LMFDB - Embedded newform 210.3.h.a.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(139,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("210.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.h (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 $ x^16 - 8x^15 + 96x^14 - 532x^13 + 3236x^12 - 12864x^11 + 49526x^10 - 141436x^9 + 362298x^8 - 722060x^7 + 1208164x^6 - 1570812x^5 + 1591101x^4 - 1183860x^3 + 619650x^2 - 202500*x + 33750
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.5
Root			$0.500000 + 2.68650i$ of defining polynomial
Character	$\chi$	$=$	210.139
Dual form			210.3.h.a.139.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +(-4.59769 + 1.96501i) q^{5} -2.44949i q^{6} +(-6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +(-4.59769 + 1.96501i) q^{5} -2.44949i q^{6} +(-6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +(2.77894 + 6.50212i) q^{10} -8.15965 q^{11} -3.46410 q^{12} -14.6064 q^{13} +(2.23278 + 9.64441i) q^{14} +(-7.96343 + 3.40349i) q^{15} +4.00000 q^{16} -5.81421 q^{17} -4.24264i q^{18} +33.7736i q^{19} +(9.19538 - 3.93001i) q^{20} +(-11.8119 + 2.73459i) q^{21} +11.5395i q^{22} -37.2576i q^{23} +4.89898i q^{24} +(17.2775 - 18.0690i) q^{25} +20.6566i q^{26} +5.19615 q^{27} +(13.6393 - 3.15763i) q^{28} -9.25305 q^{29} +(4.81326 + 11.2620i) q^{30} -19.2558i q^{31} -5.65685i q^{32} -14.1329 q^{33} +8.22253i q^{34} +(28.2522 - 20.6595i) q^{35} -6.00000 q^{36} +63.4350i q^{37} +47.7631 q^{38} -25.2990 q^{39} +(-5.55788 - 13.0042i) q^{40} +8.25880i q^{41} +(3.86729 + 16.7046i) q^{42} +42.0893i q^{43} +16.3193 q^{44} +(-13.7931 + 5.89502i) q^{45} -52.6901 q^{46} -23.3380 q^{47} +6.92820 q^{48} +(44.0147 - 21.5339i) q^{49} +(-25.5534 - 24.4341i) q^{50} -10.0705 q^{51} +29.2128 q^{52} -71.3497i q^{53} -7.34847i q^{54} +(37.5155 - 16.0337i) q^{55} +(-4.46556 - 19.2888i) q^{56} +58.4976i q^{57} +13.0858i q^{58} -42.9350i q^{59} +(15.9269 - 6.80698i) q^{60} -34.2864i q^{61} -27.2318 q^{62} +(-20.4589 + 4.73644i) q^{63} -8.00000 q^{64} +(67.1557 - 28.7017i) q^{65} +19.9870i q^{66} +4.99889i q^{67} +11.6284 q^{68} -64.5320i q^{69} +(-29.2170 - 39.9546i) q^{70} -38.8120 q^{71} +8.48528i q^{72} -124.629 q^{73} +89.7107 q^{74} +(29.9255 - 31.2964i) q^{75} -67.5472i q^{76} +(55.6458 - 12.8826i) q^{77} +35.7782i q^{78} -56.1842 q^{79} +(-18.3908 + 7.86002i) q^{80} +9.00000 q^{81} +11.6797 q^{82} +90.3980 q^{83} +(23.6239 - 5.46917i) q^{84} +(26.7319 - 11.4249i) q^{85} +59.5233 q^{86} -16.0267 q^{87} -23.0790i q^{88} +16.2289i q^{89} +(8.33681 + 19.5063i) q^{90} +(99.6102 - 23.0608i) q^{91} +74.5151i q^{92} -33.3520i q^{93} +33.0048i q^{94} +(-66.3653 - 155.280i) q^{95} -9.79796i q^{96} -82.7605 q^{97} +(-30.4535 - 62.2462i) q^{98} -24.4789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−2.00000			−0.500000
$5$	−4.59769	+	1.96501i	−0.919538	+	0.393001i
$5$	−4.59769	+	1.96501i	−0.919538	+	0.393001i
$6$		−	2.44949i		−	0.408248i
$7$	−6.81963	+	1.57881i	−0.974233	+	0.225545i
$7$	−6.81963	+	1.57881i	−0.974233	+	0.225545i
$8$			2.82843i			0.353553i
$9$	3.00000			0.333333
$10$	2.77894	+	6.50212i	0.277894	+	0.650212i
$11$	−8.15965			−0.741786			−0.370893	−	0.928676i	$-0.620948\pi$
$11$	−8.15965			−0.741786			−0.370893	+	0.928676i	$0.620948\pi$
$12$	−3.46410			−0.288675
$13$	−14.6064			−1.12357			−0.561785	−	0.827284i	$-0.689885\pi$
$13$	−14.6064			−1.12357			−0.561785	+	0.827284i	$0.689885\pi$
$14$	2.23278	+	9.64441i	0.159484	+	0.688887i
$15$	−7.96343	+	3.40349i	−0.530896	+	0.226899i
$16$	4.00000			0.250000
$17$	−5.81421			−0.342012			−0.171006	−	0.985270i	$-0.554702\pi$
$17$	−5.81421			−0.342012			−0.171006	+	0.985270i	$0.554702\pi$
$18$		−	4.24264i		−	0.235702i
$19$			33.7736i			1.77756i	0.458337	+	0.888778i	$0.348445\pi$
$19$			33.7736i			1.77756i	−0.458337	+	0.888778i	$0.651555\pi$
$20$	9.19538	−	3.93001i	0.459769	−	0.196501i
$21$	−11.8119	+	2.73459i	−0.562474	+	0.130218i
$22$			11.5395i			0.524522i
$23$		−	37.2576i		−	1.61989i	−0.586503	−	0.809947i	$-0.699496\pi$
$23$		−	37.2576i		−	1.61989i	0.586503	−	0.809947i	$-0.300504\pi$
$24$			4.89898i			0.204124i
$25$	17.2775	−	18.0690i	0.691100	−	0.722759i
$26$			20.6566i			0.794483i
$27$	5.19615			0.192450
$28$	13.6393	−	3.15763i	0.487116	−	0.112772i
$29$	−9.25305			−0.319071			−0.159535	−	0.987192i	$-0.551000\pi$
$29$	−9.25305			−0.319071			−0.159535	+	0.987192i	$0.551000\pi$
$30$	4.81326	+	11.2620i	0.160442	+	0.375400i
$31$		−	19.2558i		−	0.621154i	−0.950548	−	0.310577i	$-0.899478\pi$
$31$		−	19.2558i		−	0.621154i	0.950548	−	0.310577i	$-0.100522\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−14.1329			−0.428270
$34$			8.22253i			0.241839i
$35$	28.2522	−	20.6595i	0.807205	−	0.590272i
$36$	−6.00000			−0.166667
$37$			63.4350i			1.71446i	0.514933	+	0.857230i	$0.327817\pi$
$37$			63.4350i			1.71446i	−0.514933	+	0.857230i	$0.672183\pi$
$38$	47.7631			1.25692
$39$	−25.2990			−0.648693
$40$	−5.55788	−	13.0042i	−0.138947	−	0.325106i
$41$			8.25880i			0.201434i	0.994915	+	0.100717i	$0.0321137\pi$
$41$			8.25880i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$42$	3.86729	+	16.7046i	0.0920783	+	0.397729i
$43$			42.0893i			0.978822i	0.872053	+	0.489411i	$0.162788\pi$
$43$			42.0893i			0.978822i	−0.872053	+	0.489411i	$0.837212\pi$
$44$	16.3193			0.370893
$45$	−13.7931	+	5.89502i	−0.306513	+	0.131000i
$46$	−52.6901			−1.14544
$47$	−23.3380			−0.496552			−0.248276	−	0.968689i	$-0.579864\pi$
$47$	−23.3380			−0.496552			−0.248276	+	0.968689i	$0.579864\pi$
$48$	6.92820			0.144338
$49$	44.0147	−	21.5339i	0.898259	−	0.439466i
$50$	−25.5534	−	24.4341i	−0.511068	−	0.488682i
$51$	−10.0705			−0.197461
$52$	29.2128			0.561785
$53$		−	71.3497i		−	1.34622i	−0.739542	−	0.673110i	$-0.764958\pi$
$53$		−	71.3497i		−	1.34622i	0.739542	−	0.673110i	$-0.235042\pi$
$54$		−	7.34847i		−	0.136083i
$55$	37.5155	−	16.0337i	0.682100	−	0.291523i
$56$	−4.46556	−	19.2888i	−0.0797422	−	0.344443i
$57$			58.4976i			1.02627i
$58$			13.0858i			0.225617i
$59$		−	42.9350i		−	0.727712i	−0.931455	−	0.363856i	$-0.881460\pi$
$59$		−	42.9350i		−	0.727712i	0.931455	−	0.363856i	$-0.118540\pi$
$60$	15.9269	−	6.80698i	0.265448	−	0.113450i
$61$		−	34.2864i		−	0.562072i	−0.959697	−	0.281036i	$-0.909322\pi$
$61$		−	34.2864i		−	0.562072i	0.959697	−	0.281036i	$-0.0906781\pi$
$62$	−27.2318			−0.439222
$63$	−20.4589	+	4.73644i	−0.324744	+	0.0751816i
$64$	−8.00000			−0.125000
$65$	67.1557	−	28.7017i	1.03316	−	0.441564i
$66$			19.9870i			0.302833i
$67$			4.99889i			0.0746102i	0.999304	+	0.0373051i	$0.0118773\pi$
$67$			4.99889i			0.0746102i	−0.999304	+	0.0373051i	$0.988123\pi$
$68$	11.6284			0.171006
$69$		−	64.5320i		−	0.935246i
$70$	−29.2170	−	39.9546i	−0.417385	−	0.570780i
$71$	−38.8120			−0.546648			−0.273324	−	0.961922i	$-0.588123\pi$
$71$	−38.8120			−0.546648			−0.273324	+	0.961922i	$0.588123\pi$
$72$			8.48528i			0.117851i
$73$	−124.629			−1.70725			−0.853626	−	0.520886i	$-0.825602\pi$
$73$	−124.629			−1.70725			−0.853626	+	0.520886i	$0.825602\pi$
$74$	89.7107			1.21231
$75$	29.9255	−	31.2964i	0.399007	−	0.417285i
$76$		−	67.5472i		−	0.888778i
$77$	55.6458	−	12.8826i	0.722672	−	0.167306i
$78$			35.7782i			0.458695i
$79$	−56.1842			−0.711192			−0.355596	−	0.934640i	$-0.615722\pi$
$79$	−56.1842			−0.711192			−0.355596	+	0.934640i	$0.615722\pi$
