LMFDB - Embedded newform 490.2.e.i.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, degree $2$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	490.361
Dual form			490.2.e.i.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.414214 - 0.717439i) q^{11} +(-1.70711 - 2.95680i) q^{12} -4.82843 q^{13} +3.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 + 2.23936i) q^{17} +(4.32843 - 7.49706i) q^{18} +(-0.292893 - 0.507306i) q^{19} +1.00000 q^{20} +0.828427 q^{22} +(0.585786 + 1.01461i) q^{23} +(1.70711 - 2.95680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.41421 - 4.18154i) q^{26} +19.3137 q^{27} -4.82843 q^{29} +(1.70711 + 2.95680i) q^{30} +(1.41421 - 2.44949i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.41421 + 2.44949i) q^{33} -2.58579 q^{34} +8.65685 q^{36} +(3.82843 + 6.63103i) q^{37} +(0.292893 - 0.507306i) q^{38} +(8.24264 - 14.2767i) q^{39} +(0.500000 + 0.866025i) q^{40} -3.07107 q^{41} -8.82843 q^{43} +(0.414214 + 0.717439i) q^{44} +(-4.32843 + 7.49706i) q^{45} +(-0.585786 + 1.01461i) q^{46} +(-2.58579 - 4.47871i) q^{47} +3.41421 q^{48} -1.00000 q^{50} +(-4.41421 - 7.64564i) q^{51} +(2.41421 - 4.18154i) q^{52} +(-3.24264 + 5.61642i) q^{53} +(9.65685 + 16.7262i) q^{54} -0.828427 q^{55} +2.00000 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-4.29289 + 7.43551i) q^{59} +(-1.70711 + 2.95680i) q^{60} +(-4.65685 - 8.06591i) q^{61} +2.82843 q^{62} +1.00000 q^{64} +(2.41421 + 4.18154i) q^{65} +(-1.41421 + 2.44949i) q^{66} +(-0.828427 + 1.43488i) q^{67} +(-1.29289 - 2.23936i) q^{68} -4.00000 q^{69} -4.48528 q^{71} +(4.32843 + 7.49706i) q^{72} +(4.70711 - 8.15295i) q^{73} +(-3.82843 + 6.63103i) q^{74} +(-1.70711 - 2.95680i) q^{75} +0.585786 q^{76} +16.4853 q^{78} +(3.41421 + 5.91359i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-19.9853 + 34.6155i) q^{81} +(-1.53553 - 2.65962i) q^{82} -2.24264 q^{83} +2.58579 q^{85} +(-4.41421 - 7.64564i) q^{86} +(8.24264 - 14.2767i) q^{87} +(-0.414214 + 0.717439i) q^{88} +(-6.36396 - 11.0227i) q^{89} -8.65685 q^{90} -1.17157 q^{92} +(4.82843 + 8.36308i) q^{93} +(2.58579 - 4.47871i) q^{94} +(-0.292893 + 0.507306i) q^{95} +(1.70711 + 2.95680i) q^{96} -7.75736 q^{97} -7.17157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{8} - 6 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} + 8 q^{23} + 4 q^{24} - 2 q^{25} - 4 q^{26} + 32 q^{27} - 8 q^{29} + 4 q^{30} + 2 q^{32} - 16 q^{34} + 12 q^{36} + 4 q^{37} + 4 q^{38} + 16 q^{39} + 2 q^{40} + 16 q^{41} - 24 q^{43} - 4 q^{44} - 6 q^{45} - 8 q^{46} - 16 q^{47} + 8 q^{48} - 4 q^{50} - 12 q^{51} + 4 q^{52} + 4 q^{53} + 16 q^{54} + 8 q^{55} + 8 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} + 4 q^{61} + 4 q^{64} + 4 q^{65} + 8 q^{67} - 8 q^{68} - 16 q^{69} + 16 q^{71} + 6 q^{72} + 16 q^{73} - 4 q^{74} - 4 q^{75} + 8 q^{76} + 32 q^{78} + 8 q^{79} - 2 q^{80} - 46 q^{81} + 8 q^{82} + 8 q^{83} + 16 q^{85} - 12 q^{86} + 16 q^{87} + 4 q^{88} - 12 q^{90} - 16 q^{92} + 8 q^{93} + 16 q^{94} - 4 q^{95} + 4 q^{96} - 48 q^{97} - 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^8 - 6 * q^9 + 2 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 + 8 * q^23 + 4 * q^24 - 2 * q^25 - 4 * q^26 + 32 * q^27 - 8 * q^29 + 4 * q^30 + 2 * q^32 - 16 * q^34 + 12 * q^36 + 4 * q^37 + 4 * q^38 + 16 * q^39 + 2 * q^40 + 16 * q^41 - 24 * q^43 - 4 * q^44 - 6 * q^45 - 8 * q^46 - 16 * q^47 + 8 * q^48 - 4 * q^50 - 12 * q^51 + 4 * q^52 + 4 * q^53 + 16 * q^54 + 8 * q^55 + 8 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 + 4 * q^61 + 4 * q^64 + 4 * q^65 + 8 * q^67 - 8 * q^68 - 16 * q^69 + 16 * q^71 + 6 * q^72 + 16 * q^73 - 4 * q^74 - 4 * q^75 + 8 * q^76 + 32 * q^78 + 8 * q^79 - 2 * q^80 - 46 * q^81 + 8 * q^82 + 8 * q^83 + 16 * q^85 - 12 * q^86 + 16 * q^87 + 4 * q^88 - 12 * q^90 - 16 * q^92 + 8 * q^93 + 16 * q^94 - 4 * q^95 + 4 * q^96 - 48 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.70711	+	2.95680i	−0.985599	+	1.70711i	−0.346353	+	0.938104i	$0.612580\pi$
$3$	−1.70711	+	2.95680i	−0.985599	+	1.70711i	−0.639246	+	0.769002i	$0.720753\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.41421			−1.39385
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−4.32843	−	7.49706i	−1.44281	−	2.49902i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	−0.796800	−	0.604243i	$-0.793476\pi$
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	0.921690	+	0.387927i	$0.126809\pi$
$12$	−1.70711	−	2.95680i	−0.492799	−	0.853553i
$13$	−4.82843			−1.33916			−0.669582	−	0.742738i	$-0.733527\pi$
$13$	−4.82843			−1.33916			−0.669582	+	0.742738i	$0.733527\pi$
$14$		0			0
$15$	3.41421			0.881546
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.29289	+	2.23936i	−0.313573	+	0.543124i	−0.979133	−	0.203220i	$-0.934859\pi$
$17$	−1.29289	+	2.23936i	−0.313573	+	0.543124i	0.665560	+	0.746344i	$0.268193\pi$
$18$	4.32843	−	7.49706i	1.02022	−	1.76707i
$19$	−0.292893	−	0.507306i	−0.0671943	−	0.116384i	0.830471	−	0.557062i	$-0.188071\pi$
$19$	−0.292893	−	0.507306i	−0.0671943	−	0.116384i	−0.897665	+	0.440678i	$0.854738\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	0.828427			0.176621
$23$	0.585786	+	1.01461i	0.122145	+	0.211561i	0.920613	−	0.390476i	$-0.127689\pi$
$23$	0.585786	+	1.01461i	0.122145	+	0.211561i	−0.798468	+	0.602037i	$0.794356\pi$
$24$	1.70711	−	2.95680i	0.348462	−	0.603553i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.41421	−	4.18154i	−0.473466	−	0.820068i
$27$	19.3137			3.71692
$28$		0			0
$29$	−4.82843			−0.896616			−0.448308	−	0.893879i	$-0.647973\pi$
$29$	−4.82843			−0.896616			−0.448308	+	0.893879i	$0.647973\pi$
$30$	1.70711	+	2.95680i	0.311674	+	0.539835i
$31$	1.41421	−	2.44949i	0.254000	−	0.439941i	−0.710623	−	0.703573i	$-0.751587\pi$
$31$	1.41421	−	2.44949i	0.254000	−	0.439941i	0.964623	+	0.263631i	$0.0849203\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.41421	+	2.44949i	0.246183	+	0.426401i
$34$	−2.58579			−0.443459
$35$		0			0
$36$	8.65685			1.44281
$37$	3.82843	+	6.63103i	0.629390	+	1.09013i	0.987674	+	0.156522i	$0.0500283\pi$
$37$	3.82843	+	6.63103i	0.629390	+	1.09013i	−0.358285	+	0.933612i	$0.616638\pi$
$38$	0.292893	−	0.507306i	0.0475136	−	0.0822959i
$39$	8.24264	−	14.2767i	1.31988	−	2.28610i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−3.07107			−0.479620			−0.239810	−	0.970820i	$-0.577085\pi$
$41$	−3.07107			−0.479620			−0.239810	+	0.970820i	$0.577085\pi$
$42$		0			0
$43$	−8.82843			−1.34632			−0.673161	−	0.739496i	$-0.735064\pi$
$43$	−8.82843			−1.34632			−0.673161	+	0.739496i	$0.735064\pi$
$44$	0.414214	+	0.717439i	0.0624450	+	0.108158i
$45$	−4.32843	+	7.49706i	−0.645244	+	1.11760i
$46$	−0.585786	+	1.01461i	−0.0863695	+	0.149596i
$47$	−2.58579	−	4.47871i	−0.377176	−	0.653288i	0.613474	−	0.789715i	$-0.289771\pi$
$47$	−2.58579	−	4.47871i	−0.377176	−	0.653288i	−0.990650	+	0.136427i	$0.956438\pi$
$48$	3.41421			0.492799
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−4.41421	−	7.64564i	−0.618114	−	1.07060i
$52$	2.41421	−	4.18154i	0.334791	−	0.579875i
$53$	−3.24264	+	5.61642i	−0.445411	+	0.771474i	−0.998081	−	0.0619259i	$-0.980276\pi$
$53$	−3.24264	+	5.61642i	−0.445411	+	0.771474i	0.552670	+	0.833400i	$0.313609\pi$
$54$	9.65685	+	16.7262i	1.31413	+	2.27614i
$55$	−0.828427			−0.111705
$56$		0			0
$57$	2.00000			0.264906
$58$	−2.41421	−	4.18154i	−0.317002	−	0.549063i
$59$	−4.29289	+	7.43551i	−0.558887	+	0.968021i	0.438703	+	0.898632i	$0.355438\pi$
$59$	−4.29289	+	7.43551i	−0.558887	+	0.968021i	−0.997590	+	0.0693885i	$0.977895\pi$
$60$	−1.70711	+	2.95680i	−0.220387	+	0.381721i
$61$	−4.65685	−	8.06591i	−0.596249	−	1.03273i	−0.993369	−	0.114967i	$-0.963324\pi$
$61$	−4.65685	−	8.06591i	−0.596249	−	1.03273i	0.397120	−	0.917767i	$-0.370010\pi$
$62$	2.82843			0.359211
$63$		0			0
$64$	1.00000			0.125000
$65$	2.41421	+	4.18154i	0.299446	+	0.518656i
$66$	−1.41421	+	2.44949i	−0.174078	+	0.301511i
