LMFDB - Embedded newform 448.4.p.h.255.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(255,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("448.255");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{44} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.2
Root			$-1.75840 - 2.21540i$ of defining polynomial
Character	$\chi$	$=$	448.255
Dual form			448.4.p.h.383.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.44104 + 5.96006i) q^{3} +(4.17670 - 2.41142i) q^{5} +(5.03893 - 17.8216i) q^{7} +(-10.1816 - 17.6350i) q^{9} +(-36.6380 - 21.1529i) q^{11} -3.39776i q^{13} +33.1912i q^{15} +(101.660 + 58.6935i) q^{17} +(45.5858 + 78.9570i) q^{19} +(88.8786 + 91.3572i) q^{21} +(-147.782 + 85.3222i) q^{23} +(-50.8701 + 88.1096i) q^{25} -45.6757 q^{27} +131.473 q^{29} +(-5.70011 + 9.87288i) q^{31} +(252.146 - 145.576i) q^{33} +(-21.9293 - 86.5865i) q^{35} +(-59.2181 - 102.569i) q^{37} +(20.2508 + 11.6918i) q^{39} +109.956i q^{41} +82.5542i q^{43} +(-85.0507 - 49.1040i) q^{45} +(36.7384 + 63.6328i) q^{47} +(-292.218 - 179.603i) q^{49} +(-699.634 + 403.934i) q^{51} +(-87.2160 + 151.062i) q^{53} -204.035 q^{55} -627.451 q^{57} +(-166.628 + 288.607i) q^{59} +(-472.266 + 272.663i) q^{61} +(-365.587 + 92.5901i) q^{63} +(-8.19342 - 14.1914i) q^{65} +(516.318 + 298.096i) q^{67} -1174.39i q^{69} +384.641i q^{71} +(187.557 + 108.286i) q^{73} +(-350.092 - 606.378i) q^{75} +(-561.595 + 546.359i) q^{77} +(-868.356 + 501.346i) q^{79} +(432.074 - 748.374i) q^{81} -459.471 q^{83} +566.139 q^{85} +(-452.403 + 783.585i) q^{87} +(-771.258 + 445.286i) q^{89} +(-60.5534 - 17.1210i) q^{91} +(-39.2287 - 67.9460i) q^{93} +(380.797 + 219.853i) q^{95} +282.888i q^{97} +861.479i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5} - 56 q^{9} - 6 q^{17} - 238 q^{21} - 36 q^{25} + 352 q^{29} + 30 q^{33} - 258 q^{37} + 504 q^{45} - 644 q^{49} - 570 q^{53} + 1452 q^{57} - 294 q^{61} - 124 q^{65} + 966 q^{73} + 378 q^{77}+ \cdots + 306 q^{93}+O(q^{100}) $ 20 * q + 6 * q^5 - 56 * q^9 - 6 * q^17 - 238 * q^21 - 36 * q^25 + 352 * q^29 + 30 * q^33 - 258 * q^37 + 504 * q^45 - 644 * q^49 - 570 * q^53 + 1452 * q^57 - 294 * q^61 - 124 * q^65 + 966 * q^73 + 378 * q^77 - 1262 * q^81 + 2980 * q^85 - 3186 * q^89 + 306 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.44104	+	5.96006i	−0.662229	+	1.14701i	0.317800	+	0.948158i	$0.397056\pi$
$3$	−3.44104	+	5.96006i	−0.662229	+	1.14701i	−0.980029	+	0.198856i	$0.936277\pi$
$4$		0			0
$5$	4.17670	−	2.41142i	0.373576	−	0.215684i	−0.301444	−	0.953484i	$-0.597469\pi$
$5$	4.17670	−	2.41142i	0.373576	−	0.215684i	0.675020	+	0.737800i	$0.264135\pi$
$6$		0			0
$7$	5.03893	−	17.8216i	0.272077	−	0.962276i
$7$	5.03893	−	17.8216i	0.272077	−	0.962276i
$8$		0			0
$9$	−10.1816	−	17.6350i	−0.377094	−	0.653147i
$10$		0			0
$11$	−36.6380	−	21.1529i	−1.00425	−	0.579805i	−0.0947480	−	0.995501i	$-0.530205\pi$
$11$	−36.6380	−	21.1529i	−1.00425	−	0.579805i	−0.909503	+	0.415696i	$0.863538\pi$
$12$		0			0
$13$		−	3.39776i		−	0.0724898i	−0.999343	−	0.0362449i	$-0.988460\pi$
$13$		−	3.39776i		−	0.0724898i	0.999343	−	0.0362449i	$-0.0115396\pi$
$14$		0			0
$15$			33.1912i			0.571329i
$16$		0			0
$17$	101.660	+	58.6935i	1.45036	+	0.837369i	0.998502	−	0.0547188i	$-0.0174262\pi$
$17$	101.660	+	58.6935i	1.45036	+	0.837369i	0.451863	+	0.892087i	$0.350760\pi$
$18$		0			0
$19$	45.5858	+	78.9570i	0.550427	+	0.953367i	0.998244	+	0.0592419i	$0.0188683\pi$
$19$	45.5858	+	78.9570i	0.550427	+	0.953367i	−0.447817	+	0.894125i	$0.647798\pi$
$20$		0			0
$21$	88.8786	+	91.3572i	0.923567	+	0.949322i
$22$		0			0
$23$	−147.782	+	85.3222i	−1.33977	+	0.773518i	−0.986773	−	0.162105i	$-0.948172\pi$
$23$	−147.782	+	85.3222i	−1.33977	+	0.773518i	−0.352999	+	0.935624i	$0.614838\pi$
$24$		0			0
$25$	−50.8701	+	88.1096i	−0.406961	+	0.704877i
$26$		0			0
$27$	−45.6757			−0.325566
$28$		0			0
$29$	131.473			0.841857			0.420928	−	0.907094i	$-0.361704\pi$
$29$	131.473			0.841857			0.420928	+	0.907094i	$0.361704\pi$
$30$		0			0
$31$	−5.70011	+	9.87288i	−0.0330249	+	0.0572007i	−0.882065	−	0.471127i	$-0.843847\pi$
$31$	−5.70011	+	9.87288i	−0.0330249	+	0.0572007i	0.849041	+	0.528328i	$0.177181\pi$
$32$		0			0
$33$	252.146	−	145.576i	1.33009	−	0.767927i
$34$		0			0
$35$	−21.9293	−	86.5865i	−0.105906	−	0.418166i
$36$		0			0
$37$	−59.2181	−	102.569i	−0.263119	−	0.455735i	0.703950	−	0.710249i	$-0.251418\pi$
$37$	−59.2181	−	102.569i	−0.263119	−	0.455735i	−0.967069	+	0.254514i	$0.918085\pi$
$38$		0			0
$39$	20.2508	+	11.6918i	0.0831469	+	0.0480049i
$40$		0			0
$41$			109.956i			0.418833i	0.977826	+	0.209417i	$0.0671565\pi$
$41$			109.956i			0.418833i	−0.977826	+	0.209417i	$0.932844\pi$
$42$		0			0
$43$			82.5542i			0.292777i	0.989227	+	0.146388i	$0.0467649\pi$
$43$			82.5542i			0.292777i	−0.989227	+	0.146388i	$0.953235\pi$
$44$		0			0
$45$	−85.0507	−	49.1040i	−0.281747	−	0.162667i
$46$		0			0
$47$	36.7384	+	63.6328i	0.114018	+	0.197485i	0.917387	−	0.397997i	$-0.130294\pi$
$47$	36.7384	+	63.6328i	0.114018	+	0.197485i	−0.803369	+	0.595482i	$0.796961\pi$
$48$		0			0
$49$	−292.218	−	179.603i	−0.851949	−	0.523625i
$50$		0			0
$51$	−699.634	+	403.934i	−1.92095	+	1.10906i
$52$		0			0
$53$	−87.2160	+	151.062i	−0.226038	+	0.391510i	−0.956630	−	0.291304i	$-0.905911\pi$
$53$	−87.2160	+	151.062i	−0.226038	+	0.391510i	0.730592	+	0.682814i	$0.239244\pi$
$54$		0			0
$55$	−204.035			−0.500219
$56$		0			0
$57$	−627.451			−1.45803
$58$		0			0
$59$	−166.628	+	288.607i	−0.367679	+	0.636839i	−0.989202	−	0.146557i	$-0.953181\pi$
$59$	−166.628	+	288.607i	−0.367679	+	0.636839i	0.621523	+	0.783396i	$0.286514\pi$
$60$		0			0
$61$	−472.266	+	272.663i	−0.991271	+	0.572310i	−0.905654	−	0.424018i	$-0.860619\pi$
$61$	−472.266	+	272.663i	−0.991271	+	0.572310i	−0.0856167	+	0.996328i	$0.527286\pi$
$62$		0			0
$63$	−365.587	+	92.5901i	−0.731106	+	0.185163i
$64$		0			0
$65$	−8.19342	−	14.1914i	−0.0156349	−	0.0270805i
$66$		0			0
$67$	516.318	+	298.096i	0.941466	+	0.543556i	0.890420	−	0.455141i	$-0.150411\pi$
$67$	516.318	+	298.096i	0.941466	+	0.543556i	0.0510465	+	0.998696i	$0.483744\pi$
$68$		0			0
$69$		−	1174.39i		−	2.04898i
$70$		0			0
$71$			384.641i			0.642937i	0.946920	+	0.321468i	$0.104176\pi$
$71$			384.641i			0.642937i	−0.946920	+	0.321468i	$0.895824\pi$
$72$		0			0
$73$	187.557	+	108.286i	0.300710	+	0.173615i	0.642762	−	0.766066i	$-0.277788\pi$
$73$	187.557	+	108.286i	0.300710	+	0.173615i	−0.342052	+	0.939681i	$0.611122\pi$
$74$		0			0
$75$	−350.092	−	606.378i	−0.539002	−	0.933580i
