LMFDB - Embedded newform 105.3.h.a.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(76,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.3
Root			$0.198184 - 0.343264i$ of defining polynomial
Character	$\chi$	$=$	105.76
Dual form			105.3.h.a.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79155 q^{2} -1.73205i q^{3} +3.79273 q^{4} +2.23607i q^{5} +4.83510i q^{6} +(4.15782 - 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.79155 q^{2} -1.73205i q^{3} +3.79273 q^{4} +2.23607i q^{5} +4.83510i q^{6} +(4.15782 - 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} -6.24209i q^{10} -18.9690 q^{11} -6.56921i q^{12} -10.9807i q^{13} +(-11.6068 + 15.7203i) q^{14} +3.87298 q^{15} -16.7861 q^{16} -22.3060i q^{17} +8.37464 q^{18} -19.6057i q^{19} +8.48081i q^{20} +(-9.75385 - 7.20156i) q^{21} +52.9528 q^{22} -31.9991 q^{23} -1.00215i q^{24} -5.00000 q^{25} +30.6530i q^{26} +5.19615i q^{27} +(15.7695 - 21.3583i) q^{28} +39.9967 q^{29} -10.8116 q^{30} +36.6641i q^{31} +44.5448 q^{32} +32.8553i q^{33} +62.2683i q^{34} +(12.5922 + 9.29718i) q^{35} -11.3782 q^{36} +8.94699 q^{37} +54.7302i q^{38} -19.0191 q^{39} +1.29377i q^{40} -37.6320i q^{41} +(27.2283 + 20.1035i) q^{42} -18.8702 q^{43} -71.9443 q^{44} -6.70820i q^{45} +89.3269 q^{46} -49.3786i q^{47} +29.0744i q^{48} +(-14.4250 - 46.8286i) q^{49} +13.9577 q^{50} -38.6352 q^{51} -41.6468i q^{52} +49.2398 q^{53} -14.5053i q^{54} -42.4160i q^{55} +(2.40568 - 3.25827i) q^{56} -33.9580 q^{57} -111.653 q^{58} +35.2173i q^{59} +14.6892 q^{60} +63.4723i q^{61} -102.349i q^{62} +(-12.4735 + 16.8942i) q^{63} -57.2046 q^{64} +24.5535 q^{65} -91.7170i q^{66} +21.3544 q^{67} -84.6008i q^{68} +55.4240i q^{69} +(-35.1516 - 25.9535i) q^{70} +36.2998 q^{71} -1.73577 q^{72} -6.66818i q^{73} -24.9759 q^{74} +8.66025i q^{75} -74.3591i q^{76} +(-78.8697 + 106.822i) q^{77} +53.0926 q^{78} -16.2015 q^{79} -37.5349i q^{80} +9.00000 q^{81} +105.052i q^{82} -36.7822i q^{83} +(-36.9937 - 27.3136i) q^{84} +49.8778 q^{85} +52.6770 q^{86} -69.2763i q^{87} -10.9753 q^{88} -88.0954i q^{89} +18.7263i q^{90} +(-61.8364 - 45.6557i) q^{91} -121.364 q^{92} +63.5040 q^{93} +137.843i q^{94} +43.8396 q^{95} -77.1539i q^{96} +133.810i q^{97} +(40.2681 + 130.724i) q^{98} +56.9070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−2.79155			−1.39577			−0.697887	−	0.716208i	$-0.745876\pi$
$2$	−2.79155			−1.39577			−0.697887	+	0.716208i	$0.745876\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.79273			0.948184
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$			4.83510i			0.805850i
$7$	4.15782	−	5.63139i	0.593975	−	0.804484i
$7$	4.15782	−	5.63139i	0.593975	−	0.804484i
$8$	0.578591			0.0723239
$9$	−3.00000			−0.333333
$10$		−	6.24209i		−	0.624209i
$11$	−18.9690			−1.72445			−0.862227	−	0.506522i	$-0.830931\pi$
$11$	−18.9690			−1.72445			−0.862227	+	0.506522i	$0.830931\pi$
$12$		−	6.56921i		−	0.547434i
$13$		−	10.9807i		−	0.844667i	−0.906441	−	0.422333i	$-0.861211\pi$
$13$		−	10.9807i		−	0.844667i	0.906441	−	0.422333i	$-0.138789\pi$
$14$	−11.6068	+	15.7203i	−0.829054	+	1.12288i
$15$	3.87298			0.258199
$16$	−16.7861			−1.04913
$17$		−	22.3060i		−	1.31212i	−0.754709	−	0.656060i	$-0.772222\pi$
$17$		−	22.3060i		−	1.31212i	0.754709	−	0.656060i	$-0.227778\pi$
$18$	8.37464			0.465258
$19$		−	19.6057i		−	1.03188i	−0.856625	−	0.515939i	$-0.827443\pi$
$19$		−	19.6057i		−	1.03188i	0.856625	−	0.515939i	$-0.172557\pi$
$20$			8.48081i			0.424041i
$21$	−9.75385	−	7.20156i	−0.464469	−	0.342932i
$22$	52.9528			2.40695
$23$	−31.9991			−1.39126			−0.695632	−	0.718399i	$-0.744875\pi$
$23$	−31.9991			−1.39126			−0.695632	+	0.718399i	$0.744875\pi$
$24$		−	1.00215i		−	0.0417562i
$25$	−5.00000			−0.200000
$26$			30.6530i			1.17896i
$27$			5.19615i			0.192450i
$28$	15.7695	−	21.3583i	0.563197	−	0.762798i
$29$	39.9967			1.37920			0.689598	−	0.724192i	$-0.257787\pi$
$29$	39.9967			1.37920			0.689598	+	0.724192i	$0.257787\pi$
$30$	−10.8116			−0.360387
$31$			36.6641i			1.18271i	0.806411	+	0.591356i	$0.201407\pi$
$31$			36.6641i			1.18271i	−0.806411	+	0.591356i	$0.798593\pi$
$32$	44.5448			1.39203
$33$			32.8553i			0.995614i
$34$			62.2683i			1.83142i
$35$	12.5922	+	9.29718i	0.359776	+	0.265634i
$36$	−11.3782			−0.316061
$37$	8.94699			0.241810			0.120905	−	0.992664i	$-0.461420\pi$
$37$	8.94699			0.241810			0.120905	+	0.992664i	$0.461420\pi$
$38$			54.7302i			1.44027i
$39$	−19.0191			−0.487669
$40$			1.29377i			0.0323442i
$41$		−	37.6320i		−	0.917854i	−0.888474	−	0.458927i	$-0.848234\pi$
$41$		−	37.6320i		−	0.917854i	0.888474	−	0.458927i	$-0.151766\pi$
$42$	27.2283	+	20.1035i	0.648293	+	0.478655i
$43$	−18.8702			−0.438841			−0.219421	−	0.975630i	$-0.570417\pi$
$43$	−18.8702			−0.438841			−0.219421	+	0.975630i	$0.570417\pi$
$44$	−71.9443			−1.63510
$45$		−	6.70820i		−	0.149071i
$46$	89.3269			1.94189
$47$		−	49.3786i		−	1.05061i	−0.850914	−	0.525304i	$-0.823952\pi$
$47$		−	49.3786i		−	1.05061i	0.850914	−	0.525304i	$-0.176048\pi$
$48$			29.0744i			0.605716i
$49$	−14.4250	−	46.8286i	−0.294388	−	0.955686i
$50$	13.9577			0.279155
$51$	−38.6352			−0.757552
$52$		−	41.6468i		−	0.800899i
$53$	49.2398			0.929052			0.464526	−	0.885559i	$-0.346225\pi$
$53$	49.2398			0.929052			0.464526	+	0.885559i	$0.346225\pi$
$54$		−	14.5053i		−	0.268617i
$55$		−	42.4160i		−	0.771199i
$56$	2.40568	−	3.25827i	0.0429586	−	0.0581834i
$57$	−33.9580			−0.595755
$58$	−111.653			−1.92505
$59$			35.2173i			0.596903i	0.954425	+	0.298452i	$0.0964701\pi$
$59$			35.2173i			0.596903i	−0.954425	+	0.298452i	$0.903530\pi$
$60$	14.6892			0.244820
$61$			63.4723i			1.04053i	0.854005	+	0.520265i	$0.174167\pi$
$61$			63.4723i			1.04053i	−0.854005	+	0.520265i	$0.825833\pi$
$62$		−	102.349i		−	1.65080i
$63$	−12.4735	+	16.8942i	−0.197992	+	0.268161i
$64$	−57.2046			−0.893821
$65$	24.5535			0.377746
$66$		−	91.7170i		−	1.38965i
$67$	21.3544			0.318723			0.159361	−	0.987220i	$-0.449057\pi$
$67$	21.3544			0.318723			0.159361	+	0.987220i	$0.449057\pi$
$68$		−	84.6008i		−	1.24413i
$69$			55.4240i			0.803246i
$70$	−35.1516	−	25.9535i	−0.502166	−	0.370764i
$71$	36.2998			0.511265			0.255632	−	0.966774i	$-0.417716\pi$
$71$	36.2998			0.511265			0.255632	+	0.966774i	$0.417716\pi$
$72$	−1.73577			−0.0241080
$73$		−	6.66818i		−	0.0913449i	−0.998956	−	0.0456725i	$-0.985457\pi$
$73$		−	6.66818i		−	0.0913449i	0.998956	−	0.0456725i	$-0.0145431\pi$
$74$	−24.9759			−0.337513
$75$			8.66025i			0.115470i
$76$		−	74.3591i		−	0.978409i
$77$	−78.8697	+	106.822i	−1.02428	+	1.38729i
$78$	53.0926			0.680675
$79$	−16.2015			−0.205082			−0.102541	−	0.994729i	$-0.532697\pi$
$79$	−16.2015			−0.205082			−0.102541	+	0.994729i	$0.532697\pi$
