LMFDB - Embedded newform 26.3.f.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,3,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, 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:	$0.708448687337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.3.f.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.73205 - 1.73205i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-2.03590 + 7.59808i) q^{7} +(2.00000 + 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.73205 - 1.73205i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-2.03590 + 7.59808i) q^{7} +(2.00000 + 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(-4.96410 + 1.33013i) q^{11} +3.46410i q^{12} +(-9.92820 - 8.39230i) q^{13} +11.1244 q^{14} +(-1.09808 - 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(24.6962 - 14.2583i) q^{17} +(6.00000 - 6.00000i) q^{18} +(-24.8923 - 6.66987i) q^{19} +(-1.26795 + 4.73205i) q^{20} +(9.63397 + 9.63397i) q^{21} +(3.63397 + 6.29423i) q^{22} +(-15.1865 - 8.76795i) q^{23} +(4.73205 - 1.26795i) q^{24} +19.0000i q^{25} +(-7.83013 + 16.6340i) q^{26} +25.9808 q^{27} +(-4.07180 - 15.1962i) q^{28} +(0.356406 - 0.617314i) q^{29} +(-5.19615 + 3.00000i) q^{30} +(-23.3397 + 23.3397i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-2.30385 + 8.59808i) q^{33} +(-28.5167 - 28.5167i) q^{34} +(9.63397 + 16.6865i) q^{35} +(-10.3923 - 6.00000i) q^{36} +(21.2583 - 5.69615i) q^{37} +36.4449i q^{38} +(-21.1865 + 7.62436i) q^{39} +6.92820 q^{40} +(-11.2583 - 42.0167i) q^{41} +(9.63397 - 16.6865i) q^{42} +(63.7750 - 36.8205i) q^{43} +(7.26795 - 7.26795i) q^{44} +(14.1962 + 3.80385i) q^{45} +(-6.41858 + 23.9545i) q^{46} +(33.0000 + 33.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-11.1506 - 6.43782i) q^{49} +(25.9545 - 6.95448i) q^{50} -49.3923i q^{51} +(25.5885 + 4.60770i) q^{52} -80.1051 q^{53} +(-9.50962 - 35.4904i) q^{54} +(-6.29423 + 10.9019i) q^{55} +(-19.2679 + 11.1244i) q^{56} +(-31.5622 + 31.5622i) q^{57} +(-0.973721 - 0.260908i) q^{58} +(10.1603 - 37.9186i) q^{59} +(6.00000 + 6.00000i) q^{60} +(14.3038 + 24.7750i) q^{61} +(40.4256 + 23.3397i) q^{62} +(-45.5885 + 12.2154i) q^{63} +8.00000i q^{64} +(-31.7321 + 2.66025i) q^{65} +12.5885 q^{66} +(12.8397 + 47.9186i) q^{67} +(-28.5167 + 49.3923i) q^{68} +(-26.3038 + 15.1865i) q^{69} +(19.2679 - 19.2679i) q^{70} +(7.03590 + 1.88526i) q^{71} +(-4.39230 + 16.3923i) q^{72} +(12.7654 + 12.7654i) q^{73} +(-15.5622 - 26.9545i) q^{74} +(28.5000 + 16.4545i) q^{75} +(49.7846 - 13.3397i) q^{76} -40.4256i q^{77} +(18.1699 + 26.1506i) q^{78} -14.3538 q^{79} +(-2.53590 - 9.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-53.2750 + 30.7583i) q^{82} +(87.8372 - 87.8372i) q^{83} +(-26.3205 - 7.05256i) q^{84} +(18.0788 - 67.4711i) q^{85} +(-73.6410 - 73.6410i) q^{86} +(-0.617314 - 1.06922i) q^{87} +(-12.5885 - 7.26795i) q^{88} +(-52.2391 + 13.9974i) q^{89} -20.7846i q^{90} +(83.9782 - 58.3494i) q^{91} +35.0718 q^{92} +(14.7968 + 55.2224i) q^{93} +(33.0000 - 57.1577i) q^{94} +(-54.6673 + 31.5622i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(131.488 + 35.2321i) q^{97} +(-4.71281 + 17.5885i) q^{98} +(-21.8038 - 21.8038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{6} - 22 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^6 - 22 * q^7 + 8 * q^8 + 12 * q^9	$ 4 q + 2 q^{2} - 6 q^{6} - 22 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} + 6 q^{15} + 8 q^{16} + 78 q^{17} + 24 q^{18} - 58 q^{19} - 12 q^{20} + 42 q^{21} + 18 q^{22} + 12 q^{23} + 12 q^{24} - 14 q^{26} - 44 q^{28} - 54 q^{29} - 128 q^{31} - 8 q^{32} - 30 q^{33} - 24 q^{34} + 42 q^{35} + 40 q^{37} - 12 q^{39} + 42 q^{42} + 120 q^{43} + 36 q^{44} + 36 q^{45} + 54 q^{46} + 132 q^{47} + 42 q^{49} + 38 q^{50} + 40 q^{52} - 168 q^{53} - 90 q^{54} + 6 q^{55} - 84 q^{56} - 102 q^{57} - 42 q^{58} + 6 q^{59} + 24 q^{60} + 78 q^{61} - 60 q^{62} - 120 q^{63} - 120 q^{65} - 12 q^{66} + 86 q^{67} - 24 q^{68} - 126 q^{69} + 84 q^{70} + 42 q^{71} + 24 q^{72} - 136 q^{73} - 38 q^{74} + 114 q^{75} + 116 q^{76} + 90 q^{78} + 192 q^{79} - 24 q^{80} - 18 q^{81} - 78 q^{82} + 192 q^{83} - 36 q^{84} - 42 q^{85} - 156 q^{86} - 96 q^{87} + 12 q^{88} - 60 q^{89} + 38 q^{91} + 168 q^{92} + 222 q^{93} + 132 q^{94} - 42 q^{95} + 280 q^{97} + 92 q^{98} - 108 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^6 - 22 * q^7 + 8 * q^8 + 12 * q^9 - 12 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 + 6 * q^15 + 8 * q^16 + 78 * q^17 + 24 * q^18 - 58 * q^19 - 12 * q^20 + 42 * q^21 + 18 * q^22 + 12 * q^23 + 12 * q^24 - 14 * q^26 - 44 * q^28 - 54 * q^29 - 128 * q^31 - 8 * q^32 - 30 * q^33 - 24 * q^34 + 42 * q^35 + 40 * q^37 - 12 * q^39 + 42 * q^42 + 120 * q^43 + 36 * q^44 + 36 * q^45 + 54 * q^46 + 132 * q^47 + 42 * q^49 + 38 * q^50 + 40 * q^52 - 168 * q^53 - 90 * q^54 + 6 * q^55 - 84 * q^56 - 102 * q^57 - 42 * q^58 + 6 * q^59 + 24 * q^60 + 78 * q^61 - 60 * q^62 - 120 * q^63 - 120 * q^65 - 12 * q^66 + 86 * q^67 - 24 * q^68 - 126 * q^69 + 84 * q^70 + 42 * q^71 + 24 * q^72 - 136 * q^73 - 38 * q^74 + 114 * q^75 + 116 * q^76 + 90 * q^78 + 192 * q^79 - 24 * q^80 - 18 * q^81 - 78 * q^82 + 192 * q^83 - 36 * q^84 - 42 * q^85 - 156 * q^86 - 96 * q^87 + 12 * q^88 - 60 * q^89 + 38 * q^91 + 168 * q^92 + 222 * q^93 + 132 * q^94 - 42 * q^95 + 280 * q^97 + 92 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	1.73205	−	1.73205i	0.346410	−	0.346410i	−0.512360	−	0.858771i	$-0.671229\pi$
$5$	1.73205	−	1.73205i	0.346410	−	0.346410i	0.858771	+	0.512360i	$0.171229\pi$
$6$	−2.36603	−	0.633975i	−0.394338	−	0.105662i
$7$	−2.03590	+	7.59808i	−0.290843	+	1.08544i	0.653621	+	0.756822i	$0.273249\pi$
$7$	−2.03590	+	7.59808i	−0.290843	+	1.08544i	−0.944463	+	0.328617i	$0.893417\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	3.00000	+	5.19615i	0.333333	+	0.577350i
$10$	−3.00000	−	1.73205i	−0.300000	−	0.173205i
$11$	−4.96410	+	1.33013i	−0.451282	+	0.120921i	−0.477299	−	0.878741i	$-0.658384\pi$
$11$	−4.96410	+	1.33013i	−0.451282	+	0.120921i	0.0260172	+	0.999661i	$0.491718\pi$
$12$			3.46410i			0.288675i
$13$	−9.92820	−	8.39230i	−0.763708	−	0.645562i
$13$	−9.92820	−	8.39230i	−0.763708	−	0.645562i
$14$	11.1244			0.794597
$15$	−1.09808	−	4.09808i	−0.0732051	−	0.273205i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	24.6962	−	14.2583i	1.45271	−	0.838725i	0.454080	−	0.890961i	$-0.349968\pi$
$17$	24.6962	−	14.2583i	1.45271	−	0.838725i	0.998635	+	0.0522356i	$0.0166347\pi$
$18$	6.00000	−	6.00000i	0.333333	−	0.333333i
$19$	−24.8923	−	6.66987i	−1.31012	−	0.351046i	−0.464853	−	0.885388i	$-0.653893\pi$
$19$	−24.8923	−	6.66987i	−1.31012	−	0.351046i	−0.845268	+	0.534342i	$0.820559\pi$
$20$	−1.26795	+	4.73205i	−0.0633975	+	0.236603i
$21$	9.63397	+	9.63397i	0.458761	+	0.458761i
$22$	3.63397	+	6.29423i	0.165181	+	0.286101i
$23$	−15.1865	−	8.76795i	−0.660284	−	0.381215i	0.132101	−	0.991236i	$-0.457828\pi$
$23$	−15.1865	−	8.76795i	−0.660284	−	0.381215i	−0.792385	+	0.610021i	$0.791161\pi$
$24$	4.73205	−	1.26795i	0.197169	−	0.0528312i
$25$			19.0000i			0.760000i
$26$	−7.83013	+	16.6340i	−0.301159	+	0.639768i
$27$	25.9808			0.962250
$28$	−4.07180	−	15.1962i	−0.145421	−	0.542720i
$29$	0.356406	−	0.617314i	0.0122899	−	0.0212867i	−0.859815	−	0.510606i	$-0.829421\pi$
$29$	0.356406	−	0.617314i	0.0122899	−	0.0212867i	0.872105	+	0.489319i	$0.162755\pi$
$30$	−5.19615	+	3.00000i	−0.173205	+	0.100000i
$31$	−23.3397	+	23.3397i	−0.752895	+	0.752895i	−0.975019	−	0.222124i	$-0.928701\pi$
