LMFDB - Embedded newform 77.5.c.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,5,Mod(43,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	77.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:	$7.95948715746$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	77.43
Dual form			77.5.c.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.80284i q^{2} -16.4118 q^{3} -7.06726 q^{4} -41.5497 q^{5} -78.8230i q^{6} +18.5203i q^{7} +42.9025i q^{8} +188.346 q^{9} +O(q^{10})$	\(q+4.80284i q^{2} -16.4118 q^{3} -7.06726 q^{4} -41.5497 q^{5} -78.8230i q^{6} +18.5203i q^{7} +42.9025i q^{8} +188.346 q^{9} -199.556i q^{10} +(14.2125 - 120.162i) q^{11} +115.986 q^{12} +220.703i q^{13} -88.9498 q^{14} +681.903 q^{15} -319.130 q^{16} -256.104i q^{17} +904.594i q^{18} -61.6604i q^{19} +293.643 q^{20} -303.950i q^{21} +(577.121 + 68.2602i) q^{22} -0.958516 q^{23} -704.105i q^{24} +1101.38 q^{25} -1060.00 q^{26} -1761.73 q^{27} -130.888i q^{28} -384.050i q^{29} +3275.07i q^{30} +551.032 q^{31} -846.290i q^{32} +(-233.252 + 1972.08i) q^{33} +1230.03 q^{34} -769.511i q^{35} -1331.09 q^{36} -1461.16 q^{37} +296.145 q^{38} -3622.13i q^{39} -1782.58i q^{40} -2814.90i q^{41} +1459.82 q^{42} -486.541i q^{43} +(-100.443 + 849.220i) q^{44} -7825.70 q^{45} -4.60360i q^{46} +2634.42 q^{47} +5237.48 q^{48} -343.000 q^{49} +5289.73i q^{50} +4203.12i q^{51} -1559.77i q^{52} -1298.32 q^{53} -8461.31i q^{54} +(-590.524 + 4992.71i) q^{55} -794.565 q^{56} +1011.95i q^{57} +1844.53 q^{58} -1215.85 q^{59} -4819.19 q^{60} +5050.50i q^{61} +2646.52i q^{62} +3488.21i q^{63} -1041.48 q^{64} -9170.16i q^{65} +(-9471.56 - 1120.27i) q^{66} +5677.07 q^{67} +1809.96i q^{68} +15.7309 q^{69} +3695.84 q^{70} -269.277 q^{71} +8080.50i q^{72} -1226.73i q^{73} -7017.69i q^{74} -18075.5 q^{75} +435.770i q^{76} +(2225.44 + 263.219i) q^{77} +17396.5 q^{78} +1432.44i q^{79} +13259.7 q^{80} +13657.1 q^{81} +13519.5 q^{82} -9000.91i q^{83} +2148.09i q^{84} +10641.1i q^{85} +2336.78 q^{86} +6302.93i q^{87} +(5155.27 + 609.751i) q^{88} +3085.68 q^{89} -37585.6i q^{90} -4087.49 q^{91} +6.77408 q^{92} -9043.40 q^{93} +12652.7i q^{94} +2561.97i q^{95} +13889.1i q^{96} -14882.2 q^{97} -1647.37i q^{98} +(2676.86 - 22632.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 198 q^{4} + 6 q^{5} + 982 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 198 * q^4 + 6 * q^5 + 982 * q^9	$ 24 q - 6 q^{3} - 198 q^{4} + 6 q^{5} + 982 q^{9} - 336 q^{11} - 656 q^{12} - 294 q^{14} + 1118 q^{15} + 1882 q^{16} + 588 q^{20} - 1824 q^{22} - 1458 q^{23} + 2262 q^{25} + 2004 q^{26} - 2322 q^{27} + 3514 q^{31} - 4078 q^{33} + 172 q^{34} - 7050 q^{36} - 1826 q^{37} + 120 q^{38} + 4290 q^{44} + 4092 q^{45} - 11028 q^{47} + 19104 q^{48} - 8232 q^{49} - 10896 q^{53} - 1534 q^{55} - 1470 q^{56} + 30440 q^{58} - 1926 q^{59} - 33544 q^{60} - 17566 q^{64} - 1896 q^{66} + 22526 q^{67} - 6570 q^{69} - 13916 q^{70} + 5454 q^{71} - 12544 q^{75} + 5292 q^{77} - 15080 q^{78} + 71676 q^{80} - 5740 q^{81} + 59836 q^{82} - 24120 q^{86} + 42880 q^{88} + 36318 q^{89} + 11172 q^{91} + 25188 q^{92} - 47362 q^{93} - 26466 q^{97} - 39930 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 - 198 * q^4 + 6 * q^5 + 982 * q^9 - 336 * q^11 - 656 * q^12 - 294 * q^14 + 1118 * q^15 + 1882 * q^16 + 588 * q^20 - 1824 * q^22 - 1458 * q^23 + 2262 * q^25 + 2004 * q^26 - 2322 * q^27 + 3514 * q^31 - 4078 * q^33 + 172 * q^34 - 7050 * q^36 - 1826 * q^37 + 120 * q^38 + 4290 * q^44 + 4092 * q^45 - 11028 * q^47 + 19104 * q^48 - 8232 * q^49 - 10896 * q^53 - 1534 * q^55 - 1470 * q^56 + 30440 * q^58 - 1926 * q^59 - 33544 * q^60 - 17566 * q^64 - 1896 * q^66 + 22526 * q^67 - 6570 * q^69 - 13916 * q^70 + 5454 * q^71 - 12544 * q^75 + 5292 * q^77 - 15080 * q^78 + 71676 * q^80 - 5740 * q^81 + 59836 * q^82 - 24120 * q^86 + 42880 * q^88 + 36318 * q^89 + 11172 * q^91 + 25188 * q^92 - 47362 * q^93 - 26466 * q^97 - 39930 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$-1$

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 $

$2$			4.80284i			1.20071i	0.799734	+	0.600355i	$0.204974\pi$
$2$			4.80284i			1.20071i	−0.799734	+	0.600355i	$0.795026\pi$
$3$	−16.4118			−1.82353			−0.911764	−	0.410714i	$-0.865279\pi$
$3$	−16.4118			−1.82353			−0.911764	+	0.410714i	$0.865279\pi$
$4$	−7.06726			−0.441704
$5$	−41.5497			−1.66199			−0.830994	−	0.556282i	$-0.812227\pi$
$5$	−41.5497			−1.66199			−0.830994	+	0.556282i	$0.812227\pi$
$6$		−	78.8230i		−	2.18953i
$7$			18.5203i			0.377964i
$7$			18.5203i			0.377964i
$8$			42.9025i			0.670351i
$9$	188.346			2.32525
$10$		−	199.556i		−	1.99556i
$11$	14.2125	−	120.162i	0.117458	−	0.993078i
$11$	14.2125	−	120.162i	0.117458	−	0.993078i
$12$	115.986			0.805460
$13$			220.703i			1.30594i	0.757385	+	0.652969i	$0.226477\pi$
$13$			220.703i			1.30594i	−0.757385	+	0.652969i	$0.773523\pi$
$14$	−88.9498			−0.453826
$15$	681.903			3.03068
$16$	−319.130			−1.24660
$17$		−	256.104i		−	0.886175i	−0.896478	−	0.443087i	$-0.853883\pi$
$17$		−	256.104i		−	0.886175i	0.896478	−	0.443087i	$-0.146117\pi$
$18$			904.594i			2.79196i
$19$		−	61.6604i		−	0.170804i	−0.996347	−	0.0854022i	$-0.972782\pi$
$19$		−	61.6604i		−	0.170804i	0.996347	−	0.0854022i	$-0.0272175\pi$
$20$	293.643			0.734106
$21$		−	303.950i		−	0.689229i
$22$	577.121	+	68.2602i	1.19240	+	0.141034i
$23$	−0.958516			−0.00181194			−0.000905969	−	1.00000i	$-0.500288\pi$
$23$	−0.958516			−0.00181194			−0.000905969		1.00000i	$0.500288\pi$
$24$		−	704.105i		−	1.22240i
$25$	1101.38			1.76220
$26$	−1060.00			−1.56805
$27$	−1761.73			−2.41664
$28$		−	130.888i		−	0.166948i
$29$		−	384.050i		−	0.456659i	−0.973584	−	0.228329i	$-0.926674\pi$
$29$		−	384.050i		−	0.456659i	0.973584	−	0.228329i	$-0.0733263\pi$
$30$			3275.07i			3.63897i
$31$	551.032			0.573394			0.286697	−	0.958021i	$-0.407443\pi$
$31$	551.032			0.573394			0.286697	+	0.958021i	$0.407443\pi$
$32$		−	846.290i		−	0.826455i
$33$	−233.252	+	1972.08i	−0.214189	+	1.81091i
$34$	1230.03			1.06404
$35$		−	769.511i		−	0.628172i
$36$	−1331.09			−1.02707
$37$	−1461.16			−1.06732			−0.533658	−	0.845700i	$-0.679183\pi$
$37$	−1461.16			−1.06732			−0.533658	+	0.845700i	$0.679183\pi$
$38$	296.145			0.205086
$39$		−	3622.13i		−	2.38141i
$40$		−	1782.58i		−	1.11412i
$41$		−	2814.90i		−	1.67454i	−0.546789	−	0.837271i	$-0.684150\pi$
$41$		−	2814.90i		−	1.67454i	0.546789	−	0.837271i	$-0.315850\pi$
$42$	1459.82			0.827564
$43$		−	486.541i		−	0.263138i	−0.991307	−	0.131569i	$-0.957999\pi$
$43$		−	486.541i		−	0.263138i	0.991307	−	0.131569i	$-0.0420014\pi$
$44$	−100.443	+	849.220i	−0.0518819	+	0.438646i
$45$	−7825.70			−3.86454
$46$		−	4.60360i		−	0.00217561i
$47$	2634.42			1.19259			0.596293	−	0.802767i	$-0.296640\pi$
$47$	2634.42			1.19259			0.596293	+	0.802767i	$0.296640\pi$
$48$	5237.48			2.27321
$49$	−343.000			−0.142857
$50$			5289.73i			2.11589i
$51$			4203.12i			1.61596i
$52$		−	1559.77i		−	0.576838i
