LMFDB - Embedded newform 156.4.q.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,4,Mod(49,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("156.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	156.q (of order $6$, degree $2$, 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:	$9.20429796090$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 443x^{4} + 53128x^{2} + 1862832 $ x^6 + 443x^4 + 53128x^2 + 1862832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$-16.5475i$ of defining polynomial
Character	$\chi$	$=$	156.49
Dual form			156.4.q.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 2.59808i) q^{3} +14.8155i q^{5} +(3.28368 + 1.89583i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-3.38576 + 1.95477i) q^{11} +(-44.4652 - 14.8273i) q^{13} +(-38.4917 + 22.2232i) q^{15} +(-33.6203 + 58.2320i) q^{17} +(-9.91216 - 5.72279i) q^{19} +11.3750i q^{21} +(26.4388 + 45.7933i) q^{23} -94.4977 q^{25} -27.0000 q^{27} +(29.3449 + 50.8269i) q^{29} +182.725i q^{31} +(-10.1573 - 5.86431i) q^{33} +(-28.0876 + 48.6492i) q^{35} +(-33.9350 + 19.5924i) q^{37} +(-28.1754 - 137.765i) q^{39} +(197.469 - 114.009i) q^{41} +(-178.087 + 308.456i) q^{43} +(-115.475 - 66.6695i) q^{45} -108.483i q^{47} +(-164.312 - 284.596i) q^{49} -201.722 q^{51} +642.753 q^{53} +(-28.9608 - 50.1616i) q^{55} -34.3367i q^{57} +(550.716 + 317.956i) q^{59} +(-9.62421 + 16.6696i) q^{61} +(-29.5531 + 17.0625i) q^{63} +(219.673 - 658.772i) q^{65} +(421.110 - 243.128i) q^{67} +(-79.3163 + 137.380i) q^{69} +(331.280 + 191.264i) q^{71} -1057.00i q^{73} +(-141.747 - 245.512i) q^{75} -14.8237 q^{77} +460.065 q^{79} +(-40.5000 - 70.1481i) q^{81} +268.768i q^{83} +(-862.734 - 498.100i) q^{85} +(-88.0347 + 152.481i) q^{87} +(659.691 - 380.873i) q^{89} +(-117.899 - 132.987i) q^{91} +(-474.733 + 274.087i) q^{93} +(84.7857 - 146.853i) q^{95} +(-613.504 - 354.207i) q^{97} -35.1859i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 9 q^{7} - 27 q^{9} - 120 q^{11} - 77 q^{13} + 36 q^{15} + 32 q^{17} - 24 q^{19} + 104 q^{23} - 166 q^{25} - 162 q^{27} + 220 q^{29} - 360 q^{33} - 88 q^{35} - 684 q^{37} - 66 q^{39} + 576 q^{41}+ \cdots - 873 q^{97}+O(q^{100}) $ 6 * q + 9 * q^3 + 9 * q^7 - 27 * q^9 - 120 * q^11 - 77 * q^13 + 36 * q^15 + 32 * q^17 - 24 * q^19 + 104 * q^23 - 166 * q^25 - 162 * q^27 + 220 * q^29 - 360 * q^33 - 88 * q^35 - 684 * q^37 - 66 * q^39 + 576 * q^41 + 233 * q^43 + 108 * q^45 + 38 * q^49 + 192 * q^51 + 732 * q^53 + 702 * q^55 - 1458 * q^59 + 595 * q^61 - 81 * q^63 + 698 * q^65 - 1869 * q^67 - 312 * q^69 + 2280 * q^71 - 249 * q^75 + 2076 * q^77 + 2222 * q^79 - 243 * q^81 - 3564 * q^85 - 660 * q^87 - 384 * q^89 + 3833 * q^91 - 189 * q^93 - 90 * q^95 - 873 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$			14.8155i			1.32513i	0.749002	+	0.662567i	$0.230533\pi$
$5$			14.8155i			1.32513i	−0.749002	+	0.662567i	$0.769467\pi$
$6$		0			0
$7$	3.28368	+	1.89583i	0.177302	+	0.102365i	0.586024	−	0.810293i	$-0.300692\pi$
$7$	3.28368	+	1.89583i	0.177302	+	0.102365i	−0.408722	+	0.912659i	$0.634026\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.38576	+	1.95477i	−0.0928041	+	0.0535805i	−0.545684	−	0.837991i	$-0.683730\pi$
$11$	−3.38576	+	1.95477i	−0.0928041	+	0.0535805i	0.452880	+	0.891572i	$0.350397\pi$
$12$		0			0
$13$	−44.4652	−	14.8273i	−0.948648	−	0.316334i
$13$	−44.4652	−	14.8273i	−0.948648	−	0.316334i
$14$		0			0
$15$	−38.4917	+	22.2232i	−0.662567	+	0.382533i
$16$		0			0
$17$	−33.6203	+	58.2320i	−0.479654	+	0.830785i	−0.999728	−	0.0233367i	$-0.992571\pi$
$17$	−33.6203	+	58.2320i	−0.479654	+	0.830785i	0.520074	+	0.854121i	$0.325904\pi$
$18$		0			0
$19$	−9.91216	−	5.72279i	−0.119685	−	0.0690999i	0.438963	−	0.898505i	$-0.355346\pi$
$19$	−9.91216	−	5.72279i	−0.119685	−	0.0690999i	−0.558647	+	0.829405i	$0.688679\pi$
$20$		0			0
$21$			11.3750i			0.118201i
$22$		0			0
$23$	26.4388	+	45.7933i	0.239690	+	0.415155i	0.960625	−	0.277847i	$-0.0896209\pi$
$23$	26.4388	+	45.7933i	0.239690	+	0.415155i	−0.720935	+	0.693002i	$0.756288\pi$
$24$		0			0
$25$	−94.4977			−0.755982
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	29.3449	+	50.8269i	0.187904	+	0.325459i	0.944551	−	0.328364i	$-0.106497\pi$
$29$	29.3449	+	50.8269i	0.187904	+	0.325459i	−0.756647	+	0.653823i	$0.773164\pi$
$30$		0			0
$31$			182.725i			1.05866i	0.848417	+	0.529329i	$0.177556\pi$
$31$			182.725i			1.05866i	−0.848417	+	0.529329i	$0.822444\pi$
$32$		0			0
$33$	−10.1573	−	5.86431i	−0.0535805	−	0.0309347i
$34$		0			0
$35$	−28.0876	+	48.6492i	−0.135648	+	0.234949i
$36$		0			0
$37$	−33.9350	+	19.5924i	−0.150781	+	0.0870533i	−0.573492	−	0.819211i	$-0.694412\pi$
$37$	−33.9350	+	19.5924i	−0.150781	+	0.0870533i	0.422711	+	0.906264i	$0.361078\pi$
$38$		0			0
$39$	−28.1754	−	137.765i	−0.115684	−	0.565642i
$40$		0			0
$41$	197.469	−	114.009i	0.752183	−	0.434273i	−0.0742993	−	0.997236i	$-0.523672\pi$
$41$	197.469	−	114.009i	0.752183	−	0.434273i	0.826482	+	0.562963i	$0.190339\pi$
$42$		0			0
$43$	−178.087	+	308.456i	−0.631582	+	1.09393i	0.355647	+	0.934620i	$0.384261\pi$
$43$	−178.087	+	308.456i	−0.631582	+	1.09393i	−0.987228	+	0.159311i	$0.949073\pi$
$44$		0			0
$45$	−115.475	−	66.6695i	−0.382533	−	0.220856i
$46$		0			0
$47$		−	108.483i		−	0.336678i	−0.985729	−	0.168339i	$-0.946160\pi$
$47$		−	108.483i		−	0.336678i	0.985729	−	0.168339i	$-0.0538403\pi$
$48$		0			0
$49$	−164.312	−	284.596i	−0.479043	−	0.829726i
$50$		0			0
$51$	−201.722			−0.553856
$52$		0			0
$53$	642.753			1.66583			0.832914	−	0.553402i	$-0.186671\pi$
$53$	642.753			1.66583			0.832914	+	0.553402i	$0.186671\pi$
$54$		0			0
$55$	−28.9608	−	50.1616i	−0.0710013	−	0.122978i
$56$		0			0
$57$		−	34.3367i		−	0.0797897i
$58$		0			0
$59$	550.716	+	317.956i	1.21520	+	0.701599i	0.963888	−	0.266307i	$-0.0858033\pi$
$59$	550.716	+	317.956i	1.21520	+	0.701599i	0.251316	+	0.967905i	$0.419137\pi$
$60$		0			0
$61$	−9.62421	+	16.6696i	−0.0202009	+	0.0349890i	−0.875949	−	0.482403i	$-0.839764\pi$
$61$	−9.62421	+	16.6696i	−0.0202009	+	0.0349890i	0.855748	+	0.517392i	$0.173097\pi$
$62$		0			0
$63$	−29.5531	+	17.0625i	−0.0591007	+	0.0341218i
$64$		0			0
$65$	219.673	−	658.772i	0.419186	−	1.25709i
$66$		0			0
$67$	421.110	−	243.128i	0.767862	−	0.443325i	−0.0642496	−	0.997934i	$-0.520465\pi$
$67$	421.110	−	243.128i	0.767862	−	0.443325i	0.832111	+	0.554609i	$0.187132\pi$
$68$		0			0
$69$	−79.3163	+	137.380i	−0.138385	+	0.239690i
$70$		0			0
$71$	331.280	+	191.264i	0.553742	+	0.319703i	0.750630	−	0.660723i	$-0.229750\pi$
