LMFDB - Embedded newform 700.2.c.i.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:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			$-0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.i.699.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599676 - 1.28078i) q^{2} +0.936426i q^{3} +(-1.28078 + 1.53610i) q^{4} +(1.19935 - 0.561553i) q^{6} +(0.468213 + 2.60399i) q^{7} +(2.73546 + 0.719224i) q^{8} +2.12311 q^{9} +O(q^{10})$	\(q+(-0.599676 - 1.28078i) q^{2} +0.936426i q^{3} +(-1.28078 + 1.53610i) q^{4} +(1.19935 - 0.561553i) q^{6} +(0.468213 + 2.60399i) q^{7} +(2.73546 + 0.719224i) q^{8} +2.12311 q^{9} +2.39871i q^{11} +(-1.43845 - 1.19935i) q^{12} -2.00000 q^{13} +(3.05436 - 2.16123i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311 q^{17} +(-1.27318 - 2.71922i) q^{18} -2.39871 q^{19} +(-2.43845 + 0.438447i) q^{21} +(3.07221 - 1.43845i) q^{22} -5.73384 q^{23} +(-0.673500 + 2.56155i) q^{24} +(1.19935 + 2.56155i) q^{26} +4.79741i q^{27} +(-4.59968 - 2.61591i) q^{28} +2.00000 q^{29} +6.67026 q^{31} +(-4.60831 + 3.28078i) q^{32} -2.24621 q^{33} +(4.27156 + 9.12311i) q^{34} +(-2.71922 + 3.26131i) q^{36} -2.00000i q^{37} +(1.43845 + 3.07221i) q^{38} -1.87285i q^{39} +7.12311i q^{41} +(2.02383 + 2.86018i) q^{42} +7.60669 q^{43} +(-3.68466 - 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} +10.0054i q^{47} +(3.68466 - 0.673500i) q^{48} +(-6.56155 + 2.43845i) q^{49} -6.67026i q^{51} +(2.56155 - 3.07221i) q^{52} +2.00000i q^{53} +(6.14441 - 2.87689i) q^{54} +(-0.592076 + 7.45986i) q^{56} -2.24621i q^{57} +(-1.19935 - 2.56155i) q^{58} -10.9418 q^{59} +2.00000i q^{61} +(-4.00000 - 8.54312i) q^{62} +(0.994066 + 5.52855i) q^{63} +(6.96543 + 3.93481i) q^{64} +(1.34700 + 2.87689i) q^{66} -14.2770 q^{67} +(9.12311 - 10.9418i) q^{68} -5.36932i q^{69} +6.14441i q^{71} +(5.80766 + 1.52699i) q^{72} +9.36932 q^{73} +(-2.56155 + 1.19935i) q^{74} +(3.07221 - 3.68466i) q^{76} +(-6.24621 + 1.12311i) q^{77} +(-2.39871 + 1.12311i) q^{78} +4.27156i q^{79} +1.87689 q^{81} +(9.12311 - 4.27156i) q^{82} +0.936426i q^{83} +(2.44961 - 4.30726i) q^{84} +(-4.56155 - 9.74247i) q^{86} +1.87285i q^{87} +(-1.72521 + 6.56155i) q^{88} -12.0000i q^{89} +(-0.936426 - 5.20798i) q^{91} +(7.34376 - 8.80776i) q^{92} +6.24621i q^{93} +(12.8147 - 6.00000i) q^{94} +(-3.07221 - 4.31534i) q^{96} +7.12311 q^{97} +(7.05791 + 6.94160i) q^{98} +5.09271i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 16 * q^9	$ 8 q - 2 q^{4} - 16 q^{9} - 28 q^{12} - 16 q^{13} + 6 q^{14} - 14 q^{16} - 24 q^{17} - 36 q^{21} - 32 q^{28} + 16 q^{29} + 48 q^{33} - 30 q^{36} + 28 q^{38} - 12 q^{42} + 20 q^{44} + 44 q^{46} - 20 q^{48} - 36 q^{49} + 4 q^{52} + 2 q^{56} - 32 q^{62} - 2 q^{64} + 40 q^{68} - 24 q^{73} - 4 q^{74} + 16 q^{77} + 48 q^{81} + 40 q^{82} - 8 q^{84} - 20 q^{86} + 24 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^4 - 16 * q^9 - 28 * q^12 - 16 * q^13 + 6 * q^14 - 14 * q^16 - 24 * q^17 - 36 * q^21 - 32 * q^28 + 16 * q^29 + 48 * q^33 - 30 * q^36 + 28 * q^38 - 12 * q^42 + 20 * q^44 + 44 * q^46 - 20 * q^48 - 36 * q^49 + 4 * q^52 + 2 * q^56 - 32 * q^62 - 2 * q^64 + 40 * q^68 - 24 * q^73 - 4 * q^74 + 16 * q^77 + 48 * q^81 + 40 * q^82 - 8 * q^84 - 20 * q^86 + 24 * q^97 - 8 * 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 $

$2$	−0.599676	−	1.28078i	−0.424035	−	0.905646i
$2$	−0.599676	−	1.28078i	−0.424035	−	0.905646i
$3$			0.936426i			0.540646i	0.962770	+	0.270323i	$0.0871305\pi$
$3$			0.936426i			0.540646i	−0.962770	+	0.270323i	$0.912870\pi$
$4$	−1.28078	+	1.53610i	−0.640388	+	0.768051i
$5$		0			0
$5$		0			0
$6$	1.19935	−	0.561553i	0.489634	−	0.229253i
$7$	0.468213	+	2.60399i	0.176968	+	0.984217i
$7$	0.468213	+	2.60399i	0.176968	+	0.984217i
$8$	2.73546	+	0.719224i	0.967130	+	0.254284i
$9$	2.12311			0.707702
$10$		0			0
$11$			2.39871i			0.723237i	0.932326	+	0.361618i	$0.117776\pi$
$11$			2.39871i			0.723237i	−0.932326	+	0.361618i	$0.882224\pi$
$12$	−1.43845	−	1.19935i	−0.415244	−	0.346223i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	3.05436	−	2.16123i	0.816311	−	0.577613i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$	−7.12311			−1.72761			−0.863803	−	0.503829i	$-0.831924\pi$
$17$	−7.12311			−1.72761			−0.863803	+	0.503829i	$0.831924\pi$
$18$	−1.27318	−	2.71922i	−0.300091	−	0.640927i
$19$	−2.39871			−0.550301			−0.275150	−	0.961401i	$-0.588728\pi$
$19$	−2.39871			−0.550301			−0.275150	+	0.961401i	$0.588728\pi$
$20$		0			0
$21$	−2.43845	+	0.438447i	−0.532113	+	0.0956770i
$22$	3.07221	−	1.43845i	0.654996	−	0.306678i
$23$	−5.73384			−1.19559			−0.597794	−	0.801650i	$-0.703956\pi$
$23$	−5.73384			−1.19559			−0.597794	+	0.801650i	$0.703956\pi$
$24$	−0.673500	+	2.56155i	−0.137478	+	0.522875i
$25$		0			0
$26$	1.19935	+	2.56155i	0.235212	+	0.502362i
$27$			4.79741i			0.923262i
$28$	−4.59968	−	2.61591i	−0.869257	−	0.494360i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	6.67026			1.19801			0.599007	−	0.800743i	$-0.295562\pi$
$31$	6.67026			1.19801			0.599007	+	0.800743i	$0.295562\pi$
$32$	−4.60831	+	3.28078i	−0.814642	+	0.579965i
$33$	−2.24621			−0.391015
$34$	4.27156	+	9.12311i	0.732566	+	1.56460i
$35$		0			0
$36$	−2.71922	+	3.26131i	−0.453204	+	0.543551i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	1.43845	+	3.07221i	0.233347	+	0.498378i
$39$		−	1.87285i		−	0.299896i
$40$		0			0
$41$			7.12311i			1.11244i	0.831034	+	0.556221i	$0.187749\pi$
$41$			7.12311i			1.11244i	−0.831034	+	0.556221i	$0.812251\pi$
$42$	2.02383	+	2.86018i	0.312284	+	0.441335i
$43$	7.60669			1.16001			0.580005	−	0.814613i	$-0.303051\pi$
$43$	7.60669			1.16001			0.580005	+	0.814613i	$0.303051\pi$
$44$	−3.68466	−	3.07221i	−0.555483	−	0.463152i
$45$		0			0
$46$	3.43845	+	7.34376i	0.506971	+	1.08278i
$47$			10.0054i			1.45944i	0.683748	+	0.729719i	$0.260349\pi$
$47$			10.0054i			1.45944i	−0.683748	+	0.729719i	$0.739651\pi$
$48$	3.68466	−	0.673500i	0.531835	−	0.0972113i
$49$	−6.56155	+	2.43845i	−0.937365	+	0.348350i
$50$		0			0
$51$		−	6.67026i		−	0.934024i
$52$	2.56155	−	3.07221i	0.355223	−	0.426038i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	6.14441	−	2.87689i	0.836148	−	0.391496i
$55$		0			0
$56$	−0.592076	+	7.45986i	−0.0791195	+	0.996865i
$57$		−	2.24621i		−	0.297518i
$58$	−1.19935	−	2.56155i	−0.157483	−	0.336348i
$59$	−10.9418			−1.42450			−0.712252	−	0.701924i	$-0.752325\pi$
$59$	−10.9418			−1.42450			−0.712252	+	0.701924i	$0.752325\pi$
$60$		0			0
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	−4.00000	−	8.54312i	−0.508001	−	1.08498i
$63$	0.994066	+	5.52855i	0.125241	+	0.696532i
$64$	6.96543	+	3.93481i	0.870679	+	0.491851i
$65$		0			0
$66$	1.34700	+	2.87689i	0.165804	+	0.354121i
$67$	−14.2770			−1.74421			−0.872104	−	0.489321i	$-0.837245\pi$
$67$	−14.2770			−1.74421			−0.872104	+	0.489321i	$0.837245\pi$
$68$	9.12311	−	10.9418i	1.10634	−	1.32689i
$69$		−	5.36932i		−	0.646390i
$70$		0			0
$71$			6.14441i			0.729207i	0.931163	+	0.364604i	$0.118796\pi$
$71$			6.14441i			0.729207i	−0.931163	+	0.364604i	$0.881204\pi$
$72$	5.80766	+	1.52699i	0.684439	+	0.179957i
$73$	9.36932			1.09660			0.548298	−	0.836283i	$-0.315276\pi$
$73$	9.36932			1.09660			0.548298	+	0.836283i	$0.315276\pi$
$74$	−2.56155	+	1.19935i	−0.297774	+	0.139422i
$75$		0			0
$76$	3.07221	−	3.68466i	0.352406	−	0.422659i
$77$	−6.24621	+	1.12311i	−0.711822	+	0.127990i
