LMFDB - Embedded newform 115.5.f.a.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(47,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("115.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	115.47
Dual form			115.5.f.a.93.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.73356 - 4.73356i) q^{2} +(-10.2373 + 10.2373i) q^{3} +28.8132i q^{4} +(11.3791 - 22.2602i) q^{5} +96.9182 q^{6} +(-46.2071 - 46.2071i) q^{7} +(60.6523 - 60.6523i) q^{8} -128.606i q^{9} +(-159.234 + 51.5063i) q^{10} -142.458 q^{11} +(-294.971 - 294.971i) q^{12} +(170.253 - 170.253i) q^{13} +437.449i q^{14} +(111.393 + 344.377i) q^{15} -113.191 q^{16} +(-307.132 - 307.132i) q^{17} +(-608.766 + 608.766i) q^{18} +365.421i q^{19} +(641.388 + 327.869i) q^{20} +946.077 q^{21} +(674.334 + 674.334i) q^{22} +(-77.9968 + 77.9968i) q^{23} +1241.84i q^{24} +(-366.032 - 506.602i) q^{25} -1611.80 q^{26} +(487.362 + 487.362i) q^{27} +(1331.38 - 1331.38i) q^{28} +814.293i q^{29} +(1102.84 - 2157.42i) q^{30} +792.560 q^{31} +(-434.639 - 434.639i) q^{32} +(1458.39 - 1458.39i) q^{33} +2907.66i q^{34} +(-1554.38 + 502.784i) q^{35} +3705.57 q^{36} +(1164.78 + 1164.78i) q^{37} +(1729.74 - 1729.74i) q^{38} +3485.87i q^{39} +(-659.964 - 2040.30i) q^{40} +607.580 q^{41} +(-4478.31 - 4478.31i) q^{42} +(-2209.30 + 2209.30i) q^{43} -4104.68i q^{44} +(-2862.80 - 1463.42i) q^{45} +738.406 q^{46} +(394.124 + 394.124i) q^{47} +(1158.78 - 1158.78i) q^{48} +1869.20i q^{49} +(-665.395 + 4130.67i) q^{50} +6288.43 q^{51} +(4905.54 + 4905.54i) q^{52} +(-3207.52 + 3207.52i) q^{53} -4613.92i q^{54} +(-1621.04 + 3171.14i) q^{55} -5605.14 q^{56} +(-3740.94 - 3740.94i) q^{57} +(3854.51 - 3854.51i) q^{58} -646.937i q^{59} +(-9922.62 + 3209.61i) q^{60} -362.470 q^{61} +(-3751.63 - 3751.63i) q^{62} +(-5942.53 + 5942.53i) q^{63} +5925.84i q^{64} +(-1852.54 - 5727.18i) q^{65} -13806.8 q^{66} +(383.721 + 383.721i) q^{67} +(8849.48 - 8849.48i) q^{68} -1596.96i q^{69} +(9737.70 + 4977.77i) q^{70} +1269.41 q^{71} +(-7800.27 - 7800.27i) q^{72} +(53.1213 - 53.1213i) q^{73} -11027.2i q^{74} +(8933.45 + 1439.06i) q^{75} -10529.0 q^{76} +(6582.58 + 6582.58i) q^{77} +(16500.6 - 16500.6i) q^{78} -3461.26i q^{79} +(-1288.02 + 2519.66i) q^{80} +438.526 q^{81} +(-2876.02 - 2876.02i) q^{82} +(3869.32 - 3869.32i) q^{83} +27259.5i q^{84} +(-10331.7 + 3341.93i) q^{85} +20915.7 q^{86} +(-8336.20 - 8336.20i) q^{87} +(-8640.41 + 8640.41i) q^{88} -10803.4i q^{89} +(6624.04 + 20478.5i) q^{90} -15733.8 q^{91} +(-2247.34 - 2247.34i) q^{92} +(-8113.71 + 8113.71i) q^{93} -3731.23i q^{94} +(8134.34 + 4158.16i) q^{95} +8899.09 q^{96} +(4239.27 + 4239.27i) q^{97} +(8847.98 - 8847.98i) q^{98} +18321.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) $ 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−4.73356	−	4.73356i	−1.18339	−	1.18339i	−0.978860	−	0.204531i	$-0.934433\pi$
$2$	−4.73356	−	4.73356i	−1.18339	−	1.18339i	−0.204531	−	0.978860i	$-0.565567\pi$
$3$	−10.2373	+	10.2373i	−1.13748	+	1.13748i	−0.148582	+	0.988900i	$0.547471\pi$
$3$	−10.2373	+	10.2373i	−1.13748	+	1.13748i	−0.988900	+	0.148582i	$0.952529\pi$
$4$			28.8132i			1.80083i
$5$	11.3791	−	22.2602i	0.455164	−	0.890408i
$5$	11.3791	−	22.2602i	0.455164	−	0.890408i
$6$	96.9182			2.69217
$7$	−46.2071	−	46.2071i	−0.943003	−	0.943003i	0.0554581	−	0.998461i	$-0.482338\pi$
$7$	−46.2071	−	46.2071i	−0.943003	−	0.943003i	−0.998461	+	0.0554581i	$0.982338\pi$
$8$	60.6523	−	60.6523i	0.947693	−	0.947693i
$9$		−	128.606i		−	1.58773i
$10$	−159.234	+	51.5063i	−1.59234	+	0.515063i
$11$	−142.458			−1.17734			−0.588669	−	0.808374i	$-0.700348\pi$
$11$	−142.458			−1.17734			−0.588669	+	0.808374i	$0.700348\pi$
$12$	−294.971	−	294.971i	−2.04841	−	2.04841i
$13$	170.253	−	170.253i	1.00741	−	1.00741i	0.00744072	−	0.999972i	$-0.497632\pi$
$13$	170.253	−	170.253i	1.00741	−	1.00741i	0.999972	−	0.00744072i	$-0.00236848\pi$
$14$			437.449i			2.23188i
$15$	111.393	+	344.377i	0.495082	+	1.53056i
$16$	−113.191			−0.442154
$17$	−307.132	−	307.132i	−1.06274	−	1.06274i	−0.997895	−	0.0648457i	$-0.979344\pi$
$17$	−307.132	−	307.132i	−1.06274	−	1.06274i	−0.0648457	−	0.997895i	$-0.520656\pi$
$18$	−608.766	+	608.766i	−1.87891	+	1.87891i
$19$			365.421i			1.01225i	0.862461	+	0.506123i	$0.168922\pi$
$19$			365.421i			1.01225i	−0.862461	+	0.506123i	$0.831078\pi$
$20$	641.388	+	327.869i	1.60347	+	0.819672i
$21$	946.077			2.14530
$22$	674.334	+	674.334i	1.39325	+	1.39325i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			1241.84i			2.15597i
$25$	−366.032	−	506.602i	−0.585652	−	0.810563i
$26$	−1611.80			−2.38433
$27$	487.362	+	487.362i	0.668535	+	0.668535i
$28$	1331.38	−	1331.38i	1.69819	−	1.69819i
$29$			814.293i			0.968244i	0.875001	+	0.484122i	$0.160861\pi$
$29$			814.293i			0.968244i	−0.875001	+	0.484122i	$0.839139\pi$
$30$	1102.84	−	2157.42i	1.22538	−	2.39713i
$31$	792.560			0.824724			0.412362	−	0.911020i	$-0.364704\pi$
$31$	792.560			0.824724			0.412362	+	0.911020i	$0.364704\pi$
$32$	−434.639	−	434.639i	−0.424452	−	0.424452i
$33$	1458.39	−	1458.39i	1.33920	−	1.33920i
$34$			2907.66i			2.51528i
$35$	−1554.38	+	502.784i	−1.26888	+	0.410436i
$36$	3705.57			2.85923
$37$	1164.78	+	1164.78i	0.850829	+	0.850829i	0.990235	−	0.139407i	$-0.0445195\pi$
$37$	1164.78	+	1164.78i	0.850829	+	0.850829i	−0.139407	+	0.990235i	$0.544520\pi$
$38$	1729.74	−	1729.74i	1.19788	−	1.19788i
$39$			3485.87i			2.29183i
$40$	−659.964	−	2040.30i	−0.412477	−	1.27519i
$41$	607.580			0.361440			0.180720	−	0.983535i	$-0.442157\pi$
$41$	607.580			0.361440			0.180720	+	0.983535i	$0.442157\pi$
$42$	−4478.31	−	4478.31i	−2.53873	−	2.53873i
$43$	−2209.30	+	2209.30i	−1.19486	+	1.19486i	−0.219178	+	0.975685i	$0.570337\pi$
$43$	−2209.30	+	2209.30i	−1.19486	+	1.19486i	−0.975685	+	0.219178i	$0.929663\pi$
$44$		−	4104.68i		−	2.12018i
$45$	−2862.80	−	1463.42i	−1.41373	−	0.722679i
$46$	738.406			0.348963
$47$	394.124	+	394.124i	0.178418	+	0.178418i	0.790666	−	0.612248i	$-0.209735\pi$
$47$	394.124	+	394.124i	0.178418	+	0.178418i	−0.612248	+	0.790666i	$0.709735\pi$
$48$	1158.78	−	1158.78i	0.502942	−	0.502942i
$49$			1869.20i			0.778509i
$50$	−665.395	+	4130.67i	−0.266158	+	1.65227i
$51$	6288.43			2.41770
$52$	4905.54	+	4905.54i	1.81418	+	1.81418i
$53$	−3207.52	+	3207.52i	−1.14187	+	1.14187i	−0.153767	+	0.988107i	$0.549141\pi$
$53$	−3207.52	+	3207.52i	−1.14187	+	1.14187i	−0.988107	+	0.153767i	$0.950859\pi$
$54$		−	4613.92i		−	1.58228i
$55$	−1621.04	+	3171.14i	−0.535882	+	1.04831i
$56$	−5605.14			−1.78735
$57$	−3740.94	−	3740.94i	−1.15141	−	1.15141i
$58$	3854.51	−	3854.51i	1.14581	−	1.14581i
$59$		−	646.937i		−	0.185848i	−0.995673	−	0.0929241i	$-0.970379\pi$
$59$		−	646.937i		−	0.185848i	0.995673	−	0.0929241i	$-0.0296214\pi$
$60$	−9922.62	+	3209.61i	−2.75628	+	0.891558i
$61$	−362.470			−0.0974121			−0.0487061	−	0.998813i	$-0.515510\pi$
$61$	−362.470			−0.0974121			−0.0487061	+	0.998813i	$0.515510\pi$
$62$	−3751.63	−	3751.63i	−0.975971	−	0.975971i
$63$	−5942.53	+	5942.53i	−1.49724	+	1.49724i
$64$			5925.84i			1.44674i
$65$	−1852.54	−	5727.18i	−0.438470	−	1.35555i
$66$	−13806.8			−3.16960
$67$	383.721	+	383.721i	0.0854803	+	0.0854803i	0.748554	−	0.663074i	$-0.230748\pi$
$67$	383.721	+	383.721i	0.0854803	+	0.0854803i	−0.663074	+	0.748554i	$0.730748\pi$
$68$	8849.48	−	8849.48i	1.91381	−	1.91381i
$69$		−	1596.96i		−	0.335425i
$70$	9737.70	+	4977.77i	1.98728	+	1.01587i
$71$	1269.41			0.251817			0.125908	−	0.992042i	$-0.459815\pi$
$71$	1269.41			0.251817			0.125908	+	0.992042i	$0.459815\pi$
$72$	−7800.27	−	7800.27i	−1.50468	−	1.50468i
$73$	53.1213	−	53.1213i	0.00996834	−	0.00996834i	−0.702105	−	0.712073i	$-0.747756\pi$
$73$	53.1213	−	53.1213i	0.00996834	−	0.00996834i	0.712073	+	0.702105i	$0.247756\pi$
$74$		−	11027.2i		−	2.01373i
$75$	8933.45	+	1439.06i	1.58817	+	0.255833i
$76$	−10529.0			−1.82288
$77$	6582.58	+	6582.58i	1.11023	+	1.11023i
$78$	16500.6	−	16500.6i	2.71213	−	2.71213i
$79$		−	3461.26i		−	0.554600i	−0.960783	−	0.277300i	$-0.910560\pi$
