LMFDB - Embedded newform 450.2.p.h.443.4

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			443.4
Root			$0.500000 + 1.74530i$ of defining polynomial
Character	$\chi$	$=$	450.443
Dual form			450.2.p.h.257.4

$q$-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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	0.845347	+	0.534217i	$0.179394\pi$
$7$	1.00635	+	3.75574i	0.380364	+	1.41954i	−0.464984	+	0.885319i	$0.653940\pi$
$8$	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	−0.118430	−	0.992962i	$-0.537786\pi$
$11$	−3.44125	−	1.98681i	−1.03758	−	0.599044i	−0.919145	+	0.393918i	$0.871119\pi$
$12$	1.53819	−	0.796225i	0.444037	−	0.229850i
$13$	0.256253	−	0.956351i	0.0710719	−	0.265244i	−0.921242	−	0.388990i	$-0.872824\pi$
$13$	0.256253	−	0.956351i	0.0710719	−	0.265244i	0.992314	+	0.123746i	$0.0394908\pi$
$14$	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	0.692375	−	0.721538i	$-0.256564\pi$
$17$	−0.120239	−	0.120239i	−0.0291622	−	0.0291622i	−0.721538	+	0.692375i	$0.756564\pi$
$18$	2.95680	−	0.507306i	0.696923	−	0.119573i
$19$			1.88492i			0.432431i	0.976346	+	0.216216i	$0.0693714\pi$
$19$			1.88492i			0.432431i	−0.976346	+	0.216216i	$0.930629\pi$
$20$		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	−0.314299	−	0.949324i	$-0.601770\pi$
$23$	−5.08911	−	1.36362i	−1.06115	−	0.284335i	−0.746853	+	0.664989i	$0.768436\pi$
$24$	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	−0.593381	−	0.804922i	$-0.702207\pi$
$29$	2.15618	−	3.73461i	0.400392	−	0.693499i	0.993773	+	0.111422i	$0.0355406\pi$
$30$		0			0
$31$	−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	$-0.486741\pi$
$32$	0.258819	−	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	−0.922753	−	0.385393i	$-0.874066\pi$
$37$	−3.26863	+	3.26863i	−0.537360	+	0.537360i	0.385393	+	0.922753i	$0.374066\pi$
$38$	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	0.177001	−	0.984211i	$-0.443360\pi$
$41$	7.15775	−	4.13253i	1.11785	−	0.645393i	0.940852	+	0.338818i	$0.110027\pi$
$42$	3.09591	+	5.98083i	0.477709	+	0.922862i
$43$	1.99285	−	0.533983i	0.303907	−	0.0814316i	−0.103643	−	0.994615i	$-0.533050\pi$
$43$	1.99285	−	0.533983i	0.303907	−	0.0814316i	0.407550	+	0.913183i	$0.366383\pi$
$44$	−3.97361			−0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	−3.34787	+	0.897060i	−0.488338	+	0.130850i	−0.494582	−	0.869131i	$-0.664679\pi$
$47$	−3.34787	+	0.897060i	−0.488338	+	0.130850i	0.00624459	+	0.999981i	$0.498012\pi$
$48$	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	−0.912531	−	0.409007i	$-0.865875\pi$
$53$	−3.66571	+	3.66571i	−0.503524	+	0.503524i	0.409007	+	0.912531i	$0.365875\pi$
$54$	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	0.631906	−	0.775045i	$-0.282273\pi$
$59$	−2.72877	−	4.72637i	−0.355255	−	0.615320i	−0.987162	+	0.159724i	$0.948939\pi$
$60$		0			0
$61$	−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
$63$	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	−0.255942	−	0.966692i	$-0.582385\pi$
$67$	−7.86563	−	2.10759i	−0.960940	−	0.257483i	−0.704998	+	0.709209i	$0.749052\pi$
$68$	−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	$0.135293\pi$
$71$			6.94911i			0.824708i	−0.911024	+	0.412354i	$0.864707\pi$
$72$	2.30701	−	1.91774i	0.271883	−	0.226008i
$73$	8.27728	+	8.27728i	0.968783	+	0.968783i	0.999527	−	0.0307446i	$-0.00978785\pi$
$73$	8.27728	+	8.27728i	0.968783	+	0.968783i	−0.0307446	+	0.999527i	$0.509788\pi$
$74$	−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	0.984095	−	0.177641i	$-0.0568465\pi$
$79$	11.7529	+	6.78553i	1.32230	+	0.763431i	0.338206	+	0.941072i	$0.390180\pi$
$80$		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	−0.991252	−	0.131984i	$-0.957865\pi$
