LMFDB - Embedded newform 210.3.l.b.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(43,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, 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("210.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.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:	$5.72208555157$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.6
Root			$5.71348 + 5.71348i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.20256 + 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.20256 + 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.69129 - 2.28617i) q^{10} +15.1276 q^{11} +(2.44949 + 2.44949i) q^{12} +(14.6465 - 14.6465i) q^{13} +3.74166i q^{14} +(2.79998 + 8.19513i) q^{15} -4.00000 q^{16} +(15.9948 + 15.9948i) q^{17} +(-3.00000 + 3.00000i) q^{18} +2.05015i q^{19} +(-8.97747 - 4.40512i) q^{20} -4.58258 q^{21} +(-15.1276 - 15.1276i) q^{22} +(19.4933 - 19.4933i) q^{23} -4.89898i q^{24} +(-15.2975 - 19.7734i) q^{25} -29.2929 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +33.1037i q^{29} +(5.39515 - 10.9951i) q^{30} +27.8179 q^{31} +(4.00000 + 4.00000i) q^{32} +(18.5275 - 18.5275i) q^{33} -31.9896i q^{34} +(12.5183 - 4.27704i) q^{35} +6.00000 q^{36} +(-30.4627 - 30.4627i) q^{37} +(2.05015 - 2.05015i) q^{38} -35.8763i q^{39} +(4.57235 + 13.3826i) q^{40} -26.6233 q^{41} +(4.58258 + 4.58258i) q^{42} +(7.89901 - 7.89901i) q^{43} +30.2553i q^{44} +(13.4662 + 6.60768i) q^{45} -38.9867 q^{46} +(33.8904 + 33.8904i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-4.47595 + 35.0709i) q^{50} +39.1791 q^{51} +(29.2929 + 29.2929i) q^{52} +(5.60358 - 5.60358i) q^{53} +7.34847i q^{54} +(-33.3195 + 67.9040i) q^{55} -7.48331 q^{56} +(2.51091 + 2.51091i) q^{57} +(33.1037 - 33.1037i) q^{58} +5.80696i q^{59} +(-16.3903 + 5.59996i) q^{60} -98.2160 q^{61} +(-27.8179 - 27.8179i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(33.4843 + 98.0037i) q^{65} -37.0550 q^{66} +(51.6510 + 51.6510i) q^{67} +(-31.9896 + 31.9896i) q^{68} -47.7487i q^{69} +(-16.7953 - 8.24122i) q^{70} -120.447 q^{71} +(-6.00000 - 6.00000i) q^{72} +(81.9558 - 81.9558i) q^{73} +60.9253i q^{74} +(-42.9529 - 5.48190i) q^{75} -4.10030 q^{76} +(-28.3012 - 28.3012i) q^{77} +(-35.8763 + 35.8763i) q^{78} +33.0831i q^{79} +(8.81024 - 17.9549i) q^{80} -9.00000 q^{81} +(26.6233 + 26.6233i) q^{82} +(-97.0860 + 97.0860i) q^{83} -9.16515i q^{84} +(-107.026 + 36.5669i) q^{85} -15.7980 q^{86} +(40.5435 + 40.5435i) q^{87} +(30.2553 - 30.2553i) q^{88} -34.2132i q^{89} +(-6.85852 - 20.0739i) q^{90} -54.8020 q^{91} +(38.9867 + 38.9867i) q^{92} +(34.0699 - 34.0699i) q^{93} -67.7807i q^{94} +(-9.20257 - 4.51558i) q^{95} +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} - 16 q^{5} + 32 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$5$	−2.20256	+	4.48873i	−0.440512	+	0.897747i
$5$	−2.20256	+	4.48873i	−0.440512	+	0.897747i
$6$	−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
$10$	6.69129	−	2.28617i	0.669129	−	0.228617i
$11$	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	0.135932	−	0.990718i	$-0.456597\pi$
$13$	14.6465	−	14.6465i	1.12665	−	1.12665i	0.990718	−	0.135932i	$-0.0434028\pi$
$14$			3.74166i			0.267261i
$15$	2.79998	+	8.19513i	0.186665	+	0.546342i
$16$	−4.00000			−0.250000
$17$	15.9948	+	15.9948i	0.940872	+	0.940872i	0.998347	−	0.0574751i	$-0.0183050\pi$
$17$	15.9948	+	15.9948i	0.940872	+	0.940872i	−0.0574751	+	0.998347i	$0.518305\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			2.05015i			0.107903i	0.998544	+	0.0539513i	$0.0171816\pi$
$19$			2.05015i			0.107903i	−0.998544	+	0.0539513i	$0.982818\pi$
$20$	−8.97747	−	4.40512i	−0.448873	−	0.220256i
$21$	−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	$-0.545446\pi$
$23$	19.4933	−	19.4933i	0.847536	−	0.847536i	0.989825	+	0.142289i	$0.0454462\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−15.2975	−	19.7734i	−0.611898	−	0.790936i
$26$	−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	$0.193349\pi$
$29$			33.1037i			1.14151i	−0.821122	+	0.570753i	$0.806651\pi$
$30$	5.39515	−	10.9951i	0.179838	−	0.366504i
$31$	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
$35$	12.5183	−	4.27704i	0.357665	−	0.122201i
$36$	6.00000			0.166667
$37$	−30.4627	−	30.4627i	−0.823315	−	0.823315i	0.163267	−	0.986582i	$-0.447797\pi$
$37$	−30.4627	−	30.4627i	−0.823315	−	0.823315i	−0.986582	+	0.163267i	$0.947797\pi$
$38$	2.05015	−	2.05015i	0.0539513	−	0.0539513i
$39$		−	35.8763i		−	0.919906i
$40$	4.57235	+	13.3826i	0.114309	+	0.334565i
$41$	−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	$-0.708536\pi$
$43$	7.89901	−	7.89901i	0.183698	−	0.183698i	0.792965	+	0.609267i	$0.208536\pi$
$44$			30.2553i			0.687620i
$45$	13.4662	+	6.60768i	0.299249	+	0.146837i
$46$	−38.9867			−0.847536
$47$	33.8904	+	33.8904i	0.721072	+	0.721072i	0.968824	−	0.247752i	$-0.0796918\pi$
$47$	33.8904	+	33.8904i	0.721072	+	0.721072i	−0.247752	+	0.968824i	$0.579692\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$	−4.47595	+	35.0709i	−0.0895190	+	0.701417i
$51$	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	$-0.726181\pi$
$53$	5.60358	−	5.60358i	0.105728	−	0.105728i	0.757992	+	0.652264i	$0.226181\pi$
$54$			7.34847i			0.136083i
$55$	−33.3195	+	67.9040i	−0.605810	+	1.23462i
$56$	−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	$0.0156709\pi$
$59$			5.80696i			0.0984231i	−0.998788	+	0.0492115i	$0.984329\pi$
$60$	−16.3903	+	5.59996i	−0.273171	+	0.0933326i
$61$	−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
$65$	33.4843	+	98.0037i	0.515144	+	1.50775i
$66$	−37.0550			−0.561440
$67$	51.6510	+	51.6510i	0.770910	+	0.770910i	0.978266	−	0.207356i	$-0.0664858\pi$
$67$	51.6510	+	51.6510i	0.770910	+	0.770910i	−0.207356	+	0.978266i	$0.566486\pi$
