LMFDB - Embedded newform 450.2.p.h.293.4

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			293.4
Root			$0.500000 - 0.410882i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.h.407.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.69185 + 0.370982i) q^{6} +(-3.75574 - 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.69185 + 0.370982i) q^{6} +(-3.75574 - 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +(-3.44125 + 1.98681i) q^{11} +(0.796225 - 1.53819i) q^{12} +(-0.956351 + 0.256253i) q^{13} +(-1.94411 + 3.36730i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +(-0.507306 + 2.95680i) q^{18} +1.88492i q^{19} +(1.44246 - 6.57832i) q^{21} +(1.02845 + 3.83821i) q^{22} +(-1.36362 - 5.08911i) q^{23} +(-1.27970 - 1.16721i) q^{24} +0.990087i q^{26} +(-0.713876 - 5.14688i) q^{27} +(2.74939 + 2.74939i) q^{28} +(-2.15618 - 3.73461i) q^{29} +(-4.70172 + 8.14362i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-3.71134 - 5.79609i) q^{33} +(0.147262 - 0.0850217i) q^{34} +(2.72474 + 1.25529i) q^{36} +(-3.26863 + 3.26863i) q^{37} +(1.82070 + 0.487854i) q^{38} +(-0.519447 - 1.63432i) q^{39} +(7.15775 + 4.13253i) q^{41} +(-5.98083 - 3.09591i) q^{42} +(-0.533983 + 1.99285i) q^{43} +3.97361 q^{44} -5.26863 q^{46} +(-0.897060 + 3.34787i) q^{47} +(-1.45865 + 0.933998i) q^{48} +(7.03067 + 4.05916i) q^{49} +(-0.198476 + 0.217604i) q^{51} +(0.956351 + 0.256253i) q^{52} +(3.66571 - 3.66571i) q^{53} +(-5.15627 - 0.642559i) q^{54} +(3.36730 - 1.94411i) q^{56} +(-3.26134 + 0.149933i) q^{57} +(-4.16541 + 1.11612i) q^{58} +(2.72877 - 4.72637i) q^{59} +(-4.35623 - 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} +(11.4967 + 1.97252i) q^{63} -1.00000i q^{64} +(-6.55916 + 2.08475i) q^{66} +(2.10759 + 7.86563i) q^{67} +(-0.0440105 - 0.164249i) q^{68} +(8.69683 - 2.76418i) q^{69} -6.94911i q^{71} +(1.91774 - 2.30701i) q^{72} +(8.27728 + 8.27728i) q^{73} +(2.31127 + 4.00324i) q^{74} +(0.942462 - 1.63239i) q^{76} +(14.9238 - 3.99883i) q^{77} +(-1.71307 + 0.0787547i) q^{78} +(-11.7529 + 6.78553i) q^{79} +(8.84847 - 1.64456i) q^{81} +(5.84428 - 5.84428i) q^{82} +(-6.75913 - 1.81110i) q^{83} +(-4.53837 + 4.97576i) q^{84} +(1.78674 + 1.03157i) q^{86} +(6.29020 - 4.02773i) q^{87} +(1.02845 - 3.83821i) q^{88} +4.87832 q^{89} +3.84968 q^{91} +(-1.36362 + 5.08911i) q^{92} +(-14.4643 - 7.48725i) q^{93} +(3.00162 + 1.73299i) q^{94} +(0.524648 + 1.65068i) q^{96} +(-1.44518 - 0.387234i) q^{97} +(5.74052 - 5.74052i) q^{98} +(9.73332 - 6.88249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.69185	+	0.370982i	0.690697	+	0.151453i
$7$	−3.75574	−	1.00635i	−1.41954	−	0.380364i	−0.534217	−	0.845347i	$-0.679394\pi$
$7$	−3.75574	−	1.00635i	−1.41954	−	0.380364i	−0.885319	+	0.464984i	$0.846060\pi$
$8$	−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	$0.537786\pi$
$12$	0.796225	−	1.53819i	0.229850	−	0.444037i
$13$	−0.956351	+	0.256253i	−0.265244	+	0.0710719i	−0.388990	−	0.921242i	$-0.627176\pi$
$13$	−0.956351	+	0.256253i	−0.265244	+	0.0710719i	0.123746	+	0.992314i	$0.460509\pi$
$14$	−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	$-0.243436\pi$
$17$	0.120239	+	0.120239i	0.0291622	+	0.0291622i	−0.692375	+	0.721538i	$0.743436\pi$
$18$	−0.507306	+	2.95680i	−0.119573	+	0.696923i
$19$			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
$22$	1.02845	+	3.83821i	0.219265	+	0.818310i
$23$	−1.36362	−	5.08911i	−0.284335	−	1.06115i	−0.949324	−	0.314299i	$-0.898230\pi$
$23$	−1.36362	−	5.08911i	−0.284335	−	1.06115i	0.664989	−	0.746853i	$-0.268436\pi$
$24$	−1.27970	−	1.16721i	−0.261217	−	0.238255i
$25$		0			0
$26$			0.990087i			0.194172i
$27$	−0.713876	−	5.14688i	−0.137386	−	0.990518i
$28$	2.74939	+	2.74939i	0.519586	+	0.519586i
$29$	−2.15618	−	3.73461i	−0.400392	−	0.693499i	0.593381	−	0.804922i	$-0.297793\pi$
$29$	−2.15618	−	3.73461i	−0.400392	−	0.693499i	−0.993773	+	0.111422i	$0.964459\pi$
$30$		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	$0.846592\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−3.71134	−	5.79609i	−0.646062	−	1.00897i
$34$	0.147262	−	0.0850217i	0.0252552	−	0.0145811i
$35$		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	$0.374066\pi$
$38$	1.82070	+	0.487854i	0.295356	+	0.0791404i
$39$	−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	$0.443360\pi$
$42$	−5.98083	−	3.09591i	−0.922862	−	0.477709i
$43$	−0.533983	+	1.99285i	−0.0814316	+	0.303907i	−0.994615	−	0.103643i	$-0.966950\pi$
$43$	−0.533983	+	1.99285i	−0.0814316	+	0.303907i	0.913183	+	0.407550i	$0.133617\pi$
$44$	3.97361			0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	−0.897060	+	3.34787i	−0.130850	+	0.488338i	−0.999981	−	0.00624459i	$-0.998012\pi$
$47$	−0.897060	+	3.34787i	−0.130850	+	0.488338i	0.869131	+	0.494582i	$0.164679\pi$
$48$	−1.45865	+	0.933998i	−0.210537	+	0.134811i
$49$	7.03067	+	4.05916i	1.00438	+	0.579880i
$50$		0			0
$51$	−0.198476	+	0.217604i	−0.0277922	+	0.0304707i
$52$	0.956351	+	0.256253i	0.132622	+	0.0355359i
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	−0.409007	−	0.912531i	$-0.634125\pi$
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	0.912531	+	0.409007i	$0.134125\pi$
$54$	−5.15627	−	0.642559i	−0.701679	−	0.0874413i
$55$		0			0
$56$	3.36730	−	1.94411i	0.449975	−	0.259793i
$57$	−3.26134	+	0.149933i	−0.431975	+	0.0198591i
$58$	−4.16541	+	1.11612i	−0.546946	+	0.146554i
$59$	2.72877	−	4.72637i	0.355255	−	0.615320i	−0.631906	−	0.775045i	$-0.717727\pi$
$59$	2.72877	−	4.72637i	0.355255	−	0.615320i	0.987162	+	0.159724i	$0.0510606\pi$
$60$		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
$63$	11.4967	+	1.97252i	1.44845	+	0.248514i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−6.55916	+	2.08475i	−0.807377	+	0.256614i
$67$	2.10759	+	7.86563i	0.257483	+	0.960940i	0.966692	+	0.255942i	$0.0823855\pi$
$67$	2.10759	+	7.86563i	0.257483	+	0.960940i	−0.709209	+	0.704998i	$0.750948\pi$
$68$	−0.0440105	−	0.164249i	−0.00533705	−	0.0199182i
$69$	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	$-0.135293\pi$
$72$	1.91774	−	2.30701i	0.226008	−	0.271883i
$73$	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
$77$	14.9238	−	3.99883i	1.70073	−	0.455709i
$78$	−1.71307	+	0.0787547i	−0.193967	+	0.00891722i
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.984095	−	0.177641i	$-0.943153\pi$
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.338206	+	0.941072i	$0.609820\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$	5.84428	−	5.84428i	0.645393	−	0.645393i
$83$	−6.75913	−	1.81110i	−0.741911	−	0.198795i	−0.131984	−	0.991252i	$-0.542135\pi$
$83$	−6.75913	−	1.81110i	−0.741911	−	0.198795i	−0.609927	+	0.792457i	$0.708801\pi$
$84$	−4.53837	+	4.97576i	−0.495176	+	0.542900i
$85$		0			0
