LMFDB - Embedded newform 450.2.p.h.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (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:	$3.59326809096$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.4
Root			$0.500000 - 1.74530i$ of defining polynomial
Character	$\chi$	$=$	450.257
Dual form			450.2.p.h.443.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	1.73022	−	0.0795432i	0.998945	−	0.0459243i
$3$	1.73022	−	0.0795432i	0.998945	−	0.0459243i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.69185	+	0.370982i	0.690697	+	0.151453i
$7$	1.00635	−	3.75574i	0.380364	−	1.41954i	−0.464984	−	0.885319i	$-0.653940\pi$
$7$	1.00635	−	3.75574i	0.380364	−	1.41954i	0.845347	−	0.534217i	$-0.179394\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.98735	−	0.275255i	0.995782	−	0.0917517i
$10$		0			0
$11$	−3.44125	+	1.98681i	−1.03758	+	0.599044i	−0.919145	−	0.393918i	$-0.871119\pi$
$11$	−3.44125	+	1.98681i	−1.03758	+	0.599044i	−0.118430	+	0.992962i	$0.537786\pi$
$12$	1.53819	+	0.796225i	0.444037	+	0.229850i
$13$	0.256253	+	0.956351i	0.0710719	+	0.265244i	0.992314	−	0.123746i	$-0.0394908\pi$
$13$	0.256253	+	0.956351i	0.0710719	+	0.265244i	−0.921242	+	0.388990i	$0.872824\pi$
$14$	1.94411	−	3.36730i	0.519586	−	0.899950i
$15$		0			0
$16$	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	$0.256564\pi$
$18$	2.95680	+	0.507306i	0.696923	+	0.119573i
$19$		−	1.88492i		−	0.432431i	−0.976346	−	0.216216i	$-0.930629\pi$
$19$		−	1.88492i		−	0.432431i	0.976346	−	0.216216i	$-0.0693714\pi$
$20$		0			0
$21$	1.44246	−	6.57832i	0.314771	−	1.43551i
$22$	−3.83821	+	1.02845i	−0.818310	+	0.219265i
$23$	−5.08911	+	1.36362i	−1.06115	+	0.284335i	−0.746853	−	0.664989i	$-0.768436\pi$
$23$	−5.08911	+	1.36362i	−1.06115	+	0.284335i	−0.314299	+	0.949324i	$0.601770\pi$
$24$	1.27970	+	1.16721i	0.261217	+	0.238255i
$25$		0			0
$26$			0.990087i			0.194172i
$27$	5.14688	−	0.713876i	0.990518	−	0.137386i
$28$	2.74939	−	2.74939i	0.519586	−	0.519586i
$29$	2.15618	+	3.73461i	0.400392	+	0.693499i	0.993773	−	0.111422i	$-0.0355406\pi$
$29$	2.15618	+	3.73461i	0.400392	+	0.693499i	−0.593381	+	0.804922i	$0.702207\pi$
$30$		0			0
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	0.0416413	+	0.999133i	$0.486741\pi$
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	−0.886095	+	0.463504i	$0.846592\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−5.79609	+	3.71134i	−1.00897	+	0.646062i
$34$	−0.147262	+	0.0850217i	−0.0252552	+	0.0145811i
$35$		0			0
$36$	2.72474	+	1.25529i	0.454124	+	0.209216i
$37$	−3.26863	−	3.26863i	−0.537360	−	0.537360i	0.385393	−	0.922753i	$-0.374066\pi$
$37$	−3.26863	−	3.26863i	−0.537360	−	0.537360i	−0.922753	+	0.385393i	$0.874066\pi$
$38$	0.487854	−	1.82070i	0.0791404	−	0.295356i
$39$	0.519447	+	1.63432i	0.0831781	+	0.261700i
$40$		0			0
$41$	7.15775	+	4.13253i	1.11785	+	0.645393i	0.940852	−	0.338818i	$-0.110027\pi$
$41$	7.15775	+	4.13253i	1.11785	+	0.645393i	0.177001	+	0.984211i	$0.443360\pi$
$42$	3.09591	−	5.98083i	0.477709	−	0.922862i
$43$	1.99285	+	0.533983i	0.303907	+	0.0814316i	0.407550	−	0.913183i	$-0.366383\pi$
$43$	1.99285	+	0.533983i	0.303907	+	0.0814316i	−0.103643	+	0.994615i	$0.533050\pi$
$44$	−3.97361			−0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	−3.34787	−	0.897060i	−0.488338	−	0.130850i	0.00624459	−	0.999981i	$-0.498012\pi$
$47$	−3.34787	−	0.897060i	−0.488338	−	0.130850i	−0.494582	+	0.869131i	$0.664679\pi$
$48$	0.933998	+	1.45865i	0.134811	+	0.210537i
$49$	−7.03067	−	4.05916i	−1.00438	−	0.579880i
$50$		0			0
$51$	−0.198476	+	0.217604i	−0.0277922	+	0.0304707i
$52$	−0.256253	+	0.956351i	−0.0355359	+	0.132622i
$53$	−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
$55$		0			0
$56$	3.36730	−	1.94411i	0.449975	−	0.259793i
$57$	−0.149933	−	3.26134i	−0.0198591	−	0.431975i
$58$	1.11612	+	4.16541i	0.146554	+	0.546946i
$59$	−2.72877	+	4.72637i	−0.355255	+	0.615320i	−0.987162	−	0.159724i	$-0.948939\pi$
$59$	−2.72877	+	4.72637i	−0.355255	+	0.615320i	0.631906	+	0.775045i	$0.282273\pi$
$60$		0			0
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	−0.997683	−	0.0680302i	$-0.978329\pi$
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	0.439926	−	0.898034i	$-0.355005\pi$
$62$	−6.64923	+	6.64923i	−0.844454	+	0.844454i
$63$	1.97252	−	11.4967i	0.248514	−	1.44845i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−6.55916	+	2.08475i	−0.807377	+	0.256614i
$67$	−7.86563	+	2.10759i	−0.960940	+	0.257483i	−0.704998	−	0.709209i	$-0.749052\pi$
$67$	−7.86563	+	2.10759i	−0.960940	+	0.257483i	−0.255942	+	0.966692i	$0.582385\pi$
$68$	−0.164249	+	0.0440105i	−0.0199182	+	0.00533705i
$69$	−8.69683	+	2.76418i	−1.04698	+	0.332768i
$70$		0			0
$71$		−	6.94911i		−	0.824708i	−0.911024	−	0.412354i	$-0.864707\pi$
$71$		−	6.94911i		−	0.824708i	0.911024	−	0.412354i	$-0.135293\pi$
$72$	2.30701	+	1.91774i	0.271883	+	0.226008i
$73$	8.27728	−	8.27728i	0.968783	−	0.968783i	−0.0307446	−	0.999527i	$-0.509788\pi$
$73$	8.27728	−	8.27728i	0.968783	−	0.968783i	0.999527	+	0.0307446i	$0.00978785\pi$
$74$	−2.31127	−	4.00324i	−0.268680	−	0.465368i
$75$		0			0
$76$	0.942462	−	1.63239i	0.108108	−	0.187248i
$77$	3.99883	+	14.9238i	0.455709	+	1.70073i
$78$	0.0787547	+	1.71307i	0.00891722	+	0.193967i
$79$	11.7529	−	6.78553i	1.32230	−	0.763431i	0.338206	−	0.941072i	$-0.390180\pi$
$79$	11.7529	−	6.78553i	1.32230	−	0.763431i	0.984095	+	0.177641i	$0.0568465\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$	5.84428	+	5.84428i	0.645393	+	0.645393i
$83$	−1.81110	+	6.75913i	−0.198795	+	0.741911i	0.792457	+	0.609927i	$0.208801\pi$
$83$	−1.81110	+	6.75913i	−0.198795	+	0.741911i	−0.991252	+	0.131984i	$0.957865\pi$
$84$	4.53837	−	4.97576i	0.495176	−	0.542900i
$85$		0			0
$86$	1.78674	+	1.03157i	0.192669	+	0.111238i
$87$	4.02773	+	6.29020i	0.431818	+	0.674380i
$88$	−3.83821	−	1.02845i	−0.409155	−	0.109633i
$89$	−4.87832			−0.517100			−0.258550	−	0.965998i	$-0.583245\pi$
$89$	−4.87832			−0.517100			−0.258550	+	0.965998i	$0.583245\pi$
$90$		0			0
$91$	3.84968			0.403557
$92$	−5.08911	−	1.36362i	−0.530576	−	0.142168i
$93$	−7.48725	+	14.4643i	−0.776392	+	1.49987i
$94$	−3.00162	−	1.73299i	−0.309594	−	0.178744i
$95$		0			0
$96$	0.524648	+	1.65068i	0.0535466	+	0.168472i
$97$	0.387234	−	1.44518i	0.0393177	−	0.146736i	−0.943477	−	0.331439i	$-0.892466\pi$
$97$	0.387234	−	1.44518i	0.0393177	−	0.146736i	0.982794	+	0.184704i	$0.0591325\pi$
$98$	−5.74052	−	5.74052i	−0.579880	−	0.579880i
$99$	−9.73332	+	6.88249i	−0.978235	+	0.691717i
$100$		0			0
$101$	−8.91944	+	5.14964i	−0.887517	+	0.512408i	−0.873130	−	0.487488i	$-0.837913\pi$
$101$	−8.91944	+	5.14964i	−0.887517	+	0.512408i	−0.0143875	+	0.999896i	$0.504580\pi$
$102$	−0.248033	+	0.158820i	−0.0245589	+	0.0157255i
$103$	−1.67823	−	6.26326i	−0.165361	−	0.617137i	−0.997994	−	0.0633111i	$-0.979834\pi$
$103$	−1.67823	−	6.26326i	−0.165361	−	0.617137i	0.832632	−	0.553826i	$-0.186833\pi$
$104$	−0.495044	+	0.857441i	−0.0485430	+	0.0840790i
$105$		0			0
$106$	−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	$0.168594\pi$
$108$	4.81427	+	1.95521i	0.463253	+	0.188140i
$109$			7.30160i			0.699367i	0.936868	+	0.349683i	$0.113711\pi$
$109$			7.30160i			0.699367i	−0.936868	+	0.349683i	$0.886289\pi$
$110$		0			0
$111$	−5.91546	−	5.39547i	−0.561471	−	0.512115i
$112$	3.75574	−	1.00635i	0.354884	−	0.0950909i
