LMFDB - Embedded newform 177.11.c.a.58.7

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			58.7
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.94

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} -201708. i q^{10} +312528. i q^{11} +301880. q^{12} -359669. i q^{13} -428840. i q^{14} -502165. q^{15} +1.37801e6 q^{16} +567921. q^{17} -1.10921e6i q^{18} -397324. q^{19} -7.70175e6 q^{20} -1.06762e6 q^{21} +1.76121e7 q^{22} -1.14802e7i q^{23} -8.91609e6i q^{24} +3.04592e6 q^{25} -2.02686e7 q^{26} -2.76145e6 q^{27} -1.63743e7 q^{28} -1.45674e6 q^{29} +2.82988e7i q^{30} -1.04454e7i q^{31} -1.25786e7i q^{32} -4.38465e7i q^{33} -3.20044e7i q^{34} +2.72379e7 q^{35} -4.23526e7 q^{36} +1.11352e8i q^{37} +2.23906e7i q^{38} +5.04601e7i q^{39} +2.27473e8i q^{40} -1.09214e8 q^{41} +6.01645e7i q^{42} +2.71906e8i q^{43} -6.72478e8i q^{44} +7.04518e7 q^{45} -6.46953e8 q^{46} +1.44150e8i q^{47} -1.93329e8 q^{48} -2.24566e8 q^{49} -1.71649e8i q^{50} -7.96771e7 q^{51} +7.73911e8i q^{52} +1.14733e8 q^{53} +1.55618e8i q^{54} +1.11864e9i q^{55} +4.83617e8i q^{56} +5.57430e7 q^{57} +8.20924e7i q^{58} +(-7.13172e8 - 5.00283e7i) q^{59} +1.08053e9 q^{60} -7.51127e8i q^{61} -5.88636e8 q^{62} +1.49784e8 q^{63} +7.02230e8 q^{64} -1.28737e9i q^{65} -2.47091e9 q^{66} +6.46732e8i q^{67} -1.22201e9 q^{68} +1.61063e9i q^{69} -1.53495e9i q^{70} -1.38039e9 q^{71} +1.25089e9i q^{72} +2.57637e9i q^{73} +6.27507e9 q^{74} -4.27330e8 q^{75} +8.54935e8 q^{76} +2.37828e9i q^{77} +2.84361e9 q^{78} +4.01132e9 q^{79} +4.93233e9 q^{80} +3.87420e8 q^{81} +6.15460e9i q^{82} -1.17721e9i q^{83} +2.29724e9 q^{84} +2.03277e9 q^{85} +1.53229e10 q^{86} +2.04374e8 q^{87} -1.98618e10 q^{88} +5.40845e9i q^{89} -3.97022e9i q^{90} -2.73700e9i q^{91} +2.47024e10i q^{92} +1.46545e9i q^{93} +8.12336e9 q^{94} -1.42215e9 q^{95} +1.76473e9i q^{96} -8.97393e8i q^{97} +1.26551e10i q^{98} +6.15149e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	56.3537i		−	1.76105i	−0.473998	−	0.880526i	$-0.657190\pi$
$2$		−	56.3537i		−	1.76105i	0.473998	−	0.880526i	$-0.342810\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−2151.73			−2.10130
$5$	3579.32			1.14538			0.572691	−	0.819771i	$-0.305899\pi$
$5$	3579.32			1.14538			0.572691	+	0.819771i	$0.305899\pi$
$6$			7906.20i			1.01674i
$7$	7609.79			0.452775			0.226388	−	0.974037i	$-0.427308\pi$
$7$	7609.79			0.452775			0.226388	+	0.974037i	$0.427308\pi$
$8$			63551.9i			1.93945i
$9$	19683.0			0.333333
$10$		−	201708.i		−	2.01708i
$11$			312528.i			1.94055i	0.241996	+	0.970277i	$0.422198\pi$
$11$			312528.i			1.94055i	−0.241996	+	0.970277i	$0.577802\pi$
$12$	301880.			1.21319
$13$		−	359669.i		−	0.968692i	−0.874877	−	0.484346i	$-0.839058\pi$
$13$		−	359669.i		−	0.968692i	0.874877	−	0.484346i	$-0.160942\pi$
$14$		−	428840.i		−	0.797361i
$15$	−502165.			−0.661287
$16$	1.37801e6			1.31417
$17$	567921.			0.399984			0.199992	−	0.979797i	$-0.435908\pi$
$17$	567921.			0.399984			0.199992	+	0.979797i	$0.435908\pi$
$18$		−	1.10921e6i		−	0.587017i
$19$	−397324.			−0.160464			−0.0802318	−	0.996776i	$-0.525566\pi$
$19$	−397324.			−0.160464			−0.0802318	+	0.996776i	$0.525566\pi$
$20$	−7.70175e6			−2.40680
$21$	−1.06762e6			−0.261410
$22$	1.76121e7			3.41742
$23$		−	1.14802e7i		−	1.78366i	−0.452373	−	0.891829i	$-0.649423\pi$
$23$		−	1.14802e7i		−	1.78366i	0.452373	−	0.891829i	$-0.350577\pi$
$24$		−	8.91609e6i		−	1.11974i
$25$	3.04592e6			0.311902
$26$	−2.02686e7			−1.70592
$27$	−2.76145e6			−0.192450
$28$	−1.63743e7			−0.951418
$29$	−1.45674e6			−0.0710216			−0.0355108	−	0.999369i	$-0.511306\pi$
$29$	−1.45674e6			−0.0710216			−0.0355108	+	0.999369i	$0.511306\pi$
$30$			2.82988e7i			1.16456i
$31$		−	1.04454e7i		−	0.364852i	−0.983220	−	0.182426i	$-0.941605\pi$
$31$		−	1.04454e7i		−	0.364852i	0.983220	−	0.182426i	$-0.0583950\pi$
$32$		−	1.25786e7i		−	0.374872i
$33$		−	4.38465e7i		−	1.12038i
$34$		−	3.20044e7i		−	0.704393i
$35$	2.72379e7			0.518601
$36$	−4.23526e7			−0.700434
$37$			1.11352e8i			1.60579i	0.596122	+	0.802894i	$0.296707\pi$
$37$			1.11352e8i			1.60579i	−0.596122	+	0.802894i	$0.703293\pi$
$38$			2.23906e7i			0.282585i
$39$			5.04601e7i			0.559275i
$40$			2.27473e8i			2.22141i
$41$	−1.09214e8			−0.942668			−0.471334	−	0.881955i	$-0.656227\pi$
$41$	−1.09214e8			−0.942668			−0.471334	+	0.881955i	$0.656227\pi$
$42$			6.01645e7i			0.460356i
$43$			2.71906e8i			1.84960i	0.380457	+	0.924799i	$0.375767\pi$
$43$			2.71906e8i			1.84960i	−0.380457	+	0.924799i	$0.624233\pi$
$44$		−	6.72478e8i		−	4.07769i
$45$	7.04518e7			0.381794
$46$	−6.46953e8			−3.14111
$47$			1.44150e8i			0.628528i	0.949336	+	0.314264i	$0.101758\pi$
$47$			1.44150e8i			0.628528i	−0.949336	+	0.314264i	$0.898242\pi$
$48$	−1.93329e8			−0.758737
$49$	−2.24566e8			−0.794995
$50$		−	1.71649e8i		−	0.549275i
$51$	−7.96771e7			−0.230931
$52$			7.73911e8i			2.03552i
$53$	1.14733e8			0.274352			0.137176	−	0.990547i	$-0.456197\pi$
$53$	1.14733e8			0.274352			0.137176	+	0.990547i	$0.456197\pi$
$54$			1.55618e8i			0.338915i
$55$			1.11864e9i			2.22268i
$56$			4.83617e8i			0.878135i
$57$	5.57430e7			0.0926437
$58$			8.20924e7i			0.125073i
$59$	−7.13172e8	−	5.00283e7i	−0.997549	−	0.0699770i
$59$	−7.13172e8	−	5.00283e7i	−0.997549	−	0.0699770i
$60$	1.08053e9			1.38956
$61$		−	7.51127e8i		−	0.889333i	−0.895696	−	0.444667i	$-0.853322\pi$
$61$		−	7.51127e8i		−	0.889333i	0.895696	−	0.444667i	$-0.146678\pi$
$62$	−5.88636e8			−0.642523
$63$	1.49784e8			0.150925
$64$	7.02230e8			0.654003
$65$		−	1.28737e9i		−	1.10952i
$66$	−2.47091e9			−1.97305
$67$			6.46732e8i			0.479017i	0.970894	+	0.239508i	$0.0769862\pi$
$67$			6.46732e8i			0.479017i	−0.970894	+	0.239508i	$0.923014\pi$
$68$	−1.22201e9			−0.840488
$69$			1.61063e9i			1.02980i
$70$		−	1.53495e9i		−	0.913283i
$71$	−1.38039e9			−0.765088			−0.382544	−	0.923937i	$-0.624952\pi$
$71$	−1.38039e9			−0.765088			−0.382544	+	0.923937i	$0.624952\pi$
$72$			1.25089e9i			0.646484i
$73$			2.57637e9i			1.24278i	0.783502	+	0.621389i	$0.213431\pi$
$73$			2.57637e9i			1.24278i	−0.783502	+	0.621389i	$0.786569\pi$
$74$	6.27507e9			2.82787
$75$	−4.27330e8			−0.180077
$76$	8.54935e8			0.337183
$77$			2.37828e9i			0.878635i
$78$	2.84361e9			0.984911
$79$	4.01132e9			1.30362			0.651811	−	0.758382i	$-0.274010\pi$
$79$	4.01132e9			1.30362			0.651811	+	0.758382i	$0.274010\pi$
$80$	4.93233e9			1.50523
$81$	3.87420e8			0.111111
$82$			6.15460e9i			1.66009i
$83$		−	1.17721e9i		−	0.298857i	−0.988773	−	0.149428i	$-0.952257\pi$
$83$		−	1.17721e9i		−	0.298857i	0.988773	−	0.149428i	$-0.0477434\pi$
$84$	2.29724e9			0.549301
$85$	2.03277e9			0.458135
$86$	1.53229e10			3.25724