$86$	1.78674	+	1.03157i	0.192669	+	0.111238i
$87$	6.29020	−	4.02773i	0.674380	−	0.431818i
$88$	1.02845	−	3.83821i	0.109633	−	0.409155i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	3.84968			0.403557
$92$	−1.36362	+	5.08911i	−0.142168	+	0.530576i
$93$	−14.4643	−	7.48725i	−1.49987	−	0.776392i
$94$	3.00162	+	1.73299i	0.309594	+	0.178744i
$95$		0			0
$96$	0.524648	+	1.65068i	0.0535466	+	0.168472i
$97$	−1.44518	−	0.387234i	−0.146736	−	0.0393177i	0.184704	−	0.982794i	$-0.440868\pi$
$97$	−1.44518	−	0.387234i	−0.146736	−	0.0393177i	−0.331439	+	0.943477i	$0.607534\pi$
$98$	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	$0.504580\pi$
$102$	0.158820	+	0.248033i	0.0157255	+	0.0245589i
$103$	6.26326	−	1.67823i	0.617137	−	0.165361i	0.0633111	−	0.997994i	$-0.479834\pi$
$103$	6.26326	−	1.67823i	0.617137	−	0.165361i	0.553826	+	0.832632i	$0.313167\pi$
$104$	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	$-0.331406\pi$
$107$	−3.70057	−	3.70057i	−0.357747	−	0.357747i	−0.862982	+	0.505235i	$0.831406\pi$
$108$	−1.95521	+	4.81427i	−0.188140	+	0.463253i
$109$		−	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
$112$	−1.00635	−	3.75574i	−0.0950909	−	0.354884i
$113$	1.09205	+	4.07557i	0.102731	+	0.383397i	0.998078	−	0.0619722i	$-0.0197390\pi$
$113$	1.09205	+	4.07557i	0.102731	+	0.383397i	−0.895347	+	0.445369i	$0.853072\pi$
$114$	−0.699273	+	3.18902i	−0.0654929	+	0.298679i
$115$		0			0
$116$			4.31235i			0.400392i
$117$	2.78641	−	1.02876i	0.257604	−	0.0951087i
$118$	−3.85906	−	3.85906i	−0.355255	−	0.355255i
$119$	−0.330584	−	0.572588i	−0.0303046	−	0.0524891i
$120$		0			0
$121$	2.39479	−	4.14790i	0.217708	−	0.377081i
$122$	−8.41558	+	2.25495i	−0.761911	+	0.204153i
$123$	−6.58085	+	12.7132i	−0.593375	+	1.14631i
$124$	8.14362	−	4.70172i	0.731318	−	0.422227i
$125$		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	$0.917266\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−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	$0.729412\pi$
$132$	0.316074	+	6.87523i	0.0275107	+	0.598412i
$133$	1.89689	−	7.07929i	0.164481	−	0.613852i
$134$	8.14310			0.703457
$135$		0			0
$136$	−0.170043			−0.0145811
$137$	3.23492	−	12.0729i	0.276378	−	1.03146i	−0.678534	−	0.734569i	$-0.737384\pi$
$137$	3.23492	−	12.0729i	0.276378	−	1.03146i	0.954912	−	0.296888i	$-0.0959489\pi$
$138$	−0.419084	−	9.11591i	−0.0356748	−	0.775998i
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	0.645008	−	0.764176i	$-0.276854\pi$
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	−0.339291	+	0.940681i	$0.610187\pi$
$140$		0			0
$141$	−5.86393	−	1.28581i	−0.493832	−	0.108285i
$142$	−6.71233	−	1.79856i	−0.563286	−	0.150932i
$143$	2.78191	−	2.78191i	0.232635	−	0.232635i
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$		0			0
$146$	10.1376	−	5.85292i	0.838990	−	0.484391i
$147$	−6.46401	+	12.4875i	−0.533143	+	1.02995i
$148$	4.46504	−	1.19640i	0.367024	−	0.0983437i
$149$	0.518244	−	0.897625i	0.0424562	−	0.0735363i	−0.844016	−	0.536317i	$-0.819815\pi$
$149$	0.518244	−	0.897625i	0.0424562	−	0.0735363i	0.886473	+	0.462781i	$0.153148\pi$
$150$		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
$153$	−0.392291	−	0.326099i	−0.0317149	−	0.0263635i
$154$		−	15.4503i		−	1.24502i
$155$		0			0
$156$	−0.367304	+	1.67508i	−0.0294079	+	0.134114i
$157$	−2.36186	−	8.81460i	−0.188497	−	0.703481i	−0.993855	−	0.110692i	$-0.964693\pi$
$157$	−2.36186	−	8.81460i	−0.188497	−	0.703481i	0.805357	−	0.592789i	$-0.201973\pi$
$158$	3.51245	+	13.1086i	0.279435	+	1.04287i
$159$	6.63408	+	6.05092i	0.526117	+	0.479869i
$160$		0			0
$161$			20.4857i			1.61450i
$162$	0.701625	−	8.97261i	0.0551249	−	0.704955i
$163$	−5.03848	−	5.03848i	−0.394644	−	0.394644i	0.481695	−	0.876339i	$-0.340021\pi$
$163$	−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
$167$	10.4641	−	2.80384i	0.809734	−	0.216968i	0.169881	−	0.985465i	$-0.445662\pi$
$167$	10.4641	−	2.80384i	0.809734	−	0.216968i	0.639853	+	0.768497i	$0.278995\pi$
$168$	3.63160	+	5.67155i	0.280184	+	0.437569i
$169$	−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
$173$	−3.64139	−	0.975709i	−0.276850	−	0.0741818i	0.117722	−	0.993047i	$-0.462441\pi$
$173$	−3.64139	−	0.975709i	−0.276850	−	0.0741818i	−0.394573	+	0.918865i	$0.629107\pi$
$174$	−2.26247	−	7.11832i	−0.171517	−	0.539638i
$175$		0			0
$176$	−3.44125	−	1.98681i	−0.259394	−	0.149761i
$177$	8.39472	+	4.34543i	0.630986	+	0.326622i
$178$	1.26260	−	4.71209i	0.0946359	−	0.353186i
$179$	−12.8952			−0.963836			−0.481918	−	0.876216i	$-0.660060\pi$
$179$	−12.8952			−0.963836			−0.481918	+	0.876216i	$0.660060\pi$
$180$		0			0
$181$	24.3197			1.80767			0.903835	−	0.427881i	$-0.140740\pi$
$181$	24.3197			1.80767			0.903835	+	0.427881i	$0.140740\pi$
$182$	0.996372	−	3.71851i	0.0738560	−	0.275634i
$183$	12.7084	−	8.13741i	0.939430	−	0.601535i
$184$	4.56277	+	2.63432i	0.336372	+	0.194204i
$185$		0			0
$186$	−10.9758	+	12.0336i	−0.804782	+	0.882344i
$187$	−0.652663	−	0.174880i	−0.0477274	−	0.0127885i
$188$	2.45081	−	2.45081i	0.178744	−	0.178744i
$189$	−2.49842	+	20.0488i	−0.181733	+	1.45833i
$190$		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	$0.169197\pi$
$192$	1.73022	−	0.0795432i	0.124868	−	0.00574054i
$193$	−15.6521	+	4.19397i	−1.12666	+	0.301889i	−0.773577	−	0.633702i	$-0.781534\pi$
$193$	−15.6521	+	4.19397i	−1.12666	+	0.301889i	−0.353086	+	0.935591i	$0.614868\pi$
$194$	−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	$-0.268626\pi$
$197$	−1.16085	−	1.16085i	−0.0827072	−	0.0827072i	−0.747250	+	0.664543i	$0.768626\pi$
$198$	−4.12881	−	11.1830i	−0.293422	−	0.794740i
$199$			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
$202$	2.66565	+	9.94834i	0.187554	+	0.699963i
$203$	4.33973	+	16.1961i	0.304589	+	1.13674i
$204$	0.280687	−	0.0892129i	0.0196520	−	0.00624615i
$205$		0			0
$206$		−	6.48420i		−	0.451776i
$207$	5.47442	+	14.8276i	0.380498	+	1.03059i
$208$	−0.700097	−	0.700097i	−0.0485430	−	0.0485430i
$209$	−3.74498	−	6.48649i	−0.259046	−	0.448680i
$210$		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	$0.950914\pi$
$212$	−5.00745	+	1.34174i	−0.343913	+	0.0921513i
$213$	12.0235	−	0.552755i	0.823838	−	0.0378741i
$214$	−4.53225	+	2.61670i	−0.309818	+	0.178874i
$215$		0			0
$216$	4.14418	+	3.13461i	0.281976	+	0.213283i
$217$	25.8537	−	25.8537i	1.75507	−	1.75507i
$218$	−7.05281	−	1.88979i	−0.477676	−	0.127993i
$219$	−13.6631	+	14.9799i	−0.923270	+	1.01225i
$220$		0			0
$221$	−0.145802	−	0.0841789i	−0.00980771	−	0.00566249i
$222$	−6.74266	+	4.31745i	−0.452538	+	0.289768i
$223$	−1.21534	+	4.53570i	−0.0813849	+	0.303733i	−0.994605	−	0.103734i	$-0.966921\pi$
$223$	−1.21534	+	4.53570i	−0.0813849	+	0.303733i	0.913220	+	0.407466i	$0.133588\pi$
