LMFDB - Embedded newform 177.11.c.a.58.15

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			58.15
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.86

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +58292.2i q^{10} -33949.7i q^{11} +180483. q^{12} -413622. i q^{13} +203835. i q^{14} +170141. q^{15} -710959. q^{16} -2.03662e6 q^{17} -946104. i q^{18} +946849. q^{19} +1.56010e6 q^{20} +594944. q^{21} -1.63186e6 q^{22} +2.44743e6i q^{23} -1.76981e6i q^{24} -8.29492e6 q^{25} -1.98816e7 q^{26} -2.76145e6 q^{27} +5.45533e6 q^{28} -1.24602e7 q^{29} -8.17817e6i q^{30} +3.60531e7i q^{31} +4.70913e7i q^{32} +4.76302e6i q^{33} +9.78945e7i q^{34} +5.14273e6 q^{35} -2.53210e7 q^{36} -1.04163e8i q^{37} -4.55123e7i q^{38} +5.80296e7i q^{39} -1.52984e7i q^{40} +2.63018e7 q^{41} -2.85972e7i q^{42} +1.45679e8i q^{43} +4.36744e7i q^{44} -2.38701e7 q^{45} +1.17641e8 q^{46} +2.23833e8i q^{47} +9.97448e7 q^{48} -2.64492e8 q^{49} +3.98712e8i q^{50} +2.85730e8 q^{51} +5.32101e8i q^{52} -3.03978e8 q^{53} +1.32735e8i q^{54} +4.11717e7i q^{55} -5.34949e7i q^{56} -1.32839e8 q^{57} +5.98926e8i q^{58} +(-3.68406e8 - 6.12694e8i) q^{59} -2.18876e8 q^{60} -1.36135e9i q^{61} +1.73296e9 q^{62} -8.34684e7 q^{63} +1.53552e9 q^{64} +5.01610e8i q^{65} +2.28944e8 q^{66} +2.43057e9i q^{67} +2.62000e9 q^{68} -3.43365e8i q^{69} -2.47196e8i q^{70} +2.64328e9 q^{71} +2.48298e8i q^{72} -8.53440e8i q^{73} -5.00680e9 q^{74} +1.16374e9 q^{75} -1.21807e9 q^{76} +1.43968e8i q^{77} +2.78931e9 q^{78} +4.49737e7 q^{79} +8.62199e8 q^{80} +3.87420e8 q^{81} -1.26425e9i q^{82} +1.00500e9i q^{83} -7.65362e8 q^{84} +2.46987e9 q^{85} +7.00236e9 q^{86} +1.74812e9 q^{87} +4.28271e8 q^{88} -3.83266e9i q^{89} +1.14737e9i q^{90} +1.75402e9i q^{91} -3.14848e9i q^{92} -5.05810e9i q^{93} +1.07590e10 q^{94} -1.14827e9 q^{95} -6.60673e9i q^{96} +2.35025e9i q^{97} +1.27134e10i q^{98} -6.68233e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	48.0671i		−	1.50210i	−0.660248	−	0.751048i	$-0.729549\pi$
$2$		−	48.0671i		−	1.50210i	0.660248	−	0.751048i	$-0.270451\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−1286.44			−1.25629
$5$	−1212.73			−0.388073			−0.194036	−	0.980994i	$-0.562158\pi$
$5$	−1212.73			−0.388073			−0.194036	+	0.980994i	$0.562158\pi$
$6$			6743.62i			0.867235i
$7$	−4240.63			−0.252313			−0.126157	−	0.992010i	$-0.540264\pi$
$7$	−4240.63			−0.252313			−0.126157	+	0.992010i	$0.540264\pi$
$8$			12614.8i			0.384974i
$9$	19683.0			0.333333
$10$			58292.2i			0.582922i
$11$		−	33949.7i		−	0.210801i	−0.994430	−	0.105401i	$-0.966388\pi$
$11$		−	33949.7i		−	0.210801i	0.994430	−	0.105401i	$-0.0336125\pi$
$12$	180483.			0.725320
$13$		−	413622.i		−	1.11400i	−0.830511	−	0.557002i	$-0.811952\pi$
$13$		−	413622.i		−	1.11400i	0.830511	−	0.557002i	$-0.188048\pi$
$14$			203835.i			0.378999i
$15$	170141.			0.224054
$16$	−710959.			−0.678023
$17$	−2.03662e6			−1.43439			−0.717193	−	0.696874i	$-0.754573\pi$
$17$	−2.03662e6			−1.43439			−0.717193	+	0.696874i	$0.754573\pi$
$18$		−	946104.i		−	0.500699i
$19$	946849.			0.382396			0.191198	−	0.981552i	$-0.438763\pi$
$19$	946849.			0.382396			0.191198	+	0.981552i	$0.438763\pi$
$20$	1.56010e6			0.487532
$21$	594944.			0.145673
$22$	−1.63186e6			−0.316643
$23$			2.44743e6i			0.380251i	0.981760	+	0.190126i	$0.0608895\pi$
$23$			2.44743e6i			0.380251i	−0.981760	+	0.190126i	$0.939110\pi$
$24$		−	1.76981e6i		−	0.222265i
$25$	−8.29492e6			−0.849400
$26$	−1.98816e7			−1.67334
$27$	−2.76145e6			−0.192450
$28$	5.45533e6			0.316979
$29$	−1.24602e7			−0.607485			−0.303743	−	0.952754i	$-0.598236\pi$
$29$	−1.24602e7			−0.607485			−0.303743	+	0.952754i	$0.598236\pi$
$30$		−	8.17817e6i		−	0.336550i
$31$			3.60531e7i			1.25931i	0.776874	+	0.629657i	$0.216804\pi$
$31$			3.60531e7i			1.25931i	−0.776874	+	0.629657i	$0.783196\pi$
$32$			4.70913e7i			1.40343i
$33$			4.76302e6i			0.121706i
$34$			9.78945e7i			2.15459i
$35$	5.14273e6			0.0979159
$36$	−2.53210e7			−0.418764
$37$		−	1.04163e8i		−	1.50212i	−0.660236	−	0.751058i	$-0.729544\pi$
$37$		−	1.04163e8i		−	1.50212i	0.660236	−	0.751058i	$-0.270456\pi$
$38$		−	4.55123e7i		−	0.574395i
$39$			5.80296e7i			0.643171i
$40$		−	1.52984e7i		−	0.149398i
$41$	2.63018e7			0.227021			0.113510	−	0.993537i	$-0.463790\pi$
$41$	2.63018e7			0.227021			0.113510	+	0.993537i	$0.463790\pi$
$42$		−	2.85972e7i		−	0.218815i
$43$			1.45679e8i			0.990957i	0.868620	+	0.495478i	$0.165007\pi$
$43$			1.45679e8i			0.990957i	−0.868620	+	0.495478i	$0.834993\pi$
$44$			4.36744e7i			0.264828i
$45$	−2.38701e7			−0.129358
$46$	1.17641e8			0.571174
$47$			2.23833e8i			0.975968i	0.872853	+	0.487984i	$0.162268\pi$
$47$			2.23833e8i			0.975968i	−0.872853	+	0.487984i	$0.837732\pi$
$48$	9.97448e7			0.391457
$49$	−2.64492e8			−0.936338
$50$			3.98712e8i			1.27588i
$51$	2.85730e8			0.828143
$52$			5.32101e8i			1.39951i
$53$	−3.03978e8			−0.726880			−0.363440	−	0.931618i	$-0.618398\pi$
$53$	−3.03978e8			−0.726880			−0.363440	+	0.931618i	$0.618398\pi$
$54$			1.32735e8i			0.289078i
$55$			4.11717e7i			0.0818061i
$56$		−	5.34949e7i		−	0.0971342i
$57$	−1.32839e8			−0.220776
$58$			5.98926e8i			0.912501i
$59$	−3.68406e8	−	6.12694e8i	−0.515308	−	0.857005i
$59$	−3.68406e8	−	6.12694e8i	−0.515308	−	0.857005i
$60$	−2.18876e8			−0.281477
$61$		−	1.36135e9i		−	1.61183i	−0.592029	−	0.805917i	$-0.701673\pi$
$61$		−	1.36135e9i		−	1.61183i	0.592029	−	0.805917i	$-0.298327\pi$
$62$	1.73296e9			1.89161
$63$	−8.34684e7			−0.0841045
$64$	1.53552e9			1.43006
$65$			5.01610e8i			0.432314i
$66$	2.28944e8			0.182814
$67$			2.43057e9i			1.80025i	0.435628	+	0.900127i	$0.356526\pi$
$67$			2.43057e9i			1.80025i	−0.435628	+	0.900127i	$0.643474\pi$
$68$	2.62000e9			1.80201
$69$		−	3.43365e8i		−	0.219538i
$70$		−	2.47196e8i		−	0.147079i
$71$	2.64328e9			1.46504			0.732522	−	0.680743i	$-0.238343\pi$
$71$	2.64328e9			1.46504			0.732522	+	0.680743i	$0.238343\pi$
$72$			2.48298e8i			0.128325i
$73$		−	8.53440e8i		−	0.411679i	−0.978586	−	0.205839i	$-0.934008\pi$
$73$		−	8.53440e8i		−	0.411679i	0.978586	−	0.205839i	$-0.0659925\pi$
$74$	−5.00680e9			−2.25632
$75$	1.16374e9			0.490401
$76$	−1.21807e9			−0.480400
$77$			1.43968e8i			0.0531880i
$78$	2.78931e9			0.966104
$79$	4.49737e7			0.0146158			0.00730792	−	0.999973i	$-0.497674\pi$
$79$	4.49737e7			0.0146158			0.00730792	+	0.999973i	$0.497674\pi$
$80$	8.62199e8			0.263122
$81$	3.87420e8			0.111111
$82$		−	1.26425e9i		−	0.341007i
$83$			1.00500e9i			0.255138i	0.991830	+	0.127569i	$0.0407175\pi$
$83$			1.00500e9i			0.255138i	−0.991830	+	0.127569i	$0.959283\pi$
$84$	−7.65362e8			−0.183008
$85$	2.46987e9			0.556646
$86$	7.00236e9			1.48851
$87$	1.74812e9			0.350732
