LMFDB - Embedded newform 1890.2.i.i.991.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(991,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 4]))

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

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

chi := DirichletCharacter("1890.991");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1890.i (of order $3$ , degree $2$ , not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561$ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$3^{5}$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.3
Root			$1.67659 - 0.434811i$ of defining polynomial
Character	$\chi$	$=$	1890.991
Dual form			1890.2.i.i.1171.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.09594 + 2.40809i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.554785 + 0.960915i) q^{11} +(-1.64072 - 2.84181i) q^{13} +(-1.09594 + 2.40809i) q^{14} +1.00000 q^{16} +(-2.19747 + 3.80613i) q^{17} +(-0.622647 - 1.07846i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.554785 + 0.960915i) q^{22} +(-3.14773 + 5.45204i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.64072 - 2.84181i) q^{26} +(-1.09594 + 2.40809i) q^{28} +(-3.26879 + 5.66171i) q^{29} +3.10957 q^{31} +1.00000 q^{32} +(-2.19747 + 3.80613i) q^{34} +(-1.53750 - 2.15316i) q^{35} +(0.659906 + 1.14299i) q^{37} +(-0.622647 - 1.07846i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-3.60559 - 6.24507i) q^{41} +(-4.88416 + 8.45961i) q^{43} +(0.554785 + 0.960915i) q^{44} +(-3.14773 + 5.45204i) q^{46} +11.4617 q^{47} +(-4.59781 - 5.27827i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.64072 - 2.84181i) q^{52} +(-2.73283 + 4.73340i) q^{53} -1.10957 q^{55} +(-1.09594 + 2.40809i) q^{56} +(-3.26879 + 5.66171i) q^{58} -6.46993 q^{59} +4.40470 q^{61} +3.10957 q^{62} +1.00000 q^{64} +3.28143 q^{65} -5.23241 q^{67} +(-2.19747 + 3.80613i) q^{68} +(-1.53750 - 2.15316i) q^{70} -16.3046 q^{71} +(-0.731993 + 1.26785i) q^{73} +(0.659906 + 1.14299i) q^{74} +(-0.622647 - 1.07846i) q^{76} +(-2.92199 + 0.282863i) q^{77} +3.41668 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.60559 - 6.24507i) q^{82} +(4.06648 - 7.04336i) q^{83} +(-2.19747 - 3.80613i) q^{85} +(-4.88416 + 8.45961i) q^{86} +(0.554785 + 0.960915i) q^{88} +(1.42132 + 2.46180i) q^{89} +(8.64146 - 0.836537i) q^{91} +(-3.14773 + 5.45204i) q^{92} +11.4617 q^{94} +1.24529 q^{95} +(-8.54592 + 14.8020i) q^{97} +(-4.59781 - 5.27827i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 16 q^{2} + 16 q^{4} - 8 q^{5} + 4 q^{7} + 16 q^{8} - 8 q^{10} - q^{11} + 2 q^{13} + 4 q^{14} + 16 q^{16} - 11 q^{17} - 2 q^{19} - 8 q^{20} - q^{22} - 11 q^{23} - 8 q^{25} + 2 q^{26} + 4 q^{28}+ \cdots - 14 q^{98}+O(q^{100})$ 16 * q + 16 * q^2 + 16 * q^4 - 8 * q^5 + 4 * q^7 + 16 * q^8 - 8 * q^10 - q^11 + 2 * q^13 + 4 * q^14 + 16 * q^16 - 11 * q^17 - 2 * q^19 - 8 * q^20 - q^22 - 11 * q^23 - 8 * q^25 + 2 * q^26 + 4 * q^28 - 17 * q^29 + 30 * q^31 + 16 * q^32 - 11 * q^34 + 4 * q^35 - 2 * q^37 - 2 * q^38 - 8 * q^40 - 7 * q^41 - 13 * q^43 - q^44 - 11 * q^46 - 10 * q^47 - 14 * q^49 - 8 * q^50 + 2 * q^52 - 18 * q^53 + 2 * q^55 + 4 * q^56 - 17 * q^58 + 2 * q^59 + 54 * q^61 + 30 * q^62 + 16 * q^64 - 4 * q^65 + 20 * q^67 - 11 * q^68 + 4 * q^70 + 38 * q^71 - 8 * q^73 - 2 * q^74 - 2 * q^76 + 7 * q^77 + 50 * q^79 - 8 * q^80 - 7 * q^82 - 2 * q^83 - 11 * q^85 - 13 * q^86 - q^88 + 6 * q^89 + 14 * q^91 - 11 * q^92 - 10 * q^94 + 4 * q^95 + 26 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$ .

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.09594	+	2.40809i	−0.414228	+	0.910173i
$7$	−1.09594	+	2.40809i	−0.414228	+	0.910173i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.554785	+	0.960915i	0.167274	+	0.289727i	0.937460	−	0.348092i	$-0.113170\pi$
$11$	0.554785	+	0.960915i	0.167274	+	0.289727i	−0.770187	+	0.637819i	$0.779837\pi$
$12$		0			0
$13$	−1.64072	−	2.84181i	−0.455053	−	0.788175i	0.543638	−	0.839320i	$-0.317046\pi$
$13$	−1.64072	−	2.84181i	−0.455053	−	0.788175i	−0.998691	+	0.0511446i	$0.983713\pi$
$14$	−1.09594	+	2.40809i	−0.292903	+	0.643590i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.19747	+	3.80613i	−0.532964	+	0.923121i	0.466294	+	0.884630i	$0.345589\pi$
$17$	−2.19747	+	3.80613i	−0.532964	+	0.923121i	−0.999259	+	0.0384919i	$0.987745\pi$
$18$		0			0
$19$	−0.622647	−	1.07846i	−0.142845	−	0.247415i	0.785722	−	0.618580i	$-0.212292\pi$
$19$	−0.622647	−	1.07846i	−0.142845	−	0.247415i	−0.928567	+	0.371165i	$0.878958\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	0.554785	+	0.960915i	0.118281	+	0.204868i
$23$	−3.14773	+	5.45204i	−0.656348	+	1.13683i	0.325206	+	0.945643i	$0.394566\pi$
$23$	−3.14773	+	5.45204i	−0.656348	+	1.13683i	−0.981554	+	0.191185i	$0.938767\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.64072	−	2.84181i	−0.321771	−	0.557324i
$27$		0			0
$28$	−1.09594	+	2.40809i	−0.207114	+	0.455087i
$29$	−3.26879	+	5.66171i	−0.606999	+	1.05135i	0.384733	+	0.923028i	$0.374293\pi$
$29$	−3.26879	+	5.66171i	−0.606999	+	1.05135i	−0.991732	+	0.128325i	$0.959040\pi$
$30$		0			0
$31$	3.10957			0.558495			0.279248	−	0.960219i	$-0.409915\pi$
$31$	3.10957			0.558495			0.279248	+	0.960219i	$0.409915\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.19747	+	3.80613i	−0.376863	+	0.652745i
$35$	−1.53750	−	2.15316i	−0.259884	−	0.363951i
$36$		0			0
$37$	0.659906	+	1.14299i	0.108488	+	0.187907i	0.915158	−	0.403096i	$-0.132066\pi$
$37$	0.659906	+	1.14299i	0.108488	+	0.187907i	−0.806670	+	0.591002i	$0.798732\pi$
$38$	−0.622647	−	1.07846i	−0.101007	−	0.174949i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.60559	−	6.24507i	−0.563099	−	0.975317i	−0.997224	−	0.0744637i	$-0.976276\pi$
$41$	−3.60559	−	6.24507i	−0.563099	−	0.975317i	0.434124	−	0.900853i	$-0.357058\pi$
$42$		0			0
$43$	−4.88416	+	8.45961i	−0.744827	+	1.29008i	0.205448	+	0.978668i	$0.434135\pi$
$43$	−4.88416	+	8.45961i	−0.744827	+	1.29008i	−0.950275	+	0.311411i	$0.899198\pi$
$44$	0.554785	+	0.960915i	0.0836370	+	0.144863i
$45$		0			0
$46$	−3.14773	+	5.45204i	−0.464108	+	0.803859i
$47$	11.4617			1.67186			0.835929	−	0.548838i	$-0.184930\pi$
$47$	11.4617			1.67186			0.835929	+	0.548838i	$0.184930\pi$
$48$		0			0
$49$	−4.59781	−	5.27827i	−0.656830	−	0.754038i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−1.64072	−	2.84181i	−0.227527	−	0.394088i
$53$	−2.73283	+	4.73340i	−0.375383	+	0.650182i	−0.990384	−	0.138344i	$-0.955822\pi$
$53$	−2.73283	+	4.73340i	−0.375383	+	0.650182i	0.615002	+	0.788526i	$0.289155\pi$
$54$		0			0
$55$	−1.10957			−0.149614
$56$	−1.09594	+	2.40809i	−0.146452	+	0.321795i
$57$		0			0
$58$	−3.26879	+	5.66171i	−0.429213	+	0.743419i
$59$	−6.46993			−0.842313			−0.421157	−	0.906988i	$-0.638376\pi$
$59$	−6.46993			−0.842313			−0.421157	+	0.906988i	$0.638376\pi$
$60$		0			0
$61$	4.40470			0.563964			0.281982	−	0.959420i	$-0.409008\pi$
