LMFDB - Embedded newform 1148.2.k.b.337.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.14
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62776 + 1.62776i) q^{3} +3.63967i q^{5} +(0.707107 + 0.707107i) q^{7} +2.29923i q^{9} +O(q^{10})$	\(q+(1.62776 + 1.62776i) q^{3} +3.63967i q^{5} +(0.707107 + 0.707107i) q^{7} +2.29923i q^{9} +(1.60909 + 1.60909i) q^{11} +(2.83000 + 2.83000i) q^{13} +(-5.92453 + 5.92453i) q^{15} +(2.68616 - 2.68616i) q^{17} +(4.94910 - 4.94910i) q^{19} +2.30201i q^{21} -4.18481 q^{23} -8.24722 q^{25} +(1.14069 - 1.14069i) q^{27} +(-1.01640 - 1.01640i) q^{29} -6.11889 q^{31} +5.23843i q^{33} +(-2.57364 + 2.57364i) q^{35} -1.89269 q^{37} +9.21314i q^{39} +(5.19627 + 3.74150i) q^{41} -6.11098i q^{43} -8.36844 q^{45} +(-1.11039 + 1.11039i) q^{47} +1.00000i q^{49} +8.74486 q^{51} +(-6.21475 - 6.21475i) q^{53} +(-5.85655 + 5.85655i) q^{55} +16.1119 q^{57} -2.32994 q^{59} -10.9365i q^{61} +(-1.62580 + 1.62580i) q^{63} +(-10.3003 + 10.3003i) q^{65} +(-3.50751 + 3.50751i) q^{67} +(-6.81188 - 6.81188i) q^{69} +(1.61276 + 1.61276i) q^{71} -3.53090i q^{73} +(-13.4245 - 13.4245i) q^{75} +2.27559i q^{77} +(-7.22498 - 7.22498i) q^{79} +10.6112 q^{81} +0.636038 q^{83} +(9.77673 + 9.77673i) q^{85} -3.30891i q^{87} +(-2.14544 - 2.14544i) q^{89} +4.00222i q^{91} +(-9.96011 - 9.96011i) q^{93} +(18.0131 + 18.0131i) q^{95} +(-11.3830 + 11.3830i) q^{97} +(-3.69966 + 3.69966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.62776	+	1.62776i	0.939790	+	0.939790i	0.998288	−	0.0584977i	$-0.0186310\pi$
$3$	1.62776	+	1.62776i	0.939790	+	0.939790i	−0.0584977	+	0.998288i	$0.518631\pi$
$4$		0			0
$5$			3.63967i			1.62771i	0.581067	+	0.813856i	$0.302635\pi$
$5$			3.63967i			1.62771i	−0.581067	+	0.813856i	$0.697365\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$			2.29923i			0.766410i
$10$		0			0
$11$	1.60909	+	1.60909i	0.485158	+	0.485158i	0.906774	−	0.421616i	$-0.138537\pi$
$11$	1.60909	+	1.60909i	0.485158	+	0.485158i	−0.421616	+	0.906774i	$0.638537\pi$
$12$		0			0
$13$	2.83000	+	2.83000i	0.784900	+	0.784900i	0.980653	−	0.195753i	$-0.0627151\pi$
$13$	2.83000	+	2.83000i	0.784900	+	0.784900i	−0.195753	+	0.980653i	$0.562715\pi$
$14$		0			0
$15$	−5.92453	+	5.92453i	−1.52971	+	1.52971i
$16$		0			0
$17$	2.68616	−	2.68616i	0.651489	−	0.651489i	−0.301863	−	0.953351i	$-0.597608\pi$
$17$	2.68616	−	2.68616i	0.651489	−	0.651489i	0.953351	+	0.301863i	$0.0976084\pi$
$18$		0			0
$19$	4.94910	−	4.94910i	1.13540	−	1.13540i	0.146138	−	0.989264i	$-0.453316\pi$
$19$	4.94910	−	4.94910i	1.13540	−	1.13540i	0.989264	−	0.146138i	$-0.0466844\pi$
$20$		0			0
$21$			2.30201i			0.502339i
$22$		0			0
$23$	−4.18481			−0.872593			−0.436297	−	0.899803i	$-0.643710\pi$
$23$	−4.18481			−0.872593			−0.436297	+	0.899803i	$0.643710\pi$
$24$		0			0
$25$	−8.24722			−1.64944
$26$		0			0
$27$	1.14069	−	1.14069i	0.219526	−	0.219526i
$28$		0			0
$29$	−1.01640	−	1.01640i	−0.188740	−	0.188740i	0.606411	−	0.795151i	$-0.292609\pi$
$29$	−1.01640	−	1.01640i	−0.188740	−	0.188740i	−0.795151	+	0.606411i	$0.792609\pi$
$30$		0			0
$31$	−6.11889			−1.09899			−0.549493	−	0.835499i	$-0.685179\pi$
$31$	−6.11889			−1.09899			−0.549493	+	0.835499i	$0.685179\pi$
$32$		0			0
$33$			5.23843i			0.911893i
$34$		0			0
$35$	−2.57364	+	2.57364i	−0.435024	+	0.435024i
$36$		0			0
$37$	−1.89269			−0.311157			−0.155578	−	0.987824i	$-0.549724\pi$
$37$	−1.89269			−0.311157			−0.155578	+	0.987824i	$0.549724\pi$
$38$		0			0
$39$			9.21314i			1.47528i
$40$		0			0
$41$	5.19627	+	3.74150i	0.811521	+	0.584323i
$41$	5.19627	+	3.74150i	0.811521	+	0.584323i
$42$		0			0
$43$		−	6.11098i		−	0.931916i	−0.884807	−	0.465958i	$-0.845710\pi$
$43$		−	6.11098i		−	0.931916i	0.884807	−	0.465958i	$-0.154290\pi$
$44$		0			0
$45$	−8.36844			−1.24749
$46$		0			0
$47$	−1.11039	+	1.11039i	−0.161967	+	0.161967i	−0.783438	−	0.621470i	$-0.786536\pi$
$47$	−1.11039	+	1.11039i	−0.161967	+	0.161967i	0.621470	+	0.783438i	$0.286536\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	8.74486			1.22452
$52$		0			0
$53$	−6.21475	−	6.21475i	−0.853661	−	0.853661i	0.136921	−	0.990582i	$-0.456279\pi$
$53$	−6.21475	−	6.21475i	−0.853661	−	0.853661i	−0.990582	+	0.136921i	$0.956279\pi$
$54$		0			0
$55$	−5.85655	+	5.85655i	−0.789697	+	0.789697i
$56$		0			0
$57$	16.1119			2.13408
$58$		0			0
$59$	−2.32994			−0.303332			−0.151666	−	0.988432i	$-0.548464\pi$
$59$	−2.32994			−0.303332			−0.151666	+	0.988432i	$0.548464\pi$
$60$		0			0
$61$		−	10.9365i		−	1.40027i	−0.714009	−	0.700136i	$-0.753123\pi$
$61$		−	10.9365i		−	1.40027i	0.714009	−	0.700136i	$-0.246877\pi$
$62$		0			0
$63$	−1.62580	+	1.62580i	−0.204832	+	0.204832i
$64$		0			0
$65$	−10.3003	+	10.3003i	−1.27759	+	1.27759i
$66$		0			0
$67$	−3.50751	+	3.50751i	−0.428511	+	0.428511i	−0.888121	−	0.459610i	$-0.847989\pi$
$67$	−3.50751	+	3.50751i	−0.428511	+	0.428511i	0.459610	+	0.888121i	$0.347989\pi$
$68$		0			0
$69$	−6.81188	−	6.81188i	−0.820054	−	0.820054i
$70$		0			0
$71$	1.61276	+	1.61276i	0.191399	+	0.191399i	0.796301	−	0.604901i	$-0.206787\pi$
$71$	1.61276	+	1.61276i	0.191399	+	0.191399i	−0.604901	+	0.796301i	$0.706787\pi$
$72$		0			0
$73$		−	3.53090i		−	0.413260i	−0.978419	−	0.206630i	$-0.933750\pi$
$73$		−	3.53090i		−	0.413260i	0.978419	−	0.206630i	$-0.0662497\pi$
$74$		0			0
$75$	−13.4245	−	13.4245i	−1.55013	−	1.55013i
$76$		0			0
$77$			2.27559i			0.259328i
$78$		0			0
$79$	−7.22498	−	7.22498i	−0.812874	−	0.812874i	0.172190	−	0.985064i	$-0.444916\pi$
$79$	−7.22498	−	7.22498i	−0.812874	−	0.812874i	−0.985064	+	0.172190i	$0.944916\pi$
$80$		0			0
$81$	10.6112			1.17903
$82$		0			0
$83$	0.636038			0.0698142			0.0349071	−	0.999391i	$-0.488886\pi$
$83$	0.636038			0.0698142			0.0349071	+	0.999391i	$0.488886\pi$
$84$		0			0
$85$	9.77673	+	9.77673i	1.06044	+	1.06044i
$86$		0			0
$87$		−	3.30891i		−	0.354752i
$88$		0			0