$80$		−	37.5349i		−	0.469186i
$81$	9.00000			0.111111
$82$			105.052i			1.28112i
$83$		−	36.7822i		−	0.443159i	−0.975142	−	0.221579i	$-0.928879\pi$
$83$		−	36.7822i		−	0.443159i	0.975142	−	0.221579i	$-0.0711212\pi$
$84$	−36.9937	−	27.3136i	−0.440402	−	0.325162i
$85$	49.8778			0.586798
$86$	52.6770			0.612523
$87$		−	69.2763i		−	0.796279i
$88$	−10.9753			−0.124719
$89$		−	88.0954i		−	0.989836i	−0.868940	−	0.494918i	$-0.835198\pi$
$89$		−	88.0954i		−	0.989836i	0.868940	−	0.494918i	$-0.164802\pi$
$90$			18.7263i			0.208070i
$91$	−61.8364	−	45.6557i	−0.679520	−	0.501711i
$92$	−121.364			−1.31917
$93$	63.5040			0.682839
$94$			137.843i			1.46641i
$95$	43.8396			0.461470
$96$		−	77.1539i		−	0.803687i
$97$			133.810i			1.37948i	0.724055	+	0.689742i	$0.242276\pi$
$97$			133.810i			1.37948i	−0.724055	+	0.689742i	$0.757724\pi$
$98$	40.2681	+	130.724i	0.410899	+	1.33392i
$99$	56.9070			0.574818
$100$	−18.9637			−0.189637
$101$			194.903i			1.92973i	0.262743	+	0.964866i	$0.415373\pi$
$101$			194.903i			1.92973i	−0.262743	+	0.964866i	$0.584627\pi$
$102$	107.852			1.05737
$103$		−	41.2629i		−	0.400610i	−0.979734	−	0.200305i	$-0.935807\pi$
$103$		−	41.2629i		−	0.400610i	0.979734	−	0.200305i	$-0.0641933\pi$
$104$		−	6.35332i		−	0.0610896i
$105$	16.1032	−	21.8103i	0.153364	−	0.207717i
$106$	−137.455			−1.29675
$107$	29.7031			0.277599			0.138799	−	0.990321i	$-0.455676\pi$
$107$	29.7031			0.277599			0.138799	+	0.990321i	$0.455676\pi$
$108$			19.7076i			0.182478i
$109$	91.7028			0.841310			0.420655	−	0.907221i	$-0.361800\pi$
$109$	91.7028			0.841310			0.420655	+	0.907221i	$0.361800\pi$
$110$			118.406i			1.07642i
$111$		−	15.4966i		−	0.139609i
$112$	−69.7937	+	94.5290i	−0.623158	+	0.844009i
$113$	2.98301			0.0263983			0.0131992	−	0.999913i	$-0.495798\pi$
$113$	2.98301			0.0263983			0.0131992	+	0.999913i	$0.495798\pi$
$114$	94.7954			0.831539
$115$		−	71.5521i		−	0.622192i
$116$	151.697			1.30773
$117$			32.9420i			0.281556i
$118$		−	98.3107i		−	0.833142i
$119$	−125.614	−	92.7445i	−1.05558	−	0.779366i
$120$	2.24087			0.0186739
$121$	238.823			1.97374
$122$		−	177.186i		−	1.45234i
$123$	−65.1806			−0.529923
$124$			139.057i			1.12143i
$125$		−	11.1803i		−	0.0894427i
$126$	34.8203	−	47.1608i	0.276351	−	0.374292i
$127$	104.651			0.824023			0.412012	−	0.911179i	$-0.364826\pi$
$127$	104.651			0.824023			0.412012	+	0.911179i	$0.364826\pi$
$128$	−18.4901			−0.144454
$129$			32.6841i			0.253365i
$130$	−68.5423			−0.527248
$131$		−	70.8051i		−	0.540497i	−0.962791	−	0.270249i	$-0.912894\pi$
$131$		−	70.8051i		−	0.540497i	0.962791	−	0.270249i	$-0.0871059\pi$
$132$			124.611i			0.944025i
$133$	−110.407	−	81.5169i	−0.830129	−	0.612909i
$134$	−59.6118			−0.444864
$135$	−11.6190			−0.0860663
$136$		−	12.9061i		−	0.0948976i
$137$	−158.673			−1.15820			−0.579100	−	0.815256i	$-0.696596\pi$
$137$	−158.673			−1.15820			−0.579100	+	0.815256i	$0.696596\pi$
$138$		−	154.719i		−	1.12115i
$139$			54.4253i			0.391549i	0.980649	+	0.195774i	$0.0627220\pi$
$139$			54.4253i			0.391549i	−0.980649	+	0.195774i	$0.937278\pi$
$140$	47.7587	+	35.2617i	0.341134	+	0.251869i
$141$	−85.5262			−0.606569
$142$	−101.333			−0.713610
$143$			208.292i			1.45659i
$144$	50.3583			0.349710
$145$			89.4353i			0.616795i
$146$			18.6145i			0.127497i
$147$	−81.1095	+	24.9848i	−0.551766	+	0.169965i
$148$	33.9335			0.229281
$149$	229.102			1.53760			0.768799	−	0.639490i	$-0.220854\pi$
$149$	229.102			1.53760			0.768799	+	0.639490i	$0.220854\pi$
$150$		−	24.1755i		−	0.161170i
$151$	−197.735			−1.30950			−0.654750	−	0.755845i	$-0.727226\pi$
$151$	−197.735			−1.30950			−0.654750	+	0.755845i	$0.727226\pi$
$152$		−	11.3437i		−	0.0746294i
$153$			66.9181i			0.437373i
$154$	220.169	−	298.198i	1.42967	−	1.93635i
$155$	−81.9833			−0.528925
$156$	−72.1343			−0.462399
$157$		−	211.036i		−	1.34418i	−0.740470	−	0.672089i	$-0.765397\pi$
$157$		−	211.036i		−	1.34418i	0.740470	−	0.672089i	$-0.234603\pi$
$158$	45.2271			0.286248
$159$		−	85.2858i		−	0.536389i
$160$			99.6053i			0.622533i
$161$	−133.046	+	180.199i	−0.826375	+	1.11925i
$162$	−25.1239			−0.155086
$163$	181.823			1.11548			0.557741	−	0.830015i	$-0.311668\pi$
$163$	181.823			1.11548			0.557741	+	0.830015i	$0.311668\pi$
$164$		−	142.728i		−	0.870295i
$165$	−73.4666			−0.445252
$166$			102.679i			0.618549i
$167$		−	101.160i		−	0.605751i	−0.953030	−	0.302876i	$-0.902053\pi$
$167$		−	101.160i		−	0.605751i	0.953030	−	0.302876i	$-0.0979467\pi$
$168$	−5.64349	−	4.16676i	−0.0335922	−	0.0248021i
$169$	48.4250			0.286538
$170$	−139.236			−0.819037
$171$			58.8170i			0.343959i
$172$	−71.5696			−0.416102
$173$		−	109.976i		−	0.635702i	−0.948141	−	0.317851i	$-0.897039\pi$
$173$		−	109.976i		−	0.635702i	0.948141	−	0.317851i	$-0.102961\pi$
$174$			193.388i			1.11143i
$175$	−20.7891	+	28.1569i	−0.118795	+	0.160897i
$176$	318.415			1.80918
$177$	60.9981			0.344622
$178$			245.922i			1.38159i
$179$	91.8832			0.513314			0.256657	−	0.966503i	$-0.417379\pi$
$179$	91.8832			0.513314			0.256657	+	0.966503i	$0.417379\pi$
$180$		−	25.4424i		−	0.141347i
$181$		−	62.8649i		−	0.347320i	−0.984806	−	0.173660i	$-0.944441\pi$
$181$		−	62.8649i		−	0.347320i	0.984806	−	0.173660i	$-0.0555594\pi$
$182$	172.619	+	127.450i	0.948457	+	0.700275i
$183$	109.937			0.600750
$184$	−18.5144			−0.100622
$185$			20.0061i			0.108141i
$186$	−177.274			−0.953088
$187$			423.123i			2.26269i
$188$		−	187.280i		−	0.996170i
$189$	29.2615	+	21.6047i	0.154823	+	0.114311i
$190$	−122.380			−0.644107
$191$	−75.9925			−0.397866			−0.198933	−	0.980013i	$-0.563748\pi$
$191$	−75.9925			−0.397866			−0.198933	+	0.980013i	$0.563748\pi$
$192$			99.0812i			0.516048i
$193$	22.7530			0.117891			0.0589456	−	0.998261i	$-0.481226\pi$
$193$	22.7530			0.117891			0.0589456	+	0.998261i	$0.481226\pi$
$194$		−	373.537i		−	1.92545i
$195$		−	42.5279i		−	0.218092i
$196$	−54.7102	−	177.609i	−0.279134	−	0.906166i
$197$	−137.485			−0.697891			−0.348946	−	0.937143i	$-0.613460\pi$
$197$	−137.485			−0.697891			−0.348946	+	0.937143i	$0.613460\pi$
$198$	−158.858			−0.802316
$199$		−	267.299i		−	1.34321i	−0.740909	−	0.671606i	$-0.765605\pi$
$199$		−	267.299i		−	1.34321i	0.740909	−	0.671606i	$-0.234395\pi$
$200$	−2.89296			−0.0144648
$201$		−	36.9869i		−	0.184015i
$202$		−	544.081i		−	2.69347i
$203$	166.299	−	225.237i	0.819208	−	1.10954i
$204$	−146.533			−0.718299
$205$	84.1478			0.410477
$206$			115.187i			0.559161i
$207$	95.9972			0.463754
$208$			184.323i			0.886166i
$209$			371.900i			1.77943i
$210$	−44.9528	+	60.8844i	−0.214061	+	0.289926i
$211$	−366.610			−1.73749			−0.868744	−	0.495261i	$-0.835073\pi$
$211$	−366.610			−1.73749			−0.868744	+	0.495261i	$0.835073\pi$
