LMFDB - Embedded newform 700.2.c.e.699.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.3
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.e.699.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.633975 - 2.36603i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.633975 - 2.36603i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +0.267949i q^{11} +(-1.73205 - 3.00000i) q^{12} -0.464102 q^{13} +(3.36603 + 1.63397i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410 q^{17} -6.00000 q^{19} +(3.00000 - 3.46410i) q^{21} +(0.0980762 + 0.366025i) q^{22} -1.46410 q^{23} +(-3.46410 - 3.46410i) q^{24} +(-0.633975 + 0.169873i) q^{26} -5.19615i q^{27} +(5.19615 + 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(1.46410 - 5.46410i) q^{32} +0.464102 q^{33} +(8.83013 - 2.36603i) q^{34} +9.46410i q^{37} +(-8.19615 + 2.19615i) q^{38} +0.803848i q^{39} +3.46410i q^{41} +(2.83013 - 5.83013i) q^{42} -2.00000 q^{43} +(0.267949 + 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} -1.73205i q^{47} +(-6.00000 - 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} -11.1962i q^{51} +(-0.803848 + 0.464102i) q^{52} +2.00000i q^{53} +(-1.90192 - 7.09808i) q^{54} +(7.46410 - 0.535898i) q^{56} +10.3923i q^{57} +(-10.8301 + 2.90192i) q^{58} +3.46410 q^{59} -9.46410i q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(0.633975 - 0.169873i) q^{66} -3.46410 q^{67} +(11.1962 - 6.46410i) q^{68} +2.53590i q^{69} +7.46410i q^{71} +12.9282 q^{73} +(3.46410 + 12.9282i) q^{74} +(-10.3923 + 6.00000i) q^{76} +(-0.464102 + 0.535898i) q^{77} +(0.294229 + 1.09808i) q^{78} -14.6603i q^{79} -9.00000 q^{81} +(1.26795 + 4.73205i) q^{82} +15.4641i q^{83} +(1.73205 - 9.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} +13.7321i q^{87} +(0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(-0.928203 - 0.803848i) q^{91} +(-2.53590 + 1.46410i) q^{92} +10.3923i q^{93} +(-0.633975 - 2.36603i) q^{94} +(-9.46410 - 2.53590i) q^{96} +13.3923 q^{97} +(3.90192 + 9.09808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^6 + 8 * q^7 + 8 * q^8	$ 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{13} + 10 q^{14} + 8 q^{16} + 12 q^{17} - 24 q^{19} + 12 q^{21} - 10 q^{22} + 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} - 8 q^{32} - 12 q^{33} + 18 q^{34} - 12 q^{38} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 24 q^{48} + 4 q^{49} - 24 q^{52} - 18 q^{54} + 16 q^{56} - 26 q^{58} - 12 q^{62} + 6 q^{66} + 24 q^{68} + 24 q^{73} + 12 q^{77} - 30 q^{78} - 36 q^{81} + 12 q^{82} - 4 q^{86} + 16 q^{88} + 24 q^{91} - 24 q^{92} - 6 q^{94} - 24 q^{96} + 12 q^{97} + 26 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^13 + 10 * q^14 + 8 * q^16 + 12 * q^17 - 24 * q^19 + 12 * q^21 - 10 * q^22 + 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 - 8 * q^32 - 12 * q^33 + 18 * q^34 - 12 * q^38 - 6 * q^42 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 24 * q^48 + 4 * q^49 - 24 * q^52 - 18 * q^54 + 16 * q^56 - 26 * q^58 - 12 * q^62 + 6 * q^66 + 24 * q^68 + 24 * q^73 + 12 * q^77 - 30 * q^78 - 36 * q^81 + 12 * q^82 - 4 * q^86 + 16 * q^88 + 24 * q^91 - 24 * q^92 - 6 * q^94 - 24 * q^96 + 12 * q^97 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$		−	1.73205i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$		−	1.73205i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	−0.633975	−	2.36603i	−0.258819	−	0.965926i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$		0			0
$11$			0.267949i			0.0807897i	0.999184	+	0.0403949i	$0.0128616\pi$
$11$			0.267949i			0.0807897i	−0.999184	+	0.0403949i	$0.987138\pi$
$12$	−1.73205	−	3.00000i	−0.500000	−	0.866025i
$13$	−0.464102			−0.128719			−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	−0.464102			−0.128719			−0.0643593	+	0.997927i	$0.520500\pi$
$14$	3.36603	+	1.63397i	0.899608	+	0.436698i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	6.46410			1.56777			0.783887	−	0.620903i	$-0.213234\pi$
$17$	6.46410			1.56777			0.783887	+	0.620903i	$0.213234\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$		0			0
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	0.0980762	+	0.366025i	0.0209099	+	0.0780369i
$23$	−1.46410			−0.305286			−0.152643	−	0.988281i	$-0.548779\pi$
$23$	−1.46410			−0.305286			−0.152643	+	0.988281i	$0.548779\pi$
$24$	−3.46410	−	3.46410i	−0.707107	−	0.707107i
$25$		0			0
$26$	−0.633975	+	0.169873i	−0.124333	+	0.0333148i
$27$		−	5.19615i		−	1.00000i
$28$	5.19615	+	1.00000i	0.981981	+	0.188982i
$29$	−7.92820			−1.47223			−0.736115	−	0.676856i	$-0.763342\pi$
$29$	−7.92820			−1.47223			−0.736115	+	0.676856i	$0.763342\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$	0.464102			0.0807897
$34$	8.83013	−	2.36603i	1.51435	−	0.405770i
$35$		0			0
$36$		0			0
$37$			9.46410i			1.55589i	0.628333	+	0.777944i	$0.283737\pi$
$37$			9.46410i			1.55589i	−0.628333	+	0.777944i	$0.716263\pi$
$38$	−8.19615	+	2.19615i	−1.32959	+	0.356263i
$39$			0.803848i			0.128719i
$40$		0			0
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$	2.83013	−	5.83013i	0.436698	−	0.899608i
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$	0.267949	+	0.464102i	0.0403949	+	0.0699660i
$45$		0			0
$46$	−2.00000	+	0.535898i	−0.294884	+	0.0790139i
$47$		−	1.73205i		−	0.252646i	−0.991989	−	0.126323i	$-0.959682\pi$
$47$		−	1.73205i		−	0.252646i	0.991989	−	0.126323i	$-0.0403175\pi$
$48$	−6.00000	−	3.46410i	−0.866025	−	0.500000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		−	11.1962i		−	1.56777i
$52$	−0.803848	+	0.464102i	−0.111474	+	0.0643593i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−1.90192	−	7.09808i	−0.258819	−	0.965926i
$55$		0			0
$56$	7.46410	−	0.535898i	0.997433	−	0.0716124i
$57$			10.3923i			1.37649i
$58$	−10.8301	+	2.90192i	−1.42207	+	0.381041i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$		0			0
$61$		−	9.46410i		−	1.21175i	−0.795558	−	0.605877i	$-0.792822\pi$
$61$		−	9.46410i		−	1.21175i	0.795558	−	0.605877i	$-0.207178\pi$
$62$	−8.19615	+	2.19615i	−1.04091	+	0.278912i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	0.633975	−	0.169873i	0.0780369	−	0.0209099i
$67$	−3.46410			−0.423207			−0.211604	−	0.977356i	$-0.567869\pi$
$67$	−3.46410			−0.423207			−0.211604	+	0.977356i	$0.567869\pi$
$68$	11.1962	−	6.46410i	1.35773	−	0.783887i
$69$			2.53590i			0.305286i
$70$		0			0
$71$			7.46410i			0.885826i	0.896565	+	0.442913i	$0.146055\pi$
$71$			7.46410i			0.885826i	−0.896565	+	0.442913i	$0.853945\pi$
$72$		0			0
$73$	12.9282			1.51313			0.756566	−	0.653917i	$-0.226876\pi$
$73$	12.9282			1.51313			0.756566	+	0.653917i	$0.226876\pi$
$74$	3.46410	+	12.9282i	0.402694	+	1.50287i
$75$		0			0
$76$	−10.3923	+	6.00000i	−1.19208	+	0.688247i
$77$	−0.464102	+	0.535898i	−0.0528893	+	0.0610713i
$78$	0.294229	+	1.09808i	0.0333148	+	0.124333i
$79$		−	14.6603i		−	1.64941i	−0.565565	−	0.824704i	$-0.691342\pi$
$79$		−	14.6603i		−	1.64941i	0.565565	−	0.824704i	$-0.308658\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	1.26795	+	4.73205i	0.140022	+	0.522568i
