LMFDB - Embedded newform 177.11.c.a.58.88

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			58.88
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} +7140.06i q^{6} -26451.4 q^{7} -27587.7i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} +7140.06i q^{6} -26451.4 q^{7} -27587.7i q^{8} +19683.0 q^{9} +107235. i q^{10} +141491. i q^{11} -219714. q^{12} +258539. i q^{13} -1.34619e6i q^{14} +295614. q^{15} -199646. q^{16} +600229. q^{17} +1.00172e6i q^{18} -43051.6 q^{19} -3.29983e6 q^{20} -3.71103e6 q^{21} -7.20088e6 q^{22} +1.84919e6i q^{23} -3.87045e6i q^{24} -5.32588e6 q^{25} -1.31578e7 q^{26} +2.76145e6 q^{27} +4.14249e7 q^{28} +3.28651e6 q^{29} +1.50446e7i q^{30} +6.86797e6i q^{31} -3.84104e7i q^{32} +1.98507e7i q^{33} +3.05473e7i q^{34} -5.57350e7 q^{35} -3.08250e7 q^{36} +3.37758e7i q^{37} -2.19102e6i q^{38} +3.62720e7i q^{39} -5.81292e7i q^{40} -1.94974e8 q^{41} -1.88865e8i q^{42} +7.75843e7i q^{43} -2.21586e8i q^{44} +4.14735e7 q^{45} -9.41104e7 q^{46} -1.56607e8i q^{47} -2.80096e7 q^{48} +4.17203e8 q^{49} -2.71049e8i q^{50} +8.42097e7 q^{51} -4.04891e8i q^{52} -1.74257e8 q^{53} +1.40538e8i q^{54} +2.98132e8i q^{55} +7.29734e8i q^{56} -6.03998e6 q^{57} +1.67260e8i q^{58} +(6.14004e8 + 3.66219e8i) q^{59} -4.62953e8 q^{60} +1.60873e8i q^{61} -3.49530e8 q^{62} -5.20644e8 q^{63} +1.75037e9 q^{64} +5.44760e8i q^{65} -1.01026e9 q^{66} -1.29604e9i q^{67} -9.40003e8 q^{68} +2.59434e8i q^{69} -2.83651e9i q^{70} -1.68138e9 q^{71} -5.43009e8i q^{72} -3.06702e9i q^{73} -1.71895e9 q^{74} -7.47200e8 q^{75} +6.74221e7 q^{76} -3.74264e9i q^{77} -1.84598e9 q^{78} +1.15229e9 q^{79} -4.20669e8 q^{80} +3.87420e8 q^{81} -9.92277e9i q^{82} -7.52537e9i q^{83} +5.81176e9 q^{84} +1.26472e9 q^{85} -3.94848e9 q^{86} +4.61085e8 q^{87} +3.90341e9 q^{88} -5.42130e9i q^{89} +2.11070e9i q^{90} -6.83873e9i q^{91} -2.89597e9i q^{92} +9.63549e8i q^{93} +7.97019e9 q^{94} -9.07128e7 q^{95} -5.38882e9i q^{96} +3.52047e9i q^{97} +2.12326e10i q^{98} +2.78497e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			50.8928i			1.59040i	0.606348	+	0.795200i	$0.292634\pi$
$2$			50.8928i			1.59040i	−0.606348	+	0.795200i	$0.707366\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−1566.07			−1.52937
$5$	2107.07			0.674262			0.337131	−	0.941458i	$-0.390543\pi$
$5$	2107.07			0.674262			0.337131	+	0.941458i	$0.390543\pi$
$6$			7140.06i			0.918217i
$7$	−26451.4			−1.57383			−0.786917	−	0.617059i	$-0.788324\pi$
$7$	−26451.4			−1.57383			−0.786917	+	0.617059i	$0.788324\pi$
$8$		−	27587.7i		−	0.841910i
$9$	19683.0			0.333333
$10$			107235.i			1.07235i
$11$			141491.i			0.878549i	0.898353	+	0.439274i	$0.144764\pi$
$11$			141491.i			0.878549i	−0.898353	+	0.439274i	$0.855236\pi$
$12$	−219714.			−0.882982
$13$			258539.i			0.696320i	0.937435	+	0.348160i	$0.113193\pi$
$13$			258539.i			0.696320i	−0.937435	+	0.348160i	$0.886807\pi$
$14$		−	1.34619e6i		−	2.50303i
$15$	295614.			0.389286
$16$	−199646.			−0.190398
$17$	600229.			0.422739			0.211369	−	0.977406i	$-0.432208\pi$
$17$	600229.			0.422739			0.211369	+	0.977406i	$0.432208\pi$
$18$			1.00172e6i			0.530133i
$19$	−43051.6			−0.0173869			−0.00869344	−	0.999962i	$-0.502767\pi$
$19$	−43051.6			−0.0173869			−0.00869344	+	0.999962i	$0.502767\pi$
$20$	−3.29983e6			−1.03120
$21$	−3.71103e6			−0.908654
$22$	−7.20088e6			−1.39724
$23$			1.84919e6i			0.287304i	0.989628	+	0.143652i	$0.0458846\pi$
$23$			1.84919e6i			0.287304i	−0.989628	+	0.143652i	$0.954115\pi$
$24$		−	3.87045e6i		−	0.486077i
$25$	−5.32588e6			−0.545370
$26$	−1.31578e7			−1.10743
$27$	2.76145e6			0.192450
$28$	4.14249e7			2.40698
$29$	3.28651e6			0.160231			0.0801153	−	0.996786i	$-0.474471\pi$
$29$	3.28651e6			0.160231			0.0801153	+	0.996786i	$0.474471\pi$
$30$			1.50446e7i			0.619120i
$31$			6.86797e6i			0.239894i	0.992780	+	0.119947i	$0.0382725\pi$
$31$			6.86797e6i			0.239894i	−0.992780	+	0.119947i	$0.961728\pi$
$32$		−	3.84104e7i		−	1.14472i
$33$			1.98507e7i			0.507230i
$34$			3.05473e7i			0.672323i
$35$	−5.57350e7			−1.06118
$36$	−3.08250e7			−0.509790
$37$			3.37758e7i			0.487077i	0.969891	+	0.243538i	$0.0783082\pi$
$37$			3.37758e7i			0.487077i	−0.969891	+	0.243538i	$0.921692\pi$
$38$		−	2.19102e6i		−	0.0276521i
$39$			3.62720e7i			0.402021i
$40$		−	5.81292e7i		−	0.567668i
$41$	−1.94974e8			−1.68290			−0.841448	−	0.540338i	$-0.818297\pi$
$41$	−1.94974e8			−1.68290			−0.841448	+	0.540338i	$0.818297\pi$
$42$		−	1.88865e8i		−	1.44512i
$43$			7.75843e7i			0.527754i	0.964556	+	0.263877i	$0.0850014\pi$
$43$			7.75843e7i			0.527754i	−0.964556	+	0.263877i	$0.914999\pi$
$44$		−	2.21586e8i		−	1.34363i
$45$	4.14735e7			0.224754
$46$	−9.41104e7			−0.456929
$47$		−	1.56607e8i		−	0.682846i	−0.939910	−	0.341423i	$-0.889091\pi$
$47$		−	1.56607e8i		−	0.682846i	0.939910	−	0.341423i	$-0.110909\pi$
$48$	−2.80096e7			−0.109926
$49$	4.17203e8			1.47696
$50$		−	2.71049e8i		−	0.867356i
$51$	8.42097e7			0.244068
$52$		−	4.04891e8i		−	1.06493i
$53$	−1.74257e8			−0.416688			−0.208344	−	0.978056i	$-0.566807\pi$
$53$	−1.74257e8			−0.416688			−0.208344	+	0.978056i	$0.566807\pi$
$54$			1.40538e8i			0.306072i
$55$			2.98132e8i			0.592372i
$56$			7.29734e8i			1.32503i
$57$	−6.03998e6			−0.0100383
$58$			1.67260e8i			0.254831i
$59$	6.14004e8	+	3.66219e8i	0.858837	+	0.512249i
$59$	6.14004e8	+	3.66219e8i	0.858837	+	0.512249i
$60$	−4.62953e8			−0.595362
$61$			1.60873e8i			0.190473i	0.995455	+	0.0952365i	$0.0303607\pi$
$61$			1.60873e8i			0.190473i	−0.995455	+	0.0952365i	$0.969639\pi$
$62$	−3.49530e8			−0.381528
$63$	−5.20644e8			−0.524611
$64$	1.75037e9			1.63016
$65$			5.44760e8i			0.469503i
$66$	−1.01026e9			−0.806699
$67$		−	1.29604e9i		−	0.959938i	−0.877285	−	0.479969i	$-0.840648\pi$
$67$		−	1.29604e9i		−	0.959938i	0.877285	−	0.479969i	$-0.159352\pi$
$68$	−9.40003e8			−0.646524
$69$			2.59434e8i			0.165875i
$70$		−	2.83651e9i		−	1.68770i
$71$	−1.68138e9			−0.931910			−0.465955	−	0.884808i	$-0.654289\pi$
$71$	−1.68138e9			−0.931910			−0.465955	+	0.884808i	$0.654289\pi$
$72$		−	5.43009e8i		−	0.280637i
$73$		−	3.06702e9i		−	1.47946i	−0.672905	−	0.739729i	$-0.734954\pi$
$73$		−	3.06702e9i		−	1.47946i	0.672905	−	0.739729i	$-0.265046\pi$
$74$	−1.71895e9			−0.774647
$75$	−7.47200e8			−0.314870
$76$	6.74221e7			0.0265910
$77$		−	3.74264e9i		−	1.38269i
$78$	−1.84598e9			−0.639374
$79$	1.15229e9			0.374476			0.187238	−	0.982315i	$-0.440046\pi$
$79$	1.15229e9			0.374476			0.187238	+	0.982315i	$0.440046\pi$
$80$	−4.20669e8			−0.128378
$81$	3.87420e8			0.111111
$82$		−	9.92277e9i		−	2.67648i
$83$		−	7.52537e9i		−	1.91046i	−0.295867	−	0.955229i	$-0.595608\pi$
$83$		−	7.52537e9i		−	1.91046i	0.295867	−	0.955229i	$-0.404392\pi$