$31$	−23.3397	+	23.3397i	−0.752895	+	0.752895i	0.222124	+	0.975019i	$0.428701\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	−2.30385	+	8.59808i	−0.0698136	+	0.260548i
$34$	−28.5167	−	28.5167i	−0.838725	−	0.838725i
$35$	9.63397	+	16.6865i	0.275256	+	0.476758i
$36$	−10.3923	−	6.00000i	−0.288675	−	0.166667i
$37$	21.2583	−	5.69615i	0.574549	−	0.153950i	0.0401672	−	0.999193i	$-0.487211\pi$
$37$	21.2583	−	5.69615i	0.574549	−	0.153950i	0.534382	+	0.845243i	$0.320544\pi$
$38$			36.4449i			0.959075i
$39$	−21.1865	+	7.62436i	−0.543244	+	0.195496i
$40$	6.92820			0.173205
$41$	−11.2583	−	42.0167i	−0.274593	−	1.02480i	−0.956113	−	0.292997i	$-0.905347\pi$
$41$	−11.2583	−	42.0167i	−0.274593	−	1.02480i	0.681520	−	0.731800i	$-0.261319\pi$
$42$	9.63397	−	16.6865i	0.229380	−	0.397298i
$43$	63.7750	−	36.8205i	1.48314	−	0.856291i	0.483323	−	0.875442i	$-0.339430\pi$
$43$	63.7750	−	36.8205i	1.48314	−	0.856291i	0.999817	+	0.0191514i	$0.00609644\pi$
$44$	7.26795	−	7.26795i	0.165181	−	0.165181i
$45$	14.1962	+	3.80385i	0.315470	+	0.0845299i
$46$	−6.41858	+	23.9545i	−0.139534	+	0.520750i
$47$	33.0000	+	33.0000i	0.702128	+	0.702128i	0.964867	−	0.262739i	$-0.0846259\pi$
$47$	33.0000	+	33.0000i	0.702128	+	0.702128i	−0.262739	+	0.964867i	$0.584626\pi$
$48$	−3.46410	−	6.00000i	−0.0721688	−	0.125000i
$49$	−11.1506	−	6.43782i	−0.227564	−	0.131384i
$50$	25.9545	−	6.95448i	0.519090	−	0.139090i
$51$		−	49.3923i		−	0.968477i
$52$	25.5885	+	4.60770i	0.492086	+	0.0886095i
$53$	−80.1051			−1.51142			−0.755709	−	0.654908i	$-0.772707\pi$
$53$	−80.1051			−1.51142			−0.755709	+	0.654908i	$0.772707\pi$
$54$	−9.50962	−	35.4904i	−0.176104	−	0.657229i
$55$	−6.29423	+	10.9019i	−0.114441	+	0.198217i
$56$	−19.2679	+	11.1244i	−0.344071	+	0.198649i
$57$	−31.5622	+	31.5622i	−0.553722	+	0.553722i
$58$	−0.973721	−	0.260908i	−0.0167883	−	0.00449841i
$59$	10.1603	−	37.9186i	0.172208	−	0.642688i	−0.824803	−	0.565421i	$-0.808714\pi$
$59$	10.1603	−	37.9186i	0.172208	−	0.642688i	0.997010	−	0.0772673i	$-0.0246195\pi$
$60$	6.00000	+	6.00000i	0.100000	+	0.100000i
$61$	14.3038	+	24.7750i	0.234489	+	0.406147i	0.959124	−	0.282986i	$-0.0913249\pi$
$61$	14.3038	+	24.7750i	0.234489	+	0.406147i	−0.724635	+	0.689133i	$0.757992\pi$
$62$	40.4256	+	23.3397i	0.652026	+	0.376448i
$63$	−45.5885	+	12.2154i	−0.723626	+	0.193895i
$64$			8.00000i			0.125000i
$65$	−31.7321	+	2.66025i	−0.488185	+	0.0409270i
$66$	12.5885			0.190734
$67$	12.8397	+	47.9186i	0.191638	+	0.715203i	0.993112	+	0.117173i	$0.0373831\pi$
$67$	12.8397	+	47.9186i	0.191638	+	0.715203i	−0.801474	+	0.598030i	$0.795950\pi$
$68$	−28.5167	+	49.3923i	−0.419363	+	0.726357i
$69$	−26.3038	+	15.1865i	−0.381215	+	0.220095i
$70$	19.2679	−	19.2679i	0.275256	−	0.275256i
$71$	7.03590	+	1.88526i	0.0990972	+	0.0265530i	0.308027	−	0.951378i	$-0.400331\pi$
$71$	7.03590	+	1.88526i	0.0990972	+	0.0265530i	−0.208930	+	0.977931i	$0.566998\pi$
$72$	−4.39230	+	16.3923i	−0.0610042	+	0.227671i
$73$	12.7654	+	12.7654i	0.174868	+	0.174868i	0.789114	−	0.614246i	$-0.210540\pi$
$73$	12.7654	+	12.7654i	0.174868	+	0.174868i	−0.614246	+	0.789114i	$0.710540\pi$
$74$	−15.5622	−	26.9545i	−0.210300	−	0.364250i
$75$	28.5000	+	16.4545i	0.380000	+	0.219393i
$76$	49.7846	−	13.3397i	0.655061	−	0.175523i
$77$		−	40.4256i		−	0.525008i
$78$	18.1699	+	26.1506i	0.232947	+	0.335265i
$79$	−14.3538			−0.181694			−0.0908470	−	0.995865i	$-0.528957\pi$
$79$	−14.3538			−0.181694			−0.0908470	+	0.995865i	$0.528957\pi$
$80$	−2.53590	−	9.46410i	−0.0316987	−	0.118301i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−53.2750	+	30.7583i	−0.649695	+	0.375102i
$83$	87.8372	−	87.8372i	1.05828	−	1.05828i	0.0600859	−	0.998193i	$-0.480863\pi$
$83$	87.8372	−	87.8372i	1.05828	−	1.05828i	0.998193	−	0.0600859i	$-0.0191375\pi$
$84$	−26.3205	−	7.05256i	−0.313339	−	0.0839590i
$85$	18.0788	−	67.4711i	0.212692	−	0.793778i
$86$	−73.6410	−	73.6410i	−0.856291	−	0.856291i
$87$	−0.617314	−	1.06922i	−0.00709556	−	0.0122899i
$88$	−12.5885	−	7.26795i	−0.143051	−	0.0825903i
$89$	−52.2391	+	13.9974i	−0.586956	+	0.157274i	−0.540062	−	0.841625i	$-0.681599\pi$
$89$	−52.2391	+	13.9974i	−0.586956	+	0.157274i	−0.0468944	+	0.998900i	$0.514932\pi$
$90$		−	20.7846i		−	0.230940i
$91$	83.9782	−	58.3494i	0.922837	−	0.641202i
$92$	35.0718			0.381215
$93$	14.7968	+	55.2224i	0.159105	+	0.593790i
$94$	33.0000	−	57.1577i	0.351064	−	0.608060i
$95$	−54.6673	+	31.5622i	−0.575445	+	0.332233i
$96$	−6.92820	+	6.92820i	−0.0721688	+	0.0721688i
$97$	131.488	+	35.2321i	1.35554	+	0.363217i	0.862178	−	0.506605i	$-0.169100\pi$
$97$	131.488	+	35.2321i	1.35554	+	0.363217i	0.493366	+	0.869822i	$0.335766\pi$
$98$	−4.71281	+	17.5885i	−0.0480899	+	0.179474i
$99$	−21.8038	−	21.8038i	−0.220241	−	0.220241i
$100$	−19.0000	−	32.9090i	−0.190000	−	0.329090i
$101$	53.2461	+	30.7417i	0.527189	+	0.304373i	0.739871	−	0.672749i	$-0.234886\pi$
$101$	53.2461	+	30.7417i	0.527189	+	0.304373i	−0.212682	+	0.977122i	$0.568220\pi$
$102$	−67.4711	+	18.0788i	−0.661482	+	0.177244i
$103$			23.3205i			0.226413i	0.993571	+	0.113206i	$0.0361121\pi$
$103$			23.3205i			0.226413i	−0.993571	+	0.113206i	$0.963888\pi$
$104$	−3.07180	−	36.6410i	−0.0295365	−	0.352317i
$105$	33.3731			0.317839
$106$	29.3205	+	109.426i	0.276609	+	1.03232i
$107$	−39.8660	+	69.0500i	−0.372580	+	0.645327i	−0.989962	−	0.141337i	$-0.954860\pi$
$107$	−39.8660	+	69.0500i	−0.372580	+	0.645327i	0.617382	+	0.786664i	$0.288193\pi$
$108$	−45.0000	+	25.9808i	−0.416667	+	0.240563i
$109$	−103.655	+	103.655i	−0.950964	+	0.950964i	−0.998853	−	0.0478885i	$-0.984751\pi$
$109$	−103.655	+	103.655i	−0.950964	+	0.950964i	0.0478885	+	0.998853i	$0.484751\pi$
$110$	17.1962	+	4.60770i	0.156329	+	0.0418881i
$111$	9.86603	−	36.8205i	0.0888831	−	0.331716i
$112$	22.2487	+	22.2487i	0.198649	+	0.198649i
$113$	−88.5000	−	153.286i	−0.783186	−	1.35652i	−0.930077	−	0.367365i	$-0.880260\pi$
$113$	−88.5000	−	153.286i	−0.783186	−	1.35652i	0.146891	−	0.989153i	$-0.453073\pi$
$114$	54.6673	+	31.5622i	0.479538	+	0.276861i
$115$	−41.4904	+	11.1173i	−0.360786	+	0.0966723i
$116$			1.42563i			0.0122899i
$117$	13.8231	−	76.7654i	0.118146	−	0.656114i
$118$	−55.5167			−0.470480
$119$	58.0570	+	216.672i	0.487874	+	1.82077i
$120$	6.00000	−	10.3923i	0.0500000	−	0.0866025i
$121$	−81.9160	+	47.2942i	−0.676992	+	0.390861i
$122$	28.6077	−	28.6077i	0.234489	−	0.234489i
$123$	−72.7750	−	19.5000i	−0.591667	−	0.158537i
$124$	17.0859	−	63.7654i	0.137789	−	0.514237i
$125$	76.2102	+	76.2102i	0.609682	+	0.609682i
$126$	33.3731	+	57.8038i	0.264866	+	0.458761i
$127$	−147.651	−	85.2461i	−1.16260	−	0.671229i	−0.210677	−	0.977556i	$-0.567567\pi$
$127$	−147.651	−	85.2461i	−1.16260	−	0.671229i	−0.951927	+	0.306326i	$0.900900\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$		−	127.550i		−	0.988760i
$130$	15.2487	+	42.3731i	0.117298	+	0.325947i
$131$	−44.8513			−0.342376			−0.171188	−	0.985238i	$-0.554761\pi$
$131$	−44.8513			−0.342376			−0.171188	+	0.985238i	$0.554761\pi$
$132$	−4.60770	−	17.1962i	−0.0349068	−	0.130274i
$133$	101.356	−	175.554i	0.762078	−	1.31996i
$134$	60.7583	−	35.0788i	0.453420	−	0.261782i
$135$	45.0000	−	45.0000i	0.333333	−	0.333333i
$136$	77.9090	+	20.8756i	0.572860	+	0.153497i
$137$	−24.3775	+	90.9782i	−0.177938	+	0.664074i	0.818094	+	0.575084i	$0.195031\pi$
$137$	−24.3775	+	90.9782i	−0.177938	+	0.664074i	−0.996032	+	0.0889903i	$0.971636\pi$
$138$	30.3731	+	30.3731i	0.220095	+	0.220095i
$139$	−9.59808	−	16.6244i	−0.0690509	−	0.119600i	0.829433	−	0.558606i	$-0.188664\pi$
$139$	−9.59808	−	16.6244i	−0.0690509	−	0.119600i	−0.898484	+	0.439007i	$0.855330\pi$
