LMFDB - Embedded newform 912.3.be.j.145.5

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.5
Root			$-0.113972 + 0.197406i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(0.113972 + 0.197406i) q^{5} +2.53976 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(0.113972 + 0.197406i) q^{5} +2.53976 q^{7} +(1.50000 - 2.59808i) q^{9} -11.3468 q^{11} +(-8.88485 - 5.12967i) q^{13} +(0.341917 + 0.197406i) q^{15} +(8.13510 + 14.0904i) q^{17} +(-11.5684 - 15.0722i) q^{19} +(3.80963 - 2.19949i) q^{21} +(16.8349 - 29.1589i) q^{23} +(12.4740 - 21.6056i) q^{25} -5.19615i q^{27} +(-38.9436 - 22.4841i) q^{29} -46.5422i q^{31} +(-17.0202 + 9.82661i) q^{33} +(0.289462 + 0.501362i) q^{35} +72.5910i q^{37} -17.7697 q^{39} +(17.8447 - 10.3026i) q^{41} +(-28.2849 - 48.9909i) q^{43} +0.683834 q^{45} +(-10.5900 + 18.3424i) q^{47} -42.5496 q^{49} +(24.4053 + 14.0904i) q^{51} +(49.1444 + 28.3735i) q^{53} +(-1.29322 - 2.23992i) q^{55} +(-30.4055 - 12.5899i) q^{57} +(91.4280 - 52.7860i) q^{59} +(7.75850 - 13.4381i) q^{61} +(3.80963 - 6.59848i) q^{63} -2.33856i q^{65} +(-90.4495 - 52.2210i) q^{67} -58.3179i q^{69} +(16.0856 - 9.28705i) q^{71} +(17.3422 + 30.0375i) q^{73} -43.2113i q^{75} -28.8181 q^{77} +(53.8915 - 31.1143i) q^{79} +(-4.50000 - 7.79423i) q^{81} -112.649 q^{83} +(-1.85435 + 3.21183i) q^{85} -77.8872 q^{87} +(-64.7775 - 37.3993i) q^{89} +(-22.5653 - 13.0281i) q^{91} +(-40.3067 - 69.8133i) q^{93} +(1.65687 - 4.00148i) q^{95} +(-63.2948 + 36.5433i) q^{97} +(-17.0202 + 29.4798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * 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
$5$	0.113972	+	0.197406i	0.0227945	+	0.0394811i	0.877198	−	0.480130i	$-0.159410\pi$
$5$	0.113972	+	0.197406i	0.0227945	+	0.0394811i	−0.854403	+	0.519611i	$0.826077\pi$
$6$		0			0
$7$	2.53976			0.362822			0.181411	−	0.983407i	$-0.441934\pi$
$7$	2.53976			0.362822			0.181411	+	0.983407i	$0.441934\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−11.3468			−1.03153			−0.515763	−	0.856731i	$-0.672492\pi$
$11$	−11.3468			−1.03153			−0.515763	+	0.856731i	$0.672492\pi$
$12$		0			0
$13$	−8.88485	−	5.12967i	−0.683450	−	0.394590i	0.117704	−	0.993049i	$-0.462447\pi$
$13$	−8.88485	−	5.12967i	−0.683450	−	0.394590i	−0.801154	+	0.598459i	$0.795780\pi$
$14$		0			0
$15$	0.341917	+	0.197406i	0.0227945	+	0.0131604i
$16$		0			0
$17$	8.13510	+	14.0904i	0.478535	+	0.828847i	0.999697	−	0.0246104i	$-0.00783453\pi$
$17$	8.13510	+	14.0904i	0.478535	+	0.828847i	−0.521162	+	0.853458i	$0.674501\pi$
$18$		0			0
$19$	−11.5684	−	15.0722i	−0.608862	−	0.793276i
$19$	−11.5684	−	15.0722i	−0.608862	−	0.793276i
$20$		0			0
$21$	3.80963	−	2.19949i	0.181411	−	0.104738i
$22$		0			0
$23$	16.8349	−	29.1589i	0.731953	−	1.26778i	−0.224095	−	0.974567i	$-0.571942\pi$
$23$	16.8349	−	29.1589i	0.731953	−	1.26778i	0.956047	−	0.293212i	$-0.0947242\pi$
$24$		0			0
$25$	12.4740	−	21.6056i	0.498961	−	0.864226i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−38.9436	−	22.4841i	−1.34288	−	0.775314i	−0.355654	−	0.934618i	$-0.615742\pi$
$29$	−38.9436	−	22.4841i	−1.34288	−	0.775314i	−0.987230	+	0.159304i	$0.949075\pi$
$30$		0			0
$31$		−	46.5422i		−	1.50136i	−0.660665	−	0.750681i	$-0.729726\pi$
$31$		−	46.5422i		−	1.50136i	0.660665	−	0.750681i	$-0.270274\pi$
$32$		0			0
$33$	−17.0202	+	9.82661i	−0.515763	+	0.297776i
$34$		0			0
$35$	0.289462	+	0.501362i	0.00827033	+	0.0143246i
$36$		0			0
$37$			72.5910i			1.96192i	0.194215	+	0.980959i	$0.437784\pi$
$37$			72.5910i			1.96192i	−0.194215	+	0.980959i	$0.562216\pi$
$38$		0			0
$39$	−17.7697			−0.455633
$40$		0			0
$41$	17.8447	−	10.3026i	0.435237	−	0.251284i	−0.266338	−	0.963880i	$-0.585814\pi$
$41$	17.8447	−	10.3026i	0.435237	−	0.251284i	0.701575	+	0.712596i	$0.252481\pi$
$42$		0			0
$43$	−28.2849	−	48.9909i	−0.657789	−	1.13932i	−0.981187	−	0.193060i	$-0.938159\pi$
$43$	−28.2849	−	48.9909i	−0.657789	−	1.13932i	0.323398	−	0.946263i	$-0.395175\pi$
$44$		0			0
$45$	0.683834			0.0151963
$46$		0			0
$47$	−10.5900	+	18.3424i	−0.225319	+	0.390265i	−0.956415	−	0.292010i	$-0.905676\pi$
$47$	−10.5900	+	18.3424i	−0.225319	+	0.390265i	0.731096	+	0.682275i	$0.239009\pi$
$48$		0			0
$49$	−42.5496			−0.868360
$50$		0			0
$51$	24.4053	+	14.0904i	0.478535	+	0.276282i
$52$		0			0
$53$	49.1444	+	28.3735i	0.927253	+	0.535350i	0.885942	−	0.463797i	$-0.153513\pi$
$53$	49.1444	+	28.3735i	0.927253	+	0.535350i	0.0413110	+	0.999146i	$0.486847\pi$
$54$		0			0
$55$	−1.29322	−	2.23992i	−0.0235131	−	0.0407259i
$56$		0			0
$57$	−30.4055	−	12.5899i	−0.533430	−	0.220875i
$58$		0			0
$59$	91.4280	−	52.7860i	1.54963	−	0.894677i	0.551457	−	0.834203i	$-0.314072\pi$
$59$	91.4280	−	52.7860i	1.54963	−	0.894677i	0.998170	−	0.0604742i	$-0.0192613\pi$
$60$		0			0
$61$	7.75850	−	13.4381i	0.127189	−	0.220297i	−0.795398	−	0.606088i	$-0.792738\pi$
$61$	7.75850	−	13.4381i	0.127189	−	0.220297i	0.922586	+	0.385791i	$0.126071\pi$
$62$		0			0
$63$	3.80963	−	6.59848i	0.0604704	−	0.104738i
$64$		0			0
$65$		−	2.33856i		−	0.0359779i
$66$		0			0
$67$	−90.4495	−	52.2210i	−1.34999	−	0.779418i	−0.361744	−	0.932277i	$-0.617819\pi$
$67$	−90.4495	−	52.2210i	−1.34999	−	0.779418i	−0.988248	+	0.152859i	$0.951152\pi$
$68$		0			0
$69$		−	58.3179i		−	0.845186i
$70$		0			0
$71$	16.0856	−	9.28705i	0.226558	−	0.130803i	−0.382425	−	0.923987i	$-0.624911\pi$
$71$	16.0856	−	9.28705i	0.226558	−	0.130803i	0.608983	+	0.793183i	$0.291578\pi$
$72$		0			0
$73$	17.3422	+	30.0375i	0.237564	+	0.411473i	0.960015	−	0.279949i	$-0.0903177\pi$
$73$	17.3422	+	30.0375i	0.237564	+	0.411473i	−0.722451	+	0.691422i	$0.756984\pi$
$74$		0			0
$75$		−	43.2113i		−	0.576150i
$76$		0			0
$77$	−28.8181			−0.374261
$78$		0			0
$79$	53.8915	−	31.1143i	0.682171	−	0.393852i	−0.118501	−	0.992954i	$-0.537809\pi$
$79$	53.8915	−	31.1143i	0.682171	−	0.393852i	0.800673	+	0.599102i	$0.204476\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−112.649			−1.35722			−0.678608	−	0.734500i	$-0.737417\pi$
$83$	−112.649			−1.35722			−0.678608	+	0.734500i	$0.737417\pi$
$84$		0			0
$85$	−1.85435	+	3.21183i	−0.0218159	+	0.0377862i
$86$		0			0
$87$	−77.8872			−0.895256
$88$		0			0
$89$	−64.7775	−	37.3993i	−0.727837	−	0.420217i	0.0897935	−	0.995960i	$-0.471379\pi$
