LMFDB - Embedded newform 912.3.be.g.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.520060207104.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 44x^{6} + 664x^{4} - 3528x^{2} + 8100 $ x^8 - 44x^6 + 664x^4 - 3528*x^2 + 8100
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$-2.03753 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.g.673.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(4.62659 + 8.01349i) q^{5} +1.36330 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(4.62659 + 8.01349i) q^{5} +1.36330 q^{7} +(1.50000 - 2.59808i) q^{9} -3.17812 q^{11} +(-17.9474 - 10.3620i) q^{13} +(-13.8798 - 8.01349i) q^{15} +(-15.5951 - 27.0114i) q^{17} +(-14.8244 - 11.8844i) q^{19} +(-2.04494 + 1.18065i) q^{21} +(-0.507413 + 0.878866i) q^{23} +(-30.3107 + 52.4997i) q^{25} +5.19615i q^{27} +(-3.56164 - 2.05632i) q^{29} -41.8036i q^{31} +(4.76719 - 2.75234i) q^{33} +(6.30742 + 10.9248i) q^{35} -2.95906i q^{37} +35.8949 q^{39} +(39.4367 - 22.7688i) q^{41} +(28.2202 + 48.8787i) q^{43} +27.7596 q^{45} +(31.5546 - 54.6542i) q^{47} -47.1414 q^{49} +(46.7852 + 27.0114i) q^{51} +(20.8782 + 12.0540i) q^{53} +(-14.7039 - 25.4679i) q^{55} +(32.5287 + 4.98830i) q^{57} +(-60.2185 + 34.7672i) q^{59} +(-17.6592 + 30.5866i) q^{61} +(2.04494 - 3.54195i) q^{63} -191.762i q^{65} +(-53.1711 - 30.6984i) q^{67} -1.75773i q^{69} +(-45.8511 + 26.4721i) q^{71} +(16.5353 + 28.6401i) q^{73} -104.999i q^{75} -4.33272 q^{77} +(-17.0102 + 9.82086i) q^{79} +(-4.50000 - 7.79423i) q^{81} -35.3054 q^{83} +(144.304 - 249.942i) q^{85} +7.12329 q^{87} +(18.8431 + 10.8791i) q^{89} +(-24.4677 - 14.1264i) q^{91} +(36.2029 + 62.7053i) q^{93} +(26.6491 - 173.779i) q^{95} +(-26.1736 + 15.1113i) q^{97} +(-4.76719 + 8.25701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	4.62659	+	8.01349i	0.925319	+	1.60270i	0.791048	+	0.611754i	$0.209536\pi$
$5$	4.62659	+	8.01349i	0.925319	+	1.60270i	0.134271	+	0.990945i	$0.457131\pi$
$6$		0			0
$7$	1.36330			0.194757			0.0973783	−	0.995247i	$-0.468954\pi$
$7$	1.36330			0.194757			0.0973783	+	0.995247i	$0.468954\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−3.17812			−0.288920			−0.144460	−	0.989511i	$-0.546145\pi$
$11$	−3.17812			−0.288920			−0.144460	+	0.989511i	$0.546145\pi$
$12$		0			0
$13$	−17.9474	−	10.3620i	−1.38057	−	0.797073i	−0.388344	−	0.921514i	$-0.626953\pi$
$13$	−17.9474	−	10.3620i	−1.38057	−	0.797073i	−0.992227	+	0.124441i	$0.960286\pi$
$14$		0			0
$15$	−13.8798	−	8.01349i	−0.925319	−	0.534233i
$16$		0			0
$17$	−15.5951	−	27.0114i	−0.917357	−	1.58891i	−0.803413	−	0.595421i	$-0.796985\pi$
$17$	−15.5951	−	27.0114i	−0.917357	−	1.58891i	−0.113943	−	0.993487i	$-0.536348\pi$
$18$		0			0
$19$	−14.8244	−	11.8844i	−0.780229	−	0.625494i
$19$	−14.8244	−	11.8844i	−0.780229	−	0.625494i
$20$		0			0
$21$	−2.04494	+	1.18065i	−0.0973783	+	0.0562214i
$22$		0			0
$23$	−0.507413	+	0.878866i	−0.0220615	+	0.0382116i	−0.876845	−	0.480773i	$-0.840356\pi$
$23$	−0.507413	+	0.878866i	−0.0220615	+	0.0382116i	0.854784	+	0.518984i	$0.173690\pi$
$24$		0			0
$25$	−30.3107	+	52.4997i	−1.21243	+	2.09999i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−3.56164	−	2.05632i	−0.122815	−	0.0709074i	0.437334	−	0.899299i	$-0.355923\pi$
$29$	−3.56164	−	2.05632i	−0.122815	−	0.0709074i	−0.560149	+	0.828392i	$0.689256\pi$
$30$		0			0
$31$		−	41.8036i		−	1.34850i	−0.738502	−	0.674251i	$-0.764467\pi$
$31$		−	41.8036i		−	1.34850i	0.738502	−	0.674251i	$-0.235533\pi$
$32$		0			0
$33$	4.76719	−	2.75234i	0.144460	−	0.0834041i
$34$		0			0
$35$	6.30742	+	10.9248i	0.180212	+	0.312136i
$36$		0			0
$37$		−	2.95906i		−	0.0799745i	−0.999200	−	0.0399873i	$-0.987268\pi$
$37$		−	2.95906i		−	0.0799745i	0.999200	−	0.0399873i	$-0.0127317\pi$
$38$		0			0
$39$	35.8949			0.920381
$40$		0			0
$41$	39.4367	−	22.7688i	0.961872	−	0.555337i	0.0651230	−	0.997877i	$-0.479256\pi$
$41$	39.4367	−	22.7688i	0.961872	−	0.555337i	0.896749	+	0.442540i	$0.145923\pi$
$42$		0			0
$43$	28.2202	+	48.8787i	0.656283	+	1.13671i	0.981571	+	0.191100i	$0.0612054\pi$
$43$	28.2202	+	48.8787i	0.656283	+	1.13671i	−0.325288	+	0.945615i	$0.605461\pi$
$44$		0			0
$45$	27.7596			0.616879
$46$		0			0
$47$	31.5546	−	54.6542i	0.671375	−	1.16286i	−0.306139	−	0.951987i	$-0.599037\pi$
$47$	31.5546	−	54.6542i	0.671375	−	1.16286i	0.977514	−	0.210869i	$-0.0676293\pi$
$48$		0			0
$49$	−47.1414			−0.962070
$50$		0			0
$51$	46.7852	+	27.0114i	0.917357	+	0.529636i
$52$		0			0
$53$	20.8782	+	12.0540i	0.393927	+	0.227434i	0.683860	−	0.729613i	$-0.260300\pi$
$53$	20.8782	+	12.0540i	0.393927	+	0.227434i	−0.289933	+	0.957047i	$0.593633\pi$
$54$		0			0
$55$	−14.7039	−	25.4679i	−0.267343	−	0.463052i
$56$		0			0
$57$	32.5287	+	4.98830i	0.570679	+	0.0875140i
$58$		0			0
$59$	−60.2185	+	34.7672i	−1.02065	+	0.589274i	−0.914293	−	0.405054i	$-0.867253\pi$
$59$	−60.2185	+	34.7672i	−1.02065	+	0.589274i	−0.106359	+	0.994328i	$0.533919\pi$
$60$		0			0
$61$	−17.6592	+	30.5866i	−0.289495	+	0.501420i	−0.973689	−	0.227880i	$-0.926821\pi$
$61$	−17.6592	+	30.5866i	−0.289495	+	0.501420i	0.684194	+	0.729300i	$0.260154\pi$
$62$		0			0
$63$	2.04494	−	3.54195i	0.0324594	−	0.0562214i
$64$		0			0
$65$		−	191.762i		−	2.95019i
$66$		0			0
$67$	−53.1711	−	30.6984i	−0.793599	−	0.458184i	0.0476293	−	0.998865i	$-0.484833\pi$
$67$	−53.1711	−	30.6984i	−0.793599	−	0.458184i	−0.841228	+	0.540681i	$0.818167\pi$
$68$		0			0
$69$		−	1.75773i		−	0.0254744i
$70$		0			0
$71$	−45.8511	+	26.4721i	−0.645790	+	0.372847i	−0.786841	−	0.617155i	$-0.788285\pi$
$71$	−45.8511	+	26.4721i	−0.645790	+	0.372847i	0.141052	+	0.990002i	$0.454952\pi$
$72$		0			0
$73$	16.5353	+	28.6401i	0.226512	+	0.392330i	0.956772	−	0.290839i	$-0.0939345\pi$
$73$	16.5353	+	28.6401i	0.226512	+	0.392330i	−0.730260	+	0.683169i	$0.760601\pi$
$74$		0			0
$75$		−	104.999i		−	1.39999i
$76$		0			0
$77$	−4.33272			−0.0562691
$78$		0			0
$79$	−17.0102	+	9.82086i	−0.215319	+	0.124315i	−0.603781	−	0.797150i	$-0.706340\pi$
$79$	−17.0102	+	9.82086i	−0.215319	+	0.124315i	0.388462	+	0.921465i	$0.373007\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−35.3054			−0.425367			−0.212683	−	0.977121i	$-0.568220\pi$
$83$	−35.3054			−0.425367			−0.212683	+	0.977121i	$0.568220\pi$
$84$		0			0
$85$	144.304	−	249.942i	1.69769	−	2.94049i
