LMFDB - Embedded newform 177.11.c.a.58.14

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			58.14
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.87

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} -37466.0i q^{10} +265503. i q^{11} +218454. q^{12} +470017. i q^{13} +1.08186e6i q^{14} -103462. q^{15} -218501. q^{16} -1.88282e6 q^{17} -999984. i q^{18} -4.41356e6 q^{19} -1.14829e6 q^{20} +2.98754e6 q^{21} +1.34887e7 q^{22} +1.07346e7i q^{23} -3.79971e6i q^{24} -9.22178e6 q^{25} +2.38790e7 q^{26} -2.76145e6 q^{27} +3.31576e7 q^{28} +1.25709e7 q^{29} +5.25634e6i q^{30} -4.28985e7i q^{31} +3.88343e7i q^{32} -3.72490e7i q^{33} +9.56558e7i q^{34} -1.57038e7 q^{35} -3.06483e7 q^{36} +2.69313e7i q^{37} +2.24228e8i q^{38} -6.59416e7i q^{39} +1.99729e7i q^{40} +4.52994e6 q^{41} -1.51780e8i q^{42} -1.84390e8i q^{43} -4.13412e8i q^{44} +1.45153e7 q^{45} +5.45366e8 q^{46} +1.36961e8i q^{47} +3.06549e7 q^{48} +1.70982e8 q^{49} +4.68508e8i q^{50} +2.64153e8 q^{51} -7.31860e8i q^{52} -4.28407e7 q^{53} +1.40294e8i q^{54} +1.95796e8i q^{55} -5.76730e8i q^{56} +6.19205e8 q^{57} -6.38655e8i q^{58} +(6.78517e8 - 2.25236e8i) q^{59} +1.61100e8 q^{60} +4.89796e8i q^{61} -2.17943e9 q^{62} -4.19140e8 q^{63} +1.74921e9 q^{64} +3.46617e8i q^{65} -1.89242e9 q^{66} +8.12593e8i q^{67} +2.93173e9 q^{68} -1.50603e9i q^{69} +7.97821e8i q^{70} -2.09745e9 q^{71} +5.33084e8i q^{72} -3.96104e9i q^{73} +1.36823e9 q^{74} +1.29378e9 q^{75} +6.87232e9 q^{76} -5.65376e9i q^{77} -3.35012e9 q^{78} -2.20220e9 q^{79} -1.61135e8 q^{80} +3.87420e8 q^{81} -2.30141e8i q^{82} -2.68481e9i q^{83} -4.65188e9 q^{84} -1.38850e9 q^{85} -9.36785e9 q^{86} -1.76364e9 q^{87} -7.19074e9 q^{88} -3.26412e9i q^{89} -7.37444e8i q^{90} -1.00088e10i q^{91} -1.67148e10i q^{92} +6.01849e9i q^{93} +6.95822e9 q^{94} -3.25480e9 q^{95} -5.44831e9i q^{96} +1.33057e10i q^{97} -8.68665e9i q^{98} +5.22589e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	50.8045i		−	1.58764i	−0.608153	−	0.793820i	$-0.708089\pi$
$2$		−	50.8045i		−	1.58764i	0.608153	−	0.793820i	$-0.291911\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−1557.09			−1.52060
$5$	737.455			0.235986			0.117993	−	0.993014i	$-0.462354\pi$
$5$	737.455			0.235986			0.117993	+	0.993014i	$0.462354\pi$
$6$			7127.67i			0.916624i
$7$	−21294.5			−1.26700			−0.633502	−	0.773741i	$-0.718383\pi$
$7$	−21294.5			−1.26700			−0.633502	+	0.773741i	$0.718383\pi$
$8$			27083.5i			0.826522i
$9$	19683.0			0.333333
$10$		−	37466.0i		−	0.374660i
$11$			265503.i			1.64856i	0.566180	+	0.824282i	$0.308421\pi$
$11$			265503.i			1.64856i	−0.566180	+	0.824282i	$0.691579\pi$
$12$	218454.			0.877918
$13$			470017.i			1.26589i	0.774196	+	0.632946i	$0.218155\pi$
$13$			470017.i			1.26589i	−0.774196	+	0.632946i	$0.781845\pi$
$14$			1.08186e6i			2.01155i
$15$	−103462.			−0.136246
$16$	−218501.			−0.208379
$17$	−1.88282e6			−1.32606			−0.663032	−	0.748591i	$-0.730731\pi$
$17$	−1.88282e6			−1.32606			−0.663032	+	0.748591i	$0.730731\pi$
$18$		−	999984.i		−	0.529213i
$19$	−4.41356e6			−1.78246			−0.891232	−	0.453547i	$-0.850158\pi$
$19$	−4.41356e6			−1.78246			−0.891232	+	0.453547i	$0.850158\pi$
$20$	−1.14829e6			−0.358839
$21$	2.98754e6			0.731505
$22$	1.34887e7			2.61732
$23$			1.07346e7i			1.66781i	0.551906	+	0.833907i	$0.313901\pi$
$23$			1.07346e7i			1.66781i	−0.551906	+	0.833907i	$0.686099\pi$
$24$		−	3.79971e6i		−	0.477193i
$25$	−9.22178e6			−0.944311
$26$	2.38790e7			2.00978
$27$	−2.76145e6			−0.192450
$28$	3.31576e7			1.92660
$29$	1.25709e7			0.612879			0.306440	−	0.951890i	$-0.400862\pi$
$29$	1.25709e7			0.612879			0.306440	+	0.951890i	$0.400862\pi$
$30$			5.25634e6i			0.216310i
$31$		−	4.28985e7i		−	1.49842i	−0.662333	−	0.749209i	$-0.730434\pi$
$31$		−	4.28985e7i		−	1.49842i	0.662333	−	0.749209i	$-0.269566\pi$
$32$			3.88343e7i			1.15735i
$33$		−	3.72490e7i		−	0.951798i
$34$			9.56558e7i			2.10531i
$35$	−1.57038e7			−0.298995
$36$	−3.06483e7			−0.506866
$37$			2.69313e7i			0.388372i	0.980965	+	0.194186i	$0.0622066\pi$
$37$			2.69313e7i			0.388372i	−0.980965	+	0.194186i	$0.937793\pi$
$38$			2.24228e8i			2.82991i
$39$		−	6.59416e7i		−	0.730863i
$40$			1.99729e7i			0.195047i
$41$	4.52994e6			0.0390997			0.0195499	−	0.999809i	$-0.493777\pi$
$41$	4.52994e6			0.0390997			0.0195499	+	0.999809i	$0.493777\pi$
$42$		−	1.51780e8i		−	1.16137i
$43$		−	1.84390e8i		−	1.25428i	−0.778905	−	0.627142i	$-0.784225\pi$
$43$		−	1.84390e8i		−	1.25428i	0.778905	−	0.627142i	$-0.215775\pi$
$44$		−	4.13412e8i		−	2.50680i
$45$	1.45153e7			0.0786619
$46$	5.45366e8			2.64789
$47$			1.36961e8i			0.597183i	0.954381	+	0.298591i	$0.0965168\pi$
$47$			1.36961e8i			0.597183i	−0.954381	+	0.298591i	$0.903483\pi$
$48$	3.06549e7			0.120308
$49$	1.70982e8			0.605299
$50$			4.68508e8i			1.49922i
$51$	2.64153e8			0.765604
$52$		−	7.31860e8i		−	1.92491i
$53$	−4.28407e7			−0.102442			−0.0512209	−	0.998687i	$-0.516311\pi$
$53$	−4.28407e7			−0.102442			−0.0512209	+	0.998687i	$0.516311\pi$
$54$			1.40294e8i			0.305541i
$55$			1.95796e8i			0.389037i
$56$		−	5.76730e8i		−	1.04721i
$57$	6.19205e8			1.02911
$58$		−	6.38655e8i		−	0.973031i
$59$	6.78517e8	−	2.25236e8i	0.949076	−	0.315048i
$59$	6.78517e8	−	2.25236e8i	0.949076	−	0.315048i
$60$	1.61100e8			0.207176
$61$			4.89796e8i			0.579917i	0.957039	+	0.289959i	$0.0936415\pi$
$61$			4.89796e8i			0.579917i	−0.957039	+	0.289959i	$0.906358\pi$
$62$	−2.17943e9			−2.37895
$63$	−4.19140e8			−0.422335
$64$	1.74921e9			1.62908
$65$			3.46617e8i			0.298732i
$66$	−1.89242e9			−1.51111
$67$			8.12593e8i			0.601865i	0.953645	+	0.300933i	$0.0972979\pi$
$67$			8.12593e8i			0.601865i	−0.953645	+	0.300933i	$0.902702\pi$
$68$	2.93173e9			2.01641
$69$		−	1.50603e9i		−	0.962912i
$70$			7.97821e8i			0.474696i
$71$	−2.09745e9			−1.16252			−0.581259	−	0.813719i	$-0.697440\pi$
$71$	−2.09745e9			−1.16252			−0.581259	+	0.813719i	$0.697440\pi$
$72$			5.33084e8i			0.275507i
$73$		−	3.96104e9i		−	1.91071i	−0.295461	−	0.955355i	$-0.595473\pi$
$73$		−	3.96104e9i		−	1.91071i	0.295461	−	0.955355i	$-0.404527\pi$
$74$	1.36823e9			0.616595
$75$	1.29378e9			0.545198
$76$	6.87232e9			2.71041
$77$		−	5.65376e9i		−	2.08874i
$78$	−3.35012e9			−1.16035
$79$	−2.20220e9			−0.715683			−0.357841	−	0.933782i	$-0.616487\pi$
$79$	−2.20220e9			−0.715683			−0.357841	+	0.933782i	$0.616487\pi$
$80$	−1.61135e8			−0.0491745
$81$	3.87420e8			0.111111
$82$		−	2.30141e8i		−	0.0620762i
$83$		−	2.68481e9i		−	0.681589i	−0.940138	−	0.340794i	$-0.889304\pi$
$83$		−	2.68481e9i		−	0.681589i	0.940138	−	0.340794i	$-0.110696\pi$
$84$	−4.65188e9			−1.11233
$85$	−1.38850e9			−0.312932
$86$	−9.36785e9			−1.99135
