LMFDB - Embedded newform 912.3.be.i.145.1

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} - 2 x^{19} - 51 x^{18} + 314 x^{17} + 631 x^{16} - 7264 x^{15} + 8030 x^{14} + 12664 x^{13} + \cdots + 26753228352 $ x^20 - 2x^19 - 51x^18 + 314x^17 + 631x^16 - 7264x^15 + 8030x^14 + 12664x^13 + 393231x^12 - 447686x^11 - 9929427x^10 + 44358366x^9 - 34218119x^8 - 65904712x^7 + 1769085384x^6 - 7530122944x^5 + 6630672896x^4 + 46763900480x^3 - 4377536384x^2 - 53791886208*x + 26753228352
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$3.07263 - 3.70568i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.i.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-4.28133 - 7.41548i) q^{5} +10.9641 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-4.28133 - 7.41548i) q^{5} +10.9641 q^{7} +(1.50000 - 2.59808i) q^{9} -6.12457 q^{11} +(3.96581 + 2.28966i) q^{13} +(12.8440 + 7.41548i) q^{15} +(11.9946 + 20.7753i) q^{17} +(18.8674 + 2.24086i) q^{19} +(-16.4462 + 9.49523i) q^{21} +(20.6373 - 35.7448i) q^{23} +(-24.1596 + 41.8457i) q^{25} +5.19615i q^{27} +(-15.3416 - 8.85749i) q^{29} +0.0804213i q^{31} +(9.18686 - 5.30403i) q^{33} +(-46.9411 - 81.3044i) q^{35} -19.7392i q^{37} -7.93162 q^{39} +(-1.52912 + 0.882837i) q^{41} +(22.4714 + 38.9217i) q^{43} -25.6880 q^{45} +(6.58360 - 11.4031i) q^{47} +71.2124 q^{49} +(-35.9839 - 20.7753i) q^{51} +(-79.1928 - 45.7220i) q^{53} +(26.2213 + 45.4167i) q^{55} +(-30.2417 + 12.9783i) q^{57} +(-1.30913 + 0.755827i) q^{59} +(39.8636 - 69.0458i) q^{61} +(16.4462 - 28.4857i) q^{63} -39.2112i q^{65} +(-56.2170 - 32.4569i) q^{67} +71.4896i q^{69} +(48.2800 - 27.8745i) q^{71} +(-23.6845 - 41.0228i) q^{73} -83.6913i q^{75} -67.1507 q^{77} +(107.238 - 61.9137i) q^{79} +(-4.50000 - 7.79423i) q^{81} +66.8531 q^{83} +(102.706 - 177.892i) q^{85} +30.6832 q^{87} +(35.8903 + 20.7213i) q^{89} +(43.4817 + 25.1042i) q^{91} +(-0.0696469 - 0.120632i) q^{93} +(-64.1605 - 149.505i) q^{95} +(-24.2833 + 14.0200i) q^{97} +(-9.18686 + 15.9121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * 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
$5$	−4.28133	−	7.41548i	−0.856266	−	1.48310i	−0.875465	−	0.483281i	$-0.839445\pi$
$5$	−4.28133	−	7.41548i	−0.856266	−	1.48310i	0.0191989	−	0.999816i	$-0.493888\pi$
$6$		0			0
$7$	10.9641			1.56631			0.783153	−	0.621829i	$-0.213610\pi$
$7$	10.9641			1.56631			0.783153	+	0.621829i	$0.213610\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−6.12457			−0.556779			−0.278390	−	0.960468i	$-0.589801\pi$
$11$	−6.12457			−0.556779			−0.278390	+	0.960468i	$0.589801\pi$
$12$		0			0
$13$	3.96581	+	2.28966i	0.305062	+	0.176128i	0.644715	−	0.764423i	$-0.276976\pi$
$13$	3.96581	+	2.28966i	0.305062	+	0.176128i	−0.339652	+	0.940551i	$0.610309\pi$
$14$		0			0
$15$	12.8440	+	7.41548i	0.856266	+	0.494366i
$16$		0			0
$17$	11.9946	+	20.7753i	0.705567	+	1.22208i	0.966486	+	0.256718i	$0.0826411\pi$
$17$	11.9946	+	20.7753i	0.705567	+	1.22208i	−0.260919	+	0.965361i	$0.584026\pi$
$18$		0			0
$19$	18.8674	+	2.24086i	0.993021	+	0.117940i
$19$	18.8674	+	2.24086i	0.993021	+	0.117940i
$20$		0			0
$21$	−16.4462	+	9.49523i	−0.783153	+	0.452154i
$22$		0			0
$23$	20.6373	−	35.7448i	0.897273	−	1.55412i	0.0663072	−	0.997799i	$-0.478878\pi$
$23$	20.6373	−	35.7448i	0.897273	−	1.55412i	0.830966	−	0.556323i	$-0.187788\pi$
$24$		0			0
$25$	−24.1596	+	41.8457i	−0.966384	+	1.67383i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−15.3416	−	8.85749i	−0.529021	−	0.305431i	0.211596	−	0.977357i	$-0.432134\pi$
$29$	−15.3416	−	8.85749i	−0.529021	−	0.305431i	−0.740618	+	0.671926i	$0.765467\pi$
$30$		0			0
$31$			0.0804213i			0.00259424i	0.999999	+	0.00129712i	$0.000412885\pi$
$31$			0.0804213i			0.00259424i	−0.999999	+	0.00129712i	$0.999587\pi$
$32$		0			0
$33$	9.18686	−	5.30403i	0.278390	−	0.160728i
$34$		0			0
$35$	−46.9411	−	81.3044i	−1.34118	−	2.32298i
$36$		0			0
$37$		−	19.7392i		−	0.533491i	−0.963767	−	0.266746i	$-0.914052\pi$
$37$		−	19.7392i		−	0.533491i	0.963767	−	0.266746i	$-0.0859483\pi$
$38$		0			0
$39$	−7.93162			−0.203375
$40$		0			0
$41$	−1.52912	+	0.882837i	−0.0372956	+	0.0215326i	−0.518532	−	0.855058i	$-0.673521\pi$
$41$	−1.52912	+	0.882837i	−0.0372956	+	0.0215326i	0.481236	+	0.876591i	$0.340188\pi$
$42$		0			0
$43$	22.4714	+	38.9217i	0.522592	+	0.905155i	0.999654	+	0.0262859i	$0.00836804\pi$
$43$	22.4714	+	38.9217i	0.522592	+	0.905155i	−0.477063	+	0.878869i	$0.658299\pi$
$44$		0			0
$45$	−25.6880			−0.570844
$46$		0			0
$47$	6.58360	−	11.4031i	0.140077	−	0.242620i	−0.787449	−	0.616380i	$-0.788598\pi$
$47$	6.58360	−	11.4031i	0.140077	−	0.242620i	0.927525	+	0.373760i	$0.121932\pi$
$48$		0			0
$49$	71.2124			1.45331
$50$		0			0
$51$	−35.9839	−	20.7753i	−0.705567	−	0.407360i
$52$		0			0
$53$	−79.1928	−	45.7220i	−1.49420	−	0.862679i	−0.494225	−	0.869334i	$-0.664548\pi$
$53$	−79.1928	−	45.7220i	−1.49420	−	0.862679i	−0.999978	+	0.00665516i	$0.997882\pi$
$54$		0			0
$55$	26.2213	+	45.4167i	0.476751	+	0.825757i
$56$		0			0
$57$	−30.2417	+	12.9783i	−0.530557	+	0.227690i
$58$		0			0
$59$	−1.30913	+	0.755827i	−0.0221887	+	0.0128106i	−0.511053	−	0.859549i	$-0.670745\pi$
$59$	−1.30913	+	0.755827i	−0.0221887	+	0.0128106i	0.488865	+	0.872360i	$0.337411\pi$
$60$		0			0
$61$	39.8636	−	69.0458i	0.653502	−	1.13190i	−0.328765	−	0.944412i	$-0.606632\pi$
$61$	39.8636	−	69.0458i	0.653502	−	1.13190i	0.982267	−	0.187487i	$-0.0600342\pi$
$62$		0			0
$63$	16.4462	−	28.4857i	0.261051	−	0.452154i
$64$		0			0
$65$		−	39.2112i		−	0.603249i
$66$		0			0
$67$	−56.2170	−	32.4569i	−0.839059	−	0.484431i	0.0178850	−	0.999840i	$-0.494307\pi$
$67$	−56.2170	−	32.4569i	−0.839059	−	0.484431i	−0.856944	+	0.515409i	$0.827640\pi$
$68$		0			0
$69$			71.4896i			1.03608i
$70$		0			0
$71$	48.2800	−	27.8745i	0.680000	−	0.392598i	−0.119855	−	0.992791i	$-0.538243\pi$
$71$	48.2800	−	27.8745i	0.680000	−	0.392598i	0.799855	+	0.600193i	$0.204910\pi$
$72$		0			0
$73$	−23.6845	−	41.0228i	−0.324445	−	0.561956i	0.656955	−	0.753930i	$-0.271844\pi$
$73$	−23.6845	−	41.0228i	−0.324445	−	0.561956i	−0.981400	+	0.191974i	$0.938511\pi$
$74$		0			0
$75$		−	83.6913i		−	1.11588i
$76$		0			0
$77$	−67.1507			−0.872087
$78$		0			0
$79$	107.238	−	61.9137i	1.35744	−	0.783717i	0.368160	−	0.929762i	$-0.379988\pi$