$68$	−31.9896	+	31.9896i	−0.470436	+	0.470436i
$69$		−	47.7487i		−	0.692010i
$70$	−16.7953	−	8.24122i	−0.239933	−	0.117732i
$71$	−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	0.131346	−	0.991337i	$-0.458070\pi$
$73$	81.9558	−	81.9558i	1.12268	−	1.12268i	0.991337	−	0.131346i	$-0.0419299\pi$
$74$			60.9253i			0.823315i
$75$	−42.9529	−	5.48190i	−0.572705	−	0.0730920i
$76$	−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	$0.0671468\pi$
$79$			33.0831i			0.418774i	−0.977833	+	0.209387i	$0.932853\pi$
$80$	8.81024	−	17.9549i	0.110128	−	0.224437i
$81$	−9.00000			−0.111111
$82$	26.6233	+	26.6233i	0.324674	+	0.324674i
$83$	−97.0860	+	97.0860i	−1.16971	+	1.16971i	−0.187433	+	0.982277i	$0.560017\pi$
$83$	−97.0860	+	97.0860i	−1.16971	+	1.16971i	−0.982277	+	0.187433i	$0.939983\pi$
$84$		−	9.16515i		−	0.109109i
$85$	−107.026	+	36.5669i	−1.25913	+	0.430199i
$86$	−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	$-0.938435\pi$
$89$		−	34.2132i		−	0.384418i	0.981354	−	0.192209i	$-0.0615652\pi$
$90$	−6.85852	−	20.0739i	−0.0762058	−	0.223043i
$91$	−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
$95$	−9.20257	−	4.51558i	−0.0968692	−	0.0475324i
$96$	9.79796			0.102062
$97$	104.393	+	104.393i	1.07622	+	1.07622i	0.996845	+	0.0793705i	$0.0252910\pi$
$97$	104.393	+	104.393i	1.07622	+	1.07622i	0.0793705	+	0.996845i	$0.474709\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		−	45.3829i		−	0.458413i
$100$	39.5468	−	30.5949i	0.395468	−	0.305949i
$101$	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	$-0.734447\pi$
$103$	7.11461	−	7.11461i	0.0690739	−	0.0690739i	0.740800	+	0.671726i	$0.234447\pi$
$104$		−	58.5858i		−	0.563325i
$105$	10.0934	−	20.5700i	0.0961276	−	0.195904i
$106$	−11.2072			−0.105728
$107$	−4.56425	−	4.56425i	−0.0426566	−	0.0426566i	0.685457	−	0.728113i	$-0.259603\pi$
$107$	−4.56425	−	4.56425i	−0.0426566	−	0.0426566i	−0.728113	+	0.685457i	$0.759603\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	58.0783i		−	0.532829i	−0.963859	−	0.266414i	$-0.914161\pi$
$109$		−	58.0783i		−	0.532829i	0.963859	−	0.266414i	$-0.0858389\pi$
$110$	101.224	−	34.5844i	0.920214	−	0.314404i
$111$	−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	$-0.730893\pi$
$113$	9.58688	−	9.58688i	0.0848396	−	0.0848396i	0.748253	+	0.663413i	$0.230893\pi$
$114$		−	5.02182i		−	0.0440511i
$115$	44.5651	+	130.436i	0.387523	+	1.13422i
$116$	−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
$120$	21.9902	+	10.7903i	0.183252	+	0.0899191i
$121$	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
$125$	122.451	−	25.1141i	0.979609	−	0.200913i
$126$	11.2250			0.0890871
$127$	−140.998	−	140.998i	−1.11022	−	1.11022i	−0.993120	−	0.117097i	$-0.962641\pi$
$127$	−140.998	−	140.998i	−1.11022	−	1.11022i	−0.117097	−	0.993120i	$-0.537359\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	19.3485i		−	0.149989i
$130$	64.5194	−	131.488i	0.496303	−	1.01145i
$131$	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
$135$	24.5854	−	8.39994i	0.182114	−	0.0622218i
$136$	63.9793			0.470436
$137$	−170.364	−	170.364i	−1.24353	−	1.24353i	−0.958527	−	0.285002i	$-0.908006\pi$
$137$	−170.364	−	170.364i	−1.24353	−	1.24353i	−0.285002	−	0.958527i	$-0.591994\pi$
$138$	−47.7487	+	47.7487i	−0.346005	+	0.346005i
$139$			110.608i			0.795741i	0.917442	+	0.397870i	$0.130251\pi$
$139$			110.608i			0.795741i	−0.917442	+	0.397870i	$0.869749\pi$
$140$	8.55408	+	25.0365i	0.0611006	+	0.178832i
$141$	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
$145$	−148.594	−	72.9128i	−1.02478	−	0.502847i
$146$	−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	$-0.831227\pi$
$149$		−	150.705i		−	1.01144i	0.862697	−	0.505721i	$-0.168773\pi$
$150$	37.4710	+	48.4348i	0.249806	+	0.322898i
$151$	−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
$155$	−61.2706	+	124.867i	−0.395294	+	0.805595i
$156$	71.7527			0.459953
$157$	−28.5711	−	28.5711i	−0.181981	−	0.181981i	0.610237	−	0.792219i	$-0.291074\pi$
$157$	−28.5711	−	28.5711i	−0.181981	−	0.181981i	−0.792219	+	0.610237i	$0.791074\pi$
$158$	33.0831	−	33.0831i	0.209387	−	0.209387i
$159$		−	13.7259i		−	0.0863265i
$160$	−26.7652	+	9.14469i	−0.167282	+	0.0571543i
$161$	−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	$-0.801720\pi$
$163$	−37.2908	+	37.2908i	−0.228778	+	0.228778i	0.583404	+	0.812182i	$0.301720\pi$
$164$		−	53.2466i		−	0.324674i
$165$	42.3571	+	123.973i	0.256710	+	0.751351i
$166$	194.172			1.16971
$167$	−70.7467	−	70.7467i	−0.423633	−	0.423633i	0.462820	−	0.886453i	$-0.346838\pi$
$167$	−70.7467	−	70.7467i	−0.423633	−	0.423633i	−0.886453	+	0.462820i	$0.846838\pi$
$168$	−9.16515	+	9.16515i	−0.0545545	+	0.0545545i
$169$		−	260.037i		−	1.53868i
$170$	143.593	+	70.4591i	0.844665	+	0.414465i
$171$	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	$-0.652321\pi$
$173$	73.9048	−	73.9048i	0.427196	−	0.427196i	0.887672	+	0.460476i	$0.152321\pi$
$174$		−	81.0871i		−	0.466018i
$175$	−8.37374	+	65.6116i	−0.0478499	+	0.374923i
$176$	−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	$0.286280\pi$
$179$			280.292i			1.56588i	−0.622100	+	0.782938i	$0.713720\pi$
$180$	−13.2154	+	26.9324i	−0.0734187	+	0.149624i
$181$	−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
$185$	203.835	−	69.6430i	1.10181	−	0.376448i
$186$	−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
$190$	4.68700	+	13.7182i	0.0246684	+	0.0722008i
$191$	−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	$-0.933797\pi$
$193$	−148.989	+	148.989i	−0.771962	+	0.771962i	0.206488	+	0.978449i	$0.433797\pi$
$194$		−	208.786i		−	1.07622i
$195$	161.039	+	79.0198i	0.825842	+	0.405230i
$196$	−14.0000			−0.0714286
$197$	−255.090	−	255.090i	−1.29487	−	1.29487i	−0.931736	−	0.363135i	$-0.881706\pi$
