LMFDB - Embedded newform 177.11.c.a.58.10

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			58.10
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.91

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +245660. i q^{10} -21424.0i q^{11} +277891. q^{12} -309118. i q^{13} +1.50037e6i q^{14} +628748. q^{15} +846494. q^{16} +1.91085e6 q^{17} -1.07893e6i q^{18} -675482. q^{19} +8.87686e6 q^{20} +3.84007e6 q^{21} -1.17437e6 q^{22} -4.00666e6i q^{23} -7.35777e6i q^{24} +1.03189e7 q^{25} -1.69445e7 q^{26} -2.76145e6 q^{27} +5.42154e7 q^{28} +1.18366e7 q^{29} -3.44652e7i q^{30} -1.59663e7i q^{31} +7.30219e6i q^{32} +3.00570e6i q^{33} -1.04745e8i q^{34} +1.22666e8 q^{35} -3.89870e7 q^{36} -7.63595e7i q^{37} +3.70269e7i q^{38} +4.33680e7i q^{39} -2.35034e8i q^{40} +4.81846e7 q^{41} -2.10496e8i q^{42} +1.47581e8i q^{43} +4.24354e7i q^{44} -8.82109e7 q^{45} -2.19627e8 q^{46} -8.31364e7i q^{47} -1.18760e8 q^{48} +4.66708e8 q^{49} -5.65637e8i q^{50} -2.68085e8 q^{51} +6.12284e8i q^{52} +5.12608e8 q^{53} +1.51370e8i q^{54} +9.60132e7i q^{55} -1.43547e9i q^{56} +9.47675e7 q^{57} -6.48828e8i q^{58} +(4.98252e8 + 5.12701e8i) q^{59} -1.24539e9 q^{60} +2.96707e8i q^{61} -8.75202e8 q^{62} -5.38747e8 q^{63} +1.26708e9 q^{64} +1.38533e9i q^{65} +1.64759e8 q^{66} +5.57657e8i q^{67} -3.78492e9 q^{68} +5.62119e8i q^{69} -6.72401e9i q^{70} -6.33242e8 q^{71} +1.03227e9i q^{72} -6.09409e8i q^{73} -4.18569e9 q^{74} -1.44770e9 q^{75} +1.33796e9 q^{76} +5.86400e8i q^{77} +2.37724e9 q^{78} -1.56682e9 q^{79} -3.79363e9 q^{80} +3.87420e8 q^{81} -2.64126e9i q^{82} -1.79188e9i q^{83} -7.60621e9 q^{84} -8.56364e9 q^{85} +8.08972e9 q^{86} -1.66062e9 q^{87} +1.12357e9 q^{88} +9.80823e9i q^{89} +4.83533e9i q^{90} +8.46093e9i q^{91} +7.93617e9i q^{92} +2.24001e9i q^{93} -4.55717e9 q^{94} +3.02722e9 q^{95} -1.02447e9i q^{96} -7.87880e9i q^{97} -2.55828e10i q^{98} -4.21688e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	54.8156i		−	1.71299i	−0.516158	−	0.856493i	$-0.672638\pi$
$2$		−	54.8156i		−	1.71299i	0.516158	−	0.856493i	$-0.327362\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−1980.75			−1.93432
$5$	−4481.58			−1.43410			−0.717052	−	0.697019i	$-0.754509\pi$
$5$	−4481.58			−1.43410			−0.717052	+	0.697019i	$0.754509\pi$
$6$			7690.41i			0.988993i
$7$	−27371.2			−1.62856			−0.814280	−	0.580472i	$-0.802868\pi$
$7$	−27371.2			−1.62856			−0.814280	+	0.580472i	$0.802868\pi$
$8$			52444.5i			1.60048i
$9$	19683.0			0.333333
$10$			245660.i			2.45660i
$11$		−	21424.0i		−	0.133026i	−0.997786	−	0.0665130i	$-0.978813\pi$
$11$		−	21424.0i		−	0.133026i	0.997786	−	0.0665130i	$-0.0211874\pi$
$12$	277891.			1.11678
$13$		−	309118.i		−	0.832544i	−0.909240	−	0.416272i	$-0.863336\pi$
$13$		−	309118.i		−	0.832544i	0.909240	−	0.416272i	$-0.136664\pi$
$14$			1.50037e6i			2.78970i
$15$	628748.			0.827981
$16$	846494.			0.807279
$17$	1.91085e6			1.34581			0.672904	−	0.739730i	$-0.265047\pi$
$17$	1.91085e6			1.34581			0.672904	+	0.739730i	$0.265047\pi$
$18$		−	1.07893e6i		−	0.570995i
$19$	−675482.			−0.272801			−0.136400	−	0.990654i	$-0.543553\pi$
$19$	−675482.			−0.272801			−0.136400	+	0.990654i	$0.543553\pi$
$20$	8.87686e6			2.77402
$21$	3.84007e6			0.940249
$22$	−1.17437e6			−0.227872
$23$		−	4.00666e6i		−	0.622505i	−0.950327	−	0.311253i	$-0.899251\pi$
$23$		−	4.00666e6i		−	0.622505i	0.950327	−	0.311253i	$-0.100749\pi$
$24$		−	7.35777e6i		−	0.924038i
$25$	1.03189e7			1.05666
$26$	−1.69445e7			−1.42614
$27$	−2.76145e6			−0.192450
$28$	5.42154e7			3.15016
$29$	1.18366e7			0.577080			0.288540	−	0.957468i	$-0.406830\pi$
$29$	1.18366e7			0.577080			0.288540	+	0.957468i	$0.406830\pi$
$30$		−	3.44652e7i		−	1.41832i
$31$		−	1.59663e7i		−	0.557694i	−0.960336	−	0.278847i	$-0.910048\pi$
$31$		−	1.59663e7i		−	0.557694i	0.960336	−	0.278847i	$-0.0899522\pi$
$32$			7.30219e6i			0.217622i
$33$			3.00570e6i			0.0768026i
$34$		−	1.04745e8i		−	2.30535i
$35$	1.22666e8			2.33553
$36$	−3.89870e7			−0.644774
$37$		−	7.63595e7i		−	1.10117i	−0.834779	−	0.550585i	$-0.814405\pi$
$37$		−	7.63595e7i		−	1.10117i	0.834779	−	0.550585i	$-0.185595\pi$
$38$			3.70269e7i			0.467304i
$39$			4.33680e7i			0.480669i
$40$		−	2.35034e8i		−	2.29526i
$41$	4.81846e7			0.415900			0.207950	−	0.978139i	$-0.433321\pi$
$41$	4.81846e7			0.415900			0.207950	+	0.978139i	$0.433321\pi$
$42$		−	2.10496e8i		−	1.61063i
$43$			1.47581e8i			1.00389i	0.864899	+	0.501946i	$0.167383\pi$
$43$			1.47581e8i			1.00389i	−0.864899	+	0.501946i	$0.832617\pi$
$44$			4.24354e7i			0.257315i
$45$	−8.82109e7			−0.478035
$46$	−2.19627e8			−1.06634
$47$		−	8.31364e7i		−	0.362495i	−0.983438	−	0.181248i	$-0.941986\pi$
$47$		−	8.31364e7i		−	0.362495i	0.983438	−	0.181248i	$-0.0580135\pi$
$48$	−1.18760e8			−0.466083
$49$	4.66708e8			1.65221
$50$		−	5.65637e8i		−	1.81004i
$51$	−2.68085e8			−0.777002
$52$			6.12284e8i			1.61041i
$53$	5.12608e8			1.22576			0.612881	−	0.790176i	$-0.290011\pi$
$53$	5.12608e8			1.22576			0.612881	+	0.790176i	$0.290011\pi$
$54$			1.51370e8i			0.329664i
$55$			9.60132e7i			0.190773i
$56$		−	1.43547e9i		−	2.60648i
$57$	9.47675e7			0.157502
$58$		−	6.48828e8i		−	0.988529i
$59$	4.98252e8	+	5.12701e8i	0.696929	+	0.717140i
$59$	4.98252e8	+	5.12701e8i	0.696929	+	0.717140i
$60$	−1.24539e9			−1.60158
$61$			2.96707e8i			0.351301i	0.984453	+	0.175650i	$0.0562028\pi$
$61$			2.96707e8i			0.351301i	−0.984453	+	0.175650i	$0.943797\pi$
$62$	−8.75202e8			−0.955322
$63$	−5.38747e8			−0.542853
$64$	1.26708e9			1.18006
$65$			1.38533e9i			1.19396i
$66$	1.64759e8			0.131562
$67$			5.57657e8i			0.413041i	0.978442	+	0.206520i	$0.0662140\pi$
$67$			5.57657e8i			0.413041i	−0.978442	+	0.206520i	$0.933786\pi$
$68$	−3.78492e9			−2.60322
$69$			5.62119e8i			0.359404i
$70$		−	6.72401e9i		−	4.00072i
$71$	−6.33242e8			−0.350976			−0.175488	−	0.984482i	$-0.556150\pi$
$71$	−6.33242e8			−0.350976			−0.175488	+	0.984482i	$0.556150\pi$
$72$			1.03227e9i			0.533493i
$73$		−	6.09409e8i		−	0.293964i	−0.989139	−	0.146982i	$-0.953044\pi$
$73$		−	6.09409e8i		−	0.293964i	0.989139	−	0.146982i	$-0.0469560\pi$
$74$	−4.18569e9			−1.88629
$75$	−1.44770e9			−0.610061
$76$	1.33796e9			0.527685
$77$			5.86400e8i			0.216641i
$78$	2.37724e9			0.823380
$79$	−1.56682e9			−0.509196			−0.254598	−	0.967047i	$-0.581943\pi$
$79$	−1.56682e9			−0.509196			−0.254598	+	0.967047i	$0.581943\pi$
$80$	−3.79363e9			−1.15772
$81$	3.87420e8			0.111111
$82$		−	2.64126e9i		−	0.712431i
$83$		−	1.79188e9i		−	0.454903i	−0.973789	−	0.227451i	$-0.926961\pi$
$83$		−	1.79188e9i		−	0.454903i	0.973789	−	0.227451i	$-0.0730393\pi$
$84$	−7.60621e9			−1.81875
$85$	−8.56364e9			−1.93003
$86$	8.08972e9			1.71965