$79$	107.238	−	61.9137i	1.35744	−	0.783717i	0.989278	+	0.146045i	$0.0466546\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	66.8531			0.805459			0.402729	−	0.915319i	$-0.368062\pi$
$83$	66.8531			0.805459			0.402729	+	0.915319i	$0.368062\pi$
$84$		0			0
$85$	102.706	−	177.892i	1.20831	−	2.09285i
$86$		0			0
$87$	30.6832			0.352681
$88$		0			0
$89$	35.8903	+	20.7213i	0.403262	+	0.232823i	0.687890	−	0.725815i	$-0.258537\pi$
$89$	35.8903	+	20.7213i	0.403262	+	0.232823i	−0.284629	+	0.958638i	$0.591870\pi$
$90$		0			0
$91$	43.4817	+	25.1042i	0.477821	+	0.275870i
$92$		0			0
$93$	−0.0696469	−	0.120632i	−0.000748891	−	0.00129712i
$94$		0			0
$95$	−64.1605	−	149.505i	−0.675373	−	1.57373i
$96$		0			0
$97$	−24.2833	+	14.0200i	−0.250343	+	0.144536i	−0.619921	−	0.784664i	$-0.712836\pi$
$97$	−24.2833	+	14.0200i	−0.250343	+	0.144536i	0.369578	+	0.929200i	$0.379502\pi$
$98$		0			0
$99$	−9.18686	+	15.9121i	−0.0927965	+	0.160728i
$100$		0			0
$101$	31.2764	−	54.1724i	0.309668	−	0.536360i	−0.668622	−	0.743603i	$-0.733115\pi$
$101$	31.2764	−	54.1724i	0.309668	−	0.536360i	0.978290	+	0.207242i	$0.0664488\pi$
$102$		0			0
$103$		−	66.0766i		−	0.641521i	−0.947160	−	0.320760i	$-0.896062\pi$
$103$		−	66.0766i		−	0.641521i	0.947160	−	0.320760i	$-0.103938\pi$
$104$		0			0
$105$	140.823	+	81.3044i	1.34118	+	0.774328i
$106$		0			0
$107$		−	167.243i		−	1.56302i	−0.623893	−	0.781510i	$-0.714450\pi$
$107$		−	167.243i		−	1.56302i	0.623893	−	0.781510i	$-0.285550\pi$
$108$		0			0
$109$	3.46512	−	2.00059i	0.0317901	−	0.0183540i	−0.484021	−	0.875057i	$-0.660824\pi$
$109$	3.46512	−	2.00059i	0.0317901	−	0.0183540i	0.515811	+	0.856703i	$0.327491\pi$
$110$		0			0
$111$	17.0946	+	29.6088i	0.154006	+	0.266746i
$112$		0			0
$113$		−	200.732i		−	1.77639i	−0.459463	−	0.888197i	$-0.651958\pi$
$113$		−	200.732i		−	1.77639i	0.459463	−	0.888197i	$-0.348042\pi$
$114$		0			0
$115$	−353.420			−3.07322
$116$		0			0
$117$	11.8974	−	6.86899i	0.101687	−	0.0587093i
$118$		0			0
$119$	131.511	+	227.784i	1.10513	+	1.91415i
$120$		0			0
$121$	−83.4896			−0.689997
$122$		0			0
$123$	1.52912	−	2.64851i	0.0124319	−	0.0215326i
$124$		0			0
$125$	199.674			1.59740
$126$		0			0
$127$	97.1071	+	56.0648i	0.764623	+	0.441455i	0.830953	−	0.556342i	$-0.187796\pi$
$127$	97.1071	+	56.0648i	0.764623	+	0.441455i	−0.0663300	+	0.997798i	$0.521129\pi$
$128$		0			0
$129$	−67.4143	−	38.9217i	−0.522592	−	0.301718i
$130$		0			0
$131$	89.3401	+	154.742i	0.681985	+	1.18123i	0.974374	+	0.224934i	$0.0722165\pi$
$131$	89.3401	+	154.742i	0.681985	+	1.18123i	−0.292389	+	0.956299i	$0.594450\pi$
$132$		0			0
$133$	206.865	+	24.5691i	1.55537	+	0.184730i
$134$		0			0
$135$	38.5320	−	22.2465i	0.285422	−	0.164789i
$136$		0			0
$137$	−98.8222	+	171.165i	−0.721330	+	1.24938i	0.239137	+	0.970986i	$0.423136\pi$
$137$	−98.8222	+	171.165i	−0.721330	+	1.24938i	−0.960467	+	0.278395i	$0.910198\pi$
$138$		0			0
$139$	−17.2696	+	29.9118i	−0.124242	+	0.215193i	−0.921436	−	0.388530i	$-0.872983\pi$
$139$	−17.2696	+	29.9118i	−0.124242	+	0.215193i	0.797195	+	0.603722i	$0.206316\pi$
$140$		0			0
$141$			22.8063i			0.161747i
$142$		0			0
$143$	−24.2889	−	14.0232i	−0.169852	−	0.0980643i
$144$		0			0
$145$			151.687i			1.04612i
$146$		0			0
$147$	−106.819	+	61.6717i	−0.726657	+	0.419536i
$148$		0			0
$149$	117.283	+	203.141i	0.787137	+	1.36336i	0.927714	+	0.373292i	$0.121771\pi$
$149$	117.283	+	203.141i	0.787137	+	1.36336i	−0.140577	+	0.990070i	$0.544896\pi$
$150$		0			0
$151$			287.390i			1.90324i	0.307271	+	0.951622i	$0.400584\pi$
$151$			287.390i			1.90324i	−0.307271	+	0.951622i	$0.599416\pi$
$152$		0			0
$153$	71.9679			0.470378
$154$		0			0
$155$	0.596363	−	0.344310i	0.00384750	−	0.00222136i
$156$		0			0
$157$	−54.5862	−	94.5460i	−0.347683	−	0.602204i	0.638155	−	0.769908i	$-0.279698\pi$
$157$	−54.5862	−	94.5460i	−0.347683	−	0.602204i	−0.985837	+	0.167704i	$0.946365\pi$
$158$		0			0
$159$	158.386			0.996135
$160$		0			0
$161$	226.270	−	391.911i	1.40540	−	2.43423i
$162$		0			0
$163$	99.0052			0.607394			0.303697	−	0.952769i	$-0.401779\pi$
$163$	99.0052			0.607394			0.303697	+	0.952769i	$0.401779\pi$
$164$		0			0
$165$	−78.6640	−	45.4167i	−0.476751	−	0.275252i
$166$		0			0
$167$	−262.234	−	151.401i	−1.57026	−	0.906591i	−0.996136	−	0.0878249i	$-0.972008\pi$
$167$	−262.234	−	151.401i	−1.57026	−	0.906591i	−0.574127	−	0.818767i	$-0.694658\pi$
$168$		0			0
$169$	−74.0149	−	128.198i	−0.437958	−	0.758565i
$170$		0			0
$171$	34.1230	−	45.6576i	0.199550	−	0.267004i
$172$		0			0
$173$	−196.513	+	113.457i	−1.13591	+	0.655819i	−0.945415	−	0.325869i	$-0.894343\pi$
$173$	−196.513	+	113.457i	−1.13591	+	0.655819i	−0.190496	+	0.981688i	$0.561010\pi$
$174$		0			0
$175$	−264.889	+	458.802i	−1.51365	+	2.62172i
$176$		0			0
$177$	1.30913	−	2.26748i	0.00739622	−	0.0128106i
$178$		0			0
$179$		−	62.8016i		−	0.350847i	−0.984493	−	0.175423i	$-0.943871\pi$
$179$		−	62.8016i		−	0.350847i	0.984493	−	0.175423i	$-0.0561295\pi$
$180$		0			0
$181$	−307.003	−	177.248i	−1.69615	−	0.979272i	−0.949349	−	0.314225i	$-0.898255\pi$
$181$	−307.003	−	177.248i	−1.69615	−	0.979272i	−0.746801	−	0.665047i	$-0.768411\pi$
$182$		0			0
$183$			138.092i			0.754599i
$184$		0			0
$185$	−146.375	+	84.5099i	−0.791219	+	0.456810i
$186$		0			0
$187$	−73.4621	−	127.240i	−0.392845	−	0.680428i
$188$		0			0
$189$			56.9714i			0.301436i
$190$		0			0
$191$	−245.098			−1.28324			−0.641618	−	0.767024i	$-0.721737\pi$
$191$	−245.098			−1.28324			−0.641618	+	0.767024i	$0.721737\pi$
$192$		0			0
$193$	217.732	−	125.708i	1.12815	−	0.651336i	0.184679	−	0.982799i	$-0.440876\pi$
$193$	217.732	−	125.708i	1.12815	−	0.651336i	0.943468	+	0.331463i	$0.107542\pi$
$194$		0			0
$195$	33.9579	+	58.8168i	0.174143	+	0.301625i
$196$		0			0
$197$	203.438			1.03268			0.516340	−	0.856384i	$-0.327294\pi$
$197$	203.438			1.03268			0.516340	+	0.856384i	$0.327294\pi$
$198$		0			0
$199$	80.4856	−	139.405i	0.404450	−	0.700529i	−0.589807	−	0.807544i	$-0.700796\pi$
$199$	80.4856	−	139.405i	0.404450	−	0.700529i	0.994257	+	0.107016i	$0.0341295\pi$
$200$		0			0
$201$	112.434			0.559373
$202$		0			0
$203$	−168.208	−	97.1148i	−0.828609	−	0.478398i
$204$		0			0
$205$	13.0933	+	7.55944i	0.0638699	+	0.0368753i
$206$		0			0
$207$	−61.9118	−	107.234i	−0.299091	−	0.518041i
$208$		0			0
$209$	−115.555	−	13.7243i	−0.552893	−	0.0656667i
