LMFDB - Embedded newform 177.7.c.a.58.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,7,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, 7, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
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:	$40.7195728007$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.45
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} +138.972i q^{6} -256.162 q^{7} +432.577i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} +138.972i q^{6} -256.162 q^{7} +432.577i q^{8} +243.000 q^{9} +1565.81i q^{10} +678.296i q^{11} -241.276 q^{12} +219.397i q^{13} -2283.69i q^{14} +2737.91 q^{15} -4847.02 q^{16} +1384.65 q^{17} +2166.35i q^{18} -9224.48 q^{19} -2718.49 q^{20} -3993.17 q^{21} -6047.03 q^{22} +14351.5i q^{23} +6743.20i q^{24} +15223.4 q^{25} -1955.93 q^{26} +3788.00 q^{27} +3964.84 q^{28} +34382.4 q^{29} +24408.6i q^{30} +22681.2i q^{31} -15526.5i q^{32} +10573.6i q^{33} +12344.2i q^{34} -44991.6 q^{35} -3761.12 q^{36} +50818.4i q^{37} -82236.5i q^{38} +3420.06i q^{39} +75976.5i q^{40} +111962. q^{41} -35599.2i q^{42} +5490.26i q^{43} -10498.6i q^{44} +42679.8 q^{45} -127944. q^{46} +114737. i q^{47} -75557.6 q^{48} -52030.1 q^{49} +135717. i q^{50} +21584.5 q^{51} -3395.80i q^{52} +74936.6 q^{53} +33770.1i q^{54} +119134. i q^{55} -110810. i q^{56} -143795. q^{57} +306521. i q^{58} +(-175598. - 106518. i) q^{59} -42377.1 q^{60} +190413. i q^{61} -202203. q^{62} -62247.3 q^{63} -171790. q^{64} +38534.3i q^{65} -94263.9 q^{66} -421892. i q^{67} -21431.4 q^{68} +223717. i q^{69} -401101. i q^{70} -35267.8 q^{71} +105116. i q^{72} -698205. i q^{73} -453048. q^{74} +237310. q^{75} +142775. q^{76} -173754. i q^{77} -30490.0 q^{78} +263165. q^{79} -851317. q^{80} +59049.0 q^{81} +998142. i q^{82} -251366. i q^{83} +61805.7 q^{84} +243196. q^{85} -48945.9 q^{86} +535969. q^{87} -293415. q^{88} -429340. i q^{89} +380492. i q^{90} -56201.1i q^{91} -222130. i q^{92} +353565. i q^{93} -1.02288e6 q^{94} -1.62016e6 q^{95} -242033. i q^{96} -198287. i q^{97} -463850. i q^{98} +164826. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * 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 $

$2$			8.91504i			1.11438i	0.830385	+	0.557190i	$0.188120\pi$
$2$			8.91504i			1.11438i	−0.830385	+	0.557190i	$0.811880\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−15.4779			−0.241842
$5$	175.637			1.40510			0.702549	−	0.711635i	$-0.252045\pi$
$5$	175.637			1.40510			0.702549	+	0.711635i	$0.252045\pi$
$6$			138.972i			0.643387i
$7$	−256.162			−0.746827			−0.373414	−	0.927665i	$-0.621813\pi$
$7$	−256.162			−0.746827			−0.373414	+	0.927665i	$0.621813\pi$
$8$			432.577i			0.844876i
$9$	243.000			0.333333
$10$			1565.81i			1.56581i
$11$			678.296i			0.509614i	0.966992	+	0.254807i	$0.0820119\pi$
$11$			678.296i			0.509614i	−0.966992	+	0.254807i	$0.917988\pi$
$12$	−241.276			−0.139627
$13$			219.397i			0.0998621i	0.998753	+	0.0499310i	$0.0159002\pi$
$13$			219.397i			0.0998621i	−0.998753	+	0.0499310i	$0.984100\pi$
$14$		−	2283.69i		−	0.832249i
$15$	2737.91			0.811234
$16$	−4847.02			−1.18335
$17$	1384.65			0.281833			0.140917	−	0.990021i	$-0.454995\pi$
$17$	1384.65			0.281833			0.140917	+	0.990021i	$0.454995\pi$
$18$			2166.35i			0.371460i
$19$	−9224.48			−1.34487			−0.672436	−	0.740155i	$-0.734752\pi$
$19$	−9224.48			−1.34487			−0.672436	+	0.740155i	$0.734752\pi$
$20$	−2718.49			−0.339811
$21$	−3993.17			−0.431181
$22$	−6047.03			−0.567903
$23$			14351.5i			1.17954i	0.807571	+	0.589770i	$0.200782\pi$
$23$			14351.5i			1.17954i	−0.807571	+	0.589770i	$0.799218\pi$
$24$			6743.20i			0.487789i
$25$	15223.4			0.974300
$26$	−1955.93			−0.111284
$27$	3788.00			0.192450
$28$	3964.84			0.180614
$29$	34382.4			1.40975			0.704876	−	0.709331i	$-0.251003\pi$
$29$	34382.4			1.40975			0.704876	+	0.709331i	$0.251003\pi$
$30$			24408.6i			0.904022i
$31$			22681.2i			0.761343i	0.924710	+	0.380672i	$0.124307\pi$
$31$			22681.2i			0.761343i	−0.924710	+	0.380672i	$0.875693\pi$
$32$		−	15526.5i		−	0.473830i
$33$			10573.6i			0.294226i
$34$			12344.2i			0.314069i
$35$	−44991.6			−1.04937
$36$	−3761.12			−0.0806139
$37$			50818.4i			1.00326i	0.865081	+	0.501632i	$0.167267\pi$
$37$			50818.4i			1.00326i	−0.865081	+	0.501632i	$0.832733\pi$
$38$		−	82236.5i		−	1.49870i
$39$			3420.06i			0.0576554i
$40$			75976.5i			1.18713i
$41$	111962.			1.62449			0.812246	−	0.583315i	$-0.198245\pi$
$41$	111962.			1.62449			0.812246	+	0.583315i	$0.198245\pi$
$42$		−	35599.2i		−	0.480499i
$43$			5490.26i			0.0690538i	0.999404	+	0.0345269i	$0.0109924\pi$
$43$			5490.26i			0.0690538i	−0.999404	+	0.0345269i	$0.989008\pi$
$44$		−	10498.6i		−	0.123246i
$45$	42679.8			0.468366
$46$	−127944.			−1.31445
$47$			114737.i			1.10512i	0.833473	+	0.552561i	$0.186349\pi$
$47$			114737.i			1.10512i	−0.833473	+	0.552561i	$0.813651\pi$
$48$	−75557.6			−0.683210
$49$	−52030.1			−0.442249
$50$			135717.i			1.08574i
$51$	21584.5			0.162717
$52$		−	3395.80i		−	0.0241508i
$53$	74936.6			0.503346			0.251673	−	0.967812i	$-0.419019\pi$
$53$	74936.6			0.503346			0.251673	+	0.967812i	$0.419019\pi$
$54$			33770.1i			0.214462i
$55$			119134.i			0.716057i
$56$		−	110810.i		−	0.630977i
$57$	−143795.			−0.776462
$58$			306521.i			1.57100i
$59$	−175598.	−	106518.i	−0.854993	−	0.518639i
$59$	−175598.	−	106518.i	−0.854993	−	0.518639i
$60$	−42377.1			−0.196190
$61$			190413.i			0.838896i	0.907779	+	0.419448i	$0.137776\pi$
$61$			190413.i			0.838896i	−0.907779	+	0.419448i	$0.862224\pi$
$62$	−202203.			−0.848425
$63$	−62247.3			−0.248942
$64$	−171790.			−0.655328
$65$			38534.3i			0.140316i
$66$	−94263.9			−0.327879
$67$		−	421892.i		−	1.40274i	−0.712798	−	0.701370i	$-0.752572\pi$
$67$		−	421892.i		−	1.40274i	0.712798	−	0.701370i	$-0.247428\pi$
$68$	−21431.4			−0.0681591
$69$			223717.i			0.681007i
$70$		−	401101.i		−	1.16939i
$71$	−35267.8			−0.0985379			−0.0492689	−	0.998786i	$-0.515689\pi$
$71$	−35267.8			−0.0985379			−0.0492689	+	0.998786i	$0.515689\pi$
$72$			105116.i			0.281625i
$73$		−	698205.i		−	1.79479i	−0.441226	−	0.897396i	$-0.645456\pi$
$73$		−	698205.i		−	1.79479i	0.441226	−	0.897396i	$-0.354544\pi$
$74$	−453048.			−1.11802
$75$	237310.			0.562512
$76$	142775.			0.325246
$77$		−	173754.i		−	0.380594i
$78$	−30490.0			−0.0642500
$79$	263165.			0.533762			0.266881	−	0.963730i	$-0.414007\pi$
$79$	263165.			0.533762			0.266881	+	0.963730i	$0.414007\pi$
$80$	−851317.			−1.66273
$81$	59049.0			0.111111
$82$			998142.i			1.81030i
