LMFDB - Embedded newform 177.11.c.a.58.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,11,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, 11, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 11 $
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:	$112.458233723$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.95

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +26424.5i q^{10} +193821. i q^{11} -332756. q^{12} -998.798i q^{13} -935510. i q^{14} -63618.1 q^{15} +2.14819e6 q^{16} +1.44654e6 q^{17} -1.14700e6i q^{18} -1.03387e6 q^{19} +1.07551e6 q^{20} +2.25228e6 q^{21} +1.12947e7 q^{22} +3.69797e6i q^{23} +1.10191e7i q^{24} -9.56000e6 q^{25} -58203.6 q^{26} +2.76145e6 q^{27} -3.80765e7 q^{28} -1.48845e7 q^{29} +3.70726e6i q^{30} -2.62609e7i q^{31} -4.47557e7i q^{32} +2.71924e7i q^{33} -8.42951e7i q^{34} -7.27967e6 q^{35} -4.66844e7 q^{36} -9.93025e7i q^{37} +6.02473e7i q^{38} -140127. i q^{39} -3.56153e7i q^{40} -2.16870e8 q^{41} -1.31248e8i q^{42} +5.20592e7i q^{43} -4.59709e8i q^{44} -8.92538e6 q^{45} +2.15494e8 q^{46} -4.33749e8i q^{47} +3.01383e8 q^{48} -2.47522e7 q^{49} +5.57096e8i q^{50} +2.02944e8 q^{51} +2.36896e6i q^{52} -4.32486e8 q^{53} -1.60920e8i q^{54} -8.78895e7i q^{55} +1.26089e9i q^{56} -1.45048e8 q^{57} +8.67376e8i q^{58} +(-7.62493e7 - 7.10847e8i) q^{59} +1.50890e8 q^{60} +5.30576e8i q^{61} -1.53032e9 q^{62} +3.15986e8 q^{63} -4.08332e8 q^{64} +452911. i q^{65} +1.58460e9 q^{66} -1.25723e9i q^{67} -3.43092e9 q^{68} +5.18810e8i q^{69} +4.24213e8i q^{70} -5.22195e8 q^{71} +1.54594e9i q^{72} -3.99640e8i q^{73} -5.78672e9 q^{74} -1.34123e9 q^{75} +2.45215e9 q^{76} +3.11156e9i q^{77} -8.16573e6 q^{78} -4.13264e9 q^{79} -9.74109e8 q^{80} +3.87420e8 q^{81} +1.26378e10i q^{82} +1.61202e9i q^{83} -5.34199e9 q^{84} -6.55942e8 q^{85} +3.03368e9 q^{86} -2.08824e9 q^{87} -1.52231e10 q^{88} +5.28076e9i q^{89} +5.20114e8i q^{90} -1.60345e7i q^{91} -8.77089e9i q^{92} -3.68430e9i q^{93} -2.52761e10 q^{94} +4.68815e8 q^{95} -6.27905e9i q^{96} -8.89000e9i q^{97} +1.44240e9i q^{98} +3.81499e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * 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 $

$2$		−	58.2736i		−	1.82105i	−0.413454	−	0.910525i	$-0.635678\pi$
$2$		−	58.2736i		−	1.82105i	0.413454	−	0.910525i	$-0.364322\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−2371.81			−2.31622
$5$	−453.456			−0.145106			−0.0725530	−	0.997365i	$-0.523115\pi$
$5$	−453.456			−0.145106			−0.0725530	+	0.997365i	$0.523115\pi$
$6$		−	8175.56i		−	1.05138i
$7$	16053.8			0.955183			0.477591	−	0.878582i	$-0.341510\pi$
$7$	16053.8			0.955183			0.477591	+	0.878582i	$0.341510\pi$
$8$			78542.0i			2.39691i
$9$	19683.0			0.333333
$10$			26424.5i			0.264245i
$11$			193821.i			1.20348i	0.798692	+	0.601739i	$0.205525\pi$
$11$			193821.i			1.20348i	−0.798692	+	0.601739i	$0.794475\pi$
$12$	−332756.			−1.33727
$13$		−	998.798i		−	0.00269005i	−0.999999	−	0.00134503i	$-0.999572\pi$
$13$		−	998.798i		−	0.00269005i	0.999999	−	0.00134503i	$-0.000428135\pi$
$14$		−	935510.i		−	1.73944i
$15$	−63618.1			−0.0837770
$16$	2.14819e6			2.04867
$17$	1.44654e6			1.01879			0.509396	−	0.860532i	$-0.329869\pi$
$17$	1.44654e6			1.01879			0.509396	+	0.860532i	$0.329869\pi$
$18$		−	1.14700e6i		−	0.607017i
$19$	−1.03387e6			−0.417540			−0.208770	−	0.977965i	$-0.566946\pi$
$19$	−1.03387e6			−0.417540			−0.208770	+	0.977965i	$0.566946\pi$
$20$	1.07551e6			0.336098
$21$	2.25228e6			0.551475
$22$	1.12947e7			2.19160
$23$			3.69797e6i			0.574545i	0.957849	+	0.287272i	$0.0927485\pi$
$23$			3.69797e6i			0.574545i	−0.957849	+	0.287272i	$0.907252\pi$
$24$			1.10191e7i			1.38386i
$25$	−9.56000e6			−0.978944
$26$	−58203.6			−0.00489872
$27$	2.76145e6			0.192450
$28$	−3.80765e7			−2.21242
$29$	−1.48845e7			−0.725681			−0.362840	−	0.931851i	$-0.618193\pi$
$29$	−1.48845e7			−0.725681			−0.362840	+	0.931851i	$0.618193\pi$
$30$			3.70726e6i			0.152562i
$31$		−	2.62609e7i		−	0.917279i	−0.888622	−	0.458640i	$-0.848337\pi$
$31$		−	2.62609e7i		−	0.917279i	0.888622	−	0.458640i	$-0.151663\pi$
$32$		−	4.47557e7i		−	1.33382i
$33$			2.71924e7i			0.694829i
$34$		−	8.42951e7i		−	1.85527i
$35$	−7.27967e6			−0.138603
$36$	−4.66844e7			−0.772075
$37$		−	9.93025e7i		−	1.43203i	−0.698086	−	0.716014i	$-0.745965\pi$
$37$		−	9.93025e7i		−	1.43203i	0.698086	−	0.716014i	$-0.254035\pi$
$38$			6.02473e7i			0.760361i
$39$		−	140127.i		−	0.00155310i
$40$		−	3.56153e7i		−	0.347806i
$41$	−2.16870e8			−1.87189			−0.935944	−	0.352150i	$-0.885451\pi$
$41$	−2.16870e8			−1.87189			−0.935944	+	0.352150i	$0.885451\pi$
$42$		−	1.31248e8i		−	1.00426i
$43$			5.20592e7i			0.354124i	0.984200	+	0.177062i	$0.0566593\pi$
$43$			5.20592e7i			0.354124i	−0.984200	+	0.177062i	$0.943341\pi$
$44$		−	4.59709e8i		−	2.78753i
$45$	−8.92538e6			−0.0483686
$46$	2.15494e8			1.04627
$47$		−	4.33749e8i		−	1.89125i	−0.325260	−	0.945625i	$-0.605452\pi$
$47$		−	4.33749e8i		−	1.89125i	0.325260	−	0.945625i	$-0.394548\pi$
$48$	3.01383e8			1.18280
$49$	−2.47522e7			−0.0876260
$50$			5.57096e8i			1.78271i
$51$	2.02944e8			0.588200
$52$			2.36896e6i			0.00623077i
$53$	−4.32486e8			−1.03417			−0.517086	−	0.855934i	$-0.672983\pi$
$53$	−4.32486e8			−1.03417			−0.517086	+	0.855934i	$0.672983\pi$
$54$		−	1.60920e8i		−	0.350461i
$55$		−	8.78895e7i		−	0.174632i
$56$			1.26089e9i			2.28949i
$57$	−1.45048e8			−0.241067
$58$			8.67376e8i			1.32150i
$59$	−7.62493e7	−	7.10847e8i	−0.106654	−	0.994296i
$59$	−7.62493e7	−	7.10847e8i	−0.106654	−	0.994296i
$60$	1.50890e8			0.194046
$61$			5.30576e8i			0.628201i	0.949390	+	0.314100i	$0.101703\pi$
$61$			5.30576e8i			0.628201i	−0.949390	+	0.314100i	$0.898297\pi$
$62$	−1.53032e9			−1.67041
$63$	3.15986e8			0.318394
$64$	−4.08332e8			−0.380288
$65$			452911.i			0.000390343i
$66$	1.58460e9			1.26532
$67$		−	1.25723e9i		−	0.931196i	−0.884996	−	0.465598i	$-0.845839\pi$
$67$		−	1.25723e9i		−	0.931196i	0.884996	−	0.465598i	$-0.154161\pi$
$68$	−3.43092e9			−2.35975
$69$			5.18810e8i			0.331714i
$70$			4.24213e8i			0.252403i
$71$	−5.22195e8			−0.289428			−0.144714	−	0.989474i	$-0.546226\pi$
$71$	−5.22195e8			−0.289428			−0.144714	+	0.989474i	$0.546226\pi$
$72$			1.54594e9i			0.798971i
$73$		−	3.99640e8i		−	0.192777i	−0.995344	−	0.0963885i	$-0.969271\pi$
$73$		−	3.99640e8i		−	0.192777i	0.995344	−	0.0963885i	$-0.0307291\pi$
$74$	−5.78672e9			−2.60780
$75$	−1.34123e9			−0.565194
$76$	2.45215e9			0.967116
$77$			3.11156e9i			1.14954i
$78$	−8.16573e6			−0.00282828
$79$	−4.13264e9			−1.34305			−0.671526	−	0.740981i	$-0.734361\pi$
$79$	−4.13264e9			−1.34305			−0.671526	+	0.740981i	$0.734361\pi$
$80$	−9.74109e8			−0.297275
$81$	3.87420e8			0.111111
$82$			1.26378e10i			3.40880i
