LMFDB - Embedded newform 177.5.c.a.58.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, 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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.10
Character	$\chi$	$=$	177.58
Dual form			177.5.c.a.58.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +3.21498i q^{10} -74.8765i q^{11} -29.0796 q^{12} +105.330i q^{13} +353.662i q^{14} -3.59476 q^{15} -314.223 q^{16} -141.930 q^{17} -125.474i q^{18} -170.820 q^{19} +3.87164 q^{20} -395.439 q^{21} -347.966 q^{22} -226.464i q^{23} -251.222i q^{24} -624.521 q^{25} +489.487 q^{26} +140.296 q^{27} +425.897 q^{28} -677.129 q^{29} +16.7055i q^{30} +114.554i q^{31} +686.691i q^{32} -389.070i q^{33} +659.575i q^{34} +52.6484 q^{35} -151.102 q^{36} -488.383i q^{37} +793.831i q^{38} +547.309i q^{39} +33.4475i q^{40} -1825.63 q^{41} +1837.68i q^{42} -527.862i q^{43} +419.037i q^{44} -18.6789 q^{45} -1052.42 q^{46} +1903.37i q^{47} -1632.75 q^{48} +3390.55 q^{49} +2902.27i q^{50} -737.489 q^{51} -589.465i q^{52} +4683.03 q^{53} -651.983i q^{54} +51.8005i q^{55} +3679.36i q^{56} -887.604 q^{57} +3146.75i q^{58} +(2331.20 + 2585.12i) q^{59} +20.1176 q^{60} -6414.67i q^{61} +532.355 q^{62} -2054.76 q^{63} -1836.38 q^{64} -72.8684i q^{65} -1808.08 q^{66} +1772.67i q^{67} +794.294 q^{68} -1176.74i q^{69} -244.667i q^{70} +170.581 q^{71} -1305.39i q^{72} -8999.83i q^{73} -2269.61 q^{74} -3245.11 q^{75} +955.971 q^{76} +5698.27i q^{77} +2543.45 q^{78} -204.796 q^{79} +217.383 q^{80} +729.000 q^{81} +8484.05i q^{82} -1391.38i q^{83} +2213.03 q^{84} +98.1888 q^{85} -2453.07 q^{86} -3518.47 q^{87} -3620.10 q^{88} -3001.60i q^{89} +86.8045i q^{90} -8015.83i q^{91} +1267.38i q^{92} +595.241i q^{93} +8845.32 q^{94} +118.175 q^{95} +3568.15i q^{96} -9224.90i q^{97} -15756.5i q^{98} -2021.67i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9} + 360 q^{12} + 144 q^{15} + 3944 q^{16} - 528 q^{17} + 444 q^{19} + 444 q^{20} + 1304 q^{22} + 4880 q^{25} - 1452 q^{26} - 1160 q^{28} - 996 q^{29} + 10320 q^{35} - 8640 q^{36} - 5196 q^{41} - 10476 q^{46} + 576 q^{48} + 5104 q^{49} + 936 q^{51} - 2184 q^{53} - 2520 q^{57} - 11736 q^{59} - 11448 q^{60} + 15240 q^{62} + 2160 q^{63} - 81012 q^{64} + 17352 q^{66} + 29568 q^{68} - 5964 q^{71} + 14376 q^{74} - 2736 q^{75} + 3480 q^{76} + 37692 q^{78} + 19020 q^{79} + 33096 q^{80} + 29160 q^{81} + 25128 q^{84} + 20220 q^{85} - 65880 q^{86} + 1512 q^{87} - 14932 q^{88} - 17864 q^{94} + 11004 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9 + 360 * q^12 + 144 * q^15 + 3944 * q^16 - 528 * q^17 + 444 * q^19 + 444 * q^20 + 1304 * q^22 + 4880 * q^25 - 1452 * q^26 - 1160 * q^28 - 996 * q^29 + 10320 * q^35 - 8640 * q^36 - 5196 * q^41 - 10476 * q^46 + 576 * q^48 + 5104 * q^49 + 936 * q^51 - 2184 * q^53 - 2520 * q^57 - 11736 * q^59 - 11448 * q^60 + 15240 * q^62 + 2160 * q^63 - 81012 * q^64 + 17352 * q^66 + 29568 * q^68 - 5964 * q^71 + 14376 * q^74 - 2736 * q^75 + 3480 * q^76 + 37692 * q^78 + 19020 * q^79 + 33096 * q^80 + 29160 * q^81 + 25128 * q^84 + 20220 * q^85 - 65880 * q^86 + 1512 * q^87 - 14932 * q^88 - 17864 * q^94 + 11004 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	4.64719i		−	1.16180i	−0.813976	−	0.580899i	$-0.802701\pi$
$2$		−	4.64719i		−	1.16180i	0.813976	−	0.580899i	$-0.197299\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−5.59638			−0.349774
$5$	−0.691812			−0.0276725			−0.0138362	−	0.999904i	$-0.504404\pi$
$5$	−0.691812			−0.0276725			−0.0138362	+	0.999904i	$0.504404\pi$
$6$		−	24.1475i		−	0.670764i
$7$	−76.1022			−1.55311			−0.776553	−	0.630051i	$-0.783034\pi$
$7$	−76.1022			−1.55311			−0.776553	+	0.630051i	$0.783034\pi$
$8$		−	48.3476i		−	0.755431i
$9$	27.0000			0.333333
$10$			3.21498i			0.0321498i
$11$		−	74.8765i		−	0.618814i	−0.950930	−	0.309407i	$-0.899869\pi$
$11$		−	74.8765i		−	0.618814i	0.950930	−	0.309407i	$-0.100131\pi$
$12$	−29.0796			−0.201942
$13$			105.330i			0.623253i	0.950205	+	0.311626i	$0.100874\pi$
$13$			105.330i			0.623253i	−0.950205	+	0.311626i	$0.899126\pi$
$14$			353.662i			1.80440i
$15$	−3.59476			−0.0159767
$16$	−314.223			−1.22743
$17$	−141.930			−0.491107			−0.245553	−	0.969383i	$-0.578970\pi$
$17$	−141.930			−0.491107			−0.245553	+	0.969383i	$0.578970\pi$
$18$		−	125.474i		−	0.387266i
$19$	−170.820			−0.473184			−0.236592	−	0.971609i	$-0.576031\pi$
$19$	−170.820			−0.473184			−0.236592	+	0.971609i	$0.576031\pi$
$20$	3.87164			0.00967911
$21$	−395.439			−0.896687
$22$	−347.966			−0.718937
$23$		−	226.464i		−	0.428098i	−0.976823	−	0.214049i	$-0.931335\pi$
$23$		−	226.464i		−	0.428098i	0.976823	−	0.214049i	$-0.0686653\pi$
$24$		−	251.222i		−	0.436149i
$25$	−624.521			−0.999234
$26$	489.487			0.724093
$27$	140.296			0.192450
$28$	425.897			0.543236
$29$	−677.129			−0.805148			−0.402574	−	0.915388i	$-0.631884\pi$
$29$	−677.129			−0.805148			−0.402574	+	0.915388i	$0.631884\pi$
$30$			16.7055i			0.0185617i
$31$			114.554i			0.119203i	0.998222	+	0.0596016i	$0.0189830\pi$
$31$			114.554i			0.119203i	−0.998222	+	0.0596016i	$0.981017\pi$
$32$			686.691i			0.670596i
$33$		−	389.070i		−	0.357273i
$34$			659.575i			0.570567i
$35$	52.6484			0.0429783
$36$	−151.102			−0.116591
$37$		−	488.383i		−	0.356745i	−0.983963	−	0.178372i	$-0.942917\pi$
$37$		−	488.383i		−	0.356745i	0.983963	−	0.178372i	$-0.0570831\pi$
$38$			793.831i			0.549744i
$39$			547.309i			0.359835i
$40$			33.4475i			0.0209047i
$41$	−1825.63			−1.08604			−0.543019	−	0.839720i	$-0.682719\pi$
$41$	−1825.63			−1.08604			−0.543019	+	0.839720i	$0.682719\pi$
$42$			1837.68i			1.04177i
$43$		−	527.862i		−	0.285485i	−0.989760	−	0.142742i	$-0.954408\pi$
$43$		−	527.862i		−	0.285485i	0.989760	−	0.142742i	$-0.0455921\pi$
$44$			419.037i			0.216445i
$45$	−18.6789			−0.00922416
$46$	−1052.42			−0.497364
$47$			1903.37i			0.861643i	0.902437	+	0.430822i	$0.141776\pi$
$47$			1903.37i			0.861643i	−0.902437	+	0.430822i	$0.858224\pi$
$48$	−1632.75			−0.708658
$49$	3390.55			1.41214
$50$			2902.27i			1.16091i
$51$	−737.489			−0.283541
$52$		−	589.465i		−	0.217997i
$53$	4683.03			1.66715			0.833576	−	0.552404i	$-0.186290\pi$
$53$	4683.03			1.66715			0.833576	+	0.552404i	$0.186290\pi$
$54$		−	651.983i		−	0.223588i
$55$			51.8005i			0.0171241i
$56$			3679.36i			1.17327i
$57$	−887.604			−0.273193
$58$			3146.75i			0.935419i
$59$	2331.20	+	2585.12i	0.669693	+	0.742638i
$59$	2331.20	+	2585.12i	0.669693	+	0.742638i
$60$	20.1176			0.00558823
$61$		−	6414.67i		−	1.72391i	−0.506985	−	0.861955i	$-0.669240\pi$
$61$		−	6414.67i		−	1.72391i	0.506985	−	0.861955i	$-0.330760\pi$
