LMFDB - Embedded newform 128.5.f.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{42} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$0.153862 - 2.82424i$ of defining polynomial
Character	$\chi$	$=$	128.31
Dual form			128.5.f.a.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.42589 - 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} +76.7794 q^{7} +96.6949i q^{9} +O(q^{10})$	\(q+(-9.42589 - 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} +76.7794 q^{7} +96.6949i q^{9} +(121.488 - 121.488i) q^{11} +(-27.1604 + 27.1604i) q^{13} -53.6729i q^{15} -88.0613 q^{17} +(-261.112 - 261.112i) q^{19} +(-723.714 - 723.714i) q^{21} -93.4210 q^{23} -608.788i q^{25} +(147.938 - 147.938i) q^{27} +(-272.522 + 272.522i) q^{29} -1232.20i q^{31} -2290.26 q^{33} +(218.599 + 218.599i) q^{35} +(1046.16 + 1046.16i) q^{37} +512.021 q^{39} -915.267i q^{41} +(1116.82 - 1116.82i) q^{43} +(-275.300 + 275.300i) q^{45} -1720.70i q^{47} +3494.07 q^{49} +(830.056 + 830.056i) q^{51} +(-734.019 - 734.019i) q^{53} +691.775 q^{55} +4922.43i q^{57} +(-1202.73 + 1202.73i) q^{59} +(-580.221 + 580.221i) q^{61} +7424.17i q^{63} -154.657 q^{65} +(-1483.97 - 1483.97i) q^{67} +(880.576 + 880.576i) q^{69} -5571.73 q^{71} -6615.21i q^{73} +(-5738.37 + 5738.37i) q^{75} +(9327.75 - 9327.75i) q^{77} +5391.66i q^{79} +5043.39 q^{81} +(-2554.07 - 2554.07i) q^{83} +(-250.719 - 250.719i) q^{85} +5137.52 q^{87} +10962.7i q^{89} +(-2085.35 + 2085.35i) q^{91} +(-11614.6 + 11614.6i) q^{93} -1486.83i q^{95} +4713.20 q^{97} +(11747.2 + 11747.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 94 q^{11} + 2 q^{13} - 4 q^{17} - 706 q^{19} + 164 q^{21} - 1148 q^{23} - 1664 q^{27} - 862 q^{29} - 4 q^{33} + 1340 q^{35} + 1826 q^{37} - 2684 q^{39} + 1694 q^{43} - 1410 q^{45} + 682 q^{49} - 3012 q^{51} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} + 3778 q^{61} - 2020 q^{65} + 7998 q^{67} - 9628 q^{69} - 19964 q^{71} + 17570 q^{75} + 9508 q^{77} + 1454 q^{81} - 17282 q^{83} - 9948 q^{85} + 49284 q^{87} - 28036 q^{91} - 8896 q^{93} - 4 q^{97} + 49214 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 94 * q^11 + 2 * q^13 - 4 * q^17 - 706 * q^19 + 164 * q^21 - 1148 * q^23 - 1664 * q^27 - 862 * q^29 - 4 * q^33 + 1340 * q^35 + 1826 * q^37 - 2684 * q^39 + 1694 * q^43 - 1410 * q^45 + 682 * q^49 - 3012 * q^51 + 482 * q^53 + 11780 * q^55 - 2786 * q^59 + 3778 * q^61 - 2020 * q^65 + 7998 * q^67 - 9628 * q^69 - 19964 * q^71 + 17570 * q^75 + 9508 * q^77 + 1454 * q^81 - 17282 * q^83 - 9948 * q^85 + 49284 * q^87 - 28036 * q^91 - 8896 * q^93 - 4 * q^97 + 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	−9.42589	−	9.42589i	−1.04732	−	1.04732i	−0.998823	−	0.0484980i	$-0.984557\pi$
$3$	−9.42589	−	9.42589i	−1.04732	−	1.04732i	−0.0484980	−	0.998823i	$-0.515443\pi$
$4$		0			0
$5$	2.84710	+	2.84710i	0.113884	+	0.113884i	0.761752	−	0.647868i	$-0.224339\pi$
$5$	2.84710	+	2.84710i	0.113884	+	0.113884i	−0.647868	+	0.761752i	$0.724339\pi$
$6$		0			0
$7$	76.7794			1.56693			0.783463	−	0.621439i	$-0.213451\pi$
$7$	76.7794			1.56693			0.783463	+	0.621439i	$0.213451\pi$
$8$		0			0
$9$			96.6949i			1.19376i
$10$		0			0
$11$	121.488	−	121.488i	1.00403	−	1.00403i	0.00403849	−	0.999992i	$-0.498715\pi$
$11$	121.488	−	121.488i	1.00403	−	1.00403i	0.999992	−	0.00403849i	$-0.00128549\pi$
$12$		0			0
$13$	−27.1604	+	27.1604i	−0.160712	+	0.160712i	−0.782882	−	0.622170i	$-0.786251\pi$
$13$	−27.1604	+	27.1604i	−0.160712	+	0.160712i	0.622170	+	0.782882i	$0.286251\pi$
$14$		0			0
$15$		−	53.6729i		−	0.238546i
$16$		0			0
$17$	−88.0613			−0.304710			−0.152355	−	0.988326i	$-0.548686\pi$
$17$	−88.0613			−0.304710			−0.152355	+	0.988326i	$0.548686\pi$
$18$		0			0
$19$	−261.112	−	261.112i	−0.723302	−	0.723302i	0.245974	−	0.969276i	$-0.420892\pi$
$19$	−261.112	−	261.112i	−0.723302	−	0.723302i	−0.969276	+	0.245974i	$0.920892\pi$
$20$		0			0
$21$	−723.714	−	723.714i	−1.64107	−	1.64107i
$22$		0			0
$23$	−93.4210			−0.176599			−0.0882996	−	0.996094i	$-0.528143\pi$
$23$	−93.4210			−0.176599			−0.0882996	+	0.996094i	$0.528143\pi$
$24$		0			0
$25$		−	608.788i		−	0.974061i
$26$		0			0
$27$	147.938	−	147.938i	0.202933	−	0.202933i
$28$		0			0
$29$	−272.522	+	272.522i	−0.324045	+	0.324045i	−0.850316	−	0.526272i	$-0.823590\pi$
$29$	−272.522	+	272.522i	−0.324045	+	0.324045i	0.526272	+	0.850316i	$0.323590\pi$
$30$		0			0
$31$		−	1232.20i		−	1.28220i	−0.767455	−	0.641102i	$-0.778477\pi$
$31$		−	1232.20i		−	1.28220i	0.767455	−	0.641102i	$-0.221523\pi$
$32$		0			0
$33$	−2290.26			−2.10308
$34$		0			0
$35$	218.599	+	218.599i	0.178448	+	0.178448i
$36$		0			0
$37$	1046.16	+	1046.16i	0.764177	+	0.764177i	0.977075	−	0.212898i	$-0.0682901\pi$
$37$	1046.16	+	1046.16i	0.764177	+	0.764177i	−0.212898	+	0.977075i	$0.568290\pi$
$38$		0			0
$39$	512.021			0.336635
$40$		0			0
$41$		−	915.267i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$41$		−	915.267i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$42$		0			0
$43$	1116.82	−	1116.82i	0.604013	−	0.604013i	−0.337362	−	0.941375i	$-0.609535\pi$
$43$	1116.82	−	1116.82i	0.604013	−	0.604013i	0.941375	+	0.337362i	$0.109535\pi$
$44$		0			0
$45$	−275.300	+	275.300i	−0.135951	+	0.135951i
$46$		0			0
$47$		−	1720.70i		−	0.778949i	−0.921037	−	0.389475i	$-0.872657\pi$
$47$		−	1720.70i		−	0.778949i	0.921037	−	0.389475i	$-0.127343\pi$
$48$		0			0
$49$	3494.07			1.45526
$50$		0			0
$51$	830.056	+	830.056i	0.319130	+	0.319130i
$52$		0			0
$53$	−734.019	−	734.019i	−0.261310	−	0.261310i	0.564276	−	0.825586i	$-0.309155\pi$
$53$	−734.019	−	734.019i	−0.261310	−	0.261310i	−0.825586	+	0.564276i	$0.809155\pi$
$54$		0			0
$55$	691.775			0.228686
$56$		0			0
$57$			4922.43i			1.51506i
$58$		0			0
$59$	−1202.73	+	1202.73i	−0.345512	+	0.345512i	−0.858435	−	0.512923i	$-0.828563\pi$
$59$	−1202.73	+	1202.73i	−0.345512	+	0.345512i	0.512923	+	0.858435i	$0.328563\pi$
$60$		0			0
$61$	−580.221	+	580.221i	−0.155932	+	0.155932i	−0.780761	−	0.624830i	$-0.785168\pi$
$61$	−580.221	+	580.221i	−0.155932	+	0.155932i	0.624830	+	0.780761i	$0.285168\pi$
$62$		0			0
$63$			7424.17i			1.87054i
$64$		0			0
$65$	−154.657			−0.0366051
$66$		0			0
$67$	−1483.97	−	1483.97i	−0.330580	−	0.330580i	0.522227	−	0.852807i	$-0.325101\pi$
$67$	−1483.97	−	1483.97i	−0.330580	−	0.330580i	−0.852807	+	0.522227i	$0.825101\pi$