$83$			15.4641i			1.69741i	0.528870	+	0.848703i	$0.322616\pi$
$83$			15.4641i			1.69741i	−0.528870	+	0.848703i	$0.677384\pi$
$84$	1.73205	−	9.00000i	0.188982	−	0.981981i
$85$		0			0
$86$	−2.73205	+	0.732051i	−0.294605	+	0.0789391i
$87$			13.7321i			1.47223i
$88$	0.535898	+	0.535898i	0.0571270	+	0.0571270i
$89$			2.53590i			0.268805i	0.990927	+	0.134402i	$0.0429115\pi$
$89$			2.53590i			0.268805i	−0.990927	+	0.134402i	$0.957089\pi$
$90$		0			0
$91$	−0.928203	−	0.803848i	−0.0973021	−	0.0842661i
$92$	−2.53590	+	1.46410i	−0.264386	+	0.152643i
$93$			10.3923i			1.07763i
$94$	−0.633975	−	2.36603i	−0.0653895	−	0.244037i
$95$		0			0
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$	13.3923			1.35978			0.679891	−	0.733313i	$-0.262027\pi$
$97$	13.3923			1.35978			0.679891	+	0.733313i	$0.262027\pi$
$98$	3.90192	+	9.09808i	0.394154	+	0.919044i
$99$		0			0
$100$		0			0
$101$			15.4641i			1.53874i	0.638806	+	0.769368i	$0.279429\pi$
$101$			15.4641i			1.53874i	−0.638806	+	0.769368i	$0.720571\pi$
$102$	−4.09808	−	15.2942i	−0.405770	−	1.51435i
$103$		−	6.80385i		−	0.670403i	−0.942146	−	0.335202i	$-0.891196\pi$
$103$		−	6.80385i		−	0.670403i	0.942146	−	0.335202i	$-0.108804\pi$
$104$	−0.928203	+	0.928203i	−0.0910178	+	0.0910178i
$105$		0			0
$106$	0.732051	+	2.73205i	0.0711031	+	0.265360i
$107$	−2.39230			−0.231273			−0.115636	−	0.993292i	$-0.536891\pi$
$107$	−2.39230			−0.231273			−0.115636	+	0.993292i	$0.536891\pi$
$108$	−5.19615	−	9.00000i	−0.500000	−	0.866025i
$109$	−2.07180			−0.198442			−0.0992211	−	0.995065i	$-0.531635\pi$
$109$	−2.07180			−0.198442			−0.0992211	+	0.995065i	$0.531635\pi$
$110$		0			0
$111$	16.3923			1.55589
$112$	10.0000	−	3.46410i	0.944911	−	0.327327i
$113$			5.46410i			0.514019i	0.966409	+	0.257010i	$0.0827372\pi$
$113$			5.46410i			0.514019i	−0.966409	+	0.257010i	$0.917263\pi$
$114$	3.80385	+	14.1962i	0.356263	+	1.32959i
$115$		0			0
$116$	−13.7321	+	7.92820i	−1.27499	+	0.736115i
$117$		0			0
$118$	4.73205	−	1.26795i	0.435621	−	0.116724i
$119$	12.9282	+	11.1962i	1.18513	+	1.02635i
$120$		0			0
$121$	10.9282			0.993473
$122$	−3.46410	−	12.9282i	−0.313625	−	1.17046i
$123$	6.00000			0.541002
$124$	−10.3923	+	6.00000i	−0.933257	+	0.538816i
$125$		0			0
$126$		0			0
$127$	−15.4641			−1.37222			−0.686109	−	0.727499i	$-0.740683\pi$
$127$	−15.4641			−1.37222			−0.686109	+	0.727499i	$0.740683\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$			3.46410i			0.304997i
$130$		0			0
$131$	2.53590			0.221562			0.110781	−	0.993845i	$-0.464665\pi$
$131$	2.53590			0.221562			0.110781	+	0.993845i	$0.464665\pi$
$132$	0.803848	−	0.464102i	0.0699660	−	0.0403949i
$133$	−12.0000	−	10.3923i	−1.04053	−	0.901127i
$134$	−4.73205	+	1.26795i	−0.408787	+	0.109534i
$135$		0			0
$136$	12.9282	−	12.9282i	1.10858	−	1.10858i
$137$		−	20.3923i		−	1.74223i	−0.491077	−	0.871116i	$-0.663397\pi$
$137$		−	20.3923i		−	1.74223i	0.491077	−	0.871116i	$-0.336603\pi$
$138$	0.928203	+	3.46410i	0.0790139	+	0.294884i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	2.73205	+	10.1962i	0.229269	+	0.855642i
$143$		−	0.124356i		−	0.0103991i
$144$		0			0
$145$		0			0
$146$	17.6603	−	4.73205i	1.46157	−	0.391627i
$147$	12.0000	−	1.73205i	0.989743	−	0.142857i
$148$	9.46410	+	16.3923i	0.777944	+	1.34744i
$149$	−3.07180			−0.251651			−0.125826	−	0.992052i	$-0.540158\pi$
$149$	−3.07180			−0.251651			−0.125826	+	0.992052i	$0.540158\pi$
$150$		0			0
$151$			15.1962i			1.23665i	0.785924	+	0.618323i	$0.212188\pi$
$151$			15.1962i			1.23665i	−0.785924	+	0.618323i	$0.787812\pi$
$152$	−12.0000	+	12.0000i	−0.973329	+	0.973329i
$153$		0			0
$154$	−0.437822	+	0.901924i	−0.0352807	+	0.0726791i
$155$		0			0
$156$	0.803848	+	1.39230i	0.0643593	+	0.111474i
$157$	−7.85641			−0.627009			−0.313505	−	0.949587i	$-0.601503\pi$
$157$	−7.85641			−0.627009			−0.313505	+	0.949587i	$0.601503\pi$
$158$	−5.36603	−	20.0263i	−0.426898	−	1.59321i
$159$	3.46410			0.274721
$160$		0			0
$161$	−2.92820	−	2.53590i	−0.230775	−	0.199857i
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$	20.7846			1.62798			0.813988	−	0.580881i	$-0.197292\pi$
$163$	20.7846			1.62798			0.813988	+	0.580881i	$0.197292\pi$
$164$	3.46410	+	6.00000i	0.270501	+	0.468521i
$165$		0			0
$166$	5.66025	+	21.1244i	0.439321	+	1.63957i
$167$			5.19615i			0.402090i	0.979582	+	0.201045i	$0.0644338\pi$
$167$			5.19615i			0.402090i	−0.979582	+	0.201045i	$0.935566\pi$
$168$	−0.928203	−	12.9282i	−0.0716124	−	0.997433i
$169$	−12.7846			−0.983432
$170$		0			0
$171$		0			0
$172$	−3.46410	+	2.00000i	−0.264135	+	0.152499i
$173$	−14.3205			−1.08877			−0.544384	−	0.838836i	$-0.683237\pi$
$173$	−14.3205			−1.08877			−0.544384	+	0.838836i	$0.683237\pi$
$174$	5.02628	+	18.7583i	0.381041	+	1.42207i
$175$		0			0
$176$	0.928203	+	0.535898i	0.0699660	+	0.0403949i
$177$		−	6.00000i		−	0.450988i
$178$	0.928203	+	3.46410i	0.0695718	+	0.259645i
$179$			6.39230i			0.477783i	0.971046	+	0.238892i	$0.0767841\pi$
$179$			6.39230i			0.477783i	−0.971046	+	0.238892i	$0.923216\pi$
$180$		0			0
$181$			0.928203i			0.0689928i	0.999405	+	0.0344964i	$0.0109827\pi$
$181$			0.928203i			0.0689928i	−0.999405	+	0.0344964i	$0.989017\pi$
$182$	−1.56218	−	0.758330i	−0.115796	−	0.0562112i
$183$	−16.3923			−1.21175
$184$	−2.92820	+	2.92820i	−0.215870	+	0.215870i
$185$		0			0
$186$	3.80385	+	14.1962i	0.278912	+	1.04091i
$187$			1.73205i			0.126660i
$188$	−1.73205	−	3.00000i	−0.126323	−	0.218797i
$189$	9.00000	−	10.3923i	0.654654	−	0.755929i
$190$		0			0
$191$			7.19615i			0.520695i	0.965515	+	0.260348i	$0.0838372\pi$
$191$			7.19615i			0.520695i	−0.965515	+	0.260348i	$0.916163\pi$
$192$	−13.8564			−1.00000
$193$		−	9.46410i		−	0.681241i	−0.940201	−	0.340620i	$-0.889363\pi$
$193$		−	9.46410i		−	0.681241i	0.940201	−	0.340620i	$-0.110637\pi$
$194$	18.2942	−	4.90192i	1.31345	−	0.351938i
$195$		0			0
$196$	8.66025	+	11.0000i	0.618590	+	0.785714i
$197$			13.3205i			0.949047i	0.880243	+	0.474523i	$0.157380\pi$
$197$			13.3205i			0.949047i	−0.880243	+	0.474523i	$0.842620\pi$
$198$		0			0
$199$	−3.46410			−0.245564			−0.122782	−	0.992434i	$-0.539182\pi$
$199$	−3.46410			−0.245564			−0.122782	+	0.992434i	$0.539182\pi$
$200$		0			0
$201$			6.00000i			0.423207i
$202$	5.66025	+	21.1244i	0.398254	+	1.48630i
$203$	−15.8564	−	13.7321i	−1.11290	−	0.963801i
$204$	−11.1962	−	19.3923i	−0.783887	−	1.35773i
$205$		0			0
$206$	−2.49038	−	9.29423i	−0.173513	−	0.647560i
$207$		0			0
$208$	−0.928203	+	1.60770i	−0.0643593	+	0.111474i
$209$		−	1.60770i		−	0.111207i
$210$		0			0
$211$			3.19615i			0.220032i	0.993930	+	0.110016i	$0.0350902\pi$
$211$			3.19615i			0.220032i	−0.993930	+	0.110016i	$0.964910\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$	12.9282			0.885826
$214$	−3.26795	+	0.875644i	−0.223392	+	0.0598578i
$215$		0			0
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	−12.0000	−	10.3923i	−0.814613	−	0.705476i
$218$	−2.83013	+	0.758330i	−0.191680	+	0.0513606i
$219$		−	22.3923i		−	1.51313i
$220$		0			0
$221$	−3.00000			−0.201802
$222$	22.3923	−	6.00000i	1.50287	−	0.402694i
$223$		−	13.7321i		−	0.919566i	−0.888031	−	0.459783i	$-0.847927\pi$
