LMFDB - Embedded newform 177.3.b.a.119.36

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			119.36
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.55815i q^{2} +(-1.69290 + 2.47671i) q^{3} -8.66046 q^{4} -6.82324i q^{5} +(-8.81252 - 6.02359i) q^{6} +0.148532 q^{7} -16.5826i q^{8} +(-3.26820 - 8.38564i) q^{9} +O(q^{10})$	\(q+3.55815i q^{2} +(-1.69290 + 2.47671i) q^{3} -8.66046 q^{4} -6.82324i q^{5} +(-8.81252 - 6.02359i) q^{6} +0.148532 q^{7} -16.5826i q^{8} +(-3.26820 - 8.38564i) q^{9} +24.2782 q^{10} +1.80659i q^{11} +(14.6613 - 21.4495i) q^{12} -17.1364 q^{13} +0.528501i q^{14} +(16.8992 + 11.5511i) q^{15} +24.3617 q^{16} -18.3201i q^{17} +(29.8374 - 11.6287i) q^{18} -19.6285 q^{19} +59.0924i q^{20} +(-0.251450 + 0.367871i) q^{21} -6.42813 q^{22} +40.3036i q^{23} +(41.0704 + 28.0727i) q^{24} -21.5567 q^{25} -60.9738i q^{26} +(26.3015 + 6.10165i) q^{27} -1.28636 q^{28} -33.8473i q^{29} +(-41.1004 + 60.1300i) q^{30} -46.0774 q^{31} +20.3523i q^{32} +(-4.47440 - 3.05837i) q^{33} +65.1857 q^{34} -1.01347i q^{35} +(28.3041 + 72.6235i) q^{36} +40.6329 q^{37} -69.8412i q^{38} +(29.0101 - 42.4418i) q^{39} -113.147 q^{40} +21.3927i q^{41} +(-1.30894 - 0.894697i) q^{42} +4.07233 q^{43} -15.6459i q^{44} +(-57.2172 + 22.2997i) q^{45} -143.406 q^{46} -45.7277i q^{47} +(-41.2419 + 60.3370i) q^{48} -48.9779 q^{49} -76.7019i q^{50} +(45.3736 + 31.0140i) q^{51} +148.409 q^{52} -29.4395i q^{53} +(-21.7106 + 93.5849i) q^{54} +12.3268 q^{55} -2.46306i q^{56} +(33.2290 - 48.6141i) q^{57} +120.434 q^{58} +7.68115i q^{59} +(-146.355 - 100.037i) q^{60} -28.5354 q^{61} -163.950i q^{62} +(-0.485432 - 1.24554i) q^{63} +25.0305 q^{64} +116.926i q^{65} +(10.8822 - 15.9206i) q^{66} -6.55405 q^{67} +158.660i q^{68} +(-99.8203 - 68.2298i) q^{69} +3.60609 q^{70} -11.4894i q^{71} +(-139.056 + 54.1953i) q^{72} -113.523 q^{73} +144.578i q^{74} +(36.4932 - 53.3896i) q^{75} +169.992 q^{76} +0.268337i q^{77} +(151.014 + 103.222i) q^{78} -32.0057 q^{79} -166.226i q^{80} +(-59.6378 + 54.8118i) q^{81} -76.1184 q^{82} +145.911i q^{83} +(2.17767 - 3.18594i) q^{84} -125.002 q^{85} +14.4900i q^{86} +(83.8300 + 57.3000i) q^{87} +29.9580 q^{88} +148.358i q^{89} +(-79.3458 - 203.588i) q^{90} -2.54530 q^{91} -349.048i q^{92} +(78.0043 - 114.120i) q^{93} +162.706 q^{94} +133.930i q^{95} +(-50.4066 - 34.4543i) q^{96} -133.709 q^{97} -174.271i q^{98} +(15.1494 - 5.90429i) 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 $

$2$			3.55815i			1.77908i	0.456860	+	0.889539i	$0.348974\pi$
$2$			3.55815i			1.77908i	−0.456860	+	0.889539i	$0.651026\pi$
$3$	−1.69290	+	2.47671i	−0.564299	+	0.825570i
$3$	−1.69290	+	2.47671i	−0.564299	+	0.825570i
$4$	−8.66046			−2.16512
$5$		−	6.82324i		−	1.36465i	−0.731049	−	0.682324i	$-0.760969\pi$
$5$		−	6.82324i		−	1.36465i	0.731049	−	0.682324i	$-0.239031\pi$
$6$	−8.81252	−	6.02359i	−1.46875	−	1.00393i
$7$	0.148532			0.0212189			0.0106094	−	0.999944i	$-0.496623\pi$
$7$	0.148532			0.0212189			0.0106094	+	0.999944i	$0.496623\pi$
$8$		−	16.5826i		−	2.07283i
$9$	−3.26820	−	8.38564i	−0.363133	−	0.931737i
$10$	24.2782			2.42782
$11$			1.80659i			0.164235i	0.996623	+	0.0821177i	$0.0261684\pi$
$11$			1.80659i			0.164235i	−0.996623	+	0.0821177i	$0.973832\pi$
$12$	14.6613	−	21.4495i	1.22177	−	1.78745i
$13$	−17.1364			−1.31818			−0.659091	−	0.752064i	$-0.729059\pi$
$13$	−17.1364			−1.31818			−0.659091	+	0.752064i	$0.729059\pi$
$14$			0.528501i			0.0377500i
$15$	16.8992	+	11.5511i	1.12661	+	0.770070i
$16$	24.3617			1.52261
$17$		−	18.3201i		−	1.07765i	−0.842417	−	0.538826i	$-0.818868\pi$
$17$		−	18.3201i		−	1.07765i	0.842417	−	0.538826i	$-0.181132\pi$
$18$	29.8374	−	11.6287i	1.65763	−	0.646041i
$19$	−19.6285			−1.03308			−0.516539	−	0.856264i	$-0.672780\pi$
$19$	−19.6285			−1.03308			−0.516539	+	0.856264i	$0.672780\pi$
$20$			59.0924i			2.95462i
$21$	−0.251450	+	0.367871i	−0.0119738	+	0.0175177i
$22$	−6.42813			−0.292188
$23$			40.3036i			1.75233i	0.482012	+	0.876165i	$0.339906\pi$
$23$			40.3036i			1.75233i	−0.482012	+	0.876165i	$0.660094\pi$
$24$	41.0704	+	28.0727i	1.71127	+	1.16970i
$25$	−21.5567			−0.862267
$26$		−	60.9738i		−	2.34515i
$27$	26.3015	+	6.10165i	0.974130	+	0.225987i
$28$	−1.28636			−0.0459413
$29$		−	33.8473i		−	1.16715i	−0.812060	−	0.583574i	$-0.801654\pi$
$29$		−	33.8473i		−	1.16715i	0.812060	−	0.583574i	$-0.198346\pi$
$30$	−41.1004	+	60.1300i	−1.37001	+	2.00433i
$31$	−46.0774			−1.48637			−0.743184	−	0.669087i	$-0.766685\pi$
$31$	−46.0774			−1.48637			−0.743184	+	0.669087i	$0.766685\pi$
$32$			20.3523i			0.636008i
$33$	−4.47440	−	3.05837i	−0.135588	−	0.0926779i
$34$	65.1857			1.91723
$35$		−	1.01347i		−	0.0289563i
$36$	28.3041	+	72.6235i	0.786224	+	2.01732i
$37$	40.6329			1.09819			0.549093	−	0.835761i	$-0.314973\pi$
$37$	40.6329			1.09819			0.549093	+	0.835761i	$0.314973\pi$
$38$		−	69.8412i		−	1.83793i
$39$	29.0101	−	42.4418i	0.743849	−	1.08825i
$40$	−113.147			−2.82868
$41$			21.3927i			0.521772i	0.965370	+	0.260886i	$0.0840147\pi$
$41$			21.3927i			0.521772i	−0.965370	+	0.260886i	$0.915985\pi$
$42$	−1.30894	−	0.894697i	−0.0311653	−	0.0213023i
$43$	4.07233			0.0947053			0.0473527	−	0.998878i	$-0.484922\pi$
$43$	4.07233			0.0947053			0.0473527	+	0.998878i	$0.484922\pi$
$44$		−	15.6459i		−	0.355589i
$45$	−57.2172	+	22.2997i	−1.27149	+	0.495549i
$46$	−143.406			−3.11753
$47$		−	45.7277i		−	0.972930i	−0.873700	−	0.486465i	$-0.838286\pi$
$47$		−	45.7277i		−	0.972930i	0.873700	−	0.486465i	$-0.161714\pi$
$48$	−41.2419	+	60.3370i	−0.859207	+	1.25702i
$49$	−48.9779			−0.999550
$50$		−	76.7019i		−	1.53404i
$51$	45.3736	+	31.0140i	0.889678	+	0.608118i
$52$	148.409			2.85401
$53$		−	29.4395i		−	0.555462i	−0.960659	−	0.277731i	$-0.910418\pi$
$53$		−	29.4395i		−	0.555462i	0.960659	−	0.277731i	$-0.0895823\pi$
$54$	−21.7106	+	93.5849i	−0.402048	+	1.73305i
$55$	12.3268			0.224124
$56$		−	2.46306i		−	0.0439831i
$57$	33.2290	−	48.6141i	0.582965	−	0.852879i
$58$	120.434			2.07645
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−146.355	−	100.037i	−2.43925	−	1.66729i
$61$	−28.5354			−0.467793			−0.233897	−	0.972261i	$-0.575148\pi$
$61$	−28.5354			−0.467793			−0.233897	+	0.972261i	$0.575148\pi$
$62$		−	163.950i		−	2.64436i
$63$	−0.485432	−	1.24554i	−0.00770528	−	0.0197704i
$64$	25.0305			0.391101
$65$			116.926i			1.79885i
$66$	10.8822	−	15.9206i	0.164881	−	0.241221i
$67$	−6.55405			−0.0978217			−0.0489108	−	0.998803i	$-0.515575\pi$
$67$	−6.55405			−0.0978217			−0.0489108	+	0.998803i	$0.515575\pi$
$68$			158.660i			2.33324i
$69$	−99.8203	−	68.2298i	−1.44667	−	0.988838i
$70$	3.60609			0.0515155
$71$		−	11.4894i		−	0.161823i	−0.996721	−	0.0809115i	$-0.974217\pi$
$71$		−	11.4894i		−	0.161823i	0.996721	−	0.0809115i	$-0.0257831\pi$
$72$	−139.056	+	54.1953i	−1.93133	+	0.752712i
$73$	−113.523			−1.55510			−0.777552	−	0.628818i	$-0.783539\pi$
$73$	−113.523			−1.55510			−0.777552	+	0.628818i	$0.783539\pi$
$74$			144.578i			1.95376i
$75$	36.4932	−	53.3896i	0.486576	−	0.711862i
$76$	169.992			2.23673
$77$			0.268337i			0.00348489i
$78$	151.014	+	103.222i	1.93608	+	1.32336i