$61$	4.40470			0.563964			0.281982	+	0.959420i	$0.409008\pi$
$62$	3.10957			0.394916
$63$		0			0
$64$	1.00000			0.125000
$65$	3.28143			0.407012
$66$		0			0
$67$	−5.23241			−0.639241			−0.319620	−	0.947546i	$-0.603555\pi$
$67$	−5.23241			−0.639241			−0.319620	+	0.947546i	$0.603555\pi$
$68$	−2.19747	+	3.80613i	−0.266482	+	0.461561i
$69$		0			0
$70$	−1.53750	−	2.15316i	−0.183766	−	0.257352i
$71$	−16.3046			−1.93501			−0.967503	−	0.252860i	$-0.918629\pi$
$71$	−16.3046			−1.93501			−0.967503	+	0.252860i	$0.918629\pi$
$72$		0			0
$73$	−0.731993	+	1.26785i	−0.0856733	+	0.148391i	−0.905678	−	0.423966i	$-0.860637\pi$
$73$	−0.731993	+	1.26785i	−0.0856733	+	0.148391i	0.820005	+	0.572357i	$0.193971\pi$
$74$	0.659906	+	1.14299i	0.0767126	+	0.132870i
$75$		0			0
$76$	−0.622647	−	1.07846i	−0.0714225	−	0.123707i
$77$	−2.92199	+	0.282863i	−0.332991	+	0.0322352i
$78$		0			0
$79$	3.41668			0.384407			0.192204	−	0.981355i	$-0.438437\pi$
$79$	3.41668			0.384407			0.192204	+	0.981355i	$0.438437\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−3.60559	−	6.24507i	−0.398171	−	0.689653i
$83$	4.06648	−	7.04336i	0.446355	−	0.773109i	−0.551791	−	0.833983i	$-0.686055\pi$
$83$	4.06648	−	7.04336i	0.446355	−	0.773109i	0.998145	+	0.0608736i	$0.0193887\pi$
$84$		0			0
$85$	−2.19747	−	3.80613i	−0.238349	−	0.412832i
$86$	−4.88416	+	8.45961i	−0.526672	+	0.912223i
$87$		0			0
$88$	0.554785	+	0.960915i	0.0591403	+	0.102434i
$89$	1.42132	+	2.46180i	0.150660	+	0.260950i	0.931470	−	0.363818i	$-0.118527\pi$
$89$	1.42132	+	2.46180i	0.150660	+	0.260950i	−0.780810	+	0.624768i	$0.785194\pi$
$90$		0			0
$91$	8.64146	−	0.836537i	0.905872	−	0.0876929i
$92$	−3.14773	+	5.45204i	−0.328174	+	0.568414i
$93$		0			0
$94$	11.4617			1.18218
$95$	1.24529			0.127764
$96$		0			0
$97$	−8.54592	+	14.8020i	−0.867707	+	1.50291i	−0.00337237	+	0.999994i	$0.501073\pi$
$97$	−8.54592	+	14.8020i	−0.867707	+	1.50291i	−0.864334	+	0.502918i	$0.832260\pi$
$98$	−4.59781	−	5.27827i	−0.464449	−	0.533186i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.73642	+	6.47167i	0.371788	+	0.643955i	0.989841	−	0.142181i	$-0.0454117\pi$
$101$	3.73642	+	6.47167i	0.371788	+	0.643955i	−0.618053	+	0.786136i	$0.712078\pi$
$102$		0			0
$103$	2.48518	−	4.30445i	0.244872	−	0.424130i	−0.717224	−	0.696843i	$-0.754587\pi$
$103$	2.48518	−	4.30445i	0.244872	−	0.424130i	0.962096	+	0.272713i	$0.0879208\pi$
$104$	−1.64072	−	2.84181i	−0.160886	−	0.278662i
$105$		0			0
$106$	−2.73283	+	4.73340i	−0.265436	+	0.459748i
$107$	3.51531	+	6.08870i	0.339838	+	0.588617i	0.984402	−	0.175934i	$-0.0562944\pi$
$107$	3.51531	+	6.08870i	0.339838	+	0.588617i	−0.644564	+	0.764550i	$0.722961\pi$
$108$		0			0
$109$	−5.12829	+	8.88245i	−0.491201	+	0.850785i	−0.999949	−	0.0101309i	$-0.996775\pi$
$109$	−5.12829	+	8.88245i	−0.491201	+	0.850785i	0.508748	+	0.860916i	$0.330109\pi$
$110$	−1.10957			−0.105793
$111$		0			0
$112$	−1.09594	+	2.40809i	−0.103557	+	0.227543i
$113$	−3.64304	−	6.30993i	−0.342708	−	0.593588i	0.642226	−	0.766515i	$-0.278011\pi$
$113$	−3.64304	−	6.30993i	−0.342708	−	0.593588i	−0.984935	+	0.172927i	$0.944678\pi$
$114$		0			0
$115$	−3.14773	−	5.45204i	−0.293528	−	0.508405i
$116$	−3.26879	+	5.66171i	−0.303499	+	0.525677i
$117$		0			0
$118$	−6.46993			−0.595605
$119$	−6.75720	−	9.46301i	−0.619432	−	0.867473i
$120$		0			0
$121$	4.88443	−	8.46008i	0.444039	−	0.769098i
$122$	4.40470			0.398783
$123$		0			0
$124$	3.10957			0.279248
$125$	1.00000			0.0894427
$126$		0			0
$127$	20.9242			1.85673			0.928363	−	0.371674i	$-0.121216\pi$
$127$	20.9242			1.85673			0.928363	+	0.371674i	$0.121216\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	3.28143			0.287801
$131$	7.41195	−	12.8379i	0.647585	−	1.12165i	−0.336113	−	0.941822i	$-0.609112\pi$
$131$	7.41195	−	12.8379i	0.647585	−	1.12165i	0.983698	−	0.179828i	$-0.0575542\pi$
$132$		0			0
$133$	3.27941	−	0.317463i	0.284361	−	0.0275275i
$134$	−5.23241			−0.452011
$135$		0			0
$136$	−2.19747	+	3.80613i	−0.188431	+	0.326373i
$137$	6.20268	+	10.7434i	0.529931	+	0.917867i	0.999390	+	0.0349133i	$0.0111155\pi$
$137$	6.20268	+	10.7434i	0.529931	+	0.917867i	−0.469459	+	0.882954i	$0.655551\pi$
$138$		0			0
$139$	11.5310	+	19.9723i	0.978047	+	1.69403i	0.669491	+	0.742820i	$0.266512\pi$
$139$	11.5310	+	19.9723i	0.978047	+	1.69403i	0.308555	+	0.951206i	$0.400155\pi$
$140$	−1.53750	−	2.15316i	−0.129942	−	0.181975i
$141$		0			0
$142$	−16.3046			−1.36826
$143$	1.82049	−	3.15318i	0.152237	−	0.263682i
$144$		0			0
$145$	−3.26879	−	5.66171i	−0.271458	−	0.470179i
$146$	−0.731993	+	1.26785i	−0.0605802	+	0.104928i
$147$		0			0
$148$	0.659906	+	1.14299i	0.0542440	+	0.0939533i
$149$	1.37460	−	2.38087i	0.112611	−	0.195048i	−0.804211	−	0.594344i	$-0.797412\pi$
$149$	1.37460	−	2.38087i	0.112611	−	0.195048i	0.916822	+	0.399295i	$0.130745\pi$
$150$		0			0
$151$	9.23849	+	16.0015i	0.751818	+	1.30219i	0.946941	+	0.321408i	$0.104156\pi$
$151$	9.23849	+	16.0015i	0.751818	+	1.30219i	−0.195123	+	0.980779i	$0.562511\pi$
$152$	−0.622647	−	1.07846i	−0.0505033	−	0.0874743i
$153$		0			0
$154$	−2.92199	+	0.282863i	−0.235460	+	0.0227937i
$155$	−1.55478	+	2.69297i	−0.124883	+	0.216304i
$156$		0			0
$157$	−4.29934			−0.343124			−0.171562	−	0.985173i	$-0.554881\pi$
$157$	−4.29934			−0.343124			−0.171562	+	0.985173i	$0.554881\pi$
$158$	3.41668			0.271817
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−9.67926	−	13.5552i	−0.762833	−	1.06830i
$162$		0			0
$163$	6.23750	+	10.8037i	0.488558	+	0.846208i	0.999913	−	0.0131616i	$-0.00418959\pi$
$163$	6.23750	+	10.8037i	0.488558	+	0.846208i	−0.511355	+	0.859370i	$0.670856\pi$
$164$	−3.60559	−	6.24507i	−0.281550	−	0.487658i
$165$		0			0
$166$	4.06648	−	7.04336i	0.315620	−	0.546671i
$167$	−3.40584	−	5.89909i	−0.263552	−	0.456486i	0.703631	−	0.710565i	$-0.251561\pi$
$167$	−3.40584	−	5.89909i	−0.263552	−	0.456486i	−0.967183	+	0.254080i	$0.918227\pi$
$168$		0			0
$169$	1.11609	−	1.93313i	0.0858534	−	0.148702i
$170$	−2.19747	−	3.80613i	−0.168538	−	0.291917i
$171$		0			0
$172$	−4.88416	+	8.45961i	−0.372414	+	0.645039i
$173$	8.41334			0.639655			0.319827	−	0.947476i	$-0.396375\pi$
$173$	8.41334			0.639655			0.319827	+	0.947476i	$0.396375\pi$
$174$		0			0
$175$	2.63344	−	0.254930i	0.199069	−	0.0192709i
$176$	0.554785	+	0.960915i	0.0418185	+	0.0724317i
$177$		0			0
$178$	1.42132	+	2.46180i	0.106533	+	0.184520i
$179$	11.0539	−	19.1459i	0.826205	−	1.43103i	−0.0747893	−	0.997199i	$-0.523828\pi$
$179$	11.0539	−	19.1459i	0.826205	−	1.43103i	0.900995	−	0.433830i	$-0.142838\pi$
$180$		0			0
$181$	6.82038			0.506955			0.253477	−	0.967341i	$-0.418426\pi$
$181$	6.82038			0.506955			0.253477	+	0.967341i	$0.418426\pi$
$182$	8.64146	−	0.836537i	0.640548	−	0.0620082i
$183$		0			0
$184$	−3.14773	+	5.45204i	−0.232054	+	0.401929i
$185$	−1.31981			−0.0970346
$186$		0			0
$187$	−4.87649			−0.356604
$188$	11.4617			0.835929
$189$		0			0
$190$	1.24529			0.0903431
$191$	−3.93174			−0.284491			−0.142245	−	0.989831i	$-0.545432\pi$
