LMFDB - Embedded newform 287.3.g.a.132.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.9
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69918i q^{2} +(-0.291651 + 0.291651i) q^{3} -3.28560 q^{4} -0.108748 q^{5} +(0.787221 + 0.787221i) q^{6} +(-6.97500 + 0.591083i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +O(q^{10})$	\(q-2.69918i q^{2} +(-0.291651 + 0.291651i) q^{3} -3.28560 q^{4} -0.108748 q^{5} +(0.787221 + 0.787221i) q^{6} +(-6.97500 + 0.591083i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +0.293532i q^{10} +(-7.82173 - 7.82173i) q^{11} +(0.958249 - 0.958249i) q^{12} +(-9.60641 + 9.60641i) q^{13} +(1.59544 + 18.8268i) q^{14} +(0.0317166 - 0.0317166i) q^{15} -18.3472 q^{16} +(14.4061 + 14.4061i) q^{17} +23.8335 q^{18} +(-11.9254 - 11.9254i) q^{19} +0.357303 q^{20} +(1.86188 - 2.20666i) q^{21} +(-21.1123 + 21.1123i) q^{22} -19.1262 q^{23} +(0.562394 + 0.562394i) q^{24} -24.9882 q^{25} +(25.9295 + 25.9295i) q^{26} +(-5.20011 - 5.20011i) q^{27} +(22.9170 - 1.94206i) q^{28} +(9.29385 + 9.29385i) q^{29} +(-0.0856089 - 0.0856089i) q^{30} +44.5464i q^{31} +41.8094i q^{32} +4.56244 q^{33} +(38.8847 - 38.8847i) q^{34} +(0.758519 - 0.0642793i) q^{35} -29.0114i q^{36} +41.3202 q^{37} +(-32.1889 + 32.1889i) q^{38} -5.60345i q^{39} +0.209700i q^{40} +(18.0276 - 36.8240i) q^{41} +(-5.95618 - 5.02555i) q^{42} -39.6527i q^{43} +(25.6991 + 25.6991i) q^{44} -0.960234i q^{45} +51.6252i q^{46} +(-56.4163 - 56.4163i) q^{47} +(5.35100 - 5.35100i) q^{48} +(48.3012 - 8.24561i) q^{49} +67.4477i q^{50} -8.40311 q^{51} +(31.5628 - 31.5628i) q^{52} +(11.3804 + 11.3804i) q^{53} +(-14.0361 + 14.0361i) q^{54} +(0.850600 + 0.850600i) q^{55} +(1.13979 + 13.4500i) q^{56} +6.95613 q^{57} +(25.0858 - 25.0858i) q^{58} +33.0737i q^{59} +(-0.104208 + 0.104208i) q^{60} -105.098 q^{61} +120.239 q^{62} +(-5.21919 - 61.5884i) q^{63} +39.4622 q^{64} +(1.04468 - 1.04468i) q^{65} -12.3149i q^{66} +(50.4349 - 50.4349i) q^{67} +(-47.3326 - 47.3326i) q^{68} +(5.57819 - 5.57819i) q^{69} +(-0.173502 - 2.04738i) q^{70} +(-20.3541 - 20.3541i) q^{71} +17.0267 q^{72} -25.5463 q^{73} -111.531i q^{74} +(7.28784 - 7.28784i) q^{75} +(39.1821 + 39.1821i) q^{76} +(59.1799 + 49.9333i) q^{77} -15.1247 q^{78} +(-62.8822 - 62.8822i) q^{79} +1.99523 q^{80} -76.4357 q^{81} +(-99.3947 - 48.6599i) q^{82} +118.307i q^{83} +(-6.11738 + 7.25019i) q^{84} +(-1.56664 - 1.56664i) q^{85} -107.030 q^{86} -5.42113 q^{87} +(-15.0827 + 15.0827i) q^{88} +(-59.8987 + 59.8987i) q^{89} -2.59185 q^{90} +(61.3265 - 72.6829i) q^{91} +62.8410 q^{92} +(-12.9920 - 12.9920i) q^{93} +(-152.278 + 152.278i) q^{94} +(1.29687 + 1.29687i) q^{95} +(-12.1938 - 12.1938i) q^{96} +(-73.7946 - 73.7946i) q^{97} +(-22.2564 - 130.374i) q^{98} +(69.0650 - 69.0650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	2.69918i		−	1.34959i	−0.738004	−	0.674796i	$-0.764232\pi$
