LMFDB - Embedded newform 1050.3.l.h.757.7

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			757.7
Root			$-3.99135 + 3.99135i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.h.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -3.32459 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.80162 - 7.80162i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(13.6628 + 13.6628i) q^{17} +(3.00000 - 3.00000i) q^{18} -37.1623i q^{19} +4.58258 q^{21} +(-3.32459 - 3.32459i) q^{22} +(31.5017 - 31.5017i) q^{23} +4.89898i q^{24} +15.6032 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +55.3464i q^{29} -4.54280 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.07177 + 4.07177i) q^{33} +27.3257i q^{34} +6.00000 q^{36} +(46.8661 + 46.8661i) q^{37} +(37.1623 - 37.1623i) q^{38} -19.1100i q^{39} +9.94537 q^{41} +(4.58258 + 4.58258i) q^{42} +(-23.0431 + 23.0431i) q^{43} -6.64917i q^{44} +63.0035 q^{46} +(6.38149 + 6.38149i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +33.4670 q^{51} +(15.6032 + 15.6032i) q^{52} +(42.9239 - 42.9239i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-45.5143 - 45.5143i) q^{57} +(-55.3464 + 55.3464i) q^{58} -59.2884i q^{59} +47.1648 q^{61} +(-4.54280 - 4.54280i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} -8.14354 q^{66} +(-8.48975 - 8.48975i) q^{67} +(-27.3257 + 27.3257i) q^{68} -77.1632i q^{69} +85.6769 q^{71} +(6.00000 + 6.00000i) q^{72} +(34.7848 - 34.7848i) q^{73} +93.7322i q^{74} +74.3246 q^{76} +(-6.21973 - 6.21973i) q^{77} +(19.1100 - 19.1100i) q^{78} +96.4868i q^{79} -9.00000 q^{81} +(9.94537 + 9.94537i) q^{82} +(-19.6272 + 19.6272i) q^{83} +9.16515i q^{84} -46.0863 q^{86} +(67.7852 + 67.7852i) q^{87} +(6.64917 - 6.64917i) q^{88} +43.0279i q^{89} +29.1910 q^{91} +(63.0035 + 63.0035i) q^{92} +(-5.56377 + 5.56377i) q^{93} +12.7630i q^{94} -9.79796 q^{96} +(-88.5610 - 88.5610i) q^{97} +(-7.00000 + 7.00000i) q^{98} +9.97376i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−3.32459			−0.302235			−0.151118	−	0.988516i	$-0.548287\pi$
$11$	−3.32459			−0.302235			−0.151118	+	0.988516i	$0.548287\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	7.80162	−	7.80162i	0.600124	−	0.600124i	−0.340221	−	0.940345i	$-0.610502\pi$
$13$	7.80162	−	7.80162i	0.600124	−	0.600124i	0.940345	+	0.340221i	$0.110502\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	13.6628	+	13.6628i	0.803697	+	0.803697i	0.983671	−	0.179975i	$-0.0576016\pi$
$17$	13.6628	+	13.6628i	0.803697	+	0.803697i	−0.179975	+	0.983671i	$0.557602\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	37.1623i		−	1.95591i	−0.208817	−	0.977955i	$-0.566961\pi$
$19$		−	37.1623i		−	1.95591i	0.208817	−	0.977955i	$-0.433039\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−3.32459	−	3.32459i	−0.151118	−	0.151118i
$23$	31.5017	−	31.5017i	1.36964	−	1.36964i	0.508693	−	0.860948i	$-0.330129\pi$
$23$	31.5017	−	31.5017i	1.36964	−	1.36964i	0.860948	−	0.508693i	$-0.169871\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	15.6032			0.600124
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$			55.3464i			1.90850i	0.299016	+	0.954248i	$0.403342\pi$
$29$			55.3464i			1.90850i	−0.299016	+	0.954248i	$0.596658\pi$
$30$		0			0
$31$	−4.54280			−0.146542			−0.0732710	−	0.997312i	$-0.523344\pi$
$31$	−4.54280			−0.146542			−0.0732710	+	0.997312i	$0.523344\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−4.07177	+	4.07177i	−0.123387	+	0.123387i
$34$			27.3257i			0.803697i
$35$		0			0
$36$	6.00000			0.166667
$37$	46.8661	+	46.8661i	1.26665	+	1.26665i	0.947807	+	0.318843i	$0.103294\pi$
$37$	46.8661	+	46.8661i	1.26665	+	1.26665i	0.318843	+	0.947807i	$0.396706\pi$
$38$	37.1623	−	37.1623i	0.977955	−	0.977955i
$39$		−	19.1100i		−	0.489999i
$40$		0			0
$41$	9.94537			0.242570			0.121285	−	0.992618i	$-0.461298\pi$
$41$	9.94537			0.242570			0.121285	+	0.992618i	$0.461298\pi$
$42$	4.58258	+	4.58258i	0.109109	+	0.109109i
$43$	−23.0431	+	23.0431i	−0.535887	+	0.535887i	−0.922318	−	0.386431i	$-0.873708\pi$
$43$	−23.0431	+	23.0431i	−0.535887	+	0.535887i	0.386431	+	0.922318i	$0.373708\pi$
$44$		−	6.64917i		−	0.151118i
$45$		0			0
$46$	63.0035			1.36964
$47$	6.38149	+	6.38149i	0.135776	+	0.135776i	0.771728	−	0.635952i	$-0.219392\pi$
$47$	6.38149	+	6.38149i	0.135776	+	0.135776i	−0.635952	+	0.771728i	$0.719392\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	33.4670			0.656216
$52$	15.6032	+	15.6032i	0.300062	+	0.300062i
$53$	42.9239	−	42.9239i	0.809885	−	0.809885i	−0.174731	−	0.984616i	$-0.555906\pi$
$53$	42.9239	−	42.9239i	0.809885	−	0.809885i	0.984616	+	0.174731i	$0.0559055\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−7.48331			−0.133631
$57$	−45.5143	−	45.5143i	−0.798497	−	0.798497i
$58$	−55.3464	+	55.3464i	−0.954248	+	0.954248i
$59$		−	59.2884i		−	1.00489i	−0.864610	−	0.502444i	$-0.832434\pi$
$59$		−	59.2884i		−	1.00489i	0.864610	−	0.502444i	$-0.167566\pi$
$60$		0			0
$61$	47.1648			0.773193			0.386596	−	0.922249i	$-0.373651\pi$
$61$	47.1648			0.773193			0.386596	+	0.922249i	$0.373651\pi$
$62$	−4.54280	−	4.54280i	−0.0732710	−	0.0732710i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−8.14354			−0.123387
$67$	−8.48975	−	8.48975i	−0.126713	−	0.126713i	0.640906	−	0.767619i	$-0.278559\pi$
$67$	−8.48975	−	8.48975i	−0.126713	−	0.126713i	−0.767619	+	0.640906i	$0.778559\pi$
$68$	−27.3257	+	27.3257i	−0.401848	+	0.401848i
$69$		−	77.1632i		−	1.11831i
$70$		0			0
$71$	85.6769			1.20672			0.603358	−	0.797470i	$-0.293829\pi$
$71$	85.6769			1.20672			0.603358	+	0.797470i	$0.293829\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	34.7848	−	34.7848i	0.476505	−	0.476505i	−0.427507	−	0.904012i	$-0.640608\pi$
$73$	34.7848	−	34.7848i	0.476505	−	0.476505i	0.904012	+	0.427507i	$0.140608\pi$
$74$			93.7322i			1.26665i
$75$		0			0
$76$	74.3246			0.977955
$77$	−6.21973	−	6.21973i	−0.0807757	−	0.0807757i
$78$	19.1100	−	19.1100i	0.245000	−	0.245000i
$79$			96.4868i			1.22135i	0.791880	+	0.610676i	$0.209102\pi$
$79$			96.4868i			1.22135i	−0.791880	+	0.610676i	$0.790898\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	9.94537	+	9.94537i	0.121285	+	0.121285i
$83$	−19.6272	+	19.6272i	−0.236472	+	0.236472i	−0.815388	−	0.578915i	$-0.803476\pi$
$83$	−19.6272	+	19.6272i	−0.236472	+	0.236472i	0.578915	+	0.815388i	$0.303476\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	−46.0863			−0.535887
$87$	67.7852	+	67.7852i	0.779140	+	0.779140i
$88$	6.64917	−	6.64917i	0.0755588	−	0.0755588i
$89$			43.0279i			0.483460i	0.970344	+	0.241730i	$0.0777148\pi$
$89$			43.0279i			0.483460i	−0.970344	+	0.241730i	$0.922285\pi$
$90$		0			0
$91$	29.1910			0.320780
$92$	63.0035	+	63.0035i	0.684820	+	0.684820i
$93$	−5.56377	+	5.56377i	−0.0598255	+	0.0598255i
$94$			12.7630i			0.135776i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−88.5610	−	88.5610i	−0.913000	−	0.913000i	0.0835068	−	0.996507i	$-0.473388\pi$