$83$		−	251366.i		−	0.439615i	−0.975543	−	0.219807i	$-0.929457\pi$
$83$		−	251366.i		−	0.439615i	0.975543	−	0.219807i	$-0.0705429\pi$
$84$	61805.7			0.104278
$85$	243196.			0.396004
$86$	−48945.9			−0.0769521
$87$	535969.			0.813921
$88$	−293415.			−0.430560
$89$		−	429340.i		−	0.609019i	−0.952509	−	0.304510i	$-0.901507\pi$
$89$		−	429340.i		−	0.609019i	0.952509	−	0.304510i	$-0.0984926\pi$
$90$			380492.i			0.521937i
$91$		−	56201.1i		−	0.0745798i
$92$		−	222130.i		−	0.285262i
$93$			353565.i			0.439562i
$94$	−1.02288e6			−1.23152
$95$	−1.62016e6			−1.88968
$96$		−	242033.i		−	0.273566i
$97$		−	198287.i		−	0.217260i	−0.994082	−	0.108630i	$-0.965354\pi$
$97$		−	198287.i		−	0.217260i	0.994082	−	0.108630i	$-0.0346464\pi$
$98$		−	463850.i		−	0.492833i
$99$			164826.i			0.169871i
$100$	−235626.			−0.235626
$101$			1.38896e6i			1.34811i	0.738680	+	0.674056i	$0.235449\pi$
$101$			1.38896e6i			1.34811i	−0.738680	+	0.674056i	$0.764551\pi$
$102$			192427.i			0.181328i
$103$		−	213622.i		−	0.195495i	−0.995211	−	0.0977473i	$-0.968836\pi$
$103$		−	213622.i		−	0.195495i	0.995211	−	0.0977473i	$-0.0311637\pi$
$104$	−94906.0			−0.0843711
$105$	−701349.			−0.605852
$106$			668063.i			0.560918i
$107$	−1.16918e6			−0.954402			−0.477201	−	0.878794i	$-0.658349\pi$
$107$	−1.16918e6			−0.954402			−0.477201	+	0.878794i	$0.658349\pi$
$108$	−58630.1			−0.0465425
$109$			622536.i			0.480712i	0.970685	+	0.240356i	$0.0772642\pi$
$109$			622536.i			0.480712i	−0.970685	+	0.240356i	$0.922736\pi$
$110$	−1.06208e6			−0.797959
$111$			792180.i			0.579235i
$112$	1.24162e6			0.883762
$113$		−	882546.i		−	0.611649i	−0.952088	−	0.305824i	$-0.901068\pi$
$113$		−	882546.i		−	0.611649i	0.952088	−	0.305824i	$-0.0989320\pi$
$114$		−	1.28194e6i		−	0.865274i
$115$			2.52065e6i			1.65737i
$116$	−532167.			−0.340937
$117$			53313.5i			0.0332874i
$118$	949608.	−	1.56546e6i	0.577961	−	0.952787i
$119$	−354694.			−0.210481
$120$			1.18436e6i			0.685392i
$121$	1.31148e6			0.740294
$122$	−1.69754e6			−0.934848
$123$	1.74531e6			0.937901
$124$		−	351056.i		−	0.184125i
$125$	−70530.1			−0.0361114
$126$		−	554937.i		−	0.277416i
$127$	2.98914e6			1.45927			0.729634	−	0.683838i	$-0.239691\pi$
$127$	2.98914e6			1.45927			0.729634	+	0.683838i	$0.239691\pi$
$128$		−	2.52521e6i		−	1.20411i
$129$			85584.7i			0.0398682i
$130$	−343535.			−0.156365
$131$			1.34600e6i			0.598732i	0.954138	+	0.299366i	$0.0967752\pi$
$131$			1.34600e6i			0.598732i	−0.954138	+	0.299366i	$0.903225\pi$
$132$		−	163657.i		−	0.0711560i
$133$	2.36296e6			1.00439
$134$	3.76118e6			1.56318
$135$	665313.			0.270411
$136$			598966.i			0.238114i
$137$	1.88396e6			0.732673			0.366336	−	0.930483i	$-0.380612\pi$
$137$	1.88396e6			0.732673			0.366336	+	0.930483i	$0.380612\pi$
$138$	−1.99445e6			−0.758901
$139$	−860345.			−0.320353			−0.160176	−	0.987088i	$-0.551206\pi$
$139$	−860345.			−0.320353			−0.160176	+	0.987088i	$0.551206\pi$
$140$	696373.			0.253780
$141$			1.78857e6i			0.638042i
$142$		−	314414.i		−	0.109809i
$143$	−148816.			−0.0508911
$144$	−1.17783e6			−0.394451
$145$	6.03884e6			1.98084
$146$	6.22452e6			2.00008
$147$	−811069.			−0.255332
$148$		−	786560.i		−	0.242631i
$149$		−	2.72310e6i		−	0.823199i	−0.911365	−	0.411599i	$-0.864970\pi$
$149$		−	2.72310e6i		−	0.823199i	0.911365	−	0.411599i	$-0.135030\pi$
$150$			2.11563e6i			0.626852i
$151$			825040.i			0.239632i	0.992796	+	0.119816i	$0.0382304\pi$
$151$			825040.i			0.239632i	−0.992796	+	0.119816i	$0.961770\pi$
$152$		−	3.99029e6i		−	1.13625i
$153$	336469.			0.0939445
$154$	1.54902e6			0.424126
$155$			3.98366e6i			1.06976i
$156$		−	52935.3i		−	0.0139435i
$157$		−	5.37648e6i		−	1.38931i	−0.719343	−	0.694655i	$-0.755557\pi$
$157$		−	5.37648e6i		−	1.38931i	0.719343	−	0.694655i	$-0.244443\pi$
$158$			2.34613e6i			0.594813i
$159$	1.16815e6			0.290607
$160$		−	2.72702e6i		−	0.665777i
$161$		−	3.67630e6i		−	0.880913i
$162$			526424.i			0.123820i
$163$	5193.54			0.00119923			0.000599613	−	1.00000i	$-0.499809\pi$
$163$	5193.54			0.00119923			0.000599613		1.00000i	$0.499809\pi$
$164$	−1.73293e6			−0.392870
$165$			1.85712e6i			0.413416i
$166$	2.24094e6			0.489898
$167$	−2.00433e6			−0.430347			−0.215174	−	0.976576i	$-0.569032\pi$
$167$	−2.00433e6			−0.430347			−0.215174	+	0.976576i	$0.569032\pi$
$168$		−	1.72735e6i		−	0.364295i
$169$	4.77867e6			0.990028
$170$			2.16810e6i			0.441298i
$171$	−2.24155e6			−0.448291
$172$		−	84977.5i		−	0.0167001i
$173$			8.23796e6i			1.59104i	0.605926	+	0.795521i	$0.292803\pi$
$173$			8.23796e6i			1.59104i	−0.605926	+	0.795521i	$0.707197\pi$
$174$			4.77818e6i			0.907016i
$175$	−3.89966e6			−0.727634
$176$		−	3.28771e6i		−	0.603054i
$177$	−2.73730e6	−	1.66044e6i	−0.493631	−	0.299436i
$178$	3.82758e6			0.678679
$179$		−	1.00882e7i		−	1.75896i	−0.475935	−	0.879481i	$-0.657890\pi$
$179$		−	1.00882e7i		−	1.75896i	0.475935	−	0.879481i	$-0.342110\pi$
$180$	−660593.			−0.113270
$181$	−1.21608e6			−0.205081			−0.102540	−	0.994729i	$-0.532697\pi$
$181$	−1.21608e6			−0.205081			−0.102540	+	0.994729i	$0.532697\pi$
$182$	501035.			0.0831102
$183$			2.96825e6i			0.484337i
$184$	−6.20810e6			−0.996565
$185$			8.92560e6i			1.40969i
$186$	−3.15204e6			−0.489839
$187$			939201.i			0.143626i
$188$		−	1.77588e6i		−	0.267264i
$189$	−970340.			−0.143727
$190$		−	1.44438e7i		−	2.10582i
$191$		−	5.16473e6i		−	0.741221i	−0.928788	−	0.370610i	$-0.879149\pi$
$191$		−	5.16473e6i		−	0.741221i	0.928788	−	0.370610i	$-0.120851\pi$
$192$	−2.67795e6			−0.378354
$193$	6.15505e6			0.856169			0.428085	−	0.903739i	$-0.359189\pi$
$193$	6.15505e6			0.856169			0.428085	+	0.903739i	$0.359189\pi$
$194$	1.76774e6			0.242110
$195$			600690.i			0.0810115i
$196$	805315.			0.106954
$197$	1.40188e6			0.183363			0.0916815	−	0.995788i	$-0.470776\pi$
$197$	1.40188e6			0.183363			0.0916815	+	0.995788i	$0.470776\pi$
$198$	−1.46943e6			−0.189301
$199$	−3.86038e6			−0.489858			−0.244929	−	0.969541i	$-0.578765\pi$
$199$	−3.86038e6			−0.489858			−0.244929	+	0.969541i	$0.578765\pi$
$200$			6.58530e6i			0.823163i
$201$		−	6.57665e6i		−	0.809872i
$202$	−1.23826e7			−1.50231
$203$	−8.80747e6			−1.05284
$204$	−334082.			−0.0393517
$205$	1.96646e7			2.28257
$206$	1.90445e6			0.217855
$207$			3.48740e6i			0.393180i
$208$		−	1.06342e6i		−	0.118172i
$209$		−	6.25693e6i		−	0.685365i
$210$		−	6.25255e6i		−	0.675149i
$211$			1.32505e6i			0.141054i	0.997510	+	0.0705269i	$0.0224680\pi$
$211$			1.32505e6i			0.141054i	−0.997510	+	0.0705269i	$0.977532\pi$
$212$	−1.15986e6			−0.121730