$212$	186.753			0.880912
$213$		−	62.8731i		−	0.295179i
$214$	−82.9175			−0.387465
$215$		−	42.1950i		−	0.196256i
$216$			3.00645i			0.0139187i
$217$	206.469	+	152.443i	0.951472	+	0.702501i
$218$	−255.993			−1.17428
$219$	−11.5496			−0.0527380
$220$		−	160.872i		−	0.731238i
$221$	−244.935			−1.10830
$222$			43.2596i			0.194863i
$223$		−	282.872i		−	1.26848i	−0.773134	−	0.634242i	$-0.781312\pi$
$223$		−	282.872i		−	1.26848i	0.773134	−	0.634242i	$-0.218688\pi$
$224$	185.210	−	250.849i	0.826828	−	1.11986i
$225$	15.0000			0.0666667
$226$	−8.32722			−0.0368461
$227$		−	210.777i		−	0.928534i	−0.885695	−	0.464267i	$-0.846318\pi$
$227$		−	210.777i		−	0.928534i	0.885695	−	0.464267i	$-0.153682\pi$
$228$	−128.794			−0.564885
$229$		−	137.506i		−	0.600464i	−0.953866	−	0.300232i	$-0.902936\pi$
$229$		−	137.506i		−	0.600464i	0.953866	−	0.300232i	$-0.0970641\pi$
$230$			199.741i			0.868439i
$231$	185.021	+	136.606i	0.800955	+	0.591370i
$232$	23.1417			0.0997488
$233$	−77.7682			−0.333769			−0.166884	−	0.985976i	$-0.553371\pi$
$233$	−77.7682			−0.333769			−0.166884	+	0.985976i	$0.553371\pi$
$234$		−	91.9591i		−	0.392988i
$235$	110.414			0.469846
$236$			133.570i			0.565974i
$237$			28.0618i			0.118404i
$238$	350.657	+	258.901i	1.47335	+	1.08782i
$239$	−123.843			−0.518173			−0.259086	−	0.965854i	$-0.583421\pi$
$239$	−123.843			−0.518173			−0.259086	+	0.965854i	$0.583421\pi$
$240$	−65.0123			−0.270885
$241$		−	155.802i		−	0.646481i	−0.946317	−	0.323240i	$-0.895228\pi$
$241$		−	155.802i		−	0.646481i	0.946317	−	0.323240i	$-0.104772\pi$
$242$	−666.684			−2.75489
$243$		−	15.5885i		−	0.0641500i
$244$			240.734i			0.986613i
$245$	104.712	−	32.2553i	0.427396	−	0.131654i
$246$	181.955			0.739653
$247$	−215.283			−0.871593
$248$			21.2135i			0.0855383i
$249$	−63.7086			−0.255858
$250$			31.2104i			0.124842i
$251$			278.340i			1.10892i	0.832210	+	0.554461i	$0.187076\pi$
$251$			278.340i			1.10892i	−0.832210	+	0.554461i	$0.812924\pi$
$252$	−47.3086	+	64.0750i	−0.187732	+	0.254266i
$253$	606.990			2.39917
$254$	−292.138			−1.15015
$255$		−	86.3909i		−	0.338788i
$256$	280.434			1.09545
$257$			220.802i			0.859151i	0.903031	+	0.429575i	$0.141337\pi$
$257$			220.802i			0.859151i	−0.903031	+	0.429575i	$0.858663\pi$
$258$		−	91.2392i		−	0.353640i
$259$	37.2000	−	50.3839i	0.143629	−	0.194533i
$260$	93.1250			0.358173
$261$	−119.990			−0.459732
$262$			197.656i			0.754412i
$263$	−17.3477			−0.0659609			−0.0329804	−	0.999456i	$-0.510500\pi$
$263$	−17.3477			−0.0659609			−0.0329804	+	0.999456i	$0.510500\pi$
$264$			19.0098i			0.0720067i
$265$			110.103i			0.415485i
$266$	308.207	+	227.558i	1.15867	+	0.855483i
$267$	−152.586			−0.571482
$268$	80.9916			0.302207
$269$			499.213i			1.85581i	0.372816	+	0.927905i	$0.378392\pi$
$269$			499.213i			1.85581i	−0.372816	+	0.927905i	$0.621608\pi$
$270$	32.4348			0.120129
$271$		−	330.005i		−	1.21773i	−0.793273	−	0.608866i	$-0.791625\pi$
$271$		−	330.005i		−	1.21773i	0.793273	−	0.608866i	$-0.208375\pi$
$272$			374.431i			1.37659i
$273$	−79.0780	+	107.104i	−0.289663	+	0.392321i
$274$	442.944			1.61659
$275$	94.8449			0.344891
$276$			210.209i			0.761625i
$277$	147.766			0.533452			0.266726	−	0.963772i	$-0.414058\pi$
$277$	147.766			0.533452			0.266726	+	0.963772i	$0.414058\pi$
$278$		−	151.931i		−	0.546513i
$279$		−	109.992i		−	0.394237i
$280$	7.28571	+	5.37926i	0.0260204	+	0.0192117i
$281$	353.405			1.25767			0.628834	−	0.777540i	$-0.283533\pi$
$281$	353.405			1.25767			0.628834	+	0.777540i	$0.283533\pi$
$282$	238.751			0.846633
$283$			428.203i			1.51308i	0.653945	+	0.756542i	$0.273113\pi$
$283$			428.203i			1.51308i	−0.653945	+	0.756542i	$0.726887\pi$
$284$	137.675			0.484773
$285$		−	75.9325i		−	0.266430i
$286$		−	581.457i		−	2.03307i
$287$	−211.920	−	156.467i	−0.738399	−	0.545182i
$288$	−133.634			−0.464009
$289$	−208.559			−0.721657
$290$		−	249.663i		−	0.860906i
$291$	231.766			0.796446
$292$		−	25.2906i		−	0.0866117i
$293$		−	402.632i		−	1.37417i	−0.726577	−	0.687085i	$-0.758890\pi$
$293$		−	402.632i		−	1.37417i	0.726577	−	0.687085i	$-0.241110\pi$
$294$	226.421	−	69.7463i	0.770140	−	0.237232i
$295$	−78.7483			−0.266943
$296$	5.17665			0.0174887
$297$		−	98.5658i		−	0.331871i
$298$	−639.550			−2.14614
$299$			351.371i			1.17515i
$300$			32.8460i			0.109487i
$301$	−78.4589	+	106.265i	−0.260661	+	0.353041i
$302$	551.986			1.82777
$303$	337.582			1.11413
$304$			329.103i			1.08258i
$305$	−141.928			−0.465339
$306$		−	186.805i		−	0.610474i
$307$		−	92.7330i		−	0.302062i	−0.988529	−	0.151031i	$-0.951741\pi$
$307$		−	92.7330i		−	0.302062i	0.988529	−	0.151031i	$-0.0482593\pi$
$308$	−299.132	+	405.146i	−0.971207	+	1.31541i
$309$	−71.4694			−0.231292
$310$	228.860			0.738259
$311$		−	218.118i		−	0.701343i	−0.936498	−	0.350672i	$-0.885953\pi$
$311$		−	218.118i		−	0.701343i	0.936498	−	0.350672i	$-0.114047\pi$
$312$	−11.0043			−0.0352701
$313$			293.684i			0.938288i	0.883122	+	0.469144i	$0.155438\pi$
$313$			293.684i			0.938288i	−0.883122	+	0.469144i	$0.844562\pi$
$314$			589.117i			1.87617i
$315$	−37.7765	−	27.8915i	−0.119925	−	0.0885445i
$316$	−61.4479			−0.194455
$317$	109.074			0.344081			0.172041	−	0.985090i	$-0.444964\pi$
$317$	109.074			0.344081			0.172041	+	0.985090i	$0.444964\pi$
$318$			238.079i			0.748677i
$319$	−758.697			−2.37836
$320$		−	127.913i		−	0.399729i
$321$		−	51.4472i		−	0.160272i
$322$	371.405	−	503.034i	1.15343	−	1.56222i
$323$	−437.325			−1.35395
$324$	34.1346			0.105354
$325$			54.9033i			0.168933i
$326$	−507.569			−1.55696
$327$		−	158.834i		−	0.485731i
$328$		−	21.7736i		−	0.0663828i
$329$	−278.070	−	205.308i	−0.845197	−	0.624035i
$330$	205.085			0.621471
$331$	408.913			1.23539			0.617694	−	0.786419i	$-0.288067\pi$
$331$	408.913			1.23539			0.617694	+	0.786419i	$0.288067\pi$
$332$		−	139.505i		−	0.420196i
$333$	−26.8410			−0.0806035
$334$			282.394i			0.845492i
$335$			47.7499i			0.142537i
$336$	163.729	+	120.886i	0.487289	+	0.359780i
$337$	−299.269			−0.888040			−0.444020	−	0.896017i	$-0.646448\pi$
$337$	−299.269			−0.888040			−0.444020	+	0.896017i	$0.646448\pi$
$338$	−135.181			−0.399942
$339$		−	5.16673i		−	0.0152411i
$340$	189.173			0.556392
$341$		−	695.480i		−	2.03953i
$342$		−	164.190i		−	0.480089i
$343$	−323.687	−	113.472i	−0.943693	−	0.330823i
$344$	−10.9181			−0.0317387
$345$	−123.932			−0.359223
$346$			307.004i			0.887296i
$347$	567.731			1.63611			0.818056	−	0.575138i	$-0.195052\pi$
$347$	567.731			1.63611			0.818056	+	0.575138i	$0.195052\pi$
$348$		−	262.747i		−	0.755019i
$349$		−	141.703i		−	0.406025i	−0.979176	−	0.203012i	$-0.934927\pi$
$349$		−	141.703i		−	0.406025i	0.979176	−	0.203012i	$-0.0650732\pi$