$76$		0			0
$77$	−561.595	+	546.359i	−0.831165	+	0.808615i
$78$		0			0
$79$	−868.356	+	501.346i	−1.23668	+	0.713997i	−0.968414	−	0.249347i	$-0.919784\pi$
$79$	−868.356	+	501.346i	−1.23668	+	0.713997i	−0.268266	+	0.963345i	$0.586451\pi$
$80$		0			0
$81$	432.074	−	748.374i	0.592694	−	1.02658i
$82$		0			0
$83$	−459.471			−0.607632			−0.303816	−	0.952731i	$-0.598261\pi$
$83$	−459.471			−0.607632			−0.303816	+	0.952731i	$0.598261\pi$
$84$		0			0
$85$	566.139			0.722428
$86$		0			0
$87$	−452.403	+	783.585i	−0.557502	+	0.965622i
$88$		0			0
$89$	−771.258	+	445.286i	−0.918575	+	0.530340i	−0.883180	−	0.469034i	$-0.844602\pi$
$89$	−771.258	+	445.286i	−0.918575	+	0.530340i	−0.0353951	+	0.999373i	$0.511269\pi$
$90$		0			0
$91$	−60.5534	−	17.1210i	−0.0697552	−	0.0197228i
$92$		0			0
$93$	−39.2287	−	67.9460i	−0.0437400	−	0.0757600i
$94$		0			0
$95$	380.797	+	219.853i	0.411252	+	0.237437i
$96$		0			0
$97$			282.888i			0.296113i	0.988979	+	0.148056i	$0.0473017\pi$
$97$			282.888i			0.296113i	−0.988979	+	0.148056i	$0.952698\pi$
$98$		0			0
$99$			861.479i			0.874565i
$100$		0			0
$101$	696.516	+	402.134i	0.686197	+	0.396176i	0.802186	−	0.597074i	$-0.203670\pi$
$101$	696.516	+	402.134i	0.686197	+	0.396176i	−0.115988	+	0.993251i	$0.537004\pi$
$102$		0			0
$103$	−887.054	−	1536.42i	−0.848583	−	1.46979i	−0.882473	−	0.470363i	$-0.844123\pi$
$103$	−887.054	−	1536.42i	−0.848583	−	1.46979i	0.0338902	−	0.999426i	$-0.489210\pi$
$104$		0			0
$105$	591.520	+	167.248i	0.549776	+	0.155445i
$106$		0			0
$107$	−64.5675	+	37.2781i	−0.0583362	+	0.0336804i	−0.528884	−	0.848694i	$-0.677390\pi$
$107$	−64.5675	+	37.2781i	−0.0583362	+	0.0336804i	0.470548	+	0.882374i	$0.344056\pi$
$108$		0			0
$109$	38.8638	−	67.3141i	0.0341512	−	0.0591516i	−0.848445	−	0.529284i	$-0.822461\pi$
$109$	38.8638	−	67.3141i	0.0341512	−	0.0591516i	0.882596	+	0.470133i	$0.155794\pi$
$110$		0			0
$111$	815.089			0.696980
$112$		0			0
$113$	1026.99			0.854969			0.427484	−	0.904023i	$-0.359400\pi$
$113$	1026.99			0.854969			0.427484	+	0.904023i	$0.359400\pi$
$114$		0			0
$115$	−411.496	+	712.732i	−0.333671	+	0.577935i
$116$		0			0
$117$	−59.9193	+	34.5944i	−0.0473465	+	0.0273355i
$118$		0			0
$119$	1558.27	−	1515.99i	1.20039	−	1.16782i
$120$		0			0
$121$	229.394	+	397.322i	0.172347	+	0.298514i
$122$		0			0
$123$	−655.342	−	378.362i	−0.480408	−	0.277364i
$124$		0			0
$125$			1093.53i			0.782468i
$126$		0			0
$127$			1645.64i			1.14982i	0.818217	+	0.574909i	$0.194963\pi$
$127$			1645.64i			1.14982i	−0.818217	+	0.574909i	$0.805037\pi$
$128$		0			0
$129$	−492.028	−	284.072i	−0.335819	−	0.193885i
$130$		0			0
$131$	−381.520	−	660.812i	−0.254455	−	0.440729i	0.710293	−	0.703907i	$-0.248563\pi$
$131$	−381.520	−	660.812i	−0.254455	−	0.440729i	−0.964747	+	0.263178i	$0.915229\pi$
$132$		0			0
$133$	1636.84	−	414.554i	1.06716	−	0.270273i
$134$		0			0
$135$	−190.774	+	110.143i	−0.121624	+	0.0702195i
$136$		0			0
$137$	−361.462	+	626.070i	−0.225414	+	0.390429i	−0.956444	−	0.291917i	$-0.905707\pi$
$137$	−361.462	+	626.070i	−0.225414	+	0.390429i	0.731029	+	0.682346i	$0.239040\pi$
$138$		0			0
$139$	1639.34			1.00034			0.500168	−	0.865928i	$-0.333271\pi$
$139$	1639.34			1.00034			0.500168	+	0.865928i	$0.333271\pi$
$140$		0			0
$141$	−505.674			−0.302024
$142$		0			0
$143$	−71.8725	+	124.487i	−0.0420300	+	0.0727980i
$144$		0			0
$145$	549.122	−	317.036i	0.314497	−	0.181575i
$146$		0			0
$147$	2075.98	−	1123.62i	1.16479	−	0.630437i
$148$		0			0
$149$	30.1479	+	52.2177i	0.0165759	+	0.0287103i	0.874194	−	0.485576i	$-0.161390\pi$
$149$	30.1479	+	52.2177i	0.0165759	+	0.0287103i	−0.857618	+	0.514286i	$0.828057\pi$
$150$		0			0
$151$	816.384	+	471.339i	0.439976	+	0.254020i	0.703587	−	0.710609i	$-0.251580\pi$
$151$	816.384	+	471.339i	0.439976	+	0.254020i	−0.263611	+	0.964629i	$0.584914\pi$
$152$		0			0
$153$		−	2390.36i		−	1.26307i
$154$		0			0
$155$			54.9815i			0.0284917i
$156$		0			0
$157$	−1152.45	−	665.369i	−0.585833	−	0.338231i	0.177615	−	0.984100i	$-0.443162\pi$
$157$	−1152.45	−	665.369i	−0.585833	−	0.338231i	−0.763448	+	0.645869i	$0.776495\pi$
$158$		0			0
$159$	−600.228	−	1039.62i	−0.299378	−	0.518538i
$160$		0			0
$161$	775.913	+	3063.65i	0.379817	+	1.49969i
$162$		0			0
$163$	−853.496	+	492.766i	−0.410129	+	0.236788i	−0.690845	−	0.723003i	$-0.742761\pi$
$163$	−853.496	+	492.766i	−0.410129	+	0.236788i	0.280716	+	0.959791i	$0.409428\pi$
$164$		0			0
$165$	702.092	−	1216.06i	0.331259	−	0.573758i
$166$		0			0
$167$	−1020.34			−0.472793			−0.236396	−	0.971657i	$-0.575966\pi$
$167$	−1020.34			−0.472793			−0.236396	+	0.971657i	$0.575966\pi$
$168$		0			0
$169$	2185.46			0.994745
$170$		0			0
$171$	928.269	−	1607.81i	0.415126	−	0.719019i
$172$		0			0
$173$	1538.61	−	888.319i	0.676177	−	0.390391i	−0.122236	−	0.992501i	$-0.539007\pi$
$173$	1538.61	−	888.319i	0.676177	−	0.390391i	0.798413	+	0.602110i	$0.205673\pi$
$174$		0			0
$175$	1313.92	+	1350.56i	0.567561	+	0.583389i
$176$		0			0
$177$	−1146.74	−	1986.22i	−0.486975	−	0.843466i
$178$		0			0
$179$	3863.93	+	2230.84i	1.61343	+	0.931513i	0.988568	+	0.150777i	$0.0481775\pi$
$179$	3863.93	+	2230.84i	1.61343	+	0.931513i	0.624860	+	0.780736i	$0.285156\pi$
$180$		0			0
$181$			2630.44i			1.08021i	0.841596	+	0.540107i	$0.181616\pi$
$181$			2630.44i			1.08021i	−0.841596	+	0.540107i	$0.818384\pi$
$182$		0			0
$183$		−	3752.98i		−	1.51600i
$184$		0			0
$185$	−494.673	−	285.600i	−0.196590	−	0.113501i
$186$		0			0
$187$	−2483.08	−	4300.82i	−0.971021	−	1.68186i
$188$		0			0
$189$	−230.157	+	814.014i	−0.0885790	+	0.313285i
$190$		0			0
$191$	−350.362	+	202.282i	−0.132729	+	0.0766313i	−0.564894	−	0.825163i	$-0.691083\pi$
$191$	−350.362	+	202.282i	−0.132729	+	0.0766313i	0.432165	+	0.901795i	$0.357750\pi$
$192$		0			0
$193$	−1508.72	+	2613.17i	−0.562693	+	0.974613i	0.434567	+	0.900640i	$0.356901\pi$
$193$	−1508.72	+	2613.17i	−0.562693	+	0.974613i	−0.997260	+	0.0739738i	$0.976432\pi$
$194$		0			0
$195$	112.776			0.0414156
$196$		0			0
$197$	−2643.88			−0.956185			−0.478093	−	0.878309i	$-0.658672\pi$
$197$	−2643.88			−0.956185			−0.478093	+	0.878309i	$0.658672\pi$
$198$		0			0
$199$	2077.01	−	3597.48i	0.739875	−	1.28150i	−0.212676	−	0.977123i	$-0.568218\pi$
$199$	2077.01	−	3597.48i	0.739875	−	1.28150i	0.952551	−	0.304378i	$-0.0984487\pi$
$200$		0			0
$201$	−3553.34	+	2051.52i	−1.24693	+	0.719917i
$202$		0			0
$203$	662.481	−	2343.05i	0.229049	−	0.810098i
$204$		0			0
$205$	265.149	+	459.252i	0.0903357	+	0.156466i
$206$		0			0
