LMFDB - Embedded newform 136.2.n.c.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 28x^{10} + 258x^{8} + 880x^{6} + 1033x^{4} + 132x^{2} + 4 $ x^12 + 28x^10 + 258x^8 + 880x^6 + 1033x^4 + 132*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			25.2
Root			$0.216105i$ of defining polynomial
Character	$\chi$	$=$	136.25
Dual form			136.2.n.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.152809 - 0.368914i) q^{3} +(-1.09698 - 0.454383i) q^{5} +(4.72436 - 1.95689i) q^{7} +(2.00857 + 2.00857i) q^{9} +O(q^{10})$	\(q+(0.152809 - 0.368914i) q^{3} +(-1.09698 - 0.454383i) q^{5} +(4.72436 - 1.95689i) q^{7} +(2.00857 + 2.00857i) q^{9} +(-1.79540 - 4.33449i) q^{11} +3.10860i q^{13} +(-0.335257 + 0.335257i) q^{15} +(-3.95613 + 1.16149i) q^{17} +(-3.07309 + 3.07309i) q^{19} -2.04192i q^{21} +(0.603641 + 1.45732i) q^{23} +(-2.53864 - 2.53864i) q^{25} +(2.15466 - 0.892490i) q^{27} +(2.98947 + 1.23828i) q^{29} +(-1.26977 + 3.06549i) q^{31} -1.87341 q^{33} -6.07170 q^{35} +(-2.51119 + 6.06255i) q^{37} +(1.14680 + 0.475022i) q^{39} +(-6.91009 + 2.86225i) q^{41} +(-3.39207 - 3.39207i) q^{43} +(-1.29070 - 3.11602i) q^{45} +1.50021i q^{47} +(13.5404 - 13.5404i) q^{49} +(-0.176043 + 1.63696i) q^{51} +(1.24574 - 1.24574i) q^{53} +5.57064i q^{55} +(0.664109 + 1.60330i) q^{57} +(2.56364 + 2.56364i) q^{59} +(10.3831 - 4.30081i) q^{61} +(13.4198 + 5.55866i) q^{63} +(1.41249 - 3.41006i) q^{65} -10.8688 q^{67} +0.629868 q^{69} +(3.11619 - 7.52315i) q^{71} +(8.17226 + 3.38506i) q^{73} +(-1.32447 + 0.548612i) q^{75} +(-16.9643 - 16.9643i) q^{77} +(-0.507386 - 1.22494i) q^{79} +7.59039i q^{81} +(3.71066 - 3.71066i) q^{83} +(4.86755 + 0.523469i) q^{85} +(0.913637 - 0.913637i) q^{87} +10.9766i q^{89} +(6.08319 + 14.6861i) q^{91} +(0.936870 + 0.936870i) q^{93} +(4.76747 - 1.97475i) q^{95} +(-3.27075 - 1.35479i) q^{97} +(5.09994 - 12.3123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^5 - 8 * q^9	$ 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45} + 44 q^{49} - 8 q^{51} - 8 q^{53} - 12 q^{57} + 16 q^{59} + 44 q^{61} + 100 q^{63} - 20 q^{65} - 40 q^{67} + 56 q^{69} + 32 q^{71} + 8 q^{73} + 92 q^{75} - 12 q^{77} - 8 q^{79} + 40 q^{83} + 40 q^{85} - 84 q^{87} - 40 q^{91} - 76 q^{93} + 28 q^{95} - 16 q^{97} - 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.152809	−	0.368914i	0.0882245	−	0.212993i	−0.873609	−	0.486629i	$-0.838226\pi$
$3$	0.152809	−	0.368914i	0.0882245	−	0.212993i	0.961833	+	0.273636i	$0.0882264\pi$
$4$		0			0
$5$	−1.09698	−	0.454383i	−0.490584	−	0.203206i	0.123657	−	0.992325i	$-0.460538\pi$
$5$	−1.09698	−	0.454383i	−0.490584	−	0.203206i	−0.614241	+	0.789119i	$0.710538\pi$
$6$		0			0
$7$	4.72436	−	1.95689i	1.78564	−	0.739637i	0.794428	−	0.607358i	$-0.207771\pi$
$7$	4.72436	−	1.95689i	1.78564	−	0.739637i	0.991213	−	0.132278i	$-0.0422292\pi$
$8$		0			0
$9$	2.00857	+	2.00857i	0.669524	+	0.669524i
$10$		0			0
$11$	−1.79540	−	4.33449i	−0.541335	−	1.30690i	−0.923781	−	0.382920i	$-0.874918\pi$
$11$	−1.79540	−	4.33449i	−0.541335	−	1.30690i	0.382447	−	0.923978i	$-0.375082\pi$
$12$		0			0
$13$			3.10860i			0.862169i	0.902312	+	0.431085i	$0.141869\pi$
$13$			3.10860i			0.862169i	−0.902312	+	0.431085i	$0.858131\pi$
$14$		0			0
$15$	−0.335257	+	0.335257i	−0.0865629	+	0.0865629i
$16$		0			0
$17$	−3.95613	+	1.16149i	−0.959502	+	0.281703i
$17$	−3.95613	+	1.16149i	−0.959502	+	0.281703i
$18$		0			0
$19$	−3.07309	+	3.07309i	−0.705014	+	0.705014i	−0.965482	−	0.260468i	$-0.916123\pi$
$19$	−3.07309	+	3.07309i	−0.705014	+	0.705014i	0.260468	+	0.965482i	$0.416123\pi$
$20$		0			0
$21$		−	2.04192i		−	0.445582i
$22$		0			0
$23$	0.603641	+	1.45732i	0.125868	+	0.303872i	0.974235	−	0.225537i	$-0.0724137\pi$
$23$	0.603641	+	1.45732i	0.125868	+	0.303872i	−0.848367	+	0.529409i	$0.822414\pi$
$24$		0			0
$25$	−2.53864	−	2.53864i	−0.507727	−	0.507727i
$26$		0			0
$27$	2.15466	−	0.892490i	0.414665	−	0.171760i
$28$		0			0
$29$	2.98947	+	1.23828i	0.555130	+	0.229943i	0.642570	−	0.766227i	$-0.277868\pi$
$29$	2.98947	+	1.23828i	0.555130	+	0.229943i	−0.0874392	+	0.996170i	$0.527868\pi$
$30$		0			0
$31$	−1.26977	+	3.06549i	−0.228057	+	0.550578i	−0.995941	−	0.0900110i	$-0.971310\pi$
$31$	−1.26977	+	3.06549i	−0.228057	+	0.550578i	0.767884	+	0.640589i	$0.221310\pi$
$32$		0			0
$33$	−1.87341			−0.326119
$34$		0			0
$35$	−6.07170			−1.02630
$36$		0			0
$37$	−2.51119	+	6.06255i	−0.412837	+	0.996678i	0.571535	+	0.820578i	$0.306348\pi$
$37$	−2.51119	+	6.06255i	−0.412837	+	0.996678i	−0.984372	+	0.176100i	$0.943652\pi$
$38$		0			0
$39$	1.14680	+	0.475022i	0.183636	+	0.0760644i
$40$		0			0
$41$	−6.91009	+	2.86225i	−1.07917	+	0.447009i	−0.850219	−	0.526429i	$-0.823531\pi$
$41$	−6.91009	+	2.86225i	−1.07917	+	0.447009i	−0.228955	+	0.973437i	$0.573531\pi$
$42$		0			0
$43$	−3.39207	−	3.39207i	−0.517285	−	0.517285i	0.399464	−	0.916749i	$-0.369196\pi$
$43$	−3.39207	−	3.39207i	−0.517285	−	0.517285i	−0.916749	+	0.399464i	$0.869196\pi$
$44$		0			0
$45$	−1.29070	−	3.11602i	−0.192406	−	0.464509i
$46$		0			0
$47$			1.50021i			0.218828i	0.993996	+	0.109414i	$0.0348974\pi$
$47$			1.50021i			0.218828i	−0.993996	+	0.109414i	$0.965103\pi$
$48$		0			0
$49$	13.5404	−	13.5404i	1.93434	−	1.93434i
$50$		0			0
$51$	−0.176043	+	1.63696i	−0.0246509	+	0.229220i
$52$		0			0
$53$	1.24574	−	1.24574i	0.171116	−	0.171116i	−0.616354	−	0.787470i	$-0.711391\pi$
$53$	1.24574	−	1.24574i	0.171116	−	0.171116i	0.787470	+	0.616354i	$0.211391\pi$
$54$		0			0
$55$			5.57064i			0.751145i
$56$		0			0
$57$	0.664109	+	1.60330i	0.0879633	+	0.212362i
$58$		0			0
$59$	2.56364	+	2.56364i	0.333757	+	0.333757i	0.854011	−	0.520254i	$-0.174163\pi$
$59$	2.56364	+	2.56364i	0.333757	+	0.333757i	−0.520254	+	0.854011i	$0.674163\pi$
$60$		0			0
$61$	10.3831	−	4.30081i	1.32942	−	0.550662i	0.398927	−	0.916983i	$-0.369383\pi$
$61$	10.3831	−	4.30081i	1.32942	−	0.550662i	0.930489	+	0.366321i	$0.119383\pi$
$62$		0			0
$63$	13.4198	+	5.55866i	1.69073	+	0.700325i
$64$		0			0
$65$	1.41249	−	3.41006i	0.175198	−	0.422966i
$66$		0			0
$67$	−10.8688			−1.32784			−0.663918	−	0.747805i	$-0.731108\pi$
$67$	−10.8688			−1.32784			−0.663918	+	0.747805i	$0.731108\pi$
$68$		0			0
$69$	0.629868			0.0758271
$70$		0			0
$71$	3.11619	−	7.52315i	0.369824	−	0.892834i	−0.623955	−	0.781460i	$-0.714475\pi$
$71$	3.11619	−	7.52315i	0.369824	−	0.892834i	0.993779	−	0.111373i	$-0.0355249\pi$
$72$		0			0
$73$	8.17226	+	3.38506i	0.956490	+	0.396191i	0.805667	−	0.592369i	$-0.201807\pi$
$73$	8.17226	+	3.38506i	0.956490	+	0.396191i	0.150824	+	0.988561i	$0.451807\pi$
$74$		0			0
$75$	−1.32447	+	0.548612i	−0.152936	+	0.0633482i
