LMFDB - Embedded newform 76.5.j.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	76.53
Dual form			76.5.j.a.33.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.48759 - 1.32026i) q^{3} +(-18.9121 + 15.8691i) q^{5} +(-39.3870 + 68.2202i) q^{7} +(-21.7942 + 7.93242i) q^{9} +O(q^{10})$	\(q+(7.48759 - 1.32026i) q^{3} +(-18.9121 + 15.8691i) q^{5} +(-39.3870 + 68.2202i) q^{7} +(-21.7942 + 7.93242i) q^{9} +(20.6645 + 35.7920i) q^{11} +(132.868 + 23.4283i) q^{13} +(-120.655 + 143.791i) q^{15} +(120.095 + 43.7109i) q^{17} +(-321.938 - 163.330i) q^{19} +(-204.845 + 562.806i) q^{21} +(360.226 + 302.265i) q^{23} +(-2.69215 + 15.2679i) q^{25} +(-686.056 + 396.094i) q^{27} +(15.3762 + 42.2458i) q^{29} +(469.811 + 271.246i) q^{31} +(201.983 + 240.714i) q^{33} +(-337.706 - 1915.22i) q^{35} -1450.25i q^{37} +1025.80 q^{39} +(-1484.76 + 261.803i) q^{41} +(2135.35 - 1791.77i) q^{43} +(286.292 - 495.873i) q^{45} +(3369.92 - 1226.55i) q^{47} +(-1902.17 - 3294.65i) q^{49} +(956.931 + 168.733i) q^{51} +(-3048.52 + 3633.09i) q^{53} +(-958.798 - 348.974i) q^{55} +(-2626.18 - 797.908i) q^{57} +(-165.867 + 455.717i) q^{59} +(4390.65 + 3684.20i) q^{61} +(317.254 - 1799.24i) q^{63} +(-2884.61 + 1665.43i) q^{65} +(-1803.52 - 4955.13i) q^{67} +(3096.29 + 1787.65i) q^{69} +(4213.11 + 5020.99i) q^{71} +(746.251 + 4232.20i) q^{73} +117.875i q^{75} -3255.66 q^{77} +(-2534.46 + 446.894i) q^{79} +(-3174.85 + 2664.01i) q^{81} +(424.803 - 735.780i) q^{83} +(-2964.90 + 1079.13i) q^{85} +(170.906 + 296.019i) q^{87} +(-2584.79 - 455.768i) q^{89} +(-6831.56 + 8141.54i) q^{91} +(3875.87 + 1410.70i) q^{93} +(8680.44 - 2019.96i) q^{95} +(-1831.36 + 5031.61i) q^{97} +(-734.284 - 616.138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	7.48759	−	1.32026i	0.831955	−	0.146696i	0.258581	−	0.965990i	$-0.416745\pi$
$3$	7.48759	−	1.32026i	0.831955	−	0.146696i	0.573374	+	0.819294i	$0.305634\pi$
$4$		0			0
$5$	−18.9121	+	15.8691i	−0.756484	+	0.634765i	−0.937209	−	0.348768i	$-0.886600\pi$
$5$	−18.9121	+	15.8691i	−0.756484	+	0.634765i	0.180725	+	0.983534i	$0.442156\pi$
$6$		0			0
$7$	−39.3870	+	68.2202i	−0.803816	+	1.39225i	0.113272	+	0.993564i	$0.463867\pi$
$7$	−39.3870	+	68.2202i	−0.803816	+	1.39225i	−0.917088	+	0.398686i	$0.869466\pi$
$8$		0			0
$9$	−21.7942	+	7.93242i	−0.269064	+	0.0979312i
$10$		0			0
$11$	20.6645	+	35.7920i	0.170781	+	0.295802i	0.938693	−	0.344753i	$-0.112037\pi$
$11$	20.6645	+	35.7920i	0.170781	+	0.295802i	−0.767912	+	0.640555i	$0.778704\pi$
$12$		0			0
$13$	132.868	+	23.4283i	0.786203	+	0.138629i	0.552316	−	0.833635i	$-0.313744\pi$
$13$	132.868	+	23.4283i	0.786203	+	0.138629i	0.233887	+	0.972264i	$0.424855\pi$
$14$		0			0
$15$	−120.655	+	143.791i	−0.536243	+	0.639069i
$16$		0			0
$17$	120.095	+	43.7109i	0.415553	+	0.151249i	0.541331	−	0.840809i	$-0.317921\pi$
$17$	120.095	+	43.7109i	0.415553	+	0.151249i	−0.125778	+	0.992058i	$0.540143\pi$
$18$		0			0
$19$	−321.938	−	163.330i	−0.891795	−	0.452439i
$19$	−321.938	−	163.330i	−0.891795	−	0.452439i
$20$		0			0
$21$	−204.845	+	562.806i	−0.464501	+	1.27621i
$22$		0			0
$23$	360.226	+	302.265i	0.680956	+	0.571390i	0.916285	−	0.400526i	$-0.131173\pi$
$23$	360.226	+	302.265i	0.680956	+	0.571390i	−0.235330	+	0.971916i	$0.575617\pi$
$24$		0			0
$25$	−2.69215	+	15.2679i	−0.00430744	+	0.0244287i
$26$		0			0
$27$	−686.056	+	396.094i	−0.941091	+	0.543339i
$28$		0			0
$29$	15.3762	+	42.2458i	0.0182833	+	0.0502328i	0.948499	−	0.316782i	$-0.102602\pi$
$29$	15.3762	+	42.2458i	0.0182833	+	0.0502328i	−0.930215	+	0.367014i	$0.880380\pi$
$30$		0			0
$31$	469.811	+	271.246i	0.488877	+	0.282254i	0.724109	−	0.689686i	$-0.242251\pi$
$31$	469.811	+	271.246i	0.488877	+	0.282254i	−0.235231	+	0.971939i	$0.575585\pi$
$32$		0			0
$33$	201.983	+	240.714i	0.185475	+	0.221041i
$34$		0			0
$35$	−337.706	−	1915.22i	−0.275678	−	1.56345i
$36$		0			0
$37$		−	1450.25i		−	1.05935i	−0.848201	−	0.529675i	$-0.822314\pi$
$37$		−	1450.25i		−	1.05935i	0.848201	−	0.529675i	$-0.177686\pi$
$38$		0			0
$39$	1025.80			0.674422
$40$		0			0
$41$	−1484.76	+	261.803i	−0.883258	+	0.155742i	−0.596838	−	0.802362i	$-0.703576\pi$
$41$	−1484.76	+	261.803i	−0.883258	+	0.155742i	−0.286420	+	0.958104i	$0.592465\pi$
$42$		0			0
$43$	2135.35	−	1791.77i	1.15487	−	0.969051i	0.155047	−	0.987907i	$-0.450447\pi$
$43$	2135.35	−	1791.77i	1.15487	−	0.969051i	0.999822	+	0.0188565i	$0.00600256\pi$
$44$		0			0
$45$	286.292	−	495.873i	0.141379	−	0.244876i
$46$		0			0
$47$	3369.92	−	1226.55i	1.52554	−	0.555251i	0.563016	−	0.826446i	$-0.309641\pi$
$47$	3369.92	−	1226.55i	1.52554	−	0.555251i	0.962524	+	0.271195i	$0.0874189\pi$
$48$		0			0
$49$	−1902.17	−	3294.65i	−0.792239	−	1.37220i
$50$		0			0
$51$	956.931	+	168.733i	0.367909	+	0.0648723i
$52$		0			0
$53$	−3048.52	+	3633.09i	−1.08527	+	1.29337i	−0.132002	+	0.991249i	$0.542141\pi$
$53$	−3048.52	+	3633.09i	−1.08527	+	1.29337i	−0.953268	+	0.302126i	$0.902304\pi$
$54$		0			0
$55$	−958.798	−	348.974i	−0.316958	−	0.115363i
$56$		0			0
$57$	−2626.18	−	797.908i	−0.808304	−	0.245586i
$58$		0			0
$59$	−165.867	+	455.717i	−0.0476494	+	0.130916i	−0.961235	−	0.275732i	$-0.911080\pi$
$59$	−165.867	+	455.717i	−0.0476494	+	0.130916i	0.913585	+	0.406647i	$0.133302\pi$
$60$		0			0
$61$	4390.65	+	3684.20i	1.17997	+	0.990109i	0.999979	+	0.00643989i	$0.00204990\pi$
$61$	4390.65	+	3684.20i	1.17997	+	0.990109i	0.179987	+	0.983669i	$0.442395\pi$
$62$		0			0
$63$	317.254	−	1799.24i	0.0799330	−	0.453322i
$64$		0			0
$65$	−2884.61	+	1665.43i	−0.682747	+	0.394184i
$66$		0			0
$67$	−1803.52	−	4955.13i	−0.401764	−	1.10384i	−0.961413	−	0.275109i	$-0.911286\pi$
$67$	−1803.52	−	4955.13i	−0.401764	−	1.10384i	0.559649	−	0.828730i	$-0.310936\pi$
$68$		0			0
$69$	3096.29	+	1787.65i	0.650345	+	0.375477i
$70$		0			0
$71$	4213.11	+	5020.99i	0.835769	+	0.996031i	0.999954	+	0.00960122i	$0.00305621\pi$
$71$	4213.11	+	5020.99i	0.835769	+	0.996031i	−0.164185	+	0.986430i	$0.552499\pi$
$72$		0			0
$73$	746.251	+	4232.20i	0.140036	+	0.794182i	0.971220	+	0.238185i	$0.0765524\pi$
$73$	746.251	+	4232.20i	0.140036	+	0.794182i	−0.831184	+	0.555997i	$0.812336\pi$
$74$		0			0
$75$			117.875i			0.0209555i
$76$		0			0
$77$	−3255.66			−0.549107
$78$		0			0
$79$	−2534.46	+	446.894i	−0.406099	+	0.0716062i	−0.372967	−	0.927845i	$-0.621659\pi$
$79$	−2534.46	+	446.894i	−0.406099	+	0.0716062i	−0.0331324	+	0.999451i	$0.510548\pi$
$80$		0			0
$81$	−3174.85	+	2664.01i	−0.483897	+	0.406038i
$82$		0			0
$83$	424.803	−	735.780i	0.0616640	−	0.106805i	−0.833545	−	0.552451i	$-0.813693\pi$
$83$	424.803	−	735.780i	0.0616640	−	0.106805i	0.895209	+	0.445646i	$0.147026\pi$
