LMFDB - Embedded newform 177.11.c.a.58.100

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			58.100
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} -8904.65i q^{6} +20957.7 q^{7} -125703. i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} -8904.65i q^{6} +20957.7 q^{7} -125703. i q^{8} +19683.0 q^{9} -370712. i q^{10} -183897. i q^{11} +421519. q^{12} -55809.3i q^{13} +1.33019e6i q^{14} +819427. q^{15} +4.90180e6 q^{16} -2.25099e6 q^{17} +1.24929e6i q^{18} +54241.4 q^{19} +1.75483e7 q^{20} -2.94028e6 q^{21} +1.16720e7 q^{22} -8.37467e6i q^{23} +1.76356e7i q^{24} +2.43481e7 q^{25} +3.54224e6 q^{26} -2.76145e6 q^{27} -6.29672e7 q^{28} -1.62454e7 q^{29} +5.20094e7i q^{30} -1.95114e6i q^{31} +1.82400e8i q^{32} +2.58000e7i q^{33} -1.42871e8i q^{34} -1.22408e8 q^{35} -5.91374e7 q^{36} -1.62653e7i q^{37} +3.44273e6i q^{38} +7.82982e6i q^{39} +7.34192e8i q^{40} -7.41830e7 q^{41} -1.86621e8i q^{42} -2.14172e8i q^{43} +5.52517e8i q^{44} -1.14962e8 q^{45} +5.31543e8 q^{46} -3.95183e7i q^{47} -6.87704e8 q^{48} +1.56749e8 q^{49} +1.54539e9i q^{50} +3.15805e8 q^{51} +1.67679e8i q^{52} +5.95662e8 q^{53} -1.75270e8i q^{54} +1.07409e9i q^{55} -2.63444e9i q^{56} -7.60986e6 q^{57} -1.03110e9i q^{58} +(-137790. - 7.14924e8i) q^{59} -2.46196e9 q^{60} +2.70096e8i q^{61} +1.23840e8 q^{62} +4.12510e8 q^{63} -6.55754e9 q^{64} +3.25965e8i q^{65} -1.63754e9 q^{66} +1.14991e9i q^{67} +6.76308e9 q^{68} +1.17493e9i q^{69} -7.76925e9i q^{70} +1.55702e9 q^{71} -2.47421e9i q^{72} +2.37906e9i q^{73} +1.03237e9 q^{74} -3.41595e9 q^{75} -1.62968e8 q^{76} -3.85406e9i q^{77} -4.96962e8 q^{78} +6.62017e8 q^{79} -2.86299e10 q^{80} +3.87420e8 q^{81} -4.70842e9i q^{82} -6.82031e9i q^{83} +8.83405e9 q^{84} +1.31474e10 q^{85} +1.35936e10 q^{86} +2.27916e9 q^{87} -2.31164e10 q^{88} +5.62841e9i q^{89} -7.29672e9i q^{90} -1.16963e9i q^{91} +2.51616e10i q^{92} +2.73737e8i q^{93} +2.50824e9 q^{94} -3.16808e8 q^{95} -2.55900e10i q^{96} -1.89903e9i q^{97} +9.94893e9i q^{98} -3.61965e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			63.4704i			1.98345i	0.128379	+	0.991725i	$0.459023\pi$
$2$			63.4704i			1.98345i	−0.128379	+	0.991725i	$0.540977\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−3004.49			−2.93408
$5$	−5840.70			−1.86902			−0.934512	−	0.355932i	$-0.884164\pi$
$5$	−5840.70			−1.86902			−0.934512	+	0.355932i	$0.884164\pi$
$6$		−	8904.65i		−	1.14515i
$7$	20957.7			1.24696			0.623481	−	0.781839i	$-0.285718\pi$
$7$	20957.7			1.24696			0.623481	+	0.781839i	$0.285718\pi$
$8$		−	125703.i		−	3.83614i
$9$	19683.0			0.333333
$10$		−	370712.i		−	3.70712i
$11$		−	183897.i		−	1.14186i	−0.821000	−	0.570928i	$-0.806584\pi$
$11$		−	183897.i		−	1.14186i	0.821000	−	0.570928i	$-0.193416\pi$
$12$	421519.			1.69399
$13$		−	55809.3i		−	0.150311i	−0.997172	−	0.0751553i	$-0.976055\pi$
$13$		−	55809.3i		−	0.150311i	0.997172	−	0.0751553i	$-0.0239452\pi$
$14$			1.33019e6i			2.47329i
$15$	819427.			1.07908
$16$	4.90180e6			4.67472
$17$	−2.25099e6			−1.58536			−0.792682	−	0.609636i	$-0.791316\pi$
$17$	−2.25099e6			−1.58536			−0.792682	+	0.609636i	$0.791316\pi$
$18$			1.24929e6i			0.661150i
$19$	54241.4			0.0219060			0.0109530	−	0.999940i	$-0.496513\pi$
$19$	54241.4			0.0219060			0.0109530	+	0.999940i	$0.496513\pi$
$20$	1.75483e7			5.48386
$21$	−2.94028e6			−0.719933
$22$	1.16720e7			2.26481
$23$		−	8.37467e6i		−	1.30115i	−0.759441	−	0.650576i	$-0.774527\pi$
$23$		−	8.37467e6i		−	1.30115i	0.759441	−	0.650576i	$-0.225473\pi$
$24$			1.76356e7i			2.21480i
$25$	2.43481e7			2.49325
$26$	3.54224e6			0.298134
$27$	−2.76145e6			−0.192450
$28$	−6.29672e7			−3.65868
$29$	−1.62454e7			−0.792027			−0.396014	−	0.918245i	$-0.629607\pi$
$29$	−1.62454e7			−0.792027			−0.396014	+	0.918245i	$0.629607\pi$
$30$			5.20094e7i			2.14030i
$31$		−	1.95114e6i		−	0.0681522i	−0.999419	−	0.0340761i	$-0.989151\pi$
$31$		−	1.95114e6i		−	0.0681522i	0.999419	−	0.0340761i	$-0.0108489\pi$
$32$			1.82400e8i			5.43594i
$33$			2.58000e7i			0.659251i
$34$		−	1.42871e8i		−	3.14449i
$35$	−1.22408e8			−2.33060
$36$	−5.91374e7			−0.978025
$37$		−	1.62653e7i		−	0.234560i	−0.993099	−	0.117280i	$-0.962583\pi$
$37$		−	1.62653e7i		−	0.234560i	0.993099	−	0.117280i	$-0.0374175\pi$
$38$			3.44273e6i			0.0434495i
$39$			7.82982e6i			0.0867818i
$40$			7.34192e8i			7.16984i
$41$	−7.41830e7			−0.640302			−0.320151	−	0.947366i	$-0.603734\pi$
$41$	−7.41830e7			−0.640302			−0.320151	+	0.947366i	$0.603734\pi$
$42$		−	1.86621e8i		−	1.42795i
$43$		−	2.14172e8i		−	1.45687i	−0.685117	−	0.728433i	$-0.740249\pi$
$43$		−	2.14172e8i		−	1.45687i	0.685117	−	0.728433i	$-0.259751\pi$
$44$			5.52517e8i			3.35029i
$45$	−1.14962e8			−0.623008
$46$	5.31543e8			2.58077
$47$		−	3.95183e7i		−	0.172309i	−0.996282	−	0.0861547i	$-0.972542\pi$
$47$		−	3.95183e7i		−	0.172309i	0.996282	−	0.0861547i	$-0.0274579\pi$
$48$	−6.87704e8			−2.69895
$49$	1.56749e8			0.554913
$50$			1.54539e9i			4.94524i
$51$	3.15805e8			0.915310
$52$			1.67679e8i			0.441022i
$53$	5.95662e8			1.42436			0.712182	−	0.701995i	$-0.247707\pi$
$53$	5.95662e8			1.42436			0.712182	+	0.701995i	$0.247707\pi$
$54$		−	1.75270e8i		−	0.381715i
$55$			1.07409e9i			2.13416i
$56$		−	2.63444e9i		−	4.78352i
$57$	−7.60986e6			−0.0126474
$58$		−	1.03110e9i		−	1.57095i
$59$	−137790.	−	7.14924e8i	−0.000192734	−	1.00000i
$59$	−137790.	−	7.14924e8i	−0.000192734	−	1.00000i
$60$	−2.46196e9			−3.16611
$61$			2.70096e8i			0.319793i	0.987134	+	0.159896i	$0.0511160\pi$
$61$			2.70096e8i			0.319793i	−0.987134	+	0.159896i	$0.948884\pi$
$62$	1.23840e8			0.135176
$63$	4.12510e8			0.415654
$64$	−6.55754e9			−6.10719
$65$			3.25965e8i			0.280934i
$66$	−1.63754e9			−1.30759
$67$			1.14991e9i			0.851707i	0.904792	+	0.425853i	$0.140026\pi$
$67$			1.14991e9i			0.851707i	−0.904792	+	0.425853i	$0.859974\pi$
$68$	6.76308e9			4.65158
$69$			1.17493e9i			0.751221i
$70$		−	7.76925e9i		−	4.62263i
$71$	1.55702e9			0.862981			0.431491	−	0.902117i	$-0.357988\pi$
$71$	1.55702e9			0.862981			0.431491	+	0.902117i	$0.357988\pi$
$72$		−	2.47421e9i		−	1.27871i
$73$			2.37906e9i			1.14760i	0.818994	+	0.573802i	$0.194532\pi$
$73$			2.37906e9i			1.14760i	−0.818994	+	0.573802i	$0.805468\pi$
$74$	1.03237e9			0.465238
$75$	−3.41595e9			−1.43948
$76$	−1.62968e8			−0.0642738
$77$		−	3.85406e9i		−	1.42385i
$78$	−4.96962e8			−0.172127
$79$	6.62017e8			0.215146			0.107573	−	0.994197i	$-0.465692\pi$
$79$	6.62017e8			0.215146			0.107573	+	0.994197i	$0.465692\pi$
$80$	−2.86299e10			−8.73717
$81$	3.87420e8			0.111111
$82$		−	4.70842e9i		−	1.27001i
$83$		−	6.82031e9i		−	1.73146i	−0.500507	−	0.865732i	$-0.666853\pi$
$83$		−	6.82031e9i		−	1.73146i	0.500507	−	0.865732i	$-0.333147\pi$