$53$	−1298.32			−0.462199			−0.231100	−	0.972930i	$-0.574232\pi$
$53$	−1298.32			−0.462199			−0.231100	+	0.972930i	$0.574232\pi$
$54$		−	8461.31i		−	2.90168i
$55$	−590.524	+	4992.71i	−0.195214	+	1.65048i
$56$	−794.565			−0.253369
$57$			1011.95i			0.311467i
$58$	1844.53			0.548315
$59$	−1215.85			−0.349281			−0.174640	−	0.984632i	$-0.555876\pi$
$59$	−1215.85			−0.349281			−0.174640	+	0.984632i	$0.555876\pi$
$60$	−4819.19			−1.33866
$61$			5050.50i			1.35730i	0.734463	+	0.678648i	$0.237434\pi$
$61$			5050.50i			1.35730i	−0.734463	+	0.678648i	$0.762566\pi$
$62$			2646.52i			0.688480i
$63$			3488.21i			0.878864i
$64$	−1041.48			−0.254269
$65$		−	9170.16i		−	2.17045i
$66$	−9471.56	−	1120.27i	−2.17437	−	0.257179i
$67$	5677.07			1.26466			0.632331	−	0.774699i	$-0.282098\pi$
$67$	5677.07			1.26466			0.632331	+	0.774699i	$0.282098\pi$
$68$			1809.96i			0.391427i
$69$	15.7309			0.00330412
$70$	3695.84			0.754252
$71$	−269.277			−0.0534174			−0.0267087	−	0.999643i	$-0.508503\pi$
$71$	−269.277			−0.0534174			−0.0267087	+	0.999643i	$0.508503\pi$
$72$			8080.50i			1.55874i
$73$		−	1226.73i		−	0.230200i	−0.993354	−	0.115100i	$-0.963281\pi$
$73$		−	1226.73i		−	0.230200i	0.993354	−	0.115100i	$-0.0367188\pi$
$74$		−	7017.69i		−	1.28154i
$75$	−18075.5			−3.21342
$76$			435.770i			0.0754450i
$77$	2225.44	+	263.219i	0.375348	+	0.0443951i
$78$	17396.5			2.85939
$79$			1432.44i			0.229520i	0.993393	+	0.114760i	$0.0366099\pi$
$79$			1432.44i			0.229520i	−0.993393	+	0.114760i	$0.963390\pi$
$80$	13259.7			2.07184
$81$	13657.1			2.08155
$82$	13519.5			2.01064
$83$		−	9000.91i		−	1.30656i	−0.757115	−	0.653281i	$-0.773392\pi$
$83$		−	9000.91i		−	1.30656i	0.757115	−	0.653281i	$-0.226608\pi$
$84$			2148.09i			0.304435i
$85$			10641.1i			1.47281i
$86$	2336.78			0.315952
$87$			6302.93i			0.832730i
$88$	5155.27	+	609.751i	0.665711	+	0.0787385i
$89$	3085.68			0.389557			0.194779	−	0.980847i	$-0.437601\pi$
$89$	3085.68			0.389557			0.194779	+	0.980847i	$0.437601\pi$
$90$		−	37585.6i		−	4.64019i
$91$	−4087.49			−0.493598
$92$	6.77408			0.000800341
$93$	−9043.40			−1.04560
$94$			12652.7i			1.43195i
$95$			2561.97i			0.283875i
$96$			13889.1i			1.50706i
$97$	−14882.2			−1.58169			−0.790847	−	0.612014i	$-0.790360\pi$
$97$	−14882.2			−1.58169			−0.790847	+	0.612014i	$0.790360\pi$
$98$		−	1647.37i		−	0.171530i
$99$	2676.86	−	22632.1i	0.273121	−	2.30916i
$100$	−7783.71			−0.778371
$101$		−	6949.35i		−	0.681242i	−0.940201	−	0.340621i	$-0.889363\pi$
$101$		−	6949.35i		−	0.681242i	0.940201	−	0.340621i	$-0.110637\pi$
$102$	−20186.9			−1.94030
$103$	17338.6			1.63433			0.817166	−	0.576403i	$-0.195544\pi$
$103$	17338.6			1.63433			0.817166	+	0.576403i	$0.195544\pi$
$104$	−9468.73			−0.875437
$105$			12629.0i			1.14549i
$106$		−	6235.61i		−	0.554967i
$107$		−	590.793i		−	0.0516021i	−0.999667	−	0.0258011i	$-0.991786\pi$
$107$		−	590.793i		−	0.0516021i	0.999667	−	0.0258011i	$-0.00821364\pi$
$108$	12450.6			1.06744
$109$		−	16523.6i		−	1.39076i	−0.718642	−	0.695381i	$-0.755236\pi$
$109$		−	16523.6i		−	1.39076i	0.718642	−	0.695381i	$-0.244764\pi$
$110$	−23979.2	−	2836.19i	−1.98175	−	0.234396i
$111$	23980.1			1.94628
$112$		−	5910.37i		−	0.471171i
$113$	−5041.75			−0.394843			−0.197421	−	0.980319i	$-0.563257\pi$
$113$	−5041.75			−0.394843			−0.197421	+	0.980319i	$0.563257\pi$
$114$	−4860.26			−0.373981
$115$	39.8260			0.00301142
$116$			2714.18i			0.201708i
$117$			41568.5i			3.03664i
$118$		−	5839.51i		−	0.419385i
$119$	4743.12			0.334942
$120$			29255.3i			2.03162i
$121$	−14237.0	−	3415.61i	−0.972407	−	0.233291i
$122$	−24256.7			−1.62972
$123$			46197.5i			3.05357i
$124$	−3894.29			−0.253271
$125$	−19793.3			−1.26677
$126$	−16753.3			−1.05526
$127$		−	19433.1i		−	1.20485i	−0.798175	−	0.602426i	$-0.794201\pi$
$127$		−	19433.1i		−	1.20485i	0.798175	−	0.602426i	$-0.205799\pi$
$128$		−	18542.7i		−	1.13176i
$129$			7985.00i			0.479839i
$130$	44042.8			2.60608
$131$		−	12225.9i		−	0.712426i	−0.934405	−	0.356213i	$-0.884068\pi$
$131$		−	12225.9i		−	0.712426i	0.934405	−	0.356213i	$-0.115932\pi$
$132$	1648.45	−	13937.2i	0.0946081	−	0.799884i
$133$	1141.97			0.0645580
$134$			27266.0i			1.51849i
$135$	73199.3			4.01642
$136$	10987.5			0.594048
$137$	−31621.2			−1.68476			−0.842378	−	0.538886i	$-0.818845\pi$
$137$	−31621.2			−1.68476			−0.842378	+	0.538886i	$0.818845\pi$
$138$			75.5531i			0.00396729i
$139$		−	21133.1i		−	1.09379i	−0.837201	−	0.546895i	$-0.815810\pi$
$139$		−	21133.1i		−	1.09379i	0.837201	−	0.546895i	$-0.184190\pi$
$140$			5438.34i			0.277466i
$141$	−43235.5			−2.17471
$142$		−	1293.29i		−	0.0641387i
$143$	26520.3	+	3136.74i	1.29690	+	0.153393i
$144$	−60106.7			−2.89867
$145$			15957.2i			0.758961i
$146$	5891.81			0.276403
$147$	5629.23			0.260504
$148$	10326.4			0.471438
$149$			30858.7i			1.38997i	0.719024	+	0.694986i	$0.244589\pi$
$149$			30858.7i			1.38997i	−0.719024	+	0.694986i	$0.755411\pi$
$150$		−	86813.7i		−	3.85839i
$151$		−	15267.2i		−	0.669585i	−0.942292	−	0.334793i	$-0.891334\pi$
$151$		−	15267.2i		−	0.669585i	0.942292	−	0.334793i	$-0.108666\pi$
$152$	2645.38			0.114499
$153$		−	48236.2i		−	2.06058i
$154$	−1264.20	+	10688.4i	−0.0533057	+	0.450684i
$155$	−22895.2			−0.952974
$156$			25598.6i			1.05188i
$157$	−16784.0			−0.680920			−0.340460	−	0.940259i	$-0.610583\pi$
$157$	−16784.0			−0.680920			−0.340460	+	0.940259i	$0.610583\pi$
$158$	−6879.76			−0.275587
$159$	21307.7			0.842834
$160$			35163.1i			1.37356i
$161$		−	17.7520i		−	0.000684849i
$162$			65592.8i			2.49934i
$163$	12619.3			0.474964			0.237482	−	0.971392i	$-0.423678\pi$
$163$	12619.3			0.474964			0.237482	+	0.971392i	$0.423678\pi$
$164$			19893.7i			0.739652i
$165$	9691.53	−	81939.1i	0.355979	−	3.00970i
$166$	43229.9			1.56880
$167$			6586.85i			0.236181i	0.993003	+	0.118091i	$0.0376773\pi$
$167$			6586.85i			0.236181i	−0.993003	+	0.118091i	$0.962323\pi$
$168$	13040.2			0.462026
$169$	−20149.0			−0.705474
$170$	−51107.3			−1.76842
$171$		−	11613.5i		−	0.397164i
$172$			3438.52i			0.116229i
$173$		−	32549.8i		−	1.08757i	−0.839225	−	0.543784i	$-0.816991\pi$
$173$		−	32549.8i		−	1.08757i	0.839225	−	0.543784i	$-0.183009\pi$
$174$	−30272.0			−0.999867
$175$			20397.8i			0.666049i
$176$	−4535.63	+	38347.4i	−0.146424	+	1.23797i
$177$	19954.2			0.636923
$178$			14820.0i			0.467746i
$179$	10834.8			0.338153			0.169077	−	0.985603i	$-0.445921\pi$
$179$	10834.8			0.338153			0.169077	+	0.985603i	$0.445921\pi$
$180$	55306.3			1.70698
$181$	12231.6			0.373358			0.186679	−	0.982421i	$-0.440228\pi$
$181$	12231.6			0.373358			0.186679	+	0.982421i	$0.440228\pi$
$182$		−	19631.5i		−	0.592668i
$183$		−	82887.6i		−	2.47507i
$184$		−	41.1227i		−	0.00121464i
$185$	60710.5			1.77387
$186$		−	43434.0i		−	1.25546i
$187$	−30774.1	−	3639.88i	−0.880040	−	0.104089i
$188$	−18618.2			−0.526770
$189$		−	32627.7i		−	0.913404i
$190$	−12304.7			−0.340851