$87$	2.04374e8			0.0410044
$88$	−1.98618e10			−3.76361
$89$			5.40845e9i			0.968551i	0.874915	+	0.484276i	$0.160917\pi$
$89$			5.40845e9i			0.968551i	−0.874915	+	0.484276i	$0.839083\pi$
$90$		−	3.97022e9i		−	0.672359i
$91$		−	2.73700e9i		−	0.438600i
$92$			2.47024e10i			3.74800i
$93$			1.46545e9i			0.210647i
$94$	8.12336e9			1.10687
$95$	−1.42215e9			−0.183792
$96$			1.76473e9i			0.216432i
$97$		−	8.97393e8i		−	0.104502i	−0.998634	−	0.0522509i	$-0.983360\pi$
$97$		−	8.97393e8i		−	0.104502i	0.998634	−	0.0522509i	$-0.0166396\pi$
$98$			1.26551e10i			1.40003i
$99$			6.15149e9i			0.646851i
$100$	−6.55400e9			−0.655400
$101$		−	6.21405e9i		−	0.591245i	−0.955305	−	0.295623i	$-0.904473\pi$
$101$		−	6.21405e9i		−	0.591245i	0.955305	−	0.295623i	$-0.0955271\pi$
$102$			4.49009e9i			0.406682i
$103$		−	8.01555e9i		−	0.691428i	−0.938340	−	0.345714i	$-0.887637\pi$
$103$		−	8.01555e9i		−	0.691428i	0.938340	−	0.345714i	$-0.112363\pi$
$104$	2.28576e10			1.87873
$105$	−3.82137e9			−0.299414
$106$		−	6.46561e9i		−	0.483148i
$107$	−1.84063e10			−1.31234			−0.656171	−	0.754612i	$-0.727825\pi$
$107$	−1.84063e10			−1.31234			−0.656171	+	0.754612i	$0.727825\pi$
$108$	5.94190e9			0.404396
$109$			7.40048e9i			0.480981i	0.970652	+	0.240490i	$0.0773082\pi$
$109$			7.40048e9i			0.480981i	−0.970652	+	0.240490i	$0.922692\pi$
$110$	6.30394e10			3.91425
$111$		−	1.56222e10i		−	0.927102i
$112$	1.04864e10			0.595024
$113$			1.01481e10i			0.550798i	0.961330	+	0.275399i	$0.0888100\pi$
$113$			1.01481e10i			0.550798i	−0.961330	+	0.275399i	$0.911190\pi$
$114$		−	3.14132e9i		−	0.163150i
$115$		−	4.10914e10i		−	2.04297i
$116$	3.13451e9			0.149238
$117$		−	7.07936e9i		−	0.322897i
$118$	−2.81928e9	+	4.01898e10i	−0.123233	+	1.75673i
$119$	4.32176e9			0.181103
$120$		−	3.19136e10i		−	1.28253i
$121$	−7.17365e10			−2.76575
$122$	−4.23288e10			−1.56616
$123$	1.53223e10			0.544250
$124$			2.24757e10i			0.766664i
$125$	−2.40520e10			−0.788136
$126$		−	8.44085e9i		−	0.265787i
$127$	−1.88317e10			−0.569994			−0.284997	−	0.958528i	$-0.591993\pi$
$127$	−1.88317e10			−0.569994			−0.284997	+	0.958528i	$0.591993\pi$
$128$		−	5.24537e10i		−	1.52660i
$129$		−	3.81474e10i		−	1.06787i
$130$	−7.25480e10			−1.95393
$131$			6.32170e10i			1.63862i	0.573352	+	0.819309i	$0.305643\pi$
$131$			6.32170e10i			1.63862i	−0.573352	+	0.819309i	$0.694357\pi$
$132$			9.43460e10i			2.35426i
$133$	−3.02355e9			−0.0726539
$134$	3.64457e10			0.843573
$135$	−9.88411e9			−0.220429
$136$			3.60925e10i			0.775750i
$137$	2.38705e10			0.494606			0.247303	−	0.968938i	$-0.420456\pi$
$137$	2.38705e10			0.494606			0.247303	+	0.968938i	$0.420456\pi$
$138$	9.07650e10			1.81352
$139$	−1.68211e10			−0.324175			−0.162087	−	0.986776i	$-0.551823\pi$
$139$	−1.68211e10			−0.324175			−0.162087	+	0.986776i	$0.551823\pi$
$140$	−5.86087e10			−1.08974
$141$		−	2.02236e10i		−	0.362881i
$142$			7.77903e10i			1.34736i
$143$	1.12407e11			1.87980
$144$	2.71233e10			0.438057
$145$	−5.21412e9			−0.0813470
$146$	1.45188e11			2.18860
$147$	3.15058e10			0.458990
$148$		−	2.39599e11i		−	3.37425i
$149$		−	9.47892e10i		−	1.29071i	−0.763884	−	0.645353i	$-0.776710\pi$
$149$		−	9.47892e10i		−	1.29071i	0.763884	−	0.645353i	$-0.223290\pi$
$150$			2.40816e10i			0.317124i
$151$			1.93435e9i			0.0246405i	0.999924	+	0.0123202i	$0.00392176\pi$
$151$			1.93435e9i			0.0246405i	−0.999924	+	0.0123202i	$0.996078\pi$
$152$		−	2.52507e10i		−	0.311211i
$153$	1.11784e10			0.133328
$154$	1.34024e11			1.54732
$155$		−	3.73874e10i		−	0.417895i
$156$		−	1.08577e11i		−	1.17521i
$157$		−	6.15912e9i		−	0.0645684i	−0.999479	−	0.0322842i	$-0.989722\pi$
$157$		−	6.15912e9i		−	0.0645684i	0.999479	−	0.0322842i	$-0.0102782\pi$
$158$		−	2.26052e11i		−	2.29575i
$159$	−1.60966e10			−0.158397
$160$		−	4.50229e10i		−	0.429372i
$161$		−	8.73622e10i		−	0.807596i
$162$		−	2.18326e10i		−	0.195672i
$163$	3.96458e9			0.0344555			0.0172278	−	0.999852i	$-0.494516\pi$
$163$	3.96458e9			0.0344555			0.0172278	+	0.999852i	$0.494516\pi$
$164$	2.34999e11			1.98083
$165$		−	1.56941e11i		−	1.28326i
$166$	−6.63400e10			−0.526302
$167$	4.04658e10			0.311534			0.155767	−	0.987794i	$-0.450215\pi$
$167$	4.04658e10			0.311534			0.155767	+	0.987794i	$0.450215\pi$
$168$		−	6.78496e10i		−	0.506992i
$169$	8.49702e9			0.0616358
$170$		−	1.14554e11i		−	0.806800i
$171$	−7.82052e9			−0.0534878
$172$		−	5.85070e11i		−	3.88656i
$173$			2.16660e11i			1.39813i	0.715058	+	0.699065i	$0.246400\pi$
$173$			2.16660e11i			1.39813i	−0.715058	+	0.699065i	$0.753600\pi$
$174$		−	1.15172e10i		−	0.0722108i
$175$	2.31788e10			0.141221
$176$			4.30666e11i			2.55022i
$177$	1.00055e11	+	7.01877e9i	0.575935	+	0.0404013i
$178$	3.04786e11			1.70567
$179$			2.69806e11i			1.46820i	0.679039	+	0.734102i	$0.262397\pi$
$179$			2.69806e11i			1.46820i	−0.679039	+	0.734102i	$0.737603\pi$
$180$	−1.51594e11			−0.802265
$181$	2.59874e11			1.33773			0.668867	−	0.743383i	$-0.266780\pi$
$181$	2.59874e11			1.33773			0.668867	+	0.743383i	$0.266780\pi$
$182$	−1.54240e11			−0.772397
$183$			1.05380e11i			0.513457i
$184$	7.29591e11			3.45932
$185$			3.98563e11i			1.83924i
$186$	8.25834e10			0.370961
$187$			1.77491e11i			0.776191i
$188$		−	3.10172e11i		−	1.32073i
$189$	−2.10141e10			−0.0871366
$190$			8.01433e10i			0.323668i
$191$			1.17487e11i			0.462191i	0.972931	+	0.231096i	$0.0742310\pi$
$191$			1.17487e11i			0.462191i	−0.972931	+	0.231096i	$0.925769\pi$
$192$	−9.85201e10			−0.377589
$193$	−3.98870e11			−1.48951			−0.744757	−	0.667336i	$-0.767435\pi$
$193$	−3.98870e11			−1.48951			−0.744757	+	0.667336i	$0.767435\pi$
$194$	−5.05714e10			−0.184033
$195$			1.80613e11i			0.640584i
$196$	4.83207e11			1.67052
$197$	−1.34625e11			−0.453726			−0.226863	−	0.973927i	$-0.572847\pi$
$197$	−1.34625e11			−0.453726			−0.226863	+	0.973927i	$0.572847\pi$
$198$	3.46659e11			1.13914
$199$	−1.69369e11			−0.542710			−0.271355	−	0.962479i	$-0.587472\pi$
$199$	−1.69369e11			−0.542710			−0.271355	+	0.962479i	$0.587472\pi$
$200$			1.93574e11i			0.604918i
$201$		−	9.07340e10i		−	0.276560i
$202$	−3.50184e11			−1.04121
$203$	−1.10855e10			−0.0321568
$204$	1.71444e11			0.485256
$205$	−3.90912e11			−1.07972
$206$	−4.51706e11			−1.21764
$207$		−	2.25965e11i		−	0.594552i
$208$		−	4.95626e11i		−	1.27303i
$209$		−	1.24175e11i		−	0.311388i
$210$			2.15348e11i			0.527284i
$211$			7.72111e11i			1.84615i	0.384617	+	0.923076i	$0.374334\pi$
$211$			7.72111e11i			1.84615i	−0.384617	+	0.923076i	$0.625666\pi$
$212$	−2.46874e11			−0.576496
$213$	1.93664e11			0.441724
$214$			1.03726e12i			2.31110i
$215$			9.73241e11i			2.11850i
$216$		−	1.75495e11i		−	0.373248i