$113$	4.07557	−	1.09205i	0.383397	−	0.102731i	−0.0619722	−	0.998078i	$-0.519739\pi$
$113$	4.07557	−	1.09205i	0.383397	−	0.102731i	0.445369	+	0.895347i	$0.353072\pi$
$114$	0.699273	−	3.18902i	0.0654929	−	0.298679i
$115$		0			0
$116$			4.31235i			0.400392i
$117$	1.02876	+	2.78641i	0.0951087	+	0.257604i
$118$	−3.85906	+	3.85906i	−0.355255	+	0.355255i
$119$	0.330584	+	0.572588i	0.0303046	+	0.0524891i
$120$		0			0
$121$	2.39479	−	4.14790i	0.217708	−	0.377081i
$122$	−2.25495	−	8.41558i	−0.204153	−	0.761911i
$123$	12.7132	+	6.58085i	1.14631	+	0.593375i
$124$	−8.14362	+	4.70172i	−0.731318	+	0.422227i
$125$		0			0
$126$	4.88087	−	10.5944i	0.434823	−	0.943827i
$127$	−13.7871	−	13.7871i	−1.22341	−	1.22341i	−0.966411	−	0.257000i	$-0.917266\pi$
$127$	−13.7871	−	13.7871i	−1.22341	−	1.22341i	−0.257000	−	0.966411i	$-0.582734\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	3.49055	+	0.765391i	0.307326	+	0.0673889i
$130$		0			0
$131$	−3.88249	−	2.24156i	−0.339215	−	0.195846i	0.320710	−	0.947178i	$-0.396079\pi$
$131$	−3.88249	−	2.24156i	−0.339215	−	0.195846i	−0.659925	+	0.751332i	$0.729412\pi$
$132$	−6.87523	+	0.316074i	−0.598412	+	0.0275107i
$133$	−7.07929	−	1.89689i	−0.613852	−	0.164481i
$134$	−8.14310			−0.703457
$135$		0			0
$136$	−0.170043			−0.0145811
$137$	12.0729	+	3.23492i	1.03146	+	0.276378i	0.734569	−	0.678534i	$-0.237384\pi$
$137$	12.0729	+	3.23492i	1.03146	+	0.276378i	0.296888	+	0.954912i	$0.404051\pi$
$138$	−9.11591	+	0.419084i	−0.775998	+	0.0356748i
$139$	−3.60435	−	2.08097i	−0.305717	−	0.176506i	0.339291	−	0.940681i	$-0.389813\pi$
$139$	−3.60435	−	2.08097i	−0.305717	−	0.176506i	−0.645008	+	0.764176i	$0.723146\pi$
$140$		0			0
$141$	−5.86393	−	1.28581i	−0.493832	−	0.108285i
$142$	1.79856	−	6.71233i	0.150932	−	0.563286i
$143$	−2.78191	−	2.78191i	−0.232635	−	0.232635i
$144$	1.73205	+	2.44949i	0.144338	+	0.204124i
$145$		0			0
$146$	10.1376	−	5.85292i	0.838990	−	0.484391i
$147$	−12.4875	−	6.46401i	−1.02995	−	0.533143i
$148$	−1.19640	−	4.46504i	−0.0983437	−	0.367024i
$149$	−0.518244	+	0.897625i	−0.0424562	+	0.0735363i	−0.886473	−	0.462781i	$-0.846852\pi$
$149$	−0.518244	+	0.897625i	−0.0424562	+	0.0735363i	0.844016	+	0.536317i	$0.180185\pi$
$150$		0			0
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	0.771290	−	0.636484i	$-0.219612\pi$
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	−0.936856	+	0.349715i	$0.886278\pi$
$152$	1.33284	−	1.33284i	0.108108	−	0.108108i
$153$	−0.326099	+	0.392291i	−0.0263635	+	0.0317149i
$154$			15.4503i			1.24502i
$155$		0			0
$156$	−0.367304	+	1.67508i	−0.0294079	+	0.134114i
$157$	8.81460	−	2.36186i	0.703481	−	0.188497i	0.110692	−	0.993855i	$-0.464693\pi$
$157$	8.81460	−	2.36186i	0.703481	−	0.188497i	0.592789	+	0.805357i	$0.298027\pi$
$158$	13.1086	−	3.51245i	1.04287	−	0.279435i
$159$	−6.63408	−	6.05092i	−0.526117	−	0.479869i
$160$		0			0
$161$			20.4857i			1.61450i
$162$	8.97261	+	0.701625i	0.704955	+	0.0551249i
$163$	−5.03848	+	5.03848i	−0.394644	+	0.394644i	−0.876339	−	0.481695i	$-0.840021\pi$
$163$	−5.03848	+	5.03848i	−0.394644	+	0.394644i	0.481695	+	0.876339i	$0.340021\pi$
$164$	4.13253	+	7.15775i	0.322696	+	0.558926i
$165$		0			0
$166$	−3.49878	+	6.06007i	−0.271558	+	0.470353i
$167$	2.80384	+	10.4641i	0.216968	+	0.809734i	0.985465	+	0.169881i	$0.0543382\pi$
$167$	2.80384	+	10.4641i	0.216968	+	0.809734i	−0.768497	+	0.639853i	$0.778995\pi$
$168$	5.67155	−	3.63160i	0.437569	−	0.280184i
$169$	10.4094	−	6.00986i	0.800722	−	0.462297i
$170$		0			0
$171$	−0.518835	−	5.63092i	−0.0396763	−	0.430607i
$172$	1.45887	+	1.45887i	0.111238	+	0.111238i
$173$	−0.975709	+	3.64139i	−0.0741818	+	0.276850i	−0.993047	−	0.117722i	$-0.962441\pi$
$173$	−0.975709	+	3.64139i	−0.0741818	+	0.276850i	0.918865	+	0.394573i	$0.129107\pi$
$174$	2.26247	+	7.11832i	0.171517	+	0.539638i
$175$		0			0
$176$	−3.44125	−	1.98681i	−0.259394	−	0.149761i
$177$	−4.34543	+	8.39472i	−0.326622	+	0.630986i
$178$	−4.71209	−	1.26260i	−0.353186	−	0.0946359i
$179$	12.8952			0.963836			0.481918	−	0.876216i	$-0.339940\pi$
$179$	12.8952			0.963836			0.481918	+	0.876216i	$0.339940\pi$
$180$		0			0
$181$	24.3197			1.80767			0.903835	−	0.427881i	$-0.140740\pi$
$181$	24.3197			1.80767			0.903835	+	0.427881i	$0.140740\pi$
$182$	3.71851	+	0.996372i	0.275634	+	0.0738560i
$183$	−8.13741	−	12.7084i	−0.601535	−	0.939430i
$184$	−4.56277	−	2.63432i	−0.336372	−	0.194204i
$185$		0			0
$186$	−10.9758	+	12.0336i	−0.804782	+	0.882344i
$187$	0.174880	−	0.652663i	0.0127885	−	0.0477274i
$188$	−2.45081	−	2.45081i	−0.178744	−	0.178744i
$189$	2.49842	−	20.0488i	0.181733	−	1.45833i
$190$		0			0
$191$	11.8036	−	6.81478i	0.854075	−	0.493100i	−0.00794868	−	0.999968i	$-0.502530\pi$
$191$	11.8036	−	6.81478i	0.854075	−	0.493100i	0.862024	+	0.506868i	$0.169197\pi$
$192$	0.0795432	+	1.73022i	0.00574054	+	0.124868i
$193$	4.19397	+	15.6521i	0.301889	+	1.12666i	0.935591	+	0.353086i	$0.114868\pi$
$193$	4.19397	+	15.6521i	0.301889	+	1.12666i	−0.633702	+	0.773577i	$0.718466\pi$
$194$	0.748079	−	1.29571i	0.0537090	−	0.0930267i
$195$		0			0
$196$	−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	$0.231374\pi$
$198$	−11.1830	+	4.12881i	−0.794740	+	0.293422i
$199$		−	17.1733i		−	1.21738i	−0.793407	−	0.608691i	$-0.791695\pi$
$199$		−	17.1733i		−	1.21738i	0.793407	−	0.608691i	$-0.208305\pi$
$200$		0			0
$201$	−13.4417	+	4.27226i	−0.948101	+	0.301342i
$202$	−9.94834	+	2.66565i	−0.699963	+	0.187554i
$203$	16.1961	−	4.33973i	1.13674	−	0.304589i
$204$	−0.280687	+	0.0892129i	−0.0196520	+	0.00624615i
$205$		0			0
$206$		−	6.48420i		−	0.451776i
$207$	−14.8276	+	5.47442i	−1.03059	+	0.380498i
$208$	−0.700097	+	0.700097i	−0.0485430	+	0.0485430i
$209$	3.74498	+	6.48649i	0.259046	+	0.448680i
$210$		0			0
$211$	−9.10894	+	15.7771i	−0.627085	+	1.08614i	0.361048	+	0.932547i	$0.382419\pi$
$211$	−9.10894	+	15.7771i	−0.627085	+	1.08614i	−0.988134	+	0.153597i	$0.950914\pi$
$212$	−1.34174	−	5.00745i	−0.0921513	−	0.343913i
$213$	−0.552755	−	12.0235i	−0.0378741	−	0.823838i
$214$	4.53225	−	2.61670i	0.309818	−	0.178874i
$215$		0			0
$216$	4.14418	+	3.13461i	0.281976	+	0.213283i
$217$	25.8537	+	25.8537i	1.75507	+	1.75507i
$218$	−1.88979	+	7.05281i	−0.127993	+	0.477676i
$219$	13.6631	−	14.9799i	0.923270	−	1.01225i
$220$		0			0
$221$	−0.145802	−	0.0841789i	−0.00980771	−	0.00566249i
$222$	−4.31745	−	6.74266i	−0.289768	−	0.452538i
$223$	4.53570	+	1.21534i	0.303733	+	0.0813849i	0.407466	−	0.913220i	$-0.366412\pi$
$223$	4.53570	+	1.21534i	0.303733	+	0.0813849i	−0.103734	+	0.994605i	$0.533079\pi$
$224$	3.88823			0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	−24.1784	−	6.47859i	−1.60478	−	0.429999i	−0.658297	−	0.752758i	$-0.728723\pi$
$227$	−24.1784	−	6.47859i	−1.60478	−	0.429999i	−0.946481	+	0.322759i	$0.895390\pi$
$228$	1.50082	−	2.89937i	0.0993945	−	0.192015i
$229$	19.7350	+	11.3940i	1.30412	+	0.752935i	0.981108	−	0.193459i	$-0.0619706\pi$
$229$	19.7350	+	11.3940i	1.30412	+	0.752935i	0.323014	+	0.946394i	$0.395304\pi$
$230$		0			0
$231$	8.10596	+	25.5035i	0.533333	+	1.67801i
$232$	−1.11612	+	4.16541i	−0.0732768	+	0.273473i
$233$	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
$235$		0			0
$236$	−4.72637	+	2.72877i	−0.307660	+	0.177628i
$237$	19.7954	−	12.6753i	1.28585	−	0.823352i
$238$	0.171123	+	0.638639i	0.0110922	+	0.0413968i
$239$	4.56277	−	7.90295i	0.295141	−	0.511199i	−0.679877	−	0.733327i	$-0.737967\pi$