$207$	3009.31	+	1737.43i	1.01044	+	0.583379i
$208$		0			0
$209$		−	3857.10i		−	1.27656i
$210$		0			0
$211$			592.260i			0.193236i	0.995322	+	0.0966182i	$0.0308026\pi$
$211$			592.260i			0.193236i	−0.995322	+	0.0966182i	$0.969197\pi$
$212$		0			0
$213$	−2292.49	−	1323.57i	−0.737458	−	0.425771i
$214$		0			0
$215$	199.073	+	344.804i	0.0631473	+	0.109374i
$216$		0			0
$217$	147.228	+	151.334i	0.0460576	+	0.0473420i
$218$		0			0
$219$	−1290.78	+	745.233i	−0.398278	+	0.229946i
$220$		0			0
$221$	199.426	−	345.416i	0.0607007	−	0.105137i
$222$		0			0
$223$	3985.59			1.19684			0.598419	−	0.801183i	$-0.295796\pi$
$223$	3985.59			1.19684			0.598419	+	0.801183i	$0.295796\pi$
$224$		0			0
$225$	2071.75			0.613851
$226$		0			0
$227$	−119.836	+	207.561i	−0.0350386	+	0.0606887i	−0.883013	−	0.469349i	$-0.844489\pi$
$227$	−119.836	+	207.561i	−0.0350386	+	0.0606887i	0.847974	+	0.530037i	$0.177822\pi$
$228$		0			0
$229$	−3722.53	+	2149.20i	−1.07420	+	0.620190i	−0.929326	−	0.369261i	$-0.879611\pi$
$229$	−3722.53	+	2149.20i	−1.07420	+	0.620190i	−0.144874	+	0.989450i	$0.546278\pi$
$230$		0			0
$231$	−1323.86	−	5227.19i	−0.377072	−	1.48885i
$232$		0			0
$233$	−617.944	−	1070.31i	−0.173746	−	0.300937i	0.765981	−	0.642864i	$-0.222254\pi$
$233$	−617.944	−	1070.31i	−0.173746	−	0.300937i	−0.939727	+	0.341927i	$0.888921\pi$
$234$		0			0
$235$	306.891	+	177.184i	0.0851888	+	0.0491838i
$236$		0			0
$237$		−	6900.61i		−	1.89132i
$238$		0			0
$239$			1777.38i			0.481042i	0.970644	+	0.240521i	$0.0773183\pi$
$239$			1777.38i			0.481042i	−0.970644	+	0.240521i	$0.922682\pi$
$240$		0			0
$241$	−4291.94	−	2477.95i	−1.14717	−	0.662320i	−0.198975	−	0.980005i	$-0.563761\pi$
$241$	−4291.94	−	2477.95i	−1.14717	−	0.662320i	−0.948196	+	0.317685i	$0.897095\pi$
$242$		0			0
$243$	2356.95	+	4082.35i	0.622215	+	1.07771i
$244$		0			0
$245$	−1653.61	−	45.4889i	−0.431205	−	0.0118620i
$246$		0			0
$247$	268.277	−	154.890i	0.0691094	−	0.0399003i
$248$		0			0
$249$	1581.06	−	2738.47i	0.402392	−	0.696963i
$250$		0			0
$251$	5191.12			1.30542			0.652710	−	0.757608i	$-0.273632\pi$
$251$	5191.12			1.30542			0.652710	+	0.757608i	$0.273632\pi$
$252$		0			0
$253$	7219.27			1.79396
$254$		0			0
$255$	−1948.11	+	3374.22i	−0.478413	+	0.828636i
$256$		0			0
$257$	−3574.00	+	2063.45i	−0.867471	+	0.500835i	−0.866507	−	0.499165i	$-0.833640\pi$
$257$	−3574.00	+	2063.45i	−0.867471	+	0.500835i	−0.000963893		1.00000i	$0.500307\pi$
$258$		0			0
$259$	−2126.34	+	538.525i	−0.510132	+	0.129198i
$260$		0			0
$261$	−1338.59	−	2318.51i	−0.317459	−	0.549856i
$262$		0			0
$263$	543.813	+	313.970i	0.127502	+	0.0736131i	0.562394	−	0.826869i	$-0.309880\pi$
$263$	543.813	+	313.970i	0.127502	+	0.0736131i	−0.434893	+	0.900482i	$0.643214\pi$
$264$		0			0
$265$			841.258i			0.195012i
$266$		0			0
$267$		−	6128.99i		−	1.40483i
$268$		0			0
$269$	2662.88	+	1537.42i	0.603565	+	0.348468i	0.770443	−	0.637509i	$-0.220035\pi$
$269$	2662.88	+	1537.42i	0.603565	+	0.348468i	−0.166878	+	0.985978i	$0.553369\pi$
$270$		0			0
$271$	−944.601	−	1636.10i	−0.211736	−	0.366737i	0.740522	−	0.672032i	$-0.234578\pi$
$271$	−944.601	−	1636.10i	−0.211736	−	0.366737i	−0.952258	+	0.305295i	$0.901245\pi$
$272$		0			0
$273$	310.409	−	301.988i	0.0688162	−	0.0669492i
$274$		0			0
$275$	3727.55	−	2152.10i	0.817382	−	0.471916i
$276$		0			0
$277$	−4255.31	+	7370.41i	−0.923020	+	1.59872i	−0.128305	+	0.991735i	$0.540954\pi$
$277$	−4255.31	+	7370.41i	−0.923020	+	1.59872i	−0.794715	+	0.606983i	$0.792380\pi$
$278$		0			0
$279$	232.144			0.0498140
$280$		0			0
$281$	6028.10			1.27974			0.639869	−	0.768484i	$-0.278989\pi$
$281$	6028.10			1.27974			0.639869	+	0.768484i	$0.278989\pi$
$282$		0			0
$283$	2229.39	−	3861.42i	0.468281	−	0.811087i	−0.531062	−	0.847333i	$-0.678207\pi$
$283$	2229.39	−	3861.42i	0.468281	−	0.811087i	0.999343	+	0.0362463i	$0.0115401\pi$
$284$		0			0
$285$	−2620.68	+	1513.05i	−0.544686	+	0.314475i
$286$		0			0
$287$	1959.58	+	554.058i	0.403033	+	0.113955i
$288$		0			0
$289$	4433.35	+	7678.80i	0.902372	+	1.56295i
$290$		0			0
$291$	−1686.03	−	973.430i	−0.339646	−	0.196094i
$292$		0			0
$293$		−	3220.71i		−	0.642171i	−0.947050	−	0.321085i	$-0.895952\pi$
$293$		−	3220.71i		−	0.642171i	0.947050	−	0.321085i	$-0.104048\pi$
$294$		0			0
$295$			1607.24i			0.317210i
$296$		0			0
$297$	1673.47	+	966.176i	0.326951	+	0.188765i
$298$		0			0
$299$	289.904	+	502.129i	0.0560722	+	0.0971199i
$300$		0			0
$301$	1471.25	+	415.985i	0.281732	+	0.0796577i
$302$		0			0
$303$	−4793.48	+	2767.52i	−0.908840	+	0.524719i
$304$		0			0
$305$	−1315.01	+	2277.67i	−0.246876	+	0.427603i
$306$		0			0
$307$	−6242.78			−1.16057			−0.580284	−	0.814414i	$-0.697058\pi$
$307$	−6242.78			−1.16057			−0.580284	+	0.814414i	$0.697058\pi$
$308$		0			0
$309$	12209.6			2.24782
$310$		0			0
$311$	1146.70	−	1986.14i	0.209078	−	0.362134i	−0.742346	−	0.670016i	$-0.766287\pi$
$311$	1146.70	−	1986.14i	0.209078	−	0.362134i	0.951424	+	0.307883i	$0.0996204\pi$
$312$		0			0
$313$	4989.49	−	2880.68i	0.901030	−	0.520210i	0.0234959	−	0.999724i	$-0.492520\pi$
$313$	4989.49	−	2880.68i	0.901030	−	0.520210i	0.877534	+	0.479514i	$0.159187\pi$
$314$		0			0
$315$	−1303.68	+	1268.31i	−0.233187	+	0.226860i
$316$		0			0
$317$	2197.71	+	3806.54i	0.389386	+	0.674437i	0.992367	−	0.123319i	$-0.0393538\pi$
$317$	2197.71	+	3806.54i	0.389386	+	0.674437i	−0.602981	+	0.797756i	$0.706020\pi$
$318$		0			0
$319$	−4816.89	−	2781.03i	−0.845436	−	0.488113i
$320$		0			0
$321$		−	513.102i		−	0.0892166i
$322$		0			0
$323$			10702.4i			1.84364i
$324$		0			0
$325$	299.375	+	172.844i	0.0510964	+	0.0295005i
$326$		0			0
$327$	267.464	+	463.262i	0.0452318	+	0.0783438i
$328$		0			0
$329$	1319.16	−	334.096i	0.221057	−	0.0559857i
$330$		0			0
$331$	−5522.08	+	3188.18i	−0.916983	+	0.529420i	−0.882671	−	0.469991i	$-0.844257\pi$
$331$	−5522.08	+	3188.18i	−0.916983	+	0.529420i	−0.0343114	+	0.999411i	$0.510924\pi$
$332$		0			0
$333$	−1205.87	+	2088.62i	−0.198441	+	0.343711i
$334$		0			0
$335$	2875.34			0.468945
$336$		0			0
$337$	−5111.05			−0.826163			−0.413081	−	0.910694i	$-0.635547\pi$
$337$	−5111.05			−0.826163			−0.413081	+	0.910694i	$0.635547\pi$
$338$		0			0
$339$	−3533.93	+	6120.95i	−0.566185	+	0.980661i
$340$		0			0
$341$	417.681	−	241.148i	0.0663305	−	0.0382959i
$342$		0			0
$343$	−4673.29	+	4302.79i	−0.735667	+	0.677343i
$344$		0			0
$345$	−2831.95	−	4905.08i	−0.441933	−	0.765451i
$346$		0			0
$347$	−4393.00	−	2536.30i	−0.679621	−	0.392379i	0.120091	−	0.992763i	$-0.461681\pi$