$71$	331.280	+	191.264i	0.553742	+	0.319703i	−0.196888	+	0.980426i	$0.563084\pi$
$72$		0			0
$73$		−	1057.00i		−	1.69469i	−0.531043	−	0.847345i	$-0.678200\pi$
$73$		−	1057.00i		−	1.69469i	0.531043	−	0.847345i	$-0.321800\pi$
$74$		0			0
$75$	−141.747	−	245.512i	−0.218233	−	0.377991i
$76$		0			0
$77$	−14.8237			−0.0219391
$78$		0			0
$79$	460.065			0.655207			0.327603	−	0.944815i	$-0.393759\pi$
$79$	460.065			0.655207			0.327603	+	0.944815i	$0.393759\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			268.768i			0.355436i	0.984081	+	0.177718i	$0.0568714\pi$
$83$			268.768i			0.355436i	−0.984081	+	0.177718i	$0.943129\pi$
$84$		0			0
$85$	−862.734	−	498.100i	−1.10090	−	0.635606i
$86$		0			0
$87$	−88.0347	+	152.481i	−0.108486	+	0.187904i
$88$		0			0
$89$	659.691	−	380.873i	0.785698	−	0.453623i	−0.0527478	−	0.998608i	$-0.516798\pi$
$89$	659.691	−	380.873i	0.785698	−	0.453623i	0.838446	+	0.544985i	$0.183465\pi$
$90$		0			0
$91$	−117.899	−	132.987i	−0.135815	−	0.153195i
$92$		0			0
$93$	−474.733	+	274.087i	−0.529329	+	0.305608i
$94$		0			0
$95$	84.7857	−	146.853i	0.0915667	−	0.158598i
$96$		0			0
$97$	−613.504	−	354.207i	−0.642185	−	0.370766i	0.143271	−	0.989684i	$-0.454238\pi$
$97$	−613.504	−	354.207i	−0.642185	−	0.370766i	−0.785456	+	0.618918i	$0.787571\pi$
$98$		0			0
$99$		−	35.1859i		−	0.0357203i
$100$		0			0
$101$	−149.067	−	258.191i	−0.146859	−	0.254366i	0.783206	−	0.621762i	$-0.213583\pi$
$101$	−149.067	−	258.191i	−0.146859	−	0.254366i	−0.930065	+	0.367396i	$0.880250\pi$
$102$		0			0
$103$	664.955			0.636116			0.318058	−	0.948071i	$-0.396969\pi$
$103$	664.955			0.636116			0.318058	+	0.948071i	$0.396969\pi$
$104$		0			0
$105$	−168.526			−0.156633
$106$		0			0
$107$	1044.66	+	1809.40i	0.943839	+	1.63478i	0.758058	+	0.652187i	$0.226148\pi$
$107$	1044.66	+	1809.40i	0.943839	+	1.63478i	0.185781	+	0.982591i	$0.440518\pi$
$108$		0			0
$109$			910.270i			0.799890i	0.916539	+	0.399945i	$0.130971\pi$
$109$			910.270i			0.799890i	−0.916539	+	0.399945i	$0.869029\pi$
$110$		0			0
$111$	−101.805	−	58.7772i	−0.0870533	−	0.0502602i
$112$		0			0
$113$	−28.0095	+	48.5138i	−0.0233178	+	0.0403876i	−0.877449	−	0.479670i	$-0.840756\pi$
$113$	−28.0095	+	48.5138i	−0.0233178	+	0.0403876i	0.854131	+	0.520058i	$0.174090\pi$
$114$		0			0
$115$	−678.449	+	391.702i	−0.550136	+	0.317621i
$116$		0			0
$117$	315.660	−	279.849i	0.249426	−	0.221129i
$118$		0			0
$119$	−220.796	+	127.477i	−0.170087	+	0.0981999i
$120$		0			0
$121$	−657.858	+	1139.44i	−0.494258	+	0.856080i
$122$		0			0
$123$	592.407	+	342.027i	0.434273	+	0.250728i
$124$		0			0
$125$			451.905i			0.323357i
$126$		0			0
$127$	958.890	+	1660.85i	0.669982	+	1.16044i	0.977909	+	0.209033i	$0.0670317\pi$
$127$	958.890	+	1660.85i	0.669982	+	1.16044i	−0.307926	+	0.951410i	$0.599635\pi$
$128$		0			0
$129$	−1068.52			−0.729288
$130$		0			0
$131$	−308.770			−0.205934			−0.102967	−	0.994685i	$-0.532834\pi$
$131$	−308.770			−0.205934			−0.102967	+	0.994685i	$0.532834\pi$
$132$		0			0
$133$	−21.6989	−	37.5836i	−0.0141469	−	0.0245031i
$134$		0			0
$135$		−	400.017i		−	0.255022i
$136$		0			0
$137$	−2570.07	−	1483.83i	−1.60275	−	0.925346i	−0.990935	−	0.134341i	$-0.957108\pi$
$137$	−2570.07	−	1483.83i	−1.60275	−	0.925346i	−0.611811	−	0.791004i	$-0.709559\pi$
$138$		0			0
$139$	−1129.30	+	1956.00i	−0.689108	+	1.19357i	0.283019	+	0.959114i	$0.408664\pi$
$139$	−1129.30	+	1956.00i	−0.689108	+	1.19357i	−0.972127	+	0.234455i	$0.924669\pi$
$140$		0			0
$141$	281.847	−	162.724i	0.168339	−	0.0971905i
$142$		0			0
$143$	179.532	−	36.7176i	0.104988	−	0.0214719i
$144$		0			0
$145$	−753.023	+	434.758i	−0.431277	+	0.248998i
$146$		0			0
$147$	492.935	−	853.788i	0.276575	−	0.479043i
$148$		0			0
$149$	406.075	+	234.447i	0.223268	+	0.128904i	0.607463	−	0.794348i	$-0.292187\pi$
$149$	406.075	+	234.447i	0.223268	+	0.128904i	−0.384195	+	0.923252i	$0.625521\pi$
$150$		0			0
$151$		−	2143.41i		−	1.15516i	−0.816336	−	0.577578i	$-0.803998\pi$
$151$		−	2143.41i		−	1.15516i	0.816336	−	0.577578i	$-0.196002\pi$
$152$		0			0
$153$	−302.582	−	524.088i	−0.159885	−	0.276928i
$154$		0			0
$155$	−2707.15			−1.40286
$156$		0			0
$157$	701.045			0.356366			0.178183	−	0.983997i	$-0.442978\pi$
$157$	701.045			0.356366			0.178183	+	0.983997i	$0.442978\pi$
$158$		0			0
$159$	964.129	+	1669.92i	0.480883	+	0.832914i
$160$		0			0
$161$			200.494i			0.0981437i
$162$		0			0
$163$	−2655.81	−	1533.33i	−1.27619	−	0.736808i	−0.300044	−	0.953925i	$-0.597001\pi$
$163$	−2655.81	−	1533.33i	−1.27619	−	0.736808i	−0.976146	+	0.217117i	$0.930335\pi$
$164$		0			0
$165$	86.8824	−	150.485i	0.0409926	−	0.0710013i
$166$		0			0
$167$	−2085.46	+	1204.04i	−0.966334	+	0.557913i	−0.898117	−	0.439758i	$-0.855064\pi$
$167$	−2085.46	+	1204.04i	−0.966334	+	0.557913i	−0.0682170	+	0.997671i	$0.521731\pi$
$168$		0			0
$169$	1757.30	+	1318.60i	0.799865	+	0.600180i
$170$		0			0
$171$	89.2095	−	51.5051i	0.0398948	−	0.0230333i
$172$		0			0
$173$	1601.64	−	2774.12i	0.703876	−	1.21915i	−0.263220	−	0.964736i	$-0.584784\pi$
$173$	1601.64	−	2774.12i	0.703876	−	1.21915i	0.967096	−	0.254413i	$-0.0818822\pi$
$174$		0			0
$175$	−310.300	−	179.152i	−0.134037	−	0.0773863i
$176$		0			0
$177$			1907.73i			0.810136i
$178$		0			0
$179$	778.970	+	1349.22i	0.325268	+	0.563381i	0.981567	−	0.191121i	$-0.0612121\pi$
$179$	778.970	+	1349.22i	0.325268	+	0.563381i	−0.656299	+	0.754501i	$0.727879\pi$
$180$		0			0
$181$	4053.88			1.66476			0.832382	−	0.554203i	$-0.186977\pi$
$181$	4053.88			1.66476			0.832382	+	0.554203i	$0.186977\pi$
$182$		0			0
$183$	−57.7453			−0.0233260
$184$		0			0
$185$	−290.270	−	502.763i	−0.115357	−	0.199805i
$186$		0			0
$187$		−	262.880i		−	0.102800i
$188$		0			0
$189$	−88.6593	−	51.1875i	−0.0341218	−	0.0197002i
$190$		0			0
$191$	−1416.11	+	2452.77i	−0.536470	+	0.929194i	0.462620	+	0.886556i	$0.346909\pi$
$191$	−1416.11	+	2452.77i	−0.536470	+	0.929194i	−0.999091	+	0.0426372i	$0.986424\pi$
$192$		0			0
$193$	466.890	−	269.559i	0.174132	−	0.100535i	−0.410401	−	0.911905i	$-0.634611\pi$
$193$	466.890	−	269.559i	0.174132	−	0.100535i	0.584533	+	0.811370i	$0.301278\pi$
$194$		0			0
$195$	2041.05	−	417.431i	0.749551	−	0.153297i
$196$		0			0
$197$	−72.9076	+	42.0932i	−0.0263678	+	0.0152234i	−0.513126	−	0.858313i	$-0.671513\pi$
$197$	−72.9076	+	42.0932i	−0.0263678	+	0.0152234i	0.486758	+	0.873537i	$0.338179\pi$
$198$		0			0
$199$	2734.73	−	4736.69i	0.974171	−	1.68731i	0.291525	−	0.956563i	$-0.405837\pi$
$199$	2734.73	−	4736.69i	0.974171	−	1.68731i	0.682646	−	0.730750i	$-0.260829\pi$
$200$		0			0