$62$	532.355			0.138490
$63$	−2054.76			−0.517702
$64$	−1836.38			−0.448335
$65$		−	72.8684i		−	0.0172469i
$66$	−1808.08			−0.415078
$67$			1772.67i			0.394892i	0.980314	+	0.197446i	$0.0632647\pi$
$67$			1772.67i			0.394892i	−0.980314	+	0.197446i	$0.936735\pi$
$68$	794.294			0.171776
$69$		−	1176.74i		−	0.247163i
$70$		−	244.667i		−	0.0499321i
$71$	170.581			0.0338387			0.0169193	−	0.999857i	$-0.494614\pi$
$71$	170.581			0.0338387			0.0169193	+	0.999857i	$0.494614\pi$
$72$		−	1305.39i		−	0.251810i
$73$		−	8999.83i		−	1.68884i	−0.535682	−	0.844420i	$-0.679945\pi$
$73$		−	8999.83i		−	1.68884i	0.535682	−	0.844420i	$-0.320055\pi$
$74$	−2269.61			−0.414465
$75$	−3245.11			−0.576908
$76$	955.971			0.165507
$77$			5698.27i			0.961085i
$78$	2543.45			0.418056
$79$	−204.796			−0.0328146			−0.0164073	−	0.999865i	$-0.505223\pi$
$79$	−204.796			−0.0328146			−0.0164073	+	0.999865i	$0.505223\pi$
$80$	217.383			0.0339661
$81$	729.000			0.111111
$82$			8484.05i			1.26176i
$83$		−	1391.38i		−	0.201971i	−0.994888	−	0.100986i	$-0.967800\pi$
$83$		−	1391.38i		−	0.201971i	0.994888	−	0.100986i	$-0.0321996\pi$
$84$	2213.03			0.313637
$85$	98.1888			0.0135901
$86$	−2453.07			−0.331676
$87$	−3518.47			−0.464852
$88$	−3620.10			−0.467472
$89$		−	3001.60i		−	0.378942i	−0.981886	−	0.189471i	$-0.939323\pi$
$89$		−	3001.60i		−	0.378942i	0.981886	−	0.189471i	$-0.0606773\pi$
$90$			86.8045i			0.0107166i
$91$		−	8015.83i		−	0.967978i
$92$			1267.38i			0.149738i
$93$			595.241i			0.0688220i
$94$	8845.32			1.00105
$95$	118.175			0.0130942
$96$			3568.15i			0.387169i
$97$		−	9224.90i		−	0.980434i	−0.871600	−	0.490217i	$-0.836918\pi$
$97$		−	9224.90i		−	0.980434i	0.871600	−	0.490217i	$-0.163082\pi$
$98$		−	15756.5i		−	1.64062i
$99$		−	2021.67i		−	0.206271i
$100$	3495.06			0.349506
$101$		−	15773.4i		−	1.54626i	−0.634250	−	0.773128i	$-0.718691\pi$
$101$		−	15773.4i		−	1.54626i	0.634250	−	0.773128i	$-0.281309\pi$
$102$			3427.25i			0.329417i
$103$		−	12464.1i		−	1.17486i	−0.809273	−	0.587432i	$-0.800139\pi$
$103$		−	12464.1i		−	1.17486i	0.809273	−	0.587432i	$-0.199861\pi$
$104$	5092.44			0.470825
$105$	273.569			0.0248135
$106$		−	21762.9i		−	1.93689i
$107$	−5179.20			−0.452372			−0.226186	−	0.974084i	$-0.572626\pi$
$107$	−5179.20			−0.452372			−0.226186	+	0.974084i	$0.572626\pi$
$108$	−785.150			−0.0673140
$109$		−	653.130i		−	0.0549727i	−0.999622	−	0.0274863i	$-0.991250\pi$
$109$		−	653.130i		−	0.0549727i	0.999622	−	0.0274863i	$-0.00875028\pi$
$110$	240.727			0.0198948
$111$		−	2537.71i		−	0.205967i
$112$	23913.0			1.90633
$113$			12708.3i			0.995247i	0.867393	+	0.497623i	$0.165794\pi$
$113$			12708.3i			0.995247i	−0.867393	+	0.497623i	$0.834206\pi$
$114$			4124.87i			0.317395i
$115$			156.671i			0.0118465i
$116$	3789.47			0.281619
$117$			2843.90i			0.207751i
$118$	12013.6	−	10833.5i	0.862795	−	0.778048i
$119$	10801.2			0.762742
$120$			173.798i			0.0120693i
$121$	9034.50			0.617069
$122$	−29810.2			−2.00283
$123$	−9486.25			−0.627024
$124$		−	641.089i		−	0.0416941i
$125$	864.434			0.0553238
$126$			9548.86i			0.601465i
$127$	−3763.18			−0.233318			−0.116659	−	0.993172i	$-0.537218\pi$
$127$	−3763.18			−0.233318			−0.116659	+	0.993172i	$0.537218\pi$
$128$			19521.1i			1.19147i
$129$		−	2742.85i		−	0.164825i
$130$	−338.633			−0.0200375
$131$			1872.87i			0.109135i	0.998510	+	0.0545677i	$0.0173781\pi$
$131$			1872.87i			0.109135i	−0.998510	+	0.0545677i	$0.982622\pi$
$132$			2177.38i			0.124965i
$133$	12999.7			0.734906
$134$	8237.93			0.458784
$135$	−97.0585			−0.00532557
$136$			6861.97i			0.370998i
$137$	−7217.96			−0.384568			−0.192284	−	0.981339i	$-0.561590\pi$
$137$	−7217.96			−0.384568			−0.192284	+	0.981339i	$0.561590\pi$
$138$	−5468.54			−0.287153
$139$	−4580.22			−0.237059			−0.118530	−	0.992951i	$-0.537818\pi$
$139$	−4580.22			−0.237059			−0.118530	+	0.992951i	$0.537818\pi$
$140$	−294.641			−0.0150327
$141$			9890.20i			0.497470i
$142$		−	792.721i		−	0.0393137i
$143$	7886.72			0.385678
$144$	−8484.01			−0.409144
$145$	468.446			0.0222804
$146$	−41823.9			−1.96209
$147$	17617.8			0.815300
$148$			2733.18i			0.124780i
$149$		−	26501.4i		−	1.19370i	−0.802352	−	0.596851i	$-0.796418\pi$
$149$		−	26501.4i		−	1.19370i	0.802352	−	0.596851i	$-0.203582\pi$
$150$			15080.6i			0.670251i
$151$			28179.8i			1.23590i	0.786217	+	0.617950i	$0.212037\pi$
$151$			28179.8i			1.23590i	−0.786217	+	0.617950i	$0.787963\pi$
$152$			8258.72i			0.357458i
$153$	−3832.11			−0.163702
$154$	26481.0			1.11659
$155$		−	79.2500i		−	0.00329865i
$156$		−	3062.95i		−	0.125861i
$157$			12508.2i			0.507452i	0.967276	+	0.253726i	$0.0816562\pi$
$157$			12508.2i			0.507452i	−0.967276	+	0.253726i	$0.918344\pi$
$158$			951.725i			0.0381239i
$159$	24333.7			0.962531
$160$		−	475.061i		−	0.0185571i
$161$			17234.4i			0.664882i
$162$		−	3387.80i		−	0.129089i
$163$	−17112.4			−0.644075			−0.322038	−	0.946727i	$-0.604368\pi$
$163$	−17112.4			−0.644075			−0.322038	+	0.946727i	$0.604368\pi$
$164$	10216.9			0.379867
$165$			269.163i			0.00988662i
$166$	−6466.00			−0.234650
$167$	−5275.71			−0.189168			−0.0945841	−	0.995517i	$-0.530152\pi$
$167$	−5275.71			−0.189168			−0.0945841	+	0.995517i	$0.530152\pi$
$168$			19118.5i			0.677385i
$169$	17466.7			0.611556
$170$		−	456.302i		−	0.0157890i
$171$	−4612.13			−0.157728
$172$			2954.11i			0.0998551i
$173$			19148.2i			0.639786i	0.947454	+	0.319893i	$0.103647\pi$
$173$			19148.2i			0.639786i	−0.947454	+	0.319893i	$0.896353\pi$
$174$			16351.0i			0.540064i
$175$	47527.5			1.55192
$176$			23527.9i			0.759553i
$177$	12113.3	+	13432.7i	0.386648	+	0.428762i
$178$	−13949.0			−0.440254
$179$		−	59089.1i		−	1.84417i	−0.386987	−	0.922085i	$-0.626484\pi$
$179$		−	59089.1i		−	1.84417i	0.386987	−	0.922085i	$-0.373516\pi$
$180$	104.534			0.00322637
$181$	21278.1			0.649494			0.324747	−	0.945801i	$-0.394721\pi$
$181$	21278.1			0.649494			0.324747	+	0.945801i	$0.394721\pi$
$182$	−37251.1			−1.12459
$183$		−	33331.6i		−	0.995300i
$184$	−10949.0			−0.323399
$185$			337.869i			0.00987201i
$186$	2766.20			0.0799572
$187$			10627.2i			0.303904i
$188$		−	10652.0i		−	0.301380i
$189$	−10676.8			−0.298896
$190$		−	549.182i		−	0.0152128i
$191$		−	12072.7i		−	0.330932i	−0.986215	−	0.165466i	$-0.947087\pi$
$191$		−	12072.7i		−	0.330932i	0.986215	−	0.165466i	$-0.0529129\pi$
$192$	−9542.11			−0.258846
$193$	−43480.2			−1.16728			−0.583642	−	0.812011i	$-0.698373\pi$
$193$	−43480.2			−1.16728			−0.583642	+	0.812011i	$0.698373\pi$
$194$	−42869.9			−1.13907
$195$		−	378.635i		−	0.00995753i
$196$	−18974.8			−0.493930
