LMFDB - Embedded newform 177.3.b.a.119.2

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			119.2
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +O(q^{10})$	\(q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +10.1850 q^{10} +19.0108i q^{11} +(18.0974 - 20.4837i) q^{12} +8.47140 q^{13} -32.5842i q^{14} +(-6.32386 - 5.58714i) q^{15} +30.5668 q^{16} -19.9551i q^{17} +(-32.3399 + 4.01593i) q^{18} +16.3132 q^{19} -25.6276i q^{20} +(-17.8746 + 20.2316i) q^{21} +68.8365 q^{22} +10.3343i q^{23} +(-41.6072 - 36.7600i) q^{24} +17.0881 q^{25} -30.6742i q^{26} +(22.2829 + 15.2471i) q^{27} -81.9891 q^{28} +47.7591i q^{29} +(-20.2306 + 22.8982i) q^{30} +4.05578 q^{31} -36.6533i q^{32} +(-42.7407 - 37.7615i) q^{33} -72.2559 q^{34} +25.3122i q^{35} +(10.1050 + 81.3743i) q^{36} -13.8783 q^{37} -59.0688i q^{38} +(-16.8269 + 19.0457i) q^{39} -52.0557 q^{40} +55.0214i q^{41} +(73.2568 + 64.7226i) q^{42} +44.9435 q^{43} -173.208i q^{44} +(25.1224 - 3.11967i) q^{45} +37.4197 q^{46} +2.46701i q^{47} +(-60.7153 + 68.7212i) q^{48} +31.9799 q^{49} -61.8745i q^{50} +(44.8638 + 39.6372i) q^{51} -77.1832 q^{52} -74.2215i q^{53} +(55.2084 - 80.6844i) q^{54} -53.4739 q^{55} +166.539i q^{56} +(-32.4032 + 36.6759i) q^{57} +172.932 q^{58} +7.68115i q^{59} +(57.6169 + 50.9046i) q^{60} +32.9933 q^{61} -14.6856i q^{62} +(-9.98059 - 80.3726i) q^{63} -10.4513 q^{64} +23.8285i q^{65} +(-136.731 + 154.760i) q^{66} -51.8358 q^{67} +181.812i q^{68} +(-23.2340 - 20.5273i) q^{69} +91.6533 q^{70} -95.1596i q^{71} +(165.290 - 20.5256i) q^{72} -123.796 q^{73} +50.2521i q^{74} +(-33.9423 + 38.4179i) q^{75} -148.630 q^{76} +171.076i q^{77} +(68.9627 + 60.9287i) q^{78} -138.482 q^{79} +85.9787i q^{80} +(-78.5398 + 19.8115i) q^{81} +199.228 q^{82} +27.4328i q^{83} +(162.856 - 184.331i) q^{84} +56.1301 q^{85} -162.737i q^{86} +(-107.374 - 94.8648i) q^{87} -351.826 q^{88} -89.1780i q^{89} +(-11.2961 - 90.9660i) q^{90} +76.2331 q^{91} -94.1564i q^{92} +(-8.05606 + 9.11833i) q^{93} +8.93283 q^{94} +45.8861i q^{95} +(82.4051 + 72.8050i) q^{96} +17.0787 q^{97} -115.797i q^{98} +(169.793 - 21.0847i) 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 $

$2$		−	3.62092i		−	1.81046i	−0.424924	−	0.905229i	$-0.639699\pi$
$2$		−	3.62092i		−	1.81046i	0.424924	−	0.905229i	$-0.360301\pi$
$3$	−1.98632	+	2.24823i	−0.662106	+	0.749411i
$3$	−1.98632	+	2.24823i	−0.662106	+	0.749411i
$4$	−9.11103			−2.27776
$5$			2.81281i			0.562563i	0.959625	+	0.281281i	$0.0907595\pi$
$5$			2.81281i			0.562563i	−0.959625	+	0.281281i	$0.909241\pi$
$6$	8.14066	+	7.19229i	1.35678	+	1.19871i
$7$	8.99888			1.28555			0.642777	−	0.766053i	$-0.277782\pi$
$7$	8.99888			1.28555			0.642777	+	0.766053i	$0.277782\pi$
$8$			18.5066i			2.31333i
$9$	−1.10909	−	8.93140i	−0.123232	−	0.992378i
$10$	10.1850			1.01850
$11$			19.0108i			1.72825i	0.503273	+	0.864127i	$0.332129\pi$
$11$			19.0108i			1.72825i	−0.503273	+	0.864127i	$0.667871\pi$
$12$	18.0974	−	20.4837i	1.50812	−	1.70698i
$13$	8.47140			0.651646			0.325823	−	0.945431i	$-0.394359\pi$
$13$	8.47140			0.651646			0.325823	+	0.945431i	$0.394359\pi$
$14$		−	32.5842i		−	2.32744i
$15$	−6.32386	−	5.58714i	−0.421591	−	0.372476i
$16$	30.5668			1.91042
$17$		−	19.9551i		−	1.17383i	−0.809648	−	0.586916i	$-0.800342\pi$
$17$		−	19.9551i		−	1.17383i	0.809648	−	0.586916i	$-0.199658\pi$
$18$	−32.3399	+	4.01593i	−1.79666	+	0.223107i
$19$	16.3132			0.858591			0.429295	−	0.903164i	$-0.358762\pi$
$19$	16.3132			0.858591			0.429295	+	0.903164i	$0.358762\pi$
$20$		−	25.6276i		−	1.28138i
$21$	−17.8746	+	20.2316i	−0.851173	+	0.963409i
$22$	68.8365			3.12893
$23$			10.3343i			0.449319i	0.974437	+	0.224659i	$0.0721269\pi$
$23$			10.3343i			0.449319i	−0.974437	+	0.224659i	$0.927873\pi$
$24$	−41.6072	−	36.7600i	−1.73363	−	1.53167i
$25$	17.0881			0.683523
$26$		−	30.6742i		−	1.17978i
$27$	22.2829	+	15.2471i	0.825291	+	0.564707i
$28$	−81.9891			−2.92818
$29$			47.7591i			1.64687i	0.567413	+	0.823434i	$0.307944\pi$
$29$			47.7591i			1.64687i	−0.567413	+	0.823434i	$0.692056\pi$
$30$	−20.2306	+	22.8982i	−0.674352	+	0.763272i
$31$	4.05578			0.130832			0.0654158	−	0.997858i	$-0.479163\pi$
$31$	4.05578			0.130832			0.0654158	+	0.997858i	$0.479163\pi$
$32$		−	36.6533i		−	1.14542i
$33$	−42.7407	−	37.7615i	−1.29517	−	1.14429i
$34$	−72.2559			−2.12517
$35$			25.3122i			0.723206i
$36$	10.1050	+	81.3743i	0.280694	+	2.26040i
$37$	−13.8783			−0.375088			−0.187544	−	0.982256i	$-0.560053\pi$
$37$	−13.8783			−0.375088			−0.187544	+	0.982256i	$0.560053\pi$
$38$		−	59.0688i		−	1.55444i
$39$	−16.8269	+	19.0457i	−0.431458	+	0.488350i
$40$	−52.0557			−1.30139
$41$			55.0214i			1.34199i	0.741464	+	0.670993i	$0.234132\pi$
$41$			55.0214i			1.34199i	−0.741464	+	0.670993i	$0.765868\pi$
$42$	73.2568	+	64.7226i	1.74421	+	1.54101i
$43$	44.9435			1.04520			0.522599	−	0.852579i	$-0.324963\pi$
$43$	44.9435			1.04520			0.522599	+	0.852579i	$0.324963\pi$
$44$		−	173.208i		−	3.93655i
$45$	25.1224	−	3.11967i	0.558275	−	0.0693260i
$46$	37.4197			0.813473
$47$			2.46701i			0.0524895i	0.999656	+	0.0262448i	$0.00835493\pi$
$47$			2.46701i			0.0524895i	−0.999656	+	0.0262448i	$0.991645\pi$
$48$	−60.7153	+	68.7212i	−1.26490	+	1.43169i
$49$	31.9799			0.652652
$50$		−	61.8745i		−	1.23749i
$51$	44.8638	+	39.6372i	0.879682	+	0.777200i
$52$	−77.1832			−1.48429
$53$		−	74.2215i		−	1.40040i	−0.713944	−	0.700202i	$-0.753093\pi$
$53$		−	74.2215i		−	1.40040i	0.713944	−	0.700202i	$-0.246907\pi$
$54$	55.2084	−	80.6844i	1.02238	−	1.49416i
$55$	−53.4739			−0.972252
$56$			166.539i			2.97391i
$57$	−32.4032	+	36.6759i	−0.568478	+	0.643437i
$58$	172.932			2.98158
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	57.6169	+	50.9046i	0.960282	+	0.848410i
$61$	32.9933			0.540873			0.270437	−	0.962738i	$-0.412832\pi$
$61$	32.9933			0.540873			0.270437	+	0.962738i	$0.412832\pi$
$62$		−	14.6856i		−	0.236865i
$63$	−9.98059	−	80.3726i	−0.158422	−	1.27576i
$64$	−10.4513			−0.163302
$65$			23.8285i			0.366592i
$66$	−136.731	+	154.760i	−2.07168	+	2.34486i
$67$	−51.8358			−0.773669			−0.386834	−	0.922149i	$-0.626431\pi$
$67$	−51.8358			−0.773669			−0.386834	+	0.922149i	$0.626431\pi$
$68$			181.812i			2.67370i
$69$	−23.2340	−	20.5273i	−0.336724	−	0.297496i
$70$	91.6533			1.30933
$71$		−	95.1596i		−	1.34028i	−0.742236	−	0.670138i	$-0.766235\pi$
$71$		−	95.1596i		−	1.34028i	0.742236	−	0.670138i	$-0.233765\pi$
$72$	165.290	−	20.5256i	2.29569	−	0.285077i
$73$	−123.796			−1.69583			−0.847915	−	0.530131i	$-0.822143\pi$
$73$	−123.796			−1.69583			−0.847915	+	0.530131i	$0.822143\pi$
$74$			50.2521i			0.679082i
$75$	−33.9423	+	38.4179i	−0.452564	+	0.512239i
$76$	−148.630			−1.95566
$77$			171.076i			2.22177i
$78$	68.9627	+	60.9287i	0.884138	+	0.781137i
$79$	−138.482			−1.75293			−0.876466	−	0.481463i	$-0.840106\pi$
$79$	−138.482			−1.75293			−0.876466	+	0.481463i	$0.840106\pi$
$80$			85.9787i			1.07473i
$81$	−78.5398	+	19.8115i	−0.969628	+	0.244586i
$82$	199.228			2.42961
$83$			27.4328i			0.330516i	0.986250	+	0.165258i	$0.0528457\pi$