$201$	1263.33	+	729.383i	0.443325	+	0.255954i
$202$		0			0
$203$			222.532i			0.0769394i
$204$		0			0
$205$	1689.09	+	2925.59i	0.575470	+	0.996743i
$206$		0			0
$207$	−475.898			−0.159793
$208$		0			0
$209$	44.7469			0.0148096
$210$		0			0
$211$	−29.7642	−	51.5532i	−0.00971116	−	0.0168202i	0.861129	−	0.508387i	$-0.169758\pi$
$211$	−29.7642	−	51.5532i	−0.00971116	−	0.0168202i	−0.870840	+	0.491566i	$0.836425\pi$
$212$		0			0
$213$			1147.59i			0.369161i
$214$		0			0
$215$	−4569.91	−	2638.44i	−1.44961	−	0.836931i
$216$		0			0
$217$	−346.416	+	600.010i	−0.108370	+	0.187702i
$218$		0			0
$219$	2746.16	−	1585.50i	0.847345	−	0.489215i
$220$		0			0
$221$	2358.35	−	2090.80i	0.717828	−	0.636391i
$222$		0			0
$223$	4032.25	−	2328.02i	1.21085	−	0.699084i	0.247905	−	0.968784i	$-0.420258\pi$
$223$	4032.25	−	2328.02i	1.21085	−	0.699084i	0.962944	+	0.269700i	$0.0869247\pi$
$224$		0			0
$225$	425.240	−	736.537i	0.125997	−	0.218233i
$226$		0			0
$227$	−3194.70	−	1844.46i	−0.934095	−	0.539300i	−0.0459906	−	0.998942i	$-0.514644\pi$
$227$	−3194.70	−	1844.46i	−0.934095	−	0.539300i	−0.888104	+	0.459642i	$0.847978\pi$
$228$		0			0
$229$		−	3641.69i		−	1.05087i	−0.850833	−	0.525436i	$-0.823902\pi$
$229$		−	3641.69i		−	1.05087i	0.850833	−	0.525436i	$-0.176098\pi$
$230$		0			0
$231$	−22.2355	−	38.5130i	−0.00633328	−	0.0109696i
$232$		0			0
$233$	−4462.98			−1.25485			−0.627424	−	0.778678i	$-0.715891\pi$
$233$	−4462.98			−1.25485			−0.627424	+	0.778678i	$0.715891\pi$
$234$		0			0
$235$	1607.22			0.446143
$236$		0			0
$237$	690.097	+	1195.28i	0.189142	+	0.327603i
$238$		0			0
$239$		−	643.226i		−	0.174087i	−0.996205	−	0.0870436i	$-0.972258\pi$
$239$		−	643.226i		−	0.174087i	0.996205	−	0.0870436i	$-0.0277419\pi$
$240$		0			0
$241$	−4264.45	−	2462.08i	−1.13982	−	0.658078i	−0.193437	−	0.981113i	$-0.561964\pi$
$241$	−4264.45	−	2462.08i	−1.13982	−	0.658078i	−0.946387	+	0.323035i	$0.895297\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	4216.42	−	2434.35i	1.09950	−	0.634796i
$246$		0			0
$247$	355.893	+	401.435i	0.0916798	+	0.103412i
$248$		0			0
$249$	−698.281	+	403.152i	−0.177718	+	0.102605i
$250$		0			0
$251$	1493.42	−	2586.68i	0.375553	−	0.650478i	−0.614856	−	0.788639i	$-0.710786\pi$
$251$	1493.42	−	2586.68i	0.375553	−	0.650478i	0.990410	+	0.138162i	$0.0441193\pi$
$252$		0			0
$253$	−179.031	−	103.363i	−0.0444884	−	0.0256854i
$254$		0			0
$255$		−	2988.60i		−	0.733934i
$256$		0			0
$257$	157.195	+	272.270i	0.0381539	+	0.0660846i	0.884472	−	0.466594i	$-0.154519\pi$
$257$	157.195	+	272.270i	0.0381539	+	0.0660846i	−0.846318	+	0.532678i	$0.821186\pi$
$258$		0			0
$259$	−148.576			−0.0356450
$260$		0			0
$261$	−528.208			−0.125269
$262$		0			0
$263$	564.595	+	977.908i	0.132374	+	0.229279i	0.924591	−	0.380960i	$-0.124407\pi$
$263$	564.595	+	977.908i	0.132374	+	0.229279i	−0.792217	+	0.610239i	$0.791073\pi$
$264$		0			0
$265$			9522.68i			2.20745i
$266$		0			0
$267$	1979.07	+	1142.62i	0.453623	+	0.261899i
$268$		0			0
$269$	−44.5279	+	77.1246i	−0.0100926	+	0.0174809i	−0.871028	−	0.491234i	$-0.836546\pi$
$269$	−44.5279	+	77.1246i	−0.0100926	+	0.0174809i	0.860935	+	0.508715i	$0.169879\pi$
$270$		0			0
$271$	4564.74	−	2635.45i	1.02320	−	0.590747i	0.108174	−	0.994132i	$-0.465500\pi$
$271$	4564.74	−	2635.45i	1.02320	−	0.590747i	0.915030	+	0.403385i	$0.132166\pi$
$272$		0			0
$273$	168.660	−	505.791i	0.0373912	−	0.112131i
$274$		0			0
$275$	319.947	−	184.721i	0.0701582	−	0.0405059i
$276$		0			0
$277$	−2173.97	+	3765.42i	−0.471556	+	0.816760i	−0.999470	−	0.0325382i	$-0.989641\pi$
$277$	−2173.97	+	3765.42i	−0.471556	+	0.816760i	0.527914	+	0.849298i	$0.322974\pi$
$278$		0			0
$279$	−1424.20	−	822.262i	−0.305608	−	0.176443i
$280$		0			0
$281$			3386.80i			0.719002i	0.933145	+	0.359501i	$0.117053\pi$
$281$			3386.80i			0.719002i	−0.933145	+	0.359501i	$0.882947\pi$
$282$		0			0
$283$	1045.84	+	1811.45i	0.219678	+	0.380494i	0.954710	−	0.297539i	$-0.0961659\pi$
$283$	1045.84	+	1811.45i	0.219678	+	0.380494i	−0.735031	+	0.678033i	$0.762833\pi$
$284$		0			0
$285$	508.714			0.105732
$286$		0			0
$287$	864.567			0.177818
$288$		0			0
$289$	195.855	+	339.231i	0.0398647	+	0.0690476i
$290$		0			0
$291$		−	2125.24i		−	0.428123i
$292$		0			0
$293$	−2041.92	−	1178.90i	−0.407134	−	0.235059i	0.282424	−	0.959290i	$-0.408862\pi$
$293$	−2041.92	−	1178.90i	−0.407134	−	0.235059i	−0.689558	+	0.724231i	$0.742195\pi$
$294$		0			0
$295$	−4710.66	+	8159.10i	−0.929713	+	1.61031i
$296$		0			0
$297$	91.4155	−	52.7788i	0.0178602	−	0.0103116i
$298$		0			0
$299$	−496.615	−	2428.22i	−0.0960534	−	0.469658i
$300$		0			0
$301$	−1169.56	+	675.246i	−0.223961	+	0.129304i
$302$		0			0
$303$	447.201	−	774.574i	0.0847888	−	0.146859i
$304$		0			0
$305$	−246.968	−	142.587i	−0.0463651	−	0.0267689i
$306$		0			0
$307$		−	6738.19i		−	1.25267i	−0.779555	−	0.626334i	$-0.784555\pi$
$307$		−	6738.19i		−	1.25267i	0.779555	−	0.626334i	$-0.215445\pi$
$308$		0			0
$309$	997.433	+	1727.60i	0.183631	+	0.318058i
$310$		0			0
$311$	−8796.16			−1.60381			−0.801904	−	0.597453i	$-0.796179\pi$
$311$	−8796.16			−1.60381			−0.801904	+	0.597453i	$0.796179\pi$
$312$		0			0
$313$	−1286.70			−0.232360			−0.116180	−	0.993228i	$-0.537065\pi$
$313$	−1286.70			−0.232360			−0.116180	+	0.993228i	$0.537065\pi$
$314$		0			0
$315$	−252.789	−	437.843i	−0.0452160	−	0.0783163i
$316$		0			0
$317$			10694.6i			1.89486i	0.319960	+	0.947431i	$0.396331\pi$
$317$			10694.6i			1.89486i	−0.319960	+	0.947431i	$0.603669\pi$
$318$		0			0
$319$	−198.710	−	114.725i	−0.0348765	−	0.0201360i
$320$		0			0
$321$	−3133.97	+	5428.20i	−0.544926	+	0.943839i
$322$		0			0
$323$	666.499	−	384.803i	0.114814	−	0.0662880i
$324$		0			0
$325$	4201.86	+	1401.14i	0.717160	+	0.239143i
$326$		0			0
$327$	−2364.95	+	1365.40i	−0.399945	+	0.230908i
$328$		0			0
$329$	205.665	−	356.223i	0.0344641	−	0.0596937i
$330$		0			0
$331$	−3605.97	−	2081.91i	−0.598798	−	0.345716i	0.169771	−	0.985484i	$-0.445697\pi$
$331$	−3605.97	−	2081.91i	−0.598798	−	0.345716i	−0.768568	+	0.639768i	$0.779031\pi$
$332$		0			0
$333$		−	352.663i		−	0.0580355i
$334$		0			0
$335$	3602.05	+	6238.93i	0.587465	+	1.01752i
$336$		0			0
$337$	−12074.9			−1.95182			−0.975909	−	0.218177i	$-0.929989\pi$
$337$	−12074.9			−1.95182			−0.975909	+	0.218177i	$0.929989\pi$
$338$		0			0
$339$	−168.057			−0.0269251
$340$		0			0
$341$	−357.185	−	618.663i	−0.0567234	−	0.0982477i
$342$		0			0
$343$		−	2546.57i		−	0.400880i
$344$		0			0
$345$	−2035.35	−	1175.11i	−0.317621	−	0.183379i
$346$		0			0