$89$	−2.14544	−	2.14544i	−0.227417	−	0.227417i	0.584196	−	0.811613i	$-0.301410\pi$
$89$	−2.14544	−	2.14544i	−0.227417	−	0.227417i	−0.811613	+	0.584196i	$0.801410\pi$
$90$		0			0
$91$			4.00222i			0.419547i
$92$		0			0
$93$	−9.96011	−	9.96011i	−1.03282	−	1.03282i
$94$		0			0
$95$	18.0131	+	18.0131i	1.84811	+	1.84811i
$96$		0			0
$97$	−11.3830	+	11.3830i	−1.15577	+	1.15577i	−0.170397	+	0.985375i	$0.554505\pi$
$97$	−11.3830	+	11.3830i	−1.15577	+	1.15577i	−0.985375	+	0.170397i	$0.945495\pi$
$98$		0			0
$99$	−3.69966	+	3.69966i	−0.371830	+	0.371830i
$100$		0			0
$101$	−2.60851	+	2.60851i	−0.259556	+	0.259556i	−0.824873	−	0.565317i	$-0.808754\pi$
$101$	−2.60851	+	2.60851i	−0.259556	+	0.259556i	0.565317	+	0.824873i	$0.308754\pi$
$102$		0			0
$103$		−	13.7456i		−	1.35439i	−0.735803	−	0.677196i	$-0.763195\pi$
$103$		−	13.7456i		−	1.35439i	0.735803	−	0.677196i	$-0.236805\pi$
$104$		0			0
$105$	−8.37855			−0.817662
$106$		0			0
$107$	9.85969			0.953172			0.476586	−	0.879128i	$-0.341874\pi$
$107$	9.85969			0.953172			0.476586	+	0.879128i	$0.341874\pi$
$108$		0			0
$109$	2.42649	−	2.42649i	0.232415	−	0.232415i	−0.581285	−	0.813700i	$-0.697450\pi$
$109$	2.42649	−	2.42649i	0.232415	−	0.232415i	0.813700	+	0.581285i	$0.197450\pi$
$110$		0			0
$111$	−3.08085	−	3.08085i	−0.292422	−	0.292422i
$112$		0			0
$113$	16.3563			1.53867			0.769334	−	0.638846i	$-0.220588\pi$
$113$	16.3563			1.53867			0.769334	+	0.638846i	$0.220588\pi$
$114$		0			0
$115$		−	15.2313i		−	1.42033i
$116$		0			0
$117$	−6.50681	+	6.50681i	−0.601555	+	0.601555i
$118$		0			0
$119$	3.79880			0.348235
$120$		0			0
$121$		−	5.82168i		−	0.529243i
$122$		0			0
$123$	2.36803	+	14.5486i	0.213518	+	1.31180i
$124$		0			0
$125$		−	11.8188i		−	1.05711i
$126$		0			0
$127$	21.0335			1.86642			0.933212	−	0.359326i	$-0.116993\pi$
$127$	21.0335			1.86642			0.933212	+	0.359326i	$0.116993\pi$
$128$		0			0
$129$	9.94723	−	9.94723i	0.875805	−	0.875805i
$130$		0			0
$131$		−	2.42453i		−	0.211832i	−0.994375	−	0.105916i	$-0.966223\pi$
$131$		−	2.42453i		−	0.211832i	0.994375	−	0.105916i	$-0.0337774\pi$
$132$		0			0
$133$	6.99909			0.606898
$134$		0			0
$135$	4.15174	+	4.15174i	0.357325	+	0.357325i
$136$		0			0
$137$	−9.63456	+	9.63456i	−0.823136	+	0.823136i	−0.986557	−	0.163420i	$-0.947747\pi$
$137$	−9.63456	+	9.63456i	−0.823136	+	0.823136i	0.163420	+	0.986557i	$0.447747\pi$
$138$		0			0
$139$	6.81013			0.577628			0.288814	−	0.957385i	$-0.406739\pi$
$139$	6.81013			0.577628			0.288814	+	0.957385i	$0.406739\pi$
$140$		0			0
$141$	−3.61491			−0.304431
$142$		0			0
$143$			9.10743i			0.761601i
$144$		0			0
$145$	3.69935	−	3.69935i	0.307215	−	0.307215i
$146$		0			0
$147$	−1.62776	+	1.62776i	−0.134256	+	0.134256i
$148$		0			0
$149$	−16.7060	+	16.7060i	−1.36861	+	1.36861i	−0.506183	+	0.862426i	$0.668944\pi$
$149$	−16.7060	+	16.7060i	−1.36861	+	1.36861i	−0.862426	+	0.506183i	$0.831056\pi$
$150$		0			0
$151$	11.6674	+	11.6674i	0.949483	+	0.949483i	0.998784	−	0.0493013i	$-0.0156995\pi$
$151$	11.6674	+	11.6674i	0.949483	+	0.949483i	−0.0493013	+	0.998784i	$0.515699\pi$
$152$		0			0
$153$	6.17609	+	6.17609i	0.499307	+	0.499307i
$154$		0			0
$155$		−	22.2708i		−	1.78883i
$156$		0			0
$157$	10.7274	+	10.7274i	0.856137	+	0.856137i	0.990880	−	0.134744i	$-0.0430211\pi$
$157$	10.7274	+	10.7274i	0.856137	+	0.856137i	−0.134744	+	0.990880i	$0.543021\pi$
$158$		0			0
$159$		−	20.2323i		−	1.60452i
$160$		0			0
$161$	−2.95911	−	2.95911i	−0.233210	−	0.233210i
$162$		0			0
$163$	−7.02604			−0.550322			−0.275161	−	0.961398i	$-0.588731\pi$
$163$	−7.02604			−0.550322			−0.275161	+	0.961398i	$0.588731\pi$
$164$		0			0
$165$	−19.0662			−1.48430
$166$		0			0
$167$	4.17785	+	4.17785i	0.323292	+	0.323292i	0.850028	−	0.526737i	$-0.176585\pi$
$167$	4.17785	+	4.17785i	0.323292	+	0.323292i	−0.526737	+	0.850028i	$0.676585\pi$
$168$		0			0
$169$			3.01778i			0.232137i
$170$		0			0
$171$	11.3791	+	11.3791i	0.870183	+	0.870183i
$172$		0			0
$173$			11.6029i			0.882151i	0.897470	+	0.441075i	$0.145403\pi$
$173$			11.6029i			0.882151i	−0.897470	+	0.441075i	$0.854597\pi$
$174$		0			0
$175$	−5.83166	−	5.83166i	−0.440832	−	0.440832i
$176$		0			0
$177$	−3.79258	−	3.79258i	−0.285068	−	0.285068i
$178$		0			0
$179$	5.87965	−	5.87965i	0.439465	−	0.439465i	−0.452367	−	0.891832i	$-0.649420\pi$
$179$	5.87965	−	5.87965i	0.439465	−	0.439465i	0.891832	+	0.452367i	$0.149420\pi$
$180$		0			0
$181$	−16.7368	+	16.7368i	−1.24404	+	1.24404i	−0.285723	+	0.958312i	$0.592234\pi$
$181$	−16.7368	+	16.7368i	−1.24404	+	1.24404i	−0.958312	+	0.285723i	$0.907766\pi$
$182$		0			0
$183$	17.8020	−	17.8020i	1.31596	−	1.31596i
$184$		0			0
$185$		−	6.88878i		−	0.506473i
$186$		0			0
$187$	8.64452			0.632150
$188$		0			0
$189$	1.61318			0.117341
$190$		0			0
$191$	−12.0435	+	12.0435i	−0.871436	+	0.871436i	−0.992629	−	0.121193i	$-0.961328\pi$
$191$	−12.0435	+	12.0435i	−0.871436	+	0.871436i	0.121193	+	0.992629i	$0.461328\pi$
$192$		0			0
$193$	−17.3747	−	17.3747i	−1.25066	−	1.25066i	−0.955424	−	0.295236i	$-0.904602\pi$
$193$	−17.3747	−	17.3747i	−1.25066	−	1.25066i	−0.295236	−	0.955424i	$-0.595398\pi$
$194$		0			0
$195$	−33.5328			−2.40133
$196$		0			0
$197$			8.37995i			0.597047i	0.954402	+	0.298523i	$0.0964941\pi$
$197$			8.37995i			0.597047i	−0.954402	+	0.298523i	$0.903506\pi$
$198$		0			0
$199$	13.2564	−	13.2564i	0.939721	−	0.939721i	−0.0585626	−	0.998284i	$-0.518652\pi$
$199$	13.2564	−	13.2564i	0.939721	−	0.939721i	0.998284	+	0.0585626i	$0.0186517\pi$
$200$		0			0
$201$	−11.4188			−0.805421
$202$		0			0
$203$		−	1.43740i		−	0.100886i
$204$		0			0
$205$	−13.6178	+	18.9127i	−0.951110	+	1.32092i
$206$		0			0
$207$		−	9.62184i		−	0.668764i
$208$		0			0
$209$	15.9271			1.10170
$210$		0			0
$211$	12.1193	−	12.1193i	0.834330	−	0.834330i	−0.153776	−	0.988106i	$-0.549143\pi$
$211$	12.1193	−	12.1193i	0.834330	−	0.834330i	0.988106	+	0.153776i	$0.0491434\pi$
$212$		0			0
$213$			5.25038i			0.359750i
