LMFDB - Embedded newform 1050.3.l.h.43.4

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			43.4
Root			$-3.48873 - 3.48873i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.h.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +15.1276 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-14.6465 - 14.6465i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-15.9948 + 15.9948i) q^{17} +(3.00000 + 3.00000i) q^{18} -2.05015i q^{19} -4.58258 q^{21} +(15.1276 - 15.1276i) q^{22} +(-19.4933 - 19.4933i) q^{23} +4.89898i q^{24} -29.2929 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -33.1037i q^{29} +27.8179 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-18.5275 - 18.5275i) q^{33} +31.9896i q^{34} +6.00000 q^{36} +(30.4627 - 30.4627i) q^{37} +(-2.05015 - 2.05015i) q^{38} +35.8763i q^{39} -26.6233 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-7.89901 - 7.89901i) q^{43} -30.2553i q^{44} -38.9867 q^{46} +(-33.8904 + 33.8904i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +39.1791 q^{51} +(-29.2929 + 29.2929i) q^{52} +(-5.60358 - 5.60358i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-2.51091 + 2.51091i) q^{57} +(-33.1037 - 33.1037i) q^{58} -5.80696i q^{59} -98.2160 q^{61} +(27.8179 - 27.8179i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -37.0550 q^{66} +(-51.6510 + 51.6510i) q^{67} +(31.9896 + 31.9896i) q^{68} +47.7487i q^{69} -120.447 q^{71} +(6.00000 - 6.00000i) q^{72} +(-81.9558 - 81.9558i) q^{73} -60.9253i q^{74} -4.10030 q^{76} +(28.3012 - 28.3012i) q^{77} +(35.8763 + 35.8763i) q^{78} -33.0831i q^{79} -9.00000 q^{81} +(-26.6233 + 26.6233i) q^{82} +(97.0860 + 97.0860i) q^{83} +9.16515i q^{84} -15.7980 q^{86} +(-40.5435 + 40.5435i) q^{87} +(-30.2553 - 30.2553i) q^{88} +34.2132i q^{89} -54.8020 q^{91} +(-38.9867 + 38.9867i) q^{92} +(-34.0699 - 34.0699i) q^{93} +67.7807i q^{94} +9.79796 q^{96} +(-104.393 + 104.393i) q^{97} +(-7.00000 - 7.00000i) q^{98} +45.3829i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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
$11$	15.1276			1.37524			0.687620	−	0.726071i	$-0.258655\pi$
$11$	15.1276			1.37524			0.687620	+	0.726071i	$0.258655\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−14.6465	−	14.6465i	−1.12665	−	1.12665i	−0.990718	−	0.135932i	$-0.956597\pi$
$13$	−14.6465	−	14.6465i	−1.12665	−	1.12665i	−0.135932	−	0.990718i	$-0.543403\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−15.9948	+	15.9948i	−0.940872	+	0.940872i	−0.998347	−	0.0574751i	$-0.981695\pi$
$17$	−15.9948	+	15.9948i	−0.940872	+	0.940872i	0.0574751	+	0.998347i	$0.481695\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$		−	2.05015i		−	0.107903i	−0.998544	−	0.0539513i	$-0.982818\pi$
$19$		−	2.05015i		−	0.107903i	0.998544	−	0.0539513i	$-0.0171816\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	15.1276	−	15.1276i	0.687620	−	0.687620i
$23$	−19.4933	−	19.4933i	−0.847536	−	0.847536i	0.142289	−	0.989825i	$-0.454554\pi$
$23$	−19.4933	−	19.4933i	−0.847536	−	0.847536i	−0.989825	+	0.142289i	$0.954554\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−29.2929			−1.12665
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	33.1037i		−	1.14151i	−0.821122	−	0.570753i	$-0.806651\pi$
$29$		−	33.1037i		−	1.14151i	0.821122	−	0.570753i	$-0.193349\pi$
$30$		0			0
$31$	27.8179			0.897352			0.448676	−	0.893694i	$-0.351896\pi$
$31$	27.8179			0.897352			0.448676	+	0.893694i	$0.351896\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−18.5275	−	18.5275i	−0.561440	−	0.561440i
$34$			31.9896i			0.940872i
$35$		0			0
$36$	6.00000			0.166667
$37$	30.4627	−	30.4627i	0.823315	−	0.823315i	−0.163267	−	0.986582i	$-0.552203\pi$
$37$	30.4627	−	30.4627i	0.823315	−	0.823315i	0.986582	+	0.163267i	$0.0522031\pi$
$38$	−2.05015	−	2.05015i	−0.0539513	−	0.0539513i
$39$			35.8763i			0.919906i
$40$		0			0
$41$	−26.6233			−0.649348			−0.324674	−	0.945826i	$-0.605255\pi$
$41$	−26.6233			−0.649348			−0.324674	+	0.945826i	$0.605255\pi$
$42$	−4.58258	+	4.58258i	−0.109109	+	0.109109i
$43$	−7.89901	−	7.89901i	−0.183698	−	0.183698i	0.609267	−	0.792965i	$-0.291464\pi$
$43$	−7.89901	−	7.89901i	−0.183698	−	0.183698i	−0.792965	+	0.609267i	$0.791464\pi$
$44$		−	30.2553i		−	0.687620i
$45$		0			0
$46$	−38.9867			−0.847536
$47$	−33.8904	+	33.8904i	−0.721072	+	0.721072i	−0.968824	−	0.247752i	$-0.920308\pi$
$47$	−33.8904	+	33.8904i	−0.721072	+	0.721072i	0.247752	+	0.968824i	$0.420308\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	39.1791			0.768219
$52$	−29.2929	+	29.2929i	−0.563325	+	0.563325i
$53$	−5.60358	−	5.60358i	−0.105728	−	0.105728i	0.652264	−	0.757992i	$-0.273819\pi$
$53$	−5.60358	−	5.60358i	−0.105728	−	0.105728i	−0.757992	+	0.652264i	$0.773819\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−7.48331			−0.133631
$57$	−2.51091	+	2.51091i	−0.0440511	+	0.0440511i
$58$	−33.1037	−	33.1037i	−0.570753	−	0.570753i
$59$		−	5.80696i		−	0.0984231i	−0.998788	−	0.0492115i	$-0.984329\pi$
$59$		−	5.80696i		−	0.0984231i	0.998788	−	0.0492115i	$-0.0156709\pi$
$60$		0			0
$61$	−98.2160			−1.61010			−0.805049	−	0.593208i	$-0.797861\pi$
$61$	−98.2160			−1.61010			−0.805049	+	0.593208i	$0.797861\pi$
$62$	27.8179	−	27.8179i	0.448676	−	0.448676i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−37.0550			−0.561440
$67$	−51.6510	+	51.6510i	−0.770910	+	0.770910i	−0.978266	−	0.207356i	$-0.933514\pi$
$67$	−51.6510	+	51.6510i	−0.770910	+	0.770910i	0.207356	+	0.978266i	$0.433514\pi$
$68$	31.9896	+	31.9896i	0.470436	+	0.470436i
$69$			47.7487i			0.692010i
$70$		0			0
$71$	−120.447			−1.69643			−0.848216	−	0.529651i	$-0.822323\pi$
$71$	−120.447			−1.69643			−0.848216	+	0.529651i	$0.822323\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−81.9558	−	81.9558i	−1.12268	−	1.12268i	−0.991337	−	0.131346i	$-0.958070\pi$
$73$	−81.9558	−	81.9558i	−1.12268	−	1.12268i	−0.131346	−	0.991337i	$-0.541930\pi$
$74$		−	60.9253i		−	0.823315i
$75$		0			0
$76$	−4.10030			−0.0539513
$77$	28.3012	−	28.3012i	0.367548	−	0.367548i
$78$	35.8763	+	35.8763i	0.459953	+	0.459953i
$79$		−	33.0831i		−	0.418774i	−0.977833	−	0.209387i	$-0.932853\pi$
$79$		−	33.0831i		−	0.418774i	0.977833	−	0.209387i	$-0.0671468\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−26.6233	+	26.6233i	−0.324674	+	0.324674i
$83$	97.0860	+	97.0860i	1.16971	+	1.16971i	0.982277	+	0.187433i	$0.0600167\pi$
$83$	97.0860	+	97.0860i	1.16971	+	1.16971i	0.187433	+	0.982277i	$0.439983\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	−15.7980			−0.183698
$87$	−40.5435	+	40.5435i	−0.466018	+	0.466018i
$88$	−30.2553	−	30.2553i	−0.343810	−	0.343810i
$89$			34.2132i			0.384418i	0.981354	+	0.192209i	$0.0615652\pi$
$89$			34.2132i			0.384418i	−0.981354	+	0.192209i	$0.938435\pi$
$90$		0			0
$91$	−54.8020			−0.602220
$92$	−38.9867	+	38.9867i	−0.423768	+	0.423768i
$93$	−34.0699	−	34.0699i	−0.366343	−	0.366343i
$94$			67.7807i			0.721072i
$95$		0			0
$96$	9.79796			0.102062