$80$	−18.3908	+	7.86002i	−0.229884	+	0.0982503i
$81$	9.00000			0.111111
$82$	11.6797			0.142435
$83$	90.3980			1.08913			0.544566	−	0.838718i	$-0.316694\pi$
$83$	90.3980			1.08913			0.544566	+	0.838718i	$0.316694\pi$
$84$	23.6239	−	5.46917i	0.281237	−	0.0651092i
$85$	26.7319	−	11.4249i	0.314493	−	0.134411i
$86$	59.5233			0.692131
$87$	−16.0267			−0.184215
$88$		−	23.0790i		−	0.262261i
$89$			16.2289i			0.182347i	0.995835	+	0.0911736i	$0.0290618\pi$
$89$			16.2289i			0.182347i	−0.995835	+	0.0911736i	$0.970938\pi$
$90$	8.33681	+	19.5063i	0.0926313	+	0.216737i
$91$	99.6102	−	23.0608i	1.09462	−	0.253415i
$92$			74.5151i			0.809947i
$93$		−	33.3520i		−	0.358624i
$94$			33.0048i			0.351115i
$95$	−66.3653	−	155.280i	−0.698582	−	1.63453i
$96$		−	9.79796i		−	0.102062i
$97$	−82.7605			−0.853201			−0.426601	−	0.904440i	$-0.640289\pi$
$97$	−82.7605			−0.853201			−0.426601	+	0.904440i	$0.640289\pi$
$98$	−30.4535	−	62.2462i	−0.310750	−	0.635165i
$99$	−24.4789			−0.247262
$100$	−34.5550	+	36.1379i	−0.345550	+	0.361379i
$101$		−	87.2055i		−	0.863420i	−0.902012	−	0.431710i	$-0.857910\pi$
$101$		−	87.2055i		−	0.863420i	0.902012	−	0.431710i	$-0.142090\pi$
$102$			14.2418i			0.139626i
$103$	187.567			1.82104			0.910521	−	0.413462i	$-0.135681\pi$
$103$	187.567			1.82104			0.910521	+	0.413462i	$0.135681\pi$
$104$		−	41.3131i		−	0.397242i
$105$	48.9342	−	35.7833i	0.466040	−	0.340794i
$106$	−100.904			−0.951922
$107$			157.858i			1.47531i	0.675180	+	0.737653i	$0.264066\pi$
$107$			157.858i			1.47531i	−0.675180	+	0.737653i	$0.735934\pi$
$108$	−10.3923			−0.0962250
$109$	−112.073			−1.02819			−0.514097	−	0.857732i	$-0.671873\pi$
$109$	−112.073			−1.02819			−0.514097	+	0.857732i	$0.671873\pi$
$110$	−22.6751	−	53.0550i	−0.206138	−	0.482318i
$111$			109.873i			0.989844i
$112$	−27.2785	+	6.31526i	−0.243558	+	0.0563862i
$113$			141.987i			1.25653i	0.778001	+	0.628263i	$0.216234\pi$
$113$			141.987i			1.25653i	−0.778001	+	0.628263i	$0.783766\pi$
$114$	82.7280			0.725684
$115$	73.2113	+	171.299i	0.636620	+	1.48955i
$116$	18.5061			0.159535
$117$	−43.8192			−0.374523
$118$	−60.7192			−0.514570
$119$	39.6507	−	9.17955i	0.333199	−	0.0771391i
$120$	−9.62652	−	22.5240i	−0.0802210	−	0.187700i
$121$	−54.4202			−0.449754
$122$	−48.4883			−0.397445
$123$			14.3047i			0.116298i
$124$			38.5116i			0.310577i
$125$	−43.9310	+	117.026i	−0.351448	+	0.936207i
$126$	6.69834	+	28.9332i	0.0531614	+	0.229629i
$127$			202.414i			1.59381i	0.604104	+	0.796905i	$0.293531\pi$
$127$			202.414i			1.59381i	−0.604104	+	0.796905i	$0.706469\pi$
$128$			11.3137i			0.0883883i
$129$			72.9008i			0.565123i
$130$	−40.5903	−	94.9725i	−0.312233	−	0.730558i
$131$			141.260i			1.07832i	0.842203	+	0.539160i	$0.181258\pi$
$131$			141.260i			1.07832i	−0.842203	+	0.539160i	$0.818742\pi$
$132$	28.2658			0.214135
$133$	−53.3222	−	230.323i	−0.400919	−	1.73175i
$134$	7.06949			0.0527574
$135$	−23.8903	+	10.2105i	−0.176965	+	0.0756331i
$136$		−	16.4451i		−	0.120920i
$137$		−	50.6430i		−	0.369657i	−0.982771	−	0.184829i	$-0.940827\pi$
$137$		−	50.6430i		−	0.369657i	0.982771	−	0.184829i	$-0.0591730\pi$
$138$	−91.2620			−0.661319
$139$			74.0256i			0.532559i	0.963896	+	0.266279i	$0.0857943\pi$
$139$			74.0256i			0.532559i	−0.963896	+	0.266279i	$0.914206\pi$
$140$	−56.5043	+	41.3190i	−0.403602	+	0.295136i
$141$	−40.4225			−0.286685
$142$			54.8885i			0.386538i
$143$	119.183			0.833448
$144$	12.0000			0.0833333
$145$	42.5426	−	18.1823i	0.293397	−	0.125395i
$146$			176.253i			1.20721i
$147$	76.2357	−	37.2977i	0.518610	−	0.253726i
$148$		−	126.870i		−	0.857230i
$149$	−226.979			−1.52335			−0.761676	−	0.647958i	$-0.775623\pi$
$149$	−226.979			−1.52335			−0.761676	+	0.647958i	$0.775623\pi$
$150$	−44.2598	−	42.3211i	−0.295065	−	0.282140i
$151$	294.426			1.94984			0.974920	−	0.222558i	$-0.0714406\pi$
$151$	294.426			1.94984			0.974920	+	0.222558i	$0.0714406\pi$
$152$	−95.5261			−0.628461
$153$	−17.4426			−0.114004
$154$	−18.2187	−	78.6950i	−0.118303	−	0.511006i
$155$	37.8377	+	88.5321i	0.244114	+	0.571175i
$156$	50.5981			0.324346
$157$	65.8596			0.419488			0.209744	−	0.977756i	$-0.432737\pi$
$157$	65.8596			0.419488			0.209744	+	0.977756i	$0.432737\pi$
$158$			79.4564i			0.502889i
$159$		−	123.581i		−	0.777241i
$160$	11.1158	+	26.0085i	0.0694734	+	0.162553i
$161$	58.8227	+	254.083i	0.365359	+	1.57815i
$162$		−	12.7279i		−	0.0785674i
$163$			28.2075i			0.173052i	0.996250	+	0.0865260i	$0.0275766\pi$
$163$			28.2075i			0.173052i	−0.996250	+	0.0865260i	$0.972423\pi$
$164$		−	16.5176i		−	0.100717i
$165$	64.9788	−	27.7713i	0.393811	−	0.168311i
$166$		−	127.842i		−	0.770133i
$167$	−128.461			−0.769227			−0.384614	−	0.923078i	$-0.625665\pi$
$167$	−128.461			−0.769227			−0.384614	+	0.923078i	$0.625665\pi$
$168$	−7.73458	−	33.4092i	−0.0460392	−	0.198864i
$169$	44.3469			0.262408
$170$	−16.1573	−	37.8046i	−0.0950431	−	0.222380i
$171$			101.321i			0.592519i
$172$		−	84.1786i		−	0.489411i
$173$	−112.446			−0.649976			−0.324988	−	0.945718i	$-0.605360\pi$
$173$	−112.446			−0.649976			−0.324988	+	0.945718i	$0.605360\pi$
$174$			22.6652i			0.130260i
$175$	−89.2986	+	150.502i	−0.510278	+	0.860010i
$176$	−32.6386			−0.185446
$177$		−	74.3656i		−	0.420144i
$178$	22.9511			0.128939
$179$	−68.9019			−0.384927			−0.192464	−	0.981304i	$-0.561648\pi$
$179$	−68.9019			−0.384927			−0.192464	+	0.981304i	$0.561648\pi$
$180$	27.5861	−	11.7900i	0.153256	−	0.0655002i
$181$		−	166.537i		−	0.920094i	−0.887895	−	0.460047i	$-0.847833\pi$
$181$		−	166.537i		−	0.920094i	0.887895	−	0.460047i	$-0.152167\pi$
$182$	−32.6129	−	140.870i	−0.179192	−	0.774012i
$183$		−	59.3858i		−	0.324513i
$184$	105.380			0.572719
$185$	−124.650	−	291.655i	−0.673785	−	1.57651i
$186$	−47.1668			−0.253585
$187$	47.4419			0.253700
$188$	46.6759			0.248276
$189$	−35.4358	+	8.20376i	−0.187491	+	0.0434061i
$190$	−219.600	+	93.8547i	−1.15579	+	0.493972i
$191$	−148.289			−0.776382			−0.388191	−	0.921579i	$-0.626900\pi$
$191$	−148.289			−0.776382			−0.388191	+	0.921579i	$0.626900\pi$
$192$	−13.8564			−0.0721688
$193$		−	35.1886i		−	0.182324i	−0.995836	−	0.0911622i	$-0.970942\pi$
$193$		−	35.1886i		−	0.182324i	0.995836	−	0.0911622i	$-0.0290582\pi$
$194$			117.041i			0.603304i
$195$	116.317	−	49.7127i	0.596498	−	0.254937i
$196$	−88.0294	+	43.0677i	−0.449130	+	0.219733i
$197$			193.634i			0.982915i	0.870902	+	0.491457i	$0.163536\pi$
$197$			193.634i			0.982915i	−0.870902	+	0.491457i	$0.836464\pi$
$198$			34.6184i			0.174841i
$199$			181.838i			0.913759i	0.889529	+	0.456880i	$0.151033\pi$
$199$			181.838i			0.913759i	−0.889529	+	0.456880i	$0.848967\pi$
$200$	51.1068	+	48.8682i	0.255534	+	0.244341i
$201$			8.65832i			0.0430762i
$202$	−123.327			−0.610530
$203$	63.1023	−	14.6088i	0.310849	−	0.0719647i
$204$	20.1410			0.0987304
$205$	−16.2286	−	37.9714i	−0.0791638	−	0.185226i
$206$		−	265.260i		−	1.28767i
$207$		−	111.773i		−	0.539965i
$208$	−58.4256			−0.280892
$209$		−	275.580i		−	1.31857i
$210$	−50.6053	−	69.2034i	−0.240977	−	0.329540i
$211$	175.914			0.833717			0.416859	−	0.908971i	$-0.363131\pi$
$211$	175.914			0.833717			0.416859	+	0.908971i	$0.363131\pi$
$212$			142.699i			0.673110i
$213$	−67.2244			−0.315607
$214$	223.244			1.04320
$215$	−82.7058	−	193.514i	−0.384678	−	0.900064i
$216$			14.6969i			0.0680414i
$217$	30.4013	+	131.317i	0.140098	+	0.605149i