$223$		−	13.7321i		−	0.919566i	0.888031	−	0.459783i	$-0.152073\pi$
$224$	12.3923	−	8.39230i	0.827996	−	0.560734i
$225$		0			0
$226$	2.00000	+	7.46410i	0.133038	+	0.496505i
$227$		−	20.6603i		−	1.37127i	−0.727946	−	0.685635i	$-0.759525\pi$
$227$		−	20.6603i		−	1.37127i	0.727946	−	0.685635i	$-0.240475\pi$
$228$	10.3923	+	18.0000i	0.688247	+	1.19208i
$229$		−	8.53590i		−	0.564068i	−0.959404	−	0.282034i	$-0.908991\pi$
$229$		−	8.53590i		−	0.564068i	0.959404	−	0.282034i	$-0.0910091\pi$
$230$		0			0
$231$	0.928203	+	0.803848i	0.0610713	+	0.0528893i
$232$	−15.8564	+	15.8564i	−1.04102	+	1.04102i
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$	−25.3923			−1.64941
$238$	21.7583	+	10.5622i	1.41038	+	0.684644i
$239$			23.9808i			1.55119i	0.631233	+	0.775593i	$0.282549\pi$
$239$			23.9808i			1.55119i	−0.631233	+	0.775593i	$0.717451\pi$
$240$		0			0
$241$		−	16.3923i		−	1.05592i	−0.849269	−	0.527961i	$-0.822957\pi$
$241$		−	16.3923i		−	1.05592i	0.849269	−	0.527961i	$-0.177043\pi$
$242$	14.9282	−	4.00000i	0.959621	−	0.257130i
$243$		0			0
$244$	−9.46410	−	16.3923i	−0.605877	−	1.04941i
$245$		0			0
$246$	8.19615	−	2.19615i	0.522568	−	0.140022i
$247$	2.78461			0.177180
$248$	−12.0000	+	12.0000i	−0.762001	+	0.762001i
$249$	26.7846			1.69741
$250$		0			0
$251$	−25.8564			−1.63204			−0.816021	−	0.578022i	$-0.803825\pi$
$251$	−25.8564			−1.63204			−0.816021	+	0.578022i	$0.803825\pi$
$252$		0			0
$253$		−	0.392305i		−	0.0246640i
$254$	−21.1244	+	5.66025i	−1.32546	+	0.355156i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$	1.26795	+	4.73205i	0.0789391	+	0.294605i
$259$	−16.3923	+	18.9282i	−1.01857	+	1.17614i
$260$		0			0
$261$		0			0
$262$	3.46410	−	0.928203i	0.214013	−	0.0573446i
$263$	11.4641			0.706907			0.353453	−	0.935452i	$-0.385007\pi$
$263$	11.4641			0.706907			0.353453	+	0.935452i	$0.385007\pi$
$264$	0.928203	−	0.928203i	0.0571270	−	0.0571270i
$265$		0			0
$266$	−20.1962	−	9.80385i	−1.23831	−	0.601112i
$267$	4.39230			0.268805
$268$	−6.00000	+	3.46410i	−0.366508	+	0.211604i
$269$		−	12.0000i		−	0.731653i	−0.930683	−	0.365826i	$-0.880786\pi$
$269$		−	12.0000i		−	0.731653i	0.930683	−	0.365826i	$-0.119214\pi$
$270$		0			0
$271$	9.46410			0.574903			0.287452	−	0.957795i	$-0.407192\pi$
$271$	9.46410			0.574903			0.287452	+	0.957795i	$0.407192\pi$
$272$	12.9282	−	22.3923i	0.783887	−	1.35773i
$273$	−1.39230	+	1.60770i	−0.0842661	+	0.0973021i
$274$	−7.46410	−	27.8564i	−0.450923	−	1.68287i
$275$		0			0
$276$	2.53590	+	4.39230i	0.152643	+	0.264386i
$277$		−	16.7846i		−	1.00849i	−0.863561	−	0.504245i	$-0.831771\pi$
$277$		−	16.7846i		−	1.00849i	0.863561	−	0.504245i	$-0.168229\pi$
$278$	−9.46410	+	2.53590i	−0.567619	+	0.152093i
$279$		0			0
$280$		0			0
$281$	−7.92820			−0.472957			−0.236478	−	0.971637i	$-0.575993\pi$
$281$	−7.92820			−0.472957			−0.236478	+	0.971637i	$0.575993\pi$
$282$	−4.09808	+	1.09808i	−0.244037	+	0.0653895i
$283$			12.1244i			0.720718i	0.932814	+	0.360359i	$0.117346\pi$
$283$			12.1244i			0.720718i	−0.932814	+	0.360359i	$0.882654\pi$
$284$	7.46410	+	12.9282i	0.442913	+	0.767148i
$285$		0			0
$286$	−0.0455173	−	0.169873i	−0.00269150	−	0.0100448i
$287$	−6.00000	+	6.92820i	−0.354169	+	0.408959i
$288$		0			0
$289$	24.7846			1.45792
$290$		0			0
$291$		−	23.1962i		−	1.35978i
$292$	22.3923	−	12.9282i	1.31041	−	0.756566i
$293$	20.3205			1.18714			0.593568	−	0.804784i	$-0.297719\pi$
$293$	20.3205			1.18714			0.593568	+	0.804784i	$0.297719\pi$
$294$	15.7583	−	6.75833i	0.919044	−	0.394154i
$295$		0			0
$296$	18.9282	+	18.9282i	1.10018	+	1.10018i
$297$	1.39230			0.0807897
$298$	−4.19615	+	1.12436i	−0.243077	+	0.0651322i
$299$	0.679492			0.0392960
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	5.56218	+	20.7583i	0.320067	+	1.19451i
$303$	26.7846			1.53874
$304$	−12.0000	+	20.7846i	−0.688247	+	1.19208i
$305$		0			0
$306$		0			0
$307$		−	1.73205i		−	0.0988534i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$		−	1.73205i		−	0.0988534i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$	−0.267949	+	1.39230i	−0.0152678	+	0.0793339i
$309$	−11.7846			−0.670403
$310$		0			0
$311$	7.85641			0.445496			0.222748	−	0.974876i	$-0.428497\pi$
$311$	7.85641			0.445496			0.222748	+	0.974876i	$0.428497\pi$
$312$	1.60770	+	1.60770i	0.0910178	+	0.0910178i
$313$	−17.5359			−0.991188			−0.495594	−	0.868554i	$-0.665050\pi$
$313$	−17.5359			−0.991188			−0.495594	+	0.868554i	$0.665050\pi$
$314$	−10.7321	+	2.87564i	−0.605645	+	0.162282i
$315$		0			0
$316$	−14.6603	−	25.3923i	−0.824704	−	1.42843i
$317$			3.07180i			0.172529i	0.996272	+	0.0862646i	$0.0274931\pi$
$317$			3.07180i			0.172529i	−0.996272	+	0.0862646i	$0.972507\pi$
$318$	4.73205	−	1.26795i	0.265360	−	0.0711031i
$319$		−	2.12436i		−	0.118941i
$320$		0			0
$321$			4.14359i			0.231273i
$322$	−4.92820	−	2.39230i	−0.274638	−	0.133318i
$323$	−38.7846			−2.15803
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$		0			0
$326$	28.3923	−	7.60770i	1.57250	−	0.421351i
$327$			3.58846i			0.198442i
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$	3.00000	−	3.46410i	0.165395	−	0.190982i
$330$		0			0
$331$		−	26.3923i		−	1.45065i	−0.688405	−	0.725326i	$-0.741689\pi$
$331$		−	26.3923i		−	1.45065i	0.688405	−	0.725326i	$-0.258311\pi$
$332$	15.4641	+	26.7846i	0.848703	+	1.47000i
$333$		0			0
$334$	1.90192	+	7.09808i	0.104069	+	0.388389i
$335$		0			0
$336$	−6.00000	−	17.3205i	−0.327327	−	0.944911i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−17.4641	+	4.67949i	−0.949922	+	0.254531i
$339$	9.46410			0.514019
$340$		0			0
$341$		−	1.60770i		−	0.0870616i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−4.00000	+	4.00000i	−0.215666	+	0.215666i
$345$		0			0
$346$	−19.5622	+	5.24167i	−1.05167	+	0.281794i
$347$	34.2487			1.83857			0.919284	−	0.393596i	$-0.128769\pi$
$347$	34.2487			1.83857			0.919284	+	0.393596i	$0.128769\pi$
$348$	13.7321	+	23.7846i	0.736115	+	1.27499i
$349$		−	5.32051i		−	0.284800i	−0.989809	−	0.142400i	$-0.954518\pi$
$349$		−	5.32051i		−	0.284800i	0.989809	−	0.142400i	$-0.0454820\pi$
$350$		0			0
$351$			2.41154i			0.128719i
$352$	1.46410	+	0.392305i	0.0780369	+	0.0209099i
$353$	−7.39230			−0.393453			−0.196726	−	0.980458i	$-0.563031\pi$
$353$	−7.39230			−0.393453			−0.196726	+	0.980458i	$0.563031\pi$
$354$	−2.19615	−	8.19615i	−0.116724	−	0.435621i
$355$		0			0
$356$	2.53590	+	4.39230i	0.134402	+	0.232792i
$357$	19.3923	−	22.3923i	1.02635	−	1.18513i
$358$	2.33975	+	8.73205i	0.123659	+	0.461503i
$359$		−	25.3205i		−	1.33637i	−0.743997	−	0.668183i	$-0.767072\pi$
$359$		−	25.3205i		−	1.33637i	0.743997	−	0.668183i	$-0.232928\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	0.339746	+	1.26795i	0.0178567	+	0.0666419i
$363$		−	18.9282i		−	0.993473i
$364$	−2.41154	−	0.464102i	−0.126399	−	0.0243255i
$365$		0			0
$366$	−22.3923	+	6.00000i	−1.17046	+	0.313625i
$367$		−	11.8756i		−	0.619904i	−0.950752	−	0.309952i	$-0.899687\pi$
$367$		−	11.8756i		−	0.619904i	0.950752	−	0.309952i	$-0.100313\pi$
$368$	−2.92820	+	5.07180i	−0.152643	+	0.264386i
$369$		0			0
$370$		0			0
