LMFDB - Embedded newform 1920.2.w.i.1663.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1663.1
Root			$0.741252i$ of defining polynomial
Character	$\chi$	$=$	1920.1663
Dual form			1920.2.w.i.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-1.80858 + 1.31492i) q^{5} +(-3.60601 - 3.60601i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80858 + 1.31492i) q^{5} +(-3.60601 - 3.60601i) q^{7} -1.00000i q^{9} -3.09967i q^{11} +(0.859584 + 0.859584i) q^{13} +(0.349069 - 2.20865i) q^{15} +(0.342087 - 0.342087i) q^{17} +4.33324 q^{19} +5.09967 q^{21} +(-4.66545 + 4.66545i) q^{23} +(1.54195 - 4.75630i) q^{25} +(0.707107 + 0.707107i) q^{27} +1.52059i q^{29} -8.74220i q^{31} +(2.19180 + 2.19180i) q^{33} +(11.2634 + 1.78014i) q^{35} +(-6.86993 + 6.86993i) q^{37} -1.21564 q^{39} -8.60830 q^{41} +(0.517497 - 0.517497i) q^{43} +(1.31492 + 1.80858i) q^{45} +(7.53389 + 7.53389i) q^{47} +19.0066i q^{49} +0.483785i q^{51} +(2.39166 + 2.39166i) q^{53} +(4.07583 + 5.60601i) q^{55} +(-3.06406 + 3.06406i) q^{57} +6.26279 q^{59} +12.4864 q^{61} +(-3.60601 + 3.60601i) q^{63} +(-2.68492 - 0.424341i) q^{65} +(0.431271 + 0.431271i) q^{67} -6.59795i q^{69} -0.121941i q^{71} +(1.61407 + 1.61407i) q^{73} +(2.27289 + 4.45353i) q^{75} +(-11.1774 + 11.1774i) q^{77} -16.5190 q^{79} -1.00000 q^{81} +(-6.11235 + 6.11235i) q^{83} +(-0.168874 + 1.06851i) q^{85} +(-1.07522 - 1.07522i) q^{87} +5.61174i q^{89} -6.19934i q^{91} +(6.18167 + 6.18167i) q^{93} +(-7.83703 + 5.69789i) q^{95} +(-3.89074 + 3.89074i) q^{97} -3.09967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−1.80858	+	1.31492i	−0.808823	+	0.588052i
$5$	−1.80858	+	1.31492i	−0.808823	+	0.588052i
$6$		0			0
$7$	−3.60601	−	3.60601i	−1.36294	−	1.36294i	−0.870141	−	0.492803i	$-0.835972\pi$
$7$	−3.60601	−	3.60601i	−1.36294	−	1.36294i	−0.492803	−	0.870141i	$-0.664028\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	3.09967i		−	0.934586i	−0.884103	−	0.467293i	$-0.845229\pi$
$11$		−	3.09967i		−	0.934586i	0.884103	−	0.467293i	$-0.154771\pi$
$12$		0			0
$13$	0.859584	+	0.859584i	0.238406	+	0.238406i	0.816190	−	0.577784i	$-0.196082\pi$
$13$	0.859584	+	0.859584i	0.238406	+	0.238406i	−0.577784	+	0.816190i	$0.696082\pi$
$14$		0			0
$15$	0.349069	−	2.20865i	0.0901293	−	0.570272i
$16$		0			0
$17$	0.342087	−	0.342087i	0.0829684	−	0.0829684i	−0.664405	−	0.747373i	$-0.731315\pi$
$17$	0.342087	−	0.342087i	0.0829684	−	0.0829684i	0.747373	+	0.664405i	$0.231315\pi$
$18$		0			0
$19$	4.33324			0.994114			0.497057	−	0.867718i	$-0.334414\pi$
$19$	4.33324			0.994114			0.497057	+	0.867718i	$0.334414\pi$
$20$		0			0
$21$	5.09967			1.11284
$22$		0			0
$23$	−4.66545	+	4.66545i	−0.972815	+	0.972815i	−0.999640	−	0.0268256i	$-0.991460\pi$
$23$	−4.66545	+	4.66545i	−0.972815	+	0.972815i	0.0268256	+	0.999640i	$0.491460\pi$
$24$		0			0
$25$	1.54195	−	4.75630i	0.308389	−	0.951260i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			1.52059i			0.282367i	0.989983	+	0.141183i	$0.0450907\pi$
$29$			1.52059i			0.282367i	−0.989983	+	0.141183i	$0.954909\pi$
$30$		0			0
$31$		−	8.74220i		−	1.57015i	−0.619403	−	0.785073i	$-0.712625\pi$
$31$		−	8.74220i		−	1.57015i	0.619403	−	0.785073i	$-0.287375\pi$
$32$		0			0
$33$	2.19180	+	2.19180i	0.381543	+	0.381543i
$34$		0			0
$35$	11.2634	+	1.78014i	1.90386	+	0.300898i
$36$		0			0
$37$	−6.86993	+	6.86993i	−1.12941	+	1.12941i	−0.139137	+	0.990273i	$0.544433\pi$
$37$	−6.86993	+	6.86993i	−1.12941	+	1.12941i	−0.990273	+	0.139137i	$0.955567\pi$
$38$		0			0
$39$	−1.21564			−0.194657
$40$		0			0
$41$	−8.60830			−1.34439			−0.672195	−	0.740374i	$-0.734648\pi$
$41$	−8.60830			−1.34439			−0.672195	+	0.740374i	$0.734648\pi$
$42$		0			0
$43$	0.517497	−	0.517497i	0.0789175	−	0.0789175i	−0.666546	−	0.745464i	$-0.732228\pi$
$43$	0.517497	−	0.517497i	0.0789175	−	0.0789175i	0.745464	+	0.666546i	$0.232228\pi$
$44$		0			0
$45$	1.31492	+	1.80858i	0.196017	+	0.269608i
$46$		0			0
$47$	7.53389	+	7.53389i	1.09893	+	1.09893i	0.994536	+	0.104394i	$0.0332903\pi$
$47$	7.53389	+	7.53389i	1.09893	+	1.09893i	0.104394	+	0.994536i	$0.466710\pi$
$48$		0			0
$49$			19.0066i			2.71523i
$50$		0			0
$51$			0.483785i			0.0677434i
$52$		0			0
$53$	2.39166	+	2.39166i	0.328519	+	0.328519i	0.852023	−	0.523504i	$-0.175375\pi$
$53$	2.39166	+	2.39166i	0.328519	+	0.328519i	−0.523504	+	0.852023i	$0.675375\pi$
$54$		0			0
$55$	4.07583	+	5.60601i	0.549585	+	0.755914i
$56$		0			0
$57$	−3.06406	+	3.06406i	−0.405845	+	0.405845i
$58$		0			0
$59$	6.26279			0.815346			0.407673	−	0.913128i	$-0.366340\pi$
$59$	6.26279			0.815346			0.407673	+	0.913128i	$0.366340\pi$
$60$		0			0
$61$	12.4864			1.59871			0.799357	−	0.600856i	$-0.205174\pi$
$61$	12.4864			1.59871			0.799357	+	0.600856i	$0.205174\pi$
$62$		0			0
$63$	−3.60601	+	3.60601i	−0.454315	+	0.454315i
$64$		0			0
$65$	−2.68492	−	0.424341i	−0.333023	−	0.0526330i
$66$		0			0
$67$	0.431271	+	0.431271i	0.0526881	+	0.0526881i	0.732960	−	0.680272i	$-0.238138\pi$
$67$	0.431271	+	0.431271i	0.0526881	+	0.0526881i	−0.680272	+	0.732960i	$0.738138\pi$
$68$		0			0
$69$		−	6.59795i		−	0.794300i
$70$		0			0
$71$		−	0.121941i		−	0.0144718i	−0.999974	−	0.00723589i	$-0.997697\pi$
$71$		−	0.121941i		−	0.0144718i	0.999974	−	0.00723589i	$-0.00230328\pi$
$72$		0			0
$73$	1.61407	+	1.61407i	0.188913	+	0.188913i	0.795226	−	0.606313i	$-0.207352\pi$
$73$	1.61407	+	1.61407i	0.188913	+	0.188913i	−0.606313	+	0.795226i	$0.707352\pi$
$74$		0			0
$75$	2.27289	+	4.45353i	0.262451	+	0.514250i
$76$		0			0
$77$	−11.1774	+	11.1774i	−1.27379	+	1.27379i
$78$		0			0
$79$	−16.5190			−1.85853			−0.929267	−	0.369408i	$-0.879561\pi$
$79$	−16.5190			−1.85853			−0.929267	+	0.369408i	$0.879561\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−6.11235	+	6.11235i	−0.670918	+	0.670918i	−0.957928	−	0.287010i	$-0.907339\pi$
$83$	−6.11235	+	6.11235i	−0.670918	+	0.670918i	0.287010	+	0.957928i	$0.407339\pi$
$84$		0			0
$85$	−0.168874	+	1.06851i	−0.0183170	+	0.115897i
$86$		0			0
$87$	−1.07522	−	1.07522i	−0.115276	−	0.115276i
$88$		0			0
$89$			5.61174i			0.594843i	0.954746	+	0.297422i	$0.0961267\pi$
