LMFDB - Embedded newform 1050.2.bc.h.493.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.2
Root			$-0.709944 + 0.925217i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.h.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.582897 - 1.00961i) q^{11} +(0.258819 - 0.965926i) q^{12} +(1.92501 - 1.92501i) q^{13} +(-0.756134 - 2.53540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.0209315 - 0.00560858i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.989363 - 1.71363i) q^{19} +(1.81766 - 1.92253i) q^{21} +(-0.824341 + 0.824341i) q^{22} +(-1.85829 + 6.93525i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.35765 + 1.36119i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.0741591 + 2.64471i) q^{28} -5.60604i q^{29} +(6.86850 + 3.96553i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.12607 - 0.301730i) q^{33} -0.0216699 q^{34} -1.00000 q^{36} +(10.2592 + 2.74894i) q^{37} +(0.512132 + 1.91130i) q^{38} +(-2.35765 - 1.36119i) q^{39} +2.48977i q^{41} +(-2.25331 + 1.38658i) q^{42} +(7.87756 + 7.87756i) q^{43} +(1.00961 - 0.582897i) q^{44} +(3.58995 - 6.21797i) q^{46} +(1.05773 - 3.94750i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-3.15479 + 6.24878i) q^{49} +(-0.0108349 - 0.0187667i) q^{51} +(2.62962 - 0.704604i) q^{52} +(-2.82745 + 0.757613i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.612870 - 2.57379i) q^{56} +(-1.39917 + 1.39917i) q^{57} +(-1.45095 + 5.41502i) q^{58} +(5.34623 - 9.25995i) q^{59} +(-3.15795 + 1.82324i) q^{61} +(-5.60811 - 5.60811i) q^{62} +(-2.32747 - 1.25813i) q^{63} +1.00000i q^{64} +(1.00961 + 0.582897i) q^{66} +(-3.76794 - 14.0621i) q^{67} +(0.0209315 + 0.00560858i) q^{68} +7.17989 q^{69} +7.51848 q^{71} +(0.965926 + 0.258819i) q^{72} +(-0.969376 - 3.61776i) q^{73} +(-9.19815 - 5.31055i) q^{74} -1.97873i q^{76} +(3.08319 - 0.0864543i) q^{77} +(1.92501 + 1.92501i) q^{78} +(-1.39464 + 0.805197i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.644400 - 2.40493i) q^{82} +(9.74815 - 9.74815i) q^{83} +(2.53540 - 0.756134i) q^{84} +(-5.57028 - 9.64800i) q^{86} +(-5.41502 + 1.45095i) q^{87} +(-1.12607 + 0.301730i) q^{88} +(1.80255 + 3.12211i) q^{89} +(7.00683 + 1.66846i) q^{91} +(-5.07695 + 5.07695i) q^{92} +(2.05271 - 7.66082i) q^{93} +(-2.04338 + 3.53923i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(0.265501 + 0.265501i) q^{97} +(4.66460 - 5.21934i) q^{98} +1.16579i 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} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	1.38658	+	2.25331i	0.524078	+	0.851670i
$7$	1.38658	+	2.25331i	0.524078	+	0.851670i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	0.582897	−	1.00961i	0.175750	−	0.304408i	−0.764670	−	0.644422i	$-0.777098\pi$
$11$	0.582897	−	1.00961i	0.175750	−	0.304408i	0.940421	+	0.340013i	$0.110432\pi$
$12$	0.258819	−	0.965926i	0.0747146	−	0.278839i
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	−0.387829	−	0.921731i	$-0.626775\pi$
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	0.921731	+	0.387829i	$0.126775\pi$
$14$	−0.756134	−	2.53540i	−0.202085	−	0.677615i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.0209315	−	0.00560858i	0.00507664	−	0.00136028i	−0.256280	−	0.966603i	$-0.582497\pi$
$17$	0.0209315	−	0.00560858i	0.00507664	−	0.00136028i	0.261356	+	0.965242i	$0.415830\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−0.989363	−	1.71363i	−0.226976	−	0.393133i	0.729935	−	0.683517i	$-0.239550\pi$
$19$	−0.989363	−	1.71363i	−0.226976	−	0.393133i	−0.956910	+	0.290384i	$0.906217\pi$
$20$		0			0
$21$	1.81766	−	1.92253i	0.396645	−	0.419531i
$22$	−0.824341	+	0.824341i	−0.175750	+	0.175750i
$23$	−1.85829	+	6.93525i	−0.387481	+	1.44610i	0.446738	+	0.894665i	$0.352586\pi$
$23$	−1.85829	+	6.93525i	−0.387481	+	1.44610i	−0.834219	+	0.551434i	$0.814081\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−2.35765	+	1.36119i	−0.462373	+	0.266951i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.0741591	+	2.64471i	0.0140148	+	0.499804i
$29$		−	5.60604i		−	1.04102i	−0.853857	−	0.520508i	$-0.825743\pi$
$29$		−	5.60604i		−	1.04102i	0.853857	−	0.520508i	$-0.174257\pi$
$30$		0			0
$31$	6.86850	+	3.96553i	1.23362	+	0.712231i	0.967783	−	0.251787i	$-0.0810183\pi$
$31$	6.86850	+	3.96553i	1.23362	+	0.712231i	0.265837	+	0.964018i	$0.414352\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.12607	−	0.301730i	−0.196024	−	0.0525244i
$34$	−0.0216699			−0.00371636
$35$		0			0
$36$	−1.00000			−0.166667
$37$	10.2592	+	2.74894i	1.68660	+	0.451924i	0.969509	−	0.245054i	$-0.0788057\pi$
$37$	10.2592	+	2.74894i	1.68660	+	0.451924i	0.717093	+	0.696978i	$0.245472\pi$
$38$	0.512132	+	1.91130i	0.0830788	+	0.310054i
$39$	−2.35765	−	1.36119i	−0.377526	−	0.217965i
$40$		0			0
$41$			2.48977i			0.388837i	0.980919	+	0.194418i	$0.0622819\pi$
$41$			2.48977i			0.388837i	−0.980919	+	0.194418i	$0.937718\pi$
$42$	−2.25331	+	1.38658i	−0.347693	+	0.213954i
$43$	7.87756	+	7.87756i	1.20132	+	1.20132i	0.973766	+	0.227550i	$0.0730716\pi$
$43$	7.87756	+	7.87756i	1.20132	+	1.20132i	0.227550	+	0.973766i	$0.426928\pi$
$44$	1.00961	−	0.582897i	0.152204	−	0.0878751i
$45$		0			0
$46$	3.58995	−	6.21797i	0.529309	−	0.916790i
$47$	1.05773	−	3.94750i	0.154286	−	0.575802i	−0.844880	−	0.534956i	$-0.820328\pi$
$47$	1.05773	−	3.94750i	0.154286	−	0.575802i	0.999165	−	0.0408457i	$-0.0130052\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	−3.15479	+	6.24878i	−0.450685	+	0.892683i
$50$		0			0
$51$	−0.0108349	−	0.0187667i	−0.00151720	−	0.00262786i
$52$	2.62962	−	0.704604i	0.364662	−	0.0977110i
$53$	−2.82745	+	0.757613i	−0.388380	+	0.104066i	−0.447725	−	0.894171i	$-0.647766\pi$
$53$	−2.82745	+	0.757613i	−0.388380	+	0.104066i	0.0593446	+	0.998238i	$0.481099\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	0.612870	−	2.57379i	0.0818981	−	0.343937i
$57$	−1.39917	+	1.39917i	−0.185325	+	0.185325i
$58$	−1.45095	+	5.41502i	−0.190519	+	0.711027i
$59$	5.34623	−	9.25995i	0.696020	−	1.20554i	−0.273815	−	0.961782i	$-0.588286\pi$
$59$	5.34623	−	9.25995i	0.696020	−	1.20554i	0.969835	−	0.243760i	$-0.0783810\pi$
$60$		0			0
$61$	−3.15795	+	1.82324i	−0.404334	+	0.233442i	−0.688352	−	0.725376i	$-0.741666\pi$
$61$	−3.15795	+	1.82324i	−0.404334	+	0.233442i	0.284018	+	0.958819i	$0.408332\pi$
$62$	−5.60811	−	5.60811i	−0.712231	−	0.712231i
$63$	−2.32747	−	1.25813i	−0.293233	−	0.158510i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	1.00961	+	0.582897i	0.124274	+	0.0717497i
$67$	−3.76794	−	14.0621i	−0.460327	−	1.71796i	−0.671935	−	0.740610i	$-0.734537\pi$
$67$	−3.76794	−	14.0621i	−0.460327	−	1.71796i	0.211608	−	0.977355i	$-0.432130\pi$
$68$	0.0209315	+	0.00560858i	0.00253832	+	0.000680140i
$69$	7.17989			0.864358
$70$		0			0
$71$	7.51848			0.892280			0.446140	−	0.894963i	$-0.352798\pi$
$71$	7.51848			0.892280			0.446140	+	0.894963i	$0.352798\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−0.969376	−	3.61776i	−0.113457	−	0.423427i	0.885710	−	0.464239i	$-0.153672\pi$
$73$	−0.969376	−	3.61776i	−0.113457	−	0.423427i	−0.999167	+	0.0408122i	$0.987005\pi$
$74$	−9.19815	−	5.31055i	−1.06926	−	0.617339i
$75$		0			0
$76$		−	1.97873i		−	0.226976i
$77$	3.08319	−	0.0864543i	0.351362	−	0.00985238i
$78$	1.92501	+	1.92501i	0.217965	+	0.217965i
$79$	−1.39464	+	0.805197i	−0.156910	+	0.0905918i	−0.576399	−	0.817169i	$-0.695543\pi$
$79$	−1.39464	+	0.805197i	−0.156910	+	0.0905918i	0.419489	+	0.907760i	$0.362209\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.644400	−	2.40493i	0.0711620	−	0.265580i
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.0726405	−	0.997358i	$-0.476857\pi$
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.997358	−	0.0726405i	$-0.0231426\pi$
$84$	2.53540	−	0.756134i	0.276635	−	0.0825010i
$85$		0			0
$86$	−5.57028	−	9.64800i	−0.600658	−	1.04037i
$87$	−5.41502	+	1.45095i	−0.580551	+	0.155558i
$88$	−1.12607	+	0.301730i	−0.120040	+	0.0321645i
$89$	1.80255	+	3.12211i	0.191070	+	0.330943i	0.945605	−	0.325317i	$-0.105471\pi$
$89$	1.80255	+	3.12211i	0.191070	+	0.330943i	−0.754535	+	0.656260i	$0.772138\pi$
$90$		0			0