$191$	−3.93174			−0.284491			−0.142245	+	0.989831i	$0.545432\pi$
$192$		0			0
$193$	5.85359			0.421351			0.210675	−	0.977556i	$-0.432434\pi$
$193$	5.85359			0.421351			0.210675	+	0.977556i	$0.432434\pi$
$194$	−8.54592	+	14.8020i	−0.613561	+	1.06272i
$195$		0			0
$196$	−4.59781	−	5.27827i	−0.328415	−	0.377019i
$197$	−1.71845			−0.122435			−0.0612174	−	0.998124i	$-0.519498\pi$
$197$	−1.71845			−0.122435			−0.0612174	+	0.998124i	$0.519498\pi$
$198$		0			0
$199$	2.00694	−	3.47612i	0.142268	−	0.246415i	−0.786082	−	0.618122i	$-0.787894\pi$
$199$	2.00694	−	3.47612i	0.142268	−	0.246415i	0.928350	+	0.371706i	$0.121227\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	3.73642	+	6.47167i	0.262893	+	0.455345i
$203$	−10.0515	−	14.0765i	−0.705477	−	0.987974i
$204$		0			0
$205$	7.21119			0.503651
$206$	2.48518	−	4.30445i	0.173150	−	0.299905i
$207$		0			0
$208$	−1.64072	−	2.84181i	−0.113763	−	0.197044i
$209$	0.690870	−	1.19662i	0.0477885	−	0.0827720i
$210$		0			0
$211$	−2.32892	−	4.03380i	−0.160329	−	0.277698i	0.774657	−	0.632381i	$-0.217922\pi$
$211$	−2.32892	−	4.03380i	−0.160329	−	0.277698i	−0.934987	+	0.354683i	$0.884589\pi$
$212$	−2.73283	+	4.73340i	−0.187691	+	0.325091i
$213$		0			0
$214$	3.51531	+	6.08870i	0.240302	+	0.416215i
$215$	−4.88416	−	8.45961i	−0.333097	−	0.576941i
$216$		0			0
$217$	−3.40792	+	7.48813i	−0.231344	+	0.508327i
$218$	−5.12829	+	8.88245i	−0.347331	+	0.601596i
$219$		0			0
$220$	−1.10957			−0.0748072
$221$	14.4217			0.970108
$222$		0			0
$223$	13.3981	−	23.2061i	0.897201	−	1.55400i	0.0661434	−	0.997810i	$-0.478931\pi$
$223$	13.3981	−	23.2061i	0.897201	−	1.55400i	0.831057	−	0.556187i	$-0.187736\pi$
$224$	−1.09594	+	2.40809i	−0.0732259	+	0.160897i
$225$		0			0
$226$	−3.64304	−	6.30993i	−0.242331	−	0.419730i
$227$	6.05706	+	10.4911i	0.402021	+	0.696322i	0.993970	−	0.109654i	$-0.0349744\pi$
$227$	6.05706	+	10.4911i	0.402021	+	0.696322i	−0.591948	+	0.805976i	$0.701641\pi$
$228$		0			0
$229$	8.07886	−	13.9930i	0.533866	−	0.924683i	−0.465351	−	0.885126i	$-0.654072\pi$
$229$	8.07886	−	13.9930i	0.533866	−	0.924683i	0.999217	−	0.0395568i	$-0.0125946\pi$
$230$	−3.14773	−	5.45204i	−0.207555	−	0.359497i
$231$		0			0
$232$	−3.26879	+	5.66171i	−0.214607	+	0.371709i
$233$	−8.65151	−	14.9849i	−0.566779	−	0.981691i	−0.996882	−	0.0789105i	$-0.974856\pi$
$233$	−8.65151	−	14.9849i	−0.566779	−	0.981691i	0.430102	−	0.902780i	$-0.358477\pi$
$234$		0			0
$235$	−5.73084	+	9.92610i	−0.373839	+	0.647508i
$236$	−6.46993			−0.421157
$237$		0			0
$238$	−6.75720	−	9.46301i	−0.438004	−	0.613396i
$239$	−0.644644	−	1.11656i	−0.0416985	−	0.0722240i	0.844423	−	0.535677i	$-0.179944\pi$
$239$	−0.644644	−	1.11656i	−0.0416985	−	0.0722240i	−0.886121	+	0.463453i	$0.846610\pi$
$240$		0			0
$241$	0.200516	+	0.347304i	0.0129164	+	0.0223718i	0.872411	−	0.488772i	$-0.162555\pi$
$241$	0.200516	+	0.347304i	0.0129164	+	0.0223718i	−0.859495	+	0.511144i	$0.829222\pi$
$242$	4.88443	−	8.46008i	0.313983	−	0.543834i
$243$		0			0
$244$	4.40470			0.281982
$245$	6.87002	−	1.34269i	0.438910	−	0.0857811i
$246$		0			0
$247$	−2.04317	+	3.53888i	−0.130004	+	0.225174i
$248$	3.10957			0.197458
$249$		0			0
$250$	1.00000			0.0632456
$251$	−6.00739			−0.379183			−0.189592	−	0.981863i	$-0.560716\pi$
$251$	−6.00739			−0.379183			−0.189592	+	0.981863i	$0.560716\pi$
$252$		0			0
$253$	−6.98526			−0.439160
$254$	20.9242			1.31290
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.2294	+	21.1819i	−0.762848	+	1.32129i	0.178528	+	0.983935i	$0.442866\pi$
$257$	−12.2294	+	21.1819i	−0.762848	+	1.32129i	−0.941377	+	0.337357i	$0.890467\pi$
$258$		0			0
$259$	−3.47565	+	0.336460i	−0.215966	+	0.0209066i
$260$	3.28143			0.203506
$261$		0			0
$262$	7.41195	−	12.8379i	0.457912	−	0.793126i
$263$	−12.0119	−	20.8052i	−0.740684	−	1.28290i	−0.952184	−	0.305524i	$-0.901168\pi$
$263$	−12.0119	−	20.8052i	−0.740684	−	1.28290i	0.211500	−	0.977378i	$-0.432165\pi$
$264$		0			0
$265$	−2.73283	−	4.73340i	−0.167876	−	0.290770i
$266$	3.27941	−	0.317463i	0.201073	−	0.0194649i
$267$		0			0
$268$	−5.23241			−0.319620
$269$	8.24890	−	14.2875i	0.502944	−	0.871125i	−0.497050	−	0.867722i	$-0.665583\pi$
$269$	8.24890	−	14.2875i	0.502944	−	0.871125i	0.999994	−	0.00340330i	$-0.00108331\pi$
$270$		0			0
$271$	−14.6982	−	25.4580i	−0.892852	−	1.54646i	−0.836441	−	0.548057i	$-0.815368\pi$
$271$	−14.6982	−	25.4580i	−0.892852	−	1.54646i	−0.0564111	−	0.998408i	$-0.517966\pi$
$272$	−2.19747	+	3.80613i	−0.133241	+	0.230780i
$273$		0			0
$274$	6.20268	+	10.7434i	0.374718	+	0.649030i
$275$	0.554785	−	0.960915i	0.0334548	−	0.0579454i
$276$		0			0
$277$	4.86992	+	8.43495i	0.292605	+	0.506807i	0.974425	−	0.224713i	$-0.0721445\pi$
$277$	4.86992	+	8.43495i	0.292605	+	0.506807i	−0.681820	+	0.731520i	$0.738811\pi$
$278$	11.5310	+	19.9723i	0.691583	+	1.19786i
$279$		0			0
$280$	−1.53750	−	2.15316i	−0.0918830	−	0.128676i
$281$	−11.2140	+	19.4232i	−0.668970	+	1.15869i	0.309223	+	0.950990i	$0.399931\pi$
$281$	−11.2140	+	19.4232i	−0.668970	+	1.15869i	−0.978193	+	0.207700i	$0.933402\pi$
$282$		0			0
$283$	−18.4120			−1.09448			−0.547240	−	0.836976i	$-0.684322\pi$
$283$	−18.4120			−1.09448			−0.547240	+	0.836976i	$0.684322\pi$
$284$	−16.3046			−0.967503
$285$		0			0
$286$	1.82049	−	3.15318i	0.107648	−	0.186452i
$287$	18.9902	−	1.83835i	1.12096	−	0.108514i
$288$		0			0
$289$	−1.15774	−	2.00526i	−0.0681021	−	0.117956i
$290$	−3.26879	−	5.66171i	−0.191950	−	0.332467i
$291$		0			0
$292$	−0.731993	+	1.26785i	−0.0428366	+	0.0741953i
$293$	9.32830	+	16.1571i	0.544965	+	0.943907i	0.998609	+	0.0527239i	$0.0167903\pi$
$293$	9.32830	+	16.1571i	0.544965	+	0.943907i	−0.453644	+	0.891183i	$0.649876\pi$
$294$		0			0
$295$	3.23497	−	5.60312i	0.188347	−	0.326226i
$296$	0.659906	+	1.14299i	0.0383563	+	0.0664350i
$297$		0			0
$298$	1.37460	−	2.38087i	0.0796282	−	0.137920i
$299$	20.6582			1.19469
$300$		0			0
$301$	−15.0188	−	21.0328i	−0.865667	−	1.21231i
$302$	9.23849	+	16.0015i	0.531616	+	0.920785i
$303$		0			0
$304$	−0.622647	−	1.07846i	−0.0357112	−	0.0618537i
$305$	−2.20235	+	3.81458i	−0.126106	+	0.218422i
$306$		0			0
$307$	25.9429			1.48064			0.740320	−	0.672255i	$-0.234674\pi$
$307$	25.9429			1.48064			0.740320	+	0.672255i	$0.234674\pi$
$308$	−2.92199	+	0.282863i	−0.166496	+	0.0161176i
$309$		0			0
$310$	−1.55478	+	2.69297i	−0.0883058	+	0.152950i
$311$	−9.38608			−0.532236			−0.266118	−	0.963940i	$-0.585741\pi$
$311$	−9.38608			−0.532236			−0.266118	+	0.963940i	$0.585741\pi$
$312$		0			0
$313$	0.317071			0.0179219			0.00896097	−	0.999960i	$-0.497148\pi$
$313$	0.317071			0.0179219			0.00896097	+	0.999960i	$0.497148\pi$
$314$	−4.29934			−0.242626
$315$		0			0
$316$	3.41668			0.192204
$317$	−4.25665			−0.239077			−0.119539	−	0.992830i	$-0.538141\pi$
$317$	−4.25665			−0.239077			−0.119539	+	0.992830i	$0.538141\pi$
$318$		0			0
$319$	−7.25390			−0.406140
