LMFDB - Embedded newform 115.5.f.a.47.3

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			47.3
Character	$\chi$	$=$	115.47
Dual form			115.5.f.a.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.97771 - 4.97771i) q^{2} +(7.01798 - 7.01798i) q^{3} +33.5552i q^{4} +(-23.4643 + 8.62722i) q^{5} -69.8670 q^{6} +(-45.7084 - 45.7084i) q^{7} +(87.3849 - 87.3849i) q^{8} -17.5042i q^{9} +(159.742 + 73.8545i) q^{10} -60.0183 q^{11} +(235.490 + 235.490i) q^{12} +(35.2905 - 35.2905i) q^{13} +455.046i q^{14} +(-104.126 + 225.217i) q^{15} -333.070 q^{16} +(160.917 + 160.917i) q^{17} +(-87.1308 + 87.1308i) q^{18} +466.169i q^{19} +(-289.488 - 787.349i) q^{20} -641.562 q^{21} +(298.754 + 298.754i) q^{22} +(77.9968 - 77.9968i) q^{23} -1226.53i q^{24} +(476.142 - 404.862i) q^{25} -351.332 q^{26} +(445.613 + 445.613i) q^{27} +(1533.76 - 1533.76i) q^{28} +100.966i q^{29} +(1639.38 - 602.758i) q^{30} +352.856 q^{31} +(259.769 + 259.769i) q^{32} +(-421.207 + 421.207i) q^{33} -1602.00i q^{34} +(1466.85 + 678.177i) q^{35} +587.357 q^{36} +(1480.63 + 1480.63i) q^{37} +(2320.46 - 2320.46i) q^{38} -495.336i q^{39} +(-1296.53 + 2804.31i) q^{40} -2637.08 q^{41} +(3193.51 + 3193.51i) q^{42} +(-377.184 + 377.184i) q^{43} -2013.93i q^{44} +(151.012 + 410.723i) q^{45} -776.491 q^{46} +(-2531.67 - 2531.67i) q^{47} +(-2337.48 + 2337.48i) q^{48} +1777.51i q^{49} +(-4385.39 - 354.810i) q^{50} +2258.63 q^{51} +(1184.18 + 1184.18i) q^{52} +(-2413.27 + 2413.27i) q^{53} -4436.26i q^{54} +(1408.28 - 517.791i) q^{55} -7988.45 q^{56} +(3271.57 + 3271.57i) q^{57} +(502.578 - 502.578i) q^{58} +2795.50i q^{59} +(-7557.22 - 3493.97i) q^{60} +5911.03 q^{61} +(-1756.42 - 1756.42i) q^{62} +(-800.088 + 800.088i) q^{63} +2743.01i q^{64} +(-523.606 + 1132.52i) q^{65} +4193.30 q^{66} +(-153.737 - 153.737i) q^{67} +(-5399.62 + 5399.62i) q^{68} -1094.76i q^{69} +(-3925.79 - 10677.3i) q^{70} -4449.97 q^{71} +(-1529.60 - 1529.60i) q^{72} +(-6661.36 + 6661.36i) q^{73} -14740.3i q^{74} +(500.240 - 6182.88i) q^{75} -15642.4 q^{76} +(2743.34 + 2743.34i) q^{77} +(-2465.64 + 2465.64i) q^{78} +7130.60i q^{79} +(7815.24 - 2873.47i) q^{80} +7672.44 q^{81} +(13126.6 + 13126.6i) q^{82} +(176.164 - 176.164i) q^{83} -21527.8i q^{84} +(-5164.08 - 2387.54i) q^{85} +3755.03 q^{86} +(708.576 + 708.576i) q^{87} +(-5244.69 + 5244.69i) q^{88} +11243.3i q^{89} +(1292.76 - 2796.16i) q^{90} -3226.14 q^{91} +(2617.20 + 2617.20i) q^{92} +(2476.34 - 2476.34i) q^{93} +25203.8i q^{94} +(-4021.74 - 10938.3i) q^{95} +3646.11 q^{96} +(9789.11 + 9789.11i) q^{97} +(8847.96 - 8847.96i) q^{98} +1050.57i 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 $

$2$	−4.97771	−	4.97771i	−1.24443	−	1.24443i	−0.958145	−	0.286283i	$-0.907580\pi$
$2$	−4.97771	−	4.97771i	−1.24443	−	1.24443i	−0.286283	−	0.958145i	$-0.592420\pi$
$3$	7.01798	−	7.01798i	0.779776	−	0.779776i	−0.200017	−	0.979793i	$-0.564100\pi$
$3$	7.01798	−	7.01798i	0.779776	−	0.779776i	0.979793	+	0.200017i	$0.0640996\pi$
$4$			33.5552i			2.09720i
$5$	−23.4643	+	8.62722i	−0.938570	+	0.345089i
$5$	−23.4643	+	8.62722i	−0.938570	+	0.345089i
$6$	−69.8670			−1.94075
$7$	−45.7084	−	45.7084i	−0.932824	−	0.932824i	0.0650572	−	0.997882i	$-0.479277\pi$
$7$	−45.7084	−	45.7084i	−0.932824	−	0.932824i	−0.997882	+	0.0650572i	$0.979277\pi$
$8$	87.3849	−	87.3849i	1.36539	−	1.36539i
$9$		−	17.5042i		−	0.216101i
$10$	159.742	+	73.8545i	1.59742	+	0.738545i
$11$	−60.0183			−0.496019			−0.248009	−	0.968758i	$-0.579776\pi$
$11$	−60.0183			−0.496019			−0.248009	+	0.968758i	$0.579776\pi$
$12$	235.490	+	235.490i	1.63535	+	1.63535i
$13$	35.2905	−	35.2905i	0.208819	−	0.208819i	−0.594946	−	0.803766i	$-0.702827\pi$
$13$	35.2905	−	35.2905i	0.208819	−	0.208819i	0.803766	+	0.594946i	$0.202827\pi$
$14$			455.046i			2.32167i
$15$	−104.126	+	225.217i	−0.462782	+	1.00097i
$16$	−333.070			−1.30106
$17$	160.917	+	160.917i	0.556808	+	0.556808i	0.928397	−	0.371590i	$-0.121187\pi$
$17$	160.917	+	160.917i	0.556808	+	0.556808i	−0.371590	+	0.928397i	$0.621187\pi$
$18$	−87.1308	+	87.1308i	−0.268922	+	0.268922i
$19$			466.169i			1.29133i	0.763622	+	0.645663i	$0.223419\pi$
$19$			466.169i			1.29133i	−0.763622	+	0.645663i	$0.776581\pi$
$20$	−289.488	−	787.349i	−0.723721	−	1.96837i
$21$	−641.562			−1.45479
$22$	298.754	+	298.754i	0.617260	+	0.617260i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	1226.53i		−	2.12940i
$25$	476.142	−	404.862i	0.761828	−	0.647780i
$26$	−351.332			−0.519721
$27$	445.613	+	445.613i	0.611266	+	0.611266i
$28$	1533.76	−	1533.76i	1.95632	−	1.95632i
$29$			100.966i			0.120054i	0.998197	+	0.0600272i	$0.0191187\pi$
$29$			100.966i			0.120054i	−0.998197	+	0.0600272i	$0.980881\pi$
$30$	1639.38	−	602.758i	1.82153	−	0.669731i
$31$	352.856			0.367176			0.183588	−	0.983003i	$-0.441229\pi$
$31$	352.856			0.367176			0.183588	+	0.983003i	$0.441229\pi$
$32$	259.769	+	259.769i	0.253680	+	0.253680i
$33$	−421.207	+	421.207i	−0.386784	+	0.386784i
$34$		−	1602.00i		−	1.38581i
$35$	1466.85	+	678.177i	1.19743	+	0.553614i
$36$	587.357			0.453208
$37$	1480.63	+	1480.63i	1.08154	+	1.08154i	0.996366	+	0.0851786i	$0.0271461\pi$
$37$	1480.63	+	1480.63i	1.08154	+	1.08154i	0.0851786	+	0.996366i	$0.472854\pi$
$38$	2320.46	−	2320.46i	1.60696	−	1.60696i
$39$		−	495.336i		−	0.325665i
$40$	−1296.53	+	2804.31i	−0.810333	+	1.75269i
$41$	−2637.08			−1.56875			−0.784377	−	0.620284i	$-0.787017\pi$
$41$	−2637.08			−1.56875			−0.784377	+	0.620284i	$0.787017\pi$
$42$	3193.51	+	3193.51i	1.81038	+	1.81038i
$43$	−377.184	+	377.184i	−0.203994	+	0.203994i	−0.801709	−	0.597715i	$-0.796075\pi$
$43$	−377.184	+	377.184i	−0.203994	+	0.203994i	0.597715	+	0.801709i	$0.296075\pi$
$44$		−	2013.93i		−	1.04025i
$45$	151.012	+	410.723i	0.0745741	+	0.202826i
$46$	−776.491			−0.366962
$47$	−2531.67	−	2531.67i	−1.14607	−	1.14607i	−0.987319	−	0.158750i	$-0.949254\pi$
$47$	−2531.67	−	2531.67i	−1.14607	−	1.14607i	−0.158750	−	0.987319i	$-0.550746\pi$
$48$	−2337.48	+	2337.48i	−1.01453	+	1.01453i
$49$			1777.51i			0.740323i
$50$	−4385.39	−	354.810i	−1.75416	−	0.141924i
$51$	2258.63			0.868370
$52$	1184.18	+	1184.18i	0.437936	+	0.437936i
$53$	−2413.27	+	2413.27i	−0.859121	+	0.859121i	−0.991235	−	0.132114i	$-0.957824\pi$
$53$	−2413.27	+	2413.27i	−0.859121	+	0.859121i	0.132114	+	0.991235i	$0.457824\pi$
$54$		−	4436.26i		−	1.52135i
$55$	1408.28	−	517.791i	0.465549	−	0.171171i
$56$	−7988.45			−2.54734
$57$	3271.57	+	3271.57i	1.00695	+	1.00695i
$58$	502.578	−	502.578i	0.149399	−	0.149399i
$59$			2795.50i			0.803075i	0.915843	+	0.401538i	$0.131524\pi$
$59$			2795.50i			0.803075i	−0.915843	+	0.401538i	$0.868476\pi$
$60$	−7557.22	−	3493.97i	−2.09923	−	0.970549i
$61$	5911.03			1.58856			0.794280	−	0.607552i	$-0.207848\pi$
$61$	5911.03			1.58856			0.794280	+	0.607552i	$0.207848\pi$
$62$	−1756.42	−	1756.42i	−0.456924	−	0.456924i
$63$	−800.088	+	800.088i	−0.201584	+	0.201584i
$64$			2743.01i			0.669681i
$65$	−523.606	+	1132.52i	−0.123930	+	0.268053i
$66$	4193.30			0.962649
$67$	−153.737	−	153.737i	−0.0342474	−	0.0342474i	0.689776	−	0.724023i	$-0.257709\pi$
$67$	−153.737	−	153.737i	−0.0342474	−	0.0342474i	−0.724023	+	0.689776i	$0.757709\pi$
$68$	−5399.62	+	5399.62i	−1.16774	+	1.16774i
$69$		−	1094.76i		−	0.229943i
$70$	−3925.79	−	10677.3i	−0.801181	−	2.17905i
$71$	−4449.97			−0.882756			−0.441378	−	0.897321i	$-0.645510\pi$
$71$	−4449.97			−0.882756			−0.441378	+	0.897321i	$0.645510\pi$
$72$	−1529.60	−	1529.60i	−0.295062	−	0.295062i
$73$	−6661.36	+	6661.36i	−1.25002	+	1.25002i	−0.294312	+	0.955710i	$0.595090\pi$
$73$	−6661.36	+	6661.36i	−1.25002	+	1.25002i	−0.955710	+	0.294312i	$0.904910\pi$
$74$		−	14740.3i		−	2.69181i
$75$	500.240	−	6182.88i	0.0889316	−	1.09918i
$76$	−15642.4			−2.70817
$77$	2743.34	+	2743.34i	0.462699	+	0.462699i
$78$	−2465.64	+	2465.64i	−0.405266	+	0.405266i
$79$			7130.60i			1.14254i	0.820762	+	0.571270i	$0.193549\pi$
$79$			7130.60i			1.14254i	−0.820762	+	0.571270i	$0.806451\pi$
$80$	7815.24	−	2873.47i	1.22113	−	0.448980i
