LMFDB - Embedded newform 1050.3.l.h.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.l (of order $4$, degree $2$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			757.1
Root			$-1.37832 + 1.37832i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.h.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -14.7776 q^{11} +(-2.44949 - 2.44949i) q^{12} +(13.2827 - 13.2827i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-1.17963 - 1.17963i) q^{17} +(3.00000 - 3.00000i) q^{18} +15.1298i q^{19} +4.58258 q^{21} +(-14.7776 - 14.7776i) q^{22} +(22.5070 - 22.5070i) q^{23} -4.89898i q^{24} +26.5654 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -3.29748i q^{29} +50.0892 q^{31} +(-4.00000 - 4.00000i) q^{32} +(18.0988 - 18.0988i) q^{33} -2.35927i q^{34} +6.00000 q^{36} +(-6.15735 - 6.15735i) q^{37} +(-15.1298 + 15.1298i) q^{38} +32.5359i q^{39} -35.1369 q^{41} +(4.58258 + 4.58258i) q^{42} +(58.9417 - 58.9417i) q^{43} -29.5552i q^{44} +45.0141 q^{46} +(20.1645 + 20.1645i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +2.88950 q^{51} +(26.5654 + 26.5654i) q^{52} +(-10.9028 + 10.9028i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-18.5302 - 18.5302i) q^{57} +(3.29748 - 3.29748i) q^{58} -66.6774i q^{59} -4.45593 q^{61} +(50.0892 + 50.0892i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +36.1976 q^{66} +(88.4424 + 88.4424i) q^{67} +(2.35927 - 2.35927i) q^{68} +55.1307i q^{69} +69.3188 q^{71} +(6.00000 + 6.00000i) q^{72} +(-58.4166 + 58.4166i) q^{73} -12.3147i q^{74} -30.2597 q^{76} +(27.6464 + 27.6464i) q^{77} +(-32.5359 + 32.5359i) q^{78} -52.8307i q^{79} -9.00000 q^{81} +(-35.1369 - 35.1369i) q^{82} +(53.4286 - 53.4286i) q^{83} +9.16515i q^{84} +117.883 q^{86} +(4.03857 + 4.03857i) q^{87} +(29.5552 - 29.5552i) q^{88} -21.3553i q^{89} -49.6994 q^{91} +(45.0141 + 45.0141i) q^{92} +(-61.3464 + 61.3464i) q^{93} +40.3290i q^{94} +9.79796 q^{96} +(-90.3562 - 90.3562i) q^{97} +(-7.00000 + 7.00000i) q^{98} +44.3328i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 - 32 * q^8	$ 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−14.7776			−1.34342			−0.671710	−	0.740814i	$-0.734440\pi$
$11$	−14.7776			−1.34342			−0.671710	+	0.740814i	$0.734440\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	13.2827	−	13.2827i	1.02175	−	1.02175i	0.0219895	−	0.999758i	$-0.493000\pi$
$13$	13.2827	−	13.2827i	1.02175	−	1.02175i	0.999758	−	0.0219895i	$-0.00700004\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−1.17963	−	1.17963i	−0.0693902	−	0.0693902i	0.671560	−	0.740950i	$-0.265625\pi$
$17$	−1.17963	−	1.17963i	−0.0693902	−	0.0693902i	−0.740950	+	0.671560i	$0.765625\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			15.1298i			0.796307i	0.917319	+	0.398154i	$0.130349\pi$
$19$			15.1298i			0.796307i	−0.917319	+	0.398154i	$0.869651\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−14.7776	−	14.7776i	−0.671710	−	0.671710i
$23$	22.5070	−	22.5070i	0.978567	−	0.978567i	−0.0212084	−	0.999775i	$-0.506751\pi$
$23$	22.5070	−	22.5070i	0.978567	−	0.978567i	0.999775	+	0.0212084i	$0.00675136\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	26.5654			1.02175
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$		−	3.29748i		−	0.113706i	−0.998383	−	0.0568530i	$-0.981893\pi$
$29$		−	3.29748i		−	0.113706i	0.998383	−	0.0568530i	$-0.0181066\pi$
$30$		0			0
$31$	50.0892			1.61578			0.807890	−	0.589334i	$-0.200610\pi$
$31$	50.0892			1.61578			0.807890	+	0.589334i	$0.200610\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	18.0988	−	18.0988i	0.548449	−	0.548449i
$34$		−	2.35927i		−	0.0693902i
$35$		0			0
$36$	6.00000			0.166667
$37$	−6.15735	−	6.15735i	−0.166415	−	0.166415i	0.618987	−	0.785401i	$-0.287543\pi$
$37$	−6.15735	−	6.15735i	−0.166415	−	0.166415i	−0.785401	+	0.618987i	$0.787543\pi$
$38$	−15.1298	+	15.1298i	−0.398154	+	0.398154i
$39$			32.5359i			0.834254i
$40$		0			0
$41$	−35.1369			−0.856998			−0.428499	−	0.903542i	$-0.640957\pi$
$41$	−35.1369			−0.856998			−0.428499	+	0.903542i	$0.640957\pi$
$42$	4.58258	+	4.58258i	0.109109	+	0.109109i
$43$	58.9417	−	58.9417i	1.37074	−	1.37074i	0.511388	−	0.859350i	$-0.329131\pi$
$43$	58.9417	−	58.9417i	1.37074	−	1.37074i	0.859350	−	0.511388i	$-0.170869\pi$
$44$		−	29.5552i		−	0.671710i
$45$		0			0
$46$	45.0141			0.978567
$47$	20.1645	+	20.1645i	0.429032	+	0.429032i	0.888299	−	0.459266i	$-0.151888\pi$
$47$	20.1645	+	20.1645i	0.429032	+	0.429032i	−0.459266	+	0.888299i	$0.651888\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	2.88950			0.0566569
$52$	26.5654	+	26.5654i	0.510874	+	0.510874i
$53$	−10.9028	+	10.9028i	−0.205712	+	0.205712i	−0.802442	−	0.596730i	$-0.796466\pi$
$53$	−10.9028	+	10.9028i	−0.205712	+	0.205712i	0.596730	+	0.802442i	$0.296466\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	−18.5302	−	18.5302i	−0.325091	−	0.325091i
$58$	3.29748	−	3.29748i	0.0568530	−	0.0568530i
$59$		−	66.6774i		−	1.13013i	−0.825048	−	0.565063i	$-0.808852\pi$
$59$		−	66.6774i		−	1.13013i	0.825048	−	0.565063i	$-0.191148\pi$
$60$		0			0
$61$	−4.45593			−0.0730481			−0.0365241	−	0.999333i	$-0.511629\pi$
$61$	−4.45593			−0.0730481			−0.0365241	+	0.999333i	$0.511629\pi$
$62$	50.0892	+	50.0892i	0.807890	+	0.807890i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	36.1976			0.548449
$67$	88.4424	+	88.4424i	1.32004	+	1.32004i	0.913743	+	0.406293i	$0.133179\pi$
$67$	88.4424	+	88.4424i	1.32004	+	1.32004i	0.406293	+	0.913743i	$0.366821\pi$
$68$	2.35927	−	2.35927i	0.0346951	−	0.0346951i
$69$			55.1307i			0.798996i
$70$		0			0
$71$	69.3188			0.976321			0.488161	−	0.872754i	$-0.337668\pi$
$71$	69.3188			0.976321			0.488161	+	0.872754i	$0.337668\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−58.4166	+	58.4166i	−0.800227	+	0.800227i	−0.983131	−	0.182903i	$-0.941450\pi$
$73$	−58.4166	+	58.4166i	−0.800227	+	0.800227i	0.182903	+	0.983131i	$0.441450\pi$
$74$		−	12.3147i		−	0.166415i
$75$		0			0
$76$	−30.2597			−0.398154
$77$	27.6464	+	27.6464i	0.359044	+	0.359044i
$78$	−32.5359	+	32.5359i	−0.417127	+	0.417127i
$79$		−	52.8307i		−	0.668744i	−0.942441	−	0.334372i	$-0.891476\pi$
$79$		−	52.8307i		−	0.668744i	0.942441	−	0.334372i	$-0.108524\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−35.1369	−	35.1369i	−0.428499	−	0.428499i
$83$	53.4286	−	53.4286i	0.643718	−	0.643718i	−0.307749	−	0.951468i	$-0.599576\pi$
$83$	53.4286	−	53.4286i	0.643718	−	0.643718i	0.951468	+	0.307749i	$0.0995758\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	117.883			1.37074
$87$	4.03857	+	4.03857i	0.0464203	+	0.0464203i
$88$	29.5552	−	29.5552i	0.335855	−	0.335855i
$89$		−	21.3553i		−	0.239947i	−0.992777	−	0.119973i	$-0.961719\pi$
$89$		−	21.3553i		−	0.239947i	0.992777	−	0.119973i	$-0.0382809\pi$
$90$		0			0
$91$	−49.6994			−0.546147
$92$	45.0141	+	45.0141i	0.489283	+	0.489283i
$93$	−61.3464	+	61.3464i	−0.659639	+	0.659639i
$94$			40.3290i			0.429032i
$95$		0			0
$96$	9.79796			0.102062