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−9.67926	−	13.5552i	−0.539404	−	0.755400i
$323$	5.47299			0.304525
$324$		0			0
$325$	−1.64072	+	2.84181i	−0.0910106	+	0.157635i
$326$	6.23750	+	10.8037i	0.345463	+	0.598359i
$327$		0			0
$328$	−3.60559	−	6.24507i	−0.199086	−	0.344827i
$329$	−12.5614	+	27.6008i	−0.692530	+	1.52168i
$330$		0			0
$331$	6.77455			0.372363			0.186181	−	0.982515i	$-0.440389\pi$
$331$	6.77455			0.372363			0.186181	+	0.982515i	$0.440389\pi$
$332$	4.06648	−	7.04336i	0.223177	−	0.386554i
$333$		0			0
$334$	−3.40584	−	5.89909i	−0.186359	−	0.322784i
$335$	2.61620	−	4.53140i	0.142939	−	0.247577i
$336$		0			0
$337$	7.69796	+	13.3333i	0.419335	+	0.726309i	0.995873	−	0.0907613i	$-0.0289300\pi$
$337$	7.69796	+	13.3333i	0.419335	+	0.726309i	−0.576538	+	0.817070i	$0.695597\pi$
$338$	1.11609	−	1.93313i	0.0607075	−	0.105148i
$339$		0			0
$340$	−2.19747	−	3.80613i	−0.119174	−	0.206416i
$341$	1.72514	+	2.98803i	0.0934217	+	0.161811i
$342$		0			0
$343$	17.7495	−	5.28726i	0.958383	−	0.285485i
$344$	−4.88416	+	8.45961i	−0.263336	+	0.456112i
$345$		0			0
$346$	8.41334			0.452304
$347$	4.27257			0.229363			0.114682	−	0.993402i	$-0.463415\pi$
$347$	4.27257			0.229363			0.114682	+	0.993402i	$0.463415\pi$
$348$		0			0
$349$	3.08538	−	5.34404i	0.165157	−	0.286060i	−0.771554	−	0.636164i	$-0.780520\pi$
$349$	3.08538	−	5.34404i	0.165157	−	0.286060i	0.936711	+	0.350104i	$0.113854\pi$
$350$	2.63344	−	0.254930i	0.140763	−	0.0136266i
$351$		0			0
$352$	0.554785	+	0.960915i	0.0295701	+	0.0512170i
$353$	−6.21075	−	10.7573i	−0.330565	−	0.572555i	0.652058	−	0.758169i	$-0.273906\pi$
$353$	−6.21075	−	10.7573i	−0.330565	−	0.572555i	−0.982623	+	0.185614i	$0.940573\pi$
$354$		0			0
$355$	8.15232	−	14.1202i	0.432680	−	0.749424i
$356$	1.42132	+	2.46180i	0.0753299	+	0.130475i
$357$		0			0
$358$	11.0539	−	19.1459i	0.584215	−	1.01189i
$359$	−11.9318	−	20.6665i	−0.629738	−	1.09074i	−0.987604	−	0.156965i	$-0.949829\pi$
$359$	−11.9318	−	20.6665i	−0.629738	−	1.09074i	0.357867	−	0.933773i	$-0.383504\pi$
$360$		0			0
$361$	8.72462	−	15.1115i	0.459191	−	0.795342i
$362$	6.82038			0.358471
$363$		0			0
$364$	8.64146	−	0.836537i	0.452936	−	0.0438464i
$365$	−0.731993	−	1.26785i	−0.0383143	−	0.0663622i
$366$		0			0
$367$	−3.98627	−	6.90443i	−0.208082	−	0.360408i	0.743028	−	0.669260i	$-0.233389\pi$
$367$	−3.98627	−	6.90443i	−0.208082	−	0.360408i	−0.951110	+	0.308852i	$0.900055\pi$
$368$	−3.14773	+	5.45204i	−0.164087	+	0.284207i
$369$		0			0
$370$	−1.31981			−0.0686138
$371$	−8.40343	−	11.7684i	−0.436284	−	0.610987i
$372$		0			0
$373$	2.25724	−	3.90965i	0.116875	−	0.202434i	−0.801653	−	0.597790i	$-0.796046\pi$
$373$	2.25724	−	3.90965i	0.116875	−	0.202434i	0.918528	+	0.395356i	$0.129379\pi$
$374$	−4.87649			−0.252157
$375$		0			0
$376$	11.4617			0.591091
$377$	21.4526			1.10487
$378$		0			0
$379$	−7.52115			−0.386336			−0.193168	−	0.981166i	$-0.561876\pi$
$379$	−7.52115			−0.386336			−0.193168	+	0.981166i	$0.561876\pi$
$380$	1.24529			0.0638822
$381$		0			0
$382$	−3.93174			−0.201165
$383$	8.53489	−	14.7829i	0.436113	−	0.755369i	−0.561273	−	0.827631i	$-0.689688\pi$
$383$	8.53489	−	14.7829i	0.436113	−	0.755369i	0.997386	+	0.0722614i	$0.0230216\pi$
$384$		0			0
$385$	1.21603	−	2.67195i	0.0619744	−	0.136175i
$386$	5.85359			0.297940
$387$		0			0
$388$	−8.54592	+	14.8020i	−0.433853	+	0.751456i
$389$	18.3046	+	31.7044i	0.928078	+	1.60748i	0.786535	+	0.617545i	$0.211873\pi$
$389$	18.3046	+	31.7044i	0.928078	+	1.60748i	0.141542	+	0.989932i	$0.454794\pi$
$390$		0			0
$391$	−13.8341	−	23.9614i	−0.699620	−	1.21178i
$392$	−4.59781	−	5.27827i	−0.232225	−	0.266593i
$393$		0			0
$394$	−1.71845			−0.0865745
$395$	−1.70834	+	2.95894i	−0.0859560	+	0.148880i
$396$		0			0
$397$	3.55157	+	6.15150i	0.178248	+	0.308735i	0.941281	−	0.337625i	$-0.109624\pi$
$397$	3.55157	+	6.15150i	0.178248	+	0.308735i	−0.763032	+	0.646360i	$0.776290\pi$
$398$	2.00694	−	3.47612i	0.100599	−	0.174242i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−14.8674	+	25.7511i	−0.742442	+	1.28595i	0.208939	+	0.977929i	$0.432999\pi$
$401$	−14.8674	+	25.7511i	−0.742442	+	1.28595i	−0.951381	+	0.308018i	$0.900334\pi$
$402$		0			0
$403$	−5.10192	−	8.83679i	−0.254145	−	0.440192i
$404$	3.73642	+	6.47167i	0.185894	+	0.321977i
$405$		0			0
$406$	−10.0515	−	14.0765i	−0.498848	−	0.698603i
$407$	−0.732212	+	1.26823i	−0.0362944	+	0.0628638i
$408$		0			0
$409$	−34.4783			−1.70484			−0.852422	−	0.522855i	$-0.824867\pi$
$409$	−34.4783			−1.70484			−0.852422	+	0.522855i	$0.824867\pi$
$410$	7.21119			0.356135
$411$		0			0
$412$	2.48518	−	4.30445i	0.122436	−	0.212065i
$413$	7.09068	−	15.5802i	0.348910	−	0.766651i
$414$		0			0
$415$	4.06648	+	7.04336i	0.199616	+	0.345745i
$416$	−1.64072	−	2.84181i	−0.0804428	−	0.139331i
$417$		0			0
$418$	0.690870	−	1.19662i	0.0337915	−	0.0585287i
$419$	6.08528	+	10.5400i	0.297285	+	0.514913i	0.975514	−	0.219938i	$-0.0705855\pi$
$419$	6.08528	+	10.5400i	0.297285	+	0.514913i	−0.678229	+	0.734851i	$0.737252\pi$
$420$		0			0
$421$	−4.27799	+	7.40969i	−0.208496	+	0.361126i	−0.951241	−	0.308449i	$-0.900190\pi$
$421$	−4.27799	+	7.40969i	−0.208496	+	0.361126i	0.742745	+	0.669575i	$0.233524\pi$
$422$	−2.32892	−	4.03380i	−0.113370	−	0.196362i
$423$		0			0
$424$	−2.73283	+	4.73340i	−0.132718	+	0.229874i
$425$	4.39494			0.213186
$426$		0			0
$427$	−4.82730	+	10.6069i	−0.233610	+	0.513305i
$428$	3.51531	+	6.08870i	0.169919	+	0.294308i
$429$		0			0
$430$	−4.88416	−	8.45961i	−0.235535	−	0.407959i
$431$	12.6727	−	21.9497i	0.610422	−	1.05728i	−0.380747	−	0.924679i	$-0.624333\pi$
$431$	12.6727	−	21.9497i	0.610422	−	1.05728i	0.991169	−	0.132603i	$-0.0423334\pi$
$432$		0			0
$433$	−17.9795			−0.864041			−0.432020	−	0.901864i	$-0.642199\pi$
$433$	−17.9795			−0.864041			−0.432020	+	0.901864i	$0.642199\pi$
$434$	−3.40792	+	7.48813i	−0.163585	+	0.359442i
$435$		0			0
$436$	−5.12829	+	8.88245i	−0.245600	+	0.425392i
$437$	7.83971			0.375024
$438$		0			0
$439$	−4.23398			−0.202077			−0.101038	−	0.994883i	$-0.532217\pi$
$439$	−4.23398			−0.202077			−0.101038	+	0.994883i	$0.532217\pi$
$440$	−1.10957			−0.0528967
$441$		0			0
$442$	14.4217			0.685970
$443$	21.7581			1.03376			0.516879	−	0.856059i	$-0.327094\pi$
$443$	21.7581			1.03376			0.516879	+	0.856059i	$0.327094\pi$
$444$		0			0
$445$	−2.84264			−0.134754
$446$	13.3981	−	23.2061i	0.634417	−	1.09884i
$447$		0			0
$448$	−1.09594	+	2.40809i	−0.0517785	+	0.113772i
$449$	29.3888			1.38694			0.693471	−	0.720485i	$-0.256081\pi$
$449$	29.3888			1.38694			0.693471	+	0.720485i	$0.256081\pi$
$450$		0			0
$451$	4.00066	−	6.92934i	0.188384	−	0.326290i
$452$	−3.64304	−	6.30993i	−0.171354	−	0.296794i
$453$		0			0
$454$	6.05706	+	10.4911i	0.284272	+	0.492374i
$455$	−3.59627	+	7.90200i	−0.168596	+	0.370451i
$456$		0			0
$457$	27.7640			1.29875			0.649373	−	0.760470i	$-0.275032\pi$
$457$	27.7640			1.29875			0.649373	+	0.760470i	$0.275032\pi$