$140$	−33.3731	−	19.2679i	−0.238379	−	0.137628i
$141$	78.0788	−	20.9212i	0.553751	−	0.148377i
$142$		−	10.3013i		−	0.0725442i
$143$	60.4474	+	28.4545i	0.422709	+	0.198982i
$144$	24.0000			0.166667
$145$	−0.451905	−	1.68653i	−0.00311659	−	0.0116313i
$146$	12.7654	−	22.1103i	0.0874341	−	0.151440i
$147$	−19.3135	+	11.1506i	−0.131384	+	0.0758547i
$148$	−31.1244	+	31.1244i	−0.210300	+	0.210300i
$149$	36.0622	+	9.66283i	0.242028	+	0.0648512i	0.377794	−	0.925890i	$-0.376683\pi$
$149$	36.0622	+	9.66283i	0.242028	+	0.0648512i	−0.135766	+	0.990741i	$0.543349\pi$
$150$	12.0455	−	44.9545i	0.0803034	−	0.299697i
$151$	−161.406	−	161.406i	−1.06892	−	1.06892i	−0.997442	−	0.0714740i	$-0.977230\pi$
$151$	−161.406	−	161.406i	−1.06892	−	1.06892i	−0.0714740	−	0.997442i	$-0.522770\pi$
$152$	−36.4449	−	63.1244i	−0.239769	−	0.415292i
$153$	148.177	+	85.5500i	0.968477	+	0.559150i
$154$	−55.2224	+	14.7968i	−0.358587	+	0.0960832i
$155$			80.8513i			0.521621i
$156$	29.0718	−	34.3923i	0.186358	−	0.220463i
$157$	−14.4308			−0.0919158			−0.0459579	−	0.998943i	$-0.514634\pi$
$157$	−14.4308			−0.0919158			−0.0459579	+	0.998943i	$0.514634\pi$
$158$	5.25387	+	19.6077i	0.0332523	+	0.124099i
$159$	−69.3731	+	120.158i	−0.436309	+	0.755709i
$160$	−12.0000	+	6.92820i	−0.0750000	+	0.0433013i
$161$	97.5378	−	97.5378i	0.605825	−	0.605825i
$162$	12.2942	+	3.29423i	0.0758903	+	0.0203347i
$163$	6.40381	−	23.8993i	0.0392872	−	0.146622i	−0.943496	−	0.331383i	$-0.892485\pi$
$163$	6.40381	−	23.8993i	0.0392872	−	0.146622i	0.982783	+	0.184762i	$0.0591513\pi$
$164$	61.5167	+	61.5167i	0.375102	+	0.375102i
$165$	10.9019	+	18.8827i	0.0660723	+	0.114441i
$166$	−152.138	−	87.8372i	−0.916497	−	0.529140i
$167$	56.6769	−	15.1865i	0.339383	−	0.0909373i	−0.0851025	−	0.996372i	$-0.527122\pi$
$167$	56.6769	−	15.1865i	0.339383	−	0.0909373i	0.424485	+	0.905435i	$0.360455\pi$
$168$			38.5359i			0.229380i
$169$	28.1384	+	166.641i	0.166500	+	0.986042i
$170$	−98.7846			−0.581086
$171$	−40.0192	−	149.354i	−0.234031	−	0.873414i
$172$	−73.6410	+	127.550i	−0.428145	+	0.741570i
$173$	−62.1462	+	35.8801i	−0.359226	+	0.207399i	−0.668741	−	0.743495i	$-0.733167\pi$
$173$	−62.1462	+	35.8801i	−0.359226	+	0.207399i	0.309515	+	0.950895i	$0.399833\pi$
$174$	−1.23463	+	1.23463i	−0.00709556	+	0.00709556i
$175$	−144.363	−	38.6821i	−0.824934	−	0.221040i
$176$	−5.32051	+	19.8564i	−0.0302302	+	0.112820i
$177$	−48.0788	−	48.0788i	−0.271632	−	0.271632i
$178$	38.2417	+	66.2365i	0.214841	+	0.372115i
$179$	139.148	+	80.3372i	0.777363	+	0.448811i	0.835495	−	0.549498i	$-0.185181\pi$
$179$	139.148	+	80.3372i	0.777363	+	0.448811i	−0.0581316	+	0.998309i	$0.518514\pi$
$180$	−28.3923	+	7.60770i	−0.157735	+	0.0422650i
$181$			143.072i			0.790452i	0.918584	+	0.395226i	$0.129334\pi$
$181$			143.072i			0.790452i	−0.918584	+	0.395226i	$0.870666\pi$
$182$	−110.445	−	93.3590i	−0.606840	−	0.512961i
$183$	49.5500			0.270765
$184$	−12.8372	−	47.9090i	−0.0697672	−	0.260375i
$185$	26.9545	−	46.6865i	0.145700	−	0.252360i
$186$	70.0192	−	40.4256i	0.376448	−	0.217342i
$187$	−103.629	+	103.629i	−0.554165	+	0.554165i
$188$	−90.1577	−	24.1577i	−0.479562	−	0.128498i
$189$	−52.8942	+	197.404i	−0.279863	+	1.04446i
$190$	63.1244	+	63.1244i	0.332233	+	0.332233i
$191$	142.703	+	247.169i	0.747137	+	1.29408i	0.949190	+	0.314705i	$0.101906\pi$
$191$	142.703	+	247.169i	0.747137	+	1.29408i	−0.202052	+	0.979375i	$0.564761\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	85.5070	−	22.9115i	0.443042	−	0.118713i	−0.0304000	−	0.999538i	$-0.509678\pi$
$193$	85.5070	−	22.9115i	0.443042	−	0.118713i	0.473442	+	0.880825i	$0.343011\pi$
$194$		−	192.512i		−	0.992327i
$195$	−23.4904	+	49.9019i	−0.120463	+	0.255907i
$196$	25.7513			0.131384
$197$	−97.1725	−	362.653i	−0.493261	−	1.84088i	−0.539559	−	0.841948i	$-0.681409\pi$
$197$	−97.1725	−	362.653i	−0.493261	−	1.84088i	0.0462974	−	0.998928i	$-0.485258\pi$
$198$	−21.8038	+	37.7654i	−0.110120	+	0.190734i
$199$	257.789	−	148.835i	1.29542	−	0.747913i	0.315813	−	0.948822i	$-0.397723\pi$
$199$	257.789	−	148.835i	1.29542	−	0.747913i	0.979610	+	0.200909i	$0.0643896\pi$
$200$	−38.0000	+	38.0000i	−0.190000	+	0.190000i
$201$	82.9974	+	22.2391i	0.412923	+	0.110642i
$202$	22.5045	−	83.9878i	0.111408	−	0.415781i
$203$	3.96479	+	3.96479i	0.0195310	+	0.0195310i
$204$	49.3923	+	85.5500i	0.242119	+	0.419363i
$205$	−92.2750	−	53.2750i	−0.450122	−	0.259878i
$206$	31.8564	−	8.53590i	0.154643	−	0.0414364i
$207$		−	105.215i		−	0.508287i
$208$	−48.9282	+	17.6077i	−0.235232	+	0.0846524i
$209$	132.440			0.633683
$210$	−12.2154	−	45.5885i	−0.0581685	−	0.217088i
$211$	−27.2532	+	47.2039i	−0.129162	+	0.223715i	−0.923352	−	0.383954i	$-0.874562\pi$
$211$	−27.2532	+	47.2039i	−0.129162	+	0.223715i	0.794190	+	0.607669i	$0.207895\pi$
$212$	138.746	−	80.1051i	0.654463	−	0.377854i
$213$	8.92116	−	8.92116i	0.0418834	−	0.0418834i
$214$	108.916	+	29.1840i	0.508953	+	0.136374i
$215$	46.6865	−	174.237i	0.217147	−	0.810402i
$216$	51.9615	+	51.9615i	0.240563	+	0.240563i
$217$	−129.820	−	224.855i	−0.598248	−	1.03620i
$218$	179.536	+	103.655i	0.823559	+	0.475482i
$219$	30.2032	−	8.09292i	0.137914	−	0.0369540i
$220$		−	25.1769i		−	0.114441i
$221$	−364.849	−	65.6980i	−1.65090	−	0.297276i
$222$	−53.9090			−0.242833
$223$	−39.3949	−	147.024i	−0.176659	−	0.659299i	−0.996263	−	0.0863694i	$-0.972473\pi$
$223$	−39.3949	−	147.024i	−0.176659	−	0.659299i	0.819605	−	0.572930i	$-0.194193\pi$
$224$	22.2487	−	38.5359i	0.0993246	−	0.172035i
$225$	−98.7269	+	57.0000i	−0.438786	+	0.253333i
$226$	−177.000	+	177.000i	−0.783186	+	0.783186i
$227$	−207.978	−	55.7276i	−0.916203	−	0.245496i	−0.230242	−	0.973133i	$-0.573952\pi$
$227$	−207.978	−	55.7276i	−0.916203	−	0.245496i	−0.685962	+	0.727638i	$0.740618\pi$
$228$	23.1051	−	86.2295i	0.101338	−	0.378199i
$229$	9.23463	+	9.23463i	0.0403259	+	0.0403259i	0.726982	−	0.686656i	$-0.240922\pi$
$229$	9.23463	+	9.23463i	0.0403259	+	0.0403259i	−0.686656	+	0.726982i	$0.740922\pi$
$230$	30.3731	+	52.6077i	0.132057	+	0.228729i
$231$	−60.6384	−	35.0096i	−0.262504	−	0.151557i
$232$	1.94744	−	0.521815i	0.00839414	−	0.00224920i
$233$			397.061i			1.70413i	0.523439	+	0.852063i	$0.324649\pi$
$233$			397.061i			1.70413i	−0.523439	+	0.852063i	$0.675351\pi$
$234$	−109.923	+	9.21539i	−0.469757	+	0.0393820i
$235$	114.315			0.486448
$236$	20.3205	+	75.8372i	0.0861038	+	0.321344i
$237$	−12.4308	+	21.5307i	−0.0524506	+	0.0908470i
$238$	274.729	−	158.615i	1.15432	−	0.666448i
$239$	198.688	−	198.688i	0.831332	−	0.831332i	−0.156367	−	0.987699i	$-0.549978\pi$
$239$	198.688	−	198.688i	0.831332	−	0.831332i	0.987699	+	0.156367i	$0.0499782\pi$
$240$	−16.3923	−	4.39230i	−0.0683013	−	0.0183013i
$241$	−84.6699	+	315.992i	−0.351327	+	1.31117i	0.533717	+	0.845663i	$0.320795\pi$
$241$	−84.6699	+	315.992i	−0.351327	+	1.31117i	−0.885044	+	0.465508i	$0.845872\pi$
$242$	94.5885	+	94.5885i	0.390861	+	0.390861i
$243$	124.708	+	216.000i	0.513200	+	0.888889i
$244$	−49.5500	−	28.6077i	−0.203074	−	0.117245i
$245$	−30.4641	+	8.16283i	−0.124343	+	0.0333177i
$246$			106.550i			0.433130i
$247$	191.160	+	275.124i	0.773928	+	1.11386i
$248$	−93.3590			−0.376448
$249$	−55.6865	−	207.825i	−0.223641	−	0.834638i
$250$	76.2102	−	132.000i	0.304841	−	0.528000i
$251$	−134.267	+	77.5192i	−0.534929	+	0.308842i	−0.743021	−	0.669268i	$-0.766608\pi$
$251$	−134.267	+	77.5192i	−0.534929	+	0.308842i	0.208092	+	0.978109i	$0.433275\pi$
$252$	66.7461	−	66.7461i	0.264866	−	0.264866i
$253$	87.0500	+	23.3250i	0.344071	+	0.0921936i
$254$	−62.4045	+	232.897i	−0.245687	+	0.916916i