$197$	28225.1			0.727283			0.363642	−	0.931539i	$-0.381533\pi$
$197$	28225.1			0.727283			0.363642	+	0.931539i	$0.381533\pi$
$198$	−9395.07			−0.239646
$199$	−46347.4			−1.17036			−0.585180	−	0.810903i	$-0.698976\pi$
$199$	−46347.4			−1.17036			−0.585180	+	0.810903i	$0.698976\pi$
$200$			30194.1i			0.754853i
$201$			9211.06i			0.227991i
$202$	−73301.8			−1.79644
$203$	51531.0			1.25048
$204$	4127.27			0.0991751
$205$	1262.99			0.0300534
$206$	−57923.2			−1.36495
$207$		−	6114.53i		−	0.142699i
$208$		−	33097.0i		−	0.765000i
$209$			12790.4i			0.292813i
$210$		−	1271.33i		−	0.0288283i
$211$			49595.9i			1.11399i	0.830516	+	0.556994i	$0.188045\pi$
$211$			49595.9i			1.11399i	−0.830516	+	0.556994i	$0.811955\pi$
$212$	−26208.0			−0.583126
$213$	886.363			0.0195368
$214$			24068.7i			0.525564i
$215$			365.181i			0.00790008i
$216$		−	6782.98i		−	0.145383i
$217$		−	8717.83i		−	0.185135i
$218$	−3035.22			−0.0638671
$219$		−	46764.5i		−	0.975052i
$220$		−	289.895i		−	0.00598957i
$221$		−	14949.4i		−	0.306084i
$222$	−11793.2			−0.239291
$223$	27897.9			0.560998			0.280499	−	0.959854i	$-0.409500\pi$
$223$	27897.9			0.560998			0.280499	+	0.959854i	$0.409500\pi$
$224$		−	52258.7i		−	1.04151i
$225$	−16862.1			−0.333078
$226$	59057.9			1.15628
$227$			34726.4i			0.673919i	0.941519	+	0.336960i	$0.109399\pi$
$227$			34726.4i			0.673919i	−0.941519	+	0.336960i	$0.890601\pi$
$228$	4967.37			0.0955557
$229$		−	57357.6i		−	1.09376i	−0.837212	−	0.546878i	$-0.815816\pi$
$229$		−	57357.6i		−	1.09376i	0.837212	−	0.546878i	$-0.184184\pi$
$230$	728.078			0.0137633
$231$			29609.1i			0.554883i
$232$			32737.6i			0.608234i
$233$			64148.1i			1.18160i	0.806816	+	0.590802i	$0.201189\pi$
$233$			64148.1i			1.18160i	−0.806816	+	0.590802i	$0.798811\pi$
$234$	13216.2			0.241364
$235$		−	1316.77i		−	0.0238438i
$236$	−13046.3	−	14467.3i	−0.234241	−	0.259755i
$237$	−1064.15			−0.0189455
$238$		−	50195.2i		−	0.886151i
$239$	−33929.5			−0.593994			−0.296997	−	0.954878i	$-0.595985\pi$
$239$	−33929.5			−0.593994			−0.296997	+	0.954878i	$0.595985\pi$
$240$	1129.56			0.0196103
$241$	−35255.6			−0.607007			−0.303503	−	0.952830i	$-0.598156\pi$
$241$	−35255.6			−0.607007			−0.303503	+	0.952830i	$0.598156\pi$
$242$		−	41985.1i		−	0.716909i
$243$	3788.00			0.0641500
$244$			35898.9i			0.602978i
$245$	−2345.62			−0.0390775
$246$			44084.4i			0.728475i
$247$		−	17992.4i		−	0.294913i
$248$	5538.42			0.0900498
$249$		−	7229.82i		−	0.116608i
$250$		−	4017.19i		−	0.0642750i
$251$	57278.6			0.909170			0.454585	−	0.890703i	$-0.349788\pi$
$251$	57278.6			0.909170			0.454585	+	0.890703i	$0.349788\pi$
$252$	11499.2			0.181079
$253$	−16956.8			−0.264913
$254$			17488.2i			0.271068i
$255$	510.204			0.00784628
$256$	61336.0			0.935913
$257$	−15290.7			−0.231506			−0.115753	−	0.993278i	$-0.536928\pi$
$257$	−15290.7			−0.231506			−0.115753	+	0.993278i	$0.536928\pi$
$258$	−12746.5			−0.191493
$259$			37167.1i			0.554062i
$260$			407.799i			0.00603253i
$261$	−18282.5			−0.268383
$262$	8703.60			0.126793
$263$	90982.9			1.31537			0.657685	−	0.753293i	$-0.271536\pi$
$263$	90982.9			1.31537			0.657685	+	0.753293i	$0.271536\pi$
$264$	−18810.6			−0.269895
$265$	−3239.78			−0.0461342
$266$		−	60412.3i		−	0.853812i
$267$		−	15596.8i		−	0.218782i
$268$		−	9920.53i		−	0.138123i
$269$			68865.4i			0.951692i	0.879529	+	0.475846i	$0.157858\pi$
$269$			68865.4i			0.951692i	−0.879529	+	0.475846i	$0.842142\pi$
$270$			451.050i			0.00618724i
$271$	−120932.			−1.64666			−0.823330	−	0.567563i	$-0.807886\pi$
$271$	−120932.			−1.64666			−0.823330	+	0.567563i	$0.807886\pi$
$272$	44597.6			0.602800
$273$		−	41651.5i		−	0.558862i
$274$			33543.2i			0.446790i
$275$			46762.0i			0.618340i
$276$			6585.49i			0.0864510i
$277$	81260.6			1.05906			0.529530	−	0.848291i	$-0.322368\pi$
$277$	81260.6			1.05906			0.529530	+	0.848291i	$0.322368\pi$
$278$			21285.1i			0.275415i
$279$			3092.96i			0.0397344i
$280$		−	2545.43i		−	0.0324672i
$281$	−58788.8			−0.744530			−0.372265	−	0.928127i	$-0.621419\pi$
$281$	−58788.8			−0.744530			−0.372265	+	0.928127i	$0.621419\pi$
$282$	45961.6			0.577959
$283$		−	74223.1i		−	0.926757i	−0.886160	−	0.463379i	$-0.846637\pi$
$283$		−	74223.1i		−	0.926757i	0.886160	−	0.463379i	$-0.153363\pi$
$284$	−954.634			−0.0118359
$285$	614.055			0.00755993
$286$		−	36651.1i		−	0.448079i
$287$	138934.			1.68673
$288$			18540.6i			0.223532i
$289$	−63376.9			−0.758814
$290$		−	2176.96i		−	0.0258854i
$291$		−	47934.0i		−	0.566054i
$292$			50366.4i			0.590712i
$293$	105265.			1.22617			0.613083	−	0.790019i	$-0.289929\pi$
$293$	105265.			1.22617			0.613083	+	0.790019i	$0.289929\pi$
$294$		−	81873.4i		−	0.947214i
$295$	−1612.75	−	1788.42i	−0.0185321	−	0.0205506i
$296$	−23612.2			−0.269496
$297$		−	10504.9i		−	0.119091i
$298$	−123157.			−1.38684
$299$	23853.4			0.266813
$300$	18160.9			0.201787
$301$			40171.5i			0.443389i
$302$	130957.			1.43587
$303$		−	81960.7i		−	0.892731i
$304$	53675.4			0.580802
$305$			4437.75i			0.0477049i
$306$			17808.5i			0.190189i
$307$	3547.26			0.0376371			0.0188185	−	0.999823i	$-0.494010\pi$
$307$	3547.26			0.0376371			0.0188185	+	0.999823i	$0.494010\pi$
$308$		−	31889.7i		−	0.336162i
$309$		−	64765.5i		−	0.678308i
$310$	−368.290			−0.00383236
$311$	151291.			1.56420			0.782102	−	0.623150i	$-0.214147\pi$
$311$	151291.			1.56420			0.782102	+	0.623150i	$0.214147\pi$
$312$	26461.1			0.271831
$313$			25650.3i			0.261821i	0.991394	+	0.130911i	$0.0417901\pi$
$313$			25650.3i			0.261821i	−0.991394	+	0.130911i	$0.958210\pi$
$314$	58128.0			0.589557
$315$	1421.51			0.0143261
$316$	1146.11			0.0114777
$317$	129307.			1.28677			0.643387	−	0.765541i	$-0.277529\pi$
$317$	129307.			1.28677			0.643387	+	0.765541i	$0.277529\pi$
$318$		−	113084.i		−	1.11827i
$319$			50701.1i			0.498237i
$320$	1270.43			0.0124065
$321$	−26911.9			−0.261177
$322$	80091.6			0.772459
$323$	24244.4			0.232384
$324$	−4079.76			−0.0388637
$325$		−	65780.6i		−	0.622775i
$326$			79524.7i			0.748285i
$327$		−	3393.77i		−	0.0317385i
$328$			88264.8i			0.820427i
$329$		−	144851.i		−	1.33822i
$330$	1250.85			0.0114863
$331$	−132570.			−1.21001			−0.605004	−	0.796223i	$-0.706828\pi$
$331$	−132570.			−1.21001			−0.605004	+	0.796223i	$0.706828\pi$
$332$			7786.68i			0.0706442i
$333$		−	13186.3i		−	0.118915i
$334$			24517.2i			0.219775i
$335$		−	1226.35i		−	0.0109276i
$336$	124256.			1.10062
$337$			182026.i			1.60277i	0.598146	+	0.801387i	$0.295904\pi$
$337$			182026.i			1.60277i	−0.598146	+	0.801387i	$0.704096\pi$
$338$		−	81170.9i		−	0.710505i
$339$			66034.3i			0.574606i