$2$		−	2.69918i		−	1.34959i	0.738004	−	0.674796i	$-0.235768\pi$
$3$	−0.291651	+	0.291651i	−0.0972171	+	0.0972171i	−0.754043	−	0.656825i	$-0.771899\pi$
$3$	−0.291651	+	0.291651i	−0.0972171	+	0.0972171i	0.656825	+	0.754043i	$0.271899\pi$
$4$	−3.28560			−0.821399
$5$	−0.108748			−0.0217497			−0.0108748	−	0.999941i	$-0.503462\pi$
$5$	−0.108748			−0.0217497			−0.0108748	+	0.999941i	$0.503462\pi$
$6$	0.787221	+	0.787221i	0.131203	+	0.131203i
$7$	−6.97500	+	0.591083i	−0.996429	+	0.0844404i
$7$	−6.97500	+	0.591083i	−0.996429	+	0.0844404i
$8$		−	1.92831i		−	0.241039i
$9$			8.82988i			0.981098i
$10$			0.293532i			0.0293532i
$11$	−7.82173	−	7.82173i	−0.711067	−	0.711067i	0.255692	−	0.966758i	$-0.417697\pi$
$11$	−7.82173	−	7.82173i	−0.711067	−	0.711067i	−0.966758	+	0.255692i	$0.917697\pi$
$12$	0.958249	−	0.958249i	0.0798540	−	0.0798540i
$13$	−9.60641	+	9.60641i	−0.738955	+	0.738955i	−0.972376	−	0.233421i	$-0.925008\pi$
$13$	−9.60641	+	9.60641i	−0.738955	+	0.738955i	0.233421	+	0.972376i	$0.425008\pi$
$14$	1.59544	+	18.8268i	0.113960	+	1.34477i
$15$	0.0317166	−	0.0317166i	0.00211444	−	0.00211444i
$16$	−18.3472			−1.14670
$17$	14.4061	+	14.4061i	0.847416	+	0.847416i	0.989810	−	0.142394i	$-0.0454799\pi$
$17$	14.4061	+	14.4061i	0.847416	+	0.847416i	−0.142394	+	0.989810i	$0.545480\pi$
$18$	23.8335			1.32408
$19$	−11.9254	−	11.9254i	−0.627654	−	0.627654i	0.319823	−	0.947477i	$-0.396376\pi$
$19$	−11.9254	−	11.9254i	−0.627654	−	0.627654i	−0.947477	+	0.319823i	$0.896376\pi$
$20$	0.357303			0.0178651
$21$	1.86188	−	2.20666i	0.0886609	−	0.105079i
$22$	−21.1123	+	21.1123i	−0.959650	+	0.959650i
$23$	−19.1262			−0.831575			−0.415787	−	0.909462i	$-0.636494\pi$
$23$	−19.1262			−0.831575			−0.415787	+	0.909462i	$0.636494\pi$
$24$	0.562394	+	0.562394i	0.0234331	+	0.0234331i
$25$	−24.9882			−0.999527
$26$	25.9295	+	25.9295i	0.997287	+	0.997287i
$27$	−5.20011	−	5.20011i	−0.192597	−	0.192597i
$28$	22.9170	−	1.94206i	0.818465	−	0.0693593i
$29$	9.29385	+	9.29385i	0.320478	+	0.320478i	0.848950	−	0.528473i	$-0.177235\pi$
$29$	9.29385	+	9.29385i	0.320478	+	0.320478i	−0.528473	+	0.848950i	$0.677235\pi$
$30$	−0.0856089	−	0.0856089i	−0.00285363	−	0.00285363i
$31$			44.5464i			1.43698i	0.695536	+	0.718491i	$0.255167\pi$
$31$			44.5464i			1.43698i	−0.695536	+	0.718491i	$0.744833\pi$
$32$			41.8094i			1.30654i
$33$	4.56244			0.138256
$34$	38.8847	−	38.8847i	1.14367	−	1.14367i