$97$	−88.5610	−	88.5610i	−0.913000	−	0.913000i	−0.996507	+	0.0835068i	$0.973388\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$			9.97376i			0.100745i
$100$		0			0
$101$	−101.113			−1.00112			−0.500558	−	0.865703i	$-0.666872\pi$
$101$	−101.113			−1.00112			−0.500558	+	0.865703i	$0.666872\pi$
$102$	33.4670	+	33.4670i	0.328108	+	0.328108i
$103$	48.7475	−	48.7475i	0.473276	−	0.473276i	−0.429697	−	0.902973i	$-0.641380\pi$
$103$	48.7475	−	48.7475i	0.473276	−	0.473276i	0.902973	+	0.429697i	$0.141380\pi$
$104$			31.2065i			0.300062i
$105$		0			0
$106$	85.8479			0.809885
$107$	11.0826	+	11.0826i	0.103576	+	0.103576i	0.756996	−	0.653420i	$-0.226666\pi$
$107$	11.0826	+	11.0826i	0.103576	+	0.103576i	−0.653420	+	0.756996i	$0.726666\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	1.00349i		−	0.00920630i	−0.999989	−	0.00460315i	$-0.998535\pi$
$109$		−	1.00349i		−	0.00920630i	0.999989	−	0.00460315i	$-0.00146523\pi$
$110$		0			0
$111$	114.798			1.03422
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	129.405	−	129.405i	1.14517	−	1.14517i	0.157683	−	0.987490i	$-0.449598\pi$
$113$	129.405	−	129.405i	1.14517	−	1.14517i	0.987490	−	0.157683i	$-0.0504024\pi$
$114$		−	91.0286i		−	0.798497i
$115$		0			0
$116$	−110.693			−0.954248
$117$	−23.4048	−	23.4048i	−0.200041	−	0.200041i
$118$	59.2884	−	59.2884i	0.502444	−	0.502444i
$119$			51.1217i			0.429594i
$120$		0			0
$121$	−109.947			−0.908654
$122$	47.1648	+	47.1648i	0.386596	+	0.386596i
$123$	12.1805	−	12.1805i	0.0990288	−	0.0990288i
$124$		−	9.08560i		−	0.0732710i
$125$		0			0
$126$	11.2250			0.0890871
$127$	−124.878	−	124.878i	−0.983289	−	0.983289i	0.0165736	−	0.999863i	$-0.494724\pi$
$127$	−124.878	−	124.878i	−0.983289	−	0.983289i	−0.999863	+	0.0165736i	$0.994724\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			56.4439i			0.437550i
$130$		0			0
$131$	137.486			1.04951			0.524754	−	0.851254i	$-0.324157\pi$
$131$	137.486			1.04951			0.524754	+	0.851254i	$0.324157\pi$
$132$	−8.14354	−	8.14354i	−0.0616935	−	0.0616935i
$133$	69.5243	−	69.5243i	0.522739	−	0.522739i
$134$		−	16.9795i		−	0.126713i
$135$		0			0
$136$	−54.6514			−0.401848
$137$	−69.9065	−	69.9065i	−0.510267	−	0.510267i	0.404341	−	0.914608i	$-0.367501\pi$
$137$	−69.9065	−	69.9065i	−0.510267	−	0.510267i	−0.914608	+	0.404341i	$0.867501\pi$
$138$	77.1632	−	77.1632i	0.559154	−	0.559154i
$139$			121.192i			0.871888i	0.899974	+	0.435944i	$0.143585\pi$
$139$			121.192i			0.871888i	−0.899974	+	0.435944i	$0.856415\pi$
$140$		0			0
$141$	15.6314			0.110861
$142$	85.6769	+	85.6769i	0.603358	+	0.603358i
$143$	−25.9372	+	25.9372i	−0.181379	+	0.181379i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	69.5697			0.476505
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	−93.7322	+	93.7322i	−0.633325	+	0.633325i
$149$			131.094i			0.879823i	0.898041	+	0.439911i	$0.144990\pi$
$149$			131.094i			0.879823i	−0.898041	+	0.439911i	$0.855010\pi$
$150$		0			0
$151$	−105.336			−0.697586			−0.348793	−	0.937200i	$-0.613408\pi$
$151$	−105.336			−0.697586			−0.348793	+	0.937200i	$0.613408\pi$
$152$	74.3246	+	74.3246i	0.488977	+	0.488977i
$153$	40.9885	−	40.9885i	0.267899	−	0.267899i
$154$		−	12.4395i		−	0.0807757i
$155$		0			0
$156$	38.2200			0.245000
$157$	34.7788	+	34.7788i	0.221521	+	0.221521i	0.809139	−	0.587618i	$-0.199934\pi$
$157$	34.7788	+	34.7788i	0.221521	+	0.221521i	−0.587618	+	0.809139i	$0.699934\pi$
$158$	−96.4868	+	96.4868i	−0.610676	+	0.610676i
$159$		−	105.142i		−	0.661269i
$160$		0			0
$161$	117.869			0.732104
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−71.0414	+	71.0414i	−0.435837	+	0.435837i	−0.890608	−	0.454771i	$-0.849721\pi$
$163$	−71.0414	+	71.0414i	−0.435837	+	0.435837i	0.454771	+	0.890608i	$0.349721\pi$
$164$			19.8907i			0.121285i
$165$		0			0
$166$	−39.2544			−0.236472
$167$	155.443	+	155.443i	0.930797	+	0.930797i	0.997756	−	0.0669588i	$-0.0213296\pi$
$167$	155.443	+	155.443i	0.930797	+	0.930797i	−0.0669588	+	0.997756i	$0.521330\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$			47.2696i			0.279702i
$170$		0			0
$171$	−111.487			−0.651970
$172$	−46.0863	−	46.0863i	−0.267944	−	0.267944i
$173$	16.5518	−	16.5518i	0.0956751	−	0.0956751i	−0.657649	−	0.753324i	$-0.728449\pi$
$173$	16.5518	−	16.5518i	0.0956751	−	0.0956751i	0.753324	+	0.657649i	$0.228449\pi$
$174$			135.570i			0.779140i
$175$		0			0
$176$	13.2983			0.0755588
$177$	−72.6131	−	72.6131i	−0.410244	−	0.410244i
$178$	−43.0279	+	43.0279i	−0.241730	+	0.241730i
$179$		−	184.541i		−	1.03096i	−0.856903	−	0.515478i	$-0.827614\pi$
$179$		−	184.541i		−	1.03096i	0.856903	−	0.515478i	$-0.172386\pi$
$180$		0			0
$181$	−73.9362			−0.408488			−0.204244	−	0.978920i	$-0.565474\pi$
$181$	−73.9362			−0.408488			−0.204244	+	0.978920i	$0.565474\pi$
$182$	29.1910	+	29.1910i	0.160390	+	0.160390i
$183$	57.7648	−	57.7648i	0.315655	−	0.315655i
$184$			126.007i			0.684820i
$185$		0			0
$186$	−11.1275			−0.0598255
$187$	−45.4233	−	45.4233i	−0.242905	−	0.242905i
$188$	−12.7630	+	12.7630i	−0.0678882	+	0.0678882i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	−255.605			−1.33825			−0.669123	−	0.743152i	$-0.733330\pi$
$191$	−255.605			−1.33825			−0.669123	+	0.743152i	$0.733330\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−153.794	+	153.794i	−0.796858	+	0.796858i	−0.982599	−	0.185741i	$-0.940532\pi$
$193$	−153.794	+	153.794i	−0.796858	+	0.796858i	0.185741	+	0.982599i	$0.440532\pi$
$194$		−	177.122i		−	0.913000i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−132.071	−	132.071i	−0.670411	−	0.670411i	0.287400	−	0.957811i	$-0.407209\pi$
$197$	−132.071	−	132.071i	−0.670411	−	0.670411i	−0.957811	+	0.287400i	$0.907209\pi$
$198$	−9.97376	+	9.97376i	−0.0503725	+	0.0503725i
$199$		−	223.530i		−	1.12327i	−0.827387	−	0.561633i	$-0.810173\pi$
$199$		−	223.530i		−	1.12327i	0.827387	−	0.561633i	$-0.189827\pi$
$200$		0			0
$201$	−20.7956			−0.103460
$202$	−101.113	−	101.113i	−0.500558	−	0.500558i
$203$	−103.544	+	103.544i	−0.510067	+	0.510067i
$204$			66.9340i			0.328108i
$205$		0			0
$206$	97.4950			0.473276
$207$	−94.5052	−	94.5052i	−0.456547	−	0.456547i
$208$	−31.2065	+	31.2065i	−0.150031	+	0.150031i
$209$			123.549i			0.591145i
$210$		0			0
$211$	−122.409			−0.580137			−0.290069	−	0.957006i	$-0.593678\pi$
$211$	−122.409			−0.580137			−0.290069	+	0.957006i	$0.593678\pi$
$212$	85.8479	+	85.8479i	0.404943	+	0.404943i
$213$	104.932	−	104.932i	0.492640	−	0.492640i
$214$			22.1652i			0.103576i
$215$		0			0
$216$	14.6969			0.0680414
$217$	−8.49880	−	8.49880i	−0.0391650	−	0.0391650i
$218$	1.00349	−	1.00349i	0.00460315	−	0.00460315i
$219$		−	85.2051i		−	0.389064i
$220$		0			0
$221$	213.185			0.964636
$222$	114.798	+	114.798i	0.517108	+	0.517108i
$223$	−139.840	+	139.840i	−0.627083	+	0.627083i	−0.947333	−	0.320250i	$-0.896233\pi$
$223$	−139.840	+	139.840i	−0.627083	+	0.627083i	0.320250	+	0.947333i	$0.396233\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	258.809			1.14517