$89$	−64.7775	−	37.3993i	−0.727837	−	0.420217i	−0.817630	+	0.575744i	$0.804713\pi$
$90$		0			0
$91$	−22.5653	−	13.0281i	−0.247971	−	0.143166i
$92$		0			0
$93$	−40.3067	−	69.8133i	−0.433406	−	0.750681i
$94$		0			0
$95$	1.65687	−	4.00148i	0.0174408	−	0.0421209i
$96$		0			0
$97$	−63.2948	+	36.5433i	−0.652524	+	0.376735i	−0.789422	−	0.613850i	$-0.789620\pi$
$97$	−63.2948	+	36.5433i	−0.652524	+	0.376735i	0.136899	+	0.990585i	$0.456286\pi$
$98$		0			0
$99$	−17.0202	+	29.4798i	−0.171921	+	0.297776i
$100$		0			0
$101$	1.43834	−	2.49127i	0.0142410	−	0.0246661i	−0.858817	−	0.512282i	$-0.828800\pi$
$101$	1.43834	−	2.49127i	0.0142410	−	0.0246661i	0.873058	+	0.487616i	$0.162133\pi$
$102$		0			0
$103$		−	9.27523i		−	0.0900508i	−0.998986	−	0.0450254i	$-0.985663\pi$
$103$		−	9.27523i		−	0.0900508i	0.998986	−	0.0450254i	$-0.0143369\pi$
$104$		0			0
$105$	0.868385	+	0.501362i	0.00827033	+	0.00477488i
$106$		0			0
$107$			159.630i			1.49187i	0.666020	+	0.745934i	$0.267997\pi$
$107$			159.630i			1.49187i	−0.666020	+	0.745934i	$0.732003\pi$
$108$		0			0
$109$	159.958	−	92.3516i	1.46750	−	0.847263i	0.468164	−	0.883642i	$-0.344916\pi$
$109$	159.958	−	92.3516i	1.46750	−	0.847263i	0.999338	+	0.0363790i	$0.0115824\pi$
$110$		0			0
$111$	62.8656	+	108.886i	0.566357	+	0.980959i
$112$		0			0
$113$		−	212.319i		−	1.87893i	−0.342640	−	0.939467i	$-0.611321\pi$
$113$		−	212.319i		−	1.87893i	0.342640	−	0.939467i	$-0.388679\pi$
$114$		0			0
$115$	7.67485			0.0667379
$116$		0			0
$117$	−26.6546	+	15.3890i	−0.227817	+	0.131530i
$118$		0			0
$119$	20.6612	+	35.7862i	0.173623	+	0.300724i
$120$		0			0
$121$	7.74976			0.0640476
$122$		0			0
$123$	17.8447	−	30.9079i	0.145079	−	0.251284i
$124$		0			0
$125$	11.3854			0.0910831
$126$		0			0
$127$	−142.063	−	82.0201i	−1.11861	−	0.645827i	−0.177561	−	0.984110i	$-0.556821\pi$
$127$	−142.063	−	82.0201i	−1.11861	−	0.645827i	−0.941045	+	0.338283i	$0.890154\pi$
$128$		0			0
$129$	−84.8547	−	48.9909i	−0.657789	−	0.379774i
$130$		0			0
$131$	5.60178	+	9.70256i	0.0427617	+	0.0740654i	0.886614	−	0.462510i	$-0.153051\pi$
$131$	5.60178	+	9.70256i	0.0427617	+	0.0740654i	−0.843852	+	0.536575i	$0.819718\pi$
$132$		0			0
$133$	−29.3809	−	38.2798i	−0.220909	−	0.287818i
$134$		0			0
$135$	1.02575	−	0.592217i	0.00759815	−	0.00438679i
$136$		0			0
$137$	−6.01934	+	10.4258i	−0.0439368	+	0.0761007i	−0.887157	−	0.461467i	$-0.847323\pi$
$137$	−6.01934	+	10.4258i	−0.0439368	+	0.0761007i	0.843221	+	0.537568i	$0.180657\pi$
$138$		0			0
$139$	−37.6936	+	65.2873i	−0.271177	+	0.469693i	−0.969164	−	0.246418i	$-0.920746\pi$
$139$	−37.6936	+	65.2873i	−0.271177	+	0.469693i	0.697986	+	0.716111i	$0.254080\pi$
$140$		0			0
$141$			36.6849i			0.260176i
$142$		0			0
$143$	100.815	+	58.2053i	0.704997	+	0.407030i
$144$		0			0
$145$		−	10.2503i		−	0.0706914i
$146$		0			0
$147$	−63.8245	+	36.8491i	−0.434180	+	0.250674i
$148$		0			0
$149$	57.5075	+	99.6059i	0.385956	+	0.668496i	0.991901	−	0.127010i	$-0.0405382\pi$
$149$	57.5075	+	99.6059i	0.385956	+	0.668496i	−0.605945	+	0.795507i	$0.707205\pi$
$150$		0			0
$151$		−	40.7153i		−	0.269638i	−0.990870	−	0.134819i	$-0.956955\pi$
$151$		−	40.7153i		−	0.269638i	0.990870	−	0.134819i	$-0.0430452\pi$
$152$		0			0
$153$	48.8106			0.319024
$154$		0			0
$155$	9.18770	−	5.30452i	0.0592755	−	0.0342227i
$156$		0			0
$157$	70.8465	+	122.710i	0.451252	+	0.781591i	0.998464	−	0.0554027i	$-0.0176443\pi$
$157$	70.8465	+	122.710i	0.451252	+	0.781591i	−0.547212	+	0.836994i	$0.684311\pi$
$158$		0			0
$159$	98.2888			0.618168
$160$		0			0
$161$	42.7566	−	74.0565i	0.265569	−	0.459979i
$162$		0			0
$163$	−67.9562			−0.416909			−0.208455	−	0.978032i	$-0.566843\pi$
$163$	−67.9562			−0.416909			−0.208455	+	0.978032i	$0.566843\pi$
$164$		0			0
$165$	−3.87966	−	2.23992i	−0.0235131	−	0.0135753i
$166$		0			0
$167$	234.059	+	135.134i	1.40155	+	0.809187i	0.994552	−	0.104241i	$-0.0332412\pi$
$167$	234.059	+	135.134i	1.40155	+	0.809187i	0.407001	+	0.913428i	$0.366575\pi$
$168$		0			0
$169$	−31.8730	−	55.2056i	−0.188597	−	0.326660i
$170$		0			0
$171$	−56.5114	+	7.44716i	−0.330476	+	0.0435507i
$172$		0			0
$173$	54.9568	−	31.7293i	0.317669	−	0.183406i	−0.332684	−	0.943038i	$-0.607954\pi$
$173$	54.9568	−	31.7293i	0.317669	−	0.183406i	0.650353	+	0.759632i	$0.274621\pi$
$174$		0			0
$175$	31.6810	−	54.8730i	0.181034	−	0.313560i
$176$		0			0
$177$	91.4280	−	158.358i	0.516542	−	0.894677i
$178$		0			0
$179$			201.356i			1.12490i	0.826832	+	0.562448i	$0.190140\pi$
$179$			201.356i			1.12490i	−0.826832	+	0.562448i	$0.809860\pi$
$180$		0			0
$181$	−286.428	−	165.370i	−1.58248	−	0.913644i	−0.994497	−	0.104770i	$-0.966590\pi$
$181$	−286.428	−	165.370i	−1.58248	−	0.913644i	−0.587981	−	0.808874i	$-0.700077\pi$
$182$		0			0
$183$		−	26.8762i		−	0.146865i
$184$		0			0
$185$	−14.3299	+	8.27336i	−0.0774588	+	0.0447208i
$186$		0			0
$187$	−92.3073	−	159.881i	−0.493622	−	0.854978i
$188$		0			0
$189$		−	13.1970i		−	0.0698252i
$190$		0			0
$191$	40.5904			0.212515			0.106258	−	0.994339i	$-0.466113\pi$
$191$	40.5904			0.212515			0.106258	+	0.994339i	$0.466113\pi$
$192$		0			0
$193$	−200.963	+	116.026i	−1.04126	+	0.601170i	−0.920189	−	0.391474i	$-0.871965\pi$
$193$	−200.963	+	116.026i	−1.04126	+	0.601170i	−0.121068	+	0.992644i	$0.538632\pi$
$194$		0			0
$195$	−2.02525	−	3.50784i	−0.0103859	−	0.0179889i
$196$		0			0
$197$	110.600			0.561419			0.280710	−	0.959793i	$-0.409430\pi$
$197$	110.600			0.561419			0.280710	+	0.959793i	$0.409430\pi$
$198$		0			0
$199$	6.75910	−	11.7071i	0.0339653	−	0.0588297i	−0.848543	−	0.529126i	$-0.822520\pi$
$199$	6.75910	−	11.7071i	0.0339653	−	0.0588297i	0.882508	+	0.470297i	$0.155853\pi$
$200$		0			0
$201$	−180.899			−0.899995
$202$		0			0
$203$	−98.9073	−	57.1041i	−0.487228	−	0.281301i
$204$		0			0
$205$	4.06760	+	2.34843i	0.0198420	+	0.0114558i
$206$		0			0
$207$	−50.5047	−	87.4768i	−0.243984	−	0.422593i
$208$		0			0
$209$	131.264	+	171.022i	0.628058	+	0.818286i
$210$		0			0
$211$	−217.335	+	125.478i	−1.03002	+	0.594684i	−0.916991	−	0.398907i	$-0.869390\pi$
$211$	−217.335	+	125.478i	−1.03002	+	0.594684i	−0.113032	+	0.993591i	$0.536056\pi$
$212$		0			0
$213$	16.0856	−	27.8611i	0.0755194	−	0.130803i
$214$		0			0
$215$	6.44739	−	11.1672i	0.0299879	−	0.0519405i
$216$		0			0
$217$		−	118.206i		−	0.544727i