$35$	0.758519	−	0.0642793i	0.0216720	−	0.00183655i
$36$		−	29.0114i		−	0.805873i
$37$	41.3202			1.11676			0.558381	−	0.829585i	$-0.311423\pi$
$37$	41.3202			1.11676			0.558381	+	0.829585i	$0.311423\pi$
$38$	−32.1889	+	32.1889i	−0.847077	+	0.847077i
$39$		−	5.60345i		−	0.143678i
$40$			0.209700i			0.00524250i
$41$	18.0276	−	36.8240i	0.439699	−	0.898145i
$41$	18.0276	−	36.8240i	0.439699	−	0.898145i
$42$	−5.95618	−	5.02555i	−0.141814	−	0.119656i
$43$		−	39.6527i		−	0.922156i	−0.887360	−	0.461078i	$-0.847463\pi$
$43$		−	39.6527i		−	0.922156i	0.887360	−	0.461078i	$-0.152537\pi$
$44$	25.6991	+	25.6991i	0.584070	+	0.584070i
$45$		−	0.960234i		−	0.0213385i
$46$			51.6252i			1.12229i
$47$	−56.4163	−	56.4163i	−1.20035	−	1.20035i	−0.974061	−	0.226285i	$-0.927342\pi$
$47$	−56.4163	−	56.4163i	−1.20035	−	1.20035i	−0.226285	−	0.974061i	$-0.572658\pi$
$48$	5.35100	−	5.35100i	0.111479	−	0.111479i
$49$	48.3012	−	8.24561i	0.985740	−	0.168278i
$50$			67.4477i			1.34895i
$51$	−8.40311			−0.164767
$52$	31.5628	−	31.5628i	0.606977	−	0.606977i
$53$	11.3804	+	11.3804i	0.214725	+	0.214725i	0.806271	−	0.591546i	$-0.201482\pi$
$53$	11.3804	+	11.3804i	0.214725	+	0.214725i	−0.591546	+	0.806271i	$0.701482\pi$
$54$	−14.0361	+	14.0361i	−0.259927	+	0.259927i
$55$	0.850600	+	0.850600i	0.0154655	+	0.0154655i
$56$	1.13979	+	13.4500i	0.0203534	+	0.240178i
$57$	6.95613			0.122037
$58$	25.0858	−	25.0858i	0.432514	−	0.432514i
$59$			33.0737i			0.560571i	0.959917	+	0.280286i	$0.0904292\pi$
$59$			33.0737i			0.560571i	−0.959917	+	0.280286i	$0.909571\pi$
$60$	−0.104208	+	0.104208i	−0.00173680	+	0.00173680i
$61$	−105.098			−1.72292			−0.861461	−	0.507824i	$-0.830450\pi$
$61$	−105.098			−1.72292			−0.861461	+	0.507824i	$0.830450\pi$
$62$	120.239			1.93934
$63$	−5.21919	−	61.5884i	−0.0828443	−	0.977594i
$64$	39.4622			0.616597
$65$	1.04468	−	1.04468i	0.0160720	−	0.0160720i
$66$		−	12.3149i		−	0.186589i
$67$	50.4349	−	50.4349i	0.752760	−	0.752760i	−0.222233	−	0.974994i	$-0.571335\pi$
$67$	50.4349	−	50.4349i	0.752760	−	0.752760i	0.974994	+	0.222233i	$0.0713347\pi$
$68$	−47.3326	−	47.3326i	−0.696067	−	0.696067i
$69$	5.57819	−	5.57819i	0.0808433	−	0.0808433i
$70$	−0.173502	−	2.04738i	−0.00247859	−	0.0292483i
$71$	−20.3541	−	20.3541i	−0.286677	−	0.286677i	0.549088	−	0.835765i	$-0.314975\pi$
$71$	−20.3541	−	20.3541i	−0.286677	−	0.286677i	−0.835765	+	0.549088i	$0.814975\pi$
$72$	17.0267			0.236482
$73$	−25.5463			−0.349949			−0.174974	−	0.984573i	$-0.555984\pi$
$73$	−25.5463			−0.349949			−0.174974	+	0.984573i	$0.555984\pi$
$74$		−	111.531i		−	1.50717i
$75$	7.28784	−	7.28784i	0.0971711	−	0.0971711i