$214$		0			0
$215$	22.2420			1.51689
$216$		0			0
$217$	−4.32671	−	4.32671i	−0.293716	−	0.293716i
$218$		0			0
$219$	5.74747	−	5.74747i	0.388378	−	0.388378i
$220$		0			0
$221$	15.2036			1.02271
$222$		0			0
$223$	−14.5490			−0.974274			−0.487137	−	0.873326i	$-0.661959\pi$
$223$	−14.5490			−0.974274			−0.487137	+	0.873326i	$0.661959\pi$
$224$		0			0
$225$		−	18.9622i		−	1.26415i
$226$		0			0
$227$	7.25739	−	7.25739i	0.481690	−	0.481690i	−0.423981	−	0.905671i	$-0.639368\pi$
$227$	7.25739	−	7.25739i	0.481690	−	0.481690i	0.905671	+	0.423981i	$0.139368\pi$
$228$		0			0
$229$	6.97691	−	6.97691i	0.461047	−	0.461047i	−0.437952	−	0.898999i	$-0.644296\pi$
$229$	6.97691	−	6.97691i	0.461047	−	0.461047i	0.898999	+	0.437952i	$0.144296\pi$
$230$		0			0
$231$	−3.70413	+	3.70413i	−0.243714	+	0.243714i
$232$		0			0
$233$	21.2203	+	21.2203i	1.39018	+	1.39018i	0.824887	+	0.565298i	$0.191239\pi$
$233$	21.2203	+	21.2203i	1.39018	+	1.39018i	0.565298	+	0.824887i	$0.308761\pi$
$234$		0			0
$235$	−4.04146	−	4.04146i	−0.263636	−	0.263636i
$236$		0			0
$237$		−	23.5211i		−	1.52786i
$238$		0			0
$239$	−5.63864	−	5.63864i	−0.364733	−	0.364733i	0.500819	−	0.865552i	$-0.333032\pi$
$239$	−5.63864	−	5.63864i	−0.364733	−	0.364733i	−0.865552	+	0.500819i	$0.833032\pi$
$240$		0			0
$241$		−	6.54156i		−	0.421379i	−0.977553	−	0.210690i	$-0.932429\pi$
$241$		−	6.54156i		−	0.421379i	0.977553	−	0.210690i	$-0.0675709\pi$
$242$		0			0
$243$	13.8505	+	13.8505i	0.888511	+	0.888511i
$244$		0			0
$245$	−3.63967			−0.232530
$246$		0			0
$247$	28.0119			1.78236
$248$		0			0
$249$	1.03532	+	1.03532i	0.0656107	+	0.0656107i
$250$		0			0
$251$		−	11.2434i		−	0.709675i	−0.934928	−	0.354837i	$-0.884536\pi$
$251$		−	11.2434i		−	0.709675i	0.934928	−	0.354837i	$-0.115464\pi$
$252$		0			0
$253$	−6.73372	−	6.73372i	−0.423346	−	0.423346i
$254$		0			0
$255$			31.8284i			1.99317i
$256$		0			0
$257$	−7.84302	−	7.84302i	−0.489234	−	0.489234i	0.418830	−	0.908064i	$-0.362440\pi$
$257$	−7.84302	−	7.84302i	−0.489234	−	0.489234i	−0.908064	+	0.418830i	$0.862440\pi$
$258$		0			0
$259$	−1.33833	−	1.33833i	−0.0831601	−	0.0831601i
$260$		0			0
$261$	2.33693	−	2.33693i	0.144652	−	0.144652i
$262$		0			0
$263$	16.0480	−	16.0480i	0.989564	−	0.989564i	−0.0103825	−	0.999946i	$-0.503305\pi$
$263$	16.0480	−	16.0480i	0.989564	−	0.989564i	0.999946	+	0.0103825i	$0.00330491\pi$
$264$		0			0
$265$	22.6197	−	22.6197i	1.38951	−	1.38951i
$266$		0			0
$267$		−	6.98455i		−	0.427448i
$268$		0			0
$269$	10.8937			0.664201			0.332100	−	0.943244i	$-0.392243\pi$
$269$	10.8937			0.664201			0.332100	+	0.943244i	$0.392243\pi$
$270$		0			0
$271$	−10.1897			−0.618982			−0.309491	−	0.950902i	$-0.600159\pi$
$271$	−10.1897			−0.618982			−0.309491	+	0.950902i	$0.600159\pi$
$272$		0			0
$273$	−6.51467	+	6.51467i	−0.394286	+	0.394286i
$274$		0			0
$275$	−13.2705	−	13.2705i	−0.800241	−	0.800241i
$276$		0			0
$277$	−16.1367			−0.969562			−0.484781	−	0.874636i	$-0.661101\pi$
$277$	−16.1367			−0.969562			−0.484781	+	0.874636i	$0.661101\pi$
$278$		0			0
$279$		−	14.0687i		−	0.842273i
$280$		0			0
$281$	−17.6513	+	17.6513i	−1.05299	+	1.05299i	−0.0544708	+	0.998515i	$0.517347\pi$
$281$	−17.6513	+	17.6513i	−1.05299	+	1.05299i	−0.998515	+	0.0544708i	$0.982653\pi$
$282$		0			0
$283$	−24.0875			−1.43185			−0.715925	−	0.698177i	$-0.753995\pi$
$283$	−24.0875			−1.43185			−0.715925	+	0.698177i	$0.753995\pi$
$284$		0			0
$285$			58.6422i			3.47366i
$286$		0			0
$287$	1.02868	+	6.31995i	0.0607211	+	0.373055i
$288$		0			0
$289$			2.56913i			0.151125i
$290$		0			0
$291$	−37.0578			−2.17237
$292$		0			0
$293$	8.67027	−	8.67027i	0.506523	−	0.506523i	−0.406935	−	0.913457i	$-0.633402\pi$
$293$	8.67027	−	8.67027i	0.506523	−	0.506523i	0.913457	+	0.406935i	$0.133402\pi$
$294$		0			0
$295$		−	8.48020i		−	0.493737i
$296$		0			0
$297$	3.67094			0.213009
$298$		0			0
$299$	−11.8430	−	11.8430i	−0.684899	−	0.684899i
$300$		0			0
$301$	4.32112	−	4.32112i	0.249065	−	0.249065i
$302$		0			0
$303$	−8.49206			−0.487856
$304$		0			0
$305$	39.8052			2.27924
$306$		0			0
$307$			32.9525i			1.88070i	0.340211	+	0.940349i	$0.389501\pi$
$307$			32.9525i			1.88070i	−0.340211	+	0.940349i	$0.610499\pi$
$308$		0			0
$309$	22.3745	−	22.3745i	1.27284	−	1.27284i
$310$		0			0
$311$	−1.89889	+	1.89889i	−0.107676	+	0.107676i	−0.758892	−	0.651216i	$-0.774259\pi$
$311$	−1.89889	+	1.89889i	−0.107676	+	0.107676i	0.651216	+	0.758892i	$0.274259\pi$
$312$		0			0
$313$	−10.6576	+	10.6576i	−0.602403	+	0.602403i	−0.940950	−	0.338547i	$-0.890065\pi$
$313$	−10.6576	+	10.6576i	−0.602403	+	0.602403i	0.338547	+	0.940950i	$0.390065\pi$
$314$		0			0
$315$	−5.91738	−	5.91738i	−0.333407	−	0.333407i
$316$		0			0
$317$	3.86773	+	3.86773i	0.217233	+	0.217233i	0.807332	−	0.590098i	$-0.200911\pi$
$317$	3.86773	+	3.86773i	0.217233	+	0.217233i	−0.590098	+	0.807332i	$0.700911\pi$
$318$		0			0
$319$		−	3.27094i		−	0.183138i
$320$		0			0
$321$	16.0492	+	16.0492i	0.895782	+	0.895782i
$322$		0			0
$323$		−	26.5881i		−	1.47940i
$324$		0			0
$325$	−23.3396	−	23.3396i	−1.29465	−	1.29465i
$326$		0			0
$327$	7.89950			0.436843
$328$		0			0
$329$	−1.57033			−0.0865752
$330$		0			0
$331$	−17.7620	−	17.7620i	−0.976289	−	0.976289i	0.0234362	−	0.999725i	$-0.492539\pi$
$331$	−17.7620	−	17.7620i	−0.976289	−	0.976289i	−0.999725	+	0.0234362i	$0.992539\pi$
$332$		0			0
$333$		−	4.35173i		−	0.238473i
$334$		0			0
$335$	−12.7662	−	12.7662i	−0.697492	−	0.697492i
$336$		0			0
$337$			14.8935i			0.811302i	0.914028	+	0.405651i	$0.132955\pi$
$337$			14.8935i			0.811302i	−0.914028	+	0.405651i	$0.867045\pi$
$338$		0			0
$339$	26.6242	+	26.6242i	1.44603	+	1.44603i
$340$		0			0
$341$	−9.84583	−	9.84583i	−0.533181	−	0.533181i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	24.7930	−	24.7930i	1.33481	−	1.33481i
$346$		0			0
$347$	16.3099	−	16.3099i	0.875563	−	0.875563i	−0.117508	−	0.993072i	$-0.537491\pi$