$197$	−255.090	−	255.090i	−1.29487	−	1.29487i	−0.363135	−	0.931736i	$-0.618294\pi$
$198$	−45.3829	+	45.3829i	−0.229207	+	0.229207i
$199$			321.154i			1.61384i	0.590660	+	0.806920i	$0.298867\pi$
$199$			321.154i			1.61384i	−0.590660	+	0.806920i	$0.701133\pi$
$200$	−70.1417	−	8.95190i	−0.350709	−	0.0447595i
$201$	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
$205$	58.6394	−	119.505i	0.286046	−	0.582950i
$206$	−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
$210$	−30.6634	+	10.4766i	−0.146016	+	0.0498884i
$211$	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
$215$	18.0585	+	52.8546i	0.0839931	+	0.245835i
$216$	−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
$220$	−135.808	−	66.6391i	−0.617309	−	0.302905i
$221$	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	$-0.581835\pi$
$223$	158.968	−	158.968i	0.712863	−	0.712863i	0.967133	+	0.254270i	$0.0818353\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	−59.3202	+	45.8924i	−0.263645	+	0.203966i
$226$	−19.1738			−0.0848396
$227$	−52.1650	−	52.1650i	−0.229802	−	0.229802i	0.582808	−	0.812610i	$-0.301954\pi$
$227$	−52.1650	−	52.1650i	−0.229802	−	0.229802i	−0.812610	+	0.582808i	$0.801954\pi$
$228$	−5.02182	+	5.02182i	−0.0220255	+	0.0220255i
$229$			115.486i			0.504305i	0.967688	+	0.252152i	$0.0811384\pi$
$229$			115.486i			0.504305i	−0.967688	+	0.252152i	$0.918862\pi$
$230$	85.8705	−	175.001i	0.373350	−	0.760873i
$231$	−69.3236			−0.300102
$232$	66.2073	+	66.2073i	0.285376	+	0.285376i
$233$	−297.575	+	297.575i	−1.27714	+	1.27714i	−0.334885	+	0.942259i	$0.608698\pi$
$233$	−297.575	+	297.575i	−1.27714	+	1.27714i	−0.942259	+	0.334885i	$0.891302\pi$
$234$			87.8787i			0.375550i
$235$	−226.770	+	77.4793i	−0.964980	+	0.329699i
$236$	−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	$0.0922198\pi$
$239$			136.556i			0.571362i	−0.958325	+	0.285681i	$0.907780\pi$
$240$	−11.1999	−	32.7805i	−0.0466663	−	0.136585i
$241$	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
$245$	−31.4211	−	15.4179i	−0.128250	−	0.0629303i
$246$	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
$250$	−147.565	−	97.3370i	−0.590261	−	0.389348i
$251$	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
$255$	−86.2944	+	175.865i	−0.338410	+	0.689666i
$256$	16.0000			0.0625000
$257$	−144.579	−	144.579i	−0.562564	−	0.562564i	0.367471	−	0.930035i	$-0.380224\pi$
$257$	−144.579	−	144.579i	−0.562564	−	0.562564i	−0.930035	+	0.367471i	$0.880224\pi$
$258$	−19.3485	+	19.3485i	−0.0749944	+	0.0749944i
$259$			113.981i			0.440081i
$260$	−196.007	+	66.9687i	−0.753875	+	0.257572i
$261$	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	$-0.750333\pi$
$263$	−0.389678	+	0.389678i	−0.00148167	+	0.00148167i	0.706366	+	0.707847i	$0.250333\pi$
$264$		−	74.1100i		−	0.280720i
$265$	12.8108	+	37.4952i	0.0483425	+	0.141491i
$266$	−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	$0.169376\pi$
$269$			272.956i			1.01471i	−0.861738	+	0.507353i	$0.830624\pi$
$270$	−32.9853	−	16.1854i	−0.122168	−	0.0599461i
$271$	−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
$275$	−231.415	−	299.125i	−0.841507	−	1.08773i
$276$	95.4974			0.346005
$277$	−203.152	−	203.152i	−0.733402	−	0.733402i	0.237890	−	0.971292i	$-0.423544\pi$
$277$	−203.152	−	203.152i	−0.733402	−	0.733402i	−0.971292	+	0.237890i	$0.923544\pi$
$278$	110.608	−	110.608i	0.397870	−	0.397870i
$279$		−	83.4538i		−	0.299117i
$280$	16.4824	−	33.5906i	0.0588659	−	0.119966i
$281$	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	0.491888	−	0.870659i	$-0.336307\pi$
$283$	385.601	−	385.601i	1.36255	−	1.36255i	0.870659	−	0.491888i	$-0.163693\pi$
$284$		−	240.893i		−	0.848216i
$285$	−16.8012	+	5.74038i	−0.0589517	+	0.0201417i
$286$	−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
$290$	75.6807	+	221.506i	0.260968	+	0.763815i
$291$	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	$-0.948195\pi$
$293$	−241.653	+	241.653i	−0.824754	+	0.824754i	0.162032	+	0.986786i	$0.448195\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	−26.0659	−	12.7902i	−0.0883590	−	0.0433566i
$296$	−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
$300$	10.9638	−	85.9057i	0.0365460	−	0.286352i
$301$	−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
$305$	216.327	−	440.865i	0.709268	−	1.44546i
$306$	−95.9689			−0.313624
$307$	315.513	+	315.513i	1.02773	+	1.02773i	0.999604	+	0.0281252i	$0.00895372\pi$
$307$	315.513	+	315.513i	1.02773	+	1.02773i	0.0281252	+	0.999604i	$0.491046\pi$
$308$	56.6025	−	56.6025i	0.183774	−	0.183774i
$309$		−	17.4272i		−	0.0563986i
$310$	186.138	−	63.5966i	0.600445	−	0.205150i
$311$	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	$-0.890829\pi$
$313$	−189.513	+	189.513i	−0.605474	+	0.605474i	0.336286	+	0.941760i	$0.390829\pi$
$314$			57.1422i			0.181981i
$315$	−12.8311	−	37.5548i	−0.0407337	−	0.119222i
$316$	−66.1663			−0.209387
$317$	−21.9357	−	21.9357i	−0.0691977	−	0.0691977i	0.671661	−	0.740859i	$-0.265581\pi$
$317$	−21.9357	−	21.9357i	−0.0691977	−	0.0691977i	−0.740859	+	0.671661i	$0.765581\pi$
$318$	−13.7259	+	13.7259i	−0.0431633	+	0.0431633i
$319$			500.780i			1.56984i
$320$	35.9099	+	17.6205i	0.112218	+	0.0550640i
$321$	−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
$325$	−513.664	−	65.5568i	−1.58050	−	0.201713i
$326$	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
$330$	81.6159	−	166.330i	0.247321	−	0.504030i
$331$	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
$335$	−345.612	+	118.083i	−1.03168	+	0.352487i
$336$	18.3303			0.0545545
$337$	73.8705	+	73.8705i	0.219200	+	0.219200i	0.808161	−	0.588961i	$-0.200463\pi$
$337$	73.8705	+	73.8705i	0.219200	+	0.219200i	−0.588961	+	0.808161i	$0.700463\pi$
$338$	−260.037	+	260.037i	−0.769340	+	0.769340i
$339$		−	23.4830i		−	0.0692713i
