LMFDB - Embedded newform 418.2.b.c.417.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(417,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("418.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14584320320.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} + 11x^{5} - 11x^{4} + 32x^{3} + 44x^{2} - 18x + 46 $ x^8 - x^7 + 4x^6 + 11x^5 - 11x^4 + 32x^3 + 44x^2 - 18x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			417.5
Root			$1.20394 - 1.50360i$ of defining polynomial
Character	$\chi$	$=$	418.417
Dual form			418.2.b.c.417.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.04112i q^{3} +1.00000 q^{4} +2.40788 q^{5} -1.04112i q^{6} +3.19266i q^{7} -1.00000 q^{8} +1.91607 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.04112i q^{3} +1.00000 q^{4} +2.40788 q^{5} -1.04112i q^{6} +3.19266i q^{7} -1.00000 q^{8} +1.91607 q^{9} -2.40788 q^{10} +(-2.74140 + 1.86674i) q^{11} +1.04112i q^{12} +0.0126910 q^{13} -3.19266i q^{14} +2.50690i q^{15} +1.00000 q^{16} -1.96608i q^{17} -1.91607 q^{18} +(3.20578 - 2.95347i) q^{19} +2.40788 q^{20} -3.32395 q^{21} +(2.74140 - 1.86674i) q^{22} -1.11817 q^{23} -1.04112i q^{24} +0.797897 q^{25} -0.0126910 q^{26} +5.11822i q^{27} +3.19266i q^{28} -1.28971 q^{29} -2.50690i q^{30} +8.41384i q^{31} -1.00000 q^{32} +(-1.94350 - 2.85413i) q^{33} +1.96608i q^{34} +7.68755i q^{35} +1.91607 q^{36} -1.37153i q^{37} +(-3.20578 + 2.95347i) q^{38} +0.0132128i q^{39} -2.40788 q^{40} +5.68490 q^{41} +3.32395 q^{42} +4.28751i q^{43} +(-2.74140 + 1.86674i) q^{44} +4.61366 q^{45} +1.11817 q^{46} -2.23634 q^{47} +1.04112i q^{48} -3.19309 q^{49} -0.797897 q^{50} +2.04693 q^{51} +0.0126910 q^{52} +6.07048i q^{53} -5.11822i q^{54} +(-6.60097 + 4.49489i) q^{55} -3.19266i q^{56} +(3.07492 + 3.33761i) q^{57} +1.28971 q^{58} -12.6071i q^{59} +2.50690i q^{60} -6.10561i q^{61} -8.41384i q^{62} +6.11735i q^{63} +1.00000 q^{64} +0.0305584 q^{65} +(1.94350 + 2.85413i) q^{66} +2.91295i q^{67} -1.96608i q^{68} -1.16415i q^{69} -7.68755i q^{70} -9.82353i q^{71} -1.91607 q^{72} +6.87241i q^{73} +1.37153i q^{74} +0.830708i q^{75} +(3.20578 - 2.95347i) q^{76} +(-5.95987 - 8.75237i) q^{77} -0.0132128i q^{78} +14.1307 q^{79} +2.40788 q^{80} +0.419508 q^{81} -5.68490 q^{82} -9.28506i q^{83} -3.32395 q^{84} -4.73408i q^{85} -4.28751i q^{86} -1.34275i q^{87} +(2.74140 - 1.86674i) q^{88} -6.49279i q^{89} -4.61366 q^{90} +0.0405180i q^{91} -1.11817 q^{92} -8.75982 q^{93} +2.23634 q^{94} +(7.71914 - 7.11161i) q^{95} -1.04112i q^{96} +4.73408i q^{97} +3.19309 q^{98} +(-5.25271 + 3.57680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.04112i			0.601092i	0.953767	+	0.300546i	$0.0971688\pi$
$3$			1.04112i			0.601092i	−0.953767	+	0.300546i	$0.902831\pi$
$4$	1.00000			0.500000
$5$	2.40788			1.07684			0.538419	−	0.842677i	$-0.319022\pi$
$5$	2.40788			1.07684			0.538419	+	0.842677i	$0.319022\pi$
$6$		−	1.04112i		−	0.425036i
$7$			3.19266i			1.20671i	0.797472	+	0.603356i	$0.206170\pi$
$7$			3.19266i			1.20671i	−0.797472	+	0.603356i	$0.793830\pi$
$8$	−1.00000			−0.353553
$9$	1.91607			0.638689
$10$	−2.40788			−0.761439
$11$	−2.74140	+	1.86674i	−0.826563	+	0.562843i
$11$	−2.74140	+	1.86674i	−0.826563	+	0.562843i
$12$			1.04112i			0.300546i
$13$	0.0126910			0.00351984			0.00175992	−	0.999998i	$-0.499440\pi$
$13$	0.0126910			0.00351984			0.00175992	+	0.999998i	$0.499440\pi$
$14$		−	3.19266i		−	0.853275i
$15$			2.50690i			0.647278i
$16$	1.00000			0.250000
$17$		−	1.96608i		−	0.476844i	−0.971162	−	0.238422i	$-0.923370\pi$
$17$		−	1.96608i		−	0.476844i	0.971162	−	0.238422i	$-0.0766301\pi$
$18$	−1.91607			−0.451621
$19$	3.20578	−	2.95347i	0.735456	−	0.677572i
$19$	3.20578	−	2.95347i	0.735456	−	0.677572i
$20$	2.40788			0.538419
$21$	−3.32395			−0.725345
$22$	2.74140	−	1.86674i	0.584469	−	0.397990i
$23$	−1.11817			−0.233154			−0.116577	−	0.993182i	$-0.537192\pi$
$23$	−1.11817			−0.233154			−0.116577	+	0.993182i	$0.537192\pi$
$24$		−	1.04112i		−	0.212518i
$25$	0.797897			0.159579
$26$	−0.0126910			−0.00248891
$27$			5.11822i			0.985002i
$28$			3.19266i			0.603356i
$29$	−1.28971			−0.239494			−0.119747	−	0.992804i	$-0.538208\pi$
$29$	−1.28971			−0.239494			−0.119747	+	0.992804i	$0.538208\pi$
$30$		−	2.50690i		−	0.457695i
$31$			8.41384i			1.51117i	0.655051	+	0.755585i	$0.272647\pi$
$31$			8.41384i			1.51117i	−0.655051	+	0.755585i	$0.727353\pi$
$32$	−1.00000			−0.176777
$33$	−1.94350	−	2.85413i	−0.338321	−	0.496840i
$34$			1.96608i			0.337180i
$35$			7.68755i			1.29943i
$36$	1.91607			0.319344
$37$		−	1.37153i		−	0.225478i	−0.993625	−	0.112739i	$-0.964038\pi$
$37$		−	1.37153i		−	0.225478i	0.993625	−	0.112739i	$-0.0359624\pi$
$38$	−3.20578	+	2.95347i	−0.520046	+	0.479116i
$39$			0.0132128i			0.00211575i
$40$	−2.40788			−0.380720
$41$	5.68490			0.887833			0.443916	−	0.896068i	$-0.353589\pi$
$41$	5.68490			0.887833			0.443916	+	0.896068i	$0.353589\pi$
$42$	3.32395			0.512896
$43$			4.28751i			0.653840i	0.945052	+	0.326920i	$0.106011\pi$
$43$			4.28751i			0.653840i	−0.945052	+	0.326920i	$0.893989\pi$
$44$	−2.74140	+	1.86674i	−0.413282	+	0.281422i
$45$	4.61366			0.687764
$46$	1.11817			0.164865
$47$	−2.23634			−0.326203			−0.163102	−	0.986609i	$-0.552150\pi$
$47$	−2.23634			−0.326203			−0.163102	+	0.986609i	$0.552150\pi$
$48$			1.04112i			0.150273i
$49$	−3.19309			−0.456156
$50$	−0.797897			−0.112840
$51$	2.04693			0.286627
$52$	0.0126910			0.00175992
$53$			6.07048i			0.833845i	0.908942	+	0.416923i	$0.136891\pi$
$53$			6.07048i			0.833845i	−0.908942	+	0.416923i	$0.863109\pi$
$54$		−	5.11822i		−	0.696502i
$55$	−6.60097	+	4.49489i	−0.890075	+	0.606091i
$56$		−	3.19266i		−	0.426637i
$57$	3.07492	+	3.33761i	0.407283	+	0.442077i
$58$	1.28971			0.169348
$59$		−	12.6071i		−	1.64130i	−0.571428	−	0.820652i	$-0.693610\pi$
$59$		−	12.6071i		−	1.64130i	0.571428	−	0.820652i	$-0.306390\pi$
$60$			2.50690i			0.323639i
$61$		−	6.10561i		−	0.781744i	−0.920445	−	0.390872i	$-0.872174\pi$
$61$		−	6.10561i		−	0.781744i	0.920445	−	0.390872i	$-0.127826\pi$
$62$		−	8.41384i		−	1.06856i
$63$			6.11735i			0.770714i
$64$	1.00000			0.125000
$65$	0.0305584			0.00379030
$66$	1.94350	+	2.85413i	0.239229	+	0.351319i
$67$			2.91295i			0.355874i	0.984042	+	0.177937i	$0.0569423\pi$
$67$			2.91295i			0.355874i	−0.984042	+	0.177937i	$0.943058\pi$
$68$		−	1.96608i		−	0.238422i
$69$		−	1.16415i		−	0.140147i
$70$		−	7.68755i		−	0.918838i
$71$		−	9.82353i		−	1.16584i	−0.812530	−	0.582919i	$-0.801910\pi$
$71$		−	9.82353i		−	1.16584i	0.812530	−	0.582919i	$-0.198090\pi$
$72$	−1.91607			−0.225811
$73$			6.87241i			0.804355i	0.915562	+	0.402178i	$0.131747\pi$
$73$			6.87241i			0.804355i	−0.915562	+	0.402178i	$0.868253\pi$
$74$			1.37153i			0.159437i
$75$			0.830708i			0.0959219i