$88$	4.28271e8			0.0811531
$89$		−	3.83266e9i		−	0.686358i	−0.939270	−	0.343179i	$-0.888496\pi$
$89$		−	3.83266e9i		−	0.686358i	0.939270	−	0.343179i	$-0.111504\pi$
$90$			1.14737e9i			0.194307i
$91$			1.75402e9i			0.281078i
$92$		−	3.14848e9i		−	0.477707i
$93$		−	5.05810e9i		−	0.727065i
$94$	1.07590e10			1.46600
$95$	−1.14827e9			−0.148397
$96$		−	6.60673e9i		−	0.810271i
$97$			2.35025e9i			0.273687i	0.990593	+	0.136844i	$0.0436958\pi$
$97$			2.35025e9i			0.273687i	−0.990593	+	0.136844i	$0.956304\pi$
$98$			1.27134e10i			1.40647i
$99$		−	6.68233e8i		−	0.0702670i
$100$	1.06709e10			1.06709
$101$			1.81712e9i			0.172893i	0.996256	+	0.0864466i	$0.0275512\pi$
$101$			1.81712e9i			0.172893i	−0.996256	+	0.0864466i	$0.972449\pi$
$102$		−	1.37342e10i		−	1.24395i
$103$		−	1.59866e9i		−	0.137901i	−0.997620	−	0.0689507i	$-0.978035\pi$
$103$		−	1.59866e9i		−	0.137901i	0.997620	−	0.0689507i	$-0.0219651\pi$
$104$	5.21778e9			0.428863
$105$	−7.21505e8			−0.0565318
$106$			1.46113e10i			1.09184i
$107$	2.24233e10			1.59875			0.799376	−	0.600832i	$-0.205164\pi$
$107$	2.24233e10			1.59875			0.799376	+	0.600832i	$0.205164\pi$
$108$	3.55244e9			0.241773
$109$			2.20040e10i			1.43011i	0.699069	+	0.715054i	$0.253598\pi$
$109$			2.20040e10i			1.43011i	−0.699069	+	0.715054i	$0.746402\pi$
$110$	1.97900e9			0.122881
$111$			1.46136e10i			0.867248i
$112$	3.01491e9			0.171074
$113$		−	3.36947e10i		−	1.82881i	−0.404796	−	0.914407i	$-0.632658\pi$
$113$		−	3.36947e10i		−	1.82881i	0.404796	−	0.914407i	$-0.367342\pi$
$114$			6.38519e9i			0.331627i
$115$		−	2.96806e9i		−	0.147565i
$116$	1.60294e10			0.763178
$117$		−	8.14132e9i		−	0.371335i
$118$	−2.94504e10	+	1.77082e10i	−1.28730	+	0.774041i
$119$	8.63657e9			0.361915
$120$			2.14630e9i			0.0862550i
$121$	2.47848e10			0.955563
$122$	−6.54360e10			−2.42113
$123$	−3.69004e9			−0.131071
$124$		−	4.63802e10i		−	1.58206i
$125$	2.19025e10			0.717701
$126$			4.01208e9i			0.126333i
$127$	−5.61401e10			−1.69924			−0.849619	−	0.527396i	$-0.823168\pi$
$127$	−5.61401e10			−1.69924			−0.849619	+	0.527396i	$0.823168\pi$
$128$		−	2.55864e10i		−	0.744662i
$129$		−	2.04382e10i		−	0.572129i
$130$	2.41109e10			0.649378
$131$			2.34480e10i			0.607785i	0.952706	+	0.303892i	$0.0982863\pi$
$131$			2.34480e10i			0.607785i	−0.952706	+	0.303892i	$0.901714\pi$
$132$		−	6.12735e9i		−	0.152898i
$133$	−4.01524e9			−0.0964835
$134$	1.16830e11			2.70415
$135$	3.34888e9			0.0746846
$136$		−	2.56917e10i		−	0.552202i
$137$	−1.20211e10			−0.249082			−0.124541	−	0.992214i	$-0.539746\pi$
$137$	−1.20211e10			−0.249082			−0.124541	+	0.992214i	$0.539746\pi$
$138$	−1.65045e10			−0.329767
$139$	−9.25758e10			−1.78412			−0.892059	−	0.451920i	$-0.850739\pi$
$139$	−9.25758e10			−1.78412			−0.892059	+	0.451920i	$0.850739\pi$
$140$	−6.61582e9			−0.123011
$141$		−	3.14030e10i		−	0.563475i
$142$		−	1.27054e11i		−	2.20064i
$143$	−1.40424e10			−0.234833
$144$	−1.39938e10			−0.226008
$145$	1.51108e10			0.235748
$146$	−4.10224e10			−0.618381
$147$	3.71072e10			0.540595
$148$			1.33999e11i			1.88710i
$149$		−	6.09103e10i		−	0.829391i	−0.909960	−	0.414696i	$-0.863888\pi$
$149$		−	6.09103e10i		−	0.829391i	0.909960	−	0.414696i	$-0.136112\pi$
$150$		−	5.59378e10i		−	0.736629i
$151$		−	8.17973e10i		−	1.04197i	−0.853567	−	0.520984i	$-0.825565\pi$
$151$		−	8.17973e10i		−	1.04197i	0.853567	−	0.520984i	$-0.174435\pi$
$152$			1.19444e10i			0.147213i
$153$	−4.00869e10			−0.478129
$154$	6.92014e9			0.0798934
$155$		−	4.37225e10i		−	0.488705i
$156$		−	7.46517e10i		−	0.808010i
$157$		−	6.19935e10i		−	0.649902i	−0.945731	−	0.324951i	$-0.894652\pi$
$157$		−	6.19935e10i		−	0.649902i	0.945731	−	0.324951i	$-0.105348\pi$
$158$		−	2.16176e9i		−	0.0219544i
$159$	4.26469e10			0.419664
$160$		−	5.71089e10i		−	0.544633i
$161$		−	1.03786e10i		−	0.0959425i
$162$		−	1.86222e10i		−	0.166900i
$163$	−1.91119e11			−1.66099			−0.830493	−	0.557029i	$-0.811941\pi$
$163$	−1.91119e11			−1.66099			−0.830493	+	0.557029i	$0.811941\pi$
$164$	−3.38357e10			−0.285204
$165$		−	5.77624e9i		−	0.0472308i
$166$	4.83074e10			0.383242
$167$	2.21143e11			1.70251			0.851257	−	0.524749i	$-0.175841\pi$
$167$	2.21143e11			1.70251			0.851257	+	0.524749i	$0.175841\pi$
$168$			7.50513e9i			0.0560805i
$169$	−3.32246e10			−0.241005
$170$		−	1.18719e11i		−	0.836135i
$171$	1.86368e10			0.127465
$172$		−	1.87408e11i		−	1.24493i
$173$		−	2.47462e11i		−	1.59690i	−0.602062	−	0.798450i	$-0.705654\pi$
$173$		−	2.47462e11i		−	1.59690i	0.602062	−	0.798450i	$-0.294346\pi$
$174$		−	8.40270e10i		−	0.526833i
$175$	3.51757e10			0.214315
$176$			2.41369e10i			0.142928i
$177$	5.16859e10	+	8.59586e10i	0.297513	+	0.494792i
$178$	−1.84225e11			−1.03098
$179$		−	1.41480e11i		−	0.769893i	−0.922939	−	0.384947i	$-0.874220\pi$
$179$		−	1.41480e11i		−	0.769893i	0.922939	−	0.384947i	$-0.125780\pi$
$180$	3.07075e10			0.162511
$181$	4.38883e10			0.225920			0.112960	−	0.993600i	$-0.463967\pi$
$181$	4.38883e10			0.225920			0.112960	+	0.993600i	$0.463967\pi$
$182$	8.43105e10			0.422206
$183$			1.90992e11i			0.930592i
$184$	−3.08739e10			−0.146387
$185$			1.26321e11i			0.582930i
$186$	−2.43128e11			−1.09212
$187$			6.91428e10i			0.302370i
$188$		−	2.87949e11i		−	1.22610i
$189$	1.17103e10			0.0485577
$190$			5.51939e10i			0.222907i
$191$			4.46656e11i			1.75714i	0.477612	+	0.878571i	$0.341502\pi$
$191$			4.46656e11i			1.75714i	−0.477612	+	0.878571i	$0.658498\pi$
$192$	−2.15427e11			−0.825647
$193$	2.57216e10			0.0960529			0.0480265	−	0.998846i	$-0.484707\pi$
$193$	2.57216e10			0.0960529			0.0480265	+	0.998846i	$0.484707\pi$
$194$	1.12969e11			0.411105
$195$		−	7.03740e10i		−	0.249597i
$196$	3.40254e11			1.17631
$197$	1.77712e11			0.598943			0.299471	−	0.954105i	$-0.403190\pi$
$197$	1.77712e11			0.598943			0.299471	+	0.954105i	$0.403190\pi$
$198$	−3.21200e10			−0.105548
$199$	5.37426e11			1.72208			0.861039	−	0.508539i	$-0.169814\pi$
$199$	5.37426e11			1.72208			0.861039	+	0.508539i	$0.169814\pi$
$200$		−	1.04639e11i		−	0.326997i
$201$		−	3.40999e11i		−	1.03938i
$202$	8.73439e10			0.259702
$203$	5.28392e10			0.153277
$204$	−3.67576e11			−1.04039
$205$	−3.18969e10			−0.0881006
$206$	−7.68427e10			−0.207141
$207$			4.81727e10i			0.126750i
$208$			2.94068e11i			0.755321i
$209$		−	3.21453e10i		−	0.0806094i
$210$			3.46806e10i			0.0849161i
$211$		−	5.80157e11i		−	1.38718i	−0.720370	−	0.693590i	$-0.756028\pi$
$211$		−	5.80157e11i		−	1.38718i	0.720370	−	0.693590i	$-0.243972\pi$
$212$	3.91050e11			0.913173
$213$	−3.70841e11			−0.845844
$214$		−	1.07782e12i		−	2.40148i
$215$		−	1.76669e11i		−	0.384563i
$216$		−	3.48352e10i		−	0.0740884i
$217$		−	1.52888e11i		−	0.317742i
