LMFDB - Embedded newform 252.7.z.e.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,7,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	252.z (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:	$57.9736290722$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + 1061 x^{6} + 35442 x^{5} + 1155979 x^{4} + 17325616 x^{3} + 201523590 x^{2} + \cdots + 5192355364 $ x^8 - 2x^7 + 1061x^6 + 35442x^5 + 1155979x^4 + 17325616x^3 + 201523590x^2 + 1200774512*x + 5192355364
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$-5.94197 - 10.2918i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.7.z.e.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0783677 - 0.0452456i) q^{5} +(-218.562 - 264.348i) q^{7} +O(q^{10})$	$q+(0.0783677 - 0.0452456i) q^{5} +(-218.562 - 264.348i) q^{7} +(1139.94 - 1974.43i) q^{11} +11.1483i q^{13} +(4462.04 + 2576.16i) q^{17} +(-1501.28 + 866.766i) q^{19} +(-1173.42 - 2032.43i) q^{23} +(-7812.50 + 13531.6i) q^{25} +13880.2 q^{29} +(-35997.5 - 20783.2i) q^{31} +(-29.0887 - 10.8274i) q^{35} +(-1039.36 - 1800.23i) q^{37} -33805.2i q^{41} -105285. q^{43} +(86534.1 - 49960.5i) q^{47} +(-22110.6 + 115553. i) q^{49} +(-52238.9 + 90480.4i) q^{53} -206.309i q^{55} +(-194414. - 112245. i) q^{59} +(266700. - 153979. i) q^{61} +(0.504411 + 0.873666i) q^{65} +(118138. - 204621. i) q^{67} -586114. q^{71} +(-558139. - 322242. i) q^{73} +(-771084. + 130195. i) q^{77} +(269093. + 466084. i) q^{79} -602657. i q^{83} +466.240 q^{85} +(-1.06824e6 + 616746. i) q^{89} +(2947.03 - 2436.59i) q^{91} +(-78.4346 + 135.853i) q^{95} -339514. i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 294 q^{5} + 232 q^{7}+O(q^{10}) $ 8 * q + 294 * q^5 + 232 * q^7	$ 8 q + 294 q^{5} + 232 q^{7} - 378 q^{11} - 852 q^{17} + 3690 q^{19} - 15600 q^{23} + 3386 q^{25} + 68604 q^{29} + 23028 q^{31} - 93828 q^{35} + 15914 q^{37} - 170044 q^{43} - 102180 q^{47} + 157340 q^{49} - 196410 q^{53} + 662550 q^{59} - 23928 q^{61} - 14892 q^{65} + 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 1584738 q^{77} - 493868 q^{79} - 1329816 q^{85} - 604260 q^{89} + 3831690 q^{91} - 448944 q^{95}+O(q^{100}) $ 8 * q + 294 * q^5 + 232 * q^7 - 378 * q^11 - 852 * q^17 + 3690 * q^19 - 15600 * q^23 + 3386 * q^25 + 68604 * q^29 + 23028 * q^31 - 93828 * q^35 + 15914 * q^37 - 170044 * q^43 - 102180 * q^47 + 157340 * q^49 - 196410 * q^53 + 662550 * q^59 - 23928 * q^61 - 14892 * q^65 + 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 1584738 * q^77 - 493868 * q^79 - 1329816 * q^85 - 604260 * q^89 + 3831690 * q^91 - 448944 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0783677	−	0.0452456i	0.000626941	−	0.000361965i	−0.499686	−	0.866206i	$-0.666551\pi$
$5$	0.0783677	−	0.0452456i	0.000626941	−	0.000361965i	0.500313	+	0.865844i	$0.333218\pi$
$6$		0			0
$7$	−218.562	−	264.348i	−0.637206	−	0.770693i
$7$	−218.562	−	264.348i	−0.637206	−	0.770693i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1139.94	−	1974.43i	0.856453	−	1.48342i	−0.0188378	−	0.999823i	$-0.505997\pi$
$11$	1139.94	−	1974.43i	0.856453	−	1.48342i	0.875291	−	0.483597i	$-0.160670\pi$
$12$		0			0
$13$			11.1483i			0.00507433i	0.999997	+	0.00253716i	$0.000807605\pi$
$13$			11.1483i			0.00507433i	−0.999997	+	0.00253716i	$0.999192\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4462.04	+	2576.16i	0.908211	+	0.524356i	0.879855	−	0.475242i	$-0.157639\pi$
$17$	4462.04	+	2576.16i	0.908211	+	0.524356i	0.0283562	+	0.999598i	$0.490973\pi$
$18$		0			0
$19$	−1501.28	+	866.766i	−0.218878	+	0.126369i	−0.605430	−	0.795898i	$-0.706999\pi$
$19$	−1501.28	+	866.766i	−0.218878	+	0.126369i	0.386553	+	0.922267i	$0.373666\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1173.42	−	2032.43i	−0.0964432	−	0.167045i	0.813767	−	0.581192i	$-0.197413\pi$
$23$	−1173.42	−	2032.43i	−0.0964432	−	0.167045i	−0.910210	+	0.414147i	$0.864080\pi$
$24$		0			0
$25$	−7812.50	+	13531.6i	−0.500000	+	0.866025i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	13880.2			0.569116			0.284558	−	0.958659i	$-0.408153\pi$
$29$	13880.2			0.569116			0.284558	+	0.958659i	$0.408153\pi$
$30$		0			0
$31$	−35997.5	−	20783.2i	−1.20834	−	0.697633i	−0.245940	−	0.969285i	$-0.579097\pi$
$31$	−35997.5	−	20783.2i	−1.20834	−	0.697633i	−0.962396	+	0.271652i	$0.912430\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−29.0887	−	10.8274i	−0.000678455	−	0.000252533i
$36$		0			0
$37$	−1039.36	−	1800.23i	−0.0205193	−	0.0355404i	0.855583	−	0.517665i	$-0.173199\pi$
$37$	−1039.36	−	1800.23i	−0.0205193	−	0.0355404i	−0.876103	+	0.482125i	$0.839865\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	33805.2i		−	0.490492i	−0.969461	−	0.245246i	$-0.921131\pi$
$41$		−	33805.2i		−	0.490492i	0.969461	−	0.245246i	$-0.0788688\pi$
$42$		0			0
$43$	−105285.			−1.32423			−0.662114	−	0.749404i	$-0.730340\pi$
$43$	−105285.			−1.32423			−0.662114	+	0.749404i	$0.730340\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	86534.1	−	49960.5i	0.833477	−	0.481208i	−0.0215644	−	0.999767i	$-0.506865\pi$
$47$	86534.1	−	49960.5i	0.833477	−	0.481208i	0.855042	+	0.518559i	$0.173531\pi$
$48$		0			0
$49$	−22110.6	+	115553.i	−0.187937	+	0.982181i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−52238.9	+	90480.4i	−0.350886	+	0.607753i	−0.986405	−	0.164333i	$-0.947453\pi$
$53$	−52238.9	+	90480.4i	−0.350886	+	0.607753i	0.635519	+	0.772085i	$0.280786\pi$
$54$		0			0
$55$		−	206.309i		−	0.00124002i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−194414.	−	112245.i	−0.946610	−	0.546526i	−0.0545841	−	0.998509i	$-0.517383\pi$
$59$	−194414.	−	112245.i	−0.946610	−	0.546526i	−0.892026	+	0.451983i	$0.850717\pi$
$60$		0			0
$61$	266700.	−	153979.i	1.17499	−	0.678380i	0.220138	−	0.975469i	$-0.429349\pi$
$61$	266700.	−	153979.i	1.17499	−	0.678380i	0.954850	+	0.297089i	$0.0960158\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.504411	+	0.873666i	1.83673e−6	+	3.18131e-6i
$66$		0			0
$67$	118138.	−	204621.i	0.392795	−	0.680341i	−0.600022	−	0.799983i	$-0.704842\pi$
$67$	118138.	−	204621.i	0.392795	−	0.680341i	0.992817	+	0.119643i	$0.0381749\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−586114.			−1.63760			−0.818799	−	0.574081i	$-0.805360\pi$