$87$	−1.76364e9			−0.353846
$88$	−7.19074e9			−1.36257
$89$		−	3.26412e9i		−	0.584542i	−0.956335	−	0.292271i	$-0.905589\pi$
$89$		−	3.26412e9i		−	0.584542i	0.956335	−	0.292271i	$-0.0944110\pi$
$90$		−	7.37444e8i		−	0.124887i
$91$		−	1.00088e10i		−	1.60389i
$92$		−	1.67148e10i		−	2.53607i
$93$			6.01849e9i			0.865112i
$94$	6.95822e9			0.948111
$95$	−3.25480e9			−0.420636
$96$		−	5.44831e9i		−	0.668198i
$97$			1.33057e10i			1.54946i	0.632295	+	0.774728i	$0.282113\pi$
$97$			1.33057e10i			1.54946i	−0.632295	+	0.774728i	$0.717887\pi$
$98$		−	8.68665e9i		−	0.960997i
$99$			5.22589e9i			0.549521i
$100$	1.43592e10			1.43592
$101$			9.24528e9i			0.879656i	0.898082	+	0.439828i	$0.144961\pi$
$101$			9.24528e9i			0.879656i	−0.898082	+	0.439828i	$0.855039\pi$
$102$		−	1.34201e10i		−	1.21550i
$103$		−	1.21978e10i		−	1.05220i	−0.850424	−	0.526098i	$-0.823655\pi$
$103$		−	1.21978e10i		−	1.05220i	0.850424	−	0.526098i	$-0.176345\pi$
$104$	−1.27297e10			−1.04629
$105$	2.20318e9			0.172625
$106$			2.17650e9i			0.162641i
$107$	−1.87753e10			−1.33866			−0.669328	−	0.742967i	$-0.733418\pi$
$107$	−1.87753e10			−1.33866			−0.669328	+	0.742967i	$0.733418\pi$
$108$	4.29983e9			0.292639
$109$			4.37724e9i			0.284490i	0.989831	+	0.142245i	$0.0454322\pi$
$109$			4.37724e9i			0.284490i	−0.989831	+	0.142245i	$0.954568\pi$
$110$	9.94733e9			0.617651
$111$		−	3.77835e9i		−	0.224227i
$112$	4.65289e9			0.264017
$113$			9.12797e8i			0.0495430i	0.999693	+	0.0247715i	$0.00788582\pi$
$113$			9.12797e8i			0.0495430i	−0.999693	+	0.0247715i	$0.992114\pi$
$114$		−	3.14584e10i		−	1.63385i
$115$			7.91630e9i			0.393580i
$116$	−1.95740e10			−0.931943
$117$			9.25134e9i			0.421964i
$118$	−1.14430e10	−	3.44717e10i	−0.500183	−	1.50679i
$119$	4.00938e10			1.68013
$120$		−	2.80211e9i		−	0.112611i
$121$	−4.45543e10			−1.71776
$122$	2.48838e10			0.920699
$123$	−6.35534e8			−0.0225742
$124$			6.67969e10i			2.27849i
$125$	−1.40024e10			−0.458830
$126$			2.12942e10i			0.670515i
$127$	2.76027e10			0.835474			0.417737	−	0.908568i	$-0.362823\pi$
$127$	2.76027e10			0.835474			0.417737	+	0.908568i	$0.362823\pi$
$128$		−	4.91014e10i		−	1.42904i
$129$			2.58692e10i			0.724161i
$130$	1.76097e10			0.474279
$131$			1.39688e10i			0.362079i	0.983476	+	0.181039i	$0.0579461\pi$
$131$			1.39688e10i			0.362079i	−0.983476	+	0.181039i	$0.942054\pi$
$132$			5.80001e10i			1.44730i
$133$	9.39847e10			2.25839
$134$	4.12834e10			0.955545
$135$	−2.03644e9			−0.0454155
$136$		−	5.09934e10i		−	1.09602i
$137$	−1.40192e10			−0.290483			−0.145241	−	0.989396i	$-0.546396\pi$
$137$	−1.40192e10			−0.290483			−0.145241	+	0.989396i	$0.546396\pi$
$138$	−7.65128e10			−1.52876
$139$	−5.80410e10			−1.11856			−0.559282	−	0.828978i	$-0.688923\pi$
$139$	−5.80410e10			−1.11856			−0.559282	+	0.828978i	$0.688923\pi$
$140$	2.44522e10			0.454651
$141$		−	1.92151e10i		−	0.344784i
$142$			1.06560e11i			1.84566i
$143$	−1.24791e11			−2.08690
$144$	−4.30076e9			−0.0694598
$145$	9.27044e9			0.144631
$146$	−2.01238e11			−3.03352
$147$	−2.39881e10			−0.349470
$148$		−	4.19345e10i		−	0.590558i
$149$			1.28271e11i			1.74661i	0.487170	+	0.873307i	$0.338029\pi$
$149$			1.28271e11i			1.74661i	−0.487170	+	0.873307i	$0.661971\pi$
$150$		−	6.57298e10i		−	0.865578i
$151$			4.39180e10i			0.559445i	0.960081	+	0.279722i	$0.0902425\pi$
$151$			4.39180e10i			0.559445i	−0.960081	+	0.279722i	$0.909758\pi$
$152$		−	1.19535e11i		−	1.47325i
$153$	−3.70596e10			−0.442022
$154$	−2.87236e11			−3.31616
$155$		−	3.16357e10i		−	0.353605i
$156$			1.02677e11i			1.11135i
$157$		−	4.40831e9i		−	0.0462141i	−0.999733	−	0.0231070i	$-0.992644\pi$
$157$		−	4.40831e9i		−	0.0462141i	0.999733	−	0.0231070i	$-0.00735585\pi$
$158$			1.11881e11i			1.13625i
$159$	6.01038e9			0.0591448
$160$			2.86386e10i			0.273119i
$161$		−	2.28589e11i		−	2.11313i
$162$		−	1.96827e10i		−	0.176404i
$163$	9.45102e10			0.821374			0.410687	−	0.911776i	$-0.365289\pi$
$163$	9.45102e10			0.821374			0.410687	+	0.911776i	$0.365289\pi$
$164$	−7.05354e9			−0.0594550
$165$		−	2.74695e10i		−	0.224611i
$166$	−1.36400e11			−1.08212
$167$	3.78770e10			0.291604			0.145802	−	0.989314i	$-0.453424\pi$
$167$	3.78770e10			0.291604			0.145802	+	0.989314i	$0.453424\pi$
$168$			8.09130e10i			0.604605i
$169$	−8.30574e10			−0.602483
$170$			7.05418e10i			0.496824i
$171$	−8.68721e10			−0.594155
$172$			2.87113e11i			1.90726i
$173$			2.01673e11i			1.30142i	0.759326	+	0.650710i	$0.225529\pi$
$173$			2.01673e11i			1.30142i	−0.759326	+	0.650710i	$0.774471\pi$
$174$			8.96009e10i			0.561780i
$175$	1.96374e11			1.19645
$176$		−	5.80127e10i		−	0.343526i
$177$	−9.51933e10	+	3.15997e10i	−0.547949	+	0.181893i
$178$	−1.65832e11			−0.928042
$179$		−	2.07742e10i		−	0.113047i	−0.998401	−	0.0565236i	$-0.981998\pi$
$179$		−	2.07742e10i		−	0.113047i	0.998401	−	0.0565236i	$-0.0180016\pi$
$180$	−2.26017e10			−0.119613
$181$	−8.19283e10			−0.421737			−0.210868	−	0.977514i	$-0.567629\pi$
$181$	−8.19283e10			−0.421737			−0.210868	+	0.977514i	$0.567629\pi$
$182$	−5.08491e11			−2.54640
$183$		−	6.87164e10i		−	0.334815i
$184$	−2.90731e11			−1.37848
$185$			1.98606e10i			0.0916503i
$186$	3.05766e11			1.37349
$187$		−	4.99894e11i		−	2.18610i
$188$		−	2.13261e11i		−	0.908075i
$189$	5.88038e10			0.243835
$190$			1.65358e11i			0.667819i
$191$		−	7.73059e9i		−	0.0304121i	−0.999884	−	0.0152060i	$-0.995160\pi$
$191$		−	7.73059e9i		−	0.0304121i	0.999884	−	0.0152060i	$-0.00484042\pi$
$192$	−2.45408e11			−0.940550
$193$	1.50108e11			0.560553			0.280276	−	0.959919i	$-0.409574\pi$
$193$	1.50108e11			0.560553			0.280276	+	0.959919i	$0.409574\pi$
$194$	6.75989e11			2.45998
$195$		−	4.86290e10i		−	0.172473i
$196$	−2.66235e11			−0.920417
$197$	4.73540e11			1.59597			0.797986	−	0.602676i	$-0.205899\pi$
$197$	4.73540e11			1.59597			0.797986	+	0.602676i	$0.205899\pi$
$198$	2.65499e11			0.872441
$199$	−4.86539e10			−0.155902			−0.0779511	−	0.996957i	$-0.524838\pi$
$199$	−4.86539e10			−0.155902			−0.0779511	+	0.996957i	$0.524838\pi$
$200$		−	2.49758e11i		−	0.780494i
$201$		−	1.14004e11i		−	0.347487i
$202$	4.69701e11			1.39658
$203$	−2.67690e11			−0.776520
$204$	−4.11310e11			−1.16418
$205$	3.34063e9			0.00922697
$206$	−6.19704e11			−1.67051
$207$			2.11289e11i			0.555938i
$208$		−	1.02699e11i		−	0.263786i
$209$		−	1.17181e12i		−	2.93851i
$210$		−	1.11931e11i		−	0.274066i
$211$			4.12413e10i			0.0986099i	0.998784	+	0.0493050i	$0.0157006\pi$
$211$			4.12413e10i			0.0986099i	−0.998784	+	0.0493050i	$0.984299\pi$
$212$	6.67069e10			0.155773
$213$	2.94264e11			0.671180
$214$			9.53871e11i			2.12530i
$215$		−	1.35980e11i		−	0.295993i
$216$		−	7.47896e10i		−	0.159064i
