LMFDB - Embedded newform 504.2.j.a.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(323,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.j (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25516 + 0.651592i) q^{2} +(1.15086 - 1.63571i) q^{4} -1.82464 q^{5} -1.00000i q^{7} +(-0.378695 + 2.80296i) q^{8} +O(q^{10})$	\(q+(-1.25516 + 0.651592i) q^{2} +(1.15086 - 1.63571i) q^{4} -1.82464 q^{5} -1.00000i q^{7} +(-0.378695 + 2.80296i) q^{8} +(2.29021 - 1.18892i) q^{10} +0.868419i q^{11} +0.873281i q^{13} +(0.651592 + 1.25516i) q^{14} +(-1.35106 - 3.76492i) q^{16} -4.00897i q^{17} -3.39311 q^{19} +(-2.09990 + 2.98457i) q^{20} +(-0.565855 - 1.09001i) q^{22} -3.82976 q^{23} -1.67069 q^{25} +(-0.569023 - 1.09611i) q^{26} +(-1.63571 - 1.15086i) q^{28} -7.14742 q^{29} -4.04081i q^{31} +(4.14900 + 3.84524i) q^{32} +(2.61221 + 5.03190i) q^{34} +1.82464i q^{35} +2.16498i q^{37} +(4.25890 - 2.21092i) q^{38} +(0.690982 - 5.11439i) q^{40} -8.89325i q^{41} -9.10026 q^{43} +(1.42048 + 0.999425i) q^{44} +(4.80697 - 2.49544i) q^{46} -7.42621 q^{47} -1.00000 q^{49} +(2.09699 - 1.08861i) q^{50} +(1.42843 + 1.00502i) q^{52} +9.49922 q^{53} -1.58455i q^{55} +(2.80296 + 0.378695i) q^{56} +(8.97116 - 4.65720i) q^{58} -7.42621i q^{59} +2.29285i q^{61} +(2.63296 + 5.07187i) q^{62} +(-7.71318 - 2.12293i) q^{64} -1.59342i q^{65} -12.6278 q^{67} +(-6.55750 - 4.61375i) q^{68} +(-1.18892 - 2.29021i) q^{70} -3.29541 q^{71} +15.2867 q^{73} +(-1.41068 - 2.71740i) q^{74} +(-3.90498 + 5.55013i) q^{76} +0.868419 q^{77} -3.11668i q^{79} +(2.46521 + 6.86962i) q^{80} +(5.79478 + 11.1625i) q^{82} -0.0325150i q^{83} +7.31492i q^{85} +(11.4223 - 5.92966i) q^{86} +(-2.43414 - 0.328866i) q^{88} -13.6593i q^{89} +0.873281 q^{91} +(-4.40750 + 6.26436i) q^{92} +(9.32108 - 4.83886i) q^{94} +6.19120 q^{95} -3.79074 q^{97} +(1.25516 - 0.651592i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−1.25516	+	0.651592i	−0.887532	+	0.460745i
$2$	−1.25516	+	0.651592i	−0.887532	+	0.460745i
$3$		0			0
$3$		0			0
$4$	1.15086	−	1.63571i	0.575428	−	0.817853i
$5$	−1.82464			−0.816003			−0.408002	−	0.912981i	$-0.633774\pi$
$5$	−1.82464			−0.816003			−0.408002	+	0.912981i	$0.633774\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.378695	+	2.80296i	−0.133889	+	0.990996i
$9$		0			0
$10$	2.29021	−	1.18892i	0.724229	−	0.375970i
$11$			0.868419i			0.261838i	0.991393	+	0.130919i	$0.0417928\pi$
$11$			0.868419i			0.261838i	−0.991393	+	0.130919i	$0.958207\pi$
$12$		0			0
$13$			0.873281i			0.242204i	0.992640	+	0.121102i	$0.0386429\pi$
$13$			0.873281i			0.242204i	−0.992640	+	0.121102i	$0.961357\pi$
$14$	0.651592	+	1.25516i	0.174145	+	0.335456i
$15$		0			0
$16$	−1.35106	−	3.76492i	−0.337766	−	0.941230i
$17$		−	4.00897i		−	0.972318i	−0.873870	−	0.486159i	$-0.838398\pi$
$17$		−	4.00897i		−	0.972318i	0.873870	−	0.486159i	$-0.161602\pi$
$18$		0			0
$19$	−3.39311			−0.778433			−0.389216	−	0.921146i	$-0.627254\pi$
$19$	−3.39311			−0.778433			−0.389216	+	0.921146i	$0.627254\pi$
$20$	−2.09990	+	2.98457i	−0.469551	+	0.667371i
$21$		0			0
$22$	−0.565855	−	1.09001i	−0.120641	−	0.232390i
$23$	−3.82976			−0.798561			−0.399280	−	0.916829i	$-0.630740\pi$
$23$	−3.82976			−0.798561			−0.399280	+	0.916829i	$0.630740\pi$
$24$		0			0
$25$	−1.67069			−0.334138
$26$	−0.569023	−	1.09611i	−0.111595	−	0.214964i
$27$		0			0
$28$	−1.63571	−	1.15086i	−0.309119	−	0.217491i
$29$	−7.14742			−1.32724			−0.663621	−	0.748069i	$-0.730981\pi$
$29$	−7.14742			−1.32724			−0.663621	+	0.748069i	$0.730981\pi$
$30$		0			0
$31$		−	4.04081i		−	0.725751i	−0.931838	−	0.362876i	$-0.881795\pi$
$31$		−	4.04081i		−	0.725751i	0.931838	−	0.362876i	$-0.118205\pi$
$32$	4.14900	+	3.84524i	0.733446	+	0.679748i
$33$		0			0
$34$	2.61221	+	5.03190i	0.447991	+	0.862964i
$35$			1.82464i			0.308420i
$36$		0			0
$37$			2.16498i			0.355921i	0.984038	+	0.177960i	$0.0569499\pi$
$37$			2.16498i			0.355921i	−0.984038	+	0.177960i	$0.943050\pi$
$38$	4.25890	−	2.21092i	0.690885	−	0.358659i
$39$		0			0
$40$	0.690982	−	5.11439i	0.109254	−	0.808656i
$41$		−	8.89325i		−	1.38889i	−0.719544	−	0.694446i	$-0.755649\pi$
$41$		−	8.89325i		−	1.38889i	0.719544	−	0.694446i	$-0.244351\pi$
$42$		0			0
$43$	−9.10026			−1.38778			−0.693888	−	0.720083i	$-0.744104\pi$
$43$	−9.10026			−1.38778			−0.693888	+	0.720083i	$0.744104\pi$
$44$	1.42048	+	0.999425i	0.214145	+	0.150669i
$45$		0			0
$46$	4.80697	−	2.49544i	0.708749	−	0.367933i
$47$	−7.42621			−1.08322			−0.541612	−	0.840629i	$-0.682186\pi$
$47$	−7.42621			−1.08322			−0.541612	+	0.840629i	$0.682186\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	2.09699	−	1.08861i	0.296559	−	0.153953i
$51$		0			0
$52$	1.42843	+	1.00502i	0.198088	+	0.139371i
$53$	9.49922			1.30482			0.652409	−	0.757867i	$-0.273758\pi$
$53$	9.49922			1.30482			0.652409	+	0.757867i	$0.273758\pi$
$54$		0			0
$55$		−	1.58455i		−	0.213661i
$56$	2.80296	+	0.378695i	0.374561	+	0.0506052i
$57$		0			0
$58$	8.97116	−	4.65720i	1.17797	−	0.611521i
$59$		−	7.42621i		−	0.966810i	−0.875397	−	0.483405i	$-0.839400\pi$
$59$		−	7.42621i		−	0.966810i	0.875397	−	0.483405i	$-0.160600\pi$
$60$		0			0
$61$			2.29285i			0.293570i	0.989168	+	0.146785i	$0.0468925\pi$
$61$			2.29285i			0.293570i	−0.989168	+	0.146785i	$0.953108\pi$
$62$	2.63296	+	5.07187i	0.334386	+	0.644128i
$63$		0			0
$64$	−7.71318	−	2.12293i	−0.964148	−	0.265367i
$65$		−	1.59342i		−	0.197640i
$66$		0			0
$67$	−12.6278			−1.54273			−0.771366	−	0.636391i	$-0.780426\pi$
$67$	−12.6278			−1.54273			−0.771366	+	0.636391i	$0.780426\pi$
$68$	−6.55750	−	4.61375i	−0.795213	−	0.559499i
$69$		0			0
$70$	−1.18892	−	2.29021i	−0.142103	−	0.273733i
$71$	−3.29541			−0.391094			−0.195547	−	0.980694i	$-0.562648\pi$
$71$	−3.29541			−0.391094			−0.195547	+	0.980694i	$0.562648\pi$
$72$		0			0
$73$	15.2867			1.78917			0.894584	−	0.446900i	$-0.147472\pi$
$73$	15.2867			1.78917			0.894584	+	0.446900i	$0.147472\pi$
$74$	−1.41068	−	2.71740i	−0.163989	−	0.315891i
$75$		0			0
$76$	−3.90498	+	5.55013i	−0.447932	+	0.636644i
$77$	0.868419			0.0989655
$78$		0			0
$79$		−	3.11668i		−	0.350654i	−0.984510	−	0.175327i	$-0.943902\pi$
$79$		−	3.11668i		−	0.350654i	0.984510	−	0.175327i	$-0.0560983\pi$
$80$	2.46521	+	6.86962i	0.275618	+	0.768047i
$81$		0			0
$82$	5.79478	+	11.1625i	0.639926	+	1.23269i
$83$		−	0.0325150i		−	0.00356899i	−0.999998	−	0.00178449i	$-0.999432\pi$