$84$	8.83405e9			2.11234
$85$	1.31474e10			2.96308
$86$	1.35936e10			2.88962
$87$	2.27916e9			0.457277
$88$	−2.31164e10			−4.38032
$89$			5.62841e9i			1.00794i	0.863721	+	0.503971i	$0.168128\pi$
$89$			5.62841e9i			1.00794i	−0.863721	+	0.503971i	$0.831872\pi$
$90$		−	7.29672e9i		−	1.23571i
$91$		−	1.16963e9i		−	0.187431i
$92$			2.51616e10i			3.81768i
$93$			2.73737e8i			0.0393477i
$94$	2.50824e9			0.341767
$95$	−3.16808e8			−0.0409428
$96$		−	2.55900e10i		−	3.13844i
$97$		−	1.89903e9i		−	0.221143i	−0.993868	−	0.110572i	$-0.964732\pi$
$97$		−	1.89903e9i		−	0.221143i	0.993868	−	0.110572i	$-0.0352681\pi$
$98$			9.94893e9i			1.10064i
$99$		−	3.61965e9i		−	0.380619i
$100$	−7.31538e10			−7.31538
$101$			4.43475e9i			0.421952i	0.977491	+	0.210976i	$0.0676641\pi$
$101$			4.43475e9i			0.421952i	−0.977491	+	0.210976i	$0.932336\pi$
$102$			2.00443e10i			1.81547i
$103$		−	1.25631e10i		−	1.08370i	−0.840475	−	0.541851i	$-0.817724\pi$
$103$		−	1.25631e10i		−	1.08370i	0.840475	−	0.541851i	$-0.182276\pi$
$104$	−7.01537e9			−0.576613
$105$	1.71733e10			1.34557
$106$			3.78069e10i			2.82515i
$107$	3.56452e9			0.254145			0.127073	−	0.991893i	$-0.459442\pi$
$107$	3.56452e9			0.254145			0.127073	+	0.991893i	$0.459442\pi$
$108$	8.29675e9			0.564663
$109$		−	7.75157e9i		−	0.503799i	−0.967753	−	0.251899i	$-0.918945\pi$
$109$		−	7.75157e9i		−	0.503799i	0.967753	−	0.251899i	$-0.0810552\pi$
$110$	−6.81728e10			−4.23299
$111$			2.28196e9i			0.135423i
$112$	1.02730e11			5.82920
$113$		−	2.55116e10i		−	1.38467i	−0.721577	−	0.692334i	$-0.756582\pi$
$113$		−	2.55116e10i		−	1.38467i	0.721577	−	0.692334i	$-0.243418\pi$
$114$		−	4.83001e8i		−	0.0250856i
$115$			4.89139e10i			2.43189i
$116$	4.88091e10			2.32387
$117$		−	1.09849e9i		−	0.0501035i
$118$	4.53765e10	−	8.74559e6i	1.98345	−	0.000382278i
$119$	−4.71755e10			−1.97689
$120$		−	1.03004e11i		−	4.13951i
$121$	−7.88070e9			−0.303835
$122$	−1.71431e10			−0.634293
$123$	1.04076e10			0.369679
$124$			5.86218e9i			0.199964i
$125$	−8.51721e10			−2.79092
$126$			2.61822e10i			0.824429i
$127$	3.90746e10			1.18270			0.591351	−	0.806414i	$-0.298595\pi$
$127$	3.90746e10			1.18270			0.591351	+	0.806414i	$0.298595\pi$
$128$		−	2.29433e11i		−	6.67737i
$129$			3.00475e10i			0.841122i
$130$	−2.06891e10			−0.557219
$131$			2.22871e10i			0.577693i	0.957375	+	0.288847i	$0.0932717\pi$
$131$			2.22871e10i			0.577693i	−0.957375	+	0.288847i	$0.906728\pi$
$132$		−	7.75160e10i		−	1.93429i
$133$	1.13677e9			0.0273159
$134$	−7.29853e10			−1.68932
$135$	1.61288e10			0.359694
$136$			2.82955e11i			6.08168i
$137$	1.26596e10			0.262311			0.131155	−	0.991362i	$-0.458131\pi$
$137$	1.26596e10			0.262311			0.131155	+	0.991362i	$0.458131\pi$
$138$	−7.45735e10			−1.49001
$139$	−7.67885e10			−1.47986			−0.739932	−	0.672681i	$-0.765142\pi$
$139$	−7.67885e10			−1.47986			−0.739932	+	0.672681i	$0.765142\pi$
$140$	3.67772e11			6.83816
$141$			5.54427e9i			0.0994829i
$142$			9.88244e10i			1.71168i
$143$	−1.02632e10			−0.171633
$144$	9.64822e10			1.55824
$145$	9.48844e10			1.48032
$146$	−1.51000e11			−2.27622
$147$	−2.19913e10			−0.320379
$148$			4.88690e10i			0.688216i
$149$		−	3.94754e10i		−	0.537521i	−0.963207	−	0.268760i	$-0.913386\pi$
$149$		−	3.94754e10i		−	0.537521i	0.963207	−	0.268760i	$-0.0866140\pi$
$150$		−	2.16812e11i		−	2.85513i
$151$		−	1.80185e10i		−	0.229527i	−0.993393	−	0.114763i	$-0.963389\pi$
$151$		−	1.80185e10i		−	0.229527i	0.993393	−	0.114763i	$-0.0366110\pi$
$152$		−	6.81829e9i		−	0.0840345i
$153$	−4.43062e10			−0.528454
$154$	2.44618e11			2.82414
$155$			1.13960e10i			0.127378i
$156$		−	2.35246e10i		−	0.254624i
$157$		−	1.64815e11i		−	1.72782i	−0.503645	−	0.863911i	$-0.668008\pi$
$157$		−	1.64815e11i		−	1.72782i	0.503645	−	0.863911i	$-0.331992\pi$
$158$			4.20185e10i			0.426732i
$159$	−8.35691e10			−0.822357
$160$		−	1.06534e12i		−	10.1599i
$161$		−	1.75514e11i		−	1.62249i
$162$			2.45897e10i			0.220383i
$163$	−6.49298e10			−0.564295			−0.282147	−	0.959371i	$-0.591047\pi$
$163$	−6.49298e10			−0.564295			−0.282147	+	0.959371i	$0.591047\pi$
$164$	2.22882e11			1.87869
$165$		−	1.50690e11i		−	1.23216i
$166$	4.32888e11			3.43427
$167$	−1.16113e11			−0.893916			−0.446958	−	0.894555i	$-0.647493\pi$
$167$	−1.16113e11			−0.893916			−0.446958	+	0.894555i	$0.647493\pi$
$168$			3.69601e11i			2.76177i
$169$	1.34744e11			0.977407
$170$			8.34468e11i			5.87713i
$171$	1.06763e9			0.00730200
$172$			6.43477e11i			4.27456i
$173$		−	2.85927e11i		−	1.84512i	−0.385852	−	0.922561i	$-0.626092\pi$
$173$		−	2.85927e11i		−	1.84512i	0.385852	−	0.922561i	$-0.373908\pi$
$174$			1.44659e11i			0.906986i
$175$	5.10281e11			3.10899
$176$		−	9.01427e11i		−	5.33786i
$177$	1.93314e7	+	1.00301e11i	0.000111275	+	0.577350i
$178$	−3.57237e11			−1.99920
$179$			5.43921e10i			0.295986i	0.988988	+	0.147993i	$0.0472813\pi$
$179$			5.43921e10i			0.295986i	−0.988988	+	0.147993i	$0.952719\pi$
$180$	3.45404e11			1.82795
$181$	−1.48809e11			−0.766016			−0.383008	−	0.923745i	$-0.625112\pi$
$181$	−1.48809e11			−0.766016			−0.383008	+	0.923745i	$0.625112\pi$
$182$	7.42371e10			0.371761
$183$		−	3.78934e10i		−	0.184632i
$184$	−1.05272e12			−4.99141
$185$			9.50008e10i			0.438398i
$186$	−1.73742e10			−0.0780441
$187$			4.13950e11i			1.81026i
$188$			1.18733e11i			0.505569i
$189$	−5.78736e10			−0.239978
$190$		−	2.01079e10i		−	0.0812081i
$191$			3.61209e10i			0.142099i	0.997473	+	0.0710497i	$0.0226349\pi$
$191$			3.61209e10i			0.142099i	−0.997473	+	0.0710497i	$0.977365\pi$
$192$	9.19998e11			3.52599
$193$	3.48242e11			1.30045			0.650226	−	0.759741i	$-0.274674\pi$
$193$	3.48242e11			1.30045			0.650226	+	0.759741i	$0.274674\pi$
$194$	1.20532e11			0.438626
$195$		−	4.57316e10i		−	0.162197i
$196$	−4.70951e11			−1.62816
$197$	−3.92258e11			−1.32203			−0.661014	−	0.750373i	$-0.729874\pi$
$197$	−3.92258e11			−1.32203			−0.661014	+	0.750373i	$0.729874\pi$
$198$	2.29740e11			0.754938
$199$	−3.08718e11			−0.989228			−0.494614	−	0.869113i	$-0.664691\pi$
$199$	−3.08718e11			−0.989228			−0.494614	+	0.869113i	$0.664691\pi$
$200$		−	3.06063e12i		−	9.56446i
$201$		−	1.61328e11i		−	0.491733i
$202$	−2.81476e11			−0.836920
$203$	−3.40466e11			−0.987627
$204$	−9.48834e11			−2.68559
$205$	4.33281e11			1.19674
$206$	7.97383e11			2.14947
$207$		−	1.64839e11i		−	0.433718i
$208$		−	2.73566e11i		−	0.702660i
$209$		−	9.97484e9i		−	0.0250135i
$210$			1.09000e12i			2.66888i
$211$			3.20677e11i			0.766754i	0.923592	+	0.383377i	$0.125239\pi$
$211$			3.20677e11i			0.766754i	−0.923592	+	0.383377i	$0.874761\pi$
$212$	−1.78966e12			−4.17919
$213$	−2.18443e11			−0.498242
$214$			2.26242e11i			0.504085i