$239$	4.56277	−	7.90295i	0.295141	−	0.511199i	0.975018	+	0.222127i	$0.0713000\pi$
$240$		0			0
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	0.892675	−	0.450701i	$-0.148826\pi$
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	−0.836656	+	0.547729i	$0.815492\pi$
$242$	3.38674	−	3.38674i	0.217708	−	0.217708i
$243$	15.1790	−	3.54930i	0.973734	−	0.227688i
$244$		−	8.71245i		−	0.557758i
$245$		0			0
$246$	10.5768	+	9.64703i	0.674351	+	0.615072i
$247$	1.80265	−	0.483018i	0.114700	−	0.0307337i
$248$	−9.08302	+	2.43379i	−0.576773	+	0.154546i
$249$	−2.59597	+	11.8389i	−0.164513	+	0.750258i
$250$		0			0
$251$		−	6.16751i		−	0.389290i	−0.980874	−	0.194645i	$-0.937645\pi$
$251$		−	6.16751i		−	0.389290i	0.980874	−	0.194645i	$-0.0623555\pi$
$252$	7.45660	−	8.97017i	0.469722	−	0.565068i
$253$	14.8036	−	14.8036i	0.930696	−	0.930696i
$254$	−9.74898	−	16.8857i	−0.611706	−	1.05951i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.51956	−	28.0634i	−0.469057	−	1.75055i	−0.643075	−	0.765803i	$-0.722342\pi$
$257$	−7.51956	−	28.0634i	−0.469057	−	1.75055i	0.174018	−	0.984743i	$-0.444325\pi$
$258$	3.17351	+	1.64273i	0.197574	+	0.102272i
$259$	−15.5655	+	8.98676i	−0.967194	+	0.558410i
$260$		0			0
$261$	7.46922	+	10.5631i	0.462333	+	0.653838i
$262$	−3.17004	−	3.17004i	−0.195846	−	0.195846i
$263$	4.82975	−	18.0249i	0.297815	−	1.11146i	−0.641141	−	0.767424i	$-0.721538\pi$
$263$	4.82975	−	18.0249i	0.297815	−	1.11146i	0.938956	−	0.344038i	$-0.111795\pi$
$264$	−6.72277	−	1.47414i	−0.413758	−	0.0907269i
$265$		0			0
$266$	−6.34711	−	3.66451i	−0.389167	−	0.224685i
$267$	−8.44057	+	0.388037i	−0.516555	+	0.0237475i
$268$	−7.86563	−	2.10759i	−0.480470	−	0.128742i
$269$	15.5553			0.948425			0.474212	−	0.880411i	$-0.342733\pi$
$269$	15.5553			0.948425			0.474212	+	0.880411i	$0.342733\pi$
$270$		0			0
$271$	−1.87184			−0.113706			−0.0568532	−	0.998383i	$-0.518107\pi$
$271$	−1.87184			−0.113706			−0.0568532	+	0.998383i	$0.518107\pi$
$272$	−0.164249	−	0.0440105i	−0.00995908	−	0.00266853i
$273$	6.66081	−	0.306216i	0.403131	−	0.0185331i
$274$	10.8243	+	6.24939i	0.653918	+	0.377540i
$275$		0			0
$276$	−8.91376	−	1.95457i	−0.536545	−	0.117651i
$277$	1.06921	−	3.99035i	0.0642426	−	0.239757i	−0.926337	−	0.376696i	$-0.877060\pi$
$277$	1.06921	−	3.99035i	0.0642426	−	0.239757i	0.990579	+	0.136940i	$0.0437267\pi$
$278$	−2.94294	−	2.94294i	−0.176506	−	0.176506i
$279$	−11.8041	+	25.6220i	−0.706692	+	1.53395i
$280$		0			0
$281$	0.248640	−	0.143552i	0.0148326	−	0.00856361i	−0.492565	−	0.870275i	$-0.663941\pi$
$281$	0.248640	−	0.143552i	0.0148326	−	0.00856361i	0.507398	+	0.861712i	$0.330607\pi$
$282$	−5.33132	−	2.75970i	−0.317476	−	0.164338i
$283$	4.68527	+	17.4857i	0.278510	+	1.03941i	0.953452	+	0.301544i	$0.0975019\pi$
$283$	4.68527	+	17.4857i	0.278510	+	1.03941i	−0.674942	+	0.737871i	$0.735831\pi$
$284$	3.47456	−	6.01811i	0.206177	−	0.357109i
$285$		0			0
$286$	−1.96711	−	3.40713i	−0.116318	−	0.201468i
$287$	22.7239	−	22.7239i	1.34135	−	1.34135i
$288$	1.03906	+	2.81431i	0.0612271	+	0.165835i
$289$			16.9711i			0.998299i
$290$		0			0
$291$	0.555048	−	2.53128i	0.0325375	−	0.148386i
$292$	11.3070	−	3.02970i	0.661691	−	0.177300i
$293$	−20.6663	+	5.53752i	−1.20734	+	0.323505i	−0.805717	−	0.592300i	$-0.798220\pi$
$293$	−20.6663	+	5.53752i	−1.20734	+	0.323505i	−0.401621	+	0.915806i	$0.631553\pi$
$294$	−10.3890	−	9.47576i	−0.605899	−	0.552637i
$295$		0			0
$296$		−	4.62255i		−	0.268680i
$297$	−16.2934	+	12.6825i	−0.945436	+	0.735912i
$298$	−0.732907	+	0.732907i	−0.0424562	+	0.0424562i
$299$	−2.60820	−	4.51754i	−0.150836	−	0.261256i
$300$		0			0
$301$	4.01100	−	6.94725i	0.231190	−	0.400433i
$302$	−1.05314	−	3.93037i	−0.0606014	−	0.226168i
$303$	−15.0230	+	9.61951i	−0.863049	+	0.552626i
$304$	1.63239	−	0.942462i	0.0936241	−	0.0540539i
$305$		0			0
$306$	−0.416520	+	0.294524i	−0.0238108	+	0.0168368i
$307$	20.2953	+	20.2953i	1.15831	+	1.15831i	0.984838	+	0.173476i	$0.0555001\pi$
$307$	20.2953	+	20.2953i	1.15831	+	1.15831i	0.173476	+	0.984838i	$0.444500\pi$
$308$	−3.99883	+	14.9238i	−0.227855	+	0.850365i
$309$	−3.40192	−	10.7033i	−0.193528	−	0.608892i
$310$		0			0
$311$	−11.9868	−	6.92056i	−0.679707	−	0.392429i	0.120038	−	0.992769i	$-0.461698\pi$
$311$	−11.9868	−	6.92056i	−0.679707	−	0.392429i	−0.799745	+	0.600340i	$0.795032\pi$
$312$	−0.788332	+	1.52294i	−0.0446305	+	0.0862196i
$313$	−17.9081	−	4.79847i	−1.01223	−	0.271226i	−0.285668	−	0.958329i	$-0.592215\pi$
$313$	−17.9081	−	4.79847i	−1.01223	−	0.271226i	−0.726560	+	0.687103i	$0.758882\pi$
$314$	9.12554			0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	−0.811966	−	0.217566i	−0.0456046	−	0.0122197i	0.235945	−	0.971766i	$-0.424182\pi$
$317$	−0.811966	−	0.217566i	−0.0456046	−	0.0122197i	−0.281549	+	0.959547i	$0.590848\pi$
$318$	−4.84194	−	7.56176i	−0.271522	−	0.424043i
$319$	−14.8399	−	8.56781i	−0.830874	−	0.479705i
$320$		0			0
$321$	6.10845	−	6.69716i	0.340941	−	0.373799i
$322$	−5.30208	+	19.7876i	−0.295473	+	1.10272i
$323$	0.226641	+	0.226641i	0.0126107	+	0.0126107i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$		0			0
$326$	−6.17086	+	3.56275i	−0.341772	+	0.197322i
$327$	0.580793	+	12.6334i	0.0321179	+	0.698629i
$328$	2.13915	+	7.98343i	0.118115	+	0.440811i
$329$	−6.73825	+	11.6710i	−0.371492	+	0.643443i
$330$		0			0
$331$	2.08211	+	3.60631i	0.114443	+	0.198221i	0.917557	−	0.397604i	$-0.130158\pi$
$331$	2.08211	+	3.60631i	0.114443	+	0.198221i	−0.803114	+	0.595825i	$0.796825\pi$
$332$	−4.94803	+	4.94803i	−0.271558	+	0.271558i
$333$	−10.6642	−	8.86483i	−0.584397	−	0.485790i
$334$			10.8332i			0.592766i
$335$		0			0
$336$	6.41822	−	2.03995i	0.350143	−	0.111288i
$337$	−3.13777	+	0.840764i	−0.170925	+	0.0457993i	−0.343267	−	0.939238i	$-0.611533\pi$
$337$	−3.13777	+	0.840764i	−0.170925	+	0.0457993i	0.172341	+	0.985037i	$0.444867\pi$
$338$	11.6102	−	3.11093i	0.631510	−	0.169213i
$339$	6.96478	−	2.21367i	0.378275	−	0.120230i
$340$		0			0
$341$		−	37.3656i		−	2.02346i
$342$	0.956233	−	5.57334i	0.0517072	−	0.301372i
$343$	−3.07470	+	3.07470i	−0.166018	+	0.166018i
$344$	1.03157	+	1.78674i	0.0556188	+	0.0963346i
$345$		0			0
$346$	−1.88492	+	3.26478i	−0.101334	+	0.175516i
$347$	−1.21470	−	4.53334i	−0.0652087	−	0.243362i	0.925627	−	0.378438i	$-0.123539\pi$
$347$	−1.21470	−	4.53334i	−0.0652087	−	0.243362i	−0.990835	+	0.135076i	$0.956872\pi$
$348$	0.343019	+	7.46134i	0.0183877	+	0.399970i
$349$	8.42818	−	4.86601i	0.451150	−	0.260472i	−0.257166	−	0.966367i	$-0.582789\pi$
$349$	8.42818	−	4.86601i	0.451150	−	0.260472i	0.708316	+	0.705896i	$0.249455\pi$
$350$		0			0
$351$	2.00162	+	4.73929i	0.106839	+	0.252965i
$352$	−2.80977	−	2.80977i	−0.149761	−	0.149761i
$353$	1.32049	−	4.92815i	0.0702827	−	0.262299i	−0.921840	−	0.387572i	$-0.873314\pi$
$353$	1.32049	−	4.92815i	0.0702827	−	0.262299i	0.992122	+	0.125273i	$0.0399806\pi$
$354$	−6.37008	+	6.98400i	−0.338566	+	0.371195i
$355$		0			0
$356$	−4.22474	−	2.43916i	−0.223911	−	0.129275i
$357$	0.617529	+	0.964409i	0.0326831	+	0.0510420i
$358$	12.4559	+	3.33754i	0.658312	+	0.176394i
$359$	1.27697			0.0673957			0.0336978	−	0.999432i	$-0.489272\pi$
$359$	1.27697			0.0673957			0.0336978	+	0.999432i	$0.489272\pi$
$360$		0			0
$361$	15.4471			0.813003
$362$	23.4910	+	6.29441i	1.23466	+	0.330827i
$363$	3.81358	−	7.36727i	0.200161	−	0.386682i
$364$	3.33392	+	1.92484i	0.174745	+	0.100889i