$78$	−2.39871	+	1.12311i	−0.271600	+	0.127167i
$79$			4.27156i			0.480588i	0.970700	+	0.240294i	$0.0772438\pi$
$79$			4.27156i			0.480588i	−0.970700	+	0.240294i	$0.922756\pi$
$80$		0			0
$81$	1.87689			0.208544
$82$	9.12311	−	4.27156i	1.00748	−	0.471715i
$83$			0.936426i			0.102786i	0.998679	+	0.0513931i	$0.0163661\pi$
$83$			0.936426i			0.102786i	−0.998679	+	0.0513931i	$0.983634\pi$
$84$	2.44961	−	4.30726i	0.267274	−	0.469960i
$85$		0			0
$86$	−4.56155	−	9.74247i	−0.491885	−	1.05056i
$87$			1.87285i			0.200791i
$88$	−1.72521	+	6.56155i	−0.183908	+	0.699464i
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$	−0.936426	−	5.20798i	−0.0981642	−	0.545945i
$92$	7.34376	−	8.80776i	0.765640	−	0.918273i
$93$			6.24621i			0.647702i
$94$	12.8147	−	6.00000i	1.32173	−	0.618853i
$95$		0			0
$96$	−3.07221	−	4.31534i	−0.313556	−	0.440433i
$97$	7.12311			0.723242			0.361621	−	0.932325i	$-0.382223\pi$
$97$	7.12311			0.723242			0.361621	+	0.932325i	$0.382223\pi$
$98$	7.05791	+	6.94160i	0.712957	+	0.701208i
$99$			5.09271i			0.511836i
$100$		0			0
$101$		−	6.87689i		−	0.684277i	−0.939650	−	0.342138i	$-0.888849\pi$
$101$		−	6.87689i		−	0.684277i	0.939650	−	0.342138i	$-0.111151\pi$
$102$	−8.54312	+	4.00000i	−0.845895	+	0.396059i
$103$			1.46228i			0.144083i	0.997402	+	0.0720413i	$0.0229513\pi$
$103$			1.46228i			0.144083i	−0.997402	+	0.0720413i	$0.977049\pi$
$104$	−5.47091	−	1.43845i	−0.536467	−	0.141051i
$105$		0			0
$106$	2.56155	−	1.19935i	0.248800	−	0.116491i
$107$	9.47954			0.916422			0.458211	−	0.888843i	$-0.348490\pi$
$107$	9.47954			0.916422			0.458211	+	0.888843i	$0.348490\pi$
$108$	−7.36932	−	6.14441i	−0.709113	−	0.591246i
$109$	−1.12311			−0.107574			−0.0537870	−	0.998552i	$-0.517129\pi$
$109$	−1.12311			−0.107574			−0.0537870	+	0.998552i	$0.517129\pi$
$110$		0			0
$111$	1.87285			0.177763
$112$	9.90946	−	3.71518i	0.936356	−	0.351052i
$113$		−	14.4924i		−	1.36333i	−0.731663	−	0.681666i	$-0.761256\pi$
$113$		−	14.4924i		−	1.36333i	0.731663	−	0.681666i	$-0.238744\pi$
$114$	−2.87689	+	1.34700i	−0.269446	+	0.126158i
$115$		0			0
$116$	−2.56155	+	3.07221i	−0.237834	+	0.285247i
$117$	−4.24621			−0.392562
$118$	6.56155	+	14.0140i	0.604040	+	1.29010i
$119$	−3.33513	−	18.5485i	−0.305731	−	1.70034i
$120$		0			0
$121$	5.24621			0.476928
$122$	2.56155	−	1.19935i	0.231912	−	0.108584i
$123$	−6.67026			−0.601437
$124$	−8.54312	+	10.2462i	−0.767195	+	0.920137i
$125$		0			0
$126$	6.48472	−	4.58852i	0.577705	−	0.408778i
$127$	13.2252			1.17355			0.586776	−	0.809750i	$-0.300397\pi$
$127$	13.2252			1.17355			0.586776	+	0.809750i	$0.300397\pi$
$128$	0.862603	−	11.2808i	0.0762440	−	0.997089i
$129$			7.12311i			0.627154i
$130$		0			0
$131$	−13.8664			−1.21151			−0.605756	−	0.795651i	$-0.707129\pi$
$131$	−13.8664			−1.21151			−0.605756	+	0.795651i	$0.707129\pi$
$132$	2.87689	−	3.45041i	0.250402	−	0.300320i
$133$	−1.12311	−	6.24621i	−0.0973856	−	0.541615i
$134$	8.56155	+	18.2856i	0.739606	+	1.57963i
$135$		0			0
$136$	−19.4849	−	5.12311i	−1.67082	−	0.439303i
$137$			14.0000i			1.19610i	0.801459	+	0.598050i	$0.204058\pi$
$137$			14.0000i			1.19610i	−0.801459	+	0.598050i	$0.795942\pi$
$138$	−6.87689	+	3.21985i	−0.585400	+	0.274092i
$139$	−1.34700			−0.114251			−0.0571255	−	0.998367i	$-0.518194\pi$
$139$	−1.34700			−0.114251			−0.0571255	+	0.998367i	$0.518194\pi$
$140$		0			0
$141$	−9.36932			−0.789039
$142$	7.86962	−	3.68466i	0.660404	−	0.309210i
$143$		−	4.79741i		−	0.401180i
$144$	−1.52699	−	8.35401i	−0.127249	−	0.696168i
$145$		0			0
$146$	−5.61856	−	12.0000i	−0.464995	−	0.993127i
$147$	−2.28343	−	6.14441i	−0.188334	−	0.506782i
$148$	3.07221	+	2.56155i	0.252534	+	0.210558i
$149$	19.3693			1.58680			0.793398	−	0.608703i	$-0.208310\pi$
$149$	19.3693			1.58680			0.793398	+	0.608703i	$0.208310\pi$
$150$		0			0
$151$			14.6875i			1.19525i	0.801774	+	0.597627i	$0.203890\pi$
$151$			14.6875i			1.19525i	−0.801774	+	0.597627i	$0.796110\pi$
$152$	−6.56155	−	1.72521i	−0.532212	−	0.139933i
$153$	−15.1231			−1.22263
$154$	5.18415	+	7.32650i	0.417751	+	0.590386i
$155$		0			0
$156$	2.87689	+	2.39871i	0.230336	+	0.192050i
$157$	16.2462			1.29659			0.648294	−	0.761390i	$-0.275483\pi$
$157$	16.2462			1.29659			0.648294	+	0.761390i	$0.275483\pi$
$158$	5.47091	−	2.56155i	0.435242	−	0.203786i
$159$	−1.87285			−0.148527
$160$		0			0
$161$	−2.68466	−	14.9309i	−0.211581	−	1.17672i
$162$	−1.12553	−	2.40388i	−0.0884299	−	0.188867i
$163$	0.936426			0.0733466			0.0366733	−	0.999327i	$-0.488324\pi$
$163$	0.936426			0.0733466			0.0366733	+	0.999327i	$0.488324\pi$
$164$	−10.9418	−	9.12311i	−0.854413	−	0.712395i
$165$		0			0
$166$	1.19935	−	0.561553i	0.0930878	−	0.0435850i
$167$			2.28343i			0.176697i	0.996090	+	0.0883484i	$0.0281589\pi$
$167$			2.28343i			0.176697i	−0.996090	+	0.0883484i	$0.971841\pi$
$168$	−6.98561	−	0.554436i	−0.538951	−	0.0427757i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−5.09271			−0.389449
$172$	−9.74247	+	11.6847i	−0.742856	+	0.890947i
$173$	−0.246211			−0.0187191			−0.00935955	−	0.999956i	$-0.502979\pi$
$173$	−0.246211			−0.0187191			−0.00935955	+	0.999956i	$0.502979\pi$
$174$	2.39871	−	1.12311i	0.181845	−	0.0851424i
$175$		0			0
$176$	9.43845	−	1.72521i	0.711450	−	0.130042i
$177$		−	10.2462i		−	0.770152i
$178$	−15.3693	+	7.19612i	−1.15198	+	0.539372i
$179$			0.525853i			0.0393041i	0.999807	+	0.0196520i	$0.00625584\pi$
$179$			0.525853i			0.0393041i	−0.999807	+	0.0196520i	$0.993744\pi$
$180$		0			0
$181$		−	6.87689i		−	0.511156i	−0.966789	−	0.255578i	$-0.917734\pi$
$181$		−	6.87689i		−	0.511156i	0.966789	−	0.255578i	$-0.0822657\pi$
$182$	−6.10871	+	4.32246i	−0.452808	+	0.320402i
$183$	−1.87285			−0.138445
$184$	−15.6847	−	4.12391i	−1.15629	−	0.304019i
$185$		0			0
$186$	8.00000	−	3.74571i	0.586588	−	0.274648i
$187$		−	17.0862i		−	1.24947i
$188$	−15.3693	−	12.8147i	−1.12092	−	0.934606i
$189$	−12.4924	+	2.24621i	−0.908690	+	0.163388i
$190$		0			0
$191$		−	1.34700i		−	0.0974655i	−0.998812	−	0.0487327i	$-0.984482\pi$
$191$		−	1.34700i		−	0.0974655i	0.998812	−	0.0487327i	$-0.0155183\pi$
$192$	−3.68466	+	6.52262i	−0.265917	+	0.470729i
$193$			10.4924i			0.755261i	0.925956	+	0.377631i	$0.123261\pi$
$193$			10.4924i			0.755261i	−0.925956	+	0.377631i	$0.876739\pi$
$194$	−4.27156	−	9.12311i	−0.306680	−	0.655001i
$195$		0			0
$196$	4.65818	−	13.2023i	0.332727	−	0.943023i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	6.52262	−	3.05398i	0.463542	−	0.217037i
$199$	16.0345			1.13666			0.568329	−	0.822802i	$-0.307590\pi$
$199$	16.0345			1.13666			0.568329	+	0.822802i	$0.307590\pi$
$200$		0			0
$201$		−	13.3693i		−	0.942999i
$202$	−8.80776	+	4.12391i	−0.619712	+	0.290157i
$203$	0.936426	+	5.20798i	0.0657242	+	0.365529i
$204$	10.2462	+	8.54312i	0.717378	+	0.598138i
$205$		0			0
$206$	1.87285	−	0.876894i	0.130488	−	0.0610961i
$207$	−12.1735			−0.846120
$208$	1.43845	+	7.86962i	0.0997384	+	0.545660i
$209$		−	5.75379i		−	0.397998i
$210$		0			0
$211$		−	18.4332i		−	1.26900i	−0.772924	−	0.634498i	$-0.781207\pi$
$211$		−	18.4332i		−	1.26900i	0.772924	−	0.634498i	$-0.218793\pi$
$212$	−3.07221	−	2.56155i	−0.211000	−	0.175928i
$213$	−5.75379			−0.394243
$214$	−5.68466	−	12.1412i	−0.388595	−	0.829954i
$215$		0			0
$216$	−3.45041	+	13.1231i	−0.234771	+	0.892914i
$217$	3.12311	+	17.3693i	0.212010	+	1.17911i
$218$	0.673500	+	1.43845i	0.0456152	+	0.0974239i