$347$	16.3099	−	16.3099i	0.875563	−	0.875563i	0.993072	+	0.117508i	$0.0374907\pi$
$348$		0			0
$349$		−	30.6680i		−	1.64162i	−0.571203	−	0.820809i	$-0.693523\pi$
$349$		−	30.6680i		−	1.64162i	0.571203	−	0.820809i	$-0.306477\pi$
$350$		0			0
$351$	6.45630			0.344612
$352$		0			0
$353$	−1.68699			−0.0897895			−0.0448948	−	0.998992i	$-0.514295\pi$
$353$	−1.68699			−0.0897895			−0.0448948	+	0.998992i	$0.514295\pi$
$354$		0			0
$355$	−5.86992	+	5.86992i	−0.311543	+	0.311543i
$356$		0			0
$357$	6.18355	+	6.18355i	0.327268	+	0.327268i
$358$		0			0
$359$	6.47232			0.341596			0.170798	−	0.985306i	$-0.445365\pi$
$359$	6.47232			0.341596			0.170798	+	0.985306i	$0.445365\pi$
$360$		0			0
$361$		−	29.9873i		−	1.57828i
$362$		0			0
$363$	9.47632	−	9.47632i	0.497378	−	0.497378i
$364$		0			0
$365$	12.8513			0.672669
$366$		0			0
$367$		−	0.243504i		−	0.0127108i	−0.999980	−	0.00635539i	$-0.997977\pi$
$367$		−	0.243504i		−	0.0127108i	0.999980	−	0.00635539i	$-0.00202300\pi$
$368$		0			0
$369$	−8.60256	+	11.9474i	−0.447831	+	0.621958i
$370$		0			0
$371$		−	8.78898i		−	0.456301i
$372$		0			0
$373$	−5.21111			−0.269821			−0.134910	−	0.990858i	$-0.543075\pi$
$373$	−5.21111			−0.269821			−0.134910	+	0.990858i	$0.543075\pi$
$374$		0			0
$375$	19.2382	−	19.2382i	0.993459	−	0.993459i
$376$		0			0
$377$		−	5.75280i		−	0.296284i
$378$		0			0
$379$	24.5983			1.26353			0.631764	−	0.775161i	$-0.282331\pi$
$379$	24.5983			1.26353			0.631764	+	0.775161i	$0.282331\pi$
$380$		0			0
$381$	34.2376	+	34.2376i	1.75405	+	1.75405i
$382$		0			0
$383$	13.9311	−	13.9311i	0.711845	−	0.711845i	−0.255076	−	0.966921i	$-0.582101\pi$
$383$	13.9311	−	13.9311i	0.711845	−	0.711845i	0.966921	+	0.255076i	$0.0821005\pi$
$384$		0			0
$385$	−8.28241			−0.422111
$386$		0			0
$387$	14.0505			0.714230
$388$		0			0
$389$			16.3575i			0.829360i	0.909967	+	0.414680i	$0.136106\pi$
$389$			16.3575i			0.829360i	−0.909967	+	0.414680i	$0.863894\pi$
$390$		0			0
$391$	−11.2411	+	11.2411i	−0.568485	+	0.568485i
$392$		0			0
$393$	3.94655	−	3.94655i	0.199077	−	0.199077i
$394$		0			0
$395$	26.2966	−	26.2966i	1.32312	−	1.32312i
$396$		0			0
$397$	−11.1771	−	11.1771i	−0.560963	−	0.560963i	0.368618	−	0.929581i	$-0.379831\pi$
$397$	−11.1771	−	11.1771i	−0.560963	−	0.560963i	−0.929581	+	0.368618i	$0.879831\pi$
$398$		0			0
$399$	11.3929	+	11.3929i	0.570357	+	0.570357i
$400$		0			0
$401$			13.6373i			0.681013i	0.940242	+	0.340507i	$0.110599\pi$
$401$			13.6373i			0.681013i	−0.940242	+	0.340507i	$0.889401\pi$
$402$		0			0
$403$	−17.3164	−	17.3164i	−0.862594	−	0.862594i
$404$		0			0
$405$			38.6214i			1.91911i
$406$		0			0
$407$	−3.04551	−	3.04551i	−0.150960	−	0.150960i
$408$		0			0
$409$	−8.52231			−0.421401			−0.210701	−	0.977551i	$-0.567575\pi$
$409$	−8.52231			−0.421401			−0.210701	+	0.977551i	$0.567575\pi$
$410$		0			0
$411$	−31.3656			−1.54715
$412$		0			0
$413$	−1.64751	−	1.64751i	−0.0810688	−	0.0810688i
$414$		0			0
$415$			2.31497i			0.113637i
$416$		0			0
$417$	11.0853	+	11.0853i	0.542849	+	0.542849i
$418$		0			0
$419$		−	16.8391i		−	0.822642i	−0.911491	−	0.411321i	$-0.865067\pi$
$419$		−	16.8391i		−	0.822642i	0.911491	−	0.411321i	$-0.134933\pi$
$420$		0			0
$421$	−7.80018	−	7.80018i	−0.380157	−	0.380157i	0.491001	−	0.871159i	$-0.336631\pi$
$421$	−7.80018	−	7.80018i	−0.380157	−	0.380157i	−0.871159	+	0.491001i	$0.836631\pi$
$422$		0			0
$423$	−2.55305	−	2.55305i	−0.124133	−	0.124133i
$424$		0			0
$425$	−22.1533	+	22.1533i	−1.07459	+	1.07459i
$426$		0			0
$427$	7.73326	−	7.73326i	0.374239	−	0.374239i
$428$		0			0
$429$	−14.8247	+	14.8247i	−0.715745	+	0.715745i
$430$		0			0
$431$		−	5.40983i		−	0.260582i	−0.991476	−	0.130291i	$-0.958409\pi$
$431$		−	5.40983i		−	0.260582i	0.991476	−	0.130291i	$-0.0415912\pi$
$432$		0			0
$433$	−15.6205			−0.750671			−0.375336	−	0.926889i	$-0.622473\pi$
$433$	−15.6205			−0.750671			−0.375336	+	0.926889i	$0.622473\pi$
$434$		0			0
$435$	12.0433			0.577434
$436$		0			0
$437$	−20.7111	+	20.7111i	−0.990745	+	0.990745i
$438$		0			0
$439$	−10.4882	−	10.4882i	−0.500575	−	0.500575i	0.411041	−	0.911617i	$-0.365165\pi$
$439$	−10.4882	−	10.4882i	−0.500575	−	0.500575i	−0.911617	+	0.411041i	$0.865165\pi$
$440$		0			0
$441$	−2.29923			−0.109487
$442$		0			0
$443$		−	22.0107i		−	1.04576i	−0.852406	−	0.522880i	$-0.824858\pi$
$443$		−	22.0107i		−	1.04576i	0.852406	−	0.522880i	$-0.175142\pi$
$444$		0			0
$445$	7.80872	−	7.80872i	0.370169	−	0.370169i
$446$		0			0
$447$	−54.3869			−2.57241
$448$		0			0
$449$			27.4642i			1.29611i	0.761591	+	0.648057i	$0.224418\pi$
$449$			27.4642i			1.29611i	−0.761591	+	0.648057i	$0.775582\pi$
$450$		0			0
$451$	2.34086	+	14.3816i	0.110227	+	0.677205i
$452$		0			0
$453$			37.9837i			1.78463i
$454$		0			0
$455$	−14.5668			−0.682901
$456$		0			0
$457$	−15.3741	+	15.3741i	−0.719172	+	0.719172i	−0.968436	−	0.249264i	$-0.919811\pi$
$457$	−15.3741	+	15.3741i	−0.719172	+	0.719172i	0.249264	+	0.968436i	$0.419811\pi$
$458$		0			0
$459$		−	6.12814i		−	0.286037i
$460$		0			0
$461$	−7.51081			−0.349814			−0.174907	−	0.984585i	$-0.555962\pi$
$461$	−7.51081			−0.349814			−0.174907	+	0.984585i	$0.555962\pi$
$462$		0			0
$463$	26.1709	+	26.1709i	1.21627	+	1.21627i	0.968930	+	0.247336i	$0.0795550\pi$
$463$	26.1709	+	26.1709i	1.21627	+	1.21627i	0.247336	+	0.968930i	$0.420445\pi$
$464$		0			0
$465$	36.2515	−	36.2515i	1.68112	−	1.68112i
$466$		0			0
$467$	−25.7958			−1.19369			−0.596844	−	0.802358i	$-0.703579\pi$
$467$	−25.7958			−1.19369			−0.596844	+	0.802358i	$0.703579\pi$
$468$		0			0
$469$	−4.96037			−0.229049
$470$		0			0
$471$			34.9232i			1.60918i
$472$		0			0
$473$	9.83310	−	9.83310i	0.452126	−	0.452126i
$474$		0			0
$475$	−40.8164	+	40.8164i	−1.87278	+	1.87278i
$476$		0			0
$477$	14.2891	−	14.2891i	0.654254	−	0.654254i
$478$		0			0
$479$	−20.7038	−	20.7038i	−0.945981	−	0.945981i	0.0526329	−	0.998614i	$-0.483239\pi$