$255$	−85.5500	−	85.5500i	−0.335490	−	0.335490i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−262.012	−	151.272i	−1.01950	−	0.588609i	−0.105541	−	0.994415i	$-0.533657\pi$
$257$	−262.012	−	151.272i	−1.01950	−	0.588609i	−0.913959	+	0.405806i	$0.866991\pi$
$258$	−174.237	+	46.6865i	−0.675335	+	0.180956i
$259$			173.119i			0.668414i
$260$	52.3013	−	36.3397i	0.201159	−	0.139768i
$261$	4.27688			0.0163865
$262$	16.4167	+	61.2679i	0.0626592	+	0.233847i
$263$	−25.2968	+	43.8154i	−0.0961856	+	0.166598i	−0.910103	−	0.414383i	$-0.863998\pi$
$263$	−25.2968	+	43.8154i	−0.0961856	+	0.166598i	0.813917	+	0.580981i	$0.197331\pi$
$264$	−21.8038	+	12.5885i	−0.0825903	+	0.0476836i
$265$	−138.746	+	138.746i	−0.523570	+	0.523570i
$266$	−276.911	−	74.1980i	−1.04102	−	0.278940i
$267$	−24.2442	+	90.4808i	−0.0908024	+	0.338879i
$268$	−70.1577	−	70.1577i	−0.261782	−	0.261782i
$269$	21.4474	+	37.1481i	0.0797303	+	0.138097i	0.903134	−	0.429360i	$-0.141261\pi$
$269$	21.4474	+	37.1481i	0.0797303	+	0.138097i	−0.823403	+	0.567457i	$0.807927\pi$
$270$	−77.9423	−	45.0000i	−0.288675	−	0.166667i
$271$	478.614	−	128.244i	1.76610	−	0.473226i	0.778163	−	0.628062i	$-0.216152\pi$
$271$	478.614	−	128.244i	1.76610	−	0.473226i	0.987940	+	0.154836i	$0.0494849\pi$
$272$		−	114.067i		−	0.419363i
$273$	−14.7968	−	176.499i	−0.0542008	−	0.646518i
$274$	133.201			0.486136
$275$	−25.2724	−	94.3179i	−0.0918997	−	0.342974i
$276$	30.3731	−	52.6077i	0.110047	−	0.190608i
$277$	184.227	−	106.363i	0.665079	−	0.383984i	−0.129130	−	0.991628i	$-0.541219\pi$
$277$	184.227	−	106.363i	0.665079	−	0.383984i	0.794209	+	0.607644i	$0.207885\pi$
$278$	−19.1962	+	19.1962i	−0.0690509	+	0.0690509i
$279$	−191.296	−	51.2576i	−0.685649	−	0.183719i
$280$	−14.1051	+	52.6410i	−0.0503754	+	0.188004i
$281$	27.2243	+	27.2243i	0.0968837	+	0.0968837i	0.753887	−	0.657004i	$-0.228176\pi$
$281$	27.2243	+	27.2243i	0.0968837	+	0.0968837i	−0.657004	+	0.753887i	$0.728176\pi$
$282$	−57.1577	−	99.0000i	−0.202687	−	0.351064i
$283$	−126.526	−	73.0500i	−0.447089	−	0.258127i	0.259511	−	0.965740i	$-0.416439\pi$
$283$	−126.526	−	73.0500i	−0.447089	−	0.258127i	−0.706600	+	0.707613i	$0.749772\pi$
$284$	−14.0718	+	3.77053i	−0.0495486	+	0.0132765i
$285$			109.335i			0.383630i
$286$	16.7442	−	92.9878i	0.0585463	−	0.325132i
$287$	342.167			1.19222
$288$	−8.78461	−	32.7846i	−0.0305021	−	0.113835i
$289$	262.100	−	453.970i	0.906920	−	1.57083i
$290$	−2.13844	+	1.23463i	−0.00737393	+	0.00425734i
$291$	166.720	−	166.720i	0.572920	−	0.572920i
$292$	−34.8756	−	9.34490i	−0.119437	−	0.0320031i
$293$	25.3212	−	94.5000i	0.0864205	−	0.322526i	−0.909159	−	0.416449i	$-0.863274\pi$
$293$	25.3212	−	94.5000i	0.0864205	−	0.322526i	0.995579	+	0.0939237i	$0.0299410\pi$
$294$	22.3013	+	22.3013i	0.0758547	+	0.0758547i
$295$	−48.0788	−	83.2750i	−0.162979	−	0.282288i
$296$	53.9090	+	31.1244i	0.182125	+	0.105150i
$297$	−128.971	+	34.5577i	−0.434246	+	0.116356i
$298$		−	52.7987i		−	0.177177i
$299$	77.1917	+	214.500i	0.258166	+	0.717391i
$300$	−65.8179			−0.219393
$301$	149.926	+	559.530i	0.498092	+	1.85890i
$302$	−161.406	+	279.564i	−0.534458	+	0.925709i
$303$	92.2250	−	53.2461i	0.304373	−	0.175730i
$304$	−72.8897	+	72.8897i	−0.239769	+	0.239769i
$305$	67.6865	+	18.1366i	0.221923	+	0.0594641i
$306$	62.6269	−	233.727i	0.204663	−	0.763813i
$307$	−2.62178	−	2.62178i	−0.00853999	−	0.00853999i	0.702824	−	0.711364i	$-0.251922\pi$
$307$	−2.62178	−	2.62178i	−0.00853999	−	0.00853999i	−0.711364	+	0.702824i	$0.751922\pi$
$308$	40.4256	+	70.0192i	0.131252	+	0.227335i
$309$	34.9808	+	20.1962i	0.113206	+	0.0653597i
$310$	110.445	−	29.5936i	0.356274	−	0.0954633i
$311$		−	386.038i		−	1.24128i	−0.784095	−	0.620641i	$-0.786873\pi$
$311$		−	386.038i		−	1.24128i	0.784095	−	0.620641i	$-0.213127\pi$
$312$	−57.6218	−	27.1244i	−0.184685	−	0.0869370i
$313$	−35.1384			−0.112263			−0.0561317	−	0.998423i	$-0.517877\pi$
$313$	−35.1384			−0.112263			−0.0561317	+	0.998423i	$0.517877\pi$
$314$	5.28203	+	19.7128i	0.0168218	+	0.0627797i
$315$	−57.8038	+	100.119i	−0.183504	+	0.317839i
$316$	24.8616	−	14.3538i	0.0786758	−	0.0454235i
$317$	−12.5307	+	12.5307i	−0.0395292	+	0.0395292i	−0.726595	−	0.687066i	$-0.758898\pi$
$317$	−12.5307	+	12.5307i	−0.0395292	+	0.0395292i	0.687066	+	0.726595i	$0.258898\pi$
$318$	189.531	+	50.7846i	0.596009	+	0.159700i
$319$	−0.948132	+	3.53848i	−0.00297220	+	0.0110924i
$320$	13.8564	+	13.8564i	0.0433013	+	0.0433013i
$321$	69.0500	+	119.598i	0.215109	+	0.372580i
$322$	−168.940	−	97.5378i	−0.524660	−	0.302912i
$323$	−709.845	+	190.203i	−2.19766	+	0.588862i
$324$		−	18.0000i		−	0.0555556i
$325$	159.454	−	188.636i	0.490627	−	0.580418i
$326$	−34.9911			−0.107335
$327$	65.7147	+	245.251i	0.200962	+	0.750002i
$328$	61.5167	−	106.550i	0.187551	−	0.324848i
$329$	−317.921	+	183.552i	−0.966326	+	0.557908i
$330$	21.8038	−	21.8038i	0.0660723	−	0.0660723i
$331$	−249.959	−	66.9763i	−0.755163	−	0.202345i	−0.139356	−	0.990242i	$-0.544503\pi$
$331$	−249.959	−	66.9763i	−0.755163	−	0.202345i	−0.615807	+	0.787897i	$0.711170\pi$
$332$	−64.3013	+	239.976i	−0.193679	+	0.722818i
$333$	93.3731	+	93.3731i	0.280400	+	0.280400i
$334$	−41.4904	−	71.8634i	−0.124223	−	0.215160i
$335$	105.237	+	60.7583i	0.314139	+	0.181368i
$336$	52.6410	−	14.1051i	0.156670	−	0.0419795i
$337$		−	94.9461i		−	0.281739i	−0.990028	−	0.140870i	$-0.955010\pi$
$337$		−	94.9461i		−	0.281739i	0.990028	−	0.140870i	$-0.0449898\pi$
$338$	217.336	−	99.4327i	0.643007	−	0.294179i
$339$	−306.573			−0.904345
$340$	36.1577	+	134.942i	0.106346	+	0.396889i
$341$	84.8160	−	146.906i	0.248727	−	0.430808i
$342$	−189.373	+	109.335i	−0.553722	+	0.319692i
$343$	−200.930	+	200.930i	−0.585802	+	0.585802i
$344$	201.191	+	53.9090i	0.584858	+	0.156712i
$345$	−19.2558	+	71.8634i	−0.0558138	+	0.208300i
$346$	71.7602	+	71.7602i	0.207399	+	0.207399i
$347$	−52.2302	−	90.4653i	−0.150519	−	0.260707i	0.780899	−	0.624657i	$-0.214761\pi$
$347$	−52.2302	−	90.4653i	−0.150519	−	0.260707i	−0.931418	+	0.363950i	$0.881428\pi$
$348$	2.13844	+	1.23463i	0.00614494	+	0.00354778i
$349$	−78.0763	+	20.9205i	−0.223714	+	0.0599440i	−0.368935	−	0.929455i	$-0.620277\pi$
$349$	−78.0763	+	20.9205i	−0.223714	+	0.0599440i	0.145221	+	0.989399i	$0.453611\pi$
$350$			211.363i			0.603894i
$351$	−257.942	−	218.038i	−0.734878	−	0.621192i
$352$	29.0718			0.0825903
$353$	−44.1429	−	164.744i	−0.125051	−	0.466696i	0.874791	−	0.484501i	$-0.160999\pi$
$353$	−44.1429	−	164.744i	−0.125051	−	0.466696i	−0.999841	+	0.0178053i	$0.994332\pi$
$354$	−48.0788	+	83.2750i	−0.135816	+	0.235240i
$355$	15.4519	−	8.92116i	0.0435265	−	0.0251300i
$356$	76.4833	−	76.4833i	0.214841	−	0.214841i
$357$	375.286	+	100.558i	1.05122	+	0.281674i
$358$	58.8109	−	219.485i	0.164276	−	0.613087i
$359$	−102.058	−	102.058i	−0.284283	−	0.284283i	0.550531	−	0.834815i	$-0.314425\pi$
$359$	−102.058	−	102.058i	−0.284283	−	0.284283i	−0.834815	+	0.550531i	$0.814425\pi$
$360$	20.7846	+	36.0000i	0.0577350	+	0.100000i
$361$	262.504	+	151.557i	0.727159	+	0.419826i
$362$	195.440	−	52.3679i	0.539889	−	0.144663i
$363$			163.832i			0.451328i
$364$	−87.1051	+	185.042i	−0.239300	+	0.508358i
$365$	44.2205			0.121152
$366$	−18.1366	−	67.6865i	−0.0495534	−	0.184936i
$367$	−238.856	+	413.710i	−0.650833	+	1.12728i	0.332088	+	0.943248i	$0.392247\pi$
$367$	−238.856	+	413.710i	−0.650833	+	1.12728i	−0.982921	+	0.184027i	$0.941086\pi$
$368$	−60.7461	+	35.0718i	−0.165071	+	0.0953038i
$369$	184.550	−	184.550i	0.500135	−	0.500135i
$370$	−73.6410	−	19.7321i	−0.199030	−	0.0533299i
$371$	163.086	−	608.645i	0.439585	−	1.64055i