$224$	−3.88823			−0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	−6.47859	+	24.1784i	−0.429999	+	1.60478i	0.322759	+	0.946481i	$0.395390\pi$
$227$	−6.47859	+	24.1784i	−0.429999	+	1.60478i	−0.752758	+	0.658297i	$0.771277\pi$
$228$	2.89937	+	1.50082i	0.192015	+	0.0993945i
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.323014	−	0.946394i	$-0.604696\pi$
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.981108	+	0.193459i	$0.938029\pi$
$230$		0			0
$231$	8.10596	+	25.5035i	0.533333	+	1.67801i
$232$	4.16541	+	1.11612i	0.273473	+	0.0732768i
$233$	−20.6491	+	20.6491i	−1.35277	+	1.35277i	−0.470214	+	0.882553i	$0.655823\pi$
$233$	−20.6491	+	20.6491i	−1.35277	+	1.35277i	−0.882553	+	0.470214i	$0.844177\pi$
$234$	−0.272527	−	2.95773i	−0.0178156	−	0.193353i
$235$		0			0
$236$	−4.72637	+	2.72877i	−0.307660	+	0.177628i
$237$	−12.6753	−	19.7954i	−0.823352	−	1.28585i
$238$	−0.638639	+	0.171123i	−0.0413968	+	0.0110922i
$239$	−4.56277	+	7.90295i	−0.295141	+	0.511199i	−0.975018	−	0.222127i	$-0.928700\pi$
$239$	−4.56277	+	7.90295i	−0.295141	+	0.511199i	0.679877	+	0.733327i	$0.262033\pi$
$240$		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
$243$	3.54930	+	15.1790i	0.227688	+	0.973734i
$244$			8.71245i			0.557758i
$245$		0			0
$246$	10.5768	+	9.64703i	0.674351	+	0.615072i
$247$	−0.483018	−	1.80265i	−0.0307337	−	0.114700i
$248$	−2.43379	−	9.08302i	−0.154546	−	0.576773i
$249$	2.59597	−	11.8389i	0.164513	−	0.750258i
$250$		0			0
$251$		−	6.16751i		−	0.389290i	−0.980874	−	0.194645i	$-0.937645\pi$
$251$		−	6.16751i		−	0.389290i	0.980874	−	0.194645i	$-0.0623555\pi$
$252$	−8.97017	−	7.45660i	−0.565068	−	0.469722i
$253$	14.8036	+	14.8036i	0.930696	+	0.930696i
$254$	9.74898	+	16.8857i	0.611706	+	1.05951i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−28.0634	+	7.51956i	−1.75055	+	0.469057i	−0.984743	−	0.174018i	$-0.944325\pi$
$257$	−28.0634	+	7.51956i	−1.75055	+	0.469057i	−0.765803	+	0.643075i	$0.777658\pi$
$258$	−1.64273	+	3.17351i	−0.102272	+	0.197574i
$259$	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
$263$	18.0249	+	4.82975i	1.11146	+	0.297815i	0.767424	−	0.641141i	$-0.221538\pi$
$263$	18.0249	+	4.82975i	1.11146	+	0.297815i	0.344038	+	0.938956i	$0.388205\pi$
$264$	6.72277	+	1.47414i	0.413758	+	0.0907269i
$265$		0			0
$266$	−6.34711	−	3.66451i	−0.389167	−	0.224685i
$267$	0.388037	+	8.44057i	0.0237475	+	0.516555i
$268$	2.10759	−	7.86563i	0.128742	−	0.480470i
$269$	−15.5553			−0.948425			−0.474212	−	0.880411i	$-0.657267\pi$
$269$	−15.5553			−0.948425			−0.474212	+	0.880411i	$0.657267\pi$
$270$		0			0
$271$	−1.87184			−0.113706			−0.0568532	−	0.998383i	$-0.518107\pi$
$271$	−1.87184			−0.113706			−0.0568532	+	0.998383i	$0.518107\pi$
$272$	−0.0440105	+	0.164249i	−0.00266853	+	0.00995908i
$273$	0.306216	+	6.66081i	0.0185331	+	0.403131i
$274$	−10.8243	−	6.24939i	−0.653918	−	0.377540i
$275$		0			0
$276$	−8.91376	−	1.95457i	−0.536545	−	0.117651i
$277$	−3.99035	−	1.06921i	−0.239757	−	0.0642426i	0.136940	−	0.990579i	$-0.456273\pi$
$277$	−3.99035	−	1.06921i	−0.239757	−	0.0642426i	−0.376696	+	0.926337i	$0.622940\pi$
$278$	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	$0.330607\pi$
$282$	−2.75970	+	5.33132i	−0.164338	+	0.317476i
$283$	−17.4857	+	4.68527i	−1.03941	+	0.278510i	−0.737871	−	0.674942i	$-0.764169\pi$
$283$	−17.4857	+	4.68527i	−1.03941	+	0.278510i	−0.301544	+	0.953452i	$0.597502\pi$
$284$	−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
$288$	−2.81431	+	1.03906i	−0.165835	+	0.0612271i
$289$		−	16.9711i		−	0.998299i
$290$		0			0
$291$	0.555048	−	2.53128i	0.0325375	−	0.148386i
$292$	−3.02970	−	11.3070i	−0.177300	−	0.661691i
$293$	−5.53752	−	20.6663i	−0.323505	−	1.20734i	−0.915806	−	0.401621i	$-0.868447\pi$
$293$	−5.53752	−	20.6663i	−0.323505	−	1.20734i	0.592300	−	0.805717i	$-0.298220\pi$
$294$	10.3890	+	9.47576i	0.605899	+	0.552637i
$295$		0			0
$296$		−	4.62255i		−	0.268680i
$297$	12.6825	+	16.2934i	0.735912	+	0.945436i
$298$	−0.732907	−	0.732907i	−0.0424562	−	0.0424562i
$299$	2.60820	+	4.51754i	0.150836	+	0.261256i
$300$		0			0
$301$	4.01100	−	6.94725i	0.231190	−	0.400433i
$302$	−3.93037	+	1.05314i	−0.226168	+	0.0606014i
$303$	−9.61951	−	15.0230i	−0.552626	−	0.863049i
$304$	−1.63239	+	0.942462i	−0.0936241	+	0.0540539i
$305$		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	$-0.0555001\pi$
$308$	−14.9238	−	3.99883i	−0.850365	−	0.227855i
$309$	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	$0.795032\pi$
$312$	1.52294	+	0.788332i	0.0862196	+	0.0446305i
$313$	4.79847	−	17.9081i	0.271226	−	1.01223i	−0.687103	−	0.726560i	$-0.741118\pi$
$313$	4.79847	−	17.9081i	0.271226	−	1.01223i	0.958329	−	0.285668i	$-0.0922154\pi$
$314$	−9.12554			−0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	−0.217566	+	0.811966i	−0.0122197	+	0.0456046i	−0.971766	−	0.235945i	$-0.924182\pi$
$317$	−0.217566	+	0.811966i	−0.0122197	+	0.0456046i	0.959547	+	0.281549i	$0.0908483\pi$
$318$	7.56176	−	4.84194i	0.424043	−	0.271522i
$319$	14.8399	+	8.56781i	0.830874	+	0.479705i
$320$		0			0
$321$	6.10845	−	6.69716i	0.340941	−	0.373799i
$322$	19.7876	+	5.30208i	1.10272	+	0.295473i
$323$	−0.226641	+	0.226641i	−0.0126107	+	0.0126107i
$324$	−8.48528	−	3.00000i	−0.471405	−	0.166667i
$325$		0			0
$326$	−6.17086	+	3.56275i	−0.341772	+	0.197322i
$327$	12.6334	−	0.580793i	0.698629	−	0.0321179i
$328$	−7.98343	+	2.13915i	−0.440811	+	0.118115i
$329$	6.73825	−	11.6710i	0.371492	−	0.643443i
$330$		0			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
$333$	8.86483	−	10.6642i	0.485790	−	0.584397i
$334$		−	10.8332i		−	0.592766i
$335$		0			0
$336$	6.41822	−	2.03995i	0.350143	−	0.111288i
$337$	0.840764	+	3.13777i	0.0457993	+	0.170925i	0.985037	−	0.172341i	$-0.0551332\pi$
$337$	0.840764	+	3.13777i	0.0457993	+	0.170925i	−0.939238	+	0.343267i	$0.888467\pi$
$338$	3.11093	+	11.6102i	0.169213	+	0.631510i
$339$	−6.96478	+	2.21367i	−0.378275	+	0.120230i
$340$		0			0
$341$		−	37.3656i		−	2.02346i
$342$	−5.57334	−	0.956233i	−0.301372	−	0.0517072i
$343$	−3.07470	−	3.07470i	−0.166018	−	0.166018i
$344$	−1.03157	−	1.78674i	−0.0556188	−	0.0963346i
$345$		0			0
$346$	−1.88492	+	3.26478i	−0.101334	+	0.175516i
$347$	−4.53334	+	1.21470i	−0.243362	+	0.0652087i	−0.378438	−	0.925627i	$-0.623539\pi$
$347$	−4.53334	+	1.21470i	−0.243362	+	0.0652087i	0.135076	+	0.990835i	$0.456872\pi$
$348$	−7.46134	+	0.343019i	−0.399970	+	0.0183877i
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	−0.708316	−	0.705896i	$-0.750545\pi$
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	0.257166	+	0.966367i	$0.417211\pi$
$350$		0			0
$351$	2.00162	+	4.73929i	0.106839	+	0.252965i
$352$	−2.80977	+	2.80977i	−0.149761	+	0.149761i