$219$			8.77368i			0.592870i
$220$		0			0
$221$	14.2462			0.958304
$222$	−1.12311	−	2.39871i	−0.0753779	−	0.160991i
$223$		−	12.9300i		−	0.865854i	−0.901429	−	0.432927i	$-0.857481\pi$
$223$		−	12.9300i		−	0.865854i	0.901429	−	0.432927i	$-0.142519\pi$
$224$	−10.7008	−	10.4639i	−0.714976	−	0.699149i
$225$		0			0
$226$	−18.5616	+	8.69076i	−1.23470	+	0.578101i
$227$		−	14.2770i		−	0.947595i	−0.880634	−	0.473797i	$-0.842883\pi$
$227$		−	14.2770i		−	0.947595i	0.880634	−	0.473797i	$-0.157117\pi$
$228$	3.45041	+	2.87689i	0.228509	+	0.190527i
$229$			21.1231i			1.39585i	0.716169	+	0.697927i	$0.245894\pi$
$229$			21.1231i			1.39585i	−0.716169	+	0.697927i	$0.754106\pi$
$230$		0			0
$231$	−1.05171	−	5.84912i	−0.0691972	−	0.384844i
$232$	5.47091	+	1.43845i	0.359183	+	0.0944387i
$233$			24.2462i			1.58842i	0.607642	+	0.794211i	$0.292116\pi$
$233$			24.2462i			1.58842i	−0.607642	+	0.794211i	$0.707884\pi$
$234$	2.54635	+	5.43845i	0.166460	+	0.355522i
$235$		0			0
$236$	14.0140	−	16.8078i	0.912236	−	1.09409i
$237$	−4.00000			−0.259828
$238$	−21.7565	+	15.3947i	−1.41026	+	0.997888i
$239$			12.8147i			0.828912i	0.910069	+	0.414456i	$0.136028\pi$
$239$			12.8147i			0.828912i	−0.910069	+	0.414456i	$0.863972\pi$
$240$		0			0
$241$			15.6155i			1.00588i	0.864320	+	0.502942i	$0.167749\pi$
$241$			15.6155i			1.00588i	−0.864320	+	0.502942i	$0.832251\pi$
$242$	−3.14603	−	6.71922i	−0.202234	−	0.431928i
$243$			16.1498i			1.03601i
$244$	−3.07221	−	2.56155i	−0.196678	−	0.163987i
$245$		0			0
$246$	4.00000	+	8.54312i	0.255031	+	0.544689i
$247$	4.79741			0.305252
$248$	18.2462	+	4.79741i	1.15864	+	0.304636i
$249$	−0.876894			−0.0555709
$250$		0			0
$251$	−16.5604			−1.04528			−0.522641	−	0.852553i	$-0.675053\pi$
$251$	−16.5604			−1.04528			−0.522641	+	0.852553i	$0.675053\pi$
$252$	−9.76560	−	5.55385i	−0.615175	−	0.349860i
$253$		−	13.7538i		−	0.864693i
$254$	−7.93087	−	16.9386i	−0.497627	−	1.06282i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$	13.3693			0.833955			0.416978	−	0.908917i	$-0.363089\pi$
$257$	13.3693			0.833955			0.416978	+	0.908917i	$0.363089\pi$
$258$	9.12311	−	4.27156i	0.567980	−	0.265936i
$259$	5.20798	−	0.936426i	0.323608	−	0.0581867i
$260$		0			0
$261$	4.24621			0.262834
$262$	8.31534	+	17.7597i	0.513724	+	1.09720i
$263$	1.98813			0.122593			0.0612967	−	0.998120i	$-0.480476\pi$
$263$	1.98813			0.122593			0.0612967	+	0.998120i	$0.480476\pi$
$264$	−6.14441	−	1.61553i	−0.378162	−	0.0994289i
$265$		0			0
$266$	−7.32650	+	5.18415i	−0.449217	+	0.317861i
$267$	11.2371			0.687700
$268$	18.2856	−	21.9309i	1.11697	−	1.33964i
$269$		−	16.2462i		−	0.990549i	−0.868737	−	0.495274i	$-0.835067\pi$
$269$		−	16.2462i		−	0.990549i	0.868737	−	0.495274i	$-0.164933\pi$
$270$		0			0
$271$	23.7565			1.44310			0.721552	−	0.692360i	$-0.243429\pi$
$271$	23.7565			1.44310			0.721552	+	0.692360i	$0.243429\pi$
$272$	5.12311	+	28.0281i	0.310634	+	1.69945i
$273$	4.87689	−	0.876894i	0.295163	−	0.0530721i
$274$	17.9309	−	8.39547i	1.08324	−	0.507189i
$275$		0			0
$276$	8.24782	+	6.87689i	0.496461	+	0.413940i
$277$			4.24621i			0.255130i	0.991830	+	0.127565i	$0.0407162\pi$
$277$			4.24621i			0.255130i	−0.991830	+	0.127565i	$0.959284\pi$
$278$	0.807764	+	1.72521i	0.0484465	+	0.103471i
$279$	14.1617			0.847837
$280$		0			0
$281$	−4.63068			−0.276243			−0.138122	−	0.990415i	$-0.544107\pi$
$281$	−4.63068			−0.276243			−0.138122	+	0.990415i	$0.544107\pi$
$282$	5.61856	+	12.0000i	0.334580	+	0.714590i
$283$		−	24.6929i		−	1.46784i	−0.679235	−	0.733921i	$-0.737688\pi$
$283$		−	24.6929i		−	1.46784i	0.679235	−	0.733921i	$-0.262312\pi$
$284$	−9.43845	−	7.86962i	−0.560069	−	0.466976i
$285$		0			0
$286$	−6.14441	+	2.87689i	−0.363327	+	0.170114i
$287$	−18.5485	+	3.33513i	−1.09488	+	0.196867i
$288$	−9.78393	+	6.96543i	−0.576523	+	0.410442i
$289$	33.7386			1.98463
$290$		0			0
$291$			6.67026i			0.391018i
$292$	−12.0000	+	14.3922i	−0.702247	+	0.842242i
$293$	32.2462			1.88384			0.941922	−	0.335832i	$-0.109017\pi$
$293$	32.2462			1.88384			0.941922	+	0.335832i	$0.109017\pi$
$294$	−6.50030	+	6.60922i	−0.379105	+	0.385457i
$295$		0			0
$296$	1.43845	−	5.47091i	0.0836080	−	0.317990i
$297$	−11.5076			−0.667737
$298$	−11.6153	−	24.8078i	−0.672858	−	1.43708i
$299$	11.4677			0.663193
$300$		0			0
$301$	3.56155	+	19.8078i	0.205284	+	1.14170i
$302$	18.8114	−	8.80776i	1.08248	−	0.506830i
$303$	6.43971			0.369951
$304$	1.72521	+	9.43845i	0.0989473	+	0.541332i
$305$		0			0
$306$	9.06897	+	19.3693i	0.518438	+	1.10727i
$307$		−	31.3632i		−	1.78999i	−0.446074	−	0.894996i	$-0.647178\pi$
$307$		−	31.3632i		−	1.78999i	0.446074	−	0.894996i	$-0.352822\pi$
$308$	6.27479	−	11.0333i	0.357540	−	0.628679i
$309$	−1.36932			−0.0778977
$310$		0			0
$311$	9.36426			0.530999			0.265499	−	0.964111i	$-0.414463\pi$
$311$	9.36426			0.530999			0.265499	+	0.964111i	$0.414463\pi$
$312$	1.34700	−	5.12311i	0.0762589	−	0.290039i
$313$	7.61553			0.430455			0.215228	−	0.976564i	$-0.430951\pi$
$313$	7.61553			0.430455			0.215228	+	0.976564i	$0.430951\pi$
$314$	−9.74247	−	20.8078i	−0.549799	−	1.17425i
$315$		0			0
$316$	−6.56155	−	5.47091i	−0.369116	−	0.307763i
$317$			4.24621i			0.238491i	0.992865	+	0.119245i	$0.0380476\pi$
$317$			4.24621i			0.238491i	−0.992865	+	0.119245i	$0.961952\pi$
$318$	1.12311	+	2.39871i	0.0629806	+	0.134513i
$319$			4.79741i			0.268603i
$320$		0			0
$321$			8.87689i			0.495460i
$322$	−17.5132	+	12.3921i	−0.975971	+	0.690587i
$323$	17.0862			0.950703
$324$	−2.40388	+	2.88310i	−0.133549	+	0.160172i
$325$		0			0
$326$	−0.561553	−	1.19935i	−0.0311015	−	0.0664260i
$327$		−	1.05171i		−	0.0581595i
$328$	−5.12311	+	19.4849i	−0.282876	+	1.07588i
$329$	−26.0540	+	4.68466i	−1.43640	+	0.258274i
$330$		0			0
$331$			29.0798i			1.59837i	0.601086	+	0.799184i	$0.294735\pi$
$331$			29.0798i			1.59837i	−0.601086	+	0.799184i	$0.705265\pi$
$332$	−1.43845	−	1.19935i	−0.0789450	−	0.0658230i
$333$		−	4.24621i		−	0.232691i
$334$	2.92456	−	1.36932i	0.160025	−	0.0749257i
$335$		0			0
$336$	3.47899	+	9.27948i	0.189795	+	0.506237i
$337$		−	4.24621i		−	0.231306i	−0.993290	−	0.115653i	$-0.963104\pi$
$337$		−	4.24621i		−	0.231306i	0.993290	−	0.115653i	$-0.0368960\pi$
$338$	5.39709	+	11.5270i	0.293563	+	0.626985i
$339$	13.5711			0.737080
$340$		0			0
$341$			16.0000i			0.866449i
$342$	3.05398	+	6.52262i	0.165140	+	0.352703i
$343$	−9.42190	−	15.9445i	−0.508735	−	0.860923i
$344$	20.8078	+	5.47091i	1.12188	+	0.294972i
$345$		0			0
$346$	0.147647	+	0.315342i	0.00793756	+	0.0169529i
$347$	9.47954			0.508889			0.254444	−	0.967087i	$-0.418107\pi$
$347$	9.47954			0.508889			0.254444	+	0.967087i	$0.418107\pi$
$348$	−2.87689	−	2.39871i	−0.154218	−	0.128584i
$349$			27.8617i			1.49140i	0.666279	+	0.745702i	$0.267886\pi$
$349$			27.8617i			1.49140i	−0.666279	+	0.745702i	$0.732114\pi$
$350$		0			0
$351$		−	9.59482i		−	0.512134i
$352$	−7.86962	−	11.0540i	−0.419452	−	0.589179i
$353$	−5.36932			−0.285780			−0.142890	−	0.989739i	$-0.545639\pi$
$353$	−5.36932			−0.285780			−0.142890	+	0.989739i	$0.545639\pi$
$354$	−13.1231	+	6.14441i	−0.697485	+	0.326572i
$355$		0			0
$356$	18.4332	+	15.3693i	0.976959	+	0.814572i
$357$	17.3693	−	3.12311i	0.919282	−	0.165292i
$358$	0.673500	−	0.315342i	0.0355956	−	0.0166663i
$359$			16.5604i			0.874023i	0.899456	+	0.437012i	$0.143963\pi$
$359$			16.5604i			0.874023i	−0.899456	+	0.437012i	$0.856037\pi$