$67$	−0.828427	+	1.43488i	−0.101208	+	0.175298i	−0.912183	−	0.409784i	$-0.865604\pi$
$67$	−0.828427	+	1.43488i	−0.101208	+	0.175298i	0.810974	+	0.585082i	$0.198938\pi$
$68$	−1.29289	−	2.23936i	−0.156786	−	0.271562i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	−4.48528			−0.532305			−0.266152	−	0.963931i	$-0.585752\pi$
$71$	−4.48528			−0.532305			−0.266152	+	0.963931i	$0.585752\pi$
$72$	4.32843	+	7.49706i	0.510110	+	0.883536i
$73$	4.70711	−	8.15295i	0.550925	−	0.954230i	−0.447283	−	0.894393i	$-0.647608\pi$
$73$	4.70711	−	8.15295i	0.550925	−	0.954230i	0.998208	−	0.0598379i	$-0.0190584\pi$
$74$	−3.82843	+	6.63103i	−0.445046	+	0.770842i
$75$	−1.70711	−	2.95680i	−0.197120	−	0.341421i
$76$	0.585786			0.0671943
$77$		0			0
$78$	16.4853			1.86659
$79$	3.41421	+	5.91359i	0.384129	+	0.665331i	0.991648	−	0.128974i	$-0.0411684\pi$
$79$	3.41421	+	5.91359i	0.384129	+	0.665331i	−0.607519	+	0.794305i	$0.707835\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−19.9853	+	34.6155i	−2.22059	+	3.84617i
$82$	−1.53553	−	2.65962i	−0.169571	−	0.293706i
$83$	−2.24264			−0.246162			−0.123081	−	0.992397i	$-0.539277\pi$
$83$	−2.24264			−0.246162			−0.123081	+	0.992397i	$0.539277\pi$
$84$		0			0
$85$	2.58579			0.280468
$86$	−4.41421	−	7.64564i	−0.475997	−	0.824451i
$87$	8.24264	−	14.2767i	0.883704	−	1.53062i
$88$	−0.414214	+	0.717439i	−0.0441553	+	0.0764792i
$89$	−6.36396	−	11.0227i	−0.674579	−	1.16840i	−0.976592	−	0.215101i	$-0.930992\pi$
$89$	−6.36396	−	11.0227i	−0.674579	−	1.16840i	0.302013	−	0.953304i	$-0.402341\pi$
$90$	−8.65685			−0.912513
$91$		0			0
$92$	−1.17157			−0.122145
$93$	4.82843	+	8.36308i	0.500685	+	0.867211i
$94$	2.58579	−	4.47871i	0.266704	−	0.461944i
$95$	−0.292893	+	0.507306i	−0.0300502	+	0.0520485i
$96$	1.70711	+	2.95680i	0.174231	+	0.301777i
$97$	−7.75736			−0.787641			−0.393820	−	0.919187i	$-0.628847\pi$
$97$	−7.75736			−0.787641			−0.393820	+	0.919187i	$0.628847\pi$
$98$		0			0
$99$	−7.17157			−0.720770
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.65685	+	11.5300i	−0.662382	+	1.14728i	0.317606	+	0.948223i	$0.397121\pi$
$101$	−6.65685	+	11.5300i	−0.662382	+	1.14728i	−0.979988	+	0.199056i	$0.936212\pi$
$102$	4.41421	−	7.64564i	0.437072	−	0.757031i
$103$	7.41421	+	12.8418i	0.730544	+	1.26534i	0.956651	+	0.291237i	$0.0940669\pi$
$103$	7.41421	+	12.8418i	0.730544	+	1.26534i	−0.226107	+	0.974103i	$0.572600\pi$
$104$	4.82843			0.473466
$105$		0			0
$106$	−6.48528			−0.629906
$107$	−4.82843	−	8.36308i	−0.466782	−	0.808490i	0.532498	−	0.846431i	$-0.321253\pi$
$107$	−4.82843	−	8.36308i	−0.466782	−	0.808490i	−0.999280	+	0.0379415i	$0.987920\pi$
$108$	−9.65685	+	16.7262i	−0.929231	+	1.60948i
$109$	−1.24264	+	2.15232i	−0.119023	+	0.206155i	−0.919381	−	0.393368i	$-0.871310\pi$
$109$	−1.24264	+	2.15232i	−0.119023	+	0.206155i	0.800358	+	0.599523i	$0.204643\pi$
$110$	−0.414214	−	0.717439i	−0.0394937	−	0.0684051i
$111$	−26.1421			−2.48130
$112$		0			0
$113$	−15.3137			−1.44059			−0.720296	−	0.693667i	$-0.755994\pi$
$113$	−15.3137			−1.44059			−0.720296	+	0.693667i	$0.755994\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	0.585786	−	1.01461i	0.0546249	−	0.0946130i
$116$	2.41421	−	4.18154i	0.224154	−	0.388246i
$117$	20.8995	+	36.1990i	1.93216	+	3.34660i
$118$	−8.58579			−0.790386
$119$		0			0
$120$	−3.41421			−0.311674
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$	4.65685	−	8.06591i	0.421612	−	0.730253i
$123$	5.24264	−	9.08052i	0.472713	−	0.818763i
$124$	1.41421	+	2.44949i	0.127000	+	0.219971i
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.82843			0.250982			0.125491	−	0.992095i	$-0.459949\pi$
$127$	2.82843			0.250982			0.125491	+	0.992095i	$0.459949\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	15.0711	−	26.1039i	1.32693	−	2.29832i
$130$	−2.41421	+	4.18154i	−0.211741	+	0.366745i
$131$	3.12132	+	5.40629i	0.272711	+	0.472349i	0.969555	−	0.244873i	$-0.0787464\pi$
$131$	3.12132	+	5.40629i	0.272711	+	0.472349i	−0.696844	+	0.717223i	$0.745413\pi$
$132$	−2.82843			−0.246183
$133$		0			0
$134$	−1.65685			−0.143130
$135$	−9.65685	−	16.7262i	−0.831130	−	1.43956i
$136$	1.29289	−	2.23936i	0.110865	−	0.192023i
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$	−2.00000	−	3.46410i	−0.170251	−	0.294884i
$139$	19.8995			1.68785			0.843927	−	0.536459i	$-0.180238\pi$
$139$	19.8995			1.68785			0.843927	+	0.536459i	$0.180238\pi$
$140$		0			0
$141$	17.6569			1.48698
$142$	−2.24264	−	3.88437i	−0.188198	−	0.325969i
$143$	−2.00000	+	3.46410i	−0.167248	+	0.289683i
$144$	−4.32843	+	7.49706i	−0.360702	+	0.624755i
$145$	2.41421	+	4.18154i	0.200490	+	0.347258i
$146$	9.41421			0.779126
$147$		0			0
$148$	−7.65685			−0.629390
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	1.70711	−	2.95680i	0.139385	−	0.241421i
$151$	5.65685	−	9.79796i	0.460348	−	0.797347i	−0.538630	−	0.842542i	$-0.681058\pi$
$151$	5.65685	−	9.79796i	0.460348	−	0.797347i	0.998978	+	0.0451959i	$0.0143912\pi$
$152$	0.292893	+	0.507306i	0.0237568	+	0.0411479i
$153$	22.3848			1.80970
$154$		0			0
$155$	−2.82843			−0.227185
$156$	8.24264	+	14.2767i	0.659939	+	1.14305i
$157$	−3.24264	+	5.61642i	−0.258791	+	0.448239i	−0.965918	−	0.258847i	$-0.916657\pi$
$157$	−3.24264	+	5.61642i	−0.258791	+	0.448239i	0.707127	+	0.707086i	$0.249991\pi$
$158$	−3.41421	+	5.91359i	−0.271620	+	0.470460i
$159$	−11.0711	−	19.1757i	−0.877993	−	1.52073i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−39.9706			−3.14038
$163$	10.0711	+	17.4436i	0.788827	+	1.36629i	0.926686	+	0.375836i	$0.122645\pi$
$163$	10.0711	+	17.4436i	0.788827	+	1.36629i	−0.137859	+	0.990452i	$0.544022\pi$
$164$	1.53553	−	2.65962i	0.119905	−	0.207682i
$165$	1.41421	−	2.44949i	0.110096	−	0.190693i
$166$	−1.12132	−	1.94218i	−0.0870313	−	0.150743i
$167$	15.7990			1.22256			0.611281	−	0.791413i	$-0.290654\pi$
$167$	15.7990			1.22256			0.611281	+	0.791413i	$0.290654\pi$
$168$		0			0
$169$	10.3137			0.793362
$170$	1.29289	+	2.23936i	0.0991604	+	0.171751i
$171$	−2.53553	+	4.39167i	−0.193897	+	0.335840i
$172$	4.41421	−	7.64564i	0.336581	−	0.582975i
$173$	4.41421	+	7.64564i	0.335606	+	0.581287i	0.983601	−	0.180357i	$-0.0577254\pi$
$173$	4.41421	+	7.64564i	0.335606	+	0.581287i	−0.647995	+	0.761645i	$0.724392\pi$
$174$	16.4853			1.24975
$175$		0			0
$176$	−0.828427			−0.0624450
$177$	−14.6569	−	25.3864i	−1.10168	−	1.90816i
$178$	6.36396	−	11.0227i	0.476999	−	0.826187i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	−4.32843	−	7.49706i	−0.322622	−	0.558798i
$181$	−2.48528			−0.184730			−0.0923648	−	0.995725i	$-0.529443\pi$
$181$	−2.48528			−0.184730			−0.0923648	+	0.995725i	$0.529443\pi$
$182$		0			0
$183$	31.7990			2.35065
$184$	−0.585786	−	1.01461i	−0.0431847	−	0.0747982i
$185$	3.82843	−	6.63103i	0.281472	−	0.487523i
$186$	−4.82843	+	8.36308i	−0.354037	+	0.613211i
$187$	1.07107	+	1.85514i	0.0783242	+	0.135662i
$188$	5.17157			0.377176
$189$		0			0
$190$	−0.585786			−0.0424974
$191$	−5.07107	−	8.78335i	−0.366930	−	0.635541i	0.622154	−	0.782895i	$-0.286258\pi$
$191$	−5.07107	−	8.78335i	−0.366930	−	0.635541i	−0.989084	+	0.147354i	$0.952924\pi$
$192$	−1.70711	+	2.95680i	−0.123200	+	0.213388i
$193$	−2.82843	+	4.89898i	−0.203595	+	0.352636i	−0.949684	−	0.313210i	$-0.898596\pi$
$193$	−2.82843	+	4.89898i	−0.203595	+	0.352636i	0.746089	+	0.665846i	$0.231929\pi$
$194$	−3.87868	−	6.71807i	−0.278473	−	0.482329i
$195$	−16.4853			−1.18054
$196$		0			0
$197$	−25.7990			−1.83810			−0.919051	−	0.394139i	$-0.871043\pi$
$197$	−25.7990			−1.83810			−0.919051	+	0.394139i	$0.871043\pi$
$198$	−3.58579	−	6.21076i	−0.254831	−	0.441380i
$199$	−8.24264	+	14.2767i	−0.584305	+	1.01205i	0.410656	+	0.911790i	$0.365300\pi$
$199$	−8.24264	+	14.2767i	−0.584305	+	1.01205i	−0.994962	+	0.100256i	$0.968034\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−2.82843	−	4.89898i	−0.199502	−	0.345547i
$202$	−13.3137			−0.936749
$203$		0			0
$204$	8.82843			0.618114
$205$	1.53553	+	2.65962i	0.107246	+	0.185756i