$79$	−32.0057			−0.405135			−0.202568	−	0.979268i	$-0.564929\pi$
$79$	−32.0057			−0.405135			−0.202568	+	0.979268i	$0.564929\pi$
$80$		−	166.226i		−	2.07783i
$81$	−59.6378	+	54.8118i	−0.736269	+	0.676689i
$82$	−76.1184			−0.928273
$83$			145.911i			1.75797i	0.476854	+	0.878983i	$0.341777\pi$
$83$			145.911i			1.75797i	−0.476854	+	0.878983i	$0.658223\pi$
$84$	2.17767	−	3.18594i	0.0259247	−	0.0379278i
$85$	−125.002			−1.47062
$86$			14.4900i			0.168488i
$87$	83.8300	+	57.3000i	0.963563	+	0.658621i
$88$	29.9580			0.340432
$89$			148.358i			1.66695i	0.552560	+	0.833473i	$0.313651\pi$
$89$			148.358i			1.66695i	−0.552560	+	0.833473i	$0.686349\pi$
$90$	−79.3458	−	203.588i	−0.881620	−	2.26209i
$91$	−2.54530			−0.0279703
$92$		−	349.048i		−	3.79399i
$93$	78.0043	−	114.120i	0.838756	−	1.22710i
$94$	162.706			1.73092
$95$			133.930i			1.40979i
$96$	−50.4066	−	34.4543i	−0.525069	−	0.358899i
$97$	−133.709			−1.37844			−0.689222	−	0.724550i	$-0.742048\pi$
$97$	−133.709			−1.37844			−0.689222	+	0.724550i	$0.742048\pi$
$98$		−	174.271i		−	1.77828i
$99$	15.1494	−	5.90429i	0.153024	−	0.0596393i
$100$	186.691			1.86691
$101$			98.8253i			0.978468i	0.872152	+	0.489234i	$0.162724\pi$
$101$			98.8253i			0.978468i	−0.872152	+	0.489234i	$0.837276\pi$
$102$	−110.353	+	161.446i	−1.08189	+	1.58281i
$103$	9.65442			0.0937322			0.0468661	−	0.998901i	$-0.485077\pi$
$103$	9.65442			0.0937322			0.0468661	+	0.998901i	$0.485077\pi$
$104$			284.166i			2.73236i
$105$	2.51008	+	1.71570i	0.0239055	+	0.0163400i
$106$	104.750			0.988209
$107$		−	179.075i		−	1.67360i	−0.547510	−	0.836799i	$-0.684424\pi$
$107$		−	179.075i		−	1.67360i	0.547510	−	0.836799i	$-0.315576\pi$
$108$	−227.783	−	52.8431i	−2.10910	−	0.489288i
$109$	173.922			1.59561			0.797805	−	0.602915i	$-0.205994\pi$
$109$	173.922			1.59561			0.797805	+	0.602915i	$0.205994\pi$
$110$			43.8607i			0.398733i
$111$	−68.7873	+	100.636i	−0.619705	+	0.906629i
$112$	3.61850			0.0323081
$113$		−	119.474i		−	1.05729i	−0.848843	−	0.528646i	$-0.822700\pi$
$113$		−	119.474i		−	1.05729i	0.848843	−	0.528646i	$-0.177300\pi$
$114$	172.976	+	118.234i	1.51734	+	1.03714i
$115$	275.001			2.39131
$116$			293.133i			2.52701i
$117$	56.0050	+	143.699i	0.478675	+	1.22820i
$118$	−27.3307			−0.231616
$119$		−	2.72112i		−	0.0228666i
$120$	191.547	−	280.233i	1.59622	−	2.33528i
$121$	117.736			0.973027
$122$		−	101.533i		−	0.832241i
$123$	−52.9835	−	36.2156i	−0.430760	−	0.294436i
$124$	399.051			3.21816
$125$		−	23.4947i		−	0.187958i
$126$	4.43181	−	1.72724i	0.0351731	−	0.0137083i
$127$	4.26470			0.0335803			0.0167902	−	0.999859i	$-0.494655\pi$
$127$	4.26470			0.0335803			0.0167902	+	0.999859i	$0.494655\pi$
$128$			170.471i			1.33181i
$129$	−6.89404	+	10.0860i	−0.0534421	+	0.0781859i
$130$	−416.039			−3.20030
$131$		−	177.455i		−	1.35462i	−0.735697	−	0.677311i	$-0.763145\pi$
$131$		−	177.455i		−	1.35462i	0.735697	−	0.677311i	$-0.236855\pi$
$132$	38.7504	+	26.4869i	0.293563	+	0.200658i
$133$	−2.91546			−0.0219208
$134$		−	23.3203i		−	0.174032i
$135$	41.6330	−	179.462i	0.308393	−	1.32935i
$136$	−303.795			−2.23379
$137$		−	75.8430i		−	0.553599i	−0.960928	−	0.276799i	$-0.910726\pi$
$137$		−	75.8430i		−	0.553599i	0.960928	−	0.276799i	$-0.0892737\pi$
$138$	242.772	−	355.176i	1.75922	−	2.57374i
$139$	−75.6188			−0.544020			−0.272010	−	0.962294i	$-0.587688\pi$
$139$	−75.6188			−0.544020			−0.272010	+	0.962294i	$0.587688\pi$
$140$			8.77713i			0.0626938i
$141$	113.254	+	77.4123i	0.803222	+	0.549024i
$142$	40.8812			0.287896
$143$		−	30.9584i		−	0.216492i
$144$	−79.6189	−	204.289i	−0.552909	−	1.41867i
$145$	−230.948			−1.59275
$146$		−	403.931i		−	2.76665i
$147$	82.9146	−	121.304i	0.564045	−	0.825199i
$148$	−351.899			−2.37770
$149$			186.834i			1.25392i	0.779051	+	0.626960i	$0.215701\pi$
$149$			186.834i			1.25392i	−0.779051	+	0.626960i	$0.784299\pi$
$150$	189.969	+	129.849i	1.26646	+	0.865657i
$151$	−59.5580			−0.394424			−0.197212	−	0.980361i	$-0.563189\pi$
$151$	−59.5580			−0.394424			−0.197212	+	0.980361i	$0.563189\pi$
$152$			325.492i			2.14140i
$153$	−153.626	+	59.8736i	−1.00409	+	0.391331i
$154$	−0.954784			−0.00619989
$155$			314.397i			2.02837i
$156$	−251.241	+	367.566i	−1.61052	+	2.35619i
$157$	163.179			1.03936			0.519679	−	0.854362i	$-0.326052\pi$
$157$	163.179			1.03936			0.519679	+	0.854362i	$0.326052\pi$
$158$		−	113.881i		−	0.720767i
$159$	72.9131	+	49.8380i	0.458573	+	0.313447i
$160$	138.868			0.867927
$161$			5.98638i			0.0371825i
$162$	−195.029	−	212.200i	−1.20388	−	1.30988i
$163$	121.738			0.746856			0.373428	−	0.927659i	$-0.378182\pi$
$163$	121.738			0.746856			0.373428	+	0.927659i	$0.378182\pi$
$164$		−	185.270i		−	1.12970i
$165$	−20.8680	+	30.5299i	−0.126473	+	0.185030i
$166$	−519.174			−3.12756
$167$		−	53.8804i		−	0.322637i	−0.986902	−	0.161319i	$-0.948425\pi$
$167$		−	53.8804i		−	0.322637i	0.986902	−	0.161319i	$-0.0515747\pi$
$168$	6.10028	+	4.16970i	0.0363112	+	0.0248196i
$169$	124.655			0.737601
$170$		−	444.778i		−	2.61634i
$171$	64.1497	+	164.597i	0.375145	+	0.962558i
$172$	−35.2682			−0.205048
$173$			116.857i			0.675472i	0.941241	+	0.337736i	$0.109661\pi$
$173$			116.857i			0.675472i	−0.941241	+	0.337736i	$0.890339\pi$
$174$	−203.882	+	298.280i	−1.17174	+	1.71425i
$175$	−3.20186			−0.0182963
$176$			44.0117i			0.250066i
$177$	−19.0240	−	13.0034i	−0.107480	−	0.0734655i
$178$	−527.881			−2.96563
$179$		−	200.408i		−	1.11960i	−0.828628	−	0.559800i	$-0.810878\pi$
$179$		−	200.408i		−	1.11960i	0.828628	−	0.559800i	$-0.189122\pi$
$180$	495.528	−	193.126i	2.75293	−	1.07292i
$181$	−188.879			−1.04353			−0.521765	−	0.853089i	$-0.674726\pi$
$181$	−188.879			−1.04353			−0.521765	+	0.853089i	$0.674726\pi$
$182$		−	9.05657i		−	0.0497614i
$183$	48.3075	−	70.6739i	0.263975	−	0.386196i
$184$	668.340			3.63228
$185$		−	277.248i		−	1.49864i
$186$	406.058	+	277.551i	2.18311	+	1.49221i
$187$	33.0969			0.176989
$188$			396.023i			2.10651i
$189$	3.90662	+	0.906291i	0.0206700	+	0.00479519i
$190$	−476.543			−2.50812
$191$			334.562i			1.75163i	0.482646	+	0.875816i	$0.339676\pi$
$191$			334.562i			1.75163i	−0.482646	+	0.875816i	$0.660324\pi$
$192$	−42.3740	+	61.9933i	−0.220698	+	0.322882i
$193$	258.231			1.33798			0.668991	−	0.743270i	$-0.266726\pi$
$193$	258.231			1.33798			0.668991	+	0.743270i	$0.266726\pi$
$194$		−	475.757i		−	2.45236i
$195$	−289.591	−	197.943i	−1.48508	−	1.01509i
$196$	424.171			2.16414
$197$		−	88.8263i		−	0.450895i	−0.974255	−	0.225447i	$-0.927616\pi$
$197$		−	88.8263i		−	0.450895i	0.974255	−	0.225447i	$-0.0723844\pi$
$198$	21.0084	+	53.9039i	0.106103	+	0.272242i
$199$	−49.8385			−0.250445			−0.125222	−	0.992129i	$-0.539964\pi$
$199$	−49.8385			−0.250445			−0.125222	+	0.992129i	$0.539964\pi$
$200$			357.466i			1.78733i
$201$	11.0953	−	16.2325i	0.0552007	−	0.0807587i
$202$	−351.636			−1.74077
$203$		−	5.02742i		−	0.0247656i
$204$	−392.956	−	268.596i	−1.92625	−	1.31665i
$205$	145.967			0.712036
$206$			34.3519i			0.166757i
$207$	337.971	−	131.720i	1.63271	−	0.636328i
$208$	−417.471			−2.00707
$209$		−	35.4606i		−	0.169668i
$210$	−6.10474	+	8.93124i	−0.0290702	+	0.0425297i