$360$		0			0
$361$	−13.2462			−0.697169
$362$	−8.80776	+	4.12391i	−0.462926	+	0.216748i
$363$			4.91269i			0.257849i
$364$	9.19935	+	5.23182i	0.482177	+	0.274222i
$365$		0			0
$366$	1.12311	+	2.39871i	0.0587057	+	0.125382i
$367$			7.08084i			0.369617i	0.982775	+	0.184808i	$0.0591664\pi$
$367$			7.08084i			0.369617i	−0.982775	+	0.184808i	$0.940834\pi$
$368$	4.12391	+	22.5616i	0.214974	+	1.17610i
$369$			15.1231i			0.787277i
$370$		0			0
$371$	−5.20798	+	0.936426i	−0.270385	+	0.0486168i
$372$	−9.59482	−	8.00000i	−0.497468	−	0.414781i
$373$			22.4924i			1.16461i	0.812969	+	0.582307i	$0.197850\pi$
$373$			22.4924i			1.16461i	−0.812969	+	0.582307i	$0.802150\pi$
$374$	−21.8836	+	10.2462i	−1.13158	+	0.529819i
$375$		0			0
$376$	−7.19612	+	27.3693i	−0.371111	+	1.41146i
$377$	−4.00000			−0.206010
$378$	10.3683	+	14.6530i	0.533288	+	0.753669i
$379$		−	22.4095i		−	1.15110i	−0.817767	−	0.575549i	$-0.804788\pi$
$379$		−	22.4095i		−	1.15110i	0.817767	−	0.575549i	$-0.195212\pi$
$380$		0			0
$381$			12.3845i			0.634476i
$382$	−1.72521	+	0.807764i	−0.0882692	+	0.0413288i
$383$		−	17.4968i		−	0.894045i	−0.894523	−	0.447023i	$-0.852484\pi$
$383$		−	17.4968i		−	0.894045i	0.894523	−	0.447023i	$-0.147516\pi$
$384$	10.5636	+	0.807764i	0.539072	+	0.0412210i
$385$		0			0
$386$	13.4384	−	6.29206i	0.683999	−	0.320257i
$387$	16.1498			0.820941
$388$	−9.12311	+	10.9418i	−0.463156	+	0.555487i
$389$	−1.12311			−0.0569437			−0.0284719	−	0.999595i	$-0.509064\pi$
$389$	−1.12311			−0.0569437			−0.0284719	+	0.999595i	$0.509064\pi$
$390$		0			0
$391$	40.8427			2.06551
$392$	−19.7026	+	1.95104i	−0.995133	+	0.0985424i
$393$		−	12.9848i		−	0.654999i
$394$	−23.0540	+	10.7942i	−1.16144	+	0.543803i
$395$		0			0
$396$	−7.82292	−	6.52262i	−0.393116	−	0.327774i
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	−9.61553	−	20.5366i	−0.481983	−	1.02941i
$399$	5.84912	−	1.05171i	0.292822	−	0.0526511i
$400$		0			0
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−17.1231	+	8.01726i	−0.854023	+	0.399865i
$403$	−13.3405			−0.664539
$404$	10.5636	+	8.80776i	0.525560	+	0.438203i
$405$		0			0
$406$	6.10871	−	4.32246i	0.303170	−	0.214520i
$407$	4.79741			0.237799
$408$	4.79741	−	18.2462i	0.237507	−	0.903322i
$409$			8.87689i			0.438934i	0.975620	+	0.219467i	$0.0704319\pi$
$409$			8.87689i			0.438934i	−0.975620	+	0.219467i	$0.929568\pi$
$410$		0			0
$411$	−13.1100			−0.646667
$412$	−2.24621	−	1.87285i	−0.110663	−	0.0922688i
$413$	−5.12311	−	28.4924i	−0.252092	−	1.40202i
$414$	7.30019	+	15.5916i	0.358785	+	0.766285i
$415$		0			0
$416$	9.21662	−	6.56155i	0.451882	−	0.321707i
$417$		−	1.26137i		−	0.0617694i
$418$	−7.36932	+	3.45041i	−0.360445	+	0.168765i
$419$	−11.9935			−0.585922			−0.292961	−	0.956124i	$-0.594641\pi$
$419$	−11.9935			−0.585922			−0.292961	+	0.956124i	$0.594641\pi$
$420$		0			0
$421$	−17.6155			−0.858528			−0.429264	−	0.903179i	$-0.641227\pi$
$421$	−17.6155			−0.858528			−0.429264	+	0.903179i	$0.641227\pi$
$422$	−23.6089	+	11.0540i	−1.14926	+	0.538099i
$423$			21.2425i			1.03285i
$424$	−1.43845	+	5.47091i	−0.0698572	+	0.265691i
$425$		0			0
$426$	3.45041	+	7.36932i	0.167173	+	0.357045i
$427$	−5.20798	+	0.936426i	−0.252032	+	0.0453168i
$428$	−12.1412	+	14.5616i	−0.586866	+	0.703859i
$429$	4.49242			0.216896
$430$		0			0
$431$		−	36.5712i		−	1.76157i	−0.473515	−	0.880786i	$-0.657015\pi$
$431$		−	36.5712i		−	1.76157i	0.473515	−	0.880786i	$-0.342985\pi$
$432$	18.8769	−	3.45041i	0.908215	−	0.166008i
$433$	11.6155			0.558207			0.279103	−	0.960261i	$-0.409963\pi$
$433$	11.6155			0.558207			0.279103	+	0.960261i	$0.409963\pi$
$434$	20.3734	−	14.4160i	0.977953	−	0.691989i
$435$		0			0
$436$	1.43845	−	1.72521i	0.0688891	−	0.0826224i
$437$	13.7538			0.657933
$438$	11.2371	−	5.26137i	0.536930	−	0.251398i
$439$	18.1379			0.865677			0.432838	−	0.901472i	$-0.357512\pi$
$439$	18.1379			0.865677			0.432838	+	0.901472i	$0.357512\pi$
$440$		0			0
$441$	−13.9309	+	5.17708i	−0.663375	+	0.246528i
$442$	−8.54312	−	18.2462i	−0.406355	−	0.867884i
$443$	−30.3115			−1.44014			−0.720071	−	0.693900i	$-0.755891\pi$
$443$	−30.3115			−1.44014			−0.720071	+	0.693900i	$0.755891\pi$
$444$	−2.39871	+	2.87689i	−0.113838	+	0.136531i
$445$		0			0
$446$	−16.5604	+	7.75379i	−0.784157	+	0.367153i
$447$			18.1379i			0.857895i
$448$	−6.98490	+	19.9803i	−0.330006	+	0.943979i
$449$	−25.6155			−1.20887			−0.604436	−	0.796654i	$-0.706601\pi$
$449$	−25.6155			−1.20887			−0.604436	+	0.796654i	$0.706601\pi$
$450$		0			0
$451$	−17.0862			−0.804559
$452$	22.2619	+	18.5616i	1.04711	+	0.873062i
$453$	−13.7538			−0.646209
$454$	−18.2856	+	8.56155i	−0.858185	+	0.401814i
$455$		0			0
$456$	1.61553	−	6.14441i	0.0756540	−	0.287738i
$457$		−	6.00000i		−	0.280668i	−0.990104	−	0.140334i	$-0.955182\pi$
$457$		−	6.00000i		−	0.280668i	0.990104	−	0.140334i	$-0.0448177\pi$
$458$	27.0540	−	12.6670i	1.26415	−	0.591891i
$459$		−	34.1725i		−	1.59503i
$460$		0			0
$461$		−	37.6155i		−	1.75193i	−0.482375	−	0.875965i	$-0.660226\pi$
$461$		−	37.6155i		−	1.75193i	0.482375	−	0.875965i	$-0.339774\pi$
$462$	−6.86073	+	4.85458i	−0.319190	+	0.225855i
$463$	21.9989			1.02238			0.511188	−	0.859469i	$-0.329205\pi$
$463$	21.9989			1.02238			0.511188	+	0.859469i	$0.329205\pi$
$464$	−1.43845	−	7.86962i	−0.0667782	−	0.365338i
$465$		0			0
$466$	31.0540	−	14.5399i	1.43855	−	0.673547i
$467$			1.98813i			0.0919998i	0.998941	+	0.0459999i	$0.0146474\pi$
$467$			1.98813i			0.0919998i	−0.998941	+	0.0459999i	$0.985353\pi$
$468$	5.43845	−	6.52262i	0.251392	−	0.301508i
$469$	−6.68466	−	37.1771i	−0.308669	−	1.71668i
$470$		0			0
$471$			15.2134i			0.700996i
$472$	−29.9309	−	7.86962i	−1.37768	−	0.362228i
$473$			18.2462i			0.838962i
$474$	2.39871	+	5.12311i	0.110176	+	0.235312i
$475$		0			0
$476$	32.7640	+	18.6334i	1.50173	+	0.854060i
$477$			4.24621i			0.194421i
$478$	16.4127	−	7.68466i	0.750701	−	0.351488i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$			4.00000i			0.182384i
$482$	20.0000	−	9.36426i	0.910975	−	0.426531i
$483$	13.9817	−	2.51398i	0.636188	−	0.114390i
$484$	−6.71922	+	8.05872i	−0.305419	+	0.366305i
$485$		0			0
$486$	20.6843	−	9.68466i	0.938259	−	0.439305i
$487$	19.0744			0.864342			0.432171	−	0.901792i	$-0.357748\pi$
$487$	19.0744			0.864342			0.432171	+	0.901792i	$0.357748\pi$
$488$	−1.43845	+	5.47091i	−0.0651154	+	0.247657i
$489$			0.876894i			0.0396545i
$490$		0			0
$491$			13.6358i			0.615376i	0.951487	+	0.307688i	$0.0995553\pi$
$491$			13.6358i			0.615376i	−0.951487	+	0.307688i	$0.900445\pi$
$492$	8.54312	−	10.2462i	0.385153	−	0.461935i
$493$	−14.2462			−0.641617
$494$	−2.87689	−	6.14441i	−0.129438	−	0.276450i
$495$		0			0
$496$	−4.79741	−	26.2462i	−0.215410	−	1.17849i
$497$	−16.0000	+	2.87689i	−0.717698	+	0.129046i
$498$	0.525853	+	1.12311i	0.0235640	+	0.0503276i
$499$			27.2069i			1.21795i	0.793190	+	0.608974i	$0.208419\pi$
$499$			27.2069i			1.21795i	−0.793190	+	0.608974i	$0.791581\pi$
$500$		0			0
$501$	−2.13826			−0.0955304
$502$	9.93087	+	21.2101i	0.443236	+	0.946655i
$503$			21.4731i			0.957437i	0.877968	+	0.478718i	$0.158899\pi$
$503$			21.4731i			0.957437i	−0.877968	+	0.478718i	$0.841101\pi$
$504$	−1.25704	+	15.8381i	−0.0559930	+	0.705483i
$505$		0			0
$506$	−17.6155	+	8.24782i	−0.783106	+	0.366660i
$507$		−	8.42784i		−	0.374293i
$508$	−16.9386	+	20.3153i	−0.751528	+	0.901348i