$83$	−1.81110	−	6.75913i	−0.198795	−	0.741911i	0.792457	−	0.609927i	$-0.208801\pi$
$84$	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	0.982794	−	0.184704i	$-0.0591325\pi$
$97$	0.387234	+	1.44518i	0.0393177	+	0.146736i	−0.943477	+	0.331439i	$0.892466\pi$
$98$	−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	−0.0143875	−	0.999896i	$-0.504580\pi$
$101$	−8.91944	−	5.14964i	−0.887517	−	0.512408i	−0.873130	+	0.487488i	$0.837913\pi$
$102$	−0.248033	−	0.158820i	−0.0245589	−	0.0157255i
$103$	−1.67823	+	6.26326i	−0.165361	+	0.617137i	0.832632	+	0.553826i	$0.186833\pi$
$103$	−1.67823	+	6.26326i	−0.165361	+	0.617137i	−0.997994	+	0.0633111i	$0.979834\pi$
$104$	−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	0.862982	−	0.505235i	$-0.168594\pi$
$107$	3.70057	+	3.70057i	0.357747	+	0.357747i	−0.505235	+	0.862982i	$0.668594\pi$
$108$	4.81427	−	1.95521i	0.463253	−	0.188140i
$109$		−	7.30160i		−	0.699367i	−0.936868	−	0.349683i	$-0.886289\pi$
$109$		−	7.30160i		−	0.699367i	0.936868	−	0.349683i	$-0.113711\pi$
$110$		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	0.445369	−	0.895347i	$-0.353072\pi$
$113$	4.07557	+	1.09205i	0.383397	+	0.102731i	−0.0619722	+	0.998078i	$0.519739\pi$
$114$	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	−0.257000	+	0.966411i	$0.582734\pi$
$127$	−13.7871	+	13.7871i	−1.22341	+	1.22341i	−0.966411	+	0.257000i	$0.917266\pi$
$128$	−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	−0.659925	−	0.751332i	$-0.729412\pi$
$131$	−3.88249	+	2.24156i	−0.339215	+	0.195846i	0.320710	+	0.947178i	$0.396079\pi$
$132$	−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	0.296888	−	0.954912i	$-0.404051\pi$
$137$	12.0729	−	3.23492i	1.03146	−	0.276378i	0.734569	+	0.678534i	$0.237384\pi$
$138$	−9.11591	−	0.419084i	−0.775998	−	0.0356748i
$139$	−3.60435	+	2.08097i	−0.305717	+	0.176506i	−0.645008	−	0.764176i	$-0.723146\pi$
$139$	−3.60435	+	2.08097i	−0.305717	+	0.176506i	0.339291	+	0.940681i	$0.389813\pi$
$140$		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	0.844016	−	0.536317i	$-0.180185\pi$
$149$	−0.518244	−	0.897625i	−0.0424562	−	0.0735363i	−0.886473	+	0.462781i	$0.846852\pi$
$150$		0			0
$151$	−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
$153$	−0.326099	−	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	0.592789	−	0.805357i	$-0.298027\pi$
$157$	8.81460	+	2.36186i	0.703481	+	0.188497i	0.110692	+	0.993855i	$0.464693\pi$
$158$	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	0.481695	−	0.876339i	$-0.340021\pi$
$163$	−5.03848	−	5.03848i	−0.394644	−	0.394644i	−0.876339	+	0.481695i	$0.840021\pi$
$164$	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	−0.768497	−	0.639853i	$-0.778995\pi$
$167$	2.80384	−	10.4641i	0.216968	−	0.809734i	0.985465	−	0.169881i	$-0.0543382\pi$
$168$	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	0.918865	−	0.394573i	$-0.129107\pi$
$173$	−0.975709	−	3.64139i	−0.0741818	−	0.276850i	−0.993047	+	0.117722i	$0.962441\pi$
$174$	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	0.862024	−	0.506868i	$-0.169197\pi$
$191$	11.8036	+	6.81478i	0.854075	+	0.493100i	−0.00794868	+	0.999968i	$0.502530\pi$
$192$	0.0795432	−	1.73022i	0.00574054	−	0.124868i
$193$	4.19397	−	15.6521i	0.301889	−	1.12666i	−0.633702	−	0.773577i	$-0.718466\pi$
$193$	4.19397	−	15.6521i	0.301889	−	1.12666i	0.935591	−	0.353086i	$-0.114868\pi$
$194$	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	0.747250	−	0.664543i	$-0.231374\pi$
$197$	1.16085	+	1.16085i	0.0827072	+	0.0827072i	−0.664543	+	0.747250i	$0.731374\pi$
$198$	−11.1830	−	4.12881i	−0.794740	−	0.293422i
