LMFDB - Embedded newform 177.9.c.a.58.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,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, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
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:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.66
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} +972.254i q^{6} +1280.77 q^{7} +1658.51i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q+20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} +972.254i q^{6} +1280.77 q^{7} +1658.51i q^{8} +2187.00 q^{9} -12521.6i q^{10} +19456.6i q^{11} -8241.26 q^{12} -31433.4i q^{13} +26627.3i q^{14} -28166.2 q^{15} -79594.3 q^{16} +137031. q^{17} +45467.8i q^{18} -149188. q^{19} +106139. q^{20} +59895.7 q^{21} -404503. q^{22} +411676. i q^{23} +77561.0i q^{24} -27873.9 q^{25} +653501. q^{26} +102276. q^{27} -225705. q^{28} -288373. q^{29} -585577. i q^{30} +1.63017e6i q^{31} -1.23019e6i q^{32} +909895. i q^{33} +2.84888e6i q^{34} -771393. q^{35} -385405. q^{36} -2.14787e6i q^{37} -3.10163e6i q^{38} -1.46999e6i q^{39} -998903. i q^{40} +960198. q^{41} +1.24523e6i q^{42} -21546.2i q^{43} -3.42875e6i q^{44} -1.31720e6 q^{45} -8.55876e6 q^{46} +106905. i q^{47} -3.72226e6 q^{48} -4.12443e6 q^{49} -579499. i q^{50} +6.40830e6 q^{51} +5.53937e6i q^{52} -1.48206e7 q^{53} +2.12632e6i q^{54} -1.17185e7i q^{55} +2.12417e6i q^{56} -6.97686e6 q^{57} -5.99529e6i q^{58} +(4.18654e6 - 1.13712e7i) q^{59} +4.96361e6 q^{60} +1.74260e6i q^{61} -3.38914e7 q^{62} +2.80104e6 q^{63} +5.19953e6 q^{64} +1.89320e7i q^{65} -1.89168e7 q^{66} -5.44049e6i q^{67} -2.41483e7 q^{68} +1.92522e7i q^{69} -1.60373e7i q^{70} -2.69743e7 q^{71} +3.62717e6i q^{72} +2.23392e7i q^{73} +4.46544e7 q^{74} -1.30353e6 q^{75} +2.62908e7 q^{76} +2.49194e7i q^{77} +3.05612e7 q^{78} -1.27758e7 q^{79} +4.79387e7 q^{80} +4.78297e6 q^{81} +1.99625e7i q^{82} -6.43241e7i q^{83} -1.05552e7 q^{84} -8.25321e7 q^{85} +447946. q^{86} -1.34859e7 q^{87} -3.22690e7 q^{88} -3.11328e7i q^{89} -2.73847e7i q^{90} -4.02589e7i q^{91} -7.25479e7i q^{92} +7.62357e7i q^{93} -2.22255e6 q^{94} +8.98545e7 q^{95} -5.75302e7i q^{96} +3.65832e7i q^{97} -8.57470e7i q^{98} +4.25516e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * 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 $

$2$			20.7900i			1.29938i	0.760200	+	0.649689i	$0.225101\pi$
$2$			20.7900i			1.29938i	−0.760200	+	0.649689i	$0.774899\pi$
$3$	46.7654			0.577350
$3$	46.7654			0.577350
$4$	−176.226			−0.688381
$5$	−602.288			−0.963661			−0.481831	−	0.876264i	$-0.660028\pi$
$5$	−602.288			−0.963661			−0.481831	+	0.876264i	$0.660028\pi$
$6$			972.254i			0.750196i
$7$	1280.77			0.533432			0.266716	−	0.963775i	$-0.414061\pi$
$7$	1280.77			0.533432			0.266716	+	0.963775i	$0.414061\pi$
$8$			1658.51i			0.404910i
$9$	2187.00			0.333333
$10$		−	12521.6i		−	1.25216i
$11$			19456.6i			1.32891i	0.747327	+	0.664456i	$0.231337\pi$
$11$			19456.6i			1.32891i	−0.747327	+	0.664456i	$0.768663\pi$
$12$	−8241.26			−0.397437
$13$		−	31433.4i		−	1.10057i	−0.834977	−	0.550285i	$-0.814519\pi$
$13$		−	31433.4i		−	1.10057i	0.834977	−	0.550285i	$-0.185481\pi$
$14$			26627.3i			0.693130i
$15$	−28166.2			−0.556370
$16$	−79594.3			−1.21451
$17$	137031.			1.64068			0.820338	−	0.571879i	$-0.193785\pi$
$17$	137031.			1.64068			0.820338	+	0.571879i	$0.193785\pi$
$18$			45467.8i			0.433126i
$19$	−149188.			−1.14478			−0.572389	−	0.819983i	$-0.693983\pi$
$19$	−149188.			−1.14478			−0.572389	+	0.819983i	$0.693983\pi$
$20$	106139.			0.663366
$21$	59895.7			0.307977
$22$	−404503.			−1.72676
$23$			411676.i			1.47111i	0.677466	+	0.735554i	$0.263078\pi$
$23$			411676.i			1.47111i	−0.677466	+	0.735554i	$0.736922\pi$
$24$			77561.0i			0.233775i
$25$	−27873.9			−0.0713572
$26$	653501.			1.43006
$27$	102276.			0.192450
$28$	−225705.			−0.367205
$29$	−288373.			−0.407721			−0.203861	−	0.979000i	$-0.565349\pi$
$29$	−288373.			−0.407721			−0.203861	+	0.979000i	$0.565349\pi$
$30$		−	585577.i		−	0.722935i
$31$			1.63017e6i			1.76517i	0.470150	+	0.882587i	$0.344200\pi$
$31$			1.63017e6i			1.76517i	−0.470150	+	0.882587i	$0.655800\pi$
$32$		−	1.23019e6i		−	1.17320i
$33$			909895.i			0.767248i
$34$			2.84888e6i			2.13186i
$35$	−771393.			−0.514048
$36$	−385405.			−0.229460
$37$		−	2.14787e6i		−	1.14605i	−0.819540	−	0.573023i	$-0.805771\pi$
$37$		−	2.14787e6i		−	1.14605i	0.819540	−	0.573023i	$-0.194229\pi$
$38$		−	3.10163e6i		−	1.48750i
$39$		−	1.46999e6i		−	0.635414i
$40$		−	998903.i		−	0.390196i
$41$	960198.			0.339801			0.169901	−	0.985461i	$-0.445655\pi$
$41$	960198.			0.339801			0.169901	+	0.985461i	$0.445655\pi$
$42$			1.24523e6i			0.400179i
$43$		−	21546.2i		−	0.00630227i	−0.999995	−	0.00315113i	$-0.998997\pi$
$43$		−	21546.2i		−	0.00630227i	0.999995	−	0.00315113i	$-0.00100304\pi$
$44$		−	3.42875e6i		−	0.914798i
$45$	−1.31720e6			−0.321220
$46$	−8.55876e6			−1.91152
$47$			106905.i			0.0219081i	0.999940	+	0.0109541i	$0.00348686\pi$
$47$			106905.i			0.0219081i	−0.999940	+	0.0109541i	$0.996513\pi$
$48$	−3.72226e6			−0.701199
$49$	−4.12443e6			−0.715450
$50$		−	579499.i		−	0.0927199i
$51$	6.40830e6			0.947244
$52$			5.53937e6i			0.757612i
$53$	−1.48206e7			−1.87828			−0.939142	−	0.343528i	$-0.888378\pi$
$53$	−1.48206e7			−1.87828			−0.939142	+	0.343528i	$0.888378\pi$
$54$			2.12632e6i			0.250065i
$55$		−	1.17185e7i		−	1.28062i
$56$			2.12417e6i			0.215992i
$57$	−6.97686e6			−0.660937
$58$		−	5.99529e6i		−	0.529784i
$59$	4.18654e6	−	1.13712e7i	0.345500	−	0.938419i
$59$	4.18654e6	−	1.13712e7i	0.345500	−	0.938419i
$60$	4.96361e6			0.382995
$61$			1.74260e6i			0.125857i	0.998018	+	0.0629285i	$0.0200440\pi$
$61$			1.74260e6i			0.125857i	−0.998018	+	0.0629285i	$0.979956\pi$
$62$	−3.38914e7			−2.29363
$63$	2.80104e6			0.177811
$64$	5.19953e6			0.309916
$65$			1.89320e7i			1.06058i
$66$	−1.89168e7			−0.996944
$67$		−	5.44049e6i		−	0.269984i	−0.990847	−	0.134992i	$-0.956899\pi$
$67$		−	5.44049e6i		−	0.269984i	0.990847	−	0.134992i	$-0.0431009\pi$
$68$	−2.41483e7			−1.12941
$69$			1.92522e7i			0.849344i
$70$		−	1.60373e7i		−	0.667942i
$71$	−2.69743e7			−1.06149			−0.530746	−	0.847531i	$-0.678088\pi$
$71$	−2.69743e7			−1.06149			−0.530746	+	0.847531i	$0.678088\pi$
$72$			3.62717e6i			0.134970i
$73$			2.23392e7i			0.786639i	0.919402	+	0.393319i	$0.128673\pi$
$73$			2.23392e7i			0.786639i	−0.919402	+	0.393319i	$0.871327\pi$
$74$	4.46544e7			1.48915
$75$	−1.30353e6			−0.0411981
$76$	2.62908e7			0.788043
$77$			2.49194e7i			0.708884i
$78$	3.05612e7			0.825643
$79$	−1.27758e7			−0.328005			−0.164003	−	0.986460i	$-0.552441\pi$
$79$	−1.27758e7			−0.328005			−0.164003	+	0.986460i	$0.552441\pi$
