LMFDB - Embedded newform 448.4.p.h.383.4

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			383.4
Root			$-2.26510 - 1.69390i$ of defining polynomial
Character	$\chi$	$=$	448.383
Dual form			448.4.p.h.255.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67134 - 2.89484i) q^{3} +(15.9583 + 9.21354i) q^{5} +(15.4841 - 10.1609i) q^{7} +(7.91327 - 13.7062i) q^{9} +(35.6274 - 20.5695i) q^{11} +24.8455i q^{13} -61.5957i q^{15} +(-41.3826 + 23.8923i) q^{17} +(30.9150 - 53.5464i) q^{19} +(-55.2933 - 27.8416i) q^{21} +(64.3994 + 37.1810i) q^{23} +(107.279 + 185.812i) q^{25} -143.155 q^{27} -28.8513 q^{29} +(-11.5660 - 20.0328i) q^{31} +(-119.091 - 68.7571i) q^{33} +(340.717 - 19.4877i) q^{35} +(-51.8900 + 89.8761i) q^{37} +(71.9237 - 41.5252i) q^{39} -96.1780i q^{41} +195.747i q^{43} +(252.565 - 145.818i) q^{45} +(-89.8186 + 155.570i) q^{47} +(136.513 - 314.664i) q^{49} +(138.329 + 79.8641i) q^{51} +(218.681 + 378.767i) q^{53} +758.071 q^{55} -206.678 q^{57} +(-286.640 - 496.475i) q^{59} +(-368.470 - 212.736i) q^{61} +(-16.7374 - 292.633i) q^{63} +(-228.915 + 396.492i) q^{65} +(728.093 - 420.365i) q^{67} -248.568i q^{69} -1179.04i q^{71} +(716.185 - 413.489i) q^{73} +(358.597 - 621.109i) q^{75} +(342.652 - 680.505i) q^{77} +(282.007 + 162.817i) q^{79} +(25.6023 + 44.3445i) q^{81} +507.854 q^{83} -880.530 q^{85} +(48.2202 + 83.5198i) q^{87} +(-176.826 - 102.090i) q^{89} +(252.452 + 384.709i) q^{91} +(-38.6612 + 66.9632i) q^{93} +(986.704 - 569.674i) q^{95} +1116.33i q^{97} -651.087i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	0.659179	−	0.751986i	$-0.270904\pi$
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	−0.980828	+	0.194873i	$0.937570\pi$
$4$		0			0
$5$	15.9583	+	9.21354i	1.42736	+	0.824084i	0.996911	−	0.0785333i	$-0.0250237\pi$
$5$	15.9583	+	9.21354i	1.42736	+	0.824084i	0.430444	+	0.902617i	$0.358357\pi$
$6$		0			0
$7$	15.4841	−	10.1609i	0.836061	−	0.548636i
$7$	15.4841	−	10.1609i	0.836061	−	0.548636i
$8$		0			0
$9$	7.91327	−	13.7062i	0.293084	−	0.507636i
$10$		0			0
$11$	35.6274	−	20.5695i	0.976551	−	0.563812i	0.0753237	−	0.997159i	$-0.476001\pi$
$11$	35.6274	−	20.5695i	0.976551	−	0.563812i	0.901227	+	0.433347i	$0.142668\pi$
$12$		0			0
$13$			24.8455i			0.530069i	0.964239	+	0.265035i	$0.0853834\pi$
$13$			24.8455i			0.530069i	−0.964239	+	0.265035i	$0.914617\pi$
$14$		0			0
$15$		−	61.5957i		−	1.06026i
$16$		0			0
$17$	−41.3826	+	23.8923i	−0.590398	+	0.340866i	−0.765255	−	0.643728i	$-0.777387\pi$
$17$	−41.3826	+	23.8923i	−0.590398	+	0.340866i	0.174857	+	0.984594i	$0.444054\pi$
$18$		0			0
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	−0.616785	−	0.787132i	$-0.711565\pi$
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	0.990069	+	0.140585i	$0.0448984\pi$
$20$		0			0
$21$	−55.2933	−	27.8416i	−0.574570	−	0.289312i
$22$		0			0
$23$	64.3994	+	37.1810i	0.583835	+	0.337077i	0.762656	−	0.646804i	$-0.223895\pi$
$23$	64.3994	+	37.1810i	0.583835	+	0.337077i	−0.178821	+	0.983882i	$0.557228\pi$
$24$		0			0
$25$	107.279	+	185.812i	0.858229	+	1.48650i
$26$		0			0
$27$	−143.155			−1.02038
$28$		0			0
$29$	−28.8513			−0.184743			−0.0923715	−	0.995725i	$-0.529445\pi$
$29$	−28.8513			−0.184743			−0.0923715	+	0.995725i	$0.529445\pi$
$30$		0			0
$31$	−11.5660	−	20.0328i	−0.0670099	−	0.116065i	0.830574	−	0.556908i	$-0.188013\pi$
$31$	−11.5660	−	20.0328i	−0.0670099	−	0.116065i	−0.897584	+	0.440844i	$0.854679\pi$
$32$		0			0
$33$	−119.091	−	68.7571i	−0.628213	−	0.362699i
$34$		0			0
$35$	340.717	−	19.4877i	1.64548	−	0.0941147i
$36$		0			0
$37$	−51.8900	+	89.8761i	−0.230558	+	0.399339i	−0.957973	−	0.286860i	$-0.907389\pi$
$37$	−51.8900	+	89.8761i	−0.230558	+	0.399339i	0.727414	+	0.686199i	$0.240722\pi$
$38$		0			0
$39$	71.9237	−	41.5252i	0.295308	−	0.170496i
$40$		0			0
$41$		−	96.1780i		−	0.366353i	−0.983080	−	0.183177i	$-0.941362\pi$
$41$		−	96.1780i		−	0.366353i	0.983080	−	0.183177i	$-0.0586380\pi$
$42$		0			0
$43$			195.747i			0.694213i	0.937826	+	0.347107i	$0.112836\pi$
$43$			195.747i			0.694213i	−0.937826	+	0.347107i	$0.887164\pi$
$44$		0			0
$45$	252.565	−	145.818i	0.836670	−	0.483052i
$46$		0			0
$47$	−89.8186	+	155.570i	−0.278753	+	0.482815i	−0.971075	−	0.238774i	$-0.923254\pi$
$47$	−89.8186	+	155.570i	−0.278753	+	0.482815i	0.692322	+	0.721589i	$0.256588\pi$
$48$		0			0
$49$	136.513	−	314.664i	0.397996	−	0.917387i
$50$		0			0
$51$	138.329	+	79.8641i	0.379802	+	0.219279i
$52$		0			0
$53$	218.681	+	378.767i	0.566758	+	0.981654i	0.996884	+	0.0788851i	$0.0251360\pi$
$53$	218.681	+	378.767i	0.566758	+	0.981654i	−0.430125	+	0.902769i	$0.641531\pi$
$54$		0			0
$55$	758.071			1.85851
$56$		0			0
$57$	−206.678			−0.480266
$58$		0			0
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	−0.987040	−	0.160477i	$-0.948697\pi$
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	0.354542	−	0.935040i	$-0.384637\pi$
$60$		0			0
$61$	−368.470	−	212.736i	−0.773405	−	0.446526i	0.0606829	−	0.998157i	$-0.480672\pi$
$61$	−368.470	−	212.736i	−0.773405	−	0.446526i	−0.834088	+	0.551632i	$0.814005\pi$
$62$		0			0
$63$	−16.7374	−	292.633i	−0.0334717	−	0.585211i
$64$		0			0
$65$	−228.915	+	396.492i	−0.436822	+	0.756597i
$66$		0			0
$67$	728.093	−	420.365i	1.32762	−	0.766504i	0.342692	−	0.939448i	$-0.388661\pi$
$67$	728.093	−	420.365i	1.32762	−	0.766504i	0.984932	+	0.172944i	$0.0553281\pi$
$68$		0			0
$69$		−	248.568i		−	0.433682i
$70$		0			0
$71$		−	1179.04i		−	1.97079i	−0.170279	−	0.985396i	$-0.554467\pi$
$71$		−	1179.04i		−	1.97079i	0.170279	−	0.985396i	$-0.445533\pi$
$72$		0			0
$73$	716.185	−	413.489i	1.14826	−	0.662949i	0.199798	−	0.979837i	$-0.435971\pi$
$73$	716.185	−	413.489i	1.14826	−	0.662949i	0.948463	+	0.316888i	$0.102638\pi$
$74$		0			0
$75$	358.597	−	621.109i	0.552097	−	0.956260i
$76$		0			0
$77$	342.652	−	680.505i	0.507128	−	1.00715i
$78$		0			0
$79$	282.007	+	162.817i	0.401623	+	0.231877i	0.687184	−	0.726483i	$-0.258847\pi$
$79$	282.007	+	162.817i	0.401623	+	0.231877i	−0.285561	+	0.958361i	$0.592180\pi$
$80$		0			0
$81$	25.6023	+	44.3445i	0.0351198	+	0.0608292i
$82$		0			0
$83$	507.854			0.671617			0.335808	−	0.941930i	$-0.390991\pi$
$83$	507.854			0.671617			0.335808	+	0.941930i	$0.390991\pi$
$84$		0			0
$85$	−880.530			−1.12361
$86$		0			0
$87$	48.2202	+	83.5198i	0.0594224	+	0.102923i
$88$		0			0
$89$	−176.826	−	102.090i	−0.210601	−	0.121590i	0.390990	−	0.920395i	$-0.372133\pi$