$97$	−104.393	+	104.393i	−1.07622	+	1.07622i	−0.0793705	+	0.996845i	$0.525291\pi$
$97$	−104.393	+	104.393i	−1.07622	+	1.07622i	−0.996845	+	0.0793705i	$0.974709\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$			45.3829i			0.458413i
$100$		0			0
$101$	50.2854			0.497876			0.248938	−	0.968519i	$-0.419919\pi$
$101$	50.2854			0.497876			0.248938	+	0.968519i	$0.419919\pi$
$102$	39.1791	−	39.1791i	0.384109	−	0.384109i
$103$	−7.11461	−	7.11461i	−0.0690739	−	0.0690739i	0.671726	−	0.740800i	$-0.265553\pi$
$103$	−7.11461	−	7.11461i	−0.0690739	−	0.0690739i	−0.740800	+	0.671726i	$0.765553\pi$
$104$			58.5858i			0.563325i
$105$		0			0
$106$	−11.2072			−0.105728
$107$	4.56425	−	4.56425i	0.0426566	−	0.0426566i	−0.685457	−	0.728113i	$-0.740397\pi$
$107$	4.56425	−	4.56425i	0.0426566	−	0.0426566i	0.728113	+	0.685457i	$0.240397\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			58.0783i			0.532829i	0.963859	+	0.266414i	$0.0858389\pi$
$109$			58.0783i			0.532829i	−0.963859	+	0.266414i	$0.914161\pi$
$110$		0			0
$111$	−74.6180			−0.672234
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	−9.58688	−	9.58688i	−0.0848396	−	0.0848396i	0.663413	−	0.748253i	$-0.269107\pi$
$113$	−9.58688	−	9.58688i	−0.0848396	−	0.0848396i	−0.748253	+	0.663413i	$0.769107\pi$
$114$			5.02182i			0.0440511i
$115$		0			0
$116$	−66.2073			−0.570753
$117$	43.9394	−	43.9394i	0.375550	−	0.375550i
$118$	−5.80696	−	5.80696i	−0.0492115	−	0.0492115i
$119$			59.8471i			0.502917i
$120$		0			0
$121$	107.846			0.891286
$122$	−98.2160	+	98.2160i	−0.805049	+	0.805049i
$123$	32.6067	+	32.6067i	0.265095	+	0.265095i
$124$		−	55.6358i		−	0.448676i
$125$		0			0
$126$	11.2250			0.0890871
$127$	140.998	−	140.998i	1.11022	−	1.11022i	0.117097	−	0.993120i	$-0.462641\pi$
$127$	140.998	−	140.998i	1.11022	−	1.11022i	0.993120	−	0.117097i	$-0.0373590\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			19.3485i			0.149989i
$130$		0			0
$131$	184.764			1.41041			0.705205	−	0.709004i	$-0.250855\pi$
$131$	184.764			1.41041			0.705205	+	0.709004i	$0.250855\pi$
$132$	−37.0550	+	37.0550i	−0.280720	+	0.280720i
$133$	−3.83548	−	3.83548i	−0.0288382	−	0.0288382i
$134$			103.302i			0.770910i
$135$		0			0
$136$	63.9793			0.470436
$137$	170.364	−	170.364i	1.24353	−	1.24353i	0.285002	−	0.958527i	$-0.408006\pi$
$137$	170.364	−	170.364i	1.24353	−	1.24353i	0.958527	−	0.285002i	$-0.0919944\pi$
$138$	47.7487	+	47.7487i	0.346005	+	0.346005i
$139$		−	110.608i		−	0.795741i	−0.917442	−	0.397870i	$-0.869749\pi$
$139$		−	110.608i		−	0.795741i	0.917442	−	0.397870i	$-0.130251\pi$
$140$		0			0
$141$	83.0141			0.588753
$142$	−120.447	+	120.447i	−0.848216	+	0.848216i
$143$	−221.566	−	221.566i	−1.54941	−	1.54941i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	−163.912			−1.12268
$147$	−8.57321	+	8.57321i	−0.0583212	+	0.0583212i
$148$	−60.9253	−	60.9253i	−0.411658	−	0.411658i
$149$			150.705i			1.01144i	0.862697	+	0.505721i	$0.168773\pi$
$149$			150.705i			1.01144i	−0.862697	+	0.505721i	$0.831227\pi$
$150$		0			0
$151$	−190.444			−1.26122			−0.630610	−	0.776100i	$-0.717195\pi$
$151$	−190.444			−1.26122			−0.630610	+	0.776100i	$0.717195\pi$
$152$	−4.10030	+	4.10030i	−0.0269756	+	0.0269756i
$153$	−47.9845	−	47.9845i	−0.313624	−	0.313624i
$154$		−	56.6025i		−	0.367548i
$155$		0			0
$156$	71.7527			0.459953
$157$	28.5711	−	28.5711i	0.181981	−	0.181981i	−0.610237	−	0.792219i	$-0.708926\pi$
$157$	28.5711	−	28.5711i	0.181981	−	0.181981i	0.792219	+	0.610237i	$0.208926\pi$
$158$	−33.0831	−	33.0831i	−0.209387	−	0.209387i
$159$			13.7259i			0.0863265i
$160$		0			0
$161$	−72.9374			−0.453027
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	37.2908	+	37.2908i	0.228778	+	0.228778i	0.812182	−	0.583404i	$-0.198280\pi$
$163$	37.2908	+	37.2908i	0.228778	+	0.228778i	−0.583404	+	0.812182i	$0.698280\pi$
$164$			53.2466i			0.324674i
$165$		0			0
$166$	194.172			1.16971
$167$	70.7467	−	70.7467i	0.423633	−	0.423633i	−0.462820	−	0.886453i	$-0.653162\pi$
$167$	70.7467	−	70.7467i	0.423633	−	0.423633i	0.886453	+	0.462820i	$0.153162\pi$
$168$	9.16515	+	9.16515i	0.0545545	+	0.0545545i
$169$			260.037i			1.53868i
$170$		0			0
$171$	6.15045			0.0359675
$172$	−15.7980	+	15.7980i	−0.0918489	+	0.0918489i
$173$	−73.9048	−	73.9048i	−0.427196	−	0.427196i	0.460476	−	0.887672i	$-0.347679\pi$
$173$	−73.9048	−	73.9048i	−0.427196	−	0.427196i	−0.887672	+	0.460476i	$0.847679\pi$
$174$			81.0871i			0.466018i
$175$		0			0
$176$	−60.5106			−0.343810
$177$	−7.11205	+	7.11205i	−0.0401811	+	0.0401811i
$178$	34.2132	+	34.2132i	0.192209	+	0.192209i
$179$		−	280.292i		−	1.56588i	−0.622100	−	0.782938i	$-0.713720\pi$
$179$		−	280.292i		−	1.56588i	0.622100	−	0.782938i	$-0.286280\pi$
$180$		0			0
$181$	−139.086			−0.768430			−0.384215	−	0.923244i	$-0.625528\pi$
$181$	−139.086			−0.768430			−0.384215	+	0.923244i	$0.625528\pi$
$182$	−54.8020	+	54.8020i	−0.301110	+	0.301110i
$183$	120.290	+	120.290i	0.657320	+	0.657320i
$184$			77.9733i			0.423768i
$185$		0			0
$186$	−68.1397			−0.366343
$187$	−241.964	+	241.964i	−1.29392	+	1.29392i
$188$	67.7807	+	67.7807i	0.360536	+	0.360536i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	−231.713			−1.21316			−0.606580	−	0.795023i	$-0.707459\pi$
$191$	−231.713			−1.21316			−0.606580	+	0.795023i	$0.707459\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	148.989	+	148.989i	0.771962	+	0.771962i	0.978449	−	0.206488i	$-0.0662033\pi$
$193$	148.989	+	148.989i	0.771962	+	0.771962i	−0.206488	+	0.978449i	$0.566203\pi$
$194$			208.786i			1.07622i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	255.090	−	255.090i	1.29487	−	1.29487i	0.363135	−	0.931736i	$-0.381706\pi$
$197$	255.090	−	255.090i	1.29487	−	1.29487i	0.931736	−	0.363135i	$-0.118294\pi$
$198$	45.3829	+	45.3829i	0.229207	+	0.229207i
$199$		−	321.154i		−	1.61384i	−0.590660	−	0.806920i	$-0.701133\pi$
$199$		−	321.154i		−	1.61384i	0.590660	−	0.806920i	$-0.298867\pi$
$200$		0			0
$201$	126.518			0.629445
$202$	50.2854	−	50.2854i	0.248938	−	0.248938i
$203$	−61.9313	−	61.9313i	−0.305080	−	0.305080i
$204$		−	78.3583i		−	0.384109i
$205$		0			0
$206$	−14.2292			−0.0690739
$207$	58.4800	−	58.4800i	0.282512	−	0.282512i
$208$	58.5858	+	58.5858i	0.281663	+	0.281663i
$209$		−	31.0139i		−	0.148392i
$210$		0			0
$211$	22.7166			0.107662			0.0538308	−	0.998550i	$-0.482857\pi$
$211$	22.7166			0.107662			0.0538308	+	0.998550i	$0.482857\pi$
$212$	−11.2072	+	11.2072i	−0.0528640	+	0.0528640i
$213$	147.516	+	147.516i	0.692565	+	0.692565i
$214$		−	9.12850i		−	0.0426566i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	52.0426	−	52.0426i	0.239828	−	0.239828i
$218$	58.0783	+	58.0783i	0.266414	+	0.266414i
$219$			200.750i			0.916667i
$220$		0			0
$221$	468.535			2.12007
$222$	−74.6180	+	74.6180i	−0.336117	+	0.336117i
$223$	−158.968	−	158.968i	−0.712863	−	0.712863i	0.254270	−	0.967133i	$-0.418165\pi$
$223$	−158.968	−	158.968i	−0.712863	−	0.712863i	−0.967133	+	0.254270i	$0.918165\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−19.1738			−0.0848396