$350$	58.0338	−	78.6014i	0.165811	−	0.224575i
$351$	57.0572			0.162556
$352$	−844.970			−2.40048
$353$		−	452.435i		−	1.28169i	−0.767672	−	0.640843i	$-0.778585\pi$
$353$		−	452.435i		−	1.28169i	0.767672	−	0.640843i	$-0.221415\pi$
$354$	−170.279			−0.481015
$355$			81.1688i			0.228644i
$356$		−	334.123i		−	0.938546i
$357$	−160.638	+	217.570i	−0.449967	+	0.609439i
$358$	−256.496			−0.716470
$359$	174.670			0.486546			0.243273	−	0.969958i	$-0.421779\pi$
$359$	174.670			0.486546			0.243273	+	0.969958i	$0.421779\pi$
$360$		−	3.88131i		−	0.0107814i
$361$	−23.3825			−0.0647714
$362$			175.490i			0.484780i
$363$		−	413.653i		−	1.13954i
$364$	−234.529	−	173.160i	−0.644310	−	0.475714i
$365$	14.9105			0.0408507
$366$	−306.895			−0.838511
$367$			121.147i			0.330101i	0.986285	+	0.165051i	$0.0527788\pi$
$367$			121.147i			0.330101i	−0.986285	+	0.165051i	$0.947221\pi$
$368$	537.139			1.45962
$369$			112.896i			0.305951i
$370$		−	55.8479i		−	0.150940i
$371$	204.730	−	277.288i	0.551834	−	0.747407i
$372$	240.854			0.647456
$373$	−90.9075			−0.243720			−0.121860	−	0.992547i	$-0.538886\pi$
$373$	−90.9075			−0.243720			−0.121860	+	0.992547i	$0.538886\pi$
$374$		−	1181.17i		−	3.15820i
$375$	−19.3649			−0.0516398
$376$		−	28.5700i		−	0.0759841i
$377$		−	439.190i		−	1.16496i
$378$	−81.6850	−	60.3105i	−0.216098	−	0.159552i
$379$	−638.344			−1.68429			−0.842143	−	0.539254i	$-0.818706\pi$
$379$	−638.344			−1.68429			−0.842143	+	0.539254i	$0.818706\pi$
$380$	166.272			0.437558
$381$		−	181.261i		−	0.475750i
$382$	212.137			0.555331
$383$			176.395i			0.460561i	0.973124	+	0.230281i	$0.0739644\pi$
$383$			176.395i			0.460561i	−0.973124	+	0.230281i	$0.926036\pi$
$384$			32.0257i			0.0834003i
$385$	−238.861	−	176.358i	−0.620417	−	0.458073i
$386$	−63.5160			−0.164549
$387$	56.6105			0.146280
$388$			507.506i			1.30800i
$389$	249.521			0.641442			0.320721	−	0.947174i	$-0.396075\pi$
$389$	249.521			0.641442			0.320721	+	0.947174i	$0.396075\pi$
$390$			118.719i			0.304407i
$391$			713.772i			1.82550i
$392$	−8.34618	−	27.0946i	−0.0212913	−	0.0691189i
$393$	−122.638			−0.312056
$394$	383.795			0.974098
$395$		−	36.2276i		−	0.0917154i
$396$	215.833			0.545033
$397$		−	186.071i		−	0.468694i	−0.972153	−	0.234347i	$-0.924705\pi$
$397$		−	186.071i		−	0.468694i	0.972153	−	0.234347i	$-0.0752951\pi$
$398$			746.178i			1.87482i
$399$	−141.191	+	191.231i	−0.353863	+	0.479275i
$400$	83.9305			0.209826
$401$	−188.067			−0.468996			−0.234498	−	0.972117i	$-0.575345\pi$
$401$	−188.067			−0.468996			−0.234498	+	0.972117i	$0.575345\pi$
$402$			103.251i			0.256843i
$403$	402.596			0.998997
$404$			739.215i			1.82974i
$405$			20.1246i			0.0496904i
$406$	−464.232	+	628.759i	−1.14343	+	1.54867i
$407$	−169.715			−0.416991
$408$	−22.3540			−0.0547891
$409$		−	512.173i		−	1.25226i	−0.779720	−	0.626128i	$-0.784639\pi$
$409$		−	512.173i		−	1.25226i	0.779720	−	0.626128i	$-0.215361\pi$
$410$	−234.902			−0.572933
$411$			274.831i			0.668687i
$412$		−	156.499i		−	0.379852i
$413$	198.322	+	146.427i	0.480199	+	0.354545i
$414$	−267.981			−0.647296
$415$	82.2475			0.198187
$416$		−	489.132i		−	1.17580i
$417$	94.2673			0.226061
$418$		−	1038.18i		−	2.48367i
$419$			323.661i			0.772461i	0.922402	+	0.386231i	$0.126223\pi$
$419$			323.661i			0.772461i	−0.922402	+	0.386231i	$0.873777\pi$
$420$	61.0751	−	82.7205i	0.145417	−	0.196954i
$421$	−503.872			−1.19685			−0.598423	−	0.801180i	$-0.704206\pi$
$421$	−503.872			−1.19685			−0.598423	+	0.801180i	$0.704206\pi$
$422$	1023.41			2.42514
$423$			148.136i			0.350203i
$424$	28.4897			0.0671927
$425$			111.530i			0.262424i
$426$			175.513i			0.412003i
$427$	357.437	+	263.907i	0.837089	+	0.618049i
$428$	112.656			0.263215
$429$	360.773			0.840962
$430$			117.789i			0.273929i
$431$	317.731			0.737195			0.368597	−	0.929589i	$-0.379838\pi$
$431$	317.731			0.737195			0.368597	+	0.929589i	$0.379838\pi$
$432$		−	87.2231i		−	0.201905i
$433$		−	261.387i		−	0.603665i	−0.953361	−	0.301833i	$-0.902402\pi$
$433$		−	261.387i		−	0.603665i	0.953361	−	0.301833i	$-0.0975984\pi$
$434$	−576.369	−	425.551i	−1.32804	−	0.980532i
$435$	154.906			0.356107
$436$	347.805			0.797717
$437$			627.363i			1.43561i
$438$	32.2413			0.0736103
$439$			789.513i			1.79844i	0.437501	+	0.899218i	$0.355863\pi$
$439$			789.513i			1.79844i	−0.437501	+	0.899218i	$0.644137\pi$
$440$		−	24.5415i		−	0.0557761i
$441$	43.2750	+	140.486i	0.0981293	+	0.318562i
$442$	683.748			1.54694
$443$	585.242			1.32109			0.660544	−	0.750787i	$-0.270326\pi$
$443$	585.242			1.32109			0.660544	+	0.750787i	$0.270326\pi$
$444$		−	58.7746i		−	0.132375i
$445$	196.987			0.442668
$446$			789.651i			1.77052i
$447$		−	396.817i		−	0.887733i
$448$	−237.847	+	322.141i	−0.530907	+	0.719065i
$449$	528.147			1.17627			0.588137	−	0.808761i	$-0.299862\pi$
$449$	528.147			1.17627			0.588137	+	0.808761i	$0.299862\pi$
$450$	−41.8732			−0.0930516
$451$			713.842i			1.58280i
$452$	11.3138			0.0250305
$453$			342.486i			0.756041i
$454$			588.395i			1.29602i
$455$	102.089	−	138.270i	0.224372	−	0.303891i
$456$	−19.6478			−0.0430873
$457$	−164.041			−0.358953			−0.179476	−	0.983762i	$-0.557440\pi$
$457$	−164.041			−0.358953			−0.179476	+	0.983762i	$0.557440\pi$
$458$			383.855i			0.838112i
$459$	115.906			0.252517
$460$		−	271.378i		−	0.589952i
$461$			399.626i			0.866867i	0.901186	+	0.433434i	$0.142698\pi$
$461$			399.626i			0.866867i	−0.901186	+	0.433434i	$0.857302\pi$
$462$	−516.494	−	381.343i	−1.11795	−	0.825418i
$463$	−680.267			−1.46926			−0.734630	−	0.678468i	$-0.762644\pi$
$463$	−680.267			−1.46926			−0.734630	+	0.678468i	$0.762644\pi$
$464$	−671.388			−1.44696
$465$			141.999i			0.305375i
$466$	217.093			0.465866
$467$		−	725.217i		−	1.55293i	−0.630162	−	0.776464i	$-0.717011\pi$
$467$		−	725.217i		−	1.55293i	0.630162	−	0.776464i	$-0.282989\pi$
$468$			124.940i			0.266966i
$469$	88.7879	−	120.255i	0.189313	−	0.256407i
$470$	−308.226			−0.655799
$471$	−365.525			−0.776062
$472$			20.3764i			0.0431704i
$473$	357.948			0.756762
$474$		−	78.3357i		−	0.165265i
$475$			98.0284i			0.206376i
$476$	−476.420	−	351.755i	−1.00088	−	0.738982i
$477$	−147.719			−0.309684
$478$	345.714			0.723252
$479$		−	317.103i		−	0.662010i	−0.943629	−	0.331005i	$-0.892612\pi$
$479$		−	317.103i		−	0.662010i	0.943629	−	0.331005i	$-0.107388\pi$
$480$	172.521			0.359420
$481$		−	98.2439i		−	0.204249i
$482$			434.928i			0.902341i
$483$	312.114	+	230.443i	0.646198	+	0.477108i
$484$	905.791			1.87147
$485$	−299.208			−0.616924
$486$			43.5159i			0.0895389i
$487$	353.125			0.725103			0.362551	−	0.931964i	$-0.381906\pi$
$487$	353.125			0.725103			0.362551	+	0.931964i	$0.381906\pi$