$340$	−73.1339	−	214.052i	−0.215100	−	0.629565i
$341$	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
$345$	214.331	+	105.169i	0.621250	+	0.304839i
$346$	−147.810			−0.427196
$347$	31.2699	+	31.2699i	0.0901149	+	0.0901149i	0.750727	−	0.660612i	$-0.229703\pi$
$347$	31.2699	+	31.2699i	0.0901149	+	0.0901149i	−0.660612	+	0.750727i	$0.729703\pi$
$348$	−81.0871	+	81.0871i	−0.233009	+	0.233009i
$349$		−	546.387i		−	1.56558i	−0.622287	−	0.782789i	$-0.713796\pi$
$349$		−	546.387i		−	1.56558i	0.622287	−	0.782789i	$-0.286204\pi$
$350$	73.9853	−	57.2379i	0.211387	−	0.163537i
$351$	−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	$-0.870382\pi$
$353$	−184.331	+	184.331i	−0.522184	+	0.522184i	0.396046	+	0.918231i	$0.370382\pi$
$354$		−	14.2241i		−	0.0401811i
$355$	265.291	−	540.653i	0.747298	−	1.52297i
$356$	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	$0.146659\pi$
$359$			319.232i			0.889226i	−0.895723	+	0.444613i	$0.853341\pi$
$360$	40.1478	−	13.7170i	0.111522	−	0.0381029i
$361$	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
$365$	187.365	+	548.391i	0.513330	+	1.50244i
$366$	240.579			0.657320
$367$	116.440	+	116.440i	0.317276	+	0.317276i	0.847720	−	0.530444i	$-0.177975\pi$
$367$	116.440	+	116.440i	0.317276	+	0.317276i	−0.530444	+	0.847720i	$0.677975\pi$
$368$	−77.9733	+	77.9733i	−0.211884	+	0.211884i
$369$			79.8698i			0.216449i
$370$	−273.478	−	134.192i	−0.739129	−	0.362680i
$371$	−20.9667			−0.0565140
$372$	68.1397	+	68.1397i	0.183171	+	0.183171i
$373$	380.962	−	380.962i	1.02135	−	1.02135i	0.0215784	−	0.999767i	$-0.493131\pi$
$373$	380.962	−	380.962i	1.02135	−	1.02135i	0.999767	−	0.0215784i	$-0.00686914\pi$
$374$		−	483.928i		−	1.29392i
$375$	119.213	−	180.730i	0.317901	−	0.481946i
$376$	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	$0.0804489\pi$
$379$			189.542i			0.500111i	−0.968231	+	0.250056i	$0.919551\pi$
$380$	9.03115	−	18.4051i	0.0237662	−	0.0484346i
$381$	−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	$-0.941176\pi$
$383$	−306.102	+	306.102i	−0.799222	+	0.799222i	0.183751	+	0.982973i	$0.441176\pi$
$384$			19.5959i			0.0510310i
$385$	189.372	−	64.7015i	0.491875	−	0.168056i
$386$	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	$0.133219\pi$
$389$			316.187i			0.812819i	−0.913691	+	0.406410i	$0.866781\pi$
$390$	−82.0195	−	240.059i	−0.210306	−	0.615536i
$391$	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
$395$	−148.501	−	72.8676i	−0.375953	−	0.184475i
$396$	90.7659			0.229207
$397$	−134.126	−	134.126i	−0.337849	−	0.337849i	0.517709	−	0.855557i	$-0.326785\pi$
$397$	−134.126	−	134.126i	−0.337849	−	0.337849i	−0.855557	+	0.517709i	$0.826785\pi$
$398$	321.154	−	321.154i	0.806920	−	0.806920i
$399$		−	9.39496i		−	0.0235463i
$400$	61.1898	+	79.0936i	0.152975	+	0.197734i
$401$	−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
$405$	19.8230	−	40.3986i	0.0489458	−	0.0997496i
$406$	−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	$0.0439145\pi$
$409$			112.495i			0.275048i	−0.990498	+	0.137524i	$0.956086\pi$
$410$	−178.144	+	60.8654i	−0.434498	+	0.148452i
$411$	−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
$415$	−221.955	−	649.631i	−0.534832	−	1.56538i
$416$	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	$0.0863545\pi$
$419$			224.563i			0.535950i	−0.963426	+	0.267975i	$0.913645\pi$
$420$	41.1399	+	20.1868i	0.0979522	+	0.0480638i
$421$	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
$425$	71.5920	−	560.952i	0.168452	−	1.31989i
$426$	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
$430$	34.7961	−	70.9131i	0.0809211	−	0.164914i
$431$	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	$-0.870597\pi$
$433$	−226.490	+	226.490i	−0.523072	+	0.523072i	0.395426	+	0.918498i	$0.370597\pi$
$434$			104.085i			0.239828i
$435$	−271.289	+	92.6896i	−0.623652	+	0.213079i
$436$	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	$0.0848774\pi$
$439$			231.354i			0.527003i	−0.964659	+	0.263502i	$0.915123\pi$
$440$	69.1688	+	202.447i	0.157202	+	0.460107i
$441$	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	$-0.904047\pi$
$443$	−291.498	+	291.498i	−0.658008	+	0.658008i	0.296900	+	0.954909i	$0.404047\pi$
$444$		−	149.236i		−	0.336117i
$445$	153.574	+	75.3567i	0.345110	+	0.169341i
$446$	−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	$0.0667448\pi$
$449$			186.920i			0.416303i	−0.978097	+	0.208152i	$0.933255\pi$
$450$	105.213	+	13.4279i	0.233806	+	0.0298397i
$451$	−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
$455$	120.705	−	245.992i	0.265285	−	0.540641i
$456$	10.0436			0.0220255
$457$	−358.683	−	358.683i	−0.784865	−	0.784865i	0.195782	−	0.980647i	$-0.437275\pi$
$457$	−358.683	−	358.683i	−0.784865	−	0.784865i	−0.980647	+	0.195782i	$0.937275\pi$
$458$	115.486	−	115.486i	0.252152	−	0.252152i
$459$		−	117.537i		−	0.256073i
$460$	−260.871	+	89.1303i	−0.567111	+	0.193761i
$461$	−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	$-0.628287\pi$
$463$	244.313	−	244.313i	0.527675	−	0.527675i	0.919878	+	0.392204i	$0.128287\pi$
$464$		−	132.415i		−	0.285376i
$465$	77.8896	+	227.971i	0.167505	+	0.490261i
$466$	595.149			1.27714
$467$	165.494	+	165.494i	0.354377	+	0.354377i	0.861735	−	0.507358i	$-0.169378\pi$
$467$	165.494	+	165.494i	0.354377	+	0.354377i	−0.507358	+	0.861735i	$0.669378\pi$
$468$	87.8787	−	87.8787i	0.187775	−	0.187775i
$469$		−	193.260i		−	0.412069i
$470$	304.250	+	149.291i	0.647340	+	0.317641i
$471$	−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
$475$	40.5384	−	31.3621i	0.0853441	−	0.0660254i
$476$	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	$-0.889353\pi$
$479$		−	326.343i		−	0.681300i	0.940190	−	0.340650i	$-0.110647\pi$
$480$	−21.5806	+	43.9804i	−0.0449596	+	0.0916259i