$71$	−586114.			−1.63760			−0.818799	+	0.574081i	$0.805360\pi$
$72$		0			0
$73$	−558139.	−	322242.i	−1.43474	−	0.828348i	−0.437264	−	0.899333i	$-0.644052\pi$
$73$	−558139.	−	322242.i	−1.43474	−	0.828348i	−0.997477	+	0.0709851i	$0.977386\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−771084.	+	130195.i	−1.68900	+	0.285182i
$78$		0			0
$79$	269093.	+	466084.i	0.545785	+	0.945328i	0.998557	+	0.0537014i	$0.0171019\pi$
$79$	269093.	+	466084.i	0.545785	+	0.945328i	−0.452772	+	0.891626i	$0.649565\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	602657.i		−	1.05399i	−0.849869	−	0.526994i	$-0.823319\pi$
$83$		−	602657.i		−	1.05399i	0.849869	−	0.526994i	$-0.176681\pi$
$84$		0			0
$85$	466.240			0.000759194
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.06824e6	+	616746.i	−1.51529	+	0.874856i	−0.515456	+	0.856916i	$0.672377\pi$
$89$	−1.06824e6	+	616746.i	−1.51529	+	0.874856i	−0.999839	+	0.0179396i	$0.994289\pi$
$90$		0			0
$91$	2947.03	−	2436.59i	0.00391075	−	0.00323339i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−78.4346	+	135.853i	−9.14823e−5	+	0.000158452i
$96$		0			0
$97$		−	339514.i		−	0.372000i	−0.982550	−	0.186000i	$-0.940448\pi$
$97$		−	339514.i		−	0.372000i	0.982550	−	0.186000i	$-0.0595524\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−479993.	−	277124.i	−0.465877	−	0.268974i	0.248635	−	0.968597i	$-0.420018\pi$
$101$	−479993.	−	277124.i	−0.465877	−	0.268974i	−0.714512	+	0.699623i	$0.753351\pi$
$102$		0			0
$103$	−785695.	+	453621.i	−0.719022	+	0.415128i	−0.814393	−	0.580314i	$-0.802930\pi$
$103$	−785695.	+	453621.i	−0.719022	+	0.415128i	0.0953705	+	0.995442i	$0.469596\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−362326.	−	627566.i	−0.295766	−	0.512281i	0.679397	−	0.733771i	$-0.262241\pi$
$107$	−362326.	−	627566.i	−0.295766	−	0.512281i	−0.975163	+	0.221490i	$0.928908\pi$
$108$		0			0
$109$	−77877.9	+	134889.i	−0.0601360	+	0.104159i	−0.894526	−	0.447016i	$-0.852487\pi$
$109$	−77877.9	+	134889.i	−0.0601360	+	0.104159i	0.834390	+	0.551174i	$0.185820\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	225088.			0.155997			0.0779987	−	0.996953i	$-0.475147\pi$
$113$	225088.			0.155997			0.0779987	+	0.996953i	$0.475147\pi$
$114$		0			0
$115$	−183.917	−	106.185i	−0.000120929	−	6.98181e-5i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−294229.	−	1.74258e6i	−0.174600	−	1.03408i
$120$		0			0
$121$	−1.71314e6	−	2.96725e6i	−0.967023	−	1.67493i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2827.85i			0.00144786i
$126$		0			0
$127$	−2.95637e6			−1.44327			−0.721635	−	0.692274i	$-0.756609\pi$
$127$	−2.95637e6			−1.44327			−0.721635	+	0.692274i	$0.756609\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−289300.	+	167028.i	−0.128687	+	0.0742976i	−0.562962	−	0.826483i	$-0.690338\pi$
$131$	−289300.	+	167028.i	−0.128687	+	0.0742976i	0.434274	+	0.900781i	$0.357005\pi$
$132$		0			0
$133$	557250.	+	207419.i	0.236862	+	0.0881644i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	116799.	−	202301.i	0.0454231	−	0.0786751i	−0.842420	−	0.538821i	$-0.818870\pi$
$137$	116799.	−	202301.i	0.0454231	−	0.0786751i	0.887843	+	0.460146i	$0.152203\pi$
$138$		0			0
$139$			2.77347e6i			1.03271i	0.856374	+	0.516355i	$0.172712\pi$
$139$			2.77347e6i			1.03271i	−0.856374	+	0.516355i	$0.827288\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	22011.6	+	12708.4i	0.00752736	+	0.00434592i
$144$		0			0
$145$	1087.76	−	628.017i	0.000356803	−	0.000206000i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	399353.	+	691700.i	0.120725	+	0.209102i	0.920054	−	0.391792i	$-0.128145\pi$
$149$	399353.	+	691700.i	0.120725	+	0.209102i	−0.799329	+	0.600894i	$0.794811\pi$
$150$		0			0
$151$	−2.96924e6	+	5.14288e6i	−0.862412	+	1.49374i	0.00718135	+	0.999974i	$0.497714\pi$
$151$	−2.96924e6	+	5.14288e6i	−0.862412	+	1.49374i	−0.869594	+	0.493768i	$0.835619\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3761.39			−0.00101007
$156$		0			0
$157$	−333838.	−	192741.i	−0.0862654	−	0.0498054i	0.456247	−	0.889853i	$-0.349193\pi$
$157$	−333838.	−	192741.i	−0.0862654	−	0.0498054i	−0.542512	+	0.840048i	$0.682527\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−280803.	+	754404.i	−0.0672860	+	0.180770i
$162$		0			0
$163$	−2.99408e6	−	5.18591e6i	−0.691355	−	1.19746i	−0.971394	−	0.237474i	$-0.923681\pi$
$163$	−2.99408e6	−	5.18591e6i	−0.691355	−	1.19746i	0.280039	−	0.959989i	$-0.409653\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	1.39878e6i		−	0.300332i	−0.988661	−	0.150166i	$-0.952019\pi$
$167$		−	1.39878e6i		−	0.300332i	0.988661	−	0.150166i	$-0.0479808\pi$
$168$		0			0
$169$	4.82668e6			0.999974
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.81139e6	+	5.08726e6i	−1.70179	+	0.982530i	−0.757843	+	0.652437i	$0.773747\pi$
$173$	−8.81139e6	+	5.08726e6i	−1.70179	+	0.982530i	−0.943949	+	0.330092i	$0.892920\pi$
$174$		0			0
$175$	5.28457e6	−	892282.i	0.986043	−	0.166490i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.27964e6	−	7.41256e6i	0.746188	−	1.29244i	−0.203450	−	0.979085i	$-0.565215\pi$
$179$	4.27964e6	−	7.41256e6i	0.746188	−	1.29244i	0.949638	−	0.313350i	$-0.101451\pi$
$180$		0			0
$181$		−	3.19101e6i		−	0.538137i	−0.963121	−	0.269068i	$-0.913284\pi$
$181$		−	3.19101e6i		−	0.538137i	0.963121	−	0.269068i	$-0.0867158\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−162.905	−	94.0531i	−2.57288e−5	−	1.48545e-5i
$186$		0			0
$187$	1.01729e7	−	5.87333e6i	1.55568	−	0.898173i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.67455e6	+	8.09655e6i	0.670871	+	1.16198i	0.977657	+	0.210205i	$0.0674131\pi$
$191$	4.67455e6	+	8.09655e6i	0.670871	+	1.16198i	−0.306786	+	0.951779i	$0.599254\pi$
$192$		0			0
$193$	−977142.	+	1.69246e6i	−0.135921	+	0.235422i	−0.925949	−	0.377649i	$-0.876733\pi$
$193$	−977142.	+	1.69246e6i	−0.135921	+	0.235422i	0.790028	+	0.613071i	$0.210066\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.09910e6			0.797750			0.398875	−	0.917005i	$-0.369401\pi$
$197$	6.09910e6			0.797750			0.398875	+	0.917005i	$0.369401\pi$
$198$		0			0
$199$	8.27147e6	+	4.77554e6i	1.04960	+	0.605987i	0.922537	−	0.385908i	$-0.126112\pi$