$89$	−176.826	−	102.090i	−0.210601	−	0.121590i	−0.601591	+	0.798805i	$0.705466\pi$
$90$		0			0
$91$	252.452	+	384.709i	0.290815	+	0.443170i
$92$		0			0
$93$	−38.6612	+	66.9632i	−0.0431074	+	0.0746641i
$94$		0			0
$95$	986.704	−	569.674i	1.06562	−	0.615235i
$96$		0			0
$97$			1116.33i			1.16852i	0.811566	+	0.584261i	$0.198615\pi$
$97$			1116.33i			1.16852i	−0.811566	+	0.584261i	$0.801385\pi$
$98$		0			0
$99$		−	651.087i		−	0.660977i
$100$		0			0
$101$	3.43081	−	1.98078i	0.00337999	−	0.00195144i	−0.498309	−	0.866999i	$-0.666046\pi$
$101$	3.43081	−	1.98078i	0.00337999	−	0.00195144i	0.501689	+	0.865048i	$0.332712\pi$
$102$		0			0
$103$	−179.406	+	310.741i	−0.171626	+	0.297264i	−0.938988	−	0.343949i	$-0.888235\pi$
$103$	−179.406	+	310.741i	−0.171626	+	0.297264i	0.767363	+	0.641213i	$0.221569\pi$
$104$		0			0
$105$	−625.867	−	953.752i	−0.581699	−	0.886445i
$106$		0			0
$107$	−803.472	−	463.885i	−0.725931	−	0.419116i	0.0910010	−	0.995851i	$-0.470993\pi$
$107$	−803.472	−	463.885i	−0.725931	−	0.419116i	−0.816932	+	0.576735i	$0.804327\pi$
$108$		0			0
$109$	594.270	+	1029.31i	0.522209	+	0.904492i	0.999666	+	0.0258371i	$0.00822512\pi$
$109$	594.270	+	1029.31i	0.522209	+	0.904492i	−0.477458	+	0.878655i	$0.658442\pi$
$110$		0			0
$111$	346.903			0.296635
$112$		0			0
$113$	−662.367			−0.551418			−0.275709	−	0.961241i	$-0.588913\pi$
$113$	−662.367			−0.551418			−0.275709	+	0.961241i	$0.588913\pi$
$114$		0			0
$115$	685.137	+	1186.69i	0.555560	+	0.962258i
$116$		0			0
$117$	340.537	+	196.609i	0.269082	+	0.155355i
$118$		0			0
$119$	−398.005	+	790.434i	−0.306597	+	0.608899i
$120$		0			0
$121$	180.707	−	312.993i	0.135768	−	0.235156i
$122$		0			0
$123$	−278.420	+	160.746i	−0.204100	+	0.117837i
$124$		0			0
$125$			1650.28i			1.18084i
$126$		0			0
$127$			1496.04i			1.04529i	0.852549	+	0.522647i	$0.175055\pi$
$127$			1496.04i			1.04529i	−0.852549	+	0.522647i	$0.824945\pi$
$128$		0			0
$129$	566.657	−	327.160i	0.386755	−	0.223293i
$130$		0			0
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	0.324630	+	0.945841i	$0.394760\pi$
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	−0.981437	+	0.191783i	$0.938573\pi$
$132$		0			0
$133$	−65.3887	−	1143.24i	−0.0426310	−	0.745350i
$134$		0			0
$135$	−2284.52	−	1318.97i	−1.45644	−	0.840878i
$136$		0			0
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	0.997559	+	0.0698322i	$0.0222464\pi$
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	−0.438303	+	0.898827i	$0.644420\pi$
$138$		0			0
$139$	306.409			0.186973			0.0934867	−	0.995621i	$-0.470199\pi$
$139$	306.409			0.186973			0.0934867	+	0.995621i	$0.470199\pi$
$140$		0			0
$141$	600.469			0.358643
$142$		0			0
$143$	511.059	+	885.180i	0.298859	+	0.517639i
$144$		0			0
$145$	−460.418	−	265.822i	−0.263694	−	0.152244i
$146$		0			0
$147$	−1139.06	+	130.727i	−0.639103	+	0.0733481i
$148$		0			0
$149$	−714.928	+	1238.29i	−0.393082	+	0.680838i	−0.992854	−	0.119333i	$-0.961924\pi$
$149$	−714.928	+	1238.29i	−0.393082	+	0.680838i	0.599773	+	0.800171i	$0.295258\pi$
$150$		0			0
$151$	−1079.16	+	623.054i	−0.581595	+	0.335784i	−0.761767	−	0.647851i	$-0.775668\pi$
$151$	−1079.16	+	623.054i	−0.581595	+	0.335784i	0.180172	+	0.983635i	$0.442335\pi$
$152$		0			0
$153$			756.264i			0.399610i
$154$		0			0
$155$		−	426.254i		−	0.220887i
$156$		0			0
$157$	2201.64	−	1271.12i	1.11917	−	0.646154i	0.177982	−	0.984034i	$-0.443043\pi$
$157$	2201.64	−	1271.12i	1.11917	−	0.646154i	0.941189	+	0.337880i	$0.109710\pi$
$158$		0			0
$159$	730.980	−	1266.10i	0.364594	−	0.631496i
$160$		0			0
$161$	1374.96	−	78.6420i	0.673054	−	0.0384960i
$162$		0			0
$163$	−637.434	−	368.022i	−0.306305	−	0.176845i	0.338967	−	0.940798i	$-0.389922\pi$
$163$	−637.434	−	368.022i	−0.306305	−	0.176845i	−0.645272	+	0.763953i	$0.723256\pi$
$164$		0			0
$165$	−1266.99	−	2194.49i	−0.597789	−	1.03540i
$166$		0			0
$167$	−3110.82			−1.44145			−0.720726	−	0.693220i	$-0.756191\pi$
$167$	−3110.82			−1.44145			−0.720726	+	0.693220i	$0.756191\pi$
$168$		0			0
$169$	1579.70			0.719027
$170$		0			0
$171$	−489.278	−	847.454i	−0.218807	−	0.378985i
$172$		0			0
$173$	−2719.50	−	1570.10i	−1.19514	−	0.690015i	−0.235674	−	0.971832i	$-0.575730\pi$
$173$	−2719.50	−	1570.10i	−1.19514	−	0.690015i	−0.959468	+	0.281817i	$0.909063\pi$
$174$		0			0
$175$	3549.12	+	1787.08i	1.53308	+	0.771946i
$176$		0			0
$177$	−958.144	+	1659.55i	−0.406884	+	0.704744i
$178$		0			0
$179$	−206.742	+	119.362i	−0.0863274	+	0.0498411i	−0.542542	−	0.840028i	$-0.682538\pi$
$179$	−206.742	+	119.362i	−0.0863274	+	0.0498411i	0.456215	+	0.889870i	$0.349205\pi$
$180$		0			0
$181$			1947.09i			0.799591i	0.916604	+	0.399796i	$0.130919\pi$
$181$			1947.09i			0.799591i	−0.916604	+	0.399796i	$0.869081\pi$
$182$		0			0
$183$			1422.21i			0.574498i
$184$		0			0
$185$	−1656.15	+	956.181i	−0.658177	+	0.379999i
$186$		0			0
$187$	−982.903	+	1702.44i	−0.384369	+	0.665746i
$188$		0			0
$189$	−2216.62	+	1454.58i	−0.853099	+	0.559817i
$190$		0			0
$191$	−393.391	−	227.124i	−0.149030	−	0.0860427i	0.423631	−	0.905835i	$-0.360755\pi$
$191$	−393.391	−	227.124i	−0.149030	−	0.0860427i	−0.572661	+	0.819792i	$0.694089\pi$
$192$		0			0
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	−0.993023	−	0.117921i	$-0.962377\pi$
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	0.394389	−	0.918944i	$-0.370956\pi$
$194$		0			0
$195$	1530.38			0.562013
$196$		0			0
$197$	4173.52			1.50940			0.754698	−	0.656073i	$-0.227784\pi$
$197$	4173.52			1.50940			0.754698	+	0.656073i	$0.227784\pi$
$198$		0			0
$199$	−2639.30	−	4571.40i	−0.940176	−	1.62843i	−0.765134	−	0.643871i	$-0.777327\pi$
$199$	−2639.30	−	4571.40i	−0.940176	−	1.62843i	−0.175042	−	0.984561i	$-0.556006\pi$
$200$		0			0
$201$	−2433.78	−	1405.14i	−0.854057	−	0.493090i
$202$		0			0
$203$	−446.735	+	293.155i	−0.154456	+	0.101357i
$204$		0			0
$205$	886.140	−	1534.84i	0.301906	−	0.522916i
$206$		0			0
$207$	1019.22	−	588.446i	0.342225	−	0.197584i
$208$		0			0
$209$		−	2543.62i		−	0.841848i
$210$		0			0
$211$		−	871.583i		−	0.284371i	−0.989840	−	0.142185i	$-0.954587\pi$
$211$		−	871.583i		−	0.284371i	0.989840	−	0.142185i	$-0.0454130\pi$
$212$		0			0
$213$	−3413.13	+	1970.57i	−1.09795	+	0.633903i
$214$		0			0
$215$	−1803.53	+	3123.80i	−0.572090	+	0.990889i
$216$		0			0
$217$	−382.640	−	192.669i	−0.119702	−	0.0602730i
$218$		0			0
$219$	−2393.97	−	1382.16i	−0.738674	−	0.426474i
$220$		0			0
$221$	−593.615	−	1028.17i	−0.180683	−	0.312952i
$222$		0			0