$218$	1.05767e12			2.14816
$219$			1.19734e11i			0.237683i
$220$		−	5.29651e10i		−	0.102772i
$221$			8.42392e11i			1.59791i
$222$	7.02434e11			1.30269
$223$	6.90723e11			1.25250			0.626252	−	0.779620i	$-0.284588\pi$
$223$	6.90723e11			1.25250			0.626252	+	0.779620i	$0.284588\pi$
$224$		−	1.99697e11i		−	0.354104i
$225$	−1.63269e11			−0.283133
$226$	−1.61961e12			−2.74705
$227$			9.05355e11i			1.50207i	0.660263	+	0.751034i	$0.270445\pi$
$227$			9.05355e11i			1.50207i	−0.660263	+	0.751034i	$0.729555\pi$
$228$	1.70890e11			0.277359
$229$		−	2.08438e10i		−	0.0330978i	−0.999863	−	0.0165489i	$-0.994732\pi$
$229$		−	2.08438e10i		−	0.0330978i	0.999863	−	0.0165489i	$-0.00526792\pi$
$230$	−1.42666e11			−0.221657
$231$		−	2.01982e10i		−	0.0307081i
$232$		−	1.57184e11i		−	0.233866i
$233$			1.06421e12i			1.54970i	0.632144	+	0.774851i	$0.282175\pi$
$233$			1.06421e12i			1.54970i	−0.632144	+	0.774851i	$0.717825\pi$
$234$	−3.91329e11			−0.557780
$235$		−	2.71449e11i		−	0.378746i
$236$	4.73933e11	+	7.88195e11i	0.647377	+	1.07665i
$237$	−6.30964e9			−0.00843846
$238$		−	4.15135e11i		−	0.543631i
$239$	5.41434e11			0.694314			0.347157	−	0.937807i	$-0.387147\pi$
$239$	5.41434e11			0.694314			0.347157	+	0.937807i	$0.387147\pi$
$240$	−1.20963e11			−0.151914
$241$	6.09091e11			0.749199			0.374599	−	0.927187i	$-0.377780\pi$
$241$	6.09091e11			0.749199			0.374599	+	0.927187i	$0.377780\pi$
$242$		−	1.19133e12i		−	1.43535i
$243$	−5.43536e10			−0.0641500
$244$			1.75130e12i			2.02493i
$245$	3.20757e11			0.363367
$246$			1.77369e11i			0.196881i
$247$		−	3.91638e11i		−	0.425990i
$248$	−4.54804e11			−0.484803
$249$		−	1.40998e11i		−	0.147304i
$250$		−	1.05279e12i		−	1.07806i
$251$	1.61926e12			1.62536			0.812678	−	0.582713i	$-0.198009\pi$
$251$	1.61926e12			1.62536			0.812678	+	0.582713i	$0.198009\pi$
$252$	1.07377e11			0.105660
$253$	8.30895e10			0.0801574
$254$			2.69849e12i			2.55242i
$255$	−3.46513e11			−0.321380
$256$	3.42509e11			0.311510
$257$	1.41412e12			1.26130			0.630652	−	0.776066i	$-0.282787\pi$
$257$	1.41412e12			1.26130			0.630652	+	0.776066i	$0.282787\pi$
$258$	−9.82404e11			−0.859393
$259$			4.41716e11i			0.379004i
$260$		−	6.45293e11i		−	0.543113i
$261$	−2.45254e11			−0.202495
$262$	1.12708e12			0.912951
$263$	1.67899e11			0.133434			0.0667172	−	0.997772i	$-0.478747\pi$
$263$	1.67899e11			0.133434			0.0667172	+	0.997772i	$0.478747\pi$
$264$	−6.00847e10			−0.0468537
$265$	3.68642e11			0.282082
$266$			1.93001e11i			0.144928i
$267$			5.37708e11i			0.396269i
$268$		−	3.12679e12i		−	2.26164i
$269$			5.89368e10i			0.0418432i	0.999781	+	0.0209216i	$0.00666004\pi$
$269$			5.89368e10i			0.0418432i	−0.999781	+	0.0209216i	$0.993340\pi$
$270$		−	1.60971e11i		−	0.112183i
$271$	−1.49409e12			−1.02219			−0.511093	−	0.859525i	$-0.670759\pi$
$271$	−1.49409e12			−1.02219			−0.511093	+	0.859525i	$0.670759\pi$
$272$	1.44796e12			0.972547
$273$		−	2.46082e11i		−	0.162281i
$274$			5.77819e11i			0.374144i
$275$			2.81610e11i			0.179054i
$276$			4.41719e11i			0.275804i
$277$	−1.48765e12			−0.912224			−0.456112	−	0.889922i	$-0.650758\pi$
$277$	−1.48765e12			−0.912224			−0.456112	+	0.889922i	$0.650758\pi$
$278$			4.44985e12i			2.67992i
$279$			7.09632e11i			0.419771i
$280$			6.48747e10i			0.0376951i
$281$	2.32124e12			1.32492			0.662458	−	0.749099i	$-0.269513\pi$
$281$	2.32124e12			1.32492			0.662458	+	0.749099i	$0.269513\pi$
$282$	−1.50945e12			−0.846394
$283$		−	1.72438e12i		−	0.949948i	−0.880000	−	0.474974i	$-0.842458\pi$
$283$		−	1.72438e12i		−	0.949948i	0.880000	−	0.474974i	$-0.157542\pi$
$284$	−3.40042e12			−1.84052
$285$	1.61098e11			0.0856772
$286$			6.74975e11i			0.352742i
$287$	−1.11536e11			−0.0572804
$288$			9.26898e11i			0.467810i
$289$	2.13184e12			1.05746
$290$		−	7.26334e11i		−	0.354117i
$291$		−	3.29730e11i		−	0.158013i
$292$			1.09790e12i			0.517189i
$293$	−2.39530e12			−1.10923			−0.554615	−	0.832107i	$-0.687134\pi$
$293$	−2.39530e12			−1.10923			−0.554615	+	0.832107i	$0.687134\pi$
$294$		−	1.78364e12i		−	0.812025i
$295$	4.46776e11	+	7.43030e11i	0.199977	+	0.332580i
$296$	1.31400e12			0.578277
$297$			9.37504e10i			0.0405687i
$298$	−2.92778e12			−1.24582
$299$	1.01231e12			0.423602
$300$	−1.49709e12			−0.616087
$301$		−	6.17771e11i		−	0.250032i
$302$	−3.93176e12			−1.56514
$303$		−	2.54936e11i		−	0.0998199i
$304$	−6.73171e11			−0.259273
$305$			1.65094e12i			0.625508i
$306$			1.92686e12i			0.718195i
$307$	−2.92215e12			−1.07154			−0.535772	−	0.844363i	$-0.679979\pi$
$307$	−2.92215e12			−1.07154			−0.535772	+	0.844363i	$0.679979\pi$
$308$		−	1.85207e11i		−	0.0668196i
$309$			2.24285e11i			0.0796174i
$310$	−2.10161e12			−0.734081
$311$	3.22319e12			1.10786			0.553928	−	0.832565i	$-0.313128\pi$
$311$	3.22319e12			1.10786			0.553928	+	0.832565i	$0.313128\pi$
$312$	−7.32034e11			−0.247604
$313$			1.49286e12i			0.496931i	0.968641	+	0.248465i	$0.0799262\pi$
$313$			1.49286e12i			0.496931i	−0.968641	+	0.248465i	$0.920074\pi$
$314$	−2.97985e12			−0.976215
$315$	1.01224e11			0.0326386
$316$	−5.78561e10			−0.0183617
$317$	−4.43107e12			−1.38424			−0.692122	−	0.721781i	$-0.743324\pi$
$317$	−4.43107e12			−1.38424			−0.692122	+	0.721781i	$0.743324\pi$
$318$		−	2.04991e12i		−	0.630376i
$319$			4.23021e11i			0.128059i
$320$	−1.86216e12			−0.554968
$321$	−3.14590e12			−0.923039
$322$	−4.98871e11			−0.144115
$323$	−1.92838e12			−0.548503
$324$	−4.98394e11			−0.139588
$325$			3.43096e12i			0.946235i
$326$			9.18654e12i			2.49496i
$327$		−	3.08707e12i		−	0.825673i
$328$			3.31793e11i			0.0873972i
$329$		−	9.49195e11i		−	0.246250i
$330$	−2.77647e11			−0.0709452
$331$	4.35658e12			1.09649			0.548246	−	0.836317i	$-0.315296\pi$
$331$	4.35658e12			1.09649			0.548246	+	0.836317i	$0.315296\pi$
$332$		−	1.29288e12i		−	0.320528i
$333$		−	2.05024e12i		−	0.500706i
$334$		−	1.06297e13i		−	2.55734i
$335$		−	2.94761e12i		−	0.698629i
$336$	−4.22981e11			−0.0987698
$337$			4.08576e12i			0.939989i	0.882669	+	0.469995i	$0.155744\pi$
$337$			4.08576e12i			0.939989i	−0.882669	+	0.469995i	$0.844256\pi$
$338$			1.59701e12i			0.362013i
$339$			4.72724e12i			1.05587i
$340$	−3.17734e12			−0.699310
$341$	1.22399e12			0.265465
$342$		−	8.95818e11i		−	0.191465i
$343$	2.31949e12			0.488564
$344$	−1.83772e12			−0.381493
$345$			4.16407e11i			0.0851967i
$346$	−1.18948e13			−2.39870
$347$		−	4.87568e12i		−	0.969144i	−0.874751	−	0.484572i	$-0.838975\pi$
$347$		−	4.87568e12i		−	0.969144i	0.874751	−	0.484572i	$-0.161025\pi$
$348$	−2.24886e12			−0.440621
$349$			4.70800e12i			0.909305i	0.890669	+	0.454652i	$0.150237\pi$
$349$			4.70800e12i			0.909305i	−0.890669	+	0.454652i	$0.849763\pi$
$350$		−	1.69079e12i		−	0.321922i