$79$		−	3461.26i		−	0.554600i	0.960783	−	0.277300i	$-0.0894396\pi$
$80$	−1288.02	+	2519.66i	−0.201252	+	0.393697i
$81$	438.526			0.0668383
$82$	−2876.02	−	2876.02i	−0.427724	−	0.427724i
$83$	3869.32	−	3869.32i	0.561667	−	0.561667i	−0.368114	−	0.929781i	$-0.619996\pi$
$83$	3869.32	−	3869.32i	0.561667	−	0.561667i	0.929781	+	0.368114i	$0.119996\pi$
$84$			27259.5i			3.86331i
$85$	−10331.7	+	3341.93i	−1.42999	+	0.462551i
$86$	20915.7			2.82798
$87$	−8336.20	−	8336.20i	−1.10136	−	1.10136i
$88$	−8640.41	+	8640.41i	−1.11576	+	1.11576i
$89$		−	10803.4i		−	1.36390i	−0.731399	−	0.681950i	$-0.761132\pi$
$89$		−	10803.4i		−	1.36390i	0.731399	−	0.681950i	$-0.238868\pi$
$90$	6624.04	+	20478.5i	0.817783	+	2.52821i
$91$	−15733.8			−1.89999
$92$	−2247.34	−	2247.34i	−0.265518	−	0.265518i
$93$	−8113.71	+	8113.71i	−0.938109	+	0.938109i
$94$		−	3731.23i		−	0.422276i
$95$	8134.34	+	4158.16i	0.901312	+	0.460738i
$96$	8899.09			0.965613
$97$	4239.27	+	4239.27i	0.450555	+	0.450555i	0.895539	−	0.444984i	$-0.146790\pi$
$97$	4239.27	+	4239.27i	0.450555	+	0.450555i	−0.444984	+	0.895539i	$0.646790\pi$
$98$	8847.98	−	8847.98i	0.921280	−	0.921280i
$99$			18321.0i			1.86930i
$100$	14596.8	−	10546.6i	1.45968	−	1.05466i
$101$	−1961.58			−0.192293			−0.0961467	−	0.995367i	$-0.530652\pi$
$101$	−1961.58			−0.192293			−0.0961467	+	0.995367i	$0.530652\pi$
$102$	−29766.7	−	29766.7i	−2.86108	−	2.86108i
$103$	2578.93	−	2578.93i	0.243089	−	0.243089i	−0.575038	−	0.818127i	$-0.695013\pi$
$103$	2578.93	−	2578.93i	0.243089	−	0.243089i	0.818127	+	0.575038i	$0.195013\pi$
$104$		−	20652.5i		−	1.90944i
$105$	10765.5	−	21059.8i	0.976463	−	1.91019i
$106$	30366.0			2.70257
$107$	3976.50	+	3976.50i	0.347323	+	0.347323i	0.859111	−	0.511789i	$-0.171017\pi$
$107$	3976.50	+	3976.50i	0.347323	+	0.347323i	−0.511789	+	0.859111i	$0.671017\pi$
$108$	−14042.5	+	14042.5i	−1.20392	+	1.20392i
$109$			11571.5i			0.973949i	0.873416	+	0.486974i	$0.161900\pi$
$109$			11571.5i			0.973949i	−0.873416	+	0.486974i	$0.838100\pi$
$110$	22684.1	−	7337.49i	1.87472	−	0.606404i
$111$	−23848.6			−1.93560
$112$	5230.25	+	5230.25i	0.416952	+	0.416952i
$113$	3371.82	−	3371.82i	0.264063	−	0.264063i	−0.562640	−	0.826702i	$-0.690214\pi$
$113$	3371.82	−	3371.82i	0.264063	−	0.264063i	0.826702	+	0.562640i	$0.190214\pi$
$114$			35416.0i			2.72514i
$115$	848.690	+	2623.76i	0.0641732	+	0.198394i
$116$	−23462.4			−1.74364
$117$	−21895.6	−	21895.6i	−1.59950	−	1.59950i
$118$	−3062.32	+	3062.32i	−0.219931	+	0.219931i
$119$			28383.4i			2.00434i
$120$	27643.5	+	14131.0i	1.91969	+	0.981319i
$121$	5653.28			0.386126
$122$	1715.78	+	1715.78i	0.115277	+	0.115277i
$123$	−6220.00	+	6220.00i	−0.411131	+	0.411131i
$124$			22836.2i			1.48519i
$125$	−15442.2	+	2383.27i	−0.988299	+	0.152530i
$126$	56258.7			3.54363
$127$	5027.61	+	5027.61i	0.311712	+	0.311712i	0.845573	−	0.533860i	$-0.179259\pi$
$127$	5027.61	+	5027.61i	0.311712	+	0.311712i	−0.533860	+	0.845573i	$0.679259\pi$
$128$	21096.1	−	21096.1i	1.28761	−	1.28761i
$129$		−	45234.7i		−	2.71827i
$130$	−18340.9	+	35879.1i	−1.08526	+	2.12302i
$131$	−25770.7			−1.50170			−0.750850	−	0.660473i	$-0.770356\pi$
$131$	−25770.7			−1.50170			−0.750850	+	0.660473i	$0.770356\pi$
$132$	42021.0	+	42021.0i	2.41167	+	2.41167i
$133$	16885.1	−	16885.1i	0.954552	−	0.954552i
$134$		−	3632.74i		−	0.202313i
$135$	16394.5	−	5303.03i	0.899562	−	0.290976i
$136$	−37256.6			−2.01430
$137$	14491.9	+	14491.9i	0.772121	+	0.772121i	0.978477	−	0.206356i	$-0.0661605\pi$
$137$	14491.9	+	14491.9i	0.772121	+	0.772121i	−0.206356	+	0.978477i	$0.566161\pi$
$138$	−7559.31	+	7559.31i	−0.396939	+	0.396939i
$139$			5423.14i			0.280686i	0.990103	+	0.140343i	$0.0448206\pi$
$139$			5423.14i			0.280686i	−0.990103	+	0.140343i	$0.955179\pi$
$140$	−14486.8	−	44786.6i	−0.739125	−	2.28503i
$141$	−8069.57			−0.405894
$142$	−6008.82	−	6008.82i	−0.297998	−	0.297998i
$143$	−24253.9	+	24253.9i	−1.18607	+	1.18607i
$144$			14557.1i			0.702022i
$145$	18126.3	+	9265.92i	0.862132	+	0.440710i
$146$	−502.906			−0.0235929
$147$	−19135.6	−	19135.6i	−0.885540	−	0.885540i
$148$	−33561.2	+	33561.2i	−1.53220	+	1.53220i
$149$			20447.5i			0.921017i	0.887655	+	0.460509i	$0.152333\pi$
$149$			20447.5i			0.921017i	−0.887655	+	0.460509i	$0.847667\pi$
$150$	−35475.2	−	49098.9i	−1.57667	−	2.18218i
$151$	30628.2			1.34328			0.671642	−	0.740876i	$-0.265589\pi$
$151$	30628.2			1.34328			0.671642	+	0.740876i	$0.265589\pi$
$152$	22163.6	+	22163.6i	0.959299	+	0.959299i
$153$	−39499.1	+	39499.1i	−1.68735	+	1.68735i
$154$		−	62318.1i		−	2.62768i
$155$	9018.62	−	17642.5i	0.375385	−	0.734341i
$156$	−100439.			−4.12719
$157$	13826.1	+	13826.1i	0.560921	+	0.560921i	0.929569	−	0.368648i	$-0.120179\pi$
$157$	13826.1	+	13826.1i	0.560921	+	0.560921i	−0.368648	+	0.929569i	$0.620179\pi$
$158$	−16384.1	+	16384.1i	−0.656309	+	0.656309i
$159$		−	65673.1i		−	2.59772i
$160$	−14620.9	+	4729.35i	−0.571131	+	0.184740i
$161$	7208.02			0.278076
$162$	−2075.79	−	2075.79i	−0.0790958	−	0.0790958i
$163$	−14717.4	+	14717.4i	−0.553930	+	0.553930i	−0.927573	−	0.373643i	$-0.878109\pi$
$163$	−14717.4	+	14717.4i	−0.553930	+	0.553930i	0.373643	+	0.927573i	$0.378109\pi$
$164$			17506.4i			0.650891i
$165$	−15868.9	−	49059.2i	−0.582879	−	1.80199i
$166$	−36631.4			−1.32934
$167$	10153.6	+	10153.6i	0.364071	+	0.364071i	0.865309	−	0.501238i	$-0.167122\pi$
$167$	10153.6	+	10153.6i	0.364071	+	0.364071i	−0.501238	+	0.865309i	$0.667122\pi$
$168$	57381.7	−	57381.7i	2.03308	−	2.03308i
$169$		−	29411.0i		−	1.02976i
$170$	64725.0	+	33086.5i	2.23962	+	1.14486i
$171$	46995.5			1.60718
$172$	−63657.1	−	63657.1i	−2.15174	−	2.15174i
$173$	36871.1	−	36871.1i	1.23195	−	1.23195i	0.268739	−	0.963213i	$-0.413393\pi$
$173$	36871.1	−	36871.1i	1.23195	−	1.23195i	0.963213	−	0.268739i	$-0.0866068\pi$
$174$			78919.8i			2.60668i
$175$	−6495.32	+	40321.9i	−0.212092	+	1.31663i
$176$	16125.0			0.520565
$177$	6622.92	+	6622.92i	0.211399	+	0.211399i
$178$	−51138.8	+	51138.8i	−1.61403	+	1.61403i
$179$			4934.93i			0.154019i	0.997030	+	0.0770096i	$0.0245372\pi$
$179$			4934.93i			0.154019i	−0.997030	+	0.0770096i	$0.975463\pi$
$180$	42166.0	−	82486.6i	1.30142	−	2.54588i
$181$	62544.2			1.90911			0.954553	−	0.298040i	$-0.0963329\pi$
$181$	62544.2			1.90911			0.954553	+	0.298040i	$0.0963329\pi$
$182$	74476.9	+	74476.9i	2.24843	+	2.24843i
$183$	3710.73	−	3710.73i	0.110805	−	0.110805i
$184$			9461.37i			0.279459i
$185$	39182.5	−	12674.1i	1.14485	−	0.370318i
$186$	76813.5			2.22030
$187$	43753.4	+	43753.4i	1.25121	+	1.25121i
$188$	−11356.0	+	11356.0i	−0.321299	+	0.321299i
$189$		−	45039.2i		−	1.26086i
$190$	−18821.5	−	58187.4i	−0.521371	−	1.61184i
$191$	−38100.5			−1.04439			−0.522197	−	0.852825i	$-0.674887\pi$
$191$	−38100.5			−1.04439			−0.522197	+	0.852825i	$0.674887\pi$
$192$	−60664.9	−	60664.9i	−1.64564	−	1.64564i
$193$	−29741.2	+	29741.2i	−0.798442	+	0.798442i	−0.982850	−	0.184408i	$-0.940963\pi$
$193$	−29741.2	+	29741.2i	−0.798442	+	0.798442i	0.184408	+	0.982850i	$0.440963\pi$
$194$		−	40133.7i		−	1.06637i
$195$	77596.2	+	39666.1i	2.04066	+	1.04316i
$196$	−53857.7			−1.40196
$197$	−31841.1	−	31841.1i	−0.820456	−	0.820456i	0.165717	−	0.986173i	$-0.447006\pi$
$197$	−31841.1	−	31841.1i	−0.820456	−	0.820456i	−0.986173	+	0.165717i	$0.947006\pi$
$198$	86723.6	−	86723.6i	2.21211	−	2.21211i
$199$			4926.58i			0.124406i	0.998064	+	0.0622028i	$0.0198125\pi$
$199$			4926.58i			0.124406i	−0.998064	+	0.0622028i	$0.980187\pi$
$200$	−52927.3	−	8525.88i	−1.32318	−	0.213147i
$201$	−7856.57			−0.194465
$202$	9285.28	+	9285.28i	0.227558	+	0.227558i
$203$	37626.2	−	37626.2i	0.913057	−	0.913057i
$204$			181190.i			4.35386i
$205$	6913.71	−	13524.8i	0.164514	−	0.321829i
$206$	−24415.1			−0.575338
$207$	10030.9	+	10030.9i	0.234098	+	0.234098i
$208$	−19271.1	+	19271.1i	−0.445431	+	0.445431i
$209$		−	52057.1i		−	1.19176i
$210$	−150647.	+	48728.9i	−3.41604	+	1.10496i
$211$	7081.56			0.159061			0.0795306	−	0.996832i	$-0.474658\pi$
$211$	7081.56			0.159061			0.0795306	+	0.996832i	$0.474658\pi$