$217$			9.13503e11i			1.89850i
$218$	2.22383e11			0.451668
$219$			5.55718e11i			1.10315i
$220$		−	3.04873e11i		−	0.591570i
$221$		−	8.84958e11i		−	1.67865i
$222$	−1.91957e11			−0.355991
$223$	−1.00117e12			−1.81545			−0.907723	−	0.419570i	$-0.862181\pi$
$223$	−1.00117e12			−1.81545			−0.907723	+	0.419570i	$0.862181\pi$
$224$		−	8.26959e11i		−	1.46637i
$225$	−1.81512e11			−0.314770
$226$	4.63742e10			0.0786564
$227$		−	7.87897e10i		−	0.130719i	−0.997862	−	0.0653597i	$-0.979181\pi$
$227$		−	7.87897e10i		−	0.130719i	0.997862	−	0.0653597i	$-0.0208195\pi$
$228$	−9.64160e11			−1.56486
$229$		−	5.49767e10i		−	0.0872975i	−0.999047	−	0.0436487i	$-0.986102\pi$
$229$		−	5.49767e10i		−	0.0872975i	0.999047	−	0.0436487i	$-0.0138982\pi$
$230$	4.02183e11			0.624863
$231$			7.93200e11i			1.20593i
$232$			3.40462e11i			0.506558i
$233$		−	2.97509e11i		−	0.433232i	−0.976257	−	0.216616i	$-0.930498\pi$
$233$		−	2.97509e11i		−	0.433232i	0.976257	−	0.216616i	$-0.0695020\pi$
$234$	4.70009e11			0.669927
$235$			1.01003e11i			0.140927i
$236$	−1.05651e12	+	3.50713e11i	−1.44316	+	0.479062i
$237$	3.08960e11			0.413200
$238$		−	2.03694e12i		−	2.66744i
$239$	1.29232e12			1.65722			0.828611	−	0.559825i	$-0.189132\pi$
$239$	1.29232e12			1.65722			0.828611	+	0.559825i	$0.189132\pi$
$240$	2.26066e10			0.0283909
$241$	−7.85630e10			−0.0966347			−0.0483173	−	0.998832i	$-0.515386\pi$
$241$	−7.85630e10			−0.0966347			−0.0483173	+	0.998832i	$0.515386\pi$
$242$			2.26356e12i			2.72718i
$243$	−5.43536e10			−0.0641500
$244$		−	7.62657e11i		−	0.881821i
$245$	1.26092e11			0.142842
$246$			3.22879e10i			0.0358397i
$247$		−	2.07445e12i		−	2.25641i
$248$	1.16184e12			1.23848
$249$			3.76668e11i			0.393516i
$250$			7.11383e11i			0.728456i
$251$	1.77996e12			1.78665			0.893327	−	0.449407i	$-0.148365\pi$
$251$	1.77996e12			1.78665			0.893327	+	0.449407i	$0.148365\pi$
$252$	6.52640e11			0.642201
$253$	−2.85007e12			−2.74950
$254$		−	1.40234e12i		−	1.32643i
$255$	1.94801e11			0.180672
$256$	−7.03376e11			−0.639717
$257$	1.30368e12			1.16280			0.581401	−	0.813617i	$-0.302505\pi$
$257$	1.30368e12			1.16280			0.581401	+	0.813617i	$0.302505\pi$
$258$	1.31427e12			1.14971
$259$		−	5.73489e11i		−	0.492069i
$260$		−	5.39714e11i		−	0.454252i
$261$	2.47432e11			0.204293
$262$	7.09678e11			0.574850
$263$	−1.34743e12			−1.07085			−0.535424	−	0.844583i	$-0.679848\pi$
$263$	−1.34743e12			−1.07085			−0.535424	+	0.844583i	$0.679848\pi$
$264$	1.00883e12			0.786682
$265$	−3.15931e10			−0.0241748
$266$		−	4.77484e12i		−	3.58551i
$267$			4.57943e11i			0.337486i
$268$		−	1.26528e12i		−	0.915195i
$269$		−	2.05438e12i		−	1.45854i	−0.684226	−	0.729270i	$-0.739860\pi$
$269$		−	2.05438e12i		−	1.45854i	0.684226	−	0.729270i	$-0.260140\pi$
$270$			1.03460e11i			0.0721034i
$271$	−2.88296e12			−1.97239			−0.986195	−	0.165590i	$-0.947047\pi$
$271$	−2.88296e12			−1.97239			−0.986195	+	0.165590i	$0.947047\pi$
$272$	4.11399e11			0.276324
$273$			1.40419e12i			0.926007i
$274$			7.12238e11i			0.461182i
$275$		−	2.44841e12i		−	1.55676i
$276$			2.34502e12i			1.46420i
$277$	−1.28054e12			−0.785227			−0.392614	−	0.919704i	$-0.628429\pi$
$277$	−1.28054e12			−0.785227			−0.392614	+	0.919704i	$0.628429\pi$
$278$			2.94874e12i			1.77588i
$279$		−	8.44370e11i		−	0.499473i
$280$		−	4.25313e11i		−	0.247126i
$281$	1.63468e12			0.933044			0.466522	−	0.884510i	$-0.345507\pi$
$281$	1.63468e12			0.933044			0.466522	+	0.884510i	$0.345507\pi$
$282$	−9.76212e11			−0.547392
$283$		−	2.29521e12i		−	1.26442i	−0.774799	−	0.632208i	$-0.782149\pi$
$283$		−	2.29521e12i		−	1.26442i	0.774799	−	0.632208i	$-0.217851\pi$
$284$	3.26592e12			1.76772
$285$	4.56636e11			0.242854
$286$			6.33993e12i			3.31325i
$287$	−9.64631e10			−0.0495395
$288$			7.64376e11i			0.385784i
$289$	1.52903e12			0.758447
$290$		−	4.70980e11i		−	0.229621i
$291$		−	1.86674e12i		−	0.894579i
$292$			6.16770e12i			2.90542i
$293$	−1.27557e12			−0.590701			−0.295351	−	0.955389i	$-0.595436\pi$
$293$	−1.27557e12			−0.590701			−0.295351	+	0.955389i	$0.595436\pi$
$294$			1.21870e12i			0.554832i
$295$	5.00376e11	−	1.66101e11i	0.223968	−	0.0743469i
$296$	−7.29392e11			−0.320998
$297$		−	7.33172e11i		−	0.317266i
$298$	6.51674e12			2.77299
$299$	−5.04545e12			−2.11127
$300$	−2.01454e12			−0.829027
$301$			3.92650e12i			1.58918i
$302$	2.23123e12			0.888197
$303$		−	1.29708e12i		−	0.507870i
$304$	9.64369e11			0.371429
$305$			3.61203e11i			0.136852i
$306$			1.88279e12i			0.701771i
$307$	3.69241e12			1.35400			0.677000	−	0.735983i	$-0.263280\pi$
$307$	3.69241e12			1.35400			0.677000	+	0.735983i	$0.263280\pi$
$308$			8.80342e12i			3.17613i
$309$			1.71131e12i			0.607485i
$310$	−1.60723e12			−0.561398
$311$	2.89941e11			0.0996568			0.0498284	−	0.998758i	$-0.484133\pi$
$311$	2.89941e11			0.0996568			0.0498284	+	0.998758i	$0.484133\pi$
$312$	1.78593e12			0.604075
$313$			1.31084e12i			0.436342i	0.975911	+	0.218171i	$0.0700091\pi$
$313$			1.31084e12i			0.436342i	−0.975911	+	0.218171i	$0.929991\pi$
$314$	−2.23962e11			−0.0733713
$315$	−3.09097e11			−0.0996649
$316$	3.42902e12			1.08827
$317$	−2.03370e11			−0.0635316			−0.0317658	−	0.999495i	$-0.510113\pi$
$317$	−2.03370e11			−0.0635316			−0.0317658	+	0.999495i	$0.510113\pi$
$318$		−	3.05354e11i		−	0.0939006i
$319$			3.33760e12i			1.01037i
$320$	1.28997e12			0.384440
$321$	2.63411e12			0.772873
$322$	−1.16133e13			−3.35488
$323$	8.30995e12			2.36366
$324$	−6.03250e11			−0.168955
$325$		−	4.33440e12i		−	1.19540i
$326$		−	4.80154e12i		−	1.30405i
$327$		−	6.14109e11i		−	0.164251i
$328$			1.22687e11i			0.0323168i
$329$		−	2.91652e12i		−	0.756633i
$330$	−1.39557e12			−0.356601
$331$	−4.34702e12			−1.09409			−0.547043	−	0.837105i	$-0.684246\pi$
$331$	−4.34702e12			−1.09409			−0.547043	+	0.837105i	$0.684246\pi$
$332$			4.18049e12i			1.03642i
$333$			5.30088e11i			0.129457i
$334$		−	1.92432e12i		−	0.462961i
$335$			5.99251e11i			0.142032i
$336$	−6.52782e11			−0.152430
$337$			1.60227e12i			0.368626i	0.982868	+	0.184313i	$0.0590060\pi$
$337$			1.60227e12i			0.368626i	−0.982868	+	0.184313i	$0.940994\pi$
$338$			4.21969e12i			0.956526i
$339$		−	1.28062e11i		−	0.0286036i
$340$	2.16202e12			0.475844
$341$	1.13897e13			2.47024
$342$			4.41349e12i			0.943304i
$343$	2.37420e12			0.500088
$344$	4.99393e12			1.03669
$345$		−	1.11063e12i		−	0.227234i
$346$	1.02459e13			2.06619
$347$		−	2.33249e12i		−	0.463630i	−0.972760	−	0.231815i	$-0.925534\pi$
$347$		−	2.33249e12i		−	0.463630i	0.972760	−	0.231815i	$-0.0744664\pi$
$348$	2.74615e12			0.538057
$349$			1.84957e12i			0.357227i	0.983919	+	0.178613i	$0.0571611\pi$
$349$			1.84957e12i			0.357227i	−0.983919	+	0.178613i	$0.942839\pi$