$84$		0			0
$85$	−2964.90	+	1079.13i	−0.410367	+	0.149361i
$86$		0			0
$87$	170.906	+	296.019i	0.0225798	+	0.0391094i
$88$		0			0
$89$	−2584.79	−	455.768i	−0.326321	−	0.0575393i	0.00808769	−	0.999967i	$-0.497426\pi$
$89$	−2584.79	−	455.768i	−0.326321	−	0.0575393i	−0.334409	+	0.942428i	$0.608537\pi$
$90$		0			0
$91$	−6831.56	+	8141.54i	−0.824969	+	0.983159i
$92$		0			0
$93$	3875.87	+	1410.70i	0.448129	+	0.163106i
$94$		0			0
$95$	8680.44	−	2019.96i	0.961821	−	0.223818i
$96$		0			0
$97$	−1831.36	+	5031.61i	−0.194639	+	0.534766i	−0.998168	−	0.0604994i	$-0.980731\pi$
$97$	−1831.36	+	5031.61i	−0.194639	+	0.534766i	0.803529	+	0.595265i	$0.202953\pi$
$98$		0			0
$99$	−734.284	−	616.138i	−0.0749193	−	0.0628648i
$100$		0			0
$101$	−520.903	+	2954.19i	−0.0510639	+	0.289598i	−0.999636	−	0.0269621i	$-0.991417\pi$
$101$	−520.903	+	2954.19i	−0.0510639	+	0.289598i	0.948573	+	0.316560i	$0.102528\pi$
$102$		0			0
$103$	10090.0	−	5825.48i	0.951081	−	0.549107i	0.0576645	−	0.998336i	$-0.481635\pi$
$103$	10090.0	−	5825.48i	0.951081	−	0.549107i	0.893417	+	0.449229i	$0.148301\pi$
$104$		0			0
$105$	−5057.21	−	13894.6i	−0.458703	−	1.26028i
$106$		0			0
$107$	17390.7	+	10040.5i	1.51897	+	0.876977i	0.999751	+	0.0223345i	$0.00710988\pi$
$107$	17390.7	+	10040.5i	1.51897	+	0.876977i	0.519218	+	0.854642i	$0.326223\pi$
$108$		0			0
$109$	−5451.03	−	6496.28i	−0.458802	−	0.546779i	0.486198	−	0.873849i	$-0.338383\pi$
$109$	−5451.03	−	6496.28i	−0.458802	−	0.546779i	−0.945000	+	0.327070i	$0.893939\pi$
$110$		0			0
$111$	−1914.71	−	10858.9i	−0.155403	−	0.881331i
$112$		0			0
$113$			17452.2i			1.36677i	0.730060	+	0.683383i	$0.239492\pi$
$113$			17452.2i			1.36677i	−0.730060	+	0.683383i	$0.760508\pi$
$114$		0			0
$115$	−11609.3			−0.877830
$116$		0			0
$117$	−3081.60	+	543.369i	−0.225115	+	0.0396938i
$118$		0			0
$119$	−7712.14	+	6471.25i	−0.544604	+	0.456977i
$120$		0			0
$121$	6466.45	−	11200.2i	0.441667	−	0.764990i
$122$		0			0
$123$	−10771.6	+	3920.54i	−0.711984	+	0.259141i
$124$		0			0
$125$	−7906.37	−	13694.2i	−0.506008	−	0.876431i
$126$		0			0
$127$	−9694.89	−	1709.47i	−0.601084	−	0.105987i	−0.135178	−	0.990821i	$-0.543161\pi$
$127$	−9694.89	−	1709.47i	−0.601084	−	0.105987i	−0.465906	+	0.884834i	$0.654272\pi$
$128$		0			0
$129$	13623.0	−	16235.3i	0.818643	−	0.975621i
$130$		0			0
$131$	6197.68	+	2255.77i	0.361149	+	0.131448i	0.516221	−	0.856456i	$-0.327338\pi$
$131$	6197.68	+	2255.77i	0.361149	+	0.131448i	−0.155071	+	0.987903i	$0.549561\pi$
$132$		0			0
$133$	23822.6	−	15529.6i	1.34675	−	0.877924i
$134$		0			0
$135$	6689.07	−	18378.1i	0.367027	−	1.00840i
$136$		0			0
$137$	8187.49	+	6870.12i	0.436224	+	0.366035i	0.834294	−	0.551320i	$-0.185875\pi$
$137$	8187.49	+	6870.12i	0.436224	+	0.366035i	−0.398070	+	0.917355i	$0.630320\pi$
$138$		0			0
$139$	3216.04	−	18239.1i	0.166453	−	0.944002i	−0.781101	−	0.624405i	$-0.785341\pi$
$139$	3216.04	−	18239.1i	0.166453	−	0.944002i	0.947554	−	0.319597i	$-0.103547\pi$
$140$		0			0
$141$	23613.2	−	13633.1i	1.18773	−	0.685735i
$142$		0			0
$143$	1907.12	+	5239.77i	0.0932622	+	0.256236i
$144$		0			0
$145$	−961.200	−	554.949i	−0.0457170	−	0.0263947i
$146$		0			0
$147$	−18592.5	−	22157.6i	−0.860403	−	1.02539i
$148$		0			0
$149$	6952.63	+	39430.3i	0.313167	+	1.77606i	0.582317	+	0.812962i	$0.302146\pi$
$149$	6952.63	+	39430.3i	0.313167	+	1.77606i	−0.269150	+	0.963098i	$0.586743\pi$
$150$		0			0
$151$		−	13836.8i		−	0.606853i	−0.952855	−	0.303426i	$-0.901869\pi$
$151$		−	13836.8i		−	0.606853i	0.952855	−	0.303426i	$-0.0981306\pi$
$152$		0			0
$153$	−2964.10			−0.126622
$154$		0			0
$155$	−13189.5	+	2325.67i	−0.548993	+	0.0968022i
$156$		0			0
$157$	17234.5	−	14461.4i	0.699196	−	0.586695i	−0.222349	−	0.974967i	$-0.571372\pi$
$157$	17234.5	−	14461.4i	0.699196	−	0.586695i	0.921545	+	0.388272i	$0.126928\pi$
$158$		0			0
$159$	−18029.5	+	31228.0i	−0.713163	+	1.23523i
$160$		0			0
$161$	−34808.8	+	12669.4i	−1.34288	+	0.488768i
$162$		0			0
$163$	13640.6	+	23626.2i	0.513403	+	0.889240i	0.999879	+	0.0155464i	$0.00494877\pi$
$163$	13640.6	+	23626.2i	0.513403	+	0.889240i	−0.486476	+	0.873694i	$0.661718\pi$
$164$		0			0
$165$	−7639.83	−	1347.11i	−0.280618	−	0.0494806i
$166$		0			0
$167$	−34444.7	+	41049.6i	−1.23506	+	1.47189i	−0.404910	+	0.914357i	$0.632697\pi$
$167$	−34444.7	+	41049.6i	−1.23506	+	1.47189i	−0.830154	+	0.557535i	$0.811747\pi$
$168$		0			0
$169$	−9733.44	−	3542.68i	−0.340795	−	0.124039i
$170$		0			0
$171$	8311.98	+	1005.90i	0.284258	+	0.0344003i
$172$		0			0
$173$	−2130.96	+	5854.77i	−0.0712006	+	0.195622i	−0.970189	−	0.242351i	$-0.922081\pi$
$173$	−2130.96	+	5854.77i	−0.0712006	+	0.195622i	0.898988	+	0.437973i	$0.144304\pi$
$174$		0			0
$175$	−935.547	−	785.017i	−0.0305485	−	0.0256332i
$176$		0			0
$177$	−640.281	+	3631.21i	−0.0204373	+	0.115906i
$178$		0			0
$179$	−5998.31	+	3463.13i	−0.187207	+	0.108084i	−0.590675	−	0.806910i	$-0.701138\pi$
$179$	−5998.31	+	3463.13i	−0.187207	+	0.108084i	0.403467	+	0.914994i	$0.367805\pi$
$180$		0			0
$181$	8398.82	+	23075.6i	0.256367	+	0.704361i	0.999384	+	0.0350894i	$0.0111716\pi$
$181$	8398.82	+	23075.6i	0.256367	+	0.704361i	−0.743018	+	0.669272i	$0.766606\pi$
$182$		0			0
$183$	37739.5	+	21788.9i	1.12692	+	0.650629i
$184$		0			0
$185$	23014.2	+	27427.3i	0.672439	+	0.801381i
$186$		0			0
$187$	917.201	+	5201.71i	0.0262290	+	0.148752i
$188$		0			0
$189$		−	62403.8i		−	1.74698i
$190$		0			0
$191$	45795.4			1.25532			0.627661	−	0.778487i	$-0.284012\pi$
$191$	45795.4			1.25532			0.627661	+	0.778487i	$0.284012\pi$
$192$		0			0
$193$	−38103.8	+	6718.72i	−1.02295	+	0.180373i	−0.659865	−	0.751384i	$-0.729387\pi$
$193$	−38103.8	+	6718.72i	−1.02295	+	0.180373i	−0.363082	+	0.931757i	$0.618275\pi$
$194$		0			0
$195$	−19399.9	+	16278.5i	−0.510189	+	0.428100i
$196$		0			0
$197$	−14114.3	+	24446.7i	−0.363687	+	0.629924i	−0.988564	−	0.150799i	$-0.951815\pi$
$197$	−14114.3	+	24446.7i	−0.363687	+	0.629924i	0.624878	+	0.780722i	$0.285149\pi$
$198$		0			0
$199$	−21991.3	+	8004.19i	−0.555322	+	0.202121i	−0.604410	−	0.796674i	$-0.706591\pi$
$199$	−21991.3	+	8004.19i	−0.555322	+	0.202121i	0.0490873	+	0.998794i	$0.484369\pi$
$200$		0			0
$201$	−20046.1	−	34720.9i	−0.496179	−	0.859407i
$202$		0			0
$203$	−3487.64	−	614.965i	−0.0846330	−	0.0149231i
$204$		0			0
$205$	23925.3	−	28513.0i	0.569310	−	0.678478i
$206$		0			0
$207$	−10248.5	−	3730.15i	−0.239177	−	0.0870534i
$208$		0			0
$209$	−806.775	−	14898.0i	−0.0184697	−	0.341063i
$210$		0			0
$211$	15192.6	−	41741.4i	0.341246	−	0.937566i	−0.643788	−	0.765204i	$-0.722638\pi$