$212$	−92419.2	−	92419.2i	−2.05632	−	2.05632i
$213$	−12995.4	+	12995.4i	−0.286437	+	0.286437i
$214$		−	37646.0i		−	0.822038i
$215$	24039.6	+	74319.3i	0.520056	+	1.60777i
$216$	59119.3			1.26713
$217$	−36621.9	−	36621.9i	−0.777717	−	0.777717i
$218$	54774.4	−	54774.4i	1.15256	−	1.15256i
$219$			1087.64i			0.0226776i
$220$	−91370.9	−	46707.5i	−1.88783	−	0.965032i
$221$	−104580.			−2.14124
$222$	112889.	+	112889.i	2.29058	+	2.29058i
$223$	−48475.1	+	48475.1i	−0.974786	+	0.974786i	−0.999690	−	0.0249041i	$-0.992072\pi$
$223$	−48475.1	+	48475.1i	−0.974786	+	0.974786i	0.0249041	+	0.999690i	$0.492072\pi$
$224$			40166.8i			0.800519i
$225$	−65152.2	+	47074.1i	−1.28696	+	0.929858i
$226$	−31921.4			−0.624979
$227$	−2510.05	−	2510.05i	−0.0487113	−	0.0487113i	0.682332	−	0.731043i	$-0.260966\pi$
$227$	−2510.05	−	2510.05i	−0.0487113	−	0.0487113i	−0.731043	+	0.682332i	$0.760966\pi$
$228$	107789.	−	107789.i	2.07350	−	2.07350i
$229$			20794.8i			0.396537i	0.980148	+	0.198268i	$0.0635318\pi$
$229$			20794.8i			0.396537i	−0.980148	+	0.198268i	$0.936468\pi$
$230$	8402.39	−	16437.0i	0.158835	−	0.310719i
$231$	−134776.			−2.52574
$232$	49388.8	+	49388.8i	0.917598	+	0.917598i
$233$	−36321.7	+	36321.7i	−0.669044	+	0.669044i	−0.957495	−	0.288451i	$-0.906860\pi$
$233$	−36321.7	+	36321.7i	−0.669044	+	0.669044i	0.288451	+	0.957495i	$0.406860\pi$
$234$			207288.i			3.78567i
$235$	13258.1	−	4288.50i	0.240074	−	0.0776551i
$236$	18640.4			0.334680
$237$	35434.1	+	35434.1i	0.630848	+	0.630848i
$238$	134355.	−	134355.i	2.37191	−	2.37191i
$239$		−	105212.i		−	1.84192i	−0.389654	−	0.920961i	$-0.627405\pi$
$239$		−	105212.i		−	1.84192i	0.389654	−	0.920961i	$-0.372595\pi$
$240$	−12608.8	−	38980.5i	−0.218902	−	0.676744i
$241$	−84303.8			−1.45149			−0.725744	−	0.687965i	$-0.758504\pi$
$241$	−84303.8			−1.45149			−0.725744	+	0.687965i	$0.758504\pi$
$242$	−26760.1	−	26760.1i	−0.456938	−	0.456938i
$243$	−43965.7	+	43965.7i	−0.744563	+	0.744563i
$244$		−	10444.0i		−	0.175422i
$245$	41608.8	+	21269.8i	0.693190	+	0.354349i
$246$	58885.6			0.973058
$247$	62214.0	+	62214.0i	1.01975	+	1.01975i
$248$	48070.6	−	48070.6i	0.781585	−	0.781585i
$249$			79223.1i			1.27777i
$250$	84377.9	+	61815.1i	1.35005	+	0.989042i
$251$	−58444.7			−0.927679			−0.463840	−	0.885919i	$-0.653529\pi$
$251$	−58444.7			−0.927679			−0.463840	+	0.885919i	$0.653529\pi$
$252$	−171224.	−	171224.i	−2.69627	−	2.69627i
$253$	11111.3	−	11111.3i	0.173589	−	0.173589i
$254$		−	47597.0i		−	0.737755i
$255$	71556.7	−	139982.i	1.10045	−	2.15274i
$256$	−104906.			−1.60074
$257$	−48778.1	−	48778.1i	−0.738513	−	0.738513i	0.233777	−	0.972290i	$-0.424891\pi$
$257$	−48778.1	−	48778.1i	−0.738513	−	0.738513i	−0.972290	+	0.233777i	$0.924891\pi$
$258$	−214122.	+	214122.i	−3.21678	+	3.21678i
$259$		−	107643.i		−	1.60467i
$260$	165019.	−	53377.6i	2.44111	−	0.789609i
$261$	104723.			1.53731
$262$	121987.	+	121987.i	1.77710	+	1.77710i
$263$	−15907.6	+	15907.6i	−0.229981	+	0.229981i	−0.812685	−	0.582704i	$-0.801995\pi$
$263$	−15907.6	+	15907.6i	−0.229981	+	0.229981i	0.582704	+	0.812685i	$0.301995\pi$
$264$		−	176910.i		−	2.53830i
$265$	34901.4	+	107899.i	0.496994	+	1.53647i
$266$	−159853.			−2.25922
$267$	110599.	+	110599.i	1.55141	+	1.55141i
$268$	−11056.2	+	11056.2i	−0.153935	+	0.153935i
$269$			28292.8i			0.390995i	0.980704	+	0.195498i	$0.0626322\pi$
$269$			28292.8i			0.390995i	−0.980704	+	0.195498i	$0.937368\pi$
$270$	−102707.	−	52502.3i	−1.40887	−	0.720195i
$271$	−29275.0			−0.398619			−0.199310	−	0.979937i	$-0.563870\pi$
$271$	−29275.0			−0.398619			−0.199310	+	0.979937i	$0.563870\pi$
$272$	34764.7	+	34764.7i	0.469895	+	0.469895i
$273$	161072.	−	161072.i	2.16120	−	2.16120i
$274$		−	137197.i		−	1.82744i
$275$	52144.2	+	72169.5i	0.689510	+	0.954307i
$276$	46013.6			0.604043
$277$	−47465.6	−	47465.6i	−0.618614	−	0.618614i	0.326562	−	0.945176i	$-0.394110\pi$
$277$	−47465.6	−	47465.6i	−0.618614	−	0.618614i	−0.945176	+	0.326562i	$0.894110\pi$
$278$	25670.8	−	25670.8i	0.332162	−	0.332162i
$279$		−	101928.i		−	1.30944i
$280$	−63781.5	+	124772.i	−0.813539	+	1.59147i
$281$	47712.1			0.604249			0.302125	−	0.953268i	$-0.402304\pi$
$281$	47712.1			0.604249			0.302125	+	0.953268i	$0.402304\pi$
$282$	38197.8	+	38197.8i	0.480331	+	0.480331i
$283$	−22714.7	+	22714.7i	−0.283619	+	0.283619i	−0.834550	−	0.550932i	$-0.814273\pi$
$283$	−22714.7	+	22714.7i	−0.283619	+	0.283619i	0.550932	+	0.834550i	$0.314273\pi$
$284$			36575.8i			0.453479i
$285$	−125843.	+	40705.5i	−1.54931	+	0.501145i
$286$	229614.			2.80716
$287$	−28074.5	−	28074.5i	−0.340839	−	0.340839i
$288$	−55897.3	+	55897.3i	−0.673916	+	0.673916i
$289$			105139.i			1.25884i
$290$	−41941.3	−	129663.i	−0.498707	−	1.54177i
$291$	−86797.8			−1.02500
$292$	1530.60	+	1530.60i	0.0179513	+	0.0179513i
$293$	−80200.5	+	80200.5i	−0.934204	+	0.934204i	−0.997965	−	0.0637611i	$-0.979690\pi$
$293$	−80200.5	+	80200.5i	−0.934204	+	0.934204i	0.0637611	+	0.997965i	$0.479690\pi$
$294$			181160.i			2.09588i
$295$	−14400.9	−	7361.56i	−0.165481	−	0.0845914i
$296$	141294.			1.61265
$297$	−69428.6	−	69428.6i	−0.787092	−	0.787092i
$298$	96789.6	−	96789.6i	1.08992	−	1.08992i
$299$			26558.3i			0.297070i
$300$	−41464.0	+	257402.i	−0.460711	+	2.86002i
$301$	204171.			2.25352
$302$	−144981.	−	144981.i	−1.58963	−	1.58963i
$303$	20081.4	−	20081.4i	0.218730	−	0.218730i
$304$		−	41362.5i		−	0.447569i
$305$	−4124.59	+	8068.66i	−0.0443385	+	0.0867365i
$306$	373943.			3.99359
$307$	−31258.9	−	31258.9i	−0.331663	−	0.331663i	0.521555	−	0.853218i	$-0.325352\pi$
$307$	−31258.9	−	31258.9i	−0.331663	−	0.331663i	−0.853218	+	0.521555i	$0.825352\pi$
$308$	−189665.	+	189665.i	−1.99934	+	1.99934i
$309$			52802.8i			0.553019i
$310$	−126202.	+	40821.9i	−1.31324	+	0.424785i
$311$	165260.			1.70863			0.854315	−	0.519755i	$-0.173977\pi$
$311$	165260.			1.70863			0.854315	+	0.519755i	$0.173977\pi$
$312$	211426.	+	211426.i	2.17195	+	2.17195i
$313$	45420.9	−	45420.9i	0.463626	−	0.463626i	−0.436216	−	0.899842i	$-0.643682\pi$
$313$	45420.9	−	45420.9i	0.463626	−	0.463626i	0.899842	+	0.436216i	$0.143682\pi$
$314$		−	130894.i		−	1.32758i
$315$	64661.2	+	199903.i	0.651663	+	2.01464i
$316$	99730.1			0.998739
$317$	135278.	+	135278.i	1.34619	+	1.34619i	0.889754	+	0.456441i	$0.150876\pi$
$317$	135278.	+	135278.i	1.34619	+	1.34619i	0.456441	+	0.889754i	$0.349124\pi$
$318$	−310868.	+	310868.i	−3.07412	+	3.07412i
$319$		−	116003.i		−	1.13995i
$320$	131910.	+	67430.8i	1.28819	+	0.658503i
$321$	−81417.6			−0.790147
$322$	−34119.6	−	34119.6i	−0.329073	−	0.329073i
$323$	112233.	−	112233.i	1.07576	−	1.07576i
$324$			12635.4i			0.120364i
$325$	−148568.	−	23932.4i	−1.40656	−	0.226579i
$326$	139331.			1.31103
$327$	−118461.	−	118461.i	−1.10785	−	1.10785i
$328$	36851.1	−	36851.1i	0.342534	−	0.342534i
$329$		−	36422.7i		−	0.336497i
$330$	−157109.	+	307341.i	−1.44269	+	2.82224i
$331$	195713.			1.78633			0.893167	−	0.449725i	$-0.148478\pi$
$331$	195713.			1.78633			0.893167	+	0.449725i	$0.148478\pi$
$332$	111488.	+	111488.i	1.01147	+	1.01147i
$333$	149799.	−	149799.i	1.35089	−	1.35089i
$334$		−	96125.1i		−	0.861676i
$335$	12908.1	−	4175.30i	0.115020	−	0.0372048i
$336$	−107088.			−0.948551
$337$	−42300.4	−	42300.4i	−0.372465	−	0.372465i	0.495910	−	0.868374i	$-0.334835\pi$
$337$	−42300.4	−	42300.4i	−0.372465	−	0.372465i	−0.868374	+	0.495910i	$0.834835\pi$
$338$	−139219.	+	139219.i	−1.21861	+	1.21861i
$339$			69036.9i			0.600734i
$340$	−96291.9	−	297690.i	−0.832975	−	2.57517i
$341$	−112906.			−0.970980
$342$	−222456.	−	222456.i	−1.90192	−	1.90192i
$343$	−24573.0	+	24573.0i	−0.208867	+	0.208867i
$344$			267999.i			2.26473i
$345$	−35548.6	−	18172.0i	−0.298665	−	0.152673i
$346$	−349063.			−2.91576
$347$	−7623.30	−	7623.30i	−0.0633117	−	0.0633117i	0.674742	−	0.738054i	$-0.264255\pi$
$347$	−7623.30	−	7623.30i	−0.0633117	−	0.0633117i	−0.738054	+	0.674742i	$0.764255\pi$
$348$	240193.	−	240193.i	1.98336	−	1.98336i
$349$		−	226743.i		−	1.86159i	−0.365544	−	0.930794i	$-0.619117\pi$