$479$	−20.7038	−	20.7038i	−0.945981	−	0.945981i	−0.998614	+	0.0526329i	$0.983239\pi$
$480$		0			0
$481$	−5.35631	−	5.35631i	−0.244227	−	0.244227i
$482$		0			0
$483$		−	9.63346i		−	0.438338i
$484$		0			0
$485$	−41.4305	−	41.4305i	−1.88126	−	1.88126i
$486$		0			0
$487$			14.0123i			0.634957i	0.948265	+	0.317479i	$0.102836\pi$
$487$			14.0123i			0.634957i	−0.948265	+	0.317479i	$0.897164\pi$
$488$		0			0
$489$	−11.4367	−	11.4367i	−0.517187	−	0.517187i
$490$		0			0
$491$	0.776362			0.0350367			0.0175184	−	0.999847i	$-0.494423\pi$
$491$	0.776362			0.0350367			0.0175184	+	0.999847i	$0.494423\pi$
$492$		0			0
$493$	−5.46040			−0.245924
$494$		0			0
$495$	−13.4656	−	13.4656i	−0.605232	−	0.605232i
$496$		0			0
$497$			2.28079i			0.102307i
$498$		0			0
$499$	−1.01843	−	1.01843i	−0.0455911	−	0.0455911i	0.683944	−	0.729535i	$-0.260263\pi$
$499$	−1.01843	−	1.01843i	−0.0455911	−	0.0455911i	−0.729535	+	0.683944i	$0.760263\pi$
$500$		0			0
$501$			13.6011i			0.607653i
$502$		0			0
$503$	29.3217	+	29.3217i	1.30739	+	1.30739i	0.923294	+	0.384094i	$0.125486\pi$
$503$	29.3217	+	29.3217i	1.30739	+	1.30739i	0.384094	+	0.923294i	$0.374514\pi$
$504$		0			0
$505$	−9.49411	−	9.49411i	−0.422482	−	0.422482i
$506$		0			0
$507$	−4.91223	+	4.91223i	−0.218160	+	0.218160i
$508$		0			0
$509$	−21.7571	+	21.7571i	−0.964366	+	0.964366i	−0.999387	−	0.0350207i	$-0.988850\pi$
$509$	−21.7571	+	21.7571i	−0.964366	+	0.964366i	0.0350207	+	0.999387i	$0.488850\pi$
$510$		0			0
$511$	2.49672	−	2.49672i	0.110448	−	0.110448i
$512$		0			0
$513$		−	11.2908i		−	0.498500i
$514$		0			0
$515$	50.0294			2.20456
$516$		0			0
$517$	−3.57344			−0.157159
$518$		0			0
$519$	−18.8867	+	18.8867i	−0.829036	+	0.829036i
$520$		0			0
$521$	17.2837	+	17.2837i	0.757211	+	0.757211i	0.975814	−	0.218603i	$-0.0701500\pi$
$521$	17.2837	+	17.2837i	0.757211	+	0.757211i	−0.218603	+	0.975814i	$0.570150\pi$
$522$		0			0
$523$	−16.1813			−0.707558			−0.353779	−	0.935329i	$-0.615103\pi$
$523$	−16.1813			−0.707558			−0.353779	+	0.935329i	$0.615103\pi$
$524$		0			0
$525$		−	18.9851i		−	0.828580i
$526$		0			0
$527$	−16.4363	+	16.4363i	−0.715976	+	0.715976i
$528$		0			0
$529$	−5.48736			−0.238581
$530$		0			0
$531$		−	5.35706i		−	0.232476i
$532$		0			0
$533$	4.11701	+	25.2939i	0.178327	+	1.09560i
$534$		0			0
$535$			35.8861i			1.55149i
$536$		0			0
$537$	19.1414			0.826010
$538$		0			0
$539$	−1.60909	+	1.60909i	−0.0693083	+	0.0693083i
$540$		0			0
$541$			32.8080i			1.41053i	0.708945	+	0.705263i	$0.249171\pi$
$541$			32.8080i			1.41053i	−0.708945	+	0.705263i	$0.750829\pi$
$542$		0			0
$543$	−54.4870			−2.33826
$544$		0			0
$545$	8.83162	+	8.83162i	0.378305	+	0.378305i
$546$		0			0
$547$	12.0579	−	12.0579i	0.515559	−	0.515559i	−0.400666	−	0.916224i	$-0.631221\pi$
$547$	12.0579	−	12.0579i	0.515559	−	0.515559i	0.916224	+	0.400666i	$0.131221\pi$
$548$		0			0
$549$	25.1455			1.07318
$550$		0			0
$551$	−10.0605			−0.428592
$552$		0			0
$553$		−	10.2177i		−	0.434499i
$554$		0			0
$555$	11.2133	−	11.2133i	0.475978	−	0.475978i
$556$		0			0
$557$	21.9362	−	21.9362i	0.929467	−	0.929467i	−0.0682046	−	0.997671i	$-0.521727\pi$
$557$	21.9362	−	21.9362i	0.929467	−	0.929467i	0.997671	+	0.0682046i	$0.0217271\pi$
$558$		0			0
$559$	17.2941	−	17.2941i	0.731461	−	0.731461i
$560$		0			0
$561$	14.0712	+	14.0712i	0.594088	+	0.594088i
$562$		0			0
$563$	23.4245	+	23.4245i	0.987226	+	0.987226i	0.999919	−	0.0126939i	$-0.00404070\pi$
$563$	23.4245	+	23.4245i	0.987226	+	0.987226i	−0.0126939	+	0.999919i	$0.504041\pi$
$564$		0			0
$565$			59.5315i			2.50451i
$566$		0			0
$567$	7.50327	+	7.50327i	0.315108	+	0.315108i
$568$		0			0
$569$		−	28.7285i		−	1.20436i	−0.798359	−	0.602181i	$-0.794298\pi$
$569$		−	28.7285i		−	1.20436i	0.798359	−	0.602181i	$-0.205702\pi$
$570$		0			0
$571$	−1.55817	−	1.55817i	−0.0652073	−	0.0652073i	0.673751	−	0.738958i	$-0.264682\pi$
$571$	−1.55817	−	1.55817i	−0.0652073	−	0.0652073i	−0.738958	+	0.673751i	$0.764682\pi$
$572$		0			0
$573$	−39.2079			−1.63793
$574$		0			0
$575$	34.5131			1.43929
$576$		0			0
$577$	8.67296	+	8.67296i	0.361060	+	0.361060i	0.864203	−	0.503143i	$-0.167823\pi$
$577$	8.67296	+	8.67296i	0.361060	+	0.361060i	−0.503143	+	0.864203i	$0.667823\pi$
$578$		0			0
$579$		−	56.5639i		−	2.35072i
$580$		0			0
$581$	0.449747	+	0.449747i	0.0186586	+	0.0186586i
$582$		0			0
$583$		−	20.0001i		−	0.828321i
$584$		0			0
$585$	−23.6827	−	23.6827i	−0.979158	−	0.979158i
$586$		0			0
$587$	31.3864	+	31.3864i	1.29545	+	1.29545i	0.931363	+	0.364091i	$0.118620\pi$
$587$	31.3864	+	31.3864i	1.29545	+	1.29545i	0.364091	+	0.931363i	$0.381380\pi$
$588$		0			0
$589$	−30.2830	+	30.2830i	−1.24779	+	1.24779i
$590$		0			0
$591$	−13.6406	+	13.6406i	−0.561099	+	0.561099i
$592$		0			0
$593$	8.43599	−	8.43599i	0.346424	−	0.346424i	−0.512351	−	0.858776i	$-0.671225\pi$
$593$	8.43599	−	8.43599i	0.346424	−	0.346424i	0.858776	+	0.512351i	$0.171225\pi$
$594$		0			0
$595$			13.8264i			0.566827i
$596$		0			0
$597$	43.1566			1.76628
$598$		0			0
$599$	−21.7287			−0.887811			−0.443905	−	0.896074i	$-0.646407\pi$
$599$	−21.7287			−0.887811			−0.443905	+	0.896074i	$0.646407\pi$
$600$		0			0
$601$	−2.87854	+	2.87854i	−0.117418	+	0.117418i	−0.763374	−	0.645956i	$-0.776459\pi$
$601$	−2.87854	+	2.87854i	−0.117418	+	0.117418i	0.645956	+	0.763374i	$0.276459\pi$
$602$		0			0
$603$	−8.06458	−	8.06458i	−0.328415	−	0.328415i
$604$		0			0
$605$	21.1890			0.861456
$606$		0			0
$607$			34.7827i			1.41179i	0.708319	+	0.705893i	$0.249454\pi$
$607$			34.7827i			1.41179i	−0.708319	+	0.705893i	$0.750546\pi$
$608$		0			0
$609$	2.33975	−	2.33975i	0.0948115	−	0.0948115i
$610$		0			0
$611$	−6.28482			−0.254256
$612$		0			0
$613$			38.3345i			1.54832i	0.632992	+	0.774158i	$0.281826\pi$
$613$			38.3345i			1.54832i	−0.632992	+	0.774158i	$0.718174\pi$
$614$		0			0
$615$	−52.9520	+	8.61885i	−2.13523	+	0.347546i
$616$		0			0