$218$		0			0
$219$	52.0265	+	30.0375i	0.237564	+	0.137158i
$220$		0			0
$221$		−	166.922i		−	0.755301i
$222$		0			0
$223$	188.055	−	108.574i	0.843297	−	0.486878i	−0.0150863	−	0.999886i	$-0.504802\pi$
$223$	188.055	−	108.574i	0.843297	−	0.486878i	0.858384	+	0.513008i	$0.171469\pi$
$224$		0			0
$225$	−37.4221	−	64.8169i	−0.166320	−	0.288075i
$226$		0			0
$227$		−	115.952i		−	0.510801i	−0.966835	−	0.255401i	$-0.917793\pi$
$227$		−	115.952i		−	0.510801i	0.966835	−	0.255401i	$-0.0822074\pi$
$228$		0			0
$229$	351.432			1.53464			0.767318	−	0.641267i	$-0.221591\pi$
$229$	351.432			1.53464			0.767318	+	0.641267i	$0.221591\pi$
$230$		0			0
$231$	−43.2271	+	24.9572i	−0.187130	+	0.108040i
$232$		0			0
$233$	74.3898	+	128.847i	0.319269	+	0.552991i	0.980336	−	0.197337i	$-0.0632292\pi$
$233$	74.3898	+	128.847i	0.319269	+	0.552991i	−0.661066	+	0.750327i	$0.729896\pi$
$234$		0			0
$235$	−4.82787			−0.0205441
$236$		0			0
$237$	53.8915	−	93.3429i	0.227390	−	0.393852i
$238$		0			0
$239$	369.603			1.54645			0.773227	−	0.634129i	$-0.218641\pi$
$239$	369.603			1.54645			0.773227	+	0.634129i	$0.218641\pi$
$240$		0			0
$241$	303.016	+	174.947i	1.25733	+	0.725920i	0.972555	−	0.232675i	$-0.0747478\pi$
$241$	303.016	+	174.947i	1.25733	+	0.725920i	0.284775	+	0.958594i	$0.408081\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−4.84948	−	8.39954i	−0.0197938	−	0.0342839i
$246$		0			0
$247$	25.4677	+	193.257i	0.103108	+	0.782416i
$248$		0			0
$249$	−168.973	+	97.5569i	−0.678608	+	0.391795i
$250$		0			0
$251$	131.262	−	227.352i	0.522955	−	0.905785i	−0.476688	−	0.879073i	$-0.658163\pi$
$251$	131.262	−	227.352i	0.522955	−	0.905785i	0.999643	−	0.0267127i	$-0.00850393\pi$
$252$		0			0
$253$	−191.022	+	330.860i	−0.755029	+	1.30775i
$254$		0			0
$255$			6.42366i			0.0251908i
$256$		0			0
$257$	317.548	+	183.336i	1.23559	+	0.713370i	0.968190	−	0.250214i	$-0.0805011\pi$
$257$	317.548	+	183.336i	1.23559	+	0.713370i	0.267403	+	0.963585i	$0.413834\pi$
$258$		0			0
$259$			184.363i			0.711827i
$260$		0			0
$261$	−116.831	+	67.4523i	−0.447628	+	0.258438i
$262$		0			0
$263$	225.395	+	390.395i	0.857015	+	1.48439i	0.874763	+	0.484551i	$0.161017\pi$
$263$	225.395	+	390.395i	0.857015	+	1.48439i	−0.0177483	+	0.999842i	$0.505650\pi$
$264$		0			0
$265$			12.9352i			0.0488120i
$266$		0			0
$267$	−129.555			−0.485225
$268$		0			0
$269$	−271.691	+	156.861i	−1.01000	+	0.583127i	−0.911193	−	0.411980i	$-0.864838\pi$
$269$	−271.691	+	156.861i	−1.01000	+	0.583127i	−0.0988118	+	0.995106i	$0.531504\pi$
$270$		0			0
$271$	−6.94062	−	12.0215i	−0.0256111	−	0.0443598i	0.852936	−	0.522016i	$-0.174820\pi$
$271$	−6.94062	−	12.0215i	−0.0256111	−	0.0443598i	−0.878547	+	0.477656i	$0.841486\pi$
$272$		0			0
$273$	−45.1307			−0.165314
$274$		0			0
$275$	−141.540	+	245.155i	−0.514691	+	0.891472i
$276$		0			0
$277$	−9.62542			−0.0347488			−0.0173744	−	0.999849i	$-0.505531\pi$
$277$	−9.62542			−0.0347488			−0.0173744	+	0.999849i	$0.505531\pi$
$278$		0			0
$279$	−120.920	−	69.8133i	−0.433406	−	0.250227i
$280$		0			0
$281$	285.205	+	164.663i	1.01497	+	0.585991i	0.912642	−	0.408761i	$-0.134039\pi$
$281$	285.205	+	164.663i	1.01497	+	0.585991i	0.102324	+	0.994751i	$0.467372\pi$
$282$		0			0
$283$	−147.441	−	255.376i	−0.520994	−	0.902388i	−0.999702	−	0.0244137i	$-0.992228\pi$
$283$	−147.441	−	255.376i	−0.520994	−	0.902388i	0.478708	−	0.877974i	$-0.341105\pi$
$284$		0			0
$285$	−0.980075	−	7.43712i	−0.00343886	−	0.0260952i
$286$		0			0
$287$	45.3212	−	26.1662i	0.157914	−	0.0911714i
$288$		0			0
$289$	12.1403	−	21.0276i	0.0420079	−	0.0727598i
$290$		0			0
$291$	−63.2948	+	109.630i	−0.217508	+	0.376735i
$292$		0			0
$293$			303.093i			1.03445i	0.855850	+	0.517224i	$0.173034\pi$
$293$			303.093i			1.03445i	−0.855850	+	0.517224i	$0.826966\pi$
$294$		0			0
$295$	20.8405	+	12.0323i	0.0706458	+	0.0407874i
$296$		0			0
$297$			58.9597i			0.198517i
$298$		0			0
$299$	−299.151	+	172.715i	−1.00051	+	0.577643i
$300$		0			0
$301$	−71.8368	−	124.425i	−0.238660	−	0.413372i
$302$		0			0
$303$		−	4.98255i		−	0.0164440i
$304$		0			0
$305$	3.53701			0.0115968
$306$		0			0
$307$	275.694	−	159.172i	0.898027	−	0.518476i	0.0214677	−	0.999770i	$-0.493166\pi$
$307$	275.694	−	159.172i	0.898027	−	0.518476i	0.876560	+	0.481293i	$0.159833\pi$
$308$		0			0
$309$	−8.03259	−	13.9128i	−0.0259954	−	0.0450254i
$310$		0			0
$311$	−46.7663			−0.150374			−0.0751870	−	0.997169i	$-0.523955\pi$
$311$	−46.7663			−0.150374			−0.0751870	+	0.997169i	$0.523955\pi$
$312$		0			0
$313$	49.6649	−	86.0221i	0.158674	−	0.274831i	−0.775717	−	0.631081i	$-0.782612\pi$
$313$	49.6649	−	86.0221i	0.158674	−	0.274831i	0.934391	+	0.356250i	$0.115945\pi$
$314$		0			0
$315$	1.73677			0.00551355
$316$		0			0
$317$	164.225	+	94.8151i	0.518059	+	0.299101i	0.736140	−	0.676829i	$-0.236647\pi$
$317$	164.225	+	94.8151i	0.518059	+	0.299101i	−0.218081	+	0.975931i	$0.569980\pi$
$318$		0			0
$319$	441.885	+	255.123i	1.38522	+	0.799757i
$320$		0			0
$321$	138.244	+	239.445i	0.430665	+	0.745934i
$322$		0			0
$323$	118.264	−	285.617i	0.366143	−	0.884264i
$324$		0			0
$325$	−221.660	+	127.975i	−0.682030	+	0.393770i
$326$		0			0
$327$	159.958	−	277.055i	0.489167	−	0.847263i
$328$		0			0
$329$	−26.8960	+	46.5853i	−0.0817509	+	0.141597i
$330$		0			0
$331$		−	310.272i		−	0.937376i	−0.883364	−	0.468688i	$-0.844727\pi$
$331$		−	310.272i		−	0.937376i	0.883364	−	0.468688i	$-0.155273\pi$
$332$		0			0
$333$	188.597	+	108.886i	0.566357	+	0.326986i
$334$		0			0
$335$		−	23.8070i		−	0.0710656i
$336$		0			0
$337$	−169.924	+	98.1059i	−0.504227	+	0.291115i	−0.730457	−	0.682958i	$-0.760693\pi$
$337$	−169.924	+	98.1059i	−0.504227	+	0.291115i	0.226231	+	0.974074i	$0.427360\pi$
$338$		0			0
$339$	−183.874	−	318.479i	−0.542401	−	0.939467i
$340$		0			0
$341$			528.105i			1.54869i
$342$		0			0
$343$	−232.514			−0.677882
$344$		0			0
$345$	11.5123	−	6.64662i	0.0333689	−	0.0192656i
$346$		0			0
$347$	177.109	+	306.761i	0.510399	+	0.884037i	0.999927	+	0.0120499i	$0.00383571\pi$
$347$	177.109	+	306.761i	0.510399	+	0.884037i	−0.489528	+	0.871987i	$0.662831\pi$
$348$		0			0
$349$	204.053			0.584678			0.292339	−	0.956315i	$-0.405566\pi$
$349$	204.053			0.584678			0.292339	+	0.956315i	$0.405566\pi$
$350$		0			0