$87$	−1.66062e9			−0.333177
$88$	1.12357e9			0.212906
$89$			9.80823e9i			1.75647i	0.478230	+	0.878235i	$0.341279\pi$
$89$			9.80823e9i			1.75647i	−0.478230	+	0.878235i	$0.658721\pi$
$90$			4.83533e9i			0.818867i
$91$			8.46093e9i			1.35585i
$92$			7.93617e9i			1.20413i
$93$			2.24001e9i			0.321985i
$94$	−4.55717e9			−0.620949
$95$	3.02722e9			0.391225
$96$		−	1.02447e9i		−	0.125644i
$97$		−	7.87880e9i		−	0.917490i	−0.888568	−	0.458745i	$-0.848299\pi$
$97$		−	7.87880e9i		−	0.917490i	0.888568	−	0.458745i	$-0.151701\pi$
$98$		−	2.55828e10i		−	2.83021i
$99$		−	4.21688e8i		−	0.0443420i
$100$	−2.04391e10			−2.04391
$101$		−	1.38657e10i		−	1.31927i	−0.751584	−	0.659637i	$-0.770710\pi$
$101$		−	1.38657e10i		−	1.31927i	0.751584	−	0.659637i	$-0.229290\pi$
$102$			1.46952e10i			1.33099i
$103$		−	7.33673e9i		−	0.632872i	−0.948614	−	0.316436i	$-0.897514\pi$
$103$		−	7.33673e9i		−	0.632872i	0.948614	−	0.316436i	$-0.102486\pi$
$104$	1.62115e10			1.33247
$105$	−1.72096e10			−1.34842
$106$		−	2.80989e10i		−	2.09971i
$107$	−1.43613e10			−1.02394			−0.511971	−	0.859003i	$-0.671085\pi$
$107$	−1.43613e10			−1.02394			−0.511971	+	0.859003i	$0.671085\pi$
$108$	5.46973e9			0.372260
$109$		−	1.28408e10i		−	0.834562i	−0.908777	−	0.417281i	$-0.862983\pi$
$109$		−	1.28408e10i		−	0.834562i	0.908777	−	0.417281i	$-0.137017\pi$
$110$	5.26302e9			0.326792
$111$			1.07129e10i			0.635761i
$112$	−2.31696e10			−1.31470
$113$			4.19928e9i			0.227920i	0.993485	+	0.113960i	$0.0363536\pi$
$113$			4.19928e9i			0.227920i	−0.993485	+	0.113960i	$0.963646\pi$
$114$		−	5.19473e9i		−	0.269798i
$115$			1.79561e10i			0.892738i
$116$	−2.34452e10			−1.11626
$117$		−	6.08436e9i		−	0.277515i
$118$	2.81040e10	−	2.73119e10i	1.22845	−	1.19383i
$119$	−5.23024e10			−2.19173
$120$			3.29744e10i			1.32517i
$121$	2.54784e10			0.982304
$122$	1.62642e10			0.601773
$123$	−6.76011e9			−0.240120
$124$			3.16252e10i			1.07876i
$125$	−2.47957e9			−0.0812505
$126$			2.95317e10i			0.929900i
$127$	4.28326e10			1.29645			0.648225	−	0.761449i	$-0.275511\pi$
$127$	4.28326e10			1.29645			0.648225	+	0.761449i	$0.275511\pi$
$128$		−	6.19784e10i		−	1.80381i
$129$		−	2.07050e10i		−	0.579598i
$130$	7.59379e10			2.04523
$131$			7.08750e10i			1.83712i	0.395285	+	0.918558i	$0.370646\pi$
$131$			7.08750e10i			1.83712i	−0.395285	+	0.918558i	$0.629354\pi$
$132$		−	5.95353e9i		−	0.148561i
$133$	1.84888e10			0.444272
$134$	3.05683e10			0.707534
$135$	1.23756e10			0.275994
$136$			1.00214e11i			2.15394i
$137$	6.98990e10			1.44833			0.724166	−	0.689625i	$-0.242225\pi$
$137$	6.98990e10			1.44833			0.724166	+	0.689625i	$0.242225\pi$
$138$	3.08128e10			0.615654
$139$	1.83568e7			0.000353771			0.000176886	−	1.00000i	$-0.499944\pi$
$139$	1.83568e7			0.000353771			0.000176886		1.00000i	$0.499944\pi$
$140$	−2.42970e11			−4.51766
$141$			1.16637e10i			0.209287i
$142$			3.47115e10i			0.601218i
$143$	−6.62253e9			−0.110750
$144$	1.66615e10			0.269093
$145$	−5.30465e10			−0.827593
$146$	−3.34051e10			−0.503556
$147$	−6.54773e10			−0.953902
$148$			1.51249e11i			2.13002i
$149$		−	6.81370e10i		−	0.927795i	−0.885889	−	0.463897i	$-0.846451\pi$
$149$		−	6.81370e10i		−	0.927795i	0.885889	−	0.463897i	$-0.153549\pi$
$150$			7.93566e10i			1.04503i
$151$			1.12413e11i			1.43196i	0.698119	+	0.715981i	$0.254020\pi$
$151$			1.12413e11i			1.43196i	−0.698119	+	0.715981i	$0.745980\pi$
$152$		−	3.54253e10i		−	0.436612i
$153$	3.76113e10			0.448602
$154$	3.21438e10			0.371103
$155$			7.15542e10i			0.799791i
$156$		−	8.59010e10i		−	0.929769i
$157$			1.54822e11i			1.62306i	0.584313	+	0.811528i	$0.301364\pi$
$157$			1.54822e11i			1.62306i	−0.584313	+	0.811528i	$0.698636\pi$
$158$			8.58864e10i			0.872246i
$159$	−7.19169e10			−0.707693
$160$		−	3.27253e10i		−	0.312093i
$161$			1.09667e11i			1.01379i
$162$		−	2.12367e10i		−	0.190332i
$163$	2.52617e10			0.219545			0.109773	−	0.993957i	$-0.464988\pi$
$163$	2.52617e10			0.219545			0.109773	+	0.993957i	$0.464988\pi$
$164$	−9.54414e10			−0.804484
$165$		−	1.34703e10i		−	0.110143i
$166$	−9.82229e10			−0.779242
$167$	−8.02086e9			−0.0617502			−0.0308751	−	0.999523i	$-0.509829\pi$
$167$	−8.02086e9			−0.0617502			−0.0308751	+	0.999523i	$0.509829\pi$
$168$			2.01391e11i			1.50485i
$169$	4.23047e10			0.306871
$170$			4.69421e11i			3.30611i
$171$	−1.32955e10			−0.0909336
$172$		−	2.92320e11i		−	1.94185i
$173$		−	2.51337e11i		−	1.62190i	−0.585113	−	0.810952i	$-0.698950\pi$
$173$		−	2.51337e11i		−	1.62190i	0.585113	−	0.810952i	$-0.301050\pi$
$174$			9.10280e10i			0.570728i
$175$	−2.82441e11			−1.72083
$176$		−	1.81353e10i		−	0.107389i
$177$	−6.99028e10	−	7.19299e10i	−0.402372	−	0.414041i
$178$	5.37644e11			3.00881
$179$			1.16008e11i			0.631283i	0.948878	+	0.315642i	$0.102220\pi$
$179$			1.16008e11i			0.631283i	−0.948878	+	0.315642i	$0.897780\pi$
$180$	1.74723e11			0.924673
$181$	1.96522e11			1.01162			0.505811	−	0.862644i	$-0.331193\pi$
$181$	1.96522e11			1.01162			0.505811	+	0.862644i	$0.331193\pi$
$182$	4.63790e11			2.32255
$183$		−	4.16269e10i		−	0.202824i
$184$	2.10127e11			0.996308
$185$			3.42211e11i			1.57919i
$186$	1.22787e11			0.551555
$187$		−	4.09381e10i		−	0.179027i
$188$			1.64672e11i			0.701182i
$189$	7.55842e10			0.313416
$190$		−	1.65939e11i		−	0.670163i
$191$		−	4.12495e11i		−	1.62275i	−0.584524	−	0.811376i	$-0.698719\pi$
$191$		−	4.12495e11i		−	1.62275i	0.584524	−	0.811376i	$-0.301281\pi$
$192$	−1.77767e11			−0.681310
$193$	−2.45939e11			−0.918418			−0.459209	−	0.888328i	$-0.651867\pi$
$193$	−2.45939e11			−0.918418			−0.459209	+	0.888328i	$0.651867\pi$
$194$	−4.31881e11			−1.57165
$195$		−	1.94357e11i		−	0.689330i
$196$	−9.24429e11			−3.19590
$197$	−3.72976e10			−0.125704			−0.0628521	−	0.998023i	$-0.520020\pi$
$197$	−3.72976e10			−0.125704			−0.0628521	+	0.998023i	$0.520020\pi$
$198$	−2.31151e10			−0.0759573
$199$	4.63716e11			1.48589			0.742946	−	0.669352i	$-0.233428\pi$
$199$	4.63716e11			1.48589			0.742946	+	0.669352i	$0.233428\pi$
$200$			5.41170e11i			1.69116i
$201$		−	7.82371e10i		−	0.238469i
$202$	−7.60056e11			−2.25990
$203$	−3.23981e11			−0.939809
$204$	5.31009e11			1.50297
$205$	−2.15943e11			−0.596444
$206$	−4.02167e11			−1.08410
$207$		−	7.88631e10i		−	0.207502i
$208$		−	2.61666e11i		−	0.672095i
$209$			1.44715e10i			0.0362896i
$210$			9.43353e11i			2.30982i
$211$		−	7.10941e11i		−	1.69989i	−0.526871	−	0.849946i	$-0.676635\pi$
$211$		−	7.10941e11i		−	1.69989i	0.526871	−	0.849946i	$-0.323365\pi$
$212$	−1.01535e12			−2.37102
$213$	8.88414e10			0.202636
$214$			7.87224e11i			1.75400i
$215$		−	6.61394e11i		−	1.43969i
$216$		−	1.44823e11i		−	0.308013i
$217$			4.37017e11i			0.908238i