$340$	−549.502			−0.00475348
$341$	8577.42			0.0737646
$342$			21433.4i			0.183248i
$343$	−75307.0			−0.640099
$344$	−25520.8			−0.215664
$345$			814.084i			0.00683960i
$346$	88985.1			0.743302
$347$			36084.6i			0.299684i	0.988710	+	0.149842i	$0.0478765\pi$
$347$			36084.6i			0.299684i	−0.988710	+	0.149842i	$0.952124\pi$
$348$	19690.7			0.162593
$349$		−	155958.i		−	1.28043i	−0.768194	−	0.640217i	$-0.778844\pi$
$349$		−	155958.i		−	1.28043i	0.768194	−	0.640217i	$-0.221156\pi$
$350$		−	220869.i		−	1.80301i
$351$			14777.3i			0.119945i
$352$	51417.0			0.414975
$353$		−	106349.i		−	0.853464i	−0.904378	−	0.426732i	$-0.859665\pi$
$353$		−	106349.i		−	0.853464i	0.904378	−	0.426732i	$-0.140335\pi$
$354$	62424.3	−	56292.7i	0.498135	−	0.449206i
$355$	−118.010			−0.000936400
$356$			16798.1i			0.132544i
$357$	56124.6			0.440369
$358$	−274598.			−2.14255
$359$	−221323.			−1.71726			−0.858632	−	0.512592i	$-0.828685\pi$
$359$	−221323.			−1.71726			−0.858632	+	0.512592i	$0.828685\pi$
$360$			903.081i			0.00696822i
$361$	−101142.			−0.776097
$362$		−	98883.2i		−	0.754580i
$363$	46944.7			0.356265
$364$			44859.6i			0.338573i
$365$			6226.19i			0.0467344i
$366$	−154898.			−1.15634
$367$			231374.i			1.71784i	0.512108	+	0.858921i	$0.328865\pi$
$367$			231374.i			1.71784i	−0.512108	+	0.858921i	$0.671135\pi$
$368$			71160.1i			0.525462i
$369$	−49292.0			−0.362013
$370$	1570.14			0.0114693
$371$	−356389.			−2.58927
$372$		−	3331.19i		−	0.0240721i
$373$	129853.			0.933327			0.466663	−	0.884435i	$-0.345456\pi$
$373$	129853.			0.933327			0.466663	+	0.884435i	$0.345456\pi$
$374$	49386.7			0.353075
$375$	4491.73			0.0319412
$376$	92023.4			0.650912
$377$		−	71321.8i		−	0.501810i
$378$			49617.3i			0.347256i
$379$	−271372.			−1.88924			−0.944618	−	0.328173i	$-0.893567\pi$
$379$	−271372.			−1.88924			−0.944618	+	0.328173i	$0.893567\pi$
$380$	−661.352			−0.00458000
$381$	−19554.1			−0.134706
$382$	−56104.4			−0.384477
$383$	−228592.			−1.55834			−0.779171	−	0.626811i	$-0.784360\pi$
$383$	−228592.			−1.55834			−0.779171	+	0.626811i	$0.784360\pi$
$384$			101434.i			0.687896i
$385$		−	3942.13i		−	0.0265956i
$386$			202061.i			1.35615i
$387$		−	14252.3i		−	0.0951616i
$388$			51626.1i			0.342930i
$389$	19842.8			0.131131			0.0655654	−	0.997848i	$-0.479115\pi$
$389$	19842.8			0.131131			0.0655654	+	0.997848i	$0.479115\pi$
$390$	−1759.59			−0.0115686
$391$			32142.0i			0.210242i
$392$		−	163925.i		−	1.06678i
$393$			9731.73i			0.0630093i
$394$		−	131168.i		−	0.844956i
$395$	141.680			0.000908061
$396$			11314.0i			0.0721483i
$397$		−	286794.i		−	1.81966i	−0.414986	−	0.909828i	$-0.636213\pi$
$397$		−	286794.i		−	1.81966i	0.414986	−	0.909828i	$-0.363787\pi$
$398$			215385.i			1.35972i
$399$	67548.7			0.424298
$400$	196239.			1.22649
$401$			227378.i			1.41403i	0.707198	+	0.707016i	$0.249959\pi$
$401$			227378.i			1.41403i	−0.707198	+	0.707016i	$0.750041\pi$
$402$	42805.6			0.264879
$403$	−12066.0			−0.0742937
$404$			88273.7i			0.540839i
$405$	−504.331			−0.00307472
$406$		−	239475.i		−	1.45281i
$407$	−36568.4			−0.220759
$408$			35655.8i			0.214196i
$409$			158393.i			0.946870i	0.880829	+	0.473435i	$0.156986\pi$
$409$			158393.i			0.946870i	−0.880829	+	0.473435i	$0.843014\pi$
$410$		−	5869.37i		−	0.0349159i
$411$	−37505.6			−0.222031
$412$			69754.0i			0.410937i
$413$	−177410.	−	196734.i	−1.04011	−	1.15340i
$414$	−28415.4			−0.165788
$415$			962.573i			0.00558904i
$416$	−72328.9			−0.417951
$417$	−23799.5			−0.136866
$418$	59439.3			0.340190
$419$		−	122537.i		−	0.697976i	−0.937127	−	0.348988i	$-0.886525\pi$
$419$		−	122537.i		−	0.697976i	0.937127	−	0.348988i	$-0.113475\pi$
$420$	−1531.00			−0.00867913
$421$			46500.7i			0.262359i	0.991359	+	0.131179i	$0.0418764\pi$
$421$			46500.7i			0.262359i	−0.991359	+	0.131179i	$0.958124\pi$
$422$	230481.			1.29423
$423$			51391.0i			0.287214i
$424$		−	226413.i		−	1.25942i
$425$	88638.3			0.490731
$426$		−	4119.10i		−	0.0226978i
$427$			488171.i			2.67742i
$428$	28984.8			0.158228
$429$	40980.6			0.222671
$430$	1697.07			0.00917829
$431$			17223.7i			0.0927198i	0.998925	+	0.0463599i	$0.0147621\pi$
$431$			17223.7i			0.0927198i	−0.998925	+	0.0463599i	$0.985238\pi$
$432$	−44084.2			−0.236219
$433$	28363.6			0.151281			0.0756407	−	0.997135i	$-0.475900\pi$
$433$	28363.6			0.151281			0.0756407	+	0.997135i	$0.475900\pi$
$434$	−40513.4			−0.215090
$435$	2434.12			0.0128636
$436$			3655.17i			0.0192280i
$437$			38684.5i			0.202569i
$438$	−217323.			−1.13281
$439$	−222696.			−1.15554			−0.577769	−	0.816200i	$-0.696077\pi$
$439$	−222696.			−1.15554			−0.577769	+	0.816200i	$0.696077\pi$
$440$	2504.43			0.0129361
$441$	91544.9			0.470714
$442$	−69472.9			−0.355607
$443$			174192.i			0.887609i	0.896124	+	0.443804i	$0.146371\pi$
$443$			174192.i			0.887609i	−0.896124	+	0.443804i	$0.853629\pi$
$444$			14202.0i			0.0720417i
$445$			2076.54i			0.0104863i
$446$		−	129647.i		−	0.651766i
$447$		−	137705.i		−	0.689184i
$448$	139753.			0.696312
$449$	−24381.9			−0.120941			−0.0604706	−	0.998170i	$-0.519260\pi$
$449$	−24381.9			−0.120941			−0.0604706	+	0.998170i	$0.519260\pi$
$450$			78361.3i			0.386969i
$451$			136697.i			0.672056i
$452$		−	71120.5i		−	0.348111i
$453$			146426.i			0.713547i
$454$	161380.			0.782958
$455$			5545.44i			0.0267864i
$456$			42913.5i			0.206379i
$457$			278285.i			1.33247i	0.745741	+	0.666236i	$0.232096\pi$
$457$			278285.i			1.33247i	−0.745741	+	0.666236i	$0.767904\pi$
$458$	−266552.			−1.27072
$459$	−19912.2			−0.0945136
$460$		−	876.788i		−	0.00414361i
$461$	13805.0			0.0649581			0.0324791	−	0.999472i	$-0.489660\pi$
$461$	13805.0			0.0649581			0.0324791	+	0.999472i	$0.489660\pi$
$462$	137599.			0.644661
$463$		−	129315.i		−	0.603234i	−0.953429	−	0.301617i	$-0.902474\pi$
$463$		−	129315.i		−	0.603234i	0.953429	−	0.301617i	$-0.0975264\pi$
$464$	212769.			0.988264
$465$		−	411.795i		−	0.00190447i
$466$	298109.			1.37279
$467$			294700.i			1.35128i	0.737230	+	0.675641i	$0.236133\pi$
$467$			294700.i			1.35128i	−0.737230	+	0.675641i	$0.763867\pi$
$468$		−	15915.6i		−	0.0726658i
$469$		−	134904.i		−	0.613309i
$470$	−6119.30			−0.0277017
$471$			64994.5i			0.292978i
$472$	124984.	−	112708.i	0.561012	−	0.505907i
$473$	−39524.5			−0.176662
$474$			4945.31i			0.0220108i
$475$	106680.			0.472822
$476$	−60447.5			−0.266787
$477$	126442.			0.555717
$478$			157677.i			0.690100i
$479$	−144629.			−0.630355			−0.315177	−	0.949033i	$-0.602064\pi$
$479$	−144629.			−0.630355			−0.315177	+	0.949033i	$0.602064\pi$
$480$		−	2468.49i		−	0.0107139i