$83$		−	0.0325150i		−	0.00356899i	0.999998	−	0.00178449i	$-0.000568023\pi$
$84$		0			0
$85$			7.31492i			0.793415i
$86$	11.4223	−	5.92966i	1.23170	−	0.639411i
$87$		0			0
$88$	−2.43414	−	0.328866i	−0.259481	−	0.0350572i
$89$		−	13.6593i		−	1.44789i	−0.689860	−	0.723943i	$-0.742328\pi$
$89$		−	13.6593i		−	1.44789i	0.689860	−	0.723943i	$-0.257672\pi$
$90$		0			0
$91$	0.873281			0.0915447
$92$	−4.40750	+	6.26436i	−0.459514	+	0.653105i
$93$		0			0
$94$	9.32108	−	4.83886i	0.961396	−	0.499090i
$95$	6.19120			0.635204
$96$		0			0
$97$	−3.79074			−0.384891			−0.192446	−	0.981308i	$-0.561642\pi$
$97$	−3.79074			−0.384891			−0.192446	+	0.981308i	$0.561642\pi$
$98$	1.25516	−	0.651592i	0.126790	−	0.0658208i
$99$		0			0
$100$	−1.92273	+	2.73276i	−0.192273	+	0.273276i
$101$	5.74466			0.571615			0.285807	−	0.958287i	$-0.407738\pi$
$101$	5.74466			0.571615			0.285807	+	0.958287i	$0.407738\pi$
$102$		0			0
$103$			18.9154i			1.86379i	0.362730	+	0.931894i	$0.381845\pi$
$103$			18.9154i			1.86379i	−0.362730	+	0.931894i	$0.618155\pi$
$104$	−2.44777	−	0.330707i	−0.240024	−	0.0324285i
$105$		0			0
$106$	−11.9230	+	6.18962i	−1.15807	+	0.601189i
$107$			6.43014i			0.621625i	0.950471	+	0.310812i	$0.100601\pi$
$107$			6.43014i			0.621625i	−0.950471	+	0.310812i	$0.899399\pi$
$108$		0			0
$109$			9.43392i			0.903606i	0.892118	+	0.451803i	$0.149219\pi$
$109$			9.43392i			0.903606i	−0.892118	+	0.451803i	$0.850781\pi$
$110$	1.03248	+	1.98887i	0.0984432	+	0.189631i
$111$		0			0
$112$	−3.76492	+	1.35106i	−0.355752	+	0.127664i
$113$			8.36855i			0.787247i	0.919272	+	0.393624i	$0.128779\pi$
$113$			8.36855i			0.787247i	−0.919272	+	0.393624i	$0.871221\pi$
$114$		0			0
$115$	6.98793			0.651628
$116$	−8.22565	+	11.6911i	−0.763732	+	1.08549i
$117$		0			0
$118$	4.83886	+	9.32108i	0.445453	+	0.858075i
$119$	−4.00897			−0.367502
$120$		0			0
$121$	10.2458			0.931441
$122$	−1.49400	−	2.87790i	−0.135261	−	0.260552i
$123$		0			0
$124$	−6.60958	−	4.65039i	−0.593558	−	0.417617i
$125$	12.1716			1.08866
$126$		0			0
$127$			6.53098i			0.579531i	0.957098	+	0.289765i	$0.0935772\pi$
$127$			6.53098i			0.579531i	−0.957098	+	0.289765i	$0.906423\pi$
$128$	11.0646	−	2.36122i	0.977979	−	0.208705i
$129$		0			0
$130$	1.03826	+	2.00000i	0.0910615	+	0.175412i
$131$			16.1448i			1.41058i	0.708920	+	0.705289i	$0.249183\pi$
$131$			16.1448i			1.41058i	−0.708920	+	0.705289i	$0.750817\pi$
$132$		0			0
$133$			3.39311i			0.294220i
$134$	15.8499	−	8.22818i	1.36923	−	0.710807i
$135$		0			0
$136$	11.2370	+	1.51818i	0.963564	+	0.130183i
$137$			7.12878i			0.609053i	0.952504	+	0.304527i	$0.0984982\pi$
$137$			7.12878i			0.609053i	−0.952504	+	0.304527i	$0.901502\pi$
$138$		0			0
$139$	−18.2465			−1.54765			−0.773824	−	0.633401i	$-0.781659\pi$
$139$	−18.2465			−1.54765			−0.773824	+	0.633401i	$0.781659\pi$
$140$	2.98457	+	2.09990i	0.252242	+	0.177474i
$141$		0			0
$142$	4.13627	−	2.14727i	0.347108	−	0.180195i
$143$	−0.758374			−0.0634184
$144$		0			0
$145$	13.0415			1.08303
$146$	−19.1872	+	9.96067i	−1.58794	+	0.824351i
$147$		0			0
$148$	3.54127	+	2.49158i	0.291091	+	0.204807i
$149$	8.34991			0.684051			0.342026	−	0.939691i	$-0.388887\pi$
$149$	8.34991			0.684051			0.342026	+	0.939691i	$0.388887\pi$
$150$		0			0
$151$		−	22.2465i		−	1.81039i	−0.424992	−	0.905197i	$-0.639723\pi$
$151$		−	22.2465i		−	1.81039i	0.424992	−	0.905197i	$-0.360277\pi$
$152$	1.28495	−	9.51076i	0.104224	−	0.771424i
$153$		0			0
$154$	−1.09001	+	0.565855i	−0.0878351	+	0.0455979i
$155$			7.37302i			0.592215i
$156$		0			0
$157$			3.25089i			0.259449i	0.991550	+	0.129725i	$0.0414093\pi$
$157$			3.25089i			0.259449i	−0.991550	+	0.129725i	$0.958591\pi$
$158$	2.03080	+	3.91193i	0.161562	+	0.311217i
$159$		0			0
$160$	−7.57042	−	7.01617i	−0.598494	−	0.554677i
$161$			3.82976i			0.301828i
$162$		0			0
$163$	16.1209			1.26269			0.631344	−	0.775502i	$-0.282503\pi$
$163$	16.1209			1.26269			0.631344	+	0.775502i	$0.282503\pi$
$164$	−14.5467	−	10.2348i	−1.13591	−	0.799207i
$165$		0			0
$166$	0.0211865	+	0.0408116i	0.00164439	+	0.00316759i
$167$	14.7290			1.13976			0.569881	−	0.821727i	$-0.306989\pi$
$167$	14.7290			1.13976			0.569881	+	0.821727i	$0.306989\pi$
$168$		0			0
$169$	12.2374			0.941337
$170$	−4.76635	−	9.18140i	−0.365562	−	0.704182i
$171$		0			0
$172$	−10.4731	+	14.8853i	−0.798565	+	1.13500i
$173$	−21.5005			−1.63465			−0.817327	−	0.576175i	$-0.804545\pi$
$173$	−21.5005			−1.63465			−0.817327	+	0.576175i	$0.804545\pi$
$174$		0			0
$175$			1.67069i			0.126292i
$176$	3.26953	−	1.17329i	0.246450	−	0.0884401i
$177$		0			0
$178$	8.90031	+	17.1446i	0.667106	+	1.28505i
$179$			3.87443i			0.289588i	0.989462	+	0.144794i	$0.0462520\pi$
$179$			3.87443i			0.289588i	−0.989462	+	0.144794i	$0.953748\pi$
$180$		0			0
$181$		−	25.4192i		−	1.88939i	−0.327944	−	0.944697i	$-0.606356\pi$
$181$		−	25.4192i		−	1.88939i	0.327944	−	0.944697i	$-0.393644\pi$
$182$	−1.09611	+	0.569023i	−0.0812489	+	0.0421788i
$183$		0			0
$184$	1.45031	−	10.7347i	0.106918	−	0.791371i
$185$		−	3.95031i		−	0.290432i
$186$		0			0
$187$	3.48147			0.254590
$188$	−8.54649	+	12.1471i	−0.623317	+	0.885917i
$189$		0			0
$190$	−7.77095	+	4.03414i	−0.563764	+	0.292667i
$191$	−9.48860			−0.686571			−0.343285	−	0.939231i	$-0.611540\pi$
$191$	−9.48860			−0.686571			−0.343285	+	0.939231i	$0.611540\pi$
$192$		0			0
$193$	−14.1615			−1.01937			−0.509684	−	0.860362i	$-0.670238\pi$
$193$	−14.1615			−1.01937			−0.509684	+	0.860362i	$0.670238\pi$
$194$	4.75799	−	2.47002i	0.341603	−	0.177337i
$195$		0			0
$196$	−1.15086	+	1.63571i	−0.0822039	+	0.116836i
$197$	−3.81914			−0.272103			−0.136051	−	0.990702i	$-0.543441\pi$
$197$	−3.81914			−0.272103			−0.136051	+	0.990702i	$0.543441\pi$
$198$		0			0
$199$		−	18.4493i		−	1.30784i	−0.756565	−	0.653919i	$-0.773124\pi$
$199$		−	18.4493i		−	1.30784i	0.756565	−	0.653919i	$-0.226876\pi$
$200$	0.632683	−	4.68289i	0.0447374	−	0.331130i
$201$		0			0
$202$	−7.21046	+	3.74317i	−0.507326	+	0.263369i
$203$			7.14742i			0.501651i
$204$		0			0
$205$			16.2270i			1.13334i
$206$	−12.3251	−	23.7418i	−0.858732	−	1.65417i
$207$		0			0
$208$	3.28783	−	1.17986i	0.227970	−	0.0818085i
$209$		−	2.94664i		−	0.203824i
$210$		0			0
$211$	−8.14222			−0.560534			−0.280267	−	0.959922i	$-0.590423\pi$
$211$	−8.14222			−0.560534			−0.280267	+	0.959922i	$0.590423\pi$
$212$	10.9322	−	15.5379i	0.750828	−	1.06715i
$213$		0			0
$214$	−4.18983	−	8.07085i	−0.286411	−	0.551712i