$227$	61.8255	+	61.8255i	0.272359	+	0.272359i	0.830049	−	0.557690i	$-0.188312\pi$
$227$	61.8255	+	61.8255i	0.272359	+	0.272359i	−0.557690	+	0.830049i	$0.688312\pi$
$228$	91.0286	−	91.0286i	0.399248	−	0.399248i
$229$			145.539i			0.635540i	0.948168	+	0.317770i	$0.102934\pi$
$229$			145.539i			0.635540i	−0.948168	+	0.317770i	$0.897066\pi$
$230$		0			0
$231$	−15.2352			−0.0659531
$232$	−110.693	−	110.693i	−0.477124	−	0.477124i
$233$	−78.2015	+	78.2015i	−0.335629	+	0.335629i	−0.854719	−	0.519090i	$-0.826271\pi$
$233$	−78.2015	+	78.2015i	−0.335629	+	0.335629i	0.519090	+	0.854719i	$0.326271\pi$
$234$		−	46.8097i		−	0.200041i
$235$		0			0
$236$	118.577			0.502444
$237$	118.172	+	118.172i	0.498615	+	0.498615i
$238$	−51.1217	+	51.1217i	−0.214797	+	0.214797i
$239$		−	183.007i		−	0.765720i	−0.923806	−	0.382860i	$-0.874939\pi$
$239$		−	183.007i		−	0.765720i	0.923806	−	0.382860i	$-0.125061\pi$
$240$		0			0
$241$	39.6298			0.164439			0.0822194	−	0.996614i	$-0.473799\pi$
$241$	39.6298			0.164439			0.0822194	+	0.996614i	$0.473799\pi$
$242$	−109.947	−	109.947i	−0.454327	−	0.454327i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			94.3295i			0.386596i
$245$		0			0
$246$	24.3611			0.0990288
$247$	−289.926	−	289.926i	−1.17379	−	1.17379i
$248$	9.08560	−	9.08560i	0.0366355	−	0.0366355i
$249$			48.0766i			0.193079i
$250$		0			0
$251$	−15.9671			−0.0636141			−0.0318070	−	0.999494i	$-0.510126\pi$
$251$	−15.9671			−0.0636141			−0.0318070	+	0.999494i	$0.510126\pi$
$252$	11.2250	+	11.2250i	0.0445435	+	0.0445435i
$253$	−104.730	+	104.730i	−0.413954	+	0.413954i
$254$		−	249.755i		−	0.983289i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−59.0712	−	59.0712i	−0.229849	−	0.229849i	0.582781	−	0.812630i	$-0.301965\pi$
$257$	−59.0712	−	59.0712i	−0.229849	−	0.229849i	−0.812630	+	0.582781i	$0.801965\pi$
$258$	−56.4439	+	56.4439i	−0.218775	+	0.218775i
$259$			175.357i			0.677053i
$260$		0			0
$261$	166.039			0.636165
$262$	137.486	+	137.486i	0.524754	+	0.524754i
$263$	−186.291	+	186.291i	−0.708330	+	0.708330i	−0.966184	−	0.257854i	$-0.916985\pi$
$263$	−186.291	+	186.291i	−0.708330	+	0.708330i	0.257854	+	0.966184i	$0.416985\pi$
$264$		−	16.2871i		−	0.0616935i
$265$		0			0
$266$	139.049			0.522739
$267$	52.6982	+	52.6982i	0.197372	+	0.197372i
$268$	16.9795	−	16.9795i	0.0633563	−	0.0633563i
$269$			120.015i			0.446153i	0.974801	+	0.223077i	$0.0716100\pi$
$269$			120.015i			0.446153i	−0.974801	+	0.223077i	$0.928390\pi$
$270$		0			0
$271$	−457.758			−1.68914			−0.844571	−	0.535444i	$-0.820144\pi$
$271$	−457.758			−1.68914			−0.844571	+	0.535444i	$0.820144\pi$
$272$	−54.6514	−	54.6514i	−0.200924	−	0.200924i
$273$	35.7515	−	35.7515i	0.130958	−	0.130958i
$274$		−	139.813i		−	0.510267i
$275$		0			0
$276$	154.326			0.559154
$277$	−2.98510	−	2.98510i	−0.0107766	−	0.0107766i	0.701698	−	0.712475i	$-0.252426\pi$
$277$	−2.98510	−	2.98510i	−0.0107766	−	0.0107766i	−0.712475	+	0.701698i	$0.752426\pi$
$278$	−121.192	+	121.192i	−0.435944	+	0.435944i
$279$			13.6284i			0.0488473i
$280$		0			0
$281$	−196.044			−0.697666			−0.348833	−	0.937185i	$-0.613422\pi$
$281$	−196.044			−0.697666			−0.348833	+	0.937185i	$0.613422\pi$
$282$	15.6314	+	15.6314i	0.0554305	+	0.0554305i
$283$	226.011	−	226.011i	0.798627	−	0.798627i	−0.184252	−	0.982879i	$-0.558986\pi$
$283$	226.011	−	226.011i	0.798627	−	0.798627i	0.982879	+	0.184252i	$0.0589863\pi$
$284$			171.354i			0.603358i
$285$		0			0
$286$	−51.8743			−0.181379
$287$	18.6061	+	18.6061i	0.0648296	+	0.0648296i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			84.3465i			0.291856i
$290$		0			0
$291$	−216.929			−0.745462
$292$	69.5697	+	69.5697i	0.238252	+	0.238252i
$293$	106.875	−	106.875i	0.364762	−	0.364762i	−0.500801	−	0.865563i	$-0.666961\pi$
$293$	106.875	−	106.875i	0.364762	−	0.364762i	0.865563	+	0.500801i	$0.166961\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−187.464			−0.633325
$297$	12.2153	+	12.2153i	0.0411290	+	0.0411290i
$298$	−131.094	+	131.094i	−0.439911	+	0.439911i
$299$		−	491.529i		−	1.64391i
$300$		0			0
$301$	−86.2196			−0.286444
$302$	−105.336	−	105.336i	−0.348793	−	0.348793i
$303$	−123.837	+	123.837i	−0.408704	+	0.408704i
$304$			148.649i			0.488977i
$305$		0			0
$306$	81.9771			0.267899
$307$	169.042	+	169.042i	0.550624	+	0.550624i	0.926621	−	0.375997i	$-0.122700\pi$
$307$	169.042	+	169.042i	0.550624	+	0.550624i	−0.375997	+	0.926621i	$0.622700\pi$
$308$	12.4395	−	12.4395i	0.0403879	−	0.0403879i
$309$		−	119.406i		−	0.386429i
$310$		0			0
$311$	184.053			0.591810			0.295905	−	0.955217i	$-0.404379\pi$
$311$	184.053			0.591810			0.295905	+	0.955217i	$0.404379\pi$
$312$	38.2200	+	38.2200i	0.122500	+	0.122500i
$313$	−208.497	+	208.497i	−0.666124	+	0.666124i	−0.956817	−	0.290692i	$-0.906114\pi$
$313$	−208.497	+	208.497i	−0.666124	+	0.666124i	0.290692	+	0.956817i	$0.406114\pi$
$314$			69.5576i			0.221521i
$315$		0			0
$316$	−192.974			−0.610676
$317$	403.707	+	403.707i	1.27352	+	1.27352i	0.944227	+	0.329296i	$0.106811\pi$
$317$	403.707	+	403.707i	1.27352	+	1.27352i	0.329296	+	0.944227i	$0.393189\pi$
$318$	105.142	−	105.142i	0.330634	−	0.330634i
$319$		−	184.004i		−	0.576815i
$320$		0			0
$321$	27.1467			0.0845691
$322$	117.869	+	117.869i	0.366052	+	0.366052i
$323$	507.742	−	507.742i	1.57196	−	1.57196i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	−142.083			−0.435837
$327$	−1.22901	−	1.22901i	−0.00375846	−	0.00375846i
$328$	−19.8907	+	19.8907i	−0.0606425	+	0.0606425i
$329$			23.8773i			0.0725755i
$330$		0			0
$331$	−26.7859			−0.0809241			−0.0404620	−	0.999181i	$-0.512883\pi$
$331$	−26.7859			−0.0809241			−0.0404620	+	0.999181i	$0.512883\pi$
$332$	−39.2544	−	39.2544i	−0.118236	−	0.118236i
$333$	140.598	−	140.598i	0.422217	−	0.422217i
$334$			310.886i			0.930797i
$335$		0			0
$336$	−18.3303			−0.0545545
$337$	−325.031	−	325.031i	−0.964485	−	0.964485i	0.0349056	−	0.999391i	$-0.488887\pi$
$337$	−325.031	−	325.031i	−0.964485	−	0.964485i	−0.999391	+	0.0349056i	$0.988887\pi$
$338$	−47.2696	+	47.2696i	−0.139851	+	0.139851i
$339$		−	316.975i		−	0.935030i
$340$		0			0
$341$	15.1029			0.0442901
$342$	−111.487	−	111.487i	−0.325985	−	0.325985i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	92.1726i		−	0.267944i
$345$		0			0
$346$	33.1036			0.0956751
$347$	119.676	+	119.676i	0.344887	+	0.344887i	0.858201	−	0.513314i	$-0.171582\pi$
$347$	119.676	+	119.676i	0.344887	+	0.344887i	−0.513314	+	0.858201i	$0.671582\pi$
$348$	−135.570	+	135.570i	−0.389570	+	0.389570i
$349$		−	592.030i		−	1.69636i	−0.529708	−	0.848180i	$-0.677698\pi$
$349$		−	592.030i		−	1.69636i	0.529708	−	0.848180i	$-0.322302\pi$
$350$		0			0
$351$	−57.3299			−0.163333
$352$	13.2983	+	13.2983i	0.0377794	+	0.0377794i
$353$	−92.2147	+	92.2147i	−0.261231	+	0.261231i	−0.825554	−	0.564323i	$-0.809137\pi$
$353$	−92.2147	+	92.2147i	−0.261231	+	0.261231i	0.564323	+	0.825554i	$0.309137\pi$
$354$		−	145.226i		−	0.410244i
$355$		0			0
$356$	−86.0558			−0.241730
$357$	62.6110	+	62.6110i	0.175381	+	0.175381i
