LMFDB - Embedded newform 700.2.g.g.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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, 0, 1]))

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

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (of order $2$, degree $1$, 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.g.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.267949i q^{11} +(3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-2.09808 + 3.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410i q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} +(0.633975 - 0.169873i) q^{26} +5.19615 q^{27} +(5.00000 + 1.73205i) q^{28} +7.92820 q^{29} +6.00000 q^{31} +(-5.46410 - 1.46410i) q^{32} -0.464102i q^{33} +(8.83013 - 2.36603i) q^{34} +9.46410 q^{37} +(2.19615 + 8.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(3.63397 - 5.36603i) q^{42} -2.00000i q^{43} +(-0.267949 - 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} +1.73205 q^{47} +(-3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} -11.1962i q^{51} +(-0.464102 - 0.803848i) q^{52} -2.00000 q^{53} +(-1.90192 - 7.09808i) q^{54} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(-2.90192 - 10.8301i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(-2.19615 - 8.19615i) q^{62} +8.00000i q^{64} +(-0.633975 + 0.169873i) q^{66} +3.46410i q^{67} +(-6.46410 - 11.1962i) q^{68} +2.53590i q^{69} +7.46410i q^{71} -12.9282i q^{73} +(-3.46410 - 12.9282i) q^{74} +(10.3923 - 6.00000i) q^{76} +(0.535898 - 0.464102i) q^{77} +(-1.09808 + 0.294229i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(-4.73205 + 1.26795i) q^{82} +15.4641 q^{83} +(-8.66025 - 3.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} -13.7321 q^{87} +(-0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(0.928203 - 0.803848i) q^{91} +(1.46410 + 2.53590i) q^{92} -10.3923 q^{93} +(-0.633975 - 2.36603i) q^{94} +(9.46410 + 2.53590i) q^{96} +13.3923i q^{97} +(9.83013 - 1.16987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8	$ 4 q + 2 q^{2} + 6 q^{6} + 8 q^{8} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 24 q^{19} + 12 q^{21} - 2 q^{22} + 6 q^{26} + 20 q^{28} + 4 q^{29} + 24 q^{31} - 8 q^{32} + 18 q^{34} + 24 q^{37} - 12 q^{38} + 18 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 12 q^{52} - 8 q^{53} - 18 q^{54} + 16 q^{56} - 22 q^{58} + 12 q^{62} - 6 q^{66} - 12 q^{68} + 16 q^{77} + 6 q^{78} - 36 q^{81} - 12 q^{82} + 48 q^{83} - 4 q^{86} - 48 q^{87} - 16 q^{88} - 24 q^{91} - 8 q^{92} - 6 q^{94} + 24 q^{96} + 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 24 * q^19 + 12 * q^21 - 2 * q^22 + 6 * q^26 + 20 * q^28 + 4 * q^29 + 24 * q^31 - 8 * q^32 + 18 * q^34 + 24 * q^37 - 12 * q^38 + 18 * q^42 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 12 * q^52 - 8 * q^53 - 18 * q^54 + 16 * q^56 - 22 * q^58 + 12 * q^62 - 6 * q^66 - 12 * q^68 + 16 * q^77 + 6 * q^78 - 36 * q^81 - 12 * q^82 + 48 * q^83 - 4 * q^86 - 48 * q^87 - 16 * q^88 - 24 * q^91 - 8 * q^92 - 6 * q^94 + 24 * q^96 + 22 * 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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$	−1.73205			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−1.73205			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$		0			0
$5$		0			0
$6$	0.633975	+	2.36603i	0.258819	+	0.965926i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$	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	$0.987138\pi$
$12$	3.00000	−	1.73205i	0.866025	−	0.500000i
$13$			0.464102i			0.128719i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$			0.464102i			0.128719i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−2.09808	+	3.09808i	−0.560734	+	0.827996i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$			6.46410i			1.56777i	0.620903	+	0.783887i	$0.286766\pi$
$17$			6.46410i			1.56777i	−0.620903	+	0.783887i	$0.713234\pi$
$18$		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
$22$	0.366025	−	0.0980762i	0.0780369	−	0.0209099i
$23$		−	1.46410i		−	0.305286i	−0.988281	−	0.152643i	$-0.951221\pi$
$23$		−	1.46410i		−	0.305286i	0.988281	−	0.152643i	$-0.0487785\pi$
$24$	−3.46410	−	3.46410i	−0.707107	−	0.707107i
$25$		0			0
$26$	0.633975	−	0.169873i	0.124333	−	0.0333148i
$27$	5.19615			1.00000
$28$	5.00000	+	1.73205i	0.944911	+	0.327327i
$29$	7.92820			1.47223			0.736115	−	0.676856i	$-0.236658\pi$
$29$	7.92820			1.47223			0.736115	+	0.676856i	$0.236658\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		−	0.464102i		−	0.0807897i
$34$	8.83013	−	2.36603i	1.51435	−	0.405770i
$35$		0			0
$36$		0			0
$37$	9.46410			1.55589			0.777944	−	0.628333i	$-0.216263\pi$
$37$	9.46410			1.55589			0.777944	+	0.628333i	$0.216263\pi$
$38$	2.19615	+	8.19615i	0.356263	+	1.32959i
$39$		−	0.803848i		−	0.128719i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$	3.63397	−	5.36603i	0.560734	−	0.827996i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−0.267949	−	0.464102i	−0.0403949	−	0.0699660i
