LMFDB - Embedded newform 177.3.b.a.119.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(119,177)]

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([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.b (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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.10
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +O(q^{10})$	\(q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +10.9755 q^{10} -15.4011i q^{11} +(1.57703 - 0.175964i) q^{12} +18.6528 q^{13} -5.72689i q^{14} +(-1.71571 - 15.3766i) q^{15} -17.8360 q^{16} +4.88346i q^{17} +(-4.22163 - 18.6821i) q^{18} +3.41065 q^{19} -2.72792i q^{20} +(-8.02334 + 0.895238i) q^{21} -32.7756 q^{22} -15.9679i q^{23} +(2.45741 + 22.0239i) q^{24} -1.59821 q^{25} -39.6955i q^{26} +(-25.5136 + 8.83491i) q^{27} -1.42340 q^{28} -24.8107i q^{29} +(-32.7234 + 3.65126i) q^{30} +28.0319 q^{31} +8.40981i q^{32} +(5.12354 + 45.9184i) q^{33} +10.3926 q^{34} +13.8786i q^{35} +(-4.64338 + 1.04927i) q^{36} +60.2239 q^{37} -7.25831i q^{38} +(-55.6131 + 6.20527i) q^{39} +38.0966 q^{40} +37.6168i q^{41} +(1.90518 + 17.0747i) q^{42} -15.8209 q^{43} +8.14626i q^{44} +(10.2308 + 45.2746i) q^{45} -33.9818 q^{46} -13.1463i q^{47} +(53.1779 - 5.93355i) q^{48} -41.7583 q^{49} +3.40120i q^{50} +(-1.62460 - 14.5600i) q^{51} -9.86617 q^{52} +35.0364i q^{53} +(18.8018 + 54.2963i) q^{54} +79.4290 q^{55} -19.8784i q^{56} +(-10.1688 + 1.13463i) q^{57} -52.8004 q^{58} +7.68115i q^{59} +(0.907507 + 8.13330i) q^{60} -83.7144 q^{61} -59.6555i q^{62} +(23.6238 - 5.33830i) q^{63} -53.4467 q^{64} +96.1987i q^{65} +(97.7204 - 10.9036i) q^{66} +72.8285 q^{67} -2.58305i q^{68} +(5.31210 + 47.6083i) q^{69} +29.5356 q^{70} +27.7175i q^{71} +(-14.6535 - 64.8468i) q^{72} +54.4224 q^{73} -128.164i q^{74} +(4.76507 - 0.531683i) q^{75} -1.80403 q^{76} -41.4451i q^{77} +(13.2056 + 118.352i) q^{78} -123.594 q^{79} -91.9863i q^{80} +(73.1296 - 34.8290i) q^{81} +80.0535 q^{82} +143.471i q^{83} +(4.24386 - 0.473527i) q^{84} -25.1857 q^{85} +33.6690i q^{86} +(8.25385 + 73.9730i) q^{87} -113.766 q^{88} -21.8428i q^{89} +(96.3502 - 21.7724i) q^{90} +50.1954 q^{91} +8.44606i q^{92} +(-83.5770 + 9.32545i) q^{93} -27.9771 q^{94} +17.5899i q^{95} +(-2.79772 - 25.0738i) q^{96} -98.9417 q^{97} +88.8671i q^{98} +(-30.5517 - 135.201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

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 $

$2$		−	2.12813i		−	1.06407i	−0.846724	−	0.532033i	$-0.821428\pi$
$2$		−	2.12813i		−	1.06407i	0.846724	−	0.532033i	$-0.178572\pi$
$3$	−2.98150	+	0.332673i	−0.993833	+	0.110891i
$3$	−2.98150	+	0.332673i	−0.993833	+	0.110891i
$4$	−0.528939			−0.132235
$5$			5.15735i			1.03147i	0.856748	+	0.515735i	$0.172481\pi$
$5$			5.15735i			1.03147i	−0.856748	+	0.515735i	$0.827519\pi$
$6$	0.707972	+	6.34502i	0.117995	+	1.05750i
$7$	2.69104			0.384435			0.192217	−	0.981352i	$-0.438432\pi$
$7$	2.69104			0.384435			0.192217	+	0.981352i	$0.438432\pi$
$8$		−	7.38687i		−	0.923359i
$9$	8.77866	−	1.98373i	0.975406	−	0.220414i
$10$	10.9755			1.09755
$11$		−	15.4011i		−	1.40010i	−0.714092	−	0.700051i	$-0.753160\pi$
$11$		−	15.4011i		−	1.40010i	0.714092	−	0.700051i	$-0.246840\pi$
$12$	1.57703	−	0.175964i	0.131419	−	0.0146637i
$13$	18.6528			1.43483			0.717414	−	0.696648i	$-0.245326\pi$
$13$	18.6528			1.43483			0.717414	+	0.696648i	$0.245326\pi$
$14$		−	5.72689i		−	0.409064i
$15$	−1.71571	−	15.3766i	−0.114381	−	1.02511i
$16$	−17.8360			−1.11475
$17$			4.88346i			0.287262i	0.989631	+	0.143631i	$0.0458779\pi$
$17$			4.88346i			0.287262i	−0.989631	+	0.143631i	$0.954122\pi$
$18$	−4.22163	−	18.6821i	−0.234535	−	1.03790i
$19$	3.41065			0.179508			0.0897540	−	0.995964i	$-0.471392\pi$
$19$	3.41065			0.179508			0.0897540	+	0.995964i	$0.471392\pi$
$20$		−	2.72792i		−	0.136396i
$21$	−8.02334	+	0.895238i	−0.382064	+	0.0426304i
$22$	−32.7756			−1.48980
$23$		−	15.9679i		−	0.694257i	−0.937818	−	0.347129i	$-0.887157\pi$
$23$		−	15.9679i		−	0.694257i	0.937818	−	0.347129i	$-0.112843\pi$
$24$	2.45741	+	22.0239i	0.102392	+	0.917664i
$25$	−1.59821			−0.0639285
$26$		−	39.6955i		−	1.52675i
$27$	−25.5136	+	8.83491i	−0.944949	+	0.327219i
$28$	−1.42340			−0.0508357
$29$		−	24.8107i		−	0.855541i	−0.903887	−	0.427770i	$-0.859299\pi$
$29$		−	24.8107i		−	0.855541i	0.903887	−	0.427770i	$-0.140701\pi$
$30$	−32.7234	+	3.65126i	−1.09078	+	0.121709i
$31$	28.0319			0.904254			0.452127	−	0.891954i	$-0.350665\pi$
$31$	28.0319			0.904254			0.452127	+	0.891954i	$0.350665\pi$
$32$			8.40981i			0.262807i
$33$	5.12354	+	45.9184i	0.155259	+	1.39147i
$34$	10.3926			0.305666
$35$			13.8786i			0.396533i
$36$	−4.64338	+	1.04927i	−0.128983	+	0.0291465i
$37$	60.2239			1.62767			0.813837	−	0.581093i	$-0.197375\pi$
$37$	60.2239			1.62767			0.813837	+	0.581093i	$0.197375\pi$
$38$		−	7.25831i		−	0.191008i
$39$	−55.6131	+	6.20527i	−1.42598	+	0.159110i
$40$	38.0966			0.952416
$41$			37.6168i			0.917483i	0.888570	+	0.458742i	$0.151700\pi$
$41$			37.6168i			0.917483i	−0.888570	+	0.458742i	$0.848300\pi$
$42$	1.90518	+	17.0747i	0.0453615	+	0.406541i
$43$	−15.8209			−0.367928			−0.183964	−	0.982933i	$-0.558893\pi$
$43$	−15.8209			−0.367928			−0.183964	+	0.982933i	$0.558893\pi$
$44$			8.14626i			0.185142i
$45$	10.2308	+	45.2746i	0.227351	+	1.00610i
$46$	−33.9818			−0.738735
$47$		−	13.1463i		−	0.279709i	−0.990172	−	0.139854i	$-0.955337\pi$
$47$		−	13.1463i		−	0.279709i	0.990172	−	0.139854i	$-0.0446634\pi$
$48$	53.1779	−	5.93355i	1.10787	−	0.123616i
$49$	−41.7583			−0.852210
$50$			3.40120i			0.0680241i
$51$	−1.62460	−	14.5600i	−0.0318548	−	0.285490i
$52$	−9.86617			−0.189734
$53$			35.0364i			0.661065i	0.943795	+	0.330532i	$0.107228\pi$
$53$			35.0364i			0.661065i	−0.943795	+	0.330532i	$0.892772\pi$
$54$	18.8018	+	54.2963i	0.348182	+	1.00549i
$55$	79.4290			1.44416
$56$		−	19.8784i		−	0.354971i
$57$	−10.1688	+	1.13463i	−0.178401	+	0.0199058i
$58$	−52.8004			−0.910351
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	0.907507	+	8.13330i	0.0151251	+	0.135555i
$61$	−83.7144			−1.37237			−0.686183	−	0.727429i	$-0.740715\pi$
$61$	−83.7144			−1.37237			−0.686183	+	0.727429i	$0.740715\pi$
$62$		−	59.6555i		−	0.962185i
$63$	23.6238	−	5.33830i	0.374980	−	0.0847350i
$64$	−53.4467			−0.835105
$65$			96.1987i			1.47998i
$66$	97.7204	−	10.9036i	1.48061	−	0.165206i
$67$	72.8285			1.08699			0.543497	−	0.839411i	$-0.317100\pi$
$67$	72.8285			1.08699			0.543497	+	0.839411i	$0.317100\pi$
$68$		−	2.58305i		−	0.0379861i
$69$	5.31210	+	47.6083i	0.0769869	+	0.689975i
$70$	29.5356			0.421937
$71$			27.7175i			0.390387i	0.980765	+	0.195193i	$0.0625334\pi$
$71$			27.7175i			0.390387i	−0.980765	+	0.195193i	$0.937467\pi$
$72$	−14.6535	−	64.8468i	−0.203522	−	0.900650i
$73$	54.4224			0.745513			0.372756	−	0.927929i	$-0.378413\pi$
$73$	54.4224			0.745513			0.372756	+	0.927929i	$0.378413\pi$
$74$		−	128.164i		−	1.73195i
$75$	4.76507	−	0.531683i	0.0635342	−	0.00708910i
$76$	−1.80403			−0.0237372
$77$		−	41.4451i		−	0.538248i
$78$	13.2056	+	118.352i	0.169303	+	1.51733i