$76$	39.1821	+	39.1821i	0.515554	+	0.515554i
$77$	59.1799	+	49.9333i	0.768570	+	0.648484i
$78$	−15.1247			−0.193907
$79$	−62.8822	−	62.8822i	−0.795978	−	0.795978i	0.186481	−	0.982459i	$-0.440292\pi$
$79$	−62.8822	−	62.8822i	−0.795978	−	0.795978i	−0.982459	+	0.186481i	$0.940292\pi$
$80$	1.99523			0.0249404
$81$	−76.4357			−0.943650
$82$	−99.3947	−	48.6599i	−1.21213	−	0.593414i
$83$			118.307i			1.42538i	0.701479	+	0.712691i	$0.252524\pi$
$83$			118.307i			1.42538i	−0.701479	+	0.712691i	$0.747476\pi$
$84$	−6.11738	+	7.25019i	−0.0728259	+	0.0863118i
$85$	−1.56664	−	1.56664i	−0.0184310	−	0.0184310i
$86$	−107.030			−1.24453
$87$	−5.42113			−0.0623118
$88$	−15.0827	+	15.0827i	−0.171395	+	0.171395i
$89$	−59.8987	+	59.8987i	−0.673019	+	0.673019i	−0.958411	−	0.285392i	$-0.907876\pi$
$89$	−59.8987	+	59.8987i	−0.673019	+	0.673019i	0.285392	+	0.958411i	$0.407876\pi$
$90$	−2.59185			−0.0287983
$91$	61.3265	−	72.6829i	0.673918	−	0.798713i
$92$	62.8410			0.683055
$93$	−12.9920	−	12.9920i	−0.139699	−	0.139699i
$94$	−152.278	+	152.278i	−1.61998	+	1.61998i
$95$	1.29687	+	1.29687i	0.0136513	+	0.0136513i
$96$	−12.1938	−	12.1938i	−0.127018	−	0.127018i
$97$	−73.7946	−	73.7946i	−0.760769	−	0.760769i	0.215693	−	0.976461i	$-0.430799\pi$
$97$	−73.7946	−	73.7946i	−0.760769	−	0.760769i	−0.976461	+	0.215693i	$0.930799\pi$
$98$	−22.2564	−	130.374i	−0.227106	−	1.33035i
$99$	69.0650	−	69.0650i	0.697626	−	0.697626i
$100$	82.1010			0.821010
$101$	−17.6949	−	17.6949i	−0.175197	−	0.175197i	0.614062	−	0.789258i	$-0.289535\pi$
$101$	−17.6949	−	17.6949i	−0.175197	−	0.175197i	−0.789258	+	0.614062i	$0.789535\pi$
$102$			22.6815i			0.222368i
$103$	−62.5855			−0.607626			−0.303813	−	0.952732i	$-0.598260\pi$
$103$	−62.5855			−0.607626			−0.303813	+	0.952732i	$0.598260\pi$
$104$	18.5241	+	18.5241i	0.178117	+	0.178117i
$105$	−0.202476	+	0.239970i	−0.00192834	+	0.00228543i
$106$	30.7178	−	30.7178i	0.289791	−	0.289791i
$107$	102.020			0.953460			0.476730	−	0.879050i	$-0.341822\pi$
$107$	102.020			0.953460			0.476730	+	0.879050i	$0.341822\pi$
$108$	17.0855	+	17.0855i	0.158199	+	0.158199i
$109$	18.7353	−	18.7353i	0.171883	−	0.171883i	−0.615923	−	0.787806i	$-0.711217\pi$
$109$	18.7353	−	18.7353i	0.171883	−	0.171883i	0.787806	+	0.615923i	$0.211217\pi$
$110$	2.29593	−	2.29593i	0.0208721	−	0.0208721i
$111$	−12.0511	+	12.0511i	−0.108568	+	0.108568i
$112$	127.972	−	10.8447i	1.14261	−	0.0968281i
$113$	−160.745			−1.42252			−0.711261	−	0.702928i	$-0.751876\pi$
$113$	−160.745			−1.42252			−0.711261	+	0.702928i	$0.751876\pi$
$114$		−	18.7759i		−	0.164701i
$115$	2.07994			0.0180865
