LMFDB - Embedded newform 177.3.b.a.119.22

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			119.22
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} +O(q^{10})$	\(q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} -3.61168 q^{10} -2.06521i q^{11} +(-5.02278 + 10.1551i) q^{12} +15.4082 q^{13} -4.35364i q^{14} +(-20.5417 - 10.1600i) q^{15} +13.3675 q^{16} -15.6666i q^{17} +(3.38192 - 2.58245i) q^{18} -31.9933 q^{19} +28.8484i q^{20} +(12.2472 - 24.7617i) q^{21} +0.976424 q^{22} +41.9436i q^{23} +(-9.88681 - 4.89007i) q^{24} -33.3541 q^{25} +7.28491i q^{26} +(26.4996 - 5.17418i) q^{27} -34.7748 q^{28} +41.7036i q^{29} +(4.80362 - 9.71202i) q^{30} -6.91310 q^{31} +21.0268i q^{32} +(5.55348 + 2.74678i) q^{33} +7.40712 q^{34} -70.3421i q^{35} +(-20.6274 - 27.0131i) q^{36} +63.0547 q^{37} -15.1263i q^{38} +(-20.4932 + 41.4335i) q^{39} -28.0861 q^{40} -28.7568i q^{41} +(11.7072 + 5.79044i) q^{42} +59.9306 q^{43} -7.79920i q^{44} +(54.6418 - 41.7248i) q^{45} -19.8308 q^{46} +37.1422i q^{47} +(-17.7791 + 35.9461i) q^{48} +35.7927 q^{49} -15.7697i q^{50} +(42.1285 + 20.8370i) q^{51} +58.1884 q^{52} -0.0188512i q^{53} +(2.44633 + 12.5289i) q^{54} +15.7761 q^{55} -33.8560i q^{56} +(42.5519 - 86.0320i) q^{57} -19.7173 q^{58} -7.68115i q^{59} +(-77.5750 - 38.3690i) q^{60} -21.9824 q^{61} -3.26849i q^{62} +(50.2965 + 65.8671i) q^{63} +43.5288 q^{64} +117.703i q^{65} +(-1.29867 + 2.62566i) q^{66} +25.9477 q^{67} -59.1645i q^{68} +(-112.789 - 55.7860i) q^{69} +33.2574 q^{70} +40.5584i q^{71} +(26.2994 - 20.0823i) q^{72} -42.2494 q^{73} +29.8120i q^{74} +(44.3618 - 89.6913i) q^{75} -120.822 q^{76} +19.0171i q^{77} +(-19.5896 - 9.68910i) q^{78} +32.2588 q^{79} +102.114i q^{80} +(-21.3314 + 78.1407i) q^{81} +13.5961 q^{82} -19.0053i q^{83} +(46.2513 - 93.5115i) q^{84} +119.677 q^{85} +28.3349i q^{86} +(-112.144 - 55.4667i) q^{87} +7.59312 q^{88} -77.7511i q^{89} +(19.7273 + 25.8344i) q^{90} -141.883 q^{91} +158.399i q^{92} +(9.19458 - 18.5897i) q^{93} -17.5607 q^{94} -244.397i q^{95} +(-56.5424 - 27.9662i) q^{96} +123.092 q^{97} +16.9226i q^{98} +(-14.7725 + 11.2804i) 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 $

$2$			0.472796i			0.236398i	0.992990	+	0.118199i	$0.0377121\pi$
$2$			0.472796i			0.236398i	−0.992990	+	0.118199i	$0.962288\pi$
$3$	−1.33002	+	2.68906i	−0.443341	+	0.896353i
$3$	−1.33002	+	2.68906i	−0.443341	+	0.896353i
$4$	3.77646			0.944116
$5$			7.63899i			1.52780i	0.645336	+	0.763899i	$0.276717\pi$
$5$			7.63899i			1.52780i	−0.645336	+	0.763899i	$0.723283\pi$
$6$	−1.27138	−	0.628829i	−0.211896	−	0.104805i
$7$	−9.20830			−1.31547			−0.657735	−	0.753249i	$-0.728486\pi$
$7$	−9.20830			−1.31547			−0.657735	+	0.753249i	$0.728486\pi$
$8$			3.67668i			0.459585i
$9$	−5.46208	−	7.15302i	−0.606898	−	0.794780i
$10$	−3.61168			−0.361168
$11$		−	2.06521i		−	0.187747i	−0.995584	−	0.0938733i	$-0.970075\pi$
$11$		−	2.06521i		−	0.187747i	0.995584	−	0.0938733i	$-0.0299249\pi$
$12$	−5.02278	+	10.1551i	−0.418565	+	0.846261i
$13$	15.4082			1.18524			0.592621	−	0.805481i	$-0.298093\pi$
$13$	15.4082			1.18524			0.592621	+	0.805481i	$0.298093\pi$
$14$		−	4.35364i		−	0.310975i
$15$	−20.5417	−	10.1600i	−1.36945	−	0.677335i
$16$	13.3675			0.835471
$17$		−	15.6666i		−	0.921567i	−0.887513	−	0.460783i	$-0.847569\pi$
$17$		−	15.6666i		−	0.921567i	0.887513	−	0.460783i	$-0.152431\pi$
$18$	3.38192	−	2.58245i	0.187884	−	0.143469i
$19$	−31.9933			−1.68386			−0.841930	−	0.539586i	$-0.818581\pi$
$19$	−31.9933			−1.68386			−0.841930	+	0.539586i	$0.818581\pi$
$20$			28.8484i			1.44242i
$21$	12.2472	−	24.7617i	0.583202	−	1.17913i
$22$	0.976424			0.0443829
$23$			41.9436i			1.82364i	0.410595	+	0.911818i	$0.365321\pi$
$23$			41.9436i			1.82364i	−0.410595	+	0.911818i	$0.634679\pi$
$24$	−9.88681	−	4.89007i	−0.411950	−	0.203753i
$25$	−33.3541			−1.33417
$26$			7.28491i			0.280189i
$27$	26.4996	−	5.17418i	0.981466	−	0.191636i
$28$	−34.7748			−1.24196
$29$			41.7036i			1.43806i	0.694981	+	0.719028i	$0.255413\pi$
$29$			41.7036i			1.43806i	−0.694981	+	0.719028i	$0.744587\pi$
$30$	4.80362	−	9.71202i	0.160121	−	0.323734i
$31$	−6.91310			−0.223003			−0.111502	−	0.993764i	$-0.535566\pi$
$31$	−6.91310			−0.223003			−0.111502	+	0.993764i	$0.535566\pi$
$32$			21.0268i			0.657088i
$33$	5.55348	+	2.74678i	0.168287	+	0.0832357i
$34$	7.40712			0.217856
$35$		−	70.3421i		−	2.00977i
$36$	−20.6274	−	27.0131i	−0.572982	−	0.750364i
$37$	63.0547			1.70418			0.852091	−	0.523394i	$-0.175334\pi$
$37$	63.0547			1.70418			0.852091	+	0.523394i	$0.175334\pi$
$38$		−	15.1263i		−	0.398061i
$39$	−20.4932	+	41.4335i	−0.525467	+	1.06240i
$40$	−28.0861			−0.702153
$41$		−	28.7568i		−	0.701384i	−0.936491	−	0.350692i	$-0.885946\pi$
$41$		−	28.7568i		−	0.701384i	0.936491	−	0.350692i	$-0.114054\pi$
$42$	11.7072	+	5.79044i	0.278743	+	0.137868i
$43$	59.9306			1.39373			0.696867	−	0.717200i	$-0.254577\pi$
$43$	59.9306			1.39373			0.696867	+	0.717200i	$0.254577\pi$
$44$		−	7.79920i		−	0.177255i
$45$	54.6418	−	41.7248i	1.21426	−	0.927217i
$46$	−19.8308			−0.431104
$47$			37.1422i			0.790259i	0.918625	+	0.395129i	$0.129300\pi$
$47$			37.1422i			0.790259i	−0.918625	+	0.395129i	$0.870700\pi$
$48$	−17.7791	+	35.9461i	−0.370398	+	0.748877i
$49$	35.7927			0.730464
$50$		−	15.7697i		−	0.315394i
$51$	42.1285	+	20.8370i	0.826049	+	0.408568i
$52$	58.1884			1.11901
$53$		−	0.0188512i		−	0.000355682i	−1.00000		0.000177841i	$-0.999943\pi$
$53$		−	0.0188512i		−	0.000355682i	1.00000		0.000177841i	$-5.66086e-5\pi$
$54$	2.44633	+	12.5289i	0.0453024	+	0.232016i
$55$	15.7761			0.286839
$56$		−	33.8560i		−	0.604571i
$57$	42.5519	−	86.0320i	0.746524	−	1.50933i
$58$	−19.7173			−0.339953
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−77.5750	−	38.3690i	−1.29292	−	0.639483i
$61$	−21.9824			−0.360367			−0.180184	−	0.983633i	$-0.557669\pi$
$61$	−21.9824			−0.360367			−0.180184	+	0.983633i	$0.557669\pi$
$62$		−	3.26849i		−	0.0527175i
$63$	50.2965	+	65.8671i	0.798356	+	1.04551i
$64$	43.5288			0.680137
$65$			117.703i			1.81081i
$66$	−1.29867	+	2.62566i	−0.0196768	+	0.0397827i
$67$	25.9477			0.387279			0.193639	−	0.981073i	$-0.437971\pi$
$67$	25.9477			0.387279			0.193639	+	0.981073i	$0.437971\pi$
$68$		−	59.1645i		−	0.870066i
$69$	−112.789	−	55.7860i	−1.63462	−	0.808492i
$70$	33.2574			0.475106
$71$			40.5584i			0.571245i	0.958342	+	0.285623i	$0.0922004\pi$
$71$			40.5584i			0.571245i	−0.958342	+	0.285623i	$0.907800\pi$
$72$	26.2994	−	20.0823i	0.365269	−	0.278921i
$73$	−42.2494			−0.578759			−0.289379	−	0.957215i	$-0.593449\pi$
$73$	−42.2494			−0.578759			−0.289379	+	0.957215i	$0.593449\pi$
$74$			29.8120i			0.402865i
$75$	44.3618	−	89.6913i	0.591490	−	1.19588i
$76$	−120.822			−1.58976
$77$			19.0171i			0.246975i
$78$	−19.5896	−	9.68910i	−0.251148	−	0.124219i
$79$	32.2588			0.408340			0.204170	−	0.978935i	$-0.434551\pi$
$79$	32.2588			0.408340			0.204170	+	0.978935i	$0.434551\pi$
$80$			102.114i			1.27643i
$81$	−21.3314	+	78.1407i	−0.263350	+	0.964700i
$82$	13.5961			0.165806
$83$		−	19.0053i		−	0.228980i	−0.993424	−	0.114490i	$-0.963477\pi$