$481$	51441.3			0.222342
$482$			163839.i			0.705219i
$483$			89552.7i			0.383870i
$484$	−50560.5			−0.215834
$485$			6381.90i			0.0271310i
$486$		−	17603.5i		−	0.0745294i
$487$	−275005.			−1.15953			−0.579766	−	0.814783i	$-0.696856\pi$
$487$	−275005.			−1.15953			−0.579766	+	0.814783i	$0.696856\pi$
$488$	−310134.			−1.30230
$489$	−88918.8			−0.371857
$490$			10900.6i			0.0454001i
$491$	32951.9			0.136684			0.0683419	−	0.997662i	$-0.478229\pi$
$491$	32951.9			0.136684			0.0683419	+	0.997662i	$0.478229\pi$
$492$	53088.6			0.219317
$493$	96104.9			0.395414
$494$	−83614.0			−0.342630
$495$			1398.61i			0.00570804i
$496$		−	35995.5i		−	0.146314i
$497$	−12981.6			−0.0525551
$498$	−33598.3			−0.135475
$499$	−17305.7			−0.0695005			−0.0347503	−	0.999396i	$-0.511064\pi$
$499$	−17305.7			−0.0695005			−0.0347503	+	0.999396i	$0.511064\pi$
$500$	−4837.70			−0.0193508
$501$	−27413.4			−0.109216
$502$		−	266185.i		−	1.05627i
$503$		−	264972.i		−	1.04728i	−0.851938	−	0.523642i	$-0.824573\pi$
$503$		−	264972.i		−	1.04728i	0.851938	−	0.523642i	$-0.175427\pi$
$504$			99342.8i			0.391089i
$505$			10912.2i			0.0427887i
$506$			78801.7i			0.307776i
$507$	90759.4			0.353082
$508$	21060.2			0.0816084
$509$		−	446664.i		−	1.72403i	−0.506882	−	0.862015i	$-0.669202\pi$
$509$		−	446664.i		−	1.72403i	0.506882	−	0.862015i	$-0.330798\pi$
$510$		−	2371.02i		−	0.00911578i
$511$			684907.i			2.62295i
$512$			27296.9i			0.104129i
$513$	−23965.3			−0.0910644
$514$			71059.0i			0.268963i
$515$			8622.84i			0.0325114i
$516$			15350.0i			0.0576514i
$517$	142518.			0.533197
$518$	172722.			0.643708
$519$			99496.7i			0.369381i
$520$	−3523.01			−0.0130289
$521$	14595.5			0.0537703			0.0268852	−	0.999639i	$-0.491441\pi$
$521$	14595.5			0.0537703			0.0268852	+	0.999639i	$0.491441\pi$
$522$			84962.2i			0.311806i
$523$	−40396.8			−0.147687			−0.0738437	−	0.997270i	$-0.523527\pi$
$523$	−40396.8			−0.147687			−0.0738437	+	0.997270i	$0.523527\pi$
$524$		−	10481.3i		−	0.0381727i
$525$	246960.			0.896000
$526$		−	422815.i		−	1.52819i
$527$		−	16258.7i		−	0.0585415i
$528$			122255.i			0.438528i
$529$	228555.			0.816732
$530$			15055.9i			0.0535987i
$531$	62942.5	+	69798.3i	0.223231	+	0.247546i
$532$	−72751.5			−0.257051
$533$		−	192293.i		−	0.676876i
$534$	−72481.2			−0.254181
$535$	3583.03			0.0125182
$536$	85704.3			0.298314
$537$		−	307036.i		−	1.06473i
$538$	320030.			1.10567
$539$		−	253873.i		−	0.873853i
$540$	543.176			0.00186274
$541$		−	528895.i		−	1.80707i	−0.428513	−	0.903536i	$-0.640962\pi$
$541$		−	528895.i		−	1.80707i	0.428513	−	0.903536i	$-0.359038\pi$
$542$			561996.i			1.91309i
$543$	110564.			0.374985
$544$		−	97461.9i		−	0.329334i
$545$			451.843i			0.00152123i
$546$	−193562.			−0.649285
$547$	−223190.			−0.745935			−0.372967	−	0.927844i	$-0.621660\pi$
$547$	−223190.			−0.745935			−0.372967	+	0.927844i	$0.621660\pi$
$548$	40394.4			0.134512
$549$		−	173196.i		−	0.574637i
$550$	217312.			0.718386
$551$	115667.			0.380983
$552$	−56892.6			−0.186714
$553$	15585.4			0.0509645
$554$		−	377634.i		−	1.23041i
$555$			1755.62i			0.00569961i
$556$	25632.6			0.0829170
$557$	497882.			1.60478			0.802392	−	0.596798i	$-0.203561\pi$
$557$	497882.			1.60478			0.802392	+	0.596798i	$0.203561\pi$
$558$	14373.6			0.0461633
$559$	55599.5			0.177929
$560$	−16543.3			−0.0527530
$561$			55220.6i			0.175459i
$562$			273203.i			0.864993i
$563$			268686.i			0.847671i	0.905739	+	0.423836i	$0.139317\pi$
$563$			268686.i			0.847671i	−0.905739	+	0.423836i	$0.860683\pi$
$564$		−	55349.3i		−	0.174002i
$565$		−	8791.76i		−	0.0275409i
$566$	−344929.			−1.07670
$567$	−55478.5			−0.172567
$568$		−	8247.17i		−	0.0255628i
$569$		−	122187.i		−	0.377398i	−0.982035	−	0.188699i	$-0.939573\pi$
$569$		−	122187.i		−	0.377398i	0.982035	−	0.188699i	$-0.0604271\pi$
$570$		−	2853.63i		−	0.00878311i
$571$		−	20881.3i		−	0.0640449i	−0.999487	−	0.0320224i	$-0.989805\pi$
$571$		−	20881.3i		−	0.0640449i	0.999487	−	0.0320224i	$-0.0101948\pi$
$572$	−44137.1			−0.134900
$573$		−	62731.8i		−	0.191064i
$574$		−	645655.i		−	1.95964i
$575$			141432.i			0.427770i
$576$	−49582.3			−0.149445
$577$	−309645.			−0.930063			−0.465032	−	0.885294i	$-0.653957\pi$
$577$	−309645.			−0.930063			−0.465032	+	0.885294i	$0.653957\pi$
$578$			294525.i			0.881588i
$579$	−225930.			−0.673932
$580$	−2621.60			−0.00779311
$581$			105887.i			0.313683i
$582$	−222758.			−0.657640
$583$		−	350649.i		−	1.03166i
$584$	−435120.			−1.27580
$585$		−	1967.45i		−	0.00574898i
$586$		−	489187.i		−	1.42456i
$587$		−	245888.i		−	0.713611i	−0.934179	−	0.356806i	$-0.883866\pi$
$587$		−	245888.i		−	0.713611i	0.934179	−	0.356806i	$-0.116134\pi$
$588$	−98596.0			−0.285171
$589$		−	19568.1i		−	0.0564050i
$590$	−8311.12	+	7494.77i	−0.0238757	+	0.0215305i
$591$	146662.			0.419897
$592$			153461.i			0.437880i
$593$	396294.			1.12696			0.563480	−	0.826130i	$-0.309462\pi$
$593$	396294.			1.12696			0.563480	+	0.826130i	$0.309462\pi$
$594$	−48818.2			−0.138359
$595$	−7472.39			−0.0211070
$596$			148312.i			0.417526i
$597$	−240828.			−0.675708
$598$		−	110851.i		−	0.309983i
$599$	−107130.			−0.298579			−0.149289	−	0.988794i	$-0.547699\pi$
$599$	−107130.			−0.298579			−0.149289	+	0.988794i	$0.547699\pi$
$600$			156893.i			0.435815i
$601$		−	479681.i		−	1.32802i	−0.747725	−	0.664008i	$-0.768854\pi$
$601$		−	479681.i		−	1.32802i	0.747725	−	0.664008i	$-0.231146\pi$
$602$	186684.			0.515128
$603$			47862.1i			0.131631i
$604$		−	157705.i		−	0.432285i
$605$	−6250.18			−0.0170758
$606$	−380887.			−1.03717
$607$	−182930.			−0.496486			−0.248243	−	0.968698i	$-0.579853\pi$
$607$	−182930.			−0.496486			−0.248243	+	0.968698i	$0.579853\pi$
$608$		−	117300.i		−	0.317316i
$609$	267763.			0.721965
$610$	20623.1			0.0554234
$611$	−200481.			−0.537021
$612$	21445.9			0.0572588
$613$			474523.i			1.26281i	0.775455	+	0.631403i	$0.217521\pi$
$613$			474523.i			1.26281i	−0.775455	+	0.631403i	$0.782479\pi$
$614$		−	16484.8i		−	0.0437267i
$615$	6562.70			0.0173513
$616$	275498.			0.726034
$617$	−339241.			−0.891123			−0.445562	−	0.895251i	$-0.646996\pi$
$617$	−339241.			−0.891123			−0.445562	+	0.895251i	$0.646996\pi$
$618$	−300978.			−0.788057
$619$	307348.			0.802137			0.401069	−	0.916048i	$-0.368639\pi$
$619$	307348.			0.802137			0.401069	+	0.916048i	$0.368639\pi$
$620$			443.513i			0.00115378i
$621$		−	31772.0i		−	0.0823876i
$622$		−	703080.i		−	1.81729i
$623$			228429.i			0.588538i
$624$		−	171977.i		−	0.441673i
$625$	389728.			0.997703
$626$	119202.			0.304183
$627$			66460.7i			0.169056i
$628$		−	70000.6i		−	0.177493i