$84$	5.81176e9			1.38967
$85$	1.26472e9			0.285037
$86$	−3.94848e9			−0.839340
$87$	4.61085e8			0.0925092
$88$	3.90341e9			0.739658
$89$		−	5.42130e9i		−	0.970854i	−0.874277	−	0.485427i	$-0.838664\pi$
$89$		−	5.42130e9i		−	0.970854i	0.874277	−	0.485427i	$-0.161336\pi$
$90$			2.11070e9i			0.357449i
$91$		−	6.83873e9i		−	1.09589i
$92$		−	2.89597e9i		−	0.439395i
$93$			9.63549e8i			0.138503i
$94$	7.97019e9			1.08600
$95$	−9.07128e7			−0.0117233
$96$		−	5.38882e9i		−	0.660903i
$97$			3.52047e9i			0.409961i	0.978766	+	0.204980i	$0.0657131\pi$
$97$			3.52047e9i			0.409961i	−0.978766	+	0.204980i	$0.934287\pi$
$98$			2.12326e10i			2.34895i
$99$			2.78497e9i			0.292850i
$100$	8.34073e9			0.834073
$101$		−	1.23159e10i		−	1.17182i	−0.810377	−	0.585909i	$-0.800738\pi$
$101$		−	1.23159e10i		−	1.17182i	0.810377	−	0.585909i	$-0.199262\pi$
$102$			4.28567e9i			0.388166i
$103$		−	4.05209e9i		−	0.349537i	−0.984610	−	0.174769i	$-0.944082\pi$
$103$		−	4.05209e9i		−	0.349537i	0.984610	−	0.174769i	$-0.0559177\pi$
$104$	7.13249e9			0.586239
$105$	−7.81941e9			−0.612671
$106$		−	8.86843e9i		−	0.662701i
$107$	−1.04529e10			−0.745277			−0.372638	−	0.927977i	$-0.621547\pi$
$107$	−1.04529e10			−0.745277			−0.372638	+	0.927977i	$0.621547\pi$
$108$	−4.32463e9			−0.294327
$109$		−	1.90603e10i		−	1.23879i	−0.785080	−	0.619395i	$-0.787378\pi$
$109$		−	1.90603e10i		−	1.23879i	0.785080	−	0.619395i	$-0.212622\pi$
$110$	−1.51728e10			−0.942109
$111$			4.73862e9i			0.281214i
$112$	5.28093e9			0.299654
$113$			2.03020e10i			1.10191i	0.834534	+	0.550956i	$0.185737\pi$
$113$			2.03020e10i			1.10191i	−0.834534	+	0.550956i	$0.814263\pi$
$114$		−	3.07391e8i		−	0.0159649i
$115$			3.89637e9i			0.193718i
$116$	−5.14693e9			−0.245052
$117$			5.08882e9i			0.232107i
$118$	−1.86379e10	+	3.12483e10i	−0.814680	+	1.36589i
$119$	−1.58769e10			−0.665321
$120$		−	8.15530e9i		−	0.327743i
$121$	5.91768e9			0.228152
$122$	−8.18726e9			−0.302928
$123$	−2.73541e10			−0.971621
$124$		−	1.07558e10i		−	0.366887i
$125$	−3.17989e10			−1.04199
$126$		−	2.64970e10i		−	0.834342i
$127$	4.04217e10			1.22348			0.611738	−	0.791060i	$-0.290470\pi$
$127$	4.04217e10			1.22348			0.611738	+	0.791060i	$0.290470\pi$
$128$			4.97491e10i			1.44789i
$129$			1.08848e10i			0.304699i
$130$	−2.77243e10			−0.746697
$131$			3.47554e10i			0.900877i	0.892807	+	0.450439i	$0.148732\pi$
$131$			3.47554e10i			0.900877i	−0.892807	+	0.450439i	$0.851268\pi$
$132$		−	3.10876e10i		−	0.775743i
$133$	1.13878e9			0.0273641
$134$	6.59589e10			1.52669
$135$	5.81857e9			0.129762
$136$		−	1.65589e10i		−	0.355908i
$137$	6.12256e10			1.26862			0.634308	−	0.773080i	$-0.281285\pi$
$137$	6.12256e10			1.26862			0.634308	+	0.773080i	$0.281285\pi$
$138$	−1.32033e10			−0.263808
$139$	−1.49800e10			−0.288694			−0.144347	−	0.989527i	$-0.546108\pi$
$139$	−1.49800e10			−0.288694			−0.144347	+	0.989527i	$0.546108\pi$
$140$	8.72852e10			1.62293
$141$		−	2.19714e10i		−	0.394242i
$142$		−	8.55701e10i		−	1.48211i
$143$	−3.65810e10			−0.611751
$144$	−3.92964e9			−0.0634659
$145$	6.92491e9			0.108037
$146$	1.56089e11			2.35293
$147$	5.85320e10			0.852720
$148$		−	5.28955e10i		−	0.744921i
$149$			1.48074e10i			0.201626i	0.994905	+	0.100813i	$0.0321444\pi$
$149$			1.48074e10i			0.201626i	−0.994905	+	0.100813i	$0.967856\pi$
$150$		−	3.80271e10i		−	0.500768i
$151$			5.55513e10i			0.707635i	0.935314	+	0.353818i	$0.115117\pi$
$151$			5.55513e10i			0.707635i	−0.935314	+	0.353818i	$0.884883\pi$
$152$			1.18770e9i			0.0146382i
$153$	1.18143e10			0.140913
$154$	1.90474e11			2.19903
$155$			1.44713e10i			0.161752i
$156$		−	5.68047e10i		−	0.614838i
$157$			1.11194e11i			1.16570i	0.812582	+	0.582848i	$0.198062\pi$
$157$			1.11194e11i			1.16570i	−0.812582	+	0.582848i	$0.801938\pi$
$158$			5.86430e10i			0.595567i
$159$	−2.44476e10			−0.240575
$160$		−	8.09333e10i		−	0.771840i
$161$		−	4.89137e10i		−	0.452169i
$162$			1.97169e10i			0.176711i
$163$	6.14155e10			0.533753			0.266876	−	0.963731i	$-0.414008\pi$
$163$	6.14155e10			0.533753			0.266876	+	0.963731i	$0.414008\pi$
$164$	3.05344e11			2.57377
$165$			4.18267e10i			0.342006i
$166$	3.82987e11			3.03839
$167$	−6.25161e10			−0.481293			−0.240646	−	0.970613i	$-0.577359\pi$
$167$	−6.25161e10			−0.481293			−0.240646	+	0.970613i	$0.577359\pi$
$168$			1.02379e11i			0.765004i
$169$	7.10161e10			0.515138
$170$			6.43653e10i			0.453322i
$171$	−8.47385e8			−0.00579563
$172$		−	1.21503e11i		−	0.807132i
$173$		−	1.32957e11i		−	0.857987i	−0.903307	−	0.428994i	$-0.858868\pi$
$173$		−	1.32957e11i		−	0.857987i	0.903307	−	0.428994i	$-0.141132\pi$
$174$			2.34659e10i			0.147127i
$175$	1.40877e11			0.858322
$176$		−	2.82482e10i		−	0.167274i
$177$	8.61423e10	+	5.13791e10i	0.495850	+	0.295747i
$178$	2.75905e11			1.54405
$179$			9.63839e9i			0.0524493i	0.999656	+	0.0262246i	$0.00834852\pi$
$179$			9.63839e9i			0.0524493i	−0.999656	+	0.0262246i	$0.991651\pi$
$180$	−6.49505e10			−0.343732
$181$	−1.12840e11			−0.580857			−0.290429	−	0.956897i	$-0.593798\pi$
$181$	−1.12840e11			−0.580857			−0.290429	+	0.956897i	$0.593798\pi$
$182$	3.48042e11			1.74291
$183$			2.25698e10i			0.109970i
$184$	5.10149e10			0.241884
$185$			7.11681e10i			0.328418i
$186$	−4.90377e10			−0.220275
$187$			8.49270e10i			0.371397i
$188$			2.45259e11i			1.04432i
$189$	−7.30443e10			−0.302885
$190$		−	4.61663e9i		−	0.0186448i
$191$		−	4.37205e11i		−	1.71996i	−0.510329	−	0.859979i	$-0.670476\pi$
$191$		−	4.37205e11i		−	1.71996i	0.510329	−	0.859979i	$-0.329524\pi$
$192$	2.45570e11			0.941174
$193$	−4.25062e11			−1.58732			−0.793662	−	0.608359i	$-0.791828\pi$
$193$	−4.25062e11			−1.58732			−0.793662	+	0.608359i	$0.791828\pi$
$194$	−1.79167e11			−0.652001
$195$			7.64277e10i			0.271068i
$196$	−6.53371e11			−2.25881
$197$	−8.09420e10			−0.272799			−0.136400	−	0.990654i	$-0.543553\pi$
$197$	−8.09420e10			−0.272799			−0.136400	+	0.990654i	$0.543553\pi$
$198$	−1.41735e11			−0.465748
$199$	−4.10305e11			−1.31475			−0.657373	−	0.753566i	$-0.728332\pi$
$199$	−4.10305e11			−1.31475			−0.657373	+	0.753566i	$0.728332\pi$
$200$			1.46929e11i			0.459152i
$201$		−	1.81829e11i		−	0.554221i
$202$	6.26791e11			1.86366
$203$	−8.69330e10			−0.252176
$204$	−1.31879e11			−0.373271
$205$	−4.10824e11			−1.13471
$206$	2.06222e11			0.555904
$207$			3.63976e10i			0.0957681i
$208$		−	5.16164e10i		−	0.132578i
$209$		−	6.09143e9i		−	0.0152752i
$210$		−	3.97951e11i		−	0.974392i
$211$		−	4.72052e10i		−	0.112870i	−0.998406	−	0.0564348i	$-0.982027\pi$
$211$		−	4.72052e10i		−	0.112870i	0.998406	−	0.0564348i	$-0.0179733\pi$
$212$	2.72900e11			0.637271
$213$	−2.35891e11			−0.538039
$214$		−	5.31977e11i		−	1.18529i
$215$			1.63476e11i			0.355845i