$215$			1.25091e12i			2.72292i
$216$			3.47122e11i			0.738266i
$217$		−	4.08913e10i		−	0.0849831i
$218$	4.91995e11			0.999260
$219$		−	3.33774e11i		−	0.662569i
$220$		−	3.22709e12i		−	6.26177i
$221$			1.25626e11i			0.238297i
$222$	−1.44837e11			−0.268605
$223$	2.51695e10			0.0456405			0.0228202	−	0.999740i	$-0.492735\pi$
$223$	2.51695e10			0.0456405			0.0228202	+	0.999740i	$0.492735\pi$
$224$			3.82268e12i			6.77840i
$225$	4.79245e11			0.831083
$226$	1.61923e12			2.74642
$227$		−	6.00998e11i		−	0.997111i	−0.866858	−	0.498556i	$-0.833864\pi$
$227$		−	6.00998e11i		−	0.997111i	0.866858	−	0.498556i	$-0.166136\pi$
$228$	2.28638e10			0.0371085
$229$			7.01238e10i			0.111349i	0.998449	+	0.0556747i	$0.0177310\pi$
$229$			7.01238e10i			0.111349i	−0.998449	+	0.0556747i	$0.982269\pi$
$230$	−3.10459e12			−4.82352
$231$			5.40709e11i			0.822060i
$232$			2.04209e12i			3.03833i
$233$		−	1.94015e11i		−	0.282524i	−0.989972	−	0.141262i	$-0.954884\pi$
$233$		−	1.94015e11i		−	0.282524i	0.989972	−	0.141262i	$-0.0451160\pi$
$234$	6.97218e10			0.0993778
$235$			2.30815e11i			0.322051i
$236$	4.13989e8	+	2.14798e12i	0.000565495	+	2.93408i
$237$	−9.28784e10			−0.124215
$238$		−	2.99425e12i		−	3.92106i
$239$	−7.58340e11			−0.972465			−0.486233	−	0.873829i	$-0.661629\pi$
$239$	−7.58340e11			−0.972465			−0.486233	+	0.873829i	$0.661629\pi$
$240$	4.01667e12			5.04441
$241$	−2.40298e11			−0.295574			−0.147787	−	0.989019i	$-0.547215\pi$
$241$	−2.40298e11			−0.295574			−0.147787	+	0.989019i	$0.547215\pi$
$242$		−	5.00191e11i		−	0.602642i
$243$	−5.43536e10			−0.0641500
$244$		−	8.11500e11i		−	0.938295i
$245$	−9.15524e11			−1.03714
$246$			6.60574e11i			0.733239i
$247$		−	3.02717e9i		−	0.00329270i
$248$	−2.45263e11			−0.261441
$249$			9.56863e11i			0.999662i
$250$		−	5.40591e12i		−	5.53565i
$251$	−1.40436e11			−0.140965			−0.0704825	−	0.997513i	$-0.522454\pi$
$251$	−1.40436e11			−0.140965			−0.0704825	+	0.997513i	$0.522454\pi$
$252$	−1.23938e12			−1.21956
$253$	−1.54008e12			−1.48573
$254$			2.48008e12i			2.34583i
$255$	−1.84452e12			−1.71074
$256$	7.84726e12			7.13704
$257$	−1.16156e12			−1.03604			−0.518019	−	0.855369i	$-0.673331\pi$
$257$	−1.16156e12			−1.03604			−0.518019	+	0.855369i	$0.673331\pi$
$258$	−1.90712e12			−1.66832
$259$		−	3.40883e11i		−	0.292487i
$260$		−	9.79360e11i		−	0.824281i
$261$	−3.19758e11			−0.264009
$262$	−1.41457e12			−1.14583
$263$	−1.88757e10			−0.0150011			−0.00750055	−	0.999972i	$-0.502388\pi$
$263$	−1.88757e10			−0.0150011			−0.00750055	+	0.999972i	$0.502388\pi$
$264$	3.24313e12			2.52898
$265$	−3.47908e12			−2.66217
$266$			7.21515e10i			0.0541798i
$267$		−	7.89644e11i		−	0.581936i
$268$		−	3.45490e12i		−	2.49897i
$269$			1.76049e12i			1.24989i	0.780668	+	0.624946i	$0.214879\pi$
$269$			1.76049e12i			1.24989i	−0.780668	+	0.624946i	$0.785121\pi$
$270$			1.02370e12i			0.713435i
$271$	−3.04638e11			−0.208419			−0.104210	−	0.994555i	$-0.533231\pi$
$271$	−3.04638e11			−0.208419			−0.104210	+	0.994555i	$0.533231\pi$
$272$	−1.10339e13			−7.41113
$273$			1.64095e11i			0.108214i
$274$			8.03508e11i			0.520280i
$275$		−	4.47755e12i		−	2.84693i
$276$		−	3.53008e12i		−	2.20414i
$277$	2.34538e12			1.43818			0.719091	−	0.694916i	$-0.244558\pi$
$277$	2.34538e12			1.43818			0.719091	+	0.694916i	$0.244558\pi$
$278$		−	4.87380e12i		−	2.93524i
$279$		−	3.84043e10i		−	0.0227174i
$280$			1.53870e13i			8.94051i
$281$	9.95023e11			0.567939			0.283969	−	0.958833i	$-0.408349\pi$
$281$	9.95023e11			0.567939			0.283969	+	0.958833i	$0.408349\pi$
$282$	−3.51897e11			−0.197319
$283$			2.65918e12i			1.46493i	0.680806	+	0.732464i	$0.261630\pi$
$283$			2.65918e12i			1.46493i	−0.680806	+	0.732464i	$0.738370\pi$
$284$	−4.67804e12			−2.53205
$285$	4.44469e10			0.0236384
$286$		−	6.51407e11i		−	0.340426i
$287$	−1.55470e12			−0.798432
$288$			3.59017e12i			1.81198i
$289$	3.05096e12			1.51338
$290$			6.02235e12i			2.93614i
$291$			2.66427e11i			0.127677i
$292$		−	7.14788e12i		−	3.36716i
$293$	1.26058e12			0.583758			0.291879	−	0.956455i	$-0.405720\pi$
$293$	1.26058e12			0.583758			0.291879	+	0.956455i	$0.405720\pi$
$294$		−	1.39580e12i		−	0.635456i
$295$	8.04790e8	+	4.17566e12i	0.000360224	+	1.86902i
$296$	−2.04459e12			−0.899805
$297$			5.07822e11i			0.219750i
$298$	2.50552e12			1.06615
$299$	−4.67384e11			−0.195577
$300$	1.02632e13			4.22354
$301$		−	4.48854e12i		−	1.81666i
$302$	1.14364e12			0.455255
$303$		−	6.22179e11i		−	0.243614i
$304$	2.65881e11			0.102404
$305$		−	1.57755e12i		−	0.597700i
$306$		−	2.81213e12i		−	1.04816i
$307$	−2.99927e12			−1.09983			−0.549913	−	0.835222i	$-0.685339\pi$
$307$	−2.99927e12			−1.09983			−0.549913	+	0.835222i	$0.685339\pi$
$308$			1.15795e13i			4.17768i
$309$			1.76255e12i			0.625675i
$310$	−7.23310e11			−0.252648
$311$	1.87385e12			0.644070			0.322035	−	0.946728i	$-0.395633\pi$
$311$	1.87385e12			0.644070			0.322035	+	0.946728i	$0.395633\pi$
$312$	9.84230e11			0.332907
$313$			5.09208e11i			0.169501i	0.996402	+	0.0847507i	$0.0270094\pi$
$313$			5.09208e11i			0.169501i	−0.996402	+	0.0847507i	$0.972991\pi$
$314$	1.04609e13			3.42705
$315$	−2.40935e12			−0.776867
$316$	−1.98903e12			−0.631255
$317$	7.06424e11			0.220683			0.110342	−	0.993894i	$-0.464806\pi$
$317$	7.06424e11			0.220683			0.110342	+	0.993894i	$0.464806\pi$
$318$		−	5.30417e12i		−	1.63110i
$319$			2.98748e12i			0.904381i
$320$	3.83006e13			11.4145
$321$	−5.00089e11			−0.146731
$322$	1.11399e13			3.21812
$323$	−1.22097e11			−0.0347290
$324$	−1.16400e12			−0.326008
$325$		−	1.35885e12i		−	0.374762i
$326$		−	4.12112e12i		−	1.11925i
$327$			1.08751e12i			0.290868i
$328$			9.32500e12i			2.45629i
$329$		−	8.28212e11i		−	0.214863i
$330$	9.56437e12			2.44392
$331$	−1.03489e12			−0.260468			−0.130234	−	0.991483i	$-0.541573\pi$
$331$	−1.03489e12			−0.260468			−0.130234	+	0.991483i	$0.541573\pi$
$332$			2.04916e13i			5.08025i
$333$		−	3.20150e11i		−	0.0781866i
$334$		−	7.36971e12i		−	1.77304i
$335$		−	6.71628e12i		−	1.59186i
$336$	−1.44127e13			−3.36549
$337$			7.07662e12i			1.62808i	0.580807	+	0.814041i	$0.302737\pi$
$337$			7.07662e12i			1.62808i	−0.580807	+	0.814041i	$0.697263\pi$
$338$			8.55225e12i			1.93864i
$339$			3.57918e12i			0.799439i
$340$	−3.95011e13			−8.69391
$341$	−3.58809e11			−0.0778199
$342$			6.77632e10i			0.0144832i
$343$	−2.63493e12			−0.555007
$344$	−2.69220e13			−5.58875
$345$		−	6.86243e12i		−	1.40405i
$346$	1.81479e13			3.65971
$347$		−	5.98851e12i		−	1.19034i	−0.803600	−	0.595170i	$-0.797085\pi$
$347$		−	5.98851e12i		−	1.19034i	0.803600	−	0.595170i	$-0.202915\pi$
$348$	−6.84773e12			−1.34169
$349$		−	3.89345e12i		−	0.751981i	−0.926623	−	0.375991i	$-0.877302\pi$