$206$	−7.41421	+	12.8418i	−0.516573	+	0.894730i
$207$	5.07107	−	8.78335i	0.352464	−	0.610485i
$208$	2.41421	+	4.18154i	0.167396	+	0.289938i
$209$	−0.485281			−0.0335676
$210$		0			0
$211$	18.6274			1.28236			0.641182	−	0.767389i	$-0.278444\pi$
$211$	18.6274			1.28236			0.641182	+	0.767389i	$0.278444\pi$
$212$	−3.24264	−	5.61642i	−0.222705	−	0.385737i
$213$	7.65685	−	13.2621i	0.524639	−	0.908701i
$214$	4.82843	−	8.36308i	0.330064	−	0.571688i
$215$	4.41421	+	7.64564i	0.301047	+	0.521428i
$216$	−19.3137			−1.31413
$217$		0			0
$218$	−2.48528			−0.168324
$219$	16.0711	+	27.8359i	1.08598	+	1.88098i
$220$	0.414214	−	0.717439i	0.0279263	−	0.0483697i
$221$	6.24264	−	10.8126i	0.419925	−	0.727332i
$222$	−13.0711	−	22.6398i	−0.877273	−	1.51948i
$223$	−7.31371			−0.489762			−0.244881	−	0.969553i	$-0.578749\pi$
$223$	−7.31371			−0.489762			−0.244881	+	0.969553i	$0.578749\pi$
$224$		0			0
$225$	8.65685			0.577124
$226$	−7.65685	−	13.2621i	−0.509326	−	0.882179i
$227$	−9.12132	+	15.7986i	−0.605403	+	1.04859i	0.386584	+	0.922254i	$0.373655\pi$
$227$	−9.12132	+	15.7986i	−0.605403	+	1.04859i	−0.991988	+	0.126335i	$0.959679\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	8.07107	+	13.9795i	0.533351	+	0.923791i	0.999241	+	0.0389487i	$0.0124009\pi$
$229$	8.07107	+	13.9795i	0.533351	+	0.923791i	−0.465890	+	0.884843i	$0.654266\pi$
$230$	1.17157			0.0772512
$231$		0			0
$232$	4.82843			0.317002
$233$	−11.6569	−	20.1903i	−0.763666	−	1.32271i	−0.940949	−	0.338548i	$-0.890064\pi$
$233$	−11.6569	−	20.1903i	−0.763666	−	1.32271i	0.177283	−	0.984160i	$-0.443269\pi$
$234$	−20.8995	+	36.1990i	−1.36624	+	2.36640i
$235$	−2.58579	+	4.47871i	−0.168678	+	0.292159i
$236$	−4.29289	−	7.43551i	−0.279444	−	0.484010i
$237$	−23.3137			−1.51439
$238$		0			0
$239$	1.65685			0.107173			0.0535865	−	0.998563i	$-0.482935\pi$
$239$	1.65685			0.107173			0.0535865	+	0.998563i	$0.482935\pi$
$240$	−1.70711	−	2.95680i	−0.110193	−	0.190860i
$241$	6.70711	−	11.6170i	0.432043	−	0.748320i	−0.565006	−	0.825087i	$-0.691126\pi$
$241$	6.70711	−	11.6170i	0.432043	−	0.748320i	0.997049	+	0.0767666i	$0.0244596\pi$
$242$	−5.15685	+	8.93193i	−0.331495	+	0.574166i
$243$	−39.2635	−	68.0063i	−2.51875	−	4.36261i
$244$	9.31371			0.596249
$245$		0			0
$246$	10.4853			0.668517
$247$	1.41421	+	2.44949i	0.0899843	+	0.155857i
$248$	−1.41421	+	2.44949i	−0.0898027	+	0.155543i
$249$	3.82843	−	6.63103i	0.242617	−	0.420224i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	0.585786			0.0369745			0.0184873	−	0.999829i	$-0.494115\pi$
$251$	0.585786			0.0369745			0.0184873	+	0.999829i	$0.494115\pi$
$252$		0			0
$253$	0.970563			0.0610188
$254$	1.41421	+	2.44949i	0.0887357	+	0.153695i
$255$	−4.41421	+	7.64564i	−0.276429	+	0.478789i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.94975	+	8.57321i	0.308757	+	0.534782i	0.978091	−	0.208179i	$-0.0667538\pi$
$257$	4.94975	+	8.57321i	0.308757	+	0.534782i	−0.669334	+	0.742962i	$0.733420\pi$
$258$	30.1421			1.87657
$259$		0			0
$260$	−4.82843			−0.299446
$261$	20.8995	+	36.1990i	1.29365	+	2.24066i
$262$	−3.12132	+	5.40629i	−0.192836	+	0.334001i
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	0.00547092	+	0.999985i	$0.498259\pi$
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	−0.868748	+	0.495255i	$0.835075\pi$
$264$	−1.41421	−	2.44949i	−0.0870388	−	0.150756i
$265$	6.48528			0.398388
$266$		0			0
$267$	43.4558			2.65945
$268$	−0.828427	−	1.43488i	−0.0506042	−	0.0876491i
$269$	−9.24264	+	16.0087i	−0.563534	+	0.976069i	0.433651	+	0.901081i	$0.357225\pi$
$269$	−9.24264	+	16.0087i	−0.563534	+	0.976069i	−0.997184	+	0.0749880i	$0.976108\pi$
$270$	9.65685	−	16.7262i	0.587697	−	1.01792i
$271$	−6.00000	−	10.3923i	−0.364474	−	0.631288i	0.624218	−	0.781251i	$-0.285418\pi$
$271$	−6.00000	−	10.3923i	−0.364474	−	0.631288i	−0.988692	+	0.149963i	$0.952085\pi$
$272$	2.58579			0.156786
$273$		0			0
$274$	16.0000			0.966595
$275$	0.414214	+	0.717439i	0.0249780	+	0.0432632i
$276$	2.00000	−	3.46410i	0.120386	−	0.208514i
$277$	4.07107	−	7.05130i	0.244607	−	0.423671i	−0.717414	−	0.696647i	$-0.754674\pi$
$277$	4.07107	−	7.05130i	0.244607	−	0.423671i	0.962021	+	0.272976i	$0.0880078\pi$
$278$	9.94975	+	17.2335i	0.596746	+	1.03359i
$279$	−24.4853			−1.46590
$280$		0			0
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$	8.82843	+	15.2913i	0.525725	+	0.910583i
$283$	1.12132	−	1.94218i	0.0666556	−	0.115451i	−0.830772	−	0.556613i	$-0.812100\pi$
$283$	1.12132	−	1.94218i	0.0666556	−	0.115451i	0.897427	+	0.441163i	$0.145434\pi$
$284$	2.24264	−	3.88437i	0.133076	−	0.230495i
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$	−4.00000			−0.236525
$287$		0			0
$288$	−8.65685			−0.510110
$289$	5.15685	+	8.93193i	0.303344	+	0.525408i
$290$	−2.41421	+	4.18154i	−0.141768	+	0.245549i
$291$	13.2426	−	22.9369i	0.776297	−	1.34459i
$292$	4.70711	+	8.15295i	0.275463	+	0.477115i
$293$	−8.34315			−0.487412			−0.243706	−	0.969849i	$-0.578363\pi$
$293$	−8.34315			−0.487412			−0.243706	+	0.969849i	$0.578363\pi$
$294$		0			0
$295$	8.58579			0.499884
$296$	−3.82843	−	6.63103i	−0.222523	−	0.385421i
$297$	8.00000	−	13.8564i	0.464207	−	0.804030i
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	−2.82843	−	4.89898i	−0.163572	−	0.283315i
$300$	3.41421			0.197120
$301$		0			0
$302$	11.3137			0.651031
$303$	−22.7279	−	39.3659i	−1.30569	−	2.26151i
$304$	−0.292893	+	0.507306i	−0.0167986	+	0.0290960i
$305$	−4.65685	+	8.06591i	−0.266651	+	0.461853i
$306$	11.1924	+	19.3858i	0.639826	+	1.10821i
$307$	14.9289			0.852039			0.426020	−	0.904714i	$-0.359915\pi$
$307$	14.9289			0.852039			0.426020	+	0.904714i	$0.359915\pi$
$308$		0			0
$309$	−50.6274			−2.88009
$310$	−1.41421	−	2.44949i	−0.0803219	−	0.139122i
$311$	−2.00000	+	3.46410i	−0.113410	+	0.196431i	−0.917143	−	0.398559i	$-0.869511\pi$
$311$	−2.00000	+	3.46410i	−0.113410	+	0.196431i	0.803733	+	0.594990i	$0.202844\pi$
$312$	−8.24264	+	14.2767i	−0.466648	+	0.808257i
$313$	−7.19239	−	12.4576i	−0.406538	−	0.704144i	0.587961	−	0.808889i	$-0.299931\pi$
$313$	−7.19239	−	12.4576i	−0.406538	−	0.704144i	−0.994499	+	0.104745i	$0.966597\pi$
$314$	−6.48528			−0.365986
$315$		0			0
$316$	−6.82843			−0.384129
$317$	−5.24264	−	9.08052i	−0.294456	−	0.510013i	0.680402	−	0.732839i	$-0.261805\pi$
$317$	−5.24264	−	9.08052i	−0.294456	−	0.510013i	−0.974858	+	0.222826i	$0.928472\pi$
$318$	11.0711	−	19.1757i	0.620835	−	1.07532i
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	32.9706			1.84024
$322$		0			0
$323$	1.51472			0.0842812
$324$	−19.9853	−	34.6155i	−1.11029	−	1.92308i
$325$	2.41421	−	4.18154i	0.133916	−	0.231950i
$326$	−10.0711	+	17.4436i	−0.557785	+	0.966112i
$327$	−4.24264	−	7.34847i	−0.234619	−	0.406371i
$328$	3.07107			0.169571
$329$		0			0
$330$	2.82843			0.155700
$331$	−16.8995	−	29.2708i	−0.928880	−	1.60887i	−0.785199	−	0.619244i	$-0.787439\pi$
$331$	−16.8995	−	29.2708i	−0.928880	−	1.60887i	−0.143681	−	0.989624i	$-0.545894\pi$
$332$	1.12132	−	1.94218i	0.0615404	−	0.106591i
$333$	33.1421	−	57.4039i	1.81618	−	3.14571i
$334$	7.89949	+	13.6823i	0.432241	+	0.748664i
$335$	1.65685			0.0905236
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	5.15685	+	8.93193i	0.280496	+	0.485833i
$339$	26.1421	−	45.2795i	1.41985	−	2.45925i
$340$	−1.29289	+	2.23936i	−0.0701170	+	0.121446i
$341$	−1.17157	−	2.02922i	−0.0634442	−	0.109889i
$342$	−5.07107			−0.274212
$343$		0			0
$344$	8.82843			0.475997
$345$	2.00000	+	3.46410i	0.107676	+	0.186501i
$346$	−4.41421	+	7.64564i	−0.237310	+	0.411032i
$347$	1.58579	−	2.74666i	0.0851295	−	0.147449i	−0.820317	−	0.571909i	$-0.806203\pi$
$347$	1.58579	−	2.74666i	0.0851295	−	0.147449i	0.905446	+	0.424461i	$0.139536\pi$
$348$	8.24264	+	14.2767i	0.441852	+	0.765310i
$349$	2.48528			0.133034			0.0665170	−	0.997785i	$-0.478811\pi$
$349$	2.48528			0.133034			0.0665170	+	0.997785i	$0.478811\pi$
$350$		0			0
$351$	−93.2548			−4.97757
$352$	−0.414214	−	0.717439i	−0.0220777	−	0.0382396i