$83$			27.4328i			0.330516i	−0.986250	+	0.165258i	$0.947154\pi$
$84$	162.856	−	184.331i	1.93877	−	2.19441i
$85$	56.1301			0.660354
$86$		−	162.737i		−	1.89229i
$87$	−107.374	−	94.8648i	−1.23418	−	1.09040i
$88$	−351.826			−3.99802
$89$		−	89.1780i		−	1.00200i	−0.865447	−	0.501000i	$-0.832966\pi$
$89$		−	89.1780i		−	1.00200i	0.865447	−	0.501000i	$-0.167034\pi$
$90$	−11.2961	−	90.9660i	−0.125512	−	1.01073i
$91$	76.2331			0.837727
$92$		−	94.1564i		−	1.02344i
$93$	−8.05606	+	9.11833i	−0.0866244	+	0.0980466i
$94$	8.93283			0.0950301
$95$			45.8861i			0.483011i
$96$	82.4051	+	72.8050i	0.858386	+	0.758386i
$97$	17.0787			0.176069			0.0880345	−	0.996117i	$-0.471941\pi$
$97$	17.0787			0.176069			0.0880345	+	0.996117i	$0.471941\pi$
$98$		−	115.797i		−	1.18160i
$99$	169.793	−	21.0847i	1.71508	−	0.212977i
$100$	−155.690			−1.55690
$101$			67.1513i			0.664865i	0.943127	+	0.332432i	$0.107869\pi$
$101$			67.1513i			0.664865i	−0.943127	+	0.332432i	$0.892131\pi$
$102$	143.523	−	162.448i	1.40709	−	1.59263i
$103$	167.112			1.62245			0.811225	−	0.584734i	$-0.198801\pi$
$103$	167.112			1.62245			0.811225	+	0.584734i	$0.198801\pi$
$104$			156.777i			1.50747i
$105$	−56.9077	−	50.2780i	−0.541978	−	0.478838i
$106$	−268.750			−2.53537
$107$		−	41.9211i		−	0.391786i	−0.980625	−	0.195893i	$-0.937239\pi$
$107$		−	41.9211i		−	0.391786i	0.980625	−	0.195893i	$-0.0627605\pi$
$108$	−203.020	−	138.917i	−1.87981	−	1.28627i
$109$	−14.5692			−0.133662			−0.0668311	−	0.997764i	$-0.521289\pi$
$109$	−14.5692			−0.133662			−0.0668311	+	0.997764i	$0.521289\pi$
$110$			193.624i			1.76022i
$111$	27.5666	−	31.2016i	0.248348	−	0.281095i
$112$	275.067			2.45596
$113$			0.786761i			0.00696249i	0.999994	+	0.00348124i	$0.00110812\pi$
$113$			0.786761i			0.00696249i	−0.999994	+	0.00348124i	$0.998892\pi$
$114$	132.800	+	117.329i	1.16492	+	1.02921i
$115$	−29.0686			−0.252770
$116$		−	435.135i		−	3.75117i
$117$	−9.39556	−	75.6614i	−0.0803039	−	0.646679i
$118$	27.8128			0.235702
$119$		−	179.574i		−	1.50902i
$120$	103.399	−	117.033i	0.861659	−	0.975277i
$121$	−240.411			−1.98686
$122$		−	119.466i		−	0.979228i
$123$	−123.701	−	109.290i	−1.00570	−	0.888536i
$124$	−36.9524			−0.298003
$125$			118.386i			0.947088i
$126$	−291.023	+	36.1389i	−2.30970	+	0.286817i
$127$	189.829			1.49472			0.747358	−	0.664421i	$-0.231322\pi$
$127$	189.829			1.49472			0.747358	+	0.664421i	$0.231322\pi$
$128$		−	108.770i		−	0.849764i
$129$	−89.2720	+	101.043i	−0.692031	+	0.783282i
$130$	86.2809			0.663699
$131$		−	126.252i		−	0.963753i	−0.876239	−	0.481876i	$-0.839955\pi$
$131$		−	126.252i		−	0.963753i	0.876239	−	0.481876i	$-0.160045\pi$
$132$	389.412	+	344.046i	2.95009	+	2.60641i
$133$	146.801			1.10377
$134$			187.693i			1.40069i
$135$	−42.8872	+	62.6776i	−0.317683	+	0.464278i
$136$	369.302			2.71546
$137$			74.7474i			0.545601i	0.962071	+	0.272801i	$0.0879500\pi$
$137$			74.7474i			0.545601i	−0.962071	+	0.272801i	$0.912050\pi$
$138$	−74.3275	+	84.1283i	−0.538605	+	0.609625i
$139$	−80.8582			−0.581714			−0.290857	−	0.956767i	$-0.593940\pi$
$139$	−80.8582			−0.581714			−0.290857	+	0.956767i	$0.593940\pi$
$140$		−	230.620i		−	1.64729i
$141$	−5.54641	−	4.90026i	−0.0393362	−	0.0347536i
$142$	−344.565			−2.42651
$143$			161.048i			1.12621i
$144$	−33.9014	−	273.004i	−0.235426	−	1.89586i
$145$	−134.338			−0.926466
$146$			448.254i			3.07023i
$147$	−63.5223	+	71.8983i	−0.432124	+	0.489104i
$148$	126.445			0.854361
$149$		−	175.759i		−	1.17959i	−0.807552	−	0.589797i	$-0.799208\pi$
$149$		−	175.759i		−	1.17959i	0.807552	−	0.589797i	$-0.200792\pi$
$150$	139.108	+	122.902i	0.927388	+	0.819349i
$151$	195.888			1.29727			0.648635	−	0.761100i	$-0.275340\pi$
$151$	195.888			1.29727			0.648635	+	0.761100i	$0.275340\pi$
$152$			301.903i			1.98620i
$153$	−178.227	+	22.1321i	−1.16488	+	0.144654i
$154$	619.452			4.02241
$155$			11.4082i			0.0736010i
$156$	153.310	−	173.526i	0.982758	−	1.11234i
$157$	−137.817			−0.877813			−0.438907	−	0.898533i	$-0.644634\pi$
$157$	−137.817			−0.877813			−0.438907	+	0.898533i	$0.644634\pi$
$158$			501.431i			3.17361i
$159$	166.867	+	147.427i	1.04948	+	0.927216i
$160$	103.099			0.644368
$161$			92.9975i			0.577624i
$162$	71.7358	+	284.386i	0.442813	+	1.75547i
$163$	265.663			1.62984			0.814919	−	0.579576i	$-0.196782\pi$
$163$	265.663			1.62984			0.814919	+	0.579576i	$0.196782\pi$
$164$		−	501.302i		−	3.05672i
$165$	106.216	−	120.222i	0.643734	−	0.728616i
$166$	99.3320			0.598386
$167$		−	114.909i		−	0.688078i	−0.938955	−	0.344039i	$-0.888205\pi$
$167$		−	114.909i		−	0.688078i	0.938955	−	0.344039i	$-0.111795\pi$
$168$	−374.418	−	330.799i	−2.22868	−	1.96904i
$169$	−97.2355			−0.575358
$170$		−	203.242i		−	1.19554i
$171$	−18.0929	−	145.700i	−0.105806	−	0.852047i
$172$	−409.482			−2.38071
$173$			67.7045i			0.391356i	0.980668	+	0.195678i	$0.0626907\pi$
$173$			67.7045i			0.391356i	−0.980668	+	0.195678i	$0.937309\pi$
$174$	−343.497	+	388.791i	−1.97412	+	2.23443i
$175$	153.774			0.878706
$176$			581.099i			3.30170i
$177$	−17.2690	−	15.2572i	−0.0975649	−	0.0861988i
$178$	−322.906			−1.81408
$179$		−	210.640i		−	1.17676i	−0.808585	−	0.588380i	$-0.799766\pi$
$179$		−	210.640i		−	1.17676i	0.808585	−	0.588380i	$-0.200234\pi$
$180$	−228.891	+	28.4234i	−1.27162	+	0.157908i
$181$	−91.8129			−0.507254			−0.253627	−	0.967302i	$-0.581624\pi$
$181$	−91.8129			−0.507254			−0.253627	+	0.967302i	$0.581624\pi$
$182$		−	276.034i		−	1.51667i
$183$	−65.5351	+	74.1765i	−0.358115	+	0.405336i
$184$	−191.254			−1.03942
$185$		−	39.0370i		−	0.211011i
$186$	33.0167	+	29.1703i	0.177509	+	0.156830i
$187$	379.363			2.02868
$188$		−	22.4770i		−	0.119558i
$189$	200.521	+	137.207i	1.06096	+	0.725962i
$190$	166.150			0.874472
$191$		−	59.8897i		−	0.313559i	−0.987634	−	0.156779i	$-0.949889\pi$
$191$		−	59.8897i		−	0.313559i	0.987634	−	0.156779i	$-0.0501111\pi$
$192$	20.7596	−	23.4970i	0.108123	−	0.122380i
$193$	−29.7862			−0.154333			−0.0771664	−	0.997018i	$-0.524587\pi$
$193$	−29.7862			−0.154333			−0.0771664	+	0.997018i	$0.524587\pi$
$194$		−	61.8405i		−	0.318765i
$195$	−53.5719	−	47.3309i	−0.274728	−	0.242722i
$196$	−291.370			−1.48658
$197$		−	179.374i		−	0.910528i	−0.890357	−	0.455264i	$-0.849545\pi$
$197$		−	179.374i		−	0.910528i	0.890357	−	0.455264i	$-0.150455\pi$
$198$	−76.3461	−	614.807i	−0.385586	−	3.10508i
$199$	63.2008			0.317592			0.158796	−	0.987311i	$-0.449239\pi$
$199$	63.2008			0.317592			0.158796	+	0.987311i	$0.449239\pi$
$200$			316.242i			1.58121i
$201$	102.962	−	116.539i	0.512250	−	0.579796i
$202$	243.149			1.20371
$203$			429.779i			2.11714i
$204$	−408.755	−	361.136i	−2.00370	−	1.77027i
$205$	−154.765			−0.754952
$206$		−	605.100i		−	2.93738i
$207$	92.3001	−	11.4617i	0.445894	−	0.0553707i
$208$	258.943			1.24492
$209$			310.128i			1.48386i
$210$	−182.053	+	206.058i	−0.866917	+	0.981228i
$211$	−100.345			−0.475567			−0.237783	−	0.971318i	$-0.576421\pi$
$211$	−100.345			−0.475567			−0.237783	+	0.971318i	$0.576421\pi$
$212$			676.234i			3.18978i