$76$	3.20578	−	2.95347i	0.367728	−	0.338786i
$77$	−5.95987	−	8.75237i	−0.679190	−	0.997425i
$78$		−	0.0132128i		−	0.00149606i
$79$	14.1307			1.58983			0.794914	−	0.606722i	$-0.207516\pi$
$79$	14.1307			1.58983			0.794914	+	0.606722i	$0.207516\pi$
$80$	2.40788			0.269209
$81$	0.419508			0.0466120
$82$	−5.68490			−0.627793
$83$		−	9.28506i		−	1.01917i	−0.860421	−	0.509584i	$-0.829799\pi$
$83$		−	9.28506i		−	1.01917i	0.860421	−	0.509584i	$-0.170201\pi$
$84$	−3.32395			−0.362673
$85$		−	4.73408i		−	0.513484i
$86$		−	4.28751i		−	0.462335i
$87$		−	1.34275i		−	0.143958i
$88$	2.74140	−	1.86674i	0.292234	−	0.198995i
$89$		−	6.49279i		−	0.688234i	−0.938927	−	0.344117i	$-0.888178\pi$
$89$		−	6.49279i		−	0.688234i	0.938927	−	0.344117i	$-0.111822\pi$
$90$	−4.61366			−0.486323
$91$			0.0405180i			0.00424744i
$92$	−1.11817			−0.116577
$93$	−8.75982			−0.908351
$94$	2.23634			0.230661
$95$	7.71914	−	7.11161i	0.791967	−	0.729635i
$96$		−	1.04112i		−	0.106259i
$97$			4.73408i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$97$			4.73408i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$98$	3.19309			0.322551
$99$	−5.25271	+	3.57680i	−0.527917	+	0.359482i
$100$	0.797897			0.0797897
$101$		−	6.49279i		−	0.646056i	−0.946389	−	0.323028i	$-0.895299\pi$
$101$		−	6.49279i		−	0.646056i	0.946389	−	0.323028i	$-0.104701\pi$
$102$	−2.04693			−0.202676
$103$		−	11.3673i		−	1.12005i	−0.828474	−	0.560027i	$-0.810791\pi$
$103$		−	11.3673i		−	1.12005i	0.828474	−	0.560027i	$-0.189209\pi$
$104$	−0.0126910			−0.00124445
$105$	−8.00368			−0.781079
$106$		−	6.07048i		−	0.589618i
$107$	−0.794220			−0.0767802			−0.0383901	−	0.999263i	$-0.512223\pi$
$107$	−0.794220			−0.0767802			−0.0383901	+	0.999263i	$0.512223\pi$
$108$			5.11822i			0.492501i
$109$	−5.38100			−0.515406			−0.257703	−	0.966224i	$-0.582966\pi$
$109$	−5.38100			−0.515406			−0.257703	+	0.966224i	$0.582966\pi$
$110$	6.60097	−	4.49489i	0.629378	−	0.428571i
$111$	1.42793			0.135533
$112$			3.19266i			0.301678i
$113$		−	12.2010i		−	1.14778i	−0.818933	−	0.573889i	$-0.805434\pi$
$113$		−	12.2010i		−	1.14778i	0.818933	−	0.573889i	$-0.194566\pi$
$114$	−3.07492	−	3.33761i	−0.287993	−	0.312595i
$115$	−2.69242			−0.251069
$116$	−1.28971			−0.119747
$117$	0.0243168			0.00224808
$118$			12.6071i			1.16058i
$119$	6.27702			0.575414
$120$		−	2.50690i		−	0.228847i
$121$	4.03056	−	10.2350i	0.366414	−	0.930452i
$122$			6.10561i			0.552776i
$123$			5.91868i			0.533669i
$124$			8.41384i			0.755585i
$125$	−10.1182			−0.904997
$126$		−	6.11735i		−	0.544977i
$127$	−19.7622			−1.75361			−0.876807	−	0.480842i	$-0.840331\pi$
$127$	−19.7622			−1.75361			−0.876807	+	0.480842i	$0.840331\pi$
$128$	−1.00000			−0.0883883
$129$	−4.46382			−0.393018
$130$	−0.0305584			−0.00268015
$131$		−	14.9066i		−	1.30240i	−0.758907	−	0.651199i	$-0.774266\pi$
$131$		−	14.9066i		−	1.30240i	0.758907	−	0.651199i	$-0.225734\pi$
$132$	−1.94350	−	2.85413i	−0.169160	−	0.248420i
$133$	9.42943	+	10.2350i	0.817635	+	0.887484i
$134$		−	2.91295i		−	0.251641i
$135$			12.3241i			1.06069i
$136$			1.96608i			0.168590i
$137$	3.70645			0.316663			0.158332	−	0.987386i	$-0.449388\pi$
$137$	3.70645			0.316663			0.158332	+	0.987386i	$0.449388\pi$
$138$			1.16415i			0.0990990i
$139$			12.7388i			1.08049i	0.841507	+	0.540247i	$0.181669\pi$
$139$			12.7388i			1.08049i	−0.841507	+	0.540247i	$0.818331\pi$
$140$			7.68755i			0.649717i
$141$		−	2.32830i		−	0.196078i
$142$			9.82353i			0.824372i
$143$	−0.0347911	+	0.0236908i	−0.00290937	+	0.00198112i
$144$	1.91607			0.159672
$145$	−3.10548			−0.257896
$146$		−	6.87241i		−	0.568765i
$147$		−	3.32439i		−	0.274191i
$148$		−	1.37153i		−	0.112739i
$149$		−	1.19928i		−	0.0982487i	−0.998793	−	0.0491244i	$-0.984357\pi$
$149$		−	1.19928i		−	0.0982487i	0.998793	−	0.0491244i	$-0.0156431\pi$
$150$		−	0.830708i		−	0.0678270i
$151$	−7.89436			−0.642434			−0.321217	−	0.947006i	$-0.604092\pi$
$151$	−7.89436			−0.642434			−0.321217	+	0.947006i	$0.604092\pi$
$152$	−3.20578	+	2.95347i	−0.260023	+	0.239558i
$153$		−	3.76714i		−	0.304555i
$154$	5.95987	+	8.75237i	0.480260	+	0.705286i
$155$			20.2595i			1.62728i
$156$			0.0132128i			0.00105787i
$157$	22.3453			1.78335			0.891676	−	0.452675i	$-0.149530\pi$
$157$	22.3453			1.78335			0.891676	+	0.452675i	$0.149530\pi$
$158$	−14.1307			−1.12418
$159$	−6.32011			−0.501217
$160$	−2.40788			−0.190360
$161$		−	3.56994i		−	0.281350i
$162$	−0.419508			−0.0329597
$163$	11.3403			0.888242			0.444121	−	0.895967i	$-0.353516\pi$
$163$	11.3403			0.888242			0.444121	+	0.895967i	$0.353516\pi$
$164$	5.68490			0.443916
$165$	−4.67973	−	6.87241i	−0.364316	−	0.535017i
$166$			9.28506i			0.720661i
$167$	13.6580			1.05689			0.528445	−	0.848968i	$-0.322775\pi$
$167$	13.6580			1.05689			0.528445	+	0.848968i	$0.322775\pi$
$168$	3.32395			0.256448
$169$	−12.9998			−0.999988
$170$			4.73408i			0.363088i
$171$	6.14249	−	5.65904i	0.469728	−	0.432758i
$172$			4.28751i			0.326920i
$173$	12.1524			0.923930			0.461965	−	0.886898i	$-0.347145\pi$
$173$	12.1524			0.923930			0.461965	+	0.886898i	$0.347145\pi$
$174$			1.34275i			0.101793i
$175$			2.54742i			0.192567i
$176$	−2.74140	+	1.86674i	−0.206641	+	0.140711i
$177$	13.1255			0.986575
$178$			6.49279i			0.486655i
$179$		−	5.15874i		−	0.385582i	−0.981240	−	0.192791i	$-0.938246\pi$
$179$		−	5.15874i		−	0.385582i	0.981240	−	0.192791i	$-0.0617540\pi$
$180$	4.61366			0.343882
$181$		−	15.1164i		−	1.12359i	−0.827277	−	0.561795i	$-0.810111\pi$
$181$		−	15.1164i		−	1.12359i	0.827277	−	0.561795i	$-0.189889\pi$
$182$		−	0.0405180i		−	0.00300339i
$183$	6.35668			0.469900
$184$	1.11817			0.0824325
$185$		−	3.30248i		−	0.242803i
$186$	8.75982			0.642301
$187$	3.67016	+	5.38981i	0.268389	+	0.394142i
$188$	−2.23634			−0.163102
$189$	−16.3408			−1.18861
$190$	−7.71914	+	7.11161i	−0.560005	+	0.515930i
$191$	−17.8905			−1.29451			−0.647256	−	0.762272i	$-0.724084\pi$
$191$	−17.8905			−1.29451			−0.647256	+	0.762272i	$0.724084\pi$
$192$			1.04112i			0.0751365i
$193$	0.178898			0.0128774			0.00643868	−	0.999979i	$-0.497950\pi$
$193$	0.178898			0.0128774			0.00643868	+	0.999979i	$0.497950\pi$
$194$		−	4.73408i		−	0.339887i
$195$			0.0318150i			0.00227832i
$196$	−3.19309			−0.228078
$197$		−	4.16449i		−	0.296707i	−0.988934	−	0.148354i	$-0.952603\pi$
$197$		−	4.16449i		−	0.296707i	0.988934	−	0.148354i	$-0.0473974\pi$
$198$	5.25271	−	3.57680i	0.373294	−	0.254192i
$199$	25.3365			1.79606			0.898028	−	0.439939i	$-0.145000\pi$
$199$	25.3365			1.79606			0.898028	+	0.439939i	$0.145000\pi$
$200$	−0.797897			−0.0564199
$201$	−3.03274			−0.213913
$202$			6.49279i			0.456831i
$203$		−	4.11762i		−	0.289000i
$204$	2.04693			0.143313
$205$	13.6886			0.956052
$206$			11.3673i			0.791998i