$80$	4.79387e7			1.17038
$81$	4.78297e6			0.111111
$82$			1.99625e7i			0.441530i
$83$		−	6.43241e7i		−	1.35538i	−0.735347	−	0.677691i	$-0.762981\pi$
$83$		−	6.43241e7i		−	1.35538i	0.735347	−	0.677691i	$-0.237019\pi$
$84$	−1.05552e7			−0.212006
$85$	−8.25321e7			−1.58106
$86$	447946.			0.00818902
$87$	−1.34859e7			−0.235398
$88$	−3.22690e7			−0.538090
$89$		−	3.11328e7i		−	0.496202i	−0.968734	−	0.248101i	$-0.920194\pi$
$89$		−	3.11328e7i		−	0.496202i	0.968734	−	0.248101i	$-0.0798064\pi$
$90$		−	2.73847e7i		−	0.417386i
$91$		−	4.02589e7i		−	0.587079i
$92$		−	7.25479e7i		−	1.01268i
$93$			7.62357e7i			1.01912i
$94$	−2.22255e6			−0.0284669
$95$	8.98545e7			1.10318
$96$		−	5.75302e7i		−	0.677347i
$97$			3.65832e7i			0.413233i	0.978422	+	0.206617i	$0.0662453\pi$
$97$			3.65832e7i			0.413233i	−0.978422	+	0.206617i	$0.933755\pi$
$98$		−	8.57470e7i		−	0.929640i
$99$			4.25516e7i			0.442971i
$100$	4.91209e6			0.0491209
$101$			7.05978e6i			0.0678431i	0.999424	+	0.0339216i	$0.0107996\pi$
$101$			7.05978e6i			0.0678431i	−0.999424	+	0.0339216i	$0.989200\pi$
$102$			1.33229e8i			1.23083i
$103$		−	6.68911e7i		−	0.594319i	−0.954828	−	0.297159i	$-0.903961\pi$
$103$		−	6.68911e7i		−	0.594319i	0.954828	−	0.297159i	$-0.0960393\pi$
$104$	5.21327e7			0.445632
$105$	−3.60745e7			−0.296786
$106$		−	3.08120e8i		−	2.44060i
$107$	−2.26559e8			−1.72841			−0.864206	−	0.503139i	$-0.832178\pi$
$107$	−2.26559e8			−1.72841			−0.864206	+	0.503139i	$0.832178\pi$
$108$	−1.80236e7			−0.132479
$109$			6.94363e6i			0.0491904i	0.999697	+	0.0245952i	$0.00782969\pi$
$109$			6.94363e6i			0.0491904i	−0.999697	+	0.0245952i	$0.992170\pi$
$110$	2.43628e8			1.66401
$111$		−	1.00446e8i		−	0.661670i
$112$	−1.01942e8			−0.647860
$113$		−	1.80429e8i		−	1.10661i	−0.832980	−	0.553304i	$-0.813367\pi$
$113$		−	1.80429e8i		−	1.10661i	0.832980	−	0.553304i	$-0.186633\pi$
$114$		−	1.45049e8i		−	0.858807i
$115$		−	2.47948e8i		−	1.41765i
$116$	5.08188e7			0.280668
$117$		−	6.87448e7i		−	0.366857i
$118$	2.36407e8	+	8.70384e7i	1.21936	+	0.448934i
$119$	1.75505e8			0.875189
$120$		−	4.67141e7i		−	0.225280i
$121$	−1.64201e8			−0.766007
$122$	−3.62287e7			−0.163536
$123$	4.49040e7			0.196184
$124$		−	2.87278e8i		−	1.21511i
$125$	2.52057e8			1.03243
$126$			5.82338e7i			0.231043i
$127$	1.91244e7			0.0735144			0.0367572	−	0.999324i	$-0.488297\pi$
$127$	1.91244e7			0.0735144			0.0367572	+	0.999324i	$0.488297\pi$
$128$		−	2.06830e8i		−	0.770501i
$129$		−	1.00762e6i		−	0.00363862i
$130$	−3.93596e8			−1.37809
$131$		−	1.24907e8i		−	0.424133i	−0.977255	−	0.212066i	$-0.931981\pi$
$131$		−	1.24907e8i		−	0.424133i	0.977255	−	0.212066i	$-0.0680193\pi$
$132$		−	1.60347e8i		−	0.528159i
$133$	−1.91076e8			−0.610661
$134$	1.13108e8			0.350811
$135$	−6.15996e7			−0.185457
$136$			2.27267e8i			0.664326i
$137$	−1.18066e8			−0.335153			−0.167577	−	0.985859i	$-0.553594\pi$
$137$	−1.18066e8			−0.335153			−0.167577	+	0.985859i	$0.553594\pi$
$138$	−4.00254e8			−1.10362
$139$	5.31707e8			1.42434			0.712170	−	0.702007i	$-0.247713\pi$
$139$	5.31707e8			1.42434			0.712170	+	0.702007i	$0.247713\pi$
$140$	1.35939e8			0.353861
$141$			4.99944e6i			0.0126487i
$142$		−	5.60797e8i		−	1.37928i
$143$	6.11587e8			1.46256
$144$	−1.74073e8			−0.404838
$145$	1.73684e8			0.392905
$146$	−4.64432e8			−1.02214
$147$	−1.92880e8			−0.413065
$148$			3.78510e8i			0.788916i
$149$			5.45532e8i			1.10681i	0.832911	+	0.553407i	$0.186673\pi$
$149$			5.45532e8i			1.10681i	−0.832911	+	0.553407i	$0.813327\pi$
$150$		−	2.71005e7i		−	0.0535319i
$151$		−	2.12379e8i		−	0.408511i	−0.978918	−	0.204255i	$-0.934523\pi$
$151$		−	2.12379e8i		−	0.408511i	0.978918	−	0.204255i	$-0.0654773\pi$
$152$		−	2.47431e8i		−	0.463532i
$153$	2.99686e8			0.546892
$154$	−5.18076e8			−0.921108
$155$		−	9.81835e8i		−	1.70103i
$156$			2.59051e8i			0.437407i
$157$			8.76380e8i			1.44243i	0.692713	+	0.721213i	$0.256415\pi$
$157$			8.76380e8i			1.44243i	−0.692713	+	0.721213i	$0.743585\pi$
$158$		−	2.65610e8i		−	0.426203i
$159$	−6.93089e8			−1.08443
$160$			7.40928e8i			1.13057i
$161$			5.27263e8i			0.784736i
$162$			9.94381e7i			0.144375i
$163$	−8.37355e8			−1.18620			−0.593101	−	0.805128i	$-0.702097\pi$
$163$	−8.37355e8			−1.18620			−0.593101	+	0.805128i	$0.702097\pi$
$164$	−1.69211e8			−0.233913
$165$		−	5.48019e8i		−	0.739367i
$166$	1.33730e9			1.76115
$167$	1.08575e9			1.39593			0.697963	−	0.716133i	$-0.254090\pi$
$167$	1.08575e9			1.39593			0.697963	+	0.716133i	$0.254090\pi$
$168$			9.93378e7i			0.124703i
$169$	−1.72327e8			−0.211254
$170$		−	1.71584e9i		−	2.05439i
$171$	−3.26275e8			−0.381592
$172$			3.79699e6i			0.00433836i
$173$			4.68803e8i			0.523367i	0.965154	+	0.261683i	$0.0842776\pi$
$173$			4.68803e8i			0.523367i	−0.965154	+	0.261683i	$0.915722\pi$
$174$		−	2.80372e8i		−	0.305871i
$175$	−3.57001e7			−0.0380642
$176$		−	1.54863e9i		−	1.61398i
$177$	1.95785e8	−	5.31777e8i	0.199474	−	0.541796i
$178$	6.47252e8			0.644753
$179$			1.14428e9i			1.11460i	0.830310	+	0.557302i	$0.188164\pi$
$179$			1.14428e9i			1.11460i	−0.830310	+	0.557302i	$0.811836\pi$
$180$	2.32125e8			0.221122
$181$	−1.96453e9			−1.83039			−0.915197	−	0.403006i	$-0.867965\pi$
$181$	−1.96453e9			−1.83039			−0.915197	+	0.403006i	$0.867965\pi$
$182$	8.36985e8			0.762838
$183$			8.14932e7i			0.0726636i
$184$	−6.82770e8			−0.595667
$185$			1.29364e9i			1.10440i
$186$	−1.58494e9			−1.32423
$187$			2.66615e9i			2.18031i
$188$		−	1.88393e7i		−	0.0150812i
$189$	1.30992e8			0.102659
$190$			1.86808e9i			1.43344i
$191$			2.38546e9i			1.79241i	0.443638	+	0.896206i	$0.353688\pi$
$191$			2.38546e9i			1.79241i	−0.443638	+	0.896206i	$0.646312\pi$
$192$	2.43158e8			0.178930
$193$	−2.68938e9			−1.93831			−0.969155	−	0.246451i	$-0.920735\pi$
$193$	−2.68938e9			−1.93831			−0.969155	+	0.246451i	$0.920735\pi$
$194$	−7.60567e8			−0.536946
$195$			8.85360e8i			0.612324i
$196$	7.26830e8			0.492502
$197$	−1.73442e9			−1.15157			−0.575784	−	0.817602i	$-0.695303\pi$
$197$	−1.73442e9			−1.15157			−0.575784	+	0.817602i	$0.695303\pi$
$198$	−8.84649e8			−0.575586
$199$	1.06579e9			0.679610			0.339805	−	0.940496i	$-0.389639\pi$
$199$	1.06579e9			0.679610			0.339805	+	0.940496i	$0.389639\pi$
$200$		−	4.62292e7i		−	0.0288933i
$201$		−	2.54426e8i		−	0.155875i
$202$	−1.46773e8			−0.0881538
$203$	−3.69340e8			−0.217492
$204$	−1.12931e9			−0.652065
$205$	−5.78316e8			−0.327453
$206$	1.39067e9			0.772244
$207$			9.00336e8i			0.490369i
$208$			2.50192e9i			1.33666i
$209$		−	2.90270e9i		−	1.52131i
$210$		−	7.49990e8i		−	0.385636i
$211$			1.55428e9i			0.784149i	0.919933	+	0.392075i	$0.128243\pi$