$481$	−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
$485$	−698.524	+	238.660i	−1.44026	+	0.492083i
$486$	22.0454			0.0453609
$487$	−373.708	−	373.708i	−0.767367	−	0.767367i	0.210275	−	0.977642i	$-0.432564\pi$
$487$	−373.708	−	373.708i	−0.767367	−	0.767367i	−0.977642	+	0.210275i	$0.932564\pi$
$488$	−196.432	+	196.432i	−0.402525	+	0.402525i
$489$			91.3435i			0.186797i
$490$	16.0032	+	46.8391i	0.0326596	+	0.0955899i
$491$	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
$495$	203.712	+	99.9586i	0.411539	+	0.201937i
$496$	−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	$-0.817358\pi$
$499$		−	541.732i		−	1.08563i	0.839851	−	0.542817i	$-0.182642\pi$
$500$	50.2282	+	244.902i	0.100456	+	0.489805i
$501$	−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	$-0.950647\pi$
$503$	−419.289	+	419.289i	−0.833578	+	0.833578i	0.154427	+	0.988004i	$0.450647\pi$
$504$			22.4499i			0.0445435i
$505$	−110.757	+	225.718i	−0.219320	+	0.446966i
$506$	−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	$0.108568\pi$
$509$			340.522i			0.669002i	−0.942395	+	0.334501i	$0.891432\pi$
$510$	262.159	−	89.5703i	0.514038	−	0.175628i
$511$	−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
$515$	16.2652	+	47.6060i	0.0315830	+	0.0924388i
$516$	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
$520$	262.976	+	129.039i	0.505723	+	0.248151i
$521$	−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	$-0.876796\pi$
$523$	−286.897	+	286.897i	−0.548561	+	0.548561i	0.377464	+	0.926024i	$0.376796\pi$
$524$			369.527i			0.705205i
$525$	70.1018	+	90.6131i	0.133527	+	0.172596i
$526$	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
$530$	24.6845	−	50.3060i	0.0465744	−	0.0949169i
$531$	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
$535$	30.5407	−	10.4347i	0.0570855	−	0.0195041i
$536$	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
$540$	16.7999	+	49.1708i	0.0311109	+	0.0910570i
$541$	−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
$545$	260.698	+	127.921i	0.478345	+	0.234717i
$546$	134.237			0.245855
$547$	298.464	+	298.464i	0.545637	+	0.545637i	0.925176	−	0.379539i	$-0.123917\pi$
$547$	298.464	+	298.464i	0.545637	+	0.545637i	−0.379539	+	0.925176i	$0.623917\pi$
$548$	340.727	−	340.727i	0.621765	−	0.621765i
$549$			294.648i			0.536699i
$550$	−67.7106	+	530.540i	−0.123110	+	0.964617i
$551$	−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
$555$	164.351	−	334.940i	0.296127	−	0.603496i
$556$	−221.216			−0.397870
$557$	392.034	+	392.034i	0.703831	+	0.703831i	0.965231	−	0.261400i	$-0.0841841\pi$
$557$	392.034	+	392.034i	0.703831	+	0.703831i	−0.261400	+	0.965231i	$0.584184\pi$
$558$	−83.4538	+	83.4538i	−0.149559	+	0.149559i
$559$		−	231.385i		−	0.413926i
$560$	−50.0731	+	17.1082i	−0.0894162	+	0.0305503i
$561$	592.688			1.05649
$562$	−368.543	−	368.543i	−0.655770	−	0.655770i
$563$	575.129	−	575.129i	1.02154	−	1.02154i	0.0217803	−	0.999763i	$-0.493067\pi$
$563$	575.129	−	575.129i	1.02154	−	1.02154i	0.999763	−	0.0217803i	$-0.00693342\pi$
$564$			166.028i			0.294376i
$565$	21.9173	+	64.1486i	0.0387916	+	0.113537i
$566$	−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	$0.0543745\pi$
$569$			193.452i			0.339986i	−0.985445	+	0.169993i	$0.945625\pi$
$570$	22.5416	+	11.0609i	0.0395467	+	0.0194050i
$571$	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
$575$	−683.648	−	87.2512i	−1.18895	−	0.151741i
$576$	−24.0000			−0.0416667
$577$	−703.423	−	703.423i	−1.21910	−	1.21910i	−0.967946	−	0.251157i	$-0.919189\pi$
$577$	−703.423	−	703.423i	−1.21910	−	1.21910i	−0.251157	−	0.967946i	$-0.580811\pi$
$578$	222.669	−	222.669i	0.385240	−	0.385240i
$579$			364.946i			0.630304i
$580$	145.826	−	297.187i	0.251423	−	0.512391i
$581$	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
$585$	294.011	−	100.453i	0.502583	−	0.171715i
$586$	483.306			0.824754
$587$	−180.492	−	180.492i	−0.307483	−	0.307483i	0.536450	−	0.843932i	$-0.319765\pi$
$587$	−180.492	−	180.492i	−0.307483	−	0.307483i	−0.843932	+	0.536450i	$0.819765\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$			57.0309i			0.0968267i
$590$	13.2757	+	38.8561i	0.0225012	+	0.0658578i
$591$	−624.840			−1.05726
$592$	121.851	+	121.851i	0.205829	+	0.205829i
$593$	−701.554	+	701.554i	−1.18306	+	1.18306i	−0.204111	+	0.978948i	$0.565430\pi$
$593$	−701.554	+	701.554i	−1.18306	+	1.18306i	−0.978948	+	0.204111i	$0.934570\pi$
$594$			111.165i			0.187147i
$595$	268.638	+	131.817i	0.451492	+	0.221541i
$596$	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	$-0.905701\pi$
$599$		−	349.739i		−	0.583871i	0.956438	−	0.291935i	$-0.0942992\pi$
$600$	−96.8695	+	74.9419i	−0.161449	+	0.124903i
$601$	−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
$605$	−237.536	+	484.090i	−0.392622	+	0.800149i
$606$	−123.174			−0.203257
$607$	13.0530	+	13.0530i	0.0215042	+	0.0215042i	0.717777	−	0.696273i	$-0.245160\pi$
$607$	13.0530	+	13.0530i	0.0215042	+	0.0215042i	−0.696273	+	0.717777i	$0.745160\pi$
$608$	−8.20060	+	8.20060i	−0.0134878	+	0.0134878i
$609$		−	151.700i		−	0.249097i
$610$	−657.192	+	224.539i	−1.07736	+	0.368096i
$611$	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	$-0.863035\pi$
$613$	−301.420	+	301.420i	−0.491713	+	0.491713i	0.417133	+	0.908846i	$0.363035\pi$
$614$		−	631.026i		−	1.02773i
$615$	−74.5446	−	218.181i	−0.121211	−	0.354766i
$616$	−113.205			−0.183774
$617$	−676.069	−	676.069i	−1.09574	−	1.09574i	−0.994904	−	0.100832i	$-0.967850\pi$
$617$	−676.069	−	676.069i	−1.09574	−	1.09574i	−0.100832	−	0.994904i	$-0.532150\pi$
$618$	−17.4272	+	17.4272i	−0.0281993	+	0.0281993i
$619$		−	180.575i		−	0.291721i	−0.989305	−	0.145860i	$-0.953405\pi$
$619$		−	180.575i		−	0.291721i	0.989305	−	0.145860i	$-0.0465950\pi$
$620$	−249.735	−	122.541i	−0.402798	−	0.197647i