$213$	213.941	+	189.017i	1.00442	+	0.887405i
$214$	−151.793			−0.709312
$215$			126.418i			0.587990i
$216$	−282.172	+	412.381i	−1.30635	+	1.90917i
$217$	36.4975			0.168191
$218$			52.7538i			0.241990i
$219$	245.897	−	278.321i	1.12282	−	1.27087i
$220$	487.202			2.21456
$221$		−	169.048i		−	0.764922i
$222$	−112.978	−	99.8165i	−0.508911	−	0.449624i
$223$	−207.548			−0.930710			−0.465355	−	0.885124i	$-0.654073\pi$
$223$	−207.548			−0.930710			−0.465355	+	0.885124i	$0.654073\pi$
$224$		−	329.839i		−	1.47249i
$225$	−18.9523	−	152.620i	−0.0842322	−	0.678313i
$226$	2.84880			0.0126053
$227$			405.735i			1.78738i	0.448687	+	0.893689i	$0.351892\pi$
$227$			405.735i			1.78738i	−0.448687	+	0.893689i	$0.648108\pi$
$228$	295.227	−	334.155i	1.29486	−	1.46559i
$229$	−178.686			−0.780288			−0.390144	−	0.920754i	$-0.627575\pi$
$229$	−178.686			−0.780288			−0.390144	+	0.920754i	$0.627575\pi$
$230$			105.255i			0.457630i
$231$	−384.619	−	339.811i	−1.66502	−	1.47104i
$232$	−883.860			−3.80974
$233$			88.5617i			0.380093i	0.981775	+	0.190046i	$0.0608639\pi$
$233$			88.5617i			0.380093i	−0.981775	+	0.190046i	$0.939136\pi$
$234$	−273.964	+	34.0205i	−1.17078	+	0.145387i
$235$	−6.93924			−0.0295287
$236$		−	69.9832i		−	0.296539i
$237$	275.068	−	311.339i	1.16063	−	1.31367i
$238$	−650.222			−2.73203
$239$		−	204.857i		−	0.857144i	−0.903508	−	0.428572i	$-0.859017\pi$
$239$		−	204.857i		−	0.857144i	0.903508	−	0.428572i	$-0.140983\pi$
$240$	−193.300	−	170.781i	−0.805417	−	0.711587i
$241$	255.665			1.06085			0.530425	−	0.847732i	$-0.322032\pi$
$241$	255.665			1.06085			0.530425	+	0.847732i	$0.322032\pi$
$242$			870.507i			3.59713i
$243$	111.464	−	215.928i	0.458700	−	0.888591i
$244$	−300.603			−1.23198
$245$			89.9536i			0.367158i
$246$	−395.730	+	447.911i	−1.60866	+	1.82078i
$247$	138.196			0.559497
$248$			75.0588i			0.302656i
$249$	−61.6754	−	54.4903i	−0.247692	−	0.218837i
$250$	428.666			1.71466
$251$		−	208.746i		−	0.831659i	−0.909443	−	0.415830i	$-0.863491\pi$
$251$		−	208.746i		−	0.831659i	0.909443	−	0.415830i	$-0.136509\pi$
$252$	90.9335	+	732.278i	0.360847	+	2.90586i
$253$	−196.464			−0.776537
$254$		−	687.355i		−	2.70612i
$255$	−111.492	+	126.193i	−0.437224	+	0.494876i
$256$	−435.652			−1.70176
$257$		−	111.276i		−	0.432981i	−0.976285	−	0.216491i	$-0.930539\pi$
$257$		−	111.276i		−	0.432981i	0.976285	−	0.216491i	$-0.0694611\pi$
$258$	365.870	+	323.247i	1.41810	+	1.25289i
$259$	−124.889			−0.482197
$260$		−	217.102i		−	0.835007i
$261$	426.556	−	52.9693i	1.63431	−	0.202948i
$262$	−457.146			−1.74483
$263$		−	58.7836i		−	0.223512i	−0.993736	−	0.111756i	$-0.964353\pi$
$263$		−	58.7836i		−	0.223512i	0.993736	−	0.111756i	$-0.0356475\pi$
$264$	698.837	−	790.986i	2.64711	−	2.99616i
$265$	208.771			0.787816
$266$		−	531.554i		−	1.99832i
$267$	200.493	+	177.136i	0.750910	+	0.663430i
$268$	472.278			1.76223
$269$			68.0727i			0.253058i	0.991963	+	0.126529i	$0.0403837\pi$
$269$			68.0727i			0.253058i	−0.991963	+	0.126529i	$0.959616\pi$
$270$	226.950	+	155.291i	0.840556	+	0.575152i
$271$	154.616			0.570540			0.285270	−	0.958447i	$-0.407917\pi$
$271$	154.616			0.570540			0.285270	+	0.958447i	$0.407917\pi$
$272$		−	609.964i		−	2.24252i
$273$	−151.423	+	171.390i	−0.554663	+	0.627801i
$274$	270.654			0.987788
$275$			324.858i			1.18130i
$276$	211.686	+	187.025i	0.766976	+	0.677625i
$277$	482.276			1.74107			0.870534	−	0.492109i	$-0.163774\pi$
$277$	482.276			1.74107			0.870534	+	0.492109i	$0.163774\pi$
$278$			292.781i			1.05317i
$279$	−4.49824	−	36.2238i	−0.0161227	−	0.129834i
$280$	−468.443			−1.67301
$281$		−	7.90211i		−	0.0281214i	−0.999901	−	0.0140607i	$-0.995524\pi$
$281$		−	7.90211i		−	0.0281214i	0.999901	−	0.0140607i	$-0.00447581\pi$
$282$	−17.7434	+	20.0831i	−0.0629200	+	0.0712166i
$283$	342.096			1.20882			0.604410	−	0.796673i	$-0.293409\pi$
$283$	342.096			1.20882			0.604410	+	0.796673i	$0.293409\pi$
$284$			867.003i			3.05283i
$285$	−103.163	−	91.1443i	−0.361974	−	0.319805i
$286$	583.141			2.03896
$287$			495.132i			1.72520i
$288$	−327.365	+	40.6519i	−1.13668	+	0.141152i
$289$	−109.207			−0.377880
$290$			486.425i			1.67733i
$291$	−33.9237	+	38.3969i	−0.116576	+	0.131948i
$292$	1127.91			3.86269
$293$			58.8955i			0.201009i	0.994937	+	0.100504i	$0.0320456\pi$
$293$			58.8955i			0.201009i	−0.994937	+	0.100504i	$0.967954\pi$
$294$	260.338	+	230.009i	0.885502	+	0.782343i
$295$	−21.6056			−0.0732395
$296$		−	256.840i		−	0.867702i
$297$	−289.859	+	423.615i	−0.975958	+	1.42631i
$298$	−636.410			−2.13560
$299$			87.5462i			0.292797i
$300$	309.250	−	350.027i	1.03083	−	1.16676i
$301$	404.441			1.34366
$302$		−	709.293i		−	2.34865i
$303$	−150.972	−	133.384i	−0.498257	−	0.440211i
$304$	498.643			1.64027
$305$			92.8039i			0.304275i
$306$	80.1384	+	645.346i	0.261890	+	2.10897i
$307$	−597.151			−1.94512			−0.972559	−	0.232656i	$-0.925258\pi$
$307$	−597.151			−1.94512			−0.972559	+	0.232656i	$0.925258\pi$
$308$		−	1558.68i		−	5.06065i
$309$	−331.938	+	375.707i	−1.07423	+	1.21588i
$310$	41.3080			0.133252
$311$		−	29.6874i		−	0.0954578i	−0.998860	−	0.0477289i	$-0.984802\pi$
$311$		−	29.6874i		−	0.0954578i	0.998860	−	0.0477289i	$-0.0151983\pi$
$312$	−352.471	−	311.409i	−1.12971	−	0.998104i
$313$	−167.252			−0.534351			−0.267176	−	0.963648i	$-0.586090\pi$
$313$	−167.252			−0.534351			−0.267176	+	0.963648i	$0.586090\pi$
$314$			499.023i			1.58924i
$315$	226.073	−	28.0736i	0.717693	−	0.0891224i
$316$	1261.71			3.99276
$317$		−	395.131i		−	1.24647i	−0.782035	−	0.623234i	$-0.785818\pi$
$317$		−	395.131i		−	1.24647i	0.782035	−	0.623234i	$-0.214182\pi$
$318$	533.822	−	604.212i	1.67869	−	1.90004i
$319$	−907.940			−2.84621
$320$		−	29.3976i		−	0.0918676i
$321$	94.2484	+	83.2686i	0.293609	+	0.259404i
$322$	336.736			1.04576
$323$		−	325.533i		−	1.00784i
$324$	715.579	−	180.503i	2.20858	−	0.557109i
$325$	144.760			0.445415
$326$		−	961.945i		−	2.95075i
$327$	28.9390	−	32.7549i	0.0884985	−	0.100168i
$328$	−1018.26			−3.10445
$329$			22.2003i			0.0674782i
$330$	−435.312	−	384.599i	−1.31913	−	1.16545i
$331$	−260.174			−0.786025			−0.393013	−	0.919533i	$-0.628567\pi$
$331$	−260.174			−0.786025			−0.393013	+	0.919533i	$0.628567\pi$
$332$		−	249.942i		−	0.752836i
$333$	15.3923	+	123.952i	0.0462231	+	0.372229i
$334$	−416.076			−1.24574
$335$		−	145.805i		−	0.435237i
$336$	−546.370	+	618.414i	−1.62610	+	1.84052i
$337$	98.0518			0.290955			0.145477	−	0.989362i	$-0.453528\pi$
$337$	98.0518			0.290955			0.145477	+	0.989362i	$0.453528\pi$
$338$			352.081i			1.04166i
$339$	−1.76882	−	1.56276i	−0.00521776	−	0.00460990i
$340$	−511.403			−1.50413
$341$			77.1036i			0.226110i
$342$	−527.567	+	65.5128i	−1.54259	+	0.191558i
$343$	−153.162			−0.446535
$344$			831.752i			2.41789i
$345$	57.7394	−	65.3529i	0.167360	−	0.189429i
$346$	245.152			0.708533
$347$		−	386.618i		−	1.11417i	−0.830454	−	0.557087i	$-0.811919\pi$
$347$		−	386.618i		−	1.11417i	0.830454	−	0.557087i	$-0.188081\pi$
$348$	978.285	+	864.316i	2.81116	+	2.48367i