$347$	−4917.13	+	8516.73i	−0.760708	+	1.31758i	0.181778	+	0.983340i	$0.441815\pi$
$347$	−4917.13	+	8516.73i	−0.760708	+	1.31758i	−0.942486	+	0.334245i	$0.891519\pi$
$348$		0			0
$349$	6376.59	−	3681.52i	0.978026	−	0.564663i	0.0763521	−	0.997081i	$-0.475673\pi$
$349$	6376.59	−	3681.52i	0.978026	−	0.564663i	0.901673	+	0.432418i	$0.142339\pi$
$350$		0			0
$351$	1200.56	+	400.337i	0.182567	+	0.0608786i
$352$		0			0
$353$	4691.43	−	2708.60i	0.707365	−	0.408397i	−0.102720	−	0.994710i	$-0.532755\pi$
$353$	4691.43	−	2708.60i	0.707365	−	0.408397i	0.810084	+	0.586313i	$0.199421\pi$
$354$		0			0
$355$	−2833.67	+	4908.06i	−0.423649	+	0.733782i
$356$		0			0
$357$	−662.389	−	382.431i	−0.0981999	−	0.0566957i
$358$		0			0
$359$		−	660.418i		−	0.0970907i	−0.998821	−	0.0485453i	$-0.984541\pi$
$359$		−	660.418i		−	0.0970907i	0.998821	−	0.0485453i	$-0.0154585\pi$
$360$		0			0
$361$	−3364.00	−	5826.62i	−0.490450	−	0.849485i
$362$		0			0
$363$	−3947.15			−0.570720
$364$		0			0
$365$	15659.9			2.24569
$366$		0			0
$367$	1288.28	+	2231.36i	0.183236	+	0.317374i	0.942981	−	0.332848i	$-0.108010\pi$
$367$	1288.28	+	2231.36i	0.183236	+	0.317374i	−0.759745	+	0.650221i	$0.774676\pi$
$368$		0			0
$369$			2052.16i			0.289515i
$370$		0			0
$371$	2110.59	+	1218.55i	0.295355	+	0.170523i
$372$		0			0
$373$	−2587.69	+	4482.01i	−0.359210	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$373$	−2587.69	+	4482.01i	−0.359210	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$374$		0			0
$375$	−1174.08	+	677.858i	−0.161679	+	0.0933452i
$376$		0			0
$377$	−551.202	−	2695.13i	−0.0753007	−	0.368186i
$378$		0			0
$379$	5345.24	−	3086.07i	0.724449	−	0.418261i	−0.0919388	−	0.995765i	$-0.529306\pi$
$379$	5345.24	−	3086.07i	0.724449	−	0.418261i	0.816388	+	0.577504i	$0.195973\pi$
$380$		0			0
$381$	−2876.67	+	4982.54i	−0.386815	+	0.669982i
$382$		0			0
$383$	−4584.41	−	2646.81i	−0.611625	−	0.353122i	0.161976	−	0.986795i	$-0.448213\pi$
$383$	−4584.41	−	2646.81i	−0.611625	−	0.353122i	−0.773601	+	0.633673i	$0.781547\pi$
$384$		0			0
$385$		−	219.619i		−	0.0290723i
$386$		0			0
$387$	−1602.78	−	2776.10i	−0.210527	−	0.364644i
$388$		0			0
$389$	7481.61			0.975148			0.487574	−	0.873082i	$-0.337882\pi$
$389$	7481.61			0.975148			0.487574	+	0.873082i	$0.337882\pi$
$390$		0			0
$391$	−3555.51			−0.459872
$392$		0			0
$393$	−463.156	−	802.209i	−0.0594481	−	0.102967i
$394$		0			0
$395$			6816.07i			0.868237i
$396$		0			0
$397$	−827.803	−	477.932i	−0.104650	−	0.0604200i	0.446761	−	0.894653i	$-0.352577\pi$
$397$	−827.803	−	477.932i	−0.104650	−	0.0604200i	−0.551412	+	0.834233i	$0.685911\pi$
$398$		0			0
$399$	65.0967	−	112.751i	0.00816770	−	0.0141469i
$400$		0			0
$401$	6919.93	−	3995.22i	0.861758	−	0.497536i	−0.00284281	−	0.999996i	$-0.500905\pi$
$401$	6919.93	−	3995.22i	0.861758	−	0.497536i	0.864600	+	0.502460i	$0.167572\pi$
$402$		0			0
$403$	2709.31	−	8124.90i	0.334890	−	1.00429i
$404$		0			0
$405$	1039.28	−	600.026i	0.127511	−	0.0736186i
$406$		0			0
$407$	76.5973	−	132.670i	0.00932871	−	0.0161578i
$408$		0			0
$409$	−5914.45	−	3414.71i	−0.715039	−	0.412828i	0.0978850	−	0.995198i	$-0.468792\pi$
$409$	−5914.45	−	3414.71i	−0.715039	−	0.412828i	−0.812924	+	0.582370i	$0.802126\pi$
$410$		0			0
$411$		−	8902.99i		−	1.06850i
$412$		0			0
$413$	1205.58	+	2088.13i	0.143639	+	0.248790i
$414$		0			0
$415$	−3981.92			−0.471000
$416$		0			0
$417$	−6775.80			−0.795713
$418$		0			0
$419$	−1601.07	−	2773.13i	−0.186676	−	0.323332i	0.757464	−	0.652877i	$-0.226438\pi$
$419$	−1601.07	−	2773.13i	−0.186676	−	0.323332i	−0.944140	+	0.329545i	$0.893105\pi$
$420$		0			0
$421$			3408.00i			0.394527i	0.980351	+	0.197263i	$0.0632054\pi$
$421$			3408.00i			0.394527i	−0.980351	+	0.197263i	$0.936795\pi$
$422$		0			0
$423$	845.541	+	488.173i	0.0971905	+	0.0561130i
$424$		0			0
$425$	3177.04	−	5502.79i	0.362609	−	0.628058i
$426$		0			0
$427$	−63.2056	+	36.4918i	−0.00716332	+	0.00413574i
$428$		0			0
$429$	364.694	+	411.362i	0.0410433	+	0.0462955i
$430$		0			0
$431$	8669.72	−	5005.46i	0.968922	−	0.559408i	0.0700148	−	0.997546i	$-0.477695\pi$
$431$	8669.72	−	5005.46i	0.968922	−	0.559408i	0.898908	+	0.438138i	$0.144362\pi$
$432$		0			0
$433$	6353.96	−	11005.4i	0.705201	−	1.22144i	−0.261418	−	0.965226i	$-0.584190\pi$
$433$	6353.96	−	11005.4i	0.705201	−	1.22144i	0.966619	−	0.256218i	$-0.0824765\pi$
$434$		0			0
$435$	−2259.07	−	1304.27i	−0.248998	−	0.143759i
$436$		0			0
$437$		−	605.214i		−	0.0662502i
$438$		0			0
$439$	−1396.56	−	2418.90i	−0.151831	−	0.262980i	0.780069	−	0.625693i	$-0.215184\pi$
$439$	−1396.56	−	2418.90i	−0.151831	−	0.262980i	−0.931901	+	0.362713i	$0.881850\pi$
$440$		0			0
$441$	2957.61			0.319362
$442$		0			0
$443$	16148.4			1.73191			0.865953	−	0.500126i	$-0.166713\pi$
$443$	16148.4			1.73191			0.865953	+	0.500126i	$0.166713\pi$
$444$		0			0
$445$	5642.81	+	9773.63i	0.601112	+	1.04116i
$446$		0			0
$447$			1406.68i			0.148845i
$448$		0			0
$449$	−12559.3	−	7251.13i	−1.32007	−	0.762142i	−0.336330	−	0.941744i	$-0.609186\pi$
$449$	−12559.3	−	7251.13i	−1.32007	−	0.762142i	−0.983739	+	0.179602i	$0.942519\pi$
$450$		0			0
$451$	−445.722	+	772.013i	−0.0465371	+	0.0806046i
$452$		0			0
$453$	5568.75	−	3215.12i	0.577578	−	0.333465i
$454$		0			0
$455$	1970.26	−	1746.73i	0.203005	−	0.179974i
$456$		0			0
$457$	−10615.6	+	6128.91i	−1.08660	+	0.627349i	−0.932669	−	0.360733i	$-0.882527\pi$
$457$	−10615.6	+	6128.91i	−1.08660	+	0.627349i	−0.153931	+	0.988082i	$0.549193\pi$
$458$		0			0
$459$	907.747	−	1572.26i	0.0923094	−	0.159885i
$460$		0			0
$461$	4391.44	+	2535.40i	0.443665	+	0.256150i	0.705151	−	0.709057i	$-0.250879\pi$
$461$	4391.44	+	2535.40i	0.443665	+	0.256150i	−0.261486	+	0.965207i	$0.584212\pi$
$462$		0			0
$463$			5871.79i			0.589385i	0.955592	+	0.294693i	$0.0952173\pi$
$463$			5871.79i			0.589385i	−0.955592	+	0.294693i	$0.904783\pi$
$464$		0			0
$465$	−4060.73	−	7033.39i	−0.404972	−	0.701432i
$466$		0			0
$467$	4555.36			0.451385			0.225693	−	0.974199i	$-0.427535\pi$
$467$	4555.36			0.451385			0.225693	+	0.974199i	$0.427535\pi$
$468$		0			0
$469$	1843.72			0.181525
$470$		0			0
$471$	1051.57	+	1821.37i	0.102874	+	0.178183i
$472$		0			0
$473$		−	1392.48i		−	0.135362i
$474$		0			0
$475$	936.677	+	540.791i	0.0904793	+	0.0522383i
$476$		0			0
$477$	−2892.39	+	5009.76i	−0.277638	+	0.480883i
$478$		0			0
$479$	−4109.82	+	2372.80i	−0.392030	+	0.226339i	−0.683039	−	0.730382i	$-0.739342\pi$
$479$	−4109.82	+	2372.80i	−0.392030	+	0.226339i	0.291009	+	0.956720i	$0.406009\pi$
$480$		0			0
$481$	1799.43	−	368.015i	0.170576	−	0.0348858i