$629$			69316.2i			0.175200i
$630$		−	6606.02i		−	0.0166440i
$631$	478230.			1.20110			0.600548	−	0.799589i	$-0.294949\pi$
$631$	478230.			1.20110			0.600548	+	0.799589i	$0.294949\pi$
$632$			9901.38i			0.0247892i
$633$			257708.i			0.643161i
$634$		−	600913.i		−	1.49497i
$635$	2603.41			0.00645648
$636$	−136181.			−0.336668
$637$			357126.i			0.880121i
$638$	235618.			0.578850
$639$	4605.68			0.0112796
$640$		−	13504.9i		−	0.0329710i
$641$	84112.5			0.204713			0.102356	−	0.994748i	$-0.467362\pi$
$641$	84112.5			0.204713			0.102356	+	0.994748i	$0.467362\pi$
$642$			125065.i			0.303435i
$643$	202387.			0.489508			0.244754	−	0.969585i	$-0.421293\pi$
$643$	202387.			0.489508			0.244754	+	0.969585i	$0.421293\pi$
$644$		−	96450.3i		−	0.232558i
$645$			1897.54i			0.00456111i
$646$		−	112668.i		−	0.269983i
$647$	729383.			1.74240			0.871199	−	0.490930i	$-0.163343\pi$
$647$	729383.			1.74240			0.871199	+	0.490930i	$0.163343\pi$
$648$		−	35245.4i		−	0.0839368i
$649$	193565.	−	174552.i	0.459555	−	0.414416i
$650$	−305695.			−0.723539
$651$		−	45299.2i		−	0.106888i
$652$	95767.6			0.225280
$653$	−33872.3			−0.0794362			−0.0397181	−	0.999211i	$-0.512646\pi$
$653$	−33872.3			−0.0794362			−0.0397181	+	0.999211i	$0.512646\pi$
$654$	−15771.5			−0.0368737
$655$		−	1295.68i		−	0.00302005i
$656$	573654.			1.33304
$657$		−	242995.i		−	0.562947i
$658$	−673149.			−1.55475
$659$			12252.6i			0.0282134i	0.999900	+	0.0141067i	$0.00449046\pi$
$659$			12252.6i			0.0282134i	−0.999900	+	0.0141067i	$0.995510\pi$
$660$		−	1506.34i		−	0.00345808i
$661$	−193919.			−0.443832			−0.221916	−	0.975066i	$-0.571231\pi$
$661$	−193919.			−0.443832			−0.221916	+	0.975066i	$0.571231\pi$
$662$			616076.i			1.40578i
$663$		−	77679.5i		−	0.176717i
$664$	−67269.8			−0.152575
$665$	−8993.38			−0.0203367
$666$	−61279.5			−0.138155
$667$			153345.i			0.344682i
$668$	29524.9			0.0661660
$669$	144962.			0.323892
$670$	−5699.10			−0.0126957
$671$	−480308.			−1.06678
$672$		−	271544.i		−	0.601315i
$673$		−	527119.i		−	1.16380i	−0.813260	−	0.581900i	$-0.802310\pi$
$673$		−	527119.i		−	1.16380i	0.813260	−	0.581900i	$-0.197690\pi$
$674$	845907.			1.86210
$675$	−87617.9			−0.192303
$676$	−97750.0			−0.213906
$677$	160122.			0.349359			0.174680	−	0.984625i	$-0.444111\pi$
$677$	160122.			0.349359			0.174680	+	0.984625i	$0.444111\pi$
$678$	306874.			0.667576
$679$			702036.i			1.52272i
$680$		−	4747.19i		−	0.0102664i
$681$			180444.i			0.389088i
$682$		−	39860.9i		−	0.0856995i
$683$		−	96946.8i		−	0.207822i	−0.994587	−	0.103911i	$-0.966864\pi$
$683$		−	96946.8i		−	0.207822i	0.994587	−	0.103911i	$-0.0331358\pi$
$684$	25811.2			0.0551691
$685$	4993.47			0.0106420
$686$			349966.i			0.743666i
$687$		−	298039.i		−	0.631480i
$688$			165866.i			0.350413i
$689$			493262.i			1.03906i
$690$	3783.20			0.00794624
$691$		−	292122.i		−	0.611798i	−0.952064	−	0.305899i	$-0.901043\pi$
$691$		−	292122.i		−	0.611798i	0.952064	−	0.305899i	$-0.0989570\pi$
$692$		−	107160.i		−	0.223780i
$693$			153853.i			0.320362i
$694$	167692.			0.348172
$695$	3168.65			0.00656001
$696$			170109.i			0.351164i
$697$	259111.			0.533361
$698$	−724767.			−1.48761
$699$			333323.i			0.682200i
$700$	−265982.			−0.542820
$701$		−	761446.i		−	1.54954i	−0.632243	−	0.774770i	$-0.717866\pi$
$701$		−	761446.i		−	1.54954i	0.632243	−	0.774770i	$-0.282134\pi$
$702$	68673.1			0.139352
$703$			83425.4i			0.168806i
$704$			137502.i			0.277436i
$705$		−	6842.16i		−	0.0137662i
$706$	−494225.			−0.991552
$707$			1.20039e6i			2.40150i
$708$	−67790.5	−	75174.4i	−0.135239	−	0.149970i
$709$	9379.41			0.0186588			0.00932938	−	0.999956i	$-0.497030\pi$
$709$	9379.41			0.0186588			0.00932938	+	0.999956i	$0.497030\pi$
$710$			548.414i			0.00108791i
$711$	−5529.48			−0.0109382
$712$	−145120.			−0.286265
$713$	25942.4			0.0510307
$714$		−	260822.i		−	0.511620i
$715$	−5456.13			−0.0106727
$716$			330685.i			0.645042i
$717$	−176303.			−0.342942
$718$			1.02853e6i			1.99511i
$719$		−	474152.i		−	0.917192i	−0.888645	−	0.458596i	$-0.848353\pi$
$719$		−	474152.i		−	0.917192i	0.888645	−	0.458596i	$-0.151647\pi$
$720$	5869.34			0.0113220
$721$			948549.i			1.82469i
$722$			470025.i			0.901667i
$723$	−183193.			−0.350455
$724$	−119080.			−0.227176
$725$	422882.			0.804531
$726$		−	218161.i		−	0.413908i
$727$	−172753.			−0.326857			−0.163429	−	0.986555i	$-0.552255\pi$
$727$	−172753.			−0.326857			−0.163429	+	0.986555i	$0.552255\pi$
$728$	−387546.			−0.731241
$729$	19683.0			0.0370370
$730$	28934.3			0.0542959
$731$			74919.4i			0.140204i
$732$			186536.i			0.348130i
$733$	192952.			0.359122			0.179561	−	0.983747i	$-0.442532\pi$
$733$	192952.			0.359122			0.179561	+	0.983747i	$0.442532\pi$
$734$	1.07524e6			1.99578
$735$	−12188.2			−0.0225614
$736$	155511.			0.287081
$737$	132731.			0.244365
$738$			229069.i			0.420585i
$739$		−	894229.i		−	1.63742i	−0.574208	−	0.818709i	$-0.694690\pi$
$739$		−	894229.i		−	1.63742i	0.574208	−	0.818709i	$-0.305310\pi$
$740$		−	1890.85i		−	0.00345297i
$741$		−	93491.1i		−	0.170268i
$742$			1.65621e6i			3.00820i
$743$	−814173.			−1.47482			−0.737410	−	0.675445i	$-0.763952\pi$
$743$	−814173.			−1.47482			−0.737410	+	0.675445i	$0.763952\pi$
$744$	28778.5			0.0519903
$745$			18334.0i			0.0330327i
$746$		−	603451.i		−	1.08434i
$747$		−	37567.2i		−	0.0673237i
$748$		−	59473.9i		−	0.106298i
$749$	394149.			0.702582
$750$		−	20873.9i		−	0.0371092i
$751$			417689.i			0.740581i	0.928916	+	0.370291i	$0.120742\pi$
$751$			417689.i			0.740581i	−0.928916	+	0.370291i	$0.879258\pi$
$752$		−	598082.i		−	1.05761i
$753$	297628.			0.524910
$754$	−331446.			−0.583002
$755$		−	19495.1i		−	0.0342004i
$756$	59751.7			0.104546
$757$	−999639.			−1.74442			−0.872210	−	0.489131i	$-0.837314\pi$
$757$	−999639.			−1.74442			−0.872210	+	0.489131i	$0.837314\pi$
$758$			1.26112e6i			2.19491i
$759$	−88110.3			−0.152948
$760$		−	5713.48i		−	0.00989176i
$761$	−698337.			−1.20586			−0.602928	−	0.797795i	$-0.705999\pi$
$761$	−698337.			−1.20586			−0.602928	+	0.797795i	$0.705999\pi$
$762$			90871.4i			0.156501i
$763$			49704.7i			0.0853784i
$764$			67563.7i			0.115751i
$765$	2651.10			0.00453005
$766$			1.06231e6i			1.81048i
$767$	−272290.	+	245545.i	−0.462851	+	0.417388i
$768$	318711.			0.540350
$769$		−	1.02416e6i		−	1.73187i	−0.500155	−	0.865936i	$-0.666724\pi$
$769$		−	1.02416e6i		−	1.73187i	0.500155	−	0.865936i	$-0.333276\pi$
$770$	−18319.8			−0.0308987
$771$	−79453.0			−0.133660
$772$	243332.			0.408286
$773$		−	907633.i		−	1.51898i	−0.650521	−	0.759488i	$-0.725449\pi$
$773$		−	907633.i		−	1.51898i	0.650521	−	0.759488i	$-0.274551\pi$