$45$		0			0
$46$	−2.00000	+	0.535898i	−0.294884	+	0.0790139i
$47$	1.73205			0.252646			0.126323	−	0.991989i	$-0.459682\pi$
$47$	1.73205			0.252646			0.126323	+	0.991989i	$0.459682\pi$
$48$	−3.46410	+	6.00000i	−0.500000	+	0.866025i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$		−	11.1962i		−	1.56777i
$52$	−0.464102	−	0.803848i	−0.0643593	−	0.111474i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.90192	−	7.09808i	−0.258819	−	0.965926i
$55$		0			0
$56$	0.535898	−	7.46410i	0.0716124	−	0.997433i
$57$	10.3923			1.37649
$58$	−2.90192	−	10.8301i	−0.381041	−	1.42207i
$59$	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	$0.207178\pi$
$61$			9.46410i			1.21175i	−0.795558	+	0.605877i	$0.792822\pi$
$62$	−2.19615	−	8.19615i	−0.278912	−	1.04091i
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$	−0.633975	+	0.169873i	−0.0780369	+	0.0209099i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−6.46410	−	11.1962i	−0.783887	−	1.35773i
$69$			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
$73$		−	12.9282i		−	1.51313i	−0.653917	−	0.756566i	$-0.726876\pi$
$73$		−	12.9282i		−	1.51313i	0.653917	−	0.756566i	$-0.273124\pi$
$74$	−3.46410	−	12.9282i	−0.402694	−	1.50287i
$75$		0			0
$76$	10.3923	−	6.00000i	1.19208	−	0.688247i
$77$	0.535898	−	0.464102i	0.0610713	−	0.0528893i
$78$	−1.09808	+	0.294229i	−0.124333	+	0.0333148i
$79$			14.6603i			1.64941i	0.565565	+	0.824704i	$0.308658\pi$
$79$			14.6603i			1.64941i	−0.565565	+	0.824704i	$0.691342\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−4.73205	+	1.26795i	−0.522568	+	0.140022i
$83$	15.4641			1.69741			0.848703	−	0.528870i	$-0.177384\pi$
$83$	15.4641			1.69741			0.848703	+	0.528870i	$0.177384\pi$
$84$	−8.66025	−	3.00000i	−0.944911	−	0.327327i
$85$		0			0
$86$	−2.73205	+	0.732051i	−0.294605	+	0.0789391i
$87$	−13.7321			−1.47223
$88$	−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
$92$	1.46410	+	2.53590i	0.152643	+	0.264386i
$93$	−10.3923			−1.07763
$94$	−0.633975	−	2.36603i	−0.0653895	−	0.244037i
$95$		0			0
$96$	9.46410	+	2.53590i	0.965926	+	0.258819i
$97$			13.3923i			1.35978i	0.733313	+	0.679891i	$0.237973\pi$
$97$			13.3923i			1.35978i	−0.733313	+	0.679891i	$0.762027\pi$
$98$	9.83013	−	1.16987i	0.992993	−	0.118175i
$99$		0			0
$100$		0			0
$101$		−	15.4641i		−	1.53874i	−0.638806	−	0.769368i	$-0.720571\pi$
$101$		−	15.4641i		−	1.53874i	0.638806	−	0.769368i	$-0.279429\pi$
$102$	−15.2942	+	4.09808i	−1.51435	+	0.405770i
$103$	−6.80385			−0.670403			−0.335202	−	0.942146i	$-0.608804\pi$
$103$	−6.80385			−0.670403			−0.335202	+	0.942146i	$0.608804\pi$
$104$	−0.928203	+	0.928203i	−0.0910178	+	0.0910178i
$105$		0			0
$106$	0.732051	+	2.73205i	0.0711031	+	0.265360i
$107$			2.39230i			0.231273i	0.993292	+	0.115636i	$0.0368907\pi$
$107$			2.39230i			0.231273i	−0.993292	+	0.115636i	$0.963109\pi$
$108$	−9.00000	+	5.19615i	−0.866025	+	0.500000i
$109$	2.07180			0.198442			0.0992211	−	0.995065i	$-0.468365\pi$
$109$	2.07180			0.198442			0.0992211	+	0.995065i	$0.468365\pi$
$110$		0			0
$111$	−16.3923			−1.55589
$112$	−10.3923	+	2.00000i	−0.981981	+	0.188982i
$113$	−5.46410			−0.514019			−0.257010	−	0.966409i	$-0.582737\pi$
$113$	−5.46410			−0.514019			−0.257010	+	0.966409i	$0.582737\pi$
$114$	−3.80385	−	14.1962i	−0.356263	−	1.32959i
$115$		0			0
$116$	−13.7321	+	7.92820i	−1.27499	+	0.736115i
$117$		0			0
$118$	−1.26795	−	4.73205i	−0.116724	−	0.435621i
$119$	12.9282	−	11.1962i	1.18513	−	1.02635i
$120$		0			0
$121$	10.9282			0.993473
$122$	12.9282	−	3.46410i	1.17046	−	0.313625i
$123$			6.00000i			0.541002i
$124$	−10.3923	+	6.00000i	−0.933257	+	0.538816i
$125$		0			0
$126$		0			0
$127$			15.4641i			1.37222i	0.727499	+	0.686109i	$0.240683\pi$
$127$			15.4641i			1.37222i	−0.727499	+	0.686109i	$0.759317\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$			3.46410i			0.304997i
$130$		0			0
$131$	−2.53590			−0.221562			−0.110781	−	0.993845i	$-0.535335\pi$
$131$	−2.53590			−0.221562			−0.110781	+	0.993845i	$0.535335\pi$
$132$	0.464102	+	0.803848i	0.0403949	+	0.0699660i
$133$	10.3923	+	12.0000i	0.901127	+	1.04053i
$134$	4.73205	−	1.26795i	0.408787	−	0.109534i
$135$		0			0
$136$	−12.9282	+	12.9282i	−1.10858	+	1.10858i
$137$	−20.3923			−1.74223			−0.871116	−	0.491077i	$-0.836603\pi$
$137$	−20.3923			−1.74223			−0.871116	+	0.491077i	$0.836603\pi$
$138$	3.46410	−	0.928203i	0.294884	−	0.0790139i
$139$	−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
$142$	10.1962	−	2.73205i	0.855642	−	0.229269i
$143$	−0.124356			−0.0103991
$144$		0			0
$145$		0			0
$146$	−17.6603	+	4.73205i	−1.46157	+	0.391627i
$147$	1.73205	−	12.0000i	0.142857	−	0.989743i
$148$	−16.3923	+	9.46410i	−1.34744	+	0.777944i
$149$	3.07180			0.251651			0.125826	−	0.992052i	$-0.459842\pi$
$149$	3.07180			0.251651			0.125826	+	0.992052i	$0.459842\pi$
$150$		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
$154$	−0.830127	−	0.562178i	−0.0668935	−	0.0453016i
$155$		0			0
$156$	0.803848	+	1.39230i	0.0643593	+	0.111474i