$353$	4.92815	+	1.32049i	0.262299	+	0.0702827i	0.387572	−	0.921840i	$-0.373314\pi$
$353$	4.92815	+	1.32049i	0.262299	+	0.0702827i	−0.125273	+	0.992122i	$0.539981\pi$
$354$	6.37008	−	6.98400i	0.338566	−	0.371195i
$355$		0			0
$356$	−4.22474	−	2.43916i	−0.223911	−	0.129275i
$357$	0.964409	−	0.617529i	0.0510420	−	0.0326831i
$358$	−3.33754	+	12.4559i	−0.176394	+	0.658312i
$359$	−1.27697			−0.0673957			−0.0336978	−	0.999432i	$-0.510728\pi$
$359$	−1.27697			−0.0673957			−0.0336978	+	0.999432i	$0.510728\pi$
$360$		0			0
$361$	15.4471			0.813003
$362$	6.29441	−	23.4910i	0.330827	−	1.23466i
$363$	7.36727	+	3.81358i	0.386682	+	0.200161i
$364$	−3.33392	−	1.92484i	−0.174745	−	0.100889i
$365$		0			0
$366$	−4.57097	−	14.3815i	−0.238928	−	0.751731i
$367$	−9.74300	−	2.61063i	−0.508581	−	0.136274i	−0.00460117	−	0.999989i	$-0.501465\pi$
$367$	−9.74300	−	2.61063i	−0.508581	−	0.136274i	−0.503979	+	0.863716i	$0.668131\pi$
$368$	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
$372$	8.78279	+	13.7163i	0.455367	+	0.711156i
$373$	−12.6656	+	3.39374i	−0.655801	+	0.175721i	−0.571350	−	0.820706i	$-0.693580\pi$
$373$	−12.6656	+	3.39374i	−0.655801	+	0.175721i	−0.0844507	+	0.996428i	$0.526914\pi$
$374$	−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
$378$	18.7190	+	7.60229i	0.962800	+	0.391019i
$379$		−	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
$382$	−3.52759	−	13.1652i	−0.180487	−	0.673588i
$383$	−3.75319	−	14.0071i	−0.191779	−	0.715729i	−0.993077	−	0.117464i	$-0.962524\pi$
$383$	−3.75319	−	14.0071i	−0.191779	−	0.715729i	0.801298	−	0.598265i	$-0.204143\pi$
$384$	0.370982	−	1.69185i	0.0189316	−	0.0863371i
$385$		0			0
$386$			16.2043i			0.824775i
$387$	1.04665	−	6.10031i	0.0532041	−	0.310096i
$388$	1.05794	+	1.05794i	0.0537090	+	0.0537090i
$389$	10.3789	+	17.9767i	0.526230	+	0.911456i	0.999533	+	0.0305570i	$0.00972810\pi$
$389$	10.3789	+	17.9767i	0.526230	+	0.911456i	−0.473303	+	0.880899i	$0.656939\pi$
$390$		0			0
$391$	0.447948	−	0.775869i	0.0226537	−	0.0392374i
$392$	−7.84169	+	2.10118i	−0.396065	+	0.106125i
$393$	3.56957	−	6.89588i	0.180061	−	0.347851i
$394$	−1.42175	+	0.820845i	−0.0716265	+	0.0413536i
$395$		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	$0.438699\pi$
$398$	16.5881	+	4.44477i	0.831487	+	0.222796i
$399$	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	$0.628791\pi$
$402$	0.647729	+	14.0894i	0.0323058	+	0.702715i
$403$	2.40966	−	8.99298i	0.120034	−	0.447972i
$404$	10.2993			0.512408
$405$		0			0
$406$	16.7674			0.832153
$407$	4.75404	−	17.7423i	0.235649	−	0.879454i
$408$	−0.0135258	−	0.294213i	−0.000669627	−	0.0145657i
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.976787	−	0.214211i	$-0.0687180\pi$
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.302882	+	0.953028i	$0.402051\pi$
$410$		0			0
$411$	21.1461	+	4.63682i	1.04306	+	0.228718i
$412$	−6.26326	−	1.67823i	−0.308568	−	0.0826807i
$413$	−15.0049	+	15.0049i	−0.738343	+	0.738343i
$414$	15.7392	−	1.45022i	0.773541	−	0.0712744i
$415$		0			0
$416$	−0.857441	+	0.495044i	−0.0420395	+	0.0242715i
$417$	−3.31384	+	6.40185i	−0.162280	+	0.313500i
$418$	−7.23474	+	1.93854i	−0.353863	+	0.0948172i
$419$	−8.81638	+	15.2704i	−0.430708	+	0.746009i	−0.996934	−	0.0782412i	$-0.975070\pi$
$419$	−8.81638	+	15.2704i	−0.430708	+	0.746009i	0.566226	+	0.824250i	$0.308403\pi$
$420$		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
$423$	1.75831	−	10.2482i	0.0854919	−	0.498284i
$424$			5.18410i			0.251762i
$425$		0			0
$426$	2.57799	−	11.7569i	0.124904	−	0.569623i
$427$	8.76775	+	32.7217i	0.424301	+	1.58351i
$428$	1.35450	+	5.05507i	0.0654723	+	0.244346i
$429$	5.03461	+	4.59205i	0.243073	+	0.221706i
$430$		0			0
$431$		−	19.2910i		−	0.929215i	−0.885517	−	0.464608i	$-0.846195\pi$
$431$		−	19.2910i		−	0.929215i	0.885517	−	0.464608i	$-0.153805\pi$
$432$	4.10039	−	3.19168i	0.197280	−	0.153560i
$433$	−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
$437$	9.59259	−	2.57033i	0.458876	−	0.122955i
$438$	10.9332	+	17.0747i	0.522410	+	0.815860i
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.488285	−	0.872684i	$-0.337623\pi$
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.999909	+	0.0134750i	$0.00428934\pi$
$440$		0			0
$441$	−22.1203	−	10.1909i	−1.05335	−	0.485280i
$442$	−0.119047	+	0.119047i	−0.00566249	+	0.00566249i
$443$	25.9195	+	6.94511i	1.23147	+	0.329972i	0.815153	−	0.579246i	$-0.196653\pi$
$443$	25.9195	+	6.94511i	1.23147	+	0.329972i	0.416320	+	0.909218i	$0.363320\pi$
$444$	2.42521	+	7.63035i	0.115095	+	0.362120i
$445$		0			0
$446$	4.06659	+	2.34785i	0.192559	+	0.111174i
$447$	1.59431	+	0.825278i	0.0754085	+	0.0390343i
$448$	−1.00635	+	3.75574i	−0.0475455	+	0.177442i
$449$	41.3392			1.95092			0.975459	−	0.220182i	$-0.0706652\pi$
$449$	41.3392			1.95092			0.975459	+	0.220182i	$0.0706652\pi$
$450$		0			0
$451$	−32.8421			−1.54647
$452$	1.09205	−	4.07557i	0.0513655	−	0.191699i
$453$	5.93526	−	3.80046i	0.278863	−	0.178561i
$454$	21.6778	+	12.5157i	1.01739	+	0.587390i
$455$		0			0
$456$	2.20010	−	2.41213i	0.103029	−	0.112959i
$457$	20.8557	+	5.58827i	0.975589	+	0.261408i	0.711186	−	0.703004i	$-0.248158\pi$
$457$	20.8557	+	5.58827i	0.975589	+	0.261408i	0.264403	+	0.964412i	$0.414825\pi$
$458$	−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	$0.427757\pi$
$462$	26.7325	−	1.22897i	1.24371	−	0.0571767i
$463$	21.3514	−	5.72110i	0.992286	−	0.265882i	0.274076	−	0.961708i	$-0.411628\pi$
$463$	21.3514	−	5.72110i	0.992286	−	0.265882i	0.718210	+	0.695826i	$0.244962\pi$
$464$	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	$-0.213661\pi$
$467$	3.48137	+	3.48137i	0.161099	+	0.161099i	−0.621955	+	0.783053i	$0.713661\pi$
$468$	−2.92749	−	0.502277i	−0.135323	−	0.0232178i
$469$		−	31.6622i		−	1.46203i
$470$		0			0
$471$	15.0634	−	4.78769i	0.694083	−	0.220605i
$472$	1.41251	+	5.27158i	0.0650163	+	0.242644i
$473$	−2.12184	−	7.91881i	−0.0975622	−	0.364107i
$474$	−22.4015	+	7.12002i	−1.02893	+	0.327033i
$475$		0			0
$476$			0.661168i			0.0303046i
$477$	−9.94174	+	11.9598i	−0.455201	+	0.547599i
$478$	6.45273	+	6.45273i	0.295141	+	0.295141i
$479$	1.35673	+	2.34993i	0.0619906	+	0.107371i	0.895355	−	0.445353i	$-0.146922\pi$
$479$	1.35673	+	2.34993i	0.0619906	+	0.107371i	−0.833364	+	0.552724i	$0.813588\pi$
$480$		0			0
$481$	2.28836	−	3.96356i	0.104340	−	0.180723i
$482$	1.68004	−	0.450166i	0.0765239	−	0.0205045i
$483$	−35.4448	+	1.62949i	−1.61279	+	0.0741446i
$484$	−4.14790	+	2.39479i	−0.188541	+	0.108854i
$485$		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	$0.165288\pi$
$488$	8.41558	+	2.25495i	0.380955	+	0.102077i
$489$	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	$0.631091\pi$
$492$	12.0558	−	7.71955i	0.543517	−	0.348024i
$493$	0.189789	−	0.708301i	0.00854766	−	0.0319003i