$211$	−162.127			−0.768375			−0.384187	−	0.923255i	$-0.625518\pi$
$211$	−162.127			−0.768375			−0.384187	+	0.923255i	$0.625518\pi$
$212$			254.959i			1.20264i
$213$	28.4560	+	19.4504i	0.133596	+	0.0913166i
$214$	637.176			2.97746
$215$		−	27.7865i		−	0.129240i
$216$	101.181	−	436.149i	0.468432	−	2.01921i
$217$	−6.84398			−0.0315391
$218$			618.840i			2.83871i
$219$	192.182	−	281.163i	0.877544	−	1.28385i
$220$	−106.756			−0.485254
$221$			313.939i			1.42054i
$222$	−358.078	−	244.756i	−1.61296	−	1.10250i
$223$	−132.740			−0.595248			−0.297624	−	0.954683i	$-0.596194\pi$
$223$	−132.740			−0.595248			−0.297624	+	0.954683i	$0.596194\pi$
$224$			3.02297i			0.0134954i
$225$	70.4514	+	180.766i	0.313117	+	0.803406i
$226$	425.107			1.88100
$227$		−	104.312i		−	0.459525i	−0.973247	−	0.229762i	$-0.926205\pi$
$227$		−	104.312i		−	0.459525i	0.973247	−	0.229762i	$-0.0737949\pi$
$228$	−287.779	+	421.020i	−1.26219	+	1.84658i
$229$	62.2509			0.271838			0.135919	−	0.990720i	$-0.456601\pi$
$229$	62.2509			0.271838			0.135919	+	0.990720i	$0.456601\pi$
$230$			978.496i			4.25433i
$231$	−0.664593	−	0.454267i	−0.00287703	−	0.00196652i
$232$	−561.277			−2.41930
$233$			18.0515i			0.0774742i	0.999249	+	0.0387371i	$0.0123335\pi$
$233$			18.0515i			0.0774742i	−0.999249	+	0.0387371i	$0.987667\pi$
$234$	−511.304	+	199.274i	−2.18506	+	0.851599i
$235$	−312.011			−1.32771
$236$		−	66.5223i		−	0.281874i
$237$	54.1824	−	79.2689i	0.228618	−	0.334468i
$238$	9.68217			0.0406814
$239$		−	17.4492i		−	0.0730091i	−0.999333	−	0.0365045i	$-0.988378\pi$
$239$		−	17.4492i		−	0.0730091i	0.999333	−	0.0365045i	$-0.0116223\pi$
$240$	411.694	+	281.404i	1.71539	+	1.17252i
$241$	−211.523			−0.877689			−0.438845	−	0.898563i	$-0.644612\pi$
$241$	−211.523			−0.877689			−0.438845	+	0.898563i	$0.644612\pi$
$242$			418.924i			1.73109i
$243$	−34.7923	−	240.496i	−0.143178	−	0.989697i
$244$	247.130			1.01283
$245$			334.188i			1.36403i
$246$	128.861	−	188.523i	0.523824	−	0.766355i
$247$	336.361			1.36178
$248$			764.085i			3.08099i
$249$	−361.380	−	247.013i	−1.45132	−	0.992018i
$250$	83.5978			0.334391
$251$		−	127.331i		−	0.507295i	−0.967297	−	0.253647i	$-0.918370\pi$
$251$		−	127.331i		−	0.507295i	0.967297	−	0.253647i	$-0.0816303\pi$
$252$	4.20407	+	10.7869i	0.0166828	+	0.0428053i
$253$	−72.8120			−0.287795
$254$			15.1745i			0.0597419i
$255$	211.616	−	309.595i	0.829868	−	1.21410i
$256$	−506.441			−1.97829
$257$		−	136.584i		−	0.531457i	−0.964048	−	0.265729i	$-0.914388\pi$
$257$		−	136.584i		−	0.531457i	0.964048	−	0.265729i	$-0.0856125\pi$
$258$	−35.8875	−	24.5300i	−0.139099	−	0.0950777i
$259$	6.03529			0.0233023
$260$		−	1012.63i		−	3.89473i
$261$	−283.831	+	110.620i	−1.08748	+	0.423830i
$262$	631.414			2.40998
$263$		−	232.681i		−	0.884718i	−0.896838	−	0.442359i	$-0.854142\pi$
$263$		−	232.681i		−	0.884718i	0.896838	−	0.442359i	$-0.145858\pi$
$264$	−50.7159	+	74.1974i	−0.192106	+	0.281051i
$265$	−200.873			−0.758010
$266$		−	10.3737i		−	0.0389987i
$267$	−367.440	−	251.155i	−1.37618	−	0.940656i
$268$	56.7611			0.211795
$269$			139.297i			0.517832i	0.965900	+	0.258916i	$0.0833652\pi$
$269$			139.297i			0.517832i	−0.965900	+	0.258916i	$0.916635\pi$
$270$	638.552	+	148.137i	2.36501	+	0.548655i
$271$	340.939			1.25808			0.629038	−	0.777375i	$-0.283449\pi$
$271$	340.939			1.25808			0.629038	+	0.777375i	$0.283449\pi$
$272$		−	446.309i		−	1.64084i
$273$	4.30893	−	6.30397i	0.0157836	−	0.0230915i
$274$	269.861			0.984895
$275$		−	38.9441i		−	0.141615i
$276$	864.490	+	590.902i	3.13221	+	2.14095i
$277$	−181.171			−0.654047			−0.327024	−	0.945016i	$-0.606046\pi$
$277$	−181.171			−0.654047			−0.327024	+	0.945016i	$0.606046\pi$
$278$		−	269.063i		−	0.967853i
$279$	150.590	+	386.388i	0.539749	+	1.38490i
$280$	−16.8060			−0.0600215
$281$		−	382.735i		−	1.36205i	−0.732262	−	0.681023i	$-0.761535\pi$
$281$		−	382.735i		−	1.36205i	0.732262	−	0.681023i	$-0.238465\pi$
$282$	−275.445	+	402.976i	−0.976755	+	1.42899i
$283$	−35.7887			−0.126462			−0.0632309	−	0.997999i	$-0.520140\pi$
$283$	−35.7887			−0.126462			−0.0632309	+	0.997999i	$0.520140\pi$
$284$			99.5038i			0.350365i
$285$	−331.706	−	226.730i	−1.16388	−	0.795543i
$286$	110.155			0.385156
$287$			3.17750i			0.0110714i
$288$	170.667	−	66.5151i	0.592592	−	0.230955i
$289$	−46.6255			−0.161334
$290$		−	821.750i		−	2.83362i
$291$	226.356	−	331.159i	0.777855	−	1.13800i
$292$	983.158			3.36698
$293$		−	243.685i		−	0.831688i	−0.909436	−	0.415844i	$-0.863486\pi$
$293$		−	243.685i		−	0.831688i	0.909436	−	0.415844i	$-0.136514\pi$
$294$	431.619	+	295.023i	1.46809	+	1.00348i
$295$	52.4103			0.177662
$296$		−	673.800i		−	2.27635i
$297$	−11.0232	+	47.5161i	−0.0371151	+	0.159987i
$298$	−664.785			−2.23082
$299$		−	690.656i		−	2.30989i
$300$	−316.048	+	462.379i	−1.05349	+	1.54126i
$301$	0.604872			0.00200954
$302$		−	211.917i		−	0.701711i
$303$	−244.762	−	167.301i	−0.807794	−	0.552149i
$304$	−478.184			−1.57297
$305$			194.704i			0.638374i
$306$	−213.040	−	546.623i	−0.696208	−	1.78635i
$307$	153.107			0.498718			0.249359	−	0.968411i	$-0.419780\pi$
$307$	153.107			0.498718			0.249359	+	0.968411i	$0.419780\pi$
$308$		−	2.32392i		−	0.00754520i
$309$	−16.3439	+	23.9112i	−0.0528930	+	0.0773825i
$310$	−1118.67			−3.60863
$311$			173.317i			0.557290i	0.960394	+	0.278645i	$0.0898853\pi$
$311$			173.317i			0.557290i	−0.960394	+	0.278645i	$0.910115\pi$
$312$	−703.797	−	481.064i	−2.25576	−	1.54187i
$313$	440.611			1.40770			0.703851	−	0.710347i	$-0.251462\pi$
$313$	440.611			1.40770			0.703851	+	0.710347i	$0.251462\pi$
$314$			580.617i			1.84910i
$315$	−8.49860	+	3.31222i	−0.0269797	+	0.0105150i
$316$	277.184			0.877165
$317$		−	122.299i		−	0.385800i	−0.981218	−	0.192900i	$-0.938211\pi$
$317$		−	122.299i		−	0.385800i	0.981218	−	0.192900i	$-0.0617894\pi$
$318$	−177.331	+	259.436i	−0.557646	+	0.815836i
$319$	61.1482			0.191687
$320$		−	170.789i		−	0.533716i
$321$	443.517	+	303.156i	1.38167	+	0.944410i
$322$	−21.3005			−0.0661505
$323$			359.596i			1.11330i
$324$	516.491	−	474.695i	1.59411	−	1.46511i
$325$	369.403			1.13662
$326$			433.161i			1.32872i
$327$	−294.431	+	430.753i	−0.900402	+	1.31729i
$328$	354.747			1.08155
$329$		−	6.79204i		−	0.0206445i
$330$	−108.630	−	74.2516i	−0.329182	−	0.225005i
$331$	198.661			0.600183			0.300092	−	0.953910i	$-0.402983\pi$
$331$	198.661			0.600183			0.300092	+	0.953910i	$0.402983\pi$
$332$		−	1263.66i		−	3.80620i
$333$	−132.796	−	340.732i	−0.398787	−	1.02322i
$334$	191.715			0.573996
$335$			44.7199i			0.133492i
$336$	−6.12575	+	8.96198i	−0.0182314	+	0.0266726i
$337$	−31.0112			−0.0920215			−0.0460108	−	0.998941i	$-0.514651\pi$
$337$	−31.0112			−0.0920215			−0.0460108	+	0.998941i	$0.514651\pi$
$338$			443.540i			1.31225i
$339$	295.902	+	202.257i	0.872868	+	0.596629i
$340$	1082.58			3.18405
$341$		−	83.2430i		−	0.244114i
$342$	−585.663	+	228.255i	−1.71246	+	0.667411i
$343$	−14.5529			−0.0424282
$344$		−	67.5300i		−	0.196308i
$345$	−465.549	+	681.098i	−1.34942	+	1.97420i
$346$	−415.794			−1.20172
$347$			384.717i			1.10869i	0.832286	+	0.554347i	$0.187032\pi$
$347$			384.717i			1.10869i	−0.832286	+	0.554347i	$0.812968\pi$