$81$	7672.44			1.16940
$82$	13126.6	+	13126.6i	1.95220	+	1.95220i
$83$	176.164	−	176.164i	0.0255718	−	0.0255718i	−0.694205	−	0.719777i	$-0.744244\pi$
$83$	176.164	−	176.164i	0.0255718	−	0.0255718i	0.719777	+	0.694205i	$0.244244\pi$
$84$		−	21527.8i		−	3.05099i
$85$	−5164.08	−	2387.54i	−0.714751	−	0.330455i
$86$	3755.03			0.507711
$87$	708.576	+	708.576i	0.0936155	+	0.0936155i
$88$	−5244.69	+	5244.69i	−0.677259	+	0.677259i
$89$			11243.3i			1.41943i	0.704489	+	0.709715i	$0.251176\pi$
$89$			11243.3i			1.41943i	−0.704489	+	0.709715i	$0.748824\pi$
$90$	1292.76	−	2796.16i	0.159600	−	0.345204i
$91$	−3226.14			−0.389583
$92$	2617.20	+	2617.20i	0.309216	+	0.309216i
$93$	2476.34	−	2476.34i	0.286315	−	0.286315i
$94$			25203.8i			2.85240i
$95$	−4021.74	−	10938.3i	−0.445622	−	1.21200i
$96$	3646.11			0.395628
$97$	9789.11	+	9789.11i	1.04040	+	1.04040i	0.999149	+	0.0412500i	$0.0131340\pi$
$97$	9789.11	+	9789.11i	1.04040	+	1.04040i	0.0412500	+	0.999149i	$0.486866\pi$
$98$	8847.96	−	8847.96i	0.921278	−	0.921278i
$99$			1050.57i			0.107190i
$100$	13585.3	+	15977.1i	1.35853	+	1.59771i
$101$	5330.19			0.522517			0.261258	−	0.965269i	$-0.415863\pi$
$101$	5330.19			0.522517			0.261258	+	0.965269i	$0.415863\pi$
$102$	−11242.8	−	11242.8i	−1.08062	−	1.08062i
$103$	−1060.81	+	1060.81i	−0.0999914	+	0.0999914i	−0.755333	−	0.655341i	$-0.772525\pi$
$103$	−1060.81	+	1060.81i	−0.0999914	+	0.0999914i	0.655341	+	0.755333i	$0.272525\pi$
$104$		−	6167.71i		−	0.570239i
$105$	15053.8	−	5534.89i	1.36542	−	0.502031i
$106$	24025.1			2.13823
$107$	−9773.94	−	9773.94i	−0.853694	−	0.853694i	0.136892	−	0.990586i	$-0.456289\pi$
$107$	−9773.94	−	9773.94i	−0.853694	−	0.853694i	−0.990586	+	0.136892i	$0.956289\pi$
$108$	−14952.6	+	14952.6i	−1.28195	+	1.28195i
$109$		−	15885.8i		−	1.33708i	−0.743677	−	0.668539i	$-0.766920\pi$
$109$		−	15885.8i		−	1.33708i	0.743677	−	0.668539i	$-0.233080\pi$
$110$	−9587.45	−	4432.62i	−0.792351	−	0.366332i
$111$	20782.1			1.68672
$112$	15224.1	+	15224.1i	1.21366	+	1.21366i
$113$	−6261.34	+	6261.34i	−0.490355	+	0.490355i	−0.908418	−	0.418063i	$-0.862709\pi$
$113$	−6261.34	+	6261.34i	−0.490355	+	0.490355i	0.418063	+	0.908418i	$0.362709\pi$
$114$		−	32569.8i		−	2.50614i
$115$	−1157.24	+	2503.03i	−0.0875040	+	0.189265i
$116$	−3387.93			−0.251778
$117$	−617.731	−	617.731i	−0.0451261	−	0.0451261i
$118$	13915.2	−	13915.2i	0.999369	−	0.999369i
$119$		−	14710.6i		−	1.03881i
$120$	10581.6	+	28779.7i	0.734830	+	1.99859i
$121$	−11038.8			−0.753965
$122$	−29423.4	−	29423.4i	−1.97685	−	1.97685i
$123$	−18507.0	+	18507.0i	−1.22328	+	1.22328i
$124$			11840.2i			0.770043i
$125$	−7679.48	+	13607.6i	−0.491487	+	0.870885i
$126$	7965.22			0.501715
$127$	−2516.45	−	2516.45i	−0.156020	−	0.156020i	0.624780	−	0.780801i	$-0.285189\pi$
$127$	−2516.45	−	2516.45i	−0.156020	−	0.156020i	−0.780801	+	0.624780i	$0.785189\pi$
$128$	17810.2	−	17810.2i	1.08705	−	1.08705i
$129$			5294.15i			0.318139i
$130$	8243.73	−	3031.01i	0.487795	−	0.179350i
$131$	743.202			0.0433076			0.0216538	−	0.999766i	$-0.493107\pi$
$131$	743.202			0.0433076			0.0216538	+	0.999766i	$0.493107\pi$
$132$	−14133.7	−	14133.7i	−0.811164	−	0.811164i
$133$	21307.8	−	21307.8i	1.20458	−	1.20458i
$134$			1530.51i			0.0852370i
$135$	−14300.4	−	6611.57i	−0.784656	−	0.362775i
$136$	28123.5			1.52052
$137$	−11236.6	−	11236.6i	−0.598680	−	0.598680i	0.341281	−	0.939961i	$-0.389139\pi$
$137$	−11236.6	−	11236.6i	−0.598680	−	0.598680i	−0.939961	+	0.341281i	$0.889139\pi$
$138$	−5449.40	+	5449.40i	−0.286148	+	0.286148i
$139$		−	19759.8i		−	1.02271i	−0.859370	−	0.511355i	$-0.829144\pi$
$139$		−	19759.8i		−	1.02271i	0.859370	−	0.511355i	$-0.170856\pi$
$140$	−22756.4	+	49220.5i	−1.16104	+	2.51125i
$141$	−35534.4			−1.78735
$142$	22150.7	+	22150.7i	1.09853	+	1.09853i
$143$	−2118.07	+	2118.07i	−0.103578	+	0.103578i
$144$			5830.12i			0.281160i
$145$	−871.053	−	2369.09i	−0.0414294	−	0.112679i
$146$	66316.7			3.11112
$147$	12474.6	+	12474.6i	0.577286	+	0.577286i
$148$	−49683.0	+	49683.0i	−2.26822	+	2.26822i
$149$			24570.0i			1.10671i	0.832946	+	0.553354i	$0.186652\pi$
$149$			24570.0i			1.10671i	−0.832946	+	0.553354i	$0.813348\pi$
$150$	−33266.6	+	28286.5i	−1.47852	+	1.25718i
$151$	−40561.2			−1.77892			−0.889461	−	0.457011i	$-0.848920\pi$
$151$	−40561.2			−1.77892			−0.889461	+	0.457011i	$0.848920\pi$
$152$	40736.1	+	40736.1i	1.76316	+	1.76316i
$153$	2816.73	−	2816.73i	0.120327	−	0.120327i
$154$		−	27311.1i		−	1.15159i
$155$	−8279.51	+	3044.17i	−0.344621	+	0.126708i
$156$	16621.1			0.682984
$157$	10156.0	+	10156.0i	0.412025	+	0.412025i	0.882443	−	0.470418i	$-0.155897\pi$
$157$	10156.0	+	10156.0i	0.412025	+	0.412025i	−0.470418	+	0.882443i	$0.655897\pi$
$158$	35494.1	−	35494.1i	1.42181	−	1.42181i
$159$			33872.6i			1.33984i
$160$	−8336.36	−	3854.20i	−0.325639	−	0.150555i
$161$	−7130.22			−0.275075
$162$	−38191.2	−	38191.2i	−1.45524	−	1.45524i
$163$	19169.4	−	19169.4i	0.721495	−	0.721495i	−0.247415	−	0.968910i	$-0.579581\pi$
$163$	19169.4	−	19169.4i	0.721495	−	0.721495i	0.968910	+	0.247415i	$0.0795810\pi$
$164$		−	88487.7i		−	3.29000i
$165$	6249.47	−	13517.2i	0.229549	−	0.496498i
$166$	−1753.79			−0.0636444
$167$	11211.5	+	11211.5i	0.402005	+	0.402005i	0.878939	−	0.476934i	$-0.158252\pi$
$167$	11211.5	+	11211.5i	0.402005	+	0.402005i	−0.476934	+	0.878939i	$0.658252\pi$
$168$	−56062.8	+	56062.8i	−1.98635	+	1.98635i
$169$			26070.2i			0.912789i
$170$	13820.8	+	37589.8i	0.478229	+	1.30068i
$171$	8159.91			0.279057
$172$	−12656.5	−	12656.5i	−0.427816	−	0.427816i
$173$	−10692.3	+	10692.3i	−0.357255	+	0.357255i	−0.862800	−	0.505545i	$-0.831291\pi$
$173$	−10692.3	+	10692.3i	−0.357255	+	0.357255i	0.505545	+	0.862800i	$0.331291\pi$
$174$		−	7054.17i		−	0.232996i
$175$	−40269.3	−	3258.08i	−1.31492	−	0.106386i
$176$	19990.3			0.645348
$177$	19618.8	+	19618.8i	0.626219	+	0.626219i
$178$	55965.9	−	55965.9i	1.76638	−	1.76638i
$179$			48056.2i			1.49983i	0.661532	+	0.749917i	$0.269906\pi$
$179$			48056.2i			1.49983i	−0.661532	+	0.749917i	$0.730094\pi$
$180$	−13781.9	+	5067.26i	−0.425367	+	0.156397i
$181$	−44271.2			−1.35134			−0.675669	−	0.737205i	$-0.736145\pi$
$181$	−44271.2			−1.35134			−0.675669	+	0.737205i	$0.736145\pi$
$182$	16058.8	+	16058.8i	0.484809	+	0.484809i
$183$	41483.5	−	41483.5i	1.23872	−	1.23872i
$184$		−	13631.5i		−	0.402631i
$185$	−47515.7	−	21968.2i	−1.38833	−	0.641876i
$186$	−24653.0			−0.712597
$187$	−9657.99	−	9657.99i	−0.276187	−	0.276187i
$188$	84950.6	−	84950.6i	2.40354	−	2.40354i
$189$		−	40736.5i		−	1.14041i
$190$	−34428.7	+	74466.8i	−0.953703	+	2.06279i
$191$	46411.0			1.27220			0.636099	−	0.771608i	$-0.280547\pi$
$191$	46411.0			1.27220			0.636099	+	0.771608i	$0.280547\pi$
$192$	19250.4	+	19250.4i	0.522201	+	0.522201i
$193$	29350.6	−	29350.6i	0.787957	−	0.787957i	−0.193202	−	0.981159i	$-0.561887\pi$
$193$	29350.6	−	29350.6i	0.787957	−	0.787957i	0.981159	+	0.193202i	$0.0618874\pi$
$194$		−	97454.8i		−	2.58940i
$195$	4273.37	+	11622.7i	0.112383	+	0.305659i
$196$	−59644.9			−1.55261
$197$	22713.0	+	22713.0i	0.585252	+	0.585252i	0.936342	−	0.351090i	$-0.114189\pi$
$197$	22713.0	+	22713.0i	0.585252	+	0.585252i	−0.351090	+	0.936342i	$0.614189\pi$
$198$	5229.44	−	5229.44i	0.133391	−	0.133391i
$199$		−	33260.6i		−	0.839894i	−0.907549	−	0.419947i	$-0.862049\pi$
$199$		−	33260.6i		−	0.839894i	0.907549	−	0.419947i	$-0.137951\pi$
$200$	6228.78	−	76986.5i	0.155719	−	1.92466i
$201$	−2157.84			−0.0534107
$202$	−26532.2	−	26532.2i	−0.650234	−	0.650234i
$203$	4614.98	−	4614.98i	0.111990	−	0.111990i
$204$			75788.9i			1.82115i
$205$	61877.0	−	22750.6i	1.47239	−	0.541359i
$206$	10560.8			0.248864
$207$	−1365.27	−	1365.27i	−0.0318624	−	0.0318624i
$208$	−11754.2	+	11754.2i	−0.271686	+	0.271686i
$209$		−	27978.7i		−	0.640523i
$210$	−102484.	−	47382.2i	−2.32391	−	1.07443i
$211$	−23473.0			−0.527234			−0.263617	−	0.964627i	$-0.584915\pi$
$211$	−23473.0			−0.527234			−0.263617	+	0.964627i	$0.584915\pi$