$482$		0			0
$483$	−520.899	+	300.741i	−0.0490719	+	0.0283317i
$484$		0			0
$485$	5247.74	−	9089.35i	0.491314	−	0.850981i
$486$		0			0
$487$	13274.6	+	7664.07i	1.23517	+	0.713125i	0.968103	−	0.250553i	$-0.0806125\pi$
$487$	13274.6	+	7664.07i	1.23517	+	0.713125i	0.267066	+	0.963678i	$0.413946\pi$
$488$		0			0
$489$		−	9199.99i		−	0.850793i
$490$		0			0
$491$	9269.93	+	16056.0i	0.852029	+	1.47576i	0.879374	+	0.476131i	$0.157961\pi$
$491$	9269.93	+	16056.0i	0.852029	+	1.47576i	−0.0273459	+	0.999626i	$0.508706\pi$
$492$		0			0
$493$	−3946.33			−0.360515
$494$		0			0
$495$	521.294			0.0473342
$496$		0			0
$497$	725.211	+	1256.10i	0.0654530	+	0.113368i
$498$		0			0
$499$		−	10245.7i		−	0.919156i	−0.888137	−	0.459578i	$-0.848001\pi$
$499$		−	10245.7i		−	0.919156i	0.888137	−	0.459578i	$-0.151999\pi$
$500$		0			0
$501$	−6256.38	−	3612.12i	−0.557913	−	0.322111i
$502$		0			0
$503$	4421.17	−	7657.68i	0.391909	−	0.678806i	−0.600793	−	0.799405i	$-0.705148\pi$
$503$	4421.17	−	7657.68i	0.391909	−	0.678806i	0.992701	+	0.120599i	$0.0384816\pi$
$504$		0			0
$505$	3825.22	−	2208.49i	0.337070	−	0.194607i
$506$		0			0
$507$	−789.855	+	6543.50i	−0.0691887	+	0.573190i
$508$		0			0
$509$	15791.0	−	9116.96i	1.37510	−	0.793914i	0.383534	−	0.923527i	$-0.374707\pi$
$509$	15791.0	−	9116.96i	1.37510	−	0.793914i	0.991565	+	0.129613i	$0.0413735\pi$
$510$		0			0
$511$	2003.89	−	3470.84i	0.173478	−	0.300472i
$512$		0			0
$513$	267.628	+	154.515i	0.0230333	+	0.0132983i
$514$		0			0
$515$			9851.61i			0.842940i
$516$		0			0
$517$	212.059	+	367.297i	0.0180394	+	0.0312451i
$518$		0			0
$519$	9609.85			0.812766
$520$		0			0
$521$	−7109.30			−0.597819			−0.298910	−	0.954281i	$-0.596623\pi$
$521$	−7109.30			−0.597819			−0.298910	+	0.954281i	$0.596623\pi$
$522$		0			0
$523$	−999.051	−	1730.41i	−0.0835286	−	0.144676i	0.821235	−	0.570591i	$-0.193286\pi$
$523$	−999.051	−	1730.41i	−0.0835286	−	0.144676i	−0.904763	+	0.425915i	$0.859952\pi$
$524$		0			0
$525$		−	1074.91i		−	0.0893581i
$526$		0			0
$527$	−10640.4	−	6143.26i	−0.879516	−	0.507789i
$528$		0			0
$529$	4685.48	−	8115.49i	0.385098	−	0.667009i
$530$		0			0
$531$	−4956.44	+	2861.60i	−0.405068	+	0.233866i
$532$		0			0
$533$	−10470.9	+	2141.49i	−0.850932	+	0.174031i
$534$		0			0
$535$	−26807.1	+	15477.1i	−2.16630	+	1.25071i
$536$		0			0
$537$	−2336.91	+	4047.65i	−0.187794	+	0.325268i
$538$		0			0
$539$	1112.64	+	642.383i	0.0889142	+	0.0513347i
$540$		0			0
$541$		−	12689.9i		−	1.00847i	−0.863567	−	0.504234i	$-0.831775\pi$
$541$		−	12689.9i		−	1.00847i	0.863567	−	0.504234i	$-0.168225\pi$
$542$		0			0
$543$	6080.81	+	10532.3i	0.480576	+	0.832382i
$544$		0			0
$545$	−13486.1			−1.05996
$546$		0			0
$547$	−8535.41			−0.667180			−0.333590	−	0.942718i	$-0.608260\pi$
$547$	−8535.41			−0.667180			−0.333590	+	0.942718i	$0.608260\pi$
$548$		0			0
$549$	−86.6179	−	150.027i	−0.00673363	−	0.0116630i
$550$		0			0
$551$		−	671.739i		−	0.0519366i
$552$		0			0
$553$	1510.71	+	872.206i	0.116169	+	0.0670705i
$554$		0			0
$555$	870.811	−	1508.29i	0.0666016	−	0.115357i
$556$		0			0
$557$	−22101.0	+	12760.0i	−1.68124	+	0.970663i	−0.720397	+	0.693561i	$0.756041\pi$
$557$	−22101.0	+	12760.0i	−1.68124	+	0.970663i	−0.960841	+	0.277102i	$0.910626\pi$
$558$		0			0
$559$	12492.2	−	11075.0i	0.945197	−	0.837965i
$560$		0			0
$561$	682.981	−	394.319i	0.0514001	−	0.0296759i
$562$		0			0
$563$	−2965.67	+	5136.70i	−0.222004	+	0.384522i	−0.955416	−	0.295262i	$-0.904593\pi$
$563$	−2965.67	+	5136.70i	−0.222004	+	0.384522i	0.733412	+	0.679784i	$0.237926\pi$
$564$		0			0
$565$	−718.754	−	414.973i	−0.0535190	−	0.0308992i
$566$		0			0
$567$		−	307.125i		−	0.0227479i
$568$		0			0
$569$	−3205.89	−	5552.76i	−0.236200	−	0.409111i	0.723421	−	0.690407i	$-0.242569\pi$
$569$	−3205.89	−	5552.76i	−0.236200	−	0.409111i	−0.959621	+	0.281297i	$0.909235\pi$
$570$		0			0
$571$	4364.14			0.319849			0.159924	−	0.987129i	$-0.448875\pi$
$571$	4364.14			0.319849			0.159924	+	0.987129i	$0.448875\pi$
$572$		0			0
$573$	−8496.63			−0.619462
$574$		0			0
$575$	−2498.40	−	4327.36i	−0.181201	−	0.313849i
$576$		0			0
$577$		−	9544.78i		−	0.688656i	−0.938849	−	0.344328i	$-0.888107\pi$
$577$		−	9544.78i		−	0.688656i	0.938849	−	0.344328i	$-0.111893\pi$
$578$		0			0
$579$	1400.67	+	808.678i	0.100535	+	0.0580440i
$580$		0			0
$581$	−509.540	+	882.549i	−0.0363843	+	0.0630195i
$582$		0			0
$583$	−2176.21	+	1256.43i	−0.154596	+	0.0892559i
$584$		0			0
$585$	4146.09	+	4676.65i	0.293025	+	0.330523i
$586$		0			0
$587$	−12963.5	+	7484.47i	−0.911517	+	0.526264i	−0.880919	−	0.473267i	$-0.843074\pi$
$587$	−12963.5	+	7484.47i	−0.911517	+	0.526264i	−0.0305979	+	0.999532i	$0.509741\pi$
$588$		0			0
$589$	1045.70	−	1811.20i	0.0731531	−	0.126705i
$590$		0			0
$591$	−218.723	−	126.280i	−0.0152234	−	0.00878926i
$592$		0			0
$593$			22985.5i			1.59174i	0.605468	+	0.795869i	$0.292986\pi$
$593$			22985.5i			1.59174i	−0.605468	+	0.795869i	$0.707014\pi$
$594$		0			0
$595$	−1888.63	−	3271.20i	−0.130128	−	0.225388i
$596$		0			0
$597$	16408.4			1.12488
$598$		0			0
$599$	12936.8			0.882446			0.441223	−	0.897397i	$-0.354545\pi$
$599$	12936.8			0.882446			0.441223	+	0.897397i	$0.354545\pi$
$600$		0			0
$601$	13153.7	+	22782.9i	0.892764	+	1.54631i	0.836547	+	0.547894i	$0.184570\pi$
$601$	13153.7	+	22782.9i	0.892764	+	1.54631i	0.0562168	+	0.998419i	$0.482096\pi$
$602$		0			0
$603$			4376.30i			0.295550i
$604$		0			0
$605$	−16881.4	−	9746.46i	−1.13442	−	0.654959i
$606$		0			0
$607$	−13036.5	+	22579.9i	−0.871722	+	1.50987i	−0.0115075	+	0.999934i	$0.503663\pi$
$607$	−13036.5	+	22579.9i	−0.871722	+	1.50987i	−0.860214	+	0.509933i	$0.829670\pi$
$608$		0			0
$609$	−578.156	+	333.798i	−0.0384697	+	0.0222105i
$610$		0			0
$611$	−1608.51	+	4823.71i	−0.106503	+	0.319389i
$612$		0			0
$613$	13208.8	−	7626.08i	0.870305	−	0.502471i	0.00285537	−	0.999996i	$-0.499091\pi$
$613$	13208.8	−	7626.08i	0.870305	−	0.502471i	0.867450	+	0.497525i	$0.165758\pi$
$614$		0			0
$615$	−5067.28	+	8776.78i	−0.332248	+	0.575470i
$616$		0			0
$617$	3054.01	+	1763.23i	0.199270	+	0.115049i	0.596315	−	0.802751i	$-0.296631\pi$
$617$	3054.01	+	1763.23i	0.199270	+	0.115049i	−0.397045	+	0.917799i	$0.629964\pi$
$618$		0			0
$619$			9081.76i			0.589704i	0.955543	+	0.294852i	$0.0952703\pi$
$619$			9081.76i			0.589704i	−0.955543	+	0.294852i	$0.904730\pi$
$620$		0			0
$621$	−713.847	−	1236.42i	−0.0461283	−	0.0798966i
$622$		0			0
$623$	2888.29			0.185741
$624$		0			0
$625$	−18507.4			−1.18447
$626$		0			0
$627$	67.1204	+	116.256i	0.00427517	+	0.00740481i