$89$			5.61174i			0.594843i	−0.954746	+	0.297422i	$0.903873\pi$
$90$		0			0
$91$		−	6.19934i		−	0.649867i
$92$		0			0
$93$	6.18167	+	6.18167i	0.641009	+	0.641009i
$94$		0			0
$95$	−7.83703	+	5.69789i	−0.804062	+	0.584591i
$96$		0			0
$97$	−3.89074	+	3.89074i	−0.395045	+	0.395045i	−0.876481	−	0.481436i	$-0.840115\pi$
$97$	−3.89074	+	3.89074i	−0.395045	+	0.395045i	0.481436	+	0.876481i	$0.340115\pi$
$98$		0			0
$99$	−3.09967			−0.311529
$100$		0			0
$101$	−12.8607			−1.27969			−0.639846	−	0.768503i	$-0.721002\pi$
$101$	−12.8607			−1.27969			−0.639846	+	0.768503i	$0.721002\pi$
$102$		0			0
$103$	3.00806	−	3.00806i	0.296393	−	0.296393i	−0.543206	−	0.839599i	$-0.682790\pi$
$103$	3.00806	−	3.00806i	0.296393	−	0.296393i	0.839599	+	0.543206i	$0.182790\pi$
$104$		0			0
$105$	−9.22318	+	6.70568i	−0.900090	+	0.654407i
$106$		0			0
$107$	1.53094	+	1.53094i	0.148002	+	0.148002i	0.777225	−	0.629223i	$-0.216627\pi$
$107$	1.53094	+	1.53094i	0.148002	+	0.148002i	−0.629223	+	0.777225i	$0.716627\pi$
$108$		0			0
$109$			3.57748i			0.342660i	0.985214	+	0.171330i	$0.0548065\pi$
$109$			3.57748i			0.342660i	−0.985214	+	0.171330i	$0.945194\pi$
$110$		0			0
$111$		−	9.71556i		−	0.922160i
$112$		0			0
$113$	12.4672	+	12.4672i	1.17281	+	1.17281i	0.981536	+	0.191276i	$0.0612624\pi$
$113$	12.4672	+	12.4672i	1.17281	+	1.17281i	0.191276	+	0.981536i	$0.438738\pi$
$114$		0			0
$115$	2.30314	−	14.5726i	0.214769	−	1.35890i
$116$		0			0
$117$	0.859584	−	0.859584i	0.0794686	−	0.0794686i
$118$		0			0
$119$	−2.46714			−0.226163
$120$		0			0
$121$	1.39205			0.126550
$122$		0			0
$123$	6.08699	−	6.08699i	0.548845	−	0.548845i
$124$		0			0
$125$	3.46544	+	10.6297i	0.309958	+	0.950750i
$126$		0			0
$127$	−3.68379	−	3.68379i	−0.326883	−	0.326883i	0.524517	−	0.851400i	$-0.324246\pi$
$127$	−3.68379	−	3.68379i	−0.326883	−	0.326883i	−0.851400	+	0.524517i	$0.824246\pi$
$128$		0			0
$129$			0.731851i			0.0644359i
$130$		0			0
$131$			12.4414i			1.08701i	0.839405	+	0.543506i	$0.182904\pi$
$131$			12.4414i			1.08701i	−0.839405	+	0.543506i	$0.817096\pi$
$132$		0			0
$133$	−15.6257	−	15.6257i	−1.35492	−	1.35492i
$134$		0			0
$135$	−2.20865	−	0.349069i	−0.190091	−	0.0300431i
$136$		0			0
$137$	6.44485	−	6.44485i	0.550621	−	0.550621i	−0.375999	−	0.926620i	$-0.622700\pi$
$137$	6.44485	−	6.44485i	0.550621	−	0.550621i	0.926620	+	0.375999i	$0.122700\pi$
$138$		0			0
$139$	1.29206			0.109591			0.0547956	−	0.998498i	$-0.482549\pi$
$139$	1.29206			0.109591			0.0547956	+	0.998498i	$0.482549\pi$
$140$		0			0
$141$	−10.6545			−0.897273
$142$		0			0
$143$	2.66443	−	2.66443i	0.222811	−	0.222811i
$144$		0			0
$145$	−1.99946	−	2.75011i	−0.166046	−	0.228385i
$146$		0			0
$147$	−13.4397	−	13.4397i	−1.10849	−	1.10849i
$148$		0			0
$149$			3.51898i			0.288286i	0.989557	+	0.144143i	$0.0460426\pi$
$149$			3.51898i			0.288286i	−0.989557	+	0.144143i	$0.953957\pi$
$150$		0			0
$151$			1.72333i			0.140243i	0.997538	+	0.0701214i	$0.0223387\pi$
$151$			1.72333i			0.140243i	−0.997538	+	0.0701214i	$0.977661\pi$
$152$		0			0
$153$	−0.342087	−	0.342087i	−0.0276561	−	0.0276561i
$154$		0			0
$155$	11.4953	+	15.8110i	0.923328	+	1.26997i
$156$		0			0
$157$	−10.3021	+	10.3021i	−0.822196	+	0.822196i	−0.986423	−	0.164227i	$-0.947487\pi$
$157$	−10.3021	+	10.3021i	−0.822196	+	0.822196i	0.164227	+	0.986423i	$0.447487\pi$
$158$		0			0
$159$	−3.38231			−0.268235
$160$		0			0
$161$	33.6474			2.65178
$162$		0			0
$163$	−9.48250	+	9.48250i	−0.742727	+	0.742727i	−0.973102	−	0.230375i	$-0.926005\pi$
$163$	−9.48250	+	9.48250i	−0.742727	+	0.742727i	0.230375	+	0.973102i	$0.426005\pi$
$164$		0			0
$165$	−6.84610	−	1.08200i	−0.532968	−	0.0842336i
$166$		0			0
$167$	−5.77471	−	5.77471i	−0.446861	−	0.446861i	0.447449	−	0.894310i	$-0.352333\pi$
$167$	−5.77471	−	5.77471i	−0.446861	−	0.446861i	−0.894310	+	0.447449i	$0.852333\pi$
$168$		0			0
$169$		−	11.5222i		−	0.886325i
$170$		0			0
$171$		−	4.33324i		−	0.331371i
$172$		0			0
$173$	15.8338	+	15.8338i	1.20382	+	1.20382i	0.972995	+	0.230828i	$0.0741433\pi$
$173$	15.8338	+	15.8338i	1.20382	+	1.20382i	0.230828	+	0.972995i	$0.425857\pi$
$174$		0			0
$175$	−22.7116	+	11.5910i	−1.71683	+	0.876197i
$176$		0			0
$177$	−4.42846	+	4.42846i	−0.332864	+	0.332864i
$178$		0			0
$179$	11.2216			0.838743			0.419371	−	0.907815i	$-0.362251\pi$
$179$	11.2216			0.838743			0.419371	+	0.907815i	$0.362251\pi$
$180$		0			0
$181$	17.0890			1.27022			0.635108	−	0.772423i	$-0.280956\pi$
$181$	17.0890			1.27022			0.635108	+	0.772423i	$0.280956\pi$
$182$		0			0
$183$	−8.82919	+	8.82919i	−0.652672	+	0.652672i
$184$		0			0
$185$	3.39140	−	21.4583i	0.249341	−	1.57765i
$186$		0			0
$187$	−1.06036	−	1.06036i	−0.0775411	−	0.0775411i
$188$		0			0
$189$		−	5.09967i		−	0.370946i
$190$		0			0
$191$		−	9.62530i		−	0.696462i	−0.937409	−	0.348231i	$-0.886782\pi$
$191$		−	9.62530i		−	0.696462i	0.937409	−	0.348231i	$-0.113218\pi$
$192$		0			0
$193$	−2.69797	−	2.69797i	−0.194204	−	0.194204i	0.603306	−	0.797510i	$-0.293850\pi$
$193$	−2.69797	−	2.69797i	−0.194204	−	0.194204i	−0.797510	+	0.603306i	$0.793850\pi$
$194$		0			0
$195$	2.19858	−	1.59847i	0.157443	−	0.114469i
$196$		0			0
$197$	1.92038	−	1.92038i	0.136822	−	0.136822i	−0.635379	−	0.772201i	$-0.719156\pi$
$197$	1.92038	−	1.92038i	0.136822	−	0.136822i	0.772201	+	0.635379i	$0.219156\pi$
$198$		0			0
$199$	3.85352			0.273168			0.136584	−	0.990628i	$-0.456388\pi$
$199$	3.85352			0.273168			0.136584	+	0.990628i	$0.456388\pi$
$200$		0			0
$201$	−0.609909			−0.0430197
$202$		0			0
$203$	5.48327	−	5.48327i	0.384850	−	0.384850i
$204$		0			0
$205$	15.5688	−	11.3193i	1.08737	−	0.790572i
$206$		0			0
$207$	4.66545	+	4.66545i	0.324272	+	0.324272i
$208$		0			0
$209$		−	13.4316i		−	0.929084i
$210$		0			0
$211$			6.10998i			0.420628i	0.977634	+	0.210314i	$0.0674487\pi$
$211$			6.10998i			0.420628i	−0.977634	+	0.210314i	$0.932551\pi$
$212$		0			0
$213$	0.0862256	+	0.0862256i	0.00590808	+	0.00590808i
$214$		0			0
$215$	−0.255467	+	1.61640i	−0.0174227	+	0.110238i
$216$		0			0
$217$	−31.5245	+	31.5245i	−2.14002	+	2.14002i