$365$		0			0
$366$	−4.57097	−	14.3815i	−0.238928	−	0.751731i
$367$	2.61063	−	9.74300i	0.136274	−	0.508581i	−0.863716	−	0.503979i	$-0.831869\pi$
$367$	2.61063	−	9.74300i	0.136274	−	0.508581i	0.999989	−	0.00460117i	$-0.00146460\pi$
$368$	−3.72549	−	3.72549i	−0.194204	−	0.194204i
$369$	22.5202	+	10.3751i	1.17235	+	0.540105i
$370$		0			0
$371$	−17.4564	+	10.0785i	−0.906293	+	0.523249i
$372$	−13.7163	+	8.78279i	−0.711156	+	0.455367i
$373$	3.39374	+	12.6656i	0.175721	+	0.655801i	0.996428	+	0.0844507i	$0.0269135\pi$
$373$	3.39374	+	12.6656i	0.175721	+	0.655801i	−0.820706	+	0.571350i	$0.806420\pi$
$374$	0.337843	−	0.585162i	0.0174695	−	0.0302580i
$375$		0			0
$376$	−1.73299	−	3.00162i	−0.0893720	−	0.154797i
$377$	−3.01907	+	3.01907i	−0.155490	+	0.155490i
$378$	7.60229	−	18.7190i	0.391019	−	0.962800i
$379$			0.587648i			0.0301854i	0.999886	+	0.0150927i	$0.00480434\pi$
$379$			0.587648i			0.0301854i	−0.999886	+	0.0150927i	$0.995196\pi$
$380$		0			0
$381$	−24.9515	−	22.7582i	−1.27830	−	1.16594i
$382$	13.1652	−	3.52759i	0.673588	−	0.180487i
$383$	−14.0071	+	3.75319i	−0.715729	+	0.191779i	−0.598265	−	0.801298i	$-0.704143\pi$
$383$	−14.0071	+	3.75319i	−0.715729	+	0.191779i	−0.117464	+	0.993077i	$0.537476\pi$
$384$	−0.370982	+	1.69185i	−0.0189316	+	0.0863371i
$385$		0			0
$386$			16.2043i			0.824775i
$387$	6.10031	+	1.04665i	0.310096	+	0.0532041i
$388$	1.05794	−	1.05794i	0.0537090	−	0.0537090i
$389$	−10.3789	−	17.9767i	−0.526230	−	0.911456i	−0.999533	−	0.0305570i	$-0.990272\pi$
$389$	−10.3789	−	17.9767i	−0.526230	−	0.911456i	0.473303	−	0.880899i	$-0.343061\pi$
$390$		0			0
$391$	0.447948	−	0.775869i	0.0226537	−	0.0392374i
$392$	−2.10118	−	7.84169i	−0.106125	−	0.396065i
$393$	−6.89588	−	3.56957i	−0.347851	−	0.180061i
$394$	1.42175	−	0.820845i	0.0716265	−	0.0413536i
$395$		0			0
$396$	−11.8705	+	1.09376i	−0.596517	+	0.0549633i
$397$	−15.7430	−	15.7430i	−0.790118	−	0.790118i	0.191395	−	0.981513i	$-0.438699\pi$
$397$	−15.7430	−	15.7430i	−0.790118	−	0.790118i	−0.981513	+	0.191395i	$0.938699\pi$
$398$	4.44477	−	16.5881i	0.222796	−	0.831487i
$399$	−12.3996	−	2.71893i	−0.620758	−	0.136117i
$400$		0			0
$401$	4.11737	+	2.37716i	0.205612	+	0.118710i	0.599270	−	0.800547i	$-0.295457\pi$
$401$	4.11737	+	2.37716i	0.205612	+	0.118710i	−0.393659	+	0.919257i	$0.628791\pi$
$402$	−14.0894	+	0.647729i	−0.702715	+	0.0323058i
$403$	−8.99298	−	2.40966i	−0.447972	−	0.120034i
$404$	−10.2993			−0.512408
$405$		0			0
$406$	16.7674			0.832153
$407$	17.7423	+	4.75404i	0.879454	+	0.235649i
$408$	−0.294213	+	0.0135258i	−0.0145657	+	0.000669627i
$409$	−25.8797	−	14.9417i	−1.27967	−	0.738817i	−0.302882	−	0.953028i	$-0.597949\pi$
$409$	−25.8797	−	14.9417i	−1.27967	−	0.738817i	−0.976787	+	0.214211i	$0.931282\pi$
$410$		0			0
$411$	21.1461	+	4.63682i	1.04306	+	0.228718i
$412$	1.67823	−	6.26326i	0.0826807	−	0.308568i
$413$	15.0049	+	15.0049i	0.738343	+	0.738343i
$414$	−15.7392	+	1.45022i	−0.773541	+	0.0712744i
$415$		0			0
$416$	−0.857441	+	0.495044i	−0.0420395	+	0.0242715i
$417$	−6.40185	−	3.31384i	−0.313500	−	0.162280i
$418$	1.93854	+	7.23474i	0.0948172	+	0.353863i
$419$	8.81638	−	15.2704i	0.430708	−	0.746009i	−0.566226	−	0.824250i	$-0.691597\pi$
$419$	8.81638	−	15.2704i	0.430708	−	0.746009i	0.996934	+	0.0782412i	$0.0249304\pi$
$420$		0			0
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	0.975072	+	0.221887i	$0.0712215\pi$
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	−0.295377	+	0.955381i	$0.595445\pi$
$422$	−12.8820	+	12.8820i	−0.627085	+	0.627085i
$423$	−10.2482	−	1.75831i	−0.498284	−	0.0854919i
$424$		−	5.18410i		−	0.251762i
$425$		0			0
$426$	2.57799	−	11.7569i	0.124904	−	0.569623i
$427$	−32.7217	+	8.76775i	−1.58351	+	0.424301i
$428$	5.05507	−	1.35450i	0.244346	−	0.0654723i
$429$	−5.03461	−	4.59205i	−0.243073	−	0.221706i
$430$		0			0
$431$		−	19.2910i		−	0.929215i	−0.885517	−	0.464608i	$-0.846195\pi$
$431$		−	19.2910i		−	0.929215i	0.885517	−	0.464608i	$-0.153805\pi$
$432$	3.19168	+	4.10039i	0.153560	+	0.197280i
$433$	−16.7154	+	16.7154i	−0.803292	+	0.803292i	−0.983609	−	0.180316i	$-0.942288\pi$
$433$	−16.7154	+	16.7154i	−0.803292	+	0.803292i	0.180316	+	0.983609i	$0.442288\pi$
$434$	18.2814	+	31.6642i	0.877533	+	1.51993i
$435$		0			0
$436$	−3.65080	+	6.32337i	−0.174842	+	0.302835i
$437$	2.57033	+	9.59259i	0.122955	+	0.458876i
$438$	17.0747	−	10.9332i	0.815860	−	0.522410i
$439$	−31.1811	+	18.0024i	−1.48819	+	0.859209i	−0.999909	−	0.0134750i	$-0.995711\pi$
$439$	−31.1811	+	18.0024i	−1.48819	+	0.859209i	−0.488285	+	0.872684i	$0.662377\pi$
$440$		0			0
$441$	−22.1203	−	10.1909i	−1.05335	−	0.485280i
$442$	−0.119047	−	0.119047i	−0.00566249	−	0.00566249i
$443$	6.94511	−	25.9195i	0.329972	−	1.23147i	−0.579246	−	0.815153i	$-0.696653\pi$
$443$	6.94511	−	25.9195i	0.329972	−	1.23147i	0.909218	−	0.416320i	$-0.136680\pi$
$444$	−2.42521	−	7.63035i	−0.115095	−	0.362120i
$445$		0			0
$446$	4.06659	+	2.34785i	0.192559	+	0.111174i
$447$	−0.825278	+	1.59431i	−0.0390343	+	0.0754085i
$448$	3.75574	+	1.00635i	0.177442	+	0.0475455i
$449$	−41.3392			−1.95092			−0.975459	−	0.220182i	$-0.929335\pi$
$449$	−41.3392			−1.95092			−0.975459	+	0.220182i	$0.929335\pi$
$450$		0			0
$451$	−32.8421			−1.54647
$452$	4.07557	+	1.09205i	0.191699	+	0.0513655i
$453$	−3.80046	−	5.93526i	−0.178561	−	0.278863i
$454$	−21.6778	−	12.5157i	−1.01739	−	0.587390i
$455$		0			0
$456$	2.20010	−	2.41213i	0.103029	−	0.112959i
$457$	−5.58827	+	20.8557i	−0.261408	+	0.975589i	0.703004	+	0.711186i	$0.251842\pi$
$457$	−5.58827	+	20.8557i	−0.261408	+	0.975589i	−0.964412	+	0.264403i	$0.914825\pi$
$458$	16.1135	+	16.1135i	0.752935	+	0.752935i
$459$	−0.533019	+	0.704691i	−0.0248792	+	0.0328921i
$460$		0			0
$461$	−10.8706	+	6.27615i	−0.506295	+	0.292309i	−0.731309	−	0.682046i	$-0.761090\pi$
$461$	−10.8706	+	6.27615i	−0.506295	+	0.292309i	0.225015	+	0.974355i	$0.427757\pi$
$462$	1.22897	+	26.7325i	0.0571767	+	1.24371i
$463$	−5.72110	−	21.3514i	−0.265882	−	0.992286i	−0.961708	−	0.274076i	$-0.911628\pi$
$463$	−5.72110	−	21.3514i	−0.265882	−	0.992286i	0.695826	−	0.718210i	$-0.255038\pi$
$464$	−2.15618	+	3.73461i	−0.100098	+	0.173375i
$465$		0			0
$466$	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	$0.286339\pi$
$468$	−0.502277	+	2.92749i	−0.0232178	+	0.135323i
$469$			31.6622i			1.46203i
$470$		0			0
$471$	15.0634	−	4.78769i	0.694083	−	0.220605i
$472$	−5.27158	+	1.41251i	−0.242644	+	0.0650163i
$473$	−7.91881	+	2.12184i	−0.364107	+	0.0975622i
$474$	22.4015	−	7.12002i	1.02893	−	0.327033i
$475$		0			0
$476$			0.661168i			0.0303046i
$477$	−11.9598	−	9.94174i	−0.547599	−	0.455201i
$478$	6.45273	−	6.45273i	0.295141	−	0.295141i
$479$	−1.35673	−	2.34993i	−0.0619906	−	0.107371i	0.833364	−	0.552724i	$-0.186412\pi$
$479$	−1.35673	−	2.34993i	−0.0619906	−	0.107371i	−0.895355	+	0.445353i	$0.853078\pi$
$480$		0			0
$481$	2.28836	−	3.96356i	0.104340	−	0.180723i
$482$	0.450166	+	1.68004i	0.0205045	+	0.0765239i
$483$	1.62949	+	35.4448i	0.0741446	+	1.61279i
$484$	4.14790	−	2.39479i	0.188541	−	0.108854i
$485$		0			0
$486$	15.5804	+	0.500258i	0.706743	+	0.0226921i
$487$	8.20799	+	8.20799i	0.371940	+	0.371940i	0.868183	−	0.496244i	$-0.165288\pi$
$487$	8.20799	+	8.20799i	0.371940	+	0.371940i	−0.496244	+	0.868183i	$0.665288\pi$
$488$	2.25495	−	8.41558i	0.102077	−	0.380955i
$489$	−8.31692	+	9.11848i	−0.376104	+	0.412352i