$83$			1.61202e9i			0.409243i	0.978841	+	0.204621i	$0.0655963\pi$
$83$			1.61202e9i			0.409243i	−0.978841	+	0.204621i	$0.934404\pi$
$84$	−5.34199e9			−1.27734
$85$	−6.55942e8			−0.147833
$86$	3.03368e9			0.644878
$87$	−2.08824e9			−0.418972
$88$	−1.52231e10			−2.88463
$89$			5.28076e9i			0.945685i	0.881147	+	0.472842i	$0.156772\pi$
$89$			5.28076e9i			0.945685i	−0.881147	+	0.472842i	$0.843228\pi$
$90$			5.20114e8i			0.0880818i
$91$		−	1.60345e7i		−	0.00256949i
$92$		−	8.77089e9i		−	1.33077i
$93$		−	3.68430e9i		−	0.529591i
$94$	−2.52761e10			−3.44406
$95$	4.68815e8			0.0605875
$96$		−	6.27905e9i		−	0.770084i
$97$		−	8.89000e9i		−	1.03525i	−0.855609	−	0.517623i	$-0.826817\pi$
$97$		−	8.89000e9i		−	1.03525i	0.855609	−	0.517623i	$-0.173183\pi$
$98$			1.44240e9i			0.159571i
$99$			3.81499e9i			0.401160i
$100$	2.26745e10			2.26745
$101$		−	1.39205e10i		−	1.32449i	−0.749288	−	0.662245i	$-0.769604\pi$
$101$		−	1.39205e10i		−	1.32449i	0.749288	−	0.662245i	$-0.230396\pi$
$102$		−	1.18263e10i		−	1.07114i
$103$			3.01374e9i			0.259968i	0.991516	+	0.129984i	$0.0414925\pi$
$103$			3.01374e9i			0.259968i	−0.991516	+	0.129984i	$0.958507\pi$
$104$	7.84476e7			0.00644782
$105$	−1.02131e9			−0.0800223
$106$			2.52025e10i			1.88328i
$107$	1.02881e10			0.733526			0.366763	−	0.930314i	$-0.380466\pi$
$107$	1.02881e10			0.733526			0.366763	+	0.930314i	$0.380466\pi$
$108$	−6.54964e9			−0.445758
$109$		−	7.35418e9i		−	0.477971i	−0.971023	−	0.238986i	$-0.923185\pi$
$109$		−	7.35418e9i		−	0.477971i	0.971023	−	0.238986i	$-0.0768149\pi$
$110$	−5.12164e9			−0.318014
$111$		−	1.39318e10i		−	0.826782i
$112$	3.44865e10			1.95686
$113$		−	5.92428e9i		−	0.321546i	−0.986991	−	0.160773i	$-0.948601\pi$
$113$		−	5.92428e9i		−	0.321546i	0.986991	−	0.160773i	$-0.0513987\pi$
$114$			8.45247e9i			0.438995i
$115$		−	1.67687e9i		−	0.0833699i
$116$	3.53034e10			1.68084
$117$		−	1.96593e7i		−	0.000896684i
$118$	−4.14236e10	+	4.44332e9i	−1.81066	+	0.194222i
$119$	2.32224e10			0.973133
$120$		−	4.99670e9i		−	0.200806i
$121$	−1.16293e10			−0.448362
$122$	3.09186e10			1.14399
$123$	−3.04260e10			−1.08073
$124$			6.22860e10i			2.12462i
$125$	8.76332e9			0.287157
$126$		−	1.84137e10i		−	0.579812i
$127$	−3.03560e10			−0.918809			−0.459405	−	0.888227i	$-0.651937\pi$
$127$	−3.03560e10			−0.918809			−0.459405	+	0.888227i	$0.651937\pi$
$128$		−	2.20349e10i		−	0.641300i
$129$			7.30371e9i			0.204454i
$130$	2.63928e7			0.000710834
$131$		−	2.23580e10i		−	0.579531i	−0.957098	−	0.289766i	$-0.906423\pi$
$131$		−	2.23580e10i		−	0.579531i	0.957098	−	0.289766i	$-0.0935773\pi$
$132$		−	6.44953e10i		−	1.60938i
$133$	−1.65975e10			−0.398827
$134$	−7.32634e10			−1.69575
$135$	−1.25220e9			−0.0279257
$136$			1.13614e11i			2.44196i
$137$	−1.67018e9			−0.0346068			−0.0173034	−	0.999850i	$-0.505508\pi$
$137$	−1.67018e9			−0.0346068			−0.0173034	+	0.999850i	$0.505508\pi$
$138$	3.02330e10			0.604067
$139$	−2.92344e10			−0.563404			−0.281702	−	0.959502i	$-0.590899\pi$
$139$	−2.92344e10			−0.563404			−0.281702	+	0.959502i	$0.590899\pi$
$140$	1.72660e10			0.321035
$141$		−	6.08532e10i		−	1.09191i
$142$			3.04302e10i			0.527063i
$143$	1.93588e8			0.00323742
$144$	4.22828e10			0.682891
$145$	6.74949e9			0.105301
$146$	−2.32885e10			−0.351057
$147$	−3.47263e9			−0.0505909
$148$			2.35527e11i			3.31690i
$149$			3.42814e10i			0.466796i	0.972381	+	0.233398i	$0.0749845\pi$
$149$			3.42814e10i			0.466796i	−0.972381	+	0.233398i	$0.925015\pi$
$150$			7.81584e10i			1.02925i
$151$			1.37379e11i			1.75000i	0.484127	+	0.874998i	$0.339137\pi$
$151$			1.37379e11i			1.75000i	−0.484127	+	0.874998i	$0.660863\pi$
$152$		−	8.12022e10i		−	1.00081i
$153$	2.84722e10			0.339598
$154$	1.81322e11			2.09337
$155$			1.19082e10i			0.133103i
$156$			3.32356e8i			0.00359734i
$157$			2.67147e10i			0.280060i	0.990147	+	0.140030i	$0.0447199\pi$
$157$			2.67147e10i			0.280060i	−0.990147	+	0.140030i	$0.955280\pi$
$158$			2.40824e11i			2.44576i
$159$	−6.06761e10			−0.597079
$160$			2.02947e10i			0.193546i
$161$			5.93663e10i			0.548795i
$162$		−	2.25764e10i		−	0.202339i
$163$	−3.14499e10			−0.273326			−0.136663	−	0.990618i	$-0.543638\pi$
$163$	−3.14499e10			−0.273326			−0.136663	+	0.990618i	$0.543638\pi$
$164$	5.14375e11			4.33571
$165$		−	1.23306e10i		−	0.100824i
$166$	9.39384e10			0.745251
$167$	1.78444e11			1.37379			0.686894	−	0.726757i	$-0.258974\pi$
$167$	1.78444e11			1.37379			0.686894	+	0.726757i	$0.258974\pi$
$168$			1.76899e11i			1.32184i
$169$	1.37857e11			0.999993
$170$			3.82241e10i			0.269211i
$171$	−2.03497e10			−0.139180
$172$		−	1.23475e11i		−	0.820231i
$173$		−	1.88237e11i		−	1.21472i	−0.794428	−	0.607358i	$-0.792229\pi$
$173$		−	1.88237e11i		−	1.21472i	0.794428	−	0.607358i	$-0.207771\pi$
$174$			1.21689e11i			0.762969i
$175$	−1.53474e11			−0.935071
$176$			4.16365e11i			2.46553i
$177$	−1.06975e10	−	9.97290e10i	−0.0615765	−	0.574057i
$178$	3.07729e11			1.72214
$179$			1.10184e11i			0.599588i	0.954004	+	0.299794i	$0.0969179\pi$
$179$			1.10184e11i			0.599588i	−0.954004	+	0.299794i	$0.903082\pi$
$180$	2.11693e10			0.112033
$181$	−1.39727e11			−0.719265			−0.359632	−	0.933094i	$-0.617098\pi$
$181$	−1.39727e11			−0.719265			−0.359632	+	0.933094i	$0.617098\pi$
$182$	−9.34386e8			−0.00467917
$183$			7.44378e10i			0.362692i
$184$	−2.90446e11			−1.37713
$185$			4.50293e10i			0.207796i
$186$	−2.14698e11			−0.964412
$187$			2.80371e11i			1.22610i
$188$			1.02877e12i			4.38056i
$189$	4.43316e10			0.183825
$190$		−	2.73195e10i		−	0.110333i
$191$		−	3.88976e11i		−	1.53023i	−0.643896	−	0.765113i	$-0.722683\pi$
$191$		−	3.88976e11i		−	1.53023i	0.643896	−	0.765113i	$-0.277317\pi$
$192$	−5.72873e10			−0.219560
$193$	1.03390e11			0.386092			0.193046	−	0.981190i	$-0.438163\pi$
$193$	1.03390e11			0.386092			0.193046	+	0.981190i	$0.438163\pi$
$194$	−5.18053e11			−1.88523
$195$			6.35416e7i			0.000225364i
$196$	5.87075e10			0.202961
$197$	3.84746e11			1.29671			0.648355	−	0.761338i	$-0.275457\pi$
$197$	3.84746e11			1.29671			0.648355	+	0.761338i	$0.275457\pi$
$198$	2.22313e11			0.730532
$199$	−2.30471e10			−0.0738499			−0.0369250	−	0.999318i	$-0.511756\pi$
$199$	−2.30471e10			−0.0738499			−0.0369250	+	0.999318i	$0.511756\pi$
$200$		−	7.50862e11i		−	2.34644i
$201$		−	1.76385e11i		−	0.537626i
$202$	−8.11199e11			−2.41196
$203$	−2.38953e11			−0.693158
$204$	−4.81345e11			−1.36240
$205$	9.83409e10			0.271622
$206$	1.75621e11			0.473414
$207$			7.27871e10i			0.191515i
$208$		−	2.14561e9i		−	0.00551104i
$209$		−	2.00386e11i		−	0.502500i
$210$			5.95154e10i			0.145725i
$211$		−	7.28762e11i		−	1.74250i	−0.490838	−	0.871251i	$-0.663309\pi$
$211$		−	7.28762e11i		−	1.74250i	0.490838	−	0.871251i	$-0.336691\pi$
