LMFDB - Embedded newform 177.9.c.a.58.78

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			58.78
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} +1397.90i q^{6} +4057.23 q^{7} -11404.3i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q+29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} +1397.90i q^{6} +4057.23 q^{7} -11404.3i q^{8} +2187.00 q^{9} -7402.10i q^{10} +21197.9i q^{11} -29813.9 q^{12} -21525.6i q^{13} +121278. i q^{14} -11580.5 q^{15} +177691. q^{16} -95116.6 q^{17} +65373.4i q^{18} -41670.2 q^{19} +157869. q^{20} +189738. q^{21} -633643. q^{22} -492438. i q^{23} -533328. i q^{24} -329304. q^{25} +643438. q^{26} +102276. q^{27} -2.58657e6 q^{28} -1.25263e6 q^{29} -346162. i q^{30} -1.66108e6i q^{31} +2.39199e6i q^{32} +991326. i q^{33} -2.84321e6i q^{34} -1.00469e6 q^{35} -1.39426e6 q^{36} +889974. i q^{37} -1.24560e6i q^{38} -1.00665e6i q^{39} +2.82405e6i q^{40} +1.19968e6 q^{41} +5.67161e6i q^{42} +2.01013e6i q^{43} -1.35141e7i q^{44} -541566. q^{45} +1.47199e7 q^{46} +2.76926e6i q^{47} +8.30977e6 q^{48} +1.06963e7 q^{49} -9.84351e6i q^{50} -4.44816e6 q^{51} +1.37230e7i q^{52} -8.79299e6 q^{53} +3.05721e6i q^{54} -5.24922e6i q^{55} -4.62700e7i q^{56} -1.94872e6 q^{57} -3.74433e7i q^{58} +(-1.17794e7 - 2.84185e6i) q^{59} +7.38280e6 q^{60} +1.24584e7i q^{61} +4.96526e7 q^{62} +8.87316e6 q^{63} -2.60121e7 q^{64} +5.33037e6i q^{65} -2.96325e7 q^{66} -2.43467e7i q^{67} +6.06387e7 q^{68} -2.30290e7i q^{69} -3.00320e7i q^{70} -4.11384e7 q^{71} -2.49413e7i q^{72} -2.32169e7i q^{73} -2.66029e7 q^{74} -1.54000e7 q^{75} +2.65656e7 q^{76} +8.60046e7i q^{77} +3.00906e7 q^{78} +2.79916e6 q^{79} -4.40015e7 q^{80} +4.78297e6 q^{81} +3.58607e7i q^{82} +2.03547e6i q^{83} -1.20962e8 q^{84} +2.35537e7 q^{85} -6.00863e7 q^{86} -5.85796e7 q^{87} +2.41747e8 q^{88} -2.00226e6i q^{89} -1.61884e7i q^{90} -8.73341e7i q^{91} +3.13939e8i q^{92} -7.76809e7i q^{93} -8.27781e7 q^{94} +1.03188e7 q^{95} +1.11862e8i q^{96} +3.90744e7i q^{97} +3.19732e8i q^{98} +4.63598e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			29.8918i			1.86824i	0.356962	+	0.934119i	$0.383813\pi$
$2$			29.8918i			1.86824i	−0.356962	+	0.934119i	$0.616187\pi$
$3$	46.7654			0.577350
$3$	46.7654			0.577350
$4$	−637.520			−2.49031
$5$	−247.630			−0.396208			−0.198104	−	0.980181i	$-0.563478\pi$
$5$	−247.630			−0.396208			−0.198104	+	0.980181i	$0.563478\pi$
$6$			1397.90i			1.07863i
$7$	4057.23			1.68981			0.844904	−	0.534918i	$-0.179657\pi$
$7$	4057.23			1.68981			0.844904	+	0.534918i	$0.179657\pi$
$8$		−	11404.3i		−	2.78426i
$9$	2187.00			0.333333
$10$		−	7402.10i		−	0.740210i
$11$			21197.9i			1.44784i	0.689882	+	0.723922i	$0.257662\pi$
$11$			21197.9i			1.44784i	−0.689882	+	0.723922i	$0.742338\pi$
$12$	−29813.9			−1.43778
$13$		−	21525.6i		−	0.753669i	−0.926281	−	0.376835i	$-0.877012\pi$
$13$		−	21525.6i		−	0.753669i	0.926281	−	0.376835i	$-0.122988\pi$
$14$			121278.i			3.15696i
$15$	−11580.5			−0.228751
$16$	177691.			2.71135
$17$	−95116.6			−1.13883			−0.569417	−	0.822049i	$-0.692831\pi$
$17$	−95116.6			−1.13883			−0.569417	+	0.822049i	$0.692831\pi$
$18$			65373.4i			0.622746i
$19$	−41670.2			−0.319750			−0.159875	−	0.987137i	$-0.551109\pi$
$19$	−41670.2			−0.319750			−0.159875	+	0.987137i	$0.551109\pi$
$20$	157869.			0.986681
$21$	189738.			0.975611
$22$	−633643.			−2.70492
$23$		−	492438.i		−	1.75971i	−0.475246	−	0.879853i	$-0.657641\pi$
$23$		−	492438.i		−	1.75971i	0.475246	−	0.879853i	$-0.342359\pi$
$24$		−	533328.i		−	1.60749i
$25$	−329304.			−0.843020
$26$	643438.			1.40803
$27$	102276.			0.192450
$28$	−2.58657e6			−4.20815
$29$	−1.25263e6			−1.77105			−0.885523	−	0.464595i	$-0.846200\pi$
$29$	−1.25263e6			−1.77105			−0.885523	+	0.464595i	$0.846200\pi$
$30$		−	346162.i		−	0.427361i
$31$		−	1.66108e6i		−	1.79864i	−0.437296	−	0.899318i	$-0.644064\pi$
$31$		−	1.66108e6i		−	1.79864i	0.437296	−	0.899318i	$-0.355936\pi$
$32$			2.39199e6i			2.28118i
$33$			991326.i			0.835913i
$34$		−	2.84321e6i		−	2.12761i
$35$	−1.00469e6			−0.669515
$36$	−1.39426e6			−0.830104
$37$			889974.i			0.474865i	0.971404	+	0.237433i	$0.0763059\pi$
$37$			889974.i			0.474865i	−0.971404	+	0.237433i	$0.923694\pi$
$38$		−	1.24560e6i		−	0.597370i
$39$		−	1.00665e6i		−	0.435131i
$40$			2.82405e6i			1.10314i
$41$	1.19968e6			0.424552			0.212276	−	0.977210i	$-0.431912\pi$
$41$	1.19968e6			0.424552			0.212276	+	0.977210i	$0.431912\pi$
$42$			5.67161e6i			1.82267i
$43$			2.01013e6i			0.587963i	0.955811	+	0.293981i	$0.0949803\pi$
$43$			2.01013e6i			0.587963i	−0.955811	+	0.293981i	$0.905020\pi$
$44$		−	1.35141e7i		−	3.60558i
$45$	−541566.			−0.132069
$46$	1.47199e7			3.28755
$47$			2.76926e6i			0.567508i	0.958897	+	0.283754i	$0.0915799\pi$
$47$			2.76926e6i			0.567508i	−0.958897	+	0.283754i	$0.908420\pi$
$48$	8.30977e6			1.56540
$49$	1.06963e7			1.85545
$50$		−	9.84351e6i		−	1.57496i
$51$	−4.44816e6			−0.657506
$52$			1.37230e7i			1.87687i
$53$	−8.79299e6			−1.11438			−0.557190	−	0.830385i	$-0.688120\pi$
$53$	−8.79299e6			−1.11438			−0.557190	+	0.830385i	$0.688120\pi$
$54$			3.05721e6i			0.359543i
$55$		−	5.24922e6i		−	0.573647i
$56$		−	4.62700e7i		−	4.70486i
$57$	−1.94872e6			−0.184608
$58$		−	3.74433e7i		−	3.30874i
$59$	−1.17794e7	−	2.84185e6i	−0.972110	−	0.234527i
$59$	−1.17794e7	−	2.84185e6i	−0.972110	−	0.234527i
$60$	7.38280e6			0.569661
$61$			1.24584e7i			0.899793i	0.893081	+	0.449896i	$0.148539\pi$
$61$			1.24584e7i			0.899793i	−0.893081	+	0.449896i	$0.851461\pi$
$62$	4.96526e7			3.36028
$63$	8.87316e6			0.563269
$64$	−2.60121e7			−1.55044
$65$			5.33037e6i			0.298610i
$66$	−2.96325e7			−1.56168
$67$		−	2.43467e7i		−	1.20820i	−0.796907	−	0.604102i	$-0.793532\pi$
$67$		−	2.43467e7i		−	1.20820i	0.796907	−	0.604102i	$-0.206468\pi$
$68$	6.06387e7			2.83605
$69$		−	2.30290e7i		−	1.01597i
$70$		−	3.00320e7i		−	1.25081i
$71$	−4.11384e7			−1.61888			−0.809439	−	0.587205i	$-0.800228\pi$
$71$	−4.11384e7			−1.61888			−0.809439	+	0.587205i	$0.800228\pi$
$72$		−	2.49413e7i		−	0.928086i
$73$		−	2.32169e7i		−	0.817547i	−0.912636	−	0.408773i	$-0.865957\pi$
$73$		−	2.32169e7i		−	0.817547i	0.912636	−	0.408773i	$-0.134043\pi$
$74$	−2.66029e7			−0.887161
$75$	−1.54000e7			−0.486718
$76$	2.65656e7			0.796279
$77$			8.60046e7i			2.44658i
$78$	3.00906e7			0.812929
$79$	2.79916e6			0.0718652			0.0359326	−	0.999354i	$-0.488560\pi$
$79$	2.79916e6			0.0718652			0.0359326	+	0.999354i	$0.488560\pi$
$80$	−4.40015e7			−1.07426
$81$	4.78297e6			0.111111
$82$			3.58607e7i			0.793165i
$83$			2.03547e6i			0.0428896i	0.999770	+	0.0214448i	$0.00682661\pi$