$218$	−7.03874e11			−1.42959
$219$			8.54977e10i			0.169720i
$220$		−	1.90178e11i		−	0.369017i
$221$		−	5.90679e11i		−	1.12044i
$222$	5.87236e11			1.08905
$223$	8.81026e11			1.59759			0.798794	−	0.601605i	$-0.205472\pi$
$223$	8.81026e11			1.59759			0.798794	+	0.601605i	$0.205472\pi$
$224$		−	1.99870e11i		−	0.354411i
$225$	2.03107e11			0.352219
$226$	2.30186e11			0.390424
$227$		−	5.30184e11i		−	0.879625i	−0.898090	−	0.439813i	$-0.855045\pi$
$227$		−	5.30184e11i		−	0.879625i	0.898090	−	0.439813i	$-0.144955\pi$
$228$	−1.87710e11			−0.304659
$229$			5.38590e11i			0.855226i	0.903962	+	0.427613i	$0.140645\pi$
$229$			5.38590e11i			0.855226i	−0.903962	+	0.427613i	$0.859355\pi$
$230$	9.84276e11			1.52925
$231$		−	8.22697e10i		−	0.125078i
$232$			6.20763e11i			0.923605i
$233$		−	3.84999e11i		−	0.560635i	−0.959907	−	0.280318i	$-0.909560\pi$
$233$		−	3.84999e11i		−	0.560635i	0.959907	−	0.280318i	$-0.0904398\pi$
$234$	−3.33518e11			−0.475379
$235$			3.72582e11i			0.519856i
$236$	−9.86910e11	−	1.01553e12i	−1.34809	−	1.38718i
$237$	2.19819e11			0.293984
$238$			2.86698e12i			3.75440i
$239$	−1.14818e12			−1.47238			−0.736190	−	0.676775i	$-0.763377\pi$
$239$	−1.14818e12			−1.47238			−0.736190	+	0.676775i	$0.763377\pi$
$240$	5.32231e11			0.668412
$241$	−4.12541e11			−0.507436			−0.253718	−	0.967278i	$-0.581654\pi$
$241$	−4.12541e11			−0.507436			−0.253718	+	0.967278i	$0.581654\pi$
$242$		−	1.39661e12i		−	1.68267i
$243$	−5.43536e10			−0.0641500
$244$		−	5.87702e11i		−	0.679529i
$245$	−2.09159e12			−2.36944
$246$			3.70559e11i			0.411322i
$247$			2.08803e11i			0.227119i
$248$	8.37345e11			0.892578
$249$			2.51394e11i			0.262638i
$250$			1.35919e11i			0.139181i
$251$	−7.38749e11			−0.741530			−0.370765	−	0.928727i	$-0.620904\pi$
$251$	−7.38749e11			−0.741530			−0.370765	+	0.928727i	$0.620904\pi$
$252$	1.06712e12			1.05005
$253$	−8.58386e10			−0.0828094
$254$		−	2.34789e12i		−	2.22080i
$255$	1.20145e12			1.11430
$256$	−2.09989e12			−1.90984
$257$	1.59405e12			1.42180			0.710898	−	0.703296i	$-0.248289\pi$
$257$	1.59405e12			1.42180			0.710898	+	0.703296i	$0.248289\pi$
$258$	−1.13496e12			−0.992843
$259$			2.09005e12i			1.79332i
$260$		−	2.74400e12i		−	2.30949i
$261$	2.32979e11			0.192360
$262$	3.88505e12			3.14696
$263$	−1.52501e12			−1.21197			−0.605987	−	0.795475i	$-0.707222\pi$
$263$	−1.52501e12			−1.21197			−0.605987	+	0.795475i	$0.707222\pi$
$264$	−1.57633e11			−0.122921
$265$	−2.29729e12			−1.75787
$266$		−	1.01347e12i		−	0.761033i
$267$		−	1.37606e12i		−	1.01410i
$268$		−	1.10458e12i		−	0.798954i
$269$		−	2.61925e12i		−	1.85959i	−0.368083	−	0.929793i	$-0.619986\pi$
$269$		−	2.61925e12i		−	1.85959i	0.368083	−	0.929793i	$-0.380014\pi$
$270$		−	6.78378e11i		−	0.472773i
$271$	−2.22168e12			−1.51997			−0.759984	−	0.649942i	$-0.774793\pi$
$271$	−2.22168e12			−1.51997			−0.759984	+	0.649942i	$0.774793\pi$
$272$	1.61753e12			1.08644
$273$		−	1.18703e12i		−	0.782799i
$274$		−	3.83155e12i		−	2.48097i
$275$		−	2.21072e11i		−	0.140563i
$276$		−	1.11341e12i		−	0.695202i
$277$	1.07104e12			0.656758			0.328379	−	0.944546i	$-0.393498\pi$
$277$	1.07104e12			0.656758			0.328379	+	0.944546i	$0.393498\pi$
$278$		−	1.00624e9i		−	0.000606006i
$279$		−	3.14265e11i		−	0.185898i
$280$			6.43317e12i			3.73796i
$281$	−9.21119e11			−0.525756			−0.262878	−	0.964829i	$-0.584672\pi$
$281$	−9.21119e11			−0.525756			−0.262878	+	0.964829i	$0.584672\pi$
$282$	6.39353e11			0.358505
$283$			1.71565e12i			0.945142i	0.881293	+	0.472571i	$0.156674\pi$
$283$			1.71565e12i			0.945142i	−0.881293	+	0.472571i	$0.843326\pi$
$284$	1.25429e12			0.678901
$285$	−4.24708e11			−0.225874
$286$			3.63018e11i			0.189713i
$287$	−1.31887e12			−0.677318
$288$			1.43729e11i			0.0725408i
$289$	1.63537e12			0.811197
$290$			2.90777e12i			1.41765i
$291$			1.10536e12i			0.529713i
$292$			1.20708e12i			0.568621i
$293$	9.31552e10			0.0431389			0.0215694	−	0.999767i	$-0.493134\pi$
$293$	9.31552e10			0.0431389			0.0215694	+	0.999767i	$0.493134\pi$
$294$			3.58917e12i			1.63402i
$295$	−2.23295e12	−	2.29771e12i	−0.999470	−	1.02845i
$296$	4.00464e12			1.76240
$297$			5.91612e10i			0.0256009i
$298$	−3.73497e12			−1.58930
$299$	−1.23853e12			−0.518263
$300$	2.86753e12			1.18005
$301$		−	4.03946e12i		−	1.63490i
$302$	6.16198e12			2.45293
$303$			1.94530e12i			0.761683i
$304$	−5.71791e11			−0.220226
$305$		−	1.32972e12i		−	0.503802i
$306$		−	2.06169e12i		−	0.768450i
$307$	−1.27727e12			−0.468374			−0.234187	−	0.972192i	$-0.575243\pi$
$307$	−1.27727e12			−0.468374			−0.234187	+	0.972192i	$0.575243\pi$
$308$		−	1.16151e12i		−	0.419053i
$309$			1.02931e12i			0.365389i
$310$	3.92228e12			1.37003
$311$	2.75148e12			0.945723			0.472862	−	0.881137i	$-0.343221\pi$
$311$	2.75148e12			0.945723			0.472862	+	0.881137i	$0.343221\pi$
$312$	−2.27442e12			−0.769302
$313$			2.13941e12i			0.712151i	0.934457	+	0.356075i	$0.115885\pi$
$313$			2.13941e12i			0.712151i	−0.934457	+	0.356075i	$0.884115\pi$
$314$	8.48664e12			2.78027
$315$	2.41444e12			0.778508
$316$	3.10348e12			0.984949
$317$	1.34809e12			0.421137			0.210568	−	0.977579i	$-0.432469\pi$
$317$	1.34809e12			0.421137			0.210568	+	0.977579i	$0.432469\pi$
$318$			3.94216e12i			1.21227i
$319$		−	2.53586e11i		−	0.0767666i
$320$	−5.67853e12			−1.69233
$321$	2.01484e12			0.591174
$322$	6.01146e12			1.73660
$323$	−1.29075e12			−0.367137
$324$	−7.67381e11			−0.214925
$325$		−	3.18976e12i		−	0.879712i
$326$		−	1.38473e12i		−	0.376078i
$327$			1.80151e12i			0.481835i
$328$			2.52702e12i			0.665639i
$329$			2.27554e12i			0.590345i
$330$	−7.38381e11			−0.188673
$331$	5.34528e12			1.34534			0.672668	−	0.739944i	$-0.265148\pi$
$331$	5.34528e12			1.34534			0.672668	+	0.739944i	$0.265148\pi$
$332$			3.54926e12i			0.879928i
$333$		−	1.50298e12i		−	0.367057i
$334$			4.39668e11i			0.105777i
$335$		−	2.49918e12i		−	0.592344i
$336$	3.25060e12			0.759044
$337$			5.65028e11i			0.129993i	0.997885	+	0.0649965i	$0.0207036\pi$
$337$			5.65028e11i			0.129993i	−0.997885	+	0.0649965i	$0.979296\pi$
$338$		−	2.31896e12i		−	0.525665i
$339$		−	5.89143e11i		−	0.131590i
$340$	1.69624e13			3.73330
$341$	−3.42062e11			−0.0741878
$342$			7.28801e11i			0.155768i
$343$	−5.04266e12			−1.06216
$344$	−7.73980e12			−1.60671
$345$		−	2.51918e12i		−	0.515422i
$346$	−1.37772e13			−2.77830
$347$			3.89130e12i			0.773476i	0.922190	+	0.386738i	$0.126398\pi$
$347$			3.89130e12i			0.773476i	−0.922190	+	0.386738i	$0.873602\pi$
$348$	3.28927e12			0.644472
$349$		−	1.06678e12i		−	0.206039i	−0.994679	−	0.103020i	$-0.967150\pi$
$349$		−	1.06678e12i		−	0.206039i	0.994679	−	0.103020i	$-0.0328504\pi$
$350$			1.54822e13i			2.94775i