$218$		0			0
$219$	−2.28264			−0.154247
$220$		0			0
$221$	0.588106			0.0395603
$222$		0			0
$223$	10.5045	−	10.5045i	0.703436	−	0.703436i	−0.261710	−	0.965146i	$-0.584287\pi$
$223$	10.5045	−	10.5045i	0.703436	−	0.703436i	0.965146	+	0.261710i	$0.0842865\pi$
$224$		0			0
$225$	−4.75630	−	1.54195i	−0.317087	−	0.102796i
$226$		0			0
$227$	7.42221	+	7.42221i	0.492630	+	0.492630i	0.909134	−	0.416504i	$-0.136745\pi$
$227$	7.42221	+	7.42221i	0.492630	+	0.492630i	−0.416504	+	0.909134i	$0.636745\pi$
$228$		0			0
$229$		−	11.7507i		−	0.776509i	−0.921552	−	0.388255i	$-0.873078\pi$
$229$		−	11.7507i		−	0.776509i	0.921552	−	0.388255i	$-0.126922\pi$
$230$		0			0
$231$		−	15.8073i		−	1.04004i
$232$		0			0
$233$	9.70681	+	9.70681i	0.635914	+	0.635914i	0.949545	−	0.313631i	$-0.101545\pi$
$233$	9.70681	+	9.70681i	0.635914	+	0.635914i	−0.313631	+	0.949545i	$0.601545\pi$
$234$		0			0
$235$	−23.5321	−	3.71917i	−1.53507	−	0.242612i
$236$		0			0
$237$	11.6807	−	11.6807i	0.758744	−	0.758744i
$238$		0			0
$239$	27.2248			1.76103			0.880514	−	0.474020i	$-0.157197\pi$
$239$	27.2248			1.76103			0.880514	+	0.474020i	$0.157197\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−24.9923	−	34.3751i	−1.59670	−	2.19614i
$246$		0			0
$247$	3.72479	+	3.72479i	0.237002	+	0.237002i
$248$		0			0
$249$		−	8.64417i		−	0.547802i
$250$		0			0
$251$			22.1409i			1.39752i	0.715357	+	0.698759i	$0.246264\pi$
$251$			22.1409i			1.39752i	−0.715357	+	0.698759i	$0.753736\pi$
$252$		0			0
$253$	14.4614	+	14.4614i	0.909179	+	0.909179i
$254$		0			0
$255$	−0.636140	−	0.874965i	−0.0398367	−	0.0547924i
$256$		0			0
$257$	−0.350539	+	0.350539i	−0.0218660	+	0.0218660i	−0.717955	−	0.696089i	$-0.754922\pi$
$257$	−0.350539	+	0.350539i	−0.0218660	+	0.0218660i	0.696089	+	0.717955i	$0.254922\pi$
$258$		0			0
$259$	49.5461			3.07865
$260$		0			0
$261$	1.52059			0.0941222
$262$		0			0
$263$	6.24599	−	6.24599i	0.385144	−	0.385144i	−0.487807	−	0.872951i	$-0.662203\pi$
$263$	6.24599	−	6.24599i	0.385144	−	0.385144i	0.872951	+	0.487807i	$0.162203\pi$
$264$		0			0
$265$	−7.47036	−	1.18066i	−0.458901	−	0.0725275i
$266$		0			0
$267$	−3.96810	−	3.96810i	−0.242844	−	0.242844i
$268$		0			0
$269$		−	9.41209i		−	0.573865i	−0.957951	−	0.286933i	$-0.907364\pi$
$269$		−	9.41209i		−	0.573865i	0.957951	−	0.286933i	$-0.0926355\pi$
$270$		0			0
$271$			20.2076i			1.22752i	0.789492	+	0.613761i	$0.210344\pi$
$271$			20.2076i			1.22752i	−0.789492	+	0.613761i	$0.789656\pi$
$272$		0			0
$273$	4.38360	+	4.38360i	0.265307	+	0.265307i
$274$		0			0
$275$	−14.7430	−	4.77953i	−0.889034	−	0.288216i
$276$		0			0
$277$	5.80113	−	5.80113i	0.348556	−	0.348556i	−0.511016	−	0.859571i	$-0.670731\pi$
$277$	5.80113	−	5.80113i	0.348556	−	0.348556i	0.859571	+	0.511016i	$0.170731\pi$
$278$		0			0
$279$	−8.74220			−0.523382
$280$		0			0
$281$	12.7542			0.760849			0.380425	−	0.924812i	$-0.375778\pi$
$281$	12.7542			0.760849			0.380425	+	0.924812i	$0.375778\pi$
$282$		0			0
$283$	−13.6402	+	13.6402i	−0.810828	+	0.810828i	−0.984758	−	0.173930i	$-0.944353\pi$
$283$	−13.6402	+	13.6402i	−0.810828	+	0.810828i	0.173930	+	0.984758i	$0.444353\pi$
$284$		0			0
$285$	1.51260	−	9.57063i	0.0895988	−	0.566915i
$286$		0			0
$287$	31.0416	+	31.0416i	1.83233	+	1.83233i
$288$		0			0
$289$			16.7660i			0.986232i
$290$		0			0
$291$		−	5.50234i		−	0.322553i
$292$		0			0
$293$	17.0940	+	17.0940i	0.998640	+	0.998640i	0.999999	−	0.00135864i	$-0.000432469\pi$
$293$	17.0940	+	17.0940i	0.998640	+	0.998640i	−0.00135864	+	0.999999i	$0.500432\pi$
$294$		0			0
$295$	−11.3268	+	8.23510i	−0.659471	+	0.479466i
$296$		0			0
$297$	2.19180	−	2.19180i	0.127181	−	0.127181i
$298$		0			0
$299$	−8.02070			−0.463849
$300$		0			0
$301$	−3.73220			−0.215120
$302$		0			0
$303$	9.09392	−	9.09392i	0.522432	−	0.522432i
$304$		0			0
$305$	−22.5826	+	16.4186i	−1.29308	+	0.940127i
$306$		0			0
$307$	−20.1644	−	20.1644i	−1.15084	−	1.15084i	−0.986384	−	0.164460i	$-0.947412\pi$
$307$	−20.1644	−	20.1644i	−1.15084	−	1.15084i	−0.164460	−	0.986384i	$-0.552588\pi$
$308$		0			0
$309$			4.25404i			0.242004i
$310$		0			0
$311$			13.0740i			0.741356i	0.928761	+	0.370678i	$0.120875\pi$
$311$			13.0740i			0.741356i	−0.928761	+	0.370678i	$0.879125\pi$
$312$		0			0
$313$	−23.6218	−	23.6218i	−1.33518	−	1.33518i	−0.900662	−	0.434520i	$-0.856918\pi$
$313$	−23.6218	−	23.6218i	−1.33518	−	1.33518i	−0.434520	−	0.900662i	$-0.643082\pi$
$314$		0			0
$315$	1.78014	−	11.2634i	0.100299	−	0.634621i
$316$		0			0
$317$	−13.1778	+	13.1778i	−0.740141	+	0.740141i	−0.972605	−	0.232464i	$-0.925321\pi$
$317$	−13.1778	+	13.1778i	−0.740141	+	0.740141i	0.232464	+	0.972605i	$0.425321\pi$
$318$		0			0
$319$	4.71333			0.263896
$320$		0			0
$321$	−2.16508			−0.120843
$322$		0			0
$323$	1.48235	−	1.48235i	0.0824800	−	0.0824800i
$324$		0			0
$325$	5.41387	−	2.76301i	0.300308	−	0.153264i
$326$		0			0
$327$	−2.52966	−	2.52966i	−0.139890	−	0.139890i
$328$		0			0
$329$		−	54.3345i		−	2.99556i
$330$		0			0
$331$			18.6942i			1.02753i	0.857932	+	0.513763i	$0.171749\pi$
$331$			18.6942i			1.02753i	−0.857932	+	0.513763i	$0.828251\pi$
$332$		0			0
$333$	6.86993	+	6.86993i	0.376470	+	0.376470i
$334$		0			0
$335$	−1.34708	−	0.212901i	−0.0735988	−	0.0116320i
$336$		0			0
$337$	10.5857	−	10.5857i	0.576641	−	0.576641i	−0.357336	−	0.933976i	$-0.616315\pi$
$337$	10.5857	−	10.5857i	0.576641	−	0.576641i	0.933976	+	0.357336i	$0.116315\pi$
$338$		0			0
$339$	−17.6312			−0.957597
$340$		0			0
$341$	−27.0979			−1.46744
$342$		0			0
$343$	43.2961	−	43.2961i	2.33777	−	2.33777i
$344$		0			0
$345$	8.67581	+	11.9329i	0.467090	+	0.642448i
$346$		0			0
$347$	−8.68055	−	8.68055i	−0.465996	−	0.465996i	0.434618	−	0.900615i	$-0.356883\pi$
$347$	−8.68055	−	8.68055i	−0.465996	−	0.465996i	−0.900615	+	0.434618i	$0.856883\pi$
$348$		0			0
$349$		−	21.6852i		−	1.16078i	−0.814337	−	0.580392i	$-0.802899\pi$
$349$		−	21.6852i		−	1.16078i	0.814337	−	0.580392i	$-0.197101\pi$
$350$		0			0
$351$			1.21564i			0.0648858i
$352$		0			0
$353$	−20.8289	−	20.8289i	−1.10861	−	1.10861i	−0.993333	−	0.115277i	$-0.963225\pi$
