LMFDB - Embedded newform 1050.3.l.a.43.2

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.a.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -3.02424 q^{11} +(-2.44949 + 2.44949i) q^{12} +(2.99455 + 2.99455i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-13.0622 + 13.0622i) q^{17} +(-3.00000 - 3.00000i) q^{18} -29.5080i q^{19} -4.58258 q^{21} +(3.02424 - 3.02424i) q^{22} +(-2.34455 - 2.34455i) q^{23} -4.89898i q^{24} -5.98911 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -24.4595i q^{29} +46.7091 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.70392 + 3.70392i) q^{33} -26.1244i q^{34} +6.00000 q^{36} +(-30.6893 + 30.6893i) q^{37} +(29.5080 + 29.5080i) q^{38} -7.33513i q^{39} +11.9782 q^{41} +(4.58258 - 4.58258i) q^{42} +(0.402550 + 0.402550i) q^{43} +6.04847i q^{44} +4.68911 q^{46} +(-46.4173 + 46.4173i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +31.9957 q^{51} +(5.98911 - 5.98911i) q^{52} +(-11.9515 - 11.9515i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-36.1398 + 36.1398i) q^{57} +(24.4595 + 24.4595i) q^{58} -32.2897i q^{59} -78.3977 q^{61} +(-46.7091 + 46.7091i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -7.40784 q^{66} +(17.3609 - 17.3609i) q^{67} +(26.1244 + 26.1244i) q^{68} +5.74296i q^{69} -43.2246 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-39.4074 - 39.4074i) q^{73} -61.3787i q^{74} -59.0160 q^{76} +(-5.65783 + 5.65783i) q^{77} +(7.33513 + 7.33513i) q^{78} +0.100902i q^{79} -9.00000 q^{81} +(-11.9782 + 11.9782i) q^{82} +(15.9969 + 15.9969i) q^{83} +9.16515i q^{84} -0.805100 q^{86} +(-29.9567 + 29.9567i) q^{87} +(-6.04847 - 6.04847i) q^{88} +91.4648i q^{89} +11.2046 q^{91} +(-4.68911 + 4.68911i) q^{92} +(-57.2067 - 57.2067i) q^{93} -92.8346i q^{94} -9.79796 q^{96} +(-14.1758 + 14.1758i) q^{97} +(7.00000 + 7.00000i) q^{98} -9.07271i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$11$	−3.02424			−0.274931			−0.137465	−	0.990507i	$-0.543896\pi$
$11$	−3.02424			−0.274931			−0.137465	+	0.990507i	$0.543896\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	2.99455	+	2.99455i	0.230350	+	0.230350i	0.812839	−	0.582489i	$-0.197921\pi$
$13$	2.99455	+	2.99455i	0.230350	+	0.230350i	−0.582489	+	0.812839i	$0.697921\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−13.0622	+	13.0622i	−0.768365	+	0.768365i	−0.977819	−	0.209454i	$-0.932831\pi$
$17$	−13.0622	+	13.0622i	−0.768365	+	0.768365i	0.209454	+	0.977819i	$0.432831\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	29.5080i		−	1.55305i	−0.630085	−	0.776526i	$-0.716980\pi$
$19$		−	29.5080i		−	1.55305i	0.630085	−	0.776526i	$-0.283020\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	3.02424	−	3.02424i	0.137465	−	0.137465i
$23$	−2.34455	−	2.34455i	−0.101937	−	0.101937i	0.654299	−	0.756236i	$-0.272964\pi$
$23$	−2.34455	−	2.34455i	−0.101937	−	0.101937i	−0.756236	+	0.654299i	$0.772964\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	−5.98911			−0.230350
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	24.4595i		−	0.843432i	−0.906728	−	0.421716i	$-0.861428\pi$
$29$		−	24.4595i		−	0.843432i	0.906728	−	0.421716i	$-0.138572\pi$
$30$		0			0
$31$	46.7091			1.50674			0.753372	−	0.657594i	$-0.228426\pi$
$31$	46.7091			1.50674			0.753372	+	0.657594i	$0.228426\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	3.70392	+	3.70392i	0.112240	+	0.112240i
$34$		−	26.1244i		−	0.768365i
$35$		0			0
$36$	6.00000			0.166667
$37$	−30.6893	+	30.6893i	−0.829442	+	0.829442i	−0.987439	−	0.157998i	$-0.949496\pi$
$37$	−30.6893	+	30.6893i	−0.829442	+	0.829442i	0.157998	+	0.987439i	$0.449496\pi$
$38$	29.5080	+	29.5080i	0.776526	+	0.776526i
$39$		−	7.33513i		−	0.188080i
$40$		0			0
$41$	11.9782			0.292152			0.146076	−	0.989273i	$-0.453336\pi$
$41$	11.9782			0.292152			0.146076	+	0.989273i	$0.453336\pi$
$42$	4.58258	−	4.58258i	0.109109	−	0.109109i
$43$	0.402550	+	0.402550i	0.00936162	+	0.00936162i	0.711772	−	0.702410i	$-0.247893\pi$
$43$	0.402550	+	0.402550i	0.00936162	+	0.00936162i	−0.702410	+	0.711772i	$0.747893\pi$
$44$			6.04847i			0.137465i
$45$		0			0
$46$	4.68911			0.101937
$47$	−46.4173	+	46.4173i	−0.987602	+	0.987602i	−0.999924	−	0.0123220i	$-0.996078\pi$
$47$	−46.4173	+	46.4173i	−0.987602	+	0.987602i	0.0123220	+	0.999924i	$0.496078\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	31.9957			0.627367
$52$	5.98911	−	5.98911i	0.115175	−	0.115175i
$53$	−11.9515	−	11.9515i	−0.225501	−	0.225501i	0.585309	−	0.810810i	$-0.300973\pi$
$53$	−11.9515	−	11.9515i	−0.225501	−	0.225501i	−0.810810	+	0.585309i	$0.800973\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	−36.1398	+	36.1398i	−0.634031	+	0.634031i
$58$	24.4595	+	24.4595i	0.421716	+	0.421716i
$59$		−	32.2897i		−	0.547284i	−0.961832	−	0.273642i	$-0.911772\pi$
$59$		−	32.2897i		−	0.547284i	0.961832	−	0.273642i	$-0.0882283\pi$
$60$		0			0
$61$	−78.3977			−1.28521			−0.642604	−	0.766198i	$-0.722146\pi$
$61$	−78.3977			−1.28521			−0.642604	+	0.766198i	$0.722146\pi$
$62$	−46.7091	+	46.7091i	−0.753372	+	0.753372i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−7.40784			−0.112240
$67$	17.3609	−	17.3609i	0.259118	−	0.259118i	−0.565577	−	0.824695i	$-0.691347\pi$
$67$	17.3609	−	17.3609i	0.259118	−	0.259118i	0.824695	+	0.565577i	$0.191347\pi$
$68$	26.1244	+	26.1244i	0.384182	+	0.384182i
$69$			5.74296i			0.0832313i
$70$		0			0
$71$	−43.2246			−0.608797			−0.304398	−	0.952545i	$-0.598455\pi$
$71$	−43.2246			−0.608797			−0.304398	+	0.952545i	$0.598455\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−39.4074	−	39.4074i	−0.539827	−	0.539827i	0.383651	−	0.923478i	$-0.374667\pi$
$73$	−39.4074	−	39.4074i	−0.539827	−	0.539827i	−0.923478	+	0.383651i	$0.874667\pi$
$74$		−	61.3787i		−	0.829442i
$75$		0			0
$76$	−59.0160			−0.776526
$77$	−5.65783	+	5.65783i	−0.0734783	+	0.0734783i
$78$	7.33513	+	7.33513i	0.0940401	+	0.0940401i
$79$			0.100902i			0.00127724i	1.00000		0.000638622i	$0.000203280\pi$
$79$			0.100902i			0.00127724i	−1.00000		0.000638622i	$0.999797\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−11.9782	+	11.9782i	−0.146076	+	0.146076i
$83$	15.9969	+	15.9969i	0.192734	+	0.192734i	0.796876	−	0.604142i	$-0.206484\pi$
$83$	15.9969	+	15.9969i	0.192734	+	0.192734i	−0.604142	+	0.796876i	$0.706484\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	−0.805100			−0.00936162
$87$	−29.9567	+	29.9567i	−0.344330	+	0.344330i
$88$	−6.04847	−	6.04847i	−0.0687326	−	0.0687326i
$89$			91.4648i			1.02769i	0.857882	+	0.513847i	$0.171780\pi$
$89$			91.4648i			1.02769i	−0.857882	+	0.513847i	$0.828220\pi$
$90$		0			0
$91$	11.2046			0.123127
$92$	−4.68911	+	4.68911i	−0.0509686	+	0.0509686i
$93$	−57.2067	−	57.2067i	−0.615126	−	0.615126i
$94$		−	92.8346i		−	0.987602i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−14.1758	+	14.1758i	−0.146142	+	0.146142i	−0.776392	−	0.630250i	$-0.782952\pi$