$217$		−	7.94873e10i		−	0.165196i
$218$	4.17044e11			0.847032
$219$		−	3.61454e11i		−	0.717518i
$220$		−	2.40701e12i		−	4.67052i
$221$		−	2.04263e11i		−	0.387462i
$222$	−8.80368e11			−1.63267
$223$	8.40189e11			1.52354			0.761768	−	0.647850i	$-0.224331\pi$
$223$	8.40189e11			1.52354			0.761768	+	0.647850i	$0.224331\pi$
$224$		−	9.57206e10i		−	0.169733i
$225$	5.99528e10			0.103967
$226$	5.71883e11			0.969984
$227$			8.38688e11i			1.39146i	0.718303	+	0.695731i	$0.244919\pi$
$227$			8.38688e11i			1.39146i	−0.718303	+	0.695731i	$0.755081\pi$
$228$	−1.19944e11			−0.194672
$229$		−	8.90372e11i		−	1.41382i	−0.707303	−	0.706910i	$-0.750088\pi$
$229$		−	8.90372e11i		−	1.41382i	0.707303	−	0.706910i	$-0.249912\pi$
$230$	−2.31565e12			−3.59778
$231$		−	3.33663e11i		−	0.507280i
$232$		−	9.25784e10i		−	0.137743i
$233$		−	1.17803e12i		−	1.71544i	−0.514117	−	0.857720i	$-0.671880\pi$
$233$		−	1.17803e12i		−	1.71544i	0.514117	−	0.857720i	$-0.328120\pi$
$234$	−3.98948e11			−0.568639
$235$			5.15958e11i			0.719905i
$236$	1.53456e12	+	1.07648e11i	2.09615	+	0.147043i
$237$	−5.62772e11			−0.752646
$238$		−	2.43547e11i		−	0.318932i
$239$	5.86280e11			0.751823			0.375911	−	0.926656i	$-0.377330\pi$
$239$	5.86280e11			0.751823			0.375911	+	0.926656i	$0.377330\pi$
$240$	−6.91987e11			−0.869044
$241$	8.89255e11			1.09381			0.546904	−	0.837195i	$-0.315806\pi$
$241$	8.89255e11			1.09381			0.546904	+	0.837195i	$0.315806\pi$
$242$			4.04261e12i			4.87063i
$243$	−5.43536e10			−0.0641500
$244$			1.61623e12i			1.86876i
$245$	−8.03795e11			−0.910573
$246$		−	8.63467e11i		−	0.958452i
$247$			1.42905e11i			0.155440i
$248$	6.63825e11			0.707612
$249$			1.65158e11i			0.172545i
$250$			1.35542e12i			1.38795i
$251$	3.74763e11			0.376173			0.188087	−	0.982152i	$-0.439771\pi$
$251$	3.74763e11			0.376173			0.188087	+	0.982152i	$0.439771\pi$
$252$	−3.22294e11			−0.317139
$253$	3.58790e12			3.46128
$254$			1.06123e12i			1.00379i
$255$	−2.85190e11			−0.264505
$256$	−2.23687e12			−2.03443
$257$	−6.70538e11			−0.598078			−0.299039	−	0.954241i	$-0.596666\pi$
$257$	−6.70538e11			−0.598078			−0.299039	+	0.954241i	$0.596666\pi$
$258$	−2.14975e12			−1.88057
$259$			8.47363e11i			0.727061i
$260$			2.77008e12i			2.33144i
$261$	−2.86729e10			−0.0236739
$262$	3.56251e12			2.88569
$263$	1.25767e12			0.999510			0.499755	−	0.866167i	$-0.333423\pi$
$263$	1.25767e12			0.999510			0.499755	+	0.866167i	$0.333423\pi$
$264$	2.78653e12			2.17292
$265$	4.10665e11			0.314238
$266$			1.70388e11i			0.127947i
$267$		−	7.58784e11i		−	0.559193i
$268$		−	1.39160e12i		−	1.00656i
$269$			1.43473e12i			1.01861i	0.860586	+	0.509305i	$0.170097\pi$
$269$			1.43473e12i			1.01861i	−0.860586	+	0.509305i	$0.829903\pi$
$270$			5.57006e11i			0.388187i
$271$	1.13752e12			0.778240			0.389120	−	0.921187i	$-0.372779\pi$
$271$	1.13752e12			0.778240			0.389120	+	0.921187i	$0.372779\pi$
$272$	7.82599e11			0.525648
$273$			3.83991e11i			0.253226i
$274$		−	1.34519e12i		−	0.871027i
$275$			9.51935e11i			0.605263i
$276$		−	3.46565e12i		−	2.16391i
$277$	−2.30586e12			−1.41395			−0.706974	−	0.707240i	$-0.749940\pi$
$277$	−2.30586e12			−1.41395			−0.706974	+	0.707240i	$0.749940\pi$
$278$			9.47928e11i			0.570889i
$279$		−	2.05597e11i		−	0.121617i
$280$			1.73102e12i			1.00580i
$281$	1.30397e12			0.744280			0.372140	−	0.928177i	$-0.378624\pi$
$281$	1.30397e12			0.744280			0.372140	+	0.928177i	$0.378624\pi$
$282$	−1.13968e12			−0.639051
$283$			3.12895e12i			1.72372i	0.507149	+	0.861859i	$0.330699\pi$
$283$			3.12895e12i			1.72372i	−0.507149	+	0.861859i	$0.669301\pi$
$284$	2.97024e12			1.60768
$285$	1.99522e11			0.106112
$286$		−	6.33452e12i		−	3.31042i
$287$	−8.31095e11			−0.426817
$288$		−	2.47585e11i		−	0.124957i
$289$	−1.69346e12			−0.840012
$290$			2.93835e11i			0.143256i
$291$			1.25901e11i			0.0603342i
$292$		−	5.54366e12i		−	2.61145i
$293$	−3.07266e12			−1.42291			−0.711454	−	0.702732i	$-0.751963\pi$
$293$	−3.07266e12			−1.42291			−0.711454	+	0.702732i	$0.751963\pi$
$294$		−	1.77547e12i		−	0.808306i
$295$	−2.55267e12	−	1.79067e11i	−1.14258	−	0.0801505i
$296$	−7.07661e12			−3.11435
$297$		−	8.63031e11i		−	0.373460i
$298$	−5.34172e12			−2.27300
$299$	−4.12908e12			−1.72781
$300$	9.19501e11			0.378396
$301$			2.06915e12i			0.837452i
$302$	1.09007e11			0.0433932
$303$			8.71807e11i			0.341356i
$304$	−5.47515e11			−0.210877
$305$		−	2.68853e12i		−	1.01863i
$306$		−	6.29943e11i		−	0.234798i
$307$	3.48971e12			1.27967			0.639835	−	0.768513i	$-0.279003\pi$
$307$	3.48971e12			1.27967			0.639835	+	0.768513i	$0.279003\pi$
$308$		−	5.11742e12i		−	1.84628i
$309$			1.12455e12i			0.399196i
$310$	−2.10692e12			−0.735935
$311$	4.02825e12			1.38457			0.692284	−	0.721625i	$-0.256605\pi$
$311$	4.02825e12			1.38457			0.692284	+	0.721625i	$0.256605\pi$
$312$	−3.20684e12			−1.08469
$313$		−	1.84973e12i		−	0.615724i	−0.951431	−	0.307862i	$-0.900387\pi$
$313$		−	1.84973e12i		−	0.615724i	0.951431	−	0.307862i	$-0.0996135\pi$
$314$	−3.47089e11			−0.113708
$315$	5.36123e11			0.172867
$316$	−8.63129e12			−2.73930
$317$	1.74556e12			0.545304			0.272652	−	0.962113i	$-0.412099\pi$
$317$	1.74556e12			0.545304			0.272652	+	0.962113i	$0.412099\pi$
$318$			9.07100e11i			0.278945i
$319$		−	4.55271e11i		−	0.137821i
$320$	2.51351e12			0.749083
$321$	2.58233e12			0.757681
$322$	−4.92318e12			−1.42222
$323$	−2.25648e11			−0.0641829
$324$	−8.33626e11			−0.233478
$325$		−	1.09552e12i		−	0.302137i
$326$		−	2.23418e11i		−	0.0606779i
$327$		−	1.03826e12i		−	0.277694i
$328$		−	6.94076e12i		−	1.82826i
$329$			1.09695e12i			0.284582i
$330$	−8.84418e12			−2.25989
$331$	−2.18072e12			−0.548859			−0.274429	−	0.961607i	$-0.588489\pi$
$331$	−2.18072e12			−0.548859			−0.274429	+	0.961607i	$0.588489\pi$
$332$			2.53304e12i			0.627989i
$333$			2.19173e12i			0.535262i
$334$		−	2.28040e12i		−	0.548628i
$335$			2.31486e12i			0.548657i
$336$	−1.47120e12			−0.343537
$337$		−	2.89610e12i		−	0.666292i	−0.942875	−	0.333146i	$-0.891890\pi$
$337$		−	2.89610e12i		−	0.666292i	0.942875	−	0.333146i	$-0.108110\pi$
$338$		−	4.78838e11i		−	0.108544i
$339$		−	1.42374e12i		−	0.318003i
$340$	−4.37398e12			−0.962681
$341$	3.26448e12			0.708015
$342$			4.40715e11i			0.0941949i
$343$	−3.85848e12			−0.812729
$344$	−1.72802e13			−3.58720
$345$			5.76497e12i			1.17951i
$346$	1.22096e13			2.46218
$347$			4.24749e12i			0.844277i	0.906531	+	0.422138i	$0.138720\pi$
$347$			4.24749e12i			0.844277i	−0.906531	+	0.422138i	$0.861280\pi$
$348$	−4.39759e11			−0.0861626
$349$			9.95896e12i			1.92348i	0.273969	+	0.961739i	$0.411663\pi$
$349$			9.95896e12i			1.92348i	−0.273969	+	0.961739i	$0.588337\pi$