$350$		−	9.97665e12i		−	1.89952i
$351$		−	1.29793e12i		−	0.243621i
$352$	−1.03106e13			−1.90797
$353$			8.17195e12i			1.49091i	0.666555	+	0.745456i	$0.267768\pi$
$353$			8.17195e12i			1.49091i	−0.666555	+	0.745456i	$0.732232\pi$
$354$	1.60541e12	+	4.83625e12i	0.288781	+	0.869945i
$355$	−1.54677e12			−0.274337
$356$			5.08254e12i			0.888854i
$357$	−5.62501e12			−0.970023
$358$	−1.05542e12			−0.179478
$359$	−1.10519e13			−1.85338			−0.926692	−	0.375821i	$-0.877361\pi$
$359$	−1.10519e13			−1.85338			−0.926692	+	0.375821i	$0.877361\pi$
$360$			3.93126e11i			0.0650158i
$361$	1.33484e13			2.17718
$362$			4.16232e12i			0.669566i
$363$	6.25079e12			0.991750
$364$			1.55846e13i			2.43887i
$365$		−	2.92109e12i		−	0.450900i
$366$	−3.49110e12			−0.531566
$367$		−	1.43915e12i		−	0.216161i	−0.994142	−	0.108080i	$-0.965530\pi$
$367$		−	1.43915e12i		−	0.216161i	0.994142	−	0.108080i	$-0.0344704\pi$
$368$		−	2.34553e12i		−	0.347538i
$369$	8.91629e10			0.0130332
$370$	1.00901e12			0.145508
$371$	9.12273e11			0.129794
$372$		−	9.37134e12i		−	1.31549i
$373$	7.89849e12			1.09396			0.546978	−	0.837147i	$-0.315778\pi$
$373$	7.89849e12			1.09396			0.546978	+	0.837147i	$0.315778\pi$
$374$	−2.53969e13			−3.47074
$375$	1.96448e12			0.264905
$376$	−3.70938e12			−0.493585
$377$			5.90851e12i			0.775839i
$378$		−	2.98749e12i		−	0.387122i
$379$	1.41936e12			0.181508			0.0907539	−	0.995873i	$-0.471072\pi$
$379$	1.41936e12			0.181508			0.0907539	+	0.995873i	$0.471072\pi$
$380$	5.06803e12			0.639619
$381$	−3.87255e12			−0.482361
$382$	−3.92749e11			−0.0482834
$383$	−1.32733e13			−1.61059			−0.805293	−	0.592877i	$-0.797992\pi$
$383$	−1.32733e13			−1.61059			−0.805293	+	0.592877i	$0.797992\pi$
$384$			6.88873e12i			0.825056i
$385$		−	4.16939e12i		−	0.492912i
$386$		−	7.62614e12i		−	0.889956i
$387$		−	3.62935e12i		−	0.418094i
$388$		−	2.07182e13i		−	2.35610i
$389$	1.36976e13			1.53778			0.768892	−	0.639379i	$-0.220808\pi$
$389$	1.36976e13			1.53778			0.768892	+	0.639379i	$0.220808\pi$
$390$	−2.47057e12			−0.273825
$391$		−	2.02114e13i		−	2.21163i
$392$			4.63079e12i			0.500293i
$393$		−	1.95977e12i		−	0.209046i
$394$		−	2.40579e13i		−	2.53383i
$395$	−1.62402e12			−0.168891
$396$		−	8.13720e12i		−	0.835601i
$397$			1.94529e13i			1.97257i	0.165064	+	0.986283i	$0.447217\pi$
$397$			1.94529e13i			1.97257i	−0.165064	+	0.986283i	$0.552783\pi$
$398$			2.47183e12i			0.247516i
$399$	−1.31857e13			−1.30388
$400$	2.01497e12			0.196775
$401$			8.82993e12i			0.851600i	0.904817	+	0.425800i	$0.140007\pi$
$401$			8.82993e12i			0.851600i	−0.904817	+	0.425800i	$0.859993\pi$
$402$	−5.79190e12			−0.551684
$403$	2.01630e13			1.89684
$404$		−	1.43958e13i		−	1.33760i
$405$	2.85705e11			0.0262206
$406$			1.35999e13i			1.23283i
$407$	−7.15032e12			−0.640256
$408$			7.15417e12i			0.632788i
$409$		−	1.47875e13i		−	1.29205i	−0.763317	−	0.646024i	$-0.776430\pi$
$409$		−	1.47875e13i		−	1.29205i	0.763317	−	0.646024i	$-0.223570\pi$
$410$		−	1.69719e11i		−	0.0146491i
$411$	1.96684e12			0.167710
$412$			1.89932e13i			1.59997i
$413$	−1.44487e13	+	4.79629e12i	−1.20248	+	0.399168i
$414$	1.07344e13			0.882629
$415$		−	1.97992e12i		−	0.160845i
$416$	−1.82528e13			−1.46508
$417$	8.14292e12			0.645803
$418$	−5.95333e13			−4.66529
$419$		−	4.70785e12i		−	0.364546i	−0.983248	−	0.182273i	$-0.941654\pi$
$419$		−	4.70785e12i		−	0.364546i	0.983248	−	0.182273i	$-0.0583455\pi$
$420$	−3.43055e12			−0.262493
$421$		−	1.07219e13i		−	0.810705i	−0.914160	−	0.405352i	$-0.867149\pi$
$421$		−	1.07219e13i		−	0.810705i	0.914160	−	0.405352i	$-0.132851\pi$
$422$	2.09524e12			0.156557
$423$			2.69580e12i			0.199061i
$424$		−	1.16028e12i		−	0.0846704i
$425$	1.73630e13			1.25222
$426$		−	1.49499e13i		−	1.06559i
$427$		−	1.04300e13i		−	0.734757i
$428$	2.92349e13			2.03556
$429$	1.75077e13			1.20487
$430$	−6.90837e12			−0.469930
$431$			3.83070e12i			0.257568i	0.991673	+	0.128784i	$0.0411074\pi$
$431$			3.83070e12i			0.257568i	−0.991673	+	0.128784i	$0.958893\pi$
$432$	6.03381e11			0.0401026
$433$	−1.83002e13			−1.20231			−0.601155	−	0.799132i	$-0.705293\pi$
$433$	−1.83002e13			−1.20231			−0.601155	+	0.799132i	$0.705293\pi$
$434$	4.64100e13			3.01414
$435$	−1.30061e12			−0.0835026
$436$		−	6.81576e12i		−	0.432596i
$437$		−	4.73779e13i		−	2.97282i
$438$	2.82330e13			1.75140
$439$	1.76364e12			0.108165			0.0540826	−	0.998536i	$-0.482777\pi$
$439$	1.76364e12			0.108165			0.0540826	+	0.998536i	$0.482777\pi$
$440$	−5.30285e12			−0.321548
$441$	3.36544e12			0.201766
$442$	−4.49598e13			−2.66510
$443$			1.89410e13i			1.11016i	0.831799	+	0.555078i	$0.187311\pi$
$443$			1.89410e13i			1.11016i	−0.831799	+	0.555078i	$0.812689\pi$
$444$			5.88324e12i			0.340959i
$445$		−	2.40714e12i		−	0.137944i
$446$			5.08639e13i			2.88227i
$447$		−	1.79959e13i		−	1.00841i
$448$	−3.72486e13			−2.06405
$449$	3.00893e13			1.64884			0.824422	−	0.565975i	$-0.191500\pi$
$449$	3.00893e13			1.64884			0.824422	+	0.565975i	$0.191500\pi$
$450$			9.22164e12i			0.499742i
$451$			1.20271e12i			0.0644584i
$452$		−	1.42131e12i		−	0.0753350i
$453$		−	6.16152e12i		−	0.322996i
$454$	−4.00287e12			−0.207535
$455$		−	7.38104e12i		−	0.378495i
$456$			1.67702e13i			0.850579i
$457$		−	1.19194e13i		−	0.597959i	−0.954259	−	0.298980i	$-0.903354\pi$
$457$		−	1.19194e13i		−	0.597959i	0.954259	−	0.298980i	$-0.0966463\pi$
$458$	−2.79306e12			−0.138597
$459$	5.19932e12			0.255201
$460$		−	1.23264e13i		−	0.598477i
$461$	1.70479e13			0.818781			0.409390	−	0.912359i	$-0.365741\pi$
$461$	1.70479e13			0.818781			0.409390	+	0.912359i	$0.365741\pi$
$462$	4.02981e13			1.91459
$463$		−	9.18157e12i		−	0.431531i	−0.976445	−	0.215765i	$-0.930775\pi$
$463$		−	9.18157e12i		−	0.431531i	0.976445	−	0.215765i	$-0.0692246\pi$
$464$	−2.74675e12			−0.127711
$465$			4.43836e12i			0.204154i
$466$	−1.51148e13			−0.687816
$467$			1.00375e13i			0.451901i	0.974139	+	0.225951i	$0.0725488\pi$
$467$			1.00375e13i			0.451901i	−0.974139	+	0.225951i	$0.927451\pi$
$468$		−	1.44052e13i		−	0.641638i
$469$		−	1.73038e13i		−	0.762566i
$470$	5.13138e12			0.223741
$471$			6.18469e11i			0.0266817i
$472$	6.10017e12	+	1.83766e13i	0.260395	+	0.784432i
$473$	4.89561e13			2.06777
$474$		−	1.56965e13i		−	0.656012i
$475$	4.07009e13			1.68320
$476$	−6.24298e13			−2.55480
$477$	−8.43234e11			−0.0341473
$478$		−	6.56556e13i		−	2.63107i
$479$	−7.90833e12			−0.313622			−0.156811	−	0.987629i	$-0.550121\pi$
$479$	−7.90833e12			−0.313622			−0.156811	+	0.987629i	$0.550121\pi$
$480$		−	4.01788e12i		−	0.157685i
$481$	−1.26582e13			−0.491637
$482$			3.99135e12i			0.153421i
$483$			3.20701e13i			1.22001i
$484$	6.93751e13			2.61202