$223$	−1930.21			−0.579624			−0.289812	−	0.957084i	$-0.593593\pi$
$223$	−1930.21			−0.579624			−0.289812	+	0.957084i	$0.593593\pi$
$224$		0			0
$225$	3395.70			1.00613
$226$		0			0
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	0.973559	−	0.228436i	$-0.0733612\pi$
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	−0.684611	+	0.728909i	$0.740028\pi$
$228$		0			0
$229$	2237.66	+	1291.92i	0.645716	+	0.372804i	0.786813	−	0.617192i	$-0.211730\pi$
$229$	2237.66	+	1291.92i	0.645716	+	0.372804i	−0.141097	+	0.989996i	$0.545063\pi$
$230$		0			0
$231$	−2542.64	+	145.429i	−0.724214	+	0.0414221i
$232$		0			0
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	−0.515052	−	0.857159i	$-0.672227\pi$
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	0.999847	+	0.0174686i	$0.00556071\pi$
$234$		0			0
$235$	−2866.71	+	1655.10i	−0.795759	+	0.459432i
$236$		0			0
$237$		−	1088.49i		−	0.298333i
$238$		0			0
$239$			3647.94i			0.987304i	0.869659	+	0.493652i	$0.164338\pi$
$239$			3647.94i			0.987304i	−0.869659	+	0.493652i	$0.835662\pi$
$240$		0			0
$241$	−2194.49	+	1266.99i	−0.586553	+	0.338646i	−0.763733	−	0.645532i	$-0.776636\pi$
$241$	−2194.49	+	1266.99i	−0.586553	+	0.338646i	0.177180	+	0.984178i	$0.443302\pi$
$242$		0			0
$243$	−1847.01	+	3199.12i	−0.487597	+	0.844542i
$244$		0			0
$245$	5077.68	−	3763.74i	1.32409	−	0.981455i
$246$		0			0
$247$	1330.39	+	768.099i	0.342714	+	0.197866i
$248$		0			0
$249$	−848.795	−	1470.16i	−0.216025	−	0.374166i
$250$		0			0
$251$	−5658.23			−1.42289			−0.711443	−	0.702744i	$-0.751958\pi$
$251$	−5658.23			−1.42289			−0.711443	+	0.702744i	$0.751958\pi$
$252$		0			0
$253$	3059.18			0.760193
$254$		0			0
$255$	1471.66	+	2548.99i	0.361408	+	0.625977i
$256$		0			0
$257$	4328.82	+	2499.25i	1.05068	+	0.606610i	0.922840	−	0.385185i	$-0.125862\pi$
$257$	4328.82	+	2499.25i	1.05068	+	0.606610i	0.127840	+	0.991795i	$0.459196\pi$
$258$		0			0
$259$	109.753	+	1918.90i	0.0263310	+	0.460364i
$260$		0			0
$261$	−228.308	+	395.441i	−0.0541452	+	0.0937822i
$262$		0			0
$263$	−1646.99	+	950.892i	−0.386152	+	0.222945i	−0.680491	−	0.732756i	$-0.738234\pi$
$263$	−1646.99	+	950.892i	−0.386152	+	0.222945i	0.294340	+	0.955701i	$0.404900\pi$
$264$		0			0
$265$			8059.32i			1.86823i
$266$		0			0
$267$			682.509i			0.156438i
$268$		0			0
$269$	−6976.20	+	4027.71i	−1.58121	+	0.912913i	−0.586530	+	0.809928i	$0.699506\pi$
$269$	−6976.20	+	4027.71i	−1.58121	+	0.912913i	−0.994683	+	0.102986i	$0.967160\pi$
$270$		0			0
$271$	−2189.04	+	3791.53i	−0.490682	+	0.849886i	−0.999942	−	0.0107264i	$-0.996586\pi$
$271$	−2189.04	+	3791.53i	−0.490682	+	0.849886i	0.509261	+	0.860612i	$0.329919\pi$
$272$		0			0
$273$	691.739	−	1373.79i	0.153355	−	0.304562i
$274$		0			0
$275$	7644.11	+	4413.33i	1.67621	+	0.967759i
$276$		0			0
$277$	−1602.26	−	2775.19i	−0.347547	−	0.601968i	0.638266	−	0.769815i	$-0.279652\pi$
$277$	−1602.26	−	2775.19i	−0.347547	−	0.601968i	−0.985813	+	0.167847i	$0.946318\pi$
$278$		0			0
$279$	−366.098			−0.0785581
$280$		0			0
$281$	6258.33			1.32861			0.664307	−	0.747460i	$-0.268727\pi$
$281$	6258.33			1.32861			0.664307	+	0.747460i	$0.268727\pi$
$282$		0			0
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	−0.986235	−	0.165351i	$-0.947124\pi$
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	0.349919	−	0.936780i	$-0.386209\pi$
$284$		0			0
$285$	−3298.23	−	1904.23i	−0.685510	−	0.395779i
$286$		0			0
$287$	−977.254	−	1489.23i	−0.200995	−	0.306294i
$288$		0			0
$289$	−1314.82	+	2277.33i	−0.267620	+	0.463532i
$290$		0			0
$291$	3231.61	−	1865.77i	0.650998	−	0.375854i
$292$		0			0
$293$			457.644i			0.0912486i	0.998959	+	0.0456243i	$0.0145277\pi$
$293$			457.644i			0.0912486i	−0.998959	+	0.0456243i	$0.985472\pi$
$294$		0			0
$295$		−	10563.9i		−	2.08492i
$296$		0			0
$297$	−5100.24	+	2944.63i	−0.996451	+	0.575301i
$298$		0			0
$299$	−923.780	+	1600.03i	−0.178674	+	0.309473i
$300$		0			0
$301$	1988.97	+	3030.96i	0.380871	+	0.580405i
$302$		0			0
$303$	−11.4681	−	6.62110i	−0.00217434	−	0.00125535i
$304$		0			0
$305$	−3920.10	−	6789.82i	−0.735949	−	1.27470i
$306$		0			0
$307$	4195.62			0.779989			0.389995	−	0.920817i	$-0.372477\pi$
$307$	4195.62			0.779989			0.389995	+	0.920817i	$0.372477\pi$
$308$		0			0
$309$	1199.39			0.220813
$310$		0			0
$311$	3254.20	+	5636.44i	0.593341	+	1.02770i	0.993779	+	0.111372i	$0.0355246\pi$
$311$	3254.20	+	5636.44i	0.593341	+	1.02770i	−0.400438	+	0.916324i	$0.631142\pi$
$312$		0			0
$313$	−7481.59	−	4319.50i	−1.35107	−	0.780040i	−0.362670	−	0.931918i	$-0.618135\pi$
$313$	−7481.59	−	4319.50i	−1.35107	−	0.780040i	−0.988399	+	0.151878i	$0.951468\pi$
$314$		0			0
$315$	2429.09	−	4824.14i	0.434487	−	0.862888i
$316$		0			0
$317$	463.165	−	802.226i	0.0820629	−	0.142137i	−0.822073	−	0.569382i	$-0.807182\pi$
$317$	463.165	−	802.226i	0.0820629	−	0.142137i	0.904136	+	0.427245i	$0.140516\pi$
$318$		0			0
$319$	−1027.90	+	593.455i	−0.180411	+	0.104160i
$320$		0			0
$321$			3101.23i			0.539233i
$322$		0			0
$323$			2954.52i			0.508960i
$324$		0			0
$325$	−4616.59	+	2665.39i	−0.787946	+	0.454921i
$326$		0			0
$327$	1986.45	−	3440.63i	0.335936	−	0.581858i
$328$		0			0
$329$	189.976	+	3321.50i	0.0318351	+	0.556596i
$330$		0			0
$331$	−8260.72	−	4769.33i	−1.37175	−	0.791982i	−0.380604	−	0.924738i	$-0.624284\pi$
$331$	−8260.72	−	4769.33i	−1.37175	−	0.791982i	−0.991149	+	0.132756i	$0.957617\pi$
$332$		0			0
$333$	821.238	+	1422.43i	0.135146	+	0.234080i
$334$		0			0
$335$	15492.2			2.52665
$336$		0			0
$337$	4736.32			0.765589			0.382795	−	0.923833i	$-0.374962\pi$
$337$	4736.32			0.765589			0.382795	+	0.923833i	$0.374962\pi$
$338$		0			0
$339$	1107.04	+	1917.45i	0.177363	+	0.307202i
$340$		0			0
$341$	−824.130	−	475.812i	−0.130877	−	0.0755620i
$342$		0			0
$343$	−1083.49	−	6259.36i	−0.170563	−	0.985347i
$344$		0			0
$345$	2290.19	−	3966.73i	0.357391	−	0.619019i
$346$		0			0
$347$	1694.40	−	978.260i	0.262133	−	0.151342i	−0.363174	−	0.931721i	$-0.618307\pi$
$347$	1694.40	−	978.260i	0.262133	−	0.151342i	0.625307	+	0.780379i	$0.284974\pi$
$348$		0			0
$349$			9739.50i			1.49382i	0.664924	+	0.746911i	$0.268464\pi$
$349$			9739.50i			1.49382i	−0.664924	+	0.746911i	$0.731536\pi$
$350$		0			0
$351$		−	3556.76i		−	0.540871i
$352$		0			0
$353$	−2590.09	+	1495.39i	−0.390528	+	0.225471i	−0.682389	−	0.730989i	$-0.739059\pi$
$353$	−2590.09	+	1495.39i	−0.390528	+	0.225471i	0.291861	+	0.956461i	$0.405726\pi$
$354$		0			0