$350$		−	1.30621e12i		−	0.248698i
$351$			9.93206e11i			0.186425i
$352$	3.93117e12			0.727459
$353$			2.06879e12i			0.377436i	0.982031	+	0.188718i	$0.0604332\pi$
$353$			2.06879e12i			0.377436i	−0.982031	+	0.188718i	$0.939567\pi$
$354$	3.95534e11	−	5.63848e12i	0.0711487	−	1.01425i
$355$	−4.94087e12			−0.876319
$356$		−	1.16375e13i		−	2.03522i
$357$	−6.06326e11			−0.104560
$358$	1.52046e13			2.58558
$359$	−7.55431e12			−1.26684			−0.633421	−	0.773807i	$-0.718350\pi$
$359$	−7.55431e12			−1.26684			−0.633421	+	0.773807i	$0.718350\pi$
$360$			4.47735e12i			0.740471i
$361$	−5.97320e12			−0.974251
$362$		−	1.46448e13i		−	2.35582i
$363$	1.00643e13			1.59681
$364$			5.88930e12i			0.921631i
$365$			9.22165e12i			1.42346i
$366$	5.93856e12			0.904224
$367$		−	5.34957e12i		−	0.803505i	−0.915748	−	0.401752i	$-0.868401\pi$
$367$		−	5.34957e12i		−	0.803505i	0.915748	−	0.401752i	$-0.131599\pi$
$368$		−	1.58199e13i		−	2.34403i
$369$	−2.14966e12			−0.314223
$370$	2.24605e13			3.23900
$371$	8.73092e11			0.124220
$372$		−	3.15326e12i		−	0.442634i
$373$	−5.75490e12			−0.797064			−0.398532	−	0.917154i	$-0.630480\pi$
$373$	−5.75490e12			−0.797064			−0.398532	+	0.917154i	$0.630480\pi$
$374$	1.00023e13			1.36691
$375$	3.37440e12			0.455030
$376$	−9.16099e12			−1.21900
$377$			5.23942e11i			0.0687981i
$378$			1.18422e12i			0.153452i
$379$	5.45963e11			0.0698180			0.0349090	−	0.999390i	$-0.488886\pi$
$379$	5.45963e11			0.0698180			0.0349090	+	0.999390i	$0.488886\pi$
$380$	3.06009e12			0.386203
$381$	2.64201e12			0.329086
$382$	6.62080e12			0.813942
$383$	6.53010e11			0.0792367			0.0396183	−	0.999215i	$-0.487386\pi$
$383$	6.53010e11			0.0792367			0.0396183	+	0.999215i	$0.487386\pi$
$384$			7.35905e12i			0.881385i
$385$			8.51261e12i			1.00637i
$386$			2.24778e13i			2.62311i
$387$			5.35193e12i			0.616532i
$388$			1.93095e12i			0.219590i
$389$	−4.40465e12			−0.494496			−0.247248	−	0.968952i	$-0.579526\pi$
$389$	−4.40465e12			−0.494496			−0.247248	+	0.968952i	$0.579526\pi$
$390$	1.01782e13			1.12810
$391$		−	6.51986e12i		−	0.713435i
$392$		−	1.42716e13i		−	1.54185i
$393$		−	8.86910e12i		−	0.946056i
$394$			7.58660e12i			0.799036i
$395$	1.43578e13			1.49315
$396$		−	1.32364e13i		−	1.35923i
$397$			5.60159e12i			0.568014i	0.958822	+	0.284007i	$0.0916639\pi$
$397$			5.60159e12i			0.568014i	−0.958822	+	0.284007i	$0.908336\pi$
$398$			9.54455e12i			0.955740i
$399$	4.24192e11			0.0419468
$400$	4.19730e12			0.409892
$401$			1.14235e12i			0.110174i	0.998482	+	0.0550869i	$0.0175436\pi$
$401$			1.14235e12i			0.110174i	−0.998482	+	0.0550869i	$0.982456\pi$
$402$	−5.11319e12			−0.487037
$403$	−3.75688e12			−0.353429
$404$			1.33710e13i			1.24239i
$405$	1.38670e12			0.127265
$406$			6.24706e11i			0.0566298i
$407$	−3.48005e13			−3.11612
$408$		−	5.06363e12i		−	0.447880i
$409$		−	1.51003e13i		−	1.31938i	−0.751540	−	0.659688i	$-0.770689\pi$
$409$		−	1.51003e13i		−	1.31938i	0.751540	−	0.659688i	$-0.229311\pi$
$410$			2.20293e13i			1.90143i
$411$	−3.34895e12			−0.285561
$412$			1.72473e13i			1.45290i
$413$	−5.42709e12	−	3.80705e11i	−0.451665	−	0.0316839i
$414$	−1.27340e13			−1.04704
$415$		−	4.21361e12i		−	0.342305i
$416$	−4.52413e12			−0.363135
$417$	2.35993e12			0.187163
$418$	−6.99771e12			−0.548371
$419$		−	2.95169e12i		−	0.228560i	−0.993449	−	0.114280i	$-0.963544\pi$
$419$		−	2.95169e12i		−	0.228560i	0.993449	−	0.114280i	$-0.0364561\pi$
$420$	8.22257e12			0.629160
$421$			2.32447e13i			1.75758i	0.477212	+	0.878788i	$0.341647\pi$
$421$			2.32447e13i			1.75758i	−0.477212	+	0.878788i	$0.658353\pi$
$422$	4.35113e13			3.25117
$423$			2.83730e12i			0.209509i
$424$			7.29149e12i			0.532092i
$425$	1.72984e12			0.124756
$426$		−	1.09137e13i		−	0.777898i
$427$		−	5.71592e12i		−	0.402668i
$428$	3.96054e13			2.75763
$429$	−1.57702e13			−1.08530
$430$	5.48457e13			3.73078
$431$		−	7.31565e12i		−	0.491889i	−0.969284	−	0.245944i	$-0.920902\pi$
$431$		−	7.31565e12i		−	0.491889i	0.969284	−	0.245944i	$-0.0790980\pi$
$432$	−3.80530e12			−0.252912
$433$	−6.64971e12			−0.436881			−0.218441	−	0.975850i	$-0.570097\pi$
$433$	−6.64971e12			−0.436881			−0.218441	+	0.975850i	$0.570097\pi$
$434$	−4.47940e12			−0.290918
$435$	7.31521e11			0.0469657
$436$		−	1.59239e13i		−	1.01069i
$437$			4.56137e12i			0.286212i
$438$	−2.03693e13			−1.26359
$439$	2.67460e13			1.64035			0.820173	−	0.572115i	$-0.193877\pi$
$439$	2.67460e13			1.64035			0.820173	+	0.572115i	$0.193877\pi$
$440$	−7.10917e13			−4.31078
$441$	−4.42014e12			−0.264998
$442$	−1.15110e13			−0.682340
$443$			2.16431e13i			1.26853i	0.773116	+	0.634265i	$0.218697\pi$
$443$			2.16431e13i			1.26853i	−0.773116	+	0.634265i	$0.781303\pi$
$444$			3.36148e13i			1.94812i
$445$			1.93586e13i			1.10936i
$446$		−	4.73477e13i		−	2.68303i
$447$			1.32986e13i			0.745189i
$448$	5.34382e12			0.296116
$449$	1.39716e13			0.765623			0.382811	−	0.923827i	$-0.374956\pi$
$449$	1.39716e13			0.765623			0.382811	+	0.923827i	$0.374956\pi$
$450$		−	3.37856e12i		−	0.183092i
$451$		−	3.41324e13i		−	1.82930i
$452$		−	2.18360e13i		−	1.15739i
$453$		−	2.71381e11i		−	0.0142262i
$454$	4.72631e13			2.45044
$455$		−	9.79661e12i		−	0.502365i
$456$			3.54257e12i			0.179678i
$457$			9.56294e12i			0.479745i	0.970804	+	0.239872i	$0.0771056\pi$
$457$			9.56294e12i			0.479745i	−0.970804	+	0.239872i	$0.922894\pi$
$458$	−5.01757e13			−2.48981
$459$	−1.56828e12			−0.0769770
$460$			8.84178e13i			4.29290i
$461$	−1.15043e13			−0.552531			−0.276265	−	0.961081i	$-0.589097\pi$
$461$	−1.15043e13			−0.552531			−0.276265	+	0.961081i	$0.589097\pi$
$462$	−1.88031e13			−0.893346
$463$			1.08243e13i			0.508738i	0.967107	+	0.254369i	$0.0818678\pi$
$463$			1.08243e13i			0.508738i	−0.967107	+	0.254369i	$0.918132\pi$
$464$	−2.00739e12			−0.0933346
$465$			5.24531e12i			0.241272i
$466$	−6.63861e13			−3.02098
$467$			2.55968e13i			1.15239i	0.817311	+	0.576196i	$0.195464\pi$
$467$			2.55968e13i			1.15239i	−0.817311	+	0.576196i	$0.804536\pi$
$468$			1.52329e13i			0.678505i
$469$			4.92150e12i			0.216887i
$470$	2.90761e13			1.26779
$471$			8.64100e11i			0.0372786i
$472$	3.17939e12	−	4.53234e13i	0.135717	−	1.93470i
$473$	−8.49784e13			−3.58924
$474$			3.17143e13i			1.32545i
$475$	−1.21021e12			−0.0500489
$476$	−9.29928e12			−0.380552
$477$	2.25828e12			0.0914506
$478$		−	3.30390e13i		−	1.32400i
$479$	5.80320e12			0.230139			0.115069	−	0.993357i	$-0.463291\pi$
$479$	5.80320e12			0.230139			0.115069	+	0.993357i	$0.463291\pi$
$480$			6.31653e12i			0.247898i
$481$	4.00497e13			1.55551
$482$		−	5.01128e13i		−	1.92625i
$483$			1.22566e13i			0.466266i
$484$	1.54358e14			5.81168