$68$		0			0
$69$	880.576	+	880.576i	0.184956	+	0.184956i
$70$		0			0
$71$	−5571.73			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$71$	−5571.73			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$72$		0			0
$73$		−	6615.21i		−	1.24136i	−0.784064	−	0.620681i	$-0.786856\pi$
$73$		−	6615.21i		−	1.24136i	0.784064	−	0.620681i	$-0.213144\pi$
$74$		0			0
$75$	−5738.37	+	5738.37i	−1.02015	+	1.02015i
$76$		0			0
$77$	9327.75	−	9327.75i	1.57324	−	1.57324i
$78$		0			0
$79$			5391.66i			0.863910i	0.901895	+	0.431955i	$0.142176\pi$
$79$			5391.66i			0.863910i	−0.901895	+	0.431955i	$0.857824\pi$
$80$		0			0
$81$	5043.39			0.768692
$82$		0			0
$83$	−2554.07	−	2554.07i	−0.370747	−	0.370747i	0.497002	−	0.867749i	$-0.334434\pi$
$83$	−2554.07	−	2554.07i	−0.370747	−	0.370747i	−0.867749	+	0.497002i	$0.834434\pi$
$84$		0			0
$85$	−250.719	−	250.719i	−0.0347017	−	0.0347017i
$86$		0			0
$87$	5137.52			0.678758
$88$		0			0
$89$			10962.7i			1.38400i	0.721898	+	0.691999i	$0.243270\pi$
$89$			10962.7i			1.38400i	−0.721898	+	0.691999i	$0.756730\pi$
$90$		0			0
$91$	−2085.35	+	2085.35i	−0.251824	+	0.251824i
$92$		0			0
$93$	−11614.6	+	11614.6i	−1.34288	+	1.34288i
$94$		0			0
$95$		−	1486.83i		−	0.164745i
$96$		0			0
$97$	4713.20			0.500925			0.250462	−	0.968126i	$-0.419417\pi$
$97$	4713.20			0.500925			0.250462	+	0.968126i	$0.419417\pi$
$98$		0			0
$99$	11747.2	+	11747.2i	1.19858	+	1.19858i
$100$		0			0
$101$	11381.0	+	11381.0i	1.11568	+	1.11568i	0.992369	+	0.123307i	$0.0393499\pi$
$101$	11381.0	+	11381.0i	1.11568	+	1.11568i	0.123307	+	0.992369i	$0.460650\pi$
$102$		0			0
$103$	−175.758			−0.0165668			−0.00828342	−	0.999966i	$-0.502637\pi$
$103$	−175.758			−0.0165668			−0.00828342	+	0.999966i	$0.502637\pi$
$104$		0			0
$105$		−	4120.97i		−	0.373784i
$106$		0			0
$107$	15151.8	−	15151.8i	1.32342	−	1.32342i	0.412432	−	0.910988i	$-0.364679\pi$
$107$	15151.8	−	15151.8i	1.32342	−	1.32342i	0.910988	−	0.412432i	$-0.135321\pi$
$108$		0			0
$109$	2349.51	−	2349.51i	0.197754	−	0.197754i	−0.601283	−	0.799036i	$-0.705343\pi$
$109$	2349.51	−	2349.51i	0.197754	−	0.197754i	0.799036	+	0.601283i	$0.205343\pi$
$110$		0			0
$111$		−	19721.9i		−	1.60068i
$112$		0			0
$113$	−8526.30			−0.667734			−0.333867	−	0.942620i	$-0.608354\pi$
$113$	−8526.30			−0.667734			−0.333867	+	0.942620i	$0.608354\pi$
$114$		0			0
$115$	−265.979	−	265.979i	−0.0201118	−	0.0201118i
$116$		0			0
$117$	−2626.27	−	2626.27i	−0.191852	−	0.191852i
$118$		0			0
$119$	−6761.29			−0.477459
$120$		0			0
$121$		−	14877.5i		−	1.01615i
$122$		0			0
$123$	−8627.21	+	8627.21i	−0.570243	+	0.570243i
$124$		0			0
$125$	3512.72	−	3512.72i	0.224814	−	0.224814i
$126$		0			0
$127$		−	2844.31i		−	0.176347i	−0.996105	−	0.0881737i	$-0.971897\pi$
$127$		−	2844.31i		−	0.176347i	0.996105	−	0.0881737i	$-0.0281031\pi$
$128$		0			0
$129$	−21054.1			−1.26519
$130$		0			0
$131$	−6989.87	−	6989.87i	−0.407311	−	0.407311i	0.473489	−	0.880800i	$-0.342994\pi$
$131$	−6989.87	−	6989.87i	−0.407311	−	0.407311i	−0.880800	+	0.473489i	$0.842994\pi$
$132$		0			0
$133$	−20048.0	−	20048.0i	−1.13336	−	1.13336i
$134$		0			0
$135$	842.390			0.0462217
$136$		0			0
$137$			3669.69i			0.195519i	0.995210	+	0.0977594i	$0.0311676\pi$
$137$			3669.69i			0.195519i	−0.995210	+	0.0977594i	$0.968832\pi$
$138$		0			0
$139$	4401.33	−	4401.33i	0.227800	−	0.227800i	−0.583973	−	0.811773i	$-0.698503\pi$
$139$	4401.33	−	4401.33i	0.227800	−	0.227800i	0.811773	+	0.583973i	$0.198503\pi$
$140$		0			0
$141$	−16219.1	+	16219.1i	−0.815810	+	0.815810i
$142$		0			0
$143$			6599.30i			0.322720i
$144$		0			0
$145$	−1551.79			−0.0738071
$146$		0			0
$147$	−32934.7	−	32934.7i	−1.52412	−	1.52412i
$148$		0			0
$149$	−15737.5	−	15737.5i	−0.708863	−	0.708863i	0.257433	−	0.966296i	$-0.417123\pi$
$149$	−15737.5	−	15737.5i	−0.708863	−	0.708863i	−0.966296	+	0.257433i	$0.917123\pi$
$150$		0			0
$151$	41972.2			1.84080			0.920402	−	0.390974i	$-0.127862\pi$
$151$	41972.2			1.84080			0.920402	+	0.390974i	$0.127862\pi$
$152$		0			0
$153$		−	8515.08i		−	0.363752i
$154$		0			0
$155$	3508.19	−	3508.19i	0.146023	−	0.146023i
$156$		0			0
$157$	24735.4	−	24735.4i	1.00351	−	1.00351i	0.00351271	−	0.999994i	$-0.498882\pi$
$157$	24735.4	−	24735.4i	1.00351	−	1.00351i	0.999994	−	0.00351271i	$-0.00111813\pi$
$158$		0			0
$159$			13837.6i			0.547350i
$160$		0			0
$161$	−7172.80			−0.276718
$162$		0			0
$163$	24429.8	+	24429.8i	0.919483	+	0.919483i	0.996992	−	0.0775084i	$-0.0246965\pi$
$163$	24429.8	+	24429.8i	0.919483	+	0.919483i	−0.0775084	+	0.996992i	$0.524696\pi$
$164$		0			0
$165$	−6520.60	−	6520.60i	−0.239508	−	0.239508i
$166$		0			0
$167$	−52178.2			−1.87093			−0.935463	−	0.353425i	$-0.885017\pi$
$167$	−52178.2			−1.87093			−0.935463	+	0.353425i	$0.885017\pi$
$168$		0			0
$169$			27085.6i			0.948343i
$170$		0			0
$171$	25248.2	−	25248.2i	0.863452	−	0.863452i
$172$		0			0
$173$	−26316.2	+	26316.2i	−0.879289	+	0.879289i	−0.993461	−	0.114172i	$-0.963578\pi$
$173$	−26316.2	+	26316.2i	−0.879289	+	0.879289i	0.114172	+	0.993461i	$0.463578\pi$
$174$		0			0
$175$		−	46742.4i		−	1.52628i
$176$		0			0
$177$	22673.5			0.723723
$178$		0			0
$179$	4815.78	+	4815.78i	0.150301	+	0.150301i	0.778252	−	0.627952i	$-0.216106\pi$
$179$	4815.78	+	4815.78i	0.150301	+	0.150301i	−0.627952	+	0.778252i	$0.716106\pi$
$180$		0			0
$181$	23924.9	+	23924.9i	0.730286	+	0.730286i	0.970676	−	0.240391i	$-0.0772755\pi$
$181$	23924.9	+	23924.9i	0.730286	+	0.730286i	−0.240391	+	0.970676i	$0.577276\pi$
$182$		0			0
$183$	10938.2			0.326621
$184$		0			0
$185$			5957.04i			0.174055i
$186$		0			0
$187$	−10698.4	+	10698.4i	−0.305939	+	0.305939i
$188$		0			0
$189$	11358.6	−	11358.6i	0.317981	−	0.317981i
$190$		0			0
$191$			45079.4i			1.23569i	0.786298	+	0.617847i	$0.211995\pi$
$191$			45079.4i			1.23569i	−0.786298	+	0.617847i	$0.788005\pi$
$192$		0			0
$193$	50286.0			1.34999			0.674997	−	0.737820i	$-0.264145\pi$
$193$	50286.0			1.34999			0.674997	+	0.737820i	$0.264145\pi$
$194$		0			0
$195$	1457.78	+	1457.78i	0.0383373	+	0.0383373i
$196$		0			0
$197$	25662.2	+	25662.2i	0.661243	+	0.661243i	0.955673	−	0.294430i	$-0.0951297\pi$
$197$	25662.2	+	25662.2i	0.661243	+	0.661243i	−0.294430	+	0.955673i	$0.595130\pi$
$198$		0			0