$86$		0			0
$87$	7.12329			0.0818768
$88$		0			0
$89$	18.8431	+	10.8791i	0.211721	+	0.122237i	0.602111	−	0.798413i	$-0.294327\pi$
$89$	18.8431	+	10.8791i	0.211721	+	0.122237i	−0.390390	+	0.920649i	$0.627660\pi$
$90$		0			0
$91$	−24.4677	−	14.1264i	−0.268875	−	0.155235i
$92$		0			0
$93$	36.2029	+	62.7053i	0.389279	+	0.674251i
$94$		0			0
$95$	26.6491	−	173.779i	0.280517	−	1.82925i
$96$		0			0
$97$	−26.1736	+	15.1113i	−0.269831	+	0.155787i	−0.628811	−	0.777558i	$-0.716458\pi$
$97$	−26.1736	+	15.1113i	−0.269831	+	0.155787i	0.358980	+	0.933345i	$0.383125\pi$
$98$		0			0
$99$	−4.76719	+	8.25701i	−0.0481534	+	0.0834041i
$100$		0			0
$101$	−29.6255	+	51.3128i	−0.293321	+	0.508047i	−0.974593	−	0.223983i	$-0.928094\pi$
$101$	−29.6255	+	51.3128i	−0.293321	+	0.508047i	0.681272	+	0.732031i	$0.261427\pi$
$102$		0			0
$103$			2.50848i			0.0243542i	0.999926	+	0.0121771i	$0.00387618\pi$
$103$			2.50848i			0.0243542i	−0.999926	+	0.0121771i	$0.996124\pi$
$104$		0			0
$105$	−18.9222	−	10.9248i	−0.180212	−	0.104045i
$106$		0			0
$107$			29.4168i			0.274923i	0.990507	+	0.137461i	$0.0438943\pi$
$107$			29.4168i			0.274923i	−0.990507	+	0.137461i	$0.956106\pi$
$108$		0			0
$109$	88.1110	−	50.8709i	0.808357	−	0.466705i	−0.0380277	−	0.999277i	$-0.512108\pi$
$109$	88.1110	−	50.8709i	0.808357	−	0.466705i	0.846385	+	0.532571i	$0.178774\pi$
$110$		0			0
$111$	2.56262	+	4.43859i	0.0230867	+	0.0399873i
$112$		0			0
$113$		−	128.658i		−	1.13857i	−0.822141	−	0.569284i	$-0.807220\pi$
$113$		−	128.658i		−	1.13857i	0.822141	−	0.569284i	$-0.192780\pi$
$114$		0			0
$115$	−9.39038			−0.0816555
$116$		0			0
$117$	−53.8423	+	31.0859i	−0.460190	+	0.265691i
$118$		0			0
$119$	−21.2607	−	36.8246i	−0.178661	−	0.309450i
$120$		0			0
$121$	−110.900			−0.916525
$122$		0			0
$123$	−39.4367	+	68.3064i	−0.320624	+	0.555337i
$124$		0			0
$125$	−329.612			−2.63689
$126$		0			0
$127$	58.5464	+	33.8018i	0.460995	+	0.266156i	0.712463	−	0.701710i	$-0.247580\pi$
$127$	58.5464	+	33.8018i	0.460995	+	0.266156i	−0.251467	+	0.967866i	$0.580913\pi$
$128$		0			0
$129$	−84.6605	−	48.8787i	−0.656283	−	0.378905i
$130$		0			0
$131$	−90.9593	−	157.546i	−0.694346	−	1.20264i	−0.970401	−	0.241500i	$-0.922361\pi$
$131$	−90.9593	−	157.546i	−0.694346	−	1.20264i	0.276055	−	0.961142i	$-0.410973\pi$
$132$		0			0
$133$	−20.2100	−	16.2019i	−0.151955	−	0.121819i
$134$		0			0
$135$	−41.6393	+	24.0405i	−0.308440	+	0.178078i
$136$		0			0
$137$	−77.6805	+	134.547i	−0.567011	+	0.982091i	0.429849	+	0.902901i	$0.358567\pi$
$137$	−77.6805	+	134.547i	−0.567011	+	0.982091i	−0.996860	+	0.0791904i	$0.974766\pi$
$138$		0			0
$139$	−39.6830	+	68.7329i	−0.285489	+	0.494481i	−0.972728	−	0.231950i	$-0.925489\pi$
$139$	−39.6830	+	68.7329i	−0.285489	+	0.494481i	0.687239	+	0.726432i	$0.258823\pi$
$140$		0			0
$141$			109.308i			0.775237i
$142$		0			0
$143$	57.0392	+	32.9316i	0.398875	+	0.230291i
$144$		0			0
$145$		−	38.0549i		−	0.262448i
$146$		0			0
$147$	70.7121	−	40.8257i	0.481035	−	0.277726i
$148$		0			0
$149$	−63.1838	−	109.438i	−0.424052	−	0.734480i	0.572279	−	0.820059i	$-0.306059\pi$
$149$	−63.1838	−	109.438i	−0.424052	−	0.734480i	−0.996331	+	0.0855788i	$0.972726\pi$
$150$		0			0
$151$		−	195.697i		−	1.29601i	−0.761638	−	0.648003i	$-0.775604\pi$
$151$		−	195.697i		−	1.29601i	0.761638	−	0.648003i	$-0.224396\pi$
$152$		0			0
$153$	−93.5704			−0.611571
$154$		0			0
$155$	334.993	−	193.408i	2.16124	−	1.24779i
$156$		0			0
$157$	87.6860	+	151.877i	0.558509	+	0.967367i	0.997621	+	0.0689342i	$0.0219598\pi$
$157$	87.6860	+	151.877i	0.558509	+	0.967367i	−0.439112	+	0.898432i	$0.644707\pi$
$158$		0			0
$159$	−41.7563			−0.262618
$160$		0			0
$161$	−0.691755	+	1.19815i	−0.00429661	+	0.00744195i
$162$		0			0
$163$	242.052			1.48498			0.742490	−	0.669857i	$-0.233645\pi$
$163$	242.052			1.48498			0.742490	+	0.669857i	$0.233645\pi$
$164$		0			0
$165$	44.1117	+	25.4679i	0.267343	+	0.154351i
$166$		0			0
$167$	−234.730	−	135.521i	−1.40557	−	0.811505i	−0.410611	−	0.911811i	$-0.634684\pi$
$167$	−234.730	−	135.521i	−1.40557	−	0.811505i	−0.994957	+	0.100306i	$0.968018\pi$
$168$		0			0
$169$	130.240	+	225.582i	0.770651	+	1.33481i
$170$		0			0
$171$	−53.1131	+	20.6882i	−0.310603	+	0.120984i
$172$		0			0
$173$	140.548	−	81.1456i	0.812418	−	0.469050i	−0.0353768	−	0.999374i	$-0.511263\pi$
$173$	140.548	−	81.1456i	0.812418	−	0.469050i	0.847795	+	0.530324i	$0.177930\pi$
$174$		0			0
$175$	−41.3225	+	71.5726i	−0.236128	+	0.408987i
$176$		0			0
$177$	60.2185	−	104.301i	0.340217	−	0.589274i
$178$		0			0
$179$			315.878i			1.76468i	0.470609	+	0.882342i	$0.344034\pi$
$179$			315.878i			1.76468i	−0.470609	+	0.882342i	$0.655966\pi$
$180$		0			0
$181$	−175.927	−	101.571i	−0.971972	−	0.561168i	−0.0721353	−	0.997395i	$-0.522981\pi$
$181$	−175.927	−	101.571i	−0.971972	−	0.561168i	−0.899837	+	0.436226i	$0.856315\pi$
$182$		0			0
$183$		−	61.1732i		−	0.334280i
$184$		0			0
$185$	23.7124	−	13.6904i	0.128175	−	0.0740019i
$186$		0			0
$187$	49.5631	+	85.8457i	0.265043	+	0.459068i
$188$		0			0
$189$			7.08389i			0.0374809i
$190$		0			0
$191$	−334.615			−1.75191			−0.875955	−	0.482392i	$-0.839768\pi$
$191$	−334.615			−1.75191			−0.875955	+	0.482392i	$0.839768\pi$
$192$		0			0
$193$	152.795	−	88.2162i	0.791683	−	0.457079i	−0.0488715	−	0.998805i	$-0.515562\pi$
$193$	152.795	−	88.2162i	0.791683	−	0.457079i	0.840555	+	0.541726i	$0.182229\pi$
$194$		0			0
$195$	166.071	+	287.643i	0.851645	+	1.47509i
$196$		0			0
$197$	−4.83053			−0.0245205			−0.0122602	−	0.999925i	$-0.503903\pi$
$197$	−4.83053			−0.0245205			−0.0122602	+	0.999925i	$0.503903\pi$
$198$		0			0
$199$	−47.2231	+	81.7927i	−0.237302	+	0.411019i	−0.959939	−	0.280209i	$-0.909596\pi$
$199$	−47.2231	+	81.7927i	−0.237302	+	0.411019i	0.722637	+	0.691227i	$0.242930\pi$
$200$		0			0
$201$	106.342			0.529066
$202$		0			0
$203$	−4.85557	−	2.80337i	−0.0239191	−	0.0138097i
$204$		0			0
$205$	364.915	+	210.684i	1.78008	+	1.02773i
$206$		0			0
$207$	1.52224	+	2.63660i	0.00735382	+	0.0127372i
$208$		0			0
$209$	47.1137	+	37.7700i	0.225424	+	0.180718i
$210$		0			0
$211$	277.971	−	160.487i	1.31740	−	0.760601i	0.334091	−	0.942541i	$-0.391571\pi$
$211$	277.971	−	160.487i	1.31740	−	0.760601i	0.983310	+	0.181939i	$0.0582375\pi$