$212$	1.02578e12			2.39537
$213$	−7.32619e10			−0.167101
$214$		−	5.99524e11i		−	1.33579i
$215$		−	2.36066e10i		−	0.0513855i
$216$			2.16890e11i			0.461286i
$217$		−	4.21586e11i		−	0.876169i
$218$	−4.28555e11			−0.870410
$219$		−	5.60680e10i		−	0.111300i
$220$			2.08458e11i			0.404487i
$221$		−	1.44480e9i		−	0.00274061i
$222$	−8.11854e11			−1.50561
$223$	−8.96759e11			−1.62612			−0.813058	−	0.582183i	$-0.802199\pi$
$223$	−8.96759e11			−1.62612			−0.813058	+	0.582183i	$0.802199\pi$
$224$		−	7.18497e11i		−	1.27405i
$225$	−1.88170e11			−0.326315
$226$	−3.45229e11			−0.585551
$227$		−	2.55999e11i		−	0.424726i	−0.977191	−	0.212363i	$-0.931884\pi$
$227$		−	2.55999e11i		−	0.424726i	0.977191	−	0.212363i	$-0.0681160\pi$
$228$	3.44027e11			0.558365
$229$			3.03874e10i			0.0482521i	0.999709	+	0.0241260i	$0.00768030\pi$
$229$			3.03874e10i			0.0482521i	−0.999709	+	0.0241260i	$0.992320\pi$
$230$	−9.77170e10			−0.151821
$231$			4.36540e11i			0.663689i
$232$		−	1.16906e12i		−	1.73939i
$233$			5.98615e11i			0.871702i	0.900019	+	0.435851i	$0.143552\pi$
$233$			5.98615e11i			0.871702i	−0.900019	+	0.435851i	$0.856448\pi$
$234$	−1.14562e9			−0.00163291
$235$			1.96686e11i			0.274432i
$236$	1.80849e11	+	1.68600e12i	0.247034	+	2.30301i
$237$	−5.79794e11			−0.775411
$238$		−	1.35325e12i		−	1.77212i
$239$	−1.31673e10			−0.0168852			−0.00844262	−	0.999964i	$-0.502687\pi$
$239$	−1.31673e10			−0.0168852			−0.00844262	+	0.999964i	$0.502687\pi$
$240$	−1.36664e11			−0.171632
$241$	1.79766e11			0.221118			0.110559	−	0.993870i	$-0.464736\pi$
$241$	1.79766e11			0.221118			0.110559	+	0.993870i	$0.464736\pi$
$242$			6.77684e11i			0.816489i
$243$	5.43536e10			0.0641500
$244$		−	1.25843e12i		−	1.45505i
$245$	1.12240e10			0.0127150
$246$			1.77303e12i			1.96807i
$247$			1.03263e9i			0.00112320i
$248$	2.06259e12			2.19864
$249$			2.26161e11i			0.236276i
$250$		−	5.10671e11i		−	0.522927i
$251$	8.07379e11			0.810418			0.405209	−	0.914224i	$-0.367199\pi$
$251$	8.07379e11			0.810418			0.405209	+	0.914224i	$0.367199\pi$
$252$	−7.49460e11			−0.737473
$253$	−7.16746e11			−0.691453
$254$			1.76895e12i			1.67320i
$255$	−9.20262e10			−0.0853513
$256$	−1.70218e12			−1.54813
$257$	−7.25110e11			−0.646753			−0.323377	−	0.946270i	$-0.604818\pi$
$257$	−7.25110e11			−0.646753			−0.323377	+	0.946270i	$0.604818\pi$
$258$	4.25614e11			0.372320
$259$		−	1.59418e12i		−	1.36785i
$260$		−	1.07422e9i		−	0.000904121i
$261$	−2.92972e11			−0.241894
$262$	−1.30288e12			−1.05536
$263$	4.72240e10			0.0375305			0.0187652	−	0.999824i	$-0.494026\pi$
$263$	4.72240e10			0.0375305			0.0187652	+	0.999824i	$0.494026\pi$
$264$	−2.13575e12			−1.66544
$265$	1.96113e11			0.150064
$266$			9.67196e11i			0.726284i
$267$			7.40870e11i			0.545991i
$268$			2.98192e12i			2.15686i
$269$			7.51336e11i			0.533424i	0.963776	+	0.266712i	$0.0859373\pi$
$269$			7.51336e11i			0.533424i	−0.963776	+	0.266712i	$0.914063\pi$
$270$			7.29700e10i			0.0508540i
$271$	−1.14249e12			−0.781640			−0.390820	−	0.920467i	$-0.627809\pi$
$271$	−1.14249e12			−0.781640			−0.390820	+	0.920467i	$0.627809\pi$
$272$	3.10744e12			2.08717
$273$		−	2.24957e9i		−	0.00148350i
$274$			9.73277e10i			0.0630208i
$275$		−	1.85293e12i		−	1.17814i
$276$		−	1.23052e12i		−	0.768323i
$277$	−2.06781e12			−1.26798			−0.633990	−	0.773341i	$-0.718584\pi$
$277$	−2.06781e12			−1.26798			−0.633990	+	0.773341i	$0.718584\pi$
$278$			1.70359e12i			1.02599i
$279$		−	5.16894e11i		−	0.305760i
$280$		−	5.71760e11i		−	0.332218i
$281$	3.12787e12			1.78533			0.892663	−	0.450724i	$-0.148834\pi$
$281$	3.12787e12			1.78533			0.892663	+	0.450724i	$0.148834\pi$
$282$	−3.54614e12			−1.98843
$283$		−	4.01605e11i		−	0.221242i	−0.993863	−	0.110621i	$-0.964716\pi$
$283$		−	4.01605e11i		−	0.221242i	0.993863	−	0.110621i	$-0.0352839\pi$
$284$	1.23855e12			0.670381
$285$	6.57729e10			0.0349802
$286$		−	1.12811e10i		−	0.00589551i
$287$	−3.48157e12			−1.78799
$288$		−	8.80927e11i		−	0.444608i
$289$	7.64837e10			0.0379384
$290$		−	3.93317e11i		−	0.191758i
$291$		−	1.24723e12i		−	0.597699i
$292$			9.47873e11i			0.446515i
$293$	−3.65208e12			−1.69123			−0.845615	−	0.533793i	$-0.820766\pi$
$293$	−3.65208e12			−1.69123			−0.845615	+	0.533793i	$0.820766\pi$
$294$			2.02363e11i			0.0921285i
$295$	3.45757e10	+	3.22338e11i	0.0154761	+	0.144278i
$296$	7.79942e12			3.43244
$297$			5.35228e11i			0.231610i
$298$	1.99770e12			0.850059
$299$	3.69352e9			0.00154556
$300$	3.18115e12			1.30912
$301$			8.35746e11i			0.338253i
$302$	8.00560e12			3.18683
$303$		−	1.95299e12i		−	0.764694i
$304$	−2.22095e12			−0.855402
$305$		−	2.40593e11i		−	0.0911557i
$306$		−	1.65918e12i		−	0.618424i
$307$	−9.35620e11			−0.343090			−0.171545	−	0.985176i	$-0.554876\pi$
$307$	−9.35620e11			−0.343090			−0.171545	+	0.985176i	$0.554876\pi$
$308$		−	7.38005e12i		−	2.66260i
$309$			4.22815e11i			0.150092i
$310$	6.93932e11			0.242387
$311$	−3.68900e12			−1.26797			−0.633983	−	0.773347i	$-0.718581\pi$
$311$	−3.68900e12			−1.26797			−0.633983	+	0.773347i	$0.718581\pi$
$312$	1.10059e10			0.00372265
$313$			4.34246e12i			1.44549i	0.691116	+	0.722744i	$0.257119\pi$
$313$			4.34246e12i			1.44549i	−0.691116	+	0.722744i	$0.742881\pi$
$314$	1.55676e12			0.510004
$315$	−1.43286e11			−0.0462009
$316$	9.80186e12			3.11081
$317$	−2.26865e12			−0.708714			−0.354357	−	0.935110i	$-0.615300\pi$
$317$	−2.26865e12			−0.708714			−0.354357	+	0.935110i	$0.615300\pi$
$318$			3.53581e12i			1.08731i
$319$		−	2.88494e12i		−	0.873341i
$320$	1.85160e11			0.0551821
$321$	1.44338e12			0.423502
$322$	3.45949e12			0.999384
$323$	−1.49553e12			−0.425386
$324$	−9.18889e11			−0.257358
$325$			9.54851e9i			0.00263341i
$326$			1.83270e12i			0.497741i
$327$		−	1.03176e12i		−	0.275957i
$328$		−	1.70334e13i		−	4.48675i
$329$		−	6.96329e12i		−	1.80649i
$330$	−7.18546e11			−0.183605
$331$	7.43069e12			1.87021			0.935103	−	0.354376i	$-0.115307\pi$
$331$	7.43069e12			1.87021			0.935103	+	0.354376i	$0.115307\pi$
$332$		−	3.82342e12i		−	0.947898i
$333$		−	1.95457e12i		−	0.477343i
$334$		−	1.03986e13i		−	2.50174i
$335$			5.70099e11i			0.135122i
$336$	4.83832e12			1.12979
$337$			4.75034e12i			1.09289i	0.837496	+	0.546443i	$0.184019\pi$
$337$			4.75034e12i			1.09289i	−0.837496	+	0.546443i	$0.815981\pi$
$338$		−	8.03345e12i		−	1.82104i
$339$		−	8.31153e11i		−	0.185645i
$340$	1.55577e12			0.342414
$341$	5.08993e12			1.10393
$342$			1.18585e12i			0.253454i
$343$	−4.93215e12			−1.03888
$344$	−4.08884e12			−0.848804
$345$		−	2.35258e11i		−	0.0481336i
$346$	−1.09693e13			−2.21206
$347$		−	2.93340e12i		−	0.583074i	−0.956560	−	0.291537i	$-0.905833\pi$
$347$		−	2.93340e12i		−	0.583074i	0.956560	−	0.291537i	$-0.0941667\pi$
$348$	4.95293e12			0.970433