$212$	−80977.8	−	80977.8i	−1.80175	−	1.80175i
$213$	−31229.8	+	31229.8i	−0.688352	+	0.688352i
$214$			97303.7i			2.12472i
$215$	5596.30	−	12104.4i	0.121066	−	0.261858i
$216$	77879.6			1.66923
$217$	−16128.5	−	16128.5i	−0.342511	−	0.342511i
$218$	−79075.1	+	79075.1i	−1.66390	+	1.66390i
$219$			93498.7i			1.94947i
$220$	17374.6	+	47255.3i	0.358979	+	0.976349i
$221$	11357.7			0.232544
$222$	−103447.	−	103447.i	−2.09901	−	2.09901i
$223$	20418.7	−	20418.7i	0.410600	−	0.410600i	−0.471348	−	0.881947i	$-0.656232\pi$
$223$	20418.7	−	20418.7i	0.410600	−	0.410600i	0.881947	+	0.471348i	$0.156232\pi$
$224$		−	23747.2i		−	0.473279i
$225$	−7086.79	−	8334.48i	−0.139986	−	0.164632i
$226$	62334.3			1.22042
$227$	−38746.4	−	38746.4i	−0.751934	−	0.751934i	0.222906	−	0.974840i	$-0.428446\pi$
$227$	−38746.4	−	38746.4i	−0.751934	−	0.751934i	−0.974840	+	0.222906i	$0.928446\pi$
$228$	−109778.	+	109778.i	−2.11177	+	2.11177i
$229$			102170.i			1.94829i	0.225922	+	0.974145i	$0.427460\pi$
$229$			102170.i			1.94829i	−0.225922	+	0.974145i	$0.572540\pi$
$230$	18219.8	−	6698.96i	0.344419	−	0.126634i
$231$	38505.4			0.721602
$232$	8822.88	+	8822.88i	0.163921	+	0.163921i
$233$	−2305.59	+	2305.59i	−0.0424689	+	0.0424689i	−0.728022	−	0.685553i	$-0.759560\pi$
$233$	−2305.59	+	2305.59i	−0.0424689	+	0.0424689i	0.685553	+	0.728022i	$0.259560\pi$
$234$			6149.77i			0.112312i
$235$	81244.9	+	37562.4i	1.47116	+	0.680170i
$236$	−93803.8			−1.68421
$237$	50042.4	+	50042.4i	0.890926	+	0.890926i
$238$	−73224.9	+	73224.9i	−1.29272	+	1.29272i
$239$		−	12622.0i		−	0.220969i	−0.993878	−	0.110484i	$-0.964760\pi$
$239$		−	12622.0i		−	0.220969i	0.993878	−	0.110484i	$-0.0352402\pi$
$240$	34681.3	−	75013.2i	0.602106	−	1.30231i
$241$	−86507.2			−1.48942			−0.744712	−	0.667387i	$-0.767413\pi$
$241$	−86507.2			−1.48942			−0.744712	+	0.667387i	$0.767413\pi$
$242$	54948.0	+	54948.0i	0.938255	+	0.938255i
$243$	17750.5	−	17750.5i	0.300606	−	0.300606i
$244$			198346.i			3.33153i
$245$	−15335.0	−	41708.1i	−0.255477	−	0.694845i
$246$	184245.			3.04456
$247$	16451.3	+	16451.3i	0.269654	+	0.269654i
$248$	30834.3	−	30834.3i	0.501338	−	0.501338i
$249$		−	2472.63i		−	0.0398805i
$250$	105961.	−	29508.3i	1.69537	−	0.472133i
$251$	36484.6			0.579111			0.289556	−	0.957161i	$-0.406492\pi$
$251$	36484.6			0.579111			0.289556	+	0.957161i	$0.406492\pi$
$252$	−26847.2	−	26847.2i	−0.422763	−	0.422763i
$253$	−4681.23	+	4681.23i	−0.0731340	+	0.0731340i
$254$			25052.4i			0.388312i
$255$	−52997.1	+	19485.7i	−0.815026	+	0.299665i
$256$	−133420.			−2.03583
$257$	18324.1	+	18324.1i	0.277431	+	0.277431i	0.832083	−	0.554651i	$-0.187148\pi$
$257$	18324.1	+	18324.1i	0.277431	+	0.277431i	−0.554651	+	0.832083i	$0.687148\pi$
$258$	26352.7	−	26352.7i	0.395901	−	0.395901i
$259$		−	135355.i		−	2.01778i
$260$	−38002.1	−	17569.7i	−0.562161	−	0.259907i
$261$	1767.32			0.0259439
$262$	−3699.44	−	3699.44i	−0.0538932	−	0.0538932i
$263$	81083.1	−	81083.1i	1.17225	−	1.17225i	0.190574	−	0.981673i	$-0.438965\pi$
$263$	81083.1	−	81083.1i	1.17225	−	1.17225i	0.981673	−	0.190574i	$-0.0610349\pi$
$264$			73614.3i			1.05622i
$265$	35805.8	−	77445.4i	0.509872	−	1.10282i
$266$	−212129.			−2.99803
$267$	78905.3	+	78905.3i	1.10684	+	1.10684i
$268$	5158.67	−	5158.67i	0.0718238	−	0.0718238i
$269$		−	71105.8i		−	0.982654i	−0.870975	−	0.491327i	$-0.836512\pi$
$269$		−	71105.8i		−	0.982654i	0.870975	−	0.491327i	$-0.163488\pi$
$270$	38272.6	+	104094.i	0.525001	+	1.42790i
$271$	29491.8			0.401571			0.200786	−	0.979635i	$-0.435651\pi$
$271$	29491.8			0.401571			0.200786	+	0.979635i	$0.435651\pi$
$272$	−53596.8	−	53596.8i	−0.724438	−	0.724438i
$273$	−22641.0	+	22641.0i	−0.303788	+	0.303788i
$274$			111865.i			1.49003i
$275$	−28577.2	+	24299.2i	−0.377881	+	0.321311i
$276$	36734.9			0.482238
$277$	−80229.2	−	80229.2i	−1.04562	−	1.04562i	−0.998909	−	0.0467095i	$-0.985126\pi$
$277$	−80229.2	−	80229.2i	−1.04562	−	1.04562i	−0.0467095	−	0.998909i	$-0.514874\pi$
$278$	−98358.4	+	98358.4i	−1.27269	+	1.27269i
$279$		−	6176.46i		−	0.0793472i
$280$	187443.	−	68918.1i	2.39085	−	0.879057i
$281$	−38447.2			−0.486914			−0.243457	−	0.969912i	$-0.578281\pi$
$281$	−38447.2			−0.486914			−0.243457	+	0.969912i	$0.578281\pi$
$282$	176880.	+	176880.i	2.22423	+	2.22423i
$283$	1680.86	−	1680.86i	0.0209874	−	0.0209874i	−0.696535	−	0.717523i	$-0.745276\pi$
$283$	1680.86	−	1680.86i	0.0209874	−	0.0209874i	0.717523	+	0.696535i	$0.245276\pi$
$284$		−	149320.i		−	1.85132i
$285$	−104989.	−	48540.3i	−1.29257	−	0.597603i
$286$	21086.3			0.257792
$287$	120537.	+	120537.i	1.46337	+	1.46337i
$288$	4547.04	−	4547.04i	0.0548206	−	0.0548206i
$289$		−	31732.2i		−	0.379931i
$290$	−7456.77	+	16128.5i	−0.0886655	+	0.191777i
$291$	137400.			1.62256
$292$	−223524.	−	223524.i	−2.62155	−	2.62155i
$293$	72597.7	−	72597.7i	0.845644	−	0.845644i	−0.143942	−	0.989586i	$-0.545978\pi$
$293$	72597.7	−	72597.7i	0.845644	−	0.845644i	0.989586	+	0.143942i	$0.0459779\pi$
$294$		−	124190.i		−	1.43678i
$295$	−24117.4	−	65594.4i	−0.277132	−	0.753742i
$296$	258770.			2.95346
$297$	−26744.9	−	26744.9i	−0.303199	−	0.303199i
$298$	122302.	−	122302.i	1.37722	−	1.37722i
$299$		−	5505.09i		−	0.0615775i
$300$	207468.	+	16785.7i	2.30520	+	0.186508i
$301$	34481.0			0.380581
$302$	201902.	+	201902.i	2.21374	+	2.21374i
$303$	37407.2	−	37407.2i	0.407446	−	0.407446i
$304$		−	155267.i		−	1.68009i
$305$	−138698.	+	50995.8i	−1.49098	+	0.548194i
$306$	−28041.7			−0.299476
$307$	94937.4	+	94937.4i	1.00730	+	1.00730i	0.999973	+	0.00733124i	$0.00233363\pi$
$307$	94937.4	+	94937.4i	1.00730	+	1.00730i	0.00733124	+	0.999973i	$0.497666\pi$
$308$	−92053.4	+	92053.4i	−0.970372	+	0.970372i
$309$			14889.5i			0.155942i
$310$	56366.0	+	26060.0i	0.586535	+	0.271176i
$311$	3371.20			0.0348549			0.0174274	−	0.999848i	$-0.494452\pi$
$311$	3371.20			0.0348549			0.0174274	+	0.999848i	$0.494452\pi$
$312$	−43284.9	−	43284.9i	−0.444659	−	0.444659i
$313$	−68614.1	+	68614.1i	−0.700366	+	0.700366i	−0.964489	−	0.264123i	$-0.914917\pi$
$313$	−68614.1	+	68614.1i	−0.700366	+	0.700366i	0.264123	+	0.964489i	$0.414917\pi$
$314$		−	101107.i		−	1.02547i
$315$	11870.9	−	25676.0i	0.119637	−	0.258766i
$316$	−239269.			−2.39614
$317$	−53889.7	−	53889.7i	−0.536275	−	0.536275i	0.386158	−	0.922433i	$-0.373802\pi$
$317$	−53889.7	−	53889.7i	−0.536275	−	0.536275i	−0.922433	+	0.386158i	$0.873802\pi$
$318$	168608.	−	168608.i	1.66734	−	1.66734i
$319$		−	6059.79i		−	0.0595492i
$320$	−23664.6	−	64362.8i	−0.231099	−	0.628543i
$321$	−137187.			−1.33138
$322$	35492.2	+	35492.2i	0.342311	+	0.342311i
$323$	−75014.7	+	75014.7i	−0.719021	+	0.719021i
$324$			257451.i			2.45247i
$325$	2515.50	−	31091.1i	0.0238153	−	0.294353i
$326$	−190840.			−1.79570
$327$	−111487.	−	111487.i	−1.04262	−	1.04262i
$328$	−230441.	+	230441.i	−2.14196	+	2.14196i
$329$			231437.i			2.13816i
$330$	−98392.6	+	36176.5i	−0.903513	+	0.332199i
$331$	−12140.8			−0.110813			−0.0554066	−	0.998464i	$-0.517646\pi$
$331$	−12140.8			−0.110813			−0.0554066	+	0.998464i	$0.517646\pi$
$332$	5911.22	+	5911.22i	0.0536291	+	0.0536291i
$333$	25917.3	−	25917.3i	0.233723	−	0.233723i
$334$		−	111615.i		−	1.00053i
$335$	4933.64	+	2281.00i	0.0439620	+	0.0203252i
$336$	213685.			1.89276
$337$	157442.	+	157442.i	1.38631	+	1.38631i	0.832927	+	0.553383i	$0.186663\pi$
$337$	157442.	+	157442.i	1.38631	+	1.38631i	0.553383	+	0.832927i	$0.313337\pi$
$338$	129770.	−	129770.i	1.13590	−	1.13590i
$339$			87884.0i			0.764734i
$340$	80114.4	−	173282.i	0.693031	−	1.49898i
$341$	−21177.8			−0.182126
$342$	−40617.7	−	40617.7i	−0.347267	−	0.347267i
$343$	−28498.5	+	28498.5i	−0.242233	+	0.242233i
$344$			65920.5i			0.557062i
$345$	9444.74	+	25687.7i	0.0793509	+	0.215818i
$346$	106446.			0.889155
$347$	−61285.3	−	61285.3i	−0.508976	−	0.508976i	0.405236	−	0.914212i	$-0.367189\pi$
$347$	−61285.3	−	61285.3i	−0.508976	−	0.508976i	−0.914212	+	0.405236i	$0.867189\pi$
$348$	−23776.4	+	23776.4i	−0.196331	+	0.196331i
$349$		−	155263.i		−	1.27473i	−0.770564	−	0.637363i	$-0.780025\pi$