$213$	−549770.			−0.0568909
$214$		−	1.04233e7i		−	1.06357i
$215$			964294.i			0.0970273i
$216$			1.63860e6i			0.162596i
$217$		−	5.81005e6i		−	0.568592i
$218$	−5.54993e6			−0.535696
$219$		−	1.08839e7i		−	1.03622i
$220$		−	1.84394e6i		−	0.173173i
$221$			303788.i			0.0281445i
$222$	−7.06231e6			−0.645488
$223$	1.32277e7			1.19281			0.596403	−	0.802685i	$-0.296596\pi$
$223$	1.32277e7			1.19281			0.596403	+	0.802685i	$0.296596\pi$
$224$			3.97728e6i			0.353869i
$225$	3.69929e6			0.324767
$226$	7.86793e6			0.681609
$227$			2.00790e7i			1.71659i	0.513160	+	0.858293i	$0.328475\pi$
$227$			2.00790e7i			1.71659i	−0.513160	+	0.858293i	$0.671525\pi$
$228$	2.22565e6			0.187781
$229$		−	2.04020e7i		−	1.69889i	−0.527675	−	0.849446i	$-0.676936\pi$
$229$		−	2.04020e7i		−	1.69889i	0.527675	−	0.849446i	$-0.323064\pi$
$230$	−2.24717e7			−1.84694
$231$		−	2.70855e6i		−	0.219736i
$232$			1.48730e7i			1.19107i
$233$		−	1.71127e7i		−	1.35285i	−0.736511	−	0.676426i	$-0.763528\pi$
$233$		−	1.71127e7i		−	1.35285i	0.736511	−	0.676426i	$-0.236472\pi$
$234$	−475292.			−0.0370948
$235$			2.01521e7i			1.55280i
$236$	2.71788e6	+	1.64866e6i	0.206773	+	0.125429i
$237$	4.10234e6			0.308167
$238$		−	3.16211e6i		−	0.234556i
$239$	1.54360e7			1.13068			0.565341	−	0.824858i	$-0.308745\pi$
$239$	1.54360e7			1.13068			0.565341	+	0.824858i	$0.308745\pi$
$240$	−1.32707e7			−0.959977
$241$	9.78176e6			0.698821			0.349410	−	0.936970i	$-0.386382\pi$
$241$	9.78176e6			0.698821			0.349410	+	0.936970i	$0.386382\pi$
$242$			1.16919e7i			0.824968i
$243$	920483.			0.0641500
$244$		−	2.94719e6i		−	0.202880i
$245$	−9.13843e6			−0.621403
$246$			1.55595e7i			1.04518i
$247$		−	2.02382e6i		−	0.134302i
$248$	−9.81134e6			−0.643241
$249$		−	3.91841e6i		−	0.253812i
$250$		−	628778.i		−	0.0402418i
$251$	880652.			0.0556908			0.0278454	−	0.999612i	$-0.491135\pi$
$251$	880652.			0.0556908			0.0278454	+	0.999612i	$0.491135\pi$
$252$	963456.			0.0602047
$253$	−9.73454e6			−0.601110
$254$			2.66483e7i			1.62618i
$255$	3.79105e6			0.228633
$256$	1.15178e7			0.686512
$257$	2.44085e7			1.43794			0.718971	−	0.695040i	$-0.244614\pi$
$257$	2.44085e7			1.43794			0.718971	+	0.695040i	$0.244614\pi$
$258$	−762990.			−0.0444283
$259$		−	1.30177e7i		−	0.749266i
$260$		−	596429.i		−	0.0339343i
$261$	8.35493e6			0.469917
$262$	−1.19997e7			−0.667215
$263$	−3.37403e6			−0.185474			−0.0927368	−	0.995691i	$-0.529562\pi$
$263$	−3.37403e6			−0.185474			−0.0927368	+	0.995691i	$0.529562\pi$
$264$	−4.57389e6			−0.248584
$265$	1.31617e7			0.707250
$266$			2.10659e7i			1.11927i
$267$		−	6.69274e6i		−	0.351617i
$268$			6.52999e6i			0.339241i
$269$			2.59519e7i			1.33325i	0.745392	+	0.666626i	$0.232262\pi$
$269$			2.59519e7i			1.33325i	−0.745392	+	0.666626i	$0.767738\pi$
$270$			5.93129e6i			0.301341i
$271$	−6.90104e6			−0.346742			−0.173371	−	0.984857i	$-0.555466\pi$
$271$	−6.90104e6			−0.346742			−0.173371	+	0.984857i	$0.555466\pi$
$272$	−6.71142e6			−0.333509
$273$		−	876089.i		−	0.0430586i
$274$			1.67956e7i			0.816475i
$275$			1.03260e7i			0.496517i
$276$		−	3.46266e6i		−	0.164696i
$277$	−2.79897e7			−1.31692			−0.658459	−	0.752617i	$-0.728791\pi$
$277$	−2.79897e7			−1.31692			−0.658459	+	0.752617i	$0.728791\pi$
$278$		−	7.67001e6i		−	0.356994i
$279$			5.51153e6i			0.253781i
$280$		−	1.94623e7i		−	0.886584i
$281$	−2.13816e7			−0.963654			−0.481827	−	0.876266i	$-0.660027\pi$
$281$	−2.13816e7			−0.963654			−0.481827	+	0.876266i	$0.660027\pi$
$282$	−1.59452e7			−0.711021
$283$		−	1.30117e7i		−	0.574082i	−0.957918	−	0.287041i	$-0.907328\pi$
$283$		−	1.30117e7i		−	0.574082i	0.957918	−	0.287041i	$-0.0926715\pi$
$284$	545870.			0.0238306
$285$	−2.52558e7			−1.09101
$286$		−	1.32670e6i		−	0.0567120i
$287$	−2.86803e7			−1.21322
$288$		−	3.77293e6i		−	0.157943i
$289$	−2.22203e7			−0.920570
$290$			5.38364e7i			2.20741i
$291$		−	3.09100e6i		−	0.125435i
$292$			1.08067e7i			0.434056i
$293$	594514.			0.0236352			0.0118176	−	0.999930i	$-0.496238\pi$
$293$	594514.			0.0236352			0.0118176	+	0.999930i	$0.496238\pi$
$294$		−	7.23071e6i		−	0.284537i
$295$	−3.08415e7	−	1.87084e7i	−1.20135	−	0.728738i
$296$	−2.19828e7			−0.847634
$297$			2.56938e6i			0.0980752i
$298$	2.42765e7			0.917356
$299$	−3.14867e6			−0.117791
$300$	−3.67305e6			−0.136039
$301$		−	1.40639e6i		−	0.0515713i
$302$	−7.35526e6			−0.267040
$303$			2.16518e7i			0.778333i
$304$	4.47112e7			1.59146
$305$			3.34437e7i			1.17873i
$306$			2.99964e6i			0.104690i
$307$	3.44659e7			1.19117			0.595585	−	0.803292i	$-0.296920\pi$
$307$	3.44659e7			1.19117			0.595585	+	0.803292i	$0.296920\pi$
$308$			2.68933e6i			0.0920434i
$309$		−	3.33004e6i		−	0.112869i
$310$	−3.55145e7			−1.19212
$311$	3.44883e7			1.14654			0.573272	−	0.819365i	$-0.305674\pi$
$311$	3.44883e7			1.14654			0.573272	+	0.819365i	$0.305674\pi$
$312$	−1.47944e6			−0.0487117
$313$		−	2.97001e7i		−	0.968558i	−0.874914	−	0.484279i	$-0.839082\pi$
$313$		−	2.97001e7i		−	0.968558i	0.874914	−	0.484279i	$-0.160918\pi$
$314$	4.79315e7			1.54822
$315$	−1.09329e7			−0.349789
$316$	−4.07324e6			−0.129086
$317$	4.48502e7			1.40795			0.703973	−	0.710226i	$-0.251407\pi$
$317$	4.48502e7			1.40795			0.703973	+	0.710226i	$0.251407\pi$
$318$			1.04141e7i			0.323846i
$319$			2.33215e7i			0.718429i
$320$	−3.01728e7			−0.920800
$321$	−1.82258e7			−0.551024
$322$	3.27743e7			0.981671
$323$	−1.27727e7			−0.379030
$324$	−913953.			−0.0268713
$325$			3.33998e6i			0.0972956i
$326$			46300.6i			0.00133639i
$327$			9.70438e6i			0.277539i
$328$			4.84320e7i			1.37249i
$329$		−	2.93912e7i		−	0.825335i
$330$	−1.65563e7			−0.460702
$331$	−2.90849e6			−0.0802018			−0.0401009	−	0.999196i	$-0.512768\pi$
$331$	−2.90849e6			−0.0802018			−0.0401009	+	0.999196i	$0.512768\pi$
$332$			3.89061e6i			0.106317i
$333$			1.23489e7i			0.334422i
$334$		−	1.78686e7i		−	0.479570i
$335$		−	7.40999e7i		−	1.97099i
$336$	1.93550e7			0.510240
$337$			4.52124e7i			1.18132i	0.806921	+	0.590660i	$0.201132\pi$
$337$			4.52124e7i			1.18132i	−0.806921	+	0.590660i	$0.798868\pi$
$338$			4.26021e7i			1.10327i
$339$		−	1.37575e7i		−	0.353135i
$340$	−3.76415e6			−0.0957702
$341$	−1.53845e7			−0.387991
$342$		−	1.99835e7i		−	0.499566i
$343$	4.34653e7			1.07711
$344$	−2.37496e6			−0.0583419
$345$			3.92930e7i			0.956882i
$346$	−7.34417e7			−1.77302
$347$		−	4.88593e7i		−	1.16939i	−0.811253	−	0.584695i	$-0.801214\pi$
$347$		−	4.88593e7i		−	1.16939i	0.811253	−	0.584695i	$-0.198786\pi$
$348$	−8.29566e6			−0.196840
$349$			693047.i			0.0163037i	0.999967	+	0.00815185i	$0.00259484\pi$