$199$			17.1733i			1.21738i	0.793407	+	0.608691i	$0.208305\pi$
$199$			17.1733i			1.21738i	−0.793407	+	0.608691i	$0.791695\pi$
$200$		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	−0.988134	−	0.153597i	$-0.950914\pi$
$211$	−9.10894	−	15.7771i	−0.627085	−	1.08614i	0.361048	−	0.932547i	$-0.382419\pi$
$212$	−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	−0.103734	−	0.994605i	$-0.533079\pi$
$223$	4.53570	−	1.21534i	0.303733	−	0.0813849i	0.407466	+	0.913220i	$0.366412\pi$
$224$	3.88823			0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	−24.1784	+	6.47859i	−1.60478	+	0.429999i	−0.946481	−	0.322759i	$-0.895390\pi$
$227$	−24.1784	+	6.47859i	−1.60478	+	0.429999i	−0.658297	+	0.752758i	$0.728723\pi$
$228$	1.50082	+	2.89937i	0.0993945	+	0.192015i
$229$	19.7350	−	11.3940i	1.30412	−	0.752935i	0.323014	−	0.946394i	$-0.395304\pi$
$229$	19.7350	−	11.3940i	1.30412	−	0.752935i	0.981108	+	0.193459i	$0.0619706\pi$
$230$		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	0.470214	−	0.882553i	$-0.344177\pi$
$233$	20.6491	−	20.6491i	1.35277	−	1.35277i	0.882553	−	0.470214i	$-0.155823\pi$
$234$	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	0.975018	−	0.222127i	$-0.0713000\pi$
$239$	4.56277	+	7.90295i	0.295141	+	0.511199i	−0.679877	+	0.733327i	$0.737967\pi$
$240$		0			0
$241$	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
$243$	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	$0.0623555\pi$
$251$			6.16751i			0.389290i	−0.980874	+	0.194645i	$0.937645\pi$
$252$	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	0.174018	+	0.984743i	$0.444325\pi$
$257$	−7.51956	+	28.0634i	−0.469057	+	1.75055i	−0.643075	+	0.765803i	$0.722342\pi$
$258$	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	0.938956	+	0.344038i	$0.111795\pi$
$263$	4.82975	+	18.0249i	0.297815	+	1.11146i	−0.641141	+	0.767424i	$0.721538\pi$
$264$	−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	0.990579	−	0.136940i	$-0.0437267\pi$
$277$	1.06921	+	3.99035i	0.0642426	+	0.239757i	−0.926337	+	0.376696i	$0.877060\pi$
$278$	−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	0.507398	−	0.861712i	$-0.330607\pi$
$281$	0.248640	+	0.143552i	0.0148326	+	0.00856361i	−0.492565	+	0.870275i	$0.663941\pi$
$282$	−5.33132	+	2.75970i	−0.317476	+	0.164338i
$283$	4.68527	−	17.4857i	0.278510	−	1.03941i	−0.674942	−	0.737871i	$-0.735831\pi$
$283$	4.68527	−	17.4857i	0.278510	−	1.03941i	0.953452	−	0.301544i	$-0.0975019\pi$
$284$	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	−0.401621	−	0.915806i	$-0.631553\pi$
$293$	−20.6663	−	5.53752i	−1.20734	−	0.323505i	−0.805717	+	0.592300i	$0.798220\pi$
$294$	−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	0.173476	−	0.984838i	$-0.444500\pi$
$307$	20.2953	−	20.2953i	1.15831	−	1.15831i	0.984838	−	0.173476i	$-0.0555001\pi$
$308$	−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	−0.799745	−	0.600340i	$-0.795032\pi$
$311$	−11.9868	+	6.92056i	−0.679707	+	0.392429i	0.120038	+	0.992769i	$0.461698\pi$
$312$	−0.788332	−	1.52294i	−0.0446305	−	0.0862196i
$313$	−17.9081	+	4.79847i	−1.01223	+	0.271226i	−0.726560	−	0.687103i	$-0.758882\pi$
$313$	−17.9081	+	4.79847i	−1.01223	+	0.271226i	−0.285668	+	0.958329i	$0.592215\pi$
$314$	9.12554			0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	−0.811966	+	0.217566i	−0.0456046	+	0.0122197i	−0.281549	−	0.959547i	$-0.590848\pi$
$317$	−0.811966	+	0.217566i	−0.0456046	+	0.0122197i	0.235945	+	0.971766i	$0.424182\pi$
$318$	−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	−0.803114	−	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
$333$	−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	0.172341	−	0.985037i	$-0.444867\pi$