$79$	−123.594			−1.56448			−0.782242	−	0.622975i	$-0.785924\pi$
$79$	−123.594			−1.56448			−0.782242	+	0.622975i	$0.785924\pi$
$80$		−	91.9863i		−	1.14983i
$81$	73.1296	−	34.8290i	0.902835	−	0.429987i
$82$	80.0535			0.976262
$83$			143.471i			1.72857i	0.503003	+	0.864285i	$0.332228\pi$
$83$			143.471i			1.72857i	−0.503003	+	0.864285i	$0.667772\pi$
$84$	4.24386	−	0.473527i	0.0505222	−	0.00563722i
$85$	−25.1857			−0.296302
$86$			33.6690i			0.391500i
$87$	8.25385	+	73.9730i	0.0948718	+	0.850264i
$88$	−113.766			−1.29280
$89$		−	21.8428i		−	0.245425i	−0.992442	−	0.122713i	$-0.960841\pi$
$89$		−	21.8428i		−	0.245425i	0.992442	−	0.122713i	$-0.0391593\pi$
$90$	96.3502	−	21.7724i	1.07056	−	0.241916i
$91$	50.1954			0.551598
$92$			8.44606i			0.0918050i
$93$	−83.5770	+	9.32545i	−0.898677	+	0.100274i
$94$	−27.9771			−0.297628
$95$			17.5899i			0.185157i
$96$	−2.79772	−	25.0738i	−0.0291429	−	0.261186i
$97$	−98.9417			−1.02002			−0.510009	−	0.860169i	$-0.670358\pi$
$97$	−98.9417			−1.02002			−0.510009	+	0.860169i	$0.670358\pi$
$98$			88.8671i			0.906807i
$99$	−30.5517	−	135.201i	−0.308603	−	1.36567i
$100$	0.845357			0.00845357
$101$			11.1986i			0.110877i	0.998462	+	0.0554386i	$0.0176557\pi$
$101$			11.1986i			0.110877i	−0.998462	+	0.0554386i	$0.982344\pi$
$102$	−30.9856	+	3.45735i	−0.303780	+	0.0338956i
$103$	−103.065			−1.00064			−0.500318	−	0.865842i	$-0.666783\pi$
$103$	−103.065			−1.00064			−0.500318	+	0.865842i	$0.666783\pi$
$104$		−	137.785i		−	1.32486i
$105$	−4.61705	−	41.3791i	−0.0439719	−	0.394087i
$106$	74.5621			0.703416
$107$		−	159.235i		−	1.48818i	−0.668081	−	0.744089i	$-0.732884\pi$
$107$		−	159.235i		−	1.48818i	0.668081	−	0.744089i	$-0.267116\pi$
$108$	13.4952	−	4.67313i	0.124955	−	0.0432697i
$109$	−106.870			−0.980461			−0.490230	−	0.871593i	$-0.663087\pi$
$109$	−106.870			−0.980461			−0.490230	+	0.871593i	$0.663087\pi$
$110$		−	169.035i		−	1.53668i
$111$	−179.558	+	20.0349i	−1.61764	+	0.180495i
$112$	−47.9974			−0.428548
$113$			163.994i			1.45127i	0.688079	+	0.725636i	$0.258454\pi$
$113$			163.994i			1.45127i	−0.688079	+	0.725636i	$0.741546\pi$
$114$	2.41465	+	21.6406i	0.0211811	+	0.189830i
$115$	82.3520			0.716105
$116$			13.1233i			0.113132i
$117$	163.746	−	37.0020i	1.39954	−	0.316256i
$118$	16.3465			0.138529
$119$			13.1416i			0.110434i
$120$	−113.585	+	12.6737i	−0.946542	+	0.105614i
$121$	−116.195			−0.960288
$122$			178.155i			1.46029i
$123$	−12.5141	−	112.154i	−0.101741	−	0.911825i
$124$	−14.8272			−0.119574
$125$			120.691i			0.965529i
$126$	−11.3606	−	50.2744i	−0.0901635	−	0.399003i
$127$	150.567			1.18556			0.592782	−	0.805363i	$-0.298029\pi$
$127$	150.567			1.18556			0.592782	+	0.805363i	$0.298029\pi$
$128$			147.381i			1.15141i
$129$	47.1700	−	5.26319i	0.365659	−	0.0407999i
$130$	204.723			1.57480
$131$		−	245.946i		−	1.87745i	−0.344669	−	0.938724i	$-0.612009\pi$
$131$		−	245.946i		−	1.87745i	0.344669	−	0.938724i	$-0.387991\pi$
$132$	−2.71004	−	24.2881i	−0.0205306	−	0.184001i
$133$	9.17821			0.0690091
$134$		−	154.989i		−	1.15663i
$135$	−45.5647	−	131.583i	−0.337516	−	0.974685i
$136$	36.0735			0.265246
$137$			196.040i			1.43095i	0.698640	+	0.715474i	$0.253789\pi$
$137$			196.040i			1.43095i	−0.698640	+	0.715474i	$0.746211\pi$
$138$	101.317	−	11.3048i	0.734179	−	0.0819191i
$139$	81.6219			0.587208			0.293604	−	0.955927i	$-0.405145\pi$
$139$	81.6219			0.587208			0.293604	+	0.955927i	$0.405145\pi$
$140$		−	7.34096i		−	0.0524354i
$141$	4.37343	+	39.1957i	0.0310172	+	0.277984i
$142$	58.9864			0.415397
$143$		−	287.273i		−	2.00891i
$144$	−156.576	+	35.3818i	−1.08733	+	0.245707i
$145$	127.957			0.882464
$146$		−	115.818i		−	0.793274i
$147$	124.502	−	13.8919i	0.846954	−	0.0945025i
$148$	−31.8548			−0.215235
$149$		−	244.737i		−	1.64253i	−0.570545	−	0.821266i	$-0.693268\pi$
$149$		−	244.737i		−	1.64253i	0.570545	−	0.821266i	$-0.306732\pi$
$150$	−1.13149	−	10.1407i	−0.00754327	−	0.0676046i
$151$	−140.296			−0.929114			−0.464557	−	0.885543i	$-0.653786\pi$
$151$	−140.296			−0.929114			−0.464557	+	0.885543i	$0.653786\pi$
$152$		−	25.1940i		−	0.165750i
$153$	9.68745	+	42.8702i	0.0633167	+	0.280197i
$154$	−88.2006			−0.572731
$155$			144.570i			0.932710i
$156$	29.4160	−	3.28221i	0.188564	−	0.0210398i
$157$	101.021			0.643443			0.321721	−	0.946834i	$-0.395739\pi$
$157$	101.021			0.643443			0.321721	+	0.946834i	$0.395739\pi$
$158$			263.025i			1.66471i
$159$	−11.6557	−	104.461i	−0.0733062	−	0.656988i
$160$	−43.3723			−0.271077
$161$		−	42.9704i		−	0.266897i
$162$	−74.1206	−	155.629i	−0.457534	−	0.960675i
$163$	36.6971			0.225135			0.112568	−	0.993644i	$-0.464092\pi$
$163$	36.6971			0.225135			0.112568	+	0.993644i	$0.464092\pi$
$164$		−	19.8970i		−	0.121323i
$165$	−236.817	+	26.4239i	−1.43526	+	0.160145i
$166$	305.326			1.83931
$167$			91.5908i			0.548448i	0.961666	+	0.274224i	$0.0884210\pi$
$167$			91.5908i			0.548448i	−0.961666	+	0.274224i	$0.911579\pi$
$168$	6.61301	+	59.2674i	0.0393631	+	0.352782i
$169$	178.925			1.05873
$170$			53.5984i			0.315285i
$171$	29.9409	−	6.76581i	0.175093	−	0.0395661i
$172$	8.36830			0.0486529
$173$			32.3306i			0.186882i	0.995625	+	0.0934411i	$0.0297867\pi$
$173$			32.3306i			0.186882i	−0.995625	+	0.0934411i	$0.970213\pi$
$174$	157.424	−	17.5653i	0.904736	−	0.100950i
$175$	−4.30086			−0.0245763
$176$			274.694i			1.56076i
$177$	−2.55531	−	22.9013i	−0.0144368	−	0.129386i
$178$	−46.4844			−0.261148
$179$			265.603i			1.48382i	0.670502	+	0.741908i	$0.266079\pi$
$179$			265.603i			1.48382i	−0.670502	+	0.741908i	$0.733921\pi$
$180$	−5.41146	−	23.9475i	−0.0300637	−	0.133042i
$181$	−208.834			−1.15378			−0.576888	−	0.816823i	$-0.695733\pi$
$181$	−208.834			−1.15378			−0.576888	+	0.816823i	$0.695733\pi$
$182$		−	106.822i		−	0.586936i
$183$	249.594	−	27.8495i	1.36390	−	0.152183i
$184$	−117.953			−0.641048
$185$			310.596i			1.67890i
$186$	19.8458	+	177.863i	0.106698	+	0.956251i
$187$	75.2108			0.402197
$188$			6.95360i			0.0369872i
$189$	−68.6583	+	23.7751i	−0.363271	+	0.125794i
$190$	37.4336			0.197019
$191$		−	35.2665i		−	0.184641i	−0.995729	−	0.0923207i	$-0.970572\pi$
$191$		−	35.2665i		−	0.184641i	0.995729	−	0.0923207i	$-0.0294285\pi$
$192$	159.351	−	17.7803i	0.829955	−	0.0926057i
$193$	24.8793			0.128908			0.0644541	−	0.997921i	$-0.479469\pi$
$193$	24.8793			0.128908			0.0644541	+	0.997921i	$0.479469\pi$
$194$			210.561i			1.08536i
$195$	−32.0027	−	286.816i	−0.164117	−	1.47085i
$196$	22.0876			0.112692
$197$			26.9086i			0.136592i	0.997665	+	0.0682959i	$0.0217562\pi$
$197$			26.9086i			0.136592i	−0.997665	+	0.0682959i	$0.978244\pi$
$198$	−287.726	+	65.0179i	−1.45316	+	0.328373i
$199$	−142.574			−0.716453			−0.358226	−	0.933635i	$-0.616618\pi$
$199$	−142.574			−0.716453			−0.358226	+	0.933635i	$0.616618\pi$
$200$			11.8058i			0.0590289i
$201$	−217.138	+	24.2281i	−1.08029	+	0.120538i
$202$	23.8321			0.117981
$203$		−	66.7666i		−	0.328900i
$204$	0.859312	+	7.70136i	0.00421232	+	0.0377518i
$205$	−194.003			−0.946356
$206$			219.337i			1.06474i
$207$	−31.6760	−	140.177i	−0.153024	−	0.677183i
$208$	−332.690			−1.59947
$209$		−	52.5279i		−	0.251330i