$116$	−30.5358	−	30.5358i	−0.263240	−	0.263240i
$117$	−84.8234	−	84.8234i	−0.724987	−	0.724987i
$118$	89.2721			0.756543
$119$	−108.998	−	91.9672i	−0.915946	−	0.772834i
$120$	−0.0611593	−	0.0611593i	−0.000509661	−	0.000509661i
$121$			1.35906i			0.0112319i
$122$			283.679i			2.32524i
$123$	5.48197	+	15.9975i	0.0445689	+	0.130061i
$124$		−	146.362i		−	1.18034i
$125$	5.43613			0.0434890
$126$	−166.238	+	14.0876i	−1.31935	+	0.111806i
$127$	120.546			0.949183			0.474592	−	0.880206i	$-0.342596\pi$
$127$	120.546			0.949183			0.474592	+	0.880206i	$0.342596\pi$
$128$			60.7217i			0.474388i
$129$	11.5648	+	11.5648i	0.0896494	+	0.0896494i
$130$	−2.81979	−	2.81979i	−0.0216907	−	0.0216907i
$131$	−81.5428			−0.622464			−0.311232	−	0.950334i	$-0.600742\pi$
$131$	−81.5428			−0.622464			−0.311232	+	0.950334i	$0.600742\pi$
$132$	−14.9903			−0.113563
$133$	90.2287	+	76.1309i	0.678411	+	0.572413i
$134$	−136.133	−	136.133i	−1.01592	−	1.01592i
$135$	0.565503	+	0.565503i	0.00418891	+	0.00418891i
$136$	27.7794	−	27.7794i	0.204260	−	0.204260i
$137$	163.629	−	163.629i	1.19437	−	1.19437i	0.218548	−	0.975826i	$-0.429868\pi$
$137$	163.629	−	163.629i	1.19437	−	1.19437i	0.975826	−	0.218548i	$-0.0701320\pi$
$138$	−15.0566	−	15.0566i	−0.109106	−	0.109106i
$139$		−	214.428i		−	1.54265i	−0.636444	−	0.771323i	$-0.719595\pi$
$139$		−	214.428i		−	1.54265i	0.636444	−	0.771323i	$-0.280405\pi$
$140$	−2.49219	+	0.211196i	−0.0178013	+	0.00150854i
$141$	32.9078			0.233388
$142$	−54.9394	+	54.9394i	−0.386897	+	0.386897i
$143$	150.278			1.05089
$144$		−	162.004i		−	1.12503i
$145$	−1.01069	−	1.01069i	−0.00697028	−	0.00697028i
$146$			68.9541i			0.472288i
$147$	−11.6823	+	16.4920i	−0.0794713	+	0.112190i
$148$	−135.761			−0.917307
$149$	−27.0851	+	27.0851i	−0.181779	+	0.181779i	−0.792131	−	0.610351i	$-0.791028\pi$
$149$	−27.0851	+	27.0851i	−0.181779	+	0.181779i	0.610351	+	0.792131i	$0.291028\pi$
$150$	−19.6712	−	19.6712i	−0.131141	−	0.131141i
$151$	187.870	+	187.870i	1.24417	+	1.24417i	0.958255	+	0.285914i	$0.0922971\pi$
$151$	187.870	+	187.870i	1.24417	+	1.24417i	0.285914	+	0.958255i	$0.407703\pi$
$152$	−22.9959	+	22.9959i	−0.151289	+	0.151289i
$153$	−127.204	+	127.204i	−0.831398	+	0.831398i
$154$	134.779	−	159.737i	0.875190	−	1.03726i
$155$		−	4.84435i		−	0.0312539i
$156$			18.4107i			0.118017i
$157$	26.4949	−	26.4949i	0.168758	−	0.168758i	−0.617676	−	0.786433i	$-0.711925\pi$
$157$	26.4949	−	26.4949i	0.168758	−	0.168758i	0.786433	+	0.617676i	$0.211925\pi$
$158$	−169.731	+	169.731i	−1.07425	+	1.07425i
$159$	−6.63822			−0.0417498
$160$		−	4.54670i		−	0.0284168i
$161$	133.405	−	11.3052i	0.828605	−	0.0702185i
$162$			206.314i			1.27354i