$216$		−	7.61820e10i		−	0.162026i
$217$		−	1.81668e11i		−	0.377554i
$218$	9.70032e11			1.97017
$219$		−	4.30291e11i		−	0.854165i
$220$		−	4.66897e11i		−	0.905957i
$221$			1.55182e11i			0.294362i
$222$	−2.41161e11			−0.447242
$223$	−3.57720e11			−0.648663			−0.324331	−	0.945943i	$-0.605139\pi$
$223$	−3.57720e11			−0.648663			−0.324331	+	0.945943i	$0.605139\pi$
$224$			1.01601e12i			1.80160i
$225$	−1.04829e11			−0.181790
$226$	−1.03323e12			−1.75248
$227$			2.97110e11i			0.492933i	0.969151	+	0.246466i	$0.0792695\pi$
$227$			2.97110e11i			0.492933i	−0.969151	+	0.246466i	$0.920731\pi$
$228$	9.45906e9			0.0153523
$229$			6.05682e11i			0.961761i	0.876786	+	0.480880i	$0.159683\pi$
$229$			6.05682e11i			0.961761i	−0.876786	+	0.480880i	$0.840317\pi$
$230$	−1.98297e11			−0.308090
$231$		−	5.25078e11i		−	0.798297i
$232$		−	9.06673e10i		−	0.134900i
$233$			5.51638e11i			0.803294i	0.915795	+	0.401647i	$0.131562\pi$
$233$			5.51638e11i			0.803294i	−0.915795	+	0.401647i	$0.868438\pi$
$234$	−2.58984e11			−0.369143
$235$		−	3.29983e11i		−	0.460418i
$236$	−9.61576e11	−	5.73526e11i	−1.31348	−	0.783418i
$237$	1.61661e11			0.216204
$238$		−	8.08020e11i		−	1.05813i
$239$	9.48583e11			1.21643			0.608213	−	0.793774i	$-0.291887\pi$
$239$	9.48583e11			1.21643			0.608213	+	0.793774i	$0.291887\pi$
$240$	−5.90182e10			−0.0741190
$241$	−4.19889e11			−0.516475			−0.258238	−	0.966081i	$-0.583142\pi$
$241$	−4.19889e11			−0.516475			−0.258238	+	0.966081i	$0.583142\pi$
$242$			3.01167e11i			0.362853i
$243$	5.43536e10			0.0641500
$244$		−	2.51939e11i		−	0.291304i
$245$	8.79077e11			0.995855
$246$		−	1.39213e12i		−	1.54526i
$247$		−	1.11305e10i		−	0.0121068i
$248$	1.89471e11			0.201969
$249$		−	1.05578e12i		−	1.10300i
$250$		−	1.61833e12i		−	1.65717i
$251$	1.00757e12			1.01136			0.505680	−	0.862721i	$-0.331242\pi$
$251$	1.00757e12			1.01136			0.505680	+	0.862721i	$0.331242\pi$
$252$	8.15367e11			0.802325
$253$	−2.61644e11			−0.252411
$254$			2.05717e12i			1.94582i
$255$	1.77436e11			0.164566
$256$	−7.39488e11			−0.672560
$257$	−9.37522e11			−0.836211			−0.418105	−	0.908399i	$-0.637306\pi$
$257$	−9.37522e11			−0.836211			−0.418105	+	0.908399i	$0.637306\pi$
$258$	−5.53957e11			−0.484593
$259$		−	8.93419e11i		−	0.766578i
$260$		−	8.53134e11i		−	0.718043i
$261$	6.46884e10			0.0534102
$262$	−1.76880e12			−1.43275
$263$	5.91121e11			0.469784			0.234892	−	0.972022i	$-0.424526\pi$
$263$	5.91121e11			0.469784			0.234892	+	0.972022i	$0.424526\pi$
$264$	5.47634e11			0.427042
$265$	−3.67172e11			−0.280957
$266$			5.79556e10i			0.0435198i
$267$		−	7.60588e11i		−	0.560523i
$268$			2.02969e12i			1.46810i
$269$		−	6.67313e11i		−	0.473771i	−0.971538	−	0.236885i	$-0.923873\pi$
$269$		−	6.67313e11i		−	0.473771i	0.971538	−	0.236885i	$-0.0761266\pi$
$270$			2.96123e11i			0.206373i
$271$	−1.30064e12			−0.889837			−0.444918	−	0.895571i	$-0.646767\pi$
$271$	−1.30064e12			−0.889837			−0.444918	+	0.895571i	$0.646767\pi$
$272$	−1.19833e11			−0.0804884
$273$		−	9.59447e11i		−	0.632714i
$274$			3.11594e12i			2.01761i
$275$		−	7.53565e11i		−	0.479134i
$276$		−	4.06293e11i		−	0.253685i
$277$	1.95780e11			0.120052			0.0600261	−	0.998197i	$-0.480882\pi$
$277$	1.95780e11			0.120052			0.0600261	+	0.998197i	$0.480882\pi$
$278$		−	7.62375e11i		−	0.459140i
$279$			1.35182e11i			0.0799647i
$280$			1.53760e12i			0.893415i
$281$	−2.19824e12			−1.25471			−0.627354	−	0.778734i	$-0.715862\pi$
$281$	−2.19824e12			−1.25471			−0.627354	+	0.778734i	$0.715862\pi$
$282$	1.11819e12			0.627001
$283$		−	6.67958e11i		−	0.367974i	−0.982929	−	0.183987i	$-0.941100\pi$
$283$		−	6.67958e11i		−	0.367974i	0.982929	−	0.183987i	$-0.0589004\pi$
$284$	2.63317e12			1.42524
$285$	−1.27267e10			−0.00676846
$286$		−	1.86171e12i		−	0.972929i
$287$	5.15734e12			2.64860
$288$		−	7.56031e11i		−	0.381573i
$289$	−1.65572e12			−0.821292
$290$			3.52428e11i			0.171823i
$291$			4.93909e11i			0.236691i
$292$			4.80318e12i			2.26264i
$293$	1.38989e12			0.643639			0.321820	−	0.946801i	$-0.395706\pi$
$293$	1.38989e12			0.643639			0.321820	+	0.946801i	$0.395706\pi$
$294$			2.97886e12i			1.35617i
$295$	1.29375e12	+	7.71649e11i	0.579082	+	0.345390i
$296$	9.31797e11			0.410075
$297$			3.90720e11i			0.169077i
$298$	−7.53588e11			−0.320666
$299$	−4.78087e11			−0.200056
$300$	1.17017e12			0.481552
$301$		−	2.05222e12i		−	0.830598i
$302$	−2.82716e12			−1.12542
$303$		−	1.72788e12i		−	0.676549i
$304$	8.59510e9			0.00331042
$305$			3.38970e11i			0.128429i
$306$			6.01262e11i			0.224108i
$307$	−9.19052e11			−0.337014			−0.168507	−	0.985700i	$-0.553895\pi$
$307$	−9.19052e11			−0.337014			−0.168507	+	0.985700i	$0.553895\pi$
$308$			5.86126e12i			2.11464i
$309$		−	5.68493e11i		−	0.201805i
$310$	−7.36484e11			−0.257250
$311$	−2.50050e12			−0.859458			−0.429729	−	0.902958i	$-0.641391\pi$
$311$	−2.50050e12			−0.859458			−0.429729	+	0.902958i	$0.641391\pi$
$312$	1.00066e12			0.338465
$313$		−	2.73877e12i		−	0.911664i	−0.890066	−	0.455832i	$-0.849342\pi$
$313$		−	2.73877e12i		−	0.911664i	0.890066	−	0.455832i	$-0.150658\pi$
$314$	−5.65900e12			−1.85392
$315$	−1.09703e12			−0.353726
$316$	−1.80456e12			−0.572713
$317$	−5.65807e12			−1.76755			−0.883776	−	0.467911i	$-0.845007\pi$
$317$	−5.65807e12			−1.76755			−0.883776	+	0.467911i	$0.845007\pi$
$318$		−	1.24421e12i		−	0.382611i
$319$			4.65012e11i			0.140770i
$320$	3.68816e12			1.09916
$321$	−1.46650e12			−0.430286
$322$	2.48935e12			0.719130
$323$	−2.58408e10			−0.00735011
$324$	−6.06729e11			−0.169930
$325$		−	1.37695e12i		−	0.379752i
$326$			3.12561e12i			0.848880i
$327$		−	2.67409e12i		−	0.715215i
$328$			5.37888e12i			1.41685i
$329$			4.14249e12i			1.07469i
$330$	−2.12868e12			−0.543927
$331$	−5.78557e12			−1.45615			−0.728075	−	0.685498i	$-0.759585\pi$
$331$	−5.78557e12			−1.45615			−0.728075	+	0.685498i	$0.759585\pi$
$332$			1.17853e13i			2.92180i
$333$			6.64810e11i			0.162359i
$334$		−	3.18162e12i		−	0.765448i
$335$		−	2.73084e12i		−	0.647250i
$336$	7.40894e11			0.173006
$337$			3.77177e12i			0.867752i	0.900973	+	0.433876i	$0.142854\pi$
$337$			3.77177e12i			0.867752i	−0.900973	+	0.433876i	$0.857146\pi$
$338$			3.61421e12i			0.819275i
$339$			2.84830e12i			0.636190i
$340$	−1.98065e12			−0.435927
$341$	−9.71757e11			−0.210759
$342$		−	4.31258e10i		−	0.00921736i
$343$	−3.56375e12			−0.750648
$344$	2.14037e12			0.444321
$345$			5.46646e11i			0.111843i
$346$	6.76655e12			1.36454
$347$			1.54001e12i			0.306109i	0.988218	+	0.153054i	$0.0489109\pi$
$347$			1.54001e12i			0.306109i	−0.988218	+	0.153054i	$0.951089\pi$
$348$	−7.22094e11			−0.141481
$349$			4.66261e10i			0.00900538i	0.999990	+	0.00450269i	$0.00143326\pi$
$349$			4.66261e10i			0.00900538i	−0.999990	+	0.00450269i	$0.998567\pi$