$349$		−	226743.i		−	1.86159i	0.365544	−	0.930794i	$-0.380883\pi$
$350$	221612.	−	160120.i	1.80908	−	1.30711i
$351$	165950.			1.34698
$352$	61917.8	+	61917.8i	0.499724	+	0.499724i
$353$	−130258.	+	130258.i	−1.04534	+	1.04534i	−0.0464135	+	0.998922i	$0.514779\pi$
$353$	−130258.	+	130258.i	−1.04534	+	1.04534i	−0.998922	+	0.0464135i	$0.985221\pi$
$354$		−	62700.0i		−	0.500335i
$355$	14444.7	−	28257.3i	0.114618	−	0.224220i
$356$	311282.			2.45615
$357$	−290571.	−	290571.i	−2.27990	−	2.27990i
$358$	23359.8	−	23359.8i	0.182265	−	0.182265i
$359$		−	196175.i		−	1.52214i	−0.648670	−	0.761070i	$-0.724674\pi$
$359$		−	196175.i		−	1.52214i	0.648670	−	0.761070i	$-0.275326\pi$
$360$	−262396.	+	84875.5i	−2.02466	+	0.654903i
$361$	−3211.57			−0.0246435
$362$	−296057.	−	296057.i	−2.25922	−	2.25922i
$363$	−57874.5	+	57874.5i	−0.439212	+	0.439212i
$364$		−	453342.i		−	3.42155i
$365$	−578.018	−	1786.96i	−0.00433866	−	0.0134131i
$366$	−35130.0			−0.262250
$367$	64533.9	+	64533.9i	0.479133	+	0.479133i	0.904854	−	0.425722i	$-0.139980\pi$
$367$	64533.9	+	64533.9i	0.479133	+	0.479133i	−0.425722	+	0.904854i	$0.639980\pi$
$368$	8828.56	−	8828.56i	0.0651920	−	0.0651920i
$369$		−	78138.6i		−	0.573869i
$370$	−245467.	−	125479.i	−1.79304	−	0.916575i
$371$	296421.			2.15358
$372$	−233782.	−	233782.i	−1.68937	−	1.68937i
$373$	−120200.	+	120200.i	−0.863947	+	0.863947i	−0.991794	−	0.127847i	$-0.959193\pi$
$373$	−120200.	+	120200.i	−0.863947	+	0.863947i	0.127847	+	0.991794i	$0.459193\pi$
$374$		−	414219.i		−	2.96133i
$375$	133688.	−	182485.i	0.950673	−	1.29767i
$376$	47809.1			0.338170
$377$	138636.	+	138636.i	0.975421	+	0.975421i
$378$	−213196.	+	213196.i	−1.49209	+	1.49209i
$379$			197801.i			1.37705i	0.725212	+	0.688526i	$0.241742\pi$
$379$			197801.i			1.37705i	−0.725212	+	0.688526i	$0.758258\pi$
$380$	−119810.	+	234377.i	−0.829710	+	1.62311i
$381$	−102939.			−0.709134
$382$	180351.	+	180351.i	1.23593	+	1.23593i
$383$	−120092.	+	120092.i	−0.818686	+	0.818686i	−0.985918	−	0.167232i	$-0.946517\pi$
$383$	−120092.	+	120092.i	−0.818686	+	0.818686i	0.167232	+	0.985918i	$0.446517\pi$
$384$			431937.i			2.92926i
$385$	221433.	−	71625.6i	1.49390	−	0.483222i
$386$	281563.			1.88974
$387$	284130.	+	284130.i	1.89712	+	1.89712i
$388$	−122147.	+	122147.i	−0.811372	+	0.811372i
$389$			173105.i			1.14396i	0.820269	+	0.571978i	$0.193824\pi$
$389$			173105.i			1.14396i	−0.820269	+	0.571978i	$0.806176\pi$
$390$	−179545.	−	555068.i	−1.18044	−	3.64936i
$391$	47910.6			0.313385
$392$	113371.	+	113371.i	0.737787	+	0.737787i
$393$	263823.	−	263823.i	1.70816	−	1.70816i
$394$			301444.i			1.94184i
$395$	−77048.3	−	39386.0i	−0.493820	−	0.252434i
$396$	−527887.			−3.36629
$397$	−73626.1	−	73626.1i	−0.467144	−	0.467144i	0.433844	−	0.900988i	$-0.357157\pi$
$397$	−73626.1	−	73626.1i	−0.467144	−	0.467144i	−0.900988	+	0.433844i	$0.857157\pi$
$398$	23320.3	−	23320.3i	0.147220	−	0.147220i
$399$			345716.i			2.17157i
$400$	41431.7	+	57342.9i	0.258948	+	0.358393i
$401$	−299883.			−1.86494			−0.932468	−	0.361253i	$-0.882349\pi$
$401$	−299883.			−1.86494			−0.932468	+	0.361253i	$0.882349\pi$
$402$	37189.6	+	37189.6i	0.230128	+	0.230128i
$403$	134936.	−	134936.i	0.830838	−	0.830838i
$404$		−	56519.6i		−	0.346287i
$405$	4990.03	−	9761.67i	0.0304224	−	0.0595133i
$406$	−356212.			−2.16101
$407$	−165933.	−	165933.i	−1.00171	−	1.00171i
$408$	381408.	−	381408.i	2.29123	−	2.29123i
$409$			174665.i			1.04414i	0.852902	+	0.522070i	$0.174840\pi$
$409$			174665.i			1.04414i	−0.852902	+	0.522070i	$0.825160\pi$
$410$	−96747.2	+	31294.2i	−0.575534	+	0.186164i
$411$	−296718.			−1.75655
$412$	74307.4	+	74307.4i	0.437761	+	0.437761i
$413$	−29893.1	+	29893.1i	−0.175255	+	0.175255i
$414$		−	94963.6i		−	0.554060i
$415$	−42102.4	−	130161.i	−0.244462	−	0.755763i
$416$	−147997.			−0.855197
$417$	−55518.6	−	55518.6i	−0.319276	−	0.319276i
$418$	−246416.	+	246416.i	−1.41031	+	1.41031i
$419$		−	77120.5i		−	0.439280i	−0.975581	−	0.219640i	$-0.929512\pi$
$419$		−	77120.5i		−	0.439280i	0.975581	−	0.219640i	$-0.0704883\pi$
$420$	606803.	+	310189.i	3.43992	+	1.75844i
$421$	−82817.6			−0.467260			−0.233630	−	0.972326i	$-0.575060\pi$
$421$	−82817.6			−0.467260			−0.233630	+	0.972326i	$0.575060\pi$
$422$	−33521.0	−	33521.0i	−0.188232	−	0.188232i
$423$	50686.9	−	50686.9i	0.283279	−	0.283279i
$424$			389088.i			2.16429i
$425$	−43173.5	+	268014.i	−0.239023	+	1.48381i
$426$	123029.			0.677934
$427$	16748.7	+	16748.7i	0.0918599	+	0.0918599i
$428$	−114576.	+	114576.i	−0.625469	+	0.625469i
$429$		−	496590.i		−	2.69826i
$430$	238002.	−	465588.i	1.28719	−	2.51805i
$431$	−98817.1			−0.531958			−0.265979	−	0.963979i	$-0.585695\pi$
$431$	−98817.1			−0.531958			−0.265979	+	0.963979i	$0.585695\pi$
$432$	−55165.2	−	55165.2i	−0.295595	−	0.295595i
$433$	−13130.9	+	13130.9i	−0.0700355	+	0.0700355i	−0.741257	−	0.671221i	$-0.765770\pi$
$433$	−13130.9	+	13130.9i	−0.0700355	+	0.0700355i	0.671221	+	0.741257i	$0.265770\pi$
$434$			346704.i			1.84069i
$435$	−280424.	+	90706.9i	−1.48196	+	0.479360i
$436$	−333412.			−1.75391
$437$	−28501.7	−	28501.7i	−0.149248	−	0.149248i
$438$	5148.42	−	5148.42i	0.0268365	−	0.0268365i
$439$			25353.4i			0.131555i	0.997834	+	0.0657775i	$0.0209527\pi$
$439$			25353.4i			0.131555i	−0.997834	+	0.0657775i	$0.979047\pi$
$440$	94017.1	+	290657.i	0.485625	+	1.50133i
$441$	240391.			1.23606
$442$	495037.	+	495037.i	2.53392	+	2.53392i
$443$	113239.	−	113239.i	0.577019	−	0.577019i	−0.357062	−	0.934081i	$-0.616221\pi$
$443$	113239.	−	113239.i	0.577019	−	0.577019i	0.934081	+	0.357062i	$0.116221\pi$
$444$		−	687155.i		−	3.48569i
$445$	−240487.	−	122934.i	−1.21443	−	0.620798i
$446$	458920.			2.30711
$447$	−209328.	−	209328.i	−1.04764	−	1.04764i
$448$	273816.	−	273816.i	1.36428	−	1.36428i
$449$			227928.i			1.13059i	0.824888	+	0.565296i	$0.191238\pi$
$449$			227928.i			1.13059i	−0.824888	+	0.565296i	$0.808762\pi$
$450$	531230.	+	85574.1i	2.62336	+	0.422588i
$451$	−86554.6			−0.425537
$452$	97153.0	+	97153.0i	0.475532	+	0.475532i
$453$	−313551.	+	313551.i	−1.52796	+	1.52796i
$454$			23762.9i			0.115289i
$455$	−179036.	+	350237.i	−0.864806	+	1.69176i
$456$	−453793.			−2.18237
$457$	−105591.	−	105591.i	−0.505585	−	0.505585i	0.407583	−	0.913168i	$-0.366372\pi$
$457$	−105591.	−	105591.i	−0.505585	−	0.505585i	−0.913168	+	0.407583i	$0.866372\pi$
$458$	98433.5	−	98433.5i	0.469258	−	0.469258i
$459$		−	299369.i		−	1.42096i
$460$	−75599.0	+	24453.5i	−0.357273	+	0.115565i
$461$	140726.			0.662174			0.331087	−	0.943600i	$-0.392585\pi$
$461$	140726.			0.662174			0.331087	+	0.943600i	$0.392585\pi$
$462$	637972.	+	637972.i	2.98894	+	2.98894i
$463$	−67629.9	+	67629.9i	−0.315484	+	0.315484i	−0.847030	−	0.531546i	$-0.821611\pi$
$463$	−67629.9	+	67629.9i	−0.315484	+	0.315484i	0.531546	+	0.847030i	$0.321611\pi$
$464$		−	92170.9i		−	0.428113i
$465$	88286.0	+	272939.i	0.408306	+	1.26229i
$466$	343862.			1.58348
$467$	11535.9	+	11535.9i	0.0528954	+	0.0528954i	0.733060	−	0.680164i	$-0.238092\pi$
$467$	11535.9	+	11535.9i	0.0528954	+	0.0528954i	−0.680164	+	0.733060i	$0.738092\pi$
$468$	630883.	−	630883.i	2.88043	−	2.88043i
$469$		−	35461.3i		−	0.161216i
$470$	−83057.8	−	42458.0i	−0.375997	−	0.192205i
$471$	−283086.			−1.27608
$472$	−39238.3	−	39238.3i	−0.176127	−	0.176127i
$473$	314733.	−	314733.i	1.40676	−	1.40676i
$474$		−	335459.i		−	1.49308i
$475$	185123.	−	133756.i	0.820490	−	0.592824i
$476$	−817818.			−3.60946
$477$	412508.	+	412508.i	1.81299	+	1.81299i
$478$	−498030.	+	498030.i	−2.17971	+	2.17971i
$479$			129152.i			0.562900i	0.959576	+	0.281450i	$0.0908153\pi$
$479$			129152.i			0.562900i	−0.959576	+	0.281450i	$0.909185\pi$
$480$	101264.	−	198096.i	0.439512	−	0.859790i
$481$	396616.			1.71427
$482$	399057.	+	399057.i	1.71768	+	1.71768i
$483$	−73790.9	+	73790.9i	−0.316307	+	0.316307i
$484$			162889.i			0.695347i
$485$	142606.	−	46127.9i	0.606254	−	0.196101i
$486$	416229.			1.76222
$487$	−147088.	−	147088.i	−0.620183	−	0.620183i	0.325395	−	0.945578i	$-0.394503\pi$