$353$	1.19239	−	2.06528i	0.0634644	−	0.109924i	−0.832547	−	0.553954i	$-0.813118\pi$
$353$	1.19239	−	2.06528i	0.0634644	−	0.109924i	0.896012	+	0.444030i	$0.146452\pi$
$354$	14.6569	−	25.3864i	0.779003	−	1.34927i
$355$	2.24264	+	3.88437i	0.119027	+	0.206161i
$356$	12.7279			0.674579
$357$		0			0
$358$	−4.00000			−0.211407
$359$	−14.1421	−	24.4949i	−0.746393	−	1.29279i	−0.949541	−	0.313643i	$-0.898450\pi$
$359$	−14.1421	−	24.4949i	−0.746393	−	1.29279i	0.203148	−	0.979148i	$-0.434883\pi$
$360$	4.32843	−	7.49706i	0.228128	−	0.395130i
$361$	9.32843	−	16.1573i	0.490970	−	0.850385i
$362$	−1.24264	−	2.15232i	−0.0653117	−	0.113123i
$363$	−35.2132			−1.84821
$364$		0			0
$365$	−9.41421			−0.492762
$366$	15.8995	+	27.5387i	0.831080	+	1.43947i
$367$	−12.4853	+	21.6251i	−0.651726	+	1.12882i	0.330977	+	0.943639i	$0.392622\pi$
$367$	−12.4853	+	21.6251i	−0.651726	+	1.12882i	−0.982704	+	0.185185i	$0.940712\pi$
$368$	0.585786	−	1.01461i	0.0305362	−	0.0528903i
$369$	13.2929	+	23.0240i	0.692000	+	1.19858i
$370$	7.65685			0.398061
$371$		0			0
$372$	−9.65685			−0.500685
$373$	15.2426	+	26.4010i	0.789234	+	1.36699i	0.926437	+	0.376450i	$0.122855\pi$
$373$	15.2426	+	26.4010i	0.789234	+	1.36699i	−0.137203	+	0.990543i	$0.543811\pi$
$374$	−1.07107	+	1.85514i	−0.0553836	+	0.0959272i
$375$	−1.70711	+	2.95680i	−0.0881546	+	0.152688i
$376$	2.58579	+	4.47871i	0.133352	+	0.230972i
$377$	23.3137			1.20072
$378$		0			0
$379$	34.4853			1.77139			0.885695	−	0.464268i	$-0.153682\pi$
$379$	34.4853			1.77139			0.885695	+	0.464268i	$0.153682\pi$
$380$	−0.292893	−	0.507306i	−0.0150251	−	0.0260242i
$381$	−4.82843	+	8.36308i	−0.247368	+	0.428454i
$382$	5.07107	−	8.78335i	0.259458	−	0.449395i
$383$	16.2426	+	28.1331i	0.829960	+	1.43753i	0.898069	+	0.439855i	$0.144970\pi$
$383$	16.2426	+	28.1331i	0.829960	+	1.43753i	−0.0681085	+	0.997678i	$0.521696\pi$
$384$	−3.41421			−0.174231
$385$		0			0
$386$	−5.65685			−0.287926
$387$	38.2132	+	66.1872i	1.94249	+	3.36448i
$388$	3.87868	−	6.71807i	0.196910	−	0.341058i
$389$	−14.0711	+	24.3718i	−0.713431	+	1.23570i	0.250130	+	0.968212i	$0.419527\pi$
$389$	−14.0711	+	24.3718i	−0.713431	+	1.23570i	−0.963561	+	0.267487i	$0.913807\pi$
$390$	−8.24264	−	14.2767i	−0.417382	−	0.722927i
$391$	−3.02944			−0.153205
$392$		0			0
$393$	−21.3137			−1.07513
$394$	−12.8995	−	22.3426i	−0.649867	−	1.12560i
$395$	3.41421	−	5.91359i	0.171788	−	0.297545i
$396$	3.58579	−	6.21076i	0.180193	−	0.312103i
$397$	−16.8995	−	29.2708i	−0.848161	−	1.46906i	−0.882847	−	0.469660i	$-0.844376\pi$
$397$	−16.8995	−	29.2708i	−0.848161	−	1.46906i	0.0346859	−	0.999398i	$-0.488957\pi$
$398$	−16.4853			−0.826332
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	2.82843	−	4.89898i	0.141069	−	0.244339i
$403$	−6.82843	+	11.8272i	−0.340148	+	0.589154i
$404$	−6.65685	−	11.5300i	−0.331191	−	0.573639i
$405$	39.9706			1.98615
$406$		0			0
$407$	6.34315			0.314418
$408$	4.41421	+	7.64564i	0.218536	+	0.378516i
$409$	5.29289	−	9.16756i	0.261717	−	0.453307i	−0.704981	−	0.709226i	$-0.749045\pi$
$409$	5.29289	−	9.16756i	0.261717	−	0.453307i	0.966698	+	0.255919i	$0.0823781\pi$
$410$	−1.53553	+	2.65962i	−0.0758346	+	0.131349i
$411$	27.3137	+	47.3087i	1.34729	+	2.33357i
$412$	−14.8284			−0.730544
$413$		0			0
$414$	10.1421			0.498459
$415$	1.12132	+	1.94218i	0.0550435	+	0.0953381i
$416$	−2.41421	+	4.18154i	−0.118367	+	0.205017i
$417$	−33.9706	+	58.8387i	−1.66355	+	2.88135i
$418$	−0.242641	−	0.420266i	−0.0118679	−	0.0205559i
$419$	−20.8701			−1.01957			−0.509785	−	0.860302i	$-0.670275\pi$
$419$	−20.8701			−1.01957			−0.509785	+	0.860302i	$0.670275\pi$
$420$		0			0
$421$	17.3137			0.843819			0.421909	−	0.906638i	$-0.361360\pi$
$421$	17.3137			0.843819			0.421909	+	0.906638i	$0.361360\pi$
$422$	9.31371	+	16.1318i	0.453384	+	0.785285i
$423$	−22.3848	+	38.7716i	−1.08839	+	1.88514i
$424$	3.24264	−	5.61642i	0.157477	−	0.272757i
$425$	−1.29289	−	2.23936i	−0.0627145	−	0.108625i
$426$	15.3137			0.741952
$427$		0			0
$428$	9.65685			0.466782
$429$	−6.82843	−	11.8272i	−0.329680	−	0.571022i
$430$	−4.41421	+	7.64564i	−0.212872	+	0.368706i
$431$	11.1716	−	19.3497i	0.538116	−	0.932044i	−0.460890	−	0.887457i	$-0.652470\pi$
$431$	11.1716	−	19.3497i	0.538116	−	0.932044i	0.999006	−	0.0445864i	$-0.0141970\pi$
$432$	−9.65685	−	16.7262i	−0.464616	−	0.804738i
$433$	10.5858			0.508720			0.254360	−	0.967110i	$-0.418135\pi$
$433$	10.5858			0.508720			0.254360	+	0.967110i	$0.418135\pi$
$434$		0			0
$435$	−16.4853			−0.790409
$436$	−1.24264	−	2.15232i	−0.0595117	−	0.103077i
$437$	0.343146	−	0.594346i	0.0164149	−	0.0284314i
$438$	−16.0711	+	27.8359i	−0.767905	+	1.33005i
$439$	12.4853	+	21.6251i	0.595890	+	1.03211i	0.993421	+	0.114523i	$0.0365339\pi$
$439$	12.4853	+	21.6251i	0.595890	+	1.03211i	−0.397531	+	0.917589i	$0.630133\pi$
$440$	0.828427			0.0394937
$441$		0			0
$442$	12.4853			0.593864
$443$	−1.51472	−	2.62357i	−0.0719665	−	0.124650i	0.827797	−	0.561028i	$-0.189594\pi$
$443$	−1.51472	−	2.62357i	−0.0719665	−	0.124650i	−0.899763	+	0.436379i	$0.856261\pi$
$444$	13.0711	−	22.6398i	0.620325	−	1.07444i
$445$	−6.36396	+	11.0227i	−0.301681	+	0.522526i
$446$	−3.65685	−	6.33386i	−0.173157	−	0.299917i
$447$	−20.4853			−0.968921
$448$		0			0
$449$	−16.6274			−0.784696			−0.392348	−	0.919817i	$-0.628337\pi$
$449$	−16.6274			−0.784696			−0.392348	+	0.919817i	$0.628337\pi$
$450$	4.32843	+	7.49706i	0.204044	+	0.353415i
$451$	−1.27208	+	2.20330i	−0.0598998	+	0.103750i
$452$	7.65685	−	13.2621i	0.360148	−	0.623795i
$453$	19.3137	+	33.4523i	0.907437	+	1.57173i
$454$	−18.2426			−0.856170
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−10.8284	−	18.7554i	−0.506532	−	0.877340i	−0.999971	−	0.00755953i	$-0.997594\pi$
$457$	−10.8284	−	18.7554i	−0.506532	−	0.877340i	0.493439	−	0.869780i	$-0.335740\pi$
$458$	−8.07107	+	13.9795i	−0.377136	+	0.653219i
$459$	−24.9706	+	43.2503i	−1.16553	+	2.01875i
$460$	0.585786	+	1.01461i	0.0273124	+	0.0473065i
$461$	−12.8284			−0.597479			−0.298740	−	0.954335i	$-0.596566\pi$
$461$	−12.8284			−0.597479			−0.298740	+	0.954335i	$0.596566\pi$
$462$		0			0
$463$	−16.9706			−0.788689			−0.394344	−	0.918963i	$-0.629028\pi$
$463$	−16.9706			−0.788689			−0.394344	+	0.918963i	$0.629028\pi$
$464$	2.41421	+	4.18154i	0.112077	+	0.194123i
$465$	4.82843	−	8.36308i	0.223913	−	0.387829i
$466$	11.6569	−	20.1903i	0.539993	−	0.935296i
$467$	7.94975	+	13.7694i	0.367870	+	0.637170i	0.989232	−	0.146353i	$-0.0467537\pi$
$467$	7.94975	+	13.7694i	0.367870	+	0.637170i	−0.621362	+	0.783524i	$0.713420\pi$
$468$	−41.7990			−1.93216
$469$		0			0
$470$	−5.17157			−0.238547
$471$	−11.0711	−	19.1757i	−0.510128	−	0.883567i
$472$	4.29289	−	7.43551i	0.197596	−	0.342247i
$473$	−3.65685	+	6.33386i	−0.168142	+	0.291231i
$474$	−11.6569	−	20.1903i	−0.535417	−	0.927370i
$475$	0.585786			0.0268777
$476$		0			0
$477$	56.1421			2.57057
$478$	0.828427	+	1.43488i	0.0378914	+	0.0656298i
$479$	8.58579	−	14.8710i	0.392295	−	0.679474i	−0.600457	−	0.799657i	$-0.705015\pi$
$479$	8.58579	−	14.8710i	0.392295	−	0.679474i	0.992752	+	0.120183i	$0.0383480\pi$
$480$	1.70711	−	2.95680i	0.0779184	−	0.134959i
$481$	−18.4853	−	32.0174i	−0.842856	−	1.45987i
$482$	13.4142			0.611001
$483$		0			0
$484$	−10.3137			−0.468805
$485$	3.87868	+	6.71807i	0.176122	+	0.305052i
$486$	39.2635	−	68.0063i	1.78103	−	3.08483i
$487$	−15.8995	+	27.5387i	−0.720475	+	1.24790i	0.240335	+	0.970690i	$0.422743\pi$
$487$	−15.8995	+	27.5387i	−0.720475	+	1.24790i	−0.960810	+	0.277209i	$0.910591\pi$
$488$	4.65685	+	8.06591i	0.210806	+	0.365127i
$489$	−68.7696			−3.10987
$490$		0			0
$491$	32.2843			1.45697			0.728484	−	0.685062i	$-0.240225\pi$
$491$	32.2843			1.45697			0.728484	+	0.685062i	$0.240225\pi$
$492$	5.24264	+	9.08052i	0.236356	+	0.409381i
$493$	6.24264	−	10.8126i	0.281154	−	0.486974i
$494$	−1.41421	+	2.44949i	−0.0636285	+	0.110208i
$495$	3.58579	+	6.21076i	0.161169	+	0.279153i
$496$	−2.82843			−0.127000
$497$		0			0
$498$	7.65685			0.343112