$211$			1.55428e9i			0.784149i	−0.919933	+	0.392075i	$0.871757\pi$
$212$	2.61176e9			1.29298
$213$	−1.26146e9			−0.612853
$214$		−	4.71018e9i		−	2.24586i
$215$			1.29770e7i			0.00607325i
$216$			1.69626e8i			0.0779250i
$217$			2.08788e9i			0.941600i
$218$	−1.44358e8			−0.0639169
$219$			1.04470e9i			0.454166i
$220$			2.06510e9i			0.881555i
$221$		−	4.30734e9i		−	1.80568i
$222$	2.08828e9			0.859758
$223$	8.02134e8			0.324360			0.162180	−	0.986761i	$-0.448147\pi$
$223$	8.02134e8			0.324360			0.162180	+	0.986761i	$0.448147\pi$
$224$		−	1.57559e9i		−	0.625822i
$225$	−6.09602e7			−0.0237857
$226$	3.75113e9			1.43790
$227$			7.27978e7i			0.0274167i	0.999906	+	0.0137083i	$0.00436364\pi$
$227$			7.27978e7i			0.0274167i	−0.999906	+	0.0137083i	$0.995636\pi$
$228$	1.22950e9			0.454977
$229$		−	2.46205e9i		−	0.895271i	−0.894216	−	0.447635i	$-0.852266\pi$
$229$		−	2.46205e9i		−	0.895271i	0.894216	−	0.447635i	$-0.147734\pi$
$230$	5.15484e9			1.84206
$231$			1.16537e9i			0.409275i
$232$		−	4.78271e8i		−	0.165090i
$233$			4.04138e9i			1.37122i	0.727971	+	0.685608i	$0.240464\pi$
$233$			4.04138e9i			1.37122i	−0.727971	+	0.685608i	$0.759536\pi$
$234$	1.42921e9			0.476685
$235$		−	6.43875e7i		−	0.0211120i
$236$	−7.37776e8	+	2.00389e9i	−0.237835	+	0.645990i
$237$	−5.97467e8			−0.189374
$238$			3.64876e9i			1.13720i
$239$	2.73887e9			0.839421			0.419711	−	0.907658i	$-0.362132\pi$
$239$	2.73887e9			0.839421			0.419711	+	0.907658i	$0.362132\pi$
$240$	2.24187e9			0.675718
$241$	1.16077e9			0.344094			0.172047	−	0.985089i	$-0.444962\pi$
$241$	1.16077e9			0.344094			0.172047	+	0.985089i	$0.444962\pi$
$242$		−	3.41373e9i		−	0.995333i
$243$	2.23677e8			0.0641500
$244$		−	3.07090e8i		−	0.0866376i
$245$	2.48409e9			0.689452
$246$			9.33556e8i			0.254918i
$247$			4.68950e9i			1.25991i
$248$	−2.70366e9			−0.714737
$249$		−	3.00814e9i		−	0.782530i
$250$			5.24027e9i			1.34151i
$251$	−2.40560e9			−0.606077			−0.303039	−	0.952978i	$-0.598001\pi$
$251$	−2.40560e9			−0.606077			−0.303039	+	0.952978i	$0.598001\pi$
$252$	−4.93616e8			−0.122402
$253$	−8.00982e9			−1.95497
$254$			3.97597e8i			0.0955230i
$255$	−3.85964e9			−0.912823
$256$	5.63108e9			1.31109
$257$	−4.85521e9			−1.11295			−0.556475	−	0.830864i	$-0.687846\pi$
$257$	−4.85521e9			−1.11295			−0.556475	+	0.830864i	$0.687846\pi$
$258$	2.09484e7			0.00472793
$259$		−	2.75093e9i		−	0.611337i
$260$		−	3.33630e9i		−	0.730081i
$261$	−6.30673e8			−0.135907
$262$	2.59682e9			0.551108
$263$	3.33459e9			0.696978			0.348489	−	0.937313i	$-0.386695\pi$
$263$	3.33459e9			0.696978			0.348489	+	0.937313i	$0.386695\pi$
$264$	−1.50907e9			−0.310667
$265$	8.92625e9			1.81003
$266$		−	3.97248e9i		−	0.793479i
$267$		−	1.45594e9i		−	0.286482i
$268$			9.58753e8i			0.185852i
$269$			4.70921e9i			0.899370i	0.893187	+	0.449685i	$0.148464\pi$
$269$			4.70921e9i			0.899370i	−0.893187	+	0.449685i	$0.851536\pi$
$270$		−	1.28066e9i		−	0.240978i
$271$	2.40442e9			0.445793			0.222896	−	0.974842i	$-0.428449\pi$
$271$	2.40442e9			0.445793			0.222896	+	0.974842i	$0.428449\pi$
$272$	−1.09069e10			−1.99262
$273$		−	1.88272e9i		−	0.338950i
$274$		−	2.45460e9i		−	0.435490i
$275$		−	5.42331e8i		−	0.0948274i
$276$		−	3.39273e9i		−	0.584673i
$277$	−4.90773e8			−0.0833608			−0.0416804	−	0.999131i	$-0.513271\pi$
$277$	−4.90773e8			−0.0833608			−0.0416804	+	0.999131i	$0.513271\pi$
$278$			1.10542e10i			1.85075i
$279$			3.56519e9i			0.588391i
$280$		−	1.27937e9i		−	0.208143i
$281$	1.05372e10			1.69006			0.845028	−	0.534723i	$-0.179584\pi$
$281$	1.05372e10			1.69006			0.845028	+	0.534723i	$0.179584\pi$
$282$	−1.03939e8			−0.0164354
$283$			3.49969e8i			0.0545611i	0.999628	+	0.0272806i	$0.00868475\pi$
$283$			3.49969e8i			0.0545611i	−0.999628	+	0.0272806i	$0.991315\pi$
$284$	4.75357e9			0.730712
$285$	4.20208e9			0.636920
$286$			1.27149e10i			1.90042i
$287$	1.22979e9			0.181261
$288$		−	2.69042e9i		−	0.391067i
$289$	1.18017e10			1.69182
$290$			3.61089e9i			0.510532i
$291$			1.71083e9i			0.238580i
$292$		−	3.93673e9i		−	0.541507i
$293$	−3.02477e9			−0.410414			−0.205207	−	0.978719i	$-0.565787\pi$
$293$	−3.02477e9			−0.410414			−0.205207	+	0.978719i	$0.565787\pi$
$294$		−	4.00999e9i		−	0.536728i
$295$	−2.52151e9	+	6.84872e9i	−0.332944	+	0.904318i
$296$	3.56228e9			0.464046
$297$			1.98994e9i			0.255749i
$298$	−1.13416e10			−1.43817
$299$	1.29404e10			1.61906
$300$	2.29716e8			0.0283600
$301$		−	2.75957e7i		−	0.00336183i
$302$	4.41536e9			0.530810
$303$			3.30153e8i			0.0391692i
$304$	1.18746e10			1.39035
$305$		−	1.04955e9i		−	0.121284i
$306$			6.23049e9i			0.710619i
$307$	−1.28019e10			−1.44118			−0.720592	−	0.693359i	$-0.756130\pi$
$307$	−1.28019e10			−1.44118			−0.720592	+	0.693359i	$0.756130\pi$
$308$		−	4.39144e9i		−	0.487983i
$309$		−	3.12819e9i		−	0.343130i
$310$	2.04124e10			2.21028
$311$	−5.47848e9			−0.585623			−0.292812	−	0.956170i	$-0.594591\pi$
$311$	−5.47848e9			−0.585623			−0.292812	+	0.956170i	$0.594591\pi$
$312$	2.43800e9			0.257286
$313$		−	3.97064e9i		−	0.413698i	−0.978373	−	0.206849i	$-0.933679\pi$
$313$		−	3.97064e9i		−	0.413698i	0.978373	−	0.206849i	$-0.0663209\pi$
$314$	−1.82200e10			−1.87426
$315$	−1.68704e9			−0.171349
$316$	2.25143e9			0.225793
$317$	−5.72571e9			−0.567012			−0.283506	−	0.958970i	$-0.591498\pi$
$317$	−5.72571e9			−0.567012			−0.283506	+	0.958970i	$0.591498\pi$
$318$		−	1.44094e10i		−	1.40908i
$319$		−	5.61077e9i		−	0.541826i
$320$	−3.13162e9			−0.298654
$321$	−1.05951e10			−0.997899
$322$	−1.09618e10			−1.01967
$323$	−2.04434e10			−1.87821
$324$	−8.42882e8			−0.0764868
$325$			8.76171e8i			0.0785336i
$326$		−	1.74086e10i		−	1.54133i
$327$			3.24721e8i			0.0284001i
$328$			1.59250e9i			0.137589i
$329$			1.36920e8i			0.0116865i
$330$	1.13933e10			0.960717
$331$	−1.50335e10			−1.25241			−0.626207	−	0.779657i	$-0.715393\pi$
$331$	−1.50335e10			−1.25241			−0.626207	+	0.779657i	$0.715393\pi$
$332$			1.13356e10i			0.933019i
$333$		−	4.69740e9i		−	0.382015i
$334$			2.25727e10i			1.81384i
$335$			3.27674e9i			0.260173i
$336$	−4.76736e9			−0.374042
$337$		−	1.42090e10i		−	1.10165i	−0.834622	−	0.550824i	$-0.814314\pi$
$337$		−	1.42090e10i		−	1.10165i	0.834622	−	0.550824i	$-0.185686\pi$
$338$		−	3.58268e9i		−	0.274499i
$339$		−	8.43785e9i		−	0.638900i
$340$	1.45443e10			1.08837
$341$	−3.17177e10			−2.34576
$342$		−	6.78327e9i		−	0.495832i
$343$	−1.26658e10			−0.915076
$344$	3.57346e7			0.00255185
$345$		−	1.15954e10i		−	0.818480i
$346$	−9.74643e9			−0.680051
$347$			2.07944e10i			1.43426i	0.696938	+	0.717131i	$0.254545\pi$
$347$			2.07944e10i			1.43426i	−0.696938	+	0.717131i	$0.745455\pi$
$348$	2.37656e9			0.162043
$349$			2.15161e10i			1.45032i	0.688582	+	0.725158i	$0.258233\pi$