$91$	7.00683	+	1.66846i	0.734516	+	0.174903i
$92$	−5.07695	+	5.07695i	−0.529309	+	0.529309i
$93$	2.05271	−	7.66082i	0.212856	−	0.794390i
$94$	−2.04338	+	3.53923i	−0.210758	+	0.365044i
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	0.720457	−	0.693500i	$-0.243932\pi$
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	−0.693500	+	0.720457i	$0.743932\pi$
$98$	4.66460	−	5.21934i	0.471196	−	0.527233i
$99$			1.16579i			0.117167i
$100$		0			0
$101$	12.0515	+	6.95796i	1.19917	+	0.692343i	0.960371	−	0.278725i	$-0.0899119\pi$
$101$	12.0515	+	6.95796i	1.19917	+	0.692343i	0.238802	+	0.971068i	$0.423245\pi$
$102$	0.00560858	+	0.0209315i	0.000555332	+	0.00207253i
$103$	11.5757	+	3.10171i	1.14059	+	0.305621i	0.779189	−	0.626789i	$-0.215631\pi$
$103$	11.5757	+	3.10171i	1.14059	+	0.305621i	0.361403	+	0.932410i	$0.382298\pi$
$104$	−2.72238			−0.266951
$105$		0			0
$106$	2.92719			0.284314
$107$	6.67031	+	1.78730i	0.644843	+	0.172785i	0.566396	−	0.824133i	$-0.308337\pi$
$107$	6.67031	+	1.78730i	0.644843	+	0.172785i	0.0784469	+	0.996918i	$0.475004\pi$
$108$	0.258819	+	0.965926i	0.0249049	+	0.0929463i
$109$	−0.499969	−	0.288657i	−0.0478883	−	0.0276483i	0.475865	−	0.879519i	$-0.342135\pi$
$109$	−0.499969	−	0.288657i	−0.0478883	−	0.0276483i	−0.523753	+	0.851870i	$0.675469\pi$
$110$		0			0
$111$		−	10.6211i		−	1.00811i
$112$	−1.25813	+	2.32747i	−0.118882	+	0.219925i
$113$	−13.2689	−	13.2689i	−1.24823	−	1.24823i	−0.956501	−	0.291728i	$-0.905770\pi$
$113$	−13.2689	−	13.2689i	−1.24823	−	1.24823i	−0.291728	−	0.956501i	$-0.594230\pi$
$114$	1.71363	−	0.989363i	0.160496	−	0.0926624i
$115$		0			0
$116$	2.80302	−	4.85498i	0.260254	−	0.450773i
$117$	−0.704604	+	2.62962i	−0.0651406	+	0.243108i
$118$	−7.56072	+	7.56072i	−0.696020	+	0.696020i
$119$	0.0416611	+	0.0393884i	0.00381906	+	0.00361073i
$120$		0			0
$121$	4.82046	+	8.34928i	0.438224	+	0.759026i
$122$	3.52224	−	0.943781i	0.318888	−	0.0854459i
$123$	2.40493	−	0.644400i	0.216845	−	0.0581036i
$124$	3.96553	+	6.86850i	0.356115	+	0.616810i
$125$		0			0
$126$	1.92253	+	1.81766i	0.171273	+	0.161930i
$127$	−1.36110	+	1.36110i	−0.120778	+	0.120778i	−0.764912	−	0.644134i	$-0.777218\pi$
$127$	−1.36110	+	1.36110i	−0.120778	+	0.120778i	0.644134	+	0.764912i	$0.277218\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	5.57028	−	9.64800i	0.490435	−	0.849459i
$130$		0			0
$131$	−14.8522	+	8.57489i	−1.29764	+	0.749192i	−0.979996	−	0.199019i	$-0.936225\pi$
$131$	−14.8522	+	8.57489i	−1.29764	+	0.749192i	−0.317643	+	0.948210i	$0.602891\pi$
$132$	−0.824341	−	0.824341i	−0.0717497	−	0.0717497i
$133$	2.48950	−	4.60542i	0.215867	−	0.399341i
$134$			14.5582i			1.25764i
$135$		0			0
$136$	−0.0187667	−	0.0108349i	−0.00160923	−	0.000929089i
$137$	−2.64921	−	9.88699i	−0.226337	−	0.844702i	−0.981864	−	0.189585i	$-0.939286\pi$
$137$	−2.64921	−	9.88699i	−0.226337	−	0.844702i	0.755527	−	0.655117i	$-0.227381\pi$
$138$	−6.93525	−	1.85829i	−0.590367	−	0.158188i
$139$	5.65119			0.479327			0.239664	−	0.970856i	$-0.422963\pi$
$139$	5.65119			0.479327			0.239664	+	0.970856i	$0.422963\pi$
$140$		0			0
$141$	−4.08675			−0.344166
$142$	−7.26230	−	1.94593i	−0.609439	−	0.163299i
$143$	−0.821423	−	3.06559i	−0.0686909	−	0.256358i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$			3.74538i			0.309970i
$147$	6.85238	+	1.42999i	0.565175	+	0.117944i
$148$	7.51026	+	7.51026i	0.617339	+	0.617339i
$149$	0.191221	−	0.110402i	0.0156655	−	0.00904446i	−0.492147	−	0.870512i	$-0.663788\pi$
$149$	0.191221	−	0.110402i	0.0156655	−	0.00904446i	0.507812	+	0.861468i	$0.330454\pi$
$150$		0			0
$151$	3.18442	−	5.51559i	0.259145	−	0.448852i	−0.706868	−	0.707345i	$-0.749893\pi$
$151$	3.18442	−	5.51559i	0.259145	−	0.448852i	0.966013	+	0.258493i	$0.0832260\pi$
$152$	−0.512132	+	1.91130i	−0.0415394	+	0.155027i
$153$	−0.0153229	+	0.0153229i	−0.00123879	+	0.00123879i
$154$	−3.00051	−	0.714480i	−0.241788	−	0.0575745i
$155$		0			0
$156$	−1.36119	−	2.35765i	−0.108982	−	0.188763i
$157$	13.9830	−	3.74673i	1.11596	−	0.299022i	0.346715	−	0.937970i	$-0.387297\pi$
$157$	13.9830	−	3.74673i	1.11596	−	0.299022i	0.769249	+	0.638949i	$0.220630\pi$
$158$	1.55552	−	0.416801i	0.123751	−	0.0331589i
$159$	1.46360	+	2.53502i	0.116071	+	0.201040i
$160$		0			0
$161$	−18.2039	+	5.42896i	−1.43467	+	0.427862i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−5.66960	+	21.1592i	−0.444078	+	1.65732i	0.274283	+	0.961649i	$0.411560\pi$
$163$	−5.66960	+	21.1592i	−0.444078	+	1.65732i	−0.718360	+	0.695671i	$0.755107\pi$
$164$	−1.24488	+	2.15620i	−0.0972091	+	0.168371i
$165$		0			0
$166$	−11.9390	+	6.89298i	−0.926646	+	0.534999i
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	0.993689	−	0.112174i	$-0.0357814\pi$
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	−0.112174	+	0.993689i	$0.535781\pi$
$168$	−2.64471	+	0.0741591i	−0.204044	+	0.00572150i
$169$			5.58865i			0.429896i
$170$		0			0
$171$	1.71363	+	0.989363i	0.131044	+	0.0756585i
$172$	2.88339	+	10.7609i	0.219856	+	0.820515i
$173$	−10.0874	−	2.70291i	−0.766932	−	0.205499i	−0.145916	−	0.989297i	$-0.546613\pi$
$173$	−10.0874	−	2.70291i	−0.766932	−	0.205499i	−0.621016	+	0.783798i	$0.713280\pi$
$174$	5.60604			0.424993
$175$		0			0
$176$	1.16579			0.0878751
$177$	−10.3281	−	2.76741i	−0.776310	−	0.208012i
$178$	−0.933068	−	3.48226i	−0.0699364	−	0.261006i
$179$	1.30513	+	0.753516i	0.0975498	+	0.0563204i	0.547981	−	0.836491i	$-0.315397\pi$
$179$	1.30513	+	0.753516i	0.0975498	+	0.0563204i	−0.450431	+	0.892811i	$0.648730\pi$
$180$		0			0
$181$		−	21.3457i		−	1.58662i	−0.608821	−	0.793308i	$-0.708357\pi$
$181$		−	21.3457i		−	1.58662i	0.608821	−	0.793308i	$-0.291643\pi$
$182$	−6.33625	−	3.42511i	−0.469674	−	0.253886i
$183$	2.57846	+	2.57846i	0.190605	+	0.190605i
$184$	6.21797	−	3.58995i	0.458395	−	0.264654i
$185$		0			0
$186$	−3.96553	+	6.86850i	−0.290767	+	0.503623i
$187$	0.00653845	−	0.0244018i	0.000478139	−	0.00178444i
$188$	2.88977	−	2.88977i	0.210758	−	0.210758i
$189$	−0.612870	+	2.57379i	−0.0445797	+	0.187216i
$190$		0			0
$191$	−3.22543	−	5.58661i	−0.233384	−	0.404233i	0.725418	−	0.688309i	$-0.241647\pi$
$191$	−3.22543	−	5.58661i	−0.233384	−	0.404233i	−0.958802	+	0.284076i	$0.908313\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	−4.96349	+	1.32996i	−0.357280	+	0.0957328i	−0.432994	−	0.901397i	$-0.642543\pi$
$193$	−4.96349	+	1.32996i	−0.357280	+	0.0957328i	0.0757145	+	0.997130i	$0.475876\pi$
$194$	−0.187737	−	0.325171i	−0.0134788	−	0.0233459i
$195$		0			0
$196$	−5.85652	+	3.83421i	−0.418323	+	0.273872i
$197$	−17.8347	+	17.8347i	−1.27067	+	1.27067i	−0.324931	+	0.945738i	$0.605341\pi$
$197$	−17.8347	+	17.8347i	−1.27067	+	1.27067i	−0.945738	+	0.324931i	$0.894659\pi$
$198$	0.301730	−	1.12607i	0.0214430	−	0.0800264i
$199$	−2.47098	+	4.27987i	−0.175163	+	0.303392i	−0.940218	−	0.340574i	$-0.889379\pi$
$199$	−2.47098	+	4.27987i	−0.175163	+	0.303392i	0.765054	+	0.643966i	$0.222712\pi$
$200$		0			0
$201$	−12.6078	+	7.27910i	−0.889284	+	0.513428i
$202$	−9.84004	−	9.84004i	−0.692343	−	0.692343i
$203$	12.6321	−	7.77323i	0.886603	−	0.545574i
$204$		−	0.0216699i		−	0.00151720i
$205$		0			0
$206$	−10.3785	−	5.99204i	−0.723106	−	0.417485i
$207$	−1.85829	−	6.93525i	−0.129160	−	0.482033i
$208$	2.62962	+	0.704604i	0.182331	+	0.0488555i
$209$	−2.30679			−0.159564
$210$		0			0
$211$	−19.0455			−1.31115			−0.655574	−	0.755131i	$-0.727573\pi$
$211$	−19.0455			−1.31115			−0.655574	+	0.755131i	$0.727573\pi$
$212$	−2.82745	−	0.757613i	−0.194190	−	0.0520331i
$213$	−1.94593	−	7.26230i	−0.133333	−	0.497604i
$214$	−5.98043	−	3.45281i	−0.408814	−	0.236029i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	0.588161	+	20.9754i	0.0399270	+	1.42390i
$218$	0.408223	+	0.408223i	0.0276483	+	0.0276483i
$219$	−3.24360	+	1.87269i	−0.219182	+	0.126545i
$220$		0			0
$221$	0.0294968	−	0.0510900i	0.00198417	−	0.00343669i
$222$	−2.74894	+	10.2592i	−0.184497	+	0.688553i
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	−0.798801	−	0.601596i	$-0.794532\pi$
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	0.601596	+	0.798801i	$0.294532\pi$