$157$		−	7.85641i		−	0.627009i	−0.949587	−	0.313505i	$-0.898497\pi$
$157$		−	7.85641i		−	0.627009i	0.949587	−	0.313505i	$-0.101503\pi$
$158$	20.0263	−	5.36603i	1.59321	−	0.426898i
$159$	3.46410			0.274721
$160$		0			0
$161$	−2.92820	+	2.53590i	−0.230775	+	0.199857i
$162$	3.29423	+	12.2942i	0.258819	+	0.965926i
$163$			20.7846i			1.62798i	0.580881	+	0.813988i	$0.302708\pi$
$163$			20.7846i			1.62798i	−0.580881	+	0.813988i	$0.697292\pi$
$164$	3.46410	+	6.00000i	0.270501	+	0.468521i
$165$		0			0
$166$	−5.66025	−	21.1244i	−0.439321	−	1.63957i
$167$	−5.19615			−0.402090			−0.201045	−	0.979582i	$-0.564434\pi$
$167$	−5.19615			−0.402090			−0.201045	+	0.979582i	$0.564434\pi$
$168$	−0.928203	+	12.9282i	−0.0716124	+	0.997433i
$169$	12.7846			0.983432
$170$		0			0
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$			14.3205i			1.08877i	0.838836	+	0.544384i	$0.183237\pi$
$173$			14.3205i			1.08877i	−0.838836	+	0.544384i	$0.816763\pi$
$174$	5.02628	+	18.7583i	0.381041	+	1.42207i
$175$		0			0
$176$	0.928203	+	0.535898i	0.0699660	+	0.0403949i
$177$	−6.00000			−0.450988
$178$	3.46410	−	0.928203i	0.259645	−	0.0695718i
$179$		−	6.39230i		−	0.477783i	−0.971046	−	0.238892i	$-0.923216\pi$
$179$		−	6.39230i		−	0.477783i	0.971046	−	0.238892i	$-0.0767841\pi$
$180$		0			0
$181$		−	0.928203i		−	0.0689928i	−0.999405	−	0.0344964i	$-0.989017\pi$
$181$		−	0.928203i		−	0.0689928i	0.999405	−	0.0344964i	$-0.0109827\pi$
$182$	−1.43782	−	0.973721i	−0.106578	−	0.0721770i
$183$		−	16.3923i		−	1.21175i
$184$	2.92820	−	2.92820i	0.215870	−	0.215870i
$185$		0			0
$186$	3.80385	+	14.1962i	0.278912	+	1.04091i
$187$	−1.73205			−0.126660
$188$	−3.00000	+	1.73205i	−0.218797	+	0.126323i
$189$	−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	$0.916163\pi$
$192$		−	13.8564i		−	1.00000i
$193$	9.46410			0.681241			0.340620	−	0.940201i	$-0.389363\pi$
$193$	9.46410			0.681241			0.340620	+	0.940201i	$0.389363\pi$
$194$	18.2942	−	4.90192i	1.31345	−	0.351938i
$195$		0			0
$196$	−5.19615	−	13.0000i	−0.371154	−	0.928571i
$197$	13.3205			0.949047			0.474523	−	0.880243i	$-0.342620\pi$
$197$	13.3205			0.949047			0.474523	+	0.880243i	$0.342620\pi$
$198$		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
$202$	−21.1244	+	5.66025i	−1.48630	+	0.398254i
$203$	−13.7321	−	15.8564i	−0.963801	−	1.11290i
$204$	11.1962	+	19.3923i	0.783887	+	1.35773i
$205$		0			0
$206$	2.49038	+	9.29423i	0.173513	+	0.647560i
$207$		0			0
$208$	1.60770	+	0.928203i	0.111474	+	0.0643593i
$209$		−	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	$0.964910\pi$
$212$	3.46410	−	2.00000i	0.237915	−	0.137361i
$213$		−	12.9282i		−	0.885826i
$214$	3.26795	−	0.875644i	0.223392	−	0.0598578i
$215$		0			0
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$	−10.3923	−	12.0000i	−0.705476	−	0.814613i
$218$	−0.758330	−	2.83013i	−0.0513606	−	0.191680i
$219$			22.3923i			1.51313i
$220$		0			0
$221$	−3.00000			−0.201802
$222$	6.00000	+	22.3923i	0.402694	+	1.50287i
$223$	−13.7321			−0.919566			−0.459783	−	0.888031i	$-0.652073\pi$
$223$	−13.7321			−0.919566			−0.459783	+	0.888031i	$0.652073\pi$
$224$	6.53590	+	13.4641i	0.436698	+	0.899608i
$225$		0			0
$226$	2.00000	+	7.46410i	0.133038	+	0.496505i
$227$	20.6603			1.37127			0.685635	−	0.727946i	$-0.259525\pi$
$227$	20.6603			1.37127			0.685635	+	0.727946i	$0.259525\pi$
$228$	−18.0000	+	10.3923i	−1.19208	+	0.688247i
$229$		−	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
$233$	9.07180			0.594313			0.297157	−	0.954829i	$-0.403962\pi$
$233$	9.07180			0.594313			0.297157	+	0.954829i	$0.403962\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	+	3.46410i	−0.390567	+	0.225494i
$237$		−	25.3923i		−	1.64941i
$238$	−20.0263	−	13.5622i	−1.29811	−	0.879105i
$239$		−	23.9808i		−	1.55119i	−0.631233	−	0.775593i	$-0.717451\pi$
$239$		−	23.9808i		−	1.55119i	0.631233	−	0.775593i	$-0.282549\pi$
$240$		0			0
$241$			16.3923i			1.05592i	0.849269	+	0.527961i	$0.177043\pi$
$241$			16.3923i			1.05592i	−0.849269	+	0.527961i	$0.822957\pi$
$242$	−4.00000	−	14.9282i	−0.257130	−	0.959621i
$243$		0			0
$244$	−9.46410	−	16.3923i	−0.605877	−	1.04941i
$245$		0			0
$246$	8.19615	−	2.19615i	0.522568	−	0.140022i
$247$		−	2.78461i		−	0.177180i
$248$	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	$-0.196175\pi$
$251$	25.8564			1.63204			0.816021	+	0.578022i	$0.196175\pi$
$252$		0			0
$253$	0.392305			0.0246640
$254$	21.1244	−	5.66025i	1.32546	−	0.355156i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		−	6.00000i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$		−	6.00000i		−	0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	4.73205	−	1.26795i	0.294605	−	0.0789391i
$259$	−16.3923	−	18.9282i	−1.01857	−	1.17614i
$260$		0			0
$261$		0			0
$262$	0.928203	+	3.46410i	0.0573446	+	0.214013i
$263$			11.4641i			0.706907i	0.935452	+	0.353453i	$0.114993\pi$
$263$			11.4641i			0.706907i	−0.935452	+	0.353453i	$0.885007\pi$
$264$	0.928203	−	0.928203i	0.0571270	−	0.0571270i
$265$		0			0
