58351i
$428$	−1.35450	+	5.05507i	−0.0654723	+	0.244346i
$429$	5.03461	−	4.59205i	0.243073	−	0.221706i
$430$	3.38546	+	3.13395i	0.163261	+	0.151132i
$431$			19.2910i			0.929215i	0.885517	+	0.464608i	$0.153805\pi$
$431$			19.2910i			0.929215i	−0.885517	+	0.464608i	$0.846195\pi$
$432$	−4.10039	−	3.19168i	−0.197280	−	0.153560i
$433$	16.7154	−	16.7154i	0.803292	−	0.803292i	−0.180316	−	0.983609i	$-0.557712\pi$
$433$	16.7154	−	16.7154i	0.803292	−	0.803292i	0.983609	+	0.180316i	$0.0577122\pi$
$434$	−18.2814	+	31.6642i	−0.877533	+	1.51993i
$435$	4.44167	−	16.1002i	0.212962	−	0.771947i
$436$	−3.65080	−	6.32337i	−0.174842	−	0.302835i
$437$	−9.59259	−	2.57033i	−0.458876	−	0.122955i
$438$	−10.9332	+	17.0747i	−0.522410	+	0.815860i
$439$	31.1811	+	18.0024i	1.48819	+	0.859209i	0.999909	−	0.0134750i	$-0.00428934\pi$
$439$	31.1811	+	18.0024i	1.48819	+	0.859209i	0.488285	+	0.872684i	$0.337623\pi$
$440$	7.51788	−	4.73597i	0.358401	−	0.225778i
$441$	−22.1203	+	10.1909i	−1.05335	+	0.485280i
$442$	0.119047	+	0.119047i	0.00566249	+	0.00566249i
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.815153	−	0.579246i	$-0.803347\pi$
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.416320	+	0.909218i	$0.636680\pi$
$444$	2.42521	−	7.63035i	0.115095	−	0.362120i
$445$	3.22735	+	10.4199i	0.152991	+	0.493950i
$446$	4.06659	−	2.34785i	0.192559	−	0.111174i
$447$	−1.59431	+	0.825278i	−0.0754085	+	0.0390343i
$448$	1.00635	+	3.75574i	0.0475455	+	0.177442i
$449$	41.3392			1.95092			0.975459	−	0.220182i	$-0.0706652\pi$
$449$	41.3392			1.95092			0.975459	+	0.220182i	$0.0706652\pi$
$450$	−10.4489	−	10.7620i	−0.492565	−	0.507326i
$451$	−32.8421			−1.54647
$452$	−1.09205	−	4.07557i	−0.0513655	−	0.191699i
$453$	−5.93526	−	3.80046i	−0.278863	−	0.178561i
$454$	21.6778	−	12.5157i	1.01739	−	0.587390i
$455$	2.54684	+	8.22277i	0.119398	+	0.385489i
$456$	2.20010	+	2.41213i	0.103029	+	0.112959i
$457$	−20.8557	+	5.58827i	−0.975589	+	0.261408i	−0.711186	−	0.703004i	$-0.751842\pi$
$457$	−20.8557	+	5.58827i	−0.975589	+	0.261408i	−0.264403	+	0.964412i	$0.585175\pi$
$458$	16.1135	+	16.1135i	0.752935	+	0.752935i
$459$	0.533019	+	0.704691i	0.0248792	+	0.0328921i
$460$	−9.96800	+	6.27945i	−0.464761	+	0.292781i
$461$	−10.8706	−	6.27615i	−0.506295	−	0.292309i	0.225015	−	0.974355i	$-0.427757\pi$
$461$	−10.8706	−	6.27615i	−0.506295	−	0.292309i	−0.731309	+	0.682046i	$0.761090\pi$
$462$	−26.7325	−	1.22897i	−1.24371	−	0.0571767i
$463$	−21.3514	−	5.72110i	−0.992286	−	0.265882i	−0.274076	−	0.961708i	$-0.588372\pi$
$463$	−21.3514	−	5.72110i	−0.992286	−	0.265882i	−0.718210	+	0.695826i	$0.755038\pi$
$464$	2.15618	+	3.73461i	0.100098	+	0.173375i
$465$	25.5616	+	25.9417i	1.18539	+	1.20302i
$466$	14.6011	−	25.2899i	0.676383	−	1.17153i
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	−0.783053	−	0.621955i	$-0.786339\pi$
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	0.621955	+	0.783053i	$0.286339\pi$
$468$	2.92749	−	0.502277i	0.135323	−	0.0232178i
$469$			31.6622i			1.46203i
$470$	5.68738	+	5.26485i	0.262339	+	0.242850i
$471$	15.0634	+	4.78769i	0.694083	+	0.220605i
$472$	−1.41251	+	5.27158i	−0.0650163	+	0.242644i
$473$	2.12184	−	7.91881i	0.0975622	−	0.364107i
$474$	−22.4015	−	7.12002i	−1.02893	−	0.327033i
$475$	5.32713	+	7.77465i	0.244425	+	0.356726i
$476$		−	0.661168i		−	0.0303046i
$477$	9.94174	+	11.9598i	0.455201	+	0.547599i
$478$	−6.45273	+	6.45273i	−0.295141	+	0.295141i
$479$	1.35673	−	2.34993i	0.0619906	−	0.107371i	−0.833364	−	0.552724i	$-0.813588\pi$
$479$	1.35673	−	2.34993i	0.0619906	−	0.107371i	0.895355	+	0.445353i	$0.146922\pi$
$480$	3.87288	+	0.0285858i	0.176772	+	0.00130476i
$481$	2.28836	+	3.96356i	0.104340	+	0.180723i
$482$	−1.68004	−	0.450166i	−0.0765239	−	0.0205045i
$483$	35.4448	+	1.62949i	1.61279	+	0.0741446i
$484$	−4.14790	−	2.39479i	−0.188541	−	0.108854i
$485$	1.78320	+	2.83066i	0.0809711	+	0.128534i
$486$	15.5804	−	0.500258i	0.706743	−	0.0226921i
$487$	−8.20799	−	8.20799i	−0.371940	−	0.371940i	0.496244	−	0.868183i	$-0.334712\pi$
$487$	−8.20799	−	8.20799i	−0.371940	−	0.371940i	−0.868183	+	0.496244i	$0.834712\pi$
$488$	−8.41558	+	2.25495i	−0.380955	+	0.102077i
$489$	8.31692	+	9.11848i	0.376104	+	0.412352i
$490$	8.46376	−	16.0593i	0.382354	−	0.725484i
$491$	4.28058	−	2.47139i	0.193180	−	0.111532i	−0.400290	−	0.916388i	$-0.631091\pi$
$491$	4.28058	−	2.47139i	0.193180	−	0.111532i	0.593470	+	0.804856i	$0.297757\pi$
$492$	−12.0558	−	7.71955i	−0.543517	−	0.348024i
$493$	−0.189789	−	0.708301i	−0.00854766	−	0.0319003i
$494$	−1.86624			−0.0839661
$495$	−8.26146	+	25.3432i	−0.371325	+	1.13909i
$496$	−9.40344			−0.422227
$497$	6.99322	+	26.0991i	0.313689	+	1.17070i
$498$	10.7636	−	5.57164i	0.482328	−	0.249671i
$499$	−28.1148	+	16.2321i	−1.25859	+	0.726649i	−0.972801	−	0.231643i	$-0.925590\pi$
$499$	−28.1148	+	16.2321i	−1.25859	+	0.726649i	−0.285791	+	0.958292i	$0.592256\pi$
$500$	11.0612	+	1.62787i	0.494672	+	0.0728006i
$501$	5.68361	−	17.8821i	0.253925	−	0.798915i
$502$	5.95736	−	1.59627i	0.265890	−	0.0712450i
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	0.115717	−	0.993282i	$-0.463083\pi$
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	−0.993282	+	0.115717i	$0.963083\pi$
$504$	−9.52417	−	6.73461i	−0.424240	−	0.299983i
$505$	5.09859	−	22.4584i	0.226884	−	0.999386i