$76$		0			0
$77$	−16.9643	−	16.9643i	−1.93326	−	1.93326i
$78$		0			0
$79$	−0.507386	−	1.22494i	−0.0570854	−	0.137816i	0.892763	−	0.450526i	$-0.148763\pi$
$79$	−0.507386	−	1.22494i	−0.0570854	−	0.137816i	−0.949849	+	0.312709i	$0.898763\pi$
$80$		0			0
$81$			7.59039i			0.843377i
$82$		0			0
$83$	3.71066	−	3.71066i	0.407298	−	0.407298i	−0.473498	−	0.880795i	$-0.657009\pi$
$83$	3.71066	−	3.71066i	0.407298	−	0.407298i	0.880795	+	0.473498i	$0.157009\pi$
$84$		0			0
$85$	4.86755	+	0.523469i	0.527960	+	0.0567781i
$86$		0			0
$87$	0.913637	−	0.913637i	0.0979521	−	0.0979521i
$88$		0			0
$89$			10.9766i			1.16351i	0.813363	+	0.581756i	$0.197634\pi$
$89$			10.9766i			1.16351i	−0.813363	+	0.581756i	$0.802366\pi$
$90$		0			0
$91$	6.08319	+	14.6861i	0.637692	+	1.53952i
$92$		0			0
$93$	0.936870	+	0.936870i	0.0971489	+	0.0971489i
$94$		0			0
$95$	4.76747	−	1.97475i	0.489132	−	0.202605i
$96$		0			0
$97$	−3.27075	−	1.35479i	−0.332094	−	0.137558i	0.210405	−	0.977614i	$-0.432522\pi$
$97$	−3.27075	−	1.35479i	−0.332094	−	0.137558i	−0.542499	+	0.840057i	$0.682522\pi$
$98$		0			0
$99$	5.09994	−	12.3123i	0.512563	−	1.23744i
$100$		0			0
$101$	−1.42719			−0.142010			−0.0710052	−	0.997476i	$-0.522621\pi$
$101$	−1.42719			−0.142010			−0.0710052	+	0.997476i	$0.522621\pi$
$102$		0			0
$103$	−3.29319			−0.324488			−0.162244	−	0.986751i	$-0.551873\pi$
$103$	−3.29319			−0.324488			−0.162244	+	0.986751i	$0.551873\pi$
$104$		0			0
$105$	−0.927812	+	2.23994i	−0.0905452	+	0.218595i
$106$		0			0
$107$	−16.5302	−	6.84704i	−1.59804	−	0.661928i	−0.606900	−	0.794778i	$-0.707587\pi$
$107$	−16.5302	−	6.84704i	−1.59804	−	0.661928i	−0.991136	+	0.132850i	$0.957587\pi$
$108$		0			0
$109$	6.76072	−	2.80038i	0.647560	−	0.268228i	−0.0346335	−	0.999400i	$-0.511026\pi$
$109$	6.76072	−	2.80038i	0.647560	−	0.268228i	0.682193	+	0.731172i	$0.261026\pi$
$110$		0			0
$111$	1.85283	+	1.85283i	0.175863	+	0.175863i
$112$		0			0
$113$	−5.38551	−	13.0018i	−0.506626	−	1.22310i	−0.945814	−	0.324708i	$-0.894734\pi$
$113$	−5.38551	−	13.0018i	−0.506626	−	1.22310i	0.439188	−	0.898395i	$-0.355266\pi$
$114$		0			0
$115$		−	1.87293i		−	0.174652i
$116$		0			0
$117$	−6.24384	+	6.24384i	−0.577243	+	0.577243i
$118$		0			0
$119$	−16.4173	+	13.2290i	−1.50497	+	1.21270i
$120$		0			0
$121$	−7.78615	+	7.78615i	−0.707832	+	0.707832i
$122$		0			0
$123$			2.98661i			0.269293i
$124$		0			0
$125$	3.90323	+	9.42324i	0.349116	+	0.842840i
$126$		0			0
$127$	−9.00989	−	9.00989i	−0.799499	−	0.799499i	0.183518	−	0.983016i	$-0.441252\pi$
$127$	−9.00989	−	9.00989i	−0.799499	−	0.799499i	−0.983016	+	0.183518i	$0.941252\pi$
$128$		0			0
$129$	−1.76972	+	0.733042i	−0.155815	+	0.0645407i
$130$		0			0
$131$	8.49881	+	3.52032i	0.742544	+	0.307572i	0.721695	−	0.692211i	$-0.243363\pi$
$131$	8.49881	+	3.52032i	0.742544	+	0.307572i	0.0208488	+	0.999783i	$0.493363\pi$
$132$		0			0
$133$	−8.50466	+	20.5321i	−0.737448	+	1.78036i
$134$		0			0
$135$	−2.76915			−0.238331
$136$		0			0
$137$	0.408294			0.0348829			0.0174415	−	0.999848i	$-0.494448\pi$
$137$	0.408294			0.0348829			0.0174415	+	0.999848i	$0.494448\pi$
$138$		0			0
$139$	1.37502	−	3.31960i	0.116628	−	0.281564i	−0.854776	−	0.518997i	$-0.826306\pi$
$139$	1.37502	−	3.31960i	0.116628	−	0.281564i	0.971404	+	0.237432i	$0.0763057\pi$
$140$		0			0
$141$	0.553449	+	0.229246i	0.0466088	+	0.0193060i
$142$		0			0
$143$	13.4742	−	5.58119i	1.12677	−	0.466722i
$144$		0			0
$145$	−2.71673	−	2.71673i	−0.225612	−	0.225612i
$146$		0			0
$147$	−2.92615	−	7.06434i	−0.241345	−	0.582657i
$148$		0			0
$149$			17.2461i			1.41286i	0.707784	+	0.706429i	$0.249695\pi$
$149$			17.2461i			1.41286i	−0.707784	+	0.706429i	$0.750305\pi$
$150$		0			0
$151$	8.03403	−	8.03403i	0.653800	−	0.653800i	−0.300106	−	0.953906i	$-0.597022\pi$
$151$	8.03403	−	8.03403i	0.653800	−	0.653800i	0.953906	+	0.300106i	$0.0970221\pi$
$152$		0			0
$153$	−10.2791	−	5.61323i	−0.831017	−	0.453803i
$154$		0			0
$155$	2.78581	−	2.78581i	0.223762	−	0.223762i
$156$		0			0
$157$		−	16.9303i		−	1.35119i	−0.737275	−	0.675593i	$-0.763888\pi$
$157$		−	16.9303i		−	1.35119i	0.737275	−	0.675593i	$-0.236112\pi$
$158$		0			0
$159$	−0.269211	−	0.649933i	−0.0213498	−	0.0515431i
$160$		0			0
$161$	5.70364	+	5.70364i	0.449510	+	0.449510i
$162$		0			0
$163$	4.49132	−	1.86036i	0.351787	−	0.145715i	−0.199790	−	0.979839i	$-0.564026\pi$
$163$	4.49132	−	1.86036i	0.351787	−	0.145715i	0.551577	+	0.834124i	$0.314026\pi$
$164$		0			0
$165$	2.05509	+	0.851246i	0.159988	+	0.0662694i
$166$		0			0
$167$	−2.09576	+	5.05962i	−0.162175	+	0.391525i	−0.983989	−	0.178231i	$-0.942962\pi$
$167$	−2.09576	+	5.05962i	−0.162175	+	0.391525i	0.821814	+	0.569756i	$0.192962\pi$
$168$		0			0
$169$	3.33664			0.256664
$170$		0			0
$171$	−12.3450			−0.944048
$172$		0			0
$173$	−4.42913	+	10.6929i	−0.336741	+	0.812964i	0.661284	+	0.750136i	$0.270012\pi$
$173$	−4.42913	+	10.6929i	−0.336741	+	0.812964i	−0.998024	+	0.0628281i	$0.979988\pi$
$174$		0			0
$175$	−16.9613	−	7.02559i	−1.28215	−	0.531085i
$176$		0			0
$177$	1.33751	−	0.554015i	0.100533	−	0.0416423i
$178$		0			0
$179$	16.9028	+	16.9028i	1.26338	+	1.26338i	0.949446	+	0.313931i	$0.101646\pi$
$179$	16.9028	+	16.9028i	1.26338	+	1.26338i	0.313931	+	0.949446i	$0.398354\pi$
$180$		0			0
$181$	−2.96795	−	7.16528i	−0.220606	−	0.532591i	0.774366	−	0.632738i	$-0.218069\pi$
$181$	−2.96795	−	7.16528i	−0.220606	−	0.532591i	−0.994973	+	0.100147i	$0.968069\pi$
$182$		0			0
$183$		−	4.48766i		−	0.331738i
$184$		0			0
$185$	5.50945	−	5.50945i	0.405063	−	0.405063i
$186$		0			0
$187$	12.1373	+	15.0624i	0.887568	+	1.10148i
$188$		0			0
$189$	8.43289	−	8.43289i	0.613403	−	0.613403i
$190$		0			0
$191$		−	19.7913i		−	1.43205i	−0.698076	−	0.716023i	$-0.745960\pi$
$191$		−	19.7913i		−	1.43205i	0.698076	−	0.716023i	$-0.254040\pi$
$192$		0			0
$193$	−5.25191	−	12.6792i	−0.378041	−	0.912671i	−0.992333	−	0.123593i	$-0.960558\pi$
$193$	−5.25191	−	12.6792i	−0.378041	−	0.912671i	0.614292	−	0.789079i	$-0.289442\pi$
$194$		0			0
$195$	−1.04218	−	1.04218i	−0.0746319	−	0.0746319i
$196$		0			0
$197$	15.3222	−	6.34666i	1.09166	−	0.452181i	0.237075	−	0.971491i	$-0.423811\pi$
$197$	15.3222	−	6.34666i	1.09166	−	0.452181i	0.854586	+	0.519311i	$0.173811\pi$
$198$		0			0
$199$	−0.395509	−	0.163825i	−0.0280369	−	0.0116133i	0.368621	−	0.929580i	$-0.379830\pi$
$199$	−0.395509	−	0.163825i	−0.0280369	−	0.0116133i	−0.396658	+	0.917967i	$0.629830\pi$
$200$		0			0
$201$	−1.66085	+	4.00966i	−0.117148	+	0.282819i
$202$		0			0
$203$	16.5465			1.16134
$204$		0			0
$205$	8.88077			0.620260
$206$		0			0
$207$	−1.71467	+	4.13959i	−0.119178	+	0.287721i