$207$	−2.14249			−0.148913
$208$	0.0126910			0.000879961
$209$	−3.27497	+	14.0810i	−0.226534	+	0.974003i
$210$	8.00368			0.552306
$211$	12.7865			0.880262			0.440131	−	0.897934i	$-0.354932\pi$
$211$	12.7865			0.880262			0.440131	+	0.897934i	$0.354932\pi$
$212$			6.07048i			0.416923i
$213$	10.2275			0.700776
$214$	0.794220			0.0542918
$215$			10.3238i			0.704079i
$216$		−	5.11822i		−	0.348251i
$217$	−26.8625			−1.82355
$218$	5.38100			0.364447
$219$	−7.15502			−0.483491
$220$	−6.60097	+	4.49489i	−0.445037	+	0.303046i
$221$		−	0.0249515i		−	0.00167842i
$222$	−1.42793			−0.0958362
$223$			26.7742i			1.79293i	0.443110	+	0.896467i	$0.353875\pi$
$223$			26.7742i			1.79293i	−0.443110	+	0.896467i	$0.646125\pi$
$224$		−	3.19266i		−	0.213319i
$225$	1.52882			0.101922
$226$			12.2010i			0.811602i
$227$	−20.5829			−1.36614			−0.683069	−	0.730354i	$-0.739355\pi$
$227$	−20.5829			−1.36614			−0.683069	+	0.730354i	$0.739355\pi$
$228$	3.07492	+	3.33761i	0.203642	+	0.221038i
$229$	2.86914			0.189598			0.0947991	−	0.995496i	$-0.469779\pi$
$229$	2.86914			0.189598			0.0947991	+	0.995496i	$0.469779\pi$
$230$	2.69242			0.177533
$231$	9.11228	−	6.20495i	0.599544	−	0.408256i
$232$	1.28971			0.0846738
$233$			22.4711i			1.47213i	0.676909	+	0.736067i	$0.263319\pi$
$233$			22.4711i			1.47213i	−0.676909	+	0.736067i	$0.736681\pi$
$234$	−0.0243168			−0.00158964
$235$	−5.38484			−0.351268
$236$		−	12.6071i		−	0.820652i
$237$			14.7118i			0.955632i
$238$	−6.27702			−0.406879
$239$			4.25239i			0.275064i	0.990497	+	0.137532i	$0.0439170\pi$
$239$			4.25239i			0.275064i	−0.990497	+	0.137532i	$0.956083\pi$
$240$			2.50690i			0.161820i
$241$	−29.6974			−1.91298			−0.956490	−	0.291765i	$-0.905757\pi$
$241$	−29.6974			−1.91298			−0.956490	+	0.291765i	$0.905757\pi$
$242$	−4.03056	+	10.2350i	−0.259094	+	0.657929i
$243$			15.7914i			1.01302i
$244$		−	6.10561i		−	0.390872i
$245$	−7.68858			−0.491205
$246$		−	5.91868i		−	0.377361i
$247$	0.0406845	−	0.0374824i	0.00258869	−	0.00238495i
$248$		−	8.41384i		−	0.534279i
$249$	9.66688			0.612613
$250$	10.1182			0.639929
$251$	1.98197			0.125101			0.0625505	−	0.998042i	$-0.480077\pi$
$251$	1.98197			0.125101			0.0625505	+	0.998042i	$0.480077\pi$
$252$			6.11735i			0.385357i
$253$	3.06535	−	2.08733i	0.192717	−	0.131229i
$254$	19.7622			1.23999
$255$	4.92876			0.308651
$256$	1.00000			0.0625000
$257$		−	25.9459i		−	1.61846i	−0.587493	−	0.809230i	$-0.699885\pi$
$257$		−	25.9459i		−	1.61846i	0.587493	−	0.809230i	$-0.300115\pi$
$258$	4.46382			0.277905
$259$	4.37882			0.272087
$260$	0.0305584			0.00189515
$261$	−2.47118			−0.152962
$262$			14.9066i			0.920934i
$263$			2.58889i			0.159638i	0.996809	+	0.0798190i	$0.0254342\pi$
$263$			2.58889i			0.159638i	−0.996809	+	0.0798190i	$0.974566\pi$
$264$	1.94350	+	2.85413i	0.119614	+	0.175660i
$265$			14.6170i			0.897916i
$266$	−9.42943	−	10.2350i	−0.578155	−	0.627546i
$267$	6.75978			0.413692
$268$			2.91295i			0.177937i
$269$			13.9597i			0.851141i	0.904925	+	0.425570i	$0.139927\pi$
$269$			13.9597i			0.851141i	−0.904925	+	0.425570i	$0.860073\pi$
$270$		−	12.3241i		−	0.750019i
$271$		−	3.53245i		−	0.214581i	−0.994228	−	0.107291i	$-0.965782\pi$
$271$		−	3.53245i		−	0.214581i	0.994228	−	0.107291i	$-0.0342175\pi$
$272$		−	1.96608i		−	0.119211i
$273$	−0.0421842			−0.00255310
$274$	−3.70645			−0.223915
$275$	−2.18736	+	1.48947i	−0.131903	+	0.0898183i
$276$		−	1.16415i		−	0.0700736i
$277$		−	18.1242i		−	1.08898i	−0.838767	−	0.544490i	$-0.816723\pi$
$277$		−	18.1242i		−	1.08898i	0.838767	−	0.544490i	$-0.183277\pi$
$278$		−	12.7388i		−	0.764024i
$279$			16.1215i			0.965167i
$280$		−	7.68755i		−	0.459419i
$281$	24.3199			1.45081			0.725403	−	0.688324i	$-0.241653\pi$
$281$	24.3199			1.45081			0.725403	+	0.688324i	$0.241653\pi$
$282$			2.32830i			0.138648i
$283$		−	32.2463i		−	1.91685i	−0.285352	−	0.958423i	$-0.592111\pi$
$283$		−	32.2463i		−	1.91685i	0.285352	−	0.958423i	$-0.407889\pi$
$284$		−	9.82353i		−	0.582919i
$285$	7.40404	+	8.03656i	0.438578	+	0.476045i
$286$	0.0347911	−	0.0236908i	0.00205724	−	0.00140086i
$287$			18.1500i			1.07136i
$288$	−1.91607			−0.112905
$289$	13.1345			0.772620
$290$	3.10548			0.182360
$291$	−4.92876			−0.288929
$292$			6.87241i			0.402178i
$293$	−7.04677			−0.411676			−0.205838	−	0.978586i	$-0.565992\pi$
$293$	−7.04677			−0.411676			−0.205838	+	0.978586i	$0.565992\pi$
$294$			3.32439i			0.193883i
$295$		−	30.3564i		−	1.76742i
$296$			1.37153i			0.0797184i
$297$	−9.55439	−	14.0311i	−0.554402	−	0.814167i
$298$			1.19928i			0.0694723i
$299$	−0.0141907			−0.000820667
$300$			0.830708i			0.0479609i
$301$	−13.6886			−0.788997
$302$	7.89436			0.454269
$303$	6.75978			0.388339
$304$	3.20578	−	2.95347i	0.183864	−	0.169393i
$305$		−	14.7016i		−	0.841811i
$306$			3.76714i			0.215353i
$307$	−18.1042			−1.03326			−0.516631	−	0.856208i	$-0.672814\pi$
$307$	−18.1042			−1.03326			−0.516631	+	0.856208i	$0.672814\pi$
$308$	−5.95987	−	8.75237i	−0.339595	−	0.498712i
$309$	11.8347			0.673255
$310$		−	20.2595i		−	1.15066i
$311$	−28.0024			−1.58787			−0.793935	−	0.608002i	$-0.791971\pi$
$311$	−28.0024			−1.58787			−0.793935	+	0.608002i	$0.791971\pi$
$312$		−	0.0132128i		−	0.000748030i
$313$	−12.1117			−0.684595			−0.342297	−	0.939592i	$-0.611205\pi$
$313$	−12.1117			−0.684595			−0.342297	+	0.939592i	$0.611205\pi$
$314$	−22.3453			−1.26102
$315$			14.7299i			0.829934i
$316$	14.1307			0.794914
$317$			25.9810i			1.45924i	0.683854	+	0.729619i	$0.260303\pi$
$317$			25.9810i			1.45924i	−0.683854	+	0.729619i	$0.739697\pi$
$318$	6.32011			0.354414
$319$	3.53562	−	2.40756i	0.197957	−	0.134798i
$320$	2.40788			0.134605
$321$		−	0.826880i		−	0.0461519i
$322$			3.56994i			0.198945i
$323$	−5.80675	−	6.30281i	−0.323096	−	0.350698i
$324$	0.419508			0.0233060
$325$	0.0101261			0.000561695
$326$	−11.3403			−0.628082
$327$		−	5.60228i		−	0.309807i
$328$	−5.68490			−0.313896
$329$		−	7.13987i		−	0.393634i
$330$	4.67973	+	6.87241i	0.257611	+	0.378314i
$331$		−	11.2200i		−	0.616707i	−0.951272	−	0.308354i	$-0.900222\pi$
$331$		−	11.2200i		−	0.616707i	0.951272	−	0.308354i	$-0.0997780\pi$
$332$		−	9.28506i		−	0.509584i
$333$		−	2.62794i		−	0.144010i
$334$	−13.6580			−0.747334
$335$			7.01404i			0.383218i
$336$	−3.32395			−0.181336
$337$	3.59729			0.195957			0.0979785	−	0.995189i	$-0.468762\pi$
$337$	3.59729			0.195957			0.0979785	+	0.995189i	$0.468762\pi$
$338$	12.9998			0.707098
$339$	12.7028			0.689920
$340$		−	4.73408i		−	0.256742i
$341$	−15.7064	−	23.0657i	−0.850552	−	1.24908i
$342$	−6.14249	+	5.65904i	−0.332148	+	0.306006i
$343$			12.1542i			0.656264i
$344$		−	4.28751i		−	0.231167i
$345$		−	2.80314i		−	0.150916i
$346$	−12.1524			−0.653317
$347$		−	20.4964i		−	1.10030i	−0.835065	−	0.550151i	$-0.814570\pi$