$774$	−66233.0			−0.110559
$775$		−	71541.5i		−	0.119112i
$776$	−446002.			−0.740651
$777$			193126.i			0.319888i
$778$		−	92213.4i		−	0.152347i
$779$	311853.			0.513896
$780$			2118.99i			0.00348288i
$781$		−	12772.5i		−	0.0209399i
$782$	149370.			0.244259
$783$	−94998.6			−0.154951
$784$	−1.06539e6			−1.73331
$785$		−	8653.32i		−	0.0140425i
$786$	45225.2			0.0732041
$787$	418956.			0.676423			0.338212	−	0.941070i	$-0.390178\pi$
$787$	418956.			0.676423			0.338212	+	0.941070i	$0.390178\pi$
$788$	−157959.			−0.254385
$789$	472761.			0.759430
$790$		−	658.415i		−	0.00105498i
$791$		−	967131.i		−	1.54572i
$792$	−97742.7			−0.155824
$793$	675655.			1.07443
$794$	−1.33279e6			−2.11407
$795$	−16834.4			−0.0266356
$796$	259378.			0.409361
$797$			429165.i			0.675628i	0.941213	+	0.337814i	$0.109688\pi$
$797$			429165.i			0.675628i	−0.941213	+	0.337814i	$0.890312\pi$
$798$		−	313912.i		−	0.492948i
$799$		−	270145.i		−	0.423159i
$800$		−	428853.i		−	0.670083i
$801$		−	81043.2i		−	0.126314i
$802$	1.05667e6			1.64282
$803$	−673876.			−1.04508
$804$		−	51548.6i		−	0.0797452i
$805$		−	11923.0i		−	0.0183989i
$806$			56072.8i			0.0863142i
$807$			357835.i			0.549460i
$808$	−762604.			−1.16809
$809$		−	94992.3i		−	0.145141i	−0.997363	−	0.0725707i	$-0.976880\pi$
$809$		−	94992.3i		−	0.145141i	0.997363	−	0.0725707i	$-0.0231203\pi$
$810$			2343.72i			0.00357220i
$811$		−	738552.i		−	1.12290i	−0.827512	−	0.561448i	$-0.810244\pi$
$811$		−	738552.i		−	1.12290i	0.827512	−	0.561448i	$-0.189756\pi$
$812$	−288387.			−0.437385
$813$	−628383.			−0.950699
$814$			169941.i			0.256477i
$815$	11838.6			0.0178232
$816$	231736.			0.348027
$817$			90169.1i			0.135087i
$818$	736084.			1.10007
$819$		−	216427.i		−	0.322659i
$820$	−7068.18			−0.0105119
$821$		−	29461.7i		−	0.0437091i	−0.999761	−	0.0218545i	$-0.993043\pi$
$821$		−	29461.7i		−	0.0437091i	0.999761	−	0.0218545i	$-0.00695707\pi$
$822$			174296.i			0.257955i
$823$			130911.i			0.193275i	0.995320	+	0.0966375i	$0.0308087\pi$
$823$			130911.i			0.193275i	−0.995320	+	0.0966375i	$0.969191\pi$
$824$	−602611.			−0.887529
$825$			242982.i			0.356999i
$826$	−914258.	+	824457.i	−1.34001	+	1.20839i
$827$	238564.			0.348813			0.174407	−	0.984674i	$-0.444199\pi$
$827$	238564.			0.348813			0.174407	+	0.984674i	$0.444199\pi$
$828$			34219.2i			0.0499125i
$829$	1.03043e6			1.49937			0.749685	−	0.661795i	$-0.230205\pi$
$829$	1.03043e6			1.49937			0.749685	+	0.661795i	$0.230205\pi$
$830$	4473.26			0.00649333
$831$	422243.			0.611449
$832$		−	193425.i		−	0.279426i
$833$	−481221.			−0.693512
$834$			110601.i			0.159011i
$835$	3649.80			0.00523475
$836$		−	71579.8i		−	0.102418i
$837$			16071.5i			0.0229407i
$838$	−569454.			−0.810906
$839$		−	199610.i		−	0.283568i	−0.989898	−	0.141784i	$-0.954716\pi$
$839$		−	199610.i		−	0.283568i	0.989898	−	0.141784i	$-0.0452839\pi$
$840$		−	13226.4i		−	0.0187449i
$841$	−248777.			−0.351737
$842$	216098.			0.304808
$843$	−305476.			−0.429855
$844$		−	277557.i		−	0.389644i
$845$	−12083.6			−0.0169233
$846$	238824.			0.333685
$847$	−687546.			−0.958374
$848$	−1.47151e6			−2.04632
$849$		−	385674.i		−	0.535064i
$850$		−	411919.i		−	0.570130i
$851$	−110601.			−0.152722
$852$	−4960.43			−0.00683345
$853$	−667639.			−0.917580			−0.458790	−	0.888545i	$-0.651717\pi$
$853$	−667639.			−0.917580			−0.458790	+	0.888545i	$0.651717\pi$
$854$	2.26862e6			3.11062
$855$	3190.73			0.00436473
$856$			250402.i			0.341736i
$857$		−	470276.i		−	0.640312i	−0.947365	−	0.320156i	$-0.896265\pi$
$857$		−	470276.i		−	0.640312i	0.947365	−	0.320156i	$-0.103735\pi$
$858$		−	190445.i		−	0.258699i
$859$			919460.i			1.24608i	0.782189	+	0.623041i	$0.214103\pi$
$859$			919460.i			1.24608i	−0.782189	+	0.623041i	$0.785897\pi$
$860$		−	2043.69i		−	0.00276324i
$861$	721925.			0.973836
$862$	80041.9			0.107722
$863$			344188.i			0.462141i	0.972937	+	0.231071i	$0.0742228\pi$
$863$			344188.i			0.462141i	−0.972937	+	0.231071i	$0.925777\pi$
$864$			96340.0i			0.129056i
$865$		−	13246.9i		−	0.0177045i
$866$		−	131811.i		−	0.175758i
$867$	−329316.			−0.438101
$868$			48788.3i			0.0647554i
$869$			15334.4i			0.0203061i
$870$		−	11311.8i		−	0.0149449i
$871$	−186715.			−0.246117
$872$	−31577.3			−0.0415281
$873$		−	249072.i		−	0.326811i
$874$	179774.			0.235345
$875$	−65785.4			−0.0859237
$876$			261712.i			0.341048i
$877$	−826042.			−1.07400			−0.536998	−	0.843583i	$-0.680442\pi$
$877$	−826042.			−1.07400			−0.536998	+	0.843583i	$0.680442\pi$
$878$			1.03491e6i			1.34250i
$879$	546974.			0.707927
$880$		−	16276.9i		−	0.0210187i
$881$		−	737152.i		−	0.949742i	−0.880056	−	0.474871i	$-0.842495\pi$
$881$		−	737152.i		−	0.949742i	0.880056	−	0.474871i	$-0.157505\pi$
$882$		−	425426.i		−	0.546874i
$883$	−310160.			−0.397800			−0.198900	−	0.980020i	$-0.563737\pi$
$883$	−310160.			−0.397800			−0.198900	+	0.980020i	$0.563737\pi$
$884$			83662.7i			0.107060i
$885$	−8380.12	−	9292.90i	−0.0106995	−	0.0118649i
$886$	809505.			1.03122
$887$		−	959122.i		−	1.21906i	−0.792762	−	0.609532i	$-0.791357\pi$
$887$		−	959122.i		−	1.21906i	0.792762	−	0.609532i	$-0.208643\pi$
$888$	−122692.			−0.155594
$889$	286386.			0.362367
$890$	9650.09			0.0121829
$891$		−	54585.0i		−	0.0687571i
$892$	−156127.			−0.196222
$893$		−	325133.i		−	0.407716i
$894$	−639942.			−0.800692
$895$			40878.5i			0.0510328i
$896$		−	1.48560e6i		−	1.85048i
$897$	123946.			0.154045
$898$			113307.i			0.140509i
$899$		−	77568.0i		−	0.0959761i
$900$	94366.6			0.116502
$901$	−664662.			−0.818750
$902$	635256.			0.780793
$903$			208737.i			0.255991i
$904$	614416.			0.751841
$905$	−14720.4			−0.0179731
$906$	680471.			0.828998
$907$	11680.6			0.0141988			0.00709939	−	0.999975i	$-0.497740\pi$
$907$	11680.6			0.0141988			0.00709939	+	0.999975i	$0.497740\pi$
$908$		−	194342.i		−	0.235719i
$909$		−	425880.i		−	0.515418i
$910$	25770.7			0.0311203
$911$	637090.			0.767651			0.383826	−	0.923406i	$-0.374606\pi$
$911$	637090.			0.767651			0.383826	+	0.923406i	$0.374606\pi$
$912$	278905.			0.335326
$913$	−104182.			−0.124983
$914$	1.29325e6			1.54806
$915$			23059.2i			0.0275424i
$916$			320995.i			0.382567i
$917$		−	142530.i		−	0.169499i
$918$			92535.8i			0.109806i
$919$			702495.i			0.831787i	0.909413	+	0.415893i	$0.136531\pi$
$919$			702495.i			0.831787i	−0.909413	+	0.415893i	$0.863469\pi$
$920$	7574.64			0.00894925
$921$	18432.1			0.0217298
$922$		−	64154.3i		−	0.0754682i
$923$			17967.2i			0.0210900i
$924$		−	165704.i		−	0.194083i
$925$			305006.i			0.356471i
$926$	−600950.			−0.700836
