LMFDB - Embedded newform 740.2.l.a.413.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(413,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("740.413");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.79423744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 10x^{3} + 36x^{2} - 12x + 2 $ x^6 - 2x^5 + 2x^4 + 10x^3 + 36x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			413.3
Root			$2.23976 - 2.23976i$ of defining polynomial
Character	$\chi$	$=$	740.413
Dual form			740.2.l.a.697.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.23976 - 2.23976i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(1.23976 - 1.23976i) q^{7} -7.03304i q^{9} +4.47952i q^{11} -2.92599i q^{13} +(2.23976 + 6.71928i) q^{15} +6.03304 q^{17} +(3.79328 - 3.79328i) q^{19} -5.55352i q^{21} -6.47952i q^{23} +(-3.00000 - 4.00000i) q^{25} +(-9.03304 - 9.03304i) q^{27} +(-3.00000 - 3.00000i) q^{29} +(-3.68624 + 3.68624i) q^{31} +(10.0330 + 10.0330i) q^{33} +(1.23976 + 3.71928i) q^{35} +(4.55352 - 4.03304i) q^{37} +(-6.55352 - 6.55352i) q^{39} +9.58657i q^{41} +1.37247i q^{43} +(14.0661 + 7.03304i) q^{45} +(-9.27280 + 9.27280i) q^{47} +3.92599i q^{49} +(13.5126 - 13.5126i) q^{51} +(5.92599 + 5.92599i) q^{53} +(-8.95904 - 4.47952i) q^{55} -16.9921i q^{57} +(-4.16575 + 4.16575i) q^{59} +(-6.10705 + 6.10705i) q^{61} +(-8.71928 - 8.71928i) q^{63} +(5.85199 + 2.92599i) q^{65} +(-1.31376 - 1.31376i) q^{67} +(-14.5126 - 14.5126i) q^{69} -5.10705 q^{71} +(1.92599 - 1.92599i) q^{73} +(-15.6783 - 2.23976i) q^{75} +(5.55352 + 5.55352i) q^{77} +(1.71928 - 1.71928i) q^{79} -19.3645 q^{81} +(8.90033 + 8.90033i) q^{83} +(-6.03304 + 12.0661i) q^{85} -13.4386 q^{87} +(3.03304 + 3.03304i) q^{89} +(-3.62753 - 3.62753i) q^{91} +16.5126i q^{93} +(3.79328 + 11.3798i) q^{95} +5.37247 q^{97} +31.5046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - 6 q^{5} - 4 q^{7} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 18 q^{25} - 22 q^{27} - 18 q^{29} - 20 q^{31} + 28 q^{33} - 4 q^{35} + 18 q^{37} - 30 q^{39} + 20 q^{45} - 12 q^{47} + 26 q^{51} + 22 q^{53}+ \cdots + 56 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 - 6 * q^5 - 4 * q^7 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 18 * q^25 - 22 * q^27 - 18 * q^29 - 20 * q^31 + 28 * q^33 - 4 * q^35 + 18 * q^37 - 30 * q^39 + 20 * q^45 - 12 * q^47 + 26 * q^51 + 22 * q^53 - 8 * q^55 - 18 * q^61 - 18 * q^63 + 8 * q^65 - 10 * q^67 - 32 * q^69 - 12 * q^71 - 2 * q^73 - 14 * q^75 + 24 * q^77 - 24 * q^79 - 34 * q^81 + 14 * q^83 - 4 * q^85 - 12 * q^87 - 14 * q^89 - 26 * q^91 + 2 * q^95 + 28 * q^97 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	2.23976	−	2.23976i	1.29313	−	1.29313i	0.360282	−	0.932843i	$-0.382680\pi$
$3$	2.23976	−	2.23976i	1.29313	−	1.29313i	0.932843	−	0.360282i	$-0.117320\pi$
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	1.23976	−	1.23976i	0.468585	−	0.468585i	−0.432871	−	0.901456i	$-0.642499\pi$
$7$	1.23976	−	1.23976i	0.468585	−	0.468585i	0.901456	+	0.432871i	$0.142499\pi$
$8$		0			0
$9$		−	7.03304i		−	2.34435i
$10$		0			0
$11$			4.47952i			1.35063i	0.737531	+	0.675313i	$0.235991\pi$
$11$			4.47952i			1.35063i	−0.737531	+	0.675313i	$0.764009\pi$
$12$		0			0
$13$		−	2.92599i		−	0.811525i	−0.913979	−	0.405762i	$-0.867006\pi$
$13$		−	2.92599i		−	0.811525i	0.913979	−	0.405762i	$-0.132994\pi$
$14$		0			0
$15$	2.23976	+	6.71928i	0.578303	+	1.73491i
$16$		0			0
$17$	6.03304			1.46323			0.731614	−	0.681719i	$-0.238767\pi$
$17$	6.03304			1.46323			0.731614	+	0.681719i	$0.238767\pi$
$18$		0			0
$19$	3.79328	−	3.79328i	0.870239	−	0.870239i	−0.122259	−	0.992498i	$-0.539014\pi$
$19$	3.79328	−	3.79328i	0.870239	−	0.870239i	0.992498	+	0.122259i	$0.0390140\pi$
$20$		0			0
$21$		−	5.55352i		−	1.21188i
$22$		0			0
$23$		−	6.47952i		−	1.35107i	−0.737327	−	0.675536i	$-0.763912\pi$
$23$		−	6.47952i		−	1.35107i	0.737327	−	0.675536i	$-0.236088\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	−9.03304	−	9.03304i	−1.73841	−	1.73841i
$28$		0			0
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		0			0
$31$	−3.68624	+	3.68624i	−0.662067	+	0.662067i	−0.955867	−	0.293800i	$-0.905080\pi$
$31$	−3.68624	+	3.68624i	−0.662067	+	0.662067i	0.293800	+	0.955867i	$0.405080\pi$
$32$		0			0
$33$	10.0330	+	10.0330i	1.74653	+	1.74653i
$34$		0			0
$35$	1.23976	+	3.71928i	0.209558	+	0.628673i
$36$		0			0
$37$	4.55352	−	4.03304i	0.748595	−	0.663028i
$37$	4.55352	−	4.03304i	0.748595	−	0.663028i
$38$		0			0
$39$	−6.55352	−	6.55352i	−1.04940	−	1.04940i
$40$		0			0
$41$			9.58657i			1.49717i	0.663039	+	0.748585i	$0.269266\pi$
$41$			9.58657i			1.49717i	−0.663039	+	0.748585i	$0.730734\pi$
$42$		0			0
$43$			1.37247i			0.209300i	0.994509	+	0.104650i	$0.0333722\pi$
$43$			1.37247i			0.209300i	−0.994509	+	0.104650i	$0.966628\pi$
$44$		0			0
$45$	14.0661	+	7.03304i	2.09685	+	1.04842i
$46$		0			0
$47$	−9.27280	+	9.27280i	−1.35258	+	1.35258i	−0.469809	+	0.882768i	$0.655677\pi$
$47$	−9.27280	+	9.27280i	−1.35258	+	1.35258i	−0.882768	+	0.469809i	$0.844323\pi$
$48$		0			0
$49$			3.92599i			0.560856i
$50$		0			0
$51$	13.5126	−	13.5126i	1.89214	−	1.89214i
$52$		0			0
$53$	5.92599	+	5.92599i	0.813998	+	0.813998i	0.985231	−	0.171233i	$-0.0547750\pi$
$53$	5.92599	+	5.92599i	0.813998	+	0.813998i	−0.171233	+	0.985231i	$0.554775\pi$
$54$		0			0
$55$	−8.95904	−	4.47952i	−1.20804	−	0.604018i
$56$		0			0
$57$		−	16.9921i		−	2.25066i
$58$		0			0
$59$	−4.16575	+	4.16575i	−0.542335	+	0.542335i	−0.924213	−	0.381878i	$-0.875278\pi$
$59$	−4.16575	+	4.16575i	−0.542335	+	0.542335i	0.381878	+	0.924213i	$0.375278\pi$
$60$		0			0
$61$	−6.10705	+	6.10705i	−0.781927	+	0.781927i	−0.980156	−	0.198229i	$-0.936481\pi$
$61$	−6.10705	+	6.10705i	−0.781927	+	0.781927i	0.198229	+	0.980156i	$0.436481\pi$
$62$		0			0
$63$	−8.71928	−	8.71928i	−1.09853	−	1.09853i
$64$		0			0
$65$	5.85199	+	2.92599i	0.725850	+	0.362925i
$66$		0			0
$67$	−1.31376	−	1.31376i	−0.160502	−	0.160502i	0.622287	−	0.782789i	$-0.286204\pi$
$67$	−1.31376	−	1.31376i	−0.160502	−	0.160502i	−0.782789	+	0.622287i	$0.786204\pi$
$68$		0			0
$69$	−14.5126	−	14.5126i	−1.74711	−	1.74711i
$70$		0			0
$71$	−5.10705			−0.606095			−0.303047	−	0.952975i	$-0.598004\pi$