$485$			9.81236e12i			0.365649i
$486$			2.76140e12i			0.101847i
$487$	−5.02388e13			−1.83398			−0.916990	−	0.398910i	$-0.869389\pi$
$487$	−5.02388e13			−1.83398			−0.916990	+	0.398910i	$0.869389\pi$
$488$	−1.32654e13			−0.479314
$489$	−1.32594e13			−0.474220
$490$		−	6.40602e12i		−	0.226781i
$491$	−2.51290e13			−0.880578			−0.440289	−	0.897856i	$-0.645124\pi$
$491$	−2.51290e13			−0.880578			−0.440289	+	0.897856i	$0.645124\pi$
$492$	9.89585e11			0.0343263
$493$	−2.36687e13			−0.812717
$494$	−1.05391e14			−3.58236
$495$			3.85386e12i			0.129679i
$496$			9.37338e12i			0.312239i
$497$	4.46642e13			1.47291
$498$	1.91364e13			0.624761
$499$	−2.88039e13			−0.930996			−0.465498	−	0.885049i	$-0.654125\pi$
$499$	−2.88039e13			−0.930996			−0.465498	+	0.885049i	$0.654125\pi$
$500$	2.18030e13			0.697695
$501$	−5.31399e12			−0.168357
$502$		−	9.04296e13i		−	2.83656i
$503$			3.68002e13i			1.14290i	0.820635	+	0.571452i	$0.193620\pi$
$503$			3.68002e13i			1.14290i	−0.820635	+	0.571452i	$0.806380\pi$
$504$		−	1.13518e13i		−	0.349069i
$505$			6.81798e12i			0.207586i
$506$			1.44796e14i			4.36521i
$507$	1.16526e13			0.347844
$508$	−4.29800e13			−1.27042
$509$		−	2.32005e13i		−	0.679059i	−0.940595	−	0.339530i	$-0.889732\pi$
$509$		−	2.32005e13i		−	0.679059i	0.940595	−	0.339530i	$-0.110268\pi$
$510$		−	9.89675e12i		−	0.286841i
$511$			8.43485e13i			2.42088i
$512$		−	1.45452e13i		−	0.413398i
$513$	1.21878e13			0.343036
$514$		−	6.62328e13i		−	1.84611i
$515$		−	8.99536e12i		−	0.248303i
$516$		−	4.02808e13i		−	1.10116i
$517$	−3.63635e13			−0.984493
$518$	−2.91358e13			−0.781228
$519$		−	2.82940e13i		−	0.751376i
$520$	−9.38758e12			−0.246909
$521$	−5.31516e13			−1.38461			−0.692305	−	0.721605i	$-0.743405\pi$
$521$	−5.31516e13			−1.38461			−0.692305	+	0.721605i	$0.743405\pi$
$522$		−	1.25707e13i		−	0.324344i
$523$	4.18890e13			1.07051			0.535256	−	0.844690i	$-0.320215\pi$
$523$	4.18890e13			1.07051			0.535256	+	0.844690i	$0.320215\pi$
$524$		−	2.17507e13i		−	0.550576i
$525$	−2.75505e13			−0.690768
$526$			6.84555e13i			1.70012i
$527$			8.07702e13i			1.98700i
$528$			8.13896e12i			0.198335i
$529$	−7.38055e13			−1.78160
$530$			1.60507e12i			0.0383809i
$531$	1.33553e13	−	4.43332e12i	0.316359	−	0.105016i
$532$	−1.46343e14			−3.43410
$533$			2.12915e12i			0.0494960i
$534$	2.32656e13			0.535805
$535$	−1.38460e13			−0.315904
$536$	−2.20079e13			−0.497455
$537$			2.91454e12i			0.0652678i
$538$	−1.04371e14			−2.31564
$539$			4.53962e13i			0.997874i
$540$	3.17093e12			0.0690587
$541$			3.34393e13i			0.721557i	0.932652	+	0.360778i	$0.117489\pi$
$541$			3.34393e13i			0.721557i	−0.932652	+	0.360778i	$0.882511\pi$
$542$			1.46467e14i			3.13144i
$543$	1.14942e13			0.243490
$544$		−	7.31181e13i		−	1.53473i
$545$			3.22802e12i			0.0671357i
$546$	7.13393e13			1.47016
$547$	2.71848e13			0.555124			0.277562	−	0.960708i	$-0.410474\pi$
$547$	2.71848e13			0.555124			0.277562	+	0.960708i	$0.410474\pi$
$548$	2.18292e13			0.441707
$549$			9.64065e12i			0.193306i
$550$	−1.24390e14			−2.47157
$551$	−5.54822e13			−1.09244
$552$	4.07884e13			0.795868
$553$	4.68948e13			0.906773
$554$			6.50573e13i			1.24666i
$555$		−	2.78637e12i		−	0.0529143i
$556$	9.03752e13			1.70089
$557$	2.55587e13			0.476720			0.238360	−	0.971177i	$-0.423390\pi$
$557$	2.55587e13			0.476720			0.238360	+	0.971177i	$0.423390\pi$
$558$	−4.28978e13			−0.792983
$559$	8.66665e13			1.58779
$560$	3.43130e12			0.0623043
$561$			7.01333e13i			1.26215i
$562$		−	8.30492e13i		−	1.48134i
$563$		−	6.99852e13i		−	1.23727i	−0.785679	−	0.618635i	$-0.787686\pi$
$563$		−	6.99852e13i		−	1.23727i	0.785679	−	0.618635i	$-0.212314\pi$
$564$			2.99197e13i			0.524277i
$565$			6.73147e11i			0.0116914i
$566$	−1.16607e14			−2.00744
$567$	−8.24994e12			−0.140778
$568$		−	5.68062e13i		−	0.960846i
$569$		−	3.54639e13i		−	0.594600i	−0.954784	−	0.297300i	$-0.903914\pi$
$569$		−	3.54639e13i		−	0.594600i	0.954784	−	0.297300i	$-0.0960861\pi$
$570$		−	2.31992e13i		−	0.385565i
$571$			3.19129e13i			0.525757i	0.964829	+	0.262879i	$0.0846719\pi$
$571$			3.19129e13i			0.525757i	−0.964829	+	0.262879i	$0.915328\pi$
$572$	1.94311e14			3.17334
$573$			1.08457e12i			0.0175584i
$574$			4.90075e12i			0.0786508i
$575$		−	9.89923e13i		−	1.57493i
$576$	3.44297e13			0.543027
$577$	7.85901e13			1.22882			0.614411	−	0.788986i	$-0.289394\pi$
$577$	7.85901e13			1.22882			0.614411	+	0.788986i	$0.289394\pi$
$578$		−	7.76813e13i		−	1.20414i
$579$	−2.10595e13			−0.323635
$580$	−1.44349e13			−0.219925
$581$			5.71717e13i			0.863576i
$582$	−9.48386e13			−1.42027
$583$		−	1.13743e13i		−	0.168882i
$584$	1.07279e14			1.57924
$585$			6.82245e12i			0.0995775i
$586$			6.48049e13i			0.937820i
$587$			3.43134e13i			0.492349i	0.969226	+	0.246174i	$0.0791736\pi$
$587$			3.43134e13i			0.492349i	−0.969226	+	0.246174i	$0.920826\pi$
$588$	3.73517e13			0.531403
$589$			1.89335e14i			2.67088i
$590$	−8.43869e12	−	2.54213e13i	−0.118036	−	0.355581i
$591$	−6.64358e13			−0.921435
$592$		−	5.88452e12i		−	0.0809287i
$593$	−3.65885e13			−0.498967			−0.249483	−	0.968379i	$-0.580261\pi$
$593$	−3.65885e13			−0.498967			−0.249483	+	0.968379i	$0.580261\pi$
$594$	−3.72484e13			−0.503704
$595$	2.95674e13			0.396486
$596$		−	1.99730e14i		−	2.65590i
$597$	6.82595e12			0.0900101
$598$			2.56331e14i			3.35194i
$599$	1.08094e14			1.40174			0.700870	−	0.713289i	$-0.252795\pi$
$599$	1.08094e14			1.40174			0.700870	+	0.713289i	$0.252795\pi$
$600$			3.50401e13i			0.450618i
$601$		−	1.29552e14i		−	1.65223i	−0.563499	−	0.826117i	$-0.690545\pi$
$601$		−	1.29552e14i		−	1.65223i	0.563499	−	0.826117i	$-0.309455\pi$
$602$	1.99484e14			2.52305
$603$			1.59943e13i			0.200622i
$604$		−	6.83843e13i		−	0.850691i
$605$	−3.28568e13			−0.405367
$606$	−6.58973e13			−0.806314
$607$	−8.69381e13			−1.05503			−0.527517	−	0.849544i	$-0.676877\pi$
$607$	−8.69381e13			−1.05503			−0.527517	+	0.849544i	$0.676877\pi$
$608$		−	1.71398e14i		−	2.06294i
$609$	3.75559e13			0.448324
$610$	1.83507e13			0.217272
$611$	−6.43739e13			−0.755969
$612$	5.77052e13			0.672137
$613$			1.13794e14i			1.31467i	0.753598	+	0.657336i	$0.228317\pi$
$613$			1.13794e14i			1.31467i	−0.753598	+	0.657336i	$0.771683\pi$
$614$		−	1.87591e14i		−	2.14966i
$615$	−4.68678e11			−0.00532720
$616$	1.53123e14			1.72639
$617$	−2.54094e13			−0.284163			−0.142082	−	0.989855i	$-0.545380\pi$
$617$	−2.54094e13			−0.284163			−0.142082	+	0.989855i	$0.545380\pi$
$618$	8.69421e13			0.964468
$619$	1.45010e14			1.59567			0.797837	−	0.602873i	$-0.205977\pi$
$619$	1.45010e14			1.59567			0.797837	+	0.602873i	$0.205977\pi$
$620$			4.92597e13i			0.537692i
$621$		−	2.96431e13i		−	0.320971i