$191$	−44428.5			−1.21785			−0.608926	−	0.793227i	$-0.708399\pi$
$191$	−44428.5			−1.21785			−0.608926	+	0.793227i	$0.708399\pi$
$192$	17092.6			0.463666
$193$		−	39414.8i		−	1.05814i	−0.848577	−	0.529072i	$-0.822540\pi$
$193$		−	39414.8i		−	1.05814i	0.848577	−	0.529072i	$-0.177460\pi$
$194$		−	71476.6i		−	1.89916i
$195$			150498.i			3.95788i
$196$	2424.07			0.0631006
$197$			55219.9i			1.42286i	0.702755	+	0.711432i	$0.251953\pi$
$197$			55219.9i			1.42286i	−0.702755	+	0.711432i	$0.748047\pi$
$198$	108698.	+	12856.5i	2.77263	+	0.327939i
$199$	65267.0			1.64811			0.824057	−	0.566507i	$-0.191706\pi$
$199$	65267.0			1.64811			0.824057	+	0.566507i	$0.191706\pi$
$200$			47251.8i			1.18129i
$201$	−93170.6			−2.30615
$202$	33376.6			0.817974
$203$	7112.71			0.172601
$204$		−	29704.6i		−	0.713778i
$205$			116958.i			2.78307i
$206$			83274.6i			1.96236i
$207$	−180.532			−0.00421322
$208$		−	70433.1i		−	1.62798i
$209$	−7409.26	−	876.347i	−0.169622	−	0.0200624i
$210$	−60655.2			−1.37540
$211$		−	34912.0i		−	0.784169i	−0.919929	−	0.392085i	$-0.871754\pi$
$211$		−	34912.0i		−	0.784169i	0.919929	−	0.392085i	$-0.128246\pi$
$212$	9175.56			0.204155
$213$	4419.31			0.0974080
$214$	2837.48			0.0619592
$215$			20215.6i			0.437331i
$216$		−	75582.6i		−	1.62000i
$217$			10205.3i			0.216723i
$218$	79360.3			1.66990
$219$			20132.9i			0.419776i
$220$	4173.39	−	35284.8i	0.0862270	−	0.729025i
$221$	56523.1			1.15729
$222$			115173.i			2.33692i
$223$	17404.5			0.349987			0.174994	−	0.984570i	$-0.444010\pi$
$223$	17404.5			0.349987			0.174994	+	0.984570i	$0.444010\pi$
$224$	15673.5			0.312371
$225$	207439.			4.09757
$226$		−	24214.7i		−	0.474091i
$227$		−	1895.79i		−	0.0367907i	−0.999831	−	0.0183954i	$-0.994144\pi$
$227$		−	1895.79i		−	0.0367907i	0.999831	−	0.0183954i	$-0.00585575\pi$
$228$		−	7151.75i		−	0.137576i
$229$	−10285.9			−0.196142			−0.0980711	−	0.995179i	$-0.531267\pi$
$229$	−10285.9			−0.196142			−0.0980711	+	0.995179i	$0.531267\pi$
$230$			191.278i			0.00361584i
$231$	−36523.4	−	4319.88i	−0.684458	−	0.0809558i
$232$	16476.7			0.306122
$233$			7645.45i			0.140829i	0.997518	+	0.0704144i	$0.0224322\pi$
$233$			7645.45i			0.140829i	−0.997518	+	0.0704144i	$0.977568\pi$
$234$	−199647.			−3.64612
$235$	−109459.			−1.98206
$236$	8592.70			0.154279
$237$		−	23508.8i		−	0.418537i
$238$			22780.4i			0.402169i
$239$		−	5523.86i		−	0.0967045i	−0.998830	−	0.0483522i	$-0.984603\pi$
$239$		−	5523.86i		−	0.0967045i	0.998830	−	0.0483522i	$-0.0153970\pi$
$240$	−217616.			−3.77805
$241$		−	64575.9i		−	1.11182i	−0.831241	−	0.555912i	$-0.812369\pi$
$241$		−	64575.9i		−	1.11182i	0.831241	−	0.555912i	$-0.187631\pi$
$242$	16404.6	−	68378.1i	0.280115	−	1.16758i
$243$	−81436.5			−1.37913
$244$		−	35693.2i		−	0.599523i
$245$	14251.5			0.237427
$246$	−221879.			−3.66646
$247$	13608.7			0.223060
$248$			23640.6i			0.384376i
$249$			147721.i			2.38255i
$250$		−	95063.8i		−	1.52102i
$251$	−82339.5			−1.30696			−0.653478	−	0.756946i	$-0.726691\pi$
$251$	−82339.5			−1.30696			−0.653478	+	0.756946i	$0.726691\pi$
$252$		−	24652.1i		−	0.388198i
$253$	−13.6229	+	115.178i	−0.000212828	+	0.00179940i
$254$	93333.9			1.44668
$255$		−	174638.i		−	2.68571i
$256$	72394.0			1.10464
$257$	42079.7			0.637098			0.318549	−	0.947906i	$-0.396804\pi$
$257$	42079.7			0.637098			0.318549	+	0.947906i	$0.396804\pi$
$258$	−38350.7			−0.576147
$259$		−	27061.0i		−	0.403407i
$260$			64807.9i			0.958697i
$261$		−	72334.1i		−	1.06185i
$262$	58719.2			0.855417
$263$			36605.8i			0.529223i	0.964355	+	0.264612i	$0.0852438\pi$
$263$			36605.8i			0.529223i	−0.964355	+	0.264612i	$0.914756\pi$
$264$	−84607.0	−	10007.1i	−1.21394	−	0.143582i
$265$	53944.7			0.768170
$266$			5484.68i			0.0775154i
$267$	−50641.5			−0.710369
$268$	−40121.3			−0.558606
$269$	−78557.0			−1.08563			−0.542813	−	0.839854i	$-0.682641\pi$
$269$	−78557.0			−1.08563			−0.542813	+	0.839854i	$0.682641\pi$
$270$			351565.i			4.82256i
$271$			110204.i			1.50059i	0.661106	+	0.750293i	$0.270087\pi$
$271$			110204.i			1.50059i	−0.661106	+	0.750293i	$0.729913\pi$
$272$			81730.6i			1.10471i
$273$	67082.8			0.900090
$274$		−	151872.i		−	2.02290i
$275$	15653.3	−	132344.i	0.206985	−	1.75000i
$276$	−111.175			−0.00145944
$277$		−	39975.2i		−	0.520992i	−0.965475	−	0.260496i	$-0.916114\pi$
$277$		−	39975.2i		−	0.520992i	0.965475	−	0.260496i	$-0.0838861\pi$
$278$	101499.			1.31333
$279$	103784.			1.33329
$280$	33013.9			0.421096
$281$			19630.2i			0.248606i	0.992244	+	0.124303i	$0.0396695\pi$
$281$			19630.2i			0.248606i	−0.992244	+	0.124303i	$0.960331\pi$
$282$		−	207653.i		−	2.61120i
$283$			120981.i			1.51058i	0.655392	+	0.755289i	$0.272503\pi$
$283$			120981.i			1.51058i	−0.655392	+	0.755289i	$0.727497\pi$
$284$	1903.05			0.0235947
$285$		−	42046.4i		−	0.517653i
$286$	−15065.3	+	127373.i	−0.184181	+	1.55720i
$287$	52132.8			0.632917
$288$		−	159395.i		−	1.92172i
$289$	17931.5			0.214695
$290$	−76639.6			−0.911292
$291$	244242.			2.88426
$292$			8669.66i			0.101680i
$293$			3034.73i			0.0353496i	0.999844	+	0.0176748i	$0.00562635\pi$
$293$			3034.73i			0.0353496i	−0.999844	+	0.0176748i	$0.994374\pi$
$294$			27036.3i			0.312790i
$295$	50518.0			0.580500
$296$		−	62687.2i		−	0.715477i
$297$	−25038.5	+	211694.i	−0.283855	+	2.39991i
$298$	−148210.			−1.66895
$299$		−	211.548i		−	0.00236628i
$300$	127744.			1.41938
$301$	9010.87			0.0994567
$302$	73326.0			0.803978
$303$			114051.i			1.24226i
$304$			19677.7i			0.212925i
$305$		−	209847.i		−	2.25581i
$306$	231670.			2.47416
$307$			74789.0i			0.793526i	0.917921	+	0.396763i	$0.129867\pi$
$307$			74789.0i			0.793526i	−0.917921	+	0.396763i	$0.870133\pi$
$308$	−15727.8	−	1860.24i	−0.165793	−	0.0196095i
$309$	−284557.			−2.98025
$310$		−	109962.i		−	1.14425i
$311$	−140477.			−1.45239			−0.726197	−	0.687487i	$-0.758714\pi$
$311$	−140477.			−1.45239			−0.726197	+	0.687487i	$0.758714\pi$
$312$	155398.			1.59638
$313$	−109132.			−1.11394			−0.556972	−	0.830531i	$-0.688037\pi$
$313$	−109132.			−1.11394			−0.556972	+	0.830531i	$0.688037\pi$
$314$		−	80610.9i		−	0.817588i
$315$		−	144934.i		−	1.46066i
$316$		−	10123.4i		−	0.101380i
$317$	−63089.8			−0.627828			−0.313914	−	0.949452i	$-0.601640\pi$
$317$	−63089.8			−0.627828			−0.313914	+	0.949452i	$0.601640\pi$
$318$			102337.i			1.01200i
$319$	−46148.4	−	5458.30i	−0.453498	−	0.0536384i
$320$	43273.3			0.422591
$321$			9695.94i			0.0940979i
$322$	85.2598			0.000822304
$323$	−15791.5			−0.151362
$324$	−96518.2			−0.919431
$325$			243077.i			2.30132i
$326$			60608.6i			0.570294i
$327$			271182.i			2.53609i
$328$	120766.			1.12253
$329$			48790.2i			0.450755i
$330$	393540.	+	46546.9i	3.61378	+	0.427428i
$331$	−26454.7			−0.241461			−0.120730	−	0.992685i	$-0.538524\pi$
$331$	−26454.7			−0.241461			−0.120730	+	0.992685i	$0.538524\pi$
$332$			63611.8i			0.577114i
$333$	−275202.			−2.48178
$334$	−31635.6			−0.283585
$335$	−235880.			−2.10185
$336$			96999.5i			0.859194i