$210$	−88.0602	+	9.82569i	−0.419334	+	0.0467890i
$211$	279.331			1.32384			0.661921	−	0.749574i	$-0.269742\pi$
$211$	279.331			1.32384			0.661921	+	0.749574i	$0.269742\pi$
$212$		−	18.5322i		−	0.0874158i
$213$	−9.22085	−	82.6395i	−0.0432904	−	0.387979i
$214$	−338.873			−1.58352
$215$		−	81.5939i		−	0.379506i
$216$	65.2623	+	188.466i	0.302140	+	0.872527i
$217$	75.4350			0.347627
$218$			227.434i			1.04327i
$219$	−162.260	+	18.1049i	−0.740915	+	0.0826707i
$220$	−42.0131			−0.190969
$221$			91.0899i			0.412172i
$222$	42.6369	+	382.122i	0.192058	+	1.72127i
$223$	−189.218			−0.848512			−0.424256	−	0.905542i	$-0.639464\pi$
$223$	−189.218			−0.848512			−0.424256	+	0.905542i	$0.639464\pi$
$224$			22.6312i			0.101032i
$225$	−14.0302	+	3.17042i	−0.0623563	+	0.0140908i
$226$	349.000			1.54425
$227$		−	388.040i		−	1.70943i	−0.519101	−	0.854713i	$-0.673733\pi$
$227$		−	388.040i		−	1.70943i	0.519101	−	0.854713i	$-0.326267\pi$
$228$	5.37870	−	0.600152i	0.0235908	−	0.00263224i
$229$	377.427			1.64815			0.824076	−	0.566479i	$-0.191695\pi$
$229$	377.427			1.64815			0.824076	+	0.566479i	$0.191695\pi$
$230$		−	175.256i		−	0.761982i
$231$	13.7877	+	123.569i	0.0596869	+	0.534929i
$232$	−183.273			−0.789971
$233$			369.450i			1.58562i	0.609468	+	0.792811i	$0.291383\pi$
$233$			369.450i			1.58562i	−0.609468	+	0.792811i	$0.708617\pi$
$234$	−78.7451	−	348.473i	−0.336518	−	1.48920i
$235$	67.8001			0.288511
$236$		−	4.06286i		−	0.0172155i
$237$	368.496	−	41.1165i	1.55484	−	0.173487i
$238$	27.9670			0.117509
$239$			456.633i			1.91060i	0.295640	+	0.955299i	$0.404467\pi$
$239$			456.633i			1.91060i	−0.295640	+	0.955299i	$0.595533\pi$
$240$	30.6014	+	274.257i	0.127506	+	1.14274i
$241$	−221.449			−0.918876			−0.459438	−	0.888210i	$-0.651949\pi$
$241$	−221.449			−0.918876			−0.459438	+	0.888210i	$0.651949\pi$
$242$			247.278i			1.02181i
$243$	−206.449	+	128.171i	−0.849585	+	0.527452i
$244$	44.2798			0.181475
$245$		−	215.362i		−	0.879028i
$246$	−238.679	+	26.6317i	−0.970241	+	0.108259i
$247$	63.6180			0.257563
$248$		−	207.068i		−	0.834951i
$249$	−47.7290	−	427.759i	−0.191683	−	1.71791i
$250$	256.846			1.02739
$251$		−	245.569i		−	0.978362i	−0.872182	−	0.489181i	$-0.837296\pi$
$251$		−	245.569i		−	0.978362i	0.872182	−	0.489181i	$-0.162704\pi$
$252$	−12.4955	+	2.82364i	−0.0495854	+	0.0112049i
$253$	−245.924			−0.972031
$254$		−	320.426i		−	1.26152i
$255$	75.0910	−	8.37860i	0.294475	−	0.0328573i
$256$	99.8588			0.390073
$257$			47.6112i			0.185258i	0.995701	+	0.0926288i	$0.0295270\pi$
$257$			47.6112i			0.185258i	−0.995701	+	0.0926288i	$0.970473\pi$
$258$	−11.2008	−	100.384i	−0.0434138	−	0.389085i
$259$	162.065			0.625735
$260$		−	50.8833i		−	0.195705i
$261$	−49.2177	−	217.804i	−0.188573	−	0.834500i
$262$	−523.405			−1.99773
$263$			24.3897i			0.0927366i	0.998924	+	0.0463683i	$0.0147648\pi$
$263$			24.3897i			0.0927366i	−0.998924	+	0.0463683i	$0.985235\pi$
$264$	339.194	−	37.8470i	1.28482	−	0.143360i
$265$	−180.695			−0.681868
$266$		−	19.5324i		−	0.0734302i
$267$	7.26653	+	65.1244i	0.0272155	+	0.243911i
$268$	−38.5219			−0.143738
$269$			77.7143i			0.288901i	0.989512	+	0.144450i	$0.0461414\pi$
$269$			77.7143i			0.288901i	−0.989512	+	0.144450i	$0.953859\pi$
$270$	−280.025	+	96.9676i	−1.03713	+	0.359139i
$271$	400.159			1.47660			0.738302	−	0.674471i	$-0.235628\pi$
$271$	400.159			1.47660			0.738302	+	0.674471i	$0.235628\pi$
$272$		−	87.1012i		−	0.320225i
$273$	−149.657	+	16.6987i	−0.548196	+	0.0611672i
$274$	417.198			1.52262
$275$			24.6143i			0.0895065i
$276$	−2.80978	−	25.1819i	−0.0101804	−	0.0912388i
$277$	397.402			1.43466			0.717332	−	0.696731i	$-0.245363\pi$
$277$	397.402			1.43466			0.717332	+	0.696731i	$0.245363\pi$
$278$		−	173.702i		−	0.624827i
$279$	246.082	−	55.6076i	0.882015	−	0.199311i
$280$	102.520			0.366142
$281$			83.6606i			0.297725i	0.988858	+	0.148862i	$0.0475611\pi$
$281$			83.6606i			0.297725i	−0.988858	+	0.148862i	$0.952439\pi$
$282$	83.4136	−	9.30722i	0.295793	−	0.0330043i
$283$	−105.287			−0.372039			−0.186020	−	0.982546i	$-0.559559\pi$
$283$	−105.287			−0.372039			−0.186020	+	0.982546i	$0.559559\pi$
$284$		−	14.6609i		−	0.0516227i
$285$	−5.85169	−	52.4443i	−0.0205323	−	0.184015i
$286$	−611.355			−2.13761
$287$			101.229i			0.352713i
$288$	16.6828	+	73.8269i	0.0579264	+	0.256343i
$289$	265.152			0.917480
$290$		−	272.310i		−	0.938999i
$291$	294.994	−	32.9152i	1.01373	−	0.113111i
$292$	−28.7862			−0.0985828
$293$			53.8078i			0.183644i	0.995775	+	0.0918221i	$0.0292691\pi$
$293$			53.8078i			0.183644i	−0.995775	+	0.0918221i	$0.970731\pi$
$294$	−29.5637	−	264.957i	−0.100557	−	0.901214i
$295$	−39.6143			−0.134286
$296$		−	444.866i		−	1.50293i
$297$	136.068	+	392.938i	0.458140	+	1.32303i
$298$	−520.833			−1.74776
$299$		−	297.846i		−	0.996139i
$300$	−2.52043	+	0.281228i	−0.00840144	+	0.000937426i
$301$	−42.5748			−0.141444
$302$			298.569i			0.988638i
$303$	−3.72547	−	33.3886i	−0.0122953	−	0.110193i
$304$	−60.8323			−0.200106
$305$		−	431.744i		−	1.41555i
$306$	91.2334	−	20.6162i	0.298148	−	0.0673731i
$307$	203.837			0.663963			0.331982	−	0.943286i	$-0.392283\pi$
$307$	203.837			0.663963			0.331982	+	0.943286i	$0.392283\pi$
$308$			21.9220i			0.0711752i
$309$	307.289	−	34.2871i	0.994464	−	0.110962i
$310$	307.664			0.992464
$311$			503.727i			1.61970i	0.586636	+	0.809851i	$0.300452\pi$
$311$			503.727i			1.61970i	−0.586636	+	0.809851i	$0.699548\pi$
$312$	45.8375	+	410.807i	0.146915	+	1.31669i
$313$	212.727			0.679638			0.339819	−	0.940491i	$-0.389634\pi$
$313$	212.727			0.679638			0.339819	+	0.940491i	$0.389634\pi$
$314$		−	214.985i		−	0.684665i
$315$	27.5315	+	121.836i	0.0874015	+	0.386780i
$316$	65.3739			0.206879
$317$		−	460.556i		−	1.45286i	−0.687242	−	0.726428i	$-0.741179\pi$
$317$		−	460.556i		−	1.45286i	0.687242	−	0.726428i	$-0.258821\pi$
$318$	−222.307	+	24.8048i	−0.699078	+	0.0780026i
$319$	−382.112			−1.19784
$320$		−	275.643i		−	0.861385i
$321$	52.9732	+	474.759i	0.165026	+	1.47900i
$322$	−91.4465			−0.283995
$323$			16.6558i			0.0515658i
$324$	−38.6811	+	18.4224i	−0.119386	+	0.0568593i
$325$	−29.8111			−0.0917263
$326$		−	78.0961i		−	0.239559i
$327$	318.633	−	35.5529i	0.974414	−	0.108724i
$328$	277.871			0.847166
$329$		−	35.3773i		−	0.107530i
$330$	56.2335	+	503.978i	0.170404	+	1.52721i
$331$	−414.786			−1.25313			−0.626565	−	0.779369i	$-0.715540\pi$
$331$	−414.786			−1.25313			−0.626565	+	0.779369i	$0.715540\pi$
$332$		−	75.8876i		−	0.228577i
$333$	528.685	−	119.468i	1.58764	−	0.358763i
$334$	194.917			0.583585
$335$			375.602i			1.12120i
$336$	143.104	−	15.9675i	0.425905	−	0.0475222i
$337$	−343.388			−1.01896			−0.509478	−	0.860484i	$-0.670161\pi$
$337$	−343.388			−1.01896			−0.509478	+	0.860484i	$0.670161\pi$
$338$		−	380.776i		−	1.12656i
$339$	−54.5563	−	488.947i	−0.160933	−	1.44232i
$340$	13.3217			0.0391814
$341$		−	431.723i		−	1.26605i
$342$	−14.3985	−	63.7182i	−0.0421009	−	0.186311i
$343$	−244.235			−0.712054
$344$			116.867i			0.339730i
$345$	−245.532	+	27.3963i	−0.711688	+	0.0794096i
$346$	68.8038			0.198855
$347$			6.99097i			0.0201469i	0.999949	+	0.0100734i	$0.00320653\pi$