$211$	15192.6	−	41741.4i	0.341246	−	0.937566i	0.985034	−	0.172362i	$-0.0551398\pi$
$212$		0			0
$213$	38175.1	+	32032.7i	0.841436	+	0.706049i
$214$		0			0
$215$	−11950.1	+	67772.4i	−0.258520	+	1.46614i
$216$		0			0
$217$	−37008.9	+	21367.1i	−0.785935	+	0.453760i
$218$		0			0
$219$	11175.2	+	30703.7i	0.233007	+	0.640181i
$220$		0			0
$221$	14932.7	+	8621.42i	0.305742	+	0.176520i
$222$		0			0
$223$	−41501.0	−	49459.0i	−0.834544	−	0.994570i	−0.999965	−	0.00834740i	$-0.997343\pi$
$223$	−41501.0	−	49459.0i	−0.834544	−	0.994570i	0.165422	−	0.986223i	$-0.447102\pi$
$224$		0			0
$225$	−62.4387	−	354.107i	−0.00123336	−	0.00699471i
$226$		0			0
$227$		−	89792.7i		−	1.74257i	−0.490780	−	0.871284i	$-0.663288\pi$
$227$		−	89792.7i		−	1.74257i	0.490780	−	0.871284i	$-0.336712\pi$
$228$		0			0
$229$	77612.5			1.48000			0.739999	−	0.672608i	$-0.234826\pi$
$229$	77612.5			1.48000			0.739999	+	0.672608i	$0.234826\pi$
$230$		0			0
$231$	−24377.0	+	4298.33i	−0.456832	+	0.0805518i
$232$		0			0
$233$	73056.6	−	61301.8i	1.34570	−	1.12918i	0.365576	−	0.930781i	$-0.380872\pi$
$233$	73056.6	−	61301.8i	1.34570	−	1.12918i	0.980122	−	0.198394i	$-0.0635724\pi$
$234$		0			0
$235$	−44267.9	+	76674.3i	−0.801592	+	1.38840i
$236$		0			0
$237$	−18387.0	+	6692.33i	−0.327352	+	0.119146i
$238$		0			0
$239$	−13947.0	−	24156.9i	−0.244166	−	0.422907i	0.717731	−	0.696320i	$-0.245181\pi$
$239$	−13947.0	−	24156.9i	−0.244166	−	0.422907i	−0.961897	+	0.273413i	$0.911847\pi$
$240$		0			0
$241$	−55198.3	−	9732.94i	−0.950367	−	0.167575i	−0.323087	−	0.946369i	$-0.604721\pi$
$241$	−55198.3	−	9732.94i	−0.950367	−	0.167575i	−0.627280	+	0.778794i	$0.715832\pi$
$242$		0			0
$243$	20991.2	−	25016.3i	0.355487	−	0.423653i
$244$		0			0
$245$	88257.2	+	32123.0i	1.47034	+	0.535160i
$246$		0			0
$247$	−38948.8	−	29243.9i	−0.638411	−	0.479338i
$248$		0			0
$249$	2209.33	−	6070.08i	0.0356337	−	0.0979029i
$250$		0			0
$251$	−28520.0	−	23931.1i	−0.452691	−	0.379852i	0.387743	−	0.921768i	$-0.373255\pi$
$251$	−28520.0	−	23931.1i	−0.452691	−	0.379852i	−0.840433	+	0.541915i	$0.817699\pi$
$252$		0			0
$253$	−3374.79	+	19139.4i	−0.0527237	+	0.299011i
$254$		0			0
$255$	−20775.2	+	11994.6i	−0.319496	+	0.184461i
$256$		0			0
$257$	−24905.4	−	68427.0i	−0.377074	−	1.03600i	−0.972563	−	0.232639i	$-0.925264\pi$
$257$	−24905.4	−	68427.0i	−0.377074	−	1.03600i	0.595489	−	0.803364i	$-0.296958\pi$
$258$		0			0
$259$	98936.4	+	57121.0i	1.47488	+	0.851522i
$260$		0			0
$261$	−670.223	−	798.741i	−0.00983872	−	0.0117253i
$262$		0			0
$263$	−13676.0	−	77560.4i	−0.197718	−	1.12132i	−0.908494	−	0.417898i	$-0.862767\pi$
$263$	−13676.0	−	77560.4i	−0.197718	−	1.12132i	0.710775	−	0.703419i	$-0.248344\pi$
$264$		0			0
$265$		−	117087.i		−	1.66731i
$266$		0			0
$267$	−19955.6			−0.279925
$268$		0			0
$269$	102925.	−	18148.5i	1.42239	−	0.250805i	0.591078	−	0.806615i	$-0.298703\pi$
$269$	102925.	−	18148.5i	1.42239	−	0.250805i	0.831310	+	0.555809i	$0.187592\pi$
$270$		0			0
$271$	31987.2	−	26840.5i	0.435550	−	0.365470i	−0.398491	−	0.917172i	$-0.630466\pi$
$271$	31987.2	−	26840.5i	0.435550	−	0.365470i	0.834041	+	0.551702i	$0.186022\pi$
$272$		0			0
$273$	−40403.0	+	69980.0i	−0.542111	+	0.938964i
$274$		0			0
$275$	−602.103	+	219.148i	−0.00796169	+	0.00289782i
$276$		0			0
$277$	−38102.9	−	65996.2i	−0.496591	−	0.860121i	0.503401	−	0.864053i	$-0.332082\pi$
$277$	−38102.9	−	65996.2i	−0.496591	−	0.860121i	−0.999992	+	0.00393174i	$0.998748\pi$
$278$		0			0
$279$	−12390.8	−	2184.83i	−0.159181	−	0.0280678i
$280$		0			0
$281$	−80364.3	+	95774.4i	−1.01777	+	1.21293i	−0.0408877	+	0.999164i	$0.513019\pi$
$281$	−80364.3	+	95774.4i	−1.01777	+	1.21293i	−0.976884	+	0.213769i	$0.931426\pi$
$282$		0			0
$283$	118315.	+	43063.3i	1.47730	+	0.537693i	0.950072	−	0.312031i	$-0.101009\pi$
$283$	118315.	+	43063.3i	1.47730	+	0.537693i	0.527228	+	0.849724i	$0.323231\pi$
$284$		0			0
$285$	62328.7	−	26585.1i	0.767358	−	0.327302i
$286$		0			0
$287$	40619.8	−	111602.i	0.493145	−	1.35490i
$288$		0			0
$289$	−51468.7	−	43187.3i	−0.616236	−	0.517084i
$290$		0			0
$291$	−7069.39	+	40092.5i	−0.0834826	+	0.473453i
$292$		0			0
$293$	−72370.8	+	41783.3i	−0.843001	+	0.486707i	−0.858283	−	0.513177i	$-0.828469\pi$
$293$	−72370.8	+	41783.3i	−0.843001	+	0.486707i	0.0152825	+	0.999883i	$0.495135\pi$
$294$		0			0
$295$	−4094.93	−	11250.7i	−0.0470547	−	0.129282i
$296$		0			0
$297$	−28354.1	−	16370.2i	−0.321442	−	0.185584i
$298$		0			0
$299$	40781.0	+	48600.9i	0.456159	+	0.543629i
$300$		0			0
$301$	38130.2	+	216247.i	0.420858	+	2.38680i
$302$		0			0
$303$			22807.5i			0.248423i
$304$		0			0
$305$	−141501.			−1.52111
$306$		0			0
$307$	13430.9	−	2368.23i	0.142504	−	0.0251274i	−0.101941	−	0.994790i	$-0.532505\pi$
$307$	13430.9	−	2368.23i	0.142504	−	0.0251274i	0.244445	+	0.969663i	$0.421394\pi$
$308$		0			0
$309$	67858.8	−	56940.3i	0.710705	−	0.596352i
$310$		0			0
$311$	−8649.51	+	14981.4i	−0.0894274	+	0.154893i	−0.907269	−	0.420550i	$-0.861837\pi$
$311$	−8649.51	+	14981.4i	−0.0894274	+	0.154893i	0.817842	+	0.575443i	$0.195170\pi$
$312$		0			0
$313$	−154613.	+	56274.6i	−1.57818	+	0.574412i	−0.974808	−	0.223045i	$-0.928400\pi$
$313$	−154613.	+	56274.6i	−1.57818	+	0.574412i	−0.603376	+	0.797457i	$0.706178\pi$
$314$		0			0
$315$	22552.4	+	39061.9i	0.227285	+	0.393670i
$316$		0			0
$317$	−105079.	−	18528.2i	−1.04567	−	0.184380i	−0.375681	−	0.926749i	$-0.622591\pi$
$317$	−105079.	−	18528.2i	−1.04567	−	0.184380i	−0.669991	+	0.742369i	$0.733702\pi$
$318$		0			0
$319$	−1194.32	+	1423.34i	−0.0117365	+	0.0139871i
$320$		0			0
$321$	143470.	+	52218.9i	1.39236	+	0.506778i
$322$		0			0
$323$	−31523.8	−	33687.4i	−0.302157	−	0.322895i
$324$		0			0
$325$	−715.403	+	1965.55i	−0.00677305	+	0.0186088i
$326$		0			0
$327$	−49391.9	−	41444.7i	−0.461913	−	0.387591i
$328$		0			0
$329$	−49055.3	+	278207.i	−0.453205	+	2.57025i
$330$		0			0
$331$	130677.	−	75446.6i	1.19274	−	0.688626i	0.233810	−	0.972282i	$-0.424881\pi$
$331$	130677.	−	75446.6i	1.19274	−	0.688626i	0.958926	+	0.283656i	$0.0915474\pi$
$332$		0			0
$333$	11504.0	+	31607.0i	0.103743	+	0.285033i
$334$		0			0
$335$	112742.	+	65091.6i	1.00461	+	0.580010i
$336$		0			0
$337$	−47743.1	−	56898.0i	−0.420388	−	0.500999i	0.513735	−	0.857949i	$-0.328261\pi$
$337$	−47743.1	−	56898.0i	−0.420388	−	0.500999i	−0.934124	+	0.356949i	$0.883817\pi$
$338$		0			0
$339$	23041.6	+	130675.i	0.200499	+	1.13709i
$340$		0			0
$341$			22420.7i			0.192815i
$342$		0			0
$343$	110546.			0.939626
$344$		0			0
$345$	−86925.7	+	15327.4i	−0.730315	+	0.128774i
$346$		0			0
$347$	−19642.1	+	16481.7i	−0.163128	+	0.136881i	−0.720698	−	0.693249i	$-0.756178\pi$