$83$		−	19.0053i		−	0.228980i	0.993424	−	0.114490i	$-0.0365233\pi$
$84$	46.2513	−	93.5115i	0.550610	−	1.11323i
$85$	119.677			1.40797
$86$			28.3349i			0.329476i
$87$	−112.144	−	55.4667i	−1.28901	−	0.637549i
$88$	7.59312			0.0862855
$89$		−	77.7511i		−	0.873608i	−0.899557	−	0.436804i	$-0.856110\pi$
$89$		−	77.7511i		−	0.873608i	0.899557	−	0.436804i	$-0.143890\pi$
$90$	19.7273	+	25.8344i	0.219192	+	0.287049i
$91$	−141.883			−1.55915
$92$			158.399i			1.72172i
$93$	9.19458	−	18.5897i	0.0988665	−	0.199890i
$94$	−17.5607			−0.186816
$95$		−	244.397i		−	2.57260i
$96$	−56.5424	−	27.9662i	−0.588983	−	0.291314i
$97$	123.092			1.26899			0.634496	−	0.772926i	$-0.281208\pi$
$97$	123.092			1.26899			0.634496	+	0.772926i	$0.281208\pi$
$98$			16.9226i			0.172680i
$99$	−14.7725	+	11.2804i	−0.149217	+	0.113943i
$100$	−125.961			−1.25961
$101$		−	73.9979i		−	0.732653i	−0.930486	−	0.366326i	$-0.880615\pi$
$101$		−	73.9979i		−	0.732653i	0.930486	−	0.366326i	$-0.119385\pi$
$102$	−9.85163	+	19.9182i	−0.0965846	+	0.195276i
$103$	93.7664			0.910353			0.455176	−	0.890401i	$-0.349576\pi$
$103$	93.7664			0.910353			0.455176	+	0.890401i	$0.349576\pi$
$104$			56.6509i			0.544720i
$105$	189.154	+	93.5565i	1.80147	+	0.891015i
$106$	0.00891275			8.40825e−5
$107$		−	51.8016i		−	0.484127i	−0.970260	−	0.242063i	$-0.922176\pi$
$107$		−	51.8016i		−	0.484127i	0.970260	−	0.242063i	$-0.0778242\pi$
$108$	100.075	−	19.5401i	0.926618	−	0.180927i
$109$	29.7585			0.273014			0.136507	−	0.990639i	$-0.456412\pi$
$109$	29.7585			0.273014			0.136507	+	0.990639i	$0.456412\pi$
$110$			7.45889i			0.0678081i
$111$	−83.8642	+	169.558i	−0.755533	+	1.52755i
$112$	−123.092			−1.09904
$113$			114.745i			1.01544i	0.861523	+	0.507719i	$0.169511\pi$
$113$			114.745i			1.01544i	−0.861523	+	0.507719i	$0.830489\pi$
$114$	40.6756	+	20.1183i	0.356803	+	0.176477i
$115$	−320.407			−2.78615
$116$			157.492i			1.35769i
$117$	−84.1606	−	110.215i	−0.719321	−	0.942007i
$118$	3.63161			0.0307764
$119$			144.263i			1.21229i
$120$	37.3552	−	75.5252i	0.311293	−	0.629377i
$121$	116.735			0.964751
$122$		−	10.3932i		−	0.0851900i
$123$	77.3286	+	38.2471i	0.628688	+	0.310952i
$124$	−26.1071			−0.210541
$125$		−	63.8172i		−	0.510537i
$126$	−31.1417	+	23.7800i	−0.247156	+	0.188730i
$127$	−70.5037			−0.555147			−0.277574	−	0.960704i	$-0.589530\pi$
$127$	−70.5037			−0.555147			−0.277574	+	0.960704i	$0.589530\pi$
$128$			104.688i			0.817871i
$129$	−79.7090	+	161.157i	−0.617900	+	1.24928i
$130$	−55.6494			−0.428072
$131$		−	169.629i		−	1.29488i	−0.762116	−	0.647441i	$-0.775839\pi$
$131$		−	169.629i		−	1.29488i	0.762116	−	0.647441i	$-0.224161\pi$
$132$	20.9725	+	10.3731i	0.158883	+	0.0785842i
$133$	294.604			2.21507
$134$			12.2680i			0.0915519i
$135$	39.5255	+	202.430i	0.292782	+	1.49948i
$136$	57.6012			0.423538
$137$		−	92.5010i		−	0.675189i	−0.941292	−	0.337595i	$-0.890387\pi$
$137$		−	92.5010i		−	0.675189i	0.941292	−	0.337595i	$-0.109613\pi$
$138$	26.3754	−	53.3261i	0.191126	−	0.386421i
$139$	−132.666			−0.954432			−0.477216	−	0.878786i	$-0.658354\pi$
$139$	−132.666			−0.954432			−0.477216	+	0.878786i	$0.658354\pi$
$140$		−	265.644i		−	1.89746i
$141$	−99.8775	−	49.3999i	−0.708351	−	0.350354i
$142$	−19.1758			−0.135041
$143$		−	31.8211i		−	0.222525i
$144$	−73.0146	−	95.6183i	−0.507046	−	0.664016i
$145$	−318.573			−2.19706
$146$		−	19.9753i		−	0.136817i
$147$	−47.6051	+	96.2488i	−0.323844	+	0.654753i
$148$	238.124			1.60895
$149$			38.9276i			0.261259i	0.991431	+	0.130630i	$0.0416999\pi$
$149$			38.9276i			0.261259i	−0.991431	+	0.130630i	$0.958300\pi$
$150$	42.4056	+	20.9740i	0.282704	+	0.139827i
$151$	−187.145			−1.23937			−0.619685	−	0.784851i	$-0.712740\pi$
$151$	−187.145			−1.23937			−0.619685	+	0.784851i	$0.712740\pi$
$152$		−	117.629i		−	0.773877i
$153$	−112.064	+	85.5724i	−0.732443	+	0.559297i
$154$	−8.99120			−0.0583844
$155$		−	52.8091i		−	0.340704i
$156$	−77.3918	+	156.472i	−0.496101	+	1.00303i
$157$	−88.9609			−0.566630			−0.283315	−	0.959027i	$-0.591434\pi$
$157$	−88.9609			−0.566630			−0.283315	+	0.959027i	$0.591434\pi$
$158$			15.2518i			0.0965306i
$159$	0.0506919	+	0.0250725i	0.000318817	+	0.000157688i
$160$	−160.624			−1.00390
$161$		−	386.229i		−	2.39894i
$162$	−36.9446	−	10.0854i	−0.228053	−	0.0622554i
$163$	−192.945			−1.18371			−0.591857	−	0.806043i	$-0.701605\pi$
$163$	−192.945			−1.18371			−0.591857	+	0.806043i	$0.701605\pi$
$164$		−	108.599i		−	0.662188i
$165$	−20.9826	+	42.4230i	−0.127167	+	0.257109i
$166$	8.98563			0.0541303
$167$			131.823i			0.789358i	0.918819	+	0.394679i	$0.129144\pi$
$167$			131.823i			0.789358i	−0.918819	+	0.394679i	$0.870856\pi$
$168$	91.0407	+	45.0292i	0.541909	+	0.268031i
$169$	68.4113			0.404801
$170$			56.5829i			0.332840i
$171$	174.750	+	228.849i	1.02193	+	1.33830i
$172$	226.326			1.31585
$173$		−	117.008i		−	0.676348i	−0.941084	−	0.338174i	$-0.890191\pi$
$173$		−	117.008i		−	0.676348i	0.941084	−	0.338174i	$-0.109809\pi$
$174$	26.2244	−	53.0210i	0.150715	−	0.304718i
$175$	307.135			1.75506
$176$		−	27.6068i		−	0.156857i
$177$	20.6551	+	10.2161i	0.116695	+	0.0577181i
$178$	36.7604			0.206519
$179$			15.2966i			0.0854561i	0.999087	+	0.0427280i	$0.0136049\pi$
$179$			15.2966i			0.0854561i	−0.999087	+	0.0427280i	$0.986395\pi$
$180$	206.353	−	157.572i	1.14640	−	0.875401i
$181$	339.189			1.87397			0.936986	−	0.349366i	$-0.113603\pi$
$181$	339.189			1.87397			0.936986	+	0.349366i	$0.113603\pi$
$182$		−	67.0816i		−	0.368580i
$183$	29.2371	−	59.1120i	0.159765	−	0.323016i
$184$	−154.213			−0.838116
$185$			481.674i			2.60364i
$186$	8.78915	+	4.34716i	0.0472535	+	0.0233718i
$187$	−32.3549			−0.173021
$188$			140.266i			0.746096i
$189$	−244.016	+	47.6454i	−1.29109	+	0.252092i
$190$	115.550			0.608157
$191$		−	210.673i		−	1.10300i	−0.834175	−	0.551500i	$-0.814056\pi$
$191$		−	210.673i		−	1.10300i	0.834175	−	0.551500i	$-0.185944\pi$
$192$	−57.8942	+	117.051i	−0.301532	+	0.609643i
$193$	127.355			0.659871			0.329936	−	0.944003i	$-0.392973\pi$
$193$	127.355			0.659871			0.329936	+	0.944003i	$0.392973\pi$
$194$			58.1975i			0.299987i
$195$	−316.510	−	156.547i	−1.62313	−	0.802807i
$196$	135.170			0.689643
$197$			153.834i			0.780882i	0.920628	+	0.390441i	$0.127677\pi$
$197$			153.834i			0.780882i	−0.920628	+	0.390441i	$0.872323\pi$
$198$	−5.33331	−	6.98438i	−0.0269359	−	0.0352746i
$199$	139.680			0.701910			0.350955	−	0.936392i	$-0.385857\pi$
$199$	139.680			0.701910			0.350955	+	0.936392i	$0.385857\pi$
$200$		−	122.632i		−	0.613162i
$201$	−34.5110	+	69.7749i	−0.171697	+	0.347139i
$202$	34.9859			0.173198
$203$		−	384.019i		−	1.89172i
$204$	159.097	+	78.6901i	0.779886	+	0.385736i
$205$	219.673			1.07157
$206$			44.3323i			0.215206i
$207$	300.024	−	229.099i	1.44939	−	1.10676i
$208$	205.969			0.990236
$209$			66.0731i			0.316139i
$210$	−44.2331	+	89.4312i	−0.210634	+	0.425863i
$211$	350.086			1.65918			0.829588	−	0.558375i	$-0.188575\pi$
$211$	350.086			1.65918			0.829588	+	0.558375i	$0.188575\pi$
$212$		−	0.0711907i		−	0.000335805i