$509$		−	17.6155i		−	0.780795i	−0.920646	−	0.390397i	$-0.872338\pi$
$509$		−	17.6155i		−	0.780795i	0.920646	−	0.390397i	$-0.127662\pi$
$510$		0			0
$511$	4.38684	+	24.3976i	0.194062	+	1.07929i
$512$	16.2236	+	15.7732i	0.716990	+	0.697083i
$513$		−	11.5076i		−	0.508072i
$514$	−8.01726	−	17.1231i	−0.353626	−	0.755268i
$515$		0			0
$516$	−10.9418	−	9.12311i	−0.481687	−	0.401622i
$517$	−24.0000			−1.05552
$518$	−4.32246	−	6.10871i	−0.189918	−	0.268401i
$519$		−	0.230559i		−	0.0101204i
$520$		0			0
$521$		−	26.2462i		−	1.14987i	−0.818200	−	0.574934i	$-0.805028\pi$
$521$		−	26.2462i		−	1.14987i	0.818200	−	0.574934i	$-0.194972\pi$
$522$	−2.54635	−	5.43845i	−0.111451	−	0.238034i
$523$		−	17.2015i		−	0.752170i	−0.926585	−	0.376085i	$-0.877270\pi$
$523$		−	17.2015i		−	0.752170i	0.926585	−	0.376085i	$-0.122730\pi$
$524$	17.7597	−	21.3002i	0.775838	−	0.930503i
$525$		0			0
$526$	−1.19224	−	2.54635i	−0.0519840	−	0.111026i
$527$	−47.5130			−2.06970
$528$	1.61553	+	8.83841i	0.0703068	+	0.384642i
$529$	9.87689			0.429430
$530$		0			0
$531$	−23.2306			−1.00812
$532$	11.0333	+	6.27479i	0.478353	+	0.272047i
$533$		−	14.2462i		−	0.617072i
$534$	−6.73863	−	14.3922i	−0.291609	−	0.622813i
$535$		0			0
$536$	−39.0540	−	10.2683i	−1.68687	−	0.443524i
$537$	−0.492423			−0.0212496
$538$	−20.8078	+	9.74247i	−0.897086	+	0.420028i
$539$	−5.84912	−	15.7392i	−0.251939	−	0.677937i
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	−14.2462	−	30.4268i	−0.611927	−	1.30694i
$543$	6.43971			0.276354
$544$	32.8255	−	23.3693i	1.40738	−	1.00195i
$545$		0			0
$546$	−4.04766	−	5.72036i	−0.173224	−	0.244809i
$547$	−1.75757			−0.0751484			−0.0375742	−	0.999294i	$-0.511963\pi$
$547$	−1.75757			−0.0751484			−0.0375742	+	0.999294i	$0.511963\pi$
$548$	−21.5054	−	17.9309i	−0.918667	−	0.765969i
$549$			4.24621i			0.181224i
$550$		0			0
$551$	−4.79741			−0.204377
$552$	3.86174	−	14.6875i	0.164367	−	0.625143i
$553$	−11.1231	+	2.00000i	−0.473003	+	0.0850487i
$554$	5.43845	−	2.54635i	0.231057	−	0.108184i
$555$		0			0
$556$	1.72521	−	2.06913i	0.0731650	−	0.0877507i
$557$		−	6.49242i		−	0.275093i	−0.990495	−	0.137546i	$-0.956078\pi$
$557$		−	6.49242i		−	0.275093i	0.990495	−	0.137546i	$-0.0439216\pi$
$558$	−8.49242	−	18.1379i	−0.359513	−	0.767840i
$559$	−15.2134			−0.643457
$560$		0			0
$561$	16.0000			0.675521
$562$	2.77691	+	5.93087i	0.117137	+	0.250179i
$563$			26.7963i			1.12933i	0.825320	+	0.564665i	$0.190995\pi$
$563$			26.7963i			1.12933i	−0.825320	+	0.564665i	$0.809005\pi$
$564$	12.0000	−	14.3922i	0.505291	−	0.606022i
$565$		0			0
$566$	−31.6261	+	14.8078i	−1.32934	+	0.622417i
$567$	0.878787	+	4.88742i	0.0369056	+	0.205252i
$568$	−4.41921	+	16.8078i	−0.185426	+	0.705238i
$569$	37.1231			1.55628			0.778141	−	0.628090i	$-0.216163\pi$
$569$	37.1231			1.55628			0.778141	+	0.628090i	$0.216163\pi$
$570$		0			0
$571$		−	28.0281i		−	1.17294i	−0.809972	−	0.586469i	$-0.800518\pi$
$571$		−	28.0281i		−	1.17294i	0.809972	−	0.586469i	$-0.199482\pi$
$572$	7.36932	+	6.14441i	0.308127	+	0.256911i
$573$	1.26137			0.0526943
$574$	15.3947	+	21.7565i	0.642561	+	0.908099i
$575$		0			0
$576$	14.7884	+	8.35401i	0.616181	+	0.348084i
$577$	4.38447			0.182528			0.0912640	−	0.995827i	$-0.470909\pi$
$577$	4.38447			0.182528			0.0912640	+	0.995827i	$0.470909\pi$
$578$	−20.2323	−	43.2116i	−0.841551	−	1.79737i
$579$	−9.82538			−0.408329
$580$		0			0
$581$	−2.43845	+	0.438447i	−0.101164	+	0.0181899i
$582$	8.54312	−	4.00000i	0.354124	−	0.165805i
$583$	−4.79741			−0.198688
$584$	25.6294	+	6.73863i	1.06055	+	0.278847i
$585$		0			0
$586$	−19.3373	−	41.3002i	−0.798816	−	1.70609i
$587$		−	8.65840i		−	0.357370i	−0.983906	−	0.178685i	$-0.942816\pi$
$587$		−	8.65840i		−	0.357370i	0.983906	−	0.178685i	$-0.0571843\pi$
$588$	12.3630	+	4.36204i	0.509842	+	0.179887i
$589$	−16.0000			−0.659269
$590$		0			0
$591$	16.8557			0.693350
$592$	−7.86962	+	1.43845i	−0.323439	+	0.0591198i
$593$	−13.3693			−0.549012			−0.274506	−	0.961585i	$-0.588514\pi$
$593$	−13.3693			−0.549012			−0.274506	+	0.961585i	$0.588514\pi$
$594$	6.90082	+	14.7386i	0.283144	+	0.604733i
$595$		0			0
$596$	−24.8078	+	29.7533i	−1.01617	+	1.21874i
$597$			15.0152i			0.614529i
$598$	−6.87689	−	14.6875i	−0.281217	−	0.600618i
$599$			10.1207i			0.413520i	0.978392	+	0.206760i	$0.0662919\pi$
$599$			10.1207i			0.413520i	−0.978392	+	0.206760i	$0.933708\pi$
$600$		0			0
$601$			8.87689i			0.362096i	0.983474	+	0.181048i	$0.0579489\pi$
$601$			8.87689i			0.362096i	−0.983474	+	0.181048i	$0.942051\pi$
$602$	23.2335	−	16.4398i	0.946928	−	0.670036i
$603$	−30.3115			−1.23438
$604$	−22.5616	−	18.8114i	−0.918017	−	0.765427i
$605$		0			0
$606$	−3.86174	−	8.24782i	−0.156872	−	0.335045i
$607$			7.90198i			0.320732i	0.987058	+	0.160366i	$0.0512674\pi$
$607$			7.90198i			0.320732i	−0.987058	+	0.160366i	$0.948733\pi$
$608$	11.0540	−	7.86962i	0.448298	−	0.319155i
$609$	−4.87689	+	0.876894i	−0.197622	+	0.0355336i
$610$		0			0
$611$		−	20.0108i		−	0.809550i
$612$	19.3693	−	23.2306i	0.782958	−	0.939043i
$613$			11.7538i			0.474731i	0.971420	+	0.237366i	$0.0762839\pi$
$613$			11.7538i			0.474731i	−0.971420	+	0.237366i	$0.923716\pi$
$614$	−40.1692	+	18.8078i	−1.62110	+	0.759020i
$615$		0			0
$616$	−17.8940	−	1.42022i	−0.720970	−	0.0572222i
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$	0.821147	+	1.75379i	0.0330314	+	0.0705477i
$619$	−48.8600			−1.96385			−0.981925	−	0.189273i	$-0.939387\pi$
$619$	−48.8600			−1.96385			−0.981925	+	0.189273i	$0.939387\pi$
$620$		0			0
$621$		−	27.5076i		−	1.10384i
$622$	−5.61553	−	11.9935i	−0.225162	−	0.480897i
$623$	31.2479	−	5.61856i	1.25192	−	0.225103i
$624$	−7.36932	+	1.34700i	−0.295009	+	0.0539232i
$625$		0			0
$626$	−4.56685	−	9.75379i	−0.182528	−	0.389840i
$627$	5.38800			0.215176
$628$	−20.8078	+	24.9559i	−0.830320	+	0.995847i
$629$			14.2462i			0.568034i
$630$		0			0
$631$		−	7.19612i		−	0.286473i	−0.989688	−	0.143236i	$-0.954249\pi$
$631$		−	7.19612i		−	0.286473i	0.989688	−	0.143236i	$-0.0457509\pi$
$632$	−3.07221	+	11.6847i	−0.122206	+	0.464791i
$633$	17.2614			0.686078
$634$	5.43845	−	2.54635i	0.215988	−	0.101129i
$635$		0			0
$636$	2.39871	−	2.87689i	0.0951149	−	0.114076i
$637$	13.1231	−	4.87689i	0.519956	−	0.193230i
$638$	6.14441	−	2.87689i	0.243260	−	0.113897i
$639$			13.0452i			0.516061i
$640$		0			0
$641$	1.12311			0.0443600			0.0221800	−	0.999754i	$-0.492939\pi$
$641$	1.12311			0.0443600			0.0221800	+	0.999754i	$0.492939\pi$
$642$	11.3693	−	5.32326i	0.448711	−	0.210092i
$643$		−	4.91269i		−	0.193738i	−0.995297	−	0.0968688i	$-0.969117\pi$
$643$		−	4.91269i		−	0.193738i	0.995297	−	0.0968688i	$-0.0308827\pi$
$644$	26.3738	+	14.9992i	1.03927	+	0.591051i
$645$		0			0
$646$	−10.2462	−	21.8836i	−0.403132	−	0.861000i
$647$			37.7382i			1.48364i	0.670599	+	0.741820i	$0.266037\pi$
$647$			37.7382i			1.48364i	−0.670599	+	0.741820i	$0.733963\pi$
$648$	5.13416	+	1.34991i	0.201689	+	0.0530293i
$649$		−	26.2462i		−	1.03025i
$650$		0			0
$651$	−16.2651	+	2.92456i	−0.637479	+	0.114622i
$652$	−1.19935	+	1.43845i	−0.0469703	+	0.0563339i
$653$			42.9848i			1.68213i	0.540936	+	0.841063i	$0.318070\pi$
$653$			42.9848i			1.68213i	−0.540936	+	0.841063i	$0.681930\pi$
$654$	−1.34700	+	0.630683i	−0.0526719	+	0.0246617i
$655$		0			0
$656$	28.0281	−	5.12311i	1.09431	−	0.200024i
$657$	19.8920			0.776063
$658$	21.6240	+	30.5600i	0.842990	+	1.19135i