$349$			9.46228e11i			0.182755i	0.995816	+	0.0913774i	$0.0291270\pi$
$349$			9.46228e11i			0.182755i	−0.995816	+	0.0913774i	$0.970873\pi$
$350$			8.94348e12i			1.70281i
$351$		−	2.75813e9i		−	0.000517701i
$352$	8.67462e12			1.60523
$353$			7.08157e12i			1.29198i	0.763346	+	0.645990i	$0.223555\pi$
$353$			7.08157e12i			1.29198i	−0.763346	+	0.645990i	$0.776445\pi$
$354$	−5.81157e12	+	6.23381e11i	−1.04539	+	0.112134i
$355$	2.36792e11			0.0419978
$356$		−	1.25250e13i		−	2.19042i
$357$	3.25801e12			0.561839
$358$	6.42081e12			1.09188
$359$	−9.87389e12			−1.65583			−0.827916	−	0.560852i	$-0.810474\pi$
$359$	−9.87389e12			−1.65583			−0.827916	+	0.560852i	$0.810474\pi$
$360$		−	7.01017e11i		−	0.115935i
$361$	−5.06218e12			−0.825661
$362$			8.14242e12i			1.30982i
$363$	−1.63155e12			−0.258862
$364$			3.80308e10i			0.00595152i
$365$			1.81219e11i			0.0279731i
$366$	4.33776e12			0.660480
$367$			5.63992e12i			0.847115i	0.905869	+	0.423557i	$0.139219\pi$
$367$			5.63992e12i			0.847115i	−0.905869	+	0.423557i	$0.860781\pi$
$368$			7.94393e12i			1.17705i
$369$	−4.26865e12			−0.623962
$370$	2.62402e12			0.378407
$371$	−6.94302e12			−0.987822
$372$			8.73849e12i			1.22665i
$373$	−1.28318e13			−1.77724			−0.888618	−	0.458648i	$-0.848334\pi$
$373$	−1.28318e13			−1.77724			−0.888618	+	0.458648i	$0.848334\pi$
$374$	1.63382e13			2.23278
$375$	1.22946e12			0.165790
$376$	3.40675e13			4.53316
$377$			1.48666e10i			0.00195212i
$378$		−	2.58336e12i		−	0.334755i
$379$	−5.10730e12			−0.653124			−0.326562	−	0.945176i	$-0.605890\pi$
$379$	−5.10730e12			−0.653124			−0.326562	+	0.945176i	$0.605890\pi$
$380$	−1.11194e12			−0.140334
$381$	−4.25882e12			−0.530475
$382$	−2.26670e13			−2.78662
$383$	−2.03408e12			−0.246816			−0.123408	−	0.992356i	$-0.539382\pi$
$383$	−2.03408e12			−0.246816			−0.123408	+	0.992356i	$0.539382\pi$
$384$		−	3.09141e12i		−	0.370254i
$385$		−	1.41096e12i		−	0.166805i
$386$		−	6.02490e12i		−	0.703094i
$387$			1.02468e12i			0.118041i
$388$			2.10854e13i			2.39786i
$389$	1.38866e13			1.55900			0.779502	−	0.626399i	$-0.215472\pi$
$389$	1.38866e13			1.55900			0.779502	+	0.626399i	$0.215472\pi$
$390$	3.70280e9			0.000410400
$391$			5.34926e12i			0.585342i
$392$		−	1.94408e12i		−	0.210032i
$393$		−	3.13674e12i		−	0.334592i
$394$		−	2.24205e13i		−	2.36137i
$395$	1.87397e12			0.194885
$396$		−	9.04844e12i		−	0.929176i
$397$			5.08486e12i			0.515616i	0.966196	+	0.257808i	$0.0830002\pi$
$397$			5.08486e12i			0.515616i	−0.966196	+	0.257808i	$0.917000\pi$
$398$			1.34303e12i			0.134484i
$399$	−2.32856e12			−0.230263
$400$	−2.05367e13			−2.00554
$401$		−	9.39192e12i		−	0.905800i	−0.891561	−	0.452900i	$-0.850389\pi$
$401$		−	9.39192e12i		−	0.905800i	0.891561	−	0.452900i	$-0.149611\pi$
$402$	−1.02786e13			−0.979044
$403$	−2.62293e10			−0.00246753
$404$			3.30169e13i			3.06781i
$405$	−1.75678e11			−0.0161229
$406$			1.39246e13i			1.26227i
$407$	1.92470e13			1.72342
$408$			1.59396e13i			1.40986i
$409$			2.20792e12i			0.192916i	0.995337	+	0.0964578i	$0.0307513\pi$
$409$			2.20792e12i			0.192916i	−0.995337	+	0.0964578i	$0.969249\pi$
$410$		−	5.73068e12i		−	0.494637i
$411$	−2.34320e11			−0.0199803
$412$		−	7.14802e12i		−	0.602143i
$413$	−1.22409e12	−	1.14118e13i	−0.101874	−	0.949735i
$414$	4.24157e12			0.348758
$415$		−	7.30982e11i		−	0.0593835i
$416$	−4.47019e10			−0.00358806
$417$	−4.10147e12			−0.325281
$418$	−1.16772e13			−0.915079
$419$			1.34513e13i			1.04158i	0.853684	+	0.520792i	$0.174363\pi$
$419$			1.34513e13i			1.04158i	−0.853684	+	0.520792i	$0.825637\pi$
$420$	2.42236e12			0.185350
$421$			9.57556e12i			0.724025i	0.932173	+	0.362013i	$0.117910\pi$
$421$			9.57556e12i			0.724025i	−0.932173	+	0.362013i	$0.882090\pi$
$422$	−4.24676e13			−3.17318
$423$		−	8.53747e12i		−	0.630417i
$424$		−	3.39683e13i		−	2.47882i
$425$	−1.38289e13			−0.997341
$426$			4.26924e12i			0.304300i
$427$			8.51774e12i			0.600047i
$428$	−2.44014e13			−1.69901
$429$	2.71597e10			0.00186913
$430$	−1.37564e12			−0.0935756
$431$			3.96460e12i			0.266571i	0.991078	+	0.133285i	$0.0425527\pi$
$431$			3.96460e12i			0.266571i	−0.991078	+	0.133285i	$0.957447\pi$
$432$	5.93211e12			0.394267
$433$	−1.24379e13			−0.817162			−0.408581	−	0.912722i	$-0.633976\pi$
$433$	−1.24379e13			−0.817162			−0.408581	+	0.912722i	$0.633976\pi$
$434$	−2.45674e13			−1.59555
$435$	9.46927e11			0.0607953
$436$			1.74427e13i			1.10709i
$437$		−	3.82322e12i		−	0.239895i
$438$	−3.26728e12			−0.202683
$439$	1.48417e13			0.910252			0.455126	−	0.890427i	$-0.349594\pi$
$439$	1.48417e13			0.910252			0.455126	+	0.890427i	$0.349594\pi$
$440$	6.90302e12			0.418577
$441$	−4.87197e11			−0.0292087
$442$	−8.41938e10			−0.00499078
$443$		−	6.54734e12i		−	0.383748i	−0.981420	−	0.191874i	$-0.938543\pi$
$443$		−	6.54734e12i		−	0.383748i	0.981420	−	0.191874i	$-0.0614565\pi$
$444$			3.30435e13i			1.91501i
$445$		−	2.39459e12i		−	0.137224i
$446$			5.22574e13i			2.96124i
$447$			4.80955e12i			0.269505i
$448$	−6.55526e12			−0.363245
$449$	−6.92776e12			−0.379631			−0.189815	−	0.981820i	$-0.560789\pi$
$449$	−6.92776e12			−0.379631			−0.189815	+	0.981820i	$0.560789\pi$
$450$			1.09653e13i			0.594236i
$451$		−	4.20340e13i		−	2.25278i
$452$			1.40513e13i			0.744773i
$453$			1.92738e13i			1.01036i
$454$	−1.49180e13			−0.773448
$455$			7.27092e9i			0.000372849i
$456$		−	1.13924e13i		−	0.577816i
$457$		−	2.41663e13i		−	1.21235i	−0.795330	−	0.606176i	$-0.792703\pi$
$457$		−	2.41663e13i		−	1.21235i	0.795330	−	0.606176i	$-0.207297\pi$
$458$	1.77078e12			0.0878695
$459$	3.99455e12			0.196067
$460$			3.97721e12i			0.193103i
$461$	−2.45000e13			−1.17669			−0.588345	−	0.808610i	$-0.700220\pi$
$461$	−2.45000e13			−1.17669			−0.588345	+	0.808610i	$0.700220\pi$
$462$	2.54388e13			1.20861
$463$		−	2.87034e13i		−	1.34905i	−0.738252	−	0.674525i	$-0.764348\pi$
$463$		−	2.87034e13i		−	1.34905i	0.738252	−	0.674525i	$-0.235652\pi$
$464$	−3.19748e13			−1.48668
$465$			1.67067e12i			0.0768468i
$466$	3.48834e13			1.58741
$467$			4.39060e11i			0.0197669i	0.999951	+	0.00988347i	$0.00314606\pi$
$467$			4.39060e11i			0.0197669i	−0.999951	+	0.00988347i	$0.996854\pi$
$468$			4.66283e10i			0.00207692i
$469$		−	2.01833e13i		−	0.889462i
$470$	1.14616e13			0.499754
$471$			3.74796e12i			0.161693i
$472$	5.58313e13	−	5.98877e12i	2.38324	−	0.255639i
$473$	−1.00902e13			−0.426181
$474$			3.37867e13i			1.41206i
$475$	9.88380e12			0.408748
$476$	−5.50792e13			−2.25400
$477$	−8.51262e12			−0.344724
$478$			7.67306e11i			0.0307489i
$479$	3.31370e13			1.31412			0.657062	−	0.753837i	$-0.271799\pi$
$479$	3.31370e13			1.31412			0.657062	+	0.753837i	$0.271799\pi$
$480$			2.84727e12i			0.111744i
$481$	−9.91831e10			−0.00385223