$71$	−5.10705			−0.606095			−0.303047	+	0.952975i	$0.598004\pi$
$72$		0			0
$73$	1.92599	−	1.92599i	0.225421	−	0.225421i	−0.585356	−	0.810776i	$-0.699045\pi$
$73$	1.92599	−	1.92599i	0.225421	−	0.225421i	0.810776	+	0.585356i	$0.199045\pi$
$74$		0			0
$75$	−15.6783	−	2.23976i	−1.81038	−	0.258625i
$76$		0			0
$77$	5.55352	+	5.55352i	0.632883	+	0.632883i
$78$		0			0
$79$	1.71928	−	1.71928i	0.193434	−	0.193434i	−0.603744	−	0.797178i	$-0.706325\pi$
$79$	1.71928	−	1.71928i	0.193434	−	0.193434i	0.797178	+	0.603744i	$0.206325\pi$
$80$		0			0
$81$	−19.3645			−2.15162
$82$		0			0
$83$	8.90033	+	8.90033i	0.976938	+	0.976938i	0.999740	−	0.0228019i	$-0.00725871\pi$
$83$	8.90033	+	8.90033i	0.976938	+	0.976938i	−0.0228019	+	0.999740i	$0.507259\pi$
$84$		0			0
$85$	−6.03304	+	12.0661i	−0.654375	+	1.30875i
$86$		0			0
$87$	−13.4386			−1.44076
$88$		0			0
$89$	3.03304	+	3.03304i	0.321502	+	0.321502i	0.849343	−	0.527841i	$-0.176998\pi$
$89$	3.03304	+	3.03304i	0.321502	+	0.321502i	−0.527841	+	0.849343i	$0.676998\pi$
$90$		0			0
$91$	−3.62753	−	3.62753i	−0.380268	−	0.380268i
$92$		0			0
$93$			16.5126i			1.71227i
$94$		0			0
$95$	3.79328	+	11.3798i	0.389183	+	1.16755i
$96$		0			0
$97$	5.37247			0.545492			0.272746	−	0.962086i	$-0.412068\pi$
$97$	5.37247			0.545492			0.272746	+	0.962086i	$0.412068\pi$
$98$		0			0
$99$	31.5046			3.16634
$100$		0			0
$101$		−	16.0991i		−	1.60192i	−0.598716	−	0.800961i	$-0.704322\pi$
$101$		−	16.0991i		−	1.60192i	0.598716	−	0.800961i	$-0.295678\pi$
$102$		0			0
$103$	−7.10705			−0.700278			−0.350139	−	0.936698i	$-0.613866\pi$
$103$	−7.10705			−0.700278			−0.350139	+	0.936698i	$0.613866\pi$
$104$		0			0
$105$	11.1070	+	5.55352i	1.08394	+	0.541968i
$106$		0			0
$107$	10.8263	−	10.8263i	1.04662	−	1.04662i	0.0477615	−	0.998859i	$-0.484791\pi$
$107$	10.8263	−	10.8263i	1.04662	−	1.04662i	0.998859	−	0.0477615i	$-0.0152087\pi$
$108$		0			0
$109$	−4.40551	+	4.40551i	−0.421972	+	0.421972i	−0.885882	−	0.463910i	$-0.846446\pi$
$109$	−4.40551	+	4.40551i	−0.421972	+	0.421972i	0.463910	+	0.885882i	$0.346446\pi$
$110$		0			0
$111$	1.16575	−	19.2318i	0.110648	−	1.82541i
$112$		0			0
$113$	−5.88503			−0.553617			−0.276809	−	0.960925i	$-0.589277\pi$
$113$	−5.88503			−0.553617			−0.276809	+	0.960925i	$0.589277\pi$
$114$		0			0
$115$	12.9590	+	6.47952i	1.20844	+	0.604218i
$116$		0			0
$117$	−20.5786			−1.90250
$118$		0			0
$119$	7.47952	−	7.47952i	0.685646	−	0.685646i
$120$		0			0
$121$	−9.06608			−0.824189
$122$		0			0
$123$	21.4716	+	21.4716i	1.93603	+	1.93603i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−4.42081	+	4.42081i	−0.392284	+	0.392284i	−0.875501	−	0.483217i	$-0.839468\pi$
$127$	−4.42081	+	4.42081i	−0.392284	+	0.392284i	0.483217	+	0.875501i	$0.339468\pi$
$128$		0			0
$129$	3.07401	+	3.07401i	0.270651	+	0.270651i
$130$		0			0
$131$	2.71928	−	2.71928i	0.237584	−	0.237584i	−0.578265	−	0.815849i	$-0.696270\pi$
$131$	2.71928	−	2.71928i	0.237584	−	0.237584i	0.815849	+	0.578265i	$0.196270\pi$
$132$		0			0
$133$		−	9.40551i		−	0.815561i
$134$		0			0
$135$	27.0991	−	9.03304i	2.33232	−	0.777440i
$136$		0			0
$137$	−8.55352	+	8.55352i	−0.730777	+	0.730777i	−0.970774	−	0.239997i	$-0.922854\pi$
$137$	−8.55352	+	8.55352i	−0.730777	+	0.730777i	0.239997	+	0.970774i	$0.422854\pi$
$138$		0			0
$139$	2.21409			0.187797			0.0938985	−	0.995582i	$-0.470067\pi$
$139$	2.21409			0.187797			0.0938985	+	0.995582i	$0.470067\pi$
$140$		0			0
$141$			41.5377i			3.49810i
$142$		0			0
$143$	13.1070			1.09607
$144$		0			0
$145$	9.00000	−	3.00000i	0.747409	−	0.249136i
$146$		0			0
$147$	8.79328	+	8.79328i	0.725258	+	0.725258i
$148$		0			0
$149$			5.14009i			0.421092i	0.977584	+	0.210546i	$0.0675242\pi$
$149$			5.14009i			0.421092i	−0.977584	+	0.210546i	$0.932476\pi$
$150$		0			0
$151$			15.5205i			1.26304i	0.775360	+	0.631519i	$0.217568\pi$
$151$			15.5205i			1.26304i	−0.775360	+	0.631519i	$0.782432\pi$
$152$		0			0
$153$		−	42.4306i		−	3.43031i
$154$		0			0
$155$	−3.68624	−	11.0587i	−0.296086	−	0.888257i
$156$		0			0
$157$	−11.0330	+	11.0330i	−0.880533	+	0.880533i	−0.993589	−	0.113056i	$-0.963936\pi$
$157$	−11.0330	+	11.0330i	−0.880533	+	0.880533i	0.113056	+	0.993589i	$0.463936\pi$
$158$		0			0
$159$	26.5456			2.10520
$160$		0			0
$161$	−8.03304	−	8.03304i	−0.633092	−	0.633092i
$162$		0			0
$163$	−9.04096			−0.708143			−0.354071	−	0.935218i	$-0.615203\pi$
$163$	−9.04096			−0.708143			−0.354071	+	0.935218i	$0.615203\pi$
$164$		0			0
$165$	−30.0991	+	10.0330i	−2.34321	+	0.781071i
$166$		0			0
$167$	3.93392			0.304416			0.152208	−	0.988349i	$-0.451362\pi$
$167$	3.93392			0.304416			0.152208	+	0.988349i	$0.451362\pi$
$168$		0			0
$169$	4.43855			0.341427
$170$		0			0
$171$	−26.6783	−	26.6783i	−2.04014	−	2.04014i
$172$		0			0
$173$	−0.107047	+	0.107047i	−0.00813862	+	0.00813862i	−0.711164	−	0.703026i	$-0.751832\pi$
$173$	−0.107047	+	0.107047i	−0.00813862	+	0.00813862i	0.703026	+	0.711164i	$0.251832\pi$
$174$		0			0
$175$	−8.67831	−	1.23976i	−0.656019	−	0.0937170i
$176$		0			0
$177$			18.6606i			1.40261i
$178$		0			0
$179$	−17.8594	−	17.8594i	−1.33487	−	1.33487i	−0.900951	−	0.433921i	$-0.857130\pi$
$179$	−17.8594	−	17.8594i	−1.33487	−	1.33487i	−0.433921	−	0.900951i	$-0.642870\pi$
$180$		0			0
$181$	9.81895			0.729837			0.364918	−	0.931040i	$-0.381097\pi$
$181$	9.81895			0.729837			0.364918	+	0.931040i	$0.381097\pi$
$182$		0			0
$183$			27.3566i			2.02226i
$184$		0			0
$185$	3.51256	+	13.1401i	0.258249	+	0.966079i
$186$		0			0
$187$			27.0251i			1.97627i
$188$		0			0
$189$	−22.3976			−1.62919
$190$		0			0
$191$	14.1988	+	14.1988i	1.02739	+	1.02739i	0.999614	+	0.0277746i	$0.00884206\pi$
$191$	14.1988	+	14.1988i	1.02739	+	1.02739i	0.0277746	+	0.999614i	$0.491158\pi$
$192$		0			0
$193$		−	0.959036i		−	0.0690329i	−0.999404	−	0.0345165i	$-0.989011\pi$
$193$		−	0.959036i		−	0.0690329i	0.999404	−	0.0345165i	$-0.0109891\pi$
$194$		0			0
$195$	19.6606	−	6.55352i	1.40792	−	0.469308i
$196$		0			0
$197$	1.47952	−	1.47952i	0.105411	−	0.105411i	−0.652434	−	0.757845i	$-0.726252\pi$
$197$	1.47952	−	1.47952i	0.105411	−	0.105411i	0.757845	+	0.652434i	$0.226252\pi$
$198$		0			0
$199$	−7.34681	−	7.34681i	−0.520801	−	0.520801i	0.397012	−	0.917813i	$-0.370047\pi$