$212$		0			0
$213$	45.8511	−	79.4164i	0.215263	−	0.372847i
$214$		0			0
$215$	−261.126	+	452.284i	−1.21454	+	2.10365i
$216$		0			0
$217$		−	56.9906i		−	0.262630i
$218$		0			0
$219$	−49.6060	−	28.6401i	−0.226512	−	0.130777i
$220$		0			0
$221$			646.381i			2.92480i
$222$		0			0
$223$	−219.762	+	126.880i	−0.985480	+	0.568967i	−0.903920	−	0.427701i	$-0.859324\pi$
$223$	−219.762	+	126.880i	−0.985480	+	0.568967i	−0.0815602	+	0.996668i	$0.525990\pi$
$224$		0			0
$225$	90.9322	+	157.499i	0.404143	+	0.699996i
$226$		0			0
$227$		−	435.226i		−	1.91729i	−0.284597	−	0.958647i	$-0.591860\pi$
$227$		−	435.226i		−	1.91729i	0.284597	−	0.958647i	$-0.408140\pi$
$228$		0			0
$229$	−26.2474			−0.114618			−0.0573088	−	0.998357i	$-0.518252\pi$
$229$	−26.2474			−0.114618			−0.0573088	+	0.998357i	$0.518252\pi$
$230$		0			0
$231$	6.49909	−	3.75225i	0.0281346	−	0.0162435i
$232$		0			0
$233$	−39.9516	−	69.1983i	−0.171466	−	0.296988i	0.767466	−	0.641089i	$-0.221517\pi$
$233$	−39.9516	−	69.1983i	−0.171466	−	0.296988i	−0.938933	+	0.344101i	$0.888184\pi$
$234$		0			0
$235$	583.962			2.48494
$236$		0			0
$237$	17.0102	−	29.4626i	0.0717731	−	0.124315i
$238$		0			0
$239$	−93.3900			−0.390753			−0.195377	−	0.980728i	$-0.562593\pi$
$239$	−93.3900			−0.390753			−0.195377	+	0.980728i	$0.562593\pi$
$240$		0			0
$241$	92.8891	+	53.6296i	0.385432	+	0.222529i	0.680179	−	0.733046i	$-0.261902\pi$
$241$	92.8891	+	53.6296i	0.385432	+	0.222529i	−0.294747	+	0.955575i	$0.595235\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−218.104	−	377.768i	−0.890221	−	1.54191i
$246$		0			0
$247$	142.914	+	366.903i	0.578598	+	1.48544i
$248$		0			0
$249$	52.9582	−	30.5754i	0.212683	−	0.122793i
$250$		0			0
$251$	66.1623	−	114.596i	0.263595	−	0.456559i	−0.703600	−	0.710596i	$-0.748425\pi$
$251$	66.1623	−	114.596i	0.263595	−	0.456559i	0.967194	+	0.254037i	$0.0817585\pi$
$252$		0			0
$253$	1.61262	−	2.79314i	0.00637400	−	0.0110401i
$254$		0			0
$255$			499.884i			1.96033i
$256$		0			0
$257$	38.1498	+	22.0258i	0.148443	+	0.0857035i	0.572382	−	0.819987i	$-0.306020\pi$
$257$	38.1498	+	22.0258i	0.148443	+	0.0857035i	−0.423939	+	0.905691i	$0.639353\pi$
$258$		0			0
$259$		−	4.03407i		−	0.0155756i
$260$		0			0
$261$	−10.6849	+	6.16895i	−0.0409384	+	0.0236358i
$262$		0			0
$263$	1.79623	+	3.11116i	0.00682978	+	0.0118295i	0.869420	−	0.494074i	$-0.164493\pi$
$263$	1.79623	+	3.11116i	0.00682978	+	0.0118295i	−0.862590	+	0.505903i	$0.831159\pi$
$264$		0			0
$265$			223.076i			0.841796i
$266$		0			0
$267$	−37.6863			−0.141147
$268$		0			0
$269$	274.602	−	158.542i	1.02083	−	0.589374i	0.106483	−	0.994315i	$-0.466041\pi$
$269$	274.602	−	158.542i	1.02083	−	0.589374i	0.914343	+	0.404941i	$0.132708\pi$
$270$		0			0
$271$	40.3436	+	69.8772i	0.148869	+	0.257849i	0.930810	−	0.365504i	$-0.119103\pi$
$271$	40.3436	+	69.8772i	0.148869	+	0.257849i	−0.781940	+	0.623353i	$0.785770\pi$
$272$		0			0
$273$	48.9353			0.179250
$274$		0			0
$275$	96.3312	−	166.851i	0.350295	−	0.606730i
$276$		0			0
$277$	−437.705			−1.58016			−0.790082	−	0.613001i	$-0.789962\pi$
$277$	−437.705			−1.58016			−0.790082	+	0.613001i	$0.789962\pi$
$278$		0			0
$279$	−108.609	−	62.7053i	−0.389279	−	0.224750i
$280$		0			0
$281$	−231.422	−	133.611i	−0.823565	−	0.475486i	0.0280791	−	0.999606i	$-0.491061\pi$
$281$	−231.422	−	133.611i	−0.823565	−	0.475486i	−0.851644	+	0.524120i	$0.824394\pi$
$282$		0			0
$283$	265.986	+	460.702i	0.939881	+	1.62792i	0.765690	+	0.643210i	$0.222398\pi$
$283$	265.986	+	460.702i	0.939881	+	1.62792i	0.174191	+	0.984712i	$0.444269\pi$
$284$		0			0
$285$	110.523	+	283.747i	0.387801	+	0.995605i
$286$		0			0
$287$	53.7639	−	31.0406i	0.187331	−	0.108155i
$288$		0			0
$289$	−341.912	+	592.209i	−1.18309	+	2.04917i
$290$		0			0
$291$	26.1736	−	45.3340i	0.0899436	−	0.155787i
$292$		0			0
$293$			112.392i			0.383590i	0.981435	+	0.191795i	$0.0614309\pi$
$293$			112.392i			0.383590i	−0.981435	+	0.191795i	$0.938569\pi$
$294$		0			0
$295$	−557.213	−	321.707i	−1.88886	−	1.09053i
$296$		0			0
$297$		−	16.5140i		−	0.0556028i
$298$		0			0
$299$	18.2135	−	10.5156i	0.0609148	−	0.0351692i
$300$		0			0
$301$	38.4724	+	66.6362i	0.127815	+	0.221383i
$302$		0			0
$303$		−	102.626i		−	0.338698i
$304$		0			0
$305$	−326.808			−1.07150
$306$		0			0
$307$	−220.594	+	127.360i	−0.718546	+	0.414853i	−0.814217	−	0.580560i	$-0.802833\pi$
$307$	−220.594	+	127.360i	−0.718546	+	0.414853i	0.0956715	+	0.995413i	$0.469500\pi$
$308$		0			0
$309$	−2.17241	−	3.76272i	−0.00703044	−	0.0121771i
$310$		0			0
$311$	−69.9227			−0.224832			−0.112416	−	0.993661i	$-0.535859\pi$
$311$	−69.9227			−0.224832			−0.112416	+	0.993661i	$0.535859\pi$
$312$		0			0
$313$	145.286	−	251.644i	0.464174	−	0.803973i	−0.534990	−	0.844859i	$-0.679685\pi$
$313$	145.286	−	251.644i	0.464174	−	0.803973i	0.999164	+	0.0408855i	$0.0130179\pi$
$314$		0			0
$315$	37.8445			0.120141
$316$		0			0
$317$	−304.859	−	176.010i	−0.961700	−	0.555238i	−0.0650044	−	0.997885i	$-0.520706\pi$
$317$	−304.859	−	176.010i	−0.961700	−	0.555238i	−0.896696	+	0.442647i	$0.854039\pi$
$318$		0			0
$319$	11.3193	+	6.53523i	0.0354838	+	0.0204866i
$320$		0			0
$321$	−25.4757	−	44.1251i	−0.0793634	−	0.137461i
$322$		0			0
$323$	−89.8274	+	585.765i	−0.278103	+	1.81351i
$324$		0			0
$325$	1088.00	−	628.156i	3.34769	−	1.93279i
$326$		0			0
$327$	−88.1110	+	152.613i	−0.269452	+	0.466705i
$328$		0			0
$329$	43.0183	−	74.5099i	0.130755	−	0.226474i
$330$		0			0
$331$		−	314.043i		−	0.948771i	−0.880317	−	0.474386i	$-0.842670\pi$
$331$		−	314.043i		−	0.948771i	0.880317	−	0.474386i	$-0.157330\pi$
$332$		0			0
$333$	−7.68786	−	4.43859i	−0.0230867	−	0.0133291i
$334$		0			0
$335$		−	568.115i		−	1.69587i
$336$		0			0
$337$	−212.744	+	122.828i	−0.631288	+	0.364474i	−0.781251	−	0.624217i	$-0.785418\pi$
$337$	−212.744	+	122.828i	−0.631288	+	0.364474i	0.149963	+	0.988692i	$0.452085\pi$
$338$		0			0
$339$	111.421	+	192.987i	0.328676	+	0.569284i
$340$		0			0
$341$			132.857i			0.389610i
$342$		0			0
$343$	−131.069			−0.382126
$344$		0			0
$345$	14.0856	−	8.13231i	0.0408277	−	0.0235719i
$346$		0			0
$347$	163.135	+	282.558i	0.470129	+	0.814288i	0.999417	−	0.0341550i	$-0.0108740\pi$
$347$	163.135	+	282.558i	0.470129	+	0.814288i	−0.529287	+	0.848443i	$0.677541\pi$