$482$		−	1.04756e13i		−	0.402666i
$483$			8.32886e12i			0.316847i
$484$	2.75827e13			1.03851
$485$			4.03123e12i			0.150220i
$486$		−	3.16738e12i		−	0.116820i
$487$	2.45975e12			0.0897939			0.0448970	−	0.998992i	$-0.485704\pi$
$487$	2.45975e12			0.0897939			0.0448970	+	0.998992i	$0.485704\pi$
$488$	−4.16725e13			−1.50574
$489$	−4.41230e12			−0.157805
$490$		−	6.54064e11i		−	0.0231547i
$491$	−1.84615e13			−0.646933			−0.323467	−	0.946240i	$-0.604848\pi$
$491$	−1.84615e13			−0.646933			−0.323467	+	0.946240i	$0.604848\pi$
$492$	7.21648e13			2.50322
$493$	−2.15311e13			−0.739318
$494$	6.01749e10			0.00204541
$495$		−	1.72993e12i		−	0.0582107i
$496$		−	5.64134e13i		−	1.87920i
$497$	−8.38319e12			−0.276457
$498$	1.31792e13			0.430271
$499$	3.38598e13			1.09441			0.547206	−	0.836998i	$-0.315691\pi$
$499$	3.38598e13			1.09441			0.547206	+	0.836998i	$0.315691\pi$
$500$	−2.07850e13			−0.665119
$501$	2.50350e13			0.793157
$502$		−	4.70489e13i		−	1.47581i
$503$		−	2.88342e13i		−	0.895504i	−0.894158	−	0.447752i	$-0.852225\pi$
$503$		−	2.88342e13i		−	0.895504i	0.894158	−	0.447752i	$-0.147775\pi$
$504$			2.48182e13i			0.763163i
$505$			6.31234e12i			0.192191i
$506$			4.17674e13i			1.25917i
$507$	1.93409e13			0.577346
$508$	7.19987e13			2.12817
$509$			3.13949e13i			0.918905i	0.888202	+	0.459452i	$0.151954\pi$
$509$			3.13949e13i			0.918905i	−0.888202	+	0.459452i	$0.848046\pi$
$510$			5.36270e12i			0.155429i
$511$		−	6.41573e12i		−	0.184137i
$512$			7.66287e13i			2.17792i
$513$	−2.85498e12			−0.0803556
$514$			4.22548e13i			1.17777i
$515$		−	1.36660e12i		−	0.0377228i
$516$		−	1.73230e13i		−	0.473561i
$517$	8.40698e13			2.27608
$518$	−9.28985e13			−2.49092
$519$		−	2.64090e13i		−	0.701317i
$520$	−3.55725e10			−0.000935617
$521$	4.01429e13			1.04573			0.522865	−	0.852415i	$-0.324863\pi$
$521$	4.01429e13			1.04573			0.522865	+	0.852415i	$0.324863\pi$
$522$			1.70726e13i			0.440500i
$523$	−4.64938e13			−1.18819			−0.594095	−	0.804395i	$-0.702490\pi$
$523$	−4.64938e13			−1.18819			−0.594095	+	0.804395i	$0.702490\pi$
$524$			5.30291e13i			1.34232i
$525$	−2.15318e13			−0.539863
$526$		−	2.75191e12i		−	0.0683448i
$527$		−	3.79875e13i		−	0.934517i
$528$			5.84144e13i			1.42348i
$529$	2.77516e13			0.669898
$530$		−	1.14282e13i		−	0.273275i
$531$	−1.50081e12	−	1.39916e13i	−0.0355512	−	0.331432i
$532$	3.93662e13			0.923772
$533$			2.16609e11i			0.00503548i
$534$	4.31732e13			0.994278
$535$	−4.66519e12			−0.106439
$536$	9.87454e13			2.23199
$537$			1.54584e13i			0.346172i
$538$	4.37831e13			0.971393
$539$		−	4.79750e12i		−	0.105456i
$540$	2.96998e12			0.0646821
$541$			3.31324e13i			0.714934i	0.933926	+	0.357467i	$0.116360\pi$
$541$			3.31324e13i			0.714934i	−0.933926	+	0.357467i	$0.883640\pi$
$542$			6.65772e13i			1.42341i
$543$	−1.96032e13			−0.415268
$544$		−	6.47409e13i		−	1.35889i
$545$			3.33480e12i			0.0693565i
$546$	−1.31091e11			−0.00270152
$547$	−5.13121e13			−1.04781			−0.523906	−	0.851776i	$-0.675526\pi$
$547$	−5.13121e13			−1.04781			−0.523906	+	0.851776i	$0.675526\pi$
$548$	3.96137e12			0.0801572
$549$			1.04433e13i			0.209400i
$550$	−1.07977e14			−2.14545
$551$	1.53887e13			0.303001
$552$	−4.07484e13			−0.795088
$553$	−6.63445e13			−1.28286
$554$			1.20499e14i			2.30906i
$555$			6.31744e12i			0.119971i
$556$	6.93385e13			1.30497
$557$	7.43485e13			1.38674			0.693372	−	0.720580i	$-0.256124\pi$
$557$	7.43485e13			1.38674			0.693372	+	0.720580i	$0.256124\pi$
$558$	−3.01213e13			−0.556804
$559$	5.19967e10			0.000952613
$560$	−1.56381e13			−0.283952
$561$			3.93349e13i			0.707887i
$562$		−	1.82273e14i		−	3.25117i
$563$		−	8.25542e12i		−	0.145948i	−0.997334	−	0.0729738i	$-0.976751\pi$
$563$		−	8.25542e12i		−	0.145948i	0.997334	−	0.0729738i	$-0.0232490\pi$
$564$			1.44333e14i			2.52912i
$565$			2.68640e12i			0.0466582i
$566$	−2.34030e13			−0.402893
$567$	6.21955e12			0.106131
$568$		−	4.10142e13i		−	0.693734i
$569$		−	2.89565e13i		−	0.485495i	−0.970089	−	0.242748i	$-0.921951\pi$
$569$		−	2.89565e13i		−	0.485495i	0.970089	−	0.242748i	$-0.0780487\pi$
$570$		−	3.83282e12i		−	0.0637007i
$571$			8.69719e12i			0.143284i	0.997430	+	0.0716421i	$0.0228240\pi$
$571$			8.69719e12i			0.143284i	−0.997430	+	0.0716421i	$0.977176\pi$
$572$	−4.59156e11			−0.00749860
$573$		−	5.45718e13i		−	0.883476i
$574$			2.02884e14i			3.25603i
$575$		−	3.53526e13i		−	0.562447i
$576$	−8.03719e12			−0.126763
$577$	6.26532e12			0.0979635			0.0489818	−	0.998800i	$-0.484402\pi$
$577$	6.26532e12			0.0979635			0.0489818	+	0.998800i	$0.484402\pi$
$578$		−	4.45698e12i		−	0.0690878i
$579$	1.45052e13			0.222911
$580$	−1.60085e13			−0.243900
$581$			2.58790e13i			0.390901i
$582$	−7.26808e13			−1.08844
$583$		−	8.38250e13i		−	1.24460i
$584$	3.13886e13			0.462069
$585$			8.91465e9i			0.000130114i
$586$			2.12820e14i			3.07982i
$587$		−	3.89264e13i		−	0.558539i	−0.960213	−	0.279270i	$-0.909908\pi$
$587$		−	3.89264e13i		−	0.558539i	0.960213	−	0.279270i	$-0.0900923\pi$
$588$	8.23644e12			0.117180
$589$			2.71504e13i			0.383000i
$590$	1.87838e13	−	2.01485e12i	0.262738	−	0.0281827i
$591$	5.39784e13			0.748656
$592$		−	2.13320e14i		−	2.93376i
$593$	3.62556e13			0.494426			0.247213	−	0.968961i	$-0.420485\pi$
$593$	3.62556e13			0.494426			0.247213	+	0.968961i	$0.420485\pi$
$594$	3.11897e13			0.421773
$595$	−1.05303e13			−0.141207
$596$		−	8.13091e13i		−	1.08120i
$597$	−3.23341e12			−0.0426373
$598$		−	2.15235e11i		−	0.00281454i
$599$	−8.15328e12			−0.105730			−0.0528650	−	0.998602i	$-0.516835\pi$
$599$	−8.15328e12			−0.105730			−0.0528650	+	0.998602i	$0.516835\pi$
$600$		−	1.05343e14i		−	1.35472i
$601$			7.92561e12i			0.101079i	0.998722	+	0.0505394i	$0.0160941\pi$
$601$			7.92561e12i			0.101079i	−0.998722	+	0.0505394i	$0.983906\pi$
$602$	4.87020e13			0.615976
$603$		−	2.47461e13i		−	0.310399i
$604$		−	3.25839e14i		−	4.05338i
$605$	5.27340e12			0.0650600
$606$	−1.13808e14			−1.39255
$607$	3.53230e13			0.428661			0.214331	−	0.976761i	$-0.431243\pi$
$607$	3.53230e13			0.428661			0.214331	+	0.976761i	$0.431243\pi$
$608$			4.62716e13i			0.556925i
$609$	−3.35242e13			−0.400195
$610$	−1.40202e13			−0.165999
$611$	−4.33227e11			−0.00508756
$612$	−6.75309e13			−0.786584
$613$		−	7.66908e13i		−	0.886015i	−0.896518	−	0.443007i	$-0.853912\pi$
$613$		−	7.66908e13i		−	0.886015i	0.896518	−	0.443007i	$-0.146088\pi$
$614$			5.45220e13i			0.624784i
$615$	1.37968e13			0.156821
$616$	−2.44388e14			−2.75535
$617$	7.45415e13			0.833628			0.416814	−	0.908992i	$-0.363147\pi$
$617$	7.45415e13			0.833628			0.416814	+	0.908992i	$0.363147\pi$
$618$	2.46390e13			0.273326
$619$	1.57891e14			1.73741			0.868707	−	0.495327i	$-0.164952\pi$
$619$	1.57891e14			1.73741			0.868707	+	0.495327i	$0.164952\pi$