$199$	−7.34681	−	7.34681i	−0.520801	−	0.520801i	−0.917813	+	0.397012i	$0.870047\pi$
$200$		0			0
$201$	−5.88503			−0.415098
$202$		0			0
$203$	−7.43855			−0.522084
$204$		0			0
$205$	−19.1731	−	9.58657i	−1.33911	−	0.669555i
$206$		0			0
$207$	−45.5707			−3.16738
$208$		0			0
$209$	16.9921	+	16.9921i	1.17537	+	1.17537i
$210$		0			0
$211$	14.8110			1.01963			0.509817	−	0.860283i	$-0.329713\pi$
$211$	14.8110			1.01963			0.509817	+	0.860283i	$0.329713\pi$
$212$		0			0
$213$	−11.4386	+	11.4386i	−0.783757	+	0.783757i
$214$		0			0
$215$	−2.74494	−	1.37247i	−0.187204	−	0.0936018i
$216$		0			0
$217$			9.14009i			0.620470i
$218$		0			0
$219$		−	8.62753i		−	0.582994i
$220$		0			0
$221$		−	17.6526i		−	1.18745i
$222$		0			0
$223$	−11.8594	−	11.8594i	−0.794162	−	0.794162i	0.188006	−	0.982168i	$-0.439798\pi$
$223$	−11.8594	−	11.8594i	−0.794162	−	0.794162i	−0.982168	+	0.188006i	$0.939798\pi$
$224$		0			0
$225$	−28.1322	+	21.0991i	−1.87548	+	1.40661i
$226$		0			0
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$		0			0
$229$		−	8.62753i		−	0.570123i	−0.958509	−	0.285062i	$-0.907986\pi$
$229$		−	8.62753i		−	0.570123i	0.958509	−	0.285062i	$-0.0920140\pi$
$230$		0			0
$231$	24.8771			1.63679
$232$		0			0
$233$	−21.4306	+	21.4306i	−1.40397	+	1.40397i	−0.617020	+	0.786948i	$0.711660\pi$
$233$	−21.4306	+	21.4306i	−1.40397	+	1.40397i	−0.786948	+	0.617020i	$0.788340\pi$
$234$		0			0
$235$	−9.27280	−	27.8184i	−0.604891	−	1.81467i
$236$		0			0
$237$		−	7.70153i		−	0.500268i
$238$		0			0
$239$	−6.71928	+	6.71928i	−0.434634	+	0.434634i	−0.890201	−	0.455567i	$-0.849436\pi$
$239$	−6.71928	+	6.71928i	−0.434634	+	0.434634i	0.455567	+	0.890201i	$0.349436\pi$
$240$		0			0
$241$	−4.88503	−	4.88503i	−0.314673	−	0.314673i	0.532044	−	0.846717i	$-0.321424\pi$
$241$	−4.88503	−	4.88503i	−0.314673	−	0.314673i	−0.846717	+	0.532044i	$0.821424\pi$
$242$		0			0
$243$	−16.2728	+	16.2728i	−1.04390	+	1.04390i
$244$		0			0
$245$	−7.85199	−	3.92599i	−0.501645	−	0.250823i
$246$		0			0
$247$	−11.0991	−	11.0991i	−0.706220	−	0.706220i
$248$		0			0
$249$	39.8692			2.52661
$250$		0			0
$251$	3.97433	−	3.97433i	0.250858	−	0.250858i	−0.570464	−	0.821322i	$-0.693237\pi$
$251$	3.97433	−	3.97433i	0.250858	−	0.250858i	0.821322	+	0.570464i	$0.193237\pi$
$252$		0			0
$253$	29.0251			1.82479
$254$		0			0
$255$	13.5126	+	40.5377i	0.846189	+	2.53857i
$256$		0			0
$257$	15.7370			0.981648			0.490824	−	0.871259i	$-0.336696\pi$
$257$	15.7370			0.981648			0.490824	+	0.871259i	$0.336696\pi$
$258$		0			0
$259$	0.645272	−	10.6453i	0.0400953	−	0.661465i
$260$		0			0
$261$	−21.0991	+	21.0991i	−1.30600	+	1.30600i
$262$		0			0
$263$	−5.19880	+	5.19880i	−0.320571	+	0.320571i	−0.848986	−	0.528415i	$-0.822787\pi$
$263$	−5.19880	+	5.19880i	−0.320571	+	0.320571i	0.528415	+	0.848986i	$0.322787\pi$
$264$		0			0
$265$	−17.7780	+	5.92599i	−1.09209	+	0.364031i
$266$		0			0
$267$	13.5866			0.831484
$268$		0			0
$269$		−	11.1401i		−	0.679223i	−0.940566	−	0.339612i	$-0.889704\pi$
$269$		−	11.1401i		−	0.679223i	0.940566	−	0.339612i	$-0.110296\pi$
$270$		0			0
$271$	−0.892953			−0.0542430			−0.0271215	−	0.999632i	$-0.508634\pi$
$271$	−0.892953			−0.0542430			−0.0271215	+	0.999632i	$0.508634\pi$
$272$		0			0
$273$	−16.2496			−0.983469
$274$		0			0
$275$	17.9181	−	13.4386i	1.08050	−	0.810375i
$276$		0			0
$277$			16.0330i			0.963332i	0.876355	+	0.481666i	$0.159968\pi$
$277$			16.0330i			0.963332i	−0.876355	+	0.481666i	$0.840032\pi$
$278$		0			0
$279$	25.9254	+	25.9254i	1.55212	+	1.55212i
$280$		0			0
$281$	6.40551	+	6.40551i	0.382121	+	0.382121i	0.871866	−	0.489745i	$-0.162910\pi$
$281$	6.40551	+	6.40551i	0.382121	+	0.382121i	−0.489745	+	0.871866i	$0.662910\pi$
$282$		0			0
$283$	−23.3211			−1.38630			−0.693149	−	0.720794i	$-0.743777\pi$
$283$	−23.3211			−1.38630			−0.693149	+	0.720794i	$0.743777\pi$
$284$		0			0
$285$	33.9842	+	16.9921i	2.01305	+	1.00652i
$286$		0			0
$287$	11.8850	+	11.8850i	0.701551	+	0.701551i
$288$		0			0
$289$	19.3976			1.14103
$290$		0			0
$291$	12.0330	−	12.0330i	0.705389	−	0.705389i
$292$		0			0
$293$	−3.41343	−	3.41343i	−0.199415	−	0.199415i	0.600334	−	0.799749i	$-0.295034\pi$
$293$	−3.41343	−	3.41343i	−0.199415	−	0.199415i	−0.799749	+	0.600334i	$0.795034\pi$
$294$		0			0
$295$	−4.16575	−	12.4973i	−0.242540	−	0.727619i
$296$		0			0
$297$	40.4637	−	40.4637i	2.34794	−	2.34794i
$298$		0			0
$299$	−18.9590			−1.09643
$300$		0			0
$301$	1.70153	+	1.70153i	0.0980748	+	0.0980748i
$302$		0			0
$303$	−36.0582	−	36.0582i	−2.07149	−	2.07149i
$304$		0			0
$305$	−6.10705	−	18.3211i	−0.349688	−	1.04907i
$306$		0			0
$307$	−18.2318	−	18.2318i	−1.04055	−	1.04055i	−0.999143	−	0.0414034i	$-0.986817\pi$
$307$	−18.2318	−	18.2318i	−1.04055	−	1.04055i	−0.0414034	−	0.999143i	$-0.513183\pi$
$308$		0			0
$309$	−15.9181	+	15.9181i	−0.905548	+	0.905548i
$310$		0			0
$311$	14.6783	−	14.6783i	0.832331	−	0.832331i	−0.155504	−	0.987835i	$-0.549700\pi$
$311$	14.6783	−	14.6783i	0.832331	−	0.832331i	0.987835	+	0.155504i	$0.0497003\pi$
$312$		0			0
$313$			6.41343i			0.362509i	0.983436	+	0.181254i	$0.0580157\pi$
$313$			6.41343i			0.362509i	−0.983436	+	0.181254i	$0.941984\pi$
$314$		0			0
$315$	26.1578	−	8.71928i	1.47383	−	0.491276i
$316$		0			0
$317$	−2.00792	−	2.00792i	−0.112776	−	0.112776i	0.648467	−	0.761243i	$-0.275411\pi$
$317$	−2.00792	−	2.00792i	−0.112776	−	0.112776i	−0.761243	+	0.648467i	$0.775411\pi$
$318$		0			0
$319$	13.4386	−	13.4386i	0.752415	−	0.752415i
$320$		0			0
$321$		−	48.4967i		−	2.70682i
$322$		0			0
$323$	22.8850	−	22.8850i	1.27336	−	1.27336i
$324$		0			0
$325$	−11.7040	+	8.77798i	−0.649220	+	0.486915i
$326$		0			0
$327$			19.7346i			1.09132i
$328$		0			0
$329$			22.9921i			1.26759i
$330$		0			0
$331$	−4.65319	−	4.65319i	−0.255763	−	0.255763i	0.567566	−	0.823328i	$-0.307885\pi$
$331$	−4.65319	−	4.65319i	−0.255763	−	0.255763i	−0.823328	+	0.567566i	$0.807885\pi$
$332$		0			0
$333$	−28.3645	−	32.0251i	−1.55437	−	1.75497i
$334$		0			0
$335$	3.94129	−	1.31376i	0.215336	−	0.0717786i
$336$		0			0
$337$	14.4055	+	14.4055i	0.784718	+	0.784718i	0.980623	−	0.195905i	$-0.0627643\pi$
$337$	14.4055	+	14.4055i	0.784718	+	0.784718i	−0.195905	+	0.980623i	$0.562764\pi$
$338$		0			0
$339$	−13.1811	+	13.1811i	−0.715896	+	0.715896i