$499$	−15.1716	−	26.2779i	−0.679173	−	1.17636i	−0.975230	−	0.221192i	$-0.929005\pi$
$499$	−15.1716	−	26.2779i	−0.679173	−	1.17636i	0.296057	−	0.955170i	$-0.404328\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−26.9706	+	46.7144i	−1.20496	+	2.08704i
$502$	0.292893	+	0.507306i	0.0130725	+	0.0226422i
$503$	17.6569			0.787280			0.393640	−	0.919265i	$-0.371216\pi$
$503$	17.6569			0.787280			0.393640	+	0.919265i	$0.371216\pi$
$504$		0			0
$505$	13.3137			0.592452
$506$	0.485281	+	0.840532i	0.0215734	+	0.0373662i
$507$	−17.6066	+	30.4955i	−0.781937	+	1.35435i
$508$	−1.41421	+	2.44949i	−0.0627456	+	0.108679i
$509$	−2.89949	−	5.02207i	−0.128518	−	0.222599i	0.794585	−	0.607153i	$-0.207689\pi$
$509$	−2.89949	−	5.02207i	−0.128518	−	0.222599i	−0.923103	+	0.384554i	$0.874355\pi$
$510$	−8.82843			−0.390929
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−5.65685	−	9.79796i	−0.249756	−	0.432590i
$514$	−4.94975	+	8.57321i	−0.218324	+	0.378148i
$515$	7.41421	−	12.8418i	0.326709	−	0.565877i
$516$	15.0711	+	26.1039i	0.663467	+	1.14916i
$517$	−4.28427			−0.188422
$518$		0			0
$519$	−30.1421			−1.32309
$520$	−2.41421	−	4.18154i	−0.105870	−	0.183373i
$521$	−9.53553	+	16.5160i	−0.417759	+	0.723580i	−0.995714	−	0.0924887i	$-0.970518\pi$
$521$	−9.53553	+	16.5160i	−0.417759	+	0.723580i	0.577954	+	0.816069i	$0.303851\pi$
$522$	−20.8995	+	36.1990i	−0.914746	+	1.58439i
$523$	−11.9497	−	20.6976i	−0.522526	−	0.905042i	−0.999656	−	0.0262091i	$-0.991656\pi$
$523$	−11.9497	−	20.6976i	−0.522526	−	0.905042i	0.477131	−	0.878832i	$-0.341677\pi$
$524$	−6.24264			−0.272711
$525$		0			0
$526$	−28.0000			−1.22086
$527$	3.65685	+	6.33386i	0.159295	+	0.275907i
$528$	1.41421	−	2.44949i	0.0615457	−	0.106600i
$529$	10.8137	−	18.7299i	0.470161	−	0.814343i
$530$	3.24264	+	5.61642i	0.140851	+	0.243962i
$531$	74.3259			3.22547
$532$		0			0
$533$	14.8284			0.642290
$534$	21.7279	+	37.6339i	0.940259	+	1.62858i
$535$	−4.82843	+	8.36308i	−0.208751	+	0.361568i
$536$	0.828427	−	1.43488i	0.0357826	−	0.0619773i
$537$	−6.82843	−	11.8272i	−0.294668	−	0.510381i
$538$	−18.4853			−0.796957
$539$		0			0
$540$	19.3137			0.831130
$541$	7.48528	+	12.9649i	0.321817	+	0.557404i	0.980863	−	0.194699i	$-0.0623730\pi$
$541$	7.48528	+	12.9649i	0.321817	+	0.557404i	−0.659046	+	0.752103i	$0.729040\pi$
$542$	6.00000	−	10.3923i	0.257722	−	0.446388i
$543$	4.24264	−	7.34847i	0.182069	−	0.315353i
$544$	1.29289	+	2.23936i	0.0554323	+	0.0960116i
$545$	2.48528			0.106458
$546$		0			0
$547$	−10.4853			−0.448318			−0.224159	−	0.974553i	$-0.571964\pi$
$547$	−10.4853			−0.448318			−0.224159	+	0.974553i	$0.571964\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	−40.3137	+	69.8254i	−1.72055	+	2.98008i
$550$	−0.414214	+	0.717439i	−0.0176621	+	0.0305917i
$551$	1.41421	+	2.44949i	0.0602475	+	0.104352i
$552$	4.00000			0.170251
$553$		0			0
$554$	8.14214			0.345926
$555$	13.0711	+	22.6398i	0.554836	+	0.961004i
$556$	−9.94975	+	17.2335i	−0.421963	+	0.730862i
$557$	−7.58579	+	13.1390i	−0.321420	+	0.556716i	−0.980781	−	0.195110i	$-0.937493\pi$
$557$	−7.58579	+	13.1390i	−0.321420	+	0.556716i	0.659361	+	0.751826i	$0.270827\pi$
$558$	−12.2426	−	21.2049i	−0.518272	−	0.897674i
$559$	42.6274			1.80295
$560$		0			0
$561$	−7.31371			−0.308785
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	18.2929	−	31.6842i	0.770954	−	1.33533i	−0.166087	−	0.986111i	$-0.553113\pi$
$563$	18.2929	−	31.6842i	0.770954	−	1.33533i	0.937041	−	0.349220i	$-0.113553\pi$
$564$	−8.82843	+	15.2913i	−0.371744	+	0.643879i
$565$	7.65685	+	13.2621i	0.322126	+	0.557939i
$566$	2.24264			0.0942652
$567$		0			0
$568$	4.48528			0.188198
$569$	14.6569	+	25.3864i	0.614447	+	1.06425i	0.990481	+	0.137648i	$0.0439543\pi$
$569$	14.6569	+	25.3864i	0.614447	+	1.06425i	−0.376034	+	0.926606i	$0.622712\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	1.10051	−	1.90613i	0.0460547	−	0.0797691i	−0.842079	−	0.539354i	$-0.818668\pi$
$571$	1.10051	−	1.90613i	0.0460547	−	0.0797691i	0.888134	+	0.459585i	$0.152002\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$	34.6274			1.44658
$574$		0			0
$575$	−1.17157			−0.0488580
$576$	−4.32843	−	7.49706i	−0.180351	−	0.312377i
$577$	−3.05025	+	5.28319i	−0.126984	+	0.219942i	−0.922507	−	0.385981i	$-0.873863\pi$
$577$	−3.05025	+	5.28319i	−0.126984	+	0.219942i	0.795523	+	0.605923i	$0.207196\pi$
$578$	−5.15685	+	8.93193i	−0.214497	+	0.371519i
$579$	−9.65685	−	16.7262i	−0.401325	−	0.695116i
$580$	−4.82843			−0.200490
$581$		0			0
$582$	26.4853			1.09785
$583$	2.68629	+	4.65279i	0.111255	+	0.192699i
$584$	−4.70711	+	8.15295i	−0.194781	+	0.337371i
$585$	20.8995	−	36.1990i	0.864088	−	1.49664i
$586$	−4.17157	−	7.22538i	−0.172326	−	0.298478i
$587$	17.0711			0.704598			0.352299	−	0.935887i	$-0.385400\pi$
$587$	17.0711			0.704598			0.352299	+	0.935887i	$0.385400\pi$
$588$		0			0
$589$	−1.65685			−0.0682695
$590$	4.29289	+	7.43551i	0.176736	+	0.306115i
$591$	44.0416	−	76.2823i	1.81163	−	3.13784i
$592$	3.82843	−	6.63103i	0.157347	−	0.272534i
$593$	−1.63604	−	2.83370i	−0.0671841	−	0.116366i	0.830477	−	0.557053i	$-0.188068\pi$
$593$	−1.63604	−	2.83370i	−0.0671841	−	0.116366i	−0.897661	+	0.440687i	$0.854735\pi$
$594$	16.0000			0.656488
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−28.1421	−	48.7436i	−1.15178	−	1.99494i
$598$	2.82843	−	4.89898i	0.115663	−	0.200334i
$599$	5.41421	−	9.37769i	0.221219	−	0.383162i	−0.733960	−	0.679193i	$-0.762330\pi$
$599$	5.41421	−	9.37769i	0.221219	−	0.383162i	0.955178	+	0.296031i	$0.0956632\pi$
$600$	1.70711	+	2.95680i	0.0696923	+	0.120711i
$601$	6.58579			0.268640			0.134320	−	0.990938i	$-0.457115\pi$
$601$	6.58579			0.268640			0.134320	+	0.990938i	$0.457115\pi$
$602$		0			0
$603$	14.3431			0.584098
$604$	5.65685	+	9.79796i	0.230174	+	0.398673i
$605$	5.15685	−	8.93193i	0.209656	−	0.363135i
$606$	22.7279	−	39.3659i	0.923259	−	1.59913i
$607$	−8.14214	−	14.1026i	−0.330479	−	0.572407i	0.652127	−	0.758110i	$-0.273877\pi$
$607$	−8.14214	−	14.1026i	−0.330479	−	0.572407i	−0.982606	+	0.185703i	$0.940544\pi$
$608$	−0.585786			−0.0237568
$609$		0			0
$610$	−9.31371			−0.377101
$611$	12.4853	+	21.6251i	0.505100	+	0.874860i
$612$	−11.1924	+	19.3858i	−0.452425	+	0.783624i
$613$	6.17157	−	10.6895i	0.249267	−	0.431744i	−0.714055	−	0.700089i	$-0.753144\pi$
$613$	6.17157	−	10.6895i	0.249267	−	0.431744i	0.963323	+	0.268345i	$0.0864768\pi$
$614$	7.46447	+	12.9288i	0.301241	+	0.521765i
$615$	−10.4853			−0.422807
$616$		0			0
$617$	−33.3137			−1.34116			−0.670580	−	0.741837i	$-0.733955\pi$
$617$	−33.3137			−1.34116			−0.670580	+	0.741837i	$0.733955\pi$
$618$	−25.3137	−	43.8446i	−1.01827	−	1.76369i
$619$	−14.5355	+	25.1763i	−0.584232	+	1.01192i	0.410738	+	0.911753i	$0.365271\pi$
$619$	−14.5355	+	25.1763i	−0.584232	+	1.01192i	−0.994971	+	0.100167i	$0.968062\pi$
$620$	1.41421	−	2.44949i	0.0567962	−	0.0983739i
$621$	11.3137	+	19.5959i	0.454003	+	0.786357i
$622$	−4.00000			−0.160385
$623$		0			0
$624$	−16.4853			−0.659939
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.19239	−	12.4576i	0.287466	−	0.497905i
$627$	0.828427	−	1.43488i	0.0330842	−	0.0573035i
$628$	−3.24264	−	5.61642i	−0.129395	−	0.224119i
$629$	−19.7990			−0.789437
$630$		0			0
$631$	−12.4853			−0.497031			−0.248516	−	0.968628i	$-0.579943\pi$
$631$	−12.4853			−0.497031			−0.248516	+	0.968628i	$0.579943\pi$
$632$	−3.41421	−	5.91359i	−0.135810	−	0.235230i
$633$	−31.7990	+	55.0775i	−1.26390	+	2.18913i
$634$	5.24264	−	9.08052i	0.208212	−	0.360634i
$635$	−1.41421	−	2.44949i	−0.0561214	−	0.0972050i
$636$	22.1421			0.877993
$637$		0			0
$638$	−4.00000			−0.158362
$639$	19.4142	+	33.6264i	0.768014	+	1.33024i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	12.3137	−	21.3280i	0.486362	−	0.842404i	−0.513515	−	0.858081i	$-0.671657\pi$
$641$	12.3137	−	21.3280i	0.486362	−	0.842404i	0.999877	+	0.0156766i	$0.00499021\pi$
$642$	16.4853	+	28.5533i	0.650622	+	1.12691i
$643$	4.78680			0.188773			0.0943864	−	0.995536i	$-0.469911\pi$