$351$	−26.6546	+	46.1670i	−0.0759389	+	0.131530i
$352$		0			0
$353$	15.7739			0.0446852			0.0223426	−	0.999750i	$-0.492888\pi$
$353$	15.7739			0.0446852			0.0223426	+	0.999750i	$0.492888\pi$
$354$		0			0
$355$	3.66663	+	2.11693i	0.0103285	+	0.00596319i
$356$		0			0
$357$	61.9835	+	35.7862i	0.173623	+	0.100241i
$358$		0			0
$359$	2.54805	+	4.41335i	0.00709763	+	0.0122934i	0.869552	−	0.493841i	$-0.164407\pi$
$359$	2.54805	+	4.41335i	0.00709763	+	0.0122934i	−0.862455	+	0.506134i	$0.831074\pi$
$360$		0			0
$361$	−93.3452	+	348.723i	−0.258574	+	0.965991i
$362$		0			0
$363$	11.6246	−	6.71149i	0.0320238	−	0.0184890i
$364$		0			0
$365$	−3.95306	+	6.84689i	−0.0108303	+	0.0187586i
$366$		0			0
$367$	−298.547	+	517.099i	−0.813480	+	1.40899i	0.0969349	+	0.995291i	$0.469096\pi$
$367$	−298.547	+	517.099i	−0.813480	+	1.40899i	−0.910414	+	0.413697i	$0.864237\pi$
$368$		0			0
$369$		−	61.8159i		−	0.167523i
$370$		0			0
$371$	124.815	+	72.0618i	0.336428	+	0.194237i
$372$		0			0
$373$		−	338.589i		−	0.907746i	−0.891066	−	0.453873i	$-0.850042\pi$
$373$		−	338.589i		−	0.907746i	0.891066	−	0.453873i	$-0.149958\pi$
$374$		0			0
$375$	17.0781	−	9.86003i	0.0455415	−	0.0262934i
$376$		0			0
$377$	230.672	+	399.536i	0.611862	+	1.05978i
$378$		0			0
$379$			484.312i			1.27787i	0.769261	+	0.638935i	$0.220625\pi$
$379$			484.312i			1.27787i	−0.769261	+	0.638935i	$0.779375\pi$
$380$		0			0
$381$	−284.126			−0.745737
$382$		0			0
$383$	480.546	−	277.443i	1.25469	−	0.724395i	0.282652	−	0.959223i	$-0.408786\pi$
$383$	480.546	−	277.443i	1.25469	−	0.724395i	0.972037	+	0.234827i	$0.0754525\pi$
$384$		0			0
$385$	−3.28446	−	5.68885i	−0.00853107	−	0.0147762i
$386$		0			0
$387$	−169.709			−0.438526
$388$		0			0
$389$	26.5072	−	45.9118i	0.0681419	−	0.118025i	−0.829941	−	0.557850i	$-0.811626\pi$
$389$	26.5072	−	45.9118i	0.0681419	−	0.118025i	0.898083	+	0.439825i	$0.144960\pi$
$390$		0			0
$391$	547.815			1.40106
$392$		0			0
$393$	16.8053	+	9.70256i	0.0427617	+	0.0246885i
$394$		0			0
$395$	12.2843	+	7.09233i	0.0310994	+	0.0179553i
$396$		0			0
$397$	9.00574	+	15.5984i	0.0226845	+	0.0392907i	0.877145	−	0.480226i	$-0.159445\pi$
$397$	9.00574	+	15.5984i	0.0226845	+	0.0392907i	−0.854460	+	0.519517i	$0.826112\pi$
$398$		0			0
$399$	−77.2226	−	31.9752i	−0.193540	−	0.0801382i
$400$		0			0
$401$	−82.3855	+	47.5653i	−0.205450	+	0.118617i	−0.599195	−	0.800603i	$-0.704513\pi$
$401$	−82.3855	+	47.5653i	−0.205450	+	0.118617i	0.393745	+	0.919220i	$0.371179\pi$
$402$		0			0
$403$	−238.746	+	413.521i	−0.592422	+	1.02611i
$404$		0			0
$405$	1.02575	−	1.77665i	0.00253272	−	0.00438679i
$406$		0			0
$407$		−	823.675i		−	2.02377i
$408$		0			0
$409$	−364.357	−	210.362i	−0.890849	−	0.514332i	−0.0166292	−	0.999862i	$-0.505293\pi$
$409$	−364.357	−	210.362i	−0.890849	−	0.514332i	−0.874220	+	0.485530i	$0.838627\pi$
$410$		0			0
$411$			20.8516i			0.0507338i
$412$		0			0
$413$	232.205	−	134.063i	0.562239	−	0.324609i
$414$		0			0
$415$	−12.8389	−	22.2376i	−0.0309370	−	0.0535845i
$416$		0			0
$417$			130.575i			0.313128i
$418$		0			0
$419$	−213.786			−0.510229			−0.255115	−	0.966911i	$-0.582113\pi$
$419$	−213.786			−0.510229			−0.255115	+	0.966911i	$0.582113\pi$
$420$		0			0
$421$	−10.2415	+	5.91291i	−0.0243265	+	0.0140449i	−0.512114	−	0.858918i	$-0.671137\pi$
$421$	−10.2415	+	5.91291i	−0.0243265	+	0.0140449i	0.487787	+	0.872962i	$0.337804\pi$
$422$		0			0
$423$	31.7700	+	55.0273i	0.0751065	+	0.130088i
$424$		0			0
$425$	405.910			0.955081
$426$		0			0
$427$	19.7047	−	34.1295i	0.0461468	−	0.0799286i
$428$		0			0
$429$	201.629			0.469998
$430$		0			0
$431$	−80.8061	−	46.6534i	−0.187485	−	0.108245i	0.403320	−	0.915059i	$-0.367856\pi$
$431$	−80.8061	−	46.6534i	−0.187485	−	0.108245i	−0.590805	+	0.806815i	$0.701190\pi$
$432$		0			0
$433$	56.2884	+	32.4981i	0.129996	+	0.0750533i	0.563588	−	0.826056i	$-0.309421\pi$
$433$	56.2884	+	32.4981i	0.129996	+	0.0750533i	−0.433592	+	0.901109i	$0.642754\pi$
$434$		0			0
$435$	−8.87698	−	15.3754i	−0.0204069	−	0.0353457i
$436$		0			0
$437$	−634.243	+	83.5816i	−1.45136	+	0.191262i
$438$		0			0
$439$	508.293	−	293.463i	1.15784	−	0.668481i	0.207056	−	0.978329i	$-0.433612\pi$
$439$	508.293	−	293.463i	1.15784	−	0.668481i	0.950786	+	0.309848i	$0.100278\pi$
$440$		0			0
$441$	−63.8245	+	110.547i	−0.144727	+	0.250674i
$442$		0			0
$443$	−134.256	+	232.539i	−0.303061	+	0.524918i	−0.976828	−	0.214027i	$-0.931342\pi$
$443$	−134.256	+	232.539i	−0.303061	+	0.524918i	0.673766	+	0.738944i	$0.264675\pi$
$444$		0			0
$445$		−	17.0499i		−	0.0383144i
$446$		0			0
$447$	172.523	+	99.6059i	0.385956	+	0.222832i
$448$		0			0
$449$		−	833.742i		−	1.85689i	−0.371473	−	0.928444i	$-0.621147\pi$
$449$		−	833.742i		−	1.85689i	0.371473	−	0.928444i	$-0.378853\pi$
$450$		0			0
$451$	−202.480	+	116.902i	−0.448958	+	0.259206i
$452$		0			0
$453$	−35.2605	−	61.0729i	−0.0778377	−	0.134819i
$454$		0			0
$455$		−	5.93937i		−	0.0130536i
$456$		0			0
$457$	−578.406			−1.26566			−0.632829	−	0.774292i	$-0.718106\pi$
$457$	−578.406			−1.26566			−0.632829	+	0.774292i	$0.718106\pi$
$458$		0			0
$459$	73.2159	−	42.2712i	0.159512	−	0.0920942i
$460$		0			0
$461$	245.193	+	424.686i	0.531871	+	0.921228i	0.999308	+	0.0372015i	$0.0118443\pi$
$461$	245.193	+	424.686i	0.531871	+	0.921228i	−0.467436	+	0.884027i	$0.654822\pi$
$462$		0			0
$463$	57.8388			0.124922			0.0624609	−	0.998047i	$-0.480105\pi$
$463$	57.8388			0.124922			0.0624609	+	0.998047i	$0.480105\pi$
$464$		0			0
$465$	9.18770	−	15.9136i	0.0197585	−	0.0342227i
$466$		0			0
$467$	−698.074			−1.49481			−0.747403	−	0.664371i	$-0.768699\pi$
$467$	−698.074			−1.49481			−0.747403	+	0.664371i	$0.768699\pi$
$468$		0			0
$469$	−229.719	−	132.629i	−0.489807	−	0.282790i
$470$		0			0
$471$	212.540	+	122.710i	0.451252	+	0.260530i
$472$		0			0
$473$	320.943	+	555.890i	0.678527	+	1.17524i
$474$		0			0
$475$	−469.950	+	61.9307i	−0.989368	+	0.130380i
$476$		0			0
$477$	147.433	−	85.1206i	0.309084	−	0.178450i
$478$		0			0
$479$	−264.997	+	458.988i	−0.553229	+	0.958221i	0.444809	+	0.895625i	$0.353271\pi$
$479$	−264.997	+	458.988i	−0.553229	+	0.958221i	−0.998039	+	0.0625963i	$0.980062\pi$
$480$		0			0
$481$	372.368	−	644.960i	0.774153	−	1.34087i
$482$		0			0
$483$		−	148.113i		−	0.306652i
$484$		0			0