$347$		−	20.4964i		−	1.10030i	0.835065	−	0.550151i	$-0.185430\pi$
$348$		−	1.34275i		−	0.0719789i
$349$		−	3.30248i		−	0.176778i	−0.996086	−	0.0883888i	$-0.971828\pi$
$349$		−	3.30248i		−	0.176778i	0.996086	−	0.0883888i	$-0.0281718\pi$
$350$		−	2.54742i		−	0.136165i
$351$			0.0649552i			0.00346705i
$352$	2.74140	−	1.86674i	0.146117	−	0.0994976i
$353$	−6.33814			−0.337345			−0.168673	−	0.985672i	$-0.553948\pi$
$353$	−6.33814			−0.337345			−0.168673	+	0.985672i	$0.553948\pi$
$354$	−13.1255			−0.697614
$355$		−	23.6539i		−	1.25542i
$356$		−	6.49279i		−	0.344117i
$357$			6.53514i			0.345876i
$358$			5.15874i			0.272648i
$359$			30.4580i			1.60751i	0.594960	+	0.803755i	$0.297168\pi$
$359$			30.4580i			1.60751i	−0.594960	+	0.803755i	$0.702832\pi$
$360$	−4.61366			−0.243161
$361$	1.55404	−	18.9363i	0.0817918	−	0.996649i
$362$			15.1164i			0.794498i
$363$	10.6558	+	4.19630i	0.559287	+	0.220249i
$364$			0.0405180i			0.00212372i
$365$			16.5480i			0.866160i
$366$	−6.35668			−0.332269
$367$	10.0104			0.522536			0.261268	−	0.965266i	$-0.415859\pi$
$367$	10.0104			0.522536			0.261268	+	0.965266i	$0.415859\pi$
$368$	−1.11817			−0.0582886
$369$	10.8927			0.567049
$370$			3.30248i			0.171688i
$371$	−19.3810			−1.00621
$372$	−8.75982			−0.454176
$373$	16.3418			0.846147			0.423074	−	0.906095i	$-0.360951\pi$
$373$	16.3418			0.846147			0.423074	+	0.906095i	$0.360951\pi$
$374$	−3.67016	−	5.38981i	−0.189779	−	0.278700i
$375$		−	10.5342i		−	0.543986i
$376$	2.23634			0.115330
$377$	−0.0163677			−0.000842981
$378$	16.3408			0.840478
$379$		−	15.9032i		−	0.816894i	−0.912782	−	0.408447i	$-0.866070\pi$
$379$		−	15.9032i		−	0.816894i	0.912782	−	0.408447i	$-0.133930\pi$
$380$	7.71914	−	7.11161i	0.395984	−	0.364818i
$381$		−	20.5749i		−	1.05408i
$382$	17.8905			0.915359
$383$			11.8886i			0.607477i	0.952755	+	0.303739i	$0.0982349\pi$
$383$			11.8886i			0.607477i	−0.952755	+	0.303739i	$0.901765\pi$
$384$		−	1.04112i		−	0.0531295i
$385$	−14.3507	−	21.0747i	−0.731378	−	1.07406i
$386$	−0.178898			−0.00910566
$387$			8.21516i			0.417600i
$388$			4.73408i			0.240337i
$389$	−15.6290			−0.792420			−0.396210	−	0.918160i	$-0.629675\pi$
$389$	−15.6290			−0.792420			−0.396210	+	0.918160i	$0.629675\pi$
$390$		−	0.0318150i		−	0.00161101i
$391$			2.19841i			0.111178i
$392$	3.19309			0.161275
$393$	15.5196			0.782860
$394$			4.16449i			0.209804i
$395$	34.0251			1.71199
$396$	−5.25271	+	3.57680i	−0.263958	+	0.179741i
$397$	1.62892			0.0817530			0.0408765	−	0.999164i	$-0.486985\pi$
$397$	1.62892			0.0817530			0.0408765	+	0.999164i	$0.486985\pi$
$398$	−25.3365			−1.27000
$399$	−10.6558	+	9.81718i	−0.533460	+	0.491474i
$400$	0.797897			0.0398949
$401$		−	22.0666i		−	1.10195i	−0.834521	−	0.550976i	$-0.814256\pi$
$401$		−	22.0666i		−	1.10195i	0.834521	−	0.550976i	$-0.185744\pi$
$402$	3.03274			0.151259
$403$			0.106780i			0.00531908i
$404$		−	6.49279i		−	0.323028i
$405$	1.01013			0.0501936
$406$			4.11762i			0.204354i
$407$	2.56029	+	3.75991i	0.126909	+	0.186372i
$408$	−2.04693			−0.101338
$409$	−9.16988			−0.453422			−0.226711	−	0.973962i	$-0.572797\pi$
$409$	−9.16988			−0.453422			−0.226711	+	0.973962i	$0.572797\pi$
$410$	−13.6886			−0.676031
$411$			3.85886i			0.190344i
$412$		−	11.3673i		−	0.560027i
$413$	40.2502			1.98058
$414$	2.14249			0.105297
$415$		−	22.3573i		−	1.09748i
$416$	−0.0126910			−0.000622226
$417$	−13.2627			−0.649476
$418$	3.27497	−	14.0810i	0.160184	−	0.688724i
$419$	−17.9047			−0.874703			−0.437351	−	0.899291i	$-0.644083\pi$
$419$	−17.9047			−0.874703			−0.437351	+	0.899291i	$0.644083\pi$
$420$	−8.00368			−0.390539
$421$		−	10.6323i		−	0.518188i	−0.965852	−	0.259094i	$-0.916576\pi$
$421$		−	10.6323i		−	0.518188i	0.965852	−	0.259094i	$-0.0834239\pi$
$422$	−12.7865			−0.622439
$423$	−4.28497			−0.208342
$424$		−	6.07048i		−	0.294809i
$425$		−	1.56873i		−	0.0760945i
$426$	−10.2275			−0.495523
$427$	19.4932			0.943340
$428$	−0.794220			−0.0383901
$429$	−0.0246650	−	0.0362217i	−0.00119084	−	0.00174880i
$430$		−	10.3238i		−	0.497859i
$431$	33.5932			1.61813			0.809065	−	0.587719i	$-0.199974\pi$
$431$	33.5932			1.61813			0.809065	+	0.587719i	$0.199974\pi$
$432$			5.11822i			0.246251i
$433$			32.2063i			1.54774i	0.633346	+	0.773869i	$0.281681\pi$
$433$			32.2063i			1.54774i	−0.633346	+	0.773869i	$0.718319\pi$
$434$	26.8625			1.28944
$435$		−	3.23318i		−	0.155019i
$436$	−5.38100			−0.257703
$437$	−3.58460	+	3.30248i	−0.171475	+	0.157979i
$438$	7.15502			0.341880
$439$	23.4140			1.11749			0.558745	−	0.829340i	$-0.311283\pi$
$439$	23.4140			1.11749			0.558745	+	0.829340i	$0.311283\pi$
$440$	6.60097	−	4.49489i	0.314689	−	0.214286i
$441$	−6.11817			−0.291341
$442$			0.0249515i			0.00118682i
$443$	−0.0938522			−0.00445905			−0.00222953	−	0.999998i	$-0.500710\pi$
$443$	−0.0938522			−0.00445905			−0.00222953	+	0.999998i	$0.500710\pi$
$444$	1.42793			0.0677664
$445$		−	15.6339i		−	0.741116i
$446$		−	26.7742i		−	1.26780i
$447$	1.24859			0.0590565
$448$			3.19266i			0.150839i
$449$			40.5353i			1.91298i	0.291767	+	0.956490i	$0.405757\pi$
$449$			40.5353i			1.91298i	−0.291767	+	0.956490i	$0.594243\pi$
$450$	−1.52882			−0.0720694
$451$	−15.5846	+	10.6122i	−0.733850	+	0.499711i
$452$		−	12.2010i		−	0.573889i
$453$		−	8.21899i		−	0.386162i
$454$	20.5829			0.966005
$455$			0.0975626i			0.00457380i
$456$	−3.07492	−	3.33761i	−0.143996	−	0.156298i
$457$			26.3856i			1.23427i	0.786859	+	0.617133i	$0.211706\pi$
$457$			26.3856i			1.23427i	−0.786859	+	0.617133i	$0.788294\pi$
$458$	−2.86914			−0.134066
$459$	10.0628			0.469692
$460$	−2.69242			−0.125535
$461$			39.6386i			1.84615i	0.384615	+	0.923077i	$0.374334\pi$
$461$			39.6386i			1.84615i	−0.384615	+	0.923077i	$0.625666\pi$
$462$	−9.11228	+	6.20495i	−0.423941	+	0.288680i
$463$	−15.0595			−0.699872			−0.349936	−	0.936774i	$-0.613797\pi$
$463$	−15.0595			−0.699872			−0.349936	+	0.936774i	$0.613797\pi$
$464$	−1.28971			−0.0598734
$465$	−21.0926			−0.978147
$466$		−	22.4711i		−	1.04096i
$467$	21.0532			0.974227			0.487113	−	0.873339i	$-0.338050\pi$
$467$	21.0532			0.974227			0.487113	+	0.873339i	$0.338050\pi$
$468$	0.0243168			0.00112404
$469$	−9.30007			−0.429437
$470$	5.38484			0.248384
$471$			23.2642i			1.07196i
$472$			12.6071i			0.580289i
$473$	−8.00368	−	11.7538i	−0.368009	−	0.540440i
$474$		−	14.7118i		−	0.675734i
$475$	2.55788	−	2.35656i	0.117364	−	0.108127i
$476$	6.27702			0.287707
$477$			11.6314i			0.532567i
$478$		−	4.25239i		−	0.194500i
$479$			37.6076i			1.71833i	0.511695	+	0.859167i	$0.329018\pi$
$479$			37.6076i			1.71833i	−0.511695	+	0.859167i	$0.670982\pi$
$480$		−	2.50690i		−	0.114424i
$481$		−	0.0174060i		−	0.000793646i
$482$	29.6974			1.35268
$483$	3.71674			0.169117