$337$	−3.13777	−	0.840764i	−0.170925	−	0.0457993i	−0.343267	+	0.939238i	$0.611533\pi$
$338$	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	−0.990835	−	0.135076i	$-0.956872\pi$
$347$	−1.21470	+	4.53334i	−0.0652087	+	0.243362i	0.925627	+	0.378438i	$0.123539\pi$
$348$	0.343019	−	7.46134i	0.0183877	−	0.399970i
$349$	8.42818	+	4.86601i	0.451150	+	0.260472i	0.708316	−	0.705896i	$-0.249455\pi$
$349$	8.42818	+	4.86601i	0.451150	+	0.260472i	−0.257166	+	0.966367i	$0.582789\pi$
$350$		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	0.992122	−	0.125273i	$-0.0399806\pi$
$353$	1.32049	+	4.92815i	0.0702827	+	0.262299i	−0.921840	+	0.387572i	$0.873314\pi$
$354$	−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	0.999989	+	0.00460117i	$0.00146460\pi$
$367$	2.61063	+	9.74300i	0.136274	+	0.508581i	−0.863716	+	0.503979i	$0.831869\pi$
$368$	−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	−0.820706	−	0.571350i	$-0.806420\pi$
$373$	3.39374	−	12.6656i	0.175721	−	0.655801i	0.996428	−	0.0844507i	$-0.0269135\pi$
$374$	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	$-0.995196\pi$
$379$		−	0.587648i		−	0.0301854i	0.999886	−	0.0150927i	$-0.00480434\pi$
$380$		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	−0.117464	−	0.993077i	$-0.537476\pi$
$383$	−14.0071	−	3.75319i	−0.715729	−	0.191779i	−0.598265	+	0.801298i	$0.704143\pi$
$384$	−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	0.473303	+	0.880899i	$0.343061\pi$
$389$	−10.3789	+	17.9767i	−0.526230	+	0.911456i	−0.999533	+	0.0305570i	$0.990272\pi$
$390$		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	−0.981513	−	0.191395i	$-0.938699\pi$
$397$	−15.7430	+	15.7430i	−0.790118	+	0.790118i	0.191395	+	0.981513i	$0.438699\pi$
$398$	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	−0.393659	−	0.919257i	$-0.628791\pi$
$401$	4.11737	−	2.37716i	0.205612	−	0.118710i	0.599270	+	0.800547i	$0.295457\pi$
$402$	−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	−0.976787	−	0.214211i	$-0.931282\pi$
$409$	−25.8797	+	14.9417i	−1.27967	+	0.738817i	−0.302882	+	0.953028i	$0.597949\pi$
$410$		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	0.996934	−	0.0782412i	$-0.0249304\pi$
$419$	8.81638	+	15.2704i	0.430708	+	0.746009i	−0.566226	+	0.824250i	$0.691597\pi$
$420$		0			0
$421$	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
$423$	−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	$0.153805\pi$
$431$			19.2910i			0.929215i	−0.885517	+	0.464608i	$0.846195\pi$
$432$	3.19168	−	4.10039i	0.153560	−	0.197280i
$433$	−16.7154	−	16.7154i	−0.803292	−	0.803292i	0.180316	−	0.983609i	$-0.442288\pi$
$433$	−16.7154	−	16.7154i	−0.803292	−	0.803292i	−0.983609	+	0.180316i	$0.942288\pi$
$434$	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	−0.488285	−	0.872684i	$-0.662377\pi$
$439$	−31.1811	−	18.0024i	−1.48819	−	0.859209i	−0.999909	+	0.0134750i	$0.995711\pi$
$440$		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	0.909218	+	0.416320i	$0.136680\pi$
$443$	6.94511	+	25.9195i	0.329972	+	1.23147i	−0.579246	+	0.815153i	$0.696653\pi$
$444$	−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	−0.964412	−	0.264403i	$-0.914825\pi$
$457$	−5.58827	−	20.8557i	−0.261408	−	0.975589i	0.703004	−	0.711186i	$-0.251842\pi$
$458$	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	0.225015	−	0.974355i	$-0.427757\pi$
$461$	−10.8706	−	6.27615i	−0.506295	−	0.292309i	−0.731309	+	0.682046i	$0.761090\pi$
$462$	1.22897	−	26.7325i	0.0571767	−	1.24371i
$463$	−5.72110	+	21.3514i	−0.265882	+	0.992286i	0.695826	+	0.718210i	$0.255038\pi$
$463$	−5.72110	+	21.3514i	−0.265882	+	0.992286i	−0.961708	+	0.274076i	$0.911628\pi$