$218$			158.495i			0.727042i
$219$	−215.864			−0.985683
$220$	−75.0310	+	32.0675i	−0.341050	+	0.145761i
$221$	84.9246			0.384274
$222$	155.384			0.699926
$223$	−20.5675			−0.0922308			−0.0461154	−	0.998936i	$-0.514684\pi$
$223$	−20.5675			−0.0922308			−0.0461154	+	0.998936i	$0.514684\pi$
$224$	8.93112	+	38.5776i	0.0398711	+	0.172222i
$225$	51.8325	−	54.2069i	0.230367	−	0.240920i
$226$	200.801			0.888498
$227$	414.087			1.82417			0.912085	−	0.410001i	$-0.134472\pi$
$227$	414.087			1.82417			0.912085	+	0.410001i	$0.134472\pi$
$228$		−	116.995i		−	0.513136i
$229$			195.520i			0.853799i	0.904299	+	0.426899i	$0.140394\pi$
$229$			195.520i			0.853799i	−0.904299	+	0.426899i	$0.859606\pi$
$230$	242.253	−	103.536i	1.05327	−	0.450158i
$231$	96.3813	−	22.3133i	0.417235	−	0.0965942i
$232$		−	26.1716i		−	0.112808i
$233$		−	81.3006i		−	0.348930i	−0.984663	−	0.174465i	$-0.944180\pi$
$233$		−	81.3006i		−	0.348930i	0.984663	−	0.174465i	$-0.0558195\pi$
$234$			61.9697i			0.264828i
$235$	107.301	−	45.8592i	0.456599	−	0.195146i
$236$			85.8700i			0.363856i
$237$	−97.3138			−0.410607
$238$	−12.9818	−	56.0746i	−0.0545456	−	0.235608i
$239$	−249.265			−1.04295			−0.521475	−	0.853267i	$-0.674618\pi$
$239$	−249.265			−1.04295			−0.521475	+	0.853267i	$0.674618\pi$
$240$	−31.8537	+	13.6140i	−0.132724	+	0.0567248i
$241$		−	262.343i		−	1.08856i	−0.838904	−	0.544280i	$-0.816803\pi$
$241$		−	262.343i		−	1.08856i	0.838904	−	0.544280i	$-0.183197\pi$
$242$			76.9618i			0.318024i
$243$	15.5885			0.0641500
$244$			68.5728i			0.281036i
$245$	−160.052	+	185.495i	−0.653272	+	0.757123i
$246$	20.2298			0.0822351
$247$		−	493.310i		−	1.99721i
$248$	54.4636			0.219611
$249$	156.574			0.628811
$250$	165.500	+	62.1278i	0.661999	+	0.248511i
$251$		−	141.917i		−	0.565406i	−0.959208	−	0.282703i	$-0.908769\pi$
$251$		−	141.917i		−	0.565406i	0.959208	−	0.282703i	$-0.0912310\pi$
$252$	40.9178	−	9.47288i	0.162372	−	0.0375908i
$253$			304.008i			1.20161i
$254$	286.257			1.12699
$255$	46.3010	−	19.7886i	0.181573	−	0.0776023i
$256$	16.0000			0.0625000
$257$	−170.843			−0.664757			−0.332379	−	0.943146i	$-0.607851\pi$
$257$	−170.843			−0.664757			−0.332379	+	0.943146i	$0.607851\pi$
$258$	103.097			0.399602
$259$	−100.152	−	432.604i	−0.386688	−	1.67028i
$260$	−134.311	+	57.4033i	−0.516582	+	0.220782i
$261$	−27.7591			−0.106357
$262$	199.772			0.762488
$263$			383.417i			1.45786i	0.684588	+	0.728930i	$0.259982\pi$
$263$			383.417i			1.45786i	−0.684588	+	0.728930i	$0.740018\pi$
$264$		−	39.9739i		−	0.151416i
$265$	140.203	+	328.044i	0.529066	+	1.23790i
$266$	−325.726	+	75.4090i	−1.22454	+	0.283492i
$267$			28.1093i			0.105278i
$268$		−	9.99777i		−	0.0373051i
$269$		−	154.512i		−	0.574393i	−0.957872	−	0.287196i	$-0.907277\pi$
$269$		−	154.512i		−	0.574393i	0.957872	−	0.287196i	$-0.0927232\pi$
$270$	14.4398	+	33.7860i	0.0534807	+	0.125133i
$271$		−	320.328i		−	1.18202i	−0.806664	−	0.591010i	$-0.798729\pi$
$271$		−	320.328i		−	1.18202i	0.806664	−	0.591010i	$-0.201271\pi$
$272$	−23.2568			−0.0855030
$273$	172.530	−	39.9425i	0.631978	−	0.146309i
$274$	−71.6200			−0.261387
$275$	−140.978	+	147.436i	−0.512648	+	0.536132i
$276$			129.064i			0.467623i
$277$		−	222.854i		−	0.804526i	−0.915524	−	0.402263i	$-0.868224\pi$
$277$		−	222.854i		−	0.804526i	0.915524	−	0.402263i	$-0.131776\pi$
$278$	104.688			0.376576
$279$		−	57.7673i		−	0.207051i
$280$	58.4339	+	79.9092i	0.208693	+	0.285390i
$281$	218.973			0.779263			0.389631	−	0.920971i	$-0.372602\pi$
$281$	218.973			0.779263			0.389631	+	0.920971i	$0.372602\pi$
$282$			57.1661i			0.202717i
$283$	−36.3957			−0.128607			−0.0643034	−	0.997930i	$-0.520483\pi$
$283$	−36.3957			−0.128607			−0.0643034	+	0.997930i	$0.520483\pi$
$284$	77.6240			0.273324
$285$	−114.948	−	268.954i	−0.403326	−	0.943697i
$286$		−	168.550i		−	0.589337i
$287$	−13.0391	−	56.3219i	−0.0454324	−	0.196244i
$288$		−	16.9706i		−	0.0589256i
$289$	−255.195			−0.883028
$290$	−25.7136	−	60.1644i	−0.0886677	−	0.207463i
$291$	−143.345			−0.492596
$292$	249.259			0.853626
$293$	168.440			0.574882			0.287441	−	0.957798i	$-0.407195\pi$
$293$	168.440			0.574882			0.287441	+	0.957798i	$0.407195\pi$
$294$	−52.7470	−	107.814i	−0.179411	−	0.366713i
$295$	84.3675	+	197.402i	0.285991	+	0.669158i
$296$	−179.421			−0.606153
$297$	−42.3988			−0.142757
$298$			320.997i			1.07717i
$299$			544.199i			1.82006i
$300$	−59.8510	+	62.5928i	−0.199503	+	0.208643i
$301$	−66.4512	−	287.034i	−0.220768	−	0.953600i
$302$		−	416.381i		−	1.37874i
$303$		−	151.044i		−	0.498496i
$304$			135.094i			0.444389i
$305$	67.3730	+	157.638i	0.220895	+	0.516847i
$306$			24.6676i			0.0806130i
$307$	−223.400			−0.727688			−0.363844	−	0.931460i	$-0.618536\pi$
$307$	−223.400			−0.727688			−0.363844	+	0.931460i	$0.618536\pi$
$308$	−111.292	+	25.7651i	−0.361336	+	0.0836530i
$309$	324.876			1.05138
$310$	125.203	−	53.5106i	0.403882	−	0.172615i
$311$			46.0396i			0.148037i	0.997257	+	0.0740186i	$0.0235824\pi$
$311$			46.0396i			0.148037i	−0.997257	+	0.0740186i	$0.976418\pi$
$312$		−	71.5565i		−	0.229348i
$313$	80.0375			0.255711			0.127855	−	0.991793i	$-0.459191\pi$
$313$	80.0375			0.255711			0.127855	+	0.991793i	$0.459191\pi$
$314$		−	93.1395i		−	0.296623i
$315$	84.7565	−	61.9785i	0.269068	−	0.196757i
$316$	112.368			0.355596
$317$		−	185.237i		−	0.584343i	−0.956366	−	0.292171i	$-0.905622\pi$
$317$		−	185.237i		−	0.584343i	0.956366	−	0.292171i	$-0.0943777\pi$
$318$	−174.770			−0.549592
$319$	75.5016			0.236682
$320$	36.7815	−	15.7200i	0.114942	−	0.0491251i
$321$			273.418i			0.851768i
$322$	359.327	−	83.1879i	1.11592	−	0.258348i
$323$		−	196.367i		−	0.607946i
$324$	−18.0000			−0.0555556
$325$	−252.362	+	263.923i	−0.776499	+	0.812070i
$326$	39.8914			0.122366
$327$	−194.116			−0.593628
$328$	−23.3594			−0.0712177
$329$	159.156	−	36.8463i	0.483757	−	0.111995i
$330$	−39.2745	−	91.8939i	−0.119014	−	0.278466i
$331$	61.4686			0.185706			0.0928529	−	0.995680i	$-0.470401\pi$
$331$	61.4686			0.185706			0.0928529	+	0.995680i	$0.470401\pi$
$332$	−180.796			−0.544566
$333$			190.305i			0.571487i
$334$			181.671i			0.543926i
$335$	−9.82284	−	22.9833i	−0.0293219	−	0.0686069i
$336$	−47.2478	+	10.9383i	−0.140618	+	0.0325546i
$337$		−	656.501i		−	1.94807i	−0.226387	−	0.974037i	$-0.572691\pi$
$337$		−	656.501i		−	1.94807i	0.226387	−	0.974037i	$-0.427309\pi$
$338$		−	62.7160i		−	0.185550i
$339$			245.929i			0.725456i
$340$	−53.4638	+	22.8499i	−0.157247	+	0.0672056i
$341$			157.120i			0.460764i
$342$	143.289			0.418974
$343$	−266.166	+	216.344i	−0.775994	+	0.630740i
$344$	−119.047			−0.346066
$345$	126.806	+	296.698i	0.367553	+	0.859994i
$346$			159.022i			0.459603i
$347$		−	321.323i		−	0.926002i	−0.886358	−	0.463001i	$-0.846773\pi$
$347$		−	321.323i		−	0.926002i	0.886358	−	0.463001i	$-0.153227\pi$
$348$	32.0535			0.0921077
$349$		−	185.135i		−	0.530474i	−0.964183	−	0.265237i	$-0.914550\pi$
$349$		−	185.135i		−	0.530474i	0.964183	−	0.265237i	$-0.0854501\pi$
$350$	212.842	+	126.287i	0.608119	+	0.360821i
$351$	−75.8971			−0.216231
$352$			46.1579i			0.131130i
$353$	−597.338			−1.69218			−0.846088	−	0.533043i	$-0.821048\pi$
$353$	−597.338			−1.69218			−0.846088	+	0.533043i	$0.821048\pi$
$354$	−105.169			−0.297087
$355$	178.446	−	76.2658i	0.502664	−	0.214833i
$356$		−	32.4578i		−	0.0911736i