$484$	4.03056	−	10.2350i	0.183207	−	0.465226i
$485$			11.3991i			0.517607i
$486$		−	15.7914i		−	0.716314i
$487$		−	6.55573i		−	0.297069i	−0.988907	−	0.148534i	$-0.952544\pi$
$487$		−	6.55573i		−	0.297069i	0.988907	−	0.148534i	$-0.0474555\pi$
$488$			6.10561i			0.276388i
$489$			11.8066i			0.533915i
$490$	7.68858			0.347335
$491$		−	19.3034i		−	0.871152i	−0.900152	−	0.435576i	$-0.856545\pi$
$491$		−	19.3034i		−	0.871152i	0.900152	−	0.435576i	$-0.143455\pi$
$492$			5.91868i			0.266835i
$493$			2.53568i			0.114201i
$494$	−0.0406845	+	0.0374824i	−0.00183048	+	0.00168641i
$495$	−12.6479	+	8.61251i	−0.568481	+	0.387104i
$496$			8.41384i			0.377792i
$497$	31.3632			1.40683
$498$	−9.66688			−0.433183
$499$	−19.9923			−0.894979			−0.447490	−	0.894289i	$-0.647682\pi$
$499$	−19.9923			−0.894979			−0.447490	+	0.894289i	$0.647682\pi$
$500$	−10.1182			−0.452498
$501$			14.2197i			0.635288i
$502$	−1.98197			−0.0884597
$503$			1.34726i			0.0600713i	0.999549	+	0.0300356i	$0.00956208\pi$
$503$			1.34726i			0.0600713i	−0.999549	+	0.0300356i	$0.990438\pi$
$504$		−	6.11735i		−	0.272488i
$505$		−	15.6339i		−	0.695698i
$506$	−3.06535	+	2.08733i	−0.136271	+	0.0927932i
$507$		−	13.5344i		−	0.601084i
$508$	−19.7622			−0.876807
$509$		−	2.11338i		−	0.0936737i	−0.998903	−	0.0468369i	$-0.985086\pi$
$509$		−	2.11338i		−	0.0936737i	0.998903	−	0.0468369i	$-0.0149141\pi$
$510$	−4.92876			−0.218249
$511$	−21.9413			−0.970625
$512$	−1.00000			−0.0441942
$513$	15.1165	+	16.4079i	0.667410	+	0.724426i
$514$			25.9459i			1.14442i
$515$		−	27.3711i		−	1.20612i
$516$	−4.46382			−0.196509
$517$	6.13070	−	4.17466i	0.269628	−	0.183601i
$518$	−4.37882			−0.192394
$519$			12.6521i			0.555367i
$520$	−0.0305584			−0.00134007
$521$			14.2124i			0.622658i	0.950302	+	0.311329i	$0.100774\pi$
$521$			14.2124i			0.622658i	−0.950302	+	0.311329i	$0.899226\pi$
$522$	2.47118			0.108160
$523$	−41.0556			−1.79524			−0.897618	−	0.440773i	$-0.854704\pi$
$523$	−41.0556			−1.79524			−0.897618	+	0.440773i	$0.854704\pi$
$524$		−	14.9066i		−	0.651199i
$525$	−2.65217			−0.115750
$526$		−	2.58889i		−	0.112881i
$527$	16.5423			0.720592
$528$	−1.94350	−	2.85413i	−0.0845801	−	0.124210i
$529$	−21.7497			−0.945639
$530$		−	14.6170i		−	0.634922i
$531$		−	24.1560i		−	1.04828i
$532$	9.42943	+	10.2350i	0.408817	+	0.443742i
$533$	0.0721470			0.00312503
$534$	−6.75978			−0.292524
$535$	−1.91239			−0.0826798
$536$		−	2.91295i		−	0.125820i
$537$	5.37087			0.231770
$538$		−	13.9597i		−	0.601847i
$539$	8.75354	−	5.96067i	0.377041	−	0.256744i
$540$			12.3241i			0.530344i
$541$			11.2971i			0.485701i	0.970064	+	0.242851i	$0.0780825\pi$
$541$			11.2971i			0.485701i	−0.970064	+	0.242851i	$0.921917\pi$
$542$			3.53245i			0.151732i
$543$	15.7380			0.675380
$544$			1.96608i			0.0842949i
$545$	−12.9568			−0.555009
$546$	0.0421842			0.00180532
$547$	−36.8231			−1.57444			−0.787221	−	0.616670i	$-0.788481\pi$
$547$	−36.8231			−1.57444			−0.787221	+	0.616670i	$0.788481\pi$
$548$	3.70645			0.158332
$549$		−	11.6988i		−	0.499291i
$550$	2.18736	−	1.48947i	0.0932692	−	0.0635111i
$551$	−4.13454	+	3.80913i	−0.176137	+	0.162274i
$552$			1.16415i			0.0495495i
$553$			45.1145i			1.91847i
$554$			18.1242i			0.770025i
$555$	3.43828			0.145947
$556$			12.7388i			0.540247i
$557$		−	16.7304i		−	0.708889i	−0.935077	−	0.354445i	$-0.884670\pi$
$557$		−	16.7304i		−	0.708889i	0.935077	−	0.354445i	$-0.115330\pi$
$558$		−	16.1215i		−	0.682476i
$559$			0.0544127i			0.00230141i
$560$			7.68755i			0.324858i
$561$	−5.61145	+	3.82108i	−0.236915	+	0.161326i
$562$	−24.3199			−1.02588
$563$	−30.8029			−1.29819			−0.649093	−	0.760709i	$-0.724851\pi$
$563$	−30.8029			−1.29819			−0.649093	+	0.760709i	$0.724851\pi$
$564$		−	2.32830i		−	0.0980391i
$565$		−	29.3787i		−	1.23597i
$566$			32.2463i			1.35541i
$567$			1.33935i			0.0562473i
$568$			9.82353i			0.412186i
$569$	−16.9922			−0.712349			−0.356174	−	0.934420i	$-0.615919\pi$
$569$	−16.9922			−0.712349			−0.356174	+	0.934420i	$0.615919\pi$
$570$	−7.40404	−	8.03656i	−0.310121	−	0.336615i
$571$		−	25.0045i		−	1.04640i	−0.852209	−	0.523202i	$-0.824737\pi$
$571$		−	25.0045i		−	1.04640i	0.852209	−	0.523202i	$-0.175263\pi$
$572$	−0.0347911	+	0.0236908i	−0.00145469	+	0.000990561i
$573$		−	18.6262i		−	0.778121i
$574$		−	18.1500i		−	0.757565i
$575$	−0.892184			−0.0372066
$576$	1.91607			0.0798361
$577$	18.2195			0.758489			0.379245	−	0.925296i	$-0.376184\pi$
$577$	18.2195			0.758489			0.379245	+	0.925296i	$0.376184\pi$
$578$	−13.1345			−0.546325
$579$			0.186254i			0.00774047i
$580$	−3.10548			−0.128948
$581$	29.6441			1.22984
$582$	4.92876			0.204304
$583$	−11.3320	−	16.6416i	−0.469324	−	0.689226i
$584$		−	6.87241i		−	0.284382i
$585$	0.0585519			0.00242082
$586$	7.04677			0.291099
$587$	38.6299			1.59443			0.797213	−	0.603699i	$-0.206307\pi$
$587$	38.6299			1.59443			0.797213	+	0.603699i	$0.206307\pi$
$588$		−	3.32439i		−	0.137096i
$589$	24.8500	+	26.9729i	1.02393	+	1.11140i
$590$			30.3564i			1.24975i
$591$	4.33574			0.178348
$592$		−	1.37153i		−	0.0563694i
$593$			7.76955i			0.319057i	0.987193	+	0.159529i	$0.0509974\pi$
$593$			7.76955i			0.319057i	−0.987193	+	0.159529i	$0.949003\pi$
$594$	9.55439	+	14.0311i	0.392021	+	0.575703i
$595$	15.1143			0.619627
$596$		−	1.19928i		−	0.0491244i
$597$			26.3784i			1.07959i
$598$	0.0141907			0.000580299
$599$			29.9975i			1.22566i	0.790213	+	0.612832i	$0.209970\pi$
$599$			29.9975i			1.22566i	−0.790213	+	0.612832i	$0.790030\pi$
$600$		−	0.830708i		−	0.0339135i
$601$	18.8751			0.769930			0.384965	−	0.922931i	$-0.374214\pi$
$601$	18.8751			0.769930			0.384965	+	0.922931i	$0.374214\pi$
$602$	13.6886			0.557905
$603$			5.58141i			0.227292i
$604$	−7.89436			−0.321217
$605$	9.70511	−	24.6446i	0.394569	−	1.00195i
$606$	−6.75978			−0.274597
$607$	−33.1206			−1.34432			−0.672161	−	0.740405i	$-0.734634\pi$
$607$	−33.1206			−1.34432			−0.672161	+	0.740405i	$0.734634\pi$
$608$	−3.20578	+	2.95347i	−0.130012	+	0.119779i
$609$	4.28694			0.173716
$610$			14.7016i			0.595250i
$611$	−0.0283813			−0.00114819
$612$		−	3.76714i		−	0.152277i
$613$			31.6643i			1.27891i	0.768829	+	0.639455i	$0.220840\pi$
$613$			31.6643i			1.27891i	−0.768829	+	0.639455i	$0.779160\pi$
$614$	18.1042			0.730626
$615$			14.2515i			0.574675i
$616$	5.95987	+	8.75237i	0.240130	+	0.352643i
$617$	16.2990			0.656171			0.328086	−	0.944648i	$-0.393597\pi$
$617$	16.2990			0.656171			0.328086	+	0.944648i	$0.393597\pi$
$618$	−11.8347			−0.476063
$619$	44.1050			1.77273			0.886365	−	0.462988i	$-0.153223\pi$
$619$	44.1050			1.77273			0.886365	+	0.462988i	$0.153223\pi$
$620$			20.2595i			0.813642i
$621$		−	5.72304i		−	0.229658i
$622$	28.0024			1.12279
$623$	20.7293			0.830501
$624$			0.0132128i			0.000528937i
$625$	−28.3528			−1.13411