$224$	1.81766	−	1.92253i	0.121447	−	0.128455i
$225$		0			0
$226$	9.38250	+	16.2510i	0.624115	+	1.08100i
$227$	17.8106	−	4.77234i	1.18213	−	0.316751i	0.386360	−	0.922348i	$-0.373732\pi$
$227$	17.8106	−	4.77234i	1.18213	−	0.316751i	0.795772	+	0.605597i	$0.207065\pi$
$228$	−1.91130	+	0.512132i	−0.126579	+	0.0339168i
$229$	−2.95505	−	5.11830i	−0.195276	−	0.338227i	0.751715	−	0.659488i	$-0.229227\pi$
$229$	−2.95505	−	5.11830i	−0.195276	−	0.338227i	−0.946991	+	0.321261i	$0.895893\pi$
$230$		0			0
$231$	−0.881497	−	2.95576i	−0.0579983	−	0.194475i
$232$	−3.96407	+	3.96407i	−0.260254	+	0.260254i
$233$	−1.87264	+	6.98879i	−0.122681	+	0.457851i	−0.999746	−	0.0225196i	$-0.992831\pi$
$233$	−1.87264	+	6.98879i	−0.122681	+	0.457851i	0.877066	+	0.480371i	$0.159498\pi$
$234$	1.36119	−	2.35765i	0.0889838	−	0.154124i
$235$		0			0
$236$	9.25995	−	5.34623i	0.602771	−	0.348010i
$237$	1.13872	+	1.13872i	0.0739679	+	0.0739679i
$238$	−0.0300470	−	0.0488289i	−0.00194766	−	0.00316511i
$239$			4.20172i			0.271787i	0.990723	+	0.135893i	$0.0433904\pi$
$239$			4.20172i			0.271787i	−0.990723	+	0.135893i	$0.956610\pi$
$240$		0			0
$241$	−18.9970	−	10.9679i	−1.22371	−	0.706507i	−0.258000	−	0.966145i	$-0.583064\pi$
$241$	−18.9970	−	10.9679i	−1.22371	−	0.706507i	−0.965706	+	0.259638i	$0.916397\pi$
$242$	−2.49525	−	9.31242i	−0.160401	−	0.598625i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−3.64649			−0.233442
$245$		0			0
$246$	−2.48977			−0.158742
$247$	−5.20329	−	1.39422i	−0.331078	−	0.0887120i
$248$	−2.05271	−	7.66082i	−0.130347	−	0.486463i
$249$	−11.9390	−	6.89298i	−0.756603	−	0.436825i
$250$		0			0
$251$			15.1293i			0.954952i	0.878645	+	0.477476i	$0.158448\pi$
$251$			15.1293i			0.954952i	−0.878645	+	0.477476i	$0.841552\pi$
$252$	−1.38658	−	2.25331i	−0.0873463	−	0.141945i
$253$	5.91868	+	5.91868i	0.372105	+	0.372105i
$254$	1.66700	−	0.962442i	0.104597	−	0.0603890i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.95653	+	22.2301i	−0.371558	+	1.38667i	0.486751	+	0.873541i	$0.338182\pi$
$257$	−5.95653	+	22.2301i	−0.371558	+	1.38667i	−0.858309	+	0.513133i	$0.828485\pi$
$258$	−7.87756	+	7.87756i	−0.490435	+	0.490435i
$259$	8.03098	+	26.9288i	0.499021	+	1.67327i
$260$		0			0
$261$	2.80302	+	4.85498i	0.173503	+	0.300516i
$262$	16.5654	−	4.43869i	1.02342	−	0.274223i
$263$	−19.4349	+	5.20756i	−1.19841	+	0.321112i	−0.802203	−	0.597051i	$-0.796339\pi$
$263$	−19.4349	+	5.20756i	−1.19841	+	0.321112i	−0.396203	+	0.918163i	$0.629672\pi$
$264$	0.582897	+	1.00961i	0.0358749	+	0.0621371i
$265$		0			0
$266$	−3.59664	+	3.80417i	−0.220524	+	0.233248i
$267$	2.54919	−	2.54919i	0.156008	−	0.156008i
$268$	3.76794	−	14.0621i	0.230164	−	0.858982i
$269$	4.63479	−	8.02770i	0.282588	−	0.489457i	−0.689433	−	0.724349i	$-0.742140\pi$
$269$	4.63479	−	8.02770i	0.282588	−	0.489457i	0.972021	+	0.234892i	$0.0754736\pi$
$270$		0			0
$271$	22.7157	−	13.1149i	1.37988	−	0.796673i	0.387734	−	0.921771i	$-0.373258\pi$
$271$	22.7157	−	13.1149i	1.37988	−	0.796673i	0.992144	+	0.125098i	$0.0399244\pi$
$272$	0.0153229	+	0.0153229i	0.000929089	+	0.000929089i
$273$	−0.201889	−	7.19991i	−0.0122189	−	0.435758i
$274$			10.2358i			0.618365i
$275$		0			0
$276$	6.21797	+	3.58995i	0.374278	+	0.216089i
$277$	−3.44216	−	12.8463i	−0.206819	−	0.771860i	−0.988887	−	0.148667i	$-0.952502\pi$
$277$	−3.44216	−	12.8463i	−0.206819	−	0.771860i	0.782068	−	0.623193i	$-0.214165\pi$
$278$	−5.45863	−	1.46263i	−0.327387	−	0.0877230i
$279$	−7.93107			−0.474821
$280$		0			0
$281$	−13.5101			−0.805944			−0.402972	−	0.915212i	$-0.632023\pi$
$281$	−13.5101			−0.805944			−0.402972	+	0.915212i	$0.632023\pi$
$282$	3.94750	+	1.05773i	0.235070	+	0.0629868i
$283$	−5.14819	−	19.2133i	−0.306028	−	1.14211i	−0.932057	−	0.362313i	$-0.881987\pi$
$283$	−5.14819	−	19.2133i	−0.306028	−	1.14211i	0.626028	−	0.779800i	$-0.284679\pi$
$284$	6.51120	+	3.75924i	0.386369	+	0.223070i
$285$		0			0
$286$			3.17374i			0.187667i
$287$	−5.61022	+	3.45226i	−0.331161	+	0.203781i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−14.7220	+	8.49977i	−0.866001	+	0.499986i
$290$		0			0
$291$	0.187737	−	0.325171i	0.0110054	−	0.0190618i
$292$	0.969376	−	3.61776i	0.0567284	−	0.211713i
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.0169176	+	0.999857i	$0.505385\pi$
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.999857	+	0.0169176i	$0.994615\pi$
$294$	−6.24878	−	3.15479i	−0.364436	−	0.183991i
$295$		0			0
$296$	−5.31055	−	9.19815i	−0.308670	−	0.534632i
$297$	1.12607	−	0.301730i	0.0653413	−	0.0175081i
$298$	−0.213280	+	0.0571481i	−0.0123550	+	0.00331050i
$299$	9.77320	+	16.9277i	0.565199	+	0.978953i
$300$		0			0
$301$	−6.82771	+	28.6734i	−0.393542	+	1.65271i
$302$	−4.50346	+	4.50346i	−0.259145	+	0.259145i
$303$	3.60170	−	13.4417i	0.206913	−	0.772208i
$304$	0.989363	−	1.71363i	0.0567439	−	0.0982833i
$305$		0			0
$306$	0.0187667	−	0.0108349i	0.00107282	−	0.000619393i
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	0.723084	−	0.690760i	$-0.242724\pi$
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	−0.690760	+	0.723084i	$0.742724\pi$
$308$	2.71335	+	1.46672i	0.154607	+	0.0835744i
$309$		−	11.9841i		−	0.681751i
$310$		0			0
$311$	11.6023	+	6.69862i	0.657909	+	0.379844i	0.791480	−	0.611196i	$-0.209311\pi$
$311$	11.6023	+	6.69862i	0.657909	+	0.379844i	−0.133571	+	0.991039i	$0.542644\pi$
$312$	0.704604	+	2.62962i	0.0398903	+	0.148873i
$313$	−27.7781	−	7.44312i	−1.57011	−	0.420710i	−0.634263	−	0.773117i	$-0.718697\pi$
$313$	−27.7781	−	7.44312i	−1.57011	−	0.420710i	−0.935847	+	0.352407i	$0.885363\pi$
$314$	−14.4763			−0.816943
$315$		0			0
$316$	−1.61039			−0.0905918
$317$	−32.5854	−	8.73124i	−1.83018	−	0.490395i	−0.832232	−	0.554427i	$-0.812938\pi$
$317$	−32.5854	−	8.73124i	−1.83018	−	0.490395i	−0.997948	+	0.0640314i	$0.979604\pi$
$318$	−0.757613	−	2.82745i	−0.0424848	−	0.158556i
$319$	−5.65991	−	3.26775i	−0.316894	−	0.182959i
$320$		0			0
$321$		−	6.90561i		−	0.385434i
$322$	18.9888	−	0.532455i	1.05820	−	0.0296725i
$323$	−0.0303199	−	0.0303199i	−0.00168704	−	0.00168704i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$		0			0
$326$	10.9528	−	18.9709i	0.606621	−	1.05070i
$327$	−0.149420	+	0.557643i	−0.00826294	+	0.0308377i
$328$	1.76053	−	1.76053i	0.0972091	−	0.0972091i
$329$	10.3616	−	3.09013i	0.571251	−	0.170364i
$330$		0			0
$331$	5.46781	+	9.47053i	0.300538	+	0.520547i	0.976258	−	0.216611i	$-0.0695004\pi$
$331$	5.46781	+	9.47053i	0.300538	+	0.520547i	−0.675720	+	0.737159i	$0.736167\pi$
$332$	13.3162	−	3.56807i	0.730823	−	0.195823i
$333$	−10.2592	+	2.74894i	−0.562201	+	0.150641i
$334$	−8.05513	−	13.9519i	−0.440757	−	0.763414i
$335$		0			0
$336$	2.57379	+	0.612870i	0.140412	+	0.0334348i
$337$	10.2916	−	10.2916i	0.560617	−	0.560617i	−0.368866	−	0.929483i	$-0.620254\pi$
$337$	10.2916	−	10.2916i	0.560617	−	0.560617i	0.929483	+	0.368866i	$0.120254\pi$
$338$	1.44645	−	5.39822i	0.0786764	−	0.293624i
$339$	−9.38250	+	16.2510i	−0.509587	+	0.882631i
$340$		0			0
$341$	8.00727	−	4.62300i	0.433618	−	0.250349i
$342$	−1.39917	−	1.39917i	−0.0756585	−	0.0756585i
$343$	−18.4548	+	1.55571i	−0.996466	+	0.0840004i
$344$		−	11.1406i		−	0.600658i
$345$		0			0
$346$	9.04413	+	5.22163i	0.486215	+	0.280717i
$347$	0.661173	+	2.46753i	0.0354936	+	0.132464i	0.981399	−	0.191978i	$-0.0614902\pi$
$347$	0.661173	+	2.46753i	0.0354936	+	0.132464i	−0.945906	+	0.324442i	$0.894824\pi$
$348$	−5.41502	−	1.45095i	−0.290276	−	0.0777791i
$349$	−18.6079			−0.996058			−0.498029	−	0.867160i	$-0.665943\pi$
$349$	−18.6079			−0.996058			−0.498029	+	0.867160i	$0.665943\pi$
$350$		0			0
$351$	2.72238			0.145310
$352$	−1.12607	−	0.301730i	−0.0600198	−	0.0160823i
$353$	4.09742	+	15.2918i	0.218084	+	0.813900i	0.985058	+	0.172222i	$0.0550946\pi$
$353$	4.09742	+	15.2918i	0.218084	+	0.813900i	−0.766974	+	0.641678i	$0.778239\pi$
$354$	9.25995	+	5.34623i	0.492161	+	0.284149i
$355$		0			0
$356$			3.60510i			0.191070i
$357$	0.0272636	−	0.0504360i	0.00144294	−	0.00266935i
$358$	−1.06563	−	1.06563i	−0.0563204	−	0.0563204i
$359$	6.50055	−	3.75309i	0.343086	−	0.198081i	−0.318550	−	0.947906i	$-0.603196\pi$