$358$	184.541	−	184.541i	0.515478	−	0.515478i
$359$			464.557i			1.29403i	0.762477	+	0.647016i	$0.223983\pi$
$359$			464.557i			1.29403i	−0.762477	+	0.647016i	$0.776017\pi$
$360$		0			0
$361$	−1020.03			−2.82558
$362$	−73.9362	−	73.9362i	−0.204244	−	0.204244i
$363$	−134.657	+	134.657i	−0.370956	+	0.370956i
$364$			58.3820i			0.160390i
$365$		0			0
$366$	115.530			0.315655
$367$	−450.255	−	450.255i	−1.22685	−	1.22685i	−0.965148	−	0.261705i	$-0.915715\pi$
$367$	−450.255	−	450.255i	−1.22685	−	1.22685i	−0.261705	−	0.965148i	$-0.584285\pi$
$368$	−126.007	+	126.007i	−0.342410	+	0.342410i
$369$		−	29.8361i		−	0.0808567i
$370$		0			0
$371$	160.607			0.432902
$372$	−11.1275	−	11.1275i	−0.0299128	−	0.0299128i
$373$	−447.933	+	447.933i	−1.20089	+	1.20089i	−0.226997	+	0.973895i	$0.572891\pi$
$373$	−447.933	+	447.933i	−1.20089	+	1.20089i	−0.973895	+	0.226997i	$0.927109\pi$
$374$		−	90.8466i		−	0.242905i
$375$		0			0
$376$	−25.5259			−0.0678882
$377$	431.791	+	431.791i	1.14534	+	1.14534i
$378$	13.7477	−	13.7477i	0.0363696	−	0.0363696i
$379$		−	200.204i		−	0.528242i	−0.964490	−	0.264121i	$-0.914918\pi$
$379$		−	200.204i		−	0.528242i	0.964490	−	0.264121i	$-0.0850818\pi$
$380$		0			0
$381$	−305.887			−0.802852
$382$	−255.605	−	255.605i	−0.669123	−	0.669123i
$383$	260.633	−	260.633i	0.680503	−	0.680503i	−0.279610	−	0.960114i	$-0.590205\pi$
$383$	260.633	−	260.633i	0.680503	−	0.680503i	0.960114	+	0.279610i	$0.0902053\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−307.587			−0.796858
$387$	69.1294	+	69.1294i	0.178629	+	0.178629i
$388$	177.122	−	177.122i	0.456500	−	0.456500i
$389$		−	192.566i		−	0.495028i	−0.968884	−	0.247514i	$-0.920386\pi$
$389$		−	192.566i		−	0.495028i	0.968884	−	0.247514i	$-0.0796136\pi$
$390$		0			0
$391$	860.807			2.20155
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	168.385	−	168.385i	0.428460	−	0.428460i
$394$		−	264.142i		−	0.670411i
$395$		0			0
$396$	−19.9475			−0.0503725
$397$	183.256	+	183.256i	0.461602	+	0.461602i	0.899180	−	0.437578i	$-0.144164\pi$
$397$	183.256	+	183.256i	0.461602	+	0.461602i	−0.437578	+	0.899180i	$0.644164\pi$
$398$	223.530	−	223.530i	0.561633	−	0.561633i
$399$		−	170.299i		−	0.426814i
$400$		0			0
$401$	−327.614			−0.816992			−0.408496	−	0.912760i	$-0.633947\pi$
$401$	−327.614			−0.816992			−0.408496	+	0.912760i	$0.633947\pi$
$402$	−20.7956	−	20.7956i	−0.0517302	−	0.0517302i
$403$	−35.4412	+	35.4412i	−0.0879434	+	0.0879434i
$404$		−	202.225i		−	0.500558i
$405$		0			0
$406$	−207.087			−0.510067
$407$	−155.810	−	155.810i	−0.382826	−	0.382826i
$408$	−66.9340	+	66.9340i	−0.164054	+	0.164054i
$409$			637.257i			1.55809i	0.626971	+	0.779043i	$0.284295\pi$
$409$			637.257i			1.55809i	−0.626971	+	0.779043i	$0.715705\pi$
$410$		0			0
$411$	−171.235			−0.416631
$412$	97.4950	+	97.4950i	0.236638	+	0.236638i
$413$	110.918	−	110.918i	0.268568	−	0.268568i
$414$		−	189.010i		−	0.456547i
$415$		0			0
$416$	−62.4129			−0.150031
$417$	148.430	+	148.430i	0.355947	+	0.355947i
$418$	−123.549	+	123.549i	−0.295572	+	0.295572i
$419$		−	332.788i		−	0.794244i	−0.917766	−	0.397122i	$-0.870009\pi$
$419$		−	332.788i		−	0.794244i	0.917766	−	0.397122i	$-0.129991\pi$
$420$		0			0
$421$	−287.551			−0.683018			−0.341509	−	0.939879i	$-0.610938\pi$
$421$	−287.551			−0.683018			−0.341509	+	0.939879i	$0.610938\pi$
$422$	−122.409	−	122.409i	−0.290069	−	0.290069i
$423$	19.1445	−	19.1445i	0.0452588	−	0.0452588i
$424$			171.696i			0.404943i
$425$		0			0
$426$	209.865			0.492640
$427$	88.2372	+	88.2372i	0.206645	+	0.206645i
$428$	−22.1652	+	22.1652i	−0.0517878	+	0.0517878i
$429$			63.5328i			0.148095i
$430$		0			0
$431$	−321.978			−0.747049			−0.373524	−	0.927620i	$-0.621851\pi$
$431$	−321.978			−0.747049			−0.373524	+	0.927620i	$0.621851\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−285.044	+	285.044i	−0.658300	+	0.658300i	−0.954978	−	0.296678i	$-0.904121\pi$
$433$	−285.044	+	285.044i	−0.658300	+	0.658300i	0.296678	+	0.954978i	$0.404121\pi$
$434$		−	16.9976i		−	0.0391650i
$435$		0			0
$436$	2.00697			0.00460315
$437$	−1170.68	−	1170.68i	−2.67889	−	2.67889i
$438$	85.2051	−	85.2051i	0.194532	−	0.194532i
$439$			342.297i			0.779721i	0.920874	+	0.389860i	$0.127477\pi$
$439$			342.297i			0.779721i	−0.920874	+	0.389860i	$0.872523\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	213.185	+	213.185i	0.482318	+	0.482318i
$443$	545.221	−	545.221i	1.23075	−	1.23075i	0.267070	−	0.963677i	$-0.413945\pi$
$443$	545.221	−	545.221i	1.23075	−	1.23075i	0.963677	−	0.267070i	$-0.0860554\pi$
$444$			229.596i			0.517108i
$445$		0			0
$446$	−279.679			−0.627083
$447$	160.556	+	160.556i	0.359186	+	0.359186i
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$		−	65.3316i		−	0.145505i	−0.997350	−	0.0727523i	$-0.976822\pi$
$449$		−	65.3316i		−	0.145505i	0.997350	−	0.0727523i	$-0.0231783\pi$
$450$		0			0
$451$	−33.0643			−0.0733132
$452$	258.809	+	258.809i	0.572586	+	0.572586i
$453$	−129.009	+	129.009i	−0.284788	+	0.284788i
$454$			123.651i			0.272359i
$455$		0			0
$456$	182.057			0.399248
$457$	−147.331	−	147.331i	−0.322387	−	0.322387i	0.527295	−	0.849682i	$-0.323206\pi$
$457$	−147.331	−	147.331i	−0.322387	−	0.322387i	−0.849682	+	0.527295i	$0.823206\pi$
$458$	−145.539	+	145.539i	−0.317770	+	0.317770i
$459$		−	100.401i		−	0.218739i
$460$		0			0
$461$	−52.5087			−0.113902			−0.0569509	−	0.998377i	$-0.518138\pi$
$461$	−52.5087			−0.113902			−0.0569509	+	0.998377i	$0.518138\pi$
$462$	−15.2352	−	15.2352i	−0.0329766	−	0.0329766i
$463$	76.6237	−	76.6237i	0.165494	−	0.165494i	−0.619502	−	0.784995i	$-0.712665\pi$
$463$	76.6237	−	76.6237i	0.165494	−	0.165494i	0.784995	+	0.619502i	$0.212665\pi$
$464$		−	221.386i		−	0.477124i
$465$		0			0
$466$	−156.403			−0.335629
$467$	−54.4091	−	54.4091i	−0.116508	−	0.116508i	0.646449	−	0.762957i	$-0.276253\pi$
$467$	−54.4091	−	54.4091i	−0.116508	−	0.116508i	−0.762957	+	0.646449i	$0.776253\pi$
$468$	46.8097	−	46.8097i	0.100021	−	0.100021i
$469$		−	31.7657i		−	0.0677308i
$470$		0			0
$471$	85.1904			0.180871
$472$	118.577	+	118.577i	0.251222	+	0.251222i
$473$	76.6089	−	76.6089i	0.161964	−	0.161964i
$474$			236.343i			0.498615i
$475$		0			0
$476$	−102.243			−0.214797
$477$	−128.772	−	128.772i	−0.269962	−	0.269962i
$478$	183.007	−	183.007i	0.382860	−	0.382860i
$479$		−	165.940i		−	0.346430i	−0.984884	−	0.173215i	$-0.944584\pi$
$479$		−	165.940i		−	0.346430i	0.984884	−	0.173215i	$-0.0554156\pi$
$480$		0			0
$481$	731.262			1.52030
$482$	39.6298	+	39.6298i	0.0822194	+	0.0822194i
$483$	144.359	−	144.359i	0.298880	−	0.298880i
$484$		−	219.894i		−	0.454327i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	49.2440	+	49.2440i	0.101117	+	0.101117i	0.755856	−	0.654738i	$-0.227221\pi$
$487$	49.2440	+	49.2440i	0.101117	+	0.101117i	−0.654738	+	0.755856i	$0.727221\pi$
$488$	−94.3295	+	94.3295i	−0.193298	+	0.193298i
$489$			174.015i			0.355859i
$490$		0			0
$491$	−207.513			−0.422633			−0.211316	−	0.977418i	$-0.567775\pi$