$227$	52.1650	−	52.1650i	0.229802	−	0.229802i	−0.582808	−	0.812610i	$-0.698046\pi$
$227$	52.1650	−	52.1650i	0.229802	−	0.229802i	0.812610	+	0.582808i	$0.198046\pi$
$228$	5.02182	+	5.02182i	0.0220255	+	0.0220255i
$229$		−	115.486i		−	0.504305i	−0.967688	−	0.252152i	$-0.918862\pi$
$229$		−	115.486i		−	0.504305i	0.967688	−	0.252152i	$-0.0811384\pi$
$230$		0			0
$231$	−69.3236			−0.300102
$232$	−66.2073	+	66.2073i	−0.285376	+	0.285376i
$233$	297.575	+	297.575i	1.27714	+	1.27714i	0.942259	+	0.334885i	$0.108698\pi$
$233$	297.575	+	297.575i	1.27714	+	1.27714i	0.334885	+	0.942259i	$0.391302\pi$
$234$		−	87.8787i		−	0.375550i
$235$		0			0
$236$	−11.6139			−0.0492115
$237$	−40.5184	+	40.5184i	−0.170964	+	0.170964i
$238$	59.8471	+	59.8471i	0.251459	+	0.251459i
$239$		−	136.556i		−	0.571362i	−0.958325	−	0.285681i	$-0.907780\pi$
$239$		−	136.556i		−	0.571362i	0.958325	−	0.285681i	$-0.0922198\pi$
$240$		0			0
$241$	61.0110			0.253157			0.126579	−	0.991957i	$-0.459600\pi$
$241$	61.0110			0.253157			0.126579	+	0.991957i	$0.459600\pi$
$242$	107.846	−	107.846i	0.445643	−	0.445643i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			196.432i			0.805049i
$245$		0			0
$246$	65.2134			0.265095
$247$	−30.0274	+	30.0274i	−0.121568	+	0.121568i
$248$	−55.6358	−	55.6358i	−0.224338	−	0.224338i
$249$		−	237.811i		−	0.955064i
$250$		0			0
$251$	215.934			0.860295			0.430147	−	0.902759i	$-0.358462\pi$
$251$	215.934			0.860295			0.430147	+	0.902759i	$0.358462\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	−294.888	−	294.888i	−1.16557	−	1.16557i
$254$		−	281.995i		−	1.11022i
$255$		0			0
$256$	16.0000			0.0625000
$257$	144.579	−	144.579i	0.562564	−	0.562564i	−0.367471	−	0.930035i	$-0.619776\pi$
$257$	144.579	−	144.579i	0.562564	−	0.562564i	0.930035	+	0.367471i	$0.119776\pi$
$258$	19.3485	+	19.3485i	0.0749944	+	0.0749944i
$259$		−	113.981i		−	0.440081i
$260$		0			0
$261$	99.3110			0.380502
$262$	184.764	−	184.764i	0.705205	−	0.705205i
$263$	0.389678	+	0.389678i	0.00148167	+	0.00148167i	0.707847	−	0.706366i	$-0.249667\pi$
$263$	0.389678	+	0.389678i	0.00148167	+	0.00148167i	−0.706366	+	0.707847i	$0.749667\pi$
$264$			74.1100i			0.280720i
$265$		0			0
$266$	−7.67096			−0.0288382
$267$	41.9025	−	41.9025i	0.156938	−	0.156938i
$268$	103.302	+	103.302i	0.385455	+	0.385455i
$269$		−	272.956i		−	1.01471i	−0.861738	−	0.507353i	$-0.830624\pi$
$269$		−	272.956i		−	1.01471i	0.861738	−	0.507353i	$-0.169376\pi$
$270$		0			0
$271$	−176.708			−0.652058			−0.326029	−	0.945360i	$-0.605711\pi$
$271$	−176.708			−0.652058			−0.326029	+	0.945360i	$0.605711\pi$
$272$	63.9793	−	63.9793i	0.235218	−	0.235218i
$273$	67.1185	+	67.1185i	0.245855	+	0.245855i
$274$		−	340.727i		−	1.24353i
$275$		0			0
$276$	95.4974			0.346005
$277$	203.152	−	203.152i	0.733402	−	0.733402i	−0.237890	−	0.971292i	$-0.576456\pi$
$277$	203.152	−	203.152i	0.733402	−	0.733402i	0.971292	+	0.237890i	$0.0764559\pi$
$278$	−110.608	−	110.608i	−0.397870	−	0.397870i
$279$			83.4538i			0.299117i
$280$		0			0
$281$	368.543			1.31154			0.655770	−	0.754961i	$-0.272344\pi$
$281$	368.543			1.31154			0.655770	+	0.754961i	$0.272344\pi$
$282$	83.0141	−	83.0141i	0.294376	−	0.294376i
$283$	−385.601	−	385.601i	−1.36255	−	1.36255i	−0.870659	−	0.491888i	$-0.836307\pi$
$283$	−385.601	−	385.601i	−1.36255	−	1.36255i	−0.491888	−	0.870659i	$-0.663693\pi$
$284$			240.893i			0.848216i
$285$		0			0
$286$	−443.133			−1.54941
$287$	−49.8076	+	49.8076i	−0.173546	+	0.173546i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	222.669i		−	0.770480i
$290$		0			0
$291$	255.709			0.878726
$292$	−163.912	+	163.912i	−0.561341	+	0.561341i
$293$	241.653	+	241.653i	0.824754	+	0.824754i	0.986786	−	0.162032i	$-0.0518048\pi$
$293$	241.653	+	241.653i	0.824754	+	0.824754i	−0.162032	+	0.986786i	$0.551805\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−121.851			−0.411658
$297$	55.5825	−	55.5825i	0.187147	−	0.187147i
$298$	150.705	+	150.705i	0.505721	+	0.505721i
$299$			571.016i			1.90975i
$300$		0			0
$301$	−29.5554			−0.0981907
$302$	−190.444	+	190.444i	−0.630610	+	0.630610i
$303$	−61.5868	−	61.5868i	−0.203257	−	0.203257i
$304$			8.20060i			0.0269756i
$305$		0			0
$306$	−95.9689			−0.313624
$307$	−315.513	+	315.513i	−1.02773	+	1.02773i	−0.0281252	+	0.999604i	$0.508954\pi$
$307$	−315.513	+	315.513i	−1.02773	+	1.02773i	−0.999604	+	0.0281252i	$0.991046\pi$
$308$	−56.6025	−	56.6025i	−0.183774	−	0.183774i
$309$			17.4272i			0.0563986i
$310$		0			0
$311$	84.6545			0.272201			0.136101	−	0.990695i	$-0.456543\pi$
$311$	84.6545			0.272201			0.136101	+	0.990695i	$0.456543\pi$
$312$	71.7527	−	71.7527i	0.229976	−	0.229976i
$313$	189.513	+	189.513i	0.605474	+	0.605474i	0.941760	−	0.336286i	$-0.109171\pi$
$313$	189.513	+	189.513i	0.605474	+	0.605474i	−0.336286	+	0.941760i	$0.609171\pi$
$314$		−	57.1422i		−	0.181981i
$315$		0			0
$316$	−66.1663			−0.209387
$317$	21.9357	−	21.9357i	0.0691977	−	0.0691977i	−0.671661	−	0.740859i	$-0.734419\pi$
$317$	21.9357	−	21.9357i	0.0691977	−	0.0691977i	0.740859	+	0.671661i	$0.234419\pi$
$318$	13.7259	+	13.7259i	0.0431633	+	0.0431633i
$319$		−	500.780i		−	1.56984i
$320$		0			0
$321$	−11.1801			−0.0348289
$322$	−72.9374	+	72.9374i	−0.226514	+	0.226514i
$323$	32.7918	+	32.7918i	0.101523	+	0.101523i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	74.5817			0.228778
$327$	71.1311	−	71.1311i	0.217526	−	0.217526i
$328$	53.2466	+	53.2466i	0.162337	+	0.162337i
$329$			126.806i			0.385429i
$330$		0			0
$331$	165.937			0.501320			0.250660	−	0.968075i	$-0.419352\pi$
$331$	165.937			0.501320			0.250660	+	0.968075i	$0.419352\pi$
$332$	194.172	−	194.172i	0.584855	−	0.584855i
$333$	91.3880	+	91.3880i	0.274438	+	0.274438i
$334$		−	141.493i		−	0.423633i
$335$		0			0
$336$	18.3303			0.0545545
$337$	−73.8705	+	73.8705i	−0.219200	+	0.219200i	−0.808161	−	0.588961i	$-0.799537\pi$
$337$	−73.8705	+	73.8705i	−0.219200	+	0.219200i	0.588961	+	0.808161i	$0.299537\pi$
$338$	260.037	+	260.037i	0.769340	+	0.769340i
$339$			23.4830i			0.0692713i
$340$		0			0
$341$	420.820			1.23408
$342$	6.15045	−	6.15045i	0.0179838	−	0.0179838i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			31.5960i			0.0918489i
$345$		0			0
$346$	−147.810			−0.427196
$347$	−31.2699	+	31.2699i	−0.0901149	+	0.0901149i	−0.750727	−	0.660612i	$-0.770297\pi$
$347$	−31.2699	+	31.2699i	−0.0901149	+	0.0901149i	0.660612	+	0.750727i	$0.270297\pi$
$348$	81.0871	+	81.0871i	0.233009	+	0.233009i
$349$			546.387i			1.56558i	0.622287	+	0.782789i	$0.286204\pi$
$349$			546.387i			1.56558i	−0.622287	+	0.782789i	$0.713796\pi$
$350$		0			0
$351$	−107.629			−0.306635
$352$	−60.5106	+	60.5106i	−0.171905	+	0.171905i
$353$	184.331	+	184.331i	0.522184	+	0.522184i	0.918231	−	0.396046i	$-0.129618\pi$
$353$	184.331	+	184.331i	0.522184	+	0.522184i	−0.396046	+	0.918231i	$0.629618\pi$
$354$			14.2241i			0.0401811i
$355$		0			0