$353$	−20.8289	−	20.8289i	−1.10861	−	1.10861i	−0.115277	−	0.993333i	$-0.536775\pi$
$354$		0			0
$355$	0.160344	+	0.220541i	0.00851016	+	0.0117051i
$356$		0			0
$357$	1.74453	−	1.74453i	0.0923305	−	0.0923305i
$358$		0			0
$359$	7.78498			0.410876			0.205438	−	0.978670i	$-0.434138\pi$
$359$	7.78498			0.410876			0.205438	+	0.978670i	$0.434138\pi$
$360$		0			0
$361$	−0.223020			−0.0117379
$362$		0			0
$363$	−0.984325	+	0.984325i	−0.0516637	+	0.0516637i
$364$		0			0
$365$	−5.04157	−	0.796801i	−0.263888	−	0.0417065i
$366$		0			0
$367$	−11.7295	−	11.7295i	−0.612274	−	0.612274i	0.331264	−	0.943538i	$-0.392525\pi$
$367$	−11.7295	−	11.7295i	−0.612274	−	0.612274i	−0.943538	+	0.331264i	$0.892525\pi$
$368$		0			0
$369$			8.60830i			0.448130i
$370$		0			0
$371$		−	17.2487i		−	0.895507i
$372$		0			0
$373$	−5.28095	−	5.28095i	−0.273437	−	0.273437i	0.557045	−	0.830482i	$-0.311935\pi$
$373$	−5.28095	−	5.28095i	−0.273437	−	0.273437i	−0.830482	+	0.557045i	$0.811935\pi$
$374$		0			0
$375$	−9.96677	−	5.06591i	−0.514682	−	0.261602i
$376$		0			0
$377$	−1.30708	+	1.30708i	−0.0673178	+	0.0673178i
$378$		0			0
$379$	−18.5979			−0.955310			−0.477655	−	0.878547i	$-0.658513\pi$
$379$	−18.5979			−0.955310			−0.477655	+	0.878547i	$0.658513\pi$
$380$		0			0
$381$	5.20966			0.266899
$382$		0			0
$383$	−7.16843	+	7.16843i	−0.366290	+	0.366290i	−0.866122	−	0.499832i	$-0.833395\pi$
$383$	−7.16843	+	7.16843i	−0.366290	+	0.366290i	0.499832	+	0.866122i	$0.333395\pi$
$384$		0			0
$385$	5.51784	−	34.9128i	0.281215	−	1.77932i
$386$		0			0
$387$	−0.517497	−	0.517497i	−0.0263058	−	0.0263058i
$388$		0			0
$389$			26.9941i			1.36866i	0.729174	+	0.684328i	$0.239904\pi$
$389$			26.9941i			1.36866i	−0.729174	+	0.684328i	$0.760096\pi$
$390$		0			0
$391$			3.19199i			0.161426i
$392$		0			0
$393$	−8.79742	−	8.79742i	−0.443771	−	0.443771i
$394$		0			0
$395$	29.8760	−	21.7213i	1.50323	−	1.09292i
$396$		0			0
$397$	−12.8659	+	12.8659i	−0.645722	+	0.645722i	−0.951956	−	0.306234i	$-0.900931\pi$
$397$	−12.8659	+	12.8659i	−0.645722	+	0.645722i	0.306234	+	0.951956i	$0.400931\pi$
$398$		0			0
$399$	22.0981			1.10629
$400$		0			0
$401$	32.6062			1.62828			0.814138	−	0.580672i	$-0.197210\pi$
$401$	32.6062			1.62828			0.814138	+	0.580672i	$0.197210\pi$
$402$		0			0
$403$	7.51466	−	7.51466i	0.374332	−	0.374332i
$404$		0			0
$405$	1.80858	−	1.31492i	0.0898692	−	0.0653391i
$406$		0			0
$407$	21.2945	+	21.2945i	1.05553	+	1.05553i
$408$		0			0
$409$		−	3.85184i		−	0.190461i	−0.995455	−	0.0952305i	$-0.969641\pi$
$409$		−	3.85184i		−	0.190461i	0.995455	−	0.0952305i	$-0.0303588\pi$
$410$		0			0
$411$			9.11440i			0.449580i
$412$		0			0
$413$	−22.5837	−	22.5837i	−1.11127	−	1.11127i
$414$		0			0
$415$	3.01742	−	19.0920i	0.148119	−	0.937188i
$416$		0			0
$417$	−0.913625	+	0.913625i	−0.0447404	+	0.0447404i
$418$		0			0
$419$	−21.6800			−1.05914			−0.529568	−	0.848268i	$-0.677646\pi$
$419$	−21.6800			−1.05914			−0.529568	+	0.848268i	$0.677646\pi$
$420$		0			0
$421$	33.6816			1.64154			0.820771	−	0.571257i	$-0.193544\pi$
$421$	33.6816			1.64154			0.820771	+	0.571257i	$0.193544\pi$
$422$		0			0
$423$	7.53389	−	7.53389i	0.366310	−	0.366310i
$424$		0			0
$425$	−1.09959	−	2.15455i	−0.0533380	−	0.104511i
$426$		0			0
$427$	−45.0259	−	45.0259i	−2.17896	−	2.17896i
$428$		0			0
$429$			3.76807i			0.181924i
$430$		0			0
$431$		−	8.74443i		−	0.421205i	−0.977572	−	0.210602i	$-0.932458\pi$
$431$		−	8.74443i		−	0.421205i	0.977572	−	0.210602i	$-0.0675425\pi$
$432$		0			0
$433$	19.8491	+	19.8491i	0.953888	+	0.953888i	0.998983	−	0.0450945i	$-0.0143589\pi$
$433$	19.8491	+	19.8491i	0.953888	+	0.953888i	−0.0450945	+	0.998983i	$0.514359\pi$
$434$		0			0
$435$	3.35846	+	0.530792i	0.161026	+	0.0254495i
$436$		0			0
$437$	−20.2165	+	20.2165i	−0.967088	+	0.967088i
$438$		0			0
$439$	−1.36950			−0.0653629			−0.0326814	−	0.999466i	$-0.510405\pi$
$439$	−1.36950			−0.0653629			−0.0326814	+	0.999466i	$0.510405\pi$
$440$		0			0
$441$	19.0066			0.905078
$442$		0			0
$443$	−10.8482	+	10.8482i	−0.515412	+	0.515412i	−0.916180	−	0.400767i	$-0.868744\pi$
$443$	−10.8482	+	10.8482i	−0.515412	+	0.515412i	0.400767	+	0.916180i	$0.368744\pi$
$444$		0			0
$445$	−7.37902	−	10.1493i	−0.349799	−	0.481123i
$446$		0			0
$447$	−2.48830	−	2.48830i	−0.117692	−	0.117692i
$448$		0			0
$449$		−	4.15152i		−	0.195922i	−0.995190	−	0.0979611i	$-0.968768\pi$
$449$		−	4.15152i		−	0.195922i	0.995190	−	0.0979611i	$-0.0312321\pi$
$450$		0			0
$451$			26.6829i			1.25645i
$452$		0			0
$453$	−1.21858	−	1.21858i	−0.0572539	−	0.0572539i
$454$		0			0
$455$	8.15166	+	11.2120i	0.382156	+	0.525628i
$456$		0			0
$457$	8.00496	−	8.00496i	0.374456	−	0.374456i	−0.494641	−	0.869097i	$-0.664700\pi$
$457$	8.00496	−	8.00496i	0.374456	−	0.374456i	0.869097	+	0.494641i	$0.164700\pi$
$458$		0			0
$459$	0.483785			0.0225811
$460$		0			0
$461$	8.23392			0.383492			0.191746	−	0.981445i	$-0.438585\pi$
$461$	8.23392			0.383492			0.191746	+	0.981445i	$0.438585\pi$
$462$		0			0
$463$	−10.6260	+	10.6260i	−0.493830	+	0.493830i	−0.909511	−	0.415681i	$-0.863543\pi$
$463$	−10.6260	+	10.6260i	−0.493830	+	0.493830i	0.415681	+	0.909511i	$0.363543\pi$
$464$		0			0
$465$	−19.3085	−	3.05164i	−0.895410	−	0.141516i
$466$		0			0
$467$	−27.6803	−	27.6803i	−1.28089	−	1.28089i	−0.940160	−	0.340733i	$-0.889325\pi$
$467$	−27.6803	−	27.6803i	−1.28089	−	1.28089i	−0.340733	−	0.940160i	$-0.610675\pi$
$468$		0			0
$469$		−	3.11034i		−	0.143622i
$470$		0			0
$471$		−	14.5693i		−	0.671320i
$472$		0			0
$473$	−1.60407	−	1.60407i	−0.0737552	−	0.0737552i
$474$		0			0
$475$	6.68163	−	20.6102i	0.306574	−	0.945661i
$476$		0			0
$477$	2.39166	−	2.39166i	0.109506	−	0.109506i
$478$		0			0
$479$	−16.5477			−0.756086			−0.378043	−	0.925788i	$-0.623403\pi$
$479$	−16.5477			−0.756086			−0.378043	+	0.925788i	$0.623403\pi$
$480$		0			0
$481$	−11.8106			−0.538516
$482$		0			0
$483$	−23.7923	+	23.7923i	−1.08259	+	1.08259i
$484$		0			0
$485$	1.92070	−	12.1528i	0.0872144	−	0.551828i
$486$		0			0
$487$	28.2693	+	28.2693i	1.28100	+	1.28100i	0.940097	+	0.340906i	$0.110734\pi$