$458$	8.07886	−	13.9930i	0.377500	−	0.653850i
$459$		0			0
$460$	−3.14773	−	5.45204i	−0.146764	−	0.254202i
$461$	4.36929	−	7.56783i	0.203498	−	0.352469i	−0.746155	−	0.665772i	$-0.768102\pi$
$461$	4.36929	−	7.56783i	0.203498	−	0.352469i	0.949653	+	0.313303i	$0.101436\pi$
$462$		0			0
$463$	17.2947	+	29.9553i	0.803753	+	1.39214i	0.917129	+	0.398590i	$0.130500\pi$
$463$	17.2947	+	29.9553i	0.803753	+	1.39214i	−0.113376	+	0.993552i	$0.536166\pi$
$464$	−3.26879	+	5.66171i	−0.151750	+	0.262838i
$465$		0			0
$466$	−8.65151	−	14.9849i	−0.400774	−	0.694160i
$467$	17.2500	+	29.8779i	0.798236	+	1.38259i	0.920764	+	0.390121i	$0.127567\pi$
$467$	17.2500	+	29.8779i	0.798236	+	1.38259i	−0.122527	+	0.992465i	$0.539100\pi$
$468$		0			0
$469$	5.73443	−	12.6001i	0.264791	−	0.581820i
$470$	−5.73084	+	9.92610i	−0.264344	+	0.457857i
$471$		0			0
$472$	−6.46993			−0.297803
$473$	−10.8386			−0.498361
$474$		0			0
$475$	−0.622647	+	1.07846i	−0.0285690	+	0.0494829i
$476$	−6.75720	−	9.46301i	−0.309716	−	0.433736i
$477$		0			0
$478$	−0.644644	−	1.11656i	−0.0294853	−	0.0510701i
$479$	1.60798	+	2.78510i	0.0734703	+	0.127254i	0.900420	−	0.435022i	$-0.143259\pi$
$479$	1.60798	+	2.78510i	0.0734703	+	0.127254i	−0.826950	+	0.562276i	$0.809926\pi$
$480$		0			0
$481$	2.16544	−	3.75065i	0.0987356	−	0.171015i
$482$	0.200516	+	0.347304i	0.00913326	+	0.0158193i
$483$		0			0
$484$	4.88443	−	8.46008i	0.222019	−	0.384549i
$485$	−8.54592	−	14.8020i	−0.388050	−	0.672123i
$486$		0			0
$487$	−7.44719	+	12.8989i	−0.337465	+	0.584506i	−0.983955	−	0.178416i	$-0.942903\pi$
$487$	−7.44719	+	12.8989i	−0.337465	+	0.584506i	0.646491	+	0.762922i	$0.276236\pi$
$488$	4.40470			0.199391
$489$		0			0
$490$	6.87002	−	1.34269i	0.310356	−	0.0606564i
$491$	−21.6718	−	37.5367i	−0.978035	−	1.69401i	−0.669532	−	0.742783i	$-0.733505\pi$
$491$	−21.6718	−	37.5367i	−0.978035	−	1.69401i	−0.308503	−	0.951223i	$-0.599828\pi$
$492$		0			0
$493$	−14.3661	−	24.8829i	−0.647018	−	1.12067i
$494$	−2.04317	+	3.53888i	−0.0919268	+	0.159222i
$495$		0			0
$496$	3.10957			0.139624
$497$	17.8690	−	39.2631i	0.801534	−	1.76119i
$498$		0			0
$499$	−21.8828	+	37.9022i	−0.979611	+	1.69674i	−0.315817	+	0.948820i	$0.602278\pi$
$499$	−21.8828	+	37.9022i	−0.979611	+	1.69674i	−0.663794	+	0.747915i	$0.731055\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$	−6.00739			−0.268123
$503$	22.8379			1.01829			0.509147	−	0.860680i	$-0.329961\pi$
$503$	22.8379			1.01829			0.509147	+	0.860680i	$0.329961\pi$
$504$		0			0
$505$	−7.47284			−0.332537
$506$	−6.98526			−0.310533
$507$		0			0
$508$	20.9242			0.928363
$509$	8.35737	−	14.4754i	0.370434	−	0.641610i	−0.619198	−	0.785235i	$-0.712542\pi$
$509$	8.35737	−	14.4754i	0.370434	−	0.641610i	0.989632	+	0.143624i	$0.0458757\pi$
$510$		0			0
$511$	−2.25087	−	3.15220i	−0.0995728	−	0.139445i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−12.2294	+	21.1819i	−0.539415	+	0.934295i
$515$	2.48518	+	4.30445i	0.109510	+	0.189677i
$516$		0			0
$517$	6.35876	+	11.0137i	0.279658	+	0.484382i
$518$	−3.47565	+	0.336460i	−0.152711	+	0.0147832i
$519$		0			0
$520$	3.28143			0.143900
$521$	−9.95880	+	17.2491i	−0.436303	+	0.755699i	−0.997401	−	0.0720506i	$-0.977046\pi$
$521$	−9.95880	+	17.2491i	−0.436303	+	0.755699i	0.561098	+	0.827749i	$0.310379\pi$
$522$		0			0
$523$	−10.8121	−	18.7270i	−0.472778	−	0.818876i	0.526736	−	0.850029i	$-0.323416\pi$
$523$	−10.8121	−	18.7270i	−0.472778	−	0.818876i	−0.999515	+	0.0311527i	$0.990082\pi$
$524$	7.41195	−	12.8379i	0.323792	−	0.560825i
$525$		0			0
$526$	−12.0119	−	20.8052i	−0.523743	−	0.907149i
$527$	−6.83318	+	11.8354i	−0.297658	+	0.515559i
$528$		0			0
$529$	−8.31647	−	14.4045i	−0.361585	−	0.626284i
$530$	−2.73283	−	4.73340i	−0.118706	−	0.205606i
$531$		0			0
$532$	3.27941	−	0.317463i	0.142180	−	0.0137638i
$533$	−11.8315	+	20.4928i	−0.512480	+	0.887642i
$534$		0			0
$535$	−7.03063			−0.303960
$536$	−5.23241			−0.226006
$537$		0			0
$538$	8.24890	−	14.2875i	0.355635	−	0.615979i
$539$	2.52117	−	7.34641i	0.108595	−	0.316432i
$540$		0			0
$541$	4.89248	+	8.47403i	0.210344	+	0.364327i	0.951822	−	0.306650i	$-0.0992082\pi$
$541$	4.89248	+	8.47403i	0.210344	+	0.364327i	−0.741478	+	0.670977i	$0.765875\pi$
$542$	−14.6982	−	25.4580i	−0.631342	−	1.09352i
$543$		0			0
$544$	−2.19747	+	3.80613i	−0.0942157	+	0.163186i
$545$	−5.12829	−	8.88245i	−0.219672	−	0.380482i
$546$		0			0
$547$	−7.90117	+	13.6852i	−0.337830	+	0.585138i	−0.984024	−	0.178034i	$-0.943026\pi$
$547$	−7.90117	+	13.6852i	−0.337830	+	0.585138i	0.646194	+	0.763173i	$0.276360\pi$
$548$	6.20268	+	10.7434i	0.264965	+	0.458934i
$549$		0			0
$550$	0.554785	−	0.960915i	0.0236561	−	0.0409736i
$551$	8.14120			0.346827
$552$		0			0
$553$	−3.74450	+	8.22769i	−0.159232	+	0.349877i
$554$	4.86992	+	8.43495i	0.206903	+	0.358367i
$555$		0			0
$556$	11.5310	+	19.9723i	0.489023	+	0.847013i
$557$	−22.5882	+	39.1239i	−0.957093	+	1.65773i	−0.227589	+	0.973757i	$0.573084\pi$
$557$	−22.5882	+	39.1239i	−0.957093	+	1.65773i	−0.729504	+	0.683976i	$0.760249\pi$
$558$		0			0
$559$	32.0541			1.35574
$560$	−1.53750	−	2.15316i	−0.0649711	−	0.0909877i
$561$		0			0
$562$	−11.2140	+	19.4232i	−0.473033	+	0.819318i
$563$	−15.1412			−0.638128			−0.319064	−	0.947733i	$-0.603368\pi$
$563$	−15.1412			−0.638128			−0.319064	+	0.947733i	$0.603368\pi$
$564$		0			0
$565$	7.28608			0.306528
$566$	−18.4120			−0.773914
$567$		0			0
$568$	−16.3046			−0.684128
$569$	24.5423			1.02887			0.514434	−	0.857530i	$-0.328002\pi$
$569$	24.5423			1.02887			0.514434	+	0.857530i	$0.328002\pi$
$570$		0			0
$571$	9.54361			0.399387			0.199694	−	0.979858i	$-0.436005\pi$
$571$	9.54361			0.399387			0.199694	+	0.979858i	$0.436005\pi$
$572$	1.82049	−	3.15318i	0.0761185	−	0.131841i
$573$		0			0
$574$	18.9902	−	1.83835i	0.792637	−	0.0767313i
$575$	6.29547			0.262539
$576$		0			0
$577$	−7.75559	+	13.4331i	−0.322869	+	0.559226i	−0.981079	−	0.193609i	$-0.937981\pi$
$577$	−7.75559	+	13.4331i	−0.322869	+	0.559226i	0.658210	+	0.752835i	$0.271314\pi$
$578$	−1.15774	−	2.00526i	−0.0481555	−	0.0834078i
$579$		0			0
$580$	−3.26879	−	5.66171i	−0.135729	−	0.235090i
$581$	12.5044	+	17.5116i	0.518770	+	0.726503i
$582$		0			0
$583$	−6.06452			−0.251167
$584$	−0.731993	+	1.26785i	−0.0302901	+	0.0524640i
$585$		0			0
$586$	9.32830	+	16.1571i	0.385348	+	0.667443i
$587$	−5.40254	+	9.35747i	−0.222987	+	0.386224i	−0.955713	−	0.294299i	$-0.904914\pi$
$587$	−5.40254	+	9.35747i	−0.222987	+	0.386224i	0.732727	+	0.680523i	$0.238247\pi$
$588$		0			0
$589$	−1.93616	−	3.35353i	−0.0797782	−	0.138180i
$590$	3.23497	−	5.60312i	0.133181	−	0.230677i
$591$		0			0
$592$	0.659906	+	1.14299i	0.0271220	+	0.0469767i
$593$	−3.55908	−	6.16452i	−0.146154	−	0.253146i	0.783649	−	0.621204i	$-0.213356\pi$
$593$	−3.55908	−	6.16452i	−0.146154	−	0.253146i	−0.929803	+	0.368058i	$0.880023\pi$
$594$		0			0
$595$	11.5738	−	1.12040i	0.474480	−	0.0459320i
$596$	1.37460	−	2.38087i	0.0563056	−	0.0975242i