$351$			1.14220e12i			0.214390i
$352$	1.59874e12			0.295845
$353$			4.05744e12i			0.740250i	0.928982	+	0.370125i	$0.120685\pi$
$353$			4.05744e12i			0.740250i	−0.928982	+	0.370125i	$0.879315\pi$
$354$	4.13178e12	−	2.48439e12i	0.743225	−	0.446893i
$355$	−3.20557e12			−0.568543
$356$			4.93050e12i			0.862266i
$357$	−1.21168e12			−0.208952
$358$	−6.80054e12			−1.15645
$359$	8.17182e12			1.37040			0.685199	−	0.728356i	$-0.259715\pi$
$359$	8.17182e12			1.37040			0.685199	+	0.728356i	$0.259715\pi$
$360$		−	3.01118e11i		−	0.0497993i
$361$	−5.23454e12			−0.853774
$362$		−	2.10958e12i		−	0.339354i
$363$	−3.47722e12			−0.551694
$364$		−	2.25644e12i		−	0.353116i
$365$			1.03499e12i			0.159761i
$366$	9.18042e12			1.39784
$367$			6.99731e12i			1.05100i	0.850795	+	0.525498i	$0.176121\pi$
$367$			6.99731e12i			1.05100i	−0.850795	+	0.525498i	$0.823879\pi$
$368$		−	1.74002e12i		−	0.257819i
$369$	5.17698e11			0.0756736
$370$	6.07188e12			0.875617
$371$	1.28906e12			0.183402
$372$			6.50696e12i			0.913405i
$373$	1.07780e13			1.49278			0.746388	−	0.665511i	$-0.231786\pi$
$373$	1.07780e13			1.49278			0.746388	+	0.665511i	$0.231786\pi$
$374$	3.32349e12			0.454189
$375$	−3.07284e12			−0.414365
$376$	−2.82362e12			−0.375723
$377$			5.15382e12i			0.676741i
$378$		−	5.62879e11i		−	0.0729384i
$379$	−1.18081e13			−1.51003			−0.755015	−	0.655708i	$-0.772370\pi$
$379$	−1.18081e13			−1.51003			−0.755015	+	0.655708i	$0.772370\pi$
$380$	1.47718e12			0.186430
$381$	7.87624e12			0.981056
$382$	2.14695e13			2.63939
$383$	−4.15695e12			−0.504407			−0.252204	−	0.967674i	$-0.581155\pi$
$383$	−4.15695e12			−0.504407			−0.252204	+	0.967674i	$0.581155\pi$
$384$			3.58967e12i			0.429931i
$385$		−	1.74594e11i		−	0.0206408i
$386$		−	1.23636e12i		−	0.144281i
$387$			2.86740e12i			0.330319i
$388$		−	3.02346e12i		−	0.343831i
$389$	9.22414e11			0.103557			0.0517783	−	0.998659i	$-0.483511\pi$
$389$	9.22414e11			0.103557			0.0517783	+	0.998659i	$0.483511\pi$
$390$	−3.38267e12			−0.374918
$391$		−	4.98449e12i		−	0.545427i
$392$		−	3.33653e12i		−	0.360466i
$393$		−	3.28967e12i		−	0.350905i
$394$		−	8.54209e12i		−	0.899669i
$395$	−5.45409e10			−0.00567200
$396$			8.59643e11i			0.0882759i
$397$			6.05681e11i			0.0614174i	0.999528	+	0.0307087i	$0.00977641\pi$
$397$			6.05681e11i			0.0614174i	−0.999528	+	0.0307087i	$0.990224\pi$
$398$		−	2.58325e13i		−	2.58673i
$399$	5.63322e11			0.0557048
$400$	5.89735e12			0.575913
$401$			9.92611e11i			0.0957321i	0.998854	+	0.0478660i	$0.0152421\pi$
$401$			9.92611e11i			0.0957321i	−0.998854	+	0.0478660i	$0.984758\pi$
$402$	−1.63908e13			−1.56124
$403$	1.49123e13			1.40288
$404$		−	2.33763e12i		−	0.217204i
$405$	−4.69835e11			−0.0431192
$406$		−	2.53983e12i		−	0.230236i
$407$	−3.53630e12			−0.316648
$408$			3.60444e12i			0.318814i
$409$			5.50739e12i			0.481204i	0.970624	+	0.240602i	$0.0773449\pi$
$409$			5.50739e12i			0.481204i	−0.970624	+	0.240602i	$0.922655\pi$
$410$			1.53319e12i			0.132335i
$411$	1.68651e12			0.143807
$412$			2.05658e12i			0.173244i
$413$	1.56227e12	+	2.59821e12i	0.130019	+	0.216234i
$414$	2.31552e12			0.190391
$415$		−	1.21879e12i		−	0.0990122i
$416$	1.94780e13			1.56343
$417$	1.29880e13			1.03006
$418$	−1.54513e12			−0.121083
$419$			1.35032e13i			1.04560i	0.852454	+	0.522802i	$0.175113\pi$
$419$			1.35032e13i			1.04560i	−0.852454	+	0.522802i	$0.824887\pi$
$420$	9.28174e11			0.0710204
$421$		−	1.71630e13i		−	1.29772i	−0.760906	−	0.648862i	$-0.775245\pi$
$421$		−	1.71630e13i		−	1.29772i	0.760906	−	0.648862i	$-0.224755\pi$
$422$	−2.78864e13			−2.08368
$423$			4.40571e12i			0.325323i
$424$		−	3.83463e12i		−	0.279830i
$425$	1.68936e13			1.21837
$426$			1.78253e13i			1.27054i
$427$			5.77298e12i			0.406687i
$428$	−2.88463e13			−2.00850
$429$	1.97009e12			0.135581
$430$	−8.49195e12			−0.577650
$431$			6.74475e11i			0.0453502i	0.999743	+	0.0226751i	$0.00721833\pi$
$431$			6.74475e11i			0.0453502i	−0.999743	+	0.0226751i	$0.992782\pi$
$432$	1.96328e12			0.130486
$433$	1.25185e13			0.822454			0.411227	−	0.911533i	$-0.365100\pi$
$433$	1.25185e13			0.822454			0.411227	+	0.911533i	$0.365100\pi$
$434$	−7.34887e12			−0.477278
$435$	−2.11999e12			−0.136109
$436$		−	2.83069e13i		−	1.79663i
$437$			2.31735e12i			0.145406i
$438$	5.75528e12			0.357023
$439$	2.48488e13			1.52399			0.761997	−	0.647581i	$-0.224219\pi$
$439$	2.48488e13			1.52399			0.761997	+	0.647581i	$0.224219\pi$
$440$	−5.19375e11			−0.0314933
$441$	−5.20600e12			−0.312113
$442$	4.04913e13			2.40022
$443$			1.48108e13i			0.868079i	0.900894	+	0.434040i	$0.142912\pi$
$443$			1.48108e13i			0.868079i	−0.900894	+	0.434040i	$0.857088\pi$
$444$		−	1.87996e13i		−	1.08952i
$445$			4.64797e12i			0.266357i
$446$		−	3.32010e13i		−	1.88138i
$447$			8.54548e12i			0.478849i
$448$	−6.51157e12			−0.360824
$449$	2.59038e12			0.141949			0.0709744	−	0.997478i	$-0.477389\pi$
$449$	2.59038e12			0.141949			0.0709744	+	0.997478i	$0.477389\pi$
$450$			7.84786e12i			0.425293i
$451$		−	8.92938e11i		−	0.0478563i
$452$			4.33463e13i			2.29752i
$453$			1.14758e13i			0.601580i
$454$	4.35178e13			2.25625
$455$		−	2.12714e12i		−	0.109079i
$456$		−	1.67575e12i		−	0.0849932i
$457$			2.99458e12i			0.150230i	0.997175	+	0.0751148i	$0.0239323\pi$
$457$			2.99458e12i			0.150230i	−0.997175	+	0.0751148i	$0.976068\pi$
$458$	−1.00190e12			−0.0497161
$459$	5.62403e12			0.276048
$460$			3.81824e12i			0.185385i
$461$	−1.22054e13			−0.586201			−0.293101	−	0.956082i	$-0.594687\pi$
$461$	−1.22054e13			−0.586201			−0.293101	+	0.956082i	$0.594687\pi$
$462$	−9.70868e11			−0.0461265
$463$			1.22561e13i			0.576031i	0.957626	+	0.288016i	$0.0929955\pi$
$463$			1.22561e13i			0.576031i	−0.957626	+	0.288016i	$0.907004\pi$
$464$	8.85870e12			0.411889
$465$			6.13410e12i			0.282154i
$466$	5.11535e13			2.32780
$467$			1.45069e13i			0.653118i	0.945177	+	0.326559i	$0.105889\pi$
$467$			1.45069e13i			0.653118i	−0.945177	+	0.326559i	$0.894111\pi$
$468$			1.04733e13i			0.466505i
$469$		−	1.03071e13i		−	0.454228i
$470$	−1.30477e13			−0.568913
$471$			8.69745e12i			0.375221i
$472$	7.72904e12	−	4.64738e12i	0.329925	−	0.198380i
$473$	4.94576e12			0.208895
$474$			3.03286e11i			0.0126754i
$475$	−7.85404e12			−0.324807
$476$	−1.11105e13			−0.454671
$477$	−5.98320e12			−0.242293
$478$		−	2.60251e13i		−	1.04293i
$479$	−2.73650e13			−1.08522			−0.542610	−	0.839985i	$-0.682564\pi$
$479$	−2.73650e13			−1.08522			−0.542610	+	0.839985i	$0.682564\pi$
$480$			8.01215e12i			0.314444i
$481$	−4.30840e13			−1.67336
$482$		−	2.92772e13i		−	1.12537i
$483$			1.45608e12i			0.0553924i
$484$	−3.18843e13			−1.20047
$485$		−	2.85021e12i		−	0.106211i
$486$			2.61262e12i			0.0963595i