$340$		0			0
$341$	−16.5126	−	16.5126i	−0.894205	−	0.894205i
$342$		0			0
$343$	13.5456	+	13.5456i	0.731394	+	0.731394i
$344$		0			0
$345$	43.5377	−	14.5126i	2.34399	−	0.781330i
$346$		0			0
$347$		−	15.5866i		−	0.836731i	−0.908279	−	0.418365i	$-0.862603\pi$
$347$		−	15.5866i		−	0.836731i	0.908279	−	0.418365i	$-0.137397\pi$
$348$		0			0
$349$		−	1.28810i		−	0.0689504i	−0.999406	−	0.0344752i	$-0.989024\pi$
$349$		−	1.28810i		−	0.0689504i	0.999406	−	0.0344752i	$-0.0109760\pi$
$350$		0			0
$351$	−26.4306	+	26.4306i	−1.41076	+	1.41076i
$352$		0			0
$353$	12.2141			0.650091			0.325045	−	0.945698i	$-0.394620\pi$
$353$	12.2141			0.650091			0.325045	+	0.945698i	$0.394620\pi$
$354$		0			0
$355$	5.10705	−	10.2141i	0.271054	−	0.542108i
$356$		0			0
$357$		−	33.5046i		−	1.77325i
$358$		0			0
$359$			1.37247i			0.0724363i	0.999344	+	0.0362181i	$0.0115311\pi$
$359$			1.37247i			0.0724363i	−0.999344	+	0.0362181i	$0.988469\pi$
$360$		0			0
$361$		−	9.77798i		−	0.514631i
$362$		0			0
$363$	−20.3058	+	20.3058i	−1.06578	+	1.06578i
$364$		0			0
$365$	1.92599	+	5.77798i	0.100811	+	0.302434i
$366$		0			0
$367$	1.76024	−	1.76024i	0.0918838	−	0.0918838i	−0.659671	−	0.751555i	$-0.729304\pi$
$367$	1.76024	−	1.76024i	0.0918838	−	0.0918838i	0.751555	+	0.659671i	$0.229304\pi$
$368$		0			0
$369$	67.4227			3.50989
$370$		0			0
$371$	14.6936			0.762854
$372$		0			0
$373$	4.76762	−	4.76762i	0.246858	−	0.246858i	−0.572822	−	0.819680i	$-0.694151\pi$
$373$	4.76762	−	4.76762i	0.246858	−	0.246858i	0.819680	+	0.572822i	$0.194151\pi$
$374$		0			0
$375$	20.1578	−	29.1169i	1.04095	−	1.50359i
$376$		0			0
$377$	−8.77798	+	8.77798i	−0.452089	+	0.452089i
$378$		0			0
$379$		−	14.6117i		−	0.750552i	−0.926913	−	0.375276i	$-0.877548\pi$
$379$		−	14.6117i		−	0.750552i	0.926913	−	0.375276i	$-0.122452\pi$
$380$		0			0
$381$			19.8031i			1.01454i
$382$		0			0
$383$			7.66849i			0.391842i	0.980620	+	0.195921i	$0.0627696\pi$
$383$			7.66849i			0.391842i	−0.980620	+	0.195921i	$0.937230\pi$
$384$		0			0
$385$	−16.6606	+	5.55352i	−0.849101	+	0.283034i
$386$		0			0
$387$	9.65265			0.490672
$388$		0			0
$389$	1.51256	−	1.51256i	0.0766898	−	0.0766898i	−0.667721	−	0.744411i	$-0.732730\pi$
$389$	1.51256	−	1.51256i	0.0766898	−	0.0766898i	0.744411	+	0.667721i	$0.232730\pi$
$390$		0			0
$391$		−	39.0912i		−	1.97693i
$392$		0			0
$393$		−	12.1811i		−	0.614453i
$394$		0			0
$395$	1.71928	+	5.15783i	0.0865062	+	0.259519i
$396$		0			0
$397$	24.6857	+	24.6857i	1.23894	+	1.23894i	0.960435	+	0.278504i	$0.0898386\pi$
$397$	24.6857	+	24.6857i	1.23894	+	1.23894i	0.278504	+	0.960435i	$0.410161\pi$
$398$		0			0
$399$	−21.0661	−	21.0661i	−1.05462	−	1.05462i
$400$		0			0
$401$	22.7701	−	22.7701i	1.13708	−	1.13708i	0.148112	−	0.988971i	$-0.452680\pi$
$401$	22.7701	−	22.7701i	1.13708	−	1.13708i	0.988971	−	0.148112i	$-0.0473196\pi$
$402$		0			0
$403$	10.7859	+	10.7859i	0.537284	+	0.537284i
$404$		0			0
$405$	19.3645	−	38.7291i	0.962232	−	1.92446i
$406$		0			0
$407$	18.0661	+	20.3976i	0.895502	+	1.01107i
$408$		0			0
$409$	−22.8520	−	22.8520i	−1.12996	−	1.12996i	−0.990183	−	0.139775i	$-0.955362\pi$
$409$	−22.8520	−	22.8520i	−1.12996	−	1.12996i	−0.139775	−	0.990183i	$-0.544638\pi$
$410$		0			0
$411$			38.3157i			1.88997i
$412$		0			0
$413$			10.3291i			0.508260i
$414$		0			0
$415$	−26.7010	+	8.90033i	−1.31070	+	0.436900i
$416$		0			0
$417$	4.95904	−	4.95904i	0.242845	−	0.242845i
$418$		0			0
$419$			32.4795i			1.58673i	0.608747	+	0.793364i	$0.291672\pi$
$419$			32.4795i			1.58673i	−0.608747	+	0.793364i	$0.708328\pi$
$420$		0			0
$421$	−25.4306	+	25.4306i	−1.23941	+	1.23941i	−0.279172	+	0.960241i	$0.590060\pi$
$421$	−25.4306	+	25.4306i	−1.23941	+	1.23941i	−0.960241	+	0.279172i	$0.909940\pi$
$422$		0			0
$423$	65.2160	+	65.2160i	3.17091	+	3.17091i
$424$		0			0
$425$	−18.0991	−	24.1322i	−0.877937	−	1.17058i
$426$		0			0
$427$			15.1425i			0.732799i
$428$		0			0
$429$	29.3566	−	29.3566i	1.41735	−	1.41735i
$430$		0			0
$431$	14.2318	−	14.2318i	0.685523	−	0.685523i	−0.275716	−	0.961239i	$-0.588915\pi$
$431$	14.2318	−	14.2318i	0.685523	−	0.685523i	0.961239	+	0.275716i	$0.0889148\pi$
$432$		0			0
$433$	8.91807	+	8.91807i	0.428575	+	0.428575i	0.888143	−	0.459568i	$-0.151996\pi$
$433$	8.91807	+	8.91807i	0.428575	+	0.428575i	−0.459568	+	0.888143i	$0.651996\pi$
$434$		0			0
$435$	13.4386	−	26.8771i	0.644329	−	1.28866i
$436$		0			0
$437$	−24.5786	−	24.5786i	−1.17576	−	1.17576i
$438$		0			0
$439$	−11.1658	−	11.1658i	−0.532912	−	0.532912i	0.388526	−	0.921438i	$-0.372985\pi$
$439$	−11.1658	−	11.1658i	−0.532912	−	0.532912i	−0.921438	+	0.388526i	$0.872985\pi$
$440$		0			0
$441$	27.6117			1.31484
$442$		0			0
$443$	15.1248	−	15.1248i	0.718600	−	0.718600i	−0.249718	−	0.968319i	$-0.580338\pi$
$443$	15.1248	−	15.1248i	0.718600	−	0.718600i	0.968319	+	0.249718i	$0.0803380\pi$
$444$		0			0
$445$	−9.09912	+	3.03304i	−0.431340	+	0.143780i
$446$		0			0
$447$	11.5126	+	11.5126i	0.544525	+	0.544525i
$448$		0			0
$449$	−29.0661	+	29.0661i	−1.37171	+	1.37171i	−0.513808	+	0.857905i	$0.671766\pi$
$449$	−29.0661	+	29.0661i	−1.37171	+	1.37171i	−0.857905	+	0.513808i	$0.828234\pi$
$450$		0			0
$451$	−42.9432			−2.02212
$452$		0			0
$453$	34.7621	+	34.7621i	1.63327	+	1.63327i
$454$		0			0
$455$	10.8826	−	3.62753i	0.510183	−	0.170061i
$456$		0			0
$457$	8.18350			0.382808			0.191404	−	0.981511i	$-0.438696\pi$
$457$	8.18350			0.382808			0.191404	+	0.981511i	$0.438696\pi$
$458$		0			0
$459$	−54.4967	−	54.4967i	−2.54369	−	2.54369i
$460$		0			0
$461$	−0.818948	−	0.818948i	−0.0381422	−	0.0381422i	0.687778	−	0.725921i	$-0.258586\pi$
$461$	−0.818948	−	0.818948i	−0.0381422	−	0.0381422i	−0.725921	+	0.687778i	$0.758586\pi$
$462$		0			0
$463$		−	37.3566i		−	1.73611i	−0.496468	−	0.868055i	$-0.665370\pi$
$463$		−	37.3566i		−	1.73611i	0.496468	−	0.868055i	$-0.334630\pi$
$464$		0			0
$465$	−33.0251	−	16.5126i	−1.53150	−	0.765752i
$466$		0			0
$467$	17.3211			0.801527			0.400763	−	0.916182i	$-0.368745\pi$
$467$	17.3211			0.801527			0.400763	+	0.916182i	$0.368745\pi$
$468$		0			0
$469$	−3.25750			−0.150417
$470$		0			0
$471$			49.4227i			2.27728i
$472$		0			0
$473$	−6.14801			−0.282686
$474$		0			0
$475$	−26.5530	−	3.79328i	−1.21833	−	0.174048i