$266$	12.5885	−	18.5885i	0.771848	−	1.13973i
$267$		−	4.39230i		−	0.268805i
$268$	−3.46410	−	6.00000i	−0.211604	−	0.366508i
$269$		−	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	$-0.592808\pi$
$271$	−9.46410			−0.574903			−0.287452	+	0.957795i	$0.592808\pi$
$272$	22.3923	+	12.9282i	1.35773	+	0.783887i
$273$	−1.60770	+	1.39230i	−0.0973021	+	0.0842661i
$274$	7.46410	+	27.8564i	0.450923	+	1.68287i
$275$		0			0
$276$	−2.53590	−	4.39230i	−0.152643	−	0.264386i
$277$	−16.7846			−1.00849			−0.504245	−	0.863561i	$-0.668229\pi$
$277$	−16.7846			−1.00849			−0.504245	+	0.863561i	$0.668229\pi$
$278$	2.53590	+	9.46410i	0.152093	+	0.567619i
$279$		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	$0.575993\pi$
$282$	1.09808	+	4.09808i	0.0653895	+	0.244037i
$283$	12.1244			0.720718			0.360359	−	0.932814i	$-0.382654\pi$
$283$	12.1244			0.720718			0.360359	+	0.932814i	$0.382654\pi$
$284$	−7.46410	−	12.9282i	−0.442913	−	0.767148i
$285$		0			0
$286$	0.0455173	+	0.169873i	0.00269150	+	0.0100448i
$287$	−6.92820	+	6.00000i	−0.408959	+	0.354169i
$288$		0			0
$289$	−24.7846			−1.45792
$290$		0			0
$291$		−	23.1962i		−	1.35978i
$292$	12.9282	+	22.3923i	0.756566	+	1.31041i
$293$		−	20.3205i		−	1.18714i	−0.804784	−	0.593568i	$-0.797719\pi$
$293$		−	20.3205i		−	1.18714i	0.804784	−	0.593568i	$-0.202281\pi$
$294$	−17.0263	+	2.02628i	−0.992993	+	0.118175i
$295$		0			0
$296$	18.9282	+	18.9282i	1.10018	+	1.10018i
$297$			1.39230i			0.0807897i
$298$	−1.12436	−	4.19615i	−0.0651322	−	0.243077i
$299$	0.679492			0.0392960
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$	20.7583	−	5.56218i	1.19451	−	0.320067i
$303$			26.7846i			1.53874i
$304$	−12.0000	+	20.7846i	−0.688247	+	1.19208i
$305$		0			0
$306$		0			0
$307$	1.73205			0.0988534			0.0494267	−	0.998778i	$-0.484261\pi$
$307$	1.73205			0.0988534			0.0494267	+	0.998778i	$0.484261\pi$
$308$	−0.464102	+	1.33975i	−0.0264446	+	0.0763391i
$309$	11.7846			0.670403
$310$		0			0
$311$	−7.85641			−0.445496			−0.222748	−	0.974876i	$-0.571503\pi$
$311$	−7.85641			−0.445496			−0.222748	+	0.974876i	$0.571503\pi$
$312$	1.60770	−	1.60770i	0.0910178	−	0.0910178i
$313$			17.5359i			0.991188i	0.868554	+	0.495594i	$0.165050\pi$
$313$			17.5359i			0.991188i	−0.868554	+	0.495594i	$0.834950\pi$
$314$	−10.7321	+	2.87564i	−0.605645	+	0.162282i
$315$		0			0
$316$	−14.6603	−	25.3923i	−0.824704	−	1.42843i
$317$	3.07180			0.172529			0.0862646	−	0.996272i	$-0.472507\pi$
$317$	3.07180			0.172529			0.0862646	+	0.996272i	$0.472507\pi$
$318$	−1.26795	−	4.73205i	−0.0711031	−	0.265360i
$319$			2.12436i			0.118941i
$320$		0			0
$321$		−	4.14359i		−	0.231273i
$322$	4.53590	+	3.07180i	0.252776	+	0.171185i
$323$		−	38.7846i		−	2.15803i
$324$	15.5885	−	9.00000i	0.866025	−	0.500000i
$325$		0			0
$326$	28.3923	−	7.60770i	1.57250	−	0.421351i
$327$	−3.58846			−0.198442
$328$	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	$-0.258311\pi$
$332$	−26.7846	+	15.4641i	−1.47000	+	0.848703i
$333$		0			0
$334$	1.90192	+	7.09808i	0.104069	+	0.388389i
$335$		0			0
$336$	18.0000	−	3.46410i	0.981981	−	0.188982i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−4.67949	−	17.4641i	−0.254531	−	0.949922i
$339$	9.46410			0.514019
$340$		0			0
$341$			1.60770i			0.0870616i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	4.00000	−	4.00000i	0.215666	−	0.215666i
$345$		0			0
$346$	19.5622	−	5.24167i	1.05167	−	0.281794i
$347$		−	34.2487i		−	1.83857i	−0.393596	−	0.919284i	$-0.628769\pi$
$347$		−	34.2487i		−	1.83857i	0.393596	−	0.919284i	$-0.371231\pi$
$348$	23.7846	−	13.7321i	1.27499	−	0.736115i
$349$		−	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
$352$	0.392305	−	1.46410i	0.0209099	−	0.0780369i
$353$			7.39230i			0.393453i	0.980458	+	0.196726i	$0.0630311\pi$
$353$			7.39230i			0.393453i	−0.980458	+	0.196726i	$0.936969\pi$
$354$	2.19615	+	8.19615i	0.116724	+	0.435621i
$355$		0			0
$356$	−2.53590	−	4.39230i	−0.134402	−	0.232792i
$357$	−22.3923	+	19.3923i	−1.18513	+	1.02635i
$358$	−8.73205	+	2.33975i	−0.461503	+	0.123659i
$359$			25.3205i			1.33637i	0.743997	+	0.668183i	$0.232928\pi$
$359$			25.3205i			1.33637i	−0.743997	+	0.668183i	$0.767072\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−1.26795	+	0.339746i	−0.0666419	+	0.0178567i
$363$	−18.9282			−0.993473
$364$	−0.803848	+	2.32051i	−0.0421331	+	0.121628i
$365$		0			0
$366$	−22.3923	+	6.00000i	−1.17046	+	0.313625i
$367$	11.8756			0.619904			0.309952	−	0.950752i	$-0.399687\pi$
$367$	11.8756			0.619904			0.309952	+	0.950752i	$0.399687\pi$
$368$	−5.07180	−	2.92820i	−0.264386	−	0.152643i
$369$		0			0
$370$		0			0
$371$	3.46410	+	4.00000i	0.179847	+	0.207670i
$372$	18.0000	−	10.3923i	0.933257	−	0.538816i
$373$	3.60770			0.186799			0.0933997	−	0.995629i	$-0.470227\pi$
$373$	3.60770			0.186799			0.0933997	+	0.995629i	$0.470227\pi$
$374$	0.633975	+	2.36603i	0.0327820	+	0.122344i
$375$		0			0
$376$	3.46410	+	3.46410i	0.178647	+	0.178647i
$377$			3.67949i			0.189503i
$378$	−10.9019	+	16.0981i	−0.560734	+	0.827996i