$347$			6.99097i			0.0201469i	−0.999949	+	0.0100734i	$0.996793\pi$
$348$	−4.36579	−	39.1272i	−0.0125454	−	0.112435i
$349$	−445.031			−1.27516			−0.637580	−	0.770384i	$-0.720065\pi$
$349$	−445.031			−1.27516			−0.637580	+	0.770384i	$0.720065\pi$
$350$			9.15279i			0.0261508i
$351$	−475.899	+	164.795i	−1.35584	+	0.469502i
$352$	129.521			0.367956
$353$			247.520i			0.701190i	0.936527	+	0.350595i	$0.114021\pi$
$353$			247.520i			0.701190i	−0.936527	+	0.350595i	$0.885979\pi$
$354$	−48.7370	+	5.43804i	−0.137675	+	0.0153617i
$355$	−142.948			−0.402672
$356$			11.5535i			0.0324537i
$357$	−4.37186	−	39.1816i	−0.0122461	−	0.109752i
$358$	565.238			1.57888
$359$		−	336.875i		−	0.938370i	−0.883100	−	0.469185i	$-0.844548\pi$
$359$		−	336.875i		−	0.938370i	0.883100	−	0.469185i	$-0.155452\pi$
$360$	334.437	−	75.5734i	0.928993	−	0.209926i
$361$	−349.367			−0.967777
$362$			444.425i			1.22769i
$363$	346.435	−	38.6549i	0.954365	−	0.106487i
$364$	−26.5503			−0.0729404
$365$			280.675i			0.768973i
$366$	−59.2674	−	531.169i	−0.161933	−	1.45128i
$367$	−407.857			−1.11133			−0.555663	−	0.831407i	$-0.687536\pi$
$367$	−407.857			−1.11133			−0.555663	+	0.831407i	$0.687536\pi$
$368$			284.803i			0.773922i
$369$	74.6216	+	330.225i	0.202227	+	0.894919i
$370$	660.988			1.78645
$371$			94.2846i			0.254136i
$372$	44.2071	−	4.93260i	0.118836	−	0.0132597i
$373$	−86.5149			−0.231943			−0.115972	−	0.993253i	$-0.536998\pi$
$373$	−86.5149			−0.231943			−0.115972	+	0.993253i	$0.536998\pi$
$374$		−	160.058i		−	0.427963i
$375$	−40.1507	−	359.840i	−0.107069	−	0.959574i
$376$	−97.1101			−0.258272
$377$		−	462.787i		−	1.22755i
$378$	50.5966	+	146.114i	0.133853	+	0.386544i
$379$	−444.400			−1.17256			−0.586279	−	0.810109i	$-0.699408\pi$
$379$	−444.400			−1.17256			−0.586279	+	0.810109i	$0.699408\pi$
$380$		−	9.30399i		−	0.0244842i
$381$	−448.914	+	50.0895i	−1.17825	+	0.131469i
$382$	−75.0517			−0.196470
$383$			11.2111i			0.0292719i	0.999893	+	0.0146359i	$0.00465893\pi$
$383$			11.2111i			0.0292719i	−0.999893	+	0.0146359i	$0.995341\pi$
$384$	−49.0297	−	439.416i	−0.127681	−	1.14431i
$385$	213.747			0.555186
$386$		−	52.9463i		−	0.137167i
$387$	−138.886	+	31.3844i	−0.358879	+	0.0810966i
$388$	52.3341			0.134882
$389$		−	343.975i		−	0.884255i	−0.896952	−	0.442127i	$-0.854224\pi$
$389$		−	343.975i		−	0.884255i	0.896952	−	0.442127i	$-0.145776\pi$
$390$	−610.382	+	68.1060i	−1.56508	+	0.174631i
$391$	77.9786			0.199434
$392$			308.463i			0.786895i
$393$	81.8196	+	733.287i	0.208192	+	1.86587i
$394$	57.2649			0.145343
$395$		−	637.418i		−	1.61372i
$396$	16.1600	+	71.5133i	0.0408080	+	0.180589i
$397$	1.87556			0.00472433			0.00236216	−	0.999997i	$-0.499248\pi$
$397$	1.87556			0.00472433			0.00236216	+	0.999997i	$0.499248\pi$
$398$			303.416i			0.762353i
$399$	−27.3648	+	3.05335i	−0.0685835	+	0.00765250i
$400$	28.5057			0.0712642
$401$		−	366.293i		−	0.913450i	−0.889608	−	0.456725i	$-0.849022\pi$
$401$		−	366.293i		−	0.913450i	0.889608	−	0.456725i	$-0.150978\pi$
$402$	51.5606	+	462.098i	0.128260	+	1.14950i
$403$	522.872			1.29745
$404$		−	5.92338i		−	0.0146618i
$405$	179.625	+	377.155i	0.443518	+	0.931246i
$406$	−142.088			−0.349971
$407$		−	927.517i		−	2.27891i
$408$	−107.553	+	12.0007i	−0.263610	+	0.0294134i
$409$	−246.497			−0.602682			−0.301341	−	0.953516i	$-0.597434\pi$
$409$	−246.497			−0.602682			−0.301341	+	0.953516i	$0.597434\pi$
$410$			412.864i			1.00698i
$411$	−65.2172	−	584.492i	−0.158679	−	1.42212i
$412$	54.5154			0.132319
$413$			20.6703i			0.0500492i
$414$	−298.315	+	67.4107i	−0.720567	+	0.162828i
$415$	−739.931			−1.78297
$416$			156.866i			0.377082i
$417$	−243.355	+	27.1534i	−0.583586	+	0.0651161i
$418$	−111.786			−0.267431
$419$			560.527i			1.33777i	0.743364	+	0.668887i	$0.233229\pi$
$419$			560.527i			1.33777i	−0.743364	+	0.668887i	$0.766771\pi$
$420$	2.44214	+	21.8871i	0.00581462	+	0.0521120i
$421$	657.045			1.56068			0.780339	−	0.625357i	$-0.215047\pi$
$421$	657.045			1.56068			0.780339	+	0.625357i	$0.215047\pi$
$422$		−	594.452i		−	1.40865i
$423$	−26.0787	−	115.407i	−0.0616518	−	0.272830i
$424$	258.810			0.610400
$425$		−	7.80480i		−	0.0183642i
$426$	−175.868	+	19.6232i	−0.412835	+	0.0460638i
$427$	−225.279			−0.527586
$428$			84.2256i			0.196789i
$429$	95.5682	+	856.505i	0.222770	+	1.99652i
$430$	−173.642			−0.403820
$431$			805.638i			1.86923i	0.355662	+	0.934615i	$0.384255\pi$
$431$			805.638i			1.86923i	−0.355662	+	0.934615i	$0.615745\pi$
$432$	455.060	−	157.579i	1.05338	−	0.364767i
$433$	17.6191			0.0406907			0.0203454	−	0.999793i	$-0.493523\pi$
$433$	17.6191			0.0406907			0.0203454	+	0.999793i	$0.493523\pi$
$434$		−	160.536i		−	0.369898i
$435$	−381.504	+	42.5679i	−0.877021	+	0.0978574i
$436$	56.5279			0.129651
$437$		−	54.4610i		−	0.124625i
$438$	38.5296	+	345.311i	0.0879670	+	0.788382i
$439$	−159.746			−0.363887			−0.181943	−	0.983309i	$-0.558239\pi$
$439$	−159.746			−0.363887			−0.181943	+	0.983309i	$0.558239\pi$
$440$		−	586.731i		−	1.33348i
$441$	−366.582	+	82.8371i	−0.831251	+	0.187839i
$442$	193.851			0.438577
$443$			421.604i			0.951702i	0.879526	+	0.475851i	$0.157860\pi$
$443$			421.604i			0.951702i	−0.879526	+	0.475851i	$0.842140\pi$
$444$	94.9750	−	10.5972i	0.213908	−	0.0238677i
$445$	112.651			0.253148
$446$			402.681i			0.902872i
$447$	81.4175	+	729.684i	0.182142	+	1.63240i
$448$	−143.828			−0.321044
$449$			148.008i			0.329638i	0.986324	+	0.164819i	$0.0527040\pi$
$449$			148.008i			0.329638i	−0.986324	+	0.164819i	$0.947296\pi$
$450$	6.74707	+	29.8580i	0.0149935	+	0.0663511i
$451$	579.342			1.28457
$452$		−	86.7428i		−	0.191909i
$453$	418.293	−	46.6728i	0.923384	−	0.103030i
$454$	−825.799			−1.81894
$455$			258.875i			0.568956i
$456$	8.38138	+	75.1160i	0.0183802	+	0.164728i
$457$	−47.4974			−0.103933			−0.0519665	−	0.998649i	$-0.516549\pi$
$457$	−47.4974			−0.103933			−0.0519665	+	0.998649i	$0.516549\pi$
$458$		−	803.213i		−	1.75374i
$459$	−43.1449	−	124.595i	−0.0939976	−	0.271448i
$460$	−43.5592			−0.0946940
$461$			510.179i			1.10668i	0.832956	+	0.553340i	$0.186647\pi$
$461$			510.179i			1.10668i	−0.832956	+	0.553340i	$0.813353\pi$
$462$	262.970	−	29.3420i	0.569199	−	0.0635108i
$463$	470.002			1.01512			0.507562	−	0.861615i	$-0.330547\pi$
$463$	470.002			1.01512			0.507562	+	0.861615i	$0.330547\pi$
$464$			442.523i			0.953713i
$465$	−48.0946	−	431.035i	−0.103429	−	0.926958i
$466$	786.238			1.68721
$467$			534.667i			1.14490i	0.819941	+	0.572449i	$0.194006\pi$
$467$			534.667i			1.14490i	−0.819941	+	0.572449i	$0.805994\pi$
$468$	−86.6118	+	19.5718i	−0.185068	+	0.0418201i
$469$	195.985			0.417878
$470$		−	144.287i		−	0.306994i
$471$	−301.192	+	33.6068i	−0.639474	+	0.0713521i
$472$	56.7396			0.120211
$473$			243.660i			0.515137i
$474$	−87.5013	−	784.207i	−0.184602	−	1.65445i
$475$	−5.45095			−0.0114757
$476$		−	6.95111i		−	0.0146032i
$477$	69.5028	+	307.573i	0.145708	+	0.644807i
$478$	971.775			2.03300
$479$		−	399.048i		−	0.833085i	−0.909116	−	0.416542i	$-0.863242\pi$
$479$		−	399.048i		−	0.833085i	0.909116	−	0.416542i	$-0.136758\pi$