$372$	−80.8513	−	80.8513i	−0.217342	−	0.217342i
$373$	−257.744	−	446.425i	−0.691001	−	1.19685i	−0.971510	−	0.236998i	$-0.923836\pi$
$373$	−257.744	−	446.425i	−0.691001	−	1.19685i	0.280509	−	0.959852i	$-0.409497\pi$
$374$	179.490	+	103.629i	0.479921	+	0.277082i
$375$	180.315	−	48.3154i	0.480841	−	0.128841i
$376$			132.000i			0.351064i
$377$	−8.71916	+	3.13775i	−0.0231278	+	0.00832294i
$378$	289.019			0.764601
$379$	70.8449	+	264.397i	0.186926	+	0.697617i	0.994210	+	0.107454i	$0.0342698\pi$
$379$	70.8449	+	264.397i	0.186926	+	0.697617i	−0.807284	+	0.590163i	$0.799064\pi$
$380$	63.1244	−	109.335i	0.166117	−	0.287723i
$381$	−255.738	+	147.651i	−0.671229	+	0.387534i
$382$	285.406	−	285.406i	0.747137	−	0.747137i
$383$	451.791	+	121.057i	1.17961	+	0.316076i	0.794772	−	0.606908i	$-0.207590\pi$
$383$	451.791	+	121.057i	1.17961	+	0.316076i	0.384839	+	0.922984i	$0.374257\pi$
$384$	5.07180	−	18.9282i	0.0132078	−	0.0492922i
$385$	−70.0192	−	70.0192i	−0.181868	−	0.181868i
$386$	−62.5955	−	108.419i	−0.162165	−	0.280877i
$387$	382.650	+	220.923i	0.988760	+	0.570861i
$388$	−262.976	+	70.4641i	−0.677772	+	0.181609i
$389$		−	572.687i		−	1.47220i	−0.676871	−	0.736102i	$-0.736665\pi$
$389$		−	572.687i		−	1.47220i	0.676871	−	0.736102i	$-0.263335\pi$
$390$	76.7654	+	13.8231i	0.196834	+	0.0354438i
$391$	−500.065			−1.27894
$392$	−9.42563	−	35.1769i	−0.0240450	−	0.0897370i
$393$	−38.8423	+	67.2769i	−0.0988354	+	0.171188i
$394$	−459.825	+	265.480i	−1.16707	+	0.673807i
$395$	−24.8616	+	24.8616i	−0.0629407	+	0.0629407i
$396$	59.5692	+	15.9615i	0.150427	+	0.0403069i
$397$	15.8275	−	59.0692i	0.0398679	−	0.148789i	−0.943123	−	0.332445i	$-0.892127\pi$
$397$	15.8275	−	59.0692i	0.0398679	−	0.148789i	0.982991	+	0.183656i	$0.0587932\pi$
$398$	−297.669	−	297.669i	−0.747913	−	0.747913i
$399$	−175.554	−	304.069i	−0.439986	−	0.762078i
$400$	65.8179	+	38.0000i	0.164545	+	0.0950000i
$401$	521.798	−	139.815i	1.30124	−	0.348667i	0.459322	−	0.888270i	$-0.348092\pi$
$401$	521.798	−	139.815i	1.30124	−	0.348667i	0.841920	+	0.539603i	$0.181426\pi$
$402$		−	121.517i		−	0.302280i
$403$	427.596	−	35.8475i	1.06103	−	0.0889516i
$404$	−122.967			−0.304373
$405$	5.70577	+	21.2942i	0.0140883	+	0.0525783i
$406$	3.96479	−	6.86722i	0.00976550	−	0.0169143i
$407$	−97.9519	+	56.5526i	−0.240668	+	0.138950i
$408$	98.7846	−	98.7846i	0.242119	−	0.242119i
$409$	−20.0237	−	5.36533i	−0.0489577	−	0.0131182i	0.234257	−	0.972175i	$-0.424734\pi$
$409$	−20.0237	−	5.36533i	−0.0489577	−	0.0131182i	−0.283215	+	0.959057i	$0.591401\pi$
$410$	−39.0000	+	145.550i	−0.0951220	+	0.355000i
$411$	115.356	+	115.356i	0.280671	+	0.280671i
$412$	−23.3205	−	40.3923i	−0.0566032	−	0.0980396i
$413$	267.423	+	154.397i	0.647513	+	0.373842i
$414$	−143.727	+	38.5115i	−0.347166	+	0.0930230i
$415$		−	304.277i		−	0.733197i
$416$	41.9615	+	60.3923i	0.100869	+	0.145174i
$417$	−33.2487			−0.0797331
$418$	−48.4763	−	180.916i	−0.115972	−	0.432813i
$419$	−173.598	+	300.681i	−0.414315	+	0.717615i	−0.995356	−	0.0962592i	$-0.969312\pi$
$419$	−173.598	+	300.681i	−0.414315	+	0.717615i	0.581041	+	0.813874i	$0.302646\pi$
$420$	−57.8038	+	33.3731i	−0.137628	+	0.0794597i
$421$	−286.555	+	286.555i	−0.680654	+	0.680654i	−0.960147	−	0.279494i	$-0.909833\pi$
$421$	−286.555	+	286.555i	−0.680654	+	0.680654i	0.279494	+	0.960147i	$0.409833\pi$
$422$	74.4571	+	19.9507i	0.176439	+	0.0472766i
$423$	−72.4730	+	270.473i	−0.171331	+	0.639416i
$424$	−160.210	−	160.210i	−0.377854	−	0.377854i
$425$	270.908	+	469.227i	0.637431	+	1.10406i
$426$	−15.4519	−	8.92116i	−0.0362721	−	0.0209417i
$427$	−217.363	+	58.2424i	−0.509048	+	0.136399i
$428$		−	159.464i		−	0.372580i
$429$	95.0307	−	66.0289i	0.221517	−	0.153913i
$430$	−255.100			−0.593256
$431$	79.3602	+	296.176i	0.184130	+	0.687184i	0.994815	+	0.101701i	$0.0324284\pi$
$431$	79.3602	+	296.176i	0.184130	+	0.687184i	−0.810685	+	0.585483i	$0.800905\pi$
$432$	51.9615	−	90.0000i	0.120281	−	0.208333i
$433$	−73.2757	+	42.3057i	−0.169228	+	0.0977038i	−0.582222	−	0.813030i	$-0.697816\pi$
$433$	−73.2757	+	42.3057i	−0.169228	+	0.0977038i	0.412994	+	0.910734i	$0.364483\pi$
$434$	−259.640	+	259.640i	−0.598248	+	0.598248i
$435$	−2.92116	−	0.782723i	−0.00671531	−	0.00179936i
$436$	75.8808	−	283.191i	0.174039	−	0.649521i
$437$	319.547	+	319.547i	0.731228	+	0.731228i
$438$	−22.1103	−	38.2961i	−0.0504801	−	0.0874341i
$439$	−379.794	−	219.274i	−0.865135	−	0.499486i	0.000593556	−	1.00000i	$-0.499811\pi$
$439$	−379.794	−	219.274i	−0.865135	−	0.499486i	−0.865728	+	0.500514i	$0.833144\pi$
$440$	−34.3923	+	9.21539i	−0.0781643	+	0.0209441i
$441$		−	77.2539i		−	0.175179i
$442$	43.7987	+	522.440i	0.0990921	+	1.18199i
$443$	−323.836			−0.731006			−0.365503	−	0.930810i	$-0.619103\pi$
$443$	−323.836			−0.731006			−0.365503	+	0.930810i	$0.619103\pi$
$444$	19.7321	+	73.6410i	0.0444416	+	0.165858i
$445$	−66.2365	+	114.725i	−0.148846	+	0.257809i
$446$	−186.419	+	107.629i	−0.417979	+	0.241320i
$447$	45.7250	−	45.7250i	0.102293	−	0.102293i
$448$	−60.7846	−	16.2872i	−0.135680	−	0.0363553i
$449$	91.5122	−	341.528i	0.203813	−	0.760642i	−0.785995	−	0.618233i	$-0.787849\pi$
$449$	91.5122	−	341.528i	0.203813	−	0.760642i	0.989808	−	0.142408i	$-0.0454847\pi$
$450$	114.000	+	114.000i	0.253333	+	0.253333i
$451$	111.775	+	193.600i	0.247838	+	0.429268i
$452$	306.573	+	177.000i	0.678259	+	0.391593i
$453$	−381.892	+	102.328i	−0.843028	+	0.225889i
$454$			304.501i			0.670707i
$455$	44.3904	−	246.519i	0.0975614	−	0.541799i
$456$	−126.249			−0.276861
$457$	68.8763	+	257.050i	0.150714	+	0.562473i	0.999434	+	0.0336305i	$0.0107070\pi$
$457$	68.8763	+	257.050i	0.150714	+	0.562473i	−0.848720	+	0.528842i	$0.822626\pi$
$458$	9.23463	−	15.9948i	0.0201629	−	0.0349232i
$459$	641.625	−	370.442i	1.39788	−	0.807064i
$460$	60.7461	−	60.7461i	0.132057	−	0.132057i
$461$	145.521	+	38.9923i	0.315664	+	0.0845819i	0.413173	−	0.910653i	$-0.364421\pi$
$461$	145.521	+	38.9923i	0.315664	+	0.0845819i	−0.0975085	+	0.995235i	$0.531087\pi$
$462$	−25.6288	+	95.6481i	−0.0554736	+	0.207030i
$463$	48.4115	+	48.4115i	0.104561	+	0.104561i	0.757452	−	0.652891i	$-0.226444\pi$
$463$	48.4115	+	48.4115i	0.104561	+	0.104561i	−0.652891	+	0.757452i	$0.726444\pi$
$464$	−1.42563	−	2.46926i	−0.00307247	−	0.00532167i
$465$	121.277	+	70.0192i	0.260810	+	0.150579i
$466$	542.396	−	145.335i	1.16394	−	0.311877i
$467$		−	138.764i		−	0.297139i	−0.988902	−	0.148570i	$-0.952533\pi$
$467$		−	138.764i		−	0.297139i	0.988902	−	0.148570i	$-0.0474669\pi$
$468$	52.8231	+	146.785i	0.112870	+	0.313642i
$469$	−390.229			−0.832046
$470$	−41.8423	−	156.158i	−0.0890262	−	0.332250i
$471$	−12.4974	+	21.6462i	−0.0265338	+	0.0459579i
$472$	96.1577	−	55.5167i	0.203724	−	0.117620i
$473$	−267.610	+	267.610i	−0.565771	+	0.565771i
$474$	33.9615	+	9.09996i	0.0716488	+	0.0191982i
$475$	126.728	−	472.954i	0.266795	−	0.995692i
$476$	−317.229	−	317.229i	−0.666448	−	0.666448i
$477$	−240.315	−	416.238i	−0.503806	−	0.872617i
$478$	−344.138	−	198.688i	−0.719955	−	0.415666i
$479$	−221.959	+	59.4737i	−0.463380	+	0.124162i	−0.482953	−	0.875646i	$-0.660436\pi$
$479$	−221.959	+	59.4737i	−0.463380	+	0.124162i	0.0195733	+	0.999808i	$0.493769\pi$
$480$			24.0000i			0.0500000i
$481$	−258.861	−	121.854i	−0.538172	−	0.253334i
$482$	462.645			0.959844
$483$	−61.8365	−	230.777i	−0.128026	−	0.477799i
$484$	94.5885	−	163.832i	0.195431	−	0.338496i
$485$	288.767	−	166.720i	0.595396	−	0.343752i
$486$	249.415	−	249.415i	0.513200	−	0.513200i
$487$	471.064	+	126.221i	0.967277	+	0.259181i	0.707678	−	0.706535i	$-0.249743\pi$