$349$			2.15161e10i			1.45032i	−0.688582	+	0.725158i	$0.741767\pi$
$350$		−	7.42206e8i		−	0.0494598i
$351$		−	3.21488e9i		−	0.211805i
$352$	2.39353e10			1.55908
$353$			1.48394e9i			0.0955693i	0.998858	+	0.0477847i	$0.0152161\pi$
$353$			1.48394e9i			0.0955693i	−0.998858	+	0.0477847i	$0.984784\pi$
$354$	1.10557e10	+	4.07038e9i	0.703998	+	0.259192i
$355$	1.62463e10			1.02292
$356$			5.48640e9i			0.341576i
$357$	8.20756e9			0.505291
$358$	−2.37897e10			−1.44829
$359$	4.06704e9			0.244851			0.122425	−	0.992478i	$-0.460933\pi$
$359$	4.06704e9			0.244851			0.122425	+	0.992478i	$0.460933\pi$
$360$		−	2.18460e9i		−	0.130065i
$361$	5.27364e9			0.310515
$362$		−	4.08427e10i		−	2.37837i
$363$	−7.67890e9			−0.442255
$364$			7.09466e9i			0.404134i
$365$		−	1.34546e10i		−	0.758053i
$366$	−1.69425e9			−0.0944174
$367$		−	5.50301e9i		−	0.303345i	−0.988431	−	0.151672i	$-0.951534\pi$
$367$		−	5.50301e9i		−	0.303345i	0.988431	−	0.151672i	$-0.0484658\pi$
$368$		−	3.27671e10i		−	1.78668i
$369$	2.09995e9			0.113267
$370$	−2.68948e10			−1.43503
$371$	−1.89817e10			−1.00194
$372$		−	1.34347e10i		−	0.701545i
$373$	3.30749e10			1.70869			0.854346	−	0.519705i	$-0.173958\pi$
$373$	3.30749e10			1.70869			0.854346	+	0.519705i	$0.173958\pi$
$374$	−5.54295e10			−2.83305
$375$	1.17875e10			0.596071
$376$	−1.77303e8			−0.00887083
$377$			9.06455e9i			0.448726i
$378$			2.72333e9i			0.133393i
$379$	1.41681e10			0.686679			0.343339	−	0.939211i	$-0.388442\pi$
$379$	1.41681e10			0.686679			0.343339	+	0.939211i	$0.388442\pi$
$380$	−1.58347e10			−0.759407
$381$	8.94359e8			0.0424436
$382$	−4.95937e10			−2.32902
$383$	−8.97160e9			−0.416941			−0.208471	−	0.978029i	$-0.566849\pi$
$383$	−8.97160e9			−0.416941			−0.208471	+	0.978029i	$0.566849\pi$
$384$		−	9.67248e9i		−	0.444849i
$385$		−	1.50087e10i		−	0.683124i
$386$		−	5.59124e10i		−	2.51860i
$387$		−	4.71215e7i		−	0.00210076i
$388$		−	6.44690e9i		−	0.284462i
$389$	3.52009e9			0.153729			0.0768644	−	0.997042i	$-0.475509\pi$
$389$	3.52009e9			0.153729			0.0768644	+	0.997042i	$0.475509\pi$
$390$	−1.84067e10			−0.795640
$391$			5.64123e10i			2.41361i
$392$		−	6.84042e9i		−	0.289693i
$393$		−	5.84132e9i		−	0.244873i
$394$		−	3.60587e10i		−	1.49632i
$395$	7.69474e9			0.316086
$396$		−	7.49868e9i		−	0.304933i
$397$		−	1.68100e10i		−	0.676716i	−0.941017	−	0.338358i	$-0.890128\pi$
$397$		−	1.68100e10i		−	0.676716i	0.941017	−	0.338358i	$-0.109872\pi$
$398$			2.21578e10i			0.883070i
$399$	−8.93575e9			−0.352565
$400$	2.21860e9			0.0866642
$401$			4.92452e10i			1.90452i	0.305281	+	0.952262i	$0.401249\pi$
$401$			4.92452e10i			1.90452i	−0.305281	+	0.952262i	$0.598751\pi$
$402$	5.28953e9			0.202541
$403$	5.12419e10			1.94270
$404$		−	1.24411e9i		−	0.0467019i
$405$	−2.88073e9			−0.107073
$406$		−	7.67859e9i		−	0.282604i
$407$	4.17903e10			1.52299
$408$			1.06282e10i			0.383549i
$409$			1.58367e9i			0.0565941i	0.999600	+	0.0282970i	$0.00900843\pi$
$409$			1.58367e9i			0.0565941i	−0.999600	+	0.0282970i	$0.990992\pi$
$410$		−	1.20232e10i		−	0.425486i
$411$	−5.52141e9			−0.193501
$412$			1.17879e10i			0.409118i
$413$	5.36200e9	−	1.45638e10i	0.184301	−	0.500583i
$414$	−1.87180e10			−0.637174
$415$			3.87417e10i			1.30613i
$416$	−3.86690e10			−1.29119
$417$	2.48655e10			0.822343
$418$	6.03473e10			1.97675
$419$			5.04742e10i			1.63762i	0.574064	+	0.818811i	$0.305366\pi$
$419$			5.04742e10i			1.63762i	−0.574064	+	0.818811i	$0.694634\pi$
$420$	6.35725e9			0.204302
$421$			6.73644e9i			0.214438i	0.994235	+	0.107219i	$0.0341946\pi$
$421$			6.73644e9i			0.214438i	−0.994235	+	0.107219i	$0.965805\pi$
$422$	−3.23135e10			−1.01891
$423$			2.33801e8i			0.00730271i
$424$		−	2.45801e10i		−	0.760537i
$425$	−3.81958e9			−0.117074
$426$		−	2.62259e10i		−	0.796328i
$427$			2.23187e9i			0.0671362i
$428$	3.99256e10			1.18981
$429$	2.86011e10			0.844410
$430$	−2.69793e8			−0.00789144
$431$		−	6.35021e10i		−	1.84026i	−0.391615	−	0.920129i	$-0.628083\pi$
$431$		−	6.35021e10i		−	1.84026i	0.391615	−	0.920129i	$-0.371917\pi$
$432$	−8.14058e9			−0.233733
$433$	−4.18521e10			−1.19060			−0.595300	−	0.803503i	$-0.702967\pi$
$433$	−4.18521e10			−1.19060			−0.595300	+	0.803503i	$0.702967\pi$
$434$	−4.34071e10			−1.22349
$435$	8.12239e9			0.226844
$436$		−	1.22364e9i		−	0.0338618i
$437$		−	6.14173e10i		−	1.68409i
$438$	−2.17193e10			−0.590133
$439$	7.14779e10			1.92448			0.962241	−	0.272200i	$-0.0877513\pi$
$439$	7.14779e10			1.92448			0.962241	+	0.272200i	$0.0877513\pi$
$440$	1.94353e10			0.518537
$441$	−9.02012e9			−0.238483
$442$	8.95498e10			2.34626
$443$		−	5.53832e10i		−	1.43801i	−0.695003	−	0.719007i	$-0.744597\pi$
$443$		−	5.53832e10i		−	1.43801i	0.695003	−	0.719007i	$-0.255403\pi$
$444$			1.77012e10i			0.455481i
$445$			1.87509e10i			0.478170i
$446$			1.66764e10i			0.421466i
$447$			2.55120e10i			0.639020i
$448$	6.65941e9			0.165319
$449$	4.87436e10			1.19931			0.599657	−	0.800257i	$-0.295304\pi$
$449$	4.87436e10			1.19931			0.599657	+	0.800257i	$0.295304\pi$
$450$		−	1.26737e9i		−	0.0309066i
$451$			1.86822e10i			0.451566i
$452$			3.17963e10i			0.761768i
$453$		−	9.93198e9i		−	0.235854i
$454$	−1.51347e9			−0.0356246
$455$			2.42475e10i			0.565746i
$456$		−	1.15712e10i		−	0.267620i
$457$			4.73704e10i			1.08603i	0.839722	+	0.543016i	$0.182718\pi$
$457$			4.73704e10i			1.08603i	−0.839722	+	0.543016i	$0.817282\pi$
$458$	5.11860e10			1.16329
$459$	1.40149e10			0.315748
$460$			4.36947e10i			0.975883i
$461$	6.58324e10			1.45759			0.728796	−	0.684731i	$-0.240080\pi$
$461$	6.58324e10			1.45759			0.728796	+	0.684731i	$0.240080\pi$
$462$	−2.42280e10			−0.531802
$463$			6.41251e10i			1.39542i	0.716381	+	0.697709i	$0.245797\pi$
$463$			6.41251e10i			1.39542i	−0.716381	+	0.697709i	$0.754203\pi$
$464$	2.29529e10			0.495182
$465$		−	4.59159e10i		−	0.982089i
$466$	−8.40204e10			−1.78173
$467$		−	2.86597e10i		−	0.602566i	−0.953535	−	0.301283i	$-0.902585\pi$
$467$		−	2.86597e10i		−	0.602566i	0.953535	−	0.301283i	$-0.0974148\pi$
$468$			1.21146e10i			0.252537i
$469$		−	6.96801e9i		−	0.144018i
$470$	1.33862e9			0.0274325
$471$			4.09842e10i			0.832785i
$472$	1.88592e10	+	6.94343e9i	0.379976	+	0.139896i
$473$	4.19216e8			0.00837516
$474$		−	1.24214e10i		−	0.246068i
$475$	4.15846e9			0.0816881
$476$	−3.09285e10			−0.602464
$477$	−3.24126e10			−0.626095
$478$			5.69412e10i			1.09072i
$479$	7.46400e10			1.41785			0.708924	−	0.705285i	$-0.249181\pi$
$479$	7.46400e10			1.41785			0.708924	+	0.705285i	$0.249181\pi$
$480$			3.46498e10i			0.652733i
$481$	−6.75149e10			−1.26130
$482$			2.41324e10i			0.447108i
$483$			2.46576e10i			0.453067i
$484$	2.89363e10			0.527305
$485$		−	2.20337e10i		−	0.398217i