$620$		−	2.82440e13i		−	0.308296i
$621$			1.02117e13i			0.110571i
$622$			2.14972e14i			2.30903i
$623$			8.47760e13i			0.903302i
$624$		−	3.01020e11i		−	0.00318180i
$625$	8.93856e13			0.937276
$626$	2.53051e14			2.63231
$627$		−	2.81134e13i		−	0.290119i
$628$		−	6.33622e13i		−	0.648682i
$629$		−	1.43645e14i		−	1.45894i
$630$			8.34978e12i			0.0841342i
$631$	−1.06377e13			−0.106341			−0.0531703	−	0.998585i	$-0.516933\pi$
$631$	−1.06377e13			−0.106341			−0.0531703	+	0.998585i	$0.516933\pi$
$632$		−	3.24586e14i		−	3.21918i
$633$		−	1.02242e14i		−	1.00603i
$634$			1.32202e14i			1.29060i
$635$	1.37651e13			0.133325
$636$	1.43912e14			1.38297
$637$			2.47224e10i			0.000235718i
$638$	−1.68116e14			−1.59040
$639$	−1.02784e13			−0.0964761
$640$			9.99185e12i			0.0930564i
$641$	1.97871e14			1.82849			0.914245	−	0.405163i	$-0.132785\pi$
$641$	1.97871e14			1.82849			0.914245	+	0.405163i	$0.132785\pi$
$642$		−	8.41109e13i		−	0.771218i
$643$	−6.34533e13			−0.577297			−0.288648	−	0.957435i	$-0.593206\pi$
$643$	−6.34533e13			−0.577297			−0.288648	+	0.957435i	$0.593206\pi$
$644$		−	1.40806e14i		−	1.27113i
$645$		−	3.31191e12i		−	0.0296674i
$646$			8.71502e13i			0.774650i
$647$	1.30597e14			1.15189			0.575947	−	0.817487i	$-0.304633\pi$
$647$	1.30597e14			1.15189			0.575947	+	0.817487i	$0.304633\pi$
$648$			3.04288e13i			0.266324i
$649$	1.37777e14	−	1.47787e13i	1.19661	−	0.128355i
$650$	5.56426e11			0.00479558
$651$		−	5.91469e13i		−	0.505856i
$652$	7.45934e13			0.633085
$653$	−1.54474e14			−1.30104			−0.650519	−	0.759490i	$-0.725449\pi$
$653$	−1.54474e14			−1.30104			−0.650519	+	0.759490i	$0.725449\pi$
$654$	−6.01245e13			−0.502531
$655$			1.01384e13i			0.0840934i
$656$	−4.65877e14			−3.83488
$657$		−	7.86612e12i		−	0.0642590i
$658$	−4.05776e14			−3.28971
$659$			1.03024e14i			0.828915i	0.910069	+	0.414458i	$0.136029\pi$
$659$			1.03024e14i			0.828915i	−0.910069	+	0.414458i	$0.863971\pi$
$660$			2.92458e13i			0.233531i
$661$	−8.55031e13			−0.677602			−0.338801	−	0.940858i	$-0.610021\pi$
$661$	−8.55031e13			−0.677602			−0.338801	+	0.940858i	$0.610021\pi$
$662$		−	4.33013e14i		−	3.40574i
$663$		−	2.02700e11i		−	0.00158229i
$664$	−1.26612e14			−0.980918
$665$	7.52623e12			0.0578721
$666$	−1.13900e14			−0.869265
$667$		−	5.50425e13i		−	0.416936i
$668$	−4.23236e14			−3.18200
$669$	−1.25812e14			−0.938838
$670$	3.32217e13			0.246064
$671$	−1.02837e14			−0.756027
$672$		−	1.00802e14i		−	0.735571i
$673$		−	3.05917e13i		−	0.221579i	−0.993844	−	0.110790i	$-0.964662\pi$
$673$		−	3.05917e13i		−	0.221579i	0.993844	−	0.110790i	$-0.0353379\pi$
$674$	2.76819e14			1.99020
$675$	−2.63995e13			−0.188398
$676$	−3.26972e14			−2.31621
$677$	8.09365e13			0.569116			0.284558	−	0.958659i	$-0.408153\pi$
$677$	8.09365e13			0.569116			0.284558	+	0.958659i	$0.408153\pi$
$678$	−4.84343e13			−0.338068
$679$		−	1.42718e14i		−	0.988848i
$680$		−	5.15190e13i		−	0.354342i
$681$		−	3.59157e13i		−	0.245216i
$682$		−	2.96609e14i		−	2.01031i
$683$			4.74853e13i			0.319489i	0.987158	+	0.159744i	$0.0510670\pi$
$683$			4.74853e13i			0.319489i	−0.987158	+	0.159744i	$0.948933\pi$
$684$	4.82656e13			0.322372
$685$	7.57355e11			0.00502166
$686$			2.87414e14i			1.89186i
$687$			4.26323e12i			0.0278584i
$688$			1.11833e14i			0.725484i
$689$			4.31966e11i			0.00278197i
$690$	−1.37093e13			−0.0876537
$691$			2.57228e14i			1.63278i	0.577500	+	0.816391i	$0.304028\pi$
$691$			2.57228e14i			1.63278i	−0.577500	+	0.816391i	$0.695972\pi$
$692$			4.46464e14i			2.81356i
$693$			6.12449e13i			0.383181i
$694$	−1.70940e14			−1.06181
$695$	1.32565e13			0.0817533
$696$		−	1.64015e14i		−	1.00424i
$697$	−3.13711e14			−1.90706
$698$	5.51401e13			0.332806
$699$			8.39833e13i			0.503277i
$700$	3.64012e14			2.16583
$701$		−	4.15156e13i		−	0.245257i	−0.992453	−	0.122628i	$-0.960868\pi$
$701$		−	4.15156e13i		−	0.245257i	0.992453	−	0.122628i	$-0.0391323\pi$
$702$	−1.60726e11			−0.000942759
$703$			1.02666e14i			0.597929i
$704$		−	7.91434e13i		−	0.457669i
$705$			2.75943e13i			0.158443i
$706$	4.12668e14			2.35276
$707$		−	2.23477e14i		−	1.26513i
$708$	2.53724e13	+	2.36539e14i	0.142625	+	1.32965i
$709$	−2.09515e14			−1.16946			−0.584729	−	0.811229i	$-0.698799\pi$
$709$	−2.09515e14			−1.16946			−0.584729	+	0.811229i	$0.698799\pi$
$710$		−	1.37988e13i		−	0.0764800i
$711$	−8.13428e13			−0.447684
$712$	−4.14761e14			−2.26672
$713$	9.71120e13			0.527018
$714$		−	1.89856e14i		−	1.02314i
$715$	−8.77839e10			−0.000469769
$716$		−	2.61336e14i		−	1.38878i
$717$	−1.84732e12			−0.00974869
$718$			5.75387e14i			3.01535i
$719$		−	1.97557e14i		−	1.02813i	−0.857752	−	0.514064i	$-0.828139\pi$
$719$		−	1.97557e14i		−	1.02813i	0.857752	−	0.514064i	$-0.171861\pi$
$720$	−1.91734e13			−0.0990915
$721$			4.83818e13i			0.248317i
$722$			2.94991e14i			1.50357i
$723$	2.52205e13			0.127662
$724$	3.31408e14			1.66598
$725$	1.42296e14			0.710401
$726$			9.50765e13i			0.471400i
$727$	2.12601e14			1.04687			0.523435	−	0.852066i	$-0.324650\pi$
$727$	2.12601e14			1.04687			0.523435	+	0.852066i	$0.324650\pi$
$728$	1.25938e12			0.00615885
$729$	7.62560e12			0.0370370
$730$	1.05603e13			0.0509404
$731$			7.53058e13i			0.360779i
$732$		−	1.76553e14i		−	0.840076i
$733$	2.62897e14			1.24241			0.621207	−	0.783646i	$-0.286642\pi$
$733$	2.62897e14			1.24241			0.621207	+	0.783646i	$0.286642\pi$
$734$	3.28658e14			1.54264
$735$	1.57469e12			0.00734104
$736$	1.65505e14			0.766342
$737$	2.43678e14			1.12067
$738$			2.48749e14i			1.13627i
$739$		−	4.13594e14i		−	1.87651i	−0.345939	−	0.938257i	$-0.612440\pi$
$739$		−	4.13594e14i		−	1.87651i	0.345939	−	0.938257i	$-0.387560\pi$
$740$		−	1.06801e14i		−	0.481302i
$741$			1.44874e11i			0.000648482i
$742$			4.04595e14i			1.79887i
$743$	1.23128e14			0.543768			0.271884	−	0.962330i	$-0.412353\pi$
$743$	1.23128e14			0.543768			0.271884	+	0.962330i	$0.412353\pi$
$744$	2.89373e14			1.26938
$745$		−	1.55451e13i		−	0.0677349i
$746$			7.47758e14i			3.23644i
$747$			3.17295e13i			0.136414i
$748$		−	6.64987e14i		−	2.83991i
$749$	1.65162e14			0.700652
$750$		−	7.16451e13i		−	0.301912i
$751$			8.48640e13i			0.355241i	0.984099	+	0.177621i	$0.0568400\pi$
$751$			8.48640e13i			0.355241i	−0.984099	+	0.177621i	$0.943160\pi$
$752$		−	9.31774e14i		−	3.87455i
$753$	1.13272e14			0.467895
$754$	8.66333e11			0.00355491
$755$		−	6.22955e13i		−	0.253935i
$756$	−1.05146e14			−0.425780
$757$	8.05195e13			0.323908			0.161954	−	0.986798i	$-0.448220\pi$
$757$	8.05195e13			0.323908			0.161954	+	0.986798i	$0.448220\pi$
$758$			2.97621e14i			1.18937i
$759$	−1.00557e14			−0.399210
$760$			3.68216e13i			0.145223i
$761$	4.06457e14			1.59254			0.796272	−	0.604938i	$-0.206802\pi$
$761$	4.06457e14			1.59254			0.796272	+	0.604938i	$0.206802\pi$