$337$			81990.2i			0.721942i	0.932577	+	0.360971i	$0.117555\pi$
$337$			81990.2i			0.721942i	−0.932577	+	0.360971i	$0.882445\pi$
$338$		−	96772.5i		−	0.847069i
$339$	82743.9			0.720007
$340$		−	75203.2i		−	0.650546i
$341$	7831.53	−	66213.3i	0.0673500	−	0.569425i
$342$	55777.6			0.476878
$343$		−	6352.45i		−	0.0539949i
$344$	20873.8			0.176395
$345$	−653.615			−0.00549141
$346$	156332.			1.30585
$347$		−	97203.3i		−	0.807276i	−0.914919	−	0.403638i	$-0.867745\pi$
$347$		−	97203.3i		−	0.807276i	0.914919	−	0.403638i	$-0.132255\pi$
$348$		−	44544.5i		−	0.367820i
$349$		−	163630.i		−	1.34342i	−0.740814	−	0.671710i	$-0.765560\pi$
$349$		−	163630.i		−	1.34342i	0.740814	−	0.671710i	$-0.234440\pi$
$350$	−97967.2			−0.799732
$351$		−	388820.i		−	3.15598i
$352$	−101692.	−	12027.9i	−0.820734	−	0.0970742i
$353$	−12833.9			−0.102993			−0.0514967	−	0.998673i	$-0.516399\pi$
$353$	−12833.9			−0.102993			−0.0514967	+	0.998673i	$0.516399\pi$
$354$			95836.6i			0.764760i
$355$	11188.4			0.0887789
$356$	−21807.4			−0.172069
$357$	−77842.9			−0.610777
$358$			52037.7i			0.406024i
$359$			20603.9i			0.159868i	0.996800	+	0.0799339i	$0.0254709\pi$
$359$			20603.9i			0.159868i	−0.996800	+	0.0799339i	$0.974529\pi$
$360$		−	335742.i		−	2.59060i
$361$	126519.			0.970826
$362$			58746.2i			0.448294i
$363$	233654.	+	56056.2i	1.77321	+	0.425412i
$364$	28887.3			0.218024
$365$			50970.4i			0.382589i
$366$	398096.			2.97184
$367$	−168195.			−1.24877			−0.624383	−	0.781118i	$-0.714650\pi$
$367$	−168195.			−1.24877			−0.624383	+	0.781118i	$0.714650\pi$
$368$	305.891			0.00225877
$369$		−	530175.i		−	3.89374i
$370$			291583.i			2.12990i
$371$		−	24045.2i		−	0.174695i
$372$	63912.1			0.461846
$373$		−	207412.i		−	1.49079i	−0.666625	−	0.745393i	$-0.732262\pi$
$373$		−	207412.i		−	1.49079i	0.666625	−	0.745393i	$-0.267738\pi$
$374$	17481.8	−	147803.i	0.124980	−	1.05667i
$375$	324842.			2.30999
$376$			113023.i			0.799452i
$377$	84761.2			0.596368
$378$	156706.			1.09673
$379$	−14641.1			−0.101928			−0.0509641	−	0.998700i	$-0.516229\pi$
$379$	−14641.1			−0.101928			−0.0509641	+	0.998700i	$0.516229\pi$
$380$		−	18106.1i		−	0.125389i
$381$			318931.i			2.19708i
$382$		−	213383.i		−	1.46229i
$383$	−50760.4			−0.346041			−0.173020	−	0.984918i	$-0.555353\pi$
$383$	−50760.4			−0.346041			−0.173020	+	0.984918i	$0.555353\pi$
$384$			304319.i			2.06379i
$385$	−92466.3	−	10936.7i	−0.623824	−	0.0737841i
$386$	189303.			1.27052
$387$		−	91638.0i		−	0.611862i
$388$	105176.			0.698641
$389$	96905.7			0.640398			0.320199	−	0.947350i	$-0.396250\pi$
$389$	96905.7			0.640398			0.320199	+	0.947350i	$0.396250\pi$
$390$	−722819.			−4.75226
$391$			245.480i			0.00160569i
$392$		−	14715.6i		−	0.0957645i
$393$			200649.i			1.29913i
$394$	−265212.			−1.70845
$395$		−	59517.3i		−	0.381460i
$396$	−18918.1	+	159947.i	−0.120639	+	1.01996i
$397$	−268070.			−1.70086			−0.850428	−	0.526092i	$-0.823657\pi$
$397$	−268070.			−1.70086			−0.850428	+	0.526092i	$0.823657\pi$
$398$			313467.i			1.97891i
$399$	−18741.7			−0.117723
$400$	−351482.			−2.19676
$401$	271016.			1.68541			0.842706	−	0.538374i	$-0.180961\pi$
$401$	271016.			1.68541			0.842706	+	0.538374i	$0.180961\pi$
$402$		−	447483.i		−	2.76901i
$403$			121615.i			0.748817i
$404$			49112.9i			0.300907i
$405$	−567447.			−3.45952
$406$			34161.2i			0.207243i
$407$	−20766.6	+	175576.i	−0.125365	+	1.05993i
$408$	−180324.			−1.08326
$409$			20451.6i			0.122259i	0.998130	+	0.0611295i	$0.0194703\pi$
$409$			20451.6i			0.122259i	−0.998130	+	0.0611295i	$0.980530\pi$
$410$	−561732.			−3.34165
$411$	518959.			3.07220
$412$	−122537.			−0.721891
$413$		−	22517.8i		−	0.132016i
$414$		−	867.067i		−	0.00505885i
$415$			373985.i			2.17149i
$416$	186779.			1.07930
$417$			346832.i			1.99456i
$418$	4208.95	−	35585.5i	0.0240891	−	0.203667i
$419$	39939.2			0.227495			0.113747	−	0.993510i	$-0.463715\pi$
$419$	39939.2			0.227495			0.113747	+	0.993510i	$0.463715\pi$
$420$		−	89252.6i		−	0.505967i
$421$	−150079.			−0.846750			−0.423375	−	0.905955i	$-0.639155\pi$
$421$	−150079.			−0.846750			−0.423375	+	0.905955i	$0.639155\pi$
$422$	167677.			0.941560
$423$	496182.			2.77307
$424$		−	55701.1i		−	0.309836i
$425$		−	282067.i		−	1.56162i
$426$			21225.2i			0.116959i
$427$	−93536.6			−0.513010
$428$			4175.29i			0.0227929i
$429$	−435244.	−	51479.5i	−2.36493	−	0.279717i
$430$	−97092.5			−0.525108
$431$		−	353709.i		−	1.90411i	−0.305933	−	0.952053i	$-0.598968\pi$
$431$		−	353709.i		−	1.90411i	0.305933	−	0.952053i	$-0.401032\pi$
$432$	562221.			3.01259
$433$	150722.			0.803898			0.401949	−	0.915662i	$-0.368333\pi$
$433$	150722.			0.803898			0.401949	+	0.915662i	$0.368333\pi$
$434$	−49014.2			−0.260221
$435$		−	261885.i		−	1.38399i
$436$			116777.i			0.614305i
$437$			59.1024i			0.000309487i
$438$	−96694.9			−0.504029
$439$		−	153395.i		−	0.795946i	−0.917397	−	0.397973i	$-0.869714\pi$
$439$		−	153395.i		−	0.795946i	0.917397	−	0.397973i	$-0.130286\pi$
$440$	−214200.	−	25334.9i	−1.10640	−	0.130862i
$441$	−64602.6			−0.332179
$442$			271472.i			1.38957i
$443$	−4780.99			−0.0243619			−0.0121809	−	0.999926i	$-0.503877\pi$
$443$	−4780.99			−0.0243619			−0.0121809	+	0.999926i	$0.503877\pi$
$444$	−169474.			−0.859680
$445$	−128209.			−0.647440
$446$			83591.1i			0.420233i
$447$		−	506446.i		−	2.53465i
$448$		−	19288.6i		−	0.0961045i
$449$	55475.5			0.275175			0.137587	−	0.990490i	$-0.456065\pi$
$449$	55475.5			0.275175			0.137587	+	0.990490i	$0.456065\pi$
$450$			996298.i			4.91999i
$451$	−338246.	−	40006.8i	−1.66295	−	0.196689i
$452$	35631.4			0.174404
$453$			250562.i			1.22101i
$454$	9105.17			0.0441750
$455$	169834.			0.820354
$456$	−43415.4			−0.208792
$457$			22432.9i			0.107412i	0.998557	+	0.0537061i	$0.0171034\pi$
$457$			22432.9i			0.107412i	−0.998557	+	0.0537061i	$0.982897\pi$
$458$		−	49401.5i		−	0.235510i
$459$			451187.i			2.14156i
$460$	−281.461			−0.00133016
$461$			125828.i			0.592071i	0.955177	+	0.296035i	$0.0956647\pi$
$461$			125828.i			0.592071i	−0.955177	+	0.296035i	$0.904335\pi$
$462$	20747.7	−	175416.i	0.0972044	−	0.821835i
$463$	36498.6			0.170261			0.0851304	−	0.996370i	$-0.472869\pi$
$463$	36498.6			0.170261			0.0851304	+	0.996370i	$0.472869\pi$
$464$			122562.i			0.569272i
$465$	375750.			1.73778
$466$	−36719.9			−0.169094
$467$	157203.			0.720822			0.360411	−	0.932794i	$-0.382636\pi$
$467$	157203.			0.720822			0.360411	+	0.932794i	$0.382636\pi$
$468$		−	293776.i		−	1.34130i
$469$			105141.i			0.477997i
$470$		−	525716.i		−	2.37988i
$471$	275455.			1.24168
$472$		−	52162.8i		−	0.234141i
$473$	−58464.0	−	6914.96i	−0.261316	−	0.0309077i
$474$	112909.			0.502541
$475$		−	67911.2i		−	0.300992i
$476$	−33520.9			−0.147945
$477$	−244533.			−1.07473
$478$	26530.2			0.116114
$479$			196920.i			0.858258i	0.903243	+	0.429129i	$0.141179\pi$
$479$			196920.i			0.858258i	−0.903243	+	0.429129i	$0.858821\pi$
$480$		−	577088.i		−	2.50472i