$349$		−	3.89345e12i		−	0.751981i	0.926623	−	0.375991i	$-0.122698\pi$
$350$			3.23877e13i			6.16652i
$351$			1.54114e11i			0.0289273i
$352$	3.35428e13			6.20706
$353$			2.56602e12i			0.468152i	0.972218	+	0.234076i	$0.0752065\pi$
$353$			2.56602e12i			0.468152i	−0.972218	+	0.234076i	$0.924793\pi$
$354$	−6.36615e12	+	1.22697e9i	−1.14515	+	0.000220708i
$355$	−9.09406e12			−1.61293
$356$		−	1.69105e13i		−	2.95738i
$357$	6.61854e12			1.14136
$358$	−3.45229e12			−0.587073
$359$	4.72954e12			0.793134			0.396567	−	0.918006i	$-0.370202\pi$
$359$	4.72954e12			0.793134			0.396567	+	0.918006i	$0.370202\pi$
$360$			1.44511e13i			2.38995i
$361$	−6.12812e12			−0.999520
$362$		−	9.44500e12i		−	1.51935i
$363$	1.10563e12			0.175419
$364$			3.51415e12i			0.549938i
$365$		−	1.38954e13i		−	2.14490i
$366$	2.40511e12			0.366209
$367$		−	3.31765e12i		−	0.498311i	−0.968463	−	0.249155i	$-0.919847\pi$
$367$		−	3.31765e12i		−	0.498311i	0.968463	−	0.249155i	$-0.0801530\pi$
$368$		−	4.10509e13i		−	6.08253i
$369$	−1.46014e12			−0.213434
$370$	−6.02974e12			−0.869541
$371$	1.24837e13			1.77613
$372$		−	8.22441e11i		−	0.115449i
$373$	−4.54427e12			−0.629391			−0.314695	−	0.949193i	$-0.601902\pi$
$373$	−4.54427e12			−0.629391			−0.314695	+	0.949193i	$0.601902\pi$
$374$	−2.62736e13			−3.59055
$375$	1.19493e13			1.61134
$376$	−4.96756e12			−0.661004
$377$			9.06643e11i			0.119050i
$378$		−	3.67326e12i		−	0.475984i
$379$	−1.16208e13			−1.48607			−0.743036	−	0.669252i	$-0.766615\pi$
$379$	−1.16208e13			−1.48607			−0.743036	+	0.669252i	$0.766615\pi$
$380$	9.51847e11			0.120129
$381$	−5.48201e12			−0.682834
$382$	−2.29261e12			−0.281847
$383$	−8.53173e12			−1.03524			−0.517622	−	0.855609i	$-0.673183\pi$
$383$	−8.53173e12			−1.03524			−0.517622	+	0.855609i	$0.673183\pi$
$384$			3.21885e13i			3.85518i
$385$			2.25104e13i			2.66121i
$386$			2.21031e13i			2.57938i
$387$		−	4.21554e12i		−	0.485622i
$388$			5.70563e12i			0.648851i
$389$	−8.89190e12			−0.998266			−0.499133	−	0.866525i	$-0.666348\pi$
$389$	−8.89190e12			−0.998266			−0.499133	+	0.866525i	$0.666348\pi$
$390$	2.90261e12			0.321710
$391$			1.88513e13i			2.06280i
$392$		−	1.97038e13i		−	2.12872i
$393$		−	3.12679e12i		−	0.333531i
$394$		−	2.48968e13i		−	2.62218i
$395$	−3.86664e12			−0.402113
$396$			1.08752e13i			1.11676i
$397$		−	6.74847e12i		−	0.684309i	−0.939644	−	0.342155i	$-0.888843\pi$
$397$		−	6.74847e12i		−	0.684309i	0.939644	−	0.342155i	$-0.111157\pi$
$398$		−	1.95945e13i		−	1.96209i
$399$	−1.59485e11			−0.0157709
$400$	1.19350e14			11.6553
$401$			1.84643e12i			0.178079i	0.996028	+	0.0890393i	$0.0283797\pi$
$401$			1.84643e12i			0.178079i	−0.996028	+	0.0890393i	$0.971620\pi$
$402$	1.02396e13			0.975328
$403$	−1.08892e11			−0.0102440
$404$		−	1.33242e13i		−	1.23804i
$405$	−2.26281e12			−0.207669
$406$		−	2.16095e13i		−	1.95891i
$407$	−2.99114e12			−0.267834
$408$		−	3.96976e13i		−	3.51126i
$409$		−	2.04755e13i		−	1.78903i	−0.447039	−	0.894515i	$-0.647521\pi$
$409$		−	2.04755e13i		−	1.78903i	0.447039	−	0.894515i	$-0.352479\pi$
$410$			2.75005e13i			2.37367i
$411$	−1.77609e12			−0.151445
$412$			3.77457e13i			3.17966i
$413$	−2.88776e9	−	1.49832e13i	−0.000240331	−	1.24696i
$414$	1.04624e13			0.860257
$415$			3.98354e13i			3.23615i
$416$	1.01796e13			0.817079
$417$	1.07731e13			0.854400
$418$	6.33107e11			0.0496130
$419$			2.40803e12i			0.186463i	0.995644	+	0.0932313i	$0.0297196\pi$
$419$			2.40803e12i			0.186463i	−0.995644	+	0.0932313i	$0.970280\pi$
$420$	−5.15971e13			−3.94801
$421$		−	1.89761e13i		−	1.43482i	−0.696653	−	0.717408i	$-0.745328\pi$
$421$		−	1.89761e13i		−	1.43482i	0.696653	−	0.717408i	$-0.254672\pi$
$422$	−2.03535e13			−1.52082
$423$		−	7.77839e11i		−	0.0574365i
$424$		−	7.48764e13i		−	5.46406i
$425$	−5.48074e13			−3.95271
$426$		−	1.38647e13i		−	0.988239i
$427$			5.66058e12i			0.398769i
$428$	−1.07096e13			−0.745682
$429$	1.43988e12			0.0990924
$430$	−7.93959e13			−5.40077
$431$			6.83772e12i			0.459753i	0.973220	+	0.229877i	$0.0738323\pi$
$431$			6.83772e12i			0.459753i	−0.973220	+	0.229877i	$0.926168\pi$
$432$	−1.35361e13			−0.899651
$433$	−8.12277e12			−0.533660			−0.266830	−	0.963744i	$-0.585976\pi$
$433$	−8.12277e12			−0.533660			−0.266830	+	0.963744i	$0.585976\pi$
$434$	2.59539e12			0.168560
$435$	−1.33119e13			−0.854662
$436$			2.32895e13i			1.47818i
$437$		−	4.54254e11i		−	0.0285030i
$438$	2.11847e13			1.31417
$439$	−1.54335e13			−0.946549			−0.473274	−	0.880915i	$-0.656928\pi$
$439$	−1.54335e13			−0.946549			−0.473274	+	0.880915i	$0.656928\pi$
$440$	1.35016e14			8.18693
$441$	3.08529e12			0.184971
$442$	−7.97354e12			−0.472650
$443$			8.81273e12i			0.516525i	0.966075	+	0.258263i	$0.0831500\pi$
$443$			8.81273e12i			0.516525i	−0.966075	+	0.258263i	$0.916850\pi$
$444$		−	6.85613e12i		−	0.397342i
$445$		−	3.28738e13i		−	1.88387i
$446$			1.59752e12i			0.0905256i
$447$			5.53824e12i			0.310338i
$448$	−1.37431e14			−7.61543
$449$	−2.17822e13			−1.19363			−0.596816	−	0.802378i	$-0.703568\pi$
$449$	−2.17822e13			−1.19363			−0.596816	+	0.802378i	$0.703568\pi$
$450$			3.04178e13i			1.64841i
$451$			1.36420e13i			0.731133i
$452$			7.66495e13i			4.06272i
$453$			2.52792e12i			0.132517i
$454$	3.81456e13			1.97772
$455$			6.83147e12i			0.350314i
$456$			9.56580e11i			0.0485173i
$457$		−	2.13151e13i		−	1.06932i	−0.845068	−	0.534659i	$-0.820440\pi$
$457$		−	2.13151e13i		−	1.06932i	0.845068	−	0.534659i	$-0.179560\pi$
$458$	−4.45079e12			−0.220856
$459$	6.21599e12			0.305103
$460$		−	1.46961e14i		−	7.13534i
$461$	3.42266e13			1.64384			0.821920	−	0.569603i	$-0.192903\pi$
$461$	3.42266e13			1.64384			0.821920	+	0.569603i	$0.192903\pi$
$462$	−3.43190e13			−1.63052
$463$			3.60218e13i			1.69302i	0.532377	+	0.846508i	$0.321299\pi$
$463$			3.60218e13i			1.69302i	−0.532377	+	0.846508i	$0.678701\pi$
$464$	−7.96316e13			−3.70251
$465$		−	1.59882e12i		−	0.0735417i
$466$	1.23142e13			0.560372
$467$		−	5.76659e12i		−	0.259618i	−0.991539	−	0.129809i	$-0.958564\pi$
$467$		−	5.76659e12i		−	0.259618i	0.991539	−	0.129809i	$-0.0414364\pi$
$468$			3.30042e12i			0.147007i
$469$			2.40995e13i			1.06205i
$470$	−1.46499e13			−0.638771
$471$			2.31229e13i			0.997558i
$472$	−8.98679e13	+	1.73206e10i	−3.83614	+	0.000739354i
$473$	−3.93855e13			−1.66353
$474$		−	5.89503e12i		−	0.246374i
$475$	1.32068e12			0.0546171
$476$	1.41739e14			5.80034
$477$	1.17244e13			0.474788
$478$		−	4.81321e13i		−	1.92884i
$479$	7.47303e12			0.296360			0.148180	−	0.988960i	$-0.452659\pi$
$479$	7.47303e12			0.296360			0.148180	+	0.988960i	$0.452659\pi$
$480$			1.49463e14i			5.86582i
$481$	−9.07755e11			−0.0352568
$482$		−	1.52518e13i		−	0.586256i