$83$			2.03547e6i			0.0428896i	−0.999770	+	0.0214448i	$0.993173\pi$
$84$	−1.20962e8			−2.42958
$85$	2.35537e7			0.451215
$86$	−6.00863e7			−1.09845
$87$	−5.85796e7			−1.02251
$88$	2.41747e8			4.03117
$89$		−	2.00226e6i		−	0.0319124i	−0.999873	−	0.0159562i	$-0.994921\pi$
$89$		−	2.00226e6i		−	0.0319124i	0.999873	−	0.0159562i	$-0.00507924\pi$
$90$		−	1.61884e7i		−	0.246737i
$91$		−	8.73341e7i		−	1.27356i
$92$			3.13939e8i			4.38222i
$93$		−	7.76809e7i		−	1.03844i
$94$	−8.27781e7			−1.06024
$95$	1.03188e7			0.126688
$96$			1.11862e8i			1.31704i
$97$			3.90744e7i			0.441373i	0.975345	+	0.220686i	$0.0708297\pi$
$97$			3.90744e7i			0.441373i	−0.975345	+	0.220686i	$0.929170\pi$
$98$			3.19732e8i			3.46642i
$99$			4.63598e7i			0.482614i
$100$	2.09938e8			2.09938
$101$		−	1.41791e8i		−	1.36258i	−0.732012	−	0.681291i	$-0.761419\pi$
$101$		−	1.41791e8i		−	1.36258i	0.732012	−	0.681291i	$-0.238581\pi$
$102$		−	1.32964e8i		−	1.22838i
$103$		−	2.84725e7i		−	0.252975i	−0.991968	−	0.126487i	$-0.959630\pi$
$103$		−	2.84725e7i		−	0.252975i	0.991968	−	0.126487i	$-0.0403703\pi$
$104$	−2.45484e8			−2.09841
$105$	−4.69847e7			−0.386545
$106$		−	2.62838e8i		−	2.08193i
$107$	1.77416e8			1.35350			0.676748	−	0.736215i	$-0.263389\pi$
$107$	1.77416e8			1.35350			0.676748	+	0.736215i	$0.263389\pi$
$108$	−6.52029e7			−0.479261
$109$		−	1.88778e8i		−	1.33735i	−0.743555	−	0.668675i	$-0.766862\pi$
$109$		−	1.88778e8i		−	1.33735i	0.743555	−	0.668675i	$-0.233138\pi$
$110$	1.56909e8			1.07171
$111$			4.16200e7i			0.274164i
$112$	7.20932e8			4.58165
$113$		−	1.94290e8i		−	1.19162i	−0.803127	−	0.595808i	$-0.796832\pi$
$113$		−	1.94290e8i		−	1.19162i	0.803127	−	0.595808i	$-0.203168\pi$
$114$		−	5.82508e7i		−	0.344892i
$115$			1.21942e8i			0.697209i
$116$	7.98575e8			4.41046
$117$		−	4.70764e7i		−	0.251223i
$118$	8.49479e7	−	3.52108e8i	0.438152	−	1.81613i
$119$	−3.85910e8			−1.92441
$120$			1.32068e8i			0.636901i
$121$	−2.34991e8			−1.09625
$122$	−3.72404e8			−1.68103
$123$	5.61037e7			0.245115
$124$			1.05897e9i			4.47917i
$125$	1.78276e8			0.730218
$126$			2.65235e8i			1.05232i
$127$	1.85538e8			0.713210			0.356605	−	0.934255i	$-0.383934\pi$
$127$	1.85538e8			0.713210			0.356605	+	0.934255i	$0.383934\pi$
$128$		−	1.65199e8i		−	0.615413i
$129$			9.40043e7i			0.339460i
$130$	−1.59334e8			−0.557874
$131$			5.84623e8i			1.98514i	0.121683	+	0.992569i	$0.461171\pi$
$131$			5.84623e8i			1.98514i	−0.121683	+	0.992569i	$0.538829\pi$
$132$		−	6.31991e8i		−	2.08168i
$133$	−1.69066e8			−0.540317
$134$	7.27766e8			2.25721
$135$	−2.53266e7			−0.0762502
$136$			1.08474e9i			3.17081i
$137$	−3.84843e8			−1.09245			−0.546224	−	0.837639i	$-0.683935\pi$
$137$	−3.84843e8			−1.09245			−0.546224	+	0.837639i	$0.683935\pi$
$138$	6.88379e8			1.89807
$139$	1.34828e8			0.361179			0.180589	−	0.983559i	$-0.442199\pi$
$139$	1.34828e8			0.361179			0.180589	+	0.983559i	$0.442199\pi$
$140$	6.40511e8			1.66730
$141$			1.29505e8i			0.327651i
$142$		−	1.22970e9i		−	3.02445i
$143$	4.56296e8			1.09120
$144$	3.88610e8			0.903782
$145$	3.10188e8			0.701702
$146$	6.93995e8			1.52737
$147$	5.00217e8			1.07125
$148$		−	5.67376e8i		−	1.18256i
$149$			4.99204e8i			1.01282i	0.862292	+	0.506411i	$0.169028\pi$
$149$			4.99204e8i			1.01282i	−0.862292	+	0.506411i	$0.830972\pi$
$150$		−	4.60335e8i		−	0.909304i
$151$			6.49690e8i			1.24968i	0.780754	+	0.624839i	$0.214835\pi$
$151$			6.49690e8i			1.24968i	−0.780754	+	0.624839i	$0.785165\pi$
$152$			4.75221e8i			0.890268i
$153$	−2.08020e8			−0.379611
$154$	−2.57083e9			−4.57079
$155$			4.11332e8i			0.712633i
$156$			6.41760e8i			1.08361i
$157$		−	3.80148e8i		−	0.625683i	−0.949805	−	0.312842i	$-0.898719\pi$
$157$		−	3.80148e8i		−	0.625683i	0.949805	−	0.312842i	$-0.101281\pi$
$158$			8.36718e7i			0.134261i
$159$	−4.11207e8			−0.643387
$160$		−	5.92328e8i		−	0.903821i
$161$		−	1.99793e9i		−	2.97356i
$162$			1.42972e8i			0.207582i
$163$	4.70927e8			0.667119			0.333560	−	0.942729i	$-0.391750\pi$
$163$	4.70927e8			0.667119			0.333560	+	0.942729i	$0.391750\pi$
$164$	−7.64823e8			−1.05727
$165$		−	2.45482e8i		−	0.331195i
$166$	−6.08438e7			−0.0801280
$167$	−1.19539e9			−1.53689			−0.768444	−	0.639917i	$-0.778969\pi$
$167$	−1.19539e9			−1.53689			−0.768444	+	0.639917i	$0.778969\pi$
$168$		−	2.16383e9i		−	2.71635i
$169$	3.52381e8			0.431982
$170$			7.04063e8i			0.842977i
$171$	−9.11327e7			−0.106583
$172$		−	1.28150e9i		−	1.46421i
$173$			2.68426e8i			0.299668i	0.988711	+	0.149834i	$0.0478740\pi$
$173$			2.68426e8i			0.299668i	−0.988711	+	0.149834i	$0.952126\pi$
$174$		−	1.75105e9i		−	1.91030i
$175$	−1.33606e9			−1.42454
$176$			3.76667e9i			3.92560i
$177$	−5.50868e8	−	1.32900e8i	−0.561248	−	0.135404i
$178$	5.98511e7			0.0596200
$179$		−	5.25010e8i		−	0.511394i	−0.966757	−	0.255697i	$-0.917695\pi$
$179$		−	5.25010e8i		−	0.511394i	0.966757	−	0.255697i	$-0.0823049\pi$
$180$	3.45259e8			0.328894
$181$	1.34593e9			1.25403			0.627017	−	0.779006i	$-0.284276\pi$
$181$	1.34593e9			1.25403			0.627017	+	0.779006i	$0.284276\pi$
$182$	2.61057e9			2.37931
$183$			5.82621e8i			0.519496i
$184$	−5.61592e9			−4.89948
$185$		−	2.20384e8i		−	0.188145i
$186$	2.32202e9			1.94006
$187$		−	2.01627e9i		−	1.64885i
$188$		−	1.76546e9i		−	1.41327i
$189$	4.14957e8			0.325204
$190$			3.08447e8i			0.236683i
$191$		−	3.31156e8i		−	0.248828i	−0.992230	−	0.124414i	$-0.960295\pi$
$191$		−	3.31156e8i		−	0.248828i	0.992230	−	0.124414i	$-0.0397051\pi$
$192$	−1.21646e9			−0.895148
$193$	−2.19184e9			−1.57972			−0.789859	−	0.613289i	$-0.789846\pi$
$193$	−2.19184e9			−1.57972			−0.789859	+	0.613289i	$0.789846\pi$
$194$	−1.16801e9			−0.824590
$195$			2.49277e8i			0.172402i
$196$	−6.81911e9			−4.62065
$197$	1.88008e9			1.24828			0.624139	−	0.781313i	$-0.285450\pi$
$197$	1.88008e9			1.24828			0.624139	+	0.781313i	$0.285450\pi$
$198$	−1.38578e9			−0.901639
$199$	−1.84676e9			−1.17760			−0.588799	−	0.808279i	$-0.700399\pi$
$199$	−1.84676e9			−1.17760			−0.588799	+	0.808279i	$0.700399\pi$
$200$			3.75550e9i			2.34718i
$201$		−	1.13858e9i		−	0.697557i
$202$	4.23839e9			2.54563
$203$	−5.08220e9			−2.99273
$204$	2.83579e9			1.63740
$205$	−2.97077e8			−0.168211
$206$	8.51096e8			0.472617
$207$		−	1.07696e9i		−	0.586568i
$208$		−	3.82489e9i		−	2.04346i
$209$		−	8.83320e8i		−	0.462949i
$210$		−	1.40446e9i		−	0.722157i
$211$		−	1.12595e9i		−	0.568056i	−0.958816	−	0.284028i	$-0.908329\pi$
$211$		−	1.12595e9i		−	0.568056i	0.958816	−	0.284028i	$-0.0916708\pi$
$212$	5.60571e9			2.77515
$213$	−1.92385e9			−0.934659
$214$			5.30328e9i			2.52865i
$215$		−	4.97767e8i		−	0.232955i
$216$		−	1.16639e9i		−	0.535831i
$217$		−	6.73937e9i		−	3.03935i