$199$	44599.1			1.12621			0.563106	−	0.826385i	$-0.309606\pi$
$199$	44599.1			1.12621			0.563106	+	0.826385i	$0.309606\pi$
$200$		0			0
$201$			27975.5i			0.692447i
$202$		0			0
$203$	−20924.0	+	20924.0i	−0.507754	+	0.507754i
$204$		0			0
$205$	2605.86	−	2605.86i	0.0620073	−	0.0620073i
$206$		0			0
$207$		−	9033.33i		−	0.210818i
$208$		0			0
$209$	−63443.8			−1.45244
$210$		0			0
$211$	25828.5	+	25828.5i	0.580143	+	0.580143i	0.934942	−	0.354800i	$-0.115451\pi$
$211$	25828.5	+	25828.5i	0.580143	+	0.580143i	−0.354800	+	0.934942i	$0.615451\pi$
$212$		0			0
$213$	52518.5	+	52518.5i	1.15759	+	1.15759i
$214$		0			0
$215$	6359.40			0.137575
$216$		0			0
$217$		−	94607.4i		−	2.00912i
$218$		0			0
$219$	−62354.3	+	62354.3i	−1.30010	+	1.30010i
$220$		0			0
$221$	2391.78	−	2391.78i	0.0489707	−	0.0489707i
$222$		0			0
$223$			72650.0i			1.46092i	0.682957	+	0.730459i	$0.260694\pi$
$223$			72650.0i			1.46092i	−0.682957	+	0.730459i	$0.739306\pi$
$224$		0			0
$225$	58866.7			1.16280
$226$		0			0
$227$	18858.2	+	18858.2i	0.365972	+	0.365972i	0.866006	−	0.500034i	$-0.166679\pi$
$227$	18858.2	+	18858.2i	0.365972	+	0.365972i	−0.500034	+	0.866006i	$0.666679\pi$
$228$		0			0
$229$	−41675.9	−	41675.9i	−0.794721	−	0.794721i	0.187537	−	0.982258i	$-0.439950\pi$
$229$	−41675.9	−	41675.9i	−0.794721	−	0.794721i	−0.982258	+	0.187537i	$0.939950\pi$
$230$		0			0
$231$	−175845.			−3.29538
$232$		0			0
$233$			2767.61i			0.0509792i	0.999675	+	0.0254896i	$0.00811447\pi$
$233$			2767.61i			0.0509792i	−0.999675	+	0.0254896i	$0.991886\pi$
$234$		0			0
$235$	4899.00	−	4899.00i	0.0887099	−	0.0887099i
$236$		0			0
$237$	50821.2	−	50821.2i	0.904791	−	0.904791i
$238$		0			0
$239$		−	49981.8i		−	0.875016i	−0.899215	−	0.437508i	$-0.855861\pi$
$239$		−	49981.8i		−	0.875016i	0.899215	−	0.437508i	$-0.144139\pi$
$240$		0			0
$241$	−44076.0			−0.758872			−0.379436	−	0.925218i	$-0.623882\pi$
$241$	−44076.0			−0.758872			−0.379436	+	0.925218i	$0.623882\pi$
$242$		0			0
$243$	−59521.4	−	59521.4i	−1.00800	−	1.00800i
$244$		0			0
$245$	9947.97	+	9947.97i	0.165730	+	0.165730i
$246$		0			0
$247$	14183.8			0.232487
$248$		0			0
$249$			48148.8i			0.776582i
$250$		0			0
$251$	−31786.2	+	31786.2i	−0.504534	+	0.504534i	−0.912844	−	0.408309i	$-0.866119\pi$
$251$	−31786.2	+	31786.2i	−0.504534	+	0.504534i	0.408309	+	0.912844i	$0.366119\pi$
$252$		0			0
$253$	−11349.5	+	11349.5i	−0.177311	+	0.177311i
$254$		0			0
$255$			4726.51i			0.0726876i
$256$		0			0
$257$	70865.6			1.07292			0.536462	−	0.843924i	$-0.319760\pi$
$257$	70865.6			1.07292			0.536462	+	0.843924i	$0.319760\pi$
$258$		0			0
$259$	80323.4	+	80323.4i	1.19741	+	1.19741i
$260$		0			0
$261$	−26351.5	−	26351.5i	−0.386833	−	0.386833i
$262$		0			0
$263$	113289.			1.63786			0.818929	−	0.573894i	$-0.194568\pi$
$263$	113289.			1.63786			0.818929	+	0.573894i	$0.194568\pi$
$264$		0			0
$265$		−	4179.65i		−	0.0595180i
$266$		0			0
$267$	103333.	−	103333.i	1.44949	−	1.44949i
$268$		0			0
$269$	−70652.7	+	70652.7i	−0.976393	+	0.976393i	−0.999728	−	0.0233352i	$-0.992572\pi$
$269$	−70652.7	+	70652.7i	−0.976393	+	0.976393i	0.0233352	+	0.999728i	$0.492572\pi$
$270$		0			0
$271$			110180.i			1.50025i	0.661294	+	0.750126i	$0.270007\pi$
$271$			110180.i			1.50025i	−0.661294	+	0.750126i	$0.729993\pi$
$272$		0			0
$273$	39312.7			0.527481
$274$		0			0
$275$	−73960.2	−	73960.2i	−0.977987	−	0.977987i
$276$		0			0
$277$	−34611.0	−	34611.0i	−0.451081	−	0.451081i	0.444632	−	0.895713i	$-0.353334\pi$
$277$	−34611.0	−	34611.0i	−0.451081	−	0.451081i	−0.895713	+	0.444632i	$0.853334\pi$
$278$		0			0
$279$	119147.			1.53065
$280$		0			0
$281$			147980.i			1.87408i	0.349216	+	0.937042i	$0.386448\pi$
$281$			147980.i			1.87408i	−0.349216	+	0.937042i	$0.613552\pi$
$282$		0			0
$283$	39761.2	−	39761.2i	0.496463	−	0.496463i	−0.413872	−	0.910335i	$-0.635824\pi$
$283$	39761.2	−	39761.2i	0.496463	−	0.496463i	0.910335	+	0.413872i	$0.135824\pi$
$284$		0			0
$285$	−14014.7	+	14014.7i	−0.172541	+	0.172541i
$286$		0			0
$287$		−	70273.6i		−	0.853156i
$288$		0			0
$289$	−75766.2			−0.907152
$290$		0			0
$291$	−44426.1	−	44426.1i	−0.524629	−	0.524629i
$292$		0			0
$293$	708.909	+	708.909i	0.00825763	+	0.00825763i	0.711224	−	0.702966i	$-0.248141\pi$
$293$	708.909	+	708.909i	0.00825763	+	0.00825763i	−0.702966	+	0.711224i	$0.748141\pi$
$294$		0			0
$295$	−6848.56			−0.0786965
$296$		0			0
$297$		−	35945.3i		−	0.407502i
$298$		0			0
$299$	2537.35	−	2537.35i	0.0283816	−	0.0283816i
$300$		0			0
$301$	85748.8	−	85748.8i	0.946444	−	0.946444i
$302$		0			0
$303$		−	214552.i		−	2.33694i
$304$		0			0
$305$	−3303.90			−0.0355162
$306$		0			0
$307$	−20597.1	−	20597.1i	−0.218539	−	0.218539i	0.589344	−	0.807883i	$-0.299386\pi$
$307$	−20597.1	−	20597.1i	−0.218539	−	0.218539i	−0.807883	+	0.589344i	$0.799386\pi$
$308$		0			0
$309$	1656.67	+	1656.67i	0.0173508	+	0.0173508i
$310$		0			0
$311$	−82310.6			−0.851011			−0.425505	−	0.904956i	$-0.639904\pi$
$311$	−82310.6			−0.851011			−0.425505	+	0.904956i	$0.639904\pi$
$312$		0			0
$313$		−	120415.i		−	1.22911i	−0.788872	−	0.614557i	$-0.789335\pi$
$313$		−	120415.i		−	1.22911i	0.788872	−	0.614557i	$-0.210665\pi$
$314$		0			0
$315$	−21137.4	+	21137.4i	−0.213025	+	0.213025i
$316$		0			0
$317$	−14795.3	+	14795.3i	−0.147233	+	0.147233i	−0.776881	−	0.629648i	$-0.783199\pi$
$317$	−14795.3	+	14795.3i	−0.147233	+	0.147233i	0.629648	+	0.776881i	$0.283199\pi$
$318$		0			0
$319$			66216.1i			0.650702i
$320$		0			0
$321$	−285639.			−2.77209
$322$		0			0
$323$	22993.9	+	22993.9i	0.220398	+	0.220398i
$324$		0			0
$325$	16534.9	+	16534.9i	0.156543	+	0.156543i
$326$		0			0
$327$	−44292.5			−0.414224
$328$		0			0
$329$		−	132114.i		−	1.22056i
$330$		0			0
$331$	82868.2	−	82868.2i	0.756366	−	0.756366i	−0.219293	−	0.975659i	$-0.570375\pi$
$331$	82868.2	−	82868.2i	0.756366	−	0.756366i	0.975659	+	0.219293i	$0.0703752\pi$
$332$		0			0
$333$	−101158.	+	101158.i	−0.912247	+	0.912247i
$334$		0			0
$335$		−	8450.04i		−	0.0752955i
$336$		0			0
$337$	78854.4			0.694331			0.347165	−	0.937804i	$-0.387144\pi$
$337$	78854.4			0.694331			0.347165	+	0.937804i	$0.387144\pi$
$338$		0			0
$339$	80368.0	+	80368.0i	0.699332	+	0.699332i
$340$		0			0
$341$	−149697.	−	149697.i	−1.28737	−	1.28737i
$342$		0			0
$343$	83925.2			0.713352
$344$		0			0
$345$			5014.18i			0.0421271i