$762$			2.48177e14i			0.966021i
$763$		−	1.18062e14i		−	0.456550i
$764$			9.22578e14i			3.54435i
$765$	−1.29109e13			−0.0492776
$766$			1.18533e14i			0.449464i
$767$	−7.09992e11	+	7.61576e10i	−0.00267471	+	0.000286904i
$768$	−2.38810e14			−0.893812
$769$		−	4.75763e13i		−	0.176913i	−0.996080	−	0.0884563i	$-0.971807\pi$
$769$		−	4.75763e13i		−	0.176913i	0.996080	−	0.0884563i	$-0.0281934\pi$
$770$	−8.22216e13			−0.303761
$771$	−1.01730e14			−0.373403
$772$	−2.45221e14			−0.894277
$773$			3.40471e13i			0.123362i	0.998096	+	0.0616811i	$0.0196462\pi$
$773$			3.40471e13i			0.123362i	−0.998096	+	0.0616811i	$0.980354\pi$
$774$	5.97119e13			0.214959
$775$			2.51054e14i			0.897965i
$776$	6.98239e14			2.48139
$777$		−	2.23657e14i		−	0.789728i
$778$		−	8.09222e14i		−	2.83903i
$779$	2.24215e14			0.781587
$780$		−	1.50709e11i		−	0.000521995i
$781$		−	1.01213e14i		−	0.348321i
$782$	3.11721e14			1.06594
$783$	−4.11029e13			−0.139657
$784$	−5.31723e13			−0.179517
$785$		−	1.21139e13i		−	0.0406384i
$786$	−1.82789e14			−0.609310
$787$	−2.52016e14			−0.834745			−0.417372	−	0.908736i	$-0.637049\pi$
$787$	−2.52016e14			−0.834745			−0.417372	+	0.908736i	$0.637049\pi$
$788$	−9.12546e14			−3.00347
$789$	6.62534e12			0.0216682
$790$		−	1.09203e14i		−	0.354895i
$791$		−	9.51069e13i		−	0.307135i
$792$	−2.99637e14			−0.961544
$793$	5.29938e11			0.00168989
$794$	2.96313e14			0.938963
$795$	2.75139e13			0.0866397
$796$	5.46633e13			0.171053
$797$		−	2.64907e14i		−	0.823762i	−0.911238	−	0.411881i	$-0.864872\pi$
$797$		−	2.64907e14i		−	0.823762i	0.911238	−	0.411881i	$-0.135128\pi$
$798$			1.35694e14i			0.419320i
$799$		−	6.27435e14i		−	1.92679i
$800$			4.27865e14i			1.30574i
$801$			1.03941e14i			0.315228i
$802$	−5.47301e14			−1.64951
$803$	7.74589e13			0.232003
$804$			4.18352e14i			1.24526i
$805$		−	2.69200e13i		−	0.0796335i
$806$			1.52848e12i			0.00449349i
$807$			1.05410e14i			0.307973i
$808$	1.09335e15			3.17468
$809$		−	3.41795e14i		−	0.986333i	−0.869935	−	0.493166i	$-0.835839\pi$
$809$		−	3.41795e14i		−	0.986333i	0.869935	−	0.493166i	$-0.164161\pi$
$810$			1.02374e13i			0.0293606i
$811$		−	1.51189e14i		−	0.430939i	−0.976511	−	0.215470i	$-0.930872\pi$
$811$		−	1.51189e14i		−	0.430939i	0.976511	−	0.215470i	$-0.0691282\pi$
$812$	5.66752e14			1.60551
$813$	−1.60287e14			−0.451280
$814$		−	1.12159e15i		−	3.13843i
$815$	1.42612e13			0.0396613
$816$	4.35962e14			1.20503
$817$		−	5.38225e13i		−	0.147861i
$818$	1.28664e14			0.351309
$819$		−	3.15606e11i		−	0.000856497i
$820$	−2.33246e14			−0.629138
$821$			6.50259e14i			1.74329i	0.490135	+	0.871646i	$0.336947\pi$
$821$			6.50259e14i			1.74329i	−0.490135	+	0.871646i	$0.663053\pi$
$822$			1.36547e13i			0.0363851i
$823$		−	1.01778e14i		−	0.269559i	−0.990876	−	0.134779i	$-0.956967\pi$
$823$		−	1.01778e14i		−	0.269559i	0.990876	−	0.134779i	$-0.0430325\pi$
$824$	−2.36705e14			−0.623119
$825$		−	2.59959e14i		−	0.680199i
$826$	−6.65004e14	+	7.13320e13i	−1.72951	+	0.185517i
$827$	−3.45495e14			−0.893129			−0.446564	−	0.894751i	$-0.647353\pi$
$827$	−3.45495e14			−0.893129			−0.446564	+	0.894751i	$0.647353\pi$
$828$		−	1.72637e14i		−	0.443592i
$829$	3.04468e14			0.777623			0.388811	−	0.921317i	$-0.372886\pi$
$829$	3.04468e14			0.777623			0.388811	+	0.921317i	$0.372886\pi$
$830$	−4.25969e13			−0.108140
$831$	−2.90106e14			−0.732069
$832$			4.07841e11i			0.00102300i
$833$	−3.58050e13			−0.0892727
$834$			2.39008e14i			0.592354i
$835$	−8.09166e13			−0.199345
$836$			4.75279e14i			1.16390i
$837$		−	7.25182e13i		−	0.176530i
$838$	7.83856e14			1.89678
$839$			7.45091e13i			0.179225i	0.995977	+	0.0896126i	$0.0285629\pi$
$839$			7.45091e13i			0.179225i	−0.995977	+	0.0896126i	$0.971437\pi$
$840$		−	8.02157e13i		−	0.191806i
$841$	−1.99158e14			−0.473388
$842$	5.58003e14			1.31849
$843$	4.38829e14			1.03076
$844$			1.72849e15i			4.03603i
$845$	−6.25123e13			−0.145105
$846$	−4.97509e14			−1.14802
$847$	−1.86695e14			−0.428267
$848$	−9.29061e14			−2.11868
$849$		−	5.63437e13i		−	0.127734i
$850$			8.05861e14i			1.81621i
$851$	3.67217e14			0.822764
$852$	1.73764e14			0.387045
$853$	−4.34487e14			−0.962125			−0.481062	−	0.876686i	$-0.659749\pi$
$853$	−4.34487e14			−0.962125			−0.481062	+	0.876686i	$0.659749\pi$
$854$	4.96359e14			1.09272
$855$	9.22768e12			0.0201958
$856$			8.08047e14i			1.75820i
$857$		−	1.13827e14i		−	0.246229i	−0.992392	−	0.123115i	$-0.960712\pi$
$857$		−	1.13827e14i		−	0.246229i	0.992392	−	0.123115i	$-0.0392883\pi$
$858$		−	1.58269e12i		−	0.00340377i
$859$			9.07308e14i			1.93994i	0.243221	+	0.969971i	$0.421796\pi$
$859$			9.07308e14i			1.93994i	−0.243221	+	0.969971i	$0.578204\pi$
$860$			5.59904e13i			0.119020i
$861$	−4.88451e14			−1.03230
$862$	2.31031e14			0.485439
$863$			5.15222e14i			1.07632i	0.842844	+	0.538158i	$0.180880\pi$
$863$			5.15222e14i			1.07632i	−0.842844	+	0.538158i	$0.819120\pi$
$864$		−	1.23591e14i		−	0.256695i
$865$			8.53573e13i			0.176263i
$866$			7.24803e14i			1.48809i
$867$	1.07304e13			0.0219038
$868$			9.99925e14i			2.02940i
$869$		−	8.00995e14i		−	1.61633i
$870$		−	5.51808e13i		−	0.110711i
$871$	−1.25572e12			−0.00250497
$872$	5.77612e14			1.14565
$873$		−	1.74982e14i		−	0.345082i
$874$	−2.22793e14			−0.436861
$875$	1.40684e14			0.274287
$876$			1.32983e14i			0.257795i
$877$	−5.12074e14			−0.987041			−0.493520	−	0.869734i	$-0.664290\pi$
$877$	−5.12074e14			−0.987041			−0.493520	+	0.869734i	$0.664290\pi$
$878$		−	8.64881e14i		−	1.65762i
$879$	−5.12373e14			−0.976432
$880$		−	1.88803e14i		−	0.357764i
$881$			2.22749e14i			0.419698i	0.977734	+	0.209849i	$0.0672972\pi$
$881$			2.22749e14i			0.419698i	−0.977734	+	0.209849i	$0.932703\pi$
$882$			2.83907e13i			0.0531904i
$883$	1.94880e14			0.363048			0.181524	−	0.983387i	$-0.441897\pi$
$883$	1.94880e14			0.363048			0.181524	+	0.983387i	$0.441897\pi$
$884$			3.42680e12i			0.00634786i
$885$	4.85084e12	+	4.52227e13i	0.00893512	+	0.0832991i
$886$	−3.81537e14			−0.698825
$887$		−	7.94886e14i		−	1.44773i	−0.689943	−	0.723864i	$-0.742364\pi$
$887$		−	7.94886e14i		−	1.44773i	0.689943	−	0.723864i	$-0.257636\pi$
$888$	1.09423e15			1.98172
$889$	−4.87327e14			−0.877631
$890$	−1.39542e14			−0.249893
$891$			7.50904e13i			0.133720i
$892$	2.12695e15			3.76645
$893$			4.48440e14i			0.789672i
$894$	2.80270e14			0.490782
$895$		−	4.99635e13i		−	0.0870038i
$896$		−	3.53743e14i		−	0.612558i
$897$	5.18187e11			0.000892327
$898$			4.03706e14i			0.691327i
$899$			3.90882e14i			0.665652i
$900$	4.46303e14			0.755818
$901$	−6.25608e14			−1.05361
$902$	−2.44947e15			−4.10242
$903$			1.17252e14i			0.195291i
$904$	4.65305e14			0.770717
$905$	6.33603e13			0.104370
$906$	1.12315e15			1.83992