$213$	−109.064	−	53.9436i	−0.512037	−	0.253256i
$214$	24.4916			0.114447
$215$			457.809i			2.12934i
$216$	19.0238	+	97.4305i	0.0880732	+	0.451067i
$217$	63.6579			0.293354
$218$			14.0697i			0.0645399i
$219$	56.1926	−	113.611i	0.256587	−	0.518772i
$220$	59.5780			0.270809
$221$		−	241.394i		−	1.09228i
$222$	−80.1662	−	39.6506i	−0.361109	−	0.178606i
$223$	−190.680			−0.855069			−0.427534	−	0.903999i	$-0.640618\pi$
$223$	−190.680			−0.855069			−0.427534	+	0.903999i	$0.640618\pi$
$224$		−	193.621i		−	0.864381i
$225$	182.183	+	238.583i	0.809702	+	1.06037i
$226$	−54.2507			−0.240047
$227$		−	255.387i		−	1.12505i	−0.826779	−	0.562526i	$-0.809829\pi$
$227$		−	255.387i		−	1.12505i	0.826779	−	0.562526i	$-0.190171\pi$
$228$	160.696	−	324.897i	0.704805	−	1.42499i
$229$	−57.9236			−0.252942			−0.126471	−	0.991970i	$-0.540365\pi$
$229$	−57.9236			−0.252942			−0.126471	+	0.991970i	$0.540365\pi$
$230$		−	151.487i		−	0.658639i
$231$	−51.1381	−	25.2932i	−0.221377	−	0.109494i
$232$	−153.331			−0.660909
$233$		−	53.0200i		−	0.227553i	−0.993506	−	0.113777i	$-0.963705\pi$
$233$		−	53.0200i		−	0.227553i	0.993506	−	0.113777i	$-0.0362949\pi$
$234$	52.1091	−	39.7908i	0.222688	−	0.170046i
$235$	−283.729			−1.20736
$236$		−	29.0076i		−	0.122913i
$237$	−42.9050	+	86.7459i	−0.181034	+	0.366016i
$238$	−68.2069			−0.286584
$239$		−	313.540i		−	1.31188i	−0.754813	−	0.655940i	$-0.772272\pi$
$239$		−	313.540i		−	1.31188i	0.754813	−	0.655940i	$-0.227728\pi$
$240$	−274.592	−	135.815i	−1.14413	−	0.565894i
$241$	−189.180			−0.784980			−0.392490	−	0.919756i	$-0.628386\pi$
$241$	−189.180			−0.784980			−0.392490	+	0.919756i	$0.628386\pi$
$242$			55.1918i			0.228065i
$243$	−181.754	−	161.290i	−0.747958	−	0.663746i
$244$	−83.0157			−0.340228
$245$			273.420i			1.11600i
$246$	−18.0831	+	36.5606i	−0.0735085	+	0.148621i
$247$	−492.959			−1.99578
$248$		−	25.4173i		−	0.102489i
$249$	51.1064	+	25.2775i	0.205247	+	0.101516i
$250$	30.1725			0.120690
$251$			0.0945816i			0.000376819i	1.00000		0.000188410i	$5.99726e-5\pi$
$251$			0.0945816i			0.000376819i	−1.00000		0.000188410i	$0.999940\pi$
$252$	189.943	+	248.745i	0.753741	+	0.987083i
$253$	86.6225			0.342381
$254$		−	33.3338i		−	0.131236i
$255$	−159.173	+	321.819i	−0.624209	+	1.26204i
$256$	124.619			0.486794
$257$			1.58343i			0.00616119i	0.999995	+	0.00308059i	$0.000980585\pi$
$257$			1.58343i			0.00616119i	−0.999995	+	0.00308059i	$0.999019\pi$
$258$	−76.1943	−	37.6861i	−0.295327	−	0.146070i
$259$	−580.627			−2.24180
$260$			444.500i			1.70962i
$261$	298.307	−	227.789i	1.14294	−	0.872753i
$262$	80.2001			0.306107
$263$			335.725i			1.27652i	0.769820	+	0.638261i	$0.220346\pi$
$263$			335.725i			1.27652i	−0.769820	+	0.638261i	$0.779654\pi$
$264$	−10.0990	+	20.4184i	−0.0382539	+	0.0773423i
$265$	0.144004			0.000543411
$266$			139.288i			0.523638i
$267$	209.077	+	103.411i	0.783061	+	0.387306i
$268$	97.9905			0.365636
$269$		−	211.343i		−	0.785663i	−0.919610	−	0.392831i	$-0.871496\pi$
$269$		−	211.343i		−	0.785663i	0.919610	−	0.392831i	$-0.128504\pi$
$270$	−95.7080	+	18.6875i	−0.354474	+	0.0692130i
$271$	71.0257			0.262087			0.131044	−	0.991377i	$-0.458167\pi$
$271$	71.0257			0.262087			0.131044	+	0.991377i	$0.458167\pi$
$272$		−	209.424i		−	0.769942i
$273$	188.707	−	381.532i	0.691236	−	1.39755i
$274$	43.7341			0.159613
$275$			68.8834i			0.250485i
$276$	−425.943	−	210.674i	−1.54327	−	0.763311i
$277$	−7.50451			−0.0270921			−0.0135460	−	0.999908i	$-0.504312\pi$
$277$	−7.50451			−0.0270921			−0.0135460	+	0.999908i	$0.504312\pi$
$278$		−	62.7239i		−	0.225626i
$279$	37.7599	+	49.4495i	0.135340	+	0.177239i
$280$	258.625			0.923661
$281$		−	354.561i		−	1.26178i	−0.775871	−	0.630891i	$-0.782690\pi$
$281$		−	354.561i		−	1.26178i	0.775871	−	0.630891i	$-0.217310\pi$
$282$	23.3561	−	47.2217i	0.0828229	−	0.167453i
$283$	−7.69162			−0.0271789			−0.0135894	−	0.999908i	$-0.504326\pi$
$283$	−7.69162			−0.0271789			−0.0135894	+	0.999908i	$0.504326\pi$
$284$			153.167i			0.539322i
$285$	657.198	+	325.053i	2.30596	+	1.14054i
$286$	15.0449			0.0526045
$287$			264.801i			0.922651i
$288$	150.405	−	114.850i	0.522241	−	0.398786i
$289$	43.5566			0.150715
$290$		−	150.620i		−	0.519380i
$291$	−163.716	+	331.002i	−0.562596	+	1.13747i
$292$	−159.553			−0.546415
$293$		−	234.206i		−	0.799339i	−0.916659	−	0.399670i	$-0.869125\pi$
$293$		−	234.206i		−	0.799339i	0.916659	−	0.399670i	$-0.130875\pi$
$294$	−45.5060	−	22.5075i	−0.154782	−	0.0765561i
$295$	58.6762			0.198902
$296$			231.832i			0.783216i
$297$	−10.6858	−	54.7273i	−0.0359791	−	0.184267i
$298$	−18.4048			−0.0617611
$299$			646.274i			2.16145i
$300$	167.531	−	338.716i	0.558435	−	1.12905i
$301$	−551.859			−1.83342
$302$		−	88.4813i		−	0.292984i
$303$	198.985	+	98.4189i	0.656716	+	0.324815i
$304$	−427.672			−1.40682
$305$		−	167.923i		−	0.550568i
$306$	−40.4583	−	52.9832i	−0.132217	−	0.173148i
$307$	323.794			1.05470			0.527351	−	0.849647i	$-0.323185\pi$
$307$	323.794			1.05470			0.527351	+	0.849647i	$0.323185\pi$
$308$			71.8174i			0.233173i
$309$	−124.711	+	252.143i	−0.403597	+	0.815998i
$310$	24.9679			0.0805417
$311$		−	288.450i		−	0.927493i	−0.885968	−	0.463746i	$-0.846505\pi$
$311$		−	288.450i		−	0.927493i	0.885968	−	0.463746i	$-0.153495\pi$
$312$	−152.338	−	75.3469i	−0.488261	−	0.241496i
$313$	86.2308			0.275498			0.137749	−	0.990467i	$-0.456013\pi$
$313$	86.2308			0.275498			0.137749	+	0.990467i	$0.456013\pi$
$314$		−	42.0603i		−	0.133950i
$315$	−503.158	+	384.214i	−1.59733	+	1.21973i
$316$	121.824			0.385520
$317$			382.059i			1.20523i	0.798031	+	0.602617i	$0.205875\pi$
$317$			382.059i			1.20523i	−0.798031	+	0.602617i	$0.794125\pi$
$318$	−0.0118542	+	0.0239669i	−3.72772e−5	+	7.53676e-5i
$319$	86.1268			0.269990
$320$			332.516i			1.03911i
$321$	139.297	+	68.8972i	0.433949	+	0.214633i
$322$	182.608			0.567104
$323$			501.228i			1.55179i
$324$	−80.5571	+	295.096i	−0.248633	+	0.910789i
$325$	−513.926			−1.58131
$326$		−	91.2237i		−	0.279827i
$327$	−39.5795	+	80.0225i	−0.121038	+	0.244717i
$328$	105.729			0.322346
$329$		−	342.016i		−	1.03956i
$330$	−20.0574	−	9.92049i	−0.0607800	−	0.0300621i
$331$	71.0716			0.214718			0.107359	−	0.994220i	$-0.465761\pi$
$331$	71.0716			0.214718			0.107359	+	0.994220i	$0.465761\pi$
$332$		−	71.7729i		−	0.216183i
$333$	−344.410	−	451.032i	−1.03426	−	1.35445i
$334$	−62.3252			−0.186603
$335$			198.214i			0.591684i
$336$	163.715	−	331.002i	0.487248	−	0.985126i
$337$	−374.174			−1.11031			−0.555155	−	0.831747i	$-0.687341\pi$
$337$	−374.174			−1.11031			−0.555155	+	0.831747i	$0.687341\pi$
$338$			32.3446i			0.0956940i
$339$	−308.555	−	152.613i	−0.910191	−	0.450185i
$340$	451.957			1.32928
$341$			14.2770i			0.0418681i
$342$	−108.199	+	82.6212i	−0.316371	+	0.241582i
$343$	121.617			0.354567
$344$			220.346i			0.640540i
$345$	426.148	−	861.593i	1.23521	−	2.49737i
$346$	55.3209			0.159887
$347$			363.525i			1.04762i	0.851834	+	0.523812i	$0.175491\pi$
$347$			363.525i			1.04762i	−0.851834	+	0.523812i	$0.824509\pi$
$348$	−423.506	−	209.468i	−1.21697	−	0.601920i