$97$	−14.1758	+	14.1758i	−0.146142	+	0.146142i	0.630250	+	0.776392i	$0.282952\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		−	9.07271i		−	0.0916435i
$100$		0			0
$101$	−121.663			−1.20458			−0.602291	−	0.798277i	$-0.705745\pi$
$101$	−121.663			−1.20458			−0.602291	+	0.798277i	$0.705745\pi$
$102$	−31.9957	+	31.9957i	−0.313684	+	0.313684i
$103$	−78.3209	−	78.3209i	−0.760397	−	0.760397i	0.215997	−	0.976394i	$-0.430700\pi$
$103$	−78.3209	−	78.3209i	−0.760397	−	0.760397i	−0.976394	+	0.215997i	$0.930700\pi$
$104$			11.9782i			0.115175i
$105$		0			0
$106$	23.9031			0.225501
$107$	−125.259	+	125.259i	−1.17064	+	1.17064i	−0.188586	+	0.982057i	$0.560390\pi$
$107$	−125.259	+	125.259i	−1.17064	+	1.17064i	−0.982057	+	0.188586i	$0.939610\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	181.318i		−	1.66347i	−0.555176	−	0.831733i	$-0.687349\pi$
$109$		−	181.318i		−	1.66347i	0.555176	−	0.831733i	$-0.312651\pi$
$110$		0			0
$111$	75.1732			0.677236
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	−16.7553	−	16.7553i	−0.148277	−	0.148277i	0.629071	−	0.777348i	$-0.283436\pi$
$113$	−16.7553	−	16.7553i	−0.148277	−	0.148277i	−0.777348	+	0.629071i	$0.783436\pi$
$114$		−	72.2796i		−	0.634031i
$115$		0			0
$116$	−48.9191			−0.421716
$117$	−8.98366	+	8.98366i	−0.0767834	+	0.0767834i
$118$	32.2897	+	32.2897i	0.273642	+	0.273642i
$119$			48.8743i			0.410708i
$120$		0			0
$121$	−111.854			−0.924413
$122$	78.3977	−	78.3977i	0.642604	−	0.642604i
$123$	−14.6703	−	14.6703i	−0.119270	−	0.119270i
$124$		−	93.4182i		−	0.753372i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	−3.42855	+	3.42855i	−0.0269964	+	0.0269964i	−0.720476	−	0.693480i	$-0.756077\pi$
$127$	−3.42855	+	3.42855i	−0.0269964	+	0.0269964i	0.693480	+	0.720476i	$0.256077\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	0.986041i		−	0.00764373i
$130$		0			0
$131$	−201.822			−1.54063			−0.770314	−	0.637665i	$-0.779901\pi$
$131$	−201.822			−1.54063			−0.770314	+	0.637665i	$0.779901\pi$
$132$	7.40784	−	7.40784i	0.0561200	−	0.0561200i
$133$	−55.2044	−	55.2044i	−0.415071	−	0.415071i
$134$			34.7218i			0.259118i
$135$		0			0
$136$	−52.2488			−0.384182
$137$	−150.398	+	150.398i	−1.09779	+	1.09779i	−0.103123	+	0.994669i	$0.532884\pi$
$137$	−150.398	+	150.398i	−1.09779	+	1.09779i	−0.994669	+	0.103123i	$0.967116\pi$
$138$	−5.74296	−	5.74296i	−0.0416157	−	0.0416157i
$139$			120.042i			0.863613i	0.901966	+	0.431806i	$0.142124\pi$
$139$			120.042i			0.863613i	−0.901966	+	0.431806i	$0.857876\pi$
$140$		0			0
$141$	113.699			0.806374
$142$	43.2246	−	43.2246i	0.304398	−	0.304398i
$143$	−9.05624	−	9.05624i	−0.0633303	−	0.0633303i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	78.8147			0.539827
$147$	−8.57321	+	8.57321i	−0.0583212	+	0.0583212i
$148$	61.3787	+	61.3787i	0.414721	+	0.414721i
$149$		−	37.0923i		−	0.248942i	−0.992223	−	0.124471i	$-0.960277\pi$
$149$		−	37.0923i		−	0.248942i	0.992223	−	0.124471i	$-0.0397234\pi$
$150$		0			0
$151$	−133.681			−0.885306			−0.442653	−	0.896693i	$-0.645963\pi$
$151$	−133.681			−0.885306			−0.442653	+	0.896693i	$0.645963\pi$
$152$	59.0160	−	59.0160i	0.388263	−	0.388263i
$153$	−39.1866	−	39.1866i	−0.256122	−	0.256122i
$154$		−	11.3157i		−	0.0734783i
$155$		0			0
$156$	−14.6703			−0.0940401
$157$	125.140	−	125.140i	0.797067	−	0.797067i	−0.185565	−	0.982632i	$-0.559412\pi$
$157$	125.140	−	125.140i	0.797067	−	0.797067i	0.982632	+	0.185565i	$0.0594115\pi$
$158$	−0.100902	−	0.100902i	−0.000638622	−	0.000638622i
$159$			29.2751i			0.184120i
$160$		0			0
$161$	−8.77252			−0.0544877
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−157.323	−	157.323i	−0.965174	−	0.965174i	0.0342396	−	0.999414i	$-0.489099\pi$
$163$	−157.323	−	157.323i	−0.965174	−	0.965174i	−0.999414	+	0.0342396i	$0.989099\pi$
$164$		−	23.9564i		−	0.146076i
$165$		0			0
$166$	−31.9939			−0.192734
$167$	−24.3702	+	24.3702i	−0.145929	+	0.145929i	−0.776297	−	0.630368i	$-0.782904\pi$
$167$	−24.3702	+	24.3702i	−0.145929	+	0.145929i	0.630368	+	0.776297i	$0.282904\pi$
$168$	−9.16515	−	9.16515i	−0.0545545	−	0.0545545i
$169$		−	151.065i		−	0.893878i
$170$		0			0
$171$	88.5240			0.517684
$172$	0.805100	−	0.805100i	0.00468081	−	0.00468081i
$173$	44.2512	+	44.2512i	0.255787	+	0.255787i	0.823338	−	0.567551i	$-0.192109\pi$
$173$	44.2512	+	44.2512i	0.255787	+	0.255787i	−0.567551	+	0.823338i	$0.692109\pi$
$174$		−	59.9134i		−	0.344330i
$175$		0			0
$176$	12.0969			0.0687326
$177$	−39.5467	+	39.5467i	−0.223428	+	0.223428i
$178$	−91.4648	−	91.4648i	−0.513847	−	0.513847i
$179$		−	101.526i		−	0.567183i	−0.958945	−	0.283592i	$-0.908474\pi$
$179$		−	101.526i		−	0.567183i	0.958945	−	0.283592i	$-0.0915260\pi$
$180$		0			0
$181$	−138.946			−0.767659			−0.383829	−	0.923404i	$-0.625395\pi$
$181$	−138.946			−0.767659			−0.383829	+	0.923404i	$0.625395\pi$
$182$	−11.2046	+	11.2046i	−0.0615637	+	0.0615637i
$183$	96.0172	+	96.0172i	0.524684	+	0.524684i
$184$		−	9.37822i		−	0.0509686i
$185$		0			0
$186$	114.413			0.615126
$187$	39.5032	−	39.5032i	0.211247	−	0.211247i
$188$	92.8346	+	92.8346i	0.493801	+	0.493801i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	299.678			1.56899			0.784497	−	0.620133i	$-0.212921\pi$
$191$	299.678			1.56899			0.784497	+	0.620133i	$0.212921\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−136.927	−	136.927i	−0.709467	−	0.709467i	0.256956	−	0.966423i	$-0.417280\pi$
$193$	−136.927	−	136.927i	−0.709467	−	0.709467i	−0.966423	+	0.256956i	$0.917280\pi$
$194$		−	28.3516i		−	0.146142i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	127.476	−	127.476i	0.647088	−	0.647088i	−0.305200	−	0.952288i	$-0.598723\pi$
$197$	127.476	−	127.476i	0.647088	−	0.647088i	0.952288	+	0.305200i	$0.0987234\pi$
$198$	9.07271	+	9.07271i	0.0458218	+	0.0458218i
$199$			173.636i			0.872543i	0.899815	+	0.436272i	$0.143701\pi$
$199$			173.636i			0.872543i	−0.899815	+	0.436272i	$0.856299\pi$
$200$		0			0
$201$	−42.5253			−0.211569
$202$	121.663	−	121.663i	0.602291	−	0.602291i
$203$	−45.7596	−	45.7596i	−0.225417	−	0.225417i
$204$		−	63.9915i		−	0.313684i
$205$		0			0
$206$	156.642			0.760397
$207$	7.03366	−	7.03366i	0.0339791	−	0.0339791i
$208$	−11.9782	−	11.9782i	−0.0575876	−	0.0575876i
$209$			89.2392i			0.426982i
$210$		0			0
$211$	−146.655			−0.695047			−0.347524	−	0.937671i	$-0.612977\pi$
$211$	−146.655			−0.695047			−0.347524	+	0.937671i	$0.612977\pi$
$212$	−23.9031	+	23.9031i	−0.112750	+	0.112750i
$213$	52.9391	+	52.9391i	0.248540	+	0.248540i
$214$		−	250.518i		−	1.17064i
$215$		0			0
$216$	14.6969			0.0680414
$217$	87.3847	−	87.3847i	0.402694	−	0.402694i
$218$	181.318	+	181.318i	0.831733	+	0.831733i
$219$			96.5280i			0.440767i
$220$		0			0
$221$	−78.2309			−0.353986
$222$	−75.1732	+	75.1732i	−0.338618	+	0.338618i
$223$	−86.4182	−	86.4182i	−0.387526	−	0.387526i	0.486278	−	0.873804i	$-0.338354\pi$
$223$	−86.4182	−	86.4182i	−0.387526	−	0.387526i	−0.873804	+	0.486278i	$0.838354\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	33.5107			0.148277