$485$	−14.4277	−	8.32984i	−0.0297478	−	0.0171749i
$486$		0			0
$487$			342.480i			0.703245i	0.936142	+	0.351623i	$0.114370\pi$
$487$			342.480i			0.703245i	−0.936142	+	0.351623i	$0.885630\pi$
$488$		0			0
$489$	−101.934	+	58.8518i	−0.208455	+	0.120351i
$490$		0			0
$491$	46.1248	+	79.8905i	0.0939405	+	0.162710i	0.909166	−	0.416434i	$-0.136720\pi$
$491$	46.1248	+	79.8905i	0.0939405	+	0.162710i	−0.815225	+	0.579144i	$0.803387\pi$
$492$		0			0
$493$		−	731.642i		−	1.48406i
$494$		0			0
$495$	−7.75932			−0.0156754
$496$		0			0
$497$	40.8536	−	23.5868i	0.0822004	−	0.0474584i
$498$		0			0
$499$	−381.668	−	661.068i	−0.764866	−	1.32479i	−0.940318	−	0.340298i	$-0.889472\pi$
$499$	−381.668	−	661.068i	−0.764866	−	1.32479i	0.175452	−	0.984488i	$-0.443861\pi$
$500$		0			0
$501$	468.119			0.934369
$502$		0			0
$503$	−273.702	+	474.066i	−0.544139	+	0.942477i	0.454521	+	0.890736i	$0.349810\pi$
$503$	−273.702	+	474.066i	−0.544139	+	0.942477i	−0.998661	+	0.0517409i	$0.983523\pi$
$504$		0			0
$505$	0.655722			0.00129846
$506$		0			0
$507$	−95.6189	−	55.2056i	−0.188597	−	0.108887i
$508$		0			0
$509$	−845.154	−	487.950i	−1.66042	−	0.958645i	−0.972514	−	0.232846i	$-0.925196\pi$
$509$	−845.154	−	487.950i	−1.66042	−	0.958645i	−0.687908	−	0.725798i	$-0.741471\pi$
$510$		0			0
$511$	44.0449	+	76.2880i	0.0861935	+	0.149292i
$512$		0			0
$513$	−78.3177	+	60.1111i	−0.152666	+	0.117176i
$514$		0			0
$515$	1.83098	−	1.05712i	0.00355531	−	0.00205266i
$516$		0			0
$517$	120.163	−	208.128i	0.232423	−	0.402569i
$518$		0			0
$519$	54.9568	−	95.1879i	0.105890	−	0.183406i
$520$		0			0
$521$		−	840.053i		−	1.61238i	−0.591653	−	0.806192i	$-0.701525\pi$
$521$		−	840.053i		−	1.61238i	0.591653	−	0.806192i	$-0.298475\pi$
$522$		0			0
$523$	663.433	+	383.033i	1.26851	+	0.732377i	0.974707	−	0.223488i	$-0.0717443\pi$
$523$	663.433	+	383.033i	1.26851	+	0.732377i	0.293807	+	0.955865i	$0.405078\pi$
$524$		0			0
$525$		−	109.746i		−	0.209040i
$526$		0			0
$527$	655.799	−	378.626i	1.24440	−	0.718455i
$528$		0			0
$529$	−302.329	−	523.649i	−0.571510	−	0.989884i
$530$		0			0
$531$		−	316.716i		−	0.596452i
$532$		0			0
$533$	−211.397			−0.396617
$534$		0			0
$535$	−31.5118	+	18.1934i	−0.0589007	+	0.0340063i
$536$		0			0
$537$	174.380	+	302.035i	0.324730	+	0.562448i
$538$		0			0
$539$	482.802			0.895737
$540$		0			0
$541$	407.326	−	705.509i	0.752913	−	1.30408i	−0.193492	−	0.981102i	$-0.561981\pi$
$541$	407.326	−	705.509i	0.752913	−	1.30408i	0.946405	−	0.322982i	$-0.104685\pi$
$542$		0			0
$543$	−572.857			−1.05499
$544$		0			0
$545$	36.4615	+	21.0510i	0.0669018	+	0.0386258i
$546$		0			0
$547$	218.364	+	126.072i	0.399203	+	0.230480i	0.686140	−	0.727470i	$-0.259304\pi$
$547$	218.364	+	126.072i	0.399203	+	0.230480i	−0.286937	+	0.957949i	$0.592637\pi$
$548$		0			0
$549$	−23.2755	−	40.3143i	−0.0423962	−	0.0734323i
$550$		0			0
$551$	111.629	+	847.072i	0.202593	+	1.53734i
$552$		0			0
$553$	136.871	−	79.0227i	0.247507	−	0.142898i
$554$		0			0
$555$	−14.3299	+	24.8201i	−0.0258196	+	0.0447208i
$556$		0			0
$557$	513.710	−	889.772i	0.922281	−	1.59744i	0.126403	−	0.991979i	$-0.459657\pi$
$557$	513.710	−	889.772i	0.922281	−	1.59744i	0.795877	−	0.605458i	$-0.207010\pi$
$558$		0			0
$559$			580.369i			1.03823i
$560$		0			0
$561$	−276.922	−	159.881i	−0.493622	−	0.284993i
$562$		0			0
$563$		−	316.046i		−	0.561361i	−0.959801	−	0.280681i	$-0.909440\pi$
$563$		−	316.046i		−	0.561361i	0.959801	−	0.280681i	$-0.0905601\pi$
$564$		0			0
$565$	41.9131	−	24.1985i	0.0741824	−	0.0428293i
$566$		0			0
$567$	−11.4289	−	19.7954i	−0.0201568	−	0.0349126i
$568$		0			0
$569$		−	133.675i		−	0.234930i	−0.993077	−	0.117465i	$-0.962523\pi$
$569$		−	133.675i		−	0.234930i	0.993077	−	0.117465i	$-0.0374768\pi$
$570$		0			0
$571$	−318.271			−0.557393			−0.278696	−	0.960379i	$-0.589902\pi$
$571$	−318.271			−0.557393			−0.278696	+	0.960379i	$0.589902\pi$
$572$		0			0
$573$	60.8857	−	35.1523i	0.106258	−	0.0613479i
$574$		0			0
$575$	−419.998	−	727.458i	−0.730432	−	1.26514i
$576$		0			0
$577$	546.899			0.947833			0.473916	−	0.880570i	$-0.342840\pi$
$577$	546.899			0.947833			0.473916	+	0.880570i	$0.342840\pi$
$578$		0			0
$579$	−200.963	+	348.078i	−0.347086	+	0.601170i
$580$		0			0
$581$	−286.101			−0.492428
$582$		0			0
$583$	−557.631	−	321.949i	−0.956486	−	0.552227i
$584$		0			0
$585$	−6.07576	−	3.50784i	−0.0103859	−	0.00599631i
$586$		0			0
$587$	−543.475	−	941.326i	−0.925852	−	1.60362i	−0.790185	−	0.612868i	$-0.790016\pi$
$587$	−543.475	−	941.326i	−0.925852	−	1.60362i	−0.135667	−	0.990755i	$-0.543318\pi$
$588$		0			0
$589$	−701.496	+	538.418i	−1.19099	+	0.914122i
$590$		0			0
$591$	165.899	−	95.7821i	0.280710	−	0.162068i
$592$		0			0
$593$	−41.0118	+	71.0346i	−0.0691599	+	0.119789i	−0.898532	−	0.438909i	$-0.855365\pi$
$593$	−41.0118	+	71.0346i	−0.0691599	+	0.119789i	0.829372	+	0.558697i	$0.188699\pi$
$594$		0			0
$595$	−4.70960	+	8.15726i	−0.00791529	+	0.0137097i
$596$		0			0
$597$		−	23.4142i		−	0.0392198i
$598$		0			0
$599$	−8.06111	−	4.65408i	−0.0134576	−	0.00776975i	0.493256	−	0.869884i	$-0.335807\pi$
$599$	−8.06111	−	4.65408i	−0.0134576	−	0.00776975i	−0.506714	+	0.862114i	$0.669140\pi$
$600$		0			0
$601$			329.699i			0.548584i	0.961647	+	0.274292i	$0.0884434\pi$
$601$			329.699i			0.548584i	−0.961647	+	0.274292i	$0.911557\pi$
$602$		0			0
$603$	−271.348	+	156.663i	−0.449997	+	0.259806i
$604$		0			0
$605$	0.883258	+	1.52985i	0.00145993	+	0.00252867i
$606$		0			0
$607$		−	647.408i		−	1.06657i	−0.845936	−	0.533285i	$-0.820957\pi$
$607$		−	647.408i		−	1.06657i	0.845936	−	0.533285i	$-0.179043\pi$
$608$		0			0
$609$	−197.815			−0.324819
$610$		0			0
$611$	188.181	−	108.647i	0.307989	−	0.177818i
$612$		0			0
$613$	−382.146	−	661.897i	−0.623403	−	1.07977i	−0.988847	−	0.148933i	$-0.952416\pi$
$613$	−382.146	−	661.897i	−0.623403	−	1.07977i	0.365444	−	0.930833i	$-0.380917\pi$
$614$		0			0
$615$	8.13520			0.0132280
$616$		0			0
$617$	189.818	−	328.775i	0.307647	−	0.532860i	−0.670200	−	0.742180i	$-0.733792\pi$
$617$	189.818	−	328.775i	0.307647	−	0.532860i	0.977847	+	0.209320i	$0.0671251\pi$
$618$		0			0
$619$	1180.13			1.90652			0.953258	−	0.302157i	$-0.0977065\pi$
$619$	1180.13			1.90652			0.953258	+	0.302157i	$0.0977065\pi$
$620$		0			0