$359$	6.50055	−	3.75309i	0.343086	−	0.198081i	0.661636	+	0.749825i	$0.269863\pi$
$360$		0			0
$361$	7.54232	−	13.0637i	0.396964	−	0.687562i
$362$	−5.52468	+	20.6184i	−0.290371	+	1.08368i
$363$	6.81716	−	6.81716i	0.357808	−	0.357808i
$364$	5.23386	+	4.94835i	0.274329	+	0.259364i
$365$		0			0
$366$	−1.82324	−	3.15795i	−0.0953025	−	0.165069i
$367$	−3.81343	+	1.02181i	−0.199060	+	0.0533379i	−0.356971	−	0.934115i	$-0.616191\pi$
$367$	−3.81343	+	1.02181i	−0.199060	+	0.0533379i	0.157912	+	0.987453i	$0.449524\pi$
$368$	−6.93525	+	1.85829i	−0.361525	+	0.0968702i
$369$	−1.24488	−	2.15620i	−0.0648061	−	0.112247i
$370$		0			0
$371$	−5.62762	−	5.32063i	−0.292172	−	0.276233i
$372$	5.60811	−	5.60811i	0.290767	−	0.290767i
$373$	−1.39610	+	5.21031i	−0.0722872	+	0.269780i	−0.992605	−	0.121393i	$-0.961264\pi$
$373$	−1.39610	+	5.21031i	−0.0722872	+	0.269780i	0.920317	+	0.391173i	$0.127931\pi$
$374$	−0.0126313	+	0.0218781i	−0.000653150	+	0.00113129i
$375$		0			0
$376$	−3.53923	+	2.04338i	−0.182522	+	0.105379i
$377$	−10.7917	−	10.7917i	−0.555801	−	0.555801i
$378$	1.25813	−	2.32747i	0.0647113	−	0.119712i
$379$			2.47403i			0.127082i	0.997979	+	0.0635411i	$0.0202394\pi$
$379$			2.47403i			0.127082i	−0.997979	+	0.0635411i	$0.979761\pi$
$380$		0			0
$381$	1.66700	+	0.962442i	0.0854029	+	0.0493074i
$382$	1.66960	+	6.23105i	0.0854244	+	0.318808i
$383$	23.2872	+	6.23980i	1.18992	+	0.318839i	0.798855	−	0.601524i	$-0.205439\pi$
$383$	23.2872	+	6.23980i	1.18992	+	0.318839i	0.391067	+	0.920362i	$0.372106\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	5.13858			0.261547
$387$	−10.7609	−	2.88339i	−0.547010	−	0.146571i
$388$	0.0971800	+	0.362681i	0.00493357	+	0.0184123i
$389$	5.58638	+	3.22530i	0.283241	+	0.163529i	0.634890	−	0.772603i	$-0.281046\pi$
$389$	5.58638	+	3.22530i	0.283241	+	0.163529i	−0.351649	+	0.936132i	$0.614379\pi$
$390$		0			0
$391$			0.155588i			0.00786840i
$392$	6.64933	−	2.18778i	0.335842	−	0.110500i
$393$	12.1267	+	12.1267i	0.611713	+	0.611713i
$394$	21.8429	−	12.6110i	1.10043	−	0.635334i
$395$		0			0
$396$	−0.582897	+	1.00961i	−0.0292917	+	0.0507347i
$397$	−4.84423	+	18.0789i	−0.243125	+	0.907354i	0.731192	+	0.682172i	$0.238964\pi$
$397$	−4.84423	+	18.0789i	−0.243125	+	0.907354i	−0.974317	+	0.225182i	$0.927702\pi$
$398$	3.49450	−	3.49450i	0.175163	−	0.175163i
$399$	−5.09283	−	1.21270i	−0.254960	−	0.0607110i
$400$		0			0
$401$	9.36968	+	16.2288i	0.467900	+	0.810426i	0.999327	−	0.0366779i	$-0.0116776\pi$
$401$	9.36968	+	16.2288i	0.467900	+	0.810426i	−0.531428	+	0.847104i	$0.678344\pi$
$402$	14.0621	−	3.76794i	0.701356	−	0.187928i
$403$	20.8557	−	5.58826i	1.03889	−	0.278371i
$404$	6.95796	+	12.0515i	0.346171	+	0.599587i
$405$		0			0
$406$	−14.2136	+	4.23892i	−0.705408	+	0.210374i
$407$	8.75542	−	8.75542i	0.433990	−	0.433990i
$408$	−0.00560858	+	0.0209315i	−0.000277666	+	0.00103626i
$409$	11.6768	−	20.2248i	0.577381	−	1.00005i	−0.418398	−	0.908264i	$-0.637408\pi$
$409$	11.6768	−	20.2248i	0.577381	−	1.00005i	0.995778	−	0.0917890i	$-0.0292585\pi$
$410$		0			0
$411$	−8.86443	+	5.11788i	−0.437250	+	0.252446i
$412$	8.47403	+	8.47403i	0.417485	+	0.417485i
$413$	28.2785	−	0.792944i	1.39149	−	0.0390182i
$414$			7.17989i			0.352873i
$415$		0			0
$416$	−2.35765	−	1.36119i	−0.115593	−	0.0667378i
$417$	−1.46263	−	5.45863i	−0.0716255	−	0.267310i
$418$	2.22819	+	0.597041i	0.108984	+	0.0292022i
$419$	8.27092			0.404061			0.202030	−	0.979379i	$-0.435246\pi$
$419$	8.27092			0.404061			0.202030	+	0.979379i	$0.435246\pi$
$420$		0			0
$421$	−33.3728			−1.62649			−0.813246	−	0.581920i	$-0.802302\pi$
$421$	−33.3728			−1.62649			−0.813246	+	0.581920i	$0.802302\pi$
$422$	18.3966	+	4.92934i	0.895530	+	0.239957i
$423$	1.05773	+	3.94750i	0.0514285	+	0.191934i
$424$	2.53502	+	1.46360i	0.123112	+	0.0710785i
$425$		0			0
$426$			7.51848i			0.364272i
$427$	−8.48708	−	4.58776i	−0.410719	−	0.222017i
$428$	4.88300	+	4.88300i	0.236029	+	0.236029i
$429$	−2.74854	+	1.58687i	−0.132701	+	0.0766147i
$430$		0			0
$431$	12.1733	−	21.0848i	0.586369	−	1.01562i	−0.408334	−	0.912832i	$-0.633890\pi$
$431$	12.1733	−	21.0848i	0.586369	−	1.01562i	0.994703	−	0.102788i	$-0.0327764\pi$
$432$	−0.258819	+	0.965926i	−0.0124524	+	0.0464731i
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	−0.123464	−	0.992349i	$-0.539400\pi$
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	0.992349	+	0.123464i	$0.0394002\pi$
$434$	4.86071	−	20.4129i	0.233322	−	0.979850i
$435$		0			0
$436$	−0.288657	−	0.499969i	−0.0138242	−	0.0239442i
$437$	13.7230	−	3.67705i	0.656458	−	0.175897i
$438$	3.61776	−	0.969376i	0.172863	−	0.0463186i
$439$	−8.11012	−	14.0471i	−0.387075	−	0.670433i	0.604980	−	0.796241i	$-0.293181\pi$
$439$	−8.11012	−	14.0471i	−0.387075	−	0.670433i	−0.992055	+	0.125808i	$0.959848\pi$
$440$		0			0
$441$	−0.392259	−	6.98900i	−0.0186790	−	0.332810i
$442$	−0.0417148	+	0.0417148i	−0.00198417	+	0.00198417i
$443$	−5.63860	+	21.0436i	−0.267898	+	0.999810i	0.692554	+	0.721366i	$0.256485\pi$
$443$	−5.63860	+	21.0436i	−0.267898	+	0.999810i	−0.960452	+	0.278444i	$0.910181\pi$
$444$	5.31055	−	9.19815i	0.252028	−	0.436525i
$445$		0			0
$446$	3.60676	−	2.08236i	0.170785	−	0.0986027i
$447$	−0.156132	−	0.156132i	−0.00738477	−	0.00738477i
$448$	−2.25331	+	1.38658i	−0.106459	+	0.0655097i
$449$		−	10.1648i		−	0.479708i	−0.970809	−	0.239854i	$-0.922900\pi$
$449$		−	10.1648i		−	0.479708i	0.970809	−	0.239854i	$-0.0770996\pi$
$450$		0			0
$451$	2.51369	+	1.45128i	0.118365	+	0.0683381i
$452$	−4.85674	−	18.1256i	−0.228442	−	0.852556i
$453$	−6.15184	−	1.64838i	−0.289038	−	0.0774476i
$454$	−18.4389			−0.865381
$455$		0			0
$456$	1.97873			0.0926624
$457$	−27.5526	−	7.38270i	−1.28886	−	0.345348i	−0.451631	−	0.892205i	$-0.649158\pi$
$457$	−27.5526	−	7.38270i	−1.28886	−	0.345348i	−0.837226	+	0.546856i	$0.815824\pi$
$458$	1.52965	+	5.70873i	0.0714758	+	0.266751i
$459$	0.0187667	+	0.0108349i	0.000875953	+	0.000505732i
$460$		0			0
$461$		−	20.0972i		−	0.936022i	−0.883723	−	0.468011i	$-0.844971\pi$
$461$		−	20.0972i		−	0.936022i	0.883723	−	0.468011i	$-0.155029\pi$
$462$	0.0864543	+	3.08319i	0.00402222	+	0.143443i
$463$	7.34462	+	7.34462i	0.341334	+	0.341334i	0.856869	−	0.515535i	$-0.172407\pi$
$463$	7.34462	+	7.34462i	0.341334	+	0.341334i	−0.515535	+	0.856869i	$0.672407\pi$
$464$	4.85498	−	2.80302i	0.225387	−	0.130127i
$465$		0			0
$466$	3.61767	−	6.26598i	0.167585	−	0.290266i
$467$	6.10926	−	22.8001i	0.282703	−	1.05506i	−0.667799	−	0.744342i	$-0.732763\pi$
$467$	6.10926	−	22.8001i	0.282703	−	1.05506i	0.950502	−	0.310720i	$-0.100570\pi$
$468$	−1.92501	+	1.92501i	−0.0889838	+	0.0889838i
$469$	26.4618	−	27.9886i	1.22189	−	1.29239i
$470$		0			0
$471$	−7.23813	−	12.5368i	−0.333515	−	0.577666i
$472$	−10.3281	+	2.76741i	−0.475391	+	0.127381i
$473$	12.5451	−	3.36144i	0.576822	−	0.154559i
$474$	−0.805197	−	1.39464i	−0.0369839	−	0.0640581i
$475$		0			0
$476$	0.0163853	+	0.0549419i	0.000751021	+	0.00251826i
$477$	2.06984	−	2.06984i	0.0947714	−	0.0947714i
$478$	1.08748	−	4.05855i	0.0497404	−	0.185634i
$479$	−12.3892	+	21.4588i	−0.566079	+	0.980478i	0.430869	+	0.902414i	$0.358207\pi$
$479$	−12.3892	+	21.4588i	−0.566079	+	0.980478i	−0.996948	+	0.0780633i	$0.975126\pi$
$480$		0			0
$481$	25.0409	−	14.4573i	1.14176	−	0.659198i
$482$	15.5110	+	15.5110i	0.706507	+	0.706507i
$483$	9.95550	+	16.1785i	0.452991	+	0.736148i
$484$			9.64092i			0.438224i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−6.15129	−	22.9569i	−0.278741	−	1.04028i	−0.953292	−	0.302049i	$-0.902329\pi$
$487$	−6.15129	−	22.9569i	−0.278741	−	1.04028i	0.674551	−	0.738228i	$-0.264337\pi$
$488$	3.52224	+	0.943781i	0.159444	+	0.0427229i
$489$	21.9057			0.990608
$490$		0			0
$491$	−0.386093			−0.0174242			−0.00871208	−	0.999962i	$-0.502773\pi$
$491$	−0.386093			−0.0174242			−0.00871208	+	0.999962i	$0.502773\pi$
$492$	2.40493	+	0.644400i	0.108423	+	0.0290518i
$493$	−0.0314419	−	0.117343i	−0.00141607	−	0.00528486i
$494$	4.66514	+	2.69342i	0.209895	+	0.121183i
$495$		0			0
$496$			7.93107i			0.356115i
$497$	10.4250	+	16.9415i	0.467624	+	0.759928i