$487$	28.2693	+	28.2693i	1.28100	+	1.28100i	0.340906	+	0.940097i	$0.389266\pi$
$488$		0			0
$489$		−	13.4103i		−	0.606434i
$490$		0			0
$491$			20.4660i			0.923616i	0.886980	+	0.461808i	$0.152799\pi$
$491$			20.4660i			0.923616i	−0.886980	+	0.461808i	$0.847201\pi$
$492$		0			0
$493$	0.520175	+	0.520175i	0.0234275	+	0.0234275i
$494$		0			0
$495$	5.60601	−	4.07583i	0.251971	−	0.183195i
$496$		0			0
$497$	−0.439722	+	0.439722i	−0.0197242	+	0.0197242i
$498$		0			0
$499$	−27.2991			−1.22207			−0.611037	−	0.791602i	$-0.709247\pi$
$499$	−27.2991			−1.22207			−0.611037	+	0.791602i	$0.709247\pi$
$500$		0			0
$501$	8.16668			0.364860
$502$		0			0
$503$	−0.997587	+	0.997587i	−0.0444802	+	0.0444802i	−0.728997	−	0.684517i	$-0.760013\pi$
$503$	−0.997587	+	0.997587i	−0.0444802	+	0.0444802i	0.684517	+	0.728997i	$0.260013\pi$
$504$		0			0
$505$	23.2597	−	16.9109i	1.03504	−	0.752525i
$506$		0			0
$507$	8.14745	+	8.14745i	0.361841	+	0.361841i
$508$		0			0
$509$		−	36.5048i		−	1.61804i	−0.587778	−	0.809022i	$-0.699997\pi$
$509$		−	36.5048i		−	1.61804i	0.587778	−	0.809022i	$-0.300003\pi$
$510$		0			0
$511$		−	11.6407i		−	0.514956i
$512$		0			0
$513$	3.06406	+	3.06406i	0.135282	+	0.135282i
$514$		0			0
$515$	−1.48496	+	9.39570i	−0.0654350	+	0.414024i
$516$		0			0
$517$	23.3526	−	23.3526i	1.02704	−	1.02704i
$518$		0			0
$519$	−22.3924			−0.982917
$520$		0			0
$521$	−24.0893			−1.05537			−0.527686	−	0.849440i	$-0.676940\pi$
$521$	−24.0893			−1.05537			−0.527686	+	0.849440i	$0.676940\pi$
$522$		0			0
$523$	3.69578	−	3.69578i	0.161605	−	0.161605i	−0.621672	−	0.783277i	$-0.713546\pi$
$523$	3.69578	−	3.69578i	0.161605	−	0.161605i	0.783277	+	0.621672i	$0.213546\pi$
$524$		0			0
$525$	7.86342	−	24.2556i	0.343188	−	1.05860i
$526$		0			0
$527$	−2.99060	−	2.99060i	−0.130272	−	0.130272i
$528$		0			0
$529$		−	20.5329i		−	0.892736i
$530$		0			0
$531$		−	6.26279i		−	0.271782i
$532$		0			0
$533$	−7.39956	−	7.39956i	−0.320510	−	0.320510i
$534$		0			0
$535$	−4.78191	−	0.755762i	−0.206740	−	0.0326745i
$536$		0			0
$537$	−7.93488	+	7.93488i	−0.342415	+	0.342415i
$538$		0			0
$539$	58.9143			2.53762
$540$		0			0
$541$	1.02368			0.0440115			0.0220057	−	0.999758i	$-0.492995\pi$
$541$	1.02368			0.0440115			0.0220057	+	0.999758i	$0.492995\pi$
$542$		0			0
$543$	−12.0838	+	12.0838i	−0.518563	+	0.518563i
$544$		0			0
$545$	−4.70411	−	6.47017i	−0.201502	−	0.277152i
$546$		0			0
$547$	20.8148	+	20.8148i	0.889975	+	0.889975i	0.994520	−	0.104545i	$-0.0333385\pi$
$547$	20.8148	+	20.8148i	0.889975	+	0.889975i	−0.104545	+	0.994520i	$0.533339\pi$
$548$		0			0
$549$		−	12.4864i		−	0.532905i
$550$		0			0
$551$			6.58908i			0.280704i
$552$		0			0
$553$	59.5678	+	59.5678i	2.53308	+	2.53308i
$554$		0			0
$555$	12.7752	+	17.5714i	0.542278	+	0.745864i
$556$		0			0
$557$	9.09814	−	9.09814i	0.385501	−	0.385501i	−0.487578	−	0.873079i	$-0.662120\pi$
$557$	9.09814	−	9.09814i	0.385501	−	0.385501i	0.873079	+	0.487578i	$0.162120\pi$
$558$		0			0
$559$	0.889664			0.0376288
$560$		0			0
$561$	1.49957			0.0633120
$562$		0			0
$563$	−16.3958	+	16.3958i	−0.691003	+	0.691003i	−0.962453	−	0.271450i	$-0.912497\pi$
$563$	−16.3958	+	16.3958i	−0.691003	+	0.691003i	0.271450	+	0.962453i	$0.412497\pi$
$564$		0			0
$565$	−38.9413	−	6.15452i	−1.63827	−	0.258923i
$566$		0			0
$567$	3.60601	+	3.60601i	0.151438	+	0.151438i
$568$		0			0
$569$			8.89595i			0.372938i	0.982461	+	0.186469i	$0.0597043\pi$
$569$			8.89595i			0.372938i	−0.982461	+	0.186469i	$0.940296\pi$
$570$		0			0
$571$			31.9927i			1.33885i	0.742879	+	0.669426i	$0.233460\pi$
$571$			31.9927i			1.33885i	−0.742879	+	0.669426i	$0.766540\pi$
$572$		0			0
$573$	6.80612	+	6.80612i	0.284330	+	0.284330i
$574$		0			0
$575$	14.9964	+	29.3842i	0.625394	+	1.22541i
$576$		0			0
$577$	2.72588	−	2.72588i	0.113480	−	0.113480i	−0.648087	−	0.761567i	$-0.724431\pi$
$577$	2.72588	−	2.72588i	0.113480	−	0.113480i	0.761567	+	0.648087i	$0.224431\pi$
$578$		0			0
$579$	3.81550			0.158567
$580$		0			0
$581$	44.0824			1.82885
$582$		0			0
$583$	7.41335	−	7.41335i	0.307029	−	0.307029i
$584$		0			0
$585$	−0.424341	+	2.68492i	−0.0175443	+	0.111008i
$586$		0			0
$587$	1.80347	+	1.80347i	0.0744371	+	0.0744371i	0.743345	−	0.668908i	$-0.233238\pi$
$587$	1.80347	+	1.80347i	0.0744371	+	0.0744371i	−0.668908	+	0.743345i	$0.733238\pi$
$588$		0			0
$589$		−	37.8821i		−	1.56090i
$590$		0			0
$591$			2.71583i			0.111714i
$592$		0			0
$593$	−29.7050	−	29.7050i	−1.21984	−	1.21984i	−0.967688	−	0.252150i	$-0.918862\pi$
$593$	−29.7050	−	29.7050i	−1.21984	−	1.21984i	−0.252150	−	0.967688i	$-0.581138\pi$
$594$		0			0
$595$	4.46203	−	3.24411i	0.182926	−	0.132995i
$596$		0			0
$597$	−2.72485	+	2.72485i	−0.111521	+	0.111521i
$598$		0			0
$599$	−24.4275			−0.998082			−0.499041	−	0.866578i	$-0.666314\pi$
$599$	−24.4275			−0.998082			−0.499041	+	0.866578i	$0.666314\pi$
$600$		0			0
$601$	−27.5835			−1.12515			−0.562577	−	0.826745i	$-0.690190\pi$
$601$	−27.5835			−1.12515			−0.562577	+	0.826745i	$0.690190\pi$
$602$		0			0
$603$	0.431271	−	0.431271i	0.0175627	−	0.0175627i
$604$		0			0
$605$	−2.51763	+	1.83044i	−0.102356	+	0.0744178i
$606$		0			0
$607$	−5.67600	−	5.67600i	−0.230382	−	0.230382i	0.582470	−	0.812852i	$-0.302086\pi$
$607$	−5.67600	−	5.67600i	−0.230382	−	0.230382i	−0.812852	+	0.582470i	$0.802086\pi$
$608$		0			0
$609$			7.75451i			0.314229i
$610$		0			0
$611$			12.9520i			0.523982i
$612$		0			0
$613$	−5.46062	−	5.46062i	−0.220552	−	0.220552i	0.588179	−	0.808731i	$-0.299845\pi$
$613$	−5.46062	−	5.46062i	−0.220552	−	0.220552i	−0.808731	+	0.588179i	$0.799845\pi$
$614$		0			0
$615$	−3.00489	+	19.0128i	−0.121169	+	0.766668i
$616$		0			0
$617$	−26.1780	+	26.1780i	−1.05389	+	1.05389i	−0.0554248	+	0.998463i	$0.517651\pi$
$617$	−26.1780	+	26.1780i	−1.05389	+	1.05389i	−0.998463	+	0.0554248i	$0.982349\pi$
$618$		0			0
$619$	−14.7286			−0.591994			−0.295997	−	0.955189i	$-0.595652\pi$
$619$	−14.7286			−0.591994			−0.295997	+	0.955189i	$0.595652\pi$
$620$		0			0
$621$	−6.59795			−0.264767
$622$		0			0
$623$	20.2360	−	20.2360i	0.810738	−	0.810738i