$506$	18.1307	+	10.4677i	0.806007	+	0.465348i
$507$	11.2264	−	17.5325i	0.498582	−	0.778647i
$508$	−18.8336	−	5.04645i	−0.835606	−	0.223900i
$509$	5.25069	+	9.09446i	0.232733	+	0.403105i	0.958611	−	0.284718i	$-0.0918999\pi$
$509$	5.25069	+	9.09446i	0.232733	+	0.403105i	−0.725879	+	0.687823i	$0.758567\pi$
$510$	−0.634860	−	0.175142i	−0.0281121	−	0.00775544i
$511$	−22.7575	+	39.4171i	−1.00673	+	1.74371i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−9.70148	−	1.34560i	−0.428331	−	0.0594098i
$514$		−	29.0534i		−	1.28149i
$515$	−0.558941	−	14.4883i	−0.0246299	−	0.638432i
$516$	2.64021	−	2.40812i	0.116229	−	0.106012i
$517$	3.56457	−	13.3031i	0.156770	−	0.585072i
$518$	4.65189	−	17.3611i	0.204392	−	0.762802i
$519$	1.39855	+	6.37804i	0.0613893	+	0.279965i
$520$	−1.50395	+	1.62465i	−0.0659527	+	0.0712456i
$521$		−	28.2545i		−	1.23785i	−0.785450	−	0.618925i	$-0.787568\pi$
$521$		−	28.2545i		−	1.23785i	0.785450	−	0.618925i	$-0.212432\pi$
$522$	−12.1363	−	4.48079i	−0.531192	−	0.196119i
$523$	13.6590	−	13.6590i	0.597266	−	0.597266i	−0.342318	−	0.939584i	$-0.611212\pi$
$523$	13.6590	−	13.6590i	0.597266	−	0.597266i	0.939584	+	0.342318i	$0.111212\pi$
$524$	2.24156	−	3.88249i	0.0979230	−	0.169608i
$525$	−24.5411	−	23.0566i	−1.07106	−	1.00627i
$526$	9.33036	+	16.1607i	0.406823	+	0.704638i
$527$	1.54451	+	0.413850i	0.0672798	+	0.0180276i
$528$	−3.16389	−	6.11216i	−0.137691	−	0.265998i
$529$	−4.12099	−	2.37925i	−0.179173	−	0.103446i
$530$	−11.3043	−	2.56635i	−0.491029	−	0.111475i
$531$	−6.85082	−	14.8704i	−0.297300	−	0.645320i
$532$	5.18240	+	5.18240i	0.224685	+	0.224685i
$533$	7.90429	−	2.11795i	0.342373	−	0.0917385i
$534$	8.25340	−	1.80977i	0.357160	−	0.0783163i
$535$	10.3525	+	5.45608i	0.447575	+	0.235887i
$536$	−7.05213	+	4.07155i	−0.304606	+	0.175864i
$537$	1.02573	−	22.3117i	0.0442635	−	0.962819i
$538$	4.02601	+	15.0253i	0.173574	+	0.647786i
$539$	−32.2590			−1.38949
$540$	−8.98958	+	7.36122i	−0.386850	+	0.316776i
$541$	−26.7216			−1.14885			−0.574427	−	0.818556i	$-0.694775\pi$
$541$	−26.7216			−1.14885			−0.574427	+	0.818556i	$0.694775\pi$
$542$	0.484468	+	1.80806i	0.0208097	+	0.0776628i
$543$	−1.93447	+	42.0785i	−0.0830160	+	1.80576i
$544$	0.147262	−	0.0850217i	0.00631380	−	0.00364528i
$545$	−15.5959	+	4.83052i	−0.668056	+	0.206917i
$546$	6.51311	−	1.42816i	0.278735	−	0.0611197i
$547$	−0.234244	+	0.0627654i	−0.0100155	+	0.00268365i	−0.263823	−	0.964571i	$-0.584984\pi$
$547$	−0.234244	+	0.0627654i	−0.0100155	+	0.00268365i	0.253808	+	0.967255i	$0.418317\pi$
$548$	8.83798	+	8.83798i	0.377540	+	0.377540i
$549$	15.0904	−	21.3411i	0.644043	−	0.910814i
$550$	−6.60548	−	18.7379i	−0.281659	−	0.798985i
$551$	7.03946	+	4.06423i	0.299891	+	0.173142i
$552$	4.19502	+	8.10415i	0.178552	+	0.344936i
$553$	−50.9693	−	13.6572i	−2.16744	−	0.580763i
$554$	−2.06556	−	3.57765i	−0.0877571	−	0.152000i
$555$	−15.4380	−	9.06571i	−0.655307	−	0.384818i
$556$	−2.08097	+	3.60435i	−0.0882528	+	0.152858i
$557$	−31.4838	+	31.4838i	−1.33401	+	1.33401i	−0.432266	+	0.901746i	$0.642286\pi$
$557$	−31.4838	+	31.4838i	−1.33401	+	1.33401i	−0.901746	+	0.432266i	$0.857714\pi$
$558$	21.6938	−	18.0333i	0.918372	−	0.763412i
$559$			2.04270i			0.0863969i
$560$	8.68788	−	0.335167i	0.367130	−	0.0141634i
$561$	0.250667	+	1.14316i	0.0105832	+	0.0482644i
$562$	0.0743081	−	0.277322i	0.00313450	−	0.0116981i
$563$	8.35388	−	31.1771i	0.352074	−	1.31396i	−0.532053	−	0.846711i	$-0.678579\pi$
$563$	8.35388	−	31.1771i	0.352074	−	1.31396i	0.884127	−	0.467247i	$-0.154754\pi$
$564$	4.43540	−	4.04551i	0.186764	−	0.170347i
$565$	−9.42772	+	0.363709i	−0.396627	+	0.0153014i
$566$		−	18.1025i		−	0.760904i
$567$	34.8876	−	2.72808i	1.46514	−	0.114569i
$568$	−4.91376	+	4.91376i	−0.206177	+	0.206177i
$569$	16.1545	−	27.9804i	0.677232	−	1.17300i	−0.298580	−	0.954385i	$-0.596513\pi$
$569$	16.1545	−	27.9804i	0.677232	−	1.17300i	0.975811	−	0.218615i	$-0.0701538\pi$
$570$	6.34900	−	3.60338i	0.265930	−	0.150929i
$571$	12.9565	+	22.4413i	0.542213	+	0.939141i	0.998777	+	0.0494501i	$0.0157469\pi$
$571$	12.9565	+	22.4413i	0.542213	+	0.939141i	−0.456563	+	0.889691i	$0.650920\pi$
$572$	3.80016	+	1.01825i	0.158893	+	0.0425752i
$573$	−12.7300	+	19.8807i	−0.531803	+	0.830529i
$574$	−27.8310	−	16.0682i	−1.16164	−	0.670674i
$575$	8.75824	+	24.8446i	0.365244	+	1.03609i
$576$	0.275255	−	2.98735i	0.0114690	−	0.124473i
$577$	6.10724	+	6.10724i	0.254248	+	0.254248i	0.822710	−	0.568462i	$-0.192461\pi$
$577$	6.10724	+	6.10724i	0.254248	+	0.254248i	−0.568462	+	0.822710i	$0.692461\pi$
$578$	16.3928	−	4.39244i	0.681851	−	0.182701i
$579$	−8.50152	+	26.7480i	−0.353311	+	1.11161i
$580$	9.21102	−	2.85292i	0.382467	−	0.118461i
$581$	23.5629	−	13.6041i	0.977556	−	0.564392i
$582$	2.30138	−	1.19128i	0.0953951	−	0.0493801i
$583$	5.33157	+	19.8977i	0.220811	+	0.824077i
$584$	−11.7058			−0.484391
$585$	0.353977	−	6.63227i	0.0146351	−	0.274210i
$586$	−21.3953			−0.883833
$587$	0.490414	+	1.83025i	0.0202415	+	0.0755424i	0.975308	−	0.220850i	$-0.0708831\pi$
$587$	0.490414	+	1.83025i	0.0202415	+	0.0755424i	−0.955066	+	0.296392i	$0.904216\pi$
$588$	−11.8418	−	7.58249i	−0.488346	−	0.312697i
$589$	−15.3501	+	8.86238i	−0.632490	+	0.365168i
$590$	10.7958	+	5.68976i	0.444458	+	0.234244i
$591$	1.91619	+	2.10087i	0.0788217	+	0.0864182i