$351$			8.53613e11i			0.160223i
$352$	1.56442e11			0.0289494
$353$		−	4.84504e11i		−	0.0883942i	−0.999023	−	0.0441971i	$-0.985927\pi$
$353$		−	4.84504e11i		−	0.0883942i	0.999023	−	0.0441971i	$-0.0140730\pi$
$354$	−3.94288e12	+	3.83176e12i	−0.709246	+	0.689258i
$355$	2.83792e12			0.503337
$356$		−	1.94276e13i		−	3.39758i
$357$	7.33782e12			1.26539
$358$	6.35907e12			1.08138
$359$	1.04808e13			1.75762			0.878808	−	0.477175i	$-0.158339\pi$
$359$	1.04808e13			1.75762			0.878808	+	0.477175i	$0.158339\pi$
$360$		−	4.62618e12i		−	0.765085i
$361$	−5.67479e12			−0.925580
$362$		−	1.07725e13i		−	1.73290i
$363$	−3.57453e12			−0.567134
$364$		−	1.67589e13i		−	2.62265i
$365$			2.73111e12i			0.421575i
$366$	−2.28180e12			−0.347434
$367$		−	8.72911e12i		−	1.31111i	−0.755147	−	0.655555i	$-0.772435\pi$
$367$		−	8.72911e12i		−	1.31111i	0.755147	−	0.655555i	$-0.227565\pi$
$368$		−	3.39161e12i		−	0.502536i
$369$	9.48417e11			0.138633
$370$	1.87585e13			2.70514
$371$	−1.40307e13			−1.99623
$372$		−	4.43689e12i		−	0.622822i
$373$	7.39620e12			1.02439			0.512194	−	0.858870i	$-0.328833\pi$
$373$	7.39620e12			1.02439			0.512194	+	0.858870i	$0.328833\pi$
$374$	−2.24404e12			−0.306671
$375$	3.47874e11			0.0469100
$376$	4.36005e12			0.580166
$377$		−	3.65889e12i		−	0.480444i
$378$		−	4.14319e12i		−	0.536878i
$379$	−2.11206e12			−0.270091			−0.135045	−	0.990839i	$-0.543118\pi$
$379$	−2.11206e12			−0.270091			−0.135045	+	0.990839i	$0.543118\pi$
$380$	−5.99616e12			−0.756755
$381$	−6.00925e12			−0.748506
$382$	−2.26112e13			−2.77975
$383$	−1.52770e12			−0.185372			−0.0926862	−	0.995695i	$-0.529545\pi$
$383$	−1.52770e12			−0.185372			−0.0926862	+	0.995695i	$0.529545\pi$
$384$			8.69533e12i			1.04143i
$385$		−	2.62800e12i		−	0.310686i
$386$			1.34813e13i			1.57324i
$387$			2.90483e12i			0.334631i
$388$			1.56059e13i			1.77472i
$389$	−6.15791e12			−0.691329			−0.345665	−	0.938358i	$-0.612347\pi$
$389$	−6.15791e12			−0.691329			−0.345665	+	0.938358i	$0.612347\pi$
$390$	−1.06538e13			−1.18081
$391$		−	7.65614e12i		−	0.837772i
$392$			2.44763e13i			2.64433i
$393$		−	9.94349e12i		−	1.06066i
$394$			2.04449e12i			0.215330i
$395$	7.02185e12			0.730240
$396$			8.35257e11i			0.0857717i
$397$			2.95400e12i			0.299543i	0.988721	+	0.149771i	$0.0478537\pi$
$397$			2.95400e12i			0.299543i	−0.988721	+	0.149771i	$0.952146\pi$
$398$		−	2.54189e13i		−	2.54531i
$399$	−2.59390e12			−0.256501
$400$	8.73489e12			0.853016
$401$			1.10122e13i			1.06206i	0.847352	+	0.531032i	$0.178196\pi$
$401$			1.10122e13i			1.06206i	−0.847352	+	0.531032i	$0.821804\pi$
$402$	−4.28861e12			−0.408495
$403$	−4.93547e12			−0.464305
$404$			2.74644e13i			2.55190i
$405$	−1.73625e12			−0.159345
$406$			1.77592e13i			1.60988i
$407$	−1.63592e12			−0.146484
$408$		−	1.40596e13i		−	1.24358i
$409$		−	1.11556e13i		−	0.974708i	−0.873204	−	0.487354i	$-0.837962\pi$
$409$		−	1.11556e13i		−	0.974708i	0.873204	−	0.487354i	$-0.162038\pi$
$410$			1.18370e13i			1.02170i
$411$	−9.80656e12			−0.836195
$412$			1.45322e13i			1.22418i
$413$	−1.36378e13	−	1.40332e13i	−1.13499	−	1.16791i
$414$	−4.32292e12			−0.355448
$415$			8.03045e12i			0.652378i
$416$	2.25724e12			0.181180
$417$	−2.57539e9			−0.000204250
$418$	7.93264e11			0.0621636
$419$			5.63550e12i			0.436377i	0.975907	+	0.218189i	$0.0700148\pi$
$419$			5.63550e12i			0.436377i	−0.975907	+	0.218189i	$0.929985\pi$
$420$	3.40878e13			2.60827
$421$			1.37108e12i			0.103670i	0.998656	+	0.0518349i	$0.0165070\pi$
$421$			1.37108e12i			0.103670i	−0.998656	+	0.0518349i	$0.983493\pi$
$422$	−3.89706e13			−2.91189
$423$		−	1.63637e12i		−	0.120832i
$424$			2.68835e13i			1.96181i
$425$	1.97179e13			1.42206
$426$		−	4.86989e12i		−	0.347113i
$427$		−	8.12124e12i		−	0.572114i
$428$	2.84461e13			1.98063
$429$	9.29115e11			0.0639416
$430$	−3.62547e13			−2.46616
$431$			2.81455e13i			1.89244i	0.323525	+	0.946219i	$0.395132\pi$
$431$			2.81455e13i			1.89244i	−0.323525	+	0.946219i	$0.604868\pi$
$432$	−2.33755e12			−0.155361
$433$	−1.64021e13			−1.07760			−0.538802	−	0.842432i	$-0.681123\pi$
$433$	−1.64021e13			−1.07760			−0.538802	+	0.842432i	$0.681123\pi$
$434$	2.39553e13			1.55580
$435$	7.44221e12			0.477811
$436$			2.54343e13i			1.61431i
$437$			2.70642e12i			0.169820i
$438$	4.68660e12			0.290728
$439$	−2.05239e13			−1.25875			−0.629373	−	0.777103i	$-0.716688\pi$
$439$	−2.05239e13			−1.25875			−0.629373	+	0.777103i	$0.716688\pi$
$440$	−5.03537e12			−0.305329
$441$	9.18621e12			0.550736
$442$	−3.23784e13			−1.91930
$443$		−	3.21792e13i		−	1.88606i	−0.332704	−	0.943031i	$-0.607961\pi$
$443$		−	3.21792e13i		−	1.88606i	0.332704	−	0.943031i	$-0.392039\pi$
$444$		−	2.12196e13i		−	1.22977i
$445$		−	4.39563e13i		−	2.51896i
$446$		−	4.82940e13i		−	2.73665i
$447$			9.55936e12i			0.535662i
$448$	−3.46816e13			−1.92180
$449$	−2.00652e13			−1.09954			−0.549772	−	0.835315i	$-0.685285\pi$
$449$	−2.00652e13			−1.09954			−0.549772	+	0.835315i	$0.685285\pi$
$450$		−	1.11334e13i		−	0.603346i
$451$		−	1.03231e12i		−	0.0553255i
$452$		−	8.31771e12i		−	0.440871i
$453$		−	1.57711e13i		−	0.826744i
$454$	−2.90624e13			−1.50679
$455$		−	3.79183e13i		−	1.94443i
$456$			4.97004e12i			0.252078i
$457$		−	1.86358e13i		−	0.934905i	−0.884018	−	0.467453i	$-0.845172\pi$
$457$		−	1.86358e13i		−	0.934905i	0.884018	−	0.467453i	$-0.154828\pi$
$458$	2.95231e13			1.46499
$459$	−5.27672e12			−0.259001
$460$		−	3.55666e13i		−	1.72684i
$461$	−1.98467e13			−0.953201			−0.476601	−	0.879120i	$-0.658131\pi$
$461$	−1.98467e13			−0.953201			−0.476601	+	0.879120i	$0.658131\pi$
$462$	−4.50966e12			−0.214256
$463$		−	9.83106e12i		−	0.462057i	−0.972947	−	0.231028i	$-0.925791\pi$
$463$		−	9.83106e12i		−	0.462057i	0.972947	−	0.231028i	$-0.0742090\pi$
$464$	1.00196e13			0.465864
$465$		−	1.00388e13i		−	0.461760i
$466$	−2.11040e13			−0.960361
$467$			7.05766e12i			0.317743i	0.987299	+	0.158872i	$0.0507856\pi$
$467$			7.05766e12i			0.317743i	−0.987299	+	0.158872i	$0.949214\pi$
$468$			1.20516e13i			0.536803i
$469$		−	1.52637e13i		−	0.672662i
$470$	2.04233e13			0.890506
$471$		−	2.17209e13i		−	0.937072i
$472$	−2.68884e13	+	2.61306e13i	−1.14777	+	1.11542i
$473$	3.16177e12			0.133544
$474$		−	1.20495e13i		−	0.503591i
$475$	−6.97023e12			−0.288257
$476$	1.03598e14			4.23951
$477$	1.00897e13			0.408587
$478$			6.29380e13i			2.52217i
$479$	−1.57057e13			−0.622844			−0.311422	−	0.950272i	$-0.600805\pi$
$479$	−1.57057e13			−0.622844			−0.311422	+	0.950272i	$0.600805\pi$
$480$			4.59124e12i			0.180187i
$481$	−2.36041e13			−0.916773
$482$			2.26136e13i			0.869231i
$483$		−	1.53859e13i		−	0.585310i
$484$	−5.04663e13			−1.90009
$485$			3.53094e13i			1.31578i