$481$		−	322482.i		−	1.39385i
$482$	310148.			1.33498
$483$			291.341i			0.00124884i
$484$	100617.	+	24139.0i	0.429516	+	0.103045i
$485$	618349.			2.62876
$486$		−	391126.i		−	1.65594i
$487$	345689.			1.45756			0.728781	−	0.684747i	$-0.240087\pi$
$487$	345689.			1.45756			0.728781	+	0.684747i	$0.240087\pi$
$488$	−216679.			−0.909866
$489$	−207105.			−0.866110
$490$			68447.9i			0.285081i
$491$			5945.12i			0.0246602i	0.999924	+	0.0123301i	$0.00392490\pi$
$491$			5945.12i			0.0246602i	−0.999924	+	0.0123301i	$0.996075\pi$
$492$		−	326490.i		−	1.34878i
$493$	−98356.9			−0.404679
$494$			65360.2i			0.267830i
$495$	−111223.	+	940355.i	−0.453923	+	3.83779i
$496$	−175851.			−0.714794
$497$		−	4987.08i		−	0.0201899i
$498$	−709479.			−2.86076
$499$	223341.			0.896947			0.448473	−	0.893796i	$-0.351968\pi$
$499$	223341.			0.896947			0.448473	+	0.893796i	$0.351968\pi$
$500$	139884.			0.559537
$501$		−	108102.i		−	0.430683i
$502$		−	395463.i		−	1.56927i
$503$		−	380573.i		−	1.50419i	−0.659056	−	0.752094i	$-0.729044\pi$
$503$		−	380573.i		−	1.50419i	0.659056	−	0.752094i	$-0.270956\pi$
$504$	−149653.			−0.589148
$505$			288743.i			1.13222i
$506$	−553.179	−	65.4285i	−0.00216055	−	0.000255544i
$507$	330681.			1.28645
$508$			137339.i			0.532188i
$509$	389419.			1.50308			0.751540	−	0.659688i	$-0.229312\pi$
$509$	389419.			1.50308			0.751540	+	0.659688i	$0.229312\pi$
$510$	838760.			3.22476
$511$	22719.4			0.0870073
$512$			51013.0i			0.194599i
$513$			108629.i			0.412772i
$514$			202102.i			0.764970i
$515$	−720414.			−2.71624
$516$		−	56432.1i		−	0.211947i
$517$	37441.7	−	316559.i	0.140079	−	1.18433i
$518$	129970.			0.484375
$519$			534200.i			1.98321i
$520$	393423.			1.45497
$521$	−86995.3			−0.320494			−0.160247	−	0.987077i	$-0.551229\pi$
$521$	−86995.3			−0.320494			−0.160247	+	0.987077i	$0.551229\pi$
$522$	347409.			1.27497
$523$		−	400358.i		−	1.46368i	−0.681478	−	0.731839i	$-0.738662\pi$
$523$		−	400358.i		−	1.46368i	0.681478	−	0.731839i	$-0.261338\pi$
$524$			86404.0i			0.314681i
$525$		−	334763.i		−	1.21456i
$526$	−175812.			−0.635444
$527$		−	141122.i		−	0.508128i
$528$	74437.6	−	629349.i	0.267008	−	2.25748i
$529$	−279840.			−0.999997
$530$			259088.i			0.922349i
$531$	−228999.			−0.812166
$532$	−8070.58			−0.0285155
$533$	621259.			2.18685
$534$		−	243223.i		−	0.852947i
$535$			24547.2i			0.0857620i
$536$			243560.i			0.847768i
$537$	−177818.			−0.616632
$538$		−	377296.i		−	1.30352i
$539$	−4874.88	+	41215.7i	−0.0167798	+	0.141868i
$540$	−517319.			−1.77407
$541$		−	187163.i		−	0.639477i	−0.947506	−	0.319739i	$-0.896405\pi$
$541$		−	187163.i		−	0.639477i	0.947506	−	0.319739i	$-0.103595\pi$
$542$	−529294.			−1.80177
$543$	−200741.			−0.680828
$544$	−216739.			−0.732384
$545$			686552.i			2.31143i
$546$			322188.i			1.08075i
$547$		−	537671.i		−	1.79698i	−0.438999	−	0.898488i	$-0.644667\pi$
$547$		−	537671.i		−	1.79698i	0.438999	−	0.898488i	$-0.355333\pi$
$548$	223475.			0.744164
$549$			951240.i			3.15606i
$550$	635627.	+	75180.2i	2.10125	+	0.248529i
$551$	−23680.7			−0.0779993
$552$			674.896i			0.00221492i
$553$	−26529.1			−0.0867505
$554$	191994.			0.625560
$555$	−996366.			−3.23469
$556$			149353.i			0.483132i
$557$		−	278707.i		−	0.898332i	−0.893448	−	0.449166i	$-0.851721\pi$
$557$		−	278707.i		−	0.898332i	0.893448	−	0.449166i	$-0.148279\pi$
$558$			498460.i			1.60089i
$559$	107381.			0.343641
$560$			245574.i			0.783080i
$561$	505057.	+	59736.8i	1.60478	+	0.189809i
$562$	−94280.6			−0.298504
$563$			132404.i			0.417719i	0.977946	+	0.208859i	$0.0669751\pi$
$563$			132404.i			0.417719i	−0.977946	+	0.208859i	$0.933025\pi$
$564$	305557.			0.960580
$565$	209483.			0.656223
$566$	−581050.			−1.81376
$567$			252933.i			0.786754i
$568$		−	11552.6i		−	0.0358084i
$569$		−	510101.i		−	1.57555i	−0.615964	−	0.787774i	$-0.711233\pi$
$569$		−	510101.i		−	1.57555i	0.615964	−	0.787774i	$-0.288767\pi$
$570$	201942.			0.621551
$571$			343088.i			1.05228i	0.850397	+	0.526142i	$0.176362\pi$
$571$			343088.i			1.05228i	−0.850397	+	0.526142i	$0.823638\pi$
$572$	−187426.	−	22168.2i	−0.572845	−	0.0677545i
$573$	729149.			2.22079
$574$			250385.i			0.759950i
$575$	−1055.69			−0.00319300
$576$	−196159.			−0.591239
$577$	−288388.			−0.866215			−0.433108	−	0.901342i	$-0.642583\pi$
$577$	−288388.			−0.866215			−0.433108	+	0.901342i	$0.642583\pi$
$578$			86122.2i			0.257786i
$579$			646866.i			1.92955i
$580$		−	112773.i		−	0.335236i
$581$	166699.			0.493834
$582$			1.17306e6i			3.46316i
$583$	−18452.3	+	156009.i	−0.0542893	+	0.459000i
$584$	52630.0			0.154315
$585$		−	1.72716e6i		−	5.04685i
$586$	−14575.3			−0.0424446
$587$	−197313.			−0.572638			−0.286319	−	0.958134i	$-0.592432\pi$
$587$	−197313.			−0.572638			−0.286319	+	0.958134i	$0.592432\pi$
$588$	−39783.3			−0.115066
$589$		−	33976.8i		−	0.0979383i
$590$			242630.i			0.697012i
$591$		−	906256.i		−	2.59463i
$592$	466299.			1.33052
$593$			440367.i			1.25229i	0.779706	+	0.626146i	$0.215368\pi$
$593$			440367.i			1.25229i	−0.779706	+	0.626146i	$0.784632\pi$
$594$	−1.01673e6	−	120256.i	−2.88160	−	0.340827i
$595$	−197075.			−0.556670
$596$		−	218087.i		−	0.613956i
$597$	−1.07115e6			−3.00538
$598$	1016.03			0.00284121
$599$	−343935.			−0.958566			−0.479283	−	0.877660i	$-0.659103\pi$
$599$	−343935.			−0.958566			−0.479283	+	0.877660i	$0.659103\pi$
$600$		−	775484.i		−	2.15412i
$601$			464276.i			1.28537i	0.766132	+	0.642683i	$0.222179\pi$
$601$			464276.i			1.28537i	−0.766132	+	0.642683i	$0.777821\pi$
$602$			43277.8i			0.119419i
$603$	1.06925e6			2.94066
$604$			107897.i			0.295759i
$605$	591543.	+	141918.i	1.61613	+	0.387726i
$606$	−547769.			−1.49160
$607$		−	95742.7i		−	0.259853i	−0.991524	−	0.129927i	$-0.958526\pi$
$607$		−	95742.7i		−	0.259853i	0.991524	−	0.129927i	$-0.0414742\pi$
$608$	−52182.6			−0.141162
$609$	−116732.			−0.314742
$610$	1.00786e6			2.70857
$611$			581426.i			1.55744i
$612$			340898.i			0.910167i
$613$			6154.82i			0.0163793i	0.999966	+	0.00818963i	$0.00260687\pi$
$613$			6154.82i			0.0163793i	−0.999966	+	0.00818963i	$0.997393\pi$
$614$	−359200.			−0.952794
$615$		−	1.91949e6i		−	5.07500i
$616$	−11292.7	+	95476.9i	−0.0297603	+	0.251615i
$617$	−452445.			−1.18849			−0.594245	−	0.804284i	$-0.702549\pi$
$617$	−452445.			−1.18849			−0.594245	+	0.804284i	$0.702549\pi$
$618$		−	1.36668e6i		−	3.57841i
$619$	278607.			0.727127			0.363564	−	0.931569i	$-0.381560\pi$
$619$	278607.			0.727127			0.363564	+	0.931569i	$0.381560\pi$
$620$	161806.			0.420932
$621$	1688.65			0.00437880
$622$		−	674688.i		−	1.74390i
$623$			57147.7i			0.147239i
$624$			1.15593e6i			2.96867i
$625$	134043.			0.343151
$626$		−	524144.i		−	1.33752i
$627$	121599.	+	14382.4i	0.309310	+	0.0365844i
$628$	118617.			0.300765
$629$			374208.i			0.945828i
$630$	696095.			1.75383
$631$	−410981.			−1.03220			−0.516099	−	0.856529i	$-0.672616\pi$
$631$	−410981.			−1.03220			−0.516099	+	0.856529i	$0.672616\pi$