$486$			4.65026e9i			0.0833551i
$487$	−6.01198e9			−0.106881			−0.0534406	−	0.998571i	$-0.517019\pi$
$487$	−6.01198e9			−0.106881			−0.0534406	+	0.998571i	$0.517019\pi$
$488$	−2.89012e9			−0.0509608
$489$	−3.91592e10			−0.684855
$490$			5.16444e10i			0.895858i
$491$	1.02951e11			1.77136			0.885679	−	0.464299i	$-0.153694\pi$
$491$	1.02951e11			1.77136			0.885679	+	0.464299i	$0.153694\pi$
$492$	−7.91323e9			−0.135050
$493$	−3.95161e10			−0.668938
$494$	−9.74948e10			−1.63709
$495$		−	2.56283e10i		−	0.426874i
$496$		−	1.29753e11i		−	2.14382i
$497$	−3.45479e10			−0.566234
$498$	6.25394e10			1.01680
$499$	−8.73352e10			−1.40860			−0.704299	−	0.709903i	$-0.748739\pi$
$499$	−8.73352e10			−1.40860			−0.704299	+	0.709903i	$0.748739\pi$
$500$	−4.44189e10			−0.710702
$501$	5.07753e10			0.805939
$502$		−	5.00124e10i		−	0.787523i
$503$			9.91846e9i			0.154943i	0.996995	+	0.0774716i	$0.0246847\pi$
$503$			9.91846e9i			0.154943i	−0.996995	+	0.0774716i	$0.975315\pi$
$504$			4.64557e9i			0.0719974i
$505$		−	4.25202e9i		−	0.0653778i
$506$		−	1.66524e11i		−	2.54025i
$507$	−8.05892e9			−0.121968
$508$	−3.37021e9			−0.0506059
$509$			8.51383e10i			1.26839i	0.773172	+	0.634197i	$0.218669\pi$
$509$			8.51383e10i			1.26839i	−0.773172	+	0.634197i	$0.781331\pi$
$510$		−	8.02421e10i		−	1.18610i
$511$			2.86113e10i			0.419618i
$512$			6.41219e10i			0.933097i
$513$	−1.52584e10			−0.220312
$514$		−	1.00940e11i		−	1.44614i
$515$			4.02877e10i			0.572722i
$516$			1.77568e8i			0.00250475i
$517$	−2.08000e9			−0.0291140
$518$	5.71920e10			0.794358
$519$			2.19238e10i			0.302166i
$520$	−3.13989e10			−0.429438
$521$	−2.11893e10			−0.287585			−0.143792	−	0.989608i	$-0.545930\pi$
$521$	−2.11893e10			−0.287585			−0.143792	+	0.989608i	$0.545930\pi$
$522$		−	1.31117e10i		−	0.176595i
$523$	4.36038e10			0.582798			0.291399	−	0.956602i	$-0.405879\pi$
$523$	4.36038e10			0.582798			0.291399	+	0.956602i	$0.405879\pi$
$524$			2.20118e10i			0.291965i
$525$	−1.66953e9			−0.0219764
$526$			6.93262e10i			0.905638i
$527$			2.23384e11i			2.89608i
$528$		−	7.24225e10i		−	0.931832i
$529$	−9.11662e10			−1.16416
$530$			1.85577e11i			2.35191i
$531$	9.15597e9	−	2.48687e10i	0.115167	−	0.312806i
$532$	3.36725e10			0.420367
$533$		−	3.01823e10i		−	0.373975i
$534$	3.02690e10			0.372248
$535$	1.36454e11			1.66560
$536$	9.02311e9			0.109319
$537$			5.35128e10i			0.643517i
$538$	−9.79045e10			−1.16862
$539$		−	8.02474e10i		−	0.950770i
$540$	1.08554e10			0.127665
$541$			4.90102e10i			0.572133i	0.958210	+	0.286067i	$0.0923479\pi$
$541$			4.90102e10i			0.572133i	−0.958210	+	0.286067i	$0.907652\pi$
$542$			4.99880e10i			0.579253i
$543$	−9.18721e10			−1.05678
$544$		−	1.68574e11i		−	1.92484i
$545$		−	4.18207e9i		−	0.0474029i
$546$	3.91419e10			0.440424
$547$	4.37934e10			0.489169			0.244585	−	0.969628i	$-0.421348\pi$
$547$	4.37934e10			0.489169			0.244585	+	0.969628i	$0.421348\pi$
$548$	2.08063e10			0.230713
$549$			3.81106e9i			0.0419524i
$550$	1.12751e10			0.123217
$551$	4.30220e10			0.466750
$552$	−3.19300e10			−0.343908
$553$	−1.63629e10			−0.174969
$554$		−	1.02032e10i		−	0.108317i
$555$			6.04975e10i			0.637625i
$556$	−9.37005e10			−0.980489
$557$	1.51954e11			1.57867			0.789333	−	0.613965i	$-0.210427\pi$
$557$	1.51954e11			1.57867			0.789333	+	0.613965i	$0.210427\pi$
$558$	−7.41205e10			−0.764542
$559$	−6.77270e8			−0.00693609
$560$	6.13985e10			0.624317
$561$			1.24684e11i			1.25880i
$562$			2.19069e11i			2.19602i
$563$		−	1.75330e11i		−	1.74511i	−0.488515	−	0.872555i	$-0.662461\pi$
$563$		−	1.75330e11i		−	1.74511i	0.488515	−	0.872555i	$-0.337539\pi$
$564$		−	8.81029e8i		−	0.00870711i
$565$			1.08671e11i			1.06639i
$566$	−7.27586e9			−0.0708955
$567$	6.12589e9			0.0592702
$568$		−	4.47373e10i		−	0.429809i
$569$			5.01500e10i			0.478434i	0.970966	+	0.239217i	$0.0768907\pi$
$569$			5.01500e10i			0.478434i	−0.970966	+	0.239217i	$0.923109\pi$
$570$			8.73614e10i			0.827599i
$571$			5.51474e10i			0.518777i	0.965773	+	0.259389i	$0.0835210\pi$
$571$			5.51474e10i			0.518777i	−0.965773	+	0.259389i	$0.916479\pi$
$572$	−1.07777e11			−1.00680
$573$			1.11557e11i			1.03485i
$574$			2.55674e10i			0.235526i
$575$		−	1.14750e10i		−	0.104974i
$576$	1.13714e10			0.103305
$577$	−4.02122e10			−0.362789			−0.181395	−	0.983410i	$-0.558061\pi$
$577$	−4.02122e10			−0.362789			−0.181395	+	0.983410i	$0.558061\pi$
$578$			2.45358e11i			2.19831i
$579$	−1.25770e11			−1.11908
$580$	−3.06076e10			−0.270468
$581$		−	8.23844e10i		−	0.723004i
$582$	−3.55682e10			−0.310006
$583$		−	2.88358e11i		−	2.49608i
$584$	−3.70498e10			−0.318518
$585$			4.14042e10i			0.353526i
$586$		−	6.28852e10i		−	0.533283i
$587$			1.68429e11i			1.41862i	0.704898	+	0.709309i	$0.250993\pi$
$587$			1.68429e11i			1.41862i	−0.704898	+	0.709309i	$0.749007\pi$
$588$	3.39905e10			0.284346
$589$		−	2.43203e11i		−	2.02073i
$590$	−1.42385e11	−	5.24222e10i	−1.17505	−	0.432620i
$591$	−8.11109e10			−0.664858
$592$			1.70958e11i			1.39189i
$593$	2.68170e10			0.216866			0.108433	−	0.994104i	$-0.465417\pi$
$593$	2.68170e10			0.216866			0.108433	+	0.994104i	$0.465417\pi$
$594$	−4.13709e10			−0.332315
$595$	−1.05705e11			−0.843386
$596$		−	9.61366e10i		−	0.761910i
$597$	4.98421e10			0.392373
$598$			2.69031e11i			2.10377i
$599$	2.26978e11			1.76310			0.881549	−	0.472092i	$-0.156501\pi$
$599$	2.26978e11			1.76310			0.881549	+	0.472092i	$0.156501\pi$
$600$		−	2.16193e9i		−	0.0166815i
$601$		−	1.68922e11i		−	1.29475i	−0.762170	−	0.647377i	$-0.775866\pi$
$601$		−	1.68922e11i		−	1.29475i	0.762170	−	0.647377i	$-0.224134\pi$
$602$	5.73716e8			0.00436829
$603$		−	1.18983e10i		−	0.0899948i
$604$			3.74266e10i			0.281211i
$605$	9.88960e10			0.738172
$606$	−6.86390e9			−0.0508956
$607$	1.62456e11			1.19669			0.598344	−	0.801239i	$-0.295826\pi$
$607$	1.62456e11			1.19669			0.598344	+	0.801239i	$0.295826\pi$
$608$			1.83530e11i			1.34305i
$609$	−1.72723e10			−0.125569
$610$	2.18201e10			0.157593
$611$	3.36038e9			0.0241114
$612$	−5.28124e10			−0.376470
$613$			1.28216e11i			0.908027i	0.890995	+	0.454013i	$0.150008\pi$
$613$			1.28216e11i			0.908027i	−0.890995	+	0.454013i	$0.849992\pi$
$614$		−	2.66151e11i		−	1.87264i
$615$	−2.70451e10			−0.189055
$616$	−4.13292e10			−0.287035
$617$	3.11451e10			0.214906			0.107453	−	0.994210i	$-0.465730\pi$
$617$	3.11451e10			0.214906			0.107453	+	0.994210i	$0.465730\pi$
$618$	6.50351e10			0.445856
$619$	−2.72037e11			−1.85296			−0.926480	−	0.376344i	$-0.877181\pi$
$619$	−2.72037e11			−1.85296			−0.926480	+	0.376344i	$0.877181\pi$
$620$			1.73024e11i			1.17096i
$621$			4.21045e10i			0.283115i
$622$		−	1.13898e11i		−	0.760945i
$623$		−	3.98740e10i		−	0.264690i