$628$		0			0
$629$		−	2634.81i		−	0.167022i
$630$		0			0
$631$	11545.3	+	6665.70i	0.728387	+	0.420534i	0.817832	−	0.575457i	$-0.195176\pi$
$631$	11545.3	+	6665.70i	0.728387	+	0.420534i	−0.0894450	+	0.995992i	$0.528509\pi$
$632$		0			0
$633$	89.2927	−	154.659i	0.00560674	−	0.00971116i
$634$		0			0
$635$	−24606.2	+	14206.4i	−1.53774	+	0.887817i
$636$		0			0
$637$	3086.36	+	15090.9i	0.191972	+	0.938656i
$638$		0			0
$639$	−2981.52	+	1721.38i	−0.184581	+	0.106568i
$640$		0			0
$641$	2246.03	−	3890.24i	0.138398	−	0.239712i	−0.788493	−	0.615044i	$-0.789138\pi$
$641$	2246.03	−	3890.24i	0.138398	−	0.239712i	0.926890	+	0.375333i	$0.122472\pi$
$642$		0			0
$643$	21952.2	+	12674.1i	1.34636	+	0.777323i	0.987732	−	0.156156i	$-0.0499102\pi$
$643$	21952.2	+	12674.1i	1.34636	+	0.777323i	0.358631	+	0.933479i	$0.383244\pi$
$644$		0			0
$645$		−	15830.6i		−	0.966404i
$646$		0			0
$647$	5405.35	+	9362.34i	0.328449	+	0.568890i	0.982204	−	0.187816i	$-0.0601409\pi$
$647$	5405.35	+	9362.34i	0.328449	+	0.568890i	−0.653756	+	0.756706i	$0.726808\pi$
$648$		0			0
$649$	−2486.12			−0.150368
$650$		0			0
$651$	−2078.50			−0.125135
$652$		0			0
$653$	−5024.03	−	8701.87i	−0.301080	−	0.521486i	0.675301	−	0.737542i	$-0.264014\pi$
$653$	−5024.03	−	8701.87i	−0.301080	−	0.521486i	−0.976381	+	0.216056i	$0.930680\pi$
$654$		0			0
$655$		−	4574.57i		−	0.272891i
$656$		0			0
$657$	8238.49	+	4756.49i	0.489215	+	0.282448i
$658$		0			0
$659$	10461.2	−	18119.3i	0.618376	−	1.07106i	−0.371406	−	0.928471i	$-0.621124\pi$
$659$	10461.2	−	18119.3i	0.618376	−	1.07106i	0.989782	−	0.142589i	$-0.0455426\pi$
$660$		0			0
$661$	−14162.0	+	8176.43i	−0.833340	+	0.481129i	−0.854995	−	0.518637i	$-0.826440\pi$
$661$	−14162.0	+	8176.43i	−0.833340	+	0.481129i	0.0216550	+	0.999766i	$0.493106\pi$
$662$		0			0
$663$	8969.59	+	2990.98i	0.525415	+	0.175204i
$664$		0			0
$665$	556.818	−	321.479i	0.0324699	−	0.0187465i
$666$		0			0
$667$	−1551.69	+	2687.60i	−0.0900773	+	0.156018i
$668$		0			0
$669$	12096.7	+	6984.06i	0.699084	+	0.403616i
$670$		0			0
$671$		−	75.2525i		−	0.00432949i
$672$		0			0
$673$	−8681.74	−	15037.2i	−0.497261	−	0.861281i	0.502734	−	0.864441i	$-0.332327\pi$
$673$	−8681.74	−	15037.2i	−0.497261	−	0.861281i	−0.999995	+	0.00316005i	$0.998994\pi$
$674$		0			0
$675$	2551.44			0.145489
$676$		0			0
$677$	−15301.1			−0.868639			−0.434320	−	0.900759i	$-0.643011\pi$
$677$	−15301.1			−0.868639			−0.434320	+	0.900759i	$0.643011\pi$
$678$		0			0
$679$	−1343.03	−	2326.20i	−0.0759071	−	0.131475i
$680$		0			0
$681$		−	11066.8i		−	0.622730i
$682$		0			0
$683$	−3082.15	−	1779.48i	−0.172672	−	0.0996923i	0.411173	−	0.911557i	$-0.365119\pi$
$683$	−3082.15	−	1779.48i	−0.172672	−	0.0996923i	−0.583845	+	0.811865i	$0.698453\pi$
$684$		0			0
$685$	21983.7	−	38076.8i	1.22621	−	2.12385i
$686$		0			0
$687$	9461.39	−	5462.54i	0.525436	−	0.303361i
$688$		0			0
$689$	−28580.1	−	9530.28i	−1.58028	−	0.526959i
$690$		0			0
$691$	−15496.5	+	8946.91i	−0.853132	+	0.492556i	−0.861707	−	0.507407i	$-0.830604\pi$
$691$	−15496.5	+	8946.91i	−0.853132	+	0.492556i	0.00857407	+	0.999963i	$0.497271\pi$
$692$		0			0
$693$	66.7065	−	115.539i	0.00365652	−	0.00633328i
$694$		0			0
$695$	−28979.1	−	16731.1i	−1.58164	−	0.913160i
$696$		0			0
$697$			15332.0i			0.833202i
$698$		0			0
$699$	−6694.47	−	11595.2i	−0.362243	−	0.627424i
$700$		0			0
$701$	16354.9			0.881194			0.440597	−	0.897705i	$-0.354767\pi$
$701$	16354.9			0.881194			0.440597	+	0.897705i	$0.354767\pi$
$702$		0			0
$703$	448.493			0.0240615
$704$		0			0
$705$	2410.84	+	4175.69i	0.128791	+	0.223072i
$706$		0			0
$707$		−	1130.42i		−	0.0601329i
$708$		0			0
$709$	10044.0	+	5798.90i	0.532031	+	0.307168i	0.741843	−	0.670573i	$-0.233952\pi$
$709$	10044.0	+	5798.90i	0.532031	+	0.307168i	−0.209812	+	0.977742i	$0.567285\pi$
$710$		0			0
$711$	−2070.29	+	3585.85i	−0.109201	+	0.189142i
$712$		0			0
$713$	−8367.58	+	4831.02i	−0.439507	+	0.253749i
$714$		0			0
$715$	543.987	+	2659.85i	0.0284531	+	0.139123i
$716$		0			0
$717$	1671.15	−	964.839i	0.0870436	−	0.0502546i
$718$		0			0
$719$	11713.7	−	20288.7i	0.607577	−	1.05235i	−0.384062	−	0.923307i	$-0.625475\pi$
$719$	11713.7	−	20288.7i	0.607577	−	1.05235i	0.991639	−	0.129047i	$-0.0411917\pi$
$720$		0			0
$721$	2183.50	+	1260.64i	0.112785	+	0.0651163i
$722$		0			0
$723$		−	14772.5i		−	0.759883i
$724$		0			0
$725$	−2773.03	−	4803.02i	−0.142052	−	0.246041i
$726$		0			0
$727$	17357.7			0.885503			0.442752	−	0.896644i	$-0.354002\pi$
$727$	17357.7			0.885503			0.442752	+	0.896644i	$0.354002\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−11974.7	−	20740.7i	−0.605881	−	1.04942i
$732$		0			0
$733$		−	842.308i		−	0.0424438i	−0.999775	−	0.0212219i	$-0.993244\pi$
$733$		−	842.308i		−	0.0424438i	0.999775	−	0.0212219i	$-0.00675565\pi$
$734$		0			0
$735$	12649.3	+	7303.05i	0.634796	+	0.366500i
$736$		0			0
$737$	−950.517	+	1646.34i	−0.0475071	+	0.0822848i
$738$		0			0
$739$	31137.8	−	17977.4i	1.54996	−	0.894873i	0.551822	−	0.833962i	$-0.313933\pi$
$739$	31137.8	−	17977.4i	1.54996	−	0.894873i	0.998143	−	0.0609105i	$-0.0194004\pi$
$740$		0			0
$741$	−509.120	+	1526.79i	−0.0252402	+	0.0756923i
$742$		0			0
$743$	9844.48	−	5683.72i	0.486082	−	0.280640i	−0.236865	−	0.971542i	$-0.576120\pi$
$743$	9844.48	−	5683.72i	0.486082	−	0.280640i	0.722948	+	0.690903i	$0.242787\pi$
$744$		0			0
$745$	−3473.44	+	6016.18i	−0.170815	+	0.295860i
$746$		0			0
$747$	−2094.84	−	1209.46i	−0.102605	−	0.0592393i
$748$		0			0
$749$			7921.98i			0.386466i
$750$		0			0
$751$	−6487.12	−	11236.0i	−0.315204	−	0.545950i	0.664277	−	0.747487i	$-0.268740\pi$
$751$	−6487.12	−	11236.0i	−0.315204	−	0.545950i	−0.979481	+	0.201537i	$0.935406\pi$
$752$		0			0
$753$	8960.53			0.433652
$754$		0			0
$755$	31755.7			1.53074
$756$		0			0
$757$	1209.83	+	2095.49i	0.0580872	+	0.100610i	0.893607	−	0.448851i	$-0.148167\pi$
$757$	1209.83	+	2095.49i	0.0580872	+	0.100610i	−0.835520	+	0.549461i	$0.814833\pi$
$758$		0			0
$759$		−	620.180i		−	0.0296589i
$760$		0			0
$761$	24443.6	+	14112.5i	1.16436	+	0.672246i	0.952346	−	0.305020i	$-0.0986631\pi$
$761$	24443.6	+	14112.5i	1.16436	+	0.672246i	0.212018	+	0.977266i	$0.431996\pi$
$762$		0			0
$763$	−1725.72	+	2989.03i	−0.0818811	+	0.141822i
$764$		0			0
$765$	7764.60	−	4482.90i	0.366967	−	0.211869i
$766$		0			0
$767$	−19773.2	−	22303.6i	−0.930861	−	1.04998i
$768$		0			0
$769$	14068.7	−	8122.55i	0.659726	−	0.380893i	−0.132447	−	0.991190i	$-0.542283\pi$
$769$	14068.7	−	8122.55i	0.659726	−	0.380893i	0.792172	+	0.610297i	$0.208950\pi$