$617$			2.75803i			0.111034i	0.998458	+	0.0555171i	$0.0176807\pi$
$617$			2.75803i			0.111034i	−0.998458	+	0.0555171i	$0.982319\pi$
$618$		0			0
$619$	−16.4276			−0.660282			−0.330141	−	0.943932i	$-0.607096\pi$
$619$	−16.4276			−0.660282			−0.330141	+	0.943932i	$0.607096\pi$
$620$		0			0
$621$	−4.77357	+	4.77357i	−0.191557	+	0.191557i
$622$		0			0
$623$		−	3.03412i		−	0.121559i
$624$		0			0
$625$	1.78053			0.0712213
$626$		0			0
$627$	25.9255	+	25.9255i	1.03537	+	1.03537i
$628$		0			0
$629$	−5.08407	+	5.08407i	−0.202715	+	0.202715i
$630$		0			0
$631$	−17.8966			−0.712451			−0.356225	−	0.934400i	$-0.615936\pi$
$631$	−17.8966			−0.712451			−0.356225	+	0.934400i	$0.615936\pi$
$632$		0			0
$633$	39.4548			1.56819
$634$		0			0
$635$			76.5552i			3.03800i
$636$		0			0
$637$	−2.83000	+	2.83000i	−0.112129	+	0.112129i
$638$		0			0
$639$	−3.70811	+	3.70811i	−0.146690	+	0.146690i
$640$		0			0
$641$	−25.2395	+	25.2395i	−0.996902	+	0.996902i	−0.999995	−	0.00309336i	$-0.999015\pi$
$641$	−25.2395	+	25.2395i	−0.996902	+	0.996902i	0.00309336	+	0.999995i	$0.499015\pi$
$642$		0			0
$643$	29.6138	+	29.6138i	1.16785	+	1.16785i	0.982712	+	0.185143i	$0.0592749\pi$
$643$	29.6138	+	29.6138i	1.16785	+	1.16785i	0.185143	+	0.982712i	$0.440725\pi$
$644$		0			0
$645$	36.2047	+	36.2047i	1.42556	+	1.42556i
$646$		0			0
$647$		−	12.6871i		−	0.498781i	−0.968403	−	0.249390i	$-0.919770\pi$
$647$		−	12.6871i		−	0.498781i	0.968403	−	0.249390i	$-0.0802302\pi$
$648$		0			0
$649$	−3.74907	−	3.74907i	−0.147164	−	0.147164i
$650$		0			0
$651$		−	14.0857i		−	0.552063i
$652$		0			0
$653$	−28.0097	−	28.0097i	−1.09610	−	1.09610i	−0.994862	−	0.101242i	$-0.967718\pi$
$653$	−28.0097	−	28.0097i	−1.09610	−	1.09610i	−0.101242	−	0.994862i	$-0.532282\pi$
$654$		0			0
$655$	8.82448			0.344801
$656$		0			0
$657$	8.11835			0.316727
$658$		0			0
$659$	−15.5178	−	15.5178i	−0.604489	−	0.604489i	0.337011	−	0.941501i	$-0.390584\pi$
$659$	−15.5178	−	15.5178i	−0.604489	−	0.604489i	−0.941501	+	0.337011i	$0.890584\pi$
$660$		0			0
$661$		−	41.7422i		−	1.62358i	−0.583947	−	0.811792i	$-0.698492\pi$
$661$		−	41.7422i		−	1.62358i	0.583947	−	0.811792i	$-0.301508\pi$
$662$		0			0
$663$	24.7479	+	24.7479i	0.961130	+	0.961130i
$664$		0			0
$665$			25.4744i			0.987855i
$666$		0			0
$667$	4.25343	+	4.25343i	0.164693	+	0.164693i
$668$		0			0
$669$	−23.6824	−	23.6824i	−0.915613	−	0.915613i
$670$		0			0
$671$	17.5977	−	17.5977i	0.679353	−	0.679353i
$672$		0			0
$673$	25.9004	−	25.9004i	0.998388	−	0.998388i	−0.00161040	−	0.999999i	$-0.500513\pi$
$673$	25.9004	−	25.9004i	0.998388	−	0.998388i	0.999999	+	0.00161040i	$0.000512606\pi$
$674$		0			0
$675$	−9.40751	+	9.40751i	−0.362095	+	0.362095i
$676$		0			0
$677$		−	19.8641i		−	0.763438i	−0.924278	−	0.381719i	$-0.875332\pi$
$677$		−	19.8641i		−	0.763438i	0.924278	−	0.381719i	$-0.124668\pi$
$678$		0			0
$679$	−16.0980			−0.617786
$680$		0			0
$681$	23.6266			0.905374
$682$		0			0
$683$	−21.5579	+	21.5579i	−0.824890	+	0.824890i	−0.986805	−	0.161915i	$-0.948233\pi$
$683$	−21.5579	+	21.5579i	−0.824890	+	0.824890i	0.161915	+	0.986805i	$0.448233\pi$
$684$		0			0
$685$	−35.0667	−	35.0667i	−1.33983	−	1.33983i
$686$		0			0
$687$	22.7135			0.866575
$688$		0			0
$689$		−	35.1755i		−	1.34008i
$690$		0			0
$691$	−10.1740	+	10.1740i	−0.387036	+	0.387036i	−0.873629	−	0.486593i	$-0.838240\pi$
$691$	−10.1740	+	10.1740i	−0.387036	+	0.387036i	0.486593	+	0.873629i	$0.338240\pi$
$692$		0			0
$693$	−5.23211			−0.198751
$694$		0			0
$695$			24.7867i			0.940212i
$696$		0			0
$697$	24.0082	−	3.90775i	0.909377	−	0.148017i
$698$		0			0
$699$			69.0831i			2.61296i
$700$		0			0
$701$	8.57891			0.324021			0.162010	−	0.986789i	$-0.448202\pi$
$701$	8.57891			0.324021			0.162010	+	0.986789i	$0.448202\pi$
$702$		0			0
$703$	−9.36713	+	9.36713i	−0.353288	+	0.353288i
$704$		0			0
$705$		−	13.1571i		−	0.495525i
$706$		0			0
$707$	−3.68899			−0.138739
$708$		0			0
$709$	12.4042	+	12.4042i	0.465848	+	0.465848i	0.900566	−	0.434718i	$-0.143152\pi$
$709$	12.4042	+	12.4042i	0.465848	+	0.465848i	−0.434718	+	0.900566i	$0.643152\pi$
$710$		0			0
$711$	16.6119	−	16.6119i	0.622994	−	0.622994i
$712$		0			0
$713$	25.6064			0.958967
$714$		0			0
$715$	−33.1481			−1.23967
$716$		0			0
$717$		−	18.3567i		−	0.685545i
$718$		0			0
$719$	−34.7937	+	34.7937i	−1.29759	+	1.29759i	−0.367606	+	0.929982i	$0.619822\pi$
$719$	−34.7937	+	34.7937i	−1.29759	+	1.29759i	−0.929982	+	0.367606i	$0.880178\pi$
$720$		0			0
$721$	9.71958	−	9.71958i	0.361976	−	0.361976i
$722$		0			0
$723$	10.6481	−	10.6481i	0.396008	−	0.396008i
$724$		0			0
$725$	8.38245	+	8.38245i	0.311316	+	0.311316i
$726$		0			0
$727$	−26.7208	−	26.7208i	−0.991021	−	0.991021i	0.00893861	−	0.999960i	$-0.497155\pi$
$727$	−26.7208	−	26.7208i	−0.991021	−	0.991021i	−0.999960	+	0.00893861i	$0.997155\pi$
$728$		0			0
$729$			13.2570i			0.491001i
$730$		0			0
$731$	−16.4151	−	16.4151i	−0.607133	−	0.607133i
$732$		0			0
$733$		−	14.6974i		−	0.542862i	−0.962458	−	0.271431i	$-0.912503\pi$
$733$		−	14.6974i		−	0.542862i	0.962458	−	0.271431i	$-0.0874969\pi$
$734$		0			0
$735$	−5.92453	−	5.92453i	−0.218529	−	0.218529i
$736$		0			0
$737$	−11.2878			−0.415791
$738$		0			0
$739$	9.00515			0.331260			0.165630	−	0.986188i	$-0.447034\pi$
$739$	9.00515			0.331260			0.165630	+	0.986188i	$0.447034\pi$
$740$		0			0
$741$	45.5968	+	45.5968i	1.67504	+	1.67504i
$742$		0			0
$743$			27.0326i			0.991731i	0.868399	+	0.495865i	$0.165149\pi$
$743$			27.0326i			0.991731i	−0.868399	+	0.495865i	$0.834851\pi$
$744$		0			0
$745$	−60.8044	−	60.8044i	−2.22770	−	2.22770i
$746$		0			0
$747$			1.46240i			0.0535063i
$748$		0			0
$749$	6.97186	+	6.97186i	0.254746	+	0.254746i
$750$		0			0
$751$	2.38522	+	2.38522i	0.0870379	+	0.0870379i	0.749285	−	0.662247i	$-0.230397\pi$
$751$	2.38522	+	2.38522i	0.0870379	+	0.0870379i	−0.662247	+	0.749285i	$0.730397\pi$
$752$		0			0
$753$	18.3015	−	18.3015i	0.666945	−	0.666945i