$215$	16.6047			1.13243
$216$		0			0
$217$	−4.04081			−0.274308
$218$	−6.14707	−	11.8411i	−0.416332	−	0.801980i
$219$		0			0
$220$	−2.59186	−	1.82359i	−0.174743	−	0.122946i
$221$	3.50096			0.235500
$222$		0			0
$223$		−	13.2068i		−	0.884396i	−0.896918	−	0.442198i	$-0.854199\pi$
$223$		−	13.2068i		−	0.884396i	0.896918	−	0.442198i	$-0.145801\pi$
$224$	3.84524	−	4.14900i	0.256921	−	0.277216i
$225$		0			0
$226$	−5.45288	−	10.5039i	−0.362720	−	0.698707i
$227$		−	13.5471i		−	0.899156i	−0.893241	−	0.449578i	$-0.851574\pi$
$227$		−	13.5471i		−	0.899156i	0.893241	−	0.449578i	$-0.148426\pi$
$228$		0			0
$229$		−	23.7835i		−	1.57166i	−0.618444	−	0.785829i	$-0.712237\pi$
$229$		−	23.7835i		−	1.57166i	0.618444	−	0.785829i	$-0.287763\pi$
$230$	−8.77098	+	4.55328i	−0.578341	+	0.300235i
$231$		0			0
$232$	2.70669	−	20.0339i	0.177703	−	1.31529i
$233$			0.124045i			0.00812644i	0.999992	+	0.00406322i	$0.00129337\pi$
$233$			0.124045i			0.00812644i	−0.999992	+	0.00406322i	$0.998707\pi$
$234$		0			0
$235$	13.5501			0.883914
$236$	−12.1471	−	8.54649i	−0.790708	−	0.556329i
$237$		0			0
$238$	5.03190	−	2.61221i	0.326170	−	0.169325i
$239$	8.41079			0.544049			0.272024	−	0.962290i	$-0.412307\pi$
$239$	8.41079			0.544049			0.272024	+	0.962290i	$0.412307\pi$
$240$		0			0
$241$	−3.31950			−0.213828			−0.106914	−	0.994268i	$-0.534097\pi$
$241$	−3.31950			−0.213828			−0.106914	+	0.994268i	$0.534097\pi$
$242$	−12.8602	+	6.67611i	−0.826684	+	0.429157i
$243$		0			0
$244$	3.75043	+	2.63874i	0.240097	+	0.168928i
$245$	1.82464			0.116572
$246$		0			0
$247$		−	2.96314i		−	0.188540i
$248$	11.3262	+	1.53024i	0.719217	+	0.0971700i
$249$		0			0
$250$	−15.2773	+	7.93092i	−0.966222	+	0.501596i
$251$			7.22229i			0.455867i	0.973677	+	0.227934i	$0.0731969\pi$
$251$			7.22229i			0.455867i	−0.973677	+	0.227934i	$0.926803\pi$
$252$		0			0
$253$		−	3.32584i		−	0.209094i
$254$	−4.25553	−	8.19742i	−0.267016	−	0.514352i
$255$		0			0
$256$	−12.3492	+	10.1733i	−0.771828	+	0.635831i
$257$			8.06495i			0.503077i	0.967847	+	0.251539i	$0.0809366\pi$
$257$			8.06495i			0.503077i	−0.967847	+	0.251539i	$0.919063\pi$
$258$		0			0
$259$	2.16498			0.134525
$260$	−2.60637	−	1.83380i	−0.161640	−	0.113727i
$261$		0			0
$262$	−10.5198	−	20.2643i	−0.649917	−	1.25193i
$263$	−6.65564			−0.410404			−0.205202	−	0.978720i	$-0.565785\pi$
$263$	−6.65564			−0.410404			−0.205202	+	0.978720i	$0.565785\pi$
$264$		0			0
$265$	−17.3326			−1.06474
$266$	−2.21092	−	4.25890i	−0.135560	−	0.261130i
$267$		0			0
$268$	−14.5328	+	20.6554i	−0.887731	+	1.26173i
$269$	2.79311			0.170299			0.0851494	−	0.996368i	$-0.472863\pi$
$269$	2.79311			0.170299			0.0851494	+	0.996368i	$0.472863\pi$
$270$		0			0
$271$			4.32479i			0.262712i	0.991335	+	0.131356i	$0.0419331\pi$
$271$			4.32479i			0.262712i	−0.991335	+	0.131356i	$0.958067\pi$
$272$	−15.0935	+	5.41638i	−0.915175	+	0.328416i
$273$		0			0
$274$	−4.64506	−	8.94777i	−0.280618	−	0.540554i
$275$		−	1.45086i		−	0.0874902i
$276$		0			0
$277$		−	11.6978i		−	0.702853i	−0.936215	−	0.351427i	$-0.885697\pi$
$277$		−	11.6978i		−	0.702853i	0.936215	−	0.351427i	$-0.114303\pi$
$278$	22.9023	−	11.8893i	1.37359	−	0.713072i
$279$		0			0
$280$	−5.11439	−	0.690982i	−0.305643	−	0.0412941i
$281$			26.2705i			1.56717i	0.621287	+	0.783583i	$0.286610\pi$
$281$			26.2705i			1.56717i	−0.621287	+	0.783583i	$0.713390\pi$
$282$		0			0
$283$	10.2545			0.609570			0.304785	−	0.952421i	$-0.401415\pi$
$283$	10.2545			0.609570			0.304785	+	0.952421i	$0.401415\pi$
$284$	−3.79255	+	5.39033i	−0.225046	+	0.319857i
$285$		0			0
$286$	0.951880	−	0.494150i	0.0562859	−	0.0292197i
$287$	−8.89325			−0.524952
$288$		0			0
$289$	0.928152			0.0545972
$290$	−16.3691	+	8.49772i	−0.961228	+	0.499003i
$291$		0			0
$292$	17.5927	−	25.0045i	1.02954	−	1.46328i
$293$	20.8121			1.21585			0.607927	−	0.793993i	$-0.292001\pi$
$293$	20.8121			1.21585			0.607927	+	0.793993i	$0.292001\pi$
$294$		0			0
$295$			13.5501i			0.788920i
$296$	−6.06836	−	0.819867i	−0.352716	−	0.0476538i
$297$		0			0
$298$	−10.4805	+	5.44074i	−0.607118	+	0.315173i
$299$		−	3.34446i		−	0.193415i
$300$		0			0
$301$			9.10026i			0.524530i
$302$	14.4956	+	27.9229i	0.834131	+	1.60678i
$303$		0			0
$304$	4.58431	+	12.7748i	0.262928	+	0.732685i
$305$		−	4.18363i		−	0.239554i
$306$		0			0
$307$	−2.60226			−0.148519			−0.0742593	−	0.997239i	$-0.523659\pi$
$307$	−2.60226			−0.148519			−0.0742593	+	0.997239i	$0.523659\pi$
$308$	0.999425	−	1.42048i	0.0569475	−	0.0809392i
$309$		0			0
$310$	−4.80420	−	9.25433i	−0.272860	−	0.525610i
$311$	−0.876014			−0.0496742			−0.0248371	−	0.999692i	$-0.507907\pi$
$311$	−0.876014			−0.0496742			−0.0248371	+	0.999692i	$0.507907\pi$
$312$		0			0
$313$	17.6207			0.995982			0.497991	−	0.867182i	$-0.334071\pi$
$313$	17.6207			0.995982			0.497991	+	0.867182i	$0.334071\pi$
$314$	−2.11825	−	4.08039i	−0.119540	−	0.230270i
$315$		0			0
$316$	−5.09797	−	3.58685i	−0.286783	−	0.201776i
$317$	−27.6841			−1.55489			−0.777447	−	0.628948i	$-0.783486\pi$
$317$	−27.6841			−1.55489			−0.777447	+	0.628948i	$0.783486\pi$
$318$		0			0
$319$		−	6.20696i		−	0.347523i
$320$	14.0738	+	3.87359i	0.786748	+	0.216540i
$321$		0			0
$322$	−2.49544	−	4.80697i	−0.139066	−	0.267882i
$323$			13.6029i			0.756885i
$324$		0			0
$325$		−	1.45898i		−	0.0809298i
$326$	−20.2344	+	10.5043i	−1.12068	+	0.581778i
$327$		0			0
$328$	24.9274	+	3.36783i	1.37639	+	0.185957i
$329$			7.42621i			0.409420i
$330$		0			0
$331$	22.7716			1.25164			0.625820	−	0.779967i	$-0.284764\pi$
$331$	22.7716			1.25164			0.625820	+	0.779967i	$0.284764\pi$
$332$	−0.0531850	−	0.0374201i	−0.00291891	−	0.00205370i
$333$		0			0
$334$	−18.4872	+	9.59728i	−1.01158	+	0.525140i
$335$	23.0412			1.25888
$336$		0			0
$337$	−5.99770			−0.326715			−0.163358	−	0.986567i	$-0.552232\pi$
$337$	−5.99770			−0.326715			−0.163358	+	0.986567i	$0.552232\pi$
$338$	−15.3599	+	7.97378i	−0.835467	+	0.433717i
$339$		0			0
$340$	11.9651	+	8.41842i	0.648897	+	0.456553i
$341$	3.50912			0.190029
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	3.44622	−	25.5077i	0.185808	−	1.37528i
$345$		0			0
$346$	26.9866	−	14.0096i	1.45081	−	0.753159i
$347$		−	30.6132i		−	1.64340i	−0.569919	−	0.821701i	$-0.693025\pi$
$347$		−	30.6132i		−	1.64340i	0.569919	−	0.821701i	$-0.306975\pi$
$348$		0			0
$349$		−	4.49337i		−	0.240525i	−0.992742	−	0.120262i	$-0.961626\pi$
$349$		−	4.49337i		−	0.240525i	0.992742	−	0.120262i	$-0.0383736\pi$