$227$	2.32591	−	2.32591i	0.0102463	−	0.0102463i	−0.701965	−	0.712211i	$-0.747694\pi$
$227$	2.32591	−	2.32591i	0.0102463	−	0.0102463i	0.712211	+	0.701965i	$0.247694\pi$
$228$	72.2796	+	72.2796i	0.317016	+	0.317016i
$229$			345.111i			1.50704i	0.657427	+	0.753518i	$0.271645\pi$
$229$			345.111i			1.50704i	−0.657427	+	0.753518i	$0.728355\pi$
$230$		0			0
$231$	13.8588			0.0599948
$232$	48.9191	−	48.9191i	0.210858	−	0.210858i
$233$	97.4876	+	97.4876i	0.418402	+	0.418402i	0.884653	−	0.466251i	$-0.154396\pi$
$233$	97.4876	+	97.4876i	0.418402	+	0.418402i	−0.466251	+	0.884653i	$0.654396\pi$
$234$		−	17.9673i		−	0.0767834i
$235$		0			0
$236$	−64.5795			−0.273642
$237$	0.123580	−	0.123580i	0.000521433	−	0.000521433i
$238$	−48.8743	−	48.8743i	−0.205354	−	0.205354i
$239$			155.285i			0.649730i	0.945760	+	0.324865i	$0.105319\pi$
$239$			155.285i			0.649730i	−0.945760	+	0.324865i	$0.894681\pi$
$240$		0			0
$241$	−46.6435			−0.193542			−0.0967708	−	0.995307i	$-0.530851\pi$
$241$	−46.6435			−0.193542			−0.0967708	+	0.995307i	$0.530851\pi$
$242$	111.854	−	111.854i	0.462207	−	0.462207i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			156.795i			0.642604i
$245$		0			0
$246$	29.3405			0.119270
$247$	88.3633	−	88.3633i	0.357746	−	0.357746i
$248$	93.4182	+	93.4182i	0.376686	+	0.376686i
$249$		−	39.1843i		−	0.157367i
$250$		0			0
$251$	−110.354			−0.439657			−0.219829	−	0.975539i	$-0.570550\pi$
$251$	−110.354			−0.439657			−0.219829	+	0.975539i	$0.570550\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	7.09049	+	7.09049i	0.0280256	+	0.0280256i
$254$		−	6.85709i		−	0.0269964i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−248.411	+	248.411i	−0.966580	+	0.966580i	−0.999459	−	0.0328796i	$-0.989532\pi$
$257$	−248.411	+	248.411i	−0.966580	+	0.966580i	0.0328796	+	0.999459i	$0.489532\pi$
$258$	0.986041	+	0.986041i	0.00382187	+	0.00382187i
$259$			114.829i			0.443355i
$260$		0			0
$261$	73.3786			0.281144
$262$	201.822	−	201.822i	0.770314	−	0.770314i
$263$	32.6076	+	32.6076i	0.123983	+	0.123983i	0.766376	−	0.642392i	$-0.222058\pi$
$263$	32.6076	+	32.6076i	0.123983	+	0.123983i	−0.642392	+	0.766376i	$0.722058\pi$
$264$			14.8157i			0.0561200i
$265$		0			0
$266$	110.409			0.415071
$267$	112.021	−	112.021i	0.419554	−	0.419554i
$268$	−34.7218	−	34.7218i	−0.129559	−	0.129559i
$269$		−	109.536i		−	0.407197i	−0.979054	−	0.203598i	$-0.934736\pi$
$269$		−	109.536i		−	0.407197i	0.979054	−	0.203598i	$-0.0652637\pi$
$270$		0			0
$271$	−105.472			−0.389195			−0.194597	−	0.980883i	$-0.562340\pi$
$271$	−105.472			−0.389195			−0.194597	+	0.980883i	$0.562340\pi$
$272$	52.2488	−	52.2488i	0.192091	−	0.192091i
$273$	−13.7228	−	13.7228i	−0.0502665	−	0.0502665i
$274$		−	300.795i		−	1.09779i
$275$		0			0
$276$	11.4859			0.0416157
$277$	172.034	−	172.034i	0.621061	−	0.621061i	−0.324742	−	0.945803i	$-0.605277\pi$
$277$	172.034	−	172.034i	0.621061	−	0.621061i	0.945803	+	0.324742i	$0.105277\pi$
$278$	−120.042	−	120.042i	−0.431806	−	0.431806i
$279$			140.127i			0.502248i
$280$		0			0
$281$	−88.5422			−0.315097			−0.157548	−	0.987511i	$-0.550359\pi$
$281$	−88.5422			−0.315097			−0.157548	+	0.987511i	$0.550359\pi$
$282$	−113.699	+	113.699i	−0.403187	+	0.403187i
$283$	187.561	+	187.561i	0.662758	+	0.662758i	0.956029	−	0.293271i	$-0.0947439\pi$
$283$	187.561	+	187.561i	0.662758	+	0.662758i	−0.293271	+	0.956029i	$0.594744\pi$
$284$			86.4492i			0.304398i
$285$		0			0
$286$	18.1125			0.0633303
$287$	22.4092	−	22.4092i	0.0780808	−	0.0780808i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	52.2423i		−	0.180769i
$290$		0			0
$291$	34.7235			0.119325
$292$	−78.8147	+	78.8147i	−0.269914	+	0.269914i
$293$	−237.252	−	237.252i	−0.809733	−	0.809733i	0.174861	−	0.984593i	$-0.444053\pi$
$293$	−237.252	−	237.252i	−0.809733	−	0.809733i	−0.984593	+	0.174861i	$0.944053\pi$
$294$		−	17.1464i		−	0.0583212i
$295$		0			0
$296$	−122.757			−0.414721
$297$	−11.1118	+	11.1118i	−0.0374133	+	0.0374133i
$298$	37.0923	+	37.0923i	0.124471	+	0.124471i
$299$		−	14.0418i		−	0.0469625i
$300$		0			0
$301$	1.50620			0.00500400
$302$	133.681	−	133.681i	0.442653	−	0.442653i
$303$	149.006	+	149.006i	0.491768	+	0.491768i
$304$			118.032i			0.388263i
$305$		0			0
$306$	78.3732			0.256122
$307$	49.8059	−	49.8059i	0.162234	−	0.162234i	−0.621322	−	0.783556i	$-0.713404\pi$
$307$	49.8059	−	49.8059i	0.162234	−	0.162234i	0.783556	+	0.621322i	$0.213404\pi$
$308$	11.3157	+	11.3157i	0.0367391	+	0.0367391i
$309$			191.846i			0.620862i
$310$		0			0
$311$	607.147			1.95224			0.976121	−	0.217226i	$-0.0697009\pi$
$311$	607.147			1.95224			0.976121	+	0.217226i	$0.0697009\pi$
$312$	14.6703	−	14.6703i	0.0470200	−	0.0470200i
$313$	−67.5533	−	67.5533i	−0.215825	−	0.215825i	0.590911	−	0.806737i	$-0.298768\pi$
$313$	−67.5533	−	67.5533i	−0.215825	−	0.215825i	−0.806737	+	0.590911i	$0.798768\pi$
$314$			250.279i			0.797067i
$315$		0			0
$316$	0.201805			0.000638622
$317$	−86.6951	+	86.6951i	−0.273486	+	0.273486i	−0.830502	−	0.557016i	$-0.811946\pi$
$317$	−86.6951	+	86.6951i	−0.273486	+	0.273486i	0.557016	+	0.830502i	$0.311946\pi$
$318$	−29.2751	−	29.2751i	−0.0920602	−	0.0920602i
$319$			73.9714i			0.231885i
$320$		0			0
$321$	306.820			0.955826
$322$	8.77252	−	8.77252i	0.0272439	−	0.0272439i
$323$	385.440	+	385.440i	1.19331	+	1.19331i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	314.647			0.965174
$327$	−222.068	+	222.068i	−0.679107	+	0.679107i
$328$	23.9564	+	23.9564i	0.0730379	+	0.0730379i
$329$			173.678i			0.527896i
$330$		0			0
$331$	591.123			1.78587			0.892935	−	0.450185i	$-0.148642\pi$
$331$	591.123			1.78587			0.892935	+	0.450185i	$0.148642\pi$
$332$	31.9939	−	31.9939i	0.0963671	−	0.0963671i
$333$	−92.0680	−	92.0680i	−0.276481	−	0.276481i
$334$		−	48.7404i		−	0.145929i
$335$		0			0
$336$	18.3303			0.0545545
$337$	383.876	−	383.876i	1.13910	−	1.13910i	0.150485	−	0.988612i	$-0.451916\pi$
$337$	383.876	−	383.876i	1.13910	−	1.13910i	0.988612	−	0.150485i	$-0.0480836\pi$
$338$	151.065	+	151.065i	0.446939	+	0.446939i
$339$			41.0420i			0.121068i
$340$		0			0
$341$	−141.259			−0.414250
$342$	−88.5240	+	88.5240i	−0.258842	+	0.258842i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			1.61020i			0.00468081i
$345$		0			0
$346$	−88.5024			−0.255787
$347$	−424.033	+	424.033i	−1.22200	+	1.22200i	−0.255075	+	0.966921i	$0.582100\pi$
$347$	−424.033	+	424.033i	−1.22200	+	1.22200i	−0.966921	+	0.255075i	$0.917900\pi$
$348$	59.9134	+	59.9134i	0.172165	+	0.172165i
$349$			450.441i			1.29066i	0.763903	+	0.645331i	$0.223281\pi$
$349$			450.441i			1.29066i	−0.763903	+	0.645331i	$0.776719\pi$
$350$		0			0
$351$	22.0054			0.0626934
$352$	−12.0969	+	12.0969i	−0.0343663	+	0.0343663i
$353$	332.857	+	332.857i	0.942937	+	0.942937i	0.998458	−	0.0555202i	$-0.0176817\pi$
$353$	332.857	+	332.857i	0.942937	+	0.942937i	−0.0555202	+	0.998458i	$0.517682\pi$
$354$		−	79.0934i		−	0.223428i
$355$		0			0
$356$	182.930			0.513847