$349$	−447.308			−1.28168			−0.640842	−	0.767673i	$-0.721415\pi$
$349$	−447.308			−1.28168			−0.640842	+	0.767673i	$0.721415\pi$
$350$		−	556.801i		−	1.59086i
$351$	188.767	+	129.164i	0.537798	+	0.367989i
$352$	696.808			1.97957
$353$			468.936i			1.32843i	0.747541	+	0.664216i	$0.231234\pi$
$353$			468.936i			1.32843i	−0.747541	+	0.664216i	$0.768766\pi$
$354$	−55.2450	+	62.5296i	−0.156059	+	0.176637i
$355$	267.666			0.753990
$356$			812.504i			2.28231i
$357$	403.724	+	356.691i	1.13088	+	0.999134i
$358$	−762.710			−2.13047
$359$		−	59.9848i		−	0.167088i	−0.996504	−	0.0835442i	$-0.973376\pi$
$359$		−	59.9848i		−	0.167088i	0.996504	−	0.0835442i	$-0.0266240\pi$
$360$	57.7346	+	464.930i	0.160374	+	1.29147i
$361$	−94.8786			−0.262822
$362$			332.447i			0.918361i
$363$	477.532	−	540.499i	1.31551	−	1.48898i
$364$	−694.562			−1.90814
$365$		−	348.214i		−	0.954012i
$366$	268.587	+	237.297i	0.733844	+	0.648352i
$367$	42.3632			0.115431			0.0577155	−	0.998333i	$-0.481618\pi$
$367$	42.3632			0.115431			0.0577155	+	0.998333i	$0.481618\pi$
$368$			315.887i			0.858390i
$369$	491.418	−	61.0238i	1.33176	−	0.165376i
$370$	−141.350			−0.382026
$371$		−	667.910i		−	1.80030i
$372$	73.3991	−	83.0774i	0.197309	−	0.223326i
$373$	−210.832			−0.565232			−0.282616	−	0.959233i	$-0.591202\pi$
$373$	−210.832			−0.565232			−0.282616	+	0.959233i	$0.591202\pi$
$374$		−	1373.64i		−	3.67284i
$375$	−266.159	−	235.152i	−0.709758	−	0.627072i
$376$	−45.6560			−0.121425
$377$			404.587i			1.07317i
$378$	496.814	−	726.070i	1.31432	−	1.92082i
$379$	142.841			0.376890			0.188445	−	0.982084i	$-0.439655\pi$
$379$	142.841			0.376890			0.188445	+	0.982084i	$0.439655\pi$
$380$		−	418.070i		−	1.10018i
$381$	−377.060	+	426.780i	−0.989660	+	1.12016i
$382$	−216.856			−0.567685
$383$			215.564i			0.562830i	0.959586	+	0.281415i	$0.0908038\pi$
$383$			215.564i			0.562830i	−0.959586	+	0.281415i	$0.909196\pi$
$384$	244.540	+	216.051i	0.636822	+	0.562633i
$385$	−481.205			−1.24988
$386$			107.853i			0.279413i
$387$	−49.8465	−	401.408i	−0.128802	−	1.03723i
$388$	−155.605			−0.401043
$389$			377.794i			0.971193i	0.874183	+	0.485596i	$0.161398\pi$
$389$			377.794i			0.971193i	−0.874183	+	0.485596i	$0.838602\pi$
$390$	−171.381	+	193.979i	−0.439439	+	0.497383i
$391$	206.223			0.527425
$392$			591.840i			1.50980i
$393$	283.843	+	250.776i	0.722246	+	0.638106i
$394$	−649.498			−1.64847
$395$		−	389.523i		−	0.986135i
$396$	−1546.99	+	192.104i	−3.90654	+	0.485110i
$397$	−420.666			−1.05961			−0.529806	−	0.848119i	$-0.677735\pi$
$397$	−420.666			−1.05961			−0.529806	+	0.848119i	$0.677735\pi$
$398$		−	228.845i		−	0.574987i
$399$	−291.593	+	330.042i	−0.730810	+	0.827174i
$400$	522.327			1.30582
$401$		−	762.529i		−	1.90157i	−0.309854	−	0.950784i	$-0.600280\pi$
$401$		−	762.529i		−	1.90157i	0.309854	−	0.950784i	$-0.399720\pi$
$402$	−421.978	−	372.818i	−1.04970	−	0.927408i
$403$	34.3581			0.0852559
$404$		−	611.818i		−	1.51440i
$405$	−55.7261	−	220.918i	−0.137595	−	0.545477i
$406$	1556.19			3.83299
$407$		−	263.837i		−	0.648248i
$408$	−733.551	+	830.277i	−1.79792	+	2.03499i
$409$	389.355			0.951968			0.475984	−	0.879454i	$-0.342092\pi$
$409$	389.355			0.951968			0.475984	+	0.879454i	$0.342092\pi$
$410$			560.391i			1.36681i
$411$	−168.049	−	148.472i	−0.408879	−	0.361246i
$412$	−1522.57			−3.69555
$413$			69.1217i			0.167365i
$414$	−41.5020	−	334.211i	−0.100246	−	0.807272i
$415$	−77.1635			−0.185936
$416$		−	310.504i		−	0.746405i
$417$	160.610	−	181.788i	0.385156	−	0.435942i
$418$	1122.95			2.68647
$419$		−	170.383i		−	0.406641i	−0.979112	−	0.203320i	$-0.934827\pi$
$419$		−	170.383i		−	0.406641i	0.979112	−	0.203320i	$-0.0651733\pi$
$420$	518.488	+	458.085i	1.23449	+	1.09068i
$421$	−211.619			−0.502657			−0.251329	−	0.967902i	$-0.580867\pi$
$421$	−211.619			−0.502657			−0.251329	+	0.967902i	$0.580867\pi$
$422$			363.339i			0.860994i
$423$	22.0338	−	2.73614i	0.0520894	−	0.00646842i
$424$	1373.59			3.23960
$425$		−	340.995i		−	0.802341i
$426$	684.415	−	774.662i	1.60661	−	1.81846i
$427$	296.903			0.695322
$428$			381.945i			0.892394i
$429$	−362.073	−	319.892i	−0.843994	−	0.745670i
$430$	457.748			1.06453
$431$			319.026i			0.740199i	0.928992	+	0.370100i	$0.120676\pi$
$431$			319.026i			0.740199i	−0.928992	+	0.370100i	$0.879324\pi$
$432$	681.116	+	466.055i	1.57666	+	1.07883i
$433$	−86.0871			−0.198815			−0.0994077	−	0.995047i	$-0.531695\pi$
$433$	−86.0871			−0.198815			−0.0994077	+	0.995047i	$0.531695\pi$
$434$		−	132.154i		−	0.304503i
$435$	266.837	−	302.022i	0.613419	−	0.694304i
$436$	132.740			0.304450
$437$			168.586i			0.385781i
$438$	−1007.78	−	890.374i	−2.30086	−	2.03282i
$439$	−334.000			−0.760821			−0.380410	−	0.924818i	$-0.624217\pi$
$439$	−334.000			−0.760821			−0.380410	+	0.924818i	$0.624217\pi$
$440$		−	989.621i		−	2.24914i
$441$	−35.4687	−	285.626i	−0.0804279	−	0.647677i
$442$	−612.108			−1.38486
$443$			503.833i			1.13732i	0.822573	+	0.568660i	$0.192538\pi$
$443$			503.833i			1.13732i	−0.822573	+	0.568660i	$0.807462\pi$
$444$	−251.161	+	284.279i	−0.565677	+	0.640267i
$445$	250.841			0.563688
$446$			751.515i			1.68501i
$447$	395.148	+	349.114i	0.884000	+	0.781015i
$448$	−94.0503			−0.209934
$449$		−	532.639i		−	1.18628i	−0.805100	−	0.593139i	$-0.797888\pi$
$449$		−	532.639i		−	1.18628i	0.805100	−	0.593139i	$-0.202112\pi$
$450$	−552.626	+	68.6245i	−1.22806	+	0.152499i
$451$	−1046.00			−2.31929
$452$		−	7.16821i		−	0.0158589i
$453$	−389.095	+	440.401i	−0.858930	+	0.972188i
$454$	1469.13			3.23597
$455$			214.430i			0.471274i
$456$	−678.747	−	599.674i	−1.48848	−	1.31508i
$457$	−52.1223			−0.114053			−0.0570266	−	0.998373i	$-0.518162\pi$
$457$	−52.1223			−0.114053			−0.0570266	+	0.998373i	$0.518162\pi$
$458$			647.007i			1.41268i
$459$	304.258	−	444.658i	0.662871	−	0.968753i
$460$	264.845			0.575749
$461$		−	830.105i		−	1.80066i	−0.435207	−	0.900330i	$-0.643325\pi$
$461$		−	830.105i		−	1.80066i	0.435207	−	0.900330i	$-0.356675\pi$
$462$	−1230.43	+	1392.67i	−2.66326	+	3.01444i
$463$	185.779			0.401250			0.200625	−	0.979668i	$-0.435703\pi$
$463$	185.779			0.401250			0.200625	+	0.979668i	$0.435703\pi$
$464$			1459.84i			3.14621i
$465$	−25.6482	−	22.6602i	−0.0551574	−	0.0487317i
$466$	320.674			0.688142
$467$			834.915i			1.78783i	0.448239	+	0.893914i	$0.352051\pi$
$467$			834.915i			1.78783i	−0.448239	+	0.893914i	$0.647949\pi$
$468$	85.6032	+	689.354i	0.182913	+	1.47298i
$469$	−466.464			−0.994594
$470$			25.1264i			0.0534604i
$471$	273.748	−	309.844i	0.581205	−	0.657843i
$472$	−142.152			−0.301170
$473$			854.412i			1.80637i
$474$	−1127.33	−	996.000i	−2.37834	−	2.10127i
$475$	278.762			0.586867
$476$			1636.10i			3.43719i
$477$	−662.902	+	82.3185i	−1.38973	+	0.172575i
$478$	−741.771			−1.55182
$479$			3.76008i			0.00784985i	0.999992	+	0.00392492i	$0.00124935\pi$
$479$			3.76008i			0.00784985i	−0.999992	+	0.00392492i	$0.998751\pi$
$480$	−204.787	+	231.790i	−0.426640	+	0.482896i
$481$	−117.568			−0.244425
$482$		−	925.741i		−	1.92063i
$483$	−209.080	−	184.722i	−0.432878	−	0.382448i