$488$			36.7245i			0.0752552i
$489$		−	314.927i		−	0.644023i
$490$	−292.308	+	90.0421i	−0.596548	+	0.183759i
$491$	−343.280			−0.699145			−0.349572	−	0.936909i	$-0.613673\pi$
$491$	−343.280			−0.699145			−0.349572	+	0.936909i	$0.613673\pi$
$492$	−247.213			−0.502465
$493$		−	892.167i		−	1.80967i
$494$	600.974			1.21655
$495$			127.248i			0.257066i
$496$		−	615.447i		−	1.24082i
$497$	150.928	−	204.418i	0.303678	−	0.411304i
$498$	177.846			0.357120
$499$	−420.584			−0.842853			−0.421427	−	0.906863i	$-0.638470\pi$
$499$	−420.584			−0.842853			−0.421427	+	0.906863i	$0.638470\pi$
$500$		−	42.4041i		−	0.0848081i
$501$	−175.215			−0.349731
$502$		−	776.998i		−	1.54780i
$503$		−	183.030i		−	0.363876i	−0.983310	−	0.181938i	$-0.941763\pi$
$503$		−	183.030i		−	0.363876i	0.983310	−	0.181938i	$-0.0582370\pi$
$504$	−7.21704	+	9.77481i	−0.0143195	+	0.0193945i
$505$	−435.816			−0.863002
$506$	−1694.44			−3.34870
$507$		−	83.8745i		−	0.165433i
$508$	396.913			0.781326
$509$		−	261.854i		−	0.514448i	−0.966352	−	0.257224i	$-0.917192\pi$
$509$		−	261.854i		−	0.514448i	0.966352	−	0.257224i	$-0.0828079\pi$
$510$			241.164i			0.472871i
$511$	−37.5511	−	27.7251i	−0.0734855	−	0.0542566i
$512$	−708.885			−1.38454
$513$	101.874			0.198585
$514$		−	616.378i		−	1.19918i
$515$	92.2665			0.179158
$516$			123.962i			0.240237i
$517$			936.662i			1.81173i
$518$	−103.846	+	140.649i	−0.200474	+	0.271523i
$519$	−190.485			−0.367023
$520$	14.2064			0.0273201
$521$			477.677i			0.916846i	0.888734	+	0.458423i	$0.151586\pi$
$521$			477.677i			0.916846i	−0.888734	+	0.458423i	$0.848414\pi$
$522$	334.958			0.641682
$523$			770.784i			1.47377i	0.676016	+	0.736887i	$0.263705\pi$
$523$			770.784i			1.47377i	−0.676016	+	0.736887i	$0.736295\pi$
$524$		−	268.545i		−	0.512491i
$525$	48.7692	+	36.0078i	0.0928938	+	0.0685863i
$526$	48.4269			0.0920664
$527$	817.829			1.55186
$528$		−	551.512i		−	1.04453i
$529$	494.940			0.935614
$530$		−	307.359i		−	0.579923i
$531$		−	105.652i		−	0.198968i
$532$	−418.745	−	309.172i	−0.787114	−	0.581151i
$533$	−413.225			−0.775281
$534$	425.950			0.797660
$535$			66.4181i			0.124146i
$536$	12.3555			0.0230513
$537$		−	159.146i		−	0.296362i
$538$		−	1393.58i		−	2.59029i
$539$	273.628	+	888.292i	0.507658	+	1.64804i
$540$	−44.0676			−0.0816067
$541$	1054.53			1.94922			0.974609	−	0.223912i	$-0.0718828\pi$
$541$	1054.53			1.94922			0.974609	+	0.223912i	$0.0718828\pi$
$542$			921.225i			1.69968i
$543$	−108.885			−0.200525
$544$		−	993.618i		−	1.82650i
$545$			205.054i			0.376245i
$546$	220.750	−	298.985i	0.404304	−	0.547592i
$547$	697.821			1.27572			0.637862	−	0.770151i	$-0.279819\pi$
$547$	697.821			1.27572			0.637862	+	0.770151i	$0.279819\pi$
$548$	−601.806			−1.09819
$549$		−	190.417i		−	0.346843i
$550$	−264.764			−0.481389
$551$		−	784.162i		−	1.42316i
$552$			32.0678i			0.0580939i
$553$	−67.3628	+	91.2367i	−0.121813	+	0.164985i
$554$	−412.496			−0.744578
$555$	34.6515			0.0624352
$556$			206.421i			0.371260i
$557$	−941.244			−1.68985			−0.844923	−	0.534888i	$-0.820354\pi$
$557$	−941.244			−1.68985			−0.844923	+	0.534888i	$0.820354\pi$
$558$			307.048i			0.550266i
$559$			207.207i			0.370675i
$560$	−211.373	−	156.063i	−0.377452	−	0.278685i
$561$	732.870			1.30636
$562$	−986.545			−1.75542
$563$			768.996i			1.36589i	0.730470	+	0.682945i	$0.239301\pi$
$563$			768.996i			1.36589i	−0.730470	+	0.682945i	$0.760699\pi$
$564$	−324.378			−0.575139
$565$			6.67022i			0.0118057i
$566$		−	1195.35i		−	2.11192i
$567$	37.4204	−	50.6825i	0.0659972	−	0.0893871i
$568$	21.0027			0.0369766
$569$	−46.4935			−0.0817108			−0.0408554	−	0.999165i	$-0.513008\pi$
$569$	−46.4935			−0.0817108			−0.0408554	+	0.999165i	$0.513008\pi$
$570$			211.969i			0.371875i
$571$	774.153			1.35578			0.677892	−	0.735161i	$-0.262894\pi$
$571$	774.153			1.35578			0.677892	+	0.735161i	$0.262894\pi$
$572$			789.997i			1.38111i
$573$			131.623i			0.229708i
$574$	591.586	+	436.786i	1.03064	+	0.760951i
$575$	159.995			0.278253
$576$	171.614			0.297940
$577$		−	66.7246i		−	0.115641i	−0.998327	−	0.0578203i	$-0.981585\pi$
$577$		−	66.7246i		−	0.115641i	0.998327	−	0.0578203i	$-0.0184150\pi$
$578$	582.202			1.00727
$579$		−	39.4093i		−	0.0680645i
$580$			339.204i			0.584835i
$581$	−207.135	−	152.934i	−0.356514	−	0.263225i
$582$	−646.985			−1.11166
$583$	−934.029			−1.60211
$584$		−	3.85815i		−	0.00660642i
$585$	−73.6606			−0.125915
$586$			1123.97i			1.91803i
$587$			678.789i			1.15637i	0.815906	+	0.578185i	$0.196239\pi$
$587$			678.789i			1.15637i	−0.815906	+	0.578185i	$0.803761\pi$
$588$	−307.627	+	94.7608i	−0.523175	+	0.161158i
$589$	718.823			1.22041
$590$	219.829			0.372592
$591$			238.130i			0.402928i
$592$	−150.185			−0.253691
$593$			289.610i			0.488381i	0.969727	+	0.244190i	$0.0785222\pi$
$593$			289.610i			0.488381i	−0.969727	+	0.244190i	$0.921478\pi$
$594$			275.151i			0.463217i
$595$	207.383	−	280.881i	0.348543	−	0.472069i
$596$	868.924			1.45793
$597$	−462.976			−0.775503
$598$		−	980.869i		−	1.64025i
$599$	384.076			0.641195			0.320598	−	0.947216i	$-0.396116\pi$
$599$	384.076			0.641195			0.320598	+	0.947216i	$0.396116\pi$
$600$			5.01075i			0.00835124i
$601$		−	37.4083i		−	0.0622434i	−0.999516	−	0.0311217i	$-0.990092\pi$
$601$		−	37.4083i		−	0.0622434i	0.999516	−	0.0311217i	$-0.00990794\pi$
$602$	219.022	−	296.644i	0.363823	−	0.492765i
$603$	−64.0632			−0.106241
$604$	−749.955			−1.24165
$605$			534.023i			0.882683i
$606$	−942.375			−1.55507
$607$		−	876.691i		−	1.44430i	−0.691736	−	0.722150i	$-0.743154\pi$
$607$		−	876.691i		−	1.44430i	0.691736	−	0.722150i	$-0.256846\pi$
$608$		−	873.331i		−	1.43640i
$609$	−390.121	−	288.039i	−0.640594	−	0.472970i
$610$	396.200			0.649508
$611$	−542.210			−0.887414
$612$			253.803i			0.414710i
$613$	−591.071			−0.964226			−0.482113	−	0.876109i	$-0.660131\pi$
$613$	−591.071			−0.964226			−0.482113	+	0.876109i	$0.660131\pi$
$614$			258.868i			0.421610i
$615$		−	145.748i		−	0.236989i
$616$	−45.6333	+	61.8061i	−0.0740801	+	0.100335i
$617$	−744.668			−1.20692			−0.603459	−	0.797394i	$-0.706211\pi$
$617$	−744.668			−1.20692			−0.603459	+	0.797394i	$0.706211\pi$
$618$	199.510			0.322832
$619$		−	851.811i		−	1.37611i	−0.725659	−	0.688054i	$-0.758465\pi$
$619$		−	851.811i		−	1.37611i	0.725659	−	0.688054i	$-0.241535\pi$
$620$	−310.941			−0.501518
$621$		−	166.272i		−	0.267749i
$622$			608.886i			0.978917i
$623$	−496.099	−	366.285i	−0.796307	−	0.587938i
$624$	319.256			0.511628
$625$	25.0000			0.0400000
$626$		−	819.833i		−	1.30964i
$627$	644.149			1.02735
$628$		−	800.404i		−	1.27453i
$629$		−	199.572i		−	0.317284i
$630$	105.455	+	77.8605i	0.167389	+	0.123588i