$621$	−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
$625$	−156.975	+	604.966i	−0.251161	+	0.967945i
$626$	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
$630$	−24.7237	+	50.3859i	−0.0392439	+	0.0799776i
$631$	−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
$635$	943.457	−	322.345i	1.48576	−	0.507630i
$636$	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
$640$	−18.2894	−	53.5303i	−0.0285772	−	0.0836412i
$641$	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	$-0.545447\pi$
$643$	544.963	−	544.963i	0.847532	−	0.847532i	0.989825	+	0.142292i	$0.0454473\pi$
$644$		−	145.875i		−	0.226514i
$645$	86.8505	+	42.6163i	0.134652	+	0.0660718i
$646$	65.5835			0.101523
$647$	−654.936	−	654.936i	−1.01227	−	1.01227i	−0.999924	−	0.0123424i	$-0.996071\pi$
$647$	−654.936	−	654.936i	−1.01227	−	1.01227i	−0.0123424	−	0.999924i	$-0.503929\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			87.8457i			0.135355i
$650$	448.107	+	579.221i	0.689395	+	0.891109i
$651$	−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	$-0.933796\pi$
$653$	−504.090	+	504.090i	−0.771960	+	0.771960i	0.206489	+	0.978449i	$0.433796\pi$
$654$			142.262i			0.217526i
$655$	−406.953	+	829.355i	−0.621302	+	1.26619i
$656$	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	$-0.814155\pi$
$659$		−	726.533i		−	1.10248i	0.834347	−	0.551239i	$-0.185845\pi$
$660$	−247.946	+	84.7142i	−0.375676	+	0.128355i
$661$	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
$665$	8.76857	+	25.6643i	0.0131858	+	0.0385929i
$666$	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
$670$	463.695	+	227.529i	0.692082	+	0.339595i
$671$	−1485.78			−2.21427
$672$	−18.3303	−	18.3303i	−0.0272772	−	0.0272772i
$673$	743.671	−	743.671i	1.10501	−	1.10501i	0.111212	−	0.993797i	$-0.464527\pi$
$673$	743.671	−	743.671i	1.10501	−	1.10501i	0.993797	−	0.111212i	$-0.0354732\pi$
$674$		−	147.741i		−	0.219200i
$675$	−16.4457	+	128.859i	−0.0243640	+	0.190902i
$676$	520.074			0.769340
$677$	−182.111	−	182.111i	−0.268997	−	0.268997i	0.559699	−	0.828696i	$-0.310917\pi$
$677$	−182.111	−	182.111i	−0.268997	−	0.268997i	−0.828696	+	0.559699i	$0.810917\pi$
$678$	−23.4830	+	23.4830i	−0.0346356	+	0.0346356i
$679$		−	390.603i		−	0.575261i
$680$	−140.918	+	287.186i	−0.207233	+	0.422332i
$681$	−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	$-0.646297\pi$
$683$	309.149	−	309.149i	0.452634	−	0.452634i	0.896228	+	0.443594i	$0.146297\pi$
$684$			12.3009i			0.0179838i
$685$	1139.95	−	389.481i	1.66416	−	0.568585i
$686$	−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
$690$	−109.162	−	319.501i	−0.158206	−	0.463044i
$691$	−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
$695$	−496.490	−	243.621i	−0.714373	−	0.350533i
$696$	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
$700$	−131.223	−	16.7475i	−0.187462	−	0.0239250i
$701$	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
$705$	−182.844	+	372.628i	−0.259353	+	0.528551i
$706$	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	$-0.847561\pi$
$709$		−	653.419i		−	0.921607i	0.887502	−	0.460803i	$-0.152439\pi$
$710$	−805.944	+	275.362i	−1.13513	+	0.387834i
$711$	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
$715$	506.539	+	1482.56i	0.708446	+	2.07352i
$716$	−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	$-0.766790\pi$
$719$		−	961.796i		−	1.33769i	0.743404	−	0.668843i	$-0.233210\pi$
$720$	−53.8648	−	26.4307i	−0.0748122	−	0.0367093i
$721$	−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
$725$	654.572	−	506.402i	0.902858	−	0.698485i
$726$	−264.167			−0.363866
$727$	948.990	+	948.990i	1.30535	+	1.30535i	0.924733	+	0.380618i	$0.124289\pi$
$727$	948.990	+	948.990i	1.30535	+	1.30535i	0.380618	+	0.924733i	$0.375711\pi$
$728$	−109.604	+	109.604i	−0.150555	+	0.150555i
$729$			27.0000i			0.0370370i
$730$	361.025	−	735.756i	0.494555	−	1.00788i
$731$	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	$-0.500656\pi$
$733$	731.489	−	731.489i	0.997938	−	0.997938i	0.999998	+	0.00205981i	$0.000655659\pi$
$734$		−	232.880i		−	0.317276i
$735$	−57.3659	+	19.5999i	−0.0780488	+	0.0266665i
$736$	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	$0.00728924\pi$
$739$			33.8430i			0.0457956i	−0.999738	+	0.0228978i	$0.992711\pi$
$740$	139.286	+	407.669i	0.188224	+	0.550905i
$741$	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	$-0.737956\pi$
$743$	39.7475	−	39.7475i	0.0534959	−	0.0534959i	0.733349	+	0.679853i	$0.237956\pi$
$744$		−	136.279i		−	0.183171i
$745$	676.474	+	331.936i	0.908018	+	0.445552i
$746$	−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
$750$	−299.943	+	61.5167i	−0.399924	+	0.0820223i
$751$	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
$755$	419.465	−	854.853i	0.555582	−	1.13226i
$756$	−27.4955			−0.0363696
$757$	114.632	+	114.632i	0.151429	+	0.151429i	0.778756	−	0.627327i	$-0.215851\pi$
$757$	114.632	+	114.632i	0.151429	+	0.151429i	−0.627327	+	0.778756i	$0.715851\pi$
$758$	189.542	−	189.542i	0.250056	−	0.250056i
$759$		−	722.326i		−	0.951681i
$760$	−27.4363	+	9.37400i	−0.0361004	+	0.0123342i
$761$	−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
$765$	109.701	+	321.078i	0.143400	+	0.419710i
$766$	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	$-0.830535\pi$
$769$		−	780.679i		−	1.01519i	0.861596	−	0.507594i	$-0.169465\pi$
$770$	−254.073	−	124.670i	−0.329965	−	0.161909i
$771$	−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	$-0.531536\pi$
$773$	692.751	−	692.751i	0.896186	−	0.896186i	0.995096	+	0.0989107i	$0.0315358\pi$
$774$			47.3941i			0.0612326i
$775$	−425.544	−	550.055i	−0.549088	−	0.709749i
$776$	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
$780$	−158.040	+	322.079i	−0.202615	+	0.412921i
$781$	−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