$348$		0			0
$349$	−676.762			−1.93914			−0.969572	−	0.244805i	$-0.921276\pi$
$349$	−676.762			−1.93914			−0.969572	+	0.244805i	$0.921276\pi$
$350$		0			0
$351$	53.8423	−	93.2576i	0.153397	−	0.265691i
$352$		0			0
$353$	362.476			1.02684			0.513422	−	0.858136i	$-0.328377\pi$
$353$	362.476			1.02684			0.513422	+	0.858136i	$0.328377\pi$
$354$		0			0
$355$	−424.268	−	244.952i	−1.19512	−	0.690004i
$356$		0			0
$357$	63.7821	+	36.8246i	0.178661	+	0.103150i
$358$		0			0
$359$	−101.986	−	176.644i	−0.284082	−	0.492045i	0.688304	−	0.725423i	$-0.258356\pi$
$359$	−101.986	−	176.644i	−0.284082	−	0.492045i	−0.972386	+	0.233377i	$0.925022\pi$
$360$		0			0
$361$	78.5231	+	352.357i	0.217516	+	0.976057i
$362$		0			0
$363$	166.349	−	96.0418i	0.458262	−	0.264578i
$364$		0			0
$365$	−153.005	+	265.012i	−0.419191	+	0.726060i
$366$		0			0
$367$	−141.857	+	245.703i	−0.386531	+	0.669491i	−0.991980	−	0.126393i	$-0.959660\pi$
$367$	−141.857	+	245.703i	−0.386531	+	0.669491i	0.605449	+	0.795884i	$0.292993\pi$
$368$		0			0
$369$		−	136.613i		−	0.370225i
$370$		0			0
$371$	28.4631	+	16.4332i	0.0767200	+	0.0442943i
$372$		0			0
$373$			157.943i			0.423439i	0.977331	+	0.211719i	$0.0679063\pi$
$373$			157.943i			0.423439i	−0.977331	+	0.211719i	$0.932094\pi$
$374$		0			0
$375$	494.418	−	285.452i	1.31845	−	0.761206i
$376$		0			0
$377$	42.6149	+	73.8111i	0.113037	+	0.195786i
$378$		0			0
$379$			277.361i			0.731823i	0.930650	+	0.365912i	$0.119243\pi$
$379$			277.361i			0.731823i	−0.930650	+	0.365912i	$0.880757\pi$
$380$		0			0
$381$	−117.093			−0.307330
$382$		0			0
$383$	122.058	−	70.4705i	0.318690	−	0.183996i	−0.332118	−	0.943238i	$-0.607763\pi$
$383$	122.058	−	70.4705i	0.318690	−	0.183996i	0.650809	+	0.759242i	$0.274430\pi$
$384$		0			0
$385$	−20.0458	−	34.7203i	−0.0520669	−	0.0901825i
$386$		0			0
$387$	169.321			0.437522
$388$		0			0
$389$	77.7966	−	134.748i	0.199991	−	0.346395i	−0.748534	−	0.663096i	$-0.769242\pi$
$389$	77.7966	−	134.748i	0.199991	−	0.346395i	0.948525	+	0.316701i	$0.102575\pi$
$390$		0			0
$391$	31.6526			0.0809529
$392$		0			0
$393$	272.878	+	157.546i	0.694346	+	0.400881i
$394$		0			0
$395$	−157.399	−	90.8743i	−0.398478	−	0.230061i
$396$		0			0
$397$	−50.8916	−	88.1469i	−0.128191	−	0.222033i	0.794785	−	0.606891i	$-0.207584\pi$
$397$	−50.8916	−	88.1469i	−0.128191	−	0.222033i	−0.922976	+	0.384859i	$0.874250\pi$
$398$		0			0
$399$	44.3463	+	6.80053i	0.111144	+	0.0170439i
$400$		0			0
$401$	−567.442	+	327.613i	−1.41507	+	0.816990i	−0.995860	−	0.0909007i	$-0.971025\pi$
$401$	−567.442	+	327.613i	−1.41507	+	0.816990i	−0.419208	+	0.907890i	$0.637692\pi$
$402$		0			0
$403$	−433.166	+	750.266i	−1.07485	+	1.86170i
$404$		0			0
$405$	41.6393	−	72.1214i	0.102813	−	0.178078i
$406$		0			0
$407$			9.40425i			0.0231063i
$408$		0			0
$409$	74.9537	+	43.2745i	0.183261	+	0.105806i	0.588824	−	0.808261i	$-0.299591\pi$
$409$	74.9537	+	43.2745i	0.183261	+	0.105806i	−0.405563	+	0.914067i	$0.632925\pi$
$410$		0			0
$411$		−	269.093i		−	0.654728i
$412$		0			0
$413$	−82.0956	+	47.3979i	−0.198779	+	0.114765i
$414$		0			0
$415$	−163.344	−	282.920i	−0.393600	−	0.681735i
$416$		0			0
$417$		−	137.466i		−	0.329654i
$418$		0			0
$419$	591.331			1.41129			0.705645	−	0.708565i	$-0.250657\pi$
$419$	591.331			1.41129			0.705645	+	0.708565i	$0.250657\pi$
$420$		0			0
$421$	−204.434	+	118.030i	−0.485592	+	0.280357i	−0.722744	−	0.691116i	$-0.757119\pi$
$421$	−204.434	+	118.030i	−0.485592	+	0.280357i	0.237152	+	0.971473i	$0.423786\pi$
$422$		0			0
$423$	−94.6639	−	163.963i	−0.223792	−	0.387619i
$424$		0			0
$425$	1890.79			4.44892
$426$		0			0
$427$	−24.0747	+	41.6986i	−0.0563810	+	0.0976548i
$428$		0			0
$429$	−114.078			−0.265917
$430$		0			0
$431$	239.740	+	138.414i	0.556240	+	0.321145i	0.751635	−	0.659579i	$-0.229266\pi$
$431$	239.740	+	138.414i	0.556240	+	0.321145i	−0.195395	+	0.980725i	$0.562599\pi$
$432$		0			0
$433$	−466.441	−	269.300i	−1.07723	−	0.621940i	−0.147083	−	0.989124i	$-0.546989\pi$
$433$	−466.441	−	269.300i	−1.07723	−	0.621940i	−0.930148	+	0.367184i	$0.880322\pi$
$434$		0			0
$435$	32.9565	+	57.0824i	0.0757622	+	0.131224i
$436$		0			0
$437$	17.9668	−	6.99833i	0.0411141	−	0.0160145i
$438$		0			0
$439$	237.003	−	136.834i	0.539870	−	0.311694i	−0.205156	−	0.978729i	$-0.565770\pi$
$439$	237.003	−	136.834i	0.539870	−	0.311694i	0.745026	+	0.667035i	$0.232437\pi$
$440$		0			0
$441$	−70.7121	+	122.477i	−0.160345	+	0.277726i
$442$		0			0
$443$	−273.233	+	473.254i	−0.616779	+	1.06829i	0.373290	+	0.927715i	$0.378230\pi$
$443$	−273.233	+	473.254i	−0.616779	+	1.06829i	−0.990070	+	0.140578i	$0.955104\pi$
$444$		0			0
$445$			201.332i			0.452432i
$446$		0			0
$447$	189.551	+	109.438i	0.424052	+	0.244827i
$448$		0			0
$449$		−	860.002i		−	1.91537i	−0.287815	−	0.957686i	$-0.592929\pi$
$449$		−	860.002i		−	1.91537i	0.287815	−	0.957686i	$-0.407071\pi$
$450$		0			0
$451$	−125.335	+	72.3621i	−0.277904	+	0.160448i
$452$		0			0
$453$	169.479	+	293.545i	0.374125	+	0.648003i
$454$		0			0
$455$		−	261.429i		−	0.574568i
$456$		0			0
$457$	492.364			1.07738			0.538691	−	0.842503i	$-0.318919\pi$
$457$	492.364			1.07738			0.538691	+	0.842503i	$0.318919\pi$
$458$		0			0
$459$	140.356	−	81.0343i	0.305786	−	0.176545i
$460$		0			0
$461$	−76.5184	−	132.534i	−0.165984	−	0.287492i	0.771021	−	0.636810i	$-0.219747\pi$
$461$	−76.5184	−	132.534i	−0.165984	−	0.287492i	−0.937004	+	0.349318i	$0.886413\pi$
$462$		0			0
$463$	130.850			0.282612			0.141306	−	0.989966i	$-0.454870\pi$
$463$	130.850			0.282612			0.141306	+	0.989966i	$0.454870\pi$
$464$		0			0
$465$	−334.993	+	580.224i	−0.720414	+	1.24779i
$466$		0			0
$467$	384.553			0.823455			0.411727	−	0.911307i	$-0.364926\pi$
$467$	384.553			0.823455			0.411727	+	0.911307i	$0.364926\pi$
$468$		0			0
$469$	−72.4880	−	41.8509i	−0.154559	−	0.0892344i
$470$		0			0
$471$	−263.058	−	151.877i	−0.558509	−	0.322456i
$472$		0			0
$473$	−89.6872	−	155.343i	−0.189613	−	0.328420i
$474$		0			0
$475$	1073.26	−	418.050i	2.25950	−	0.880106i
$476$		0			0
$477$	62.6345	−	36.1620i	0.131309	−	0.0758114i
$478$		0			0
$479$	194.165	−	336.304i	0.405356	−	0.702097i	−0.589007	−	0.808128i	$-0.700481\pi$
$479$	194.165	−	336.304i	0.405356	−	0.702097i	0.994363	+	0.106031i	$0.0338144\pi$
$480$		0			0