$347$	−19642.1	+	16481.7i	−0.163128	+	0.136881i	0.557569	+	0.830130i	$0.311734\pi$
$348$		0			0
$349$	−2917.56	+	5053.35i	−0.0239535	+	0.0414886i	−0.877754	−	0.479112i	$-0.840959\pi$
$349$	−2917.56	+	5053.35i	−0.0239535	+	0.0414886i	0.853800	+	0.520601i	$0.174292\pi$
$350$		0			0
$351$	−100435.	+	36555.3i	−0.815212	+	0.296713i
$352$		0			0
$353$	−104577.	−	181132.i	−0.839238	−	1.45360i	−0.890533	−	0.454919i	$-0.849668\pi$
$353$	−104577.	−	181132.i	−0.839238	−	1.45360i	0.0512945	−	0.998684i	$-0.483665\pi$
$354$		0			0
$355$	−159358.	−	28099.0i	−1.26449	−	0.222964i
$356$		0			0
$357$	−49201.6	+	58636.2i	−0.386049	+	0.460076i
$358$		0			0
$359$	187053.	+	68081.7i	1.45136	+	0.528253i	0.942971	−	0.332874i	$-0.108018\pi$
$359$	187053.	+	68081.7i	1.45136	+	0.528253i	0.508391	+	0.861127i	$0.330241\pi$
$360$		0			0
$361$	76967.3	+	105165.i	0.590598	+	0.806966i
$362$		0			0
$363$	33630.9	−	92400.2i	0.255226	−	0.701228i
$364$		0			0
$365$	−81274.5	−	68197.4i	−0.610054	−	0.511896i
$366$		0			0
$367$	−13863.0	+	78620.8i	−0.102926	+	0.583721i	0.889103	+	0.457707i	$0.151329\pi$
$367$	−13863.0	+	78620.8i	−0.102926	+	0.583721i	−0.992029	+	0.126013i	$0.959782\pi$
$368$		0			0
$369$	30282.3	−	17483.5i	0.222401	−	0.128403i
$370$		0			0
$371$	−127778.	−	351067.i	−0.928343	−	2.55060i
$372$		0			0
$373$	178067.	+	102807.i	1.27987	+	0.738932i	0.976824	−	0.214044i	$-0.0686637\pi$
$373$	178067.	+	102807.i	1.27987	+	0.738932i	0.303044	+	0.952976i	$0.401997\pi$
$374$		0			0
$375$	−77279.7	−	92098.3i	−0.549544	−	0.654922i
$376$		0			0
$377$	1053.27	+	5973.37i	0.00741063	+	0.0420278i
$378$		0			0
$379$		−	55178.6i		−	0.384143i	−0.981381	−	0.192071i	$-0.938480\pi$
$379$		−	55178.6i		−	0.384143i	0.981381	−	0.192071i	$-0.0615205\pi$
$380$		0			0
$381$	−74848.3			−0.515623
$382$		0			0
$383$	73791.5	−	13011.4i	0.503047	−	0.0887008i	0.0836346	−	0.996496i	$-0.473347\pi$
$383$	73791.5	−	13011.4i	0.503047	−	0.0887008i	0.419413	+	0.907796i	$0.362236\pi$
$384$		0			0
$385$	61571.3	−	51664.4i	0.415390	−	0.348554i
$386$		0			0
$387$	−32325.1	+	55988.7i	−0.215833	+	0.373834i
$388$		0			0
$389$	175467.	−	63864.7i	1.15957	−	0.422048i	0.310624	−	0.950533i	$-0.399462\pi$
$389$	175467.	−	63864.7i	1.15957	−	0.422048i	0.848942	+	0.528485i	$0.177240\pi$
$390$		0			0
$391$	30048.9	+	52046.3i	0.196551	+	0.340437i
$392$		0			0
$393$	49383.9	+	8707.72i	0.319743	+	0.0563793i
$394$		0			0
$395$	40840.2	−	48671.4i	0.261754	−	0.311946i
$396$		0			0
$397$	−184423.	−	67124.6i	−1.17013	−	0.425893i	−0.317425	−	0.948283i	$-0.602818\pi$
$397$	−184423.	−	67124.6i	−1.17013	−	0.425893i	−0.852706	+	0.522391i	$0.825040\pi$
$398$		0			0
$399$	157871.	−	147731.i	0.991644	−	0.927956i
$400$		0			0
$401$	63372.6	−	174115.i	0.394106	−	1.08280i	−0.571003	−	0.820948i	$-0.693446\pi$
$401$	63372.6	−	174115.i	0.394106	−	1.08280i	0.965109	−	0.261849i	$-0.0843321\pi$
$402$		0			0
$403$	56068.2	+	47046.8i	0.345229	+	0.289681i
$404$		0			0
$405$	17767.4	−	100764.i	0.108322	−	0.614322i
$406$		0			0
$407$	51907.4	−	29968.8i	0.313358	−	0.180917i
$408$		0			0
$409$	25696.6	+	70600.7i	0.153613	+	0.422049i	0.992498	−	0.122260i	$-0.0390142\pi$
$409$	25696.6	+	70600.7i	0.153613	+	0.422049i	−0.838885	+	0.544309i	$0.816792\pi$
$410$		0			0
$411$	70375.0	+	40631.0i	0.416615	+	0.240533i
$412$		0			0
$413$	−24556.1	−	29264.8i	−0.143966	−	0.171572i
$414$		0			0
$415$	3642.28	+	20656.4i	0.0211484	+	0.119938i
$416$		0			0
$417$		−	140813.i		−	0.809785i
$418$		0			0
$419$	124576.			0.709588			0.354794	−	0.934945i	$-0.384551\pi$
$419$	124576.			0.709588			0.354794	+	0.934945i	$0.384551\pi$
$420$		0			0
$421$	1648.98	−	290.759i	0.00930359	−	0.00164047i	−0.168994	−	0.985617i	$-0.554052\pi$
$421$	1648.98	−	290.759i	0.00930359	−	0.00164047i	0.178298	+	0.983977i	$0.442941\pi$
$422$		0			0
$423$	−63715.0	+	53463.2i	−0.356091	+	0.298796i
$424$		0			0
$425$	−990.690	+	1715.92i	−0.00548479	+	0.00949993i
$426$		0			0
$427$	−424271.	+	154422.i	−2.32695	+	0.846942i
$428$		0			0
$429$	21197.6	+	36715.3i	0.115179	+	0.199495i
$430$		0			0
$431$	−261976.	−	46193.4i	−1.41028	−	0.248671i	−0.583922	−	0.811810i	$-0.698482\pi$
$431$	−261976.	−	46193.4i	−1.41028	−	0.248671i	−0.826362	+	0.563139i	$0.809594\pi$
$432$		0			0
$433$	−77709.0	+	92610.0i	−0.414472	+	0.493949i	−0.932376	−	0.361490i	$-0.882268\pi$
$433$	−77709.0	+	92610.0i	−0.414472	+	0.493949i	0.517904	+	0.855439i	$0.326713\pi$
$434$		0			0
$435$	−7929.76	−	2886.20i	−0.0419065	−	0.0152527i
$436$		0			0
$437$	−66601.2	−	156146.i	−0.348754	−	0.817654i
$438$		0			0
$439$	−74737.9	+	205341.i	−0.387804	+	1.06548i	0.580184	+	0.814485i	$0.302981\pi$
$439$	−74737.9	+	205341.i	−0.387804	+	1.06548i	−0.967988	+	0.250997i	$0.919242\pi$
$440$		0			0
$441$	67590.7	+	56715.3i	0.347544	+	0.291624i
$442$		0			0
$443$	35869.4	−	203426.i	0.182775	−	1.03657i	−0.746006	−	0.665939i	$-0.768031\pi$
$443$	35869.4	−	203426.i	0.182775	−	1.03657i	0.928781	−	0.370629i	$-0.120858\pi$
$444$		0			0
$445$	56116.5	−	32398.9i	0.283381	−	0.163610i
$446$		0			0
$447$	104117.	+	286059.i	0.521082	+	1.43166i
$448$		0			0
$449$	140035.	+	80849.4i	0.694616	+	0.401037i	0.805339	−	0.592815i	$-0.201983\pi$
$449$	140035.	+	80849.4i	0.694616	+	0.401037i	−0.110723	+	0.993851i	$0.535317\pi$
$450$		0			0
$451$	−40052.3	−	47732.4i	−0.196913	−	0.234672i
$452$		0			0
$453$	−18268.3	−	103605.i	−0.0890229	−	0.504874i
$454$		0			0
$455$		−	262385.i		−	1.26741i
$456$		0			0
$457$	102385.			0.490234			0.245117	−	0.969493i	$-0.421174\pi$
$457$	102385.			0.490234			0.245117	+	0.969493i	$0.421174\pi$
$458$		0			0
$459$	−99705.4	+	17580.7i	−0.473253	+	0.0834472i
$460$		0			0
$461$	98923.7	−	83006.9i	0.465477	−	0.390582i	−0.379664	−	0.925124i	$-0.623960\pi$
$461$	98923.7	−	83006.9i	0.465477	−	0.390582i	0.845142	+	0.534542i	$0.179516\pi$
$462$		0			0
$463$	−89167.8	+	154443.i	−0.415955	+	0.720454i	−0.995528	−	0.0944655i	$-0.969886\pi$
$463$	−89167.8	+	154443.i	−0.415955	+	0.720454i	0.579574	+	0.814920i	$0.303219\pi$
$464$		0			0
$465$	−95687.4	+	34827.4i	−0.442536	+	0.161070i
$466$		0			0
$467$	−88798.3	−	153803.i	−0.407165	−	0.705231i	0.587405	−	0.809293i	$-0.300149\pi$
$467$	−88798.3	−	153803.i	−0.407165	−	0.705231i	−0.994571	+	0.104062i	$0.966816\pi$
$468$		0			0
$469$	409075.	+	72131.0i	1.85976	+	0.327926i
$470$		0			0
$471$	109952.	−	131036.i	0.495634	−	0.590673i
$472$		0			0
$473$	108257.	+	39402.5i	0.483877	+	0.176117i
$474$		0			0
$475$	3360.43	−	4475.62i	0.0148939	−	0.0198366i
$476$		0			0
$477$	37620.8	−	103362.i	0.165345	−	0.454282i
$478$		0			0
$479$	347713.	+	291766.i	1.51548	+	1.27164i	0.852137	+	0.523318i	$0.175306\pi$