$346$		0			0
$347$	−59543.0	+	59543.0i	−0.494506	+	0.494506i	−0.909723	−	0.415216i	$-0.863706\pi$
$347$	−59543.0	+	59543.0i	−0.494506	+	0.494506i	0.415216	+	0.909723i	$0.363706\pi$
$348$		0			0
$349$	756.172	−	756.172i	0.00620826	−	0.00620826i	−0.703996	−	0.710204i	$-0.748603\pi$
$349$	756.172	−	756.172i	0.00620826	−	0.00620826i	0.710204	+	0.703996i	$0.248603\pi$
$350$		0			0
$351$			8036.11i			0.0652276i
$352$		0			0
$353$	23723.5			0.190384			0.0951918	−	0.995459i	$-0.469654\pi$
$353$	23723.5			0.190384			0.0951918	+	0.995459i	$0.469654\pi$
$354$		0			0
$355$	−15863.3	−	15863.3i	−0.125874	−	0.125874i
$356$		0			0
$357$	63731.2	+	63731.2i	0.500053	+	0.500053i
$358$		0			0
$359$	−146064.			−1.13333			−0.566663	−	0.823950i	$-0.691766\pi$
$359$	−146064.			−1.13333			−0.566663	+	0.823950i	$0.691766\pi$
$360$		0			0
$361$			6038.12i			0.0463327i
$362$		0			0
$363$	−140234.	+	140234.i	−1.06424	+	1.06424i
$364$		0			0
$365$	18834.2	−	18834.2i	0.141371	−	0.141371i
$366$		0			0
$367$		−	151129.i		−	1.12206i	−0.827797	−	0.561028i	$-0.810406\pi$
$367$		−	151129.i		−	1.12206i	0.827797	−	0.561028i	$-0.189594\pi$
$368$		0			0
$369$	88501.7			0.649978
$370$		0			0
$371$	−56357.5	−	56357.5i	−0.409453	−	0.409453i
$372$		0			0
$373$	−26207.7	−	26207.7i	−0.188370	−	0.188370i	0.606621	−	0.794991i	$-0.292524\pi$
$373$	−26207.7	−	26207.7i	−0.188370	−	0.188370i	−0.794991	+	0.606621i	$0.792524\pi$
$374$		0			0
$375$	−66221.0			−0.470905
$376$		0			0
$377$		−	14803.6i		−	0.104156i
$378$		0			0
$379$	110424.	−	110424.i	0.768752	−	0.768752i	−0.209135	−	0.977887i	$-0.567065\pi$
$379$	110424.	−	110424.i	0.768752	−	0.768752i	0.977887	+	0.209135i	$0.0670647\pi$
$380$		0			0
$381$	−26810.1	+	26810.1i	−0.184692	+	0.184692i
$382$		0			0
$383$			10514.9i			0.0716819i	0.999358	+	0.0358409i	$0.0114110\pi$
$383$			10514.9i			0.0716819i	−0.999358	+	0.0358409i	$0.988589\pi$
$384$		0			0
$385$	53114.1			0.358334
$386$		0			0
$387$	107991.	+	107991.i	0.721049	+	0.721049i
$388$		0			0
$389$	166762.	+	166762.i	1.10204	+	1.10204i	0.994164	+	0.107877i	$0.0344054\pi$
$389$	166762.	+	166762.i	1.10204	+	1.10204i	0.107877	+	0.994164i	$0.465595\pi$
$390$		0			0
$391$	8226.78			0.0538116
$392$		0			0
$393$			131772.i			0.853172i
$394$		0			0
$395$	−15350.6	+	15350.6i	−0.0983855	+	0.0983855i
$396$		0			0
$397$	192542.	−	192542.i	1.22164	−	1.22164i	0.254594	−	0.967048i	$-0.418058\pi$
$397$	192542.	−	192542.i	1.22164	−	1.22164i	0.967048	−	0.254594i	$-0.0819419\pi$
$398$		0			0
$399$			377941.i			2.37399i
$400$		0			0
$401$	91157.6			0.566897			0.283448	−	0.958987i	$-0.408522\pi$
$401$	91157.6			0.566897			0.283448	+	0.958987i	$0.408522\pi$
$402$		0			0
$403$	33467.0	+	33467.0i	0.206066	+	0.206066i
$404$		0			0
$405$	14359.0	+	14359.0i	0.0875417	+	0.0875417i
$406$		0			0
$407$	254191.			1.53451
$408$		0			0
$409$			107774.i			0.644272i	0.946693	+	0.322136i	$0.104401\pi$
$409$			107774.i			0.644272i	−0.946693	+	0.322136i	$0.895599\pi$
$410$		0			0
$411$	34590.1	−	34590.1i	0.204771	−	0.204771i
$412$		0			0
$413$	−92344.5	+	92344.5i	−0.541391	+	0.541391i
$414$		0			0
$415$		−	14543.4i		−	0.0844442i
$416$		0			0
$417$	−82972.9			−0.477160
$418$		0			0
$419$	−118524.	−	118524.i	−0.675115	−	0.675115i	0.283776	−	0.958891i	$-0.408413\pi$
$419$	−118524.	−	118524.i	−0.675115	−	0.675115i	−0.958891	+	0.283776i	$0.908413\pi$
$420$		0			0
$421$	226616.	+	226616.i	1.27858	+	1.27858i	0.941464	+	0.337113i	$0.109451\pi$
$421$	226616.	+	226616.i	1.27858	+	1.27858i	0.337113	+	0.941464i	$0.390549\pi$
$422$		0			0
$423$	166383.			0.929882
$424$		0			0
$425$			53610.7i			0.296807i
$426$		0			0
$427$	−44549.0	+	44549.0i	−0.244333	+	0.244333i
$428$		0			0
$429$	62204.3	−	62204.3i	0.337991	−	0.337991i
$430$		0			0
$431$		−	5397.51i		−	0.0290562i	−0.999894	−	0.0145281i	$-0.995375\pi$
$431$		−	5397.51i		−	0.0290562i	0.999894	−	0.0145281i	$-0.00462460\pi$
$432$		0			0
$433$	163835.			0.873840			0.436920	−	0.899500i	$-0.356069\pi$
$433$	163835.			0.873840			0.436920	+	0.899500i	$0.356069\pi$
$434$		0			0
$435$	14627.0	+	14627.0i	0.0772997	+	0.0772997i
$436$		0			0
$437$	24393.4	+	24393.4i	0.127735	+	0.127735i
$438$		0			0
$439$	−158472.			−0.822289			−0.411144	−	0.911570i	$-0.634871\pi$
$439$	−158472.			−0.822289			−0.411144	+	0.911570i	$0.634871\pi$
$440$		0			0
$441$			337859.i			1.73723i
$442$		0			0
$443$	−137929.	+	137929.i	−0.702826	+	0.702826i	−0.965016	−	0.262190i	$-0.915555\pi$
$443$	−137929.	+	137929.i	−0.702826	+	0.702826i	0.262190	+	0.965016i	$0.415555\pi$
$444$		0			0
$445$	−31211.8	+	31211.8i	−0.157615	+	0.157615i
$446$		0			0
$447$			296680.i			1.48482i
$448$		0			0
$449$	327336.			1.62368			0.811841	−	0.583879i	$-0.198466\pi$
$449$	327336.			1.62368			0.811841	+	0.583879i	$0.198466\pi$
$450$		0			0
$451$	−111194.	−	111194.i	−0.546672	−	0.546672i
$452$		0			0
$453$	−395625.	−	395625.i	−1.92791	−	1.92791i
$454$		0			0
$455$	−11874.4			−0.0573575
$456$		0			0
$457$		−	154510.i		−	0.739817i	−0.929068	−	0.369909i	$-0.879389\pi$
$457$		−	154510.i		−	0.739817i	0.929068	−	0.369909i	$-0.120611\pi$
$458$		0			0
$459$	−13027.6	+	13027.6i	−0.0618358	+	0.0618358i
$460$		0			0
$461$	−19296.3	+	19296.3i	−0.0907971	+	0.0907971i	−0.751046	−	0.660249i	$-0.770451\pi$
$461$	−19296.3	+	19296.3i	−0.0907971	+	0.0907971i	0.660249	+	0.751046i	$0.270451\pi$
$462$		0			0
$463$			26503.6i			0.123635i	0.998087	+	0.0618176i	$0.0196897\pi$
$463$			26503.6i			0.123635i	−0.998087	+	0.0618176i	$0.980310\pi$
$464$		0			0
$465$	−66135.7			−0.305865
$466$		0			0
$467$	111797.	+	111797.i	0.512622	+	0.512622i	0.915329	−	0.402707i	$-0.131931\pi$
$467$	111797.	+	111797.i	0.512622	+	0.512622i	−0.402707	+	0.915329i	$0.631931\pi$
$468$		0			0
$469$	−113939.	−	113939.i	−0.517994	−	0.517994i
$470$		0			0
$471$	−466307.			−2.10199
$472$		0			0
$473$		−	271360.i		−	1.21290i
$474$		0			0
$475$	−158962.	+	158962.i	−0.704541	+	0.704541i
$476$		0			0
$477$	70975.8	−	70975.8i	0.311942	−	0.311942i
$478$		0			0
$479$		−	225380.i		−	0.982301i	−0.871075	−	0.491150i	$-0.836577\pi$
$479$		−	225380.i		−	0.982301i	0.871075	−	0.491150i	$-0.163423\pi$
$480$		0			0
$481$	−56828.1			−0.245625
$482$		0			0
$483$	67610.1	+	67610.1i	0.289813	+	0.289813i
$484$		0			0
$485$	13419.0	+	13419.0i	0.0570473	+	0.0570473i