$481$	−30.6616	+	53.1075i	−0.0637455	+	0.110411i
$482$		0			0
$483$		−	2.39631i		−	0.00496130i
$484$		0			0
$485$	−242.189	−	139.828i	−0.499359	−	0.288305i
$486$		0			0
$487$			418.397i			0.859131i	0.903036	+	0.429566i	$0.141333\pi$
$487$			418.397i			0.859131i	−0.903036	+	0.429566i	$0.858667\pi$
$488$		0			0
$489$	−363.078	+	209.623i	−0.742490	+	0.428677i
$490$		0			0
$491$	−214.588	−	371.678i	−0.437043	−	0.756981i	0.560417	−	0.828211i	$-0.310641\pi$
$491$	−214.588	−	371.678i	−0.437043	−	0.756981i	−0.997460	+	0.0712296i	$0.977308\pi$
$492$		0			0
$493$			128.274i			0.260190i
$494$		0			0
$495$	−88.2233			−0.178229
$496$		0			0
$497$	−62.5086	+	36.0893i	−0.125772	+	0.0726144i
$498$		0			0
$499$	−347.677	−	602.194i	−0.696747	−	1.20680i	−0.969588	−	0.244742i	$-0.921297\pi$
$499$	−347.677	−	602.194i	−0.696747	−	1.20680i	0.272841	−	0.962059i	$-0.412037\pi$
$500$		0			0
$501$	469.459			0.937045
$502$		0			0
$503$	−38.1027	+	65.9959i	−0.0757510	+	0.131205i	−0.901413	−	0.432961i	$-0.857469\pi$
$503$	−38.1027	+	65.9959i	−0.0757510	+	0.131205i	0.825662	+	0.564166i	$0.190802\pi$
$504$		0			0
$505$	−548.260			−1.08566
$506$		0			0
$507$	−390.720	−	225.582i	−0.770651	−	0.444936i
$508$		0			0
$509$	−435.453	−	251.409i	−0.855508	−	0.493928i	0.00699762	−	0.999976i	$-0.497773\pi$
$509$	−435.453	−	251.409i	−0.855508	−	0.493928i	−0.862505	+	0.506048i	$0.831106\pi$
$510$		0			0
$511$	22.5426	+	39.0449i	0.0441146	+	0.0764088i
$512$		0			0
$513$	61.7530	−	77.0296i	0.120376	−	0.150155i
$514$		0			0
$515$	−20.1017	+	11.6057i	−0.0390324	+	0.0225354i
$516$		0			0
$517$	−100.285	+	173.698i	−0.193974	+	0.335973i
$518$		0			0
$519$	−140.548	+	243.437i	−0.270806	+	0.469050i
$520$		0			0
$521$			166.183i			0.318970i	0.987200	+	0.159485i	$0.0509833\pi$
$521$			166.183i			0.318970i	−0.987200	+	0.159485i	$0.949017\pi$
$522$		0			0
$523$	638.397	+	368.578i	1.22064	+	0.704739i	0.965055	−	0.262047i	$-0.0843975\pi$
$523$	638.397	+	368.578i	1.22064	+	0.704739i	0.255588	+	0.966786i	$0.417731\pi$
$524$		0			0
$525$		−	143.145i		−	0.272658i
$526$		0			0
$527$	−1129.17	+	651.929i	−2.14265	+	1.23706i
$528$		0			0
$529$	263.985	+	457.236i	0.499027	+	0.864339i
$530$		0			0
$531$			208.603i			0.392849i
$532$		0			0
$533$	−943.717			−1.77058
$534$		0			0
$535$	−235.731	+	136.099i	−0.440619	+	0.254391i
$536$		0			0
$537$	−273.559	−	473.818i	−0.509420	−	0.882342i
$538$		0			0
$539$	149.821			0.277962
$540$		0			0
$541$	473.431	−	820.007i	0.875104	−	1.51572i	0.0184517	−	0.999830i	$-0.494126\pi$
$541$	473.431	−	820.007i	0.875104	−	1.51572i	0.856652	−	0.515895i	$-0.172540\pi$
$542$		0			0
$543$	351.854			0.647982
$544$		0			0
$545$	815.307	+	470.718i	1.49598	+	0.863702i
$546$		0			0
$547$	336.629	+	194.353i	0.615409	+	0.355306i	0.775079	−	0.631864i	$-0.217710\pi$
$547$	336.629	+	194.353i	0.615409	+	0.355306i	−0.159671	+	0.987170i	$0.551043\pi$
$548$		0			0
$549$	52.9776	+	91.7599i	0.0964983	+	0.167140i
$550$		0			0
$551$	28.3610	+	72.8115i	0.0514719	+	0.132144i
$552$		0			0
$553$	−23.1900	+	13.3887i	−0.0419349	+	0.0242111i
$554$		0			0
$555$	−23.7124	+	41.0711i	−0.0427250	+	0.0740019i
$556$		0			0
$557$	−197.907	+	342.784i	−0.355308	+	0.615412i	−0.987171	−	0.159669i	$-0.948957\pi$
$557$	−197.907	+	342.784i	−0.355308	+	0.615412i	0.631862	+	0.775081i	$0.282291\pi$
$558$		0			0
$559$		−	1169.66i		−	2.09242i
$560$		0			0
$561$	−148.689	−	85.8457i	−0.265043	−	0.153023i
$562$		0			0
$563$			86.2538i			0.153204i	0.997062	+	0.0766019i	$0.0244071\pi$
$563$			86.2538i			0.153204i	−0.997062	+	0.0766019i	$0.975593\pi$
$564$		0			0
$565$	1031.00	−	595.249i	1.82478	−	1.05354i
$566$		0			0
$567$	−6.13483	−	10.6258i	−0.0108198	−	0.0187405i
$568$		0			0
$569$		−	488.821i		−	0.859089i	−0.903046	−	0.429544i	$-0.858674\pi$
$569$		−	488.821i		−	0.859089i	0.903046	−	0.429544i	$-0.141326\pi$
$570$		0			0
$571$	−48.6050			−0.0851226			−0.0425613	−	0.999094i	$-0.513552\pi$
$571$	−48.6050			−0.0851226			−0.0425613	+	0.999094i	$0.513552\pi$
$572$		0			0
$573$	501.922	−	289.785i	0.875955	−	0.505733i
$574$		0			0
$575$	−30.7601	−	53.2781i	−0.0534959	−	0.0926576i
$576$		0			0
$577$	112.577			0.195107			0.0975534	−	0.995230i	$-0.468898\pi$
$577$	112.577			0.195107			0.0975534	+	0.995230i	$0.468898\pi$
$578$		0			0
$579$	−152.795	+	264.649i	−0.263894	+	0.457079i
$580$		0			0
$581$	−48.1318			−0.0828430
$582$		0			0
$583$	−66.3534	−	38.3091i	−0.113814	−	0.0657104i
$584$		0			0
$585$	−498.213	−	287.643i	−0.851645	−	0.491698i
$586$		0			0
$587$	−265.035	−	459.054i	−0.451508	−	0.782034i	0.546972	−	0.837151i	$-0.315780\pi$
$587$	−265.035	−	459.054i	−0.451508	−	0.782034i	−0.998480	+	0.0551166i	$0.982447\pi$
$588$		0			0
$589$	−496.809	+	619.711i	−0.843479	+	1.05214i
$590$		0			0
$591$	7.24579	−	4.18336i	0.0122602	−	0.00707845i
$592$		0			0
$593$	−113.699	+	196.932i	−0.191735	+	0.332094i	−0.945825	−	0.324676i	$-0.894745\pi$
$593$	−113.699	+	196.932i	−0.191735	+	0.332094i	0.754091	+	0.656770i	$0.228078\pi$
$594$		0			0
$595$	196.729	−	340.745i	0.330637	−	0.572680i
$596$		0			0
$597$		−	163.585i		−	0.274013i
$598$		0			0
$599$	239.473	+	138.260i	0.399788	+	0.230818i	0.686392	−	0.727231i	$-0.259193\pi$
$599$	239.473	+	138.260i	0.399788	+	0.230818i	−0.286605	+	0.958049i	$0.592527\pi$
$600$		0			0
$601$		−	583.913i		−	0.971570i	−0.874078	−	0.485785i	$-0.838534\pi$
$601$		−	583.913i		−	0.971570i	0.874078	−	0.485785i	$-0.161466\pi$
$602$		0			0
$603$	−159.513	+	92.0951i	−0.264533	+	0.152728i
$604$		0			0
$605$	−513.087	−	888.693i	−0.848078	−	1.46891i
$606$		0			0
$607$		−	233.406i		−	0.384524i	−0.981344	−	0.192262i	$-0.938418\pi$
$607$		−	233.406i		−	0.384524i	0.981344	−	0.192262i	$-0.0615823\pi$
$608$		0			0
$609$	9.71115			0.0159461
$610$		0			0
$611$	−1132.65	+	653.935i	−1.85376	+	1.07027i
$612$		0			0
$613$	125.901	+	218.068i	0.205386	+	0.355738i	0.950256	−	0.311471i	$-0.100822\pi$
$613$	125.901	+	218.068i	0.205386	+	0.355738i	−0.744870	+	0.667210i	$0.767488\pi$
$614$		0			0
$615$	−729.831			−1.18672
$616$		0			0
$617$	−120.017	+	207.875i	−0.194517	+	0.336913i	−0.946742	−	0.321993i	$-0.895647\pi$
$617$	−120.017	+	207.875i	−0.194517	+	0.336913i	0.752225	+	0.658906i	$0.228981\pi$
$618$		0			0
$619$	−1112.30			−1.79693			−0.898467	−	0.439042i	$-0.855318\pi$