$349$	−277.377			−0.794776			−0.397388	−	0.917651i	$-0.630083\pi$
$349$	−277.377			−0.794776			−0.397388	+	0.917651i	$0.630083\pi$
$350$			145.212i			0.414892i
$351$	408.310	−	79.7246i	1.16328	−	0.227136i
$352$	43.4249			0.123366
$353$			453.778i			1.28549i	0.766080	+	0.642745i	$0.222205\pi$
$353$			453.778i			1.28549i	−0.766080	+	0.642745i	$0.777795\pi$
$354$	−4.83013	+	9.76562i	−0.0136444	+	0.0275865i
$355$	−309.825			−0.872747
$356$		−	293.624i		−	0.824787i
$357$	−387.932	−	191.873i	−1.08664	−	0.537459i
$358$	−7.23218			−0.0202016
$359$		−	288.922i		−	0.804798i	−0.915464	−	0.402399i	$-0.868177\pi$
$359$		−	288.922i		−	0.804798i	0.915464	−	0.402399i	$-0.131823\pi$
$360$	153.409	+	200.900i	0.426135	+	0.558057i
$361$	662.574			1.83539
$362$			160.367i			0.443003i
$363$	−155.260	+	313.907i	−0.427714	+	0.864758i
$364$	−535.816			−1.47202
$365$		−	322.742i		−	0.884226i
$366$	27.9479	+	13.8232i	0.0763604	+	0.0377682i
$367$	89.6102			0.244169			0.122085	−	0.992520i	$-0.461042\pi$
$367$	89.6102			0.244169			0.122085	+	0.992520i	$0.461042\pi$
$368$			560.683i			1.52360i
$369$	−205.698	+	157.072i	−0.557446	+	0.425669i
$370$	−227.734			−0.615496
$371$			0.173587i			0.000467890i
$372$	34.7230	−	70.2035i	0.0933414	−	0.188719i
$373$	106.852			0.286466			0.143233	−	0.989689i	$-0.454250\pi$
$373$	106.852			0.286466			0.143233	+	0.989689i	$0.454250\pi$
$374$		−	15.2973i		−	0.0409018i
$375$	171.608	+	84.8783i	0.457622	+	0.226342i
$376$	−136.560			−0.363191
$377$			642.576i			1.70445i
$378$	−22.5265	−	115.370i	−0.0595940	−	0.305211i
$379$	72.5836			0.191513			0.0957567	−	0.995405i	$-0.469473\pi$
$379$	72.5836			0.191513			0.0957567	+	0.995405i	$0.469473\pi$
$380$		−	922.956i		−	2.42883i
$381$	93.7715	−	189.589i	0.246119	−	0.497608i
$382$	99.6053			0.260747
$383$		−	560.752i		−	1.46411i	−0.681248	−	0.732053i	$-0.738563\pi$
$383$		−	560.752i		−	1.46411i	0.681248	−	0.732053i	$-0.261437\pi$
$384$	−281.511	−	139.237i	−0.733102	−	0.362596i
$385$	−145.271			−0.377328
$386$			60.2130i			0.155992i
$387$	−327.346	−	428.685i	−0.845855	−	1.10771i
$388$	464.854			1.19808
$389$		−	258.485i		−	0.664487i	−0.943194	−	0.332244i	$-0.892194\pi$
$389$		−	258.485i		−	0.664487i	0.943194	−	0.332244i	$-0.107806\pi$
$390$	74.0149	−	149.644i	0.189782	−	0.383704i
$391$	657.115			1.68060
$392$			131.598i			0.335710i
$393$	456.144	+	225.611i	1.16067	+	0.574074i
$394$	−72.7319			−0.184599
$395$			246.425i			0.623860i
$396$	−55.7878	+	42.5999i	−0.140878	+	0.107575i
$397$	−181.745			−0.457796			−0.228898	−	0.973450i	$-0.573512\pi$
$397$	−181.745			−0.457796			−0.228898	+	0.973450i	$0.573512\pi$
$398$			66.0402i			0.165930i
$399$	−391.830	+	792.208i	−0.982031	+	1.98548i
$400$	−445.863			−1.11466
$401$		−	401.247i		−	1.00061i	−0.865848	−	0.500307i	$-0.833220\pi$
$401$		−	401.247i		−	1.00061i	0.865848	−	0.500307i	$-0.166780\pi$
$402$	−32.9893	−	16.3167i	−0.0820628	−	0.0405887i
$403$	−106.518			−0.264313
$404$		−	279.451i		−	0.691709i
$405$	−596.916	−	162.950i	−1.47387	−	0.402346i
$406$	181.563			0.447199
$407$		−	130.221i		−	0.319954i
$408$	−76.6109	+	154.893i	−0.187772	+	0.379640i
$409$	399.897			0.977744			0.488872	−	0.872356i	$-0.337409\pi$
$409$	399.897			0.977744			0.488872	+	0.872356i	$0.337409\pi$
$410$			103.860i			0.253318i
$411$	248.741	+	123.028i	0.605208	+	0.299339i
$412$	354.105			0.859479
$413$			70.7303i			0.171260i
$414$	108.317	+	141.850i	0.261636	+	0.342633i
$415$	145.181			0.349834
$416$			323.985i			0.778809i
$417$	176.449	−	356.747i	0.423138	−	0.855508i
$418$	−31.2391			−0.0747346
$419$			355.555i			0.848579i	0.905527	+	0.424290i	$0.139476\pi$
$419$			355.555i			0.848579i	−0.905527	+	0.424290i	$0.860524\pi$
$420$	714.333	+	353.313i	1.70079	+	0.841221i
$421$	−123.497			−0.293343			−0.146671	−	0.989185i	$-0.546856\pi$
$421$	−123.497			−0.293343			−0.146671	+	0.989185i	$0.546856\pi$
$422$			165.519i			0.392226i
$423$	265.679	−	202.874i	0.628082	−	0.479606i
$424$	0.0693097			0.000163466
$425$			522.547i			1.22952i
$426$	25.5043	−	51.5650i	0.0598693	−	0.121045i
$427$	202.420			0.474053
$428$		−	195.627i		−	0.457072i
$429$	85.5689	+	42.3228i	0.199461	+	0.0986546i
$430$	−216.450			−0.503373
$431$			275.384i			0.638942i	0.947596	+	0.319471i	$0.103505\pi$
$431$			275.384i			0.638942i	−0.947596	+	0.319471i	$0.896495\pi$
$432$	354.234	−	69.1661i	0.819987	−	0.160107i
$433$	172.056			0.397357			0.198679	−	0.980065i	$-0.436335\pi$
$433$	172.056			0.397357			0.198679	+	0.980065i	$0.436335\pi$
$434$			30.0972i			0.0693483i
$435$	423.710	−	856.663i	0.974046	−	1.96934i
$436$	112.382			0.257757
$437$		−	1341.92i		−	3.07075i
$438$	53.7148	+	26.5676i	0.122637	+	0.0606567i
$439$	−69.7491			−0.158882			−0.0794409	−	0.996840i	$-0.525313\pi$
$439$	−69.7491			−0.158882			−0.0794409	+	0.996840i	$0.525313\pi$
$440$			58.0038i			0.131827i
$441$	−195.503	−	256.026i	−0.443317	−	0.580558i
$442$	114.130			0.258213
$443$		−	524.445i		−	1.18385i	−0.805994	−	0.591924i	$-0.798369\pi$
$443$		−	524.445i		−	1.18385i	0.805994	−	0.591924i	$-0.201631\pi$
$444$	−316.710	+	640.329i	−0.713311	+	1.44218i
$445$	593.940			1.33470
$446$		−	90.1529i		−	0.202136i
$447$	−104.679	−	51.7746i	−0.234180	−	0.115827i
$448$	−400.826			−0.894700
$449$			36.1045i			0.0804109i	0.999191	+	0.0402055i	$0.0128012\pi$
$449$			36.1045i			0.0804109i	−0.999191	+	0.0402055i	$0.987199\pi$
$450$	−112.801	+	86.1353i	−0.250669	+	0.191412i
$451$	−59.3888			−0.131683
$452$			433.329i			0.958692i
$453$	248.907	−	503.243i	0.549463	−	1.11091i
$454$	120.746			0.265960
$455$		−	1083.84i		−	2.38207i
$456$	316.312	+	156.450i	0.693667	+	0.343091i
$457$	−163.409			−0.357569			−0.178784	−	0.983888i	$-0.557216\pi$
$457$	−163.409			−0.357569			−0.178784	+	0.983888i	$0.557216\pi$
$458$		−	27.3861i		−	0.0597949i
$459$	−81.0620	−	415.159i	−0.176606	−	0.904486i
$460$	−1210.01			−2.63045
$461$			297.609i			0.645572i	0.946472	+	0.322786i	$0.104619\pi$
$461$			297.609i			0.645572i	−0.946472	+	0.322786i	$0.895381\pi$
$462$	11.9585	−	24.1779i	0.0258842	−	0.0523330i
$463$	−442.567			−0.955868			−0.477934	−	0.878396i	$-0.658614\pi$
$463$	−442.567			−0.955868			−0.477934	+	0.878396i	$0.658614\pi$
$464$			557.475i			1.20145i
$465$	142.007	+	70.2373i	0.305391	+	0.151048i
$466$	25.0676			0.0537932
$467$			244.305i			0.523136i	0.965185	+	0.261568i	$0.0842396\pi$
$467$			244.305i			0.523136i	−0.965185	+	0.261568i	$0.915760\pi$
$468$	−317.829	−	416.222i	−0.679123	−	0.889364i
$469$	−238.934			−0.509454
$470$		−	134.146i		−	0.285416i
$471$	118.320	−	239.221i	0.251210	−	0.507901i
$472$	28.2411			0.0598329
$473$		−	123.769i		−	0.261669i
$474$	−41.0131	−	20.2853i	−0.0865255	−	0.0427959i
$475$	1067.11			2.24655
$476$			544.804i			1.14455i
$477$	−0.134843	+	0.102967i	−0.000282689	+	0.000215863i
$478$	148.240			0.310126
$479$			639.138i			1.33432i	0.744915	+	0.667159i	$0.232490\pi$
$479$			639.138i			1.33432i	−0.744915	+	0.667159i	$0.767510\pi$
$480$	213.633	−	431.927i	0.445069	−	0.899847i
$481$	971.557			2.01987
$482$		−	89.4436i		−	0.185568i
$483$	1038.59	+	513.694i	2.15030	+	1.06355i
$484$	440.845			0.910837