$199$	8.27147e6	+	4.77554e6i	1.04960	+	0.605987i	0.127062	+	0.991895i	$0.459445\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.03368e6	−	3.66920e6i	−0.362644	−	0.438614i
$204$		0			0
$205$	−1529.54	−	2649.24i	−0.000177541	−	0.000307510i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			3.95224e6i			0.432917i
$210$		0			0
$211$	−3.50535e6			−0.373151			−0.186575	−	0.982441i	$-0.559739\pi$
$211$	−3.50535e6			−0.373151			−0.186575	+	0.982441i	$0.559739\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8250.97	+	4763.70i	−0.000830213	+	0.000479324i
$216$		0			0
$217$	2.37369e6	+	1.40583e7i	0.232298	+	1.37579i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−28719.8	+	49744.2i	−0.00266075	+	0.00460856i
$222$		0			0
$223$			3.12055e6i			0.281395i	0.990053	+	0.140698i	$0.0449345\pi$
$223$			3.12055e6i			0.281395i	−0.990053	+	0.140698i	$0.955066\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.46876e6	+	3.73474e6i	0.553023	+	0.319288i	0.750340	−	0.661052i	$-0.229890\pi$
$227$	6.46876e6	+	3.73474e6i	0.553023	+	0.319288i	−0.197317	+	0.980340i	$0.563223\pi$
$228$		0			0
$229$	7.96006e6	−	4.59574e6i	0.662841	−	0.382692i	−0.130517	−	0.991446i	$-0.541664\pi$
$229$	7.96006e6	−	4.59574e6i	0.662841	−	0.382692i	0.793359	+	0.608754i	$0.208330\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.17134e6	+	1.41532e7i	0.645990	+	1.11889i	0.984072	+	0.177771i	$0.0568885\pi$
$233$	8.17134e6	+	1.41532e7i	0.645990	+	1.11889i	−0.338082	+	0.941117i	$0.609778\pi$
$234$		0			0
$235$	4520.99	−	7830.58i	0.000348361	−	0.000603379i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.11658e7			1.55039			0.775196	−	0.631721i	$-0.217651\pi$
$239$	2.11658e7			1.55039			0.775196	+	0.631721i	$0.217651\pi$
$240$		0			0
$241$	−1.13158e7	−	6.53316e6i	−0.808412	−	0.466737i	0.0379922	−	0.999278i	$-0.487904\pi$
$241$	−1.13158e7	−	6.53316e6i	−0.808412	−	0.466737i	−0.846404	+	0.532541i	$0.821237\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3495.49	+	10056.0i	0.000237690	+	0.000683796i
$246$		0			0
$247$	−9662.96	−	16736.7i	−0.000641238	−	0.00111066i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.43596e7i		−	0.908077i	−0.890982	−	0.454038i	$-0.849983\pi$
$251$		−	1.43596e7i		−	0.908077i	0.890982	−	0.454038i	$-0.150017\pi$
$252$		0			0
$253$	−5.35053e6			−0.330396
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.51641e6	+	1.45285e6i	−0.148246	+	0.0855896i	−0.572288	−	0.820053i	$-0.693944\pi$
$257$	−2.51641e6	+	1.45285e6i	−0.148246	+	0.0855896i	0.424042	+	0.905642i	$0.360611\pi$
$258$		0			0
$259$	−248722.	+	668214.i	−0.0143158	+	0.0384606i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.34154e7	−	2.32361e7i	0.737456	−	1.27731i	−0.216182	−	0.976353i	$-0.569360\pi$
$263$	1.34154e7	−	2.32361e7i	0.737456	−	1.27731i	0.953638	−	0.300957i	$-0.0973062\pi$
$264$		0			0
$265$			9454.32i			0.000508034i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.58515e7	+	9.15186e6i	0.814354	+	0.470168i	0.848466	−	0.529250i	$-0.177527\pi$
$269$	1.58515e7	+	9.15186e6i	0.814354	+	0.470168i	−0.0341115	+	0.999418i	$0.510860\pi$
$270$		0			0
$271$	2.11779e7	−	1.22270e7i	1.06408	−	0.614347i	0.137522	−	0.990499i	$-0.456086\pi$
$271$	2.11779e7	−	1.22270e7i	1.06408	−	0.614347i	0.926558	+	0.376152i	$0.122753\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.78115e7	+	3.08505e7i	0.856452	+	1.48342i
$276$		0			0
$277$	−1.53590e7	+	2.66025e7i	−0.722642	+	1.25165i	0.237296	+	0.971438i	$0.423739\pi$
$277$	−1.53590e7	+	2.66025e7i	−0.722642	+	1.25165i	−0.959937	+	0.280215i	$0.909594\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.13967e7			0.964333			0.482167	−	0.876080i	$-0.339850\pi$
$281$	2.13967e7			0.964333			0.482167	+	0.876080i	$0.339850\pi$
$282$		0			0
$283$	−2.02749e7	−	1.17057e7i	−0.894541	−	0.516464i	−0.0191160	−	0.999817i	$-0.506085\pi$
$283$	−2.02749e7	−	1.17057e7i	−0.894541	−	0.516464i	−0.875425	+	0.483354i	$0.839419\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.93634e6	+	7.38853e6i	−0.378019	+	0.312545i
$288$		0			0
$289$	1.20443e6	+	2.08614e6i	0.0498986	+	0.0864270i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	2.62759e7i		−	1.04461i	−0.852759	−	0.522305i	$-0.825072\pi$
$293$		−	2.62759e7i		−	1.04461i	0.852759	−	0.522305i	$-0.174928\pi$
$294$		0			0
$295$	−20314.4			−0.000791292
$296$		0			0
$297$		0			0
$298$		0			0
$299$	22658.2	−	13081.7i	0.000847639	−	0.000489385i
$300$		0			0
$301$	2.30113e7	+	2.78319e7i	0.843806	+	1.02057i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	13933.8	−	24134.0i	0.000491099	−	0.000850609i
$306$		0			0
$307$			1.25570e7i			0.433981i	0.976174	+	0.216990i	$0.0696241\pi$
$307$			1.25570e7i			0.433981i	−0.976174	+	0.216990i	$0.930376\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.02129e6	−	589640.i	−0.0339521	−	0.0196023i	0.482928	−	0.875660i	$-0.339573\pi$
$311$	−1.02129e6	−	589640.i	−0.0339521	−	0.0196023i	−0.516880	+	0.856058i	$0.672907\pi$
$312$		0			0
$313$	−7.70433e6	+	4.44810e6i	−0.251248	+	0.145058i	−0.620335	−	0.784337i	$-0.713004\pi$
$313$	−7.70433e6	+	4.44810e6i	−0.251248	+	0.145058i	0.369088	+	0.929395i	$0.379670\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.59927e6	−	1.48944e7i	−0.269950	−	0.467568i	0.698898	−	0.715221i	$-0.253674\pi$
$317$	−8.59927e6	−	1.48944e7i	−0.269950	−	0.467568i	−0.968849	+	0.247653i	$0.920341\pi$
$318$		0			0
$319$	1.58226e7	−	2.74055e7i	0.487421	−	0.844238i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.93171e6			−0.265050
$324$		0			0
$325$	−150855.	−	87096.0i	−0.00439449	−	0.00253716i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.21200e7	−	1.19557e7i	−0.901961	−	0.335727i
$330$		0			0
$331$	−2.93149e7	−	5.07749e7i	−0.808359	−	1.40012i	−0.914000	−	0.405714i	$-0.867023\pi$
$331$	−2.93149e7	−	5.07749e7i	−0.808359	−	1.40012i	0.105642	−	0.994404i	$-0.466310\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	21380.9i		−	0.000568712i
$336$		0			0
$337$	−5.26755e6			−0.137632			−0.0688159	−	0.997629i	$-0.521922\pi$
$337$	−5.26755e6			−0.137632			−0.0688159	+	0.997629i	$0.521922\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.20700e7	+	4.73831e7i	−2.06977	+	1.19498i
$342$		0			0