$927$		−	336532.i		−	0.391621i
$928$		−	464978.i		−	0.539929i
$929$		−	631639.i		−	0.731875i	−0.930639	−	0.365938i	$-0.880748\pi$
$929$		−	631639.i		−	0.731875i	0.930639	−	0.365938i	$-0.119252\pi$
$930$	−1913.69			−0.00221261
$931$	−579172.			−0.668203
$932$		−	358997.i		−	0.413294i
$933$	786133.			0.903094
$934$	1.36953e6			1.56992
$935$		−	7352.04i		−	0.00840978i
$936$	137496.			0.156942
$937$		−	550717.i		−	0.627263i	−0.949545	−	0.313631i	$-0.898454\pi$
$937$		−	550717.i		−	0.627263i	0.949545	−	0.313631i	$-0.101546\pi$
$938$	−626925.			−0.712541
$939$			133283.i			0.151162i
$940$			7369.17i			0.00833994i
$941$		−	625271.i		−	0.706137i	−0.935597	−	0.353069i	$-0.885138\pi$
$941$		−	625271.i		−	0.706137i	0.935597	−	0.353069i	$-0.114862\pi$
$942$	302042.			0.340381
$943$			413439.i			0.464931i
$944$	−732516.	−	812304.i	−0.822003	−	0.911537i
$945$	7386.37			0.00827118
$946$			183678.i			0.205246i
$947$	62423.0			0.0696057			0.0348028	−	0.999394i	$-0.488920\pi$
$947$	62423.0			0.0696057			0.0348028	+	0.999394i	$0.488920\pi$
$948$	5955.39			0.00662664
$949$	947949.			1.05257
$950$		−	495764.i		−	0.549323i
$951$	671897.			0.742919
$952$		−	522211.i		−	0.576199i
$953$	817236.			0.899832			0.449916	−	0.893071i	$-0.351454\pi$
$953$	817236.			0.899832			0.449916	+	0.893071i	$0.351454\pi$
$954$		−	587599.i		−	0.645631i
$955$			8352.07i			0.00915772i
$956$	189882.			0.207763
$957$			263451.i			0.287657i
$958$			672119.i			0.732344i
$959$	549303.			0.597276
$960$	6601.35			0.00716292
$961$	910398.			0.985791
$962$		−	239057.i		−	0.258316i
$963$	−139838.			−0.150791
$964$	197303.			0.212315
$965$	30080.1			0.0323017
$966$	416168.			0.445979
$967$		−	991071.i		−	1.05987i	−0.848039	−	0.529934i	$-0.822217\pi$
$967$		−	991071.i		−	1.05987i	0.848039	−	0.529934i	$-0.177783\pi$
$968$		−	436797.i		−	0.466153i
$969$	125978.			0.134167
$970$	29657.9			0.0315208
$971$	−1.08960e6			−1.15566			−0.577829	−	0.816158i	$-0.696100\pi$
$971$	−1.08960e6			−1.15566			−0.577829	+	0.816158i	$0.696100\pi$
$972$	−21199.1			−0.0224380
$973$	348565.			0.368178
$974$			1.27800e6i			1.34714i
$975$		−	341806.i		−	0.359560i
$976$			2.01563e6i			2.11598i
$977$			10538.2i			0.0110402i	0.999985	+	0.00552010i	$0.00175711\pi$
$977$			10538.2i			0.0110402i	−0.999985	+	0.00552010i	$0.998243\pi$
$978$			413223.i			0.432022i
$979$	−224749.			−0.234495
$980$	13127.0			0.0136683
$981$		−	17634.5i		−	0.0183242i
$982$		−	153134.i		−	0.158799i
$983$			825144.i			0.853931i	0.904268	+	0.426965i	$0.140417\pi$
$983$			825144.i			0.853931i	−0.904268	+	0.426965i	$0.859583\pi$
$984$			458637.i			0.473674i
$985$	−19526.5			−0.0201257
$986$		−	446618.i		−	0.459391i
$987$		−	752666.i		−	0.772624i
$988$			100692.i			0.103153i
$989$	−119542.			−0.122216
$990$	6499.62			0.00663159
$991$			1.64789e6i			1.67795i	0.544167	+	0.838977i	$0.316846\pi$
$991$			1.64789e6i			1.67795i	−0.544167	+	0.838977i	$0.683154\pi$
$992$	−78663.3			−0.0799372
$993$	−688852.			−0.698598
$994$			60327.8i			0.0610584i
$995$	32063.7			0.0323868
$996$			40460.8i			0.0407864i
$997$	596888.			0.600486			0.300243	−	0.953863i	$-0.402932\pi$
$997$	596888.			0.600486			0.300243	+	0.953863i	$0.402932\pi$
$998$			80422.9i			0.0807456i
$999$		−	68518.3i		−	0.0686555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.c.a.58.10	✓	40
3.2	odd	2		531.5.c.d.235.31		40
59.58	odd	2	inner	177.5.c.a.58.31	yes	40
177.176	even	2		531.5.c.d.235.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.c.a.58.10	✓	40	1.1	even	1	trivial
177.5.c.a.58.31	yes	40	59.58	odd	2	inner
531.5.c.d.235.10		40	177.176	even	2
531.5.c.d.235.31		40	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +3.21498i q^{10} -74.8765i q^{11} -29.0796 q^{12} +105.330i q^{13} +353.662i q^{14} -3.59476 q^{15} -314.223 q^{16} -141.930 q^{17} -125.474i q^{18} -170.820 q^{19} +3.87164 q^{20} -395.439 q^{21} -347.966 q^{22} -226.464i q^{23} -251.222i q^{24} -624.521 q^{25} +489.487 q^{26} +140.296 q^{27} +425.897 q^{28} -677.129 q^{29} +16.7055i q^{30} +114.554i q^{31} +686.691i q^{32} -389.070i q^{33} +659.575i q^{34} +52.6484 q^{35} -151.102 q^{36} -488.383i q^{37} +793.831i q^{38} +547.309i q^{39} +33.4475i q^{40} -1825.63 q^{41} +1837.68i q^{42} -527.862i q^{43} +419.037i q^{44} -18.6789 q^{45} -1052.42 q^{46} +1903.37i q^{47} -1632.75 q^{48} +3390.55 q^{49} +2902.27i q^{50} -737.489 q^{51} -589.465i q^{52} +4683.03 q^{53} -651.983i q^{54} +51.8005i q^{55} +3679.36i q^{56} -887.604 q^{57} +3146.75i q^{58} +(2331.20 + 2585.12i) q^{59} +20.1176 q^{60} -6414.67i q^{61} +532.355 q^{62} -2054.76 q^{63} -1836.38 q^{64} -72.8684i q^{65} -1808.08 q^{66} +1772.67i q^{67} +794.294 q^{68} -1176.74i q^{69} -244.667i q^{70} +170.581 q^{71} -1305.39i q^{72} -8999.83i q^{73} -2269.61 q^{74} -3245.11 q^{75} +955.971 q^{76} +5698.27i q^{77} +2543.45 q^{78} -204.796 q^{79} +217.383 q^{80} +729.000 q^{81} +8484.05i q^{82} -1391.38i q^{83} +2213.03 q^{84} +98.1888 q^{85} -2453.07 q^{86} -3518.47 q^{87} -3620.10 q^{88} -3001.60i q^{89} +86.8045i q^{90} -8015.83i q^{91} +1267.38i q^{92} +595.241i q^{93} +8845.32 q^{94} +118.175 q^{95} +3568.15i q^{96} -9224.90i q^{97} -15756.5i q^{98} -2021.67i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9} + 360 q^{12} + 144 q^{15} + 3944 q^{16} - 528 q^{17} + 444 q^{19} + 444 q^{20} + 1304 q^{22} + 4880 q^{25} - 1452 q^{26} - 1160 q^{28} - 996 q^{29} + 10320 q^{35} - 8640 q^{36} - 5196 q^{41} - 10476 q^{46} + 576 q^{48} + 5104 q^{49} + 936 q^{51} - 2184 q^{53} - 2520 q^{57} - 11736 q^{59} - 11448 q^{60} + 15240 q^{62} + 2160 q^{63} - 81012 q^{64} + 17352 q^{66} + 29568 q^{68} - 5964 q^{71} + 14376 q^{74} - 2736 q^{75} + 3480 q^{76} + 37692 q^{78} + 19020 q^{79} + 33096 q^{80} + 29160 q^{81} + 25128 q^{84} + 20220 q^{85} - 65880 q^{86} + 1512 q^{87} - 14932 q^{88} - 17864 q^{94} + 11004 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9 + 360 * q^12 + 144 * q^15 + 3944 * q^16 - 528 * q^17 + 444 * q^19 + 444 * q^20 + 1304 * q^22 + 4880 * q^25 - 1452 * q^26 - 1160 * q^28 - 996 * q^29 + 10320 * q^35 - 8640 * q^36 - 5196 * q^41 - 10476 * q^46 + 576 * q^48 + 5104 * q^49 + 936 * q^51 - 2184 * q^53 - 2520 * q^57 - 11736 * q^59 - 11448 * q^60 + 15240 * q^62 + 2160 * q^63 - 81012 * q^64 + 17352 * q^66 + 29568 * q^68 - 5964 * q^71 + 14376 * q^74 - 2736 * q^75 + 3480 * q^76 + 37692 * q^78 + 19020 * q^79 + 33096 * q^80 + 29160 * q^81 + 25128 * q^84 + 20220 * q^85 - 65880 * q^86 + 1512 * q^87 - 14932 * q^88 - 17864 * q^94 + 11004 * q^95

Introduction

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