$621$	−151.514	−	87.4768i	−0.243984	−	0.140864i
$622$		0			0
$623$	−164.519	−	94.9850i	−0.264075	−	0.152464i
$624$		0			0
$625$	−310.553	−	537.893i	−0.496885	−	0.860629i
$626$		0			0
$627$	345.005	+	142.855i	0.550247	+	0.227838i
$628$		0			0
$629$	−1022.84	+	590.535i	−1.62613	+	0.938847i
$630$		0			0
$631$	180.322	−	312.327i	0.285772	−	0.494971i	−0.687024	−	0.726634i	$-0.741083\pi$
$631$	180.322	−	312.327i	0.285772	−	0.494971i	0.972796	+	0.231663i	$0.0744168\pi$
$632$		0			0
$633$	−217.335	+	376.435i	−0.343341	+	0.594684i
$634$		0			0
$635$		−	37.3920i		−	0.0588851i
$636$		0			0
$637$	378.047	+	218.266i	0.593481	+	0.342646i
$638$		0			0
$639$		−	55.7223i		−	0.0872023i
$640$		0			0
$641$	999.927	−	577.308i	1.55995	−	0.900636i	0.562687	−	0.826670i	$-0.309768\pi$
$641$	999.927	−	577.308i	1.55995	−	0.900636i	0.997261	−	0.0739666i	$-0.0235658\pi$
$642$		0			0
$643$	426.427	+	738.593i	0.663183	+	1.14867i	0.979774	+	0.200105i	$0.0641283\pi$
$643$	426.427	+	738.593i	0.663183	+	1.14867i	−0.316591	+	0.948562i	$0.602538\pi$
$644$		0			0
$645$		−	22.3344i		−	0.0346270i
$646$		0			0
$647$	−541.000			−0.836167			−0.418084	−	0.908409i	$-0.637298\pi$
$647$	−541.000			−0.836167			−0.418084	+	0.908409i	$0.637298\pi$
$648$		0			0
$649$	−1037.41	+	598.952i	−1.59848	+	0.922884i
$650$		0			0
$651$	−102.369	−	177.309i	−0.157249	−	0.272364i
$652$		0			0
$653$	−429.105			−0.657129			−0.328564	−	0.944482i	$-0.606565\pi$
$653$	−429.105			−0.657129			−0.328564	+	0.944482i	$0.606565\pi$
$654$		0			0
$655$	−1.27689	+	2.21165i	−0.00194946	+	0.00337656i
$656$		0			0
$657$	104.053			0.158376
$658$		0			0
$659$	−655.348	−	378.366i	−0.994459	−	0.574151i	−0.0878548	−	0.996133i	$-0.528001\pi$
$659$	−655.348	−	378.366i	−0.994459	−	0.574151i	−0.906604	+	0.421982i	$0.861334\pi$
$660$		0			0
$661$	918.616	+	530.363i	1.38974	+	0.802365i	0.993285	−	0.115691i	$-0.0369082\pi$
$661$	918.616	+	530.363i	1.38974	+	0.802365i	0.396451	+	0.918056i	$0.370242\pi$
$662$		0			0
$663$	−144.558	−	250.382i	−0.218037	−	0.377651i
$664$		0			0
$665$	4.20805	−	10.1628i	0.00632790	−	0.0152824i
$666$		0			0
$667$	−1311.23	+	757.036i	−1.96585	+	1.13499i
$668$		0			0
$669$	188.055	−	325.721i	0.281099	−	0.486878i
$670$		0			0
$671$	−88.0341	+	152.480i	−0.131198	+	0.227242i
$672$		0			0
$673$		−	29.6113i		−	0.0439990i	−0.999758	−	0.0219995i	$-0.992997\pi$
$673$		−	29.6113i		−	0.0439990i	0.999758	−	0.0219995i	$-0.00700322\pi$
$674$		0			0
$675$	−112.266	−	64.8169i	−0.166320	−	0.0960251i
$676$		0			0
$677$		−	62.5572i		−	0.0924036i	−0.998932	−	0.0462018i	$-0.985288\pi$
$677$		−	62.5572i		−	0.0924036i	0.998932	−	0.0462018i	$-0.0147117\pi$
$678$		0			0
$679$	−160.753	+	92.8109i	−0.236750	+	0.136688i
$680$		0			0
$681$	−100.417	−	173.928i	−0.147456	−	0.255401i
$682$		0			0
$683$		−	208.329i		−	0.305021i	−0.988302	−	0.152510i	$-0.951264\pi$
$683$		−	208.329i		−	0.305021i	0.988302	−	0.152510i	$-0.0487358\pi$
$684$		0			0
$685$	−2.74415			−0.00400606
$686$		0			0
$687$	527.147	−	304.349i	0.767318	−	0.443011i
$688$		0			0
$689$	−291.094	−	504.189i	−0.422487	−	0.731769i
$690$		0			0
$691$	−302.278			−0.437451			−0.218725	−	0.975786i	$-0.570190\pi$
$691$	−302.278			−0.437451			−0.218725	+	0.975786i	$0.570190\pi$
$692$		0			0
$693$	−43.2271	+	74.8716i	−0.0623768	+	0.108040i
$694$		0			0
$695$	−17.1841			−0.0247253
$696$		0			0
$697$	290.337	+	167.626i	0.416552	+	0.240497i
$698$		0			0
$699$	223.169	+	128.847i	0.319269	+	0.184330i
$700$		0			0
$701$	425.857	+	737.606i	0.607500	+	1.05222i	0.991651	+	0.128950i	$0.0411607\pi$
$701$	425.857	+	737.606i	0.607500	+	1.05222i	−0.384152	+	0.923270i	$0.625506\pi$
$702$		0			0
$703$	1094.11	−	839.760i	1.55634	−	1.19454i
$704$		0			0
$705$	−7.24181	+	4.18106i	−0.0102721	+	0.00593058i
$706$		0			0
$707$	3.65302	−	6.32722i	0.00516694	−	0.00894940i
$708$		0			0
$709$	137.196	−	237.630i	0.193506	−	0.335163i	−0.752904	−	0.658131i	$-0.771347\pi$
$709$	137.196	−	237.630i	0.193506	−	0.335163i	0.946410	+	0.322968i	$0.104681\pi$
$710$		0			0
$711$		−	186.686i		−	0.262568i
$712$		0			0
$713$	−1357.12	−	783.534i	−1.90340	−	1.09893i
$714$		0			0
$715$			26.5352i			0.0371121i
$716$		0			0
$717$	554.404	−	320.085i	0.773227	−	0.446423i
$718$		0			0
$719$	252.002	+	436.480i	0.350490	+	0.607066i	0.986335	−	0.164750i	$-0.0526818\pi$
$719$	252.002	+	436.480i	0.350490	+	0.607066i	−0.635846	+	0.771816i	$0.719348\pi$
$720$		0			0
$721$		−	23.5568i		−	0.0326724i
$722$		0			0
$723$	606.033			0.838220
$724$		0			0
$725$	−971.567	+	560.934i	−1.34009	+	0.773703i
$726$		0			0
$727$	−163.960	−	283.986i	−0.225529	−	0.390628i	0.730949	−	0.682432i	$-0.239078\pi$
$727$	−163.960	−	283.986i	−0.225529	−	0.390628i	−0.956478	+	0.291804i	$0.905744\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	460.201	−	797.092i	0.629550	−	1.09041i
$732$		0			0
$733$	116.751			0.159278			0.0796389	−	0.996824i	$-0.474623\pi$
$733$	116.751			0.159278			0.0796389	+	0.996824i	$0.474623\pi$
$734$		0			0
$735$	−14.5484	−	8.39954i	−0.0197938	−	0.0114280i
$736$		0			0
$737$	1026.31	+	592.541i	1.39255	+	0.803991i
$738$		0			0
$739$	−414.877	−	718.588i	−0.561403	−	0.972379i	−0.997374	−	0.0724181i	$-0.976928\pi$
$739$	−414.877	−	718.588i	−0.561403	−	0.972379i	0.435971	−	0.899961i	$-0.356405\pi$
$740$		0			0
$741$	205.567	+	267.829i	0.277418	+	0.361443i
$742$		0			0
$743$	−20.9818	+	12.1138i	−0.0282393	+	0.0163040i	−0.514053	−	0.857758i	$-0.671857\pi$
$743$	−20.9818	+	12.1138i	−0.0282393	+	0.0163040i	0.485814	+	0.874062i	$0.338523\pi$
$744$		0			0
$745$	−13.1085	+	22.7046i	−0.0175953	+	0.0304760i
$746$		0			0
$747$	−168.973	+	292.671i	−0.226203	+	0.391795i
$748$		0			0
$749$			405.421i			0.541283i
$750$		0			0
$751$	722.134	+	416.924i	0.961563	+	0.555159i	0.896654	−	0.442732i	$-0.145991\pi$
$751$	722.134	+	416.924i	0.961563	+	0.555159i	0.0649094	+	0.997891i	$0.479324\pi$
$752$		0			0
$753$		−	454.704i		−	0.603857i
$754$		0			0
$755$	8.03743	−	4.64041i	0.0106456	−	0.00614624i
$756$		0			0
$757$	597.525	+	1034.94i	0.789333	+	1.36716i	0.926376	+	0.376600i	$0.122907\pi$
$757$	597.525	+	1034.94i	0.789333	+	1.36716i	−0.137043	+	0.990565i	$0.543760\pi$
$758$		0			0
$759$			661.721i			0.871832i
$760$		0			0
$761$	−857.853			−1.12727			−0.563635	−	0.826024i	$-0.690598\pi$