$97$	−90.3562	−	90.3562i	−0.931507	−	0.931507i	0.0662929	−	0.997800i	$-0.478883\pi$
$97$	−90.3562	−	90.3562i	−0.931507	−	0.931507i	−0.997800	+	0.0662929i	$0.978883\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$			44.3328i			0.447806i
$100$		0			0
$101$	43.6109			0.431791			0.215896	−	0.976416i	$-0.430733\pi$
$101$	43.6109			0.431791			0.215896	+	0.976416i	$0.430733\pi$
$102$	2.88950	+	2.88950i	0.0283284	+	0.0283284i
$103$	48.8638	−	48.8638i	0.474405	−	0.474405i	−0.428932	−	0.903337i	$-0.641110\pi$
$103$	48.8638	−	48.8638i	0.474405	−	0.474405i	0.903337	+	0.428932i	$0.141110\pi$
$104$			53.1309i			0.510874i
$105$		0			0
$106$	−21.8055			−0.205712
$107$	−23.1497	−	23.1497i	−0.216352	−	0.216352i	0.590607	−	0.806959i	$-0.298888\pi$
$107$	−23.1497	−	23.1497i	−0.216352	−	0.216352i	−0.806959	+	0.590607i	$0.798888\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			141.834i			1.30123i	0.759409	+	0.650613i	$0.225488\pi$
$109$			141.834i			1.30123i	−0.759409	+	0.650613i	$0.774512\pi$
$110$		0			0
$111$	15.0824			0.135877
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	113.746	−	113.746i	1.00660	−	1.00660i	0.00662298	−	0.999978i	$-0.497892\pi$
$113$	113.746	−	113.746i	1.00660	−	1.00660i	0.999978	−	0.00662298i	$-0.00210818\pi$
$114$		−	37.0604i		−	0.325091i
$115$		0			0
$116$	6.59495			0.0568530
$117$	−39.8482	−	39.8482i	−0.340583	−	0.340583i
$118$	66.6774	−	66.6774i	0.565063	−	0.565063i
$119$			4.41379i			0.0370906i
$120$		0			0
$121$	97.3779			0.804776
$122$	−4.45593	−	4.45593i	−0.0365241	−	0.0365241i
$123$	43.0338	−	43.0338i	0.349868	−	0.349868i
$124$			100.178i			0.807890i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	172.678	+	172.678i	1.35967	+	1.35967i	0.874325	+	0.485341i	$0.161305\pi$
$127$	172.678	+	172.678i	1.35967	+	1.35967i	0.485341	+	0.874325i	$0.338695\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			144.377i			1.11920i
$130$		0			0
$131$	147.540			1.12626			0.563129	−	0.826369i	$-0.309597\pi$
$131$	147.540			1.12626			0.563129	+	0.826369i	$0.309597\pi$
$132$	36.1976	+	36.1976i	0.274224	+	0.274224i
$133$	28.3053	−	28.3053i	0.212822	−	0.212822i
$134$			176.885i			1.32004i
$135$		0			0
$136$	4.71854			0.0346951
$137$	−96.5907	−	96.5907i	−0.705042	−	0.705042i	0.260447	−	0.965488i	$-0.416130\pi$
$137$	−96.5907	−	96.5907i	−0.705042	−	0.705042i	−0.965488	+	0.260447i	$0.916130\pi$
$138$	−55.1307	+	55.1307i	−0.399498	+	0.399498i
$139$		−	184.197i		−	1.32516i	−0.748993	−	0.662578i	$-0.769462\pi$
$139$		−	184.197i		−	1.32516i	0.748993	−	0.662578i	$-0.230538\pi$
$140$		0			0
$141$	−49.3928			−0.350303
$142$	69.3188	+	69.3188i	0.488161	+	0.488161i
$143$	−196.287	+	196.287i	−1.37264	+	1.37264i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	−116.833			−0.800227
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	12.3147	−	12.3147i	0.0832074	−	0.0832074i
$149$			206.358i			1.38495i	0.721442	+	0.692475i	$0.243480\pi$
$149$			206.358i			1.38495i	−0.721442	+	0.692475i	$0.756520\pi$
$150$		0			0
$151$	51.4825			0.340944			0.170472	−	0.985363i	$-0.445471\pi$
$151$	51.4825			0.340944			0.170472	+	0.985363i	$0.445471\pi$
$152$	−30.2597	−	30.2597i	−0.199077	−	0.199077i
$153$	−3.53890	+	3.53890i	−0.0231301	+	0.0231301i
$154$			55.2928i			0.359044i
$155$		0			0
$156$	−65.0718			−0.417127
$157$	−91.7859	−	91.7859i	−0.584624	−	0.584624i	0.351547	−	0.936170i	$-0.385656\pi$
$157$	−91.7859	−	91.7859i	−0.584624	−	0.584624i	−0.936170	+	0.351547i	$0.885656\pi$
$158$	52.8307	−	52.8307i	0.334372	−	0.334372i
$159$		−	26.7062i		−	0.167963i
$160$		0			0
$161$	−84.2136			−0.523066
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	11.1451	−	11.1451i	0.0683748	−	0.0683748i	−0.672092	−	0.740467i	$-0.734604\pi$
$163$	11.1451	−	11.1451i	0.0683748	−	0.0683748i	0.740467	+	0.672092i	$0.234604\pi$
$164$		−	70.2739i		−	0.428499i
$165$		0			0
$166$	106.857			0.643718
$167$	−224.811	−	224.811i	−1.34617	−	1.34617i	−0.889776	−	0.456397i	$-0.849140\pi$
$167$	−224.811	−	224.811i	−1.34617	−	1.34617i	−0.456397	−	0.889776i	$-0.650860\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$		−	183.861i		−	1.08794i
$170$		0			0
$171$	45.3895			0.265436
$172$	117.883	+	117.883i	0.685369	+	0.685369i
$173$	−43.4546	+	43.4546i	−0.251183	+	0.251183i	−0.821455	−	0.570273i	$-0.806838\pi$
$173$	−43.4546	+	43.4546i	−0.251183	+	0.251183i	0.570273	+	0.821455i	$0.306838\pi$
$174$			8.07713i			0.0464203i
$175$		0			0
$176$	59.1105			0.335855
$177$	81.6628	+	81.6628i	0.461372	+	0.461372i
$178$	21.3553	−	21.3553i	0.119973	−	0.119973i
$179$			167.373i			0.935046i	0.883981	+	0.467523i	$0.154854\pi$
$179$			167.373i			0.935046i	−0.883981	+	0.467523i	$0.845146\pi$
$180$		0			0
$181$	225.762			1.24730			0.623652	−	0.781702i	$-0.285648\pi$
$181$	225.762			1.24730			0.623652	+	0.781702i	$0.285648\pi$
$182$	−49.6994	−	49.6994i	−0.273074	−	0.273074i
$183$	5.45738	−	5.45738i	0.0298218	−	0.0298218i
$184$			90.0281i			0.489283i
$185$		0			0
$186$	−122.693			−0.659639
$187$	17.4322	+	17.4322i	0.0932202	+	0.0932202i
$188$	−40.3290	+	40.3290i	−0.214516	+	0.214516i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	−148.626			−0.778145			−0.389073	−	0.921207i	$-0.627204\pi$
$191$	−148.626			−0.778145			−0.389073	+	0.921207i	$0.627204\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	158.063	−	158.063i	0.818979	−	0.818979i	−0.166982	−	0.985960i	$-0.553402\pi$
$193$	158.063	−	158.063i	0.818979	−	0.818979i	0.985960	+	0.166982i	$0.0534020\pi$
$194$		−	180.712i		−	0.931507i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−26.7707	−	26.7707i	−0.135892	−	0.135892i	0.635889	−	0.771781i	$-0.280634\pi$
$197$	−26.7707	−	26.7707i	−0.135892	−	0.135892i	−0.771781	+	0.635889i	$0.780634\pi$
$198$	−44.3328	+	44.3328i	−0.223903	+	0.223903i
$199$		−	171.790i		−	0.863269i	−0.902049	−	0.431634i	$-0.857937\pi$
$199$		−	171.790i		−	0.863269i	0.902049	−	0.431634i	$-0.142063\pi$
$200$		0			0
$201$	−216.639			−1.07780
$202$	43.6109	+	43.6109i	0.215896	+	0.215896i
$203$	−6.16901	+	6.16901i	−0.0303892	+	0.0303892i
$204$			5.77900i			0.0283284i
$205$		0			0
$206$	97.7275			0.474405
$207$	−67.5211	−	67.5211i	−0.326189	−	0.326189i
$208$	−53.1309	+	53.1309i	−0.255437	+	0.255437i
$209$		−	223.583i		−	1.06977i
$210$		0			0
$211$	−302.432			−1.43333			−0.716664	−	0.697419i	$-0.754332\pi$
$211$	−302.432			−1.43333			−0.716664	+	0.697419i	$0.754332\pi$
$212$	−21.8055	−	21.8055i	−0.102856	−	0.102856i
$213$	−84.8978	+	84.8978i	−0.398581	+	0.398581i
$214$		−	46.2994i		−	0.216352i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−93.7082	−	93.7082i	−0.431835	−	0.431835i
$218$	−141.834	+	141.834i	−0.650613	+	0.650613i
$219$		−	143.091i		−	0.653383i
$220$		0			0
$221$	−31.3375			−0.141799
$222$	15.0824	+	15.0824i	0.0679385	+	0.0679385i
$223$	170.784	−	170.784i	0.765850	−	0.765850i	−0.211523	−	0.977373i	$-0.567842\pi$
$223$	170.784	−	170.784i	0.765850	−	0.765850i	0.977373	+	0.211523i	$0.0678424\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	227.492			1.00660