$626$	12.1117			0.484082
$627$	−14.6600	−	3.40964i	−0.585465	−	0.136168i
$628$	22.3453			0.891676
$629$	−2.69653			−0.107518
$630$		−	14.7299i		−	0.586852i
$631$	38.3608			1.52712			0.763560	−	0.645737i	$-0.223450\pi$
$631$	38.3608			1.52712			0.763560	+	0.645737i	$0.223450\pi$
$632$	−14.1307			−0.562089
$633$			13.3123i			0.529118i
$634$		−	25.9810i		−	1.03184i
$635$	−47.5851			−1.88836
$636$	−6.32011			−0.250609
$637$	−0.0405234			−0.00160560
$638$	−3.53562	+	2.40756i	−0.139977	+	0.0953162i
$639$		−	18.8225i		−	0.744608i
$640$	−2.40788			−0.0951799
$641$		−	15.7562i		−	0.622333i	−0.950355	−	0.311166i	$-0.899280\pi$
$641$		−	15.7562i		−	0.622333i	0.950355	−	0.311166i	$-0.100720\pi$
$642$			0.826880i			0.0326343i
$643$	16.2975			0.642709			0.321354	−	0.946959i	$-0.395862\pi$
$643$	16.2975			0.642709			0.321354	+	0.946959i	$0.395862\pi$
$644$		−	3.56994i		−	0.140675i
$645$	−10.7484			−0.423216
$646$	5.80675	+	6.30281i	0.228464	+	0.247981i
$647$	−17.0166			−0.668993			−0.334497	−	0.942397i	$-0.608566\pi$
$647$	−17.0166			−0.668993			−0.334497	+	0.942397i	$0.608566\pi$
$648$	−0.419508			−0.0164798
$649$	23.5342	+	34.5611i	0.923798	+	1.35664i
$650$	−0.0101261			−0.000397178
$651$		−	27.9672i		−	1.09612i
$652$	11.3403			0.444121
$653$	1.16035			0.0454081			0.0227041	−	0.999742i	$-0.492772\pi$
$653$	1.16035			0.0454081			0.0227041	+	0.999742i	$0.492772\pi$
$654$			5.60228i			0.219066i
$655$		−	35.8934i		−	1.40247i
$656$	5.68490			0.221958
$657$			13.1680i			0.513732i
$658$			7.13987i			0.278341i
$659$	−46.1615			−1.79820			−0.899098	−	0.437747i	$-0.855776\pi$
$659$	−46.1615			−1.79820			−0.899098	+	0.437747i	$0.855776\pi$
$660$	−4.67973	−	6.87241i	−0.182158	−	0.267508i
$661$		−	12.5807i		−	0.489332i	−0.969607	−	0.244666i	$-0.921322\pi$
$661$		−	12.5807i		−	0.489332i	0.969607	−	0.244666i	$-0.0786782\pi$
$662$			11.2200i			0.436078i
$663$	0.0259775			0.00100888
$664$			9.28506i			0.360330i
$665$	22.7049	+	24.6446i	0.880460	+	0.955677i
$666$			2.62794i			0.101831i
$667$	1.44212			0.0558390
$668$	13.6580			0.528445
$669$	−27.8752			−1.07772
$670$		−	7.01404i		−	0.270976i
$671$	11.3976	+	16.7379i	0.439999	+	0.646161i
$672$	3.32395			0.128224
$673$	11.2185			0.432440			0.216220	−	0.976345i	$-0.430627\pi$
$673$	11.2185			0.432440			0.216220	+	0.976345i	$0.430627\pi$
$674$	−3.59729			−0.138563
$675$			4.08381i			0.157186i
$676$	−12.9998			−0.499994
$677$	5.87949			0.225967			0.112984	−	0.993597i	$-0.463959\pi$
$677$	5.87949			0.225967			0.112984	+	0.993597i	$0.463959\pi$
$678$	−12.7028			−0.487847
$679$	−15.1143			−0.580035
$680$			4.73408i			0.181544i
$681$		−	21.4293i		−	0.821174i
$682$	15.7064	+	23.0657i	0.601431	+	0.883231i
$683$		−	37.0017i		−	1.41583i	−0.706298	−	0.707914i	$-0.749636\pi$
$683$		−	37.0017i		−	1.41583i	0.706298	−	0.707914i	$-0.250364\pi$
$684$	6.14249	−	5.65904i	0.234864	−	0.216379i
$685$	8.92469			0.340995
$686$		−	12.1542i		−	0.464049i
$687$			2.98712i			0.113966i
$688$			4.28751i			0.163460i
$689$			0.0770404i			0.00293500i
$690$			2.80314i			0.106714i
$691$	−36.4366			−1.38611			−0.693057	−	0.720883i	$-0.743737\pi$
$691$	−36.4366			−1.38611			−0.693057	+	0.720883i	$0.743737\pi$
$692$	12.1524			0.461965
$693$	−11.4195	−	16.7701i	−0.433791	−	0.637044i
$694$			20.4964i			0.778031i
$695$			30.6736i			1.16352i
$696$			1.34275i			0.0508967i
$697$		−	11.1770i		−	0.423358i
$698$			3.30248i			0.125001i
$699$	−23.3952			−0.884887
$700$			2.54742i			0.0962833i
$701$			30.4476i			1.14999i	0.818157	+	0.574996i	$0.194996\pi$
$701$			30.4476i			1.14999i	−0.818157	+	0.574996i	$0.805004\pi$
$702$		−	0.0649552i		−	0.00245158i
$703$	−4.05076	−	4.39682i	−0.152777	−	0.165829i
$704$	−2.74140	+	1.86674i	−0.103320	+	0.0703554i
$705$		−	5.60627i		−	0.211144i
$706$	6.33814			0.238539
$707$	20.7293			0.779604
$708$	13.1255			0.493287
$709$	6.92402			0.260037			0.130018	−	0.991512i	$-0.458496\pi$
$709$	6.92402			0.260037			0.130018	+	0.991512i	$0.458496\pi$
$710$			23.6539i			0.887715i
$711$	27.0754			1.01541
$712$			6.49279i			0.243327i
$713$		−	9.40809i		−	0.352336i
$714$		−	6.53514i		−	0.244572i
$715$	−0.0837728	+	0.0570446i	−0.00313292	+	0.00213335i
$716$		−	5.15874i		−	0.192791i
$717$	−4.42725			−0.165339
$718$		−	30.4580i		−	1.13668i
$719$	−24.8922			−0.928322			−0.464161	−	0.885751i	$-0.653644\pi$
$719$	−24.8922			−0.928322			−0.464161	+	0.885751i	$0.653644\pi$
$720$	4.61366			0.171941
$721$	36.2920			1.35158
$722$	−1.55404	+	18.9363i	−0.0578356	+	0.704738i
$723$		−	30.9186i		−	1.14988i
$724$		−	15.1164i		−	0.561795i
$725$	−1.02906			−0.0382183
$726$	−10.6558	−	4.19630i	−0.395476	−	0.155739i
$727$	−24.6525			−0.914312			−0.457156	−	0.889387i	$-0.651132\pi$
$727$	−24.6525			−0.914312			−0.457156	+	0.889387i	$0.651132\pi$
$728$		−	0.0405180i		−	0.00150170i
$729$	−15.1823			−0.562306
$730$		−	16.5480i		−	0.612467i
$731$	8.42959			0.311780
$732$	6.35668			0.234950
$733$			48.5372i			1.79276i	0.443285	+	0.896381i	$0.353813\pi$
$733$			48.5372i			1.79276i	−0.443285	+	0.896381i	$0.646187\pi$
$734$	−10.0104			−0.369489
$735$		−	8.00475i		−	0.295260i
$736$	1.11817			0.0412163
$737$	−5.43772	−	7.98557i	−0.200301	−	0.294152i
$738$	−10.8927			−0.400964
$739$		−	44.5869i		−	1.64016i	−0.572251	−	0.820078i	$-0.693930\pi$
$739$		−	44.5869i		−	1.64016i	0.572251	−	0.820078i	$-0.306070\pi$
$740$		−	3.30248i		−	0.121401i
$741$	0.0390237	+	0.0423575i	0.00143357	+	0.00155604i
$742$	19.3810			0.711499
$743$	−41.7483			−1.53160			−0.765798	−	0.643081i	$-0.777656\pi$
$743$	−41.7483			−1.53160			−0.765798	+	0.643081i	$0.777656\pi$
$744$	8.75982			0.321151
$745$		−	2.88772i		−	0.105798i
$746$	−16.3418			−0.598316
$747$		−	17.7908i		−	0.650931i
$748$	3.67016	+	5.38981i	0.134194	+	0.197071i
$749$		−	2.53568i		−	0.0926516i
$750$			10.5342i			0.384656i
$751$			4.07798i			0.148808i	0.997228	+	0.0744038i	$0.0237054\pi$
$751$			4.07798i			0.148808i	−0.997228	+	0.0744038i	$0.976295\pi$
$752$	−2.23634			−0.0815509
$753$			2.06347i			0.0751971i
$754$	0.0163677			0.000596077
$755$	−19.0087			−0.691797
$756$	−16.3408			−0.594307
$757$	−11.8473			−0.430596			−0.215298	−	0.976548i	$-0.569072\pi$
$757$	−11.8473			−0.430596			−0.215298	+	0.976548i	$0.569072\pi$
$758$			15.9032i			0.577631i
$759$	2.17317	+	3.19140i	0.0788809	+	0.115841i
$760$	−7.71914	+	7.11161i	−0.280003	+	0.257965i
$761$			4.89156i			0.177319i	0.996062	+	0.0886595i	$0.0282583\pi$
$761$			4.89156i			0.177319i	−0.996062	+	0.0886595i	$0.971742\pi$
$762$			20.5749i			0.745349i
$763$		−	17.1797i		−	0.621947i
$764$	−17.8905			−0.647256
$765$		−	9.07082i		−	0.327956i
$766$		−	11.8886i		−	0.429551i
$767$		−	0.159996i		−	0.00577714i
$768$			1.04112i			0.0375682i
$769$			12.3462i			0.445214i	0.974908	+	0.222607i	$0.0714567\pi$