$479$	347713.	+	291766.i	1.51548	+	1.27164i	0.663340	+	0.748318i	$0.269138\pi$
$480$		0			0
$481$	33976.9	−	192692.i	0.146857	−	0.832865i
$482$		0			0
$483$	−243907.	+	140820.i	−1.04551	+	0.603628i
$484$		0			0
$485$	−45212.5	−	124220.i	−0.192210	−	0.528091i
$486$		0			0
$487$	21316.0	+	12306.8i	0.0898767	+	0.0518904i	0.544265	−	0.838914i	$-0.316809\pi$
$487$	21316.0	+	12306.8i	0.0898767	+	0.0518904i	−0.454388	+	0.890804i	$0.650142\pi$
$488$		0			0
$489$	133328.	+	158894.i	0.557576	+	0.664493i
$490$		0			0
$491$	217.503	+	1233.52i	0.000902200	+	0.00511663i	0.985256	−	0.171089i	$-0.0547287\pi$
$491$	217.503	+	1233.52i	0.000902200	+	0.00511663i	−0.984353	+	0.176206i	$0.943618\pi$
$492$		0			0
$493$			5745.61i			0.0236397i
$494$		0			0
$495$	23664.4			0.0965796
$496$		0			0
$497$	−508475.	+	89657.8i	−2.05853	+	0.362974i
$498$		0			0
$499$	−104194.	+	87429.0i	−0.418447	+	0.351119i	−0.827572	−	0.561360i	$-0.810278\pi$
$499$	−104194.	+	87429.0i	−0.418447	+	0.351119i	0.409125	+	0.912478i	$0.365834\pi$
$500$		0			0
$501$	−203711.	+	352839.i	−0.811596	+	1.40573i
$502$		0			0
$503$	60501.9	−	22020.9i	0.239129	−	0.0870360i	−0.219676	−	0.975573i	$-0.570500\pi$
$503$	60501.9	−	22020.9i	0.239129	−	0.0870360i	0.458805	+	0.888537i	$0.348278\pi$
$504$		0			0
$505$	−37029.0	−	64136.1i	−0.145198	−	0.251489i
$506$		0			0
$507$	−77557.3	−	13675.5i	−0.301722	−	0.0532017i
$508$		0			0
$509$	−262556.	+	312902.i	−1.01341	+	1.20774i	−0.0353598	+	0.999375i	$0.511258\pi$
$509$	−262556.	+	312902.i	−1.01341	+	1.20774i	−0.978052	+	0.208362i	$0.933187\pi$
$510$		0			0
$511$	−318114.	−	115784.i	−1.21826	−	0.443411i
$512$		0			0
$513$	285562.	−	15464.1i	1.08509	−	0.0587612i
$514$		0			0
$515$	−98378.1	+	270292.i	−0.370923	+	1.01910i
$516$		0			0
$517$	113539.	+	95270.2i	0.424778	+	0.356431i
$518$		0			0
$519$	−8225.93	+	46651.6i	−0.0305387	+	0.173193i
$520$		0			0
$521$	−60388.8	+	34865.5i	−0.222475	+	0.128446i	−0.607096	−	0.794629i	$-0.707666\pi$
$521$	−60388.8	+	34865.5i	−0.222475	+	0.128446i	0.384621	+	0.923075i	$0.374332\pi$
$522$		0			0
$523$	166145.	+	456479.i	0.607411	+	1.66885i	0.735861	+	0.677133i	$0.236778\pi$
$523$	166145.	+	456479.i	0.607411	+	1.66885i	−0.128449	+	0.991716i	$0.541000\pi$
$524$		0			0
$525$	−8041.43	−	4642.72i	−0.0291752	−	0.0168443i
$526$		0			0
$527$	44565.5	+	53111.1i	0.160464	+	0.191233i
$528$		0			0
$529$	−10195.6	−	57822.3i	−0.0364337	−	0.206626i
$530$		0			0
$531$		−	11247.7i		−	0.0398910i
$532$		0			0
$533$	−203411.			−0.716011
$534$		0			0
$535$	−488228.	+	86087.8i	−1.70575	+	0.300770i
$536$		0			0
$537$	−40340.7	+	33849.8i	−0.139893	+	0.117384i
$538$		0			0
$539$	78614.8	−	136165.i	0.270599	−	0.468692i
$540$		0			0
$541$	381671.	−	138917.i	1.30405	−	0.474636i	0.405737	−	0.913990i	$-0.367015\pi$
$541$	381671.	−	138917.i	1.30405	−	0.474636i	0.898314	+	0.439354i	$0.144793\pi$
$542$		0			0
$543$	93352.8	+	161692.i	0.316612	+	0.548389i
$544$		0			0
$545$	206181.	+	36355.2i	0.694152	+	0.122398i
$546$		0			0
$547$	46267.0	−	55138.9i	0.154631	−	0.184282i	−0.683167	−	0.730262i	$-0.739398\pi$
$547$	46267.0	−	55138.9i	0.154631	−	0.184282i	0.837798	+	0.545980i	$0.183842\pi$
$548$		0			0
$549$	−124915.	−	45465.4i	−0.414448	−	0.150847i
$550$		0			0
$551$	1949.84	−	16111.9i	0.00642236	−	0.0530695i
$552$		0			0
$553$	69337.6	−	190504.i	0.226735	−	0.622949i
$554$		0			0
$555$	208532.	+	174979.i	0.676998	+	0.568069i
$556$		0			0
$557$	−23478.0	+	133150.i	−0.0756746	+	0.429172i	0.923307	+	0.384062i	$0.125475\pi$
$557$	−23478.0	+	133150.i	−0.0756746	+	0.429172i	−0.998982	+	0.0451101i	$0.985636\pi$
$558$		0			0
$559$	325699.	−	188042.i	1.04230	−	0.601773i
$560$		0			0
$561$	13735.3	+	37737.3i	0.0436426	+	0.119907i
$562$		0			0
$563$	−35448.6	−	20466.2i	−0.111836	−	0.0645686i	0.443039	−	0.896503i	$-0.353900\pi$
$563$	−35448.6	−	20466.2i	−0.111836	−	0.0645686i	−0.554875	+	0.831934i	$0.687234\pi$
$564$		0			0
$565$	−276952.	−	330058.i	−0.867575	−	1.03394i
$566$		0			0
$567$	−56692.0	−	321516.i	−0.176342	−	1.00008i
$568$		0			0
$569$		−	103071.i		−	0.318355i	−0.987250	−	0.159178i	$-0.949116\pi$
$569$		−	103071.i		−	0.318355i	0.987250	−	0.159178i	$-0.0508842\pi$
$570$		0			0
$571$	425127.			1.30391			0.651954	−	0.758259i	$-0.273950\pi$
$571$	425127.			1.30391			0.651954	+	0.758259i	$0.273950\pi$
$572$		0			0
$573$	342897.	−	60462.1i	1.04437	−	0.184151i
$574$		0			0
$575$	−5584.75	+	4686.16i	−0.0168915	+	0.0141736i
$576$		0			0
$577$	222629.	−	385604.i	0.668697	−	1.15822i	−0.309571	−	0.950876i	$-0.600186\pi$
$577$	222629.	−	385604.i	0.668697	−	1.15822i	0.978269	−	0.207341i	$-0.0664811\pi$
$578$		0			0
$579$	−276435.	+	100614.i	−0.824586	+	0.300125i
$580$		0			0
$581$	33463.4	+	57960.3i	0.0991329	+	0.171703i
$582$		0			0
$583$	−193032.	−	34036.8i	−0.567927	−	0.100141i
$584$		0			0
$585$	49656.7	−	59178.5i	0.145099	−	0.172923i
$586$		0			0
$587$	−397261.	−	144591.i	−1.15292	−	0.419630i	−0.306359	−	0.951916i	$-0.599111\pi$
$587$	−397261.	−	144591.i	−1.15292	−	0.419630i	−0.846564	+	0.532287i	$0.821333\pi$
$588$		0			0
$589$	−106947.	−	164059.i	−0.308276	−	0.472900i
$590$		0			0
$591$	−73406.1	+	201682.i	−0.210163	+	0.577419i
$592$		0			0
$593$	−100063.	−	83962.7i	−0.284553	−	0.238768i	0.489327	−	0.872100i	$-0.337242\pi$
$593$	−100063.	−	83962.7i	−0.284553	−	0.238768i	−0.773880	+	0.633332i	$0.781687\pi$
$594$		0			0
$595$	43159.5	−	244770.i	0.121911	−	0.691392i
$596$		0			0
$597$	−154094.	+	88966.5i	−0.432353	+	0.249619i
$598$		0			0
$599$	−216612.	−	595136.i	−0.603710	−	1.65868i	−0.743689	−	0.668526i	$-0.766926\pi$
$599$	−216612.	−	595136.i	−0.603710	−	1.65868i	0.139979	−	0.990154i	$-0.455296\pi$
$600$		0			0
$601$	−31516.2	−	18195.9i	−0.0872540	−	0.0503761i	0.455738	−	0.890114i	$-0.349375\pi$
$601$	−31516.2	−	18195.9i	−0.0872540	−	0.0503761i	−0.542992	+	0.839738i	$0.682709\pi$
$602$		0			0
$603$	78612.4	+	93686.6i	0.216200	+	0.257658i
$604$		0			0
$605$	55443.7	+	314437.i	0.151475	+	0.859058i
$606$		0			0
$607$			176712.i			0.479610i	0.970821	+	0.239805i	$0.0770835\pi$
$607$			176712.i			0.479610i	−0.970821	+	0.239805i	$0.922916\pi$
$608$		0			0
$609$	−26925.9			−0.0726000
$610$		0			0
$611$	476491.	−	84018.3i	1.27636	−	0.225056i
$612$		0			0
$613$	122043.	−	102407.i	0.324783	−	0.272525i	−0.465787	−	0.884897i	$-0.654229\pi$
$613$	122043.	−	102407.i	0.324783	−	0.272525i	0.790570	+	0.612371i	$0.209784\pi$
$614$		0			0
$615$	141498.	−	245082.i	0.374111	−	0.647978i
$616$		0			0
$617$	398569.	−	145067.i	1.04697	−	0.381065i	0.239451	−	0.970909i	$-0.423033\pi$