$484$	2190.39			4.52560
$485$			48.0392i			0.0990499i
$486$	−781.856	−	403.602i	−1.60876	−	0.830457i
$487$	532.953			1.09436			0.547180	−	0.837015i	$-0.315701\pi$
$487$	532.953			1.09436			0.547180	+	0.837015i	$0.315701\pi$
$488$			610.594i			1.25122i
$489$	−527.692	+	597.273i	−1.07912	+	1.22142i
$490$	325.715			0.664723
$491$			457.567i			0.931907i	0.884809	+	0.465954i	$0.154289\pi$
$491$			457.567i			0.931907i	−0.884809	+	0.465954i	$0.845711\pi$
$492$	1127.04	+	995.745i	2.29074	+	2.02387i
$493$	953.040			1.93314
$494$		−	500.395i		−	1.01295i
$495$	59.3075	+	477.596i	0.119813	+	0.964841i
$496$	123.972			0.249944
$497$		−	856.331i		−	1.72300i
$498$	−197.305	+	223.321i	−0.396195	+	0.448437i
$499$	838.159			1.67968			0.839839	−	0.542836i	$-0.182649\pi$
$499$	838.159			1.67968			0.839839	+	0.542836i	$0.182649\pi$
$500$		−	1078.62i		−	2.15724i
$501$	258.342	+	228.246i	0.515653	+	0.455580i
$502$	−755.853			−1.50568
$503$			85.9693i			0.170913i	0.996342	+	0.0854566i	$0.0272349\pi$
$503$			85.9693i			0.170913i	−0.996342	+	0.0854566i	$0.972765\pi$
$504$	1487.43	−	184.707i	2.95124	−	0.366482i
$505$	−188.884			−0.374028
$506$			711.379i			1.40589i
$507$	193.140	−	218.608i	0.380948	−	0.431179i
$508$	−1729.54			−3.40460
$509$			788.265i			1.54865i	0.632786	+	0.774327i	$0.281911\pi$
$509$			788.265i			1.54865i	−0.632786	+	0.774327i	$0.718089\pi$
$510$	456.936	+	403.704i	0.895953	+	0.791576i
$511$	−1114.02			−2.18008
$512$			1142.38i			2.23121i
$513$	363.505	+	248.729i	0.708588	+	0.484852i
$514$	−402.922			−0.783894
$515$			470.056i			0.912731i
$516$	813.360	−	920.610i	1.57628	−	1.78413i
$517$	−46.8998			−0.0907153
$518$			452.212i			0.872997i
$519$	−152.216	−	134.483i	−0.293286	−	0.259119i
$520$	−440.984			−0.848047
$521$		−	764.944i		−	1.46822i	−0.679029	−	0.734111i	$-0.737599\pi$
$521$		−	764.944i		−	1.46822i	0.679029	−	0.734111i	$-0.262401\pi$
$522$	−191.797	−	1544.52i	−0.367428	−	2.95886i
$523$	−901.245			−1.72322			−0.861611	−	0.507569i	$-0.830544\pi$
$523$	−901.245			−1.72322			−0.861611	+	0.507569i	$0.830544\pi$
$524$			1150.28i			2.19520i
$525$	−305.443	+	345.719i	−0.581796	+	0.658512i
$526$	−212.851			−0.404659
$527$		−	80.9337i		−	0.153574i
$528$	−1306.45	−	1154.25i	−2.47433	−	2.18607i
$529$	422.202			0.798113
$530$		−	755.943i		−	1.42631i
$531$	68.6034	−	8.51910i	0.129197	−	0.0160435i
$532$	−1337.51			−2.51411
$533$			466.108i			0.874500i
$534$	641.394	−	725.968i	1.20111	−	1.35949i
$535$	117.916			0.220404
$536$		−	959.306i		−	1.78975i
$537$	473.567	+	418.398i	0.881876	+	0.779139i
$538$	246.486			0.458152
$539$			607.964i			1.12795i
$540$	390.747	−	571.057i	0.723606	−	1.05751i
$541$	660.541			1.22096			0.610482	−	0.792030i	$-0.290976\pi$
$541$	660.541			1.22096			0.610482	+	0.792030i	$0.290976\pi$
$542$		−	559.852i		−	1.03294i
$543$	182.370	−	206.417i	0.335855	−	0.380141i
$544$	−731.421			−1.34452
$545$		−	40.9804i		−	0.0751934i
$546$	620.588	+	548.290i	1.13661	+	1.00419i
$547$	−446.351			−0.815998			−0.407999	−	0.912982i	$-0.633773\pi$
$547$	−446.351			−0.815998			−0.407999	+	0.912982i	$0.633773\pi$
$548$		−	681.026i		−	1.24275i
$549$	−36.5926	−	294.676i	−0.0666531	−	0.536750i
$550$	1176.28			2.13870
$551$			779.106i			1.41399i
$552$	379.890	−	429.982i	0.688207	−	0.778954i
$553$	−1246.18			−2.25349
$554$		−	1746.28i		−	3.15213i
$555$	87.7642	+	77.5399i	0.158134	+	0.139711i
$556$	736.702			1.32500
$557$		−	426.163i		−	0.765104i	−0.923934	−	0.382552i	$-0.875045\pi$
$557$		−	426.163i		−	0.765104i	0.923934	−	0.382552i	$-0.124955\pi$
$558$	−131.163	+	16.2877i	−0.235060	+	0.0291895i
$559$	380.734			0.681099
$560$			773.713i			1.38163i
$561$	−753.535	+	852.896i	−1.34320	+	1.52031i
$562$	−28.6129			−0.0509126
$563$			128.538i			0.228309i	0.993463	+	0.114155i	$0.0364160\pi$
$563$			128.538i			0.228309i	−0.993463	+	0.114155i	$0.963584\pi$
$564$	50.5335	+	44.6464i	0.0895984	+	0.0791603i
$565$	−2.21301			−0.00391684
$566$		−	1238.70i		−	2.18852i
$567$	−706.771	+	178.281i	−1.24651	+	0.314429i
$568$	1761.08			3.10050
$569$		−	276.291i		−	0.485572i	−0.970080	−	0.242786i	$-0.921939\pi$
$569$		−	276.291i		−	0.485572i	0.970080	−	0.242786i	$-0.0780613\pi$
$570$	−330.026	+	373.543i	−0.578993	+	0.655339i
$571$	−148.282			−0.259689			−0.129844	−	0.991534i	$-0.541448\pi$
$571$	−148.282			−0.259689			−0.129844	+	0.991534i	$0.541448\pi$
$572$		−	1467.31i		−	2.56523i
$573$	134.646	+	118.960i	0.234984	+	0.207609i
$574$	1792.83			3.12340
$575$			176.594i			0.307120i
$576$	11.5915	+	93.3450i	0.0201241	+	0.162057i
$577$	−186.092			−0.322516			−0.161258	−	0.986912i	$-0.551555\pi$
$577$	−186.092			−0.322516			−0.161258	+	0.986912i	$0.551555\pi$
$578$			395.431i			0.684137i
$579$	59.1649	−	66.9664i	0.102185	−	0.115659i
$580$	1223.95			2.11027
$581$			246.865i			0.424897i
$582$	139.032	+	122.835i	0.238886	+	0.211056i
$583$	1411.01			2.42026
$584$		−	2291.04i		−	3.92301i
$585$	212.822	−	26.4280i	0.363798	−	0.0451760i
$586$	213.256			0.363918
$587$		−	985.876i		−	1.67952i	−0.542960	−	0.839758i	$-0.682697\pi$
$587$		−	985.876i		−	1.67952i	0.542960	−	0.839758i	$-0.317303\pi$
$588$	578.753	−	655.068i	0.984275	−	1.11406i
$589$	66.1629			0.112331
$590$			78.2322i			0.132597i
$591$	403.274	+	356.293i	0.682359	+	0.602865i
$592$	−424.214			−0.716578
$593$		−	366.566i		−	0.618155i	−0.951037	−	0.309078i	$-0.899980\pi$
$593$		−	366.566i		−	0.618155i	0.951037	−	0.309078i	$-0.100020\pi$
$594$	1533.87	+	1049.56i	2.58228	+	1.76693i
$595$	505.108			0.848922
$596$			1601.35i			2.68683i
$597$	−125.537	+	142.090i	−0.210279	+	0.238007i
$598$	316.997			0.530096
$599$			544.283i			0.908653i	0.890835	+	0.454327i	$0.150120\pi$
$599$			544.283i			0.908653i	−0.890835	+	0.454327i	$0.849880\pi$
$600$	−710.986	−	628.158i	−1.18498	−	1.04693i
$601$	−648.078			−1.07833			−0.539166	−	0.842199i	$-0.681261\pi$
$601$	−648.078			−1.07833			−0.539166	+	0.842199i	$0.681261\pi$
$602$		−	1464.45i		−	2.43264i
$603$	57.4907	+	462.966i	0.0953411	+	0.767772i
$604$	−1784.74			−2.95487
$605$		−	676.230i		−	1.11774i
$606$	−482.972	+	546.656i	−0.796983	+	0.902073i
$607$	−288.308			−0.474972			−0.237486	−	0.971391i	$-0.576323\pi$
$607$	−288.308			−0.474972			−0.237486	+	0.971391i	$0.576323\pi$
$608$		−	597.933i		−	0.983443i
$609$	−966.243	−	853.677i	−1.58661	−	1.40177i
$610$	336.035			0.550877
$611$			20.8990i			0.0342046i
$612$	1623.83	−	201.646i	2.65332	−	0.329487i
$613$	259.679			0.423620			0.211810	−	0.977311i	$-0.432064\pi$
$613$	259.679			0.423620			0.211810	+	0.977311i	$0.432064\pi$
$614$			2162.23i			3.52156i
$615$	307.412	−	347.948i	0.499858	−	0.565769i
$616$	−3166.04			−5.13967
$617$		−	622.301i		−	1.00859i	−0.863531	−	0.504296i	$-0.831752\pi$
$617$		−	622.301i		−	1.00859i	0.863531	−	0.504296i	$-0.168248\pi$
$618$	1360.41	+	1201.92i	2.20130	+	1.94485i
$619$	605.489			0.978172			0.489086	−	0.872236i	$-0.337330\pi$
$619$	605.489			0.978172			0.489086	+	0.872236i	$0.337330\pi$
$620$		−	103.940i		−	0.167645i
$621$	−157.569	+	230.279i	−0.253734	+	0.370819i