$350$			7.16963e12i			1.36508i
$351$			7.13942e11i			0.134007i
$352$	5.43472e12			1.00569
$353$			1.25736e12i			0.229396i	0.993400	+	0.114698i	$0.0365900\pi$
$353$			1.25736e12i			0.229396i	−0.993400	+	0.114698i	$0.963410\pi$
$354$	−2.61483e12	+	4.38402e12i	−0.470356	+	0.788599i
$355$	−3.54278e12			−0.628352
$356$			8.49017e12i			1.48479i
$357$	−2.22747e12			−0.384123
$358$	−4.90525e11			−0.0834153
$359$	2.11731e12			0.355068			0.177534	−	0.984115i	$-0.443188\pi$
$359$	2.11731e12			0.355068			0.177534	+	0.984115i	$0.443188\pi$
$360$		−	1.14416e12i		−	0.189223i
$361$	−6.12921e12			−0.999698
$362$		−	5.74273e12i		−	0.923795i
$363$	8.30228e11			0.131724
$364$			1.07100e13i			1.67603i
$365$		−	6.46243e12i		−	0.997542i
$366$	−1.14864e12			−0.174896
$367$		−	3.76611e12i		−	0.565669i	−0.959169	−	0.282834i	$-0.908725\pi$
$367$		−	3.76611e12i		−	0.565669i	0.959169	−	0.282834i	$-0.0912747\pi$
$368$		−	3.69184e11i		−	0.0547020i
$369$	−3.83767e12			−0.560966
$370$	−3.62194e12			−0.522315
$371$	4.60935e12			0.655799
$372$		−	1.50899e12i		−	0.211822i
$373$	−7.08756e12			−0.981641			−0.490821	−	0.871261i	$-0.663303\pi$
$373$	−7.08756e12			−0.981641			−0.490821	+	0.871261i	$0.663303\pi$
$374$	−4.32217e12			−0.590669
$375$	−4.46126e12			−0.601590
$376$	−4.32044e12			−0.574895
$377$			8.49691e11i			0.111572i
$378$		−	3.71743e12i		−	0.481707i
$379$	1.17226e13			1.49910			0.749548	−	0.661950i	$-0.230271\pi$
$379$	1.17226e13			1.49910			0.749548	+	0.661950i	$0.230271\pi$
$380$	1.42063e11			0.0179293
$381$	5.67100e12			0.706375
$382$	2.22506e13			2.73542
$383$	9.52031e12			1.15520			0.577600	−	0.816320i	$-0.303989\pi$
$383$	9.52031e12			1.15520			0.577600	+	0.816320i	$0.303989\pi$
$384$			6.97960e12i			0.835939i
$385$		−	7.88601e12i		−	0.932296i
$386$		−	2.16326e13i		−	2.52448i
$387$			1.52709e12i			0.175918i
$388$		−	5.51332e12i		−	0.626982i
$389$	−7.50109e12			−0.842125			−0.421063	−	0.907032i	$-0.638343\pi$
$389$	−7.50109e12			−0.842125			−0.421063	+	0.907032i	$0.638343\pi$
$390$	−3.88962e12			−0.431106
$391$			1.10994e12i			0.121455i
$392$		−	1.15097e13i		−	1.24346i
$393$			4.87605e12i			0.520122i
$394$		−	4.11936e12i		−	0.433859i
$395$	2.42795e12			0.252495
$396$		−	4.36147e12i		−	0.447875i
$397$		−	6.39193e12i		−	0.648156i	−0.946030	−	0.324078i	$-0.894946\pi$
$397$		−	6.39193e12i		−	0.648156i	0.946030	−	0.324078i	$-0.105054\pi$
$398$		−	2.08816e13i		−	2.09097i
$399$	1.59766e11			0.0157987
$400$	1.06329e12			0.103837
$401$		−	3.14324e12i		−	0.303148i	−0.988446	−	0.151574i	$-0.951566\pi$
$401$		−	3.14324e12i		−	0.303148i	0.988446	−	0.151574i	$-0.0484342\pi$
$402$	9.25378e12			0.881432
$403$	−1.77564e12			−0.167043
$404$			1.92876e13i			1.79214i
$405$	8.16322e11			0.0749181
$406$		−	4.42426e12i		−	0.401061i
$407$	−4.77898e12			−0.427921
$408$		−	2.32315e12i		−	0.205483i
$409$			2.02712e13i			1.77118i	0.464471	+	0.885588i	$0.346244\pi$
$409$			2.02712e13i			1.77118i	−0.464471	+	0.885588i	$0.653756\pi$
$410$		−	2.09080e13i		−	1.80465i
$411$	8.58972e12			0.732436
$412$			6.34588e12i			0.534572i
$413$	−1.62413e13	−	9.68702e12i	−1.35167	−	0.806195i
$414$	−1.85237e12			−0.152310
$415$		−	1.58565e13i		−	1.28815i
$416$	9.93057e12			0.797090
$417$	−2.10164e12			−0.166678
$418$	3.10010e11			0.0242937
$419$		−	1.62123e13i		−	1.25538i	−0.778465	−	0.627688i	$-0.784001\pi$
$419$		−	1.62123e13i		−	1.25538i	0.778465	−	0.627688i	$-0.215999\pi$
$420$	1.22458e13			0.937001
$421$			2.28667e13i			1.72899i	0.502642	+	0.864495i	$0.332361\pi$
$421$			2.28667e13i			1.72899i	−0.502642	+	0.864495i	$0.667639\pi$
$422$	2.40240e12			0.179508
$423$		−	3.08250e12i		−	0.227615i
$424$			4.80735e12i			0.350814i
$425$	−3.19675e12			−0.230549
$426$		−	1.20051e13i		−	0.855696i
$427$		−	4.25532e12i		−	0.299773i
$428$	1.63700e13			1.13980
$429$	−5.13217e12			−0.353195
$430$	−8.31973e12			−0.565936
$431$		−	3.91398e12i		−	0.263167i	−0.991305	−	0.131584i	$-0.957994\pi$
$431$		−	3.91398e12i		−	0.263167i	0.991305	−	0.131584i	$-0.0420062\pi$
$432$	−5.51313e11			−0.0366420
$433$	−2.66348e13			−1.74988			−0.874942	−	0.484227i	$-0.839101\pi$
$433$	−2.66348e13			−1.74988			−0.874942	+	0.484227i	$0.839101\pi$
$434$	9.24557e12			0.600461
$435$	9.71538e11			0.0623755
$436$			2.98499e13i			1.89457i
$437$		−	7.96106e10i		−	0.00499533i
$438$	2.18987e13			1.35846
$439$	1.22436e13			0.750910			0.375455	−	0.926841i	$-0.377486\pi$
$439$	1.22436e13			0.750910			0.375455	+	0.926841i	$0.377486\pi$
$440$	8.22477e12			0.498724
$441$	8.21181e12			0.492318
$442$	−7.89766e12			−0.468152
$443$		−	8.44368e12i		−	0.494895i	−0.968901	−	0.247447i	$-0.920408\pi$
$443$		−	8.44368e12i		−	0.494895i	0.968901	−	0.247447i	$-0.0795918\pi$
$444$		−	7.42103e12i		−	0.430080i
$445$		−	1.14231e13i		−	0.654610i
$446$		−	1.82054e13i		−	1.03163i
$447$			2.07742e12i			0.116409i
$448$	−4.62998e13			−2.56560
$449$	−2.90029e12			−0.158931			−0.0794657	−	0.996838i	$-0.525321\pi$
$449$	−2.90029e12			−0.158931			−0.0794657	+	0.996838i	$0.525321\pi$
$450$		−	5.33505e12i		−	0.289119i
$451$		−	2.75871e13i		−	1.47851i
$452$		−	3.17945e13i		−	1.68523i
$453$			7.79363e12i			0.408553i
$454$	−1.51207e13			−0.783960
$455$		−	1.44097e13i		−	0.738920i
$456$			1.66629e11i			0.00845136i
$457$			4.37141e12i			0.219301i	0.993970	+	0.109650i	$0.0349731\pi$
$457$			4.37141e12i			0.219301i	−0.993970	+	0.109650i	$0.965027\pi$
$458$	−3.08248e13			−1.52958
$459$	1.65750e12			0.0813561
$460$		−	6.10201e12i		−	0.296267i
$461$	2.45776e12			0.118042			0.0590208	−	0.998257i	$-0.481202\pi$
$461$	2.45776e12			0.118042			0.0590208	+	0.998257i	$0.481202\pi$
$462$	2.67227e13			1.26961
$463$		−	6.09401e12i		−	0.286417i	−0.989693	−	0.143208i	$-0.954258\pi$
$463$		−	6.09401e12i		−	0.286417i	0.989693	−	0.143208i	$-0.0457419\pi$
$464$	−6.56140e11			−0.0305075
$465$			2.03027e12i			0.0933874i
$466$	−2.80744e13			−1.27756
$467$			6.90328e12i			0.310793i	0.987852	+	0.155396i	$0.0496655\pi$
$467$			6.90328e12i			0.310793i	−0.987852	+	0.155396i	$0.950335\pi$
$468$		−	7.96947e12i		−	0.354977i
$469$			3.42820e13i			1.51078i
$470$	1.67937e13			0.732248
$471$			1.56002e13i			0.673014i
$472$	1.01031e13	−	1.69389e13i	0.431267	−	0.723063i
$473$	−1.09775e13			−0.463658
$474$			8.22738e12i			0.343851i
$475$	2.29288e11			0.00948229
$476$	2.48644e13			1.01752
$477$	−3.42991e12			−0.138896
$478$			4.82760e13i			1.93460i
$479$	−1.35835e13			−0.538686			−0.269343	−	0.963044i	$-0.586806\pi$
$479$	−1.35835e13			−0.538686			−0.269343	+	0.963044i	$0.586806\pi$
$480$		−	1.13546e13i		−	0.445622i
$481$	−8.73237e12			−0.339162
$482$		−	2.13693e13i		−	0.821402i
$483$		−	6.86240e12i		−	0.261060i