$487$	2.31886e13			0.846504			0.423252	−	0.906012i	$-0.360889\pi$
$487$	2.31886e13			0.846504			0.423252	+	0.906012i	$0.360889\pi$
$488$	1.71732e13			0.620515
$489$	2.68133e13			0.958971
$490$		−	1.54178e13i		−	0.545812i
$491$	−2.44864e13			−0.858058			−0.429029	−	0.903291i	$-0.641144\pi$
$491$	−2.44864e13			−0.858058			−0.429029	+	0.903291i	$0.641144\pi$
$492$	4.74702e12			0.164663
$493$	2.53768e13			0.871368
$494$	−1.88249e13			−0.639878
$495$			8.10384e11i			0.0272687i
$496$		−	2.56322e13i		−	0.853843i
$497$	−1.12092e13			−0.369650
$498$	−6.77734e12			−0.221265
$499$	−1.95409e13			−0.631601			−0.315800	−	0.948826i	$-0.602273\pi$
$499$	−1.95409e13			−0.631601			−0.315800	+	0.948826i	$0.602273\pi$
$500$	−2.81763e13			−0.901642
$501$	−3.10255e13			−0.982947
$502$		−	7.78332e13i		−	2.44144i
$503$		−	4.04475e13i		−	1.25618i	−0.778141	−	0.628090i	$-0.783837\pi$
$503$		−	4.04475e13i		−	1.25618i	0.778141	−	0.628090i	$-0.216163\pi$
$504$		−	1.05294e12i		−	0.0323781i
$505$		−	2.20368e12i		−	0.0670951i
$506$		−	3.99387e12i		−	0.120404i
$507$	4.66129e12			0.139144
$508$	7.22210e13			2.13474
$509$			4.75133e13i			1.39068i	0.718682	+	0.695339i	$0.244746\pi$
$509$			4.75133e13i			1.39068i	−0.718682	+	0.695339i	$0.755254\pi$
$510$			1.66559e13i			0.482743i
$511$			3.61912e12i			0.103872i
$512$		−	4.26638e13i		−	1.21258i
$513$	−2.61468e12			−0.0735921
$514$		−	6.79725e13i		−	1.89460i
$515$			1.93873e12i			0.0535157i
$516$			2.62926e13i			0.718761i
$517$	7.59909e12			0.205735
$518$	2.12320e13			0.569301
$519$			3.47179e13i			0.921970i
$520$	−6.32774e12			−0.166430
$521$	−4.64189e13			−1.20922			−0.604611	−	0.796521i	$-0.706671\pi$
$521$	−4.64189e13			−1.20922			−0.604611	+	0.796521i	$0.706671\pi$
$522$			1.17887e13i			0.304167i
$523$	−1.77026e13			−0.452407			−0.226204	−	0.974080i	$-0.572631\pi$
$523$	−1.77026e13			−0.452407			−0.226204	+	0.974080i	$0.572631\pi$
$524$		−	3.01645e13i		−	0.763555i
$525$	−4.93501e12			−0.123735
$526$		−	8.07039e12i		−	0.200431i
$527$		−	7.34265e13i		−	1.80634i
$528$		−	3.38631e12i		−	0.0825195i
$529$	3.54366e13			0.855409
$530$		−	1.77195e13i		−	0.423714i
$531$	−7.25133e12	−	1.20597e13i	−0.171769	−	0.285668i
$532$	5.16537e12			0.121211
$533$		−	1.08790e13i		−	0.252902i
$534$	2.58460e13			0.595234
$535$	−2.71933e13			−0.620431
$536$	−3.06612e13			−0.693052
$537$			1.98491e13i			0.444498i
$538$	2.83292e12			0.0628525
$539$			8.97944e12i			0.197381i
$540$	−4.30814e12			−0.0938256
$541$		−	7.67384e13i		−	1.65587i	−0.560824	−	0.827935i	$-0.689516\pi$
$541$		−	7.67384e13i		−	1.65587i	0.560824	−	0.827935i	$-0.310484\pi$
$542$			7.18165e13i			1.53542i
$543$	−6.15735e12			−0.130435
$544$		−	9.59072e13i		−	2.01306i
$545$		−	2.66848e13i		−	0.554986i
$546$	−1.18284e13			−0.243761
$547$	−5.33433e13			−1.08929			−0.544644	−	0.838667i	$-0.683335\pi$
$547$	−5.33433e13			−1.08929			−0.544644	+	0.838667i	$0.683335\pi$
$548$	1.54645e13			0.312919
$549$		−	2.67954e13i		−	0.537278i
$550$	1.35362e13			0.268957
$551$	−1.17979e13			−0.232300
$552$	4.33149e12			0.0845166
$553$	−1.90717e11			−0.00368777
$554$			7.15069e13i			1.37025i
$555$		−	1.77223e13i		−	0.336555i
$556$	1.19093e14			2.24137
$557$	−8.38263e13			−1.56352			−0.781761	−	0.623578i	$-0.785679\pi$
$557$	−8.38263e13			−1.56352			−0.781761	+	0.623578i	$0.785679\pi$
$558$	3.41099e13			0.630536
$559$	6.02560e13			1.10393
$560$	−3.65627e12			−0.0663893
$561$		−	9.70047e12i		−	0.174574i
$562$		−	1.11575e14i		−	1.99015i
$563$			8.01858e13i			1.41761i	0.705407	+	0.708803i	$0.250764\pi$
$563$			8.01858e13i			1.41761i	−0.705407	+	0.708803i	$0.749236\pi$
$564$			4.03981e13i			0.707889i
$565$			4.08625e13i			0.709712i
$566$	−8.28857e13			−1.42691
$567$	−1.64291e12			−0.0280348
$568$			3.33445e13i			0.564004i
$569$		−	4.44464e13i		−	0.745203i	−0.927991	−	0.372602i	$-0.878466\pi$
$569$		−	4.44464e13i		−	0.745203i	0.927991	−	0.372602i	$-0.121534\pi$
$570$		−	7.74349e12i		−	0.128695i
$571$		−	5.25658e12i		−	0.0866009i	−0.999062	−	0.0433005i	$-0.986213\pi$
$571$		−	5.25658e12i		−	0.0866009i	0.999062	−	0.0433005i	$-0.0137873\pi$
$572$	1.80647e13			0.295019
$573$		−	6.26642e13i		−	1.01449i
$574$			5.36121e12i			0.0860407i
$575$		−	2.03012e13i		−	0.322985i
$576$	3.02236e13			0.476688
$577$	−1.09977e14			−1.71958			−0.859790	−	0.510648i	$-0.829405\pi$
$577$	−1.09977e14			−1.71958			−0.859790	+	0.510648i	$0.829405\pi$
$578$		−	1.02471e14i		−	1.58841i
$579$	−3.60863e12			−0.0554562
$580$	−1.94392e13			−0.296169
$581$		−	4.26184e12i		−	0.0643748i
$582$	−1.58492e13			−0.237351
$583$			1.03200e13i			0.153227i
$584$	1.07660e13			0.158486
$585$			9.87320e12i			0.144105i
$586$			1.15135e14i			1.66617i
$587$			3.08123e13i			0.442113i	0.975261	+	0.221056i	$0.0709505\pi$
$587$			3.08123e13i			0.442113i	−0.975261	+	0.221056i	$0.929050\pi$
$588$	−4.77363e13			−0.679145
$589$			3.41368e13i			0.481556i
$590$	3.57153e13	−	2.14752e13i	0.499567	−	0.300384i
$591$	−2.49323e13			−0.345800
$592$			7.40554e13i			1.01847i
$593$	1.74470e13			0.237929			0.118964	−	0.992899i	$-0.462043\pi$
$593$	1.74470e13			0.237929			0.118964	+	0.992899i	$0.462043\pi$
$594$	4.50631e12			0.0609381
$595$	−1.04738e13			−0.140449
$596$			7.83576e13i			1.04196i
$597$	−7.53987e13			−0.994242
$598$		−	4.86588e13i		−	0.636290i
$599$	2.40542e13			0.311929			0.155965	−	0.987763i	$-0.450151\pi$
$599$	2.40542e13			0.311929			0.155965	+	0.987763i	$0.450151\pi$
$600$			1.46805e13i			0.188792i
$601$		−	3.18260e13i		−	0.405891i	−0.979190	−	0.202945i	$-0.934949\pi$
$601$		−	3.18260e13i		−	0.405891i	0.979190	−	0.202945i	$-0.0650514\pi$
$602$	−2.96944e13			−0.375571
$603$			4.78409e13i			0.600085i
$604$			1.05228e14i			1.30902i
$605$	−3.00572e13			−0.370828
$606$	−1.22540e13			−0.149939
$607$	−7.13963e13			−0.866427			−0.433214	−	0.901291i	$-0.642620\pi$
$607$	−7.13963e13			−0.866427			−0.433214	+	0.901291i	$0.642620\pi$
$608$			4.45884e13i			0.536665i
$609$	−7.41314e12			−0.0884943
$610$	7.93560e13			0.939573
$611$	9.25824e13			1.08723
$612$	5.15694e13			0.600669
$613$			2.52653e13i			0.291892i	0.989293	+	0.145946i	$0.0466226\pi$
$613$			2.52653e13i			0.291892i	−0.989293	+	0.145946i	$0.953377\pi$
$614$			1.40459e14i			1.60956i
$615$	4.47501e12			0.0508649
$616$	−1.81614e12			−0.0204760
$617$	4.37750e13			0.489554			0.244777	−	0.969579i	$-0.421285\pi$
$617$	4.37750e13			0.489554			0.244777	+	0.969579i	$0.421285\pi$
$618$	1.07807e13			0.119593
$619$	−1.60155e14			−1.76233			−0.881165	−	0.472809i	$-0.843240\pi$
$619$	−1.60155e14			−1.76233			−0.881165	+	0.472809i	$0.843240\pi$
$620$			5.62465e13i			0.613956i
$621$		−	6.75845e12i		−	0.0731794i
$622$		−	1.54929e14i		−	1.66411i
$623$			1.62529e13i			0.173177i