$622$		−	1.47303e13i		−	0.158219i
$623$			6.95079e13i			0.740617i
$624$			1.44083e13i			0.152297i
$625$	7.97304e13			0.836034
$626$	6.65964e13			0.692754
$627$			1.64401e14i			1.69655i
$628$			6.86415e12i			0.0702730i
$629$		−	5.07068e13i		−	0.515007i
$630$			1.57035e13i			0.158232i
$631$	9.63252e13			0.962927			0.481463	−	0.876466i	$-0.340105\pi$
$631$	9.63252e13			0.962927			0.481463	+	0.876466i	$0.340105\pi$
$632$		−	5.96432e13i		−	0.591528i
$633$		−	5.78600e12i		−	0.0569325i
$634$			1.03321e13i			0.100865i
$635$	2.03558e13			0.197160
$636$	−9.35873e12			−0.0899355
$637$			8.03644e13i			0.766243i
$638$	1.69565e14			1.60410
$639$	−4.12841e13			−0.387506
$640$		−	3.62101e13i		−	0.337233i
$641$	9.08204e13			0.839253			0.419627	−	0.907697i	$-0.362161\pi$
$641$	9.08204e13			0.839253			0.419627	+	0.907697i	$0.362161\pi$
$642$		−	1.33824e14i		−	1.22704i
$643$	5.76101e13			0.524136			0.262068	−	0.965049i	$-0.415596\pi$
$643$	5.76101e13			0.524136			0.262068	+	0.965049i	$0.415596\pi$
$644$			3.55934e14i			3.21322i
$645$			1.90774e13i			0.170892i
$646$		−	4.22182e14i		−	3.75265i
$647$	6.00411e13			0.529575			0.264788	−	0.964307i	$-0.414698\pi$
$647$	6.00411e13			0.529575			0.264788	+	0.964307i	$0.414698\pi$
$648$			1.04927e13i			0.0918358i
$649$	5.98007e13	+	1.80148e14i	0.519377	+	1.56461i
$650$	−2.20207e14			−1.89786
$651$		−	1.28161e14i		−	1.09610i
$652$	−1.47161e14			−1.24898
$653$	1.80413e14			1.51950			0.759751	−	0.650215i	$-0.225321\pi$
$653$	1.80413e14			1.51950			0.759751	+	0.650215i	$0.225321\pi$
$654$	−3.11995e13			−0.260771
$655$			1.03014e13i			0.0854454i
$656$	−9.89800e11			−0.00814757
$657$		−	7.79651e13i		−	0.636903i
$658$	−1.48172e14			−1.20126
$659$		−	2.13417e14i		−	1.71712i	−0.512709	−	0.858562i	$-0.671358\pi$
$659$		−	2.13417e14i		−	1.71712i	0.512709	−	0.858562i	$-0.328642\pi$
$660$			4.27725e13i			0.341543i
$661$	−1.04672e14			−0.829510			−0.414755	−	0.909933i	$-0.636133\pi$
$661$	−1.04672e14			−0.829510			−0.414755	+	0.909933i	$0.636133\pi$
$662$			2.20848e14i			1.73701i
$663$			1.24156e14i			0.969172i
$664$	7.27139e13			0.563348
$665$	6.93095e13			0.532948
$666$	2.69308e13			0.205532
$667$			1.34943e14i			1.02217i
$668$	−5.89780e13			−0.443412
$669$	1.40460e14			1.04815
$670$	3.04446e13			0.225495
$671$	−1.30042e14			−0.956030
$672$			1.16019e14i			0.846610i
$673$			3.77116e13i			0.273149i	0.990630	+	0.136574i	$0.0436093\pi$
$673$			3.77116e13i			0.273149i	−0.990630	+	0.136574i	$0.956391\pi$
$674$	8.14025e13			0.585245
$675$	2.54655e13			0.181733
$676$	1.29328e14			0.916135
$677$	−1.41601e14			−0.995687			−0.497844	−	0.867267i	$-0.665875\pi$
$677$	−1.41601e14			−0.995687			−0.497844	+	0.867267i	$0.665875\pi$
$678$	−6.50611e12			−0.0454123
$679$		−	2.83339e14i		−	1.96317i
$680$		−	3.76053e13i		−	0.258645i
$681$			1.10539e13i			0.0754709i
$682$		−	5.78645e14i		−	3.92185i
$683$		−	2.66011e11i		−	0.00178977i	−1.00000		0.000894883i	$-0.999715\pi$
$683$		−	2.66011e11i		−	0.00178977i	1.00000		0.000894883i	$-0.000284850\pi$
$684$	1.35268e14			0.903471
$685$	−1.03385e13			−0.0685498
$686$		−	1.20620e14i		−	0.793959i
$687$			7.71302e12i			0.0504012i
$688$			4.02895e13i			0.261367i
$689$		−	2.01359e13i		−	0.129680i
$690$	−5.64248e13			−0.360765
$691$			1.09596e14i			0.695672i	0.937555	+	0.347836i	$0.113083\pi$
$691$			1.09596e14i			0.695672i	−0.937555	+	0.347836i	$0.886917\pi$
$692$		−	3.14024e14i		−	1.97894i
$693$		−	1.11283e14i		−	0.696245i
$694$	−1.18501e14			−0.736077
$695$	−4.28026e13			−0.263965
$696$		−	4.77656e13i		−	0.292461i
$697$	−8.52908e12			−0.0518488
$698$	9.39664e13			0.567147
$699$			4.17394e13i			0.250127i
$700$	−3.05772e14			−1.81931
$701$		−	1.21445e14i		−	0.717444i	−0.933444	−	0.358722i	$-0.883213\pi$
$701$		−	1.21445e14i		−	0.717444i	0.933444	−	0.358722i	$-0.116787\pi$
$702$	−6.59405e13			−0.386782
$703$		−	1.18863e14i		−	0.692260i
$704$			4.64420e14i			2.68564i
$705$		−	1.41703e13i		−	0.0813640i
$706$	4.15171e14			2.36703
$707$		−	1.96874e14i		−	1.11453i
$708$	1.48225e14	−	4.92037e13i	0.833210	−	0.276587i
$709$	3.72063e13			0.207676			0.103838	−	0.994594i	$-0.466888\pi$
$709$	3.72063e13			0.207676			0.103838	+	0.994594i	$0.466888\pi$
$710$			7.85830e13i			0.435549i
$711$	−4.33458e13			−0.238561
$712$	8.84037e13			0.483137
$713$	4.60499e14			2.49908
$714$			2.85775e14i			1.54005i
$715$	−9.20276e13			−0.492479
$716$			3.23474e13i			0.171899i
$717$	−1.81307e14			−0.956797
$718$			5.61487e14i			2.94251i
$719$			1.17385e14i			0.610899i	0.952208	+	0.305449i	$0.0988067\pi$
$719$			1.17385e14i			0.610899i	−0.952208	+	0.305449i	$0.901193\pi$
$720$	−3.17162e12			−0.0163915
$721$			2.59747e14i			1.33314i
$722$		−	6.78160e14i		−	3.45658i
$723$	1.10221e13			0.0557921
$724$	1.27570e14			0.641292
$725$	−1.15926e14			−0.578748
$726$		−	3.17568e14i		−	1.57454i
$727$	−2.78503e14			−1.37138			−0.685689	−	0.727894i	$-0.740499\pi$
$727$	−2.78503e14			−1.37138			−0.685689	+	0.727894i	$0.740499\pi$
$728$	2.71073e14			1.32565
$729$	7.62560e12			0.0370370
$730$	−1.48404e14			−0.715867
$731$			3.47174e14i			1.66326i
$732$			1.06998e14i			0.509119i
$733$	−1.01510e14			−0.479720			−0.239860	−	0.970807i	$-0.577102\pi$
$733$	−1.01510e14			−0.479720			−0.239860	+	0.970807i	$0.577102\pi$
$734$	−7.31155e13			−0.343186
$735$	−1.76902e13			−0.0824698
$736$	−4.16872e14			−1.93025
$737$	−2.15746e14			−0.992213
$738$		−	4.52987e12i		−	0.0206921i
$739$		−	2.86584e14i		−	1.30026i	−0.759824	−	0.650129i	$-0.774715\pi$
$739$		−	2.86584e14i		−	1.30026i	0.759824	−	0.650129i	$-0.225285\pi$
$740$		−	3.09248e13i		−	0.139363i
$741$			2.91037e14i			1.30274i
$742$		−	4.63475e13i		−	0.206066i
$743$	−7.90605e13			−0.349153			−0.174576	−	0.984644i	$-0.555856\pi$
$743$	−7.90605e13			−0.349153			−0.174576	+	0.984644i	$0.555856\pi$
$744$	−1.63002e14			−0.715035
$745$			9.45941e13i			0.412176i
$746$		−	4.01279e14i		−	1.73681i
$747$		−	5.28450e13i		−	0.227196i
$748$			7.78382e14i			3.32418i
$749$	3.99812e14			1.69608
$750$		−	9.98042e13i		−	0.420574i
$751$			3.25139e13i			0.136104i	0.997682	+	0.0680518i	$0.0216783\pi$
$751$			3.25139e13i			0.136104i	−0.997682	+	0.0680518i	$0.978322\pi$
$752$		−	2.99262e13i		−	0.124440i
$753$	−2.49721e14			−1.03153
$754$	3.00179e14			1.23175
$755$			3.23875e13i			0.132021i
$756$	−9.15629e13			−0.370775
$757$	6.85566e13			0.275785			0.137892	−	0.990447i	$-0.455967\pi$
$757$	6.85566e13			0.275785			0.137892	+	0.990447i	$0.455967\pi$
$758$		−	7.21096e13i		−	0.288169i
$759$	3.99854e14			1.58742
$760$		−	8.81514e13i		−	0.347665i
$761$	−2.11057e14			−0.826947			−0.413473	−	0.910516i	$-0.635684\pi$