$597$		0			0
$598$	20.6582			0.844775
$599$	22.4482			0.917208			0.458604	−	0.888641i	$-0.348350\pi$
$599$	22.4482			0.917208			0.458604	+	0.888641i	$0.348350\pi$
$600$		0			0
$601$	−7.16754	+	12.4145i	−0.292370	+	0.506400i	−0.974370	−	0.224953i	$-0.927777\pi$
$601$	−7.16754	+	12.4145i	−0.292370	+	0.506400i	0.682000	+	0.731353i	$0.261111\pi$
$602$	−15.0188	−	21.0328i	−0.612119	−	0.857232i
$603$		0			0
$604$	9.23849	+	16.0015i	0.375909	+	0.651093i
$605$	4.88443	+	8.46008i	0.198580	+	0.343951i
$606$		0			0
$607$	16.8347	−	29.1586i	0.683300	−	1.18351i	−0.290667	−	0.956824i	$-0.593877\pi$
$607$	16.8347	−	29.1586i	0.683300	−	1.18351i	0.973968	−	0.226687i	$-0.0727893\pi$
$608$	−0.622647	−	1.07846i	−0.0252517	−	0.0437371i
$609$		0			0
$610$	−2.20235	+	3.81458i	−0.0891705	+	0.154448i
$611$	−18.8054	−	32.5719i	−0.760784	−	1.31772i
$612$		0			0
$613$	2.64921	−	4.58857i	0.107001	−	0.185331i	−0.807553	−	0.589795i	$-0.799209\pi$
$613$	2.64921	−	4.58857i	0.107001	−	0.185331i	0.914554	+	0.404464i	$0.132542\pi$
$614$	25.9429			1.04697
$615$		0			0
$616$	−2.92199	+	0.282863i	−0.117730	+	0.0113969i
$617$	−2.92877	−	5.07278i	−0.117908	−	0.204222i	0.801031	−	0.598623i	$-0.204285\pi$
$617$	−2.92877	−	5.07278i	−0.117908	−	0.204222i	−0.918938	+	0.394401i	$0.870952\pi$
$618$		0			0
$619$	−13.9169	−	24.1049i	−0.559369	−	0.968856i	−0.997549	−	0.0699689i	$-0.977710\pi$
$619$	−13.9169	−	24.1049i	−0.559369	−	0.968856i	0.438180	−	0.898887i	$-0.355623\pi$
$620$	−1.55478	+	2.69297i	−0.0624417	+	0.108152i
$621$		0			0
$622$	−9.38608			−0.376347
$623$	−7.48593	+	0.724676i	−0.299918	+	0.0290335i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.317071			0.0126727
$627$		0			0
$628$	−4.29934			−0.171562
$629$	−5.80049			−0.231281
$630$		0			0
$631$	27.1850			1.08222			0.541109	−	0.840952i	$-0.318005\pi$
$631$	27.1850			1.08222			0.541109	+	0.840952i	$0.318005\pi$
$632$	3.41668			0.135908
$633$		0			0
$634$	−4.25665			−0.169053
$635$	−10.4621	+	18.1209i	−0.415177	+	0.719107i
$636$		0			0
$637$	−7.45611	+	21.7262i	−0.295422	+	0.860825i
$638$	−7.25390			−0.287185
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	6.21099	+	10.7578i	0.245319	+	0.424906i	0.962221	−	0.272268i	$-0.0877738\pi$
$641$	6.21099	+	10.7578i	0.245319	+	0.424906i	−0.716902	+	0.697174i	$0.754440\pi$
$642$		0			0
$643$	15.6754	+	27.1506i	0.618177	+	1.07071i	0.989818	+	0.142337i	$0.0454618\pi$
$643$	15.6754	+	27.1506i	0.618177	+	1.07071i	−0.371641	+	0.928376i	$0.621205\pi$
$644$	−9.67926	−	13.5552i	−0.381416	−	0.534148i
$645$		0			0
$646$	5.47299			0.215332
$647$	−0.918400	+	1.59071i	−0.0361060	+	0.0625374i	−0.883514	−	0.468405i	$-0.844829\pi$
$647$	−0.918400	+	1.59071i	−0.0361060	+	0.0625374i	0.847408	+	0.530943i	$0.178162\pi$
$648$		0			0
$649$	−3.58942	−	6.21706i	−0.140897	−	0.244041i
$650$	−1.64072	+	2.84181i	−0.0643542	+	0.111465i
$651$		0			0
$652$	6.23750	+	10.8037i	0.244279	+	0.423104i
$653$	7.84443	−	13.5870i	0.306976	−	0.531699i	−0.670723	−	0.741708i	$-0.734016\pi$
$653$	7.84443	−	13.5870i	0.306976	−	0.531699i	0.977699	+	0.210009i	$0.0673494\pi$
$654$		0			0
$655$	7.41195	+	12.8379i	0.289609	+	0.501617i
$656$	−3.60559	−	6.24507i	−0.140775	−	0.243829i
$657$		0			0
$658$	−12.5614	+	27.6008i	−0.489693	+	1.07599i
$659$	−7.26080	+	12.5761i	−0.282841	+	0.489894i	−0.972083	−	0.234636i	$-0.924610\pi$
$659$	−7.26080	+	12.5761i	−0.282841	+	0.489894i	0.689243	+	0.724531i	$0.257943\pi$
$660$		0			0
$661$	−48.7637			−1.89669			−0.948344	−	0.317244i	$-0.897242\pi$
$661$	−48.7637			−1.89669			−0.948344	+	0.317244i	$0.897242\pi$
$662$	6.77455			0.263300
$663$		0			0
$664$	4.06648	−	7.04336i	0.157810	−	0.273335i
$665$	−1.36477	+	2.99878i	−0.0529236	+	0.116288i
$666$		0			0
$667$	−20.5786	−	35.6431i	−0.796805	−	1.38011i
$668$	−3.40584	−	5.89909i	−0.131776	−	0.228243i
$669$		0			0
$670$	2.61620	−	4.53140i	0.101073	−	0.175063i
$671$	2.44366	+	4.23254i	0.0943364	+	0.163395i
$672$		0			0
$673$	−19.7658	+	34.2354i	−0.761915	+	1.31968i	0.179947	+	0.983676i	$0.442407\pi$
$673$	−19.7658	+	34.2354i	−0.761915	+	1.31968i	−0.941862	+	0.335999i	$0.890926\pi$
$674$	7.69796	+	13.3333i	0.296514	+	0.513578i
$675$		0			0
$676$	1.11609	−	1.93313i	0.0429267	−	0.0743512i
$677$	−44.9411			−1.72723			−0.863614	−	0.504153i	$-0.831805\pi$
$677$	−44.9411			−1.72723			−0.863614	+	0.504153i	$0.831805\pi$
$678$		0			0
$679$	−26.2786	−	36.8015i	−1.00848	−	1.41231i
$680$	−2.19747	−	3.80613i	−0.0842691	−	0.145958i
$681$		0			0
$682$	1.72514	+	2.98803i	0.0660591	+	0.114418i
$683$	−17.3244	+	30.0068i	−0.662900	+	1.14818i	0.316950	+	0.948442i	$0.397341\pi$
$683$	−17.3244	+	30.0068i	−0.662900	+	1.14818i	−0.979850	+	0.199734i	$0.935992\pi$
$684$		0			0
$685$	−12.4054			−0.473985
$686$	17.7495	−	5.28726i	0.677679	−	0.201869i
$687$		0			0
$688$	−4.88416	+	8.45961i	−0.186207	+	0.322520i
$689$	17.9352			0.683276
$690$		0			0
$691$	45.7430			1.74015			0.870073	−	0.492923i	$-0.164071\pi$
$691$	45.7430			1.74015			0.870073	+	0.492923i	$0.164071\pi$
$692$	8.41334			0.319827
$693$		0			0
$694$	4.27257			0.162184
$695$	−23.0620			−0.874791
$696$		0			0
$697$	31.6927			1.20045
$698$	3.08538	−	5.34404i	0.116783	−	0.202275i
$699$		0			0
$700$	2.63344	−	0.254930i	0.0995347	−	0.00963546i
$701$	−24.6901			−0.932533			−0.466267	−	0.884644i	$-0.654401\pi$
$701$	−24.6901			−0.932533			−0.466267	+	0.884644i	$0.654401\pi$
$702$		0			0
$703$	0.821777	−	1.42336i	0.0309939	−	0.0536830i
$704$	0.554785	+	0.960915i	0.0209092	+	0.0362159i
$705$		0			0
$706$	−6.21075	−	10.7573i	−0.233745	−	0.404857i
$707$	−19.6793	+	1.90505i	−0.740115	+	0.0716469i
$708$		0			0
$709$	−36.8564			−1.38417			−0.692086	−	0.721815i	$-0.743308\pi$
$709$	−36.8564			−1.38417			−0.692086	+	0.721815i	$0.743308\pi$
$710$	8.15232	−	14.1202i	0.305951	−	0.529923i
$711$		0			0
$712$	1.42132	+	2.46180i	0.0532663	+	0.0922599i
$713$	−9.78810	+	16.9535i	−0.366567	+	0.634913i
$714$		0			0
$715$	1.82049	+	3.15318i	0.0680825	+	0.117922i
$716$	11.0539	−	19.1459i	0.413103	−	0.715515i
$717$		0			0
$718$	−11.9318	−	20.6665i	−0.445292	−	0.771268i
$719$	20.1527	+	34.9055i	0.751569	+	1.30176i	0.947062	+	0.321051i	$0.104036\pi$
$719$	20.1527	+	34.9055i	0.751569	+	1.30176i	−0.195492	+	0.980705i	$0.562631\pi$
$720$		0			0
$721$	7.64190	+	10.7020i	0.284599	+	0.398562i
$722$	8.72462	−	15.1115i	0.324697	−	0.562391i
$723$		0			0
$724$	6.82038			0.253477
$725$	6.53758			0.242800
$726$		0			0
$727$	−6.90054	+	11.9521i	−0.255927	+	0.443278i	−0.965147	−	0.261709i	$-0.915714\pi$
$727$	−6.90054	+	11.9521i	−0.255927	+	0.443278i	0.709220	+	0.704987i	$0.249047\pi$
$728$	8.64146	−	0.836537i	0.320274	−	0.0310041i
$729$		0			0
$730$	−0.731993	−	1.26785i	−0.0270923	−	0.0469252i
$731$	−21.4656	−	37.1795i	−0.793933	−	1.37513i
$732$		0			0
$733$	−14.8346	+	25.6942i	−0.547928	+	0.949038i	0.450489	+	0.892782i	$0.351250\pi$
$733$	−14.8346	+	25.6942i	−0.547928	+	0.949038i	−0.998416	+	0.0562563i	$0.982084\pi$