$486$			2.97942e12i			0.109888i
$487$	3.55340e13			1.29718			0.648589	−	0.761139i	$-0.275359\pi$
$487$	3.55340e13			1.29718			0.648589	+	0.761139i	$0.275359\pi$
$488$	−1.55607e13			−0.562250
$489$	−3.54412e12			−0.126755
$490$			1.14651e14i			4.05881i
$491$	4.49539e13			1.57529			0.787644	−	0.616131i	$-0.211301\pi$
$491$	4.49539e13			1.57529			0.787644	+	0.616131i	$0.211301\pi$
$492$	1.33901e13			0.464469
$493$	2.26179e13			0.776638
$494$	1.14457e13			0.389051
$495$			1.88983e12i			0.0635911i
$496$		−	1.35154e13i		−	0.450215i
$497$	1.73326e13			0.571586
$498$	1.37803e13			0.449896
$499$	5.61991e13			1.81646			0.908232	−	0.418467i	$-0.137432\pi$
$499$	5.61991e13			1.81646			0.908232	+	0.418467i	$0.137432\pi$
$500$	4.91139e12			0.157165
$501$	1.12529e12			0.0356515
$502$			4.04950e13i			1.27023i
$503$			1.85153e12i			0.0575030i	0.999587	+	0.0287515i	$0.00915316\pi$
$503$			1.85153e12i			0.0575030i	−0.999587	+	0.0287515i	$0.990847\pi$
$504$		−	2.82544e13i		−	0.868826i
$505$			6.21402e13i			1.89198i
$506$			4.70529e12i			0.141851i
$507$	−5.93519e12			−0.177172
$508$	−8.48405e13			−2.50775
$509$			6.65068e13i			1.94660i	0.229530	+	0.973302i	$0.426281\pi$
$509$			6.65068e13i			1.94660i	−0.229530	+	0.973302i	$0.573719\pi$
$510$		−	6.58579e13i		−	1.90878i
$511$			1.66802e13i			0.478738i
$512$			5.16407e13i			1.46772i
$513$	1.86531e12			0.0525005
$514$		−	8.73789e13i		−	2.43552i
$515$			3.28801e13i			0.907605i
$516$			4.10113e13i			1.12113i
$517$	−1.78111e12			−0.0482213
$518$	1.14567e14			3.07193
$519$			3.52615e13i			0.936407i
$520$	−7.26533e13			−1.91090
$521$	7.49443e13			1.95232			0.976158	−	0.217060i	$-0.0696467\pi$
$521$	7.49443e13			1.95232			0.976158	+	0.217060i	$0.0696467\pi$
$522$		−	1.27709e13i		−	0.329510i
$523$	−2.65517e13			−0.678554			−0.339277	−	0.940686i	$-0.610182\pi$
$523$	−2.65517e13			−0.678554			−0.339277	+	0.940686i	$0.610182\pi$
$524$		−	1.40385e14i		−	3.55358i
$525$	3.96254e13			0.993520
$526$			8.35941e13i			2.07609i
$527$		−	3.05093e13i		−	0.750548i
$528$			2.54431e12i			0.0620012i
$529$	2.53732e13			0.612487
$530$			1.25927e14i			3.01121i
$531$	9.80709e12	+	1.00915e13i	0.232310	+	0.239047i
$532$	−3.66215e13			−0.859366
$533$		−	1.48947e13i		−	0.346255i
$534$	−7.54293e13			−1.73714
$535$	6.43614e13			1.46844
$536$	−2.92461e13			−0.661064
$537$		−	1.62755e13i		−	0.364472i
$538$	−1.43576e14			−3.18544
$539$		−	9.99873e12i		−	0.219787i
$540$	−2.45130e13			−0.533860
$541$			8.54421e13i			1.84368i	0.387570	+	0.921840i	$0.373315\pi$
$541$			8.54421e13i			1.84368i	−0.387570	+	0.921840i	$0.626685\pi$
$542$			1.21782e14i			2.60368i
$543$	−2.75713e13			−0.584061
$544$			1.39534e13i			0.292878i
$545$			5.75469e13i			1.19685i
$546$	−6.50680e13			−1.34092
$547$	−3.36039e13			−0.686205			−0.343102	−	0.939298i	$-0.611478\pi$
$547$	−3.36039e13			−0.686205			−0.343102	+	0.939298i	$0.611478\pi$
$548$	−1.38452e14			−2.80154
$549$			5.84009e12i			0.117100i
$550$	−1.21182e13			−0.240782
$551$	−7.99539e12			−0.157428
$552$	−2.94801e13			−0.575219
$553$	4.28859e13			0.829256
$554$		−	5.87095e13i		−	1.12502i
$555$		−	4.80109e13i		−	0.911748i
$556$	−3.63601e10			−0.000684308
$557$	−6.37800e13			−1.18962			−0.594810	−	0.803866i	$-0.702773\pi$
$557$	−6.37800e13			−1.18962			−0.594810	+	0.803866i	$0.702773\pi$
$558$	−1.72266e13			−0.318441
$559$	4.56198e13			0.835785
$560$	1.03836e14			1.88542
$561$			5.74345e12i			0.103362i
$562$			5.04917e13i			0.900613i
$563$		−	5.16188e13i		−	0.912570i	−0.889834	−	0.456285i	$-0.849180\pi$
$563$		−	5.16188e13i		−	0.912570i	0.889834	−	0.456285i	$-0.150820\pi$
$564$		−	2.31029e13i		−	0.404828i
$565$		−	1.88194e13i		−	0.326862i
$566$	9.40445e13			1.61902
$567$	−1.06042e13			−0.180951
$568$		−	3.32101e13i		−	0.561731i
$569$		−	1.06813e14i		−	1.79087i	−0.445190	−	0.895436i	$-0.646864\pi$
$569$		−	1.06813e14i		−	1.79087i	0.445190	−	0.895436i	$-0.353136\pi$
$570$			2.32806e13i			0.386919i
$571$			5.47878e13i			0.902616i	0.892368	+	0.451308i	$0.149042\pi$
$571$			5.47878e13i			0.902616i	−0.892368	+	0.451308i	$0.850958\pi$
$572$	1.31175e13			0.214226
$573$			5.78715e13i			0.936896i
$574$			7.22946e13i			1.16024i
$575$		−	4.13443e13i		−	0.657774i
$576$	2.49400e13			0.393354
$577$	7.67946e13			1.20075			0.600373	−	0.799720i	$-0.295019\pi$
$577$	7.67946e13			1.20075			0.600373	+	0.799720i	$0.295019\pi$
$578$		−	8.96436e13i		−	1.38957i
$579$	3.45042e13			0.530249
$580$	1.05072e14			1.60083
$581$			4.90459e13i			0.740836i
$582$	6.05912e13			0.907391
$583$		−	1.09821e13i		−	0.163058i
$584$	3.19602e13			0.470484
$585$			2.72675e13i			0.397985i
$586$		−	5.10635e12i		−	0.0738963i
$587$		−	2.35646e13i		−	0.338119i	−0.985606	−	0.169059i	$-0.945927\pi$
$587$		−	2.35646e13i		−	0.338119i	0.985606	−	0.169059i	$-0.0540729\pi$
$588$	1.29694e14			1.84515
$589$			1.07849e13i			0.152139i
$590$	−1.25950e14	+	1.22401e14i	−1.76173	+	1.71208i
$591$	5.23271e12			0.0725754
$592$		−	6.46378e13i		−	0.888952i
$593$	−3.97416e12			−0.0541966			−0.0270983	−	0.999633i	$-0.508627\pi$
$593$	−3.97416e12			−0.0541966			−0.0270983	+	0.999633i	$0.508627\pi$
$594$	3.24295e12			0.0438539
$595$	2.34397e14			3.14317
$596$			1.34962e14i			1.79465i
$597$	−6.50576e13			−0.857880
$598$			6.78907e13i			0.887778i
$599$	9.56501e13			1.24037			0.620185	−	0.784455i	$-0.287057\pi$
$599$	9.56501e13			1.24037			0.620185	+	0.784455i	$0.287057\pi$
$600$		−	7.59241e13i		−	0.976390i
$601$		−	1.19763e14i		−	1.52739i	−0.645578	−	0.763694i	$-0.723384\pi$
$601$		−	1.19763e14i		−	1.52739i	0.645578	−	0.763694i	$-0.276616\pi$
$602$	−2.21425e14			−2.80056
$603$			1.09764e13i			0.137680i
$604$		−	2.22662e14i		−	2.76988i
$605$	−1.14184e14			−1.40873
$606$	1.06633e14			1.30475
$607$	9.12510e13			1.10737			0.553687	−	0.832725i	$-0.313221\pi$
$607$	9.12510e13			1.10737			0.553687	+	0.832725i	$0.313221\pi$
$608$		−	4.93250e12i		−	0.0593675i
$609$	4.54533e13			0.542599
$610$	−7.28892e13			−0.863006
$611$	−2.56989e13			−0.301793
$612$	−7.44985e13			−0.867741
$613$			1.62743e14i			1.88018i	0.340928	+	0.940089i	$0.389259\pi$
$613$			1.62743e14i			1.88018i	−0.340928	+	0.940089i	$0.610741\pi$
$614$			7.00145e13i			0.802317i
$615$	3.02959e13			0.344357
$616$	−3.07535e13			−0.346729
$617$	−1.37883e13			−0.154200			−0.0771002	−	0.997023i	$-0.524566\pi$
$617$	−1.37883e13			−0.154200			−0.0771002	+	0.997023i	$0.524566\pi$
$618$	5.64224e13			0.625906
$619$	2.94466e13			0.324028			0.162014	−	0.986788i	$-0.448201\pi$
$619$	2.94466e13			0.324028			0.162014	+	0.986788i	$0.448201\pi$
$620$		−	1.41731e14i		−	1.54705i
$621$			1.10642e13i			0.119801i
$622$		−	1.50824e14i		−	1.62001i