$355$	10863.1	−	18815.5i	1.62410	−	2.81302i
$356$		0			0
$357$	2953.38	−	168.921i	0.437842	−	0.0250428i
$358$		0			0
$359$	1144.24	+	660.628i	0.168219	+	0.0971215i	0.581746	−	0.813371i	$-0.302370\pi$
$359$	1144.24	+	660.628i	0.168219	+	0.0971215i	−0.413527	+	0.910492i	$0.635703\pi$
$360$		0			0
$361$	1518.02	+	2629.29i	0.221318	+	0.383334i
$362$		0			0
$363$	−1208.09			−0.174678
$364$		0			0
$365$	15238.8			2.18530
$366$		0			0
$367$	−3367.76	−	5833.14i	−0.479008	−	0.829666i	0.520703	−	0.853738i	$-0.325670\pi$
$367$	−3367.76	−	5833.14i	−0.479008	−	0.829666i	−0.999710	+	0.0240726i	$0.992337\pi$
$368$		0			0
$369$	−1318.23	−	761.082i	−0.185974	−	0.107372i
$370$		0			0
$371$	7234.69	+	3642.86i	1.01242	+	0.509779i
$372$		0			0
$373$	104.742	−	181.419i	0.0145398	−	0.0251837i	−0.858664	−	0.512539i	$-0.828705\pi$
$373$	104.742	−	181.419i	0.0145398	−	0.0251837i	0.873204	+	0.487355i	$0.162038\pi$
$374$		0			0
$375$	4777.29	−	2758.17i	0.657862	−	0.379817i
$376$		0			0
$377$		−	716.824i		−	0.0979265i
$378$		0			0
$379$			1205.99i			0.163450i	0.996655	+	0.0817250i	$0.0260429\pi$
$379$			1205.99i			0.163450i	−0.996655	+	0.0817250i	$0.973957\pi$
$380$		0			0
$381$	4330.81	−	2500.39i	0.582346	−	0.336218i
$382$		0			0
$383$	1590.45	−	2754.73i	0.212188	−	0.367520i	−0.740211	−	0.672375i	$-0.765274\pi$
$383$	1590.45	−	2754.73i	0.212188	−	0.367520i	0.952399	+	0.304854i	$0.0986078\pi$
$384$		0			0
$385$	11738.0	−	7702.67i	1.55383	−	1.01965i
$386$		0			0
$387$	2682.95	+	1549.00i	0.352408	+	0.203463i
$388$		0			0
$389$	−4006.02	−	6938.63i	−0.522142	−	0.904377i	−0.999668	−	0.0257595i	$-0.991800\pi$
$389$	−4006.02	−	6938.63i	−0.522142	−	0.904377i	0.477526	−	0.878618i	$-0.341534\pi$
$390$		0			0
$391$	−3553.36			−0.459593
$392$		0			0
$393$	6583.69			0.845046
$394$		0			0
$395$	3000.24	+	5196.56i	0.382173	+	0.661943i
$396$		0			0
$397$	−10496.5	−	6060.15i	−1.32696	−	0.766121i	−0.342132	−	0.939652i	$-0.611149\pi$
$397$	−10496.5	−	6060.15i	−1.32696	−	0.766121i	−0.984828	+	0.173531i	$0.944482\pi$
$398$		0			0
$399$	−3200.21	+	2100.03i	−0.401531	+	0.263491i
$400$		0			0
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	0.288998	+	0.957330i	$0.406678\pi$
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	−0.973571	+	0.228385i	$0.926655\pi$
$402$		0			0
$403$	497.726	−	287.362i	0.0615223	−	0.0355199i
$404$		0			0
$405$			943.552i			0.115767i
$406$		0			0
$407$			4269.40i			0.519966i
$408$		0			0
$409$	−1739.78	+	1004.46i	−0.210333	+	0.121436i	−0.601466	−	0.798898i	$-0.705417\pi$
$409$	−1739.78	+	1004.46i	−0.210333	+	0.121436i	0.391133	+	0.920334i	$0.372083\pi$
$410$		0			0
$411$	2997.68	−	5192.14i	0.359768	−	0.623137i
$412$		0			0
$413$	−9482.98	−	4774.93i	−1.12985	−	0.568908i
$414$		0			0
$415$	8104.49	+	4679.13i	0.958636	+	0.553469i
$416$		0			0
$417$	−512.113	−	887.006i	−0.0601398	−	0.104165i
$418$		0			0
$419$	−6662.83			−0.776850			−0.388425	−	0.921480i	$-0.626981\pi$
$419$	−6662.83			−0.776850			−0.388425	+	0.921480i	$0.626981\pi$
$420$		0			0
$421$	−5859.67			−0.678344			−0.339172	−	0.940724i	$-0.610147\pi$
$421$	−5859.67			−0.678344			−0.339172	+	0.940724i	$0.610147\pi$
$422$		0			0
$423$	1421.52	+	2462.14i	0.163396	+	0.283010i
$424$		0			0
$425$	−8878.94	−	5126.26i	−1.01339	−	0.585083i
$426$		0			0
$427$	−7867.00	+	449.960i	−0.891594	+	0.0509956i
$428$		0			0
$429$	1708.30	−	2958.87i	0.192256	−	0.332996i
$430$		0			0
$431$	−3178.02	+	1834.83i	−0.355174	+	0.205060i	−0.666962	−	0.745092i	$-0.732406\pi$
$431$	−3178.02	+	1834.83i	−0.355174	+	0.205060i	0.311788	+	0.950152i	$0.399072\pi$
$432$		0			0
$433$			8282.34i			0.919224i	0.888120	+	0.459612i	$0.152011\pi$
$433$			8282.34i			0.919224i	−0.888120	+	0.459612i	$0.847989\pi$
$434$		0			0
$435$			1777.11i			0.195876i
$436$		0			0
$437$	3981.82	−	2298.90i	0.435872	−	0.251651i
$438$		0			0
$439$	4840.93	−	8384.73i	0.526298	−	0.911575i	−0.473233	−	0.880938i	$-0.656913\pi$
$439$	4840.93	−	8384.73i	0.526298	−	0.911575i	0.999531	−	0.0306374i	$-0.00975370\pi$
$440$		0			0
$441$	−3232.58	−	4361.08i	−0.349053	−	0.470909i
$442$		0			0
$443$	7154.34	+	4130.56i	0.767298	+	0.443000i	0.831910	−	0.554911i	$-0.187248\pi$
$443$	7154.34	+	4130.56i	0.767298	+	0.443000i	−0.0646117	+	0.997910i	$0.520581\pi$
$444$		0			0
$445$	−1881.23	−	3258.38i	−0.200402	−	0.347106i
$446$		0			0
$447$	4779.54			0.505737
$448$		0			0
$449$	−73.1562			−0.00768921			−0.00384461	−	0.999993i	$-0.501224\pi$
$449$	−73.1562			−0.00768921			−0.00384461	+	0.999993i	$0.501224\pi$
$450$		0			0
$451$	−1978.33	−	3426.57i	−0.206554	−	0.357762i
$452$		0			0
$453$	3607.28	+	2082.67i	0.374139	+	0.216009i
$454$		0			0
$455$	484.180	+	8465.29i	0.0498873	+	0.872217i
$456$		0			0
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	−0.302563	−	0.953129i	$-0.597842\pi$
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	0.976716	−	0.214538i	$-0.0688245\pi$
$458$		0			0
$459$	5924.14	−	3420.30i	0.602429	−	0.347813i
$460$		0			0
$461$			12655.0i			1.27853i	0.768985	+	0.639267i	$0.220762\pi$
$461$			12655.0i			1.27853i	−0.768985	+	0.639267i	$0.779238\pi$
$462$		0			0
$463$			852.596i			0.0855799i	0.999084	+	0.0427899i	$0.0136246\pi$
$463$			852.596i			0.0855799i	−0.999084	+	0.0427899i	$0.986375\pi$
$464$		0			0
$465$	−1233.94	+	712.414i	−0.123059	+	0.0710482i
$466$		0			0
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	0.457549	+	0.889185i	$0.348728\pi$
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	−0.998831	+	0.0483436i	$0.984606\pi$
$468$		0			0
$469$	7002.56	−	13907.0i	0.689442	−	1.36923i
$470$		0			0
$471$	−7359.36	−	4248.93i	−0.719961	−	0.415669i
$472$		0			0
$473$	4026.42	+	6973.96i	0.391406	+	0.677935i
$474$		0			0
$475$	13266.1			1.28145
$476$		0			0
$477$	6921.93			0.664431
$478$		0			0
$479$	5330.56	+	9232.81i	0.508475	+	0.880705i	0.999952	+	0.00981425i	$0.00312402\pi$
$479$	5330.56	+	9232.81i	0.508475	+	0.880705i	−0.491477	+	0.870891i	$0.663543\pi$
$480$		0			0
$481$	−2233.01	−	1289.23i	−0.211677	−	0.122212i
$482$		0			0
$483$	−2525.67	−	3848.84i	−0.237934	−	0.362585i
$484$		0			0
$485$	−10285.4	+	17814.8i	−0.962960	+	1.66789i
$486$		0			0
$487$	46.9282	−	27.0940i	0.00436657	−	0.00252104i	−0.497815	−	0.867283i	$-0.665864\pi$
$487$	46.9282	−	27.0940i	0.00436657	−	0.00252104i	0.502182	+	0.864762i	$0.332531\pi$
$488$		0			0
$489$			2460.36i			0.227528i
$490$		0			0
$491$			5628.07i			0.517294i	0.965972	+	0.258647i	$0.0832766\pi$