$347$	−4393.00	−	2536.30i	−0.679621	−	0.392379i	−0.799712	+	0.600384i	$0.795015\pi$
$348$		0			0
$349$		−	11661.1i		−	1.78856i	−0.447512	−	0.894278i	$-0.647690\pi$
$349$		−	11661.1i		−	1.78856i	0.447512	−	0.894278i	$-0.352310\pi$
$350$		0			0
$351$			155.195i			0.0236003i
$352$		0			0
$353$	5552.29	+	3205.62i	0.837163	+	0.483337i	0.856299	−	0.516480i	$-0.172758\pi$
$353$	5552.29	+	3205.62i	0.837163	+	0.483337i	−0.0191356	+	0.999817i	$0.506091\pi$
$354$		0			0
$355$	927.532	+	1606.53i	0.138671	+	0.240186i
$356$		0			0
$357$	3673.34	+	14504.0i	0.544576	+	2.15023i
$358$		0			0
$359$	8337.73	−	4813.79i	1.22576	−	0.707694i	0.259621	−	0.965711i	$-0.416402\pi$
$359$	8337.73	−	4813.79i	1.22576	−	0.707694i	0.966140	+	0.258017i	$0.0830690\pi$
$360$		0			0
$361$	−726.638	+	1258.57i	−0.105939	+	0.183492i
$362$		0			0
$363$	−3157.42			−0.456533
$364$		0			0
$365$	1044.49			0.149784
$366$		0			0
$367$	−1753.92	+	3037.88i	−0.249466	+	0.432087i	−0.963378	−	0.268148i	$-0.913588\pi$
$367$	−1753.92	+	3037.88i	−0.249466	+	0.432087i	0.713912	+	0.700235i	$0.246922\pi$
$368$		0			0
$369$	1939.06	−	1119.52i	0.273560	−	0.157940i
$370$		0			0
$371$	2252.70	+	2315.52i	0.315241	+	0.324032i
$372$		0			0
$373$	−4053.65	−	7021.12i	−0.562707	−	0.974638i	−0.997259	−	0.0739909i	$-0.976426\pi$
$373$	−4053.65	−	7021.12i	−0.562707	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$374$		0			0
$375$	−6517.52	−	3762.89i	−0.897502	−	0.518173i
$376$		0			0
$377$		−	446.712i		−	0.0610261i
$378$		0			0
$379$		−	6838.23i		−	0.926798i	−0.886150	−	0.463399i	$-0.846630\pi$
$379$		−	6838.23i		−	0.926798i	0.886150	−	0.463399i	$-0.153370\pi$
$380$		0			0
$381$	−9808.11	−	5662.71i	−1.31886	−	0.761443i
$382$		0			0
$383$	6010.60	+	10410.7i	0.801899	+	1.38893i	0.918365	+	0.395735i	$0.129510\pi$
$383$	6010.60	+	10410.7i	0.801899	+	1.38893i	−0.116466	+	0.993195i	$0.537157\pi$
$384$		0			0
$385$	−1028.12	+	3636.22i	−0.136098	+	0.481348i
$386$		0			0
$387$	1455.84	−	840.530i	0.191226	−	0.110404i
$388$		0			0
$389$	1922.93	−	3330.62i	0.250634	−	0.434111i	−0.713067	−	0.701096i	$-0.752694\pi$
$389$	1922.93	−	3330.62i	0.250634	−	0.434111i	0.963701	+	0.266986i	$0.0860276\pi$
$390$		0			0
$391$	−20031.4			−2.59088
$392$		0			0
$393$	5251.31			0.674029
$394$		0			0
$395$	−2417.91	+	4187.95i	−0.307996	+	0.533464i
$396$		0			0
$397$	−10023.9	+	5787.30i	−1.26722	+	0.731628i	−0.974460	−	0.224560i	$-0.927906\pi$
$397$	−10023.9	+	5787.30i	−1.26722	+	0.731628i	−0.292756	+	0.956187i	$0.594572\pi$
$398$		0			0
$399$	−3161.68	+	11182.2i	−0.396697	+	1.40303i
$400$		0			0
$401$	−6583.03	−	11402.1i	−0.819803	−	1.41994i	−0.905827	−	0.423647i	$-0.860750\pi$
$401$	−6583.03	−	11402.1i	−0.819803	−	1.41994i	0.0860245	−	0.996293i	$-0.472584\pi$
$402$		0			0
$403$	33.5456	+	19.3676i	0.00414647	+	0.00239397i
$404$		0			0
$405$		−	4167.65i		−	0.511339i
$406$		0			0
$407$			5010.55i			0.610231i
$408$		0			0
$409$	−9916.78	−	5725.46i	−1.19891	−	0.692190i	−0.238596	−	0.971119i	$-0.576687\pi$
$409$	−9916.78	−	5725.46i	−1.19891	−	0.692190i	−0.960312	+	0.278929i	$0.910021\pi$
$410$		0			0
$411$	−2487.61	−	4308.67i	−0.298552	−	0.517107i
$412$		0			0
$413$	4303.82	+	4423.84i	0.512777	+	0.527077i
$414$		0			0
$415$	−1919.07	+	1107.98i	−0.226997	+	0.131057i
$416$		0			0
$417$	−5641.03	+	9770.55i	−0.662452	+	1.14740i
$418$		0			0
$419$	−4195.08			−0.489124			−0.244562	−	0.969634i	$-0.578644\pi$
$419$	−4195.08			−0.489124			−0.244562	+	0.969634i	$0.578644\pi$
$420$		0			0
$421$	3710.27			0.429520			0.214760	−	0.976667i	$-0.431103\pi$
$421$	3710.27			0.429520			0.214760	+	0.976667i	$0.431103\pi$
$422$		0			0
$423$	748.108	−	1295.76i	0.0859912	−	0.148941i
$424$		0			0
$425$	−10342.9	+	5971.49i	−1.18048	+	0.681552i
$426$		0			0
$427$	2479.57	+	9790.47i	0.281019	+	1.10959i
$428$		0			0
$429$	−494.633	−	856.729i	−0.0556669	−	0.0964179i
$430$		0			0
$431$	2084.43	+	1203.45i	0.232955	+	0.134497i	0.611935	−	0.790908i	$-0.290392\pi$
$431$	2084.43	+	1203.45i	0.232955	+	0.134497i	−0.378979	+	0.925405i	$0.623725\pi$
$432$		0			0
$433$		−	15138.8i		−	1.68019i	−0.542436	−	0.840097i	$-0.682498\pi$
$433$		−	15138.8i		−	1.68019i	0.542436	−	0.840097i	$-0.317502\pi$
$434$		0			0
$435$			4363.74i			0.480977i
$436$		0			0
$437$	−13473.6	−	7778.97i	−1.47489	−	0.851530i
$438$		0			0
$439$	−2889.10	−	5004.08i	−0.314099	−	0.544035i	0.665147	−	0.746713i	$-0.268369\pi$
$439$	−2889.10	−	5004.08i	−0.314099	−	0.544035i	−0.979246	+	0.202677i	$0.935036\pi$
$440$		0			0
$441$	−192.064	+	6981.90i	−0.0207390	+	0.753904i
$442$		0			0
$443$	7143.22	−	4124.14i	0.766106	−	0.442311i	−0.0653780	−	0.997861i	$-0.520825\pi$
$443$	7143.22	−	4124.14i	0.766106	−	0.442311i	0.831484	+	0.555549i	$0.187492\pi$
$444$		0			0
$445$	−2147.55	+	3719.66i	−0.228772	+	0.396244i
$446$		0			0
$447$	−414.961			−0.0439082
$448$		0			0
$449$	6493.19			0.682478			0.341239	−	0.939977i	$-0.389153\pi$
$449$	6493.19			0.682478			0.341239	+	0.939977i	$0.389153\pi$
$450$		0			0
$451$	2325.88	−	4028.55i	0.242842	−	0.420614i
$452$		0			0
$453$	−5618.42	+	3243.80i	−0.582730	+	0.336439i
$454$		0			0
$455$	−294.200	+	74.5103i	−0.0303127	+	0.00767713i
$456$		0			0
$457$	5548.06	+	9609.52i	0.567893	+	0.983620i	0.996774	+	0.0802591i	$0.0255748\pi$
$457$	5548.06	+	9609.52i	0.567893	+	0.983620i	−0.428881	+	0.903361i	$0.641092\pi$
$458$		0			0
$459$	−4643.40	−	2680.87i	−0.472190	−	0.272619i
$460$		0			0
$461$			4976.01i			0.502724i	0.967893	+	0.251362i	$0.0808784\pi$
$461$			4976.01i			0.502724i	−0.967893	+	0.251362i	$0.919122\pi$
$462$		0			0
$463$		−	16003.8i		−	1.60639i	−0.595716	−	0.803195i	$-0.703132\pi$
$463$		−	16003.8i		−	1.60639i	0.595716	−	0.803195i	$-0.296868\pi$
$464$		0			0
$465$	−327.693	−	189.194i	−0.0326804	−	0.0188681i
$466$		0			0
$467$	8856.55	+	15340.0i	0.877585	+	1.52002i	0.853984	+	0.520300i	$0.174180\pi$
$467$	8856.55	+	15340.0i	0.877585	+	1.52002i	0.0236011	+	0.999721i	$0.492487\pi$
$468$		0			0
$469$	7914.23	−	7699.52i	0.779201	−	0.758061i
$470$		0			0
$471$	7931.28	−	4579.13i	0.775911	−	0.447972i
$472$		0			0
$473$	1746.26	−	3024.62i	0.169753	−	0.294021i
$474$		0			0
$475$	−9275.82			−0.896008
$476$		0			0
$477$	3551.97			0.340951
$478$		0			0
$479$	−5044.30	+	8736.99i	−0.481169	+	0.833410i	−0.999766	−	0.0216091i	$-0.993121\pi$
$479$	−5044.30	+	8736.99i	−0.481169	+	0.833410i	0.518597	+	0.855019i	$0.326454\pi$
$480$		0			0
$481$	−348.504	+	201.209i	−0.0330362	+	0.0190735i
$482$		0			0
$483$	−20929.5	−	5917.67i	−1.97169	−	0.557481i
$484$		0			0
$485$	682.162	+	1181.54i	0.0638668	+	0.110621i