$487$	−147088.	−	147088.i	−0.620183	−	0.620183i	−0.945578	+	0.325395i	$0.894503\pi$
$488$	−21984.7	+	21984.7i	−0.0923167	+	0.0923167i
$489$		−	301333.i		−	1.26017i
$490$	−96275.7	−	297640.i	−0.400981	−	1.23965i
$491$	105526.			0.437720			0.218860	−	0.975756i	$-0.429766\pi$
$491$	105526.			0.437720			0.218860	+	0.975756i	$0.429766\pi$
$492$	−179218.	−	179218.i	−0.740377	−	0.740377i
$493$	250096.	−	250096.i	1.02899	−	1.02899i
$494$		−	588988.i		−	2.41353i
$495$	407829.	+	208476.i	1.66444	+	0.850837i
$496$	−89710.9			−0.364655
$497$	−58655.7	−	58655.7i	−0.237464	−	0.237464i
$498$	375008.	−	375008.i	1.51210	−	1.51210i
$499$		−	89517.0i		−	0.359505i	−0.983712	−	0.179752i	$-0.942470\pi$
$499$		−	89517.0i		−	0.359505i	0.983712	−	0.179752i	$-0.0575296\pi$
$500$	−68669.9	−	444939.i	−0.274679	−	1.77976i
$501$	−207891.			−0.828248
$502$	276652.	+	276652.i	1.09781	+	1.09781i
$503$	−292581.	+	292581.i	−1.15640	+	1.15640i	−0.171161	+	0.985243i	$0.554752\pi$
$503$	−292581.	+	292581.i	−1.15640	+	1.15640i	−0.985243	+	0.171161i	$0.945248\pi$
$504$			720857.i			2.83784i
$505$	−22321.1	+	43665.2i	−0.0875250	+	0.171219i
$506$	−105192.			−0.410848
$507$	301091.	+	301091.i	1.17134	+	1.17134i
$508$	−144862.	+	144862.i	−0.561340	+	0.561340i
$509$			408386.i			1.57629i	0.615491	+	0.788144i	$0.288958\pi$
$509$			408386.i			1.57629i	−0.615491	+	0.788144i	$0.711042\pi$
$510$	−1.00133e6	+	323894.i	−3.84979	+	1.24527i
$511$	−4909.17			−0.0188003
$512$	159042.	+	159042.i	0.606699	+	0.606699i
$513$	−178092.	+	178092.i	−0.676723	+	0.676723i
$514$			461788.i			1.74790i
$515$	−28061.6	−	86753.4i	−0.105803	−	0.327094i
$516$	1.30336e6			4.89514
$517$	−56146.2	−	56146.2i	−0.210058	−	0.210058i
$518$	−509534.	+	509534.i	−1.89895	+	1.89895i
$519$			754924.i			2.80265i
$520$	−459728.	−	235006.i	−1.70018	−	0.869106i
$521$	−113104.			−0.416679			−0.208340	−	0.978057i	$-0.566806\pi$
$521$	−113104.			−0.416679			−0.208340	+	0.978057i	$0.566806\pi$
$522$	−495714.	−	495714.i	−1.81924	−	1.81924i
$523$	347447.	−	347447.i	1.27024	−	1.27024i	0.324277	−	0.945962i	$-0.394879\pi$
$523$	347447.	−	347447.i	1.27024	−	1.27024i	0.945962	−	0.324277i	$-0.105121\pi$
$524$		−	742537.i		−	2.70430i
$525$	−346294.	−	479284.i	−1.25640	−	1.73890i
$526$	150599.			0.544315
$527$	−243421.	−	243421.i	−0.876468	−	0.876468i
$528$	−165077.	+	165077.i	−0.592133	+	0.592133i
$529$		−	12167.0i		−	0.0434783i
$530$	345538.	−	675954.i	1.23011	−	2.40639i
$531$	−83200.2			−0.295077
$532$	486514.	+	486514.i	1.71898	+	1.71898i
$533$	103442.	−	103442.i	0.364119	−	0.364119i
$534$		−	1.04705e6i		−	3.67185i
$535$	133767.	−	43268.7i	0.467348	−	0.151170i
$536$	46547.1			0.162018
$537$	−50520.6	−	50520.6i	−0.175194	−	0.175194i
$538$	133926.	−	133926.i	0.462700	−	0.462700i
$539$		−	266282.i		−	0.916569i
$540$	152798.	+	472379.i	0.523997	+	1.61996i
$541$	−75100.2			−0.256594			−0.128297	−	0.991736i	$-0.540951\pi$
$541$	−75100.2			−0.256594			−0.128297	+	0.991736i	$0.540951\pi$
$542$	138575.	+	138575.i	0.471723	+	0.471723i
$543$	−640287.	+	640287.i	−2.17158	+	2.17158i
$544$			266983.i			0.902165i
$545$	257584.	+	131673.i	0.867212	+	0.443306i
$546$	−1.52489e6			−5.11509
$547$	1626.53	+	1626.53i	0.00543609	+	0.00543609i	0.709820	−	0.704384i	$-0.248776\pi$
$547$	1626.53	+	1626.53i	0.00543609	+	0.00543609i	−0.704384	+	0.709820i	$0.748776\pi$
$548$	−417560.	+	417560.i	−1.39046	+	1.39046i
$549$			46616.0i			0.154664i
$550$	94790.9	−	588447.i	0.313358	−	1.94528i
$551$	−297560.			−0.980102
$552$	−96859.3	−	96859.3i	−0.317880	−	0.317880i
$553$	−159935.	+	159935.i	−0.522989	+	0.522989i
$554$			449363.i			1.46412i
$555$	−271375.	+	530874.i	−0.881018	+	1.72348i
$556$	−156258.			−0.505468
$557$	209155.	+	209155.i	0.674151	+	0.674151i	0.958670	−	0.284519i	$-0.0918340\pi$
$557$	209155.	+	209155.i	0.674151	+	0.674151i	−0.284519	+	0.958670i	$0.591834\pi$
$558$	−482484.	+	482484.i	−1.54958	+	1.54958i
$559$			752279.i			2.40744i
$560$	175942.	−	56910.8i	0.561039	−	0.181476i
$561$	−895838.			−2.84645
$562$	−225848.	−	225848.i	−0.715063	−	0.715063i
$563$	−127387.	+	127387.i	−0.401891	+	0.401891i	−0.878899	−	0.477008i	$-0.841721\pi$
$563$	−127387.	+	127387.i	−0.401891	+	0.401891i	0.477008	+	0.878899i	$0.341721\pi$
$564$		−	232511.i		−	0.730945i
$565$	−36689.1	−	113426.i	−0.114932	−	0.355315i
$566$	215043.			0.671264
$567$	−20263.0	−	20263.0i	−0.0630287	−	0.0630287i
$568$	76992.6	−	76992.6i	0.238645	−	0.238645i
$569$		−	304586.i		−	0.940775i	−0.882460	−	0.470388i	$-0.844114\pi$
$569$		−	304586.i		−	0.940775i	0.882460	−	0.470388i	$-0.155886\pi$
$570$	788366.	+	403002.i	2.42649	+	1.24039i
$571$	−178736.			−0.548202			−0.274101	−	0.961701i	$-0.588380\pi$
$571$	−178736.			−0.548202			−0.274101	+	0.961701i	$0.588380\pi$
$572$	−698833.	−	698833.i	−2.13590	−	2.13590i
$573$	390048.	−	390048.i	1.18798	−	1.18798i
$574$			265785.i			0.806691i
$575$	68062.7	+	10964.0i	0.205861	+	0.0331614i
$576$	762101.			2.29703
$577$	−91764.5	−	91764.5i	−0.275628	−	0.275628i	0.555733	−	0.831361i	$-0.312438\pi$
$577$	−91764.5	−	91764.5i	−0.275628	−	0.275628i	−0.831361	+	0.555733i	$0.812438\pi$
$578$	497684.	−	497684.i	1.48970	−	1.48970i
$579$		−	608941.i		−	1.81643i
$580$	−266981.	+	522278.i	−0.793642	+	1.55255i
$581$	−357581.			−1.05931
$582$	410863.	+	410863.i	1.21297	+	1.21297i
$583$	456937.	−	456937.i	1.34437	−	1.34437i
$584$		−	6443.86i		−	0.0188938i
$585$	−736552.	+	238248.i	−2.15224	+	0.696173i
$586$	759268.			2.21106
$587$	−35333.1	−	35333.1i	−0.102543	−	0.102543i	0.653974	−	0.756517i	$-0.273101\pi$
$587$	−35333.1	−	35333.1i	−0.102543	−	0.102543i	−0.756517	+	0.653974i	$0.773101\pi$
$588$	551360.	−	551360.i	1.59471	−	1.59471i
$589$			289618.i			0.834824i
$590$	33321.4	+	103014.i	0.0957236	+	0.295933i
$591$	651936.			1.86651
$592$	−131843.	−	131843.i	−0.376197	−	0.376197i
$593$	299739.	−	299739.i	0.852380	−	0.852380i	−0.138045	−	0.990426i	$-0.544082\pi$
$593$	299739.	−	299739.i	0.852380	−	0.852380i	0.990426	+	0.138045i	$0.0440820\pi$
$594$			657290.i			1.86288i
$595$	631820.	+	322978.i	1.78468	+	0.912301i
$596$	−589159.			−1.65859
$597$	−50435.1	−	50435.1i	−0.141509	−	0.141509i
$598$	125716.	−	125716.i	0.351550	−	0.351550i
$599$		−	273832.i		−	0.763187i	−0.924330	−	0.381594i	$-0.875375\pi$
$599$		−	273832.i		−	0.763187i	0.924330	−	0.381594i	$-0.124625\pi$
$600$	629117.	−	454552.i	1.74755	−	1.26265i
$601$	−78618.9			−0.217660			−0.108830	−	0.994060i	$-0.534710\pi$
$601$	−78618.9			−0.217660			−0.108830	+	0.994060i	$0.534710\pi$
$602$	−966456.	−	966456.i	−2.66679	−	2.66679i
$603$	49348.9	−	49348.9i	0.135720	−	0.135720i
$604$			882498.i			2.41902i
$605$	64329.2	−	125843.i	0.175751	−	0.343810i
$606$	−190113.			−0.517687
$607$	159790.	+	159790.i	0.433682	+	0.433682i	0.889879	−	0.456197i	$-0.150789\pi$
$607$	159790.	+	159790.i	0.433682	+	0.433682i	−0.456197	+	0.889879i	$0.650789\pi$
$608$	158826.	−	158826.i	0.429650	−	0.429650i
$609$			770384.i			2.07717i
$610$	57717.5	−	18669.5i	0.155113	−	0.0501734i
$611$	134202.			0.359480
$612$	−1.13810e6	−	1.13810e6i	−3.03862	−	3.03862i
$613$	−224399.	+	224399.i	−0.597174	+	0.597174i	−0.939559	−	0.342386i	$-0.888765\pi$
$613$	−224399.	+	224399.i	−0.597174	+	0.597174i	0.342386	+	0.939559i	$0.388765\pi$
$614$			295932.i			0.784973i
$615$	67680.4	+	209236.i	0.178942	+	0.553206i
$616$	798497.			2.10432
$617$	35222.8	+	35222.8i	0.0925238	+	0.0925238i	0.751854	−	0.659330i	$-0.229160\pi$
$617$	35222.8	+	35222.8i	0.0925238	+	0.0925238i	−0.659330	+	0.751854i	$0.729160\pi$
$618$	249945.	−	249945.i	0.654437	−	0.654437i
$619$			490494.i			1.28012i	0.768323	+	0.640062i	$0.221091\pi$
$619$			490494.i			1.28012i	−0.768323	+	0.640062i	$0.778909\pi$
$620$	508339.	+	259856.i	1.32242	+	0.676003i
$621$	−76025.4			−0.197140
$622$	−782271.	−	782271.i	−2.02198	−	2.02198i
$623$	−499197.	+	499197.i	−1.28616	+	1.28616i
$624$		−	394570.i		−	1.01334i
$625$	−122666.	+	370865.i	−0.314025	+	0.949415i
$626$	−430006.			−1.09730
$627$	532927.	+	532927.i	1.35560	+	1.35560i
$628$	−398376.	+	398376.i	−1.01012	+	1.01012i