$350$	−1.08861	−	2.09699i	−0.0581887	−	0.112089i
$351$		0			0
$352$	−3.33928	+	3.60307i	−0.177984	+	0.192044i
$353$			5.42679i			0.288839i	0.989517	+	0.144419i	$0.0461315\pi$
$353$			5.42679i			0.288839i	−0.989517	+	0.144419i	$0.953869\pi$
$354$		0			0
$355$	6.01294			0.319134
$356$	−22.3426	−	15.7199i	−1.18416	−	0.833153i
$357$		0			0
$358$	−2.52455	−	4.86303i	−0.133426	−	0.257019i
$359$	−33.4019			−1.76288			−0.881441	−	0.472294i	$-0.843426\pi$
$359$	−33.4019			−1.76288			−0.881441	+	0.472294i	$0.843426\pi$
$360$		0			0
$361$	−7.48680			−0.394042
$362$	16.5630	+	31.9052i	0.870530	+	1.67690i
$363$		0			0
$364$	1.00502	−	1.42843i	0.0526773	−	0.0748701i
$365$	−27.8926			−1.45997
$366$		0			0
$367$			13.9494i			0.728152i	0.931369	+	0.364076i	$0.118615\pi$
$367$			13.9494i			0.728152i	−0.931369	+	0.364076i	$0.881385\pi$
$368$	5.17426	+	14.4188i	0.269727	+	0.751629i
$369$		0			0
$370$	2.57399	+	4.95827i	0.133815	+	0.257768i
$371$		−	9.49922i		−	0.493175i
$372$		0			0
$373$			18.4165i			0.953569i	0.879020	+	0.476785i	$0.158198\pi$
$373$			18.4165i			0.953569i	−0.879020	+	0.476785i	$0.841802\pi$
$374$	−4.36980	+	2.26850i	−0.225957	+	0.117301i
$375$		0			0
$376$	2.81227	−	20.8154i	0.145032	−	1.07347i
$377$		−	6.24171i		−	0.321464i
$378$		0			0
$379$	4.63575			0.238123			0.119061	−	0.992887i	$-0.462011\pi$
$379$	4.63575			0.238123			0.119061	+	0.992887i	$0.462011\pi$
$380$	7.12518	−	10.1270i	0.365514	−	0.519503i
$381$		0			0
$382$	11.9097	−	6.18269i	0.609354	−	0.316334i
$383$	18.2653			0.933311			0.466656	−	0.884439i	$-0.345459\pi$
$383$	18.2653			0.933311			0.466656	+	0.884439i	$0.345459\pi$
$384$		0			0
$385$	−1.58455			−0.0807562
$386$	17.7750	−	9.22753i	0.904722	−	0.469669i
$387$		0			0
$388$	−4.36259	+	6.20053i	−0.221477	+	0.314784i
$389$	24.4390			1.23911			0.619553	−	0.784955i	$-0.287314\pi$
$389$	24.4390			1.23911			0.619553	+	0.784955i	$0.287314\pi$
$390$		0			0
$391$			15.3534i			0.776455i
$392$	0.378695	−	2.80296i	0.0191270	−	0.141571i
$393$		0			0
$394$	4.79363	−	2.48852i	0.241500	−	0.125370i
$395$			5.68682i			0.286135i
$396$		0			0
$397$		−	35.2267i		−	1.76798i	−0.467510	−	0.883988i	$-0.654849\pi$
$397$		−	35.2267i		−	1.76798i	0.467510	−	0.883988i	$-0.345151\pi$
$398$	12.0214	+	23.1569i	0.602580	+	1.16075i
$399$		0			0
$400$	2.25721	+	6.29002i	0.112861	+	0.314501i
$401$			35.7617i			1.78585i	0.450203	+	0.892926i	$0.351352\pi$
$401$			35.7617i			1.78585i	−0.450203	+	0.892926i	$0.648648\pi$
$402$		0			0
$403$	3.52876			0.175780
$404$	6.61127	−	9.39656i	0.328923	−	0.467497i
$405$		0			0
$406$	−4.65720	−	8.97116i	−0.231133	−	0.445231i
$407$	−1.88011			−0.0931936
$408$		0			0
$409$	−29.2063			−1.44416			−0.722080	−	0.691809i	$-0.756814\pi$
$409$	−29.2063			−1.44416			−0.722080	+	0.691809i	$0.756814\pi$
$410$	−10.5734	−	20.3675i	−0.522182	−	1.00588i
$411$		0			0
$412$	30.9400	+	21.7689i	1.52430	+	1.07248i
$413$	−7.42621			−0.365420
$414$		0			0
$415$			0.0593282i			0.00291231i
$416$	−3.35797	+	3.62324i	−0.164638	+	0.177644i
$417$		0			0
$418$	1.92001	+	3.69851i	0.0939107	+	0.180900i
$419$		−	33.2606i		−	1.62489i	−0.583039	−	0.812444i	$-0.698137\pi$
$419$		−	33.2606i		−	1.62489i	0.583039	−	0.812444i	$-0.301863\pi$
$420$		0			0
$421$		−	34.9320i		−	1.70248i	−0.524774	−	0.851242i	$-0.675850\pi$
$421$		−	34.9320i		−	1.70248i	0.524774	−	0.851242i	$-0.324150\pi$
$422$	10.2198	−	5.30541i	0.497492	−	0.258263i
$423$		0			0
$424$	−3.59731	+	26.6259i	−0.174701	+	1.29307i
$425$			6.69776i			0.324889i
$426$		0			0
$427$	2.29285			0.110959
$428$	10.5178	+	7.40016i	0.508398	+	0.357700i
$429$		0			0
$430$	−20.8415	+	10.8195i	−1.00507	+	0.521762i
$431$	−18.6171			−0.896756			−0.448378	−	0.893844i	$-0.647998\pi$
$431$	−18.6171			−0.896756			−0.448378	+	0.893844i	$0.647998\pi$
$432$		0			0
$433$	−5.25746			−0.252657			−0.126329	−	0.991988i	$-0.540319\pi$
$433$	−5.25746			−0.252657			−0.126329	+	0.991988i	$0.540319\pi$
$434$	5.07187	−	2.63296i	0.243457	−	0.126386i
$435$		0			0
$436$	15.4311	+	10.8571i	0.739017	+	0.519960i
$437$	12.9948			0.621626
$438$		0			0
$439$			33.8919i			1.61757i	0.588104	+	0.808785i	$0.299874\pi$
$439$			33.8919i			1.61757i	−0.588104	+	0.808785i	$0.700126\pi$
$440$	4.44144	+	0.600062i	0.211737	+	0.0286068i
$441$		0			0
$442$	−4.39426	+	2.28120i	−0.209014	+	0.108505i
$443$		−	17.6784i		−	0.839928i	−0.907541	−	0.419964i	$-0.862043\pi$
$443$		−	17.6784i		−	0.839928i	0.907541	−	0.419964i	$-0.137957\pi$
$444$		0			0
$445$			24.9233i			1.18148i
$446$	8.60548	+	16.5767i	0.407481	+	0.784930i
$447$		0			0
$448$	−2.12293	+	7.71318i	−0.100299	+	0.364414i
$449$		−	35.0517i		−	1.65419i	−0.562060	−	0.827096i	$-0.689991\pi$
$449$		−	35.0517i		−	1.65419i	0.562060	−	0.827096i	$-0.310009\pi$
$450$		0			0
$451$	7.72307			0.363665
$452$	13.6885	+	9.63099i	0.643852	+	0.453004i
$453$		0			0
$454$	8.82721	+	17.0038i	0.414282	+	0.798030i
$455$	−1.59342			−0.0747008
$456$		0			0
$457$	−29.3167			−1.37138			−0.685689	−	0.727895i	$-0.740499\pi$
$457$	−29.3167			−1.37138			−0.685689	+	0.727895i	$0.740499\pi$
$458$	15.4971	+	29.8521i	0.724134	+	1.39490i
$459$		0			0
$460$	8.04210	−	11.4302i	0.374965	−	0.532936i
$461$	−13.2335			−0.616345			−0.308172	−	0.951331i	$-0.599717\pi$
$461$	−13.2335			−0.616345			−0.308172	+	0.951331i	$0.599717\pi$
$462$		0			0
$463$			41.3986i			1.92396i	0.273125	+	0.961978i	$0.411943\pi$
$463$			41.3986i			1.92396i	−0.273125	+	0.961978i	$0.588057\pi$
$464$	9.65663	+	26.9095i	0.448298	+	1.24924i
$465$		0			0
$466$	−0.0808266	−	0.155696i	−0.00374422	−	0.00721248i
$467$			17.8192i			0.824573i	0.911054	+	0.412286i	$0.135270\pi$
$467$			17.8192i			0.824573i	−0.911054	+	0.412286i	$0.864730\pi$
$468$		0			0
$469$			12.6278i			0.583098i
$470$	−17.0076	+	8.82917i	−0.784503	+	0.407259i
$471$		0			0
$472$	20.8154	+	2.81227i	0.958105	+	0.129445i
$473$		−	7.90284i		−	0.363373i
$474$		0			0
$475$	5.66884			0.260104
$476$	−4.61375	+	6.55750i	−0.211471	+	0.300562i
$477$		0			0
$478$	−10.5569	+	5.48041i	−0.482861	+	0.250668i
$479$	13.5424			0.618767			0.309384	−	0.950937i	$-0.399877\pi$
$479$	13.5424			0.618767			0.309384	+	0.950937i	$0.399877\pi$
$480$		0			0
$481$	−1.89064			−0.0862056
$482$	4.16651	−	2.16296i	0.189779	−	0.0985202i
$483$		0			0
$484$	11.7915	−	16.7592i	0.535977	−	0.761781i
$485$	6.91673			0.314073
$486$		0			0
$487$			3.47083i			0.157278i	0.996903	+	0.0786391i	$0.0250575\pi$