$210$		0			0
$211$	9.23560	−	5.33217i	0.0437706	−	0.0252710i	−0.477955	−	0.878384i	$-0.658622\pi$
$211$	9.23560	−	5.33217i	0.0437706	−	0.0252710i	0.521726	+	0.853113i	$0.325288\pi$
$212$		0			0
$213$	−48.2800	+	83.6234i	−0.226667	+	0.392598i
$214$		0			0
$215$	192.415	−	333.273i	0.894955	−	1.55011i
$216$		0			0
$217$			0.881750i			0.00406337i
$218$		0			0
$219$	71.0535	+	41.0228i	0.324445	+	0.187319i
$220$		0			0
$221$			109.855i			0.497080i
$222$		0			0
$223$	−205.920	+	118.888i	−0.923407	+	0.533129i	−0.884720	−	0.466122i	$-0.845651\pi$
$223$	−205.920	+	118.888i	−0.923407	+	0.533129i	−0.0386865	+	0.999251i	$0.512317\pi$
$224$		0			0
$225$	72.4788	+	125.537i	0.322128	+	0.557942i
$226$		0			0
$227$		−	57.0421i		−	0.251287i	−0.992075	−	0.125643i	$-0.959900\pi$
$227$		−	57.0421i		−	0.251287i	0.992075	−	0.125643i	$-0.0400995\pi$
$228$		0			0
$229$	321.720			1.40489			0.702446	−	0.711737i	$-0.252091\pi$
$229$	321.720			1.40489			0.702446	+	0.711737i	$0.252091\pi$
$230$		0			0
$231$	100.726	−	58.1542i	0.436043	−	0.251750i
$232$		0			0
$233$	72.4503	+	125.488i	0.310946	+	0.538574i	0.978567	−	0.205927i	$-0.0660210\pi$
$233$	72.4503	+	125.488i	0.310946	+	0.538574i	−0.667622	+	0.744501i	$0.732688\pi$
$234$		0			0
$235$	−112.746			−0.479772
$236$		0			0
$237$	−107.238	+	185.741i	−0.452479	+	0.783717i
$238$		0			0
$239$	−272.906			−1.14186			−0.570932	−	0.820997i	$-0.693418\pi$
$239$	−272.906			−1.14186			−0.570932	+	0.820997i	$0.693418\pi$
$240$		0			0
$241$	−375.633	−	216.872i	−1.55864	−	0.899884i	−0.997387	−	0.0722428i	$-0.976984\pi$
$241$	−375.633	−	216.872i	−1.55864	−	0.899884i	−0.561258	−	0.827641i	$-0.689682\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−304.884	−	528.074i	−1.24442	−	2.15541i
$246$		0			0
$247$	69.6937	+	52.0868i	0.282161	+	0.210878i
$248$		0			0
$249$	−100.280	+	57.8965i	−0.402729	+	0.232516i
$250$		0			0
$251$	182.180	−	315.545i	0.725816	−	1.25715i	−0.232821	−	0.972520i	$-0.574796\pi$
$251$	182.180	−	315.545i	0.725816	−	1.25715i	0.958637	−	0.284631i	$-0.0918710\pi$
$252$		0			0
$253$	−126.395	+	218.922i	−0.499583	+	0.865303i
$254$		0			0
$255$			355.784i			1.39523i
$256$		0			0
$257$	106.638	+	61.5675i	0.414934	+	0.239562i	0.692907	−	0.721027i	$-0.256329\pi$
$257$	106.638	+	61.5675i	0.414934	+	0.239562i	−0.277974	+	0.960589i	$0.589663\pi$
$258$		0			0
$259$		−	216.423i		−	0.835610i
$260$		0			0
$261$	−46.0249	+	26.5725i	−0.176340	+	0.101810i
$262$		0			0
$263$	156.980	+	271.897i	0.596882	+	1.03383i	0.993278	+	0.115750i	$0.0369272\pi$
$263$	156.980	+	271.897i	0.596882	+	1.03383i	−0.396397	+	0.918079i	$0.629740\pi$
$264$		0			0
$265$			783.004i			2.95473i
$266$		0			0
$267$	−71.7806			−0.268841
$268$		0			0
$269$	36.4179	−	21.0259i	0.135382	−	0.0781631i	−0.430779	−	0.902457i	$-0.641761\pi$
$269$	36.4179	−	21.0259i	0.135382	−	0.0781631i	0.566161	+	0.824294i	$0.308428\pi$
$270$		0			0
$271$	110.230	+	190.924i	0.406754	+	0.704518i	0.994524	−	0.104510i	$-0.0333274\pi$
$271$	110.230	+	190.924i	0.406754	+	0.704518i	−0.587770	+	0.809028i	$0.699994\pi$
$272$		0			0
$273$	−86.9634			−0.318547
$274$		0			0
$275$	147.967	−	256.287i	0.538063	−	0.931952i
$276$		0			0
$277$	−210.452			−0.759755			−0.379877	−	0.925037i	$-0.624034\pi$
$277$	−210.452			−0.759755			−0.379877	+	0.925037i	$0.624034\pi$
$278$		0			0
$279$	0.208941	+	0.120632i	0.000748891	+	0.000432373i
$280$		0			0
$281$	−255.540	−	147.536i	−0.909397	−	0.525040i	−0.0291597	−	0.999575i	$-0.509283\pi$
$281$	−255.540	−	147.536i	−0.909397	−	0.525040i	−0.880237	+	0.474534i	$0.842616\pi$
$282$		0			0
$283$	218.410	+	378.298i	0.771767	+	1.33674i	0.936594	+	0.350418i	$0.113960\pi$
$283$	218.410	+	378.298i	0.771767	+	1.33674i	−0.164826	+	0.986323i	$0.552706\pi$
$284$		0			0
$285$	225.716	+	168.692i	0.791985	+	0.591904i
$286$		0			0
$287$	−16.7655	+	9.67955i	−0.0584163	+	0.0337267i
$288$		0			0
$289$	−143.243	+	248.104i	−0.495651	+	0.858492i
$290$		0			0
$291$	24.2833	−	42.0599i	0.0834478	−	0.144536i
$292$		0			0
$293$		−	103.704i		−	0.353939i	−0.984216	−	0.176970i	$-0.943371\pi$
$293$		−	103.704i		−	0.353939i	0.984216	−	0.176970i	$-0.0566295\pi$
$294$		0			0
$295$	11.2096	+	6.47189i	0.0379988	+	0.0219386i
$296$		0			0
$297$		−	31.8242i		−	0.107152i
$298$		0			0
$299$	163.687	−	94.5048i	0.547449	−	0.316070i
$300$		0			0
$301$	246.380	+	426.743i	0.818538	+	1.41775i
$302$		0			0
$303$			108.345i			0.357574i
$304$		0			0
$305$	−682.677			−2.23829
$306$		0			0
$307$	189.477	−	109.395i	0.617188	−	0.356334i	−0.158585	−	0.987345i	$-0.550693\pi$
$307$	189.477	−	109.395i	0.617188	−	0.356334i	0.775774	+	0.631011i	$0.217360\pi$
$308$		0			0
$309$	57.2240	+	99.1149i	0.185191	+	0.320760i
$310$		0			0
$311$	177.181			0.569715			0.284858	−	0.958570i	$-0.408054\pi$
$311$	177.181			0.569715			0.284858	+	0.958570i	$0.408054\pi$
$312$		0			0
$313$	−172.635	+	299.013i	−0.551551	+	0.955314i	0.446612	+	0.894728i	$0.352630\pi$
$313$	−172.635	+	299.013i	−0.551551	+	0.955314i	−0.998163	+	0.0605862i	$0.980703\pi$
$314$		0			0
$315$	−281.647			−0.894117
$316$		0			0
$317$	2.46052	+	1.42058i	0.00776189	+	0.00448133i	0.503876	−	0.863776i	$-0.331907\pi$
$317$	2.46052	+	1.42058i	0.00776189	+	0.00448133i	−0.496114	+	0.868257i	$0.665240\pi$
$318$		0			0
$319$	93.9608	+	54.2483i	0.294548	+	0.170057i
$320$		0			0
$321$	144.837	+	250.865i	0.451205	+	0.781510i
$322$		0			0
$323$	179.753	+	418.855i	0.556511	+	1.29676i
$324$		0			0
$325$	−191.625	+	110.635i	−0.589615	+	0.340414i
$326$		0			0
$327$	−3.46512	+	6.00176i	−0.0105967	+	0.0183540i
$328$		0			0
$329$	72.1835	−	125.026i	0.219403	−	0.380017i
$330$		0			0
$331$			90.3808i			0.273054i	0.990636	+	0.136527i	$0.0435940\pi$
$331$			90.3808i			0.273054i	−0.990636	+	0.136527i	$0.956406\pi$
$332$		0			0
$333$	−51.2839	−	29.6088i	−0.154006	−	0.0889152i
$334$		0			0
$335$			555.835i			1.65921i
$336$		0			0
$337$	271.116	−	156.529i	0.804498	−	0.464477i	−0.0405437	−	0.999178i	$-0.512909\pi$
$337$	271.116	−	156.529i	0.804498	−	0.464477i	0.845041	+	0.534701i	$0.179576\pi$
$338$		0			0
$339$	173.839	+	301.099i	0.512801	+	0.888197i
$340$		0			0
$341$		−	0.492546i		−	0.00144442i
$342$		0			0
$343$	243.540			0.710029
$344$		0			0
$345$	530.130	−	306.071i	1.53661	−	0.887162i
$346$		0			0