$494$	−1.86624			−0.0839661
$495$		0			0
$496$	−9.40344			−0.422227
$497$	−6.99322	+	26.0991i	−0.313689	+	1.17070i
$498$	−10.7636	−	5.57164i	−0.482328	−	0.249671i
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.285791	−	0.958292i	$-0.592256\pi$
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.972801	+	0.231643i	$0.925590\pi$
$500$		0			0
$501$	5.68361	+	17.8821i	0.253925	+	0.798915i
$502$	−5.95736	−	1.59627i	−0.265890	−	0.0712450i
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	−0.115717	−	0.993282i	$-0.536917\pi$
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	0.993282	+	0.115717i	$0.0369166\pi$
$504$	−9.52417	+	6.73461i	−0.424240	+	0.299983i
$505$		0			0
$506$	18.1307	−	10.4677i	0.806007	−	0.465348i
$507$	−11.2264	−	17.5325i	−0.498582	−	0.778647i
$508$	18.8336	−	5.04645i	0.835606	−	0.223900i
$509$	5.25069	−	9.09446i	0.232733	−	0.403105i	−0.725879	−	0.687823i	$-0.758567\pi$
$509$	5.25069	−	9.09446i	0.232733	−	0.403105i	0.958611	+	0.284718i	$0.0918999\pi$
$510$		0			0
$511$	−22.7575	−	39.4171i	−1.00673	−	1.74371i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	9.70148	−	1.34560i	0.428331	−	0.0594098i
$514$			29.0534i			1.28149i
$515$		0			0
$516$	2.64021	+	2.40812i	0.116229	+	0.106012i
$517$	−3.56457	−	13.3031i	−0.156770	−	0.585072i
$518$	−4.65189	−	17.3611i	−0.204392	−	0.762802i
$519$	1.39855	−	6.37804i	0.0613893	−	0.279965i
$520$		0			0
$521$			28.2545i			1.23785i	0.785450	+	0.618925i	$0.212432\pi$
$521$			28.2545i			1.23785i	−0.785450	+	0.618925i	$0.787568\pi$
$522$	12.1363	−	4.48079i	0.531192	−	0.196119i
$523$	−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
$527$	−1.54451	+	0.413850i	−0.0672798	+	0.0180276i
$528$	3.16389	−	6.11216i	0.137691	−	0.265998i
$529$	−4.12099	+	2.37925i	−0.179173	+	0.103446i
$530$		0			0
$531$	−6.85082	+	14.8704i	−0.297300	+	0.645320i
$532$	−5.18240	+	5.18240i	−0.224685	+	0.224685i
$533$	−7.90429	−	2.11795i	−0.342373	−	0.0917385i
$534$	8.25340	+	1.80977i	0.357160	+	0.0783163i
$535$		0			0
$536$	−7.05213	−	4.07155i	−0.304606	−	0.175864i
$537$	−1.02573	−	22.3117i	−0.0442635	−	0.962819i
$538$	−4.02601	+	15.0253i	−0.173574	+	0.647786i
$539$	−32.2590			−1.38949
$540$		0			0
$541$	−26.7216			−1.14885			−0.574427	−	0.818556i	$-0.694775\pi$
$541$	−26.7216			−1.14885			−0.574427	+	0.818556i	$0.694775\pi$
$542$	−0.484468	+	1.80806i	−0.0208097	+	0.0776628i
$543$	1.93447	+	42.0785i	0.0830160	+	1.80576i
$544$	0.147262	+	0.0850217i	0.00631380	+	0.00364528i
$545$		0			0
$546$	6.51311	+	1.42816i	0.278735	+	0.0611197i
$547$	0.234244	+	0.0627654i	0.0100155	+	0.00268365i	0.263823	−	0.964571i	$-0.415016\pi$
$547$	0.234244	+	0.0627654i	0.0100155	+	0.00268365i	−0.253808	+	0.967255i	$0.581683\pi$
$548$	−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
$552$	−4.19502	+	8.10415i	−0.178552	+	0.344936i
$553$	50.9693	−	13.6572i	2.16744	−	0.580763i
$554$	−2.06556	+	3.57765i	−0.0877571	+	0.152000i
$555$		0			0
$556$	−2.08097	−	3.60435i	−0.0882528	−	0.152858i
$557$	31.4838	+	31.4838i	1.33401	+	1.33401i	0.901746	+	0.432266i	$0.142286\pi$
$557$	31.4838	+	31.4838i	1.33401	+	1.33401i	0.432266	+	0.901746i	$0.357714\pi$
$558$	−21.6938	−	18.0333i	−0.918372	−	0.763412i
$559$		−	2.04270i		−	0.0863969i
$560$		0			0
$561$	0.250667	−	1.14316i	0.0105832	−	0.0482644i
$562$	−0.0743081	−	0.277322i	−0.00313450	−	0.0116981i
$563$	−8.35388	−	31.1771i	−0.352074	−	1.31396i	−0.884127	−	0.467247i	$-0.845246\pi$
$563$	−8.35388	−	31.1771i	−0.352074	−	1.31396i	0.532053	−	0.846711i	$-0.321421\pi$
$564$	4.43540	+	4.04551i	0.186764	+	0.170347i
$565$		0			0
$566$			18.1025i			0.760904i
$567$	−34.8876	−	2.72808i	−1.46514	−	0.114569i
$568$	4.91376	+	4.91376i	0.206177	+	0.206177i
$569$	16.1545	+	27.9804i	0.677232	+	1.17300i	0.975811	+	0.218615i	$0.0701538\pi$
$569$	16.1545	+	27.9804i	0.677232	+	1.17300i	−0.298580	+	0.954385i	$0.596513\pi$
$570$		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	$-0.0157469\pi$
$572$	−3.80016	+	1.01825i	−0.158893	+	0.0425752i
$573$	12.7300	+	19.8807i	0.531803	+	0.830529i
$574$	−27.8310	+	16.0682i	−1.16164	+	0.670674i
$575$		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	$0.307539\pi$
$578$	−16.3928	−	4.39244i	−0.681851	−	0.182701i
$579$	−8.50152	−	26.7480i	−0.353311	−	1.11161i
$580$		0			0
$581$	23.5629	+	13.6041i	0.977556	+	0.564392i
$582$	−2.30138	−	1.19128i	−0.0953951	−	0.0493801i
$583$	−5.33157	+	19.8977i	−0.220811	+	0.824077i
$584$	−11.7058			−0.484391
$585$		0			0
$586$	−21.3953			−0.883833
$587$	−0.490414	+	1.83025i	−0.0202415	+	0.0755424i	−0.975308	−	0.220850i	$-0.929117\pi$
$587$	−0.490414	+	1.83025i	−0.0202415	+	0.0755424i	0.955066	+	0.296392i	$0.0957836\pi$
$588$	11.8418	−	7.58249i	0.488346	−	0.312697i
$589$	−15.3501	−	8.86238i	−0.632490	−	0.365168i
$590$		0			0
$591$	1.91619	−	2.10087i	0.0788217	−	0.0864182i
$592$	−4.46504	−	1.19640i	−0.183512	−	0.0491719i
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	−0.896029	−	0.443996i	$-0.853561\pi$
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	0.443996	+	0.896029i	$0.353561\pi$
$594$	19.0206	−	8.03330i	0.780426	−	0.329610i
$595$		0			0
$596$	−0.897625	+	0.518244i	−0.0367681	+	0.0212281i
$597$	−29.7136	+	1.36602i	−1.21610	+	0.0559074i
$598$	5.03866	−	1.35011i	0.206046	−	0.0552099i
$599$	12.9428	−	22.4176i	0.528828	−	0.915957i	−0.470607	−	0.882343i	$-0.655965\pi$
$599$	12.9428	−	22.4176i	0.528828	−	0.915957i	0.999435	−	0.0336142i	$-0.0107018\pi$
$600$		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
$603$	−8.46115	−	22.9172i	−0.344565	−	0.933262i
$604$			4.06902i			0.165566i
$605$		0			0
$606$	−17.0008	+	5.40349i	−0.690611	+	0.219502i
$607$	−7.70972	−	28.7731i	−0.312928	−	1.16786i	−0.925903	−	0.377761i	$-0.876694\pi$
$607$	−7.70972	−	28.7731i	−0.312928	−	1.16786i	0.612975	−	0.790102i	$-0.289973\pi$
$608$	0.487854	+	1.82070i	0.0197851	+	0.0738390i
$609$	−27.6776	+	8.79699i	−1.12155	+	0.356472i
$610$		0			0
$611$		−	3.43162i		−	0.138828i
$612$	0.176685	+	0.478556i	0.00714207	+	0.0193445i
$613$	12.5028	+	12.5028i	0.504982	+	0.504982i	0.912982	−	0.408000i	$-0.133774\pi$
$613$	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
$617$	7.14621	−	1.91482i	0.287695	−	0.0770878i	−0.112085	−	0.993699i	$-0.535753\pi$
$617$	7.14621	−	1.91482i	0.287695	−	0.0770878i	0.399781	+	0.916611i	$0.369086\pi$
$618$	11.2191	−	0.515774i	0.451299	−	0.0207475i
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	−0.792917	−	0.609329i	$-0.791439\pi$
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	0.131236	+	0.991351i	$0.458105\pi$
$620$		0			0
$621$	−25.2196	+	10.6514i	−1.01203	+	0.427426i
$622$	−9.78715	+	9.78715i	−0.392429	+	0.392429i
$623$	−18.3217	−	4.90928i	−0.734043	−	0.196686i