$624$		0			0
$625$	−20.2448	−	14.6679i	−0.809792	−	0.586717i
$626$		0			0
$627$	9.49759	+	9.49759i	0.379297	+	0.379297i
$628$		0			0
$629$			4.70024i			0.187411i
$630$		0			0
$631$		−	12.3304i		−	0.490865i	−0.969414	−	0.245433i	$-0.921070\pi$
$631$		−	12.3304i		−	0.490865i	0.969414	−	0.245433i	$-0.0789300\pi$
$632$		0			0
$633$	−4.32041	−	4.32041i	−0.171721	−	0.171721i
$634$		0			0
$635$	11.5063	+	1.81853i	0.456615	+	0.0721663i
$636$		0			0
$637$	−16.3378	+	16.3378i	−0.647327	+	0.647327i
$638$		0			0
$639$	−0.121941			−0.00482393
$640$		0			0
$641$	9.58224			0.378476			0.189238	−	0.981931i	$-0.439398\pi$
$641$	9.58224			0.378476			0.189238	+	0.981931i	$0.439398\pi$
$642$		0			0
$643$	16.9307	−	16.9307i	0.667681	−	0.667681i	−0.289498	−	0.957179i	$-0.593488\pi$
$643$	16.9307	−	16.9307i	0.667681	−	0.667681i	0.957179	+	0.289498i	$0.0934882\pi$
$644$		0			0
$645$	−0.962329	−	1.32361i	−0.0378916	−	0.0521172i
$646$		0			0
$647$	17.4846	+	17.4846i	0.687391	+	0.687391i	0.961654	−	0.274264i	$-0.0884342\pi$
$647$	17.4846	+	17.4846i	0.687391	+	0.687391i	−0.274264	+	0.961654i	$0.588434\pi$
$648$		0			0
$649$		−	19.4126i		−	0.762011i
$650$		0			0
$651$		−	44.5823i		−	1.74732i
$652$		0			0
$653$	−1.76368	−	1.76368i	−0.0690180	−	0.0690180i	0.671755	−	0.740773i	$-0.265541\pi$
$653$	−1.76368	−	1.76368i	−0.0690180	−	0.0690180i	−0.740773	+	0.671755i	$0.765541\pi$
$654$		0			0
$655$	−16.3595	−	22.5014i	−0.639220	−	0.879201i
$656$		0			0
$657$	1.61407	−	1.61407i	0.0629710	−	0.0629710i
$658$		0			0
$659$	−36.0321			−1.40361			−0.701806	−	0.712369i	$-0.747622\pi$
$659$	−36.0321			−1.40361			−0.701806	+	0.712369i	$0.747622\pi$
$660$		0			0
$661$	26.9082			1.04661			0.523305	−	0.852146i	$-0.324699\pi$
$661$	26.9082			1.04661			0.523305	+	0.852146i	$0.324699\pi$
$662$		0			0
$663$	−0.415854	+	0.415854i	−0.0161504	+	0.0161504i
$664$		0			0
$665$	48.8070	+	7.71377i	1.89266	+	0.299127i
$666$		0			0
$667$	−7.09424	−	7.09424i	−0.274690	−	0.274690i
$668$		0			0
$669$			14.8557i			0.574353i
$670$		0			0
$671$		−	38.7036i		−	1.49414i
$672$		0			0
$673$	2.31292	+	2.31292i	0.0891564	+	0.0891564i	0.750278	−	0.661122i	$-0.229919\pi$
$673$	2.31292	+	2.31292i	0.0891564	+	0.0891564i	−0.661122	+	0.750278i	$0.729919\pi$
$674$		0			0
$675$	4.45353	−	2.27289i	0.171417	−	0.0874836i
$676$		0			0
$677$	17.6126	−	17.6126i	0.676907	−	0.676907i	−0.282392	−	0.959299i	$-0.591128\pi$
$677$	17.6126	−	17.6126i	0.676907	−	0.676907i	0.959299	+	0.282392i	$0.0911278\pi$
$678$		0			0
$679$	28.0601			1.07685
$680$		0			0
$681$	−10.4966			−0.402230
$682$		0			0
$683$	−26.6330	+	26.6330i	−1.01908	+	1.01908i	−0.0192681	+	0.999814i	$0.506134\pi$
$683$	−26.6330	+	26.6330i	−1.01908	+	1.01908i	−0.999814	+	0.0192681i	$0.993866\pi$
$684$		0			0
$685$	−3.18156	+	20.1305i	−0.121561	+	0.769148i
$686$		0			0
$687$	8.30901	+	8.30901i	0.317009	+	0.317009i
$688$		0			0
$689$			4.11166i			0.156642i
$690$		0			0
$691$		−	29.3954i		−	1.11825i	−0.829082	−	0.559127i	$-0.811136\pi$
$691$		−	29.3954i		−	1.11825i	0.829082	−	0.559127i	$-0.188864\pi$
$692$		0			0
$693$	11.1774	+	11.1774i	0.424596	+	0.424596i
$694$		0			0
$695$	−2.33680	+	1.69896i	−0.0886399	+	0.0644453i
$696$		0			0
$697$	−2.94479	+	2.94479i	−0.111542	+	0.111542i
$698$		0			0
$699$	−13.7275			−0.519222
$700$		0			0
$701$	15.3338			0.579149			0.289575	−	0.957155i	$-0.406486\pi$
$701$	15.3338			0.579149			0.289575	+	0.957155i	$0.406486\pi$
$702$		0			0
$703$	−29.7691	+	29.7691i	−1.12276	+	1.12276i
$704$		0			0
$705$	19.2696	−	14.0099i	0.725735	−	0.527643i
$706$		0			0
$707$	46.3760	+	46.3760i	1.74415	+	1.74415i
$708$		0			0
$709$			35.6987i			1.34069i	0.742049	+	0.670346i	$0.233854\pi$
$709$			35.6987i			1.34069i	−0.742049	+	0.670346i	$0.766146\pi$
$710$		0			0
$711$			16.5190i			0.619512i
$712$		0			0
$713$	40.7863	+	40.7863i	1.52746	+	1.52746i
$714$		0			0
$715$	−1.31532	+	8.32236i	−0.0491901	+	0.311239i
$716$		0			0
$717$	−19.2509	+	19.2509i	−0.718937	+	0.718937i
$718$		0			0
$719$	−27.2336			−1.01564			−0.507822	−	0.861462i	$-0.669549\pi$
$719$	−27.2336			−1.01564			−0.507822	+	0.861462i	$0.669549\pi$
$720$		0			0
$721$	−21.6942			−0.807935
$722$		0			0
$723$	−2.82843	+	2.82843i	−0.105190	+	0.105190i
$724$		0			0
$725$	7.23238	+	2.34467i	0.268604	+	0.0870788i
$726$		0			0
$727$	7.65384	+	7.65384i	0.283865	+	0.283865i	0.834648	−	0.550783i	$-0.185671\pi$
$727$	7.65384	+	7.65384i	0.283865	+	0.283865i	−0.550783	+	0.834648i	$0.685671\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	0.354058i		−	0.0130953i
$732$		0			0
$733$	−21.4957	−	21.4957i	−0.793962	−	0.793962i	0.188173	−	0.982136i	$-0.439743\pi$
$733$	−21.4957	−	21.4957i	−0.793962	−	0.793962i	−0.982136	+	0.188173i	$0.939743\pi$
$734$		0			0
$735$	41.9791	+	6.63463i	1.54842	+	0.244722i
$736$		0			0
$737$	1.33680	−	1.33680i	0.0492416	−	0.0492416i
$738$		0			0
$739$	27.9207			1.02708			0.513540	−	0.858066i	$-0.328334\pi$
$739$	27.9207			1.02708			0.513540	+	0.858066i	$0.328334\pi$
$740$		0			0
$741$	−5.26764			−0.193512
$742$		0			0
$743$	−17.6722	+	17.6722i	−0.648332	+	0.648332i	−0.952590	−	0.304258i	$-0.901592\pi$
$743$	−17.6722	+	17.6722i	−0.648332	+	0.648332i	0.304258	+	0.952590i	$0.401592\pi$
$744$		0			0
$745$	−4.62719	−	6.36437i	−0.169527	−	0.233172i
$746$		0			0
$747$	6.11235	+	6.11235i	0.223639	+	0.223639i
$748$		0			0
$749$		−	11.0412i		−	0.403436i
$750$		0			0
$751$			19.5214i			0.712345i	0.934420	+	0.356172i	$0.115918\pi$
$751$			19.5214i			0.712345i	−0.934420	+	0.356172i	$0.884082\pi$
$752$		0			0
$753$	−15.6559	−	15.6559i	−0.570534	−	0.570534i
$754$		0			0
$755$	−2.26605	−	3.11679i	−0.0824701	−	0.113432i
$756$		0			0
$757$	−36.4915	+	36.4915i	−1.32631	+	1.32631i	−0.417738	+	0.908567i	$0.637177\pi$
$757$	−36.4915	+	36.4915i	−1.32631	+	1.32631i	−0.908567	+	0.417738i	$0.862823\pi$
$758$		0			0
$759$	−20.4515			−0.742341
$760$		0			0
$761$	17.9113			0.649284			0.324642	−	0.945837i	$-0.394756\pi$
$761$	17.9113			0.649284			0.324642	+	0.945837i	$0.394756\pi$
$762$		0			0
$763$	12.9004	−	12.9004i	0.467027	−	0.467027i