$643$	4.78680			0.188773			0.0943864	+	0.995536i	$0.469911\pi$
$644$		0			0
$645$	−30.1421			−1.18685
$646$	0.757359	+	1.31178i	0.0297979	+	0.0516115i
$647$	11.5563	−	20.0162i	0.454327	−	0.786917i	−0.544322	−	0.838876i	$-0.683213\pi$
$647$	11.5563	−	20.0162i	0.454327	−	0.786917i	0.998649	+	0.0519588i	$0.0165465\pi$
$648$	19.9853	−	34.6155i	0.785096	−	1.35983i
$649$	3.55635	+	6.15978i	0.139599	+	0.241792i
$650$	4.82843			0.189386
$651$		0			0
$652$	−20.1421			−0.788827
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	0.820403	−	0.571786i	$-0.193749\pi$
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	−0.905383	+	0.424596i	$0.860416\pi$
$654$	4.24264	−	7.34847i	0.165900	−	0.287348i
$655$	3.12132	−	5.40629i	0.121960	−	0.211241i
$656$	1.53553	+	2.65962i	0.0599525	+	0.103841i
$657$	−81.4975			−3.17952
$658$		0			0
$659$	−27.1716			−1.05845			−0.529227	−	0.848480i	$-0.677518\pi$
$659$	−27.1716			−1.05845			−0.529227	+	0.848480i	$0.677518\pi$
$660$	1.41421	+	2.44949i	0.0550482	+	0.0953463i
$661$	19.1421	−	33.1552i	0.744543	−	1.28959i	−0.205865	−	0.978580i	$-0.566001\pi$
$661$	19.1421	−	33.1552i	0.744543	−	1.28959i	0.950408	−	0.311006i	$-0.100666\pi$
$662$	16.8995	−	29.2708i	0.656818	−	1.13764i
$663$	21.3137	+	36.9164i	0.827756	+	1.43372i
$664$	2.24264			0.0870313
$665$		0			0
$666$	66.2843			2.56846
$667$	−2.82843	−	4.89898i	−0.109517	−	0.189689i
$668$	−7.89949	+	13.6823i	−0.305641	+	0.529385i
$669$	12.4853	−	21.6251i	0.482709	−	0.836076i
$670$	0.828427	+	1.43488i	0.0320049	+	0.0554342i
$671$	−7.71573			−0.297862
$672$		0			0
$673$	−48.0000			−1.85026			−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000			−1.85026			−0.925132	+	0.379646i	$0.876046\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$	−9.65685	+	16.7262i	−0.371692	+	0.643790i
$676$	−5.15685	+	8.93193i	−0.198341	+	0.343536i
$677$	−19.7279	−	34.1698i	−0.758206	−	1.31325i	−0.943765	−	0.330618i	$-0.892743\pi$
$677$	−19.7279	−	34.1698i	−0.758206	−	1.31325i	0.185559	−	0.982633i	$-0.440590\pi$
$678$	52.2843			2.00797
$679$		0			0
$680$	−2.58579			−0.0991604
$681$	−31.1421	−	53.9398i	−1.19337	−	2.06698i
$682$	1.17157	−	2.02922i	0.0448618	−	0.0777030i
$683$	−16.8284	+	29.1477i	−0.643922	+	1.11531i	0.340628	+	0.940198i	$0.389360\pi$
$683$	−16.8284	+	29.1477i	−0.643922	+	1.11531i	−0.984549	+	0.175107i	$0.943973\pi$
$684$	−2.53553	−	4.39167i	−0.0969486	−	0.167920i
$685$	−16.0000			−0.611329
$686$		0			0
$687$	−55.1127			−2.10268
$688$	4.41421	+	7.64564i	0.168290	+	0.291487i
$689$	15.6569	−	27.1185i	0.596479	−	1.03313i
$690$	−2.00000	+	3.46410i	−0.0761387	+	0.131876i
$691$	−0.878680	−	1.52192i	−0.0334265	−	0.0578965i	0.848828	−	0.528669i	$-0.177309\pi$
$691$	−0.878680	−	1.52192i	−0.0334265	−	0.0578965i	−0.882255	+	0.470772i	$0.843975\pi$
$692$	−8.82843			−0.335606
$693$		0			0
$694$	3.17157			0.120391
$695$	−9.94975	−	17.2335i	−0.377415	−	0.653703i
$696$	−8.24264	+	14.2767i	−0.312436	+	0.541156i
$697$	3.97056	−	6.87722i	0.150396	−	0.260493i
$698$	1.24264	+	2.15232i	0.0470346	+	0.0814664i
$699$	79.5980			3.01067
$700$		0			0
$701$	2.48528			0.0938678			0.0469339	−	0.998898i	$-0.485055\pi$
$701$	2.48528			0.0938678			0.0469339	+	0.998898i	$0.485055\pi$
$702$	−46.6274	−	80.7611i	−1.75984	−	3.04813i
$703$	2.24264	−	3.88437i	0.0845828	−	0.146502i
$704$	0.414214	−	0.717439i	0.0156113	−	0.0270395i
$705$	−8.82843	−	15.2913i	−0.332498	−	0.575903i
$706$	2.38478			0.0897522
$707$		0			0
$708$	29.3137			1.10168
$709$	−22.5563	−	39.0687i	−0.847121	−	1.46726i	−0.883766	−	0.467929i	$-0.845000\pi$
$709$	−22.5563	−	39.0687i	−0.847121	−	1.46726i	0.0366445	−	0.999328i	$-0.488333\pi$
$710$	−2.24264	+	3.88437i	−0.0841648	+	0.145778i
$711$	29.5563	−	51.1931i	1.10845	−	1.91989i
$712$	6.36396	+	11.0227i	0.238500	+	0.413093i
$713$	3.31371			0.124099
$714$		0			0
$715$	4.00000			0.149592
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	−2.82843	+	4.89898i	−0.105630	+	0.182956i
$718$	14.1421	−	24.4949i	0.527780	−	0.914141i
$719$	−20.7279	−	35.9018i	−0.773021	−	1.33891i	−0.935900	−	0.352266i	$-0.885411\pi$
$719$	−20.7279	−	35.9018i	−0.773021	−	1.33891i	0.162879	−	0.986646i	$-0.447922\pi$
$720$	8.65685			0.322622
$721$		0			0
$722$	18.6569			0.694336
$723$	22.8995	+	39.6631i	0.851641	+	1.47509i
$724$	1.24264	−	2.15232i	0.0461824	−	0.0799902i
$725$	2.41421	−	4.18154i	0.0896616	−	0.155299i
$726$	−17.6066	−	30.4955i	−0.653442	−	1.13180i
$727$	−3.51472			−0.130354			−0.0651768	−	0.997874i	$-0.520761\pi$
$727$	−3.51472			−0.130354			−0.0651768	+	0.997874i	$0.520761\pi$
$728$		0			0
$729$	148.196			5.48874
$730$	−4.70711	−	8.15295i	−0.174218	−	0.301754i
$731$	11.4142	−	19.7700i	0.422170	−	0.731220i
$732$	−15.8995	+	27.5387i	−0.587662	+	1.01786i
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$	−24.9706			−0.921680
$735$		0			0
$736$	1.17157			0.0431847
$737$	0.686292	+	1.18869i	0.0252799	+	0.0437860i
$738$	−13.2929	+	23.0240i	−0.489318	+	0.847524i
$739$	−1.58579	+	2.74666i	−0.0583341	+	0.101038i	−0.893718	−	0.448630i	$-0.851912\pi$
$739$	−1.58579	+	2.74666i	−0.0583341	+	0.101038i	0.835384	+	0.549667i	$0.185246\pi$
$740$	3.82843	+	6.63103i	0.140736	+	0.243762i
$741$	−9.65685			−0.354753
$742$		0			0
$743$	51.7990			1.90032			0.950160	−	0.311762i	$-0.100919\pi$
$743$	51.7990			1.90032			0.950160	+	0.311762i	$0.100919\pi$
$744$	−4.82843	−	8.36308i	−0.177019	−	0.306605i
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$	−15.2426	+	26.4010i	−0.558073	+	0.966610i
$747$	9.70711	+	16.8132i	0.355164	+	0.615163i
$748$	−2.14214			−0.0783242
$749$		0			0
$750$	−3.41421			−0.124669
$751$	19.6569	+	34.0467i	0.717289	+	1.24238i	0.962070	+	0.272802i	$0.0879505\pi$
$751$	19.6569	+	34.0467i	0.717289	+	1.24238i	−0.244781	+	0.969578i	$0.578716\pi$
$752$	−2.58579	+	4.47871i	−0.0942939	+	0.163322i
$753$	−1.00000	+	1.73205i	−0.0364420	+	0.0631194i
$754$	11.6569	+	20.1903i	0.424518	+	0.735286i
$755$	−11.3137			−0.411748
$756$		0			0
$757$	3.65685			0.132911			0.0664553	−	0.997789i	$-0.478831\pi$
$757$	3.65685			0.132911			0.0664553	+	0.997789i	$0.478831\pi$
$758$	17.2426	+	29.8651i	0.626281	+	1.08475i
$759$	−1.65685	+	2.86976i	−0.0601400	+	0.104166i
$760$	0.292893	−	0.507306i	0.0106244	−	0.0184019i
$761$	−11.1924	−	19.3858i	−0.405724	−	0.702734i	0.588682	−	0.808365i	$-0.299647\pi$
$761$	−11.1924	−	19.3858i	−0.405724	−	0.702734i	−0.994405	+	0.105631i	$0.966314\pi$
$762$	−9.65685			−0.349831
$763$		0			0
$764$	10.1421			0.366930
$765$	−11.1924	−	19.3858i	−0.404662	−	0.700895i
$766$	−16.2426	+	28.1331i	−0.586870	+	1.01649i
$767$	20.7279	−	35.9018i	0.748442	−	1.29634i
$768$	−1.70711	−	2.95680i	−0.0615999	−	0.106694i
$769$	19.5563			0.705220			0.352610	−	0.935770i	$-0.385294\pi$
$769$	19.5563			0.705220			0.352610	+	0.935770i	$0.385294\pi$
$770$		0			0
$771$	−33.7990			−1.21724
$772$	−2.82843	−	4.89898i	−0.101797	−	0.176318i
$773$	1.00000	−	1.73205i	0.0359675	−	0.0622975i	−0.847481	−	0.530825i	$-0.821882\pi$
$773$	1.00000	−	1.73205i	0.0359675	−	0.0622975i	0.883449	+	0.468528i	$0.155215\pi$
$774$	−38.2132	+	66.1872i	−1.37355	+	2.37905i
$775$	1.41421	+	2.44949i	0.0508001	+	0.0879883i
$776$	7.75736			0.278473
$777$		0			0
$778$	−28.1421			−1.00894
$779$	0.899495	+	1.55797i	0.0322278	+	0.0558201i
$780$	8.24264	−	14.2767i	0.295134	−	0.511187i
$781$	−1.85786	+	3.21792i	−0.0664796	+	0.115146i
$782$	−1.51472	−	2.62357i	−0.0541662	−	0.0938187i
$783$	−93.2548			−3.33266
$784$		0			0
$785$	6.48528			0.231470
$786$	−10.6569	−	18.4582i	−0.380117	−	0.658383i
$787$	0.636039	−	1.10165i	0.0226723	−	0.0392696i	−0.854467	−	0.519506i	$-0.826116\pi$
$787$	0.636039	−	1.10165i	0.0226723	−	0.0392696i	0.877139	+	0.480237i	$0.159449\pi$
$788$	12.8995	−	22.3426i	0.459525	−	0.795921i
$789$	−47.7990	−	82.7903i	−1.70169	−	2.94741i
$790$	6.82843			0.242945
$791$		0			0
$792$	7.17157			0.254831
$793$	22.4853	+	38.9456i	0.798476	+	1.38300i
$794$	16.8995	−	29.2708i	0.599741	−	1.03878i