$624$	1.15564	−	1.26701i	0.0462625	−	0.0507211i
$625$		0			0
$626$	−16.0560	−	9.26994i	−0.641727	−	0.370501i
$627$	10.9252	−	6.99560i	0.436310	−	0.279378i
$628$	−2.36186	+	8.81460i	−0.0942486	+	0.351741i
$629$	−0.786034			−0.0313412
$630$		0			0
$631$	−2.22853			−0.0887165			−0.0443583	−	0.999016i	$-0.514124\pi$
$631$	−2.22853			−0.0887165			−0.0443583	+	0.999016i	$0.514124\pi$
$632$	3.51245	−	13.1086i	0.139718	−	0.521433i
$633$	−28.0225	−	14.5055i	−1.11380	−	0.576543i
$634$	0.727989	+	0.420305i	0.0289121	+	0.0166924i
$635$		0			0
$636$	−2.71982	−	8.55729i	−0.107848	−	0.339319i
$637$	−7.76396	−	2.08035i	−0.307619	−	0.0824263i
$638$	12.1167	−	12.1167i	0.479705	−	0.479705i
$639$	1.91278	+	20.7594i	0.0756683	+	0.821229i
$640$		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	$0.00212622\pi$
$642$	−4.88798	−	7.63367i	−0.192913	−	0.301277i
$643$	−29.4639	+	7.89483i	−1.16194	+	0.311342i	−0.787742	−	0.616006i	$-0.788750\pi$
$643$	−29.4639	+	7.89483i	−1.16194	+	0.311342i	−0.374202	+	0.927347i	$0.622083\pi$
$644$	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	$-0.285704\pi$
$647$	−4.02651	−	4.02651i	−0.158298	−	0.158298i	−0.781812	+	0.623514i	$0.785704\pi$
$648$	−5.09393	+	7.41970i	−0.200108	+	0.291473i
$649$			21.6861i			0.851255i
$650$		0			0
$651$	46.7892	+	42.6763i	1.83381	+	1.67261i
$652$	1.84421	+	6.88270i	0.0722249	+	0.269547i
$653$	8.44081	+	31.5015i	0.330314	+	1.23275i	0.908861	+	0.417100i	$0.136954\pi$
$653$	8.44081	+	31.5015i	0.330314	+	1.23275i	−0.578546	+	0.815650i	$0.696380\pi$
$654$	2.70876	−	12.3533i	0.105921	−	0.483050i
$655$		0			0
$656$			8.26506i			0.322696i
$657$	−27.0055	−	22.4487i	−1.05358	−	0.875809i
$658$	−9.52933	−	9.52933i	−0.371492	−	0.371492i
$659$	−7.75612	−	13.4340i	−0.302136	−	0.523314i	0.674484	−	0.738290i	$-0.264366\pi$
$659$	−7.75612	−	13.4340i	−0.302136	−	0.523314i	−0.976619	+	0.214975i	$0.931033\pi$
$660$		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	$0.0241453\pi$
$662$	4.02232	−	1.07778i	0.156332	−	0.0418890i
$663$	0.134051	−	0.258966i	0.00520610	−	0.0100574i
$664$	6.06007	−	3.49878i	0.235176	−	0.135779i
$665$		0			0
$666$	−8.00649	−	11.3229i	−0.310245	−	0.438753i
$667$	−16.0656	+	16.0656i	−0.622063	+	0.622063i
$668$	−10.4641	−	2.80384i	−0.404867	−	0.108484i
$669$	−7.94444	−	1.74202i	−0.307150	−	0.0673503i
$670$		0			0
$671$	29.9817	+	17.3099i	1.15743	+	0.668243i
$672$	−0.309282	−	6.72750i	−0.0119308	−	0.259519i
$673$	−2.49905	+	9.32657i	−0.0963312	+	0.359513i	−0.997218	−	0.0745413i	$-0.976251\pi$
$673$	−2.49905	+	9.32657i	−0.0963312	+	0.359513i	0.900887	+	0.434054i	$0.142917\pi$
$674$	3.24846			0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	−1.95869	+	7.30994i	−0.0752787	+	0.280944i	−0.993296	−	0.115596i	$-0.963122\pi$
$677$	−1.95869	+	7.30994i	−0.0752787	+	0.280944i	0.918018	+	0.396539i	$0.129789\pi$
$678$	0.335620	+	7.30040i	0.0128894	+	0.280370i
$679$	5.03802	+	2.90870i	0.193342	+	0.111626i
$680$		0			0
$681$	−42.3494	−	9.28618i	−1.62283	−	0.355847i
$682$	−36.0924	−	9.67093i	−1.38205	−	0.370319i
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	−0.549300	−	0.835625i	$-0.685106\pi$
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	0.835625	+	0.549300i	$0.185106\pi$
$684$	−2.36614	+	5.13594i	−0.0904715	+	0.196378i
$685$		0			0
$686$	−3.76572	+	2.17414i	−0.143776	+	0.0830090i
$687$	18.1443	−	35.0522i	0.692250	−	1.33732i
$688$	−1.99285	+	0.533983i	−0.0759767	+	0.0203579i
$689$	−2.56635	+	4.44506i	−0.0977703	+	0.169343i
$690$		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
$693$	−43.4820	+	16.0538i	−1.65174	+	0.609832i
$694$			4.69326i			0.178154i
$695$		0			0
$696$	−1.59981	+	7.29588i	−0.0606405	+	0.276550i
$697$	0.363749	+	1.35753i	0.0137780	+	0.0514201i
$698$	2.51883	+	9.40041i	0.0953392	+	0.355811i
$699$	−37.3700	−	34.0850i	−1.41346	−	1.28921i
$700$		0			0
$701$			36.3602i			1.37331i	0.726985	+	0.686653i	$0.240921\pi$
$701$			36.3602i			1.37331i	−0.726985	+	0.686653i	$0.759079\pi$
$702$	5.09586	−	0.706799i	0.192331	−	0.0266764i
$703$	−6.16113	−	6.16113i	−0.232371	−	0.232371i
$704$	1.98681	+	3.44125i	0.0748805	+	0.129697i
$705$		0			0
$706$	2.55100	−	4.41846i	0.0960080	−	0.166291i
$707$	38.6814	−	10.3647i	1.45476	−	0.389803i
$708$	−5.09733	−	7.96061i	−0.191569	−	0.299178i
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	−0.493288	−	0.869866i	$-0.664205\pi$
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	0.506682	+	0.862133i	$0.330872\pi$
$710$		0			0
$711$	33.2421	−	23.5057i	1.24668	−	0.881534i
$712$	−3.44949	+	3.44949i	−0.129275	+	0.129275i
$713$	47.8551	+	12.8227i	1.79219	+	0.480215i
$714$	−0.346880	−	1.09138i	−0.0129817	−	0.0408437i
$715$		0			0
$716$	11.1676	+	6.44762i	0.417353	+	0.240959i
$717$	−14.0368	−	7.26599i	−0.524214	−	0.271353i
$718$	−0.330503	+	1.23345i	−0.0123343	+	0.0460321i
$719$	34.4664			1.28538			0.642690	−	0.766126i	$-0.277818\pi$
$719$	34.4664			1.28538			0.642690	+	0.766126i	$0.277818\pi$
$720$		0			0
$721$	−25.2120			−0.938946
$722$	3.99799	−	14.9207i	0.148790	−	0.555291i
$723$	−2.53704	+	1.62451i	−0.0943534	+	0.0604162i
$724$	−21.0615	−	12.1599i	−0.782744	−	0.451918i
$725$		0			0
$726$	5.59043	−	6.12921i	0.207480	−	0.227476i
$727$	13.7902	+	3.69508i	0.511451	+	0.137043i	0.505310	−	0.862938i	$-0.331378\pi$
$727$	13.7902	+	3.69508i	0.511451	+	0.137043i	0.00614188	+	0.999981i	$0.498045\pi$
$728$	−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
$732$	−15.0745	+	0.693017i	−0.557169	+	0.0256146i
$733$	29.6676	−	7.94942i	1.09580	−	0.293618i	0.334746	−	0.942308i	$-0.391349\pi$
$733$	29.6676	−	7.94942i	1.09580	−	0.293618i	0.761053	+	0.648690i	$0.224683\pi$
$734$	−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
$738$	−15.8502	+	19.0675i	−0.583454	+	0.701886i
$739$			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
$742$	5.21700	+	19.4701i	0.191522	+	0.714771i
$743$	9.31585	+	34.7672i	0.341765	+	1.27549i	0.896346	+	0.443356i	$0.146212\pi$
$743$	9.31585	+	34.7672i	0.341765	+	1.27549i	−0.554580	+	0.832130i	$0.687121\pi$
$744$	15.5221	−	4.93349i	0.569067	−	0.180871i
$745$		0			0
$746$			13.1124i			0.480080i
$747$	20.6904	+	3.54991i	0.757022	+	0.129884i
$748$	0.477782	+	0.477782i	0.0174695	+	0.0174695i
$749$	10.1743	+	17.6224i	0.371761	+	0.643910i
$750$		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	$0.815660\pi$
$752$	−3.34787	+	0.897060i	−0.122084	+	0.0327124i
$753$	10.6712	−	0.490584i	0.388879	−	0.0178779i
$754$	3.69759	−	2.13480i	0.134658	−	0.0777449i
$755$		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	$0.450426\pi$
$758$	−0.567624	−	0.152094i	−0.0206170	−	0.00552432i
$759$	−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	$0.728282\pi$
$762$	−28.4406	+	18.2111i	−1.03030	+	0.659717i