$208$		0			0
$209$	18.8377	+	7.80282i	1.30303	+	0.539733i
$210$		0			0
$211$	11.0299	−	4.56874i	0.759331	−	0.314525i	0.0307886	−	0.999526i	$-0.490198\pi$
$211$	11.0299	−	4.56874i	0.759331	−	0.314525i	0.728542	+	0.685001i	$0.240198\pi$
$212$		0			0
$213$	−2.29921	−	2.29921i	−0.157540	−	0.157540i
$214$		0			0
$215$	2.17972	+	5.26232i	0.148656	+	0.358887i
$216$		0			0
$217$			16.9673i			1.15181i
$218$		0			0
$219$	2.49759	−	2.49759i	0.168772	−	0.168772i
$220$		0			0
$221$	−3.61060	−	12.2980i	−0.242875	−	0.827253i
$222$		0			0
$223$	−16.0555	+	16.0555i	−1.07516	+	1.07516i	−0.0782204	+	0.996936i	$0.524924\pi$
$223$	−16.0555	+	16.0555i	−1.07516	+	1.07516i	−0.996936	+	0.0782204i	$0.975076\pi$
$224$		0			0
$225$		−	10.1981i		−	0.679872i
$226$		0			0
$227$	−3.29834	−	7.96291i	−0.218919	−	0.528517i	0.775821	−	0.630953i	$-0.217336\pi$
$227$	−3.29834	−	7.96291i	−0.218919	−	0.528517i	−0.994740	+	0.102437i	$0.967336\pi$
$228$		0			0
$229$	−8.83453	−	8.83453i	−0.583802	−	0.583802i	0.352144	−	0.935946i	$-0.385453\pi$
$229$	−8.83453	−	8.83453i	−0.583802	−	0.583802i	−0.935946	+	0.352144i	$0.885453\pi$
$230$		0			0
$231$	−8.85066	+	3.66606i	−0.582331	+	0.241209i
$232$		0			0
$233$	5.20993	+	2.15803i	0.341314	+	0.141377i	0.546755	−	0.837293i	$-0.315863\pi$
$233$	5.20993	+	2.15803i	0.341314	+	0.141377i	−0.205441	+	0.978669i	$0.565863\pi$
$234$		0			0
$235$	0.681670	−	1.64570i	0.0444673	−	0.107353i
$236$		0			0
$237$	−0.529430			−0.0343902
$238$		0			0
$239$	7.52042			0.486456			0.243228	−	0.969969i	$-0.421794\pi$
$239$	7.52042			0.486456			0.243228	+	0.969969i	$0.421794\pi$
$240$		0			0
$241$	−0.620633	+	1.49834i	−0.0399785	+	0.0965166i	−0.942608	−	0.333903i	$-0.891634\pi$
$241$	−0.620633	+	1.49834i	−0.0399785	+	0.0965166i	0.902629	+	0.430419i	$0.141634\pi$
$242$		0			0
$243$	9.26419	+	3.83735i	0.594298	+	0.246166i
$244$		0			0
$245$	−21.0061	+	8.70100i	−1.34203	+	0.555886i
$246$		0			0
$247$	−9.55298	−	9.55298i	−0.607841	−	0.607841i
$248$		0			0
$249$	−0.801891	−	1.93594i	−0.0508178	−	0.122685i
$250$		0			0
$251$		−	14.2870i		−	0.901787i	−0.892578	−	0.450893i	$-0.851105\pi$
$251$		−	14.2870i		−	0.901787i	0.892578	−	0.450893i	$-0.148895\pi$
$252$		0			0
$253$	5.23295	−	5.23295i	0.328993	−	0.328993i
$254$		0			0
$255$	0.936921	−	1.71572i	0.0586723	−	0.107442i
$256$		0			0
$257$	5.51279	−	5.51279i	0.343878	−	0.343878i	−0.513945	−	0.857823i	$-0.671816\pi$
$257$	5.51279	−	5.51279i	0.343878	−	0.343878i	0.857823	+	0.513945i	$0.171816\pi$
$258$		0			0
$259$			33.5558i			2.08506i
$260$		0			0
$261$	3.51739	+	8.49174i	0.217721	+	0.525626i
$262$		0			0
$263$	4.89628	+	4.89628i	0.301917	+	0.301917i	0.841764	−	0.539846i	$-0.181518\pi$
$263$	4.89628	+	4.89628i	0.301917	+	0.301917i	−0.539846	+	0.841764i	$0.681518\pi$
$264$		0			0
$265$	−1.93260	+	0.800508i	−0.118719	+	0.0491748i
$266$		0			0
$267$	4.04941	+	1.67732i	0.247820	+	0.102650i
$268$		0			0
$269$	11.3197	−	27.3283i	0.690176	−	1.66623i	−0.0542486	−	0.998527i	$-0.517276\pi$
$269$	11.3197	−	27.3283i	0.690176	−	1.66623i	0.744425	−	0.667706i	$-0.232724\pi$
$270$		0			0
$271$	−22.1769			−1.34715			−0.673574	−	0.739120i	$-0.735242\pi$
$271$	−22.1769			−1.34715			−0.673574	+	0.739120i	$0.735242\pi$
$272$		0			0
$273$	6.34749			0.384167
$274$		0			0
$275$	−6.44581	+	15.5616i	−0.388697	+	0.938398i
$276$		0			0
$277$	−6.36330	−	2.63577i	−0.382334	−	0.158368i	0.183235	−	0.983069i	$-0.441343\pi$
$277$	−6.36330	−	2.63577i	−0.382334	−	0.158368i	−0.565568	+	0.824701i	$0.691343\pi$
$278$		0			0
$279$	−8.70768	+	3.60684i	−0.521315	+	0.215936i
$280$		0			0
$281$	−6.88677	−	6.88677i	−0.410830	−	0.410830i	0.471197	−	0.882028i	$-0.343822\pi$
$281$	−6.88677	−	6.88677i	−0.410830	−	0.410830i	−0.882028	+	0.471197i	$0.843822\pi$
$282$		0			0
$283$	1.75969	+	4.24828i	0.104603	+	0.252534i	0.967512	−	0.252826i	$-0.0813599\pi$
$283$	1.75969	+	4.24828i	0.104603	+	0.252534i	−0.862909	+	0.505360i	$0.831360\pi$
$284$		0			0
$285$		−	2.06055i		−	0.122056i
$286$		0			0
$287$	−27.0446	+	27.0446i	−1.59639	+	1.59639i
$288$		0			0
$289$	14.3019	−	9.19000i	0.841287	−	0.540589i
$290$		0			0
$291$	−0.999600	+	0.999600i	−0.0585976	+	0.0585976i
$292$		0			0
$293$			21.8373i			1.27575i	0.770140	+	0.637875i	$0.220186\pi$
$293$			21.8373i			1.27575i	−0.770140	+	0.637875i	$0.779814\pi$
$294$		0			0
$295$	−1.64738	−	3.97713i	−0.0959143	−	0.231557i
$296$		0			0
$297$	−7.73698	−	7.73698i	−0.448945	−	0.448945i
$298$		0			0
$299$	−4.53022	+	1.87648i	−0.261989	+	0.108519i
$300$		0			0
$301$	−22.6633	−	9.38743i	−1.30629	−	0.541082i
$302$		0			0
$303$	−0.218087	+	0.526510i	−0.0125288	+	0.0302472i
$304$		0			0
$305$	−13.3442			−0.764087
$306$		0			0
$307$	−17.2871			−0.986624			−0.493312	−	0.869852i	$-0.664214\pi$
$307$	−17.2871			−0.986624			−0.493312	+	0.869852i	$0.664214\pi$
$308$		0			0
$309$	−0.503230	+	1.21490i	−0.0286277	+	0.0691135i
$310$		0			0
$311$	9.88905	+	4.09618i	0.560756	+	0.232273i	0.645014	−	0.764171i	$-0.276852\pi$
$311$	9.88905	+	4.09618i	0.560756	+	0.232273i	−0.0842572	+	0.996444i	$0.526852\pi$
$312$		0			0
$313$	−14.2434	+	5.89979i	−0.805082	+	0.333476i	−0.746990	−	0.664835i	$-0.768502\pi$
$313$	−14.2434	+	5.89979i	−0.805082	+	0.333476i	−0.0580921	+	0.998311i	$0.518502\pi$
$314$		0			0
$315$	−12.1955	−	12.1955i	−0.687136	−	0.687136i
$316$		0			0
$317$	10.8401	+	26.1702i	0.608839	+	1.46987i	0.864264	+	0.503038i	$0.167784\pi$
$317$	10.8401	+	26.1702i	0.608839	+	1.46987i	−0.255426	+	0.966829i	$0.582216\pi$
$318$		0			0
$319$		−	15.1810i		−	0.849975i
$320$		0			0
$321$	−5.05194	+	5.05194i	−0.281972	+	0.281972i
$322$		0			0
$323$	8.58816	−	15.7269i	0.477858	−	0.875067i
$324$		0			0
$325$	7.89159	−	7.89159i	0.437747	−	0.437747i
$326$		0			0
$327$		−	2.92205i		−	0.161590i
$328$		0			0
$329$	2.93575	+	7.08753i	0.161853	+	0.390748i
$330$		0			0
$331$	20.8314	+	20.8314i	1.14500	+	1.14500i	0.987523	+	0.157476i	$0.0503356\pi$
$331$	20.8314	+	20.8314i	1.14500	+	1.14500i	0.157476	+	0.987523i	$0.449664\pi$
$332$		0			0
$333$	−17.2210	+	7.13317i	−0.943705	+	0.390895i
$334$		0			0
$335$	11.9228	+	4.93860i	0.651415	+	0.269825i
$336$		0			0
$337$	−2.46073	+	5.94073i	−0.134044	+	0.323612i	−0.976622	−	0.214963i	$-0.931037\pi$
$337$	−2.46073	+	5.94073i	−0.134044	+	0.323612i	0.842578	+	0.538575i	$0.181037\pi$
$338$		0			0
$339$	−5.61949			−0.305209
$340$		0			0
$341$	15.5671			0.843005
$342$		0			0
$343$	23.7744	−	57.3964i	1.28369	−	3.09911i
$344$		0			0
$345$	−0.690951	−	0.286201i	−0.0371996	−	0.0154086i
$346$		0			0
$347$	11.0943	−	4.59542i	0.595575	−	0.246695i	−0.0644720	−	0.997920i	$-0.520536\pi$