$357$	59.8585	−	59.8585i	0.167671	−	0.167671i
$358$	101.526	+	101.526i	0.283592	+	0.283592i
$359$			405.400i			1.12925i	0.825349	+	0.564623i	$0.190979\pi$
$359$			405.400i			1.12925i	−0.825349	+	0.564623i	$0.809021\pi$
$360$		0			0
$361$	−509.722			−1.41197
$362$	138.946	−	138.946i	0.383829	−	0.383829i
$363$	136.993	+	136.993i	0.377390	+	0.377390i
$364$		−	22.4092i		−	0.0615637i
$365$		0			0
$366$	−192.034			−0.524684
$367$	342.518	−	342.518i	0.933291	−	0.933291i	−0.0646188	−	0.997910i	$-0.520583\pi$
$367$	342.518	−	342.518i	0.933291	−	0.933291i	0.997910	+	0.0646188i	$0.0205831\pi$
$368$	9.37822	+	9.37822i	0.0254843	+	0.0254843i
$369$			35.9346i			0.0973838i
$370$		0			0
$371$	−44.7185			−0.120535
$372$	−114.413	+	114.413i	−0.307563	+	0.307563i
$373$	−415.273	−	415.273i	−1.11333	−	1.11333i	−0.992697	−	0.120635i	$-0.961507\pi$
$373$	−415.273	−	415.273i	−1.11333	−	1.11333i	−0.120635	−	0.992697i	$-0.538493\pi$
$374$			79.0064i			0.211247i
$375$		0			0
$376$	−185.669			−0.493801
$377$	73.2454	−	73.2454i	0.194285	−	0.194285i
$378$	13.7477	+	13.7477i	0.0363696	+	0.0363696i
$379$		−	118.806i		−	0.313473i	−0.987640	−	0.156736i	$-0.949903\pi$
$379$		−	118.806i		−	0.313473i	0.987640	−	0.156736i	$-0.0500973\pi$
$380$		0			0
$381$	8.39819			0.0220425
$382$	−299.678	+	299.678i	−0.784497	+	0.784497i
$383$	−161.764	−	161.764i	−0.422361	−	0.422361i	0.463655	−	0.886016i	$-0.346538\pi$
$383$	−161.764	−	161.764i	−0.422361	−	0.422361i	−0.886016	+	0.463655i	$0.846538\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	273.854			0.709467
$387$	−1.20765	+	1.20765i	−0.00312054	+	0.00312054i
$388$	28.3516	+	28.3516i	0.0730712	+	0.0730712i
$389$		−	314.948i		−	0.809636i	−0.914397	−	0.404818i	$-0.867335\pi$
$389$		−	314.948i		−	0.809636i	0.914397	−	0.404818i	$-0.132665\pi$
$390$		0			0
$391$	61.2501			0.156650
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	247.181	+	247.181i	0.628959	+	0.628959i
$394$			254.953i			0.647088i
$395$		0			0
$396$	−18.1454			−0.0458218
$397$	−76.9396	+	76.9396i	−0.193802	+	0.193802i	−0.797337	−	0.603534i	$-0.793759\pi$
$397$	−76.9396	+	76.9396i	−0.193802	+	0.193802i	0.603534	+	0.797337i	$0.293759\pi$
$398$	−173.636	−	173.636i	−0.436272	−	0.436272i
$399$			135.223i			0.338904i
$400$		0			0
$401$	−143.407			−0.357623			−0.178811	−	0.983883i	$-0.557225\pi$
$401$	−143.407			−0.357623			−0.178811	+	0.983883i	$0.557225\pi$
$402$	42.5253	−	42.5253i	0.105784	−	0.105784i
$403$	139.873	+	139.873i	0.347079	+	0.347079i
$404$			243.325i			0.602291i
$405$		0			0
$406$	91.5192			0.225417
$407$	92.8118	−	92.8118i	0.228039	−	0.228039i
$408$	63.9915	+	63.9915i	0.156842	+	0.156842i
$409$			444.181i			1.08602i	0.839727	+	0.543008i	$0.182715\pi$
$409$			444.181i			1.08602i	−0.839727	+	0.543008i	$0.817285\pi$
$410$		0			0
$411$	368.397			0.896343
$412$	−156.642	+	156.642i	−0.380199	+	0.380199i
$413$	−60.4086	−	60.4086i	−0.146268	−	0.146268i
$414$			14.0673i			0.0339791i
$415$		0			0
$416$	23.9564			0.0575876
$417$	147.021	−	147.021i	0.352568	−	0.352568i
$418$	−89.2392	−	89.2392i	−0.213491	−	0.213491i
$419$			550.340i			1.31346i	0.754126	+	0.656730i	$0.228061\pi$
$419$			550.340i			1.31346i	−0.754126	+	0.656730i	$0.771939\pi$
$420$		0			0
$421$	389.810			0.925914			0.462957	−	0.886381i	$-0.346788\pi$
$421$	389.810			0.925914			0.462957	+	0.886381i	$0.346788\pi$
$422$	146.655	−	146.655i	0.347524	−	0.347524i
$423$	−139.252	−	139.252i	−0.329201	−	0.329201i
$424$		−	47.8061i		−	0.112750i
$425$		0			0
$426$	−105.878			−0.248540
$427$	−146.669	+	146.669i	−0.343487	+	0.343487i
$428$	250.518	+	250.518i	0.585321	+	0.585321i
$429$			22.1832i			0.0517090i
$430$		0			0
$431$	752.470			1.74587			0.872936	−	0.487836i	$-0.162213\pi$
$431$	752.470			1.74587			0.872936	+	0.487836i	$0.162213\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−336.761	−	336.761i	−0.777740	−	0.777740i	0.201706	−	0.979446i	$-0.435351\pi$
$433$	−336.761	−	336.761i	−0.777740	−	0.777740i	−0.979446	+	0.201706i	$0.935351\pi$
$434$			174.769i			0.402694i
$435$		0			0
$436$	−362.636			−0.831733
$437$	−69.1831	+	69.1831i	−0.158314	+	0.158314i
$438$	−96.5280	−	96.5280i	−0.220383	−	0.220383i
$439$			380.190i			0.866037i	0.901385	+	0.433019i	$0.142552\pi$
$439$			380.190i			0.866037i	−0.901385	+	0.433019i	$0.857448\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	78.2309	−	78.2309i	0.176993	−	0.176993i
$443$	−548.394	−	548.394i	−1.23791	−	1.23791i	−0.960854	−	0.277055i	$-0.910642\pi$
$443$	−548.394	−	548.394i	−1.23791	−	1.23791i	−0.277055	−	0.960854i	$-0.589358\pi$
$444$		−	150.346i		−	0.338618i
$445$		0			0
$446$	172.836			0.387526
$447$	−45.4287	+	45.4287i	−0.101630	+	0.101630i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$		−	809.446i		−	1.80277i	−0.433013	−	0.901387i	$-0.642550\pi$
$449$		−	809.446i		−	1.80277i	0.433013	−	0.901387i	$-0.357450\pi$
$450$		0			0
$451$	−36.2249			−0.0803214
$452$	−33.5107	+	33.5107i	−0.0741387	+	0.0741387i
$453$	163.725	+	163.725i	0.361425	+	0.361425i
$454$			4.65182i			0.0102463i
$455$		0			0
$456$	−144.559			−0.317016
$457$	273.719	−	273.719i	0.598949	−	0.598949i	−0.341084	−	0.940033i	$-0.610794\pi$
$457$	273.719	−	273.719i	0.598949	−	0.598949i	0.940033	+	0.341084i	$0.110794\pi$
$458$	−345.111	−	345.111i	−0.753518	−	0.753518i
$459$			95.9872i			0.209122i
$460$		0			0
$461$	336.458			0.729844			0.364922	−	0.931038i	$-0.381096\pi$
$461$	336.458			0.729844			0.364922	+	0.931038i	$0.381096\pi$
$462$	−13.8588	+	13.8588i	−0.0299974	+	0.0299974i
$463$	447.621	+	447.621i	0.966785	+	0.966785i	0.999466	−	0.0326812i	$-0.0104046\pi$
$463$	447.621	+	447.621i	0.966785	+	0.966785i	−0.0326812	+	0.999466i	$0.510405\pi$
$464$			97.8381i			0.210858i
$465$		0			0
$466$	−194.975			−0.418402
$467$	185.531	−	185.531i	0.397282	−	0.397282i	−0.479991	−	0.877273i	$-0.659360\pi$
$467$	185.531	−	185.531i	0.397282	−	0.397282i	0.877273	+	0.479991i	$0.159360\pi$
$468$	17.9673	+	17.9673i	0.0383917	+	0.0383917i
$469$		−	64.9585i		−	0.138504i
$470$		0			0
$471$	−306.528			−0.650802
$472$	64.5795	−	64.5795i	0.136821	−	0.136821i
$473$	−1.21741	−	1.21741i	−0.00257380	−	0.00257380i
$474$			0.247159i			0.000521433i
$475$		0			0
$476$	97.7486			0.205354
$477$	35.8546	−	35.8546i	0.0751668	−	0.0751668i
$478$	−155.285	−	155.285i	−0.324865	−	0.324865i
$479$		−	444.150i		−	0.927244i	−0.886033	−	0.463622i	$-0.846550\pi$
$479$		−	444.150i		−	0.927244i	0.886033	−	0.463622i	$-0.153450\pi$
$480$		0			0
$481$	−183.802			−0.382124
$482$	46.6435	−	46.6435i	0.0967708	−	0.0967708i
$483$	10.7441	+	10.7441i	0.0222445	+	0.0222445i
$484$			223.708i			0.462207i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	−117.334	+	117.334i	−0.240932	+	0.240932i	−0.817236	−	0.576304i	$-0.804495\pi$
$487$	−117.334	+	117.334i	−0.240932	+	0.240932i	0.576304	+	0.817236i	$0.304495\pi$
$488$	−156.795	−	156.795i	−0.321302	−	0.321302i
$489$			385.362i			0.788061i
$490$		0			0