$349$			693047.i			0.0163037i	−0.999967	+	0.00815185i	$0.997405\pi$
$350$		−	3.47656e7i		−	0.810860i
$351$			831075.i			0.0192185i
$352$	1.05315e7			0.241470
$353$		−	8.18650e7i		−	1.86112i	−0.366140	−	0.930560i	$-0.619321\pi$
$353$		−	8.18650e7i		−	1.86112i	0.366140	−	0.930560i	$-0.380679\pi$
$354$	1.48029e7	−	2.44031e7i	0.333686	−	0.550092i
$355$	−6.19434e6			−0.138455
$356$			6.64527e6i			0.147286i
$357$	−5.52913e6			−0.121521
$358$	8.99370e7			1.96015
$359$	5.78879e6			0.125114			0.0625568	−	0.998041i	$-0.480075\pi$
$359$	5.78879e6			0.125114			0.0625568	+	0.998041i	$0.480075\pi$
$360$			1.84623e7i			0.395711i
$361$	3.80451e7			0.808680
$362$		−	1.08414e7i		−	0.228538i
$363$	2.04439e7			0.427409
$364$			869874.i			0.0180365i
$365$		−	1.22631e8i		−	2.52186i
$366$	−2.64621e7			−0.539735
$367$		−	5.60143e7i		−	1.13319i	−0.823998	−	0.566593i	$-0.808261\pi$
$367$		−	5.60143e7i		−	1.13319i	0.823998	−	0.566593i	$-0.191739\pi$
$368$		−	6.95618e7i		−	1.39581i
$369$	2.72067e7			0.541497
$370$	−7.95720e7			−1.57092
$371$	−1.91959e7			−0.375913
$372$		−	5.47243e6i		−	0.106304i
$373$	−6.78694e7			−1.30782			−0.653909	−	0.756573i	$-0.726872\pi$
$373$	−6.78694e7			−1.30782			−0.653909	+	0.756573i	$0.726872\pi$
$374$	−8.37301e6			−0.160054
$375$	−1.09946e6			−0.0208489
$376$	−4.96325e7			−0.933691
$377$			7.54340e6i			0.140781i
$378$		−	8.65061e6i		−	0.160166i
$379$	3.93573e7			0.722948			0.361474	−	0.932382i	$-0.382274\pi$
$379$	3.93573e7			0.722948			0.361474	+	0.932382i	$0.382274\pi$
$380$	2.50766e7			0.457003
$381$	4.65961e7			0.842508
$382$	4.60438e7			0.826001
$383$	1.72548e7			0.307123			0.153562	−	0.988139i	$-0.450926\pi$
$383$	1.72548e7			0.307123			0.153562	+	0.988139i	$0.450926\pi$
$384$		−	3.93641e7i		−	0.695196i
$385$		−	3.05176e7i		−	0.534771i
$386$			5.48725e7i			0.954097i
$387$			1.33413e6i			0.0230179i
$388$			3.06907e6i			0.0525426i
$389$	−3.77016e7			−0.640488			−0.320244	−	0.947335i	$-0.603765\pi$
$389$	−3.77016e7			−0.640488			−0.320244	+	0.947335i	$0.603765\pi$
$390$	−5.35517e6			−0.0902775
$391$			1.98717e7i			0.332434i
$392$		−	2.25070e7i		−	0.373645i
$393$			2.09821e7i			0.345678i
$394$			1.24978e7i			0.204336i
$395$	4.62216e7			0.749987
$396$		−	2.55115e6i		−	0.0410820i
$397$		−	4.78319e6i		−	0.0764445i	−0.999269	−	0.0382222i	$-0.987831\pi$
$397$		−	4.78319e6i		−	0.0764445i	0.999269	−	0.0382222i	$-0.0121695\pi$
$398$		−	3.44154e7i		−	0.545888i
$399$	3.68349e7			0.579883
$400$	−7.37883e7			−1.15294
$401$			3.14396e7i			0.487577i	0.969828	+	0.243789i	$0.0783903\pi$
$401$			3.14396e7i			0.487577i	−0.969828	+	0.243789i	$0.921610\pi$
$402$	5.86310e7			0.902505
$403$	−4.97618e6			−0.0760293
$404$		−	2.14982e7i		−	0.326030i
$405$	1.03712e7			0.156122
$406$		−	7.85189e7i		−	1.17326i
$407$	−3.44699e7			−0.511278
$408$			9.33696e6i			0.137475i
$409$			1.12711e8i			1.64739i	0.567033	+	0.823695i	$0.308091\pi$
$409$			1.12711e8i			1.64739i	−0.567033	+	0.823695i	$0.691909\pi$
$410$			1.75311e8i			2.54365i
$411$	2.93680e7			0.423009
$412$			3.30642e6i			0.0472788i
$413$	4.49814e7	+	2.72857e7i	0.638533	+	0.387334i
$414$	−3.10903e7			−0.438152
$415$		−	4.41492e7i		−	0.617702i
$416$	3.40646e6			0.0473176
$417$	−1.34115e7			−0.184956
$418$	5.57807e7			0.763757
$419$		−	3.52543e7i		−	0.479259i	−0.970864	−	0.239630i	$-0.922974\pi$
$419$		−	3.52543e7i		−	0.479259i	0.970864	−	0.239630i	$-0.0770260\pi$
$420$	1.08554e7			0.146520
$421$			8.97239e7i			1.20244i	0.799085	+	0.601218i	$0.205318\pi$
$421$			8.97239e7i			1.20244i	−0.799085	+	0.601218i	$0.794682\pi$
$422$	−1.18129e7			−0.157187
$423$			2.78811e7i			0.368374i
$424$			3.24158e7i			0.425265i
$425$	2.10791e7			0.274590
$426$		−	4.90122e6i		−	0.0633980i
$427$		−	4.87766e7i		−	0.626510i
$428$	1.80965e7			0.230814
$429$	−2.31981e6			−0.0293820
$430$	−8.59671e6			−0.108125
$431$		−	9.58317e7i		−	1.19695i	−0.801140	−	0.598477i	$-0.795773\pi$
$431$		−	9.58317e7i		−	1.19695i	0.801140	−	0.598477i	$-0.204227\pi$
$432$	−1.83605e7			−0.227737
$433$	−2.93429e7			−0.361443			−0.180721	−	0.983534i	$-0.557843\pi$
$433$	−2.93429e7			−0.361443			−0.180721	+	0.983534i	$0.557843\pi$
$434$	5.17968e7			0.633627
$435$	9.41361e7			1.14364
$436$		−	9.63553e6i		−	0.116256i
$437$		−	1.32385e8i		−	1.58633i
$438$	9.70307e7			1.15475
$439$	1.15409e8			1.36410			0.682050	−	0.731305i	$-0.261089\pi$
$439$	1.15409e8			1.36410			0.682050	+	0.731305i	$0.261089\pi$
$440$	−5.15346e7			−0.604980
$441$	−1.26433e7			−0.147416
$442$	−2.70828e6			−0.0313636
$443$		−	6.74042e7i		−	0.775311i	−0.921804	−	0.387656i	$-0.873285\pi$
$443$		−	6.74042e7i		−	0.775311i	0.921804	−	0.387656i	$-0.126715\pi$
$444$		−	1.22613e7i		−	0.140083i
$445$		−	7.54080e7i		−	0.855732i
$446$			1.17925e8i			1.32924i
$447$		−	4.24489e7i		−	0.475274i
$448$	4.40061e7			0.489417
$449$	1.13935e8			1.25869			0.629346	−	0.777125i	$-0.283323\pi$
$449$	1.13935e8			1.25869			0.629346	+	0.777125i	$0.283323\pi$
$450$			3.29793e7i			0.361913i
$451$			7.59431e7i			0.827864i
$452$			1.36599e7i			0.147922i
$453$			1.28611e7i			0.138351i
$454$	−1.79005e8			−1.91293
$455$		−	9.87101e6i		−	0.104792i
$456$		−	6.22025e7i		−	0.656014i
$457$		−	4.52840e7i		−	0.474456i	−0.971454	−	0.237228i	$-0.923761\pi$
$457$		−	4.52840e7i		−	0.474456i	0.971454	−	0.237228i	$-0.0762388\pi$
$458$	1.81884e8			1.89321
$459$	5.24504e6			0.0542389
$460$		−	3.90143e7i		−	0.400821i
$461$	2.51264e7			0.256465			0.128232	−	0.991744i	$-0.459070\pi$
$461$	2.51264e7			0.256465			0.128232	+	0.991744i	$0.459070\pi$
$462$	2.41468e7			0.244869
$463$			1.56900e8i			1.58081i	0.612584	+	0.790405i	$0.290130\pi$
$463$			1.56900e8i			1.58081i	−0.612584	+	0.790405i	$0.709870\pi$
$464$	−1.66652e8			−1.66824
$465$			6.20991e7i			0.617627i
$466$	1.52560e8			1.50759
$467$			1.05635e8i			1.03719i	0.855021	+	0.518593i	$0.173544\pi$
$467$			1.05635e8i			1.03719i	−0.855021	+	0.518593i	$0.826456\pi$
$468$		−	825179.i		−	0.00805027i
$469$			1.08073e8i			1.04760i
$470$	−1.79657e8			−1.73041
$471$		−	8.38110e7i		−	0.802118i
$472$	4.60770e7	−	7.59594e7i	0.438186	−	0.722363i
$473$	−3.72402e6			−0.0351908
$474$			3.65725e7i			0.343416i
$475$	−1.40428e8			−1.31031
$476$	5.48991e6			0.0509031
$477$	1.82096e7			0.167782
$478$			1.37612e8i			1.26001i
$479$	2.49010e7			0.226574			0.113287	−	0.993562i	$-0.463862\pi$
$479$	2.49010e7			0.226574			0.113287	+	0.993562i	$0.463862\pi$
$480$		−	4.25101e7i		−	0.384387i
$481$	−1.11494e7			−0.100188
$482$			8.72048e7i			0.778752i