$356$	68.4265			0.192209
$357$	73.2975	−	73.2975i	0.205315	−	0.205315i
$358$	−280.292	−	280.292i	−0.782938	−	0.782938i
$359$		−	319.232i		−	0.889226i	−0.895723	−	0.444613i	$-0.853341\pi$
$359$		−	319.232i		−	0.889226i	0.895723	−	0.444613i	$-0.146659\pi$
$360$		0			0
$361$	356.797			0.988357
$362$	−139.086	+	139.086i	−0.384215	+	0.384215i
$363$	−132.083	−	132.083i	−0.363866	−	0.363866i
$364$			109.604i			0.301110i
$365$		0			0
$366$	240.579			0.657320
$367$	−116.440	+	116.440i	−0.317276	+	0.317276i	−0.847720	−	0.530444i	$-0.822025\pi$
$367$	−116.440	+	116.440i	−0.317276	+	0.317276i	0.530444	+	0.847720i	$0.322025\pi$
$368$	77.9733	+	77.9733i	0.211884	+	0.211884i
$369$		−	79.8698i		−	0.216449i
$370$		0			0
$371$	−20.9667			−0.0565140
$372$	−68.1397	+	68.1397i	−0.183171	+	0.183171i
$373$	−380.962	−	380.962i	−1.02135	−	1.02135i	−0.999767	−	0.0215784i	$-0.993131\pi$
$373$	−380.962	−	380.962i	−1.02135	−	1.02135i	−0.0215784	−	0.999767i	$-0.506869\pi$
$374$			483.928i			1.29392i
$375$		0			0
$376$	135.561			0.360536
$377$	−484.851	+	484.851i	−1.28608	+	1.28608i
$378$	−13.7477	−	13.7477i	−0.0363696	−	0.0363696i
$379$		−	189.542i		−	0.500111i	−0.968231	−	0.250056i	$-0.919551\pi$
$379$		−	189.542i		−	0.500111i	0.968231	−	0.250056i	$-0.0804489\pi$
$380$		0			0
$381$	−345.372			−0.906489
$382$	−231.713	+	231.713i	−0.606580	+	0.606580i
$383$	306.102	+	306.102i	0.799222	+	0.799222i	0.982973	−	0.183751i	$-0.0588239\pi$
$383$	306.102	+	306.102i	0.799222	+	0.799222i	−0.183751	+	0.982973i	$0.558824\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	297.977			0.771962
$387$	23.6970	−	23.6970i	0.0612326	−	0.0612326i
$388$	208.786	+	208.786i	0.538108	+	0.538108i
$389$		−	316.187i		−	0.812819i	−0.913691	−	0.406410i	$-0.866781\pi$
$389$		−	316.187i		−	0.812819i	0.913691	−	0.406410i	$-0.133219\pi$
$390$		0			0
$391$	623.585			1.59485
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$	−226.288	−	226.288i	−0.575797	−	0.575797i
$394$		−	510.179i		−	1.29487i
$395$		0			0
$396$	90.7659			0.229207
$397$	134.126	−	134.126i	0.337849	−	0.337849i	−0.517709	−	0.855557i	$-0.673215\pi$
$397$	134.126	−	134.126i	0.337849	−	0.337849i	0.855557	+	0.517709i	$0.173215\pi$
$398$	−321.154	−	321.154i	−0.806920	−	0.806920i
$399$			9.39496i			0.0235463i
$400$		0			0
$401$	−504.024			−1.25692			−0.628459	−	0.777842i	$-0.716314\pi$
$401$	−504.024			−1.25692			−0.628459	+	0.777842i	$0.716314\pi$
$402$	126.518	−	126.518i	0.314723	−	0.314723i
$403$	−407.434	−	407.434i	−1.01100	−	1.01100i
$404$		−	100.571i		−	0.248938i
$405$		0			0
$406$	−123.863			−0.305080
$407$	460.828	−	460.828i	1.13226	−	1.13226i
$408$	−78.3583	−	78.3583i	−0.192055	−	0.192055i
$409$		−	112.495i		−	0.275048i	−0.990498	−	0.137524i	$-0.956086\pi$
$409$		−	112.495i		−	0.275048i	0.990498	−	0.137524i	$-0.0439145\pi$
$410$		0			0
$411$	−417.304			−1.01534
$412$	−14.2292	+	14.2292i	−0.0345370	+	0.0345370i
$413$	−10.8638	−	10.8638i	−0.0263047	−	0.0263047i
$414$		−	116.960i		−	0.282512i
$415$		0			0
$416$	117.172			0.281663
$417$	−135.466	+	135.466i	−0.324860	+	0.324860i
$418$	−31.0139	−	31.0139i	−0.0741960	−	0.0741960i
$419$		−	224.563i		−	0.535950i	−0.963426	−	0.267975i	$-0.913645\pi$
$419$		−	224.563i		−	0.535950i	0.963426	−	0.267975i	$-0.0863545\pi$
$420$		0			0
$421$	474.635			1.12740			0.563699	−	0.825980i	$-0.309378\pi$
$421$	474.635			1.12740			0.563699	+	0.825980i	$0.309378\pi$
$422$	22.7166	−	22.7166i	0.0538308	−	0.0538308i
$423$	−101.671	−	101.671i	−0.240357	−	0.240357i
$424$			22.4143i			0.0528640i
$425$		0			0
$426$	295.033			0.692565
$427$	−183.745	+	183.745i	−0.430317	+	0.430317i
$428$	−9.12850	−	9.12850i	−0.0213283	−	0.0213283i
$429$			542.724i			1.26509i
$430$		0			0
$431$	142.798			0.331317			0.165659	−	0.986183i	$-0.447025\pi$
$431$	142.798			0.331317			0.165659	+	0.986183i	$0.447025\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	226.490	+	226.490i	0.523072	+	0.523072i	0.918498	−	0.395426i	$-0.129403\pi$
$433$	226.490	+	226.490i	0.523072	+	0.523072i	−0.395426	+	0.918498i	$0.629403\pi$
$434$		−	104.085i		−	0.239828i
$435$		0			0
$436$	116.157			0.266414
$437$	−39.9642	+	39.9642i	−0.0914514	+	0.0914514i
$438$	200.750	+	200.750i	0.458333	+	0.458333i
$439$		−	231.354i		−	0.527003i	−0.964659	−	0.263502i	$-0.915123\pi$
$439$		−	231.354i		−	0.527003i	0.964659	−	0.263502i	$-0.0848774\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	468.535	−	468.535i	1.06003	−	1.06003i
$443$	291.498	+	291.498i	0.658008	+	0.658008i	0.954909	−	0.296900i	$-0.0959529\pi$
$443$	291.498	+	291.498i	0.658008	+	0.658008i	−0.296900	+	0.954909i	$0.595953\pi$
$444$			149.236i			0.336117i
$445$		0			0
$446$	−317.937			−0.712863
$447$	184.575	−	184.575i	0.412919	−	0.412919i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$		−	186.920i		−	0.416303i	−0.978097	−	0.208152i	$-0.933255\pi$
$449$		−	186.920i		−	0.416303i	0.978097	−	0.208152i	$-0.0667448\pi$
$450$		0			0
$451$	−402.747			−0.893010
$452$	−19.1738	+	19.1738i	−0.0424198	+	0.0424198i
$453$	233.245	+	233.245i	0.514891	+	0.514891i
$454$		−	104.330i		−	0.229802i
$455$		0			0
$456$	10.0436			0.0220255
$457$	358.683	−	358.683i	0.784865	−	0.784865i	−0.195782	−	0.980647i	$-0.562725\pi$
$457$	358.683	−	358.683i	0.784865	−	0.784865i	0.980647	+	0.195782i	$0.0627246\pi$
$458$	−115.486	−	115.486i	−0.252152	−	0.252152i
$459$			117.537i			0.256073i
$460$		0			0
$461$	−178.973			−0.388227			−0.194113	−	0.980979i	$-0.562183\pi$
$461$	−178.973			−0.388227			−0.194113	+	0.980979i	$0.562183\pi$
$462$	−69.3236	+	69.3236i	−0.150051	+	0.150051i
$463$	−244.313	−	244.313i	−0.527675	−	0.527675i	0.392204	−	0.919878i	$-0.371713\pi$
$463$	−244.313	−	244.313i	−0.527675	−	0.527675i	−0.919878	+	0.392204i	$0.871713\pi$
$464$			132.415i			0.285376i
$465$		0			0
$466$	595.149			1.27714
$467$	−165.494	+	165.494i	−0.354377	+	0.354377i	−0.861735	−	0.507358i	$-0.830622\pi$
$467$	−165.494	+	165.494i	−0.354377	+	0.354377i	0.507358	+	0.861735i	$0.330622\pi$
$468$	−87.8787	−	87.8787i	−0.187775	−	0.187775i
$469$			193.260i			0.412069i
$470$		0			0
$471$	−69.9846			−0.148587
$472$	−11.6139	+	11.6139i	−0.0246058	+	0.0246058i
$473$	−119.493	−	119.493i	−0.252629	−	0.252629i
$474$			81.0368i			0.170964i
$475$		0			0
$476$	119.694			0.251459
$477$	16.8107	−	16.8107i	0.0352427	−	0.0352427i
$478$	−136.556	−	136.556i	−0.285681	−	0.285681i
$479$			326.343i			0.681300i	0.940190	+	0.340650i	$0.110647\pi$
$479$			326.343i			0.681300i	−0.940190	+	0.340650i	$0.889353\pi$
$480$		0			0
$481$	−892.340			−1.85518
$482$	61.0110	−	61.0110i	0.126579	−	0.126579i
$483$	89.3297	+	89.3297i	0.184948	+	0.184948i
$484$		−	215.691i		−	0.445643i
$485$		0			0
$486$	22.0454			0.0453609
$487$	373.708	−	373.708i	0.767367	−	0.767367i	−0.210275	−	0.977642i	$-0.567436\pi$
$487$	373.708	−	373.708i	0.767367	−	0.767367i	0.977642	+	0.210275i	$0.0674360\pi$
$488$	196.432	+	196.432i	0.402525	+	0.402525i
$489$		−	91.3435i		−	0.186797i
$490$		0			0