$629$		−	715485.i		−	1.80842i
$630$	640173.	−	1.25233e6i	1.61293	−	3.15528i
$631$	−25166.5			−0.0632068			−0.0316034	−	0.999500i	$-0.510061\pi$
$631$	−25166.5			−0.0632068			−0.0316034	+	0.999500i	$0.510061\pi$
$632$	−209933.	−	209933.i	−0.525590	−	0.525590i
$633$	−72496.4	+	72496.4i	−0.180929	+	0.180929i
$634$		−	1.28069e6i		−	3.18615i
$635$	169125.	−	54705.8i	0.419431	−	0.135671i
$636$	1.89225e6			4.67805
$637$	318237.	+	318237.i	0.784280	+	0.784280i
$638$	−549105.	+	549105.i	−1.34901	+	1.34901i
$639$		−	163254.i		−	0.399818i
$640$	−229549.	−	709659.i	−0.560422	−	1.73257i
$641$	88357.4			0.215044			0.107522	−	0.994203i	$-0.465708\pi$
$641$	88357.4			0.215044			0.107522	+	0.994203i	$0.465708\pi$
$642$	385395.	+	385395.i	0.935053	+	0.935053i
$643$	96842.8	−	96842.8i	0.234232	−	0.234232i	−0.580225	−	0.814456i	$-0.697035\pi$
$643$	96842.8	−	96842.8i	0.234232	−	0.234232i	0.814456	+	0.580225i	$0.197035\pi$
$644$			207686.i			0.500768i
$645$	−1.00693e6	−	514731.i	−2.42037	−	1.23726i
$646$	−1.06252e6			−2.54608
$647$	−213247.	−	213247.i	−0.509417	−	0.509417i	0.404931	−	0.914347i	$-0.367296\pi$
$647$	−213247.	−	213247.i	−0.509417	−	0.509417i	−0.914347	+	0.404931i	$0.867296\pi$
$648$	26597.6	−	26597.6i	0.0633421	−	0.0633421i
$649$			92161.4i			0.218806i
$650$	589972.	+	816543.i	1.39638	+	1.93265i
$651$	749822.			1.76928
$652$	−424055.	−	424055.i	−0.997533	−	0.997533i
$653$	−90955.5	+	90955.5i	−0.213306	+	0.213306i	−0.805670	−	0.592364i	$-0.798195\pi$
$653$	−90955.5	+	90955.5i	−0.213306	+	0.213306i	0.592364	+	0.805670i	$0.298195\pi$
$654$			1.12149e6i			2.62204i
$655$	−293247.	+	573660.i	−0.683519	+	1.33712i
$656$	−68772.8			−0.159812
$657$	−6831.73	−	6831.73i	−0.0158271	−	0.0158271i
$658$	−172409.	+	172409.i	−0.398207	+	0.398207i
$659$		−	152947.i		−	0.352184i	−0.984374	−	0.176092i	$-0.943654\pi$
$659$		−	152947.i		−	0.352184i	0.984374	−	0.176092i	$-0.0563455\pi$
$660$	1.41356e6	−	457234.i	3.24508	−	1.04967i
$661$	−320167.			−0.732780			−0.366390	−	0.930461i	$-0.619406\pi$
$661$	−320167.			−0.732780			−0.366390	+	0.930461i	$0.619406\pi$
$662$	−926418.	−	926418.i	−2.11393	−	2.11393i
$663$	1.07062e6	−	1.07062e6i	2.43562	−	2.43562i
$664$		−	469367.i		−	1.06457i
$665$	−183728.	−	568002.i	−0.415463	−	1.28442i
$666$	−1.41816e6			−3.19726
$667$	−63512.3	−	63512.3i	−0.142760	−	0.142760i
$668$	−292557.	+	292557.i	−0.655629	+	0.655629i
$669$		−	992513.i		−	2.21760i
$670$	−80865.4	−	41337.3i	−0.180141	−	0.0920857i
$671$	51636.8			0.114687
$672$	−411202.	−	411202.i	−0.910576	−	0.910576i
$673$	547517.	−	547517.i	1.20884	−	1.20884i	0.237432	−	0.971404i	$-0.423694\pi$
$673$	547517.	−	547517.i	1.20884	−	1.20884i	0.971404	−	0.237432i	$-0.0763057\pi$
$674$			400464.i			0.881542i
$675$	68508.3	−	425289.i	0.150361	−	0.933419i
$676$	847427.			1.85442
$677$	425592.	+	425592.i	0.928572	+	0.928572i	0.997614	−	0.0690414i	$-0.0219940\pi$
$677$	425592.	+	425592.i	0.928572	+	0.928572i	−0.0690414	+	0.997614i	$0.521994\pi$
$678$	326791.	−	326791.i	0.710903	−	0.710903i
$679$		−	391769.i		−	0.849750i
$680$	−423946.	+	829338.i	−0.916838	+	1.79355i
$681$	51392.4			0.110817
$682$	534450.	+	534450.i	1.14905	+	1.14905i
$683$	−575602.	+	575602.i	−1.23390	+	1.23390i	−0.271449	+	0.962453i	$0.587503\pi$
$683$	−575602.	+	575602.i	−1.23390	+	1.23390i	−0.962453	+	0.271449i	$0.912497\pi$
$684$			1.35409e6i			2.89425i
$685$	487498.	−	157688.i	1.03894	−	0.336061i
$686$	232635.			0.494342
$687$	−212883.	−	212883.i	−0.451054	−	0.451054i
$688$	250074.	−	250074.i	0.528313	−	0.528313i
$689$			1.09218e6i			2.30068i
$690$	82253.5	+	254290.i	0.172765	+	0.534110i
$691$	−24090.6			−0.0504534			−0.0252267	−	0.999682i	$-0.508031\pi$
$691$	−24090.6			−0.0504534			−0.0252267	+	0.999682i	$0.508031\pi$
$692$	1.06238e6	+	1.06238e6i	2.21853	+	2.21853i
$693$	846561.	−	846561.i	1.76275	−	1.76275i
$694$			72170.7i			0.149845i
$695$	120720.	+	61710.5i	0.249925	+	0.127758i
$696$	−1.01122e6			−2.08750
$697$	−186607.	−	186607.i	−0.384117	−	0.384117i
$698$	−1.07330e6	+	1.07330e6i	−2.20299	+	2.20299i
$699$		−	743676.i		−	1.52205i
$700$	−1.16181e6	−	187151.i	−2.37103	−	0.381942i
$701$	−561691.			−1.14304			−0.571520	−	0.820588i	$-0.693646\pi$
$701$	−561691.			−1.14304			−0.571520	+	0.820588i	$0.693646\pi$
$702$	−785533.	−	785533.i	−1.59401	−	1.59401i
$703$	−425637.	+	425637.i	−0.861248	+	0.861248i
$704$		−	844184.i		−	1.70330i
$705$	−91824.5	+	179630.i	−0.184748	+	0.361411i
$706$	1.23317e6			2.47408
$707$	90639.2	+	90639.2i	0.181333	+	0.181333i
$708$	−190828.	+	190828.i	−0.380693	+	0.380693i
$709$		−	147612.i		−	0.293649i	−0.989163	−	0.146824i	$-0.953095\pi$
$709$		−	147612.i		−	0.293649i	0.989163	−	0.146824i	$-0.0469052\pi$
$710$	−202133.	+	65382.6i	−0.400977	+	0.129702i
$711$	−445140.			−0.880556
$712$	−655254.	−	655254.i	−1.29256	−	1.29256i
$713$	−61817.1	+	61817.1i	−0.121599	+	0.121599i
$714$			2.75087e6i			5.39602i
$715$	263909.	+	815883.i	0.516228	+	1.59594i
$716$	−142191.			−0.277362
$717$	1.07710e6	+	1.07710e6i	2.09515	+	2.09515i
$718$	−928606.	+	928606.i	−1.80129	+	1.80129i
$719$		−	172172.i		−	0.333046i	−0.986038	−	0.166523i	$-0.946746\pi$
$719$		−	172172.i		−	0.333046i	0.986038	−	0.166523i	$-0.0532540\pi$
$720$	324044.	+	165647.i	0.625085	+	0.319535i
$721$	−238330.			−0.458467
$722$	15202.2	+	15202.2i	0.0291629	+	0.0291629i
$723$	863047.	−	863047.i	1.65104	−	1.65104i
$724$			1.80210e6i			3.43797i
$725$	412522.	−	298057.i	0.784823	−	0.567053i
$726$	547905.			1.03952
$727$	584688.	+	584688.i	1.10625	+	1.10625i	0.993639	+	0.112616i	$0.0359231\pi$
$727$	584688.	+	584688.i	1.10625	+	1.10625i	0.112616	+	0.993639i	$0.464077\pi$
$728$	−954291.	+	954291.i	−1.80060	+	1.80060i
$729$		−	864663.i		−	1.62702i
$730$	−5722.62	+	11194.8i	−0.0107386	+	0.0210073i
$731$	1.35709e6			2.53966
$732$	106918.	+	106918.i	0.199540	+	0.199540i
$733$	622492.	−	622492.i	1.15858	−	1.15858i	0.173799	−	0.984781i	$-0.444396\pi$
$733$	622492.	−	622492.i	1.15858	−	1.15858i	0.984781	−	0.173799i	$-0.0556043\pi$
$734$		−	610951.i		−	1.13400i
$735$	−643709.	+	208217.i	−1.19156	+	0.385426i
$736$	67800.9			0.125164
$737$	−54664.1	−	54664.1i	−0.100639	−	0.100639i
$738$	−369874.	+	369874.i	−0.679112	+	0.679112i
$739$			13484.4i			0.0246913i	0.999924	+	0.0123456i	$0.00392984\pi$
$739$			13484.4i			0.0246913i	−0.999924	+	0.0123456i	$0.996070\pi$
$740$	365183.	+	1.12898e6i	0.666879	+	2.06168i
$741$	−1.27381e6			−2.31990
$742$	−1.40313e6	−	1.40313e6i	−2.54853	−	2.54853i
$743$	−459257.	+	459257.i	−0.831913	+	0.831913i	−0.987778	−	0.155866i	$-0.950183\pi$
$743$	−459257.	+	459257.i	−0.831913	+	0.831913i	0.155866	+	0.987778i	$0.450183\pi$
$744$			984230.i			1.77808i
$745$	455165.	+	232674.i	0.820081	+	0.419214i
$746$	1.13795e6			2.04477
$747$	−497619.	−	497619.i	−0.891776	−	0.891776i
$748$	−1.26068e6	+	1.26068e6i	−2.25321	+	2.25321i
$749$		−	367485.i		−	0.655053i
$750$	−1.49663e6	+	230983.i	−2.66067	+	0.410636i
$751$	−438831.			−0.778068			−0.389034	−	0.921223i	$-0.627191\pi$
$751$	−438831.			−0.778068			−0.389034	+	0.921223i	$0.627191\pi$
$752$	−44611.5	−	44611.5i	−0.0788880	−	0.0788880i
$753$	598319.	−	598319.i	1.05522	−	1.05522i
$754$		−	1.31248e6i		−	2.30861i
$755$	348521.	−	681790.i	0.611414	−	1.19607i
$756$	1.29773e6			2.27059
$757$	−435077.	−	435077.i	−0.759232	−	0.759232i	0.216951	−	0.976183i	$-0.430389\pi$
$757$	−435077.	−	435077.i	−0.759232	−	0.759232i	−0.976183	+	0.216951i	$0.930389\pi$
$758$	936304.	−	936304.i	1.62959	−	1.62959i
$759$			227500.i			0.394909i
$760$	745569.	−	241165.i	1.29081	−	0.417529i
$761$	−564600.			−0.974926			−0.487463	−	0.873144i	$-0.662078\pi$
$761$	−564600.			−0.974926			−0.487463	+	0.873144i	$0.662078\pi$
$762$	487267.	+	487267.i	0.839183	+	0.839183i
$763$	534685.	−	534685.i	0.918437	−	0.918437i
$764$		−	1.09780e6i		−	1.88077i
$765$	429794.	+	1.32872e6i	0.734408	+	2.27045i
$766$	1.13693e6			1.93765
$767$	−110143.	−	110143.i	−0.187226	−	0.187226i
$768$	1.07396e6	−	1.07396e6i	1.82082	−	1.82082i
$769$		−	415646.i		−	0.702863i	−0.936214	−	0.351431i	$-0.885695\pi$