$632$	−61455.1			−0.153859
$633$			572967.i			1.42995i
$634$		−	303010.i		−	0.753839i
$635$			807438.i			2.00245i
$636$	−150587.			−0.372283
$637$		−	75701.3i		−	0.186563i
$638$	26215.3	−	221643.i	0.0644042	−	0.544519i
$639$	−50717.1			−0.124209
$640$			770444.i			1.88097i
$641$	765643.			1.86342			0.931709	−	0.363206i	$-0.118318\pi$
$641$	765643.			1.86342			0.931709	+	0.363206i	$0.118318\pi$
$642$	−46568.0			−0.112984
$643$	207804.			0.502611			0.251306	−	0.967908i	$-0.419140\pi$
$643$	207804.			0.502611			0.251306	+	0.967908i	$0.419140\pi$
$644$			125.458i			0.000302500i
$645$		−	331774.i		−	0.797486i
$646$		−	75844.0i		−	0.181742i
$647$	−243134.			−0.580813			−0.290406	−	0.956903i	$-0.593791\pi$
$647$	−243134.			−0.580813			−0.290406	+	0.956903i	$0.593791\pi$
$648$			585923.i			1.39537i
$649$	−17280.2	+	146099.i	−0.0410260	+	0.346863i
$650$	−1.16746e6			−2.76322
$651$		−	167486.i		−	0.395200i
$652$	−89184.1			−0.209794
$653$	233977.			0.548715			0.274357	−	0.961628i	$-0.411535\pi$
$653$	233977.			0.548715			0.274357	+	0.961628i	$0.411535\pi$
$654$	−1.30244e6			−3.04511
$655$			507984.i			1.18404i
$656$			898320.i			2.08749i
$657$		−	231050.i		−	0.535273i
$658$	−234331.			−0.541226
$659$		−	858879.i		−	1.97770i	−0.148907	−	0.988851i	$-0.547575\pi$
$659$		−	858879.i		−	1.97770i	0.148907	−	0.988851i	$-0.452425\pi$
$660$	−68492.6	+	579085.i	−0.157237	+	1.32940i
$661$	50033.4			0.114514			0.0572568	−	0.998359i	$-0.481765\pi$
$661$	50033.4			0.114514			0.0572568	+	0.998359i	$0.481765\pi$
$662$		−	127058.i		−	0.289924i
$663$	−927644.			−2.11035
$664$	386162.			0.875856
$665$	−47448.3			−0.107295
$666$		−	1.32175e6i		−	2.97990i
$667$			368.118i			0.000827438i
$668$		−	46551.0i		−	0.104322i
$669$	−285639.			−0.638212
$670$		−	1.13289e6i		−	2.52371i
$671$	606880.	+	71780.1i	1.34790	+	0.159426i
$672$	−257230.			−0.569617
$673$			262811.i			0.580247i	0.956989	+	0.290123i	$0.0936964\pi$
$673$			262811.i			0.580247i	−0.956989	+	0.290123i	$0.906304\pi$
$674$	−393786.			−0.866842
$675$	−1.94033e6			−4.25860
$676$	142399.			0.311610
$677$		−	581325.i		−	1.26836i	−0.773187	−	0.634179i	$-0.781338\pi$
$677$		−	581325.i		−	1.26836i	0.773187	−	0.634179i	$-0.218662\pi$
$678$			397406.i			0.864519i
$679$		−	275622.i		−	0.597824i
$680$	−456528.			−0.987301
$681$			31113.2i			0.0670889i
$682$	318012.	+	37613.6i	0.683714	+	0.0808679i
$683$	−176335.			−0.378005			−0.189002	−	0.981977i	$-0.560525\pi$
$683$	−176335.			−0.378005			−0.189002	+	0.981977i	$0.560525\pi$
$684$			82075.4i			0.175429i
$685$	1.31385e6			2.80004
$686$	30509.8			0.0648322
$687$	168809.			0.357671
$688$			155270.i			0.328028i
$689$		−	286543.i		−	0.603604i
$690$		−	3139.21i		−	0.00659359i
$691$	−506589.			−1.06096			−0.530481	−	0.847697i	$-0.677989\pi$
$691$	−506589.			−1.06096			−0.530481	+	0.847697i	$0.677989\pi$
$692$			230038.i			0.480383i
$693$	419152.	+	49576.1i	0.872780	+	0.103230i
$694$	466852.			0.969305
$695$			878075.i			1.81787i
$696$	−270412.			−0.558222
$697$	−720909.			−1.48394
$698$	785888.			1.61306
$699$		−	125475.i		−	0.256805i
$700$		−	144156.i		−	0.294197i
$701$		−	296863.i		−	0.604116i	−0.953290	−	0.302058i	$-0.902326\pi$
$701$		−	296863.i		−	0.604116i	0.953290	−	0.302058i	$-0.0976736\pi$
$702$	1.86744e6			3.78942
$703$			90095.4i			0.182302i
$704$	−14802.1	+	125147.i	−0.0298660	+	0.252509i
$705$	1.79642e6			3.61435
$706$		−	61639.2i		−	0.123665i
$707$	128704.			0.257485
$708$	−141021.			−0.281331
$709$	497361.			0.989416			0.494708	−	0.869059i	$-0.335275\pi$
$709$	497361.			0.989416			0.494708	+	0.869059i	$0.335275\pi$
$710$			53735.9i			0.106598i
$711$			269793.i			0.533693i
$712$			132384.i			0.261140i
$713$	−528.173			−0.00103896
$714$		−	373867.i		−	0.733366i
$715$	−1.10191e6	−	130331.i	−2.15543	−	0.254938i
$716$	−76572.2			−0.149364
$717$			90656.2i			0.176343i
$718$	−98957.3			−0.191955
$719$	443090.			0.857106			0.428553	−	0.903517i	$-0.359024\pi$
$719$	443090.			0.857106			0.428553	+	0.903517i	$0.359024\pi$
$720$	2.49742e6			4.81755
$721$			321116.i			0.617719i
$722$			607650.i			1.16568i
$723$			1.05980e6i			2.02744i
$724$	−86443.7			−0.164914
$725$		−	422983.i		−	0.804725i
$726$	−269229.	+	1.12220e6i	−0.510797	+	2.12911i
$727$	−945629.			−1.78917			−0.894586	−	0.446896i	$-0.852529\pi$
$727$	−945629.			−1.78917			−0.894586	+	0.446896i	$0.852529\pi$
$728$		−	175363.i		−	0.330884i
$729$	230292.			0.433335
$730$	−244803.			−0.459378
$731$	−124605.			−0.233186
$732$			585788.i			1.09325i
$733$		−	55866.0i		−	0.103978i	−0.998648	−	0.0519888i	$-0.983444\pi$
$733$		−	55866.0i		−	0.103978i	0.998648	−	0.0519888i	$-0.0165560\pi$
$734$		−	807814.i		−	1.49941i
$735$	−233893.			−0.432954
$736$			811.182i			0.00149749i
$737$	80685.2	−	682170.i	0.148545	−	1.25591i
$738$	2.54634e6			4.67525
$739$			119234.i			0.218329i	0.994024	+	0.109165i	$0.0348176\pi$
$739$			119234.i			0.218329i	−0.994024	+	0.109165i	$0.965182\pi$
$740$	−429057.			−0.783523
$741$	−223342.			−0.406756
$742$	115485.			0.209758
$743$			675422.i			1.22348i	0.791058	+	0.611741i	$0.209530\pi$
$743$			675422.i			1.22348i	−0.791058	+	0.611741i	$0.790470\pi$
$744$		−	387984.i		−	0.700920i
$745$		−	1.28217e6i		−	2.31011i
$746$	996165.			1.79000
$747$		−	1.69528e6i		−	3.03809i
$748$	217489.	+	25724.0i	0.388717	+	0.0459764i
$749$	10941.6			0.0195038
$750$			1.56016e6i			2.77362i
$751$	−177685.			−0.315043			−0.157521	−	0.987516i	$-0.550350\pi$
$751$	−177685.			−0.315043			−0.157521	+	0.987516i	$0.550350\pi$
$752$	−840723.			−1.48668
$753$	1.35134e6			2.38327
$754$			407094.i			0.716065i
$755$			634348.i			1.11284i
$756$			230589.i			0.403454i
$757$	−353767.			−0.617341			−0.308670	−	0.951169i	$-0.599884\pi$
$757$	−353767.			−0.617341			−0.308670	+	0.951169i	$0.599884\pi$
$758$		−	70318.7i		−	0.122386i
$759$	223.575	−	1890.27i	0.000388097	−	0.00328125i
$760$	−109915.			−0.190296
$761$		−	251147.i		−	0.433669i	−0.976208	−	0.216834i	$-0.930427\pi$
$761$		−	251147.i		−	0.433669i	0.976208	−	0.216834i	$-0.0695732\pi$
$762$	−1.53177e6			−2.63806
$763$	306022.			0.525658
$764$	313988.			0.537930
$765$			2.00420e6i			3.42466i
$766$		−	243794.i		−	0.415495i
$767$		−	268341.i		−	0.456139i
$768$	−1.18811e6			−2.01435
$769$			303191.i			0.512701i	0.966584	+	0.256350i	$0.0825201\pi$
$769$			303191.i			0.512701i	−0.966584	+	0.256350i	$0.917480\pi$
$770$	52527.0	−	444101.i	0.0885933	−	0.749031i
$771$	−690601.			−1.16177
$772$			278555.i			0.467386i
$773$	−622597.			−1.04195			−0.520976	−	0.853571i	$-0.674432\pi$
$773$	−622597.			−1.04195			−0.520976	+	0.853571i	$0.674432\pi$
$774$	440122.			0.734669
$775$	606893.			1.01044
$776$		−	638482.i		−	1.06029i
$777$			444118.i			0.735625i
$778$			465422.i			0.768932i
$779$	−173568.			−0.286019
$780$		−	1.06361e6i		−	1.74821i
$781$	−3827.09	+	32357.0i	−0.00627432	+	0.0530476i
$782$	−1179.00			−0.00192797