$763$	−7.34795	+	27.4229i	−0.266014	+	0.992777i
$764$	−13.6296			−0.493100
$765$		0			0
$766$	−14.5012			−0.523950
$767$	−1.39851	+	5.21932i	−0.0504974	+	0.188459i
$768$	−1.53819	−	0.796225i	−0.0555046	−	0.0287313i
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	0.558633	−	0.829415i	$-0.311326\pi$
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	−0.438978	+	0.898498i	$0.644659\pi$
$770$		0			0
$771$	−15.2428	−	47.9578i	−0.548955	−	1.72716i
$772$	15.6521	+	4.19397i	0.563332	+	0.150944i
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	−0.252047	−	0.967715i	$-0.581104\pi$
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	0.967715	+	0.252047i	$0.0811037\pi$
$774$	−5.62156	−	2.58986i	−0.202063	−	0.0930907i
$775$		0			0
$776$	1.29571	−	0.748079i	0.0465133	−	0.0268545i
$777$	16.7872	+	26.2170i	0.602239	+	0.940529i
$778$	20.0504	−	5.37250i	0.718843	−	0.192613i
$779$	−7.78950	+	13.4918i	−0.279088	+	0.483395i
$780$		0			0
$781$	13.8065	+	23.9136i	0.494036	+	0.855696i
$782$	−0.633495	−	0.633495i	−0.0226537	−	0.0226537i
$783$	−17.6823	+	13.7636i	−0.631915	+	0.491872i
$784$			8.11832i			0.289940i
$785$		0			0
$786$	−5.73704	−	5.23273i	−0.204633	−	0.186645i
$787$	1.87155	+	6.98473i	0.0667137	+	0.248979i	0.991227	−	0.132171i	$-0.0421948\pi$
$787$	1.87155	+	6.98473i	0.0667137	+	0.248979i	−0.924513	+	0.381150i	$0.875528\pi$
$788$	0.424901	+	1.58575i	0.0151365	+	0.0564901i
$789$	−6.92279	+	31.5712i	−0.246458	+	1.12397i
$790$		0			0
$791$		−	16.4058i		−	0.583321i
$792$	−2.01584	+	11.7492i	−0.0716296	+	0.417488i
$793$	6.09956	+	6.09956i	0.216602	+	0.216602i
$794$	11.1320	+	19.2811i	0.395059	+	0.684262i
$795$		0			0
$796$	8.58664	−	14.8725i	0.304345	−	0.527142i
$797$	33.4396	−	8.96012i	1.18449	−	0.317384i	0.387786	−	0.921750i	$-0.373240\pi$
$797$	33.4396	−	8.96012i	1.18449	−	0.317384i	0.796707	+	0.604366i	$0.206573\pi$
$798$	5.83555	−	11.2734i	0.206576	−	0.399074i
$799$	−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
$803$	−44.9295	−	12.0388i	−1.58553	−	0.424841i
$804$	13.7769	+	3.02094i	0.485875	+	0.106540i
$805$		0			0
$806$	−8.06289	−	4.65511i	−0.284003	−	0.163969i
$807$	−1.23732	−	26.9142i	−0.0435557	−	0.947424i
$808$	2.66565	−	9.94834i	0.0937772	−	0.349981i
$809$	−52.6028			−1.84942			−0.924709	−	0.380675i	$-0.875692\pi$
$809$	−52.6028			−1.84942			−0.924709	+	0.380675i	$0.875692\pi$
$810$		0			0
$811$	−13.8979			−0.488021			−0.244011	−	0.969773i	$-0.578463\pi$
$811$	−13.8979			−0.488021			−0.244011	+	0.969773i	$0.578463\pi$
$812$	4.33973	−	16.1961i	0.152295	−	0.568371i
$813$	−0.148892	−	3.23870i	−0.00522188	−	0.113586i
$814$	−15.9073	−	9.18410i	−0.557551	−	0.321902i
$815$		0			0
$816$	−0.287689	−	0.0630830i	−0.0100711	−	0.00220835i
$817$	−3.75637	−	1.00652i	−0.131419	−	0.0352136i
$818$	21.1307	−	21.1307i	0.738817	−	0.738817i
$819$	−11.5003	+	1.05965i	−0.401854	+	0.0370270i
$820$		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	$0.493750\pi$
$822$	9.95185	−	19.2255i	0.347111	−	0.670566i
$823$	−29.1118	+	7.80049i	−1.01477	+	0.271908i	−0.727623	−	0.685977i	$-0.759375\pi$
$823$	−29.1118	+	7.80049i	−1.01477	+	0.271908i	−0.287151	+	0.957885i	$0.592708\pi$
$824$	−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	$-0.217866\pi$
$827$	4.09863	+	4.09863i	0.142523	+	0.142523i	−0.632245	+	0.774768i	$0.717866\pi$
$828$	2.67281	−	15.5783i	0.0928865	−	0.541382i
$829$			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
$832$	0.256253	+	0.956351i	0.00888399	+	0.0331555i
$833$	0.357291	+	1.33343i	0.0123794	+	0.0462006i
$834$	5.32603	+	4.85785i	0.184425	+	0.168213i
$835$		0			0
$836$			7.48995i			0.259046i
$837$	45.2707	+	18.3857i	1.56478	+	0.635501i
$838$	12.4682	+	12.4682i	0.430708	+	0.430708i
$839$	−16.5639	−	28.6895i	−0.571849	−	0.990471i	−0.996376	−	0.0850559i	$-0.972893\pi$
$839$	−16.5639	−	28.6895i	−0.571849	−	0.990471i	0.424527	−	0.905415i	$-0.360440\pi$
$840$		0			0
$841$	5.20180	−	9.00978i	0.179372	−	0.310682i
$842$	26.9420	−	7.21908i	0.928482	−	0.248786i
$843$	0.268155	+	0.418784i	0.00923575	+	0.0144237i
$844$	15.7771	−	9.10894i	0.543072	−	0.313543i
$845$		0			0
$846$	−9.44390	−	4.35082i	−0.324688	−	0.149584i
$847$	−13.1684	+	13.1684i	−0.452472	+	0.452472i
$848$	5.00745	+	1.34174i	0.171957	+	0.0460757i
$849$	−9.49743	−	29.8814i	−0.325951	−	1.02553i
$850$		0			0
$851$	21.0916	+	12.1773i	0.723011	+	0.417431i
$852$	−10.6890	−	5.53306i	−0.366201	−	0.189559i
$853$	−0.689663	+	2.57386i	−0.0236136	+	0.0881273i	−0.976727	−	0.214486i	$-0.931192\pi$
$853$	−0.689663	+	2.57386i	−0.0236136	+	0.0881273i	0.953113	+	0.302613i	$0.0978590\pi$
$854$	33.8760			1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	−4.05364	+	15.1284i	−0.138470	+	0.516776i	0.861490	+	0.507775i	$0.169532\pi$
$857$	−4.05364	+	15.1284i	−0.138470	+	0.516776i	−0.999959	+	0.00900123i	$0.997135\pi$
$858$	5.73863	−	3.67455i	0.195914	−	0.125447i
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	0.488162	−	0.872753i	$-0.337667\pi$
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	−0.511745	+	0.859137i	$0.671001\pi$
$860$		0			0
$861$	37.5099	−	41.1249i	1.27833	−	1.40153i
$862$	−18.6337	−	4.99288i	−0.634666	−	0.170058i
$863$	30.2854	−	30.2854i	1.03093	−	1.03093i	0.0314193	−	0.999506i	$-0.489997\pi$
$863$	30.2854	−	30.2854i	1.03093	−	1.03093i	0.999506	−	0.0314193i	$-0.0100027\pi$
$864$	−2.02166	−	4.78674i	−0.0687783	−	0.162848i
$865$		0			0
$866$	−20.4721	+	11.8196i	−0.695671	+	0.401646i
$867$	29.3638	−	1.34994i	0.997246	−	0.0458462i
$868$	−35.3169	+	9.46313i	−1.19873	+	0.321199i
$869$	26.9630	−	46.7013i	0.914658	−	1.58423i
$870$		0			0
$871$	−4.03119	−	6.98222i	−0.136592	−	0.236584i
$872$	5.16301	+	5.16301i	0.174842	+	0.174842i
$873$	4.42384	+	0.759010i	0.149724	+	0.0256886i
$874$		−	9.93098i		−	0.335920i
$875$		0			0
$876$	19.3226	−	6.14144i	0.652850	−	0.207500i
$877$	−4.48641	−	16.7435i	−0.151495	−	0.565388i	−0.999380	−	0.0352074i	$-0.988791\pi$
$877$	−4.48641	−	16.7435i	−0.151495	−	0.565388i	0.847885	−	0.530180i	$-0.177876\pi$
$878$	−9.31875	−	34.7780i	−0.314492	−	1.17370i
$879$	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	$0.918115\pi$
$882$	−15.5688	+	18.7290i	−0.524229	+	0.630639i
$883$	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
$887$	−26.4123	+	7.07714i	−0.886837	+	0.237627i	−0.673355	−	0.739320i	$-0.735147\pi$
$887$	−26.4123	+	7.07714i	−0.886837	+	0.237627i	−0.213482	+	0.976947i	$0.568481\pi$
$888$	7.99804	−	0.367692i	0.268397	−	0.0123389i
$889$	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
$893$	−6.31049	−	1.69089i	−0.211173	−	0.0565835i
$894$	1.20980	−	1.32639i	0.0404616	−	0.0443612i
$895$		0			0
$896$	3.36730	+	1.94411i	0.112494	+	0.0649483i