$486$		0			0
$487$	−8483.58			−0.0357702			−0.0178851	−	0.999840i	$-0.505693\pi$
$487$	−8483.58			−0.0357702			−0.0178851	+	0.999840i	$0.505693\pi$
$488$		0			0
$489$		−	460544.i		−	1.92599i
$490$		0			0
$491$	69265.0	−	69265.0i	0.287310	−	0.287310i	−0.548706	−	0.836016i	$-0.684879\pi$
$491$	69265.0	−	69265.0i	0.287310	−	0.287310i	0.836016	+	0.548706i	$0.184879\pi$
$492$		0			0
$493$	23998.6	−	23998.6i	0.0987399	−	0.0987399i
$494$		0			0
$495$			66891.1i			0.272997i
$496$		0			0
$497$	−427794.			−1.73190
$498$		0			0
$499$	86869.4	+	86869.4i	0.348872	+	0.348872i	0.859689	−	0.510817i	$-0.170657\pi$
$499$	86869.4	+	86869.4i	0.348872	+	0.348872i	−0.510817	+	0.859689i	$0.670657\pi$
$500$		0			0
$501$	491827.	+	491827.i	1.95946	+	1.95946i
$502$		0			0
$503$	−112271.			−0.443745			−0.221872	−	0.975076i	$-0.571217\pi$
$503$	−112271.			−0.443745			−0.221872	+	0.975076i	$0.571217\pi$
$504$		0			0
$505$			64805.7i			0.254115i
$506$		0			0
$507$	255306.	−	255306.i	0.993220	−	0.993220i
$508$		0			0
$509$	167589.	−	167589.i	0.646861	−	0.646861i	−0.305372	−	0.952233i	$-0.598781\pi$
$509$	167589.	−	167589.i	0.646861	−	0.646861i	0.952233	+	0.305372i	$0.0987808\pi$
$510$		0			0
$511$		−	507912.i		−	1.94512i
$512$		0			0
$513$	−77256.9			−0.293564
$514$		0			0
$515$	−500.399	−	500.399i	−0.00188670	−	0.00188670i
$516$		0			0
$517$	−209044.	−	209044.i	−0.782089	−	0.782089i
$518$		0			0
$519$	496108.			1.84180
$520$		0			0
$521$			287463.i			1.05903i	0.848302	+	0.529513i	$0.177625\pi$
$521$			287463.i			1.05903i	−0.848302	+	0.529513i	$0.822375\pi$
$522$		0			0
$523$	−203069.	+	203069.i	−0.742404	+	0.742404i	−0.973040	−	0.230636i	$-0.925919\pi$
$523$	−203069.	+	203069.i	−0.742404	+	0.742404i	0.230636	+	0.973040i	$0.425919\pi$
$524$		0			0
$525$	−440588.	+	440588.i	−1.59851	+	1.59851i
$526$		0			0
$527$			108509.i			0.390701i
$528$		0			0
$529$	−271114.			−0.968813
$530$		0			0
$531$	−116297.	−	116297.i	−0.412459	−	0.412459i
$532$		0			0
$533$	24859.0	+	24859.0i	0.0875042	+	0.0875042i
$534$		0			0
$535$	86277.6			0.301433
$536$		0			0
$537$		−	90786.1i		−	0.314826i
$538$		0			0
$539$	424486.	−	424486.i	1.46112	−	1.46112i
$540$		0			0
$541$	−308972.	+	308972.i	−1.05566	+	1.05566i	−0.0573036	+	0.998357i	$0.518250\pi$
$541$	−308972.	+	308972.i	−1.05566	+	1.05566i	−0.998357	+	0.0573036i	$0.981750\pi$
$542$		0			0
$543$		−	451027.i		−	1.52969i
$544$		0			0
$545$	13378.6			0.0450420
$546$		0			0
$547$	−8623.13	−	8623.13i	−0.0288198	−	0.0288198i	0.692550	−	0.721370i	$-0.256487\pi$
$547$	−8623.13	−	8623.13i	−0.0288198	−	0.0288198i	−0.721370	+	0.692550i	$0.756487\pi$
$548$		0			0
$549$	−56104.4	−	56104.4i	−0.186145	−	0.186145i
$550$		0			0
$551$	142317.			0.468765
$552$		0			0
$553$			413968.i			1.35368i
$554$		0			0
$555$	56150.4	−	56150.4i	0.182292	−	0.182292i
$556$		0			0
$557$	208785.	−	208785.i	0.672961	−	0.672961i	−0.285437	−	0.958398i	$-0.592139\pi$
$557$	208785.	−	208785.i	0.672961	−	0.672961i	0.958398	+	0.285437i	$0.0921387\pi$
$558$		0			0
$559$			60666.5i			0.194145i
$560$		0			0
$561$	201683.			0.640832
$562$		0			0
$563$	127891.	+	127891.i	0.403480	+	0.403480i	0.879458	−	0.475977i	$-0.157906\pi$
$563$	127891.	+	127891.i	0.403480	+	0.403480i	−0.475977	+	0.879458i	$0.657906\pi$
$564$		0			0
$565$	−24275.2	−	24275.2i	−0.0760443	−	0.0760443i
$566$		0			0
$567$	387228.			1.20448
$568$		0			0
$569$		−	488561.i		−	1.50902i	−0.656290	−	0.754509i	$-0.727875\pi$
$569$		−	488561.i		−	1.50902i	0.656290	−	0.754509i	$-0.272125\pi$
$570$		0			0
$571$	−17324.2	+	17324.2i	−0.0531352	+	0.0531352i	−0.733175	−	0.680040i	$-0.761962\pi$
$571$	−17324.2	+	17324.2i	−0.0531352	+	0.0531352i	0.680040	+	0.733175i	$0.261962\pi$
$572$		0			0
$573$	424913.	−	424913.i	1.29417	−	1.29417i
$574$		0			0
$575$			56873.6i			0.172018i
$576$		0			0
$577$	−9362.93			−0.0281229			−0.0140615	−	0.999901i	$-0.504476\pi$
$577$	−9362.93			−0.0281229			−0.0140615	+	0.999901i	$0.504476\pi$
$578$		0			0
$579$	−473990.	−	473990.i	−1.41388	−	1.41388i
$580$		0			0
$581$	−196100.	−	196100.i	−0.580932	−	0.580932i
$582$		0			0
$583$	−178348.			−0.524725
$584$		0			0
$585$		−	14954.5i		−	0.0436978i
$586$		0			0
$587$	46301.5	−	46301.5i	0.134375	−	0.134375i	−0.636720	−	0.771095i	$-0.719709\pi$
$587$	46301.5	−	46301.5i	0.134375	−	0.134375i	0.771095	+	0.636720i	$0.219709\pi$
$588$		0			0
$589$	−321742.	+	321742.i	−0.927422	+	0.927422i
$590$		0			0
$591$		−	483778.i		−	1.38507i
$592$		0			0
$593$	−194145.			−0.552099			−0.276049	−	0.961143i	$-0.589025\pi$
$593$	−194145.			−0.552099			−0.276049	+	0.961143i	$0.589025\pi$
$594$		0			0
$595$	−19250.1	−	19250.1i	−0.0543749	−	0.0543749i
$596$		0			0
$597$	−420387.	−	420387.i	−1.17951	−	1.17951i
$598$		0			0
$599$	−474516.			−1.32250			−0.661252	−	0.750164i	$-0.729975\pi$
$599$	−474516.			−1.32250			−0.661252	+	0.750164i	$0.729975\pi$
$600$		0			0
$601$			87515.3i			0.242290i	0.992635	+	0.121145i	$0.0386566\pi$
$601$			87515.3i			0.242290i	−0.992635	+	0.121145i	$0.961343\pi$
$602$		0			0
$603$	143493.	−	143493.i	0.394634	−	0.394634i
$604$		0			0
$605$	42357.8	−	42357.8i	0.115724	−	0.115724i
$606$		0			0
$607$			687260.i			1.86528i	0.360808	+	0.932640i	$0.382501\pi$
$607$			687260.i			1.86528i	−0.360808	+	0.932640i	$0.617499\pi$
$608$		0			0
$609$	394456.			1.06356
$610$		0			0
$611$	46734.8	+	46734.8i	0.125187	+	0.125187i
$612$		0			0
$613$	220862.	+	220862.i	0.587761	+	0.587761i	0.937025	−	0.349263i	$-0.113568\pi$
$613$	220862.	+	220862.i	0.587761	+	0.587761i	−0.349263	+	0.937025i	$0.613568\pi$
$614$		0			0
$615$	−49125.1			−0.129883
$616$		0			0
$617$			518967.i			1.36323i	0.731711	+	0.681615i	$0.238722\pi$
$617$			518967.i			1.36323i	−0.731711	+	0.681615i	$0.761278\pi$
$618$		0			0
$619$	−77555.3	+	77555.3i	−0.202409	+	0.202409i	−0.801031	−	0.598622i	$-0.795715\pi$
$619$	−77555.3	+	77555.3i	−0.202409	+	0.202409i	0.598622	+	0.801031i	$0.295715\pi$
$620$		0			0
$621$	−13820.5	+	13820.5i	−0.0358378	+	0.0358378i
$622$		0			0
$623$			841705.i			2.16862i
$624$		0			0
$625$	−360490.			−0.922855
$626$		0			0
$627$	598015.	+	598015.i	1.52117	+	1.52117i
$628$		0			0
$629$	−92126.1	−	92126.1i	−0.232853	−	0.232853i
$630$		0			0
$631$	−344653.			−0.865612			−0.432806	−	0.901487i	$-0.642477\pi$