$491$	−207.513			−0.422633			−0.211316	+	0.977418i	$0.567775\pi$
$492$	24.3611	+	24.3611i	0.0495144	+	0.0495144i
$493$	−756.189	+	756.189i	−1.53385	+	1.53385i
$494$		−	579.852i		−	1.17379i
$495$		0			0
$496$	18.1712			0.0366355
$497$	160.287	+	160.287i	0.322509	+	0.322509i
$498$	−48.0766	+	48.0766i	−0.0965393	+	0.0965393i
$499$			299.711i			0.600624i	0.953841	+	0.300312i	$0.0970908\pi$
$499$			299.711i			0.600624i	−0.953841	+	0.300312i	$0.902909\pi$
$500$		0			0
$501$	380.756			0.759993
$502$	−15.9671	−	15.9671i	−0.0318070	−	0.0318070i
$503$	354.819	−	354.819i	0.705406	−	0.705406i	−0.260160	−	0.965566i	$-0.583775\pi$
$503$	354.819	−	354.819i	0.705406	−	0.705406i	0.965566	+	0.260160i	$0.0837753\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−209.461			−0.413954
$507$	57.8932	+	57.8932i	0.114188	+	0.114188i
$508$	249.755	−	249.755i	0.491645	−	0.491645i
$509$			46.3713i			0.0911027i	0.998962	+	0.0455514i	$0.0145045\pi$
$509$			46.3713i			0.0911027i	−0.998962	+	0.0455514i	$0.985496\pi$
$510$		0			0
$511$	130.153			0.254702
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−136.543	+	136.543i	−0.266166	+	0.266166i
$514$		−	118.142i		−	0.229849i
$515$		0			0
$516$	−112.888			−0.218775
$517$	−21.2158	−	21.2158i	−0.0410364	−	0.0410364i
$518$	−175.357	+	175.357i	−0.338527	+	0.338527i
$519$		−	40.5435i		−	0.0781184i
$520$		0			0
$521$	784.619			1.50599			0.752993	−	0.658028i	$-0.228609\pi$
$521$	784.619			1.50599			0.752993	+	0.658028i	$0.228609\pi$
$522$	166.039	+	166.039i	0.318083	+	0.318083i
$523$	−271.744	+	271.744i	−0.519587	+	0.519587i	−0.917446	−	0.397859i	$-0.869753\pi$
$523$	−271.744	+	271.744i	−0.519587	+	0.519587i	0.397859	+	0.917446i	$0.369753\pi$
$524$			274.971i			0.524754i
$525$		0			0
$526$	−372.582			−0.708330
$527$	−62.0676	−	62.0676i	−0.117775	−	0.117775i
$528$	16.2871	−	16.2871i	0.0308467	−	0.0308467i
$529$		−	1455.72i		−	2.75183i
$530$		0			0
$531$	−177.865			−0.334963
$532$	139.049	+	139.049i	0.261369	+	0.261369i
$533$	77.5900	−	77.5900i	0.145572	−	0.145572i
$534$			105.396i			0.197372i
$535$		0			0
$536$	33.9590			0.0633563
$537$	−226.016	−	226.016i	−0.420886	−	0.420886i
$538$	−120.015	+	120.015i	−0.223077	+	0.223077i
$539$		−	23.2721i		−	0.0431765i
$540$		0			0
$541$	545.359			1.00806			0.504029	−	0.863687i	$-0.331851\pi$
$541$	545.359			1.00806			0.504029	+	0.863687i	$0.331851\pi$
$542$	−457.758	−	457.758i	−0.844571	−	0.844571i
$543$	−90.5530	+	90.5530i	−0.166764	+	0.166764i
$544$		−	109.303i		−	0.200924i
$545$		0			0
$546$	71.5030			0.130958
$547$	−93.2739	−	93.2739i	−0.170519	−	0.170519i	0.616688	−	0.787207i	$-0.288474\pi$
$547$	−93.2739	−	93.2739i	−0.170519	−	0.170519i	−0.787207	+	0.616688i	$0.788474\pi$
$548$	139.813	−	139.813i	0.255133	−	0.255133i
$549$		−	141.494i		−	0.257731i
$550$		0			0
$551$	2056.80			3.73285
$552$	154.326	+	154.326i	0.279577	+	0.279577i
$553$	−180.510	+	180.510i	−0.326420	+	0.326420i
$554$		−	5.97021i		−	0.0107766i
$555$		0			0
$556$	−242.385			−0.435944
$557$	−549.179	−	549.179i	−0.985958	−	0.985958i	0.0139446	−	0.999903i	$-0.495561\pi$
$557$	−549.179	−	549.179i	−0.985958	−	0.985958i	−0.999903	+	0.0139446i	$0.995561\pi$
$558$	−13.6284	+	13.6284i	−0.0244237	+	0.0244237i
$559$			359.548i			0.643198i
$560$		0			0
$561$	−111.264			−0.198331
$562$	−196.044	−	196.044i	−0.348833	−	0.348833i
$563$	45.1575	−	45.1575i	0.0802088	−	0.0802088i	−0.665864	−	0.746073i	$-0.731937\pi$
$563$	45.1575	−	45.1575i	0.0802088	−	0.0802088i	0.746073	+	0.665864i	$0.231937\pi$
$564$			31.2628i			0.0554305i
$565$		0			0
$566$	452.023			0.798627
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	−171.354	+	171.354i	−0.301679	+	0.301679i
$569$			392.758i			0.690260i	0.938555	+	0.345130i	$0.112165\pi$
$569$			392.758i			0.690260i	−0.938555	+	0.345130i	$0.887835\pi$
$570$		0			0
$571$	−0.726963			−0.00127314			−0.000636570	−	1.00000i	$-0.500203\pi$
$571$	−0.726963			−0.00127314			−0.000636570		1.00000i	$0.500203\pi$
$572$	−51.8743	−	51.8743i	−0.0906893	−	0.0906893i
$573$	−313.051	+	313.051i	−0.546337	+	0.546337i
$574$			37.2122i			0.0648296i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	184.973	+	184.973i	0.320577	+	0.320577i	0.848988	−	0.528411i	$-0.177212\pi$
$577$	184.973	+	184.973i	0.320577	+	0.320577i	−0.528411	+	0.848988i	$0.677212\pi$
$578$	−84.3465	+	84.3465i	−0.145928	+	0.145928i
$579$			376.716i			0.650632i
$580$		0			0
$581$	−73.4382			−0.126400
$582$	−216.929	−	216.929i	−0.372731	−	0.372731i
$583$	−142.704	+	142.704i	−0.244776	+	0.244776i
$584$			139.139i			0.238252i
$585$		0			0
$586$	213.751			0.364762
$587$	703.941	+	703.941i	1.19922	+	1.19922i	0.974401	+	0.224817i	$0.0721783\pi$
$587$	703.941	+	703.941i	1.19922	+	1.19922i	0.224817	+	0.974401i	$0.427822\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$			168.821i			0.286623i
$590$		0			0
$591$	−323.506			−0.547388
$592$	−187.464	−	187.464i	−0.316663	−	0.316663i
$593$	−730.917	+	730.917i	−1.23257	+	1.23257i	−0.269603	+	0.962972i	$0.586893\pi$
$593$	−730.917	+	730.917i	−1.23257	+	1.23257i	−0.962972	+	0.269603i	$0.913107\pi$
$594$			24.4306i			0.0411290i
$595$		0			0
$596$	−262.187			−0.439911
$597$	−273.767	−	273.767i	−0.458571	−	0.458571i
$598$	491.529	−	491.529i	0.821955	−	0.821955i
$599$			646.505i			1.07931i	0.841887	+	0.539654i	$0.181445\pi$
$599$			646.505i			1.07931i	−0.841887	+	0.539654i	$0.818555\pi$
$600$		0			0
$601$	−133.146			−0.221541			−0.110771	−	0.993846i	$-0.535332\pi$
$601$	−133.146			−0.221541			−0.110771	+	0.993846i	$0.535332\pi$
$602$	−86.2196	−	86.2196i	−0.143222	−	0.143222i
$603$	−25.4692	+	25.4692i	−0.0422376	+	0.0422376i
$604$		−	210.671i		−	0.348793i
$605$		0			0
$606$	−247.674			−0.408704
$607$	1.17531	+	1.17531i	0.00193627	+	0.00193627i	0.708074	−	0.706138i	$-0.249564\pi$
$607$	1.17531	+	1.17531i	0.00193627	+	0.00193627i	−0.706138	+	0.708074i	$0.749564\pi$
$608$	−148.649	+	148.649i	−0.244489	+	0.244489i
$609$			253.629i			0.416468i
$610$		0			0
$611$	99.5718			0.162965
$612$	81.9771	+	81.9771i	0.133949	+	0.133949i
$613$	464.748	−	464.748i	0.758153	−	0.758153i	−0.217833	−	0.975986i	$-0.569899\pi$
$613$	464.748	−	464.748i	0.758153	−	0.758153i	0.975986	+	0.217833i	$0.0698989\pi$
$614$			338.083i			0.550624i
$615$		0			0
$616$	24.8789			0.0403879
$617$	591.643	+	591.643i	0.958903	+	0.958903i	0.999188	−	0.0402851i	$-0.0128266\pi$
$617$	591.643	+	591.643i	0.958903	+	0.958903i	−0.0402851	+	0.999188i	$0.512827\pi$
$618$	119.406	−	119.406i	0.193214	−	0.193214i
$619$			1133.85i			1.83175i	0.401466	+	0.915874i	$0.368501\pi$
$619$			1133.85i			1.83175i	−0.401466	+	0.915874i	$0.631499\pi$
$620$		0			0
$621$	−231.490			−0.372769
$622$	184.053	+	184.053i	0.295905	+	0.295905i
$623$	−80.4978	+	80.4978i	−0.129210	+	0.129210i
$624$			76.4399i			0.122500i
$625$		0			0
$626$	−416.994			−0.666124
$627$	151.316	+	151.316i	0.241334	+	0.241334i
$628$	−69.5576	+	69.5576i	−0.110761	+	0.110761i