$486$		0			0
$487$	2053.73	+	1185.72i	0.191095	+	0.110329i	0.592495	−	0.805574i	$-0.298143\pi$
$487$	2053.73	+	1185.72i	0.191095	+	0.110329i	−0.401400	+	0.915903i	$0.631476\pi$
$488$		0			0
$489$		−	6782.52i		−	0.627231i
$490$		0			0
$491$		−	11069.3i		−	1.01741i	−0.860940	−	0.508706i	$-0.830124\pi$
$491$		−	11069.3i		−	1.01741i	0.860940	−	0.508706i	$-0.169876\pi$
$492$		0			0
$493$	13365.5	+	7716.59i	1.22100	+	0.704944i
$494$		0			0
$495$	2077.39	+	3598.14i	0.188630	+	0.326716i
$496$		0			0
$497$	6854.92	+	1938.18i	0.618682	+	0.174928i
$498$		0			0
$499$	9842.36	−	5682.49i	0.882975	−	0.509786i	0.0113371	−	0.999936i	$-0.496391\pi$
$499$	9842.36	−	5682.49i	0.882975	−	0.509786i	0.871638	+	0.490150i	$0.163058\pi$
$500$		0			0
$501$	3511.04	−	6081.30i	0.313097	−	0.542300i
$502$		0			0
$503$	11337.8			1.00503			0.502513	−	0.864570i	$-0.332409\pi$
$503$	11337.8			1.00503			0.502513	+	0.864570i	$0.332409\pi$
$504$		0			0
$505$	3878.86			0.341796
$506$		0			0
$507$	−7520.24	+	13025.4i	−0.658749	+	1.14099i
$508$		0			0
$509$	−2352.86	+	1358.43i	−0.204890	+	0.118293i	−0.598934	−	0.800798i	$-0.704409\pi$
$509$	−2352.86	+	1358.43i	−0.204890	+	0.118293i	0.394045	+	0.919091i	$0.371076\pi$
$510$		0			0
$511$	2874.91	−	2796.92i	0.248882	−	0.242130i
$512$		0			0
$513$	−2082.17	−	3606.42i	−0.179200	−	0.310384i
$514$		0			0
$515$	−7409.93	−	4278.12i	−0.634020	−	0.366052i
$516$		0			0
$517$		−	3108.50i		−	0.264433i
$518$		0			0
$519$			12227.0i			1.03411i
$520$		0			0
$521$	−6728.44	−	3884.67i	−0.565793	−	0.326661i	0.189674	−	0.981847i	$-0.439257\pi$
$521$	−6728.44	−	3884.67i	−0.565793	−	0.326661i	−0.755467	+	0.655186i	$0.772590\pi$
$522$		0			0
$523$	8189.91	+	14185.3i	0.684742	+	1.18601i	0.973518	+	0.228611i	$0.0734182\pi$
$523$	8189.91	+	14185.3i	0.684742	+	1.18601i	−0.288776	+	0.957397i	$0.593248\pi$
$524$		0			0
$525$	−12570.7	+	3183.71i	−1.04501	+	0.264664i
$526$		0			0
$527$	−1158.95	+	669.119i	−0.0957962	+	0.0553079i
$528$		0			0
$529$	8476.27	−	14681.3i	0.696661	−	1.20665i
$530$		0			0
$531$	6786.11			0.554599
$532$		0			0
$533$	373.602			0.0303612
$534$		0			0
$535$	−179.786	+	311.399i	−0.0145287	+	0.0251644i
$536$		0			0
$537$	−26591.9	+	15352.8i	−2.13692	+	1.23375i
$538$		0			0
$539$	6907.15	+	12761.6i	0.551970	+	1.01982i
$540$		0			0
$541$	−3348.80	−	5800.29i	−0.266129	−	0.460950i	0.701729	−	0.712444i	$-0.252412\pi$
$541$	−3348.80	−	5800.29i	−0.266129	−	0.460950i	−0.967859	+	0.251494i	$0.919078\pi$
$542$		0			0
$543$	−15677.6	−	9051.45i	−1.23902	−	0.715350i
$544$		0			0
$545$		−	374.868i		−	0.0294635i
$546$		0			0
$547$			2582.34i			0.201851i	0.994894	+	0.100926i	$0.0321804\pi$
$547$			2582.34i			0.201851i	−0.994894	+	0.100926i	$0.967820\pi$
$548$		0			0
$549$	9616.81	+	5552.27i	0.747605	+	0.431630i
$550$		0			0
$551$	5993.29	+	10380.7i	0.463380	+	0.802599i
$552$		0			0
$553$	4559.19	+	18001.7i	0.350591	+	1.38429i
$554$		0			0
$555$	3404.38	−	1965.52i	0.260375	−	0.150328i
$556$		0			0
$557$	224.120	−	388.188i	0.0170490	−	0.0295297i	−0.857375	−	0.514692i	$-0.827906\pi$
$557$	224.120	−	388.188i	0.0170490	−	0.0295297i	0.874424	+	0.485162i	$0.161240\pi$
$558$		0			0
$559$	280.499			0.0212233
$560$		0			0
$561$	34177.5			2.57215
$562$		0			0
$563$	12501.7	−	21653.5i	0.935849	−	1.62094i	0.162736	−	0.986670i	$-0.447968\pi$
$563$	12501.7	−	21653.5i	0.935849	−	1.62094i	0.773113	−	0.634268i	$-0.218698\pi$
$564$		0			0
$565$	4289.45	−	2476.52i	0.319396	−	0.184403i
$566$		0			0
$567$	−11160.0	−	11471.2i	−0.826591	−	0.849642i
$568$		0			0
$569$	3287.22	+	5693.64i	0.242193	+	0.419490i	0.961339	−	0.275369i	$-0.0888001\pi$
$569$	3287.22	+	5693.64i	0.242193	+	0.419490i	−0.719146	+	0.694859i	$0.755467\pi$
$570$		0			0
$571$	−9610.58	−	5548.67i	−0.704361	−	0.406663i	0.104608	−	0.994513i	$-0.466641\pi$
$571$	−9610.58	−	5548.67i	−0.704361	−	0.406663i	−0.808970	+	0.587850i	$0.799974\pi$
$572$		0			0
$573$		−	2784.24i		−	0.202990i
$574$		0			0
$575$		−	17361.4i		−	1.25917i
$576$		0			0
$577$	−1236.76	−	714.046i	−0.0892325	−	0.0515184i	0.454720	−	0.890635i	$-0.349739\pi$
$577$	−1236.76	−	714.046i	−0.0892325	−	0.0515184i	−0.543952	+	0.839116i	$0.683073\pi$
$578$		0			0
$579$	−10383.1	−	17984.1i	−0.745264	−	1.29083i
$580$		0			0
$581$	−2315.24	+	8188.50i	−0.165322	+	0.584710i
$582$		0			0
$583$	6390.83	−	3689.75i	0.453999	−	0.262116i
$584$		0			0
$585$	−166.843	+	288.981i	−0.0117917	+	0.0204238i
$586$		0			0
$587$	27212.3			1.91341			0.956704	−	0.291063i	$-0.0940089\pi$
$587$	27212.3			1.91341			0.956704	+	0.291063i	$0.0940089\pi$
$588$		0			0
$589$	−1039.38			−0.0727111
$590$		0			0
$591$	9097.69	−	15757.7i	0.633213	−	1.09676i
$592$		0			0
$593$	−7855.97	+	4535.65i	−0.544024	+	0.314092i	−0.746708	−	0.665152i	$-0.768367\pi$
$593$	−7855.97	+	4535.65i	−0.544024	+	0.314092i	0.202684	+	0.979244i	$0.435033\pi$
$594$		0			0
$595$	2852.73	−	10089.5i	0.196556	−	0.695175i
$596$		0			0
$597$	14294.1	+	24758.2i	0.979933	+	1.69729i
$598$		0			0
$599$	6261.35	+	3614.99i	0.427098	+	0.246585i	0.698110	−	0.715991i	$-0.254025\pi$
$599$	6261.35	+	3614.99i	0.427098	+	0.246585i	−0.271011	+	0.962576i	$0.587358\pi$
$600$		0			0
$601$		−	18772.6i		−	1.27413i	−0.770810	−	0.637065i	$-0.780148\pi$
$601$		−	18772.6i		−	1.27413i	0.770810	−	0.637065i	$-0.219852\pi$
$602$		0			0
$603$		−	12140.3i		−	0.819887i
$604$		0			0
$605$	1916.22	+	1106.33i	0.128770	+	0.0743451i
$606$		0			0
$607$	6114.97	+	10591.4i	0.408895	+	0.708226i	0.994766	−	0.102178i	$-0.0325810\pi$
$607$	6114.97	+	10591.4i	0.408895	+	0.708226i	−0.585871	+	0.810404i	$0.699248\pi$
$608$		0			0
$609$	11685.1	+	12011.0i	0.777511	+	0.799193i
$610$		0			0
$611$	216.209	−	124.828i	0.0143157	−	0.00826515i
$612$		0			0
$613$	5994.59	−	10382.9i	0.394974	−	0.684116i	−0.598124	−	0.801404i	$-0.704087\pi$
$613$	5994.59	−	10382.9i	0.394974	−	0.684116i	0.993098	+	0.117288i	$0.0374201\pi$
$614$		0			0
$615$	−3649.56			−0.239292
$616$		0			0
$617$	−1209.26			−0.0789030			−0.0394515	−	0.999221i	$-0.512561\pi$
$617$	−1209.26			−0.0789030			−0.0394515	+	0.999221i	$0.512561\pi$
$618$		0			0
$619$	9171.91	−	15886.2i	0.595558	−	1.03154i	−0.397910	−	0.917424i	$-0.630264\pi$
$619$	9171.91	−	15886.2i	0.595558	−	1.03154i	0.993468	−	0.114112i	$-0.0364022\pi$
$620$		0			0
$621$	6750.07	−	3897.15i	0.436185	−	0.251832i
$622$		0			0
$623$	4049.39	+	15988.8i	0.260410	+	1.02822i
$624$		0			0
$625$	−3721.79	−	6446.34i	−0.238195	−	0.412565i
$626$		0			0
$627$	22988.5	+	13272.4i	1.46423	+	0.845375i
$628$		0			0