$348$	−726.006	−	496.245i	−2.08622	−	1.42599i
$349$	122.340			0.350545			0.175273	−	0.984520i	$-0.443919\pi$
$349$	122.340			0.350545			0.175273	+	0.984520i	$0.443919\pi$
$350$		−	11.3927i		−	0.0325506i
$351$	−450.712	−	104.560i	−1.28408	−	0.297892i
$352$	−36.7682			−0.104455
$353$		−	659.650i		−	1.86870i	−0.356360	−	0.934349i	$-0.615982\pi$
$353$		−	659.650i		−	1.86870i	0.356360	−	0.934349i	$-0.384018\pi$
$354$	46.2681	−	67.6902i	0.130701	−	0.191215i
$355$	−78.3952			−0.220832
$356$		−	1284.85i		−	3.60913i
$357$	6.73944	+	4.60658i	0.0188780	+	0.0129036i
$358$	713.084			1.99186
$359$			107.767i			0.300186i	0.988672	+	0.150093i	$0.0479573\pi$
$359$			107.767i			0.300186i	−0.988672	+	0.150093i	$0.952043\pi$
$360$	369.788	+	948.813i	1.02719	+	2.63559i
$361$	24.2775			0.0672507
$362$		−	672.061i		−	1.85652i
$363$	−199.315	+	291.599i	−0.549078	+	0.803302i
$364$	22.0435			0.0605590
$365$			774.593i			2.12217i
$366$	251.469	+	171.886i	0.687073	+	0.469633i
$367$	−606.039			−1.65133			−0.825666	−	0.564159i	$-0.809201\pi$
$367$	−606.039			−1.65133			−0.825666	+	0.564159i	$0.809201\pi$
$368$			981.865i			2.66811i
$369$	179.391	−	69.9154i	0.486155	−	0.189473i
$370$	986.491			2.66619
$371$		−	4.37271i		−	0.0117863i
$372$	−675.553	+	988.335i	−1.81600	+	2.65681i
$373$	−42.6708			−0.114399			−0.0571995	−	0.998363i	$-0.518217\pi$
$373$	−42.6708			−0.114399			−0.0571995	+	0.998363i	$0.518217\pi$
$374$			117.764i			0.314877i
$375$	58.1896	+	39.7742i	0.155172	+	0.106064i
$376$	−758.286			−2.01672
$377$			580.019i			1.53851i
$378$	−3.22472	+	13.9004i	−0.00853102	+	0.0367735i
$379$	−548.047			−1.44604			−0.723018	−	0.690830i	$-0.757245\pi$
$379$	−548.047			−1.44604			−0.723018	+	0.690830i	$0.757245\pi$
$380$		−	1159.90i		−	3.05236i
$381$	−7.21970	+	10.5624i	−0.0189493	+	0.0277229i
$382$	−1190.42			−3.11629
$383$			435.197i			1.13628i	0.822931	+	0.568142i	$0.192337\pi$
$383$			435.197i			1.13628i	−0.822931	+	0.568142i	$0.807663\pi$
$384$	−422.208	−	288.590i	−1.09950	−	0.751538i
$385$	1.83093			0.00475566
$386$			918.824i			2.38037i
$387$	−13.3092	−	34.1491i	−0.0343906	−	0.0882405i
$388$	1157.98			2.98449
$389$		−	227.077i		−	0.583746i	−0.956457	−	0.291873i	$-0.905722\pi$
$389$		−	227.077i		−	0.583746i	0.956457	−	0.291873i	$-0.0942784\pi$
$390$	704.312	−	1030.41i	1.80593	−	2.64207i
$391$	738.365			1.88840
$392$			812.183i			2.07190i
$393$	439.506	+	300.414i	1.11834	+	0.764412i
$394$	316.058			0.802177
$395$			218.383i			0.552868i
$396$	−131.201	+	51.1339i	−0.331315	+	0.129126i
$397$	740.164			1.86439			0.932197	−	0.361952i	$-0.117890\pi$
$397$	740.164			1.86439			0.932197	+	0.361952i	$0.117890\pi$
$398$		−	177.333i		−	0.445560i
$399$	4.93558	−	7.22076i	0.0123699	−	0.0180971i
$400$	−525.158			−1.31289
$401$		−	306.471i		−	0.764268i	−0.924107	−	0.382134i	$-0.875189\pi$
$401$		−	306.471i		−	0.764268i	0.924107	−	0.382134i	$-0.124811\pi$
$402$	57.7577	+	39.4789i	0.143676	+	0.0982063i
$403$	789.599			1.95930
$404$		−	855.873i		−	2.11850i
$405$	373.994	+	406.923i	0.923443	+	1.00475i
$406$	17.8883			0.0440599
$407$			73.4069i			0.180361i
$408$	514.294	−	752.413i	1.26053	−	1.84415i
$409$	−572.519			−1.39980			−0.699901	−	0.714240i	$-0.746772\pi$
$409$	−572.519			−1.39980			−0.699901	+	0.714240i	$0.746772\pi$
$410$			519.374i			1.26677i
$411$	187.841	+	128.394i	0.457035	+	0.312395i
$412$	−83.6117			−0.202941
$413$			1.14090i			0.00276246i
$414$	468.680	+	1202.55i	1.13208	+	2.90472i
$415$	995.587			2.39901
$416$		−	348.763i		−	0.838374i
$417$	128.015	−	187.286i	0.306990	−	0.449127i
$418$	126.174			0.301853
$419$		−	50.8652i		−	0.121397i	−0.998156	−	0.0606984i	$-0.980667\pi$
$419$		−	50.8652i		−	0.121397i	0.998156	−	0.0606984i	$-0.0193328\pi$
$420$	−21.7384	−	14.8588i	−0.0517581	−	0.0353781i
$421$	−320.698			−0.761753			−0.380876	−	0.924626i	$-0.624378\pi$
$421$	−320.698			−0.761753			−0.380876	+	0.924626i	$0.624378\pi$
$422$		−	576.873i		−	1.36700i
$423$	−383.456	+	149.447i	−0.906515	+	0.353303i
$424$	−488.184			−1.15138
$425$			394.920i			0.929223i
$426$	−69.2076	+	101.251i	−0.162459	+	0.237678i
$427$	−4.23843			−0.00992606
$428$			1550.87i			3.62353i
$429$	76.6749	+	52.4093i	0.178729	+	0.122166i
$430$	98.8686			0.229927
$431$			137.310i			0.318584i	0.987232	+	0.159292i	$0.0509211\pi$
$431$			137.310i			0.318584i	−0.987232	+	0.159292i	$0.949079\pi$
$432$	640.751	+	148.647i	1.48322	+	0.344090i
$433$	−721.580			−1.66647			−0.833233	−	0.552921i	$-0.813513\pi$
$433$	−721.580			−1.66647			−0.833233	+	0.552921i	$0.813513\pi$
$434$		−	24.3519i		−	0.0561104i
$435$	390.972	−	571.993i	0.898786	−	1.31493i
$436$	−1506.24			−3.45468
$437$		−	791.098i		−	1.81029i
$438$	1000.42	+	683.814i	2.28407	+	1.56122i
$439$	−288.042			−0.656132			−0.328066	−	0.944655i	$-0.606397\pi$
$439$	−288.042			−0.656132			−0.328066	+	0.944655i	$0.606397\pi$
$440$		−	204.411i		−	0.464570i
$441$	160.069	+	410.711i	0.362969	+	0.931318i
$442$	−1117.05			−2.52725
$443$			656.684i			1.48236i	0.671308	+	0.741178i	$0.265733\pi$
$443$			656.684i			1.48236i	−0.671308	+	0.741178i	$0.734267\pi$
$444$	595.730	−	871.553i	1.34173	−	1.96296i
$445$	1012.28			2.27480
$446$		−	472.311i		−	1.05899i
$447$	−462.734	−	316.291i	−1.03520	−	0.707586i
$448$	3.71783			0.00829873
$449$			265.029i			0.590266i	0.955456	+	0.295133i	$0.0953640\pi$
$449$			265.029i			0.590266i	−0.955456	+	0.295133i	$0.904636\pi$
$450$	−643.195	+	250.677i	−1.42932	+	0.557060i
$451$	−38.6478			−0.0856935
$452$			1034.70i			2.28916i
$453$	100.826	−	147.508i	0.222573	−	0.325625i
$454$	371.159			0.817530
$455$			17.3672i			0.0381697i
$456$	−806.150	−	551.025i	−1.76787	−	1.20839i
$457$	−751.980			−1.64547			−0.822736	−	0.568424i	$-0.807553\pi$
$457$	−751.980			−1.64547			−0.822736	+	0.568424i	$0.807553\pi$
$458$			221.498i			0.483621i
$459$	111.783	−	481.846i	0.243535	−	1.04977i
$460$	−2381.64			−5.17747
$461$		−	342.840i		−	0.743689i	−0.928295	−	0.371844i	$-0.878726\pi$
$461$		−	342.840i		−	0.743689i	0.928295	−	0.371844i	$-0.121274\pi$
$462$	1.61635	−	2.36472i	0.00349860	−	0.00511845i
$463$	−610.900			−1.31944			−0.659719	−	0.751512i	$-0.729325\pi$
$463$	−610.900			−1.31944			−0.659719	+	0.751512i	$0.729325\pi$
$464$		−	824.579i		−	1.77711i
$465$	−778.671	−	532.242i	−1.67456	−	1.14461i
$466$	−64.2300			−0.137833
$467$			70.7483i			0.151495i	0.997127	+	0.0757477i	$0.0241344\pi$
$467$			70.7483i			0.151495i	−0.997127	+	0.0757477i	$0.975866\pi$
$468$	−485.029	−	1244.50i	−1.03639	−	2.65919i
$469$	−0.973488			−0.00207567
$470$		−	1110.18i		−	2.36209i
$471$	−276.246	+	404.148i	−0.586509	+	0.858063i
$472$	127.374			0.269859
$473$			7.35703i			0.0155540i
$474$	282.051	+	192.789i	0.595044	+	0.406728i
$475$	423.125			0.890789
$476$			23.5662i			0.0495088i
$477$	−246.869	+	96.2140i	−0.517544	+	0.201706i
$478$	62.0868			0.129889
$479$		−	86.5788i		−	0.180749i	−0.995908	−	0.0903746i	$-0.971194\pi$
$479$		−	86.5788i		−	0.180749i	0.995908	−	0.0903746i	$-0.0288064\pi$
$480$	−235.090	+	343.937i	−0.489771	+	0.716535i
$481$	−696.299			−1.44761
$482$		−	752.632i		−	1.56148i