$631$	−344653.			−0.865612			−0.432806	+	0.901487i	$0.642477\pi$
$632$		0			0
$633$		−	486914.i		−	1.21519i
$634$		0			0
$635$	8098.03	−	8098.03i	0.0200832	−	0.0200832i
$636$		0			0
$637$	−94900.2	+	94900.2i	−0.233877	+	0.233877i
$638$		0			0
$639$		−	538758.i		−	1.31945i
$640$		0			0
$641$	−183353.			−0.446243			−0.223122	−	0.974791i	$-0.571625\pi$
$641$	−183353.			−0.446243			−0.223122	+	0.974791i	$0.571625\pi$
$642$		0			0
$643$	−541900.	−	541900.i	−1.31068	−	1.31068i	−0.920913	−	0.389768i	$-0.872555\pi$
$643$	−541900.	−	541900.i	−1.31068	−	1.31068i	−0.389768	−	0.920913i	$-0.627445\pi$
$644$		0			0
$645$	−59943.0	−	59943.0i	−0.144085	−	0.144085i
$646$		0			0
$647$	358562.			0.856555			0.428278	−	0.903647i	$-0.359121\pi$
$647$	358562.			0.856555			0.428278	+	0.903647i	$0.359121\pi$
$648$		0			0
$649$			292233.i			0.693808i
$650$		0			0
$651$	−891760.	+	891760.i	−2.10419	+	2.10419i
$652$		0			0
$653$	73642.4	−	73642.4i	0.172704	−	0.172704i	−0.615463	−	0.788166i	$-0.711031\pi$
$653$	73642.4	−	73642.4i	0.172704	−	0.172704i	0.788166	+	0.615463i	$0.211031\pi$
$654$		0			0
$655$		−	39801.7i		−	0.0927725i
$656$		0			0
$657$	639657.			1.48189
$658$		0			0
$659$	22081.7	+	22081.7i	0.0508467	+	0.0508467i	0.732073	−	0.681226i	$-0.238553\pi$
$659$	22081.7	+	22081.7i	0.0508467	+	0.0508467i	−0.681226	+	0.732073i	$0.738553\pi$
$660$		0			0
$661$	−20869.3	−	20869.3i	−0.0477644	−	0.0477644i	0.682821	−	0.730586i	$-0.260753\pi$
$661$	−20869.3	−	20869.3i	−0.0477644	−	0.0477644i	−0.730586	+	0.682821i	$0.760753\pi$
$662$		0			0
$663$	−45089.3			−0.102576
$664$		0			0
$665$		−	114157.i		−	0.258143i
$666$		0			0
$667$	25459.3	−	25459.3i	0.0572261	−	0.0572261i
$668$		0			0
$669$	684791.	−	684791.i	1.53005	−	1.53005i
$670$		0			0
$671$			140979.i			0.313120i
$672$		0			0
$673$	379771.			0.838479			0.419239	−	0.907876i	$-0.362297\pi$
$673$	379771.			0.838479			0.419239	+	0.907876i	$0.362297\pi$
$674$		0			0
$675$	−90063.0	−	90063.0i	−0.197669	−	0.197669i
$676$		0			0
$677$	156167.	+	156167.i	0.340731	+	0.340731i	0.856642	−	0.515911i	$-0.172546\pi$
$677$	156167.	+	156167.i	0.340731	+	0.340731i	−0.515911	+	0.856642i	$0.672546\pi$
$678$		0			0
$679$	361877.			0.784912
$680$		0			0
$681$		−	355511.i		−	0.766581i
$682$		0			0
$683$	164044.	−	164044.i	0.351656	−	0.351656i	−0.509070	−	0.860725i	$-0.670010\pi$
$683$	164044.	−	164044.i	0.351656	−	0.351656i	0.860725	+	0.509070i	$0.170010\pi$
$684$		0			0
$685$	−10448.0	+	10448.0i	−0.0222665	+	0.0222665i
$686$		0			0
$687$			785666.i			1.66466i
$688$		0			0
$689$	39872.4			0.0839912
$690$		0			0
$691$	−288207.	−	288207.i	−0.603599	−	0.603599i	0.337667	−	0.941266i	$-0.390362\pi$
$691$	−288207.	−	288207.i	−0.603599	−	0.603599i	−0.941266	+	0.337667i	$0.890362\pi$
$692$		0			0
$693$	901945.	+	901945.i	1.87808	+	1.87808i
$694$		0			0
$695$	25062.1			0.0518856
$696$		0			0
$697$			80599.7i			0.165908i
$698$		0			0
$699$	26087.2	−	26087.2i	0.0533916	−	0.0533916i
$700$		0			0
$701$	−323248.	+	323248.i	−0.657808	+	0.657808i	−0.954861	−	0.297053i	$-0.903996\pi$
$701$	−323248.	+	323248.i	−0.657808	+	0.657808i	0.297053	+	0.954861i	$0.403996\pi$
$702$		0			0
$703$		−	546329.i		−	1.10546i
$704$		0			0
$705$	−92355.0			−0.185816
$706$		0			0
$707$	873826.	+	873826.i	1.74818	+	1.74818i
$708$		0			0
$709$	580085.	+	580085.i	1.15398	+	1.15398i	0.985747	+	0.168235i	$0.0538067\pi$
$709$	580085.	+	580085.i	1.15398	+	1.15398i	0.168235	+	0.985747i	$0.446193\pi$
$710$		0			0
$711$	−521346.			−1.03130
$712$		0			0
$713$			115113.i			0.226436i
$714$		0			0
$715$	−18788.9	+	18788.9i	−0.0367526	+	0.0367526i
$716$		0			0
$717$	−471123.	+	471123.i	−0.916423	+	0.916423i
$718$		0			0
$719$		−	332243.i		−	0.642684i	−0.946963	−	0.321342i	$-0.895866\pi$
$719$		−	332243.i		−	0.642684i	0.946963	−	0.321342i	$-0.104134\pi$
$720$		0			0
$721$	−13494.5			−0.0259590
$722$		0			0
$723$	415456.	+	415456.i	0.794783	+	0.794783i
$724$		0			0
$725$	165908.	+	165908.i	0.315639	+	0.315639i
$726$		0			0
$727$	−362311.			−0.685508			−0.342754	−	0.939425i	$-0.611360\pi$
$727$	−362311.			−0.685508			−0.342754	+	0.939425i	$0.611360\pi$
$728$		0			0
$729$			713570.i			1.34271i
$730$		0			0
$731$	−98348.7	+	98348.7i	−0.184049	+	0.184049i
$732$		0			0
$733$	−377844.	+	377844.i	−0.703242	+	0.703242i	−0.965105	−	0.261863i	$-0.915663\pi$
$733$	−377844.	+	377844.i	−0.703242	+	0.703242i	0.261863	+	0.965105i	$0.415663\pi$
$734$		0			0
$735$		−	187537.i		−	0.347146i
$736$		0			0
$737$	−360569.			−0.663825
$738$		0			0
$739$	467502.	+	467502.i	0.856042	+	0.856042i	0.990869	−	0.134828i	$-0.0430480\pi$
$739$	467502.	+	467502.i	0.856042	+	0.856042i	−0.134828	+	0.990869i	$0.543048\pi$
$740$		0			0
$741$	−133695.	−	133695.i	−0.243489	−	0.243489i
$742$		0			0
$743$	555820.			1.00683			0.503415	−	0.864045i	$-0.332077\pi$
$743$	555820.			1.00683			0.503415	+	0.864045i	$0.332077\pi$
$744$		0			0
$745$		−	89612.4i		−	0.161456i
$746$		0			0
$747$	246966.	−	246966.i	0.442584	−	0.442584i
$748$		0			0
$749$	1.16335e6	−	1.16335e6i	2.07370	−	2.07370i
$750$		0			0
$751$			308308.i			0.546644i	0.961923	+	0.273322i	$0.0881224\pi$
$751$			308308.i			0.546644i	−0.961923	+	0.273322i	$0.911878\pi$
$752$		0			0
$753$	599226.			1.05682
$754$		0			0
$755$	119499.	+	119499.i	0.209638	+	0.209638i
$756$		0			0
$757$	−34980.2	−	34980.2i	−0.0610423	−	0.0610423i	0.675927	−	0.736969i	$-0.263744\pi$
$757$	−34980.2	−	34980.2i	−0.0610423	−	0.0610423i	−0.736969	+	0.675927i	$0.763744\pi$
$758$		0			0
$759$	213958.			0.371403
$760$		0			0
$761$			545745.i			0.942368i	0.882035	+	0.471184i	$0.156173\pi$
$761$			545745.i			0.942368i	−0.882035	+	0.471184i	$0.843827\pi$
$762$		0			0
$763$	180394.	−	180394.i	0.309866	−	0.309866i
$764$		0			0
$765$	24243.3	−	24243.3i	0.0414256	−	0.0414256i
$766$		0			0
$767$		−	65332.9i		−	0.111056i
$768$		0			0
$769$	510362.			0.863030			0.431515	−	0.902106i	$-0.357979\pi$
$769$	510362.			0.863030			0.431515	+	0.902106i	$0.357979\pi$
$770$		0			0
$771$	−667972.	−	667972.i	−1.12370	−	1.12370i
$772$		0			0
$773$	−596763.	−	596763.i	−0.998718	−	0.998718i	0.00128103	−	0.999999i	$-0.499592\pi$
$773$	−596763.	−	596763.i	−0.998718	−	0.998718i	−0.999999	+	0.00128103i	$0.999592\pi$
$774$		0			0
$775$	−750148.			−1.24895
$776$		0			0
$777$		−	1.51424e6i		−	2.50814i