$491$			5628.07i			0.517294i	−0.965972	+	0.258647i	$0.916723\pi$
$492$		0			0
$493$	1193.94	−	689.322i	0.109072	−	0.0629727i
$494$		0			0
$495$	5998.81	−	10390.3i	0.544700	−	0.943449i
$496$		0			0
$497$	−11980.1	−	18256.3i	−1.08125	−	1.64770i
$498$		0			0
$499$	536.728	+	309.880i	0.0481508	+	0.0277999i	0.523882	−	0.851791i	$-0.324483\pi$
$499$	536.728	+	309.880i	0.0481508	+	0.0277999i	−0.475731	+	0.879591i	$0.657817\pi$
$500$		0			0
$501$	5199.23	+	9005.33i	0.463641	+	0.803050i
$502$		0			0
$503$	−18680.1			−1.65587			−0.827935	−	0.560823i	$-0.810485\pi$
$503$	−18680.1			−1.65587			−0.827935	+	0.560823i	$0.810485\pi$
$504$		0			0
$505$	73.0000			0.00643259
$506$		0			0
$507$	−2640.21	−	4572.98i	−0.231274	−	0.400579i
$508$		0			0
$509$	−3084.16	−	1780.64i	−0.268572	−	0.155060i	0.359667	−	0.933081i	$-0.382890\pi$
$509$	−3084.16	−	1780.64i	−0.268572	−	0.155060i	−0.628238	+	0.778021i	$0.716224\pi$
$510$		0			0
$511$	6888.03	−	13679.6i	0.596298	−	1.18424i
$512$		0			0
$513$	−4425.65	+	7665.44i	−0.380891	+	0.659722i
$514$		0			0
$515$	−5726.05	+	3305.93i	−0.489941	+	0.282868i
$516$		0			0
$517$			7390.09i			0.628657i
$518$		0			0
$519$			10496.7i			0.887771i
$520$		0			0
$521$	10004.0	−	5775.82i	0.841235	−	0.485687i	−0.0164486	−	0.999865i	$-0.505236\pi$
$521$	10004.0	−	5775.82i	0.841235	−	0.485687i	0.857684	+	0.514177i	$0.171903\pi$
$522$		0			0
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	−0.762831	−	0.646598i	$-0.776191\pi$
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	0.941386	+	0.337332i	$0.109525\pi$
$524$		0			0
$525$	−758.474	−	13261.0i	−0.0630524	−	1.10239i
$526$		0			0
$527$	957.260	+	552.674i	0.0791250	+	0.0456829i
$528$		0			0
$529$	−3318.65	−	5748.06i	−0.272758	−	0.472431i
$530$		0			0
$531$	−9073.03			−0.741499
$532$		0			0
$533$	2389.59			0.194192
$534$		0			0
$535$	−8548.04	−	14805.6i	−0.690774	−	1.19646i
$536$		0			0
$537$	691.070	+	398.990i	0.0555342	+	0.0320627i
$538$		0			0
$539$	−1608.88	−	14018.6i	−0.128570	−	1.12027i
$540$		0			0
$541$	4878.48	−	8449.78i	0.387694	−	0.671505i	−0.604445	−	0.796647i	$-0.706605\pi$
$541$	4878.48	−	8449.78i	0.387694	−	0.671505i	0.992139	+	0.125142i	$0.0399385\pi$
$542$		0			0
$543$	5636.51	−	3254.24i	0.445462	−	0.257188i
$544$		0			0
$545$			21901.3i			1.72138i
$546$		0			0
$547$		−	19891.0i		−	1.55480i	−0.629005	−	0.777401i	$-0.716537\pi$
$547$		−	19891.0i		−	1.55480i	0.629005	−	0.777401i	$-0.283463\pi$
$548$		0			0
$549$	−5831.60	+	3366.87i	−0.453345	+	0.261739i
$550$		0			0
$551$	−891.938	+	1544.88i	−0.0689616	+	0.119445i
$552$		0			0
$553$	6020.98	−	344.376i	0.462998	−	0.0264816i
$554$		0			0
$555$	5535.98	+	3196.20i	0.423404	+	0.244453i
$556$		0			0
$557$	3043.39	+	5271.30i	0.231513	+	0.400992i	0.958253	−	0.285920i	$-0.0922992\pi$
$557$	3043.39	+	5271.30i	0.231513	+	0.400992i	−0.726741	+	0.686912i	$0.758966\pi$
$558$		0			0
$559$	−4863.44			−0.367981
$560$		0			0
$561$	6571.05			0.494527
$562$		0			0
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	0.977154	−	0.212534i	$-0.0681716\pi$
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	−0.672637	+	0.739973i	$0.734838\pi$
$564$		0			0
$565$	−10570.3	−	6102.75i	−0.787070	−	0.454415i
$566$		0			0
$567$	847.008	+	426.491i	0.0627354	+	0.0315890i
$568$		0			0
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	0.0369008	+	0.999319i	$0.488251\pi$
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	−0.883886	+	0.467702i	$0.845082\pi$
$570$		0			0
$571$	−16493.6	+	9522.59i	−1.20882	+	0.697912i	−0.962501	−	0.271277i	$-0.912554\pi$
$571$	−16493.6	+	9522.59i	−1.20882	+	0.697912i	−0.246318	+	0.969189i	$0.579221\pi$
$572$		0			0
$573$			1518.41i			0.110702i
$574$		0			0
$575$			15954.9i			1.15716i
$576$		0			0
$577$	13902.1	−	8026.36i	1.00303	−	0.579102i	0.0938892	−	0.995583i	$-0.470070\pi$
$577$	13902.1	−	8026.36i	1.00303	−	0.579102i	0.909144	+	0.416481i	$0.136737\pi$
$578$		0			0
$579$	−5365.27	+	9292.92i	−0.385100	+	0.667013i
$580$		0			0
$581$	7863.64	−	5160.25i	0.561513	−	0.368473i
$582$		0			0
$583$	15582.1	+	8996.32i	1.10694	+	0.639090i
$584$		0			0
$585$	3622.93	+	6275.10i	0.256051	+	0.443493i
$586$		0			0
$587$	21155.6			1.48754			0.743770	−	0.668436i	$-0.233036\pi$
$587$	21155.6			1.48754			0.743770	+	0.668436i	$0.233036\pi$
$588$		0			0
$589$	−1430.25			−0.100055
$590$		0			0
$591$	−6975.36	−	12081.7i	−0.485495	−	0.840903i
$592$		0			0
$593$	−1240.18	−	716.018i	−0.0858821	−	0.0495840i	0.456444	−	0.889752i	$-0.349123\pi$
$593$	−1240.18	−	716.018i	−0.0858821	−	0.0495840i	−0.542326	+	0.840168i	$0.682456\pi$
$594$		0			0
$595$	−13634.2	+	8946.96i	−0.939406	+	0.616453i
$596$		0			0
$597$	−8822.32	+	15280.7i	−0.604813	+	1.04757i
$598$		0			0
$599$	−4611.09	+	2662.21i	−0.314531	+	0.181595i	−0.648952	−	0.760829i	$-0.724793\pi$
$599$	−4611.09	+	2662.21i	−0.314531	+	0.181595i	0.334421	+	0.942424i	$0.391459\pi$
$600$		0			0
$601$			8711.39i			0.591256i	0.955303	+	0.295628i	$0.0955289\pi$
$601$			8711.39i			0.591256i	−0.955303	+	0.295628i	$0.904471\pi$
$602$		0			0
$603$		−	13305.8i		−	0.898599i
$604$		0			0
$605$	5767.55	−	3329.90i	0.387577	−	0.223768i
$606$		0			0
$607$	−12379.6	+	21442.1i	−0.827796	+	1.43378i	0.0719681	+	0.997407i	$0.477072\pi$
$607$	−12379.6	+	21442.1i	−0.827796	+	1.43378i	−0.899764	+	0.436377i	$0.856261\pi$
$608$		0			0
$609$	1595.28	+	803.266i	0.106148	+	0.0534483i
$610$		0			0
$611$	−3865.22	−	2231.59i	−0.255925	−	0.147758i
$612$		0			0
$613$	3167.74	+	5486.69i	0.208717	+	0.361509i	0.951311	−	0.308233i	$-0.0997378\pi$
$613$	3167.74	+	5486.69i	0.208717	+	0.361509i	−0.742593	+	0.669743i	$0.766404\pi$
$614$		0			0
$615$	−5924.15			−0.388431
$616$		0			0
$617$	12720.7			0.830013			0.415006	−	0.909819i	$-0.363779\pi$
$617$	12720.7			0.830013			0.415006	+	0.909819i	$0.363779\pi$
$618$		0			0
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	0.959761	+	0.280820i	$0.0906063\pi$
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	−0.236683	+	0.971587i	$0.576060\pi$
$620$		0			0
$621$	−9219.10	−	5322.65i	−0.595733	−	0.343946i
$622$		0			0
$623$	−3775.31	+	215.932i	−0.242784	+	0.0138863i
$624$		0			0
$625$	−1795.08	+	3109.16i	−0.114885	+	0.198987i
$626$		0			0
$627$	−7363.39	+	4251.25i	−0.469004	+	0.270779i
$628$		0			0
$629$		−	4959.08i		−	0.314358i
$630$		0			0
$631$		−	7895.30i		−	0.498110i	−0.968489	−	0.249055i	$-0.919880\pi$
$631$		−	7895.30i		−	0.498110i	0.968489	−	0.249055i	$-0.0801199\pi$