$349$		−	155263.i		−	1.27473i	0.770564	−	0.637363i	$-0.219975\pi$
$350$	184231.	+	216667.i	1.50393	+	1.76871i
$351$	31451.7			0.255288
$352$	−15590.9	−	15590.9i	−0.125830	−	0.125830i
$353$	−45354.4	+	45354.4i	−0.363974	+	0.363974i	−0.865274	−	0.501300i	$-0.832855\pi$
$353$	−45354.4	+	45354.4i	−0.363974	+	0.363974i	0.501300	+	0.865274i	$0.332855\pi$
$354$		−	195314.i		−	1.55857i
$355$	104415.	−	38390.9i	0.828528	−	0.304629i
$356$	−377272.			−2.97683
$357$	−103238.	−	103238.i	−0.810037	−	0.810037i
$358$	239210.	−	239210.i	1.86643	−	1.86643i
$359$		−	88791.5i		−	0.688942i	−0.938797	−	0.344471i	$-0.888058\pi$
$359$		−	88791.5i		−	0.688942i	0.938797	−	0.344471i	$-0.111942\pi$
$360$	49087.2	+	22694.8i	0.378759	+	0.175114i
$361$	−86992.5			−0.667525
$362$	220369.	+	220369.i	1.68164	+	1.68164i
$363$	−77470.2	+	77470.2i	−0.587924	+	0.587924i
$364$		−	108254.i		−	0.817035i
$365$	98834.9	−	213773.i	0.741864	−	1.60460i
$366$	−412986.			−3.08300
$367$	−8186.22	−	8186.22i	−0.0607787	−	0.0607787i	0.676064	−	0.736843i	$-0.263684\pi$
$367$	−8186.22	−	8186.22i	−0.0607787	−	0.0607787i	−0.736843	+	0.676064i	$0.763684\pi$
$368$	−25978.4	+	25978.4i	−0.191830	+	0.191830i
$369$			46159.9i			0.339010i
$370$	127168.	+	345871.i	0.928913	+	2.52645i
$371$	220613.			1.60282
$372$	83094.2	+	83094.2i	0.600461	+	0.600461i
$373$	65921.2	−	65921.2i	0.473814	−	0.473814i	−0.429333	−	0.903146i	$-0.641251\pi$
$373$	65921.2	−	65921.2i	0.473814	−	0.473814i	0.903146	+	0.429333i	$0.141251\pi$
$374$			96149.4i			0.687390i
$375$	41603.3	+	149392.i	0.295845	+	1.06234i
$376$	−442459.			−3.12966
$377$	3563.13	+	3563.13i	0.0250697	+	0.0250697i
$378$	−202774.	+	202774.i	−1.41915	+	1.41915i
$379$			239280.i			1.66582i	0.553406	+	0.832911i	$0.313328\pi$
$379$			239280.i			1.66582i	−0.553406	+	0.832911i	$0.686672\pi$
$380$	367037.	−	134951.i	2.54181	−	0.934560i
$381$	−35320.9			−0.243322
$382$	−231021.	−	231021.i	−1.58316	−	1.58316i
$383$	−15711.5	+	15711.5i	−0.107107	+	0.107107i	−0.758630	−	0.651522i	$-0.774131\pi$
$383$	−15711.5	+	15711.5i	−0.107107	+	0.107107i	0.651522	+	0.758630i	$0.274131\pi$
$384$		−	249984.i		−	1.69531i
$385$	−88037.8	−	40703.0i	−0.593947	−	0.274603i
$386$	−292198.			−1.96111
$387$	6602.31	+	6602.31i	0.0440833	+	0.0440833i
$388$	−328476.	+	328476.i	−2.18193	+	2.18193i
$389$			209338.i			1.38340i	0.722184	+	0.691701i	$0.243139\pi$
$389$			209338.i			1.38340i	−0.722184	+	0.691701i	$0.756861\pi$
$390$	36582.8	−	79126.0i	0.240518	−	0.520223i
$391$	25102.1			0.164194
$392$	155328.	+	155328.i	1.01083	+	1.01083i
$393$	5215.78	−	5215.78i	0.0337702	−	0.0337702i
$394$		−	226118.i		−	1.45661i
$395$	−61517.2	−	167314.i	−0.394278	−	1.07235i
$396$	−35252.2			−0.224800
$397$	−194221.	−	194221.i	−1.23229	−	1.23229i	−0.963080	−	0.269215i	$-0.913236\pi$
$397$	−194221.	−	194221.i	−1.23229	−	1.23229i	−0.269215	−	0.963080i	$-0.586764\pi$
$398$	−165562.	+	165562.i	−1.04519	+	1.04519i
$399$		−	299076.i		−	1.87861i
$400$	−158589.	+	134848.i	−0.991180	+	0.842798i
$401$	−53436.2			−0.332313			−0.166156	−	0.986099i	$-0.553136\pi$
$401$	−53436.2			−0.332313			−0.166156	+	0.986099i	$0.553136\pi$
$402$	10741.1	+	10741.1i	0.0664657	+	0.0664657i
$403$	12452.5	−	12452.5i	0.0766735	−	0.0766735i
$404$			178856.i			1.09582i
$405$	−180028.	+	66191.8i	−1.09757	+	0.403547i
$406$	−45944.1			−0.278726
$407$	−88865.1	−	88865.1i	−0.536466	−	0.536466i
$408$	197370.	−	197370.i	1.18566	−	1.18566i
$409$		−	77180.5i		−	0.461382i	−0.973027	−	0.230691i	$-0.925901\pi$
$409$		−	77180.5i		−	0.461382i	0.973027	−	0.230691i	$-0.0740987\pi$
$410$	−421252.	−	194760.i	−2.50596	−	1.15860i
$411$	−157717.			−0.933673
$412$	−35595.7	−	35595.7i	−0.209702	−	0.209702i
$413$	127778.	−	127778.i	0.749128	−	0.749128i
$414$			13591.8i			0.0793009i
$415$	−2613.75	+	5653.36i	−0.0151764	+	0.0328254i
$416$	18334.7			0.105947
$417$	−138674.	−	138674.i	−0.797484	−	0.797484i
$418$	−139270.	+	139270.i	−0.797084	+	0.797084i
$419$			188729.i			1.07501i	0.843262	+	0.537503i	$0.180632\pi$
$419$			188729.i			1.07501i	−0.843262	+	0.537503i	$0.819368\pi$
$420$	185725.	+	505133.i	1.05286	+	2.86356i
$421$	231657.			1.30702			0.653508	−	0.756920i	$-0.273297\pi$
$421$	231657.			1.30702			0.653508	+	0.756920i	$0.273297\pi$
$422$	116842.	+	116842.i	0.656105	+	0.656105i
$423$	−44314.8	+	44314.8i	−0.247667	+	0.247667i
$424$			421767.i			2.34607i
$425$	141769.	+	11470.2i	0.784880	+	0.0635026i
$426$	310906.			1.71321
$427$	−270184.	−	270184.i	−1.48185	−	1.48185i
$428$	327967.	−	327967.i	1.79037	−	1.79037i
$429$			29729.2i			0.161536i
$430$	−88109.0	+	32395.5i	−0.476522	+	0.175205i
$431$	111516.			0.600318			0.300159	−	0.953889i	$-0.402960\pi$
$431$	111516.			0.600318			0.300159	+	0.953889i	$0.402960\pi$
$432$	−148420.	−	148420.i	−0.795290	−	0.795290i
$433$	10112.3	−	10112.3i	0.0539354	−	0.0539354i	−0.679625	−	0.733560i	$-0.737857\pi$
$433$	10112.3	−	10112.3i	0.0539354	−	0.0539354i	0.733560	+	0.679625i	$0.237857\pi$
$434$			160566.i			0.852460i
$435$	−22739.2	−	10513.2i	−0.120170	−	0.0555591i
$436$	533053.			2.80413
$437$	36359.7	+	36359.7i	0.190396	+	0.190396i
$438$	465409.	−	465409.i	2.42598	−	2.42598i
$439$			152395.i			0.790756i	0.918518	+	0.395378i	$0.129386\pi$
$439$			152395.i			0.790756i	−0.918518	+	0.395378i	$0.870614\pi$
$440$	77815.7	−	168310.i	0.401941	−	0.869369i
$441$	31114.0			0.159985
$442$	−56535.4	−	56535.4i	−0.289385	−	0.289385i
$443$	−148814.	+	148814.i	−0.758293	+	0.758293i	−0.976012	−	0.217718i	$-0.930139\pi$
$443$	−148814.	+	148814.i	−0.758293	+	0.758293i	0.217718	+	0.976012i	$0.430139\pi$
$444$			697349.i			3.53740i
$445$	−96998.4	−	263816.i	−0.489829	−	1.33223i
$446$	−203277.			−1.02192
$447$	172432.	+	172432.i	0.862984	+	0.862984i
$448$	125379.	−	125379.i	0.624695	−	0.624695i
$449$			13412.9i			0.0665320i	0.999447	+	0.0332660i	$0.0105909\pi$
$449$			13412.9i			0.0665320i	−0.999447	+	0.0332660i	$0.989409\pi$
$450$	−6210.67	+	76762.7i	−0.0306700	+	0.379075i
$451$	158273.			0.778132
$452$	−210101.	−	210101.i	−1.02837	−	1.02837i
$453$	−284658.	+	284658.i	−1.38716	+	1.38716i
$454$			385737.i			1.87146i
$455$	75699.0	−	27832.6i	0.365651	−	0.134441i
$456$	571771.			2.74975
$457$	−176842.	−	176842.i	−0.846744	−	0.846744i	0.142982	−	0.989725i	$-0.454331\pi$
$457$	−176842.	−	176842.i	−0.846744	−	0.846744i	−0.989725	+	0.142982i	$0.954331\pi$
$458$	508574.	−	508574.i	2.42451	−	2.42451i
$459$			143414.i			0.680715i
$460$	−83989.8	−	38831.5i	−0.396927	−	0.183514i
$461$	130892.			0.615903			0.307952	−	0.951402i	$-0.400356\pi$
$461$	130892.			0.615903			0.307952	+	0.951402i	$0.400356\pi$
$462$	−191669.	−	191669.i	−0.897982	−	0.897982i
$463$	238118.	−	238118.i	1.11078	−	1.11078i	0.117740	−	0.993044i	$-0.462435\pi$
$463$	238118.	−	238118.i	1.11078	−	1.11078i	0.993044	−	0.117740i	$-0.0375650\pi$
$464$		−	33628.7i		−	0.156197i
$465$	−36741.5	+	79469.4i	−0.169923	+	0.367531i
$466$	22953.2			0.105699
$467$	−186603.	−	186603.i	−0.855628	−	0.855628i	0.135191	−	0.990820i	$-0.456835\pi$
$467$	−186603.	−	186603.i	−0.855628	−	0.855628i	−0.990820	+	0.135191i	$0.956835\pi$
$468$	20728.1	−	20728.1i	0.0946385	−	0.0946385i
$469$			14054.1i			0.0638937i
$470$	−217439.	−	591388.i	−0.984331	−	2.67718i
$471$	142549.			0.642574
$472$	244285.	+	244285.i	1.09651	+	1.09651i
$473$	22638.0	−	22638.0i	0.101185	−	0.101185i
$474$		−	498193.i		−	2.21739i
$475$	188734.	+	221963.i	0.836496	+	0.983768i
$476$	493616.			2.17859
$477$	42242.3	+	42242.3i	0.185657	+	0.185657i
$478$	−62828.5	+	62828.5i	−0.274980	+	0.274980i
$479$			56312.2i			0.245432i	0.992442	+	0.122716i	$0.0391604\pi$
$479$			56312.2i			0.245432i	−0.992442	+	0.122716i	$0.960840\pi$
$480$	−85553.2	+	31455.8i	−0.371325	+	0.136527i
$481$	104505.			0.451695
$482$	430608.	+	430608.i	1.85348	+	1.85348i
$483$	−50039.7	+	50039.7i	−0.214497	+	0.214497i
$484$		−	370410.i		−	1.58122i
$485$	−314147.	−	145241.i	−1.33552	−	0.617457i
$486$	−176713.			−0.748164