$491$	418.263			0.851859			0.425930	−	0.904756i	$-0.359947\pi$
$491$	418.263			0.851859			0.425930	+	0.904756i	$0.359947\pi$
$492$	65.2134	−	65.2134i	0.132548	−	0.132548i
$493$	529.487	+	529.487i	1.07401	+	1.07401i
$494$			60.0548i			0.121568i
$495$		0			0
$496$	−111.272			−0.224338
$497$	−225.335	+	225.335i	−0.453390	+	0.453390i
$498$	−237.811	−	237.811i	−0.477532	−	0.477532i
$499$			541.732i			1.08563i	0.839851	+	0.542817i	$0.182642\pi$
$499$			541.732i			1.08563i	−0.839851	+	0.542817i	$0.817358\pi$
$500$		0			0
$501$	−173.293			−0.345895
$502$	215.934	−	215.934i	0.430147	−	0.430147i
$503$	419.289	+	419.289i	0.833578	+	0.833578i	0.988004	−	0.154427i	$-0.0493531\pi$
$503$	419.289	+	419.289i	0.833578	+	0.833578i	−0.154427	+	0.988004i	$0.549353\pi$
$504$		−	22.4499i		−	0.0445435i
$505$		0			0
$506$	−589.776			−1.16557
$507$	318.479	−	318.479i	0.628164	−	0.628164i
$508$	−281.995	−	281.995i	−0.555109	−	0.555109i
$509$		−	340.522i		−	0.669002i	−0.942395	−	0.334501i	$-0.891432\pi$
$509$		−	340.522i		−	0.669002i	0.942395	−	0.334501i	$-0.108568\pi$
$510$		0			0
$511$	−306.651			−0.600099
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−7.53273	−	7.53273i	−0.0146837	−	0.0146837i
$514$		−	289.158i		−	0.562564i
$515$		0			0
$516$	38.6971			0.0749944
$517$	−512.681	+	512.681i	−0.991647	+	0.991647i
$518$	−113.981	−	113.981i	−0.220040	−	0.220040i
$519$			181.029i			0.348804i
$520$		0			0
$521$	−507.014			−0.973155			−0.486578	−	0.873637i	$-0.661755\pi$
$521$	−507.014			−0.973155			−0.486578	+	0.873637i	$0.661755\pi$
$522$	99.3110	−	99.3110i	0.190251	−	0.190251i
$523$	286.897	+	286.897i	0.548561	+	0.548561i	0.926024	−	0.377464i	$-0.123204\pi$
$523$	286.897	+	286.897i	0.548561	+	0.548561i	−0.377464	+	0.926024i	$0.623204\pi$
$524$		−	369.527i		−	0.705205i
$525$		0			0
$526$	0.779357			0.00148167
$527$	−444.943	+	444.943i	−0.844294	+	0.844294i
$528$	74.1100	+	74.1100i	0.140360	+	0.140360i
$529$			230.980i			0.436635i
$530$		0			0
$531$	17.4209			0.0328077
$532$	−7.67096	+	7.67096i	−0.0144191	+	0.0144191i
$533$	389.937	+	389.937i	0.731588	+	0.731588i
$534$		−	83.8050i		−	0.156938i
$535$		0			0
$536$	206.604			0.385455
$537$	−343.286	+	343.286i	−0.639266	+	0.639266i
$538$	−272.956	−	272.956i	−0.507353	−	0.507353i
$539$		−	105.894i		−	0.196463i
$540$		0			0
$541$	−604.754			−1.11784			−0.558922	−	0.829220i	$-0.688785\pi$
$541$	−604.754			−1.11784			−0.558922	+	0.829220i	$0.688785\pi$
$542$	−176.708	+	176.708i	−0.326029	+	0.326029i
$543$	170.345	+	170.345i	0.313710	+	0.313710i
$544$		−	127.959i		−	0.235218i
$545$		0			0
$546$	134.237			0.245855
$547$	−298.464	+	298.464i	−0.545637	+	0.545637i	−0.925176	−	0.379539i	$-0.876083\pi$
$547$	−298.464	+	298.464i	−0.545637	+	0.545637i	0.379539	+	0.925176i	$0.376083\pi$
$548$	−340.727	−	340.727i	−0.621765	−	0.621765i
$549$		−	294.648i		−	0.536699i
$550$		0			0
$551$	−67.8675			−0.123171
$552$	95.4974	−	95.4974i	0.173003	−	0.173003i
$553$	−61.8929	−	61.8929i	−0.111922	−	0.111922i
$554$		−	406.304i		−	0.733402i
$555$		0			0
$556$	−221.216			−0.397870
$557$	−392.034	+	392.034i	−0.703831	+	0.703831i	−0.965231	−	0.261400i	$-0.915816\pi$
$557$	−392.034	+	392.034i	−0.703831	+	0.703831i	0.261400	+	0.965231i	$0.415816\pi$
$558$	83.4538	+	83.4538i	0.149559	+	0.149559i
$559$			231.385i			0.413926i
$560$		0			0
$561$	592.688			1.05649
$562$	368.543	−	368.543i	0.655770	−	0.655770i
$563$	−575.129	−	575.129i	−1.02154	−	1.02154i	−0.999763	−	0.0217803i	$-0.993067\pi$
$563$	−575.129	−	575.129i	−1.02154	−	1.02154i	−0.0217803	−	0.999763i	$-0.506933\pi$
$564$		−	166.028i		−	0.294376i
$565$		0			0
$566$	−771.201			−1.36255
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	240.893	+	240.893i	0.424108	+	0.424108i
$569$		−	193.452i		−	0.339986i	−0.985445	−	0.169993i	$-0.945625\pi$
$569$		−	193.452i		−	0.339986i	0.985445	−	0.169993i	$-0.0543745\pi$
$570$		0			0
$571$	117.456			0.205703			0.102851	−	0.994697i	$-0.467203\pi$
$571$	117.456			0.205703			0.102851	+	0.994697i	$0.467203\pi$
$572$	−443.133	+	443.133i	−0.774707	+	0.774707i
$573$	283.790	+	283.790i	0.495270	+	0.495270i
$574$			99.6152i			0.173546i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	703.423	−	703.423i	1.21910	−	1.21910i	0.251157	−	0.967946i	$-0.419189\pi$
$577$	703.423	−	703.423i	1.21910	−	1.21910i	0.967946	−	0.251157i	$-0.0808111\pi$
$578$	−222.669	−	222.669i	−0.385240	−	0.385240i
$579$		−	364.946i		−	0.630304i
$580$		0			0
$581$	363.262			0.625236
$582$	255.709	−	255.709i	0.439363	−	0.439363i
$583$	−84.7690	−	84.7690i	−0.145401	−	0.145401i
$584$			327.823i			0.561341i
$585$		0			0
$586$	483.306			0.824754
$587$	180.492	−	180.492i	0.307483	−	0.307483i	−0.536450	−	0.843932i	$-0.680235\pi$
$587$	180.492	−	180.492i	0.307483	−	0.307483i	0.843932	+	0.536450i	$0.180235\pi$
$588$	17.1464	+	17.1464i	0.0291606	+	0.0291606i
$589$		−	57.0309i		−	0.0968267i
$590$		0			0
$591$	−624.840			−1.05726
$592$	−121.851	+	121.851i	−0.205829	+	0.205829i
$593$	701.554	+	701.554i	1.18306	+	1.18306i	0.978948	+	0.204111i	$0.0654304\pi$
$593$	701.554	+	701.554i	1.18306	+	1.18306i	0.204111	+	0.978948i	$0.434570\pi$
$594$		−	111.165i		−	0.187147i
$595$		0			0
$596$	301.410			0.505721
$597$	−393.332	+	393.332i	−0.658848	+	0.658848i
$598$	571.016	+	571.016i	0.954877	+	0.954877i
$599$			349.739i			0.583871i	0.956438	+	0.291935i	$0.0942992\pi$
$599$			349.739i			0.583871i	−0.956438	+	0.291935i	$0.905701\pi$
$600$		0			0
$601$	−227.029			−0.377752			−0.188876	−	0.982001i	$-0.560484\pi$
$601$	−227.029			−0.377752			−0.188876	+	0.982001i	$0.560484\pi$
$602$	−29.5554	+	29.5554i	−0.0490953	+	0.0490953i
$603$	−154.953	−	154.953i	−0.256970	−	0.256970i
$604$			380.888i			0.630610i
$605$		0			0
$606$	−123.174			−0.203257
$607$	−13.0530	+	13.0530i	−0.0215042	+	0.0215042i	−0.717777	−	0.696273i	$-0.754840\pi$
$607$	−13.0530	+	13.0530i	−0.0215042	+	0.0215042i	0.696273	+	0.717777i	$0.254840\pi$
$608$	8.20060	+	8.20060i	0.0134878	+	0.0134878i
$609$			151.700i			0.249097i
$610$		0			0
$611$	992.747			1.62479
$612$	−95.9689	+	95.9689i	−0.156812	+	0.156812i
$613$	301.420	+	301.420i	0.491713	+	0.491713i	0.908846	−	0.417133i	$-0.136965\pi$
$613$	301.420	+	301.420i	0.491713	+	0.491713i	−0.417133	+	0.908846i	$0.636965\pi$
$614$			631.026i			1.02773i
$615$		0			0
$616$	−113.205			−0.183774
$617$	676.069	−	676.069i	1.09574	−	1.09574i	0.100832	−	0.994904i	$-0.467850\pi$
$617$	676.069	−	676.069i	1.09574	−	1.09574i	0.994904	−	0.100832i	$-0.0321503\pi$
$618$	17.4272	+	17.4272i	0.0281993	+	0.0281993i
$619$			180.575i			0.291721i	0.989305	+	0.145860i	$0.0465950\pi$
$619$			180.575i			0.291721i	−0.989305	+	0.145860i	$0.953405\pi$
$620$		0			0
$621$	−143.246			−0.230670
$622$	84.6545	−	84.6545i	0.136101	−	0.136101i
$623$	64.0071	+	64.0071i	0.102740	+	0.102740i
$624$		−	143.505i		−	0.229976i
$625$		0			0
$626$	379.027			0.605474
$627$	−37.9842	+	37.9842i	−0.0605808	+	0.0605808i
$628$	−57.1422	−	57.1422i	−0.0909907	−	0.0909907i