$487$	471.064	+	126.221i	0.967277	+	0.259181i	0.259599	+	0.965716i	$0.416409\pi$
$488$	−20.9423	+	78.1577i	−0.0429145	+	0.160159i
$489$	−30.3032	−	30.3032i	−0.0619696	−	0.0619696i
$490$	22.3013	+	38.6269i	0.0455128	+	0.0788305i
$491$	−453.156	−	261.630i	−0.922924	−	0.532850i	−0.0383572	−	0.999264i	$-0.512212\pi$
$491$	−453.156	−	261.630i	−0.922924	−	0.532850i	−0.884567	+	0.466414i	$0.845546\pi$
$492$	145.550	−	39.0000i	0.295833	−	0.0792683i
$493$		−	20.3270i		−	0.0412313i
$494$	305.856	−	361.832i	0.619143	−	0.732453i
$495$	−75.5307			−0.152587
$496$	34.1718	+	127.531i	0.0688947	+	0.257118i
$497$	−28.6487	+	49.6211i	−0.0576434	+	0.0998412i
$498$	−263.512	+	152.138i	−0.529140	+	0.305499i
$499$	108.412	−	108.412i	0.217258	−	0.217258i	−0.590084	−	0.807342i	$-0.700905\pi$
$499$	108.412	−	108.412i	0.217258	−	0.217258i	0.807342	+	0.590084i	$0.200905\pi$
$500$	−208.210	−	55.7898i	−0.416420	−	0.111580i
$501$	26.3038	−	98.1673i	0.0525027	−	0.195943i
$502$	155.038	+	155.038i	0.308842	+	0.308842i
$503$	202.861	+	351.365i	0.403302	+	0.698539i	0.994122	−	0.108264i	$-0.0345291\pi$
$503$	202.861	+	351.365i	0.403302	+	0.698539i	−0.590820	+	0.806803i	$0.701196\pi$
$504$	−115.608	−	66.7461i	−0.229380	−	0.132433i
$505$	145.471	−	38.9789i	0.288062	−	0.0771859i
$506$		−	127.450i		−	0.251878i
$507$	274.330	+	102.108i	0.541085	+	0.201396i
$508$	340.985			0.671229
$509$	−40.0814	−	149.586i	−0.0787454	−	0.293882i	0.915311	−	0.402748i	$-0.131945\pi$
$509$	−40.0814	−	149.586i	−0.0787454	−	0.293882i	−0.994056	+	0.108866i	$0.965278\pi$
$510$	−85.5500	+	148.177i	−0.167745	+	0.290543i
$511$	−122.981	+	71.0033i	−0.240668	+	0.138950i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−646.721	−	173.288i	−1.26066	−	0.337794i
$514$	−110.739	+	413.284i	−0.215446	+	0.804054i
$515$	40.3923	+	40.3923i	0.0784317	+	0.0784317i
$516$	127.550	+	220.923i	0.247190	+	0.428145i
$517$	−207.710	−	119.921i	−0.401759	−	0.231956i
$518$	236.485	−	63.3660i	0.456535	−	0.122328i
$519$			124.292i			0.239484i
$520$	−68.7846	−	58.1436i	−0.132278	−	0.111815i
$521$	−239.636			−0.459954			−0.229977	−	0.973196i	$-0.573865\pi$
$521$	−239.636			−0.459954			−0.229977	+	0.973196i	$0.573865\pi$
$522$	−1.56545	−	5.84232i	−0.00299894	−	0.0111922i
$523$	497.663	−	861.978i	0.951555	−	1.64814i	0.209494	−	0.977810i	$-0.432818\pi$
$523$	497.663	−	861.978i	0.951555	−	1.64814i	0.742061	−	0.670332i	$-0.233848\pi$
$524$	77.6846	−	44.8513i	0.148253	−	0.0855940i
$525$	−183.046	+	183.046i	−0.348658	+	0.348658i
$526$	69.1122	+	18.5185i	0.131392	+	0.0352064i
$527$	−243.616	+	909.188i	−0.462270	+	1.72521i
$528$	25.1769	+	25.1769i	0.0476836	+	0.0476836i
$529$	−110.746	−	191.818i	−0.209350	−	0.362605i
$530$	240.315	+	138.746i	0.453425	+	0.261785i
$531$	227.512	−	60.9615i	0.428459	−	0.114805i
$532$			405.426i			0.762078i
$533$	−240.842	+	511.633i	−0.451860	+	0.959912i
$534$	132.473			0.248077
$535$	50.5481	+	188.648i	0.0944824	+	0.352613i
$536$	−70.1577	+	121.517i	−0.130891	+	0.226710i
$537$	241.012	−	139.148i	0.448811	−	0.259121i
$538$	42.8949	−	42.8949i	0.0797303	−	0.0797303i
$539$	63.9160	+	17.1262i	0.118583	+	0.0317741i
$540$	−32.9423	+	122.942i	−0.0610042	+	0.227671i
$541$	74.1000	+	74.1000i	0.136969	+	0.136969i	0.772267	−	0.635298i	$-0.219123\pi$
$541$	74.1000	+	74.1000i	0.136969	+	0.136969i	−0.635298	+	0.772267i	$0.719123\pi$
$542$	−350.370	−	606.858i	−0.646439	−	1.11966i
$543$	214.608	+	123.904i	0.395226	+	0.228184i
$544$	−155.818	+	41.7513i	−0.286430	+	0.0767487i
$545$			359.072i			0.658847i
$546$	−235.687	+	84.8160i	−0.431660	+	0.155341i
$547$	961.854			1.75842			0.879208	−	0.476438i	$-0.158072\pi$
$547$	961.854			1.75842			0.879208	+	0.476438i	$0.158072\pi$
$548$	−48.7551	−	181.956i	−0.0889691	−	0.332037i
$549$	−85.8231	+	148.650i	−0.156326	+	0.270765i
$550$	−119.590	+	69.0455i	−0.217437	+	0.125537i
$551$	−12.9892	+	12.9892i	−0.0235738	+	0.0235738i
$552$	−82.9808	−	22.2346i	−0.150327	−	0.0402801i
$553$	29.2229	−	109.061i	0.0528444	−	0.197218i
$554$	−212.727	−	212.727i	−0.383984	−	0.383984i
$555$	−46.6865	−	80.8634i	−0.0841199	−	0.145700i
$556$	33.2487	+	19.1962i	0.0597998	+	0.0345255i
$557$	−729.917	+	195.581i	−1.31044	+	0.351132i	−0.845390	−	0.534150i	$-0.820632\pi$
$557$	−729.917	+	195.581i	−1.31044	+	0.351132i	−0.465054	+	0.885282i	$0.653965\pi$
$558$			280.077i			0.501930i
$559$	−942.180	−	169.658i	−1.68547	−	0.303502i
$560$	77.0718			0.137628
$561$	65.6980	+	245.188i	0.117109	+	0.437056i
$562$	27.2243	−	47.1539i	0.0484418	−	0.0839037i
$563$	−26.1250	+	15.0833i	−0.0464033	+	0.0267909i	−0.523022	−	0.852319i	$-0.675196\pi$
$563$	−26.1250	+	15.0833i	−0.0464033	+	0.0267909i	0.476619	+	0.879110i	$0.341862\pi$
$564$	−114.315	+	114.315i	−0.202687	+	0.202687i
$565$	−418.786	−	112.214i	−0.741215	−	0.198608i
$566$	−53.4763	+	199.576i	−0.0944811	+	0.352608i
$567$	−50.0596	−	50.0596i	−0.0882885	−	0.0882885i
$568$	10.3013	+	17.8423i	0.0181360	+	0.0314125i
$569$	−447.092	−	258.129i	−0.785751	−	0.453653i	0.0527137	−	0.998610i	$-0.483213\pi$
$569$	−447.092	−	258.129i	−0.785751	−	0.453653i	−0.838465	+	0.544956i	$0.816546\pi$
$570$	149.354	−	40.0192i	0.262024	−	0.0702092i
$571$			813.423i			1.42456i	0.701896	+	0.712279i	$0.252337\pi$
$571$			813.423i			1.42456i	−0.701896	+	0.712279i	$0.747663\pi$
$572$	−133.153	+	11.1628i	−0.232784	+	0.0195154i
$573$	494.338			0.862720
$574$	−125.242	−	467.408i	−0.218191	−	0.814300i
$575$	166.591	−	288.544i	0.289724	−	0.501816i
$576$	−41.5692	+	24.0000i	−0.0721688	+	0.0416667i
$577$	336.660	−	336.660i	0.583467	−	0.583467i	−0.352388	−	0.935854i	$-0.614630\pi$
$577$	336.660	−	336.660i	0.583467	−	0.583467i	0.935854	+	0.352388i	$0.114630\pi$
$578$	−716.070	−	191.870i	−1.23888	−	0.331956i
$579$	39.6840	−	148.103i	0.0685388	−	0.255790i
$580$	2.46926	+	2.46926i	0.00425734	+	0.00425734i
$581$	488.566	+	846.221i	0.840905	+	1.45649i
$582$	−288.767	−	166.720i	−0.496164	−	0.286460i
$583$	397.650	−	106.550i	0.682075	−	0.182762i
$584$			51.0615i			0.0874341i
$585$	−109.019	−	156.904i	−0.186358	−	0.268212i
$586$	−138.358			−0.236105
$587$	−154.442	−	576.386i	−0.263104	−	0.981919i	−0.963400	−	0.268066i	$-0.913615\pi$
$587$	−154.442	−	576.386i	−0.263104	−	0.981919i	0.700296	−	0.713853i	$-0.253051\pi$
$588$	22.3013	−	38.6269i	0.0379273	−	0.0656921i
$589$	736.653	−	425.307i	1.25068	−	0.722083i
$590$	−96.1577	+	96.1577i	−0.162979	+	0.162979i
$591$	−628.133	−	168.308i	−1.06283	−	0.284784i
$592$	22.7846	−	85.0333i	0.0384875	−	0.143637i
$593$	297.953	+	297.953i	0.502450	+	0.502450i	0.912198	−	0.409749i	$-0.134384\pi$
$593$	297.953	+	297.953i	0.502450	+	0.502450i	−0.409749	+	0.912198i	$0.634384\pi$
$594$	94.4134	+	163.529i	0.158945	+	0.275301i
$595$	475.844	+	274.729i	0.799738	+	0.461729i
$596$	−72.1244	+	19.3257i	−0.121014	+	0.0324256i
$597$		−	515.578i		−	0.863615i
$598$	264.758	−	183.958i	0.442740	−	0.307623i
$599$	996.169			1.66305			0.831527	−	0.555485i	$-0.187467\pi$
$599$	996.169			1.66305			0.831527	+	0.555485i	$0.187467\pi$
$600$	24.0910	+	89.9090i	0.0401517	+	0.149848i
$601$	−126.265	+	218.698i	−0.210092	+	0.363890i	−0.951743	−	0.306896i	$-0.900710\pi$
$601$	−126.265	+	218.698i	−0.210092	+	0.363890i	0.741651	+	0.670786i	$0.234043\pi$
$602$	709.456	−	409.604i	1.17850	−	0.680406i
$603$	−210.473	+	210.473i	−0.349043	+	0.349043i
$604$	440.970	+	118.158i	0.730084	+	0.195625i
$605$	−59.9667	+	223.799i	−0.0991185	+	0.369915i
$606$	−106.492	−	106.492i	−0.175730	−	0.175730i
$607$	245.321	+	424.909i	0.404154	+	0.700014i	0.994223	−	0.107338i	$-0.0342328\pi$