$785$	191.178	−	65.3185i	0.243538	−	0.0832082i
$786$	−452.577			−0.575797
$787$	505.691	+	505.691i	0.642556	+	0.642556i	0.951183	−	0.308627i	$-0.0998696\pi$
$787$	505.691	+	505.691i	0.642556	+	0.642556i	−0.308627	+	0.951183i	$0.599870\pi$
$788$	510.179	−	510.179i	0.647436	−	0.647436i
$789$			0.954513i			0.00120978i
$790$	75.6338	+	221.369i	0.0957390	+	0.280214i
$791$	−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
$795$	61.6120	+	30.2322i	0.0774994	+	0.0380279i
$796$	−642.309			−0.806920
$797$	221.290	+	221.290i	0.277654	+	0.277654i	0.832172	−	0.554518i	$-0.187097\pi$
$797$	221.290	+	221.290i	0.277654	+	0.277654i	−0.554518	+	0.832172i	$0.687097\pi$
$798$	−9.39496	+	9.39496i	−0.0117731	+	0.0117731i
$799$			1084.14i			1.35687i
$800$	17.9038	−	140.283i	0.0223798	−	0.175354i
$801$	−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
$805$	160.649	−	327.396i	0.199564	−	0.406704i
$806$	−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	$0.0639500\pi$
$809$			322.881i			0.399112i	−0.979886	+	0.199556i	$0.936050\pi$
$810$	−60.2216	+	20.5756i	−0.0743477	+	0.0254019i
$811$	−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
$815$	−85.2533	−	249.524i	−0.104605	−	0.306164i
$816$	−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
$820$	239.010	+	117.279i	0.291475	+	0.143023i
$821$	−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	−0.105414	+	0.994428i	$0.533617\pi$
$823$	−905.171	+	905.171i	−1.09984	+	1.09984i	−0.994428	+	0.105414i	$0.966383\pi$
$824$		−	28.4585i		−	0.0345370i
$825$	−649.776	−	82.9282i	−0.787607	−	0.100519i
$826$	−21.7277			−0.0263047
$827$	752.036	+	752.036i	0.909354	+	0.909354i	0.996220	−	0.0868659i	$-0.0276852\pi$
$827$	752.036	+	752.036i	0.909354	+	0.909354i	−0.0868659	+	0.996220i	$0.527685\pi$
$828$	116.960	−	116.960i	0.141256	−	0.141256i
$829$			1043.36i			1.25858i	0.777172	+	0.629288i	$0.216653\pi$
$829$			1043.36i			1.25858i	−0.777172	+	0.629288i	$0.783347\pi$
$830$	−427.675	+	871.586i	−0.515271	+	1.05010i
$831$	−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
$835$	473.387	−	161.739i	0.566931	−	0.193700i
$836$	−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	$0.00533497\pi$
$839$			28.1225i			0.0335190i	−0.999860	+	0.0167595i	$0.994665\pi$
$840$	−20.9531	−	61.3267i	−0.0249442	−	0.0730080i
$841$	−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
$845$	1167.24	+	572.747i	1.38135	+	0.677807i
$846$	−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
$850$	−632.544	+	489.360i	−0.744170	+	0.575718i
$851$	−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	$-0.825992\pi$
$853$	−285.266	+	285.266i	−0.334427	+	0.334427i	0.519838	+	0.854265i	$0.325992\pi$
$854$		−	367.491i		−	0.430317i
$855$	−13.5467	+	27.6077i	−0.0158441	+	0.0322897i
$856$	−18.2570			−0.0213283
$857$	−307.011	−	307.011i	−0.358239	−	0.358239i	0.504924	−	0.863164i	$-0.331520\pi$
$857$	−307.011	−	307.011i	−0.358239	−	0.358239i	−0.863164	+	0.504924i	$0.831520\pi$
$858$	−542.724	+	542.724i	−0.632546	+	0.632546i
$859$			875.499i			1.01921i	0.860409	+	0.509604i	$0.170208\pi$
$859$			875.499i			1.01921i	−0.860409	+	0.509604i	$0.829792\pi$
$860$	−105.709	+	36.1170i	−0.122918	+	0.0419965i
$861$	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	$-0.573443\pi$
$863$	642.774	−	642.774i	0.744814	−	0.744814i	0.973500	+	0.228686i	$0.0734430\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	168.959	+	494.519i	0.195329	+	0.571698i
$866$	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
$870$	363.978	+	178.599i	0.418366	+	0.205286i
$871$	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
$875$	−276.069	−	182.101i	−0.315508	−	0.208115i
$876$	401.500			0.458333
$877$	943.109	+	943.109i	1.07538	+	1.07538i	0.996917	+	0.0784638i	$0.0250015\pi$
$877$	943.109	+	943.109i	1.07538	+	1.07538i	0.0784638	+	0.996917i	$0.474999\pi$
$878$	231.354	−	231.354i	0.263502	−	0.263502i
$879$			591.926i			0.673408i
$880$	133.278	−	271.616i	0.151452	−	0.308654i
$881$	−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	$-0.776637\pi$
$883$	−104.376	+	104.376i	−0.118206	+	0.118206i	0.645529	+	0.763736i	$0.276637\pi$
$884$			937.069i			1.06003i
$885$	−47.5888	+	16.2594i	−0.0537727	+	0.0183722i
$886$	582.995			0.658008
$887$	530.292	+	530.292i	0.597849	+	0.597849i	0.939740	−	0.341891i	$-0.111067\pi$
$887$	530.292	+	530.292i	0.597849	+	0.597849i	−0.341891	+	0.939740i	$0.611067\pi$
$888$	−149.236	+	149.236i	−0.168059	+	0.168059i
$889$			527.565i			0.593436i
$890$	−78.2174	−	228.931i	−0.0878847	−	0.257226i
$891$	−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
$895$	−1258.15	−	617.359i	−1.40576	−	0.689787i
$896$	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
$900$	−91.7848	−	118.640i	−0.101983	−	0.131823i
$901$	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
$905$	306.345	−	624.319i	0.338503	−	0.689856i
$906$	466.491			0.514891
$907$	−460.614	−	460.614i	−0.507844	−	0.507844i	0.406020	−	0.913864i	$-0.366916\pi$
$907$	−460.614	−	460.614i	−0.507844	−	0.507844i	−0.913864	+	0.406020i	$0.866916\pi$
$908$	104.330	−	104.330i	0.114901	−	0.114901i
$909$		−	150.856i		−	0.165959i
$910$	−366.696	+	125.287i	−0.402963	+	0.137678i
$911$	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
$915$	−275.003	−	804.892i	−0.300549	−	0.879664i
$916$	−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	$-0.820742\pi$
$919$		−	981.230i		−	1.06772i	0.845574	−	0.533858i	$-0.179258\pi$
$920$	350.002	+	171.741i	0.380436	+	0.186675i
$921$	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
$925$	−136.349	+	1068.35i	−0.147405	+	1.15498i
$926$	−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	$0.162500\pi$
$929$			907.859i			0.977244i	−0.872496	+	0.488622i	$0.837500\pi$
$930$	150.082	−	305.861i	0.161378	−	0.328883i