$778$		0			0
$779$	−238987.	+	238987.i	−0.393822	+	0.393822i
$780$		0			0
$781$	−676897.	+	676897.i	−1.10974	+	1.10974i
$782$		0			0
$783$			80632.7i			0.131519i
$784$		0			0
$785$	140849.			0.228567
$786$		0			0
$787$	−463254.	−	463254.i	−0.747945	−	0.747945i	0.226148	−	0.974093i	$-0.427387\pi$
$787$	−463254.	−	463254.i	−0.747945	−	0.747945i	−0.974093	+	0.226148i	$0.927387\pi$
$788$		0			0
$789$	−1.06785e6	−	1.06785e6i	−1.71536	−	1.71536i
$790$		0			0
$791$	−654644.			−1.04629
$792$		0			0
$793$		−	31518.0i		−	0.0501202i
$794$		0			0
$795$	−39396.9	+	39396.9i	−0.0623344	+	0.0623344i
$796$		0			0
$797$	−406283.	+	406283.i	−0.639605	+	0.639605i	−0.950458	−	0.310853i	$-0.899385\pi$
$797$	−406283.	+	406283.i	−0.639605	+	0.639605i	0.310853	+	0.950458i	$0.399385\pi$
$798$		0			0
$799$			151527.i			0.237354i
$800$		0			0
$801$	−1.06003e6			−1.65217
$802$		0			0
$803$	−803667.	−	803667.i	−1.24636	−	1.24636i
$804$		0			0
$805$	−20421.7	−	20421.7i	−0.0315137	−	0.0315137i
$806$		0			0
$807$	1.33193e6			2.04519
$808$		0			0
$809$		−	766553.i		−	1.17124i	−0.810587	−	0.585619i	$-0.800852\pi$
$809$		−	766553.i		−	1.17124i	0.810587	−	0.585619i	$-0.199148\pi$
$810$		0			0
$811$	−418641.	+	418641.i	−0.636503	+	0.636503i	−0.949691	−	0.313188i	$-0.898603\pi$
$811$	−418641.	+	418641.i	−0.636503	+	0.636503i	0.313188	+	0.949691i	$0.398603\pi$
$812$		0			0
$813$	1.03855e6	−	1.03855e6i	1.57125	−	1.57125i
$814$		0			0
$815$			139108.i			0.209429i
$816$		0			0
$817$	−583231.			−0.873769
$818$		0			0
$819$	−201643.	−	201643.i	−0.300618	−	0.300618i
$820$		0			0
$821$	23229.7	+	23229.7i	0.0344633	+	0.0344633i	0.724128	−	0.689665i	$-0.242242\pi$
$821$	23229.7	+	23229.7i	0.0344633	+	0.0344633i	−0.689665	+	0.724128i	$0.742242\pi$
$822$		0			0
$823$	41797.3			0.0617090			0.0308545	−	0.999524i	$-0.490177\pi$
$823$	41797.3			0.0617090			0.0308545	+	0.999524i	$0.490177\pi$
$824$		0			0
$825$			1.39428e6i			2.04853i
$826$		0			0
$827$	−349889.	+	349889.i	−0.511587	+	0.511587i	−0.915013	−	0.403425i	$-0.867820\pi$
$827$	−349889.	+	349889.i	−0.511587	+	0.511587i	0.403425	+	0.915013i	$0.367820\pi$
$828$		0			0
$829$	−213369.	+	213369.i	−0.310472	+	0.310472i	−0.845092	−	0.534621i	$-0.820455\pi$
$829$	−213369.	+	213369.i	−0.310472	+	0.310472i	0.534621	+	0.845092i	$0.320455\pi$
$830$		0			0
$831$			652479.i			0.944853i
$832$		0			0
$833$	−307692.			−0.443432
$834$		0			0
$835$	−148557.	−	148557.i	−0.213069	−	0.213069i
$836$		0			0
$837$	−182289.	−	182289.i	−0.260202	−	0.260202i
$838$		0			0
$839$	7789.74			0.0110662			0.00553311	−	0.999985i	$-0.498239\pi$
$839$	7789.74			0.0110662			0.00553311	+	0.999985i	$0.498239\pi$
$840$		0			0
$841$			558745.i			0.789990i
$842$		0			0
$843$	1.39484e6	−	1.39484e6i	1.96277	−	1.96277i
$844$		0			0
$845$	−77115.5	+	77115.5i	−0.108001	+	0.108001i
$846$		0			0
$847$		−	1.14229e6i		−	1.59224i
$848$		0			0
$849$	−749570.			−1.03991
$850$		0			0
$851$	−97733.2	−	97733.2i	−0.134953	−	0.134953i
$852$		0			0
$853$	−485860.	−	485860.i	−0.667749	−	0.667749i	0.289445	−	0.957195i	$-0.406529\pi$
$853$	−485860.	−	485860.i	−0.667749	−	0.667749i	−0.957195	+	0.289445i	$0.906529\pi$
$854$		0			0
$855$	143768.			0.196667
$856$		0			0
$857$		−	1.01914e6i		−	1.38763i	−0.720154	−	0.693814i	$-0.755929\pi$
$857$		−	1.01914e6i		−	1.38763i	0.720154	−	0.693814i	$-0.244071\pi$
$858$		0			0
$859$	232567.	−	232567.i	0.315182	−	0.315182i	−0.531731	−	0.846913i	$-0.678458\pi$
$859$	232567.	−	232567.i	0.315182	−	0.315182i	0.846913	+	0.531731i	$0.178458\pi$
$860$		0			0
$861$	−662392.	+	662392.i	−0.893529	+	0.893529i
$862$		0			0
$863$		−	739852.i		−	0.993398i	−0.867923	−	0.496699i	$-0.834545\pi$
$863$		−	739852.i		−	0.993398i	0.867923	−	0.496699i	$-0.165455\pi$
$864$		0			0
$865$	−149850.			−0.200274
$866$		0			0
$867$	714164.	+	714164.i	0.950079	+	0.950079i
$868$		0			0
$869$	655020.	+	655020.i	0.867392	+	0.867392i
$870$		0			0
$871$	80610.5			0.106256
$872$		0			0
$873$			455742.i			0.597986i
$874$		0			0
$875$	269704.	−	269704.i	0.352267	−	0.352267i
$876$		0			0
$877$	828805.	−	828805.i	1.07759	−	1.07759i	0.0808636	−	0.996725i	$-0.474232\pi$
$877$	828805.	−	828805.i	1.07759	−	1.07759i	0.996725	−	0.0808636i	$-0.0257678\pi$
$878$		0			0
$879$		−	13364.2i		−	0.0172968i
$880$		0			0
$881$	1.20631e6			1.55420			0.777099	−	0.629379i	$-0.216690\pi$
$881$	1.20631e6			1.55420			0.777099	+	0.629379i	$0.216690\pi$
$882$		0			0
$883$	381765.	+	381765.i	0.489637	+	0.489637i	0.908192	−	0.418555i	$-0.137463\pi$
$883$	381765.	+	381765.i	0.489637	+	0.489637i	−0.418555	+	0.908192i	$0.637463\pi$
$884$		0			0
$885$	64553.8	+	64553.8i	0.0824205	+	0.0824205i
$886$		0			0
$887$	1.44154e6			1.83223			0.916113	−	0.400919i	$-0.131309\pi$
$887$	1.44154e6			1.83223			0.916113	+	0.400919i	$0.131309\pi$
$888$		0			0
$889$		−	218384.i		−	0.276323i
$890$		0			0
$891$	612709.	−	612709.i	0.771790	−	0.771790i
$892$		0			0
$893$	−449295.	+	449295.i	−0.563416	+	0.563416i
$894$		0			0
$895$			27422.0i			0.0342337i
$896$		0			0
$897$	−47833.5			−0.0594494
$898$		0			0
$899$	335801.	+	335801.i	0.415492	+	0.415492i
$900$		0			0
$901$	64638.6	+	64638.6i	0.0796238	+	0.0796238i
$902$		0			0
$903$	−1.61652e6			−1.98246
$904$		0			0
$905$			136233.i			0.166336i
$906$		0			0
$907$	−208093.	+	208093.i	−0.252955	+	0.252955i	−0.822181	−	0.569226i	$-0.807243\pi$
$907$	−208093.	+	208093.i	−0.252955	+	0.252955i	0.569226	+	0.822181i	$0.307243\pi$
$908$		0			0
$909$	−1.10048e6	+	1.10048e6i	−1.33185	+	1.33185i
$910$		0			0
$911$		−	861726.i		−	1.03832i	−0.854676	−	0.519162i	$-0.826244\pi$
$911$		−	861726.i		−	1.03832i	0.854676	−	0.519162i	$-0.173756\pi$
$912$		0			0
$913$	−620577.			−0.744482
$914$		0			0
$915$	31142.2	+	31142.2i	0.0371969	+	0.0371969i
$916$		0			0
$917$	−536678.	−	536678.i	−0.638227	−	0.638227i
$918$		0			0
$919$	368829.			0.436711			0.218355	−	0.975869i	$-0.429931\pi$
$919$	368829.			0.436711			0.218355	+	0.975869i	$0.429931\pi$
$920$		0			0
$921$			388292.i			0.457761i
$922$		0			0
$923$	151330.	−	151330.i	0.177632	−	0.177632i
$924$		0			0
$925$	636889.	−	636889.i	0.744355	−	0.744355i
$926$		0			0
$927$		−	16994.8i		−	0.0197769i
$928$		0			0
$929$	842458.			0.976151			0.488076	−	0.872801i	$-0.337699\pi$
$929$	842458.			0.976151			0.488076	+	0.872801i	$0.337699\pi$