$491$	780.904			1.59044			0.795218	−	0.606324i	$-0.207357\pi$
$491$	780.904			1.59044			0.795218	+	0.606324i	$0.207357\pi$
$492$	−29.3405	+	29.3405i	−0.0596352	+	0.0596352i
$493$	319.495	+	319.495i	0.648064	+	0.648064i
$494$			176.727i			0.357746i
$495$		0			0
$496$	−186.836			−0.376686
$497$	−80.8658	+	80.8658i	−0.162708	+	0.162708i
$498$	39.1843	+	39.1843i	0.0786834	+	0.0786834i
$499$		−	520.134i		−	1.04235i	−0.853449	−	0.521176i	$-0.825493\pi$
$499$		−	520.134i		−	1.04235i	0.853449	−	0.521176i	$-0.174507\pi$
$500$		0			0
$501$	59.6945			0.119151
$502$	110.354	−	110.354i	0.219829	−	0.219829i
$503$	−392.689	−	392.689i	−0.780693	−	0.780693i	0.199255	−	0.979948i	$-0.436148\pi$
$503$	−392.689	−	392.689i	−0.780693	−	0.780693i	−0.979948	+	0.199255i	$0.936148\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−14.1810			−0.0280256
$507$	−185.016	+	185.016i	−0.364924	+	0.364924i
$508$	6.85709	+	6.85709i	0.0134982	+	0.0134982i
$509$		−	6.30380i		−	0.0123847i	−0.999981	−	0.00619234i	$-0.998029\pi$
$509$		−	6.30380i		−	0.0123847i	0.999981	−	0.00619234i	$-0.00197110\pi$
$510$		0			0
$511$	−147.449			−0.288550
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−108.419	−	108.419i	−0.211344	−	0.211344i
$514$		−	496.822i		−	0.966580i
$515$		0			0
$516$	−1.97208			−0.00382187
$517$	140.377	−	140.377i	0.271522	−	0.271522i
$518$	−114.829	−	114.829i	−0.221678	−	0.221678i
$519$		−	108.393i		−	0.208849i
$520$		0			0
$521$	−146.807			−0.281779			−0.140890	−	0.990025i	$-0.544996\pi$
$521$	−146.807			−0.281779			−0.140890	+	0.990025i	$0.544996\pi$
$522$	−73.3786	+	73.3786i	−0.140572	+	0.140572i
$523$	96.3768	+	96.3768i	0.184277	+	0.184277i	0.793217	−	0.608940i	$-0.208405\pi$
$523$	96.3768	+	96.3768i	0.184277	+	0.184277i	−0.608940	+	0.793217i	$0.708405\pi$
$524$			403.645i			0.770314i
$525$		0			0
$526$	−65.2152			−0.123983
$527$	−610.123	+	610.123i	−1.15773	+	1.15773i
$528$	−14.8157	−	14.8157i	−0.0280600	−	0.0280600i
$529$		−	518.006i		−	0.979218i
$530$		0			0
$531$	96.8692			0.182428
$532$	−110.409	+	110.409i	−0.207535	+	0.207535i
$533$	35.8694	+	35.8694i	0.0672972	+	0.0672972i
$534$			224.042i			0.419554i
$535$		0			0
$536$	69.4436			0.129559
$537$	−124.343	+	124.343i	−0.231552	+	0.231552i
$538$	109.536	+	109.536i	0.203598	+	0.203598i
$539$			21.1697i			0.0392758i
$540$		0			0
$541$	−199.291			−0.368376			−0.184188	−	0.982891i	$-0.558966\pi$
$541$	−199.291			−0.368376			−0.184188	+	0.982891i	$0.558966\pi$
$542$	105.472	−	105.472i	0.194597	−	0.194597i
$543$	170.174	+	170.174i	0.313395	+	0.313395i
$544$			104.498i			0.192091i
$545$		0			0
$546$	27.4455			0.0502665
$547$	615.316	−	615.316i	1.12489	−	1.12489i	0.133897	−	0.990995i	$-0.457251\pi$
$547$	615.316	−	615.316i	1.12489	−	1.12489i	0.990995	−	0.133897i	$-0.0427491\pi$
$548$	300.795	+	300.795i	0.548896	+	0.548896i
$549$		−	235.193i		−	0.428403i
$550$		0			0
$551$	−721.752			−1.30989
$552$	−11.4859	+	11.4859i	−0.0208078	+	0.0208078i
$553$	0.188771	+	0.188771i	0.000341358	+	0.000341358i
$554$			344.068i			0.621061i
$555$		0			0
$556$	240.084			0.431806
$557$	505.708	−	505.708i	0.907914	−	0.907914i	−0.0881896	−	0.996104i	$-0.528108\pi$
$557$	505.708	−	505.708i	0.907914	−	0.907914i	0.996104	+	0.0881896i	$0.0281081\pi$
$558$	−140.127	−	140.127i	−0.251124	−	0.251124i
$559$			2.41091i			0.00431290i
$560$		0			0
$561$	−96.7627			−0.172482
$562$	88.5422	−	88.5422i	0.157548	−	0.157548i
$563$	526.861	+	526.861i	0.935811	+	0.935811i	0.998061	−	0.0622500i	$-0.0198276\pi$
$563$	526.861	+	526.861i	0.935811	+	0.935811i	−0.0622500	+	0.998061i	$0.519828\pi$
$564$		−	227.397i		−	0.403187i
$565$		0			0
$566$	−375.121			−0.662758
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−86.4492	−	86.4492i	−0.152199	−	0.152199i
$569$		−	829.309i		−	1.45749i	−0.684787	−	0.728743i	$-0.740105\pi$
$569$		−	829.309i		−	1.45749i	0.684787	−	0.728743i	$-0.259895\pi$
$570$		0			0
$571$	−642.527			−1.12527			−0.562633	−	0.826707i	$-0.690212\pi$
$571$	−642.527			−1.12527			−0.562633	+	0.826707i	$0.690212\pi$
$572$	−18.1125	+	18.1125i	−0.0316652	+	0.0316652i
$573$	−367.029	−	367.029i	−0.640539	−	0.640539i
$574$			44.8184i			0.0780808i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	479.432	−	479.432i	0.830904	−	0.830904i	−0.156736	−	0.987641i	$-0.550097\pi$
$577$	479.432	−	479.432i	0.830904	−	0.830904i	0.987641	+	0.156736i	$0.0500972\pi$
$578$	52.2423	+	52.2423i	0.0903846	+	0.0903846i
$579$			335.402i			0.579277i
$580$		0			0
$581$	59.8551			0.103021
$582$	−34.7235	+	34.7235i	−0.0596624	+	0.0596624i
$583$	36.1442	+	36.1442i	0.0619970	+	0.0619970i
$584$		−	157.629i		−	0.269914i
$585$		0			0
$586$	474.503			0.809733
$587$	66.4097	−	66.4097i	0.113134	−	0.113134i	−0.648273	−	0.761408i	$-0.724509\pi$
$587$	66.4097	−	66.4097i	0.113134	−	0.113134i	0.761408	+	0.648273i	$0.224509\pi$
$588$	17.1464	+	17.1464i	0.0291606	+	0.0291606i
$589$		−	1378.29i		−	2.34005i
$590$		0			0
$591$	−312.252			−0.528345
$592$	122.757	−	122.757i	0.207360	−	0.207360i
$593$	−744.586	−	744.586i	−1.25563	−	1.25563i	−0.953160	−	0.302466i	$-0.902190\pi$
$593$	−744.586	−	744.586i	−1.25563	−	1.25563i	−0.302466	−	0.953160i	$-0.597810\pi$
$594$		−	22.2235i		−	0.0374133i
$595$		0			0
$596$	−74.1847			−0.124471
$597$	212.660	−	212.660i	0.356214	−	0.356214i
$598$	14.0418	+	14.0418i	0.0234812	+	0.0234812i
$599$		−	840.233i		−	1.40273i	−0.712804	−	0.701363i	$-0.752575\pi$
$599$		−	840.233i		−	1.40273i	0.712804	−	0.701363i	$-0.247425\pi$
$600$		0			0
$601$	−739.213			−1.22997			−0.614986	−	0.788538i	$-0.710838\pi$
$601$	−739.213			−1.22997			−0.614986	+	0.788538i	$0.710838\pi$
$602$	−1.50620	+	1.50620i	−0.00250200	+	0.00250200i
$603$	52.0827	+	52.0827i	0.0863726	+	0.0863726i
$604$			267.362i			0.442653i
$605$		0			0
$606$	−298.012			−0.491768
$607$	−776.567	+	776.567i	−1.27935	+	1.27935i	−0.338323	+	0.941030i	$0.609860\pi$
$607$	−776.567	+	776.567i	−1.27935	+	1.27935i	−0.941030	+	0.338323i	$0.890140\pi$
$608$	−118.032	−	118.032i	−0.194132	−	0.194132i
$609$			112.088i			0.184052i
$610$		0			0
$611$	−277.998			−0.454989
$612$	−78.3732	+	78.3732i	−0.128061	+	0.128061i
$613$	340.874	+	340.874i	0.556075	+	0.556075i	0.928188	−	0.372113i	$-0.121367\pi$
$613$	340.874	+	340.874i	0.556075	+	0.556075i	−0.372113	+	0.928188i	$0.621367\pi$
$614$			99.6117i			0.162234i
$615$		0			0
$616$	−22.6313			−0.0367391
$617$	539.699	−	539.699i	0.874715	−	0.874715i	−0.118266	−	0.992982i	$-0.537734\pi$
$617$	539.699	−	539.699i	0.874715	−	0.874715i	0.992982	+	0.118266i	$0.0377337\pi$
$618$	−191.846	−	191.846i	−0.310431	−	0.310431i
$619$			354.188i			0.572193i	0.958201	+	0.286097i	$0.0923579\pi$
$619$			354.188i			0.572193i	−0.958201	+	0.286097i	$0.907642\pi$
$620$		0			0
$621$	−17.2289			−0.0277438
$622$	−607.147	+	607.147i	−0.976121	+	0.976121i
$623$	171.115	+	171.115i	0.274663	+	0.274663i
$624$			29.3405i			0.0470200i
$625$		0			0
$626$	135.107			0.215825
$627$	109.295	−	109.295i	0.174315	−	0.174315i