$487$	26833.4	+	26833.4i	0.113141	+	0.113141i	0.761411	−	0.648270i	$-0.224507\pi$
$487$	26833.4	+	26833.4i	0.113141	+	0.113141i	−0.648270	+	0.761411i	$0.724507\pi$
$488$	516535.	−	516535.i	2.16900	−	2.16900i
$489$		−	269061.i		−	1.12521i
$490$	−131277.	+	283944.i	−0.546761	+	1.18261i
$491$	146195.			0.606413			0.303206	−	0.952925i	$-0.401943\pi$
$491$	146195.			0.606413			0.303206	+	0.952925i	$0.401943\pi$
$492$	−621005.	−	621005.i	−2.56546	−	2.56546i
$493$	−16247.1	+	16247.1i	−0.0668472	+	0.0668472i
$494$		−	163780.i		−	0.671130i
$495$	−9063.51	−	24650.9i	−0.0369901	−	0.100606i
$496$	−117526.			−0.477717
$497$	203401.	+	203401.i	0.823456	+	0.823456i
$498$	−12308.0	+	12308.0i	−0.0496284	+	0.0496284i
$499$			283089.i			1.13690i	0.822718	+	0.568450i	$0.192457\pi$
$499$			283089.i			1.13690i	−0.822718	+	0.568450i	$0.807543\pi$
$500$	−456605.	−	257687.i	−1.82642	−	1.03075i
$501$	157364.			0.626947
$502$	−181610.	−	181610.i	−0.720662	−	0.720662i
$503$	−71282.4	+	71282.4i	−0.281738	+	0.281738i	−0.833802	−	0.552064i	$-0.813841\pi$
$503$	−71282.4	+	71282.4i	−0.281738	+	0.281738i	0.552064	+	0.833802i	$0.313841\pi$
$504$			139831.i			0.550482i
$505$	−125069.	+	45984.7i	−0.490418	+	0.180315i
$506$	46603.7			0.182020
$507$	182960.	+	182960.i	0.711771	+	0.711771i
$508$	84440.2	−	84440.2i	0.327206	−	0.327206i
$509$			377501.i			1.45708i	0.685004	+	0.728539i	$0.259801\pi$
$509$			377501.i			1.45708i	−0.685004	+	0.728539i	$0.740199\pi$
$510$	360799.	+	166810.i	1.38715	+	0.641330i
$511$	608960.			2.33210
$512$	379164.	+	379164.i	1.44640	+	1.44640i
$513$	−207731.	+	207731.i	−0.789344	+	0.789344i
$514$		−	182424.i		−	0.690487i
$515$	15739.3	−	34042.9i	0.0593430	−	0.128355i
$516$	−177646.			−0.667201
$517$	151946.	+	151946.i	0.568472	+	0.568472i
$518$	−673757.	+	673757.i	−2.51098	+	2.51098i
$519$			150076.i			0.557157i
$520$	53210.2	+	144721.i	0.196783	+	0.535210i
$521$	−158649.			−0.584469			−0.292235	−	0.956347i	$-0.594399\pi$
$521$	−158649.			−0.584469			−0.292235	+	0.956347i	$0.594399\pi$
$522$	−8797.23	−	8797.23i	−0.0322853	−	0.0322853i
$523$	−95459.9	+	95459.9i	−0.348994	+	0.348994i	−0.859735	−	0.510741i	$-0.829371\pi$
$523$	−95459.9	+	95459.9i	−0.348994	+	0.348994i	0.510741	+	0.859735i	$0.329371\pi$
$524$			24938.3i			0.0908248i
$525$	−305475.	+	259744.i	−1.10830	+	0.942382i
$526$	−807217.			−2.91755
$527$	56780.7	+	56780.7i	0.204446	+	0.204446i
$528$	140292.	−	140292.i	0.503227	−	0.503227i
$529$		−	12167.0i		−	0.0434783i
$530$	−563732.	+	207270.i	−2.00688	+	0.737878i
$531$	48933.0			0.173545
$532$	714990.	+	714990.i	2.52625	+	2.52625i
$533$	−93063.6	+	93063.6i	−0.327586	+	0.327586i
$534$		−	785536.i		−	2.75476i
$535$	313660.	+	145016.i	1.09585	+	0.506651i
$536$	−26868.6			−0.0935222
$537$	337257.	+	337257.i	1.16953	+	1.16953i
$538$	−353944.	+	353944.i	−1.22284	+	1.22284i
$539$		−	106683.i		−	0.367214i
$540$	221853.	−	479852.i	0.760812	−	1.64558i
$541$	−126526.			−0.432301			−0.216150	−	0.976360i	$-0.569350\pi$
$541$	−126526.			−0.432301			−0.216150	+	0.976360i	$0.569350\pi$
$542$	−146802.	−	146802.i	−0.499726	−	0.499726i
$543$	−310695.	+	310695.i	−1.05374	+	1.05374i
$544$			83602.6i			0.282502i
$545$	137051.	+	372749.i	0.461411	+	1.25494i
$546$	225401.			0.756084
$547$	90531.6	+	90531.6i	0.302570	+	0.302570i	0.842019	−	0.539449i	$-0.181367\pi$
$547$	90531.6	+	90531.6i	0.302570	+	0.302570i	−0.539449	+	0.842019i	$0.681367\pi$
$548$	377048.	−	377048.i	1.25555	−	1.25555i
$549$		−	103468.i		−	0.343290i
$550$	263203.	+	21295.1i	0.870094	+	0.0703970i
$551$	−47067.1			−0.155029
$552$	−95665.6	−	95665.6i	−0.313962	−	0.313962i
$553$	325928.	−	325928.i	1.06579	−	1.06579i
$554$			798716.i			2.60239i
$555$	−487637.	+	179292.i	−1.58311	+	0.582070i
$556$	663044.			2.14483
$557$	−73994.4	−	73994.4i	−0.238500	−	0.238500i	0.577729	−	0.816229i	$-0.303939\pi$
$557$	−73994.4	−	73994.4i	−0.238500	−	0.238500i	−0.816229	+	0.577729i	$0.803939\pi$
$558$	−30744.7	+	30744.7i	−0.0987419	+	0.0987419i
$559$			26622.0i			0.0851957i
$560$	−488564.	−	225881.i	−1.55792	−	0.720282i
$561$	−135559.			−0.430728
$562$	191379.	+	191379.i	0.605929	+	0.605929i
$563$	−89048.5	+	89048.5i	−0.280937	+	0.280937i	−0.833483	−	0.552545i	$-0.813657\pi$
$563$	−89048.5	+	89048.5i	−0.280937	+	0.280937i	0.552545	+	0.833483i	$0.313657\pi$
$564$		−	1.19236e6i		−	3.74844i
$565$	92899.7	−	200936.i	0.291017	−	0.629448i
$566$	−16733.7			−0.0522346
$567$	−350695.	−	350695.i	−1.09085	−	1.09085i
$568$	−388860.	+	388860.i	−1.20531	+	1.20531i
$569$			108959.i			0.336542i	0.985741	+	0.168271i	$0.0538183\pi$
$569$			108959.i			0.336542i	−0.985741	+	0.168271i	$0.946182\pi$
$570$	280987.	+	764227.i	0.864842	+	2.35219i
$571$	−24728.4			−0.0758445			−0.0379222	−	0.999281i	$-0.512074\pi$
$571$	−24728.4			−0.0758445			−0.0379222	+	0.999281i	$0.512074\pi$
$572$	−71072.5	−	71072.5i	−0.217225	−	0.217225i
$573$	325712.	−	325712.i	0.992029	−	0.992029i
$574$		−	1.19999e6i		−	3.64212i
$575$	5559.59	−	68715.5i	0.0168154	−	0.207835i
$576$	48014.2			0.144719
$577$	136086.	+	136086.i	0.408755	+	0.408755i	0.881304	−	0.472549i	$-0.156666\pi$
$577$	136086.	+	136086.i	0.408755	+	0.408755i	−0.472549	+	0.881304i	$0.656666\pi$
$578$	−157954.	+	157954.i	−0.472796	+	0.472796i
$579$		−	411964.i		−	1.22886i
$580$	79495.2	−	29228.4i	0.236312	−	0.0868859i
$581$	−16104.3			−0.0477079
$582$	−683936.	−	683936.i	−2.01915	−	2.01915i
$583$	144840.	−	144840.i	0.426140	−	0.426140i
$584$			1.16421e6i			3.41353i
$585$	19823.9	+	9165.29i	0.0579265	+	0.0267815i
$586$	−722741.			−2.10469
$587$	−428921.	−	428921.i	−1.24481	−	1.24481i	−0.957984	−	0.286822i	$-0.907401\pi$
$587$	−428921.	−	428921.i	−1.24481	−	1.24481i	−0.286822	−	0.957984i	$-0.592599\pi$
$588$	−418587.	+	418587.i	−1.21069	+	1.21069i
$589$			164491.i			0.474144i
$590$	−206461.	+	446560.i	−0.593107	+	1.28285i
$591$	318800.			0.912731
$592$	−493155.	−	493155.i	−1.40715	−	1.40715i
$593$	−194892.	+	194892.i	−0.554223	+	0.554223i	−0.927657	−	0.373434i	$-0.878180\pi$
$593$	−194892.	+	194892.i	−0.554223	+	0.554223i	0.373434	+	0.927657i	$0.378180\pi$
$594$			266257.i			0.754619i
$595$	126911.	+	345172.i	0.358481	+	0.974994i
$596$	−824453.			−2.32099
$597$	−233423.	−	233423.i	−0.654929	−	0.654929i
$598$	−27402.7	+	27402.7i	−0.0766287	+	0.0766287i
$599$			343712.i			0.957947i	0.877829	+	0.478973i	$0.158991\pi$
$599$			343712.i			0.957947i	−0.877829	+	0.478973i	$0.841009\pi$
$600$	−496577.	−	584004.i	−1.37938	−	1.62223i
$601$	−30450.5			−0.0843035			−0.0421517	−	0.999111i	$-0.513421\pi$
$601$	−30450.5			−0.0843035			−0.0421517	+	0.999111i	$0.513421\pi$
$602$	−171636.	−	171636.i	−0.473605	−	0.473605i
$603$	−2691.04	+	2691.04i	−0.00740091	+	0.00740091i
$604$		−	1.36104e6i		−	3.73076i
$605$	259017.	−	95234.2i	0.707649	−	0.260185i
$606$	−372405.			−1.01407
$607$	444668.	+	444668.i	1.20687	+	1.20687i	0.972037	+	0.234829i	$0.0754530\pi$
$607$	444668.	+	444668.i	1.20687	+	1.20687i	0.234829	+	0.972037i	$0.424547\pi$
$608$	−121096.	+	121096.i	−0.327584	+	0.327584i
$609$		−	64775.7i		−	0.174654i
$610$	944241.	+	436556.i	2.53760	+	1.17322i
$611$	−178687.			−0.478642
$612$	94516.0	+	94516.0i	0.252350	+	0.252350i
$613$	−87800.5	+	87800.5i	−0.233655	+	0.233655i	−0.814217	−	0.580561i	$-0.802833\pi$
$613$	−87800.5	+	87800.5i	−0.233655	+	0.233655i	0.580561	+	0.814217i	$0.302833\pi$
$614$		−	945142.i		−	2.50704i
$615$	274588.	−	593915.i	0.725992	−	1.57027i
$616$	479453.			1.26353
$617$	−209927.	−	209927.i	−0.551440	−	0.551440i	0.375417	−	0.926856i	$-0.377500\pi$
$617$	−209927.	−	209927.i	−0.551440	−	0.551440i	−0.926856	+	0.375417i	$0.877500\pi$
$618$	74115.5	−	74115.5i	0.194058	−	0.194058i
$619$		−	478006.i		−	1.24753i	−0.781611	−	0.623766i	$-0.785602\pi$
$619$		−	478006.i		−	1.24753i	0.781611	−	0.623766i	$-0.214398\pi$
$620$	−102148.	−	277821.i	−0.265733	−	0.722739i
$621$	69512.7			0.180252
$622$	−16780.9	−	16780.9i	−0.0433744	−	0.0433744i
$623$	513913.	−	513913.i	1.32408	−	1.32408i
$624$			164982.i			0.423708i