$629$			1280.65i			2.03601i
$630$		0			0
$631$	−383.255			−0.607377			−0.303689	−	0.952771i	$-0.598218\pi$
$631$	−383.255			−0.607377			−0.303689	+	0.952771i	$0.598218\pi$
$632$	−192.974	−	192.974i	−0.305338	−	0.305338i
$633$	−149.920	+	149.920i	−0.236840	+	0.236840i
$634$			807.414i			1.27352i
$635$		0			0
$636$	210.283			0.330634
$637$	54.6113	+	54.6113i	0.0857320	+	0.0857320i
$638$	184.004	−	184.004i	0.288407	−	0.288407i
$639$		−	257.031i		−	0.402239i
$640$		0			0
$641$	−129.610			−0.202199			−0.101100	−	0.994876i	$-0.532236\pi$
$641$	−129.610			−0.202199			−0.101100	+	0.994876i	$0.532236\pi$
$642$	27.1467	+	27.1467i	0.0422845	+	0.0422845i
$643$	−233.464	+	233.464i	−0.363085	+	0.363085i	−0.864948	−	0.501862i	$-0.832648\pi$
$643$	−233.464	+	233.464i	−0.363085	+	0.363085i	0.501862	+	0.864948i	$0.332648\pi$
$644$			235.737i			0.366052i
$645$		0			0
$646$	1015.48			1.57196
$647$	430.823	+	430.823i	0.665878	+	0.665878i	0.956759	−	0.290881i	$-0.0939484\pi$
$647$	430.823	+	430.823i	0.665878	+	0.665878i	−0.290881	+	0.956759i	$0.593948\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			197.109i			0.303712i
$650$		0			0
$651$	−20.8177			−0.0319781
$652$	−142.083	−	142.083i	−0.217918	−	0.217918i
$653$	−170.000	+	170.000i	−0.260337	+	0.260337i	−0.825191	−	0.564854i	$-0.808932\pi$
$653$	−170.000	+	170.000i	−0.260337	+	0.260337i	0.564854	+	0.825191i	$0.308932\pi$
$654$		−	2.45803i		−	0.00375846i
$655$		0			0
$656$	−39.7815			−0.0606425
$657$	−104.355	−	104.355i	−0.158835	−	0.158835i
$658$	−23.8773	+	23.8773i	−0.0362878	+	0.0362878i
$659$		−	532.095i		−	0.807429i	−0.914885	−	0.403714i	$-0.867719\pi$
$659$		−	532.095i		−	0.807429i	0.914885	−	0.403714i	$-0.132281\pi$
$660$		0			0
$661$	1235.23			1.86872			0.934362	−	0.356325i	$-0.115971\pi$
$661$	1235.23			1.86872			0.934362	+	0.356325i	$0.115971\pi$
$662$	−26.7859	−	26.7859i	−0.0404620	−	0.0404620i
$663$	261.097	−	261.097i	0.393811	−	0.393811i
$664$		−	78.5087i		−	0.118236i
$665$		0			0
$666$	281.196			0.422217
$667$	1743.51	+	1743.51i	2.61395	+	2.61395i
$668$	−310.886	+	310.886i	−0.465398	+	0.465398i
$669$			342.536i			0.512011i
$670$		0			0
$671$	−156.803			−0.233686
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	350.867	−	350.867i	0.521347	−	0.521347i	−0.396631	−	0.917978i	$-0.629821\pi$
$673$	350.867	−	350.867i	0.521347	−	0.521347i	0.917978	+	0.396631i	$0.129821\pi$
$674$		−	650.063i		−	0.964485i
$675$		0			0
$676$	−94.5391			−0.139851
$677$	721.673	+	721.673i	1.06599	+	1.06599i	0.997663	+	0.0683230i	$0.0217648\pi$
$677$	721.673	+	721.673i	1.06599	+	1.06599i	0.0683230	+	0.997663i	$0.478235\pi$
$678$	316.975	−	316.975i	0.467515	−	0.467515i
$679$		−	331.365i		−	0.488019i
$680$		0			0
$681$	151.441			0.222380
$682$	15.1029	+	15.1029i	0.0221451	+	0.0221451i
$683$	−314.116	+	314.116i	−0.459906	+	0.459906i	−0.898624	−	0.438719i	$-0.855432\pi$
$683$	−314.116	+	314.116i	−0.459906	+	0.459906i	0.438719	+	0.898624i	$0.355432\pi$
$684$		−	222.974i		−	0.325985i
$685$		0			0
$686$	−26.1916			−0.0381802
$687$	178.248	+	178.248i	0.259458	+	0.259458i
$688$	92.1726	−	92.1726i	0.133972	−	0.133972i
$689$		−	669.752i		−	0.972064i
$690$		0			0
$691$	−1255.23			−1.81654			−0.908269	−	0.418387i	$-0.862595\pi$
$691$	−1255.23			−1.81654			−0.908269	+	0.418387i	$0.862595\pi$
$692$	33.1036	+	33.1036i	0.0478376	+	0.0478376i
$693$	−18.6592	+	18.6592i	−0.0269252	+	0.0269252i
$694$			239.351i			0.344887i
$695$		0			0
$696$	−271.141			−0.389570
$697$	135.882	+	135.882i	0.194953	+	0.194953i
$698$	592.030	−	592.030i	0.848180	−	0.848180i
$699$			191.554i			0.274040i
$700$		0			0
$701$	275.772			0.393398			0.196699	−	0.980464i	$-0.436978\pi$
$701$	275.772			0.393398			0.196699	+	0.980464i	$0.436978\pi$
$702$	−57.3299	−	57.3299i	−0.0816666	−	0.0816666i
$703$	1741.65	−	1741.65i	2.47745	−	2.47745i
$704$			26.5967i			0.0377794i
$705$		0			0
$706$	−184.429			−0.261231
$707$	−189.164	−	189.164i	−0.267559	−	0.267559i
$708$	145.226	−	145.226i	0.205122	−	0.205122i
$709$			533.450i			0.752398i	0.926539	+	0.376199i	$0.122769\pi$
$709$			533.450i			0.752398i	−0.926539	+	0.376199i	$0.877231\pi$
$710$		0			0
$711$	289.460			0.407117
$712$	−86.0558	−	86.0558i	−0.120865	−	0.120865i
$713$	−143.106	+	143.106i	−0.200710	+	0.200710i
$714$			125.222i			0.175381i
$715$		0			0
$716$	369.082			0.515478
$717$	−224.137	−	224.137i	−0.312604	−	0.312604i
$718$	−464.557	+	464.557i	−0.647016	+	0.647016i
$719$			260.982i			0.362979i	0.983393	+	0.181490i	$0.0580919\pi$
$719$			260.982i			0.362979i	−0.983393	+	0.181490i	$0.941908\pi$
$720$		0			0
$721$	182.396			0.252977
$722$	−1020.03	−	1020.03i	−1.41279	−	1.41279i
$723$	48.5363	−	48.5363i	0.0671319	−	0.0671319i
$724$		−	147.872i		−	0.204244i
$725$		0			0
$726$	−269.314			−0.370956
$727$	−293.600	−	293.600i	−0.403852	−	0.403852i	0.475736	−	0.879588i	$-0.342182\pi$
$727$	−293.600	−	293.600i	−0.403852	−	0.403852i	−0.879588	+	0.475736i	$0.842182\pi$
$728$	−58.3820	+	58.3820i	−0.0801950	+	0.0801950i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−629.670			−0.861381
$732$	115.530	+	115.530i	0.157827	+	0.157827i
$733$	−416.677	+	416.677i	−0.568455	+	0.568455i	−0.931695	−	0.363241i	$-0.881670\pi$
$733$	−416.677	+	416.677i	−0.568455	+	0.568455i	0.363241	+	0.931695i	$0.381670\pi$
$734$		−	900.510i		−	1.22685i
$735$		0			0
$736$	−252.014			−0.342410
$737$	28.2249	+	28.2249i	0.0382970	+	0.0382970i
$738$	29.8361	−	29.8361i	0.0404283	−	0.0404283i
$739$		−	96.5954i		−	0.130711i	−0.997862	−	0.0653555i	$-0.979182\pi$
$739$		−	96.5954i		−	0.130711i	0.997862	−	0.0653555i	$-0.0208181\pi$
$740$		0			0
$741$	−710.170			−0.958395
$742$	160.607	+	160.607i	0.216451	+	0.216451i
$743$	517.336	−	517.336i	0.696280	−	0.696280i	−0.267326	−	0.963606i	$-0.586140\pi$
$743$	517.336	−	517.336i	0.696280	−	0.696280i	0.963606	+	0.267326i	$0.0861400\pi$
$744$		−	22.2551i		−	0.0299128i
$745$		0			0
$746$	−895.866			−1.20089
$747$	58.8816	+	58.8816i	0.0788240	+	0.0788240i
$748$	90.8466	−	90.8466i	0.121453	−	0.121453i
$749$			41.4672i			0.0553635i
$750$		0			0
$751$	429.736			0.572218			0.286109	−	0.958197i	$-0.407638\pi$
$751$	429.736			0.572218			0.286109	+	0.958197i	$0.407638\pi$
$752$	−25.5259	−	25.5259i	−0.0339441	−	0.0339441i
$753$	−19.5557	+	19.5557i	−0.0259703	+	0.0259703i
$754$			863.583i			1.14534i
$755$		0			0
$756$	27.4955			0.0363696
$757$	−400.880	−	400.880i	−0.529565	−	0.529565i	0.390878	−	0.920443i	$-0.372171\pi$
$757$	−400.880	−	400.880i	−0.529565	−	0.529565i	−0.920443	+	0.390878i	$0.872171\pi$
$758$	200.204	−	200.204i	0.264121	−	0.264121i
$759$			256.536i			0.337992i
$760$		0			0
$761$	−45.5634			−0.0598730			−0.0299365	−	0.999552i	$-0.509531\pi$
$761$	−45.5634			−0.0598730			−0.0299365	+	0.999552i	$0.509531\pi$
$762$	−305.887	−	305.887i	−0.401426	−	0.401426i
$763$	1.87735	−	1.87735i	0.00246049	−	0.00246049i
$764$		−	511.210i		−	0.669123i
$765$		0			0
$766$	521.265			0.680503