$464$	−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	0.621955	−	0.783053i	$-0.286339\pi$
$467$	−3.48137	−	3.48137i	−0.161099	−	0.161099i	−0.783053	+	0.621955i	$0.786339\pi$
$468$	−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	−0.895355	−	0.445353i	$-0.853078\pi$
$479$	−1.35673	+	2.34993i	−0.0619906	+	0.107371i	0.833364	+	0.552724i	$0.186412\pi$
$480$		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	−0.496244	−	0.868183i	$-0.665288\pi$
$487$	8.20799	−	8.20799i	0.371940	−	0.371940i	0.868183	+	0.496244i	$0.165288\pi$
$488$	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	−0.400290	−	0.916388i	$-0.631091\pi$
$491$	4.28058	−	2.47139i	0.193180	−	0.111532i	0.593470	+	0.804856i	$0.297757\pi$
$492$	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	0.285791	−	0.958292i	$-0.407744\pi$
$499$	28.1148	−	16.2321i	1.25859	−	0.726649i	0.972801	+	0.231643i	$0.0744102\pi$
$500$		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	−0.993282	−	0.115717i	$-0.963083\pi$
$503$	−19.6817	+	19.6817i	−0.877565	+	0.877565i	0.115717	+	0.993282i	$0.463083\pi$
$504$	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	0.725879	−	0.687823i	$-0.241433\pi$
$509$	−5.25069	−	9.09446i	−0.232733	−	0.403105i	−0.958611	+	0.284718i	$0.908100\pi$
$510$		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	$-0.787568\pi$
$521$		−	28.2545i		−	1.23785i	0.785450	−	0.618925i	$-0.212432\pi$
$522$	4.48079	−	12.1363i	0.196119	−	0.531192i
$523$	−13.6590	−	13.6590i	−0.597266	−	0.597266i	0.342318	−	0.939584i	$-0.388788\pi$
$523$	−13.6590	−	13.6590i	−0.597266	−	0.597266i	−0.939584	+	0.342318i	$0.888788\pi$
$524$	−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	0.964571	−	0.263823i	$-0.0849836\pi$
$547$	−0.0627654	−	0.234244i	−0.00268365	−	0.0100155i	−0.967255	+	0.253808i	$0.918317\pi$
$548$	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	−0.901746	−	0.432266i	$-0.857714\pi$
$557$	−31.4838	−	31.4838i	−1.33401	−	1.33401i	−0.432266	−	0.901746i	$-0.642286\pi$
$558$	−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	−0.467247	−	0.884127i	$-0.654754\pi$
$563$	−31.1771	−	8.35388i	−1.31396	−	0.352074i	−0.846711	+	0.532053i	$0.821421\pi$
$564$	−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	0.298580	+	0.954385i	$0.403487\pi$
$569$	−16.1545	+	27.9804i	−0.677232	+	1.17300i	−0.975811	+	0.218615i	$0.929846\pi$
$570$		0			0
$571$	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	$0.650920\pi$
$572$	−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	−0.822710	−	0.568462i	$-0.807539\pi$
$577$	−6.10724	+	6.10724i	−0.254248	+	0.254248i	0.568462	+	0.822710i	$0.307539\pi$
$578$	−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	−0.296392	−	0.955066i	$-0.595784\pi$
$587$	−1.83025	+	0.490414i	−0.0755424	+	0.0202415i	0.220850	+	0.975308i	$0.429117\pi$
$588$	−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	−0.443996	−	0.896029i	$-0.646439\pi$
$593$	11.0077	−	11.0077i	0.452033	−	0.452033i	0.896029	+	0.443996i	$0.146439\pi$
$594$	−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	−0.999435	−	0.0336142i	$-0.989298\pi$
$599$	−12.9428	−	22.4176i	−0.528828	−	0.915957i	0.470607	−	0.882343i	$-0.344035\pi$
$600$		0			0
$601$	−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
$603$	−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	0.790102	−	0.612975i	$-0.210027\pi$
$607$	28.7731	+	7.70972i	1.16786	+	0.312928i	0.377761	+	0.925903i	$0.376694\pi$
$608$	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	0.912982	−	0.408000i	$-0.133774\pi$
$613$	12.5028	+	12.5028i	0.504982	+	0.504982i	−0.408000	+	0.912982i	$0.633774\pi$