$628$	−250.279	−	250.279i	−0.398533	−	0.398533i
$629$		−	801.741i		−	1.27463i
$630$		0			0
$631$	136.968			0.217065			0.108533	−	0.994093i	$-0.465385\pi$
$631$	136.968			0.217065			0.108533	+	0.994093i	$0.465385\pi$
$632$	−0.201805	+	0.201805i	−0.000319311	+	0.000319311i
$633$	179.615	+	179.615i	0.283752	+	0.283752i
$634$		−	173.390i		−	0.273486i
$635$		0			0
$636$	58.5503			0.0920602
$637$	20.9619	−	20.9619i	0.0329072	−	0.0329072i
$638$	−73.9714	−	73.9714i	−0.115943	−	0.115943i
$639$		−	129.674i		−	0.202932i
$640$		0			0
$641$	−956.048			−1.49149			−0.745747	−	0.666229i	$-0.767907\pi$
$641$	−956.048			−1.49149			−0.745747	+	0.666229i	$0.767907\pi$
$642$	−306.820	+	306.820i	−0.477913	+	0.477913i
$643$	294.266	+	294.266i	0.457646	+	0.457646i	0.897882	−	0.440236i	$-0.145105\pi$
$643$	294.266	+	294.266i	0.457646	+	0.457646i	−0.440236	+	0.897882i	$0.645105\pi$
$644$			17.5450i			0.0272439i
$645$		0			0
$646$	−770.879			−1.19331
$647$	−786.052	+	786.052i	−1.21492	+	1.21492i	−0.245529	+	0.969389i	$0.578962\pi$
$647$	−786.052	+	786.052i	−1.21492	+	1.21492i	−0.969389	+	0.245529i	$0.921038\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			97.6518i			0.150465i
$650$		0			0
$651$	−214.048			−0.328799
$652$	−314.647	+	314.647i	−0.482587	+	0.482587i
$653$	−97.8898	−	97.8898i	−0.149908	−	0.149908i	0.628169	−	0.778077i	$-0.283805\pi$
$653$	−97.8898	−	97.8898i	−0.149908	−	0.149908i	−0.778077	+	0.628169i	$0.783805\pi$
$654$		−	444.136i		−	0.679107i
$655$		0			0
$656$	−47.9128			−0.0730379
$657$	118.222	−	118.222i	0.179942	−	0.179942i
$658$	−173.678	−	173.678i	−0.263948	−	0.263948i
$659$		−	1155.72i		−	1.75375i	−0.480718	−	0.876875i	$-0.659624\pi$
$659$		−	1155.72i		−	1.75375i	0.480718	−	0.876875i	$-0.340376\pi$
$660$		0			0
$661$	675.364			1.02173			0.510865	−	0.859661i	$-0.329325\pi$
$661$	675.364			1.02173			0.510865	+	0.859661i	$0.329325\pi$
$662$	−591.123	+	591.123i	−0.892935	+	0.892935i
$663$	95.8129	+	95.8129i	0.144514	+	0.144514i
$664$			63.9877i			0.0963671i
$665$		0			0
$666$	184.136			0.276481
$667$	−57.3467	+	57.3467i	−0.0859771	+	0.0859771i
$668$	48.7404	+	48.7404i	0.0729646	+	0.0729646i
$669$			211.681i			0.316413i
$670$		0			0
$671$	237.093			0.353343
$672$	−18.3303	+	18.3303i	−0.0272772	+	0.0272772i
$673$	258.340	+	258.340i	0.383863	+	0.383863i	0.872492	−	0.488629i	$-0.162503\pi$
$673$	258.340	+	258.340i	0.383863	+	0.383863i	−0.488629	+	0.872492i	$0.662503\pi$
$674$			767.752i			1.13910i
$675$		0			0
$676$	−302.131			−0.446939
$677$	−18.7815	+	18.7815i	−0.0277423	+	0.0277423i	−0.720842	−	0.693100i	$-0.756245\pi$
$677$	−18.7815	+	18.7815i	−0.0277423	+	0.0277423i	0.693100	+	0.720842i	$0.256245\pi$
$678$	−41.0420	−	41.0420i	−0.0605340	−	0.0605340i
$679$			53.0410i			0.0781164i
$680$		0			0
$681$	−5.69729			−0.00836607
$682$	141.259	−	141.259i	0.207125	−	0.207125i
$683$	475.671	+	475.671i	0.696443	+	0.696443i	0.963642	−	0.267198i	$-0.0860978\pi$
$683$	475.671	+	475.671i	0.696443	+	0.696443i	−0.267198	+	0.963642i	$0.586098\pi$
$684$		−	177.048i		−	0.258842i
$685$		0			0
$686$	26.1916			0.0381802
$687$	422.673	−	422.673i	0.615245	−	0.615245i
$688$	−1.61020	−	1.61020i	−0.00234041	−	0.00234041i
$689$		−	71.5790i		−	0.103888i
$690$		0			0
$691$	1301.16			1.88301			0.941507	−	0.336992i	$-0.109410\pi$
$691$	1301.16			1.88301			0.941507	+	0.336992i	$0.109410\pi$
$692$	88.5024	−	88.5024i	0.127894	−	0.127894i
$693$	−16.9735	−	16.9735i	−0.0244928	−	0.0244928i
$694$		−	848.066i		−	1.22200i
$695$		0			0
$696$	−119.827			−0.172165
$697$	−156.462	+	156.462i	−0.224479	+	0.224479i
$698$	−450.441	−	450.441i	−0.645331	−	0.645331i
$699$		−	238.795i		−	0.341623i
$700$		0			0
$701$	−1197.02			−1.70759			−0.853795	−	0.520609i	$-0.825705\pi$
$701$	−1197.02			−1.70759			−0.853795	+	0.520609i	$0.825705\pi$
$702$	−22.0054	+	22.0054i	−0.0313467	+	0.0313467i
$703$	905.581	+	905.581i	1.28817	+	1.28817i
$704$		−	24.1939i		−	0.0343663i
$705$		0			0
$706$	−665.714			−0.942937
$707$	−227.610	+	227.610i	−0.321938	+	0.321938i
$708$	79.0934	+	79.0934i	0.111714	+	0.111714i
$709$			1040.88i			1.46810i	0.679097	+	0.734049i	$0.262372\pi$
$709$			1040.88i			1.46810i	−0.679097	+	0.734049i	$0.737628\pi$
$710$		0			0
$711$	−0.302707			−0.000425748
$712$	−182.930	+	182.930i	−0.256924	+	0.256924i
$713$	−109.512	−	109.512i	−0.153593	−	0.153593i
$714$			119.717i			0.167671i
$715$		0			0
$716$	−203.052			−0.283592
$717$	190.185	−	190.185i	0.265251	−	0.265251i
$718$	−405.400	−	405.400i	−0.564623	−	0.564623i
$719$		−	670.331i		−	0.932310i	−0.884703	−	0.466155i	$-0.845639\pi$
$719$		−	670.331i		−	0.932310i	0.884703	−	0.466155i	$-0.154361\pi$
$720$		0			0
$721$	−293.050			−0.406450
$722$	509.722	−	509.722i	0.705987	−	0.705987i
$723$	57.1264	+	57.1264i	0.0790130	+	0.0790130i
$724$			277.893i			0.383829i
$725$		0			0
$726$	−273.985			−0.377390
$727$	−501.531	+	501.531i	−0.689864	+	0.689864i	−0.962202	−	0.272338i	$-0.912203\pi$
$727$	−501.531	+	501.531i	−0.689864	+	0.689864i	0.272338	+	0.962202i	$0.412203\pi$
$728$	22.4092	+	22.4092i	0.0307818	+	0.0307818i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−10.5164			−0.0143863
$732$	192.034	−	192.034i	0.262342	−	0.262342i
$733$	−370.001	−	370.001i	−0.504776	−	0.504776i	0.408142	−	0.912918i	$-0.366177\pi$
$733$	−370.001	−	370.001i	−0.504776	−	0.504776i	−0.912918	+	0.408142i	$0.866177\pi$
$734$			685.036i			0.933291i
$735$		0			0
$736$	−18.7564			−0.0254843
$737$	−52.5034	+	52.5034i	−0.0712394	+	0.0712394i
$738$	−35.9346	−	35.9346i	−0.0486919	−	0.0486919i
$739$		−	462.721i		−	0.626145i	−0.949729	−	0.313073i	$-0.898642\pi$
$739$		−	462.721i		−	0.626145i	0.949729	−	0.313073i	$-0.101358\pi$
$740$		0			0
$741$	−216.445			−0.292098
$742$	44.7185	−	44.7185i	0.0602675	−	0.0602675i
$743$	−223.221	−	223.221i	−0.300432	−	0.300432i	0.540751	−	0.841183i	$-0.318140\pi$
$743$	−223.221	−	223.221i	−0.300432	−	0.300432i	−0.841183	+	0.540751i	$0.818140\pi$
$744$		−	228.827i		−	0.307563i
$745$		0			0
$746$	830.546			1.11333
$747$	−47.9908	+	47.9908i	−0.0642447	+	0.0642447i
$748$	−79.0064	−	79.0064i	−0.105623	−	0.105623i
$749$			468.675i			0.625735i
$750$		0			0
$751$	378.724			0.504292			0.252146	−	0.967689i	$-0.418864\pi$
$751$	378.724			0.504292			0.252146	+	0.967689i	$0.418864\pi$
$752$	185.669	−	185.669i	0.246901	−	0.246901i
$753$	135.155	+	135.155i	0.179489	+	0.179489i
$754$			146.491i			0.194285i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	−698.321	+	698.321i	−0.922485	+	0.922485i	−0.997205	−	0.0747195i	$-0.976194\pi$
$757$	−698.321	+	698.321i	−0.922485	+	0.922485i	0.0747195	+	0.997205i	$0.476194\pi$
$758$	118.806	+	118.806i	0.156736	+	0.156736i
$759$		−	17.3681i		−	0.0228828i
$760$		0			0
$761$	−1211.43			−1.59189			−0.795947	−	0.605366i	$-0.793027\pi$
$761$	−1211.43			−1.59189			−0.795947	+	0.605366i	$0.793027\pi$
$762$	−8.39819	+	8.39819i	−0.0110212	+	0.0110212i
$763$	−339.215	−	339.215i	−0.444580	−	0.444580i