$767$	−462.545	−	462.545i	−0.603058	−	0.603058i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			1217.00i			1.58257i	0.611445	+	0.791287i	$0.290588\pi$
$769$			1217.00i			1.58257i	−0.611445	+	0.791287i	$0.709412\pi$
$770$		0			0
$771$	−144.694			−0.187671
$772$	−307.587	−	307.587i	−0.398429	−	0.398429i
$773$	−141.860	+	141.860i	−0.183519	+	0.183519i	−0.792887	−	0.609368i	$-0.791423\pi$
$773$	−141.860	+	141.860i	−0.183519	+	0.183519i	0.609368	+	0.792887i	$0.291423\pi$
$774$			138.259i			0.178629i
$775$		0			0
$776$	354.244			0.456500
$777$	214.767	+	214.767i	0.276406	+	0.276406i
$778$	192.566	−	192.566i	0.247514	−	0.247514i
$779$		−	369.593i		−	0.474445i
$780$		0			0
$781$	−284.840			−0.364712
$782$	860.807	+	860.807i	1.10078	+	1.10078i
$783$	203.356	−	203.356i	0.259713	−	0.259713i
$784$		−	28.0000i		−	0.0357143i
$785$		0			0
$786$	336.769			0.428460
$787$	−41.2990	−	41.2990i	−0.0524765	−	0.0524765i	0.680382	−	0.732858i	$-0.261814\pi$
$787$	−41.2990	−	41.2990i	−0.0524765	−	0.0524765i	−0.732858	+	0.680382i	$0.761814\pi$
$788$	264.142	−	264.142i	0.335205	−	0.335205i
$789$			456.317i			0.578349i
$790$		0			0
$791$	484.187			0.612121
$792$	−19.9475	−	19.9475i	−0.0251863	−	0.0251863i
$793$	367.961	−	367.961i	0.464012	−	0.464012i
$794$			366.512i			0.461602i
$795$		0			0
$796$	447.060			0.561633
$797$	320.603	+	320.603i	0.402262	+	0.402262i	0.879029	−	0.476768i	$-0.158192\pi$
$797$	320.603	+	320.603i	0.402262	+	0.402262i	−0.476768	+	0.879029i	$0.658192\pi$
$798$	170.299	−	170.299i	0.213407	−	0.213407i
$799$			174.379i			0.218246i
$800$		0			0
$801$	129.084			0.161153
$802$	−327.614	−	327.614i	−0.408496	−	0.408496i
$803$	−115.645	+	115.645i	−0.144016	+	0.144016i
$804$		−	41.5911i		−	0.0517302i
$805$		0			0
$806$	−70.8824			−0.0879434
$807$	146.988	+	146.988i	0.182141	+	0.182141i
$808$	202.225	−	202.225i	0.250279	−	0.250279i
$809$			1036.57i			1.28130i	0.767834	+	0.640649i	$0.221335\pi$
$809$			1036.57i			1.28130i	−0.767834	+	0.640649i	$0.778665\pi$
$810$		0			0
$811$	591.042			0.728782			0.364391	−	0.931246i	$-0.381277\pi$
$811$	591.042			0.728782			0.364391	+	0.931246i	$0.381277\pi$
$812$	−207.087	−	207.087i	−0.255034	−	0.255034i
$813$	−560.636	+	560.636i	−0.689589	+	0.689589i
$814$		−	311.621i		−	0.382826i
$815$		0			0
$816$	−133.868			−0.164054
$817$	856.336	+	856.336i	1.04815	+	1.04815i
$818$	−637.257	+	637.257i	−0.779043	+	0.779043i
$819$		−	87.5729i		−	0.106927i
$820$		0			0
$821$	550.566			0.670604			0.335302	−	0.942111i	$-0.391162\pi$
$821$	550.566			0.670604			0.335302	+	0.942111i	$0.391162\pi$
$822$	−171.235	−	171.235i	−0.208316	−	0.208316i
$823$	828.295	−	828.295i	1.00643	−	1.00643i	0.00645489	−	0.999979i	$-0.497945\pi$
$823$	828.295	−	828.295i	1.00643	−	1.00643i	0.999979	−	0.00645489i	$-0.00205467\pi$
$824$			194.990i			0.236638i
$825$		0			0
$826$	221.837			0.268568
$827$	−266.349	−	266.349i	−0.322066	−	0.322066i	0.527493	−	0.849559i	$-0.323132\pi$
$827$	−266.349	−	266.349i	−0.322066	−	0.322066i	−0.849559	+	0.527493i	$0.823132\pi$
$828$	189.010	−	189.010i	0.228273	−	0.228273i
$829$		−	1568.25i		−	1.89174i	−0.324551	−	0.945868i	$-0.605213\pi$
$829$		−	1568.25i		−	1.89174i	0.324551	−	0.945868i	$-0.394787\pi$
$830$		0			0
$831$	−7.31198			−0.00879902
$832$	−62.4129	−	62.4129i	−0.0750155	−	0.0750155i
$833$	−95.6399	+	95.6399i	−0.114814	+	0.114814i
$834$			296.860i			0.355947i
$835$		0			0
$836$	−247.098			−0.295572
$837$	16.6913	+	16.6913i	0.0199418	+	0.0199418i
$838$	332.788	−	332.788i	0.397122	−	0.397122i
$839$		−	660.770i		−	0.787568i	−0.919203	−	0.393784i	$-0.871166\pi$
$839$		−	660.770i		−	0.787568i	0.919203	−	0.393784i	$-0.128834\pi$
$840$		0			0
$841$	−2222.22			−2.64236
$842$	−287.551	−	287.551i	−0.341509	−	0.341509i
$843$	−240.104	+	240.104i	−0.284821	+	0.284821i
$844$		−	244.818i		−	0.290069i
$845$		0			0
$846$	38.2889			0.0452588
$847$	−205.692	−	205.692i	−0.242848	−	0.242848i
$848$	−171.696	+	171.696i	−0.202471	+	0.202471i
$849$		−	553.613i		−	0.652076i
$850$		0			0
$851$	2952.73			3.46971
$852$	209.865	+	209.865i	0.246320	+	0.246320i
$853$	338.010	−	338.010i	0.396261	−	0.396261i	−0.480651	−	0.876912i	$-0.659600\pi$
$853$	338.010	−	338.010i	0.396261	−	0.396261i	0.876912	+	0.480651i	$0.159600\pi$
$854$			176.474i			0.206645i
$855$		0			0
$856$	−44.3303			−0.0517878
$857$	19.5395	+	19.5395i	0.0227999	+	0.0227999i	0.718415	−	0.695615i	$-0.244868\pi$
$857$	19.5395	+	19.5395i	0.0227999	+	0.0227999i	−0.695615	+	0.718415i	$0.744868\pi$
$858$	−63.5328	+	63.5328i	−0.0740475	+	0.0740475i
$859$		−	749.310i		−	0.872305i	−0.899873	−	0.436153i	$-0.856341\pi$
$859$		−	749.310i		−	0.872305i	0.899873	−	0.436153i	$-0.143659\pi$
$860$		0			0
$861$	45.5754			0.0529331
$862$	−321.978	−	321.978i	−0.373524	−	0.373524i
$863$	−937.685	+	937.685i	−1.08654	+	1.08654i	−0.0906593	+	0.995882i	$0.528897\pi$
$863$	−937.685	+	937.685i	−1.08654	+	1.08654i	−0.995882	+	0.0906593i	$0.971103\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−570.087			−0.658300
$867$	103.303	+	103.303i	0.119150	+	0.119150i
$868$	16.9976	−	16.9976i	0.0195825	−	0.0195825i
$869$		−	320.779i		−	0.369136i
$870$		0			0
$871$	−132.468			−0.152087
$872$	2.00697	+	2.00697i	0.00230157	+	0.00230157i
$873$	−265.683	+	265.683i	−0.304333	+	0.304333i
$874$		−	2341.35i		−	2.67889i
$875$		0			0
$876$	170.410			0.194532
$877$	282.933	+	282.933i	0.322615	+	0.322615i	0.849769	−	0.527155i	$-0.176741\pi$
$877$	282.933	+	282.933i	0.322615	+	0.322615i	−0.527155	+	0.849769i	$0.676741\pi$
$878$	−342.297	+	342.297i	−0.389860	+	0.389860i
$879$		−	261.790i		−	0.297827i
$880$		0			0
$881$	1193.56			1.35478			0.677391	−	0.735623i	$-0.263110\pi$
$881$	1193.56			1.35478			0.677391	+	0.735623i	$0.263110\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	−28.7690	+	28.7690i	−0.0325809	+	0.0325809i	−0.723210	−	0.690629i	$-0.757334\pi$
$883$	−28.7690	+	28.7690i	−0.0325809	+	0.0325809i	0.690629	+	0.723210i	$0.257334\pi$
$884$			426.369i			0.482318i
$885$		0			0
$886$	1090.44			1.23075
$887$	774.170	+	774.170i	0.872796	+	0.872796i	0.992776	−	0.119980i	$-0.0382831\pi$
$887$	774.170	+	774.170i	0.872796	+	0.872796i	−0.119980	+	0.992776i	$0.538283\pi$
$888$	−229.596	+	229.596i	−0.258554	+	0.258554i
$889$		−	467.250i		−	0.525590i
$890$		0			0
$891$	29.9213			0.0335817
$892$	−279.679	−	279.679i	−0.313542	−	0.313542i
$893$	237.151	−	237.151i	0.265566	−	0.265566i
$894$			321.112i			0.359186i
$895$		0			0
$896$	29.9333			0.0334077
$897$	−601.998	−	601.998i	−0.671123	−	0.671123i
$898$	65.3316	−	65.3316i	0.0727523	−	0.0727523i
$899$		−	251.428i		−	0.279675i
$900$		0			0
$901$	1172.93			1.30180
$902$	−33.0643	−	33.0643i	−0.0366566	−	0.0366566i
$903$	−105.597	+	105.597i	−0.116940	+	0.116940i
$904$			517.618i			0.572586i
$905$		0			0
$906$	−258.018			−0.284788
$907$	386.610	+	386.610i	0.426252	+	0.426252i	0.887349	−	0.461098i	$-0.152544\pi$
$907$	386.610	+	386.610i	0.426252	+	0.426252i	−0.461098	+	0.887349i	$0.652544\pi$