$485$			940.301i			1.93876i
$486$	76.2573	−	85.9325i	0.156908	−	0.176816i
$487$	−485.955			−0.997855			−0.498927	−	0.866644i	$-0.666273\pi$
$487$	−485.955			−0.997855			−0.498927	+	0.866644i	$0.666273\pi$
$488$		−	80.8222i		−	0.165619i
$489$	256.622	−	518.841i	0.524789	−	1.06103i
$490$	−129.272			−0.263820
$491$			377.155i			0.768137i	0.923305	+	0.384068i	$0.125477\pi$
$491$			377.155i			0.768137i	−0.923305	+	0.384068i	$0.874523\pi$
$492$	292.029	+	144.439i	0.593555	+	0.293575i
$493$	653.355			1.32526
$494$		−	233.069i		−	0.471799i
$495$	−86.1705	−	112.847i	−0.174082	−	0.227974i
$496$	−92.4112			−0.186313
$497$		−	373.474i		−	0.751457i
$498$	−11.9511	+	24.1629i	−0.0239982	+	0.0485199i
$499$	−622.890			−1.24828			−0.624138	−	0.781314i	$-0.714550\pi$
$499$	−622.890			−1.24828			−0.624138	+	0.781314i	$0.714550\pi$
$500$		−	241.003i		−	0.482007i
$501$	−354.479	−	175.327i	−0.707543	−	0.349955i
$502$	−0.0447178			−8.90793e−5
$503$		−	941.653i		−	1.87207i	−0.351903	−	0.936036i	$-0.614465\pi$
$503$		−	941.653i		−	1.87207i	0.351903	−	0.936036i	$-0.385535\pi$
$504$	−242.172	+	184.924i	−0.480500	+	0.366913i
$505$	565.269			1.11935
$506$			40.9548i			0.0809383i
$507$	−90.9886	+	183.962i	−0.179465	+	0.362844i
$508$	−266.255			−0.524123
$509$			646.240i			1.26963i	0.772666	+	0.634813i	$0.218923\pi$
$509$			646.240i			1.26963i	−0.772666	+	0.634813i	$0.781077\pi$
$510$	−152.155	−	75.2565i	−0.298343	−	0.147562i
$511$	389.045			0.761340
$512$			477.670i			0.932948i
$513$	−847.810	+	165.539i	−1.65265	+	0.322689i
$514$	−0.748637			−0.00145649
$515$			716.280i			1.39084i
$516$	−301.018	+	608.603i	−0.583369	+	1.17946i
$517$	76.7065			0.148368
$518$		−	274.518i		−	0.529957i
$519$	314.642	+	155.623i	0.606246	+	0.299852i
$520$	−432.755			−0.832222
$521$			941.837i			1.80775i	0.427799	+	0.903874i	$0.359289\pi$
$521$			941.837i			1.80775i	−0.427799	+	0.903874i	$0.640711\pi$
$522$	107.697	+	141.038i	0.206317	+	0.270188i
$523$	−384.235			−0.734674			−0.367337	−	0.930088i	$-0.619730\pi$
$523$	−384.235			−0.734674			−0.367337	+	0.930088i	$0.619730\pi$
$524$		−	640.600i		−	1.22252i
$525$	−408.496	+	825.904i	−0.778088	+	1.57315i
$526$	−158.729			−0.301767
$527$			108.305i			0.205512i
$528$	74.2364	+	36.7177i	0.140599	+	0.0695411i
$529$	−1230.27			−2.32565
$530$			0.0680844i			0.000128461i
$531$	−54.9434	+	41.9550i	−0.103472	+	0.0790114i
$532$	1112.56			2.09128
$533$		−	443.089i		−	0.831311i
$534$	−48.8922	+	98.8509i	−0.0915583	+	0.185114i
$535$	395.712			0.739648
$536$			95.4013i			0.177988i
$537$	−41.1336	−	20.3449i	−0.0765988	−	0.0378862i
$538$	99.9222			0.185729
$539$		−	73.9196i		−	0.137142i
$540$	149.267	+	764.470i	0.276420	+	1.41568i
$541$	−498.752			−0.921908			−0.460954	−	0.887424i	$-0.652493\pi$
$541$	−498.752			−0.921908			−0.460954	+	0.887424i	$0.652493\pi$
$542$			33.5807i			0.0619569i
$543$	−451.129	+	912.099i	−0.830808	+	1.67974i
$544$	329.420			0.605551
$545$			227.325i			0.417110i
$546$	180.386	+	89.2201i	0.330378	+	0.163407i
$547$	38.8715			0.0710631			0.0355315	−	0.999369i	$-0.488688\pi$
$547$	38.8715			0.0710631			0.0355315	+	0.999369i	$0.488688\pi$
$548$		−	349.327i		−	0.637457i
$549$	120.070	+	157.240i	0.218706	+	0.286413i
$550$	−32.5678			−0.0592141
$551$		−	1334.24i		−	2.42149i
$552$	205.107	−	414.689i	0.371571	−	0.751248i
$553$	−297.049			−0.537159
$554$		−	3.54810i		−	0.00640451i
$555$	−1295.25	−	640.638i	−2.33379	−	1.15430i
$556$	−501.008			−0.901094
$557$		−	621.587i		−	1.11596i	−0.829856	−	0.557978i	$-0.811577\pi$
$557$		−	621.587i		−	1.11596i	0.829856	−	0.557978i	$-0.188423\pi$
$558$	−23.3795	+	17.8527i	−0.0418988	+	0.0319941i
$559$	923.420			1.65191
$560$		−	940.300i		−	1.67911i
$561$	43.0328	−	87.0043i	0.0767073	−	0.155088i
$562$	167.635			0.298283
$563$		−	572.900i		−	1.01758i	−0.860889	−	0.508792i	$-0.830092\pi$
$563$		−	572.900i		−	1.01758i	0.860889	−	0.508792i	$-0.169908\pi$
$564$	−377.184	−	186.557i	−0.668766	−	0.330775i
$565$	−876.532			−1.55138
$566$		−	3.63656i		−	0.00642503i
$567$	196.425	−	719.543i	0.346429	−	1.26904i
$568$	−149.120			−0.262536
$569$			880.655i			1.54772i	0.633354	+	0.773862i	$0.281678\pi$
$569$			880.655i			1.54772i	−0.633354	+	0.773862i	$0.718322\pi$
$570$	−153.684	+	310.720i	−0.269621	+	0.545123i
$571$	961.034			1.68307			0.841535	−	0.540202i	$-0.181652\pi$
$571$	961.034			1.68307			0.841535	+	0.540202i	$0.181652\pi$
$572$		−	120.171i		−	0.210090i
$573$	566.512	+	280.200i	0.988677	+	0.489005i
$574$	−125.197			−0.218113
$575$		−	1398.99i		−	2.43303i
$576$	−237.758	−	311.362i	−0.412774	−	0.540559i
$577$	−188.373			−0.326469			−0.163234	−	0.986587i	$-0.552193\pi$
$577$	−188.373			−0.326469			−0.163234	+	0.986587i	$0.552193\pi$
$578$			20.5934i			0.0356287i
$579$	−169.385	+	342.466i	−0.292548	+	0.591478i
$580$	−1203.08			−2.07428
$581$			175.006i			0.301216i
$582$	−156.497	−	77.4040i	−0.268894	−	0.132997i
$583$	−0.0389317			−6.67781e−5
$584$		−	155.337i		−	0.265989i
$585$	841.930	−	642.902i	1.43920	−	1.09898i
$586$	110.732			0.188962
$587$			523.610i			0.892010i	0.895030	+	0.446005i	$0.147154\pi$
$587$			523.610i			0.892010i	−0.895030	+	0.446005i	$0.852846\pi$
$588$	−179.779	+	363.480i	−0.305747	+	0.618163i
$589$	221.173			0.375506
$590$			27.7418i			0.0470201i
$591$	−413.668	−	204.602i	−0.699946	−	0.346197i
$592$	842.886			1.42379
$593$		−	238.602i		−	0.402364i	−0.979554	−	0.201182i	$-0.935522\pi$
$593$		−	238.602i		−	0.402364i	0.979554	−	0.201182i	$-0.0644783\pi$
$594$	25.8748	−	5.05220i	0.0435603	−	0.00850538i
$595$	−1102.02			−1.85214
$596$			147.009i			0.246659i
$597$	−185.778	+	375.608i	−0.311185	+	0.629159i
$598$	−305.556			−0.510963
$599$		−	275.680i		−	0.460234i	−0.973163	−	0.230117i	$-0.926089\pi$
$599$		−	275.680i		−	0.460234i	0.973163	−	0.230117i	$-0.0739110\pi$
$600$	329.766	+	163.104i	0.549610	+	0.271840i
$601$	−116.291			−0.193495			−0.0967477	−	0.995309i	$-0.530844\pi$
$601$	−116.291			−0.193495			−0.0967477	+	0.995309i	$0.530844\pi$
$602$		−	260.916i		−	0.433416i
$603$	−141.728	−	185.604i	−0.235039	−	0.307802i
$604$	−706.746			−1.17011
$605$			891.737i			1.47394i
$606$	−46.5321	+	94.0792i	−0.0767856	+	0.155246i
$607$	174.518			0.287508			0.143754	−	0.989613i	$-0.454083\pi$
$607$	174.518			0.287508			0.143754	+	0.989613i	$0.454083\pi$
$608$		−	672.719i		−	1.10645i
$609$	1032.65	+	510.754i	1.69565	+	0.838677i
$610$	79.3934			0.130153
$611$			572.292i			0.936649i
$612$	−423.205	+	323.161i	−0.691511	+	0.528041i
$613$	320.145			0.522259			0.261130	−	0.965304i	$-0.415905\pi$
$613$	320.145			0.522259			0.261130	+	0.965304i	$0.415905\pi$
$614$			153.088i			0.249329i
$615$	−292.169	+	590.713i	−0.475072	+	0.960508i
$616$	−69.9197			−0.113506
$617$		−	881.663i		−	1.42895i	−0.699661	−	0.714475i	$-0.746665\pi$
$617$		−	881.663i		−	1.42895i	0.699661	−	0.714475i	$-0.253335\pi$
$618$	−119.212	−	58.9630i	−0.192900	−	0.0954094i
$619$	510.282			0.824366			0.412183	−	0.911101i	$-0.364766\pi$
$619$	510.282			0.824366			0.412183	+	0.911101i	$0.364766\pi$
$620$		−	199.432i		−	0.321664i