$607$	245.321	+	424.909i	0.404154	+	0.700014i	−0.590069	+	0.807353i	$0.700899\pi$
$608$	126.249	+	72.8897i	0.207646	+	0.119884i
$609$	9.38080	−	2.51358i	0.0154036	−	0.00412739i
$610$		−	99.1000i		−	0.162459i
$611$	−50.6846	−	604.577i	−0.0829536	−	0.989487i
$612$	−342.200			−0.559150
$613$	−137.311	−	512.451i	−0.223998	−	0.835973i	−0.982803	−	0.184655i	$-0.940883\pi$
$613$	−137.311	−	512.451i	−0.223998	−	0.835973i	0.758805	−	0.651318i	$-0.225783\pi$
$614$	−2.62178	+	4.54105i	−0.00427000	+	0.00739585i
$615$	−159.825	+	92.2750i	−0.259878	+	0.150041i
$616$	80.8513	−	80.8513i	0.131252	−	0.131252i
$617$	536.185	+	143.670i	0.869020	+	0.232853i	0.665664	−	0.746252i	$-0.268148\pi$
$617$	536.185	+	143.670i	0.869020	+	0.232853i	0.203356	+	0.979105i	$0.434815\pi$
$618$	14.7846	−	55.1769i	0.0239233	−	0.0892830i
$619$	501.483	+	501.483i	0.810151	+	0.810151i	0.984656	−	0.174505i	$-0.0558327\pi$
$619$	501.483	+	501.483i	0.810151	+	0.810151i	−0.174505	+	0.984656i	$0.555833\pi$
$620$	−80.8513	−	140.038i	−0.130405	−	0.225869i
$621$	−394.558	−	227.798i	−0.635359	−	0.366824i
$622$	−527.338	+	141.300i	−0.847811	+	0.227170i
$623$		−	425.414i		−	0.682847i
$624$	−15.9615	+	88.6410i	−0.0255794	+	0.142053i
$625$	−211.000			−0.337600
$626$	12.8616	+	48.0000i	0.0205456	+	0.0766773i
$627$	114.696	−	198.660i	0.182928	−	0.316841i
$628$	24.9948	−	14.4308i	0.0398007	−	0.0229790i
$629$	443.781	−	443.781i	0.705535	−	0.705535i
$630$	157.923	+	42.3154i	0.250672	+	0.0671672i
$631$	−54.9524	+	205.085i	−0.0870878	+	0.325016i	−0.995701	−	0.0926217i	$-0.970475\pi$
$631$	−54.9524	+	205.085i	−0.0870878	+	0.325016i	0.908614	+	0.417638i	$0.137142\pi$
$632$	−28.7077	−	28.7077i	−0.0454235	−	0.0454235i
$633$	47.2039	+	81.7595i	0.0745717	+	0.129162i
$634$	21.7039	+	12.5307i	0.0342333	+	0.0197646i
$635$	−403.389	+	108.088i	−0.635258	+	0.170217i
$636$		−	277.492i		−	0.436309i
$637$	56.6776	+	157.496i	0.0889758	+	0.247246i
$638$	5.18069			0.00812020
$639$	11.3116	+	42.2154i	0.0177020	+	0.0660648i
$640$	13.8564	−	24.0000i	0.0216506	−	0.0375000i
$641$	−69.3499	+	40.0392i	−0.108190	+	0.0624636i	−0.553119	−	0.833102i	$-0.686562\pi$
$641$	−69.3499	+	40.0392i	−0.108190	+	0.0624636i	0.444929	+	0.895566i	$0.353229\pi$
$642$	138.100	−	138.100i	0.215109	−	0.215109i
$643$	−543.346	−	145.589i	−0.845017	−	0.226422i	−0.189763	−	0.981830i	$-0.560772\pi$
$643$	−543.346	−	145.589i	−0.845017	−	0.226422i	−0.655254	+	0.755408i	$0.727439\pi$
$644$	−71.4026	+	266.478i	−0.110874	+	0.413786i
$645$	−220.923	−	220.923i	−0.342516	−	0.342516i
$646$	519.643	+	900.048i	0.804401	+	1.39326i
$647$	−1005.44	−	580.493i	−1.55401	−	0.897208i	−0.997809	−	0.0661597i	$-0.978925\pi$
$647$	−1005.44	−	580.493i	−1.55401	−	0.897208i	−0.556200	−	0.831048i	$-0.687741\pi$
$648$	−24.5885	+	6.58846i	−0.0379452	+	0.0101674i
$649$			201.746i			0.310857i
$650$	−316.046	−	148.772i	−0.486224	−	0.228881i
$651$	−449.709			−0.690797
$652$	12.8076	+	47.7987i	0.0196436	+	0.0733109i
$653$	−220.045	+	381.129i	−0.336975	+	0.583658i	−0.983862	−	0.178928i	$-0.942737\pi$
$653$	−220.045	+	381.129i	−0.336975	+	0.583658i	0.646887	+	0.762586i	$0.276071\pi$
$654$	310.965	−	179.536i	0.475482	−	0.274520i
$655$	−77.6846	+	77.6846i	−0.118603	+	0.118603i
$656$	−168.067	−	45.0333i	−0.256199	−	0.0686484i
$657$	−28.0347	+	104.627i	−0.0426708	+	0.159250i
$658$	367.104	+	367.104i	0.557908	+	0.557908i
$659$	−274.521	−	475.485i	−0.416572	−	0.721524i	0.579020	−	0.815313i	$-0.303435\pi$
$659$	−274.521	−	475.485i	−0.416572	−	0.721524i	−0.995592	+	0.0937891i	$0.970102\pi$
$660$	−37.7654	−	21.8038i	−0.0572203	−	0.0330361i
$661$	784.429	−	210.187i	1.18673	−	0.317983i	0.389137	−	0.921180i	$-0.372773\pi$
$661$	784.429	−	210.187i	1.18673	−	0.317983i	0.797593	+	0.603196i	$0.206106\pi$
$662$			365.965i			0.552818i
$663$	−414.515	+	490.377i	−0.625212	+	0.739633i
$664$	351.349			0.529140
$665$	−128.515	−	479.624i	−0.193255	−	0.721239i
$666$	93.3731	−	161.727i	0.140200	−	0.242833i
$667$	−10.8252	+	6.24991i	−0.0162296	+	0.00937018i
$668$	−82.9808	+	82.9808i	−0.124223	+	0.124223i
$669$	−254.653	−	68.2339i	−0.380647	−	0.101994i
$670$	44.4782	−	165.995i	0.0663854	−	0.247754i
$671$	−103.960	−	103.960i	−0.154932	−	0.154932i
$672$	−38.5359	−	66.7461i	−0.0573451	−	0.0993246i
$673$	367.385	+	212.110i	0.545891	+	0.315170i	0.747463	−	0.664303i	$-0.231272\pi$
$673$	367.385	+	212.110i	0.545891	+	0.315170i	−0.201572	+	0.979474i	$0.564605\pi$
$674$	−129.699	+	34.7527i	−0.192431	+	0.0515618i
$675$			493.634i			0.731310i
$676$	−215.378	−	260.492i	−0.318607	−	0.385344i
$677$	124.308			0.183616			0.0918078	−	0.995777i	$-0.470735\pi$
$677$	124.308			0.183616			0.0918078	+	0.995777i	$0.470735\pi$
$678$	112.214	+	418.786i	0.165507	+	0.617679i
$679$	−535.392	+	927.325i	−0.788500	+	1.36572i
$680$	171.100	−	98.7846i	0.251618	−	0.145271i
$681$	−263.706	+	263.706i	−0.387233	+	0.387233i
$682$	−231.722	−	62.0897i	−0.339768	−	0.0910405i
$683$	−11.2551	+	42.0045i	−0.0164789	+	0.0614999i	−0.973676	−	0.227938i	$-0.926802\pi$
$683$	−11.2551	+	42.0045i	−0.0164789	+	0.0614999i	0.957197	+	0.289438i	$0.0934684\pi$
$684$	218.669	+	218.669i	0.319692	+	0.319692i
$685$	115.356	+	199.802i	0.168403	+	0.291682i
$686$	348.021	+	200.930i	0.507319	+	0.292901i
$687$	21.8494	−	5.85452i	0.0318040	−	0.00852186i
$688$		−	294.564i		−	0.428145i
$689$	795.300	+	672.267i	1.15428	+	0.975713i
$690$	105.215			0.152486
$691$	−195.327	−	728.970i	−0.282673	−	1.05495i	−0.950523	−	0.310654i	$-0.899452\pi$
$691$	−195.327	−	728.970i	−0.282673	−	1.05495i	0.667850	−	0.744295i	$-0.267215\pi$
$692$	71.7602	−	124.292i	0.103700	−	0.179613i
$693$	210.058	−	121.277i	0.303114	−	0.175003i
$694$	−104.460	+	104.460i	−0.150519	+	0.150519i
$695$	−45.4186	−	12.1699i	−0.0653505	−	0.0175106i
$696$	0.903811	−	3.37307i	0.00129858	−	0.00484636i
$697$	−877.125	−	877.125i	−1.25843	−	1.25843i
$698$	57.1558	+	98.9967i	0.0818851	+	0.141829i
$699$	595.592	+	343.865i	0.852063	+	0.491939i
$700$	288.727	−	77.3641i	0.412467	−	0.110520i
$701$			847.213i			1.20858i	0.796766	+	0.604289i	$0.206543\pi$
$701$			847.213i			1.20858i	−0.796766	+	0.604289i	$0.793457\pi$
$702$	−203.433	+	432.163i	−0.289790	+	0.615617i
$703$	−567.161			−0.806773
$704$	−10.6410	−	39.7128i	−0.0151151	−	0.0564102i
$705$	99.0000	−	171.473i	0.140426	−	0.243224i
$706$	−208.886	+	120.601i	−0.295873	+	0.170822i
$707$	−341.981	+	341.981i	−0.483708	+	0.483708i
$708$	131.354	+	35.1962i	0.185528	+	0.0497121i
$709$	−209.535	+	781.996i	−0.295536	+	1.10296i	0.645254	+	0.763968i	$0.276751\pi$
$709$	−209.535	+	781.996i	−0.295536	+	1.10296i	−0.940791	+	0.338988i	$0.889915\pi$
$710$	−17.8423	−	17.8423i	−0.0251300	−	0.0251300i
$711$	−43.0615	−	74.5847i	−0.0605647	−	0.104901i
$712$	−132.473	−	76.4833i	−0.186058	−	0.107420i
$713$	559.092	−	149.808i	0.784140	−	0.210110i
$714$		−	549.458i		−	0.769548i
$715$	153.983	−	55.4134i	0.215360	−	0.0775013i
$716$	−321.349			−0.448811
$717$	−125.963	−	470.102i	−0.175681	−	0.655651i
$718$	−102.058	+	176.769i	−0.142142	+	0.246197i
$719$	−685.421	+	395.728i	−0.953298	+	0.550387i	−0.894104	−	0.447860i	$-0.852186\pi$
$719$	−685.421	+	395.728i	−0.953298	+	0.550387i	−0.0591940	+	0.998246i	$0.518853\pi$
$720$	41.5692	−	41.5692i	0.0577350	−	0.0577350i
$721$	−177.191	−	47.4782i	−0.245757	−	0.0658505i
$722$	110.947	−	414.061i	0.153667	−	0.573492i
$723$	400.662	+	400.662i	0.554166	+	0.554166i
$724$	−143.072	−	247.808i	−0.197613	−	0.342276i
$725$	11.7290	+	6.77172i	0.0161779	+	0.00934031i
$726$	223.799	−	59.9667i	0.308263	−	0.0825987i
$727$		−	1014.52i		−	1.39549i	−0.716345	−	0.697746i	$-0.754186\pi$