$163$	145.574			0.893095			0.446548	−	0.894760i	$-0.352653\pi$
$163$	145.574			0.893095			0.446548	+	0.894760i	$0.352653\pi$
$164$	−59.2315	+	120.989i	−0.361168	+	0.737736i
$165$	−0.496157			−0.00300701
$166$	319.331			1.92368
$167$	8.20575	−	8.20575i	0.0491362	−	0.0491362i	−0.682112	−	0.731248i	$-0.738938\pi$
$167$	8.20575	−	8.20575i	0.0491362	−	0.0491362i	0.731248	+	0.682112i	$0.238938\pi$
$168$	−4.25512	−	3.59028i	−0.0253281	−	0.0213707i
$169$		−	15.5662i		−	0.0921079i
$170$	−4.22864	+	4.22864i	−0.0248743	+	0.0248743i
$171$	105.300	−	105.300i	0.615790	−	0.615790i
$172$			130.283i			0.757458i
$173$	216.974			1.25418			0.627092	−	0.778946i	$-0.284245\pi$
$173$	216.974			1.25418			0.627092	+	0.778946i	$0.284245\pi$
$174$			14.6326i			0.0840955i
$175$	174.293	−	14.7701i	0.995957	−	0.0844005i
$176$	143.507	+	143.507i	0.815382	+	0.815382i
$177$	−9.64600	−	9.64600i	−0.0544971	−	0.0544971i
$178$	161.678	+	161.678i	0.908301	+	0.908301i
$179$	−227.374	+	227.374i	−1.27025	+	1.27025i	−0.324289	+	0.945958i	$0.605125\pi$
$179$	−227.374	+	227.374i	−1.27025	+	1.27025i	−0.945958	+	0.324289i	$0.894875\pi$
$180$			3.15494i			0.0175274i
$181$	208.026	+	208.026i	1.14932	+	1.14932i	0.986687	+	0.162630i	$0.0519976\pi$
$181$	208.026	+	208.026i	1.14932	+	1.14932i	0.162630	+	0.986687i	$0.448002\pi$
$182$	−196.185	−	165.532i	−1.07794	−	0.909514i
$183$	30.6520	−	30.6520i	0.167497	−	0.167497i
$184$			36.8813i			0.200442i
$185$	−4.49350			−0.0242892
$186$	−35.0679	+	35.0679i	−0.188537	+	0.188537i
$187$		−	225.361i		−	1.20514i
$188$	185.361	+	185.361i	0.985963	+	0.985963i
$189$	39.3445	+	33.1971i	0.208172	+	0.175646i
$190$	3.50049	−	3.50049i	0.0184236	−	0.0184236i
$191$	−1.40145	+	1.40145i	−0.00733744	+	0.00733744i	−0.710766	−	0.703429i	$-0.751652\pi$
$191$	−1.40145	+	1.40145i	−0.00733744	+	0.00733744i	0.703429	+	0.710766i	$0.251652\pi$
$192$	−11.5092	+	11.5092i	−0.0599438	+	0.0599438i
$193$	86.5068	+	86.5068i	0.448222	+	0.448222i	0.894763	−	0.446541i	$-0.147344\pi$
$193$	86.5068	+	86.5068i	0.448222	+	0.448222i	−0.446541	+	0.894763i	$0.647344\pi$
$194$	−199.185	+	199.185i	−1.02673	+	1.02673i
$195$			0.609365i			0.00312495i
$196$	−158.698	+	27.0917i	−0.809686	+	0.138223i
$197$			378.741i			1.92254i	0.275602	+	0.961272i	$0.411123\pi$
$197$			378.741i			1.92254i	−0.275602	+	0.961272i	$0.588877\pi$
$198$	−186.419	−	186.419i	−0.941511	−	0.941511i
$199$	−242.699	−	242.699i	−1.21959	−	1.21959i	−0.967774	−	0.251821i	$-0.918971\pi$
$199$	−242.699	−	242.699i	−1.21959	−	1.21959i	−0.251821	−	0.967774i	$-0.581029\pi$
$200$			48.1849i			0.240925i
$201$			29.4188i			0.146362i