$483$			2.46239e13i			0.936743i
$484$	2.36775e13			0.891475
$485$			1.10917e13i			0.413322i
$486$		−	3.44984e12i		−	0.127238i
$487$	1.50255e13			0.548510			0.274255	−	0.961657i	$-0.411569\pi$
$487$	1.50255e13			0.548510			0.274255	+	0.961657i	$0.411569\pi$
$488$	3.39517e13			1.22677
$489$	9.10940e12			0.325796
$490$		−	5.81087e13i		−	2.05713i
$491$	1.44317e13			0.505718			0.252859	−	0.967503i	$-0.418629\pi$
$491$	1.44317e13			0.505718			0.252859	+	0.967503i	$0.418629\pi$
$492$	−3.12695e13			−1.08467
$493$	3.65682e13			1.25565
$494$	1.92136e11			0.00653091
$495$			2.11413e13i			0.711385i
$496$		−	9.56409e12i		−	0.318592i
$497$	3.26314e13			1.07610
$498$	−6.07325e13			−1.98278
$499$	1.90084e13			0.614387			0.307194	−	0.951647i	$-0.400610\pi$
$499$	1.90084e13			0.614387			0.307194	+	0.951647i	$0.400610\pi$
$500$	2.55899e14			8.18877
$501$	1.62901e13			0.516103
$502$		−	8.91356e12i		−	0.279597i
$503$			5.04714e13i			1.56749i	0.621081	+	0.783746i	$0.286694\pi$
$503$			5.04714e13i			1.56749i	−0.621081	+	0.783746i	$0.713306\pi$
$504$		−	5.18536e13i		−	1.59451i
$505$		−	2.59021e13i		−	0.788638i
$506$		−	9.77493e13i		−	2.94687i
$507$	−1.89040e13			−0.564306
$508$	−1.17399e14			−3.47014
$509$		−	1.15054e13i		−	0.336755i	−0.985723	−	0.168378i	$-0.946147\pi$
$509$		−	1.15054e13i		−	0.336755i	0.985723	−	0.168378i	$-0.0538528\pi$
$510$		−	1.17073e14i		−	3.39316i
$511$			4.98597e13i			1.43102i
$512$			2.63130e14i			7.47860i
$513$	−1.49785e11			−0.00421581
$514$		−	7.37247e13i		−	2.05493i
$515$			7.33771e13i			2.02546i
$516$		−	9.02774e13i		−	2.46792i
$517$	−7.26730e12			−0.196753
$518$	2.16360e13			0.580134
$519$			4.01145e13i			1.06528i
$520$	4.09747e13			1.07770
$521$	4.75369e13			1.23835			0.619173	−	0.785255i	$-0.287468\pi$
$521$	4.75369e13			1.23835			0.619173	+	0.785255i	$0.287468\pi$
$522$		−	2.02952e13i		−	0.523649i
$523$	6.54008e13			1.67138			0.835688	−	0.549204i	$-0.185069\pi$
$523$	6.54008e13			1.67138			0.835688	+	0.549204i	$0.185069\pi$
$524$		−	6.69614e13i		−	1.69499i
$525$	−7.15904e13			−1.79497
$526$		−	1.19805e12i		−	0.0297539i
$527$			4.39199e12i			0.108046i
$528$			1.26467e14i			3.08181i
$529$	−2.87085e13			−0.692999
$530$		−	2.20819e14i		−	5.28028i
$531$	−2.71212e9	−	1.40719e13i	−6.42446e−5	−	0.333333i
$532$	−3.41543e12			−0.0801470
$533$			4.14010e12i			0.0962442i
$534$	5.01190e13			1.15424
$535$	−2.08193e13			−0.475004
$536$	1.44547e14			3.26727
$537$		−	7.63100e12i		−	0.170887i
$538$	−1.11739e14			−2.47910
$539$		−	2.88257e13i		−	0.633630i
$540$	−4.84588e13			−1.05537
$541$			6.22173e13i			1.34253i	0.741216	+	0.671266i	$0.234249\pi$
$541$			6.22173e13i			1.34253i	−0.741216	+	0.671266i	$0.765751\pi$
$542$		−	1.93355e13i		−	0.413389i
$543$	2.08774e13			0.442259
$544$		−	4.10580e14i		−	8.61794i
$545$			4.52746e13i			0.941612i
$546$	−1.04152e13			−0.214636
$547$	4.77479e13			0.975029			0.487514	−	0.873115i	$-0.337904\pi$
$547$	4.77479e13			0.975029			0.487514	+	0.873115i	$0.337904\pi$
$548$	−3.80356e13			−0.769639
$549$			5.31629e12i			0.106598i
$550$	2.84192e14			5.64675
$551$	−8.81173e11			−0.0173501
$552$	1.47692e14			2.88179
$553$	1.38743e13			0.268279
$554$			1.48862e14i			2.85256i
$555$		−	1.33282e13i		−	0.253109i
$556$	2.30710e14			4.34203
$557$	−3.04354e13			−0.567679			−0.283840	−	0.958872i	$-0.591608\pi$
$557$	−3.04354e13			−0.567679			−0.283840	+	0.958872i	$0.591608\pi$
$558$	2.43753e12			0.0450588
$559$	−1.19528e13			−0.218982
$560$	−6.00017e14			−10.8949
$561$		−	5.80756e13i		−	1.04515i
$562$			6.31545e13i			1.12648i
$563$			6.02785e13i			1.06566i	0.846221	+	0.532832i	$0.178872\pi$
$563$			6.02785e13i			1.06566i	−0.846221	+	0.532832i	$0.821128\pi$
$564$		−	1.66577e13i		−	0.291890i
$565$			1.49006e14i			2.58798i
$566$	−1.68779e14			−2.90561
$567$	8.11943e12			0.138551
$568$		−	1.95721e14i		−	3.31052i
$569$			4.35597e13i			0.730338i	0.930941	+	0.365169i	$0.118989\pi$
$569$			4.35597e13i			0.730338i	−0.930941	+	0.365169i	$0.881011\pi$
$570$			2.82106e12i			0.0468855i
$571$			3.20890e13i			0.528659i	0.964432	+	0.264329i	$0.0851506\pi$
$571$			3.20890e13i			0.528659i	−0.964432	+	0.264329i	$0.914849\pi$
$572$	3.08356e13			0.503584
$573$		−	5.06762e12i		−	0.0820411i
$574$		−	9.86777e13i		−	1.58365i
$575$		−	2.03908e14i		−	3.24410i
$576$	−1.29072e14			−2.03573
$577$	5.85741e13			0.915855			0.457927	−	0.888990i	$-0.348592\pi$
$577$	5.85741e13			0.915855			0.457927	+	0.888990i	$0.348592\pi$
$578$			1.93646e14i			3.00171i
$579$	−4.88570e13			−0.750817
$580$	−2.85080e14			−4.34336
$581$		−	1.42938e14i		−	2.15907i
$582$	−1.69102e13			−0.253241
$583$		−	1.09541e14i		−	1.62642i
$584$	2.99055e14			4.40237
$585$			6.41597e12i			0.0936447i
$586$			8.00097e13i			1.15786i
$587$		−	5.30355e13i		−	0.760985i	−0.924784	−	0.380493i	$-0.875754\pi$
$587$		−	5.30355e13i		−	0.760985i	0.924784	−	0.380493i	$-0.124246\pi$
$588$	6.60727e13			0.940016
$589$		−	1.05833e11i		−	0.00149294i
$590$	−2.65031e14	+	5.10803e10i	−3.70712	+	0.000714486i
$591$	5.50323e13			0.763273
$592$		−	7.97293e13i		−	1.09650i
$593$	2.02817e13			0.276586			0.138293	−	0.990391i	$-0.455838\pi$
$593$	2.02817e13			0.276586			0.138293	+	0.990391i	$0.455838\pi$
$594$	−3.22317e13			−0.435864
$595$	2.75538e14			3.69485
$596$			1.18604e14i			1.57713i
$597$	4.33119e13			0.571131
$598$		−	2.96650e13i		−	0.387917i
$599$	5.40889e13			0.701414			0.350707	−	0.936485i	$-0.385941\pi$
$599$	5.40889e13			0.701414			0.350707	+	0.936485i	$0.385941\pi$
$600$			4.29394e14i			5.52204i
$601$		−	6.20264e13i		−	0.791050i	−0.918455	−	0.395525i	$-0.870563\pi$
$601$		−	6.20264e13i		−	0.791050i	0.918455	−	0.395525i	$-0.129437\pi$
$602$	2.84890e14			3.60325
$603$			2.26337e13i			0.283902i
$604$			5.41364e13i			0.673449i
$605$	4.60288e13			0.567875
$606$	3.94899e13			0.483196
$607$	1.23049e12			0.0149326			0.00746629	−	0.999972i	$-0.497623\pi$
$607$	1.23049e12			0.0149326			0.00746629	+	0.999972i	$0.497623\pi$
$608$			9.89362e12i			0.119080i
$609$	4.77660e13			0.570207
$610$	1.00128e14			1.18551
$611$	−2.20549e12			−0.0258999
$612$	1.33118e14			1.55053
$613$			7.83342e13i			0.905001i	0.891764	+	0.452500i	$0.149468\pi$
$613$			7.83342e13i			0.905001i	−0.891764	+	0.452500i	$0.850532\pi$
$614$		−	1.90365e14i		−	2.18145i
$615$	−6.07876e13			−0.690938
$616$	−4.84465e14			−5.46209
$617$	1.06587e14			1.19200			0.596002	−	0.802983i	$-0.296755\pi$
$617$	1.06587e14			1.19200			0.596002	+	0.802983i	$0.296755\pi$
$618$	−1.11870e14			−1.24100
$619$	−9.84942e13			−1.08382			−0.541910	−	0.840436i	$-0.682299\pi$
$619$	−9.84942e13			−1.08382			−0.541910	+	0.840436i	$0.682299\pi$
$620$		−	3.42392e13i		−	0.373737i