$347$	−9.95414	−	17.2411i	−0.0286863	−	0.0496861i	0.851326	−	0.524637i	$-0.175799\pi$
$347$	−9.95414	−	17.2411i	−0.0286863	−	0.0496861i	−0.880012	+	0.474951i	$0.842466\pi$
$348$		0			0
$349$	217.996			0.624630			0.312315	−	0.949979i	$-0.398895\pi$
$349$	217.996			0.624630			0.312315	+	0.949979i	$0.398895\pi$
$350$		0			0
$351$	−11.8974	+	20.6070i	−0.0338958	+	0.0587093i
$352$		0			0
$353$	472.812			1.33941			0.669705	−	0.742627i	$-0.266421\pi$
$353$	472.812			1.33941			0.669705	+	0.742627i	$0.266421\pi$
$354$		0			0
$355$	−413.406	−	238.680i	−1.16452	−	0.672337i
$356$		0			0
$357$	−394.533	−	227.784i	−1.10513	−	0.638050i
$358$		0			0
$359$	319.020	+	552.559i	0.888636	+	1.53916i	0.841489	+	0.540274i	$0.181680\pi$
$359$	319.020	+	552.559i	0.888636	+	1.53916i	0.0471470	+	0.998888i	$0.484987\pi$
$360$		0			0
$361$	350.957	+	84.5585i	0.972180	+	0.234234i
$362$		0			0
$363$	125.234	−	72.3041i	0.344998	−	0.199185i
$364$		0			0
$365$	−202.803	+	351.264i	−0.555623	+	0.962368i
$366$		0			0
$367$	268.439	−	464.950i	0.731442	−	1.26689i	−0.224825	−	0.974399i	$-0.572181\pi$
$367$	268.439	−	464.950i	0.731442	−	1.26689i	0.956267	−	0.292496i	$-0.0944857\pi$
$368$		0			0
$369$			5.29702i			0.0143551i
$370$		0			0
$371$	−868.281	−	501.302i	−2.34038	−	1.35122i
$372$		0			0
$373$			684.564i			1.83529i	0.397397	+	0.917647i	$0.369913\pi$
$373$			684.564i			1.83529i	−0.397397	+	0.917647i	$0.630087\pi$
$374$		0			0
$375$	−299.512	+	172.923i	−0.798698	+	0.461129i
$376$		0			0
$377$	−40.5613	−	70.2543i	−0.107590	−	0.186351i
$378$		0			0
$379$			104.581i			0.275939i	0.990436	+	0.137969i	$0.0440576\pi$
$379$			104.581i			0.275939i	−0.990436	+	0.137969i	$0.955942\pi$
$380$		0			0
$381$	−194.214			−0.509749
$382$		0			0
$383$	195.197	−	112.697i	0.509652	−	0.294248i	−0.223039	−	0.974810i	$-0.571598\pi$
$383$	195.197	−	112.697i	0.509652	−	0.294248i	0.732691	+	0.680562i	$0.238264\pi$
$384$		0			0
$385$	287.494	+	497.955i	0.746738	+	1.29339i
$386$		0			0
$387$	134.829			0.348394
$388$		0			0
$389$	−90.6057	+	156.934i	−0.232920	+	0.403429i	−0.958666	−	0.284534i	$-0.908161\pi$
$389$	−90.6057	+	156.934i	−0.232920	+	0.403429i	0.725746	+	0.687962i	$0.241495\pi$
$390$		0			0
$391$	990.148			2.53235
$392$		0			0
$393$	−268.020	−	154.742i	−0.681985	−	0.393744i
$394$		0			0
$395$	−918.239	−	530.146i	−2.32466	−	1.34214i
$396$		0			0
$397$	−42.2839	−	73.2379i	−0.106509	−	0.184478i	0.807845	−	0.589395i	$-0.200634\pi$
$397$	−42.2839	−	73.2379i	−0.106509	−	0.184478i	−0.914354	+	0.404917i	$0.867301\pi$
$398$		0			0
$399$	−331.575	+	142.296i	−0.831014	+	0.356633i
$400$		0			0
$401$	408.081	−	235.606i	1.01766	−	0.587545i	0.104233	−	0.994553i	$-0.466761\pi$
$401$	408.081	−	235.606i	1.01766	−	0.587545i	0.913425	+	0.407008i	$0.133428\pi$
$402$		0			0
$403$	−0.184138	+	0.318936i	−0.000456917	+	0.000791404i
$404$		0			0
$405$	−38.5320	+	66.7394i	−0.0951407	+	0.164789i
$406$		0			0
$407$			120.894i			0.297037i
$408$		0			0
$409$	−366.772	−	211.756i	−0.896753	−	0.517741i	−0.0206079	−	0.999788i	$-0.506560\pi$
$409$	−366.772	−	211.756i	−0.896753	−	0.517741i	−0.876145	+	0.482047i	$0.839894\pi$
$410$		0			0
$411$		−	342.330i		−	0.832920i
$412$		0			0
$413$	−14.3535	+	8.28700i	−0.0347542	+	0.0200654i
$414$		0			0
$415$	−286.220	−	495.748i	−0.689687	−	1.19457i
$416$		0			0
$417$		−	59.8236i		−	0.143462i
$418$		0			0
$419$	−47.5788			−0.113553			−0.0567766	−	0.998387i	$-0.518082\pi$
$419$	−47.5788			−0.113553			−0.0567766	+	0.998387i	$0.518082\pi$
$420$		0			0
$421$	184.109	−	106.295i	0.437313	−	0.252483i	−0.265144	−	0.964209i	$-0.585419\pi$
$421$	184.109	−	106.295i	0.437313	−	0.252483i	0.702457	+	0.711726i	$0.252086\pi$
$422$		0			0
$423$	−19.7508	−	34.2094i	−0.0466922	−	0.0808733i
$424$		0			0
$425$	−1159.14			−2.72740
$426$		0			0
$427$	437.070	−	757.028i	1.02358	−	1.77290i
$428$		0			0
$429$	48.5778			0.113235
$430$		0			0
$431$	367.151	+	211.975i	0.851859	+	0.491821i	0.861278	−	0.508134i	$-0.169665\pi$
$431$	367.151	+	211.975i	0.851859	+	0.491821i	−0.00941837	+	0.999956i	$0.502998\pi$
$432$		0			0
$433$	607.732	+	350.874i	1.40354	+	0.810333i	0.994754	−	0.102298i	$-0.0326195\pi$
$433$	607.732	+	350.874i	1.40354	+	0.810333i	0.408784	+	0.912631i	$0.365953\pi$
$434$		0			0
$435$	−131.365	−	227.531i	−0.301989	−	0.523060i
$436$		0			0
$437$	469.471	−	628.166i	1.07430	−	1.43745i
$438$		0			0
$439$	183.591	−	105.996i	0.418203	−	0.241450i	−0.276105	−	0.961127i	$-0.589044\pi$
$439$	183.591	−	105.996i	0.418203	−	0.241450i	0.694308	+	0.719678i	$0.255710\pi$
$440$		0			0
$441$	106.819	−	185.015i	0.242219	−	0.419536i
$442$		0			0
$443$	−398.107	+	689.542i	−0.898662	+	1.55653i	−0.0694561	+	0.997585i	$0.522126\pi$
$443$	−398.107	+	689.542i	−0.898662	+	1.55653i	−0.829206	+	0.558943i	$0.811207\pi$
$444$		0			0
$445$		−	354.859i		−	0.797435i
$446$		0			0
$447$	−351.850	−	203.141i	−0.787137	−	0.454454i
$448$		0			0
$449$		−	425.180i		−	0.946950i	−0.880807	−	0.473475i	$-0.842999\pi$
$449$		−	425.180i		−	0.946950i	0.880807	−	0.473475i	$-0.157001\pi$
$450$		0			0
$451$	9.36520	−	5.40700i	0.0207654	−	0.0119889i
$452$		0			0
$453$	−248.887	−	431.085i	−0.549419	−	0.951622i
$454$		0			0
$455$		−	429.917i		−	0.944873i
$456$		0			0
$457$	−95.9063			−0.209861			−0.104930	−	0.994480i	$-0.533462\pi$
$457$	−95.9063			−0.209861			−0.104930	+	0.994480i	$0.533462\pi$
$458$		0			0
$459$	−107.952	+	62.3260i	−0.235189	+	0.135787i
$460$		0			0
$461$	226.675	+	392.613i	0.491703	+	0.851655i	0.999954	−	0.00955381i	$-0.00304112\pi$
$461$	226.675	+	392.613i	0.491703	+	0.851655i	−0.508251	+	0.861209i	$0.669708\pi$
$462$		0			0
$463$	−32.0547			−0.0692327			−0.0346163	−	0.999401i	$-0.511021\pi$
$463$	−32.0547			−0.0692327			−0.0346163	+	0.999401i	$0.511021\pi$
$464$		0			0
$465$	−0.596363	+	1.03293i	−0.00128250	+	0.00222136i
$466$		0			0
$467$	−4.97056			−0.0106436			−0.00532180	−	0.999986i	$-0.501694\pi$
$467$	−4.97056			−0.0106436			−0.00532180	+	0.999986i	$0.501694\pi$
$468$		0			0
$469$	−616.371	−	355.862i	−1.31422	−	0.758767i
$470$		0			0
$471$	163.759	+	94.5460i	0.347683	+	0.200735i
$472$		0			0
$473$	−137.628	−	238.379i	−0.290968	−	0.503972i
$474$		0			0
$475$	−549.599	+	735.380i	−1.15705	+	1.54817i
$476$		0			0
$477$	−237.578	+	137.166i	−0.498068	+	0.287560i
$478$		0			0