$484$	−9.26753e12			−0.348929
$485$			7.41789e12i			0.276421i
$486$			2.76621e12i			0.102024i
$487$	4.23136e12			0.154467			0.0772334	−	0.997013i	$-0.475391\pi$
$487$	4.23136e12			0.154467			0.0772334	+	0.997013i	$0.475391\pi$
$488$	4.43811e12			0.160361
$489$	8.61636e12			0.308162
$490$			4.47386e13i			1.58381i
$491$	6.30143e12			0.220816			0.110408	−	0.993886i	$-0.464784\pi$
$491$	6.30143e12			0.220816			0.110408	+	0.993886i	$0.464784\pi$
$492$	4.28386e13			1.48597
$493$	1.97266e12			0.0677357
$494$	5.66463e11			0.0192547
$495$			5.86813e12i			0.197457i
$496$		−	1.37116e12i		−	0.0456753i
$497$	4.44749e13			1.46667
$498$	5.37316e13			1.75422
$499$	6.90808e12			0.223282			0.111641	−	0.993749i	$-0.464389\pi$
$499$	6.90808e12			0.223282			0.111641	+	0.993749i	$0.464389\pi$
$500$	4.97994e13			1.59358
$501$	−8.77077e12			−0.277875
$502$			5.12779e13i			1.60847i
$503$			5.01804e12i			0.155846i	0.996959	+	0.0779228i	$0.0248288\pi$
$503$			5.01804e12i			0.155846i	−0.996959	+	0.0779228i	$0.975171\pi$
$504$			1.43634e13i			0.441675i
$505$		−	2.59505e13i		−	0.790112i
$506$		−	1.33158e13i		−	0.401434i
$507$	9.96329e12			0.297415
$508$	−6.33034e13			−1.87115
$509$		−	3.38091e12i		−	0.0989565i	−0.998775	−	0.0494783i	$-0.984244\pi$
$509$		−	3.38091e12i		−	0.0989565i	0.998775	−	0.0494783i	$-0.0157559\pi$
$510$			9.03020e12i			0.261726i
$511$			8.11271e13i			2.32842i
$512$			1.33085e13i			0.378249i
$513$	−1.18885e11			−0.00334611
$514$		−	4.77131e13i		−	1.32991i
$515$		−	8.53805e12i		−	0.235680i
$516$		−	1.70464e13i		−	0.465998i
$517$	2.21586e13			0.599914
$518$	4.54686e13			1.21917
$519$		−	1.86534e13i		−	0.495359i
$520$	1.50287e13			0.395279
$521$	1.96892e13			0.512908			0.256454	−	0.966556i	$-0.417446\pi$
$521$	1.96892e13			0.512908			0.256454	+	0.966556i	$0.417446\pi$
$522$			3.29217e12i			0.0849435i
$523$	−1.74191e13			−0.445162			−0.222581	−	0.974914i	$-0.571448\pi$
$523$	−1.74191e13			−0.445162			−0.222581	+	0.974914i	$0.571448\pi$
$524$		−	5.44295e13i		−	1.37777i
$525$	1.97645e13			0.495553
$526$			3.00838e13i			0.747143i
$527$			4.12235e12i			0.101413i
$528$		−	3.96311e12i		−	0.0965754i
$529$	3.80070e13			0.917456
$530$		−	1.86864e13i		−	0.446834i
$531$	1.20854e13	+	7.20829e12i	0.286279	+	0.170750i
$532$	−1.78341e12			−0.0418498
$533$		−	5.04084e13i		−	1.17184i
$534$	3.87084e13			0.891455
$535$	−2.20250e13			−0.502512
$536$	−3.57547e13			−0.808181
$537$			1.35223e12i			0.0302816i
$538$	3.39614e13			0.753485
$539$			5.90306e13i			1.29758i
$540$	−9.11231e12			−0.198454
$541$			3.09098e13i			0.666976i	0.942754	+	0.333488i	$0.108226\pi$
$541$			3.09098e13i			0.666976i	−0.942754	+	0.333488i	$0.891774\pi$
$542$		−	6.61931e13i		−	1.41520i
$543$	−1.58310e13			−0.335358
$544$		−	2.30550e13i		−	0.483917i
$545$		−	4.01614e13i		−	0.835269i
$546$	4.88289e13			1.00627
$547$	9.65358e13			1.97130			0.985648	−	0.168813i	$-0.0539936\pi$
$547$	9.65358e13			1.97130			0.985648	+	0.168813i	$0.0539936\pi$
$548$	−9.58839e13			−1.94018
$549$			3.16646e12i			0.0634910i
$550$	3.83510e13			0.762015
$551$	−1.41490e11			−0.00278591
$552$	7.15719e12			0.139652
$553$	−3.04796e13			−0.589364
$554$			9.96381e12i			0.190931i
$555$			9.98460e12i			0.189612i
$556$	2.34598e13			0.441521
$557$	−8.42715e13			−1.57183			−0.785914	−	0.618336i	$-0.787807\pi$
$557$	−8.42715e13			−1.57183			−0.785914	+	0.618336i	$0.787807\pi$
$558$	−6.87980e12			−0.127176
$559$	−2.00586e13			−0.367486
$560$	1.11273e13			0.202046
$561$			1.19149e13i			0.214426i
$562$		−	1.11874e14i		−	1.99549i
$563$		−	2.46985e13i		−	0.436644i	−0.975877	−	0.218322i	$-0.929942\pi$
$563$		−	2.46985e13i		−	0.436644i	0.975877	−	0.218322i	$-0.0700584\pi$
$564$			3.44089e13i			0.602941i
$565$			4.27778e13i			0.742978i
$566$	3.39942e13			0.585225
$567$	−1.02478e13			−0.174870
$568$			4.63854e13i			0.784584i
$569$			5.13881e13i			0.861591i	0.902450	+	0.430796i	$0.141767\pi$
$569$			5.13881e13i			0.861591i	−0.902450	+	0.430796i	$0.858233\pi$
$570$		−	6.47695e11i		−	0.0107646i
$571$		−	4.30960e13i		−	0.709997i	−0.934867	−	0.354999i	$-0.884481\pi$
$571$		−	4.30960e13i		−	0.709997i	0.934867	−	0.354999i	$-0.115519\pi$
$572$	5.72885e13			0.935594
$573$		−	6.13381e13i		−	0.993019i
$574$			2.62471e14i			4.21233i
$575$		−	9.84856e12i		−	0.156687i
$576$	3.44526e13			0.543387
$577$	−3.50752e13			−0.548430			−0.274215	−	0.961668i	$-0.588418\pi$
$577$	−3.50752e13			−0.548430			−0.274215	+	0.961668i	$0.588418\pi$
$578$		−	8.42642e13i		−	1.30618i
$579$	−5.96345e13			−0.916442
$580$	−1.08449e13			−0.165229
$581$			1.99057e14i			3.00675i
$582$	−2.51364e13			−0.376433
$583$		−	2.46559e13i		−	0.366081i
$584$	−8.46120e13			−1.24557
$585$			1.07225e13i			0.156501i
$586$			7.07354e13i			1.02364i
$587$			8.69944e13i			1.24825i	0.781326	+	0.624124i	$0.214544\pi$
$587$			8.69944e13i			1.24825i	−0.781326	+	0.624124i	$0.785456\pi$
$588$	−9.16655e13			−1.30412
$589$		−	2.95677e11i		−	0.00417101i
$590$	−3.92714e13	+	6.58425e13i	−0.549308	+	0.920971i
$591$	−1.13559e13			−0.157501
$592$		−	6.74322e12i		−	0.0927383i
$593$	9.80223e13			1.33675			0.668377	−	0.743823i	$-0.266989\pi$
$593$	9.80223e13			1.33675			0.668377	+	0.743823i	$0.266989\pi$
$594$	−1.98849e13			−0.268900
$595$	−3.34538e13			−0.448601
$596$		−	2.31894e13i		−	0.308361i
$597$	−5.75642e13			−0.759069
$598$		−	2.43312e13i		−	0.318169i
$599$	−6.56015e13			−0.850706			−0.425353	−	0.905028i	$-0.639850\pi$
$599$	−6.56015e13			−0.850706			−0.425353	+	0.905028i	$0.639850\pi$
$600$			2.06135e13i			0.265092i
$601$			7.31596e13i			0.933038i	0.884511	+	0.466519i	$0.154492\pi$
$601$			7.31596e13i			0.933038i	−0.884511	+	0.466519i	$0.845508\pi$
$602$	1.04443e14			1.32098
$603$		−	2.55099e13i		−	0.319979i
$604$		−	8.69975e13i		−	1.08224i
$605$	1.24690e13			0.153834
$606$	8.79364e13			1.07598
$607$	−5.58822e13			−0.678156			−0.339078	−	0.940758i	$-0.610115\pi$
$607$	−5.58822e13			−0.678156			−0.339078	+	0.940758i	$0.610115\pi$
$608$			1.65363e12i			0.0199031i
$609$	−1.21964e13			−0.145594
$610$	−1.72511e13			−0.204253
$611$	4.04891e13			0.475480
$612$	−1.85021e13			−0.215508
$613$		−	4.28268e13i		−	0.494781i	−0.968916	−	0.247391i	$-0.920427\pi$
$613$		−	4.28268e13i		−	0.494781i	0.968916	−	0.247391i	$-0.0795731\pi$
$614$		−	4.67731e13i		−	0.535987i
$615$	−5.76370e13			−0.655127
$616$	−1.03251e14			−1.16410
$617$	−1.09740e14			−1.22727			−0.613634	−	0.789590i	$-0.710293\pi$
$617$	−1.09740e14			−1.22727			−0.613634	+	0.789590i	$0.710293\pi$
$618$	2.89322e13			0.320951
$619$	−7.95094e13			−0.874914			−0.437457	−	0.899239i	$-0.644121\pi$
$619$	−7.95094e13			−0.874914			−0.437457	+	0.899239i	$0.644121\pi$
$620$		−	2.26631e13i		−	0.247378i