$621$			2.31262e13i			0.250407i
$622$			1.18934e14i			1.27748i
$623$			1.17958e14i			1.25686i
$624$			3.83802e13i			0.405681i
$625$	2.59690e14			2.72305
$626$	−3.23196e13			−0.336198
$627$			1.39943e12i			0.0144415i
$628$			4.95186e14i			5.06956i
$629$			3.66130e13i			0.371863i
$630$		−	1.52922e14i		−	1.54088i
$631$	−9.27400e13			−0.927086			−0.463543	−	0.886074i	$-0.653422\pi$
$631$	−9.27400e13			−0.927086			−0.463543	+	0.886074i	$0.653422\pi$
$632$		−	8.32173e13i		−	0.825332i
$633$		−	4.49898e13i		−	0.442686i
$634$			4.48370e13i			0.437714i
$635$	−2.28223e14			−2.21050
$636$	2.51083e14			2.41286
$637$		−	8.74805e12i		−	0.0834092i
$638$	−1.89616e14			−1.79379
$639$	3.06467e13			0.287660
$640$			1.34005e15i			12.4802i
$641$	−9.66091e13			−0.892746			−0.446373	−	0.894847i	$-0.647284\pi$
$641$	−9.66091e13			−0.892746			−0.446373	+	0.894847i	$0.647284\pi$
$642$		−	3.17408e13i		−	0.291034i
$643$	−5.58926e13			−0.508510			−0.254255	−	0.967137i	$-0.581830\pi$
$643$	−5.58926e13			−0.508510			−0.254255	+	0.967137i	$0.581830\pi$
$644$			5.27329e14i			4.76050i
$645$		−	1.75498e14i		−	1.57208i
$646$		−	7.74954e12i		−	0.0688832i
$647$	−1.06933e14			−0.943168			−0.471584	−	0.881821i	$-0.656318\pi$
$647$	−1.06933e14			−0.943168			−0.471584	+	0.881821i	$0.656318\pi$
$648$		−	4.86998e13i		−	0.426238i
$649$	−1.31472e14	+	2.53392e10i	−1.14186	+	0.000220074i
$650$	8.62469e13			0.743321
$651$			5.73689e12i			0.0490650i
$652$	1.95081e14			1.65568
$653$	−1.12908e14			−0.950956			−0.475478	−	0.879728i	$-0.657725\pi$
$653$	−1.12908e14			−0.950956			−0.475478	+	0.879728i	$0.657725\pi$
$654$	−6.90250e13			−0.576923
$655$		−	1.30172e14i		−	1.07972i
$656$	−3.63630e14			−2.99323
$657$			4.68271e13i			0.382535i
$658$	5.25670e13			0.426171
$659$			1.35675e14i			1.09162i	0.837909	+	0.545810i	$0.183778\pi$
$659$			1.35675e14i			1.09162i	−0.837909	+	0.545810i	$0.816222\pi$
$660$			4.52748e14i			3.61524i
$661$	1.55289e14			1.23065			0.615323	−	0.788275i	$-0.289025\pi$
$661$	1.55289e14			1.23065			0.615323	+	0.788275i	$0.289025\pi$
$662$		−	6.56849e13i		−	0.516625i
$663$		−	1.76248e13i		−	0.137581i
$664$	−8.57331e14			−6.64214
$665$	−6.63956e12			−0.0510541
$666$	2.03201e13			0.155079
$667$			1.36050e14i			1.03055i
$668$	3.48859e14			2.62282
$669$	−3.53118e12			−0.0263505
$670$	4.26285e14			3.15738
$671$	4.96698e13			0.365157
$672$		−	5.36307e14i		−	3.91351i
$673$			1.74921e14i			1.26697i	0.773756	+	0.633484i	$0.218376\pi$
$673$			1.74921e14i			1.26697i	−0.773756	+	0.633484i	$0.781624\pi$
$674$	−4.49156e14			−3.22922
$675$	−6.72362e13			−0.479826
$676$	−4.04837e14			−2.86778
$677$	−4.86161e13			−0.341851			−0.170925	−	0.985284i	$-0.554676\pi$
$677$	−4.86161e13			−0.341851			−0.170925	+	0.985284i	$0.554676\pi$
$678$	−2.27172e14			−1.58565
$679$		−	3.97993e13i		−	0.275757i
$680$		−	1.65266e15i		−	11.3668i
$681$			8.43176e13i			0.575682i
$682$		−	2.27737e13i		−	0.154352i
$683$			1.55046e13i			0.104317i	0.998639	+	0.0521586i	$0.0166101\pi$
$683$			1.55046e13i			0.104317i	−0.998639	+	0.0521586i	$0.983390\pi$
$684$	−3.20770e12			−0.0214246
$685$	−7.39407e13			−0.490265
$686$		−	1.67240e14i		−	1.10083i
$687$		−	9.83810e12i		−	0.0642876i
$688$		−	1.04983e15i		−	6.81045i
$689$		−	3.32435e13i		−	0.214097i
$690$	4.35561e14			2.78486
$691$		−	2.79217e14i		−	1.77236i	−0.463343	−	0.886179i	$-0.653350\pi$
$691$		−	2.79217e14i		−	1.77236i	0.463343	−	0.886179i	$-0.346650\pi$
$692$			8.59066e14i			5.41373i
$693$		−	7.58594e13i		−	0.474617i
$694$	3.80093e14			2.36098
$695$	4.48498e14			2.76590
$696$		−	2.86497e14i		−	1.75418i
$697$	1.66985e14			1.01511
$698$	2.47119e14			1.49152
$699$			2.72195e13i			0.163115i
$700$	−1.53313e15			−9.12200
$701$		−	1.49605e14i		−	0.883804i	−0.897063	−	0.441902i	$-0.854304\pi$
$701$		−	1.49605e14i		−	0.883804i	0.897063	−	0.441902i	$-0.145696\pi$
$702$	−9.78170e12			−0.0573758
$703$		−	8.82253e11i		−	0.00513827i
$704$			1.20591e15i			6.97353i
$705$		−	3.23824e13i		−	0.185936i
$706$	−1.62867e14			−0.928557
$707$			9.29421e13i			0.526157i
$708$	−5.80810e10	−	3.01354e14i	−0.000326489	−	1.69399i
$709$	1.49929e14			0.836865			0.418433	−	0.908248i	$-0.362580\pi$
$709$	1.49929e14			0.836865			0.418433	+	0.908248i	$0.362580\pi$
$710$		−	5.77204e14i		−	3.19917i
$711$	1.30305e13			0.0717154
$712$	7.07506e14			3.86661
$713$	−1.63401e13			−0.0886764
$714$			4.20082e14i			2.26382i
$715$	5.99440e13			0.320786
$716$		−	1.63421e14i		−	0.868444i
$717$	1.06392e14			0.561453
$718$			3.00186e14i			1.57314i
$719$			1.55523e13i			0.0809375i	0.999181	+	0.0404687i	$0.0128851\pi$
$719$			1.55523e13i			0.0809375i	−0.999181	+	0.0404687i	$0.987115\pi$
$720$	−5.63523e14			−2.91239
$721$		−	2.63293e14i		−	1.35133i
$722$		−	3.88955e14i		−	1.98250i
$723$	3.37129e13			0.170650
$724$	4.47097e14			2.24755
$725$	−3.95545e14			−1.97472
$726$			7.01749e13i			0.347935i
$727$	−2.54365e14			−1.25252			−0.626261	−	0.779613i	$-0.715416\pi$
$727$	−2.54365e14			−1.25252			−0.626261	+	0.779613i	$0.715416\pi$
$728$	−1.47026e14			−0.719014
$729$	7.62560e12			0.0370370
$730$	8.81947e14			4.25430
$731$			4.82098e14i			2.30966i
$732$			1.13850e14i			0.541725i
$733$	−1.27430e14			−0.602216			−0.301108	−	0.953590i	$-0.597356\pi$
$733$	−1.27430e14			−0.602216			−0.301108	+	0.953590i	$0.597356\pi$
$734$	2.10573e14			0.988375
$735$	1.28444e14			0.598796
$736$	1.52754e15			7.07298
$737$	2.11465e14			0.972527
$738$		−	9.26759e13i		−	0.423336i
$739$			3.32416e14i			1.50820i	0.656758	+	0.754102i	$0.271927\pi$
$739$			3.32416e14i			1.50820i	−0.656758	+	0.754102i	$0.728073\pi$
$740$		−	2.85429e14i		−	1.28629i
$741$			4.24701e11i			0.00190104i
$742$			7.92346e14i			3.52286i
$743$	−2.55056e14			−1.12639			−0.563197	−	0.826322i	$-0.690429\pi$
$743$	−2.55056e14			−1.12639			−0.563197	+	0.826322i	$0.690429\pi$
$744$	3.44095e13			0.150943
$745$			2.30564e14i			1.00464i
$746$		−	2.88427e14i		−	1.24836i
$747$		−	1.34244e14i		−	0.577155i
$748$		−	1.24371e15i		−	5.31143i
$749$	7.47041e13			0.316910
$750$			7.58428e14i			3.19601i
$751$		−	3.85398e14i		−	1.61328i	−0.591043	−	0.806640i	$-0.701284\pi$
$751$		−	3.85398e14i		−	1.61328i	0.591043	−	0.806640i	$-0.298716\pi$
$752$		−	1.93711e14i		−	0.805499i
$753$	1.97027e13			0.0813861
$754$	−5.75450e13			−0.236130
$755$			1.05241e14i			0.428991i
$756$	1.73881e14			0.704113
$757$	1.20459e14			0.484574			0.242287	−	0.970205i	$-0.422102\pi$
$757$	1.20459e14			0.484574			0.242287	+	0.970205i	$0.422102\pi$
$758$		−	7.37577e14i		−	2.94755i
$759$	2.16067e14			0.857786
$760$			3.98236e13i			0.157063i
$761$	−7.56048e13			−0.296228			−0.148114	−	0.988970i	$-0.547320\pi$