$769$			12.3462i			0.445214i	−0.974908	+	0.222607i	$0.928543\pi$
$770$	14.3507	+	21.0747i	0.517162	+	0.759478i
$771$	27.0128			0.972842
$772$	0.178898			0.00643868
$773$		−	23.5854i		−	0.848308i	−0.905590	−	0.424154i	$-0.860572\pi$
$773$		−	23.5854i		−	0.848308i	0.905590	−	0.424154i	$-0.139428\pi$
$774$		−	8.21516i		−	0.295288i
$775$			6.71338i			0.241152i
$776$		−	4.73408i		−	0.169944i
$777$			4.55889i			0.163549i
$778$	15.6290			0.560326
$779$	18.2246	−	16.7902i	0.652962	−	0.601571i
$780$			0.0318150i			0.00113916i
$781$	18.3380	+	26.9302i	0.656184	+	0.963639i
$782$		−	2.19841i		−	0.0786149i
$783$		−	6.60104i		−	0.235902i
$784$	−3.19309			−0.114039
$785$	53.8049			1.92038
$786$	−15.5196			−0.553566
$787$	−19.8106			−0.706171			−0.353086	−	0.935591i	$-0.614868\pi$
$787$	−19.8106			−0.706171			−0.353086	+	0.935591i	$0.614868\pi$
$788$		−	4.16449i		−	0.148354i
$789$	−2.69535			−0.0959571
$790$	−34.0251			−1.21056
$791$	38.9538			1.38504
$792$	5.25271	−	3.57680i	0.186647	−	0.127096i
$793$		−	0.0774862i		−	0.00275162i
$794$	−1.62892			−0.0578081
$795$	−15.2181			−0.539730
$796$	25.3365			0.898028
$797$			29.4036i			1.04153i	0.853700	+	0.520765i	$0.174353\pi$
$797$			29.4036i			1.04153i	−0.853700	+	0.520765i	$0.825647\pi$
$798$	10.6558	−	9.81718i	0.377213	−	0.347524i
$799$			4.39682i			0.155548i
$800$	−0.797897			−0.0282099
$801$		−	12.4406i		−	0.439567i
$802$			22.0666i			0.779198i
$803$	−12.8290	−	18.8400i	−0.452726	−	0.664850i
$804$	−3.03274			−0.106956
$805$		−	8.59598i		−	0.302969i
$806$		−	0.106780i		−	0.00376116i
$807$	−14.5338			−0.511614
$808$			6.49279i			0.228415i
$809$			15.2014i			0.534452i	0.963634	+	0.267226i	$0.0861071\pi$
$809$			15.2014i			0.534452i	−0.963634	+	0.267226i	$0.913893\pi$
$810$	−1.01013			−0.0354922
$811$	1.09935			0.0386034			0.0193017	−	0.999814i	$-0.493856\pi$
$811$	1.09935			0.0386034			0.0193017	+	0.999814i	$0.493856\pi$
$812$		−	4.11762i		−	0.144500i
$813$	3.67771			0.128983
$814$	−2.56029	−	3.75991i	−0.0897380	−	0.131785i
$815$	27.3061			0.956493
$816$	2.04693			0.0716567
$817$	12.6630	+	13.7448i	0.443024	+	0.480871i
$818$	9.16988			0.320617
$819$			0.0776352i			0.00271279i
$820$	13.6886			0.478026
$821$		−	51.9620i		−	1.81349i	−0.421683	−	0.906743i	$-0.638561\pi$
$821$		−	51.9620i		−	1.81349i	0.421683	−	0.906743i	$-0.361439\pi$
$822$		−	3.85886i		−	0.134593i
$823$	−29.7661			−1.03758			−0.518790	−	0.854902i	$-0.673617\pi$
$823$	−29.7661			−1.03758			−0.518790	+	0.854902i	$0.673617\pi$
$824$			11.3673i			0.395999i
$825$	−1.55072	−	2.27730i	−0.0539890	−	0.0792855i
$826$	−40.2502			−1.40048
$827$	7.38100			0.256663			0.128331	−	0.991731i	$-0.459038\pi$
$827$	7.38100			0.256663			0.128331	+	0.991731i	$0.459038\pi$
$828$	−2.14249			−0.0744565
$829$			22.8435i			0.793389i	0.917951	+	0.396695i	$0.129843\pi$
$829$			22.8435i			0.793389i	−0.917951	+	0.396695i	$0.870157\pi$
$830$			22.3573i			0.776034i
$831$	18.8695			0.654577
$832$	0.0126910			0.000439980
$833$			6.27786i			0.217515i
$834$	13.2627			0.459249
$835$	32.8869			1.13810
$836$	−3.27497	+	14.0810i	−0.113267	+	0.487002i
$837$	−43.0639			−1.48851
$838$	17.9047			0.618508
$839$			36.3079i			1.25349i	0.779226	+	0.626743i	$0.215613\pi$
$839$			36.3079i			1.25349i	−0.779226	+	0.626743i	$0.784387\pi$
$840$	8.00368			0.276153
$841$	−27.3366			−0.942643
$842$			10.6323i			0.366414i
$843$			25.3200i			0.872068i
$844$	12.7865			0.440131
$845$	−31.3021			−1.07682
$846$	4.28497			0.147320
$847$	32.6768	+	12.8682i	1.12279	+	0.442157i
$848$			6.07048i			0.208461i
$849$	33.5723			1.15220
$850$			1.56873i			0.0538069i
$851$			1.53360i			0.0525711i
$852$	10.2275			0.350388
$853$		−	13.6247i		−	0.466500i	−0.972417	−	0.233250i	$-0.925064\pi$
$853$		−	13.6247i		−	0.466500i	0.972417	−	0.233250i	$-0.0749360\pi$
$854$	−19.4932			−0.667042
$855$	14.7904	−	13.6263i	0.505820	−	0.466010i
$856$	0.794220			0.0271459
$857$	−43.4586			−1.48452			−0.742259	−	0.670113i	$-0.766245\pi$
$857$	−43.4586			−1.48452			−0.742259	+	0.670113i	$0.766245\pi$
$858$	0.0246650	+	0.0362217i	0.000842048	+	0.00123659i
$859$	−4.25437			−0.145157			−0.0725786	−	0.997363i	$-0.523123\pi$
$859$	−4.25437			−0.145157			−0.0725786	+	0.997363i	$0.523123\pi$
$860$			10.3238i			0.352040i
$861$	−18.8963			−0.643985
$862$	−33.5932			−1.14419
$863$		−	14.3916i		−	0.489897i	−0.969536	−	0.244948i	$-0.921229\pi$
$863$		−	14.3916i		−	0.489897i	0.969536	−	0.244948i	$-0.0787710\pi$
$864$		−	5.11822i		−	0.174125i
$865$	29.2616			0.994923
$866$		−	32.2063i		−	1.09442i
$867$			13.6746i			0.464415i
$868$	−26.8625			−0.911774
$869$	−38.7379	+	26.3784i	−1.31409	+	0.894824i
$870$			3.23318i			0.109615i
$871$			0.0369682i			0.00125262i
$872$	5.38100			0.182224
$873$			9.07082i			0.307001i
$874$	3.58460	−	3.30248i	0.121251	−	0.111708i
$875$		−	32.3039i		−	1.09207i
$876$	−7.15502			−0.241746
$877$	41.6376			1.40600			0.703001	−	0.711189i	$-0.251843\pi$
$877$	41.6376			1.40600			0.703001	+	0.711189i	$0.251843\pi$
$878$	−23.4140			−0.790185
$879$		−	7.33654i		−	0.247455i
$880$	−6.60097	+	4.49489i	−0.222519	+	0.151523i
$881$	−32.4127			−1.09201			−0.546006	−	0.837781i	$-0.683853\pi$
$881$	−32.4127			−1.09201			−0.546006	+	0.837781i	$0.683853\pi$
$882$	6.11817			0.206009
$883$	8.49149			0.285762			0.142881	−	0.989740i	$-0.454363\pi$
$883$	8.49149			0.285762			0.142881	+	0.989740i	$0.454363\pi$
$884$		−	0.0249515i		−	0.000839208i
$885$	31.6047			1.06238
$886$	0.0938522			0.00315303
$887$	−0.936433			−0.0314423			−0.0157212	−	0.999876i	$-0.505004\pi$
$887$	−0.936433			−0.0314423			−0.0157212	+	0.999876i	$0.505004\pi$
$888$	−1.42793			−0.0479181
$889$		−	63.0941i		−	2.11611i
$890$			15.6339i			0.524048i
$891$	−1.15004	+	0.783113i	−0.0385278	+	0.0262353i
$892$			26.7742i			0.896467i
$893$	−7.16921	+	6.60495i	−0.239908	+	0.221026i
$894$	−1.24859			−0.0417592
$895$		−	12.4216i		−	0.415210i
$896$		−	3.19266i		−	0.106659i
$897$		−	0.0147742i		−	0.000493296i
$898$		−	40.5353i		−	1.35268i
$899$		−	10.8514i		−	0.361916i
$900$	1.52882			0.0509608
$901$	11.9350			0.397614
$902$	15.5846	−	10.6122i	0.518911	−	0.353349i
$903$		−	14.2515i		−	0.474259i
$904$			12.2010i			0.405801i
$905$		−	36.3984i		−	1.20992i
$906$			8.21899i			0.273058i
$907$		−	41.7860i		−	1.38748i	−0.720226	−	0.693740i	$-0.755962\pi$
$907$		−	41.7860i		−	1.38748i	0.720226	−	0.693740i	$-0.244038\pi$
$908$	−20.5829			−0.683069
$909$		−	12.4406i		−	0.412629i
$910$		−	0.0975626i		−	0.00323417i
$911$			12.7869i			0.423649i	0.977308	+	0.211824i	$0.0679405\pi$
$911$			12.7869i			0.423649i	−0.977308	+	0.211824i	$0.932060\pi$
$912$	3.07492	+	3.33761i	0.101821	+	0.110519i
$913$	17.3328	+	25.4541i	0.573632	+	0.842407i
$914$		−	26.3856i		−	0.872757i