$617$	398569.	−	145067.i	1.04697	−	0.381065i	0.807518	+	0.589843i	$0.200810\pi$
$618$		0			0
$619$	−25384.7	−	43967.7i	−0.0662509	−	0.114750i	0.830997	−	0.556276i	$-0.187770\pi$
$619$	−25384.7	−	43967.7i	−0.0662509	−	0.114750i	−0.897248	+	0.441527i	$0.854437\pi$
$620$		0			0
$621$	−366860.	−	64687.4i	−0.951300	−	0.167740i
$622$		0			0
$623$	132900.	−	158384.i	0.342411	−	0.408070i
$624$		0			0
$625$	357736.	+	130205.i	0.915805	+	0.333326i
$626$		0			0
$627$	−25710.1	−	110485.i	−0.0653986	−	0.281040i
$628$		0			0
$629$	63391.8	−	174168.i	0.160226	−	0.440216i
$630$		0			0
$631$	−118259.	−	99230.9i	−0.297012	−	0.249223i	0.482087	−	0.876123i	$-0.339879\pi$
$631$	−118259.	−	99230.9i	−0.297012	−	0.249223i	−0.779099	+	0.626900i	$0.784323\pi$
$632$		0			0
$633$	58646.5	−	332601.i	0.146364	−	0.830072i
$634$		0			0
$635$	210478.	−	121520.i	0.521988	−	0.301370i
$636$		0			0
$637$	−175550.	−	482319.i	−0.432635	−	1.18865i
$638$		0			0
$639$	−131650.	−	76008.1i	−0.322418	−	0.186148i
$640$		0			0
$641$	485190.	+	578226.i	1.18085	+	1.40728i	0.893265	+	0.449530i	$0.148409\pi$
$641$	485190.	+	578226.i	1.18085	+	1.40728i	0.287587	+	0.957755i	$0.407147\pi$
$642$		0			0
$643$	36966.7	+	209648.i	0.0894105	+	0.507072i	0.996317	+	0.0857411i	$0.0273258\pi$
$643$	36966.7	+	209648.i	0.0894105	+	0.507072i	−0.906907	+	0.421331i	$0.861563\pi$
$644$		0			0
$645$			523229.i			1.25769i
$646$		0			0
$647$	−700532.			−1.67348			−0.836738	−	0.547603i	$-0.815540\pi$
$647$	−700532.			−1.67348			−0.836738	+	0.547603i	$0.815540\pi$
$648$		0			0
$649$	−19738.6	+	3480.45i	−0.0468627	+	0.00826316i
$650$		0			0
$651$	−248897.	+	208850.i	−0.587297	+	0.492801i
$652$		0			0
$653$	93437.4	−	161838.i	0.219126	−	0.379538i	−0.735415	−	0.677617i	$-0.763013\pi$
$653$	93437.4	−	161838.i	0.219126	−	0.379538i	0.954541	+	0.298079i	$0.0963460\pi$
$654$		0			0
$655$	−153008.	+	55690.5i	−0.356642	+	0.129807i
$656$		0			0
$657$	−49835.5	−	86317.6i	−0.115454	−	0.199972i
$658$		0			0
$659$	632273.	+	111487.i	1.45591	+	0.256716i	0.844907	−	0.534913i	$-0.179656\pi$
$659$	632273.	+	111487.i	1.45591	+	0.256716i	0.611002	+	0.791629i	$0.290767\pi$
$660$		0			0
$661$	−453466.	+	540420.i	−1.03787	+	1.23688i	−0.0668781	+	0.997761i	$0.521304\pi$
$661$	−453466.	+	540420.i	−1.03787	+	1.23688i	−0.970990	+	0.239122i	$0.923141\pi$
$662$		0			0
$663$	123193.	+	44838.5i	0.280258	+	0.102006i
$664$		0			0
$665$	−204094.	+	671741.i	−0.461516	+	1.51900i
$666$		0			0
$667$	−7230.53	+	19865.7i	−0.0162524	+	0.0446532i
$668$		0			0
$669$	−376042.	−	315536.i	−0.840202	−	0.705013i
$670$		0			0
$671$	−41134.0	+	233283.i	−0.0913600	+	0.518128i
$672$		0			0
$673$	485127.	−	280088.i	1.07109	−	0.618393i	0.142610	−	0.989779i	$-0.454451\pi$
$673$	485127.	−	280088.i	1.07109	−	0.618393i	0.928479	+	0.371386i	$0.121117\pi$
$674$		0			0
$675$	−4200.58	−	11541.0i	−0.00921939	−	0.0253301i
$676$		0			0
$677$	−149773.	−	86471.5i	−0.326781	−	0.188667i	0.327630	−	0.944806i	$-0.393750\pi$
$677$	−149773.	−	86471.5i	−0.326781	−	0.188667i	−0.654411	+	0.756139i	$0.727083\pi$
$678$		0			0
$679$	−271126.	−	323115.i	−0.588073	−	0.700839i
$680$		0			0
$681$	−118550.	−	672331.i	−0.255628	−	1.44974i
$682$		0			0
$683$			561963.i			1.20466i	0.798245	+	0.602332i	$0.205762\pi$
$683$			561963.i			1.20466i	−0.798245	+	0.602332i	$0.794238\pi$
$684$		0			0
$685$	−263865.			−0.562343
$686$		0			0
$687$	581131.	−	102469.i	1.23129	−	0.217110i
$688$		0			0
$689$	−490170.	+	411301.i	−1.03254	+	0.866406i
$690$		0			0
$691$	27777.4	−	48111.9i	0.0581750	−	0.100762i	−0.835471	−	0.549534i	$-0.814805\pi$
$691$	27777.4	−	48111.9i	0.0581750	−	0.100762i	0.893646	+	0.448772i	$0.148139\pi$
$692$		0			0
$693$	70954.3	−	25825.2i	0.147745	−	0.0537747i
$694$		0			0
$695$	228616.	+	395975.i	0.473301	+	0.819781i
$696$		0			0
$697$	−189755.	−	33459.0i	−0.390596	−	0.0688727i
$698$		0			0
$699$	466084.	−	555457.i	0.953915	−	1.13683i
$700$		0			0
$701$	444283.	+	161706.i	0.904115	+	0.329071i	0.751901	−	0.659276i	$-0.229137\pi$
$701$	444283.	+	161706.i	0.904115	+	0.329071i	0.152215	+	0.988347i	$0.451359\pi$
$702$		0			0
$703$	−236870.	+	466891.i	−0.479291	+	0.944724i
$704$		0			0
$705$	−230230.	+	632551.i	−0.463216	+	1.27267i
$706$		0			0
$707$	−181018.	−	151893.i	−0.362146	−	0.303877i
$708$		0			0
$709$	−37158.9	+	210739.i	−0.0739214	+	0.419229i	0.925280	+	0.379284i	$0.123830\pi$
$709$	−37158.9	+	210739.i	−0.0739214	+	0.419229i	−0.999202	+	0.0399456i	$0.987282\pi$
$710$		0			0
$711$	51691.5	−	29844.1i	0.102254	−	0.0590364i
$712$		0			0
$713$	87249.9	+	239717.i	0.171627	+	0.471542i
$714$		0			0
$715$	−119218.	−	68830.6i	−0.233201	−	0.134639i
$716$		0			0
$717$	−136323.	−	162463.i	−0.265174	−	0.316022i
$718$		0			0
$719$	74521.0	+	422629.i	0.144152	+	0.817527i	0.968044	+	0.250780i	$0.0806871\pi$
$719$	74521.0	+	422629.i	0.144152	+	0.817527i	−0.823892	+	0.566747i	$0.808202\pi$
$720$		0			0
$721$			917791.i			1.76552i
$722$		0			0
$723$	−426152.			−0.815245
$724$		0			0
$725$	−686.402	+	121.031i	−0.00130588	+	0.000230261i
$726$		0			0
$727$	400152.	−	335767.i	0.757104	−	0.635286i	−0.180267	−	0.983618i	$-0.557696\pi$
$727$	400152.	−	335767.i	0.757104	−	0.635286i	0.937371	+	0.348332i	$0.113252\pi$
$728$		0			0
$729$	291996.	−	505752.i	0.549442	−	0.951662i
$730$		0			0
$731$	334765.	−	121845.i	0.626477	−	0.228019i
$732$		0			0
$733$	4773.63	+	8268.18i	0.00888467	+	0.0153887i	0.870434	−	0.492286i	$-0.163839\pi$
$733$	4773.63	+	8268.18i	0.00888467	+	0.0153887i	−0.861549	+	0.507675i	$0.830505\pi$
$734$		0			0
$735$	703244.	+	124001.i	1.30176	+	0.229536i
$736$		0			0
$737$	140085.	−	166947.i	0.257904	−	0.307358i
$738$		0			0
$739$	−610485.	−	222198.i	−1.11786	−	0.406867i	−0.283987	−	0.958828i	$-0.591657\pi$
$739$	−610485.	−	222198.i	−1.11786	−	0.406867i	−0.833870	+	0.551961i	$0.813880\pi$
$740$		0			0
$741$	−330243.	−	167544.i	−0.601446	−	0.305135i
$742$		0			0
$743$	20420.2	−	56103.9i	0.0369898	−	0.101629i	−0.919823	−	0.392334i	$-0.871668\pi$
$743$	20420.2	−	56103.9i	0.0369898	−	0.101629i	0.956813	+	0.290705i	$0.0938900\pi$
$744$		0			0
$745$	−757214.	−	635378.i	−1.36429	−	1.14477i
$746$		0			0
$747$	−3421.70	+	19405.4i	−0.00613198	+	0.0347762i
$748$		0			0
$749$	−1.36993e6	+	790930.i	−2.44194	+	1.40986i
$750$		0			0
$751$	211038.	+	579823.i	0.374181	+	1.02805i	0.973728	+	0.227714i	$0.0731251\pi$
$751$	211038.	+	579823.i	0.374181	+	1.02805i	−0.599547	+	0.800339i	$0.704653\pi$
$752$		0			0
$753$	−245141.	−	141532.i	−0.432341	−	0.249612i
$754$		0			0
$755$	219579.	+	261684.i	0.385209	+	0.459074i
$756$		0			0
$757$	83191.5	+	471802.i	0.145173	+	0.823319i	0.967228	+	0.253910i	$0.0817168\pi$