$624$			1.17003e11i			0.771719i
$625$	−1.40923e11			−0.923551
$626$	8.25498e10			0.537550
$627$		−	1.35746e11i		−	0.878328i
$628$		−	1.54441e11i		−	0.992939i
$629$		−	2.94325e11i		−	1.88029i
$630$		−	3.50735e10i		−	0.222647i
$631$	−1.70619e11			−1.07624			−0.538121	−	0.842867i	$-0.680866\pi$
$631$	−1.70619e11			−1.07624			−0.538121	+	0.842867i	$0.680866\pi$
$632$		−	2.11889e10i		−	0.132813i
$633$			7.26864e10i			0.452729i
$634$		−	1.19038e11i		−	0.736763i
$635$	−1.15184e10			−0.0708430
$636$	1.22140e11			0.746500
$637$			1.29645e11i			0.787403i
$638$	1.16648e11			0.704036
$639$	−5.89928e10			−0.353831
$640$			1.24571e11i			0.742502i
$641$	−9.03740e10			−0.535317			−0.267659	−	0.963514i	$-0.586250\pi$
$641$	−9.03740e10			−0.535317			−0.267659	+	0.963514i	$0.586250\pi$
$642$		−	2.20273e11i		−	1.29665i
$643$	−9.94208e10			−0.581612			−0.290806	−	0.956782i	$-0.593923\pi$
$643$	−9.94208e10			−0.581612			−0.290806	+	0.956782i	$0.593923\pi$
$644$		−	9.29172e10i		−	0.540197i
$645$			6.06875e8i			0.00350639i
$646$		−	4.25020e11i		−	2.44050i
$647$	2.16018e11			1.23274			0.616372	−	0.787455i	$-0.288602\pi$
$647$	2.16018e11			1.23274			0.616372	+	0.787455i	$0.288602\pi$
$648$			7.93261e9i			0.0449900i
$649$	2.21244e11	+	8.14559e10i	1.24708	+	0.459139i
$650$	−1.82156e10			−0.102045
$651$			9.76404e10i			0.543633i
$652$	1.47563e11			0.816560
$653$	−1.67238e10			−0.0919777			−0.0459888	−	0.998942i	$-0.514644\pi$
$653$	−1.67238e10			−0.0919777			−0.0459888	+	0.998942i	$0.514644\pi$
$654$	−6.75097e9			−0.0369024
$655$			7.52300e10i			0.408720i
$656$	−7.64262e10			−0.412693
$657$			4.88557e10i			0.262213i
$658$	−2.84658e9			−0.0151852
$659$			1.66939e11i			0.885147i	0.896732	+	0.442574i	$0.145934\pi$
$659$			1.66939e11i			0.885147i	−0.896732	+	0.442574i	$0.854066\pi$
$660$			9.65750e10i			0.508966i
$661$	2.82067e11			1.47756			0.738782	−	0.673944i	$-0.235401\pi$
$661$	2.82067e11			1.47756			0.738782	+	0.673944i	$0.235401\pi$
$662$		−	3.12547e11i		−	1.62736i
$663$		−	2.01434e11i		−	1.04251i
$664$	1.06682e11			0.548808
$665$	1.15083e11			0.588470
$666$	9.76591e10			0.496382
$667$		−	1.18716e11i		−	0.599802i
$668$	−1.91336e11			−0.960930
$669$	3.75121e10			0.187269
$670$	−6.81235e10			−0.338063
$671$	−3.39050e10			−0.167253
$672$		−	7.36830e10i		−	0.361319i
$673$		−	7.75508e10i		−	0.378030i	−0.981974	−	0.189015i	$-0.939471\pi$
$673$		−	7.75508e10i		−	0.378030i	0.981974	−	0.189015i	$-0.0605295\pi$
$674$	2.95405e11			1.43146
$675$	−2.85083e9			−0.0137327
$676$	3.03684e10			0.145424
$677$	1.51021e11			0.718921			0.359461	−	0.933160i	$-0.382961\pi$
$677$	1.51021e11			0.718921			0.359461	+	0.933160i	$0.382961\pi$
$678$	1.75423e11			0.830172
$679$			4.68547e10i			0.220432i
$680$		−	1.36880e11i		−	0.640186i
$681$			3.40442e9i			0.0158290i
$682$		−	6.59411e11i		−	3.04803i
$683$		−	2.89247e11i		−	1.32919i	−0.747206	−	0.664593i	$-0.768605\pi$
$683$		−	2.89247e11i		−	1.32919i	0.747206	−	0.664593i	$-0.231395\pi$
$684$	5.74980e10			0.262681
$685$	7.11099e10			0.322974
$686$		−	2.63323e11i		−	1.18903i
$687$		−	1.15139e11i		−	0.516885i
$688$			1.71495e9i			0.00765418i
$689$			4.65861e11i			2.06718i
$690$	2.41068e11			1.06351
$691$		−	1.18108e10i		−	0.0518046i	−0.999664	−	0.0259023i	$-0.991754\pi$
$691$		−	1.18108e10i		−	0.0518046i	0.999664	−	0.0259023i	$-0.00824587\pi$
$692$		−	8.26151e10i		−	0.360276i
$693$			5.44988e10i			0.236295i
$694$	−4.32317e11			−1.86365
$695$	−3.20241e11			−1.37258
$696$		−	2.23665e10i		−	0.0953150i
$697$	1.31577e11			0.557504
$698$	−4.47322e11			−1.88451
$699$			1.88997e11i			0.791672i
$700$	6.29127e9			0.0262027
$701$		−	3.43372e11i		−	1.42198i	−0.703203	−	0.710989i	$-0.748248\pi$
$701$		−	3.43372e11i		−	1.42198i	0.703203	−	0.710989i	$-0.251752\pi$
$702$	6.68374e10			0.275214
$703$			3.20438e11i			1.31197i
$704$			1.01165e11i			0.411852i
$705$		−	3.01110e9i		−	0.0121890i
$706$	−3.08512e10			−0.124181
$707$			9.04196e9i			0.0361897i
$708$	−3.45024e10	+	9.37126e10i	−0.137314	+	0.372962i
$709$	−4.25429e10			−0.168361			−0.0841806	−	0.996451i	$-0.526827\pi$
$709$	−4.25429e10			−0.168361			−0.0841806	+	0.996451i	$0.526827\pi$
$710$			3.37761e11i			1.32916i
$711$	−2.79408e10			−0.109335
$712$	5.16341e10			0.200917
$713$	−6.71104e11			−2.59676
$714$			1.70635e11i			0.656563i
$715$	−3.68352e11			−1.40941
$716$		−	2.01652e11i		−	0.767273i
$717$	1.28084e11			0.484640
$718$			8.45540e10i			0.318153i
$719$			2.07734e11i			0.777308i	0.921384	+	0.388654i	$0.127060\pi$
$719$			2.07734e11i			0.777308i	−0.921384	+	0.388654i	$0.872940\pi$
$720$	1.04842e11			0.390126
$721$		−	8.56722e10i		−	0.317029i
$722$			1.09639e11i			0.403476i
$723$	5.42837e10			0.198663
$724$	3.46201e11			1.26001
$725$	8.03809e9			0.0290938
$726$		−	1.59645e11i		−	0.574656i
$727$	4.48539e10			0.160569			0.0802847	−	0.996772i	$-0.474417\pi$
$727$	4.48539e10			0.160569			0.0802847	+	0.996772i	$0.474417\pi$
$728$	6.67700e10			0.237714
$729$	1.04604e10			0.0370370
$730$	2.79722e11			0.984997
$731$		−	2.95249e9i		−	0.0103400i
$732$		−	1.43612e10i		−	0.0500203i
$733$	−1.81016e11			−0.627047			−0.313523	−	0.949580i	$-0.601509\pi$
$733$	−1.81016e11			−0.627047			−0.313523	+	0.949580i	$0.601509\pi$
$734$	1.14408e11			0.394159
$735$	1.16170e11			0.398055
$736$	5.06439e11			1.72590
$737$	1.05853e11			0.358785
$738$			4.36581e10i			0.147177i
$739$			7.57291e10i			0.253913i	0.991908	+	0.126957i	$0.0405209\pi$
$739$			7.57291e10i			0.253913i	−0.991908	+	0.126957i	$0.959479\pi$
$740$		−	2.27972e11i		−	0.760248i
$741$			2.19306e11i			0.727408i
$742$		−	3.94631e11i		−	1.30189i
$743$	4.21136e11			1.38187			0.690934	−	0.722918i	$-0.257199\pi$
$743$	4.21136e11			1.38187			0.690934	+	0.722918i	$0.257199\pi$
$744$	−1.26438e11			−0.412653
$745$		−	3.28567e11i		−	1.06659i
$746$			6.87629e11i			2.22024i
$747$		−	1.40677e11i		−	0.451794i
$748$		−	4.69845e11i		−	1.50089i
$749$	−2.90171e11			−0.921990
$750$			2.45063e11i			0.774521i
$751$		−	5.28692e11i		−	1.66205i	−0.556237	−	0.831023i	$-0.687756\pi$
$751$		−	5.28692e11i		−	1.66205i	0.556237	−	0.831023i	$-0.312244\pi$
$752$		−	8.50901e9i		−	0.0266077i
$753$	−1.12499e11			−0.349919
$754$	−1.88452e11			−0.583064
$755$			1.27913e11i			0.393666i
$756$	−2.30841e10			−0.0706686
$757$	2.75157e10			0.0837910			0.0418955	−	0.999122i	$-0.486660\pi$
$757$	2.75157e10			0.0837910			0.0418955	+	0.999122i	$0.486660\pi$
$758$			2.94555e11i			0.892255i
$759$	−3.74582e11			−1.12870
$760$			1.49025e11i			0.446688i
$761$	−2.00208e11			−0.596957			−0.298479	−	0.954416i	$-0.596479\pi$
$761$	−2.00208e11			−0.596957			−0.298479	+	0.954416i	$0.596479\pi$
$762$			1.85938e10i			0.0551502i