$629$			974.490i			1.54927i
$630$		0			0
$631$	−778.962			−1.23449			−0.617244	−	0.786771i	$-0.711751\pi$
$631$	−778.962			−1.23449			−0.617244	+	0.786771i	$0.711751\pi$
$632$	−66.1663	+	66.1663i	−0.104693	+	0.104693i
$633$	−27.8220	−	27.8220i	−0.0439527	−	0.0439527i
$634$		−	43.8713i		−	0.0691977i
$635$		0			0
$636$	27.4518			0.0431633
$637$	−102.525	+	102.525i	−0.160950	+	0.160950i
$638$	−500.780	−	500.780i	−0.784922	−	0.784922i
$639$		−	361.340i		−	0.565477i
$640$		0			0
$641$	773.498			1.20671			0.603353	−	0.797475i	$-0.293831\pi$
$641$	773.498			1.20671			0.603353	+	0.797475i	$0.293831\pi$
$642$	−11.1801	+	11.1801i	−0.0174145	+	0.0174145i
$643$	−544.963	−	544.963i	−0.847532	−	0.847532i	0.142292	−	0.989825i	$-0.454553\pi$
$643$	−544.963	−	544.963i	−0.847532	−	0.847532i	−0.989825	+	0.142292i	$0.954553\pi$
$644$			145.875i			0.226514i
$645$		0			0
$646$	65.5835			0.101523
$647$	654.936	−	654.936i	1.01227	−	1.01227i	0.0123424	−	0.999924i	$-0.496071\pi$
$647$	654.936	−	654.936i	1.01227	−	1.01227i	0.999924	−	0.0123424i	$-0.00392881\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$		−	87.8457i		−	0.135355i
$650$		0			0
$651$	−127.478			−0.195818
$652$	74.5817	−	74.5817i	0.114389	−	0.114389i
$653$	504.090	+	504.090i	0.771960	+	0.771960i	0.978449	−	0.206489i	$-0.0662038\pi$
$653$	504.090	+	504.090i	0.771960	+	0.771960i	−0.206489	+	0.978449i	$0.566204\pi$
$654$		−	142.262i		−	0.217526i
$655$		0			0
$656$	106.493			0.162337
$657$	245.868	−	245.868i	0.374228	−	0.374228i
$658$	126.806	+	126.806i	0.192715	+	0.192715i
$659$			726.533i			1.10248i	0.834347	+	0.551239i	$0.185845\pi$
$659$			726.533i			1.10248i	−0.834347	+	0.551239i	$0.814155\pi$
$660$		0			0
$661$	1149.24			1.73865			0.869323	−	0.494245i	$-0.164555\pi$
$661$	1149.24			1.73865			0.869323	+	0.494245i	$0.164555\pi$
$662$	165.937	−	165.937i	0.250660	−	0.250660i
$663$	−573.835	−	573.835i	−0.865514	−	0.865514i
$664$		−	388.344i		−	0.584855i
$665$		0			0
$666$	182.776			0.274438
$667$	−645.301	+	645.301i	−0.967467	+	0.967467i
$668$	−141.493	−	141.493i	−0.211816	−	0.211816i
$669$			389.391i			0.582050i
$670$		0			0
$671$	−1485.78			−2.21427
$672$	18.3303	−	18.3303i	0.0272772	−	0.0272772i
$673$	−743.671	−	743.671i	−1.10501	−	1.10501i	−0.993797	−	0.111212i	$-0.964527\pi$
$673$	−743.671	−	743.671i	−1.10501	−	1.10501i	−0.111212	−	0.993797i	$-0.535473\pi$
$674$			147.741i			0.219200i
$675$		0			0
$676$	520.074			0.769340
$677$	182.111	−	182.111i	0.268997	−	0.268997i	−0.559699	−	0.828696i	$-0.689083\pi$
$677$	182.111	−	182.111i	0.268997	−	0.268997i	0.828696	+	0.559699i	$0.189083\pi$
$678$	23.4830	+	23.4830i	0.0346356	+	0.0346356i
$679$			390.603i			0.575261i
$680$		0			0
$681$	−127.778			−0.187632
$682$	420.820	−	420.820i	0.617038	−	0.617038i
$683$	−309.149	−	309.149i	−0.452634	−	0.452634i	0.443594	−	0.896228i	$-0.353703\pi$
$683$	−309.149	−	309.149i	−0.452634	−	0.452634i	−0.896228	+	0.443594i	$0.853703\pi$
$684$		−	12.3009i		−	0.0179838i
$685$		0			0
$686$	−26.1916			−0.0381802
$687$	−141.441	+	141.441i	−0.205882	+	0.205882i
$688$	31.5960	+	31.5960i	0.0459245	+	0.0459245i
$689$			164.145i			0.238237i
$690$		0			0
$691$	−634.866			−0.918764			−0.459382	−	0.888239i	$-0.651929\pi$
$691$	−634.866			−0.918764			−0.459382	+	0.888239i	$0.651929\pi$
$692$	−147.810	+	147.810i	−0.213598	+	0.213598i
$693$	84.9037	+	84.9037i	0.122516	+	0.122516i
$694$			62.5397i			0.0901149i
$695$		0			0
$696$	162.174			0.233009
$697$	425.835	−	425.835i	0.610953	−	0.610953i
$698$	546.387	+	546.387i	0.782789	+	0.782789i
$699$		−	728.906i		−	1.04278i
$700$		0			0
$701$	863.013			1.23112			0.615559	−	0.788091i	$-0.288930\pi$
$701$	863.013			1.23112			0.615559	+	0.788091i	$0.288930\pi$
$702$	−107.629	+	107.629i	−0.153318	+	0.153318i
$703$	−62.4530	−	62.4530i	−0.0888379	−	0.0888379i
$704$			121.021i			0.171905i
$705$		0			0
$706$	368.662			0.522184
$707$	94.0754	−	94.0754i	0.133063	−	0.133063i
$708$	14.2241	+	14.2241i	0.0200905	+	0.0200905i
$709$			653.419i			0.921607i	0.887502	+	0.460803i	$0.152439\pi$
$709$			653.419i			0.921607i	−0.887502	+	0.460803i	$0.847561\pi$
$710$		0			0
$711$	99.2494			0.139591
$712$	68.4265	−	68.4265i	0.0961046	−	0.0961046i
$713$	−542.264	−	542.264i	−0.760539	−	0.760539i
$714$		−	146.595i		−	0.205315i
$715$		0			0
$716$	−560.583			−0.782938
$717$	−167.246	+	167.246i	−0.233258	+	0.233258i
$718$	−319.232	−	319.232i	−0.444613	−	0.444613i
$719$			961.796i			1.33769i	0.743404	+	0.668843i	$0.233210\pi$
$719$			961.796i			1.33769i	−0.743404	+	0.668843i	$0.766790\pi$
$720$		0			0
$721$	−26.6204			−0.0369216
$722$	356.797	−	356.797i	0.494179	−	0.494179i
$723$	−74.7229	−	74.7229i	−0.103351	−	0.103351i
$724$			278.172i			0.384215i
$725$		0			0
$726$	−264.167			−0.363866
$727$	−948.990	+	948.990i	−1.30535	+	1.30535i	−0.380618	+	0.924733i	$0.624289\pi$
$727$	−948.990	+	948.990i	−1.30535	+	1.30535i	−0.924733	+	0.380618i	$0.875711\pi$
$728$	109.604	+	109.604i	0.150555	+	0.150555i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	252.686			0.345672
$732$	240.579	−	240.579i	0.328660	−	0.328660i
$733$	−731.489	−	731.489i	−0.997938	−	0.997938i	0.00205981	−	0.999998i	$-0.499344\pi$
$733$	−731.489	−	731.489i	−0.997938	−	0.997938i	−0.999998	+	0.00205981i	$0.999344\pi$
$734$			232.880i			0.317276i
$735$		0			0
$736$	155.947			0.211884
$737$	−781.357	+	781.357i	−1.06019	+	1.06019i
$738$	−79.8698	−	79.8698i	−0.108225	−	0.108225i
$739$		−	33.8430i		−	0.0457956i	−0.999738	−	0.0228978i	$-0.992711\pi$
$739$		−	33.8430i		−	0.0457956i	0.999738	−	0.0228978i	$-0.00728924\pi$
$740$		0			0
$741$	73.5518			0.0992602
$742$	−20.9667	+	20.9667i	−0.0282570	+	0.0282570i
$743$	−39.7475	−	39.7475i	−0.0534959	−	0.0534959i	0.679853	−	0.733349i	$-0.262044\pi$
$743$	−39.7475	−	39.7475i	−0.0534959	−	0.0534959i	−0.733349	+	0.679853i	$0.762044\pi$
$744$			136.279i			0.183171i
$745$		0			0
$746$	−761.924			−1.02135
$747$	−291.258	+	291.258i	−0.389903	+	0.389903i
$748$	483.928	+	483.928i	0.646962	+	0.646962i
$749$		−	17.0779i		−	0.0228009i
$750$		0			0
$751$	578.927			0.770874			0.385437	−	0.922734i	$-0.374051\pi$
$751$	578.927			0.770874			0.385437	+	0.922734i	$0.374051\pi$
$752$	135.561	−	135.561i	0.180268	−	0.180268i
$753$	−264.464	−	264.464i	−0.351214	−	0.351214i
$754$			969.702i			1.28608i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	−114.632	+	114.632i	−0.151429	+	0.151429i	−0.778756	−	0.627327i	$-0.784149\pi$
$757$	−114.632	+	114.632i	−0.151429	+	0.151429i	0.627327	+	0.778756i	$0.284149\pi$
$758$	−189.542	−	189.542i	−0.250056	−	0.250056i
$759$			722.326i			0.951681i
$760$		0			0
$761$	−87.5262			−0.115015			−0.0575073	−	0.998345i	$-0.518315\pi$
$761$	−87.5262			−0.115015			−0.0575073	+	0.998345i	$0.518315\pi$
$762$	−345.372	+	345.372i	−0.453245	+	0.453245i
$763$	108.655	+	108.655i	0.142404	+	0.142404i
$764$			463.427i			0.606580i
$765$		0			0
$766$	612.204			0.799222