$619$	−1112.30			−1.79693			−0.898467	+	0.439042i	$0.855318\pi$
$620$		0			0
$621$	−4.56672	−	2.63660i	−0.00735382	−	0.00424573i
$622$		0			0
$623$	25.6888	+	14.8314i	0.0412340	+	0.0238064i
$624$		0			0
$625$	−767.212	−	1328.85i	−1.22754	−	2.12616i
$626$		0			0
$627$	−103.380	−	15.8534i	−0.164881	−	0.0252846i
$628$		0			0
$629$	−79.9284	+	46.1467i	−0.127072	+	0.0733652i
$630$		0			0
$631$	33.4803	−	57.9896i	0.0530591	−	0.0919011i	−0.838276	−	0.545246i	$-0.816436\pi$
$631$	33.4803	−	57.9896i	0.0530591	−	0.0919011i	0.891335	+	0.453345i	$0.149769\pi$
$632$		0			0
$633$	−277.971	+	481.461i	−0.439133	+	0.760601i
$634$		0			0
$635$			625.548i			0.985115i
$636$		0			0
$637$	846.067	+	488.477i	1.32821	+	0.766840i
$638$		0			0
$639$			158.833i			0.248565i
$640$		0			0
$641$	464.442	−	268.145i	0.724558	−	0.418324i	−0.0918702	−	0.995771i	$-0.529284\pi$
$641$	464.442	−	268.145i	0.724558	−	0.418324i	0.816428	+	0.577447i	$0.195951\pi$
$642$		0			0
$643$	−394.740	−	683.709i	−0.613903	−	1.06331i	−0.990576	−	0.136965i	$-0.956265\pi$
$643$	−394.740	−	683.709i	−0.613903	−	1.06331i	0.376673	−	0.926346i	$-0.377068\pi$
$644$		0			0
$645$		−	904.568i		−	1.40243i
$646$		0			0
$647$	−249.048			−0.384927			−0.192464	−	0.981304i	$-0.561648\pi$
$647$	−249.048			−0.384927			−0.192464	+	0.981304i	$0.561648\pi$
$648$		0			0
$649$	191.382	−	110.494i	0.294887	−	0.170253i
$650$		0			0
$651$	49.3553	+	85.4859i	0.0758146	+	0.131315i
$652$		0			0
$653$	51.8821			0.0794520			0.0397260	−	0.999211i	$-0.487351\pi$
$653$	51.8821			0.0794520			0.0397260	+	0.999211i	$0.487351\pi$
$654$		0			0
$655$	841.663	−	1457.80i	1.28498	−	2.22565i
$656$		0			0
$657$	99.2121			0.151008
$658$		0			0
$659$	198.126	+	114.388i	0.300646	+	0.173578i	0.642733	−	0.766090i	$-0.277800\pi$
$659$	198.126	+	114.388i	0.300646	+	0.173578i	−0.342087	+	0.939668i	$0.611134\pi$
$660$		0			0
$661$	654.373	+	377.803i	0.989975	+	0.571562i	0.905267	−	0.424844i	$-0.139671\pi$
$661$	654.373	+	377.803i	0.989975	+	0.571562i	0.0847081	+	0.996406i	$0.473004\pi$
$662$		0			0
$663$	−559.783	−	969.572i	−0.844318	−	1.46240i
$664$		0			0
$665$	36.3306	−	236.912i	0.0546326	−	0.356259i
$666$		0			0
$667$	3.61445	−	2.08680i	0.00541897	−	0.00312864i
$668$		0			0
$669$	219.762	−	380.639i	0.328493	−	0.568967i
$670$		0			0
$671$	56.1231	−	97.2081i	0.0836410	−	0.144870i
$672$		0			0
$673$			146.962i			0.218369i	0.994021	+	0.109185i	$0.0348240\pi$
$673$			146.962i			0.218369i	−0.994021	+	0.109185i	$0.965176\pi$
$674$		0			0
$675$	−272.796	−	157.499i	−0.404143	−	0.233332i
$676$		0			0
$677$		−	205.384i		−	0.303374i	−0.988429	−	0.151687i	$-0.951529\pi$
$677$		−	205.384i		−	0.303374i	0.988429	−	0.151687i	$-0.0484706\pi$
$678$		0			0
$679$	−35.6823	+	20.6012i	−0.0525513	+	0.0303405i
$680$		0			0
$681$	376.917	+	652.839i	0.553475	+	0.958647i
$682$		0			0
$683$		−	73.7209i		−	0.107937i	−0.998543	−	0.0539685i	$-0.982813\pi$
$683$		−	73.7209i		−	0.107937i	0.998543	−	0.0539685i	$-0.0171870\pi$
$684$		0			0
$685$	−1437.58			−2.09866
$686$		0			0
$687$	39.3711	−	22.7309i	0.0573088	−	0.0330872i
$688$		0			0
$689$	−249.806	−	432.677i	−0.362563	−	0.627978i
$690$		0			0
$691$	−395.259			−0.572010			−0.286005	−	0.958228i	$-0.592327\pi$
$691$	−395.259			−0.572010			−0.286005	+	0.958228i	$0.592327\pi$
$692$		0			0
$693$	−6.49909	+	11.2567i	−0.00937819	+	0.0162435i
$694$		0			0
$695$	−734.388			−1.05667
$696$		0			0
$697$	−1230.04	−	710.162i	−1.76476	−	1.01888i
$698$		0			0
$699$	119.855	+	69.1983i	0.171466	+	0.0989961i
$700$		0			0
$701$	630.716	+	1092.43i	0.899737	+	1.55839i	0.827830	+	0.560980i	$0.189575\pi$
$701$	630.716	+	1092.43i	0.899737	+	1.55839i	0.0719080	+	0.997411i	$0.477091\pi$
$702$		0			0
$703$	−35.1666	+	43.8661i	−0.0500235	+	0.0623985i
$704$		0			0
$705$	−875.942	+	505.726i	−1.24247	+	0.717341i
$706$		0			0
$707$	−40.3883	+	69.9545i	−0.0571263	+	0.0989456i
$708$		0			0
$709$	−427.184	+	739.904i	−0.602516	+	1.04359i	0.389923	+	0.920847i	$0.372502\pi$
$709$	−427.184	+	739.904i	−0.602516	+	1.04359i	−0.992439	+	0.122741i	$0.960832\pi$
$710$		0			0
$711$			58.9252i			0.0828765i
$712$		0			0
$713$	36.7397	+	21.2117i	0.0515284	+	0.0297499i
$714$		0			0
$715$			609.444i			0.852369i
$716$		0			0
$717$	140.085	−	80.8781i	0.195377	−	0.112801i
$718$		0			0
$719$	−208.554	−	361.225i	−0.290061	−	0.502400i	0.683763	−	0.729704i	$-0.260342\pi$
$719$	−208.554	−	361.225i	−0.290061	−	0.502400i	−0.973824	+	0.227304i	$0.927009\pi$
$720$		0			0
$721$			3.41980i			0.00474314i
$722$		0			0
$723$	−185.778			−0.256955
$724$		0			0
$725$	215.912	−	124.657i	0.297810	−	0.171940i
$726$		0			0
$727$	222.947	+	386.155i	0.306667	+	0.531163i	0.977631	−	0.210327i	$-0.0674529\pi$
$727$	222.947	+	386.155i	0.306667	+	0.531163i	−0.670964	+	0.741490i	$0.734120\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	880.190	−	1524.53i	1.20409	−	2.08555i
$732$		0			0
$733$	−160.129			−0.218457			−0.109229	−	0.994017i	$-0.534838\pi$
$733$	−160.129			−0.218457			−0.109229	+	0.994017i	$0.534838\pi$
$734$		0			0
$735$	654.313	+	377.768i	0.890221	+	0.513969i
$736$		0			0
$737$	168.984	+	97.5632i	0.229287	+	0.132379i
$738$		0			0
$739$	395.990	+	685.875i	0.535846	+	0.928112i	0.999122	+	0.0418981i	$0.0133405\pi$
$739$	395.990	+	685.875i	0.535846	+	0.928112i	−0.463276	+	0.886214i	$0.653326\pi$
$740$		0			0
$741$	−532.118	−	426.588i	−0.718108	−	0.575692i
$742$		0			0
$743$	1081.21	−	624.235i	1.45519	−	0.840154i	0.456421	−	0.889764i	$-0.349131\pi$
$743$	1081.21	−	624.235i	1.45519	−	0.840154i	0.998769	+	0.0496094i	$0.0157976\pi$
$744$		0			0
$745$	584.651	−	1012.65i	0.784767	−	1.35926i
$746$		0			0
$747$	−52.9582	+	91.7262i	−0.0708945	+	0.122793i
$748$		0			0
$749$			40.1037i			0.0535430i
$750$		0			0
$751$	−157.512	−	90.9398i	−0.209737	−	0.121092i	0.391452	−	0.920198i	$-0.371973\pi$
$751$	−157.512	−	90.9398i	−0.209737	−	0.121092i	−0.601189	+	0.799107i	$0.705306\pi$
$752$		0			0
$753$			229.193i			0.304373i
$754$		0			0
$755$	1568.22	−	905.410i	2.07711	−	1.19922i
$756$		0			0
$757$	−440.562	−	763.076i	−0.581984	−	1.00803i	−0.995244	−	0.0974132i	$-0.968943\pi$
$757$	−440.562	−	763.076i	−0.581984	−	1.00803i	0.413260	−	0.910613i	$-0.364390\pi$
$758$		0			0
$759$			5.58629i			0.00736007i