$659$			4.27156i			0.166396i	0.996533	+	0.0831981i	$0.0265134\pi$
$659$			4.27156i			0.166396i	−0.996533	+	0.0831981i	$0.973487\pi$
$660$		0			0
$661$			4.24621i			0.165158i	0.996585	+	0.0825792i	$0.0263158\pi$
$661$			4.24621i			0.165158i	−0.996585	+	0.0825792i	$0.973684\pi$
$662$	37.2447	−	17.4384i	1.44756	−	0.677764i
$663$			13.3405i			0.518103i
$664$	−0.673500	+	2.56155i	−0.0261369	+	0.0994075i
$665$		0			0
$666$	−5.43845	+	2.54635i	−0.210736	+	0.0986692i
$667$	−11.4677			−0.444030
$668$	−3.50758	−	2.92456i	−0.135712	−	0.113155i
$669$	12.1080			0.468120
$670$		0			0
$671$	−4.79741			−0.185202
$672$	9.79867	−	10.0205i	0.377992	−	0.386549i
$673$		−	14.0000i		−	0.539660i	−0.962908	−	0.269830i	$-0.913032\pi$
$673$		−	14.0000i		−	0.539660i	0.962908	−	0.269830i	$-0.0869676\pi$
$674$	−5.43845	+	2.54635i	−0.209481	+	0.0980818i
$675$		0			0
$676$	11.5270	−	13.8249i	0.443346	−	0.531728i
$677$	16.7386			0.643318			0.321659	−	0.946856i	$-0.395760\pi$
$677$	16.7386			0.643318			0.321659	+	0.946856i	$0.395760\pi$
$678$	−8.13826	−	17.3815i	−0.312548	−	0.667534i
$679$	3.33513	+	18.5485i	0.127991	+	0.711827i
$680$		0			0
$681$	13.3693			0.512313
$682$	20.4924	−	9.59482i	0.784695	−	0.367405i
$683$	7.60669			0.291062			0.145531	−	0.989354i	$-0.453511\pi$
$683$	7.60669			0.291062			0.145531	+	0.989354i	$0.453511\pi$
$684$	6.52262	−	7.82292i	0.249398	−	0.299117i
$685$		0			0
$686$	−14.7713	+	21.6289i	−0.563970	+	0.825795i
$687$	−19.7802			−0.754663
$688$	−5.47091	−	29.9309i	−0.208577	−	1.14110i
$689$		−	4.00000i		−	0.152388i
$690$		0			0
$691$	22.4095			0.852497			0.426249	−	0.904606i	$-0.359835\pi$
$691$	22.4095			0.852497			0.426249	+	0.904606i	$0.359835\pi$
$692$	0.315342	−	0.378206i	0.0119875	−	0.0143772i
$693$	−13.2614	+	2.38447i	−0.503758	+	0.0905786i
$694$	−5.68466	−	12.1412i	−0.215787	−	0.460873i
$695$		0			0
$696$	−1.34700	+	5.12311i	−0.0510579	+	0.194191i
$697$		−	50.7386i		−	1.92186i
$698$	35.6847	−	16.7080i	1.35068	−	0.632408i
$699$	−22.7048			−0.858774
$700$		0			0
$701$	2.87689			0.108659			0.0543294	−	0.998523i	$-0.482698\pi$
$701$	2.87689			0.108659			0.0543294	+	0.998523i	$0.482698\pi$
$702$	−12.2888	+	5.75379i	−0.463812	+	0.217163i
$703$			4.79741i			0.180938i
$704$	−9.43845	+	16.7080i	−0.355725	+	0.629707i
$705$		0			0
$706$	3.21985	+	6.87689i	0.121181	+	0.258815i
$707$	17.9074	−	3.21985i	0.673476	−	0.121095i
$708$	15.7392	+	13.1231i	0.591517	+	0.493197i
$709$	4.73863			0.177963			0.0889816	−	0.996033i	$-0.471639\pi$
$709$	4.73863			0.177963			0.0889816	+	0.996033i	$0.471639\pi$
$710$		0			0
$711$			9.06897i			0.340113i
$712$	8.63068	−	32.8255i	0.323449	−	1.23019i
$713$	−38.2462			−1.43233
$714$	−14.4160	−	20.3734i	−0.539504	−	0.762454i
$715$		0			0
$716$	−0.807764	−	0.673500i	−0.0301876	−	0.0251699i
$717$	−12.0000			−0.448148
$718$	21.2101	−	9.93087i	0.791556	−	0.370617i
$719$	−37.9182			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$719$	−37.9182			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$720$		0			0
$721$	−3.80776	+	0.684658i	−0.141809	+	0.0254980i
$722$	7.94344	+	16.9654i	0.295624	+	0.631388i
$723$	−14.6228			−0.543828
$724$	10.5636	+	8.80776i	0.392594	+	0.327338i
$725$		0			0
$726$	6.29206	−	2.94602i	0.233520	−	0.109337i
$727$			22.2942i			0.826847i	0.910539	+	0.413423i	$0.135667\pi$
$727$			22.2942i			0.826847i	−0.910539	+	0.413423i	$0.864333\pi$
$728$	1.18415	−	14.9197i	0.0438876	−	0.552961i
$729$	−9.49242			−0.351571
$730$		0			0
$731$	−54.1833			−2.00404
$732$	2.39871	−	2.87689i	0.0886587	−	0.106333i
$733$	48.7386			1.80020			0.900101	−	0.435681i	$-0.143492\pi$
$733$	48.7386			1.80020			0.900101	+	0.435681i	$0.143492\pi$
$734$	9.06897	−	4.24621i	0.334742	−	0.156731i
$735$		0			0
$736$	26.4233	−	18.8114i	0.973975	−	0.693399i
$737$		−	34.2462i		−	1.26148i
$738$	19.3693	−	9.06897i	0.712994	−	0.333833i
$739$			15.5087i			0.570496i	0.958454	+	0.285248i	$0.0920759\pi$
$739$			15.5087i			0.570496i	−0.958454	+	0.285248i	$0.907924\pi$
$740$		0			0
$741$			4.49242i			0.165033i
$742$	4.32246	+	6.10871i	0.158682	+	0.224258i
$743$	15.0981			0.553896			0.276948	−	0.960885i	$-0.410677\pi$
$743$	15.0981			0.553896			0.276948	+	0.960885i	$0.410677\pi$
$744$	−4.49242	+	17.0862i	−0.164700	+	0.626412i
$745$		0			0
$746$	28.8078	−	13.4882i	1.05473	−	0.493837i
$747$			1.98813i			0.0727420i
$748$	26.2462	+	21.8836i	0.959657	+	0.800145i
$749$	4.43845	+	24.6847i	0.162177	+	0.901958i
$750$		0			0
$751$			5.09271i			0.185835i	0.995674	+	0.0929177i	$0.0296194\pi$
$751$			5.09271i			0.185835i	−0.995674	+	0.0929177i	$0.970381\pi$
$752$	39.3693	−	7.19612i	1.43565	−	0.262415i
$753$		−	15.5076i		−	0.565128i
$754$	2.39871	+	5.12311i	0.0873557	+	0.186573i
$755$		0			0
$756$	12.5496	−	22.0665i	0.456424	−	0.802552i
$757$			12.2462i			0.445096i	0.974922	+	0.222548i	$0.0714374\pi$
$757$			12.2462i			0.445096i	−0.974922	+	0.222548i	$0.928563\pi$
$758$	−28.7016	+	13.4384i	−1.04249	+	0.488106i
$759$	12.8794			0.467493
$760$		0			0
$761$			35.2311i			1.27712i	0.769570	+	0.638562i	$0.220471\pi$
$761$			35.2311i			1.27712i	−0.769570	+	0.638562i	$0.779529\pi$
$762$	15.8617	−	7.42668i	0.574610	−	0.269040i
$763$	−0.525853	−	2.92456i	−0.0190372	−	0.105876i
$764$	2.06913	+	1.72521i	0.0748585	+	0.0624158i
$765$		0			0
$766$	−22.4095	+	10.4924i	−0.809688	+	0.379107i
$767$	21.8836			0.790173
$768$	−5.30019	−	14.0140i	−0.191254	−	0.505688i
$769$		−	55.2311i		−	1.99168i	−0.0911037	−	0.995841i	$-0.529039\pi$
$769$		−	55.2311i		−	1.99168i	0.0911037	−	0.995841i	$-0.470961\pi$
$770$		0			0
$771$			12.5194i			0.450874i
$772$	−16.1174	−	13.4384i	−0.580079	−	0.483660i
$773$	−16.7386			−0.602047			−0.301023	−	0.953617i	$-0.597328\pi$
$773$	−16.7386			−0.602047			−0.301023	+	0.953617i	$0.597328\pi$
$774$	−9.68466	−	20.6843i	−0.348108	−	0.743482i
$775$		0			0
$776$	19.4849	+	5.12311i	0.699469	+	0.183909i
$777$	0.876894	+	4.87689i	0.0314584	+	0.174958i
$778$	0.673500	+	1.43845i	0.0241461	+	0.0515708i
$779$		−	17.0862i		−	0.612178i
$780$		0			0
$781$	−14.7386			−0.527390
$782$	−24.4924	−	52.3104i	−0.875847	−	1.87062i
$783$			9.59482i			0.342891i
$784$	14.3140	+	24.0647i	0.511216	+	0.859452i
$785$		0			0
$786$	−16.6307	+	7.78671i	−0.593197	+	0.277743i
$787$		−	0.936426i		−	0.0333800i	−0.999861	−	0.0166900i	$-0.994687\pi$
$787$		−	0.936426i		−	0.0333800i	0.999861	−	0.0166900i	$-0.00531284\pi$
$788$	27.6499	+	23.0540i	0.984985	+	0.821264i
$789$			1.86174i			0.0662797i
$790$		0			0
$791$	37.7382	−	6.78554i	1.34181	−	0.241266i
$792$	−3.66279	+	13.9309i	−0.130152	+	0.495012i
$793$		−	4.00000i		−	0.142044i
$794$	8.39547	+	17.9309i	0.297944	+	0.636343i
$795$		0			0
$796$	−20.5366	+	24.6307i	−0.727902	+	0.873011i
$797$	−20.2462			−0.717158			−0.358579	−	0.933499i	$-0.616739\pi$
$797$	−20.2462			−0.717158			−0.358579	+	0.933499i	$0.616739\pi$
$798$	−4.85458	−	6.86073i	−0.171850	−	0.242867i
$799$		−	71.2695i		−	2.52133i
$800$		0			0
$801$		−	25.4773i		−	0.900195i
$802$	−3.59806	−	7.68466i	−0.127052	−	0.271355i
$803$			22.4742i			0.793098i
$804$	20.5366	+	17.1231i	0.724272	+	0.603885i
$805$		0			0
$806$	8.00000	+	17.0862i	0.281788	+	0.601837i
$807$	15.2134			0.535536
$808$	4.94602	−	18.8114i	0.174001	−	0.661784i
$809$	18.9848			0.667472			0.333736	−	0.942667i	$-0.391691\pi$
$809$	18.9848			0.667472			0.333736	+	0.942667i	$0.391691\pi$
$810$		0			0