$614$	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	−0.916611	−	0.399781i	$-0.869086\pi$
$617$	1.91482	−	7.14621i	0.0770878	−	0.287695i	0.993699	+	0.112085i	$0.0357530\pi$
$618$	−0.515774	+	11.2191i	−0.0207475	+	0.451299i
$619$	16.4624	+	9.50460i	0.661682	+	0.382022i	0.792917	−	0.609329i	$-0.208561\pi$
$619$	16.4624	+	9.50460i	0.661682	+	0.382022i	−0.131236	+	0.991351i	$0.541895\pi$
$620$		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	0.999978	−	0.00667968i	$-0.00212622\pi$
$641$	37.8297	+	21.8410i	1.49418	+	0.862666i	0.494204	+	0.869346i	$0.335460\pi$
$642$	7.63367	+	4.88798i	0.301277	+	0.192913i
$643$	7.89483	−	29.4639i	0.311342	−	1.16194i	−0.616006	−	0.787742i	$-0.711250\pi$
$643$	7.89483	−	29.4639i	0.311342	−	1.16194i	0.927347	−	0.374202i	$-0.122083\pi$
$644$	−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	0.781812	−	0.623514i	$-0.214296\pi$
$647$	4.02651	+	4.02651i	0.158298	+	0.158298i	−0.623514	+	0.781812i	$0.714296\pi$
$648$	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	0.815650	−	0.578546i	$-0.196380\pi$
$653$	31.5015	+	8.44081i	1.23275	+	0.330314i	0.417100	+	0.908861i	$0.363046\pi$
$654$	−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	−0.674484	−	0.738290i	$-0.735634\pi$
$659$	7.75612	−	13.4340i	0.302136	−	0.523314i	0.976619	+	0.214975i	$0.0689671\pi$
$660$		0			0
$661$	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	$0.690812\pi$
$662$	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	−0.0745413	−	0.997218i	$-0.523749\pi$
$673$	9.32657	−	2.49905i	0.359513	−	0.0963312i	0.434054	+	0.900887i	$0.357083\pi$
$674$	−3.24846			−0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	−7.30994	+	1.95869i	−0.280944	+	0.0752787i	−0.396539	−	0.918018i	$-0.629789\pi$
$677$	−7.30994	+	1.95869i	−0.280944	+	0.0752787i	0.115596	+	0.993296i	$0.463122\pi$
$678$	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	−0.835625	−	0.549300i	$-0.814894\pi$
$683$	−7.48288	+	7.48288i	−0.286325	+	0.286325i	0.549300	+	0.835625i	$0.314894\pi$
$684$	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	−0.101975	−	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
$693$	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	$-0.759079\pi$
$701$		−	36.3602i		−	1.37331i	0.726985	−	0.686653i	$-0.240921\pi$
$702$	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	0.493288	−	0.869866i	$-0.335795\pi$
$709$	−0.356646	−	0.205910i	−0.0133941	−	0.00773310i	−0.506682	+	0.862133i	$0.669128\pi$
$710$		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	−0.999981	−	0.00614188i	$-0.998045\pi$
$727$	−3.69508	−	13.7902i	−0.137043	−	0.511451i	0.862938	−	0.505310i	$-0.168622\pi$
$728$	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	0.648690	+	0.761053i	$0.275317\pi$
$733$	−7.94942	+	29.6676i	−0.293618	+	1.09580i	−0.942308	+	0.334746i	$0.891349\pi$
$734$	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	$0.117589\pi$
$739$			19.6312i			0.722144i	−0.932538	+	0.361072i	$0.882411\pi$
$740$		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	0.832130	−	0.554580i	$-0.187121\pi$
$743$	34.7672	+	9.31585i	1.27549	+	0.341765i	0.443356	+	0.896346i	$0.353788\pi$
$744$	−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	−0.836944	−	0.547289i	$-0.815660\pi$
$751$	−24.4567	−	42.3603i	−0.892438	−	1.54575i	−0.0554938	−	0.998459i	$-0.517673\pi$
$752$	−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	−0.987897	−	0.155114i	$-0.950426\pi$
$757$	−22.9129	+	22.9129i	−0.832783	+	0.832783i	0.155114	+	0.987897i	$0.450426\pi$
$758$	−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	−0.657253	−	0.753670i	$-0.728282\pi$
$761$	−9.19124	+	5.30657i	−0.333182	+	0.192363i	0.324071	+	0.946033i	$0.394948\pi$