$592$	4.46504	−	1.19640i	0.183512	−	0.0491719i
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	0.896029	−	0.443996i	$-0.146439\pi$
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	−0.443996	+	0.896029i	$0.646439\pi$
$594$	19.0206	+	8.03330i	0.780426	+	0.329610i
$595$	−1.44173	−	0.327307i	−0.0591051	−	0.0134183i
$596$	−0.897625	−	0.518244i	−0.0367681	−	0.0212281i
$597$	29.7136	+	1.36602i	1.21610	+	0.0559074i
$598$	−5.03866	−	1.35011i	−0.206046	−	0.0552099i
$599$	12.9428	+	22.4176i	0.528828	+	0.915957i	0.999435	+	0.0336142i	$0.0107018\pi$
$599$	12.9428	+	22.4176i	0.528828	+	0.915957i	−0.470607	+	0.882343i	$0.655965\pi$
$600$	1.97958	−	8.43097i	0.0808159	−	0.344193i
$601$	−9.79604	+	16.9672i	−0.399589	+	0.692108i	−0.993675	−	0.112293i	$-0.964180\pi$
$601$	−9.79604	+	16.9672i	−0.399589	+	0.692108i	0.594086	+	0.804401i	$0.297514\pi$
$602$	5.67241	−	5.67241i	0.231190	−	0.231190i
$603$	8.46115	−	22.9172i	0.344565	−	0.933262i
$604$		−	4.06902i		−	0.165566i
$605$	−7.27542	+	7.85930i	−0.295788	+	0.319526i
$606$	−17.0008	−	5.40349i	−0.690611	−	0.219502i
$607$	7.70972	−	28.7731i	0.312928	−	1.16786i	−0.612975	−	0.790102i	$-0.710027\pi$
$607$	7.70972	−	28.7731i	0.312928	−	1.16786i	0.925903	−	0.377761i	$-0.123306\pi$
$608$	−0.487854	+	1.82070i	−0.0197851	+	0.0738390i
$609$	−27.6776	−	8.79699i	−1.12155	−	0.356472i
$610$	0.751018	+	19.4672i	0.0304078	+	0.788202i
$611$			3.43162i			0.138828i
$612$	−0.176685	+	0.478556i	−0.00714207	+	0.0193445i
$613$	−12.5028	+	12.5028i	−0.504982	+	0.504982i	−0.912982	−	0.408000i	$-0.866226\pi$
$613$	−12.5028	+	12.5028i	−0.504982	+	0.504982i	0.408000	+	0.912982i	$0.366226\pi$
$614$	−14.3510	+	24.8566i	−0.579157	+	1.00313i
$615$	−22.8012	+	22.4671i	−0.919435	+	0.905961i
$616$	−7.72515	−	13.3804i	−0.311255	−	0.539110i
$617$	−7.14621	−	1.91482i	−0.287695	−	0.0770878i	0.112085	−	0.993699i	$-0.464247\pi$
$617$	−7.14621	−	1.91482i	−0.287695	−	0.0770878i	−0.399781	+	0.916611i	$0.630914\pi$
$618$	−11.2191	−	0.515774i	−0.451299	−	0.0207475i
$619$	−16.4624	−	9.50460i	−0.661682	−	0.382022i	0.131236	−	0.991351i	$-0.458105\pi$
$619$	−16.4624	−	9.50460i	−0.661682	−	0.382022i	−0.792917	+	0.609329i	$0.791439\pi$
$620$	−4.65511	+	20.5050i	−0.186954	+	0.823499i
$621$	−25.2196	−	10.6514i	−1.01203	−	0.427426i
$622$	9.78715	+	9.78715i	0.392429	+	0.392429i
$623$	18.3217	−	4.90928i	0.734043	−	0.196686i
$624$	1.15564	+	1.26701i	0.0462625	+	0.0507211i
$625$	9.02548	−	23.3140i	0.361019	−	0.932558i
$626$	−16.0560	+	9.26994i	−0.641727	+	0.370501i
$627$	−10.9252	−	6.99560i	−0.436310	−	0.279378i
$628$	2.36186	+	8.81460i	0.0942486	+	0.351741i
$629$	−0.786034			−0.0313412
$630$	−19.4002	+	17.4343i	−0.772924	+	0.694599i
$631$	−2.22853			−0.0887165			−0.0443583	−	0.999016i	$-0.514124\pi$
$631$	−2.22853			−0.0887165			−0.0443583	+	0.999016i	$0.514124\pi$
$632$	−3.51245	−	13.1086i	−0.139718	−	0.521433i
$633$	28.0225	−	14.5055i	1.11380	−	0.576543i
$634$	0.727989	−	0.420305i	0.0289121	−	0.0166924i
$635$	−20.3276	+	38.5700i	−0.806677	+	1.53060i
$636$	−2.71982	+	8.55729i	−0.107848	+	0.339319i
$637$	7.76396	−	2.08035i	0.307619	−	0.0824263i
$638$	−12.1167	−	12.1167i	−0.479705	−	0.479705i
$639$	1.91278	−	20.7594i	0.0756683	−	0.821229i
$640$	1.19185	+	1.89195i	0.0471122	+	0.0747860i
$641$	37.8297	+	21.8410i	1.49418	+	0.862666i	0.999978	−	0.00667968i	$-0.00212622\pi$
$641$	37.8297	+	21.8410i	1.49418	+	0.862666i	0.494204	+	0.869346i	$0.335460\pi$
$642$	4.88798	−	7.63367i	0.192913	−	0.301277i
$643$	29.4639	+	7.89483i	1.16194	+	0.311342i	0.787742	−	0.616006i	$-0.211250\pi$
$643$	29.4639	+	7.89483i	1.16194	+	0.311342i	0.374202	+	0.927347i	$0.377917\pi$
$644$	10.2428	+	17.7411i	0.403624	+	0.699097i
$645$	−3.94409	−	6.94932i	−0.155298	−	0.273629i
$646$	0.160260	−	0.277578i	0.00630533	−	0.0109211i
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	−0.623514	−	0.781812i	$-0.714296\pi$
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	0.781812	+	0.623514i	$0.214296\pi$
$648$	5.09393	+	7.41970i	0.200108	+	0.291473i
$649$		−	21.6861i		−	0.851255i
$650$	2.79816	+	4.08376i	0.109753	+	0.160178i
$651$	46.7892	−	42.6763i	1.83381	−	1.67261i
$652$	−1.84421	+	6.88270i	−0.0722249	+	0.269547i
$653$	−8.44081	+	31.5015i	−0.330314	+	1.23275i	0.578546	+	0.815650i	$0.303620\pi$
$653$	−8.44081	+	31.5015i	−0.330314	+	1.23275i	−0.908861	+	0.417100i	$0.863046\pi$
$654$	2.70876	+	12.3533i	0.105921	+	0.483050i
$655$	−7.35642	−	6.80990i	−0.287439	−	0.266085i
$656$		−	8.26506i		−	0.322696i
$657$	27.0055	−	22.4487i	1.05358	−	0.875809i
$658$	9.52933	−	9.52933i	0.371492	−	0.371492i
$659$	−7.75612	+	13.4340i	−0.302136	+	0.523314i	−0.976619	−	0.214975i	$-0.931033\pi$
$659$	−7.75612	+	13.4340i	−0.302136	+	0.523314i	0.674484	+	0.738290i	$0.264366\pi$
$660$	−14.8943	+	3.87333i	−0.579761	+	0.150769i
$661$	11.1307	+	19.2789i	0.432933	+	0.749862i	0.997124	−	0.0757821i	$-0.0241453\pi$
$661$	11.1307	+	19.2789i	0.432933	+	0.749862i	−0.564191	+	0.825644i	$0.690812\pi$
$662$	−4.02232	−	1.07778i	−0.156332	−	0.0418890i
$663$	−0.134051	−	0.258966i	−0.00520610	−	0.0100574i
$664$	6.06007	+	3.49878i	0.235176	+	0.135779i
$665$	13.8661	−	8.73512i	0.537706	−	0.338734i
$666$	−8.00649	+	11.3229i	−0.310245	+	0.438753i
$667$	16.0656	+	16.0656i	0.622063	+	0.622063i
$668$	10.4641	−	2.80384i	0.404867	−	0.108484i