$625$	62797.8	−	385544.i	0.160762	−	0.986993i
$626$	683083.			1.74311
$627$	−196354.	−	196354.i	−0.499464	−	0.499464i
$628$	−340787.	+	340787.i	−0.864100	+	0.864100i
$629$			476520.i			1.20442i
$630$	−186898.	+	68717.7i	−0.470894	+	0.173136i
$631$	623875.			1.56689			0.783445	−	0.621461i	$-0.213460\pi$
$631$	623875.			1.56689			0.783445	+	0.621461i	$0.213460\pi$
$632$	623107.	+	623107.i	1.56001	+	1.56001i
$633$	−164733.	+	164733.i	−0.411124	+	0.411124i
$634$			536495.i			1.33471i
$635$	80756.7	+	37336.7i	0.200277	+	0.0925952i
$636$	−1.13660e6			−2.80992
$637$	62729.3	+	62729.3i	0.154594	+	0.154594i
$638$	−30163.9	+	30163.9i	−0.0741048	+	0.0741048i
$639$			77893.1i			0.190764i
$640$	−264251.	+	571557.i	−0.645144	+	1.39540i
$641$	226803.			0.551992			0.275996	−	0.961159i	$-0.410992\pi$
$641$	226803.			0.551992			0.275996	+	0.961159i	$0.410992\pi$
$642$	682876.	+	682876.i	1.65681	+	1.65681i
$643$	−261852.	+	261852.i	−0.633335	+	0.633335i	−0.948903	−	0.315568i	$-0.897805\pi$
$643$	−261852.	+	261852.i	−0.633335	+	0.633335i	0.315568	+	0.948903i	$0.397805\pi$
$644$		−	239256.i		−	0.576888i
$645$	−45673.8	−	124223.i	−0.109786	−	0.298596i
$646$	746803.			1.78954
$647$	93311.7	+	93311.7i	0.222909	+	0.222909i	0.809722	−	0.586813i	$-0.199618\pi$
$647$	93311.7	+	93311.7i	0.222909	+	0.222909i	−0.586813	+	0.809722i	$0.699618\pi$
$648$	670456.	−	670456.i	1.59669	−	1.59669i
$649$		−	167781.i		−	0.398340i
$650$	−167284.	+	142241.i	−0.395938	+	0.336665i
$651$	−226379.			−0.534164
$652$	643234.	+	643234.i	1.51312	+	1.51312i
$653$	168989.	−	168989.i	0.396308	−	0.396308i	−0.480621	−	0.876929i	$-0.659589\pi$
$653$	168989.	−	168989.i	0.396308	−	0.396308i	0.876929	+	0.480621i	$0.159589\pi$
$654$			1.10990e6i			2.59494i
$655$	−17438.7	+	6411.76i	−0.0406472	+	0.0149450i
$656$	878332.			2.04104
$657$	116602.	+	116602.i	0.270131	+	0.270131i
$658$	1.15203e6	−	1.15203e6i	2.66079	−	2.66079i
$659$		−	102886.i		−	0.236911i	−0.992959	−	0.118455i	$-0.962206\pi$
$659$		−	102886.i		−	0.236911i	0.992959	−	0.118455i	$-0.0377942\pi$
$660$	453572.	+	209702.i	1.04126	+	0.481410i
$661$	−813233.			−1.86128			−0.930640	−	0.365935i	$-0.880749\pi$
$661$	−813233.			−1.86128			−0.930640	+	0.365935i	$0.880749\pi$
$662$	60433.5	+	60433.5i	0.137899	+	0.137899i
$663$	79708.1	−	79708.1i	0.181333	−	0.181333i
$664$		−	30788.1i		−	0.0698308i
$665$	−316145.	+	683800.i	−0.714896	+	1.54627i
$666$	−258018.			−0.581703
$667$	7875.00	+	7875.00i	0.0177011	+	0.0177011i
$668$	−376205.	+	376205.i	−0.843085	+	0.843085i
$669$		−	286596.i		−	0.640351i
$670$	−13204.1	−	35912.4i	−0.0294143	−	0.0800009i
$671$	−354770.			−0.787956
$672$	−166658.	−	166658.i	−0.369051	−	0.369051i
$673$	−505553.	+	505553.i	−1.11619	+	1.11619i	−0.123889	+	0.992296i	$0.539537\pi$
$673$	−505553.	+	505553.i	−1.11619	+	1.11619i	−0.992296	+	0.123889i	$0.960463\pi$
$674$		−	1.56740e6i		−	3.45033i
$675$	392587.	+	31763.2i	0.861644	+	0.0697134i
$676$	−874791.			−1.91430
$677$	−216642.	−	216642.i	−0.472679	−	0.472679i	0.430102	−	0.902780i	$-0.358478\pi$
$677$	−216642.	−	216642.i	−0.472679	−	0.472679i	−0.902780	+	0.430102i	$0.858478\pi$
$678$	437461.	−	437461.i	0.951656	−	0.951656i
$679$		−	894889.i		−	1.94102i
$680$	−659897.	+	242628.i	−1.42711	+	0.524714i
$681$	−543843.			−1.17268
$682$	105417.	+	105417.i	0.226643	+	0.226643i
$683$	158119.	−	158119.i	0.338955	−	0.338955i	−0.517019	−	0.855974i	$-0.672958\pi$
$683$	158119.	−	158119.i	0.338955	−	0.338955i	0.855974	+	0.517019i	$0.172958\pi$
$684$			273808.i			0.585239i
$685$	360600.	+	166718.i	0.768501	+	0.355306i
$686$	283715.			0.602884
$687$	717030.	+	717030.i	1.51923	+	1.51923i
$688$	125629.	−	125629.i	0.265407	−	0.265407i
$689$			170331.i			0.358802i
$690$	80853.0	−	174879.i	0.169823	−	0.367316i
$691$	−239527.			−0.501647			−0.250823	−	0.968033i	$-0.580701\pi$
$691$	−239527.			−0.501647			−0.250823	+	0.968033i	$0.580701\pi$
$692$	−358782.	−	358782.i	−0.749235	−	0.749235i
$693$	48019.9	−	48019.9i	0.0999897	−	0.0999897i
$694$			610121.i			1.26677i
$695$	170472.	+	463648.i	0.352925	+	0.959884i
$696$	123838.			0.255643
$697$	−424351.	−	424351.i	−0.873494	−	0.873494i
$698$	−772854.	+	772854.i	−1.58630	+	1.58630i
$699$			32361.2i			0.0662324i
$700$	109326.	−	1.35125e6i	0.223114	−	2.75765i
$701$	−498045.			−1.01352			−0.506760	−	0.862087i	$-0.669157\pi$
$701$	−498045.			−1.01352			−0.506760	+	0.862087i	$0.669157\pi$
$702$	−156558.	−	156558.i	−0.317688	−	0.317688i
$703$	−690226.	+	690226.i	−1.39663	+	1.39663i
$704$		−	164631.i		−	0.332175i
$705$	833787.	−	306563.i	1.67756	−	0.616796i
$706$	451522.			0.905878
$707$	−243635.	−	243635.i	−0.487416	−	0.487416i
$708$	−658314.	+	658314.i	−1.31331	+	1.31331i
$709$			440566.i			0.876433i	0.898869	+	0.438217i	$0.144390\pi$
$709$			440566.i			0.876433i	−0.898869	+	0.438217i	$0.855610\pi$
$710$	−710848.	−	328650.i	−1.41013	−	0.651955i
$711$	124815.			0.246904
$712$	982495.	+	982495.i	1.93807	+	1.93807i
$713$	27521.7	−	27521.7i	0.0541372	−	0.0541372i
$714$			1.02778e6i			2.01607i
$715$	31425.9	−	67972.1i	0.0614718	−	0.132959i
$716$	−1.61254e6			−3.14545
$717$	−88580.8	−	88580.8i	−0.172306	−	0.172306i
$718$	−441979.	+	441979.i	−0.857339	+	0.857339i
$719$		−	973296.i		−	1.88273i	−0.337394	−	0.941363i	$-0.609546\pi$
$719$		−	973296.i		−	1.88273i	0.337394	−	0.941363i	$-0.390454\pi$
$720$	−50297.8	−	136799.i	−0.0970250	−	0.263888i
$721$	96975.7			0.186549
$722$	433024.	+	433024.i	0.830687	+	0.830687i
$723$	−607106.	+	607106.i	−1.16142	+	1.16142i
$724$		−	1.48553e6i		−	2.83403i
$725$	40877.2	+	48074.1i	0.0777688	+	0.0914607i
$726$	771248.			1.46326
$727$	−386495.	−	386495.i	−0.731265	−	0.731265i	0.239606	−	0.970870i	$-0.422982\pi$
$727$	−386495.	−	386495.i	−0.731265	−	0.731265i	−0.970870	+	0.239606i	$0.922982\pi$
$728$	−281916.	+	281916.i	−0.531933	+	0.531933i
$729$			372323.i			0.700591i
$730$	−1.55607e6	+	572129.i	−2.92001	+	1.07361i
$731$	−121391.			−0.227171
$732$	1.39199e6	+	1.39199e6i	2.59785	+	2.59785i
$733$	−188457.	+	188457.i	−0.350756	+	0.350756i	−0.860391	−	0.509635i	$-0.829781\pi$
$733$	−188457.	+	188457.i	−0.350756	+	0.350756i	0.509635	+	0.860391i	$0.329781\pi$
$734$			81497.3i			0.151269i
$735$	−400327.	−	185086.i	−0.741038	−	0.342608i
$736$	40522.3			0.0748063
$737$	9227.02	+	9227.02i	0.0169874	+	0.0169874i
$738$	229771.	−	229771.i	0.421873	−	0.421873i
$739$		−	374653.i		−	0.686025i	−0.939331	−	0.343013i	$-0.888553\pi$
$739$		−	374653.i		−	0.686025i	0.939331	−	0.343013i	$-0.111447\pi$
$740$	737149.	−	1.59440e6i	1.34614	−	2.91162i
$741$	230910.			0.420539
$742$	−1.09815e6	−	1.09815e6i	−1.99459	−	1.99459i
$743$	25584.3	−	25584.3i	0.0463443	−	0.0463443i	−0.683555	−	0.729899i	$-0.739567\pi$
$743$	25584.3	−	25584.3i	0.0463443	−	0.0463443i	0.729899	+	0.683555i	$0.239567\pi$
$744$		−	432790.i		−	0.781863i
$745$	−211971.	−	576517.i	−0.381912	−	1.03872i
$746$	−656274.			−1.17925
$747$	−3083.61	−	3083.61i	−0.00552608	−	0.00552608i
$748$	324076.	−	324076.i	0.579220	−	0.579220i
$749$			893502.i			1.59269i
$750$	536543.	−	950721.i	0.953853	−	1.69017i
$751$	−427072.			−0.757218			−0.378609	−	0.925557i	$-0.623597\pi$
$751$	−427072.			−0.757218			−0.378609	+	0.925557i	$0.623597\pi$
$752$	843222.	+	843222.i	1.49110	+	1.49110i
$753$	256048.	−	256048.i	0.451577	−	0.451577i
$754$		−	35472.5i		−	0.0623948i
$755$	951738.	−	349930.i	1.66964	−	0.613886i
$756$	1.36692e6			2.39166
$757$	207275.	+	207275.i	0.361705	+	0.361705i	0.864440	−	0.502735i	$-0.167673\pi$
$757$	207275.	+	207275.i	0.361705	+	0.361705i	−0.502735	+	0.864440i	$0.667673\pi$
$758$	1.19107e6	−	1.19107e6i	2.07300	−	2.07300i
$759$			65705.7i			0.114056i
$760$	−1.30728e6	−	604404.i	−2.26330	−	1.04640i
$761$	1.10227e6			1.90335			0.951676	−	0.307104i	$-0.0993601\pi$
$761$	1.10227e6			1.90335			0.951676	+	0.307104i	$0.0993601\pi$
$762$	175817.	+	175817.i	0.302797	+	0.302797i
$763$	−726116.	+	726116.i	−1.24726	+	1.24726i
$764$			1.55733e6i			2.66806i
$765$	−41791.9	+	90393.0i	−0.0714117	+	0.154458i