$483$		−	5.73078e7i		−	0.508595i
$484$	−2.02988e7			−0.179034
$485$		−	3.48267e7i		−	0.305272i
$486$			8.20614e6i			0.0714875i
$487$	2.58850e7			0.224110			0.112055	−	0.993702i	$-0.464257\pi$
$487$	2.58850e7			0.224110			0.112055	+	0.993702i	$0.464257\pi$
$488$	−8.23684e7			−0.708763
$489$	80959.3			0.000692373
$490$		−	8.14694e7i		−	0.692478i
$491$	2.98001e7			0.251753			0.125876	−	0.992046i	$-0.459826\pi$
$491$	2.98001e7			0.251753			0.125876	+	0.992046i	$0.459826\pi$
$492$	−2.70137e7			−0.226824
$493$	4.76076e7			0.397315
$494$	1.80425e7			0.149663
$495$			2.89496e7i			0.238686i
$496$		−	1.09936e8i		−	0.900939i
$497$	9.03426e6			0.0735908
$498$	3.49327e7			0.282842
$499$	−7.82912e7			−0.630103			−0.315051	−	0.949075i	$-0.602022\pi$
$499$	−7.82912e7			−0.630103			−0.315051	+	0.949075i	$0.602022\pi$
$500$	1.09166e6			0.00873325
$501$	−3.12443e7			−0.248461
$502$			7.85105e6i			0.0620607i
$503$			2.05439e7i			0.161428i	0.996737	+	0.0807140i	$0.0257200\pi$
$503$			2.05439e7i			0.161428i	−0.996737	+	0.0807140i	$0.974280\pi$
$504$		−	2.69267e7i		−	0.210326i
$505$			2.43953e8i			1.89423i
$506$		−	8.67837e7i		−	0.669864i
$507$	7.44922e7			0.571593
$508$	−4.62655e7			−0.352912
$509$		−	1.35190e8i		−	1.02516i	−0.858639	−	0.512581i	$-0.828689\pi$
$509$		−	1.35190e8i		−	1.02516i	0.858639	−	0.512581i	$-0.171311\pi$
$510$			3.37973e7i			0.254784i
$511$			1.78853e8i			1.34040i
$512$		−	5.89322e7i		−	0.439079i
$513$	−3.49423e7			−0.258821
$514$			2.17602e8i			1.60241i
$515$		−	3.75200e7i		−	0.274689i
$516$		−	1.32467e6i		−	0.00964180i
$517$	−7.78257e7			−0.563185
$518$	1.16054e8			0.834966
$519$			1.28417e8i			0.918588i
$520$	−1.66690e7			−0.118550
$521$	−2.04501e8			−1.44604			−0.723022	−	0.690825i	$-0.757248\pi$
$521$	−2.04501e8			−1.44604			−0.723022	+	0.690825i	$0.757248\pi$
$522$			7.44845e7i			0.523666i
$523$	1.61277e8			1.12737			0.563686	−	0.825989i	$-0.309383\pi$
$523$	1.61277e8			1.12737			0.563686	+	0.825989i	$0.309383\pi$
$524$		−	2.08333e7i		−	0.144798i
$525$	−6.07897e7			−0.420100
$526$		−	3.00796e7i		−	0.206688i
$527$			3.14054e7i			0.214572i
$528$		−	5.12504e7i		−	0.348173i
$529$	−5.79285e7			−0.391314
$530$			1.17337e8i			0.788145i
$531$	−4.26702e7	−	2.58838e7i	−0.284998	−	0.172880i
$532$	−3.65736e7			−0.242903
$533$			2.45640e7i			0.162225i
$534$	5.96661e7			0.391835
$535$	−2.05352e8			−1.34103
$536$	1.82501e8			1.18514
$537$		−	1.57260e8i		−	1.01554i
$538$	−2.31362e8			−1.48575
$539$		−	3.52918e7i		−	0.225376i
$540$	−1.02976e7			−0.0653967
$541$			1.33762e8i			0.844772i	0.906416	+	0.422386i	$0.138807\pi$
$541$			1.33762e8i			0.844772i	−0.906416	+	0.422386i	$0.861193\pi$
$542$		−	6.15230e7i		−	0.386402i
$543$	−1.89567e7			−0.118403
$544$		−	2.14987e7i		−	0.133541i
$545$			1.09340e8i			0.675447i
$546$	7.81037e6			0.0479837
$547$	−2.40525e8			−1.46959			−0.734797	−	0.678287i	$-0.762723\pi$
$547$	−2.40525e8			−1.46959			−0.734797	+	0.678287i	$0.762723\pi$
$548$	−2.91597e7			−0.177191
$549$			4.62705e7i			0.279632i
$550$	−9.20566e7			−0.553308
$551$	−3.17160e8			−1.89594
$552$	−9.67748e7			−0.575367
$553$	−6.74129e7			−0.398628
$554$		−	2.49529e8i		−	1.46755i
$555$			1.39136e8i			0.813882i
$556$	1.33163e7			0.0774746
$557$	5.88909e7			0.340787			0.170393	−	0.985376i	$-0.445496\pi$
$557$	5.88909e7			0.340787			0.170393	+	0.985376i	$0.445496\pi$
$558$	−4.91354e7			−0.282808
$559$	−1.20455e6			−0.00689585
$560$	2.18075e8			1.24177
$561$			1.46407e7i			0.0829226i
$562$		−	1.90618e8i		−	1.07388i
$563$			8.90157e7i			0.498817i	0.968398	+	0.249409i	$0.0802363\pi$
$563$			8.90157e7i			0.498817i	−0.968398	+	0.249409i	$0.919764\pi$
$564$		−	2.76833e7i		−	0.154305i
$565$		−	1.55008e8i		−	0.859426i
$566$	1.15999e8			0.639745
$567$	−1.51261e7			−0.0829808
$568$		−	1.52560e7i		−	0.0832523i
$569$			3.46633e8i			1.88162i	0.338929	+	0.940812i	$0.389935\pi$
$569$			3.46633e8i			1.88162i	−0.338929	+	0.940812i	$0.610065\pi$
$570$		−	2.25157e8i		−	1.21579i
$571$		−	3.04837e7i		−	0.163741i	−0.996643	−	0.0818707i	$-0.973911\pi$
$571$		−	3.04837e7i		−	0.163741i	0.996643	−	0.0818707i	$-0.0260895\pi$
$572$	2.30336e6			0.0123076
$573$		−	8.05102e7i		−	0.427944i
$574$		−	2.55686e8i		−	1.35198i
$575$			2.18478e8i			1.14923i
$576$	−4.17451e7			−0.218443
$577$	−4.21117e7			−0.219217			−0.109609	−	0.993975i	$-0.534960\pi$
$577$	−4.21117e7			−0.219217			−0.109609	+	0.993975i	$0.534960\pi$
$578$		−	1.98095e8i		−	1.02586i
$579$	9.59477e7			0.494309
$580$	−9.34683e7			−0.479050
$581$			6.43904e7i			0.328316i
$582$	2.75563e7			0.139782
$583$			5.08292e7i			0.256512i
$584$	3.02027e8			1.51638
$585$			9.36383e6i			0.0467720i
$586$			5.30011e6i			0.0263386i
$587$		−	1.34414e8i		−	0.664554i	−0.943182	−	0.332277i	$-0.892183\pi$
$587$		−	1.34414e8i		−	0.664554i	0.943182	−	0.332277i	$-0.107817\pi$
$588$	1.25536e7			0.0617500
$589$		−	2.09222e8i		−	1.02391i
$590$	1.66786e8	−	2.74953e8i	0.812091	−	1.33876i
$591$	2.18531e7			0.105865
$592$		−	2.46318e8i		−	1.18722i
$593$	−6.13574e7			−0.294241			−0.147120	−	0.989119i	$-0.547000\pi$
$593$	−6.13574e7			−0.294241			−0.147120	+	0.989119i	$0.547000\pi$
$594$	−2.29061e7			−0.109293
$595$	−6.22975e7			−0.295746
$596$			4.21478e7i			0.199084i
$597$	−6.01773e7			−0.282820
$598$		−	2.80705e7i		−	0.131264i
$599$	8.23867e6			0.0383333			0.0191667	−	0.999816i	$-0.493899\pi$
$599$	8.23867e6			0.0383333			0.0191667	+	0.999816i	$0.493899\pi$
$600$			1.02655e8i			0.475253i
$601$		−	4.33229e7i		−	0.199569i	−0.995009	−	0.0997847i	$-0.968185\pi$
$601$		−	4.33229e7i		−	0.199569i	0.995009	−	0.0997847i	$-0.0318154\pi$
$602$	1.25381e7			0.0574700
$603$		−	1.02520e8i		−	0.467580i
$604$		−	1.27699e7i		−	0.0579529i
$605$	2.30344e8			1.04019
$606$	−1.93026e8			−0.867358
$607$	−1.49938e8			−0.670417			−0.335209	−	0.942144i	$-0.608807\pi$
$607$	−1.49938e8			−0.670417			−0.335209	+	0.942144i	$0.608807\pi$
$608$			1.43223e8i			0.637240i
$609$	−1.37295e8			−0.607858
$610$	−2.98152e8			−1.31355
$611$	−2.51730e7			−0.110360
$612$	−5.20783e6			−0.0227197
$613$			2.33739e8i			1.01473i	0.861732	+	0.507363i	$0.169380\pi$
$613$			2.33739e8i			1.01473i	−0.861732	+	0.507363i	$0.830620\pi$
$614$			3.07264e8i			1.32742i
$615$	3.06541e8			1.31784
$616$	7.51617e7			0.321554
$617$	−3.31897e8			−1.41302			−0.706510	−	0.707703i	$-0.749731\pi$
$617$	−3.31897e8			−1.41302			−0.706510	+	0.707703i	$0.749731\pi$
$618$	2.96874e7			0.125779
$619$	4.22537e8			1.78153			0.890765	−	0.454464i	$-0.150169\pi$
$619$	4.22537e8			1.78153			0.890765	+	0.454464i	$0.150169\pi$