$764$		0			0
$765$	1.06851	+	0.168874i	0.0386322	+	0.00610567i
$766$		0			0
$767$	5.38340	+	5.38340i	0.194383	+	0.194383i
$768$		0			0
$769$			28.3807i			1.02343i	0.859154	+	0.511717i	$0.170990\pi$
$769$			28.3807i			1.02343i	−0.859154	+	0.511717i	$0.829010\pi$
$770$		0			0
$771$		−	0.495736i		−	0.0178535i
$772$		0			0
$773$	−5.86144	−	5.86144i	−0.210821	−	0.210821i	0.593795	−	0.804616i	$-0.297629\pi$
$773$	−5.86144	−	5.86144i	−0.210821	−	0.210821i	−0.804616	+	0.593795i	$0.797629\pi$
$774$		0			0
$775$	−41.5805	−	13.4800i	−1.49362	−	0.484216i
$776$		0			0
$777$	−35.0344	+	35.0344i	−1.25685	+	1.25685i
$778$		0			0
$779$	−37.3018			−1.33648
$780$		0			0
$781$	−0.377978			−0.0135251
$782$		0			0
$783$	−1.07522	+	1.07522i	−0.0384252	+	0.0384252i
$784$		0			0
$785$	5.08571	−	32.1786i	0.181517	−	1.14850i
$786$		0			0
$787$	11.8633	+	11.8633i	0.422882	+	0.422882i	0.886195	−	0.463313i	$-0.153339\pi$
$787$	11.8633	+	11.8633i	0.422882	+	0.422882i	−0.463313	+	0.886195i	$0.653339\pi$
$788$		0			0
$789$			8.83316i			0.314469i
$790$		0			0
$791$		−	89.9134i		−	3.19695i
$792$		0			0
$793$	10.7331	+	10.7331i	0.381143	+	0.381143i
$794$		0			0
$795$	6.11720	−	4.44749i	0.216955	−	0.157736i
$796$		0			0
$797$	−33.5114	+	33.5114i	−1.18703	+	1.18703i	−0.209150	+	0.977884i	$0.567070\pi$
$797$	−33.5114	+	33.5114i	−1.18703	+	1.18703i	−0.977884	+	0.209150i	$0.932930\pi$
$798$		0			0
$799$	5.15450			0.182353
$800$		0			0
$801$	5.61174			0.198281
$802$		0			0
$803$	5.00309	−	5.00309i	0.176555	−	0.176555i
$804$		0			0
$805$	−60.8541	+	44.2437i	−2.14482	+	1.55939i
$806$		0			0
$807$	6.65535	+	6.65535i	0.234279	+	0.234279i
$808$		0			0
$809$			21.8407i			0.767877i	0.923359	+	0.383938i	$0.125432\pi$
$809$			21.8407i			0.767877i	−0.923359	+	0.383938i	$0.874568\pi$
$810$		0			0
$811$		−	30.2170i		−	1.06106i	−0.847666	−	0.530530i	$-0.821993\pi$
$811$		−	30.2170i		−	1.06106i	0.847666	−	0.530530i	$-0.178007\pi$
$812$		0			0
$813$	−14.2889	−	14.2889i	−0.501134	−	0.501134i
$814$		0			0
$815$	4.68112	−	29.6187i	0.163973	−	1.03750i
$816$		0			0
$817$	2.24244	−	2.24244i	0.0784530	−	0.0784530i
$818$		0			0
$819$	−6.19934			−0.216622
$820$		0			0
$821$	38.9191			1.35829			0.679143	−	0.734006i	$-0.262352\pi$
$821$	38.9191			1.35829			0.679143	+	0.734006i	$0.262352\pi$
$822$		0			0
$823$	−24.1674	+	24.1674i	−0.842424	+	0.842424i	−0.989174	−	0.146750i	$-0.953119\pi$
$823$	−24.1674	+	24.1674i	−0.842424	+	0.842424i	0.146750	+	0.989174i	$0.453119\pi$
$824$		0			0
$825$	13.8045	−	7.04521i	0.480610	−	0.245283i
$826$		0			0
$827$	−28.4906	−	28.4906i	−0.990717	−	0.990717i	0.00924075	−	0.999957i	$-0.497059\pi$
$827$	−28.4906	−	28.4906i	−0.990717	−	0.990717i	−0.999957	+	0.00924075i	$0.997059\pi$
$828$		0			0
$829$		−	33.7109i		−	1.17083i	−0.810735	−	0.585413i	$-0.800932\pi$
$829$		−	33.7109i		−	1.17083i	0.810735	−	0.585413i	$-0.199068\pi$
$830$		0			0
$831$			8.20403i			0.284595i
$832$		0			0
$833$	6.50193	+	6.50193i	0.225279	+	0.225279i
$834$		0			0
$835$	18.0374	+	2.85074i	0.624209	+	0.0986539i
$836$		0			0
$837$	6.18167	−	6.18167i	0.213670	−	0.213670i
$838$		0			0
$839$	−43.1971			−1.49133			−0.745665	−	0.666321i	$-0.767868\pi$
$839$	−43.1971			−1.49133			−0.745665	+	0.666321i	$0.767868\pi$
$840$		0			0
$841$	26.6878			0.920269
$842$		0			0
$843$	−9.01855	+	9.01855i	−0.310616	+	0.310616i
$844$		0			0
$845$	15.1509	+	20.8389i	0.521206	+	0.716880i
$846$		0			0
$847$	−5.01973	−	5.01973i	−0.172480	−	0.172480i
$848$		0			0
$849$		−	19.2902i		−	0.662038i
$850$		0			0
$851$		−	64.1027i		−	2.19741i
$852$		0			0
$853$	26.6965	+	26.6965i	0.914069	+	0.914069i	0.996589	−	0.0825203i	$-0.0262969\pi$
$853$	26.6965	+	26.6965i	0.914069	+	0.914069i	−0.0825203	+	0.996589i	$0.526297\pi$
$854$		0			0
$855$	5.69789	+	7.83703i	0.194864	+	0.268021i
$856$		0			0
$857$	−21.4580	+	21.4580i	−0.732991	+	0.732991i	−0.971211	−	0.238220i	$-0.923436\pi$
$857$	−21.4580	+	21.4580i	−0.732991	+	0.732991i	0.238220	+	0.971211i	$0.423436\pi$
$858$		0			0
$859$	−21.6429			−0.738447			−0.369223	−	0.929341i	$-0.620376\pi$
$859$	−21.6429			−0.738447			−0.369223	+	0.929341i	$0.620376\pi$
$860$		0			0
$861$	−43.8995			−1.49609
$862$		0			0
$863$	21.9068	−	21.9068i	0.745715	−	0.745715i	−0.227957	−	0.973671i	$-0.573204\pi$
$863$	21.9068	−	21.9068i	0.745715	−	0.745715i	0.973671	+	0.227957i	$0.0732045\pi$
$864$		0			0
$865$	−49.4570	−	7.81650i	−1.68159	−	0.265769i
$866$		0			0
$867$	−11.8553	−	11.8553i	−0.402628	−	0.402628i
$868$		0			0
$869$			51.2035i			1.73696i
$870$		0			0
$871$			0.741427i			0.0251223i
$872$		0			0
$873$	3.89074	+	3.89074i	0.131682	+	0.131682i
$874$		0			0
$875$	25.8344	−	50.8273i	0.873364	−	1.71828i
$876$		0			0
$877$	1.92034	−	1.92034i	0.0648454	−	0.0648454i	−0.673940	−	0.738786i	$-0.735400\pi$
$877$	1.92034	−	1.92034i	0.0648454	−	0.0648454i	0.738786	+	0.673940i	$0.235400\pi$
$878$		0			0
$879$	−24.1745			−0.815387
$880$		0			0
$881$	−12.5808			−0.423858			−0.211929	−	0.977285i	$-0.567975\pi$
$881$	−12.5808			−0.423858			−0.211929	+	0.977285i	$0.567975\pi$
$882$		0			0
$883$	16.9862	−	16.9862i	0.571630	−	0.571630i	−0.360954	−	0.932584i	$-0.617549\pi$
$883$	16.9862	−	16.9862i	0.571630	−	0.571630i	0.932584	+	0.360954i	$0.117549\pi$
$884$		0			0
$885$	2.18615	−	13.8323i	0.0734866	−	0.464969i
$886$		0			0
$887$	−23.5877	−	23.5877i	−0.791999	−	0.791999i	0.189820	−	0.981819i	$-0.439210\pi$
$887$	−23.5877	−	23.5877i	−0.791999	−	0.791999i	−0.981819	+	0.189820i	$0.939210\pi$
$888$		0			0
$889$			26.5675i			0.891047i
$890$		0			0
$891$			3.09967i			0.103843i
$892$		0			0
$893$	32.6461	+	32.6461i	1.09246	+	1.09246i
$894$		0			0
$895$	−20.2952	+	14.7556i	−0.678394	+	0.493224i
$896$		0			0
$897$	5.67149	−	5.67149i	0.189366	−	0.189366i
$898$		0			0
$899$	13.2933			0.443357
$900$		0			0
$901$	1.63631			0.0545135
$902$		0			0
$903$	2.63906	−	2.63906i	0.0878225	−	0.0878225i
$904$		0			0
$905$	−30.9069	+	22.4708i	−1.02738	+	0.746953i
$906$		0			0
$907$	−3.15079	−	3.15079i	−0.104620	−	0.104620i	0.652859	−	0.757479i	$-0.273569\pi$