$485$		−	3.21206e12i		−	0.119695i
$486$			3.06302e12i			0.112972i
$487$	−6.57773e12			−0.240121			−0.120061	−	0.992767i	$-0.538309\pi$
$487$	−6.57773e12			−0.240121			−0.120061	+	0.992767i	$0.538309\pi$
$488$	4.77356e13			1.72482
$489$	−5.56215e11			−0.0198929
$490$			4.52968e13i			1.60357i
$491$	9.12416e12			0.319731			0.159866	−	0.987139i	$-0.448894\pi$
$491$	9.12416e12			0.319731			0.159866	+	0.987139i	$0.448894\pi$
$492$	−3.29695e13			−1.14363
$493$	−8.27310e11			−0.0284075
$494$	8.05321e12			0.273737
$495$			2.20182e13i			0.740893i
$496$		−	1.43938e13i		−	0.479478i
$497$	−1.05045e13			−0.346413
$498$	9.30725e12			0.303861
$499$	4.19762e13			1.35675			0.678377	−	0.734714i	$-0.262684\pi$
$499$	4.19762e13			1.35675			0.678377	+	0.734714i	$0.262684\pi$
$500$	5.17535e13			1.65611
$501$	−5.67719e12			−0.179864
$502$		−	2.11193e13i		−	0.662460i
$503$			2.75417e13i			0.855363i	0.903930	+	0.427681i	$0.140670\pi$
$503$			2.75417e13i			0.855363i	−0.903930	+	0.427681i	$0.859330\pi$
$504$			9.51904e12i			0.292712i
$505$		−	2.22421e13i		−	0.677202i
$506$		−	2.02191e14i		−	6.09550i
$507$	−1.19210e12			−0.0355855
$508$	4.05208e13			1.19773
$509$		−	2.65671e13i		−	0.777597i	−0.921323	−	0.388798i	$-0.872890\pi$
$509$		−	2.65671e13i		−	0.777597i	0.921323	−	0.388798i	$-0.127110\pi$
$510$			1.60715e13i			0.465806i
$511$			1.96056e13i			0.562699i
$512$			7.23435e13i			2.05613i
$513$	1.09719e12			0.0308812
$514$			3.77873e13i			1.05325i
$515$		−	2.86902e13i		−	0.791950i
$516$			8.20831e13i			2.24391i
$517$	−4.50508e13			−1.21969
$518$	4.77520e13			1.28039
$519$		−	3.03965e13i		−	0.807210i
$520$	8.18148e13			2.15187
$521$	2.84427e13			0.740938			0.370469	−	0.928845i	$-0.379197\pi$
$521$	2.84427e13			0.740938			0.370469	+	0.928845i	$0.379197\pi$
$522$			1.61582e12i			0.0416909i
$523$	1.96961e13			0.503352			0.251676	−	0.967812i	$-0.419018\pi$
$523$	1.96961e13			0.503352			0.251676	+	0.967812i	$0.419018\pi$
$524$		−	1.36026e14i		−	3.44323i
$525$	−3.25189e12			−0.0815342
$526$		−	7.08742e13i		−	1.76019i
$527$		−	5.93216e12i		−	0.145935i
$528$		−	6.04208e13i		−	1.47237i
$529$	−9.03692e13			−2.18143
$530$		−	2.31425e13i		−	0.553389i
$531$	−1.40374e13	−	9.84707e11i	−0.332516	−	0.0233257i
$532$	6.50588e12			0.152668
$533$			3.92808e13i			0.913155i
$534$	−4.27603e13			−0.984769
$535$	−6.58820e13			−1.50313
$536$	−4.11011e13			−0.929029
$537$		−	3.78527e13i		−	0.847668i
$538$	8.08521e13			1.79382
$539$		−	7.01833e13i		−	1.54273i
$540$	2.12680e13			0.463188
$541$		−	3.82714e12i		−	0.0825824i	−0.999147	−	0.0412912i	$-0.986853\pi$
$541$		−	3.82714e12i		−	0.0825824i	0.999147	−	0.0412912i	$-0.0131471\pi$
$542$		−	6.41036e13i		−	1.37052i
$543$	−3.64593e13			−0.772341
$544$		−	7.14365e12i		−	0.149943i
$545$			2.64887e13i			0.550907i
$546$	2.16393e13			0.445943
$547$	4.19549e13			0.856733			0.428367	−	0.903605i	$-0.359089\pi$
$547$	4.19549e13			0.856733			0.428367	+	0.903605i	$0.359089\pi$
$548$	−5.13631e13			−1.03932
$549$		−	1.47844e13i		−	0.296444i
$550$	5.36450e13			1.06590
$551$	5.78795e11			0.0113964
$552$	−1.02359e14			−1.99724
$553$	3.05253e13			0.590248
$554$			1.29943e14i			2.49003i
$555$		−	5.59169e13i		−	1.06189i
$556$	3.61945e13			0.681190
$557$	9.01920e13			1.68225			0.841127	−	0.540837i	$-0.181892\pi$
$557$	9.01920e13			1.68225			0.841127	+	0.540837i	$0.181892\pi$
$558$	−1.15861e13			−0.214174
$559$	9.77962e13			1.79169
$560$	3.75340e13			0.681530
$561$		−	2.49013e13i		−	0.448134i
$562$		−	7.34835e13i		−	1.31072i
$563$		−	4.13807e13i		−	0.731570i	−0.930699	−	0.365785i	$-0.880800\pi$
$563$		−	4.13807e13i		−	0.731570i	0.930699	−	0.365785i	$-0.119200\pi$
$564$			4.35159e13i			0.762522i
$565$			3.63233e13i			0.630875i
$566$	1.76328e14			3.03555
$567$	2.94819e12			0.0503084
$568$		−	8.77267e13i		−	1.48385i
$569$			6.24035e13i			1.04628i	0.852247	+	0.523139i	$0.175239\pi$
$569$			6.24035e13i			1.04628i	−0.852247	+	0.523139i	$0.824761\pi$
$570$		−	1.12438e13i		−	0.186870i
$571$		−	7.43307e13i		−	1.22458i	−0.790632	−	0.612291i	$-0.790248\pi$
$571$		−	7.43307e13i		−	1.22458i	0.790632	−	0.612291i	$-0.209752\pi$
$572$	−2.41869e14			−3.95003
$573$		−	1.64829e13i		−	0.266846i
$574$			4.68353e13i			0.751646i
$575$		−	3.49678e13i		−	0.556326i
$576$	1.38220e13			0.218001
$577$	−2.05474e13			−0.321276			−0.160638	−	0.987013i	$-0.551355\pi$
$577$	−2.05474e13			−0.321276			−0.160638	+	0.987013i	$0.551355\pi$
$578$			9.54327e13i			1.47931i
$579$	5.59599e13			0.859971
$580$	1.12194e13			0.170935
$581$		−	8.95832e12i		−	0.135315i
$582$	7.09497e12			0.106252
$583$			3.58572e13i			0.532395i
$584$	−1.63733e14			−2.41031
$585$		−	2.53393e13i		−	0.369841i
$586$			1.73156e14i			2.50582i
$587$		−	1.16216e14i		−	1.66753i	−0.552117	−	0.833767i	$-0.686180\pi$
$587$		−	1.16216e14i		−	1.66753i	0.552117	−	0.833767i	$-0.313820\pi$
$588$	−6.77921e13			−0.964478
$589$			4.15020e12i			0.0585454i
$590$	−1.00911e13	+	1.43852e14i	−0.141149	+	2.01213i
$591$	1.88873e13			0.261959
$592$			1.53443e14i			2.11028i
$593$	−8.87027e13			−1.20966			−0.604830	−	0.796355i	$-0.706759\pi$
$593$	−8.87027e13			−1.20966			−0.604830	+	0.796355i	$0.706759\pi$
$594$	−4.86349e13			−0.657682
$595$	1.54690e13			0.207432
$596$			2.03961e14i			2.71216i
$597$	2.37618e13			0.313334
$598$			2.32689e14i			3.04277i
$599$	−8.18429e12			−0.106132			−0.0530661	−	0.998591i	$-0.516899\pi$
$599$	−8.18429e12			−0.106132			−0.0530661	+	0.998591i	$0.516899\pi$
$600$		−	2.71577e13i		−	0.349250i
$601$		−	1.31722e14i		−	1.67991i	−0.542654	−	0.839956i	$-0.682581\pi$
$601$		−	1.31722e14i		−	1.67991i	0.542654	−	0.839956i	$-0.317419\pi$
$602$	1.16604e14			1.47480
$603$			1.27296e13i			0.159672i
$604$		−	4.16220e12i		−	0.0517771i
$605$	−2.56768e14			−3.16784
$606$	4.91295e13			0.601145
$607$	−5.27923e13			−0.640660			−0.320330	−	0.947306i	$-0.603794\pi$
$607$	−5.27923e13			−0.640660			−0.320330	+	0.947306i	$0.603794\pi$
$608$			4.99778e12i			0.0601532i
$609$	1.55525e12			0.0185658
$610$	−1.51508e14			−1.79385
$611$	5.18461e13			0.608850
$612$	−2.40529e13			−0.280163
$613$		−	1.53901e14i		−	1.77803i	−0.457878	−	0.889015i	$-0.651390\pi$
$613$		−	1.53901e14i		−	1.77803i	0.457878	−	0.889015i	$-0.348610\pi$
$614$		−	1.96658e14i		−	2.25356i
$615$	5.48434e13			0.623374
$616$	−1.51144e14			−1.70407
$617$	2.31009e13			0.258346			0.129173	−	0.991622i	$-0.458768\pi$
$617$	2.31009e13			0.258346			0.129173	+	0.991622i	$0.458768\pi$
$618$	6.33725e13			0.703005
$619$	−1.38207e14			−1.52081			−0.760407	−	0.649446i	$-0.775001\pi$
$619$	−1.38207e14			−1.52081			−0.760407	+	0.649446i	$0.775001\pi$
$620$			8.04478e13i			0.878124i