$490$		0			0
$491$	4.28058	+	2.47139i	0.193180	+	0.111532i	0.593470	−	0.804856i	$-0.297757\pi$
$491$	4.28058	+	2.47139i	0.193180	+	0.111532i	−0.400290	+	0.916388i	$0.631091\pi$
$492$	7.71955	+	12.0558i	0.348024	+	0.543517i
$493$	−0.708301	−	0.189789i	−0.0319003	−	0.00854766i
$494$	1.86624			0.0839661
$495$		0			0
$496$	−9.40344			−0.422227
$497$	−26.0991	−	6.99322i	−1.17070	−	0.313689i
$498$	−5.57164	+	10.7636i	−0.249671	+	0.482328i
$499$	28.1148	+	16.2321i	1.25859	+	0.726649i	0.972801	−	0.231643i	$-0.0744102\pi$
$499$	28.1148	+	16.2321i	1.25859	+	0.726649i	0.285791	+	0.958292i	$0.407744\pi$
$500$		0			0
$501$	5.68361	+	17.8821i	0.253925	+	0.798915i
$502$	1.59627	−	5.95736i	0.0712450	−	0.265890i
$503$	−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
$505$		0			0
$506$	18.1307	−	10.4677i	0.806007	−	0.465348i
$507$	17.5325	−	11.2264i	0.778647	−	0.498582i
$508$	−5.04645	−	18.8336i	−0.223900	−	0.835606i
$509$	−5.25069	+	9.09446i	−0.232733	+	0.403105i	−0.958611	−	0.284718i	$-0.908100\pi$
$509$	−5.25069	+	9.09446i	−0.232733	+	0.403105i	0.725879	+	0.687823i	$0.241433\pi$
$510$		0			0
$511$	−22.7575	−	39.4171i	−1.00673	−	1.74371i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.34560	−	9.70148i	−0.0594098	−	0.428331i
$514$		−	29.0534i		−	1.28149i
$515$		0			0
$516$	2.64021	+	2.40812i	0.116229	+	0.106012i
$517$	13.3031	−	3.56457i	0.585072	−	0.156770i
$518$	−17.3611	+	4.65189i	−0.762802	+	0.204392i
$519$	−1.39855	+	6.37804i	−0.0613893	+	0.279965i
$520$		0			0
$521$			28.2545i			1.23785i	0.785450	+	0.618925i	$0.212432\pi$
$521$			28.2545i			1.23785i	−0.785450	+	0.618925i	$0.787568\pi$
$522$	4.48079	+	12.1363i	0.196119	+	0.531192i
$523$	−13.6590	+	13.6590i	−0.597266	+	0.597266i	−0.939584	−	0.342318i	$-0.888788\pi$
$523$	−13.6590	+	13.6590i	−0.597266	+	0.597266i	0.342318	+	0.939584i	$0.388788\pi$
$524$	−2.24156	−	3.88249i	−0.0979230	−	0.169608i
$525$		0			0
$526$	9.33036	−	16.1607i	0.406823	−	0.704638i
$527$	−0.413850	−	1.54451i	−0.0180276	−	0.0672798i
$528$	−6.11216	−	3.16389i	−0.265998	−	0.137691i
$529$	4.12099	−	2.37925i	0.179173	−	0.103446i
$530$		0			0
$531$	−6.85082	+	14.8704i	−0.297300	+	0.645320i
$532$	−5.18240	−	5.18240i	−0.224685	−	0.224685i
$533$	−2.11795	+	7.90429i	−0.0917385	+	0.342373i
$534$	−8.25340	−	1.80977i	−0.357160	−	0.0783163i
$535$		0			0
$536$	−7.05213	−	4.07155i	−0.304606	−	0.175864i
$537$	22.3117	−	1.02573i	0.962819	−	0.0442635i
$538$	15.0253	+	4.02601i	0.647786	+	0.173574i
$539$	32.2590			1.38949
$540$		0			0
$541$	−26.7216			−1.14885			−0.574427	−	0.818556i	$-0.694775\pi$
$541$	−26.7216			−1.14885			−0.574427	+	0.818556i	$0.694775\pi$
$542$	−1.80806	−	0.484468i	−0.0776628	−	0.0208097i
$543$	42.0785	−	1.93447i	1.80576	−	0.0830160i
$544$	−0.147262	−	0.0850217i	−0.00631380	−	0.00364528i
$545$		0			0
$546$	6.51311	+	1.42816i	0.278735	+	0.0611197i
$547$	−0.0627654	+	0.234244i	−0.00268365	+	0.0100155i	−0.967255	−	0.253808i	$-0.918317\pi$
$547$	−0.0627654	+	0.234244i	−0.00268365	+	0.0100155i	0.964571	+	0.263823i	$0.0849836\pi$
$548$	8.83798	+	8.83798i	0.377540	+	0.377540i
$549$	−15.0904	−	21.3411i	−0.644043	−	0.910814i
$550$		0			0
$551$	7.03946	−	4.06423i	0.299891	−	0.173142i
$552$	−8.10415	−	4.19502i	−0.344936	−	0.178552i
$553$	−13.6572	−	50.9693i	−0.580763	−	2.16744i
$554$	2.06556	−	3.57765i	0.0877571	−	0.152000i
$555$		0			0
$556$	−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	$0.857714\pi$
$558$	−18.0333	+	21.6938i	−0.763412	+	0.918372i
$559$			2.04270i			0.0863969i
$560$		0			0
$561$	0.250667	−	1.14316i	0.0105832	−	0.0482644i
$562$	0.277322	−	0.0743081i	0.0116981	−	0.00313450i
$563$	−31.1771	+	8.35388i	−1.31396	+	0.352074i	−0.846711	−	0.532053i	$-0.821421\pi$
$563$	−31.1771	+	8.35388i	−1.31396	+	0.352074i	−0.467247	+	0.884127i	$0.654754\pi$
$564$	−4.43540	−	4.04551i	−0.186764	−	0.170347i
$565$		0			0
$566$			18.1025i			0.760904i
$567$	2.72808	−	34.8876i	0.114569	−	1.46514i
$568$	4.91376	−	4.91376i	0.206177	−	0.206177i
$569$	−16.1545	−	27.9804i	−0.677232	−	1.17300i	−0.975811	−	0.218615i	$-0.929846\pi$
$569$	−16.1545	−	27.9804i	−0.677232	−	1.17300i	0.298580	−	0.954385i	$-0.403487\pi$
$570$		0			0
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	−0.456563	−	0.889691i	$-0.650920\pi$
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	0.998777	−	0.0494501i	$-0.0157469\pi$
$572$	−1.01825	−	3.80016i	−0.0425752	−	0.158893i
$573$	19.8807	−	12.7300i	0.830529	−	0.531803i
$574$	27.8310	−	16.0682i	1.16164	−	0.670674i
$575$		0			0
$576$	0.275255	+	2.98735i	0.0114690	+	0.124473i
$577$	−6.10724	−	6.10724i	−0.254248	−	0.254248i	0.568462	−	0.822710i	$-0.307539\pi$
$577$	−6.10724	−	6.10724i	−0.254248	−	0.254248i	−0.822710	+	0.568462i	$0.807539\pi$
$578$	−4.39244	+	16.3928i	−0.182701	+	0.681851i
$579$	8.50152	+	26.7480i	0.353311	+	1.11161i
$580$		0			0
$581$	23.5629	+	13.6041i	0.977556	+	0.564392i
$582$	1.19128	−	2.30138i	0.0493801	−	0.0953951i
$583$	19.8977	+	5.33157i	0.824077	+	0.220811i
$584$	11.7058			0.484391
$585$		0			0
$586$	−21.3953			−0.883833
$587$	−1.83025	−	0.490414i	−0.0755424	−	0.0202415i	0.220850	−	0.975308i	$-0.429117\pi$
$587$	−1.83025	−	0.490414i	−0.0755424	−	0.0202415i	−0.296392	+	0.955066i	$0.595784\pi$
$588$	−7.58249	−	11.8418i	−0.312697	−	0.488346i
$589$	15.3501	+	8.86238i	0.632490	+	0.365168i
$590$		0			0
$591$	1.91619	−	2.10087i	0.0788217	−	0.0864182i
$592$	1.19640	−	4.46504i	0.0491719	−	0.183512i
$593$	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
$595$		0			0
$596$	−0.897625	+	0.518244i	−0.0367681	+	0.0212281i
$597$	−1.36602	−	29.7136i	−0.0559074	−	1.21610i
$598$	−1.35011	−	5.03866i	−0.0552099	−	0.206046i
$599$	−12.9428	+	22.4176i	−0.528828	+	0.915957i	0.470607	+	0.882343i	$0.344035\pi$
$599$	−12.9428	+	22.4176i	−0.528828	+	0.915957i	−0.999435	+	0.0336142i	$0.989298\pi$
$600$		0			0
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	0.594086	−	0.804401i	$-0.297514\pi$
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	−0.993675	+	0.112293i	$0.964180\pi$
$602$	5.67241	−	5.67241i	0.231190	−	0.231190i
$603$	−22.9172	+	8.46115i	−0.933262	+	0.344565i
$604$		−	4.06902i		−	0.165566i
$605$		0			0
$606$	−17.0008	+	5.40349i	−0.690611	+	0.219502i
$607$	28.7731	−	7.70972i	1.16786	−	0.312928i	0.377761	−	0.925903i	$-0.376694\pi$
$607$	28.7731	−	7.70972i	1.16786	−	0.312928i	0.790102	+	0.612975i	$0.210027\pi$
$608$	1.82070	−	0.487854i	0.0738390	−	0.0197851i
$609$	27.6776	−	8.79699i	1.12155	−	0.356472i
$610$		0			0
$611$		−	3.43162i		−	0.138828i
$612$	−0.478556	+	0.176685i	−0.0193445	+	0.00714207i
$613$	12.5028	−	12.5028i	0.504982	−	0.504982i	−0.408000	−	0.912982i	$-0.633774\pi$
$613$	12.5028	−	12.5028i	0.504982	−	0.504982i	0.912982	+	0.408000i	$0.133774\pi$
$614$	14.3510	+	24.8566i	0.579157	+	1.00313i
$615$		0			0
$616$	−7.72515	+	13.3804i	−0.311255	+	0.539110i
$617$	1.91482	+	7.14621i	0.0770878	+	0.287695i	0.993699	−	0.112085i	$-0.0357530\pi$
$617$	1.91482	+	7.14621i	0.0770878	+	0.287695i	−0.916611	+	0.399781i	$0.869086\pi$
$618$	−0.515774	−	11.2191i	−0.0207475	−	0.451299i
$619$	16.4624	−	9.50460i	0.661682	−	0.382022i	−0.131236	−	0.991351i	$-0.541895\pi$
$619$	16.4624	−	9.50460i	0.661682	−	0.382022i	0.792917	+	0.609329i	$0.208561\pi$
$620$		0			0
$621$	−25.2196	+	10.6514i	−1.01203	+	0.427426i
$622$	−9.78715	−	9.78715i	−0.392429	−	0.392429i
$623$	−4.90928	+	18.3217i	−0.196686	+	0.734043i