$218$	5.64291e9			2.49849
$219$		−	1.08575e9i		−	0.472011i
$220$			3.34649e9i			1.42856i
$221$			2.04744e9i			0.858305i
$222$	−1.24410e9			−0.512203
$223$	1.27587e9			0.515924			0.257962	−	0.966155i	$-0.416949\pi$
$223$	1.27587e9			0.515924			0.257962	+	0.966155i	$0.416949\pi$
$224$			9.70485e9i			3.85476i
$225$	−7.20189e8			−0.281007
$226$	5.80767e9			2.22622
$227$		−	1.10307e9i		−	0.415433i	−0.978189	−	0.207716i	$-0.933397\pi$
$227$		−	1.10307e9i		−	0.415433i	0.978189	−	0.207716i	$-0.0666031\pi$
$228$	1.24235e9			0.459732
$229$		−	1.07539e8i		−	0.0391043i	−0.999809	−	0.0195521i	$-0.993776\pi$
$229$		−	1.07539e8i		−	0.0391043i	0.999809	−	0.0195521i	$-0.00622404\pi$
$230$	−3.64507e9			−1.30255
$231$			4.02204e9i			1.41253i
$232$			1.42854e10i			4.93105i
$233$		−	8.76987e8i		−	0.297557i	−0.988871	−	0.148778i	$-0.952466\pi$
$233$		−	8.76987e8i		−	0.297557i	0.988871	−	0.148778i	$-0.0475341\pi$
$234$	1.40720e9			0.469345
$235$		−	6.85751e8i		−	0.224851i
$236$	7.50961e9	+	1.81173e9i	2.42086	+	0.584045i
$237$	1.30904e8			0.0414914
$238$		−	1.15355e10i		−	3.59526i
$239$	1.11886e9			0.342913			0.171457	−	0.985192i	$-0.445153\pi$
$239$	1.11886e9			0.342913			0.171457	+	0.985192i	$0.445153\pi$
$240$	−2.05775e9			−0.620222
$241$	3.82849e9			1.13490			0.567452	−	0.823407i	$-0.307929\pi$
$241$	3.82849e9			1.13490			0.567452	+	0.823407i	$0.307929\pi$
$242$		−	7.02431e9i		−	2.04806i
$243$	2.23677e8			0.0641500
$244$		−	7.94247e9i		−	2.24077i
$245$	−2.64872e9			−0.735144
$246$			1.67704e9i			0.457934i
$247$			8.96974e8i			0.240986i
$248$	−1.89435e10			−5.00787
$249$			9.51894e7i			0.0247623i
$250$			5.32899e9i			1.36422i
$251$	−4.29677e9			−1.08255			−0.541275	−	0.840846i	$-0.682058\pi$
$251$	−4.29677e9			−1.08255			−0.541275	+	0.840846i	$0.682058\pi$
$252$	−5.65682e9			−1.40272
$253$	1.04386e10			2.54778
$254$			5.54606e9i			1.33245i
$255$	1.10150e9			0.260509
$256$	−1.72101e9			−0.400703
$257$	5.03295e9			1.15369			0.576847	−	0.816852i	$-0.304283\pi$
$257$	5.03295e9			1.15369			0.576847	+	0.816852i	$0.304283\pi$
$258$	−2.80996e9			−0.634193
$259$			3.61083e9i			0.802431i
$260$		−	3.39822e9i		−	0.743631i
$261$	−2.73950e9			−0.590349
$262$	−1.74754e10			−3.70871
$263$	3.01837e8			0.0630884			0.0315442	−	0.999502i	$-0.489957\pi$
$263$	3.01837e8			0.0630884			0.0315442	+	0.999502i	$0.489957\pi$
$264$	1.13054e10			2.32740
$265$	2.17741e9			0.441525
$266$		−	5.05368e9i		−	1.00944i
$267$		−	9.36364e7i		−	0.0184247i
$268$			1.55215e10i			3.00881i
$269$			4.48283e9i			0.856136i	0.903747	+	0.428068i	$0.140806\pi$
$269$			4.48283e9i			0.856136i	−0.903747	+	0.428068i	$0.859194\pi$
$270$		−	7.57056e8i		−	0.142454i
$271$	−2.34851e9			−0.435427			−0.217713	−	0.976013i	$-0.569860\pi$
$271$	−2.34851e9			−0.435427			−0.217713	+	0.976013i	$0.569860\pi$
$272$	−1.69013e10			−3.08777
$273$		−	4.08421e9i		−	0.735288i
$274$		−	1.15036e10i		−	2.04095i
$275$		−	6.98056e9i		−	1.22056i
$276$			1.46815e10i			2.53007i
$277$	−7.92826e9			−1.34666			−0.673331	−	0.739341i	$-0.735137\pi$
$277$	−7.92826e9			−1.34666			−0.673331	+	0.739341i	$0.735137\pi$
$278$			4.03026e9i			0.674768i
$279$		−	3.63278e9i		−	0.599545i
$280$			1.14578e10i			1.86410i
$281$	−8.25964e9			−1.32476			−0.662378	−	0.749170i	$-0.730453\pi$
$281$	−8.25964e9			−1.32476			−0.662378	+	0.749170i	$0.730453\pi$
$282$	−3.87115e9			−0.612130
$283$		−	4.43696e8i		−	0.0691736i	−0.999402	−	0.0345868i	$-0.988988\pi$
$283$		−	4.43696e8i		−	0.0691736i	0.999402	−	0.0345868i	$-0.0110115\pi$
$284$	2.62265e10			4.03151
$285$	4.82562e8			0.0731431
$286$			1.36395e10i			2.03861i
$287$	4.86739e9			0.717412
$288$			5.23128e9i			0.760393i
$289$	2.07141e9			0.296944
$290$			9.27208e9i			1.31095i
$291$			1.82733e9i			0.254827i
$292$			1.48012e10i			2.03595i
$293$	3.14415e9			0.426612			0.213306	−	0.976985i	$-0.431577\pi$
$293$	3.14415e9			0.426612			0.213306	+	0.976985i	$0.431577\pi$
$294$			1.49524e10i			2.00134i
$295$	2.91693e9	+	7.03726e8i	0.385157	+	0.0929213i
$296$	1.01496e10			1.32215
$297$			2.16803e9i			0.278638i
$298$	−1.49221e10			−1.89219
$299$	−1.06000e10			−1.32624
$300$	9.81784e9			1.21208
$301$			8.15555e9i			0.993544i
$302$	−1.94204e10			−2.33470
$303$		−	6.63091e9i		−	0.786688i
$304$	−7.40441e9			−0.866954
$305$		−	3.08507e9i		−	0.356505i
$306$		−	6.21809e9i		−	0.709205i
$307$	−3.18785e9			−0.358876			−0.179438	−	0.983769i	$-0.557428\pi$
$307$	−3.18785e9			−0.358876			−0.179438	+	0.983769i	$0.557428\pi$
$308$		−	5.48297e10i		−	6.09274i
$309$		−	1.33153e9i		−	0.146055i
$310$	−1.22955e10			−1.33137
$311$	−1.43538e10			−1.53435			−0.767176	−	0.641437i	$-0.778339\pi$
$311$	−1.43538e10			−1.53435			−0.767176	+	0.641437i	$0.778339\pi$
$312$	−1.14802e10			−1.21152
$313$		−	6.81720e9i		−	0.710279i	−0.934813	−	0.355140i	$-0.884433\pi$
$313$		−	6.81720e9i		−	0.710279i	0.934813	−	0.355140i	$-0.115567\pi$
$314$	1.13633e10			1.16892
$315$	−2.19726e9			−0.223172
$316$	−1.78452e9			−0.178967
$317$	5.79535e9			0.573909			0.286954	−	0.957944i	$-0.407357\pi$
$317$	5.79535e9			0.573909			0.286954	+	0.957944i	$0.407357\pi$
$318$		−	1.22917e10i		−	1.20200i
$319$		−	2.65530e10i		−	2.56420i
$320$	6.44137e9			0.614297
$321$	8.29691e9			0.781441
$322$	5.97218e10			5.55533
$323$	3.96353e9			0.364143
$324$	−3.04924e9			−0.276701
$325$			7.08846e9i			0.635358i
$326$			1.40769e10i			1.24634i
$327$		−	8.82826e9i		−	0.772119i
$328$		−	1.36816e10i		−	1.18206i
$329$			1.12355e10i			0.958979i
$330$	7.33790e9			0.618751
$331$	−1.65954e10			−1.38253			−0.691266	−	0.722601i	$-0.742947\pi$
$331$	−1.65954e10			−1.38253			−0.691266	+	0.722601i	$0.742947\pi$
$332$		−	1.29765e9i		−	0.106809i
$333$			1.94637e9i			0.158288i
$334$		−	3.57322e10i		−	2.87127i
$335$			6.02896e9i			0.478700i
$336$	3.37147e10			2.64522
$337$		−	1.80474e10i		−	1.39925i	−0.714512	−	0.699623i	$-0.753351\pi$
$337$		−	1.80474e10i		−	1.39925i	0.714512	−	0.699623i	$-0.246649\pi$
$338$			1.05333e10i			0.807046i
$339$		−	9.08603e9i		−	0.687979i
$340$	−1.50160e10			−1.12367
$341$	3.52113e10			2.60414
$342$		−	2.72412e9i		−	0.199123i
$343$	2.00082e10			1.44555
$344$	2.29241e10			1.63704
$345$			5.70267e9i			0.402534i
$346$	−8.02375e9			−0.559852
$347$			2.10020e10i			1.44858i	0.689494	+	0.724292i	$0.257833\pi$
$347$			2.10020e10i			1.44858i	−0.689494	+	0.724292i	$0.742167\pi$
$348$	3.73457e10			2.54638
$349$			4.85779e9i			0.327444i	0.986507	+	0.163722i	$0.0523500\pi$
$349$			4.85779e9i			0.327444i	−0.986507	+	0.163722i	$0.947650\pi$
$350$		−	3.99374e10i		−	2.66138i
$351$		−	2.20154e9i		−	0.145044i
$352$	−5.07051e10			−3.30279