$763$			8.89319e9i			0.0262397i
$764$		−	4.20378e11i		−	1.23386i
$765$	−1.80498e11			−0.527018
$766$		−	1.86520e11i		−	0.541764i
$767$	−3.57434e11	−	1.31597e11i	−1.03280	−	0.380246i
$768$	2.63340e11			0.756957
$769$			3.28397e11i			0.939060i	0.882917	+	0.469530i	$0.155577\pi$
$769$			3.28397e11i			0.939060i	−0.882917	+	0.469530i	$0.844423\pi$
$770$	3.12031e11			0.887636
$771$	−2.27056e11			−0.642562
$772$	4.73938e11			1.33430
$773$			3.06586e11i			0.858685i	0.903142	+	0.429343i	$0.141255\pi$
$773$			3.06586e11i			0.858685i	−0.903142	+	0.429343i	$0.858745\pi$
$774$	9.79658e8			0.00272967
$775$		−	4.54393e10i		−	0.125958i
$776$	−6.06738e10			−0.167322
$777$		−	1.28648e11i		−	0.352956i
$778$			7.31828e10i			0.199752i
$779$	−1.43250e11			−0.388997
$780$		−	1.56023e11i		−	0.421512i
$781$		−	5.24829e11i		−	1.41063i
$782$	−1.17281e12			−3.13619
$783$	−2.94936e10			−0.0784660
$784$	3.28281e11			0.868923
$785$		−	5.27833e11i		−	1.39001i
$786$	1.21441e11			0.318182
$787$	−5.38886e11			−1.40475			−0.702373	−	0.711809i	$-0.747876\pi$
$787$	−5.38886e11			−1.40475			−0.702373	+	0.711809i	$0.747876\pi$
$788$	3.05649e11			0.792718
$789$	1.55943e11			0.402401
$790$			1.59974e11i			0.410715i
$791$		−	2.31089e11i		−	0.590300i
$792$	−7.05724e10			−0.179363
$793$	5.47757e10			0.138515
$794$	3.49481e11			0.879310
$795$	4.17440e11			1.04502
$796$	−1.87820e11			−0.467831
$797$			3.71574e11i			0.920898i	0.887686	+	0.460449i	$0.152312\pi$
$797$			3.71574e11i			0.920898i	−0.887686	+	0.460449i	$0.847688\pi$
$798$		−	1.85775e11i		−	0.458115i
$799$			1.46492e10i			0.0359441i
$800$			3.42902e10i			0.0837162i
$801$		−	6.80874e10i		−	0.165401i
$802$	−1.02381e12			−2.47470
$803$	−4.34644e11			−1.04537
$804$			4.48364e10i			0.107302i
$805$		−	3.17564e11i		−	0.756219i
$806$			1.06532e12i			2.52430i
$807$			2.20228e11i			0.519252i
$808$	−1.17087e10			−0.0274704
$809$			5.07981e11i			1.18591i	0.805234	+	0.592957i	$0.202040\pi$
$809$			5.07981e11i			1.18591i	−0.805234	+	0.592957i	$0.797960\pi$
$810$		−	5.98904e10i		−	0.139129i
$811$		−	6.18631e11i		−	1.43004i	−0.699104	−	0.715020i	$-0.746418\pi$
$811$		−	6.18631e11i		−	1.43004i	0.699104	−	0.715020i	$-0.253582\pi$
$812$	6.50872e10			0.149717
$813$	1.12444e11			0.257379
$814$			8.68822e11i			1.97894i
$815$	5.04329e11			1.14310
$816$	−5.10064e11			−1.15044
$817$			3.21444e9i			0.00721469i
$818$	−3.29245e10			−0.0735371
$819$		−	8.80463e10i		−	0.195693i
$820$	1.01914e11			0.225413
$821$			2.56965e11i			0.565589i	0.959181	+	0.282794i	$0.0912614\pi$
$821$			2.56965e11i			0.565589i	−0.959181	+	0.282794i	$0.908739\pi$
$822$		−	1.14790e11i		−	0.251430i
$823$		−	7.36087e10i		−	0.160446i	−0.996777	−	0.0802232i	$-0.974437\pi$
$823$		−	7.36087e10i		−	0.160446i	0.996777	−	0.0802232i	$-0.0255633\pi$
$824$	1.10940e11			0.240646
$825$		−	2.53623e10i		−	0.0547486i
$826$	3.02783e11	+	1.11476e11i	0.650446	+	0.239476i
$827$	−2.10704e11			−0.450455			−0.225227	−	0.974306i	$-0.572312\pi$
$827$	−2.10704e11			−0.450455			−0.225227	+	0.974306i	$0.572312\pi$
$828$		−	1.58662e11i		−	0.337561i
$829$	−2.48597e11			−0.526353			−0.263177	−	0.964748i	$-0.584770\pi$
$829$	−2.48597e11			−0.526353			−0.263177	+	0.964748i	$0.584770\pi$
$830$	−8.05440e11			−1.69715
$831$	−2.29512e10			−0.0481284
$832$		−	1.63439e11i		−	0.341085i
$833$	−5.65174e11			−1.17382
$834$			5.16955e11i			1.06853i
$835$	−6.53932e11			−1.34520
$836$			5.11530e11i			1.04724i
$837$			1.66727e11i			0.339708i
$838$	−1.04936e12			−2.12789
$839$			2.07856e11i			0.419482i	0.977757	+	0.209741i	$0.0672621\pi$
$839$			2.07856e11i			0.419482i	−0.977757	+	0.209741i	$0.932738\pi$
$840$		−	5.98300e10i		−	0.120172i
$841$	−4.17087e11			−0.833763
$842$	−1.40051e11			−0.278636
$843$	4.92777e11			0.975754
$844$		−	2.73903e11i		−	0.539794i
$845$	1.03790e11			0.203578
$846$	−4.86072e9			−0.00948898
$847$	−2.10303e11			−0.408613
$848$	1.17963e12			2.28120
$849$			1.63664e10i			0.0315009i
$850$		−	7.94093e10i		−	0.152123i
$851$	8.84228e11			1.68596
$852$	2.22302e11			0.421877
$853$	−3.59860e11			−0.679731			−0.339866	−	0.940474i	$-0.610382\pi$
$853$	−3.59860e11			−0.679731			−0.339866	+	0.940474i	$0.610382\pi$
$854$	−4.64006e10			−0.0872352
$855$	1.96512e11			0.367726
$856$		−	3.75752e11i		−	0.699852i
$857$		−	6.28341e11i		−	1.16486i	−0.812883	−	0.582428i	$-0.802103\pi$
$857$		−	6.28341e11i		−	1.16486i	0.812883	−	0.582428i	$-0.197897\pi$
$858$			5.94618e11i			1.09721i
$859$			3.34835e11i			0.614976i	0.951552	+	0.307488i	$0.0994884\pi$
$859$			3.34835e11i			0.614976i	−0.951552	+	0.307488i	$0.900512\pi$
$860$		−	2.28688e9i		−	0.00418071i
$861$	5.75117e10			0.104651
$862$	1.32021e12			2.39119
$863$			7.74387e11i			1.39609i	0.716052	+	0.698047i	$0.245947\pi$
$863$			7.74387e11i			1.39609i	−0.716052	+	0.698047i	$0.754053\pi$
$864$		−	1.25819e11i		−	0.225782i
$865$		−	2.82355e11i		−	0.504348i
$866$		−	8.70108e11i		−	1.54704i
$867$	5.51911e11			0.976770
$868$		−	3.67938e11i		−	0.648180i
$869$		−	2.48574e11i		−	0.435890i
$870$			1.68865e11i			0.294756i
$871$	−1.71013e11			−0.297137
$872$	−1.15161e10			−0.0199177
$873$			8.00075e10i			0.137744i
$874$	1.27687e12			2.18827
$875$	3.22827e11			0.550729
$876$		−	1.84103e11i		−	0.312639i
$877$	7.77703e11			1.31467			0.657333	−	0.753600i	$-0.271685\pi$
$877$	7.77703e11			1.31467			0.657333	+	0.753600i	$0.271685\pi$
$878$			1.48603e12i			2.50063i
$879$	−1.41455e11			−0.236953
$880$			9.32724e11i			1.55533i
$881$			1.39113e11i			0.230921i	0.993312	+	0.115461i	$0.0368344\pi$
$881$			1.39113e11i			0.230921i	−0.993312	+	0.115461i	$0.963166\pi$
$882$		−	1.87529e11i		−	0.309880i
$883$	−3.20082e11			−0.526524			−0.263262	−	0.964724i	$-0.584798\pi$
$883$	−3.20082e11			−0.526524			−0.263262	+	0.964724i	$0.584798\pi$
$884$			7.59064e11i			1.24299i
$885$	−1.17919e11	+	3.20283e11i	−0.192226	+	0.522108i
$886$	1.15142e12			1.86852
$887$			8.37930e11i			1.35367i	0.736134	+	0.676836i	$0.236649\pi$
$887$			8.37930e11i			1.35367i	−0.736134	+	0.676836i	$0.763351\pi$
$888$	1.66591e11			0.267917
$889$	2.44939e10			0.0392149
$890$	−3.89832e11			−0.621324
$891$			9.30603e10i			0.147657i
$892$	−1.41356e11			−0.223283
$893$		−	1.59490e10i		−	0.0250799i
$894$	−5.30395e11			−0.830328
$895$		−	6.89187e11i		−	1.07410i
$896$		−	2.64902e11i		−	0.411010i
$897$	6.05161e11			0.934763
$898$			1.01338e12i			1.55836i
$899$		−	4.70099e11i		−	0.719698i
$900$	1.07427e10			0.0163736
$901$	−2.03088e12			−3.08166
$902$	−3.88403e11			−0.586755
$903$		−	1.29052e9i		−	0.00194095i
$904$	2.99245e11			0.448077
$905$	1.18321e12			1.76388
$906$	2.06486e11			0.306463
$907$	6.35603e11			0.939197			0.469598	−	0.882880i	$-0.344399\pi$