$624$	−1.15564	+	1.26701i	−0.0462625	+	0.0507211i
$625$		0			0
$626$	−16.0560	−	9.26994i	−0.641727	−	0.370501i
$627$	6.99560	+	10.9252i	0.279378	+	0.436310i
$628$	8.81460	+	2.36186i	0.351741	+	0.0942486i
$629$	0.786034			0.0313412
$630$		0			0
$631$	−2.22853			−0.0887165			−0.0443583	−	0.999016i	$-0.514124\pi$
$631$	−2.22853			−0.0887165			−0.0443583	+	0.999016i	$0.514124\pi$
$632$	13.1086	+	3.51245i	0.521433	+	0.139718i
$633$	−14.5055	+	28.0225i	−0.576543	+	1.11380i
$634$	−0.727989	−	0.420305i	−0.0289121	−	0.0166924i
$635$		0			0
$636$	−2.71982	−	8.55729i	−0.107848	−	0.339319i
$637$	2.08035	−	7.76396i	0.0824263	−	0.307619i
$638$	−12.1167	−	12.1167i	−0.479705	−	0.479705i
$639$	−1.91278	−	20.7594i	−0.0756683	−	0.821229i
$640$		0			0
$641$	37.8297	−	21.8410i	1.49418	−	0.862666i	0.494204	−	0.869346i	$-0.335460\pi$
$641$	37.8297	−	21.8410i	1.49418	−	0.862666i	0.999978	+	0.00667968i	$0.00212622\pi$
$642$	7.63367	−	4.88798i	0.301277	−	0.192913i
$643$	7.89483	+	29.4639i	0.311342	+	1.16194i	0.927347	+	0.374202i	$0.122083\pi$
$643$	7.89483	+	29.4639i	0.311342	+	1.16194i	−0.616006	+	0.787742i	$0.711250\pi$
$644$	−10.2428	+	17.7411i	−0.403624	+	0.699097i
$645$		0			0
$646$	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	$0.214296\pi$
$648$	7.41970	+	5.09393i	0.291473	+	0.200108i
$649$		−	21.6861i		−	0.851255i
$650$		0			0
$651$	46.7892	+	42.6763i	1.83381	+	1.67261i
$652$	−6.88270	+	1.84421i	−0.269547	+	0.0722249i
$653$	31.5015	−	8.44081i	1.23275	−	0.330314i	0.417100	−	0.908861i	$-0.363046\pi$
$653$	31.5015	−	8.44081i	1.23275	−	0.330314i	0.815650	+	0.578546i	$0.196380\pi$
$654$	−2.70876	+	12.3533i	−0.105921	+	0.483050i
$655$		0			0
$656$			8.26506i			0.322696i
$657$	22.4487	−	27.0055i	0.875809	−	1.05358i
$658$	−9.52933	+	9.52933i	−0.371492	+	0.371492i
$659$	7.75612	+	13.4340i	0.302136	+	0.523314i	0.976619	−	0.214975i	$-0.0689671\pi$
$659$	7.75612	+	13.4340i	0.302136	+	0.523314i	−0.674484	+	0.738290i	$0.735634\pi$
$660$		0			0
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	−0.564191	−	0.825644i	$-0.690812\pi$
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	0.997124	+	0.0757821i	$0.0241453\pi$
$662$	1.07778	+	4.02232i	0.0418890	+	0.156332i
$663$	−0.258966	−	0.134051i	−0.0100574	−	0.00520610i
$664$	−6.06007	+	3.49878i	−0.235176	+	0.135779i
$665$		0			0
$666$	−8.00649	−	11.3229i	−0.310245	−	0.438753i
$667$	−16.0656	−	16.0656i	−0.622063	−	0.622063i
$668$	−2.80384	+	10.4641i	−0.108484	+	0.404867i
$669$	7.94444	+	1.74202i	0.307150	+	0.0673503i
$670$		0			0
$671$	29.9817	+	17.3099i	1.15743	+	0.668243i
$672$	6.72750	−	0.309282i	0.259519	−	0.0119308i
$673$	9.32657	+	2.49905i	0.359513	+	0.0963312i	0.434054	−	0.900887i	$-0.357083\pi$
$673$	9.32657	+	2.49905i	0.359513	+	0.0963312i	−0.0745413	+	0.997218i	$0.523749\pi$
$674$	−3.24846			−0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	−7.30994	−	1.95869i	−0.280944	−	0.0752787i	0.115596	−	0.993296i	$-0.463122\pi$
$677$	−7.30994	−	1.95869i	−0.280944	−	0.0752787i	−0.396539	+	0.918018i	$0.629789\pi$
$678$	7.30040	−	0.335620i	0.280370	−	0.0128894i
$679$	−5.03802	−	2.90870i	−0.193342	−	0.111626i
$680$		0			0
$681$	−42.3494	−	9.28618i	−1.62283	−	0.355847i
$682$	9.67093	−	36.0924i	0.370319	−	1.38205i
$683$	−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
$685$		0			0
$686$	−3.76572	+	2.17414i	−0.143776	+	0.0830090i
$687$	35.0522	+	18.1443i	1.33732	+	0.692250i
$688$	0.533983	+	1.99285i	0.0203579	+	0.0759767i
$689$	2.56635	−	4.44506i	0.0977703	−	0.169343i
$690$		0			0
$691$	21.3061	+	36.9033i	0.810523	+	1.40387i	0.912498	+	0.409080i	$0.134150\pi$
$691$	21.3061	+	36.9033i	0.810523	+	1.40387i	−0.101975	+	0.994787i	$0.532516\pi$
$692$	−2.66569	+	2.66569i	−0.101334	+	0.101334i
$693$	16.0538	+	43.4820i	0.609832	+	1.65174i
$694$		−	4.69326i		−	0.178154i
$695$		0			0
$696$	−1.59981	+	7.29588i	−0.0606405	+	0.276550i
$697$	−1.35753	+	0.363749i	−0.0514201	+	0.0137780i
$698$	9.40041	−	2.51883i	0.355811	−	0.0953392i
$699$	37.3700	+	34.0850i	1.41346	+	1.28921i
$700$		0			0
$701$			36.3602i			1.37331i	0.726985	+	0.686653i	$0.240921\pi$
$701$			36.3602i			1.37331i	−0.726985	+	0.686653i	$0.759079\pi$
$702$	0.706799	+	5.09586i	0.0266764	+	0.192331i
$703$	−6.16113	+	6.16113i	−0.232371	+	0.232371i
$704$	−1.98681	−	3.44125i	−0.0748805	−	0.129697i
$705$		0			0
$706$	2.55100	−	4.41846i	0.0960080	−	0.166291i
$707$	10.3647	+	38.6814i	0.389803	+	1.45476i
$708$	−7.96061	+	5.09733i	−0.299178	+	0.191569i
$709$	−0.356646	+	0.205910i	−0.0133941	+	0.00773310i	−0.506682	−	0.862133i	$-0.669128\pi$
$709$	−0.356646	+	0.205910i	−0.0133941	+	0.00773310i	0.493288	+	0.869866i	$0.335795\pi$
$710$		0			0
$711$	33.2421	−	23.5057i	1.24668	−	0.881534i
$712$	−3.44949	−	3.44949i	−0.129275	−	0.129275i
$713$	12.8227	−	47.8551i	0.480215	−	1.79219i
$714$	0.346880	+	1.09138i	0.0129817	+	0.0408437i
$715$		0			0
$716$	11.1676	+	6.44762i	0.417353	+	0.240959i
$717$	7.26599	−	14.0368i	0.271353	−	0.524214i
$718$	1.23345	+	0.330503i	0.0460321	+	0.0123343i
$719$	−34.4664			−1.28538			−0.642690	−	0.766126i	$-0.722182\pi$
$719$	−34.4664			−1.28538			−0.642690	+	0.766126i	$0.722182\pi$
$720$		0			0
$721$	−25.2120			−0.938946
$722$	14.9207	+	3.99799i	0.555291	+	0.148790i
$723$	1.62451	+	2.53704i	0.0604162	+	0.0943534i
$724$	21.0615	+	12.1599i	0.782744	+	0.451918i
$725$		0			0
$726$	5.59043	−	6.12921i	0.207480	−	0.227476i
$727$	−3.69508	+	13.7902i	−0.137043	+	0.511451i	0.862938	+	0.505310i	$0.168622\pi$
$727$	−3.69508	+	13.7902i	−0.137043	+	0.511451i	−0.999981	+	0.00614188i	$0.998045\pi$
$728$	2.72214	+	2.72214i	0.100889	+	0.100889i
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$		0			0
$731$	−0.303823	+	0.175413i	−0.0112373	+	0.00648787i
$732$	−0.693017	−	15.0745i	−0.0256146	−	0.557169i
$733$	−7.94942	−	29.6676i	−0.293618	−	1.09580i	−0.942308	−	0.334746i	$-0.891349\pi$
$733$	−7.94942	−	29.6676i	−0.293618	−	1.09580i	0.648690	−	0.761053i	$-0.275317\pi$
$734$	5.04335	−	8.73534i	0.186153	−	0.322427i
$735$		0			0
$736$	−2.63432	−	4.56277i	−0.0971022	−	0.168186i
$737$	22.8802	−	22.8802i	0.842803	−	0.842803i
$738$	19.0675	+	15.8502i	0.701886	+	0.583454i
$739$		−	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			0
$741$	3.08056	−	0.979118i	0.113167	−	0.0359688i
$742$	−19.4701	+	5.21700i	−0.714771	+	0.191522i
$743$	34.7672	−	9.31585i	1.27549	−	0.341765i	0.443356	−	0.896346i	$-0.353788\pi$
$743$	34.7672	−	9.31585i	1.27549	−	0.341765i	0.832130	+	0.554580i	$0.187121\pi$
$744$	−15.5221	+	4.93349i	−0.569067	+	0.180871i
$745$		0			0
$746$			13.1124i			0.480080i
$747$	−3.54991	+	20.6904i	−0.129884	+	0.757022i
$748$	0.477782	−	0.477782i	0.0174695	−	0.0174695i
$749$	−10.1743	−	17.6224i	−0.371761	−	0.643910i
$750$		0			0
$751$	−24.4567	+	42.3603i	−0.892438	+	1.54575i	−0.0554938	+	0.998459i	$0.517673\pi$
$751$	−24.4567	+	42.3603i	−0.892438	+	1.54575i	−0.836944	+	0.547289i	$0.815660\pi$
$752$	−0.897060	−	3.34787i	−0.0327124	−	0.122084i
$753$	−0.490584	−	10.6712i	−0.0178779	−	0.388879i
$754$	−3.69759	+	2.13480i	−0.134658	+	0.0777449i
$755$		0			0
$756$	12.1881	−	16.1135i	0.443276	−	0.586043i
$757$	−22.9129	−	22.9129i	−0.832783	−	0.832783i	0.155114	−	0.987897i	$-0.450426\pi$
$757$	−22.9129	−	22.9129i	−0.832783	−	0.832783i	−0.987897	+	0.155114i	$0.950426\pi$
$758$	−0.152094	+	0.567624i	−0.00552432	+	0.0206170i
$759$	24.4361	−	26.7911i	0.886973	−	0.972456i