$227$	−154.323	−	154.323i	−0.679838	−	0.679838i	0.280125	−	0.959963i	$-0.409624\pi$
$227$	−154.323	−	154.323i	−0.679838	−	0.679838i	−0.959963	+	0.280125i	$0.909624\pi$
$228$	37.0604	−	37.0604i	0.162546	−	0.162546i
$229$		−	33.7243i		−	0.147267i	−0.997285	−	0.0736337i	$-0.976540\pi$
$229$		−	33.7243i		−	0.147267i	0.997285	−	0.0736337i	$-0.0234596\pi$
$230$		0			0
$231$	−67.7195			−0.293158
$232$	6.59495	+	6.59495i	0.0284265	+	0.0284265i
$233$	207.998	−	207.998i	0.892697	−	0.892697i	−0.102079	−	0.994776i	$-0.532550\pi$
$233$	207.998	−	207.998i	0.892697	−	0.892697i	0.994776	+	0.102079i	$0.0325496\pi$
$234$		−	79.6963i		−	0.340583i
$235$		0			0
$236$	133.355			0.565063
$237$	64.7042	+	64.7042i	0.273013	+	0.273013i
$238$	−4.41379	+	4.41379i	−0.0185453	+	0.0185453i
$239$			49.7163i			0.208018i	0.994576	+	0.104009i	$0.0331670\pi$
$239$			49.7163i			0.208018i	−0.994576	+	0.104009i	$0.966833\pi$
$240$		0			0
$241$	−49.9716			−0.207351			−0.103676	−	0.994611i	$-0.533060\pi$
$241$	−49.9716			−0.207351			−0.103676	+	0.994611i	$0.533060\pi$
$242$	97.3779	+	97.3779i	0.402388	+	0.402388i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	8.91187i		−	0.0365241i
$245$		0			0
$246$	86.0675			0.349868
$247$	200.965	+	200.965i	0.813625	+	0.813625i
$248$	−100.178	+	100.178i	−0.403945	+	0.403945i
$249$			130.873i			0.525594i
$250$		0			0
$251$	−315.486			−1.25692			−0.628459	−	0.777843i	$-0.716314\pi$
$251$	−315.486			−1.25692			−0.628459	+	0.777843i	$0.716314\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	−332.600	+	332.600i	−1.31463	+	1.31463i
$254$			345.355i			1.35967i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−275.744	−	275.744i	−1.07293	−	1.07293i	−0.997122	−	0.0758107i	$-0.975846\pi$
$257$	−275.744	−	275.744i	−1.07293	−	1.07293i	−0.0758107	−	0.997122i	$-0.524154\pi$
$258$	−144.377	+	144.377i	−0.559601	+	0.559601i
$259$			23.0387i			0.0889524i
$260$		0			0
$261$	−9.89243			−0.0379020
$262$	147.540	+	147.540i	0.563129	+	0.563129i
$263$	−122.744	+	122.744i	−0.466708	+	0.466708i	−0.900846	−	0.434138i	$-0.857053\pi$
$263$	−122.744	+	122.744i	−0.466708	+	0.466708i	0.434138	+	0.900846i	$0.357053\pi$
$264$			72.3952i			0.274224i
$265$		0			0
$266$	56.6107			0.212822
$267$	26.1547	+	26.1547i	0.0979578	+	0.0979578i
$268$	−176.885	+	176.885i	−0.660018	+	0.660018i
$269$			62.3232i			0.231685i	0.993268	+	0.115842i	$0.0369567\pi$
$269$			62.3232i			0.231685i	−0.993268	+	0.115842i	$0.963043\pi$
$270$		0			0
$271$	127.663			0.471081			0.235541	−	0.971864i	$-0.424314\pi$
$271$	127.663			0.471081			0.235541	+	0.971864i	$0.424314\pi$
$272$	4.71854	+	4.71854i	0.0173476	+	0.0173476i
$273$	60.8691	−	60.8691i	0.222964	−	0.222964i
$274$		−	193.181i		−	0.705042i
$275$		0			0
$276$	−110.261			−0.399498
$277$	57.6863	+	57.6863i	0.208254	+	0.208254i	0.803525	−	0.595271i	$-0.202955\pi$
$277$	57.6863	+	57.6863i	0.208254	+	0.208254i	−0.595271	+	0.803525i	$0.702955\pi$
$278$	184.197	−	184.197i	0.662578	−	0.662578i
$279$		−	150.267i		−	0.538593i
$280$		0			0
$281$	119.372			0.424812			0.212406	−	0.977182i	$-0.431870\pi$
$281$	119.372			0.424812			0.212406	+	0.977182i	$0.431870\pi$
$282$	−49.3928	−	49.3928i	−0.175152	−	0.175152i
$283$	175.257	−	175.257i	0.619282	−	0.619282i	−0.326065	−	0.945347i	$-0.605723\pi$
$283$	175.257	−	175.257i	0.619282	−	0.619282i	0.945347	+	0.326065i	$0.105723\pi$
$284$			138.638i			0.488161i
$285$		0			0
$286$	−392.574			−1.37264
$287$	65.7352	+	65.7352i	0.229042	+	0.229042i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	286.217i		−	0.990370i
$290$		0			0
$291$	221.327			0.760572
$292$	−116.833	−	116.833i	−0.400114	−	0.400114i
$293$	−224.254	+	224.254i	−0.765372	+	0.765372i	−0.977288	−	0.211916i	$-0.932030\pi$
$293$	−224.254	+	224.254i	−0.765372	+	0.765372i	0.211916	+	0.977288i	$0.432030\pi$
$294$		−	17.1464i		−	0.0583212i
$295$		0			0
$296$	24.6294			0.0832074
$297$	−54.2964	−	54.2964i	−0.182816	−	0.182816i
$298$	−206.358	+	206.358i	−0.692475	+	0.692475i
$299$		−	597.909i		−	1.99970i
$300$		0			0
$301$	−220.540			−0.732690
$302$	51.4825	+	51.4825i	0.170472	+	0.170472i
$303$	−53.4123	+	53.4123i	−0.176278	+	0.176278i
$304$		−	60.5194i		−	0.199077i
$305$		0			0
$306$	−7.07780			−0.0231301
$307$	−202.366	−	202.366i	−0.659172	−	0.659172i	0.296012	−	0.955184i	$-0.404343\pi$
$307$	−202.366	−	202.366i	−0.659172	−	0.659172i	−0.955184	+	0.296012i	$0.904343\pi$
$308$	−55.2928	+	55.2928i	−0.179522	+	0.179522i
$309$			119.691i			0.387350i
$310$		0			0
$311$	−382.114			−1.22866			−0.614331	−	0.789049i	$-0.710574\pi$
$311$	−382.114			−1.22866			−0.614331	+	0.789049i	$0.710574\pi$
$312$	−65.0718	−	65.0718i	−0.208563	−	0.208563i
$313$	235.445	−	235.445i	0.752220	−	0.752220i	−0.222674	−	0.974893i	$-0.571478\pi$
$313$	235.445	−	235.445i	0.752220	−	0.752220i	0.974893	+	0.222674i	$0.0714784\pi$
$314$		−	183.572i		−	0.584624i
$315$		0			0
$316$	105.661			0.334372
$317$	−297.704	−	297.704i	−0.939129	−	0.939129i	0.0591213	−	0.998251i	$-0.481170\pi$
$317$	−297.704	−	297.704i	−0.939129	−	0.939129i	−0.998251	+	0.0591213i	$0.981170\pi$
$318$	26.7062	−	26.7062i	0.0839817	−	0.0839817i
$319$			48.7288i			0.152755i
$320$		0			0
$321$	56.7049			0.176651
$322$	−84.2136	−	84.2136i	−0.261533	−	0.261533i
$323$	17.8477	−	17.8477i	0.0552559	−	0.0552559i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	22.2902			0.0683748
$327$	−173.710	−	173.710i	−0.531223	−	0.531223i
$328$	70.2739	−	70.2739i	0.214250	−	0.214250i
$329$		−	75.4487i		−	0.229327i
$330$		0			0
$331$	−197.349			−0.596221			−0.298110	−	0.954531i	$-0.596356\pi$
$331$	−197.349			−0.596221			−0.298110	+	0.954531i	$0.596356\pi$
$332$	106.857	+	106.857i	0.321859	+	0.321859i
$333$	−18.4720	+	18.4720i	−0.0554716	+	0.0554716i
$334$		−	449.622i		−	1.34617i
$335$		0			0
$336$	−18.3303			−0.0545545
$337$	259.060	+	259.060i	0.768723	+	0.768723i	0.977882	−	0.209159i	$-0.0670726\pi$
$337$	259.060	+	259.060i	0.768723	+	0.768723i	−0.209159	+	0.977882i	$0.567073\pi$
$338$	183.861	−	183.861i	0.543968	−	0.543968i
$339$			278.619i			0.821886i
$340$		0			0
$341$	−740.198			−2.17067
$342$	45.3895	+	45.3895i	0.132718	+	0.132718i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			235.767i			0.685369i
$345$		0			0
$346$	−86.9092			−0.251183
$347$	316.016	+	316.016i	0.910710	+	0.910710i	0.996328	−	0.0856183i	$-0.0272866\pi$
$347$	316.016	+	316.016i	0.910710	+	0.910710i	−0.0856183	+	0.996328i	$0.527287\pi$
$348$	−8.07713	+	8.07713i	−0.0232102	+	0.0232102i
$349$		−	64.9155i		−	0.186004i	−0.995666	−	0.0930022i	$-0.970354\pi$
$349$		−	64.9155i		−	0.186004i	0.995666	−	0.0930022i	$-0.0296464\pi$
$350$		0			0
$351$	97.6077			0.278085
$352$	59.1105	+	59.1105i	0.167927	+	0.167927i
$353$	−328.571	+	328.571i	−0.930796	+	0.930796i	−0.997756	−	0.0669597i	$-0.978670\pi$
$353$	−328.571	+	328.571i	−0.930796	+	0.930796i	0.0669597	+	0.997756i	$0.478670\pi$