$483$	−14.8265	−	10.1343i	−0.0306968	−	0.0209820i
$484$	−1019.65			−2.10671
$485$			912.330i			1.88109i
$486$	855.723	−	123.796i	1.76075	−	0.254725i
$487$	167.140			0.343203			0.171601	−	0.985166i	$-0.445106\pi$
$487$	167.140			0.343203			0.171601	+	0.985166i	$0.445106\pi$
$488$			473.192i			0.969656i
$489$	−206.089	+	301.509i	−0.421450	+	0.616583i
$490$	−1189.09			−2.42672
$491$		−	732.046i		−	1.49093i	−0.666546	−	0.745464i	$-0.732228\pi$
$491$		−	732.046i		−	1.49093i	0.666546	−	0.745464i	$-0.267772\pi$
$492$	458.861	+	313.644i	0.932645	+	0.637487i
$493$	−620.085			−1.25778
$494$			1196.82i			2.42272i
$495$	−40.2864	−	103.368i	−0.0813867	−	0.208824i
$496$	−1122.53			−2.26316
$497$		−	1.70655i		−	0.00343370i
$498$	878.909	−	1285.84i	1.76488	−	2.58202i
$499$	756.899			1.51683			0.758416	−	0.651771i	$-0.225974\pi$
$499$	756.899			1.51683			0.758416	+	0.651771i	$0.225974\pi$
$500$			203.475i			0.406950i
$501$	133.446	+	91.2140i	0.266360	+	0.182064i
$502$	453.063			0.902516
$503$		−	424.962i		−	0.844856i	−0.906397	−	0.422428i	$-0.861178\pi$
$503$		−	424.962i		−	0.844856i	0.906397	−	0.422428i	$-0.138822\pi$
$504$	−20.6543	+	8.04975i	−0.0409807	+	0.0159717i
$505$	674.309			1.33527
$506$		−	259.076i		−	0.512009i
$507$	−211.028	+	308.734i	−0.416228	+	0.608942i
$508$	−36.9343			−0.0727052
$509$			163.430i			0.321081i	0.987029	+	0.160540i	$0.0513237\pi$
$509$			163.430i			0.321081i	−0.987029	+	0.160540i	$0.948676\pi$
$510$	1101.59	+	752.963i	2.15997	+	1.47640i
$511$	−16.8618			−0.0329976
$512$		−	1120.11i		−	2.18772i
$513$	−516.259	−	119.766i	−1.00635	−	0.233462i
$514$	485.989			0.945503
$515$		−	65.8744i		−	0.127912i
$516$	59.7055	−	87.3493i	0.115708	−	0.169282i
$517$	82.6112			0.159790
$518$			21.4745i			0.0414565i
$519$	−289.420	−	197.826i	−0.557650	−	0.381168i
$520$	1938.93			3.72872
$521$			643.967i			1.23602i	0.786169	+	0.618011i	$0.212061\pi$
$521$			643.967i			1.23602i	−0.786169	+	0.618011i	$0.787939\pi$
$522$	−393.602	−	1009.92i	−0.754026	−	1.93470i
$523$	371.188			0.709729			0.354864	−	0.934918i	$-0.384527\pi$
$523$	371.188			0.709729			0.354864	+	0.934918i	$0.384527\pi$
$524$			1536.85i			2.93291i
$525$	5.42042	−	7.93008i	0.0103246	−	0.0151049i
$526$	827.914			1.57398
$527$			844.142i			1.60179i
$528$	−109.004	−	74.5072i	−0.206447	−	0.141112i
$529$	−1095.38			−2.07066
$530$		−	714.736i		−	1.34856i
$531$	64.4113	−	25.1035i	0.121302	−	0.0472759i
$532$	25.2493			0.0474610
$533$		−	366.592i		−	0.687790i
$534$	893.649	−	1307.41i	1.67350	−	2.44833i
$535$	−1221.87			−2.28387
$536$			108.683i			0.202768i
$537$	496.354	+	339.271i	0.924309	+	0.631790i
$538$	−495.639			−0.921262
$539$		−	88.4831i		−	0.164162i
$540$	−360.561	+	1554.22i	−0.667706	+	2.87819i
$541$	175.446			0.324300			0.162150	−	0.986766i	$-0.448157\pi$
$541$	175.446			0.324300			0.162150	+	0.986766i	$0.448157\pi$
$542$			1213.11i			2.23821i
$543$	319.753	−	467.799i	0.588864	−	0.861508i
$544$	372.855			0.685395
$545$		−	1186.71i		−	2.17745i
$546$	22.4305	+	15.3318i	0.0410815	+	0.0280803i
$547$	209.300			0.382632			0.191316	−	0.981528i	$-0.438724\pi$
$547$	209.300			0.382632			0.191316	+	0.981528i	$0.438724\pi$
$548$			656.835i			1.19860i
$549$	93.2593	+	239.288i	0.169871	+	0.435861i
$550$	138.569			0.251944
$551$			664.371i			1.20576i
$552$	−1131.43	+	1655.28i	−2.04969	+	2.99870i
$553$	−4.75388			−0.00859652
$554$		−	644.635i		−	1.16360i
$555$	686.663	+	469.352i	1.23723	+	0.845680i
$556$	654.893			1.17787
$557$		−	46.3436i		−	0.0832022i	−0.999134	−	0.0416011i	$-0.986754\pi$
$557$		−	46.3436i		−	0.0832022i	0.999134	−	0.0416011i	$-0.0132459\pi$
$558$	−1374.83	+	535.822i	−2.46385	+	0.960255i
$559$	−69.7849			−0.124839
$560$		−	24.6899i		−	0.0440892i
$561$	−56.0296	+	81.9714i	−0.0998746	+	0.146117i
$562$	1361.83			2.42318
$563$		−	866.791i		−	1.53959i	−0.638290	−	0.769796i	$-0.720358\pi$
$563$		−	866.791i		−	1.53959i	0.638290	−	0.769796i	$-0.279642\pi$
$564$	−980.835	−	670.426i	−1.73907	−	1.18870i
$565$	−815.200			−1.44283
$566$		−	127.342i		−	0.224985i
$567$	−8.85813	+	8.14132i	−0.0156228	+	0.0143586i
$568$	−190.525			−0.335431
$569$		−	116.360i		−	0.204500i	−0.994759	−	0.102250i	$-0.967396\pi$
$569$		−	116.360i		−	0.204500i	0.994759	−	0.102250i	$-0.0326041\pi$
$570$	806.739	−	1180.26i	1.41533	−	2.07063i
$571$	487.416			0.853618			0.426809	−	0.904342i	$-0.359638\pi$
$571$	487.416			0.853618			0.426809	+	0.904342i	$0.359638\pi$
$572$			268.114i			0.468730i
$573$	−828.612	−	566.378i	−1.44609	−	0.988444i
$574$	−11.3060			−0.0196969
$575$		−	868.811i		−	1.51098i
$576$	−81.8045	−	209.897i	−0.142022	−	0.364404i
$577$	672.310			1.16518			0.582591	−	0.812766i	$-0.302039\pi$
$577$	672.310			1.16518			0.582591	+	0.812766i	$0.302039\pi$
$578$		−	165.901i		−	0.287026i
$579$	−437.158	+	639.563i	−0.755023	+	1.10460i
$580$	2000.12			3.44848
$581$			21.6725i			0.0373021i
$582$	1178.31	+	805.409i	2.02459	+	1.38386i
$583$	53.1851			0.0912265
$584$			1882.50i			3.22347i
$585$	980.495	−	382.136i	1.67606	−	0.653223i
$586$	867.067			1.47964
$587$		−	320.616i		−	0.546194i	−0.961986	−	0.273097i	$-0.911952\pi$
$587$		−	320.616i		−	0.546194i	0.961986	−	0.273097i	$-0.0880480\pi$
$588$	−718.079	+	1050.55i	−1.22122	+	1.78665i
$589$	904.429			1.53553
$590$			186.484i			0.316075i
$591$	219.997	+	150.374i	0.372245	+	0.254440i
$592$	989.887			1.67211
$593$		−	779.831i		−	1.31506i	−0.753428	−	0.657530i	$-0.771601\pi$
$593$		−	779.831i		−	1.31506i	0.753428	−	0.657530i	$-0.228399\pi$
$594$	−169.069	−	39.2222i	−0.284629	−	0.0660306i
$595$	−18.5669			−0.0312049
$596$		−	1618.07i		−	2.71488i
$597$	84.3714	−	123.436i	0.141326	−	0.206760i
$598$	2457.46			4.10947
$599$			315.093i			0.526032i	0.964791	+	0.263016i	$0.0847172\pi$
$599$			315.093i			0.526032i	−0.964791	+	0.263016i	$0.915283\pi$
$600$	−885.341	−	605.154i	−1.47557	−	1.00859i
$601$	−474.472			−0.789470			−0.394735	−	0.918795i	$-0.629164\pi$
$601$	−474.472			−0.789470			−0.394735	+	0.918795i	$0.629164\pi$
$602$			2.15223i			0.00357513i
$603$	21.4199	+	54.9599i	0.0355223	+	0.0911441i
$604$	515.800			0.853973
$605$		−	803.343i		−	1.32784i
$606$	595.283	−	870.900i	0.982315	−	1.43713i
$607$	368.145			0.606500			0.303250	−	0.952911i	$-0.401928\pi$
$607$	368.145			0.606500			0.303250	+	0.952911i	$0.401928\pi$
$608$		−	399.484i		−	0.657046i
$609$	12.4515	+	8.51090i	0.0204457	+	0.0139752i
$610$	−692.787			−1.13572
$611$			783.606i			1.28250i
$612$	1330.47	−	518.533i	2.17397	−	0.847276i
$613$	25.3403			0.0413382			0.0206691	−	0.999786i	$-0.493420\pi$
$613$	25.3403			0.0413382			0.0206691	+	0.999786i	$0.493420\pi$
$614$			544.777i			0.887259i
$615$	−247.108	+	361.519i	−0.401801	+	0.587836i
$616$	4.44973			0.00722359
$617$			410.846i			0.665876i	0.942949	+	0.332938i	$0.108040\pi$
$617$			410.846i			0.665876i	−0.942949	+	0.332938i	$0.891960\pi$
$618$	−85.0797	−	58.1543i	−0.137669	−	0.0941007i
$619$	−652.761			−1.05454			−0.527271	−	0.849697i	$-0.676785\pi$
$619$	−652.761			−1.05454			−0.527271	+	0.849697i	$0.676785\pi$
$620$		−	2722.83i		−	4.39165i
$621$	−245.918	+	1060.05i	−0.396004	+	1.70700i
$622$	−616.689			−0.991462