$727$		−	1014.52i		−	1.39549i	0.716345	−	0.697746i	$-0.245814\pi$
$728$	284.655	+	51.2576i	0.391010	+	0.0704088i
$729$	351.000			0.481481
$730$	−16.1858	−	60.4064i	−0.0221724	−	0.0827485i
$731$	1050.00	−	1818.65i	1.43639	−	2.48789i
$732$	−85.8231	+	49.5500i	−0.117245	+	0.0676912i
$733$	769.697	−	769.697i	1.05006	−	1.05006i	0.0513857	−	0.998679i	$-0.483636\pi$
$733$	769.697	−	769.697i	1.05006	−	1.05006i	0.998679	−	0.0513857i	$-0.0163638\pi$
$734$	652.566	+	174.855i	0.889054	+	0.238221i
$735$	−14.1384	+	52.7654i	−0.0192360	+	0.0717896i
$736$	70.1436	+	70.1436i	0.0953038	+	0.0953038i
$737$	−127.476	−	220.794i	−0.172966	−	0.299585i
$738$	−319.650	−	184.550i	−0.433130	−	0.250068i
$739$	−255.155	+	68.3686i	−0.345271	+	0.0925150i	−0.427287	−	0.904116i	$-0.640531\pi$
$739$	−255.155	+	68.3686i	−0.345271	+	0.0925150i	0.0820164	+	0.996631i	$0.473864\pi$
$740$			107.818i			0.145700i
$741$	578.235	−	48.4763i	0.780344	−	0.0654201i
$742$	−891.118			−1.20097
$743$	202.345	+	755.161i	0.272335	+	1.01637i	0.957606	+	0.288080i	$0.0930168\pi$
$743$	202.345	+	755.161i	0.272335	+	1.01637i	−0.685272	+	0.728287i	$0.740317\pi$
$744$	−80.8513	+	140.038i	−0.108671	+	0.188224i
$745$	79.1980	−	45.7250i	0.106306	−	0.0613759i
$746$	−515.487	+	515.487i	−0.691001	+	0.691001i
$747$	719.927	+	192.904i	0.963757	+	0.258238i
$748$	75.8616	−	283.119i	0.101419	−	0.378502i
$749$	−443.484	−	443.484i	−0.592101	−	0.592101i
$750$	−132.000	−	228.631i	−0.176000	−	0.304841i
$751$	640.663	+	369.887i	0.853080	+	0.492526i	0.861689	−	0.507437i	$-0.169407\pi$
$751$	640.663	+	369.887i	0.853080	+	0.492526i	−0.00860865	+	0.999963i	$0.502740\pi$
$752$	180.315	−	48.3154i	0.239781	−	0.0642491i
$753$			268.535i			0.356620i
$754$	7.47768	+	10.7621i	0.00991735	+	0.0142733i
$755$	−559.128			−0.740567
$756$	−105.788	−	394.808i	−0.139932	−	0.522232i
$757$	−368.437	+	638.152i	−0.486707	+	0.843001i	−0.999883	−	0.0152821i	$-0.995135\pi$
$757$	−368.437	+	638.152i	−0.486707	+	0.843001i	0.513176	+	0.858283i	$0.328469\pi$
$758$	335.242	−	193.552i	0.442271	−	0.255345i
$759$	110.375	−	110.375i	0.145422	−	0.145422i
$760$	−172.459	−	46.2102i	−0.226920	−	0.0608029i
$761$	370.661	−	1383.33i	0.487071	−	1.81777i	−0.0834780	−	0.996510i	$-0.526603\pi$
$761$	370.661	−	1383.33i	0.487071	−	1.81777i	0.570549	−	0.821264i	$-0.306731\pi$
$762$	295.301	+	295.301i	0.387534	+	0.387534i
$763$	−576.548	−	998.611i	−0.755633	−

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.73205 - 1.73205i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-2.03590 + 7.59808i) q^{7} +(2.00000 + 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.73205 - 1.73205i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-2.03590 + 7.59808i) q^{7} +(2.00000 + 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(-4.96410 + 1.33013i) q^{11} +3.46410i q^{12} +(-9.92820 - 8.39230i) q^{13} +11.1244 q^{14} +(-1.09808 - 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(24.6962 - 14.2583i) q^{17} +(6.00000 - 6.00000i) q^{18} +(-24.8923 - 6.66987i) q^{19} +(-1.26795 + 4.73205i) q^{20} +(9.63397 + 9.63397i) q^{21} +(3.63397 + 6.29423i) q^{22} +(-15.1865 - 8.76795i) q^{23} +(4.73205 - 1.26795i) q^{24} +19.0000i q^{25} +(-7.83013 + 16.6340i) q^{26} +25.9808 q^{27} +(-4.07180 - 15.1962i) q^{28} +(0.356406 - 0.617314i) q^{29} +(-5.19615 + 3.00000i) q^{30} +(-23.3397 + 23.3397i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-2.30385 + 8.59808i) q^{33} +(-28.5167 - 28.5167i) q^{34} +(9.63397 + 16.6865i) q^{35} +(-10.3923 - 6.00000i) q^{36} +(21.2583 - 5.69615i) q^{37} +36.4449i q^{38} +(-21.1865 + 7.62436i) q^{39} +6.92820 q^{40} +(-11.2583 - 42.0167i) q^{41} +(9.63397 - 16.6865i) q^{42} +(63.7750 - 36.8205i) q^{43} +(7.26795 - 7.26795i) q^{44} +(14.1962 + 3.80385i) q^{45} +(-6.41858 + 23.9545i) q^{46} +(33.0000 + 33.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-11.1506 - 6.43782i) q^{49} +(25.9545 - 6.95448i) q^{50} -49.3923i q^{51} +(25.5885 + 4.60770i) q^{52} -80.1051 q^{53} +(-9.50962 - 35.4904i) q^{54} +(-6.29423 + 10.9019i) q^{55} +(-19.2679 + 11.1244i) q^{56} +(-31.5622 + 31.5622i) q^{57} +(-0.973721 - 0.260908i) q^{58} +(10.1603 - 37.9186i) q^{59} +(6.00000 + 6.00000i) q^{60} +(14.3038 + 24.7750i) q^{61} +(40.4256 + 23.3397i) q^{62} +(-45.5885 + 12.2154i) q^{63} +8.00000i q^{64} +(-31.7321 + 2.66025i) q^{65} +12.5885 q^{66} +(12.8397 + 47.9186i) q^{67} +(-28.5167 + 49.3923i) q^{68} +(-26.3038 + 15.1865i) q^{69} +(19.2679 - 19.2679i) q^{70} +(7.03590 + 1.88526i) q^{71} +(-4.39230 + 16.3923i) q^{72} +(12.7654 + 12.7654i) q^{73} +(-15.5622 - 26.9545i) q^{74} +(28.5000 + 16.4545i) q^{75} +(49.7846 - 13.3397i) q^{76} -40.4256i q^{77} +(18.1699 + 26.1506i) q^{78} -14.3538 q^{79} +(-2.53590 - 9.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-53.2750 + 30.7583i) q^{82} +(87.8372 - 87.8372i) q^{83} +(-26.3205 - 7.05256i) q^{84} +(18.0788 - 67.4711i) q^{85} +(-73.6410 - 73.6410i) q^{86} +(-0.617314 - 1.06922i) q^{87} +(-12.5885 - 7.26795i) q^{88} +(-52.2391 + 13.9974i) q^{89} -20.7846i q^{90} +(83.9782 - 58.3494i) q^{91} +35.0718 q^{92} +(14.7968 + 55.2224i) q^{93} +(33.0000 - 57.1577i) q^{94} +(-54.6673 + 31.5622i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(131.488 + 35.2321i) q^{97} +(-4.71281 + 17.5885i) q^{98} +(-21.8038 - 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{6} - 22 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^6 - 22 * q^7 + 8 * q^8 + 12 * q^9	\( 4 q + 2 q^{2} - 6 q^{6} - 22 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} + 6 q^{15} + 8 q^{16} + 78 q^{17} + 24 q^{18} - 58 q^{19} - 12 q^{20} + 42 q^{21} + 18 q^{22} + 12 q^{23} + 12 q^{24} - 14 q^{26} - 44 q^{28} - 54 q^{29} - 128 q^{31} - 8 q^{32} - 30 q^{33} - 24 q^{34} + 42 q^{35} + 40 q^{37} - 12 q^{39} + 42 q^{42} + 120 q^{43} + 36 q^{44} + 36 q^{45} + 54 q^{46} + 132 q^{47} + 42 q^{49} + 38 q^{50} + 40 q^{52} - 168 q^{53} - 90 q^{54} + 6 q^{55} - 84 q^{56} - 102 q^{57} - 42 q^{58} + 6 q^{59} + 24 q^{60} + 78 q^{61} - 60 q^{62} - 120 q^{63} - 120 q^{65} - 12 q^{66} + 86 q^{67} - 24 q^{68} - 126 q^{69} + 84 q^{70} + 42 q^{71} + 24 q^{72} - 136 q^{73} - 38 q^{74} + 114 q^{75} + 116 q^{76} + 90 q^{78} + 192 q^{79} - 24 q^{80} - 18 q^{81} - 78 q^{82} + 192 q^{83} - 36 q^{84} - 42 q^{85} - 156 q^{86} - 96 q^{87} + 12 q^{88} - 60 q^{89} + 38 q^{91} + 168 q^{92} + 222 q^{93} + 132 q^{94} - 42 q^{95} + 280 q^{97} + 92 q^{98} - 108 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^6 - 22 * q^7 + 8 * q^8 + 12 * q^9 - 12 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 + 6 * q^15 + 8 * q^16 + 78 * q^17 + 24 * q^18 - 58 * q^19 - 12 * q^20 + 42 * q^21 + 18 * q^22 + 12 * q^23 + 12 * q^24 - 14 * q^26 - 44 * q^28 - 54 * q^29 - 128 * q^31 - 8 * q^32 - 30 * q^33 - 24 * q^34 + 42 * q^35 + 40 * q^37 - 12 * q^39 + 42 * q^42 + 120 * q^43 + 36 * q^44 + 36 * q^45 + 54 * q^46 + 132 * q^47 + 42 * q^49 + 38 * q^50 + 40 * q^52 - 168 * q^53 - 90 * q^54 + 6 * q^55 - 84 * q^56 - 102 * q^57 - 42 * q^58 + 6 * q^59 + 24 * q^60 + 78 * q^61 - 60 * q^62 - 120 * q^63 - 120 * q^65 - 12 * q^66 + 86 * q^67 - 24 * q^68 - 126 * q^69 + 84 * q^70 + 42 * q^71 + 24 * q^72 - 136 * q^73 - 38 * q^74 + 114 * q^75 + 116 * q^76 + 90 * q^78 + 192 * q^79 - 24 * q^80 - 18 * q^81 - 78 * q^82 + 192 * q^83 - 36 * q^84 - 42 * q^85 - 156 * q^86 - 96 * q^87 + 12 * q^88 - 60 * q^89 + 38 * q^91 + 168 * q^92 + 222 * q^93 + 132 * q^94 - 42 * q^95 + 280 * q^97 + 92 * q^98 - 108 * q^99

Introduction

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