$480$	129.314	−	14.4288i	0.269405	−	0.0300600i
$481$	1123.34			2.33543
$482$			471.273i			0.977744i
$483$	14.2951	+	128.116i	0.0295965	+	0.265251i
$484$	61.4600			0.126983
$485$		−	510.276i		−	1.05212i
$486$	272.764	+	439.351i	0.561243	+	0.904014i
$487$	−461.325			−0.947279			−0.473639	−	0.880719i	$-0.657060\pi$
$487$	−461.325			−0.947279			−0.473639	+	0.880719i	$0.657060\pi$
$488$			618.387i			1.26719i
$489$	−109.412	+	12.2081i	−0.223747	+	0.0249655i
$490$	−458.318			−0.935343
$491$			660.058i			1.34431i	0.740409	+	0.672156i	$0.234632\pi$
$491$			660.058i			1.34431i	−0.740409	+	0.672156i	$0.765368\pi$
$492$	6.61920	+	59.3229i	0.0134537	+	0.120575i
$493$	121.162			0.245764
$494$		−	135.387i		−	0.274064i
$495$	697.280	−	157.566i	1.40865	−	0.318314i
$496$	−499.976			−1.00802
$497$			74.5889i			0.150078i
$498$	−910.327	+	101.574i	−1.82797	+	0.203963i
$499$	131.114			0.262754			0.131377	−	0.991332i	$-0.458060\pi$
$499$	131.114			0.262754			0.131377	+	0.991332i	$0.458060\pi$
$500$		−	63.8383i		−	0.127677i
$501$	−30.4698	−	273.078i	−0.0608180	−	0.545066i
$502$	−522.603			−1.04104
$503$			7.20522i			0.0143245i	0.999974	+	0.00716225i	$0.00227983\pi$
$503$			7.20522i			0.0143245i	−0.999974	+	0.00716225i	$0.997720\pi$
$504$	−39.4333	−	174.506i	−0.0782408	−	0.346241i
$505$	−57.7551			−0.114366
$506$			523.358i			1.03430i
$507$	−533.465	+	59.5236i	−1.05220	+	0.117404i
$508$	−79.6407			−0.156773
$509$			155.141i			0.304796i	0.988319	+	0.152398i	$0.0486995\pi$
$509$			155.141i			0.304796i	−0.988319	+	0.152398i	$0.951300\pi$
$510$	−17.8308	−	159.803i	−0.0349623	−	0.313340i
$511$	146.453			0.286601
$512$			377.011i			0.736350i
$513$	−87.0180	+	30.1328i	−0.169626	+	0.0587384i
$514$	101.323			0.197126
$515$		−	531.544i		−	1.03212i
$516$	−24.9501	+	2.78391i	−0.0483529	+	0.00539517i
$517$	−202.468			−0.391621
$518$		−	344.896i		−	0.665822i
$519$	−10.7555	−	96.3936i	−0.0207236	−	0.185730i
$520$	710.607			1.36655
$521$			453.960i			0.871323i	0.900110	+	0.435662i	$0.143486\pi$
$521$			453.960i			0.871323i	−0.900110	+	0.435662i	$0.856514\pi$
$522$	−463.516	+	104.742i	−0.887962	+	0.200654i
$523$	198.044			0.378670			0.189335	−	0.981913i	$-0.439367\pi$
$523$	198.044			0.378670			0.189335	+	0.981913i	$0.439367\pi$
$524$			130.090i			0.248264i
$525$	12.8230	−	1.43078i	0.0244248	−	0.00272530i
$526$	51.9045			0.0986778
$527$			136.892i			0.259758i
$528$	−91.3834	−	819.000i	−0.173075	−	1.55114i
$529$	274.026			0.518007
$530$			384.543i			0.725552i
$531$	15.2373	+	67.4301i	0.0286955	+	0.126987i
$532$	−4.85472			−0.00912541
$533$			701.657i			1.31643i
$534$	138.593	−	15.4641i	0.259538	−	0.0289590i
$535$	821.230			1.53501
$536$		−	537.975i		−	1.00368i
$537$	−88.3590	−	791.895i	−0.164542	−	1.47466i
$538$	165.386			0.307409
$539$			643.125i			1.19318i
$540$	24.1009	+	69.5992i	0.0446314	+	0.128887i
$541$	−283.459			−0.523954			−0.261977	−	0.965074i	$-0.584374\pi$
$541$	−283.459			−0.523954			−0.261977	+	0.965074i	$0.584374\pi$
$542$		−	851.592i		−	1.57120i
$543$	622.637	−	69.4733i	1.14666	−	0.127944i
$544$	−41.0690			−0.0754944
$545$		−	551.167i		−	1.01131i
$546$	35.5369	+	318.490i	0.0650859	+	0.583316i
$547$	35.6589			0.0651899			0.0325949	−	0.999469i	$-0.489623\pi$
$547$	35.6589			0.0651899			0.0325949	+	0.999469i	$0.489623\pi$
$548$		−	103.693i		−	0.189221i
$549$	−734.900	+	166.067i	−1.33862	+	0.302489i
$550$	52.3824			0.0952407
$551$		−	84.6206i		−	0.153576i
$552$	351.676	−	39.2398i	0.637095	−	0.0710865i
$553$	−332.598			−0.601442
$554$		−	845.723i		−	1.52658i
$555$	−103.327	−	926.040i	−0.186175	−	1.66854i
$556$	−43.1730			−0.0776493
$557$			105.727i			0.189816i	0.995486	+	0.0949078i	$0.0302556\pi$
$557$			105.727i			0.189816i	−0.995486	+	0.0949078i	$0.969744\pi$
$558$	−118.340	−	523.695i	−0.212079	−	0.938522i
$559$	−295.104			−0.527913
$560$		−	247.539i		−	0.442034i
$561$	−224.241	+	25.0206i	−0.399716	+	0.0446000i
$562$	178.041			0.316799
$563$		−	521.415i		−	0.926137i	−0.886323	−	0.463068i	$-0.846748\pi$
$563$		−	521.415i		−	0.926137i	0.886323	−	0.463068i	$-0.153252\pi$
$564$	−2.31328	−	20.7321i	−0.00410155	−	0.0367591i
$565$	−845.773			−1.49694
$566$			224.065i			0.395874i
$567$	196.795	−	93.7262i	0.347081	−	0.165302i
$568$	204.745			0.360467
$569$		−	646.759i		−	1.13666i	−0.822801	−	0.568330i	$-0.807590\pi$
$569$		−	646.759i		−	1.13666i	0.822801	−	0.568330i	$-0.192410\pi$
$570$	−111.608	+	12.4532i	−0.195804	+	0.0218477i
$571$	−1073.49			−1.88002			−0.940010	−	0.341146i	$-0.889185\pi$
$571$	−1073.49			−1.88002			−0.940010	+	0.341146i	$0.889185\pi$
$572$			151.950i			0.265647i
$573$	11.7322	+	105.147i	0.0204751	+	0.183503i
$574$	215.427			0.375309
$575$			25.5201i			0.0443828i
$576$	−469.191	+	106.024i	−0.814567	+	0.184069i
$577$	−495.612			−0.858947			−0.429473	−	0.903079i	$-0.641301\pi$
$577$	−495.612			−0.858947			−0.429473	+	0.903079i	$0.641301\pi$
$578$		−	564.278i		−	0.976259i
$579$	−74.1775	+	8.27667i	−0.128113	+	0.0142948i
$580$	−67.6816			−0.116692
$581$			386.087i			0.664522i
$582$	−70.0479	−	627.786i	−0.120357	−	1.07867i
$583$	539.601			0.925559
$584$		−	402.011i		−	0.688376i
$585$	190.832	+	844.495i	0.326209	+	1.44358i
$586$	114.510			0.195410
$587$		−	219.909i		−	0.374632i	−0.982300	−	0.187316i	$-0.940021\pi$
$587$		−	219.909i		−	0.374632i	0.982300	−	0.187316i	$-0.0599788\pi$
$588$	−65.8541	+	7.34795i	−0.111997	+	0.0124965i
$589$	95.6070			0.162321
$590$			84.3044i			0.142889i
$591$	−8.95176	−	80.2278i	−0.0151468	−	0.135749i
$592$	−1074.15			−1.81445
$593$			344.715i			0.581307i	0.956828	+	0.290654i	$0.0938728\pi$
$593$			344.715i			0.581307i	−0.956828	+	0.290654i	$0.906127\pi$
$594$	836.224	−	289.570i	1.40779	−	0.487491i
$595$	−67.7758			−0.113909
$596$			129.451i			0.217200i
$597$	425.084	−	47.4306i	0.712034	−	0.0794482i
$598$	−633.854			−1.05996
$599$		−	72.2992i		−	0.120700i	−0.998177	−	0.0603499i	$-0.980778\pi$
$599$		−	72.2992i		−	0.120700i	0.998177	−	0.0603499i	$-0.0192216\pi$
$600$	−3.92747	−	35.1989i	−0.00654578	−	0.0586649i
$601$	1109.43			1.84597			0.922985	−	0.384836i	$-0.125742\pi$
$601$	1109.43			1.84597			0.922985	+	0.384836i	$0.125742\pi$
$602$			90.6047i			0.150506i
$603$	639.337	−	144.472i	1.06026	−	0.239589i
$604$	74.2082			0.122861
$605$		−	599.257i		−	0.990507i
$606$	−71.0553	+	7.92830i	−0.117253	+	0.0130830i
$607$	−311.142			−0.512589			−0.256295	−	0.966599i	$-0.582502\pi$
$607$	−311.142			−0.512589			−0.256295	+	0.966599i	$0.582502\pi$
$608$			28.6829i			0.0471759i
$609$	22.2115	+	199.065i	0.0364720	+	0.326871i
$610$	−918.808			−1.50624
$611$		−	245.215i		−	0.401334i
$612$	−5.12408	−	22.6757i	−0.00837267	−	0.0370518i
$613$	−93.5672			−0.152638			−0.0763191	−	0.997083i	$-0.524317\pi$
$613$	−93.5672			−0.152638			−0.0763191	+	0.997083i	$0.524317\pi$
$614$		−	433.791i		−	0.706500i
$615$	578.419	−	64.5396i	0.940519	−	0.104942i
$616$	−306.150			−0.496996
$617$		−	837.167i		−	1.35683i	−0.734677	−	0.678417i	$-0.762666\pi$
$617$		−	837.167i		−	1.35683i	0.734677	−	0.678417i	$-0.237334\pi$
$618$	−72.9675	−	653.952i	−0.118070	−	1.05817i