$623$		−	2.68463e14i		−	2.86052i
$624$			3.67108e13i			0.388034i
$625$	−8.96582e13			−0.940134
$626$	1.17273e14			1.21990
$627$		−	2.03030e12i		−	0.0209518i
$628$		−	3.06662e14i		−	3.13951i
$629$		−	1.45912e14i		−	1.48196i
$630$		−	1.32349e14i		−	1.33357i
$631$	5.81855e13			0.581658			0.290829	−	0.956775i	$-0.406069\pi$
$631$	5.81855e13			0.581658			0.290829	+	0.956775i	$0.406069\pi$
$632$		−	8.21714e13i		−	0.814958i
$633$			9.97422e13i			0.981433i
$634$		−	7.38964e13i		−	0.721402i
$635$	−1.91958e14			−1.85925
$636$	1.42449e14			1.36891
$637$		−	1.44268e14i		−	1.37554i
$638$	−1.39005e13			−0.131500
$639$	−1.24641e13			−0.116992
$640$			2.77761e14i			2.58685i
$641$	7.38506e13			0.682439			0.341219	−	0.939984i	$-0.389160\pi$
$641$	7.38506e13			0.682439			0.341219	+	0.939984i	$0.389160\pi$
$642$		−	1.10444e14i		−	1.01267i
$643$	−8.30666e13			−0.755739			−0.377869	−	0.925859i	$-0.623343\pi$
$643$	−8.30666e13			−0.755739			−0.377869	+	0.925859i	$0.623343\pi$
$644$		−	2.17223e14i		−	1.96099i
$645$			9.27910e13i			0.831204i
$646$			7.07530e13i			0.628901i
$647$	1.99383e14			1.75860			0.879300	−	0.476268i	$-0.158011\pi$
$647$	1.99383e14			1.75860			0.879300	+	0.476268i	$0.158011\pi$
$648$			2.03181e13i			0.177831i
$649$	1.09841e13	−	1.06745e13i	0.0953983	−	0.0927097i
$650$	−1.74848e14			−1.50694
$651$		−	6.13118e13i		−	0.524371i
$652$	−5.00370e13			−0.424671
$653$	4.42893e13			0.373021			0.186510	−	0.982453i	$-0.440282\pi$
$653$	4.42893e13			0.373021			0.186510	+	0.982453i	$0.440282\pi$
$654$	9.87508e13			0.825376
$655$		−	3.17632e14i		−	2.63462i
$656$	4.07879e13			0.335747
$657$		−	1.19950e13i		−	0.0979880i
$658$	1.24735e14			1.01125
$659$			9.75611e13i			0.784964i	0.919760	+	0.392482i	$0.128383\pi$
$659$			9.75611e13i			0.784964i	−0.919760	+	0.392482i	$0.871617\pi$
$660$			2.66812e13i			0.213052i
$661$	6.45464e12			0.0511523			0.0255761	−	0.999673i	$-0.491858\pi$
$661$	6.45464e12			0.0511523			0.0255761	+	0.999673i	$0.491858\pi$
$662$		−	2.93005e14i		−	2.30454i
$663$			8.28699e13i			0.646888i
$664$	9.39743e13			0.728063
$665$	−8.28588e13			−0.637133
$666$	−8.23869e13			−0.628763
$667$		−	4.74251e13i		−	0.359235i
$668$	1.58873e13			0.119445
$669$	−1.23605e14			−0.922367
$670$	−1.36994e14			−1.01468
$671$	6.35665e12			0.0467322
$672$			2.80410e13i			0.204619i
$673$			4.61819e13i			0.334500i	0.985914	+	0.167250i	$0.0534887\pi$
$673$			4.61819e13i			0.334500i	−0.985914	+	0.167250i	$0.946511\pi$
$674$	3.09723e13			0.222676
$675$	−2.84951e13			−0.203354
$676$	−8.37949e13			−0.593586
$677$	8.77618e13			0.617110			0.308555	−	0.951207i	$-0.400155\pi$
$677$	8.77618e13			0.617110			0.308555	+	0.951207i	$0.400155\pi$
$678$	−3.22942e13			−0.225412
$679$			2.15652e14i			1.49419i
$680$		−	4.49116e14i		−	3.08897i
$681$			7.43828e13i			0.507852i
$682$			1.87503e13i			0.127083i
$683$			2.02710e14i			1.36387i	0.731414	+	0.681933i	$0.238861\pi$
$683$			2.02710e14i			1.36387i	−0.731414	+	0.681933i	$0.761139\pi$
$684$	2.63350e13			0.175895
$685$	−3.13258e14			−2.07706
$686$			2.76416e14i			1.81946i
$687$		−	7.55621e13i		−	0.493765i
$688$			1.24926e14i			0.810422i
$689$		−	1.58456e14i		−	1.02050i
$690$	−1.38090e14			−0.882912
$691$		−	2.19696e14i		−	1.39454i	−0.716806	−	0.697272i	$-0.754397\pi$
$691$		−	2.19696e14i		−	1.39454i	0.716806	−	0.697272i	$-0.245603\pi$
$692$			4.97834e14i			3.13728i
$693$			1.15421e13i			0.0722136i
$694$	2.13304e14			1.32495
$695$	−8.22674e10			−0.000507345
$696$		−	8.70907e13i		−	0.533243i
$697$	9.20737e13			0.559721
$698$	−5.84764e13			−0.352942
$699$			5.40139e13i			0.323683i
$700$	5.59444e14			3.32863
$701$			3.01975e14i			1.78394i	0.452091	+	0.891972i	$0.350678\pi$
$701$			3.01975e14i			1.78394i	−0.452091	+	0.891972i	$0.649322\pi$
$702$	4.67913e13			0.274460
$703$			5.15794e13i			0.300400i
$704$		−	2.71460e13i		−	0.156979i
$705$		−	5.22718e13i		−	0.300139i
$706$	−2.65583e13			−0.151418
$707$			3.79521e14i			2.14852i
$708$	1.38460e14	+	1.42475e14i	0.778318	+	0.800888i
$709$	−7.73009e13			−0.431473			−0.215736	−	0.976452i	$-0.569215\pi$
$709$	−7.73009e13			−0.431473			−0.215736	+	0.976452i	$0.569215\pi$
$710$		−	1.55562e14i		−	0.862209i
$711$	−3.08398e13			−0.169732
$712$	−5.14388e14			−2.81120
$713$	−6.39715e13			−0.347167
$714$		−	4.02227e14i		−	2.16760i
$715$	2.96794e13			0.158827
$716$		−	2.29783e14i		−	1.22111i
$717$	1.61085e14			0.850079
$718$		−	5.74514e14i		−	3.01077i
$719$		−	2.62216e14i		−	1.36463i	−0.731059	−	0.682314i	$-0.760974\pi$
$719$		−	2.62216e14i		−	1.36463i	0.731059	−	0.682314i	$-0.239026\pi$
$720$	−7.46699e13			−0.385908
$721$			2.00815e14i			1.03067i
$722$			3.11067e14i			1.58551i
$723$	5.78778e13			0.292968
$724$	−3.89260e14			−1.95680
$725$	1.22140e14			0.609775
$726$			1.95940e14i			0.971492i
$727$	−1.80737e14			−0.889970			−0.444985	−	0.895538i	$-0.646791\pi$
$727$	−1.80737e14			−0.889970			−0.444985	+	0.895538i	$0.646791\pi$
$728$	−4.43729e14			−2.17001
$729$	7.62560e12			0.0370370
$730$	1.49707e14			0.722153
$731$			2.82005e14i			1.35105i
$732$			8.24523e13i			0.392326i
$733$	3.23004e14			1.52647			0.763236	−	0.646120i	$-0.223610\pi$
$733$	3.23004e14			1.52647			0.763236	+	0.646120i	$0.223610\pi$
$734$	−4.78491e14			−2.24591
$735$	2.93441e14			1.36800
$736$	2.92574e13			0.135471
$737$	1.19472e13			0.0549452
$738$		−	5.19880e13i		−	0.237477i
$739$			7.65366e13i			0.347254i	0.984812	+	0.173627i	$0.0555486\pi$
$739$			7.65366e13i			0.347254i	−0.984812	+	0.173627i	$0.944451\pi$
$740$		−	6.77833e14i		−	3.05467i
$741$		−	2.92943e13i		−	0.131127i
$742$			7.69100e14i			3.41951i
$743$	−2.02718e14			−0.895257			−0.447629	−	0.894220i	$-0.647731\pi$
$743$	−2.02718e14			−0.895257			−0.447629	+	0.894220i	$0.647731\pi$
$744$	−1.17476e14			−0.515330
$745$			3.05361e14i			1.33055i
$746$		−	4.05427e14i		−	1.75476i
$747$		−	3.52696e13i		−	0.151634i
$748$			8.10879e13i			0.346297i
$749$	3.93087e14			1.66755
$750$		−	1.90689e13i		−	0.0803562i
$751$			4.55437e14i			1.90647i	0.302238	+	0.953233i	$0.402266\pi$
$751$			4.55437e14i			1.90647i	−0.302238	+	0.953233i	$0.597734\pi$
$752$		−	7.03745e13i		−	0.292635i
$753$	1.03644e14			0.428122
$754$	−2.00564e14			−0.822994
$755$		−	5.03787e14i		−	2.05358i
$756$	−1.49713e14			−0.606248
$757$	1.19767e14			0.481788			0.240894	−	0.970551i	$-0.422559\pi$
$757$	1.19767e14			0.481788			0.240894	+	0.970551i	$0.422559\pi$
$758$			1.15774e14i			0.462662i
$759$	1.20428e13			0.0478100
$760$			1.58761e14i			0.626148i
$761$	−3.20270e14			−1.25485			−0.627427	−	0.778676i	$-0.715892\pi$
$761$	−3.20270e14			−1.25485			−0.627427	+	0.778676i	$0.715892\pi$
$762$			3.29400e14i			1.28218i
$763$			3.51468e14i			1.35913i