$760$		0			0
$761$	−9.19124	−	5.30657i	−0.333182	−	0.192363i	0.324071	−	0.946033i	$-0.394948\pi$
$761$	−9.19124	−	5.30657i	−0.333182	−	0.192363i	−0.657253	+	0.753670i	$0.728282\pi$
$762$	−18.2111	−	28.4406i	−0.659717	−	1.03030i
$763$	27.4229	+	7.34795i	0.992777	+	0.266014i
$764$	13.6296			0.493100
$765$		0			0
$766$	−14.5012			−0.523950
$767$	−5.21932	−	1.39851i	−0.188459	−	0.0504974i
$768$	−0.796225	+	1.53819i	−0.0287313	+	0.0555046i
$769$	−3.31814	−	1.91573i	−0.119655	−	0.0690830i	0.438978	−	0.898498i	$-0.355341\pi$
$769$	−3.31814	−	1.91573i	−0.119655	−	0.0690830i	−0.558633	+	0.829415i	$0.688674\pi$
$770$		0			0
$771$	−15.2428	−	47.9578i	−0.548955	−	1.72716i
$772$	−4.19397	+	15.6521i	−0.150944	+	0.563332i
$773$	−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
$775$		0			0
$776$	1.29571	−	0.748079i	0.0465133	−	0.0268545i
$777$	−26.2170	+	16.7872i	−0.940529	+	0.602239i
$778$	−5.37250	−	20.0504i	−0.192613	−	0.718843i
$779$	7.78950	−	13.4918i	0.279088	−	0.483395i
$780$		0			0
$781$	13.8065	+	23.9136i	0.494036	+	0.855696i
$782$	0.633495	−	0.633495i	0.0226537	−	0.0226537i
$783$	13.7636	+	17.6823i	0.491872	+	0.631915i
$784$		−	8.11832i		−	0.289940i
$785$		0			0
$786$	−5.73704	−	5.23273i	−0.204633	−	0.186645i
$787$	−6.98473	+	1.87155i	−0.248979	+	0.0667137i	−0.381150	−	0.924513i	$-0.624472\pi$
$787$	−6.98473	+	1.87155i	−0.248979	+	0.0667137i	0.132171	+	0.991227i	$0.457805\pi$
$788$	1.58575	−	0.424901i	0.0564901	−	0.0151365i
$789$	6.92279	−	31.5712i	0.246458	−	1.12397i
$790$		0			0
$791$		−	16.4058i		−	0.583321i
$792$	−11.7492	−	2.01584i	−0.417488	−	0.0716296i
$793$	6.09956	−	6.09956i	0.216602	−	0.216602i
$794$	−11.1320	−	19.2811i	−0.395059	−	0.684262i
$795$		0			0
$796$	8.58664	−	14.8725i	0.304345	−	0.527142i
$797$	8.96012	+	33.4396i	0.317384	+	1.18449i	0.921750	+	0.387786i	$0.126760\pi$
$797$	8.96012	+	33.4396i	0.317384	+	1.18449i	−0.604366	+	0.796707i	$0.706573\pi$
$798$	−11.2734	−	5.83555i	−0.399074	−	0.206576i
$799$	0.510406	−	0.294683i	0.0180569	−	0.0104251i
$800$		0			0
$801$	−14.5732	+	1.34278i	−0.514919	+	0.0474448i
$802$	3.36182	+	3.36182i	0.118710	+	0.118710i
$803$	−12.0388	+	44.9295i	−0.424841	+	1.58553i
$804$	−13.7769	−	3.02094i	−0.485875	−	0.106540i
$805$		0			0
$806$	−8.06289	−	4.65511i	−0.284003	−	0.163969i
$807$	26.9142	−	1.23732i	0.947424	−	0.0435557i
$808$	−9.94834	−	2.66565i	−0.349981	−	0.0937772i
$809$	52.6028			1.84942			0.924709	−	0.380675i	$-0.124308\pi$
$809$	52.6028			1.84942			0.924709	+	0.380675i	$0.124308\pi$
$810$		0			0
$811$	−13.8979			−0.488021			−0.244011	−	0.969773i	$-0.578463\pi$
$811$	−13.8979			−0.488021			−0.244011	+	0.969773i	$0.578463\pi$
$812$	16.1961	+	4.33973i	0.568371	+	0.152295i
$813$	−3.23870	+	0.148892i	−0.113586	+	0.00522188i
$814$	15.9073	+	9.18410i	0.557551	+	0.321902i
$815$		0			0
$816$	−0.287689	−	0.0630830i	−0.0100711	−	0.00220835i
$817$	1.00652	−	3.75637i	0.0352136	−	0.131419i
$818$	−21.1307	−	21.1307i	−0.738817	−	0.738817i
$819$	11.5003	−	1.05965i	0.401854	−	0.0370270i
$820$		0			0
$821$	−23.9657	+	13.8366i	−0.836408	+	0.482900i	−0.856042	−	0.516907i	$-0.827083\pi$
$821$	−23.9657	+	13.8366i	−0.836408	+	0.482900i	0.0196338	+	0.999807i	$0.493750\pi$
$822$	19.2255	+	9.95185i	0.670566	+	0.347111i
$823$	7.80049	+	29.1118i	0.271908	+	1.01477i	0.957885	+	0.287151i	$0.0927083\pi$
$823$	7.80049	+	29.1118i	0.271908	+	1.01477i	−0.685977	+	0.727623i	$0.740625\pi$
$824$	3.24210	−	5.61548i	0.112944	−	0.195625i
$825$		0			0
$826$	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	$0.282134\pi$
$828$	−15.5783	−	2.67281i	−0.541382	−	0.0928865i
$829$		−	37.6756i		−	1.30853i	−0.756266	−	0.654264i	$-0.772979\pi$
$829$		−	37.6756i		−	1.30853i	0.756266	−	0.654264i	$-0.227021\pi$
$830$		0			0
$831$	1.53257	−	6.98924i	0.0531642	−	0.242454i
$832$	−0.956351	+	0.256253i	−0.0331555	+	0.00888399i
$833$	1.33343	−	0.357291i	0.0462006	−	0.0123794i
$834$	−5.32603	−	4.85785i	−0.184425	−	0.168213i
$835$		0			0
$836$			7.48995i			0.259046i
$837$	−18.3857	+	45.2707i	−0.635501	+	1.56478i
$838$	12.4682	−	12.4682i	0.430708	−	0.430708i
$839$	16.5639	+	28.6895i	0.571849	+	0.990471i	0.996376	+	0.0850559i	$0.0271069\pi$
$839$	16.5639	+	28.6895i	0.571849	+	0.990471i	−0.424527	+	0.905415i	$0.639560\pi$
$840$		0			0
$841$	5.20180	−	9.00978i	0.179372	−	0.310682i
$842$	7.21908	+	26.9420i	0.248786	+	0.928482i
$843$	0.418784	−	0.268155i	0.0144237	−	0.00923575i
$844$	−15.7771	+	9.10894i	−0.543072	+	0.313543i
$845$		0			0
$846$	−9.44390	−	4.35082i	−0.324688	−	0.149584i
$847$	−13.1684	−	13.1684i	−0.452472	−	0.452472i
$848$	1.34174	−	5.00745i	0.0460757	−	0.171957i
$849$	9.49743	+	29.8814i	0.325951	+	1.02553i
$850$		0			0
$851$	21.0916	+	12.1773i	0.723011	+	0.417431i
$852$	5.53306	−	10.6890i	0.189559	−	0.366201i
$853$	2.57386	+	0.689663i	0.0881273	+	0.0236136i	0.302613	−	0.953113i	$-0.402141\pi$
$853$	2.57386	+	0.689663i	0.0881273	+	0.0236136i	−0.214486	+	0.976727i	$0.568808\pi$
$854$	−33.8760			−1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	−15.1284	−	4.05364i	−0.516776	−	0.138470i	−0.00900123	−	0.999959i	$-0.502865\pi$
$857$	−15.1284	−	4.05364i	−0.516776	−	0.138470i	−0.507775	+	0.861490i	$0.669532\pi$
$858$	−3.67455	−	5.73863i	−0.125447	−	0.195914i
$859$	0.691191	+	0.399059i	0.0235831	+	0.0136157i	0.511745	−	0.859137i	$-0.328999\pi$
$859$	0.691191	+	0.399059i	0.0235831	+	0.0136157i	−0.488162	+	0.872753i	$0.662333\pi$
$860$		0			0
$861$	37.5099	−	41.1249i	1.27833	−	1.40153i
$862$	4.99288	−	18.6337i	0.170058	−	0.634666i
$863$	−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
$865$		0			0
$866$	−20.4721	+	11.8196i	−0.695671	+	0.401646i
$867$	1.34994	+	29.3638i	0.0458462	+	0.997246i
$868$	9.46313	+	35.3169i	0.321199	+	1.19873i
$869$	−26.9630	+	46.7013i	−0.914658	+	1.58423i
$870$		0			0
$871$	−4.03119	−	6.98222i	−0.136592	−	0.236584i
$872$	−5.16301	+	5.16301i	−0.174842	+	0.174842i
$873$	0.759010	−	4.42384i	0.0256886	−	0.149724i
$874$			9.93098i			0.335920i
$875$		0			0
$876$	19.3226	−	6.14144i	0.652850	−	0.207500i
$877$	16.7435	−	4.48641i	0.565388	−	0.151495i	0.0352074	−	0.999380i	$-0.488791\pi$
$877$	16.7435	−	4.48641i	0.565388	−	0.151495i	0.530180	+	0.847885i	$0.322124\pi$
$878$	−34.7780	+	9.31875i	−1.17370	+	0.314492i
$879$	−35.3169	+	11.2250i	−1.19121	+	0.378610i
$880$		0			0
$881$			15.1033i			0.508843i	0.967093	+	0.254421i	$0.0818850\pi$
$881$			15.1033i			0.508843i	−0.967093	+	0.254421i	$0.918115\pi$
$882$	−18.7290	−	15.5688i	−0.630639	−	0.524229i
$883$	16.4678	−	16.4678i	0.554185	−	0.554185i	−0.373461	−	0.927646i	$-0.621829\pi$
$883$	16.4678	−	16.4678i	0.554185	−	0.554185i	0.927646	+	0.373461i	$0.121829\pi$
$884$	−0.0841789	−	0.145802i	−0.00283124	−	0.00490386i
$885$		0			0
$886$	13.4169	−	23.2388i	0.450750	−	0.780723i
$887$	−7.07714	−	26.4123i	−0.237627	−	0.886837i	−0.976947	−	0.213482i	$-0.931519\pi$
$887$	−7.07714	−	26.4123i	−0.237627	−	0.886837i	0.739320	−	0.673355i	$-0.235147\pi$
$888$	−0.367692	−	7.99804i	−0.0123389	−	0.268397i
$889$	−65.6556	+	37.9063i	−2.20202	+	1.27134i
$890$		0			0
$891$	−27.1823	+	23.2395i	−0.910643	+	0.778554i
$892$	3.32036	+	3.32036i	0.111174	+	0.111174i
$893$	−1.69089	+	6.31049i	−0.0565835	+	0.211173i
$894$	−1.20980	+	1.32639i	−0.0404616	+	0.0443612i
$895$		0			0
$896$	3.36730	+	1.94411i	0.112494	+	0.0649483i
$897$	−4.87211	−	7.60889i	−0.162675	−	0.254053i