$379$			5.60770i			0.288048i	0.989574	+	0.144024i	$0.0460042\pi$
$379$			5.60770i			0.288048i	−0.989574	+	0.144024i	$0.953996\pi$
$380$		0			0
$381$		−	26.7846i		−	1.37222i
$382$	9.83013	−	2.63397i	0.502953	−	0.134766i
$383$	27.4641			1.40335			0.701675	−	0.712497i	$-0.252436\pi$
$383$	27.4641			1.40335			0.701675	+	0.712497i	$0.252436\pi$
$384$	−18.9282	+	5.07180i	−0.965926	+	0.258819i
$385$		0			0
$386$	−3.46410	−	12.9282i	−0.176318	−	0.658028i
$387$		0			0
$388$	−13.3923	−	23.1962i	−0.679891	−	1.17761i
$389$	−20.8564			−1.05746			−0.528731	−	0.848790i	$-0.677332\pi$
$389$	−20.8564			−1.05746			−0.528731	+	0.848790i	$0.677332\pi$
$390$		0			0
$391$	9.46410			0.478620
$392$	−15.8564	+	11.8564i	−0.800869	+	0.598839i
$393$	4.39230			0.221562
$394$	−4.87564	−	18.1962i	−0.245631	−	0.916709i
$395$		0			0
$396$		0			0
$397$		−	12.4641i		−	0.625555i	−0.949826	−	0.312778i	$-0.898741\pi$
$397$		−	12.4641i		−	0.625555i	0.949826	−	0.312778i	$-0.101259\pi$
$398$	1.26795	+	4.73205i	0.0635566	+	0.237196i
$399$	−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	$0.580918\pi$
$402$	−8.19615	+	2.19615i	−0.408787	+	0.109534i
$403$			2.78461i			0.138711i
$404$	15.4641	+	26.7846i	0.769368	+	1.33258i
$405$		0			0
$406$	−16.6340	+	24.5622i	−0.825530	+	1.21900i
$407$			2.53590i			0.125700i
$408$	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
$412$	11.7846	−	6.80385i	0.580586	−	0.335202i
$413$	−6.00000	−	6.92820i	−0.295241	−	0.340915i
$414$		0			0
$415$		0			0
$416$	0.679492	−	2.53590i	0.0333148	−	0.124333i
$417$	12.0000			0.587643
$418$	−2.19615	+	0.588457i	−0.107417	+	0.0287824i
$419$	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	$0.346772\pi$
$422$	4.36603	−	1.16987i	0.212535	−	0.0569485i
$423$		0			0
$424$	−4.00000	−	4.00000i	−0.194257	−	0.194257i
$425$		0			0
$426$	−17.6603	+	4.73205i	−0.855642	+	0.229269i
$427$	18.9282	−	16.3923i	0.916000	−	0.793279i
$428$	−2.39230	−	4.14359i	−0.115636	−	0.200288i
$429$	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	$-0.106127\pi$
$432$	10.3923	−	18.0000i	0.500000	−	0.866025i
$433$			31.8564i			1.53092i	0.643483	+	0.765461i	$0.277489\pi$
$433$			31.8564i			1.53092i	−0.643483	+	0.765461i	$0.722511\pi$
$434$	−12.5885	+	18.5885i	−0.604265	+	0.892275i
$435$		0			0
$436$	−3.58846	+	2.07180i	−0.171856	+	0.0992211i
$437$			8.78461i			0.420225i
$438$	30.5885	−	8.19615i	1.46157	−	0.391627i
$439$	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
$442$	1.09808	+	4.09808i	0.0522302	+	0.194926i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$	28.3923	−	16.3923i	1.34744	−	0.777944i
$445$		0			0
$446$	5.02628	+	18.7583i	0.238001	+	0.888233i
$447$	−5.32051			−0.251651
$448$	16.0000	−	13.8564i	0.755929	−	0.654654i
$449$	11.9282			0.562927			0.281463	−	0.959572i	$-0.409180\pi$
$449$	11.9282			0.562927			0.281463	+	0.959572i	$0.409180\pi$
$450$		0			0
$451$	0.928203			0.0437074
$452$	9.46410	−	5.46410i	0.445154	−	0.257010i
$453$		−	26.3205i		−	1.23665i
$454$	−7.56218	−	28.2224i	−0.354911	−	1.32454i
$455$		0			0
$456$	20.7846	+	20.7846i	0.973329	+	0.973329i
$457$	−20.5359			−0.960629			−0.480314	−	0.877096i	$-0.659477\pi$
$457$	−20.5359			−0.960629			−0.480314	+	0.877096i	$0.659477\pi$
$458$	−11.6603	+	3.12436i	−0.544848	+	0.145992i
$459$			33.5885i			1.56777i
$460$		0			0
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$	1.43782	+	0.973721i	0.0668935	+	0.0453016i
$463$			16.3923i			0.761815i	0.924613	+	0.380908i	$0.124388\pi$
$463$			16.3923i			0.761815i	−0.924613	+	0.380908i	$0.875612\pi$
$464$	15.8564	−	27.4641i	0.736115	−	1.27499i
$465$		0			0
$466$	−3.32051	−	12.3923i	−0.153820	−	0.574062i
$467$	22.5167			1.04195			0.520973	−	0.853573i	$-0.325569\pi$
$467$	22.5167			1.04195			0.520973	+	0.853573i	$0.325569\pi$
$468$		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
$473$	0.535898			0.0246406
$474$	−34.6865	+	9.29423i	−1.59321	+	0.426898i
$475$		0			0
$476$	−11.1962	+	32.3205i	−0.513175	+	1.48141i
$477$		0			0
$478$	−32.7583	+	8.77757i	−1.49833	+	0.401477i
$479$	−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
$482$	22.3923	−	6.00000i	1.01994	−	0.273293i
$483$	5.07180	−	4.39230i	0.230775	−	0.199857i
$484$	−18.9282	+	10.9282i	−0.860373	+	0.496737i
$485$		0			0
$486$		0			0
$487$			12.7846i			0.579326i	0.957129	+	0.289663i	$0.0935432\pi$
$487$			12.7846i			0.579326i	−0.957129	+	0.289663i	$0.906457\pi$
$488$	−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	$-0.0715330\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$			51.2487i			2.30813i
$494$	−3.80385	+	1.01924i	−0.171143	+	0.0458577i
$495$		0			0
$496$	12.0000	−	20.7846i	0.538816	−	0.933257i
$497$	14.9282	−	12.9282i	0.669621	−	0.579909i
$498$	9.80385	+	36.5885i	0.439321	+	1.63957i
$499$			25.5885i			1.14550i	0.819731	+	0.572748i	$0.194123\pi$
$499$			25.5885i			1.14550i	−0.819731	+	0.572748i	$0.805877\pi$
$500$		0			0
$501$	9.00000			0.402090
$502$	−9.46410	−	35.3205i	−0.422404	−	1.57643i