$764$		−	599.356i		−	0.784497i
$765$		0			0
$766$	323.529			0.422361
$767$	96.6934	−	96.6934i	0.126067	−	0.126067i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			103.430i			0.134499i	0.997736	+	0.0672495i	$0.0214224\pi$
$769$			103.430i			0.134499i	−0.997736	+	0.0672495i	$0.978578\pi$
$770$		0			0
$771$	608.480			0.789209
$772$	−273.854	+	273.854i	−0.354734	+	0.354734i
$773$	50.4008	+	50.4008i	0.0652015	+	0.0652015i	0.738956	−	0.673754i	$-0.235319\pi$
$773$	50.4008	+	50.4008i	0.0652015	+	0.0652015i	−0.673754	+	0.738956i	$0.735319\pi$
$774$		−	2.41530i		−	0.00312054i
$775$		0			0
$776$	−56.7032			−0.0730712
$777$	140.636	−	140.636i	0.180999	−	0.180999i
$778$	314.948	+	314.948i	0.404818	+	0.404818i
$779$		−	353.453i		−	0.453727i
$780$		0			0
$781$	130.721			0.167377
$782$	−61.2501	+	61.2501i	−0.0783249	+	0.0783249i
$783$	−89.8701	−	89.8701i	−0.114777	−	0.114777i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	−494.362			−0.628959
$787$	−237.837	+	237.837i	−0.302207	+	0.302207i	−0.841877	−	0.539670i	$-0.818549\pi$
$787$	−237.837	+	237.837i	−0.302207	+	0.302207i	0.539670	+	0.841877i	$0.318549\pi$
$788$	−254.953	−	254.953i	−0.323544	−	0.323544i
$789$		−	79.8720i		−	0.101232i
$790$		0			0
$791$	−62.6927			−0.0792576
$792$	18.1454	−	18.1454i	0.0229109	−	0.0229109i
$793$	−234.766	−	234.766i	−0.296048	−	0.296048i
$794$		−	153.879i		−	0.193802i
$795$		0			0
$796$	347.272			0.436272
$797$	7.28126	−	7.28126i	0.00913584	−	0.00913584i	−0.702524	−	0.711660i	$-0.747944\pi$
$797$	7.28126	−	7.28126i	0.00913584	−	0.00913584i	0.711660	+	0.702524i	$0.247944\pi$
$798$	−135.223	−	135.223i	−0.169452	−	0.169452i
$799$		−	1212.62i		−	1.51768i
$800$		0			0
$801$	−274.394			−0.342565
$802$	143.407	−	143.407i	0.178811	−	0.178811i
$803$	119.177	+	119.177i	0.148415	+	0.148415i
$804$			85.0507i			0.105784i
$805$		0			0
$806$	−279.746			−0.347079
$807$	−134.154	+	134.154i	−0.166237	+	0.166237i
$808$	−243.325	−	243.325i	−0.301145	−	0.301145i
$809$			1185.33i			1.46517i	0.680673	+	0.732587i	$0.261687\pi$
$809$			1185.33i			1.46517i	−0.680673	+	0.732587i	$0.738313\pi$
$810$		0			0
$811$	−116.511			−0.143663			−0.0718316	−	0.997417i	$-0.522884\pi$
$811$	−116.511			−0.143663			−0.0718316	+	0.997417i	$0.522884\pi$
$812$	−91.5192	+	91.5192i	−0.112708	+	0.112708i
$813$	129.176	+	129.176i	0.158888	+	0.158888i
$814$			185.624i			0.228039i
$815$		0			0
$816$	−127.983			−0.156842
$817$	11.8784	−	11.8784i	0.0145391	−	0.0145391i
$818$	−444.181	−	444.181i	−0.543008	−	0.543008i
$819$			33.6138i			0.0410425i
$820$		0			0
$821$	676.720			0.824263			0.412131	−	0.911124i	$-0.364784\pi$
$821$	676.720			0.824263			0.412131	+	0.911124i	$0.364784\pi$
$822$	−368.397	+	368.397i	−0.448172	+	0.448172i
$823$	−102.651	−	102.651i	−0.124728	−	0.124728i	0.641988	−	0.766715i	$-0.278110\pi$
$823$	−102.651	−	102.651i	−0.124728	−	0.124728i	−0.766715	+	0.641988i	$0.778110\pi$
$824$		−	313.284i		−	0.380199i
$825$		0			0
$826$	120.817			0.146268
$827$	503.694	−	503.694i	0.609061	−	0.609061i	−0.333639	−	0.942701i	$-0.608277\pi$
$827$	503.694	−	503.694i	0.609061	−	0.609061i	0.942701	+	0.333639i	$0.108277\pi$
$828$	−14.0673	−	14.0673i	−0.0169895	−	0.0169895i
$829$		−	854.725i		−	1.03103i	−0.856880	−	0.515515i	$-0.827600\pi$
$829$		−	854.725i		−	1.03103i	0.856880	−	0.515515i	$-0.172400\pi$
$830$		0			0
$831$	−421.395			−0.507094
$832$	−23.9564	+	23.9564i	−0.0287938	+	0.0287938i
$833$	91.4354	+	91.4354i	0.109766	+	0.109766i
$834$			294.042i			0.352568i
$835$		0			0
$836$	178.478			0.213491
$837$	171.620	−	171.620i	0.205042	−	0.205042i
$838$	−550.340	−	550.340i	−0.656730	−	0.656730i
$839$		−	1149.25i		−	1.36978i	−0.728645	−	0.684892i	$-0.759850\pi$
$839$		−	1149.25i		−	1.36978i	0.728645	−	0.684892i	$-0.240150\pi$
$840$		0			0
$841$	242.731			0.288622
$842$	−389.810	+	389.810i	−0.462957	+	0.462957i
$843$	108.442	+	108.442i	0.128638	+	0.128638i
$844$			293.310i			0.347524i
$845$		0			0
$846$	278.504			0.329201
$847$	−209.260	+	209.260i	−0.247060	+	0.247060i
$848$	47.8061	+	47.8061i	0.0563751	+	0.0563751i
$849$		−	459.428i		−	0.541140i
$850$		0			0
$851$	143.906			0.169102
$852$	105.878	−	105.878i	0.124270	−	0.124270i
$853$	−234.885	−	234.885i	−0.275363	−	0.275363i	0.555892	−	0.831255i	$-0.312377\pi$
$853$	−234.885	−	234.885i	−0.275363	−	0.275363i	−0.831255	+	0.555892i	$0.812377\pi$
$854$		−	293.338i		−	0.343487i
$855$		0			0
$856$	−501.035			−0.585321
$857$	−318.679	+	318.679i	−0.371855	+	0.371855i	−0.868152	−	0.496298i	$-0.834692\pi$
$857$	−318.679	+	318.679i	−0.371855	+	0.371855i	0.496298	+	0.868152i	$0.334692\pi$
$858$	−22.1832	−	22.1832i	−0.0258545	−	0.0258545i
$859$			202.016i			0.235176i	0.993062	+	0.117588i	$0.0375162\pi$
$859$			202.016i			0.235176i	−0.993062	+	0.117588i	$0.962484\pi$
$860$		0			0
$861$	−54.8911			−0.0637527
$862$	−752.470	+	752.470i	−0.872936	+	0.872936i
$863$	−814.775	−	814.775i	−0.944120	−	0.944120i	0.0543994	−	0.998519i	$-0.482676\pi$
$863$	−814.775	−	814.775i	−0.944120	−	0.944120i	−0.998519	+	0.0543994i	$0.982676\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	673.522			0.777740
$867$	−63.9835	+	63.9835i	−0.0737987	+	0.0737987i
$868$	−174.769	−	174.769i	−0.201347	−	0.201347i
$869$		−	0.305152i		−	0.000351153i
$870$		0			0
$871$	103.976			0.119376
$872$	362.636	−	362.636i	0.415867	−	0.415867i
$873$	−42.5274	−	42.5274i	−0.0487141	−	0.0487141i
$874$		−	138.366i		−	0.158314i
$875$		0			0
$876$	193.056			0.220383
$877$	784.014	−	784.014i	0.893972	−	0.893972i	−0.100922	−	0.994894i	$-0.532179\pi$
$877$	784.014	−	784.014i	0.893972	−	0.893972i	0.994894	+	0.100922i	$0.0321792\pi$
$878$	−380.190	−	380.190i	−0.433019	−	0.433019i
$879$			581.146i			0.661144i
$880$		0			0
$881$	−630.608			−0.715786			−0.357893	−	0.933763i	$-0.616505\pi$
$881$	−630.608			−0.715786			−0.357893	+	0.933763i	$0.616505\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	612.193	+	612.193i	0.693311	+	0.693311i	0.962959	−	0.269648i	$-0.0869074\pi$
$883$	612.193	+	612.193i	0.693311	+	0.693311i	−0.269648	+	0.962959i	$0.586907\pi$
$884$			156.462i			0.176993i
$885$		0			0
$886$	1096.79			1.23791
$887$	−424.255	+	424.255i	−0.478303	+	0.478303i	−0.904589	−	0.426286i	$-0.859822\pi$
$887$	−424.255	+	424.255i	−0.478303	+	0.478303i	0.426286	+	0.904589i	$0.359822\pi$
$888$	150.346	+	150.346i	0.169309	+	0.169309i
$889$			12.8284i			0.0144302i
$890$		0			0
$891$	27.2181			0.0305478
$892$	−172.836	+	172.836i	−0.193763	+	0.193763i
$893$	1369.68	+	1369.68i	1.53380	+	1.53380i
$894$		−	90.8573i		−	0.101630i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	−17.1976	+	17.1976i	−0.0191724	+	0.0191724i
$898$	809.446	+	809.446i	0.901387	+	0.901387i
$899$		−	1142.48i		−	1.27084i
$900$		0			0
$901$	312.227			0.346533
$902$	36.2249	−	36.2249i	0.0401607	−	0.0401607i
$903$	−1.84471	−	1.84471i	−0.00204287	−	0.00204287i
$904$		−	67.0213i		−	0.0741387i
$905$		0			0
$906$	−327.451			−0.361425