$487$			3.47083i			0.157278i	−0.996903	+	0.0786391i	$0.974943\pi$
$488$	−6.42677	−	0.868291i	−0.290926	−	0.0393057i
$489$		0			0
$490$	−2.29021	+	1.18892i	−0.103461	+	0.0537100i
$491$			8.90015i			0.401658i	0.979626	+	0.200829i	$0.0643636\pi$
$491$			8.90015i			0.401658i	−0.979626	+	0.200829i	$0.935636\pi$
$492$		0			0
$493$			28.6538i			1.29050i
$494$	1.93076	+	3.71921i	0.0868689	+	0.167335i
$495$		0			0
$496$	−15.2133	+	5.45940i	−0.683099	+	0.245134i
$497$			3.29541i			0.147820i
$498$		0			0
$499$	−22.9352			−1.02672			−0.513360	−	0.858173i	$-0.671599\pi$
$499$	−22.9352			−1.02672			−0.513360	+	0.858173i	$0.671599\pi$
$500$	14.0078	−	19.9092i	0.626446	−	0.890365i
$501$		0			0
$502$	−4.70599	−	9.06514i	−0.210039	−	0.404597i
$503$	32.2317			1.43714			0.718569	−	0.695455i	$-0.244797\pi$
$503$	32.2317			1.43714			0.718569	+	0.695455i	$0.244797\pi$
$504$		0			0
$505$	−10.4819			−0.466439
$506$	2.16709	+	4.17446i	0.0963389	+	0.185577i
$507$		0			0
$508$	10.6828	+	7.51621i	0.473971	+	0.333478i
$509$	−35.2935			−1.56436			−0.782179	−	0.623054i	$-0.785892\pi$
$509$	−35.2935			−1.56436			−0.782179	+	0.623054i	$0.785892\pi$
$510$		0			0
$511$		−	15.2867i		−	0.676242i
$512$	8.87145	−	20.8158i	0.392066	−	0.919937i
$513$		0			0
$514$	−5.25506	−	10.1228i	−0.231791	−	0.446498i
$515$		−	34.5138i		−	1.52086i
$516$		0			0
$517$		−	6.44906i		−	0.283629i
$518$	−2.71740	+	1.41068i	−0.119396	+	0.0619819i
$519$		0			0
$520$	4.46630	+	0.603421i	0.195860	+	0.0264618i
$521$		−	0.819575i		−	0.0359062i	−0.999839	−	0.0179531i	$-0.994285\pi$
$521$		−	0.819575i		−	0.0359062i	0.999839	−	0.0179531i	$-0.00571496\pi$
$522$		0			0
$523$	−34.3253			−1.50094			−0.750471	−	0.660904i	$-0.770173\pi$
$523$	−34.3253			−1.50094			−0.750471	+	0.660904i	$0.770173\pi$
$524$	26.4081	+	18.5803i	1.15365	+	0.811686i
$525$		0			0
$526$	8.35389	−	4.33676i	0.364247	−	0.189092i
$527$	−16.1995			−0.705661
$528$		0			0
$529$	−8.33292			−0.362301
$530$	21.7552	−	11.2938i	0.944988	−	0.490572i
$531$		0			0
$532$	5.55013	+	3.90498i	0.240629	+	0.169302i
$533$	7.76631			0.336396
$534$		0			0
$535$		−	11.7327i		−	0.507248i
$536$	4.78209	−	35.3953i	0.206555	−	1.52884i
$537$		0			0
$538$	−3.50580	+	1.81997i	−0.151146	+	0.0784644i
$539$		−	0.868419i		−	0.0374055i
$540$		0			0
$541$			21.7178i			0.933721i	0.884331	+	0.466861i	$0.154615\pi$
$541$			21.7178i			0.933721i	−0.884331	+	0.466861i	$0.845385\pi$
$542$	−2.81800	−	5.42830i	−0.121043	−	0.233166i
$543$		0			0
$544$	15.4154	−	16.6332i	0.660931	−	0.713143i
$545$		−	17.2135i		−	0.737345i
$546$		0			0
$547$	36.8201			1.57431			0.787157	−	0.616753i	$-0.211552\pi$
$547$	36.8201			1.57431			0.787157	+	0.616753i	$0.211552\pi$
$548$	11.6606	+	8.20420i	0.498116	+	0.350466i
$549$		0			0
$550$	0.945370	+	1.82106i	0.0403107	+	0.0776504i
$551$	24.2520			1.03317
$552$		0			0
$553$	−3.11668			−0.132535
$554$	7.62220	+	14.6826i	0.323836	+	0.623805i
$555$		0			0
$556$	−20.9991	+	29.8459i	−0.890559	+	1.26575i
$557$	−5.04764			−0.213875			−0.106938	−	0.994266i	$-0.534105\pi$
$557$	−5.04764			−0.213875			−0.106938	+	0.994266i	$0.534105\pi$
$558$		0			0
$559$		−	7.94708i		−	0.336126i
$560$	6.86962	−	2.46521i	0.290294	−	0.104174i
$561$		0			0
$562$	−17.1176	−	32.9737i	−0.722064	−	1.39091i
$563$		−	17.8517i		−	0.752359i	−0.926547	−	0.376179i	$-0.877238\pi$
$563$		−	17.8517i		−	0.752359i	0.926547	−	0.376179i	$-0.122762\pi$
$564$		0			0
$565$		−	15.2696i		−	0.642396i
$566$	−12.8711	+	6.68178i	−0.541013	+	0.280856i
$567$		0			0
$568$	1.24796	−	9.23692i	0.0523631	−	0.387572i
$569$			6.17085i			0.258695i	0.991599	+	0.129348i	$0.0412883\pi$
$569$			6.17085i			0.258695i	−0.991599	+	0.129348i	$0.958712\pi$
$570$		0			0
$571$	26.3284			1.10181			0.550904	−	0.834568i	$-0.314283\pi$
$571$	26.3284			1.10181			0.550904	+	0.834568i	$0.314283\pi$
$572$	−0.872778	+	1.24048i	−0.0364927	+	0.0518669i
$573$		0			0
$574$	11.1625	−	5.79478i	0.465912	−	0.241869i
$575$	6.39836			0.266830
$576$		0			0
$577$	−26.1304			−1.08782			−0.543911	−	0.839143i	$-0.683057\pi$
$577$	−26.1304			−1.08782			−0.543911	+	0.839143i	$0.683057\pi$
$578$	−1.16498	+	0.604776i	−0.0484567	+	0.0251554i
$579$		0			0
$580$	15.0088	−	21.3320i	0.623208	−	0.885763i
$581$	−0.0325150			−0.00134895
$582$		0			0
$583$			8.24930i			0.341651i
$584$	−5.78898	+	42.8479i	−0.239550	+	1.77306i
$585$		0			0
$586$	−26.1225	+	13.5610i	−1.07911	+	0.560199i
$587$		−	37.9967i		−	1.56829i	−0.620576	−	0.784146i	$-0.713101\pi$
$587$		−	37.9967i		−	1.56829i	0.620576	−	0.784146i	$-0.286899\pi$
$588$		0			0
$589$			13.7109i			0.564949i
$590$	−8.82917	−	17.0076i	−0.363491	−	0.700192i
$591$		0			0
$592$	8.15098	−	2.92503i	0.335003	−	0.120218i
$593$		−	14.8985i		−	0.611809i	−0.952062	−	0.305905i	$-0.901041\pi$
$593$		−	14.8985i		−	0.611809i	0.952062	−	0.305905i	$-0.0989589\pi$
$594$		0			0
$595$	7.31492			0.299883
$596$	9.60954	−	13.6580i	0.393622	−	0.559453i
$597$		0			0
$598$	2.17922	+	4.19783i	0.0891150	+	0.171662i
$599$	−2.28660			−0.0934279			−0.0467140	−	0.998908i	$-0.514875\pi$
$599$	−2.28660			−0.0934279			−0.0467140	+	0.998908i	$0.514875\pi$
$600$		0			0
$601$	13.9248			0.568004			0.284002	−	0.958824i	$-0.408338\pi$
$601$	13.9248			0.568004			0.284002	+	0.958824i	$0.408338\pi$
$602$	−5.92966	−	11.4223i	−0.241675	−	0.465538i
$603$		0			0
$604$	−36.3887	−	25.6025i	−1.48064	−	1.04175i
$605$	−18.6950			−0.760059
$606$		0			0
$607$			36.9575i			1.50006i	0.661404	+	0.750029i	$0.269961\pi$
$607$			36.9575i			1.50006i	−0.661404	+	0.750029i	$0.730039\pi$
$608$	−14.0780	−	13.0473i	−0.570938	−	0.529138i
$609$		0			0
$610$	2.72602	+	5.25112i	0.110373	+	0.212612i
$611$		−	6.48516i		−	0.262362i
$612$		0			0
$613$			20.3787i			0.823090i	0.911390	+	0.411545i	$0.135011\pi$
$613$			20.3787i			0.823090i	−0.911390	+	0.411545i	$0.864989\pi$
$614$	3.26625	−	1.69561i	0.131815	−	0.0684292i
$615$		0			0
$616$	−0.328866	+	2.43414i	−0.0132504	+	0.0980745i
$617$		−	18.1491i		−	0.730656i	−0.930879	−	0.365328i	$-0.880957\pi$
$617$		−	18.1491i		−	0.730656i	0.930879	−	0.365328i	$-0.119043\pi$
$618$		0			0
$619$	−26.4388			−1.06266			−0.531332	−	0.847164i	$-0.678308\pi$
$619$	−26.4388			−1.06266			−0.531332	+	0.847164i	$0.678308\pi$
$620$	12.0601	+	8.48528i	0.484345	+	0.340777i
$621$		0			0
$622$	1.09954	−	0.570804i	0.0440875	−	0.0228872i
$623$	−13.6593			−0.547249
$624$		0			0
$625$	−13.8553			−0.554213