$907$	−3.15079	−	3.15079i	−0.104620	−	0.104620i	−0.757479	+	0.652859i	$0.773569\pi$
$908$		0			0
$909$			12.8607i			0.426564i
$910$		0			0
$911$			31.7329i			1.05136i	0.850683	+	0.525679i	$0.176189\pi$
$911$			31.7329i			1.05136i	−0.850683	+	0.525679i	$0.823811\pi$
$912$		0			0
$913$	18.9463	+	18.9463i	0.627030	+	0.627030i
$914$		0			0
$915$	4.35861	−	27.5780i	0.144091	−	0.911702i
$916$		0			0
$917$	44.8639	−	44.8639i	1.48154	−	1.48154i
$918$		0			0
$919$	19.9823			0.659154			0.329577	−	0.944129i	$-0.393094\pi$
$919$	19.9823			0.659154			0.329577	+	0.944129i	$0.393094\pi$
$920$		0			0
$921$	28.5168			0.939660
$922$		0			0
$923$	0.104819	−	0.104819i	0.00345016	−	0.00345016i
$924$		0			0
$925$	22.0824	+	43.2686i	0.726065	+	1.42266i
$926$		0			0
$927$	−3.00806	−	3.00806i	−0.0987977	−	0.0987977i
$928$		0			0
$929$			12.4814i			0.409502i	0.978814	+	0.204751i	$0.0656385\pi$
$929$			12.4814i			0.409502i	−0.978814	+	0.204751i	$0.934361\pi$
$930$		0			0
$931$			82.3603i			2.69925i
$932$		0			0
$933$	−9.24468	−	9.24468i	−0.302657	−	0.302657i
$934$		0			0
$935$	3.31204	+	0.523455i	0.108315	+	0.0171188i
$936$		0			0
$937$	21.7024	−	21.7024i	0.708986	−	0.708986i	−0.257336	−	0.966322i	$-0.582845\pi$
$937$	21.7024	−	21.7024i	0.708986	−	0.708986i	0.966322	+	0.257336i	$0.0828446\pi$
$938$		0			0
$939$	33.4062			1.09017
$940$		0			0
$941$	−47.0802			−1.53477			−0.767385	−	0.641187i	$-0.778442\pi$
$941$	−47.0802			−1.53477			−0.767385	+	0.641187i	$0.778442\pi$
$942$		0			0
$943$	40.1616	−	40.1616i	1.30784	−	1.30784i
$944$		0			0
$945$	6.70568	+	9.22318i	0.218136	+	0.300030i
$946$		0			0
$947$	5.45511	+	5.45511i	0.177267	+	0.177267i	0.790164	−	0.612896i	$-0.209996\pi$
$947$	5.45511	+	5.45511i	0.177267	+	0.177267i	−0.612896	+	0.790164i	$0.709996\pi$
$948$		0			0
$949$			2.77486i			0.0900759i
$950$		0			0
$951$		−	18.6363i		−	0.604322i
$952$		0			0
$953$	−2.58369	−	2.58369i	−0.0836941	−	0.0836941i	0.664020	−	0.747714i	$-0.268849\pi$
$953$	−2.58369	−	2.58369i	−0.0836941	−	0.0836941i	−0.747714	+	0.664020i	$0.768849\pi$
$954$		0			0
$955$	12.6565	+	17.4082i	0.409556	+	0.563315i
$956$		0			0
$957$	−3.33283	+	3.33283i	−0.107735	+	0.107735i
$958$		0			0
$959$	−46.4804			−1.50093
$960$		0			0
$961$	−45.4261			−1.46536
$962$		0			0
$963$	1.53094	−	1.53094i	0.0493339	−	0.0493339i
$964$		0			0
$965$	8.42712	+	1.33187i	0.271279	+	0.0428746i
$966$		0			0
$967$	14.6499	+	14.6499i	0.471108	+	0.471108i	0.902273	−	0.431165i	$-0.141897\pi$
$967$	14.6499	+	14.6499i	0.471108	+	0.471108i	−0.431165	+	0.902273i	$0.641897\pi$
$968$		0			0
$969$			2.09636i			0.0673447i
$970$		0			0
$971$			18.8077i			0.603568i	0.953376	+	0.301784i	$0.0975822\pi$
$971$			18.8077i			0.603568i	−0.953376	+	0.301784i	$0.902418\pi$
$972$		0			0
$973$	−4.65919	−	4.65919i	−0.149367	−	0.149367i
$974$		0			0
$975$	−1.87445	+	5.78193i	−0.0600303	+	0.185170i
$976$		0			0
$977$	−25.0396	+	25.0396i	−0.801087	+	0.801087i	−0.983266	−	0.182178i	$-0.941685\pi$
$977$	−25.0396	+	25.0396i	−0.801087	+	0.801087i	0.182178	+	0.983266i	$0.441685\pi$
$978$		0			0
$979$	17.3945			0.555932
$980$		0			0
$981$	3.57748			0.114220
$982$		0			0
$983$	−15.8725	+	15.8725i	−0.506255	+	0.506255i	−0.913375	−	0.407120i	$-0.866533\pi$
$983$	−15.8725	+	15.8725i	−0.506255	+	0.506255i	0.407120	+	0.913375i	$0.366533\pi$
$984$		0			0
$985$	−0.948014	+	5.99833i	−0.0302062	+	0.191123i
$986$		0			0
$987$	38.4203	+	38.4203i	1.22293	+	1.22293i
$988$		0			0
$989$			4.82871i			0.153544i
$990$		0			0
$991$			20.0157i			0.635821i	0.948121	+	0.317911i	$0.102981\pi$
$991$			20.0157i			0.635821i	−0.948121	+	0.317911i	$0.897019\pi$
$992$		0			0
$993$	−13.2188	−	13.2188i	−0.419485	−	0.419485i
$994$		0			0
$995$	−6.96940	+	5.06708i	−0.220945	+	0.160637i
$996$		0			0
$997$	−7.81770	+	7.81770i	−0.247589	+	0.247589i	−0.819981	−	0.572391i	$-0.806016\pi$
$997$	−7.81770	+	7.81770i	−0.247589	+	0.247589i	0.572391	+	0.819981i	$0.306016\pi$
$998$		0			0
$999$	−9.71556			−0.307387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.1663.1	yes	12
4.3	odd	2		1920.2.w.j.1663.4	yes	12
5.2	odd	4		1920.2.w.j.127.4	yes	12
8.3	odd	2		1920.2.w.l.1663.3	yes	12
8.5	even	2		1920.2.w.k.1663.6	yes	12
20.7	even	4	inner	1920.2.w.i.127.1	✓	12
40.27	even	4		1920.2.w.k.127.6	yes	12
40.37	odd	4		1920.2.w.l.127.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.1	✓	12	20.7	even	4	inner
1920.2.w.i.1663.1	yes	12	1.1	even	1	trivial
1920.2.w.j.127.4	yes	12	5.2	odd	4
1920.2.w.j.1663.4	yes	12	4.3	odd	2
1920.2.w.k.127.6	yes	12	40.27	even	4
1920.2.w.k.1663.6	yes	12	8.5	even	2
1920.2.w.l.127.3	yes	12	40.37	odd	4
1920.2.w.l.1663.3	yes	12	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80858 + 1.31492i) q^{5} +(-3.60601 - 3.60601i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.80858 + 1.31492i) q^{5} +(-3.60601 - 3.60601i) q^{7} -1.00000i q^{9} -3.09967i q^{11} +(0.859584 + 0.859584i) q^{13} +(0.349069 - 2.20865i) q^{15} +(0.342087 - 0.342087i) q^{17} +4.33324 q^{19} +5.09967 q^{21} +(-4.66545 + 4.66545i) q^{23} +(1.54195 - 4.75630i) q^{25} +(0.707107 + 0.707107i) q^{27} +1.52059i q^{29} -8.74220i q^{31} +(2.19180 + 2.19180i) q^{33} +(11.2634 + 1.78014i) q^{35} +(-6.86993 + 6.86993i) q^{37} -1.21564 q^{39} -8.60830 q^{41} +(0.517497 - 0.517497i) q^{43} +(1.31492 + 1.80858i) q^{45} +(7.53389 + 7.53389i) q^{47} +19.0066i q^{49} +0.483785i q^{51} +(2.39166 + 2.39166i) q^{53} +(4.07583 + 5.60601i) q^{55} +(-3.06406 + 3.06406i) q^{57} +6.26279 q^{59} +12.4864 q^{61} +(-3.60601 + 3.60601i) q^{63} +(-2.68492 - 0.424341i) q^{65} +(0.431271 + 0.431271i) q^{67} -6.59795i q^{69} -0.121941i q^{71} +(1.61407 + 1.61407i) q^{73} +(2.27289 + 4.45353i) q^{75} +(-11.1774 + 11.1774i) q^{77} -16.5190 q^{79} -1.00000 q^{81} +(-6.11235 + 6.11235i) q^{83} +(-0.168874 + 1.06851i) q^{85} +(-1.07522 - 1.07522i) q^{87} +5.61174i q^{89} -6.19934i q^{91} +(6.18167 + 6.18167i) q^{93} +(-7.83703 + 5.69789i) q^{95} +(-3.89074 + 3.89074i) q^{97} -3.09967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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