$357$	68.6771	−	15.8995i	0.192373	−	0.0445363i
$358$			97.4421i			0.272185i
$359$	239.446			0.666982			0.333491	−	0.942753i	$-0.391773\pi$
$359$	239.446			0.666982			0.333491	+	0.942753i	$0.391773\pi$
$360$	−16.6736	−	39.0127i	−0.0463156	−	0.108369i
$361$	−779.655			−2.15971
$362$	−235.519			−0.650604
$363$	−94.2585			−0.259665
$364$	−199.220	+	46.1216i	−0.547309	+	0.126708i
$365$	573.007	−	244.898i	1.56988	−	0.670952i
$366$	−83.9842			−0.229465
$367$	−398.743			−1.08649			−0.543246	−	0.839573i	$-0.682805\pi$
$367$	−398.743			−1.08649			−0.543246	+	0.839573i	$0.682805\pi$
$368$		−	149.030i		−	0.404973i
$369$			24.7764i			0.0671447i
$370$	−412.462	+	176.282i	−1.11476	+	0.476438i
$371$	112.648	+	486.578i	0.303633	+	1.31153i
$372$			66.7040i			0.179312i
$373$		−	34.7064i		−	0.0930466i	−0.998917	−	0.0465233i	$-0.985186\pi$
$373$		−	34.7064i		−	0.0930466i	0.998917	−	0.0465233i	$-0.0148142\pi$
$374$		−	67.0929i		−	0.179393i
$375$	−76.0907	+	202.695i	−0.202908	+	0.540520i
$376$		−	66.0097i		−	0.175558i
$377$	135.154			0.358498
$378$	11.6019	+	50.1138i	0.0306928	+	0.132576i
$379$	−109.217			−0.288172			−0.144086	−	0.989565i	$-0.546024\pi$
$379$	−109.217			−0.288172			−0.144086	+	0.989565i	$0.546024\pi$
$380$	132.731	+	310.561i	0.349291	+	0.817265i
$381$			350.591i			0.920187i
$382$			209.712i			0.548985i
$383$	−336.420			−0.878381			−0.439191	−	0.898394i	$-0.644735\pi$
$383$	−336.420			−0.878381			−0.439191	+	0.898394i	$0.644735\pi$
$384$			19.5959i			0.0510310i
$385$	−230.528	+	168.574i	−0.598773	+	0.437855i
$386$	−49.7642			−0.128923
$387$			126.268i			0.326274i
$388$	165.521			0.426601
$389$	−311.173			−0.799930			−0.399965	−	0.916530i	$-0.630978\pi$
$389$	−311.173			−0.799930			−0.399965	+	0.916530i	$0.630978\pi$
$390$	−70.3044	−	164.497i	−0.180268	−	0.421788i
$391$			216.623i			0.554023i
$392$	60.9069	+	124.492i	0.155375	+	0.317583i
$393$			244.669i			0.622568i
$394$	273.840			0.695026
$395$	258.317	−	110.402i	0.653968	−	0.279499i
$396$	48.9579			0.123631
$397$	41.2679			0.103949			0.0519747	−	0.998648i	$-0.483448\pi$
$397$	41.2679			0.103949			0.0519747	+	0.998648i	$0.483448\pi$
$398$	257.158			0.646125
$399$	−92.3568	−	398.932i	−0.231471	−	0.999829i
$400$	69.1100	−	72.2759i	0.172775	−	0.180690i
$401$	−495.642			−1.23601			−0.618007	−	0.786173i	$-0.712060\pi$
$401$	−495.642			−1.23601			−0.618007	+	0.786173i	$0.712060\pi$
$402$	12.2447			0.0304595
$403$			281.258i			0.697910i
$404$			174.411i			0.431710i
$405$	−41.3792	+	17.6851i	−0.102171	+	0.0436668i
$406$	−20.6600	−	89.2402i	−0.0508867	−	0.219803i
$407$		−	517.608i		−	1.27176i
$408$		−	28.4837i		−	0.0698129i
$409$			359.920i			0.880001i	0.897998	+	0.440000i	$0.145022\pi$
$409$			359.920i			0.880001i	−0.897998	+	0.440000i	$0.854978\pi$
$410$	−53.6997	+	22.9507i	−0.130975	+	0.0559773i
$411$		−	87.7163i		−	0.213422i
$412$	−375.135			−0.910521
$413$	67.7863	+	292.801i	0.164132	+	0.708960i
$414$	−158.070			−0.381813
$415$	−415.622	+	177.633i	−1.00150	+	0.428030i
$416$			82.6263i			0.198621i
$417$			128.216i			0.307473i
$418$	−389.730			−0.932367
$419$		−	482.910i		−	1.15253i	−0.817263	−	0.576265i	$-0.804510\pi$
$419$		−	482.910i		−	1.15253i	0.817263	−	0.576265i	$-0.195490\pi$
$420$	−97.8684	+	71.5666i	−0.233020	+	0.170397i
$421$	−523.520			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$421$	−523.520			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$422$		−	248.780i		−	0.589527i
$423$	−70.0139			−0.165517
$424$	201.807			0.475961
$425$	−100.455	+	105.057i	−0.236365	+	0.247192i
$426$			95.0696i			0.223168i
$427$	54.1319	+	233.821i	0.126773	+	0.547589i
$428$		−	315.715i		−	0.737653i
$429$	206.431			0.481191
$430$	−273.670	+	116.964i	−0.636441	+	0.272008i
$431$	517.027			1.19960			0.599799	−	0.800150i	$-0.295247\pi$
$431$	517.027			1.19960			0.599799	+	0.800150i	$0.295247\pi$
$432$	20.7846			0.0481125
$433$	567.712			1.31111			0.655557	−	0.755146i	$-0.272434\pi$
$433$	567.712			1.31111			0.655557	+	0.755146i	$0.272434\pi$
$434$	185.711	−	42.9939i	0.427905	−	0.0990644i
$435$	73.6860	−	31.4926i	0.169393	−	0.0723969i
$436$	224.146			0.514097
$437$	1258.32			2.87945
$438$			305.279i			0.696983i
$439$			622.875i			1.41885i	0.704781	+	0.709425i	$0.251045\pi$
$439$			622.875i			1.41885i	−0.704781	+	0.709425i	$0.748955\pi$
$440$	45.3503	+	106.110i	0.103069	+	0.241159i
$441$	132.044	−	64.6016i	0.299420	−	0.146489i
$442$		−	120.102i		−	0.271723i
$443$		−	476.699i		−	1.07607i	−0.842923	−	0.538035i	$-0.819167\pi$
$443$		−	476.699i		−	1.07607i	0.842923	−	0.538035i	$-0.180833\pi$
$444$		−	219.745i		−	0.494922i
$445$	−31.8899	−	74.6154i	−0.0716626	−	0.167675i
$446$			29.0868i			0.0652170i
$447$	−393.140			−0.879507
$448$	54.5570	−	12.6305i	0.121779	−	0.0281931i
$449$	861.931			1.91967			0.959834	−	0.280570i	$-0.0905233\pi$
$449$	861.931			1.91967			0.959834	+	0.280570i	$0.0905233\pi$
$450$	−76.6602	−	73.3022i	−0.170356	−	0.162894i
$451$		−	67.3889i		−	0.149421i
$452$		−	283.975i		−	0.628263i
$453$	509.960			1.12574
$454$		−	585.607i		−	1.28988i
$455$	−412.662	+	301.761i	−0.906950	+	0.663211i
$456$	−165.456			−0.362842
$457$			27.5401i			0.0602629i	0.999546	+	0.0301314i	$0.00959258\pi$
$457$			27.5401i			0.0602629i	−0.999546	+	0.0301314i	$0.990407\pi$
$458$	276.507			0.603727
$459$	−30.2115			−0.0658203
$460$	−146.423	−	342.597i	−0.318310	−	0.744777i
$461$			378.183i			0.820353i	0.912006	+	0.410176i	$0.134533\pi$
$461$			378.183i			0.820353i	−0.912006	+	0.410176i	$0.865467\pi$
$462$	−31.5557	−	136.304i	−0.0683024	−	0.295030i
$463$		−	724.994i		−	1.56586i	−0.622108	−	0.782931i	$-0.713724\pi$
$463$		−	724.994i		−	1.56586i	0.622108	−	0.782931i	$-0.286276\pi$
$464$	−37.0122			−0.0797676
$465$	65.5369	+	153.342i	0.140939	+	0.329768i
$466$	−114.976			−0.246731
$467$	371.451			0.795398			0.397699	−	0.917516i	$-0.369809\pi$
$467$	371.451			0.795398			0.397699	+	0.917516i	$0.369809\pi$
$468$	87.6384			0.187262
$469$	−7.89231	−	34.0905i	−0.0168280	−	0.0726877i
$470$	−64.8547	−	151.746i	−0.137989	−	0.322864i
$471$	114.072			0.242191
$472$	121.438			0.257285
$473$		−	343.434i		−	0.726076i
$474$			137.623i			0.290343i
$475$	610.254	+	583.523i	1.28475	+	1.22847i
$476$	−79.3015	+	18.3591i	−0.166600	+	0.0385695i
$477$		−	214.049i		−	0.448740i
$478$			352.514i			0.737477i
$479$		−	860.650i		−	1.79677i	−0.439214	−	0.898383i	$-0.644743\pi$
$479$		−	860.650i		−	1.79677i	0.439214	−	0.898383i	$-0.355257\pi$
$480$	19.2530	+	45.0480i	0.0401105	+	0.0938500i
$481$		−	926.558i		−	1.92632i
$482$	−371.009			−0.769728
$483$	101.884	+	440.084i	0.210940	+	0.911147i
$484$	108.840			0.224877
$485$	380.507	−	162.625i	0.784551	−	0.335309i
$486$		−	22.0454i		−	0.0453609i
$487$			887.173i			1.82171i	0.412726	+	0.910855i	$0.364577\pi$
$487$			887.173i			1.82171i	−0.412726	+	0.910855i	$0.635423\pi$
$488$	96.9766			0.198723
$489$			48.8568i			0.0999116i
$490$	262.330	+	226.347i	0.535367	+	0.461933i
$491$	−50.1823			−0.102204			−0.0511021	−	0.998693i	$-0.516273\pi$
$491$	−50.1823			−0.102204			−0.0511021	+	0.998693i	$0.516273\pi$
$492$		−	28.6093i		−	0.0581490i
$493$	53.7991			0.109126
$494$	−697.646			−1.41224
$495$	112.547	−	48.1012i	0.227367	−	0.0971742i
$496$		−	77.0231i		−	0.155289i
$497$	264.683	−	61.2769i	0.532562	−	0.123294i
$498$		−	221.429i		−	0.444636i