$783$			676592.i			1.10358i
$784$	109462.			0.178086
$785$	697370.			1.13168
$786$	−963686.			−1.55988
$787$		−	1.10420e6i		−	1.78277i	−0.453242	−	0.891387i	$-0.649733\pi$
$787$		−	1.10420e6i		−	1.78277i	0.453242	−	0.891387i	$-0.350267\pi$
$788$		−	390254.i		−	0.628485i
$789$		−	600766.i		−	0.965054i
$790$	285852.			0.458022
$791$		−	93374.4i		−	0.149237i
$792$	970972.	+	114844.i	1.54795	+	0.183087i
$793$	−1.11466e6			−1.77254
$794$		−	1.28750e6i		−	2.04223i
$795$	−885327.			−1.40078
$796$	−461259.			−0.727979
$797$	−980208.			−1.54313			−0.771564	−	0.636152i	$-0.780525\pi$
$797$	−980208.			−1.54313			−0.771564	+	0.636152i	$0.780525\pi$
$798$		−	90013.2i		−	0.141351i
$799$		−	674687.i		−	1.05684i
$800$		−	932083.i		−	1.45638i
$801$	581175.			0.905820
$802$			1.30165e6i			2.02369i
$803$	−147407.	−	17434.9i	−0.228606	−	0.0270389i
$804$	658461.			1.01863
$805$			737.588i			0.00113821i
$806$	−584096.			−0.899112
$807$	1.28926e6			1.97967
$808$	298145.			0.456672
$809$			198856.i			0.303838i	0.988393	+	0.151919i	$0.0485453\pi$
$809$			198856.i			0.303838i	−0.988393	+	0.151919i	$0.951455\pi$
$810$		−	2.72536e6i		−	4.15388i
$811$			1.11278e6i			1.69187i	0.533290	+	0.845933i	$0.320956\pi$
$811$			1.11278e6i			1.69187i	−0.533290	+	0.845933i	$0.679044\pi$
$812$	−50267.4			−0.0762385
$813$		−	1.80865e6i		−	2.73636i
$814$	−843263.	−	99738.8i	−1.27267	−	0.150527i
$815$	−524329.			−0.789384
$816$		−	1.34134e6i		−	2.01446i
$817$	−30000.3			−0.0449450
$818$	−98225.7			−0.146798
$819$	−769860.			−1.14774
$820$		−	826576.i		−	1.22929i
$821$			668605.i			0.991935i	0.868341	+	0.495968i	$0.165187\pi$
$821$			668605.i			0.991935i	−0.868341	+	0.495968i	$0.834813\pi$
$822$			2.49248e6i			3.68882i
$823$	−260587.			−0.384727			−0.192363	−	0.981324i	$-0.561615\pi$
$823$	−260587.			−0.384727			−0.192363	+	0.981324i	$0.561615\pi$
$824$			743870.i			1.09558i
$825$	−256898.	+	2.17200e6i	−0.377444	+	3.19118i
$826$	108149.			0.158512
$827$			278580.i			0.407323i	0.979041	+	0.203661i	$0.0652842\pi$
$827$			278580.i			0.407323i	−0.979041	+	0.203661i	$0.934716\pi$
$828$	1275.87			0.00186100
$829$	1.25461e6			1.82557			0.912784	−	0.408442i	$-0.133928\pi$
$829$	1.25461e6			1.82557			0.912784	+	0.408442i	$0.133928\pi$
$830$	−1.79619e6			−2.60733
$831$			656063.i			0.950043i
$832$		−	229859.i		−	0.332059i
$833$			87843.8i			0.126596i
$834$	−1.66578e6			−2.39489
$835$		−	273682.i		−	0.392530i
$836$	52363.2	+	6193.37i	0.0749227	+	0.00886165i
$837$	−970770.			−1.38569
$838$			191821.i			0.273155i
$839$	−536556.			−0.762239			−0.381119	−	0.924526i	$-0.624461\pi$
$839$	−536556.			−0.762239			−0.381119	+	0.924526i	$0.624461\pi$
$840$	−541816.			−0.767880
$841$	559787.			0.791463
$842$		−	720804.i		−	1.01670i
$843$		−	322166.i		−	0.453340i
$844$			246732.i			0.346371i
$845$	837186.			1.17249
$846$			2.38308e6i			3.32965i
$847$	63258.0	−	263673.i	0.0881756	−	0.367535i
$848$	414332.			0.576179
$849$		−	1.98550e6i		−	2.75458i
$850$	1.35472e6			1.87505
$851$	1400.54			0.00193391
$852$	−31232.4			−0.0430255
$853$		−	528821.i		−	0.726793i	−0.931635	−	0.363397i	$-0.881617\pi$
$853$		−	528821.i		−	0.726793i	0.931635	−	0.363397i	$-0.118383\pi$
$854$		−	449241.i		−	0.615976i
$855$			482536.i			0.660081i
$856$	25346.5			0.0345916
$857$			1.16546e6i			1.58685i	0.608670	+	0.793424i	$0.291703\pi$
$857$			1.16546e6i			1.58685i	−0.608670	+	0.793424i	$0.708297\pi$
$858$	247248.	−	2.09041e6i	0.335859	−	2.83959i
$859$	928156.			1.25787			0.628934	−	0.777459i	$-0.283492\pi$
$859$	928156.			1.25787			0.628934	+	0.777459i	$0.283492\pi$
$860$		−	142869.i		−	0.193171i
$861$	−855590.			−1.15414
$862$	1.69881e6			2.28628
$863$	352022.			0.472659			0.236329	−	0.971673i	$-0.424056\pi$
$863$	352022.			0.472659			0.236329	+	0.971673i	$0.424056\pi$
$864$			1.49093e6i			1.99724i
$865$			1.35244e6i			1.80752i
$866$			723894.i			0.965249i
$867$	−294288.			−0.391502
$868$		−	72123.2i		−	0.0957273i
$869$	172125.	+	20358.5i	0.227931	+	0.0269591i
$870$	1.25779e6			1.66177
$871$			1.25295e6i			1.65157i
$872$	708905.			0.932299
$873$	−2.80299e6			−3.67784
$874$	−283.859			−0.000371604
$875$		−	366576.i		−	0.478793i
$876$		−	142284.i		−	0.185417i
$877$			1.50226e6i			1.95319i	0.215079	+	0.976597i	$0.430999\pi$
$877$			1.50226e6i			1.95319i	−0.215079	+	0.976597i	$0.569001\pi$
$878$	736734.			0.955700
$879$		−	49805.2i		−	0.0644610i
$880$	188454.	−	1.59332e6i	0.243355	−	2.05749i
$881$	−559816.			−0.721263			−0.360631	−	0.932708i	$-0.617439\pi$
$881$	−559816.			−0.721263			−0.360631	+	0.932708i	$0.617439\pi$
$882$		−	310276.i		−	0.398851i
$883$	−89914.8			−0.115321			−0.0576607	−	0.998336i	$-0.518364\pi$
$883$	−89914.8			−0.115321			−0.0576607	+	0.998336i	$0.518364\pi$
$884$	−399464.			−0.511179
$885$	−829089.			−1.05856
$886$		−	22962.3i		−	0.0292515i
$887$		−	423496.i		−	0.538272i	−0.963102	−	0.269136i	$-0.913262\pi$
$887$		−	423496.i		−	0.538272i	0.963102	−	0.269136i	$-0.0867381\pi$
$888$			1.02881e6i			1.30469i
$889$	359905.			0.455391
$890$		−	615768.i		−	0.777387i
$891$	194101.	−	1.64107e6i	0.244496	−	2.06715i
$892$	−123002.			−0.154591
$893$		−	162439.i		−	0.203699i
$894$	2.43238e6			3.04338
$895$	−450181.			−0.562006
$896$	343416.			0.427764
$897$			3471.87i			0.00431498i
$898$			266440.i			0.330405i
$899$		−	211624.i		−	0.261846i
$900$	−1.46603e6			−1.80991
$901$			332505.i			0.409589i
$902$	192146.	−	1.62454e6i	0.236167	−	1.99672i
$903$	−147884.			−0.181362
$904$		−	216303.i		−	0.264683i
$905$	−508218.			−0.620515
$906$	−1.20341e6			−1.46608
$907$	927976.			1.12803			0.564017	−	0.825763i	$-0.309255\pi$
$907$	927976.			1.12803			0.564017	+	0.825763i	$0.309255\pi$
$908$			13398.0i			0.0162506i
$909$		−	1.30888e6i		−	1.58406i
$910$			815684.i			0.985007i
$911$	−348505.			−0.419926			−0.209963	−	0.977709i	$-0.567334\pi$
$911$	−348505.			−0.419926			−0.209963	+	0.977709i	$0.567334\pi$
$912$		−	322945.i		−	0.388275i
$913$	−1.08157e6	−	127925.i	−1.29752	−	0.153467i
$914$	−107742.			−0.128971
$915$			3.44395e6i			4.11353i
$916$	72693.1			0.0866368
$917$	226428.			0.269272
$918$	−2.16698e6			−2.57140
$919$		−	99098.0i		−	0.117337i	−0.998278	−	0.0586683i	$-0.981315\pi$
$919$		−	99098.0i		−	0.117337i	0.998278	−	0.0586683i	$-0.0186854\pi$
$920$			1708.64i			0.00201871i
$921$		−	1.22742e6i		−	1.44702i
$922$	−604329.			−0.710905
$923$		−	59430.3i		−	0.0697597i
$924$	258120.	+	30529.7i	0.302328	+	0.0357585i
$925$	−1.60928e6			−1.88083
$926$			175297.i			0.204434i
$927$	3.26565e6			3.80024
$928$	−325018.			−0.377408
$929$	−1.48364e6			−1.71909			−0.859543	−	0.511063i	$-0.829252\pi$
$929$	−1.48364e6			−1.71909			−0.859543	+	0.511063i	$0.829252\pi$
$930$			1.80467e6i			2.08656i
$931$			21149.5i			0.0244006i
$932$		−	54032.4i		−	0.0622046i
$933$	2.30547e6			2.64848
$934$			755022.i			0.865498i
$935$	1.27866e6	+	151236.i	1.46262	+	0.172994i
$936$	−1.78339e6			−2.03561