$347$	11.0943	−	4.59542i	0.595575	−	0.246695i	0.660047	+	0.751224i	$0.270536\pi$
$348$		0			0
$349$	25.2738	+	25.2738i	1.35288	+	1.35288i	0.882426	+	0.470451i	$0.155909\pi$
$349$	25.2738	+	25.2738i	1.35288	+	1.35288i	0.470451	+	0.882426i	$0.344091\pi$
$350$		0			0
$351$	2.77439	+	6.69797i	0.148086	+	0.357511i
$352$		0			0
$353$		−	21.5227i		−	1.14554i	−0.819717	−	0.572769i	$-0.805869\pi$
$353$		−	21.5227i		−	1.14554i	0.819717	−	0.572769i	$-0.194131\pi$
$354$		0			0
$355$	−6.83679	+	6.83679i	−0.362859	+	0.362859i
$356$		0			0
$357$	2.37166	+	8.07808i	0.125522	+	0.427537i
$358$		0			0
$359$	−8.33594	+	8.33594i	−0.439954	+	0.439954i	−0.891996	−	0.452042i	$-0.850696\pi$
$359$	−8.33594	+	8.33594i	−0.439954	+	0.439954i	0.452042	+	0.891996i	$0.350696\pi$
$360$		0			0
$361$			0.112296i			0.00591032i
$362$		0			0
$363$	1.68262	+	4.06221i	0.0883149	+	0.213211i
$364$		0			0
$365$	−7.42668	−	7.42668i	−0.388730	−	0.388730i
$366$		0			0
$367$	6.15964	−	2.55141i	0.321530	−	0.133182i	−0.216080	−	0.976376i	$-0.569327\pi$
$367$	6.15964	−	2.55141i	0.321530	−	0.133182i	0.537610	+	0.843193i	$0.319327\pi$
$368$		0			0
$369$	−19.6285	−	8.13037i	−1.02182	−	0.423250i
$370$		0			0
$371$	3.44755	−	8.32313i	0.178988	−	0.432115i
$372$		0			0
$373$	−2.67018			−0.138257			−0.0691283	−	0.997608i	$-0.522022\pi$
$373$	−2.67018			−0.138257			−0.0691283	+	0.997608i	$0.522022\pi$
$374$		0			0
$375$	4.07281			0.210319
$376$		0			0
$377$	−3.84931	+	9.29305i	−0.198249	+	0.478616i
$378$		0			0
$379$	−16.2015	−	6.71088i	−0.832215	−	0.344715i	−0.0744357	−	0.997226i	$-0.523716\pi$
$379$	−16.2015	−	6.71088i	−0.832215	−	0.344715i	−0.757779	+	0.652511i	$0.773716\pi$
$380$		0			0
$381$	−4.70067	+	1.94708i	−0.240823	+	0.0997520i
$382$		0			0
$383$	14.3378	+	14.3378i	0.732628	+	0.732628i	0.971140	−	0.238512i	$-0.0766596\pi$
$383$	14.3378	+	14.3378i	0.732628	+	0.732628i	−0.238512	+	0.971140i	$0.576660\pi$
$384$		0			0
$385$	10.9012	+	26.3177i	0.555575	+	1.34128i
$386$		0			0
$387$		−	13.6264i		−	0.692670i
$388$		0			0
$389$	15.7641	−	15.7641i	0.799271	−	0.799271i	−0.183709	−	0.982981i	$-0.558810\pi$
$389$	15.7641	−	15.7641i	0.799271	−	0.799271i	0.982981	+	0.183709i	$0.0588105\pi$
$390$		0			0
$391$	−4.08074	−	5.06422i	−0.206372	−	0.256108i
$392$		0			0
$393$	2.59739	−	2.59739i	0.131021	−	0.131021i
$394$		0			0
$395$			1.57428i			0.0792105i
$396$		0			0
$397$	−9.39026	−	22.6701i	−0.471284	−	1.13778i	−0.963596	−	0.267361i	$-0.913848\pi$
$397$	−9.39026	−	22.6701i	−0.471284	−	1.13778i	0.492313	−	0.870418i	$-0.336152\pi$
$398$		0			0
$399$	6.27498	+	6.27498i	0.314142	+	0.314142i
$400$		0			0
$401$	−2.01808	+	0.835915i	−0.100778	+	0.0417436i	−0.432503	−	0.901633i	$-0.642369\pi$
$401$	−2.01808	+	0.835915i	−0.100778	+	0.0417436i	0.331725	+	0.943376i	$0.392369\pi$
$402$		0			0
$403$	−9.52937	−	3.94719i	−0.474692	−	0.196624i
$404$		0			0
$405$	3.44895	−	8.32649i	0.171380	−	0.413747i
$406$		0			0
$407$	30.7867			1.52604
$408$		0			0
$409$	−7.33140			−0.362514			−0.181257	−	0.983436i	$-0.558017\pi$
$409$	−7.33140			−0.362514			−0.181257	+	0.983436i	$0.558017\pi$
$410$		0			0
$411$	0.0623911	−	0.150625i	0.00307753	−	0.00742981i
$412$		0			0
$413$	17.1283	+	7.09478i	0.842830	+	0.349111i
$414$		0			0
$415$	−5.75657	+	2.38445i	−0.282579	+	0.117048i
$416$		0			0
$417$	−1.01453	−	1.01453i	−0.0496817	−	0.0496817i
$418$		0			0
$419$	−5.84439	−	14.1096i	−0.285517	−	0.689299i	0.714429	−	0.699708i	$-0.246687\pi$
$419$	−5.84439	−	14.1096i	−0.285517	−	0.689299i	−0.999946	+	0.0104091i	$0.996687\pi$
$420$		0			0
$421$			2.47377i			0.120564i	0.998181	+	0.0602821i	$0.0192000\pi$
$421$			2.47377i			0.120564i	−0.998181	+	0.0602821i	$0.980800\pi$
$422$		0			0
$423$	−3.01328	+	3.01328i	−0.146511	+	0.146511i
$424$		0			0
$425$	12.9918	+	7.09457i	0.630193	+	0.344137i
$426$		0			0
$427$	40.6371	−	40.6371i	1.96657	−	1.96657i
$428$		0			0
$429$		−	5.82367i		−	0.281169i
$430$		0			0
$431$	−5.51828	−	13.3223i	−0.265806	−	0.641713i	0.733471	−	0.679720i	$-0.237899\pi$
$431$	−5.51828	−	13.3223i	−0.265806	−	0.641713i	−0.999277	+	0.0380076i	$0.987899\pi$
$432$		0			0
$433$	14.7495	+	14.7495i	0.708817	+	0.708817i	0.966286	−	0.257470i	$-0.0828888\pi$
$433$	14.7495	+	14.7495i	0.708817	+	0.708817i	−0.257470	+	0.966286i	$0.582889\pi$
$434$		0			0
$435$	−1.41738	+	0.587099i	−0.0679582	+	0.0281492i
$436$		0			0
$437$	−6.33351	−	2.62342i	−0.302973	−	0.125495i
$438$		0			0
$439$	−7.35074	+	17.7463i	−0.350832	+	0.846983i	0.645686	+	0.763603i	$0.276571\pi$
$439$	−7.35074	+	17.7463i	−0.350832	+	0.846983i	−0.996518	+	0.0833799i	$0.973429\pi$
$440$		0			0
$441$	54.3938			2.59018
$442$		0			0
$443$	−15.7377			−0.747719			−0.373859	−	0.927485i	$-0.621966\pi$
$443$	−15.7377			−0.747719			−0.373859	+	0.927485i	$0.621966\pi$
$444$		0			0
$445$	4.98756	−	12.0410i	0.236433	−	0.570800i
$446$		0			0
$447$	6.36234	+	2.63537i	0.300928	+	0.124649i
$448$		0			0
$449$	6.94036	−	2.87479i	0.327536	−	0.135670i	−0.212855	−	0.977084i	$-0.568276\pi$
$449$	6.94036	−	2.87479i	0.327536	−	0.135670i	0.540391	+	0.841414i	$0.318276\pi$
$450$		0			0
$451$	24.8128	+	24.8128i	1.16839	+	1.16839i
$452$		0			0
$453$	−1.73619	−	4.19154i	−0.0815734	−	0.196936i
$454$		0			0
$455$		−	18.8745i		−	0.884849i
$456$		0			0
$457$	−21.3633	+	21.3633i	−0.999331	+	0.999331i	−1.00000		0.000668656i	$-0.999787\pi$
$457$	−21.3633	+	21.3633i	−0.999331	+	0.999331i	0.000668656		1.00000i	$0.499787\pi$
$458$		0			0
$459$	−7.48750	+	6.03342i	−0.349486	+	0.281616i
$460$		0			0
$461$	−24.5916	+	24.5916i	−1.14534	+	1.14534i	−0.157887	+	0.987457i	$0.550468\pi$
$461$	−24.5916	+	24.5916i	−1.14534	+	1.14534i	−0.987457	+	0.157887i	$0.949532\pi$
$462$		0			0
$463$		−	32.9760i		−	1.53252i	−0.642529	−	0.766261i	$-0.722115\pi$
$463$		−	32.9760i		−	1.53252i	0.642529	−	0.766261i	$-0.277885\pi$
$464$		0			0
$465$	−0.602028	−	1.45342i	−0.0279184	−	0.0674010i
$466$		0			0
$467$	−14.6954	−	14.6954i	−0.680021	−	0.680021i	0.279984	−	0.960005i	$-0.409671\pi$
$467$	−14.6954	−	14.6954i	−0.680021	−	0.680021i	−0.960005	+	0.279984i	$0.909671\pi$
$468$		0			0
$469$	−51.3482	+	21.2691i	−2.37104	+	0.982116i
$470$		0			0
$471$	−6.24583	−	2.58711i	−0.287793	−	0.119208i
$472$		0			0
$473$	−8.61274	+	20.7930i	−0.396014	+	0.956063i
$474$		0			0
$475$	15.6029			0.715910
$476$		0			0
$477$	5.00433			0.229133
$478$		0			0
$479$	−5.56333	+	13.4311i	−0.254195	+	0.613681i	−0.998534	−	0.0541204i	$-0.982765\pi$
$479$	−5.56333	+	13.4311i	−0.254195	+	0.613681i	0.744339	+	0.667802i	$0.232765\pi$
$480$		0			0
$481$	−18.8460	−	7.80628i	−0.859305	−	0.355936i
$482$		0			0
$483$	2.97572	−	1.23258i	0.135400	−	0.0560845i