$354$			163.326i			0.461372i
$355$		0			0
$356$	42.7105			0.119973
$357$	−5.40576	−	5.40576i	−0.0151422	−	0.0151422i
$358$	−167.373	+	167.373i	−0.467523	+	0.467523i
$359$		−	110.889i		−	0.308883i	−0.988002	−	0.154442i	$-0.950642\pi$
$359$		−	110.889i		−	0.308883i	0.988002	−	0.154442i	$-0.0493579\pi$
$360$		0			0
$361$	132.088			0.365895
$362$	225.762	+	225.762i	0.623652	+	0.623652i
$363$	−119.263	+	119.263i	−0.328548	+	0.328548i
$364$		−	99.3988i		−	0.273074i
$365$		0			0
$366$	10.9148			0.0298218
$367$	347.342	+	347.342i	0.946436	+	0.946436i	0.998637	−	0.0522011i	$-0.0166237\pi$
$367$	347.342	+	347.342i	0.946436	+	0.946436i	−0.0522011	+	0.998637i	$0.516624\pi$
$368$	−90.0281	+	90.0281i	−0.244642	+	0.244642i
$369$			105.411i			0.285666i
$370$		0			0
$371$	40.7944			0.109958
$372$	−122.693	−	122.693i	−0.329820	−	0.329820i
$373$	433.660	−	433.660i	1.16263	−	1.16263i	0.178728	−	0.983899i	$-0.442802\pi$
$373$	433.660	−	433.660i	1.16263	−	1.16263i	0.983899	−	0.178728i	$-0.0571981\pi$
$374$			34.8644i			0.0932202i
$375$		0			0
$376$	−80.6581			−0.214516
$377$	−43.7995	−	43.7995i	−0.116179	−	0.116179i
$378$	13.7477	−	13.7477i	0.0363696	−	0.0363696i
$379$			5.82662i			0.0153737i	0.999970	+	0.00768684i	$0.00244682\pi$
$379$			5.82662i			0.0153737i	−0.999970	+	0.00768684i	$0.997553\pi$
$380$		0			0
$381$	−422.972			−1.11016
$382$	−148.626	−	148.626i	−0.389073	−	0.389073i
$383$	84.7856	−	84.7856i	0.221372	−	0.221372i	−0.587704	−	0.809076i	$-0.699968\pi$
$383$	84.7856	−	84.7856i	0.221372	−	0.221372i	0.809076	+	0.587704i	$0.199968\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	316.126			0.818979
$387$	−176.825	−	176.825i	−0.456913	−	0.456913i
$388$	180.712	−	180.712i	0.465754	−	0.465754i
$389$		−	287.140i		−	0.738150i	−0.929400	−	0.369075i	$-0.879675\pi$
$389$		−	287.140i		−	0.738150i	0.929400	−	0.369075i	$-0.120325\pi$
$390$		0			0
$391$	−53.1001			−0.135806
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	−180.699	+	180.699i	−0.459793	+	0.459793i
$394$		−	53.5413i		−	0.135892i
$395$		0			0
$396$	−88.6657			−0.223903
$397$	−89.5514	−	89.5514i	−0.225570	−	0.225570i	0.585269	−	0.810839i	$-0.300989\pi$
$397$	−89.5514	−	89.5514i	−0.225570	−	0.225570i	−0.810839	+	0.585269i	$0.800989\pi$
$398$	171.790	−	171.790i	0.431634	−	0.431634i
$399$			69.3336i			0.173768i
$400$		0			0
$401$	−649.944			−1.62081			−0.810405	−	0.585871i	$-0.800753\pi$
$401$	−649.944			−1.62081			−0.810405	+	0.585871i	$0.800753\pi$
$402$	−216.639	−	216.639i	−0.538902	−	0.538902i
$403$	665.320	−	665.320i	1.65092	−	1.65092i
$404$			87.2218i			0.215896i
$405$		0			0
$406$	−12.3380			−0.0303892
$407$	90.9909	+	90.9909i	0.223565	+	0.223565i
$408$	−5.77900	+	5.77900i	−0.0141642	+	0.0141642i
$409$			717.337i			1.75388i	0.480600	+	0.876940i	$0.340419\pi$
$409$			717.337i			1.75388i	−0.480600	+	0.876940i	$0.659581\pi$
$410$		0			0
$411$	236.598			0.575664
$412$	97.7275	+	97.7275i	0.237203	+	0.237203i
$413$	−124.742	+	124.742i	−0.302039	+	0.302039i
$414$		−	135.042i		−	0.326189i
$415$		0			0
$416$	−106.262			−0.255437
$417$	225.594	+	225.594i	0.540992	+	0.540992i
$418$	223.583	−	223.583i	0.534887	−	0.534887i
$419$			680.885i			1.62502i	0.582945	+	0.812511i	$0.301900\pi$
$419$			680.885i			1.62502i	−0.582945	+	0.812511i	$0.698100\pi$
$420$		0			0
$421$	710.333			1.68725			0.843626	−	0.536931i	$-0.180416\pi$
$421$	710.333			1.68725			0.843626	+	0.536931i	$0.180416\pi$
$422$	−302.432	−	302.432i	−0.716664	−	0.716664i
$423$	60.4936	−	60.4936i	0.143011	−	0.143011i
$424$		−	43.6110i		−	0.102856i
$425$		0			0
$426$	−169.796			−0.398581
$427$	8.33629	+	8.33629i	0.0195229	+	0.0195229i
$428$	46.2994	−	46.2994i	0.108176	−	0.108176i
$429$		−	480.803i		−	1.12075i
$430$		0			0
$431$	785.543			1.82261			0.911303	−	0.411737i	$-0.135078\pi$
$431$	785.543			1.82261			0.911303	+	0.411737i	$0.135078\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−484.429	+	484.429i	−1.11877	+	1.11877i	−0.126852	+	0.991922i	$0.540487\pi$
$433$	−484.429	+	484.429i	−1.11877	+	1.11877i	−0.991922	+	0.126852i	$0.959513\pi$
$434$		−	187.416i		−	0.431835i
$435$		0			0
$436$	−283.667			−0.650613
$437$	340.528	+	340.528i	0.779240	+	0.779240i
$438$	143.091	−	143.091i	0.326691	−	0.326691i
$439$			558.366i			1.27190i	0.771728	+	0.635952i	$0.219392\pi$
$439$			558.366i			1.27190i	−0.771728	+	0.635952i	$0.780608\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−31.3375	−	31.3375i	−0.0708993	−	0.0708993i
$443$	−94.3596	+	94.3596i	−0.213001	+	0.213001i	−0.805541	−	0.592540i	$-0.798125\pi$
$443$	−94.3596	+	94.3596i	−0.213001	+	0.213001i	0.592540	+	0.805541i	$0.298125\pi$
$444$			30.1647i			0.0679385i
$445$		0			0
$446$	341.569			0.765850
$447$	−252.735	−	252.735i	−0.565404	−	0.565404i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	642.007i		−	1.42986i	−0.699197	−	0.714929i	$-0.746459\pi$
$449$		−	642.007i		−	1.42986i	0.699197	−	0.714929i	$-0.253541\pi$
$450$		0			0
$451$	519.240			1.15131
$452$	227.492	+	227.492i	0.503301	+	0.503301i
$453$	−63.0529	+	63.0529i	−0.139190	+	0.139190i
$454$		−	308.647i		−	0.679838i
$455$		0			0
$456$	74.1208			0.162546
$457$	−320.594	−	320.594i	−0.701519	−	0.701519i	0.263218	−	0.964736i	$-0.415216\pi$
$457$	−320.594	−	320.594i	−0.701519	−	0.701519i	−0.964736	+	0.263218i	$0.915216\pi$
$458$	33.7243	−	33.7243i	0.0736337	−	0.0736337i
$459$		−	8.66850i		−	0.0188856i
$460$		0			0
$461$	−300.193			−0.651177			−0.325589	−	0.945512i	$-0.605562\pi$
$461$	−300.193			−0.651177			−0.325589	+	0.945512i	$0.605562\pi$
$462$	−67.7195	−	67.7195i	−0.146579	−	0.146579i
$463$	−58.9154	+	58.9154i	−0.127247	+	0.127247i	−0.767862	−	0.640615i	$-0.778679\pi$
$463$	−58.9154	+	58.9154i	−0.127247	+	0.127247i	0.640615	+	0.767862i	$0.278679\pi$
$464$			13.1899i			0.0284265i
$465$		0			0
$466$	415.997			0.892697
$467$	362.497	+	362.497i	0.776226	+	0.776226i	0.979187	−	0.202961i	$-0.0650565\pi$
$467$	362.497	+	362.497i	0.776226	+	0.776226i	−0.202961	+	0.979187i	$0.565057\pi$
$468$	79.6963	−	79.6963i	0.170291	−	0.170291i
$469$		−	330.921i		−	0.705589i
$470$		0			0
$471$	224.829			0.477343
$472$	133.355	+	133.355i	0.282531	+	0.282531i
$473$	−871.018	+	871.018i	−1.84148	+	1.84148i
$474$			129.408i			0.273013i
$475$		0			0
$476$	−8.82757			−0.0185453
$477$	32.7083	+	32.7083i	0.0685708	+	0.0685708i
$478$	−49.7163	+	49.7163i	−0.104009	+	0.104009i
$479$		−	233.704i		−	0.487900i	−0.969788	−	0.243950i	$-0.921557\pi$
$479$		−	233.704i		−	0.487900i	0.969788	−	0.243950i	$-0.0784433\pi$
$480$		0			0
$481$	−163.573			−0.340068
$482$	−49.9716	−	49.9716i	−0.103676	−	0.103676i
$483$	103.140	−	103.140i	0.213541	−	0.213541i
$484$			194.756i			0.402388i
$485$		0			0
$486$	22.0454			0.0453609
$487$	−234.027	−	234.027i	−0.480549	−	0.480549i	0.424758	−	0.905307i	$-0.360359\pi$
$487$	−234.027	−	234.027i	−0.480549	−	0.480549i	−0.905307	+	0.424758i	$0.860359\pi$
$488$	8.91187	−	8.91187i	0.0182620	−	0.0182620i
$489$			27.2998i			0.0558278i