$623$			22.0360i			0.0353707i
$624$	706.736	−	1033.96i	1.13259	−	1.65698i
$625$	−699.227			−1.11876
$626$			1567.76i			2.50441i
$627$	87.8257	+	60.0312i	0.140073	+	0.0957436i
$628$	−1413.21			−2.25033
$629$		−	744.398i		−	1.18346i
$630$	−11.7854	−	30.2393i	−0.0187070	−	0.0479990i
$631$	−869.264			−1.37760			−0.688799	−	0.724952i	$-0.741862\pi$
$631$	−869.264			−1.37760			−0.688799	+	0.724952i	$0.741862\pi$
$632$			530.739i			0.839777i
$633$	274.465	−	401.542i	0.433593	−	0.634347i
$634$	435.158			0.686369
$635$		−	29.0991i		−	0.0458253i
$636$	−631.461	−	431.620i	−0.992863	−	0.678648i
$637$	839.303			1.31759
$638$			217.575i			0.341026i
$639$	−96.3462	+	37.5497i	−0.150777	+	0.0587632i
$640$	1163.17			1.81745
$641$		−	252.973i		−	0.394653i	−0.980338	−	0.197327i	$-0.936774\pi$
$641$		−	252.973i		−	0.394653i	0.980338	−	0.197327i	$-0.0632259\pi$
$642$	−1078.67	+	1578.10i	−1.68018	+	2.45810i
$643$	−1098.13			−1.70782			−0.853910	−	0.520421i	$-0.825775\pi$
$643$	−1098.13			−1.70782			−0.853910	+	0.520421i	$0.825775\pi$
$644$		−	51.8448i		−	0.0805044i
$645$	68.8191	+	47.0397i	0.106696	+	0.0729298i
$646$	−1279.50			−1.98064
$647$			634.640i			0.980896i	0.871470	+	0.490448i	$0.163167\pi$
$647$			634.640i			0.980896i	−0.871470	+	0.490448i	$0.836833\pi$
$648$	908.924	+	988.952i	1.40266	+	1.52616i
$649$	−13.8767			−0.0213816
$650$			1314.39i			2.02214i
$651$	11.5862	−	16.9506i	0.0177975	−	0.0260377i
$652$	−1054.30			−1.61703
$653$			743.777i			1.13901i	0.821986	+	0.569507i	$0.192866\pi$
$653$			743.777i			1.13901i	−0.821986	+	0.569507i	$0.807134\pi$
$654$	−1532.69	−	1047.63i	−2.34356	−	1.60188i
$655$	−1210.82			−1.84858
$656$			521.162i			0.794455i
$657$	371.014	+	951.960i	0.564710	+	1.44895i
$658$	24.1671			0.0367281
$659$			9.11578i			0.0138327i	0.999976	+	0.00691637i	$0.00220157\pi$
$659$			9.11578i			0.0138327i	−0.999976	+	0.00691637i	$0.997798\pi$
$660$	180.727	−	264.403i	0.273828	−	0.400611i
$661$	−350.843			−0.530776			−0.265388	−	0.964142i	$-0.585500\pi$
$661$	−350.843			−0.530776			−0.265388	+	0.964142i	$0.585500\pi$
$662$			706.865i			1.06777i
$663$	−777.537	−	531.467i	−1.17276	−	0.801610i
$664$	2419.59			3.64396
$665$			19.8929i			0.0299142i
$666$	1212.38	−	472.509i	1.82039	−	0.709473i
$667$	1364.17			2.04523
$668$			466.629i			0.698547i
$669$	224.716	−	328.759i	0.335898	−	0.491419i
$670$	−159.120			−0.237493
$671$		−	51.5518i		−	0.0768283i
$672$	−7.48701	−	5.11757i	−0.0111414	−	0.00761543i
$673$	−1036.60			−1.54027			−0.770134	−	0.637882i	$-0.779811\pi$
$673$	−1036.60			−1.54027			−0.770134	+	0.637882i	$0.779811\pi$
$674$		−	110.343i		−	0.163713i
$675$	−566.973	−	131.531i	−0.839960	−	0.194861i
$676$	−1079.57			−1.59699
$677$		−	446.603i		−	0.659680i	−0.944037	−	0.329840i	$-0.893005\pi$
$677$		−	446.603i		−	0.659680i	0.944037	−	0.329840i	$-0.106995\pi$
$678$	−719.662	+	1052.87i	−1.06145	+	1.55290i
$679$	−19.8601			−0.0292491
$680$			2072.87i			3.04834i
$681$	258.351	+	176.590i	0.379370	+	0.259309i
$682$	296.191			0.434298
$683$		−	751.761i		−	1.10067i	−0.834942	−	0.550337i	$-0.814499\pi$
$683$		−	751.761i		−	1.10067i	0.834942	−	0.550337i	$-0.185501\pi$
$684$	−555.566	−	1425.49i	−0.812231	−	2.08405i
$685$	−517.495			−0.755468
$686$		−	51.7814i		−	0.0754831i
$687$	−105.384	+	154.178i	−0.153398	+	0.224422i
$688$	99.2090			0.144199
$689$			504.485i			0.732199i
$690$	−2423.45	−	1656.49i	−3.51225	−	2.40072i
$691$	296.414			0.428964			0.214482	−	0.976728i	$-0.431194\pi$
$691$	296.414			0.428964			0.214482	+	0.976728i	$0.431194\pi$
$692$		−	1012.03i		−	1.46247i
$693$	2.25018	−	0.876977i	0.00324701	−	0.00126548i
$694$	−1368.88			−1.97245
$695$			515.965i			0.742396i
$696$	950.185	−	1390.12i	1.36521	−	1.99730i
$697$	391.915			0.562289
$698$			435.305i			0.623647i
$699$	−44.7083	−	30.5593i	−0.0639604	−	0.0437186i
$700$	27.7296			0.0396137
$701$		−	317.412i		−	0.452799i	−0.974035	−	0.226400i	$-0.927304\pi$
$701$		−	317.412i		−	0.452799i	0.974035	−	0.226400i	$-0.0726955\pi$
$702$	372.041	−	1603.70i	0.529972	−	2.28448i
$703$	−797.562			−1.13451
$704$			45.2198i			0.0642327i
$705$	528.203	−	772.762i	0.749224	−	1.09612i
$706$	2347.14			3.32456
$707$			14.6787i			0.0207620i
$708$	164.756	+	112.615i	0.232707	+	0.159061i
$709$	−981.184			−1.38390			−0.691950	−	0.721946i	$-0.743248\pi$
$709$	−981.184			−1.38390			−0.691950	+	0.721946i	$0.743248\pi$
$710$		−	278.942i		−	0.392876i
$711$	104.601	+	268.388i	0.147118	+	0.377480i
$712$	2460.17			3.45530
$713$		−	1857.08i		−	2.60461i
$714$	−16.3909	+	23.9800i	−0.0229565	+	0.0335854i
$715$	−211.237			−0.295436
$716$			1735.63i			2.42406i
$717$	43.2165	+	29.5397i	0.0602741	+	0.0411990i
$718$	−383.450			−0.534054
$719$			73.9197i			0.102809i	0.998678	+	0.0514045i	$0.0163698\pi$
$719$			73.9197i			0.102809i	−0.998678	+	0.0514045i	$0.983630\pi$
$720$	−1393.91	+	543.259i	−1.93599	+	0.754527i
$721$	1.43399			0.00198889
$722$			86.3831i			0.119644i
$723$	358.087	−	523.882i	0.495279	−	0.724594i
$724$	1635.78			2.25936
$725$			729.635i			1.00639i
$726$	−1037.55	−	709.195i	−1.42914	−	0.976852i
$727$	1232.61			1.69547			0.847735	−	0.530420i	$-0.177966\pi$
$727$	1232.61			1.69547			0.847735	+	0.530420i	$0.177966\pi$
$728$			42.2078i			0.0579777i
$729$	654.540	+	320.965i	0.897860	+	0.440281i
$730$	−2756.12			−3.77551
$731$		−	74.6054i		−	0.102059i
$732$	−418.365	+	612.069i	−0.571537	+	0.836160i
$733$	325.363			0.443878			0.221939	−	0.975061i	$-0.428761\pi$
$733$	325.363			0.443878			0.221939	+	0.975061i	$0.428761\pi$
$734$		−	2156.38i		−	2.93785i
$735$	−827.688	−	565.747i	−1.12611	−	0.769724i
$736$	−820.269			−1.11450
$737$		−	11.8405i		−	0.0160658i
$738$	248.770	+	638.301i	0.337086	+	0.864907i
$739$	411.718			0.557129			0.278564	−	0.960418i	$-0.410141\pi$
$739$	411.718			0.557129			0.278564	+	0.960418i	$0.410141\pi$
$740$			2401.10i			3.24472i
$741$	−569.424	+	833.068i	−0.768454	+	1.12425i
$742$	15.5588			0.0209687
$743$			31.6240i			0.0425626i	0.999774	+	0.0212813i	$0.00677456\pi$
$743$			31.6240i			0.0425626i	−0.999774	+	0.0212813i	$0.993225\pi$
$744$	−1892.42	−	1293.52i	−2.54357	−	1.73860i
$745$	1274.81			1.71116
$746$		−	151.829i		−	0.203525i
$747$	1223.56	−	476.866i	1.63796	−	0.638375i
$748$	−286.634			−0.383201
$749$		−	26.5984i		−	0.0355119i
$750$	−141.523	+	207.048i	−0.188697	+	0.276064i
$751$	−827.119			−1.10136			−0.550678	−	0.834718i	$-0.685631\pi$
$751$	−827.119			−1.10136			−0.550678	+	0.834718i	$0.685631\pi$
$752$		−	1114.01i		−	1.48139i
$753$	315.362	+	215.558i	0.418807	+	0.286266i
$754$	−2063.80			−2.73713
$755$			406.379i			0.538250i
$756$	−33.8332	−	7.84890i	−0.0447528	−	0.0103821i
$757$	422.114			0.557615			0.278807	−	0.960347i	$-0.410061\pi$
$757$	422.114			0.557615			0.278807	+	0.960347i	$0.410061\pi$
$758$		−	1950.04i		−	2.57261i
$759$	123.263	−	180.334i	0.162402	−	0.237595i
$760$	2220.91			2.92225
$761$		−	37.4749i		−	0.0492443i	−0.999697	−	0.0246222i	$-0.992162\pi$
$761$		−	37.4749i		−	0.0492443i	0.999697	−	0.0246222i	$-0.00783827\pi$
$762$	−37.5827	−	25.6888i	−0.0493212	−	0.0337123i
$763$	25.8330			0.0338571
$764$		−	2897.46i		−	3.79248i