$669$	−7.94444	+	1.74202i	−0.307150	+	0.0673503i
$670$	5.38723	+	17.3933i	0.208127	+	0.671963i
$671$	29.9817	−	17.3099i	1.15743	−	0.668243i
$672$	0.309282	−	6.72750i	0.0119308	−	0.259519i
$673$	2.49905	+	9.32657i	0.0963312	+	0.359513i	0.997218	−	0.0745413i	$-0.0237493\pi$
$673$	2.49905	+	9.32657i	0.0963312	+	0.359513i	−0.900887	+	0.434054i	$0.857083\pi$
$674$	3.24846			0.125126
$675$	11.6015	+	23.2466i	0.446542	+	0.894763i
$676$	12.0197			0.462297
$677$	1.95869	+	7.30994i	0.0752787	+	0.280944i	0.993296	−	0.115596i	$-0.0368777\pi$
$677$	1.95869	+	7.30994i	0.0752787	+	0.280944i	−0.918018	+	0.396539i	$0.870211\pi$
$678$	−0.335620	+	7.30040i	−0.0128894	+	0.280370i
$679$	5.03802	−	2.90870i	0.193342	−	0.111626i
$680$	−0.112496	−	0.363206i	−0.00431401	−	0.0139283i
$681$	−42.3494	+	9.28618i	−1.62283	+	0.355847i
$682$	36.0924	−	9.67093i	1.38205	−	0.370319i
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	0.549300	−	0.835625i	$-0.314894\pi$
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	−0.835625	+	0.549300i	$0.814894\pi$
$684$	−2.36614	−	5.13594i	−0.0904715	−	0.196378i
$685$	23.6471	−	14.8967i	0.903509	−	0.569175i
$686$	−3.76572	−	2.17414i	−0.143776	−	0.0830090i
$687$	−18.1443	−	35.0522i	−0.692250	−	1.33732i
$688$	1.99285	+	0.533983i	0.0759767	+	0.0203579i
$689$	−2.56635	−	4.44506i	−0.0977703	−	0.169343i
$690$	19.7485	−	5.13567i	0.751812	−	0.195512i
$691$	21.3061	−	36.9033i	0.810523	−	1.40387i	−0.101975	−	0.994787i	$-0.532516\pi$
$691$	21.3061	−	36.9033i	0.810523	−	1.40387i	0.912498	−	0.409080i	$-0.134150\pi$
$692$	−2.66569	+	2.66569i	−0.101334	+	0.101334i
$693$	43.4820	+	16.0538i	1.65174	+	0.609832i
$694$		−	4.69326i		−	0.178154i
$695$	6.82940	+	6.32203i	0.259054	+	0.239808i
$696$	−1.59981	−	7.29588i	−0.0606405	−	0.276550i
$697$	−0.363749	+	1.35753i	−0.0137780	+	0.0514201i
$698$	−2.51883	+	9.40041i	−0.0953392	+	0.355811i
$699$	−37.3700	+	34.0850i	−1.41346	+	1.28921i
$700$	3.57002	−	19.1105i	0.134934	−	0.722311i
$701$		−	36.3602i		−	1.37331i	−0.726985	−	0.686653i	$-0.759079\pi$
$701$		−	36.3602i		−	1.37331i	0.726985	−	0.686653i	$-0.240921\pi$
$702$	−5.09586	−	0.706799i	−0.192331	−	0.0266764i
$703$	6.16113	−	6.16113i	0.232371	−	0.232371i
$704$	1.98681	−	3.44125i	0.0748805	−	0.129697i
$705$	−6.62584	−	11.6745i	−0.249544	−	0.439685i
$706$	2.55100	+	4.41846i	0.0960080	+	0.166291i
$707$	−38.6814	−	10.3647i	−1.45476	−	0.389803i
$708$	5.09733	−	7.96061i	0.191569	−	0.299178i
$709$	0.356646	+	0.205910i	0.0133941	+	0.00773310i	0.506682	−	0.862133i	$-0.330872\pi$
$709$	0.356646	+	0.205910i	0.0133941	+	0.00773310i	−0.493288	+	0.869866i	$0.664205\pi$
$710$	8.28233	+	13.1474i	0.310830	+	0.493413i
$711$	33.2421	+	23.5057i	1.24668	+	0.881534i
$712$	3.44949	+	3.44949i	0.129275	+	0.129275i
$713$	−47.8551	+	12.8227i	−1.79219	+	0.480215i
$714$	−0.346880	+	1.09138i	−0.0129817	+	0.0408437i
$715$	4.10163	−	7.78249i	0.153392	−	0.291048i
$716$	11.1676	−	6.44762i	0.417353	−	0.240959i
$717$	14.0368	−	7.26599i	0.524214	−	0.271353i
$718$	0.330503	+	1.23345i	0.0123343	+	0.0460321i
$719$	34.4664			1.28538			0.642690	−	0.766126i	$-0.277818\pi$
$719$	34.4664			1.28538			0.642690	+	0.766126i	$0.277818\pi$
$720$	−6.37789	−	2.07908i	−0.237690	−	0.0774828i
$721$	−25.2120			−0.938946
$722$	−3.99799	−	14.9207i	−0.148790	−	0.555291i
$723$	2.53704	+	1.62451i	0.0943534	+	0.0604162i
$724$	−21.0615	+	12.1599i	−0.782744	+	0.451918i
$725$	−1.66118	−	21.4977i	−0.0616946	−	0.798404i
$726$	5.59043	+	6.12921i	0.207480	+	0.227476i
$727$	−13.7902	+	3.69508i	−0.511451	+	0.137043i	−0.505310	−	0.862938i	$-0.668622\pi$
$727$	−13.7902	+	3.69508i	−0.511451	+	0.137043i	−0.00614188	+	0.999981i	$0.501955\pi$
$728$	2.72214	+	2.72214i	0.100889	+	0.100889i
$729$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$730$	−5.79490	+	25.5255i	−0.214479	+	0.944743i
$731$	−0.303823	−	0.175413i	−0.0112373	−	0.00648787i
$732$	15.0745	+	0.693017i	0.557169	+	0.0256146i
$733$	−29.6676	−	7.94942i	−1.09580	−	0.293618i	−0.334746	−	0.942308i	$-0.608651\pi$
$733$	−29.6676	−	7.94942i	−1.09580	−	0.293618i	−0.761053	+	0.648690i	$0.775317\pi$
$734$	−5.04335	−	8.73534i	−0.186153	−	0.322427i
$735$	−22.3964	+	22.0682i	−0.826104	+	0.813999i
$736$	−2.63432	+	4.56277i	−0.0971022	+	0.168186i
$737$	22.8802	−	22.8802i	0.842803	−	0.842803i
$738$	15.8502	+	19.0675i	0.583454	+	0.701886i
$739$		−	19.6312i		−	0.722144i	−0.932538	−	0.361072i	$-0.882411\pi$
$739$		−	19.6312i		−	0.722144i	0.932538	−	0.361072i	$-0.117589\pi$
$740$	−0.398466	−	10.3286i	−0.0146479	−	0.379689i
$741$	3.08056	+	0.979118i	0.113167	+	0.0359688i
$742$	−5.21700	+	19.4701i	−0.191522	+	0.714771i
$743$	−9.31585	+	34.7672i	−0.341765	+	1.27549i	0.554580	+	0.832130i	$0.312879\pi$
$743$	−9.31585	+	34.7672i	−0.341765	+	1.27549i	−0.896346	+	0.443356i	$0.853788\pi$
$744$	15.5221	+	4.93349i	0.569067	+	0.180871i
$745$	−1.57444	+	1.70079i	−0.0576829	+	0.0623121i
$746$		−	13.1124i		−	0.480080i
$747$	−20.6904	+	3.54991i	−0.757022	+	0.129884i
$748$	−0.477782	+	0.477782i	−0.0174695	+	0.0174695i
$749$	10.1743	−	17.6224i	0.371761	−	0.643910i
$750$	−17.4044	−	8.49032i	−0.635520	−	0.310023i
$751$	−24.4567	−	42.3603i	−0.892438	−	1.54575i	−0.836944	−	0.547289i	$-0.815660\pi$
$751$	−24.4567	−	42.3603i	−0.892438	−	1.54575i	−0.0554938	−	0.998459i	$-0.517673\pi$