$621$			3.17021e13i			0.343265i
$622$		−	2.27006e14i		−	2.43830i
$623$			4.11572e13i			0.438536i
$624$			6.95344e13i			0.734982i
$625$	−1.15835e14			−1.21462
$626$	−1.04239e14			−1.08432
$627$			1.74212e13i			0.179780i
$628$			1.32528e13i			0.135678i
$629$			6.32389e13i			0.642290i
$630$		−	3.02125e13i		−	0.304428i
$631$	−3.14987e13			−0.314880			−0.157440	−	0.987529i	$-0.550324\pi$
$631$	−3.14987e13			−0.314880			−0.157440	+	0.987529i	$0.550324\pi$
$632$			2.54927e14i			2.52831i
$633$		−	1.08324e14i		−	1.06588i
$634$		−	9.83688e13i		−	0.960309i
$635$	−6.74046e13			−0.652862
$636$	3.46355e13			0.332840
$637$			8.07694e13i			0.770105i
$638$	−2.56562e13			−0.242711
$639$	−2.71703e13			−0.255029
$640$		−	1.87749e14i		−	1.74855i
$641$	8.70942e13			0.804820			0.402410	−	0.915459i	$-0.368173\pi$
$641$	8.70942e13			0.804820			0.402410	+	0.915459i	$0.368173\pi$
$642$		−	1.45524e14i		−	1.33432i
$643$	−1.32562e14			−1.20605			−0.603025	−	0.797722i	$-0.706038\pi$
$643$	−1.32562e14			−1.20605			−0.603025	+	0.797722i	$0.706038\pi$
$644$			1.87980e14i			1.69700i
$645$		−	1.36542e14i		−	1.22311i
$646$			1.27161e13i			0.113029i
$647$	−5.81938e13			−0.513282			−0.256641	−	0.966507i	$-0.582616\pi$
$647$	−5.81938e13			−0.513282			−0.256641	+	0.966507i	$0.582616\pi$
$648$			2.46213e13i			0.215495i
$649$	1.56353e13	−	2.22886e14i	0.135794	−	1.93580i
$650$	−6.17366e13			−0.532079
$651$			1.11518e13i			0.0953759i
$652$	−8.53071e12			−0.0724015
$653$	1.55543e14			1.31004			0.655021	−	0.755611i	$-0.272660\pi$
$653$	1.55543e14			1.31004			0.655021	+	0.755611i	$0.272660\pi$
$654$	−5.85097e13			−0.489034
$655$			2.26274e14i			1.87684i
$656$	−1.50498e14			−1.23883
$657$			5.07107e13i			0.414259i
$658$	6.18171e13			0.501163
$659$		−	7.04034e12i		−	0.0566457i	−0.999599	−	0.0283228i	$-0.990983\pi$
$659$		−	7.04034e12i		−	0.0566457i	0.999599	−	0.0283228i	$-0.00901664\pi$
$660$			3.37695e14i			2.69653i
$661$	−1.59800e14			−1.26639			−0.633196	−	0.773991i	$-0.718257\pi$
$661$	−1.59800e14			−1.26639			−0.633196	+	0.773991i	$0.718257\pi$
$662$			1.22892e14i			0.966569i
$663$			2.86573e13i			0.223701i
$664$	7.48139e13			0.579618
$665$	−1.08223e13			−0.0832165
$666$	1.23512e14			0.942625
$667$			1.67237e13i			0.126678i
$668$	−8.70716e13			−0.654628
$669$	−1.17875e14			−0.879614
$670$	1.30451e14			0.966214
$671$	2.34749e14			1.72580
$672$			1.34292e13i			0.0979952i
$673$			1.57352e14i			1.13971i	0.821744	+	0.569857i	$0.193001\pi$
$673$			1.57352e14i			1.13971i	−0.821744	+	0.569857i	$0.806999\pi$
$674$	−1.63206e14			−1.17337
$675$	−8.41114e12			−0.0600255
$676$	−1.82833e13			−0.129516
$677$	−3.79219e12			−0.0266653			−0.0133326	−	0.999911i	$-0.504244\pi$
$677$	−3.79219e12			−0.0266653			−0.0133326	+	0.999911i	$0.504244\pi$
$678$	−8.02329e13			−0.560021
$679$		−	6.82898e12i		−	0.0473159i
$680$			1.29187e14i			0.888531i
$681$		−	1.17665e14i		−	0.803361i
$682$		−	1.83965e14i		−	1.24685i
$683$			3.83847e12i			0.0258258i	0.999917	+	0.0129129i	$0.00411042\pi$
$683$			3.83847e12i			0.0258258i	−0.999917	+	0.0129129i	$0.995890\pi$
$684$	1.68277e13			0.112394
$685$	8.54404e13			0.566513
$686$			2.17440e14i			1.43126i
$687$			1.24916e14i			0.816270i
$688$			3.74689e14i			2.43069i
$689$		−	4.12657e13i		−	0.265762i
$690$	3.24877e14			2.07718
$691$			9.70769e13i			0.616206i	0.951353	+	0.308103i	$0.0996941\pi$
$691$			9.70769e13i			0.616206i	−0.951353	+	0.308103i	$0.900306\pi$
$692$		−	4.66194e14i		−	2.93789i
$693$			4.68116e13i			0.292878i
$694$	2.39361e14			1.48681
$695$	−6.02080e13			−0.371304
$696$			1.29884e13i			0.0795260i
$697$	−6.20248e13			−0.377052
$698$	5.61224e14			3.38734
$699$			1.65273e14i			0.990410i
$700$	−4.98746e13			−0.296749
$701$			1.58415e14i			0.935848i	0.883769	+	0.467924i	$0.154998\pi$
$701$			1.58415e14i			0.935848i	−0.883769	+	0.467924i	$0.845002\pi$
$702$	5.59708e13			0.328304
$703$		−	4.42426e13i		−	0.257670i
$704$			2.19467e14i			1.26913i
$705$		−	7.23869e13i		−	0.415637i
$706$	1.16584e14			0.664685
$707$		−	4.72876e13i		−	0.267701i
$708$	−2.15292e14	−	1.51025e13i	−1.21021	−	0.0848953i
$709$	−1.37774e14			−0.769019			−0.384509	−	0.923121i	$-0.625629\pi$
$709$	−1.37774e14			−0.769019			−0.384509	+	0.923121i	$0.625629\pi$
$710$			2.78436e14i			1.54324i
$711$	7.89548e13			0.434541
$712$	−3.43717e14			−1.87846
$713$	−1.19916e14			−0.650771
$714$			3.41687e13i			0.184135i
$715$	4.02339e14			2.15309
$716$		−	5.80551e14i		−	3.08514i
$717$	−8.22528e13			−0.434065
$718$			4.25713e14i			2.23097i
$719$		−	4.09687e13i		−	0.213210i	−0.994301	−	0.106605i	$-0.966002\pi$
$719$		−	4.09687e13i		−	0.213210i	0.994301	−	0.106605i	$-0.0339980\pi$
$720$	9.70831e13			0.501743
$721$		−	6.09967e13i		−	0.313062i
$722$			3.36612e14i			1.71571i
$723$	−1.24759e14			−0.631511
$724$	−5.59179e14			−2.81098
$725$	−4.43709e12			−0.0221518
$726$		−	5.67163e14i		−	2.81206i
$727$	1.18643e14			0.584213			0.292107	−	0.956386i	$-0.405644\pi$
$727$	1.18643e14			0.584213			0.292107	+	0.956386i	$0.405644\pi$
$728$	1.73942e14			0.850643
$729$	7.62560e12			0.0370370
$730$	5.19674e14			2.50678
$731$			1.54421e14i			0.739810i
$732$		−	2.26750e14i		−	1.07893i
$733$	−2.44546e14			−1.15569			−0.577843	−	0.816148i	$-0.696106\pi$
$733$	−2.44546e14			−1.15569			−0.577843	+	0.816148i	$0.696106\pi$
$734$	−3.01468e14			−1.41501
$735$	1.12769e14			0.525720
$736$	−1.44405e14			−0.668643
$737$	−2.02122e14			−0.929558
$738$			1.21141e14i			0.553362i
$739$		−	1.15757e14i		−	0.525200i	−0.964905	−	0.262600i	$-0.915420\pi$
$739$		−	1.15757e14i		−	0.525200i	0.964905	−	0.262600i	$-0.0845800\pi$
$740$		−	8.57602e14i		−	3.86480i
$741$		−	2.00490e13i		−	0.0897432i
$742$		−	4.92019e13i		−	0.218757i
$743$	1.02803e14			0.454008			0.227004	−	0.973894i	$-0.427107\pi$
$743$	1.02803e14			0.454008			0.227004	+	0.973894i	$0.427107\pi$
$744$	−9.31321e13			−0.408540
$745$		−	3.39281e14i		−	1.47835i
$746$			3.24309e14i			1.40367i
$747$		−	2.31710e13i		−	0.0996189i
$748$		−	3.81914e14i		−	1.63101i
$749$	−1.40068e14			−0.594196
$750$		−	1.90160e14i		−	0.801332i
$751$		−	1.66524e14i		−	0.697071i	−0.937296	−	0.348536i	$-0.886679\pi$
$751$		−	1.66524e14i		−	0.697071i	0.937296	−	0.348536i	$-0.113321\pi$
$752$			1.98639e14i			0.825993i
$753$	−5.25778e13			−0.217184
$754$	2.95260e13			0.121157
$755$			6.92365e12i			0.0282228i
$756$	4.52167e13			0.183100
$757$	1.05660e14			0.425039			0.212520	−	0.977157i	$-0.431833\pi$
$757$	1.05660e14			0.425039			0.212520	+	0.977157i	$0.431833\pi$
$758$		−	3.07670e13i		−	0.122953i
$759$	−5.03368e14			−1.99837
$760$		−	9.03803e13i		−	0.356456i
$761$	2.80348e14			1.09843			0.549217	−	0.835680i	$-0.314926\pi$