$498$	9.74815	+	9.74815i	0.436825	+	0.436825i
$499$	−6.94992	+	4.01254i	−0.311121	+	0.179626i	−0.647428	−	0.762127i	$-0.724155\pi$
$499$	−6.94992	+	4.01254i	−0.311121	+	0.179626i	0.336307	+	0.941752i	$0.390822\pi$
$500$		0			0
$501$	8.05513	−	13.9519i	0.359877	−	0.623325i
$502$	3.91575	−	14.6138i	0.174768	−	0.652244i
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	−0.916594	−	0.399819i	$-0.869073\pi$
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	0.399819	+	0.916594i	$0.369073\pi$
$504$	0.756134	+	2.53540i	0.0336809	+	0.112936i
$505$		0			0
$506$	−4.18514	−	7.24888i	−0.186052	−	0.322252i
$507$	5.39822	−	1.44645i	0.239743	−	0.0642390i
$508$	−1.85929	+	0.498197i	−0.0824929	+	0.0221039i
$509$	7.77422	+	13.4654i	0.344586	+	0.596841i	0.985279	−	0.170957i	$-0.0546858\pi$
$509$	7.77422	+	13.4654i	0.344586	+	0.596841i	−0.640692	+	0.767798i	$0.721352\pi$
$510$		0			0
$511$	6.80781	−	7.20062i	0.301160	−	0.318536i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.512132	−	1.91130i	0.0226112	−	0.0843861i
$514$	11.5071	−	19.9309i	0.507558	−	0.879116i
$515$		0			0
$516$	9.64800	−	5.57028i	0.424730	−	0.245218i
$517$	−3.36888	−	3.36888i	−0.148163	−	0.148163i
$518$	−0.787652	−	28.0898i	−0.0346074	−	1.23419i
$519$			10.4433i			0.458408i
$520$		0			0
$521$	22.8573	+	13.1967i	1.00140	+	0.578156i	0.908661	−	0.417535i	$-0.137106\pi$
$521$	22.8573	+	13.1967i	1.00140	+	0.578156i	0.0927347	+	0.995691i	$0.470439\pi$
$522$	−1.45095	−	5.41502i	−0.0635064	−	0.237009i
$523$	38.1134	+	10.2125i	1.66658	+	0.446559i	0.964186	−	0.265227i	$-0.0854469\pi$
$523$	38.1134	+	10.2125i	1.66658	+	0.446559i	0.702396	+	0.711786i	$0.252114\pi$
$524$	−17.1498			−0.749192
$525$		0			0
$526$	20.1205			0.877294
$527$	0.166009	+	0.0444820i	0.00723147	+	0.00193767i
$528$	−0.301730	−	1.12607i	−0.0131311	−	0.0490060i
$529$	−24.7258	−	14.2754i	−1.07503	−	0.620671i
$530$		0			0
$531$			10.6925i			0.464014i
$532$	4.45868	−	2.74366i	0.193308	−	0.118953i
$533$	4.79284	+	4.79284i	0.207601	+	0.207601i
$534$	−3.12211	+	1.80255i	−0.135107	+	0.0780040i
$535$		0			0
$536$	−7.27910	+	12.6078i	−0.314409	+	0.544573i
$537$	0.390048	−	1.45568i	0.0168318	−	0.0628172i
$538$	−6.55459	+	6.55459i	−0.282588	+	0.282588i
$539$	4.46990	+	6.82750i	0.192532	+	0.294081i
$540$		0			0
$541$	−4.06849	−	7.04683i	−0.174918	−	0.302967i	0.765215	−	0.643775i	$-0.222633\pi$
$541$	−4.06849	−	7.04683i	−0.174918	−	0.302967i	−0.940133	+	0.340808i	$0.889299\pi$
$542$	−25.3360	+	6.78877i	−1.08828	+	0.291603i
$543$	−20.6184	+	5.52468i	−0.884820	+	0.237087i
$544$	−0.0108349	−	0.0187667i	−0.000464544	−	0.000804615i
$545$		0			0
$546$	−1.66846	+	7.00683i	−0.0714037	+	0.299865i
$547$	−12.5204	+	12.5204i	−0.535335	+	0.535335i	−0.922155	−	0.386820i	$-0.873573\pi$
$547$	−12.5204	+	12.5204i	−0.535335	+	0.535335i	0.386820	+	0.922155i	$0.373573\pi$
$548$	2.64921	−	9.88699i	0.113169	−	0.422351i
$549$	1.82324	−	3.15795i	0.0778142	−	0.134778i
$550$		0			0
$551$	−9.60667	+	5.54641i	−0.409258	+	0.236285i
$552$	−5.07695	−	5.07695i	−0.216089	−	0.216089i
$553$	−3.74814	−	2.02609i	−0.159387	−	0.0861581i
$554$			13.2995i			0.565040i
$555$		0			0
$556$	4.89407	+	2.82559i	0.207555	+	0.119832i
$557$	4.19123	+	15.6419i	0.177588	+	0.662768i	0.996096	+	0.0882732i	$0.0281348\pi$
$557$	4.19123	+	15.6419i	0.177588	+	0.662768i	−0.818508	+	0.574495i	$0.805198\pi$
$558$	7.66082	+	2.05271i	0.324308	+	0.0868982i
$559$	30.3288			1.28277
$560$		0			0
$561$	−0.0252626			−0.00106659
$562$	13.0497	+	3.49667i	0.550470	+	0.147498i
$563$	−2.26573	−	8.45582i	−0.0954892	−	0.356370i	0.901604	−	0.432562i	$-0.142390\pi$
$563$	−2.26573	−	8.45582i	−0.0954892	−	0.356370i	−0.997093	+	0.0761920i	$0.975724\pi$
$564$	−3.53923	−	2.04338i	−0.149028	−	0.0860416i
$565$		0			0
$566$			19.8911i			0.836085i
$567$	2.64471	−	0.0741591i	0.111067	−	0.00311439i
$568$	−5.31637	−	5.31637i	−0.223070	−	0.223070i
$569$	−35.9794	+	20.7727i	−1.50833	+	0.870838i	−0.508382	+	0.861132i	$0.669756\pi$
$569$	−35.9794	+	20.7727i	−1.50833	+	0.870838i	−0.999953	+	0.00970591i	$0.996910\pi$
$570$		0			0
$571$	−6.59259	+	11.4187i	−0.275891	+	0.477858i	−0.970360	−	0.241666i	$-0.922306\pi$
$571$	−6.59259	+	11.4187i	−0.275891	+	0.477858i	0.694468	+	0.719523i	$0.255640\pi$
$572$	0.821423	−	3.06559i	0.0343454	−	0.128179i
$573$	−4.56144	+	4.56144i	−0.190557	+	0.190557i
$574$	6.31256	−	1.88260i	0.263481	−	0.0785782i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−17.3319	+	4.64406i	−0.721535	+	0.193335i	−0.600857	−	0.799357i	$-0.705174\pi$
$577$	−17.3319	+	4.64406i	−0.721535	+	0.193335i	−0.120679	+	0.992692i	$0.538507\pi$
$578$	16.4203	−	4.39980i	0.682994	−	0.183008i
$579$	2.56929	+	4.45014i	0.106776	+	0.184942i
$580$		0			0
$581$	35.4822	+	8.44900i	1.47205	+	0.350524i
$582$	−0.265501	+	0.265501i	−0.0110054	+	0.0110054i
$583$	−0.883222	+	3.29623i	−0.0365793	+	0.136516i
$584$	−1.87269	+	3.24360i	−0.0774925	+	0.134221i
$585$		0			0
$586$	21.3159	−	12.3068i	0.880553	−	0.508387i
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	0.530535	−	0.847663i	$-0.321991\pi$
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	−0.847663	+	0.530535i	$0.821991\pi$
$588$	5.21934	+	4.66460i	0.215242	+	0.192365i
$589$		−	15.6934i		−	0.646636i
$590$		0			0
$591$	21.8429	+	12.6110i	0.898499	+	0.518748i
$592$	2.74894	+	10.2592i	0.112981	+	0.421651i
$593$	7.58832	+	2.03328i	0.311615	+	0.0834970i	0.411237	−	0.911528i	$-0.365097\pi$
$593$	7.58832	+	2.03328i	0.311615	+	0.0834970i	−0.0996223	+	0.995025i	$0.531763\pi$
$594$	−1.16579			−0.0478331
$595$		0			0
$596$	0.220803			0.00904446
$597$	4.77357	+	1.27908i	0.195369	+	0.0523491i
$598$	−5.05898	−	18.8804i	−0.206877	−	0.772076i
$599$	−20.5520	−	11.8657i	−0.839731	−	0.484819i	0.0174418	−	0.999848i	$-0.494448\pi$
$599$	−20.5520	−	11.8657i	−0.839731	−	0.484819i	−0.857173	+	0.515029i	$0.827781\pi$
$600$		0			0
$601$		−	14.4348i		−	0.588806i	−0.955681	−	0.294403i	$-0.904879\pi$
$601$		−	14.4348i		−	0.588806i	0.955681	−	0.294403i	$-0.0951208\pi$
$602$	14.0163	−	25.9293i	0.571261	−	1.05680i
$603$	10.2942	+	10.2942i	0.419213	+	0.419213i
$604$	5.51559	−	3.18442i	0.224426	−	0.129572i
$605$		0			0
$606$	−6.95796	+	12.0515i	−0.282648	+	0.489560i
$607$	−0.172772	+	0.644795i	−0.00701261	+	0.0261714i	−0.969343	−	0.245710i	$-0.920979\pi$
$607$	−0.172772	+	0.644795i	−0.00701261	+	0.0261714i	0.962331	+	0.271881i	$0.0876457\pi$
$608$	−1.39917	+	1.39917i	−0.0567439	+	0.0567439i
$609$	−10.7778	−	10.1899i	−0.436738	−	0.412914i
$610$		0			0
$611$	−5.56284	−	9.63513i	−0.225049	−	0.389796i
$612$	−0.0209315	+	0.00560858i	−0.000846106	+	0.000226713i
$613$	−14.2571	+	3.82018i	−0.575839	+	0.154296i	−0.534973	−	0.844869i	$-0.679678\pi$
$613$	−14.2571	+	3.82018i	−0.575839	+	0.154296i	−0.0408659	+	0.999165i	$0.513012\pi$
$614$	−0.400469	−	0.693633i	−0.0161616	−	0.0279927i
$615$		0			0
$616$	−2.24128	−	2.11901i	−0.0903037	−	0.0853775i
$617$	4.88322	−	4.88322i	0.196591	−	0.196591i	−0.601946	−	0.798537i	$-0.705608\pi$
$617$	4.88322	−	4.88322i	0.196591	−	0.196591i	0.798537	+	0.601946i	$0.205608\pi$
$618$	−3.10171	+	11.5757i	−0.124769	+	0.465644i
$619$	−13.8975	+	24.0712i	−0.558589	+	0.967504i	0.439026	+	0.898474i	$0.355324\pi$
$619$	−13.8975	+	24.0712i	−0.558589	+	0.967504i	−0.997615	+	0.0690295i	$0.978010\pi$
$620$		0			0
$621$	−6.21797	+	3.58995i	−0.249519	+	0.144060i
$622$	−9.47327	−	9.47327i	−0.379844	−	0.379844i
$623$	−4.53569	+	8.39075i	−0.181719	+	0.336168i
$624$		−	2.72238i		−	0.108982i
$625$		0			0
$626$	24.9051	+	14.3790i	0.995410	+	0.574700i
$627$	0.597041	+	2.22819i	0.0238435	+	0.0889852i
$628$	13.9830	+	3.74673i	0.557982	+	0.149511i
$629$	0.230158			0.00917701
$630$		0			0
$631$	6.30112			0.250844			0.125422	−	0.992104i	$-0.459972\pi$
$631$	6.30112			0.250844			0.125422	+	0.992104i	$0.459972\pi$
$632$	1.55552	+	0.416801i	0.0618753	+	0.0165794i
$633$	4.92934	+	18.3966i	0.195924	+	0.731197i
$634$	29.2153	+	16.8675i	1.16029	+	0.669893i
$635$		0			0
$636$			2.92719i			0.116071i
$637$	5.95597	+	18.1020i	0.235984	+	0.717228i
$638$	4.62129	+	4.62129i	0.182959	+	0.182959i