$754$		0			0
$755$	−42.4657	+	42.4657i	−1.54548	+	1.54548i
$756$		0			0
$757$	−7.65379	+	7.65379i	−0.278182	+	0.278182i	−0.832383	−	0.554201i	$-0.813024\pi$
$757$	−7.65379	+	7.65379i	−0.278182	+	0.278182i	0.554201	+	0.832383i	$0.313024\pi$
$758$		0			0
$759$		−	21.9218i		−	0.795712i
$760$		0			0
$761$	2.85100			0.103349			0.0516743	−	0.998664i	$-0.483544\pi$
$761$	2.85100			0.103349			0.0516743	+	0.998664i	$0.483544\pi$
$762$		0			0
$763$	3.43157			0.124231
$764$		0			0
$765$	−22.4789	+	22.4789i	−0.812728	+	0.812728i
$766$		0			0
$767$	−6.59371	−	6.59371i	−0.238085	−	0.238085i
$768$		0			0
$769$	−26.4780			−0.954820			−0.477410	−	0.878681i	$-0.658424\pi$
$769$	−26.4780			−0.954820			−0.477410	+	0.878681i	$0.658424\pi$
$770$		0			0
$771$		−	25.5332i		−	0.919554i
$772$		0			0
$773$	−19.9132	+	19.9132i	−0.716229	+	0.716229i	−0.967831	−	0.251602i	$-0.919043\pi$
$773$	−19.9132	+	19.9132i	−0.716229	+	0.716229i	0.251602	+	0.967831i	$0.419043\pi$
$774$		0			0
$775$	50.4638			1.81271
$776$		0			0
$777$		−	4.35699i		−	0.156306i
$778$		0			0
$779$	44.2339	−	7.19983i	1.58485	−	0.257961i
$780$		0			0
$781$			5.19014i			0.185718i
$782$		0			0
$783$	−2.31879			−0.0828667
$784$		0			0
$785$	−39.0441	+	39.0441i	−1.39354	+	1.39354i
$786$		0			0
$787$		−	44.3469i		−	1.58080i	−0.612593	−	0.790399i	$-0.709873\pi$
$787$		−	44.3469i		−	1.58080i	0.612593	−	0.790399i	$-0.290127\pi$
$788$		0			0
$789$	52.2448			1.85996
$790$		0			0
$791$	11.5656	+	11.5656i	0.411227	+	0.411227i
$792$		0			0
$793$	30.9502	−	30.9502i	1.09907	−	1.09907i
$794$		0			0
$795$	73.6389			2.61170
$796$		0			0
$797$	39.4176			1.39624			0.698122	−	0.715979i	$-0.254019\pi$
$797$	39.4176			1.39624			0.698122	+	0.715979i	$0.254019\pi$
$798$		0			0
$799$			5.96537i			0.211040i
$800$		0			0
$801$	4.93287	−	4.93287i	0.174294	−	0.174294i
$802$		0			0
$803$	5.68152	−	5.68152i	0.200497	−	0.200497i
$804$		0			0
$805$	10.7702	−	10.7702i	0.379599	−	0.379599i
$806$		0			0
$807$	17.7324	+	17.7324i	0.624209	+	0.624209i
$808$		0			0
$809$	−27.3558	−	27.3558i	−0.961778	−	0.961778i	0.0375177	−	0.999296i	$-0.488055\pi$
$809$	−27.3558	−	27.3558i	−0.961778	−	0.961778i	−0.999296	+	0.0375177i	$0.988055\pi$
$810$		0			0
$811$			4.57789i			0.160751i	0.996765	+	0.0803757i	$0.0256120\pi$
$811$			4.57789i			0.160751i	−0.996765	+	0.0803757i	$0.974388\pi$
$812$		0			0
$813$	−16.5865	−	16.5865i	−0.581713	−	0.581713i
$814$		0			0
$815$		−	25.5725i		−	0.895765i
$816$		0			0
$817$	−30.2439	−	30.2439i	−1.05810	−	1.05810i
$818$		0			0
$819$	−9.20202			−0.321545
$820$		0			0
$821$	4.37268			0.152608			0.0763038	−	0.997085i	$-0.475688\pi$
$821$	4.37268			0.152608			0.0763038	+	0.997085i	$0.475688\pi$
$822$		0			0
$823$	29.1881	+	29.1881i	1.01743	+	1.01743i	0.999845	+	0.0175871i	$0.00559845\pi$
$823$	29.1881	+	29.1881i	1.01743	+	1.01743i	0.0175871	+	0.999845i	$0.494402\pi$
$824$		0			0
$825$		−	43.2025i		−	1.50412i
$826$		0			0
$827$	−23.6341	−	23.6341i	−0.821837	−	0.821837i	0.164534	−	0.986371i	$-0.447388\pi$
$827$	−23.6341	−	23.6341i	−0.821837	−	0.821837i	−0.986371	+	0.164534i	$0.947388\pi$
$828$		0			0
$829$		−	39.1402i		−	1.35939i	−0.733493	−	0.679697i	$-0.762111\pi$
$829$		−	39.1402i		−	1.35939i	0.733493	−	0.679697i	$-0.237889\pi$
$830$		0			0
$831$	−26.2668	−	26.2668i	−0.911184	−	0.911184i
$832$		0			0
$833$	2.68616	+	2.68616i	0.0930698	+	0.0930698i
$834$		0			0
$835$	−15.2060	+	15.2060i	−0.526226	+	0.526226i
$836$		0			0
$837$	−6.97975	+	6.97975i	−0.241256	+	0.241256i
$838$		0			0
$839$	33.2900	−	33.2900i	1.14930	−	1.14930i	0.162609	−	0.986691i	$-0.448009\pi$
$839$	33.2900	−	33.2900i	1.14930	−	1.14930i	0.986691	−	0.162609i	$-0.0519910\pi$
$840$		0			0
$841$		−	26.9339i		−	0.928754i
$842$		0			0
$843$	−57.4642			−1.97917
$844$		0			0
$845$	−10.9837			−0.377851
$846$		0			0
$847$	4.11655	−	4.11655i	0.141446	−	0.141446i
$848$		0			0
$849$	−39.2087	−	39.2087i	−1.34564	−	1.34564i
$850$		0			0
$851$	7.92056			0.271513
$852$		0			0
$853$		−	54.4214i		−	1.86335i	−0.363288	−	0.931677i	$-0.618346\pi$
$853$		−	54.4214i		−	1.86335i	0.363288	−	0.931677i	$-0.381654\pi$
$854$		0			0
$855$	−41.4163	+	41.4163i	−1.41641	+	1.41641i
$856$		0			0
$857$	−26.4802			−0.904547			−0.452273	−	0.891879i	$-0.649387\pi$
$857$	−26.4802			−0.904547			−0.452273	+	0.891879i	$0.649387\pi$
$858$		0			0
$859$			22.1260i			0.754930i	0.926024	+	0.377465i	$0.123204\pi$
$859$			22.1260i			0.754930i	−0.926024	+	0.377465i	$0.876796\pi$
$860$		0			0
$861$	−8.61294	+	11.9618i	−0.293528	+	0.407658i
$862$		0			0
$863$		−	38.6192i		−	1.31461i	−0.753623	−	0.657307i	$-0.771695\pi$
$863$		−	38.6192i		−	1.31461i	0.753623	−	0.657307i	$-0.228305\pi$
$864$		0			0
$865$	−42.2307			−1.43589
$866$		0			0
$867$	−4.18193	+	4.18193i	−0.142026	+	0.142026i
$868$		0			0
$869$		−	23.2512i		−	0.788744i
$870$		0			0
$871$	−19.8525			−0.672677
$872$		0			0
$873$	−26.1722	−	26.1722i	−0.885795	−	0.885795i
$874$		0			0
$875$	8.35717	−	8.35717i	0.282524	−	0.282524i
$876$		0			0
$877$	−33.5916			−1.13431			−0.567154	−	0.823612i	$-0.691956\pi$
$877$	−33.5916			−1.13431			−0.567154	+	0.823612i	$0.691956\pi$
$878$		0			0
$879$	28.2263			0.952050
$880$		0			0
$881$			31.1561i			1.04967i	0.851203	+	0.524837i	$0.175874\pi$
$881$			31.1561i			1.04967i	−0.851203	+	0.524837i	$0.824126\pi$
$882$		0			0
$883$	−26.8878	+	26.8878i	−0.904848	+	0.904848i	−0.995851	−	0.0910028i	$-0.970993\pi$
$883$	−26.8878	+	26.8878i	−0.904848	+	0.904848i	0.0910028	+	0.995851i	$0.470993\pi$
$884$		0			0
$885$	13.8038	−	13.8038i	0.464009	−	0.464009i
$886$		0			0
$887$	39.7170	−	39.7170i	1.33357	−	1.33357i	0.431409	−	0.902157i	$-0.358017\pi$
$887$	39.7170	−	39.7170i	1.33357	−	1.33357i	0.902157	−	0.431409i	$-0.141983\pi$
$888$		0			0
$889$	14.8730	+	14.8730i	0.498823	+	0.498823i
$890$		0			0
$891$	17.0744	+	17.0744i	0.572014	+	0.572014i
$892$		0			0
$893$			10.9909i			0.367796i