$757$	83191.5	+	471802.i	0.145173	+	0.823319i	−0.822054	+	0.569409i	$0.807172\pi$
$758$		0			0
$759$			147764.i			0.256498i
$760$		0			0
$761$	351157.			0.606362			0.303181	−	0.952933i	$-0.401951\pi$
$761$	351157.			0.606362			0.303181	+	0.952933i	$0.401951\pi$
$762$		0			0
$763$	657877.	−	116001.i	1.13004	−	0.199257i
$764$		0			0
$765$	56057.3	−	47037.7i	0.0957876	−	0.0803754i
$766$		0			0
$767$	−32715.2	+	56664.4i	−0.0556108	+	0.0963207i
$768$		0			0
$769$	629039.	−	228952.i	1.06371	−	0.387160i	0.249892	−	0.968274i	$-0.419605\pi$
$769$	629039.	−	228952.i	1.06371	−	0.387160i	0.813823	+	0.581113i	$0.197383\pi$
$770$		0			0
$771$	−276823.	−	479471.i	−0.465686	−	0.806592i
$772$		0			0
$773$	−717414.	−	126499.i	−1.20064	−	0.211704i	−0.462662	−	0.886535i	$-0.653106\pi$
$773$	−717414.	−	126499.i	−1.20064	−	0.211704i	−0.737973	+	0.674830i	$0.764217\pi$
$774$		0			0
$775$	−5406.17	+	6442.82i	−0.00900090	+	0.0107269i
$776$		0			0
$777$	816210.	+	297076.i	1.35195	+	0.492069i
$778$		0			0
$779$	520760.	+	158222.i	0.858149	+	0.260730i
$780$		0			0
$781$	−92649.5	+	254552.i	−0.151894	+	0.417326i
$782$		0			0
$783$	−27282.3	−	22892.5i	−0.0444997	−	0.0373397i
$784$		0			0
$785$	−96449.5	+	546993.i	−0.156517	+	0.887651i
$786$		0			0
$787$	−359227.	+	207400.i	−0.579988	+	0.334856i	−0.761129	−	0.648601i	$-0.775354\pi$
$787$	−359227.	+	207400.i	−0.579988	+	0.334856i	0.181140	+	0.983457i	$0.442021\pi$
$788$		0			0
$789$	−204800.	−	562685.i	−0.328986	−	0.903881i
$790$		0			0
$791$	−1.19059e6	−	687390.i	−1.90288	−	1.09863i
$792$		0			0
$793$	497065.	+	592378.i	0.790435	+	0.942004i
$794$		0			0
$795$	−154586.	−	876698.i	−0.244588	−	1.38713i
$796$		0			0
$797$			448699.i			0.706380i	0.935552	+	0.353190i	$0.114903\pi$
$797$			448699.i			0.706380i	−0.935552	+	0.353190i	$0.885097\pi$
$798$		0			0
$799$	458323.			0.717924
$800$		0			0
$801$	59948.7	−	10570.6i	0.0934361	−	0.0164753i
$802$		0			0
$803$	−136058.	+	114166.i	−0.211005	+	0.177054i
$804$		0			0
$805$	457255.	−	791989.i	0.705614	−	1.22216i
$806$		0			0
$807$	746703.	−	271777.i	1.14657	−	0.417317i
$808$		0			0
$809$	412674.	+	714773.i	0.630537	+	1.09212i	0.987442	+	0.157981i	$0.0504984\pi$
$809$	412674.	+	714773.i	0.630537	+	1.09212i	−0.356906	+	0.934140i	$0.616168\pi$
$810$		0			0
$811$	422824.	+	74555.3i	0.642862	+	0.113354i	0.485570	−	0.874198i	$-0.338612\pi$
$811$	422824.	+	74555.3i	0.642862	+	0.113354i	0.157293	+	0.987552i	$0.449723\pi$
$812$		0			0
$813$	204071.	−	243202.i	0.308745	−	0.367948i
$814$		0			0
$815$	−632900.	−	230357.i	−0.952840	−	0.346805i
$816$		0			0
$817$	−980103.	+	228072.i	−1.46834	+	0.341687i
$818$		0			0
$819$	84306.0	−	231629.i	0.125687	−	0.345323i
$820$		0			0
$821$	450369.	+	377905.i	0.668163	+	0.560656i	0.912521	−	0.409030i	$-0.134133\pi$
$821$	450369.	+	377905.i	0.668163	+	0.560656i	−0.244358	+	0.969685i	$0.578577\pi$
$822$		0			0
$823$	85194.2	−	483160.i	0.125780	−	0.713331i	−0.855062	−	0.518525i	$-0.826481\pi$
$823$	85194.2	−	483160.i	0.125780	−	0.713331i	0.980842	−	0.194806i	$-0.0624077\pi$
$824$		0			0
$825$	−4218.97	+	2435.82i	−0.00619867	+	0.00357880i
$826$		0			0
$827$	268227.	+	736947.i	0.392185	+	1.07752i	0.966002	+	0.258536i	$0.0832401\pi$
$827$	268227.	+	736947.i	0.392185	+	1.07752i	−0.573816	+	0.818984i	$0.694538\pi$
$828$		0			0
$829$	−860067.	−	496560.i	−1.25148	−	0.722541i	−0.280075	−	0.959978i	$-0.590359\pi$
$829$	−860067.	−	496560.i	−1.25148	−	0.722541i	−0.971403	+	0.237437i	$0.923693\pi$
$830$		0			0
$831$	−372432.	−	443847.i	−0.539318	−	0.642734i
$832$		0			0
$833$	−84428.1	−	478816.i	−0.121674	−	0.690047i
$834$		0			0
$835$		−	1.32294e6i		−	1.89744i
$836$		0			0
$837$	−429756.			−0.613438
$838$		0			0
$839$	−435208.	+	76738.9i	−0.618262	+	0.109016i	−0.474002	−	0.880524i	$-0.657191\pi$
$839$	−435208.	+	76738.9i	−0.618262	+	0.109016i	−0.144260	+	0.989540i	$0.546080\pi$
$840$		0			0
$841$	540260.	−	453332.i	0.763855	−	0.640951i
$842$		0			0
$843$	−475287.	+	823222.i	−0.668808	+	1.15841i
$844$		0			0
$845$	240299.	−	87461.7i	0.336542	−	0.122491i
$846$		0			0
$847$	509388.	+	882286.i	0.710038	+	1.22982i
$848$		0			0
$849$	942753.	+	166233.i	1.30792	+	0.230622i
$850$		0			0
$851$	438360.	−	522417.i	0.605302	−	0.721371i
$852$		0			0
$853$	−1.29584e6	−	471646.i	−1.78095	−	0.648213i	−0.999712	−	0.0239804i	$-0.992366\pi$
$853$	−1.29584e6	−	471646.i	−1.78095	−	0.648213i	−0.781238	−	0.624233i	$-0.785412\pi$
$854$		0			0
$855$	−173160.	+	112880.i	−0.236872	+	0.154414i
$856$		0			0
$857$	−58971.8	+	162024.i	−0.0802939	+	0.220606i	−0.973343	−	0.229353i	$-0.926339\pi$
$857$	−58971.8	+	162024.i	−0.0802939	+	0.220606i	0.893049	+	0.449959i	$0.148561\pi$
$858$		0			0
$859$	−375604.	−	315169.i	−0.509030	−	0.427127i	0.351758	−	0.936091i	$-0.385584\pi$
$859$	−375604.	−	315169.i	−0.509030	−	0.427127i	−0.860788	+	0.508964i	$0.830029\pi$
$860$		0			0
$861$	156800.	−	889260.i	0.211515	−	1.19956i
$862$		0			0
$863$	1.19144e6	−	687878.i	1.59974	−	0.923613i	0.608209	−	0.793777i	$-0.291888\pi$
$863$	1.19144e6	−	687878.i	1.59974	−	0.923613i	0.991535	−	0.129836i	$-0.0414451\pi$
$864$		0			0
$865$	−52609.2	−	144542.i	−0.0703120	−	0.193181i
$866$		0			0
$867$	−442395.	−	255417.i	−0.588535	−	0.339791i
$868$		0			0
$869$	−68368.8	−	81478.8i	−0.0905354	−	0.107896i
$870$		0			0
$871$	−123541.	−	700634.i	−0.162845	−	0.923538i
$872$		0			0
$873$		−	124187.i		−	0.162947i
$874$		0			0
$875$	1.24563e6			1.62695
$876$		0			0
$877$	1.47452e6	−	259998.i	1.91713	−	0.338042i	0.918747	−	0.394847i	$-0.129202\pi$
$877$	1.47452e6	−	259998.i	1.91713	−	0.338042i	0.998385	+	0.0568051i	$0.0180914\pi$
$878$		0			0
$879$	−486718.	+	408405.i	−0.629940	+	0.528583i
$880$		0			0
$881$	117779.	−	203999.i	0.151746	−	0.262831i	−0.780124	−	0.625625i	$-0.784844\pi$
$881$	117779.	−	203999.i	0.151746	−	0.262831i	0.931869	+	0.362794i	$0.118177\pi$
$882$		0			0
$883$	422773.	−	153877.i	0.542233	−	0.197357i	−0.0563591	−	0.998411i	$-0.517949\pi$
$883$	422773.	−	153877.i	0.542233	−	0.197357i	0.598592	+	0.801054i	$0.295727\pi$
$884$		0			0
$885$	−45515.1	−	78834.5i	−0.0581125	−	0.100654i
$886$		0			0
$887$	724708.	+	127786.i	0.921120	+	0.162418i	0.614048	−	0.789268i	$-0.289540\pi$
$887$	724708.	+	127786.i	0.921120	+	0.162418i	0.307071	+	0.951687i	$0.400651\pi$
$888$		0			0
$889$	498473.	−	594057.i	0.630722	−	0.751665i
$890$		0			0
$891$	−160957.	−	58583.7i	−0.202747	−	0.0737940i
$892$		0			0
$893$	−1.28524e6	−	155537.i	−1.61169	−	0.195043i
$894$		0			0
$895$	58483.8	−	160683.i	0.0730112	−	0.200597i
$896$		0			0
$897$	369518.	+	310062.i	0.459251	+	0.385358i
$898$		0			0