$476$		0			0
$477$	41.6778	−	41.6778i	1.90829	−	1.90829i
$478$		0			0
$479$	2.32169	−	2.32169i	0.106081	−	0.106081i	−0.652074	−	0.758155i	$-0.726101\pi$
$479$	2.32169	−	2.32169i	0.106081	−	0.106081i	0.758155	+	0.652074i	$0.226101\pi$
$480$		0			0
$481$	−11.8007	−	13.3236i	−0.538064	−	0.607503i
$482$		0			0
$483$	−35.9842			−1.63734
$484$		0			0
$485$	−5.37247	+	10.7449i	−0.243951	+	0.487903i
$486$		0			0
$487$	−10.7449			−0.486900			−0.243450	−	0.969913i	$-0.578279\pi$
$487$	−10.7449			−0.486900			−0.243450	+	0.969913i	$0.578279\pi$
$488$		0			0
$489$	−20.2496	+	20.2496i	−0.915718	+	0.915718i
$490$		0			0
$491$	−32.8771			−1.48372			−0.741862	−	0.670553i	$-0.766057\pi$
$491$	−32.8771			−1.48372			−0.741862	+	0.670553i	$0.766057\pi$
$492$		0			0
$493$	−18.0991	−	18.0991i	−0.815144	−	0.815144i
$494$		0			0
$495$	−31.5046	+	63.0093i	−1.41603	+	2.83206i
$496$		0			0
$497$	−6.33151	+	6.33151i	−0.284007	+	0.284007i
$498$		0			0
$499$	−20.4129	−	20.4129i	−0.913806	−	0.913806i	0.0827629	−	0.996569i	$-0.473626\pi$
$499$	−20.4129	−	20.4129i	−0.913806	−	0.913806i	−0.996569	+	0.0827629i	$0.973626\pi$
$500$		0			0
$501$	8.81103	−	8.81103i	0.393648	−	0.393648i
$502$		0			0
$503$			8.09668i			0.361013i	0.983574	+	0.180507i	$0.0577737\pi$
$503$			8.09668i			0.361013i	−0.983574	+	0.180507i	$0.942226\pi$
$504$		0			0
$505$	32.1982	+	16.0991i	1.43280	+	0.716402i
$506$		0			0
$507$	9.94129	−	9.94129i	0.441508	−	0.441508i
$508$		0			0
$509$	0.0158440			0.000702275			0.000351138	−	1.00000i	$-0.499888\pi$
$509$	0.0158440			0.000702275			0.000351138		1.00000i	$0.499888\pi$
$510$		0			0
$511$		−	4.77554i		−	0.211257i
$512$		0			0
$513$	−68.5298			−3.02566
$514$		0			0
$515$	7.10705	−	14.2141i	0.313174	−	0.626348i
$516$		0			0
$517$	−41.5377	−	41.5377i	−1.82683	−	1.82683i
$518$		0			0
$519$			0.479518i			0.0210485i
$520$		0			0
$521$		−	20.2471i		−	0.887043i	−0.896264	−	0.443522i	$-0.853729\pi$
$521$		−	20.2471i		−	0.887043i	0.896264	−	0.443522i	$-0.146271\pi$
$522$		0			0
$523$		−	12.6117i		−	0.551470i	−0.961234	−	0.275735i	$-0.911079\pi$
$523$		−	12.6117i		−	0.551470i	0.961234	−	0.275735i	$-0.0889213\pi$
$524$		0			0
$525$	−22.2141	+	16.6606i	−0.969503	+	0.727127i
$526$		0			0
$527$	−22.2392	+	22.2392i	−0.968755	+	0.968755i
$528$		0			0
$529$	−18.9842			−0.825398
$530$		0			0
$531$	29.2979	+	29.2979i	1.27142	+	1.27142i
$532$		0			0
$533$	28.0502			1.21499
$534$		0			0
$535$	10.8263	+	32.4790i	0.468063	+	1.40419i
$536$		0			0
$537$	−80.0014			−3.45231
$538$		0			0
$539$	−17.5866			−0.757507
$540$		0			0
$541$	13.3315	+	13.3315i	0.573166	+	0.573166i	0.933012	−	0.359846i	$-0.117171\pi$
$541$	13.3315	+	13.3315i	0.573166	+	0.573166i	−0.359846	+	0.933012i	$0.617171\pi$
$542$		0			0
$543$	21.9921	−	21.9921i	0.943770	−	0.943770i
$544$		0			0
$545$	−4.40551	−	13.2165i	−0.188711	−	0.566134i
$546$		0			0
$547$		−	34.2496i		−	1.46441i	−0.681086	−	0.732203i	$-0.738492\pi$
$547$		−	34.2496i		−	1.46441i	0.681086	−	0.732203i	$-0.261508\pi$
$548$		0			0
$549$	42.9511	+	42.9511i	1.83311	+	1.83311i
$550$		0			0
$551$	−22.7597			−0.969596
$552$		0			0
$553$		−	4.26298i		−	0.181280i
$554$		0			0
$555$	37.2979	+	21.5633i	1.58321	+	0.915313i
$556$		0			0
$557$		−	39.2062i		−	1.66122i	−0.556855	−	0.830609i	$-0.687992\pi$
$557$		−	39.2062i		−	1.66122i	0.556855	−	0.830609i	$-0.312008\pi$
$558$		0			0
$559$	4.01584			0.169852
$560$		0			0
$561$	60.5298	+	60.5298i	2.55557	+	2.55557i
$562$		0			0
$563$		−	23.6526i		−	0.996840i	−0.866936	−	0.498420i	$-0.833914\pi$
$563$		−	23.6526i		−	0.996840i	0.866936	−	0.498420i	$-0.166086\pi$
$564$		0			0
$565$	5.88503	−	11.7701i	0.247585	−	0.495170i
$566$		0			0
$567$	−24.0074	+	24.0074i	−1.00822	+	1.00822i
$568$		0			0
$569$	−11.6300	−	11.6300i	−0.487554	−	0.487554i	0.419980	−	0.907534i	$-0.362037\pi$
$569$	−11.6300	−	11.6300i	−0.487554	−	0.487554i	−0.907534	+	0.419980i	$0.862037\pi$
$570$		0			0
$571$	27.1731			1.13716			0.568580	−	0.822628i	$-0.307493\pi$
$571$	27.1731			1.13716			0.568580	+	0.822628i	$0.307493\pi$
$572$		0			0
$573$	63.6038			2.65709
$574$		0			0
$575$	−25.9181	+	19.4386i	−1.08086	+	0.810644i
$576$		0			0
$577$	28.1652			1.17253			0.586266	−	0.810118i	$-0.300597\pi$
$577$	28.1652			1.17253			0.586266	+	0.810118i	$0.300597\pi$
$578$		0			0
$579$	−2.14801	−	2.14801i	−0.0892683	−	0.0892683i
$580$		0			0
$581$	22.0685			0.915557
$582$		0			0
$583$	−26.5456	+	26.5456i	−1.09941	+	1.09941i
$584$		0			0
$585$	20.5786	−	41.1573i	0.850822	−	1.70164i
$586$		0			0
$587$			38.3817i			1.58418i	0.610402	+	0.792092i	$0.291008\pi$
$587$			38.3817i			1.58418i	−0.610402	+	0.792092i	$0.708992\pi$
$588$		0			0
$589$			27.9659i			1.15231i
$590$		0			0
$591$		−	6.62753i		−	0.272620i
$592$		0			0
$593$	6.05816	+	6.05816i	0.248779	+	0.248779i	0.820469	−	0.571690i	$-0.193712\pi$
$593$	6.05816	+	6.05816i	0.248779	+	0.248779i	−0.571690	+	0.820469i	$0.693712\pi$
$594$		0			0
$595$	7.47952	+	22.4386i	0.306630	+	0.919891i
$596$		0			0
$597$	−32.9102			−1.34692
$598$		0			0
$599$			13.9487i			0.569927i	0.958538	+	0.284964i	$0.0919815\pi$
$599$			13.9487i			0.569927i	−0.958538	+	0.284964i	$0.908018\pi$
$600$		0			0
$601$	29.3542			1.19738			0.598691	−	0.800980i	$-0.295688\pi$
$601$	29.3542			1.19738			0.598691	+	0.800980i	$0.295688\pi$
$602$		0			0
$603$	−9.23976	+	9.23976i	−0.376272	+	0.376272i
$604$		0			0
$605$	9.06608	−	18.1322i	0.368589	−	0.737177i
$606$		0			0
$607$			4.84162i			0.196515i	0.995161	+	0.0982577i	$0.0313269\pi$
$607$			4.84162i			0.196515i	−0.995161	+	0.0982577i	$0.968673\pi$
$608$		0			0
$609$	−16.6606	+	16.6606i	−0.675120	+	0.675120i
$610$		0			0
$611$	27.1322	+	27.1322i	1.09765	+	1.09765i
$612$		0			0
$613$	15.8771	−	15.8771i	0.641270	−	0.641270i	−0.309597	−	0.950868i	$-0.600194\pi$
$613$	15.8771	−	15.8771i	0.641270	−	0.641270i	0.950868	+	0.309597i	$0.100194\pi$
$614$		0			0
$615$	−64.4148	+	21.4716i	−2.59745	+	0.865818i
$616$		0			0
$617$	21.2141	+	21.2141i	0.854047	+	0.854047i	0.990629	−	0.136582i	$-0.0436116\pi$
$617$	21.2141	+	21.2141i	0.854047	+	0.854047i	−0.136582	+	0.990629i	$0.543612\pi$
$618$		0			0
$619$	−11.5352			−0.463640			−0.231820	−	0.972759i	$-0.574468\pi$