$761$	−7.56048e13			−0.296228			−0.148114	+	0.988970i	$0.547320\pi$
$762$		−	3.47945e14i		−	1.35437i
$763$		−	1.62455e14i		−	0.628217i
$764$		−	1.08525e14i		−	0.416930i
$765$	2.58779e14			0.987694
$766$		−	5.41512e14i		−	2.05336i
$767$	−3.98994e13	+	7.68996e9i	−0.150311	+	2.89699e-5i
$768$	−1.10094e15			−4.12057
$769$		−	2.33655e13i		−	0.0868848i	−0.999056	−	0.0434424i	$-0.986168\pi$
$769$		−	2.33655e13i		−	0.0868848i	0.999056	−	0.0434424i	$-0.0138325\pi$
$770$	−1.42874e15			−5.27838
$771$	1.62962e14			0.598157
$772$	−1.04629e15			−3.81563
$773$			3.39985e14i			1.23186i	0.787800	+	0.615931i	$0.211220\pi$
$773$			3.39985e14i			1.23186i	−0.787800	+	0.615931i	$0.788780\pi$
$774$	2.67562e14			0.963207
$775$		−	4.75066e13i		−	0.169920i
$776$	−2.38713e14			−0.848337
$777$			4.78246e13i			0.168867i
$778$		−	5.64372e14i		−	1.98001i
$779$	−4.02379e12			−0.0140265
$780$			1.37400e14i			0.475899i
$781$		−	2.86331e14i		−	0.985400i
$782$	−1.19650e15			−4.09146
$783$	4.48608e13			0.152426
$784$	7.68353e14			2.59406
$785$			9.62636e14i			3.22934i
$786$	1.98459e14			0.661543
$787$	−4.43901e14			−1.47032			−0.735162	−	0.677892i	$-0.762894\pi$
$787$	−4.43901e14			−1.47032			−0.735162	+	0.677892i	$0.762894\pi$
$788$	1.17854e15			3.87893
$789$	2.64818e12			0.00866089
$790$		−	2.45417e14i		−	0.797572i
$791$		−	5.34664e14i		−	1.72663i
$792$	−4.54999e14			−1.46011
$793$	1.50738e13			0.0480682
$794$	4.28328e14			1.35729
$795$	4.88102e14			1.53700
$796$	9.27541e14			2.90247
$797$		−	3.14563e14i		−	0.978174i	−0.872235	−	0.489087i	$-0.837330\pi$
$797$		−	3.14563e14i		−	0.978174i	0.872235	−	0.489087i	$-0.162670\pi$
$798$		−	1.01226e13i		−	0.0312807i
$799$			8.89553e13i			0.273173i
$800$			4.44110e15i			13.5531i
$801$			1.10784e14i			0.335981i
$802$	−1.17194e14			−0.353210
$803$	4.37503e14			1.31040
$804$			4.84709e14i			1.44278i
$805$			1.02512e15i			3.03247i
$806$		−	6.91139e12i		−	0.0203184i
$807$		−	2.46990e14i		−	0.721625i
$808$	5.57460e14			1.61867
$809$			4.11525e14i			1.18755i	0.804629	+	0.593777i	$0.202364\pi$
$809$			4.11525e14i			1.18755i	−0.804629	+	0.593777i	$0.797636\pi$
$810$		−	1.43621e14i		−	0.411902i
$811$		−	1.04930e14i		−	0.299087i	−0.988755	−	0.149543i	$-0.952220\pi$
$811$		−	1.04930e14i		−	0.299087i	0.988755	−	0.149543i	$-0.0477803\pi$
$812$	1.02293e15			2.89777
$813$	4.27396e13			0.120331
$814$		−	1.89849e14i		−	0.531235i
$815$	3.79235e14			1.05468
$816$	1.54801e15			4.27882
$817$		−	1.16170e13i		−	0.0319141i
$818$	1.29959e15			3.54845
$819$		−	2.30219e13i		−	0.0624771i
$820$	−1.30179e15			−3.51133
$821$		−	4.17704e13i		−	0.111983i	−0.998431	−	0.0559916i	$-0.982168\pi$
$821$		−	4.17704e13i		−	0.111983i	0.998431	−	0.0559916i	$-0.0178320\pi$
$822$		−	1.12729e14i		−	0.300384i
$823$			6.95141e14i			1.84108i	0.390644	+	0.920542i	$0.372252\pi$
$823$			6.95141e14i			1.84108i	−0.390644	+	0.920542i	$0.627748\pi$
$824$	−1.57921e15			−4.15723
$825$			6.28183e14i			1.64368i
$826$	9.50987e14	−	1.83287e11i	2.47329	−	0.000476685i
$827$	−1.06274e14			−0.274725			−0.137362	−	0.990521i	$-0.543863\pi$
$827$	−1.06274e14			−0.274725			−0.137362	+	0.990521i	$0.543863\pi$
$828$			4.95256e14i			1.27256i
$829$	−1.30239e14			−0.332634			−0.166317	−	0.986072i	$-0.553188\pi$
$829$	−1.30239e14			−0.332634			−0.166317	+	0.986072i	$0.553188\pi$
$830$	−2.52837e15			−6.41874
$831$	−3.29047e14			−0.830335
$832$			3.65972e14i			0.917975i
$833$	−3.52841e14			−0.879738
$834$			6.83775e14i			1.69466i
$835$	6.78179e14			1.67075
$836$			2.99693e13i			0.0733915i
$837$			5.38797e12i			0.0131159i
$838$	−1.52839e14			−0.369839
$839$		−	1.79598e14i		−	0.432007i	−0.976393	−	0.216004i	$-0.930698\pi$
$839$		−	1.79598e14i		−	0.432007i	0.976393	−	0.216004i	$-0.0693023\pi$
$840$		−	2.15873e15i		−	5.16181i
$841$	−1.56795e14			−0.372693
$842$	1.20442e15			2.84589
$843$	−1.39598e14			−0.327900
$844$		−	9.63473e14i		−	2.24971i
$845$	−7.86998e14			−1.82680
$846$	4.93698e13			0.113922
$847$	−1.65161e14			−0.378871
$848$	2.91982e15			6.65850
$849$		−	3.73073e14i		−	0.845776i
$850$		−	3.47865e15i		−	7.84000i
$851$	−1.36217e14			−0.305198
$852$	6.56311e14			1.46188
$853$	1.90935e14			0.422805			0.211402	−	0.977399i	$-0.432197\pi$
$853$	1.90935e14			0.422805			0.211402	+	0.977399i	$0.432197\pi$
$854$	−3.59279e14			−0.790938
$855$	−6.23573e12			−0.0136476
$856$		−	4.48070e14i		−	0.974938i
$857$			6.13434e14i			1.32698i	0.748186	+	0.663489i	$0.230925\pi$
$857$			6.13434e14i			1.32698i	−0.748186	+	0.663489i	$0.769075\pi$
$858$			9.13898e13i			0.196545i
$859$		−	6.74774e13i		−	0.144275i	−0.997395	−	0.0721377i	$-0.977018\pi$
$859$		−	6.74774e13i		−	0.144275i	0.997395	−	0.0721377i	$-0.0229821\pi$
$860$		−	3.75836e15i		−	7.98925i
$861$	2.18119e14			0.460975
$862$	−4.33993e14			−0.911898
$863$			1.61367e14i			0.337101i	0.985693	+	0.168551i	$0.0539087\pi$
$863$			1.61367e14i			0.337101i	−0.985693	+	0.168551i	$0.946091\pi$
$864$		−	5.03688e14i		−	1.04615i
$865$			1.67002e15i			3.44858i
$866$		−	5.15556e14i		−	1.05849i
$867$	−4.28038e14			−0.873749
$868$			1.22858e14i			0.249347i
$869$		−	1.21743e14i		−	0.245666i
$870$		−	8.44913e14i		−	1.69518i
$871$	6.41757e13			0.128021
$872$	−9.74393e14			−1.93264
$873$		−	3.73786e13i		−	0.0737144i
$874$	2.88317e13			0.0565344
$875$	−1.78501e15			−3.48017
$876$			1.00282e15i			1.94403i
$877$	−7.70487e13			−0.148514			−0.0742570	−	0.997239i	$-0.523659\pi$
$877$	−7.70487e13			−0.148514			−0.0742570	+	0.997239i	$0.523659\pi$
$878$		−	9.79573e14i		−	1.87743i
$879$	−1.76855e14			−0.337033
$880$			5.26496e15i			9.97659i
$881$			3.67428e14i			0.692297i	0.938180	+	0.346148i	$0.112511\pi$
$881$			3.67428e14i			0.692297i	−0.938180	+	0.346148i	$0.887489\pi$
$882$			1.95825e14i			0.366881i
$883$	2.36063e14			0.439769			0.219884	−	0.975526i	$-0.429432\pi$
$883$	2.36063e14			0.439769			0.219884	+	0.975526i	$0.429432\pi$
$884$		−	3.77443e14i		−	0.699181i
$885$	−1.12909e11	−	5.85829e14i	−0.000207975	−	1.07908i
$886$	−5.59347e14			−1.02450
$887$		−	1.77601e14i		−	0.323465i	−0.986835	−	0.161733i	$-0.948292\pi$
$887$		−	1.77601e14i		−	0.323465i	0.986835	−	0.161733i	$-0.0517082\pi$
$888$	2.86848e14			0.519503
$889$	8.18912e14			1.47478
$890$	2.08652e15			3.73656
$891$		−	7.12455e13i		−	0.126873i
$892$	−7.56215e13			−0.133913
$893$		−	2.14353e12i		−	0.00377461i
$894$	−3.51515e14			−0.615539
$895$		−	3.17688e14i		−	0.553204i
$896$		−	4.80838e15i		−	8.32642i
$897$	6.55721e13			0.112916
$898$		−	1.38253e15i		−	2.36751i
$899$			3.16970e13i			0.0539783i
$900$	−1.43989e15			−2.43846
$901$	−1.34083e15			−2.25813
$902$	−8.65865e14			−1.45017
$903$			6.29725e14i			1.04885i
$904$	−3.20688e15			−5.31178
$905$	8.69151e14			1.43170