$632$		0			0
$633$	−2523.10	+	1456.71i	−0.158427	+	0.0914676i
$634$		0			0
$635$	−13783.8	+	23874.3i	−0.861410	+	1.49201i
$636$		0			0
$637$	7817.98	+	3391.72i	0.486279	+	0.210965i
$638$		0			0
$639$	−16160.1	−	9330.05i	−1.00045	−	0.577607i
$640$		0			0
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	0.706493	−	0.707720i	$-0.250276\pi$
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	−0.966150	+	0.257981i	$0.916943\pi$
$642$		0			0
$643$	−12838.8			−0.787424			−0.393712	−	0.919234i	$-0.628809\pi$
$643$	−12838.8			−0.787424			−0.393712	+	0.919234i	$0.628809\pi$
$644$		0			0
$645$	12057.2			0.736049
$646$		0			0
$647$	11376.3	+	19704.4i	0.691267	+	1.19731i	0.971423	+	0.237355i	$0.0762805\pi$
$647$	11376.3	+	19704.4i	0.691267	+	1.19731i	−0.280156	+	0.959955i	$0.590386\pi$
$648$		0			0
$649$	−20424.5	−	11792.1i	−1.23533	−	0.713219i
$650$		0			0
$651$	81.7728	+	1429.70i	0.00492309	+	0.0860740i
$652$		0			0
$653$	430.103	−	744.961i	0.0257753	−	0.0446441i	−0.852850	−	0.522156i	$-0.825128\pi$
$653$	430.103	−	744.961i	0.0257753	−	0.0446441i	0.878625	+	0.477512i	$0.158461\pi$
$654$		0			0
$655$	−31431.3	+	18146.9i	−1.87500	+	1.08253i
$656$		0			0
$657$		−	13088.2i		−	0.777199i
$658$		0			0
$659$			19262.8i			1.13865i	0.822111	+	0.569327i	$0.192796\pi$
$659$			19262.8i			1.13865i	−0.822111	+	0.569327i	$0.807204\pi$
$660$		0			0
$661$	−3499.64	+	2020.52i	−0.205931	+	0.118894i	−0.599419	−	0.800436i	$-0.704602\pi$
$661$	−3499.64	+	2020.52i	−0.205931	+	0.118894i	0.393488	+	0.919330i	$0.371268\pi$
$662$		0			0
$663$	−1984.26	+	3436.84i	−0.116233	+	0.201321i
$664$		0			0
$665$	9489.80	−	18846.7i	0.553381	−	1.09901i
$666$		0			0
$667$	−1858.00	−	1072.72i	−0.107859	−	0.0622727i
$668$		0			0
$669$	3226.03	+	5587.64i	0.186435	+	0.322916i
$670$		0			0
$671$	−17503.5			−1.00703
$672$		0			0
$673$	−30094.8			−1.72373			−0.861863	−	0.507141i	$-0.830702\pi$
$673$	−30094.8			−1.72373			−0.861863	+	0.507141i	$0.830702\pi$
$674$		0			0
$675$	−15357.5	−	26599.9i	−0.875718	−	1.51679i
$676$		0			0
$677$	−16898.8	−	9756.55i	−0.959343	−	0.553877i	−0.0633724	−	0.997990i	$-0.520186\pi$
$677$	−16898.8	−	9756.55i	−0.959343	−	0.553877i	−0.895971	+	0.444113i	$0.853519\pi$
$678$		0			0
$679$	11342.9	+	17285.4i	0.641093	+	0.976955i
$680$		0			0
$681$	3303.34	−	5721.55i	0.185880	−	0.321953i
$682$		0			0
$683$	−19594.6	+	11312.9i	−1.09775	+	0.633788i	−0.935630	−	0.352982i	$-0.885168\pi$
$683$	−19594.6	+	11312.9i	−1.09775	+	0.633788i	−0.162123	+	0.986771i	$0.551834\pi$
$684$		0			0
$685$			33050.5i			1.84350i
$686$		0			0
$687$		−	8636.90i		−	0.479648i
$688$		0			0
$689$	−9410.66	+	5433.24i	−0.520345	+	0.300421i
$690$		0			0
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	−0.868833	−	0.495106i	$-0.835129\pi$
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	0.863191	+	0.504878i	$0.168463\pi$
$692$		0			0
$693$	−6615.62	−	10081.5i	−0.362636	−	0.552617i
$694$		0			0
$695$	4889.78	+	2823.11i	0.266877	+	0.154082i
$696$		0			0
$697$	2297.91	+	3980.10i	0.124877	+	0.216294i
$698$		0			0
$699$	−11527.0			−0.623736
$700$		0			0
$701$	−9946.71			−0.535923			−0.267962	−	0.963430i	$-0.586350\pi$
$701$	−9946.71			−0.535923			−0.267962	+	0.963430i	$0.586350\pi$
$702$		0			0
$703$	3208.36	+	5557.04i	0.172127	+	0.298133i
$704$		0			0
$705$	9582.47	+	5532.44i	0.511910	+	0.295552i
$706$		0			0
$707$	32.9964	−	65.5307i	0.00175525	−	0.00348590i
$708$		0			0
$709$	14432.4	−	24997.6i	0.764484	−	1.32412i	−0.176035	−	0.984384i	$-0.556327\pi$
$709$	14432.4	−	24997.6i	0.764484	−	1.32412i	0.940519	−	0.339741i	$-0.110339\pi$
$710$		0			0
$711$	4463.19	−	2576.82i	0.235419	−	0.135919i
$712$		0			0
$713$		−	1720.14i		−	0.0903501i
$714$		0			0
$715$			18834.6i			0.985141i
$716$		0			0
$717$	10560.2	−	6096.94i	0.550039	−	0.317565i
$718$		0			0
$719$	3063.07	−	5305.39i	0.158878	−	0.275185i	−0.775586	−	0.631241i	$-0.782546\pi$
$719$	3063.07	−	5305.39i	0.158878	−	0.275185i	0.934464	+	0.356057i	$0.115879\pi$
$720$		0			0
$721$	379.464	+	6634.46i	0.0196005	+	0.342691i
$722$		0			0
$723$	7335.45	+	4235.12i	0.377328	+	0.217851i
$724$		0			0
$725$	−3095.12	−	5360.91i	−0.158552	−	0.274620i
$726$		0			0
$727$	20742.9			1.05820			0.529101	−	0.848559i	$-0.322529\pi$
$727$	20742.9			1.05820			0.529101	+	0.848559i	$0.322529\pi$
$728$		0			0
$729$	13730.5			0.697579
$730$		0			0
$731$	−4676.85	−	8100.54i	−0.236634	−	0.409862i
$732$		0			0
$733$	15694.9	+	9061.44i	0.790864	+	0.456606i	0.840267	−	0.542173i	$-0.182398\pi$
$733$	15694.9	+	9061.44i	0.790864	+	0.456606i	−0.0494026	+	0.998779i	$0.515732\pi$
$734$		0			0
$735$	−19381.9	−	8408.59i	−0.972672	−	0.421980i
$736$		0			0
$737$	17293.4	−	29953.0i	0.864328	−	1.49706i
$738$		0			0
$739$	32754.4	−	18910.8i	1.63043	−	0.941332i	0.646476	−	0.762934i	$-0.276242\pi$
$739$	32754.4	−	18910.8i	1.63043	−	0.941332i	0.983958	−	0.178398i	$-0.0570913\pi$
$740$		0			0
$741$		−	5135.01i		−	0.254574i
$742$		0			0
$743$			4974.35i			0.245614i	0.992431	+	0.122807i	$0.0391896\pi$
$743$			4974.35i			0.245614i	−0.992431	+	0.122807i	$0.960810\pi$
$744$		0			0
$745$	−22818.1	+	13174.0i	−1.12213	+	0.647865i
$746$		0			0
$747$	4018.78	−	6960.73i	0.196840	−	0.340937i
$748$		0			0
$749$	−17154.5	+	981.168i	−0.836865	+	0.0478653i
$750$		0			0
$751$	−19034.7	−	10989.7i	−0.924884	−	0.533982i	−0.0396939	−	0.999212i	$-0.512638\pi$
$751$	−19034.7	−	10989.7i	−0.924884	−	0.533982i	−0.885190	+	0.465230i	$0.845972\pi$
$752$		0			0
$753$	9456.81	+	16379.7i	0.457670	+	0.792707i
$754$		0			0
$755$	−22962.1			−1.10686
$756$		0			0
$757$	10241.5			0.491722			0.245861	−	0.969305i	$-0.420929\pi$
$757$	10241.5			0.491722			0.245861	+	0.969305i	$0.420929\pi$
$758$		0			0
$759$	−5112.91	−	8855.83i	−0.244515	−	0.423513i
$760$		0			0
$761$	−18578.2	−	10726.2i	−0.884968	−	0.510937i	−0.0126751	−	0.999920i	$-0.504035\pi$
$761$	−18578.2	−	10726.2i	−0.884968	−	0.510937i	−0.872293	+	0.488983i	$0.837368\pi$
$762$		0			0
$763$	19660.4	+	9899.53i	0.932836	+	0.469708i
$764$		0			0
$765$	−6967.86	+	12068.7i	−0.329312	+	0.570385i
$766$		0			0
$767$	12335.2	−	7121.71i	0.580700	−	0.335267i
$768$		0			0
$769$			26466.5i			1.24110i	0.784166	+	0.620551i	$0.213091\pi$
$769$			26466.5i			1.24110i	−0.784166	+	0.620551i	$0.786909\pi$
$770$		0			0
$771$		−	16708.3i		−	0.780462i
$772$		0			0
$773$	−9692.09	+	5595.73i	−0.450971	+	0.260368i	−0.708240	−	0.705972i	$-0.750511\pi$
$773$	−9692.09	+	5595.73i	−0.450971	+	0.260368i	0.257269	+	0.966340i	$0.417177\pi$