$761$	−857.853			−1.12727			−0.563635	+	0.826024i	$0.690598\pi$
$762$		0			0
$763$	406.253	−	234.551i	0.532442	−	0.307406i
$764$		0			0
$765$	5.56305	+	9.63549i	0.00727197	+	0.0125954i
$766$		0			0
$767$	−1083.10			−1.41212
$768$		0			0
$769$	−187.737	+	325.170i	−0.244131	+	0.422847i	−0.961887	−	0.273447i	$-0.911836\pi$
$769$	−187.737	+	325.170i	−0.244131	+	0.422847i	0.717756	+	0.696295i	$0.245169\pi$
$770$		0			0
$771$	635.095			0.823729
$772$		0			0
$773$	−73.7576	−	42.5840i	−0.0954173	−	0.0550892i	0.451532	−	0.892255i	$-0.350878\pi$
$773$	−73.7576	−	42.5840i	−0.0954173	−	0.0550892i	−0.546949	+	0.837166i	$0.684211\pi$
$774$		0			0
$775$	−1005.57	−	580.569i	−1.29752	−	0.749121i
$776$		0			0
$777$	159.663	+	276.545i	0.205487	+	0.355914i
$778$		0			0
$779$	−361.718	−	149.775i	−0.464337	−	0.192266i
$780$		0			0
$781$	−182.520	+	105.378i	−0.233701	+	0.134927i
$782$		0			0
$783$	−116.831	+	202.357i	−0.149209	+	0.258438i
$784$		0			0
$785$	−16.1491	+	27.9710i	−0.0205721	+	0.0356319i
$786$		0			0
$787$		−	857.106i		−	1.08908i	−0.838735	−	0.544540i	$-0.816704\pi$
$787$		−	857.106i		−	1.08908i	0.838735	−	0.544540i	$-0.183296\pi$
$788$		0			0
$789$	676.185	+	390.395i	0.857015	+	0.494798i
$790$		0			0
$791$		−	539.239i		−	0.681719i
$792$		0			0
$793$	−137.866	+	79.5971i	−0.173854	+	0.100375i
$794$		0			0
$795$	11.2022	+	19.4028i	0.0140908	+	0.0244060i
$796$		0			0
$797$		−	889.701i		−	1.11631i	−0.829736	−	0.558156i	$-0.811509\pi$
$797$		−	889.701i		−	1.11631i	0.829736	−	0.558156i	$-0.188491\pi$
$798$		0			0
$799$	−344.603			−0.431293
$800$		0			0
$801$	−194.332	+	112.198i	−0.242612	+	0.140072i
$802$		0			0
$803$	−196.778	−	340.830i	−0.245054	−	0.424446i
$804$		0			0
$805$	19.4922			0.0242140
$806$		0			0
$807$	−271.691	+	470.583i	−0.336668	+	0.583127i
$808$		0			0
$809$	−200.367			−0.247672			−0.123836	−	0.992303i	$-0.539520\pi$
$809$	−200.367			−0.247672			−0.123836	+	0.992303i	$0.539520\pi$
$810$		0			0
$811$	−1113.63	−	642.952i	−1.37315	−	0.792789i	−0.381827	−	0.924234i	$-0.624705\pi$
$811$	−1113.63	−	642.952i	−1.37315	−	0.792789i	−0.991323	+	0.131445i	$0.958038\pi$
$812$		0			0
$813$	−20.8218	−	12.0215i	−0.0256111	−	0.0147866i
$814$		0			0
$815$	−7.74513	−	13.4150i	−0.00950322	−	0.0164601i
$816$		0			0
$817$	−411.192	+	993.063i	−0.503295	+	1.21550i
$818$		0			0
$819$	−67.6960	+	39.0843i	−0.0826569	+	0.0477220i
$820$		0			0
$821$	−22.4395	+	38.8663i	−0.0273319	+	0.0473402i	−0.879368	−	0.476143i	$-0.842034\pi$
$821$	−22.4395	+	38.8663i	−0.0273319	+	0.0473402i	0.852036	+	0.523483i	$0.175368\pi$
$822$		0			0
$823$	−121.226	+	209.969i	−0.147297	+	0.255126i	−0.930228	−	0.366983i	$-0.880391\pi$
$823$	−121.226	+	209.969i	−0.147297	+	0.255126i	0.782930	+	0.622109i	$0.213724\pi$
$824$		0			0
$825$			490.309i			0.594315i
$826$		0			0
$827$	250.941	+	144.881i	0.303435	+	0.175188i	0.643985	−	0.765038i	$-0.277280\pi$
$827$	250.941	+	144.881i	0.303435	+	0.175188i	−0.340550	+	0.940226i	$0.610613\pi$
$828$		0			0
$829$		−	1519.45i		−	1.83287i	−0.400184	−	0.916435i	$-0.631054\pi$
$829$		−	1519.45i		−	1.83287i	0.400184	−	0.916435i	$-0.368946\pi$
$830$		0			0
$831$	−14.4381	+	8.33586i	−0.0173744	+	0.0100311i
$832$		0			0
$833$	−346.146	−	599.542i	−0.415541	−	0.719738i
$834$		0			0
$835$			61.6062i			0.0737799i
$836$		0			0
$837$	−241.840			−0.288937
$838$		0			0
$839$	−419.817	+	242.381i	−0.500377	+	0.288893i	−0.728869	−	0.684653i	$-0.759954\pi$
$839$	−419.817	+	242.381i	−0.500377	+	0.288893i	0.228492	+	0.973546i	$0.426621\pi$
$840$		0			0
$841$	590.570	+	1022.90i	0.702224	+	1.21629i
$842$		0			0
$843$	570.411			0.676644
$844$		0			0
$845$	7.26526	−	12.5838i	0.00859795	−	0.0148921i
$846$		0			0
$847$	19.6825			0.0232379
$848$		0			0
$849$	−442.324	−	255.376i	−0.520994	−	0.300796i
$850$		0			0
$851$	2116.67	+	1222.06i	2.48728	+	1.43603i
$852$		0			0
$853$	635.431	+	1100.60i	0.744937	+	1.29027i	0.950224	+	0.311566i	$0.100854\pi$
$853$	635.431	+	1100.60i	0.744937	+	1.29027i	−0.205288	+	0.978702i	$0.565813\pi$
$854$		0			0
$855$	−7.91085	−	10.3069i	−0.00925245	−	0.0120549i
$856$		0			0
$857$	431.601	−	249.185i	0.503618	−	0.290764i	−0.226588	−	0.973991i	$-0.572757\pi$
$857$	431.601	−	249.185i	0.503618	−	0.290764i	0.730206	+	0.683227i	$0.239424\pi$
$858$		0			0
$859$	343.195	−	594.431i	0.399528	−	0.692004i	−0.594139	−	0.804362i	$-0.702507\pi$
$859$	343.195	−	594.431i	0.399528	−	0.692004i	0.993668	+	0.112359i	$0.0358405\pi$
$860$		0			0
$861$	45.3212	−	78.4986i	0.0526378	−	0.0911714i
$862$		0			0
$863$		−	701.513i		−	0.812877i	−0.913678	−	0.406438i	$-0.866771\pi$
$863$		−	701.513i		−	0.812877i	0.913678	−	0.406438i	$-0.133229\pi$
$864$		0			0
$865$	12.5271	+	7.23252i	0.0144822	+	0.00836130i
$866$		0			0
$867$		−	42.0552i		−	0.0485066i
$868$		0			0
$869$	−611.496	+	353.048i	−0.703678	+	0.406269i
$870$		0			0
$871$	535.753	+	927.952i	0.615101	+	1.06539i
$872$		0			0
$873$			219.260i			0.251156i
$874$		0			0
$875$	28.9161			0.0330470
$876$		0			0
$877$	510.160	−	294.541i	0.581710	−	0.335851i	−0.180103	−	0.983648i	$-0.557643\pi$
$877$	510.160	−	294.541i	0.581710	−	0.335851i	0.761813	+	0.647797i	$0.224310\pi$
$878$		0			0
$879$	262.486	+	454.640i	0.298619	+	0.517224i
$880$		0			0
$881$	539.838			0.612756			0.306378	−	0.951910i	$-0.400883\pi$
$881$	539.838			0.612756			0.306378	+	0.951910i	$0.400883\pi$
$882$		0			0
$883$	548.990	−	950.878i	0.621732	−	1.07687i	−0.367431	−	0.930051i	$-0.619763\pi$
$883$	548.990	−	950.878i	0.621732	−	1.07687i	0.989163	−	0.146821i	$-0.0469041\pi$
$884$		0			0
$885$	41.6810			0.0470972
$886$		0			0
$887$	−631.390	−	364.533i	−0.711826	−	0.410973i	0.0999109	−	0.994996i	$-0.468144\pi$
$887$	−631.390	−	364.533i	−0.711826	−	0.410973i	−0.811737	+	0.584024i	$0.801478\pi$
$888$		0			0
$889$	−360.805	−	208.311i	−0.405855	−	0.234320i
$890$		0			0
$891$	51.0606	+	88.4395i	0.0573070	+	0.0992587i
$892$		0			0
$893$	398.971	−	52.5770i	0.446776	−	0.0588769i
$894$		0			0
$895$	−39.7489	+	22.9491i	−0.0444122	+	0.0256414i
$896$		0			0
$897$	−299.151	+	518.145i	−0.333502	+	0.577643i
$898$		0			0
$899$	−1046.46	+	1812.52i	−1.16403	+	2.01615i
$900$		0			0
$901$			923.286i			1.02473i
$902$		0			0
$903$	−215.510	−	124.425i	−0.238660	−	0.137791i
$904$		0			0