$353$		−	1.90800e10i		−	1.22879i	−0.788997	−	0.614397i	$-0.789399\pi$
$353$		−	1.90800e10i		−	1.22879i	0.788997	−	0.614397i	$-0.210601\pi$
$354$	3.97262e9	−	1.64664e10i	0.252967	−	1.04854i
$355$	1.01871e10			0.641411
$356$			1.27648e9i			0.0794720i
$357$	−1.80472e10			−1.11106
$358$	1.56935e10			0.955405
$359$	−8.81861e9			−0.530912			−0.265456	−	0.964123i	$-0.585522\pi$
$359$	−8.81861e9			−0.530912			−0.265456	+	0.964123i	$0.585522\pi$
$360$			6.17620e9i			0.367715i
$361$	−1.52472e10			−0.897760
$362$			4.02324e10i			2.34283i
$363$	−1.09894e10			−0.632920
$364$			5.56772e10i			3.17155i
$365$			5.74919e9i			0.323918i
$366$	−1.74156e10			−0.970541
$367$			1.46733e10i			0.808840i	0.914573	+	0.404420i	$0.132527\pi$
$367$			1.46733e10i			0.808840i	−0.914573	+	0.404420i	$0.867473\pi$
$368$		−	8.75016e10i		−	4.77117i
$369$	2.62371e9			0.141517
$370$	6.58768e9			0.351500
$371$	−3.56752e10			−1.88309
$372$			4.95232e10i			2.58605i
$373$	4.10565e9			0.212103			0.106051	−	0.994361i	$-0.466179\pi$
$373$	4.10565e9			0.212103			0.106051	+	0.994361i	$0.466179\pi$
$374$	6.02699e10			3.08045
$375$	8.33714e9			0.421592
$376$	3.15815e10			1.58009
$377$			2.69635e10i			1.33478i
$378$			1.24038e10i			0.607558i
$379$	−3.96543e10			−1.92191			−0.960955	−	0.276704i	$-0.910758\pi$
$379$	−3.96543e10			−1.92191			−0.960955	+	0.276704i	$0.910758\pi$
$380$	−6.57843e9			−0.315492
$381$	8.67674e9			0.411772
$382$	9.89885e9			0.464870
$383$	1.49720e10			0.695799			0.347899	−	0.937532i	$-0.386895\pi$
$383$	1.49720e10			0.695799			0.347899	+	0.937532i	$0.386895\pi$
$384$		−	7.72558e9i		−	0.355309i
$385$		−	2.12973e10i		−	0.969353i
$386$		−	6.55180e10i		−	2.95129i
$387$			4.39615e9i			0.195988i
$388$		−	2.49107e10i		−	1.09916i
$389$	3.75472e9			0.163975			0.0819877	−	0.996633i	$-0.473873\pi$
$389$	3.75472e9			0.163975			0.0819877	+	0.996633i	$0.473873\pi$
$390$	−7.45133e9			−0.322089
$391$			4.68390e10i			2.00401i
$392$		−	1.21984e11i		−	5.16606i
$393$			2.73401e10i			1.14612i
$394$			5.61990e10i			2.33208i
$395$	−6.93154e8			−0.0284735
$396$		−	2.95553e10i		−	1.20186i
$397$			5.89403e9i			0.237274i	0.992938	+	0.118637i	$0.0378525\pi$
$397$			5.89403e9i			0.237274i	−0.992938	+	0.118637i	$0.962148\pi$
$398$		−	5.52029e10i		−	2.20003i
$399$	−7.90641e9			−0.311952
$400$	−5.85144e10			−2.28572
$401$		−	3.30329e10i		−	1.27752i	−0.769404	−	0.638762i	$-0.779447\pi$
$401$		−	3.30329e10i		−	1.27752i	0.769404	−	0.638762i	$-0.220553\pi$
$402$	3.40343e10			1.30320
$403$	−3.57556e10			−1.35558
$404$			9.03946e10i			3.39326i
$405$	−1.18441e9			−0.0440231
$406$		−	1.51916e11i		−	5.59113i
$407$	−1.88656e10			−0.687530
$408$			5.07283e10i			1.83067i
$409$			3.04752e10i			1.08906i	0.838740	+	0.544532i	$0.183293\pi$
$409$			3.04752e10i			1.08906i	−0.838740	+	0.544532i	$0.816707\pi$
$410$		−	8.88018e9i		−	0.314258i
$411$	−1.79973e10			−0.630725
$412$			1.81518e10i			0.629987i
$413$	−4.77917e10	−	1.15300e10i	−1.64268	−	0.396305i
$414$	3.21923e10			1.09585
$415$		−	5.04043e8i		−	0.0169932i
$416$	5.14889e10			1.71926
$417$	6.30530e9			0.208527
$418$	2.64040e10			0.864898
$419$			1.81306e9i			0.0588241i	0.999567	+	0.0294121i	$0.00936350\pi$
$419$			1.81306e9i			0.0588241i	−0.999567	+	0.0294121i	$0.990637\pi$
$420$	2.99537e10			0.962617
$421$			3.79069e10i			1.20667i	0.797486	+	0.603337i	$0.206163\pi$
$421$			3.79069e10i			1.20667i	−0.797486	+	0.603337i	$0.793837\pi$
$422$	3.36568e10			1.06126
$423$			6.05637e9i			0.189169i
$424$			1.00278e11i			3.10272i
$425$	3.13223e10			0.960060
$426$		−	5.75074e10i		−	1.74617i
$427$			5.05465e10i			1.52048i
$428$	−1.13106e11			−3.37063
$429$	2.13388e10			0.630002
$430$	1.48792e10			0.435216
$431$			6.06752e10i			1.75834i	0.476510	+	0.879169i	$0.341902\pi$
$431$			6.06752e10i			1.75834i	−0.476510	+	0.879169i	$0.658098\pi$
$432$	1.81735e10			0.521799
$433$	−2.64222e10			−0.751653			−0.375826	−	0.926690i	$-0.622641\pi$
$433$	−2.64222e10			−0.751653			−0.375826	+	0.926690i	$0.622641\pi$
$434$	2.01452e11			5.67823
$435$	1.45061e10			0.405128
$436$			1.20350e11i			3.33042i
$437$			2.05200e10i			0.562667i
$438$	3.24549e10			0.881829
$439$	−6.36143e10			−1.71276			−0.856380	−	0.516347i	$-0.827292\pi$
$439$	−6.36143e10			−1.71276			−0.856380	+	0.516347i	$0.827292\pi$
$440$	−5.98639e10			−1.59718
$441$	2.33928e10			0.618484
$442$	−6.12016e10			−1.60352
$443$		−	3.79235e10i		−	0.984677i	−0.870404	−	0.492338i	$-0.836142\pi$
$443$		−	3.79235e10i		−	0.984677i	0.870404	−	0.492338i	$-0.163858\pi$
$444$		−	2.65336e10i		−	0.682753i
$445$			4.95819e8i			0.0126440i
$446$			3.81380e10i			0.963869i
$447$			2.33455e10i			0.584753i
$448$	−1.05537e11			−2.61995
$449$	−1.87339e10			−0.460938			−0.230469	−	0.973080i	$-0.574026\pi$
$449$	−1.87339e10			−0.460938			−0.230469	+	0.973080i	$0.574026\pi$
$450$		−	2.15277e10i		−	0.524987i
$451$			2.54307e10i			0.614685i
$452$			1.23864e11i			2.96749i
$453$			3.03830e10i			0.721502i
$454$	3.29728e10			0.776127
$455$			2.16265e10i			0.504593i
$456$			2.22239e10i			0.513997i
$457$		−	1.55748e10i		−	0.357074i	−0.983933	−	0.178537i	$-0.942864\pi$
$457$		−	1.55748e10i		−	0.357074i	0.983933	−	0.178537i	$-0.0571364\pi$
$458$	3.21454e9			0.0730561
$459$	−9.72813e9			−0.219169
$460$		−	7.77406e10i		−	1.73627i
$461$	1.36617e10			0.302484			0.151242	−	0.988497i	$-0.451673\pi$
$461$	1.36617e10			0.302484			0.151242	+	0.988497i	$0.451673\pi$
$462$	−1.20226e11			−2.63895
$463$		−	2.90985e10i		−	0.633209i	−0.948558	−	0.316604i	$-0.897457\pi$
$463$		−	2.90985e10i		−	0.633209i	0.948558	−	0.316604i	$-0.102543\pi$
$464$	−2.22580e11			−4.80192
$465$			1.92361e10i			0.411439i
$466$	2.62147e10			0.555906
$467$			9.71527e9i			0.204262i	0.994771	+	0.102131i	$0.0325661\pi$
$467$			9.71527e9i			0.204262i	−0.994771	+	0.102131i	$0.967434\pi$
$468$			3.00121e10i			0.625624i
$469$		−	9.87800e10i		−	2.04163i
$470$	2.04983e10			0.420075
$471$		−	1.77778e10i		−	0.361238i
$472$	−3.24093e10	+	1.34336e11i	−0.652984	+	2.70661i
$473$	−4.26104e10			−0.851278
$474$			3.91294e9i			0.0775158i
$475$	1.37222e10			0.269556
$476$	2.46025e11			4.79239
$477$	−1.92303e10			−0.371460
$478$			3.34448e10i			0.640644i
$479$	5.28028e10			1.00303			0.501516	−	0.865148i	$-0.332776\pi$
$479$	5.28028e10			1.00303			0.501516	+	0.865148i	$0.332776\pi$
$480$		−	2.77004e10i		−	0.521821i
$481$	1.91572e10			0.357891
$482$			1.14440e11i			2.12027i
$483$		−	9.34341e10i		−	1.71679i
$484$	1.49811e11			2.73001
$485$		−	9.67599e9i		−	0.174875i
$486$			6.68612e9i			0.119848i
$487$	6.59238e10			1.17200			0.585998	−	0.810312i	$-0.300703\pi$
$487$	6.59238e10			1.17200			0.585998	+	0.810312i	$0.300703\pi$