$795$	−11.0711	+	19.1757i	−0.392650	+	0.680090i
$796$	−8.24264	−	14.2767i	−0.292153	−	0.506023i
$797$	−41.7990			−1.48060			−0.740298	−	0.672279i	$-0.765316\pi$
$797$	−41.7990			−1.48060			−0.740298	+	0.672279i	$0.765316\pi$
$798$		0			0
$799$	13.3726			0.473088
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−55.0919	+	95.4219i	−1.94658	+	3.37157i
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	−3.89949	−	6.75412i	−0.137610	−	0.238348i
$804$	5.65685			0.199502
$805$		0			0
$806$	−13.6569			−0.481042
$807$	−31.5563	−	54.6572i	−1.11084	−	1.92402i
$808$	6.65685	−	11.5300i	0.234187	−	0.405624i
$809$	−1.51472	+	2.62357i	−0.0532547	+	0.0922398i	−0.891424	−	0.453171i	$-0.850293\pi$
$809$	−1.51472	+	2.62357i	−0.0532547	+	0.0922398i	0.838169	+	0.545410i	$0.183626\pi$
$810$	19.9853	+	34.6155i	0.702211	+	1.21627i
$811$	32.5858			1.14424			0.572121	−	0.820169i	$-0.306121\pi$
$811$	32.5858			1.14424			0.572121	+	0.820169i	$0.306121\pi$
$812$		0			0
$813$	40.9706			1.43690
$814$	3.17157	+	5.49333i	0.111164	+	0.192541i
$815$	10.0711	−	17.4436i	0.352774	−	0.611023i
$816$	−4.41421	+	7.64564i	−0.154528	+	0.267651i
$817$	2.58579	+	4.47871i	0.0904652	+	0.156690i
$818$	10.5858			0.370123
$819$		0			0
$820$	−3.07107			−0.107246
$821$	−8.65685	−	14.9941i	−0.302126	−	0.523298i	0.674491	−	0.738283i	$-0.264363\pi$
$821$	−8.65685	−	14.9941i	−0.302126	−	0.523298i	−0.976617	+	0.214985i	$0.931030\pi$
$822$	−27.3137	+	47.3087i	−0.952675	+	1.65008i
$823$	−10.1421	+	17.5667i	−0.353533	+	0.612336i	−0.986866	−	0.161543i	$-0.948353\pi$
$823$	−10.1421	+	17.5667i	−0.353533	+	0.612336i	0.633333	+	0.773879i	$0.281686\pi$
$824$	−7.41421	−	12.8418i	−0.258286	−	0.447365i
$825$	−2.82843			−0.0984732
$826$		0			0
$827$	−5.37258			−0.186823			−0.0934115	−	0.995628i	$-0.529777\pi$
$827$	−5.37258			−0.186823			−0.0934115	+	0.995628i	$0.529777\pi$
$828$	5.07107	+	8.78335i	0.176232	+	0.305242i
$829$	2.51472	−	4.35562i	0.0873398	−	0.151277i	−0.819046	−	0.573728i	$-0.805497\pi$
$829$	2.51472	−	4.35562i	0.0873398	−	0.151277i	0.906386	+	0.422451i	$0.138830\pi$
$830$	−1.12132	+	1.94218i	−0.0389216	+	0.0674142i
$831$	13.8995	+	24.0746i	0.482168	+	0.835140i
$832$	−4.82843			−0.167396
$833$		0			0
$834$	−67.9411			−2.35261
$835$	−7.89949	−	13.6823i	−0.273373	−	0.473496i
$836$	0.242641	−	0.420266i	0.00839190	−	0.0145352i
$837$	27.3137	−	47.3087i	0.944100	−	1.63523i
$838$	−10.4350	−	18.0740i	−0.360472	−	0.624356i
$839$	−42.1421			−1.45491			−0.727454	−	0.686156i	$-0.759297\pi$
$839$	−42.1421			−1.45491			−0.727454	+	0.686156i	$0.759297\pi$
$840$		0			0
$841$	−5.68629			−0.196079
$842$	8.65685	+	14.9941i	0.298335	+	0.516731i
$843$	−13.6569	+	23.6544i	−0.470367	+	0.814700i
$844$	−9.31371	+	16.1318i	−0.320591	+	0.555280i
$845$	−5.15685	−	8.93193i	−0.177401	−	0.307268i
$846$	−44.7696			−1.53921
$847$		0			0
$848$	6.48528			0.222705
$849$	3.82843	+	6.63103i	0.131391	+	0.227576i
$850$	1.29289	−	2.23936i	0.0443459	−	0.0768093i
$851$	−4.48528	+	7.76874i	−0.153753	+	0.266309i
$852$	7.65685	+	13.2621i	0.262320	+	0.454351i
$853$	−43.1716			−1.47817			−0.739083	−	0.673614i	$-0.764741\pi$
$853$	−43.1716			−1.47817			−0.739083	+	0.673614i	$0.764741\pi$
$854$		0			0
$855$	5.07107			0.173427
$856$	4.82843	+	8.36308i	0.165032	+	0.285844i
$857$	2.46447	−	4.26858i	0.0841846	−	0.145812i	−0.820859	−	0.571131i	$-0.806505\pi$
$857$	2.46447	−	4.26858i	0.0841846	−	0.145812i	0.905043	+	0.425319i	$0.139838\pi$
$858$	6.82843	−	11.8272i	0.233119	−	0.403773i
$859$	3.60660	+	6.24682i	0.123056	+	0.213139i	0.920971	−	0.389631i	$-0.127397\pi$
$859$	3.60660	+	6.24682i	0.123056	+	0.213139i	−0.797916	+	0.602769i	$0.794064\pi$
$860$	−8.82843			−0.301047
$861$		0			0
$862$	22.3431			0.761011
$863$	2.48528	+	4.30463i	0.0846000	+	0.146531i	0.905221	−	0.424942i	$-0.139705\pi$
$863$	2.48528	+	4.30463i	0.0846000	+	0.146531i	−0.820621	+	0.571473i	$0.806372\pi$
$864$	9.65685	−	16.7262i	0.328533	−	0.569036i
$865$	4.41421	−	7.64564i	0.150088	−	0.259960i
$866$	5.29289	+	9.16756i	0.179860	+	0.311526i
$867$	−35.2132			−1.19590
$868$		0			0
$869$	5.65685			0.191896
$870$	−8.24264	−	14.2767i	−0.279452	−	0.484025i
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	1.24264	−	2.15232i	0.0420811	−	0.0728866i
$873$	33.5772	+	58.1574i	1.13641	+	1.96833i
$874$	0.686292			0.0232142
$875$		0			0
$876$	−32.1421			−1.08598
$877$	15.1421	+	26.2269i	0.511314	+	0.885621i	0.999914	+	0.0131135i	$0.00417426\pi$
$877$	15.1421	+	26.2269i	0.511314	+	0.885621i	−0.488600	+	0.872508i	$0.662492\pi$
$878$	−12.4853	+	21.6251i	−0.421358	+	0.729813i
$879$	14.2426	−	24.6690i	0.480392	−	0.832064i
$880$	0.414214	+	0.717439i	0.0139631	+	0.0241849i
$881$	−2.38478			−0.0803452			−0.0401726	−	0.999193i	$-0.512791\pi$
$881$	−2.38478			−0.0803452			−0.0401726	+	0.999193i	$0.512791\pi$
$882$		0			0
$883$	−41.6569			−1.40186			−0.700932	−	0.713228i	$-0.747233\pi$
$883$	−41.6569			−1.40186			−0.700932	+	0.713228i	$0.747233\pi$
$884$	6.24264	+	10.8126i	0.209963	+	0.363666i
$885$	−14.6569	+	25.3864i	−0.492685	+	0.853355i
$886$	1.51472	−	2.62357i	0.0508880	−	0.0881405i
$887$	27.5563	+	47.7290i	0.925252	+	1.60258i	0.791156	+	0.611614i	$0.209480\pi$
$887$	27.5563	+	47.7290i	0.925252	+	1.60258i	0.134096	+	0.990968i	$0.457187\pi$
$888$	26.1421			0.877273
$889$		0			0
$890$	−12.7279			−0.426641
$891$	16.5563	+	28.6764i	0.554659	+	0.960697i
$892$	3.65685	−	6.33386i	0.122441	−	0.212073i
$893$	−1.51472	+	2.62357i	−0.0506881	+	0.0877944i
$894$	−10.2426	−	17.7408i	−0.342565	−	0.593340i
$895$	4.00000			0.133705
$896$		0			0
$897$	19.3137			0.644866
$898$	−8.31371	−	14.3998i	−0.277432	−	0.480526i
$899$	−6.82843	+	11.8272i	−0.227741	+	0.394459i
$900$	−4.32843	+	7.49706i	−0.144281	+	0.249902i
$901$	−8.38478	−	14.5229i	−0.279337	−	0.483827i
$902$	−2.54416			−0.0847111
$903$		0			0
$904$	15.3137			0.509326
$905$	1.24264	+	2.15232i	0.0413068	+	0.0715454i
$906$	−19.3137	+	33.4523i	−0.641655	+	1.11138i
$907$	−0.142136	+	0.246186i	−0.00471954	+	0.00817448i	−0.868376	−	0.495907i	$-0.834836\pi$
$907$	−0.142136	+	0.246186i	−0.00471954	+	0.00817448i	0.863656	+	0.504082i	$0.168169\pi$
$908$	−9.12132	−	15.7986i	−0.302702	−	0.524295i
$909$	115.255			3.82276
$910$		0			0
$911$	36.2843			1.20215			0.601076	−	0.799192i	$-0.294739\pi$
$911$	36.2843			1.20215			0.601076	+	0.799192i	$0.294739\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−0.928932	+	1.60896i	−0.0307432	+	0.0532487i
$914$	10.8284	−	18.7554i	0.358173	−	0.620373i
$915$	−15.8995	−	27.5387i	−0.525621	−	0.910402i
$916$	−16.1421			−0.533351
$917$		0			0
$918$	−49.9411			−1.64830
$919$	−7.75736	−	13.4361i	−0.255892	−	0.443217i	0.709246	−	0.704961i	$-0.249036\pi$
$919$	−7.75736	−	13.4361i	−0.255892	−	0.443217i	−0.965137	+	0.261744i	$0.915702\pi$
$920$	−0.585786	+	1.01461i	−0.0193128	+	0.0334508i
$921$	−25.4853	+	44.1418i	−0.839769	+	1.45452i
$922$	−6.41421	−	11.1097i	−0.211241	−	0.365880i
$923$	21.6569			0.712844
$924$		0			0
$925$	−7.65685			−0.251756
$926$	−8.48528	−	14.6969i	−0.278844	−	0.482971i
$927$	64.1838	−	111.170i	2.10807	−	3.65129i
$928$	−2.41421	+	4.18154i	−0.0792504	+	0.137266i
$929$	8.60660	+	14.9071i	0.282373	+	0.489085i	0.971969	−	0.235110i	$-0.0755449\pi$
$929$	8.60660	+	14.9071i	0.282373	+	0.489085i	−0.689595	+	0.724195i	$0.742212\pi$
$930$	9.65685			0.316661
$931$		0			0
$932$	23.3137			0.763666
$933$	−6.82843	−	11.8272i	−0.223553	−	0.387205i
$934$	−7.94975	+	13.7694i	−0.260124	+	0.450547i
$935$	1.07107	−	1.85514i	0.0350277	−	0.0606697i
$936$	−20.8995	−	36.1990i	−0.683121	−	1.18320i
$937$	20.2426			0.661298			0.330649	−	0.943754i	$-0.392732\pi$
$937$	20.2426			0.661298			0.330649	+	0.943754i	$0.392732\pi$
$938$		0			0
$939$	49.1127			1.60273
$940$	−2.58579	−	4.47871i	−0.0843391	−	0.146080i
$941$	25.0000	−	43.3013i	0.814977	−	1.41158i	−0.0943679	−	0.995537i	$-0.530083\pi$
$941$	25.0000	−	43.3013i	0.814977	−	1.41158i	0.909345	−	0.416044i	$-0.136584\pi$