$905$		−	75.3902i		−	0.0833041i
$906$		0			0
$907$	285.340	−	164.741i	0.314598	−	0.181633i	−0.334384	−	0.942437i	$-0.608528\pi$
$907$	285.340	−	164.741i	0.314598	−	0.181633i	0.648982	+	0.760804i	$0.275195\pi$
$908$		0			0
$909$	−4.31501	−	7.47382i	−0.00474699	−	0.00822202i
$910$		0			0
$911$		−	698.321i		−	0.766543i	−0.923636	−	0.383272i	$-0.874797\pi$
$911$		−	698.321i		−	0.766543i	0.923636	−	0.383272i	$-0.125203\pi$
$912$		0			0
$913$	1278.21			1.40001
$914$		0			0
$915$	5.30552	−	3.06314i	0.00579838	−	0.00334770i
$916$		0			0
$917$	14.2271	+	24.6421i	0.0155149	+	0.0268726i
$918$		0			0
$919$	−151.147			−0.164469			−0.0822347	−	0.996613i	$-0.526206\pi$
$919$	−151.147			−0.164469			−0.0822347	+	0.996613i	$0.526206\pi$
$920$		0			0
$921$	275.694	−	477.517i	0.299342	−	0.518476i
$922$		0			0
$923$	−190.558			−0.206455
$924$		0			0
$925$	1568.37	+	905.501i	1.69554	+	0.978920i
$926$		0			0
$927$	−24.0978	−	13.9128i	−0.0259954	−	0.0150085i
$928$		0			0
$929$	254.455	+	440.729i	0.273902	+	0.474413i	0.969858	−	0.243673i	$-0.0783522\pi$
$929$	254.455	+	440.729i	0.273902	+	0.474413i	−0.695955	+	0.718085i	$0.745019\pi$
$930$		0			0
$931$	492.230	+	641.319i	0.528712	+	0.688849i
$932$		0			0
$933$	−70.1495	+	40.5008i	−0.0751870	+	0.0434093i
$934$		0			0
$935$	21.0409	−	36.4440i	0.0225037	−	0.0389775i
$936$		0			0
$937$	−649.672	+	1125.27i	−0.693354	+	1.20092i	0.277379	+	0.960761i	$0.410534\pi$
$937$	−649.672	+	1125.27i	−0.693354	+	1.20092i	−0.970733	+	0.240163i	$0.922799\pi$
$938$		0			0
$939$		−	172.044i		−	0.183221i
$940$		0			0
$941$	−670.131	−	386.900i	−0.712148	−	0.411159i	0.0997080	−	0.995017i	$-0.468209\pi$
$941$	−670.131	−	386.900i	−0.712148	−	0.411159i	−0.811856	+	0.583858i	$0.801542\pi$
$942$		0			0
$943$		−	693.777i		−	0.735712i
$944$		0			0
$945$	2.60515	−	1.50409i	0.00275678	−	0.00159163i
$946$		0			0
$947$	155.193	+	268.802i	0.163878	+	0.283846i	0.936256	−	0.351317i	$-0.114266\pi$
$947$	155.193	+	268.802i	0.163878	+	0.283846i	−0.772378	+	0.635163i	$0.780933\pi$
$948$		0			0
$949$		−	355.839i		−	0.374962i
$950$		0			0
$951$	328.449			0.345372
$952$		0			0
$953$	100.592	−	58.0765i	0.105552	−	0.0609408i	−0.446294	−	0.894886i	$-0.647257\pi$
$953$	100.592	−	58.0765i	0.105552	−	0.0609408i	0.551847	+	0.833945i	$0.313923\pi$
$954$		0			0
$955$	4.62618	+	8.01278i	0.00484417	+	0.00839035i
$956$		0			0
$957$	883.771			0.923480
$958$		0			0
$959$	−15.2876	+	26.4790i	−0.0159412	+	0.0276110i
$960$		0			0
$961$	−1205.18			−1.25409
$962$		0			0
$963$	414.731	+	239.445i	0.430665	+	0.248645i
$964$		0			0
$965$	−45.8083	−	26.4475i	−0.0474698	−	0.0274067i
$966$		0			0
$967$	−188.639	−	326.732i	−0.195076	−	0.337882i	0.751849	−	0.659335i	$-0.229162\pi$
$967$	−188.639	−	326.732i	−0.195076	−	0.337882i	−0.946926	+	0.321453i	$0.895829\pi$
$968$		0			0
$969$	−69.9557	−	530.846i	−0.0721937	−	0.547829i
$970$		0			0
$971$	−154.430	+	89.1601i	−0.159042	+	0.0918229i	−0.577409	−	0.816455i	$-0.695936\pi$
$971$	−154.430	+	89.1601i	−0.159042	+	0.0918229i	0.418367	+	0.908278i	$0.362603\pi$
$972$		0			0
$973$	−95.7326	+	165.814i	−0.0983891	+	0.170415i
$974$		0			0
$975$	−221.660	+	383.926i	−0.227343	+	0.393770i
$976$		0			0
$977$			1010.90i			1.03470i	0.855775	+	0.517349i	$0.173081\pi$
$977$			1010.90i			1.03470i	−0.855775	+	0.517349i	$0.826919\pi$
$978$		0			0
$979$	735.017	+	424.362i	0.750783	+	0.433465i
$980$		0			0
$981$		−	554.110i		−	0.564842i
$982$		0			0
$983$	−289.065	+	166.892i	−0.294064	+	0.169778i	−0.639773	−	0.768564i	$-0.720972\pi$
$983$	−289.065	+	166.892i	−0.294064	+	0.169778i	0.345709	+	0.938342i	$0.387638\pi$
$984$		0			0
$985$	12.6053	+	21.8330i	0.0127972	+	0.0221655i
$986$		0			0
$987$			93.1706i			0.0943978i
$988$		0			0
$989$	−1904.70			−1.92588
$990$		0			0
$991$	−616.523	+	355.950i	−0.622122	+	0.359182i	−0.777695	−	0.628642i	$-0.783611\pi$
$991$	−616.523	+	355.950i	−0.622122	+	0.359182i	0.155573	+	0.987824i	$0.450278\pi$
$992$		0			0
$993$	−268.703	−	465.407i	−0.270597	−	0.468688i
$994$		0			0
$995$	3.08140			0.00309688
$996$		0			0
$997$	−573.369	+	993.104i	−0.575094	+	0.996092i	0.420937	+	0.907090i	$0.361701\pi$
$997$	−573.369	+	993.104i	−0.575094	+	0.996092i	−0.996031	+	0.0890024i	$0.971632\pi$
$998$		0			0
$999$	377.194			0.377571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.5		20
4.3	odd	2		456.3.w.a.145.5	✓	20
12.11	even	2		1368.3.bv.c.145.6		20
19.8	odd	6	inner	912.3.be.j.673.5		20
76.27	even	6		456.3.w.a.217.5	yes	20
228.179	odd	6		1368.3.bv.c.217.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.5	✓	20	4.3	odd	2
456.3.w.a.217.5	yes	20	76.27	even	6
912.3.be.j.145.5		20	1.1	even	1	trivial
912.3.be.j.673.5		20	19.8	odd	6	inner
1368.3.bv.c.145.6		20	12.11	even	2
1368.3.bv.c.217.6		20	228.179	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.113972 + 0.197406i) q^{5} +2.53976 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.113972 + 0.197406i) q^{5} +2.53976 q^{7} +(1.50000 - 2.59808i) q^{9} -11.3468 q^{11} +(-8.88485 - 5.12967i) q^{13} +(0.341917 + 0.197406i) q^{15} +(8.13510 + 14.0904i) q^{17} +(-11.5684 - 15.0722i) q^{19} +(3.80963 - 2.19949i) q^{21} +(16.8349 - 29.1589i) q^{23} +(12.4740 - 21.6056i) q^{25} -5.19615i q^{27} +(-38.9436 - 22.4841i) q^{29} -46.5422i q^{31} +(-17.0202 + 9.82661i) q^{33} +(0.289462 + 0.501362i) q^{35} +72.5910i q^{37} -17.7697 q^{39} +(17.8447 - 10.3026i) q^{41} +(-28.2849 - 48.9909i) q^{43} +0.683834 q^{45} +(-10.5900 + 18.3424i) q^{47} -42.5496 q^{49} +(24.4053 + 14.0904i) q^{51} +(49.1444 + 28.3735i) q^{53} +(-1.29322 - 2.23992i) q^{55} +(-30.4055 - 12.5899i) q^{57} +(91.4280 - 52.7860i) q^{59} +(7.75850 - 13.4381i) q^{61} +(3.80963 - 6.59848i) q^{63} -2.33856i q^{65} +(-90.4495 - 52.2210i) q^{67} -58.3179i q^{69} +(16.0856 - 9.28705i) q^{71} +(17.3422 + 30.0375i) q^{73} -43.2113i q^{75} -28.8181 q^{77} +(53.8915 - 31.1143i) q^{79} +(-4.50000 - 7.79423i) q^{81} -112.649 q^{83} +(-1.85435 + 3.21183i) q^{85} -77.8872 q^{87} +(-64.7775 - 37.3993i) q^{89} +(-22.5653 - 13.0281i) q^{91} +(-40.3067 - 69.8133i) q^{93} +(1.65687 - 4.00148i) q^{95} +(-63.2948 + 36.5433i) q^{97} +(-17.0202 + 29.4798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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