$621$	217.024	+	1111.49i	0.349475	+	1.78984i
$622$	136.378			0.219257
$623$			715.955i			1.14921i
$624$	−273.944	+	553.863i	−0.439012	+	0.887601i
$625$	−346.355			−0.554168
$626$			40.7696i			0.0651271i
$627$	−177.674	−	87.8787i	−0.283372	−	0.140157i
$628$	−335.958			−0.534964
$629$		−	987.855i		−	1.57052i
$630$	−181.655	−	237.891i	−0.288341	−	0.377605i
$631$	167.330			0.265182			0.132591	−	0.991171i	$-0.457670\pi$
$631$	167.330			0.265182			0.132591	+	0.991171i	$0.457670\pi$
$632$			118.605i			0.187667i
$633$	−465.623	+	941.403i	−0.735581	+	1.48721i
$634$	−180.636			−0.284915
$635$		−	538.577i		−	0.848153i
$636$	0.191436	+	0.0946853i	0.000301000	+	0.000148876i
$637$	551.500			0.865777
$638$			40.7204i			0.0638251i
$639$	290.115	−	221.533i	0.454014	−	0.346688i
$640$	−799.707			−1.24954
$641$			486.167i			0.758452i	0.925304	+	0.379226i	$0.123810\pi$
$641$			486.167i			0.758452i	−0.925304	+	0.379226i	$0.876190\pi$
$642$	−32.5743	+	65.8593i	−0.0507388	+	0.102585i
$643$	657.600			1.02271			0.511353	−	0.859371i	$-0.329144\pi$
$643$	657.600			1.02271			0.511353	+	0.859371i	$0.329144\pi$
$644$		−	1458.58i		−	2.26488i
$645$	−1231.08	−	608.896i	−1.90864	−	0.944026i
$646$	−236.978			−0.366840
$647$			1134.78i			1.75392i	0.480568	+	0.876958i	$0.340431\pi$
$647$			1134.78i			1.75392i	−0.480568	+	0.876958i	$0.659569\pi$
$648$	−287.298	−	78.4285i	−0.443362	−	0.121032i
$649$	−15.8632			−0.0244425
$650$		−	242.982i		−	0.373818i
$651$	−84.6664	+	171.180i	−0.130056	+	0.262949i
$652$	−728.651			−1.11756
$653$			572.427i			0.876611i	0.898826	+	0.438306i	$0.144421\pi$
$653$			572.427i			0.876611i	−0.898826	+	0.438306i	$0.855579\pi$
$654$	−37.8343	−	18.7130i	−0.0578506	−	0.0286132i
$655$	1295.80			1.97832
$656$		−	384.407i		−	0.585986i
$657$	230.769	+	302.211i	0.351247	+	0.459986i
$658$	161.704			0.245750
$659$		−	321.495i		−	0.487853i	−0.969794	−	0.243926i	$-0.921565\pi$
$659$		−	321.495i		−	0.487853i	0.969794	−	0.243926i	$-0.0784355\pi$
$660$	−79.2401	+	160.209i	−0.120061	+	0.242741i
$661$	−649.633			−0.982803			−0.491402	−	0.870933i	$-0.663515\pi$
$661$	−649.633			−0.982803			−0.491402	+	0.870933i	$0.663515\pi$
$662$			33.6023i			0.0507588i
$663$	649.123	+	321.059i	0.979069	+	0.484252i
$664$	69.8764			0.105236
$665$			2250.48i			3.38418i
$666$	213.246	−	162.836i	0.320189	−	0.244498i
$667$	−1749.20			−2.62249
$668$			497.824i			0.745246i
$669$	253.609	−	512.751i	0.379087	−	0.766444i
$670$	−93.7148			−0.139873
$671$			45.3983i			0.0676577i
$672$	520.659	+	257.521i	0.774790	+	0.383215i
$673$	1232.00			1.83061			0.915303	−	0.402766i	$-0.131951\pi$
$673$	1232.00			1.83061			0.915303	+	0.402766i	$0.131951\pi$
$674$		−	176.908i		−	0.262475i
$675$	−883.871	+	172.580i	−1.30944	+	0.255675i
$676$	258.353			0.382179
$677$			216.524i			0.319829i	0.987131	+	0.159915i	$0.0511219\pi$
$677$			216.524i			0.319829i	−0.987131	+	0.159915i	$0.948878\pi$
$678$	72.1547	−	145.883i	0.106423	−	0.215167i
$679$	−1133.47			−1.66932
$680$			440.015i			0.647080i
$681$	686.751	+	339.670i	1.00844	+	0.498782i
$682$	−6.75012			−0.00989753
$683$		−	1.94504i		−	0.00284779i	−0.999999	−	0.00142390i	$-0.999547\pi$
$683$		−	1.94504i		−	0.00284779i	0.999999	−	0.00142390i	$-0.000453240\pi$
$684$	659.938	+	864.240i	0.964822	+	1.26351i
$685$	706.614			1.03155
$686$			57.4998i			0.0838189i
$687$	77.0398	−	155.760i	0.112139	−	0.226725i
$688$	801.125			1.16443
$689$		−	0.290462i		−	0.000421570i
$690$	407.358	+	201.481i	0.590373	+	0.292002i
$691$	632.425			0.915232			0.457616	−	0.889150i	$-0.348704\pi$
$691$	632.425			0.915232			0.457616	+	0.889150i	$0.348704\pi$
$692$		−	441.877i		−	0.638551i
$693$	136.030	−	103.873i	0.196291	−	0.149889i
$694$	−171.873			−0.247656
$695$		−	1013.43i		−	1.45818i
$696$	203.933	−	412.316i	0.293008	−	0.592408i
$697$	−450.522			−0.646372
$698$		−	131.143i		−	0.187883i
$699$	142.574	+	70.5177i	0.203968	+	0.100884i
$700$	1159.88			1.65698
$701$			324.722i			0.463226i	0.972808	+	0.231613i	$0.0744004\pi$
$701$			324.722i			0.463226i	−0.972808	+	0.231613i	$0.925600\pi$
$702$	37.6935	+	193.047i	0.0536944	+	0.274996i
$703$	−2017.33			−2.86960
$704$		−	89.8961i		−	0.127693i
$705$	377.365	−	762.963i	0.535270	−	1.08222i
$706$	−214.544			−0.303887
$707$			681.395i			0.963784i
$708$	78.0031	+	38.5807i	0.110174	+	0.0544925i
$709$	−705.852			−0.995560			−0.497780	−	0.867303i	$-0.665851\pi$
$709$	−705.852			−0.995560			−0.497780	+	0.867303i	$0.665851\pi$
$710$		−	146.484i		−	0.206316i
$711$	−176.200	−	230.748i	−0.247820	−	0.324540i
$712$	285.866			0.401497
$713$		−	289.961i		−	0.406677i
$714$	90.7167	−	183.412i	0.127054	−	0.256880i
$715$	243.081			0.339974
$716$			57.7672i			0.0806804i
$717$	843.126	+	417.015i	1.17591	+	0.581610i
$718$	136.601			0.190252
$719$			221.233i			0.307695i	0.988095	+	0.153848i	$0.0491665\pi$
$719$			221.233i			0.307695i	−0.988095	+	0.153848i	$0.950834\pi$
$720$	730.427	−	557.757i	1.01448	−	0.774663i
$721$	−863.428			−1.19754
$722$			313.262i			0.433881i
$723$	251.614	−	508.717i	0.348014	−	0.703620i
$724$	1280.94			1.76925
$725$		−	1390.99i		−	1.91860i
$726$	−148.414	−	73.4063i	−0.204427	−	0.101111i
$727$	800.622			1.10127			0.550634	−	0.834747i	$-0.314386\pi$
$727$	800.622			1.10127			0.550634	+	0.834747i	$0.314386\pi$
$728$		−	521.658i		−	0.716563i
$729$	675.456	−	274.227i	0.926551	−	0.376169i
$730$	152.591			0.209029
$731$		−	938.911i		−	1.28442i
$732$	110.413	−	223.234i	0.150837	−	0.304965i
$733$	632.139			0.862400			0.431200	−	0.902256i	$-0.358090\pi$
$733$	632.139			0.862400			0.431200	+	0.902256i	$0.358090\pi$
$734$			42.3673i			0.0577211i
$735$	−735.243	−	363.655i	−1.00033	−	0.494769i
$736$	−881.942			−1.19829
$737$		−	53.5875i		−	0.0727103i
$738$	−74.2628	−	97.2530i	−0.100627	−	0.131779i
$739$	−431.988			−0.584558			−0.292279	−	0.956333i	$-0.594414\pi$
$739$	−431.988			−0.584558			−0.292279	+	0.956333i	$0.594414\pi$
$740$			1819.03i			2.45814i
$741$	655.646	−	1325.59i	0.884812	−	1.78893i
$742$	−0.0820712			−0.000110608
$743$		−	1135.31i		−	1.52801i	−0.645213	−	0.764003i	$-0.723231\pi$
$743$		−	1135.31i		−	1.52801i	0.645213	−	0.764003i	$-0.276769\pi$
$744$	68.3485	+	33.8055i	0.0918663	+	0.0454375i
$745$	−297.368			−0.399151
$746$			50.5192i			0.0677200i
$747$	−135.945	+	103.809i	−0.181988	+	0.138967i
$748$	−122.187			−0.163352
$749$			477.004i			0.636855i
$750$	−40.1301	+	81.1356i	−0.0535068	+	0.108181i
$751$	95.9451			0.127756			0.0638782	−	0.997958i	$-0.479653\pi$
$751$	95.9451			0.127756			0.0638782	+	0.997958i	$0.479653\pi$
$752$			496.499i			0.660239i
$753$	−0.254336	−	0.125796i	−0.000337763	−	0.000167059i
$754$	−303.807			−0.402927
$755$		−	1429.60i		−	1.89351i
$756$	−921.518	+	179.931i	−1.21894	+	0.238004i
$757$	708.368			0.935757			0.467879	−	0.883793i	$-0.345018\pi$
$757$	708.368			0.935757			0.467879	+	0.883793i	$0.345018\pi$
$758$			34.3172i			0.0452734i
$759$	−115.210	+	232.933i	−0.151792	+	0.306895i
$760$	898.569			1.18233
$761$			872.545i			1.14658i	0.819353	+	0.573289i	$0.194333\pi$
$761$			872.545i			1.14658i	−0.819353	+	0.573289i	$0.805667\pi$