$371$	−3.46410	+	4.00000i	−0.179847	+	0.207670i
$372$	10.3923	+	18.0000i	0.538816	+	0.933257i
$373$		−	3.60770i		−	0.186799i	−0.995629	−	0.0933997i	$-0.970227\pi$
$373$		−	3.60770i		−	0.186799i	0.995629	−	0.0933997i	$-0.0297734\pi$
$374$	0.633975	+	2.36603i	0.0327820	+	0.122344i
$375$		0			0
$376$	−3.46410	−	3.46410i	−0.178647	−	0.178647i
$377$	3.67949			0.189503
$378$	8.49038	−	17.4904i	0.436698	−	0.899608i
$379$		−	5.60770i		−	0.288048i	−0.989574	−	0.144024i	$-0.953996\pi$
$379$		−	5.60770i		−	0.288048i	0.989574	−	0.144024i	$-0.0460042\pi$
$380$		0			0
$381$			26.7846i			1.37222i
$382$	2.63397	+	9.83013i	0.134766	+	0.502953i
$383$			27.4641i			1.40335i	0.712497	+	0.701675i	$0.247564\pi$
$383$			27.4641i			1.40335i	−0.712497	+	0.701675i	$0.752436\pi$
$384$	−18.9282	+	5.07180i	−0.965926	+	0.258819i
$385$		0			0
$386$	−3.46410	−	12.9282i	−0.176318	−	0.658028i
$387$		0			0
$388$	23.1962	−	13.3923i	1.17761	−	0.679891i
$389$	20.8564			1.05746			0.528731	−	0.848790i	$-0.322668\pi$
$389$	20.8564			1.05746			0.528731	+	0.848790i	$0.322668\pi$
$390$		0			0
$391$	−9.46410			−0.478620
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$		−	4.39230i		−	0.221562i
$394$	4.87564	+	18.1962i	0.245631	+	0.916709i
$395$		0			0
$396$		0			0
$397$	−12.4641			−0.625555			−0.312778	−	0.949826i	$-0.601259\pi$
$397$	−12.4641			−0.625555			−0.312778	+	0.949826i	$0.601259\pi$
$398$	−4.73205	+	1.26795i	−0.237196	+	0.0635566i
$399$	−18.0000	+	20.7846i	−0.901127	+	1.04053i
$400$		0			0
$401$	−10.0718			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$401$	−10.0718			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$402$	2.19615	+	8.19615i	0.109534	+	0.408787i
$403$	2.78461			0.138711
$404$	15.4641	+	26.7846i	0.769368	+	1.33258i
$405$		0			0
$406$	−26.6865	−	12.9545i	−1.32443	−	0.642920i
$407$	−2.53590			−0.125700
$408$	−22.3923	−	22.3923i	−1.10858	−	1.10858i
$409$			4.14359i			0.204888i	0.994739	+	0.102444i	$0.0326662\pi$
$409$			4.14359i			0.204888i	−0.994739	+	0.102444i	$0.967334\pi$
$410$		0			0
$411$	−35.3205			−1.74223
$412$	−6.80385	−	11.7846i	−0.335202	−	0.580586i
$413$	6.92820	+	6.00000i	0.340915	+	0.295241i
$414$		0			0
$415$		0			0
$416$	−0.679492	+	2.53590i	−0.0333148	+	0.124333i
$417$			12.0000i			0.587643i
$418$	−0.588457	−	2.19615i	−0.0287824	−	0.107417i
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	1.16987	+	4.36603i	0.0569485	+	0.212535i
$423$		0			0
$424$	4.00000	+	4.00000i	0.194257	+	0.194257i
$425$		0			0
$426$	17.6603	−	4.73205i	0.855642	−	0.229269i
$427$	16.3923	−	18.9282i	0.793279	−	0.916000i
$428$	−4.14359	+	2.39230i	−0.200288	+	0.115636i
$429$	−0.215390			−0.0103991
$430$		0			0
$431$		−	13.5885i		−	0.654533i	−0.944932	−	0.327266i	$-0.893873\pi$
$431$		−	13.5885i		−	0.654533i	0.944932	−	0.327266i	$-0.106127\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	−31.8564			−1.53092			−0.765461	−	0.643483i	$-0.777489\pi$
$433$	−31.8564			−1.53092			−0.765461	+	0.643483i	$0.777489\pi$
$434$	−20.1962	−	9.80385i	−0.969446	−	0.470600i
$435$		0			0
$436$	−3.58846	+	2.07180i	−0.171856	+	0.0992211i
$437$	8.78461			0.420225
$438$	−8.19615	−	30.5885i	−0.391627	−	1.46157i
$439$	39.7128			1.89539			0.947695	−	0.319179i	$-0.103407\pi$
$439$	39.7128			1.89539			0.947695	+	0.319179i	$0.103407\pi$
$440$		0			0
$441$		0			0
$442$	−4.09808	+	1.09808i	−0.194926	+	0.0522302i
$443$	26.0000			1.23530			0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000			1.23530			0.617649	+	0.786454i	$0.288085\pi$
$444$	28.3923	−	16.3923i	1.34744	−	0.777944i
$445$		0			0
$446$	−5.02628	−	18.7583i	−0.238001	−	0.888233i
$447$			5.32051i			0.251651i
$448$	13.8564	−	16.0000i	0.654654	−	0.755929i
$449$	−11.9282			−0.562927			−0.281463	−	0.959572i	$-0.590820\pi$
$449$	−11.9282			−0.562927			−0.281463	+	0.959572i	$0.590820\pi$
$450$		0			0
$451$	−0.928203			−0.0437074
$452$	5.46410	+	9.46410i	0.257010	+	0.445154i
$453$	26.3205			1.23665
$454$	−7.56218	−	28.2224i	−0.354911	−	1.32454i
$455$		0			0
$456$	20.7846	+	20.7846i	0.973329	+	0.973329i
$457$		−	20.5359i		−	0.960629i	−0.877096	−	0.480314i	$-0.840523\pi$
$457$		−	20.5359i		−	0.960629i	0.877096	−	0.480314i	$-0.159477\pi$
$458$	−3.12436	−	11.6603i	−0.145992	−	0.544848i
$459$		−	33.5885i		−	1.56777i
$460$		0			0
$461$		−	27.7128i		−	1.29071i	−0.763881	−	0.645357i	$-0.776709\pi$
$461$		−	27.7128i		−	1.29071i	0.763881	−	0.645357i	$-0.223291\pi$
$462$	1.56218	+	0.758330i	0.0726791	+	0.0352807i
$463$	16.3923			0.761815			0.380908	−	0.924613i	$-0.375612\pi$
$463$	16.3923			0.761815			0.380908	+	0.924613i	$0.375612\pi$
$464$	−15.8564	+	27.4641i	−0.736115	+	1.27499i
$465$		0			0
$466$	−3.32051	−	12.3923i	−0.153820	−	0.574062i
$467$		−	22.5167i		−	1.04195i	−0.853573	−	0.520973i	$-0.825569\pi$
$467$		−	22.5167i		−	1.04195i	0.853573	−	0.520973i	$-0.174431\pi$
$468$		0			0
$469$	−6.92820	−	6.00000i	−0.319915	−	0.277054i
$470$		0			0
$471$			13.6077i			0.627009i
$472$	6.92820	−	6.92820i	0.318896	−	0.318896i
$473$		−	0.535898i		−	0.0246406i
$474$	−34.6865	+	9.29423i	−1.59321	+	0.426898i
$475$		0			0
$476$	33.5885	+	6.46410i	1.53952	+	0.296282i
$477$		0			0
$478$	8.77757	+	32.7583i	0.401477	+	1.49833i
$479$	−25.1769			−1.15036			−0.575181	−	0.818026i	$-0.695068\pi$
$479$	−25.1769			−1.15036			−0.575181	+	0.818026i	$0.695068\pi$
$480$		0			0
$481$		−	4.39230i		−	0.200272i
$482$	−6.00000	−	22.3923i	−0.273293	−	1.01994i
$483$	−4.39230	+	5.07180i	−0.199857	+	0.230775i
$484$	18.9282	−	10.9282i	0.860373	−	0.496737i
$485$		0			0
$486$		0			0
$487$	−12.7846			−0.579326			−0.289663	−	0.957129i	$-0.593543\pi$
$487$	−12.7846			−0.579326			−0.289663	+	0.957129i	$0.593543\pi$
$488$	−18.9282	−	18.9282i	−0.856840	−	0.856840i
$489$		−	36.0000i		−	1.62798i
$490$		0			0
$491$		−	9.87564i		−	0.445682i	−0.974855	−	0.222841i	$-0.928467\pi$
$491$		−	9.87564i		−	0.445682i	0.974855	−	0.222841i	$-0.0715330\pi$
$492$	10.3923	−	6.00000i	0.468521	−	0.270501i
$493$	−51.2487			−2.30813
$494$	3.80385	−	1.01924i	0.171143	−	0.0458577i
$495$		0			0
$496$	−12.0000	+	20.7846i	−0.538816	+	0.933257i
$497$	−12.9282	+	14.9282i	−0.579909	+	0.669621i
$498$	36.5885	−	9.80385i	1.63957	−	0.439321i
$499$		−	25.5885i		−	1.14550i	−0.819731	−	0.572748i	$-0.805877\pi$
$499$		−	25.5885i		−	1.14550i	0.819731	−	0.572748i	$-0.194123\pi$
$500$		0			0
$501$	9.00000			0.402090
$502$	−35.3205	+	9.46410i	−1.57643	+	0.422404i
$503$		−	15.5885i		−	0.695055i	−0.937670	−	0.347527i	$-0.887021\pi$
$503$		−	15.5885i		−	0.695055i	0.937670	−	0.347527i	$-0.112979\pi$
$504$		0			0
$505$		0			0
$506$	−0.143594	−	0.535898i	−0.00638351	−	0.0238236i
$507$			22.1436i			0.983432i
$508$	−26.7846	+	15.4641i	−1.18837	+	0.686109i
$509$			25.8564i			1.14607i	0.819533	+	0.573033i	$0.194233\pi$
$509$			25.8564i			1.14607i	−0.819533	+	0.573033i	$0.805767\pi$
$510$		0			0
$511$	25.8564	+	22.3923i	1.14382	+	0.990577i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$			31.1769i			1.37649i
$514$	−8.19615	+	2.19615i	−0.361517	+	0.0968681i
$515$		0			0
$516$	3.46410	+	6.00000i	0.152499	+	0.264135i