$624$		−	4.12566e13i		−	0.436085i
$625$	5.44433e13			0.570880
$626$	7.17572e13			0.746438
$627$			4.50986e12i			0.0465399i
$628$			7.97511e13i			0.816467i
$629$			2.12140e14i			2.15462i
$630$		−	4.86556e12i		−	0.0490264i
$631$	−3.60007e13			−0.359886			−0.179943	−	0.983677i	$-0.557591\pi$
$631$	−3.60007e13			−0.359886			−0.179943	+	0.983677i	$0.557591\pi$
$632$			5.67337e11i			0.00562672i
$633$			8.13937e13i			0.800889i
$634$			2.12989e14i			2.07927i
$635$	6.80826e13			0.659428
$636$	−5.48628e13			−0.527221
$637$			1.09400e14i			1.04308i
$638$	2.03334e13			0.192356
$639$	5.20276e13			0.488348
$640$			3.10293e13i			0.288983i
$641$	−1.24923e14			−1.15439			−0.577193	−	0.816608i	$-0.695852\pi$
$641$	−1.24923e14			−1.15439			−0.577193	+	0.816608i	$0.695852\pi$
$642$			1.51214e14i			1.38649i
$643$	−1.32175e14			−1.20253			−0.601264	−	0.799050i	$-0.705336\pi$
$643$	−1.32175e14			−1.20253			−0.601264	+	0.799050i	$0.705336\pi$
$644$			1.33515e13i			0.120532i
$645$			2.47859e13i			0.222028i
$646$			9.26913e13i			0.823904i
$647$	2.26232e14			1.99541			0.997706	−	0.0676954i	$-0.0215646\pi$
$647$	2.26232e14			1.99541			0.997706	+	0.0676954i	$0.0215646\pi$
$648$			4.88725e12i			0.0427749i
$649$	−2.08008e13	+	1.25073e13i	−0.180658	+	0.108627i
$650$	1.64916e14			1.42134
$651$			2.14496e13i			0.183448i
$652$	2.45864e14			2.08668
$653$	−1.61068e14			−1.35657			−0.678287	−	0.734797i	$-0.737277\pi$
$653$	−1.61068e14			−1.35657			−0.678287	+	0.734797i	$0.737277\pi$
$654$	−1.48387e14			−1.24024
$655$		−	2.84360e13i		−	0.235865i
$656$	−1.86995e13			−0.153925
$657$		−	1.67983e13i		−	0.137226i
$658$	−4.56250e13			−0.369891
$659$			9.82649e13i			0.790627i	0.918546	+	0.395313i	$0.129364\pi$
$659$			9.82649e13i			0.790627i	−0.918546	+	0.395313i	$0.870636\pi$
$660$			7.43080e12i			0.0593356i
$661$	1.24089e14			0.983393			0.491696	−	0.870767i	$-0.336377\pi$
$661$	1.24089e14			0.983393			0.491696	+	0.870767i	$0.336377\pi$
$662$		−	2.09408e14i		−	1.64704i
$663$		−	1.18184e14i		−	0.922555i
$664$	−1.26779e13			−0.0982217
$665$	4.86939e12			0.0374426
$666$	−9.85488e13			−0.752108
$667$		−	3.04955e13i		−	0.230997i
$668$	−2.84488e14			−2.13885
$669$	−9.69057e13			−0.723134
$670$	−1.41683e14			−1.04941
$671$	−4.62174e13			−0.339776
$672$			2.80167e13i			0.204442i
$673$			1.05709e14i			0.765662i	0.923818	+	0.382831i	$0.125051\pi$
$673$			1.05709e14i			0.765662i	−0.923818	+	0.382831i	$0.874949\pi$
$674$	1.96390e14			1.41195
$675$	2.29060e13			0.163467
$676$	4.27416e13			0.302773
$677$	1.17787e14			0.828238			0.414119	−	0.910223i	$-0.364090\pi$
$677$	1.17787e14			0.828238			0.414119	+	0.910223i	$0.364090\pi$
$678$	2.27224e14			1.58601
$679$		−	9.96653e12i		−	0.0690550i
$680$			3.11570e13i			0.214294i
$681$		−	1.27018e14i		−	0.867219i
$682$		−	5.88337e13i		−	0.398753i
$683$			1.82949e14i			1.23091i	0.788172	+	0.615455i	$0.211028\pi$
$683$			1.82949e14i			1.23091i	−0.788172	+	0.615455i	$0.788972\pi$
$684$	−2.39752e13			−0.160133
$685$	1.45783e13			0.0966617
$686$		−	1.11491e14i		−	0.733870i
$687$			2.92430e12i			0.0191090i
$688$		−	1.03572e14i		−	0.671891i
$689$			1.25732e14i			0.809747i
$690$	2.00155e13			0.127974
$691$		−	8.14976e13i		−	0.517314i	−0.965969	−	0.258657i	$-0.916720\pi$
$691$		−	8.14976e13i		−	0.517314i	0.965969	−	0.258657i	$-0.0832800\pi$
$692$			3.18345e14i			2.00617i
$693$			2.83373e12i			0.0177293i
$694$	−2.34360e14			−1.45575
$695$	1.12269e14			0.692367
$696$			2.20523e13i			0.135023i
$697$	−5.35668e13			−0.325636
$698$	2.26300e14			1.36586
$699$		−	1.49305e14i		−	0.894721i
$700$	−4.52515e13			−0.269242
$701$		−	2.29407e14i		−	1.35524i	−0.735412	−	0.677620i	$-0.763012\pi$
$701$		−	2.29407e14i		−	1.35524i	0.735412	−	0.677620i	$-0.236988\pi$
$702$	5.49020e13			0.322035
$703$		−	9.86264e13i		−	0.574403i
$704$		−	5.21304e13i		−	0.301459i
$705$			3.80832e13i			0.218669i
$706$	1.95029e14			1.11193
$707$		−	7.70576e12i		−	0.0436233i
$708$	−6.64910e13	−	1.10581e14i	−0.373763	−	0.621603i
$709$	9.37167e13			0.523101			0.261551	−	0.965190i	$-0.415766\pi$
$709$	9.37167e13			0.523101			0.261551	+	0.965190i	$0.415766\pi$
$710$			1.54082e14i			0.854006i
$711$	8.85218e11			0.00487194
$712$	4.83485e13			0.264230
$713$	−8.82373e13			−0.478855
$714$			5.82418e13i			0.313865i
$715$	1.70295e13			0.0911324
$716$			1.82006e14i			0.967211i
$717$	−7.59610e13			−0.400862
$718$		−	3.92795e14i		−	2.05847i
$719$			6.45439e13i			0.335900i	0.985795	+	0.167950i	$0.0537148\pi$
$719$			6.45439e13i			0.335900i	−0.985795	+	0.167950i	$0.946285\pi$
$720$	1.69707e13			0.0877074
$721$			6.77931e12i			0.0347944i
$722$			2.51609e14i			1.28245i
$723$	−8.54531e13			−0.432550
$724$	−5.64597e13			−0.283822
$725$	1.03357e14			0.515998
$726$			1.67140e14i			0.828698i
$727$	−2.81569e14			−1.38648			−0.693239	−	0.720708i	$-0.743817\pi$
$727$	−2.81569e14			−1.38648			−0.693239	+	0.720708i	$0.743817\pi$
$728$	−2.21267e13			−0.108208
$729$	7.62560e12			0.0370370
$730$	4.97489e13			0.239977
$731$		−	2.96693e14i		−	1.42141i
$732$		−	2.45700e14i		−	1.16910i
$733$	−1.25097e13			−0.0591188			−0.0295594	−	0.999563i	$-0.509410\pi$
$733$	−1.25097e13			−0.0591188			−0.0295594	+	0.999563i	$0.509410\pi$
$734$	3.36340e14			1.57870
$735$	−4.50009e13			−0.209790
$736$	−1.15253e14			−0.533656
$737$	8.25171e13			0.379496
$738$		−	2.48842e13i		−	0.113669i
$739$			3.10630e14i			1.40936i	0.709526	+	0.704679i	$0.248909\pi$
$739$			3.10630e14i			1.40936i	−0.709526	+	0.704679i	$0.751091\pi$
$740$		−	1.62505e14i		−	0.732330i
$741$			5.49452e13i			0.245946i
$742$		−	6.19613e13i		−	0.275487i
$743$	1.22114e13			0.0539290			0.0269645	−	0.999636i	$-0.491416\pi$
$743$	1.22114e13			0.0539290			0.0269645	+	0.999636i	$0.491416\pi$
$744$	6.38072e13			0.279901
$745$			7.38675e13i			0.321864i
$746$		−	5.18068e14i		−	2.24229i
$747$			1.97814e13i			0.0850461i
$748$		−	8.89483e13i		−	0.379865i
$749$	−9.50890e13			−0.403386
$750$			1.47702e14i			0.622416i
$751$			2.02817e14i			0.848994i	0.905429	+	0.424497i	$0.139549\pi$
$751$			2.02817e14i			0.848994i	−0.905429	+	0.424497i	$0.860451\pi$
$752$		−	1.59136e14i		−	0.661729i
$753$	−2.27176e14			−0.938400
$754$	2.47729e14			1.01653
$755$			9.91978e13i			0.404359i
$756$	−1.50646e13			−0.0610027
$757$	1.52549e14			0.613663			0.306832	−	0.951764i	$-0.400731\pi$
$757$	1.52549e14			0.613663			0.306832	+	0.951764i	$0.400731\pi$
$758$			5.67583e14i			2.26821i
$759$	−1.16571e13			−0.0462789
$760$		−	1.44852e13i		−	0.0571291i
$761$	2.28700e14			0.896072			0.448036	−	0.894016i	$-0.352124\pi$
$761$	2.28700e14			0.896072			0.448036	+	0.894016i	$0.352124\pi$
$762$		−	3.78587e14i		−	1.47364i
$763$		−	9.33108e13i		−	0.360836i