$762$	89.6367	+	44.3348i	0.117633	+	0.0581821i
$763$	−274.025			−0.359142
$764$		−	795.599i		−	1.04136i
$765$	−653.687	−	856.053i	−0.854492	−	1.11902i
$766$	265.121			0.346111
$767$		−	118.352i		−	0.154305i
$768$	−165.746	+	335.108i	−0.215816	+	0.436339i
$769$	−945.954			−1.23011			−0.615055	−	0.788484i	$-0.710866\pi$
$769$	−945.954			−1.23011			−0.615055	+	0.788484i	$0.710866\pi$
$770$		−	68.6837i		−	0.0891996i
$771$	−4.25793	−	2.10599i	−0.00552260	−	0.00273151i
$772$	480.952			0.622995
$773$			1230.18i			1.59144i	0.605665	+	0.795720i	$0.292907\pi$
$773$			1230.18i			1.59144i	−0.605665	+	0.795720i	$0.707093\pi$
$774$	202.680	−	154.768i	0.261861	−	0.199958i
$775$	230.581			0.297523
$776$			452.571i			0.583210i
$777$	772.246	−	1561.34i	0.993882	−	2.00945i
$778$	122.211			0.157083
$779$			920.025i			1.18103i
$780$	−1195.29	−	591.195i	−1.53242	−	0.757943i
$781$	83.7618			0.107249
$782$			310.681i			0.397291i
$783$	215.782	+	1105.13i	0.275584	+	1.41140i
$784$	478.461			0.610281
$785$		−	679.571i		−	0.865696i
$786$	−106.668	+	215.663i	−0.135710	+	0.274380i
$787$	−1265.82			−1.60842			−0.804208	−	0.594348i	$-0.797410\pi$
$787$	−1265.82			−1.60842			−0.804208	+	0.594348i	$0.797410\pi$
$788$			580.947i			0.737243i
$789$	−902.785	−	446.522i	−1.14421	−	0.565934i
$790$	−116.509			−0.147479
$791$		−	1056.60i		−	1.33578i
$792$	−41.4743	−	54.3138i	−0.0523665	−	0.0685780i
$793$	−338.708			−0.427123
$794$		−	85.9283i		−	0.108222i
$795$	−0.191528	+	0.387235i	−0.000240916	+	0.000487088i
$796$	527.497			0.662685
$797$			1484.95i			1.86317i	0.363523	+	0.931585i	$0.381574\pi$
$797$			1484.95i			1.86317i	−0.363523	+	0.931585i	$0.618426\pi$
$798$	−374.553	−	185.256i	−0.469364	−	0.232150i
$799$	581.893			0.728276
$800$		−	701.332i		−	0.876665i
$801$	−556.155	+	424.683i	−0.694326	+	0.530191i
$802$	189.708			0.236543
$803$			87.2539i			0.108660i
$804$	−130.330	+	263.502i	−0.162101	+	0.327739i
$805$	2950.40			3.66510
$806$		−	50.3613i		−	0.0624830i
$807$	568.315	+	281.091i	0.704231	+	0.348316i
$808$	272.067			0.336716
$809$		−	507.860i		−	0.627762i	−0.949462	−	0.313881i	$-0.898371\pi$
$809$		−	507.860i		−	0.627762i	0.949462	−	0.313881i	$-0.101629\pi$
$810$	77.0420	−	282.219i	0.0951136	−	0.348419i
$811$	416.682			0.513787			0.256894	−	0.966440i	$-0.417301\pi$
$811$	416.682			0.513787			0.256894	+	0.966440i	$0.417301\pi$
$812$		−	1450.24i		−	1.78600i
$813$	−94.4658	+	190.992i	−0.116194	+	0.234923i
$814$	61.5681			0.0756365
$815$		−	1473.91i		−	1.80847i
$816$	563.154	+	278.539i	0.690140	+	0.341347i
$817$	−1917.38			−2.34685
$818$			189.070i			0.231137i
$819$	774.976	+	1014.89i	0.946246	+	1.23918i
$820$	829.586			1.01169
$821$			98.7748i			0.120310i	0.998189	+	0.0601552i	$0.0191596\pi$
$821$			98.7748i			0.120310i	−0.998189	+	0.0601552i	$0.980840\pi$
$822$	−58.1673	+	117.603i	−0.0707631	+	0.143070i
$823$	505.968			0.614785			0.307393	−	0.951583i	$-0.400543\pi$
$823$	505.968			0.614785			0.307393	+	0.951583i	$0.400543\pi$
$824$			344.749i			0.418384i
$825$	−185.232	−	91.6165i	−0.224523	−	0.111050i
$826$	−33.4410			−0.0404854
$827$		−	600.085i		−	0.725617i	−0.931864	−	0.362808i	$-0.881818\pi$
$827$		−	600.085i		−	0.725617i	0.931864	−	0.362808i	$-0.118182\pi$
$828$	1133.03	−	865.186i	1.36839	−	1.04491i
$829$	−1485.51			−1.79193			−0.895966	−	0.444123i	$-0.853515\pi$
$829$	−1485.51			−1.79193			−0.895966	+	0.444123i	$0.853515\pi$
$830$			68.6411i			0.0827001i
$831$	9.98117	−	20.1801i	0.0120110	−	0.0242841i
$832$	670.698			0.806127
$833$		−	560.751i		−	0.673171i
$834$	168.668	+	83.4242i	0.202240	+	0.100029i
$835$	−1006.99			−1.20598
$836$			249.523i			0.298472i
$837$	−183.194	+	35.7697i	−0.218870	+	0.0427356i
$838$	−168.105			−0.200602
$839$		−	458.174i		−	0.546095i	−0.962001	−	0.273048i	$-0.911968\pi$
$839$		−	458.174i		−	0.546095i	0.962001	−	0.273048i	$-0.0880317\pi$
$840$	−343.977	+	695.459i	−0.409497	+	0.827927i
$841$	−898.192			−1.06800
$842$		−	58.3890i		−	0.0693456i
$843$	953.435	+	471.574i	1.13100	+	0.559399i
$844$	1322.09			1.56646
$845$			522.593i			0.618454i
$846$	95.9177	+	125.612i	0.113378	+	0.148477i
$847$	−1074.93			−1.26910
$848$		−	0.251994i		−	0.000297162i
$849$	10.2300	−	20.6832i	0.0120495	−	0.0243619i
$850$	−247.058			−0.290656
$851$			2644.74i			3.10781i
$852$	−411.876	−	203.716i	−0.483423	−	0.239103i
$853$	156.404			0.183358			0.0916790	−	0.995789i	$-0.470777\pi$
$853$	156.404			0.183358			0.0916790	+	0.995789i	$0.470777\pi$
$854$			95.7035i			0.112065i
$855$	−1748.17	+	1334.92i	−2.04465	+	1.56130i
$856$	190.458			0.222497
$857$		−	139.422i		−	0.162686i	−0.996686	−	0.0813432i	$-0.974079\pi$
$857$		−	139.422i		−	0.162686i	0.996686	−	0.0813432i	$-0.0259210\pi$
$858$	−20.0100	+	40.4566i	−0.0233217	+	0.0471522i
$859$	759.482			0.884147			0.442073	−	0.896979i	$-0.354243\pi$
$859$	759.482			0.884147			0.442073	+	0.896979i	$0.354243\pi$
$860$			1728.90i			2.01035i
$861$	−712.065	−	352.191i	−0.827021	−	0.409049i
$862$	−130.200			−0.151045
$863$			470.420i			0.545098i	0.962142	+	0.272549i	$0.0878667\pi$
$863$			470.420i			0.545098i	−0.962142	+	0.272549i	$0.912133\pi$
$864$	108.797	+	557.202i	0.125922	+	0.644910i
$865$	893.824			1.03332
$866$			81.3472i			0.0939344i
$867$	−57.9313	+	117.126i	−0.0668181	+	0.135094i
$868$	240.402			0.276961
$869$		−	66.6213i		−	0.0766644i
$870$	405.027	+	200.328i	0.465548	+	0.230262i
$871$	399.806			0.459020
$872$			109.413i			0.125473i
$873$	−672.340	−	880.481i	−0.770149	−	1.00857i
$874$	634.453			0.725918
$875$			587.648i			0.671597i
$876$	212.209	−	429.048i	0.242248	−	0.489781i
$877$	−778.085			−0.887212			−0.443606	−	0.896222i	$-0.646301\pi$
$877$	−778.085			−0.887212			−0.443606	+	0.896222i	$0.646301\pi$
$878$		−	32.9771i		−	0.0375593i
$879$	629.795	+	311.500i	0.716490	+	0.354380i
$880$	210.888			0.239646
$881$		−	1105.89i		−	1.25527i	−0.778509	−	0.627634i	$-0.784023\pi$
$881$		−	1105.89i		−	1.25527i	0.778509	−	0.627634i	$-0.215977\pi$
$882$	121.048	−	92.4329i	0.137243	−	0.104799i
$883$	1237.26			1.40120			0.700602	−	0.713552i	$-0.252915\pi$
$883$	1237.26			1.40120			0.700602	+	0.713552i	$0.252915\pi$
$884$		−	911.616i		−	1.03124i
$885$	−78.0406	+	157.784i	−0.0881815	+	0.178287i
$886$	247.955			0.279859
$887$		−	751.441i		−	0.847171i	−0.905856	−	0.423586i	$-0.860771\pi$
$887$		−	751.441i		−	0.847171i	0.905856	−	0.423586i	$-0.139229\pi$
$888$	−623.410	−	308.342i	−0.702038	−	0.347232i
$889$	649.219			0.730280
$890$			280.812i			0.315519i
$891$	161.377	+	44.0538i	0.181119	+	0.0494431i
$892$	−720.097			−0.807284
$893$		−	1188.30i		−	1.33069i
$894$	24.4788	−	49.4916i	0.0273812	−	0.0553598i
$895$	−116.851			−0.130560
$896$		−	963.994i		−	1.07589i
$897$	−1737.87	−	859.559i	−1.93742	−	0.958260i
$898$	−17.0701			−0.0190090
$899$		−	288.301i		−	0.320691i
$900$	688.008	+	900.999i	0.764453	+	1.00111i
$901$	−0.295334			−0.000327785
$902$		−	28.0788i		−	0.0311295i
$903$	733.985	−	1483.98i	0.812829	−	1.64339i
$904$	−421.879			−0.466680
$905$			2591.06i			2.86305i
$906$	237.931	+	117.682i	0.262617	+	0.129892i