$620$		−	6.16586e7i		−	0.258713i
$621$			5.43633e7i			0.227002i
$622$			3.07465e8i			1.27769i
$623$			1.09980e8i			0.454832i
$624$		−	1.65771e7i		−	0.0682268i
$625$	−2.50254e8			−1.02504
$626$	2.64778e8			1.07934
$627$		−	9.75358e7i		−	0.395696i
$628$			8.32164e7i			0.335993i
$629$			7.03656e7i			0.282754i
$630$		−	9.74676e7i		−	0.389797i
$631$	−3.42333e8			−1.36257			−0.681287	−	0.732016i	$-0.738580\pi$
$631$	−3.42333e8			−1.36257			−0.681287	+	0.732016i	$0.738580\pi$
$632$			1.13839e8i			0.450962i
$633$			2.06555e7i			0.0814374i
$634$			3.99841e8i			1.56899i
$635$	5.25004e8			2.05041
$636$	−1.80804e7			−0.0702809
$637$		−	1.14153e7i		−	0.0441639i
$638$	−2.07912e8			−0.800603
$639$	−8.57007e6			−0.0328460
$640$		−	4.43521e8i		−	1.69190i
$641$	−3.46348e8			−1.31504			−0.657519	−	0.753438i	$-0.728394\pi$
$641$	−3.46348e8			−1.31504			−0.657519	+	0.753438i	$0.728394\pi$
$642$		−	1.62483e8i		−	0.614050i
$643$	−2.34493e8			−0.882058			−0.441029	−	0.897493i	$-0.645386\pi$
$643$	−2.34493e8			−0.882058			−0.441029	+	0.897493i	$0.645386\pi$
$644$			5.69012e7i			0.213041i
$645$			1.50319e7i			0.0560187i
$646$		−	1.13869e8i		−	0.422383i
$647$	−3.76403e8			−1.38976			−0.694881	−	0.719125i	$-0.744543\pi$
$647$	−3.76403e8			−1.38976			−0.694881	+	0.719125i	$0.744543\pi$
$648$			2.55432e7i			0.0938751i
$649$	7.22504e7	−	1.19107e8i	0.264306	−	0.435716i
$650$	−2.97760e7			−0.108424
$651$		−	9.05697e7i		−	0.328277i
$652$	−80385.0			−0.000290023
$653$	1.07408e8			0.385742			0.192871	−	0.981224i	$-0.438220\pi$
$653$	1.07408e8			0.385742			0.192871	+	0.981224i	$0.438220\pi$
$654$	−8.65149e7			−0.309284
$655$			2.36408e8i			0.841277i
$656$	−5.42680e8			−1.92235
$657$		−	1.69664e8i		−	0.598264i
$658$	2.62024e8			0.919737
$659$			2.76117e8i			0.964801i	0.875951	+	0.482400i	$0.160235\pi$
$659$			2.76117e8i			0.964801i	−0.875951	+	0.482400i	$0.839765\pi$
$660$		−	2.87442e7i		−	0.0999812i
$661$	−4.07007e8			−1.40928			−0.704641	−	0.709564i	$-0.748892\pi$
$661$	−4.07007e8			−1.40928			−0.704641	+	0.709564i	$0.748892\pi$
$662$		−	2.59293e7i		−	0.0893753i
$663$			4.73558e6i			0.0162492i
$664$	1.08735e8			0.371420
$665$	4.15023e8			1.41126
$666$	−1.10091e8			−0.372673
$667$			4.93438e8i			1.66286i
$668$	3.10227e7			0.104076
$669$	2.06199e8			0.688667
$670$	6.60604e8			2.19643
$671$	−1.29157e8			−0.427513
$672$			6.19997e7i			0.204306i
$673$			1.63452e7i			0.0536223i	0.999641	+	0.0268112i	$0.00853528\pi$
$673$			1.63452e7i			0.0536223i	−0.999641	+	0.0268112i	$0.991465\pi$
$674$	−4.03070e8			−1.31644
$675$	5.76663e7			0.187504
$676$	−7.39637e7			−0.239430
$677$	4.66815e8			1.50445			0.752227	−	0.658904i	$-0.228980\pi$
$677$	4.66815e8			1.50445			0.752227	+	0.658904i	$0.228980\pi$
$678$	1.22649e8			0.393527
$679$			5.07937e7i			0.162256i
$680$			1.05201e8i			0.334574i
$681$			3.13001e8i			0.991071i
$682$		−	1.37154e8i		−	0.432369i
$683$			7.64516e7i			0.239952i	0.992777	+	0.119976i	$0.0382818\pi$
$683$			7.64516e7i			0.239952i	−0.992777	+	0.119976i	$0.961718\pi$
$684$	3.46944e7			0.108415
$685$	3.30893e8			1.02948
$686$			3.87495e8i			1.20031i
$687$		−	3.18035e8i		−	0.980856i
$688$		−	2.66114e7i		−	0.0817151i
$689$			1.64409e7i			0.0502652i
$690$	−3.50299e8			−1.06633
$691$		−	1.86619e8i		−	0.565615i	−0.959177	−	0.282807i	$-0.908734\pi$
$691$		−	1.86619e8i		−	0.565615i	0.959177	−	0.282807i	$-0.0912657\pi$
$692$		−	1.27506e8i		−	0.384780i
$693$		−	4.22221e7i		−	0.126865i
$694$	4.35583e8			1.30314
$695$	−1.51109e8			−0.450127
$696$			2.31848e8i			0.687662i
$697$	1.55027e8			0.457836
$698$	−6.17854e6			−0.0181685
$699$		−	2.66760e8i		−	0.781069i
$700$	6.03585e7			0.175972
$701$		−	2.64441e8i		−	0.767669i	−0.923402	−	0.383835i	$-0.874603\pi$
$701$		−	2.64441e8i		−	0.767669i	0.923402	−	0.383835i	$-0.125397\pi$
$702$	−7.40906e6			−0.0214167
$703$		−	4.68773e8i		−	1.34926i
$704$		−	1.16525e8i		−	0.333964i
$705$			3.14140e8i			0.896512i
$706$	7.29830e8			2.07399
$707$		−	3.55799e8i		−	1.00681i
$708$	4.23675e7	+	2.57001e7i	0.119380	+	0.0724162i
$709$	−2.07674e8			−0.582697			−0.291348	−	0.956617i	$-0.594104\pi$
$709$	−2.07674e8			−0.582697			−0.291348	+	0.956617i	$0.594104\pi$
$710$		−	5.52227e7i		−	0.154292i
$711$	6.39492e7			0.177921
$712$	1.85722e8			0.514546
$713$	−3.25508e8			−0.898034
$714$		−	4.92924e7i		−	0.135421i
$715$	−2.61376e7			−0.0715070
$716$			1.56144e8i			0.425390i
$717$	2.40623e8			0.652799
$718$			5.16072e7i			0.139424i
$719$			5.52111e8i			1.48539i	0.669631	+	0.742694i	$0.266452\pi$
$719$			5.52111e8i			1.48539i	−0.669631	+	0.742694i	$0.733548\pi$
$720$	−2.06870e8			−0.554243
$721$			5.47219e7i			0.146001i
$722$			3.39173e8i			0.901177i
$723$	1.52483e8			0.403464
$724$	1.88223e7			0.0495971
$725$	5.23419e8			1.37352
$726$			1.82258e8i			0.476296i
$727$	−1.55964e8			−0.405902			−0.202951	−	0.979189i	$-0.565053\pi$
$727$	−1.55964e8			−0.405902			−0.202951	+	0.979189i	$0.565053\pi$
$728$	2.43113e7			0.0630106
$729$	1.43489e7			0.0370370
$730$	1.09326e9			2.81031
$731$			7.60207e6i			0.0194617i
$732$		−	4.59422e7i		−	0.117133i
$733$	7.36970e8			1.87128			0.935638	−	0.352962i	$-0.114825\pi$
$733$	7.36970e8			1.87128			0.935638	+	0.352962i	$0.114825\pi$
$734$	4.99370e8			1.26280
$735$	−1.42454e8			−0.358767
$736$	2.22827e8			0.558901
$737$	2.86168e8			0.714855
$738$			2.42549e8i			0.603434i
$739$			3.38338e8i			0.838336i	0.907909	+	0.419168i	$0.137678\pi$
$739$			3.38338e8i			0.838336i	−0.907909	+	0.419168i	$0.862322\pi$
$740$		−	1.38149e8i		−	0.340921i
$741$		−	3.15483e7i		−	0.0775391i
$742$		−	1.71132e8i		−	0.418909i
$743$	−5.92755e8			−1.44514			−0.722568	−	0.691300i	$-0.757038\pi$
$743$	−5.92755e8			−1.44514			−0.722568	+	0.691300i	$0.757038\pi$
$744$	−1.52944e8			−0.371375
$745$		−	4.78278e8i		−	1.15667i
$746$		−	6.05058e8i		−	1.45741i
$747$		−	6.10819e7i		−	0.146538i
$748$		−	1.45368e7i		−	0.0347348i
$749$	2.99500e8			0.712773
$750$		−	9.80168e6i		−	0.0232336i
$751$		−	5.01083e8i		−	1.18301i	−0.806300	−	0.591507i	$-0.798533\pi$
$751$		−	5.01083e8i		−	1.18301i	0.806300	−	0.591507i	$-0.201467\pi$
$752$		−	5.56133e8i		−	1.30775i
$753$	1.37280e7			0.0321531
$754$	−6.72497e7			−0.156883
$755$			1.44908e8i			0.336706i
$756$	1.50188e7			0.0347592
$757$	−2.69345e8			−0.620900			−0.310450	−	0.950590i	$-0.600480\pi$
$757$	−2.69345e8			−0.620900			−0.310450	+	0.950590i	$0.600480\pi$
$758$			3.50871e8i			0.805639i
$759$	−1.51746e8			−0.347051
$760$		−	7.00844e8i		−	1.59654i
$761$	1.03962e8			0.235896			0.117948	−	0.993020i	$-0.462368\pi$