$202$	−47.7617	+	47.7617i	−0.236444	+	0.236444i
$203$	−70.3180	−	59.3312i	−0.346394	−	0.292272i
$204$	27.6092			0.135339
$205$	−1.96047	+	4.00454i	−0.00956329	+	0.0195344i
$206$			168.930i			0.820047i
$207$		−	168.882i		−	0.815856i
$208$	176.251	−	176.251i	0.847361	−	0.847361i
$209$			186.555i			0.892607i
$210$	0.647724	+	0.546520i	0.00308440	+	0.00260248i
$211$	−51.5781	+	51.5781i	−0.244446	+	0.244446i	−0.818687	−	0.574241i	$-0.805297\pi$
$211$	−51.5781	+	51.5781i	−0.244446	+	0.244446i	0.574241	+	0.818687i	$0.305297\pi$
$212$	−37.3914	−	37.3914i	−0.176375	−	0.176375i
$213$	11.8726			0.0557399
$214$		−	275.371i		−	1.28678i
$215$			4.31216i			0.0200566i
$216$	−10.0274	+	10.0274i	−0.0464232	+	0.0464232i
$217$	−26.3306	−	310.711i	−0.121339	−	1.43185i
$218$	−50.5700	−	50.5700i	−0.231973	−	0.231973i
$219$	7.45060	−	7.45060i	0.0340210	−	0.0340210i
$220$	−2.79473	−	2.79473i	−0.0127033	−	0.0127033i
$221$	−276.781			−1.25240
$222$	32.5281	+	32.5281i	0.146523	+	0.146523i
$223$			306.185i			1.37303i	0.727116	+	0.686515i	$0.240860\pi$
$223$			306.185i			1.37303i	−0.727116	+	0.686515i	$0.759140\pi$
$224$	−24.7128	−	291.620i	−0.110325	−	1.30188i
$225$		−	220.643i		−	0.980634i
$226$			433.880i			1.91982i
$227$	231.780	+	231.780i	1.02106	+	1.02106i	0.999773	+	0.0212854i	$0.00677585\pi$
$227$	231.780	+	231.780i	1.02106	+	1.02106i	0.0212854	+	0.999773i	$0.493224\pi$
$228$	−22.8550			−0.100241
$229$	−76.1497	−	76.1497i	−0.332532	−	0.332532i	0.521016	−	0.853547i	$-0.325553\pi$
$229$	−76.1497	−	76.1497i	−0.332532	−	0.332532i	−0.853547	+	0.521016i	$0.825553\pi$
$230$		−	5.61415i		−	0.0244094i
$231$	−31.8230	+	2.69678i	−0.137762	+	0.0116744i
$232$	17.9214	−	17.9214i	0.0772474	−	0.0772474i
$233$	−166.811	−	166.811i	−0.715929	−	0.715929i	0.251840	−	0.967769i	$-0.418964\pi$
$233$	−166.811	−	166.811i	−0.715929	−	0.715929i	−0.967769	+	0.251840i	$0.918964\pi$
$234$	−228.954	+	228.954i	−0.978436	+	0.978436i
$235$	6.13517	+	6.13517i	0.0261071	+	0.0261071i
$236$		−	108.667i		−	0.460453i
$237$	36.6794			0.154765
$238$	−248.236	+	294.205i	−1.04301	+	1.23615i
$239$	−56.5626	−	56.5626i	−0.236663	−	0.236663i	0.578804	−	0.815467i	$-0.303520\pi$
$239$	−56.5626	−	56.5626i	−0.236663	−	0.236663i	−0.815467	+	0.578804i	$0.803520\pi$
$240$	−0.581912	+	0.581912i	−0.00242463	+	0.00242463i
$241$	−57.5754			−0.238902			−0.119451	−	0.992840i	$-0.538113\pi$
$241$	−57.5754			−0.238902			−0.119451	+	0.992840i	$0.538113\pi$
$242$	3.66836			0.0151585
$243$	69.0935	−	69.0935i	0.284336	−	0.284336i
$244$	345.310			1.41521
$245$	−5.25268	+	0.896696i	−0.0214395	+	0.00365998i
$246$	43.1803	−	14.7969i	0.175530	−	0.0601498i