$907$	6.35603e11			0.939197			0.469598	+	0.882880i	$0.344399\pi$
$908$		−	1.28288e10i		−	0.0188731i
$909$			1.54397e10i			0.0226144i
$910$	−5.04106e11			−0.735117
$911$	−5.00033e11			−0.725981			−0.362990	−	0.931793i	$-0.618244\pi$
$911$	−5.00033e11			−0.725981			−0.362990	+	0.931793i	$0.618244\pi$
$912$	5.55318e11			0.802717
$913$	1.25153e12			1.80118
$914$	−9.84833e11			−1.41116
$915$		−	4.90824e10i		−	0.0700231i
$916$			4.33876e11i			0.616288i
$917$		−	1.59977e11i		−	0.226246i
$918$			2.91371e11i			0.410276i
$919$			1.06524e12i			1.49344i	0.665141	+	0.746718i	$0.268372\pi$
$919$			1.06524e12i			1.49344i	−0.665141	+	0.746718i	$0.731628\pi$
$920$	4.11224e11			0.574021
$921$	−5.98684e11			−0.832068
$922$			1.36866e12i			1.89396i
$923$			8.47894e11i			1.16825i
$924$		−	2.05367e11i		−	0.281737i
$925$			5.98696e10i			0.0817786i
$926$	−1.33316e12			−1.81317
$927$		−	1.46291e11i		−	0.198106i
$928$			3.54754e11i			0.478338i
$929$		−	4.28519e11i		−	0.575317i	−0.957733	−	0.287658i	$-0.907123\pi$
$929$		−	4.28519e11i		−	0.575317i	0.957733	−	0.287658i	$-0.0928768\pi$
$930$	9.54593e11			1.27610
$931$	6.15317e11			0.819031
$932$		−	7.12195e11i		−	0.943920i
$933$	−2.56203e11			−0.338110
$934$	5.95837e11			0.782960
$935$		−	1.60579e12i		−	2.10108i
$936$	1.14014e11			0.148544
$937$			3.46999e11i			0.450163i	0.974340	+	0.225082i	$0.0722648\pi$
$937$			3.46999e11i			0.450163i	−0.974340	+	0.225082i	$0.927735\pi$
$938$	1.44865e11			0.187134
$939$		−	1.85689e11i		−	0.238849i
$940$			1.13467e10i			0.0145331i
$941$			6.27418e10i			0.0800200i	0.999199	+	0.0400100i	$0.0127390\pi$
$941$			6.27418e10i			0.0800200i	−0.999199	+	0.0400100i	$0.987261\pi$
$942$	−8.52063e11			−1.08210
$943$			3.95290e11i			0.499884i
$944$	−3.33225e11	+	9.05079e11i	−0.419613	+	1.13972i
$945$	−7.88949e10			−0.0989285
$946$			8.71551e9i			0.0108825i
$947$	3.27314e11			0.406973			0.203486	−	0.979078i	$-0.434773\pi$
$947$	3.27314e11			0.406973			0.203486	+	0.979078i	$0.434773\pi$
$948$	1.05289e11			0.130362
$949$	7.02195e11			0.865751
$950$			8.64546e10i			0.106144i
$951$	−2.67765e11			−0.327365
$952$			2.91077e11i			0.354373i
$953$	5.87400e11			0.712134			0.356067	−	0.934460i	$-0.384117\pi$
$953$	5.87400e11			0.712134			0.356067	+	0.934460i	$0.384117\pi$
$954$		−	6.73859e11i		−	0.813533i
$955$		−	1.43673e12i		−	1.72728i
$956$	−4.82659e11			−0.577842
$957$		−	2.62390e11i		−	0.312823i
$958$			1.55177e12i			1.84232i
$959$	−1.51216e11			−0.178781
$960$	−1.46451e11			−0.172428
$961$	−1.80458e12			−2.11584
$962$		−	1.40364e12i		−	1.63891i
$963$	−4.95486e11			−0.576137
$964$	−2.04557e11			−0.236868
$965$	1.61978e12			1.86787
$966$	−5.12633e11			−0.588706
$967$		−	1.39417e12i		−	1.59445i	−0.603686	−	0.797223i	$-0.706302\pi$
$967$		−	1.39417e12i		−	1.59445i	0.603686	−	0.797223i	$-0.293698\pi$
$968$		−	2.72329e11i		−	0.310164i
$969$	−9.56044e11			−1.08438
$970$	4.58080e11			0.517434
$971$	1.36392e12			1.53430			0.767152	−	0.641466i	$-0.221673\pi$
$971$	1.36392e12			1.53430			0.767152	+	0.641466i	$0.221673\pi$
$972$	−3.94177e10			−0.0441597
$973$	6.80995e11			0.759788
$974$		−	1.24989e11i		−	0.138879i
$975$			4.09745e10i			0.0453414i
$976$		−	1.38701e11i		−	0.152855i
$977$			4.76857e11i			0.523372i	0.965153	+	0.261686i	$0.0842784\pi$
$977$			4.76857e11i			0.523372i	−0.965153	+	0.261686i	$0.915722\pi$
$978$		−	8.14121e11i		−	0.889884i
$979$	6.05739e11			0.659408
$980$	−4.37761e11			−0.474606
$981$			1.51857e10i			0.0163968i
$982$			2.14036e12i			2.30166i
$983$		−	1.13198e12i		−	1.21234i	−0.795336	−	0.606169i	$-0.792705\pi$
$983$		−	1.13198e12i		−	1.21234i	0.795336	−	0.606169i	$-0.207295\pi$
$984$			7.44738e10i			0.0794371i
$985$	1.04462e12			1.10972
$986$		−	8.21540e11i		−	0.869203i
$987$			6.40313e9i			0.00674721i
$988$		−	8.26410e11i		−	0.867297i
$989$	8.87006e9			0.00927131
$990$	5.32814e11			0.554670
$991$			9.47124e11i			0.982001i	0.871159	+	0.491001i	$0.163369\pi$
$991$			9.47124e11i			0.982001i	−0.871159	+	0.491001i	$0.836631\pi$
$992$	2.00542e12			2.07090
$993$	−7.03047e11			−0.723081
$994$		−	7.18252e11i		−	0.735752i
$995$	−6.41913e11			−0.654914
$996$			5.30111e11i			0.538679i
$997$	1.05186e12			1.06458			0.532291	−	0.846561i	$-0.321331\pi$
$997$	1.05186e12			1.06458			0.532291	+	0.846561i	$0.321331\pi$
$998$		−	1.81570e12i		−	1.83030i
$999$		−	2.19676e11i		−	0.220557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.66	yes	80
59.58	odd	2	inner	177.9.c.a.58.15	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.15	✓	80	59.58	odd	2	inner
177.9.c.a.58.66	yes	80	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} +972.254i q^{6} +1280.77 q^{7} +1658.51i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q+20.7900i q^{2} +46.7654 q^{3} -176.226 q^{4} -602.288 q^{5} +972.254i q^{6} +1280.77 q^{7} +1658.51i q^{8} +2187.00 q^{9} -12521.6i q^{10} +19456.6i q^{11} -8241.26 q^{12} -31433.4i q^{13} +26627.3i q^{14} -28166.2 q^{15} -79594.3 q^{16} +137031. q^{17} +45467.8i q^{18} -149188. q^{19} +106139. q^{20} +59895.7 q^{21} -404503. q^{22} +411676. i q^{23} +77561.0i q^{24} -27873.9 q^{25} +653501. q^{26} +102276. q^{27} -225705. q^{28} -288373. q^{29} -585577. i q^{30} +1.63017e6i q^{31} -1.23019e6i q^{32} +909895. i q^{33} +2.84888e6i q^{34} -771393. q^{35} -385405. q^{36} -2.14787e6i q^{37} -3.10163e6i q^{38} -1.46999e6i q^{39} -998903. i q^{40} +960198. q^{41} +1.24523e6i q^{42} -21546.2i q^{43} -3.42875e6i q^{44} -1.31720e6 q^{45} -8.55876e6 q^{46} +106905. i q^{47} -3.72226e6 q^{48} -4.12443e6 q^{49} -579499. i q^{50} +6.40830e6 q^{51} +5.53937e6i q^{52} -1.48206e7 q^{53} +2.12632e6i q^{54} -1.17185e7i q^{55} +2.12417e6i q^{56} -6.97686e6 q^{57} -5.99529e6i q^{58} +(4.18654e6 - 1.13712e7i) q^{59} +4.96361e6 q^{60} +1.74260e6i q^{61} -3.38914e7 q^{62} +2.80104e6 q^{63} +5.19953e6 q^{64} +1.89320e7i q^{65} -1.89168e7 q^{66} -5.44049e6i q^{67} -2.41483e7 q^{68} +1.92522e7i q^{69} -1.60373e7i q^{70} -2.69743e7 q^{71} +3.62717e6i q^{72} +2.23392e7i q^{73} +4.46544e7 q^{74} -1.30353e6 q^{75} +2.62908e7 q^{76} +2.49194e7i q^{77} +3.05612e7 q^{78} -1.27758e7 q^{79} +4.79387e7 q^{80} +4.78297e6 q^{81} +1.99625e7i q^{82} -6.43241e7i q^{83} -1.05552e7 q^{84} -8.25321e7 q^{85} +447946. q^{86} -1.34859e7 q^{87} -3.22690e7 q^{88} -3.11328e7i q^{89} -2.73847e7i q^{90} -4.02589e7i q^{91} -7.25479e7i q^{92} +7.62357e7i q^{93} -2.22255e6 q^{94} +8.98545e7 q^{95} -5.75302e7i q^{96} +3.65832e7i q^{97} -8.57470e7i q^{98} +4.25516e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

Modular forms

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Database

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