$621$			5.10644e12i			0.0552917i
$622$		−	1.27257e14i		−	1.36688i
$623$			1.43401e14i			1.52796i
$624$		−	7.24157e12i		−	0.0765438i
$625$	−1.49919e13			−0.157201
$626$	1.39384e14			1.44991
$627$		−	8.54603e11i		−	0.00881915i
$628$		−	1.74139e14i		−	1.78278i
$629$			2.02732e13i			0.205906i
$630$		−	5.58310e13i		−	0.562565i
$631$	−1.06133e14			−1.06097			−0.530485	−	0.847694i	$-0.677990\pi$
$631$	−1.06133e14			−1.06097			−0.530485	+	0.847694i	$0.677990\pi$
$632$		−	3.17889e13i		−	0.315275i
$633$		−	6.62270e12i		−	0.0651653i
$634$		−	2.87955e14i		−	2.81111i
$635$	8.51713e13			0.824945
$636$	3.82868e13			0.367928
$637$			1.07863e14i			1.02843i
$638$	−2.36658e13			−0.223881
$639$	−3.30946e13			−0.310637
$640$			1.04825e14i			0.976257i
$641$	−9.16379e13			−0.846808			−0.423404	−	0.905941i	$-0.639165\pi$
$641$	−9.16379e13			−0.846808			−0.423404	+	0.905941i	$0.639165\pi$
$642$		−	7.46343e13i		−	0.684326i
$643$	2.54312e13			0.231373			0.115686	−	0.993286i	$-0.463093\pi$
$643$	2.54312e13			0.231373			0.115686	+	0.993286i	$0.463093\pi$
$644$			7.66025e13i			0.691534i
$645$			2.29350e13i			0.205447i
$646$		−	1.31511e12i		−	0.0116896i
$647$	−7.95829e13			−0.701937			−0.350969	−	0.936387i	$-0.614148\pi$
$647$	−7.95829e13			−0.701937			−0.350969	+	0.936387i	$0.614148\pi$
$648$		−	1.06880e13i		−	0.0935455i
$649$	−5.18167e13	+	8.68761e13i	−0.450035	+	0.754530i
$650$	7.00767e13			0.603958
$651$		−	2.54873e13i		−	0.217981i
$652$	−9.61813e13			−0.816305
$653$	1.46937e13			0.123756			0.0618780	−	0.998084i	$-0.480291\pi$
$653$	1.46937e13			0.123756			0.0618780	+	0.998084i	$0.480291\pi$
$654$	1.36092e14			1.13748
$655$			7.32320e13i			0.607428i
$656$	3.89258e13			0.320419
$657$		−	6.03682e13i		−	0.493152i
$658$	−2.10823e14			−1.70918
$659$			3.70636e13i			0.298209i	0.988821	+	0.149105i	$0.0476391\pi$
$659$			3.70636e13i			0.298209i	−0.988821	+	0.149105i	$0.952361\pi$
$660$		−	6.55038e13i		−	0.523054i
$661$	1.96867e14			1.56015			0.780076	−	0.625685i	$-0.215181\pi$
$661$	1.96867e14			1.56015			0.780076	+	0.625685i	$0.215181\pi$
$662$		−	2.94444e14i		−	2.31586i
$663$			2.17715e13i			0.169950i
$664$	−2.07608e14			−1.60843
$665$	2.39948e12			0.0184506
$666$	−3.38340e13			−0.258216
$667$			6.07738e12i			0.0460349i
$668$	9.79049e13			0.736075
$669$	−5.01867e13			−0.374506
$670$	1.38980e14			1.02939
$671$	−2.27621e13			−0.167340
$672$			1.42542e14i			1.04015i
$673$		−	1.56435e14i		−	1.13307i	−0.824037	−	0.566536i	$-0.808283\pi$
$673$		−	1.56435e14i		−	1.13307i	0.824037	−	0.566536i	$-0.191717\pi$
$674$	−1.91956e14			−1.38007
$675$	−1.47071e13			−0.104957
$676$	−1.11217e14			−0.787836
$677$	−8.64965e13			−0.608212			−0.304106	−	0.952638i	$-0.598358\pi$
$677$	−8.64965e13			−0.608212			−0.304106	+	0.952638i	$0.598358\pi$
$678$	−1.44958e14			−1.01180
$679$		−	9.31216e13i		−	0.645211i
$680$		−	3.48908e13i		−	0.239975i
$681$			4.16833e13i			0.284595i
$682$		−	4.94554e13i		−	0.335191i
$683$			2.51796e14i			1.69412i	0.531496	+	0.847061i	$0.321630\pi$
$683$			2.51796e14i			1.69412i	−0.531496	+	0.847061i	$0.678370\pi$
$684$	1.32707e12			0.00886366
$685$	1.29007e14			0.855381
$686$		−	1.81369e14i		−	1.19383i
$687$			8.49748e13i			0.555273i
$688$		−	1.54894e13i		−	0.100483i
$689$		−	4.50523e13i		−	0.290149i
$690$	−2.78203e13			−0.177876
$691$		−	8.92973e13i		−	0.566824i	−0.958998	−	0.283412i	$-0.908534\pi$
$691$		−	8.92973e13i		−	0.566824i	0.958998	−	0.283412i	$-0.0914663\pi$
$692$			2.08221e14i			1.31218i
$693$		−	7.36665e13i		−	0.460897i
$694$	−7.83753e13			−0.486835
$695$	−3.15640e13			−0.194656
$696$		−	1.27203e13i		−	0.0778843i
$697$	−1.17029e14			−0.711426
$698$	−2.37293e12			−0.0143221
$699$			7.73926e13i			0.463782i
$700$	−2.20624e14			−1.31269
$701$		−	2.17405e14i		−	1.28434i	−0.766563	−	0.642169i	$-0.778035\pi$
$701$		−	2.17405e14i		−	1.28434i	0.766563	−	0.642169i	$-0.221965\pi$
$702$	−3.63345e13			−0.213125
$703$		−	1.45411e12i		−	0.00846875i
$704$			2.47662e14i			1.43218i
$705$		−	4.62953e13i		−	0.265822i
$706$	−6.39905e13			−0.364831
$707$			3.25774e14i			1.84425i
$708$	−1.34905e14	−	8.04635e13i	−0.758338	−	0.452306i
$709$	4.37689e13			0.244306			0.122153	−	0.992511i	$-0.461020\pi$
$709$	4.37689e13			0.244306			0.122153	+	0.992511i	$0.461020\pi$
$710$		−	1.80302e14i		−	0.999331i
$711$	2.26804e13			0.124825
$712$	−1.49561e14			−0.817371
$713$	−1.27002e13			−0.0689226
$714$		−	1.13362e14i		−	0.610909i
$715$	−7.70787e13			−0.412481
$716$		−	1.50944e13i		−	0.0802143i
$717$	1.33082e14			0.702304
$718$			1.07756e14i			0.564700i
$719$			2.73736e14i			1.42458i	0.701885	+	0.712290i	$0.252342\pi$
$719$			2.73736e14i			1.42458i	−0.701885	+	0.712290i	$0.747658\pi$
$720$	−8.28003e12			−0.0427927
$721$			1.07184e14i			0.550114i
$722$		−	3.11933e14i		−	1.58992i
$723$	−5.89089e13			−0.298187
$724$	1.76716e14			0.888345
$725$	−1.75036e13			−0.0873850
$726$			4.22526e13i			0.209493i
$727$	−6.53955e13			−0.322015			−0.161007	−	0.986953i	$-0.551474\pi$
$727$	−6.53955e13			−0.322015			−0.161007	+	0.986953i	$0.551474\pi$
$728$	−1.88665e14			−0.922643
$729$	7.62560e12			0.0370370
$730$	3.28891e14			1.58649
$731$			4.65683e13i			0.223102i
$732$		−	3.53460e13i		−	0.168184i
$733$	−6.74238e13			−0.318635			−0.159318	−	0.987227i	$-0.550929\pi$
$733$	−6.74238e13			−0.318635			−0.159318	+	0.987227i	$0.550929\pi$
$734$	1.91668e14			0.899639
$735$	1.23331e14			0.574957
$736$	7.10280e13			0.328882
$737$	1.83378e14			0.843353
$738$		−	1.95310e14i		−	0.892159i
$739$		−	1.38269e13i		−	0.0627341i	−0.999508	−	0.0313671i	$-0.990014\pi$
$739$		−	1.38269e13i		−	0.0627341i	0.999508	−	0.0313671i	$-0.00998608\pi$
$740$		−	1.11455e14i		−	0.502272i
$741$		−	1.56157e12i		−	0.00698989i
$742$			2.34583e14i			1.04298i
$743$	−3.62484e13			−0.160083			−0.0800414	−	0.996792i	$-0.525505\pi$
$743$	−3.62484e13			−0.160083			−0.0800414	+	0.996792i	$0.525505\pi$
$744$	2.65821e13			0.116607
$745$			3.12002e13i			0.135949i
$746$		−	3.60706e14i		−	1.56120i
$747$		−	1.48122e14i		−	0.636819i
$748$		−	1.33002e14i		−	0.568003i
$749$	2.76494e14			1.17294
$750$		−	2.27046e14i		−	0.956769i
$751$			1.53369e14i			0.642004i	0.947079	+	0.321002i	$0.104020\pi$
$751$			1.53369e14i			0.642004i	−0.947079	+	0.321002i	$0.895980\pi$
$752$			3.12661e13i			0.130012i
$753$	1.41358e14			0.583909
$754$	−4.32432e13			−0.177444
$755$			1.17050e14i			0.477132i
$756$	1.14393e14			0.463223
$757$	−1.02440e14			−0.412088			−0.206044	−	0.978543i	$-0.566059\pi$
$757$	−1.02440e14			−0.412088			−0.206044	+	0.978543i	$0.566059\pi$
$758$			5.96598e14i			2.38416i
$759$	−3.67076e13			−0.145729
$760$			2.50256e12i			0.00986998i
$761$	4.48293e13			0.175646			0.0878230	−	0.996136i	$-0.472009\pi$