$764$			8.17048e14i			3.13893i
$765$	−1.68558e14			−0.643343
$766$			8.37419e13i			0.317540i
$767$	1.58485e14	−	1.54018e14i	0.597050	−	0.580224i
$768$	2.94606e14			1.10265
$769$			1.47981e14i			0.550268i	0.961406	+	0.275134i	$0.0887223\pi$
$769$			1.47981e14i			0.550268i	−0.961406	+	0.275134i	$0.911278\pi$
$770$	−1.44055e14			−0.532200
$771$	−2.23639e14			−0.820874
$772$	4.87142e14			1.77652
$773$		−	4.29167e13i		−	0.155500i	−0.996973	−	0.0777498i	$-0.975226\pi$
$773$		−	4.29167e13i		−	0.155500i	0.996973	−	0.0777498i	$-0.0247735\pi$
$774$	1.59230e14			0.573218
$775$		−	1.64755e14i		−	0.589290i
$776$	4.13200e14			1.46842
$777$		−	2.93226e14i		−	1.03537i
$778$			3.37549e14i			1.18424i
$779$	−3.25478e13			−0.113458
$780$			3.84972e14i			1.33339i
$781$			1.35666e13i			0.0466890i
$782$	−4.19676e14			−1.43509
$783$	−3.26861e13			−0.111059
$784$	3.95065e14			1.33379
$785$		−	6.93846e14i		−	2.32763i
$786$	−5.45058e14			−1.81690
$787$	4.61361e14			1.52815			0.764077	−	0.645125i	$-0.223195\pi$
$787$	4.61361e14			1.52815			0.764077	+	0.645125i	$0.223195\pi$
$788$	7.38771e13			0.243153
$789$	2.13953e14			0.699733
$790$		−	3.84906e14i		−	1.25089i
$791$		−	1.14939e14i		−	0.371182i
$792$	2.21152e13			0.0709685
$793$	9.17175e13			0.292473
$794$	1.61925e14			0.513112
$795$	3.22301e14			1.01491
$796$	−9.18504e14			−2.87419
$797$			1.44143e14i			0.448231i	0.974563	+	0.224116i	$0.0719493\pi$
$797$			1.44143e14i			0.448231i	−0.974563	+	0.224116i	$0.928051\pi$
$798$			1.42186e14i			0.439382i
$799$		−	1.58862e14i		−	0.487848i
$800$			7.53506e13i			0.229952i
$801$			1.93055e14i			0.585490i
$802$	6.03638e14			1.81930
$803$	−1.30560e13			−0.0391049
$804$			1.54968e14i			0.461276i
$805$		−	4.91481e14i		−	1.45388i
$806$			2.70540e14i			0.795347i
$807$			3.67471e14i			1.07363i
$808$	7.27181e14			2.11147
$809$		−	6.54583e14i		−	1.88896i	−0.328573	−	0.944478i	$-0.606568\pi$
$809$		−	6.54583e14i		−	1.88896i	0.328573	−	0.944478i	$-0.393432\pi$
$810$			9.51738e13i			0.272956i
$811$			9.01373e13i			0.256921i	0.991715	+	0.128461i	$0.0410036\pi$
$811$			9.01373e13i			0.256921i	−0.991715	+	0.128461i	$0.958996\pi$
$812$	6.41724e14			1.81789
$813$	3.11693e14			0.877554
$814$			8.96741e13i			0.250926i
$815$	−1.13212e14			−0.314851
$816$	−2.26933e14			−0.627258
$817$		−	9.96881e13i		−	0.273863i
$818$	−6.11498e14			−1.66966
$819$			1.66536e14i			0.451949i
$820$	4.27728e14			1.15371
$821$		−	5.37663e14i		−	1.44143i	−0.693230	−	0.720716i	$-0.743813\pi$
$821$		−	5.37663e14i		−	1.44143i	0.693230	−	0.720716i	$-0.256187\pi$
$822$			5.37552e14i			1.43239i
$823$		−	2.77563e14i		−	0.735127i	−0.929998	−	0.367564i	$-0.880192\pi$
$823$		−	2.77563e14i		−	0.735127i	0.929998	−	0.367564i	$-0.119808\pi$
$824$	3.84771e14			1.01290
$825$			3.10155e13i			0.0811539i
$826$	−7.69240e14	+	7.47561e14i	−2.00061	+	1.94422i
$827$	1.24917e14			0.322920			0.161460	−	0.986879i	$-0.448380\pi$
$827$	1.24917e14			0.322920			0.161460	+	0.986879i	$0.448380\pi$
$828$			1.56208e14i			0.401375i
$829$	−1.50300e14			−0.383873			−0.191936	−	0.981407i	$-0.561477\pi$
$829$	−1.50300e14			−0.383873			−0.191936	+	0.981407i	$0.561477\pi$
$830$	4.40194e14			1.11751
$831$	−1.50262e14			−0.379179
$832$		−	3.91678e14i		−	0.982455i
$833$	8.91810e14			2.22355
$834$			1.41171e11i			0.000349878i
$835$	3.59461e13			0.0885562
$836$		−	2.86644e13i		−	0.0701958i
$837$			4.40901e13i			0.107328i
$838$	3.08913e14			0.747508
$839$		−	3.68858e14i		−	0.887257i	−0.896211	−	0.443629i	$-0.853691\pi$
$839$		−	3.68858e14i		−	0.887257i	0.896211	−	0.443629i	$-0.146309\pi$
$840$		−	9.02549e14i		−	2.15811i
$841$	−2.80603e14			−0.666979
$842$	7.51565e13			0.177585
$843$	1.29229e14			0.303545
$844$			1.40819e15i			3.28814i
$845$	−1.89592e14			−0.440084
$846$	−8.96988e13			−0.206983
$847$	−6.97376e14			−1.59974
$848$	4.33919e14			0.989531
$849$		−	2.40699e14i		−	0.545678i
$850$		−	1.08085e15i		−	2.43596i
$851$	−3.05946e14			−0.685484
$852$	−1.75972e14			−0.391964
$853$	−5.87151e14			−1.30018			−0.650092	−	0.759855i	$-0.725270\pi$
$853$	−5.87151e14			−1.30018			−0.650092	+	0.759855i	$0.725270\pi$
$854$	−4.45170e14			−0.980024
$855$	5.95848e13			0.130408
$856$		−	7.53173e14i		−	1.63880i
$857$			8.93692e13i			0.193323i	0.995317	+	0.0966616i	$0.0308164\pi$
$857$			8.93692e13i			0.193323i	−0.995317	+	0.0966616i	$0.969184\pi$
$858$		−	5.09300e13i		−	0.109531i
$859$		−	8.25451e14i		−	1.76492i	−0.470386	−	0.882461i	$-0.655885\pi$
$859$		−	8.25451e14i		−	1.76492i	0.470386	−	0.882461i	$-0.344115\pi$
$860$			1.31005e15i			2.78482i
$861$	1.85032e14			0.391050
$862$	1.54281e15			3.24172
$863$		−	9.45516e11i		−	0.00197522i	−1.00000		0.000987609i	$-0.999686\pi$
$863$		−	9.45516e11i		−	0.00197522i	1.00000		0.000987609i	$-0.000314366\pi$
$864$		−	2.01646e13i		−	0.0418814i
$865$			1.12638e15i			2.32598i
$866$			8.99089e14i			1.84592i
$867$	−2.29436e14			−0.468345
$868$		−	8.65619e14i		−	1.75682i
$869$			3.35676e13i			0.0677363i
$870$		−	4.07949e14i		−	0.818483i
$871$	1.72382e14			0.343875
$872$	6.73429e14			1.33570
$873$		−	1.55078e14i		−	0.305830i
$874$	1.48354e14			0.290899
$875$	6.78688e13			0.132321
$876$		−	1.69349e14i		−	0.328294i
$877$	5.57499e13			0.107460			0.0537299	−	0.998556i	$-0.482889\pi$
$877$	5.57499e13			0.107460			0.0537299	+	0.998556i	$0.482889\pi$
$878$			1.12503e15i			2.15621i
$879$	−1.30693e13			−0.0249063
$880$			8.12746e13i			0.154007i
$881$		−	1.10028e14i		−	0.207312i	−0.994613	−	0.103656i	$-0.966946\pi$
$881$		−	1.10028e14i		−	0.207312i	0.994613	−	0.103656i	$-0.0330541\pi$
$882$		−	5.03547e14i		−	0.943403i
$883$	2.09051e14			0.389448			0.194724	−	0.980858i	$-0.437619\pi$
$883$	2.09051e14			0.389448			0.194724	+	0.980858i	$0.437619\pi$
$884$			1.16998e15i			2.16730i
$885$	3.13275e14	+	3.22359e14i	0.577044	+	0.593778i
$886$	−1.76392e15			−3.23080
$887$		−	1.47493e14i		−	0.268630i	−0.990939	−	0.134315i	$-0.957117\pi$
$887$		−	1.47493e14i		−	0.268630i	0.990939	−	0.134315i	$-0.0428833\pi$
$888$	−5.61835e14			−1.01752
$889$	−1.17238e15			−2.11135
$890$	−2.40949e15			−4.31495
$891$		−	8.30009e12i		−	0.0147807i
$892$	−1.74509e15			−3.09025
$893$			5.61571e13i			0.0988889i
$894$	5.24002e14			0.917582
$895$		−	5.19901e14i		−	0.905326i
$896$			1.69642e15i			2.93761i
$897$	1.73761e14			0.299219
$898$			1.09989e15i			1.88350i
$899$		−	1.88986e14i		−	0.321834i
$900$	−4.02303e14			−0.681304
$901$	9.79518e14			1.64964
$902$	−5.65864e13			−0.0947718
$903$			5.66721e14i			0.943910i
$904$	−2.20230e14			−0.364782
$905$	−8.80729e14			−1.45077
$906$	−8.64502e14			−1.41620
$907$	1.13791e15			1.85384			0.926922	−	0.375254i	$-0.122444\pi$