$488$	1.42080e11			2.50526
$489$	2.20231e10			0.385162
$490$		−	7.91751e10i		−	1.37342i
$491$	1.08414e11			1.86535			0.932675	−	0.360719i	$-0.117469\pi$
$491$	1.08414e11			1.86535			0.932675	+	0.360719i	$0.117469\pi$
$492$	−3.57672e10			−0.610414
$493$	1.19146e11			2.01693
$494$	−2.68122e10			−0.450219
$495$		−	1.14801e10i		−	0.191216i
$496$		−	2.95158e11i		−	4.87672i
$497$	−1.66908e11			−2.73559
$498$	−2.84538e9			−0.0462619
$499$	−2.38659e10			−0.384925			−0.192462	−	0.981304i	$-0.561647\pi$
$499$	−2.38659e10			−0.384925			−0.192462	+	0.981304i	$0.561647\pi$
$500$	−1.13655e11			−1.81847
$501$	−5.59027e10			−0.887323
$502$		−	1.28438e11i		−	2.02246i
$503$		−	1.22240e10i		−	0.190960i	−0.995431	−	0.0954799i	$-0.969561\pi$
$503$		−	1.22240e10i		−	0.190960i	0.995431	−	0.0954799i	$-0.0304386\pi$
$504$		−	1.01192e11i		−	1.56829i
$505$			3.51117e10i			0.539866i
$506$			3.12030e11i			4.75986i
$507$	1.64792e10			0.249405
$508$	−1.18284e11			−1.77612
$509$			3.81044e10i			0.567680i	0.958872	+	0.283840i	$0.0916085\pi$
$509$			3.81044e10i			0.567680i	−0.958872	+	0.283840i	$0.908392\pi$
$510$			3.29258e10i			0.486693i
$511$		−	9.41963e10i		−	1.38150i
$512$		−	9.37349e10i		−	1.36402i
$513$	−4.26186e9			−0.0615360
$514$			1.50444e11i			2.15537i
$515$			7.05065e9i			0.100231i
$516$		−	5.99297e10i		−	0.845363i
$517$	−5.87024e10			−0.821662
$518$	−1.07934e11			−1.49913
$519$			1.25531e10i			0.173014i
$520$	6.07892e10			0.831406
$521$	−1.64846e10			−0.223732			−0.111866	−	0.993723i	$-0.535683\pi$
$521$	−1.64846e10			−0.223732			−0.111866	+	0.993723i	$0.535683\pi$
$522$		−	8.18885e10i		−	1.10291i
$523$	8.28989e9			0.110801			0.0554003	−	0.998464i	$-0.482357\pi$
$523$	8.28989e9			0.110801			0.0554003	+	0.998464i	$0.482357\pi$
$524$		−	3.72709e11i		−	4.94362i
$525$	−6.24815e10			−0.822459
$526$			9.02246e9i			0.117864i
$527$			1.57996e11i			2.04835i
$528$			1.76150e11i			2.26645i
$529$	−1.64184e11			−2.09656
$530$			6.50866e10i			0.824875i
$531$	−2.57616e10	−	6.21512e9i	−0.324037	−	0.0781756i
$532$	1.07783e11			1.34556
$533$		−	2.58239e10i		−	0.319972i
$534$	2.79896e9			0.0344216
$535$	−4.39334e10			−0.536265
$536$	−2.77657e11			−3.36395
$537$		−	2.45523e10i		−	0.295253i
$538$	−1.34000e11			−1.59947
$539$			2.26739e11i			2.68640i
$540$	1.61462e10			0.189887
$541$			9.07595e10i			1.05951i	0.848152	+	0.529753i	$0.177715\pi$
$541$			9.07595e10i			1.05951i	−0.848152	+	0.529753i	$0.822285\pi$
$542$		−	7.02012e10i		−	0.813481i
$543$	6.29431e10			0.724017
$544$		−	2.27518e11i		−	2.59789i
$545$			4.67470e10i			0.529868i
$546$	1.22084e11			1.37369
$547$	−3.63083e10			−0.405561			−0.202781	−	0.979224i	$-0.564998\pi$
$547$	−3.63083e10			−0.405561			−0.202781	+	0.979224i	$0.564998\pi$
$548$	2.45345e11			2.72054
$549$			2.72465e10i			0.299931i
$550$	2.08661e11			2.28030
$551$	5.21973e10			0.566293
$552$	−2.62631e11			−2.82871
$553$	1.13568e10			0.121438
$554$		−	2.36990e11i		−	2.51589i
$555$		−	1.03063e10i		−	0.108626i
$556$	−8.59558e10			−0.899448
$557$	−1.36428e10			−0.141737			−0.0708684	−	0.997486i	$-0.522577\pi$
$557$	−1.36428e10			−0.141737			−0.0708684	+	0.997486i	$0.522577\pi$
$558$	1.08590e11			1.12009
$559$	4.32691e10			0.443129
$560$	−1.78524e11			−1.81529
$561$		−	9.42916e10i		−	0.951966i
$562$		−	2.46895e11i		−	2.47496i
$563$		−	9.41472e9i		−	0.0937073i	−0.998902	−	0.0468537i	$-0.985081\pi$
$563$		−	9.41472e9i		−	0.0937073i	0.998902	−	0.0468537i	$-0.0149194\pi$
$564$		−	8.25623e10i		−	0.815953i
$565$			4.81119e10i			0.472127i
$566$	1.32629e10			0.129233
$567$	1.94056e10			0.187756
$568$			4.69156e11i			4.50737i
$569$			1.09073e11i			1.04056i	0.853995	+	0.520281i	$0.174173\pi$
$569$			1.09073e11i			1.04056i	−0.853995	+	0.520281i	$0.825827\pi$
$570$			1.44246e10i			0.136649i
$571$		−	1.44117e11i		−	1.35572i	−0.735189	−	0.677862i	$-0.762907\pi$
$571$		−	1.44117e11i		−	1.35572i	0.735189	−	0.677862i	$-0.237093\pi$
$572$	−2.90898e11			−2.71742
$573$		−	1.54866e10i		−	0.143661i
$574$			1.45495e11i			1.34030i
$575$			1.62162e11i			1.48347i
$576$	−5.68884e10			−0.516814
$577$	2.14805e11			1.93794			0.968972	−	0.247172i	$-0.0795013\pi$
$577$	2.14805e11			1.93794			0.968972	+	0.247172i	$0.0795013\pi$
$578$			6.19181e10i			0.554762i
$579$	−1.02502e11			−0.912050
$580$	−1.97751e11			−1.74746
$581$			8.25836e9i			0.0724752i
$582$	−5.46222e10			−0.476077
$583$		−	1.86393e11i		−	1.61345i
$584$	−2.64773e11			−2.27626
$585$			1.16575e10i			0.0995365i
$586$			9.39843e10i			0.797012i
$587$			1.59442e11i			1.34292i	0.741039	+	0.671461i	$0.234333\pi$
$587$			1.59442e11i			1.34292i	−0.741039	+	0.671461i	$0.765667\pi$
$588$	−3.18898e11			−2.66774
$589$			6.92175e10i			0.575115i
$590$	−2.10356e10	+	8.71923e10i	−0.173599	+	0.719565i
$591$	8.79227e10			0.720694
$592$			1.58140e11i			1.28752i
$593$	1.49251e11			1.20698			0.603488	−	0.797372i	$-0.293777\pi$
$593$	1.49251e11			1.20698			0.603488	+	0.797372i	$0.293777\pi$
$594$	−6.48064e10			−0.520561
$595$	9.55628e10			0.762467
$596$		−	3.18253e11i		−	2.52224i
$597$	−8.63642e10			−0.679887
$598$		−	3.16853e11i		−	2.47772i
$599$	9.04429e9			0.0702533			0.0351267	−	0.999383i	$-0.488817\pi$
$599$	9.04429e9			0.0702533			0.0351267	+	0.999383i	$0.488817\pi$
$600$			1.75627e11i			1.35515i
$601$		−	3.45042e10i		−	0.264469i	−0.991218	−	0.132234i	$-0.957785\pi$
$601$		−	3.45042e10i		−	0.264469i	0.991218	−	0.132234i	$-0.0422152\pi$
$602$	−2.43784e11			−1.85618
$603$		−	5.32462e10i		−	0.402735i
$604$		−	4.14190e11i		−	3.11209i
$605$	5.81908e10			0.434343
$606$	1.98210e11			1.46972
$607$	−1.49775e11			−1.10328			−0.551639	−	0.834083i	$-0.685997\pi$
$607$	−1.49775e11			−1.10328			−0.551639	+	0.834083i	$0.685997\pi$
$608$		−	9.96747e10i		−	0.729408i
$609$	−2.37671e11			−1.72785
$610$	9.22182e10			0.666036
$611$	5.96098e10			0.427713
$612$	1.32617e11			0.945351
$613$			7.52477e10i			0.532907i	0.963848	+	0.266453i	$0.0858518\pi$
$613$			7.52477e10i			0.532907i	−0.963848	+	0.266453i	$0.914148\pi$
$614$		−	9.52906e10i		−	0.670465i
$615$	−1.38929e10			−0.0971166
$616$	9.80825e11			6.81191
$617$	−1.95339e11			−1.34787			−0.673934	−	0.738791i	$-0.735397\pi$
$617$	−1.95339e11			−1.34787			−0.673934	+	0.738791i	$0.735397\pi$
$618$	3.98018e10			0.272866
$619$	−3.92472e10			−0.267329			−0.133664	−	0.991027i	$-0.542674\pi$
$619$	−3.92472e10			−0.267329			−0.133664	+	0.991027i	$0.542674\pi$
$620$		−	2.62233e11i		−	1.77468i
$621$		−	5.03645e10i		−	0.338655i
$622$		−	4.29060e11i		−	2.86653i
$623$		−	8.12362e9i		−	0.0539259i
$624$		−	1.78872e11i		−	1.17979i
$625$	8.44881e10			0.553701
$626$	2.03779e11			1.32697
$627$		−	4.13088e10i		−	0.267284i