$760$		0			0
$761$	961.043			1.26287			0.631434	−	0.775429i	$-0.282466\pi$
$761$	961.043			1.26287			0.631434	+	0.775429i	$0.282466\pi$
$762$		0			0
$763$	120.121	−	69.3521i	0.157433	−	0.0908939i
$764$		0			0
$765$	−432.912	−	749.826i	−0.565898	−	0.980164i
$766$		0			0
$767$	1441.02			1.87878
$768$		0			0
$769$	−32.1730	+	55.7253i	−0.0418375	+	0.0724646i	−0.886186	−	0.463330i	$-0.846654\pi$
$769$	−32.1730	+	55.7253i	−0.0418375	+	0.0724646i	0.844348	+	0.535795i	$0.179988\pi$
$770$		0			0
$771$	−76.2996			−0.0989619
$772$		0			0
$773$	1134.34	+	654.910i	1.46745	+	0.847231i	0.999336	−	0.0364384i	$-0.0116013\pi$
$773$	1134.34	+	654.910i	1.46745	+	0.847231i	0.468111	+	0.883669i	$0.344935\pi$
$774$		0			0
$775$	2194.67	+	1267.10i	2.83184	+	1.63496i
$776$		0			0
$777$	3.49361	+	6.05111i	0.00449628	+	0.00778778i
$778$		0			0
$779$	−855.217	−	131.148i	−1.09784	−	0.168354i
$780$		0			0
$781$	145.720	−	84.1317i	0.186582	−	0.107723i
$782$		0			0
$783$	10.6849	−	18.5068i	0.0136461	−	0.0236358i
$784$		0			0
$785$	−811.375	+	1405.34i	−1.03360	+	1.79024i
$786$		0			0
$787$		−	919.142i		−	1.16791i	−0.811788	−	0.583953i	$-0.801505\pi$
$787$		−	919.142i		−	1.16791i	0.811788	−	0.583953i	$-0.198495\pi$
$788$		0			0
$789$	−5.38869	−	3.11116i	−0.00682978	−	0.00394317i
$790$		0			0
$791$		−	175.399i		−	0.221744i
$792$		0			0
$793$	633.874	−	365.967i	0.799337	−	0.461497i
$794$		0			0
$795$	−193.189	−	334.614i	−0.243006	−	0.420898i
$796$		0			0
$797$		−	844.287i		−	1.05933i	−0.848207	−	0.529666i	$-0.822317\pi$
$797$		−	844.287i		−	1.05933i	0.848207	−	0.529666i	$-0.177683\pi$
$798$		0			0
$799$	−1968.39			−2.46356
$800$		0			0
$801$	56.5294	−	32.6373i	0.0705735	−	0.0407456i
$802$		0			0
$803$	−52.5514	−	91.0217i	−0.0654438	−	0.113352i
$804$		0			0
$805$	−12.8019			−0.0159029
$806$		0			0
$807$	−274.602	+	475.625i	−0.340275	+	0.589374i
$808$		0			0
$809$	24.6535			0.0304741			0.0152371	−	0.999884i	$-0.495150\pi$
$809$	24.6535			0.0304741			0.0152371	+	0.999884i	$0.495150\pi$
$810$		0			0
$811$	525.432	+	303.358i	0.647882	+	0.374055i	0.787644	−	0.616130i	$-0.211301\pi$
$811$	525.432	+	303.358i	0.647882	+	0.374055i	−0.139762	+	0.990185i	$0.544634\pi$
$812$		0			0
$813$	−121.031	−	69.8772i	−0.148869	−	0.0859498i
$814$		0			0
$815$	1119.87	+	1939.68i	1.37408	+	2.37998i
$816$		0			0
$817$	162.548	−	1059.97i	0.198957	−	1.29740i
$818$		0			0
$819$	−73.4030	+	42.3792i	−0.0896251	+	0.0517451i
$820$		0			0
$821$	210.762	−	365.051i	0.256714	−	0.444641i	−0.708646	−	0.705564i	$-0.750694\pi$
$821$	210.762	−	365.051i	0.256714	−	0.444641i	0.965360	+	0.260923i	$0.0840269\pi$
$822$		0			0
$823$	486.568	−	842.761i	0.591213	−	1.02401i	−0.402857	−	0.915263i	$-0.631983\pi$
$823$	486.568	−	842.761i	0.591213	−	1.02401i	0.994069	−	0.108747i	$-0.0346840\pi$
$824$		0			0
$825$			333.701i			0.404486i
$826$		0			0
$827$	599.496	+	346.119i	0.724904	+	0.418524i	0.816555	−	0.577268i	$-0.195881\pi$
$827$	599.496	+	346.119i	0.724904	+	0.418524i	−0.0916509	+	0.995791i	$0.529214\pi$
$828$		0			0
$829$			752.230i			0.907394i	0.891156	+	0.453697i	$0.149895\pi$
$829$			752.230i			0.907394i	−0.891156	+	0.453697i	$0.850105\pi$
$830$		0			0
$831$	656.558	−	379.064i	0.790082	−	0.456154i
$832$		0			0
$833$	735.174	+	1273.36i	0.882561	+	1.52864i
$834$		0			0
$835$		−	2508.01i		−	3.00360i
$836$		0			0
$837$	217.218			0.259519
$838$		0			0
$839$	−521.533	+	301.107i	−0.621613	+	0.358888i	−0.777497	−	0.628887i	$-0.783511\pi$
$839$	−521.533	+	301.107i	−0.621613	+	0.358888i	0.155884	+	0.987775i	$0.450177\pi$
$840$		0			0
$841$	−412.043	−	713.680i	−0.489944	−	0.848608i
$842$		0			0
$843$	462.844			0.549043
$844$		0			0
$845$	−1205.14	+	2087.36i	−1.42620	+	2.47024i
$846$		0			0
$847$	−151.189			−0.178499
$848$		0			0
$849$	−797.959	−	460.702i	−0.939881	−	0.542641i
$850$		0			0
$851$	2.60061	+	1.50146i	0.00305595	+	0.00176435i
$852$		0			0
$853$	744.725	+	1289.90i	0.873065	+	1.51219i	0.858809	+	0.512295i	$0.171205\pi$
$853$	744.725	+	1289.90i	0.873065	+	1.51219i	0.0142561	+	0.999898i	$0.495462\pi$
$854$		0			0
$855$	−411.518	−	329.905i	−0.481307	−	0.385854i
$856$		0			0
$857$	−310.639	+	179.347i	−0.362472	+	0.209273i	−0.670165	−	0.742212i	$-0.733777\pi$
$857$	−310.639	+	179.347i	−0.362472	+	0.209273i	0.307693	+	0.951486i	$0.400443\pi$
$858$		0			0
$859$	−275.224	+	476.702i	−0.320400	+	0.554950i	−0.980571	−	0.196166i	$-0.937151\pi$
$859$	−275.224	+	476.702i	−0.320400	+	0.554950i	0.660170	+	0.751116i	$0.270484\pi$
$860$		0			0
$861$	−53.7639	+	93.1219i	−0.0624436	+	0.108155i
$862$		0			0
$863$		−	64.7931i		−	0.0750789i	−0.999295	−	0.0375395i	$-0.988048\pi$
$863$		−	64.7931i		−	0.0750789i	0.999295	−	0.0375395i	$-0.0119520\pi$
$864$		0			0
$865$	1300.52	+	750.855i	1.50349	+	0.868041i
$866$		0			0
$867$		−	1184.42i		−	1.36611i
$868$		0			0
$869$	54.0606	−	31.2119i	0.0622102	−	0.0359171i
$870$		0			0
$871$	636.190	+	1101.91i	0.730413	+	1.26511i
$872$		0			0
$873$			90.6680i			0.103858i
$874$		0			0
$875$	−449.358			−0.513553
$876$		0			0
$877$	300.360	−	173.413i	0.342486	−	0.197734i	−0.318885	−	0.947793i	$-0.603308\pi$
$877$	300.360	−	173.413i	0.342486	−	0.197734i	0.661371	+	0.750059i	$0.269975\pi$
$878$		0			0
$879$	−97.3343	−	168.588i	−0.110733	−	0.191795i
$880$		0			0
$881$	578.732			0.656904			0.328452	−	0.944521i	$-0.393473\pi$
$881$	578.732			0.656904			0.328452	+	0.944521i	$0.393473\pi$
$882$		0			0
$883$	−707.145	+	1224.81i	−0.800843	+	1.38710i	0.118218	+	0.992988i	$0.462282\pi$
$883$	−707.145	+	1224.81i	−0.800843	+	1.38710i	−0.919062	+	0.394114i	$0.871052\pi$
$884$		0			0
$885$	1114.43			1.25924
$886$		0			0
$887$	−732.655	−	422.998i	−0.825992	−	0.476886i	0.0264867	−	0.999649i	$-0.491568\pi$
$887$	−732.655	−	422.998i	−0.825992	−	0.476886i	−0.852478	+	0.522763i	$0.824901\pi$
$888$		0			0
$889$	79.8160	+	46.0818i	0.0897818	+	0.0518356i
$890$		0			0
$891$	14.3016	+	24.7710i	0.0160511	+	0.0278014i
$892$		0			0
$893$	−1117.31	+	435.206i	−1.25119	+	0.487353i
$894$		0			0
$895$	−2531.29	+	1461.44i	−2.82826	+	1.63289i
$896$		0			0
$897$	−18.2135	+	31.5468i	−0.0203049	+	0.0351692i
$898$		0			0
$899$	−85.9613	+	148.889i	−0.0956188	+	0.165617i
$900$		0			0
$901$		−	751.932i		−	0.834553i
$902$		0			0