$503$	−15.5885			−0.695055			−0.347527	−	0.937670i	$-0.612979\pi$
$503$	−15.5885			−0.695055			−0.347527	+	0.937670i	$0.612979\pi$
$504$		0			0
$505$		0			0
$506$	−0.143594	−	0.535898i	−0.00638351	−	0.0238236i
$507$	−22.1436			−0.983432
$508$	−15.4641	−	26.7846i	−0.686109	−	1.18837i
$509$			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
$513$	−31.1769			−1.37649
$514$	−8.19615	+	2.19615i	−0.361517	+	0.0968681i
$515$		0			0
$516$	−3.46410	−	6.00000i	−0.152499	−	0.264135i
$517$			0.464102i			0.0204112i
$518$	−19.8564	+	29.3205i	−0.872440	+	1.28827i
$519$		−	24.8038i		−	1.08877i
$520$		0			0
$521$			13.6077i			0.596164i	0.954540	+	0.298082i	$0.0963469\pi$
$521$			13.6077i			0.596164i	−0.954540	+	0.298082i	$0.903653\pi$
$522$		0			0
$523$	−24.2487			−1.06032			−0.530161	−	0.847897i	$-0.677869\pi$
$523$	−24.2487			−1.06032			−0.530161	+	0.847897i	$0.677869\pi$
$524$	4.39230	−	2.53590i	0.191879	−	0.110781i
$525$		0			0
$526$	15.6603	−	4.19615i	0.682820	−	0.182961i
$527$			38.7846i			1.68948i
$528$	−1.60770	−	0.928203i	−0.0699660	−	0.0403949i
$529$	20.8564			0.906800
$530$		0			0
$531$		0			0
$532$	−30.0000	−	10.3923i	−1.30066	−	0.450564i
$533$	1.60770			0.0696370
$534$	−6.00000	+	1.60770i	−0.259645	+	0.0695718i
$535$		0			0
$536$	−6.92820	+	6.92820i	−0.299253	+	0.299253i
$537$			11.0718i			0.477783i
$538$	−16.3923	+	4.39230i	−0.706722	+	0.189366i
$539$	−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	$0.446481\pi$
$542$	3.46410	+	12.9282i	0.148796	+	0.555314i
$543$			1.60770i			0.0689928i
$544$	9.46410	−	35.3205i	0.405770	−	1.51435i
$545$		0			0
$546$	2.49038	+	1.68653i	0.106578	+	0.0721770i
$547$		−	21.4641i		−	0.917739i	−0.888504	−	0.458869i	$-0.848255\pi$
$547$		−	21.4641i		−	0.917739i	0.888504	−	0.458869i	$-0.151745\pi$
$548$	35.3205	−	20.3923i	1.50882	−	0.871116i
$549$		0			0
$550$		0			0
$551$	−47.5692			−2.02652
$552$	−5.07180	+	5.07180i	−0.215870	+	0.215870i
$553$	29.3205	−	25.3923i	1.24683	−	1.07979i
$554$	6.14359	+	22.9282i	0.261016	+	0.974126i
$555$		0			0
$556$	12.0000	−	6.92820i	0.508913	−	0.293821i
$557$	21.8564			0.926086			0.463043	−	0.886336i	$-0.346758\pi$
$557$	21.8564			0.926086			0.463043	+	0.886336i	$0.346758\pi$
$558$		0			0
$559$	0.928203			0.0392588
$560$		0			0
$561$	3.00000			0.126660
$562$	2.90192	+	10.8301i	0.122410	+	0.456841i
$563$	19.1769			0.808211			0.404105	−	0.914712i	$-0.367583\pi$
$563$	19.1769			0.808211			0.404105	+	0.914712i	$0.367583\pi$
$564$	5.19615	−	3.00000i	0.218797	−	0.126323i
$565$		0			0
$566$	−4.43782	−	16.5622i	−0.186536	−	0.696160i
$567$	15.5885	+	18.0000i	0.654654	+	0.755929i
$568$	−14.9282	+	14.9282i	−0.626373	+	0.626373i
$569$	7.07180			0.296465			0.148233	−	0.988953i	$-0.452642\pi$
$569$	7.07180			0.296465			0.148233	+	0.988953i	$0.452642\pi$
$570$		0			0
$571$		−	6.67949i		−	0.279528i	−0.990185	−	0.139764i	$-0.955366\pi$
$571$		−	6.67949i		−	0.279528i	0.990185	−	0.139764i	$-0.0446344\pi$
$572$	0.215390	−	0.124356i	0.00900592	−	0.00519957i
$573$		−	12.4641i		−	0.520695i
$574$	10.7321	+	7.26795i	0.447947	+	0.303358i
$575$		0			0
$576$		0			0
$577$		−	19.3923i		−	0.807312i	−0.914911	−	0.403656i	$-0.867739\pi$
$577$		−	19.3923i		−	0.807312i	0.914911	−	0.403656i	$-0.132261\pi$
$578$	9.07180	+	33.8564i	0.377337	+	1.40824i
$579$	−16.3923			−0.681241
$580$		0			0
$581$	−26.7846	−	30.9282i	−1.11121	−	1.28312i
$582$	−31.6865	+	8.49038i	−1.31345	+	0.351938i
$583$		−	0.535898i		−	0.0221946i
$584$	25.8564	−	25.8564i	1.06995	−	1.06995i
$585$		0			0
$586$	−27.7583	+	7.43782i	−1.14669	+	0.307254i
$587$	−20.5359			−0.847607			−0.423804	−	0.905754i	$-0.639305\pi$
$587$	−20.5359			−0.847607			−0.423804	+	0.905754i	$0.639305\pi$
$588$	9.00000	+	22.5167i	0.371154	+	0.928571i
$589$	−36.0000			−1.48335
$590$		0			0
$591$	−23.0718			−0.949047
$592$	18.9282	−	32.7846i	0.777944	−	1.34744i
$593$		−	30.4641i		−	1.25101i	−0.780220	−	0.625505i	$-0.784893\pi$
$593$		−	30.4641i		−	1.25101i	0.780220	−	0.625505i	$-0.215107\pi$
$594$	1.90192	−	0.509619i	0.0780369	−	0.0209099i
$595$		0			0
$596$	−5.32051	+	3.07180i	−0.217937	+	0.125826i
$597$	6.00000			0.245564
$598$	−0.248711	−	0.928203i	−0.0101706	−	0.0379571i
$599$		−	10.1244i		−	0.413670i	−0.978376	−	0.206835i	$-0.933684\pi$
$599$		−	10.1244i		−	0.413670i	0.978376	−	0.206835i	$-0.0663163\pi$
$600$		0			0
$601$		−	14.7846i		−	0.603077i	−0.953454	−	0.301538i	$-0.902500\pi$
$601$		−	14.7846i		−	0.603077i	0.953454	−	0.301538i	$-0.0975001\pi$
$602$	6.19615	+	4.19615i	0.252536	+	0.171022i
$603$		0			0
$604$	−15.1962	−	26.3205i	−0.618323	−	1.07097i
$605$		0			0
$606$	36.5885	−	9.80385i	1.48630	−	0.398254i
$607$	−29.1962			−1.18504			−0.592518	−	0.805557i	$-0.701866\pi$
$607$	−29.1962			−1.18504			−0.592518	+	0.805557i	$0.701866\pi$
$608$	32.7846	+	8.78461i	1.32959	+	0.356263i
$609$	23.7846	+	27.4641i	0.963801	+	1.11290i
$610$		0			0
$611$			0.803848i			0.0325202i
$612$		0			0
$613$	10.0000			0.403896			0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000			0.403896			0.201948	+	0.979396i	$0.435273\pi$