$484$		0			0
$485$	2.97234	+	2.97234i	0.134967	+	0.134967i
$486$		0			0
$487$	10.8162	+	26.1127i	0.490130	+	1.18328i	0.954654	+	0.297718i	$0.0962255\pi$
$487$	10.8162	+	26.1127i	0.490130	+	1.18328i	−0.464524	+	0.885561i	$0.653774\pi$
$488$		0			0
$489$		−	1.94119i		−	0.0877837i
$490$		0			0
$491$	−20.4737	+	20.4737i	−0.923965	+	0.923965i	−0.997307	−	0.0733423i	$-0.976633\pi$
$491$	−20.4737	+	20.4737i	−0.923965	+	0.923965i	0.0733423	+	0.997307i	$0.476633\pi$
$492$		0			0
$493$	−13.2650	−	1.42655i	−0.597424	−	0.0642485i
$494$		0			0
$495$	−11.1890	+	11.1890i	−0.502910	+	0.502910i
$496$		0			0
$497$		−	41.6401i		−	1.86782i
$498$		0			0
$499$	−12.7601	−	30.8056i	−0.571220	−	1.37905i	−0.900517	−	0.434821i	$-0.856812\pi$
$499$	−12.7601	−	30.8056i	−0.571220	−	1.37905i	0.329296	−	0.944227i	$-0.393188\pi$
$500$		0			0
$501$	1.54631	+	1.54631i	0.0690842	+	0.0690842i
$502$		0			0
$503$	−36.0598	+	14.9365i	−1.60783	+	0.665984i	−0.992495	−	0.122283i	$-0.960978\pi$
$503$	−36.0598	+	14.9365i	−1.60783	+	0.665984i	−0.615333	+	0.788268i	$0.710978\pi$
$504$		0			0
$505$	1.56559	+	0.648490i	0.0696680	+	0.0288574i
$506$		0			0
$507$	0.509869	−	1.23093i	0.0226441	−	0.0546676i
$508$		0			0
$509$	15.8180			0.701121			0.350560	−	0.936540i	$-0.385991\pi$
$509$	15.8180			0.701121			0.350560	+	0.936540i	$0.385991\pi$
$510$		0			0
$511$	45.2329			2.00099
$512$		0			0
$513$	−3.87876	+	9.36416i	−0.171251	+	0.413438i
$514$		0			0
$515$	3.61256	+	1.49637i	0.159188	+	0.0659380i
$516$		0			0
$517$	6.50264	−	2.69348i	0.285986	−	0.118459i
$518$		0			0
$519$	3.26794	+	3.26794i	0.143447	+	0.143447i
$520$		0			0
$521$	−2.13588	−	5.15646i	−0.0935745	−	0.225909i	0.870161	−	0.492767i	$-0.164014\pi$
$521$	−2.13588	−	5.15646i	−0.0935745	−	0.225909i	−0.963736	+	0.266858i	$0.914014\pi$
$522$		0			0
$523$			41.0233i			1.79382i	0.442208	+	0.896912i	$0.354195\pi$
$523$			41.0233i			1.79382i	−0.442208	+	0.896912i	$0.645805\pi$
$524$		0			0
$525$	−5.18368	+	5.18368i	−0.226234	+	0.226234i
$526$		0			0
$527$	1.46283	−	13.6023i	0.0637217	−	0.592525i
$528$		0			0
$529$	14.5041	−	14.5041i	0.630611	−	0.630611i
$530$		0			0
$531$			10.2985i			0.446917i
$532$		0			0
$533$	−8.89758	−	21.4807i	−0.385397	−	0.930431i
$534$		0			0
$535$	15.0221	+	15.0221i	0.649462	+	0.649462i
$536$		0			0
$537$	8.81860	−	3.65278i	0.380551	−	0.157629i
$538$		0			0
$539$	−83.0012	−	34.3802i	−3.57512	−	1.48086i
$540$		0			0
$541$	−1.89222	+	4.56822i	−0.0813528	+	0.196403i	−0.959322	−	0.282314i	$-0.908898\pi$
$541$	−1.89222	+	4.56822i	−0.0813528	+	0.196403i	0.877969	+	0.478717i	$0.158898\pi$
$542$		0			0
$543$	−3.09690			−0.132901
$544$		0			0
$545$	−8.68881			−0.372188
$546$		0			0
$547$	−10.7933	+	26.0573i	−0.461487	+	1.11413i	0.506300	+	0.862357i	$0.331013\pi$
$547$	−10.7933	+	26.0573i	−0.461487	+	1.11413i	−0.967787	+	0.251771i	$0.918987\pi$
$548$		0			0
$549$	29.4936	+	12.2167i	1.25876	+	0.521395i
$550$		0			0
$551$	−12.9922	+	5.38156i	−0.553487	+	0.229262i
$552$		0			0
$553$	−4.79415	−	4.79415i	−0.203868	−	0.203868i
$554$		0			0
$555$	−1.19062	−	2.87441i	−0.0505389	−	0.122012i
$556$		0			0
$557$		−	4.83116i		−	0.204703i	−0.994748	−	0.102351i	$-0.967363\pi$
$557$		−	4.83116i		−	0.204703i	0.994748	−	0.102351i	$-0.0326366\pi$
$558$		0			0
$559$	10.5446	−	10.5446i	0.445987	−	0.445987i
$560$		0			0
$561$	7.41144	−	2.17595i	0.312911	−	0.0918685i
$562$		0			0
$563$	−7.66980	+	7.66980i	−0.323244	+	0.323244i	−0.850010	−	0.526766i	$-0.823404\pi$
$563$	−7.66980	+	7.66980i	−0.323244	+	0.323244i	0.526766	+	0.850010i	$0.323404\pi$
$564$		0			0
$565$			16.7097i			0.702984i
$566$		0			0
$567$	14.8536	+	35.8597i	0.623792	+	1.50597i
$568$		0			0
$569$	−7.15839	−	7.15839i	−0.300095	−	0.300095i	0.540956	−	0.841051i	$-0.318063\pi$
$569$	−7.15839	−	7.15839i	−0.300095	−	0.300095i	−0.841051	+	0.540956i	$0.818063\pi$
$570$		0			0
$571$	−12.2720	+	5.08325i	−0.513569	+	0.212727i	−0.624389	−	0.781113i	$-0.714652\pi$
$571$	−12.2720	+	5.08325i	−0.513569	+	0.212727i	0.110820	+	0.993840i	$0.464652\pi$
$572$		0			0
$573$	−7.30128	−	3.02429i	−0.305015	−	0.126342i
$574$		0			0
$575$	2.16718	−	5.23203i	0.0903776	−	0.218191i
$576$		0			0
$577$	−28.7986			−1.19890			−0.599451	−	0.800412i	$-0.704614\pi$
$577$	−28.7986			−1.19890			−0.599451	+	0.800412i	$0.704614\pi$
$578$		0			0
$579$	−5.48009			−0.227745
$580$		0			0
$581$	10.2691	−	24.7919i	0.426035	−	1.02854i
$582$		0			0
$583$	−7.63627	−	3.16305i	−0.316262	−	0.131000i
$584$		0			0
$585$	9.68646	−	4.01226i	0.400486	−	0.165887i
$586$		0			0
$587$	9.26211	+	9.26211i	0.382288	+	0.382288i	0.871926	−	0.489638i	$-0.162871\pi$
$587$	9.26211	+	9.26211i	0.382288	+	0.382288i	−0.489638	+	0.871926i	$0.662871\pi$
$588$		0			0
$589$	−5.51841	−	13.3226i	−0.227382	−	0.548949i
$590$		0			0
$591$		−	6.62240i		−	0.272409i
$592$		0			0
$593$	−26.2428	+	26.2428i	−1.07766	+	1.07766i	−0.0809422	+	0.996719i	$0.525793\pi$
$593$	−26.2428	+	26.2428i	−1.07766	+	1.07766i	−0.996719	+	0.0809422i	$0.974207\pi$
$594$		0			0
$595$	24.0204	−	7.05222i	0.984741	−	0.289113i
$596$		0			0
$597$	−0.120875	+	0.120875i	−0.00494708	+	0.00494708i
$598$		0			0
$599$			11.9668i			0.488949i	0.969656	+	0.244475i	$0.0786155\pi$
$599$			11.9668i			0.488949i	−0.969656	+	0.244475i	$0.921385\pi$
$600$		0			0
$601$	−12.5930	−	30.4023i	−0.513680	−	1.24013i	−0.941727	−	0.336377i	$-0.890798\pi$
$601$	−12.5930	−	30.4023i	−0.513680	−	1.24013i	0.428047	−	0.903757i	$-0.359202\pi$
$602$		0			0
$603$	−21.8308	−	21.8308i	−0.889019	−	0.889019i
$604$		0			0
$605$	12.0791	−	5.00334i	0.491087	−	0.203415i
$606$		0			0
$607$	22.6770	+	9.39314i	0.920433	+	0.381256i	0.792041	−	0.610468i	$-0.209019\pi$
$607$	22.6770	+	9.39314i	0.920433	+	0.381256i	0.128392	+	0.991724i	$0.459019\pi$
$608$		0			0
$609$	2.52846	−	6.10424i	0.102458	−	0.247356i
$610$		0			0
$611$	−4.66354			−0.188667
$612$		0			0
$613$	16.9644			0.685187			0.342593	−	0.939484i	$-0.388695\pi$
$613$	16.9644			0.685187			0.342593	+	0.939484i	$0.388695\pi$
$614$		0			0
$615$	1.35706	−	3.27624i	0.0547221	−	0.132111i
$616$		0			0
$617$	−19.7492	−	8.18039i	−0.795074	−	0.329330i	−0.0520922	−	0.998642i	$-0.516589\pi$
$617$	−19.7492	−	8.18039i	−0.795074	−	0.329330i	−0.742981	+	0.669312i	$0.766589\pi$
$618$		0			0
$619$	−15.5069	+	6.42318i	−0.623276	+	0.258170i	−0.671893	−	0.740648i	$-0.734519\pi$
$619$	−15.5069	+	6.42318i	−0.623276	+	0.258170i	0.0486169	+	0.998818i	$0.484519\pi$
$620$		0			0
$621$	2.60129	+	2.60129i	0.104386	+	0.104386i
$622$		0			0
$623$	21.4800	+	51.8572i	0.860576	+	2.07761i
$624$		0			0
$625$			5.84022i			0.233609i
$626$		0			0