$619$	−11.5352			−0.463640			−0.231820	+	0.972759i	$0.574468\pi$
$620$		0			0
$621$	−58.5298	+	58.5298i	−2.34872	+	2.34872i
$622$		0			0
$623$	7.52048			0.301302
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	76.1163			3.03979
$628$		0			0
$629$	27.4716	−	24.3315i	1.09536	−	0.970161i
$630$		0			0
$631$	25.4459	−	25.4459i	1.01299	−	1.01299i	0.0130719	−	0.999915i	$-0.495839\pi$
$631$	25.4459	−	25.4459i	1.01299	−	1.01299i	0.999915	−	0.0130719i	$-0.00416105\pi$
$632$		0			0
$633$	33.1731	−	33.1731i	1.31851	−	1.31851i
$634$		0			0
$635$	−4.42081	−	13.2624i	−0.175435	−	0.526304i
$636$		0			0
$637$	11.4874			0.455149
$638$		0			0
$639$			35.9181i			1.42090i
$640$		0			0
$641$	−36.0833			−1.42520			−0.712602	−	0.701569i	$-0.752483\pi$
$641$	−36.0833			−1.42520			−0.712602	+	0.701569i	$0.752483\pi$
$642$		0			0
$643$	−1.77006			−0.0698044			−0.0349022	−	0.999391i	$-0.511112\pi$
$643$	−1.77006			−0.0698044			−0.0349022	+	0.999391i	$0.511112\pi$
$644$		0			0
$645$	−9.22202	+	3.07401i	−0.363117	+	0.121039i
$646$		0			0
$647$		−	11.3064i		−	0.444500i	−0.974990	−	0.222250i	$-0.928660\pi$
$647$		−	11.3064i		−	0.444500i	0.974990	−	0.222250i	$-0.0713401\pi$
$648$		0			0
$649$	−18.6606	−	18.6606i	−0.732491	−	0.732491i
$650$		0			0
$651$	20.4716	+	20.4716i	0.802345	+	0.802345i
$652$		0			0
$653$	36.2141			1.41717			0.708583	−	0.705627i	$-0.249335\pi$
$653$	36.2141			1.41717			0.708583	+	0.705627i	$0.249335\pi$
$654$		0			0
$655$	2.71928	+	8.15783i	0.106251	+	0.318753i
$656$		0			0
$657$	−13.5456	−	13.5456i	−0.528464	−	0.528464i
$658$		0			0
$659$	−20.9432			−0.815831			−0.407915	−	0.913020i	$-0.633744\pi$
$659$	−20.9432			−0.815831			−0.407915	+	0.913020i	$0.633744\pi$
$660$		0			0
$661$	23.8771	−	23.8771i	0.928712	−	0.928712i	−0.0689109	−	0.997623i	$-0.521952\pi$
$661$	23.8771	−	23.8771i	0.928712	−	0.928712i	0.997623	+	0.0689109i	$0.0219524\pi$
$662$		0			0
$663$	−39.5377	−	39.5377i	−1.53552	−	1.53552i
$664$		0			0
$665$	18.8110	+	9.40551i	0.729460	+	0.364730i
$666$		0			0
$667$	−19.4386	+	19.4386i	−0.752664	+	0.752664i
$668$		0			0
$669$	−53.1242			−2.05390
$670$		0			0
$671$	−27.3566	−	27.3566i	−1.05609	−	1.05609i
$672$		0			0
$673$	−22.0251	−	22.0251i	−0.849006	−	0.849006i	0.141003	−	0.990009i	$-0.454967\pi$
$673$	−22.0251	−	22.0251i	−0.849006	−	0.849006i	−0.990009	+	0.141003i	$0.954967\pi$
$674$		0			0
$675$	−9.03304	+	63.2313i	−0.347682	+	2.43377i
$676$		0			0
$677$	26.2575	+	26.2575i	1.00916	+	1.00916i	0.999958	+	0.00920012i	$0.00292853\pi$
$677$	26.2575	+	26.2575i	1.00916	+	1.00916i	0.00920012	+	0.999958i	$0.497071\pi$
$678$		0			0
$679$	6.66057	−	6.66057i	0.255609	−	0.255609i
$680$		0			0
$681$	−40.3157	+	40.3157i	−1.54490	+	1.54490i
$682$		0			0
$683$		−	11.7187i		−	0.448405i	−0.974543	−	0.224202i	$-0.928022\pi$
$683$		−	11.7187i		−	0.448405i	0.974543	−	0.224202i	$-0.0719777\pi$
$684$		0			0
$685$	−8.55352	−	25.6606i	−0.326813	−	0.980440i
$686$		0			0
$687$	−19.3236	−	19.3236i	−0.737241	−	0.737241i
$688$		0			0
$689$	17.3394	−	17.3394i	0.660580	−	0.660580i
$690$		0			0
$691$		−	15.9694i		−	0.607505i	−0.952751	−	0.303752i	$-0.901760\pi$
$691$		−	15.9694i		−	0.607505i	0.952751	−	0.303752i	$-0.0982396\pi$
$692$		0			0
$693$	39.0582	−	39.0582i	1.48370	−	1.48370i
$694$		0			0
$695$	−2.21409	+	4.42819i	−0.0839854	+	0.167971i
$696$		0			0
$697$			57.8361i			2.19070i
$698$		0			0
$699$			95.9989i			3.63101i
$700$		0			0
$701$	−20.3236	−	20.3236i	−0.767611	−	0.767611i	0.210074	−	0.977685i	$-0.432629\pi$
$701$	−20.3236	−	20.3236i	−0.767611	−	0.767611i	−0.977685	+	0.210074i	$0.932629\pi$
$702$		0			0
$703$	1.97433	−	32.5713i	0.0744634	−	1.22845i
$704$		0			0
$705$	−83.0754	−	41.5377i	−3.12880	−	1.56440i
$706$		0			0
$707$	−19.9590	−	19.9590i	−0.750637	−	0.750637i
$708$		0			0
$709$	24.6857	−	24.6857i	0.927091	−	0.927091i	−0.0704264	−	0.997517i	$-0.522436\pi$
$709$	24.6857	−	24.6857i	0.927091	−	0.927091i	0.997517	+	0.0704264i	$0.0224360\pi$
$710$		0			0
$711$	−12.0917	−	12.0917i	−0.453476	−	0.453476i
$712$		0			0
$713$	23.8850	+	23.8850i	0.894501	+	0.894501i
$714$		0			0
$715$	−13.1070	+	26.2141i	−0.490176	+	0.980352i
$716$		0			0
$717$			30.0991i			1.12407i
$718$		0			0
$719$		−	11.1425i		−	0.415546i	−0.978177	−	0.207773i	$-0.933378\pi$
$719$		−	11.1425i		−	0.415546i	0.978177	−	0.207773i	$-0.0666216\pi$
$720$		0			0
$721$	−8.81103	+	8.81103i	−0.328140	+	0.328140i
$722$		0			0
$723$	−21.8826			−0.813822
$724$		0			0
$725$	−3.00000	+	21.0000i	−0.111417	+	0.779920i
$726$		0			0
$727$		−	36.6778i		−	1.36030i	−0.733072	−	0.680152i	$-0.761914\pi$
$727$		−	36.6778i		−	1.36030i	0.733072	−	0.680152i	$-0.238086\pi$
$728$		0			0
$729$			14.8007i			0.548173i
$730$		0			0
$731$			8.28018i			0.306253i
$732$		0			0
$733$	25.8771	−	25.8771i	0.955793	−	0.955793i	−0.0432706	−	0.999063i	$-0.513778\pi$
$733$	25.8771	−	25.8771i	0.955793	−	0.955793i	0.999063	+	0.0432706i	$0.0137777\pi$
$734$		0			0
$735$	−26.3798	+	8.79328i	−0.973035	+	0.324345i
$736$		0			0
$737$	5.88503	−	5.88503i	0.216778	−	0.216778i
$738$		0			0
$739$	−13.7701			−0.506540			−0.253270	−	0.967396i	$-0.581506\pi$
$739$	−13.7701			−0.506540			−0.253270	+	0.967396i	$0.581506\pi$
$740$		0			0
$741$	−49.7187			−1.82646
$742$		0			0
$743$	−12.3798	+	12.3798i	−0.454173	+	0.454173i	−0.896737	−	0.442564i	$-0.854069\pi$
$743$	−12.3798	+	12.3798i	−0.454173	+	0.454173i	0.442564	+	0.896737i	$0.354069\pi$
$744$		0			0
$745$	−10.2802	−	5.14009i	−0.376637	−	0.188318i
$746$		0			0
$747$	62.5964	−	62.5964i	2.29028	−	2.29028i
$748$		0			0
$749$		−	26.8441i		−	0.980861i
$750$		0			0
$751$			15.4386i			0.563361i	0.959508	+	0.281680i	$0.0908918\pi$
$751$			15.4386i			0.563361i	−0.959508	+	0.281680i	$0.909108\pi$
$752$		0			0
$753$		−	17.8031i		−	0.648781i
$754$		0			0
$755$	−31.0410	−	15.5205i	−1.12970	−	0.564848i
$756$		0			0
$757$	18.0661			0.656623			0.328311	−	0.944570i	$-0.393520\pi$
$757$	18.0661			0.656623			0.328311	+	0.944570i	$0.393520\pi$
$758$		0			0
$759$	65.0093	−	65.0093i	2.35969	−	2.35969i
$760$		0			0
$761$			38.8110i			1.40690i	0.710745	+	0.703449i	$0.248358\pi$
$761$			38.8110i			1.40690i	−0.710745	+	0.703449i	$0.751642\pi$
$762$		0			0
$763$			10.9235i			0.395459i
$764$		0			0
$765$	84.8613	+	42.4306i	3.06817	+	1.53408i