$765$	408.532	+	1048.22i	0.534029	+	1.37023i
$766$	−1548.50			−2.02154
$767$		−	131.627i		−	0.171613i
$768$	857.353	−	1254.31i	1.11635	−	1.63321i
$769$	162.942			0.211888			0.105944	−	0.994372i	$-0.466214\pi$
$769$	162.942			0.211888			0.105944	+	0.994372i	$0.466214\pi$
$770$			6.51472i			0.00846068i
$771$	338.280	+	231.224i	0.438755	+	0.299901i
$772$	−2236.40			−2.89689
$773$		−	817.034i		−	1.05697i	−0.848944	−	0.528483i	$-0.822761\pi$
$773$		−	817.034i		−	1.05697i	0.848944	−	0.528483i	$-0.177239\pi$
$774$	121.508	−	47.3561i	0.156987	−	0.0611836i
$775$	993.275			1.28164
$776$			2217.25i			2.85728i
$777$	−10.2171	+	14.9477i	−0.0131495	+	0.0192377i
$778$	807.975			1.03853
$779$		−	419.906i		−	0.539032i
$780$	2507.99	+	1714.28i	3.21537	+	2.19779i
$781$	20.7567			0.0265771
$782$			2627.22i			3.35961i
$783$	206.524	−	890.235i	0.263760	−	1.13695i
$784$	−1193.19			−1.52192
$785$		−	1113.41i		−	1.41836i
$786$	−1068.92	+	1563.83i	−1.35995	+	1.98960i
$787$	1085.30			1.37903			0.689517	−	0.724269i	$-0.257823\pi$
$787$	1085.30			1.37903			0.689517	+	0.724269i	$0.257823\pi$
$788$			769.276i			0.976239i
$789$	576.283	+	393.905i	0.730397	+	0.499246i
$790$	−777.039			−0.983594
$791$		−	17.7457i		−	0.0224345i
$792$	−97.9087	−	251.217i	−0.123622	−	0.317193i
$793$	488.993			0.616637
$794$			2633.62i			3.31690i
$795$	340.057	−	497.504i	0.427745	−	0.625791i
$796$	431.624			0.542241
$797$		−	225.017i		−	0.282330i	−0.989986	−	0.141165i	$-0.954915\pi$
$797$		−	225.017i		−	0.282330i	0.989986	−	0.141165i	$-0.0450847\pi$
$798$	25.6926	+	17.5616i	0.0321962	+	0.0220070i
$799$	−837.736			−1.04848
$800$		−	438.727i		−	0.548408i
$801$	1244.08	−	484.864i	1.55316	−	0.605323i
$802$	1090.47			1.35969
$803$		−	205.089i		−	0.255403i
$804$	−96.0907	+	140.581i	−0.119516	+	0.174852i
$805$	40.8465			0.0507410
$806$			2809.51i			3.48575i
$807$	−344.998	−	235.815i	−0.427506	−	0.292212i
$808$	1638.78			2.02820
$809$		−	1209.09i		−	1.49454i	−0.664518	−	0.747272i	$-0.731363\pi$
$809$		−	1209.09i		−	1.49454i	0.664518	−	0.747272i	$-0.268637\pi$
$810$	−1447.90	+	1330.73i	−1.78753	+	1.64288i
$811$	−1496.07			−1.84472			−0.922360	−	0.386332i	$-0.873742\pi$
$811$	−1496.07			−1.84472			−0.922360	+	0.386332i	$0.873742\pi$
$812$			43.5397i			0.0536204i
$813$	−577.174	+	844.406i	−0.709931	+	1.03863i
$814$	−261.193			−0.320876
$815$		−	830.645i		−	1.01920i
$816$	1105.38	+	755.555i	1.35463	+	0.925926i
$817$	−79.9337			−0.0978380
$818$		−	2037.11i		−	2.49035i
$819$	8.31854	+	21.3440i	0.0101569	+	0.0260610i
$820$	−1264.14			−1.54164
$821$		−	49.1322i		−	0.0598444i	−0.999552	−	0.0299222i	$-0.990474\pi$
$821$		−	49.1322i		−	0.0598444i	0.999552	−	0.0299222i	$-0.00952595\pi$
$822$	−456.847	+	668.368i	−0.555775	+	0.813100i
$823$	−687.001			−0.834752			−0.417376	−	0.908734i	$-0.637050\pi$
$823$	−687.001			−0.834752			−0.417376	+	0.908734i	$0.637050\pi$
$824$		−	160.096i		−	0.194291i
$825$	96.4532	+	65.9283i	0.116913	+	0.0799131i
$826$	−4.05949			−0.00491464
$827$			616.530i			0.745502i	0.927931	+	0.372751i	$0.121585\pi$
$827$			616.530i			0.745502i	−0.927931	+	0.372751i	$0.878415\pi$
$828$	−2926.99	+	1140.76i	−3.53501	+	1.37772i
$829$	151.679			0.182966			0.0914830	−	0.995807i	$-0.470839\pi$
$829$	151.679			0.182966			0.0914830	+	0.995807i	$0.470839\pi$
$830$			3542.45i			4.26801i
$831$	306.704	−	448.708i	0.369078	−	0.539962i
$832$	−428.931			−0.515542
$833$			897.280i			1.07717i
$834$	666.392	+	455.496i	0.799031	+	0.546159i
$835$	−367.639			−0.440287
$836$			307.105i			0.367351i
$837$	−1211.91	−	281.148i	−1.44792	−	0.335900i
$838$	180.986			0.215974
$839$		−	334.699i		−	0.398926i	−0.979905	−	0.199463i	$-0.936080\pi$
$839$		−	334.699i		−	0.398926i	0.979905	−	0.199463i	$-0.0639198\pi$
$840$	28.4509	−	41.6237i	0.0338701	−	0.0495520i
$841$	−304.640			−0.362235
$842$		−	1141.09i		−	1.35522i
$843$	947.923	+	647.931i	1.12446	+	0.768601i
$844$	1404.10			1.66362
$845$		−	850.549i		−	1.00657i
$846$	−531.756	−	1364.40i	−0.628553	−	1.61276i
$847$	17.4876			0.0206465
$848$		−	717.197i		−	0.845751i
$849$	60.5865	−	88.6382i	0.0713622	−	0.104403i
$850$	−1405.19			−1.65316
$851$			1637.65i			1.92438i
$852$	−246.442	−	168.450i	−0.289251	−	0.197711i
$853$	1580.91			1.85336			0.926678	−	0.375857i	$-0.122652\pi$
$853$	1580.91			1.85336			0.926678	+	0.375857i	$0.122652\pi$
$854$		−	15.0810i		−	0.0176592i
$855$	1123.09	−	437.709i	1.31355	−	0.511941i
$856$	−2969.53			−3.46908
$857$			1213.06i			1.41548i	0.706475	+	0.707738i	$0.250284\pi$
$857$			1213.06i			1.41548i	−0.706475	+	0.707738i	$0.749716\pi$
$858$	−186.481	+	272.821i	−0.217343	+	0.317973i
$859$	−281.587			−0.327808			−0.163904	−	0.986476i	$-0.552409\pi$
$859$	−281.587			−0.327808			−0.163904	+	0.986476i	$0.552409\pi$
$860$			240.644i			0.279818i
$861$	−7.86975	−	5.37918i	−0.00914024	−	0.00624760i
$862$	−488.569			−0.566786
$863$			627.276i			0.726856i	0.931622	+	0.363428i	$0.118394\pi$
$863$			627.276i			0.726856i	−0.931622	+	0.363428i	$0.881606\pi$
$864$	−124.182	+	535.295i	−0.143729	+	0.619555i
$865$	797.341			0.921782
$866$		−	2567.49i		−	2.96477i
$867$	78.9323	−	115.478i	0.0910407	−	0.133193i
$868$	59.2720			0.0682857
$869$		−	57.8212i		−	0.0665376i
$870$	2035.24	+	1391.14i	2.33935	+	1.59901i
$871$	112.313			0.128947
$872$		−	2884.08i		−	3.30743i
$873$	436.987	+	1121.24i	0.500558	+	1.28435i
$874$	2814.85			3.22065
$875$		−	3.48972i		−	0.00398825i
$876$	−1664.39	+	2435.00i	−1.89998	+	2.77968i
$877$	54.0744			0.0616584			0.0308292	−	0.999525i	$-0.490185\pi$
$877$	54.0744			0.0616584			0.0308292	+	0.999525i	$0.490185\pi$
$878$		−	1024.90i		−	1.16731i
$879$	603.536	+	412.533i	0.686617	+	0.469321i
$880$	300.302			0.341253
$881$		−	720.388i		−	0.817694i	−0.912603	−	0.408847i	$-0.865931\pi$
$881$		−	720.388i		−	0.817694i	0.912603	−	0.408847i	$-0.134069\pi$
$882$	−1461.37	+	569.552i	−1.65689	+	0.645750i
$883$	91.1658			0.103246			0.0516228	−	0.998667i	$-0.483561\pi$
$883$	91.1658			0.103246			0.0516228	+	0.998667i	$0.483561\pi$
$884$		−	2718.86i		−	3.07563i
$885$	−88.7253	+	129.805i	−0.100255	+	0.146673i
$886$	−2336.58			−2.63723
$887$			169.474i			0.191065i	0.995426	+	0.0955323i	$0.0304553\pi$
$887$			169.474i			0.191065i	−0.995426	+	0.0955323i	$0.969545\pi$
$888$	1668.81	+	1140.67i	1.87929	+	1.28454i
$889$	0.633445			0.000712537
$890$			3601.86i			4.04704i
$891$	−99.0225	−	107.741i	−0.111136	−	0.120921i
$892$	1149.59			1.28878
$893$			897.566i			1.00511i
$894$	1125.41	−	1646.48i	1.25885	−	1.84170i
$895$	−1367.44			−1.52786
$896$			25.3205i			0.0282595i
$897$	1710.56	+	1169.21i	1.90697	+	1.30347i
$898$	−943.016			−1.05013
$899$			1559.60i			1.73481i
$900$	−610.142	−	1565.52i	−0.677935	−	1.73947i
$901$	−539.334			−0.598595
$902$		−	137.515i		−	0.152455i
$903$	−1.02399	+	1.49809i	−0.00113398	+	0.00165902i
$904$	−1981.19			−2.19158
$905$			1288.77i			1.42405i
$906$	524.856	+	358.753i	0.579312	+	0.395975i
$907$	542.771			0.598424			0.299212	−	0.954187i	$-0.403276\pi$
$907$	542.771			0.598424			0.299212	+	0.954187i	$0.403276\pi$
$908$			903.391i			0.994924i
$909$	828.713	−	322.980i	0.911675	−	0.355314i