$629$		−	13902.9i		−	0.881310i
$630$		0			0
$631$			7055.98i			0.445157i	0.974915	+	0.222579i	$0.0714474\pi$
$631$			7055.98i			0.445157i	−0.974915	+	0.222579i	$0.928553\pi$
$632$		0			0
$633$	−3529.91	−	2037.99i	−0.221645	−	0.127967i
$634$		0			0
$635$	3968.33	+	6873.35i	0.247997	+	0.429544i
$636$		0			0
$637$	−610.249	+	992.887i	−0.0379575	+	0.0617576i
$638$		0			0
$639$	6783.13	−	3916.24i	0.419932	−	0.242448i
$640$		0			0
$641$	−5116.60	+	8862.20i	−0.315278	+	0.546078i	−0.979497	−	0.201461i	$-0.935431\pi$
$641$	−5116.60	+	8862.20i	−0.315278	+	0.546078i	0.664218	+	0.747539i	$0.268765\pi$
$642$		0			0
$643$	−20543.5			−1.25996			−0.629982	−	0.776610i	$-0.716938\pi$
$643$	−20543.5			−1.25996			−0.629982	+	0.776610i	$0.716938\pi$
$644$		0			0
$645$	−2740.07			−0.167272
$646$		0			0
$647$	12712.8	−	22019.1i	0.772473	−	1.33796i	−0.163731	−	0.986505i	$-0.552353\pi$
$647$	12712.8	−	22019.1i	0.772473	−	1.33796i	0.936204	−	0.351457i	$-0.114314\pi$
$648$		0			0
$649$	12209.8	−	7049.33i	0.738484	−	0.426364i
$650$		0			0
$651$	−1408.58	+	356.742i	−0.0848026	+	0.0214775i
$652$		0			0
$653$	−9127.03	−	15808.5i	−0.546965	−	0.947371i	−0.998480	−	0.0551081i	$-0.982450\pi$
$653$	−9127.03	−	15808.5i	−0.546965	−	0.947371i	0.451515	−	0.892263i	$-0.350884\pi$
$654$		0			0
$655$	−3186.99	−	1840.01i	−0.190116	−	0.109764i
$656$		0			0
$657$		−	4410.08i		−	0.261877i
$658$		0			0
$659$			16252.1i			0.960683i	0.877081	+	0.480342i	$0.159487\pi$
$659$			16252.1i			0.960683i	−0.877081	+	0.480342i	$0.840513\pi$
$660$		0			0
$661$	−6622.84	−	3823.70i	−0.389711	−	0.224999i	0.292324	−	0.956319i	$-0.405571\pi$
$661$	−6622.84	−	3823.70i	−0.389711	−	0.224999i	−0.682035	+	0.731320i	$0.738905\pi$
$662$		0			0
$663$	1372.47	+	2377.18i	0.0803955	+	0.139249i
$664$		0			0
$665$	5836.95	−	5678.59i	0.340372	−	0.331137i
$666$		0			0
$667$	−19429.3	+	11217.5i	−1.12790	+	0.651191i
$668$		0			0
$669$	−13714.6	+	23754.4i	−0.792581	+	1.37279i
$670$		0			0
$671$	23070.5			1.32731
$672$		0			0
$673$	−4057.51			−0.232400			−0.116200	−	0.993226i	$-0.537071\pi$
$673$	−4057.51			−0.232400			−0.116200	+	0.993226i	$0.537071\pi$
$674$		0			0
$675$	2323.53	−	4024.47i	0.132493	−	0.229484i
$676$		0			0
$677$	−3916.39	+	2261.13i	−0.222333	+	0.128364i	−0.607030	−	0.794679i	$-0.707639\pi$
$677$	−3916.39	+	2261.13i	−0.222333	+	0.128364i	0.384697	+	0.923043i	$0.374306\pi$
$678$		0			0
$679$	5041.52	+	1425.45i	0.284942	+	0.0805653i
$680$		0			0
$681$	−824.719	−	1428.45i	−0.0464072	−	0.0803796i
$682$		0			0
$683$	12667.7	+	7313.73i	0.709690	+	0.409739i	0.810946	−	0.585121i	$-0.198953\pi$
$683$	12667.7	+	7313.73i	0.709690	+	0.409739i	−0.101257	+	0.994860i	$0.532286\pi$
$684$		0			0
$685$			3486.55i			0.194473i
$686$		0			0
$687$		−	29582.0i		−	1.64283i
$688$		0			0
$689$	513.273	+	296.339i	0.0283805	+	0.0163855i
$690$		0			0
$691$	−6100.92	−	10567.1i	−0.335875	−	0.581753i	0.647777	−	0.761830i	$-0.275699\pi$
$691$	−6100.92	−	10567.1i	−0.335875	−	0.581753i	−0.983653	+	0.180077i	$0.942365\pi$
$692$		0			0
$693$	15352.9	+	4340.93i	0.841572	+	0.237949i
$694$		0			0
$695$	6847.03	−	3953.13i	0.373702	−	0.215757i
$696$		0			0
$697$	−6453.67	+	11178.1i	−0.350718	+	0.607461i
$698$		0			0
$699$	8505.48			0.460239
$700$		0			0
$701$	31433.5			1.69362			0.846808	−	0.531898i	$-0.178521\pi$
$701$	31433.5			1.69362			0.846808	+	0.531898i	$0.178521\pi$
$702$		0			0
$703$	5399.02	−	9351.37i	0.289655	−	0.501698i
$704$		0			0
$705$	−2112.05	+	1219.39i	−0.112829	+	0.0651418i
$706$		0			0
$707$	10676.4	−	10386.7i	0.567929	−	0.552521i
$708$		0			0
$709$	−12216.8	−	21160.2i	−0.647126	−	1.12086i	−0.983806	−	0.179237i	$-0.942637\pi$
$709$	−12216.8	−	21160.2i	−0.647126	−	1.12086i	0.336680	−	0.941619i	$-0.390696\pi$
$710$		0			0
$711$	17682.4	+	10209.0i	0.932690	+	0.538489i
$712$		0			0
$713$		−	1945.39i		−	0.102181i
$714$		0			0
$715$			693.260i			0.0362608i
$716$		0			0
$717$	−10593.3	−	6116.04i	−0.551762	−	0.318560i
$718$		0			0
$719$	−14584.0	−	25260.1i	−0.756453	−	1.31021i	−0.944649	−	0.328083i	$-0.893597\pi$
$719$	−14584.0	−	25260.1i	−0.756453	−	1.31021i	0.188196	−	0.982132i	$-0.439736\pi$
$720$		0			0
$721$	−31851.3	+	8066.79i	−1.64522	+	0.416676i
$722$		0			0
$723$	29537.5	−	17053.5i	1.51938	−	0.877215i
$724$		0			0
$725$	−6688.02	+	11584.0i	−0.342603	+	0.593405i
$726$		0			0
$727$	−14802.2			−0.755135			−0.377567	−	0.925982i	$-0.623239\pi$
$727$	−14802.2			−0.755135			−0.377567	+	0.925982i	$0.623239\pi$
$728$		0			0
$729$	−9109.44			−0.462807
$730$		0			0
$731$	−4845.39	+	8392.47i	−0.245162	+	0.424633i
$732$		0			0
$733$	−24302.0	+	14030.8i	−1.22458	+	0.707010i	−0.965890	−	0.258951i	$-0.916623\pi$
$733$	−24302.0	+	14030.8i	−1.22458	+	0.707010i	−0.258687	+	0.965961i	$0.583290\pi$
$734$		0			0
$735$	5961.26	−	9699.09i	0.299162	−	0.486743i
$736$		0			0
$737$	−12611.2	−	21843.3i	−0.630312	−	1.09173i
$738$		0			0
$739$	−19623.3	−	11329.5i	−0.976798	−	0.563955i	−0.0754963	−	0.997146i	$-0.524054\pi$
$739$	−19623.3	−	11329.5i	−0.976798	−	0.563955i	−0.901302	+	0.433191i	$0.857387\pi$
$740$		0			0
$741$			2131.93i			0.105693i
$742$		0			0
$743$			36038.3i			1.77943i	0.456514	+	0.889716i	$0.349098\pi$
$743$			36038.3i			1.77943i	−0.456514	+	0.889716i	$0.650902\pi$
$744$		0			0
$745$	251.838	+	145.398i	0.0123847	+	0.00715032i
$746$		0			0
$747$	4678.13	+	8102.75i	0.229135	+	0.396873i
$748$		0			0
$749$	339.004	+	1338.54i	0.0165379	+	0.0652992i
$750$		0			0
$751$	−10031.0	+	5791.41i	−0.487399	+	0.281400i	−0.723495	−	0.690330i	$-0.757465\pi$
$751$	−10031.0	+	5791.41i	−0.487399	+	0.281400i	0.236096	+	0.971730i	$0.424132\pi$
$752$		0			0
$753$	−17862.9	+	30939.4i	−0.864487	+	1.49733i
$754$		0			0
$755$	4546.39			0.219153
$756$		0			0
$757$	−24698.1			−1.18582			−0.592910	−	0.805268i	$-0.702021\pi$
$757$	−24698.1			−1.18582			−0.592910	+	0.805268i	$0.702021\pi$
$758$		0			0
$759$	−24841.8	+	43027.3i	−1.18801	+	2.05770i
$760$		0			0
$761$	21831.6	−	12604.5i	1.03994	−	0.600410i	0.120124	−	0.992759i	$-0.461671\pi$
$761$	21831.6	−	12604.5i	1.03994	−	0.600410i	0.919816	+	0.392349i	$0.128338\pi$
$762$		0			0
$763$	−1003.81	−	1031.81i	−0.0476284	−	0.0489566i
$764$		0			0
$765$	−5764.17	−	9983.84i	−0.272424	−	0.471852i
$766$		0			0
$767$	980.617	+	566.160i	0.0461643	+	0.0266530i
$768$		0			0
$769$		−	16983.7i		−	0.796423i	−0.917294	−	0.398212i	$-0.869631\pi$
$769$		−	16983.7i		−	0.796423i	0.917294	−	0.398212i	$-0.130369\pi$
$770$		0			0
$771$		−	28401.7i		−	1.32667i
$772$		0			0