$479$	407.363	−	705.574i	0.850446	−	1.47301i	−0.0303612	−	0.999539i	$-0.509666\pi$
$479$	407.363	−	705.574i	0.850446	−	1.47301i	0.880807	−	0.473476i	$-0.157001\pi$
$480$		0			0
$481$	45.1960	−	78.2818i	0.0939626	−	0.162748i
$482$		0			0
$483$			783.823i			1.62282i
$484$		0			0
$485$	207.930	+	120.048i	0.428721	+	0.247522i
$486$		0			0
$487$			875.221i			1.79717i	0.438801	+	0.898584i	$0.355403\pi$
$487$			875.221i			1.79717i	−0.438801	+	0.898584i	$0.644597\pi$
$488$		0			0
$489$	−148.508	+	85.7410i	−0.303697	+	0.175339i
$490$		0			0
$491$	−31.4744	−	54.5152i	−0.0641026	−	0.111029i	0.832193	−	0.554486i	$-0.187085\pi$
$491$	−31.4744	−	54.5152i	−0.0641026	−	0.111029i	−0.896296	+	0.443457i	$0.853752\pi$
$492$		0			0
$493$		−	424.970i		−	0.862008i
$494$		0			0
$495$	157.328			0.317834
$496$		0			0
$497$	529.349	−	305.620i	1.06509	−	0.614929i
$498$		0			0
$499$	−6.20946	−	10.7551i	−0.0124438	−	0.0215533i	0.859736	−	0.510738i	$-0.170628\pi$
$499$	−6.20946	−	10.7551i	−0.0124438	−	0.0215533i	−0.872180	+	0.489185i	$0.837294\pi$
$500$		0			0
$501$	524.468			1.04684
$502$		0			0
$503$	116.743	−	202.205i	0.232094	−	0.401998i	−0.726330	−	0.687346i	$-0.758776\pi$
$503$	116.743	−	202.205i	0.232094	−	0.401998i	0.958424	+	0.285348i	$0.0921091\pi$
$504$		0			0
$505$	−535.619			−1.06063
$506$		0			0
$507$	222.045	+	128.198i	0.437958	+	0.252855i
$508$		0			0
$509$	546.952	+	315.783i	1.07456	+	0.620399i	0.929424	−	0.369013i	$-0.120304\pi$
$509$	546.952	+	315.783i	1.07456	+	0.620399i	0.145138	+	0.989411i	$0.453638\pi$
$510$		0			0
$511$	−259.680	−	449.780i	−0.508181	−	0.880195i
$512$		0			0
$513$	−11.6439	+	98.0379i	−0.0226976	+	0.191107i
$514$		0			0
$515$	−489.990	+	282.896i	−0.951437	+	0.549313i
$516$		0			0
$517$	−40.3217	+	69.8393i	−0.0779918	+	0.135086i
$518$		0			0
$519$	196.513	−	340.370i	0.378637	−	0.655819i
$520$		0			0
$521$			396.828i			0.761665i	0.924644	+	0.380833i	$0.124363\pi$
$521$			396.828i			0.761665i	−0.924644	+	0.380833i	$0.875637\pi$
$522$		0			0
$523$	−463.389	−	267.538i	−0.886021	−	0.511545i	−0.0133823	−	0.999910i	$-0.504260\pi$
$523$	−463.389	−	267.538i	−0.886021	−	0.511545i	−0.872639	+	0.488366i	$0.837593\pi$
$524$		0			0
$525$		−	917.603i		−	1.74782i
$526$		0			0
$527$	−1.67078	+	0.964625i	−0.00317036	+	0.00183041i
$528$		0			0
$529$	−587.295	−	1017.22i	−1.11020	−	1.92292i
$530$		0			0
$531$			4.53496i			0.00854042i
$532$		0			0
$533$	−8.08560			−0.0151700
$534$		0			0
$535$	−1240.19	+	716.023i	−2.31811	+	1.33836i
$536$		0			0
$537$	54.3878	+	94.2024i	0.101281	+	0.175423i
$538$		0			0
$539$	−436.145			−0.809175
$540$		0			0
$541$	161.126	−	279.078i	0.297830	−	0.515857i	−0.677809	−	0.735238i	$-0.737070\pi$
$541$	161.126	−	279.078i	0.297830	−	0.515857i	0.975639	+	0.219381i	$0.0704038\pi$
$542$		0			0
$543$	614.006			1.13077
$544$		0			0
$545$	−29.6706	−	17.1304i	−0.0544415	−	0.0314318i
$546$		0			0
$547$	−38.6396	−	22.3086i	−0.0706392	−	0.0407835i	0.464264	−	0.885697i	$-0.346319\pi$
$547$	−38.6396	−	22.3086i	−0.0706392	−	0.0407835i	−0.534904	+	0.844913i	$0.679652\pi$
$548$		0			0
$549$	−119.591	−	207.137i	−0.217834	−	0.377299i
$550$		0			0
$551$	−269.608	−	201.496i	−0.489307	−	0.365692i
$552$		0			0
$553$	1175.77	−	678.830i	2.12616	−	1.22754i
$554$		0			0
$555$	146.375	−	253.530i	0.263740	−	0.456810i
$556$		0			0
$557$	93.2339	−	161.486i	0.167386	−	0.289921i	−0.770114	−	0.637906i	$-0.779801\pi$
$557$	93.2339	−	161.486i	0.167386	−	0.289921i	0.937500	+	0.347985i	$0.113134\pi$
$558$		0			0
$559$			205.808i			0.368172i
$560$		0			0
$561$	220.386	+	127.240i	0.392845	+	0.226809i
$562$		0			0
$563$			439.241i			0.780179i	0.920777	+	0.390090i	$0.127556\pi$
$563$			439.241i			0.780179i	−0.920777	+	0.390090i	$0.872444\pi$
$564$		0			0
$565$	−1488.53	+	859.402i	−2.63456	+	1.52107i
$566$		0			0
$567$	−49.3386	−	85.4570i	−0.0870170	−	0.150718i
$568$		0			0
$569$			122.467i			0.215233i	0.994192	+	0.107616i	$0.0343218\pi$
$569$			122.467i			0.215233i	−0.994192	+	0.107616i	$0.965678\pi$
$570$		0			0
$571$	308.267			0.539871			0.269936	−	0.962878i	$-0.412998\pi$
$571$	308.267			0.539871			0.269936	+	0.962878i	$0.412998\pi$
$572$		0			0
$573$	367.647	−	212.261i	0.641618	−	0.370439i
$574$		0			0
$575$	997.177	+	1727.16i	1.73422	+	3.00376i
$576$		0			0
$577$	464.514			0.805051			0.402525	−	0.915409i	$-0.368133\pi$
$577$	464.514			0.805051			0.402525	+	0.915409i	$0.368133\pi$
$578$		0			0
$579$	−217.732	+	377.123i	−0.376049	+	0.651336i
$580$		0			0
$581$	732.986			1.26159
$582$		0			0
$583$	485.022	+	280.027i	0.831941	+	0.480322i
$584$		0			0
$585$	−101.874	−	58.8168i	−0.174143	−	0.100542i
$586$		0			0
$587$	−19.0488	−	32.9936i	−0.0324512	−	0.0562071i	0.849344	−	0.527840i	$-0.176998\pi$
$587$	−19.0488	−	32.9936i	−0.0324512	−	0.0562071i	−0.881795	+	0.471633i	$0.843665\pi$
$588$		0			0
$589$	−0.180213	+	1.51734i	−0.000305965	+	0.00257613i
$590$		0			0
$591$	−305.157	+	176.182i	−0.516340	+	0.298109i
$592$		0			0
$593$	369.349	−	639.732i	0.622849	−	1.07881i	−0.366104	−	0.930574i	$-0.619308\pi$
$593$	369.349	−	639.732i	0.622849	−	1.07881i	0.988953	−	0.148232i	$-0.0473582\pi$
$594$		0			0
$595$	1126.08	−	1950.44i	1.89258	−	3.27804i
$596$		0			0
$597$			278.810i			0.467019i
$598$		0			0
$599$	−261.661	−	151.070i	−0.436830	−	0.252204i	0.265422	−	0.964132i	$-0.414489\pi$
$599$	−261.661	−	151.070i	−0.436830	−	0.252204i	−0.702252	+	0.711928i	$0.747822\pi$
$600$		0			0
$601$			1018.62i			1.69487i	0.530896	+	0.847437i	$0.321855\pi$
$601$			1018.62i			1.69487i	−0.530896	+	0.847437i	$0.678145\pi$
$602$		0			0
$603$	−168.651	+	97.3707i	−0.279686	+	0.161477i
$604$		0			0
$605$	357.447	+	619.116i	0.590821	+	1.02333i
$606$		0			0
$607$		−	1049.33i		−	1.72871i	−0.502882	−	0.864355i	$-0.667727\pi$
$607$		−	1049.33i		−	1.72871i	0.502882	−	0.864355i	$-0.332273\pi$
$608$		0			0
$609$	336.415			0.552406
$610$		0			0
$611$	52.2186	−	30.1484i	0.0854642	−	0.0493428i
$612$		0			0
$613$	354.811	+	614.550i	0.578811	+	1.00253i	0.995616	+	0.0935337i	$0.0298163\pi$
$613$	354.811	+	614.550i	0.578811	+	1.00253i	−0.416806	+	0.908996i	$0.636850\pi$
$614$		0			0
$615$	−26.1867			−0.0425799
$616$		0			0
$617$	−538.505	+	932.718i	−0.872779	+	1.51170i	−0.0136695	+	0.999907i	$0.504351\pi$
$617$	−538.505	+	932.718i	−0.872779	+	1.51170i	−0.859110	+	0.511791i	$0.828982\pi$
$618$		0			0