$619$	416.723			0.673219			0.336609	−	0.941644i	$-0.390720\pi$
$619$	416.723			0.673219			0.336609	+	0.941644i	$0.390720\pi$
$620$		−	76.4688i		−	0.123337i
$621$	141.075	+	407.399i	0.227174	+	0.656037i
$622$	1072.00			1.72347
$623$		−	58.7800i		−	0.0943500i
$624$	991.915	−	110.677i	1.58961	−	0.177367i
$625$	−662.401			−1.05984
$626$		−	452.710i		−	0.723179i
$627$	17.4746	+	156.612i	0.0278702	+	0.249780i
$628$	−53.4337			−0.0850855
$629$			294.101i			0.467569i
$630$	259.283	−	58.5906i	0.411560	−	0.0930009i
$631$	609.967			0.966668			0.483334	−	0.875436i	$-0.339426\pi$
$631$	609.967			0.966668			0.483334	+	0.875436i	$0.339426\pi$
$632$			912.975i			1.44458i
$633$	−832.823	+	92.9258i	−1.31568	+	0.146802i
$634$	−980.122			−1.54593
$635$			776.525i			1.22287i
$636$	6.16515	+	55.2536i	0.00969363	+	0.0868767i
$637$	−778.907			−1.22277
$638$			813.185i			1.27458i
$639$	54.9839	+	243.322i	0.0860468	+	0.380786i
$640$	−760.094			−1.18765
$641$			1232.43i			1.92266i	0.275394	+	0.961331i	$0.411192\pi$
$641$			1232.43i			1.92266i	−0.275394	+	0.961331i	$0.588808\pi$
$642$	1010.35	−	112.734i	1.57375	−	0.175598i
$643$	−919.351			−1.42978			−0.714892	−	0.699235i	$-0.753524\pi$
$643$	−919.351			−1.42978			−0.714892	+	0.699235i	$0.753524\pi$
$644$			22.7287i			0.0352930i
$645$	27.1441	+	243.272i	0.0420839	+	0.377166i
$646$	35.4456			0.0548694
$647$			270.021i			0.417343i	0.977986	+	0.208671i	$0.0669139\pi$
$647$			270.021i			0.417343i	−0.977986	+	0.208671i	$0.933086\pi$
$648$	−257.277	−	540.199i	−0.397032	−	0.833641i
$649$	118.298			0.182278
$650$			63.4418i			0.0976028i
$651$	−224.909	+	25.0952i	−0.345483	+	0.0385487i
$652$	−19.4105			−0.0297707
$653$		−	430.290i		−	0.658943i	−0.944166	−	0.329472i	$-0.893129\pi$
$653$		−	430.290i		−	0.658943i	0.944166	−	0.329472i	$-0.106871\pi$
$654$	−75.6611	−	678.093i	−0.115690	−	1.03684i
$655$	1268.43			1.93653
$656$		−	670.933i		−	1.02276i
$657$	477.756	−	107.959i	0.727178	−	0.164322i
$658$	−75.2875			−0.114419
$659$		−	1083.87i		−	1.64473i	−0.568964	−	0.822363i	$-0.692656\pi$
$659$		−	1083.87i		−	1.64473i	0.568964	−	0.822363i	$-0.307344\pi$
$660$	125.262	−	13.9766i	0.189791	−	0.0211767i
$661$	−114.088			−0.172599			−0.0862996	−	0.996269i	$-0.527504\pi$
$661$	−114.088			−0.172599			−0.0862996	+	0.996269i	$0.527504\pi$
$662$			882.719i			1.33341i
$663$	−30.3032	−	271.584i	−0.0457061	−	0.409629i
$664$	1059.80			1.59609
$665$			47.3352i			0.0711808i
$666$	−254.243	−	1125.11i	−0.381747	−	1.68936i
$667$	−396.175			−0.593965
$668$		−	48.4460i		−	0.0725239i
$669$	564.153	−	62.9478i	0.843279	−	0.0940924i
$670$	799.330			1.19303
$671$			1289.30i			1.92145i
$672$	−7.52879	−	67.4748i	−0.0112036	−	0.100409i
$673$	340.904			0.506544			0.253272	−	0.967395i	$-0.418493\pi$
$673$	340.904			0.506544			0.253272	+	0.967395i	$0.418493\pi$
$674$			730.775i			1.08424i
$675$	40.7762	−	14.1201i	0.0604091	−	0.0209186i
$676$	−94.6406			−0.140001
$677$		−	905.939i		−	1.33817i	−0.743187	−	0.669084i	$-0.766687\pi$
$677$		−	905.939i		−	1.33817i	0.743187	−	0.669084i	$-0.233313\pi$
$678$	−1040.54	+	116.103i	−1.53472	+	0.171243i
$679$	−266.256			−0.392130
$680$			186.043i			0.273593i
$681$	129.090	+	1156.94i	0.189560	+	1.69888i
$682$	−918.762			−1.34716
$683$			172.470i			0.252518i	0.991997	+	0.126259i	$0.0402970\pi$
$683$			172.470i			0.252518i	−0.991997	+	0.126259i	$0.959703\pi$
$684$	−15.8369	+	3.57870i	−0.0231534	+	0.00523202i
$685$	−1011.05			−1.47598
$686$			519.763i			0.757672i
$687$	−1125.30	+	125.560i	−1.63799	+	0.182765i
$688$	282.181			0.410147
$689$			653.526i			0.948514i
$690$	58.3029	+	522.525i	0.0844970	+	0.757283i
$691$	−762.162			−1.10298			−0.551492	−	0.834180i	$-0.685941\pi$
$691$	−762.162			−1.10298			−0.551492	+	0.834180i	$0.685941\pi$
$692$		−	17.1009i		−	0.0247123i
$693$	−82.2159	−	363.832i	−0.118638	−	0.525011i
$694$	14.8777			0.0214376
$695$			420.952i			0.605687i
$696$	546.429	−	60.9701i	0.785099	−	0.0876007i
$697$	−183.700			−0.263558
$698$			947.084i			1.35685i
$699$	−122.906	−	1101.51i	−0.175831	−	1.57584i
$700$	2.27489			0.00324985
$701$		−	1223.58i		−	1.74548i	−0.488188	−	0.872739i	$-0.662342\pi$
$701$		−	1223.58i		−	1.74548i	0.488188	−	0.872739i	$-0.337658\pi$
$702$	350.706	+	1012.78i	0.499581	+	1.44270i
$703$	205.403			0.292180
$704$			823.140i			1.16923i
$705$	−202.146	+	22.5553i	−0.286732	+	0.0319933i
$706$	526.755			0.746112
$707$			30.1359i			0.0426251i
$708$	1.35160	+	12.1134i	0.00190905	+	0.0171093i
$709$	110.240			0.155487			0.0777435	−	0.996973i	$-0.475228\pi$
$709$	110.240			0.155487			0.0777435	+	0.996973i	$0.475228\pi$
$710$			304.213i			0.428469i
$711$	−1084.99	+	245.177i	−1.52601	+	0.344835i
$712$	−161.350			−0.226615
$713$		−	447.611i		−	0.627785i
$714$	−83.3836	+	9.30388i	−0.116784	+	0.0130306i
$715$	1481.57			2.07212
$716$		−	140.488i		−	0.196212i
$717$	−151.910	−	1361.45i	−0.211868	−	1.89882i
$718$	−716.914			−0.998487
$719$		−	663.517i		−	0.922834i	−0.887183	−	0.461417i	$-0.847341\pi$
$719$		−	663.517i		−	0.922834i	0.887183	−	0.461417i	$-0.152659\pi$
$720$	−182.476	−	807.516i	−0.253439	−	1.12155i
$721$	−277.354			−0.384679
$722$			743.500i			1.02978i
$723$	660.250	−	73.6702i	0.913209	−	0.101895i
$724$	110.460			0.152569
$725$			39.6527i			0.0546934i
$726$	−82.2627	−	737.258i	−0.113309	−	1.01551i
$727$	684.753			0.941889			0.470944	−	0.882163i	$-0.343913\pi$
$727$	684.753			0.941889			0.470944	+	0.882163i	$0.343913\pi$
$728$		−	370.787i		−	0.509322i
$729$	572.889	−	450.821i	0.785856	−	0.618410i
$730$	597.314			0.818238
$731$		−	77.2607i		−	0.105692i
$732$	−132.020	+	14.7307i	−0.180355	+	0.0201239i
$733$	981.794			1.33942			0.669709	−	0.742624i	$-0.266419\pi$
$733$	981.794			1.33942			0.669709	+	0.742624i	$0.266419\pi$
$734$			867.973i			1.18252i
$735$	71.6451	+	642.101i	0.0974764	+	0.873607i
$736$	134.287			0.182455
$737$		−	1121.64i		−	1.52190i
$738$	702.762	−	158.804i	0.952252	−	0.215182i
$739$	820.477			1.11025			0.555126	−	0.831766i	$-0.312670\pi$
$739$	820.477			1.11025			0.555126	+	0.831766i	$0.312670\pi$
$740$		−	164.286i		−	0.222008i
$741$	−189.677	+	21.1640i	−0.255974	+	0.0285614i
$742$	200.650			0.270418
$743$			252.899i			0.340376i	0.985412	+	0.170188i	$0.0544374\pi$
$743$			252.899i			0.340376i	−0.985412	+	0.170188i	$0.945563\pi$
$744$	68.8859	+	617.372i	0.0925886	+	0.829801i
$745$	1262.19			1.69422
$746$			184.115i			0.246803i
$747$	284.608	+	1259.48i	0.381001	+	1.68606i
$748$	−39.7819			−0.0531844
$749$		−	428.508i		−	0.572107i
$750$	−765.787	+	85.4459i	−1.02105	+	0.113928i
$751$	565.853			0.753466			0.376733	−	0.926322i	$-0.377047\pi$
$751$	565.853			0.753466			0.376733	+	0.926322i	$0.377047\pi$
$752$			234.477i			0.311805i
$753$	81.6942	+	732.163i	0.108492	+	0.972328i
$754$	−984.872			−1.30620
$755$		−	723.556i		−	0.958352i
$756$	36.3160	−	12.5756i	0.0480371	−	0.0166344i
$757$	366.712			0.484428			0.242214	−	0.970223i	$-0.422126\pi$
$757$	366.712			0.484428			0.242214	+	0.970223i	$0.422126\pi$
$758$			945.740i			1.24768i
$759$	733.222	−	81.8123i	0.966036	−	0.107790i
$760$	129.934			0.170966
$761$		−	246.039i		−	0.323310i	−0.986847	−	0.161655i	$-0.948317\pi$