$766$	156415.			0.266575
$767$	98654.7	+	98654.7i	0.167698	+	0.167698i
$768$	−936341.	+	936341.i	−1.58749	+	1.58749i
$769$			362301.i			0.612656i	0.951926	+	0.306328i	$0.0991005\pi$
$769$			362301.i			0.612656i	−0.951926	+	0.306328i	$0.900900\pi$
$770$	235619.	+	640835.i	0.397401	+	1.08085i
$771$	257196.			0.432669
$772$	984866.	+	984866.i	1.65250	+	1.65250i
$773$	79786.0	−	79786.0i	0.133527	−	0.133527i	−0.637185	−	0.770711i	$-0.719901\pi$
$773$	79786.0	−	79786.0i	0.133527	−	0.133527i	0.770711	+	0.637185i	$0.219901\pi$
$774$		−	65728.8i		−	0.109717i
$775$	168010.	−	142858.i	0.279725	−	0.237849i
$776$	1.71084e6			2.84110
$777$	−949918.	−	949918.i	−1.57342	−	1.57342i
$778$	1.04202e6	−	1.04202e6i	1.72155	−	1.72155i
$779$		−	1.22932e6i		−	2.02577i
$780$	−390002.	+	143394.i	−0.641029	+	0.235690i
$781$	267080.			0.437863
$782$	−124951.	−	124951.i	−0.204327	−	0.204327i
$783$	−44991.6	+	44991.6i	−0.0733851	+	0.0733851i
$784$		−	592037.i		−	0.963201i
$785$	−325921.	−	150685.i	−0.528900	−	0.244529i
$786$	−51925.3			−0.0840492
$787$	−390932.	−	390932.i	−0.631178	−	0.631178i	0.317185	−	0.948364i	$-0.397262\pi$
$787$	−390932.	−	390932.i	−0.631178	−	0.631178i	−0.948364	+	0.317185i	$0.897262\pi$
$788$	−762142.	+	762142.i	−1.22739	+	1.22739i
$789$		−	1.13808e6i		−	1.82818i
$790$	−526626.	+	1.13906e6i	−0.843817	+	1.82512i
$791$	572392.			0.914830
$792$	91804.1	+	91804.1i	0.146356	+	0.146356i
$793$	208603.	−	208603.i	0.331722	−	0.331722i
$794$			1.93355e6i			3.06700i
$795$	−292226.	−	794795.i	−0.462365	−	1.25754i
$796$	1.11607e6			1.76143
$797$	528575.	+	528575.i	0.832127	+	0.832127i	0.987807	−	0.155680i	$-0.0497570\pi$
$797$	528575.	+	528575.i	0.832127	+	0.832127i	−0.155680	+	0.987807i	$0.549757\pi$
$798$	−1.48871e6	+	1.48871e6i	−2.33779	+	2.33779i
$799$		−	814778.i		−	1.27628i
$800$	228858.	+	18516.3i	0.357590	+	0.0289317i
$801$	196805.			0.306740
$802$	265990.	+	265990.i	0.413539	+	0.413539i
$803$	399804.	−	399804.i	0.620034	−	0.620034i
$804$		−	72407.0i		−	0.112013i
$805$	167305.	−	61513.9i	0.258177	−	0.0949252i
$806$	−123970.			−0.190829
$807$	−499019.	−	499019.i	−0.766250	−	0.766250i
$808$	465778.	−	465778.i	0.713439	−	0.713439i
$809$			230834.i			0.352697i	0.984328	+	0.176349i	$0.0564286\pi$
$809$			230834.i			0.352697i	−0.984328	+	0.176349i	$0.943571\pi$
$810$	1.22561e6	+	566644.i	1.86803	+	0.863655i
$811$	451965.			0.687168			0.343584	−	0.939122i	$-0.388359\pi$
$811$	451965.			0.687168			0.343584	+	0.939122i	$0.388359\pi$
$812$	154857.	+	154857.i	0.234865	+	0.234865i
$813$	206973.	−	206973.i	0.313135	−	0.313135i
$814$			884690.i			1.33519i
$815$	−284417.	+	615174.i	−0.428194	+	0.926153i
$816$	−752283.			−1.12980
$817$	−175832.	−	175832.i	−0.263423	−	0.263423i
$818$	−384182.	+	384182.i	−0.574157	+	0.574157i
$819$			56471.0i			0.0841894i
$820$	763403.	+	2.07630e6i	1.13534	+	3.08789i
$821$	−329612.			−0.489008			−0.244504	−	0.969648i	$-0.578625\pi$
$821$	−329612.			−0.489008			−0.244504	+	0.969648i	$0.578625\pi$
$822$	785070.	+	785070.i	1.16189	+	1.16189i
$823$	−590744.	+	590744.i	−0.872167	+	0.872167i	−0.992708	−	0.120541i	$-0.961537\pi$
$823$	−590744.	+	590744.i	−0.872167	+	0.872167i	0.120541	+	0.992708i	$0.461537\pi$
$824$			185397.i			0.273054i
$825$	−30023.6	+	371086.i	−0.0441118	+	0.545213i
$826$	−1.27208e6			−1.86447
$827$	60958.3	+	60958.3i	0.0891296	+	0.0891296i	0.750266	−	0.661136i	$-0.229925\pi$
$827$	60958.3	+	60958.3i	0.0891296	+	0.0891296i	−0.661136	+	0.750266i	$0.729925\pi$
$828$	45812.0	−	45812.0i	0.0668218	−	0.0668218i
$829$		−	756707.i		−	1.10108i	−0.834809	−	0.550540i	$-0.814422\pi$
$829$		−	756707.i		−	1.10108i	0.834809	−	0.550540i	$-0.185578\pi$
$830$	41151.3	−	15130.3i	0.0597348	−	0.0219630i
$831$	−1.12609e6			−1.63070
$832$	96802.2	+	96802.2i	0.139842	+	0.139842i
$833$	−286033.	+	286033.i	−0.412217	+	0.412217i
$834$			1.38056e6i			1.98482i
$835$	−359794.	−	166346.i	−0.516037	−	0.238582i
$836$	938831.			1.34331
$837$	157237.	+	157237.i	0.224442	+	0.224442i
$838$	939440.	−	939440.i	1.33777	−	1.33777i
$839$			131846.i			0.187302i	0.995605	+	0.0936509i	$0.0298538\pi$
$839$			131846.i			0.187302i	−0.995605	+	0.0936509i	$0.970146\pi$
$840$	831806.	−	1.79914e6i	1.17886	−	2.54980i
$841$	697087.			0.985587
$842$	−1.15312e6	−	1.15312e6i	−1.62649	−	1.62649i
$843$	−269822.	+	269822.i	−0.379684	+	0.379684i
$844$		−	787641.i		−	1.10572i
$845$	−224913.	−	611717.i	−0.314993	−	0.856716i
$846$	441172.			0.616407
$847$	504566.	+	504566.i	0.703317	+	0.703317i
$848$	803788.	−	803788.i	1.11776	−	1.11776i
$849$		−	23592.5i		−	0.0327310i
$850$	−648590.	−	762780.i	−0.897702	−	1.05575i
$851$	230969.			0.318930
$852$	−1.04792e6	−	1.04792e6i	−1.44361	−	1.44361i
$853$	751333.	−	751333.i	1.03261	−	1.03261i	0.0331559	−	0.999450i	$-0.489444\pi$
$853$	751333.	−	751333.i	1.03261	−	1.03261i	0.999450	−	0.0331559i	$-0.0105558\pi$
$854$			2.68979e6i			3.68811i
$855$	−191466.	+	70397.3i	−0.261915	+	0.0962995i
$856$	−1.70819e6			−2.33125
$857$	−174736.	−	174736.i	−0.237915	−	0.237915i	0.578071	−	0.815986i	$-0.303806\pi$
$857$	−174736.	−	174736.i	−0.237915	−	0.237915i	−0.815986	+	0.578071i	$0.803806\pi$
$858$	147983.	−	147983.i	0.201020	−	0.201020i
$859$		−	477215.i		−	0.646737i	−0.946273	−	0.323368i	$-0.895185\pi$
$859$		−	477215.i		−	0.646737i	0.946273	−	0.323368i	$-0.104815\pi$
$860$	406166.	+	187785.i	0.549170	+	0.253901i
$861$	1.69185e6			2.28221
$862$	−555093.	−	555093.i	−0.747053	−	0.747053i
$863$	−460499.	+	460499.i	−0.618312	+	0.618312i	−0.945098	−	0.326787i	$-0.894034\pi$
$863$	−460499.	+	460499.i	−0.618312	+	0.618312i	0.326787	+	0.945098i	$0.394034\pi$
$864$			231513.i			0.310132i
$865$	158642.	−	343131.i	0.212024	−	0.458593i
$866$	−100672.			−0.134237
$867$	−222696.	−	222696.i	−0.296261	−	0.296261i
$868$	541196.	−	541196.i	0.718315	−	0.718315i
$869$		−	427966.i		−	0.566722i
$870$	60857.9	+	165521.i	0.0804041	+	0.218683i
$871$	−10850.9			−0.0143031
$872$	−1.38818e6	−	1.38818e6i	−1.82563	−	1.82563i
$873$	171350.	−	171350.i	0.224831	−	0.224831i
$874$		−	361976.i		−	0.473868i
$875$	972997.	−	270964.i	1.27085	−	0.353912i
$876$	−3.13737e6			−4.08844
$877$	−161437.	−	161437.i	−0.209896	−	0.209896i	0.594328	−	0.804223i	$-0.297418\pi$
$877$	−161437.	−	161437.i	−0.209896	−	0.209896i	−0.804223	+	0.594328i	$0.797418\pi$
$878$	758580.	−	758580.i	0.984039	−	0.984039i
$879$		−	1.01898e6i		−	1.31883i
$880$	−469058.	+	172461.i	−0.605704	+	0.222702i
$881$	511116.			0.658517			0.329259	−	0.944240i	$-0.393201\pi$
$881$	511116.			0.658517			0.329259	+	0.944240i	$0.393201\pi$
$882$	−154876.	−	154876.i	−0.199089	−	0.199089i
$883$	−830205.	+	830205.i	−1.06479	+	1.06479i	−0.0670391	+	0.997750i	$0.521355\pi$
$883$	−830205.	+	830205.i	−1.06479	+	1.06479i	−0.997750	+	0.0670391i	$0.978645\pi$
$884$			381110.i			0.487693i
$885$	−629596.	−	291085.i	−0.803851	−	0.371649i
$886$	1.48151e6			1.88728
$887$	894875.	+	894875.i	1.13741	+	1.13741i	0.988914	+	0.148492i	$0.0474419\pi$
$887$	894875.	+	894875.i	1.13741	+	1.13741i	0.148492	+	0.988914i	$0.452558\pi$
$888$	1.81604e6	−	1.81604e6i	2.30304	−	2.30304i
$889$			230046.i			0.291079i
$890$	−830368.	+	1.79603e6i	−1.04831	+	2.26743i
$891$	−460487.			−0.580045
$892$	685155.	+	685155.i	0.861110	+	0.861110i
$893$	1.18018e6	−	1.18018e6i	1.47995	−	1.47995i
$894$		−	1.71663e6i		−	2.14784i
$895$	−414591.	−	1.12760e6i	−0.517576	−	1.40770i
$896$	−1.62815e6			−2.02805
$897$	−38634.6	−	38634.6i	−0.0480166	−	0.0480166i
$898$	66765.7	−	66765.7i	0.0827943	−	0.0827943i
$899$			35626.4i			0.0440811i
$900$	279666.	−	237799.i	0.345266	−	0.293579i
$901$	−776674.			−0.956730
$902$	−787836.	−	787836.i	−0.968329	−	0.968329i
$903$	241987.	−	241987.i	0.296768	−	0.296768i
$904$			1.09429e6i			1.33905i
$905$	1.03879e6	−	381937.i	1.26833	−	0.466332i
$906$	2.83389e6			3.45244
$907$	−389725.	−	389725.i	−0.473744	−	0.473744i	0.429380	−	0.903124i	$-0.358732\pi$
$907$	−389725.	−	389725.i	−0.473744	−	0.473744i	−0.903124	+	0.429380i	$0.858732\pi$