$907$	−265.578			−0.292810			−0.146405	−	0.989225i	$-0.546770\pi$
$907$	−265.578			−0.292810			−0.146405	+	0.989225i	$0.546770\pi$
$908$		−	964.460i		−	1.06218i
$909$	−529.309	+	404.183i	−0.582298	+	0.444645i
$910$	512.436			0.563116
$911$		−	725.435i		−	0.796306i	−0.917319	−	0.398153i	$-0.869651\pi$
$911$		−	725.435i		−	0.796306i	0.917319	−	0.398153i	$-0.130349\pi$
$912$	568.814	−	1150.04i	0.623699	−	1.26100i
$913$	−39.2500			−0.0429901
$914$		−	77.2591i		−	0.0845285i
$915$	451.556	+	223.342i	0.493503	+	0.244089i
$916$	−218.747			−0.238806
$917$			1562.00i			1.70338i
$918$	196.285	−	38.3258i	0.213819	−	0.0417492i
$919$	1670.90			1.81817			0.909087	−	0.416606i	$-0.136780\pi$
$919$	1670.90			1.81817			0.909087	+	0.416606i	$0.136780\pi$
$920$		−	1178.03i		−	1.28047i
$921$	−430.653	+	870.700i	−0.467593	+	0.945386i
$922$	−140.708			−0.152612
$923$			624.930i			0.677064i
$924$	−193.121	−	95.5187i	−0.209006	−	0.103375i
$925$	−2103.14			−2.27366
$926$		−	209.244i		−	0.225965i
$927$	−512.159	−	670.713i	−0.552491	−	0.723530i
$928$	−876.895			−0.944930
$929$			970.713i			1.04490i	0.852670	+	0.522451i	$0.174982\pi$
$929$			970.713i			1.04490i	−0.852670	+	0.522451i	$0.825018\pi$
$930$	−33.2079	+	67.1402i	−0.0357074	+	0.0721938i
$931$	−1145.13			−1.23000
$932$		−	200.228i		−	0.214837i
$933$	775.660	+	383.645i	0.831361	+	0.411195i
$934$	−115.506			−0.123668
$935$		−	247.159i		−	0.264341i
$936$	405.225	−	309.432i	0.432932	−	0.330589i
$937$	192.193			0.205115			0.102557	−	0.994727i	$-0.467297\pi$
$937$	192.193			0.205115			0.102557	+	0.994727i	$0.467297\pi$
$938$		−	112.967i		−	0.120434i
$939$	−114.689	+	231.880i	−0.122139	+	0.246943i
$940$	−1071.49			−1.13988
$941$			521.301i			0.553986i	0.960872	+	0.276993i	$0.0893379\pi$
$941$			521.301i			0.553986i	−0.960872	+	0.276993i	$0.910662\pi$
$942$	113.103	+	55.9412i	0.120067	+	0.0593855i
$943$	1206.16			1.27907
$944$		−	102.678i		−	0.108769i
$945$	−363.963	−	1864.04i	−0.385146	−	1.97252i
$946$	58.5177			0.0618580
$947$			779.688i			0.823324i	0.911337	+	0.411662i	$0.135052\pi$
$947$			779.688i			0.823324i	−0.911337	+	0.411662i	$0.864948\pi$
$948$	−162.029	+	327.593i	−0.170917	+	0.345562i
$949$	−650.985			−0.685969
$950$			504.525i			0.531079i
$951$	−1027.38	−	508.147i	−1.08032	−	0.534329i
$952$	−530.409			−0.557152
$953$			1298.89i			1.36295i	0.731841	+	0.681475i	$0.238661\pi$
$953$			1298.89i			1.36295i	−0.731841	+	0.681475i	$0.761339\pi$
$954$	−0.0486821	−	0.0637531i	−5.10295e−5	−	6.68271e-5i
$955$	1609.33			1.68516
$956$		−	1184.07i		−	1.23857i
$957$	−114.551	+	231.600i	−0.119698	+	0.242006i
$958$	−302.182			−0.315430
$959$			851.776i			0.888192i
$960$	−894.154	−	442.253i	−0.931411	−	0.460681i
$961$	−913.209			−0.950270
$962$			459.348i			0.477493i
$963$	−370.538	+	282.944i	−0.384774	+	0.293816i
$964$	−714.432			−0.741113
$965$			972.865i			1.00815i
$966$	−242.872	+	491.043i	−0.251421	+	0.508326i
$967$	−270.268			−0.279491			−0.139746	−	0.990187i	$-0.544628\pi$
$967$	−270.268			−0.279491			−0.139746	+	0.990187i	$0.544628\pi$
$968$			429.197i			0.443385i
$969$	−1347.83	−	666.644i	−1.39095	−	0.687972i
$970$	−444.570			−0.458320
$971$		−	1459.22i		−	1.50280i	−0.659844	−	0.751402i	$-0.729378\pi$
$971$		−	1459.22i		−	1.50280i	0.659844	−	0.751402i	$-0.270622\pi$
$972$	−686.387	−	609.107i	−0.706159	−	0.626653i
$973$	1221.63			1.25553
$974$		−	229.758i		−	0.235891i
$975$	683.533	−	1381.98i	0.701059	−	1.41741i
$976$	−293.851			−0.301076
$977$		−	1189.83i		−	1.21784i	−0.793233	−	0.608918i	$-0.791604\pi$
$977$		−	1189.83i		−	1.21784i	0.793233	−	0.608918i	$-0.208396\pi$
$978$	245.306	+	121.330i	0.250824	+	0.124059i
$979$	−160.573			−0.164017
$980$			1032.56i			1.05363i
$981$	−162.543	−	212.863i	−0.165692	−	0.216986i
$982$	−178.317			−0.181586
$983$			1449.96i			1.47503i	0.675330	+	0.737515i	$0.264001\pi$
$983$			1449.96i			1.47503i	−0.675330	+	0.737515i	$0.735999\pi$
$984$	−140.622	+	284.313i	−0.142909	+	0.288936i
$985$	−1175.13			−1.19303
$986$			308.904i			0.313290i
$987$	919.702	+	454.889i	0.931815	+	0.460881i
$988$	−1861.64			−1.88425
$989$			2513.71i			2.54167i
$990$	53.3536	−	40.7411i	0.0538925	−	0.0411526i
$991$	−1027.59			−1.03692			−0.518461	−	0.855101i	$-0.673495\pi$
$991$	−1027.59			−1.03692			−0.518461	+	0.855101i	$0.673495\pi$
$992$		−	145.361i		−	0.146533i
$993$	−94.5268	+	191.116i	−0.0951931	+	0.192463i
$994$	176.577			0.177643
$995$			1067.01i			1.07238i
$996$	193.001	+	95.4595i	0.193777	+	0.0958429i
$997$	216.378			0.217029			0.108514	−	0.994095i	$-0.465391\pi$
$997$	216.378			0.217029			0.108514	+	0.994095i	$0.465391\pi$
$998$		−	294.500i		−	0.295090i
$999$	1670.92	−	326.257i	1.67260	−	0.326583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.22	yes	38
3.2	odd	2	inner	177.3.b.a.119.17	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.17	✓	38	3.2	odd	2	inner
177.3.b.a.119.22	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)

\(f(q)\)	\(=\)	\(q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} +O(q^{10})\)	\(q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} -3.61168 q^{10} -2.06521i q^{11} +(-5.02278 + 10.1551i) q^{12} +15.4082 q^{13} -4.35364i q^{14} +(-20.5417 - 10.1600i) q^{15} +13.3675 q^{16} -15.6666i q^{17} +(3.38192 - 2.58245i) q^{18} -31.9933 q^{19} +28.8484i q^{20} +(12.2472 - 24.7617i) q^{21} +0.976424 q^{22} +41.9436i q^{23} +(-9.88681 - 4.89007i) q^{24} -33.3541 q^{25} +7.28491i q^{26} +(26.4996 - 5.17418i) q^{27} -34.7748 q^{28} +41.7036i q^{29} +(4.80362 - 9.71202i) q^{30} -6.91310 q^{31} +21.0268i q^{32} +(5.55348 + 2.74678i) q^{33} +7.40712 q^{34} -70.3421i q^{35} +(-20.6274 - 27.0131i) q^{36} +63.0547 q^{37} -15.1263i q^{38} +(-20.4932 + 41.4335i) q^{39} -28.0861 q^{40} -28.7568i q^{41} +(11.7072 + 5.79044i) q^{42} +59.9306 q^{43} -7.79920i q^{44} +(54.6418 - 41.7248i) q^{45} -19.8308 q^{46} +37.1422i q^{47} +(-17.7791 + 35.9461i) q^{48} +35.7927 q^{49} -15.7697i q^{50} +(42.1285 + 20.8370i) q^{51} +58.1884 q^{52} -0.0188512i q^{53} +(2.44633 + 12.5289i) q^{54} +15.7761 q^{55} -33.8560i q^{56} +(42.5519 - 86.0320i) q^{57} -19.7173 q^{58} -7.68115i q^{59} +(-77.5750 - 38.3690i) q^{60} -21.9824 q^{61} -3.26849i q^{62} +(50.2965 + 65.8671i) q^{63} +43.5288 q^{64} +117.703i q^{65} +(-1.29867 + 2.62566i) q^{66} +25.9477 q^{67} -59.1645i q^{68} +(-112.789 - 55.7860i) q^{69} +33.2574 q^{70} +40.5584i q^{71} +(26.2994 - 20.0823i) q^{72} -42.2494 q^{73} +29.8120i q^{74} +(44.3618 - 89.6913i) q^{75} -120.822 q^{76} +19.0171i q^{77} +(-19.5896 - 9.68910i) q^{78} +32.2588 q^{79} +102.114i q^{80} +(-21.3314 + 78.1407i) q^{81} +13.5961 q^{82} -19.0053i q^{83} +(46.2513 - 93.5115i) q^{84} +119.677 q^{85} +28.3349i q^{86} +(-112.144 - 55.4667i) q^{87} +7.59312 q^{88} -77.7511i q^{89} +(19.7273 + 25.8344i) q^{90} -141.883 q^{91} +158.399i q^{92} +(9.19458 - 18.5897i) q^{93} -17.5607 q^{94} -244.397i q^{95} +(-56.5424 - 27.9662i) q^{96} +123.092 q^{97} +16.9226i q^{98} +(-14.7725 + 11.2804i) 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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