$490$		0			0
$491$	29.6268			0.0603398			0.0301699	−	0.999545i	$-0.490395\pi$
$491$	29.6268			0.0603398			0.0301699	+	0.999545i	$0.490395\pi$
$492$	86.0675	+	86.0675i	0.174934	+	0.174934i
$493$	−3.88981	+	3.88981i	−0.00789009	+	0.00789009i
$494$			401.931i			0.813625i
$495$		0			0
$496$	−200.357			−0.403945
$497$	−129.684	−	129.684i	−0.260933	−	0.260933i
$498$	−130.873	+	130.873i	−0.262797	+	0.262797i
$499$		−	322.566i		−	0.646426i	−0.946326	−	0.323213i	$-0.895237\pi$
$499$		−	322.566i		−	0.646426i	0.946326	−	0.323213i	$-0.104763\pi$
$500$		0			0
$501$	550.672			1.09915
$502$	−315.486	−	315.486i	−0.628459	−	0.628459i
$503$	350.402	−	350.402i	0.696625	−	0.696625i	−0.267056	−	0.963681i	$-0.586051\pi$
$503$	350.402	−	350.402i	0.696625	−	0.696625i	0.963681	+	0.267056i	$0.0860510\pi$
$504$		−	22.4499i		−	0.0445435i
$505$		0			0
$506$	−665.200			−1.31463
$507$	225.183	+	225.183i	0.444148	+	0.444148i
$508$	−345.355	+	345.355i	−0.679833	+	0.679833i
$509$			66.4967i			0.130642i	0.997864	+	0.0653210i	$0.0208071\pi$
$509$			66.4967i			0.130642i	−0.997864	+	0.0653210i	$0.979193\pi$
$510$		0			0
$511$	218.575			0.427740
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−55.5906	+	55.5906i	−0.108364	+	0.108364i
$514$		−	551.488i		−	1.07293i
$515$		0			0
$516$	−288.754			−0.559601
$517$	−297.983	−	297.983i	−0.576370	−	0.576370i
$518$	−23.0387	+	23.0387i	−0.0444762	+	0.0444762i
$519$		−	106.442i		−	0.205090i
$520$		0			0
$521$	−603.618			−1.15858			−0.579288	−	0.815123i	$-0.696669\pi$
$521$	−603.618			−1.15858			−0.579288	+	0.815123i	$0.696669\pi$
$522$	−9.89243	−	9.89243i	−0.0189510	−	0.0189510i
$523$	294.450	−	294.450i	0.563002	−	0.563002i	−0.367157	−	0.930159i	$-0.619669\pi$
$523$	294.450	−	294.450i	0.563002	−	0.563002i	0.930159	+	0.367157i	$0.119669\pi$
$524$			295.080i			0.563129i
$525$		0			0
$526$	−245.488			−0.466708
$527$	−59.0869	−	59.0869i	−0.112119	−	0.112119i
$528$	−72.3952	+	72.3952i	−0.137112	+	0.137112i
$529$		−	484.133i		−	0.915185i
$530$		0			0
$531$	−200.032			−0.376709
$532$	56.6107	+	56.6107i	0.106411	+	0.106411i
$533$	−466.714	+	466.714i	−0.875636	+	0.875636i
$534$			52.3095i			0.0979578i
$535$		0			0
$536$	−353.770			−0.660018
$537$	−204.990	−	204.990i	−0.381731	−	0.381731i
$538$	−62.3232	+	62.3232i	−0.115842	+	0.115842i
$539$		−	103.443i		−	0.191917i
$540$		0			0
$541$	−248.513			−0.459358			−0.229679	−	0.973266i	$-0.573768\pi$
$541$	−248.513			−0.459358			−0.229679	+	0.973266i	$0.573768\pi$
$542$	127.663	+	127.663i	0.235541	+	0.235541i
$543$	−276.501	+	276.501i	−0.509209	+	0.509209i
$544$			9.43707i			0.0173476i
$545$		0			0
$546$	121.738			0.222964
$547$	246.861	+	246.861i	0.451299	+	0.451299i	0.895786	−	0.444487i	$-0.146614\pi$
$547$	246.861	+	246.861i	0.451299	+	0.451299i	−0.444487	+	0.895786i	$0.646614\pi$
$548$	193.181	−	193.181i	0.352521	−	0.352521i
$549$			13.3678i			0.0243494i
$550$		0			0
$551$	49.8903			0.0905450
$552$	−110.261	−	110.261i	−0.199749	−	0.199749i
$553$	−98.8373	+	98.8373i	−0.178729	+	0.178729i
$554$			115.373i			0.208254i
$555$		0			0
$556$	368.393			0.662578
$557$	333.317	+	333.317i	0.598416	+	0.598416i	0.939891	−	0.341475i	$-0.110927\pi$
$557$	333.317	+	333.317i	0.598416	+	0.598416i	−0.341475	+	0.939891i	$0.610927\pi$
$558$	150.267	−	150.267i	0.269297	−	0.269297i
$559$		−	1565.81i		−	2.80110i
$560$		0			0
$561$	−42.6999			−0.0761140
$562$	119.372	+	119.372i	0.212406	+	0.212406i
$563$	−499.267	+	499.267i	−0.886798	+	0.886798i	−0.994214	−	0.107416i	$-0.965742\pi$
$563$	−499.267	+	499.267i	−0.886798	+	0.886798i	0.107416	+	0.994214i	$0.465742\pi$
$564$		−	98.7856i		−	0.175152i
$565$		0			0
$566$	350.514			0.619282
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−138.638	+	138.638i	−0.244080	+	0.244080i
$569$			990.818i			1.74133i	0.491874	+	0.870666i	$0.336312\pi$
$569$			990.818i			1.74133i	−0.491874	+	0.870666i	$0.663688\pi$
$570$		0			0
$571$	−172.474			−0.302057			−0.151028	−	0.988529i	$-0.548258\pi$
$571$	−172.474			−0.302057			−0.151028	+	0.988529i	$0.548258\pi$
$572$	−392.574	−	392.574i	−0.686318	−	0.686318i
$573$	182.029	−	182.029i	0.317676	−	0.317676i
$574$			131.470i			0.229042i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	75.2134	+	75.2134i	0.130352	+	0.130352i	0.769273	−	0.638920i	$-0.220619\pi$
$577$	75.2134	+	75.2134i	0.130352	+	0.130352i	−0.638920	+	0.769273i	$0.720619\pi$
$578$	286.217	−	286.217i	0.495185	−	0.495185i
$579$			387.173i			0.668693i
$580$		0			0
$581$	−199.912			−0.344082
$582$	221.327	+	221.327i	0.380286	+	0.380286i
$583$	161.117	−	161.117i	0.276358	−	0.276358i
$584$		−	233.666i		−	0.400114i
$585$		0			0
$586$	−448.508			−0.765372
$587$	−371.013	−	371.013i	−0.632050	−	0.632050i	0.316532	−	0.948582i	$-0.397481\pi$
$587$	−371.013	−	371.013i	−0.632050	−	0.632050i	−0.948582	+	0.316532i	$0.897481\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			757.841i			1.28666i
$590$		0			0
$591$	65.5745			0.110955
$592$	24.6294	+	24.6294i	0.0416037	+	0.0416037i
$593$	−106.940	+	106.940i	−0.180337	+	0.180337i	−0.791503	−	0.611166i	$-0.790701\pi$
$593$	−106.940	+	106.940i	−0.180337	+	0.180337i	0.611166	+	0.791503i	$0.290701\pi$
$594$		−	108.593i		−	0.182816i
$595$		0			0
$596$	−412.715			−0.692475
$597$	210.399	+	210.399i	0.352428	+	0.352428i
$598$	597.909	−	597.909i	0.999848	−	0.999848i
$599$			382.077i			0.637859i	0.947778	+	0.318929i	$0.103323\pi$
$599$			382.077i			0.637859i	−0.947778	+	0.318929i	$0.896677\pi$
$600$		0			0
$601$	618.446			1.02903			0.514514	−	0.857482i	$-0.327972\pi$
$601$	618.446			1.02903			0.514514	+	0.857482i	$0.327972\pi$
$602$	−220.540	−	220.540i	−0.366345	−	0.366345i
$603$	265.327	−	265.327i	0.440012	−	0.440012i
$604$			102.965i			0.170472i
$605$		0			0
$606$	−106.825			−0.176278
$607$	−222.670	−	222.670i	−0.366837	−	0.366837i	0.499485	−	0.866322i	$-0.333523\pi$
$607$	−222.670	−	222.670i	−0.366837	−	0.366837i	−0.866322	+	0.499485i	$0.833523\pi$
$608$	60.5194	−	60.5194i	0.0995384	−	0.0995384i
$609$		−	15.1109i		−	0.0248127i
$610$		0			0
$611$	535.679			0.876725
$612$	−7.07780	−	7.07780i	−0.0115650	−	0.0115650i
$613$	−422.055	+	422.055i	−0.688508	+	0.688508i	−0.961902	−	0.273394i	$-0.911854\pi$
$613$	−422.055	+	422.055i	−0.688508	+	0.688508i	0.273394	+	0.961902i	$0.411854\pi$
$614$		−	404.731i		−	0.659172i
$615$		0			0
$616$	−110.586			−0.179522
$617$	651.882	+	651.882i	1.05653	+	1.05653i	0.998303	+	0.0582314i	$0.0185461\pi$
$617$	651.882	+	651.882i	1.05653	+	1.05653i	0.0582314	+	0.998303i	$0.481454\pi$
$618$	−119.691	+	119.691i	−0.193675	+	0.193675i
$619$			687.434i			1.11056i	0.831665	+	0.555278i	$0.187388\pi$
$619$			687.434i			1.11056i	−0.831665	+	0.555278i	$0.812612\pi$
$620$		0			0
$621$	165.392			0.266332
$622$	−382.114	−	382.114i	−0.614331	−	0.614331i
$623$	−39.9520	+	39.9520i	−0.0641284	+	0.0641284i
$624$		−	130.144i		−	0.208563i
$625$		0			0
$626$	470.889			0.752220
$627$	273.832	+	273.832i	0.436734	+	0.436734i