$639$	−6.51120	+	3.75924i	−0.257579	+	0.148713i
$640$		0			0
$641$	−2.63684	+	4.56715i	−0.104149	+	0.180391i	−0.913390	−	0.407085i	$-0.866545\pi$
$641$	−2.63684	+	4.56715i	−0.104149	+	0.180391i	0.809241	+	0.587477i	$0.199879\pi$
$642$	−1.78730	+	6.67031i	−0.0705393	+	0.263256i
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	−0.593714	−	0.804677i	$-0.702339\pi$
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	0.804677	+	0.593714i	$0.202339\pi$
$644$	−18.4795	−	4.40034i	−0.728196	−	0.173398i
$645$		0			0
$646$	0.0214394	+	0.0371341i	0.000843522	+	0.00146102i
$647$	21.4035	−	5.73506i	0.841460	−	0.225469i	0.187753	−	0.982216i	$-0.439880\pi$
$647$	21.4035	−	5.73506i	0.841460	−	0.225469i	0.653707	+	0.756748i	$0.273213\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−6.23261	−	10.7952i	−0.244651	−	0.423749i
$650$		0			0
$651$	20.1084	−	5.99695i	0.788112	−	0.235039i
$652$	−15.4896	+	15.4896i	−0.606621	+	0.606621i
$653$	11.4754	−	42.8267i	0.449066	−	1.67594i	−0.255907	−	0.966702i	$-0.582374\pi$
$653$	11.4754	−	42.8267i	0.449066	−	1.67594i	0.704972	−	0.709235i	$-0.250959\pi$
$654$	0.288657	−	0.499969i	0.0112874	−	0.0195503i
$655$		0			0
$656$	−2.15620	+	1.24488i	−0.0841856	+	0.0486046i
$657$	2.64838	+	2.64838i	0.103323	+	0.103323i
$658$	−10.8083	+	0.303070i	−0.421351	+	0.0118149i
$659$		−	38.6387i		−	1.50515i	−0.658507	−	0.752575i	$-0.728812\pi$
$659$		−	38.6387i		−	1.50515i	0.658507	−	0.752575i	$-0.271188\pi$
$660$		0			0
$661$	−24.7737	−	14.3031i	−0.963587	−	0.556327i	−0.0663118	−	0.997799i	$-0.521123\pi$
$661$	−24.7737	−	14.3031i	−0.963587	−	0.556327i	−0.897275	+	0.441472i	$0.854457\pi$
$662$	−2.83035	−	10.5630i	−0.110005	−	0.410543i
$663$	−0.0569835	−	0.0152687i	−0.00221306	−	0.000592987i
$664$	−13.7860			−0.534999
$665$		0			0
$666$	10.6211			0.411560
$667$	38.8793	+	10.4177i	1.50541	+	0.403374i
$668$	4.16964	+	15.5613i	0.161328	+	0.602086i
$669$	3.60676	+	2.08236i	0.139445	+	0.0805088i
$670$		0			0
$671$			4.25106i			0.164110i
$672$	−2.32747	−	1.25813i	−0.0897840	−	0.0485335i
$673$	−36.6126	−	36.6126i	−1.41131	−	1.41131i	−0.750932	−	0.660379i	$-0.770396\pi$
$673$	−36.6126	−	36.6126i	−1.41131	−	1.41131i	−0.660379	−	0.750932i	$-0.729604\pi$
$674$	−12.6045	+	7.27723i	−0.485509	+	0.280309i
$675$		0			0
$676$	−2.79432	+	4.83991i	−0.107474	+	0.186150i
$677$	6.94951	−	25.9359i	0.267091	−	0.996798i	−0.693867	−	0.720104i	$-0.744094\pi$
$677$	6.94951	−	25.9359i	0.267091	−	0.996798i	0.960958	−	0.276695i	$-0.0892390\pi$
$678$	13.2689	−	13.2689i	0.509587	−	0.509587i
$679$	−0.230117	+	0.966393i	−0.00883108	+	0.0370868i
$680$		0			0
$681$	−9.21945	−	15.9686i	−0.353290	−	0.611917i
$682$	−8.93095	+	2.39304i	−0.341984	+	0.0916342i
$683$	−1.91999	+	0.514460i	−0.0734664	+	0.0196853i	−0.295365	−	0.955384i	$-0.595441\pi$
$683$	−1.91999	+	0.514460i	−0.0734664	+	0.0196853i	0.221899	+	0.975070i	$0.428775\pi$
$684$	0.989363	+	1.71363i	0.0378293	+	0.0655222i
$685$		0			0
$686$	18.2286	+	3.27375i	0.695972	+	0.124993i
$687$	−4.17908	+	4.17908i	−0.159442	+	0.159442i
$688$	−2.88339	+	10.7609i	−0.109928	+	0.410257i
$689$	−3.98446	+	6.90130i	−0.151796	+	0.262918i
$690$		0			0
$691$	−8.33571	+	4.81262i	−0.317105	+	0.183081i	−0.650102	−	0.759847i	$-0.725274\pi$
$691$	−8.33571	+	4.81262i	−0.317105	+	0.183081i	0.332996	+	0.942928i	$0.391940\pi$
$692$	−7.38450	−	7.38450i	−0.280717	−	0.280717i
$693$	−2.62690	+	1.61647i	−0.0997875	+	0.0614045i
$694$		−	2.55458i		−	0.0969703i
$695$		0			0
$696$	4.85498	+	2.80302i	0.184027	+	0.106248i
$697$	0.0139641	+	0.0521146i	0.000528927	+	0.00197398i
$698$	17.9739	+	4.81608i	0.680320	+	0.182291i
$699$	7.23533			0.273665
$700$		0			0
$701$	−12.4958			−0.471959			−0.235980	−	0.971758i	$-0.575830\pi$
$701$	−12.4958			−0.471959			−0.235980	+	0.971758i	$0.575830\pi$
$702$	−2.62962	−	0.704604i	−0.0992485	−	0.0265936i
$703$	−5.43941	−	20.3002i	−0.205151	−	0.765635i
$704$	1.00961	+	0.582897i	0.0380510	+	0.0219688i
$705$		0			0
$706$		−	15.8312i		−	0.595816i
$707$	1.03199	+	36.8036i	0.0388121	+	1.38414i
$708$	−7.56072	−	7.56072i	−0.284149	−	0.284149i
$709$	39.6174	−	22.8731i	1.48786	−	0.859018i	0.487958	−	0.872867i	$-0.337742\pi$
$709$	39.6174	−	22.8731i	1.48786	−	0.859018i	0.999904	+	0.0138494i	$0.00440856\pi$
$710$		0			0
$711$	0.805197	−	1.39464i	0.0301973	−	0.0523032i
$712$	0.933068	−	3.48226i	0.0349682	−	0.130503i
$713$	−40.2656	+	40.2656i	−1.50796	+	1.50796i
$714$	−0.0393884	+	0.0416611i	−0.00147407	+	0.00155913i
$715$		0			0
$716$	0.753516	+	1.30513i	0.0281602	+	0.0487749i
$717$	4.05855	−	1.08748i	0.151569	−	0.0406129i
$718$	−7.25042	+	1.94274i	−0.270583	+	0.0725025i
$719$	−8.05439	−	13.9506i	−0.300378	−	0.520270i	0.675844	−	0.737045i	$-0.263779\pi$
$719$	−8.05439	−	13.9506i	−0.300378	−	0.520270i	−0.976222	+	0.216775i	$0.930446\pi$
$720$		0			0
$721$	9.06157	+	30.3845i	0.337471	+	1.13158i
$722$	−10.6665	+	10.6665i	−0.396964	+	0.396964i
$723$	−5.67742	+	21.1884i	−0.211146	+	0.788006i
$724$	10.6729	−	18.4859i	0.396654	−	0.687025i
$725$		0			0
$726$	−8.34928	+	4.82046i	−0.309871	+	0.178904i
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	0.00843633	−	0.999964i	$-0.497315\pi$
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	−0.999964	+	0.00843633i	$0.997315\pi$
$728$	−3.77480	−	6.13436i	−0.139903	−	0.227355i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	0.209071	+	0.120707i	0.00773278	+	0.00446452i
$732$	0.943781	+	3.52224i	0.0348831	+	0.130186i
$733$	9.81640	+	2.63030i	0.362577	+	0.0971523i	0.435508	−	0.900185i	$-0.356569\pi$
$733$	9.81640	+	2.63030i	0.362577	+	0.0971523i	−0.0729311	+	0.997337i	$0.523235\pi$
$734$	3.94796			0.145722
$735$		0			0
$736$	7.17989			0.264654
$737$	−16.3936	−	4.39265i	−0.603865	−	0.161805i
$738$	0.644400	+	2.40493i	0.0237207	+	0.0885268i
$739$	1.51357	+	0.873858i	0.0556775	+	0.0321454i	0.527580	−	0.849505i	$-0.323099\pi$
$739$	1.51357	+	0.873858i	0.0556775	+	0.0321454i	−0.471903	+	0.881651i	$0.656433\pi$
$740$		0			0
$741$			5.38685i			0.197891i
$742$	4.05879	+	6.59587i	0.149003	+	0.242142i
$743$	−4.26452	−	4.26452i	−0.156450	−	0.156450i	0.624542	−	0.780992i	$-0.285286\pi$
$743$	−4.26452	−	4.26452i	−0.156450	−	0.156450i	−0.780992	+	0.624542i	$0.785286\pi$
$744$	−6.86850	+	3.96553i	−0.251812	+	0.145383i
$745$		0			0
$746$	2.69706	−	4.67144i	0.0987462	−	0.171033i
$747$	−3.56807	+	13.3162i	−0.130549	+	0.487215i
$748$	0.0178634	−	0.0178634i	0.000653150	−	0.000653150i
$749$	5.22157	+	17.5085i	0.190792	+	0.639747i
$750$		0			0
$751$	−7.54354	−	13.0658i	−0.275268	−	0.476778i	0.694935	−	0.719073i	$-0.255433\pi$
$751$	−7.54354	−	13.0658i	−0.275268	−	0.476778i	−0.970203	+	0.242295i	$0.922100\pi$
$752$	3.94750	−	1.05773i	0.143950	−	0.0385714i
$753$	14.6138	−	3.91575i	0.532555	−	0.142698i
$754$	7.63089	+	13.2171i	0.277901	+	0.481338i
$755$		0			0
$756$	−1.81766	+	1.92253i	−0.0661075	+	0.0699218i
$757$	7.26095	−	7.26095i	0.263904	−	0.263904i	−0.562734	−	0.826638i	$-0.690251\pi$
$757$	7.26095	−	7.26095i	0.263904	−	0.263904i	0.826638	+	0.562734i	$0.190251\pi$
$758$	0.640325	−	2.38973i	0.0232576	−	0.0867987i
$759$	4.18514	−	7.24888i	0.151911	−	0.263118i
$760$		0			0
$761$	−10.7048	+	6.18041i	−0.388048	+	0.224040i	−0.681314	−	0.731991i	$-0.738591\pi$
$761$	−10.7048	+	6.18041i	−0.388048	+	0.224040i	0.293266	+	0.956031i	$0.405258\pi$
$762$	−1.36110	−	1.36110i	−0.0493074	−	0.0493074i
$763$	−0.0428131	−	1.52683i	−0.00154994	−	0.0552750i
$764$		−	6.45086i		−	0.233384i
$765$		0			0
$766$	−20.8788	−	12.0544i	−0.754380	−	0.435542i
$767$	−7.53395	−	28.1171i	−0.272035	−	1.01525i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	17.1708			0.619196			0.309598	−	0.950867i	$-0.399805\pi$
$769$	17.1708			0.619196			0.309598	+	0.950867i	$0.399805\pi$
$770$		0			0
$771$	23.0143			0.828839
$772$	−4.96349	−	1.32996i	−0.178640	−	0.0478664i
$773$	0.327680	+	1.22292i	0.0117858	+	0.0439853i	0.971568	−	0.236759i	$-0.0760853\pi$
$773$	0.327680	+	1.22292i	0.0117858	+	0.0439853i	−0.959783	+	0.280745i	$0.909419\pi$
$774$	9.64800	+	5.57028i	0.346790	+	0.200219i
$775$		0			0