$752$	3.34787	+	0.897060i	0.122084	+	0.0327124i
$753$	−10.6712	−	0.490584i	−0.388879	−	0.0178779i
$754$	3.69759	+	2.13480i	0.134658	+	0.0777449i
$755$	−8.87283	−	2.01434i	−0.322915	−	0.0733095i
$756$	12.1881	+	16.1135i	0.443276	+	0.586043i
$757$	22.9129	+	22.9129i	0.832783	+	0.832783i	0.987897	−	0.155114i	$-0.0495745\pi$
$757$	22.9129	+	22.9129i	0.832783	+	0.832783i	−0.155114	+	0.987897i	$0.549574\pi$
$758$	0.567624	−	0.152094i	0.0206170	−	0.00552432i
$759$	−24.4361	−	26.7911i	−0.886973	−	0.972456i
$760$	3.72867	+	1.96513i	0.135253	+	0.0712828i
$761$	−9.19124	+	5.30657i	−0.333182	+	0.192363i	−0.657253	−	0.753670i	$-0.728282\pi$
$761$	−9.19124	+	5.30657i	−0.333182	+	0.192363i	0.324071	+	0.946033i	$0.394948\pi$
$762$	28.4406	+	18.2111i	1.03030	+	0.659717i
$763$	7.34795	+	27.4229i	0.266014	+	0.992777i
$764$	−13.6296			−0.493100
$765$	0.956062	+	0.622182i	0.0345665	+	0.0224950i
$766$	−14.5012			−0.523950
$767$	1.39851	+	5.21932i	0.0504974	+	0.188459i
$768$	1.53819	−	0.796225i	0.0555046	−	0.0287313i
$769$	3.31814	−	1.91573i	0.119655	−	0.0690830i	−0.438978	−	0.898498i	$-0.644659\pi$
$769$	3.31814	−	1.91573i	0.119655	−	0.0690830i	0.558633	+	0.829415i	$0.311326\pi$
$770$	−33.0012	+	10.2215i	−1.18928	+	0.368356i
$771$	−15.2428	+	47.9578i	−0.548955	+	1.72716i
$772$	−15.6521	+	4.19397i	−0.563332	+	0.150944i
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	0.252047	−	0.967715i	$-0.418896\pi$
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	−0.967715	+	0.252047i	$0.918896\pi$
$774$	−5.62156	+	2.58986i	−0.202063	+	0.0930907i
$775$	42.4082	+	20.3017i	1.52335	+	0.729258i
$776$	1.29571	+	0.748079i	0.0465133	+	0.0268545i
$777$	−16.7872	+	26.2170i	−0.602239	+	0.940529i
$778$	−20.0504	−	5.37250i	−0.718843	−	0.192613i
$779$	−7.78950	−	13.4918i	−0.279088	−	0.483395i
$780$	3.33491	−	1.89273i	0.119409	−	0.0677707i
$781$	13.8065	−	23.9136i	0.494036	−	0.855696i
$782$	0.633495	−	0.633495i	0.0226537	−	0.0226537i
$783$	17.6823	+	13.7636i	0.631915	+	0.491872i
$784$		−	8.11832i		−	0.289940i
$785$	20.3902	−	0.786626i	0.727756	−	0.0280759i
$786$	−5.73704	+	5.23273i	−0.204633	+	0.186645i
$787$	−1.87155	+	6.98473i	−0.0667137	+	0.248979i	−0.991227	−	0.132171i	$-0.957805\pi$
$787$	−1.87155	+	6.98473i	−0.0667137	+	0.248979i	0.924513	+	0.381150i	$0.124472\pi$
$788$	−0.424901	+	1.58575i	−0.0151365	+	0.0564901i
$789$	−6.92279	−	31.5712i	−0.246458	−	1.12397i
$790$	−30.3232	+	1.16983i	−1.07885	+	0.0416207i
$791$			16.4058i			0.583321i
$792$	2.01584	+	11.7492i	0.0716296	+	0.417488i
$793$	−6.09956	+	6.09956i	−0.216602	+	0.216602i
$794$	11.1320	−	19.2811i	0.395059	−	0.684262i
$795$	17.3134	+	10.1670i	0.614044	+	0.360587i
$796$	8.58664	+	14.8725i	0.304345	+	0.527142i
$797$	−33.4396	−	8.96012i	−1.18449	−	0.317384i	−0.387786	−	0.921750i	$-0.626760\pi$
$797$	−33.4396	−	8.96012i	−1.18449	−	0.317384i	−0.796707	+	0.604366i	$0.793427\pi$
$798$	−5.83555	−	11.2734i	−0.206576	−	0.399074i
$799$	−0.510406	−	0.294683i	−0.0180569	−	0.0104251i
$800$	4.71557	−	1.66234i	0.166721	−	0.0587725i
$801$	−14.5732	−	1.34278i	−0.514919	−	0.0474448i
$802$	−3.36182	−	3.36182i	−0.118710	−	0.118710i
$803$	44.9295	−	12.0388i	1.58553	−	0.424841i
$804$	13.7769	−	3.02094i	0.485875	−	0.106540i
$805$	43.7565	−	13.5527i	1.54222	−	0.477670i
$806$	−8.06289	+	4.65511i	−0.284003	+	0.163969i
$807$	1.23732	−	26.9142i	0.0435557	−	0.947424i
$808$	−2.66565	−	9.94834i	−0.0937772	−	0.349981i
$809$	−52.6028			−1.84942			−0.924709	−	0.380675i	$-0.875692\pi$
$809$	−52.6028			−1.84942			−0.924709	+	0.380675i	$0.875692\pi$
$810$	18.7010	−	7.43465i	0.657085	−	0.261227i
$811$	−13.8979			−0.488021			−0.244011	−	0.969773i	$-0.578463\pi$
$811$	−13.8979			−0.488021			−0.244011	+	0.969773i	$0.578463\pi$
$812$	−4.33973	−	16.1961i	−0.152295	−	0.568371i
$813$	0.148892	−	3.23870i	0.00522188	−	0.113586i
$814$	−15.9073	+	9.18410i	−0.557551	+	0.321902i
$815$	14.0953	+	7.42869i	0.493737	+	0.260216i
$816$	−0.287689	+	0.0630830i	−0.0100711	+	0.00220835i
$817$	3.75637	−	1.00652i	0.131419	−	0.0352136i
$818$	−21.1307	−	21.1307i	−0.738817	−	0.738817i
$819$	−11.5003	−	1.05965i	−0.401854	−	0.0370270i
$820$	−18.0226	−	4.09156i	−0.629377	−	0.142884i
$821$	−23.9657	−	13.8366i	−0.836408	−	0.482900i	0.0196338	−	0.999807i	$-0.493750\pi$
$821$	−23.9657	−	13.8366i	−0.836408	−	0.482900i	−0.856042	+	0.516907i	$0.827083\pi$
$822$	−9.95185	−	19.2255i	−0.347111	−	0.670566i
$823$	29.1118	+	7.80049i	1.01477	+	0.271908i	0.727623	−	0.685977i	$-0.240625\pi$
$823$	29.1118	+	7.80049i	1.01477	+	0.271908i	0.287151	+	0.957885i	$0.407292\pi$
$824$	−3.24210	−	5.61548i	−0.112944	−	0.195625i
$825$	1.07276	+	34.3957i	0.0373488	+	1.19751i
$826$	10.6101	−	18.3772i	0.369172	−	0.639424i
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	−0.774768	−	0.632245i	$-0.782134\pi$
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	0.632245	+	0.774768i	$0.282134\pi$
$828$	−2.67281	−	15.5783i	−0.0928865	−	0.541382i
$829$		−	37.6756i		−	1.30853i	−0.756266	−	0.654264i	$-0.772979\pi$
$829$		−	37.6756i		−	1.30853i	0.756266	−	0.654264i	$-0.227021\pi$
$830$	10.6294	−	11.4824i	0.368951	−	0.398561i
$831$	1.53257	+	6.98924i	0.0531642	+	0.242454i
$832$	−0.256253	+	0.956351i	−0.00888399	+	0.0331555i
$833$	−0.357291	+	1.33343i	−0.0123794	+	0.0462006i
$834$	5.32603	−	4.85785i	0.184425	−	0.168213i