$499$	160.443			0.321529			0.160765	−	0.986993i	$-0.448604\pi$
$499$	160.443			0.321529			0.160765	+	0.986993i	$0.448604\pi$
$500$	87.8620	−	234.052i	0.175724	−	0.468104i
$501$	−222.501			−0.444113
$502$	−200.701			−0.399802
$503$	−742.042			−1.47523			−0.737616	−	0.675220i	$-0.764049\pi$
$503$	−742.042			−1.47523			−0.737616	+	0.675220i	$0.764049\pi$
$504$	−13.3967	−	57.8665i	−0.0265807	−	0.114814i
$505$	171.359	+	400.944i	0.339325	+	0.793948i
$506$	429.933			0.849670
$507$	76.8111			0.151501
$508$		−	404.828i		−	0.796905i
$509$			978.447i			1.92229i	0.276038	+	0.961147i	$0.410979\pi$
$509$			978.447i			1.92229i	−0.276038	+	0.961147i	$0.589021\pi$
$510$	−27.9853	−	65.4796i	−0.0548731	−	0.128391i
$511$	849.927	−	196.767i	1.66326	−	0.385062i
$512$		−	22.6274i		−	0.0441942i
$513$			175.493i			0.342091i
$514$			241.608i			0.470054i
$515$	−862.377	+	368.571i	−1.67452	+	0.715672i
$516$		−	145.802i		−	0.282561i
$517$	190.429			0.368335
$518$	−611.794	+	141.637i	−1.18107	+	0.273430i
$519$	−194.762			−0.375264
$520$	81.1805	+	189.945i	0.156116	+	0.365279i
$521$		−	575.650i		−	1.10489i	−0.833548	−	0.552447i	$-0.813694\pi$
$521$		−	575.650i		−	1.10489i	0.833548	−	0.552447i	$-0.186306\pi$
$522$			39.2573i			0.0752056i
$523$	339.090			0.648355			0.324178	−	0.945996i	$-0.394912\pi$
$523$	339.090			0.648355			0.324178	+	0.945996i	$0.394912\pi$
$524$		−	282.520i		−	0.539160i
$525$	−154.670	+	260.677i	−0.294609	+	0.496527i
$526$	542.234			1.03086
$527$			111.957i			0.212442i
$528$	−56.5317			−0.107068
$529$	−859.125			−1.62406
$530$	463.924	−	198.276i	0.875328	−	0.374106i
$531$		−	128.805i		−	0.242571i
$532$	106.644	+	460.647i	0.200459	+	0.865877i
$533$		−	120.631i		−	0.226325i
$534$	39.7525			0.0744429
$535$	−310.191	−	725.781i	−0.579797	−	1.35660i
$536$	−14.1390			−0.0263787
$537$	−119.342			−0.222238
$538$	−218.512			−0.406157
$539$	−359.144	+	175.709i	−0.666316	+	0.325990i
$540$	47.7806	−	20.4209i	0.0884826	−	0.0378166i
$541$	35.8638			0.0662916			0.0331458	−	0.999451i	$-0.489447\pi$
$541$	35.8638			0.0662916			0.0331458	+	0.999451i	$0.489447\pi$
$542$	−453.012			−0.835815
$543$		−	288.450i		−	0.531216i
$544$			32.8901i			0.0604598i
$545$	515.277	−	220.224i	0.945463	−	0.404081i
$546$	−56.4872	−	243.994i	−0.103456	−	0.446876i
$547$		−	700.845i		−	1.28125i	−0.767853	−	0.640626i	$-0.778675\pi$
$547$		−	700.845i		−	1.28125i	0.767853	−	0.640626i	$-0.221325\pi$
$548$			101.286i			0.184829i
$549$		−	102.859i		−	0.187357i
$550$	208.507	+	199.373i	0.379103	+	0.362497i
$551$		−	312.508i		−	0.567166i
$552$	182.524			0.330659
$553$	383.155	−	88.7044i	0.692867	−	0.160406i
$554$	−315.163			−0.568886
$555$	−215.901	−	505.161i	−0.389010	−	0.910200i
$556$		−	148.051i		−	0.266279i
$557$			639.349i			1.14784i	0.818910	+	0.573922i	$0.194579\pi$
$557$			639.349i			1.14784i	−0.818910	+	0.573922i	$0.805421\pi$
$558$	−81.6954			−0.146407
$559$		−	614.773i		−	1.09977i
$560$	113.009	−	82.6380i	0.201801	−	0.147568i
$561$	82.1717			0.146474
$562$		−	309.674i		−	0.551022i
$563$	227.519			0.404120			0.202060	−	0.979373i	$-0.435236\pi$
$563$	227.519			0.404120			0.202060	+	0.979373i	$0.435236\pi$
$564$	80.8450			0.143342
$565$	−279.006	−	652.814i	−0.493816	−	1.15542i
$566$			51.4713i			0.0909387i
$567$	−61.3767	+	14.2093i	−0.108248	+	0.0250605i
$568$		−	109.777i		−	0.193269i
$569$	613.901			1.07891			0.539456	−	0.842014i	$-0.318630\pi$
$569$	613.901			1.07891			0.539456	+	0.842014i	$0.318630\pi$
$570$	−380.358	+	162.561i	−0.667294	+	0.285195i
$571$	366.674			0.642161			0.321081	−	0.947052i	$-0.395954\pi$
$571$	366.674			0.642161			0.321081	+	0.947052i	$0.395954\pi$
$572$	−238.366			−0.416724
$573$	−256.844			−0.448244
$574$	−79.6513	+	18.4401i	−0.138765	+	0.0321256i
$575$	−673.206	−	643.718i	−1.17079	−	1.11951i
$576$	−24.0000			−0.0416667
$577$	62.1951			0.107790			0.0538952	−	0.998547i	$-0.482836\pi$
$577$	62.1951			0.107790			0.0538952	+	0.998547i	$0.482836\pi$
$578$			360.900i			0.624395i
$579$		−	60.9485i		−	0.105265i
$580$	−85.0853	+	36.3646i	−0.146699	+	0.0626975i
$581$	−616.481	+	142.722i	−1.06107	+	0.245648i
$582$			202.721i			0.348318i
$583$			582.188i			0.998607i
$584$		−	352.505i		−	0.603605i
$585$	201.467	−	86.1050i	0.344388	−	0.147188i
$586$		−	238.211i		−	0.406503i
$587$	176.872			0.301315			0.150658	−	0.988586i	$-0.451861\pi$
$587$	176.872			0.301315			0.150658	+	0.988586i	$0.451861\pi$
$588$	−152.471	+	74.5955i	−0.259305	+	0.126863i
$589$	650.337			1.10414
$590$	279.168	−	119.314i	0.473166	−	0.202226i
$591$			335.384i			0.567486i
$592$			253.740i			0.428615i
$593$	−154.878			−0.261176			−0.130588	−	0.991437i	$-0.541687\pi$
$593$	−154.878			−0.261176			−0.130588	+	0.991437i	$0.541687\pi$
$594$			59.9609i			0.100944i
$595$	−164.264	+	120.119i	−0.276074	+	0.201880i
$596$	453.959			0.761676
$597$			314.953i			0.527559i
$598$	769.613			1.28698
$599$	900.825			1.50388			0.751940	−	0.659231i	$-0.229118\pi$
$599$	900.825			1.50388			0.751940	+	0.659231i	$0.229118\pi$
$600$	88.5195	+	84.6421i	0.147533	+	0.141070i
$601$			682.387i			1.13542i	0.823229	+	0.567710i	$0.192170\pi$
$601$			682.387i			1.13542i	−0.823229	+	0.567710i	$0.807830\pi$
$602$	−405.927	+	93.9762i	−0.674297	+	0.156107i
$603$			14.9967i			0.0248701i
$604$	−588.851			−0.974920
$605$	250.207	−	106.936i	0.413566	−	0.176754i
$606$	−213.609			−0.352490
$607$	−367.814			−0.605954			−0.302977	−	0.952998i	$-0.597981\pi$
$607$	−367.814			−0.605954			−0.302977	+	0.952998i	$0.597981\pi$
$608$	191.052			0.314231
$609$	109.296	−	25.3032i	0.179469	−	0.0415488i
$610$	222.934	−	95.2798i	0.365466	−	0.156196i
$611$	340.883			0.557911
$612$	34.8852			0.0570020
$613$			117.271i			0.191306i	0.995415	+	0.0956532i	$0.0304940\pi$
$613$			117.271i			0.191306i	−0.995415	+	0.0956532i	$0.969506\pi$
$614$			315.936i			0.514553i
$615$	−28.1087	−	65.7684i	−0.0457053	−	0.106940i
$616$	36.4374	+	157.390i	0.0591516	+	0.255503i
$617$			1070.18i			1.73449i	0.497881	+	0.867245i	$0.334112\pi$
$617$			1070.18i			1.73449i	−0.497881	+	0.867245i	$0.665888\pi$
$618$		−	459.444i		−	0.743438i
$619$			532.192i			0.859761i	0.902886	+	0.429880i	$0.141444\pi$
$619$			532.192i			0.859761i	−0.902886	+	0.429880i	$0.858556\pi$
$620$	−75.6754	−	177.064i	−0.122057	−	0.285587i
$621$		−	193.596i		−	0.311749i
$622$	65.1098			0.104678
$623$	−25.6224	−	110.675i	−0.0411275	−	0.177649i
$624$	−101.196			−0.162173
$625$	−27.9756	−	624.374i	−0.0447610	−	0.998998i
$626$		−	113.190i		−	0.180815i
$627$		−	477.319i		−	0.761275i
$628$	−131.719			−0.209744
$629$		−	368.825i		−	0.586366i
$630$	−87.6509	−	119.864i	−0.139128	−	0.190260i
$631$	472.933			0.749498			0.374749	−	0.927126i	$-0.377729\pi$
$631$	472.933			0.749498			0.374749	+	0.927126i	$0.377729\pi$
$632$		−	158.913i		−	0.251444i
$633$	304.693			0.481347
$634$	−261.964			−0.413193
$635$	−397.745	−	930.636i	−0.626369	−	1.46557i
$636$			247.163i			0.388620i
$637$	−642.896	+	314.532i	−1.00926	+	0.493771i
$638$		−	106.775i		−	0.167359i
$639$	−116.436			−0.182216
$640$	−22.2315	−	52.0169i	−0.0347367	−	0.0812764i
$641$	−486.990			−0.759734			−0.379867	−	0.925041i	$-0.624030\pi$
$641$	−486.990			−0.759734			−0.379867	+	0.925041i	$0.624030\pi$
$642$	386.671			0.602291
$643$	111.425			0.173289			0.0866447	−	0.996239i	$-0.472386\pi$
$643$	111.425			0.173289			0.0866447	+	0.996239i	$0.472386\pi$