$761$	4.48293e13			0.175646			0.0878230	+	0.996136i	$0.472009\pi$
$762$			2.88613e14i			1.12342i
$763$			5.04172e14i			1.94965i
$764$			6.84695e14i			2.63045i
$765$	2.48936e13			0.0950123
$766$			4.84515e14i			1.83723i
$767$	−9.46819e13	+	1.58744e14i	−0.356689	+	0.598026i
$768$	−1.03747e14			−0.388303
$769$		−	7.98791e13i		−	0.297031i	−0.988910	−	0.148515i	$-0.952551\pi$
$769$		−	7.98791e13i		−	0.297031i	0.988910	−	0.148515i	$-0.0474494\pi$
$770$	4.01341e14			1.48272
$771$	−1.31531e14			−0.482787
$772$	6.65679e14			2.42761
$773$			4.49751e14i			1.62958i	0.579760	+	0.814788i	$0.303146\pi$
$773$			4.49751e14i			1.62958i	−0.579760	+	0.814788i	$0.696854\pi$
$774$	−7.77180e13			−0.279780
$775$		−	3.65780e13i		−	0.130831i
$776$	9.71217e13			0.345150
$777$		−	1.25343e14i		−	0.442584i
$778$		−	3.81752e14i		−	1.33932i
$779$	8.39395e12			0.0292603
$780$		−	1.19691e14i		−	0.414563i
$781$		−	2.37900e14i		−	0.818728i
$782$	−5.64877e13			−0.193161
$783$	9.07554e12			0.0308364
$784$	−8.32931e13			−0.281209
$785$			2.34295e14i			0.785984i
$786$	−2.48155e14			−0.827201
$787$	−1.28414e14			−0.425344			−0.212672	−	0.977124i	$-0.568217\pi$
$787$	−1.28414e14			−0.425344			−0.212672	+	0.977124i	$0.568217\pi$
$788$	1.26761e14			0.417211
$789$	8.29320e13			0.271230
$790$			1.23565e14i			0.401569i
$791$		−	5.37018e14i		−	1.73423i
$792$	7.68309e13			0.246553
$793$	−4.15919e13			−0.132630
$794$	3.25303e14			1.03083
$795$	−5.15128e13			−0.162211
$796$	6.42569e14			2.01073
$797$			4.67600e14i			1.45406i	0.686605	+	0.727031i	$0.259100\pi$
$797$			4.67600e14i			1.45406i	−0.686605	+	0.727031i	$0.740900\pi$
$798$			8.13094e12i			0.0251262i
$799$		−	9.40002e13i		−	0.288666i
$800$			2.04569e14i			0.624295i
$801$		−	1.06708e14i		−	0.323618i
$802$	1.59968e14			0.482127
$803$	4.33956e14			1.29978
$804$			2.84758e14i			0.847608i
$805$		−	1.03065e14i		−	0.304881i
$806$		−	9.03671e13i		−	0.265665i
$807$		−	9.36214e13i		−	0.273532i
$808$	−3.39768e14			−0.986564
$809$		−	5.35501e14i		−	1.54532i	−0.634822	−	0.772659i	$-0.718926\pi$
$809$		−	5.35501e14i		−	1.54532i	0.634822	−	0.772659i	$-0.281074\pi$
$810$			4.15449e13i			0.119150i
$811$		−	6.40192e14i		−	1.82476i	−0.409344	−	0.912380i	$-0.634242\pi$
$811$		−	6.40192e14i		−	1.82476i	0.409344	−	0.912380i	$-0.365758\pi$
$812$	1.36144e14			0.385671
$813$	−1.82475e14			−0.513748
$814$		−	2.43216e14i		−	0.680565i
$815$	1.29407e14			0.359889
$816$	−1.68122e13			−0.0464700
$817$		−	3.34013e12i		−	0.00917600i
$818$	−1.03166e15			−2.81688
$819$		−	1.34607e14i		−	0.365298i
$820$	6.43381e14			1.73540
$821$		−	4.27084e13i		−	0.114498i	−0.998360	−	0.0572490i	$-0.981767\pi$
$821$		−	4.27084e13i		−	0.114498i	0.998360	−	0.0572490i	$-0.0182329\pi$
$822$			4.37155e14i			1.16487i
$823$		−	5.55121e14i		−	1.47024i	−0.677937	−	0.735120i	$-0.737126\pi$
$823$		−	5.55121e14i		−	1.47024i	0.677937	−	0.735120i	$-0.262874\pi$
$824$	−1.11788e14			−0.294279
$825$		−	1.05722e14i		−	0.276628i
$826$	4.92999e14	−	8.26564e14i	1.28217	−	2.14969i
$827$	−5.66330e14			−1.46400			−0.732002	−	0.681303i	$-0.761414\pi$
$827$	−5.66330e14			−1.46400			−0.732002	+	0.681303i	$0.761414\pi$
$828$		−	5.70013e13i		−	0.146465i
$829$	−6.99218e14			−1.78583			−0.892914	−	0.450227i	$-0.851343\pi$
$829$	−6.99218e14			−1.78583			−0.892914	+	0.450227i	$0.851343\pi$
$830$	8.06981e14			2.04867
$831$	2.74672e13			0.0693122
$832$			4.52539e14i			1.13511i
$833$	2.50417e14			0.624366
$834$		−	1.06958e14i		−	0.265084i
$835$	−1.31726e14			−0.324518
$836$			9.53963e12i			0.0233615i
$837$			1.89655e13i			0.0461677i
$838$	8.25087e14			1.99655
$839$			3.20522e14i			0.770989i	0.922710	+	0.385495i	$0.125969\pi$
$839$			3.20522e14i			0.770989i	−0.922710	+	0.385495i	$0.874031\pi$
$840$			2.15719e14i			0.515814i
$841$	−4.09906e14			−0.974326
$842$	−1.16375e15			−2.74978
$843$	−3.08404e14			−0.724406
$844$			7.39268e13i			0.172619i
$845$	1.49636e14			0.347338
$846$	1.56877e14			0.361999
$847$	−1.56531e14			−0.359074
$848$	3.47898e13			0.0793365
$849$		−	9.37119e13i		−	0.212450i
$850$		−	1.62691e14i		−	0.366665i
$851$	−6.24579e13			−0.139939
$852$	3.69423e14			0.822860
$853$	−2.49877e14			−0.553325			−0.276663	−	0.960967i	$-0.589228\pi$
$853$	−2.49877e14			−0.553325			−0.276663	+	0.960967i	$0.589228\pi$
$854$	2.16565e14			0.476759
$855$	−1.78550e12			−0.00390777
$856$			2.88371e14i			0.627456i
$857$			3.33483e13i			0.0721390i	0.999349	+	0.0360695i	$0.0114838\pi$
$857$			3.33483e13i			0.0721390i	−0.999349	+	0.0360695i	$0.988516\pi$
$858$		−	2.61190e14i		−	0.561721i
$859$			8.66469e14i			1.85262i	0.376758	+	0.926312i	$0.377039\pi$
$859$			8.66469e14i			1.85262i	−0.376758	+	0.926312i	$0.622961\pi$
$860$		−	2.56015e14i		−	0.544219i
$861$	7.23555e14			1.52917
$862$	1.99193e14			0.418541
$863$			1.68794e14i			0.352617i	0.984335	+	0.176309i	$0.0564157\pi$
$863$			1.68794e14i			0.352617i	−0.984335	+	0.176309i	$0.943584\pi$
$864$		−	1.06068e14i		−	0.220301i
$865$		−	2.80150e14i		−	0.578509i
$866$		−	1.35552e15i		−	2.78302i
$867$	−2.32291e14			−0.474173
$868$			2.84505e14i			0.577419i
$869$			1.63038e14i			0.328996i
$870$			4.94443e13i			0.0992019i
$871$	3.35076e14			0.668425
$872$	−5.25830e14			−1.04295
$873$			6.92935e13i			0.136654i
$874$	4.05161e12			0.00794456
$875$	8.41126e14			1.63991
$876$			6.73868e14i			1.30633i
$877$	5.35503e14			1.03220			0.516100	−	0.856528i	$-0.327383\pi$
$877$	5.35503e14			1.03220			0.516100	+	0.856528i	$0.327383\pi$
$878$			6.23113e14i			1.19425i
$879$	1.94996e14			0.371605
$880$		−	5.95209e13i		−	0.112786i
$881$		−	2.99832e12i		−	0.00564935i	−0.999996	−	0.00282468i	$-0.999101\pi$
$881$		−	2.99832e12i		−	0.00564935i	0.999996	−	0.00282468i	$-0.000899124\pi$
$882$			4.17922e14i			0.782983i
$883$	−1.14025e14			−0.212420			−0.106210	−	0.994344i	$-0.533872\pi$
$883$	−1.14025e14			−0.212420			−0.106210	+	0.994344i	$0.533872\pi$
$884$		−	2.43027e14i		−	0.450188i
$885$	1.81508e14	+	1.08259e14i	0.334333	+	0.199411i
$886$	4.29722e14			0.787081
$887$			5.14714e14i			0.937449i	0.883344	+	0.468725i	$0.155286\pi$
$887$			5.14714e14i			0.937449i	−0.883344	+	0.468725i	$0.844714\pi$
$888$	1.30728e14			0.236757
$889$	−1.06921e15			−1.92555
$890$	5.81352e14			1.04109
$891$			5.48166e13i			0.0976165i
$892$	5.60217e14			0.992046
$893$			6.74221e12i			0.0118726i
$894$	−1.05725e14			−0.185136
$895$			2.03088e13i			0.0353646i
$896$		−	1.31593e15i		−	2.27874i
$897$	−6.70738e13			−0.115502
$898$		−	1.47604e14i		−	0.252764i
$899$			2.25717e13i			0.0384384i
$900$	1.64171e14			0.278024
$901$	−1.04594e14			−0.176150
$902$	1.40398e15			2.35142
$903$		−	2.87918e14i		−	0.479546i
$904$	5.60086e14			0.927711
$905$	−2.37761e14			−0.391650
$906$	−3.96640e14			−0.649763