$907$	1.13791e15			1.85384			0.926922	+	0.375254i	$0.122444\pi$
$908$			1.05016e15i			1.70148i
$909$		−	2.72919e14i		−	0.439758i
$910$	−2.07851e15			−3.33078
$911$	4.19526e14			0.668601			0.334301	−	0.942466i	$-0.391500\pi$
$911$	4.19526e14			0.668601			0.334301	+	0.942466i	$0.391500\pi$
$912$	8.02201e13			0.127148
$913$	−3.83892e13			−0.0605139
$914$	−1.02153e15			−1.60148
$915$			1.86554e14i			0.290870i
$916$		−	1.06681e15i		−	1.65428i
$917$		−	1.93994e15i		−	2.99185i
$918$			2.89247e14i			0.443665i
$919$		−	5.23381e14i		−	0.798436i	−0.916856	−	0.399218i	$-0.869282\pi$
$919$		−	5.23381e14i		−	0.798436i	0.916856	−	0.399218i	$-0.130718\pi$
$920$	−9.41702e14			−1.42881
$921$	1.79197e14			0.270416
$922$			1.08791e15i			1.63282i
$923$			1.95746e14i			0.292203i
$924$			1.62955e14i			0.241940i
$925$		−	7.87946e14i		−	1.16356i
$926$	−5.38895e14			−0.791497
$927$		−	1.44409e14i		−	0.210957i
$928$			8.64329e13i			0.125585i
$929$			1.48309e14i			0.214333i	0.994241	+	0.107166i	$0.0341778\pi$
$929$			1.48309e14i			0.214333i	−0.994241	+	0.107166i	$0.965822\pi$
$930$	−5.50281e14			−0.790988
$931$	−3.15253e14			−0.450723
$932$			7.62586e14i			1.08445i
$933$	−3.86022e14			−0.546014
$934$	3.86869e14			0.544290
$935$			1.83467e14i			0.256744i
$936$	3.19092e14			0.444157
$937$		−	4.43050e14i		−	0.613415i	−0.951804	−	0.306708i	$-0.900773\pi$
$937$		−	4.43050e14i		−	0.613415i	0.951804	−	0.306708i	$-0.0992273\pi$
$938$	−8.36691e14			−1.15226
$939$		−	3.00151e14i		−	0.411160i
$940$		−	7.37991e14i		−	1.00557i
$941$		−	9.43694e14i		−	1.27904i	−0.768776	−	0.639518i	$-0.779134\pi$
$941$		−	9.43694e14i		−	1.27904i	0.768776	−	0.639518i	$-0.220866\pi$
$942$	−1.19064e15			−1.60519
$943$		−	1.93059e14i		−	0.258900i
$944$	4.21767e14	+	4.33998e14i	0.562617	+	0.578932i
$945$	−3.38736e14			−0.449472
$946$		−	1.73314e14i		−	0.228759i
$947$	−6.06562e13			−0.0796389			−0.0398195	−	0.999207i	$-0.512678\pi$
$947$	−6.06562e13			−0.0796389			−0.0398195	+	0.999207i	$0.512678\pi$
$948$	−4.35406e14			−0.568661
$949$	−1.88379e14			−0.244738
$950$			3.82077e14i			0.493780i
$951$	−1.89132e14			−0.243143
$952$		−	2.74297e15i		−	3.50782i
$953$	4.11774e14			0.523835			0.261918	−	0.965090i	$-0.415645\pi$
$953$	4.11774e14			0.523835			0.261918	+	0.965090i	$0.415645\pi$
$954$		−	5.53070e14i		−	0.699904i
$955$			1.84863e15i			2.32720i
$956$	2.27425e15			2.84806
$957$			3.55772e13i			0.0443212i
$958$			8.60916e14i			1.06692i
$959$	−1.91322e15			−2.35870
$960$	7.96676e14			0.977070
$961$	5.64706e14			0.688978
$962$			1.29387e15i			1.57042i
$963$	−2.82674e14			−0.341314
$964$	8.17138e14			0.981545
$965$	1.10219e15			1.31711
$966$	−8.43385e14			−1.00263
$967$		−	5.62073e14i		−	0.664753i	−0.943147	−	0.332376i	$-0.892150\pi$
$967$		−	5.62073e14i		−	0.664753i	0.943147	−	0.332376i	$-0.107850\pi$
$968$			1.33621e15i			1.57216i
$969$	1.81087e14			0.211967
$970$	1.93551e15			2.25391
$971$	−1.20236e15			−1.39296			−0.696481	−	0.717575i	$-0.745252\pi$
$971$	−1.20236e15			−1.39296			−0.696481	+	0.717575i	$0.745252\pi$
$972$	1.07661e14			0.124087
$973$	−5.02448e11			−0.000576138
$974$		−	1.94782e15i		−	2.22205i
$975$			4.47510e14i			0.507902i
$976$			2.51161e14i			0.283598i
$977$			3.27645e13i			0.0368070i	0.999831	+	0.0184035i	$0.00585835\pi$
$977$			3.27645e13i			0.0368070i	−0.999831	+	0.0184035i	$0.994142\pi$
$978$			1.94273e14i			0.217129i
$979$	2.10131e14			0.233656
$980$	4.14290e15			4.58326
$981$		−	2.52745e14i		−	0.278187i
$982$		−	2.46417e15i		−	2.69845i
$983$			3.08300e14i			0.335897i	0.985796	+	0.167948i	$0.0537142\pi$
$983$			3.08300e14i			0.335897i	−0.985796	+	0.167948i	$0.946286\pi$
$984$		−	3.54531e14i		−	0.384307i
$985$	1.67152e14			0.180273
$986$		−	1.23982e15i		−	1.33037i
$987$		−	3.19250e14i		−	0.340836i
$988$		−	4.13586e14i		−	0.439321i
$989$	5.91305e14			0.624929
$990$	1.03592e14			0.108931
$991$		−	6.90032e13i		−	0.0721940i	−0.999348	−	0.0360970i	$-0.988507\pi$
$991$		−	6.90032e13i		−	0.0721940i	0.999348	−	0.0360970i	$-0.0114925\pi$
$992$	1.16589e14			0.121367
$993$	−7.49922e14			−0.776730
$994$		−	9.50096e14i		−	0.979119i
$995$	−2.07818e15			−2.13092
$996$		−	4.97947e14i		−	0.508027i
$997$	1.52386e15			1.54693			0.773464	−	0.633841i	$-0.218523\pi$
$997$	1.52386e15			1.54693			0.773464	+	0.633841i	$0.218523\pi$
$998$		−	3.08059e15i		−	3.11158i
$999$			2.10863e14i			0.211920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.10	✓	100
59.58	odd	2	inner	177.11.c.a.58.91	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.10	✓	100	1.1	even	1	trivial
177.11.c.a.58.91	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)

\(f(q)\)	\(=\)	\(q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-54.8156i q^{2} -140.296 q^{3} -1980.75 q^{4} -4481.58 q^{5} +7690.41i q^{6} -27371.2 q^{7} +52444.5i q^{8} +19683.0 q^{9} +245660. i q^{10} -21424.0i q^{11} +277891. q^{12} -309118. i q^{13} +1.50037e6i q^{14} +628748. q^{15} +846494. q^{16} +1.91085e6 q^{17} -1.07893e6i q^{18} -675482. q^{19} +8.87686e6 q^{20} +3.84007e6 q^{21} -1.17437e6 q^{22} -4.00666e6i q^{23} -7.35777e6i q^{24} +1.03189e7 q^{25} -1.69445e7 q^{26} -2.76145e6 q^{27} +5.42154e7 q^{28} +1.18366e7 q^{29} -3.44652e7i q^{30} -1.59663e7i q^{31} +7.30219e6i q^{32} +3.00570e6i q^{33} -1.04745e8i q^{34} +1.22666e8 q^{35} -3.89870e7 q^{36} -7.63595e7i q^{37} +3.70269e7i q^{38} +4.33680e7i q^{39} -2.35034e8i q^{40} +4.81846e7 q^{41} -2.10496e8i q^{42} +1.47581e8i q^{43} +4.24354e7i q^{44} -8.82109e7 q^{45} -2.19627e8 q^{46} -8.31364e7i q^{47} -1.18760e8 q^{48} +4.66708e8 q^{49} -5.65637e8i q^{50} -2.68085e8 q^{51} +6.12284e8i q^{52} +5.12608e8 q^{53} +1.51370e8i q^{54} +9.60132e7i q^{55} -1.43547e9i q^{56} +9.47675e7 q^{57} -6.48828e8i q^{58} +(4.98252e8 + 5.12701e8i) q^{59} -1.24539e9 q^{60} +2.96707e8i q^{61} -8.75202e8 q^{62} -5.38747e8 q^{63} +1.26708e9 q^{64} +1.38533e9i q^{65} +1.64759e8 q^{66} +5.57657e8i q^{67} -3.78492e9 q^{68} +5.62119e8i q^{69} -6.72401e9i q^{70} -6.33242e8 q^{71} +1.03227e9i q^{72} -6.09409e8i q^{73} -4.18569e9 q^{74} -1.44770e9 q^{75} +1.33796e9 q^{76} +5.86400e8i q^{77} +2.37724e9 q^{78} -1.56682e9 q^{79} -3.79363e9 q^{80} +3.87420e8 q^{81} -2.64126e9i q^{82} -1.79188e9i q^{83} -7.60621e9 q^{84} -8.56364e9 q^{85} +8.08972e9 q^{86} -1.66062e9 q^{87} +1.12357e9 q^{88} +9.80823e9i q^{89} +4.83533e9i q^{90} +8.46093e9i q^{91} +7.93617e9i q^{92} +2.24001e9i q^{93} -4.55717e9 q^{94} +3.02722e9 q^{95} -1.02447e9i q^{96} -7.87880e9i q^{97} -2.55828e10i q^{98} -4.21688e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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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