$644$	−117.645	−	508.165i	−0.182679	−	0.789077i
$645$	−143.251	−	335.176i	−0.222094	−	0.519652i
$646$	−277.704			−0.429883
$647$	−737.696			−1.14018			−0.570090	−	0.821583i	$-0.693092\pi$
$647$	−737.696			−1.14018			−0.570090	+	0.821583i	$0.693092\pi$
$648$			25.4558i			0.0392837i
$649$			350.334i			0.539806i
$650$	373.243	+	356.894i	0.574220	+	0.549068i
$651$	52.6566	+	227.448i	0.0808857	+	0.349383i
$652$		−	56.4149i		−	0.0865260i
$653$			193.734i			0.296682i	0.988936	+	0.148341i	$0.0473934\pi$
$653$			193.734i			0.296682i	−0.988936	+	0.148341i	$0.952607\pi$
$654$			274.522i			0.419758i
$655$	−277.577	−	649.469i	−0.423781	−	0.991556i
$656$			33.0352i			0.0503585i
$657$	−373.888			−0.569084
$658$	−52.1085	−	225.081i	−0.0791923	−	0.342068i
$659$	−823.339			−1.24938			−0.624688	−	0.780874i	$-0.714774\pi$
$659$	−823.339			−1.24938			−0.624688	+	0.780874i	$0.714774\pi$
$660$	−129.958	+	55.5425i	−0.196905	+	0.0841554i
$661$			657.833i			0.995208i	0.867404	+	0.497604i	$0.165787\pi$
$661$			657.833i			0.995208i	−0.867404	+	0.497604i	$0.834213\pi$
$662$		−	86.9298i		−	0.131314i
$663$	147.094			0.221861
$664$			255.684i			0.385066i
$665$	697.746	+	954.177i	1.04924	+	1.43485i
$666$	269.132			0.404102
$667$			344.746i			0.516860i
$668$	256.922			0.384614
$669$	−35.6239			−0.0532495
$670$	−32.5033	+	13.8916i	−0.0485124	+	0.0207337i
$671$			279.765i			0.416937i
$672$	15.4692	+	66.8184i	0.0230196	+	0.0994322i
$673$		−	727.300i		−	1.08068i	−0.841446	−	0.540342i	$-0.818295\pi$
$673$		−	727.300i		−	1.08068i	0.841446	−	0.540342i	$-0.181705\pi$
$674$	−928.433			−1.37750
$675$	89.7766	−	93.8891i	0.133002	−	0.139095i
$676$	−88.6938			−0.131204
$677$	385.964			0.570110			0.285055	−	0.958511i	$-0.407988\pi$
$677$	385.964			0.570110			0.285055	+	0.958511i	$0.407988\pi$
$678$	347.797			0.512975
$679$	564.396	−	130.663i	0.831217	−	0.192435i
$680$	32.3146	+	75.6093i	0.0475215	+	0.111190i
$681$	717.219			1.05319
$682$	222.202			0.325809
$683$			236.488i			0.346249i	0.984900	+	0.173124i	$0.0553863\pi$
$683$			236.488i			0.346249i	−0.984900	+	0.173124i	$0.944614\pi$
$684$		−	202.641i		−	0.296259i
$685$	99.5138	+	232.841i	0.145276	+	0.339914i
$686$	305.957	+	376.415i	0.446001	+	0.548711i
$687$			338.650i			0.492941i
$688$			168.357i			0.244705i
$689$			1042.16i			1.51257i
$690$	419.594	−	179.330i	0.608108	−	0.259899i
$691$			337.426i			0.488316i	0.969735	+	0.244158i	$0.0785116\pi$
$691$			337.426i			0.488316i	−0.969735	+	0.244158i	$0.921488\pi$
$692$	224.892			0.324988
$693$	166.937	−	38.6477i	0.240891	−	0.0557687i
$694$	−454.419			−0.654782
$695$	−145.461	−	340.347i	−0.209296	−	0.489708i
$696$		−	45.3305i		−	0.0651300i
$697$		−	48.0184i		−	0.0688929i
$698$	−261.821			−0.375101
$699$		−	140.817i		−	0.201455i
$700$	178.597	−	301.003i	0.255139	−	0.430005i
$701$	89.2192			0.127274			0.0636371	−	0.997973i	$-0.479730\pi$
$701$	89.2192			0.127274			0.0636371	+	0.997973i	$0.479730\pi$
$702$			107.335i			0.152898i
$703$	−2142.43			−3.04755
$704$	65.2772			0.0927232
$705$	185.850	−	79.4305i	0.263617	−	0.112667i
$706$			844.764i			1.19655i
$707$	137.681	+	594.709i	0.194740	+	0.841172i
$708$			148.731i			0.210072i
$709$	569.646			0.803450			0.401725	−	0.915760i	$-0.368411\pi$
$709$	569.646			0.803450			0.401725	+	0.915760i	$0.368411\pi$
$710$	−107.856	−	252.360i	−0.151910	−	0.355437i
$711$	−168.552			−0.237064
$712$	−45.9023			−0.0644695
$713$	−717.423			−1.00620
$714$	−22.4852	−	97.1241i	−0.0314919	−	0.136028i
$715$	−547.967	+	234.195i	−0.766387	+	0.327546i
$716$	137.804			0.192464
$717$	−431.740			−0.602147
$718$		−	338.628i		−	0.471627i
$719$			1261.33i			1.75428i	0.480233	+	0.877141i	$0.340552\pi$
$719$			1261.33i			1.75428i	−0.480233	+	0.877141i	$0.659448\pi$
$720$	−55.1723	+	23.5801i	−0.0766282	+	0.0327501i
$721$	−1279.14	+	296.134i	−1.77412	+	0.410727i
$722$			1102.60i			1.52714i
$723$		−	454.391i		−	0.628481i
$724$			333.074i			0.460047i
$725$	−159.870	+	167.193i	−0.220510	+	0.230611i
$726$			133.302i			0.183611i
$727$	307.746			0.423310			0.211655	−	0.977344i	$-0.432115\pi$
$727$	307.746			0.423310			0.211655	+	0.977344i	$0.432115\pi$
$728$	65.2258	+	281.740i	0.0895958	+	0.387006i
$729$	27.0000			0.0370370
$730$	−346.337	−	810.355i	−0.474435	−	1.11008i
$731$		−	244.716i		−	0.334769i
$732$			118.772i			0.162256i
$733$	633.490			0.864243			0.432121	−	0.901815i	$-0.357765\pi$
$733$	633.490			0.864243			0.432121	+	0.901815i	$0.357765\pi$
$734$			563.908i			0.768266i
$735$	−277.218	+	321.287i	−0.377167	+	0.437125i
$736$	−210.761			−0.286359
$737$		−	40.7891i		−	0.0553448i
$738$	35.0391			0.0474785
$739$	749.557			1.01428			0.507142	−	0.861862i	$-0.330702\pi$
$739$	749.557			1.01428			0.507142	+	0.861862i	$0.330702\pi$
$740$	249.300	+	583.309i	0.336893	+	0.788256i
$741$		−	854.439i		−	1.15309i
$742$	688.126	−	159.308i	0.927393	−	0.214701i
$743$		−	145.699i		−	0.196095i	−0.995182	−	0.0980476i	$-0.968740\pi$
$743$		−	145.699i		−	0.196095i	0.995182	−	0.0980476i	$-0.0312597\pi$
$744$	94.3337			0.126793
$745$	1043.58	−	446.016i	1.40078	−	0.598679i
$746$	−49.0822			−0.0657939
$747$	271.194			0.363044
$748$	−94.8837			−0.126850
$749$	−249.228	−	1076.53i	−0.332748	−	1.43729i
$750$	286.654	+	107.608i	0.382205	+	0.143478i
$751$	156.811			0.208803			0.104402	−	0.994535i	$-0.466707\pi$
$751$	156.811			0.208803			0.104402	+	0.994535i	$0.466707\pi$
$752$	−93.3518			−0.124138
$753$		−	245.807i		−	0.326437i
$754$		−	191.136i		−	0.253496i
$755$	−1353.68	+	578.548i	−1.79295	+	0.766289i
$756$	70.8717	−	16.4075i	0.0937456	−	0.0217031i
$757$			296.377i			0.391515i	0.980652	+	0.195758i	$0.0627166\pi$
$757$			296.377i			0.391515i	−0.980652	+	0.195758i	$0.937283\pi$
$758$			154.457i			0.203769i
$759$			526.558i			0.693752i
$760$	439.199	−	187.709i	0.577894	−	0.246986i
$761$		−	312.747i		−	0.410968i	−0.978660	−	0.205484i	$-0.934123\pi$
$761$		−	312.747i		−	0.410968i	0.978660	−	0.205484i	$-0.0658769\pi$
$762$	495.811			0.650670
$763$	764.297	−	176.942i	1.00170	−	0.231904i
$764$	296.578			0.388191
$765$	80.1958	−	34.2748i	0.104831	−	0.0448037i
$766$			475.770i			0.621109i
$767$			627.125i			0.817634i
$768$	27.7128			0.0360844
$769$		−	91.1460i		−	0.118525i	−0.998242	−	0.0592627i	$-0.981125\pi$
$769$		−	91.1460i		−	0.118525i	0.998242	−	0.0592627i	$-0.0188750\pi$
$770$	238.400	+	326.015i	0.309610	+	0.423396i
$771$	−295.908			−0.383798
$772$			70.3772i			0.0911622i
$773$	−417.539			−0.540154			−0.270077	−	0.962839i	$-0.587049\pi$
$773$	−417.539			−0.540154			−0.270077	+	0.962839i	$0.587049\pi$
$774$	178.570			0.230710
$775$	−347.932	−	332.692i	−0.448945	−	0.429280i
$776$		−	234.082i		−	0.301652i
$777$	−173.469	−	749.291i	−0.223254	−	0.964339i
$778$			440.065i			0.565636i
$779$	−278.929			−0.358061
$780$	−232.634	+	99.4255i	−0.298249	+	0.127469i
$781$	316.692			0.405496
$782$	306.351			0.391754
$783$	−48.0802			−0.0614052
$784$	176.059	−	86.1354i	0.224565	−	0.109867i
$785$	−302.802	+	129.414i	−0.385735	+	0.164859i
$786$	346.015			0.440222
$787$	−318.111			−0.404207			−0.202104	−	0.979364i	$-0.564778\pi$
$787$	−318.111			−0.404207			−0.202104	+	0.979364i	$0.564778\pi$
$788$		−	387.268i		−	0.491457i
$789$			664.098i			0.841696i
$790$	−156.132	−	365.316i	−0.197636	−	0.462425i
$791$	−224.172	−	968.302i	−0.283403	−	1.22415i
$792$		−	69.2369i		−	0.0874203i