$898$	−39.9306	−	10.6994i	−1.33250	−	0.357043i
$899$	−40.5510			−1.35245
$900$		0			0
$901$	0.881522			0.0293678
$902$	−31.7230	−	8.50016i	−1.05626	−	0.283025i
$903$	6.38732	−	12.3393i	0.212557	−	0.410628i
$904$	3.65405	+	2.10967i	0.121532	+	0.0701666i
$905$		0			0
$906$	−2.13480	−	6.71666i	−0.0709241	−	0.223146i
$907$	−6.62626	+	24.7295i	−0.220021	+	0.821130i	0.764317	+	0.644841i	$0.223076\pi$
$907$	−6.62626	+	24.7295i	−0.220021	+	0.821130i	−0.984338	+	0.176290i	$0.943590\pi$
$908$	−17.6998	−	17.6998i	−0.587390	−	0.587390i
$909$	−25.2280	+	17.8389i	−0.836759	+	0.591678i
$910$		0			0
$911$	3.55075	−	2.05003i	0.117642	−	0.0679204i	−0.440025	−	0.897986i	$-0.645030\pi$
$911$	3.55075	−	2.05003i	0.117642	−	0.0679204i	0.557666	+	0.830065i	$0.311697\pi$
$912$	2.74944	−	1.76052i	0.0910430	−	0.0582965i
$913$	−7.19662	−	26.8582i	−0.238173	−	0.888875i
$914$	−10.7957	+	18.6987i	−0.357090	+	0.618499i
$915$		0			0
$916$	11.3940	+	19.7350i	0.376468	+	0.652061i
$917$	−12.3259	+	12.3259i	−0.407035	+	0.407035i
$918$	−0.697245	+	0.542723i	−0.0230125	+	0.0179125i
$919$			28.8740i			0.952464i	0.879320	+	0.476232i	$0.157998\pi$
$919$			28.8740i			0.952464i	−0.879320	+	0.476232i	$0.842002\pi$
$920$		0			0
$921$	36.7298	+	33.5011i	1.21029	+	1.10390i
$922$	−12.1246	+	3.24877i	−0.399302	+	0.106993i
$923$	6.64579	−	1.78073i	0.218749	−	0.0586135i
$924$	−5.73178	+	26.1397i	−0.188562	+	0.859932i
$925$		0			0
$926$		−	22.1046i		−	0.726404i
$927$	−6.73746	−	18.2486i	−0.221287	−	0.599362i
$928$	−3.04930	+	3.04930i	−0.100098	+	0.100098i
$929$	−25.1077	−	43.4879i	−0.823758	−	1.42679i	−0.902865	−	0.429925i	$-0.858540\pi$
$929$	−25.1077	−	43.4879i	−0.823758	−	1.42679i	0.0791067	−	0.996866i	$-0.474793\pi$
$930$		0			0
$931$	−7.65121	+	13.2523i	−0.250758	+	0.434326i
$932$	7.55809	+	28.2072i	0.247573	+	0.923956i
$933$	−21.2903	−	11.0206i	−0.697012	−	0.360800i
$934$	−4.26380	+	2.46170i	−0.139516	+	0.0805494i
$935$		0			0
$936$	−1.24285	+	2.69773i	−0.0406239	+	0.0881782i
$937$	0.857094	+	0.857094i	0.0280000	+	0.0280000i	0.720968	−	0.692968i	$-0.243697\pi$
$937$	0.857094	+	0.857094i	0.0280000	+	0.0280000i	−0.692968	+	0.720968i	$0.743697\pi$
$938$	−8.19479	+	30.5834i	−0.267569	+	0.998582i
$939$	−31.3668	−	6.87796i	−1.02362	−	0.224454i
$940$		0			0
$941$	−43.4478	−	25.0846i	−1.41636	−	0.817735i	−0.420382	−	0.907347i	$-0.638104\pi$
$941$	−43.4478	−	25.0846i	−1.41636	−	0.817735i	−0.995977	+	0.0896119i	$0.971437\pi$
$942$	15.7892	−	0.725875i	0.514441	−	0.0236503i
$943$	−42.0618	−	11.2704i	−1.36972	−	0.367015i
$944$	−5.45754			−0.177628
$945$		0			0
$946$	−8.19815			−0.266545
$947$	−2.54334	−	0.681485i	−0.0826473	−	0.0221453i	0.217258	−	0.976114i	$-0.430289\pi$
$947$	−2.54334	−	0.681485i	−0.0826473	−	0.0221453i	−0.299906	+	0.953969i	$0.596955\pi$
$948$	23.4809	−	1.07949i	0.762626	−	0.0350601i
$949$	10.0371	+	5.79490i	0.325817	+	0.188111i
$950$		0			0
$951$	−1.42219	−	0.311851i	−0.0461176	−	0.0101125i
$952$	−0.171123	+	0.638639i	−0.00554612	+	0.0206984i
$953$	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
$955$		0			0
$956$	7.90295	−	4.56277i	0.255600	−	0.147571i
$957$	−26.3578	−	13.6438i	−0.852027	−	0.441042i
$958$	−0.702296	−	2.62100i	−0.0226901	−	0.0846808i
$959$	24.2991	−	42.0872i	0.784658	−	1.35907i
$960$		0			0
$961$	−28.7123	−	49.7312i	−0.926204	−	1.60423i
$962$	3.23623	−	3.23623i	0.104340	−	0.104340i
$963$	10.0363	−	12.0735i	0.323414	−	0.389062i
$964$			1.73931i			0.0560194i
$965$		0			0
$966$	−7.59981	+	34.6587i	−0.244520	+	1.11513i
$967$	−1.28319	+	0.343829i	−0.0412646	+	0.0110568i	−0.279392	−	0.960177i	$-0.590133\pi$
$967$	−1.28319	+	0.343829i	−0.0412646	+	0.0110568i	0.238128	+	0.971234i	$0.423466\pi$
$968$	4.62638	−	1.23963i	0.148697	−	0.0398433i
$969$	0.410168	+	0.374112i	0.0131765	+	0.0120182i
$970$		0			0
$971$		−	38.7906i		−	1.24485i	−0.782679	−	0.622425i	$-0.786147\pi$
$971$		−	38.7906i		−	1.24485i	0.782679	−	0.622425i	$-0.213853\pi$
$972$	14.9201	+	4.51572i	0.478561	+	0.144842i
$973$	−11.4428	+	11.4428i	−0.366840	+	0.366840i
$974$	5.80393	+	10.0527i	0.185970	+	0.322109i
$975$		0			0
$976$	4.35623	−	7.54520i	0.139439	−	0.241516i
$977$	−11.0953	−	41.4084i	−0.354972	−	1.32477i	−0.880520	−	0.474009i	$-0.842807\pi$
$977$	−11.0953	−	41.4084i	−0.354972	−	1.32477i	0.525548	−	0.850764i	$-0.323860\pi$
$978$	−10.3936	+	6.65520i	−0.332350	+	0.212810i
$979$	16.7875	−	9.69226i	0.536530	−	0.309766i
$980$		0			0
$981$	2.00980	+	21.8124i	0.0641681	+	0.696417i
$982$	3.49508	+	3.49508i	0.111532	+	0.111532i
$983$	−8.34182	+	31.1321i	−0.266063	+	0.992960i	0.695534	+	0.718493i	$0.255168\pi$
$983$	−8.34182	+	31.1321i	−0.266063	+	0.992960i	−0.961597	+	0.274466i	$0.911499\pi$
$984$	4.33624	+	13.6430i	0.138234	+	0.434922i
$985$		0			0
$986$	−0.635046	−	0.366644i	−0.0202240	−	0.0116763i
$987$	−10.7303	+	20.7294i	−0.341550	+	0.659824i
$988$	1.80265	+	0.483018i	0.0573499	+	0.0153669i
$989$	−10.8700			−0.345645
$990$		0			0
$991$	20.1017			0.638551			0.319275	−	0.947662i	$-0.396561\pi$
$991$	20.1017			0.638551			0.319275	+	0.947662i	$0.396561\pi$
$992$	−9.08302	−	2.43379i	−0.288386	−	0.0772729i
$993$	3.88937	+	6.07411i	0.123425	+	0.192756i
$994$	−23.3998	−	13.5099i	−0.742196	−	0.428507i
$995$		0			0
$996$	−8.16761	+	8.95478i	−0.258801	+	0.283743i
$997$	−0.763421	+	2.84912i	−0.0241778	+	0.0902327i	−0.976960	−	0.213420i	$-0.931540\pi$
$997$	−0.763421	+	2.84912i	−0.0241778	+	0.0902327i	0.952783	+	0.303653i	$0.0982063\pi$
$998$	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	450.2.p.h.257.4		16
3.2	odd	2		1350.2.q.h.557.2		16
5.2	odd	4		90.2.l.b.23.1	✓	16
5.3	odd	4	inner	450.2.p.h.293.4		16
5.4	even	2		90.2.l.b.77.1	yes	16
9.2	odd	6	inner	450.2.p.h.407.4		16
9.7	even	3		1350.2.q.h.1007.1		16
15.2	even	4		270.2.m.b.233.3		16
15.8	even	4		1350.2.q.h.1043.1		16
15.14	odd	2		270.2.m.b.17.4		16
20.7	even	4		720.2.cu.b.113.3		16
20.19	odd	2		720.2.cu.b.257.4		16
45.2	even	12		90.2.l.b.83.1	yes	16
45.4	even	6		810.2.f.c.647.8		16
45.7	odd	12		270.2.m.b.143.4		16
45.14	odd	6		810.2.f.c.647.1		16
45.22	odd	12		810.2.f.c.323.1		16
45.29	odd	6		90.2.l.b.47.1	yes	16
45.32	even	12		810.2.f.c.323.8		16
45.34	even	6		270.2.m.b.197.3		16
45.38	even	12	inner	450.2.p.h.443.4		16
45.43	odd	12		1350.2.q.h.143.2		16
180.47	odd	12		720.2.cu.b.353.4		16
180.119	even	6		720.2.cu.b.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	5.2	odd	4
90.2.l.b.47.1	yes	16	45.29	odd	6
90.2.l.b.77.1	yes	16	5.4	even	2
90.2.l.b.83.1	yes	16	45.2	even	12
270.2.m.b.17.4		16	15.14	odd	2
270.2.m.b.143.4		16	45.7	odd	12
270.2.m.b.197.3		16	45.34	even	6
270.2.m.b.233.3		16	15.2	even	4
450.2.p.h.257.4		16	1.1	even	1	trivial
450.2.p.h.293.4		16	5.3	odd	4	inner
450.2.p.h.407.4		16	9.2	odd	6	inner
450.2.p.h.443.4		16	45.38	even	12	inner
720.2.cu.b.113.3		16	20.7	even	4
720.2.cu.b.257.4		16	20.19	odd	2
720.2.cu.b.353.4		16	180.47	odd	12
720.2.cu.b.497.3		16	180.119	even	6
810.2.f.c.323.1		16	45.22	odd	12
810.2.f.c.323.8		16	45.32	even	12
810.2.f.c.647.1		16	45.14	odd	6
810.2.f.c.647.8		16	45.4	even	6
1350.2.q.h.143.2		16	45.43	odd	12
1350.2.q.h.557.2		16	3.2	odd	2
1350.2.q.h.1007.1		16	9.7	even	3
1350.2.q.h.1043.1		16	15.8	even	4

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

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

Introduction

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