$907$	−6.33701e14			−1.03240			−0.516200	−	0.856468i	$-0.672654\pi$
$907$	−6.33701e14			−1.03240			−0.516200	+	0.856468i	$0.672654\pi$
$908$		−	4.65296e14i		−	0.753876i
$909$		−	2.42414e14i		−	0.390606i
$910$	7.33348e14			1.17518
$911$	−7.63257e14			−1.21641			−0.608203	−	0.793781i	$-0.708109\pi$
$911$	−7.63257e14			−1.21641			−0.608203	+	0.793781i	$0.708109\pi$
$912$	1.20586e12			0.00191127
$913$	1.06477e15			1.67843
$914$	−2.22473e14			−0.348776
$915$			4.75562e13i			0.0741484i
$916$		−	9.48543e14i		−	1.47089i
$917$		−	9.19330e14i		−	1.41783i
$918$			8.43548e13i			0.129389i
$919$		−	7.53959e14i		−	1.15019i	−0.818086	−	0.575096i	$-0.804965\pi$
$919$		−	7.53959e14i		−	1.15019i	0.818086	−	0.575096i	$-0.195035\pi$
$920$	1.07492e14			0.163093
$921$	−1.28939e14			−0.194575
$922$			1.25082e14i			0.187733i
$923$		−	4.34702e14i		−	0.648908i
$924$			8.22312e14i			1.22089i
$925$		−	1.79886e14i		−	0.265637i
$926$	3.10141e14			0.455517
$927$		−	7.97574e13i		−	0.116512i
$928$		−	1.26236e14i		−	0.183419i
$929$		−	1.13752e15i		−	1.64392i	−0.569548	−	0.821958i	$-0.692882\pi$
$929$		−	1.13752e15i		−	1.64392i	0.569548	−	0.821958i	$-0.307118\pi$
$930$	−1.03326e14			−0.148523
$931$	−1.79613e13			−0.0256796
$932$		−	8.63906e14i		−	1.22853i
$933$	−3.50810e14			−0.496208
$934$	−3.51327e14			−0.494285
$935$			1.78947e14i			0.250419i
$936$	1.40389e14			0.195413
$937$			6.68677e14i			0.925803i	0.886410	+	0.462901i	$0.153192\pi$
$937$			6.68677e14i			0.925803i	−0.886410	+	0.462901i	$0.846808\pi$
$938$	−1.74471e15			−2.40275
$939$		−	3.84239e14i		−	0.526349i
$940$			5.16778e14i			0.704149i
$941$		−	6.55700e13i		−	0.0888703i	−0.999012	−	0.0444352i	$-0.985851\pi$
$941$		−	6.55700e13i		−	0.0888703i	0.999012	−	0.0444352i	$-0.0141488\pi$
$942$	−7.93935e14			−1.07036
$943$		−	3.60544e14i		−	0.483503i
$944$	−1.22584e14	−	7.31143e13i	−0.163521	−	0.0975309i
$945$	−1.53909e14			−0.204224
$946$		−	5.58675e14i		−	0.737401i
$947$	4.02311e14			0.528216			0.264108	−	0.964493i	$-0.414922\pi$
$947$	4.02311e14			0.528216			0.264108	+	0.964493i	$0.414922\pi$
$948$	−2.53173e14			−0.330656
$949$	7.92944e14			1.03018
$950$			1.16691e13i			0.0150806i
$951$	−7.93805e14			−1.02050
$952$			4.38007e14i			0.560140i
$953$	8.91998e14			1.13475			0.567374	−	0.823460i	$-0.307959\pi$
$953$	8.91998e14			1.13475			0.567374	+	0.823460i	$0.307959\pi$
$954$		−	1.74557e14i		−	0.220900i
$955$		−	9.21221e14i		−	1.15970i
$956$	−1.48555e15			−1.86037
$957$			6.52394e13i			0.0812738i
$958$		−	6.91304e14i		−	0.856725i
$959$	−1.61951e15			−1.99659
$960$	5.17434e14			0.634598
$961$	7.72459e14			0.942451
$962$		−	4.44414e14i		−	0.539402i
$963$	−2.05744e14			−0.248426
$964$	6.57578e14			0.789882
$965$	−8.95635e14			−1.07027
$966$	3.49247e14			0.415190
$967$		−	3.18395e14i		−	0.376560i	−0.982115	−	0.188280i	$-0.939709\pi$
$967$		−	3.18395e14i		−	0.376560i	0.982115	−	0.188280i	$-0.0602912\pi$
$968$		−	1.63255e14i		−	0.192084i
$969$	−3.62537e12			−0.00424359
$970$	−3.77517e14			−0.439620
$971$	−1.19147e14			−0.138034			−0.0690172	−	0.997615i	$-0.521986\pi$
$971$	−1.19147e14			−0.138034			−0.0690172	+	0.997615i	$0.521986\pi$
$972$	−8.51218e13			−0.0981091
$973$	3.96243e14			0.454357
$974$			2.15346e14i			0.245664i
$975$		−	1.93180e14i		−	0.219250i
$976$		−	3.21177e13i		−	0.0362656i
$977$		−	4.28514e14i		−	0.481385i	−0.970601	−	0.240692i	$-0.922626\pi$
$977$		−	4.28514e14i		−	0.481385i	0.970601	−	0.240692i	$-0.0773745\pi$
$978$			4.38510e14i			0.490101i
$979$	7.67067e14			0.852942
$980$	−1.37670e15			−1.52303
$981$		−	3.75164e14i		−	0.412930i
$982$			3.20697e14i			0.351186i
$983$			6.67690e14i			0.727456i	0.931505	+	0.363728i	$0.118496\pi$
$983$			6.67690e14i			0.727456i	−0.931505	+	0.363728i	$0.881504\pi$
$984$			7.54636e14i			0.818017i
$985$	−1.70551e14			−0.183938
$986$			1.00394e14i			0.107727i
$987$			5.81175e14i			0.620471i
$988$			1.74312e13i			0.0185158i
$989$	−1.43468e14			−0.151626
$990$	−2.98645e14			−0.314036
$991$		−	7.41790e14i		−	0.776091i	−0.921640	−	0.388045i	$-0.873150\pi$
$991$		−	7.41790e14i		−	0.776091i	0.921640	−	0.388045i	$-0.126850\pi$
$992$	2.63801e14			0.274611
$993$	−8.11693e14			−0.840708
$994$			2.26345e15i			2.33259i
$995$	−8.64542e14			−0.886483
$996$			1.65343e15i			1.68690i
$997$	−6.46805e14			−0.656595			−0.328298	−	0.944574i	$-0.606475\pi$
$997$	−6.46805e14			−0.656595			−0.328298	+	0.944574i	$0.606475\pi$
$998$			3.51571e14i			0.355108i
$999$			9.32702e13i			0.0937380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.88	yes	100
59.58	odd	2	inner	177.11.c.a.58.13	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.13	✓	100	59.58	odd	2	inner
177.11.c.a.58.88	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} +7140.06i q^{6} -26451.4 q^{7} -27587.7i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} +7140.06i q^{6} -26451.4 q^{7} -27587.7i q^{8} +19683.0 q^{9} +107235. i q^{10} +141491. i q^{11} -219714. q^{12} +258539. i q^{13} -1.34619e6i q^{14} +295614. q^{15} -199646. q^{16} +600229. q^{17} +1.00172e6i q^{18} -43051.6 q^{19} -3.29983e6 q^{20} -3.71103e6 q^{21} -7.20088e6 q^{22} +1.84919e6i q^{23} -3.87045e6i q^{24} -5.32588e6 q^{25} -1.31578e7 q^{26} +2.76145e6 q^{27} +4.14249e7 q^{28} +3.28651e6 q^{29} +1.50446e7i q^{30} +6.86797e6i q^{31} -3.84104e7i q^{32} +1.98507e7i q^{33} +3.05473e7i q^{34} -5.57350e7 q^{35} -3.08250e7 q^{36} +3.37758e7i q^{37} -2.19102e6i q^{38} +3.62720e7i q^{39} -5.81292e7i q^{40} -1.94974e8 q^{41} -1.88865e8i q^{42} +7.75843e7i q^{43} -2.21586e8i q^{44} +4.14735e7 q^{45} -9.41104e7 q^{46} -1.56607e8i q^{47} -2.80096e7 q^{48} +4.17203e8 q^{49} -2.71049e8i q^{50} +8.42097e7 q^{51} -4.04891e8i q^{52} -1.74257e8 q^{53} +1.40538e8i q^{54} +2.98132e8i q^{55} +7.29734e8i q^{56} -6.03998e6 q^{57} +1.67260e8i q^{58} +(6.14004e8 + 3.66219e8i) q^{59} -4.62953e8 q^{60} +1.60873e8i q^{61} -3.49530e8 q^{62} -5.20644e8 q^{63} +1.75037e9 q^{64} +5.44760e8i q^{65} -1.01026e9 q^{66} -1.29604e9i q^{67} -9.40003e8 q^{68} +2.59434e8i q^{69} -2.83651e9i q^{70} -1.68138e9 q^{71} -5.43009e8i q^{72} -3.06702e9i q^{73} -1.71895e9 q^{74} -7.47200e8 q^{75} +6.74221e7 q^{76} -3.74264e9i q^{77} -1.84598e9 q^{78} +1.15229e9 q^{79} -4.20669e8 q^{80} +3.87420e8 q^{81} -9.92277e9i q^{82} -7.52537e9i q^{83} +5.81176e9 q^{84} +1.26472e9 q^{85} -3.94848e9 q^{86} +4.61085e8 q^{87} +3.90341e9 q^{88} -5.42130e9i q^{89} +2.11070e9i q^{90} -6.83873e9i q^{91} -2.89597e9i q^{92} +9.63549e8i q^{93} +7.97019e9 q^{94} -9.07128e7 q^{95} -5.38882e9i q^{96} +3.52047e9i q^{97} +2.12326e10i q^{98} +2.78497e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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