$761$		−	246.039i		−	0.323310i	0.986847	−	0.161655i	$-0.0516832\pi$
$762$	106.597	+	955.348i	0.139891	+	1.25374i
$763$	−287.592			−0.376923
$764$			18.6538i			0.0244160i
$765$	−221.096	+	49.9615i	−0.289015	+	0.0653092i
$766$	23.8587			0.0311472
$767$			143.275i			0.186799i
$768$	−297.729	+	33.2204i	−0.387668	+	0.0432557i
$769$	1153.63			1.50017			0.750083	−	0.661344i	$-0.230014\pi$
$769$	1153.63			1.50017			0.750083	+	0.661344i	$0.230014\pi$
$770$		−	454.881i		−	0.590755i
$771$	−15.8390	−	141.953i	−0.0205434	−	0.184115i
$772$	−13.1596			−0.0170461
$773$			841.471i			1.08858i	0.838898	+	0.544289i	$0.183200\pi$
$773$			841.471i			1.08858i	−0.838898	+	0.544289i	$0.816800\pi$
$774$	66.7901	+	295.568i	0.0862921	+	0.381871i
$775$	−44.8009			−0.0578076
$776$			730.869i			0.941842i
$777$	−483.197	+	53.9148i	−0.621875	+	0.0693884i
$778$	−732.024			−0.940905
$779$			128.298i			0.164696i
$780$	16.9275	+	151.708i	0.0217019	+	0.194498i
$781$	426.880			0.546581
$782$		−	165.949i		−	0.212211i
$783$	219.200	+	633.010i	0.279949	+	0.808442i
$784$	744.800			0.950000
$785$			520.998i			0.663691i
$786$	1560.53	−	174.123i	1.98541	−	0.221530i
$787$	222.739			0.283023			0.141512	−	0.989937i	$-0.454804\pi$
$787$	222.739			0.283023			0.141512	+	0.989937i	$0.454804\pi$
$788$		−	14.2330i		−	0.0180622i
$789$	−8.11381	−	72.7179i	−0.0102837	−	0.0921647i
$790$	−1356.51			−1.71710
$791$			441.314i			0.557920i
$792$	−998.714	+	225.681i	−1.26100	+	0.284951i
$793$	−1561.50			−1.96911
$794$		−	3.99143i		−	0.00502699i
$795$	538.742	−	60.1124i	0.677663	−	0.0756131i
$796$	75.4131			0.0947400
$797$		−	259.737i		−	0.325893i	−0.986635	−	0.162947i	$-0.947900\pi$
$797$		−	259.737i		−	0.325893i	0.986635	−	0.162947i	$-0.0520998\pi$
$798$	6.49792	+	58.2359i	0.00814275	+	0.0729773i
$799$	64.1994			0.0803497
$800$		−	13.4407i		−	0.0168008i
$801$	−43.3303	−	191.751i	−0.0540952	−	0.239389i
$802$	−779.520			−0.971970
$803$		−	838.167i		−	1.04379i
$804$	114.853	−	12.8152i	0.142852	−	0.0159393i
$805$	221.613			0.275296
$806$		−	1112.74i		−	1.38057i
$807$	−25.8535	−	231.705i	−0.0320365	−	0.287119i
$808$	82.7226			0.102379
$809$		−	1444.65i		−	1.78572i	−0.450333	−	0.892860i	$-0.648695\pi$
$809$		−	1444.65i		−	1.78572i	0.450333	−	0.892860i	$-0.351305\pi$
$810$	802.635	−	382.265i	0.990907	−	0.471932i
$811$	−513.040			−0.632602			−0.316301	−	0.948659i	$-0.602441\pi$
$811$	−513.040			−0.632602			−0.316301	+	0.948659i	$0.602441\pi$
$812$			35.3155i			0.0434920i
$813$	−1193.07	+	133.122i	−1.46750	+	0.163742i
$814$	−1973.88			−2.42491
$815$			189.259i			0.232220i
$816$	28.9763	+	259.692i	0.0355101	+	0.318250i
$817$	−53.9596			−0.0660460
$818$			524.577i			0.641293i
$819$	440.648	−	99.5740i	0.538032	−	0.121580i
$820$	102.616			0.125141
$821$		−	775.725i		−	0.944854i	−0.881370	−	0.472427i	$-0.843378\pi$
$821$		−	775.725i		−	0.944854i	0.881370	−	0.472427i	$-0.156622\pi$
$822$	−1243.88	+	138.791i	−1.51323	+	0.168845i
$823$	−1214.21			−1.47534			−0.737671	−	0.675161i	$-0.764074\pi$
$823$	−1214.21			−1.47534			−0.737671	+	0.675161i	$0.764074\pi$
$824$			761.331i			0.923946i
$825$	−8.18851	−	73.3874i	−0.00992547	−	0.0889544i
$826$	43.9891			0.0532556
$827$		−	389.723i		−	0.471249i	−0.971844	−	0.235625i	$-0.924286\pi$
$827$		−	389.723i		−	0.471249i	0.971844	−	0.235625i	$-0.0757136\pi$
$828$	16.7547	+	74.1450i	0.0202351	+	0.0895472i
$829$	11.2777			0.0136040			0.00680200	−	0.999977i	$-0.497835\pi$
$829$	11.2777			0.0136040			0.00680200	+	0.999977i	$0.497835\pi$
$830$			1574.67i			1.89719i
$831$	−1184.85	+	132.205i	−1.42582	+	0.159091i
$832$	−996.929			−1.19823
$833$		−	203.925i		−	0.244808i
$834$	57.7860	+	517.892i	0.0692878	+	0.620974i
$835$	−472.366			−0.565707
$836$			27.7841i			0.0332345i
$837$	−715.194	+	247.659i	−0.854474	+	0.295889i
$838$	1192.87			1.42348
$839$			548.329i			0.653551i	0.945102	+	0.326775i	$0.105962\pi$
$839$			548.329i			0.653551i	−0.945102	+	0.326775i	$0.894038\pi$
$840$	−305.662	+	34.1056i	−0.363884	+	0.0406019i
$841$	225.430			0.268050
$842$		−	1398.28i		−	1.66066i
$843$	−27.8317	−	249.434i	−0.0330150	−	0.295889i
$844$	−147.749			−0.175058
$845$			922.779i			1.09205i
$846$	−245.601	+	55.4989i	−0.290309	+	0.0656016i
$847$	−312.685			−0.369168
$848$		−	624.909i		−	0.736921i
$849$	313.913	−	35.0262i	0.369745	−	0.0412558i
$850$	−16.6096			−0.0195407
$851$		−	961.651i		−	1.13002i
$852$	4.87727	+	43.7113i	0.00572450	+	0.0513043i
$853$	6.08304			0.00713135			0.00356568	−	0.999994i	$-0.498865\pi$
$853$	6.08304			0.00713135			0.00356568	+	0.999994i	$0.498865\pi$
$854$			479.423i			0.561386i
$855$	34.8936	+	154.416i	0.0408112	+	0.180603i
$856$	−1176.25			−1.37412
$857$		−	1092.14i		−	1.27438i	−0.770708	−	0.637189i	$-0.780097\pi$
$857$		−	1092.14i		−	1.27438i	0.770708	−	0.637189i	$-0.219903\pi$
$858$	1822.75	−	203.382i	2.12442	−	0.237041i
$859$	−840.237			−0.978157			−0.489079	−	0.872240i	$-0.662667\pi$
$859$	−840.237			−0.978157			−0.489079	+	0.872240i	$0.662667\pi$
$860$			43.1582i			0.0501840i
$861$	−33.6760	−	301.813i	−0.0391127	−	0.350537i
$862$	1714.50			1.98898
$863$			1387.20i			1.60742i	0.595020	+	0.803711i	$0.297144\pi$
$863$			1387.20i			1.60742i	−0.595020	+	0.803711i	$0.702856\pi$
$864$	−74.2999	−	214.565i	−0.0859953	−	0.248339i
$865$	−166.740			−0.192763
$866$		−	37.4957i		−	0.0432976i
$867$	−790.550	+	88.2089i	−0.911822	+	0.101740i
$868$	−39.9005			−0.0459684
$869$			1903.49i			2.19044i
$870$	90.5901	+	811.891i	0.104127	+	0.933208i
$871$	1358.45			1.55965
$872$			789.436i			0.905317i
$873$	−868.575	+	196.273i	−0.994931	+	0.224826i
$874$	−115.900			−0.132609
$875$			324.785i			0.371183i
$876$	85.8259	−	9.57639i	0.0979748	−	0.0109319i
$877$	−1158.78			−1.32129			−0.660647	−	0.750696i	$-0.729718\pi$
$877$	−1158.78			−1.32129			−0.660647	+	0.750696i	$0.729718\pi$
$878$			339.961i			0.387199i
$879$	−17.9004	−	160.428i	−0.0203645	−	0.182512i
$880$	−1416.69			−1.60988
$881$		−	1694.62i		−	1.92352i	−0.273886	−	0.961762i	$-0.588309\pi$
$881$		−	1694.62i		−	1.92352i	0.273886	−	0.961762i	$-0.411691\pi$
$882$	176.288	+	780.134i	0.199873	+	0.884505i
$883$	732.068			0.829069			0.414535	−	0.910034i	$-0.363944\pi$
$883$	732.068			0.829069			0.414535	+	0.910034i	$0.363944\pi$
$884$		−	48.1810i		−	0.0545034i
$885$	118.110	−	13.1786i	0.133458	−	0.0148911i
$886$	897.229			1.01267
$887$			558.719i			0.629897i	0.949109	+	0.314948i	$0.101987\pi$
$887$			558.719i			0.629897i	−0.949109	+	0.314948i	$0.898013\pi$
$888$	147.995	+	1326.37i	0.166661	+	1.49366i
$889$	405.182			0.455772
$890$		−	239.736i		−	0.269366i
$891$	−536.405	−	1126.28i	−0.602026	−	1.26406i
$892$	100.085			0.112203
$893$		−	44.8375i		−	0.0502099i
$894$	1552.86	−	173.267i	1.73698	−	0.193811i
$895$	−1369.81			−1.53051
$896$			396.608i			0.442643i
$897$	99.0852	+	888.026i	0.110463	+	0.989995i
$898$	314.979			0.350757
$899$		−	695.490i		−	0.773626i
$900$	7.42110	−	1.67696i	0.00824567	−	0.00186329i
$901$	−171.099			−0.189899
$902$		−	1232.91i		−	1.36687i
$903$	126.937	−	14.1635i	0.140572	−	0.0156849i
$904$	1211.40			1.34005