$614$	−0.633975	−	2.36603i	−0.0255851	−	0.0954850i
$615$		0			0
$616$	2.00000	+	0.143594i	0.0805823	+	0.00578555i
$617$	22.9282			0.923055			0.461527	−	0.887126i	$-0.347302\pi$
$617$	22.9282			0.923055			0.461527	+	0.887126i	$0.347302\pi$
$618$	−4.31347	−	16.0981i	−0.173513	−	0.647560i
$619$	−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
$622$	2.87564	+	10.7321i	0.115303	+	0.430316i
$623$	5.07180	−	4.39230i	0.203197	−	0.175974i
$624$	−2.78461	−	1.60770i	−0.111474	−	0.0643593i
$625$		0			0
$626$	23.9545	−	6.41858i	0.957414	−	0.256538i
$627$			2.78461i			0.111207i
$628$	7.85641	+	13.6077i	0.313505	+	0.543006i
$629$			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
$633$		−	5.53590i		−	0.220032i
$634$	−1.12436	−	4.19615i	−0.0446539	−	0.166651i
$635$		0			0
$636$	−6.00000	+	3.46410i	−0.237915	+	0.137361i
$637$	−3.21539	−	0.464102i	−0.127398	−	0.0183884i
$638$	2.90192	−	0.777568i	0.114888	−	0.0307842i
$639$		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	$0.443580\pi$
$642$	−5.66025	+	1.51666i	−0.223392	+	0.0598578i
$643$	7.05256			0.278126			0.139063	−	0.990284i	$-0.455591\pi$
$643$	7.05256			0.278126			0.139063	+	0.990284i	$0.455591\pi$
$644$	2.53590	−	7.32051i	0.0999284	−	0.288468i
$645$		0			0
$646$	−52.9808	+	14.1962i	−2.08450	+	0.558540i
$647$	−10.3923			−0.408564			−0.204282	−	0.978912i	$-0.565486\pi$
$647$	−10.3923			−0.408564			−0.204282	+	0.978912i	$0.565486\pi$
$648$	−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
$652$	−20.7846	−	36.0000i	−0.813988	−	1.40987i
$653$	−17.6077			−0.689042			−0.344521	−	0.938779i	$-0.611959\pi$
$653$	−17.6077			−0.689042			−0.344521	+	0.938779i	$0.611959\pi$
$654$	1.31347	+	4.90192i	0.0513606	+	0.191680i
$655$		0			0
$656$	−12.0000	−	6.92820i	−0.468521	−	0.270501i
$657$		0			0
$658$	−3.63397	+	5.36603i	−0.141667	+	0.209189i
$659$		−	31.1962i		−	1.21523i	−0.794232	−	0.607615i	$-0.792126\pi$
$659$		−	31.1962i		−	1.21523i	0.794232	−	0.607615i	$-0.207874\pi$
$660$		0			0
$661$			39.7128i			1.54465i	0.635228	+	0.772325i	$0.280906\pi$
$661$			39.7128i			1.54465i	−0.635228	+	0.772325i	$0.719094\pi$
$662$	−36.0526	+	9.66025i	−1.40122	+	0.375456i
$663$	5.19615			0.201802
$664$	30.9282	+	30.9282i	1.20025	+	1.20025i
$665$		0			0
$666$		0			0
$667$		−	11.6077i		−	0.449452i
$668$	9.00000	−	5.19615i	0.348220	−	0.201045i
$669$	23.7846			0.919566
$670$		0			0
$671$	−2.53590			−0.0978973
$672$	−11.3205	−	23.3205i	−0.436698	−	0.899608i
$673$	13.1769			0.507933			0.253966	−	0.967213i	$-0.418265\pi$
$673$	13.1769			0.507933			0.253966	+	0.967213i	$0.418265\pi$
$674$		0			0
$675$		0			0
$676$	−22.1436	+	12.7846i	−0.851677	+	0.491716i
$677$			25.3923i			0.975906i	0.872870	+	0.487953i	$0.162256\pi$
$677$			25.3923i			0.975906i	−0.872870	+	0.487953i	$0.837744\pi$
$678$	−3.46410	−	12.9282i	−0.133038	−	0.496505i
$679$	26.7846	−	23.1962i	1.02790	−	0.890187i
$680$		0			0
$681$	−35.7846			−1.37127
$682$	2.19615	−	0.588457i	0.0840950	−	0.0225332i
$683$		−	7.32051i		−	0.280111i	−0.990144	−	0.140056i	$-0.955272\pi$
$683$		−	7.32051i		−	0.280111i	0.990144	−	0.140056i	$-0.0447282\pi$
$684$		0			0
$685$		0			0
$686$	−19.3660	−	17.6340i	−0.739398	−	0.673268i
$687$			14.7846i			0.564068i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$		−	0.928203i		−	0.0353617i
$690$		0			0
$691$	22.6410			0.861305			0.430652	−	0.902518i	$-0.358283\pi$
$691$	22.6410			0.861305			0.430652	+	0.902518i	$0.358283\pi$
$692$	−14.3205	−	24.8038i	−0.544384	−	0.942901i
$693$		0			0
$694$	−46.7846	+	12.5359i	−1.77592	+	0.475856i
$695$		0			0
$696$	−27.4641	−	27.4641i	−1.04102	−	1.04102i
$697$	22.3923			0.848169
$698$	−7.26795	+	1.94744i	−0.275096	+	0.0737117i
$699$	−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	$0.752915\pi$
$702$	3.29423	−	0.882686i	0.124333	−	0.0333148i
$703$	−56.7846			−2.14167
$704$	−2.14359			−0.0807897
$705$		0			0
$706$	10.0981	−	2.70577i	0.380046	−	0.101833i
$707$	−30.9282	+	26.7846i	−1.16317	+	1.00734i
$708$	10.3923	−	6.00000i	0.390567	−	0.225494i
$709$	21.0000			0.788672			0.394336	−	0.918966i	$-0.370975\pi$
$709$	21.0000			0.788672			0.394336	+	0.918966i	$0.370975\pi$
$710$		0			0
$711$		0			0
$712$	−5.07180	+	5.07180i	−0.190074	+	0.190074i
$713$		−	8.78461i		−	0.328986i
$714$	34.6865	+	23.4904i	1.29811	+	0.879105i
$715$		0			0
$716$	6.39230	+	11.0718i	0.238892	+	0.413772i
$717$			41.5359i			1.55119i
$718$	34.5885	−	9.26795i	1.29083	−	0.345877i
$719$	−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
$722$	−6.22243	−	23.2224i	−0.231575	−	0.864249i
$723$		−	28.3923i		−	1.05592i
$724$	0.928203	+	1.60770i	0.0344964	+	0.0597495i
$725$		0			0
$726$	6.92820	+	25.8564i	0.257130	+	0.959621i
$727$	−13.6077			−0.504681			−0.252341	−	0.967638i	$-0.581200\pi$
$727$	−13.6077			−0.504681			−0.252341	+	0.967638i	$0.581200\pi$
$728$	3.46410	+	0.248711i	0.128388	+	0.00921785i
$729$	27.0000			1.00000
$730$		0			0
$731$	12.9282			0.478167
$732$	16.3923	+	28.3923i	0.605877	+	1.04941i