$766$		0			0
$767$	12.1890	+	12.1890i	0.440118	+	0.440118i
$768$		0			0
$769$	35.3976	+	35.3976i	1.27647	+	1.27647i	0.942630	+	0.333840i	$0.108345\pi$
$769$	35.3976	+	35.3976i	1.27647	+	1.27647i	0.333840	+	0.942630i	$0.391655\pi$
$770$		0			0
$771$	35.2471	−	35.2471i	1.26939	−	1.26939i
$772$		0			0
$773$	24.5046	+	24.5046i	0.881371	+	0.881371i	0.993674	−	0.112303i	$-0.0358229\pi$
$773$	24.5046	+	24.5046i	0.881371	+	0.881371i	−0.112303	+	0.993674i	$0.535823\pi$
$774$		0			0
$775$	25.8036	+	3.68624i	0.926894	+	0.132413i
$776$		0			0
$777$	−22.3976	−	25.2881i	−0.803509	−	0.907205i
$778$		0			0
$779$	36.3645	+	36.3645i	1.30290	+	1.30290i
$780$		0			0
$781$		−	22.8771i		−	0.818607i
$782$		0			0
$783$			54.1982i			1.93689i
$784$		0			0
$785$	−11.0330	−	33.0991i	−0.393786	−	1.18136i
$786$		0			0
$787$	4.01774	−	4.01774i	0.143217	−	0.143217i	−0.631863	−	0.775080i	$-0.717709\pi$
$787$	4.01774	−	4.01774i	0.143217	−	0.143217i	0.775080	+	0.631863i	$0.217709\pi$
$788$		0			0
$789$			23.2881i			0.829078i
$790$		0			0
$791$	−7.29602	+	7.29602i	−0.259417	+	0.259417i
$792$		0			0
$793$	17.8692	+	17.8692i	0.634553	+	0.634553i
$794$		0			0
$795$	−26.5456	+	53.0912i	−0.941475	+	1.88295i
$796$		0			0
$797$			13.6502i			0.483515i	0.970337	+	0.241757i	$0.0777238\pi$
$797$			13.6502i			0.483515i	−0.970337	+	0.241757i	$0.922276\pi$
$798$		0			0
$799$	−55.9432	+	55.9432i	−1.97913	+	1.97913i
$800$		0			0
$801$	21.3315	−	21.3315i	0.753712	−	0.753712i
$802$		0			0
$803$	8.62753	+	8.62753i	0.304459	+	0.304459i
$804$		0			0
$805$	24.0991	−	8.03304i	0.849383	−	0.283128i
$806$		0			0
$807$	−24.9511	−	24.9511i	−0.878321	−	0.878321i
$808$		0			0
$809$	−3.00000	−	3.00000i	−0.105474	−	0.105474i	0.652400	−	0.757875i	$-0.273762\pi$
$809$	−3.00000	−	3.00000i	−0.105474	−	0.105474i	−0.757875	+	0.652400i	$0.773762\pi$
$810$		0			0
$811$	−2.95904			−0.103906			−0.0519529	−	0.998650i	$-0.516545\pi$
$811$	−2.95904			−0.103906			−0.0519529	+	0.998650i	$0.516545\pi$
$812$		0			0
$813$	−2.00000	+	2.00000i	−0.0701431	+	0.0701431i
$814$		0			0
$815$	9.04096	−	18.0819i	0.316691	−	0.633382i
$816$		0			0
$817$	5.20617	+	5.20617i	0.182141	+	0.182141i
$818$		0			0
$819$	−25.5126	+	25.5126i	−0.891481	+	0.891481i
$820$		0			0
$821$	−31.9181			−1.11395			−0.556974	−	0.830530i	$-0.688038\pi$
$821$	−31.9181			−1.11395			−0.556974	+	0.830530i	$0.688038\pi$
$822$		0			0
$823$	−20.9254	−	20.9254i	−0.729415	−	0.729415i	0.241088	−	0.970503i	$-0.422496\pi$
$823$	−20.9254	−	20.9254i	−0.729415	−	0.729415i	−0.970503	+	0.241088i	$0.922496\pi$
$824$		0			0
$825$	10.0330	−	70.2313i	0.349306	−	2.44514i
$826$		0			0
$827$	21.3053			0.740858			0.370429	−	0.928861i	$-0.379211\pi$
$827$	21.3053			0.740858			0.370429	+	0.928861i	$0.379211\pi$
$828$		0			0
$829$	−1.11741	−	1.11741i	−0.0388094	−	0.0388094i	0.687436	−	0.726245i	$-0.258736\pi$
$829$	−1.11741	−	1.11741i	−0.0388094	−	0.0388094i	−0.726245	+	0.687436i	$0.758736\pi$
$830$		0			0
$831$	35.9102	+	35.9102i	1.24571	+	1.24571i
$832$		0			0
$833$			23.6857i			0.820661i
$834$		0			0
$835$	−3.93392	+	7.86783i	−0.136139	+	0.272278i
$836$		0			0
$837$	66.5958			2.30189
$838$		0			0
$839$	−44.3304			−1.53046			−0.765228	−	0.643759i	$-0.777374\pi$
$839$	−44.3304			−1.53046			−0.765228	+	0.643759i	$0.777374\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$		0			0
$843$	28.6936			0.988260
$844$		0			0
$845$	−4.43855	+	8.87711i	−0.152691	+	0.305382i
$846$		0			0
$847$	−11.2398	+	11.2398i	−0.386203	+	0.386203i
$848$		0			0
$849$	−52.2337	+	52.2337i	−1.79266	+	1.79266i
$850$		0			0
$851$	−26.1322	−	29.5046i	−0.895799	−	1.01141i
$852$		0			0
$853$	−8.05133			−0.275672			−0.137836	−	0.990455i	$-0.544015\pi$
$853$	−8.05133			−0.275672			−0.137836	+	0.990455i	$0.544015\pi$
$854$		0			0
$855$	80.0349	−	26.6783i	2.73714	−	0.912379i
$856$		0			0
$857$	−32.8416			−1.12185			−0.560924	−	0.827867i	$-0.689554\pi$
$857$	−32.8416			−1.12185			−0.560924	+	0.827867i	$0.689554\pi$
$858$		0			0
$859$	27.0098	−	27.0098i	0.921563	−	0.921563i	−0.0755768	−	0.997140i	$-0.524080\pi$
$859$	27.0098	−	27.0098i	0.921563	−	0.921563i	0.997140	+	0.0755768i	$0.0240798\pi$
$860$		0			0
$861$	53.2392			1.81439
$862$		0			0
$863$	−1.97433	−	1.97433i	−0.0672071	−	0.0672071i	0.672704	−	0.739911i	$-0.265133\pi$
$863$	−1.97433	−	1.97433i	−0.0672071	−	0.0672071i	−0.739911	+	0.672704i	$0.765133\pi$
$864$		0			0
$865$	−0.107047	−	0.321140i	−0.00363970	−	0.0109191i
$866$		0			0
$867$	43.4459	−	43.4459i	1.47550	−	1.47550i
$868$		0			0
$869$	7.70153	+	7.70153i	0.261257	+	0.261257i
$870$		0			0
$871$	−3.84407	+	3.84407i	−0.130251	+	0.130251i
$872$		0			0
$873$		−	37.7848i		−	1.27882i
$874$		0			0
$875$	11.1578	−	16.1169i	0.377204	−	0.544850i
$876$		0			0
$877$	10.2881	−	10.2881i	0.347404	−	0.347404i	−0.511737	−	0.859142i	$-0.670998\pi$
$877$	10.2881	−	10.2881i	0.347404	−	0.347404i	0.859142	+	0.511737i	$0.170998\pi$
$878$		0			0
$879$	−15.2905			−0.515737
$880$		0			0
$881$			32.6141i			1.09880i	0.835560	+	0.549399i	$0.185143\pi$
$881$			32.6141i			1.09880i	−0.835560	+	0.549399i	$0.814857\pi$
$882$		0			0
$883$	5.17313			0.174090			0.0870448	−	0.996204i	$-0.472258\pi$
$883$	5.17313			0.174090			0.0870448	+	0.996204i	$0.472258\pi$
$884$		0			0
$885$	−37.3211	−	18.6606i	−1.25454	−	0.627268i
$886$		0			0
$887$	33.6374	+	33.6374i	1.12943	+	1.12943i	0.990270	+	0.139162i	$0.0444409\pi$
$887$	33.6374	+	33.6374i	1.12943	+	1.12943i	0.139162	+	0.990270i	$0.455559\pi$
$888$		0			0
$889$			10.9615i			0.367636i
$890$		0			0
$891$		−	86.7439i		−	2.90603i
$892$		0			0
$893$			70.3487i			2.35413i
$894$		0			0
$895$	53.5781	−	17.8594i	1.79092	−	0.596973i
$896$		0			0
$897$	−42.4637	+	42.4637i	−1.41782	+	1.41782i
$898$		0			0
$899$	22.1174			0.737657
$900$		0			0
$901$	35.7518	+	35.7518i	1.19106	+	1.19106i
$902$		0			0
$903$	7.62205			0.253646
$904$		0			0
$905$	−9.81895	+	19.6379i	−0.326393	+	0.652786i
$906$		0			0
$907$	−38.3463			−1.27327			−0.636633	−	0.771167i	$-0.719674\pi$
$907$	−38.3463			−1.27327			−0.636633	+	0.771167i	$0.719674\pi$
$908$		0			0
$909$	−113.226			−3.75546
$910$		0			0
$911$	−4.67587	−	4.67587i	−0.154918	−	0.154918i	0.625392	−	0.780311i	$-0.284939\pi$