$793$			500.801i			0.631527i
$794$		−	58.3616i		−	0.0735033i
$795$	242.838	+	568.188i	0.305456	+	0.714702i
$796$		−	363.676i		−	0.456880i
$797$	−1188.06			−1.49067			−0.745335	−	0.666690i	$-0.767711\pi$
$797$	−1188.06			−1.49067			−0.745335	+	0.666690i	$0.767711\pi$
$798$	−564.175	+	130.612i	−0.706986	+	0.163674i
$799$	135.692			0.169827
$800$	−102.214	−	97.7363i	−0.127767	−	0.122170i
$801$			48.6867i			0.0607824i
$802$			700.943i			0.873994i
$803$	1016.93			1.26642
$804$		−	17.3166i		−	0.0215381i
$805$	−769.723	−	1052.61i	−0.956177	−	1.30759i
$806$	397.758			0.493497
$807$		−	267.622i		−	0.331626i
$808$	246.654			0.305265
$809$	−223.374			−0.276111			−0.138055	−	0.990425i	$-0.544085\pi$
$809$	−223.374			−0.276111			−0.138055	+	0.990425i	$0.544085\pi$
$810$	25.0104	+	58.5190i	0.0308771	+	0.0722457i
$811$			366.185i			0.451523i	0.974183	+	0.225761i	$0.0724870\pi$
$811$			366.185i			0.451523i	−0.974183	+	0.225761i	$0.927513\pi$
$812$	−126.205	+	29.2177i	−0.155424	+	0.0359824i
$813$		−	554.824i		−	0.682440i
$814$	−732.008			−0.899272
$815$	−55.4278	−	129.689i	−0.0680096	−	0.159128i
$816$	−40.2820			−0.0493652
$817$	−1421.51			−1.73991
$818$	509.004			0.622255
$819$	298.831	−	69.1824i	0.364873	−	0.0844718i
$820$	32.4572	+	75.9428i	0.0395819	+	0.0926132i
$821$	−1547.39			−1.88476			−0.942381	−	0.334543i	$-0.891418\pi$
$821$	−1547.39			−1.88476			−0.942381	+	0.334543i	$0.891418\pi$
$822$	−124.050			−0.150912
$823$		−	1284.25i		−	1.56045i	−0.625499	−	0.780225i	$-0.715105\pi$
$823$		−	1284.25i		−	1.56045i	0.625499	−	0.780225i	$-0.284895\pi$
$824$			530.521i			0.643836i
$825$	−244.182	+	255.367i	−0.295978	+	0.309536i
$826$	414.083	−	95.8644i	0.501311	−	0.116059i
$827$			807.319i			0.976202i	0.872787	+	0.488101i	$0.162310\pi$
$827$			807.319i			0.976202i	−0.872787	+	0.488101i	$0.837690\pi$
$828$			223.545i			0.269982i
$829$		−	623.615i		−	0.752250i	−0.926569	−	0.376125i	$-0.877256\pi$
$829$		−	623.615i		−	0.752250i	0.926569	−	0.376125i	$-0.122744\pi$
$830$	251.210	+	587.778i	0.302663	+	0.708166i
$831$		−	385.994i		−	0.464493i
$832$	116.851			0.140446
$833$	−255.911	+	125.202i	−0.307216	+	0.150303i
$834$	181.325			0.217416
$835$	590.623	−	252.426i	0.707333	−	0.302307i
$836$			551.161i			0.659283i
$837$		−	100.056i		−	0.119541i
$838$	−682.938			−0.814962
$839$		−	1146.31i		−	1.36628i	−0.730286	−	0.683142i	$-0.760613\pi$
$839$		−	1146.31i		−	1.36628i	0.730286	−	0.683142i	$-0.239387\pi$
$840$	101.211	+	138.407i	0.120489	+	0.164770i
$841$	−755.381			−0.898194
$842$			740.368i			0.879297i
$843$	379.272			0.449908
$844$	−351.829			−0.416859
$845$	−203.893	+	87.1419i	−0.241294	+	0.103127i
$846$			99.0145i			0.117038i
$847$	371.126	−	85.9194i	0.438165	−	0.101440i
$848$		−	285.399i		−	0.336555i
$849$	−63.0392			−0.0742511
$850$	148.573	+	142.065i	0.174791	+	0.167135i
$851$	2363.43			2.77724
$852$	134.449			0.157804
$853$	948.920			1.11245			0.556225	−	0.831032i	$-0.312249\pi$
$853$	948.920			1.11245			0.556225	+	0.831032i	$0.312249\pi$
$854$	330.672	−	76.5540i	0.387204	−	0.0896417i
$855$	−199.096	−	465.841i	−0.232861	−	0.544844i
$856$	−446.489			−0.521599
$857$	868.842			1.01382			0.506909	−	0.862000i	$-0.330788\pi$
$857$	868.842			1.01382			0.506909	+	0.862000i	$0.330788\pi$
$858$		−	291.938i		−	0.340254i
$859$		−	119.981i		−	0.139675i	−0.997558	−	0.0698377i	$-0.977752\pi$
$859$		−	119.981i		−	0.139675i	0.997558	−	0.0698377i	$-0.0222482\pi$
$860$	165.412	+	387.027i	0.192339	+	0.450032i
$861$	−22.5844	−	97.5525i	−0.0262304	−	0.113301i
$862$		−	731.187i		−	0.848245i
$863$			788.430i			0.913592i	0.889571	+	0.456796i	$0.151003\pi$
$863$			788.430i			0.913592i	−0.889571	+	0.456796i	$0.848997\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	516.991	−	220.957i	0.597678	−	0.255441i
$866$		−	802.866i		−	0.927097i
$867$	−442.011			−0.509816
$868$	−60.8026	−	262.635i	−0.0700491	−	0.302574i
$869$	458.443			0.527552
$870$	−44.5373	−	104.208i	−0.0511923	−	0.119779i
$871$		−	73.0157i		−	0.0838298i
$872$		−	316.990i		−	0.363521i
$873$	−248.282			−0.284400
$874$		−	1779.53i		−	2.03608i
$875$	114.831	−	867.432i	0.131235	−	0.991351i
$876$	431.729			0.492841
$877$			234.663i			0.267574i	0.991010	+	0.133787i	$0.0427139\pi$
$877$			234.663i			0.267574i	−0.991010	+	0.133787i	$0.957286\pi$
$878$	880.879			1.00328
$879$	291.747			0.331908
$880$	150.062	−	64.1350i	0.170525	−	0.0728807i
$881$		−	750.816i		−	0.852232i	−0.904669	−	0.426116i	$-0.859882\pi$
$881$		−	750.816i		−	0.852232i	0.904669	−	0.426116i	$-0.140118\pi$
$882$	−91.3604	−	186.739i	−0.103583	−	0.211722i
$883$			1293.79i			1.46522i	0.680649	+	0.732610i	$0.261698\pi$
$883$			1293.79i			1.46522i	−0.680649	+	0.732610i	$0.738302\pi$
$884$	−169.849			−0.192137
$885$	146.129	+	341.910i	0.165117	+	0.386339i
$886$	−674.154			−0.760896
$887$	−728.248			−0.821024			−0.410512	−	0.911855i	$-0.634650\pi$
$887$	−728.248			−0.821024			−0.410512	+	0.911855i	$0.634650\pi$
$888$	−310.767			−0.349963
$889$	−319.574	−	1380.39i	−0.359476	−	1.55274i
$890$	−105.522	+	45.0991i	−0.118564	+	0.0506731i
$891$	−73.4368			−0.0824207
$892$	41.1349			0.0461154
$893$		−	788.206i		−	0.882650i
$894$			555.984i			0.621906i
$895$	316.790	−	135.393i	0.353955	−	0.151277i
$896$	−17.8622	−	77.1553i	−0.0199355	−	0.0861108i
$897$			942.580i			1.05081i
$898$		−	1218.95i		−	1.35741i
$899$			178.175i			0.198192i
$900$	−103.665	+	108.414i	−0.115183	+	0.120460i
$901$			414.842i			0.460424i
$902$	−95.3022			−0.105657
$903$	−115.097	−	497.157i	−0.127461	−	0.550561i
$904$	−401.601			−0.444249
$905$	327.246	+	765.685i	0.361598	+	0.846061i
$906$		−	721.193i		−	0.796018i
$907$			913.713i			1.00740i	0.863878	+	0.503700i	$0.168028\pi$
$907$			913.713i			1.00740i	−0.863878	+	0.503700i	$0.831972\pi$
$908$	−828.173			−0.912085
$909$		−	261.616i		−	0.287807i
$910$	426.755	+	583.593i	0.468961	+	0.641311i
$911$	−1331.32			−1.46138			−0.730690	−	0.682709i	$-0.760802\pi$
$911$	−1331.32			−1.46138			−0.730690	+	0.682709i	$0.760802\pi$
$912$			233.990i			0.256568i
$913$	−737.615			−0.807903
$914$	38.9476			0.0426123
$915$	116.693	+	273.037i	0.127534	+	0.298402i
$916$		−	391.040i		−	0.426899i
$917$	−223.023	−	963.341i	−0.243210	−	1.05053i
$918$			42.7255i			0.0465420i
$919$	−111.140			−0.120936			−0.0604678	−	0.998170i	$-0.519259\pi$
$919$	−111.140			−0.120936			−0.0604678	+	0.998170i	$0.519259\pi$
$920$	−484.506	+	207.073i	−0.526637	+	0.225079i
$921$	−386.941			−0.420131
$922$	534.831			0.580077
$923$	566.904			0.614197
$924$	−192.763	+	44.6265i	−0.208617	+	0.0482971i
$925$	1146.21	+	1096.00i	1.23914	+	1.18486i
$926$	−1025.30			−1.10723
$927$	562.702			0.607014
$928$			52.3431i			0.0564042i
$929$		−	571.383i		−	0.615051i	−0.951540	−	0.307526i	$-0.900499\pi$
$929$		−	571.383i		−	0.615051i	0.951540	−	0.307526i	$-0.0995010\pi$
$930$	216.859	−	92.6831i	0.233181	−	0.0996593i
$931$	727.275	+	1486.53i	0.781176	+	1.59671i
$932$			162.601i			0.174465i
$933$			79.7428i			0.0854693i
$934$		−	525.311i		−	0.562431i
$935$	−218.123	+	93.2235i	−0.233287	+	0.0997043i
$936$		−	123.939i		−	0.132414i
$937$	1657.10			1.76852			0.884259	−	0.466997i	$-0.154664\pi$
$937$	1657.10			1.76852			0.884259	+	0.466997i	$0.154664\pi$
$938$	−48.2113	+	11.1614i	−0.0513980	+	0.0118992i
$939$	138.629			0.147635
$940$	−214.601	+	91.7184i	−0.228299	+	0.0975728i