$628$	183.572	−	183.572i	0.292312	−	0.292312i
$629$			14.5268i			0.0230951i
$630$		0			0
$631$	589.381			0.934043			0.467021	−	0.884246i	$-0.345327\pi$
$631$	589.381			0.934043			0.467021	+	0.884246i	$0.345327\pi$
$632$	105.661	+	105.661i	0.167186	+	0.167186i
$633$	370.402	−	370.402i	0.585154	−	0.585154i
$634$		−	595.408i		−	0.939129i
$635$		0			0
$636$	53.4124			0.0839817
$637$	92.9790	+	92.9790i	0.145964	+	0.145964i
$638$	−48.7288	+	48.7288i	−0.0763775	+	0.0763775i
$639$		−	207.956i		−	0.325440i
$640$		0			0
$641$	410.799			0.640872			0.320436	−	0.947270i	$-0.396171\pi$
$641$	410.799			0.640872			0.320436	+	0.947270i	$0.396171\pi$
$642$	56.7049	+	56.7049i	0.0883254	+	0.0883254i
$643$	−216.800	+	216.800i	−0.337169	+	0.337169i	−0.855301	−	0.518132i	$-0.826628\pi$
$643$	−216.800	+	216.800i	−0.337169	+	0.337169i	0.518132	+	0.855301i	$0.326628\pi$
$644$		−	168.427i		−	0.261533i
$645$		0			0
$646$	35.6953			0.0552559
$647$	411.008	+	411.008i	0.635252	+	0.635252i	0.949380	−	0.314129i	$-0.101712\pi$
$647$	411.008	+	411.008i	0.635252	+	0.635252i	−0.314129	+	0.949380i	$0.601712\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			985.333i			1.51823i
$650$		0			0
$651$	229.537			0.352592
$652$	22.2902	+	22.2902i	0.0341874	+	0.0341874i
$653$	46.1020	−	46.1020i	0.0706003	−	0.0706003i	−0.670925	−	0.741525i	$-0.734103\pi$
$653$	46.1020	−	46.1020i	0.0706003	−	0.0706003i	0.741525	+	0.670925i	$0.234103\pi$
$654$		−	347.420i		−	0.531223i
$655$		0			0
$656$	140.548			0.214250
$657$	175.250	+	175.250i	0.266742	+	0.266742i
$658$	75.4487	−	75.4487i	0.114664	−	0.114664i
$659$			911.116i			1.38257i	0.722580	+	0.691287i	$0.242956\pi$
$659$			911.116i			1.38257i	−0.722580	+	0.691287i	$0.757044\pi$
$660$		0			0
$661$	24.2084			0.0366239			0.0183120	−	0.999832i	$-0.494171\pi$
$661$	24.2084			0.0366239			0.0183120	+	0.999832i	$0.494171\pi$
$662$	−197.349	−	197.349i	−0.298110	−	0.298110i
$663$	38.3804	−	38.3804i	0.0578890	−	0.0578890i
$664$			213.714i			0.321859i
$665$		0			0
$666$	−36.9441			−0.0554716
$667$	−74.2164	−	74.2164i	−0.111269	−	0.111269i
$668$	449.622	−	449.622i	0.673087	−	0.673087i
$669$			418.335i			0.625314i
$670$		0			0
$671$	65.8481			0.0981343
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	−522.406	+	522.406i	−0.776235	+	0.776235i	−0.979188	−	0.202954i	$-0.934946\pi$
$673$	−522.406	+	522.406i	−0.776235	+	0.776235i	0.202954	+	0.979188i	$0.434946\pi$
$674$			518.119i			0.768723i
$675$		0			0
$676$	367.723			0.543968
$677$	283.980	+	283.980i	0.419468	+	0.419468i	0.885020	−	0.465552i	$-0.154144\pi$
$677$	283.980	+	283.980i	0.419468	+	0.419468i	−0.465552	+	0.885020i	$0.654144\pi$
$678$	−278.619	+	278.619i	−0.410943	+	0.410943i
$679$			338.082i			0.497912i
$680$		0			0
$681$	378.013			0.555086
$682$	−740.198	−	740.198i	−1.08533	−	1.08533i
$683$	549.911	−	549.911i	0.805141	−	0.805141i	−0.178753	−	0.983894i	$-0.557206\pi$
$683$	549.911	−	549.911i	0.805141	−	0.805141i	0.983894	+	0.178753i	$0.0572064\pi$
$684$			90.7790i			0.132718i
$685$		0			0
$686$	26.1916			0.0381802
$687$	41.3036	+	41.3036i	0.0601217	+	0.0601217i
$688$	−235.767	+	235.767i	−0.342685	+	0.342685i
$689$			289.636i			0.420372i
$690$		0			0
$691$	−1119.58			−1.62023			−0.810117	−	0.586268i	$-0.800597\pi$
$691$	−1119.58			−1.62023			−0.810117	+	0.586268i	$0.800597\pi$
$692$	−86.9092	−	86.9092i	−0.125591	−	0.125591i
$693$	82.9392	−	82.9392i	0.119681	−	0.119681i
$694$			632.033i			0.910710i
$695$		0			0
$696$	−16.1543			−0.0232102
$697$	41.4487	+	41.4487i	0.0594673	+	0.0594673i
$698$	64.9155	−	64.9155i	0.0930022	−	0.0930022i
$699$			509.490i			0.728884i
$700$		0			0
$701$	693.405			0.989166			0.494583	−	0.869130i	$-0.335321\pi$
$701$	693.405			0.989166			0.494583	+	0.869130i	$0.335321\pi$
$702$	97.6077	+	97.6077i	0.139042	+	0.139042i
$703$	93.1597	−	93.1597i	0.132517	−	0.132517i
$704$			118.221i			0.167927i
$705$		0			0
$706$	−657.142			−0.930796
$707$	−81.5886	−	81.5886i	−0.115401	−	0.115401i
$708$	−163.326	+	163.326i	−0.230686	+	0.230686i
$709$			774.547i			1.09245i	0.837638	+	0.546225i	$0.183936\pi$
$709$			774.547i			1.09245i	−0.837638	+	0.546225i	$0.816064\pi$
$710$		0			0
$711$	−158.492			−0.222915
$712$	42.7105	+	42.7105i	0.0599867	+	0.0599867i
$713$	1127.36	−	1127.36i	1.58115	−	1.58115i
$714$		−	10.8115i		−	0.0151422i
$715$		0			0
$716$	−334.747			−0.467523
$717$	−60.8897	−	60.8897i	−0.0849229	−	0.0849229i
$718$	110.889	−	110.889i	0.154442	−	0.154442i
$719$		−	8.61314i		−	0.0119793i	−0.999982	−	0.00598966i	$-0.998093\pi$
$719$		−	8.61314i		−	0.0119793i	0.999982	−	0.00598966i	$-0.00190658\pi$
$720$		0			0
$721$	−182.831			−0.253580
$722$	132.088	+	132.088i	0.182947	+	0.182947i
$723$	61.2025	−	61.2025i	0.0846507	−	0.0846507i
$724$			451.524i			0.623652i
$725$		0			0
$726$	−238.526			−0.328548
$727$	305.108	+	305.108i	0.419681	+	0.419681i	0.885094	−	0.465413i	$-0.154094\pi$
$727$	305.108	+	305.108i	0.419681	+	0.419681i	−0.465413	+	0.885094i	$0.654094\pi$
$728$	99.3988	−	99.3988i	0.136537	−	0.136537i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−139.059			−0.190232
$732$	10.9148	+	10.9148i	0.0149109	+	0.0149109i
$733$	73.0619	−	73.0619i	0.0996751	−	0.0996751i	−0.655511	−	0.755186i	$-0.727547\pi$
$733$	73.0619	−	73.0619i	0.0996751	−	0.0996751i	0.755186	+	0.655511i	$0.227547\pi$
$734$			694.684i			0.946436i
$735$		0			0
$736$	−180.056			−0.244642
$737$	−1306.97	−	1306.97i	−1.77336	−	1.77336i
$738$	−105.411	+	105.411i	−0.142833	+	0.142833i
$739$			81.9526i			0.110897i	0.998462	+	0.0554483i	$0.0176588\pi$
$739$			81.9526i			0.110897i	−0.998462	+	0.0554483i	$0.982341\pi$
$740$		0			0
$741$	−492.263			−0.664322
$742$	40.7944	+	40.7944i	0.0549789	+	0.0549789i
$743$	−225.872	+	225.872i	−0.304000	+	0.304000i	−0.842577	−	0.538577i	$-0.818962\pi$
$743$	−225.872	+	225.872i	−0.304000	+	0.304000i	0.538577	+	0.842577i	$0.318962\pi$
$744$		−	245.386i		−	0.329820i
$745$		0			0
$746$	867.319			1.16263
$747$	−160.286	−	160.286i	−0.214573	−	0.214573i
$748$	−34.8644	+	34.8644i	−0.0466101	+	0.0466101i
$749$			86.6182i			0.115645i
$750$		0			0
$751$	795.157			1.05880			0.529399	−	0.848373i	$-0.322417\pi$
$751$	795.157			1.05880			0.529399	+	0.848373i	$0.322417\pi$
$752$	−80.6581	−	80.6581i	−0.107258	−	0.107258i
$753$	386.390	−	386.390i	0.513134	−	0.513134i
$754$		−	87.5989i		−	0.116179i
$755$		0			0
$756$	27.4955			0.0363696
$757$	43.3607	+	43.3607i	0.0572796	+	0.0572796i	0.735166	−	0.677887i	$-0.237104\pi$
$757$	43.3607	+	43.3607i	0.0572796	+	0.0572796i	−0.677887	+	0.735166i	$0.737104\pi$
$758$	−5.82662	+	5.82662i	−0.00768684	+	0.00768684i
$759$		−	814.701i		−	1.07339i
$760$		0			0
$761$	448.207			0.588972			0.294486	−	0.955656i	$-0.404852\pi$
$761$	448.207			0.588972			0.294486	+	0.955656i	$0.404852\pi$
$762$	−422.972	−	422.972i	−0.555081	−	0.555081i
$763$	265.346	−	265.346i	0.347767	−	0.347767i
$764$		−	297.251i		−	0.389073i
$765$		0			0
$766$	169.571			0.221372