$517$	0.464102			0.0204112
$518$	−15.4641	+	31.8564i	−0.679454	+	1.39969i
$519$			24.8038i			1.08877i
$520$		0			0
$521$		−	13.6077i		−	0.596164i	−0.954540	−	0.298082i	$-0.903653\pi$
$521$		−	13.6077i		−	0.596164i	0.954540	−	0.298082i	$-0.0963469\pi$
$522$		0			0
$523$		−	24.2487i		−	1.06032i	−0.847897	−	0.530161i	$-0.822131\pi$
$523$		−	24.2487i		−	1.06032i	0.847897	−	0.530161i	$-0.177869\pi$
$524$	4.39230	−	2.53590i	0.191879	−	0.110781i
$525$		0			0
$526$	15.6603	−	4.19615i	0.682820	−	0.182961i
$527$	−38.7846			−1.68948
$528$	0.928203	−	1.60770i	0.0403949	−	0.0699660i
$529$	−20.8564			−0.906800
$530$		0			0
$531$		0			0
$532$	−31.1769	−	6.00000i	−1.35169	−	0.260133i
$533$		−	1.60770i		−	0.0696370i
$534$	6.00000	−	1.60770i	0.259645	−	0.0695718i
$535$		0			0
$536$	−6.92820	+	6.92820i	−0.299253	+	0.299253i
$537$	11.0718			0.477783
$538$	−4.39230	−	16.3923i	−0.189366	−	0.706722i
$539$	−1.85641	+	0.267949i	−0.0799611	+	0.0115414i
$540$		0			0
$541$	7.78461			0.334687			0.167343	−	0.985899i	$-0.446481\pi$
$541$	7.78461			0.334687			0.167343	+	0.985899i	$0.446481\pi$
$542$	12.9282	−	3.46410i	0.555314	−	0.148796i
$543$	1.60770			0.0689928
$544$	9.46410	−	35.3205i	0.405770	−	1.51435i
$545$		0			0
$546$	−1.31347	+	2.70577i	−0.0562112	+	0.115796i
$547$	21.4641			0.917739			0.458869	−	0.888504i	$-0.348255\pi$
$547$	21.4641			0.917739			0.458869	+	0.888504i	$0.348255\pi$
$548$	−20.3923	−	35.3205i	−0.871116	−	1.50882i
$549$		0			0
$550$		0			0
$551$	47.5692			2.02652
$552$	5.07180	+	5.07180i	0.215870	+	0.215870i
$553$	25.3923	−	29.3205i	1.07979	−	1.24683i
$554$	−6.14359	−	22.9282i	−0.261016	−	0.974126i
$555$		0			0
$556$	−12.0000	+	6.92820i	−0.508913	+	0.293821i
$557$			21.8564i			0.926086i	0.886336	+	0.463043i	$0.153242\pi$
$557$			21.8564i			0.926086i	−0.886336	+	0.463043i	$0.846758\pi$
$558$		0			0
$559$	0.928203			0.0392588
$560$		0			0
$561$	3.00000			0.126660
$562$	−10.8301	+	2.90192i	−0.456841	+	0.122410i
$563$			19.1769i			0.808211i	0.914712	+	0.404105i	$0.132417\pi$
$563$			19.1769i			0.808211i	−0.914712	+	0.404105i	$0.867583\pi$
$564$	−5.19615	+	3.00000i	−0.218797	+	0.126323i
$565$		0			0
$566$	4.43782	+	16.5622i	0.186536	+	0.696160i
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$	14.9282	+	14.9282i	0.626373	+	0.626373i
$569$	−7.07180			−0.296465			−0.148233	−	0.988953i	$-0.547358\pi$
$569$	−7.07180			−0.296465			−0.148233	+	0.988953i	$0.547358\pi$
$570$		0			0
$571$		−	6.67949i		−	0.279528i	−0.990185	−	0.139764i	$-0.955366\pi$
$571$		−	6.67949i		−	0.279528i	0.990185	−	0.139764i	$-0.0446344\pi$
$572$	−0.124356	−	0.215390i	−0.00519957	−	0.00900592i
$573$	12.4641			0.520695
$574$	−5.66025	+	11.6603i	−0.236254	+	0.486690i
$575$		0			0
$576$		0			0
$577$	−19.3923			−0.807312			−0.403656	−	0.914911i	$-0.632261\pi$
$577$	−19.3923			−0.807312			−0.403656	+	0.914911i	$0.632261\pi$
$578$	33.8564	−	9.07180i	1.40824	−	0.377337i
$579$	−16.3923			−0.681241
$580$		0			0
$581$	−26.7846	+	30.9282i	−1.11121	+	1.28312i
$582$	−8.49038	−	31.6865i	−0.351938	−	1.31345i
$583$	−0.535898			−0.0221946
$584$	25.8564	−	25.8564i	1.06995	−	1.06995i
$585$		0			0
$586$	27.7583	−	7.43782i	1.14669	−	0.307254i
$587$			20.5359i			0.847607i	0.905754	+	0.423804i	$0.139305\pi$
$587$			20.5359i			0.847607i	−0.905754	+	0.423804i	$0.860695\pi$
$588$	19.0526	−	15.0000i	0.785714	−	0.618590i
$589$	36.0000			1.48335
$590$		0			0
$591$	23.0718			0.949047
$592$	32.7846	+	18.9282i	1.34744	+	0.777944i
$593$	30.4641			1.25101			0.625505	−	0.780220i	$-0.284893\pi$
$593$	30.4641			1.25101			0.625505	+	0.780220i	$0.284893\pi$
$594$	1.90192	−	0.509619i	0.0780369	−	0.0209099i
$595$		0			0
$596$	−5.32051	+	3.07180i	−0.217937	+	0.125826i
$597$			6.00000i			0.245564i
$598$	0.928203	−	0.248711i	0.0379571	−	0.0101706i
$599$			10.1244i			0.413670i	0.978376	+	0.206835i	$0.0663163\pi$
$599$			10.1244i			0.413670i	−0.978376	+	0.206835i	$0.933684\pi$
$600$		0			0
$601$			14.7846i			0.603077i	0.953454	+	0.301538i	$0.0975001\pi$
$601$			14.7846i			0.603077i	−0.953454	+	0.301538i	$0.902500\pi$
$602$	−6.73205	−	3.26795i	−0.274378	−	0.133192i
$603$		0			0
$604$	15.1962	+	26.3205i	0.618323	+	1.07097i
$605$		0			0
$606$	36.5885	−	9.80385i	1.48630	−	0.398254i
$607$			29.1962i			1.18504i	0.805557	+	0.592518i	$0.201866\pi$
$607$			29.1962i			1.18504i	−0.805557	+	0.592518i	$0.798134\pi$
$608$	−8.78461	+	32.7846i	−0.356263	+	1.32959i
$609$	−23.7846	+	27.4641i	−0.963801	+	1.11290i
$610$		0			0
$611$			0.803848i			0.0325202i
$612$		0			0
$613$		−	10.0000i		−	0.403896i	−0.979396	−	0.201948i	$-0.935273\pi$
$613$		−	10.0000i		−	0.403896i	0.979396	−	0.201948i	$-0.0647272\pi$
$614$	−0.633975	−	2.36603i	−0.0255851	−	0.0954850i
$615$		0			0
$616$	0.143594	+	2.00000i	0.00578555	+	0.0805823i
$617$			22.9282i			0.923055i	0.887126	+	0.461527i	$0.152698\pi$
$617$			22.9282i			0.923055i	−0.887126	+	0.461527i	$0.847302\pi$
$618$	−16.0981	+	4.31347i	−0.647560	+	0.173513i
$619$	−0.679492			−0.0273111			−0.0136555	−	0.999907i	$-0.504347\pi$
$619$	−0.679492			−0.0273111			−0.0136555	+	0.999907i	$0.504347\pi$
$620$		0			0
$621$			7.60770i			0.305286i
$622$	10.7321	−	2.87564i	0.430316	−	0.115303i
$623$	−4.39230	+	5.07180i	−0.175974	+	0.203197i
$624$	2.78461	+	1.60770i	0.111474	+	0.0643593i
$625$		0			0
$626$	−23.9545	+	6.41858i	−0.957414	+	0.256538i
$627$	−2.78461			−0.111207
$628$	−13.6077	+	7.85641i	−0.543006	+	0.313505i
$629$			61.1769i			2.43928i
$630$		0			0
$631$			38.9090i			1.54894i	0.632610	+	0.774471i	$0.281984\pi$
$631$			38.9090i			1.54894i	−0.632610	+	0.774471i	$0.718016\pi$
$632$	−29.3205	−	29.3205i	−1.16631	−	1.16631i
$633$	5.53590			0.220032
$634$	1.12436	+	4.19615i	0.0446539	+	0.166651i
$635$		0			0
$636$	6.00000	−	3.46410i	0.237915	−	0.137361i
$637$	−0.464102	−	3.21539i	−0.0183884	−	0.127398i
$638$	−0.777568	−	2.90192i	−0.0307842	−	0.114888i
$639$		0			0
$640$		0			0
$641$	8.92820			0.352643			0.176321	−	0.984333i	$-0.443580\pi$
$641$	8.92820			0.352643			0.176321	+	0.984333i	$0.443580\pi$
$642$	1.51666	+	5.66025i	0.0598578	+	0.223392i
$643$			7.05256i			0.278126i	0.990284	+	0.139063i	$0.0444090\pi$
$643$			7.05256i			0.278126i	−0.990284	+	0.139063i	$0.955591\pi$
$644$	−7.60770	−	1.46410i	−0.299785	−	0.0576937i
$645$		0			0
$646$	−52.9808	+	14.1962i	−2.08450	+	0.558540i
$647$			10.3923i			0.408564i	0.978912	+	0.204282i	$0.0654859\pi$
$647$			10.3923i			0.408564i	−0.978912	+	0.204282i	$0.934514\pi$
$648$	−18.0000	+	18.0000i	−0.707107	+	0.707107i
$649$			0.928203i			0.0364352i
$650$		0			0
$651$	−18.0000	+	20.7846i	−0.705476	+	0.814613i
$652$	36.0000	−	20.7846i	1.40987	−	0.813988i
$653$			17.6077i			0.689042i	0.938779	+	0.344521i	$0.111959\pi$
$653$			17.6077i			0.689042i	−0.938779	+	0.344521i	$0.888041\pi$
$654$	1.31347	+	4.90192i	0.0513606	+	0.191680i
$655$		0			0
$656$	12.0000	+	6.92820i	0.468521	+	0.270501i
$657$		0			0
$658$	2.83013	−	5.83013i	0.110330	−	0.227282i
$659$			31.1962i			1.21523i	0.794232	+	0.607615i	$0.207874\pi$
$659$			31.1962i			1.21523i	−0.794232	+	0.607615i	$0.792126\pi$
$660$		0			0