$931$	−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
$935$	−1619.05	+	553.172i	−1.73161	+	0.591627i
$936$	−175.757			−0.187775
$937$	−1133.74	−	1133.74i	−1.20997	−	1.20997i	−0.971035	−	0.238937i	$-0.923201\pi$
$937$	−1133.74	−	1133.74i	−1.20997	−	1.20997i	−0.238937	−	0.971035i	$-0.576799\pi$
$938$	−193.260	+	193.260i	−0.206034	+	0.206034i
$939$			464.211i			0.494367i
$940$	−154.959	−	453.541i	−0.164850	−	0.482490i
$941$	−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
$945$	−61.7099	−	30.2802i	−0.0653015	−	0.0320425i
$946$	−238.987			−0.252629
$947$	435.731	+	435.731i	0.460117	+	0.460117i	0.898694	−	0.438577i	$-0.144517\pi$
$947$	435.731	+	435.731i	0.460117	+	0.460117i	−0.438577	+	0.898694i	$0.644517\pi$
$948$	−81.0368	+	81.0368i	−0.0854819	+	0.0854819i
$949$		−	2400.72i		−	2.52974i
$950$	−71.9005	−	9.17637i	−0.0756848	−	0.00965934i
$951$	−53.7312			−0.0564996
$952$	−119.694	−	119.694i	−0.125729	−	0.125729i
$953$	1133.89	−	1133.89i	1.18981	−	1.18981i	0.212687	−	0.977120i	$-0.431778\pi$
$953$	1133.89	−	1133.89i	1.18981	−	1.18981i	0.977120	−	0.212687i	$-0.0682216\pi$
$954$			33.6215i			0.0352427i
$955$	510.363	−	1040.10i	0.534411	−	1.08911i
$956$	−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
$960$	65.5610	−	22.3998i	0.0682927	−	0.0233332i
$961$	−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
$965$	−340.614	−	996.926i	−0.352968	−	1.03308i
$966$	178.659			0.184948
$967$	−1229.34	−	1229.34i	−1.27129	−	1.27129i	−0.945411	−	0.325882i	$-0.894339\pi$
$967$	−1229.34	−	1229.34i	−1.27129	−	1.27129i	−0.325882	−	0.945411i	$-0.605661\pi$
$968$	215.691	−	215.691i	0.222821	−	0.222821i
$969$			80.3231i			0.0828928i
$970$	937.184	+	459.863i	0.966169	+	0.474086i
$971$	−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
$975$	−709.397	+	548.817i	−0.727587	+	0.562889i
$976$	392.864			0.402525
$977$	295.891	+	295.891i	0.302857	+	0.302857i	0.842131	−	0.539273i	$-0.181301\pi$
$977$	295.891	+	295.891i	0.302857	+	0.302857i	−0.539273	+	0.842131i	$0.681301\pi$
$978$	91.3435	−	91.3435i	0.0933983	−	0.0933983i
$979$		−	517.566i		−	0.528668i
$980$	30.8358	−	62.8423i	0.0314651	−	0.0641248i
$981$	−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	$-0.537809\pi$
$983$	859.585	−	859.585i	0.874451	−	0.874451i	0.992954	+	0.118503i	$0.0378094\pi$
$984$			130.427i			0.132548i
$985$	1706.88	−	583.179i	1.73287	−	0.592060i
$986$	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
$990$	−103.753	−	303.671i	−0.104801	−	0.306738i
$991$	−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
$995$	−1441.58	−	707.362i	−1.44882	−	0.710916i
$996$	−475.622			−0.477532
$997$	−251.901	−	251.901i	−0.252659	−	0.252659i	0.569401	−	0.822060i	$-0.307175\pi$
$997$	−251.901	−	251.901i	−0.252659	−	0.252659i	−0.822060	+	0.569401i	$0.807175\pi$
$998$	−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	210.3.l.b.127.6	yes	16
3.2	odd	2		630.3.o.f.127.5		16
5.2	odd	4		1050.3.l.h.43.4		16
5.3	odd	4	inner	210.3.l.b.43.6	✓	16
5.4	even	2		1050.3.l.h.757.4		16
15.8	even	4		630.3.o.f.253.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.6	✓	16	5.3	odd	4	inner
210.3.l.b.127.6	yes	16	1.1	even	1	trivial
630.3.o.f.127.5		16	3.2	odd	2
630.3.o.f.253.5		16	15.8	even	4
1050.3.l.h.43.4		16	5.2	odd	4
1050.3.l.h.757.4		16	5.4	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.20256 + 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.20256 + 4.48873i) q^{5} -2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.69129 - 2.28617i) q^{10} +15.1276 q^{11} +(2.44949 + 2.44949i) q^{12} +(14.6465 - 14.6465i) q^{13} +3.74166i q^{14} +(2.79998 + 8.19513i) q^{15} -4.00000 q^{16} +(15.9948 + 15.9948i) q^{17} +(-3.00000 + 3.00000i) q^{18} +2.05015i q^{19} +(-8.97747 - 4.40512i) q^{20} -4.58258 q^{21} +(-15.1276 - 15.1276i) q^{22} +(19.4933 - 19.4933i) q^{23} -4.89898i q^{24} +(-15.2975 - 19.7734i) q^{25} -29.2929 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +33.1037i q^{29} +(5.39515 - 10.9951i) q^{30} +27.8179 q^{31} +(4.00000 + 4.00000i) q^{32} +(18.5275 - 18.5275i) q^{33} -31.9896i q^{34} +(12.5183 - 4.27704i) q^{35} +6.00000 q^{36} +(-30.4627 - 30.4627i) q^{37} +(2.05015 - 2.05015i) q^{38} -35.8763i q^{39} +(4.57235 + 13.3826i) q^{40} -26.6233 q^{41} +(4.58258 + 4.58258i) q^{42} +(7.89901 - 7.89901i) q^{43} +30.2553i q^{44} +(13.4662 + 6.60768i) q^{45} -38.9867 q^{46} +(33.8904 + 33.8904i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-4.47595 + 35.0709i) q^{50} +39.1791 q^{51} +(29.2929 + 29.2929i) q^{52} +(5.60358 - 5.60358i) q^{53} +7.34847i q^{54} +(-33.3195 + 67.9040i) q^{55} -7.48331 q^{56} +(2.51091 + 2.51091i) q^{57} +(33.1037 - 33.1037i) q^{58} +5.80696i q^{59} +(-16.3903 + 5.59996i) q^{60} -98.2160 q^{61} +(-27.8179 - 27.8179i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(33.4843 + 98.0037i) q^{65} -37.0550 q^{66} +(51.6510 + 51.6510i) q^{67} +(-31.9896 + 31.9896i) q^{68} -47.7487i q^{69} +(-16.7953 - 8.24122i) q^{70} -120.447 q^{71} +(-6.00000 - 6.00000i) q^{72} +(81.9558 - 81.9558i) q^{73} +60.9253i q^{74} +(-42.9529 - 5.48190i) q^{75} -4.10030 q^{76} +(-28.3012 - 28.3012i) q^{77} +(-35.8763 + 35.8763i) q^{78} +33.0831i q^{79} +(8.81024 - 17.9549i) q^{80} -9.00000 q^{81} +(26.6233 + 26.6233i) q^{82} +(-97.0860 + 97.0860i) q^{83} -9.16515i q^{84} +(-107.026 + 36.5669i) q^{85} -15.7980 q^{86} +(40.5435 + 40.5435i) q^{87} +(30.2553 - 30.2553i) q^{88} -34.2132i q^{89} +(-6.85852 - 20.0739i) q^{90} -54.8020 q^{91} +(38.9867 + 38.9867i) q^{92} +(34.0699 - 34.0699i) q^{93} -67.7807i q^{94} +(-9.20257 - 4.51558i) q^{95} +9.79796 q^{96} +(104.393 + 104.393i) q^{97} +(7.00000 - 7.00000i) q^{98} -45.3829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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