$769$		−	415646.i		−	0.702863i	0.936214	−	0.351431i	$-0.114305\pi$
$770$	−1.38721e6	−	709124.i	−2.33971	−	1.19603i
$771$	998715.			1.68009
$772$	−856940.	−	856940.i	−1.43786	−	1.43786i
$773$	−90950.7	+	90950.7i	−0.152211	+	0.152211i	−0.779105	−	0.626894i	$-0.784326\pi$
$773$	−90950.7	+	90950.7i	−0.152211	+	0.152211i	0.626894	+	0.779105i	$0.284326\pi$
$774$		−	2.68990e6i		−	4.49007i
$775$	−290102.	−	401512.i	−0.483001	−	0.668491i
$776$	514244.			0.853976
$777$	1.10198e6	+	1.10198e6i	1.82528	+	1.82528i
$778$	819401.	−	819401.i	1.35375	−	1.35375i
$779$			222023.i			0.365866i
$780$	−1.14291e6	+	2.23580e6i	−1.87855	+	3.67488i
$781$	−180837.			−0.296474
$782$	−226788.	−	226788.i	−0.370857	−	0.370857i
$783$	−396856.	+	396856.i	−0.647305	+	0.647305i
$784$		−	211577.i		−	0.344221i
$785$	465102.	−	150444.i	0.754759	−	0.244137i
$786$	−2.49765e6			−4.04283
$787$	−371459.	−	371459.i	−0.599738	−	0.599738i	0.340505	−	0.940243i	$-0.389402\pi$
$787$	−371459.	−	371459.i	−0.599738	−	0.599738i	−0.940243	+	0.340505i	$0.889402\pi$
$788$	917445.	−	917445.i	1.47750	−	1.47750i
$789$		−	325702.i		−	0.523199i
$790$	178277.	+	551149.i	0.285654	+	0.883110i
$791$	−311604.			−0.498024
$792$	1.11121e6	+	1.11121e6i	1.77152	+	1.77152i
$793$	−61711.6	+	61711.6i	−0.0981342	+	0.0981342i
$794$			697027.i			1.10563i
$795$	−1.46189e6	−	747300.i	−2.31303	−	1.18239i
$796$	−141951.			−0.224033
$797$	214898.	+	214898.i	0.338311	+	0.338311i	0.855731	−	0.517420i	$-0.173108\pi$
$797$	214898.	+	214898.i	0.338311	+	0.338311i	−0.517420	+	0.855731i	$0.673108\pi$
$798$	1.63647e6	−	1.63647e6i	2.56982	−	2.56982i
$799$		−	242097.i		−	0.379223i
$800$	−61097.0	+	379281.i	−0.0954641	+	0.592626i
$801$	−1.38939e6			−2.16551
$802$	1.41952e6	+	1.41952e6i	2.20695	+	2.20695i
$803$	−7567.55	+	7567.55i	−0.0117361	+	0.0117361i
$804$		−	226373.i		−	0.350197i
$805$	82020.8	−	160452.i	0.126570	−	0.247601i
$806$	−1.27745e6			−1.96641
$807$	−289643.	−	289643.i	−0.444750	−	0.444750i
$808$	−118975.	+	118975.i	−0.182235	+	0.182235i
$809$			730130.i			1.11559i	0.829980	+	0.557793i	$0.188352\pi$
$809$			730130.i			1.11559i	−0.829980	+	0.557793i	$0.811648\pi$
$810$	−69828.1	+	22586.9i	−0.106429	+	0.0344260i
$811$	−1.10448e6			−1.67926			−0.839630	−	0.543158i	$-0.817228\pi$
$811$	−1.10448e6			−1.67926			−0.839630	+	0.543158i	$0.817228\pi$
$812$	1.08413e6	+	1.08413e6i	1.64426	+	1.64426i
$813$	299698.	−	299698.i	0.453422	−	0.453422i
$814$			1.57091e6i			2.37084i
$815$	160141.	+	495082.i	0.241095	+	0.745353i
$816$	−711796.			−1.06899
$817$	−807325.	−	807325.i	−1.20950	−	1.20950i
$818$	826787.	−	826787.i	1.23563	−	1.23563i
$819$			2.02347e6i			3.01667i
$820$	389695.	+	199207.i	0.579558	+	0.296262i
$821$	801624.			1.18928			0.594641	−	0.803992i	$-0.297294\pi$
$821$	801624.			1.18928			0.594641	+	0.803992i	$0.297294\pi$
$822$	1.40453e6	+	1.40453e6i	2.07868	+	2.07868i
$823$	382533.	−	382533.i	0.564766	−	0.564766i	−0.365891	−	0.930658i	$-0.619236\pi$
$823$	382533.	−	382533.i	0.564766	−	0.564766i	0.930658	+	0.365891i	$0.119236\pi$
$824$		−	312836.i		−	0.460747i
$825$	−1.27264e6	−	205006.i	−1.86981	−	0.301202i
$826$	283002.			0.414791
$827$	−308729.	−	308729.i	−0.451405	−	0.451405i	0.444416	−	0.895821i	$-0.353411\pi$
$827$	−308729.	−	308729.i	−0.451405	−	0.451405i	−0.895821	+	0.444416i	$0.853411\pi$
$828$	−289022.	+	289022.i	−0.421571	+	0.421571i
$829$			1.03473e6i			1.50563i	0.658229	+	0.752817i	$0.271306\pi$
$829$			1.03473e6i			1.50563i	−0.658229	+	0.752817i	$0.728694\pi$
$830$	−416832.	+	815421.i	−0.605069	+	1.18366i
$831$	971844.			1.40732
$832$	1.00889e6	+	1.00889e6i	1.45746	+	1.45746i
$833$	574091.	−	574091.i	0.827353	−	0.827353i
$834$			525601.i			0.755656i
$835$	341559.	−	110482.i	0.489883	−	0.158459i
$836$	1.49994e6			2.14615
$837$	386264.	+	386264.i	0.551357	+	0.551357i
$838$	−365055.	+	365055.i	−0.519840	+	0.519840i
$839$		−	392806.i		−	0.558025i	−0.960287	−	0.279013i	$-0.909993\pi$
$839$		−	392806.i		−	0.558025i	0.960287	−	0.279013i	$-0.0900071\pi$
$840$	−624376.	−	1.93028e6i	−0.884887	−	2.73566i
$841$	44207.8			0.0625038
$842$	392022.	+	392022.i	0.552951	+	0.552951i
$843$	−488445.	+	488445.i	−0.687323	+	0.687323i
$844$			204043.i			0.286442i
$845$	−654695.	−	334671.i	−0.916908	−	0.468711i
$846$	−479859.			−0.670460
$847$	−261222.	−	261222.i	−0.364118	−	0.364118i
$848$	363064.	−	363064.i	0.504884	−	0.504884i
$849$		−	465077.i		−	0.645223i
$850$	1.47303e6	−	1.06430e6i	2.03879	−	1.47308i
$851$	−181699.			−0.250896
$852$	−374439.	−	374439.i	−0.515824	−	0.515824i
$853$	768079.	−	768079.i	1.05562	−	1.05562i	0.0572617	−	0.998359i	$-0.481763\pi$
$853$	768079.	−	768079.i	1.05562	−	1.05562i	0.998359	−	0.0572617i	$-0.0182370\pi$
$854$		−	158562.i		−	0.217412i
$855$	534766.	−	1.04613e6i	0.731529	−	1.43104i
$856$	482368.			0.658311
$857$	210208.	+	210208.i	0.286212	+	0.286212i	0.835580	−	0.549368i	$-0.185132\pi$
$857$	210208.	+	210208.i	0.286212	+	0.286212i	−0.549368	+	0.835580i	$0.685132\pi$
$858$	−2.35064e6	+	2.35064e6i	−3.19310	+	3.19310i
$859$		−	10970.7i		−	0.0148678i	−0.999972	−	0.00743391i	$-0.997634\pi$
$859$		−	10970.7i		−	0.0148678i	0.999972	−	0.00743391i	$-0.00236631\pi$
$860$	−2.14138e6	+	692659.i	−2.89532	+	0.936532i
$861$	574817.			0.775396
$862$	467757.	+	467757.i	0.629515	+	0.629515i
$863$	−638749.	+	638749.i	−0.857647	+	0.857647i	−0.991060	−	0.133414i	$-0.957406\pi$
$863$	−638749.	+	638749.i	−0.857647	+	0.857647i	0.133414	+	0.991060i	$0.457406\pi$
$864$		−	423653.i		−	0.567522i
$865$	−401198.	−	1.24032e6i	−0.536199	−	1.65768i
$866$	124312.			0.165759
$867$	−1.07635e6	−	1.07635e6i	−1.43190	−	1.43190i
$868$	1.05520e6	−	1.05520e6i	1.40053	−	1.40053i
$869$			493084.i			0.652952i
$870$	1.75677e6	+	898037.i	2.32101	+	1.18647i
$871$	130659.			0.172228
$872$	701838.	+	701838.i	0.923004	+	0.923004i
$873$	545197.	−	545197.i	0.715361	−	0.715361i
$874$			269829.i			0.353237i
$875$	823663.	+	603414.i	1.07580	+	0.788133i
$876$	−31338.5			−0.0408385
$877$	144871.	+	144871.i	0.188358	+	0.188358i	0.794986	−	0.606628i	$-0.207478\pi$
$877$	144871.	+	144871.i	0.188358	+	0.188358i	−0.606628	+	0.794986i	$0.707478\pi$
$878$	120012.	−	120012.i	0.155681	−	0.155681i
$879$		−	1.64208e6i		−	2.12528i
$880$	183488.	−	358946.i	0.236942	−	0.463515i
$881$	−75370.9			−0.0971073			−0.0485537	−	0.998821i	$-0.515461\pi$
$881$	−75370.9			−0.0971073			−0.0485537	+	0.998821i	$0.515461\pi$
$882$	−1.13791e6	−	1.13791e6i	−1.46275	−	1.46275i
$883$	−108327.	+	108327.i	−0.138936	+	0.138936i	−0.773154	−	0.634218i	$-0.781322\pi$
$883$	−108327.	+	108327.i	−0.138936	+	0.138936i	0.634218	+	0.773154i	$0.281322\pi$
$884$		−	3.01330e6i		−	3.85600i
$885$	222790.	−	72064.6i	0.284452	−	0.0920101i
$886$	−1.07205e6			−1.36568
$887$	644895.	+	644895.i	0.819675	+	0.819675i	0.986061	−	0.166385i	$-0.0532096\pi$
$887$	644895.	+	644895.i	0.819675	+	0.819675i	−0.166385	+	0.986061i	$0.553210\pi$
$888$	−1.44647e6	+	1.44647e6i	−1.83436	+	1.83436i
$889$		−	464623.i		−	0.587891i
$890$	556446.	+	1.72027e6i	0.702495	+	2.17179i
$891$	−62471.5			−0.0786913
$892$	−1.39673e6	−	1.39673e6i	−1.75542	−	1.75542i
$893$	−144021.	+	144021.i	−0.180603	+	0.180603i
$894$			1.98174e6i			2.47954i
$895$	109853.	+	56155.1i	0.137140	+	0.0701040i
$896$	−1.94958e6			−2.42843
$897$	−271887.	−	271887.i	−0.337912	−	0.337912i
$898$	1.07891e6	−	1.07891e6i	1.33793	−	1.33793i
$899$			645376.i			0.798534i
$900$	−1.35636e6	−	1.87725e6i	−1.67451	−	2.31759i
$901$	1.97027e6			2.42703
$902$	409712.	+	409712.i	0.503576	+	0.503576i
$903$	−2.09017e6	+	2.09017e6i	−2.56334	+	2.56334i
$904$		−	409017.i		−	0.500501i
$905$	711697.	−	1.39225e6i	0.868957	−	1.69988i
$906$	2.96843e6			3.61635
$907$	−713852.	−	713852.i	−0.867748	−	0.867748i	0.124475	−	0.992223i	$-0.460275\pi$
$907$	−713852.	−	713852.i	−0.867748	−	0.867748i	−0.992223	+	0.124475i	$0.960275\pi$
$908$	72322.6	−	72322.6i	0.0877207	−	0.0877207i
$909$			252272.i			0.305310i
$910$	2.50535e6	−	810390.i	3.02542	−	0.978614i