$761$	1.03962e8			0.235896			0.117948	+	0.993020i	$0.462368\pi$
$762$			4.15406e8i			0.938874i
$763$		−	1.59470e8i		−	0.359009i
$764$			7.99390e7i			0.179258i
$765$	5.90966e7			0.132001
$766$			1.53827e8i			0.342252i
$767$	2.33696e7	−	3.85256e7i	0.0517924	−	0.0853814i
$768$	1.79544e8			0.396358
$769$		−	6.72944e7i		−	0.147979i	−0.997259	−	0.0739895i	$-0.976427\pi$
$769$		−	6.72944e7i		−	0.147979i	0.997259	−	0.0739895i	$-0.0235731\pi$
$770$	2.72065e8			0.595938
$771$	3.80490e8			0.830196
$772$	−9.52670e7			−0.207057
$773$		−	6.24379e8i		−	1.35179i	−0.736997	−	0.675896i	$-0.763757\pi$
$773$		−	6.24379e8i		−	1.35179i	0.736997	−	0.675896i	$-0.236243\pi$
$774$	−1.18938e7			−0.0256507
$775$			3.45285e8i			0.741776i
$776$	8.57745e7			0.183558
$777$		−	2.02926e8i		−	0.432589i
$778$		−	3.36111e8i		−	0.713747i
$779$	−1.03279e9			−2.18473
$780$		−	9.29740e6i		−	0.0195920i
$781$		−	2.39220e7i		−	0.0502163i
$782$	−1.77157e8			−0.370457
$783$	1.30240e8			0.271307
$784$	2.52191e8			0.523337
$785$		−	9.44310e8i		−	1.95212i
$786$	−1.87056e8			−0.385217
$787$	−5.72875e8			−1.17527			−0.587633	−	0.809128i	$-0.699940\pi$
$787$	−5.72875e8			−1.17527			−0.587633	+	0.809128i	$0.699940\pi$
$788$	−2.16981e7			−0.0443448
$789$	−5.25960e7			−0.107083
$790$			4.12067e8i			0.835771i
$791$			2.26075e8i			0.456796i
$792$	−7.12998e7			−0.143520
$793$	−4.17761e7			−0.0837739
$794$	4.26423e7			0.0851882
$795$	2.05170e8			0.408331
$796$	5.97504e7			0.118468
$797$		−	6.90958e8i		−	1.36482i	−0.730968	−	0.682412i	$-0.760931\pi$
$797$		−	6.90958e8i		−	1.36482i	0.730968	−	0.682412i	$-0.239069\pi$
$798$			3.28384e8i			0.646210i
$799$			1.58870e8i			0.311460i
$800$		−	2.36366e8i		−	0.461652i
$801$		−	1.04330e8i		−	0.203006i
$802$	−2.80285e8			−0.543346
$803$	4.73589e8			0.914651
$804$			1.01792e8i			0.195861i
$805$		−	6.45694e8i		−	1.23777i
$806$		−	4.43628e7i		−	0.0847255i
$807$			4.04550e8i			0.769754i
$808$	−6.00832e8			−1.13899
$809$			9.80021e7i			0.185093i	0.995708	+	0.0925464i	$0.0295007\pi$
$809$			9.80021e7i			0.185093i	−0.995708	+	0.0925464i	$0.970499\pi$
$810$			9.24596e7i			0.173979i
$811$			6.95316e8i			1.30353i	0.758423	+	0.651763i	$0.225970\pi$
$811$			6.95316e8i			1.30353i	−0.758423	+	0.651763i	$0.774030\pi$
$812$	1.36321e8			0.254621
$813$	−1.07577e8			−0.200192
$814$		−	3.07300e8i		−	0.569757i
$815$	912179.			0.00168503
$816$	−1.04621e8			−0.192551
$817$		−	5.06448e7i		−	0.0928685i
$818$	−1.00482e9			−1.83582
$819$		−	1.36569e7i		−	0.0248599i
$820$	−3.04367e8			−0.552021
$821$			4.72553e8i			0.853927i	0.904269	+	0.426963i	$0.140417\pi$
$821$			4.72553e8i			0.853927i	−0.904269	+	0.426963i	$0.859583\pi$
$822$			2.61817e8i			0.471392i
$823$		−	8.88715e7i		−	0.159427i	−0.996818	−	0.0797137i	$-0.974599\pi$
$823$		−	8.88715e7i		−	0.159427i	0.996818	−	0.0797137i	$-0.0254006\pi$
$824$	9.24080e7			0.165169
$825$			1.60966e8i			0.286664i
$826$	−2.43253e8	+	4.01011e8i	−0.431637	+	0.711568i
$827$	−3.98588e8			−0.704705			−0.352352	−	0.935867i	$-0.614618\pi$
$827$	−3.98588e8			−0.704705			−0.352352	+	0.935867i	$0.614618\pi$
$828$		−	5.39776e7i		−	0.0950873i
$829$	4.38027e8			0.768842			0.384421	−	0.923158i	$-0.374401\pi$
$829$	4.38027e8			0.768842			0.384421	+	0.923158i	$0.374401\pi$
$830$	3.93592e8			0.688354
$831$	−4.36316e8			−0.760323
$832$		−	3.76903e7i		−	0.0654424i
$833$	−7.20434e7			−0.124640
$834$		−	1.19564e8i		−	0.206111i
$835$	−3.52034e8			−0.604680
$836$			9.68439e7i			0.165750i
$837$			8.59162e7i			0.146521i
$838$	3.14294e8			0.534077
$839$			7.88894e8i			1.33577i	0.744263	+	0.667887i	$0.232801\pi$
$839$			7.88894e8i			1.33577i	−0.744263	+	0.667887i	$0.767199\pi$
$840$		−	3.03387e8i		−	0.511869i
$841$	5.87329e8			0.987400
$842$	−7.99892e8			−1.33997
$843$	−3.33306e8			−0.556366
$844$		−	2.05089e7i		−	0.0341127i
$845$	8.39313e8			1.39109
$846$	−2.48561e8			−0.410508
$847$	−3.35950e8			−0.552872
$848$	−3.63219e8			−0.595637
$849$		−	2.02832e8i		−	0.331446i
$850$			1.87921e8i			0.305998i
$851$	−7.29318e8			−1.18339
$852$	8.50928e6			0.0137586
$853$	1.03626e9			1.66963			0.834816	−	0.550528i	$-0.185574\pi$
$853$	1.03626e9			1.66963			0.834816	+	0.550528i	$0.185574\pi$
$854$	4.34846e8			0.698170
$855$	−3.93699e8			−0.629892
$856$		−	5.05761e8i		−	0.806351i
$857$		−	7.20612e8i		−	1.14488i	−0.819948	−	0.572439i	$-0.805997\pi$
$857$		−	7.20612e8i		−	1.14488i	0.819948	−	0.572439i	$-0.194003\pi$
$858$		−	2.06812e7i		−	0.0327427i
$859$		−	5.94338e8i		−	0.937678i	−0.883284	−	0.468839i	$-0.844672\pi$
$859$		−	5.94338e8i		−	0.937678i	0.883284	−	0.468839i	$-0.155328\pi$
$860$		−	1.49252e7i		−	0.0234652i
$861$	−4.47082e8			−0.700450
$862$	8.54343e8			1.33386
$863$		−	3.74562e8i		−	0.582763i	−0.956607	−	0.291381i	$-0.905885\pi$
$863$		−	3.74562e8i		−	0.582763i	0.956607	−	0.291381i	$-0.0941148\pi$
$864$		−	5.88141e7i		−	0.0911886i
$865$			1.44689e9i			2.23557i
$866$		−	2.61593e8i		−	0.402784i
$867$	−3.46380e8			−0.531491
$868$			8.99272e7i			0.137509i
$869$			1.78504e8i			0.272012i
$870$			8.39227e8i			1.27445i
$871$	9.25619e7			0.140080
$872$	−2.69294e8			−0.406142
$873$		−	4.81838e7i		−	0.0724200i
$874$	1.18021e9			1.76777
$875$	1.80671e7			0.0269690
$876$			1.68460e8i			0.250602i
$877$	−8.07317e8			−1.19687			−0.598433	−	0.801173i	$-0.704210\pi$
$877$	−8.07317e8			−1.19687			−0.598433	+	0.801173i	$0.704210\pi$
$878$			1.02888e9i			1.52013i
$879$	9.26756e6			0.0136458
$880$		−	5.77445e8i		−	0.847349i
$881$		−	1.27508e9i		−	1.86471i	−0.361549	−	0.932353i	$-0.617752\pi$
$881$		−	1.27508e9i		−	1.86471i	0.361549	−	0.932353i	$-0.382248\pi$
$882$		−	1.12716e8i		−	0.164278i
$883$	−9.23049e8			−1.34073			−0.670367	−	0.742029i	$-0.733863\pi$
$883$	−9.23049e8			−1.34073			−0.670367	+	0.742029i	$0.733863\pi$
$884$		−	4.70199e6i		−	0.00680651i
$885$	−4.80771e8	−	2.91636e8i	−0.693599	−	0.420737i
$886$	6.00911e8			0.863991
$887$		−	2.45974e8i		−	0.352467i	−0.984348	−	0.176233i	$-0.943609\pi$
$887$		−	2.45974e8i		−	0.352467i	0.984348	−	0.176233i	$-0.0563913\pi$
$888$	−3.42678e8			−0.489382
$889$	−7.65703e8			−1.08982
$890$	6.72265e8			0.953610
$891$			4.00527e7i			0.0566238i
$892$	−2.04737e8			−0.288470
$893$		−	1.05839e9i		−	1.48625i
$894$	3.78434e8			0.529636
$895$		−	1.77187e9i		−	2.47151i
$896$			6.46862e8i			0.899265i
$897$	−4.90829e7			−0.0680068
$898$			1.01574e9i			1.40266i
$899$			7.79834e8i			1.07330i
$900$	−5.72572e7			−0.0785421
$901$	1.03761e8			0.141860
$902$	−6.77036e8			−0.922554
$903$		−	2.19235e7i		−	0.0297747i