$343$	3.53786e7	−	1.94105e7i	0.876715	−	0.481010i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.35761e7	+	5.81555e7i	−0.803604	+	1.39188i	0.113626	+	0.993524i	$0.463754\pi$
$347$	−3.35761e7	+	5.81555e7i	−0.803604	+	1.39188i	−0.917230	+	0.398359i	$0.869580\pi$
$348$		0			0
$349$		−	4.50914e6i		−	0.106076i	−0.998592	−	0.0530380i	$-0.983110\pi$
$349$		−	4.50914e6i		−	0.106076i	0.998592	−	0.0530380i	$-0.0168905\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.90317e7	−	3.40820e7i	−1.34203	−	0.774819i	−0.354922	−	0.934896i	$-0.615493\pi$
$353$	−5.90317e7	−	3.40820e7i	−1.34203	−	0.774819i	−0.987105	+	0.160077i	$0.948826\pi$
$354$		0			0
$355$	−45932.4	+	26519.1i	−0.00102668	+	0.000592753i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.92553e7	−	5.06717e7i	−0.632298	−	1.09517i	−0.987081	−	0.160223i	$-0.948779\pi$
$359$	−2.92553e7	−	5.06717e7i	−0.632298	−	1.09517i	0.354783	−	0.934949i	$-0.384555\pi$
$360$		0			0
$361$	−2.20204e7	+	3.81404e7i	−0.468062	+	0.810707i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−58320.0			−0.00119933
$366$		0			0
$367$	5.04590e7	+	2.91325e7i	1.02080	+	0.589359i	0.914335	−	0.404958i	$-0.132714\pi$
$367$	5.04590e7	+	2.91325e7i	1.02080	+	0.589359i	0.106464	+	0.994317i	$0.466047\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.53357e7	−	5.96631e6i	0.691978	−	0.116838i
$372$		0			0
$373$	−2.16495e7	−	3.74981e7i	−0.417178	−	0.722574i	0.578476	−	0.815699i	$-0.303648\pi$
$373$	−2.16495e7	−	3.74981e7i	−0.417178	−	0.722574i	−0.995654	+	0.0931254i	$0.970314\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			154740.i			0.00288788i
$378$		0			0
$379$	3.56341e7			0.654558			0.327279	−	0.944928i	$-0.393868\pi$
$379$	3.56341e7			0.654558			0.327279	+	0.944928i	$0.393868\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.96797e6	+	3.44561e6i	−0.106226	+	0.0613295i	−0.552172	−	0.833730i	$-0.686201\pi$
$383$	−5.96797e6	+	3.44561e6i	−0.106226	+	0.0613295i	0.445946	+	0.895060i	$0.352867\pi$
$384$		0			0
$385$	−54537.3	+	45091.2i	−0.000955678	+	0.000790150i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.06591e6	+	3.57826e6i	−0.0350964	+	0.0607887i	−0.883040	−	0.469298i	$-0.844507\pi$
$389$	−2.06591e6	+	3.57826e6i	−0.0350964	+	0.0607887i	0.847944	+	0.530086i	$0.177840\pi$
$390$		0			0
$391$		−	1.20917e7i		−	0.202282i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	42176.5	+	24350.6i	0.000684351	+	0.000395110i
$396$		0			0
$397$	−7.57634e7	+	4.37420e7i	−1.21084	+	0.699081i	−0.962943	−	0.269705i	$-0.913074\pi$
$397$	−7.57634e7	+	4.37420e7i	−1.21084	+	0.699081i	−0.247900	+	0.968786i	$0.579741\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.54173e7	−	6.13446e7i	−0.549266	−	0.951356i	−0.998325	−	0.0578539i	$-0.981574\pi$
$401$	−3.54173e7	−	6.13446e7i	−0.549266	−	0.951356i	0.449060	−	0.893502i	$-0.351759\pi$
$402$		0			0
$403$	231697.	−	401311.i	0.00354002	−	0.00613149i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.73924e6			−0.0702951
$408$		0			0
$409$	−4.74349e7	−	2.73866e7i	−0.693312	−	0.400284i	0.111540	−	0.993760i	$-0.464422\pi$
$409$	−4.74349e7	−	2.73866e7i	−0.693312	−	0.400284i	−0.804851	+	0.593476i	$0.797755\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.28197e7	+	7.59253e7i	0.181982	+	1.07780i
$414$		0			0
$415$	−27267.6	−	47228.8i	−0.000381507	−	0.000660789i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	1.26910e8i		−	1.72525i	−0.505842	−	0.862626i	$-0.668818\pi$
$419$		−	1.26910e8i		−	1.72525i	0.505842	−	0.862626i	$-0.331182\pi$
$420$		0			0
$421$	−2.52286e7			−0.338102			−0.169051	−	0.985607i	$-0.554070\pi$
$421$	−2.52286e7			−0.338102			−0.169051	+	0.985607i	$0.554070\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.97194e7	+	4.02525e7i	−0.908211	+	0.524356i
$426$		0			0
$427$	−9.89945e7	−	3.68476e7i	−1.27153	−	0.473288i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.00037e7	−	1.21250e8i	0.874358	−	1.51443i	0.0169134	−	0.999857i	$-0.494616\pi$
$431$	7.00037e7	−	1.21250e8i	0.874358	−	1.51443i	0.857445	−	0.514576i	$-0.172051\pi$
$432$		0			0
$433$		−	7.55793e7i		−	0.930978i	−0.885054	−	0.465489i	$-0.845879\pi$
$433$		−	7.55793e7i		−	0.930978i	0.885054	−	0.465489i	$-0.154121\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.52328e6	+	2.03417e6i	0.0422185	+	0.0243749i
$438$		0			0
$439$	−8.60392e7	+	4.96747e7i	−1.01696	+	0.587140i	−0.913221	−	0.407465i	$-0.866413\pi$
$439$	−8.60392e7	+	4.96747e7i	−1.01696	+	0.587140i	−0.103736	+	0.994605i	$0.533080\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.18080e7	+	5.50930e7i	0.365868	+	0.633703i	0.988915	−	0.148482i	$-0.0474387\pi$
$443$	3.18080e7	+	5.50930e7i	0.365868	+	0.633703i	−0.623047	+	0.782185i	$0.714105\pi$
$444$		0			0
$445$	−55810.1	+	96665.9i	−0.000633334	+	0.00109697i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.37071e6			−0.0261903			−0.0130951	−	0.999914i	$-0.504168\pi$
$449$	−2.37071e6			−0.0261903			−0.0130951	+	0.999914i	$0.504168\pi$
$450$		0			0
$451$	−6.67461e7	−	3.85359e7i	−0.727606	−	0.420083i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	120.707	−	324.290i	1.28144e−6	−	3.44270e-6i
$456$		0			0
$457$	8.95758e7	+	1.55150e8i	0.938517	+	1.62556i	0.768239	+	0.640163i	$0.221133\pi$
$457$	8.95758e7	+	1.55150e8i	0.938517	+	1.62556i	0.170278	+	0.985396i	$0.445533\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			6.44992e7i			0.658342i	0.944270	+	0.329171i	$0.106769\pi$
$461$			6.44992e7i			0.658342i	−0.944270	+	0.329171i	$0.893231\pi$
$462$		0			0
$463$	8.12336e7			0.818451			0.409226	−	0.912433i	$-0.365799\pi$
$463$	8.12336e7			0.818451			0.409226	+	0.912433i	$0.365799\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.15323e7	−	4.70727e7i	0.800533	−	0.462188i	−0.0431244	−	0.999070i	$-0.513731\pi$
$467$	8.15323e7	−	4.70727e7i	0.800533	−	0.462188i	0.843658	+	0.536882i	$0.180398\pi$
$468$		0			0
$469$	−7.99117e7	+	1.34928e7i	−0.774625	+	0.130793i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.20019e8	+	2.07879e8i	−1.13414	+	1.96438i
$474$		0			0
$475$		−	2.70864e7i		−	0.252738i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.84049e8	−	1.06261e8i	−1.67466	−	0.966865i	−0.964974	−	0.262347i	$-0.915504\pi$