$761$	−2.11057e14			−0.826947			−0.413473	+	0.910516i	$0.635684\pi$
$762$			1.96743e14i			0.765816i
$763$		−	9.32112e13i		−	0.360451i
$764$			1.20372e13i			0.0462445i
$765$	−2.73298e13			−0.104311
$766$			6.74341e14i			2.55703i
$767$	1.05865e14	+	3.18915e14i	0.398817	+	1.20143i
$768$	9.86810e13			0.369341
$769$			1.83509e14i			0.682380i	0.939994	+	0.341190i	$0.110830\pi$
$769$			1.83509e14i			0.682380i	−0.939994	+	0.341190i	$0.889170\pi$
$770$	−2.11824e14			−0.782566
$771$	−1.82901e14			−0.671344
$772$	−2.33732e14			−0.852376
$773$		−	2.04840e14i		−	0.742195i	−0.928594	−	0.371098i	$-0.878982\pi$
$773$		−	2.04840e14i		−	0.742195i	0.928594	−	0.371098i	$-0.121018\pi$
$774$	−1.84387e14			−0.663783
$775$			3.95600e14i			1.41497i
$776$	−3.60365e14			−1.28066
$777$			8.04582e13i			0.284096i
$778$		−	6.95897e14i		−	2.44145i
$779$	−1.99932e13			−0.0696939
$780$			7.57198e13i			0.262263i
$781$		−	5.56878e14i		−	1.91648i
$782$	−1.02683e15			−3.51127
$783$	−3.47138e13			−0.117949
$784$	−3.73598e13			−0.126132
$785$		−	3.25094e12i		−	0.0109059i
$786$	−9.95650e13			−0.331890
$787$	−4.53085e13			−0.150074			−0.0750371	−	0.997181i	$-0.523908\pi$
$787$	−4.53085e13			−0.150074			−0.0750371	+	0.997181i	$0.523908\pi$
$788$	−7.37345e14			−2.42683
$789$	1.89039e14			0.618255
$790$			8.25075e13i			0.268138i
$791$		−	1.94376e13i		−	0.0627711i
$792$	−1.41535e14			−0.454191
$793$	−2.30212e14			−0.734113
$794$	9.88293e14			3.13172
$795$	4.43239e12			0.0139573
$796$	7.57586e13			0.237065
$797$			1.27648e14i			0.396938i	0.980107	+	0.198469i	$0.0635969\pi$
$797$			1.27648e14i			0.396938i	−0.980107	+	0.198469i	$0.936403\pi$
$798$			6.69892e14i			2.07009i
$799$		−	2.57873e14i		−	0.791903i
$800$		−	3.58122e14i		−	1.09290i
$801$		−	6.42476e13i		−	0.194847i
$802$	4.48600e14			1.35203
$803$	1.05167e15			3.14993
$804$			1.77514e14i			0.528388i
$805$		−	1.68574e14i		−	0.498668i
$806$		−	1.02437e15i		−	3.01149i
$807$			2.88221e14i			0.842089i
$808$	−2.50394e14			−0.727055
$809$			4.74878e13i			0.137038i	0.997650	+	0.0685188i	$0.0218273\pi$
$809$			4.74878e13i			0.137038i	−0.997650	+	0.0685188i	$0.978173\pi$
$810$		−	1.45151e13i		−	0.0416289i
$811$		−	5.33789e14i		−	1.52148i	−0.649058	−	0.760739i	$-0.724837\pi$
$811$		−	5.33789e14i		−	1.52148i	0.649058	−	0.760739i	$-0.275163\pi$
$812$	4.16819e14			1.18078
$813$	4.04469e14			1.13876
$814$			3.63268e14i			1.01650i
$815$	6.96971e13			0.193832
$816$	−5.77177e13			−0.159536
$817$			8.13817e14i			2.23572i
$818$	−7.51272e14			−2.05131
$819$		−	1.97003e14i		−	0.534630i
$820$	−5.20167e12			−0.0140305
$821$		−	2.91170e14i		−	0.780605i	−0.920687	−	0.390303i	$-0.872370\pi$
$821$		−	2.91170e14i		−	0.780605i	0.920687	−	0.390303i	$-0.127630\pi$
$822$		−	9.99242e13i		−	0.266263i
$823$			5.99064e14i			1.58662i	0.608816	+	0.793312i	$0.291645\pi$
$823$			5.99064e14i			1.58662i	−0.608816	+	0.793312i	$0.708355\pi$
$824$	3.30360e14			0.869663
$825$			3.43502e14i			0.898793i
$826$	2.43673e14	+	7.34059e14i	0.633734	+	1.90911i
$827$	4.00222e14			1.03460			0.517301	−	0.855804i	$-0.326937\pi$
$827$	4.00222e14			1.03460			0.517301	+	0.855804i	$0.326937\pi$
$828$		−	3.28997e14i		−	0.845358i
$829$	4.97802e13			0.127140			0.0635702	−	0.997977i	$-0.479751\pi$
$829$	4.97802e13			0.127140			0.0635702	+	0.997977i	$0.479751\pi$
$830$	−1.00589e14			−0.255364
$831$	1.79655e14			0.453351
$832$			8.22159e14i			2.06224i
$833$	−3.21929e14			−0.802666
$834$		−	4.13697e14i		−	1.02530i
$835$	2.79326e13			0.0688143
$836$			1.82462e15i			4.46829i
$837$			1.18462e14i			0.288371i
$838$	−2.39180e14			−0.578768
$839$		−	6.03524e14i		−	1.45173i	−0.687839	−	0.725863i	$-0.741441\pi$
$839$		−	6.03524e14i		−	1.45173i	0.687839	−	0.725863i	$-0.258559\pi$
$840$			5.96697e13i			0.142678i
$841$	−2.62681e14			−0.624379
$842$	−5.44722e14			−1.28711
$843$	−2.29340e14			−0.538693
$844$		−	6.42166e13i		−	0.149946i
$845$	−6.12512e13			−0.142177
$846$	1.36959e14			0.316037
$847$	9.48763e14			2.17641
$848$	9.36076e12			0.0213468
$849$			3.22009e14i			0.730010i
$850$		−	8.82117e14i		−	1.98807i
$851$	−2.89097e14			−0.647732
$852$	−4.58196e14			−1.02059
$853$	7.32799e14			1.62271			0.811353	−	0.584556i	$-0.198731\pi$
$853$	7.32799e14			1.62271			0.811353	+	0.584556i	$0.198731\pi$
$854$	−5.29889e14			−1.16653
$855$	−6.40643e13			−0.140212
$856$		−	5.08502e14i		−	1.10643i
$857$			3.98818e14i			0.862721i	0.902180	+	0.431361i	$0.141966\pi$
$857$			3.98818e14i			0.862721i	−0.902180	+	0.431361i	$0.858034\pi$
$858$		−	8.89467e14i		−	1.91291i
$859$		−	1.07606e13i		−	0.0230076i	−0.999934	−	0.0115038i	$-0.996338\pi$
$859$		−	1.07606e13i		−	0.0230076i	0.999934	−	0.0115038i	$-0.00366185\pi$
$860$			2.11733e14i			0.450086i
$861$	1.35334e13			0.0286016
$862$	1.94617e14			0.408925
$863$			3.48855e14i			0.728771i	0.931248	+	0.364385i	$0.118721\pi$
$863$			3.48855e14i			0.728771i	−0.931248	+	0.364385i	$0.881279\pi$
$864$		−	1.07239e14i		−	0.222733i
$865$			1.48725e14i			0.307117i
$866$			9.29732e14i			1.90884i
$867$	−2.14516e14			−0.437890
$868$		−	1.42241e15i		−	2.88686i
$869$		−	5.84689e14i		−	1.17985i
$870$			6.60766e13i			0.132572i
$871$	−3.81933e14			−0.761897
$872$	−1.18551e14			−0.235138
$873$			2.61896e14i			0.516485i
$874$	−2.40701e15			−4.71976
$875$	2.98174e14			0.581339
$876$		−	8.65305e14i		−	1.67745i
$877$	−7.01394e14			−1.35196			−0.675980	−	0.736920i	$-0.736280\pi$
$877$	−7.01394e14			−1.35196			−0.675980	+	0.736920i	$0.736280\pi$
$878$		−	8.96008e13i		−	0.171727i
$879$	1.78958e14			0.341042
$880$		−	4.27818e13i		−	0.0810673i
$881$		−	6.13603e14i		−	1.15613i	−0.815989	−	0.578067i	$-0.803807\pi$
$881$		−	6.13603e14i		−	1.15613i	0.815989	−	0.578067i	$-0.196193\pi$
$882$		−	1.70979e14i		−	0.320332i
$883$	−4.93933e14			−0.920162			−0.460081	−	0.887877i	$-0.652180\pi$
$883$	−4.93933e14			−0.920162			−0.460081	+	0.887877i	$0.652180\pi$
$884$			1.37796e15i			2.55256i
$885$	−7.02008e13	+	2.33034e13i	−0.129308	+	0.0429242i
$886$	9.62286e14			1.76253
$887$			6.08262e14i			1.10783i	0.832574	+	0.553914i	$0.186866\pi$
$887$			6.08262e14i			1.10783i	−0.832574	+	0.553914i	$0.813134\pi$
$888$	1.02331e14			0.185328
$889$	−5.87787e14			−1.05855
$890$	−1.22294e14			−0.219005
$891$			1.02861e14i			0.183174i
$892$	1.55891e15			2.76056
$893$		−	6.04485e14i		−	1.06446i
$894$	−9.14273e14			−1.60099
$895$		−	1.53201e13i		−	0.0266775i
$896$			1.04559e15i			1.81060i
$897$	7.07857e14			1.21894
$898$		−	1.52867e15i		−	2.61777i
$899$		−	5.39270e14i		−	0.918349i
$900$	2.82632e14			0.478639
$901$	8.06614e13			0.135844
$902$	6.11032e13			0.102337
$903$		−	5.50873e14i		−	0.917515i
$904$	−2.47217e13			−0.0409484
$905$	−6.04185e13			−0.0995238