$907$	5.33074e13			0.0868463			0.0434231	−	0.999057i	$-0.486174\pi$
$907$	5.33074e13			0.0868463			0.0434231	+	0.999057i	$0.486174\pi$
$908$			6.07182e14i			0.983762i
$909$		−	2.73997e14i		−	0.441496i
$910$	4.23703e11			0.000678976
$911$	−7.35383e14			−1.17198			−0.585992	−	0.810317i	$-0.699295\pi$
$911$	−7.35383e14			−1.17198			−0.585992	+	0.810317i	$0.699295\pi$
$912$	−3.11590e14			−0.493867
$913$	−3.12445e14			−0.492515
$914$	−1.40826e15			−2.20775
$915$		−	3.37543e13i		−	0.0526288i
$916$		−	7.20733e13i		−	0.111763i
$917$		−	3.58930e14i		−	0.553558i
$918$		−	2.32777e14i		−	0.357047i
$919$		−	3.60374e14i		−	0.549764i	−0.961478	−	0.274882i	$-0.911361\pi$
$919$		−	3.60374e14i		−	0.549764i	0.961478	−	0.274882i	$-0.0886388\pi$
$920$	1.31704e14			0.199830
$921$	−1.31264e14			−0.198083
$922$			1.42771e15i			2.14281i
$923$			5.21567e11i			0.000778577i
$924$		−	1.03539e15i		−	1.53725i
$925$			9.49332e14i			1.40188i
$926$	−1.67265e15			−2.45669
$927$			5.93194e13i			0.0866558i
$928$			6.66168e14i			0.967930i
$929$			7.53601e14i			1.08909i	0.838732	+	0.544544i	$0.183297\pi$
$929$			7.53601e14i			1.08909i	−0.838732	+	0.544544i	$0.816703\pi$
$930$	9.73560e13			0.139942
$931$	2.55905e13			0.0365873
$932$		−	1.41980e15i		−	2.01906i
$933$	−5.17553e14			−0.732060
$934$	2.55856e13			0.0359966
$935$		−	1.27136e14i		−	0.177914i
$936$	1.54408e12			0.00214927
$937$			2.70760e14i			0.374874i	0.982277	+	0.187437i	$0.0600181\pi$
$937$			2.70760e14i			0.374874i	−0.982277	+	0.187437i	$0.939982\pi$
$938$	−1.17615e15			−1.61976
$939$			6.09231e14i			0.834553i
$940$		−	4.66503e14i		−	0.635645i
$941$			1.26333e15i			1.71226i	0.516758	+	0.856131i	$0.327139\pi$
$941$			1.26333e15i			1.71226i	−0.516758	+	0.856131i	$0.672861\pi$
$942$	2.18407e14			0.294451
$943$		−	8.01977e14i		−	1.07548i
$944$	−1.63798e14	−	1.52703e15i	−0.218498	−	2.03699i
$945$	−2.01024e13			−0.0266741
$946$			5.87992e14i			0.776097i
$947$	−7.08836e14			−0.930670			−0.465335	−	0.885135i	$-0.654066\pi$
$947$	−7.08836e14			−0.930670			−0.465335	+	0.885135i	$0.654066\pi$
$948$	1.37516e15			1.79603
$949$	−3.99160e11			−0.000518580
$950$		−	5.75965e14i		−	0.744351i
$951$	−3.18283e14			−0.409176
$952$			1.82393e15i			2.33251i
$953$	−1.15488e15			−1.46917			−0.734583	−	0.678519i	$-0.762622\pi$
$953$	−1.15488e15			−1.46917			−0.734583	+	0.678519i	$0.762622\pi$
$954$			4.96061e14i			0.627759i
$955$			1.76383e14i			0.222045i
$956$	3.12304e13			0.0391100
$957$		−	4.04746e14i		−	0.504224i
$958$		−	1.93102e15i		−	2.39309i
$959$	−2.68127e13			−0.0330558
$960$	2.59773e13			0.0318594
$961$	1.29992e14			0.158599
$962$			5.77976e12i			0.00701511i
$963$	2.02500e14			0.244509
$964$	−4.26372e14			−0.512158
$965$	−4.68827e13			−0.0560243
$966$	4.85353e14			0.576995
$967$		−	2.41949e13i		−	0.0286149i	−0.999898	−	0.0143074i	$-0.995446\pi$
$967$		−	2.41949e13i		−	0.0286149i	0.999898	−	0.0143074i	$-0.00455436\pi$
$968$		−	9.13392e14i		−	1.07468i
$969$	−2.09818e14			−0.245597
$970$	2.34914e14			0.273559
$971$	−6.41959e14			−0.743723			−0.371862	−	0.928288i	$-0.621280\pi$
$971$	−6.41959e14			−0.743723			−0.371862	+	0.928288i	$0.621280\pi$
$972$	−1.28917e14			−0.148586
$973$	−4.69322e14			−0.538154
$974$		−	1.43339e14i		−	0.163519i
$975$			1.33962e12i			0.00152040i
$976$			1.13978e15i			1.28698i
$977$		−	6.76743e14i		−	0.760241i	−0.924937	−	0.380120i	$-0.875883\pi$
$977$		−	6.76743e14i		−	0.760241i	0.924937	−	0.380120i	$-0.124117\pi$
$978$			2.57121e14i			0.287371i
$979$	−1.02352e15			−1.13811
$980$	−2.66213e13			−0.0294509
$981$		−	1.44752e14i		−	0.159324i
$982$			1.07582e15i			1.17810i
$983$		−	1.30915e15i		−	1.42634i	−0.700991	−	0.713170i	$-0.747259\pi$
$983$		−	1.30915e15i		−	1.42634i	0.700991	−	0.713170i	$-0.252741\pi$
$984$		−	2.38972e15i		−	2.59043i
$985$	−1.74465e14			−0.188160
$986$			1.25469e15i			1.34634i
$987$		−	9.76923e14i		−	1.04298i
$988$		−	2.44920e12i		−	0.00260159i
$989$	−1.92513e14			−0.203460
$990$	−1.00809e14			−0.106005
$991$		−	5.68858e14i		−	0.595162i	−0.954697	−	0.297581i	$-0.903820\pi$
$991$		−	5.68858e14i		−	0.595162i	0.954697	−	0.297581i	$-0.0961799\pi$
$992$	−1.17533e15			−1.22349
$993$	1.04250e15			1.07976
$994$			4.88519e14i			0.503442i
$995$	1.04508e13			0.0107161
$996$		−	5.36411e14i		−	0.547269i
$997$	1.45061e14			0.147257			0.0736283	−	0.997286i	$-0.476542\pi$
$997$	1.45061e14			0.147257			0.0736283	+	0.997286i	$0.476542\pi$
$998$		−	1.97313e15i		−	1.99298i
$999$		−	2.74219e14i		−	0.275594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.6	✓	100
59.58	odd	2	inner	177.11.c.a.58.95	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.6	✓	100	1.1	even	1	trivial
177.11.c.a.58.95	yes	100	59.58	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-58.2736i q^{2} +140.296 q^{3} -2371.81 q^{4} -453.456 q^{5} -8175.56i q^{6} +16053.8 q^{7} +78542.0i q^{8} +19683.0 q^{9} +26424.5i q^{10} +193821. i q^{11} -332756. q^{12} -998.798i q^{13} -935510. i q^{14} -63618.1 q^{15} +2.14819e6 q^{16} +1.44654e6 q^{17} -1.14700e6i q^{18} -1.03387e6 q^{19} +1.07551e6 q^{20} +2.25228e6 q^{21} +1.12947e7 q^{22} +3.69797e6i q^{23} +1.10191e7i q^{24} -9.56000e6 q^{25} -58203.6 q^{26} +2.76145e6 q^{27} -3.80765e7 q^{28} -1.48845e7 q^{29} +3.70726e6i q^{30} -2.62609e7i q^{31} -4.47557e7i q^{32} +2.71924e7i q^{33} -8.42951e7i q^{34} -7.27967e6 q^{35} -4.66844e7 q^{36} -9.93025e7i q^{37} +6.02473e7i q^{38} -140127. i q^{39} -3.56153e7i q^{40} -2.16870e8 q^{41} -1.31248e8i q^{42} +5.20592e7i q^{43} -4.59709e8i q^{44} -8.92538e6 q^{45} +2.15494e8 q^{46} -4.33749e8i q^{47} +3.01383e8 q^{48} -2.47522e7 q^{49} +5.57096e8i q^{50} +2.02944e8 q^{51} +2.36896e6i q^{52} -4.32486e8 q^{53} -1.60920e8i q^{54} -8.78895e7i q^{55} +1.26089e9i q^{56} -1.45048e8 q^{57} +8.67376e8i q^{58} +(-7.62493e7 - 7.10847e8i) q^{59} +1.50890e8 q^{60} +5.30576e8i q^{61} -1.53032e9 q^{62} +3.15986e8 q^{63} -4.08332e8 q^{64} +452911. i q^{65} +1.58460e9 q^{66} -1.25723e9i q^{67} -3.43092e9 q^{68} +5.18810e8i q^{69} +4.24213e8i q^{70} -5.22195e8 q^{71} +1.54594e9i q^{72} -3.99640e8i q^{73} -5.78672e9 q^{74} -1.34123e9 q^{75} +2.45215e9 q^{76} +3.11156e9i q^{77} -8.16573e6 q^{78} -4.13264e9 q^{79} -9.74109e8 q^{80} +3.87420e8 q^{81} +1.26378e10i q^{82} +1.61202e9i q^{83} -5.34199e9 q^{84} -6.55942e8 q^{85} +3.03368e9 q^{86} -2.08824e9 q^{87} -1.52231e10 q^{88} +5.28076e9i q^{89} +5.20114e8i q^{90} -1.60345e7i q^{91} -8.77089e9i q^{92} -3.68430e9i q^{93} -2.52761e10 q^{94} +4.68815e8 q^{95} -6.27905e9i q^{96} -8.89000e9i q^{97} +1.44240e9i q^{98} +3.81499e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

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Database

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