$479$	−1.84049e8	−	1.06261e8i	−1.67466	−	0.966865i	−0.709686	−	0.704518i	$-0.751163\pi$
$480$		0			0
$481$	20069.5	−	11587.1i	0.000180344	−	0.000104121i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15361.5	−	26606.9i	−0.000134651	−	0.000233222i
$486$		0			0
$487$	1.39442e7	−	2.41521e7i	0.120728	−	0.209106i	−0.799327	−	0.600896i	$-0.794811\pi$
$487$	1.39442e7	−	2.41521e7i	0.120728	−	0.209106i	0.920055	+	0.391790i	$0.128144\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.07655e8			1.75427			0.877137	−	0.480240i	$-0.159450\pi$
$491$	2.07655e8			1.75427			0.877137	+	0.480240i	$0.159450\pi$
$492$		0			0
$493$	6.19339e7	+	3.57576e7i	0.516878	+	0.298420i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.28102e8	+	1.54938e8i	1.04349	+	1.26209i
$498$		0			0
$499$	−4.96648e6	−	8.60219e6i	−0.0399712	−	0.0692321i	0.845348	−	0.534216i	$-0.179393\pi$
$499$	−4.96648e6	−	8.60219e6i	−0.0399712	−	0.0692321i	−0.885319	+	0.464984i	$0.846060\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	1.17586e8i		−	0.923956i	−0.886891	−	0.461978i	$-0.847140\pi$
$503$		−	1.17586e8i		−	0.923956i	0.886891	−	0.461978i	$-0.152860\pi$
$504$		0			0
$505$	−50154.6			−0.000389437
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.25834e7	−	5.34530e7i	0.702069	−	0.405340i	−0.106049	−	0.994361i	$-0.533820\pi$
$509$	9.25834e7	−	5.34530e7i	0.702069	−	0.405340i	0.808117	+	0.589021i	$0.200487\pi$
$510$		0			0
$511$	3.68039e7	+	2.17972e8i	0.275823	+	1.63357i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−41048.7	+	71098.5i	−0.000300523	+	0.000520521i
$516$		0			0
$517$		−	2.27808e8i		−	1.64853i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.88379e7	−	4.55171e7i	−0.557471	−	0.321856i	0.194659	−	0.980871i	$-0.437640\pi$
$521$	−7.88379e7	−	4.55171e7i	−0.557471	−	0.321856i	−0.752130	+	0.659015i	$0.770973\pi$
$522$		0			0
$523$	4.65798e7	−	2.68929e7i	0.325606	−	0.187989i	−0.328282	−	0.944580i	$-0.606470\pi$
$523$	4.65798e7	−	2.68929e7i	0.325606	−	0.187989i	0.653889	+	0.756591i	$0.273136\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.07082e8	−	1.85471e8i	−0.731616	−	1.26720i
$528$		0			0
$529$	7.12641e7	−	1.23433e8i	0.481397	−	0.833805i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	376871.			0.00248892
$534$		0			0
$535$	−56789.2	−	32787.3i	−0.000370855	−	0.000214113i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.02946e8	+	1.75379e8i	1.29603	+	1.11998i
$540$		0			0
$541$	8.51256e7	+	1.47442e8i	0.537612	+	0.931170i	0.999032	+	0.0439889i	$0.0140066\pi$
$541$	8.51256e7	+	1.47442e8i	0.537612	+	0.931170i	−0.461421	+	0.887182i	$0.652660\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			14094.5i			8.70685e-5i
$546$		0			0
$547$	2.69779e8			1.64834			0.824170	−	0.566343i	$-0.191642\pi$
$547$	2.69779e8			1.64834			0.824170	+	0.566343i	$0.191642\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.08381e7	+	1.20309e7i	−0.124567	+	0.0719187i
$552$		0			0
$553$	6.43947e7	−	1.73002e8i	0.380780	−	1.02300i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.73125e7	+	1.51230e8i	−0.505255	+	0.875128i	0.494726	+	0.869049i	$0.335268\pi$
$557$	−8.73125e7	+	1.51230e8i	−0.505255	+	0.875128i	−0.999982	+	0.00607879i	$0.998065\pi$
$558$		0			0
$559$		−	1.17375e6i		−	0.00671956i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.68901e8	+	1.55250e8i	1.50684	+	0.869976i	0.999968	+	0.00795588i	$0.00253246\pi$
$563$	2.68901e8	+	1.55250e8i	1.50684	+	0.869976i	0.506874	+	0.862020i	$0.330801\pi$
$564$		0			0
$565$	17639.6	−	10184.3i	9.78013e−5	−	5.64656e-5i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.21511e7	−	5.56873e7i	−0.174525	−	0.302287i	0.765472	−	0.643470i	$-0.222506\pi$
$569$	−3.21511e7	−	5.56873e7i	−0.174525	−	0.302287i	−0.939997	+	0.341183i	$0.889172\pi$
$570$		0			0
$571$	2.92864e7	−	5.07255e7i	0.157310	−	0.272470i	−0.776588	−	0.630009i	$-0.783051\pi$
$571$	2.92864e7	−	5.07255e7i	0.157310	−	0.272470i	0.933898	+	0.357540i	$0.116384\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.66695e7			0.192886
$576$		0			0
$577$	1.85466e7	+	1.07079e7i	0.0965468	+	0.0557413i	0.547496	−	0.836808i	$-0.315581\pi$
$577$	1.85466e7	+	1.07079e7i	0.0965468	+	0.0557413i	−0.450949	+	0.892550i	$0.648914\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.59311e8	+	1.31718e8i	−0.812302	+	0.671608i
$582$		0			0
$583$	1.19098e8	+	2.06284e8i	0.601035	+	1.04102i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1.58381e8i		−	0.783050i	−0.920167	−	0.391525i	$-0.871948\pi$
$587$		−	1.58381e8i		−	0.783050i	0.920167	−	0.391525i	$-0.128052\pi$
$588$		0			0
$589$	7.20566e7			0.352637
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.39682e6	−	2.53850e6i	0.0210850	−	0.0121735i	−0.489420	−	0.872048i	$-0.662792\pi$
$593$	4.39682e6	−	2.53850e6i	0.0210850	−	0.0121735i	0.510505	+	0.859875i	$0.329458\pi$
$594$		0			0
$595$	−101902.	−	123250.i	−0.000483763	−	0.000585106i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.46545e8	+	2.53823e8i	−0.681850	+	1.18100i	0.292565	+	0.956246i	$0.405491\pi$
$599$	−1.46545e8	+	2.53823e8i	−0.681850	+	1.18100i	−0.974416	+	0.224754i	$0.927842\pi$
$600$		0			0
$601$			2.90021e8i			1.33600i	0.744162	+	0.667999i	$0.232849\pi$
$601$			2.90021e8i			1.33600i	−0.744162	+	0.667999i	$0.767151\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−268510.	−	155024.i	−0.00121253	−	0.000700056i
$606$		0			0
$607$	−2.64810e8	+	1.52888e8i	−1.18405	+	0.683609i	−0.956947	−	0.290263i	$-0.906257\pi$
$607$	−2.64810e8	+	1.52888e8i	−1.18405	+	0.683609i	−0.227098	+	0.973872i	$0.572924\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	556975.	+	964708.i	0.00244181	+	0.00422934i
$612$		0			0
$613$	6.23753e6	−	1.08037e7i	0.0270789	−	0.0469020i	−0.852168	−	0.523268i	$-0.824713\pi$
$613$	6.23753e6	−	1.08037e7i	0.0270789	−	0.0469020i	0.879247	+	0.476366i	$0.158046\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.75554e8			1.59888			0.799442	−	0.600743i	$-0.205129\pi$
$617$	3.75554e8			1.59888			0.799442	+	0.600743i	$0.205129\pi$
$618$		0			0
$619$	−7.09760e7	−	4.09780e7i	−0.299254	−	0.172774i	0.342854	−	0.939389i	$-0.388606\pi$