$628$			2.42352e11i			1.55815i
$629$		−	8.46513e10i		−	0.540793i
$630$		−	6.56800e10i		−	0.416938i
$631$	−1.90888e11			−1.20410			−0.602048	−	0.798460i	$-0.705648\pi$
$631$	−1.90888e11			−1.20410			−0.602048	+	0.798460i	$0.705648\pi$
$632$		−	3.19225e10i		−	0.200091i
$633$		−	5.26557e10i		−	0.327967i
$634$			1.73234e11i			1.07220i
$635$	−4.59447e10			−0.282579
$636$	2.62153e11			1.60224
$637$		−	2.30244e11i		−	1.39840i
$638$	7.93718e11			4.79053
$639$	−8.99697e10			−0.539626
$640$			4.09081e10i			0.243831i
$641$	1.74358e11			1.03278			0.516392	−	0.856352i	$-0.327275\pi$
$641$	1.74358e11			1.03278			0.516392	+	0.856352i	$0.327275\pi$
$642$			2.48010e11i			1.45992i
$643$	−1.55791e10			−0.0911376			−0.0455688	−	0.998961i	$-0.514510\pi$
$643$	−1.55791e10			−0.0911376			−0.0455688	+	0.998961i	$0.514510\pi$
$644$			1.27372e12i			7.40511i
$645$		−	2.32783e10i		−	0.134497i
$646$			1.18477e11i			0.680306i
$647$	8.29547e10			0.473395			0.236697	−	0.971583i	$-0.423935\pi$
$647$	8.29547e10			0.473395			0.236697	+	0.971583i	$0.423935\pi$
$648$		−	5.45465e10i		−	0.309362i
$649$	6.02411e10	−	2.49698e11i	0.339558	−	1.40746i
$650$	−2.11887e11			−1.18700
$651$		−	3.15169e11i		−	1.75477i
$652$	−3.00226e11			−1.66134
$653$	−2.11139e10			−0.116122			−0.0580612	−	0.998313i	$-0.518492\pi$
$653$	−2.11139e10			−0.116122			−0.0580612	+	0.998313i	$0.518492\pi$
$654$	2.63893e11			1.44250
$655$		−	1.44770e11i		−	0.786527i
$656$	2.13173e11			1.15111
$657$		−	5.07753e10i		−	0.272516i
$658$	−3.35850e11			−1.79160
$659$			2.40511e11i			1.27524i	0.770350	+	0.637622i	$0.220082\pi$
$659$			2.40511e11i			1.27524i	−0.770350	+	0.637622i	$0.779918\pi$
$660$			1.56500e11i			0.824779i
$661$	4.97787e10			0.260758			0.130379	−	0.991464i	$-0.458381\pi$
$661$	4.97787e10			0.260758			0.130379	+	0.991464i	$0.458381\pi$
$662$		−	4.96066e11i		−	2.58290i
$663$			9.57492e10i			0.495542i
$664$	2.32131e10			0.119416
$665$	4.18657e10			0.214078
$666$	−5.81806e10			−0.295720
$667$			6.16841e11i			3.11652i
$668$	7.62083e11			3.82733
$669$	5.96664e10			0.297869
$670$	−1.80217e11			−0.894325
$671$	−2.64091e11			−1.30276
$672$			4.53851e11i			2.22554i
$673$		−	3.50853e9i		−	0.0171027i	−0.999963	−	0.00855136i	$-0.997278\pi$
$673$		−	3.50853e9i		−	0.0171027i	0.999963	−	0.00855136i	$-0.00272201\pi$
$674$	5.39468e11			2.61412
$675$	−3.36799e10			−0.162239
$676$	−2.24650e11			−1.07577
$677$	−1.33644e11			−0.636200			−0.318100	−	0.948057i	$-0.603045\pi$
$677$	−1.33644e11			−0.636200			−0.318100	+	0.948057i	$0.603045\pi$
$678$	2.71598e11			1.28531
$679$			1.58534e11i			0.745835i
$680$		−	2.68614e11i		−	1.25630i
$681$		−	5.15856e10i		−	0.239850i
$682$			1.05253e12i			4.86516i
$683$		−	2.61051e11i		−	1.19962i	−0.800144	−	0.599808i	$-0.795244\pi$
$683$		−	2.61051e11i		−	1.19962i	0.800144	−	0.599808i	$-0.204756\pi$
$684$	5.80990e10			0.265426
$685$	9.52985e10			0.432836
$686$			5.98083e11i			2.70063i
$687$		−	5.02911e9i		−	0.0225769i
$688$			3.57181e11i			1.59417i
$689$			1.89274e11i			0.839873i
$690$	−1.70463e11			−0.752029
$691$		−	1.53433e11i		−	0.672987i	−0.941686	−	0.336493i	$-0.890759\pi$
$691$		−	1.53433e11i		−	0.672987i	0.941686	−	0.336493i	$-0.109241\pi$
$692$		−	1.71127e11i		−	0.746268i
$693$			1.88092e11i			0.815526i
$694$	−6.27789e11			−2.70630
$695$	−3.33875e10			−0.143102
$696$			6.68061e11i			2.84695i
$697$	−1.14110e11			−0.483495
$698$	−1.45208e11			−0.611743
$699$		−	4.10126e10i		−	0.171794i
$700$	8.51768e11			3.54755
$701$			8.71726e10i			0.361001i	0.983575	+	0.180500i	$0.0577717\pi$
$701$			8.71726e10i			0.361001i	−0.983575	+	0.180500i	$0.942228\pi$
$702$	6.58081e10			0.270976
$703$		−	3.70854e10i		−	0.151838i
$704$		−	5.51401e11i		−	2.24480i
$705$		−	3.20694e10i		−	0.129818i
$706$	5.70335e11			2.29568
$707$		−	5.75278e11i		−	2.30250i
$708$	3.51190e11	+	8.47264e10i	1.39768	+	0.337199i
$709$	3.33405e10			0.131943			0.0659717	−	0.997821i	$-0.478985\pi$
$709$	3.33405e10			0.131943			0.0659717	+	0.997821i	$0.478985\pi$
$710$			3.04511e11i			1.19831i
$711$	6.12175e9			0.0239551
$712$	−2.28344e10			−0.0888525
$713$	−8.17977e11			−3.16507
$714$		−	5.39464e11i		−	2.07572i
$715$	−1.12992e11			−0.432340
$716$			3.34704e11i			1.27353i
$717$	5.23239e10			0.197981
$718$		−	2.63604e11i		−	0.991870i
$719$			9.49106e10i			0.355140i	0.984108	+	0.177570i	$0.0568236\pi$
$719$			9.49106e10i			0.355140i	−0.984108	+	0.177570i	$0.943176\pi$
$720$	−9.62313e10			−0.358085
$721$		−	1.15520e11i		−	0.427479i
$722$		−	4.55765e11i		−	1.67723i
$723$	1.79041e11			0.655237
$724$	−8.58059e11			−3.12294
$725$	4.12496e11			1.49303
$726$		−	3.28494e11i		−	1.18245i
$727$	−1.53628e11			−0.549963			−0.274981	−	0.961450i	$-0.588672\pi$
$727$	−1.53628e11			−0.549963			−0.274981	+	0.961450i	$0.588672\pi$
$728$	−9.95987e11			−3.54591
$729$	1.04604e10			0.0370370
$730$	−1.71854e11			−0.605156
$731$		−	1.91196e11i		−	0.669592i
$732$		−	3.71433e11i		−	1.29371i
$733$	4.52962e10			0.156908			0.0784541	−	0.996918i	$-0.475002\pi$
$733$	4.52962e10			0.156908			0.0784541	+	0.996918i	$0.475002\pi$
$734$	−4.38611e11			−1.51111
$735$	−1.23869e11			−0.424436
$736$	1.17791e12			4.01420
$737$	5.16098e11			1.74929
$738$			7.84274e10i			0.264388i
$739$		−	3.89715e11i		−	1.30668i	−0.757065	−	0.653340i	$-0.773367\pi$
$739$		−	3.89715e11i		−	1.30668i	0.757065	−	0.653340i	$-0.226633\pi$
$740$			1.40499e11i			0.468541i
$741$			4.19473e10i			0.139133i
$742$		−	1.06640e12i		−	3.51805i
$743$	−2.21515e10			−0.0726854			−0.0363427	−	0.999339i	$-0.511571\pi$
$743$	−2.21515e10			−0.0726854			−0.0363427	+	0.999339i	$0.511571\pi$
$744$	−8.85899e11			−2.89129
$745$		−	1.23618e11i		−	0.401288i
$746$			1.22725e11i			0.396259i
$747$			4.45157e9i			0.0142965i
$748$			1.28541e12i			4.10616i
$749$	7.19816e11			2.28715
$750$			2.49212e11i			0.787634i
$751$			1.70755e10i			0.0536803i	0.999640	+	0.0268401i	$0.00854450\pi$
$751$			1.70755e10i			0.0536803i	−0.999640	+	0.0268401i	$0.991455\pi$
$752$			4.92071e11i			1.53871i
$753$	−2.00940e11			−0.625010
$754$	−8.05988e11			−2.49369
$755$		−	1.60882e11i		−	0.495132i
$756$	−2.64543e11			−0.809859
$757$	−3.31538e10			−0.100960			−0.0504800	−	0.998725i	$-0.516075\pi$
$757$	−3.31538e10			−0.100960			−0.0504800	+	0.998725i	$0.516075\pi$
$758$		−	1.18534e12i		−	3.59059i
$759$	4.88167e11			1.47096
$760$		−	1.17679e11i		−	0.352731i
$761$	−5.71126e11			−1.70292			−0.851458	−	0.524423i	$-0.824281\pi$
$761$	−5.71126e11			−1.70292			−0.851458	+	0.524423i	$0.824281\pi$
$762$			2.59363e11i			0.769288i
$763$		−	7.65915e11i		−	2.25986i
$764$			2.11119e11i			0.619659i
$765$	5.15119e10			0.150405