$774$		0			0
$775$	2481.56	−	4298.19i	0.115020	−	0.199220i
$776$		0			0
$777$	5371.46	−	3524.84i	0.248005	−	0.162745i
$778$		0			0
$779$	−5149.99	−	2973.35i	−0.236864	−	0.136754i
$780$		0			0
$781$	−24252.2	−	42006.1i	−1.11116	−	1.92458i
$782$		0			0
$783$	4130.21			0.188508
$784$		0			0
$785$	46845.9			2.12994
$786$		0			0
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	0.974804	+	0.223065i	$0.0716062\pi$
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	−0.294222	+	0.955737i	$0.595061\pi$
$788$		0			0
$789$	5505.36	+	3178.52i	0.248411	+	0.143420i
$790$		0			0
$791$	−10256.1	+	6730.24i	−0.461019	+	0.302528i
$792$		0			0
$793$	5285.53	−	9154.81i	0.236689	−	0.409958i
$794$		0			0
$795$	23330.4	−	13469.8i	1.04081	−	0.600913i
$796$		0			0
$797$		−	26567.8i		−	1.18078i	−0.807119	−	0.590389i	$-0.798974\pi$
$797$		−	26567.8i		−	1.18078i	0.807119	−	0.590389i	$-0.201026\pi$
$798$		0			0
$799$		−	8583.89i		−	0.380070i
$800$		0			0
$801$	−2798.54	+	1615.74i	−0.123447	+	0.0712724i
$802$		0			0
$803$	17010.5	−	29463.1i	0.747557	−	1.29481i
$804$		0			0
$805$	22666.6	+	11413.2i	0.992412	+	0.499706i
$806$		0			0
$807$	23319.1	+	13463.3i	1.01719	+	0.587275i
$808$		0			0
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	0.886543	−	0.462647i	$-0.153100\pi$
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	−0.843935	+	0.536445i	$0.819767\pi$
$810$		0			0
$811$	2633.82			0.114040			0.0570198	−	0.998373i	$-0.481840\pi$
$811$	2633.82			0.114040			0.0570198	+	0.998373i	$0.481840\pi$
$812$		0			0
$813$	14634.5			0.631309
$814$		0			0
$815$	−6781.58	−	11746.0i	−0.291470	−	0.504841i
$816$		0			0
$817$	10481.6	+	6051.53i	0.448841	+	0.259139i
$818$		0			0
$819$	7270.61	−	415.850i	0.310202	−	0.0177423i
$820$		0			0
$821$	5333.16	−	9237.30i	0.226710	−	0.392672i	−0.730121	−	0.683317i	$-0.760537\pi$
$821$	5333.16	−	9237.30i	0.226710	−	0.392672i	0.956831	+	0.290645i	$0.0938699\pi$
$822$		0			0
$823$	32943.1	−	19019.7i	1.39529	−	0.805571i	0.401395	−	0.915905i	$-0.368525\pi$
$823$	32943.1	−	19019.7i	1.39529	−	0.805571i	0.993895	+	0.110334i	$0.0351922\pi$
$824$		0			0
$825$		−	29504.6i		−	1.24512i
$826$		0			0
$827$			22277.0i			0.936697i	0.883544	+	0.468349i	$0.155151\pi$
$827$			22277.0i			0.936697i	−0.883544	+	0.468349i	$0.844849\pi$
$828$		0			0
$829$	−18752.2	+	10826.6i	−0.785633	+	0.453585i	−0.838423	−	0.545020i	$-0.816522\pi$
$829$	−18752.2	+	10826.6i	−0.785633	+	0.453585i	0.0527901	+	0.998606i	$0.483189\pi$
$830$		0			0
$831$	−5355.83	+	9276.57i	−0.223576	+	0.387245i
$832$		0			0
$833$	1868.78	+	16283.2i	0.0777304	+	0.677287i
$834$		0			0
$835$	−49643.4	−	28661.7i	−2.05746	−	1.18788i
$836$		0			0
$837$	1655.73	+	2867.80i	0.0683755	+	0.118430i
$838$		0			0
$839$	47337.4			1.94788			0.973939	−	0.226811i	$-0.0728299\pi$
$839$	47337.4			1.94788			0.973939	+	0.226811i	$0.0728299\pi$
$840$		0			0
$841$	−23556.6			−0.965870
$842$		0			0
$843$	−10459.8	−	18116.9i	−0.427347	−	0.740187i
$844$		0			0
$845$	25209.4	+	14554.6i	1.02631	+	0.592538i
$846$		0			0
$847$	−382.215	−	6682.55i	−0.0155054	−	0.271092i
$848$		0			0
$849$	−10126.2	+	17539.1i	−0.409341	+	0.708999i
$850$		0			0
$851$	−6683.37	+	3858.64i	−0.269216	+	0.155432i
$852$		0			0
$853$			16562.9i			0.664833i	0.943133	+	0.332417i	$0.107864\pi$
$853$			16562.9i			0.664833i	−0.943133	+	0.332417i	$0.892136\pi$
$854$		0			0
$855$		−	18031.9i		−	0.721261i
$856$		0			0
$857$	−28076.8	+	16210.2i	−1.11912	+	0.646124i	−0.941176	−	0.337917i	$-0.890278\pi$
$857$	−28076.8	+	16210.2i	−1.11912	+	0.646124i	−0.177944	+	0.984041i	$0.556944\pi$
$858$		0			0
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	−0.347735	−	0.937593i	$-0.613049\pi$
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	0.985847	−	0.167649i	$-0.0536177\pi$
$860$		0			0
$861$	−2677.75	+	5317.99i	−0.105990	+	0.210496i
$862$		0			0
$863$	−33292.7	−	19221.5i	−1.31320	−	0.758179i	−0.330579	−	0.943778i	$-0.607244\pi$
$863$	−33292.7	−	19221.5i	−1.31320	−	0.758179i	−0.982625	+	0.185600i	$0.940577\pi$
$864$		0			0
$865$	−28932.4	−	50112.4i	−1.13726	−	1.96979i
$866$		0			0
$867$	8790.02			0.344319
$868$		0			0
$869$	13396.2			0.522941
$870$		0			0
$871$	10444.2	+	18089.8i	0.406300	+	0.703732i
$872$		0			0
$873$	15300.7	+	8833.85i	0.593184	+	0.342475i
$874$		0			0
$875$	16768.3	+	25553.0i	0.647854	+	0.987257i
$876$		0			0
$877$	−10742.3	+	18606.2i	−0.413616	+	0.716404i	−0.995282	−	0.0970237i	$-0.969068\pi$
$877$	−10742.3	+	18606.2i	−0.413616	+	0.716404i	0.581666	+	0.813428i	$0.302401\pi$
$878$		0			0
$879$	1324.81	−	764.877i	0.0508357	−	0.0293500i
$880$		0			0
$881$		−	17193.8i		−	0.657517i	−0.944414	−	0.328759i	$-0.893370\pi$
$881$		−	17193.8i		−	0.657517i	0.944414	−	0.328759i	$-0.106630\pi$
$882$		0			0
$883$			16514.2i			0.629384i	0.949194	+	0.314692i	$0.101901\pi$
$883$			16514.2i			0.629384i	−0.949194	+	0.314692i	$0.898099\pi$
$884$		0			0
$885$	−30580.7	+	17655.8i	−1.16154	+	0.670614i
$886$		0			0
$887$	−10239.6	+	17735.5i	−0.387612	+	0.671364i	−0.992128	−	0.125229i	$-0.960033\pi$
$887$	−10239.6	+	17735.5i	−0.387612	+	0.671364i	0.604516	+	0.796593i	$0.293367\pi$
$888$		0			0
$889$	15201.1	+	23164.8i	0.573486	+	0.873929i
$890$		0			0
$891$	1824.29	+	1053.25i	0.0685925	+	0.0396019i
$892$		0			0
$893$	5553.49	+	9618.93i	0.208108	+	0.360454i
$894$		0			0
$895$	−4399.00			−0.164293
$896$		0			0
$897$	6175.79			0.229882
$898$		0			0
$899$	333.693	+	577.973i	0.0123796	+	0.0214421i
$900$		0			0
$901$	−18099.2	−	10449.6i	−0.669226	−	0.386378i
$902$		0			0
$903$	5449.92	−	10823.5i	0.200844	−	0.398874i
$904$		0			0
$905$	−17939.6	+	31072.3i	−0.658930	+	1.14130i
$906$		0			0
$907$	26983.7	−	15579.0i	0.987848	−	0.570334i	0.0832177	−	0.996531i	$-0.473480\pi$
$907$	26983.7	−	15579.0i	0.987848	−	0.570334i	0.904630	+	0.426197i	$0.140147\pi$
$908$		0			0
$909$		−	62.6978i		−	0.00228774i
$910$		0			0
$911$			412.348i			0.0149964i	0.999972	+	0.00749818i	$0.00238677\pi$
$911$			412.348i			0.0149964i	−0.999972	+	0.00749818i	$0.997613\pi$
$912$		0			0
$913$	18093.5	−	10446.3i	0.655868	−	0.378666i
$914$		0			0
$915$	−13103.6	+	22696.2i	−0.473435	+	0.820013i
$916$		0			0
$917$	2082.95	+	36417.7i	0.0750109	+	1.31147i
$918$		0			0
$919$	8444.08	+	4875.19i	0.303095	+	0.174992i	0.643832	−	0.765166i	$-0.277343\pi$
$919$	8444.08	+	4875.19i	0.303095	+	0.174992i	−0.340737	+	0.940159i	$0.610677\pi$
$920$		0			0