$619$	−733.159			−1.18442			−0.592212	−	0.805782i	$-0.701745\pi$
$619$	−733.159			−1.18442			−0.592212	+	0.805782i	$0.701745\pi$
$620$		0			0
$621$	185.736	+	107.234i	0.299091	+	0.172680i
$622$		0			0
$623$	393.506	+	227.191i	0.631631	+	0.364672i
$624$		0			0
$625$	−250.883	−	434.542i	−0.401412	−	0.695267i
$626$		0			0
$627$	185.218	−	79.4868i	0.295403	−	0.126773i
$628$		0			0
$629$	410.088	−	236.764i	0.651968	−	0.376414i
$630$		0			0
$631$	−391.977	+	678.923i	−0.621199	+	1.07595i	0.368064	+	0.929800i	$0.380021\pi$
$631$	−391.977	+	678.923i	−0.621199	+	1.07595i	−0.989263	+	0.146148i	$0.953313\pi$
$632$		0			0
$633$	−9.23560	+	15.9965i	−0.0145902	+	0.0252710i
$634$		0			0
$635$		−	960.129i		−	1.51201i
$636$		0			0
$637$	282.415	+	163.052i	0.443352	+	0.255969i
$638$		0			0
$639$		−	167.247i		−	0.261732i
$640$		0			0
$641$	−806.996	+	465.920i	−1.25896	+	0.726864i	−0.972873	−	0.231339i	$-0.925689\pi$
$641$	−806.996	+	465.920i	−1.25896	+	0.726864i	−0.286092	+	0.958202i	$0.592356\pi$
$642$		0			0
$643$	−166.175	−	287.824i	−0.258437	−	0.447626i	0.707386	−	0.706827i	$-0.249874\pi$
$643$	−166.175	−	287.824i	−0.258437	−	0.447626i	−0.965823	+	0.259201i	$0.916541\pi$
$644$		0			0
$645$			666.546i			1.03341i
$646$		0			0
$647$	−37.0987			−0.0573395			−0.0286698	−	0.999589i	$-0.509127\pi$
$647$	−37.0987			−0.0573395			−0.0286698	+	0.999589i	$0.509127\pi$
$648$		0			0
$649$	8.01787	−	4.62912i	0.0123542	−	0.00713269i
$650$		0			0
$651$	−0.763618	−	1.32263i	−0.00117299	−	0.00203168i
$652$		0			0
$653$	464.586			0.711465			0.355732	−	0.934588i	$-0.384231\pi$
$653$	464.586			0.711465			0.355732	+	0.934588i	$0.384231\pi$
$654$		0			0
$655$	764.989	−	1325.00i	1.16792	−	2.02290i
$656$		0			0
$657$	−142.107			−0.216297
$658$		0			0
$659$	737.058	+	425.541i	1.11845	+	0.645737i	0.941004	−	0.338394i	$-0.109884\pi$
$659$	737.058	+	425.541i	1.11845	+	0.645737i	0.177444	+	0.984131i	$0.443217\pi$
$660$		0			0
$661$	−618.959	−	357.356i	−0.936398	−	0.540630i	−0.0475687	−	0.998868i	$-0.515147\pi$
$661$	−618.959	−	357.356i	−0.936398	−	0.540630i	−0.888829	+	0.458238i	$0.848481\pi$
$662$		0			0
$663$	−95.1370	−	164.782i	−0.143495	−	0.248540i
$664$		0			0
$665$	−703.465	−	1639.19i	−1.05784	−	2.46495i
$666$		0			0
$667$	−633.219	+	365.589i	−0.949353	+	0.548109i
$668$		0			0
$669$	205.920	−	356.663i	0.307802	−	0.533129i
$670$		0			0
$671$	−244.148	+	422.876i	−0.363856	+	0.630218i
$672$		0			0
$673$		−	393.732i		−	0.585040i	−0.956259	−	0.292520i	$-0.905506\pi$
$673$		−	393.732i		−	0.585040i	0.956259	−	0.292520i	$-0.0944938\pi$
$674$		0			0
$675$	−217.436	−	125.537i	−0.322128	−	0.185981i
$676$		0			0
$677$			222.890i			0.329232i	0.986358	+	0.164616i	$0.0526384\pi$
$677$			222.890i			0.329232i	−0.986358	+	0.164616i	$0.947362\pi$
$678$		0			0
$679$	−266.246	+	153.717i	−0.392114	+	0.226387i
$680$		0			0
$681$	49.3999	+	85.5632i	0.0725403	+	0.125643i
$682$		0			0
$683$			401.388i			0.587684i	0.955854	+	0.293842i	$0.0949339\pi$
$683$			401.388i			0.587684i	−0.955854	+	0.293842i	$0.905066\pi$
$684$		0			0
$685$	1692.36			2.47060
$686$		0			0
$687$	−482.580	+	278.618i	−0.702446	+	0.405557i
$688$		0			0
$689$	−209.376	−	362.649i	−0.303884	−	0.526342i
$690$		0			0
$691$	−23.7065			−0.0343075			−0.0171538	−	0.999853i	$-0.505460\pi$
$691$	−23.7065			−0.0343075			−0.0171538	+	0.999853i	$0.505460\pi$
$692$		0			0
$693$	−100.726	+	174.463i	−0.145348	+	0.251750i
$694$		0			0
$695$	295.747			0.425536
$696$		0			0
$697$	−36.6825	−	21.1786i	−0.0526291	−	0.0303854i
$698$		0			0
$699$	−217.351	−	125.488i	−0.310946	−	0.179525i
$700$		0			0
$701$	−488.122	−	845.452i	−0.696322	−	1.20607i	−0.969733	−	0.244168i	$-0.921485\pi$
$701$	−488.122	−	845.452i	−0.696322	−	1.20607i	0.273410	−	0.961897i	$-0.411848\pi$
$702$		0			0
$703$	44.2328	−	372.427i	0.0629200	−	0.529768i
$704$		0			0
$705$	169.119	−	97.6412i	0.239886	−	0.138498i
$706$		0			0
$707$	342.919	−	593.954i	0.485034	−	0.840104i
$708$		0			0
$709$	76.7333	−	132.906i	0.108227	−	0.187455i	−0.806825	−	0.590791i	$-0.798816\pi$
$709$	76.7333	−	132.906i	0.108227	−	0.187455i	0.915052	+	0.403335i	$0.132149\pi$
$710$		0			0
$711$		−	371.482i		−	0.522478i
$712$		0			0
$713$	2.87464	+	1.65968i	0.00403176	+	0.00232774i
$714$		0			0
$715$			240.152i			0.335877i
$716$		0			0
$717$	409.359	−	236.343i	0.570932	−	0.329628i
$718$		0			0
$719$	−115.422	−	199.916i	−0.160531	−	0.278048i	0.774528	−	0.632539i	$-0.217987\pi$
$719$	−115.422	−	199.916i	−0.160531	−	0.278048i	−0.935059	+	0.354491i	$0.884654\pi$
$720$		0			0
$721$		−	724.474i		−	1.00482i
$722$		0			0
$723$	751.267			1.03910
$724$		0			0
$725$	741.295	−	427.987i	1.02248	−	0.590327i
$726$		0			0
$727$	−341.504	−	591.502i	−0.469744	−	0.813620i	0.529658	−	0.848212i	$-0.322320\pi$
$727$	−341.504	−	591.502i	−0.469744	−	0.813620i	−0.999402	+	0.0345912i	$0.988987\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−539.074	+	933.703i	−0.737447	+	1.27730i
$732$		0			0
$733$	−1445.93			−1.97262			−0.986310	−	0.164902i	$-0.947269\pi$
$733$	−1445.93			−1.97262			−0.986310	+	0.164902i	$0.947269\pi$
$734$		0			0
$735$	914.652	+	528.074i	1.24442	+	0.718469i
$736$		0			0
$737$	344.305	+	198.785i	0.467171	+	0.269721i
$738$		0			0
$739$	319.733	+	553.794i	0.432656	+	0.749382i	0.997101	−	0.0760883i	$-0.0242431\pi$
$739$	319.733	+	553.794i	0.432656	+	0.749382i	−0.564445	+	0.825471i	$0.690910\pi$
$740$		0			0
$741$	−149.649	−	17.7737i	−0.201956	−	0.0239861i
$742$		0			0
$743$	35.6677	−	20.5928i	0.0480050	−	0.0277157i	−0.475805	−	0.879551i	$-0.657843\pi$
$743$	35.6677	−	20.5928i	0.0480050	−	0.0277157i	0.523810	+	0.851835i	$0.324510\pi$
$744$		0			0
$745$	1004.26	−	1739.43i	1.34800	−	2.33480i
$746$		0			0
$747$	100.280	−	173.689i	0.134243	−	0.232516i
$748$		0			0
$749$		−	1833.68i		−	2.44817i
$750$		0			0
$751$	−55.3461	−	31.9541i	−0.0736965	−	0.0425487i	0.462699	−	0.886515i	$-0.346881\pi$
$751$	−55.3461	−	31.9541i	−0.0736965	−	0.0425487i	−0.536395	+	0.843967i	$0.680214\pi$
$752$		0			0
$753$			631.090i			0.838100i
$754$		0			0
$755$	2131.14	−	1230.41i	2.82270	−	1.62968i
$756$		0			0
$757$	434.877	+	753.229i	0.574474	+	0.995019i	0.996099	+	0.0882480i	$0.0281268\pi$
$757$	434.877	+	753.229i	0.574474	+	0.995019i	−0.421624	+	0.906771i	$0.638540\pi$
$758$		0			0
$759$		−	437.843i		−	0.576869i