$734$	−3.98627	−	6.90443i	−0.147136	−	0.254847i
$735$		0			0
$736$	−3.14773	+	5.45204i	−0.116027	+	0.200965i
$737$	−2.90286	−	5.02790i	−0.106928	−	0.185205i
$738$		0			0
$739$	22.7417	−	39.3898i	0.836568	−	1.44898i	−0.0561788	−	0.998421i	$-0.517892\pi$
$739$	22.7417	−	39.3898i	0.836568	−	1.44898i	0.892747	−	0.450558i	$-0.148775\pi$
$740$	−1.31981			−0.0485173
$741$		0			0
$742$	−8.40343	−	11.7684i	−0.308499	−	0.432033i
$743$	16.8783	+	29.2341i	0.619206	+	1.07250i	0.989631	+	0.143634i	$0.0458789\pi$
$743$	16.8783	+	29.2341i	0.619206	+	1.07250i	−0.370424	+	0.928863i	$0.620788\pi$
$744$		0			0
$745$	1.37460	+	2.38087i	0.0503613	+	0.0872283i
$746$	2.25724	−	3.90965i	0.0826433	−	0.143142i
$747$		0			0
$748$	−4.87649			−0.178302
$749$	−18.5147	+	1.79232i	−0.676514	+	0.0654899i
$750$		0			0
$751$	16.2454	−	28.1379i	0.592805	−	1.02677i	−0.401048	−	0.916057i	$-0.631354\pi$
$751$	16.2454	−	28.1379i	0.592805	−	1.02677i	0.993853	−	0.110711i	$-0.0353127\pi$
$752$	11.4617			0.417964
$753$		0			0
$754$	21.4526			0.781259
$755$	−18.4770			−0.672446
$756$		0			0
$757$	18.6647			0.678382			0.339191	−	0.940718i	$-0.389847\pi$
$757$	18.6647			0.678382			0.339191	+	0.940718i	$0.389847\pi$
$758$	−7.52115			−0.273181
$759$		0			0
$760$	1.24529			0.0451715
$761$	16.4080	−	28.4195i	0.594789	−	1.03021i	−0.398787	−	0.917044i	$-0.630569\pi$
$761$	16.4080	−	28.4195i	0.594789	−	1.03021i	0.993577	−	0.113162i	$-0.0360979\pi$
$762$		0			0
$763$	−15.7694	−	22.0841i	−0.570892	−	0.799497i
$764$	−3.93174			−0.142245
$765$		0			0
$766$	8.53489	−	14.7829i	0.308378	−	0.534127i
$767$	10.6153	+	18.3863i	0.383297	+	0.663890i
$768$		0			0
$769$	13.2690	+	22.9826i	0.478493	+	0.828775i	0.999696	−	0.0246581i	$-0.00784972\pi$
$769$	13.2690	+	22.9826i	0.478493	+	0.828775i	−0.521203	+	0.853433i	$0.674516\pi$
$770$	1.21603	−	2.67195i	0.0438226	−	0.0962902i
$771$		0			0
$772$	5.85359			0.210675
$773$	−24.6606	+	42.7135i	−0.886981	+	1.53630i	−0.0435555	+	0.999051i	$0.513869\pi$
$773$	−24.6606	+	42.7135i	−0.886981	+	1.53630i	−0.843426	+	0.537246i	$0.819465\pi$
$774$		0			0
$775$	−1.55478	−	2.69297i	−0.0558495	−	0.0967342i
$776$	−8.54592	+	14.8020i	−0.306781	+	0.531360i
$777$		0			0
$778$	18.3046	+	31.7044i	0.656250	+	1.13666i
$779$	−4.49002	+	7.77695i	−0.160872	+	0.278638i
$780$		0			0
$781$	−9.04557	−	15.6674i	−0.323676	−	0.560623i
$782$	−13.8341	−	23.9614i	−0.494706	−	0.856856i
$783$		0			0
$784$	−4.59781	−	5.27827i	−0.164208	−	0.188510i
$785$	2.14967	−	3.72333i	0.0767249	−	0.132891i
$786$		0			0
$787$	−40.4417			−1.44159			−0.720795	−	0.693149i	$-0.756223\pi$
$787$	−40.4417			−1.44159			−0.720795	+	0.693149i	$0.756223\pi$
$788$	−1.71845			−0.0612174
$789$		0			0
$790$	−1.70834	+	2.95894i	−0.0607801	+	0.105274i
$791$	19.1875	−	1.85744i	0.682227	−	0.0660430i
$792$		0			0
$793$	−7.22686	−	12.5173i	−0.256633	−	0.444502i
$794$	3.55157	+	6.15150i	0.126041	+	0.218309i
$795$		0			0
$796$	2.00694	−	3.47612i	0.0711340	−	0.123208i
$797$	21.8594	+	37.8616i	0.774300	+	1.34113i	0.935187	+	0.354154i	$0.115231\pi$
$797$	21.8594	+	37.8616i	0.774300	+	1.34113i	−0.160887	+	0.986973i	$0.551435\pi$
$798$		0			0
$799$	−25.1867	+	43.6246i	−0.891041	+	1.54333i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−14.8674	+	25.7511i	−0.524986	+	0.909302i
$803$	−1.62439			−0.0573236
$804$		0			0
$805$	16.5787	−	1.60491i	0.584324	−	0.0565655i
$806$	−5.10192	−	8.83679i	−0.179708	−	0.311263i
$807$		0			0
$808$	3.73642	+	6.47167i	0.131447	+	0.227672i
$809$	3.41634	−	5.91727i	0.120112	−	0.208040i	−0.799700	−	0.600400i	$-0.795008\pi$
$809$	3.41634	−	5.91727i	0.120112	−	0.208040i	0.919812	+	0.392360i	$0.128341\pi$
$810$		0			0
$811$	−43.5544			−1.52940			−0.764701	−	0.644386i	$-0.777113\pi$
$811$	−43.5544			−1.52940			−0.764701	+	0.644386i	$0.777113\pi$
$812$	−10.0515	−	14.0765i	−0.352739	−	0.493987i
$813$		0			0
$814$	−0.732212	+	1.26823i	−0.0256640	+	0.0444514i
$815$	−12.4750			−0.436980
$816$		0			0
$817$	12.1644			0.425579
$818$	−34.4783			−1.20551
$819$		0			0
$820$	7.21119			0.251826
$821$	−4.94619			−0.172623			−0.0863116	−	0.996268i	$-0.527508\pi$
$821$	−4.94619			−0.172623			−0.0863116	+	0.996268i	$0.527508\pi$
$822$		0			0
$823$	49.7275			1.73339			0.866696	−	0.498836i	$-0.166239\pi$
$823$	49.7275			1.73339			0.866696	+	0.498836i	$0.166239\pi$
$824$	2.48518	−	4.30445i	0.0865752	−	0.149953i
$825$		0			0
$826$	7.09068	−	15.5802i	0.246716	−	0.542104i
$827$	34.5238			1.20051			0.600255	−	0.799808i	$-0.295066\pi$
$827$	34.5238			1.20051			0.600255	+	0.799808i	$0.295066\pi$
$828$		0			0
$829$	−12.9897	+	22.4988i	−0.451150	+	0.781414i	−0.998458	−	0.0555170i	$-0.982319\pi$
$829$	−12.9897	+	22.4988i	−0.451150	+	0.781414i	0.547308	+	0.836931i	$0.315653\pi$
$830$	4.06648	+	7.04336i	0.141150	+	0.244478i
$831$		0			0
$832$	−1.64072	−	2.84181i	−0.0568816	−	0.0985219i
$833$	30.1933	−	5.90103i	1.04614	−	0.204458i
$834$		0			0
$835$	6.81169			0.235728
$836$	0.690870	−	1.19662i	0.0238942	−	0.0413860i
$837$		0			0
$838$	6.08528	+	10.5400i	0.210212	+	0.364098i
$839$	12.0636	−	20.8948i	0.416483	−	0.721370i	−0.579100	−	0.815257i	$-0.696596\pi$
$839$	12.0636	−	20.8948i	0.416483	−	0.721370i	0.995583	+	0.0938866i	$0.0299291\pi$
$840$		0			0
$841$	−6.86997	−	11.8991i	−0.236895	−	0.410315i
$842$	−4.27799	+	7.40969i	−0.147429	+	0.255355i
$843$		0			0
$844$	−2.32892	−	4.03380i	−0.0801646	−	0.138849i
$845$	1.11609	+	1.93313i	0.0383948	+	0.0665017i
$846$		0			0
$847$	15.0196	+	21.0339i	0.516079	+	0.722734i
$848$	−2.73283	+	4.73340i	−0.0938457	+	0.162545i
$849$		0			0
$850$	4.39494			0.150745
$851$	−8.30884			−0.284823
$852$		0			0
$853$	2.39457	−	4.14752i	0.0819886	−	0.142008i	−0.822115	−	0.569321i	$-0.807206\pi$
$853$	2.39457	−	4.14752i	0.0819886	−	0.142008i	0.904104	+	0.427312i	$0.140540\pi$
$854$	−4.82730	+	10.6069i	−0.165187	+	0.362961i
$855$		0			0
$856$	3.51531	+	6.08870i	0.120151	+	0.208107i
$857$	−14.5259	−	25.1597i	−0.496197	−	0.859438i	0.503794	−	0.863824i	$-0.331937\pi$
$857$	−14.5259	−	25.1597i	−0.496197	−	0.859438i	−0.999990	+	0.00438620i	$0.998604\pi$
$858$		0			0
$859$	−10.8654	+	18.8194i	−0.370722	+	0.642109i	−0.989677	−	0.143318i	$-0.954223\pi$
$859$	−10.8654	+	18.8194i	−0.370722	+	0.642109i	0.618955	+	0.785426i	$0.287556\pi$
$860$	−4.88416	−	8.45961i	−0.166548	−	0.288470i
$861$		0			0
$862$	12.6727	−	21.9497i	0.431633	−	0.747611i
$863$	2.46678	+	4.27259i	0.0839703	+	0.145441i	0.904952	−	0.425514i	$-0.139907\pi$
$863$	2.46678	+	4.27259i	0.0839703	+	0.145441i	−0.820982	+	0.570955i	$0.806573\pi$
$864$		0			0
$865$	−4.20667	+	7.28617i	−0.143031	+	0.247737i
$866$	−17.9795			−0.610969
$867$		0			0
$868$	−3.40792	+	7.48813i	−0.115672	+	0.254164i
$869$	1.89552	+	3.28315i	0.0643013	+	0.111373i
$870$		0			0
$871$	8.58490	+	14.8695i	0.290888	+	0.503833i
$872$	−5.12829	+	8.88245i	−0.173666	+	0.300798i
$873$		0			0
$874$	7.83971			0.265182