$626$	−22.1168	+	11.4815i	−0.883967	+	0.458894i
$627$		0			0
$628$	5.31750	+	3.74130i	0.212191	+	0.149294i
$629$	8.67934			0.346068
$630$		0			0
$631$		−	24.1890i		−	0.962948i	−0.876460	−	0.481474i	$-0.840102\pi$
$631$		−	24.1890i		−	0.962948i	0.876460	−	0.481474i	$-0.159898\pi$
$632$	8.73593	+	1.18027i	0.347497	+	0.0469487i
$633$		0			0
$634$	34.7480	−	18.0388i	1.38002	−	0.716410i
$635$		−	11.9167i		−	0.472899i
$636$		0			0
$637$		−	0.873281i		−	0.0346006i
$638$	4.04441	+	7.79073i	0.160120	+	0.308438i
$639$		0			0
$640$	−20.1888	+	4.30838i	−0.798034	+	0.170304i
$641$			12.5591i			0.496054i	0.968753	+	0.248027i	$0.0797821\pi$
$641$			12.5591i			0.496054i	−0.968753	+	0.248027i	$0.920218\pi$
$642$		0			0
$643$	−5.34203			−0.210669			−0.105334	−	0.994437i	$-0.533591\pi$
$643$	−5.34203			−0.210669			−0.105334	+	0.994437i	$0.533591\pi$
$644$	6.26436	+	4.40750i	0.246851	+	0.173680i
$645$		0			0
$646$	−8.86353	−	17.0738i	−0.348731	−	0.671760i
$647$	−42.2500			−1.66102			−0.830509	−	0.557006i	$-0.811950\pi$
$647$	−42.2500			−1.66102			−0.830509	+	0.557006i	$0.811950\pi$
$648$		0			0
$649$	6.44906			0.253148
$650$	0.950662	+	1.83126i	0.0372880	+	0.0718279i
$651$		0			0
$652$	18.5529	−	26.3691i	0.726586	−	1.03269i
$653$	5.77510			0.225997			0.112999	−	0.993595i	$-0.463954\pi$
$653$	5.77510			0.225997			0.112999	+	0.993595i	$0.463954\pi$
$654$		0			0
$655$		−	29.4584i		−	1.15104i
$656$	−33.4824	+	12.0154i	−1.30727	+	0.469121i
$657$		0			0
$658$	−4.83886	−	9.32108i	−0.188638	−	0.363374i
$659$			3.60497i			0.140430i	0.997532	+	0.0702148i	$0.0223685\pi$
$659$			3.60497i			0.140430i	−0.997532	+	0.0702148i	$0.977632\pi$
$660$		0			0
$661$		−	21.9760i		−	0.854769i	−0.904070	−	0.427384i	$-0.859435\pi$
$661$		−	21.9760i		−	0.854769i	0.904070	−	0.427384i	$-0.140565\pi$
$662$	−28.5820	+	14.8378i	−1.11087	+	0.576687i
$663$		0			0
$664$	0.0911384	+	0.0123133i	0.00353686	+	0.000477848i
$665$		−	6.19120i		−	0.240085i
$666$		0			0
$667$	27.3729			1.05988
$668$	16.9509	−	24.0922i	0.655850	−	0.932157i
$669$		0			0
$670$	−28.9204	+	15.0135i	−1.11729	+	0.580021i
$671$	−1.99116			−0.0768677
$672$		0			0
$673$	24.1597			0.931287			0.465644	−	0.884972i	$-0.345823\pi$
$673$	24.1597			0.931287			0.465644	+	0.884972i	$0.345823\pi$
$674$	7.52807	−	3.90805i	0.289971	−	0.150533i
$675$		0			0
$676$	14.0835	−	20.0168i	0.541671	−	0.769875i
$677$	−32.6288			−1.25403			−0.627013	−	0.779008i	$-0.715723\pi$
$677$	−32.6288			−1.25403			−0.627013	+	0.779008i	$0.715723\pi$
$678$		0			0
$679$			3.79074i			0.145475i
$680$	−20.5034	−	2.77013i	−0.786271	−	0.106229i
$681$		0			0
$682$	−4.40451	+	2.28651i	−0.168657	+	0.0875551i
$683$			43.5893i			1.66790i	0.551842	+	0.833948i	$0.313925\pi$
$683$			43.5893i			1.66790i	−0.551842	+	0.833948i	$0.686075\pi$
$684$		0			0
$685$		−	13.0075i		−	0.496989i
$686$	−0.651592	−	1.25516i	−0.0248779	−	0.0479222i
$687$		0			0
$688$	12.2950	+	34.2618i	0.468744	+	1.30622i
$689$			8.29548i			0.316033i
$690$		0			0
$691$	−17.5269			−0.666756			−0.333378	−	0.942793i	$-0.608188\pi$
$691$	−17.5269			−0.666756			−0.333378	+	0.942793i	$0.608188\pi$
$692$	−24.7440	+	35.1685i	−0.940625	+	1.33691i
$693$		0			0
$694$	19.9473	+	38.4245i	0.757190	+	1.45857i
$695$	33.2933			1.26289
$696$		0			0
$697$	−35.6528			−1.35045
$698$	2.92784	+	5.63990i	0.110821	+	0.213473i
$699$		0			0
$700$	2.73276	+	1.92273i	0.103289	+	0.0726722i
$701$	−15.1210			−0.571112			−0.285556	−	0.958362i	$-0.592178\pi$
$701$	−15.1210			−0.571112			−0.285556	+	0.958362i	$0.592178\pi$
$702$		0			0
$703$		−	7.34602i		−	0.277060i
$704$	1.84360	−	6.69827i	0.0694832	−	0.252451i
$705$		0			0
$706$	−3.53605	−	6.81149i	−0.133081	−	0.256354i
$707$		−	5.74466i		−	0.216050i
$708$		0			0
$709$		−	11.1649i		−	0.419307i	−0.977776	−	0.209654i	$-0.932766\pi$
$709$		−	11.1649i		−	0.419307i	0.977776	−	0.209654i	$-0.0672337\pi$
$710$	−7.54721	+	3.91799i	−0.283242	+	0.147039i
$711$		0			0
$712$	38.2865	+	5.17272i	1.43485	+	0.193856i
$713$			15.4753i			0.579556i
$714$		0			0
$715$	1.38376			0.0517496
$716$	6.33742	+	4.45890i	0.236841	+	0.166637i
$717$		0			0
$718$	41.9247	−	21.7644i	1.56462	−	0.812240i
$719$	1.96113			0.0731378			0.0365689	−	0.999331i	$-0.488357\pi$
$719$	1.96113			0.0731378			0.0365689	+	0.999331i	$0.488357\pi$
$720$		0			0
$721$	18.9154			0.704446
$722$	9.39713	−	4.87834i	0.349725	−	0.181553i
$723$		0			0
$724$	−41.5783	−	29.2538i	−1.54525	−	1.08721i
$725$	11.9411			0.443483
$726$		0			0
$727$		−	1.43512i		−	0.0532255i	−0.999646	−	0.0266128i	$-0.991528\pi$
$727$		−	1.43512i		−	0.0532255i	0.999646	−	0.0266128i	$-0.00847211\pi$
$728$	−0.330707	+	2.44777i	−0.0122568	+	0.0907204i
$729$		0			0
$730$	35.0097	−	18.1746i	1.29577	−	0.672673i
$731$			36.4827i			1.34936i
$732$		0			0
$733$			11.2055i			0.413886i	0.978353	+	0.206943i	$0.0663515\pi$
$733$			11.2055i			0.413886i	−0.978353	+	0.206943i	$0.933648\pi$
$734$	−9.08931	−	17.5087i	−0.335493	−	0.646258i
$735$		0			0
$736$	−15.8897	−	14.7263i	−0.585701	−	0.542820i
$737$		−	10.9662i		−	0.403946i
$738$		0			0
$739$	3.20841			0.118023			0.0590117	−	0.998257i	$-0.481205\pi$
$739$	3.20841			0.118023			0.0590117	+	0.998257i	$0.481205\pi$
$740$	−6.46154	−	4.54623i	−0.237531	−	0.167123i
$741$		0			0
$742$	6.18962	+	11.9230i	0.227228	+	0.437709i
$743$	−28.1666			−1.03333			−0.516666	−	0.856187i	$-0.672827\pi$
$743$	−28.1666			−1.03333			−0.516666	+	0.856187i	$0.672827\pi$
$744$		0			0
$745$	−15.2356			−0.558188
$746$	−12.0000	−	23.1156i	−0.439353	−	0.846324i
$747$		0			0
$748$	4.00666	−	5.69465i	0.146498	−	0.208217i
$749$	6.43014			0.234952
$750$		0			0
$751$		−	50.1612i		−	1.83041i	−0.402990	−	0.915204i	$-0.632029\pi$
$751$		−	50.1612i		−	1.83041i	0.402990	−	0.915204i	$-0.367971\pi$
$752$	10.0333	+	27.9591i	0.365876	+	1.01956i
$753$		0			0
$754$	4.06705	+	7.83434i	0.148113	+	0.285310i
$755$			40.5918i			1.47729i
$756$		0			0
$757$		−	28.2689i		−	1.02745i	−0.857954	−	0.513726i	$-0.828265\pi$
$757$		−	28.2689i		−	1.02745i	0.857954	−	0.513726i	$-0.171735\pi$
$758$	−5.81862	+	3.02062i	−0.211342	+	0.109714i
$759$		0			0
$760$	−2.34458	+	17.3537i	−0.0850468	+	0.629485i
$761$			25.9454i			0.940518i	0.882528	+	0.470259i	$0.155840\pi$
$761$			25.9454i			0.940518i	−0.882528	+	0.470259i	$0.844160\pi$
$762$		0			0
$763$	9.43392			0.341531
$764$	−10.9200	+	15.5205i	−0.395072	+	0.561514i
$765$		0			0
$766$	−22.9258	+	11.9015i	−0.828344	+	0.430019i