$942$	11.0711	−	19.1757i	0.360715	−	0.624777i
$943$	−1.79899	−	3.11594i	−0.0585832	−	0.101469i
$944$	8.58579			0.279444
$945$		0			0
$946$	−7.31371			−0.237789
$947$	2.41421	+	4.18154i	0.0784514	+	0.135882i	0.902582	−	0.430518i	$-0.141669\pi$
$947$	2.41421	+	4.18154i	0.0784514	+	0.135882i	−0.824131	+	0.566400i	$0.808336\pi$
$948$	11.6569	−	20.1903i	0.378597	−	0.655749i
$949$	−22.7279	+	39.3659i	−0.737780	+	1.27787i
$950$	0.292893	+	0.507306i	0.00950271	+	0.0164592i
$951$	35.7990			1.16086
$952$		0			0
$953$	0.343146			0.0111156			0.00555779	−	0.999985i	$-0.498231\pi$
$953$	0.343146			0.0111156			0.00555779	+	0.999985i	$0.498231\pi$
$954$	28.0711	+	48.6205i	0.908834	+	1.57415i
$955$	−5.07107	+	8.78335i	−0.164096	+	0.284222i
$956$	−0.828427	+	1.43488i	−0.0267932	+	0.0464073i
$957$	−6.82843	−	11.8272i	−0.220732	−	0.382319i
$958$	17.1716			0.554788
$959$		0			0
$960$	3.41421			0.110193
$961$	11.5000	+	19.9186i	0.370968	+	0.642535i
$962$	18.4853	−	32.0174i	0.595989	−	1.03228i
$963$	−41.7990	+	72.3980i	−1.34695	+	2.33299i
$964$	6.70711	+	11.6170i	0.216021	+	0.374160i
$965$	5.65685			0.182101
$966$		0			0
$967$	−37.4558			−1.20450			−0.602249	−	0.798308i	$-0.705729\pi$
$967$	−37.4558			−1.20450			−0.602249	+	0.798308i	$0.705729\pi$
$968$	−5.15685	−	8.93193i	−0.165748	−	0.287083i
$969$	−2.58579	+	4.47871i	−0.0830674	+	0.143877i
$970$	−3.87868	+	6.71807i	−0.124537	+	0.215704i
$971$	16.6777	+	28.8866i	0.535212	+	0.927014i	0.999153	+	0.0411482i	$0.0131016\pi$
$971$	16.6777	+	28.8866i	0.535212	+	0.927014i	−0.463941	+	0.885866i	$0.653565\pi$
$972$	78.5269			2.51875
$973$		0			0
$974$	−31.7990			−1.01891
$975$	8.24264	+	14.2767i	0.263976	+	0.457219i
$976$	−4.65685	+	8.06591i	−0.149062	+	0.258183i
$977$	6.34315	−	10.9867i	0.202935	−	0.351494i	−0.746538	−	0.665343i	$-0.768285\pi$
$977$	6.34315	−	10.9867i	0.202935	−	0.351494i	0.949473	+	0.313849i	$0.101619\pi$
$978$	−34.3848	−	59.5562i	−1.09950	−	1.90440i
$979$	−10.5442			−0.336993
$980$		0			0
$981$	21.5147			0.686912
$982$	16.1421	+	27.9590i	0.515116	+	0.892208i
$983$	6.10051	−	10.5664i	0.194576	−	0.337015i	−0.752186	−	0.658951i	$-0.771000\pi$
$983$	6.10051	−	10.5664i	0.194576	−	0.337015i	0.946761	+	0.321936i	$0.104334\pi$
$984$	−5.24264	+	9.08052i	−0.167129	+	0.289476i
$985$	12.8995	+	22.3426i	0.411012	+	0.711894i
$986$	12.4853			0.397612
$987$		0			0
$988$	−2.82843			−0.0899843
$989$	−5.17157	−	8.95743i	−0.164446	−	0.284830i
$990$	−3.58579	+	6.21076i	−0.113964	+	0.197391i
$991$	−22.3848	+	38.7716i	−0.711076	+	1.23162i	0.253378	+	0.967367i	$0.418458\pi$
$991$	−22.3848	+	38.7716i	−0.711076	+	1.23162i	−0.964454	+	0.264252i	$0.914875\pi$
$992$	−1.41421	−	2.44949i	−0.0449013	−	0.0777714i
$993$	115.397			3.66201
$994$		0			0
$995$	16.4853			0.522619
$996$	3.82843	+	6.63103i	0.121308	+	0.210112i
$997$	9.14214	−	15.8346i	0.289534	−	0.501488i	−0.684164	−	0.729328i	$-0.739833\pi$
$997$	9.14214	−	15.8346i	0.289534	−	0.501488i	0.973699	+	0.227840i	$0.0731662\pi$
$998$	15.1716	−	26.2779i	0.480248	−	0.831813i
$999$	73.9411	+	128.070i	2.33939	+	4.05195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.i.361.1		4
7.2	even	3	inner	490.2.e.i.471.1		4
7.3	odd	6		490.2.a.l.1.1	✓	2
7.4	even	3		490.2.a.m.1.2	yes	2
7.5	odd	6		490.2.e.j.471.2		4
7.6	odd	2		490.2.e.j.361.2		4
21.11	odd	6		4410.2.a.bt.1.2		2
21.17	even	6		4410.2.a.by.1.2		2
28.3	even	6		3920.2.a.ca.1.2		2
28.11	odd	6		3920.2.a.bm.1.1		2
35.3	even	12		2450.2.c.w.99.3		4
35.4	even	6		2450.2.a.bn.1.1		2
35.17	even	12		2450.2.c.w.99.2		4
35.18	odd	12		2450.2.c.t.99.4		4
35.24	odd	6		2450.2.a.bs.1.2		2
35.32	odd	12		2450.2.c.t.99.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.a.l.1.1	✓	2	7.3	odd	6
490.2.a.m.1.2	yes	2	7.4	even	3
490.2.e.i.361.1		4	1.1	even	1	trivial
490.2.e.i.471.1		4	7.2	even	3	inner
490.2.e.j.361.2		4	7.6	odd	2
490.2.e.j.471.2		4	7.5	odd	6
2450.2.a.bn.1.1		2	35.4	even	6
2450.2.a.bs.1.2		2	35.24	odd	6
2450.2.c.t.99.1		4	35.32	odd	12
2450.2.c.t.99.4		4	35.18	odd	12
2450.2.c.w.99.2		4	35.17	even	12
2450.2.c.w.99.3		4	35.3	even	12
3920.2.a.bm.1.1		2	28.11	odd	6
3920.2.a.ca.1.2		2	28.3	even	6
4410.2.a.bt.1.2		2	21.11	odd	6
4410.2.a.by.1.2		2	21.17	even	6

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.414214 - 0.717439i) q^{11} +(-1.70711 - 2.95680i) q^{12} -4.82843 q^{13} +3.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 + 2.23936i) q^{17} +(4.32843 - 7.49706i) q^{18} +(-0.292893 - 0.507306i) q^{19} +1.00000 q^{20} +0.828427 q^{22} +(0.585786 + 1.01461i) q^{23} +(1.70711 - 2.95680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.41421 - 4.18154i) q^{26} +19.3137 q^{27} -4.82843 q^{29} +(1.70711 + 2.95680i) q^{30} +(1.41421 - 2.44949i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.41421 + 2.44949i) q^{33} -2.58579 q^{34} +8.65685 q^{36} +(3.82843 + 6.63103i) q^{37} +(0.292893 - 0.507306i) q^{38} +(8.24264 - 14.2767i) q^{39} +(0.500000 + 0.866025i) q^{40} -3.07107 q^{41} -8.82843 q^{43} +(0.414214 + 0.717439i) q^{44} +(-4.32843 + 7.49706i) q^{45} +(-0.585786 + 1.01461i) q^{46} +(-2.58579 - 4.47871i) q^{47} +3.41421 q^{48} -1.00000 q^{50} +(-4.41421 - 7.64564i) q^{51} +(2.41421 - 4.18154i) q^{52} +(-3.24264 + 5.61642i) q^{53} +(9.65685 + 16.7262i) q^{54} -0.828427 q^{55} +2.00000 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-4.29289 + 7.43551i) q^{59} +(-1.70711 + 2.95680i) q^{60} +(-4.65685 - 8.06591i) q^{61} +2.82843 q^{62} +1.00000 q^{64} +(2.41421 + 4.18154i) q^{65} +(-1.41421 + 2.44949i) q^{66} +(-0.828427 + 1.43488i) q^{67} +(-1.29289 - 2.23936i) q^{68} -4.00000 q^{69} -4.48528 q^{71} +(4.32843 + 7.49706i) q^{72} +(4.70711 - 8.15295i) q^{73} +(-3.82843 + 6.63103i) q^{74} +(-1.70711 - 2.95680i) q^{75} +0.585786 q^{76} +16.4853 q^{78} +(3.41421 + 5.91359i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-19.9853 + 34.6155i) q^{81} +(-1.53553 - 2.65962i) q^{82} -2.24264 q^{83} +2.58579 q^{85} +(-4.41421 - 7.64564i) q^{86} +(8.24264 - 14.2767i) q^{87} +(-0.414214 + 0.717439i) q^{88} +(-6.36396 - 11.0227i) q^{89} -8.65685 q^{90} -1.17157 q^{92} +(4.82843 + 8.36308i) q^{93} +(2.58579 - 4.47871i) q^{94} +(-0.292893 + 0.507306i) q^{95} +(1.70711 + 2.95680i) q^{96} -7.75736 q^{97} -7.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{8} - 6 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} + 8 q^{23} + 4 q^{24} - 2 q^{25} - 4 q^{26} + 32 q^{27} - 8 q^{29} + 4 q^{30} + 2 q^{32} - 16 q^{34} + 12 q^{36} + 4 q^{37} + 4 q^{38} + 16 q^{39} + 2 q^{40} + 16 q^{41} - 24 q^{43} - 4 q^{44} - 6 q^{45} - 8 q^{46} - 16 q^{47} + 8 q^{48} - 4 q^{50} - 12 q^{51} + 4 q^{52} + 4 q^{53} + 16 q^{54} + 8 q^{55} + 8 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} + 4 q^{61} + 4 q^{64} + 4 q^{65} + 8 q^{67} - 8 q^{68} - 16 q^{69} + 16 q^{71} + 6 q^{72} + 16 q^{73} - 4 q^{74} - 4 q^{75} + 8 q^{76} + 32 q^{78} + 8 q^{79} - 2 q^{80} - 46 q^{81} + 8 q^{82} + 8 q^{83} + 16 q^{85} - 12 q^{86} + 16 q^{87} + 4 q^{88} - 12 q^{90} - 16 q^{92} + 8 q^{93} + 16 q^{94} - 4 q^{95} + 4 q^{96} - 48 q^{97} - 40 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^8 - 6 * q^9 + 2 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 + 8 * q^23 + 4 * q^24 - 2 * q^25 - 4 * q^26 + 32 * q^27 - 8 * q^29 + 4 * q^30 + 2 * q^32 - 16 * q^34 + 12 * q^36 + 4 * q^37 + 4 * q^38 + 16 * q^39 + 2 * q^40 + 16 * q^41 - 24 * q^43 - 4 * q^44 - 6 * q^45 - 8 * q^46 - 16 * q^47 + 8 * q^48 - 4 * q^50 - 12 * q^51 + 4 * q^52 + 4 * q^53 + 16 * q^54 + 8 * q^55 + 8 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 + 4 * q^61 + 4 * q^64 + 4 * q^65 + 8 * q^67 - 8 * q^68 - 16 * q^69 + 16 * q^71 + 6 * q^72 + 16 * q^73 - 4 * q^74 - 4 * q^75 + 8 * q^76 + 32 * q^78 + 8 * q^79 - 2 * q^80 - 46 * q^81 + 8 * q^82 + 8 * q^83 + 16 * q^85 - 12 * q^86 + 16 * q^87 + 4 * q^88 - 12 * q^90 - 16 * q^92 + 8 * q^93 + 16 * q^94 - 4 * q^95 + 4 * q^96 - 48 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more