$762$	−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	−0.558633	−	0.829415i	$-0.688674\pi$
$769$	−3.31814	+	1.91573i	−0.119655	+	0.0690830i	0.438978	+	0.898498i	$0.355341\pi$
$770$		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	−0.967715	−	0.252047i	$-0.918896\pi$
$773$	−19.8976	+	19.8976i	−0.715668	+	0.715668i	0.252047	+	0.967715i	$0.418896\pi$
$774$	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	0.132171	−	0.991227i	$-0.457805\pi$
$787$	−6.98473	−	1.87155i	−0.248979	−	0.0667137i	−0.381150	+	0.924513i	$0.624472\pi$
$788$	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	−0.604366	−	0.796707i	$-0.706573\pi$
$797$	8.96012	−	33.4396i	0.317384	−	1.18449i	0.921750	−	0.387786i	$-0.126760\pi$
$798$	−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	0.0196338	−	0.999807i	$-0.493750\pi$
$821$	−23.9657	−	13.8366i	−0.836408	−	0.482900i	−0.856042	+	0.516907i	$0.827083\pi$
$822$	19.2255	−	9.95185i	0.670566	−	0.347111i
$823$	7.80049	−	29.1118i	0.271908	−	1.01477i	−0.685977	−	0.727623i	$-0.740625\pi$
$823$	7.80049	−	29.1118i	0.271908	−	1.01477i	0.957885	−	0.287151i	$-0.0927083\pi$
$824$	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	0.632245	−	0.774768i	$-0.282134\pi$
$827$	−4.09863	−	4.09863i	−0.142523	−	0.142523i	−0.774768	+	0.632245i	$0.782134\pi$
$828$	−15.5783	+	2.67281i	−0.541382	+	0.0928865i
$829$			37.6756i			1.30853i	0.756266	+	0.654264i	$0.227021\pi$
$829$			37.6756i			1.30853i	−0.756266	+	0.654264i	$0.772979\pi$
$830$		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	−0.424527	−	0.905415i	$-0.639560\pi$
$839$	16.5639	−	28.6895i	0.571849	−	0.990471i	0.996376	−	0.0850559i	$-0.0271069\pi$
$840$		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	−0.214486	−	0.976727i	$-0.568808\pi$
$853$	2.57386	−	0.689663i	0.0881273	−	0.0236136i	0.302613	+	0.953113i	$0.402141\pi$
$854$	−33.8760			−1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	−15.1284	+	4.05364i	−0.516776	+	0.138470i	−0.507775	−	0.861490i	$-0.669532\pi$
$857$	−15.1284	+	4.05364i	−0.516776	+	0.138470i	−0.00900123	+	0.999959i	$0.502865\pi$
$858$	−3.67455	+	5.73863i	−0.125447	+	0.195914i
$859$	0.691191	−	0.399059i	0.0235831	−	0.0136157i	−0.488162	−	0.872753i	$-0.662333\pi$
$859$	0.691191	−	0.399059i	0.0235831	−	0.0136157i	0.511745	+	0.859137i	$0.328999\pi$
$860$		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	−0.0314193	+	0.999506i	$0.510003\pi$
$863$	−30.2854	+	30.2854i	−1.03093	+	1.03093i	−0.999506	+	0.0314193i	$0.989997\pi$
$864$	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	0.530180	−	0.847885i	$-0.322124\pi$
$877$	16.7435	+	4.48641i	0.565388	+	0.151495i	0.0352074	+	0.999380i	$0.488791\pi$
$878$	−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	$-0.918115\pi$
$881$		−	15.1033i		−	0.508843i	0.967093	−	0.254421i	$-0.0818850\pi$
$882$	−18.7290	+	15.5688i	−0.630639	+	0.524229i
$883$	16.4678	+	16.4678i	0.554185	+	0.554185i	0.927646	−	0.373461i	$-0.121829\pi$
$883$	16.4678	+	16.4678i	0.554185	+	0.554185i	−0.373461	+	0.927646i	$0.621829\pi$
$884$	−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	0.739320	+	0.673355i	$0.235147\pi$
$887$	−7.07714	+	26.4123i	−0.237627	+	0.886837i	−0.976947	+	0.213482i	$0.931519\pi$
$888$	−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	−0.984338	−	0.176290i	$-0.943590\pi$
$907$	−6.62626	−	24.7295i	−0.220021	−	0.821130i	0.764317	−	0.644841i	$-0.223076\pi$
$908$	−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	0.557666	−	0.830065i	$-0.311697\pi$
$911$	3.55075	+	2.05003i	0.117642	+	0.0679204i	−0.440025	+	0.897986i	$0.645030\pi$
$912$	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	$-0.842002\pi$