$937$		−	816968.i		−	0.930521i	−0.885174	−	0.465260i	$-0.845961\pi$
$937$		−	816968.i		−	0.930521i	0.885174	−	0.465260i	$-0.154039\pi$
$938$	−504974.			−0.573936
$939$	1.79105e6			2.03131
$940$	773579.			0.875485
$941$			430892.i			0.486619i	0.969949	+	0.243310i	$0.0782331\pi$
$941$			430892.i			0.486619i	−0.969949	+	0.243310i	$0.921767\pi$
$942$			1.32297e6i			1.49089i
$943$			2698.13i			0.00303417i
$944$	388013.			0.435414
$945$			1.35567e6i			1.51807i
$946$	33211.4	−	280793.i	0.0371112	−	0.313765i
$947$	−554147.			−0.617910			−0.308955	−	0.951077i	$-0.599979\pi$
$947$	−554147.			−0.617910			−0.308955	+	0.951077i	$0.599979\pi$
$948$			166143.i			0.184869i
$949$	270745.			0.300627
$950$	326167.			0.361404
$951$	1.03541e6			1.14486
$952$			203492.i			0.224529i
$953$			948578.i			1.04445i	0.852808	+	0.522225i	$0.174898\pi$
$953$			948578.i			1.04445i	−0.852808	+	0.522225i	$0.825102\pi$
$954$		−	1.17445e6i		−	1.29044i
$955$	1.84599e6			2.02405
$956$			39038.6i			0.0427148i
$957$	757376.	+	89580.3i	0.826966	+	0.0978112i
$958$	−945773.			−1.03052
$959$		−	585633.i		−	0.636778i
$960$	−710191.			−0.770607
$961$	−619885.			−0.671219
$962$	1.54883e6			1.67361
$963$		−	111273.i		−	0.119988i
$964$			456375.i			0.491097i
$965$			1.63767e6i			1.75862i
$966$	−1399.26			−0.00149950
$967$		−	47884.7i		−	0.0512087i	−0.999672	−	0.0256043i	$-0.991849\pi$
$967$		−	47884.7i		−	0.0512087i	0.999672	−	0.0256043i	$-0.00815100\pi$
$968$	146538.	−	610803.i	0.156387	−	0.651854i
$969$	259166.			0.276014
$970$			2.96983e6i			3.15637i
$971$	−337882.			−0.358366			−0.179183	−	0.983816i	$-0.557345\pi$
$971$	−337882.			−0.358366			−0.179183	+	0.983816i	$0.557345\pi$
$972$	575533.			0.609169
$973$	391391.			0.413414
$974$			1.66029e6i			1.75011i
$975$		−	3.98933e6i		−	4.19653i
$976$		−	1.61177e6i		−	1.69201i
$977$	−1.58709e6			−1.66270			−0.831349	−	0.555751i	$-0.812431\pi$
$977$	−1.58709e6			−1.66270			−0.831349	+	0.555751i	$0.812431\pi$
$978$		−	994693.i		−	1.03995i
$979$	43855.2	−	370783.i	0.0457568	−	0.386861i
$980$	−100719.			−0.104872
$981$		−	3.11215e6i		−	3.23387i
$982$	−28553.4			−0.0296098
$983$	−232850.			−0.240973			−0.120487	−	0.992715i	$-0.538445\pi$
$983$	−232850.			−0.240973			−0.120487	+	0.992715i	$0.538445\pi$
$984$	−1.98199e6			−2.04697
$985$		−	2.29437e6i		−	2.36478i
$986$		−	472392.i		−	0.485902i
$987$		−	800733.i		−	0.821965i
$988$	−96176.0			−0.0985264
$989$			466.358i			0.000476789i
$990$	−4.51637e6	−	534184.i	−4.60807	−	0.545030i
$991$	471193.			0.479790			0.239895	−	0.970799i	$-0.422887\pi$
$991$	471193.			0.479790			0.239895	+	0.970799i	$0.422887\pi$
$992$		−	466333.i		−	0.473885i
$993$	434168.			0.440311
$994$	23952.1			0.0242422
$995$	−2.71182e6			−2.73914
$996$		−	1.04398e6i		−	1.05238i
$997$			137443.i			0.138272i	0.997607	+	0.0691358i	$0.0220242\pi$
$997$			137443.i			0.138272i	−0.997607	+	0.0691358i	$0.977976\pi$
$998$			1.07267e6i			1.07697i
$999$	2.57416e6			2.57932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.5.c.a.43.20	yes	24
11.10	odd	2	inner	77.5.c.a.43.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.5.c.a.43.5	✓	24	11.10	odd	2	inner
77.5.c.a.43.20	yes	24	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	77.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.80284i q^{2} -16.4118 q^{3} -7.06726 q^{4} -41.5497 q^{5} -78.8230i q^{6} +18.5203i q^{7} +42.9025i q^{8} +188.346 q^{9} +O(q^{10})\)	\(q+4.80284i q^{2} -16.4118 q^{3} -7.06726 q^{4} -41.5497 q^{5} -78.8230i q^{6} +18.5203i q^{7} +42.9025i q^{8} +188.346 q^{9} -199.556i q^{10} +(14.2125 - 120.162i) q^{11} +115.986 q^{12} +220.703i q^{13} -88.9498 q^{14} +681.903 q^{15} -319.130 q^{16} -256.104i q^{17} +904.594i q^{18} -61.6604i q^{19} +293.643 q^{20} -303.950i q^{21} +(577.121 + 68.2602i) q^{22} -0.958516 q^{23} -704.105i q^{24} +1101.38 q^{25} -1060.00 q^{26} -1761.73 q^{27} -130.888i q^{28} -384.050i q^{29} +3275.07i q^{30} +551.032 q^{31} -846.290i q^{32} +(-233.252 + 1972.08i) q^{33} +1230.03 q^{34} -769.511i q^{35} -1331.09 q^{36} -1461.16 q^{37} +296.145 q^{38} -3622.13i q^{39} -1782.58i q^{40} -2814.90i q^{41} +1459.82 q^{42} -486.541i q^{43} +(-100.443 + 849.220i) q^{44} -7825.70 q^{45} -4.60360i q^{46} +2634.42 q^{47} +5237.48 q^{48} -343.000 q^{49} +5289.73i q^{50} +4203.12i q^{51} -1559.77i q^{52} -1298.32 q^{53} -8461.31i q^{54} +(-590.524 + 4992.71i) q^{55} -794.565 q^{56} +1011.95i q^{57} +1844.53 q^{58} -1215.85 q^{59} -4819.19 q^{60} +5050.50i q^{61} +2646.52i q^{62} +3488.21i q^{63} -1041.48 q^{64} -9170.16i q^{65} +(-9471.56 - 1120.27i) q^{66} +5677.07 q^{67} +1809.96i q^{68} +15.7309 q^{69} +3695.84 q^{70} -269.277 q^{71} +8080.50i q^{72} -1226.73i q^{73} -7017.69i q^{74} -18075.5 q^{75} +435.770i q^{76} +(2225.44 + 263.219i) q^{77} +17396.5 q^{78} +1432.44i q^{79} +13259.7 q^{80} +13657.1 q^{81} +13519.5 q^{82} -9000.91i q^{83} +2148.09i q^{84} +10641.1i q^{85} +2336.78 q^{86} +6302.93i q^{87} +(5155.27 + 609.751i) q^{88} +3085.68 q^{89} -37585.6i q^{90} -4087.49 q^{91} +6.77408 q^{92} -9043.40 q^{93} +12652.7i q^{94} +2561.97i q^{95} +13889.1i q^{96} -14882.2 q^{97} -1647.37i q^{98} +(2676.86 - 22632.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 198 q^{4} + 6 q^{5} + 982 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 198 * q^4 + 6 * q^5 + 982 * q^9	\( 24 q - 6 q^{3} - 198 q^{4} + 6 q^{5} + 982 q^{9} - 336 q^{11} - 656 q^{12} - 294 q^{14} + 1118 q^{15} + 1882 q^{16} + 588 q^{20} - 1824 q^{22} - 1458 q^{23} + 2262 q^{25} + 2004 q^{26} - 2322 q^{27} + 3514 q^{31} - 4078 q^{33} + 172 q^{34} - 7050 q^{36} - 1826 q^{37} + 120 q^{38} + 4290 q^{44} + 4092 q^{45} - 11028 q^{47} + 19104 q^{48} - 8232 q^{49} - 10896 q^{53} - 1534 q^{55} - 1470 q^{56} + 30440 q^{58} - 1926 q^{59} - 33544 q^{60} - 17566 q^{64} - 1896 q^{66} + 22526 q^{67} - 6570 q^{69} - 13916 q^{70} + 5454 q^{71} - 12544 q^{75} + 5292 q^{77} - 15080 q^{78} + 71676 q^{80} - 5740 q^{81} + 59836 q^{82} - 24120 q^{86} + 42880 q^{88} + 36318 q^{89} + 11172 q^{91} + 25188 q^{92} - 47362 q^{93} - 26466 q^{97} - 39930 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 - 198 * q^4 + 6 * q^5 + 982 * q^9 - 336 * q^11 - 656 * q^12 - 294 * q^14 + 1118 * q^15 + 1882 * q^16 + 588 * q^20 - 1824 * q^22 - 1458 * q^23 + 2262 * q^25 + 2004 * q^26 - 2322 * q^27 + 3514 * q^31 - 4078 * q^33 + 172 * q^34 - 7050 * q^36 - 1826 * q^37 + 120 * q^38 + 4290 * q^44 + 4092 * q^45 - 11028 * q^47 + 19104 * q^48 - 8232 * q^49 - 10896 * q^53 - 1534 * q^55 - 1470 * q^56 + 30440 * q^58 - 1926 * q^59 - 33544 * q^60 - 17566 * q^64 - 1896 * q^66 + 22526 * q^67 - 6570 * q^69 - 13916 * q^70 + 5454 * q^71 - 12544 * q^75 + 5292 * q^77 - 15080 * q^78 + 71676 * q^80 - 5740 * q^81 + 59836 * q^82 - 24120 * q^86 + 42880 * q^88 + 36318 * q^89 + 11172 * q^91 + 25188 * q^92 - 47362 * q^93 - 26466 * q^97 - 39930 * q^99

Introduction

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