$661$		−	39.7128i		−	1.54465i	−0.635228	−	0.772325i	$-0.719094\pi$
$661$		−	39.7128i		−	1.54465i	0.635228	−	0.772325i	$-0.280906\pi$
$662$	−9.66025	−	36.0526i	−0.375456	−	1.40122i
$663$			5.19615i			0.201802i
$664$	30.9282	+	30.9282i	1.20025	+	1.20025i
$665$		0			0
$666$		0			0
$667$	11.6077			0.449452
$668$	5.19615	+	9.00000i	0.201045	+	0.348220i
$669$	−23.7846			−0.919566
$670$		0			0
$671$	2.53590			0.0978973
$672$	−14.5359	−	21.4641i	−0.560734	−	0.827996i
$673$		−	13.1769i		−	0.507933i	−0.967213	−	0.253966i	$-0.918265\pi$
$673$		−	13.1769i		−	0.507933i	0.967213	−	0.253966i	$-0.0817353\pi$
$674$		0			0
$675$		0			0
$676$	−22.1436	+	12.7846i	−0.851677	+	0.491716i
$677$	25.3923			0.975906			0.487953	−	0.872870i	$-0.337744\pi$
$677$	25.3923			0.975906			0.487953	+	0.872870i	$0.337744\pi$
$678$	12.9282	−	3.46410i	0.496505	−	0.133038i
$679$	26.7846	+	23.1962i	1.02790	+	0.890187i
$680$		0			0
$681$	−35.7846			−1.37127
$682$	−0.588457	−	2.19615i	−0.0225332	−	0.0840950i
$683$	−7.32051			−0.280111			−0.140056	−	0.990144i	$-0.544728\pi$
$683$	−7.32051			−0.280111			−0.140056	+	0.990144i	$0.544728\pi$
$684$		0			0
$685$		0			0
$686$	−7.95448	+	24.9545i	−0.303704	+	0.952767i
$687$	−14.7846			−0.564068
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$		−	0.928203i		−	0.0353617i
$690$		0			0
$691$	−22.6410			−0.861305			−0.430652	−	0.902518i	$-0.641717\pi$
$691$	−22.6410			−0.861305			−0.430652	+	0.902518i	$0.641717\pi$
$692$	−24.8038	+	14.3205i	−0.942901	+	0.544384i
$693$		0			0
$694$	46.7846	−	12.5359i	1.77592	−	0.475856i
$695$		0			0
$696$	27.4641	+	27.4641i	1.04102	+	1.04102i
$697$			22.3923i			0.848169i
$698$	−1.94744	−	7.26795i	−0.0737117	−	0.275096i
$699$	−15.7128			−0.594313
$700$		0			0
$701$	−37.7846			−1.42711			−0.713553	−	0.700602i	$-0.752915\pi$
$701$	−37.7846			−1.42711			−0.713553	+	0.700602i	$0.752915\pi$
$702$	0.882686	+	3.29423i	0.0333148	+	0.124333i
$703$		−	56.7846i		−	2.14167i
$704$	2.14359			0.0807897
$705$		0			0
$706$	−10.0981	+	2.70577i	−0.380046	+	0.101833i
$707$	−26.7846	+	30.9282i	−1.00734	+	1.16317i
$708$	−6.00000	−	10.3923i	−0.225494	−	0.390567i
$709$	−21.0000			−0.788672			−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000			−0.788672			−0.394336	+	0.918966i	$0.629025\pi$
$710$		0			0
$711$		0			0
$712$	5.07180	+	5.07180i	0.190074	+	0.190074i
$713$	8.78461			0.328986
$714$	18.2942	−	37.6865i	0.684644	−	1.41038i
$715$		0			0
$716$	6.39230	+	11.0718i	0.238892	+	0.413772i
$717$	41.5359			1.55119
$718$	−9.26795	−	34.5885i	−0.345877	−	1.29083i
$719$	−38.5359			−1.43715			−0.718573	−	0.695451i	$-0.755205\pi$
$719$	−38.5359			−1.43715			−0.718573	+	0.695451i	$0.755205\pi$
$720$		0			0
$721$	11.7846	−	13.6077i	0.438882	−	0.506777i
$722$	23.2224	−	6.22243i	0.864249	−	0.231575i
$723$	−28.3923			−1.05592
$724$	0.928203	+	1.60770i	0.0344964	+	0.0597495i
$725$		0			0
$726$	−6.92820	−	25.8564i	−0.257130	−	0.959621i
$727$			13.6077i			0.504681i	0.967638	+	0.252341i	$0.0812004\pi$
$727$			13.6077i			0.504681i	−0.967638	+	0.252341i	$0.918800\pi$
$728$	−3.46410	+	0.248711i	−0.128388	+	0.00921785i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−12.9282			−0.478167
$732$	−28.3923	+	16.3923i	−1.04941	+	0.605877i
$733$	11.5359			0.426088			0.213044	−	0.977043i	$-0.431662\pi$
$733$	11.5359			0.426088			0.213044	+	0.977043i	$0.431662\pi$
$734$	−4.34679	−	16.2224i	−0.160443	−	0.598781i
$735$		0			0
$736$	−2.14359	+	8.00000i	−0.0790139	+	0.294884i
$737$		−	0.928203i		−	0.0341908i
$738$		0			0
$739$			4.26795i			0.156999i	0.996914	+	0.0784995i	$0.0250129\pi$
$739$			4.26795i			0.156999i	−0.996914	+	0.0784995i	$0.974987\pi$
$740$		0			0
$741$		−	4.82309i		−	0.177180i
$742$	−3.26795	+	6.73205i	−0.119970	+	0.247141i
$743$	−30.3923			−1.11499			−0.557493	−	0.830182i	$-0.688237\pi$
$743$	−30.3923			−1.11499			−0.557493	+	0.830182i	$0.688237\pi$
$744$	20.7846	+	20.7846i	0.762001	+	0.762001i
$745$		0			0
$746$	−1.32051	−	4.92820i	−0.0483472	−	0.180434i
$747$		0			0
$748$	1.73205	+	3.00000i	0.0633300	+	0.109691i
$749$	−4.78461	−	4.14359i	−0.174826	−	0.151404i
$750$		0			0
$751$		−	25.5885i		−	0.933736i	−0.884327	−	0.466868i	$-0.845382\pi$
$751$		−	25.5885i		−	0.933736i	0.884327	−	0.466868i	$-0.154618\pi$
$752$	−6.00000	−	3.46410i	−0.218797	−	0.126323i
$753$			44.7846i			1.63204i
$754$	5.02628	−	1.34679i	0.183046	−	0.0490471i
$755$		0			0
$756$	5.19615	−	27.0000i	0.188982	−	0.981981i
$757$		−	37.8564i		−	1.37591i	−0.725751	−	0.687957i	$-0.758508\pi$
$757$		−	37.8564i		−	1.37591i	0.725751	−	0.687957i	$-0.241492\pi$
$758$	−2.05256	−	7.66025i	−0.0745523	−	0.278233i
$759$	−0.679492			−0.0246640
$760$		0			0
$761$			42.2487i			1.53151i	0.643130	+	0.765757i	$0.277636\pi$
$761$			42.2487i			1.53151i	−0.643130	+	0.765757i	$0.722364\pi$
$762$	9.80385	+	36.5885i	0.355156	+	1.32546i
$763$	−4.14359	−	3.58846i	−0.150008	−	0.129911i
$764$	7.19615	+	12.4641i	0.260348	+	0.450935i
$765$		0			0
$766$	10.0526	+	37.5167i	0.363214	+	1.35553i
$767$	−1.60770			−0.0580505
$768$	−24.0000	+	13.8564i	−0.866025	+	0.500000i
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$		0			0
$771$			10.3923i			0.374270i
$772$	−9.46410	−	16.3923i	−0.340620	−	0.589972i
$773$	−5.53590			−0.199112			−0.0995562	−	0.995032i	$-0.531742\pi$
$773$	−5.53590			−0.199112			−0.0995562	+	0.995032i	$0.531742\pi$
$774$		0			0
$775$		0			0
$776$	26.7846	−	26.7846i	0.961511	−	0.961511i
$777$	32.7846	+	28.3923i	1.17614	+	1.01857i
$778$	28.4904	−	7.63397i	1.02143	−	0.273691i
$779$		−	20.7846i		−	0.744686i
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	−12.9282	+	3.46410i	−0.462312	+	0.123876i
$783$			41.1962i			1.47223i
$784$	26.0000	+	10.3923i	0.928571	+	0.371154i
$785$		0			0
$786$	−1.60770	−	6.00000i	−0.0573446	−	0.214013i
$787$		−	32.6603i		−	1.16421i	−0.813113	−	0.582106i	$-0.802229\pi$
$787$		−	32.6603i		−	1.16421i	0.813113	−	0.582106i	$-0.197771\pi$
$788$	13.3205	+	23.0718i	0.474523	+	0.821899i
$789$		−	19.8564i		−	0.706907i
$790$		0			0
$791$	−9.46410	+	10.9282i	−0.336505	+	0.388562i
$792$		0			0
$793$			4.39230i			0.155975i
$794$	−17.0263	+	4.56218i	−0.604240	+	0.161906i
$795$		0			0
$796$	−6.00000	+	3.46410i	−0.212664	+	0.122782i
$797$	22.1769			0.785547			0.392773	−	0.919635i	$-0.371516\pi$
$797$	22.1769			0.785547			0.392773	+	0.919635i	$0.371516\pi$
$798$	−16.9808	+	34.9808i	−0.601112	+	1.23831i
$799$		−	11.1962i		−	0.396091i
$800$		0			0
$801$		0			0
$802$	−13.7583	+	3.68653i	−0.485824	+	0.130176i
$803$			3.46410i			0.122245i
$804$	6.00000	+	10.3923i	0.211604	+	0.366508i
$805$		0			0
$806$	3.80385	−	1.01924i	0.133985	−	0.0359011i
$807$	−20.7846			−0.731653
$808$	30.9282	+	30.9282i	1.08805	+	1.08805i
$809$	−7.92820			−0.278741			−0.139370	−	0.990240i	$-0.544508\pi$
$809$	−7.92820			−0.278741			−0.139370	+	0.990240i	$0.544508\pi$
$810$		0			0
$811$	29.0718			1.02085			0.510424	−	0.859923i	$-0.329488\pi$
$811$	29.0718			1.02085			0.510424	+	0.859923i	$0.329488\pi$
$812$	−41.1962	−	7.92820i	−1.44570	−	0.278225i
$813$		−	16.3923i		−	0.574903i
$814$	−3.46410	+	0.928203i	−0.121417	+	0.0325335i