$627$	5.75714	−	5.75714i	0.229918	−	0.229918i
$628$		0			0
$629$	2.89300	−	26.9010i	0.115351	−	1.07261i
$630$		0			0
$631$	10.7839	−	10.7839i	0.429301	−	0.429301i	−0.459089	−	0.888390i	$-0.651824\pi$
$631$	10.7839	−	10.7839i	0.429301	−	0.429301i	0.888390	+	0.459089i	$0.151824\pi$
$632$		0			0
$633$		−	4.76724i		−	0.189481i
$634$		0			0
$635$	5.78971	+	13.9776i	0.229758	+	0.554684i
$636$		0			0
$637$	42.0916	+	42.0916i	1.66773	+	1.66773i
$638$		0			0
$639$	21.3699	−	8.85170i	0.845380	−	0.350168i
$640$		0			0
$641$	20.6657	+	8.56003i	0.816247	+	0.338101i	0.751444	−	0.659797i	$-0.229358\pi$
$641$	20.6657	+	8.56003i	0.816247	+	0.338101i	0.0648037	+	0.997898i	$0.479358\pi$
$642$		0			0
$643$	7.91554	−	19.1098i	0.312158	−	0.753617i	−0.687466	−	0.726216i	$-0.741277\pi$
$643$	7.91554	−	19.1098i	0.312158	−	0.753617i	0.999625	−	0.0274005i	$-0.00872294\pi$
$644$		0			0
$645$	2.27443			0.0895555
$646$		0			0
$647$	47.0545			1.84990			0.924951	−	0.380085i	$-0.124105\pi$
$647$	47.0545			1.84990			0.924951	+	0.380085i	$0.124105\pi$
$648$		0			0
$649$	6.50930	−	15.7148i	0.255512	−	0.616861i
$650$		0			0
$651$	6.25947	+	2.59276i	0.245328	+	0.101618i
$652$		0			0
$653$	3.91036	−	1.61973i	0.153024	−	0.0633848i	−0.304857	−	0.952398i	$-0.598609\pi$
$653$	3.91036	−	1.61973i	0.153024	−	0.0633848i	0.457881	+	0.889013i	$0.348609\pi$
$654$		0			0
$655$	−7.72343	−	7.72343i	−0.301780	−	0.301780i
$656$		0			0
$657$	9.61544	+	23.2137i	0.375134	+	0.905653i
$658$		0			0
$659$		−	19.9128i		−	0.775693i	−0.921724	−	0.387846i	$-0.873219\pi$
$659$		−	19.9128i		−	0.775693i	0.921724	−	0.387846i	$-0.126781\pi$
$660$		0			0
$661$	−16.7557	+	16.7557i	−0.651721	+	0.651721i	−0.953407	−	0.301686i	$-0.902450\pi$
$661$	−16.7557	+	16.7557i	−0.651721	+	0.651721i	0.301686	+	0.953407i	$0.402450\pi$
$662$		0			0
$663$	−5.08864	−	0.547245i	−0.197626	−	0.0212532i
$664$		0			0
$665$	18.6589	−	18.6589i	0.723559	−	0.723559i
$666$		0			0
$667$			5.10409i			0.197631i
$668$		0			0
$669$	3.46967	+	8.37653i	0.134145	+	0.323856i
$670$		0			0
$671$	−37.2836	−	37.2836i	−1.43932	−	1.43932i
$672$		0			0
$673$	25.3668	−	10.5073i	0.977818	−	0.405025i	0.164201	−	0.986427i	$-0.447495\pi$
$673$	25.3668	−	10.5073i	0.977818	−	0.405025i	0.813617	+	0.581402i	$0.197495\pi$
$674$		0			0
$675$	−7.73561	−	3.20420i	−0.297744	−	0.123330i
$676$		0			0
$677$	−0.264525	+	0.638621i	−0.0101665	+	0.0245442i	−0.928881	−	0.370378i	$-0.879228\pi$
$677$	−0.264525	+	0.638621i	−0.0101665	+	0.0245442i	0.918715	+	0.394922i	$0.129228\pi$
$678$		0			0
$679$	−18.1034			−0.694743
$680$		0			0
$681$	−3.44165			−0.131884
$682$		0			0
$683$	−2.87557	+	6.94224i	−0.110031	+	0.265637i	−0.969298	−	0.245890i	$-0.920920\pi$
$683$	−2.87557	+	6.94224i	−0.110031	+	0.265637i	0.859267	+	0.511527i	$0.170920\pi$
$684$		0			0
$685$	−0.447890	−	0.185522i	−0.0171130	−	0.00708843i
$686$		0			0
$687$	−4.60918	+	1.90918i	−0.175851	+	0.0728399i
$688$		0			0
$689$	3.87251	+	3.87251i	0.147531	+	0.147531i
$690$		0			0
$691$	−2.34522	−	5.66186i	−0.0892164	−	0.215387i	0.872973	−	0.487768i	$-0.162189\pi$
$691$	−2.34522	−	5.66186i	−0.0892164	−	0.215387i	−0.962189	+	0.272381i	$0.912189\pi$
$692$		0			0
$693$		−	68.1480i		−	2.58873i
$694$		0			0
$695$	−3.01674	+	3.01674i	−0.114431	+	0.114431i
$696$		0			0
$697$	24.0127	−	19.3494i	0.909546	−	0.732912i
$698$		0			0
$699$	1.59225	−	1.59225i	0.0602245	−	0.0602245i
$700$		0			0
$701$			20.9152i			0.789957i	0.918690	+	0.394979i	$0.129248\pi$
$701$			20.9152i			0.789957i	−0.918690	+	0.394979i	$0.870752\pi$
$702$		0			0
$703$	−10.9136	−	26.3478i	−0.411616	−	0.993728i
$704$		0			0
$705$	−0.502956	−	0.502956i	−0.0189424	−	0.0189424i
$706$		0			0
$707$	−6.74255	+	2.79286i	−0.253580	+	0.105036i
$708$		0			0
$709$	12.8569	+	5.32551i	0.482851	+	0.200004i	0.610812	−	0.791776i	$-0.290843\pi$
$709$	12.8569	+	5.32551i	0.482851	+	0.200004i	−0.127961	+	0.991779i	$0.540843\pi$
$710$		0			0
$711$	1.44126	−	3.47950i	0.0540513	−	0.130491i
$712$		0			0
$713$	−5.23388			−0.196010
$714$		0			0
$715$	−17.3169			−0.647614
$716$		0			0
$717$	1.14919	−	2.77439i	0.0429173	−	0.103612i
$718$		0			0
$719$	28.2472	+	11.7004i	1.05344	+	0.436351i	0.841120	−	0.540849i	$-0.181897\pi$
$719$	28.2472	+	11.7004i	1.05344	+	0.436351i	0.212324	+	0.977199i	$0.431897\pi$
$720$		0			0
$721$	−15.5582	+	6.44442i	−0.579418	+	0.240003i
$722$		0			0
$723$	0.457920	+	0.457920i	0.0170302	+	0.0170302i
$724$		0			0
$725$	−4.44564	−	10.7327i	−0.165107	−	0.398603i
$726$		0			0
$727$			13.4448i			0.498641i	0.968421	+	0.249321i	$0.0802073\pi$
$727$			13.4448i			0.498641i	−0.968421	+	0.249321i	$0.919793\pi$
$728$		0			0
$729$	−13.2703	+	13.2703i	−0.491494	+	0.491494i
$730$		0			0
$731$	17.3593	+	9.47959i	0.642057	+	0.350615i
$732$		0			0
$733$	−5.99912	+	5.99912i	−0.221582	+	0.221582i	−0.809165	−	0.587582i	$-0.800080\pi$
$733$	−5.99912	+	5.99912i	−0.221582	+	0.221582i	0.587582	+	0.809165i	$0.300080\pi$
$734$		0			0
$735$			9.07903i			0.334885i
$736$		0			0
$737$	19.5139	+	47.1107i	0.718804	+	1.73535i
$738$		0			0
$739$	22.3102	+	22.3102i	0.820694	+	0.820694i	0.986207	−	0.165514i	$-0.0529283\pi$
$739$	22.3102	+	22.3102i	0.820694	+	0.820694i	−0.165514	+	0.986207i	$0.552928\pi$
$740$		0			0
$741$	−4.98401	+	2.06445i	−0.183092	+	0.0758393i
$742$		0			0
$743$	28.0689	+	11.6265i	1.02975	+	0.426535i	0.832621	−	0.553843i	$-0.186839\pi$
$743$	28.0689	+	11.6265i	1.02975	+	0.426535i	0.197126	+	0.980378i	$0.436839\pi$
$744$		0			0
$745$	7.83635	−	18.9186i	0.287102	−	0.693125i
$746$		0			0
$747$	14.9063			0.545391
$748$		0			0
$749$	−91.4936			−3.34310
$750$		0			0
$751$	3.48112	−	8.40418i	0.127028	−	0.306673i	−0.847552	−	0.530712i	$-0.821924\pi$
$751$	3.48112	−	8.40418i	0.127028	−	0.306673i	0.974580	+	0.224040i	$0.0719245\pi$
$752$		0			0
$753$	−5.27067	−	2.18318i	−0.192074	−	0.0795596i
$754$		0			0
$755$	−12.4637	+	5.16263i	−0.453600	+	0.187887i
$756$		0			0
$757$	22.1908	+	22.1908i	0.806540	+	0.806540i	0.984108	−	0.177569i	$-0.0568232\pi$
$757$	22.1908	+	22.1908i	0.806540	+	0.806540i	−0.177569	+	0.984108i	$0.556823\pi$
$758$		0			0
$759$	−1.13087	−	2.73015i	−0.0410479	−	0.0990983i
$760$		0			0
$761$		−	30.8196i		−	1.11721i	−0.829434	−	0.558604i	$-0.811337\pi$
$761$		−	30.8196i		−	1.11721i	0.829434	−	0.558604i	$-0.188663\pi$
$762$		0			0
$763$	26.4600	−	26.4600i	0.957917	−	0.957917i
$764$		0			0
$765$	8.72540	+	10.8283i	0.315468	+	0.391496i
$766$		0			0
$767$	−7.96931	+	7.96931i	−0.287755	+	0.287755i
$768$		0			0
$769$			22.6483i			0.816720i	0.912821	+	0.408360i	$0.133899\pi$
$769$			22.6483i			0.816720i	−0.912821	+	0.408360i	$0.866101\pi$