$941$		−	519.083i		−	0.551629i	−0.961211	−	0.275815i	$-0.911052\pi$
$941$		−	519.083i		−	0.551629i	0.961211	−	0.275815i	$-0.0889476\pi$
$942$		−	161.322i		−	0.171255i
$943$	307.703			0.326302
$944$		−	171.740i		−	0.181928i
$945$	146.803	−	107.350i	0.155347	−	0.113598i
$946$	−485.689			−0.513413
$947$			558.258i			0.589502i	0.955574	+	0.294751i	$0.0952366\pi$
$947$			558.258i			0.589502i	−0.955574	+	0.294751i	$0.904763\pi$
$948$	194.628			0.205303
$949$	1820.39			1.91822
$950$	825.226	−	863.029i	0.868659	−	0.908452i
$951$		−	320.839i		−	0.337370i
$952$	25.9637	+	112.149i	0.0272728	+	0.117804i
$953$			291.413i			0.305784i	0.988243	+	0.152892i	$0.0488587\pi$
$953$			291.413i			0.305784i	−0.988243	+	0.152892i	$0.951141\pi$
$954$	−302.711			−0.317307
$955$	681.786	−	291.389i	0.713912	−	0.305119i
$956$	498.530			0.521475
$957$	130.773			0.136648
$958$	−1217.14			−1.27050
$959$	79.9559	+	345.367i	0.0833742	+	0.360132i
$960$	63.7075	−	27.2279i	0.0663619	−	0.0283624i
$961$	590.215			0.614167
$962$	−1310.35			−1.36211
$963$			473.573i			0.491768i
$964$			524.686i			0.544280i
$965$	69.1458	+	161.786i	0.0716537	+	0.167654i
$966$	622.373	−	144.086i	0.644278	−	0.149157i
$967$		−	323.558i		−	0.334600i	−0.985906	−	0.167300i	$-0.946495\pi$
$967$		−	323.558i		−	0.334600i	0.985906	−	0.167300i	$-0.0535048\pi$
$968$		−	153.924i		−	0.159012i
$969$		−	340.117i		−	0.350998i
$970$	−229.986	−	538.118i	−0.237099	−	0.554761i
$971$			219.659i			0.226219i	0.993583	+	0.113110i	$0.0360812\pi$
$971$			219.659i			0.226219i	−0.993583	+	0.113110i	$0.963919\pi$
$972$	−31.1769			−0.0320750
$973$	−116.873	−	504.827i	−0.120116	−	0.518836i
$974$	1254.65			1.28814
$975$	−437.104	+	457.127i	−0.448312	+	0.468849i
$976$		−	137.146i		−	0.140518i
$977$		−	1302.29i		−	1.33295i	−0.745527	−	0.666475i	$-0.767802\pi$
$977$		−	1302.29i		−	1.33295i	0.745527	−	0.666475i	$-0.232198\pi$
$978$	69.0939			0.0706482
$979$		−	132.422i		−	0.135263i
$980$	320.104	−	370.990i	0.326636	−	0.378561i
$981$	−336.219			−0.342731
$982$			70.9685i			0.0722693i
$983$	649.905			0.661144			0.330572	−	0.943781i	$-0.392758\pi$
$983$	649.905			0.661144			0.330572	+	0.943781i	$0.392758\pi$
$984$	−40.4597			−0.0411176
$985$	−380.492	−	890.270i	−0.386287	−	0.903827i
$986$		−	76.0834i		−	0.0771637i
$987$	275.667	−	63.8196i	0.279297	−	0.0646602i
$988$			986.621i			0.998604i
$989$	1568.15			1.58559
$990$	−68.0254	−	159.165i	−0.0687126	−	0.160773i
$991$	−575.568			−0.580795			−0.290397	−	0.956906i	$-0.593788\pi$
$991$	−575.568			−0.580795			−0.290397	+	0.956906i	$0.593788\pi$
$992$	−108.927			−0.109806
$993$	106.467			0.107217
$994$	−86.6587	−	374.319i	−0.0871818	−	0.376578i
$995$	−357.313	−	836.035i	−0.359108	−	0.840236i
$996$	−313.148			−0.314405
$997$	−705.512			−0.707635			−0.353817	−	0.935315i	$-0.615117\pi$
$997$	−705.512			−0.707635			−0.353817	+	0.935315i	$0.615117\pi$
$998$		−	226.901i		−	0.227355i
$999$			329.618i			0.329948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.h.a.139.5	yes	16
3.2	odd	2		630.3.h.e.559.15		16
4.3	odd	2		1680.3.bd.a.769.2		16
5.2	odd	4		1050.3.f.e.601.10		16
5.3	odd	4		1050.3.f.e.601.7		16
5.4	even	2	inner	210.3.h.a.139.12	yes	16
7.6	odd	2	inner	210.3.h.a.139.4	✓	16
15.14	odd	2		630.3.h.e.559.2		16
20.19	odd	2		1680.3.bd.a.769.16		16
21.20	even	2		630.3.h.e.559.10		16
28.27	even	2		1680.3.bd.a.769.15		16
35.13	even	4		1050.3.f.e.601.3		16
35.27	even	4		1050.3.f.e.601.14		16
35.34	odd	2	inner	210.3.h.a.139.13	yes	16
105.104	even	2		630.3.h.e.559.7		16
140.139	even	2		1680.3.bd.a.769.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.4	✓	16	7.6	odd	2	inner
210.3.h.a.139.5	yes	16	1.1	even	1	trivial
210.3.h.a.139.12	yes	16	5.4	even	2	inner
210.3.h.a.139.13	yes	16	35.34	odd	2	inner
630.3.h.e.559.2		16	15.14	odd	2
630.3.h.e.559.7		16	105.104	even	2
630.3.h.e.559.10		16	21.20	even	2
630.3.h.e.559.15		16	3.2	odd	2
1050.3.f.e.601.3		16	35.13	even	4
1050.3.f.e.601.7		16	5.3	odd	4
1050.3.f.e.601.10		16	5.2	odd	4
1050.3.f.e.601.14		16	35.27	even	4
1680.3.bd.a.769.1		16	140.139	even	2
1680.3.bd.a.769.2		16	4.3	odd	2
1680.3.bd.a.769.15		16	28.27	even	2
1680.3.bd.a.769.16		16	20.19	odd	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +(-4.59769 + 1.96501i) q^{5} -2.44949i q^{6} +(-6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +(-4.59769 + 1.96501i) q^{5} -2.44949i q^{6} +(-6.81963 + 1.57881i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +(2.77894 + 6.50212i) q^{10} -8.15965 q^{11} -3.46410 q^{12} -14.6064 q^{13} +(2.23278 + 9.64441i) q^{14} +(-7.96343 + 3.40349i) q^{15} +4.00000 q^{16} -5.81421 q^{17} -4.24264i q^{18} +33.7736i q^{19} +(9.19538 - 3.93001i) q^{20} +(-11.8119 + 2.73459i) q^{21} +11.5395i q^{22} -37.2576i q^{23} +4.89898i q^{24} +(17.2775 - 18.0690i) q^{25} +20.6566i q^{26} +5.19615 q^{27} +(13.6393 - 3.15763i) q^{28} -9.25305 q^{29} +(4.81326 + 11.2620i) q^{30} -19.2558i q^{31} -5.65685i q^{32} -14.1329 q^{33} +8.22253i q^{34} +(28.2522 - 20.6595i) q^{35} -6.00000 q^{36} +63.4350i q^{37} +47.7631 q^{38} -25.2990 q^{39} +(-5.55788 - 13.0042i) q^{40} +8.25880i q^{41} +(3.86729 + 16.7046i) q^{42} +42.0893i q^{43} +16.3193 q^{44} +(-13.7931 + 5.89502i) q^{45} -52.6901 q^{46} -23.3380 q^{47} +6.92820 q^{48} +(44.0147 - 21.5339i) q^{49} +(-25.5534 - 24.4341i) q^{50} -10.0705 q^{51} +29.2128 q^{52} -71.3497i q^{53} -7.34847i q^{54} +(37.5155 - 16.0337i) q^{55} +(-4.46556 - 19.2888i) q^{56} +58.4976i q^{57} +13.0858i q^{58} -42.9350i q^{59} +(15.9269 - 6.80698i) q^{60} -34.2864i q^{61} -27.2318 q^{62} +(-20.4589 + 4.73644i) q^{63} -8.00000 q^{64} +(67.1557 - 28.7017i) q^{65} +19.9870i q^{66} +4.99889i q^{67} +11.6284 q^{68} -64.5320i q^{69} +(-29.2170 - 39.9546i) q^{70} -38.8120 q^{71} +8.48528i q^{72} -124.629 q^{73} +89.7107 q^{74} +(29.9255 - 31.2964i) q^{75} -67.5472i q^{76} +(55.6458 - 12.8826i) q^{77} +35.7782i q^{78} -56.1842 q^{79} +(-18.3908 + 7.86002i) q^{80} +9.00000 q^{81} +11.6797 q^{82} +90.3980 q^{83} +(23.6239 - 5.46917i) q^{84} +(26.7319 - 11.4249i) q^{85} +59.5233 q^{86} -16.0267 q^{87} -23.0790i q^{88} +16.2289i q^{89} +(8.33681 + 19.5063i) q^{90} +(99.6102 - 23.0608i) q^{91} +74.5151i q^{92} -33.3520i q^{93} +33.0048i q^{94} +(-66.3653 - 155.280i) q^{95} -9.79796i q^{96} -82.7605 q^{97} +(-30.4535 - 62.2462i) q^{98} -24.4789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} + 96 q^{11} + 16 q^{14} - 24 q^{15} + 64 q^{16} + 24 q^{21} + 24 q^{25} + 64 q^{29} + 24 q^{30} - 8 q^{35} - 96 q^{36} - 144 q^{39} - 192 q^{44} - 176 q^{46} + 224 q^{49} - 96 q^{50} - 48 q^{51} - 32 q^{56} + 48 q^{60} - 128 q^{64} + 368 q^{65} - 56 q^{70} - 384 q^{71} + 224 q^{74} - 608 q^{79} + 144 q^{81} - 48 q^{84} - 440 q^{85} + 416 q^{86} + 224 q^{91} - 560 q^{95} + 288 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 + 96 * q^11 + 16 * q^14 - 24 * q^15 + 64 * q^16 + 24 * q^21 + 24 * q^25 + 64 * q^29 + 24 * q^30 - 8 * q^35 - 96 * q^36 - 144 * q^39 - 192 * q^44 - 176 * q^46 + 224 * q^49 - 96 * q^50 - 48 * q^51 - 32 * q^56 + 48 * q^60 - 128 * q^64 + 368 * q^65 - 56 * q^70 - 384 * q^71 + 224 * q^74 - 608 * q^79 + 144 * q^81 - 48 * q^84 - 440 * q^85 + 416 * q^86 + 224 * q^91 - 560 * q^95 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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