$875$	−1.09594	+	2.40809i	−0.0370497	+	0.0814084i
$876$		0			0
$877$	13.0736	−	22.6442i	0.441465	−	0.764639i	−0.556334	−	0.830959i	$-0.687792\pi$
$877$	13.0736	−	22.6442i	0.441465	−	0.764639i	0.997798	+	0.0663196i	$0.0211257\pi$
$878$	−4.23398			−0.142890
$879$		0			0
$880$	−1.10957			−0.0374036
$881$	−39.6778			−1.33678			−0.668389	−	0.743812i	$-0.733016\pi$
$881$	−39.6778			−1.33678			−0.668389	+	0.743812i	$0.733016\pi$
$882$		0			0
$883$	−26.5578			−0.893742			−0.446871	−	0.894598i	$-0.647462\pi$
$883$	−26.5578			−0.893742			−0.446871	+	0.894598i	$0.647462\pi$
$884$	14.4217			0.485054
$885$		0			0
$886$	21.7581			0.730977
$887$	17.4629	−	30.2467i	0.586348	−	1.01558i	−0.408358	−	0.912822i	$-0.633899\pi$
$887$	17.4629	−	30.2467i	0.586348	−	1.01558i	0.994706	−	0.102762i	$-0.0327681\pi$
$888$		0			0
$889$	−22.9318	+	50.3875i	−0.769108	+	1.68994i
$890$	−2.84264			−0.0952856
$891$		0			0
$892$	13.3981	−	23.2061i	0.448600	−	0.776999i
$893$	−7.13657	−	12.3609i	−0.238816	−	0.413642i
$894$		0			0
$895$	11.0539	+	19.1459i	0.369490	+	0.639976i
$896$	−1.09594	+	2.40809i	−0.0366129	+	0.0804487i
$897$		0			0
$898$	29.3888			0.980716
$899$	−10.1645	+	17.6055i	−0.339006	+	0.587176i
$900$		0			0
$901$	−12.0106	−	20.8030i	−0.400131	−	0.693048i
$902$	4.00066	−	6.92934i	0.133207	−	0.230722i
$903$		0			0
$904$	−3.64304	−	6.30993i	−0.121166	−	0.209865i
$905$	−3.41019	+	5.90662i	−0.113359	+	0.196343i
$906$		0			0
$907$	23.8443	+	41.2996i	0.791737	+	1.37133i	0.924890	+	0.380234i	$0.124157\pi$
$907$	23.8443	+	41.2996i	0.791737	+	1.37133i	−0.133153	+	0.991096i	$0.542510\pi$
$908$	6.05706	+	10.4911i	0.201011	+	0.348161i
$909$		0			0
$910$	−3.59627	+	7.90200i	−0.119215	+	0.261949i
$911$	−12.1806	+	21.0974i	−0.403561	+	0.698989i	−0.994153	−	0.107982i	$-0.965561\pi$
$911$	−12.1806	+	21.0974i	−0.403561	+	0.698989i	0.590592	+	0.806971i	$0.298894\pi$
$912$		0			0
$913$	9.02409			0.298654
$914$	27.7640			0.918352
$915$		0			0
$916$	8.07886	−	13.9930i	0.266933	−	0.462341i
$917$	22.7917	+	31.9182i	0.752648	+	1.05403i
$918$		0			0
$919$	−14.7746	−	25.5904i	−0.487369	−	0.844149i	0.512525	−	0.858672i	$-0.328710\pi$
$919$	−14.7746	−	25.5904i	−0.487369	−	0.844149i	−0.999895	+	0.0145236i	$0.995377\pi$
$920$	−3.14773	−	5.45204i	−0.103778	−	0.179748i
$921$		0			0
$922$	4.36929	−	7.56783i	0.143895	−	0.249233i
$923$	26.7513	+	46.3346i	0.880530	+	1.52512i
$924$		0			0
$925$	0.659906	−	1.14299i	0.0216976	−	0.0375813i
$926$	17.2947	+	29.9553i	0.568339	+	0.984393i
$927$		0			0
$928$	−3.26879	+	5.66171i	−0.107303	+	0.185855i
$929$	−21.3312			−0.699854			−0.349927	−	0.936777i	$-0.613794\pi$
$929$	−21.3312			−0.699854			−0.349927	+	0.936777i	$0.613794\pi$
$930$		0			0
$931$	−2.82957	+	8.24503i	−0.0927353	+	0.270220i
$932$	−8.65151	−	14.9849i	−0.283390	−	0.490845i
$933$		0			0
$934$	17.2500	+	29.8779i	0.564438	+	0.977636i
$935$	2.43824	−	4.22316i	0.0797391	−	0.138112i
$936$		0			0
$937$	5.48745			0.179267			0.0896337	−	0.995975i	$-0.471430\pi$
$937$	5.48745			0.179267			0.0896337	+	0.995975i	$0.471430\pi$
$938$	5.73443	−	12.6001i	0.187236	−	0.411409i
$939$		0			0
$940$	−5.73084	+	9.92610i	−0.186919	+	0.323754i
$941$	23.8907			0.778813			0.389407	−	0.921066i	$-0.372680\pi$
$941$	23.8907			0.778813			0.389407	+	0.921066i	$0.372680\pi$
$942$		0			0
$943$	45.3978			1.47836
$944$	−6.46993			−0.210578
$945$		0			0
$946$	−10.8386			−0.352394
$947$	−6.18056			−0.200841			−0.100421	−	0.994945i	$-0.532019\pi$
$947$	−6.18056			−0.200841			−0.100421	+	0.994945i	$0.532019\pi$
$948$		0			0
$949$	4.80397			0.155944
$950$	−0.622647	+	1.07846i	−0.0202013	+	0.0349897i
$951$		0			0
$952$	−6.75720	−	9.46301i	−0.219002	−	0.306698i
$953$	−5.30086			−0.171712			−0.0858558	−	0.996308i	$-0.527362\pi$
$953$	−5.30086			−0.171712			−0.0858558	+	0.996308i	$0.527362\pi$
$954$		0			0
$955$	1.96587	−	3.40499i	0.0636140	−	0.110183i
$956$	−0.644644	−	1.11656i	−0.0208493	−	0.0361120i
$957$		0			0
$958$	1.60798	+	2.78510i	0.0519513	+	0.0899824i
$959$	−32.6688	+	3.16250i	−1.05493	+	0.102123i
$960$		0			0
$961$	−21.3306			−0.688083
$962$	2.16544	−	3.75065i	0.0698166	−	0.120926i
$963$		0			0
$964$	0.200516	+	0.347304i	0.00645819	+	0.0111859i
$965$	−2.92679	+	5.06936i	−0.0942169	+	0.163188i
$966$		0			0
$967$	3.99630	+	6.92180i	0.128512	+	0.222590i	0.923100	−	0.384559i	$-0.125646\pi$
$967$	3.99630	+	6.92180i	0.128512	+	0.222590i	−0.794588	+	0.607149i	$0.792313\pi$
$968$	4.88443	−	8.46008i	0.156991	−	0.271917i
$969$		0			0
$970$	−8.54592	−	14.8020i	−0.274393	−	0.475263i
$971$	10.4036	+	18.0196i	0.333869	+	0.578278i	0.983267	−	0.182171i	$-0.0583124\pi$
$971$	10.4036	+	18.0196i	0.333869	+	0.578278i	−0.649398	+	0.760449i	$0.724979\pi$
$972$		0			0
$973$	−60.7324	+	5.87920i	−1.94699	+	0.188479i
$974$	−7.44719	+	12.8989i	−0.238624	+	0.413308i
$975$		0			0
$976$	4.40470			0.140991
$977$	−37.8435			−1.21072			−0.605360	−	0.795952i	$-0.706971\pi$
$977$	−37.8435			−1.21072			−0.605360	+	0.795952i	$0.706971\pi$
$978$		0			0
$979$	−1.57706	+	2.73154i	−0.0504029	+	0.0873004i
$980$	6.87002	−	1.34269i	0.219455	−	0.0428906i
$981$		0			0
$982$	−21.6718	−	37.5367i	−0.691575	−	1.19784i
$983$	−10.9759	−	19.0108i	−0.350077	−	0.606351i	0.636186	−	0.771536i	$-0.280511\pi$
$983$	−10.9759	−	19.0108i	−0.350077	−	0.606351i	−0.986263	+	0.165185i	$0.947178\pi$
$984$		0			0
$985$	0.859227	−	1.48822i	0.0273772	−	0.0474188i
$986$	−14.3661	−	24.8829i	−0.457511	−	0.792432i
$987$		0			0
$988$	−2.04317	+	3.53888i	−0.0650020	+	0.112587i
$989$	−30.7481	−	53.2572i	−0.977732	−	1.69348i
$990$		0			0
$991$	26.5988	−	46.0704i	0.844938	−	1.46348i	−0.0407375	−	0.999170i	$-0.512971\pi$
$991$	26.5988	−	46.0704i	0.844938	−	1.46348i	0.885675	−	0.464305i	$-0.153696\pi$
$992$	3.10957			0.0987289
$993$		0			0
$994$	17.8690	−	39.2631i	0.566770	−	1.24535i
$995$	2.00694	+	3.47612i	0.0636242	+	0.110200i
$996$		0			0
$997$	19.4525	+	33.6927i	0.616067	+	1.06706i	0.990196	+	0.139683i	$0.0446083\pi$
$997$	19.4525	+	33.6927i	0.616067	+	1.06706i	−0.374129	+	0.927377i	$0.622058\pi$
$998$	−21.8828	+	37.9022i	−0.692689	+	1.19977i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.i.i.991.3		16
3.2	odd	2		630.2.i.i.151.7	yes	16
7.2	even	3		1890.2.l.i.1801.3		16
9.4	even	3		1890.2.l.i.361.3		16
9.5	odd	6		630.2.l.i.571.5	yes	16
21.2	odd	6		630.2.l.i.331.5	yes	16
63.23	odd	6		630.2.i.i.121.7	✓	16
63.58	even	3	inner	1890.2.i.i.1171.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.7	✓	16	63.23	odd	6
630.2.i.i.151.7	yes	16	3.2	odd	2
630.2.l.i.331.5	yes	16	21.2	odd	6
630.2.l.i.571.5	yes	16	9.5	odd	6
1890.2.i.i.991.3		16	1.1	even	1	trivial
1890.2.i.i.1171.3		16	63.58	even	3	inner
1890.2.l.i.361.3		16	9.4	even	3
1890.2.l.i.1801.3		16	7.2	even	3

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1890.2.i.i.991.3

Level	$1890$
Weight	$2$
Character	1890.991
Analytic conductor	$15.092$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$