$835$	−0.933827	−	24.2058i	−0.0323164	−	0.837675i
$836$		−	7.48995i		−	0.259046i
$837$	−45.2707	+	18.3857i	−1.56478	+	0.635501i
$838$	−12.4682	+	12.4682i	−0.430708	+	0.430708i
$839$	−16.5639	+	28.6895i	−0.571849	+	0.990471i	0.424527	+	0.905415i	$0.360440\pi$
$839$	−16.5639	+	28.6895i	−0.571849	+	0.990471i	−0.996376	+	0.0850559i	$0.972893\pi$
$840$	−14.5168	−	4.00482i	−0.500876	−	0.138179i
$841$	5.20180	+	9.00978i	0.179372	+	0.310682i
$842$	−26.9420	−	7.21908i	−0.928482	−	0.248786i
$843$	−0.268155	+	0.418784i	−0.00923575	+	0.0144237i
$844$	15.7771	+	9.10894i	0.543072	+	0.313543i
$845$	5.95029	−	26.2100i	0.204696	−	0.901651i
$846$	−9.44390	+	4.35082i	−0.324688	+	0.149584i
$847$	13.1684	+	13.1684i	0.452472	+	0.452472i
$848$	−5.00745	+	1.34174i	−0.171957	+	0.0460757i
$849$	−9.49743	+	29.8814i	−0.325951	+	1.02553i
$850$	−0.847690	+	0.0655031i	−0.0290755	+	0.00224674i
$851$	21.0916	−	12.1773i	0.723011	−	0.417431i
$852$	10.6890	−	5.53306i	0.366201	−	0.189559i
$853$	0.689663	+	2.57386i	0.0236136	+	0.0881273i	0.976727	−	0.214486i	$-0.0688076\pi$
$853$	0.689663	+	2.57386i	0.0236136	+	0.0881273i	−0.953113	+	0.302613i	$0.902141\pi$
$854$	33.8760			1.15921
$855$	−12.3707	+	2.61704i	−0.423068	+	0.0895008i
$856$	5.23339			0.178874
$857$	4.05364	+	15.1284i	0.138470	+	0.516776i	0.999959	+	0.00900123i	$0.00286522\pi$
$857$	4.05364	+	15.1284i	0.138470	+	0.516776i	−0.861490	+	0.507775i	$0.830468\pi$
$858$	−5.73863	−	3.67455i	−0.195914	−	0.125447i
$859$	−0.691191	+	0.399059i	−0.0235831	+	0.0136157i	−0.511745	−	0.859137i	$-0.671001\pi$
$859$	−0.691191	+	0.399059i	−0.0235831	+	0.0136157i	0.488162	+	0.872753i	$0.337667\pi$
$860$	2.15094	−	4.08123i	0.0733464	−	0.139169i
$861$	37.5099	+	41.1249i	1.27833	+	1.40153i
$862$	18.6337	−	4.99288i	0.634666	−	0.170058i
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.999506	−	0.0314193i	$-0.989997\pi$
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.0314193	−	0.999506i	$-0.510003\pi$
$864$	−2.02166	+	4.78674i	−0.0687783	+	0.162848i
$865$	4.49311	+	7.13237i	0.152770	+	0.242508i
$866$	−20.4721	−	11.8196i	−0.695671	−	0.401646i
$867$	−29.3638	−	1.34994i	−0.997246	−	0.0458462i
$868$	35.3169	+	9.46313i	1.19873	+	0.321199i
$869$	26.9630	+	46.7013i	0.914658	+	1.58423i
$870$	−16.7012	−	0.123272i	−0.566224	−	0.00417931i
$871$	−4.03119	+	6.98222i	−0.136592	+	0.236584i
$872$	−5.16301	+	5.16301i	−0.174842	+	0.174842i
$873$	−4.42384	+	0.759010i	−0.149724	+	0.0256886i
$874$			9.93098i			0.335920i
$875$	−39.9048	−	17.2453i	−1.34903	−	0.582996i
$876$	19.3226	+	6.14144i	0.652850	+	0.207500i
$877$	4.48641	−	16.7435i	0.151495	−	0.565388i	−0.847885	−	0.530180i	$-0.822124\pi$
$877$	4.48641	−	16.7435i	0.151495	−	0.565388i	0.999380	−	0.0352074i	$-0.0112092\pi$
$878$	9.31875	−	34.7780i	0.314492	−	1.17370i
$879$	35.3169	+	11.2250i	1.19121	+	0.378610i
$880$	−6.52036	−	6.03596i	−0.219801	−	0.203472i
$881$		−	15.1033i		−	0.508843i	−0.967093	−	0.254421i	$-0.918115\pi$
$881$		−	15.1033i		−	0.508843i	0.967093	−	0.254421i	$-0.0818850\pi$
$882$	15.5688	+	18.7290i	0.524229	+	0.630639i
$883$	−16.4678	+	16.4678i	−0.554185	+	0.554185i	−0.927646	−	0.373461i	$-0.878171\pi$
$883$	−16.4678	+	16.4678i	−0.554185	+	0.554185i	0.373461	+	0.927646i	$0.378171\pi$
$884$	0.0841789	−	0.145802i	0.00283124	−	0.00490386i
$885$	−14.8354	−	15.0560i	−0.498685	−	0.506102i
$886$	13.4169	+	23.2388i	0.450750	+	0.780723i
$887$	26.4123	+	7.07714i	0.886837	+	0.237627i	0.673355	−	0.739320i	$-0.264853\pi$
$887$	26.4123	+	7.07714i	0.886837	+	0.237627i	0.213482	+	0.976947i	$0.431519\pi$
$888$	−7.99804	−	0.367692i	−0.268397	−	0.0123389i
$889$	65.6556	+	37.9063i	2.20202	+	1.27134i
$890$	9.22954	−	5.81424i	0.309375	−	0.194894i
$891$	−27.1823	−	23.2395i	−0.910643	−	0.778554i
$892$	−3.32036	−	3.32036i	−0.111174	−	0.111174i
$893$	6.31049	−	1.69089i	0.211173	−	0.0565835i
$894$	1.20980	+	1.32639i	0.0404616	+	0.0443612i
$895$	−8.53111	−	27.5437i	−0.285164	−	0.920686i
$896$	3.36730	−	1.94411i	0.112494	−	0.0649483i
$897$	7.60889	+	4.87211i	0.254053	+	0.162675i
$898$	−10.6994	−	39.9306i	−0.357043	−	1.33250i
$899$	40.5510			1.35245
$900$	−7.69094	+	12.8783i	−0.256365	+	0.429275i
$901$	0.881522			0.0293678
$902$	8.50016	+	31.7230i	0.283025	+	1.05626i
$903$	−12.3393	+	6.38732i	−0.410628	+	0.212557i
$904$	−3.65405	+	2.10967i	−0.121532	+	0.0701666i
$905$	16.0892	+	51.9459i	0.534823	+	1.72674i
$906$	−2.13480	+	6.71666i	−0.0709241	+	0.223146i
$907$	−24.7295	+	6.62626i	−0.821130	+	0.220021i	−0.644841	−	0.764317i	$-0.723076\pi$
$907$	−24.7295	+	6.62626i	−0.821130	+	0.220021i	−0.176290	+	0.984338i	$0.556410\pi$
$908$	−17.6998	−	17.6998i	−0.587390	−	0.587390i
$909$	25.2280	+	17.8389i	0.836759	+	0.591678i
$910$	7.28342	−	4.58826i	0.241443	−	0.152099i
$911$	3.55075	+	2.05003i	0.117642	+	0.0679204i	0.557666	−	0.830065i	$-0.311697\pi$
$911$	3.55075	+	2.05003i	0.117642	+	0.0679204i	−0.440025	+	0.897986i	$0.645030\pi$
$912$	1.76052	−	2.74944i	0.0582965	−	0.0910430i
$913$	−26.8582	−	7.19662i	−0.888875	−	0.238173i
$914$	10.7957	+	18.6987i	0.357090	+	0.618499i
$915$	8.97371	−	32.5281i	0.296662	−	1.07534i
$916$	11.3940	−	19.7350i	0.376468	−	0.652061i
$917$	−12.3259	+	12.3259i	−0.407035	+	0.407035i
$918$	0.542723	−	0.697245i	0.0179125	−	0.0230125i
$919$			28.8740i			0.952464i	0.879320	+	0.476232i	$0.157998\pi$