$921$	−7012.30	−	12145.7i	−0.250883	−	0.434542i
$922$		0			0
$923$	29293.8			1.04466
$924$		0			0
$925$	−22266.7			−0.791487
$926$		0			0
$927$	2839.38	+	4917.95i	0.100601	+	0.174247i
$928$		0			0
$929$	−19036.4	−	10990.7i	−0.672297	−	0.388151i	0.124650	−	0.992201i	$-0.460219\pi$
$929$	−19036.4	−	10990.7i	−0.672297	−	0.388151i	−0.796946	+	0.604050i	$0.793553\pi$
$930$		0			0
$931$	−12628.8	−	17037.6i	−0.444568	−	0.599769i
$932$		0			0
$933$	10877.7	−	18840.8i	0.381695	−	0.661115i
$934$		0			0
$935$	−31371.0	+	18112.0i	−1.09726	+	0.633505i
$936$		0			0
$937$			19723.5i			0.687662i	0.939032	+	0.343831i	$0.111725\pi$
$937$			19723.5i			0.687662i	−0.939032	+	0.343831i	$0.888275\pi$
$938$		0			0
$939$			28877.4i			1.00360i
$940$		0			0
$941$	9773.15	−	5642.53i	0.338571	−	0.195474i	−0.321069	−	0.947056i	$-0.604042\pi$
$941$	9773.15	−	5642.53i	0.338571	−	0.195474i	0.659640	+	0.751582i	$0.270709\pi$
$942$		0			0
$943$	3575.99	−	6193.80i	0.123489	−	0.213890i
$944$		0			0
$945$	−48775.4	+	2789.76i	−1.67901	+	0.0960327i
$946$		0			0
$947$	26386.0	+	15234.0i	0.905417	+	0.522743i	0.878954	−	0.476907i	$-0.158242\pi$
$947$	26386.0	+	15234.0i	0.905417	+	0.522743i	0.0264635	+	0.999650i	$0.491575\pi$
$948$		0			0
$949$	10273.3	+	17794.0i	0.351409	+	0.608658i
$950$		0			0
$951$	−3096.42			−0.105582
$952$		0			0
$953$	11791.2			0.400791			0.200395	−	0.979715i	$-0.435777\pi$
$953$	11791.2			0.400791			0.200395	+	0.979715i	$0.435777\pi$
$954$		0			0
$955$	−4185.24	−	7249.05i	−0.141813	−	0.245627i
$956$		0			0
$957$	3435.92	+	1983.73i	0.116058	+	0.0670061i
$958$		0			0
$959$	29668.8	+	14939.0i	0.999014	+	0.503030i
$960$		0			0
$961$	14628.0	−	25336.4i	0.491019	−	0.850470i
$962$		0			0
$963$	−12716.2	+	7341.69i	−0.425517	+	0.245672i
$964$		0			0
$965$		−	59154.0i		−	1.97330i
$966$		0			0
$967$		−	40914.1i		−	1.36061i	−0.732929	−	0.680305i	$-0.761847\pi$
$967$		−	40914.1i		−	1.36061i	0.732929	−	0.680305i	$-0.238153\pi$
$968$		0			0
$969$	8552.87	−	4938.00i	0.283548	−	0.163706i
$970$		0			0
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	−0.977610	−	0.210425i	$-0.932515\pi$
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	0.671038	+	0.741423i	$0.265849\pi$
$972$		0			0
$973$	4744.46	−	3113.39i	0.156321	−	0.102580i
$974$		0			0
$975$	15431.8	+	8909.53i	0.506884	+	0.292650i
$976$		0			0
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	0.888876	−	0.458148i	$-0.151487\pi$
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	−0.841206	+	0.540715i	$0.818154\pi$
$978$		0			0
$979$	−8399.78			−0.274217
$980$		0			0
$981$	18810.5			0.612204
$982$		0			0
$983$	18251.1	+	31611.8i	0.592186	+	1.02570i	0.993937	+	0.109947i	$0.0350682\pi$
$983$	18251.1	+	31611.8i	0.592186	+	1.02570i	−0.401752	+	0.915749i	$0.631598\pi$
$984$		0			0
$985$	66602.3	+	38452.9i	2.15444	+	1.24387i
$986$		0			0
$987$	9297.70	−	6101.30i	0.299847	−	0.196764i
$988$		0			0
$989$	−7278.08	+	12606.0i	−0.234004	+	0.405306i
$990$		0			0
$991$	31879.7	−	18405.7i	1.02189	−	0.589987i	0.107238	−	0.994233i	$-0.465799\pi$
$991$	31879.7	−	18405.7i	1.02189	−	0.589987i	0.914650	+	0.404246i	$0.132466\pi$
$992$		0			0
$993$			31884.6i			1.01896i
$994$		0			0
$995$		−	97269.2i		−	3.09914i
$996$		0			0
$997$	10060.1	−	5808.18i	0.319564	−	0.184500i	−0.331634	−	0.943408i	$-0.607600\pi$
$997$	10060.1	−	5808.18i	0.319564	−	0.184500i	0.651198	+	0.758908i	$0.274267\pi$
$998$		0			0
$999$	7428.32	−	12866.2i	0.235257	−	0.407477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.p.h.383.4		20
4.3	odd	2	inner	448.4.p.h.383.7		20
7.3	odd	6	inner	448.4.p.h.255.7		20
8.3	odd	2		28.4.f.a.19.2	yes	20
8.5	even	2		28.4.f.a.19.9	yes	20
28.3	even	6	inner	448.4.p.h.255.4		20
56.3	even	6		28.4.f.a.3.9	yes	20
56.5	odd	6		196.4.d.b.195.10		20
56.11	odd	6		196.4.f.d.31.9		20
56.13	odd	2		196.4.f.d.19.9		20
56.19	even	6		196.4.d.b.195.11		20
56.27	even	2		196.4.f.d.19.2		20
56.37	even	6		196.4.d.b.195.9		20
56.45	odd	6		28.4.f.a.3.2	✓	20
56.51	odd	6		196.4.d.b.195.12		20
56.53	even	6		196.4.f.d.31.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.2	✓	20	56.45	odd	6
28.4.f.a.3.9	yes	20	56.3	even	6
28.4.f.a.19.2	yes	20	8.3	odd	2
28.4.f.a.19.9	yes	20	8.5	even	2
196.4.d.b.195.9		20	56.37	even	6
196.4.d.b.195.10		20	56.5	odd	6
196.4.d.b.195.11		20	56.19	even	6
196.4.d.b.195.12		20	56.51	odd	6
196.4.f.d.19.2		20	56.27	even	2
196.4.f.d.19.9		20	56.13	odd	2
196.4.f.d.31.2		20	56.53	even	6
196.4.f.d.31.9		20	56.11	odd	6
448.4.p.h.255.4		20	28.3	even	6	inner
448.4.p.h.255.7		20	7.3	odd	6	inner
448.4.p.h.383.4		20	1.1	even	1	trivial
448.4.p.h.383.7		20	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.67134 - 2.89484i) q^{3} +(15.9583 + 9.21354i) q^{5} +(15.4841 - 10.1609i) q^{7} +(7.91327 - 13.7062i) q^{9} +(35.6274 - 20.5695i) q^{11} +24.8455i q^{13} -61.5957i q^{15} +(-41.3826 + 23.8923i) q^{17} +(30.9150 - 53.5464i) q^{19} +(-55.2933 - 27.8416i) q^{21} +(64.3994 + 37.1810i) q^{23} +(107.279 + 185.812i) q^{25} -143.155 q^{27} -28.8513 q^{29} +(-11.5660 - 20.0328i) q^{31} +(-119.091 - 68.7571i) q^{33} +(340.717 - 19.4877i) q^{35} +(-51.8900 + 89.8761i) q^{37} +(71.9237 - 41.5252i) q^{39} -96.1780i q^{41} +195.747i q^{43} +(252.565 - 145.818i) q^{45} +(-89.8186 + 155.570i) q^{47} +(136.513 - 314.664i) q^{49} +(138.329 + 79.8641i) q^{51} +(218.681 + 378.767i) q^{53} +758.071 q^{55} -206.678 q^{57} +(-286.640 - 496.475i) q^{59} +(-368.470 - 212.736i) q^{61} +(-16.7374 - 292.633i) q^{63} +(-228.915 + 396.492i) q^{65} +(728.093 - 420.365i) q^{67} -248.568i q^{69} -1179.04i q^{71} +(716.185 - 413.489i) q^{73} +(358.597 - 621.109i) q^{75} +(342.652 - 680.505i) q^{77} +(282.007 + 162.817i) q^{79} +(25.6023 + 44.3445i) q^{81} +507.854 q^{83} -880.530 q^{85} +(48.2202 + 83.5198i) q^{87} +(-176.826 - 102.090i) q^{89} +(252.452 + 384.709i) q^{91} +(-38.6612 + 66.9632i) q^{93} +(986.704 - 569.674i) q^{95} +1116.33i q^{97} -651.087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 56 q^{9} - 6 q^{17} - 238 q^{21} - 36 q^{25} + 352 q^{29} + 30 q^{33} - 258 q^{37} + 504 q^{45} - 644 q^{49} - 570 q^{53} + 1452 q^{57} - 294 q^{61} - 124 q^{65} + 966 q^{73} + 378 q^{77}+ \cdots + 306 q^{93}+O(q^{100}) \) 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

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Representations

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Database

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