$904$	3.81769e8			0.516767
$905$	−2.13588e8			−0.288158
$906$	−1.14657e8			−0.154176
$907$	1.08526e7			0.0145449			0.00727244	−	0.999974i	$-0.497685\pi$
$907$	1.08526e7			0.0145449			0.00727244	+	0.999974i	$0.497685\pi$
$908$		−	3.10781e8i		−	0.415142i
$909$			3.37518e8i			0.449371i
$910$	8.80004e7			0.116778
$911$	−8.15991e8			−1.07927			−0.539635	−	0.841899i	$-0.681438\pi$
$911$	−8.15991e8			−1.07927			−0.539635	+	0.841899i	$0.681438\pi$
$912$	6.96979e8			0.918830
$913$	1.70500e8			0.224034
$914$	4.03708e8			0.528724
$915$			5.21335e8i			0.680540i
$916$			3.15779e8i			0.410863i
$917$		−	3.44795e8i		−	0.447150i
$918$			4.67597e7i			0.0604427i
$919$			1.49051e9i			1.92038i	0.279346	+	0.960190i	$0.409882\pi$
$919$			1.49051e9i			1.92038i	−0.279346	+	0.960190i	$0.590118\pi$
$920$	−1.09037e9			−1.40027
$921$	5.37270e8			0.687723
$922$			2.24003e8i			0.285799i
$923$		−	7.73765e6i		−	0.00984020i
$924$			4.19226e7i			0.0531413i
$925$			7.73630e8i			0.977481i
$926$	−1.39877e9			−1.76162
$927$		−	5.19102e7i		−	0.0651649i
$928$		−	5.33837e8i		−	0.667982i
$929$			6.90383e8i			0.861079i	0.902572	+	0.430539i	$0.141677\pi$
$929$			6.90383e8i			0.861079i	−0.902572	+	0.430539i	$0.858323\pi$
$930$	−5.53616e8			−0.688271
$931$	4.79951e8			0.594768
$932$			2.64868e8i			0.327176i
$933$	5.37620e8			0.661957
$934$	−9.41739e8			−1.15582
$935$			1.64959e8i			0.201809i
$936$	−2.30622e7			−0.0281237
$937$		−	4.29772e8i		−	0.522419i	−0.965282	−	0.261210i	$-0.915879\pi$
$937$		−	4.29772e8i		−	0.522419i	0.965282	−	0.261210i	$-0.0841214\pi$
$938$	−9.63472e8			−1.16743
$939$		−	4.62979e8i		−	0.559197i
$940$		−	3.11911e8i		−	0.375533i
$941$			8.69654e8i			1.04371i	0.853036	+	0.521853i	$0.174759\pi$
$941$			8.69654e8i			1.04371i	−0.853036	+	0.521853i	$0.825241\pi$
$942$	7.47178e8			0.893864
$943$			1.60681e9i			1.91615i
$944$	8.51125e8	+	5.16293e8i	1.01176	+	0.613734i
$945$	−1.70428e8			−0.201951
$946$		−	3.31998e7i		−	0.0392159i
$947$	−1.38856e9			−1.63499			−0.817495	−	0.575936i	$-0.804638\pi$
$947$	−1.38856e9			−1.63499			−0.817495	+	0.575936i	$0.804638\pi$
$948$	−6.34955e7			−0.0745278
$949$	1.53184e8			0.179232
$950$		−	1.25192e9i		−	1.46018i
$951$	6.99145e8			0.812878
$952$		−	1.53432e8i		−	0.177830i
$953$	1.16369e9			1.34449			0.672245	−	0.740329i	$-0.265330\pi$
$953$	1.16369e9			1.34449			0.672245	+	0.740329i	$0.265330\pi$
$954$			1.62339e8i			0.186973i
$955$		−	9.07119e8i		−	1.04149i
$956$	−2.38916e8			−0.273446
$957$			3.63546e8i			0.414785i
$958$			2.21993e8i			0.252489i
$959$	−4.82599e8			−0.547180
$960$	−4.70347e8			−0.531624
$961$	3.73068e8			0.420357
$962$		−	9.93973e7i		−	0.111648i
$963$	−2.84111e8			−0.318134
$964$	−1.51401e8			−0.169004
$965$	1.08106e9			1.20300
$966$	5.10901e8			0.566768
$967$			5.55639e8i			0.614488i	0.951631	+	0.307244i	$0.0994068\pi$
$967$			5.55639e8i			0.614488i	−0.951631	+	0.307244i	$0.900593\pi$
$968$			5.67314e8i			0.625456i
$969$	−1.99106e8			−0.218833
$970$	3.10481e8			0.340189
$971$	1.53537e9			1.67709			0.838545	−	0.544832i	$-0.183407\pi$
$971$	1.53537e9			1.67709			0.838545	+	0.544832i	$0.183407\pi$
$972$	−1.42471e7			−0.0155142
$973$	2.20388e8			0.239248
$974$			2.30765e8i			0.249743i
$975$			5.20651e7i			0.0561736i
$976$		−	9.22937e8i		−	0.992711i
$977$			8.80152e8i			0.943787i	0.881656	+	0.471893i	$0.156429\pi$
$977$			8.80152e8i			0.943787i	−0.881656	+	0.471893i	$0.843571\pi$
$978$			721755.i			0.000771567i
$979$	2.91219e8			0.310365
$980$	1.41443e8			0.150281
$981$			1.51276e8i			0.160237i
$982$			2.65669e8i			0.280548i
$983$			1.20391e9i			1.26746i	0.773554	+	0.633730i	$0.218477\pi$
$983$			1.20391e9i			1.26746i	−0.773554	+	0.633730i	$0.781523\pi$
$984$			7.54980e8i			0.792410i
$985$	2.46222e8			0.257643
$986$			4.24423e8i			0.442760i
$987$		−	4.58164e8i		−	0.476507i
$988$			3.13245e7i			0.0324798i
$989$	−7.87932e7			−0.0814517
$990$	−2.58086e8			−0.265986
$991$		−	4.24826e8i		−	0.436506i	−0.975892	−	0.218253i	$-0.929964\pi$
$991$		−	4.24826e8i		−	0.436506i	0.975892	−	0.218253i	$-0.0700358\pi$
$992$	3.52158e8			0.360747
$993$	−4.53389e7			−0.0463045
$994$			8.05408e7i			0.0820081i
$995$	−6.78026e8			−0.688299
$996$			6.06486e7i			0.0613822i
$997$	−1.25628e9			−1.26766			−0.633829	−	0.773473i	$-0.718518\pi$
$997$	−1.25628e9			−1.26766			−0.633829	+	0.773473i	$0.718518\pi$
$998$		−	6.97969e8i		−	0.702174i
$999$			1.92500e8i			0.193078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.45	yes	60
59.58	odd	2	inner	177.7.c.a.58.16	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.16	✓	60	59.58	odd	2	inner
177.7.c.a.58.45	yes	60	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} +138.972i q^{6} -256.162 q^{7} +432.577i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+8.91504i q^{2} +15.5885 q^{3} -15.4779 q^{4} +175.637 q^{5} +138.972i q^{6} -256.162 q^{7} +432.577i q^{8} +243.000 q^{9} +1565.81i q^{10} +678.296i q^{11} -241.276 q^{12} +219.397i q^{13} -2283.69i q^{14} +2737.91 q^{15} -4847.02 q^{16} +1384.65 q^{17} +2166.35i q^{18} -9224.48 q^{19} -2718.49 q^{20} -3993.17 q^{21} -6047.03 q^{22} +14351.5i q^{23} +6743.20i q^{24} +15223.4 q^{25} -1955.93 q^{26} +3788.00 q^{27} +3964.84 q^{28} +34382.4 q^{29} +24408.6i q^{30} +22681.2i q^{31} -15526.5i q^{32} +10573.6i q^{33} +12344.2i q^{34} -44991.6 q^{35} -3761.12 q^{36} +50818.4i q^{37} -82236.5i q^{38} +3420.06i q^{39} +75976.5i q^{40} +111962. q^{41} -35599.2i q^{42} +5490.26i q^{43} -10498.6i q^{44} +42679.8 q^{45} -127944. q^{46} +114737. i q^{47} -75557.6 q^{48} -52030.1 q^{49} +135717. i q^{50} +21584.5 q^{51} -3395.80i q^{52} +74936.6 q^{53} +33770.1i q^{54} +119134. i q^{55} -110810. i q^{56} -143795. q^{57} +306521. i q^{58} +(-175598. - 106518. i) q^{59} -42377.1 q^{60} +190413. i q^{61} -202203. q^{62} -62247.3 q^{63} -171790. q^{64} +38534.3i q^{65} -94263.9 q^{66} -421892. i q^{67} -21431.4 q^{68} +223717. i q^{69} -401101. i q^{70} -35267.8 q^{71} +105116. i q^{72} -698205. i q^{73} -453048. q^{74} +237310. q^{75} +142775. q^{76} -173754. i q^{77} -30490.0 q^{78} +263165. q^{79} -851317. q^{80} +59049.0 q^{81} +998142. i q^{82} -251366. i q^{83} +61805.7 q^{84} +243196. q^{85} -48945.9 q^{86} +535969. q^{87} -293415. q^{88} -429340. i q^{89} +380492. i q^{90} -56201.1i q^{91} -222130. i q^{92} +353565. i q^{93} -1.02288e6 q^{94} -1.62016e6 q^{95} -242033. i q^{96} -198287. i q^{97} -463850. i q^{98} +164826. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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