$776$		−	0.375475i		−	0.0134788i
$777$	23.9326	−	14.7270i	0.858578	−	0.528329i
$778$	−4.56126	−	4.56126i	−0.163529	−	0.163529i
$779$	4.26654	−	2.46329i	0.152865	−	0.0882564i
$780$		0			0
$781$	4.38251	−	7.59072i	0.156818	−	0.271617i
$782$	0.0402690	−	0.150286i	0.00144002	−	0.00537422i
$783$	3.96407	−	3.96407i	0.141664	−	0.141664i
$784$	−6.98900	+	0.392259i	−0.249607	+	0.0140092i
$785$		0			0
$786$	−8.57489	−	14.8522i	−0.305856	−	0.529759i
$787$	−14.8015	+	3.96605i	−0.527617	+	0.141375i	−0.512788	−	0.858515i	$-0.671387\pi$
$787$	−14.8015	+	3.96605i	−0.527617	+	0.141375i	−0.0148294	+	0.999890i	$0.504721\pi$
$788$	−24.3626	+	6.52795i	−0.867883	+	0.232549i
$789$	10.0602	+	17.4248i	0.358154	+	0.620341i
$790$		0			0
$791$	11.5005	−	48.2971i	0.408911	−	1.71725i
$792$	0.824341	−	0.824341i	0.0292917	−	0.0292917i
$793$	−2.56933	+	9.58887i	−0.0912396	+	0.340511i
$794$	9.35833	−	16.2091i	0.332115	−	0.575240i
$795$		0			0
$796$	−4.27987	+	2.47098i	−0.151696	+	0.0875817i
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.933570	+	0.358396i	$0.116676\pi$
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.358396	+	0.933570i	$0.383324\pi$
$798$	4.60542	+	2.48950i	0.163030	+	0.0881273i
$799$		−	0.0885594i		−	0.00313301i
$800$		0			0
$801$	−3.12211	−	1.80255i	−0.110314	−	0.0636900i
$802$	−4.85010	−	18.1008i	−0.171263	−	0.639163i
$803$	−4.21757	−	1.13009i	−0.148835	−	0.0398801i
$804$	−14.5582			−0.513428
$805$		0			0
$806$	−21.5914			−0.760524
$807$	−8.95373	−	2.39915i	−0.315186	−	0.0844539i
$808$	−3.60170	−	13.4417i	−0.126708	−	0.472879i
$809$	−12.0158	−	6.93731i	−0.422452	−	0.243903i	0.273674	−	0.961823i	$-0.411761\pi$
$809$	−12.0158	−	6.93731i	−0.422452	−	0.243903i	−0.696126	+	0.717920i	$0.745094\pi$
$810$		0			0
$811$			18.4047i			0.646275i	0.946352	+	0.323137i	$0.104738\pi$
$811$			18.4047i			0.646275i	−0.946352	+	0.323137i	$0.895262\pi$
$812$	14.8264	−	0.415739i	0.520304	−	0.0145896i
$813$	−18.5473	−	18.5473i	−0.650481	−	0.650481i
$814$	−10.7232	+	6.19102i	−0.375846	+	0.216995i
$815$		0			0
$816$	0.0108349	−	0.0187667i	0.000379299	−	0.000656965i
$817$	5.70544	−	21.2930i	0.199608	−	0.744947i
$818$	−16.5135	+	16.5135i	−0.577381	+	0.577381i
$819$	−6.90233	+	2.05848i	−0.241187	+	0.0719292i
$820$		0			0
$821$	−16.4402	−	28.4753i	−0.573768	−	0.993796i	−0.996174	−	0.0873891i	$-0.972148\pi$
$821$	−16.4402	−	28.4753i	−0.573768	−	0.993796i	0.422406	−	0.906407i	$-0.361186\pi$
$822$	9.88699	−	2.64921i	0.344848	−	0.0924018i
$823$	−23.5835	+	6.31918i	−0.822069	+	0.220273i	−0.645251	−	0.763971i	$-0.723247\pi$
$823$	−23.5835	+	6.31918i	−0.822069	+	0.220273i	−0.176818	+	0.984244i	$0.556580\pi$
$824$	−5.99204	−	10.3785i	−0.208743	−	0.361553i
$825$		0			0
$826$	−27.5202	−	6.55309i	−0.957549	−	0.228011i
$827$	−1.94367	+	1.94367i	−0.0675881	+	0.0675881i	−0.740093	−	0.672505i	$-0.765218\pi$
$827$	−1.94367	+	1.94367i	−0.0675881	+	0.0675881i	0.672505	+	0.740093i	$0.265218\pi$
$828$	1.85829	−	6.93525i	0.0645802	−	0.241016i
$829$	−8.99161	+	15.5739i	−0.312291	+	0.540905i	−0.978858	−	0.204541i	$-0.934430\pi$
$829$	−8.99161	+	15.5739i	−0.312291	+	0.540905i	0.666567	+	0.745446i	$0.267763\pi$
$830$		0			0
$831$	−11.5177	+	6.64974i	−0.399544	+	0.230677i
$832$	1.92501	+	1.92501i	0.0667378	+	0.0667378i
$833$	−0.0309878	+	0.148490i	−0.00107366	+	0.00514489i
$834$			5.65119i			0.195685i
$835$		0			0
$836$	−1.99774	−	1.15339i	−0.0690932	−	0.0398910i
$837$	2.05271	+	7.66082i	0.0709521	+	0.264797i
$838$	−7.98909	−	2.14067i	−0.275979	−	0.0739483i
$839$	−4.25819			−0.147009			−0.0735045	−	0.997295i	$-0.523418\pi$
$839$	−4.25819			−0.147009			−0.0735045	+	0.997295i	$0.523418\pi$
$840$		0			0
$841$	−2.42773			−0.0837148
$842$	32.2357	+	8.63752i	1.11091	+	0.297669i
$843$	3.49667	+	13.0497i	0.120432	+	0.449457i
$844$	−16.4939	−	9.52276i	−0.567743	−	0.327787i
$845$		0			0
$846$		−	4.08675i		−	0.140505i
$847$	−12.1296	+	22.4389i	−0.416776	+	0.771011i
$848$	−2.06984	−	2.06984i	−0.0710785	−	0.0710785i
$849$	−17.2262	+	9.94554i	−0.591201	+	0.341330i
$850$		0			0
$851$	−38.1292	+	66.0417i	−1.30705	+	2.26388i
$852$	1.94593	−	7.26230i	0.0666664	−	0.248802i
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.295436	−	0.955362i	$-0.404535\pi$
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.955362	−	0.295436i	$-0.0954650\pi$
$854$	7.01049	+	6.62806i	0.239894	+	0.226807i
$855$		0			0
$856$	−3.45281	−	5.98043i	−0.118014	−	0.204407i
$857$	3.06389	−	0.820966i	0.104660	−	0.0280437i	−0.206109	−	0.978529i	$-0.566080\pi$
$857$	3.06389	−	0.820966i	0.104660	−	0.0280437i	0.310769	+	0.950485i	$0.399413\pi$
$858$	3.06559	−	0.821423i	0.104658	−	0.0280429i
$859$	−14.9376	−	25.8726i	−0.509663	−	0.882763i	−0.999937	−	0.0111943i	$-0.996437\pi$
$859$	−14.9376	−	25.8726i	−0.509663	−	0.882763i	0.490274	−	0.871568i	$-0.336897\pi$
$860$		0			0
$861$	4.78666	+	4.52554i	0.163129	+	0.154230i
$862$	−17.2157	+	17.2157i	−0.586369	+	0.586369i
$863$	−8.36277	+	31.2103i	−0.284672	+	1.06241i	0.664407	+	0.747371i	$0.268684\pi$
$863$	−8.36277	+	31.2103i	−0.284672	+	1.06241i	−0.949079	+	0.315039i	$0.897982\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−22.1438	+	12.7847i	−0.752477	+	0.434443i
$867$	12.0205	+	12.0205i	0.408237	+	0.408237i
$868$	−9.97833	+	18.4593i	−0.338687	+	0.626549i
$869$			1.87739i			0.0636861i
$870$		0			0
$871$	−34.3232	−	19.8165i	−1.16300	−	0.671456i
$872$	0.149420	+	0.557643i	0.00506000	+	0.0188842i
$873$	−0.362681	−	0.0971800i	−0.0122749	−	0.00328905i
$874$	−14.2070			−0.480561
$875$		0			0
$876$	−3.74538			−0.126545
$877$	3.93603	+	1.05466i	0.132910	+	0.0356132i	0.324661	−	0.945830i	$-0.394750\pi$
$877$	3.93603	+	1.05466i	0.132910	+	0.0356132i	−0.191751	+	0.981444i	$0.561416\pi$
$878$	4.19811	+	15.6675i	0.141679	+	0.528754i
$879$	21.3159	+	12.3068i	0.718968	+	0.415096i
$880$		0			0
$881$			19.0783i			0.642764i	0.946950	+	0.321382i	$0.104147\pi$
$881$			19.0783i			0.642764i	−0.946950	+	0.321382i	$0.895853\pi$
$882$	−1.42999	+	6.85238i	−0.0481504	+	0.230732i
$883$	−6.02976	−	6.02976i	−0.202918	−	0.202918i	0.598331	−	0.801249i	$-0.295831\pi$
$883$	−6.02976	−	6.02976i	−0.202918	−	0.202918i	−0.801249	+	0.598331i	$0.795831\pi$
$884$	0.0510900	−	0.0294968i	0.00171834	−	0.000992086i
$885$		0			0
$886$	10.8929	−	18.8671i	0.365956	−	0.633854i
$887$	11.2725	−	42.0695i	0.378494	−	1.41256i	−0.469679	−	0.882837i	$-0.655630\pi$
$887$	11.2725	−	42.0695i	0.378494	−	1.41256i	0.848173	−	0.529720i	$-0.177703\pi$
$888$	−7.51026	+	7.51026i	−0.252028	+	0.252028i
$889$	−4.95424	−	1.17970i	−0.166160	−	0.0395660i
$890$		0			0
$891$	−0.582897	−	1.00961i	−0.0195278	−	0.0338231i
$892$	−4.02281	+	1.07791i	−0.134694	+	0.0360911i
$893$	−7.81102	+	2.09296i	−0.261386	+	0.0700381i
$894$	0.110402	+	0.191221i	0.00369239	+	0.00639540i
$895$		0			0
$896$	2.53540	−	0.756134i	0.0847018	−	0.0252607i
$897$	13.8214	−	13.8214i	0.461483	−	0.461483i
$898$	−2.63085	+	9.81847i	−0.0877926	+	0.327647i
$899$	22.2310	−	38.5051i	0.741444	−	1.28422i
$900$		0			0
$901$	−0.0549337	+	0.0317160i	−0.00183011	+	0.00105661i
$902$	−2.05242	−	2.05242i	−0.0683381	−	0.0683381i
$903$	29.4636	−	0.826173i	0.980486	−	0.0274933i
$904$			18.7650i			0.624115i
$905$		0			0
$906$	5.51559	+	3.18442i	0.183243	+	0.105795i
$907$	14.7658	+	55.1066i	0.490290	+	1.82979i	0.554957	+	0.831879i	$0.312735\pi$
$907$	14.7658	+	55.1066i	0.490290	+	1.82979i	−0.0646668	+	0.997907i	$0.520598\pi$
$908$	17.8106	+	4.77234i	0.591066	+	0.158376i
$909$	−13.9159			−0.461562
$910$		0			0
$911$	−32.4993			−1.07675			−0.538375	−	0.842705i	$-0.680962\pi$
$911$	−32.4993			−1.07675			−0.538375	+	0.842705i	$0.680962\pi$
$912$	−1.91130	−	0.512132i	−0.0632896	−	0.0169584i
$913$	−4.15964	−	15.5240i	−0.137664	−	0.513769i
$914$	24.7030	+	14.2623i	0.817103	+	0.471755i
$915$		0			0
$916$		−	5.91011i		−	0.195276i
$917$	−39.9156	−	21.5767i	−1.31813	−	0.712525i
$918$	−0.0153229	−	0.0153229i	−0.000505732	−	0.000505732i
$919$	−1.92544	+	1.11165i	−0.0635143	+	0.0366700i	−0.531421	−	0.847108i	$-0.678342\pi$
$919$	−1.92544	+	1.11165i	−0.0635143	+	0.0366700i	0.467907	+	0.883778i	$0.345008\pi$