$770$		0			0
$771$	−1.19134	−	2.87615i	−0.0429051	−	0.103582i
$772$		0			0
$773$	−8.44322	−	8.44322i	−0.303681	−	0.303681i	0.538771	−	0.842452i	$-0.318889\pi$
$773$	−8.44322	−	8.44322i	−0.303681	−	0.303681i	−0.842452	+	0.538771i	$0.818889\pi$
$774$		0			0
$775$	11.0056	−	4.55869i	0.395334	−	0.163753i
$776$		0			0
$777$	12.3792	+	5.12764i	0.444102	+	0.183953i
$778$		0			0
$779$	12.4393	−	30.0312i	0.445686	−	1.07598i
$780$		0			0
$781$	−38.2038			−1.36704
$782$		0			0
$783$	7.54645			0.269688
$784$		0			0
$785$	−7.69285	+	18.5722i	−0.274569	+	0.662869i
$786$		0			0
$787$	−9.06855	−	3.75632i	−0.323259	−	0.133898i	0.215152	−	0.976581i	$-0.430975\pi$
$787$	−9.06855	−	3.75632i	−0.323259	−	0.133898i	−0.538411	+	0.842682i	$0.680975\pi$
$788$		0			0
$789$	2.55450	−	1.05811i	0.0909426	−	0.0376697i
$790$		0			0
$791$	−50.8862	−	50.8862i	−1.80930	−	1.80930i
$792$		0			0
$793$	13.3695	+	32.2767i	0.474764	+	1.14618i
$794$		0			0
$795$			0.835288i			0.0296246i
$796$		0			0
$797$	8.28119	−	8.28119i	0.293335	−	0.293335i	−0.545061	−	0.838396i	$-0.683494\pi$
$797$	8.28119	−	8.28119i	0.293335	−	0.293335i	0.838396	+	0.545061i	$0.183494\pi$
$798$		0			0
$799$	−1.74248	−	5.93502i	−0.0616445	−	0.209966i
$800$		0			0
$801$	−22.0472	+	22.0472i	−0.779000	+	0.779000i
$802$		0			0
$803$		−	41.5001i		−	1.46451i
$804$		0			0
$805$	−3.66513	−	8.84841i	−0.129179	−	0.311865i
$806$		0			0
$807$	−8.35202	−	8.35202i	−0.294005	−	0.294005i
$808$		0			0
$809$	−20.3450	+	8.42717i	−0.715292	+	0.296284i	−0.710492	−	0.703705i	$-0.751528\pi$
$809$	−20.3450	+	8.42717i	−0.715292	+	0.296284i	−0.00479961	+	0.999988i	$0.501528\pi$
$810$		0			0
$811$	11.3354	+	4.69528i	0.398040	+	0.164874i	0.572719	−	0.819752i	$-0.305889\pi$
$811$	11.3354	+	4.69528i	0.398040	+	0.164874i	−0.174679	+	0.984625i	$0.555889\pi$
$812$		0			0
$813$	−3.38883	+	8.18136i	−0.118851	+	0.286933i
$814$		0			0
$815$	−5.77220			−0.202191
$816$		0			0
$817$	20.8482			0.729387
$818$		0			0
$819$	−17.2796	+	41.7167i	−0.603799	+	1.45770i
$820$		0			0
$821$	−18.1822	−	7.53129i	−0.634562	−	0.262844i	0.0421283	−	0.999112i	$-0.486586\pi$
$821$	−18.1822	−	7.53129i	−0.634562	−	0.262844i	−0.676690	+	0.736268i	$0.736586\pi$
$822$		0			0
$823$	−36.6779	+	15.1925i	−1.27851	+	0.529577i	−0.915541	−	0.402224i	$-0.868237\pi$
$823$	−36.6779	+	15.1925i	−1.27851	+	0.529577i	−0.362970	+	0.931801i	$0.618237\pi$
$824$		0			0
$825$	4.75590	+	4.75590i	0.165579	+	0.165579i
$826$		0			0
$827$	−3.71499	−	8.96878i	−0.129183	−	0.311875i	0.846033	−	0.533130i	$-0.178985\pi$
$827$	−3.71499	−	8.96878i	−0.129183	−	0.311875i	−0.975216	+	0.221256i	$0.928985\pi$
$828$		0			0
$829$			22.0832i			0.766982i	0.923545	+	0.383491i	$0.125278\pi$
$829$			22.0832i			0.766982i	−0.923545	+	0.383491i	$0.874722\pi$
$830$		0			0
$831$	−1.94474	+	1.94474i	−0.0674624	+	0.0674624i
$832$		0			0
$833$	−37.8405	+	69.2946i	−1.31110	+	2.40092i
$834$		0			0
$835$	4.59801	−	4.59801i	0.159121	−	0.159121i
$836$		0			0
$837$			7.73835i			0.267476i
$838$		0			0
$839$	−9.61206	−	23.2056i	−0.331845	−	0.801146i	−0.998446	−	0.0557304i	$-0.982251\pi$
$839$	−9.61206	−	23.2056i	−0.331845	−	0.801146i	0.666601	−	0.745415i	$-0.267749\pi$
$840$		0			0
$841$	−13.1025	−	13.1025i	−0.451811	−	0.451811i
$842$		0			0
$843$	−3.59299	+	1.48826i	−0.123749	+	0.0512586i
$844$		0			0
$845$	−3.66022	−	1.51611i	−0.125915	−	0.0521558i
$846$		0			0
$847$	−21.5479	+	52.0212i	−0.740395	+	1.78747i
$848$		0			0
$849$	1.83615			0.0630164
$850$		0			0
$851$	−10.3509			−0.354825
$852$		0			0
$853$	7.16213	−	17.2909i	0.245227	−	0.592029i	−0.752560	−	0.658523i	$-0.771181\pi$
$853$	7.16213	−	17.2909i	0.245227	−	0.592029i	0.997787	+	0.0664941i	$0.0211814\pi$
$854$		0			0
$855$	13.5422	+	5.60938i	0.463135	+	0.191837i
$856$		0			0
$857$	29.1931	−	12.0922i	0.997218	−	0.413061i	0.176441	−	0.984311i	$-0.443541\pi$
$857$	29.1931	−	12.0922i	0.997218	−	0.413061i	0.820776	+	0.571250i	$0.193541\pi$
$858$		0			0
$859$	3.13197	+	3.13197i	0.106862	+	0.106862i	0.758516	−	0.651654i	$-0.225925\pi$
$859$	3.13197	+	3.13197i	0.106862	+	0.106862i	−0.651654	+	0.758516i	$0.725925\pi$
$860$		0			0
$861$	5.84447	+	14.1098i	0.199179	+	0.480861i
$862$		0			0
$863$			20.5515i			0.699580i	0.936828	+	0.349790i	$0.113747\pi$
$863$			20.5515i			0.699580i	−0.936828	+	0.349790i	$0.886253\pi$
$864$		0			0
$865$	9.71733	−	9.71733i	0.330399	−	0.330399i
$866$		0			0
$867$	−1.20486	−	6.68048i	−0.0409193	−	0.226881i
$868$		0			0
$869$	−4.39852	+	4.39852i	−0.149209	+	0.149209i
$870$		0			0
$871$		−	33.7867i		−	1.14482i
$872$		0			0
$873$	−3.84834	−	9.29072i	−0.130247	−	0.314443i
$874$		0			0
$875$	36.8806	+	36.8806i	1.24679	+	1.24679i
$876$		0			0
$877$	25.0857	−	10.3908i	0.847082	−	0.350873i	0.0834403	−	0.996513i	$-0.473409\pi$
$877$	25.0857	−	10.3908i	0.847082	−	0.350873i	0.763642	+	0.645640i	$0.223409\pi$
$878$		0			0
$879$	8.05609	+	3.33694i	0.271725	+	0.112552i
$880$		0			0
$881$	2.82787	−	6.82707i	0.0952732	−	0.230010i	−0.869057	−	0.494712i	$-0.835274\pi$
$881$	2.82787	−	6.82707i	0.0952732	−	0.230010i	0.964330	+	0.264702i	$0.0852736\pi$
$882$		0			0
$883$	1.98735			0.0668797			0.0334398	−	0.999441i	$-0.489354\pi$
$883$	1.98735			0.0668797			0.0334398	+	0.999441i	$0.489354\pi$
$884$		0			0
$885$	−1.71895			−0.0577820
$886$		0			0
$887$	9.82026	−	23.7082i	0.329732	−	0.796044i	−0.668880	−	0.743371i	$-0.733226\pi$
$887$	9.82026	−	23.7082i	0.329732	−	0.796044i	0.998612	−	0.0526732i	$-0.0167742\pi$
$888$		0			0
$889$	−60.1974	−	24.9346i	−2.01896	−	0.836279i
$890$		0			0
$891$	32.9005	−	13.6278i	1.10221	−	0.456549i
$892$		0			0
$893$	−4.61027	−	4.61027i	−0.154277	−	0.154277i
$894$		0			0
$895$	−10.8617	−	26.2224i	−0.363066	−	0.876518i
$896$		0			0
$897$			1.95800i			0.0653758i
$898$		0			0
$899$	−7.59186	+	7.59186i	−0.253203	+	0.253203i
$900$		0			0
$901$	−3.48140	+	6.37524i	−0.115982	+	0.212390i
$902$		0			0
$903$	−6.92631	+	6.92631i	−0.230493	+	0.230493i
$904$		0			0
$905$			9.20874i			0.306109i
$906$		0			0
$907$	−8.92046	−	21.5359i	−0.296199	−	0.715088i	−0.999989	−	0.00467982i	$-0.998510\pi$
$907$	−8.92046	−	21.5359i	−0.296199	−	0.715088i	0.703790	−	0.710408i	$-0.251490\pi$
$908$		0			0
$909$	−2.86661	−	2.86661i	−0.0950795	−	0.0950795i
$910$		0			0
$911$	−29.0036	+	12.0137i	−0.960932	+	0.398031i	−0.807329	−	0.590101i	$-0.799088\pi$
$911$	−29.0036	+	12.0137i	−0.960932	+	0.398031i	−0.153603	+	0.988133i	$0.549088\pi$
$912$		0			0
$913$	−22.7459	−	9.42168i	−0.752781	−	0.311812i
$914$		0			0
$915$	−2.03912	+	4.92287i	−0.0674112	+	0.162745i
$916$		0			0
$917$	47.0403			1.55341
$918$		0			0