$919$			28.8740i			0.952464i	−0.879320	+	0.476232i	$0.842002\pi$
$920$	8.64539	+	8.00311i	0.285030	+	0.263855i
$921$	36.7298	−	33.5011i	1.21029	−	1.10390i
$922$	−3.24877	+	12.1246i	−0.106993	+	0.399302i
$923$	−1.78073	+	6.64579i	−0.0586135	+	0.218749i
$924$	5.73178	+	26.1397i	0.188562	+	0.859932i
$925$	−22.7197	−	4.24424i	−0.747019	−	0.139550i
$926$			22.1046i			0.726404i
$927$	18.2486	+	6.73746i	0.599362	+	0.221287i
$928$	3.04930	−	3.04930i	0.100098	−	0.100098i
$929$	25.1077	−	43.4879i	0.823758	−	1.42679i	−0.0791067	−	0.996866i	$-0.525207\pi$
$929$	25.1077	−	43.4879i	0.823758	−	1.42679i	0.902865	−	0.429925i	$-0.141460\pi$
$930$	18.4420	−	31.4048i	0.604736	−	1.02980i
$931$	−7.65121	−	13.2523i	−0.250758	−	0.434326i
$932$	−28.2072	−	7.55809i	−0.923956	−	0.247573i
$933$	−11.0206	−	21.2903i	−0.360800	−	0.697012i
$934$	4.26380	+	2.46170i	0.139516	+	0.0805494i
$935$	0.805320	+	1.27837i	0.0263368	+	0.0418070i
$936$	−1.24285	−	2.69773i	−0.0406239	−	0.0881782i
$937$	−0.857094	−	0.857094i	−0.0280000	−	0.0280000i	0.692968	−	0.720968i	$-0.256303\pi$
$937$	−0.857094	−	0.857094i	−0.0280000	−	0.0280000i	−0.720968	+	0.692968i	$0.756303\pi$
$938$	30.5834	−	8.19479i	0.998582	−	0.267569i
$939$	31.3668	−	6.87796i	1.02362	−	0.224454i
$940$	3.61346	−	6.85623i	0.117858	−	0.223625i
$941$	−43.4478	+	25.0846i	−1.41636	+	0.817735i	−0.995977	−	0.0896119i	$-0.971437\pi$
$941$	−43.4478	+	25.0846i	−1.41636	+	0.817735i	−0.420382	+	0.907347i	$0.638104\pi$
$942$	0.725875	−	15.7892i	0.0236503	−	0.514441i
$943$	−11.2704	−	42.0618i	−0.367015	−	1.36972i
$944$	5.45754			0.177628
$945$	41.1705	−	18.6002i	1.33928	−	0.605064i
$946$	−8.19815			−0.266545
$947$	0.681485	+	2.54334i	0.0221453	+	0.0826473i	0.976114	−	0.217258i	$-0.0697114\pi$
$947$	0.681485	+	2.54334i	0.0221453	+	0.0826473i	−0.953969	+	0.299906i	$0.903045\pi$
$948$	−1.07949	+	23.4809i	−0.0350601	+	0.762626i
$949$	−10.0371	+	5.79490i	−0.325817	+	0.188111i
$950$	6.13098	−	7.15784i	0.198915	−	0.232231i
$951$	−1.42219	+	0.311851i	−0.0461176	+	0.0101125i
$952$	−0.638639	+	0.171123i	−0.0206984	+	0.00554612i
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	0.996419	−	0.0845545i	$-0.0269467\pi$
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	−0.0845545	+	0.996419i	$0.526947\pi$
$954$	8.97912	−	12.6984i	0.290710	−	0.411126i
$955$	−6.74723	+	29.7204i	−0.218335	+	0.961729i
$956$	7.90295	+	4.56277i	0.255600	+	0.147571i
$957$	13.6438	+	26.3578i	0.441042	+	0.852027i
$958$	−2.62100	−	0.702296i	−0.0846808	−	0.0226901i
$959$	−24.2991	−	42.0872i	−0.784658	−	1.35907i
$960$	−0.974763	−	3.74831i	−0.0314603	−	0.120976i
$961$	−28.7123	+	49.7312i	−0.926204	+	1.60423i
$962$	3.23623	−	3.23623i	0.104340	−	0.104340i
$963$	−12.0735	+	10.0363i	−0.389062	+	0.323414i
$964$			1.73931i			0.0560194i
$965$	1.39681	+	36.2069i	0.0449651	+	1.16554i
$966$	−7.59981	−	34.6587i	−0.244520	−	1.11513i
$967$	−0.343829	+	1.28319i	−0.0110568	+	0.0412646i	−0.971234	−	0.238128i	$-0.923466\pi$
$967$	−0.343829	+	1.28319i	−0.0110568	+	0.0412646i	0.960177	+	0.279392i	$0.0901330\pi$
$968$	−1.23963	+	4.62638i	−0.0398433	+	0.148697i
$969$	−0.410168	+	0.374112i	−0.0131765	+	0.0120182i
$970$	2.27268	−	2.45507i	0.0729714	−	0.0788276i
$971$			38.7906i			1.24485i	0.782679	+	0.622425i	$0.213853\pi$
$971$			38.7906i			1.24485i	−0.782679	+	0.622425i	$0.786147\pi$
$972$	−4.51572	−	14.9201i	−0.144842	−	0.478561i
$973$	11.4428	−	11.4428i	0.366840	−	0.366840i
$974$	−5.80393	+	10.0527i	−0.185970	+	0.322109i
$975$	−2.47633	−	8.20903i	−0.0793060	−	0.262899i
$976$	4.35623	+	7.54520i	0.139439	+	0.241516i
$977$	41.4084	+	11.0953i	1.32477	+	0.354972i	0.850764	−	0.525548i	$-0.176140\pi$
$977$	41.4084	+	11.0953i	1.32477	+	0.354972i	0.474009	+	0.880520i	$0.342807\pi$
$978$	6.65520	−	10.3936i	0.212810	−	0.332350i
$979$	−16.7875	−	9.69226i	−0.536530	−	0.309766i
$980$	−17.7026	−	4.01892i	−0.565490	−	0.128380i
$981$	2.00980	−	21.8124i	0.0641681	−	0.696417i
$982$	−3.49508	−	3.49508i	−0.111532	−	0.111532i
$983$	31.1321	−	8.34182i	0.992960	−	0.266063i	0.274466	−	0.961597i	$-0.411499\pi$
$983$	31.1321	−	8.34182i	0.992960	−	0.266063i	0.718493	+	0.695534i	$0.244832\pi$
$984$	−4.33624	+	13.6430i	−0.138234	+	0.434922i
$985$	3.24751	+	1.71155i	0.103474	+	0.0545344i
$986$	−0.635046	+	0.366644i	−0.0202240	+	0.0116763i
$987$	−20.7294	+	10.7303i	−0.659824	+	0.341550i
$988$	0.483018	+	1.80265i	0.0153669	+	0.0573499i
$989$	10.8700			0.345645
$990$	26.6179	+	1.42065i	0.845972	+	0.0451512i
$991$	20.1017			0.638551			0.319275	−	0.947662i	$-0.396561\pi$
$991$	20.1017			0.638551			0.319275	+	0.947662i	$0.396561\pi$
$992$	2.43379	+	9.08302i	0.0772729	+	0.288386i
$993$	6.07411	+	3.88937i	0.192756	+	0.123425i
$994$	23.3998	−	13.5099i	0.742196	−	0.428507i
$995$	36.6815	−	11.3613i	1.16288	−	0.360178i
$996$	−8.16761	−	8.95478i	−0.258801	−	0.283743i
$997$	−2.84912	+	0.763421i	−0.0902327	+	0.0241778i	−0.303653	−	0.952783i	$-0.598206\pi$
$997$	−2.84912	+	0.763421i	−0.0902327	+	0.0241778i	0.213420	+	0.976960i	$0.431540\pi$
$998$	22.9557	+	22.9557i	0.726649	+	0.726649i
$999$	19.1567	−	14.4899i	0.606090	−	0.458439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.b.47.1	yes	16
3.2	odd	2		270.2.m.b.197.3		16
4.3	odd	2		720.2.cu.b.497.3		16
5.2	odd	4		450.2.p.h.443.4		16