$773$	−26702.2	−	15416.5i	−1.24245	−	0.717326i	−0.272854	−	0.962056i	$-0.587967\pi$
$773$	−26702.2	−	15416.5i	−1.24245	−	0.717326i	−0.969591	+	0.244730i	$0.921301\pi$
$774$		0			0
$775$	−579.930	−	1004.47i	−0.0268796	−	0.0465569i
$776$		0			0
$777$	4107.17	−	14526.2i	0.189632	−	0.670687i
$778$		0			0
$779$	−8681.76	+	5012.41i	−0.399302	+	0.230537i
$780$		0			0
$781$	8136.30	−	14092.5i	0.372778	−	0.645670i
$782$		0			0
$783$	−6005.10			−0.274080
$784$		0			0
$785$	−6417.94			−0.291804
$786$		0			0
$787$	−7483.59	+	12962.0i	−0.338960	+	0.587095i	−0.984237	−	0.176853i	$-0.943408\pi$
$787$	−7483.59	+	12962.0i	−0.338960	+	0.587095i	0.645278	+	0.763948i	$0.276742\pi$
$788$		0			0
$789$	−3742.56	+	2160.77i	−0.168871	+	0.0974974i
$790$		0			0
$791$	5174.95	−	18302.7i	0.232617	−	0.822715i
$792$		0			0
$793$	926.443	+	1604.65i	0.0414867	+	0.0718570i
$794$		0			0
$795$	−5013.95	−	2894.80i	−0.223681	−	0.129142i
$796$		0			0
$797$		−	39166.5i		−	1.74071i	−0.492421	−	0.870357i	$-0.663888\pi$
$797$		−	39166.5i		−	1.74071i	0.492421	−	0.870357i	$-0.336112\pi$
$798$		0			0
$799$			8625.23i			0.381901i
$800$		0			0
$801$	15705.2	+	9067.41i	0.692779	+	0.399976i
$802$		0			0
$803$	−4581.13	−	7934.76i	−0.201326	−	0.348707i
$804$		0			0
$805$	10628.5	+	10924.9i	0.465349	+	0.478326i
$806$		0			0
$807$	−18326.2	+	10580.6i	−0.799396	+	0.461532i
$808$		0			0
$809$	13908.0	−	24089.3i	0.604422	−	1.04689i	−0.387720	−	0.921777i	$-0.626737\pi$
$809$	13908.0	−	24089.3i	0.604422	−	1.04689i	0.992143	−	0.125113i	$-0.0399293\pi$
$810$		0			0
$811$	20600.5			0.891962			0.445981	−	0.895042i	$-0.352855\pi$
$811$	20600.5			0.891962			0.445981	+	0.895042i	$0.352855\pi$
$812$		0			0
$813$	13001.7			0.560871
$814$		0			0
$815$	−2376.53	+	4116.28i	−0.102143	+	0.176916i
$816$		0			0
$817$	−6518.23	+	3763.30i	−0.279124	+	0.161152i
$818$		0			0
$819$	314.599	+	1242.18i	0.0134224	+	0.0529977i
$820$		0			0
$821$	8179.13	+	14166.7i	0.347690	+	0.602217i	0.985839	−	0.167696i	$-0.0536328\pi$
$821$	8179.13	+	14166.7i	0.347690	+	0.602217i	−0.638149	+	0.769913i	$0.720299\pi$
$822$		0			0
$823$	8972.43	+	5180.24i	0.380024	+	0.219407i	0.677828	−	0.735220i	$-0.262921\pi$
$823$	8972.43	+	5180.24i	0.380024	+	0.219407i	−0.297805	+	0.954627i	$0.596255\pi$
$824$		0			0
$825$			29621.9i			1.25006i
$826$		0			0
$827$			9204.30i			0.387019i	0.981098	+	0.193510i	$0.0619871\pi$
$827$			9204.30i			0.387019i	−0.981098	+	0.193510i	$0.938013\pi$
$828$		0			0
$829$	26296.5	+	15182.3i	1.10171	+	0.636071i	0.936669	−	0.350216i	$-0.113892\pi$
$829$	26296.5	+	15182.3i	1.10171	+	0.636071i	0.165039	+	0.986287i	$0.447225\pi$
$830$		0			0
$831$	−29285.4	−	50723.8i	−1.22250	−	2.11743i
$832$		0			0
$833$	−19165.4	−	35409.8i	−0.797169	−	1.47284i
$834$		0			0
$835$	−4261.66	+	2460.47i	−0.176624	+	0.101974i
$836$		0			0
$837$	260.357	−	450.951i	0.0107518	−	0.0186226i
$838$		0			0
$839$	7688.40			0.316369			0.158184	−	0.987410i	$-0.449436\pi$
$839$	7688.40			0.316369			0.158184	+	0.987410i	$0.449436\pi$
$840$		0			0
$841$	−7103.96			−0.291277
$842$		0			0
$843$	−20742.9	+	35927.8i	−0.847479	+	1.46788i
$844$		0			0
$845$	9128.00	−	5270.05i	0.371613	−	0.214551i
$846$		0			0
$847$	8236.82	−	2086.09i	0.334145	−	0.0846268i
$848$		0			0
$849$	15342.9	+	26574.6i	0.620219	+	1.07425i
$850$		0			0
$851$	17502.8	+	10105.2i	0.705039	+	0.407055i
$852$		0			0
$853$			16264.6i			0.652860i	0.945221	+	0.326430i	$0.105846\pi$
$853$			16264.6i			0.652860i	−0.945221	+	0.326430i	$0.894154\pi$
$854$		0			0
$855$		−	8953.79i		−	0.358144i
$856$		0			0
$857$	9676.46	+	5586.71i	0.385696	+	0.222682i	0.680294	−	0.732940i	$-0.261852\pi$
$857$	9676.46	+	5586.71i	0.385696	+	0.222682i	−0.294598	+	0.955621i	$0.595186\pi$
$858$		0			0
$859$	−10035.8	−	17382.6i	−0.398624	−	0.690437i	0.594932	−	0.803776i	$-0.297179\pi$
$859$	−10035.8	−	17382.6i	−0.398624	−	0.690437i	−0.993556	+	0.113339i	$0.963845\pi$
$860$		0			0
$861$	−10045.2	+	9772.69i	−0.397608	+	0.386821i
$862$		0			0
$863$	−16644.7	+	9609.81i	−0.656537	+	0.379052i	−0.790956	−	0.611873i	$-0.790416\pi$
$863$	−16644.7	+	9609.81i	−0.656537	+	0.379052i	0.134419	+	0.990925i	$0.457083\pi$
$864$		0			0
$865$	4284.22	−	7420.49i	0.168402	−	0.291681i
$866$		0			0
$867$	−61021.5			−2.39031
$868$		0			0
$869$	42419.8			1.65592
$870$		0			0
$871$	1012.86	−	1754.32i	0.0394023	−	0.0682467i
$872$		0			0
$873$	4988.72	−	2880.24i	0.193405	−	0.111662i
$874$		0			0
$875$	19488.5	+	5510.23i	0.752950	+	0.212891i
$876$		0			0
$877$	15336.1	+	26563.0i	0.590496	+	1.02277i	0.994166	+	0.107864i	$0.0344010\pi$
$877$	15336.1	+	26563.0i	0.590496	+	1.02277i	−0.403670	+	0.914905i	$0.632266\pi$
$878$		0			0
$879$	19195.6	+	11082.6i	0.736579	+	0.425264i
$880$		0			0
$881$			37453.2i			1.43227i	0.697962	+	0.716135i	$0.254091\pi$
$881$			37453.2i			1.43227i	−0.697962	+	0.716135i	$0.745909\pi$
$882$		0			0
$883$			28915.6i			1.10202i	0.834497	+	0.551012i	$0.185758\pi$
$883$			28915.6i			1.10202i	−0.834497	+	0.551012i	$0.814242\pi$
$884$		0			0
$885$	−9579.23	−	5530.57i	−0.363844	−	0.210066i
$886$		0			0
$887$	18831.9	+	32617.7i	0.712866	+	1.23472i	0.963777	+	0.266710i	$0.0859365\pi$
$887$	18831.9	+	32617.7i	0.712866	+	1.23472i	−0.250911	+	0.968010i	$0.580730\pi$
$888$		0			0
$889$	29327.9	+	8292.26i	1.10644	+	0.312838i
$890$		0			0
$891$	−31660.6	+	18279.3i	−1.19043	+	0.687294i
$892$		0			0
$893$	−3349.50	+	5801.51i	−0.125517	+	0.217402i
$894$		0			0
$895$	21518.0			0.803650
$896$		0			0
$897$	−3990.29			−0.148531
$898$		0			0
$899$	−749.408	+	1298.01i	−0.0278022	+	0.0481548i
$900$		0			0
$901$	−17732.8	+	10238.0i	−0.655676	+	0.378555i
$902$		0			0
$903$	−7541.92	+	7337.30i	−0.277939	+	0.270399i
$904$		0			0
$905$	6343.09	+	10986.6i	0.232985	+	0.403542i
$906$		0			0
$907$	18222.8	+	10520.9i	0.667119	+	0.385161i	0.794984	−	0.606630i	$-0.207479\pi$
$907$	18222.8	+	10520.9i	0.667119	+	0.385161i	−0.127865	+	0.991792i	$0.540813\pi$
$908$		0			0
$909$		−	16377.4i		−	0.597584i
$910$		0			0
$911$			9510.87i			0.345894i	0.984931	+	0.172947i	$0.0553289\pi$
$911$			9510.87i			0.345894i	−0.984931	+	0.172947i	$0.944671\pi$
$912$		0			0
$913$	16834.1	+	9719.16i	0.610215	+	0.352308i
$914$		0			0
$915$	−9050.02	−	15675.1i	−0.326978	−	0.566342i
$916$		0			0
$917$	−13699.2	+	3469.51i	−0.493333	+	0.124944i
$918$		0			0
$919$	−6898.95	+	3983.11i	−0.247634	+	0.142971i	−0.618680	−	0.785643i	$-0.712332\pi$
$919$	−6898.95	+	3983.11i	−0.247634	+	0.142971i	0.371047	+	0.928614i	$0.378999\pi$
$920$		0			0
$921$	21481.7	−	37207.4i	0.768562	−	1.33119i