$905$		−	1077.03i		−	1.19009i
$906$	−99.3258	−	890.182i	−0.109631	−	0.982540i
$907$	−528.797			−0.583018			−0.291509	−	0.956568i	$-0.594157\pi$
$907$	−528.797			−0.583018			−0.291509	+	0.956568i	$0.594157\pi$
$908$			205.250i			0.226046i
$909$	22.2150	+	98.3087i	0.0244389	+	0.108150i
$910$	550.920			0.605406
$911$			367.309i			0.403193i	0.979469	+	0.201597i	$0.0646130\pi$
$911$			367.309i			0.403193i	−0.979469	+	0.201597i	$0.935387\pi$
$912$	181.371	−	20.2373i	0.198872	−	0.0221900i
$913$	2209.62			2.42017
$914$			101.081i			0.110592i
$915$	143.630	+	1287.24i	0.156972	+	1.40682i
$916$	−199.636			−0.217943
$917$		−	661.851i		−	0.721757i
$918$	−265.154	+	91.8180i	−0.288838	+	0.100020i
$919$	44.5474			0.0484737			0.0242369	−	0.999706i	$-0.492284\pi$
$919$	44.5474			0.0484737			0.0242369	+	0.999706i	$0.492284\pi$
$920$		−	608.324i		−	0.661222i
$921$	−607.739	+	67.8110i	−0.659868	+	0.0736276i
$922$	1085.73			1.17758
$923$			517.007i			0.560137i
$924$	−7.29285	−	65.3603i	−0.00789269	−	0.0707362i
$925$	−96.2506			−0.104055
$926$		−	1000.23i		−	1.08016i
$927$	−904.776	+	204.454i	−0.976026	+	0.220554i
$928$	208.653			0.224842
$929$		−	804.136i		−	0.865593i	−0.901492	−	0.432797i	$-0.857527\pi$
$929$		−	804.136i		−	0.865593i	0.901492	−	0.432797i	$-0.142473\pi$
$930$	−917.299	+	102.352i	−0.986343	+	0.110055i
$931$	−142.423			−0.152978
$932$		−	195.417i		−	0.209674i
$933$	−167.577	−	1501.86i	−0.179610	−	1.60971i
$934$	1137.84			1.21825
$935$			387.888i			0.414853i
$936$	−273.329	−	1209.57i	−0.292018	−	1.29228i
$937$	1109.35			1.18394			0.591971	−	0.805959i	$-0.298350\pi$
$937$	1109.35			1.18394			0.591971	+	0.805959i	$0.298350\pi$
$938$		−	417.081i		−	0.444649i
$939$	−634.244	+	70.7684i	−0.675446	+	0.0753657i
$940$	−35.8621			−0.0381512
$941$		−	839.747i		−	0.892399i	−0.894934	−	0.446199i	$-0.852777\pi$
$941$		−	839.747i		−	0.892399i	0.894934	−	0.446199i	$-0.147223\pi$
$942$	71.5197	+	640.977i	0.0759232	+	0.680442i
$943$	600.662			0.636969
$944$		−	137.001i		−	0.145128i
$945$	−122.617	−	354.094i	−0.129753	−	0.374703i
$946$	518.540			0.548140
$947$		−	1351.11i		−	1.42673i	−0.700795	−	0.713363i	$-0.747171\pi$
$947$		−	1351.11i		−	1.42673i	0.700795	−	0.713363i	$-0.252829\pi$
$948$	−194.912	+	21.7481i	−0.205603	+	0.0229411i
$949$	1015.13			1.06968
$950$			11.6003i			0.0122109i
$951$	153.215	+	1373.15i	0.161109	+	1.44390i
$952$	97.0753			0.101970
$953$			67.8838i			0.0712317i	0.999366	+	0.0356158i	$0.0113393\pi$
$953$			67.8838i			0.0712317i	−0.999366	+	0.0356158i	$0.988661\pi$
$954$	654.555	−	147.911i	0.686117	−	0.155043i
$955$	181.882			0.190452
$956$		−	241.531i		−	0.252648i
$957$	1139.27	−	127.119i	1.19046	−	0.132830i
$958$	−849.225			−0.886457
$959$			527.552i			0.550106i
$960$	91.6992	+	821.830i	0.0955200	+	0.856073i
$961$	−175.214			−0.182325
$962$		−	2390.62i		−	2.48505i
$963$	−315.879	−	1397.87i	−0.328016	−	1.45158i
$964$	117.133			0.121507
$965$			128.311i			0.132965i
$966$	272.648	−	30.4218i	0.282244	−	0.0314926i
$967$	−1412.99			−1.46121			−0.730604	−	0.682801i	$-0.760761\pi$
$967$	−1412.99			−1.46121			−0.730604	+	0.682801i	$0.760761\pi$
$968$			858.316i			0.886690i
$969$	−5.54093	−	49.6591i	−0.00571819	−	0.0512478i
$970$	−1085.93			−1.11952
$971$			652.618i			0.672109i	0.941842	+	0.336055i	$0.109093\pi$
$971$			652.618i			0.672109i	−0.941842	+	0.336055i	$0.890907\pi$
$972$	109.199	−	67.7945i	0.112345	−	0.0697475i
$973$	219.648			0.225743
$974$			981.760i			1.00797i
$975$	88.8816	−	9.91734i	0.0911606	−	0.0101716i
$976$	1493.13			1.52984
$977$		−	1596.53i		−	1.63412i	−0.576554	−	0.817059i	$-0.695603\pi$
$977$		−	1596.53i		−	1.63412i	0.576554	−	0.817059i	$-0.304397\pi$
$978$	25.9805	+	232.843i	0.0265649	+	0.238081i
$979$	−336.404			−0.343620
$980$			113.913i			0.116238i
$981$	−938.177	+	212.002i	−0.956347	+	0.216108i
$982$	1404.69			1.43044
$983$		−	828.776i		−	0.843109i	−0.906803	−	0.421554i	$-0.861485\pi$
$983$		−	828.776i		−	0.843109i	0.906803	−	0.421554i	$-0.138515\pi$
$984$	−828.470	+	92.4401i	−0.841942	+	0.0939432i
$985$	−138.777			−0.140890
$986$		−	257.848i		−	0.261509i
$987$	11.7691	+	105.477i	0.0119241	+	0.106867i
$988$	−33.6501			−0.0340588
$989$			252.627i			0.255437i
$990$	−335.320	−	1483.90i	−0.338707	−	1.49889i
$991$	−676.393			−0.682535			−0.341268	−	0.939966i	$-0.610856\pi$
$991$	−676.393			−0.682535			−0.341268	+	0.939966i	$0.610856\pi$
$992$			235.743i			0.237644i
$993$	1236.68	−	137.988i	1.24540	−	0.138961i
$994$	158.735			0.159693
$995$		−	735.304i		−	0.738999i
$996$	25.2458	+	226.259i	0.0253472	+	0.227167i
$997$	1544.78			1.54943			0.774715	−	0.632310i	$-0.217893\pi$
$997$	1544.78			1.54943			0.774715	+	0.632310i	$0.217893\pi$
$998$		−	279.028i		−	0.279587i
$999$	−1536.53	+	532.073i	−1.53807	+	0.532605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.10	✓	38
3.2	odd	2	inner	177.3.b.a.119.29	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.10	✓	38	1.1	even	1	trivial
177.3.b.a.119.29	yes	38	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +O(q^{10})\)	\(q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +10.9755 q^{10} -15.4011i q^{11} +(1.57703 - 0.175964i) q^{12} +18.6528 q^{13} -5.72689i q^{14} +(-1.71571 - 15.3766i) q^{15} -17.8360 q^{16} +4.88346i q^{17} +(-4.22163 - 18.6821i) q^{18} +3.41065 q^{19} -2.72792i q^{20} +(-8.02334 + 0.895238i) q^{21} -32.7756 q^{22} -15.9679i q^{23} +(2.45741 + 22.0239i) q^{24} -1.59821 q^{25} -39.6955i q^{26} +(-25.5136 + 8.83491i) q^{27} -1.42340 q^{28} -24.8107i q^{29} +(-32.7234 + 3.65126i) q^{30} +28.0319 q^{31} +8.40981i q^{32} +(5.12354 + 45.9184i) q^{33} +10.3926 q^{34} +13.8786i q^{35} +(-4.64338 + 1.04927i) q^{36} +60.2239 q^{37} -7.25831i q^{38} +(-55.6131 + 6.20527i) q^{39} +38.0966 q^{40} +37.6168i q^{41} +(1.90518 + 17.0747i) q^{42} -15.8209 q^{43} +8.14626i q^{44} +(10.2308 + 45.2746i) q^{45} -33.9818 q^{46} -13.1463i q^{47} +(53.1779 - 5.93355i) q^{48} -41.7583 q^{49} +3.40120i q^{50} +(-1.62460 - 14.5600i) q^{51} -9.86617 q^{52} +35.0364i q^{53} +(18.8018 + 54.2963i) q^{54} +79.4290 q^{55} -19.8784i q^{56} +(-10.1688 + 1.13463i) q^{57} -52.8004 q^{58} +7.68115i q^{59} +(0.907507 + 8.13330i) q^{60} -83.7144 q^{61} -59.6555i q^{62} +(23.6238 - 5.33830i) q^{63} -53.4467 q^{64} +96.1987i q^{65} +(97.7204 - 10.9036i) q^{66} +72.8285 q^{67} -2.58305i q^{68} +(5.31210 + 47.6083i) q^{69} +29.5356 q^{70} +27.7175i q^{71} +(-14.6535 - 64.8468i) q^{72} +54.4224 q^{73} -128.164i q^{74} +(4.76507 - 0.531683i) q^{75} -1.80403 q^{76} -41.4451i q^{77} +(13.2056 + 118.352i) q^{78} -123.594 q^{79} -91.9863i q^{80} +(73.1296 - 34.8290i) q^{81} +80.0535 q^{82} +143.471i q^{83} +(4.24386 - 0.473527i) q^{84} -25.1857 q^{85} +33.6690i q^{86} +(8.25385 + 73.9730i) q^{87} -113.766 q^{88} -21.8428i q^{89} +(96.3502 - 21.7724i) q^{90} +50.1954 q^{91} +8.44606i q^{92} +(-83.5770 + 9.32545i) q^{93} -27.9771 q^{94} +17.5899i q^{95} +(-2.79772 - 25.0738i) q^{96} -98.9417 q^{97} +88.8671i q^{98} +(-30.5517 - 135.201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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