$761$	2.80348e14			1.09843			0.549217	+	0.835680i	$0.314926\pi$
$762$		−	1.48887e14i		−	0.579538i
$763$			5.63161e13i			0.217776i
$764$		−	2.52800e14i		−	0.971204i
$765$	4.00110e13			0.152712
$766$		−	3.67995e13i		−	0.139540i
$767$	−1.79936e13	+	2.56505e14i	−0.0677862	+	0.966317i
$768$	3.13825e14			1.17458
$769$			1.98347e14i			0.737555i	0.929518	+	0.368777i	$0.120224\pi$
$769$			1.98347e14i			0.737555i	−0.929518	+	0.368777i	$0.879776\pi$
$770$	4.79717e14			1.77228
$771$	9.40739e13			0.345301
$772$	8.58262e14			3.12992
$773$			1.64588e14i			0.596348i	0.954511	+	0.298174i	$0.0963776\pi$
$773$			1.64588e14i			0.596348i	−0.954511	+	0.298174i	$0.903622\pi$
$774$	3.01601e14			1.08575
$775$		−	3.18158e13i		−	0.113798i
$776$	5.70311e13			0.202676
$777$		−	1.18882e14i		−	0.419769i
$778$			2.48218e14i			0.870834i
$779$	4.33933e13			0.151264
$780$		−	3.88631e14i		−	1.34606i
$781$		−	4.31412e14i		−	1.48469i
$782$	−3.67418e14			−1.25640
$783$	4.02270e12			0.0136681
$784$	−3.09454e14			−1.04476
$785$		−	2.20455e13i		−	0.0739555i
$786$	−4.99806e14			−1.66605
$787$	−1.75590e14			−0.581603			−0.290801	−	0.956783i	$-0.593922\pi$
$787$	−1.75590e14			−0.581603			−0.290801	+	0.956783i	$0.593922\pi$
$788$	2.89677e14			0.953417
$789$	−1.76446e14			−0.577067
$790$		−	8.09114e14i		−	2.62951i
$791$			7.72249e13i			0.249388i
$792$	−3.90939e14			−1.25454
$793$	−2.70157e14			−0.861490
$794$	3.15670e14			1.00030
$795$	−5.76147e13			−0.181425
$796$	3.64436e14			1.14040
$797$			6.18648e14i			1.92376i	0.273464	+	0.961882i	$0.411831\pi$
$797$			6.18648e14i			1.92376i	−0.273464	+	0.961882i	$0.588169\pi$
$798$		−	2.39048e13i		−	0.0738704i
$799$			8.18656e13i			0.251401i
$800$		−	3.83134e13i		−	0.116923i
$801$			1.06455e14i			0.322850i
$802$	6.43757e13			0.194022
$803$	−8.05188e14			−2.41168
$804$			1.95236e14i			0.581137i
$805$		−	3.12697e14i		−	0.925006i
$806$			2.11714e14i			0.622407i
$807$		−	2.01287e14i		−	0.588095i
$808$	3.94915e14			1.14669
$809$		−	1.98976e14i		−	0.574194i	−0.957902	−	0.287097i	$-0.907310\pi$
$809$		−	1.98976e14i		−	0.574194i	0.957902	−	0.287097i	$-0.0926902\pi$
$810$		−	7.81457e13i		−	0.224120i
$811$		−	4.73787e14i		−	1.35045i	−0.737611	−	0.675226i	$-0.764046\pi$
$811$		−	4.73787e14i		−	1.35045i	0.737611	−	0.675226i	$-0.235954\pi$
$812$	2.38530e13			0.0675713
$813$	−1.59590e14			−0.449317
$814$			1.96114e15i			5.48764i
$815$	1.41905e13			0.0394648
$816$	−1.09796e14			−0.303483
$817$		−	1.08035e14i		−	0.296793i
$818$	−8.50956e14			−2.32349
$819$		−	5.38724e13i		−	0.146200i
$820$	8.41138e14			2.26881
$821$			5.82705e14i			1.56219i	0.624414	+	0.781094i	$0.285338\pi$
$821$			5.82705e14i			1.56219i	−0.624414	+	0.781094i	$0.714662\pi$
$822$			1.88725e14i			0.502888i
$823$		−	6.46238e14i		−	1.71156i	−0.517337	−	0.855782i	$-0.673077\pi$
$823$		−	6.46238e14i		−	1.71156i	0.517337	−	0.855782i	$-0.326923\pi$
$824$	5.09404e14			1.34099
$825$		−	1.33553e14i		−	0.349448i
$826$	−2.14541e13	+	3.05836e14i	−0.0557969	+	0.795406i
$827$	−1.41244e13			−0.0365125			−0.0182562	−	0.999833i	$-0.505811\pi$
$827$	−1.41244e13			−0.0365125			−0.0182562	+	0.999833i	$0.505811\pi$
$828$			4.86217e14i			1.24933i
$829$	−7.20313e14			−1.83971			−0.919853	−	0.392264i	$-0.871692\pi$
$829$	−7.20313e14			−1.83971			−0.919853	+	0.392264i	$0.871692\pi$
$830$	−2.37452e14			−0.602818
$831$	3.23503e14			0.816343
$832$		−	2.52570e14i		−	0.633527i
$833$	−1.27536e14			−0.317985
$834$		−	1.32991e14i		−	0.329603i
$835$	1.44840e14			0.356826
$836$			2.67191e14i			0.654321i
$837$			2.88444e13i			0.0702158i
$838$	−1.66338e14			−0.402506
$839$			2.42106e13i			0.0582365i	0.999576	+	0.0291183i	$0.00926994\pi$
$839$			2.42106e13i			0.0582365i	−0.999576	+	0.0291183i	$0.990730\pi$
$840$		−	2.42856e14i		−	0.580700i
$841$	−4.18585e14			−0.994956
$842$	1.30993e15			3.09518
$843$	−1.82942e14			−0.429710
$844$		−	1.66138e15i		−	3.87933i
$845$	3.04136e13			0.0705966
$846$	1.59892e14			0.368956
$847$	−5.45900e14			−1.25226
$848$	1.58103e14			0.360545
$849$		−	4.38979e14i		−	0.995189i
$850$		−	9.74827e13i		−	0.219702i
$851$	1.27834e15			2.86417
$852$	−4.16713e14			−0.928195
$853$	4.82433e14			1.06830			0.534148	−	0.845391i	$-0.320632\pi$
$853$	4.82433e14			1.06830			0.534148	+	0.845391i	$0.320632\pi$
$854$	−3.22113e14			−0.709119
$855$	−2.79922e13			−0.0612641
$856$		−	1.16976e15i		−	2.54522i
$857$			3.07177e13i			0.0664485i	0.999448	+	0.0332242i	$0.0105776\pi$
$857$			3.07177e13i			0.0664485i	−0.999448	+	0.0332242i	$0.989422\pi$
$858$			8.88709e14i			1.91127i
$859$		−	3.21195e14i		−	0.686756i	−0.939197	−	0.343378i	$-0.888429\pi$
$859$		−	3.21195e14i		−	0.686756i	0.939197	−	0.343378i	$-0.111571\pi$
$860$		−	2.09415e15i		−	4.45160i
$861$	1.16599e14			0.246423
$862$	−4.12264e14			−0.866241
$863$		−	6.19194e14i		−	1.29352i	−0.762694	−	0.646760i	$-0.776124\pi$
$863$		−	6.19194e14i		−	1.29352i	0.762694	−	0.646760i	$-0.223876\pi$
$864$			3.47352e13i			0.0721441i
$865$			7.75494e14i			1.60139i
$866$			3.74736e14i			0.769370i
$867$	2.37586e14			0.484981
$868$			1.71036e14i			0.347127i
$869$			1.25365e15i			2.52975i
$870$		−	4.12239e13i		−	0.0827090i
$871$	2.32609e14			0.464020
$872$	−4.70315e14			−0.932838
$873$		−	1.76634e13i		−	0.0348340i
$874$	2.57050e14			0.504034
$875$	−1.83031e14			−0.356848
$876$			7.77754e14i			1.50772i
$877$	−5.35228e14			−1.03167			−0.515835	−	0.856688i	$-0.672518\pi$
$877$	−5.35228e14			−1.03167			−0.515835	+	0.856688i	$0.672518\pi$
$878$		−	1.50723e15i		−	2.88874i
$879$	4.31083e14			0.821517
$880$			1.54149e15i			2.92098i
$881$		−	1.82013e14i		−	0.342944i	−0.985189	−	0.171472i	$-0.945148\pi$
$881$		−	1.82013e14i		−	0.342944i	0.985189	−	0.171472i	$-0.0548523\pi$
$882$			2.49091e14i			0.466676i
$883$	8.50408e14			1.58425			0.792126	−	0.610358i	$-0.208974\pi$
$883$	8.50408e14			1.58425			0.792126	+	0.610358i	$0.208974\pi$
$884$			4.39520e14i			0.814174i
$885$	3.58130e14	+	2.51225e13i	0.659666	+	0.0462749i
$886$	1.21967e15			2.23395
$887$			1.89602e12i			0.00345322i	0.999999	+	0.00172661i	$0.000549597\pi$
$887$			1.89602e12i			0.00345322i	−0.999999	+	0.00172661i	$0.999450\pi$
$888$	9.92821e14			1.79807
$889$	−1.43305e14			−0.258079
$890$	1.09093e15			1.95364
$891$			1.21080e14i			0.215617i
$892$	−1.80786e15			−3.20141
$893$		−	5.72741e13i		−	0.100856i
$894$	7.49422e14			1.31232
$895$			9.65722e14i			1.68166i
$896$		−	3.99162e14i		−	0.691208i
$897$	5.79294e14			0.997554
$898$		−	7.87351e14i		−	1.34830i
$899$			1.52162e13i			0.0259124i
$900$	−1.29002e14			−0.218467
$901$	6.51591e13			0.109736
$902$	−1.92349e15			−3.22149
$903$		−	2.90294e14i		−	0.483503i