$631$	316.625			0.501783			0.250891	−	0.968015i	$-0.419276\pi$
$631$	316.625			0.501783			0.250891	+	0.968015i	$0.419276\pi$
$632$	−9.37402			−0.0148323
$633$			634.987i			1.00314i
$634$	−304.485			−0.480260
$635$			234.007i			0.368514i
$636$		−	323.466i		−	0.508595i
$637$	−514.209	+	158.396i	−0.807236	+	0.248660i
$638$	2117.94			3.31965
$639$	−108.899			−0.170422
$640$		−	41.3450i		−	0.0646016i
$641$	173.979			0.271418			0.135709	−	0.990749i	$-0.456669\pi$
$641$	173.979			0.271418			0.135709	+	0.990749i	$0.456669\pi$
$642$			143.617i			0.223703i
$643$			926.785i			1.44135i	0.693275	+	0.720673i	$0.256167\pi$
$643$			926.785i			1.44135i	−0.693275	+	0.720673i	$0.743833\pi$
$644$	−504.610	+	683.447i	−0.783556	+	1.06125i
$645$	−73.0839			−0.113308
$646$	1220.81			1.88980
$647$			429.625i			0.664027i	0.943275	+	0.332013i	$0.107728\pi$
$647$			429.625i			0.664027i	−0.943275	+	0.332013i	$0.892272\pi$
$648$	5.20732			0.00803599
$649$		−	668.036i		−	1.02933i
$650$		−	153.265i		−	0.235793i
$651$	264.038	−	357.615i	0.405589	−	0.549333i
$652$	689.608			1.05768
$653$	−927.100			−1.41976			−0.709878	−	0.704325i	$-0.751250\pi$
$653$	−927.100			−1.41976			−0.709878	+	0.704325i	$0.751250\pi$
$654$			443.392i			0.677970i
$655$	158.325			0.241718
$656$			631.695i			0.962950i
$657$			20.0045i			0.0304483i
$658$	776.245	+	573.126i	1.17970	+	0.871012i
$659$	692.153			1.05031			0.525154	−	0.851007i	$-0.324008\pi$
$659$	692.153			1.05031			0.525154	+	0.851007i	$0.324008\pi$
$660$	−278.639			−0.422181
$661$		−	1101.42i		−	1.66629i	−0.553053	−	0.833146i	$-0.686537\pi$
$661$		−	1101.42i		−	1.66629i	0.553053	−	0.833146i	$-0.313463\pi$
$662$	−1141.50			−1.72432
$663$			424.240i			0.639879i
$664$		−	21.2818i		−	0.0320510i
$665$	182.277	−	246.878i	0.274101	−	0.371245i
$666$	74.9278			0.112504
$667$	−1279.86			−1.91882
$668$		−	383.675i		−	0.574364i
$669$	−489.949			−0.732360
$670$		−	133.296i		−	0.198949i
$671$		−	1204.01i		−	1.79435i
$672$	−434.483	−	320.792i	−0.646553	−	0.477370i
$673$	701.861			1.04288			0.521442	−	0.853287i	$-0.325394\pi$
$673$	701.861			1.04288			0.521442	+	0.853287i	$0.325394\pi$
$674$	835.424			1.23950
$675$		−	25.9808i		−	0.0384900i
$676$	183.663			0.271691
$677$		−	404.920i		−	0.598110i	−0.954236	−	0.299055i	$-0.903329\pi$
$677$		−	404.920i		−	0.598110i	0.954236	−	0.299055i	$-0.0966714\pi$
$678$			14.4232i			0.0212731i
$679$	753.535	+	556.358i	1.10977	+	0.819379i
$680$	28.8589			0.0424395
$681$	−365.077			−0.536090
$682$			1941.47i			2.84672i
$683$	−766.177			−1.12178			−0.560891	−	0.827890i	$-0.689541\pi$
$683$	−766.177			−1.12178			−0.560891	+	0.827890i	$0.689541\pi$
$684$			223.077i			0.326136i
$685$		−	354.805i		−	0.517963i
$686$	903.586	+	316.764i	1.31718	+	0.461754i
$687$	−238.168			−0.346678
$688$	316.757			0.460402
$689$		−	540.686i		−	0.784740i
$690$	345.962			0.501393
$691$			162.333i			0.234925i	0.993077	+	0.117462i	$0.0374760\pi$
$691$			162.333i			0.234925i	−0.993077	+	0.117462i	$0.962524\pi$
$692$		−	417.111i		−	0.602762i
$693$	236.609	−	320.465i	0.341427	−	0.462432i
$694$	−1584.85			−2.28364
$695$	−121.699			−0.175106
$696$		−	40.0826i		−	0.0575900i
$697$	−839.421			−1.20433
$698$			395.570i			0.566719i
$699$			134.698i			0.192702i
$700$	−78.8476	+	106.792i	−0.112639	+	0.152560i
$701$	−69.5098			−0.0991581			−0.0495790	−	0.998770i	$-0.515788\pi$
$701$	−69.5098			−0.0991581			−0.0495790	+	0.998770i	$0.515788\pi$
$702$	−159.278			−0.226892
$703$		−	175.412i		−	0.249519i
$704$	1085.11			1.54135
$705$		−	191.242i		−	0.271266i
$706$			1262.99i			1.78894i
$707$	1097.57	+	810.372i	1.55244	+	1.14621i
$708$	231.350			0.326765
$709$	134.839			0.190182			0.0950912	−	0.995469i	$-0.469686\pi$
$709$	134.839			0.190182			0.0950912	+	0.995469i	$0.469686\pi$
$710$		−	226.586i		−	0.319136i
$711$	48.6044			0.0683606
$712$		−	50.9712i		−	0.0715888i
$713$		−	1173.22i		−	1.64546i
$714$	448.429	−	607.356i	0.628052	−	0.850638i
$715$	−465.755			−0.651406
$716$	348.489			0.486716
$717$			214.503i			0.299167i
$718$	−487.600			−0.679109
$719$			638.863i			0.888544i	0.895892	+	0.444272i	$0.146538\pi$
$719$			638.863i			0.888544i	−0.895892	+	0.444272i	$0.853462\pi$
$720$			112.605i			0.156395i
$721$	−232.367	−	171.564i	−0.322284	−	0.237952i
$722$	65.2732			0.0904062
$723$	−269.857			−0.373246
$724$		−	238.430i		−	0.329323i
$725$	−199.983			−0.275839
$726$			1154.73i			1.59054i
$727$		−	704.430i		−	0.968955i	−0.874804	−	0.484477i	$-0.839010\pi$
$727$		−	704.430i		−	0.968955i	0.874804	−	0.484477i	$-0.160990\pi$
$728$	−35.7780	−	26.4160i	−0.0491456	−	0.0362857i
$729$	−27.0000			−0.0370370
$730$	−41.6234			−0.0570183
$731$			420.919i			0.575812i
$732$	416.963			0.569622
$733$			275.472i			0.375815i	0.982187	+	0.187907i	$0.0601705\pi$
$733$			275.472i			0.375815i	−0.982187	+	0.187907i	$0.939830\pi$
$734$		−	338.188i		−	0.460747i
$735$	−55.8678	−	181.366i	−0.0760106	−	0.246757i
$736$	−1425.39			−1.93667
$737$	−405.072			−0.549622
$738$		−	315.155i		−	0.427039i
$739$	238.655			0.322943			0.161471	−	0.986877i	$-0.448376\pi$
$739$	238.655			0.322943			0.161471	+	0.986877i	$0.448376\pi$
$740$			75.8777i			0.102537i
$741$			372.882i			0.503214i
$742$	−571.514	+	774.063i	−0.770235	+	1.04321i
$743$	221.162			0.297661			0.148831	−	0.988863i	$-0.452449\pi$
$743$	221.162			0.297661			0.148831	+	0.988863i	$0.452449\pi$
$744$	36.7429			0.0493856
$745$			512.288i			0.687635i
$746$	253.773			0.340178
$747$			110.347i			0.147720i
$748$			1604.79i			2.14544i
$749$	123.500	−	167.269i	0.164887	−	0.223324i
$750$	54.0581			0.0720774
$751$	−496.682			−0.661361			−0.330680	−	0.943743i	$-0.607278\pi$
$751$	−496.682			−0.661361			−0.330680	+	0.943743i	$0.607278\pi$
$752$			828.874i			1.10223i
$753$	482.098			0.640237
$754$			1226.02i			1.62602i
$755$		−	442.148i		−	0.585627i
$756$	110.981	+	81.9408i	0.146801	+	0.108387i
$757$	866.706			1.14492			0.572461	−	0.819932i	$-0.305989\pi$
$757$	866.706			1.14492			0.572461	+	0.819932i	$0.305989\pi$
$758$	1781.97			2.35088
$759$		−	1051.34i		−	1.38516i
$760$	25.3652			0.0333753
$761$		−	621.621i		−	0.816847i	−0.912793	−	0.408424i	$-0.866079\pi$
$761$		−	621.621i		−	0.816847i	0.912793	−	0.408424i	$-0.133921\pi$
$762$			505.998i			0.664039i
$763$	381.284	−	516.414i	0.499717	−	0.676820i
$764$	−288.219			−0.377250
$765$	−149.633			−0.195599
$766$		−	492.415i		−	0.642839i
$767$	386.709			0.504184
$768$		−	485.726i		−	0.632456i
$769$			316.574i			0.411669i	0.978587	+	0.205835i	$0.0659909\pi$
$769$			316.574i			0.411669i	−0.978587	+	0.205835i	$0.934009\pi$
$770$	666.790	+	492.312i	0.865962	+	0.639366i
$771$	382.440			0.496031
$772$	86.2961			0.111782