$815$		0			0
$816$	−38.7846	−	22.3923i	−1.35773	−	0.783887i
$817$	12.0000			0.419827
$818$	1.51666	+	5.66025i	0.0530288	+	0.197906i
$819$		0			0
$820$		0			0
$821$	27.7846			0.969690			0.484845	−	0.874600i	$-0.338876\pi$
$821$	27.7846			0.969690			0.484845	+	0.874600i	$0.338876\pi$
$822$	−48.2487	+	12.9282i	−1.68287	+	0.450923i
$823$	−11.0718			−0.385939			−0.192969	−	0.981205i	$-0.561812\pi$
$823$	−11.0718			−0.385939			−0.192969	+	0.981205i	$0.561812\pi$
$824$	−13.6077	−	13.6077i	−0.474047	−	0.474047i
$825$		0			0
$826$	11.6603	+	5.66025i	0.405712	+	0.196945i
$827$	14.1436			0.491821			0.245910	−	0.969293i	$-0.420913\pi$
$827$	14.1436			0.491821			0.245910	+	0.969293i	$0.420913\pi$
$828$		0			0
$829$			0.248711i			0.00863810i	0.999991	+	0.00431905i	$0.00137480\pi$
$829$			0.248711i			0.00863810i	−0.999991	+	0.00431905i	$0.998625\pi$
$830$		0			0
$831$	−29.0718			−1.00849
$832$			3.71281i			0.128719i
$833$	6.46410	+	44.7846i	0.223968	+	1.55169i
$834$	4.39230	+	16.3923i	0.152093	+	0.567619i
$835$		0			0
$836$	−1.60770	−	2.78461i	−0.0556033	−	0.0963077i
$837$			31.1769i			1.07763i
$838$	33.1244	−	8.87564i	1.14426	−	0.306604i
$839$	−4.39230			−0.151639			−0.0758196	−	0.997122i	$-0.524157\pi$
$839$	−4.39230			−0.151639			−0.0758196	+	0.997122i	$0.524157\pi$
$840$		0			0
$841$	33.8564			1.16746
$842$	25.9545	−	6.95448i	0.894451	−	0.239667i
$843$			13.7321i			0.472957i
$844$	3.19615	+	5.53590i	0.110016	+	0.190553i
$845$		0			0
$846$		0			0
$847$	21.8564	+	18.9282i	0.750995	+	0.650381i
$848$	6.92820	+	4.00000i	0.237915	+	0.137361i
$849$	21.0000			0.720718
$850$		0			0
$851$		−	13.8564i		−	0.474991i
$852$	22.3923	−	12.9282i	0.767148	−	0.442913i
$853$	−2.78461			−0.0953432			−0.0476716	−	0.998863i	$-0.515180\pi$
$853$	−2.78461			−0.0953432			−0.0476716	+	0.998863i	$0.515180\pi$
$854$	15.4641	−	31.8564i	0.529171	−	1.09010i
$855$		0			0
$856$	−4.78461	+	4.78461i	−0.163535	+	0.163535i
$857$	−57.7128			−1.97143			−0.985716	−	0.168416i	$-0.946135\pi$
$857$	−57.7128			−1.97143			−0.985716	+	0.168416i	$0.946135\pi$
$858$	−0.294229	+	0.0788383i	−0.0100448	+	0.00269150i
$859$	−39.7128			−1.35498			−0.677492	−	0.735530i	$-0.736933\pi$
$859$	−39.7128			−1.35498			−0.677492	+	0.735530i	$0.736933\pi$
$860$		0			0
$861$	12.0000	+	10.3923i	0.408959	+	0.354169i
$862$	−4.97372	−	18.5622i	−0.169406	−	0.632230i
$863$	39.8564			1.35673			0.678364	−	0.734726i	$-0.262689\pi$
$863$	39.8564			1.35673			0.678364	+	0.734726i	$0.262689\pi$
$864$	−28.3923	−	7.60770i	−0.965926	−	0.258819i
$865$		0			0
$866$	−43.5167	+	11.6603i	−1.47876	+	0.396232i
$867$		−	42.9282i		−	1.45792i
$868$	−31.1769	−	6.00000i	−1.05821	−	0.203653i
$869$	3.92820			0.133255
$870$		0			0
$871$	1.60770			0.0544747
$872$	−4.14359	+	4.14359i	−0.140320	+	0.140320i
$873$		0			0
$874$	12.0000	−	3.21539i	0.405906	−	0.108762i
$875$		0			0
$876$	−22.3923	−	38.7846i	−0.756566	−	1.31041i
$877$			18.3923i			0.621064i	0.950563	+	0.310532i	$0.100507\pi$
$877$			18.3923i			0.621064i	−0.950563	+	0.310532i	$0.899493\pi$
$878$	54.2487	−	14.5359i	1.83081	−	0.490563i
$879$		−	35.1962i		−	1.18714i
$880$		0			0
$881$			29.0718i			0.979454i	0.871876	+	0.489727i	$0.162904\pi$
$881$			29.0718i			0.979454i	−0.871876	+	0.489727i	$0.837096\pi$
$882$		0			0
$883$	23.6077			0.794462			0.397231	−	0.917719i	$-0.369971\pi$
$883$	23.6077			0.794462			0.397231	+	0.917719i	$0.369971\pi$
$884$	−5.19615	+	3.00000i	−0.174766	+	0.100901i
$885$		0			0
$886$	35.5167	−	9.51666i	1.19321	−	0.319718i
$887$			8.53590i			0.286607i	0.989679	+	0.143304i	$0.0457726\pi$
$887$			8.53590i			0.286607i	−0.989679	+	0.143304i	$0.954227\pi$
$888$	32.7846	−	32.7846i	1.10018	−	1.10018i
$889$	−30.9282	−	26.7846i	−1.03730	−	0.898327i
$890$		0			0
$891$		−	2.41154i		−	0.0807897i
$892$	−13.7321	−	23.7846i	−0.459783	−	0.796368i
$893$			10.3923i			0.347765i
$894$	1.94744	+	7.26795i	0.0651322	+	0.243077i
$895$		0			0
$896$	13.0718	−	26.9282i	0.436698	−	0.899608i
$897$		−	1.17691i		−	0.0392960i
$898$	−16.2942	+	4.36603i	−0.543745	+	0.145696i
$899$	47.5692			1.58652
$900$		0			0
$901$			12.9282i			0.430701i
$902$	−1.26795	+	0.339746i	−0.0422181	+	0.0113123i
$903$	−6.00000	+	6.92820i	−0.199667	+	0.230556i
$904$	10.9282	+	10.9282i	0.363467	+	0.363467i
$905$		0			0
$906$	35.9545	−	9.63397i	1.19451	−	0.320067i
$907$	−32.3923			−1.07557			−0.537784	−	0.843082i	$-0.680739\pi$
$907$	−32.3923			−1.07557			−0.537784	+	0.843082i	$0.680739\pi$
$908$	−20.6603	−	35.7846i	−0.685635	−	1.18755i
$909$		0			0
$910$		0			0
$911$		−	20.2487i		−	0.670870i	−0.942063	−	0.335435i	$-0.891117\pi$
$911$		−	20.2487i		−	0.670870i	0.942063	−	0.335435i	$-0.108883\pi$
$912$	36.0000	+	20.7846i	1.19208	+	0.688247i
$913$	−4.14359			−0.137133
$914$	−7.51666	−	28.0526i	−0.248629	−	0.927896i
$915$		0			0
$916$	−8.53590	−	14.7846i	−0.282034	−	0.488497i
$917$	5.07180	+	4.39230i	0.167485	+	0.145047i
$918$	−12.2942	−	45.8827i	−0.405770	−	1.51435i
$919$			6.41154i			0.211497i	0.994393	+	0.105749i	$0.0337239\pi$
$919$			6.41154i			0.211497i	−0.994393	+	0.105749i	$0.966276\pi$
$920$		0			0
$921$	−3.00000			−0.0988534
$922$	−10.1436	−	37.8564i	−0.334061	−	1.24673i
$923$		−	3.46410i		−	0.114022i
$924$	2.41154	+	0.464102i	0.0793339	+	0.0152678i
$925$		0			0
$926$	22.3923	−	6.00000i	0.735857	−	0.197172i
$927$		0			0
$928$	−11.6077	+	43.3205i	−0.381041	+	1.42207i
$929$		−	54.4974i		−	1.78800i	−0.448065	−	0.894001i	$-0.647887\pi$
$929$		−	54.4974i		−	1.78800i	0.448065	−	0.894001i	$-0.352113\pi$
$930$		0			0
$931$	−6.00000	−	41.5692i	−0.196642	−	1.36238i
$932$	−9.07180	−	15.7128i	−0.297157	−	0.514690i
$933$		−	13.6077i		−	0.445496i
$934$	−8.24167	−	30.7583i	−0.269676	−	1.00644i
$935$		0			0
$936$		0			0
$937$	25.3923			0.829530			0.414765	−	0.909928i	$-0.363864\pi$
$937$	25.3923			0.829530			0.414765	+	0.909928i	$0.363864\pi$
$938$	−11.6603	−	5.66025i	−0.380721	−	0.184814i
$939$			30.3731i			0.991188i
$940$		0			0
$941$		−	39.0333i		−	1.27245i	−0.771504	−	0.636225i	$-0.780495\pi$
$941$		−	39.0333i		−	1.27245i	0.771504	−	0.636225i	$-0.219505\pi$
$942$	4.98076	+	18.5885i	0.162282	+	0.605645i
$943$		−	5.07180i		−	0.165160i
$944$	6.92820	−	12.0000i	0.225494	−	0.390567i
$945$		0			0
$946$	−0.196152	−	0.732051i	−0.00637747	−	0.0238010i
$947$	22.7846			0.740400			0.370200	−	0.928952i	$-0.379289\pi$
$947$	22.7846			0.740400			0.370200	+	0.928952i	$0.379289\pi$
$948$	−43.9808	+	25.3923i	−1.42843	+	0.824704i
$949$	−6.00000			−0.194768
$950$		0			0
$951$	5.32051			0.172529
$952$	48.2487	−	3.46410i	1.56375	−	0.112272i
$953$			21.3205i			0.690639i	0.938485	+	0.345320i	$0.112229\pi$
$953$			21.3205i			0.690639i	−0.938485	+	0.345320i	$0.887771\pi$
$954$		0			0
$955$		0			0
$956$	23.9808	+	41.5359i	0.775593	+	1.34337i
$957$	−3.67949			−0.118941
$958$	−34.3923	+	9.21539i	−1.11116	+	0.297736i
$959$	35.3205	−	40.7846i	1.14056	−	1.31700i
$960$		0			0
$961$	5.00000			0.161290
$962$	−1.60770	−	6.00000i	−0.0518342	−	0.193448i
$963$		0			0
$964$	−16.3923	−	28.3923i	−0.527961	−	0.914455i
$965$		0			0
$966$	−4.14359	+	8.53590i	−0.133318	+	0.274638i