$622$	−107.495			−0.172822
$623$		−	802.503i		−	1.28813i
$624$	−514.343	+	582.165i	−0.824268	+	0.932956i
$625$	94.2041			0.150727
$626$			605.605i			0.967421i
$627$	−697.239	−	616.012i	−1.11202	−	0.982475i
$628$	1255.65			1.99945
$629$			276.943i			0.440291i
$630$	−101.652	−	818.593i	−0.161352	−	1.29935i
$631$	−941.970			−1.49282			−0.746411	−	0.665486i	$-0.768224\pi$
$631$	−941.970			−1.49282			−0.746411	+	0.665486i	$0.768224\pi$
$632$		−	2562.83i		−	4.05511i
$633$	199.316	−	225.598i	0.314875	−	0.356395i
$634$	−1430.73			−2.25668
$635$			533.954i			0.840872i
$636$	−1520.33	−	1343.22i	−2.39046	−	2.11197i
$637$	270.915			0.425298
$638$			3287.57i			5.15294i
$639$	−849.909	+	105.541i	−1.33006	+	0.165166i
$640$	305.949			0.478046
$641$		−	401.011i		−	0.625602i	−0.949819	−	0.312801i	$-0.898733\pi$
$641$		−	401.011i		−	0.625602i	0.949819	−	0.312801i	$-0.101267\pi$
$642$	301.509	−	341.265i	0.469640	−	0.531566i
$643$	851.435			1.32416			0.662080	−	0.749433i	$-0.269674\pi$
$643$	851.435			1.32416			0.662080	+	0.749433i	$0.269674\pi$
$644$		−	847.303i		−	1.31569i
$645$	−284.216	−	251.106i	−0.440646	−	0.389311i
$646$	−1178.73			−1.82465
$647$		−	221.121i		−	0.341764i	−0.985292	−	0.170882i	$-0.945338\pi$
$647$		−	221.121i		−	0.341764i	0.985292	−	0.170882i	$-0.0546617\pi$
$648$	−366.644	−	1453.51i	−0.565808	−	2.24307i
$649$	−146.025			−0.225000
$650$		−	524.163i		−	0.806405i
$651$	−72.4956	+	82.0548i	−0.111360	+	0.126044i
$652$	−2420.47			−3.71237
$653$		−	512.798i		−	0.785296i	−0.919689	−	0.392648i	$-0.871559\pi$
$653$		−	512.798i		−	0.785296i	0.919689	−	0.392648i	$-0.128441\pi$
$654$	−118.603	−	104.786i	−0.181350	−	0.160223i
$655$	355.122			0.542172
$656$			1681.83i			2.56376i
$657$	137.301	+	1105.67i	0.208981	+	1.68291i
$658$	80.3855			0.122166
$659$			241.786i			0.366898i	0.983029	+	0.183449i	$0.0587262\pi$
$659$			241.786i			0.366898i	−0.983029	+	0.183449i	$0.941274\pi$
$660$	−967.738	+	1095.34i	−1.46627	+	1.65961i
$661$	−1100.95			−1.66558			−0.832790	−	0.553590i	$-0.813258\pi$
$661$	−1100.95			−1.66558			−0.832790	+	0.553590i	$0.813258\pi$
$662$			942.070i			1.42307i
$663$	380.059	+	335.783i	0.573241	+	0.506459i
$664$	−507.689			−0.764592
$665$			412.924i			0.620938i
$666$	448.821	−	55.7342i	0.673906	−	0.0836849i
$667$	−493.559			−0.739968
$668$			1046.94i			1.56728i
$669$	412.257	−	466.617i	0.616228	−	0.697484i
$670$	−527.946			−0.787979
$671$			627.228i			0.934767i
$672$	741.554	+	655.164i	1.10350	+	0.974947i
$673$	820.295			1.21886			0.609431	−	0.792839i	$-0.291398\pi$
$673$	820.295			1.21886			0.609431	+	0.792839i	$0.291398\pi$
$674$		−	355.037i		−	0.526762i
$675$	380.771	+	260.543i	0.564106	+	0.385990i
$676$	885.915			1.31053
$677$			863.866i			1.27602i	0.770028	+	0.638010i	$0.220242\pi$
$677$			863.866i			1.27602i	−0.770028	+	0.638010i	$0.779758\pi$
$678$	−5.65861	+	6.40475i	−0.00834603	+	0.00944654i
$679$	153.689			0.226346
$680$			1038.78i			1.52762i
$681$	−912.186	−	805.918i	−1.33948	−	1.18343i
$682$	279.186			0.409363
$683$		−	1009.66i		−	1.47828i	−0.673554	−	0.739138i	$-0.735233\pi$
$683$		−	1009.66i		−	1.47828i	0.673554	−	0.739138i	$-0.264767\pi$
$684$	164.845	+	1327.48i	0.241001	+	1.94076i
$685$	−210.251			−0.306935
$686$			554.585i			0.808434i
$687$	354.927	−	401.727i	0.516633	−	0.584756i
$688$	1373.78			1.99677
$689$		−	628.759i		−	0.912568i
$690$	−236.637	−	209.069i	−0.342953	−	0.302999i
$691$	584.388			0.845714			0.422857	−	0.906196i	$-0.361027\pi$
$691$	584.388			0.845714			0.422857	+	0.906196i	$0.361027\pi$
$692$		−	616.858i		−	0.891414i
$693$	1527.95	−	189.739i	2.20483	−	0.273794i
$694$	−1399.91			−2.01716
$695$		−	227.439i		−	0.327251i
$696$	1755.63	−	1987.12i	2.52245	−	2.85506i
$697$	1097.96			1.57527
$698$			1619.66i			2.32043i
$699$	−199.107	−	175.911i	−0.284846	−	0.251662i
$700$	−1401.04			−2.00148
$701$			813.924i			1.16109i	0.814228	+	0.580545i	$0.197160\pi$
$701$			813.924i			1.16109i	−0.814228	+	0.580545i	$0.802840\pi$
$702$	467.693	−	683.509i	0.666229	−	0.973660i
$703$	−226.399			−0.322048
$704$		−	198.688i		−	0.282227i
$705$	13.7835	−	15.6010i	0.0195511	−	0.0221291i
$706$	1697.98			2.40507
$707$			604.287i			0.854720i
$708$	157.338	+	139.009i	0.222229	+	0.196340i
$709$	275.826			0.389035			0.194518	−	0.980899i	$-0.437686\pi$
$709$	275.826			0.389035			0.194518	+	0.980899i	$0.437686\pi$
$710$		−	969.198i		−	1.36507i
$711$	153.589	+	1236.84i	0.216018	+	1.73957i
$712$	1650.38			2.31796
$713$			41.9138i			0.0587851i
$714$	1291.55	−	1461.85i	1.80889	−	2.04741i
$715$	−452.998			−0.633564
$716$			1919.15i			2.68037i
$717$	460.567	+	406.912i	0.642353	+	0.567520i
$718$	−217.200			−0.302507
$719$			79.3016i			0.110294i	0.998478	+	0.0551471i	$0.0175628\pi$
$719$			79.3016i			0.110294i	−0.998478	+	0.0551471i	$0.982437\pi$
$720$	767.910	−	95.3583i	1.06654	−	0.132442i
$721$	1503.83			2.08575
$722$			343.547i			0.475827i
$723$	−507.832	+	574.794i	−0.702395	+	0.795013i
$724$	836.510			1.15540
$725$			816.112i			1.12567i
$726$	−1957.10	−	1729.10i	−2.69573	−	2.38168i
$727$	−432.390			−0.594759			−0.297380	−	0.954759i	$-0.596113\pi$
$727$	−432.390			−0.594759			−0.297380	+	0.954759i	$0.596113\pi$
$728$			1410.82i			1.93794i
$729$	264.052	+	679.498i	0.362212	+	0.932096i
$730$	−1260.85			−1.72720
$731$		−	896.854i		−	1.22689i
$732$	597.092	−	675.824i	0.815700	−	0.923257i
$733$	−700.451			−0.955595			−0.477797	−	0.878470i	$-0.658565\pi$
$733$	−700.451			−0.955595			−0.477797	+	0.878470i	$0.658565\pi$
$734$		−	153.393i		−	0.208983i
$735$	−202.237	−	178.676i	−0.275152	−	0.243097i
$736$	378.787			0.514657
$737$		−	985.440i		−	1.33710i
$738$	−220.962	−	1779.38i	−0.299407	−	2.41109i
$739$	906.590			1.22678			0.613389	−	0.789781i	$-0.289806\pi$
$739$	906.590			1.22678			0.613389	+	0.789781i	$0.289806\pi$
$740$			355.667i			0.480632i
$741$	−274.501	+	310.696i	−0.370446	+	0.419293i
$742$	−2418.45			−3.25936
$743$		−	350.702i		−	0.472008i	−0.971752	−	0.236004i	$-0.924162\pi$
$743$		−	350.702i		−	0.472008i	0.971752	−	0.236004i	$-0.0758378\pi$
$744$	−168.750	−	149.091i	−0.226814	−	0.200390i
$745$	494.379			0.663595
$746$			763.404i			1.02333i
$747$	245.014	−	30.4256i	0.327997	−	0.0407303i
$748$	−3456.39			−4.62084
$749$		−	377.243i		−	0.503663i
$750$	−851.466	+	963.740i	−1.13529	+	1.28499i
$751$	−688.234			−0.916423			−0.458212	−	0.888843i	$-0.651510\pi$
$751$	−688.234			−0.916423			−0.458212	+	0.888843i	$0.651510\pi$
$752$			75.4085i			0.100277i
$753$	469.310	+	414.637i	0.623254	+	0.550646i
$754$	1464.97			1.94294
$755$			550.996i			0.729796i
$756$	−1826.95	−	1250.10i	−2.41660	−	1.65357i
$757$	1336.84			1.76597			0.882983	−	0.469406i	$-0.155532\pi$
$757$	1336.84			1.76597			0.882983	+	0.469406i	$0.155532\pi$
$758$		−	517.217i		−	0.682344i
$759$	390.240	−	441.696i	0.514150	−	0.581945i
$760$	−849.196			−1.11736
$761$		−	882.165i		−	1.15922i	−0.814895	−	0.579609i	$-0.803205\pi$
$761$		−	882.165i		−	1.15922i	0.814895	−	0.579609i	$-0.196795\pi$
$762$	1545.33	+	1365.30i	2.02800	+	1.79174i