$773$			710.993i			0.919784i	0.887975	+	0.459892i	$0.152112\pi$
$773$			710.993i			0.919784i	−0.887975	+	0.459892i	$0.847888\pi$
$774$	−158.031			−0.204174
$775$		−	183.320i		−	0.236542i
$776$			77.4213i			0.0997697i
$777$	−87.2675	−	64.4323i	−0.112313	−	0.0829244i
$778$	−696.550			−0.895308
$779$	−737.801			−0.947113
$780$		−	161.297i		−	0.206791i
$781$	−688.570			−0.881652
$782$		−	1992.53i		−	2.54799i
$783$			207.829i			0.265426i
$784$	242.140	+	786.070i	0.308851	+	1.00264i
$785$	471.891			0.601135
$786$	342.350			0.435560
$787$		−	845.181i		−	1.07393i	−0.843605	−	0.536964i	$-0.819571\pi$
$787$		−	845.181i		−	1.07393i	0.843605	−	0.536964i	$-0.180429\pi$
$788$	−521.443			−0.661729
$789$			30.0471i			0.0380825i
$790$			101.131i			0.128014i
$791$	12.4028	−	16.7985i	0.0156799	−	0.0212370i
$792$	32.9259			0.0415731
$793$	696.968			0.878901
$794$			519.427i			0.654190i
$795$	190.705			0.239880
$796$		−	1013.79i		−	1.27361i
$797$			541.537i			0.679469i	0.940521	+	0.339734i	$0.110337\pi$
$797$			541.537i			0.679469i	−0.940521	+	0.339734i	$0.889663\pi$
$798$	394.143	−	533.830i	0.493913	−	0.668959i
$799$	−1101.44			−1.37852
$800$	−222.724			−0.278405
$801$			264.286i			0.329945i
$802$	524.999			0.654612
$803$			126.489i			0.157520i
$804$		−	140.282i		−	0.174480i
$805$	−402.937	−	297.501i	−0.500543	−	0.369566i
$806$	−1123.86			−1.39437
$807$	864.662			1.07145
$808$			112.769i			0.139566i
$809$	−363.991			−0.449927			−0.224963	−	0.974367i	$-0.572226\pi$
$809$	−363.991			−0.449927			−0.224963	+	0.974367i	$0.572226\pi$
$810$		−	56.1788i		−	0.0693565i
$811$			882.216i			1.08781i	0.839146	+	0.543906i	$0.183055\pi$
$811$			882.216i			1.08781i	−0.839146	+	0.543906i	$0.816945\pi$
$812$	630.729	−	854.263i	0.776759	−	1.05205i
$813$	−571.586			−0.703057
$814$	473.768			0.582025
$815$			406.570i			0.498858i
$816$	648.534			0.794772
$817$			369.963i			0.452831i
$818$			1429.76i			1.74787i
$819$	185.509	+	136.967i	0.226507	+	0.167237i
$820$	319.150			0.389208
$821$	681.271			0.829806			0.414903	−	0.909866i	$-0.363815\pi$
$821$	681.271			0.829806			0.414903	+	0.909866i	$0.363815\pi$
$822$		−	767.202i		−	0.933336i
$823$	−360.544			−0.438085			−0.219042	−	0.975715i	$-0.570293\pi$
$823$	−360.544			−0.438085			−0.219042	+	0.975715i	$0.570293\pi$
$824$		−	23.8743i		−	0.0289737i
$825$		−	164.276i		−	0.199123i
$826$	−553.626	−	408.759i	−0.670249	−	0.494865i
$827$	−770.095			−0.931191			−0.465596	−	0.884998i	$-0.654160\pi$
$827$	−770.095			−0.931191			−0.465596	+	0.884998i	$0.654160\pi$
$828$	364.092			0.439724
$829$		−	128.381i		−	0.154862i	−0.996998	−	0.0774312i	$-0.975328\pi$
$829$		−	128.381i		−	0.154862i	0.996998	−	0.0774312i	$-0.0246718\pi$
$830$	−229.598			−0.276624
$831$		−	255.938i		−	0.307988i
$832$			628.144i			0.754981i
$833$	−1044.56	+	321.764i	−1.25397	+	0.386272i
$834$	−263.152			−0.315530
$835$	226.202			0.270900
$836$			1410.52i			1.68722i
$837$	−190.512			−0.227613
$838$		−	903.515i		−	1.07818i
$839$		−	1367.14i		−	1.62949i	−0.579823	−	0.814743i	$-0.696878\pi$
$839$		−	1367.14i		−	1.62949i	0.579823	−	0.814743i	$-0.303122\pi$
$840$	9.31716	−	12.6192i	0.0110919	−	0.0150229i
$841$	758.735			0.902182
$842$	1406.58			1.67053
$843$		−	612.115i		−	0.726115i
$844$	−1390.46			−1.64746
$845$			108.281i			0.128144i
$846$		−	413.528i		−	0.488804i
$847$	992.982	−	1344.90i	1.17235	−	1.58784i
$848$	−826.544			−0.974698
$849$	741.669			0.873580
$850$		−	311.342i		−	0.366284i
$851$	−286.295			−0.336422
$852$		−	238.461i		−	0.279884i
$853$			797.415i			0.934836i	0.884036	+	0.467418i	$0.154816\pi$
$853$			797.415i			0.934836i	−0.884036	+	0.467418i	$0.845184\pi$
$854$	−997.803	−	736.708i	−1.16839	−	0.862656i
$855$	−131.519			−0.153823
$856$	17.1859			0.0200770
$857$		−	898.781i		−	1.04875i	−0.851486	−	0.524377i	$-0.824298\pi$
$857$		−	898.781i		−	1.04875i	0.851486	−	0.524377i	$-0.175702\pi$
$858$	−1007.11			−1.17379
$859$		−	915.157i		−	1.06537i	−0.846312	−	0.532687i	$-0.821182\pi$
$859$		−	915.157i		−	1.06537i	0.846312	−	0.532687i	$-0.178818\pi$
$860$		−	160.034i		−	0.186087i
$861$	−271.009	+	367.057i	−0.314761	+	0.426315i
$862$	−886.961			−1.02896
$863$	−1357.85			−1.57341			−0.786703	−	0.617332i	$-0.788214\pi$
$863$	−1357.85			−1.57341			−0.786703	+	0.617332i	$0.788214\pi$
$864$			231.462i			0.267896i
$865$	245.915			0.284294
$866$			729.674i			0.842580i
$867$			361.235i			0.416649i
$868$	783.084	+	578.175i	0.902170	+	0.666100i
$869$	307.325			0.353654
$870$	−432.429			−0.497045
$871$		−	234.486i		−	0.269214i
$872$	53.0584			0.0608468
$873$		−	401.430i		−	0.459828i
$874$		−	1751.31i		−	2.00379i
$875$	−62.9608	−	46.4859i	−0.0719552	−	0.0531267i
$876$	−43.8047			−0.0500053
$877$	1513.27			1.72550			0.862752	−	0.505627i	$-0.168739\pi$
$877$	1513.27			1.72550			0.862752	+	0.505627i	$0.168739\pi$
$878$		−	2203.96i		−	2.51021i
$879$	−697.379			−0.793377
$880$			711.998i			0.809089i
$881$			677.970i			0.769546i	0.923011	+	0.384773i	$0.125720\pi$
$881$			677.970i			0.769546i	−0.923011	+	0.384773i	$0.874280\pi$
$882$	−120.804	−	392.173i	−0.136966	−	0.444640i
$883$	155.548			0.176159			0.0880793	−	0.996113i	$-0.471927\pi$
$883$	155.548			0.176159			0.0880793	+	0.996113i	$0.471927\pi$
$884$	−928.974			−1.05088
$885$			136.396i			0.154120i
$886$	−1633.73			−1.84394
$887$			871.417i			0.982432i	0.871038	+	0.491216i	$0.163447\pi$
$887$			871.417i			0.982432i	−0.871038	+	0.491216i	$0.836553\pi$
$888$		−	8.96622i		−	0.0100971i
$889$	435.120	−	589.330i	0.489449	−	0.662913i
$890$	−549.899			−0.617864
$891$	−170.721			−0.191606
$892$		−	1072.86i		−	1.20276i
$893$	−968.101			−1.08410
$894$			1107.73i			1.23907i
$895$			205.457i			0.229561i
$896$	−76.8784	+	104.125i	−0.0858018	+	0.116211i
$897$	608.592			0.678475
$898$	−1474.35			−1.64181
$899$			1466.44i			1.63119i
$900$	56.8910			0.0632122
$901$		−	1098.34i		−	1.21903i
$902$		−	1992.72i		−	2.20923i
$903$	184.057	+	135.895i	0.203828	+	0.150493i
$904$	1.72594			0.00190923
$905$	140.570			0.155326
$906$		−	956.067i		−	1.05526i
$907$	−473.129			−0.521642			−0.260821	−	0.965387i	$-0.583993\pi$
$907$	−473.129			−0.521642			−0.260821	+	0.965387i	$0.583993\pi$
$908$		−	799.422i		−	0.880421i
$909$		−	584.709i		−	0.643244i
$910$	−284.987	+	385.988i	−0.313172	+	0.424163i
$911$	−676.153			−0.742210			−0.371105	−	0.928591i	$-0.621021\pi$
$911$	−676.153			−0.742210			−0.371105	+	0.928591i	$0.621021\pi$
$912$	570.023			0.625025
$913$			697.721i			0.764207i
$914$	457.929			0.501017
$915$			245.827i			0.268664i
$916$		−	521.525i		−	0.569350i
$917$	−398.731	−	294.395i	−0.434821	−	0.321042i
$918$	−323.556			−0.352457
$919$	1204.50			1.31066			0.655331	−	0.755342i	$-0.272529\pi$