$619$	−7.09760e7	−	4.09780e7i	−0.299254	−	0.172774i	−0.642108	+	0.766615i	$0.721940\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.96511e8	+	1.47589e8i	1.63980	+	0.610364i
$624$		0			0
$625$	−1.22070e8	−	2.11432e8i	−0.499999	−	0.866024i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.07103e7i		−	0.0430376i
$630$		0			0
$631$	3.38493e8			1.34729			0.673646	−	0.739054i	$-0.264727\pi$
$631$	3.38493e8			1.34729			0.673646	+	0.739054i	$0.264727\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−231684.	+	133763.i	−0.000904846	+	0.000522413i
$636$		0			0
$637$	−1.28822e6	−	246495.i	−0.00498391	−	0.000953653i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.02548e8	−	3.50823e8i	0.769048	−	1.33203i	−0.169032	−	0.985611i	$-0.554064\pi$
$641$	2.02548e8	−	3.50823e8i	0.769048	−	1.33203i	0.938080	−	0.346419i	$-0.112603\pi$
$642$		0			0
$643$		−	4.76136e8i		−	1.79101i	−0.445050	−	0.895506i	$-0.646814\pi$
$643$		−	4.76136e8i		−	1.79101i	0.445050	−	0.895506i	$-0.353186\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.52008e7	−	8.77616e6i	−0.0561245	−	0.0324035i	0.471675	−	0.881772i	$-0.343649\pi$
$647$	−1.52008e7	−	8.77616e6i	−0.0561245	−	0.0324035i	−0.527800	+	0.849369i	$0.676983\pi$
$648$		0			0
$649$	−4.43240e8	+	2.55905e8i	−1.62145	+	0.936147i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.28952e7	−	3.96557e7i	−0.0822252	−	0.142418i	0.821980	−	0.569516i	$-0.192869\pi$
$653$	−2.28952e7	−	3.96557e7i	−0.0822252	−	0.142418i	−0.904205	+	0.427098i	$0.859536\pi$
$654$		0			0
$655$	−15114.5	+	26179.1i	−5.37862e−5	+	9.31604e-5i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.26685e8			1.49091			0.745455	−	0.666556i	$-0.232232\pi$
$659$	4.26685e8			1.49091			0.745455	+	0.666556i	$0.232232\pi$
$660$		0			0
$661$	9.62322e7	+	5.55597e7i	0.333208	+	0.192378i	0.657265	−	0.753660i	$-0.271713\pi$
$661$	9.62322e7	+	5.55597e7i	0.333208	+	0.192378i	−0.324056	+	0.946038i	$0.605047\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	53055.2	−	8958.19i	0.000180411	−	3.04618e-5i
$666$		0			0
$667$	−1.62873e7	−	2.82105e7i	−0.0548874	−	0.0950678i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	7.02108e8i		−	2.32400i
$672$		0			0
$673$	−1.25013e8			−0.410119			−0.205060	−	0.978749i	$-0.565739\pi$
$673$	−1.25013e8			−0.410119			−0.205060	+	0.978749i	$0.565739\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.17878e7	+	2.41262e7i	−0.134674	+	0.0777539i	−0.565823	−	0.824527i	$-0.691442\pi$
$677$	−4.17878e7	+	2.41262e7i	−0.134674	+	0.0777539i	0.431149	+	0.902281i	$0.358108\pi$
$678$		0			0
$679$	−8.97498e7	+	7.42048e7i	−0.286698	+	0.237041i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.23115e8	+	3.86446e8i	−0.700271	+	1.21291i	0.268100	+	0.963391i	$0.413604\pi$
$683$	−2.23115e8	+	3.86446e8i	−0.700271	+	1.21291i	−0.968371	+	0.249514i	$0.919729\pi$
$684$		0			0
$685$		−	21138.5i		−	6.57662e-5i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.00870e6	−	582375.i	−0.00308394	−	0.00178051i
$690$		0			0
$691$	−4.39974e8	+	2.54019e8i	−1.33350	+	0.769897i	−0.985834	−	0.167722i	$-0.946359\pi$
$691$	−4.39974e8	+	2.54019e8i	−1.33350	+	0.769897i	−0.347666	+	0.937618i	$0.613026\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	125487.	+	217350.i	0.000373805	+	0.000647449i
$696$		0			0
$697$	8.70877e7	−	1.50840e8i	0.257193	−	0.445471i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.62305e8			1.63237			0.816183	−	0.577793i	$-0.196086\pi$
$701$	5.62305e8			1.63237			0.816183	+	0.577793i	$0.196086\pi$
$702$		0			0
$703$	3.12075e6	+	1.80177e6i	0.00898242	+	0.00518600i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.16509e7	+	1.87454e8i	0.0895630	+	0.530440i
$708$		0			0
$709$	5.94219e7	+	1.02922e8i	0.166728	+	0.288781i	0.937267	−	0.348611i	$-0.113347\pi$
$709$	5.94219e7	+	1.02922e8i	0.166728	+	0.288781i	−0.770540	+	0.637392i	$0.780013\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			9.75500e7i			0.269128i
$714$		0			0
$715$	2299.99			6.29228e−6
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.17751e8	+	2.98924e8i	−1.39295	+	0.804219i	−0.993641	−	0.112599i	$-0.964082\pi$
$719$	−5.17751e8	+	2.98924e8i	−1.39295	+	0.804219i	−0.399307	+	0.916817i	$0.630749\pi$
$720$		0			0
$721$	2.91637e8	+	1.08553e8i	0.778102	+	0.289624i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.08439e8	+	1.87822e8i	−0.284558	+	0.492869i
$726$		0			0
$727$			1.55915e8i			0.405775i	0.979202	+	0.202887i	$0.0650325\pi$
$727$			1.55915e8i			0.405775i	−0.979202	+	0.202887i	$0.934967\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.69788e8	−	2.71232e8i	−1.20268	−	0.694367i
$732$		0			0
$733$	2.33614e8	−	1.34877e8i	0.593180	−	0.342472i	−0.173174	−	0.984891i	$-0.555402\pi$
$733$	2.33614e8	−	1.34877e8i	0.593180	−	0.342472i	0.766354	+	0.642419i	$0.222069\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.69341e8	−	4.66511e8i	−0.672821	−	1.16536i
$738$		0			0
$739$	−2.68694e7	+	4.65391e7i	−0.0665770	+	0.115315i	−0.897392	−	0.441233i	$-0.854541\pi$
$739$	−2.68694e7	+	4.65391e7i	−0.0665770	+	0.115315i	0.830815	+	0.556548i	$0.187874\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.94445e8			−1.69306			−0.846528	−	0.532344i	$-0.821311\pi$
$743$	−6.94445e8			−1.69306			−0.846528	+	0.532344i	$0.821311\pi$
$744$		0			0
$745$	62592.7	+	36137.9i	0.000151375	+	8.73966e-5i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.67053e7	+	2.32942e8i	−0.206348	+	0.554373i
$750$		0			0
$751$	−3.16023e8	−	5.47368e8i	−0.746104	−	1.29229i	−0.949677	−	0.313230i	$-0.898589\pi$
$751$	−3.16023e8	−	5.47368e8i	−0.746104	−	1.29229i	0.203574	−	0.979060i	$-0.434744\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			537381.i			0.00124865i
$756$		0			0
$757$	1.00073e8			0.230691			0.115346	−	0.993325i	$-0.463202\pi$
$757$	1.00073e8			0.230691			0.115346	+	0.993325i	$0.463202\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.67004e8	+	1.54155e8i	−0.605848	+	0.349787i	−0.771339	−	0.636425i	$-0.780413\pi$
$761$	−2.67004e8	+	1.54155e8i	−0.605848	+	0.349787i	0.165491	+	0.986211i	$0.447079\pi$
$762$		0			0
$763$	5.26786e7	−	8.89460e6i	0.118593	−	0.0200241i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.25134e6	−	2.16738e6i	0.00277325	−	0.00480341i
$768$		0			0