$894$		0			0
$895$	21.4000	+	21.4000i	0.715323	+	0.715323i
$896$		0			0
$897$		−	38.5552i		−	1.28732i
$898$		0			0
$899$	6.21922	+	6.21922i	0.207423	+	0.207423i
$900$		0			0
$901$	−33.3876			−1.11230
$902$		0			0
$903$	14.0675			0.468138
$904$		0			0
$905$	−60.9164	−	60.9164i	−2.02493	−	2.02493i
$906$		0			0
$907$		−	42.3315i		−	1.40560i	−0.711390	−	0.702798i	$-0.751934\pi$
$907$		−	42.3315i		−	1.40560i	0.711390	−	0.702798i	$-0.248066\pi$
$908$		0			0
$909$	−5.99755	−	5.99755i	−0.198926	−	0.198926i
$910$		0			0
$911$			47.3218i			1.56784i	0.620860	+	0.783921i	$0.286783\pi$
$911$			47.3218i			1.56784i	−0.620860	+	0.783921i	$0.713217\pi$
$912$		0			0
$913$	1.02344	+	1.02344i	0.0338709	+	0.0338709i
$914$		0			0
$915$	64.7935	+	64.7935i	2.14201	+	2.14201i
$916$		0			0
$917$	1.71440	−	1.71440i	0.0566144	−	0.0566144i
$918$		0			0
$919$	−22.0407	+	22.0407i	−0.727056	+	0.727056i	−0.970032	−	0.242976i	$-0.921876\pi$
$919$	−22.0407	+	22.0407i	−0.727056	+	0.727056i	0.242976	+	0.970032i	$0.421876\pi$
$920$		0			0
$921$	−53.6389	+	53.6389i	−1.76746	+	1.76746i
$922$		0			0
$923$			9.12822i			0.300459i
$924$		0			0
$925$	15.6094			0.513235
$926$		0			0
$927$	31.6042			1.03802
$928$		0			0
$929$	−15.0800	+	15.0800i	−0.494759	+	0.494759i	−0.909802	−	0.415043i	$-0.863767\pi$
$929$	−15.0800	+	15.0800i	−0.494759	+	0.494759i	0.415043	+	0.909802i	$0.363767\pi$
$930$		0			0
$931$	4.94910	+	4.94910i	0.162200	+	0.162200i
$932$		0			0
$933$	−6.18189			−0.202386
$934$		0			0
$935$			31.4632i			1.02896i
$936$		0			0
$937$	8.55415	−	8.55415i	0.279452	−	0.279452i	−0.553438	−	0.832890i	$-0.686685\pi$
$937$	8.55415	−	8.55415i	0.279452	−	0.279452i	0.832890	+	0.553438i	$0.186685\pi$
$938$		0			0
$939$	−34.6961			−1.13226
$940$		0			0
$941$			22.0860i			0.719983i	0.932956	+	0.359991i	$0.117220\pi$
$941$			22.0860i			0.719983i	−0.932956	+	0.359991i	$0.882780\pi$
$942$		0			0
$943$	−21.7454	−	15.6575i	−0.708128	−	0.509877i
$944$		0			0
$945$			5.87144i			0.190998i
$946$		0			0
$947$	22.4888			0.730789			0.365394	−	0.930853i	$-0.380934\pi$
$947$	22.4888			0.730789			0.365394	+	0.930853i	$0.380934\pi$
$948$		0			0
$949$	9.99244	−	9.99244i	0.324368	−	0.324368i
$950$		0			0
$951$			12.5915i			0.408307i
$952$		0			0
$953$	38.0948			1.23401			0.617006	−	0.786959i	$-0.288346\pi$
$953$	38.0948			1.23401			0.617006	+	0.786959i	$0.288346\pi$
$954$		0			0
$955$	−43.8343	−	43.8343i	−1.41845	−	1.41845i
$956$		0			0
$957$	5.32432	−	5.32432i	0.172111	−	0.172111i
$958$		0			0
$959$	−13.6253			−0.439985
$960$		0			0
$961$	6.44082			0.207768
$962$		0			0
$963$			22.6697i			0.730521i
$964$		0			0
$965$	63.2383	−	63.2383i	2.03571	−	2.03571i
$966$		0			0
$967$	10.1237	−	10.1237i	0.325557	−	0.325557i	−0.525337	−	0.850894i	$-0.676061\pi$
$967$	10.1237	−	10.1237i	0.325557	−	0.325557i	0.850894	+	0.525337i	$0.176061\pi$
$968$		0			0
$969$	43.2792	−	43.2792i	1.39033	−	1.39033i
$970$		0			0
$971$	−31.2031	−	31.2031i	−1.00135	−	1.00135i	−0.999999	−	0.00135469i	$-0.999569\pi$
$971$	−31.2031	−	31.2031i	−1.00135	−	1.00135i	−0.00135469	−	0.999999i	$-0.500431\pi$
$972$		0			0
$973$	4.81549	+	4.81549i	0.154378	+	0.154378i
$974$		0			0
$975$		−	75.9828i		−	2.43340i
$976$		0			0
$977$	−14.6963	−	14.6963i	−0.470175	−	0.470175i	0.431796	−	0.901971i	$-0.357880\pi$
$977$	−14.6963	−	14.6963i	−0.470175	−	0.470175i	−0.901971	+	0.431796i	$0.857880\pi$
$978$		0			0
$979$		−	6.90441i		−	0.220666i
$980$		0			0
$981$	5.57905	+	5.57905i	0.178125	+	0.178125i
$982$		0			0
$983$	39.1525			1.24877			0.624385	−	0.781117i	$-0.285350\pi$
$983$	39.1525			1.24877			0.624385	+	0.781117i	$0.285350\pi$
$984$		0			0
$985$	−30.5003			−0.971820
$986$		0			0
$987$	−2.55613	−	2.55613i	−0.0813625	−	0.0813625i
$988$		0			0
$989$			25.5733i			0.813184i
$990$		0			0
$991$	22.9860	+	22.9860i	0.730173	+	0.730173i	0.970654	−	0.240481i	$-0.0773052\pi$
$991$	22.9860	+	22.9860i	0.730173	+	0.730173i	−0.240481	+	0.970654i	$0.577305\pi$
$992$		0			0
$993$		−	57.8248i		−	1.83501i
$994$		0			0
$995$	48.2490	+	48.2490i	1.52959	+	1.52959i
$996$		0			0
$997$	42.1713	+	42.1713i	1.33558	+	1.33558i	0.900291	+	0.435289i	$0.143354\pi$
$997$	42.1713	+	42.1713i	1.33558	+	1.33558i	0.435289	+	0.900291i	$0.356646\pi$
$998$		0			0
$999$	−2.15897	+	2.15897i	−0.0683069	+	0.0683069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.14	✓	36
41.32	even	4	inner	1148.2.k.b.729.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.14	✓	36	1.1	even	1	trivial
1148.2.k.b.729.14	yes	36	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62776 + 1.62776i) q^{3} +3.63967i q^{5} +(0.707107 + 0.707107i) q^{7} +2.29923i q^{9} +O(q^{10})\)	\(q+(1.62776 + 1.62776i) q^{3} +3.63967i q^{5} +(0.707107 + 0.707107i) q^{7} +2.29923i q^{9} +(1.60909 + 1.60909i) q^{11} +(2.83000 + 2.83000i) q^{13} +(-5.92453 + 5.92453i) q^{15} +(2.68616 - 2.68616i) q^{17} +(4.94910 - 4.94910i) q^{19} +2.30201i q^{21} -4.18481 q^{23} -8.24722 q^{25} +(1.14069 - 1.14069i) q^{27} +(-1.01640 - 1.01640i) q^{29} -6.11889 q^{31} +5.23843i q^{33} +(-2.57364 + 2.57364i) q^{35} -1.89269 q^{37} +9.21314i q^{39} +(5.19627 + 3.74150i) q^{41} -6.11098i q^{43} -8.36844 q^{45} +(-1.11039 + 1.11039i) q^{47} +1.00000i q^{49} +8.74486 q^{51} +(-6.21475 - 6.21475i) q^{53} +(-5.85655 + 5.85655i) q^{55} +16.1119 q^{57} -2.32994 q^{59} -10.9365i q^{61} +(-1.62580 + 1.62580i) q^{63} +(-10.3003 + 10.3003i) q^{65} +(-3.50751 + 3.50751i) q^{67} +(-6.81188 - 6.81188i) q^{69} +(1.61276 + 1.61276i) q^{71} -3.53090i q^{73} +(-13.4245 - 13.4245i) q^{75} +2.27559i q^{77} +(-7.22498 - 7.22498i) q^{79} +10.6112 q^{81} +0.636038 q^{83} +(9.77673 + 9.77673i) q^{85} -3.30891i q^{87} +(-2.14544 - 2.14544i) q^{89} +4.00222i q^{91} +(-9.96011 - 9.96011i) q^{93} +(18.0131 + 18.0131i) q^{95} +(-11.3830 + 11.3830i) q^{97} +(-3.69966 + 3.69966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more