$767$	−85.0514	+	85.0514i	−0.110888	+	0.110888i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			780.679i			1.01519i	0.861596	+	0.507594i	$0.169465\pi$
$769$			780.679i			1.01519i	−0.861596	+	0.507594i	$0.830535\pi$
$770$		0			0
$771$	−354.144			−0.459331
$772$	297.977	−	297.977i	0.385981	−	0.385981i
$773$	−692.751	−	692.751i	−0.896186	−	0.896186i	0.0989107	−	0.995096i	$-0.468464\pi$
$773$	−692.751	−	692.751i	−0.896186	−	0.896186i	−0.995096	+	0.0989107i	$0.968464\pi$
$774$		−	47.3941i		−	0.0612326i
$775$		0			0
$776$	417.572			0.538108
$777$	−139.597	+	139.597i	−0.179662	+	0.179662i
$778$	−316.187	−	316.187i	−0.406410	−	0.406410i
$779$			54.5817i			0.0700664i
$780$		0			0
$781$	−1822.07			−2.33300
$782$	623.585	−	623.585i	0.797423	−	0.797423i
$783$	−121.631	−	121.631i	−0.155339	−	0.155339i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	−452.577			−0.575797
$787$	−505.691	+	505.691i	−0.642556	+	0.642556i	−0.951183	−	0.308627i	$-0.900130\pi$
$787$	−505.691	+	505.691i	−0.642556	+	0.642556i	0.308627	+	0.951183i	$0.400130\pi$
$788$	−510.179	−	510.179i	−0.647436	−	0.647436i
$789$		−	0.954513i		−	0.00120978i
$790$		0			0
$791$	−35.8708			−0.0453487
$792$	90.7659	−	90.7659i	0.114603	−	0.114603i
$793$	1438.52	+	1438.52i	1.81402	+	1.81402i
$794$		−	268.252i		−	0.337849i
$795$		0			0
$796$	−642.309			−0.806920
$797$	−221.290	+	221.290i	−0.277654	+	0.277654i	−0.832172	−	0.554518i	$-0.812903\pi$
$797$	−221.290	+	221.290i	−0.277654	+	0.277654i	0.554518	+	0.832172i	$0.312903\pi$
$798$	9.39496	+	9.39496i	0.0117731	+	0.0117731i
$799$		−	1084.14i		−	1.35687i
$800$		0			0
$801$	−102.640			−0.128139
$802$	−504.024	+	504.024i	−0.628459	+	0.628459i
$803$	−1239.80	−	1239.80i	−1.54396	−	1.54396i
$804$		−	253.037i		−	0.314723i
$805$		0			0
$806$	−814.868			−1.01100
$807$	−334.301	+	334.301i	−0.414252	+	0.414252i
$808$	−100.571	−	100.571i	−0.124469	−	0.124469i
$809$		−	322.881i		−	0.399112i	−0.979886	−	0.199556i	$-0.936050\pi$
$809$		−	322.881i		−	0.399112i	0.979886	−	0.199556i	$-0.0639500\pi$
$810$		0			0
$811$	−1239.53			−1.52840			−0.764199	−	0.644981i	$-0.776865\pi$
$811$	−1239.53			−1.52840			−0.764199	+	0.644981i	$0.776865\pi$
$812$	−123.863	+	123.863i	−0.152540	+	0.152540i
$813$	216.422	+	216.422i	0.266202	+	0.266202i
$814$		−	921.657i		−	1.13226i
$815$		0			0
$816$	−156.717			−0.192055
$817$	−16.1941	+	16.1941i	−0.0198215	+	0.0198215i
$818$	−112.495	−	112.495i	−0.137524	−	0.137524i
$819$		−	164.406i		−	0.200740i
$820$		0			0
$821$	−887.758			−1.08131			−0.540657	−	0.841243i	$-0.681824\pi$
$821$	−887.758			−1.08131			−0.540657	+	0.841243i	$0.681824\pi$
$822$	−417.304	+	417.304i	−0.507669	+	0.507669i
$823$	905.171	+	905.171i	1.09984	+	1.09984i	0.994428	+	0.105414i	$0.0336169\pi$
$823$	905.171	+	905.171i	1.09984	+	1.09984i	0.105414	+	0.994428i	$0.466383\pi$
$824$			28.4585i			0.0345370i
$825$		0			0
$826$	−21.7277			−0.0263047
$827$	−752.036	+	752.036i	−0.909354	+	0.909354i	−0.996220	−	0.0868659i	$-0.972315\pi$
$827$	−752.036	+	752.036i	−0.909354	+	0.909354i	0.0868659	+	0.996220i	$0.472315\pi$
$828$	−116.960	−	116.960i	−0.141256	−	0.141256i
$829$		−	1043.36i		−	1.25858i	−0.777172	−	0.629288i	$-0.783347\pi$
$829$		−	1043.36i		−	1.25858i	0.777172	−	0.629288i	$-0.216653\pi$
$830$		0			0
$831$	−497.619			−0.598820
$832$	117.172	−	117.172i	0.140831	−	0.140831i
$833$	111.964	+	111.964i	0.134410	+	0.134410i
$834$			270.933i			0.324860i
$835$		0			0
$836$	−62.0279			−0.0741960
$837$	102.210	−	102.210i	0.122114	−	0.122114i
$838$	−224.563	−	224.563i	−0.267975	−	0.267975i
$839$		−	28.1225i		−	0.0335190i	−0.999860	−	0.0167595i	$-0.994665\pi$
$839$		−	28.1225i		−	0.0335190i	0.999860	−	0.0167595i	$-0.00533497\pi$
$840$		0			0
$841$	−254.852			−0.303035
$842$	474.635	−	474.635i	0.563699	−	0.563699i
$843$	−451.371	−	451.371i	−0.535434	−	0.535434i
$844$		−	45.4332i		−	0.0538308i
$845$		0			0
$846$	−203.342			−0.240357
$847$	201.761	−	201.761i	0.238206	−	0.238206i
$848$	22.4143	+	22.4143i	0.0264320	+	0.0264320i
$849$			944.525i			1.11251i
$850$		0			0
$851$	−1187.64			−1.39558
$852$	295.033	−	295.033i	0.346283	−	0.346283i
$853$	285.266	+	285.266i	0.334427	+	0.334427i	0.854265	−	0.519838i	$-0.174008\pi$
$853$	285.266	+	285.266i	0.334427	+	0.334427i	−0.519838	+	0.854265i	$0.674008\pi$
$854$			367.491i			0.430317i
$855$		0			0
$856$	−18.2570			−0.0213283
$857$	307.011	−	307.011i	0.358239	−	0.358239i	−0.504924	−	0.863164i	$-0.668480\pi$
$857$	307.011	−	307.011i	0.358239	−	0.358239i	0.863164	+	0.504924i	$0.168480\pi$
$858$	542.724	+	542.724i	0.632546	+	0.632546i
$859$		−	875.499i		−	1.01921i	−0.860409	−	0.509604i	$-0.829792\pi$
$859$		−	875.499i		−	1.01921i	0.860409	−	0.509604i	$-0.170208\pi$
$860$		0			0
$861$	122.003			0.141699
$862$	142.798	−	142.798i	0.165659	−	0.165659i
$863$	−642.774	−	642.774i	−0.744814	−	0.744814i	0.228686	−	0.973500i	$-0.426557\pi$
$863$	−642.774	−	642.774i	−0.744814	−	0.744814i	−0.973500	+	0.228686i	$0.926557\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	452.980			0.523072
$867$	−272.712	+	272.712i	−0.314547	+	0.314547i
$868$	−104.085	−	104.085i	−0.119914	−	0.119914i
$869$		−	500.470i		−	0.575915i
$870$		0			0
$871$	1513.01			1.73709
$872$	116.157	−	116.157i	0.133207	−	0.133207i
$873$	−313.179	−	313.179i	−0.358739	−	0.358739i
$874$			79.9285i			0.0914514i
$875$		0			0
$876$	401.500			0.458333
$877$	−943.109	+	943.109i	−1.07538	+	1.07538i	−0.0784638	+	0.996917i	$0.525001\pi$
$877$	−943.109	+	943.109i	−1.07538	+	1.07538i	−0.996917	+	0.0784638i	$0.974999\pi$
$878$	−231.354	−	231.354i	−0.263502	−	0.263502i
$879$		−	591.926i		−	0.673408i
$880$		0			0
$881$	−422.894			−0.480016			−0.240008	−	0.970771i	$-0.577150\pi$
$881$	−422.894			−0.480016			−0.240008	+	0.970771i	$0.577150\pi$
$882$	21.0000	−	21.0000i	0.0238095	−	0.0238095i
$883$	104.376	+	104.376i	0.118206	+	0.118206i	0.763736	−	0.645529i	$-0.223363\pi$
$883$	104.376	+	104.376i	0.118206	+	0.118206i	−0.645529	+	0.763736i	$0.723363\pi$
$884$		−	937.069i		−	1.06003i
$885$		0			0
$886$	582.995			0.658008
$887$	−530.292	+	530.292i	−0.597849	+	0.597849i	−0.939740	−	0.341891i	$-0.888933\pi$
$887$	−530.292	+	530.292i	−0.597849	+	0.597849i	0.341891	+	0.939740i	$0.388933\pi$
$888$	149.236	+	149.236i	0.168059	+	0.168059i
$889$		−	527.565i		−	0.593436i
$890$		0			0
$891$	−136.149			−0.152804
$892$	−317.937	+	317.937i	−0.356431	+	0.356431i
$893$	69.4803	+	69.4803i	0.0778055	+	0.0778055i
$894$		−	369.150i		−	0.412919i
$895$		0			0
$896$	29.9333			0.0334077
$897$	699.349	−	699.349i	0.779654	−	0.779654i
$898$	−186.920	−	186.920i	−0.208152	−	0.208152i
$899$		−	920.875i		−	1.02433i
$900$		0			0
$901$	179.257			0.198953
$902$	−402.747	+	402.747i	−0.446505	+	0.446505i
$903$	36.1978	+	36.1978i	0.0400862	+	0.0400862i
$904$			38.3475i			0.0424198i
$905$		0			0
$906$	466.491			0.514891
$907$	460.614	−	460.614i	0.507844	−	0.507844i	−0.406020	−	0.913864i	$-0.633084\pi$
$907$	460.614	−	460.614i	0.507844	−	0.507844i	0.913864	+	0.406020i	$0.133084\pi$