$908$	−123.651	+	123.651i	−0.136180	+	0.136180i
$909$			303.338i			0.333705i
$910$		0			0
$911$	1028.20			1.12865			0.564324	−	0.825553i	$-0.309137\pi$
$911$	1028.20			1.12865			0.564324	+	0.825553i	$0.309137\pi$
$912$	182.057	+	182.057i	0.199624	+	0.199624i
$913$	65.2523	−	65.2523i	0.0714702	−	0.0714702i
$914$		−	294.662i		−	0.322387i
$915$		0			0
$916$	−291.077			−0.317770
$917$	257.212	+	257.212i	0.280493	+	0.280493i
$918$	100.401	−	100.401i	0.109369	−	0.109369i
$919$			334.758i			0.364263i	0.983274	+	0.182132i	$0.0582997\pi$
$919$			334.758i			0.364263i	−0.983274	+	0.182132i	$0.941700\pi$
$920$		0			0
$921$	414.066			0.449583
$922$	−52.5087	−	52.5087i	−0.0569509	−	0.0569509i
$923$	668.418	−	668.418i	0.724180	−	0.724180i
$924$		−	30.4703i		−	0.0329766i
$925$		0			0
$926$	153.247			0.165494
$927$	−146.242	−	146.242i	−0.157759	−	0.157759i
$928$	221.386	−	221.386i	0.238562	−	0.238562i
$929$			829.100i			0.892465i	0.894917	+	0.446233i	$0.147235\pi$
$929$			829.100i			0.892465i	−0.894917	+	0.446233i	$0.852765\pi$
$930$		0			0
$931$	260.136			0.279416
$932$	−156.403	−	156.403i	−0.167814	−	0.167814i
$933$	225.418	−	225.418i	0.241605	−	0.241605i
$934$		−	108.818i		−	0.116508i
$935$		0			0
$936$	93.6194			0.100021
$937$	602.614	+	602.614i	0.643132	+	0.643132i	0.951324	−	0.308192i	$-0.0997240\pi$
$937$	602.614	+	602.614i	0.643132	+	0.643132i	−0.308192	+	0.951324i	$0.599724\pi$
$938$	31.7657	−	31.7657i	0.0338654	−	0.0338654i
$939$			510.711i			0.543888i
$940$		0			0
$941$	−1339.85			−1.42386			−0.711928	−	0.702252i	$-0.752178\pi$
$941$	−1339.85			−1.42386			−0.711928	+	0.702252i	$0.752178\pi$
$942$	85.1904	+	85.1904i	0.0904356	+	0.0904356i
$943$	313.297	−	313.297i	0.332234	−	0.332234i
$944$			237.154i			0.251222i
$945$		0			0
$946$	153.218			0.161964
$947$	617.006	+	617.006i	0.651537	+	0.651537i	0.953363	−	0.301826i	$-0.0975961\pi$
$947$	617.006	+	617.006i	0.651537	+	0.651537i	−0.301826	+	0.953363i	$0.597596\pi$
$948$	−236.343	+	236.343i	−0.249307	+	0.249307i
$949$		−	542.756i		−	0.571924i
$950$		0			0
$951$	988.876			1.03983
$952$	−102.243	−	102.243i	−0.107398	−	0.107398i
$953$	324.856	−	324.856i	0.340877	−	0.340877i	−0.515820	−	0.856697i	$-0.672513\pi$
$953$	324.856	−	324.856i	0.340877	−	0.340877i	0.856697	+	0.515820i	$0.172513\pi$
$954$		−	257.544i		−	0.269962i
$955$		0			0
$956$	366.014			0.382860
$957$	−225.358	−	225.358i	−0.235484	−	0.235484i
$958$	165.940	−	165.940i	0.173215	−	0.173215i
$959$		−	261.566i		−	0.272749i
$960$		0			0
$961$	−940.363			−0.978525
$962$	731.262	+	731.262i	0.760148	+	0.760148i
$963$	33.2478	−	33.2478i	0.0345252	−	0.0345252i
$964$			79.2595i			0.0822194i
$965$		0			0
$966$	288.718			0.298880
$967$	−834.219	−	834.219i	−0.862688	−	0.862688i	0.128962	−	0.991650i	$-0.458836\pi$
$967$	−834.219	−	834.219i	−0.862688	−	0.862688i	−0.991650	+	0.128962i	$0.958836\pi$
$968$	219.894	−	219.894i	0.227163	−	0.227163i
$969$		−	1243.71i		−	1.28350i
$970$		0			0
$971$	−1357.06			−1.39759			−0.698796	−	0.715321i	$-0.746280\pi$
$971$	−1357.06			−1.39759			−0.698796	+	0.715321i	$0.746280\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	−226.730	+	226.730i	−0.233022	+	0.233022i
$974$			98.4881i			0.101117i
$975$		0			0
$976$	−188.659			−0.193298
$977$	−1099.64	−	1099.64i	−1.12553	−	1.12553i	−0.990895	−	0.134634i	$-0.957014\pi$
$977$	−1099.64	−	1099.64i	−1.12553	−	1.12553i	−0.134634	−	0.990895i	$-0.542986\pi$
$978$	−174.015	+	174.015i	−0.177930	+	0.177930i
$979$		−	143.050i		−	0.146118i
$980$		0			0
$981$	−3.01046			−0.00306877
$982$	−207.513	−	207.513i	−0.211316	−	0.211316i
$983$	−329.200	+	329.200i	−0.334893	+	0.334893i	−0.854441	−	0.519548i	$-0.826100\pi$
$983$	−329.200	+	329.200i	−0.334893	+	0.334893i	0.519548	+	0.854441i	$0.326100\pi$
$984$			48.7222i			0.0495144i
$985$		0			0
$986$	−1512.38			−1.53385
$987$	29.2436	+	29.2436i	0.0296288	+	0.0296288i
$988$	579.852	−	579.852i	0.586894	−	0.586894i
$989$			1451.80i			1.46795i
$990$		0			0
$991$	1117.81			1.12796			0.563978	−	0.825789i	$-0.309270\pi$
$991$	1117.81			1.12796			0.563978	+	0.825789i	$0.309270\pi$
$992$	18.1712	+	18.1712i	0.0183177	+	0.0183177i
$993$	−32.8058	+	32.8058i	−0.0330371	+	0.0330371i
$994$			320.574i			0.322509i
$995$		0			0
$996$	−96.1532			−0.0965393
$997$	−1308.85	−	1308.85i	−1.31278	−	1.31278i	−0.919355	−	0.393428i	$-0.871289\pi$
$997$	−1308.85	−	1308.85i	−1.31278	−	1.31278i	−0.393428	−	0.919355i	$-0.628711\pi$
$998$	−299.711	+	299.711i	−0.300312	+	0.300312i
$999$		−	344.394i		−	0.344739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.h.757.7		16
5.2	odd	4		210.3.l.b.43.3	✓	16
5.3	odd	4	inner	1050.3.l.h.43.7		16
5.4	even	2		210.3.l.b.127.3	yes	16
15.2	even	4		630.3.o.f.253.3		16
15.14	odd	2		630.3.o.f.127.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.3	✓	16	5.2	odd	4
210.3.l.b.127.3	yes	16	5.4	even	2
630.3.o.f.127.3		16	15.14	odd	2
630.3.o.f.253.3		16	15.2	even	4
1050.3.l.h.43.7		16	5.3	odd	4	inner
1050.3.l.h.757.7		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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -3.32459 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.80162 - 7.80162i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(13.6628 + 13.6628i) q^{17} +(3.00000 - 3.00000i) q^{18} -37.1623i q^{19} +4.58258 q^{21} +(-3.32459 - 3.32459i) q^{22} +(31.5017 - 31.5017i) q^{23} +4.89898i q^{24} +15.6032 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +55.3464i q^{29} -4.54280 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.07177 + 4.07177i) q^{33} +27.3257i q^{34} +6.00000 q^{36} +(46.8661 + 46.8661i) q^{37} +(37.1623 - 37.1623i) q^{38} -19.1100i q^{39} +9.94537 q^{41} +(4.58258 + 4.58258i) q^{42} +(-23.0431 + 23.0431i) q^{43} -6.64917i q^{44} +63.0035 q^{46} +(6.38149 + 6.38149i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +33.4670 q^{51} +(15.6032 + 15.6032i) q^{52} +(42.9239 - 42.9239i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-45.5143 - 45.5143i) q^{57} +(-55.3464 + 55.3464i) q^{58} -59.2884i q^{59} +47.1648 q^{61} +(-4.54280 - 4.54280i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} -8.14354 q^{66} +(-8.48975 - 8.48975i) q^{67} +(-27.3257 + 27.3257i) q^{68} -77.1632i q^{69} +85.6769 q^{71} +(6.00000 + 6.00000i) q^{72} +(34.7848 - 34.7848i) q^{73} +93.7322i q^{74} +74.3246 q^{76} +(-6.21973 - 6.21973i) q^{77} +(19.1100 - 19.1100i) q^{78} +96.4868i q^{79} -9.00000 q^{81} +(9.94537 + 9.94537i) q^{82} +(-19.6272 + 19.6272i) q^{83} +9.16515i q^{84} -46.0863 q^{86} +(67.7852 + 67.7852i) q^{87} +(6.64917 - 6.64917i) q^{88} +43.0279i q^{89} +29.1910 q^{91} +(63.0035 + 63.0035i) q^{92} +(-5.56377 + 5.56377i) q^{93} +12.7630i q^{94} -9.79796 q^{96} +(-88.5610 - 88.5610i) q^{97} +(-7.00000 + 7.00000i) q^{98} +9.97376i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) 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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