$906$	−1.60448e14			−0.262842
$907$	−6.89276e14			−1.12294			−0.561470	−	0.827497i	$-0.689764\pi$
$907$	−6.89276e14			−1.12294			−0.561470	+	0.827497i	$0.689764\pi$
$908$			1.80569e15i			2.92560i
$909$			8.72893e13i			0.140651i
$910$	−4.33596e14			−0.694830
$911$	−1.13409e15			−1.80740			−0.903701	−	0.428163i	$-0.859161\pi$
$911$	−1.13409e15			−1.80740			−0.903701	+	0.428163i	$0.859161\pi$
$912$	−3.73020e13			−0.0591232
$913$	−1.25423e15			−1.97708
$914$	1.35288e15			2.12094
$915$			2.21324e14i			0.345082i
$916$		−	2.10686e14i		−	0.326708i
$917$			4.67086e14i			0.720361i
$918$			3.94532e14i			0.605157i
$919$		−	9.20388e14i		−	1.40408i	−0.712135	−	0.702042i	$-0.752272\pi$
$919$		−	9.20388e14i		−	1.40408i	0.712135	−	0.702042i	$-0.247728\pi$
$920$	6.14861e15			9.32906
$921$	4.20786e14			0.634985
$922$			2.17238e15i			3.26047i
$923$		−	8.68959e13i		−	0.129715i
$924$		−	1.62456e15i		−	2.41199i
$925$		−	3.96030e14i		−	0.584816i
$926$	−2.28632e15			−3.35801
$927$		−	2.47279e14i		−	0.361234i
$928$		−	2.96315e15i		−	4.30541i
$929$			1.02686e15i			1.48399i	0.670405	+	0.741995i	$0.266120\pi$
$929$			1.02686e15i			1.48399i	−0.670405	+	0.741995i	$0.733880\pi$
$930$	1.01478e14			0.145866
$931$	8.50229e12			0.0121559
$932$			5.82916e14i			0.828946i
$933$	−2.62894e14			−0.371854
$934$	3.66008e14			0.514939
$935$		−	2.41776e15i		−	3.38341i
$936$	−1.38084e14			−0.192204
$937$		−	4.38428e14i		−	0.607017i	−0.952829	−	0.303508i	$-0.901842\pi$
$937$		−	4.38428e14i		−	0.607017i	0.952829	−	0.303508i	$-0.0981581\pi$
$938$	−1.52960e15			−2.10651
$939$		−	7.14399e13i		−	0.0978617i
$940$		−	6.93481e14i		−	0.944921i
$941$			1.09395e14i			0.148268i	0.997248	+	0.0741341i	$0.0236193\pi$
$941$			1.09395e14i			0.148268i	−0.997248	+	0.0741341i	$0.976381\pi$
$942$	−1.46762e15			−1.97861
$943$			6.21258e14i			0.833131i
$944$	−6.75419e11	−	3.50442e15i	−0.000900976	−	4.67472i
$945$	3.38022e14			0.448524
$946$		−	2.49982e15i		−	3.29953i
$947$	9.67375e14			1.27012			0.635060	−	0.772462i	$-0.280975\pi$
$947$	9.67375e14			1.27012			0.635060	+	0.772462i	$0.280975\pi$
$948$	2.79053e14			0.364455
$949$	1.32774e14			0.172497
$950$			8.38240e13i			0.108330i
$951$	−9.91086e13			−0.127412
$952$			5.93009e15i			7.58362i
$953$	−3.28194e14			−0.417510			−0.208755	−	0.977968i	$-0.566941\pi$
$953$	−3.28194e14			−0.417510			−0.208755	+	0.977968i	$0.566941\pi$
$954$			7.44154e14i			0.941718i
$955$		−	2.10971e14i		−	0.265587i
$956$	2.27843e15			2.85329
$957$		−	4.19132e14i		−	0.522144i
$958$			4.74317e14i			0.587815i
$959$	2.65315e14			0.327091
$960$	−5.37343e15			−6.59015
$961$	8.15821e14			0.995355
$962$		−	5.76156e13i		−	0.0699301i
$963$	7.01605e13			0.0847152
$964$	7.21975e14			0.867235
$965$	−2.03398e15			−2.43058
$966$	−1.56289e15			−1.85798
$967$		−	1.91384e14i		−	0.226347i	−0.993575	−	0.113173i	$-0.963898\pi$
$967$		−	1.91384e14i		−	0.226347i	0.993575	−	0.113173i	$-0.0361015\pi$
$968$			9.90625e14i			1.16555i
$969$	1.71297e13			0.0200508
$970$	−7.03993e14			−0.819803
$971$	−1.61112e15			−1.86651			−0.933257	−	0.359210i	$-0.883046\pi$
$971$	−1.61112e15			−1.86651			−0.933257	+	0.359210i	$0.883046\pi$
$972$	1.63305e14			0.188221
$973$	−1.60931e15			−1.84533
$974$			9.53675e14i			1.08794i
$975$			1.90642e14i			0.216369i
$976$			1.32395e15i			1.49494i
$977$		−	6.68174e14i		−	0.750614i	−0.926901	−	0.375307i	$-0.877537\pi$
$977$		−	6.68174e14i		−	0.750614i	0.926901	−	0.375307i	$-0.122463\pi$
$978$			5.78177e14i			0.646199i
$979$	1.03505e15			1.15092
$980$	2.75069e15			3.04306
$981$		−	1.52574e14i		−	0.167933i
$982$			9.15983e14i			1.00307i
$983$			1.77138e15i			1.92994i	0.262351	+	0.964972i	$0.415502\pi$
$983$			1.77138e15i			1.92994i	−0.262351	+	0.964972i	$0.584498\pi$
$984$		−	1.30826e15i		−	1.41814i
$985$	2.29106e15			2.47090
$986$			2.32100e15i			2.49052i
$987$			1.16195e14i			0.124051i
$988$			9.09512e12i			0.00966104i
$989$	−1.79362e15			−1.89561
$990$	−1.34184e15			−1.41100
$991$		−	5.01226e14i		−	0.524403i	−0.965013	−	0.262202i	$-0.915551\pi$
$991$		−	5.01226e14i		−	0.524403i	0.965013	−	0.262202i	$-0.0844485\pi$
$992$	3.55887e14			0.370471
$993$	1.45191e14			0.150381
$994$			2.07113e15i			2.13440i
$995$	1.80313e15			1.84889
$996$		−	2.87489e15i		−	2.93308i
$997$	1.76373e15			1.79042			0.895211	−	0.445643i	$-0.147025\pi$
$997$	1.76373e15			1.79042			0.895211	+	0.445643i	$0.147025\pi$
$998$			1.20647e15i			1.21861i
$999$			4.49158e13i			0.0451411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.100	yes	100
59.58	odd	2	inner	177.11.c.a.58.1	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.1	✓	100	59.58	odd	2	inner
177.11.c.a.58.100	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} -8904.65i q^{6} +20957.7 q^{7} -125703. i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} -8904.65i q^{6} +20957.7 q^{7} -125703. i q^{8} +19683.0 q^{9} -370712. i q^{10} -183897. i q^{11} +421519. q^{12} -55809.3i q^{13} +1.33019e6i q^{14} +819427. q^{15} +4.90180e6 q^{16} -2.25099e6 q^{17} +1.24929e6i q^{18} +54241.4 q^{19} +1.75483e7 q^{20} -2.94028e6 q^{21} +1.16720e7 q^{22} -8.37467e6i q^{23} +1.76356e7i q^{24} +2.43481e7 q^{25} +3.54224e6 q^{26} -2.76145e6 q^{27} -6.29672e7 q^{28} -1.62454e7 q^{29} +5.20094e7i q^{30} -1.95114e6i q^{31} +1.82400e8i q^{32} +2.58000e7i q^{33} -1.42871e8i q^{34} -1.22408e8 q^{35} -5.91374e7 q^{36} -1.62653e7i q^{37} +3.44273e6i q^{38} +7.82982e6i q^{39} +7.34192e8i q^{40} -7.41830e7 q^{41} -1.86621e8i q^{42} -2.14172e8i q^{43} +5.52517e8i q^{44} -1.14962e8 q^{45} +5.31543e8 q^{46} -3.95183e7i q^{47} -6.87704e8 q^{48} +1.56749e8 q^{49} +1.54539e9i q^{50} +3.15805e8 q^{51} +1.67679e8i q^{52} +5.95662e8 q^{53} -1.75270e8i q^{54} +1.07409e9i q^{55} -2.63444e9i q^{56} -7.60986e6 q^{57} -1.03110e9i q^{58} +(-137790. - 7.14924e8i) q^{59} -2.46196e9 q^{60} +2.70096e8i q^{61} +1.23840e8 q^{62} +4.12510e8 q^{63} -6.55754e9 q^{64} +3.25965e8i q^{65} -1.63754e9 q^{66} +1.14991e9i q^{67} +6.76308e9 q^{68} +1.17493e9i q^{69} -7.76925e9i q^{70} +1.55702e9 q^{71} -2.47421e9i q^{72} +2.37906e9i q^{73} +1.03237e9 q^{74} -3.41595e9 q^{75} -1.62968e8 q^{76} -3.85406e9i q^{77} -4.96962e8 q^{78} +6.62017e8 q^{79} -2.86299e10 q^{80} +3.87420e8 q^{81} -4.70842e9i q^{82} -6.82031e9i q^{83} +8.83405e9 q^{84} +1.31474e10 q^{85} +1.35936e10 q^{86} +2.27916e9 q^{87} -2.31164e10 q^{88} +5.62841e9i q^{89} -7.29672e9i q^{90} -1.16963e9i q^{91} +2.51616e10i q^{92} +2.73737e8i q^{93} +2.50824e9 q^{94} -3.16808e8 q^{95} -2.55900e10i q^{96} -1.89903e9i q^{97} +9.94893e9i q^{98} -3.61965e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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