$919$	1204.50			1.31066			0.655331	+	0.755342i	$0.272529\pi$
$920$		−	41.3994i		−	0.0449993i
$921$	−160.618			−0.174395
$922$		−	1115.57i		−	1.20995i
$923$		−	398.596i		−	0.431848i
$924$	701.734	+	518.112i	0.759452	+	0.560727i
$925$	−44.7349			−0.0483621
$926$	1899.00			2.05075
$927$			123.789i			0.133537i
$928$	1781.65			1.91988
$929$			586.143i			0.630940i	0.948936	+	0.315470i	$0.102162\pi$
$929$			586.143i			0.630940i	−0.948936	+	0.315470i	$0.897838\pi$
$930$		−	396.398i		−	0.426234i
$931$	−918.107	+	282.812i	−0.986151	+	0.303772i
$932$	−294.954			−0.316474
$933$	−377.791			−0.404921
$934$			2024.48i			2.16754i
$935$	−946.131			−1.01191
$936$			19.0599i			0.0203632i
$937$			449.053i			0.479245i	0.970866	+	0.239623i	$0.0770237\pi$
$937$			449.053i			0.479245i	−0.970866	+	0.239623i	$0.922976\pi$
$938$	−247.856	+	335.697i	−0.264238	+	0.357886i
$939$	508.676			0.541721
$940$	418.771			0.445501
$941$			904.538i			0.961252i	0.876926	+	0.480626i	$0.159591\pi$
$941$			904.538i			0.961252i	−0.876926	+	0.480626i	$0.840409\pi$
$942$	1020.38			1.08321
$943$			1204.19i			1.27698i
$944$		−	591.161i		−	0.626230i
$945$	−48.3095	+	65.4308i	−0.0511212	+	0.0692389i
$946$	−999.229			−1.05627
$947$	1631.56			1.72288			0.861439	−	0.507861i	$-0.169564\pi$
$947$	1631.56			1.72288			0.861439	+	0.507861i	$0.169564\pi$
$948$			106.431i			0.112269i
$949$	−73.2210			−0.0771560
$950$		−	273.651i		−	0.288053i
$951$		−	188.921i		−	0.198656i
$952$	−72.6791	−	53.6612i	−0.0763435	−	0.0563668i
$953$	1547.14			1.62344			0.811721	−	0.584046i	$-0.198531\pi$
$953$	1547.14			1.62344			0.811721	+	0.584046i	$0.198531\pi$
$954$	412.365			0.432249
$955$		−	169.924i		−	0.177931i
$956$	−469.705			−0.491323
$957$			1314.10i			1.37315i
$958$			885.207i			0.924015i
$959$	−659.736	+	893.552i	−0.687942	+	0.931753i
$960$	−221.552			−0.230784
$961$	−383.253			−0.398806
$962$			274.252i			0.285086i
$963$	−89.1092			−0.0925329
$964$		−	590.915i		−	0.612982i
$965$			50.8772i			0.0527225i
$966$	−871.281	−	643.293i	−0.901947	−	0.665935i
$967$	282.618			0.292263			0.146131	−	0.989265i	$-0.453318\pi$
$967$	282.618			0.292263			0.146131	+	0.989265i	$0.453318\pi$
$968$	138.181			0.142749
$969$			757.469i			0.781701i
$970$	835.254			0.861086
$971$			586.935i			0.604465i	0.953234	+	0.302232i	$0.0977319\pi$
$971$			586.935i			0.604465i	−0.953234	+	0.302232i	$0.902268\pi$
$972$		−	59.1229i		−	0.0608260i
$973$	306.490	+	226.291i	0.314994	+	0.232570i
$974$	−985.765			−1.01208
$975$	95.0954			0.0975337
$976$		−	1065.45i		−	1.09165i
$977$	−651.703			−0.667045			−0.333523	−	0.942742i	$-0.608237\pi$
$977$	−651.703			−0.667045			−0.333523	+	0.942742i	$0.608237\pi$
$978$			879.135i			0.898911i
$979$			1671.08i			1.70693i
$980$	397.145	−	122.336i	0.405250	−	0.124832i
$981$	−275.109			−0.280437
$982$	958.283			0.975848
$983$		−	583.048i		−	0.593131i	−0.955013	−	0.296565i	$-0.904159\pi$
$983$		−	583.048i		−	0.593131i	0.955013	−	0.296565i	$-0.0958413\pi$
$984$	−37.7129			−0.0383261
$985$		−	307.425i		−	0.312106i
$986$			2490.53i			2.52589i
$987$	−355.603	+	481.631i	−0.360287	+	0.487975i
$988$	−816.513			−0.826430
$989$	603.828			0.610544
$990$		−	355.218i		−	0.358806i
$991$	377.146			0.380572			0.190286	−	0.981729i	$-0.439059\pi$
$991$	377.146			0.380572			0.190286	+	0.981729i	$0.439059\pi$
$992$			1633.19i			1.64636i
$993$		−	708.259i		−	0.713251i
$994$	−421.323	+	570.643i	−0.423866	+	0.574087i
$995$	597.699			0.600702
$996$	−241.630			−0.242600
$997$		−	1586.82i		−	1.59159i	−0.605565	−	0.795795i	$-0.707053\pi$
$997$		−	1586.82i		−	1.59159i	0.605565	−	0.795795i	$-0.292947\pi$
$998$	1174.08			1.17643
$999$			46.4899i			0.0465364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.h.a.76.3	✓	12
3.2	odd	2		315.3.h.d.181.9		12
4.3	odd	2		1680.3.s.c.1441.10		12
5.2	odd	4		525.3.e.c.349.7		24
5.3	odd	4		525.3.e.c.349.22		24
5.4	even	2		525.3.h.d.76.10		12
7.6	odd	2	inner	105.3.h.a.76.4	yes	12
21.20	even	2		315.3.h.d.181.10		12
28.27	even	2		1680.3.s.c.1441.1		12
35.13	even	4		525.3.e.c.349.8		24
35.27	even	4		525.3.e.c.349.21		24
35.34	odd	2		525.3.h.d.76.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.3	✓	12	1.1	even	1	trivial
105.3.h.a.76.4	yes	12	7.6	odd	2	inner
315.3.h.d.181.9		12	3.2	odd	2
315.3.h.d.181.10		12	21.20	even	2
525.3.e.c.349.7		24	5.2	odd	4
525.3.e.c.349.8		24	35.13	even	4
525.3.e.c.349.21		24	35.27	even	4
525.3.e.c.349.22		24	5.3	odd	4
525.3.h.d.76.9		12	35.34	odd	2
525.3.h.d.76.10		12	5.4	even	2
1680.3.s.c.1441.1		12	28.27	even	2
1680.3.s.c.1441.10		12	4.3	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.79155 q^{2} -1.73205i q^{3} +3.79273 q^{4} +2.23607i q^{5} +4.83510i q^{6} +(4.15782 - 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.79155 q^{2} -1.73205i q^{3} +3.79273 q^{4} +2.23607i q^{5} +4.83510i q^{6} +(4.15782 - 5.63139i) q^{7} +0.578591 q^{8} -3.00000 q^{9} -6.24209i q^{10} -18.9690 q^{11} -6.56921i q^{12} -10.9807i q^{13} +(-11.6068 + 15.7203i) q^{14} +3.87298 q^{15} -16.7861 q^{16} -22.3060i q^{17} +8.37464 q^{18} -19.6057i q^{19} +8.48081i q^{20} +(-9.75385 - 7.20156i) q^{21} +52.9528 q^{22} -31.9991 q^{23} -1.00215i q^{24} -5.00000 q^{25} +30.6530i q^{26} +5.19615i q^{27} +(15.7695 - 21.3583i) q^{28} +39.9967 q^{29} -10.8116 q^{30} +36.6641i q^{31} +44.5448 q^{32} +32.8553i q^{33} +62.2683i q^{34} +(12.5922 + 9.29718i) q^{35} -11.3782 q^{36} +8.94699 q^{37} +54.7302i q^{38} -19.0191 q^{39} +1.29377i q^{40} -37.6320i q^{41} +(27.2283 + 20.1035i) q^{42} -18.8702 q^{43} -71.9443 q^{44} -6.70820i q^{45} +89.3269 q^{46} -49.3786i q^{47} +29.0744i q^{48} +(-14.4250 - 46.8286i) q^{49} +13.9577 q^{50} -38.6352 q^{51} -41.6468i q^{52} +49.2398 q^{53} -14.5053i q^{54} -42.4160i q^{55} +(2.40568 - 3.25827i) q^{56} -33.9580 q^{57} -111.653 q^{58} +35.2173i q^{59} +14.6892 q^{60} +63.4723i q^{61} -102.349i q^{62} +(-12.4735 + 16.8942i) q^{63} -57.2046 q^{64} +24.5535 q^{65} -91.7170i q^{66} +21.3544 q^{67} -84.6008i q^{68} +55.4240i q^{69} +(-35.1516 - 25.9535i) q^{70} +36.2998 q^{71} -1.73577 q^{72} -6.66818i q^{73} -24.9759 q^{74} +8.66025i q^{75} -74.3591i q^{76} +(-78.8697 + 106.822i) q^{77} +53.0926 q^{78} -16.2015 q^{79} -37.5349i q^{80} +9.00000 q^{81} +105.052i q^{82} -36.7822i q^{83} +(-36.9937 - 27.3136i) q^{84} +49.8778 q^{85} +52.6770 q^{86} -69.2763i q^{87} -10.9753 q^{88} -88.0954i q^{89} +18.7263i q^{90} +(-61.8364 - 45.6557i) q^{91} -121.364 q^{92} +63.5040 q^{93} +137.843i q^{94} +43.8396 q^{95} -77.1539i q^{96} +133.810i q^{97} +(40.2681 + 130.724i) q^{98} +56.9070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Introduction

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