$764$		−	5.74598e14i		−	2.20748i
$765$	4.86144e13			0.185549
$766$			1.99813e14i			0.757668i
$767$	−2.53424e14	+	1.52381e14i	−0.954707	+	0.574055i
$768$	−4.80527e13			−0.179850
$769$		−	4.33481e14i		−	1.61190i	−0.591982	−	0.805951i	$-0.701654\pi$
$769$		−	4.33481e14i		−	1.61190i	0.591982	−	0.805951i	$-0.298346\pi$
$770$	−8.39223e12			−0.0310044
$771$	−1.98395e14			−0.728214
$772$	−3.30893e13			−0.120670
$773$			1.19916e14i			0.434492i	0.976117	+	0.217246i	$0.0697073\pi$
$773$			1.19916e14i			0.434492i	−0.976117	+	0.217246i	$0.930293\pi$
$774$	1.37827e14			0.496171
$775$		−	2.99057e14i		−	1.06966i
$776$	−2.96480e13			−0.105363
$777$		−	6.19710e13i		−	0.218818i
$778$		−	4.43377e13i		−	0.155552i
$779$	2.49038e13			0.0868118
$780$			9.05321e13i			0.313566i
$781$		−	8.97385e13i		−	0.308833i
$782$	−2.39590e14			−0.819284
$783$	3.44083e13			0.116911
$784$	1.88043e14			0.634859
$785$			7.51812e13i			0.252209i
$786$	−1.58125e14			−0.527092
$787$	−1.36664e14			−0.452670			−0.226335	−	0.974049i	$-0.572674\pi$
$787$	−1.36664e14			−0.452670			−0.226335	+	0.974049i	$0.572674\pi$
$788$	−2.28616e14			−0.752447
$789$	−2.35555e13			−0.0770384
$790$			2.62162e12i			0.00851989i
$791$			1.42887e14i			0.461434i
$792$	8.42965e12			0.0270510
$793$	−5.63084e14			−1.79559
$794$	2.91133e13			0.0922547
$795$	−5.17191e13			−0.162860
$796$	−6.91367e14			−2.16343
$797$			5.64804e14i			1.75633i	0.478358	+	0.878165i	$0.341232\pi$
$797$			5.64804e14i			1.75633i	−0.478358	+	0.878165i	$0.658768\pi$
$798$		−	2.70773e13i		−	0.0836739i
$799$		−	4.55864e14i		−	1.39992i
$800$		−	3.90619e14i		−	1.19207i
$801$		−	7.54383e13i		−	0.228786i
$802$	4.77119e13			0.143799
$803$	−2.89741e13			−0.0867824
$804$			4.38676e14i			1.30576i
$805$			1.25865e13i			0.0372327i
$806$		−	7.16792e14i		−	2.10726i
$807$		−	8.26860e12i		−	0.0241582i
$808$	−2.29227e13			−0.0665595
$809$			3.16395e14i			0.913034i	0.889715	+	0.456517i	$0.150903\pi$
$809$			3.16395e14i			0.913034i	−0.889715	+	0.456517i	$0.849097\pi$
$810$			2.25836e13i			0.0647691i
$811$		−	2.71723e14i		−	0.774500i	−0.921975	−	0.387250i	$-0.873425\pi$
$811$		−	2.71723e14i		−	0.774500i	0.921975	−	0.387250i	$-0.126575\pi$
$812$	−6.79746e13			−0.192560
$813$	2.09615e14			0.590160
$814$			1.69979e14i			0.475636i
$815$	2.31775e14			0.644583
$816$	−2.03142e14			−0.561500
$817$			1.37936e14i			0.378937i
$818$	2.64724e14			0.722815
$819$			3.45243e13i			0.0936927i
$820$	4.10335e13			0.110680
$821$		−	6.50932e13i		−	0.174510i	−0.996186	−	0.0872550i	$-0.972191\pi$
$821$		−	6.50932e13i		−	0.174510i	0.996186	−	0.0872550i	$-0.0278095\pi$
$822$		−	8.10658e13i		−	0.216012i
$823$			7.25621e14i			1.92181i	0.276877	+	0.960905i	$0.410701\pi$
$823$			7.25621e14i			1.92181i	−0.276877	+	0.960905i	$0.589299\pi$
$824$	2.01668e13			0.0530885
$825$		−	3.95088e13i		−	0.103377i
$826$	1.24888e14	−	7.50939e13i	0.324804	−	0.195301i
$827$	−5.15427e14			−1.33241			−0.666207	−	0.745767i	$-0.732083\pi$
$827$	−5.15427e14			−1.33241			−0.666207	+	0.745767i	$0.732083\pi$
$828$		−	6.19714e13i		−	0.159236i
$829$	−4.15282e14			−1.06065			−0.530323	−	0.847795i	$-0.677930\pi$
$829$	−4.15282e14			−1.06065			−0.530323	+	0.847795i	$0.677930\pi$
$830$	−5.85837e13			−0.148726
$831$	2.08711e14			0.526673
$832$		−	6.35124e14i		−	1.59310i
$833$	5.38671e14			1.34307
$834$		−	6.24296e14i		−	1.54725i
$835$	−2.68186e14			−0.660699
$836$			4.13531e13i			0.101269i
$837$		−	9.95587e13i		−	0.242355i
$838$	6.49060e14			1.57060
$839$			6.50012e14i			1.56355i	0.623561	+	0.781774i	$0.285685\pi$
$839$			6.50012e14i			1.56355i	−0.623561	+	0.781774i	$0.714315\pi$
$840$		−	9.10167e12i		−	0.0217633i
$841$	−2.65450e14			−0.630962
$842$	−8.24975e14			−1.94931
$843$	−3.25661e14			−0.764940
$844$			7.46338e14i			1.74270i
$845$	4.02924e13			0.0935275
$846$	2.11770e14			0.488666
$847$	−1.05103e14			−0.241101
$848$	2.16116e14			0.492842
$849$			2.41923e14i			0.548452i
$850$		−	8.12027e14i		−	1.83010i
$851$	2.54931e14			0.571182
$852$	4.77066e14			1.06263
$853$	−5.77920e14			−1.27974			−0.639871	−	0.768482i	$-0.721012\pi$
$853$	−5.77920e14			−1.27974			−0.639871	+	0.768482i	$0.721012\pi$
$854$	2.77490e14			0.610883
$855$	−2.26014e13			−0.0494657
$856$			2.82867e14i			0.615478i
$857$			1.52316e14i			0.329488i	0.986336	+	0.164744i	$0.0526799\pi$
$857$			1.52316e14i			0.329488i	−0.986336	+	0.164744i	$0.947320\pi$
$858$		−	9.46963e13i		−	0.203656i
$859$		−	2.44874e14i		−	0.523573i	−0.965126	−	0.261786i	$-0.915688\pi$
$859$		−	2.44874e14i		−	0.523573i	0.965126	−	0.261786i	$-0.0843116\pi$
$860$			2.27274e14i			0.483123i
$861$	1.56481e13			0.0330709
$862$	3.24200e13			0.0681204
$863$		−	4.22291e14i		−	0.882180i	−0.897463	−	0.441090i	$-0.854592\pi$
$863$		−	4.22291e14i		−	0.882180i	0.897463	−	0.441090i	$-0.145408\pi$
$864$		−	1.30040e14i		−	0.270090i
$865$			3.00103e14i			0.619713i
$866$		−	6.01726e14i		−	1.23540i
$867$	−2.99089e14			−0.610527
$868$			1.96681e14i			0.399176i
$869$		−	1.52685e12i		−	0.00308103i
$870$			1.01902e14i			0.204449i
$871$	1.00534e15			2.00549
$872$	−2.77577e14			−0.550555
$873$			4.62599e13i			0.0912291i
$874$	1.11388e14			0.218414
$875$	−9.28805e13			−0.181086
$876$		−	1.54031e14i		−	0.298599i
$877$	8.12428e14			1.56598			0.782991	−	0.622033i	$-0.213693\pi$
$877$	8.12428e14			1.56598			0.782991	+	0.622033i	$0.213693\pi$
$878$		−	1.19441e15i		−	2.28918i
$879$	3.36051e14			0.640414
$880$		−	2.92714e13i		−	0.0554664i
$881$			1.13539e14i			0.213927i	0.994263	+	0.106963i	$0.0341128\pi$
$881$			1.13539e14i			0.213927i	−0.994263	+	0.106963i	$0.965887\pi$
$882$			2.50237e14i			0.468823i
$883$	−1.36999e14			−0.255219			−0.127610	−	0.991824i	$-0.540730\pi$
$883$	−1.36999e14			−0.255219			−0.127610	+	0.991824i	$0.540730\pi$
$884$		−	1.08369e15i		−	2.00744i
$885$	−6.26809e13	−	1.04244e14i	−0.115457	−	0.192015i
$886$	7.11911e14			1.30394
$887$			8.10100e14i			1.47544i	0.675109	+	0.737718i	$0.264097\pi$
$887$			8.10100e14i			1.47544i	−0.675109	+	0.737718i	$0.735903\pi$
$888$	−1.84349e14			−0.333868
$889$	2.38069e14			0.428741
$890$	2.23414e14			0.400093
$891$		−	1.31528e13i		−	0.0234223i
$892$	−8.88575e14			−1.57351
$893$			2.11937e14i			0.373206i
$894$	4.10756e14			0.719277
$895$			1.71577e14i			0.298774i
$896$			1.08502e14i			0.187888i
$897$	−1.42023e14			−0.244566
$898$		−	1.24512e14i		−	0.213221i
$899$		−	4.49229e14i		−	0.765014i
$900$	2.10036e14			0.355698
$901$	6.19089e14			1.04263
$902$	−4.29209e13			−0.0718847
$903$			8.66709e13i			0.144356i
$904$	4.25053e14			0.704047
$905$	−5.32245e13			−0.0876735
$906$	5.51610e14			0.903631
$907$	6.54803e14			1.06678			0.533389	−	0.845870i	$-0.320918\pi$