$915$	15.3061			0.506006
$916$	2.86914			0.0947991
$917$	47.5918			1.57162
$918$	−10.0628			−0.332123
$919$		−	29.7800i		−	0.982350i	−0.871061	−	0.491175i	$-0.836568\pi$
$919$		−	29.7800i		−	0.982350i	0.871061	−	0.491175i	$-0.163432\pi$
$920$	2.69242			0.0887664
$921$		−	18.8487i		−	0.621085i
$922$		−	39.6386i		−	1.30543i
$923$		−	0.124670i		−	0.00410357i
$924$	9.11228	−	6.20495i	0.299772	−	0.204128i
$925$		−	1.09434i		−	0.0359816i
$926$	15.0595			0.494884
$927$		−	21.7805i		−	0.715366i
$928$	1.28971			0.0423369
$929$	−18.5730			−0.609360			−0.304680	−	0.952455i	$-0.598549\pi$
$929$	−18.5730			−0.609360			−0.304680	+	0.952455i	$0.598549\pi$
$930$	21.0926			0.691654
$931$	−10.2363	+	9.43069i	−0.335482	+	0.309078i
$932$			22.4711i			0.736067i
$933$		−	29.1539i		−	0.954456i
$934$	−21.0532			−0.688882
$935$	8.83731	+	12.9780i	0.289011	+	0.424427i
$936$	−0.0243168			−0.000794818
$937$			23.9023i			0.780854i	0.920634	+	0.390427i	$0.127673\pi$
$937$			23.9023i			0.780854i	−0.920634	+	0.390427i	$0.872327\pi$
$938$	9.30007			0.303658
$939$		−	12.6098i		−	0.411504i
$940$	−5.38484			−0.175634
$941$	−1.98359			−0.0646630			−0.0323315	−	0.999477i	$-0.510293\pi$
$941$	−1.98359			−0.0646630			−0.0323315	+	0.999477i	$0.510293\pi$
$942$		−	23.2642i		−	0.757989i
$943$	−6.35668			−0.207002
$944$		−	12.6071i		−	0.410326i
$945$	−39.3466			−1.27995
$946$	8.00368	+	11.7538i	0.260222	+	0.382149i
$947$	−50.1495			−1.62964			−0.814820	−	0.579714i	$-0.803164\pi$
$947$	−50.1495			−1.62964			−0.814820	+	0.579714i	$0.803164\pi$
$948$			14.7118i			0.477816i
$949$			0.0872176i			0.00283120i
$950$	−2.55788	+	2.35656i	−0.0829887	+	0.0764570i
$951$	−27.0494			−0.877136
$952$	−6.27702			−0.203439
$953$	−38.4609			−1.24587			−0.622935	−	0.782273i	$-0.714060\pi$
$953$	−38.4609			−1.24587			−0.622935	+	0.782273i	$0.714060\pi$
$954$		−	11.6314i		−	0.376582i
$955$	−43.0783			−1.39398
$956$			4.25239i			0.137532i
$957$	2.50656	+	3.68101i	0.0810257	+	0.118990i
$958$		−	37.6076i		−	1.21505i
$959$			11.8334i			0.382122i
$960$			2.50690i			0.0809098i
$961$	−39.7926			−1.28363
$962$			0.0174060i			0.000561193i
$963$	−1.52178			−0.0490386
$964$	−29.6974			−0.956490
$965$	0.430765			0.0138668
$966$	−3.71674			−0.119584
$967$		−	1.35309i		−	0.0435125i	−0.999763	−	0.0217563i	$-0.993074\pi$
$967$		−	1.35309i		−	0.0435125i	0.999763	−	0.0217563i	$-0.00692578\pi$
$968$	−4.03056	+	10.2350i	−0.129547	+	0.328964i
$969$	6.56199	−	6.04553i	0.210802	−	0.194210i
$970$		−	11.3991i		−	0.366004i
$971$		−	27.2856i		−	0.875636i	−0.899064	−	0.437818i	$-0.855751\pi$
$971$		−	27.2856i		−	0.875636i	0.899064	−	0.437818i	$-0.144249\pi$
$972$			15.7914i			0.506510i
$973$	−40.6708			−1.30385
$974$			6.55573i			0.210059i
$975$			0.0105425i			0.000337630i
$976$		−	6.10561i		−	0.195436i
$977$		−	0.724442i		−	0.0231770i	−0.999933	−	0.0115885i	$-0.996311\pi$
$977$		−	0.724442i		−	0.0231770i	0.999933	−	0.0115885i	$-0.00368881\pi$
$978$		−	11.8066i		−	0.377535i
$979$	12.1203	+	17.7993i	0.387368	+	0.568869i
$980$	−7.68858			−0.245603
$981$	−10.3104			−0.329184
$982$			19.3034i			0.615997i
$983$			40.7078i			1.29838i	0.760627	+	0.649189i	$0.224892\pi$
$983$			40.7078i			1.29838i	−0.760627	+	0.649189i	$0.775108\pi$
$984$		−	5.91868i		−	0.188681i
$985$		−	10.0276i		−	0.319506i
$986$		−	2.53568i		−	0.0807524i
$987$	7.43347			0.236610
$988$	0.0406845	−	0.0374824i	0.00129435	−	0.00119247i
$989$		−	4.79416i		−	0.152446i
$990$	12.6479	−	8.61251i	0.401977	−	0.273724i
$991$		−	7.70196i		−	0.244661i	−0.992489	−	0.122330i	$-0.960963\pi$
$991$		−	7.70196i		−	0.244661i	0.992489	−	0.122330i	$-0.0390368\pi$
$992$		−	8.41384i		−	0.267140i
$993$	11.6814			0.370698
$994$	−31.3632			−0.994780
$995$	61.0073			1.93406
$996$	9.66688			0.306307
$997$		−	38.9069i		−	1.23220i	−0.787670	−	0.616098i	$-0.788713\pi$
$997$		−	38.9069i		−	1.23220i	0.787670	−	0.616098i	$-0.211287\pi$
$998$	19.9923			0.632846
$999$	7.01978			0.222096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.b.c.417.5	yes	8
3.2	odd	2		3762.2.g.h.2089.2		8
11.10	odd	2		418.2.b.d.417.5	yes	8
19.18	odd	2		418.2.b.d.417.4	yes	8
33.32	even	2		3762.2.g.g.2089.1		8
57.56	even	2		3762.2.g.g.2089.2		8
209.208	even	2	inner	418.2.b.c.417.4	✓	8
627.626	odd	2		3762.2.g.h.2089.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.b.c.417.4	✓	8	209.208	even	2	inner
418.2.b.c.417.5	yes	8	1.1	even	1	trivial
418.2.b.d.417.4	yes	8	19.18	odd	2
418.2.b.d.417.5	yes	8	11.10	odd	2
3762.2.g.g.2089.1		8	33.32	even	2
3762.2.g.g.2089.2		8	57.56	even	2
3762.2.g.h.2089.1		8	627.626	odd	2
3762.2.g.h.2089.2		8	3.2	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.04112i q^{3} +1.00000 q^{4} +2.40788 q^{5} -1.04112i q^{6} +3.19266i q^{7} -1.00000 q^{8} +1.91607 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.04112i q^{3} +1.00000 q^{4} +2.40788 q^{5} -1.04112i q^{6} +3.19266i q^{7} -1.00000 q^{8} +1.91607 q^{9} -2.40788 q^{10} +(-2.74140 + 1.86674i) q^{11} +1.04112i q^{12} +0.0126910 q^{13} -3.19266i q^{14} +2.50690i q^{15} +1.00000 q^{16} -1.96608i q^{17} -1.91607 q^{18} +(3.20578 - 2.95347i) q^{19} +2.40788 q^{20} -3.32395 q^{21} +(2.74140 - 1.86674i) q^{22} -1.11817 q^{23} -1.04112i q^{24} +0.797897 q^{25} -0.0126910 q^{26} +5.11822i q^{27} +3.19266i q^{28} -1.28971 q^{29} -2.50690i q^{30} +8.41384i q^{31} -1.00000 q^{32} +(-1.94350 - 2.85413i) q^{33} +1.96608i q^{34} +7.68755i q^{35} +1.91607 q^{36} -1.37153i q^{37} +(-3.20578 + 2.95347i) q^{38} +0.0132128i q^{39} -2.40788 q^{40} +5.68490 q^{41} +3.32395 q^{42} +4.28751i q^{43} +(-2.74140 + 1.86674i) q^{44} +4.61366 q^{45} +1.11817 q^{46} -2.23634 q^{47} +1.04112i q^{48} -3.19309 q^{49} -0.797897 q^{50} +2.04693 q^{51} +0.0126910 q^{52} +6.07048i q^{53} -5.11822i q^{54} +(-6.60097 + 4.49489i) q^{55} -3.19266i q^{56} +(3.07492 + 3.33761i) q^{57} +1.28971 q^{58} -12.6071i q^{59} +2.50690i q^{60} -6.10561i q^{61} -8.41384i q^{62} +6.11735i q^{63} +1.00000 q^{64} +0.0305584 q^{65} +(1.94350 + 2.85413i) q^{66} +2.91295i q^{67} -1.96608i q^{68} -1.16415i q^{69} -7.68755i q^{70} -9.82353i q^{71} -1.91607 q^{72} +6.87241i q^{73} +1.37153i q^{74} +0.830708i q^{75} +(3.20578 - 2.95347i) q^{76} +(-5.95987 - 8.75237i) q^{77} -0.0132128i q^{78} +14.1307 q^{79} +2.40788 q^{80} +0.419508 q^{81} -5.68490 q^{82} -9.28506i q^{83} -3.32395 q^{84} -4.73408i q^{85} -4.28751i q^{86} -1.34275i q^{87} +(2.74140 - 1.86674i) q^{88} -6.49279i q^{89} -4.61366 q^{90} +0.0405180i q^{91} -1.11817 q^{92} -8.75982 q^{93} +2.23634 q^{94} +(7.71914 - 7.11161i) q^{95} -1.04112i q^{96} +4.73408i q^{97} +3.19309 q^{98} +(-5.25271 + 3.57680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

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