$910$	−61.7952			−0.0679068
$911$			1650.88i			1.81217i	0.423099	+	0.906083i	$0.360942\pi$
$911$			1650.88i			1.81217i	−0.423099	+	0.906083i	$0.639058\pi$
$912$	809.516	−	1184.32i	0.887628	−	1.29860i
$913$	−263.602			−0.288720
$914$		−	2675.66i		−	2.92742i
$915$	−482.226	−	329.614i	−0.527023	−	0.360234i
$916$	−539.122			−0.588561
$917$		−	26.3578i		−	0.0287436i
$918$	1714.48	+	397.740i	1.86763	+	0.433268i
$919$	139.132			0.151395			0.0756977	−	0.997131i	$-0.475882\pi$
$919$	139.132			0.151395			0.0756977	+	0.997131i	$0.475882\pi$
$920$		−	4560.24i		−	4.95679i
$921$	−259.194	+	379.201i	−0.281426	+	0.411727i
$922$	1219.88			1.32308
$923$			196.887i			0.213312i
$924$	5.75568	+	3.93416i	0.00622909	+	0.00425775i
$925$	−875.909			−0.946929
$926$		−	2173.68i		−	2.34738i
$927$	−31.5525	−	80.9584i	−0.0340372	−	0.0873338i
$928$	688.869			0.742316
$929$		−	378.918i		−	0.407877i	−0.978984	−	0.203939i	$-0.934626\pi$
$929$		−	378.918i		−	0.407877i	0.978984	−	0.203939i	$-0.0653743\pi$
$930$	1893.80	−	2770.63i	2.03634	−	2.97917i
$931$	961.363			1.03261
$932$		−	156.334i		−	0.167741i
$933$	−429.256	−	293.408i	−0.460082	−	0.314478i
$934$	−251.733			−0.269522
$935$		−	225.828i		−	0.241527i
$936$	2382.91	−	928.710i	2.54585	−	0.992211i
$937$	−905.019			−0.965868			−0.482934	−	0.875657i	$-0.660429\pi$
$937$	−905.019			−0.965868			−0.482934	+	0.875657i	$0.660429\pi$
$938$		−	3.46382i		−	0.00369277i
$939$	−745.909	+	1091.27i	−0.794365	+	1.16216i
$940$	2702.16			2.87464
$941$		−	1652.38i		−	1.75599i	−0.478673	−	0.877993i	$-0.658882\pi$
$941$		−	1652.38i		−	1.75599i	0.478673	−	0.877993i	$-0.341118\pi$
$942$	−1438.02	−	982.925i	−1.52656	−	1.04344i
$943$	−862.201			−0.914317
$944$			187.126i			0.198227i
$945$	6.18385	−	26.6558i	0.00654375	−	0.0282072i
$946$	−26.1774			−0.0276717
$947$		−	876.672i		−	0.925736i	−0.886427	−	0.462868i	$-0.846820\pi$
$947$		−	876.672i		−	0.925736i	0.886427	−	0.462868i	$-0.153180\pi$
$948$	−469.244	+	686.505i	−0.494983	+	0.724161i
$949$	1945.36			2.04991
$950$			1505.54i			1.58478i
$951$	302.899	+	207.039i	0.318505	+	0.217707i
$952$	−45.1234			−0.0473985
$953$		−	1421.51i		−	1.49161i	−0.666163	−	0.745806i	$-0.732065\pi$
$953$		−	1421.51i		−	1.49161i	0.666163	−	0.745806i	$-0.267935\pi$
$954$	−342.344	−	878.397i	−0.358851	−	0.920751i
$955$	2282.80			2.39036
$956$			151.118i			0.158073i
$957$	−103.518	+	151.446i	−0.108169	+	0.158251i
$958$	308.061			0.321567
$959$		−	11.2651i		−	0.0117467i
$960$	422.995	+	289.128i	0.440620	+	0.301175i
$961$	1162.13			1.20929
$962$		−	2477.54i		−	2.57541i
$963$	−1501.66	+	585.252i	−1.55935	+	0.607738i
$964$	1831.89			1.90030
$965$		−	1761.97i		−	1.82588i
$966$	36.0595	−	52.7551i	0.0373287	−	0.0546119i
$967$	−867.366			−0.896966			−0.448483	−	0.893791i	$-0.648036\pi$
$967$	−867.366			−0.896966			−0.448483	+	0.893791i	$0.648036\pi$
$968$		−	1952.38i		−	2.01692i
$969$	−890.614	−	608.758i	−0.919107	−	0.628234i
$970$	−3246.21			−3.34661
$971$			24.0015i			0.0247183i	0.999924	+	0.0123592i	$0.00393414\pi$
$971$			24.0015i			0.0247183i	−0.999924	+	0.0123592i	$0.996066\pi$
$972$	301.317	+	2082.81i	0.309997	+	2.14281i
$973$	−11.2318			−0.0115435
$974$			594.709i			0.610584i
$975$	−625.361	+	914.904i	−0.641396	+	0.938363i
$976$	−695.172			−0.712266
$977$			54.1008i			0.0553744i	0.999617	+	0.0276872i	$0.00881424\pi$
$977$			54.1008i			0.0553744i	−0.999617	+	0.0276872i	$0.991186\pi$
$978$	−1072.81	−	733.297i	−1.09695	−	0.749793i
$979$	−268.022			−0.273772
$980$		−	2894.23i		−	2.95329i
$981$	−568.410	−	1458.44i	−0.579419	−	1.48669i
$982$	2604.73			2.65248
$983$			936.220i			0.952411i	0.879334	+	0.476205i	$0.157988\pi$
$983$			936.220i			0.952411i	−0.879334	+	0.476205i	$0.842012\pi$
$984$	−600.550	+	878.605i	−0.610315	+	0.892892i
$985$	−606.083			−0.615313
$986$		−	2206.36i		−	2.23769i
$987$	16.8219	+	11.4982i	0.0170435	+	0.0116497i
$988$	−2913.04			−2.94842
$989$			164.129i			0.165955i
$990$	367.800	−	143.345i	0.371515	−	0.144793i
$991$	−282.208			−0.284771			−0.142386	−	0.989811i	$-0.545477\pi$
$991$	−282.208			−0.284771			−0.142386	+	0.989811i	$0.545477\pi$
$992$		−	937.779i		−	0.945341i
$993$	−336.312	+	492.025i	−0.338683	+	0.495494i
$994$	6.07217			0.00610882
$995$			340.060i			0.341769i
$996$	3129.71	+	2139.24i	3.14228	+	2.14783i
$997$	94.6404			0.0949252			0.0474626	−	0.998873i	$-0.484887\pi$
$997$	94.6404			0.0949252			0.0474626	+	0.998873i	$0.484887\pi$
$998$			2693.16i			2.69856i
$999$	1068.71	+	247.927i	1.06978	+	0.248176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.36	yes	38
3.2	odd	2	inner	177.3.b.a.119.3	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.3	✓	38	3.2	odd	2	inner
177.3.b.a.119.36	yes	38	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.55815i q^{2} +(-1.69290 + 2.47671i) q^{3} -8.66046 q^{4} -6.82324i q^{5} +(-8.81252 - 6.02359i) q^{6} +0.148532 q^{7} -16.5826i q^{8} +(-3.26820 - 8.38564i) q^{9} +O(q^{10})\)	\(q+3.55815i q^{2} +(-1.69290 + 2.47671i) q^{3} -8.66046 q^{4} -6.82324i q^{5} +(-8.81252 - 6.02359i) q^{6} +0.148532 q^{7} -16.5826i q^{8} +(-3.26820 - 8.38564i) q^{9} +24.2782 q^{10} +1.80659i q^{11} +(14.6613 - 21.4495i) q^{12} -17.1364 q^{13} +0.528501i q^{14} +(16.8992 + 11.5511i) q^{15} +24.3617 q^{16} -18.3201i q^{17} +(29.8374 - 11.6287i) q^{18} -19.6285 q^{19} +59.0924i q^{20} +(-0.251450 + 0.367871i) q^{21} -6.42813 q^{22} +40.3036i q^{23} +(41.0704 + 28.0727i) q^{24} -21.5567 q^{25} -60.9738i q^{26} +(26.3015 + 6.10165i) q^{27} -1.28636 q^{28} -33.8473i q^{29} +(-41.1004 + 60.1300i) q^{30} -46.0774 q^{31} +20.3523i q^{32} +(-4.47440 - 3.05837i) q^{33} +65.1857 q^{34} -1.01347i q^{35} +(28.3041 + 72.6235i) q^{36} +40.6329 q^{37} -69.8412i q^{38} +(29.0101 - 42.4418i) q^{39} -113.147 q^{40} +21.3927i q^{41} +(-1.30894 - 0.894697i) q^{42} +4.07233 q^{43} -15.6459i q^{44} +(-57.2172 + 22.2997i) q^{45} -143.406 q^{46} -45.7277i q^{47} +(-41.2419 + 60.3370i) q^{48} -48.9779 q^{49} -76.7019i q^{50} +(45.3736 + 31.0140i) q^{51} +148.409 q^{52} -29.4395i q^{53} +(-21.7106 + 93.5849i) q^{54} +12.3268 q^{55} -2.46306i q^{56} +(33.2290 - 48.6141i) q^{57} +120.434 q^{58} +7.68115i q^{59} +(-146.355 - 100.037i) q^{60} -28.5354 q^{61} -163.950i q^{62} +(-0.485432 - 1.24554i) q^{63} +25.0305 q^{64} +116.926i q^{65} +(10.8822 - 15.9206i) q^{66} -6.55405 q^{67} +158.660i q^{68} +(-99.8203 - 68.2298i) q^{69} +3.60609 q^{70} -11.4894i q^{71} +(-139.056 + 54.1953i) q^{72} -113.523 q^{73} +144.578i q^{74} +(36.4932 - 53.3896i) q^{75} +169.992 q^{76} +0.268337i q^{77} +(151.014 + 103.222i) q^{78} -32.0057 q^{79} -166.226i q^{80} +(-59.6378 + 54.8118i) q^{81} -76.1184 q^{82} +145.911i q^{83} +(2.17767 - 3.18594i) q^{84} -125.002 q^{85} +14.4900i q^{86} +(83.8300 + 57.3000i) q^{87} +29.9580 q^{88} +148.358i q^{89} +(-79.3458 - 203.588i) q^{90} -2.54530 q^{91} -349.048i q^{92} +(78.0043 - 114.120i) q^{93} +162.706 q^{94} +133.930i q^{95} +(-50.4066 - 34.4543i) q^{96} -133.709 q^{97} -174.271i q^{98} +(15.1494 - 5.90429i) 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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