$904$	−6.44931e14			−1.06825
$905$	9.30172e14			1.53222
$906$	−1.52933e13			−0.0250531
$907$	−3.15928e14			−0.514697			−0.257348	−	0.966319i	$-0.582849\pi$
$907$	−3.15928e14			−0.514697			−0.257348	+	0.966319i	$0.582849\pi$
$908$		−	1.80463e15i		−	2.92388i
$909$		−	1.22311e14i		−	0.197082i
$910$	−5.52075e14			−0.884690
$911$	−5.03868e14			−0.803017			−0.401508	−	0.915855i	$-0.631514\pi$
$911$	−5.03868e14			−0.803017			−0.401508	+	0.915855i	$0.631514\pi$
$912$	7.68143e13			0.121750
$913$	3.67911e14			0.579948
$914$	5.38906e14			0.844855
$915$			3.77190e14i			0.588105i
$916$			1.91584e15i			2.97087i
$917$			4.81069e14i			0.741925i
$918$			8.83785e13i			0.135561i
$919$		−	6.50439e14i		−	0.992268i	−0.868246	−	0.496134i	$-0.834752\pi$
$919$		−	6.50439e14i		−	0.992268i	0.868246	−	0.496134i	$-0.165248\pi$
$920$	2.61144e15			3.96224
$921$	−4.89593e14			−0.738818
$922$			6.48311e14i			0.973035i
$923$			4.96484e14i			0.741135i
$924$			7.17954e14i			1.06595i
$925$			3.39168e14i			0.500848i
$926$	6.09988e14			0.895914
$927$		−	1.57770e14i		−	0.230476i
$928$			1.83237e13i			0.0266240i
$929$			5.07384e14i			0.733260i	0.930367	+	0.366630i	$0.119489\pi$
$929$			5.07384e14i			0.733260i	−0.930367	+	0.366630i	$0.880511\pi$
$930$	2.95592e14			0.424892
$931$	8.92255e13			0.127568
$932$			2.53480e15i			3.60466i
$933$	−5.65148e14			−0.799381
$934$	1.44247e15			2.02942
$935$			6.35298e14i			0.889036i
$936$	4.49907e14			0.626244
$937$			8.68955e14i			1.20309i	0.798838	+	0.601547i	$0.205449\pi$
$937$			8.68955e14i			1.20309i	−0.798838	+	0.601547i	$0.794551\pi$
$938$	2.77344e14			0.381949
$939$			2.59510e14i			0.355488i
$940$		−	1.11020e15i		−	1.51274i
$941$		−	3.37220e14i		−	0.457052i	−0.973538	−	0.228526i	$-0.926609\pi$
$941$		−	3.37220e14i		−	0.457052i	0.973538	−	0.228526i	$-0.0733906\pi$
$942$	4.86952e13			0.0656495
$943$			1.25380e15i			1.68140i
$944$	−9.82756e14	−	6.89394e13i	−1.31095	−	0.0919618i
$945$	−7.52160e13			−0.0998048
$946$			4.78885e15i			6.32084i
$947$	−4.03885e14			−0.530283			−0.265142	−	0.964209i	$-0.585419\pi$
$947$	−4.03885e14			−0.530283			−0.265142	+	0.964209i	$0.585419\pi$
$948$	1.21094e15			1.58154
$949$	9.26639e14			1.20387
$950$			6.82000e13i			0.0881387i
$951$	−2.44896e14			−0.314832
$952$			2.74656e14i			0.351240i
$953$	−1.44962e15			−1.84412			−0.922058	−	0.387052i	$-0.873494\pi$
$953$	−1.44962e15			−1.84412			−0.922058	+	0.387052i	$0.873494\pi$
$954$		−	1.27263e14i		−	0.161049i
$955$			4.20522e14i			0.529386i
$956$	−1.26152e15			−1.57981
$957$			6.38727e13i			0.0795712i
$958$		−	3.27032e14i		−	0.405287i
$959$	1.81650e14			0.223945
$960$	−3.52635e14			−0.432483
$961$	7.10522e14			0.866883
$962$		−	2.25695e15i		−	2.73934i
$963$	−3.62291e14			−0.437448
$964$	−1.91344e15			−2.29842
$965$	−1.42768e15			−1.70606
$966$	6.90703e14			0.821118
$967$			5.11589e14i			0.605046i	0.953142	+	0.302523i	$0.0978289\pi$
$967$			5.11589e14i			0.605046i	−0.953142	+	0.302523i	$0.902171\pi$
$968$		−	4.55899e15i		−	5.36404i
$969$	3.16576e13			0.0370560
$970$	−1.81011e14			−0.210788
$971$	1.44300e15			1.67174			0.835871	−	0.548926i	$-0.184963\pi$
$971$	1.44300e15			1.67174			0.835871	+	0.548926i	$0.184963\pi$
$972$	1.16954e14			0.134799
$973$	−1.28005e14			−0.146778
$974$			3.70679e14i			0.422866i
$975$			1.53697e14i			0.174439i
$976$		−	1.03506e15i		−	1.16874i
$977$			5.80145e14i			0.651724i	0.945417	+	0.325862i	$0.105655\pi$
$977$			5.80145e14i			0.651724i	−0.945417	+	0.325862i	$0.894345\pi$
$978$			3.13447e13i			0.0350324i
$979$	−1.69029e15			−1.87953
$980$	1.72955e15			1.91339
$981$			1.45664e14i			0.160327i
$982$		−	5.14179e14i		−	0.563063i
$983$			2.43073e14i			0.264831i	0.991194	+	0.132415i	$0.0422733\pi$
$983$			2.43073e14i			0.264831i	−0.991194	+	0.132415i	$0.957727\pi$
$984$			9.73761e14i			1.05555i
$985$	−4.81866e14			−0.519690
$986$			4.66219e13i			0.0500272i
$987$		−	1.53898e14i		−	0.164303i
$988$		−	3.07493e14i		−	0.326626i
$989$	3.12155e15			3.29905
$990$	1.24080e15			1.30475
$991$		−	5.67192e14i		−	0.593419i	−0.954968	−	0.296710i	$-0.904111\pi$
$991$		−	5.67192e14i		−	0.593419i	0.954968	−	0.296710i	$-0.0958893\pi$
$992$	−1.31389e14			−0.136773
$993$	3.05947e14			0.316884
$994$			5.91968e14i			0.610051i
$995$	−6.06225e14			−0.621611
$996$		−	3.55376e14i		−	0.362569i
$997$	−1.85745e15			−1.88557			−0.942783	−	0.333406i	$-0.891802\pi$
$997$	−1.85745e15			−1.88557			−0.942783	+	0.333406i	$0.891802\pi$
$998$		−	2.36551e15i		−	2.38931i
$999$		−	3.07492e14i		−	0.309034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.7	✓	100
59.58	odd	2	inner	177.11.c.a.58.94	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.7	✓	100	1.1	even	1	trivial
177.11.c.a.58.94	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)

\(f(q)\)	\(=\)	\(q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} -201708. i q^{10} +312528. i q^{11} +301880. q^{12} -359669. i q^{13} -428840. i q^{14} -502165. q^{15} +1.37801e6 q^{16} +567921. q^{17} -1.10921e6i q^{18} -397324. q^{19} -7.70175e6 q^{20} -1.06762e6 q^{21} +1.76121e7 q^{22} -1.14802e7i q^{23} -8.91609e6i q^{24} +3.04592e6 q^{25} -2.02686e7 q^{26} -2.76145e6 q^{27} -1.63743e7 q^{28} -1.45674e6 q^{29} +2.82988e7i q^{30} -1.04454e7i q^{31} -1.25786e7i q^{32} -4.38465e7i q^{33} -3.20044e7i q^{34} +2.72379e7 q^{35} -4.23526e7 q^{36} +1.11352e8i q^{37} +2.23906e7i q^{38} +5.04601e7i q^{39} +2.27473e8i q^{40} -1.09214e8 q^{41} +6.01645e7i q^{42} +2.71906e8i q^{43} -6.72478e8i q^{44} +7.04518e7 q^{45} -6.46953e8 q^{46} +1.44150e8i q^{47} -1.93329e8 q^{48} -2.24566e8 q^{49} -1.71649e8i q^{50} -7.96771e7 q^{51} +7.73911e8i q^{52} +1.14733e8 q^{53} +1.55618e8i q^{54} +1.11864e9i q^{55} +4.83617e8i q^{56} +5.57430e7 q^{57} +8.20924e7i q^{58} +(-7.13172e8 - 5.00283e7i) q^{59} +1.08053e9 q^{60} -7.51127e8i q^{61} -5.88636e8 q^{62} +1.49784e8 q^{63} +7.02230e8 q^{64} -1.28737e9i q^{65} -2.47091e9 q^{66} +6.46732e8i q^{67} -1.22201e9 q^{68} +1.61063e9i q^{69} -1.53495e9i q^{70} -1.38039e9 q^{71} +1.25089e9i q^{72} +2.57637e9i q^{73} +6.27507e9 q^{74} -4.27330e8 q^{75} +8.54935e8 q^{76} +2.37828e9i q^{77} +2.84361e9 q^{78} +4.01132e9 q^{79} +4.93233e9 q^{80} +3.87420e8 q^{81} +6.15460e9i q^{82} -1.17721e9i q^{83} +2.29724e9 q^{84} +2.03277e9 q^{85} +1.53229e10 q^{86} +2.04374e8 q^{87} -1.98618e10 q^{88} +5.40845e9i q^{89} -3.97022e9i q^{90} -2.73700e9i q^{91} +2.47024e10i q^{92} +1.46545e9i q^{93} +8.12336e9 q^{94} -1.42215e9 q^{95} +1.76473e9i q^{96} -8.97393e8i q^{97} +1.26551e10i q^{98} +6.15149e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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