$903$	−115.417	−	66.6362i	−0.127815	−	0.0737942i
$904$		0			0
$905$		−	1879.72i		−	2.07704i
$906$		0			0
$907$	−529.221	+	305.546i	−0.583485	+	0.336875i	−0.762517	−	0.646968i	$-0.776037\pi$
$907$	−529.221	+	305.546i	−0.583485	+	0.336875i	0.179032	+	0.983843i	$0.442703\pi$
$908$		0			0
$909$	88.8764	+	153.938i	0.0977738	+	0.169349i
$910$		0			0
$911$			437.771i			0.480539i	0.970706	+	0.240270i	$0.0772359\pi$
$911$			437.771i			0.480539i	−0.970706	+	0.240270i	$0.922764\pi$
$912$		0			0
$913$	112.205			0.122897
$914$		0			0
$915$	490.211	−	283.024i	0.535750	−	0.309315i
$916$		0			0
$917$	−124.004	−	214.782i	−0.135228	−	0.234222i
$918$		0			0
$919$	−919.121			−1.00013			−0.500066	−	0.865987i	$-0.666691\pi$
$919$	−919.121			−1.00013			−0.500066	+	0.865987i	$0.666691\pi$
$920$		0			0
$921$	220.594	−	382.079i	0.239515	−	0.414853i
$922$		0			0
$923$	1097.21			1.18874
$924$		0			0
$925$	155.350	+	89.6912i	0.167946	+	0.0969634i
$926$		0			0
$927$	6.51722	+	3.76272i	0.00703044	+	0.00405903i
$928$		0			0
$929$	145.895	+	252.697i	0.157045	+	0.272010i	0.933802	−	0.357791i	$-0.116470\pi$
$929$	145.895	+	252.697i	0.157045	+	0.272010i	−0.776757	+	0.629801i	$0.783137\pi$
$930$		0			0
$931$	698.841	+	560.247i	0.750635	+	0.601769i
$932$		0			0
$933$	104.884	−	60.5548i	0.112416	−	0.0649034i
$934$		0			0
$935$	−458.616	+	794.347i	−0.490499	+	0.849569i
$936$		0			0
$937$	27.8410	−	48.2219i	0.0297129	−	0.0514642i	−0.850787	−	0.525511i	$-0.823874\pi$
$937$	27.8410	−	48.2219i	0.0297129	−	0.0514642i	0.880499	+	0.474047i	$0.157207\pi$
$938$		0			0
$939$			503.287i			0.535982i
$940$		0			0
$941$	−797.330	−	460.339i	−0.847323	−	0.489202i	0.0124240	−	0.999923i	$-0.496045\pi$
$941$	−797.330	−	460.339i	−0.847323	−	0.489202i	−0.859747	+	0.510721i	$0.829379\pi$
$942$		0			0
$943$			46.2128i			0.0490061i
$944$		0			0
$945$	−56.7667	+	32.7743i	−0.0600706	+	0.0346818i
$946$		0			0
$947$	551.083	+	954.504i	0.581925	+	1.00792i	0.995251	+	0.0973409i	$0.0310337\pi$
$947$	551.083	+	954.504i	0.581925	+	1.00792i	−0.413326	+	0.910583i	$0.635633\pi$
$948$		0			0
$949$		−	685.354i		−	0.722185i
$950$		0			0
$951$	609.718			0.641134
$952$		0			0
$953$	−323.496	+	186.770i	−0.339450	+	0.195981i	−0.660029	−	0.751240i	$-0.729456\pi$
$953$	−323.496	+	186.770i	−0.339450	+	0.195981i	0.320579	+	0.947222i	$0.396123\pi$
$954$		0			0
$955$	−1548.13	−	2681.43i	−1.62108	−	2.80779i
$956$		0			0
$957$	−22.6387			−0.0236559
$958$		0			0
$959$	−105.901	+	183.427i	−0.110429	+	0.191269i
$960$		0			0
$961$	−786.537			−0.818457
$962$		0			0
$963$	76.4270	+	44.1251i	0.0793634	+	0.0458205i
$964$		0			0
$965$	1413.84	+	816.281i	1.46512	+	0.845887i
$966$		0			0
$967$	224.199	+	388.325i	0.231850	+	0.401577i	0.958353	−	0.285587i	$-0.0921887\pi$
$967$	224.199	+	388.325i	0.231850	+	0.401577i	−0.726502	+	0.687164i	$0.758855\pi$
$968$		0			0
$969$	−372.546	−	956.440i	−0.384465	−	0.987039i
$970$		0			0
$971$	−139.523	+	80.5534i	−0.143690	+	0.0829593i	−0.570121	−	0.821561i	$-0.693104\pi$
$971$	−139.523	+	80.5534i	−0.143690	+	0.0829593i	0.426432	+	0.904520i	$0.359770\pi$
$972$		0			0
$973$	−54.0996	+	93.7033i	−0.0556008	+	0.0963035i
$974$		0			0
$975$	−1088.00	+	1884.47i	−1.11590	+	1.93279i
$976$		0			0
$977$			542.963i			0.555745i	0.960618	+	0.277872i	$0.0896292\pi$
$977$			542.963i			0.555745i	−0.960618	+	0.277872i	$0.910371\pi$
$978$		0			0
$979$	−59.8858	−	34.5751i	−0.0611704	−	0.0353167i
$980$		0			0
$981$		−	305.225i		−	0.311137i
$982$		0			0
$983$	163.495	−	94.3937i	0.166322	−	0.0960262i	−0.414528	−	0.910036i	$-0.636053\pi$
$983$	163.495	−	94.3937i	0.166322	−	0.0960262i	0.580850	+	0.814010i	$0.302720\pi$
$984$		0			0
$985$	−22.3489	−	38.7094i	−0.0226892	−	0.0392989i
$986$		0			0
$987$			149.020i			0.150982i
$988$		0			0
$989$	−57.2771			−0.0579142
$990$		0			0
$991$	−1281.93	+	740.125i	−1.29358	+	0.746846i	−0.979286	−	0.202481i	$-0.935100\pi$
$991$	−1281.93	+	740.125i	−1.29358	+	0.746846i	−0.314290	+	0.949327i	$0.601766\pi$
$992$		0			0
$993$	271.969	+	471.065i	0.273887	+	0.474386i
$994$		0			0
$995$	−873.927			−0.878319
$996$		0			0
$997$	−125.801	+	217.893i	−0.126179	+	0.218549i	−0.922193	−	0.386729i	$-0.873605\pi$
$997$	−125.801	+	217.893i	−0.126179	+	0.218549i	0.796014	+	0.605278i	$0.206938\pi$
$998$		0			0
$999$	15.3757			0.0153911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.g.145.4		8
4.3	odd	2		114.3.f.b.31.4	✓	8
12.11	even	2		342.3.m.b.145.1		8
19.8	odd	6	inner	912.3.be.g.673.4		8
76.27	even	6		114.3.f.b.103.4	yes	8
228.179	odd	6		342.3.m.b.217.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.3.f.b.31.4	✓	8	4.3	odd	2
114.3.f.b.103.4	yes	8	76.27	even	6
342.3.m.b.145.1		8	12.11	even	2
342.3.m.b.217.1		8	228.179	odd	6
912.3.be.g.145.4		8	1.1	even	1	trivial
912.3.be.g.673.4		8	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(4.62659 + 8.01349i) q^{5} +1.36330 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(4.62659 + 8.01349i) q^{5} +1.36330 q^{7} +(1.50000 - 2.59808i) q^{9} -3.17812 q^{11} +(-17.9474 - 10.3620i) q^{13} +(-13.8798 - 8.01349i) q^{15} +(-15.5951 - 27.0114i) q^{17} +(-14.8244 - 11.8844i) q^{19} +(-2.04494 + 1.18065i) q^{21} +(-0.507413 + 0.878866i) q^{23} +(-30.3107 + 52.4997i) q^{25} +5.19615i q^{27} +(-3.56164 - 2.05632i) q^{29} -41.8036i q^{31} +(4.76719 - 2.75234i) q^{33} +(6.30742 + 10.9248i) q^{35} -2.95906i q^{37} +35.8949 q^{39} +(39.4367 - 22.7688i) q^{41} +(28.2202 + 48.8787i) q^{43} +27.7596 q^{45} +(31.5546 - 54.6542i) q^{47} -47.1414 q^{49} +(46.7852 + 27.0114i) q^{51} +(20.8782 + 12.0540i) q^{53} +(-14.7039 - 25.4679i) q^{55} +(32.5287 + 4.98830i) q^{57} +(-60.2185 + 34.7672i) q^{59} +(-17.6592 + 30.5866i) q^{61} +(2.04494 - 3.54195i) q^{63} -191.762i q^{65} +(-53.1711 - 30.6984i) q^{67} -1.75773i q^{69} +(-45.8511 + 26.4721i) q^{71} +(16.5353 + 28.6401i) q^{73} -104.999i q^{75} -4.33272 q^{77} +(-17.0102 + 9.82086i) q^{79} +(-4.50000 - 7.79423i) q^{81} -35.3054 q^{83} +(144.304 - 249.942i) q^{85} +7.12329 q^{87} +(18.8431 + 10.8791i) q^{89} +(-24.4677 - 14.1264i) q^{91} +(36.2029 + 62.7053i) q^{93} +(26.6491 - 173.779i) q^{95} +(-26.1736 + 15.1113i) q^{97} +(-4.76719 + 8.25701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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