$930$		0			0
$931$	−912344.	−	912344.i	−1.05259	−	1.05259i
$932$		0			0
$933$	775851.	+	775851.i	0.891282	+	0.891282i
$934$		0			0
$935$	−60918.6			−0.0696830
$936$		0			0
$937$		−	41186.1i		−	0.0469107i	−0.999725	−	0.0234553i	$-0.992533\pi$
$937$		−	41186.1i		−	0.0469107i	0.999725	−	0.0234553i	$-0.00746675\pi$
$938$		0			0
$939$	−1.13502e6	+	1.13502e6i	−1.28728	+	1.28728i
$940$		0			0
$941$	−495362.	+	495362.i	−0.559427	+	0.559427i	−0.929144	−	0.369717i	$-0.879454\pi$
$941$	−495362.	+	495362.i	−0.559427	+	0.559427i	0.369717	+	0.929144i	$0.379454\pi$
$942$		0			0
$943$			85505.2i			0.0961544i
$944$		0			0
$945$	64678.2			0.0724259
$946$		0			0
$947$	−825578.	−	825578.i	−0.920573	−	0.920573i	0.0764965	−	0.997070i	$-0.475627\pi$
$947$	−825578.	−	825578.i	−0.920573	−	0.920573i	−0.997070	+	0.0764965i	$0.975627\pi$
$948$		0			0
$949$	179672.	+	179672.i	0.199502	+	0.199502i
$950$		0			0
$951$	278918.			0.308401
$952$		0			0
$953$		−	1.06311e6i		−	1.17055i	−0.810834	−	0.585276i	$-0.800986\pi$
$953$		−	1.06311e6i		−	1.17055i	0.810834	−	0.585276i	$-0.199014\pi$
$954$		0			0
$955$	−128345.	+	128345.i	−0.140726	+	0.140726i
$956$		0			0
$957$	624145.	−	624145.i	0.681494	−	0.681494i
$958$		0			0
$959$			281757.i			0.306364i
$960$		0			0
$961$	−594793.			−0.644050
$962$		0			0
$963$	1.46511e6	+	1.46511e6i	1.57985	+	1.57985i
$964$		0			0
$965$	143169.	+	143169.i	0.153743	+	0.153743i
$966$		0			0
$967$	−1.03910e6			−1.11123			−0.555615	−	0.831440i	$-0.687517\pi$
$967$	−1.03910e6			−1.11123			−0.555615	+	0.831440i	$0.687517\pi$
$968$		0			0
$969$		−	433476.i		−	0.461655i
$970$		0			0
$971$	624932.	−	624932.i	0.662818	−	0.662818i	−0.293225	−	0.956043i	$-0.594729\pi$
$971$	624932.	−	624932.i	0.662818	−	0.662818i	0.956043	+	0.293225i	$0.0947285\pi$
$972$		0			0
$973$	337931.	−	337931.i	0.356946	−	0.356946i
$974$		0			0
$975$		−	311712.i		−	0.327903i
$976$		0			0
$977$	1.37121e6			1.43653			0.718264	−	0.695771i	$-0.244937\pi$
$977$	1.37121e6			1.43653			0.718264	+	0.695771i	$0.244937\pi$
$978$		0			0
$979$	1.33183e6	+	1.33183e6i	1.38958	+	1.38958i
$980$		0			0
$981$	227186.	+	227186.i	0.236071	+	0.236071i
$982$		0			0
$983$	−838159.			−0.867400			−0.433700	−	0.901057i	$-0.642792\pi$
$983$	−838159.			−0.867400			−0.433700	+	0.901057i	$0.642792\pi$
$984$		0			0
$985$			146126.i			0.150610i
$986$		0			0
$987$	−1.24529e6	+	1.24529e6i	−1.27831	+	1.27831i
$988$		0			0
$989$	−104335.	+	104335.i	−0.106668	+	0.106668i
$990$		0			0
$991$			817540.i			0.832457i	0.909260	+	0.416228i	$0.136648\pi$
$991$			817540.i			0.832457i	−0.909260	+	0.416228i	$0.863352\pi$
$992$		0			0
$993$	−1.56221e6			−1.58432
$994$		0			0
$995$	126978.	+	126978.i	0.128258	+	0.128258i
$996$		0			0
$997$	243046.	+	243046.i	0.244511	+	0.244511i	0.818713	−	0.574203i	$-0.194688\pi$
$997$	243046.	+	243046.i	0.244511	+	0.244511i	−0.574203	+	0.818713i	$0.694688\pi$
$998$		0			0
$999$	309534.			0.310154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.a.31.1		14
4.3	odd	2		128.5.f.b.31.7		14
8.3	odd	2		16.5.f.a.11.2	yes	14
8.5	even	2		64.5.f.a.15.7		14
16.3	odd	4	inner	128.5.f.a.95.1		14
16.5	even	4		16.5.f.a.3.2	✓	14
16.11	odd	4		64.5.f.a.47.7		14
16.13	even	4		128.5.f.b.95.7		14
24.5	odd	2		576.5.m.a.271.4		14
24.11	even	2		144.5.m.a.91.6		14
48.5	odd	4		144.5.m.a.19.6		14
48.11	even	4		576.5.m.a.559.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.2	✓	14	16.5	even	4
16.5.f.a.11.2	yes	14	8.3	odd	2
64.5.f.a.15.7		14	8.5	even	2
64.5.f.a.47.7		14	16.11	odd	4
128.5.f.a.31.1		14	1.1	even	1	trivial
128.5.f.a.95.1		14	16.3	odd	4	inner
128.5.f.b.31.7		14	4.3	odd	2
128.5.f.b.95.7		14	16.13	even	4
144.5.m.a.19.6		14	48.5	odd	4
144.5.m.a.91.6		14	24.11	even	2
576.5.m.a.271.4		14	24.5	odd	2
576.5.m.a.559.4		14	48.11	even	4

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.42589 - 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} +76.7794 q^{7} +96.6949i q^{9} +O(q^{10})\)	\(q+(-9.42589 - 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} +76.7794 q^{7} +96.6949i q^{9} +(121.488 - 121.488i) q^{11} +(-27.1604 + 27.1604i) q^{13} -53.6729i q^{15} -88.0613 q^{17} +(-261.112 - 261.112i) q^{19} +(-723.714 - 723.714i) q^{21} -93.4210 q^{23} -608.788i q^{25} +(147.938 - 147.938i) q^{27} +(-272.522 + 272.522i) q^{29} -1232.20i q^{31} -2290.26 q^{33} +(218.599 + 218.599i) q^{35} +(1046.16 + 1046.16i) q^{37} +512.021 q^{39} -915.267i q^{41} +(1116.82 - 1116.82i) q^{43} +(-275.300 + 275.300i) q^{45} -1720.70i q^{47} +3494.07 q^{49} +(830.056 + 830.056i) q^{51} +(-734.019 - 734.019i) q^{53} +691.775 q^{55} +4922.43i q^{57} +(-1202.73 + 1202.73i) q^{59} +(-580.221 + 580.221i) q^{61} +7424.17i q^{63} -154.657 q^{65} +(-1483.97 - 1483.97i) q^{67} +(880.576 + 880.576i) q^{69} -5571.73 q^{71} -6615.21i q^{73} +(-5738.37 + 5738.37i) q^{75} +(9327.75 - 9327.75i) q^{77} +5391.66i q^{79} +5043.39 q^{81} +(-2554.07 - 2554.07i) q^{83} +(-250.719 - 250.719i) q^{85} +5137.52 q^{87} +10962.7i q^{89} +(-2085.35 + 2085.35i) q^{91} +(-11614.6 + 11614.6i) q^{93} -1486.83i q^{95} +4713.20 q^{97} +(11747.2 + 11747.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	\( 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 94 q^{11} + 2 q^{13} - 4 q^{17} - 706 q^{19} + 164 q^{21} - 1148 q^{23} - 1664 q^{27} - 862 q^{29} - 4 q^{33} + 1340 q^{35} + 1826 q^{37} - 2684 q^{39} + 1694 q^{43} - 1410 q^{45} + 682 q^{49} - 3012 q^{51} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} + 3778 q^{61} - 2020 q^{65} + 7998 q^{67} - 9628 q^{69} - 19964 q^{71} + 17570 q^{75} + 9508 q^{77} + 1454 q^{81} - 17282 q^{83} - 9948 q^{85} + 49284 q^{87} - 28036 q^{91} - 8896 q^{93} - 4 q^{97} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 94 * q^11 + 2 * q^13 - 4 * q^17 - 706 * q^19 + 164 * q^21 - 1148 * q^23 - 1664 * q^27 - 862 * q^29 - 4 * q^33 + 1340 * q^35 + 1826 * q^37 - 2684 * q^39 + 1694 * q^43 - 1410 * q^45 + 682 * q^49 - 3012 * q^51 + 482 * q^53 + 11780 * q^55 - 2786 * q^59 + 3778 * q^61 - 2020 * q^65 + 7998 * q^67 - 9628 * q^69 - 19964 * q^71 + 17570 * q^75 + 9508 * q^77 + 1454 * q^81 - 17282 * q^83 - 9948 * q^85 + 49284 * q^87 - 28036 * q^91 - 8896 * q^93 - 4 * q^97 + 49214 * q^99

Introduction

L-functions

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