$967$	31.1769			1.00258			0.501291	−	0.865279i	$-0.332859\pi$
$967$	31.1769			1.00258			0.501291	+	0.865279i	$0.332859\pi$
$968$	21.8564	−	21.8564i	0.702492	−	0.702492i
$969$			67.1769i			2.15803i
$970$		0			0
$971$	14.7846			0.474461			0.237230	−	0.971453i	$-0.423760\pi$
$971$	14.7846			0.474461			0.237230	+	0.971453i	$0.423760\pi$
$972$		0			0
$973$	−13.8564	−	12.0000i	−0.444216	−	0.384702i
$974$	−17.4641	+	4.67949i	−0.559586	+	0.149941i
$975$		0			0
$976$	−32.7846	−	18.9282i	−1.04941	−	0.605877i
$977$			4.24871i			0.135928i	0.997688	+	0.0679642i	$0.0216504\pi$
$977$			4.24871i			0.135928i	−0.997688	+	0.0679642i	$0.978350\pi$
$978$	−13.1769	−	49.1769i	−0.421351	−	1.57250i
$979$	−0.679492			−0.0217167
$980$		0			0
$981$		0			0
$982$	−3.61474	−	13.4904i	−0.115351	−	0.430495i
$983$		−	27.5885i		−	0.879935i	−0.898014	−	0.439968i	$-0.854990\pi$
$983$		−	27.5885i		−	0.879935i	0.898014	−	0.439968i	$-0.145010\pi$
$984$	12.0000	−	12.0000i	0.382546	−	0.382546i
$985$		0			0
$986$	−70.0070	+	18.7583i	−2.22948	+	0.597387i
$987$	−6.00000	−	5.19615i	−0.190982	−	0.165395i
$988$	4.82309	−	2.78461i	0.153443	−	0.0885902i
$989$	2.92820			0.0931114
$990$		0			0
$991$			47.1769i			1.49862i	0.662217	+	0.749312i	$0.269616\pi$
$991$			47.1769i			1.49862i	−0.662217	+	0.749312i	$0.730384\pi$
$992$	−8.78461	+	32.7846i	−0.278912	+	1.04091i
$993$	−45.7128			−1.45065
$994$	−12.1962	+	25.1244i	−0.386838	+	0.796896i
$995$		0			0
$996$	46.3923	−	26.7846i	1.47000	−	0.848703i
$997$	−5.53590			−0.175324			−0.0876618	−	0.996150i	$-0.527939\pi$
$997$	−5.53590			−0.175324			−0.0876618	+	0.996150i	$0.527939\pi$
$998$	−9.36603	−	34.9545i	−0.296476	−	1.10646i
$999$	49.1769			1.55589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.c.e.699.3		4
4.3	odd	2		700.2.c.c.699.1		4
5.2	odd	4		140.2.g.a.111.4	yes	4
5.3	odd	4		700.2.g.f.251.1		4
5.4	even	2		700.2.c.b.699.2		4
7.6	odd	2		700.2.c.f.699.3		4
15.2	even	4		1260.2.c.a.811.1		4
20.3	even	4		700.2.g.g.251.2		4
20.7	even	4		140.2.g.b.111.3	yes	4
20.19	odd	2		700.2.c.f.699.4		4
28.27	even	2		700.2.c.b.699.1		4
35.2	odd	12		980.2.o.c.31.1		4
35.12	even	12		980.2.o.d.31.1		4
35.13	even	4		700.2.g.g.251.1		4
35.17	even	12		980.2.o.b.411.1		4
35.27	even	4		140.2.g.b.111.4	yes	4
35.32	odd	12		980.2.o.a.411.1		4
35.34	odd	2		700.2.c.c.699.2		4
40.27	even	4		2240.2.k.b.1791.1		4
40.37	odd	4		2240.2.k.a.1791.3		4
60.47	odd	4		1260.2.c.b.811.2		4
105.62	odd	4		1260.2.c.b.811.1		4
140.27	odd	4		140.2.g.a.111.3	✓	4
140.47	odd	12		980.2.o.a.31.1		4
140.67	even	12		980.2.o.d.411.2		4
140.83	odd	4		700.2.g.f.251.2		4
140.87	odd	12		980.2.o.c.411.2		4
140.107	even	12		980.2.o.b.31.1		4
140.139	even	2	inner	700.2.c.e.699.4		4
280.27	odd	4		2240.2.k.a.1791.4		4
280.237	even	4		2240.2.k.b.1791.2		4
420.167	even	4		1260.2.c.a.811.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.3	✓	4	140.27	odd	4
140.2.g.a.111.4	yes	4	5.2	odd	4
140.2.g.b.111.3	yes	4	20.7	even	4
140.2.g.b.111.4	yes	4	35.27	even	4
700.2.c.b.699.1		4	28.27	even	2
700.2.c.b.699.2		4	5.4	even	2
700.2.c.c.699.1		4	4.3	odd	2
700.2.c.c.699.2		4	35.34	odd	2
700.2.c.e.699.3		4	1.1	even	1	trivial
700.2.c.e.699.4		4	140.139	even	2	inner
700.2.c.f.699.3		4	7.6	odd	2
700.2.c.f.699.4		4	20.19	odd	2
700.2.g.f.251.1		4	5.3	odd	4
700.2.g.f.251.2		4	140.83	odd	4
700.2.g.g.251.1		4	35.13	even	4
700.2.g.g.251.2		4	20.3	even	4
980.2.o.a.31.1		4	140.47	odd	12
980.2.o.a.411.1		4	35.32	odd	12
980.2.o.b.31.1		4	140.107	even	12
980.2.o.b.411.1		4	35.17	even	12
980.2.o.c.31.1		4	35.2	odd	12
980.2.o.c.411.2		4	140.87	odd	12
980.2.o.d.31.1		4	35.12	even	12
980.2.o.d.411.2		4	140.67	even	12
1260.2.c.a.811.1		4	15.2	even	4
1260.2.c.a.811.2		4	420.167	even	4
1260.2.c.b.811.1		4	105.62	odd	4
1260.2.c.b.811.2		4	60.47	odd	4
2240.2.k.a.1791.3		4	40.37	odd	4
2240.2.k.a.1791.4		4	280.27	odd	4
2240.2.k.b.1791.1		4	40.27	even	4
2240.2.k.b.1791.2		4	280.237	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.633975 - 2.36603i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} -1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.633975 - 2.36603i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +0.267949i q^{11} +(-1.73205 - 3.00000i) q^{12} -0.464102 q^{13} +(3.36603 + 1.63397i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410 q^{17} -6.00000 q^{19} +(3.00000 - 3.46410i) q^{21} +(0.0980762 + 0.366025i) q^{22} -1.46410 q^{23} +(-3.46410 - 3.46410i) q^{24} +(-0.633975 + 0.169873i) q^{26} -5.19615i q^{27} +(5.19615 + 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(1.46410 - 5.46410i) q^{32} +0.464102 q^{33} +(8.83013 - 2.36603i) q^{34} +9.46410i q^{37} +(-8.19615 + 2.19615i) q^{38} +0.803848i q^{39} +3.46410i q^{41} +(2.83013 - 5.83013i) q^{42} -2.00000 q^{43} +(0.267949 + 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} -1.73205i q^{47} +(-6.00000 - 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} -11.1962i q^{51} +(-0.803848 + 0.464102i) q^{52} +2.00000i q^{53} +(-1.90192 - 7.09808i) q^{54} +(7.46410 - 0.535898i) q^{56} +10.3923i q^{57} +(-10.8301 + 2.90192i) q^{58} +3.46410 q^{59} -9.46410i q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(0.633975 - 0.169873i) q^{66} -3.46410 q^{67} +(11.1962 - 6.46410i) q^{68} +2.53590i q^{69} +7.46410i q^{71} +12.9282 q^{73} +(3.46410 + 12.9282i) q^{74} +(-10.3923 + 6.00000i) q^{76} +(-0.464102 + 0.535898i) q^{77} +(0.294229 + 1.09808i) q^{78} -14.6603i q^{79} -9.00000 q^{81} +(1.26795 + 4.73205i) q^{82} +15.4641i q^{83} +(1.73205 - 9.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} +13.7321i q^{87} +(0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(-0.928203 - 0.803848i) q^{91} +(-2.53590 + 1.46410i) q^{92} +10.3923i q^{93} +(-0.633975 - 2.36603i) q^{94} +(-9.46410 - 2.53590i) q^{96} +13.3923 q^{97} +(3.90192 + 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^6 + 8 * q^7 + 8 * q^8	\( 4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{13} + 10 q^{14} + 8 q^{16} + 12 q^{17} - 24 q^{19} + 12 q^{21} - 10 q^{22} + 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} - 8 q^{32} - 12 q^{33} + 18 q^{34} - 12 q^{38} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 24 q^{48} + 4 q^{49} - 24 q^{52} - 18 q^{54} + 16 q^{56} - 26 q^{58} - 12 q^{62} + 6 q^{66} + 24 q^{68} + 24 q^{73} + 12 q^{77} - 30 q^{78} - 36 q^{81} + 12 q^{82} - 4 q^{86} + 16 q^{88} + 24 q^{91} - 24 q^{92} - 6 q^{94} - 24 q^{96} + 12 q^{97} + 26 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^13 + 10 * q^14 + 8 * q^16 + 12 * q^17 - 24 * q^19 + 12 * q^21 - 10 * q^22 + 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 - 8 * q^32 - 12 * q^33 + 18 * q^34 - 12 * q^38 - 6 * q^42 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 24 * q^48 + 4 * q^49 - 24 * q^52 - 18 * q^54 + 16 * q^56 - 26 * q^58 - 12 * q^62 + 6 * q^66 + 24 * q^68 + 24 * q^73 + 12 * q^77 - 30 * q^78 - 36 * q^81 + 12 * q^82 - 4 * q^86 + 16 * q^88 + 24 * q^91 - 24 * q^92 - 6 * q^94 - 24 * q^96 + 12 * q^97 + 26 * q^98

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