$919$		−	28.8740i		−	0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$920$		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	0.0791067	+	0.996866i	$0.474793\pi$
$929$	−25.1077	+	43.4879i	−0.823758	+	1.42679i	−0.902865	+	0.429925i	$0.858540\pi$
$930$		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	−0.692968	−	0.720968i	$-0.743697\pi$
$937$	0.857094	−	0.857094i	0.0280000	−	0.0280000i	0.720968	+	0.692968i	$0.243697\pi$
$938$	−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	−0.995977	−	0.0896119i	$-0.971437\pi$
$941$	−43.4478	+	25.0846i	−1.41636	+	0.817735i	−0.420382	+	0.907347i	$0.638104\pi$
$942$	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	−0.299906	−	0.953969i	$-0.596955\pi$
$947$	−2.54334	+	0.681485i	−0.0826473	+	0.0221453i	0.217258	+	0.976114i	$0.430289\pi$
$948$	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	−0.0845545	−	0.996419i	$-0.526947\pi$
$953$	28.1499	−	28.1499i	0.911864	−	0.911864i	0.996419	+	0.0845545i	$0.0269467\pi$
$954$	−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	0.238128	−	0.971234i	$-0.423466\pi$
$967$	−1.28319	−	0.343829i	−0.0412646	−	0.0110568i	−0.279392	+	0.960177i	$0.590133\pi$
$968$	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	$0.213853\pi$
$971$			38.7906i			1.24485i	−0.782679	+	0.622425i	$0.786147\pi$
$972$	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	0.525548	+	0.850764i	$0.323860\pi$
$977$	−11.0953	+	41.4084i	−0.354972	+	1.32477i	−0.880520	+	0.474009i	$0.842807\pi$
$978$	−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	−0.961597	−	0.274466i	$-0.911499\pi$
$983$	−8.34182	−	31.1321i	−0.266063	−	0.992960i	0.695534	−	0.718493i	$-0.255168\pi$
$984$	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	0.952783	−	0.303653i	$-0.0982063\pi$
$997$	−0.763421	−	2.84912i	−0.0241778	−	0.0902327i	−0.976960	+	0.213420i	$0.931540\pi$
$998$	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.443.4		16
3.2	odd	2		1350.2.q.h.143.2		16
5.2	odd	4	inner	450.2.p.h.407.4		16
5.3	odd	4		90.2.l.b.47.1	yes	16
5.4	even	2		90.2.l.b.83.1	yes	16
9.4	even	3		1350.2.q.h.1043.1		16
9.5	odd	6	inner	450.2.p.h.293.4		16
15.2	even	4		1350.2.q.h.1007.1		16
15.8	even	4		270.2.m.b.197.3		16
15.14	odd	2		270.2.m.b.143.4		16
20.3	even	4		720.2.cu.b.497.3		16
20.19	odd	2		720.2.cu.b.353.4		16
45.4	even	6		270.2.m.b.233.3		16
45.13	odd	12		270.2.m.b.17.4		16
45.14	odd	6		90.2.l.b.23.1	✓	16
45.22	odd	12		1350.2.q.h.557.2		16
45.23	even	12		90.2.l.b.77.1	yes	16
45.29	odd	6		810.2.f.c.323.1		16
45.32	even	12	inner	450.2.p.h.257.4		16
45.34	even	6		810.2.f.c.323.8		16
45.38	even	12		810.2.f.c.647.8		16
45.43	odd	12		810.2.f.c.647.1		16
180.23	odd	12		720.2.cu.b.257.4		16
180.59	even	6		720.2.cu.b.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	45.14	odd	6
90.2.l.b.47.1	yes	16	5.3	odd	4
90.2.l.b.77.1	yes	16	45.23	even	12
90.2.l.b.83.1	yes	16	5.4	even	2
270.2.m.b.17.4		16	45.13	odd	12
270.2.m.b.143.4		16	15.14	odd	2
270.2.m.b.197.3		16	15.8	even	4
270.2.m.b.233.3		16	45.4	even	6
450.2.p.h.257.4		16	45.32	even	12	inner
450.2.p.h.293.4		16	9.5	odd	6	inner
450.2.p.h.407.4		16	5.2	odd	4	inner
450.2.p.h.443.4		16	1.1	even	1	trivial
720.2.cu.b.113.3		16	180.59	even	6
720.2.cu.b.257.4		16	180.23	odd	12
720.2.cu.b.353.4		16	20.19	odd	2
720.2.cu.b.497.3		16	20.3	even	4
810.2.f.c.323.1		16	45.29	odd	6
810.2.f.c.323.8		16	45.34	even	6
810.2.f.c.647.1		16	45.43	odd	12
810.2.f.c.647.8		16	45.38	even	12
1350.2.q.h.143.2		16	3.2	odd	2
1350.2.q.h.557.2		16	45.22	odd	12
1350.2.q.h.1007.1		16	15.2	even	4
1350.2.q.h.1043.1		16	9.4	even	3

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more