$767$	6.48516			0.234166
$768$		0			0
$769$	40.4165			1.45746			0.728728	−	0.684803i	$-0.240112\pi$
$769$	40.4165			1.45746			0.728728	+	0.684803i	$0.240112\pi$
$770$	1.98887	−	1.03248i	0.0716738	−	0.0372080i
$771$		0			0
$772$	−16.2979	+	23.1641i	−0.586572	+	0.833693i
$773$	53.3995			1.92065			0.960324	−	0.278888i	$-0.0899658\pi$
$773$	53.3995			1.92065			0.960324	+	0.278888i	$0.0899658\pi$
$774$		0			0
$775$			6.75095i			0.242501i
$776$	1.43553	−	10.6253i	0.0515327	−	0.381426i
$777$		0			0
$778$	−30.6748	+	15.9242i	−1.09975	+	0.570912i
$779$			30.1758i			1.08116i
$780$		0			0
$781$		−	2.86180i		−	0.102403i
$782$	−10.0042	−	19.2710i	−0.357748	−	0.689129i
$783$		0			0
$784$	1.35106	+	3.76492i	0.0482523	+	0.134461i
$785$		−	5.93170i		−	0.211711i
$786$		0			0
$787$	−8.14768			−0.290434			−0.145217	−	0.989400i	$-0.546388\pi$
$787$	−8.14768			−0.290434			−0.145217	+	0.989400i	$0.546388\pi$
$788$	−4.39528	+	6.24699i	−0.156575	+	0.222540i
$789$		0			0
$790$	−3.70549	−	7.13787i	−0.131835	−	0.253954i
$791$	8.36855			0.297551
$792$		0			0
$793$	−2.00230			−0.0711039
$794$	22.9534	+	44.2151i	0.814587	+	1.56914i
$795$		0			0
$796$	−30.1777	−	21.2325i	−1.06962	−	0.752566i
$797$	−51.8938			−1.83817			−0.919086	−	0.394057i	$-0.871071\pi$
$797$	−51.8938			−1.83817			−0.919086	+	0.394057i	$0.871071\pi$
$798$		0			0
$799$			29.7715i			1.05324i
$800$	−6.93170	−	6.42421i	−0.245072	−	0.227130i
$801$		0			0
$802$	−23.3020	−	44.8866i	−0.822823	−	1.58500i
$803$			13.2752i			0.468473i
$804$		0			0
$805$		−	6.98793i		−	0.246292i
$806$	−4.42916	+	2.29931i	−0.156011	+	0.0809899i
$807$		0			0
$808$	−2.17547	+	16.1020i	−0.0765328	+	0.566468i
$809$		−	5.35164i		−	0.188154i	−0.995565	−	0.0940769i	$-0.970010\pi$
$809$		−	5.35164i		−	0.188154i	0.995565	−	0.0940769i	$-0.0299899\pi$
$810$		0			0
$811$	−10.0528			−0.353003			−0.176501	−	0.984300i	$-0.556478\pi$
$811$	−10.0528			−0.353003			−0.176501	+	0.984300i	$0.556478\pi$
$812$	11.6911	+	8.22565i	0.410276	+	0.288664i
$813$		0			0
$814$	2.35984	−	1.22507i	0.0827124	−	0.0429385i
$815$	−29.4149			−1.03036
$816$		0			0
$817$	30.8782			1.08029
$818$	36.6586	−	19.0306i	1.28174	−	0.665390i
$819$		0			0
$820$	26.5426	+	18.6749i	0.926906	+	0.652156i
$821$	35.2792			1.23125			0.615626	−	0.788039i	$-0.288903\pi$
$821$	35.2792			1.23125			0.615626	+	0.788039i	$0.288903\pi$
$822$		0			0
$823$		−	26.5569i		−	0.925715i	−0.886433	−	0.462857i	$-0.846824\pi$
$823$		−	26.5569i		−	0.925715i	0.886433	−	0.462857i	$-0.153176\pi$
$824$	−53.0191	−	7.16316i	−1.84701	−	0.249541i
$825$		0			0
$826$	9.32108	−	4.83886i	0.324322	−	0.168365i
$827$		−	22.2453i		−	0.773543i	−0.922176	−	0.386772i	$-0.873590\pi$
$827$		−	22.2453i		−	0.773543i	0.922176	−	0.386772i	$-0.126410\pi$
$828$		0			0
$829$			10.4591i			0.363258i	0.983367	+	0.181629i	$0.0581371\pi$
$829$			10.4591i			0.363258i	−0.983367	+	0.181629i	$0.941863\pi$
$830$	−0.0386578	−	0.0744664i	−0.00134183	−	0.00258477i
$831$		0			0
$832$	1.85392	−	6.73577i	0.0642730	−	0.233521i
$833$			4.00897i			0.138903i
$834$		0			0
$835$	−26.8750			−0.930049
$836$	−4.81984	−	3.39116i	−0.166698	−	0.117286i
$837$		0			0
$838$	21.6724	+	41.7474i	0.748659	+	1.44214i
$839$	−35.7724			−1.23500			−0.617500	−	0.786571i	$-0.711855\pi$
$839$	−35.7724			−1.23500			−0.617500	+	0.786571i	$0.711855\pi$
$840$		0			0
$841$	22.0856			0.761574
$842$	22.7614	+	43.8453i	0.784411	+	1.51101i
$843$		0			0
$844$	−9.37052	+	13.3183i	−0.322547	+	0.458434i
$845$	−22.3288			−0.768134
$846$		0			0
$847$		−	10.2458i		−	0.352052i
$848$	−12.8341	−	35.7638i	−0.440723	−	1.22813i
$849$		0			0
$850$	−4.36421	−	8.40676i	−0.149691	−	0.288349i
$851$		−	8.29136i		−	0.284224i
$852$		0			0
$853$		−	30.1552i		−	1.03249i	−0.856440	−	0.516247i	$-0.827329\pi$
$853$		−	30.1552i		−	1.03249i	0.856440	−	0.516247i	$-0.172671\pi$
$854$	−2.87790	+	1.49400i	−0.0984796	+	0.0511238i
$855$		0			0
$856$	−18.0234	−	2.43506i	−0.616028	−	0.0832287i
$857$			29.5149i			1.00821i	0.863642	+	0.504105i	$0.168178\pi$
$857$			29.5149i			1.00821i	−0.863642	+	0.504105i	$0.831822\pi$
$858$		0			0
$859$	−39.8863			−1.36090			−0.680452	−	0.732793i	$-0.738216\pi$
$859$	−39.8863			−1.36090			−0.680452	+	0.732793i	$0.738216\pi$
$860$	19.1096	−	27.1604i	0.651632	−	0.926161i
$861$		0			0
$862$	23.3675	−	12.1308i	0.795900	−	0.413176i
$863$	−11.0053			−0.374626			−0.187313	−	0.982300i	$-0.559978\pi$
$863$	−11.0053			−0.374626			−0.187313	+	0.982300i	$0.559978\pi$
$864$		0			0
$865$	39.2307			1.33388
$866$	6.59895	−	3.42572i	0.224242	−	0.116411i
$867$		0			0
$868$	−4.65039	+	6.60958i	−0.157844	+	0.224344i
$869$	2.70658			0.0918146
$870$		0			0
$871$		−	11.0276i		−	0.373657i
$872$	−26.4429	−	3.57258i	−0.895470	−	0.120983i
$873$		0			0
$874$	−16.3106	+	8.46732i	−0.551713	+	0.286411i
$875$		−	12.1716i		−	0.411475i
$876$		0			0
$877$			25.5930i			0.864214i	0.901822	+	0.432107i	$0.142230\pi$
$877$			25.5930i			0.864214i	−0.901822	+	0.432107i	$0.857770\pi$
$878$	−22.0837	−	42.5397i	−0.745288	−	1.43565i
$879$		0			0
$880$	−5.96571	+	2.14083i	−0.201104	+	0.0721674i
$881$		−	2.27129i		−	0.0765218i	−0.999268	−	0.0382609i	$-0.987818\pi$
$881$		−	2.27129i		−	0.0765218i	0.999268	−	0.0382609i	$-0.0121818\pi$
$882$		0			0
$883$	−5.45252			−0.183492			−0.0917459	−	0.995782i	$-0.529245\pi$
$883$	−5.45252			−0.183492			−0.0917459	+	0.995782i	$0.529245\pi$
$884$	4.02909	−	5.72653i	0.135513	−	0.192604i
$885$		0			0
$886$	11.5191	+	22.1893i	0.386993	+	0.745463i
$887$	17.1339			0.575302			0.287651	−	0.957735i	$-0.407126\pi$
$887$	17.1339			0.575302			0.287651	+	0.957735i	$0.407126\pi$
$888$		0			0
$889$	6.53098			0.219042
$890$	−16.2398	−	31.2828i	−0.544361	−	1.04860i
$891$		0			0
$892$	−21.6025	−	15.1992i	−0.723305	−	0.508906i
$893$	25.1979			0.843217
$894$		0			0
$895$		−	7.06943i		−	0.236305i
$896$	−2.36122	−	11.0646i	−0.0788830	−	0.369641i
$897$		0			0
$898$	22.8394	+	43.9955i	0.762161	+	1.46815i
$899$			28.8814i			0.963248i
$900$		0			0
$901$		−	38.0821i		−	1.26870i
$902$	−9.69369	+	5.03229i	−0.322765	+	0.167557i
$903$		0			0
$904$	−23.4567	−	3.16913i	−0.780159	−	0.105404i
$905$			46.3809i			1.54175i
$906$		0			0
$907$	5.41708			0.179871			0.0899356	−	0.995948i	$-0.471334\pi$
$907$	5.41708			0.179871			0.0899356	+	0.995948i	$0.471334\pi$
$908$	−22.1591	−	15.5908i	−0.735377	−	0.517399i
$909$		0			0
$910$	2.00000	−	1.03826i	0.0662994	−	0.0344180i