$763$	−131.106			−0.171830
$764$			545.657i			0.714211i
$765$	−62.2535	−	501.320i	−0.0813771	−	0.655321i
$766$	780.539			1.01898
$767$			65.0700i			0.0848371i
$768$	865.342	−	979.446i	1.12675	−	1.27532i
$769$	−142.803			−0.185700			−0.0928500	−	0.995680i	$-0.529598\pi$
$769$	−142.803			−0.185700			−0.0928500	+	0.995680i	$0.529598\pi$
$770$			1742.40i			2.26286i
$771$	250.175	+	221.030i	0.324481	+	0.286679i
$772$	271.383			0.351533
$773$		−	43.6724i		−	0.0564973i	−0.999601	−	0.0282486i	$-0.991007\pi$
$773$		−	43.6724i		−	0.0564973i	0.999601	−	0.0282486i	$-0.00899302\pi$
$774$	−1453.47	+	180.490i	−1.87786	+	0.233191i
$775$	69.3055			0.0894264
$776$			316.069i			0.407305i
$777$	248.069	−	280.779i	0.319265	−	0.361363i
$778$	1367.96			1.75830
$779$			897.577i			1.15222i
$780$	488.095	+	431.233i	0.625763	+	0.552863i
$781$	1809.06			2.31634
$782$		−	746.716i		−	0.954880i
$783$	−728.188	+	1064.21i	−0.929998	+	1.35915i
$784$	977.524			1.24684
$785$		−	387.653i		−	0.493825i
$786$	908.038	−	1027.77i	1.15526	−	1.30760i
$787$	−276.086			−0.350808			−0.175404	−	0.984497i	$-0.556123\pi$
$787$	−276.086			−0.350808			−0.175404	+	0.984497i	$0.556123\pi$
$788$			1634.28i			2.07396i
$789$	132.159	+	116.763i	0.167502	+	0.147988i
$790$	−1410.43			−1.78536
$791$			7.07997i			0.00895066i
$792$	390.207	+	3142.30i	0.492686	+	3.96755i
$793$	279.499			0.352458
$794$			1523.20i			1.91838i
$795$	−414.686	+	469.366i	−0.521617	+	0.590398i
$796$	−575.825			−0.723398
$797$		−	288.683i		−	0.362212i	−0.983464	−	0.181106i	$-0.942032\pi$
$797$		−	288.683i		−	0.362212i	0.983464	−	0.181106i	$-0.0579677\pi$
$798$	1195.06	+	1055.83i	1.49756	+	1.32310i
$799$	49.2295			0.0616139
$800$		−	626.334i		−	0.782918i
$801$	−796.485	+	98.9067i	−0.994363	+	0.123479i
$802$	−2761.05			−3.44271
$803$		−	2353.45i		−	2.93083i
$804$	−938.093	+	1061.79i	−1.16678	+	1.32063i
$805$	−261.585			−0.324950
$806$		−	124.408i		−	0.154352i
$807$	−153.043	−	135.214i	−0.189645	−	0.167551i
$808$	−1242.74			−1.53805
$809$			1067.95i			1.32008i	0.751228	+	0.660042i	$0.229462\pi$
$809$			1067.95i			1.32008i	−0.751228	+	0.660042i	$0.770538\pi$
$810$	−799.925	+	201.779i	−0.987562	+	0.249110i
$811$	−237.591			−0.292960			−0.146480	−	0.989214i	$-0.546794\pi$
$811$	−237.591			−0.292960			−0.146480	+	0.989214i	$0.546794\pi$
$812$		−	3915.73i		−	4.82233i
$813$	−307.117	+	347.613i	−0.377757	+	0.427568i
$814$	−955.332			−1.17363
$815$			747.262i			0.916886i
$816$	1371.34	+	1211.58i	1.68057	+	1.48478i
$817$	733.174			0.897397
$818$		−	1409.82i		−	1.72350i
$819$	−84.5496	−	680.868i	−0.103235	−	0.831341i
$820$	1410.07			1.71960
$821$		−	141.405i		−	0.172235i	−0.996285	−	0.0861173i	$-0.972554\pi$
$821$		−	141.405i		−	0.172235i	0.996285	−	0.0861173i	$-0.0274460\pi$
$822$	−537.605	+	608.493i	−0.654020	+	0.740259i
$823$	597.748			0.726304			0.363152	−	0.931730i	$-0.381701\pi$
$823$	597.748			0.726304			0.363152	+	0.931730i	$0.381701\pi$
$824$			3092.69i			3.75326i
$825$	−730.356	−	645.271i	−0.885280	−	0.782146i
$826$	250.284			0.303007
$827$		−	474.391i		−	0.573629i	−0.957986	−	0.286814i	$-0.907404\pi$
$827$		−	474.391i		−	0.573629i	0.957986	−	0.286814i	$-0.0925963\pi$
$828$	−840.949	+	104.428i	−1.01564	+	0.126121i
$829$	−384.059			−0.463280			−0.231640	−	0.972802i	$-0.574409\pi$
$829$	−384.059			−0.463280			−0.231640	+	0.972802i	$0.574409\pi$
$830$			279.403i			0.336630i
$831$	−957.952	+	1084.27i	−1.15277	+	1.30477i
$832$	−88.5373			−0.106415
$833$		−	638.164i		−	0.766103i
$834$	−658.239	−	581.555i	−0.789255	−	0.697308i
$835$	323.218			0.387087
$836$		−	2825.58i		−	3.37988i
$837$	90.3744	+	61.8389i	0.107974	+	0.0738816i
$838$	−616.941			−0.736206
$839$			1.42512i			0.00169860i	1.00000		0.000849299i	$0.000270340\pi$
$839$			1.42512i			0.00169860i	−1.00000		0.000849299i	$0.999730\pi$
$840$	930.477	−	1053.17i	1.10771	−	1.25377i
$841$	−1439.94			−1.71217
$842$			766.254i			0.910040i
$843$	17.7658	+	15.6961i	0.0210745	+	0.0186193i
$844$	914.243			1.08323
$845$		−	273.505i		−	0.323675i
$846$	−9.90733	−	79.7827i	−0.0117108	−	0.0943058i
$847$	−2163.43			−2.55422
$848$		−	2268.71i		−	2.67537i
$849$	−679.512	+	769.112i	−0.800367	+	0.905903i
$850$	−1234.71			−1.45260
$851$		−	143.423i		−	0.168534i
$852$	−1949.22	−	1722.14i	−2.28782	−	2.02129i
$853$	1057.46			1.23969			0.619846	−	0.784724i	$-0.287195\pi$
$853$	1057.46			1.23969			0.619846	+	0.784724i	$0.287195\pi$
$854$		−	1075.06i		−	1.25885i
$855$	409.827	−	50.8919i	0.479330	−	0.0595227i
$856$	775.818			0.906330
$857$		−	481.634i		−	0.562000i	−0.959708	−	0.281000i	$-0.909334\pi$
$857$		−	481.634i		−	0.562000i	0.959708	−	0.281000i	$-0.0906660\pi$
$858$	−1158.30	+	1311.04i	−1.35000	+	1.52802i
$859$	1045.33			1.21691			0.608455	−	0.793589i	$-0.291790\pi$
$859$	1045.33			1.21691			0.608455	+	0.793589i	$0.291790\pi$
$860$		−	1151.80i		−	1.33930i
$861$	−1113.17	−	983.488i	−1.29288	−	1.14226i
$862$	1155.17			1.34010
$863$		−	240.120i		−	0.278238i	−0.990276	−	0.139119i	$-0.955573\pi$
$863$		−	240.120i		−	0.278238i	0.990276	−	0.139119i	$-0.0444271\pi$
$864$	558.856	−	816.740i	0.646824	−	0.945301i
$865$	−190.440			−0.220162
$866$			311.714i			0.359947i
$867$	216.921	−	245.524i	0.250197	−	0.283188i
$868$	−332.530			−0.383099
$869$		−	2632.65i		−	3.02951i
$870$	−1093.60	−	966.195i	−1.25701	−	1.11057i
$871$	−439.122			−0.504158
$872$		−	269.626i		−	0.309204i
$873$	−18.9418	−	152.537i	−0.0216974	−	0.174727i
$874$	610.437			0.698440
$875$			1065.34i			1.21753i
$876$	−2240.38	+	2535.79i	−2.55751	+	2.89474i
$877$	−541.206			−0.617111			−0.308556	−	0.951206i	$-0.599846\pi$
$877$	−541.206			−0.617111			−0.308556	+	0.951206i	$0.599846\pi$
$878$			1209.39i			1.37743i
$879$	−132.411	−	116.985i	−0.150638	−	0.133089i
$880$	−1634.52			−1.85741
$881$			167.307i			0.189906i	0.995482	+	0.0949528i	$0.0302700\pi$
$881$			167.307i			0.189906i	−0.995482	+	0.0949528i	$0.969730\pi$
$882$	−1034.23	+	128.429i	−1.17259	+	0.145611i
$883$	850.375			0.963052			0.481526	−	0.876432i	$-0.340083\pi$
$883$	850.375			0.963052			0.481526	+	0.876432i	$0.340083\pi$
$884$			1540.20i			1.74231i
$885$	42.9156	−	48.5745i	0.0484923	−	0.0548864i
$886$	1824.34			2.05907
$887$			61.0295i			0.0688044i	0.999408	+	0.0344022i	$0.0109527\pi$
$887$			61.0295i			0.0688044i	−0.999408	+	0.0344022i	$0.989047\pi$
$888$	577.436	+	510.165i	0.650265	+	0.574511i
$889$	1708.25			1.92154
$890$		−	908.275i		−	1.02053i
$891$	−376.632	−	1493.11i	−0.422708	−	1.67576i
$892$	1890.98			2.11993
$893$			40.2449i			0.0450670i
$894$	1264.11	−	1430.80i	1.41400	−	1.60044i
$895$	592.491			0.662001
$896$		−	978.807i		−	1.09242i
$897$	−196.824	−	173.895i	−0.219425	−	0.193862i
$898$	−1928.64			−2.14771
$899$			193.701i			0.215462i
$900$	172.675	+	1390.53i	0.191861	+	1.54503i
$901$	−1481.10			−1.64384
$902$			3787.48i			4.19898i
$903$	−803.349	+	909.278i	−0.889644	+	1.00695i
$904$	−14.5603			−0.0161065
$905$		−	258.253i		−	0.285362i
$906$	1594.66	+	1408.88i	1.76011	+	1.55506i
$907$	−30.5548			−0.0336878			−0.0168439	−	0.999858i	$-0.505362\pi$