$919$	−11.4058			−0.376242			−0.188121	−	0.982146i	$-0.560240\pi$
$919$	−11.4058			−0.376242			−0.188121	+	0.982146i	$0.560240\pi$
$920$		0			0
$921$	−2.64162	+	6.37744i	−0.0870444	+	0.210144i
$922$		0			0
$923$	23.3864	+	9.68698i	0.769774	+	0.318851i
$924$		0			0
$925$	21.7656	−	9.01562i	0.715649	−	0.296432i
$926$		0			0
$927$	−6.61461	−	6.61461i	−0.217252	−	0.217252i
$928$		0			0
$929$	−23.0938	−	55.7533i	−0.757682	−	1.82921i	−0.509431	−	0.860512i	$-0.670144\pi$
$929$	−23.0938	−	55.7533i	−0.757682	−	1.82921i	−0.248252	−	0.968696i	$-0.579856\pi$
$930$		0			0
$931$			83.2216i			2.72748i
$932$		0			0
$933$	3.02228	−	3.02228i	0.0989448	−	0.0989448i
$934$		0			0
$935$	−6.47025	−	22.0382i	−0.211600	−	0.720725i
$936$		0			0
$937$	−4.33359	+	4.33359i	−0.141572	+	0.141572i	−0.774341	−	0.632769i	$-0.781918\pi$
$937$	−4.33359	+	4.33359i	−0.141572	+	0.141572i	0.632769	+	0.774341i	$0.281918\pi$
$938$		0			0
$939$			6.15612i			0.200897i
$940$		0			0
$941$	19.4053	+	46.8485i	0.632594	+	1.52722i	0.836351	+	0.548195i	$0.184685\pi$
$941$	19.4053	+	46.8485i	0.632594	+	1.52722i	−0.203757	+	0.979021i	$0.565315\pi$
$942$		0			0
$943$	−8.34243	−	8.34243i	−0.271667	−	0.271667i
$944$		0			0
$945$	−13.0825	+	5.41893i	−0.425573	+	0.176278i
$946$		0			0
$947$	−19.5357	−	8.09194i	−0.634824	−	0.262953i	0.0419773	−	0.999119i	$-0.486634\pi$
$947$	−19.5357	−	8.09194i	−0.634824	−	0.262953i	−0.676801	+	0.736166i	$0.736634\pi$
$948$		0			0
$949$	−10.5228	+	25.4042i	−0.341584	+	0.824657i
$950$		0			0
$951$	11.3110			0.366785
$952$		0			0
$953$	51.2476			1.66007			0.830037	−	0.557708i	$-0.188319\pi$
$953$	51.2476			1.66007			0.830037	+	0.557708i	$0.188319\pi$
$954$		0			0
$955$	−8.99283	+	21.7106i	−0.291001	+	0.702539i
$956$		0			0
$957$	−5.60050	−	2.31980i	−0.181038	−	0.0749885i
$958$		0			0
$959$	1.92893	−	0.798989i	0.0622884	−	0.0258007i
$960$		0			0
$961$	14.1354	+	14.1354i	0.455980	+	0.455980i
$962$		0			0
$963$	−19.4494	−	46.9549i	−0.626747	−	1.51310i
$964$		0			0
$965$			16.2952i			0.524562i
$966$		0			0
$967$	15.5365	−	15.5365i	0.499619	−	0.499619i	−0.411700	−	0.911319i	$-0.635065\pi$
$967$	15.5365	−	15.5365i	0.499619	−	0.499619i	0.911319	+	0.411700i	$0.135065\pi$
$968$		0			0
$969$	−4.48952	−	5.57150i	−0.144224	−	0.178982i
$970$		0			0
$971$	32.4309	−	32.4309i	1.04076	−	1.04076i	0.0416227	−	0.999133i	$-0.486747\pi$
$971$	32.4309	−	32.4309i	1.04076	−	1.04076i	0.999133	−	0.0416227i	$-0.0132528\pi$
$972$		0			0
$973$		−	18.3737i		−	0.589035i
$974$		0			0
$975$	−1.70541	−	4.11723i	−0.0546169	−	0.131857i
$976$		0			0
$977$	−16.0260	−	16.0260i	−0.512717	−	0.512717i	0.402641	−	0.915358i	$-0.368092\pi$
$977$	−16.0260	−	16.0260i	−0.512717	−	0.512717i	−0.915358	+	0.402641i	$0.868092\pi$
$978$		0			0
$979$	47.5778	−	19.7074i	1.52059	−	0.629850i
$980$		0			0
$981$	19.2042	+	7.95463i	0.613142	+	0.253972i
$982$		0			0
$983$	−7.25288	+	17.5100i	−0.231331	+	0.558482i	−0.996334	−	0.0855441i	$-0.972737\pi$
$983$	−7.25288	+	17.5100i	−0.231331	+	0.558482i	0.765004	+	0.644026i	$0.222737\pi$
$984$		0			0
$985$	−19.6919			−0.627437
$986$		0			0
$987$	3.06330			0.0975059
$988$		0			0
$989$	2.89573	−	6.99091i	0.0920789	−	0.222298i
$990$		0			0
$991$	29.4783	+	12.2103i	0.936409	+	0.387873i	0.798106	−	0.602517i	$-0.205835\pi$
$991$	29.4783	+	12.2103i	0.936409	+	0.387873i	0.138303	+	0.990390i	$0.455835\pi$
$992$		0			0
$993$	10.8682	−	4.50177i	0.344893	−	0.142859i
$994$		0			0
$995$	0.359426	+	0.359426i	0.0113946	+	0.0113946i
$996$		0			0
$997$	−12.5583	−	30.3184i	−0.397724	−	0.960192i	−0.988205	−	0.153140i	$-0.951062\pi$
$997$	−12.5583	−	30.3184i	−0.397724	−	0.960192i	0.590480	−	0.807052i	$-0.298938\pi$
$998$		0			0
$999$			15.3040i			0.484196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.c.25.2	✓	12
3.2	odd	2		1224.2.bq.c.433.3		12
4.3	odd	2		272.2.v.f.161.2		12
17.6	odd	16		2312.2.b.n.577.5		12
17.7	odd	16		2312.2.a.w.1.5		12
17.10	odd	16		2312.2.a.w.1.8		12
17.11	odd	16		2312.2.b.n.577.8		12
17.15	even	8	inner	136.2.n.c.49.2	yes	12
51.32	odd	8		1224.2.bq.c.865.3		12
68.7	even	16		4624.2.a.bt.1.8		12
68.15	odd	8		272.2.v.f.49.2		12
68.27	even	16		4624.2.a.bt.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.c.25.2	✓	12	1.1	even	1	trivial
136.2.n.c.49.2	yes	12	17.15	even	8	inner
272.2.v.f.49.2		12	68.15	odd	8
272.2.v.f.161.2		12	4.3	odd	2
1224.2.bq.c.433.3		12	3.2	odd	2
1224.2.bq.c.865.3		12	51.32	odd	8
2312.2.a.w.1.5		12	17.7	odd	16
2312.2.a.w.1.8		12	17.10	odd	16
2312.2.b.n.577.5		12	17.6	odd	16
2312.2.b.n.577.8		12	17.11	odd	16
4624.2.a.bt.1.5		12	68.27	even	16
4624.2.a.bt.1.8		12	68.7	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.152809 - 0.368914i) q^{3} +(-1.09698 - 0.454383i) q^{5} +(4.72436 - 1.95689i) q^{7} +(2.00857 + 2.00857i) q^{9} +O(q^{10})\)	\(q+(0.152809 - 0.368914i) q^{3} +(-1.09698 - 0.454383i) q^{5} +(4.72436 - 1.95689i) q^{7} +(2.00857 + 2.00857i) q^{9} +(-1.79540 - 4.33449i) q^{11} +3.10860i q^{13} +(-0.335257 + 0.335257i) q^{15} +(-3.95613 + 1.16149i) q^{17} +(-3.07309 + 3.07309i) q^{19} -2.04192i q^{21} +(0.603641 + 1.45732i) q^{23} +(-2.53864 - 2.53864i) q^{25} +(2.15466 - 0.892490i) q^{27} +(2.98947 + 1.23828i) q^{29} +(-1.26977 + 3.06549i) q^{31} -1.87341 q^{33} -6.07170 q^{35} +(-2.51119 + 6.06255i) q^{37} +(1.14680 + 0.475022i) q^{39} +(-6.91009 + 2.86225i) q^{41} +(-3.39207 - 3.39207i) q^{43} +(-1.29070 - 3.11602i) q^{45} +1.50021i q^{47} +(13.5404 - 13.5404i) q^{49} +(-0.176043 + 1.63696i) q^{51} +(1.24574 - 1.24574i) q^{53} +5.57064i q^{55} +(0.664109 + 1.60330i) q^{57} +(2.56364 + 2.56364i) q^{59} +(10.3831 - 4.30081i) q^{61} +(13.4198 + 5.55866i) q^{63} +(1.41249 - 3.41006i) q^{65} -10.8688 q^{67} +0.629868 q^{69} +(3.11619 - 7.52315i) q^{71} +(8.17226 + 3.38506i) q^{73} +(-1.32447 + 0.548612i) q^{75} +(-16.9643 - 16.9643i) q^{77} +(-0.507386 - 1.22494i) q^{79} +7.59039i q^{81} +(3.71066 - 3.71066i) q^{83} +(4.86755 + 0.523469i) q^{85} +(0.913637 - 0.913637i) q^{87} +10.9766i q^{89} +(6.08319 + 14.6861i) q^{91} +(0.936870 + 0.936870i) q^{93} +(4.76747 - 1.97475i) q^{95} +(-3.27075 - 1.35479i) q^{97} +(5.09994 - 12.3123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^5 - 8 * q^9	\( 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45} + 44 q^{49} - 8 q^{51} - 8 q^{53} - 12 q^{57} + 16 q^{59} + 44 q^{61} + 100 q^{63} - 20 q^{65} - 40 q^{67} + 56 q^{69} + 32 q^{71} + 8 q^{73} + 92 q^{75} - 12 q^{77} - 8 q^{79} + 40 q^{83} + 40 q^{85} - 84 q^{87} - 40 q^{91} - 76 q^{93} + 28 q^{95} - 16 q^{97} - 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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