$907$	−855.352	+	855.352i	−0.943056	+	0.943056i	−0.998464	−	0.0554075i	$-0.982354\pi$
$907$	−855.352	+	855.352i	−0.943056	+	0.943056i	0.0554075	+	0.998464i	$0.482354\pi$
$908$	−4.65182	−	4.65182i	−0.00512315	−	0.00512315i
$909$		−	364.988i		−	0.401527i
$910$		0			0
$911$	600.082			0.658707			0.329353	−	0.944207i	$-0.393169\pi$
$911$	600.082			0.658707			0.329353	+	0.944207i	$0.393169\pi$
$912$	144.559	−	144.559i	0.158508	−	0.158508i
$913$	−48.3785	−	48.3785i	−0.0529885	−	0.0529885i
$914$			547.439i			0.598949i
$915$		0			0
$916$	690.222			0.753518
$917$	−377.575	+	377.575i	−0.411750	+	0.411750i
$918$	−95.9872	−	95.9872i	−0.104561	−	0.104561i
$919$			1703.19i			1.85331i	0.375913	+	0.926655i	$0.377329\pi$
$919$			1703.19i			1.85331i	−0.375913	+	0.926655i	$0.622671\pi$
$920$		0			0
$921$	−121.999			−0.132464
$922$	−336.458	+	336.458i	−0.364922	+	0.364922i
$923$	−129.438	−	129.438i	−0.140236	−	0.140236i
$924$		−	27.7176i		−	0.0299974i
$925$		0			0
$926$	−895.243			−0.966785
$927$	234.963	−	234.963i	0.253466	−	0.253466i
$928$	−97.8381	−	97.8381i	−0.105429	−	0.105429i
$929$			1567.07i			1.68683i	0.537261	+	0.843416i	$0.319459\pi$
$929$			1567.07i			1.68683i	−0.537261	+	0.843416i	$0.680541\pi$
$930$		0			0
$931$	−206.556			−0.221865
$932$	194.975	−	194.975i	0.209201	−	0.209201i
$933$	−743.601	−	743.601i	−0.797000	−	0.797000i
$934$			371.062i			0.397282i
$935$		0			0
$936$	−35.9346			−0.0383917
$937$	−684.510	+	684.510i	−0.730533	+	0.730533i	−0.970725	−	0.240192i	$-0.922790\pi$
$937$	−684.510	+	684.510i	−0.730533	+	0.730533i	0.240192	+	0.970725i	$0.422790\pi$
$938$	64.9585	+	64.9585i	0.0692522	+	0.0692522i
$939$			165.471i			0.176221i
$940$		0			0
$941$	−1676.18			−1.78127			−0.890637	−	0.454715i	$-0.849741\pi$
$941$	−1676.18			−1.78127			−0.890637	+	0.454715i	$0.849741\pi$
$942$	306.528	−	306.528i	0.325401	−	0.325401i
$943$	−28.0836	−	28.0836i	−0.0297811	−	0.0297811i
$944$			129.159i			0.136821i
$945$		0			0
$946$	2.43481			0.00257380
$947$	−659.283	+	659.283i	−0.696180	+	0.696180i	−0.963584	−	0.267404i	$-0.913834\pi$
$947$	−659.283	+	659.283i	−0.696180	+	0.696180i	0.267404	+	0.963584i	$0.413834\pi$
$948$	−0.247159	−	0.247159i	−0.000260716	−	0.000260716i
$949$		−	236.015i		−	0.248699i
$950$		0			0
$951$	212.359			0.223300
$952$	−97.7486	+	97.7486i	−0.102677	+	0.102677i
$953$	876.383	+	876.383i	0.919604	+	0.919604i	0.997000	−	0.0773963i	$-0.0246607\pi$
$953$	876.383	+	876.383i	0.919604	+	0.919604i	−0.0773963	+	0.997000i	$0.524661\pi$
$954$			71.7092i			0.0751668i
$955$		0			0
$956$	310.571			0.324865
$957$	90.5961	−	90.5961i	0.0946668	−	0.0946668i
$958$	444.150	+	444.150i	0.463622	+	0.463622i
$959$			562.736i			0.586795i
$960$		0			0
$961$	1220.74			1.27028
$962$	183.802	−	183.802i	0.191062	−	0.191062i
$963$	−375.776	−	375.776i	−0.390214	−	0.390214i
$964$			93.2871i			0.0967708i
$965$		0			0
$966$	−21.4882			−0.0222445
$967$	−1085.32	+	1085.32i	−1.12236	+	1.12236i	−0.130970	+	0.991386i	$0.541809\pi$
$967$	−1085.32	+	1085.32i	−1.12236	+	1.12236i	−0.991386	+	0.130970i	$0.958191\pi$
$968$	−223.708	−	223.708i	−0.231103	−	0.231103i
$969$		−	944.130i		−	0.974335i
$970$		0			0
$971$	20.6475			0.0212642			0.0106321	−	0.999943i	$-0.496616\pi$
$971$	20.6475			0.0212642			0.0106321	+	0.999943i	$0.496616\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	224.578	+	224.578i	0.230810	+	0.230810i
$974$		−	234.668i		−	0.240932i
$975$		0			0
$976$	313.591			0.321302
$977$	44.9724	−	44.9724i	0.0460311	−	0.0460311i	−0.683717	−	0.729748i	$-0.739638\pi$
$977$	44.9724	−	44.9724i	0.0460311	−	0.0460311i	0.729748	+	0.683717i	$0.239638\pi$
$978$	−385.362	−	385.362i	−0.394031	−	0.394031i
$979$		−	276.611i		−	0.282544i
$980$		0			0
$981$	543.954			0.554489
$982$	−780.904	+	780.904i	−0.795218	+	0.795218i
$983$	465.720	+	465.720i	0.473774	+	0.473774i	0.903134	−	0.429360i	$-0.141261\pi$
$983$	465.720	+	465.720i	0.473774	+	0.473774i	−0.429360	+	0.903134i	$0.641261\pi$
$984$		−	58.6810i		−	0.0596352i
$985$		0			0
$986$	−638.991			−0.648064
$987$	212.711	−	212.711i	0.215512	−	0.215512i
$988$	−176.727	−	176.727i	−0.178873	−	0.178873i
$989$		−	1.88760i		−	0.00190859i
$990$		0			0
$991$	312.457			0.315295			0.157647	−	0.987495i	$-0.449609\pi$
$991$	312.457			0.315295			0.157647	+	0.987495i	$0.449609\pi$
$992$	186.836	−	186.836i	0.188343	−	0.188343i
$993$	−723.975	−	723.975i	−0.729078	−	0.729078i
$994$		−	161.732i		−	0.162708i
$995$		0			0
$996$	−78.3687			−0.0786834
$997$	814.207	−	814.207i	0.816657	−	0.816657i	−0.168965	−	0.985622i	$-0.554042\pi$
$997$	814.207	−	814.207i	0.816657	−	0.816657i	0.985622	+	0.168965i	$0.0540424\pi$
$998$	520.134	+	520.134i	0.521176	+	0.521176i
$999$			225.520i			0.225745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.a.43.2	✓	8
5.2	odd	4	inner	1050.3.l.a.757.2	yes	8
5.3	odd	4		1050.3.l.e.757.3	yes	8
5.4	even	2		1050.3.l.e.43.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.l.a.43.2	✓	8	1.1	even	1	trivial
1050.3.l.a.757.2	yes	8	5.2	odd	4	inner
1050.3.l.e.43.3	yes	8	5.4	even	2
1050.3.l.e.757.3	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -3.02424 q^{11} +(-2.44949 + 2.44949i) q^{12} +(2.99455 + 2.99455i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-13.0622 + 13.0622i) q^{17} +(-3.00000 - 3.00000i) q^{18} -29.5080i q^{19} -4.58258 q^{21} +(3.02424 - 3.02424i) q^{22} +(-2.34455 - 2.34455i) q^{23} -4.89898i q^{24} -5.98911 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -24.4595i q^{29} +46.7091 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.70392 + 3.70392i) q^{33} -26.1244i q^{34} +6.00000 q^{36} +(-30.6893 + 30.6893i) q^{37} +(29.5080 + 29.5080i) q^{38} -7.33513i q^{39} +11.9782 q^{41} +(4.58258 - 4.58258i) q^{42} +(0.402550 + 0.402550i) q^{43} +6.04847i q^{44} +4.68911 q^{46} +(-46.4173 + 46.4173i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +31.9957 q^{51} +(5.98911 - 5.98911i) q^{52} +(-11.9515 - 11.9515i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-36.1398 + 36.1398i) q^{57} +(24.4595 + 24.4595i) q^{58} -32.2897i q^{59} -78.3977 q^{61} +(-46.7091 + 46.7091i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -7.40784 q^{66} +(17.3609 - 17.3609i) q^{67} +(26.1244 + 26.1244i) q^{68} +5.74296i q^{69} -43.2246 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-39.4074 - 39.4074i) q^{73} -61.3787i q^{74} -59.0160 q^{76} +(-5.65783 + 5.65783i) q^{77} +(7.33513 + 7.33513i) q^{78} +0.100902i q^{79} -9.00000 q^{81} +(-11.9782 + 11.9782i) q^{82} +(15.9969 + 15.9969i) q^{83} +9.16515i q^{84} -0.805100 q^{86} +(-29.9567 + 29.9567i) q^{87} +(-6.04847 - 6.04847i) q^{88} +91.4648i q^{89} +11.2046 q^{91} +(-4.68911 + 4.68911i) q^{92} +(-57.2067 - 57.2067i) q^{93} -92.8346i q^{94} -9.79796 q^{96} +(-14.1758 + 14.1758i) q^{97} +(7.00000 + 7.00000i) q^{98} -9.07271i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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