$767$	−885.657	−	885.657i	−1.15470	−	1.15470i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			126.308i			0.164249i	0.996622	+	0.0821245i	$0.0261705\pi$
$769$			126.308i			0.164249i	−0.996622	+	0.0821245i	$0.973829\pi$
$770$		0			0
$771$	675.432			0.876046
$772$	316.126	+	316.126i	0.409489	+	0.409489i
$773$	534.661	−	534.661i	0.691670	−	0.691670i	−0.270929	−	0.962599i	$-0.587331\pi$
$773$	534.661	−	534.661i	0.691670	−	0.691670i	0.962599	+	0.270929i	$0.0873310\pi$
$774$		−	353.650i		−	0.456913i
$775$		0			0
$776$	361.425			0.465754
$777$	−28.2165	−	28.2165i	−0.0363147	−	0.0363147i
$778$	287.140	−	287.140i	0.369075	−	0.369075i
$779$		−	531.616i		−	0.682434i
$780$		0			0
$781$	−1024.37			−1.31161
$782$	−53.1001	−	53.1001i	−0.0679030	−	0.0679030i
$783$	12.1157	−	12.1157i	0.0154734	−	0.0154734i
$784$		−	28.0000i		−	0.0357143i
$785$		0			0
$786$	−361.397			−0.459793
$787$	1038.23	+	1038.23i	1.31922	+	1.31922i	0.914394	+	0.404825i	$0.132668\pi$
$787$	1038.23	+	1038.23i	1.31922	+	1.31922i	0.404825	+	0.914394i	$0.367332\pi$
$788$	53.5413	−	53.5413i	0.0679458	−	0.0679458i
$789$		−	300.661i		−	0.381065i
$790$		0			0
$791$	−425.598			−0.538051
$792$	−88.6657	−	88.6657i	−0.111952	−	0.111952i
$793$	−59.1869	+	59.1869i	−0.0746367	+	0.0746367i
$794$		−	179.103i		−	0.225570i
$795$		0			0
$796$	343.581			0.431634
$797$	294.158	+	294.158i	0.369081	+	0.369081i	0.867142	−	0.498061i	$-0.165954\pi$
$797$	294.158	+	294.158i	0.369081	+	0.369081i	−0.498061	+	0.867142i	$0.665954\pi$
$798$	−69.3336	+	69.3336i	−0.0868842	+	0.0868842i
$799$		−	47.5735i		−	0.0595413i
$800$		0			0
$801$	−64.0658			−0.0799822
$802$	−649.944	−	649.944i	−0.810405	−	0.810405i
$803$	863.258	−	863.258i	1.07504	−	1.07504i
$804$		−	433.278i		−	0.538902i
$805$		0			0
$806$	1330.64			1.65092
$807$	−76.3300	−	76.3300i	−0.0945849	−	0.0945849i
$808$	−87.2218	+	87.2218i	−0.107948	+	0.107948i
$809$		−	22.0860i		−	0.0273004i	−0.999907	−	0.0136502i	$-0.995655\pi$
$809$		−	22.0860i		−	0.0273004i	0.999907	−	0.0136502i	$-0.00434513\pi$
$810$		0			0
$811$	−242.865			−0.299464			−0.149732	−	0.988727i	$-0.547841\pi$
$811$	−242.865			−0.299464			−0.149732	+	0.988727i	$0.547841\pi$
$812$	−12.3380	−	12.3380i	−0.0151946	−	0.0151946i
$813$	−156.355	+	156.355i	−0.192318	+	0.192318i
$814$			181.982i			0.223565i
$815$		0			0
$816$	−11.5580			−0.0141642
$817$	891.779	+	891.779i	1.09153	+	1.09153i
$818$	−717.337	+	717.337i	−0.876940	+	0.876940i
$819$			149.098i			0.182049i
$820$		0			0
$821$	228.561			0.278394			0.139197	−	0.990265i	$-0.455548\pi$
$821$	228.561			0.278394			0.139197	+	0.990265i	$0.455548\pi$
$822$	236.598	+	236.598i	0.287832	+	0.287832i
$823$	641.691	−	641.691i	0.779698	−	0.779698i	−0.200081	−	0.979779i	$-0.564121\pi$
$823$	641.691	−	641.691i	0.779698	−	0.779698i	0.979779	+	0.200081i	$0.0641207\pi$
$824$			195.455i			0.237203i
$825$		0			0
$826$	−249.484			−0.302039
$827$	1075.03	+	1075.03i	1.29992	+	1.29992i	0.928441	+	0.371479i	$0.121149\pi$
$827$	1075.03	+	1075.03i	1.29992	+	1.29992i	0.371479	+	0.928441i	$0.378851\pi$
$828$	135.042	−	135.042i	0.163094	−	0.163094i
$829$			530.478i			0.639901i	0.947434	+	0.319950i	$0.103666\pi$
$829$			530.478i			0.639901i	−0.947434	+	0.319950i	$0.896334\pi$
$830$		0			0
$831$	−141.302			−0.170039
$832$	−106.262	−	106.262i	−0.127718	−	0.127718i
$833$	8.25744	−	8.25744i	0.00991289	−	0.00991289i
$834$			451.188i			0.540992i
$835$		0			0
$836$	447.166			0.534887
$837$	184.039	+	184.039i	0.219880	+	0.219880i
$838$	−680.885	+	680.885i	−0.812511	+	0.812511i
$839$		−	618.719i		−	0.737448i	−0.929539	−	0.368724i	$-0.879795\pi$
$839$		−	618.719i		−	0.737448i	0.929539	−	0.368724i	$-0.120205\pi$
$840$		0			0
$841$	830.127			0.987071
$842$	710.333	+	710.333i	0.843626	+	0.843626i
$843$	−146.200	+	146.200i	−0.173429	+	0.173429i
$844$		−	604.864i		−	0.716664i
$845$		0			0
$846$	120.987			0.143011
$847$	−182.177	−	182.177i	−0.215085	−	0.215085i
$848$	43.6110	−	43.6110i	0.0514281	−	0.0514281i
$849$			429.290i			0.505642i
$850$		0			0
$851$	−277.167			−0.325696
$852$	−169.796	−	169.796i	−0.199291	−	0.199291i
$853$	−164.001	+	164.001i	−0.192264	+	0.192264i	−0.796674	−	0.604410i	$-0.793409\pi$
$853$	−164.001	+	164.001i	−0.192264	+	0.192264i	0.604410	+	0.796674i	$0.293409\pi$
$854$			16.6726i			0.0195229i
$855$		0			0
$856$	92.5987			0.108176
$857$	−889.068	−	889.068i	−1.03742	−	1.03742i	−0.999272	−	0.0381473i	$-0.987854\pi$
$857$	−889.068	−	889.068i	−1.03742	−	1.03742i	−0.0381473	−	0.999272i	$-0.512146\pi$
$858$	480.803	−	480.803i	0.560376	−	0.560376i
$859$		−	1203.95i		−	1.40157i	−0.713374	−	0.700783i	$-0.752834\pi$
$859$		−	1203.95i		−	1.40157i	0.713374	−	0.700783i	$-0.247166\pi$
$860$		0			0
$861$	−161.018			−0.187012
$862$	785.543	+	785.543i	0.911303	+	0.911303i
$863$	−813.145	+	813.145i	−0.942230	+	0.942230i	−0.998420	−	0.0561900i	$-0.982105\pi$
$863$	−813.145	+	813.145i	−0.942230	+	0.942230i	0.0561900	+	0.998420i	$0.482105\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	−968.858			−1.11877
$867$	350.543	+	350.543i	0.404317	+	0.404317i
$868$	187.416	−	187.416i	0.215918	−	0.215918i
$869$			780.712i			0.898403i
$870$		0			0
$871$	2349.51			2.69749
$872$	−283.667	−	283.667i	−0.325307	−	0.325307i
$873$	−271.069	+	271.069i	−0.310502	+	0.310502i
$874$			681.056i			0.779240i
$875$		0			0
$876$	286.182			0.326691
$877$	233.930	+	233.930i	0.266739	+	0.266739i	0.827785	−	0.561046i	$-0.189601\pi$
$877$	233.930	+	233.930i	0.266739	+	0.266739i	−0.561046	+	0.827785i	$0.689601\pi$
$878$	−558.366	+	558.366i	−0.635952	+	0.635952i
$879$		−	549.308i		−	0.624923i
$880$		0			0
$881$	34.2672			0.0388957			0.0194479	−	0.999811i	$-0.493809\pi$
$881$	34.2672			0.0388957			0.0194479	+	0.999811i	$0.493809\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	−1030.29	+	1030.29i	−1.16680	+	1.16680i	−0.183846	+	0.982955i	$0.558855\pi$
$883$	−1030.29	+	1030.29i	−1.16680	+	1.16680i	−0.982955	+	0.183846i	$0.941145\pi$
$884$		−	62.6750i		−	0.0708993i
$885$		0			0
$886$	−188.719			−0.213001
$887$	129.771	+	129.771i	0.146303	+	0.146303i	0.776464	−	0.630161i	$-0.217011\pi$
$887$	129.771	+	129.771i	0.146303	+	0.146303i	−0.630161	+	0.776464i	$0.717011\pi$
$888$	−30.1647	+	30.1647i	−0.0339693	+	0.0339693i
$889$		−	646.100i		−	0.726772i
$890$		0			0
$891$	132.999			0.149269
$892$	341.569	+	341.569i	0.382925	+	0.382925i
$893$	−305.086	+	305.086i	−0.341642	+	0.341642i
$894$		−	505.471i		−	0.565404i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	732.286	+	732.286i	0.816373	+	0.816373i
$898$	642.007	−	642.007i	0.714929	−	0.714929i
$899$		−	165.168i		−	0.183724i
$900$		0			0
$901$	25.7225			0.0285489
$902$	519.240	+	519.240i	0.575654	+	0.575654i
$903$	270.105	−	270.105i	0.299120	−	0.299120i
$904$			454.984i			0.503301i
$905$		0			0
$906$	−126.106			−0.139190
$907$	914.642	+	914.642i	1.00843	+	1.00843i	0.999964	+	0.00846121i	$0.00269332\pi$
$907$	914.642	+	914.642i	1.00843	+	1.00843i	0.00846121	+	0.999964i	$0.497307\pi$