$811$	−9.06897			−0.318455			−0.159227	−	0.987242i	$-0.550900\pi$
$811$	−9.06897			−0.318455			−0.159227	+	0.987242i	$0.550900\pi$
$812$	−9.19935	−	5.23182i	−0.322834	−	0.183601i
$813$			22.2462i			0.780209i
$814$	−2.87689	−	6.14441i	−0.100835	−	0.215362i
$815$		0			0
$816$	−26.2462	+	4.79741i	−0.918801	+	0.167943i
$817$	−18.2462			−0.638354
$818$	11.3693	−	5.32326i	0.397519	−	0.186124i
$819$	−1.98813	−	11.0571i	−0.0694710	−	0.386366i
$820$		0			0
$821$	−25.6155			−0.893988			−0.446994	−	0.894537i	$-0.647505\pi$
$821$	−25.6155			−0.893988			−0.446994	+	0.894537i	$0.647505\pi$
$822$	7.86174	+	16.7909i	0.274210	+	0.585651i
$823$	−32.1843			−1.12188			−0.560938	−	0.827858i	$-0.689559\pi$
$823$	−32.1843			−1.12188			−0.560938	+	0.827858i	$0.689559\pi$
$824$	−1.05171	+	4.00000i	−0.0366379	+	0.139347i
$825$		0			0
$826$	−33.4202	+	23.6478i	−1.16284	+	0.822812i
$827$	−0.115279			−0.00400866			−0.00200433	−	0.999998i	$-0.500638\pi$
$827$	−0.115279			−0.00400866			−0.00200433	+	0.999998i	$0.500638\pi$
$828$	15.5916	−	18.6998i	0.541845	−	0.649863i
$829$		−	32.2462i		−	1.11996i	−0.828507	−	0.559979i	$-0.810809\pi$
$829$		−	32.2462i		−	1.11996i	0.828507	−	0.559979i	$-0.189191\pi$
$830$		0			0
$831$	−3.97626			−0.137935
$832$	−13.9309	−	7.86962i	−0.482966	−	0.272830i
$833$	46.7386	−	17.3693i	1.61940	−	0.601811i
$834$	−1.61553	+	0.756412i	−0.0559412	+	0.0261924i
$835$		0			0
$836$	8.83841	+	7.36932i	0.305683	+	0.254873i
$837$			32.0000i			1.10608i
$838$	7.19224	+	15.3610i	0.248452	+	0.530638i
$839$	35.2242			1.21607			0.608037	−	0.793909i	$-0.291957\pi$
$839$	35.2242			1.21607			0.608037	+	0.793909i	$0.291957\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	10.5636	+	22.5616i	0.364046	+	0.777522i
$843$		−	4.33629i		−	0.149350i
$844$	28.3153	+	23.6089i	0.974654	+	0.812650i
$845$		0			0
$846$	27.2069	−	12.7386i	0.935393	−	0.437963i
$847$	2.45635	+	13.6611i	0.0844010	+	0.469401i
$848$	7.86962	−	1.43845i	0.270244	−	0.0493965i
$849$	23.1231			0.793583
$850$		0			0
$851$			11.4677i			0.393107i
$852$	7.36932	−	8.83841i	0.252469	−	0.302799i
$853$	−7.75379			−0.265485			−0.132742	−	0.991151i	$-0.542378\pi$
$853$	−7.75379			−0.265485			−0.132742	+	0.991151i	$0.542378\pi$
$854$	4.32246	+	6.10871i	0.147911	+	0.209036i
$855$		0			0
$856$	25.9309	+	6.81791i	0.886299	+	0.233031i
$857$	−15.6155			−0.533416			−0.266708	−	0.963777i	$-0.585936\pi$
$857$	−15.6155			−0.533416			−0.266708	+	0.963777i	$0.585936\pi$
$858$	−2.69400	−	5.75379i	−0.0919716	−	0.196431i
$859$	−41.3686			−1.41148			−0.705739	−	0.708472i	$-0.749385\pi$
$859$	−41.3686			−1.41148			−0.705739	+	0.708472i	$0.749385\pi$
$860$		0			0
$861$	−3.12311	−	17.3693i	−0.106435	−	0.591945i
$862$	−46.8395	+	21.9309i	−1.59536	+	0.746968i
$863$	−41.7792			−1.42218			−0.711090	−	0.703101i	$-0.751798\pi$
$863$	−41.7792			−1.42218			−0.711090	+	0.703101i	$0.751798\pi$
$864$	−15.7392	−	22.1080i	−0.535460	−	0.752128i
$865$		0			0
$866$	−6.96556	−	14.8769i	−0.236699	−	0.505537i
$867$			31.5937i			1.07298i
$868$	−30.6811	−	17.4488i	−1.04138	−	0.592251i
$869$	−10.2462			−0.347579
$870$		0			0
$871$	28.5539			0.967512
$872$	−3.07221	−	0.807764i	−0.104038	−	0.0273543i
$873$	15.1231			0.511840
$874$	−8.24782	−	17.6155i	−0.278987	−	0.595854i
$875$		0			0
$876$	−13.4773	−	11.2371i	−0.455355	−	0.379667i
$877$			48.7386i			1.64579i	0.568196	+	0.822893i	$0.307642\pi$
$877$			48.7386i			1.64579i	−0.568196	+	0.822893i	$0.692358\pi$
$878$	−10.8769	−	23.2306i	−0.367077	−	0.783996i
$879$			30.1962i			1.01849i
$880$		0			0
$881$			6.63068i			0.223393i	0.993742	+	0.111697i	$0.0356285\pi$
$881$			6.63068i			0.223393i	−0.993742	+	0.111697i	$0.964371\pi$
$882$	14.9847	+	14.7378i	0.504561	+	0.496246i
$883$	13.4558			0.452824			0.226412	−	0.974032i	$-0.427300\pi$
$883$	13.4558			0.452824			0.226412	+	0.974032i	$0.427300\pi$
$884$	−18.2462	+	21.8836i	−0.613686	+	0.736027i
$885$		0			0
$886$	18.1771	+	38.8222i	0.610671	+	1.30426i
$887$			17.7274i			0.595227i	0.954686	+	0.297613i	$0.0961906\pi$
$887$			17.7274i			0.595227i	−0.954686	+	0.297613i	$0.903809\pi$
$888$	5.12311	+	1.34700i	0.171920	+	0.0452024i
$889$	6.19224	+	34.4384i	0.207681	+	1.15503i
$890$		0			0
$891$			4.50212i			0.150827i
$892$	19.8617	+	16.5604i	0.665020	+	0.554483i
$893$		−	24.0000i		−	0.803129i
$894$	23.2306	−	10.8769i	0.776949	−	0.363778i
$895$		0			0
$896$	29.7789	−	3.03560i	0.994844	−	0.101412i
$897$			10.7386i			0.358553i
$898$	15.3610	+	32.8078i	0.512604	+	1.09481i
$899$	13.3405			0.444932
$900$		0			0
$901$		−	14.2462i		−	0.474610i
$902$	10.2462	+	21.8836i	0.341162	+	0.728646i
$903$	−18.5485	+	3.33513i	−0.617256	+	0.110986i
$904$	10.4233	−	39.6434i	0.346674	−	1.31852i
$905$		0			0
$906$	8.24782	+	17.6155i	0.274016	+	0.585237i
$907$	14.5075			0.481714			0.240857	−	0.970561i	$-0.422572\pi$
$907$	14.5075			0.481714			0.240857	+	0.970561i	$0.422572\pi$
$908$	21.9309	+	18.2856i	0.727801	+	0.606829i
$909$		−	14.6004i		−	0.484264i
$910$		0			0
$911$			10.9418i			0.362519i	0.983435	+	0.181259i	$0.0580174\pi$
$911$			10.9418i			0.362519i	−0.983435	+	0.181259i	$0.941983\pi$
$912$	−8.83841	+	1.61553i	−0.292669	+	0.0534955i
$913$	−2.24621			−0.0743387
$914$	−7.68466	+	3.59806i	−0.254186	+	0.119013i
$915$		0			0
$916$	−32.4473	−	27.0540i	−1.07209	−	0.893889i
$917$	−6.49242	−	36.1080i	−0.214399	−	1.19239i
$918$	−43.7673	+	20.4924i	−1.44454	+	0.676351i
$919$		−	29.9009i		−	0.986340i	−0.869933	−	0.493170i	$-0.835838\pi$
$919$		−	29.9009i		−	0.986340i	0.869933	−	0.493170i	$-0.164162\pi$
$920$		0			0
$921$	29.3693			0.967752
$922$	−48.1771	+	22.5571i	−1.58663	+	0.742880i
$923$		−	12.2888i		−	0.404492i
$924$	10.3318	+	5.87588i	0.339893	+	0.193302i
$925$		0			0
$926$	−13.1922	−	28.1757i	−0.433524	−	0.925911i
$927$			3.10457i			0.101968i
$928$	−9.21662	+	6.56155i	−0.302550	+	0.215394i
$929$			12.8769i			0.422477i	0.977435	+	0.211239i	$0.0677497\pi$
$929$			12.8769i			0.422477i	−0.977435	+	0.211239i	$0.932250\pi$
$930$		0			0
$931$	15.7392	−	5.84912i	0.515833	−	0.191697i
$932$	−37.2447	−	31.0540i	−1.21999	−	1.01721i
$933$			8.76894i			0.287082i
$934$	2.54635	−	1.19224i	0.0833192	−	0.0390112i
$935$		0			0
$936$	−11.6153	−	3.05398i	−0.379659	−	0.0998223i
$937$	36.1080			1.17960			0.589798	−	0.807551i	$-0.299207\pi$
$937$	36.1080			1.17960			0.589798	+	0.807551i	$0.299207\pi$
$938$	−43.6069	+	30.8558i	−1.42382	+	1.00748i
$939$			7.13138i			0.232724i
$940$		0			0
$941$			51.3693i			1.67459i	0.546750	+	0.837296i	$0.315865\pi$
$941$			51.3693i			1.67459i	−0.546750	+	0.837296i	$0.684135\pi$
$942$	19.4849	−	9.12311i	0.634854	−	0.297247i
$943$		−	40.8427i		−	1.33002i
$944$	7.86962	+	43.0540i	0.256134	+	1.40129i
$945$		0			0
$946$	23.3693	−	10.9418i	0.759802	−	0.355749i
$947$	−18.8438			−0.612341			−0.306171	−	0.951977i	$-0.599048\pi$
$947$	−18.8438			−0.612341			−0.306171	+	0.951977i	$0.599048\pi$
$948$	5.12311	−	6.14441i	0.166391	−	0.199561i
$949$	−18.7386			−0.608282
$950$		0			0
$951$	−3.97626			−0.128939
$952$	4.21742	−	53.1373i	0.136687	−	1.72219i
$953$			11.7538i			0.380743i	0.981712	+	0.190371i	$0.0609692\pi$
$953$			11.7538i			0.380743i	−0.981712	+	0.190371i	$0.939031\pi$
$954$	5.43845	−	2.54635i	0.176076	−	0.0824412i
$955$		0			0
$956$	−19.6847	−	16.4127i	−0.636647	−	0.530826i
$957$	−4.49242			−0.145219
$958$		0			0
$959$	−36.4559	+	6.55498i	−1.17722	+	0.211671i