$760$		0			0
$761$	−501.368			−0.658828			−0.329414	−	0.944186i	$-0.606851\pi$
$761$	−501.368			−0.658828			−0.329414	+	0.944186i	$0.606851\pi$
$762$		0			0
$763$	37.9920	−	21.9347i	0.0497930	−	0.0287480i
$764$		0			0
$765$	−308.118	−	533.677i	−0.402769	−	0.697617i
$766$		0			0
$767$	−6.92236			−0.00902524
$768$		0			0
$769$	−157.943	+	273.565i	−0.205388	+	0.355742i	−0.950256	−	0.311469i	$-0.899179\pi$
$769$	−157.943	+	273.565i	−0.205388	+	0.355742i	0.744869	+	0.667211i	$0.232512\pi$
$770$		0			0
$771$	−213.276			−0.276623
$772$		0			0
$773$	703.707	+	406.285i	0.910358	+	0.525595i	0.880546	−	0.473960i	$-0.157176\pi$
$773$	703.707	+	406.285i	0.910358	+	0.525595i	0.0298115	+	0.999556i	$0.490509\pi$
$774$		0			0
$775$	−3.36528	−	1.94295i	−0.00434230	−	0.00250703i
$776$		0			0
$777$	187.428	+	324.635i	0.241220	+	0.417805i
$778$		0			0
$779$	−30.8288	+	13.2303i	−0.0395748	+	0.0169837i
$780$		0			0
$781$	−295.694	+	170.719i	−0.378610	+	0.218591i
$782$		0			0
$783$	46.0249	−	79.7174i	0.0587801	−	0.101810i
$784$		0			0
$785$	−467.403	+	809.566i	−0.595418	+	1.03129i
$786$		0			0
$787$		−	756.944i		−	0.961809i	−0.876773	−	0.480904i	$-0.840308\pi$
$787$		−	756.944i		−	0.961809i	0.876773	−	0.480904i	$-0.159692\pi$
$788$		0			0
$789$	−470.940	−	271.897i	−0.596882	−	0.344610i
$790$		0			0
$791$		−	2200.86i		−	2.78238i
$792$		0			0
$793$	316.183	−	182.548i	0.398718	−	0.230200i
$794$		0			0
$795$	−678.101	−	1174.51i	−0.852957	−	1.47737i
$796$		0			0
$797$			533.380i			0.669235i	0.942354	+	0.334617i	$0.108607\pi$
$797$			533.380i			0.669235i	−0.942354	+	0.334617i	$0.891393\pi$
$798$		0			0
$799$	315.872			0.395334
$800$		0			0
$801$	107.671	−	62.1638i	0.134421	−	0.0776078i
$802$		0			0
$803$	145.058	+	251.247i	0.180644	+	0.312885i
$804$		0			0
$805$	−3874.95			−4.81360
$806$		0			0
$807$	−36.4179	+	63.0776i	−0.0451275	+	0.0781631i
$808$		0			0
$809$	−456.724			−0.564554			−0.282277	−	0.959333i	$-0.591090\pi$
$809$	−456.724			−0.564554			−0.282277	+	0.959333i	$0.591090\pi$
$810$		0			0
$811$	793.417	+	458.080i	0.978320	+	0.564833i	0.901762	−	0.432232i	$-0.142274\pi$
$811$	793.417	+	458.080i	0.978320	+	0.564833i	0.0765574	+	0.997065i	$0.475607\pi$
$812$		0			0
$813$	−330.691	−	190.924i	−0.406754	−	0.234839i
$814$		0			0
$815$	−423.874	−	734.171i	−0.520091	−	0.900823i
$816$		0			0
$817$	336.759	+	784.706i	0.412190	+	0.960472i
$818$		0			0
$819$	130.445	−	75.3125i	0.159274	−	0.0919567i
$820$		0			0
$821$	−219.386	+	379.987i	−0.267217	+	0.462834i	−0.968142	−	0.250401i	$-0.919438\pi$
$821$	−219.386	+	379.987i	−0.267217	+	0.462834i	0.700925	+	0.713235i	$0.252771\pi$
$822$		0			0
$823$	111.152	−	192.520i	0.135057	−	0.233925i	−0.790562	−	0.612381i	$-0.790212\pi$
$823$	111.152	−	192.520i	0.135057	−	0.233925i	0.925619	+	0.378456i	$0.123545\pi$
$824$		0			0
$825$			512.573i			0.621301i
$826$		0			0
$827$	−137.528	−	79.4017i	−0.166297	−	0.0960117i	0.414542	−	0.910030i	$-0.363942\pi$
$827$	−137.528	−	79.4017i	−0.166297	−	0.0960117i	−0.580839	+	0.814019i	$0.697275\pi$
$828$		0			0
$829$		−	1100.41i		−	1.32740i	−0.748001	−	0.663698i	$-0.768986\pi$
$829$		−	1100.41i		−	1.32740i	0.748001	−	0.663698i	$-0.231014\pi$
$830$		0			0
$831$	315.678	−	182.257i	0.379877	−	0.219322i
$832$		0			0
$833$	854.168	+	1479.46i	1.02541	+	1.77606i
$834$		0			0
$835$			2592.79i			3.10514i
$836$		0			0
$837$	−0.417881			−0.000499261
$838$		0			0
$839$	−1188.13	+	685.970i	−1.41613	+	0.817604i	−0.995956	−	0.0898387i	$-0.971365\pi$
$839$	−1188.13	+	685.970i	−1.41613	+	0.817604i	−0.420176	+	0.907443i	$0.638032\pi$
$840$		0			0
$841$	−263.590	−	456.551i	−0.313424	−	0.542867i
$842$		0			0
$843$	511.081			0.606264
$844$		0			0
$845$	−633.765	+	1097.71i	−0.750017	+	1.29907i
$846$		0			0
$847$	−915.392			−1.08075
$848$		0			0
$849$	−655.231	−	378.298i	−0.771767	−	0.445580i
$850$		0			0
$851$	−705.573	−	407.363i	−0.829111	−	0.478687i
$852$		0			0
$853$	−135.668	−	234.983i	−0.159048	−	0.275479i	0.775478	−	0.631375i	$-0.217509\pi$
$853$	−135.668	−	234.983i	−0.159048	−	0.275479i	−0.934526	+	0.355896i	$0.884176\pi$
$854$		0			0
$855$	−484.665	−	57.5633i	−0.566860	−	0.0673255i
$856$		0			0
$857$	−1062.95	+	613.694i	−1.24031	+	0.716096i	−0.969158	−	0.246440i	$-0.920739\pi$
$857$	−1062.95	+	613.694i	−1.24031	+	0.716096i	−0.271156	+	0.962535i	$0.587406\pi$
$858$		0			0
$859$	413.878	−	716.858i	0.481814	−	0.834527i	−0.517968	−	0.855400i	$-0.673311\pi$
$859$	413.878	−	716.858i	0.481814	−	0.834527i	0.999782	+	0.0208735i	$0.00664471\pi$
$860$		0			0
$861$	16.7655	−	29.0387i	0.0194721	−	0.0337267i
$862$		0			0
$863$		−	490.427i		−	0.568281i	−0.958783	−	0.284141i	$-0.908292\pi$
$863$		−	490.427i		−	0.568281i	0.958783	−	0.284141i	$-0.0917082\pi$
$864$		0			0
$865$	1682.67	+	971.491i	1.94528	+	1.12311i
$866$		0			0
$867$		−	496.209i		−	0.572328i
$868$		0			0
$869$	−656.784	+	379.195i	−0.755793	+	0.436357i
$870$		0			0
$871$	−148.631	−	257.436i	−0.170644	−	0.295563i
$872$		0			0
$873$			84.1198i			0.0963572i
$874$		0			0
$875$	2189.26			2.50201
$876$		0			0
$877$	85.5065	−	49.3672i	0.0974988	−	0.0562910i	−0.450458	−	0.892798i	$-0.648739\pi$
$877$	85.5065	−	49.3672i	0.0974988	−	0.0562910i	0.547957	+	0.836507i	$0.315406\pi$
$878$		0			0
$879$	89.8105	+	155.556i	0.102173	+	0.176970i
$880$		0			0
$881$	−1023.77			−1.16205			−0.581025	−	0.813886i	$-0.697348\pi$
$881$	−1023.77			−1.16205			−0.581025	+	0.813886i	$0.697348\pi$
$882$		0			0
$883$	52.0052	−	90.0757i	0.0588960	−	0.102011i	−0.835074	−	0.550138i	$-0.814575\pi$
$883$	52.0052	−	90.0757i	0.0588960	−	0.102011i	0.893970	+	0.448127i	$0.147909\pi$
$884$		0			0
$885$	−22.4193			−0.0253325
$886$		0			0
$887$	492.674	+	284.446i	0.555439	+	0.320683i	0.751313	−	0.659946i	$-0.229421\pi$
$887$	492.674	+	284.446i	0.555439	+	0.320683i	−0.195874	+	0.980629i	$0.562754\pi$
$888$		0			0
$889$	1064.70	+	614.703i	1.19763	+	0.691454i
$890$		0			0
$891$	27.5606	+	47.7363i	0.0309322	+	0.0535761i
$892$		0			0
$893$	149.768	−	200.394i	0.167714	−	0.224406i
$894$		0			0
$895$	−465.704	+	268.874i	−0.520340	+	0.300418i
$896$		0			0
$897$	−163.687	+	283.514i	−0.182483	+	0.316070i
$898$		0			0
$899$	0.712331	−	1.23379i	0.000792359	−	0.00137241i
$900$		0			0
$901$		−	2193.68i		−	2.43471i
$902$		0			0
$903$	−739.140	−	426.743i	−0.818538	−	0.472583i