$908$	308.647	−	308.647i	0.339919	−	0.339919i
$909$		−	130.833i		−	0.143930i
$910$		0			0
$911$	75.4264			0.0827952			0.0413976	−	0.999143i	$-0.486819\pi$
$911$	75.4264			0.0827952			0.0413976	+	0.999143i	$0.486819\pi$
$912$	74.1208	+	74.1208i	0.0812728	+	0.0812728i
$913$	−789.548	+	789.548i	−0.864784	+	0.864784i
$914$		−	641.188i		−	0.701519i
$915$		0			0
$916$	67.4485			0.0736337
$917$	−276.022	−	276.022i	−0.301005	−	0.301005i
$918$	8.66850	−	8.66850i	0.00944281	−	0.00944281i
$919$		−	1008.57i		−	1.09747i	−0.835998	−	0.548733i	$-0.815111\pi$
$919$		−	1008.57i		−	1.09747i	0.835998	−	0.548733i	$-0.184889\pi$
$920$		0			0
$921$	495.693			0.538212
$922$	−300.193	−	300.193i	−0.325589	−	0.325589i
$923$	920.742	−	920.742i	0.997554	−	0.997554i
$924$		−	135.439i		−	0.146579i
$925$		0			0
$926$	−117.831			−0.127247
$927$	−146.591	−	146.591i	−0.158135	−	0.158135i
$928$	−13.1899	+	13.1899i	−0.0142133	+	0.0142133i
$929$		−	1240.03i		−	1.33480i	−0.744699	−	0.667400i	$-0.767407\pi$
$929$		−	1240.03i		−	1.33480i	0.744699	−	0.667400i	$-0.232593\pi$
$930$		0			0
$931$	−105.909			−0.113758
$932$	415.997	+	415.997i	0.446348	+	0.446348i
$933$	467.992	−	467.992i	0.501599	−	0.501599i
$934$			724.995i			0.776226i
$935$		0			0
$936$	159.393			0.170291
$937$	−239.199	−	239.199i	−0.255282	−	0.255282i	0.567850	−	0.823132i	$-0.307775\pi$
$937$	−239.199	−	239.199i	−0.255282	−	0.255282i	−0.823132	+	0.567850i	$0.807775\pi$
$938$	330.921	−	330.921i	0.352794	−	0.352794i
$939$			576.719i			0.614185i
$940$		0			0
$941$	1412.22			1.50077			0.750384	−	0.661003i	$-0.229869\pi$
$941$	1412.22			1.50077			0.750384	+	0.661003i	$0.229869\pi$
$942$	224.829	+	224.829i	0.238672	+	0.238672i
$943$	−790.828	+	790.828i	−0.838630	+	0.838630i
$944$			266.710i			0.282531i
$945$		0			0
$946$	−1742.04			−1.84148
$947$	−13.0937	−	13.0937i	−0.0138265	−	0.0138265i	0.700160	−	0.713986i	$-0.253112\pi$
$947$	−13.0937	−	13.0937i	−0.0138265	−	0.0138265i	−0.713986	+	0.700160i	$0.753112\pi$
$948$	−129.408	+	129.408i	−0.136507	+	0.136507i
$949$			1551.86i			1.63526i
$950$		0			0
$951$	729.223			0.766796
$952$	−8.82757	−	8.82757i	−0.00927266	−	0.00927266i
$953$	1186.29	−	1186.29i	1.24480	−	1.24480i	0.286809	−	0.957988i	$-0.407406\pi$
$953$	1186.29	−	1186.29i	1.24480	−	1.24480i	0.957988	−	0.286809i	$-0.0925944\pi$
$954$			65.4165i			0.0685708i
$955$		0			0
$956$	−99.4325			−0.104009
$957$	−59.6804	−	59.6804i	−0.0623619	−	0.0623619i
$958$	233.704	−	233.704i	0.243950	−	0.243950i
$959$			361.409i			0.376861i
$960$		0			0
$961$	1547.92			1.61074
$962$	−163.573	−	163.573i	−0.170034	−	0.170034i
$963$	−69.4491	+	69.4491i	−0.0721174	+	0.0721174i
$964$		−	99.9432i		−	0.103676i
$965$		0			0
$966$	206.280			0.213541
$967$	−989.527	−	989.527i	−1.02330	−	1.02330i	−0.999722	−	0.0235735i	$-0.992496\pi$
$967$	−989.527	−	989.527i	−1.02330	−	1.02330i	−0.0235735	−	0.999722i	$-0.507504\pi$
$968$	−194.756	+	194.756i	−0.201194	+	0.201194i
$969$			43.7177i			0.0451163i
$970$		0			0
$971$	104.077			0.107185			0.0535927	−	0.998563i	$-0.482933\pi$
$971$	104.077			0.107185			0.0535927	+	0.998563i	$0.482933\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−344.600	+	344.600i	−0.354163	+	0.354163i
$974$		−	468.055i		−	0.480549i
$975$		0			0
$976$	17.8237			0.0182620
$977$	635.859	+	635.859i	0.650828	+	0.650828i	0.953192	−	0.302364i	$-0.0977760\pi$
$977$	635.859	+	635.859i	0.650828	+	0.650828i	−0.302364	+	0.953192i	$0.597776\pi$
$978$	−27.2998	+	27.2998i	−0.0279139	+	0.0279139i
$979$			315.580i			0.322349i
$980$		0			0
$981$	425.501			0.433742
$982$	29.6268	+	29.6268i	0.0301699	+	0.0301699i
$983$	−1166.39	+	1166.39i	−1.18656	+	1.18656i	−0.208553	+	0.978011i	$0.566875\pi$
$983$	−1166.39	+	1166.39i	−1.18656	+	1.18656i	−0.978011	+	0.208553i	$0.933125\pi$
$984$			172.135i			0.174934i
$985$		0			0
$986$	−7.77963			−0.00789009
$987$	92.4054	+	92.4054i	0.0936225	+	0.0936225i
$988$	−401.931	+	401.931i	−0.406813	+	0.406813i
$989$		−	2653.21i		−	2.68272i
$990$		0			0
$991$	−978.880			−0.987770			−0.493885	−	0.869527i	$-0.664424\pi$
$991$	−978.880			−0.987770			−0.493885	+	0.869527i	$0.664424\pi$
$992$	−200.357	−	200.357i	−0.201972	−	0.201972i
$993$	241.702	−	241.702i	0.243406	−	0.243406i
$994$		−	259.367i		−	0.260933i
$995$		0			0
$996$	−261.746			−0.262797
$997$	−646.604	−	646.604i	−0.648550	−	0.648550i	0.304093	−	0.952642i	$-0.401647\pi$
$997$	−646.604	−	646.604i	−0.648550	−	0.648550i	−0.952642	+	0.304093i	$0.901647\pi$
$998$	322.566	−	322.566i	0.323213	−	0.323213i
$999$		−	45.2471i		−	0.0452924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.h.757.1		16
5.2	odd	4		210.3.l.b.43.5	✓	16
5.3	odd	4	inner	1050.3.l.h.43.1		16
5.4	even	2		210.3.l.b.127.5	yes	16
15.2	even	4		630.3.o.f.253.7		16
15.14	odd	2		630.3.o.f.127.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.5	✓	16	5.2	odd	4
210.3.l.b.127.5	yes	16	5.4	even	2
630.3.o.f.127.7		16	15.14	odd	2
630.3.o.f.253.7		16	15.2	even	4
1050.3.l.h.43.1		16	5.3	odd	4	inner
1050.3.l.h.757.1		16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -14.7776 q^{11} +(-2.44949 - 2.44949i) q^{12} +(13.2827 - 13.2827i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-1.17963 - 1.17963i) q^{17} +(3.00000 - 3.00000i) q^{18} +15.1298i q^{19} +4.58258 q^{21} +(-14.7776 - 14.7776i) q^{22} +(22.5070 - 22.5070i) q^{23} -4.89898i q^{24} +26.5654 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} -3.29748i q^{29} +50.0892 q^{31} +(-4.00000 - 4.00000i) q^{32} +(18.0988 - 18.0988i) q^{33} -2.35927i q^{34} +6.00000 q^{36} +(-6.15735 - 6.15735i) q^{37} +(-15.1298 + 15.1298i) q^{38} +32.5359i q^{39} -35.1369 q^{41} +(4.58258 + 4.58258i) q^{42} +(58.9417 - 58.9417i) q^{43} -29.5552i q^{44} +45.0141 q^{46} +(20.1645 + 20.1645i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +2.88950 q^{51} +(26.5654 + 26.5654i) q^{52} +(-10.9028 + 10.9028i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-18.5302 - 18.5302i) q^{57} +(3.29748 - 3.29748i) q^{58} -66.6774i q^{59} -4.45593 q^{61} +(50.0892 + 50.0892i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +36.1976 q^{66} +(88.4424 + 88.4424i) q^{67} +(2.35927 - 2.35927i) q^{68} +55.1307i q^{69} +69.3188 q^{71} +(6.00000 + 6.00000i) q^{72} +(-58.4166 + 58.4166i) q^{73} -12.3147i q^{74} -30.2597 q^{76} +(27.6464 + 27.6464i) q^{77} +(-32.5359 + 32.5359i) q^{78} -52.8307i q^{79} -9.00000 q^{81} +(-35.1369 - 35.1369i) q^{82} +(53.4286 - 53.4286i) q^{83} +9.16515i q^{84} +117.883 q^{86} +(4.03857 + 4.03857i) q^{87} +(29.5552 - 29.5552i) q^{88} -21.3553i q^{89} -49.6994 q^{91} +(45.0141 + 45.0141i) q^{92} +(-61.3464 + 61.3464i) q^{93} +40.3290i q^{94} +9.79796 q^{96} +(-90.3562 - 90.3562i) q^{97} +(-7.00000 + 7.00000i) q^{98} +44.3328i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 - 32 * q^8	\( 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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