$897$	−7.60889	+	4.87211i	−0.254053	+	0.162675i
$898$	10.6994	−	39.9306i	0.357043	−	1.33250i
$899$	40.5510			1.35245
$900$		0			0
$901$	0.881522			0.0293678
$902$	−8.50016	+	31.7230i	−0.283025	+	1.05626i
$903$	12.3393	+	6.38732i	0.410628	+	0.212557i
$904$	−3.65405	−	2.10967i	−0.121532	−	0.0701666i
$905$		0			0
$906$	−2.13480	−	6.71666i	−0.0709241	−	0.223146i
$907$	24.7295	+	6.62626i	0.821130	+	0.220021i	0.644841	−	0.764317i	$-0.276924\pi$
$907$	24.7295	+	6.62626i	0.821130	+	0.220021i	0.176290	+	0.984338i	$0.443590\pi$
$908$	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	$0.311697\pi$
$912$	−1.76052	−	2.74944i	−0.0582965	−	0.0910430i
$913$	26.8582	−	7.19662i	0.888875	−	0.238173i
$914$	10.7957	−	18.6987i	0.357090	−	0.618499i
$915$		0			0
$916$	11.3940	+	19.7350i	0.376468	+	0.652061i
$917$	12.3259	+	12.3259i	0.407035	+	0.407035i
$918$	−0.542723	−	0.697245i	−0.0179125	−	0.0230125i
$919$		−	28.8740i		−	0.952464i	−0.879320	−	0.476232i	$-0.842002\pi$
$919$		−	28.8740i		−	0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$920$		0			0
$921$	36.7298	+	33.5011i	1.21029	+	1.10390i
$922$	3.24877	+	12.1246i	0.106993	+	0.399302i
$923$	1.78073	+	6.64579i	0.0586135	+	0.218749i
$924$	5.73178	−	26.1397i	0.188562	−	0.859932i
$925$		0			0
$926$		−	22.1046i		−	0.726404i
$927$	−18.2486	+	6.73746i	−0.599362	+	0.221287i
$928$	−3.04930	−	3.04930i	−0.100098	−	0.100098i
$929$	25.1077	+	43.4879i	0.823758	+	1.42679i	0.902865	+	0.429925i	$0.141460\pi$
$929$	25.1077	+	43.4879i	0.823758	+	1.42679i	−0.0791067	+	0.996866i	$0.525207\pi$
$930$		0			0
$931$	−7.65121	+	13.2523i	−0.250758	+	0.434326i
$932$	28.2072	−	7.55809i	0.923956	−	0.247573i
$933$	11.0206	−	21.2903i	0.360800	−	0.697012i
$934$	4.26380	−	2.46170i	0.139516	−	0.0805494i
$935$		0			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	$0.243697\pi$
$938$	−30.5834	−	8.19479i	−0.998582	−	0.267569i
$939$	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	$0.971437\pi$
$942$	−0.725875	−	15.7892i	−0.0236503	−	0.514441i
$943$	11.2704	−	42.0618i	0.367015	−	1.36972i
$944$	5.45754			0.177628
$945$		0			0
$946$	−8.19815			−0.266545
$947$	−0.681485	+	2.54334i	−0.0221453	+	0.0826473i	−0.976114	−	0.217258i	$-0.930289\pi$
$947$	−0.681485	+	2.54334i	−0.0221453	+	0.0826473i	0.953969	+	0.299906i	$0.0969552\pi$
$948$	1.07949	+	23.4809i	0.0350601	+	0.762626i
$949$	−10.0371	−	5.79490i	−0.325817	−	0.188111i
$950$		0			0
$951$	−1.42219	−	0.311851i	−0.0461176	−	0.0101125i
$952$	0.638639	+	0.171123i	0.0206984	+	0.00554612i
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	−0.996419	−	0.0845545i	$-0.973053\pi$
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	0.0845545	+	0.996419i	$0.473053\pi$
$954$	8.97912	+	12.6984i	0.290710	+	0.411126i
$955$		0			0
$956$	7.90295	−	4.56277i	0.255600	−	0.147571i
$957$	−13.6438	+	26.3578i	−0.441042	+	0.852027i
$958$	2.62100	−	0.702296i	0.0846808	−	0.0226901i
$959$	−24.2991	+	42.0872i	−0.784658	+	1.35907i
$960$		0			0
$961$	−28.7123	−	49.7312i	−0.926204	−	1.60423i
$962$	−3.23623	−	3.23623i	−0.104340	−	0.104340i
$963$	12.0735	+	10.0363i	0.389062	+	0.323414i
$964$		−	1.73931i		−	0.0560194i
$965$		0			0
$966$	−7.59981	+	34.6587i	−0.244520	+	1.11513i
$967$	0.343829	+	1.28319i	0.0110568	+	0.0412646i	0.971234	−	0.238128i	$-0.0765337\pi$
$967$	0.343829	+	1.28319i	0.0110568	+	0.0412646i	−0.960177	+	0.279392i	$0.909867\pi$
$968$	1.23963	+	4.62638i	0.0398433	+	0.148697i
$969$	−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	$-0.213853\pi$
$972$	4.51572	−	14.9201i	0.144842	−	0.478561i
$973$	−11.4428	−	11.4428i	−0.366840	−	0.366840i
$974$	−5.80393	−	10.0527i	−0.185970	−	0.322109i
$975$		0			0
$976$	4.35623	−	7.54520i	0.139439	−	0.241516i
$977$	−41.4084	+	11.0953i	−1.32477	+	0.354972i	−0.850764	−	0.525548i	$-0.823860\pi$
$977$	−41.4084	+	11.0953i	−1.32477	+	0.354972i	−0.474009	+	0.880520i	$0.657193\pi$
$978$	−6.65520	−	10.3936i	−0.212810	−	0.332350i
$979$	−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
$983$	−31.1321	−	8.34182i	−0.992960	−	0.266063i	−0.274466	−	0.961597i	$-0.588501\pi$
$983$	−31.1321	−	8.34182i	−0.992960	−	0.266063i	−0.718493	+	0.695534i	$0.755168\pi$
$984$	−4.33624	−	13.6430i	−0.138234	−	0.434922i
$985$		0			0
$986$	−0.635046	−	0.366644i	−0.0202240	−	0.0116763i
$987$	20.7294	+	10.7303i	0.659824	+	0.341550i
$988$	−0.483018	+	1.80265i	−0.0153669	+	0.0573499i
$989$	10.8700			0.345645
$990$		0			0
$991$	20.1017			0.638551			0.319275	−	0.947662i	$-0.396561\pi$
$991$	20.1017			0.638551			0.319275	+	0.947662i	$0.396561\pi$
$992$	−2.43379	+	9.08302i	−0.0772729	+	0.288386i
$993$	−6.07411	+	3.88937i	−0.192756	+	0.123425i
$994$	23.3998	+	13.5099i	0.742196	+	0.428507i
$995$		0			0
$996$	−8.16761	+	8.95478i	−0.258801	+	0.283743i
$997$	2.84912	+	0.763421i	0.0902327	+	0.0241778i	0.303653	−	0.952783i	$-0.401794\pi$
$997$	2.84912	+	0.763421i	0.0902327	+	0.0241778i	−0.213420	+	0.976960i	$0.568460\pi$
$998$	−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.293.4		16
3.2	odd	2		1350.2.q.h.1043.1		16
5.2	odd	4	inner	450.2.p.h.257.4		16
5.3	odd	4		90.2.l.b.77.1	yes	16
5.4	even	2		90.2.l.b.23.1	✓	16
9.2	odd	6	inner	450.2.p.h.443.4		16
9.7	even	3		1350.2.q.h.143.2		16
15.2	even	4		1350.2.q.h.557.2		16
15.8	even	4		270.2.m.b.17.4		16
15.14	odd	2		270.2.m.b.233.3		16
20.3	even	4		720.2.cu.b.257.4		16
20.19	odd	2		720.2.cu.b.113.3		16
45.2	even	12	inner	450.2.p.h.407.4		16
45.4	even	6		810.2.f.c.323.1		16
45.7	odd	12		1350.2.q.h.1007.1		16
45.13	odd	12		810.2.f.c.647.8		16
45.14	odd	6		810.2.f.c.323.8		16
45.23	even	12		810.2.f.c.647.1		16
45.29	odd	6		90.2.l.b.83.1	yes	16
45.34	even	6		270.2.m.b.143.4		16
45.38	even	12		90.2.l.b.47.1	yes	16
45.43	odd	12		270.2.m.b.197.3		16
180.83	odd	12		720.2.cu.b.497.3		16
180.119	even	6		720.2.cu.b.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	5.4	even	2
90.2.l.b.47.1	yes	16	45.38	even	12
90.2.l.b.77.1	yes	16	5.3	odd	4
90.2.l.b.83.1	yes	16	45.29	odd	6
270.2.m.b.17.4		16	15.8	even	4
270.2.m.b.143.4		16	45.34	even	6
270.2.m.b.197.3		16	45.43	odd	12
270.2.m.b.233.3		16	15.14	odd	2
450.2.p.h.257.4		16	5.2	odd	4	inner
450.2.p.h.293.4		16	1.1	even	1	trivial
450.2.p.h.407.4		16	45.2	even	12	inner
450.2.p.h.443.4		16	9.2	odd	6	inner
720.2.cu.b.113.3		16	20.19	odd	2
720.2.cu.b.257.4		16	20.3	even	4
720.2.cu.b.353.4		16	180.119	even	6
720.2.cu.b.497.3		16	180.83	odd	12
810.2.f.c.323.1		16	45.4	even	6
810.2.f.c.323.8		16	45.14	odd	6
810.2.f.c.647.1		16	45.23	even	12
810.2.f.c.647.8		16	45.13	odd	12
1350.2.q.h.143.2		16	9.7	even	3
1350.2.q.h.557.2		16	15.2	even	4
1350.2.q.h.1007.1		16	45.7	odd	12
1350.2.q.h.1043.1		16	3.2	odd	2

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)

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