$766$			4.47539e11i			1.29992i
$767$	−6.11723e10	+	2.53558e11i	−0.176756	+	0.732649i
$768$	−8.04836e10			−0.231346
$769$			8.44024e10i			0.241351i	0.992692	+	0.120676i	$0.0385061\pi$
$769$			8.44024e10i			0.241351i	−0.992692	+	0.120676i	$0.961494\pi$
$770$	6.36615e11			1.81098
$771$	2.35368e11			0.666085
$772$	1.39734e12			3.93399
$773$			2.74428e11i			0.768618i	0.923205	+	0.384309i	$0.125560\pi$
$773$			2.74428e11i			0.768618i	−0.923205	+	0.384309i	$0.874440\pi$
$774$	−1.31409e11			−0.366151
$775$			5.47000e11i			1.51628i
$776$	4.45617e11			1.22890
$777$			1.68862e11i			0.463284i
$778$			1.12235e11i			0.306345i
$779$	−4.99911e10			−0.135751
$780$		−	1.58919e11i		−	0.429336i
$781$		−	8.72046e11i		−	2.34388i
$782$	−1.40010e12			−3.74397
$783$	−1.28114e11			−0.340838
$784$	1.90063e12			5.03077
$785$			9.41360e10i			0.247900i
$786$	−8.17245e11			−2.14122
$787$	−1.65013e11			−0.430148			−0.215074	−	0.976598i	$-0.568999\pi$
$787$	−1.65013e11			−0.430148			−0.215074	+	0.976598i	$0.568999\pi$
$788$	−1.19859e12			−3.10860
$789$	1.41155e10			0.0364241
$790$		−	2.07196e10i		−	0.0531954i
$791$		−	7.88278e11i		−	2.01360i
$792$	5.28702e11			1.34372
$793$	2.68174e11			0.678146
$794$	−1.76183e11			−0.443284
$795$	1.01827e11			0.254915
$796$	1.17734e12			2.93259
$797$			2.42268e11i			0.600430i	0.953872	+	0.300215i	$0.0970585\pi$
$797$			2.42268e11i			0.600430i	−0.953872	+	0.300215i	$0.902942\pi$
$798$		−	2.36337e11i		−	0.582801i
$799$		−	2.63402e11i		−	0.646297i
$800$		−	7.87693e11i		−	1.92308i
$801$		−	4.37894e9i		−	0.0106375i
$802$	9.87413e11			2.38672
$803$	4.92149e11			1.18368
$804$			7.25868e11i			1.73714i
$805$			4.94748e11i			1.17815i
$806$		−	1.06880e12i		−	2.53254i
$807$			2.09641e11i			0.494290i
$808$	−1.61703e12			−3.79378
$809$		−	4.60332e11i		−	1.07467i	−0.843368	−	0.537337i	$-0.819430\pi$
$809$		−	4.60332e11i		−	1.07467i	0.843368	−	0.537337i	$-0.180570\pi$
$810$		−	3.54040e10i		−	0.0822456i
$811$			2.57768e11i			0.595861i	0.954588	+	0.297931i	$0.0962964\pi$
$811$			2.57768e11i			0.595861i	−0.954588	+	0.297931i	$0.903704\pi$
$812$	3.24000e12			7.45283
$813$	−1.09829e11			−0.251394
$814$		−	5.63926e11i		−	1.28447i
$815$	−1.16616e11			−0.264318
$816$	−7.90397e11			−1.78273
$817$		−	8.37624e10i		−	0.188001i
$818$	−9.10959e11			−2.03463
$819$		−	1.91000e11i		−	0.424519i
$820$	1.89393e11			0.418898
$821$			1.74887e11i			0.384933i	0.981304	+	0.192466i	$0.0616486\pi$
$821$			1.74887e11i			0.384933i	−0.981304	+	0.192466i	$0.938351\pi$
$822$		−	5.37972e11i		−	1.17835i
$823$		−	3.23459e11i		−	0.705049i	−0.935803	−	0.352525i	$-0.885323\pi$
$823$		−	3.23459e11i		−	0.705049i	0.935803	−	0.352525i	$-0.114677\pi$
$824$	−3.24710e11			−0.704348
$825$		−	3.26448e11i		−	0.704691i
$826$	3.44653e11	−	1.42858e12i	0.740393	−	3.06891i
$827$	4.56032e11			0.974929			0.487465	−	0.873143i	$-0.337922\pi$
$827$	4.56032e11			0.974929			0.487465	+	0.873143i	$0.337922\pi$
$828$			6.86585e11i			1.46074i
$829$	3.65235e11			0.773310			0.386655	−	0.922224i	$-0.373630\pi$
$829$	3.65235e11			0.773310			0.386655	+	0.922224i	$0.373630\pi$
$830$	1.50667e10			0.0317473
$831$	−3.70768e11			−0.777496
$832$			5.59924e11i			1.16852i
$833$	−1.01740e12			−2.11305
$834$			1.88477e11i			0.389577i
$835$	2.96013e11			0.608927
$836$			5.63134e11i			1.15289i
$837$		−	1.69888e11i		−	0.346148i
$838$	−5.41956e10			−0.109897
$839$		−	2.76165e11i		−	0.557342i	−0.960387	−	0.278671i	$-0.910106\pi$
$839$		−	2.76165e11i		−	0.557342i	0.960387	−	0.278671i	$-0.0898938\pi$
$840$			5.35829e11i			1.07624i
$841$	1.06883e12			2.13661
$842$	−1.13311e12			−2.25436
$843$	−3.86265e11			−0.764848
$844$			7.17818e11i			1.41464i
$845$	−8.72601e10			−0.171155
$846$	−1.81036e11			−0.353413
$847$	−9.53412e11			−1.85245
$848$	−1.56243e12			−3.02147
$849$		−	2.07496e10i		−	0.0399374i
$850$			9.36281e11i			1.79362i
$851$	4.38257e11			0.835623
$852$	1.22649e12			2.32759
$853$	1.17242e11			0.221456			0.110728	−	0.993851i	$-0.464682\pi$
$853$	1.17242e11			0.221456			0.110728	+	0.993851i	$0.464682\pi$
$854$	−1.51093e12			−2.84061
$855$	2.25672e10			0.0422292
$856$		−	2.02331e12i		−	3.76848i
$857$			1.39151e11i			0.257966i	0.991647	+	0.128983i	$0.0411713\pi$
$857$			1.39151e11i			0.257966i	−0.991647	+	0.128983i	$0.958829\pi$
$858$			6.37857e11i			1.17699i
$859$		−	1.96043e11i		−	0.360064i	−0.983661	−	0.180032i	$-0.942380\pi$
$859$		−	1.96043e11i		−	0.360064i	0.983661	−	0.180032i	$-0.0576201\pi$
$860$			3.17337e11i			0.580132i
$861$	2.27625e11			0.414198
$862$	−1.81369e12			−3.28499
$863$		−	2.32620e11i		−	0.419376i	−0.977768	−	0.209688i	$-0.932755\pi$
$863$		−	2.32620e11i		−	0.419376i	0.977768	−	0.209688i	$-0.0672449\pi$
$864$			2.44643e11i			0.439013i
$865$		−	6.64704e10i		−	0.118731i
$866$		−	7.89807e11i		−	1.40427i
$867$	9.68702e10			0.171441
$868$			4.29649e12i			7.56893i
$869$			5.93362e10i			0.104050i
$870$			4.33612e11i			0.756875i
$871$	−5.24076e11			−0.910587
$872$	−2.15288e12			−3.72353
$873$			8.54558e10i			0.147124i
$874$	−6.13379e11			−1.05120
$875$	7.23306e11			1.23393
$876$			6.92185e11i			1.17545i
$877$	3.48906e11			0.589807			0.294903	−	0.955527i	$-0.404713\pi$
$877$	3.48906e11			0.589807			0.294903	+	0.955527i	$0.404713\pi$
$878$		−	1.90155e12i		−	3.19984i
$879$	1.47037e11			0.246304
$880$		−	9.32739e11i		−	1.55535i
$881$		−	1.10103e12i		−	1.82766i	−0.406101	−	0.913828i	$-0.633112\pi$
$881$		−	1.10103e12i		−	1.82766i	0.406101	−	0.913828i	$-0.366888\pi$
$882$			6.99254e11i			1.15547i
$883$	3.90643e11			0.642595			0.321298	−	0.946978i	$-0.395881\pi$
$883$	3.90643e11			0.642595			0.321298	+	0.946978i	$0.395881\pi$
$884$		−	1.30528e12i		−	2.13745i
$885$	1.36411e11	+	3.29100e10i	0.222371	+	0.0536482i
$886$	1.13360e12			1.83961
$887$		−	3.64372e11i		−	0.588641i	−0.955707	−	0.294321i	$-0.904907\pi$
$887$		−	3.64372e11i		−	0.588641i	0.955707	−	0.294321i	$-0.0950933\pi$
$888$	4.74648e11			0.763343
$889$	7.52769e11			1.20519
$890$	−1.48209e10			−0.0236219
$891$			1.01389e11i			0.160871i
$892$	−8.13391e11			−1.28481
$893$		−	1.15396e11i		−	0.181461i
$894$	−6.97838e11			−1.09246
$895$			1.30008e11i			0.202618i
$896$		−	6.70249e11i		−	1.03993i
$897$	−4.95713e11			−0.765703
$898$		−	5.59989e11i		−	0.861141i
$899$			2.08071e12i			3.18547i
$900$	4.59135e11			0.699794
$901$	8.36359e11			1.26909
$902$	−7.60171e11			−1.14838
$903$			3.81397e11i			0.573623i
$904$	−2.21574e12			−3.31777
$905$	−3.33293e11			−0.496858
$906$	−9.08202e11			−1.34794
$907$	6.73147e11			0.994673			0.497337	−	0.867558i	$-0.334311\pi$
$907$	6.73147e11			0.994673			0.497337	+	0.867558i	$0.334311\pi$