$906$	−3.13033e14			−0.512801
$907$	8.24849e14			1.34381			0.671905	−	0.740637i	$-0.265476\pi$
$907$	8.24849e14			1.34381			0.671905	+	0.740637i	$0.265476\pi$
$908$			1.22683e14i			0.198772i
$909$			1.81975e14i			0.293219i
$910$	−3.74990e14			−0.600914
$911$	−5.93367e14			−0.945652			−0.472826	−	0.881156i	$-0.656766\pi$
$911$	−5.93367e14			−0.945652			−0.472826	+	0.881156i	$0.656766\pi$
$912$	−1.35297e14			−0.214444
$913$	7.12823e14			1.12364
$914$	−6.05556e14			−0.949344
$915$		−	5.06753e13i		−	0.0790116i
$916$			8.56039e13i			0.132744i
$917$		−	2.97459e14i		−	0.458755i
$918$		−	2.64148e14i		−	0.405168i
$919$		−	6.41323e14i		−	0.978361i	−0.872183	−	0.489180i	$-0.837296\pi$
$919$		−	6.41323e14i		−	0.978361i	0.872183	−	0.489180i	$-0.162704\pi$
$920$	−2.14401e14			−0.325303
$921$	−5.18031e14			−0.781732
$922$		−	8.66112e14i		−	1.29993i
$923$		−	9.85836e14i		−	1.47162i
$924$		−	1.23509e15i		−	1.83374i
$925$		−	2.48354e14i		−	0.366744i
$926$	−4.66464e14			−0.685115
$927$		−	2.40090e14i		−	0.350732i
$928$			4.88181e14i			0.709318i
$929$		−	1.13270e15i		−	1.63695i	−0.574541	−	0.818475i	$-0.694820\pi$
$929$		−	1.13270e15i		−	1.63695i	0.574541	−	0.818475i	$-0.305180\pi$
$930$	2.25489e14			0.324123
$931$	−7.54639e14			−1.07892
$932$			4.63249e14i			0.658772i
$933$	−4.06775e13			−0.0575369
$934$	5.09952e14			0.717456
$935$		−	3.68650e14i		−	0.515889i
$936$	−2.50559e14			−0.348763
$937$			1.27114e15i			1.75993i	0.475038	+	0.879965i	$0.342434\pi$
$937$			1.27114e15i			1.75993i	−0.475038	+	0.879965i	$0.657566\pi$
$938$	−8.79110e14			−1.21068
$939$		−	1.83906e14i		−	0.251922i
$940$		−	1.57270e14i		−	0.214293i
$941$		−	1.14106e15i		−	1.54654i	−0.634078	−	0.773269i	$-0.718620\pi$
$941$		−	1.14106e15i		−	1.54654i	0.634078	−	0.773269i	$-0.281380\pi$
$942$	3.14210e13			0.0423609
$943$			4.86272e13i			0.0652110i
$944$	−1.48257e14	+	4.92144e13i	−0.197768	+	0.0656496i
$945$	4.33652e13			0.0575416
$946$		−	2.48719e15i		−	3.28287i
$947$	1.75091e14			0.229887			0.114943	−	0.993372i	$-0.463331\pi$
$947$	1.75091e14			0.229887			0.114943	+	0.993372i	$0.463331\pi$
$948$	−4.81079e14			−0.628311
$949$	1.86175e15			2.41875
$950$		−	2.06779e15i		−	2.67232i
$951$	2.85320e13			0.0366800
$952$			1.08588e15i			1.38866i
$953$	−4.72824e14			−0.601499			−0.300749	−	0.953703i	$-0.597237\pi$
$953$	−4.72824e14			−0.601499			−0.300749	+	0.953703i	$0.597237\pi$
$954$			4.28400e13i			0.0542135i
$955$		−	5.70097e12i		−	0.00717681i
$956$	−2.01226e15			−2.51997
$957$		−	4.68252e14i		−	0.583337i
$958$			4.01778e14i			0.497919i
$959$	2.98532e14			0.368043
$960$	−1.80977e14			−0.221956
$961$	−1.02065e15			−1.24526
$962$			6.43090e14i			0.780543i
$963$	−3.69555e14			−0.446219
$964$	1.22330e14			0.146943
$965$	1.10698e14			0.132282
$966$	1.62930e15			1.93694
$967$			3.35107e14i			0.396325i	0.980169	+	0.198162i	$0.0634974\pi$
$967$			3.35107e14i			0.396325i	−0.980169	+	0.198162i	$0.936503\pi$
$968$		−	1.20669e15i		−	1.41977i
$969$	−1.16585e15			−1.36466
$970$	4.98512e14			0.580519
$971$	−4.68900e14			−0.543231			−0.271615	−	0.962406i	$-0.587558\pi$
$971$	−4.68900e14			−0.543231			−0.271615	+	0.962406i	$0.587558\pi$
$972$	8.46336e13			0.0975464
$973$	1.23596e15			1.41722
$974$			2.55236e15i			2.91170i
$975$			6.08099e14i			0.690162i
$976$		−	1.07021e14i		−	0.120843i
$977$			5.59819e13i			0.0628891i	0.999505	+	0.0314445i	$0.0100108\pi$
$977$			5.59819e13i			0.0628891i	−0.999505	+	0.0314445i	$0.989989\pi$
$978$			6.73638e14i			0.752891i
$979$	8.66633e14			0.963655
$980$	−1.96336e14			−0.217205
$981$			8.61572e13i			0.0948301i
$982$			1.27666e15i			1.39804i
$983$			1.52718e15i			1.66388i	0.554864	+	0.831941i	$0.312770\pi$
$983$			1.52718e15i			1.66388i	−0.554864	+	0.831941i	$0.687230\pi$
$984$		−	1.72125e13i		−	0.0186581i
$985$	3.49214e14			0.376627
$986$			1.20247e15i			1.29030i
$987$			4.09176e14i			0.436842i
$988$			3.23011e15i			3.43109i
$989$	1.97936e15			2.09191
$990$	1.95793e14			0.205884
$991$			1.00761e15i			1.05420i	0.849802	+	0.527102i	$0.176721\pi$
$991$			1.00761e15i			1.05420i	−0.849802	+	0.527102i	$0.823279\pi$
$992$	1.66593e15			1.73420
$993$	6.09869e14			0.631670
$994$		−	2.26914e15i		−	2.33846i
$995$	−3.58801e13			−0.0367907
$996$		−	5.86507e14i		−	0.598379i
$997$	1.67544e15			1.70080			0.850399	−	0.526138i	$-0.176361\pi$
$997$	1.67544e15			1.70080			0.850399	+	0.526138i	$0.176361\pi$
$998$			1.46336e15i			1.47809i
$999$		−	7.43693e13i		−	0.0747423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.14	✓	100
59.58	odd	2	inner	177.11.c.a.58.87	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.14	✓	100	1.1	even	1	trivial
177.11.c.a.58.87	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)

\(f(q)\)	\(=\)	\(q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} -37466.0i q^{10} +265503. i q^{11} +218454. q^{12} +470017. i q^{13} +1.08186e6i q^{14} -103462. q^{15} -218501. q^{16} -1.88282e6 q^{17} -999984. i q^{18} -4.41356e6 q^{19} -1.14829e6 q^{20} +2.98754e6 q^{21} +1.34887e7 q^{22} +1.07346e7i q^{23} -3.79971e6i q^{24} -9.22178e6 q^{25} +2.38790e7 q^{26} -2.76145e6 q^{27} +3.31576e7 q^{28} +1.25709e7 q^{29} +5.25634e6i q^{30} -4.28985e7i q^{31} +3.88343e7i q^{32} -3.72490e7i q^{33} +9.56558e7i q^{34} -1.57038e7 q^{35} -3.06483e7 q^{36} +2.69313e7i q^{37} +2.24228e8i q^{38} -6.59416e7i q^{39} +1.99729e7i q^{40} +4.52994e6 q^{41} -1.51780e8i q^{42} -1.84390e8i q^{43} -4.13412e8i q^{44} +1.45153e7 q^{45} +5.45366e8 q^{46} +1.36961e8i q^{47} +3.06549e7 q^{48} +1.70982e8 q^{49} +4.68508e8i q^{50} +2.64153e8 q^{51} -7.31860e8i q^{52} -4.28407e7 q^{53} +1.40294e8i q^{54} +1.95796e8i q^{55} -5.76730e8i q^{56} +6.19205e8 q^{57} -6.38655e8i q^{58} +(6.78517e8 - 2.25236e8i) q^{59} +1.61100e8 q^{60} +4.89796e8i q^{61} -2.17943e9 q^{62} -4.19140e8 q^{63} +1.74921e9 q^{64} +3.46617e8i q^{65} -1.89242e9 q^{66} +8.12593e8i q^{67} +2.93173e9 q^{68} -1.50603e9i q^{69} +7.97821e8i q^{70} -2.09745e9 q^{71} +5.33084e8i q^{72} -3.96104e9i q^{73} +1.36823e9 q^{74} +1.29378e9 q^{75} +6.87232e9 q^{76} -5.65376e9i q^{77} -3.35012e9 q^{78} -2.20220e9 q^{79} -1.61135e8 q^{80} +3.87420e8 q^{81} -2.30141e8i q^{82} -2.68481e9i q^{83} -4.65188e9 q^{84} -1.38850e9 q^{85} -9.36785e9 q^{86} -1.76364e9 q^{87} -7.19074e9 q^{88} -3.26412e9i q^{89} -7.37444e8i q^{90} -1.00088e10i q^{91} -1.67148e10i q^{92} +6.01849e9i q^{93} +6.95822e9 q^{94} -3.25480e9 q^{95} -5.44831e9i q^{96} +1.33057e10i q^{97} -8.68665e9i q^{98} +5.22589e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

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Database

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