$769$		−	6.37446e8i		−	1.40173i	−0.713294	−	0.700865i	$-0.752798\pi$
$769$		−	6.37446e8i		−	1.40173i	0.713294	−	0.700865i	$-0.247202\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.94870e8	−	2.85713e8i	−1.07140	−	0.618574i	−0.142838	−	0.989746i	$-0.545623\pi$
$773$	−4.94870e8	−	2.85713e8i	−1.07140	−	0.618574i	−0.928564	+	0.371172i	$0.878956\pi$
$774$		0			0
$775$	5.62461e8	−	3.24737e8i	1.20834	−	0.697633i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.93012e7	+	5.07512e7i	0.0619831	+	0.107358i
$780$		0			0
$781$	−6.68134e8	+	1.15724e9i	−1.40253	+	2.42924i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−34882.8			−7.21111e−5
$786$		0			0
$787$	−7.50442e8	−	4.33268e8i	−1.53955	−	0.888857i	−0.998865	−	0.0476296i	$-0.984833\pi$
$787$	−7.50442e8	−	4.33268e8i	−1.53955	−	0.888857i	−0.540681	−	0.841228i	$-0.681833\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.91957e7	−	5.95016e7i	−0.0994025	−	0.120226i
$792$		0			0
$793$	1.71661e6	+	2.97325e6i	0.00344232	+	0.00596227i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	7.87468e8i		−	1.55546i	−0.628601	−	0.777728i	$-0.716372\pi$
$797$		−	7.87468e8i		−	1.55546i	0.628601	−	0.777728i	$-0.283628\pi$
$798$		0			0
$799$	5.14825e8			1.00930
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.27249e9	+	7.34671e8i	−2.45758	+	1.41888i
$804$		0			0
$805$	12127.6	+	71826.0i	2.32480e−5	+	0.000137687i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.24621e8	−	5.62259e8i	0.613099	−	1.06192i	−0.377616	−	0.925962i	$-0.623256\pi$
$809$	3.24621e8	−	5.62259e8i	0.613099	−	1.06192i	0.990715	−	0.135956i	$-0.0434106\pi$
$810$		0			0
$811$			1.94118e8i			0.363917i	0.983306	+	0.181959i	$0.0582437\pi$
$811$			1.94118e8i			0.363917i	−0.983306	+	0.181959i	$0.941756\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−469279.	−	270938.i	−0.000866878	−	0.000500492i
$816$		0			0
$817$	1.58063e8	−	9.12577e7i	0.289844	−	0.167341i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.47367e7	−	6.01658e7i	−0.0627711	−	0.108723i	0.832932	−	0.553375i	$-0.186660\pi$
$821$	−3.47367e7	−	6.01658e7i	−0.0627711	−	0.108723i	−0.895703	+	0.444653i	$0.853327\pi$
$822$		0			0
$823$	2.87144e8	−	4.97347e8i	0.515109	−	0.892196i	−0.484737	−	0.874660i	$-0.661085\pi$
$823$	2.87144e8	−	4.97347e8i	0.515109	−	0.892196i	0.999846	−	0.0175357i	$-0.00558206\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.02808e8			0.181765			0.0908826	−	0.995862i	$-0.471031\pi$
$827$	1.02808e8			0.181765			0.0908826	+	0.995862i	$0.471031\pi$
$828$		0			0
$829$	3.09922e8	+	1.78934e8i	0.543988	+	0.314071i	0.746693	−	0.665168i	$-0.231640\pi$
$829$	3.09922e8	+	1.78934e8i	0.543988	+	0.314071i	−0.202706	+	0.979240i	$0.564974\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.96341e8	+	4.58640e8i	−0.685699	+	0.793482i
$834$		0			0
$835$	−63288.8	−	109619.i	−0.000108710	−	0.000188290i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	2.36873e8i		−	0.401079i	−0.979686	−	0.200539i	$-0.935731\pi$
$839$		−	2.36873e8i		−	0.401079i	0.979686	−	0.200539i	$-0.0642694\pi$
$840$		0			0
$841$	−4.02164e8			−0.676107
$842$		0			0
$843$		0			0
$844$		0			0
$845$	378256.	−	218386.i	0.000626925	−	0.000361955i
$846$		0			0
$847$	−4.09958e8	+	1.10139e9i	−0.674667	+	1.81256i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.43923e6	+	4.22487e6i	−0.00395789	+	0.00685526i
$852$		0			0
$853$		−	6.95204e8i		−	1.12012i	−0.828451	−	0.560061i	$-0.810778\pi$
$853$		−	6.95204e8i		−	1.12012i	0.828451	−	0.560061i	$-0.189222\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.87613e8	−	3.96994e8i	−1.09245	−	0.630727i	−0.158223	−	0.987403i	$-0.550576\pi$
$857$	−6.87613e8	−	3.96994e8i	−1.09245	−	0.630727i	−0.934228	+	0.356677i	$0.883910\pi$
$858$		0			0
$859$	6.84536e8	−	3.95217e8i	1.07998	−	0.623529i	0.149092	−	0.988823i	$-0.452365\pi$
$859$	6.84536e8	−	3.95217e8i	1.07998	−	0.623529i	0.930892	+	0.365295i	$0.119032\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.33504e8	+	1.09726e9i	0.985637	+	1.70717i	0.639070	+	0.769148i	$0.279319\pi$
$863$	6.33504e8	+	1.09726e9i	0.985637	+	1.70717i	0.346567	+	0.938025i	$0.387347\pi$
$864$		0			0
$865$	−460352.	+	797354.i	−0.000711282	+	0.00123198i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.22700e9			1.86976
$870$		0			0
$871$	2.28118e6	+	1.31704e6i	0.00345227	+	0.00199317i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	747536.	−	618059.i	0.00111586	−	0.000922584i
$876$		0			0
$877$	−2.07029e8	−	3.58584e8i	−0.306924	−	0.531609i	0.670764	−	0.741671i	$-0.265967\pi$
$877$	−2.07029e8	−	3.58584e8i	−0.306924	−	0.531609i	−0.977688	+	0.210063i	$0.932633\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.11611e9i		−	1.63222i	−0.577897	−	0.816110i	$-0.696126\pi$
$881$		−	1.11611e9i		−	1.63222i	0.577897	−	0.816110i	$-0.303874\pi$
$882$		0			0
$883$	−7.77359e8			−1.12912			−0.564559	−	0.825392i	$-0.690954\pi$
$883$	−7.77359e8			−1.12912			−0.564559	+	0.825392i	$0.690954\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.79999e8	+	1.61657e8i	−0.401223	+	0.231646i	−0.687011	−	0.726647i	$-0.741078\pi$
$887$	−2.79999e8	+	1.61657e8i	−0.401223	+	0.231646i	0.285789	+	0.958293i	$0.407744\pi$
$888$		0			0
$889$	6.46149e8	+	7.81510e8i	0.919661	+	1.11232i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.66081e7	+	1.50010e8i	−0.121620	+	0.210652i
$894$		0			0
$895$		−	774540.i		−	0.00108038i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.99652e8	−	2.88474e8i	−0.687684	−	0.397034i
$900$		0			0
$901$	−4.66184e8	+	2.69152e8i	−0.637358	+	0.367979i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−144379.	−	250072.i	−0.000194787	−	0.000337380i
$906$		0			0
$907$	−5.41990e8	+	9.38754e8i	−0.726389	+	1.25814i	0.232011	+	0.972713i	$0.425470\pi$
$907$	−5.41990e8	+	9.38754e8i	−0.726389	+	1.25814i	−0.958400	+	0.285430i	$0.907864\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.83298e8			0.242439			0.121219	−	0.992626i	$-0.461320\pi$
$911$	1.83298e8			0.242439			0.121219	+	0.992626i	$0.461320\pi$
$912$		0			0
$913$	−1.18991e9	−	6.86992e8i	−1.56351	−	0.902692i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.07383e8	+	3.99701e7i	0.139261	+	0.0518355i
$918$		0			0