$960$		0			0
$961$	13.4924			0.435239
$962$	5.12311	−	2.39871i	0.165176	−	0.0773374i
$963$	20.1261			0.648554
$964$	−23.9871	−	20.0000i	−0.772571	−	0.644157i
$965$		0			0
$966$	−11.6043	−	16.3998i	−0.373363	−	0.527655i
$967$	−55.1197			−1.77253			−0.886265	−	0.463179i	$-0.846709\pi$
$967$	−55.1197			−1.77253			−0.886265	+	0.463179i	$0.846709\pi$
$968$	14.3508	+	3.77320i	0.461251	+	0.121275i
$969$			16.0000i			0.513994i
$970$		0			0
$971$	0.525853			0.0168754			0.00843771	−	0.999964i	$-0.497314\pi$
$971$	0.525853			0.0168754			0.00843771	+	0.999964i	$0.497314\pi$
$972$	−24.8078	−	20.6843i	−0.795709	−	0.663449i
$973$	−0.630683	−	3.50758i	−0.0202188	−	0.112448i
$974$	−11.4384	−	24.4300i	−0.366511	−	0.782788i
$975$		0			0
$976$	7.86962	−	1.43845i	0.251900	−	0.0460436i
$977$			10.4924i			0.335682i	0.985814	+	0.167841i	$0.0536796\pi$
$977$			10.4924i			0.335682i	−0.985814	+	0.167841i	$0.946320\pi$
$978$	1.12311	−	0.525853i	0.0359130	−	0.0168149i
$979$	28.7845			0.919956
$980$		0			0
$981$	−2.38447			−0.0761303
$982$	17.4644	−	8.17708i	0.557313	−	0.260941i
$983$			12.6994i			0.405048i	0.979277	+	0.202524i	$0.0649144\pi$
$983$			12.6994i			0.405048i	−0.979277	+	0.202524i	$0.935086\pi$
$984$	−18.2462	−	4.79741i	−0.581668	−	0.152936i
$985$		0			0
$986$	8.54312	+	18.2462i	0.272068	+	0.581078i
$987$	−4.38684	−	24.3976i	−0.139635	−	0.776585i
$988$	−6.14441	+	7.36932i	−0.195480	+	0.234449i
$989$	−43.6155			−1.38689
$990$		0			0
$991$			34.4678i			1.09490i	0.836837	+	0.547452i	$0.184402\pi$
$991$			34.4678i			1.09490i	−0.836837	+	0.547452i	$0.815598\pi$
$992$	−30.7386	+	21.8836i	−0.975953	+	0.694806i
$993$	−27.2311			−0.864151
$994$	13.2795	+	18.7672i	0.421200	+	0.595260i
$995$		0			0
$996$	1.12311	−	1.34700i	0.0355870	−	0.0426813i
$997$	−38.4924			−1.21907			−0.609534	−	0.792760i	$-0.708643\pi$
$997$	−38.4924			−1.21907			−0.609534	+	0.792760i	$0.708643\pi$
$998$	34.8460	−	16.3153i	1.10303	−	0.516453i
$999$	9.59482			0.303567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.c.i.699.3		8
4.3	odd	2	inner	700.2.c.i.699.5		8
5.2	odd	4		140.2.g.c.111.6	yes	8
5.3	odd	4		700.2.g.j.251.3		8
5.4	even	2		700.2.c.j.699.6		8
7.6	odd	2		700.2.c.j.699.3		8
15.2	even	4		1260.2.c.c.811.3		8
20.3	even	4		700.2.g.j.251.2		8
20.7	even	4		140.2.g.c.111.7	yes	8
20.19	odd	2		700.2.c.j.699.4		8
28.27	even	2		700.2.c.j.699.5		8
35.2	odd	12		980.2.o.e.31.1		16
35.12	even	12		980.2.o.e.31.2		16
35.13	even	4		700.2.g.j.251.4		8
35.17	even	12		980.2.o.e.411.6		16
35.27	even	4		140.2.g.c.111.5	✓	8
35.32	odd	12		980.2.o.e.411.5		16
35.34	odd	2	inner	700.2.c.i.699.6		8
40.27	even	4		2240.2.k.e.1791.5		8
40.37	odd	4		2240.2.k.e.1791.3		8
60.47	odd	4		1260.2.c.c.811.1		8
105.62	odd	4		1260.2.c.c.811.4		8
140.27	odd	4		140.2.g.c.111.8	yes	8
140.47	odd	12		980.2.o.e.31.5		16
140.67	even	12		980.2.o.e.411.2		16
140.83	odd	4		700.2.g.j.251.1		8
140.87	odd	12		980.2.o.e.411.1		16
140.107	even	12		980.2.o.e.31.6		16
140.139	even	2	inner	700.2.c.i.699.4		8
280.27	odd	4		2240.2.k.e.1791.4		8
280.237	even	4		2240.2.k.e.1791.6		8
420.167	even	4		1260.2.c.c.811.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.5	✓	8	35.27	even	4
140.2.g.c.111.6	yes	8	5.2	odd	4
140.2.g.c.111.7	yes	8	20.7	even	4
140.2.g.c.111.8	yes	8	140.27	odd	4
700.2.c.i.699.3		8	1.1	even	1	trivial
700.2.c.i.699.4		8	140.139	even	2	inner
700.2.c.i.699.5		8	4.3	odd	2	inner
700.2.c.i.699.6		8	35.34	odd	2	inner
700.2.c.j.699.3		8	7.6	odd	2
700.2.c.j.699.4		8	20.19	odd	2
700.2.c.j.699.5		8	28.27	even	2
700.2.c.j.699.6		8	5.4	even	2
700.2.g.j.251.1		8	140.83	odd	4
700.2.g.j.251.2		8	20.3	even	4
700.2.g.j.251.3		8	5.3	odd	4
700.2.g.j.251.4		8	35.13	even	4
980.2.o.e.31.1		16	35.2	odd	12
980.2.o.e.31.2		16	35.12	even	12
980.2.o.e.31.5		16	140.47	odd	12
980.2.o.e.31.6		16	140.107	even	12
980.2.o.e.411.1		16	140.87	odd	12
980.2.o.e.411.2		16	140.67	even	12
980.2.o.e.411.5		16	35.32	odd	12
980.2.o.e.411.6		16	35.17	even	12
1260.2.c.c.811.1		8	60.47	odd	4
1260.2.c.c.811.2		8	420.167	even	4
1260.2.c.c.811.3		8	15.2	even	4
1260.2.c.c.811.4		8	105.62	odd	4
2240.2.k.e.1791.3		8	40.37	odd	4
2240.2.k.e.1791.4		8	280.27	odd	4
2240.2.k.e.1791.5		8	40.27	even	4
2240.2.k.e.1791.6		8	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)

\(f(q)\)	\(=\)	\(q+(-0.599676 - 1.28078i) q^{2} +0.936426i q^{3} +(-1.28078 + 1.53610i) q^{4} +(1.19935 - 0.561553i) q^{6} +(0.468213 + 2.60399i) q^{7} +(2.73546 + 0.719224i) q^{8} +2.12311 q^{9} +O(q^{10})\)	\(q+(-0.599676 - 1.28078i) q^{2} +0.936426i q^{3} +(-1.28078 + 1.53610i) q^{4} +(1.19935 - 0.561553i) q^{6} +(0.468213 + 2.60399i) q^{7} +(2.73546 + 0.719224i) q^{8} +2.12311 q^{9} +2.39871i q^{11} +(-1.43845 - 1.19935i) q^{12} -2.00000 q^{13} +(3.05436 - 2.16123i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311 q^{17} +(-1.27318 - 2.71922i) q^{18} -2.39871 q^{19} +(-2.43845 + 0.438447i) q^{21} +(3.07221 - 1.43845i) q^{22} -5.73384 q^{23} +(-0.673500 + 2.56155i) q^{24} +(1.19935 + 2.56155i) q^{26} +4.79741i q^{27} +(-4.59968 - 2.61591i) q^{28} +2.00000 q^{29} +6.67026 q^{31} +(-4.60831 + 3.28078i) q^{32} -2.24621 q^{33} +(4.27156 + 9.12311i) q^{34} +(-2.71922 + 3.26131i) q^{36} -2.00000i q^{37} +(1.43845 + 3.07221i) q^{38} -1.87285i q^{39} +7.12311i q^{41} +(2.02383 + 2.86018i) q^{42} +7.60669 q^{43} +(-3.68466 - 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} +10.0054i q^{47} +(3.68466 - 0.673500i) q^{48} +(-6.56155 + 2.43845i) q^{49} -6.67026i q^{51} +(2.56155 - 3.07221i) q^{52} +2.00000i q^{53} +(6.14441 - 2.87689i) q^{54} +(-0.592076 + 7.45986i) q^{56} -2.24621i q^{57} +(-1.19935 - 2.56155i) q^{58} -10.9418 q^{59} +2.00000i q^{61} +(-4.00000 - 8.54312i) q^{62} +(0.994066 + 5.52855i) q^{63} +(6.96543 + 3.93481i) q^{64} +(1.34700 + 2.87689i) q^{66} -14.2770 q^{67} +(9.12311 - 10.9418i) q^{68} -5.36932i q^{69} +6.14441i q^{71} +(5.80766 + 1.52699i) q^{72} +9.36932 q^{73} +(-2.56155 + 1.19935i) q^{74} +(3.07221 - 3.68466i) q^{76} +(-6.24621 + 1.12311i) q^{77} +(-2.39871 + 1.12311i) q^{78} +4.27156i q^{79} +1.87689 q^{81} +(9.12311 - 4.27156i) q^{82} +0.936426i q^{83} +(2.44961 - 4.30726i) q^{84} +(-4.56155 - 9.74247i) q^{86} +1.87285i q^{87} +(-1.72521 + 6.56155i) q^{88} -12.0000i q^{89} +(-0.936426 - 5.20798i) q^{91} +(7.34376 - 8.80776i) q^{92} +6.24621i q^{93} +(12.8147 - 6.00000i) q^{94} +(-3.07221 - 4.31534i) q^{96} +7.12311 q^{97} +(7.05791 + 6.94160i) q^{98} +5.09271i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 16 * q^9	\( 8 q - 2 q^{4} - 16 q^{9} - 28 q^{12} - 16 q^{13} + 6 q^{14} - 14 q^{16} - 24 q^{17} - 36 q^{21} - 32 q^{28} + 16 q^{29} + 48 q^{33} - 30 q^{36} + 28 q^{38} - 12 q^{42} + 20 q^{44} + 44 q^{46} - 20 q^{48} - 36 q^{49} + 4 q^{52} + 2 q^{56} - 32 q^{62} - 2 q^{64} + 40 q^{68} - 24 q^{73} - 4 q^{74} + 16 q^{77} + 48 q^{81} + 40 q^{82} - 8 q^{84} - 20 q^{86} + 24 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^4 - 16 * q^9 - 28 * q^12 - 16 * q^13 + 6 * q^14 - 14 * q^16 - 24 * q^17 - 36 * q^21 - 32 * q^28 + 16 * q^29 + 48 * q^33 - 30 * q^36 + 28 * q^38 - 12 * q^42 + 20 * q^44 + 44 * q^46 - 20 * q^48 - 36 * q^49 + 4 * q^52 + 2 * q^56 - 32 * q^62 - 2 * q^64 + 40 * q^68 - 24 * q^73 - 4 * q^74 + 16 * q^77 + 48 * q^81 + 40 * q^82 - 8 * q^84 - 20 * q^86 + 24 * q^97 - 8 * q^98

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