$733$		−	11.5359i		−	0.426088i	−0.977043	−	0.213044i	$-0.931662\pi$
$733$		−	11.5359i		−	0.426088i	0.977043	−	0.213044i	$-0.0683378\pi$
$734$	−4.34679	−	16.2224i	−0.160443	−	0.598781i
$735$		0			0
$736$	−2.14359	+	8.00000i	−0.0790139	+	0.294884i
$737$	−0.928203			−0.0341908
$738$		0			0
$739$		−	4.26795i		−	0.156999i	−0.996914	−	0.0784995i	$-0.974987\pi$
$739$		−	4.26795i		−	0.156999i	0.996914	−	0.0784995i	$-0.0250129\pi$
$740$		0			0
$741$			4.82309i			0.177180i
$742$	4.19615	−	6.19615i	0.154046	−	0.227468i
$743$		−	30.3923i		−	1.11499i	−0.830182	−	0.557493i	$-0.811763\pi$
$743$		−	30.3923i		−	1.11499i	0.830182	−	0.557493i	$-0.188237\pi$
$744$	−20.7846	−	20.7846i	−0.762001	−	0.762001i
$745$		0			0
$746$	−1.32051	−	4.92820i	−0.0483472	−	0.180434i
$747$		0			0
$748$	3.00000	−	1.73205i	0.109691	−	0.0633300i
$749$	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	$-0.154618\pi$
$752$	3.46410	−	6.00000i	0.126323	−	0.218797i
$753$	−44.7846			−1.63204
$754$	5.02628	−	1.34679i	0.183046	−	0.0490471i
$755$		0			0
$756$	25.9808	+	9.00000i	0.944911	+	0.327327i
$757$	−37.8564			−1.37591			−0.687957	−	0.725751i	$-0.741492\pi$
$757$	−37.8564			−1.37591			−0.687957	+	0.725751i	$0.741492\pi$
$758$	7.66025	−	2.05256i	0.278233	−	0.0745523i
$759$	−0.679492			−0.0246640
$760$		0			0
$761$		−	42.2487i		−	1.53151i	−0.643130	−	0.765757i	$-0.722364\pi$
$761$		−	42.2487i		−	1.53151i	0.643130	−	0.765757i	$-0.277636\pi$
$762$	−36.5885	+	9.80385i	−1.32546	+	0.355156i
$763$	−3.58846	−	4.14359i	−0.129911	−	0.150008i
$764$	−7.19615	−	12.4641i	−0.260348	−	0.450935i
$765$		0			0
$766$	−10.0526	−	37.5167i	−0.363214	−	1.35553i
$767$			1.60770i			0.0580505i
$768$	13.8564	+	24.0000i	0.500000	+	0.866025i
$769$			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
$772$	−16.3923	+	9.46410i	−0.589972	+	0.340620i
$773$			5.53590i			0.199112i	0.995032	+	0.0995562i	$0.0317423\pi$
$773$			5.53590i			0.199112i	−0.995032	+	0.0995562i	$0.968258\pi$
$774$		0			0
$775$		0			0
$776$	−26.7846	+	26.7846i	−0.961511	+	0.961511i
$777$	28.3923	+	32.7846i	1.01857	+	1.17614i
$778$	7.63397	+	28.4904i	0.273691	+	1.02143i
$779$			20.7846i			0.744686i
$780$		0			0
$781$	−2.00000			−0.0715656

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.267949i q^{11} +(3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-2.09808 + 3.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410i q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} +(0.633975 - 0.169873i) q^{26} +5.19615 q^{27} +(5.00000 + 1.73205i) q^{28} +7.92820 q^{29} +6.00000 q^{31} +(-5.46410 - 1.46410i) q^{32} -0.464102i q^{33} +(8.83013 - 2.36603i) q^{34} +9.46410 q^{37} +(2.19615 + 8.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(3.63397 - 5.36603i) q^{42} -2.00000i q^{43} +(-0.267949 - 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} +1.73205 q^{47} +(-3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} -11.1962i q^{51} +(-0.464102 - 0.803848i) q^{52} -2.00000 q^{53} +(-1.90192 - 7.09808i) q^{54} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(-2.90192 - 10.8301i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(-2.19615 - 8.19615i) q^{62} +8.00000i q^{64} +(-0.633975 + 0.169873i) q^{66} +3.46410i q^{67} +(-6.46410 - 11.1962i) q^{68} +2.53590i q^{69} +7.46410i q^{71} -12.9282i q^{73} +(-3.46410 - 12.9282i) q^{74} +(10.3923 - 6.00000i) q^{76} +(0.535898 - 0.464102i) q^{77} +(-1.09808 + 0.294229i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(-4.73205 + 1.26795i) q^{82} +15.4641 q^{83} +(-8.66025 - 3.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} -13.7321 q^{87} +(-0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(0.928203 - 0.803848i) q^{91} +(1.46410 + 2.53590i) q^{92} -10.3923 q^{93} +(-0.633975 - 2.36603i) q^{94} +(9.46410 + 2.53590i) q^{96} +13.3923i q^{97} +(9.83013 - 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8	\( 4 q + 2 q^{2} + 6 q^{6} + 8 q^{8} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 24 q^{19} + 12 q^{21} - 2 q^{22} + 6 q^{26} + 20 q^{28} + 4 q^{29} + 24 q^{31} - 8 q^{32} + 18 q^{34} + 24 q^{37} - 12 q^{38} + 18 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 12 q^{52} - 8 q^{53} - 18 q^{54} + 16 q^{56} - 22 q^{58} + 12 q^{62} - 6 q^{66} - 12 q^{68} + 16 q^{77} + 6 q^{78} - 36 q^{81} - 12 q^{82} + 48 q^{83} - 4 q^{86} - 48 q^{87} - 16 q^{88} - 24 q^{91} - 8 q^{92} - 6 q^{94} + 24 q^{96} + 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 24 * q^19 + 12 * q^21 - 2 * q^22 + 6 * q^26 + 20 * q^28 + 4 * q^29 + 24 * q^31 - 8 * q^32 + 18 * q^34 + 24 * q^37 - 12 * q^38 + 18 * q^42 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 12 * q^52 - 8 * q^53 - 18 * q^54 + 16 * q^56 - 22 * q^58 + 12 * q^62 - 6 * q^66 - 12 * q^68 + 16 * q^77 + 6 * q^78 - 36 * q^81 - 12 * q^82 + 48 * q^83 - 4 * q^86 - 48 * q^87 - 16 * q^88 - 24 * q^91 - 8 * q^92 - 6 * q^94 + 24 * q^96 + 22 * q^98

Introduction

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