$907$	−30.5548			−0.0336878			−0.0168439	+	0.999858i	$0.505362\pi$
$908$		−	3696.66i		−	4.07122i
$909$	599.755	−	74.4770i	0.659797	−	0.0819329i
$910$	776.432			0.853222
$911$			656.020i			0.720110i	0.932931	+	0.360055i	$0.117242\pi$
$911$			656.020i			0.720110i	−0.932931	+	0.360055i	$0.882758\pi$
$912$	−990.463	+	1121.06i	−1.08603	+	1.22924i
$913$	−521.520			−0.571216
$914$			188.730i			0.206488i
$915$	−208.645	−	184.338i	−0.228027	−	0.201462i
$916$	1628.01			1.77731
$917$		−	1136.12i		−	1.23896i
$918$	−1610.07	−	1101.69i	−1.75389	−	1.20010i
$919$	213.211			0.232004			0.116002	−	0.993249i	$-0.462992\pi$
$919$	213.211			0.232004			0.116002	+	0.993249i	$0.462992\pi$
$920$		−	537.961i		−	0.584740i
$921$	1186.13	−	1342.53i	1.28787	−	1.45769i
$922$	−3005.74			−3.26002
$923$		−	806.135i		−	0.873386i
$924$	3504.27	+	3096.03i	3.79250	+	3.35068i
$925$	−237.153			−0.256382
$926$		−	672.689i		−	0.726446i
$927$	−185.343	−	1492.55i	−0.199939	−	1.61008i
$928$	1750.53			1.88635
$929$			188.725i			0.203149i	0.994828	+	0.101574i	$0.0323880\pi$
$929$			188.725i			0.203149i	−0.994828	+	0.101574i	$0.967612\pi$
$930$	−82.0507	+	92.8699i	−0.0882266	+	0.0998601i
$931$	521.696			0.560361
$932$		−	806.888i		−	0.865760i
$933$	66.7441	+	58.9685i	0.0715371	+	0.0632031i
$934$	3023.16			3.23679
$935$			1067.08i			1.14126i
$936$	1400.24	−	173.880i	1.49598	−	0.185769i
$937$	1234.88			1.31791			0.658956	−	0.752181i	$-0.270998\pi$
$937$	1234.88			1.31791			0.658956	+	0.752181i	$0.270998\pi$
$938$			1689.03i			1.80067i
$939$	332.215	−	376.021i	0.353797	−	0.400449i
$940$	63.2236			0.0672592
$941$			36.7630i			0.0390680i	0.999809	+	0.0195340i	$0.00621826\pi$
$941$			36.7630i			0.0390680i	−0.999809	+	0.0195340i	$0.993782\pi$
$942$	−1121.92	−	991.217i	−1.19100	−	1.05225i
$943$	−568.610			−0.602980
$944$			234.788i			0.248716i
$945$	−385.937	+	564.028i	−0.408399	+	0.596855i
$946$	3093.75			3.27035
$947$			22.9549i			0.0242397i	0.999927	+	0.0121198i	$0.00385795\pi$
$947$			22.9549i			0.0242397i	−0.999927	+	0.0121198i	$0.996142\pi$
$948$	−2506.16	+	2836.62i	−2.64363	+	2.99221i
$949$	−1048.72			−1.10508
$950$		−	1009.37i		−	1.06250i
$951$	888.345	+	784.855i	0.934117	+	0.825294i
$952$	3323.31			3.49087
$953$			86.8265i			0.0911086i	0.998962	+	0.0455543i	$0.0145054\pi$
$953$			86.8265i			0.0911086i	−0.998962	+	0.0455543i	$0.985495\pi$
$954$	298.068	+	2400.31i	0.312440	+	2.51605i
$955$	168.459			0.176396
$956$			1866.46i			1.95237i
$957$	1803.46	−	2041.26i	1.88449	−	2.13298i
$958$	13.6149			0.0142118
$959$			672.643i			0.701401i
$960$	66.0927	+	58.3930i	0.0688466	+	0.0608261i
$961$	−944.551			−0.982883
$962$			425.705i			0.442521i
$963$	−374.414	+	46.4944i	−0.388800	+	0.0482808i
$964$	−2329.37			−2.41636
$965$		−	83.7832i		−	0.0868220i
$966$	−668.864	+	757.061i	−0.692406	+	0.783707i
$967$	1078.28			1.11508			0.557541	−	0.830150i	$-0.311745\pi$
$967$	1078.28			1.11508			0.557541	+	0.830150i	$0.311745\pi$
$968$		−	4449.19i		−	4.59627i
$969$	731.873	+	646.611i	0.755287	+	0.667297i
$970$	173.946			0.179326
$971$			96.3825i			0.0992611i	0.998768	+	0.0496305i	$0.0158044\pi$
$971$			96.3825i			0.0992611i	−0.998768	+	0.0496305i	$0.984196\pi$
$972$	−1015.55	+	1967.32i	−1.04481	+	2.02400i
$973$	−727.634			−0.747825
$974$		−	1929.78i		−	1.98129i
$975$	−287.539	+	325.454i	−0.294912	+	0.333799i
$976$	1008.50			1.03330
$977$		−	127.665i		−	0.130671i	−0.997863	−	0.0653353i	$-0.979188\pi$
$977$		−	127.665i		−	0.130671i	0.997863	−	0.0653353i	$-0.0208117\pi$
$978$	2162.68	+	1910.73i	2.21132	+	1.95371i
$979$	1695.35			1.73171
$980$		−	819.570i		−	0.836296i
$981$	16.1586	+	130.123i	0.0164715	+	0.132643i
$982$	1656.81			1.68718
$983$			1003.04i			1.02038i	0.860061	+	0.510192i	$0.170426\pi$
$983$			1003.04i			1.02038i	−0.860061	+	0.510192i	$0.829574\pi$
$984$	2022.59	−	2289.29i	2.05548	−	2.32651i
$985$	504.546			0.512229
$986$		−	3450.88i		−	3.49988i
$987$	−49.9115	−	44.0969i	−0.0505689	−	0.0446777i
$988$	−1259.11			−1.27440
$989$			464.461i			0.469627i
$990$	1729.34	−	214.747i	1.74680	−	0.216916i
$991$	−1673.44			−1.68864			−0.844319	−	0.535841i	$-0.819995\pi$
$991$	−1673.44			−1.68864			−0.844319	+	0.535841i	$0.819995\pi$
$992$		−	148.658i		−	0.149857i
$993$	516.789	−	584.932i	0.520432	−	0.589056i
$994$	−3100.70			−3.11942
$995$			177.772i			0.178665i
$996$	561.927	+	496.463i	0.564183	+	0.498457i
$997$	−968.793			−0.971708			−0.485854	−	0.874040i	$-0.661491\pi$
$997$	−968.793			−0.971708			−0.485854	+	0.874040i	$0.661491\pi$
$998$		−	3034.90i		−	3.04099i
$999$	−309.248	−	211.603i	−0.309557	−	0.211815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.2	✓	38
3.2	odd	2	inner	177.3.b.a.119.37	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.2	✓	38	1.1	even	1	trivial
177.3.b.a.119.37	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)

\(f(q)\)	\(=\)	\(q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +O(q^{10})\)	\(q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +10.1850 q^{10} +19.0108i q^{11} +(18.0974 - 20.4837i) q^{12} +8.47140 q^{13} -32.5842i q^{14} +(-6.32386 - 5.58714i) q^{15} +30.5668 q^{16} -19.9551i q^{17} +(-32.3399 + 4.01593i) q^{18} +16.3132 q^{19} -25.6276i q^{20} +(-17.8746 + 20.2316i) q^{21} +68.8365 q^{22} +10.3343i q^{23} +(-41.6072 - 36.7600i) q^{24} +17.0881 q^{25} -30.6742i q^{26} +(22.2829 + 15.2471i) q^{27} -81.9891 q^{28} +47.7591i q^{29} +(-20.2306 + 22.8982i) q^{30} +4.05578 q^{31} -36.6533i q^{32} +(-42.7407 - 37.7615i) q^{33} -72.2559 q^{34} +25.3122i q^{35} +(10.1050 + 81.3743i) q^{36} -13.8783 q^{37} -59.0688i q^{38} +(-16.8269 + 19.0457i) q^{39} -52.0557 q^{40} +55.0214i q^{41} +(73.2568 + 64.7226i) q^{42} +44.9435 q^{43} -173.208i q^{44} +(25.1224 - 3.11967i) q^{45} +37.4197 q^{46} +2.46701i q^{47} +(-60.7153 + 68.7212i) q^{48} +31.9799 q^{49} -61.8745i q^{50} +(44.8638 + 39.6372i) q^{51} -77.1832 q^{52} -74.2215i q^{53} +(55.2084 - 80.6844i) q^{54} -53.4739 q^{55} +166.539i q^{56} +(-32.4032 + 36.6759i) q^{57} +172.932 q^{58} +7.68115i q^{59} +(57.6169 + 50.9046i) q^{60} +32.9933 q^{61} -14.6856i q^{62} +(-9.98059 - 80.3726i) q^{63} -10.4513 q^{64} +23.8285i q^{65} +(-136.731 + 154.760i) q^{66} -51.8358 q^{67} +181.812i q^{68} +(-23.2340 - 20.5273i) q^{69} +91.6533 q^{70} -95.1596i q^{71} +(165.290 - 20.5256i) q^{72} -123.796 q^{73} +50.2521i q^{74} +(-33.9423 + 38.4179i) q^{75} -148.630 q^{76} +171.076i q^{77} +(68.9627 + 60.9287i) q^{78} -138.482 q^{79} +85.9787i q^{80} +(-78.5398 + 19.8115i) q^{81} +199.228 q^{82} +27.4328i q^{83} +(162.856 - 184.331i) q^{84} +56.1301 q^{85} -162.737i q^{86} +(-107.374 - 94.8648i) q^{87} -351.826 q^{88} -89.1780i q^{89} +(-11.2961 - 90.9660i) q^{90} +76.2331 q^{91} -94.1564i q^{92} +(-8.05606 + 9.11833i) q^{93} +8.93283 q^{94} +45.8861i q^{95} +(82.4051 + 72.8050i) q^{96} +17.0787 q^{97} -115.797i q^{98} +(169.793 - 21.0847i) 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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