$922$		0			0
$923$	1306.92			0.0466064
$924$		0			0
$925$	12049.7			0.428316
$926$		0			0
$927$	−18063.2	+	31286.3i	−0.639992	+	1.10850i
$928$		0			0
$929$	1439.51	−	831.103i	0.0508384	−	0.0293516i	−0.474365	−	0.880328i	$-0.657322\pi$
$929$	1439.51	−	831.103i	0.0508384	−	0.0293516i	0.525204	+	0.850976i	$0.323989\pi$
$930$		0			0
$931$	859.929	−	31260.1i	0.0302718	−	1.10044i
$932$		0			0
$933$	7891.67	+	13668.8i	0.276915	+	0.479631i
$934$		0			0
$935$	−20742.2	−	11975.5i	−0.725500	−	0.418867i
$936$		0			0
$937$			11523.9i			0.401783i	0.979614	+	0.200891i	$0.0643838\pi$
$937$			11523.9i			0.401783i	−0.979614	+	0.200891i	$0.935616\pi$
$938$		0			0
$939$			39650.2i			1.37799i
$940$		0			0
$941$	13692.6	+	7905.45i	0.474354	+	0.273868i	0.718061	−	0.695981i	$-0.245030\pi$
$941$	13692.6	+	7905.45i	0.474354	+	0.273868i	−0.243707	+	0.969849i	$0.578363\pi$
$942$		0			0
$943$	−9381.65	−	16249.5i	−0.323975	−	0.561141i
$944$		0			0
$945$	1001.63	+	3954.90i	0.0344795	+	0.136141i
$946$		0			0
$947$	−20479.9	+	11824.1i	−0.702752	+	0.405734i	−0.808372	−	0.588672i	$-0.799651\pi$
$947$	−20479.9	+	11824.1i	−0.702752	+	0.405734i	0.105619	+	0.994407i	$0.466317\pi$
$948$		0			0
$949$	367.929	−	637.272i	0.0125853	−	0.0217984i
$950$		0			0
$951$	−30249.6			−1.03145
$952$		0			0
$953$	23736.6			0.806825			0.403413	−	0.915018i	$-0.367824\pi$
$953$	23736.6			0.806825			0.403413	+	0.915018i	$0.367824\pi$
$954$		0			0
$955$	−975.572	+	1689.74i	−0.0330563	+	0.0572552i
$956$		0			0
$957$	33150.2	−	19139.3i	1.11974	−	0.646485i
$958$		0			0
$959$	9336.18	+	9596.54i	0.314370	+	0.323137i
$960$		0			0
$961$	14830.5	+	25687.2i	0.497819	+	0.862247i
$962$		0			0
$963$	1314.79	+	759.097i	0.0439965	+	0.0254014i
$964$		0			0
$965$			14552.6i			0.485456i
$966$		0			0
$967$			37667.0i			1.25263i	0.779571	+	0.626314i	$0.215437\pi$
$967$			37667.0i			1.25263i	−0.779571	+	0.626314i	$0.784563\pi$
$968$		0			0
$969$	−63786.8	−	36827.3i	−2.11468	−	1.22091i
$970$		0			0
$971$	−14502.0	−	25118.3i	−0.479292	−	0.830159i	0.520426	−	0.853907i	$-0.325773\pi$
$971$	−14502.0	−	25118.3i	−0.479292	−	0.830159i	−0.999718	+	0.0237484i	$0.992440\pi$
$972$		0			0
$973$	8260.51	−	29215.6i	0.272168	−	0.962600i
$974$		0			0
$975$	−2060.32	+	1189.53i	−0.0676750	+	0.0390722i
$976$		0			0
$977$	−11699.4	+	20263.9i	−0.383108	+	0.663563i	−0.991505	−	0.130070i	$-0.958480\pi$
$977$	−11699.4	+	20263.9i	−0.383108	+	0.663563i	0.608397	+	0.793633i	$0.291813\pi$
$978$		0			0
$979$	37676.5			1.22997
$980$		0			0
$981$	−1582.78			−0.0515129
$982$		0			0
$983$	5578.49	−	9662.22i	0.181003	−	0.313507i	−0.761219	−	0.648495i	$-0.775399\pi$
$983$	5578.49	−	9662.22i	0.181003	−	0.313507i	0.942222	+	0.334988i	$0.108732\pi$
$984$		0			0
$985$	−11042.7	+	6375.50i	−0.357208	+	0.206234i
$986$		0			0
$987$	−2548.05	+	9011.91i	−0.0821737	+	0.290631i
$988$		0			0
$989$	−7043.71	−	12200.1i	−0.226468	−	0.392254i
$990$		0			0
$991$	−49165.5	−	28385.7i	−1.57598	−	0.909892i	−0.995412	−	0.0956788i	$-0.969498\pi$
$991$	−49165.5	−	28385.7i	−1.57598	−	0.909892i	−0.580566	−	0.814213i	$-0.697169\pi$
$992$		0			0
$993$		−	43882.6i		−	1.40239i
$994$		0			0
$995$		−	20034.2i		−	0.638317i
$996$		0			0
$997$	−8650.18	−	4994.18i	−0.274778	−	0.158643i	0.356279	−	0.934380i	$-0.384045\pi$
$997$	−8650.18	−	4994.18i	−0.274778	−	0.158643i	−0.631057	+	0.775736i	$0.717379\pi$
$998$		0			0
$999$	2704.83	+	4684.90i	0.0856627	+	0.148372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.p.h.255.2		20
4.3	odd	2	inner	448.4.p.h.255.9		20
7.5	odd	6	inner	448.4.p.h.383.9		20
8.3	odd	2		28.4.f.a.3.3	✓	20
8.5	even	2		28.4.f.a.3.5	yes	20
28.19	even	6	inner	448.4.p.h.383.2		20
56.3	even	6		196.4.d.b.195.17		20
56.5	odd	6		28.4.f.a.19.3	yes	20
56.11	odd	6		196.4.d.b.195.18		20
56.13	odd	2		196.4.f.d.31.5		20
56.19	even	6		28.4.f.a.19.5	yes	20
56.27	even	2		196.4.f.d.31.3		20
56.37	even	6		196.4.f.d.19.3		20
56.45	odd	6		196.4.d.b.195.20		20
56.51	odd	6		196.4.f.d.19.5		20
56.53	even	6		196.4.d.b.195.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.3	✓	20	8.3	odd	2
28.4.f.a.3.5	yes	20	8.5	even	2
28.4.f.a.19.3	yes	20	56.5	odd	6
28.4.f.a.19.5	yes	20	56.19	even	6
196.4.d.b.195.17		20	56.3	even	6
196.4.d.b.195.18		20	56.11	odd	6
196.4.d.b.195.19		20	56.53	even	6
196.4.d.b.195.20		20	56.45	odd	6
196.4.f.d.19.3		20	56.37	even	6
196.4.f.d.19.5		20	56.51	odd	6
196.4.f.d.31.3		20	56.27	even	2
196.4.f.d.31.5		20	56.13	odd	2
448.4.p.h.255.2		20	1.1	even	1	trivial
448.4.p.h.255.9		20	4.3	odd	2	inner
448.4.p.h.383.2		20	28.19	even	6	inner
448.4.p.h.383.9		20	7.5	odd	6	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.44104 + 5.96006i) q^{3} +(4.17670 - 2.41142i) q^{5} +(5.03893 - 17.8216i) q^{7} +(-10.1816 - 17.6350i) q^{9} +(-36.6380 - 21.1529i) q^{11} -3.39776i q^{13} +33.1912i q^{15} +(101.660 + 58.6935i) q^{17} +(45.5858 + 78.9570i) q^{19} +(88.8786 + 91.3572i) q^{21} +(-147.782 + 85.3222i) q^{23} +(-50.8701 + 88.1096i) q^{25} -45.6757 q^{27} +131.473 q^{29} +(-5.70011 + 9.87288i) q^{31} +(252.146 - 145.576i) q^{33} +(-21.9293 - 86.5865i) q^{35} +(-59.2181 - 102.569i) q^{37} +(20.2508 + 11.6918i) q^{39} +109.956i q^{41} +82.5542i q^{43} +(-85.0507 - 49.1040i) q^{45} +(36.7384 + 63.6328i) q^{47} +(-292.218 - 179.603i) q^{49} +(-699.634 + 403.934i) q^{51} +(-87.2160 + 151.062i) q^{53} -204.035 q^{55} -627.451 q^{57} +(-166.628 + 288.607i) q^{59} +(-472.266 + 272.663i) q^{61} +(-365.587 + 92.5901i) q^{63} +(-8.19342 - 14.1914i) q^{65} +(516.318 + 298.096i) q^{67} -1174.39i q^{69} +384.641i q^{71} +(187.557 + 108.286i) q^{73} +(-350.092 - 606.378i) q^{75} +(-561.595 + 546.359i) q^{77} +(-868.356 + 501.346i) q^{79} +(432.074 - 748.374i) q^{81} -459.471 q^{83} +566.139 q^{85} +(-452.403 + 783.585i) q^{87} +(-771.258 + 445.286i) q^{89} +(-60.5534 - 17.1210i) q^{91} +(-39.2287 - 67.9460i) q^{93} +(380.797 + 219.853i) q^{95} +282.888i q^{97} +861.479i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 56 q^{9} - 6 q^{17} - 238 q^{21} - 36 q^{25} + 352 q^{29} + 30 q^{33} - 258 q^{37} + 504 q^{45} - 644 q^{49} - 570 q^{53} + 1452 q^{57} - 294 q^{61} - 124 q^{65} + 966 q^{73} + 378 q^{77}+ \cdots + 306 q^{93}+O(q^{100}) \) 20 * q + 6 * q^5 - 56 * q^9 - 6 * q^17 - 238 * q^21 - 36 * q^25 + 352 * q^29 + 30 * q^33 - 258 * q^37 + 504 * q^45 - 644 * q^49 - 570 * q^53 + 1452 * q^57 - 294 * q^61 - 124 * q^65 + 966 * q^73 + 378 * q^77 - 1262 * q^81 + 2980 * q^85 - 3186 * q^89 + 306 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more