$911$	27.3356			0.905669			0.452834	−	0.891595i	$-0.350413\pi$
$911$	27.3356			0.905669			0.452834	+	0.891595i	$0.350413\pi$
$912$		0			0
$913$	0.0282367			0.000934498
$914$	36.7972	−	19.1025i	1.21714	−	0.631856i
$915$		0			0
$916$	−38.9028	−	27.3714i	−1.28538	−	0.904375i
$917$	16.1448			0.533148
$918$		0			0
$919$		−	2.62318i		−	0.0865307i	−0.999064	−	0.0432653i	$-0.986224\pi$
$919$		−	2.62318i		−	0.0865307i	0.999064	−	0.0432653i	$-0.0137761\pi$
$920$	−2.64630	+	19.5869i	−0.0872458	+	0.645761i
$921$		0			0
$922$	16.6101	−	8.62283i	0.547026	−	0.283978i
$923$		−	2.87782i		−	0.0947247i
$924$		0			0
$925$		−	3.61702i		−	0.118927i
$926$	−26.9750	−	51.9619i	−0.886454	−	1.70757i
$927$		0			0
$928$	−29.6546	−	27.4835i	−0.973461	−	0.902191i
$929$		−	32.5610i		−	1.06829i	−0.845393	−	0.534145i	$-0.820633\pi$
$929$		−	32.5610i		−	1.06829i	0.845393	−	0.534145i	$-0.179367\pi$
$930$		0			0
$931$	3.39311			0.111205
$932$	0.202901	+	0.142758i	0.00664623	+	0.00467618i
$933$		0			0
$934$	−11.6108	−	22.3659i	−0.379918	−	0.731835i
$935$	−6.35242			−0.207746
$936$		0			0
$937$	6.12761			0.200180			0.100090	−	0.994978i	$-0.468087\pi$
$937$	6.12761			0.200180			0.100090	+	0.994978i	$0.468087\pi$
$938$	−8.22818	−	15.8499i	−0.268660	−	0.517519i
$939$		0			0
$940$	15.5943	−	22.1641i	0.508629	−	0.722912i
$941$	11.7334			0.382497			0.191248	−	0.981542i	$-0.438746\pi$
$941$	11.7334			0.382497			0.191248	+	0.981542i	$0.438746\pi$
$942$		0			0
$943$			34.0591i			1.10912i
$944$	−27.9591	+	10.0333i	−0.909991	+	0.326556i
$945$		0			0
$946$	5.14943	+	9.91933i	0.167422	+	0.322505i
$947$		−	17.3517i		−	0.563854i	−0.959436	−	0.281927i	$-0.909026\pi$
$947$		−	17.3517i		−	0.563854i	0.959436	−	0.281927i	$-0.0909736\pi$
$948$		0			0
$949$			13.3495i			0.433345i
$950$	−7.11531	+	3.69377i	−0.230851	+	0.119842i
$951$		0			0
$952$	1.51818	−	11.2370i	0.0492044	−	0.364193i
$953$		−	52.1250i		−	1.68849i	−0.535954	−	0.844247i	$-0.680048\pi$
$953$		−	52.1250i		−	1.68849i	0.535954	−	0.844247i	$-0.319952\pi$
$954$		0			0
$955$	17.3133			0.560244
$956$	9.67960	−	13.7576i	0.313061	−	0.444952i
$957$		0			0
$958$	−16.9979	+	8.82411i	−0.549176	+	0.285094i
$959$	7.12878			0.230200
$960$		0			0
$961$	14.6718			0.473285
$962$	2.37305	−	1.23192i	0.0765102	−	0.0397188i
$963$		0			0
$964$	−3.82027	+	5.42973i	−0.123042	+	0.174880i
$965$	25.8396			0.831808
$966$		0			0
$967$		−	9.60838i		−	0.308985i	−0.987994	−	0.154492i	$-0.950626\pi$
$967$		−	9.60838i		−	0.308985i	0.987994	−	0.154492i	$-0.0493742\pi$
$968$	−3.88005	+	28.7187i	−0.124710	+	0.923054i
$969$		0			0
$970$	−8.68161	+	4.50689i	−0.278750	+	0.144707i
$971$			13.4611i			0.431986i	0.976395	+	0.215993i	$0.0692989\pi$
$971$			13.4611i			0.431986i	−0.976395	+	0.215993i	$0.930701\pi$
$972$		0			0
$973$			18.2465i			0.584956i
$974$	−2.26156	−	4.35645i	−0.0724652	−	0.139590i
$975$		0			0
$976$	8.63240	−	3.09779i	0.276316	−	0.0991578i
$977$		−	13.7483i		−	0.439848i	−0.975517	−	0.219924i	$-0.929419\pi$
$977$		−	13.7483i		−	0.439848i	0.975517	−	0.219924i	$-0.0705810\pi$
$978$		0			0
$979$	11.8620			0.379112
$980$	2.09990	−	2.98457i	0.0670787	−	0.0953387i
$981$		0			0
$982$	−5.79927	−	11.1711i	−0.185062	−	0.356485i
$983$	60.8720			1.94151			0.970757	−	0.240062i	$-0.0771679\pi$
$983$	60.8720			1.94151			0.970757	+	0.240062i	$0.0771679\pi$
$984$		0			0
$985$	6.96855			0.222037
$986$	−18.6706	−	35.9651i	−0.594593	−	1.14536i
$987$		0			0
$988$	−4.84682	−	3.41014i	−0.154198	−	0.108491i
$989$	34.8518			1.10822
$990$		0			0
$991$		−	11.5747i		−	0.367684i	−0.982956	−	0.183842i	$-0.941147\pi$
$991$		−	11.5747i		−	0.367684i	0.982956	−	0.183842i	$-0.0588535\pi$
$992$	15.5379	−	16.7653i	0.493328	−	0.532299i
$993$		0			0
$994$	−2.14727	−	4.13627i	−0.0681072	−	0.131195i
$995$			33.6634i			1.06720i
$996$		0			0
$997$			20.9122i			0.662295i	0.943579	+	0.331147i	$0.107436\pi$
$997$			20.9122i			0.662295i	−0.943579	+	0.331147i	$0.892564\pi$
$998$	28.7873	−	14.9444i	0.911247	−	0.473056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.j.a.323.4	yes	24
3.2	odd	2	inner	504.2.j.a.323.21	yes	24
4.3	odd	2		2016.2.j.a.1583.5		24
8.3	odd	2	inner	504.2.j.a.323.22	yes	24
8.5	even	2		2016.2.j.a.1583.19		24
12.11	even	2		2016.2.j.a.1583.20		24
24.5	odd	2		2016.2.j.a.1583.6		24
24.11	even	2	inner	504.2.j.a.323.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.j.a.323.3	✓	24	24.11	even	2	inner
504.2.j.a.323.4	yes	24	1.1	even	1	trivial
504.2.j.a.323.21	yes	24	3.2	odd	2	inner
504.2.j.a.323.22	yes	24	8.3	odd	2	inner
2016.2.j.a.1583.5		24	4.3	odd	2
2016.2.j.a.1583.6		24	24.5	odd	2
2016.2.j.a.1583.19		24	8.5	even	2
2016.2.j.a.1583.20		24	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25516 + 0.651592i) q^{2} +(1.15086 - 1.63571i) q^{4} -1.82464 q^{5} -1.00000i q^{7} +(-0.378695 + 2.80296i) q^{8} +O(q^{10})\)	\(q+(-1.25516 + 0.651592i) q^{2} +(1.15086 - 1.63571i) q^{4} -1.82464 q^{5} -1.00000i q^{7} +(-0.378695 + 2.80296i) q^{8} +(2.29021 - 1.18892i) q^{10} +0.868419i q^{11} +0.873281i q^{13} +(0.651592 + 1.25516i) q^{14} +(-1.35106 - 3.76492i) q^{16} -4.00897i q^{17} -3.39311 q^{19} +(-2.09990 + 2.98457i) q^{20} +(-0.565855 - 1.09001i) q^{22} -3.82976 q^{23} -1.67069 q^{25} +(-0.569023 - 1.09611i) q^{26} +(-1.63571 - 1.15086i) q^{28} -7.14742 q^{29} -4.04081i q^{31} +(4.14900 + 3.84524i) q^{32} +(2.61221 + 5.03190i) q^{34} +1.82464i q^{35} +2.16498i q^{37} +(4.25890 - 2.21092i) q^{38} +(0.690982 - 5.11439i) q^{40} -8.89325i q^{41} -9.10026 q^{43} +(1.42048 + 0.999425i) q^{44} +(4.80697 - 2.49544i) q^{46} -7.42621 q^{47} -1.00000 q^{49} +(2.09699 - 1.08861i) q^{50} +(1.42843 + 1.00502i) q^{52} +9.49922 q^{53} -1.58455i q^{55} +(2.80296 + 0.378695i) q^{56} +(8.97116 - 4.65720i) q^{58} -7.42621i q^{59} +2.29285i q^{61} +(2.63296 + 5.07187i) q^{62} +(-7.71318 - 2.12293i) q^{64} -1.59342i q^{65} -12.6278 q^{67} +(-6.55750 - 4.61375i) q^{68} +(-1.18892 - 2.29021i) q^{70} -3.29541 q^{71} +15.2867 q^{73} +(-1.41068 - 2.71740i) q^{74} +(-3.90498 + 5.55013i) q^{76} +0.868419 q^{77} -3.11668i q^{79} +(2.46521 + 6.86962i) q^{80} +(5.79478 + 11.1625i) q^{82} -0.0325150i q^{83} +7.31492i q^{85} +(11.4223 - 5.92966i) q^{86} +(-2.43414 - 0.328866i) q^{88} -13.6593i q^{89} +0.873281 q^{91} +(-4.40750 + 6.26436i) q^{92} +(9.32108 - 4.83886i) q^{94} +6.19120 q^{95} -3.79074 q^{97} +(1.25516 - 0.651592i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more