$919$	−3.97916e8	−	6.89211e8i	−0.512679	−	0.887986i	−0.999892	−	0.0147025i	$-0.995320\pi$
$919$	−3.97916e8	−	6.89211e8i	−0.512679	−	0.887986i	0.487213	−	0.873283i	$-0.338013\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	6.53418e6i		−	0.00830971i
$924$		0			0
$925$	3.24801e7			0.0410385
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.80851e8	−	1.62149e8i	0.350290	−	0.202240i	−0.314523	−	0.949250i	$-0.601844\pi$
$929$	2.80851e8	−	1.62149e8i	0.350290	−	0.202240i	0.664813	+	0.747010i	$0.268511\pi$
$930$		0			0
$931$	−6.69628e7	−	1.92642e8i	−0.0829822	−	0.238727i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	531485.	−	920559.i	0.000650214	−	0.00112620i
$936$		0			0
$937$		−	7.22586e8i		−	0.878356i	−0.898400	−	0.439178i	$-0.855270\pi$
$937$		−	7.22586e8i		−	0.878356i	0.898400	−	0.439178i	$-0.144730\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.32202e8	+	4.80472e8i	0.998757	+	0.576633i	0.907880	−	0.419229i	$-0.137700\pi$
$941$	8.32202e8	+	4.80472e8i	0.998757	+	0.576633i	0.0908770	+	0.995862i	$0.471033\pi$
$942$		0			0
$943$	−6.87068e7	+	3.96679e7i	−0.0819341	+	0.0473047i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.20174e8	+	2.08148e8i	0.141502	+	0.245088i	0.928062	−	0.372425i	$-0.121474\pi$
$947$	1.20174e8	+	2.08148e8i	0.141502	+	0.245088i	−0.786561	+	0.617513i	$0.788140\pi$
$948$		0			0
$949$	3.59244e6	−	6.22230e6i	0.00420331	−	0.00728035i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.26904e9			1.46622			0.733108	−	0.680113i	$-0.238069\pi$
$953$	1.26904e9			1.46622			0.733108	+	0.680113i	$0.238069\pi$
$954$		0			0
$955$	732667.	+	423005.i	0.000841194	+	0.000485664i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.90057e7	+	1.33398e7i	−0.0895782	+	0.0151250i
$960$		0			0
$961$	4.20130e8	+	7.27686e8i	0.473384	+	0.819925i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			176846.i			0.000196794i
$966$		0			0
$967$	2.04679e8			0.226357			0.113178	−	0.993575i	$-0.463897\pi$
$967$	2.04679e8			0.226357			0.113178	+	0.993575i	$0.463897\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−5.23119e8	+	3.02023e8i	−0.571404	+	0.329900i	−0.757710	−	0.652592i	$-0.773682\pi$
$971$	−5.23119e8	+	3.02023e8i	−0.571404	+	0.329900i	0.186306	+	0.982492i	$0.440348\pi$
$972$		0			0
$973$	7.33160e8	−	6.06174e8i	0.795903	−	0.658049i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.57469e8	−	1.31197e9i	0.812234	−	1.40683i	−0.0990637	−	0.995081i	$-0.531585\pi$
$977$	7.57469e8	−	1.31197e9i	0.812234	−	1.40683i	0.911297	−	0.411749i	$-0.135082\pi$
$978$		0			0
$979$			2.81221e9i			2.99709i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.45203e9	+	8.38332e8i	1.52868	+	0.882583i	0.999418	+	0.0341231i	$0.0108638\pi$
$983$	1.45203e9	+	8.38332e8i	1.52868	+	0.882583i	0.529260	+	0.848460i	$0.322470\pi$
$984$		0			0
$985$	477972.	−	275957.i	0.000500143	−	0.000288757i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.23544e8	+	2.13985e8i	0.127713	+	0.221205i
$990$		0			0
$991$	−3.22159e8	+	5.57995e8i	−0.331016	+	0.573336i	−0.982711	−	0.185144i	$-0.940725\pi$
$991$	−3.22159e8	+	5.57995e8i	−0.331016	+	0.573336i	0.651695	+	0.758481i	$0.274058\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	864288.			0.000877383
$996$		0			0
$997$	1.35199e9	+	7.80574e8i	1.36424	+	0.787642i	0.990185	−	0.139766i	$-0.0446351\pi$
$997$	1.35199e9	+	7.80574e8i	1.36424	+	0.787642i	0.374051	+	0.927408i	$0.377968\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.7.z.e.73.2		8
3.2	odd	2		84.7.m.b.73.3	yes	8
7.5	odd	6	inner	252.7.z.e.145.2		8
12.11	even	2		336.7.bh.a.241.3		8
21.2	odd	6		588.7.m.b.313.2		8
21.5	even	6		84.7.m.b.61.3	✓	8
21.11	odd	6		588.7.d.a.97.3		8
21.17	even	6		588.7.d.a.97.6		8
21.20	even	2		588.7.m.b.325.2		8
84.47	odd	6		336.7.bh.a.145.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.7.m.b.61.3	✓	8	21.5	even	6
84.7.m.b.73.3	yes	8	3.2	odd	2
252.7.z.e.73.2		8	1.1	even	1	trivial
252.7.z.e.145.2		8	7.5	odd	6	inner
336.7.bh.a.145.3		8	84.47	odd	6
336.7.bh.a.241.3		8	12.11	even	2
588.7.d.a.97.3		8	21.11	odd	6
588.7.d.a.97.6		8	21.17	even	6
588.7.m.b.313.2		8	21.2	odd	6
588.7.m.b.325.2		8	21.20	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0783677 - 0.0452456i) q^{5} +(-218.562 - 264.348i) q^{7} +O(q^{10})\)	\(q+(0.0783677 - 0.0452456i) q^{5} +(-218.562 - 264.348i) q^{7} +(1139.94 - 1974.43i) q^{11} +11.1483i q^{13} +(4462.04 + 2576.16i) q^{17} +(-1501.28 + 866.766i) q^{19} +(-1173.42 - 2032.43i) q^{23} +(-7812.50 + 13531.6i) q^{25} +13880.2 q^{29} +(-35997.5 - 20783.2i) q^{31} +(-29.0887 - 10.8274i) q^{35} +(-1039.36 - 1800.23i) q^{37} -33805.2i q^{41} -105285. q^{43} +(86534.1 - 49960.5i) q^{47} +(-22110.6 + 115553. i) q^{49} +(-52238.9 + 90480.4i) q^{53} -206.309i q^{55} +(-194414. - 112245. i) q^{59} +(266700. - 153979. i) q^{61} +(0.504411 + 0.873666i) q^{65} +(118138. - 204621. i) q^{67} -586114. q^{71} +(-558139. - 322242. i) q^{73} +(-771084. + 130195. i) q^{77} +(269093. + 466084. i) q^{79} -602657. i q^{83} +466.240 q^{85} +(-1.06824e6 + 616746. i) q^{89} +(2947.03 - 2436.59i) q^{91} +(-78.4346 + 135.853i) q^{95} -339514. i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 294 q^{5} + 232 q^{7}+O(q^{10}) \) 8 * q + 294 * q^5 + 232 * q^7	\( 8 q + 294 q^{5} + 232 q^{7} - 378 q^{11} - 852 q^{17} + 3690 q^{19} - 15600 q^{23} + 3386 q^{25} + 68604 q^{29} + 23028 q^{31} - 93828 q^{35} + 15914 q^{37} - 170044 q^{43} - 102180 q^{47} + 157340 q^{49} - 196410 q^{53} + 662550 q^{59} - 23928 q^{61} - 14892 q^{65} + 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 1584738 q^{77} - 493868 q^{79} - 1329816 q^{85} - 604260 q^{89} + 3831690 q^{91} - 448944 q^{95}+O(q^{100}) \) 8 * q + 294 * q^5 + 232 * q^7 - 378 * q^11 - 852 * q^17 + 3690 * q^19 - 15600 * q^23 + 3386 * q^25 + 68604 * q^29 + 23028 * q^31 - 93828 * q^35 + 15914 * q^37 - 170044 * q^43 - 102180 * q^47 + 157340 * q^49 - 196410 * q^53 + 662550 * q^59 - 23928 * q^61 - 14892 * q^65 + 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 1584738 * q^77 - 493868 * q^79 - 1329816 * q^85 - 604260 * q^89 + 3831690 * q^91 - 448944 * q^95

Introduction

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