$911$	−4.67587	−	4.67587i	−0.154918	−	0.154918i	−0.780311	+	0.625392i	$0.784939\pi$
$912$		0			0
$913$	−39.8692	+	39.8692i	−1.31948	+	1.31948i
$914$		0			0
$915$	−54.7133	−	27.3566i	−1.80876	−	0.904382i
$916$		0			0
$917$		−	6.74250i		−	0.222657i
$918$		0			0
$919$	29.9003	+	29.9003i	0.986321	+	0.986321i	0.999908	−	0.0135868i	$-0.00432496\pi$
$919$	29.9003	+	29.9003i	0.986321	+	0.986321i	−0.0135868	+	0.999908i	$0.504325\pi$
$920$		0			0
$921$	−81.6698			−2.69111
$922$		0			0
$923$			14.9432i			0.491861i
$924$		0			0
$925$	−29.7927	−	6.11497i	−0.979579	−	0.201059i
$926$		0			0
$927$			49.9842i			1.64170i
$928$		0			0
$929$	−21.5046			−0.705544			−0.352772	−	0.935709i	$-0.614761\pi$
$929$	−21.5046			−0.705544			−0.352772	+	0.935709i	$0.614761\pi$
$930$		0			0
$931$	14.8924	+	14.8924i	0.488079	+	0.488079i
$932$		0			0
$933$		−	65.7518i		−	2.15262i
$934$		0			0
$935$	−54.0502	−	27.0251i	−1.76763	−	0.883816i
$936$		0			0
$937$	2.40307	−	2.40307i	0.0785048	−	0.0785048i	−0.666764	−	0.745269i	$-0.732321\pi$
$937$	2.40307	−	2.40307i	0.0785048	−	0.0785048i	0.745269	+	0.666764i	$0.232321\pi$
$938$		0			0
$939$	14.3645	+	14.3645i	0.468769	+	0.468769i
$940$		0			0
$941$	−43.5071			−1.41829			−0.709145	−	0.705062i	$-0.750919\pi$
$941$	−43.5071			−1.41829			−0.709145	+	0.705062i	$0.750919\pi$
$942$		0			0
$943$	62.1163			2.02279
$944$		0			0
$945$	22.3976	−	44.7952i	0.728594	−	1.45719i
$946$		0			0
$947$	9.17313			0.298087			0.149043	−	0.988831i	$-0.452381\pi$
$947$	9.17313			0.298087			0.149043	+	0.988831i	$0.452381\pi$
$948$		0			0
$949$	−5.63545	−	5.63545i	−0.182934	−	0.182934i
$950$		0			0
$951$	−8.99452			−0.291667
$952$		0			0
$953$	−34.6221	+	34.6221i	−1.12152	+	1.12152i	−0.130005	+	0.991513i	$0.541499\pi$
$953$	−34.6221	+	34.6221i	−1.12152	+	1.12152i	−0.991513	+	0.130005i	$0.958501\pi$
$954$		0			0
$955$	−42.5964	+	14.1988i	−1.37839	+	0.459462i
$956$		0			0
$957$		−	60.1982i		−	1.94593i
$958$		0			0
$959$			21.2086i			0.684862i
$960$		0			0
$961$			3.82333i			0.123333i
$962$		0			0
$963$	−76.1420	−	76.1420i	−2.45364	−	2.45364i
$964$		0			0
$965$	1.91807	+	0.959036i	0.0617449	+	0.0308725i
$966$		0			0
$967$	0.892953			0.0287154			0.0143577	−	0.999897i	$-0.495430\pi$
$967$	0.892953			0.0287154			0.0143577	+	0.999897i	$0.495430\pi$
$968$		0			0
$969$		−	102.514i		−	3.29322i
$970$		0			0
$971$	47.1573			1.51335			0.756675	−	0.653792i	$-0.226823\pi$
$971$	47.1573			1.51335			0.756675	+	0.653792i	$0.226823\pi$
$972$		0			0
$973$	2.74494	−	2.74494i	0.0879988	−	0.0879988i
$974$		0			0
$975$	−6.55352	+	45.8747i	−0.209881	+	1.46917i
$976$		0			0
$977$		−	49.2905i		−	1.57694i	−0.615071	−	0.788472i	$-0.710872\pi$
$977$		−	49.2905i		−	1.57694i	0.615071	−	0.788472i	$-0.289128\pi$
$978$		0			0
$979$	−13.5866	+	13.5866i	−0.434229	+	0.434229i
$980$		0			0
$981$	30.9842	+	30.9842i	0.989248	+	0.989248i
$982$		0			0
$983$	3.08138	−	3.08138i	0.0982808	−	0.0982808i	−0.656257	−	0.754538i	$-0.727861\pi$
$983$	3.08138	−	3.08138i	0.0982808	−	0.0982808i	0.754538	+	0.656257i	$0.227861\pi$
$984$		0			0
$985$	1.47952	+	4.43855i	0.0471414	+	0.141424i
$986$		0			0
$987$	51.4967	+	51.4967i	1.63916	+	1.63916i
$988$		0			0
$989$	8.89295			0.282779
$990$		0			0
$991$	16.0917	−	16.0917i	0.511171	−	0.511171i	−0.403714	−	0.914885i	$-0.632281\pi$
$991$	16.0917	−	16.0917i	0.511171	−	0.511171i	0.914885	+	0.403714i	$0.132281\pi$
$992$		0			0
$993$	−20.8441			−0.661466
$994$		0			0
$995$	22.0404	−	7.34681i	0.698728	−	0.232909i
$996$		0			0
$997$	−22.9590			−0.727120			−0.363560	−	0.931571i	$-0.618439\pi$
$997$	−22.9590			−0.727120			−0.363560	+	0.931571i	$0.618439\pi$
$998$		0			0
$999$	−77.5628	−	4.70153i	−2.45398	−	0.148750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.l.a.413.3	✓	6
5.2	odd	4		740.2.o.a.117.1	yes	6
37.31	odd	4		740.2.o.a.253.1	yes	6
185.142	even	4	inner	740.2.l.a.697.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.l.a.413.3	✓	6	1.1	even	1	trivial
740.2.l.a.697.3	yes	6	185.142	even	4	inner
740.2.o.a.117.1	yes	6	5.2	odd	4
740.2.o.a.253.1	yes	6	37.31	odd	4

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.23976 - 2.23976i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(1.23976 - 1.23976i) q^{7} -7.03304i q^{9} +4.47952i q^{11} -2.92599i q^{13} +(2.23976 + 6.71928i) q^{15} +6.03304 q^{17} +(3.79328 - 3.79328i) q^{19} -5.55352i q^{21} -6.47952i q^{23} +(-3.00000 - 4.00000i) q^{25} +(-9.03304 - 9.03304i) q^{27} +(-3.00000 - 3.00000i) q^{29} +(-3.68624 + 3.68624i) q^{31} +(10.0330 + 10.0330i) q^{33} +(1.23976 + 3.71928i) q^{35} +(4.55352 - 4.03304i) q^{37} +(-6.55352 - 6.55352i) q^{39} +9.58657i q^{41} +1.37247i q^{43} +(14.0661 + 7.03304i) q^{45} +(-9.27280 + 9.27280i) q^{47} +3.92599i q^{49} +(13.5126 - 13.5126i) q^{51} +(5.92599 + 5.92599i) q^{53} +(-8.95904 - 4.47952i) q^{55} -16.9921i q^{57} +(-4.16575 + 4.16575i) q^{59} +(-6.10705 + 6.10705i) q^{61} +(-8.71928 - 8.71928i) q^{63} +(5.85199 + 2.92599i) q^{65} +(-1.31376 - 1.31376i) q^{67} +(-14.5126 - 14.5126i) q^{69} -5.10705 q^{71} +(1.92599 - 1.92599i) q^{73} +(-15.6783 - 2.23976i) q^{75} +(5.55352 + 5.55352i) q^{77} +(1.71928 - 1.71928i) q^{79} -19.3645 q^{81} +(8.90033 + 8.90033i) q^{83} +(-6.03304 + 12.0661i) q^{85} -13.4386 q^{87} +(3.03304 + 3.03304i) q^{89} +(-3.62753 - 3.62753i) q^{91} +16.5126i q^{93} +(3.79328 + 11.3798i) q^{95} +5.37247 q^{97} +31.5046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - 6 q^{5} - 4 q^{7} + 2 q^{15} + 4 q^{17} + 2 q^{19} - 18 q^{25} - 22 q^{27} - 18 q^{29} - 20 q^{31} + 28 q^{33} - 4 q^{35} + 18 q^{37} - 30 q^{39} + 20 q^{45} - 12 q^{47} + 26 q^{51} + 22 q^{53}+ \cdots + 56 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 - 6 * q^5 - 4 * q^7 + 2 * q^15 + 4 * q^17 + 2 * q^19 - 18 * q^25 - 22 * q^27 - 18 * q^29 - 20 * q^31 + 28 * q^33 - 4 * q^35 + 18 * q^37 - 30 * q^39 + 20 * q^45 - 12 * q^47 + 26 * q^51 + 22 * q^53 - 8 * q^55 - 18 * q^61 - 18 * q^63 + 8 * q^65 - 10 * q^67 - 32 * q^69 - 12 * q^71 - 2 * q^73 - 14 * q^75 + 24 * q^77 - 24 * q^79 - 34 * q^81 + 14 * q^83 - 4 * q^85 - 12 * q^87 - 14 * q^89 - 26 * q^91 + 2 * q^95 + 28 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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