$907$	6.54803e14			1.06678			0.533389	+	0.845870i	$0.320918\pi$
$908$		−	1.16469e15i		−	1.88704i
$909$			3.57665e13i			0.0576311i
$910$	−1.02246e14			−0.163847
$911$	9.35781e14			1.49136			0.745680	−	0.666304i	$-0.232125\pi$
$911$	9.35781e14			1.49136			0.745680	+	0.666304i	$0.232125\pi$
$912$	9.44432e13			0.149691
$913$	3.41195e13			0.0537835
$914$	1.43941e14			0.225659
$915$		−	2.31621e14i		−	0.361137i
$916$			2.68143e13i			0.0415805i
$917$		−	9.94344e13i		−	0.153352i
$918$		−	2.70331e14i		−	0.414650i
$919$			3.53276e14i			0.538936i	0.963009	+	0.269468i	$0.0868478\pi$
$919$			3.53276e14i			0.538936i	−0.963009	+	0.269468i	$0.913152\pi$
$920$	3.74416e13			0.0568088
$921$	4.09966e14			0.618656
$922$			5.86677e14i			0.880531i
$923$		−	1.09332e15i		−	1.63207i
$924$			2.59838e13i			0.0385783i
$925$			8.64021e14i			1.27590i
$926$	5.89113e14			0.865254
$927$		−	3.14663e13i		−	0.0459671i
$928$		−	5.86768e14i		−	0.852563i
$929$			3.90298e14i			0.564050i	0.959407	+	0.282025i	$0.0910061\pi$
$929$			3.90298e14i			0.564050i	−0.959407	+	0.282025i	$0.908994\pi$
$930$	2.94848e14			0.423822
$931$	−2.50434e14			−0.358051
$932$		−	1.36905e15i		−	1.94688i
$933$	−4.52200e14			−0.639621
$934$	6.97306e14			0.981045
$935$		−	8.38513e13i		−	0.117342i
$936$	1.02701e14			0.142954
$937$			1.18889e15i			1.64605i	0.568007	+	0.823024i	$0.307715\pi$
$937$			1.18889e15i			1.64605i	−0.568007	+	0.823024i	$0.692285\pi$
$938$	−4.95434e14			−0.682294
$939$		−	2.09442e14i		−	0.286903i
$940$			3.49203e14i			0.475816i
$941$		−	4.85054e13i		−	0.0657419i	−0.999460	−	0.0328709i	$-0.989535\pi$
$941$		−	4.85054e13i		−	0.0657419i	0.999460	−	0.0328709i	$-0.0104650\pi$
$942$	4.18061e14			0.563618
$943$			6.43717e13i			0.0863250i
$944$	2.61921e14	+	4.35600e14i	0.349391	+	0.581069i
$945$	−1.42014e13			−0.0188439
$946$		−	2.37728e14i		−	0.313780i
$947$	6.03885e14			0.792874			0.396437	−	0.918062i	$-0.370246\pi$
$947$	6.03885e14			0.792874			0.396437	+	0.918062i	$0.370246\pi$
$948$	8.11699e12			0.0106012
$949$	−3.53002e14			−0.458612
$950$			3.77521e14i			0.487891i
$951$	6.21662e14			0.799194
$952$			1.08949e14i			0.139328i
$953$	5.64065e14			0.717570			0.358785	−	0.933420i	$-0.383191\pi$
$953$	5.64065e14			0.717570			0.358785	+	0.933420i	$0.383191\pi$
$954$			2.87595e14i			0.363948i
$955$		−	5.41672e14i		−	0.681898i
$956$	−6.96523e14			−0.872260
$957$		−	5.93482e13i		−	0.0739347i
$958$			1.31535e15i			1.63010i
$959$	5.09771e13			0.0628466
$960$	2.61254e14			0.320411
$961$	−4.80195e14			−0.585869
$962$			2.07092e15i			2.51355i
$963$	4.41358e14			0.532917
$964$	−7.83561e14			−0.941212
$965$	−3.11932e13			−0.0372755
$966$	6.99896e13			0.0832047
$967$		−	1.21479e14i		−	0.143671i	−0.997416	−	0.0718356i	$-0.977114\pi$
$967$		−	1.21479e14i		−	0.143671i	0.997416	−	0.0718356i	$-0.0228857\pi$
$968$			3.12657e14i			0.367867i
$969$	2.70544e14			0.316678
$970$	−1.37001e14			−0.159538
$971$	7.06931e14			0.818994			0.409497	−	0.912311i	$-0.365704\pi$
$971$	7.06931e14			0.818994			0.409497	+	0.912311i	$0.365704\pi$
$972$	6.99228e13			0.0805911
$973$	3.92580e14			0.450157
$974$		−	1.11461e15i		−	1.27153i
$975$		−	4.81350e14i		−	0.546309i
$976$			9.67863e14i			1.09286i
$977$		−	1.21808e15i		−	1.36837i	−0.729310	−	0.684183i	$-0.760159\pi$
$977$		−	1.21808e15i		−	1.36837i	0.729310	−	0.684183i	$-0.239841\pi$
$978$		−	1.28884e15i		−	1.44047i
$979$	−1.30118e14			−0.144685
$980$	−4.12635e14			−0.456495
$981$			4.33105e14i			0.476703i
$982$			1.17699e15i			1.28889i
$983$		−	7.48886e12i		−	0.00815921i	−0.999992	−	0.00407961i	$-0.998701\pi$
$983$		−	7.48886e12i		−	0.00815921i	0.999992	−	0.00407961i	$-0.00129858\pi$
$984$		−	4.65492e13i		−	0.0504588i
$985$	−2.15516e14			−0.232433
$986$		−	1.21979e15i		−	1.30888i
$987$			1.33168e14i			0.142172i
$988$			5.03819e14i			0.535168i
$989$	−3.56539e14			−0.376813
$990$	3.89528e13			0.0409602
$991$		−	9.80875e13i		−	0.102623i	−0.998683	−	0.0513116i	$-0.983660\pi$
$991$		−	9.80875e13i		−	0.102623i	0.998683	−	0.0513116i	$-0.0163402\pi$
$992$	−1.69779e15			−1.76736
$993$	−6.11211e14			−0.633060
$994$			5.38791e14i			0.555250i
$995$	−6.51750e14			−0.668291
$996$			1.81385e14i			0.185057i
$997$	−1.66006e15			−1.68519			−0.842595	−	0.538548i	$-0.818973\pi$
$997$	−1.66006e15			−1.68519			−0.842595	+	0.538548i	$0.818973\pi$
$998$			9.39275e14i			0.948724i
$999$			2.87640e14i			0.289083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.15	✓	100
59.58	odd	2	inner	177.11.c.a.58.86	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.15	✓	100	1.1	even	1	trivial
177.11.c.a.58.86	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)

\(f(q)\)	\(=\)	\(q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-48.0671i q^{2} -140.296 q^{3} -1286.44 q^{4} -1212.73 q^{5} +6743.62i q^{6} -4240.63 q^{7} +12614.8i q^{8} +19683.0 q^{9} +58292.2i q^{10} -33949.7i q^{11} +180483. q^{12} -413622. i q^{13} +203835. i q^{14} +170141. q^{15} -710959. q^{16} -2.03662e6 q^{17} -946104. i q^{18} +946849. q^{19} +1.56010e6 q^{20} +594944. q^{21} -1.63186e6 q^{22} +2.44743e6i q^{23} -1.76981e6i q^{24} -8.29492e6 q^{25} -1.98816e7 q^{26} -2.76145e6 q^{27} +5.45533e6 q^{28} -1.24602e7 q^{29} -8.17817e6i q^{30} +3.60531e7i q^{31} +4.70913e7i q^{32} +4.76302e6i q^{33} +9.78945e7i q^{34} +5.14273e6 q^{35} -2.53210e7 q^{36} -1.04163e8i q^{37} -4.55123e7i q^{38} +5.80296e7i q^{39} -1.52984e7i q^{40} +2.63018e7 q^{41} -2.85972e7i q^{42} +1.45679e8i q^{43} +4.36744e7i q^{44} -2.38701e7 q^{45} +1.17641e8 q^{46} +2.23833e8i q^{47} +9.97448e7 q^{48} -2.64492e8 q^{49} +3.98712e8i q^{50} +2.85730e8 q^{51} +5.32101e8i q^{52} -3.03978e8 q^{53} +1.32735e8i q^{54} +4.11717e7i q^{55} -5.34949e7i q^{56} -1.32839e8 q^{57} +5.98926e8i q^{58} +(-3.68406e8 - 6.12694e8i) q^{59} -2.18876e8 q^{60} -1.36135e9i q^{61} +1.73296e9 q^{62} -8.34684e7 q^{63} +1.53552e9 q^{64} +5.01610e8i q^{65} +2.28944e8 q^{66} +2.43057e9i q^{67} +2.62000e9 q^{68} -3.43365e8i q^{69} -2.47196e8i q^{70} +2.64328e9 q^{71} +2.48298e8i q^{72} -8.53440e8i q^{73} -5.00680e9 q^{74} +1.16374e9 q^{75} -1.21807e9 q^{76} +1.43968e8i q^{77} +2.78931e9 q^{78} +4.49737e7 q^{79} +8.62199e8 q^{80} +3.87420e8 q^{81} -1.26425e9i q^{82} +1.00500e9i q^{83} -7.65362e8 q^{84} +2.46987e9 q^{85} +7.00236e9 q^{86} +1.74812e9 q^{87} +4.28271e8 q^{88} -3.83266e9i q^{89} +1.14737e9i q^{90} +1.75402e9i q^{91} -3.14848e9i q^{92} -5.05810e9i q^{93} +1.07590e10 q^{94} -1.14827e9 q^{95} -6.60673e9i q^{96} +2.35025e9i q^{97} +1.27134e10i q^{98} -6.68233e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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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