$770$		0			0
$771$	−471.585	+	816.810i	−0.0220282	+	0.0381539i
$772$		0			0
$773$	1680.27	+	970.103i	0.0781824	+	0.0451387i	0.538582	−	0.842573i	$-0.318960\pi$
$773$	1680.27	+	970.103i	0.0781824	+	0.0451387i	−0.460399	+	0.887712i	$0.652294\pi$
$774$		0			0
$775$		−	17267.1i		−	0.800326i
$776$		0			0
$777$	−222.864	−	386.011i	−0.0102898	−	0.0178225i
$778$		0			0
$779$	−2609.79			−0.120033
$780$		0			0
$781$	−1495.51			−0.0685193
$782$		0			0
$783$	−792.312	−	1372.33i	−0.0361621	−	0.0626346i
$784$		0			0
$785$			10386.3i			0.472233i
$786$		0			0
$787$	17188.1	+	9923.54i	0.778512	+	0.449474i	0.835903	−	0.548878i	$-0.184945\pi$
$787$	17188.1	+	9923.54i	0.778512	+	0.449474i	−0.0573908	+	0.998352i	$0.518278\pi$
$788$		0			0
$789$	−1693.79	+	2933.72i	−0.0764263	+	0.132374i
$790$		0			0
$791$	−183.948	+	106.203i	−0.00826858	+	0.00477387i
$792$		0			0
$793$	675.107	−	598.517i	0.0302317	−	0.0268020i
$794$		0			0
$795$	−24740.6	+	14284.0i	−1.10372	+	0.637235i
$796$		0			0
$797$	−17877.2	+	30964.2i	−0.794533	+	1.37617i	0.128601	+	0.991696i	$0.458951\pi$
$797$	−17877.2	+	30964.2i	−0.794533	+	1.37617i	−0.923135	+	0.384476i	$0.874382\pi$
$798$		0			0
$799$	6317.18	+	3647.22i	0.279707	+	0.161489i
$800$		0			0
$801$			6855.71i			0.302415i
$802$		0			0
$803$	2066.19	+	3578.74i	0.0908023	+	0.157274i
$804$		0			0
$805$	−2970.41			−0.130054
$806$		0			0
$807$	−267.168			−0.0116540
$808$		0			0
$809$	1708.12	+	2958.56i	0.0742329	+	0.128575i	0.900752	−	0.434333i	$-0.143016\pi$
$809$	1708.12	+	2958.56i	0.0742329	+	0.128575i	−0.826520	+	0.562908i	$0.809683\pi$
$810$		0			0
$811$		−	26171.6i		−	1.13318i	−0.823999	−	0.566591i	$-0.808262\pi$
$811$		−	26171.6i		−	1.13318i	0.823999	−	0.566591i	$-0.191738\pi$
$812$		0			0
$813$	13694.2	+	7906.36i	0.590747	+	0.341068i
$814$		0			0
$815$	22717.0	−	39347.0i	0.976370	−	1.69112i
$816$		0			0
$817$	3530.45	−	2038.31i	0.151181	−	0.0872845i
$818$		0			0
$819$	1567.07	−	320.495i	0.0668596	−	0.0136740i
$820$		0			0
$821$	34547.3	−	19945.9i	1.46859	−	0.847889i	0.469206	−	0.883089i	$-0.344540\pi$
$821$	34547.3	−	19945.9i	1.46859	−	0.847889i	0.999380	+	0.0352001i	$0.0112069\pi$
$822$		0			0
$823$	−18207.2	+	31535.8i	−0.771157	+	1.33568i	0.165772	+	0.986164i	$0.446989\pi$
$823$	−18207.2	+	31535.8i	−0.771157	+	1.33568i	−0.936929	+	0.349520i	$0.886345\pi$
$824$		0			0
$825$	959.840	+	554.164i	0.0405059	+	0.0233861i
$826$		0			0
$827$			43200.2i			1.81647i	0.418464	+	0.908234i	$0.362569\pi$
$827$			43200.2i			1.81647i	−0.418464	+	0.908234i	$0.637431\pi$
$828$		0			0
$829$	−11372.3	−	19697.3i	−0.476447	−	0.825231i	0.523188	−	0.852217i	$-0.324742\pi$
$829$	−11372.3	−	19697.3i	−0.476447	−	0.825231i	−0.999636	+	0.0269858i	$0.991409\pi$
$830$		0			0
$831$	−13043.8			−0.544506
$832$		0			0
$833$	22096.8			0.919098
$834$		0			0
$835$	−17838.4	−	30897.0i	−0.739310	−	1.28052i
$836$		0			0
$837$		−	4933.57i		−	0.203739i
$838$		0			0
$839$	14931.8	+	8620.89i	0.614426	+	0.354739i	0.774696	−	0.632334i	$-0.217903\pi$
$839$	14931.8	+	8620.89i	0.614426	+	0.354739i	−0.160270	+	0.987073i	$0.551236\pi$
$840$		0			0
$841$	10472.3	−	18138.5i	0.429384	−	0.743715i
$842$		0			0
$843$	−8799.17	+	5080.20i	−0.359501	+	0.207558i
$844$		0			0
$845$	−19535.6	+	26035.3i	−0.795319	+	1.05993i
$846$		0			0
$847$	−4320.39	+	2494.38i	−0.175266	+	0.101190i
$848$		0			0
$849$	−3137.53	+	5434.36i	−0.126831	+	0.219678i
$850$		0			0
$851$	−1794.40	−	1036.00i	−0.0722812	−	0.0417316i
$852$		0			0
$853$		−	25949.7i		−	1.04162i	−0.853673	−	0.520809i	$-0.825630\pi$
$853$		−	25949.7i		−	1.04162i	0.853673	−	0.520809i	$-0.174370\pi$
$854$		0			0
$855$	763.072	+	1321.68i	0.0305222	+	0.0528660i
$856$		0			0
$857$	−43312.3			−1.72640			−0.863198	−	0.504866i	$-0.831542\pi$
$857$	−43312.3			−1.72640			−0.863198	+	0.504866i	$0.831542\pi$
$858$		0			0
$859$	−30465.4			−1.21009			−0.605045	−	0.796191i	$-0.706845\pi$
$859$	−30465.4			−1.21009			−0.605045	+	0.796191i	$0.706845\pi$
$860$		0			0
$861$	1296.85	+	2246.21i	0.0513316	+	0.0889090i
$862$		0			0
$863$		−	34192.7i		−	1.34871i	−0.738409	−	0.674354i	$-0.764422\pi$
$863$		−	34192.7i		−	1.34871i	0.738409	−	0.674354i	$-0.235578\pi$
$864$		0			0
$865$	41099.9	+	23729.0i	1.61554	+	0.932730i
$866$		0			0
$867$	−587.565	+	1017.69i	−0.0230159	+	0.0398647i
$868$		0			0
$869$	−1557.67	+	899.321i	−0.0608059	+	0.0351063i
$870$		0			0
$871$	−22329.6	+	4566.81i	−0.868669	+	0.177658i
$872$		0			0
$873$	5521.54	−	3187.86i	0.214062	−	0.123589i
$874$		0			0
$875$	−856.737	+	1483.91i	−0.0331006	+	0.0573319i
$876$		0			0
$877$	−17808.5	−	10281.7i	−0.685690	−	0.395884i	0.116305	−	0.993214i	$-0.462895\pi$
$877$	−17808.5	−	10281.7i	−0.685690	−	0.395884i	−0.801996	+	0.597330i	$0.796228\pi$
$878$		0			0
$879$		−	7073.42i		−	0.271423i
$880$		0			0
$881$	8859.76	+	15345.6i	0.338812	+	0.586839i	0.984209	−	0.177008i	$-0.0566418\pi$
$881$	8859.76	+	15345.6i	0.338812	+	0.586839i	−0.645398	+	0.763847i	$0.723308\pi$
$882$		0			0
$883$	35140.1			1.33925			0.669625	−	0.742699i	$-0.266455\pi$
$883$	35140.1			1.33925			0.669625	+	0.742699i	$0.266455\pi$
$884$		0			0
$885$	−28264.0			−1.07354
$886$		0			0
$887$	−18493.9	−	32032.4i	−0.700072	−	1.21256i	−0.968441	−	0.249244i	$-0.919818\pi$
$887$	−18493.9	−	32032.4i	−0.700072	−	1.21256i	0.268368	−	0.963316i	$-0.413516\pi$
$888$		0			0
$889$			7271.58i			0.274332i
$890$		0			0
$891$	274.247	+	158.336i	0.0103116	+	0.00595339i
$892$		0			0
$893$	−620.825	+	1075.30i	−0.0232644	+	0.0402951i
$894$		0			0
$895$	−19989.3	+	11540.8i	−0.746555	+	0.431024i
$896$		0			0
$897$	5563.78	−	4932.58i	0.207101	−	0.183605i
$898$		0			0
$899$	−9287.34	+	5362.05i	−0.344550	+	0.198926i
$900$		0			0
$901$	−21609.5	+	37428.8i	−0.799021	+	1.38394i
$902$		0			0
$903$	−3508.68	−	2025.74i	−0.129304	−	0.0746538i
$904$		0			0
$905$			60060.0i			2.20604i
$906$		0			0
$907$	1163.43	+	2015.11i	0.0425920	+	0.0737715i	0.886536	−	0.462661i	$-0.153105\pi$
$907$	1163.43	+	2015.11i	0.0425920	+	0.0737715i	−0.843944	+	0.536432i	$0.819772\pi$
$908$		0			0
$909$	2683.20			0.0979057
$910$		0			0
$911$	34700.9			1.26201			0.631005	−	0.775779i	$-0.282643\pi$
$911$	34700.9			1.26201			0.631005	+	0.775779i	$0.282643\pi$
$912$		0			0
$913$	−525.380	−	909.985i	−0.0190444	−	0.0329859i
$914$		0			0
$915$		−	855.522i		−	0.0309101i
$916$		0			0
$917$	−1013.90	−	585.377i	−0.0365126	−	0.0210805i
$918$		0			0
$919$	−15829.7	+	27417.9i	−0.568199	+	0.984149i	0.428546	+	0.903520i	$0.359026\pi$
$919$	−15829.7	+	27417.9i	−0.568199	+	0.984149i	−0.996744	+	0.0806286i	$0.974307\pi$