$908$	1.30014e6	−	1.30014e6i	1.57696	−	1.57696i
$909$		−	93300.7i		−	0.112916i
$910$	−515351.	−	238265.i	−0.622329	−	0.287725i
$911$	−1.02058e6			−1.22973			−0.614863	−	0.788634i	$-0.710789\pi$
$911$	−1.02058e6			−1.22973			−0.614863	+	0.788634i	$0.710789\pi$
$912$	−1.08966e6	−	1.08966e6i	−1.31009	−	1.31009i
$913$	−10573.1	+	10573.1i	−0.0126841	+	0.0126841i
$914$			1.76053e6i			2.10742i
$915$	−615493.	+	1.33127e6i	−0.735158	+	1.59010i
$916$	−3.42835e6			−4.08596
$917$	−33970.5	−	33970.5i	−0.0403984	−	0.0403984i
$918$	713872.	−	713872.i	0.847100	−	0.847100i
$919$			343802.i			0.407078i	0.979067	+	0.203539i	$0.0652443\pi$
$919$			343802.i			0.407078i	−0.979067	+	0.203539i	$0.934756\pi$
$920$	117602.	+	319853.i	0.138944	+	0.377898i
$921$	1.33254e6			1.57094
$922$	−651545.	−	651545.i	−0.766447	−	0.766447i
$923$	−157042.	+	157042.i	−0.184336	+	0.184336i
$924$			1.29206e6i			1.51335i
$925$	1.30445e6	+	105539.i	1.52455	+	0.123348i
$926$	−2.37056e6			−2.76458
$927$	18568.6	+	18568.6i	0.0216082	+	0.0216082i
$928$	−26227.8	+	26227.8i	−0.0304555	+	0.0304555i
$929$			780337.i			0.904172i	0.891974	+	0.452086i	$0.149320\pi$
$929$			780337.i			0.904172i	−0.891974	+	0.452086i	$0.850680\pi$
$930$	578465.	−	212687.i	0.668822	−	0.245909i
$931$	−828622.			−0.955999
$932$	−77364.7	−	77364.7i	−0.0890658	−	0.0890658i
$933$	23659.0	−	23659.0i	0.0271790	−	0.0271790i
$934$			1.85771e6i			2.12954i
$935$	309939.	+	143296.i	0.354530	+	0.163912i
$936$	−107961.			−0.123229
$937$	225038.	+	225038.i	0.256317	+	0.256317i	0.823554	−	0.567237i	$-0.191988\pi$
$937$	225038.	+	225038.i	0.256317	+	0.256317i	−0.567237	+	0.823554i	$0.691988\pi$
$938$	69957.4	−	69957.4i	0.0795111	−	0.0795111i
$939$			963066.i			1.09226i
$940$	−1.26042e6	+	2.72619e6i	−1.42645	+	3.08532i
$941$	594421.			0.671297			0.335649	−	0.941987i	$-0.391045\pi$
$941$	594421.			0.671297			0.335649	+	0.941987i	$0.391045\pi$
$942$	−709570.	−	709570.i	−0.799638	−	0.799638i
$943$	−205683.	+	205683.i	−0.231300	+	0.231300i
$944$		−	931099.i		−	1.04485i
$945$	351442.	+	955851.i	0.393542	+	1.07035i
$946$	−225371.			−0.251834
$947$	754342.	+	754342.i	0.841140	+	0.841140i	0.989007	−	0.147867i	$-0.0472408\pi$
$947$	754342.	+	754342.i	0.841140	+	0.841140i	−0.147867	+	0.989007i	$0.547241\pi$
$948$	−1.67918e6	+	1.67918e6i	−1.86845	+	1.86845i
$949$			470165.i			0.522057i
$950$	165402.	−	2.04433e6i	0.183270	−	2.26519i
$951$	−756395.			−0.836349
$952$	−1.28548e6	−	1.28548e6i	−1.41838	−	1.41838i
$953$	421633.	−	421633.i	0.464247	−	0.464247i	−0.435798	−	0.900045i	$-0.643534\pi$
$953$	421633.	−	421633.i	0.464247	−	0.464247i	0.900045	+	0.435798i	$0.143534\pi$
$954$		−	420540.i		−	0.462073i
$955$	−1.08900e6	+	400398.i	−1.19405	+	0.439021i
$956$	423533.			0.463417
$957$	−42527.5	−	42527.5i	−0.0464351	−	0.0464351i
$958$	280306.	−	280306.i	0.305422	−	0.305422i
$959$			1.02722e6i			1.11693i
$960$	−617775.	−	285619.i	−0.670328	−	0.309917i
$961$	−799013.			−0.865182
$962$	−520193.	−	520193.i	−0.562102	−	0.562102i
$963$	−171085.	+	171085.i	−0.184484	+	0.184484i
$964$		−	2.90277e6i		−	3.12362i
$965$	−435476.	+	941904.i	−0.467638	+	1.01147i
$966$	498167.			0.533852
$967$	290811.	+	290811.i	0.310999	+	0.310999i	0.845296	−	0.534298i	$-0.179424\pi$
$967$	290811.	+	290811.i	0.310999	+	0.310999i	−0.534298	+	0.845296i	$0.679424\pi$
$968$	−964625.	+	964625.i	−1.02946	+	1.02946i
$969$			1.05290e6i			1.12135i
$970$	840764.	+	2.28670e6i	0.893574	+	2.43034i
$971$	987283.			1.04714			0.523568	−	0.851984i	$-0.324601\pi$
$971$	987283.			1.04714			0.523568	+	0.851984i	$0.324601\pi$
$972$	595621.	+	595621.i	0.630431	+	0.630431i
$973$	−903187.	+	903187.i	−0.954008	+	0.954008i
$974$		−	267138.i		−	0.281591i
$975$	−200543.	−	235850.i	−0.210959	−	0.248100i
$976$	−1.96879e6			−2.06681
$977$	−149610.	−	149610.i	−0.156737	−	0.156737i	0.624382	−	0.781119i	$-0.285351\pi$
$977$	−149610.	−	149610.i	−0.156737	−	0.156737i	−0.781119	+	0.624382i	$0.785351\pi$
$978$	−1.33931e6	+	1.33931e6i	−1.40024	+	1.40024i
$979$		−	674803.i		−	0.704064i
$980$	1.39952e6	−	514570.i	1.45723	−	0.535787i
$981$	−278069.			−0.288944
$982$	−727714.	−	727714.i	−0.754637	−	0.754637i
$983$	1.08246e6	−	1.08246e6i	1.12023	−	1.12023i	0.128522	−	0.991707i	$-0.458977\pi$
$983$	1.08246e6	−	1.08246e6i	1.12023	−	1.12023i	0.991707	−	0.128522i	$-0.0410232\pi$
$984$			3.23446e6i			3.34050i
$985$	−728895.	−	336994.i	−0.751264	−	0.347336i
$986$	161747.			0.166373
$987$	1.62422e6	+	1.62422e6i	1.66729	+	1.66729i
$988$	−552028.	+	552028.i	−0.565519	+	0.565519i
$989$			58838.3i			0.0601545i
$990$	−77589.4	+	167820.i	−0.0791648	+	0.171228i
$991$	38132.0			0.0388278			0.0194139	−	0.999812i	$-0.493820\pi$
$991$	38132.0			0.0388278			0.0194139	+	0.999812i	$0.493820\pi$
$992$	91661.1	+	91661.1i	0.0931454	+	0.0931454i
$993$	−85204.0	+	85204.0i	−0.0864095	+	0.0864095i
$994$		−	2.02494e6i		−	2.04946i
$995$	286947.	+	780436.i	0.289838	+	0.788299i
$996$	82969.7			0.0836374
$997$	−941807.	−	941807.i	−0.947483	−	0.947483i	0.0512050	−	0.998688i	$-0.483694\pi$
$997$	−941807.	−	941807.i	−0.947483	−	0.947483i	−0.998688	+	0.0512050i	$0.983694\pi$
$998$	1.40914e6	−	1.40914e6i	1.41479	−	1.41479i
$999$			1.31958e6i			1.32222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.f.a.47.3	✓	88
5.3	odd	4	inner	115.5.f.a.93.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.f.a.47.3	✓	88	1.1	even	1	trivial
115.5.f.a.93.3	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+(-4.97771 - 4.97771i) q^{2} +(7.01798 - 7.01798i) q^{3} +33.5552i q^{4} +(-23.4643 + 8.62722i) q^{5} -69.8670 q^{6} +(-45.7084 - 45.7084i) q^{7} +(87.3849 - 87.3849i) q^{8} -17.5042i q^{9} +(159.742 + 73.8545i) q^{10} -60.0183 q^{11} +(235.490 + 235.490i) q^{12} +(35.2905 - 35.2905i) q^{13} +455.046i q^{14} +(-104.126 + 225.217i) q^{15} -333.070 q^{16} +(160.917 + 160.917i) q^{17} +(-87.1308 + 87.1308i) q^{18} +466.169i q^{19} +(-289.488 - 787.349i) q^{20} -641.562 q^{21} +(298.754 + 298.754i) q^{22} +(77.9968 - 77.9968i) q^{23} -1226.53i q^{24} +(476.142 - 404.862i) q^{25} -351.332 q^{26} +(445.613 + 445.613i) q^{27} +(1533.76 - 1533.76i) q^{28} +100.966i q^{29} +(1639.38 - 602.758i) q^{30} +352.856 q^{31} +(259.769 + 259.769i) q^{32} +(-421.207 + 421.207i) q^{33} -1602.00i q^{34} +(1466.85 + 678.177i) q^{35} +587.357 q^{36} +(1480.63 + 1480.63i) q^{37} +(2320.46 - 2320.46i) q^{38} -495.336i q^{39} +(-1296.53 + 2804.31i) q^{40} -2637.08 q^{41} +(3193.51 + 3193.51i) q^{42} +(-377.184 + 377.184i) q^{43} -2013.93i q^{44} +(151.012 + 410.723i) q^{45} -776.491 q^{46} +(-2531.67 - 2531.67i) q^{47} +(-2337.48 + 2337.48i) q^{48} +1777.51i q^{49} +(-4385.39 - 354.810i) q^{50} +2258.63 q^{51} +(1184.18 + 1184.18i) q^{52} +(-2413.27 + 2413.27i) q^{53} -4436.26i q^{54} +(1408.28 - 517.791i) q^{55} -7988.45 q^{56} +(3271.57 + 3271.57i) q^{57} +(502.578 - 502.578i) q^{58} +2795.50i q^{59} +(-7557.22 - 3493.97i) q^{60} +5911.03 q^{61} +(-1756.42 - 1756.42i) q^{62} +(-800.088 + 800.088i) q^{63} +2743.01i q^{64} +(-523.606 + 1132.52i) q^{65} +4193.30 q^{66} +(-153.737 - 153.737i) q^{67} +(-5399.62 + 5399.62i) q^{68} -1094.76i q^{69} +(-3925.79 - 10677.3i) q^{70} -4449.97 q^{71} +(-1529.60 - 1529.60i) q^{72} +(-6661.36 + 6661.36i) q^{73} -14740.3i q^{74} +(500.240 - 6182.88i) q^{75} -15642.4 q^{76} +(2743.34 + 2743.34i) q^{77} +(-2465.64 + 2465.64i) q^{78} +7130.60i q^{79} +(7815.24 - 2873.47i) q^{80} +7672.44 q^{81} +(13126.6 + 13126.6i) q^{82} +(176.164 - 176.164i) q^{83} -21527.8i q^{84} +(-5164.08 - 2387.54i) q^{85} +3755.03 q^{86} +(708.576 + 708.576i) q^{87} +(-5244.69 + 5244.69i) q^{88} +11243.3i q^{89} +(1292.76 - 2796.16i) q^{90} -3226.14 q^{91} +(2617.20 + 2617.20i) q^{92} +(2476.34 - 2476.34i) q^{93} +25203.8i q^{94} +(-4021.74 - 10938.3i) q^{95} +3646.11 q^{96} +(9789.11 + 9789.11i) q^{97} +(8847.96 - 8847.96i) q^{98} +1050.57i 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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