$920$		0			0
$921$	0.400469	−	0.693633i	0.0131959	−	0.0228560i
$922$	−5.20155	+	19.4125i	−0.171304	+	0.639315i
$923$	14.4732	−	14.4732i	0.476391	−	0.476391i
$924$	0.714480	−	3.00051i	0.0235047	−	0.0987095i
$925$		0			0
$926$	−5.19343	−	8.99529i	−0.170667	−	0.295604i
$927$	−11.5757	+	3.10171i	−0.380197	+	0.101874i
$928$	−5.41502	+	1.45095i	−0.177757	+	0.0476298i
$929$	−0.358305	−	0.620603i	−0.0117556	−	0.0203613i	0.860088	−	0.510146i	$-0.170409\pi$
$929$	−0.358305	−	0.620603i	−0.0117556	−	0.0203613i	−0.871843	+	0.489785i	$0.837075\pi$
$930$		0			0
$931$	13.8293	−	0.776173i	0.453238	−	0.0254380i
$932$	−5.11615	+	5.11615i	−0.167585	+	0.167585i
$933$	3.46746	−	12.9407i	0.113520	−	0.423661i
$934$	−11.8022	+	20.4420i	−0.386179	+	0.668882i
$935$		0			0
$936$	2.35765	−	1.36119i	0.0770622	−	0.0444919i
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	0.490435	−	0.871478i	$-0.336838\pi$
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	−0.871478	+	0.490435i	$0.836838\pi$
$938$	−32.8041	+	20.1861i	−1.07109	+	0.659100i
$939$			28.7580i			0.938481i
$940$		0			0
$941$	26.7812	+	15.4621i	0.873041	+	0.504051i	0.868358	−	0.495938i	$-0.165176\pi$
$941$	26.7812	+	15.4621i	0.873041	+	0.504051i	0.00468360	+	0.999989i	$0.498509\pi$
$942$	3.74673	+	13.9830i	0.122075	+	0.455591i
$943$	−17.2672	−	4.62672i	−0.562296	−	0.150667i
$944$	10.6925			0.348010
$945$		0			0
$946$	−12.9876			−0.422263
$947$	−15.7786	−	4.22786i	−0.512735	−	0.137387i	−0.00683099	−	0.999977i	$-0.502174\pi$
$947$	−15.7786	−	4.22786i	−0.512735	−	0.137387i	−0.505904	+	0.862590i	$0.668841\pi$
$948$	0.416801	+	1.55552i	0.0135371	+	0.0505210i
$949$	−8.83030	−	5.09817i	−0.286644	−	0.165494i
$950$		0			0
$951$			33.7349i			1.09393i
$952$	−0.00160702	−	0.0573106i	−5.20838e−5	−	0.00185745i
$953$	8.22927	+	8.22927i	0.266572	+	0.266572i	0.827717	−	0.561145i	$-0.189639\pi$
$953$	8.22927	+	8.22927i	0.266572	+	0.266572i	−0.561145	+	0.827717i	$0.689639\pi$
$954$	−2.53502	+	1.46360i	−0.0820744	+	0.0473857i
$955$		0			0
$956$	−2.10086	+	3.63880i	−0.0679467	+	0.117687i
$957$	−1.69151	+	6.31281i	−0.0546788	+	0.204064i
$958$	17.5210	−	17.5210i	0.566079	−	0.566079i
$959$	18.6051	−	19.6786i	0.600789	−	0.635454i
$960$		0			0
$961$	15.9509	+	27.6278i	0.514545	+	0.891219i
$962$	−27.9294	+	7.48367i	−0.900481	+	0.241283i
$963$	−6.67031	+	1.78730i	−0.214948	+	0.0575951i
$964$	−10.9679	−	18.9970i	−0.353254	−	0.611853i
$965$		0			0
$966$	−5.42896	−	18.2039i	−0.174674	−	0.585701i
$967$	−1.15164	+	1.15164i	−0.0370342	+	0.0370342i	−0.725381	−	0.688347i	$-0.758337\pi$
$967$	−1.15164	+	1.15164i	−0.0370342	+	0.0370342i	0.688347	+	0.725381i	$0.258337\pi$
$968$	2.49525	−	9.31242i	0.0802005	−	0.299312i
$969$	−0.0214394	+	0.0371341i	−0.000688733	+	0.00119292i
$970$		0			0
$971$	12.4747	−	7.20230i	0.400334	−	0.231133i	−0.286294	−	0.958142i	$-0.592424\pi$
$971$	12.4747	−	7.20230i	0.400334	−	0.231133i	0.686628	+	0.727009i	$0.259090\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	7.83582	+	12.7339i	0.251205	+	0.408229i
$974$			23.7668i			0.761536i
$975$		0			0
$976$	−3.15795	−	1.82324i	−0.101084	−	0.0583606i
$977$	9.63078	+	35.9426i	0.308116	+	1.14990i	0.930230	+	0.366977i	$0.119607\pi$
$977$	9.63078	+	35.9426i	0.308116	+	1.14990i	−0.622114	+	0.782927i	$0.713726\pi$
$978$	−21.1592	−	5.66960i	−0.676598	−	0.181294i
$979$	4.20281			0.134322
$980$		0			0
$981$	0.577314			0.0184322
$982$	0.372938	+	0.0999283i	0.0119009	+	0.00318884i
$983$	−7.32286	−	27.3293i	−0.233563	−	0.871669i	−0.978791	−	0.204860i	$-0.934326\pi$
$983$	−7.32286	−	27.3293i	−0.233563	−	0.871669i	0.745228	−	0.666809i	$-0.232341\pi$
$984$	−2.15620	−	1.24488i	−0.0687372	−	0.0396855i
$985$		0			0
$986$			0.121482i			0.00386879i
$987$	−5.66660	−	9.20871i	−0.180370	−	0.293116i
$988$	−3.80907	−	3.80907i	−0.121183	−	0.121183i
$989$	−69.2716	+	39.9940i	−2.20271	+	1.27174i
$990$		0			0
$991$	−18.6725	+	32.3417i	−0.593151	+	1.02737i	0.400654	+	0.916230i	$0.368783\pi$
$991$	−18.6725	+	32.3417i	−0.593151	+	1.02737i	−0.993805	+	0.111139i	$0.964550\pi$
$992$	2.05271	−	7.66082i	0.0651736	−	0.243231i
$993$	7.73266	−	7.73266i	0.245388	−	0.245388i
$994$	−5.68498	−	19.0624i	−0.180317	−	0.604622i
$995$		0			0
$996$	−6.89298	−	11.9390i	−0.218413	−	0.378302i
$997$	−35.7963	+	9.59160i	−1.13368	+	0.303769i	−0.776408	−	0.630231i	$-0.782960\pi$
$997$	−35.7963	+	9.59160i	−1.13368	+	0.303769i	−0.357274	+	0.934000i	$0.616294\pi$
$998$	7.75163	−	2.07704i	0.245373	−	0.0657476i
$999$	5.31055	+	9.19815i	0.168018	+	0.291017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.h.493.2		16
5.2	odd	4		1050.2.bc.g.157.3		16
5.3	odd	4		210.2.u.b.157.1	yes	16
5.4	even	2		210.2.u.a.73.4	✓	16
7.5	odd	6		1050.2.bc.g.943.3		16
15.8	even	4		630.2.bv.b.577.4		16
15.14	odd	2		630.2.bv.a.73.1		16
35.3	even	12		1470.2.m.d.97.1		16
35.4	even	6		1470.2.m.d.1273.1		16
35.12	even	12	inner	1050.2.bc.h.607.2		16
35.18	odd	12		1470.2.m.e.97.4		16
35.19	odd	6		210.2.u.b.103.1	yes	16
35.24	odd	6		1470.2.m.e.1273.4		16
35.33	even	12		210.2.u.a.187.4	yes	16
105.68	odd	12		630.2.bv.a.397.1		16
105.89	even	6		630.2.bv.b.523.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.4	✓	16	5.4	even	2
210.2.u.a.187.4	yes	16	35.33	even	12
210.2.u.b.103.1	yes	16	35.19	odd	6
210.2.u.b.157.1	yes	16	5.3	odd	4
630.2.bv.a.73.1		16	15.14	odd	2
630.2.bv.a.397.1		16	105.68	odd	12
630.2.bv.b.523.4		16	105.89	even	6
630.2.bv.b.577.4		16	15.8	even	4
1050.2.bc.g.157.3		16	5.2	odd	4
1050.2.bc.g.943.3		16	7.5	odd	6
1050.2.bc.h.493.2		16	1.1	even	1	trivial
1050.2.bc.h.607.2		16	35.12	even	12	inner
1470.2.m.d.97.1		16	35.3	even	12
1470.2.m.d.1273.1		16	35.4	even	6
1470.2.m.e.97.4		16	35.18	odd	12
1470.2.m.e.1273.4		16	35.24	odd	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(1.38658 + 2.25331i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.582897 - 1.00961i) q^{11} +(0.258819 - 0.965926i) q^{12} +(1.92501 - 1.92501i) q^{13} +(-0.756134 - 2.53540i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.0209315 - 0.00560858i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-0.989363 - 1.71363i) q^{19} +(1.81766 - 1.92253i) q^{21} +(-0.824341 + 0.824341i) q^{22} +(-1.85829 + 6.93525i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.35765 + 1.36119i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.0741591 + 2.64471i) q^{28} -5.60604i q^{29} +(6.86850 + 3.96553i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.12607 - 0.301730i) q^{33} -0.0216699 q^{34} -1.00000 q^{36} +(10.2592 + 2.74894i) q^{37} +(0.512132 + 1.91130i) q^{38} +(-2.35765 - 1.36119i) q^{39} +2.48977i q^{41} +(-2.25331 + 1.38658i) q^{42} +(7.87756 + 7.87756i) q^{43} +(1.00961 - 0.582897i) q^{44} +(3.58995 - 6.21797i) q^{46} +(1.05773 - 3.94750i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-3.15479 + 6.24878i) q^{49} +(-0.0108349 - 0.0187667i) q^{51} +(2.62962 - 0.704604i) q^{52} +(-2.82745 + 0.757613i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.612870 - 2.57379i) q^{56} +(-1.39917 + 1.39917i) q^{57} +(-1.45095 + 5.41502i) q^{58} +(5.34623 - 9.25995i) q^{59} +(-3.15795 + 1.82324i) q^{61} +(-5.60811 - 5.60811i) q^{62} +(-2.32747 - 1.25813i) q^{63} +1.00000i q^{64} +(1.00961 + 0.582897i) q^{66} +(-3.76794 - 14.0621i) q^{67} +(0.0209315 + 0.00560858i) q^{68} +7.17989 q^{69} +7.51848 q^{71} +(0.965926 + 0.258819i) q^{72} +(-0.969376 - 3.61776i) q^{73} +(-9.19815 - 5.31055i) q^{74} -1.97873i q^{76} +(3.08319 - 0.0864543i) q^{77} +(1.92501 + 1.92501i) q^{78} +(-1.39464 + 0.805197i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.644400 - 2.40493i) q^{82} +(9.74815 - 9.74815i) q^{83} +(2.53540 - 0.756134i) q^{84} +(-5.57028 - 9.64800i) q^{86} +(-5.41502 + 1.45095i) q^{87} +(-1.12607 + 0.301730i) q^{88} +(1.80255 + 3.12211i) q^{89} +(7.00683 + 1.66846i) q^{91} +(-5.07695 + 5.07695i) q^{92} +(2.05271 - 7.66082i) q^{93} +(-2.04338 + 3.53923i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(0.265501 + 0.265501i) q^{97} +(4.66460 - 5.21934i) q^{98} +1.16579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more