$904$		0			0
$905$			3035.44i			3.35407i
$906$		0			0
$907$	−147.520	+	85.1709i	−0.162647	+	0.0939040i	−0.579114	−	0.815247i	$-0.696601\pi$
$907$	−147.520	+	85.1709i	−0.162647	+	0.0939040i	0.416467	+	0.909151i	$0.363268\pi$
$908$		0			0
$909$	−93.8293	−	162.517i	−0.103223	−	0.178787i
$910$		0			0
$911$			631.493i			0.693187i	0.938015	+	0.346593i	$0.112662\pi$
$911$			631.493i			0.693187i	−0.938015	+	0.346593i	$0.887338\pi$
$912$		0			0
$913$	−409.446			−0.448463
$914$		0			0
$915$	1024.02	−	591.216i	1.11914	−	0.646138i
$916$		0			0
$917$	979.537	+	1696.61i	1.06820	+	1.85017i
$918$		0			0
$919$	−605.939			−0.659346			−0.329673	−	0.944095i	$-0.606939\pi$
$919$	−605.939			−0.659346			−0.329673	+	0.944095i	$0.606939\pi$
$920$		0			0
$921$	−189.477	+	328.184i	−0.205729	+	0.356334i
$922$		0			0
$923$	255.293			0.276590
$924$		0			0
$925$	825.999	+	476.890i	0.892971	+	0.515557i
$926$		0			0
$927$	−171.672	−	99.1149i	−0.185191	−	0.106920i
$928$		0			0
$929$	420.152	+	727.725i	0.452263	+	0.783343i	0.998526	−	0.0542710i	$-0.0172835\pi$
$929$	420.152	+	727.725i	0.452263	+	0.783343i	−0.546263	+	0.837614i	$0.683950\pi$
$930$		0			0
$931$	1343.59	+	159.577i	1.44317	+	0.171404i
$932$		0			0
$933$	−265.772	+	153.444i	−0.284858	+	0.164463i
$934$		0			0
$935$	−629.031	+	1089.51i	−0.672760	+	1.16526i
$936$		0			0
$937$	550.700	−	953.841i	0.587727	−	1.01797i	−0.406802	−	0.913516i	$-0.633356\pi$
$937$	550.700	−	953.841i	0.587727	−	1.01797i	0.994529	−	0.104457i	$-0.0333105\pi$
$938$		0			0
$939$		−	598.026i		−	0.636876i
$940$		0			0
$941$	1357.67	+	783.850i	1.44279	+	0.832997i	0.998035	−	0.0626535i	$-0.0199563\pi$
$941$	1357.67	+	783.850i	1.44279	+	0.832997i	0.444758	+	0.895651i	$0.353290\pi$
$942$		0			0
$943$			72.8774i			0.0772825i
$944$		0			0
$945$	422.470	−	243.913i	0.447058	−	0.258109i
$946$		0			0
$947$	710.921	+	1231.35i	0.750709	+	1.30027i	0.947479	+	0.319817i	$0.103621\pi$
$947$	710.921	+	1231.35i	0.750709	+	1.30027i	−0.196771	+	0.980450i	$0.563045\pi$
$948$		0			0
$949$		−	216.918i		−	0.228576i
$950$		0			0
$951$	−4.92104			−0.00517459
$952$		0			0
$953$	−157.415	+	90.8836i	−0.165178	+	0.0953657i	−0.580310	−	0.814395i	$-0.697069\pi$
$953$	−157.415	+	90.8836i	−0.165178	+	0.0953657i	0.415132	+	0.909761i	$0.363735\pi$
$954$		0			0
$955$	1049.35	+	1817.52i	1.09879	+	1.90316i
$956$		0			0
$957$	−187.922			−0.196365
$958$		0			0
$959$	−1083.50	+	1876.68i	−1.12982	+	1.95691i
$960$		0			0
$961$	960.994			0.999993
$962$		0			0
$963$	−434.510	−	250.865i	−0.451205	−	0.260503i
$964$		0			0
$965$	−1864.37	−	1076.39i	−1.93199	−	1.11543i
$966$		0			0
$967$	22.4256	+	38.8423i	0.0231909	+	0.0401679i	0.877388	−	0.479782i	$-0.159284\pi$
$967$	22.4256	+	38.8423i	0.0231909	+	0.0401679i	−0.854197	+	0.519949i	$0.825951\pi$
$968$		0			0
$969$	−632.368	−	472.612i	−0.652599	−	0.487731i
$970$		0			0
$971$	−438.132	+	252.955i	−0.451217	+	0.260510i	−0.708344	−	0.705867i	$-0.750557\pi$
$971$	−438.132	+	252.955i	−0.451217	+	0.260510i	0.257127	+	0.966378i	$0.417224\pi$
$972$		0			0
$973$	−189.346	+	327.957i	−0.194600	+	0.337058i
$974$		0			0
$975$	191.625	−	331.904i	0.196538	−	0.340414i
$976$		0			0
$977$			429.210i			0.439314i	0.975577	+	0.219657i	$0.0704938\pi$
$977$			429.210i			0.439314i	−0.975577	+	0.219657i	$0.929506\pi$
$978$		0			0
$979$	−219.813	−	126.909i	−0.224528	−	0.129631i
$980$		0			0
$981$		−	12.0035i		−	0.0122360i
$982$		0			0
$983$	−518.890	+	299.581i	−0.527864	+	0.304762i	−0.740146	−	0.672446i	$-0.765244\pi$
$983$	−518.890	+	299.581i	−0.527864	+	0.304762i	0.212282	+	0.977208i	$0.431910\pi$
$984$		0			0
$985$	−870.985	−	1508.59i	−0.884249	−	1.53156i
$986$		0			0
$987$			250.051i			0.253345i
$988$		0			0
$989$	1855.00			1.87563
$990$		0			0
$991$	−401.611	+	231.870i	−0.405258	+	0.233976i	−0.688750	−	0.724999i	$-0.741840\pi$
$991$	−401.611	+	231.870i	−0.405258	+	0.233976i	0.283492	+	0.958975i	$0.408507\pi$
$992$		0			0
$993$	−78.2721	−	135.571i	−0.0788239	−	0.136527i
$994$		0			0
$995$	−1378.34			−1.38527
$996$		0			0
$997$	−147.980	+	256.308i	−0.148425	+	0.257080i	−0.930646	−	0.365922i	$-0.880754\pi$
$997$	−147.980	+	256.308i	−0.148425	+	0.257080i	0.782221	+	0.623002i	$0.214087\pi$
$998$		0			0
$999$	102.568			0.102670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.i.145.1		20
4.3	odd	2		456.3.w.b.145.1	✓	20
12.11	even	2		1368.3.bv.b.145.10		20
19.8	odd	6	inner	912.3.be.i.673.1		20
76.27	even	6		456.3.w.b.217.1	yes	20
228.179	odd	6		1368.3.bv.b.217.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.b.145.1	✓	20	4.3	odd	2
456.3.w.b.217.1	yes	20	76.27	even	6
912.3.be.i.145.1		20	1.1	even	1	trivial
912.3.be.i.673.1		20	19.8	odd	6	inner
1368.3.bv.b.145.10		20	12.11	even	2
1368.3.bv.b.217.10		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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-4.28133 - 7.41548i) q^{5} +10.9641 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-4.28133 - 7.41548i) q^{5} +10.9641 q^{7} +(1.50000 - 2.59808i) q^{9} -6.12457 q^{11} +(3.96581 + 2.28966i) q^{13} +(12.8440 + 7.41548i) q^{15} +(11.9946 + 20.7753i) q^{17} +(18.8674 + 2.24086i) q^{19} +(-16.4462 + 9.49523i) q^{21} +(20.6373 - 35.7448i) q^{23} +(-24.1596 + 41.8457i) q^{25} +5.19615i q^{27} +(-15.3416 - 8.85749i) q^{29} +0.0804213i q^{31} +(9.18686 - 5.30403i) q^{33} +(-46.9411 - 81.3044i) q^{35} -19.7392i q^{37} -7.93162 q^{39} +(-1.52912 + 0.882837i) q^{41} +(22.4714 + 38.9217i) q^{43} -25.6880 q^{45} +(6.58360 - 11.4031i) q^{47} +71.2124 q^{49} +(-35.9839 - 20.7753i) q^{51} +(-79.1928 - 45.7220i) q^{53} +(26.2213 + 45.4167i) q^{55} +(-30.2417 + 12.9783i) q^{57} +(-1.30913 + 0.755827i) q^{59} +(39.8636 - 69.0458i) q^{61} +(16.4462 - 28.4857i) q^{63} -39.2112i q^{65} +(-56.2170 - 32.4569i) q^{67} +71.4896i q^{69} +(48.2800 - 27.8745i) q^{71} +(-23.6845 - 41.0228i) q^{73} -83.6913i q^{75} -67.1507 q^{77} +(107.238 - 61.9137i) q^{79} +(-4.50000 - 7.79423i) q^{81} +66.8531 q^{83} +(102.706 - 177.892i) q^{85} +30.6832 q^{87} +(35.8903 + 20.7213i) q^{89} +(43.4817 + 25.1042i) q^{91} +(-0.0696469 - 0.120632i) q^{93} +(-64.1605 - 149.505i) q^{95} +(-24.2833 + 14.0200i) q^{97} +(-9.18686 + 15.9121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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