$899$	−4235.07	+	24018.3i	−0.00524012	+	0.0297182i
$900$		0			0
$901$	−524918.	+	303061.i	−0.646609	+	0.373320i
$902$		0			0
$903$	571006.	+	1.56883e6i	0.700270	+	1.92398i
$904$		0			0
$905$	−525029.	−	303125.i	−0.641041	−	0.370105i
$906$		0			0
$907$	228210.	+	271970.i	0.277409	+	0.330603i	0.886701	−	0.462343i	$-0.152991\pi$
$907$	228210.	+	271970.i	0.277409	+	0.330603i	−0.609293	+	0.792945i	$0.708547\pi$
$908$		0			0
$909$	−12081.2	−	68516.0i	−0.0146212	−	0.0829210i
$910$		0			0
$911$		−	831035.i		−	1.00134i	−0.865637	−	0.500671i	$-0.833087\pi$
$911$		−	831035.i		−	1.00134i	0.865637	−	0.500671i	$-0.166913\pi$
$912$		0			0
$913$	35113.4			0.0421242
$914$		0			0
$915$	−1.05950e6	+	186819.i	−1.26550	+	0.223141i
$916$		0			0
$917$	−397997.	+	333959.i	−0.473305	+	0.397150i
$918$		0			0
$919$	−67362.5	+	116675.i	−0.0797603	+	0.138149i	−0.903146	−	0.429333i	$-0.858749\pi$
$919$	−67362.5	+	116675.i	−0.0797603	+	0.138149i	0.823386	+	0.567481i	$0.192082\pi$
$920$		0			0
$921$	97438.4	−	35464.7i	0.114871	−	0.0418097i
$922$		0			0
$923$	442156.	+	765837.i	0.519006	+	0.898944i
$924$		0			0
$925$	22142.3	+	3904.29i	0.0258786	+	0.00456309i
$926$		0			0
$927$	−173693.	+	207000.i	−0.202127	+	0.240885i
$928$		0			0
$929$	−600073.	−	218409.i	−0.695300	−	0.253069i	−0.0298973	−	0.999553i	$-0.509518\pi$
$929$	−600073.	−	218409.i	−0.695300	−	0.253069i	−0.665403	+	0.746484i	$0.731740\pi$
$930$		0			0
$931$	74263.5	+	1.37135e6i	0.0856793	+	1.58216i
$932$		0			0
$933$	−44984.6	+	123594.i	−0.0516774	+	0.141982i
$934$		0			0
$935$	−99892.7	−	83820.0i	−0.114264	−	0.0958792i
$936$		0			0
$937$	−51925.6	+	294485.i	−0.0591429	+	0.335416i	−0.999994	−	0.00340378i	$-0.998917\pi$
$937$	−51925.6	+	294485.i	−0.0591429	+	0.335416i	0.940851	+	0.338820i	$0.110028\pi$
$938$		0			0
$939$	−1.08338e6	+	625491.i	−1.22871	+	0.709398i
$940$		0			0
$941$	322134.	+	885055.i	0.363795	+	0.999518i	0.977676	+	0.210120i	$0.0673854\pi$
$941$	322134.	+	885055.i	0.363795	+	0.999518i	−0.613881	+	0.789399i	$0.710392\pi$
$942$		0			0
$943$	−613981.	−	354482.i	−0.690449	−	0.398631i
$944$		0			0
$945$	990294.	+	1.18019e6i	1.10892	+	1.32156i
$946$		0			0
$947$	20729.8	+	117564.i	0.0231151	+	0.131092i	0.994182	−	0.107717i	$-0.0343541\pi$
$947$	20729.8	+	117564.i	0.0231151	+	0.131092i	−0.971067	+	0.238809i	$0.923243\pi$
$948$		0			0
$949$			579809.i			0.643802i
$950$		0			0
$951$	−811247.			−0.896999
$952$		0			0
$953$	−262828.	+	46343.7i	−0.289392	+	0.0510276i	−0.316460	−	0.948606i	$-0.602494\pi$
$953$	−262828.	+	46343.7i	−0.289392	+	0.0510276i	0.0270676	+	0.999634i	$0.491383\pi$
$954$		0			0
$955$	−866087.	+	726733.i	−0.949631	+	0.796835i
$956$		0			0
$957$	−7063.41	+	12234.2i	−0.00771242	+	0.0133583i
$958$		0			0
$959$	−791161.	+	287959.i	−0.860256	+	0.313108i
$960$		0			0
$961$	−314612.	−	544924.i	−0.340666	−	0.590051i
$962$		0			0
$963$	−458660.	−	80874.2i	−0.494582	−	0.0872082i
$964$		0			0
$965$	614001.	−	731738.i	0.659348	−	0.785780i
$966$		0			0
$967$	−651323.	−	237062.i	−0.696536	−	0.253518i	−0.0306049	−	0.999532i	$-0.509743\pi$
$967$	−651323.	−	237062.i	−0.696536	−	0.253518i	−0.665931	+	0.746013i	$0.731966\pi$
$968$		0			0
$969$	−280513.	−	210617.i	−0.298749	−	0.224309i
$970$		0			0
$971$	−200968.	+	552156.i	−0.213152	+	0.585630i	−0.999482	−	0.0321764i	$-0.989756\pi$
$971$	−200968.	+	552156.i	−0.213152	+	0.585630i	0.786330	+	0.617806i	$0.211978\pi$
$972$		0			0
$973$	1.11760e6	+	937780.i	1.18049	+	0.990548i
$974$		0			0
$975$	−2761.60	+	15661.8i	−0.00290503	+	0.0164753i
$976$		0			0
$977$	825474.	−	476587.i	0.864797	−	0.499291i	−0.000818797	−	1.00000i	$-0.500261\pi$
$977$	825474.	−	476587.i	0.864797	−	0.499291i	0.865616	+	0.500709i	$0.166927\pi$
$978$		0			0
$979$	−37100.7	−	101933.i	−0.0387094	−	0.106353i
$980$		0			0
$981$	170332.	+	98341.1i	0.176994	+	0.102187i
$982$		0			0
$983$	−568150.	−	677095.i	−0.587971	−	0.700717i	0.387243	−	0.921978i	$-0.373427\pi$
$983$	−568150.	−	677095.i	−0.587971	−	0.700717i	−0.975215	+	0.221260i	$0.928983\pi$
$984$		0			0
$985$	−121017.	−	686320.i	−0.124731	−	0.707383i
$986$		0			0
$987$			2.14786e6i			2.20482i
$988$		0			0
$989$	1.31080e6			1.34012
$990$		0			0
$991$	−173201.	+	30540.0i	−0.176361	+	0.0310972i	−0.261131	−	0.965303i	$-0.584096\pi$
$991$	−173201.	+	30540.0i	−0.176361	+	0.0310972i	0.0847700	+	0.996401i	$0.472984\pi$
$992$		0			0
$993$	878849.	−	737442.i	0.891283	−	0.747876i
$994$		0			0
$995$	288882.	−	500359.i	0.291793	−	0.505400i
$996$		0			0
$997$	614047.	−	223495.i	0.617748	−	0.224842i	−0.0141420	−	0.999900i	$-0.504502\pi$
$997$	614047.	−	223495.i	0.617748	−	0.224842i	0.631890	+	0.775058i	$0.282279\pi$
$998$		0			0
$999$	574436.	+	994953.i	0.575587	+	0.996945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.53.6	yes	42
19.14	odd	18	inner	76.5.j.a.33.6	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.6	✓	42	19.14	odd	18	inner
76.5.j.a.53.6	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.48759 - 1.32026i) q^{3} +(-18.9121 + 15.8691i) q^{5} +(-39.3870 + 68.2202i) q^{7} +(-21.7942 + 7.93242i) q^{9} +O(q^{10})\)	\(q+(7.48759 - 1.32026i) q^{3} +(-18.9121 + 15.8691i) q^{5} +(-39.3870 + 68.2202i) q^{7} +(-21.7942 + 7.93242i) q^{9} +(20.6645 + 35.7920i) q^{11} +(132.868 + 23.4283i) q^{13} +(-120.655 + 143.791i) q^{15} +(120.095 + 43.7109i) q^{17} +(-321.938 - 163.330i) q^{19} +(-204.845 + 562.806i) q^{21} +(360.226 + 302.265i) q^{23} +(-2.69215 + 15.2679i) q^{25} +(-686.056 + 396.094i) q^{27} +(15.3762 + 42.2458i) q^{29} +(469.811 + 271.246i) q^{31} +(201.983 + 240.714i) q^{33} +(-337.706 - 1915.22i) q^{35} -1450.25i q^{37} +1025.80 q^{39} +(-1484.76 + 261.803i) q^{41} +(2135.35 - 1791.77i) q^{43} +(286.292 - 495.873i) q^{45} +(3369.92 - 1226.55i) q^{47} +(-1902.17 - 3294.65i) q^{49} +(956.931 + 168.733i) q^{51} +(-3048.52 + 3633.09i) q^{53} +(-958.798 - 348.974i) q^{55} +(-2626.18 - 797.908i) q^{57} +(-165.867 + 455.717i) q^{59} +(4390.65 + 3684.20i) q^{61} +(317.254 - 1799.24i) q^{63} +(-2884.61 + 1665.43i) q^{65} +(-1803.52 - 4955.13i) q^{67} +(3096.29 + 1787.65i) q^{69} +(4213.11 + 5020.99i) q^{71} +(746.251 + 4232.20i) q^{73} +117.875i q^{75} -3255.66 q^{77} +(-2534.46 + 446.894i) q^{79} +(-3174.85 + 2664.01i) q^{81} +(424.803 - 735.780i) q^{83} +(-2964.90 + 1079.13i) q^{85} +(170.906 + 296.019i) q^{87} +(-2584.79 - 455.768i) q^{89} +(-6831.56 + 8141.54i) q^{91} +(3875.87 + 1410.70i) q^{93} +(8680.44 - 2019.96i) q^{95} +(-1831.36 + 5031.61i) q^{97} +(-734.284 - 616.138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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