$908$			7.03231e11i			1.03456i
$909$		−	3.10097e11i		−	0.454194i
$910$	−6.46456e11			−0.942700
$911$	−1.11052e11			−0.161232			−0.0806160	−	0.996745i	$-0.525689\pi$
$911$	−1.11052e11			−0.161232			−0.0806160	+	0.996745i	$0.525689\pi$
$912$	−3.46270e11			−0.500536
$913$	−4.31476e10			−0.0620974
$914$	4.65560e11			0.667099
$915$		−	1.44274e11i		−	0.205828i
$916$			6.85583e10i			0.0973819i
$917$			2.37195e12i			3.35450i
$918$		−	2.90791e11i		−	0.409459i
$919$			8.37123e11i			1.17362i	0.809725	+	0.586809i	$0.199616\pi$
$919$			8.37123e11i			1.17362i	−0.809725	+	0.586809i	$0.800384\pi$
$920$	1.39067e12			1.94121
$921$	−1.49081e11			−0.207197
$922$			4.08374e11i			0.565112i
$923$			8.85526e11i			1.22010i
$924$		−	2.56413e12i		−	3.51765i
$925$		−	2.93072e11i		−	0.400321i
$926$	8.69807e11			1.18298
$927$		−	6.22695e10i		−	0.0843250i
$928$		−	2.99627e12i		−	4.04008i
$929$			1.13432e12i			1.52290i	0.648224	+	0.761449i	$0.275512\pi$
$929$			1.13432e12i			1.52290i	−0.648224	+	0.761449i	$0.724488\pi$
$930$	−5.75002e11			−0.768666
$931$	−4.45717e11			−0.593281
$932$			5.59097e11i			0.741009i
$933$	−6.71260e11			−0.885858
$934$	−2.90407e11			−0.381610
$935$			4.99288e11i			0.653288i
$936$	−5.36874e11			−0.699470
$937$		−	1.22246e12i		−	1.58590i	−0.609285	−	0.792952i	$-0.708543\pi$
$937$		−	1.22246e12i		−	1.58590i	0.609285	−	0.792952i	$-0.291457\pi$
$938$	2.95271e12			3.81426
$939$		−	3.18809e11i		−	0.410080i
$940$			4.37180e11i			0.559949i
$941$			1.07347e11i			0.136909i	0.997654	+	0.0684543i	$0.0218067\pi$
$941$			1.07347e11i			0.136909i	−0.997654	+	0.0684543i	$0.978193\pi$
$942$	5.31410e11			0.674879
$943$		−	5.90770e11i		−	0.747087i
$944$	−2.09309e12	−	5.04970e11i	−2.63573	−	0.635883i
$945$	−1.02756e11			−0.128848
$946$		−	1.27370e12i		−	1.59039i
$947$	2.49539e11			0.310270			0.155135	−	0.987893i	$-0.450419\pi$
$947$	2.49539e11			0.310270			0.155135	+	0.987893i	$0.450419\pi$
$948$	−8.34537e10			−0.103327
$949$	−4.99756e11			−0.616160
$950$			4.10181e11i			0.503595i
$951$	2.71022e11			0.331346
$952$			4.40104e12i			5.35806i
$953$	1.01884e12			1.23519			0.617594	−	0.786497i	$-0.288108\pi$
$953$	1.01884e12			1.23519			0.617594	+	0.786497i	$0.288108\pi$
$954$		−	5.74827e11i		−	0.693975i
$955$			8.20040e10i			0.0985875i
$956$	−7.13296e11			−0.853962
$957$		−	1.24176e12i		−	1.48044i
$958$			1.57837e12i			1.87390i
$959$	−1.56139e12			−1.84603
$960$	3.01233e11			0.354664
$961$	−1.90629e12			−2.23509
$962$			5.72643e11i			0.668626i
$963$	3.88008e11			0.451165
$964$	−2.44074e12			−2.82626
$965$	5.42764e11			0.625896
$966$	2.79291e12			3.20737
$967$			2.25546e11i			0.257946i	0.991648	+	0.128973i	$0.0411680\pi$
$967$			2.25546e11i			0.257946i	−0.991648	+	0.128973i	$0.958832\pi$
$968$			2.67991e12i			3.05225i
$969$	1.85356e11			0.210238
$970$	2.89233e11			0.326709
$971$	−1.33335e12			−1.49992			−0.749960	−	0.661484i	$-0.769927\pi$
$971$	−1.33335e12			−1.49992			−0.749960	+	0.661484i	$0.769927\pi$
$972$	−1.42599e11			−0.159754
$973$	5.47030e11			0.610323
$974$			1.97058e12i			2.18957i
$975$			3.31495e11i			0.366824i
$976$			2.21374e12i			2.43965i
$977$			1.06416e12i			1.16796i	0.811767	+	0.583982i	$0.198506\pi$
$977$			1.06416e12i			1.16796i	−0.811767	+	0.583982i	$0.801494\pi$
$978$			6.58310e11i			0.719573i
$979$	4.24436e10			0.0462042
$980$	1.68861e12			1.83074
$981$		−	4.12857e11i		−	0.445783i
$982$			3.24070e12i			3.48492i
$983$			2.83765e9i			0.00303910i	0.999999	+	0.00151955i	$0.000483688\pi$
$983$			2.83765e9i			0.00303910i	−0.999999	+	0.00151955i	$0.999516\pi$
$984$		−	6.39824e11i		−	0.682465i
$985$	−4.65564e11			−0.494578
$986$			3.56148e12i			3.76810i
$987$			5.25433e11i			0.553667i
$988$		−	5.71839e11i		−	0.600131i
$989$	9.89862e11			1.03464
$990$	3.43160e11			0.357236
$991$			1.14914e12i			1.19146i	0.803186	+	0.595728i	$0.203136\pi$
$991$			1.14914e12i			1.19146i	−0.803186	+	0.595728i	$0.796864\pi$
$992$	3.97328e12			4.10301
$993$	−7.76089e11			−0.798205
$994$		−	4.98918e12i		−	5.11074i
$995$	4.57312e11			0.466574
$996$		−	6.06852e10i		−	0.0616659i
$997$	−1.40469e12			−1.42167			−0.710834	−	0.703360i	$-0.751682\pi$
$997$	−1.40469e12			−1.42167			−0.710834	+	0.703360i	$0.751682\pi$
$998$		−	7.13395e11i		−	0.719131i
$999$			9.10229e10i			0.0913879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.78	yes	80
59.58	odd	2	inner	177.9.c.a.58.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.3	✓	80	59.58	odd	2	inner
177.9.c.a.58.78	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)

\(f(q)\)	\(=\)	\(q+29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} +1397.90i q^{6} +4057.23 q^{7} -11404.3i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q+29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} +1397.90i q^{6} +4057.23 q^{7} -11404.3i q^{8} +2187.00 q^{9} -7402.10i q^{10} +21197.9i q^{11} -29813.9 q^{12} -21525.6i q^{13} +121278. i q^{14} -11580.5 q^{15} +177691. q^{16} -95116.6 q^{17} +65373.4i q^{18} -41670.2 q^{19} +157869. q^{20} +189738. q^{21} -633643. q^{22} -492438. i q^{23} -533328. i q^{24} -329304. q^{25} +643438. q^{26} +102276. q^{27} -2.58657e6 q^{28} -1.25263e6 q^{29} -346162. i q^{30} -1.66108e6i q^{31} +2.39199e6i q^{32} +991326. i q^{33} -2.84321e6i q^{34} -1.00469e6 q^{35} -1.39426e6 q^{36} +889974. i q^{37} -1.24560e6i q^{38} -1.00665e6i q^{39} +2.82405e6i q^{40} +1.19968e6 q^{41} +5.67161e6i q^{42} +2.01013e6i q^{43} -1.35141e7i q^{44} -541566. q^{45} +1.47199e7 q^{46} +2.76926e6i q^{47} +8.30977e6 q^{48} +1.06963e7 q^{49} -9.84351e6i q^{50} -4.44816e6 q^{51} +1.37230e7i q^{52} -8.79299e6 q^{53} +3.05721e6i q^{54} -5.24922e6i q^{55} -4.62700e7i q^{56} -1.94872e6 q^{57} -3.74433e7i q^{58} +(-1.17794e7 - 2.84185e6i) q^{59} +7.38280e6 q^{60} +1.24584e7i q^{61} +4.96526e7 q^{62} +8.87316e6 q^{63} -2.60121e7 q^{64} +5.33037e6i q^{65} -2.96325e7 q^{66} -2.43467e7i q^{67} +6.06387e7 q^{68} -2.30290e7i q^{69} -3.00320e7i q^{70} -4.11384e7 q^{71} -2.49413e7i q^{72} -2.32169e7i q^{73} -2.66029e7 q^{74} -1.54000e7 q^{75} +2.65656e7 q^{76} +8.60046e7i q^{77} +3.00906e7 q^{78} +2.79916e6 q^{79} -4.40015e7 q^{80} +4.78297e6 q^{81} +3.58607e7i q^{82} +2.03547e6i q^{83} -1.20962e8 q^{84} +2.35537e7 q^{85} -6.00863e7 q^{86} -5.85796e7 q^{87} +2.41747e8 q^{88} -2.00226e6i q^{89} -1.61884e7i q^{90} -8.73341e7i q^{91} +3.13939e8i q^{92} -7.76809e7i q^{93} -8.27781e7 q^{94} +1.03188e7 q^{95} +1.11862e8i q^{96} +3.90744e7i q^{97} +3.19732e8i q^{98} +4.63598e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 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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