$920$		0			0
$921$	17506.3	−	10107.3i	0.626334	−	0.361614i
$922$		0			0
$923$	−11894.5	−	13416.6i	−0.424173	−	0.478453i
$924$		0			0
$925$	3206.78	−	1851.44i	0.113987	−	0.0658107i
$926$		0			0
$927$	−2992.30	+	5182.81i	−0.106019	+	0.183631i
$928$		0			0
$929$	34177.5	+	19732.4i	1.20703	+	0.696877i	0.962109	−	0.272667i	$-0.0879056\pi$
$929$	34177.5	+	19732.4i	1.20703	+	0.696877i	0.244918	+	0.969544i	$0.421239\pi$
$930$		0			0
$931$			3761.28i			0.132407i
$932$		0			0
$933$	−13194.2	−	22853.1i	−0.462979	−	0.801904i
$934$		0			0
$935$	3894.68			0.136224
$936$		0			0
$937$	−572.068			−0.0199452			−0.00997260	−	0.999950i	$-0.503174\pi$
$937$	−572.068			−0.0199452			−0.00997260	+	0.999950i	$0.503174\pi$
$938$		0			0
$939$	−1930.05	−	3342.94i	−0.0670764	−	0.116180i
$940$		0			0
$941$			26136.2i			0.905437i	0.891654	+	0.452718i	$0.149546\pi$
$941$			26136.2i			0.905437i	−0.891654	+	0.452718i	$0.850454\pi$
$942$		0			0
$943$	10441.7	+	6028.51i	0.360581	+	0.208182i
$944$		0			0
$945$	758.366	−	1313.53i	0.0261054	−	0.0452160i
$946$		0			0
$947$	−8465.13	+	4887.34i	−0.290475	+	0.167706i	−0.638156	−	0.769907i	$-0.720303\pi$
$947$	−8465.13	+	4887.34i	−0.290475	+	0.167706i	0.347681	+	0.937613i	$0.386969\pi$
$948$		0			0
$949$	−15672.4	+	46999.6i	−0.536089	+	1.60766i
$950$		0			0
$951$	−27785.5	+	16042.0i	−0.947431	+	0.547000i
$952$		0			0
$953$	18961.0	−	32841.4i	0.644498	−	1.11630i	−0.339919	−	0.940455i	$-0.610400\pi$
$953$	18961.0	−	32841.4i	0.644498	−	1.11630i	0.984417	−	0.175849i	$-0.0562670\pi$
$954$		0			0
$955$	−36338.9	−	20980.2i	−1.23131	−	0.710895i
$956$		0			0
$957$		−	688.350i		−	0.0232510i
$958$		0			0
$959$	−5626.20	−	9744.86i	−0.189447	−	0.328131i
$960$		0			0
$961$	−3597.42			−0.120755
$962$		0			0
$963$	−18803.8			−0.629226
$964$		0			0
$965$	3993.64	+	6917.19i	0.133223	+	0.230749i
$966$		0			0
$967$			23198.3i			0.771467i	0.922610	+	0.385733i	$0.126052\pi$
$967$			23198.3i			0.771467i	−0.922610	+	0.385733i	$0.873948\pi$
$968$		0			0
$969$	1999.50	+	1154.41i	0.0662880	+	0.0382714i
$970$		0			0
$971$	17277.8	−	29926.0i	0.571030	−	0.989053i	−0.425430	−	0.904991i	$-0.639877\pi$
$971$	17277.8	−	29926.0i	0.571030	−	0.989053i	0.996461	−	0.0840622i	$-0.0267894\pi$
$972$		0			0
$973$	−7416.52	+	4281.93i	−0.244360	+	0.141082i
$974$		0			0
$975$	2662.51	+	13018.5i	0.0874549	+	0.427615i
$976$		0			0
$977$	26697.5	−	15413.8i	0.874236	−	0.504740i	0.00548232	−	0.999985i	$-0.498255\pi$
$977$	26697.5	−	15413.8i	0.874236	−	0.504740i	0.868754	+	0.495245i	$0.164922\pi$
$978$		0			0
$979$	−1489.04	+	2579.09i	−0.0486107	+	0.0841961i
$980$		0			0
$981$	−7094.85	−	4096.21i	−0.230908	−	0.133315i
$982$		0			0
$983$			35014.7i			1.13611i	0.822990	+	0.568055i	$0.192304\pi$
$983$			35014.7i			1.13611i	−0.822990	+	0.568055i	$0.807696\pi$
$984$		0			0
$985$	−623.630	−	1080.16i	−0.0201731	−	0.0349408i
$986$		0			0
$987$	1233.99			0.0397958
$988$		0			0
$989$	−18833.6			−0.605535
$990$		0			0
$991$	−21702.4	−	37589.7i	−0.695661	−	1.20492i	−0.969957	−	0.243275i	$-0.921778\pi$
$991$	−21702.4	−	37589.7i	−0.695661	−	1.20492i	0.274297	−	0.961645i	$-0.411555\pi$
$992$		0			0
$993$		−	12491.4i		−	0.399198i
$994$		0			0
$995$	70176.3	+	40516.3i	2.23592	+	1.29091i
$996$		0			0
$997$	−11481.0	+	19885.6i	−0.364700	+	0.631679i	−0.988728	−	0.149723i	$-0.952162\pi$
$997$	−11481.0	+	19885.6i	−0.364700	+	0.631679i	0.624028	+	0.781402i	$0.285495\pi$
$998$		0			0
$999$	916.246	−	528.995i	0.0290178	−	0.0167534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.4.q.c.49.3	✓	6
3.2	odd	2		468.4.t.f.361.1		6
4.3	odd	2		624.4.bv.f.49.3		6
13.2	odd	12		2028.4.a.o.1.6		6
13.3	even	3		2028.4.b.h.337.6		6
13.4	even	6	inner	156.4.q.c.121.1	yes	6
13.10	even	6		2028.4.b.h.337.1		6
13.11	odd	12		2028.4.a.o.1.1		6
39.17	odd	6		468.4.t.f.433.3		6
52.43	odd	6		624.4.bv.f.433.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.4.q.c.49.3	✓	6	1.1	even	1	trivial
156.4.q.c.121.1	yes	6	13.4	even	6	inner
468.4.t.f.361.1		6	3.2	odd	2
468.4.t.f.433.3		6	39.17	odd	6
624.4.bv.f.49.3		6	4.3	odd	2
624.4.bv.f.433.1		6	52.43	odd	6
2028.4.a.o.1.1		6	13.11	odd	12
2028.4.a.o.1.6		6	13.2	odd	12
2028.4.b.h.337.1		6	13.10	even	6
2028.4.b.h.337.6		6	13.3	even	3

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	156.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +14.8155i q^{5} +(3.28368 + 1.89583i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-3.38576 + 1.95477i) q^{11} +(-44.4652 - 14.8273i) q^{13} +(-38.4917 + 22.2232i) q^{15} +(-33.6203 + 58.2320i) q^{17} +(-9.91216 - 5.72279i) q^{19} +11.3750i q^{21} +(26.4388 + 45.7933i) q^{23} -94.4977 q^{25} -27.0000 q^{27} +(29.3449 + 50.8269i) q^{29} +182.725i q^{31} +(-10.1573 - 5.86431i) q^{33} +(-28.0876 + 48.6492i) q^{35} +(-33.9350 + 19.5924i) q^{37} +(-28.1754 - 137.765i) q^{39} +(197.469 - 114.009i) q^{41} +(-178.087 + 308.456i) q^{43} +(-115.475 - 66.6695i) q^{45} -108.483i q^{47} +(-164.312 - 284.596i) q^{49} -201.722 q^{51} +642.753 q^{53} +(-28.9608 - 50.1616i) q^{55} -34.3367i q^{57} +(550.716 + 317.956i) q^{59} +(-9.62421 + 16.6696i) q^{61} +(-29.5531 + 17.0625i) q^{63} +(219.673 - 658.772i) q^{65} +(421.110 - 243.128i) q^{67} +(-79.3163 + 137.380i) q^{69} +(331.280 + 191.264i) q^{71} -1057.00i q^{73} +(-141.747 - 245.512i) q^{75} -14.8237 q^{77} +460.065 q^{79} +(-40.5000 - 70.1481i) q^{81} +268.768i q^{83} +(-862.734 - 498.100i) q^{85} +(-88.0347 + 152.481i) q^{87} +(659.691 - 380.873i) q^{89} +(-117.899 - 132.987i) q^{91} +(-474.733 + 274.087i) q^{93} +(84.7857 - 146.853i) q^{95} +(-613.504 - 354.207i) q^{97} -35.1859i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 9 q^{7} - 27 q^{9} - 120 q^{11} - 77 q^{13} + 36 q^{15} + 32 q^{17} - 24 q^{19} + 104 q^{23} - 166 q^{25} - 162 q^{27} + 220 q^{29} - 360 q^{33} - 88 q^{35} - 684 q^{37} - 66 q^{39} + 576 q^{41}+ \cdots - 873 q^{97}+O(q^{100}) \) 6 * q + 9 * q^3 + 9 * q^7 - 27 * q^9 - 120 * q^11 - 77 * q^13 + 36 * q^15 + 32 * q^17 - 24 * q^19 + 104 * q^23 - 166 * q^25 - 162 * q^27 + 220 * q^29 - 360 * q^33 - 88 * q^35 - 684 * q^37 - 66 * q^39 + 576 * q^41 + 233 * q^43 + 108 * q^45 + 38 * q^49 + 192 * q^51 + 732 * q^53 + 702 * q^55 - 1458 * q^59 + 595 * q^61 - 81 * q^63 + 698 * q^65 - 1869 * q^67 - 312 * q^69 + 2280 * q^71 - 249 * q^75 + 2076 * q^77 + 2222 * q^79 - 243 * q^81 - 3564 * q^85 - 660 * q^87 - 384 * q^89 + 3833 * q^91 - 189 * q^93 - 90 * q^95 - 873 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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