$908$	−104.330	−	104.330i	−0.114901	−	0.114901i
$909$			150.856i			0.165959i
$910$		0			0
$911$	1095.00			1.20198			0.600990	−	0.799257i	$-0.294773\pi$
$911$	1095.00			1.20198			0.600990	+	0.799257i	$0.294773\pi$
$912$	10.0436	−	10.0436i	0.0110128	−	0.0110128i
$913$	1468.68	+	1468.68i	1.60863	+	1.60863i
$914$		−	717.367i		−	0.784865i
$915$		0			0
$916$	−230.972			−0.252152
$917$	345.661	−	345.661i	0.376948	−	0.376948i
$918$	117.537	+	117.537i	0.128036	+	0.128036i
$919$			981.230i			1.06772i	0.845574	+	0.533858i	$0.179258\pi$
$919$			981.230i			1.06772i	−0.845574	+	0.533858i	$0.820742\pi$
$920$		0			0
$921$	772.846			0.839138
$922$	−178.973	+	178.973i	−0.194113	+	0.194113i
$923$	1764.12	+	1764.12i	1.91128	+	1.91128i
$924$			138.647i			0.150051i
$925$		0			0
$926$	−488.627			−0.527675
$927$	21.3438	−	21.3438i	0.0230246	−	0.0230246i
$928$	132.415	+	132.415i	0.142688	+	0.142688i
$929$		−	907.859i		−	0.977244i	−0.872496	−	0.488622i	$-0.837500\pi$
$929$		−	907.859i		−	0.977244i	0.872496	−	0.488622i	$-0.162500\pi$
$930$		0			0
$931$	−14.3510			−0.0154147
$932$	595.149	−	595.149i	0.638572	−	0.638572i
$933$	−103.680	−	103.680i	−0.111126	−	0.111126i
$934$			330.988i			0.354377i
$935$		0			0
$936$	−175.757			−0.187775
$937$	1133.74	−	1133.74i	1.20997	−	1.20997i	0.238937	−	0.971035i	$-0.423201\pi$
$937$	1133.74	−	1133.74i	1.20997	−	1.20997i	0.971035	−	0.238937i	$-0.0767990\pi$
$938$	193.260	+	193.260i	0.206034	+	0.206034i
$939$		−	464.211i		−	0.494367i
$940$		0			0
$941$	−1246.83			−1.32500			−0.662501	−	0.749061i	$-0.730505\pi$
$941$	−1246.83			−1.32500			−0.662501	+	0.749061i	$0.730505\pi$
$942$	−69.9846	+	69.9846i	−0.0742936	+	0.0742936i
$943$	518.976	+	518.976i	0.550346	+	0.550346i
$944$			23.2278i			0.0246058i
$945$		0			0
$946$	−238.987			−0.252629
$947$	−435.731	+	435.731i	−0.460117	+	0.460117i	−0.898694	−	0.438577i	$-0.855483\pi$
$947$	−435.731	+	435.731i	−0.460117	+	0.460117i	0.438577	+	0.898694i	$0.355483\pi$
$948$	81.0368	+	81.0368i	0.0854819	+	0.0854819i
$949$			2400.72i			2.52974i
$950$		0			0
$951$	−53.7312			−0.0564996
$952$	119.694	−	119.694i	0.125729	−	0.125729i
$953$	−1133.89	−	1133.89i	−1.18981	−	1.18981i	−0.977120	−	0.212687i	$-0.931778\pi$
$953$	−1133.89	−	1133.89i	−1.18981	−	1.18981i	−0.212687	−	0.977120i	$-0.568222\pi$
$954$		−	33.6215i		−	0.0352427i
$955$		0			0
$956$	−273.111			−0.285681
$957$	−613.328	+	613.328i	−0.640886	+	0.640886i
$958$	326.343	+	326.343i	0.340650	+	0.340650i
$959$		−	637.442i		−	0.664694i
$960$		0			0
$961$	−187.163			−0.194759
$962$	−892.340	+	892.340i	−0.927588	+	0.927588i
$963$	13.6928	+	13.6928i	0.0142189	+	0.0142189i
$964$		−	122.022i		−	0.126579i
$965$		0			0
$966$	178.659			0.184948
$967$	1229.34	−	1229.34i	1.27129	−	1.27129i	0.325882	−	0.945411i	$-0.394339\pi$
$967$	1229.34	−	1229.34i	1.27129	−	1.27129i	0.945411	−	0.325882i	$-0.105661\pi$
$968$	−215.691	−	215.691i	−0.222821	−	0.222821i
$969$		−	80.3231i		−	0.0828928i
$970$		0			0
$971$	−990.708			−1.02030			−0.510148	−	0.860086i	$-0.670410\pi$
$971$	−990.708			−1.02030			−0.510148	+	0.860086i	$0.670410\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−206.928	−	206.928i	−0.212671	−	0.212671i
$974$		−	747.415i		−	0.767367i
$975$		0			0
$976$	392.864			0.402525
$977$	−295.891	+	295.891i	−0.302857	+	0.302857i	−0.842131	−	0.539273i	$-0.818699\pi$
$977$	−295.891	+	295.891i	−0.302857	+	0.302857i	0.539273	+	0.842131i	$0.318699\pi$
$978$	−91.3435	−	91.3435i	−0.0933983	−	0.0933983i
$979$			517.566i			0.528668i
$980$		0			0
$981$	−174.235			−0.177610
$982$	418.263	−	418.263i	0.425930	−	0.425930i
$983$	−859.585	−	859.585i	−0.874451	−	0.874451i	0.118503	−	0.992954i	$-0.462191\pi$
$983$	−859.585	−	859.585i	−0.874451	−	0.874451i	−0.992954	+	0.118503i	$0.962191\pi$
$984$		−	130.427i		−	0.132548i
$985$		0			0
$986$	1058.97			1.07401
$987$	155.305	−	155.305i	0.157351	−	0.157351i
$988$	60.0548	+	60.0548i	0.0607842	+	0.0607842i
$989$			307.956i			0.311381i
$990$		0			0
$991$	−866.595			−0.874465			−0.437233	−	0.899348i	$-0.644041\pi$
$991$	−866.595			−0.874465			−0.437233	+	0.899348i	$0.644041\pi$
$992$	−111.272	+	111.272i	−0.112169	+	0.112169i
$993$	−203.231	−	203.231i	−0.204663	−	0.204663i
$994$			450.670i			0.453390i
$995$		0			0
$996$	−475.622			−0.477532
$997$	251.901	−	251.901i	0.252659	−	0.252659i	−0.569401	−	0.822060i	$-0.692825\pi$
$997$	251.901	−	251.901i	0.252659	−	0.252659i	0.822060	+	0.569401i	$0.192825\pi$
$998$	541.732	+	541.732i	0.542817	+	0.542817i
$999$		−	223.854i		−	0.224078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.h.43.4		16
5.2	odd	4	inner	1050.3.l.h.757.4		16
5.3	odd	4		210.3.l.b.127.6	yes	16
5.4	even	2		210.3.l.b.43.6	✓	16
15.8	even	4		630.3.o.f.127.5		16
15.14	odd	2		630.3.o.f.253.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.6	✓	16	5.4	even	2
210.3.l.b.127.6	yes	16	5.3	odd	4
630.3.o.f.127.5		16	15.8	even	4
630.3.o.f.253.5		16	15.14	odd	2
1050.3.l.h.43.4		16	1.1	even	1	trivial
1050.3.l.h.757.4		16	5.2	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +15.1276 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-14.6465 - 14.6465i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-15.9948 + 15.9948i) q^{17} +(3.00000 + 3.00000i) q^{18} -2.05015i q^{19} -4.58258 q^{21} +(15.1276 - 15.1276i) q^{22} +(-19.4933 - 19.4933i) q^{23} +4.89898i q^{24} -29.2929 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -33.1037i q^{29} +27.8179 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-18.5275 - 18.5275i) q^{33} +31.9896i q^{34} +6.00000 q^{36} +(30.4627 - 30.4627i) q^{37} +(-2.05015 - 2.05015i) q^{38} +35.8763i q^{39} -26.6233 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-7.89901 - 7.89901i) q^{43} -30.2553i q^{44} -38.9867 q^{46} +(-33.8904 + 33.8904i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +39.1791 q^{51} +(-29.2929 + 29.2929i) q^{52} +(-5.60358 - 5.60358i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(-2.51091 + 2.51091i) q^{57} +(-33.1037 - 33.1037i) q^{58} -5.80696i q^{59} -98.2160 q^{61} +(27.8179 - 27.8179i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -37.0550 q^{66} +(-51.6510 + 51.6510i) q^{67} +(31.9896 + 31.9896i) q^{68} +47.7487i q^{69} -120.447 q^{71} +(6.00000 - 6.00000i) q^{72} +(-81.9558 - 81.9558i) q^{73} -60.9253i q^{74} -4.10030 q^{76} +(28.3012 - 28.3012i) q^{77} +(35.8763 + 35.8763i) q^{78} -33.0831i q^{79} -9.00000 q^{81} +(-26.6233 + 26.6233i) q^{82} +(97.0860 + 97.0860i) q^{83} +9.16515i q^{84} -15.7980 q^{86} +(-40.5435 + 40.5435i) q^{87} +(-30.2553 - 30.2553i) q^{88} +34.2132i q^{89} -54.8020 q^{91} +(-38.9867 + 38.9867i) q^{92} +(-34.0699 - 34.0699i) q^{93} +67.7807i q^{94} +9.79796 q^{96} +(-104.393 + 104.393i) q^{97} +(-7.00000 - 7.00000i) q^{98} +45.3829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) 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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