$911$	−1.51428e6			−1.82460			−0.912301	−	0.409520i	$-0.865696\pi$
$911$	−1.51428e6			−1.82460			−0.912301	+	0.409520i	$0.865696\pi$
$912$	423442.	+	423442.i	0.509101	+	0.509101i
$913$	−551216.	+	551216.i	−0.661272	+	0.661272i
$914$			999642.i			1.19661i
$915$	−40376.8	−	124826.i	−0.0482270	−	0.149095i
$916$	−599166.			−0.714095
$917$	1.19079e6	+	1.19079e6i	1.41611	+	1.41611i
$918$	−1.41708e6	+	1.41708e6i	−1.68155	+	1.68155i
$919$			786035.i			0.930702i	0.885126	+	0.465351i	$0.154072\pi$
$919$			786035.i			0.930702i	−0.885126	+	0.465351i	$0.845928\pi$
$920$	210612.	+	107662.i	0.248833	+	0.127200i
$921$	640015.			0.754521
$922$	−666135.	−	666135.i	−0.783611	−	0.783611i
$923$	216120.	−	216120.i	0.253683	−	0.253683i
$924$		−	3.88334e6i		−	4.54843i
$925$	163733.	−	1.01643e6i	0.191361	−	1.18794i
$926$	640261.			0.746681
$927$	−331667.	−	331667.i	−0.385960	−	0.385960i
$928$	353923.	−	353923.i	0.410973	−	0.410973i
$929$			462231.i			0.535584i	0.963477	+	0.267792i	$0.0862939\pi$
$929$			462231.i			0.535584i	−0.963477	+	0.267792i	$0.913706\pi$
$930$	874068.	−	1.70988e6i	1.01060	−	1.97697i
$931$	−683045.			−0.788043
$932$	−1.04655e6	−	1.04655e6i	−1.20483	−	1.20483i
$933$	−1.69183e6	+	1.69183e6i	−1.94354	+	1.94354i
$934$		−	109212.i		−	0.125192i
$935$	1.47183e6	−	476085.i	1.68359	−	0.544580i
$936$	−2.65604e6			−3.03167
$937$	16221.7	+	16221.7i	0.0184764	+	0.0184764i	0.716285	−	0.697808i	$-0.245841\pi$
$937$	16221.7	+	16221.7i	0.0184764	+	0.0184764i	−0.697808	+	0.716285i	$0.745841\pi$
$938$	−167858.	+	167858.i	−0.190782	+	0.190782i
$939$			929979.i			1.05473i
$940$	123566.	+	382008.i	0.139844	+	0.432331i
$941$	851096.			0.961168			0.480584	−	0.876949i	$-0.340425\pi$
$941$	851096.			0.961168			0.480584	+	0.876949i	$0.340425\pi$
$942$	1.34000e6	+	1.34000e6i	1.51010	+	1.51010i
$943$	−47389.3	+	47389.3i	−0.0532914	+	0.0532914i
$944$			73227.7i			0.0821734i
$945$	−1.00258e6	−	512506.i	−1.12268	−	0.573899i
$946$	−2.97961e6			−3.32949
$947$	832603.	+	832603.i	0.928407	+	0.928407i	0.997603	−	0.0691965i	$-0.0220436\pi$
$947$	832603.	+	832603.i	0.928407	+	0.928407i	−0.0691965	+	0.997603i	$0.522044\pi$
$948$	−1.02097e6	+	1.02097e6i	−1.13605	+	1.13605i
$949$		−	18088.1i		−	0.0200845i
$950$	−1.50943e6	−	243150.i	−1.67250	−	0.269418i
$951$	−2.76977e6			−3.06255
$952$	1.72152e6	+	1.72152e6i	1.89949	+	1.89949i
$953$	−905801.	+	905801.i	−0.997349	+	0.997349i	−0.999996	−	0.00264786i	$-0.999157\pi$
$953$	−905801.	+	905801.i	−0.997349	+	0.997349i	0.00264786	+	0.999996i	$0.499157\pi$
$954$		−	3.90527e6i		−	4.29095i
$955$	−433549.	+	848125.i	−0.475370	+	0.929936i
$956$	3.03151e6			3.31699
$957$	1.18756e6	+	1.18756e6i	1.29667	+	1.29667i
$958$	611350.	−	611350.i	0.666130	−	0.666130i
$959$		−	1.33926e6i		−	1.45622i
$960$	−2.04072e6	+	660100.i	−2.21433	+	0.716254i
$961$	−295370.			−0.319830
$962$	−1.87741e6	−	1.87741e6i	−2.02865	−	2.02865i
$963$	511403.	−	511403.i	0.551456	−	0.551456i
$964$		−	2.42907e6i		−	2.61388i
$965$	323616.	+	1.00047e6i	0.347517	+	1.07436i
$966$	698588.			0.748630
$967$	−1.27235e6	−	1.27235e6i	−1.36067	−	1.36067i	−0.873063	−	0.487608i	$-0.837869\pi$
$967$	−1.27235e6	−	1.27235e6i	−1.36067	−	1.36067i	−0.487608	−	0.873063i	$-0.662131\pi$
$968$	342884.	−	342884.i	0.365929	−	0.365929i
$969$			2.29793e6i			2.44731i
$970$	−893385.	−	456686.i	−0.949500	−	0.485371i
$971$	121122.			0.128465			0.0642326	−	0.997935i	$-0.479540\pi$
$971$	121122.			0.128465			0.0642326	+	0.997935i	$0.479540\pi$
$972$	−1.26679e6	−	1.26679e6i	−1.34083	−	1.34083i
$973$	250588.	−	250588.i	0.264688	−	0.264688i
$974$			1.39250e6i			1.46784i
$975$	1.76595e6	−	1.27594e6i	1.85767	−	1.34221i
$976$	41028.5			0.0430711
$977$	1.01954e6	+	1.01954e6i	1.06811	+	1.06811i	0.997505	+	0.0706025i	$0.0224922\pi$
$977$	1.01954e6	+	1.01954e6i	1.06811	+	1.06811i	0.0706025	+	0.997505i	$0.477508\pi$
$978$	−1.42638e6	+	1.42638e6i	−1.49128	+	1.49128i
$979$			1.53904e6i			1.60577i
$980$	−612852.	+	1.19888e6i	−0.638122	+	1.24832i
$981$	1.48817e6			1.54637
$982$	−499514.	−	499514.i	−0.517994	−	0.517994i
$983$	369420.	−	369420.i	0.382308	−	0.382308i	−0.489625	−	0.871933i	$-0.662866\pi$
$983$	369420.	−	369420.i	0.382308	−	0.382308i	0.871933	+	0.489625i	$0.162866\pi$
$984$			754515.i			0.779252i
$985$	−1.07111e6	+	346466.i	−1.10398	+	0.357098i
$986$	−2.36769e6			−2.43540
$987$	372872.	+	372872.i	0.382759	+	0.382759i
$988$	−1.79259e6	+	1.79259e6i	−1.83640	+	1.83640i
$989$		−	344637.i		−	0.352346i
$990$	−943647.	−	2.91732e6i	−0.962807	−	2.97655i
$991$	105984.			0.107918			0.0539588	−	0.998543i	$-0.482816\pi$
$991$	105984.			0.107918			0.0539588	+	0.998543i	$0.482816\pi$
$992$	−344477.	−	344477.i	−0.350056	−	0.350056i
$993$	−2.00358e6	+	2.00358e6i	−2.03192	+	2.03192i
$994$			555301.i			0.562025i
$995$	109667.	+	56060.1i	0.110772	+	0.0566249i
$996$	−2.28268e6			−2.30105
$997$	1.09554e6	+	1.09554e6i	1.10214	+	1.10214i	0.994152	+	0.107991i	$0.0344419\pi$
$997$	1.09554e6	+	1.09554e6i	1.10214	+	1.10214i	0.107991	+	0.994152i	$0.465558\pi$
$998$	−423735.	+	423735.i	−0.425435	+	0.425435i
$999$			1.13534e6i			1.13762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.f.a.47.5	✓	88
5.3	odd	4	inner	115.5.f.a.93.5	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.f.a.47.5	✓	88	1.1	even	1	trivial
115.5.f.a.93.5	yes	88	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.73356 - 4.73356i) q^{2} +(-10.2373 + 10.2373i) q^{3} +28.8132i q^{4} +(11.3791 - 22.2602i) q^{5} +96.9182 q^{6} +(-46.2071 - 46.2071i) q^{7} +(60.6523 - 60.6523i) q^{8} -128.606i q^{9} +(-159.234 + 51.5063i) q^{10} -142.458 q^{11} +(-294.971 - 294.971i) q^{12} +(170.253 - 170.253i) q^{13} +437.449i q^{14} +(111.393 + 344.377i) q^{15} -113.191 q^{16} +(-307.132 - 307.132i) q^{17} +(-608.766 + 608.766i) q^{18} +365.421i q^{19} +(641.388 + 327.869i) q^{20} +946.077 q^{21} +(674.334 + 674.334i) q^{22} +(-77.9968 + 77.9968i) q^{23} +1241.84i q^{24} +(-366.032 - 506.602i) q^{25} -1611.80 q^{26} +(487.362 + 487.362i) q^{27} +(1331.38 - 1331.38i) q^{28} +814.293i q^{29} +(1102.84 - 2157.42i) q^{30} +792.560 q^{31} +(-434.639 - 434.639i) q^{32} +(1458.39 - 1458.39i) q^{33} +2907.66i q^{34} +(-1554.38 + 502.784i) q^{35} +3705.57 q^{36} +(1164.78 + 1164.78i) q^{37} +(1729.74 - 1729.74i) q^{38} +3485.87i q^{39} +(-659.964 - 2040.30i) q^{40} +607.580 q^{41} +(-4478.31 - 4478.31i) q^{42} +(-2209.30 + 2209.30i) q^{43} -4104.68i q^{44} +(-2862.80 - 1463.42i) q^{45} +738.406 q^{46} +(394.124 + 394.124i) q^{47} +(1158.78 - 1158.78i) q^{48} +1869.20i q^{49} +(-665.395 + 4130.67i) q^{50} +6288.43 q^{51} +(4905.54 + 4905.54i) q^{52} +(-3207.52 + 3207.52i) q^{53} -4613.92i q^{54} +(-1621.04 + 3171.14i) q^{55} -5605.14 q^{56} +(-3740.94 - 3740.94i) q^{57} +(3854.51 - 3854.51i) q^{58} -646.937i q^{59} +(-9922.62 + 3209.61i) q^{60} -362.470 q^{61} +(-3751.63 - 3751.63i) q^{62} +(-5942.53 + 5942.53i) q^{63} +5925.84i q^{64} +(-1852.54 - 5727.18i) q^{65} -13806.8 q^{66} +(383.721 + 383.721i) q^{67} +(8849.48 - 8849.48i) q^{68} -1596.96i q^{69} +(9737.70 + 4977.77i) q^{70} +1269.41 q^{71} +(-7800.27 - 7800.27i) q^{72} +(53.1213 - 53.1213i) q^{73} -11027.2i q^{74} +(8933.45 + 1439.06i) q^{75} -10529.0 q^{76} +(6582.58 + 6582.58i) q^{77} +(16500.6 - 16500.6i) q^{78} -3461.26i q^{79} +(-1288.02 + 2519.66i) q^{80} +438.526 q^{81} +(-2876.02 - 2876.02i) q^{82} +(3869.32 - 3869.32i) q^{83} +27259.5i q^{84} +(-10331.7 + 3341.93i) q^{85} +20915.7 q^{86} +(-8336.20 - 8336.20i) q^{87} +(-8640.41 + 8640.41i) q^{88} -10803.4i q^{89} +(6624.04 + 20478.5i) q^{90} -15733.8 q^{91} +(-2247.34 - 2247.34i) q^{92} +(-8113.71 + 8113.71i) q^{93} -3731.23i q^{94} +(8134.34 + 4158.16i) q^{95} +8899.09 q^{96} +(4239.27 + 4239.27i) q^{97} +(8847.98 - 8847.98i) q^{98} +18321.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) \) 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Introduction

L-functions

Modular forms

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Database

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