5.3	odd	4	inner	90.2.l.b.83.1	yes	16
5.4	even	2		450.2.p.h.407.4		16
9.2	odd	6		810.2.f.c.647.8		16
9.4	even	3		270.2.m.b.17.4		16
9.5	odd	6	inner	90.2.l.b.77.1	yes	16
9.7	even	3		810.2.f.c.647.1		16
15.2	even	4		1350.2.q.h.143.2		16
15.8	even	4		270.2.m.b.143.4		16
15.14	odd	2		1350.2.q.h.1007.1		16
20.3	even	4		720.2.cu.b.353.4		16
36.23	even	6		720.2.cu.b.257.4		16
45.4	even	6		1350.2.q.h.557.2		16
45.13	odd	12		270.2.m.b.233.3		16
45.14	odd	6		450.2.p.h.257.4		16
45.22	odd	12		1350.2.q.h.1043.1		16
45.23	even	12	inner	90.2.l.b.23.1	✓	16
45.32	even	12		450.2.p.h.293.4		16
45.38	even	12		810.2.f.c.323.1		16
45.43	odd	12		810.2.f.c.323.8		16
180.23	odd	12		720.2.cu.b.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	45.23	even	12	inner
90.2.l.b.47.1	yes	16	1.1	even	1	trivial
90.2.l.b.77.1	yes	16	9.5	odd	6	inner
90.2.l.b.83.1	yes	16	5.3	odd	4	inner
270.2.m.b.17.4		16	9.4	even	3
270.2.m.b.143.4		16	15.8	even	4
270.2.m.b.197.3		16	3.2	odd	2
270.2.m.b.233.3		16	45.13	odd	12
450.2.p.h.257.4		16	45.14	odd	6
450.2.p.h.293.4		16	45.32	even	12
450.2.p.h.407.4		16	5.4	even	2
450.2.p.h.443.4		16	5.2	odd	4
720.2.cu.b.113.3		16	180.23	odd	12
720.2.cu.b.257.4		16	36.23	even	6
720.2.cu.b.353.4		16	20.3	even	4
720.2.cu.b.497.3		16	4.3	odd	2
810.2.f.c.323.1		16	45.38	even	12
810.2.f.c.323.8		16	45.43	odd	12
810.2.f.c.647.1		16	9.7	even	3
810.2.f.c.647.8		16	9.2	odd	6
1350.2.q.h.143.2		16	15.2	even	4
1350.2.q.h.557.2		16	45.4	even	6
1350.2.q.h.1007.1		16	15.14	odd	2
1350.2.q.h.1043.1		16	45.22	odd	12

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.661570 + 2.13596i) q^{5} +(1.69185 - 0.370982i) q^{6} +(3.75574 - 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.661570 + 2.13596i) q^{5} +(1.69185 - 0.370982i) q^{6} +(3.75574 - 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +(1.89195 - 1.19185i) q^{10} +(-3.44125 - 1.98681i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(0.956351 + 0.256253i) q^{13} +(-1.94411 - 3.36730i) q^{14} +(-3.74831 + 0.974763i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.120239 + 0.120239i) q^{17} +(0.507306 + 2.95680i) q^{18} -1.88492i q^{19} +(-1.64092 - 1.51901i) q^{20} +(1.44246 + 6.57832i) q^{21} +(-1.02845 + 3.83821i) q^{22} +(1.36362 - 5.08911i) q^{23} +(-1.27970 + 1.16721i) q^{24} +(-4.12465 + 2.82617i) q^{25} -0.990087i q^{26} +(0.713876 - 5.14688i) q^{27} +(-2.74939 + 2.74939i) q^{28} +(-2.15618 + 3.73461i) q^{29} +(1.91168 + 3.36830i) q^{30} +(-4.70172 - 8.14362i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.71134 - 5.79609i) q^{33} +(0.147262 + 0.0850217i) q^{34} +(4.63420 + 7.35634i) q^{35} +(2.72474 - 1.25529i) q^{36} +(3.26863 + 3.26863i) q^{37} +(-1.82070 + 0.487854i) q^{38} +(-0.519447 + 1.63432i) q^{39} +(-1.04255 + 1.97815i) q^{40} +(7.15775 - 4.13253i) q^{41} +(5.98083 - 3.09591i) q^{42} +(0.533983 + 1.99285i) q^{43} +3.97361 q^{44} +(-1.38840 - 6.56295i) q^{45} -5.26863 q^{46} +(0.897060 + 3.34787i) q^{47} +(1.45865 + 0.933998i) q^{48} +(7.03067 - 4.05916i) q^{49} +(3.79741 + 3.25264i) q^{50} +(-0.198476 - 0.217604i) q^{51} +(-0.956351 + 0.256253i) q^{52} +(-3.66571 - 3.66571i) q^{53} +(-5.15627 + 0.642559i) q^{54} +(1.96711 - 8.66478i) q^{55} +(3.36730 + 1.94411i) q^{56} +(3.26134 + 0.149933i) q^{57} +(4.16541 + 1.11612i) q^{58} +(2.72877 + 4.72637i) q^{59} +(2.75875 - 2.71832i) q^{60} +(-4.35623 + 7.54520i) q^{61} +(-6.64923 + 6.64923i) q^{62} +(-11.4967 + 1.97252i) q^{63} +1.00000i q^{64} +(0.0853460 + 2.21226i) q^{65} +(-6.55916 - 2.08475i) q^{66} +(-2.10759 + 7.86563i) q^{67} +(0.0440105 - 0.164249i) q^{68} +(8.69683 + 2.76418i) q^{69} +(5.90626 - 6.38026i) q^{70} +6.94911i q^{71} +(-1.91774 - 2.30701i) q^{72} +(-8.27728 + 8.27728i) q^{73} +(2.31127 - 4.00324i) q^{74} +(-4.56182 - 7.36137i) q^{75} +(0.942462 + 1.63239i) q^{76} +(-14.9238 - 3.99883i) q^{77} +(1.71307 + 0.0787547i) q^{78} +(-11.7529 - 6.78553i) q^{79} +(2.18058 + 0.495044i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-5.84428 - 5.84428i) q^{82} +(6.75913 - 1.81110i) q^{83} +(-4.53837 - 4.97576i) q^{84} +(-0.336372 - 0.177279i) q^{85} +(1.78674 - 1.03157i) q^{86} +(-6.29020 - 4.02773i) q^{87} +(-1.02845 - 3.83821i) q^{88} +4.87832 q^{89} +(-5.97998 + 3.03971i) q^{90} +3.84968 q^{91} +(1.36362 + 5.08911i) q^{92} +(14.4643 - 7.48725i) q^{93} +(3.00162 - 1.73299i) q^{94} +(4.02612 - 1.24701i) q^{95} +(0.524648 - 1.65068i) q^{96} +(1.44518 - 0.387234i) q^{97} +(-5.74052 - 5.74052i) q^{98} +(9.73332 + 6.88249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 + 8 * q^7	\( 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 8 * q^10 - 24 * q^15 + 8 * q^16 - 12 * q^20 + 24 * q^21 + 8 * q^22 - 24 * q^23 - 16 * q^25 - 16 * q^28 - 12 * q^30 - 8 * q^31 + 24 * q^36 + 24 * q^38 - 4 * q^40 + 24 * q^41 + 24 * q^42 + 36 * q^45 - 32 * q^46 + 48 * q^47 + 24 * q^50 - 48 * q^51 + 24 * q^55 + 24 * q^56 + 24 * q^57 + 16 * q^58 + 12 * q^60 - 24 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 24 * q^68 + 16 * q^70 - 24 * q^72 + 16 * q^73 + 16 * q^76 - 72 * q^77 + 24 * q^81 - 16 * q^82 + 48 * q^83 - 4 * q^85 - 48 * q^86 - 48 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^92 + 72 * q^93 + 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

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