$247$	229.121			0.927615
$248$	85.8993			0.346368
$249$	−34.5043	−	34.5043i	−0.138571	−	0.138571i
$250$		−	14.6731i		−	0.0586924i
$251$	−473.649			−1.88705			−0.943523	−	0.331306i	$-0.892511\pi$
$251$	−473.649			−1.88705			−0.943523	+	0.331306i	$0.892511\pi$
$252$	17.1482	+	202.355i	0.0680482	+	0.802994i
$253$	149.600	+	149.600i	0.591305	+	0.591305i
$254$		−	325.377i		−	1.28101i
$255$	0.913823			0.00358362
$256$	321.748			1.25683
$257$	316.912	−	316.912i	1.23312	−	1.23312i	0.270360	−	0.962759i	$-0.412857\pi$
$257$	316.912	−	316.912i	1.23312	−	1.23312i	0.962759	−	0.270360i	$-0.0871426\pi$
$258$	31.2154	−	31.2154i	0.120990	−	0.120990i
$259$	−288.208	+	24.4237i	−1.11277	+	0.0942998i
$260$	−3.43240	+	3.43240i	−0.0132015	+	0.0132015i
$261$	−82.0636	+	82.0636i	−0.314420	+	0.314420i
$262$			220.099i			0.840073i
$263$	176.315	−	176.315i	0.670398	−	0.670398i	−0.287410	−	0.957808i	$-0.592794\pi$
$263$	176.315	−	176.315i	0.670398	−	0.670398i	0.957808	+	0.287410i	$0.0927942\pi$
$264$		−	8.79779i		−	0.0333250i
$265$	−1.23760	−	1.23760i	−0.00467018	−	0.00467018i
$266$	205.491	−	243.544i	0.772524	−	0.915579i
$267$		−	34.9391i		−	0.130858i
$268$	−165.709	+	165.709i	−0.618316	+	0.618316i
$269$			310.547i			1.15445i	0.816586	+	0.577224i	$0.195864\pi$
$269$			310.547i			1.15445i	−0.816586	+	0.577224i	$0.804136\pi$
$270$	1.52640	−	1.52640i	0.00565332	−	0.00565332i
$271$			183.565i			0.677363i	0.940901	+	0.338681i	$0.109981\pi$
$271$			183.565i			0.677363i	−0.940901	+	0.338681i	$0.890019\pi$
$272$	−264.312	−	264.312i	−0.971735	−	0.971735i
$273$	3.31210	+	39.0840i	0.0121322	+	0.143165i
$274$	−441.666	−	441.666i	−1.61192	−	1.61192i
$275$	195.451	+	195.451i	0.710730	+	0.710730i
$276$	−18.3277	+	18.3277i	−0.0664046	+	0.0664046i
$277$	−92.3913			−0.333543			−0.166771	−	0.985996i	$-0.553334\pi$
$277$	−92.3913			−0.333543			−0.166771	+	0.985996i	$0.553334\pi$
$278$	−578.780			−2.08194
$279$	−393.340			−1.40982
$280$	−0.123950	−	1.46266i	−0.000442679	−	0.00522378i
$281$	−217.397	+	217.397i	−0.773656	+	0.773656i	−0.978744	−	0.205087i	$-0.934252\pi$
$281$	−217.397	+	217.397i	−0.773656	+	0.773656i	0.205087	+	0.978744i	$0.434252\pi$
$282$		−	88.8241i		−	0.314979i
$283$		−	148.412i		−	0.524425i	−0.965010	−	0.262212i	$-0.915548\pi$
$283$		−	148.412i		−	0.524425i	0.965010	−	0.262212i	$-0.0844521\pi$
$284$	66.8753	+	66.8753i	0.235476	+	0.235476i
$285$	−0.756467			−0.00265427
$286$		−	405.627i		−	1.41828i
$287$	−103.977	+	267.503i	−0.362288	+	0.932066i
$288$	−369.172			−1.28185
$289$			126.070i			0.436229i
$290$	−2.72804	+	2.72804i	−0.00940703	+	0.00940703i
$291$	43.0446			0.147919
$292$	83.9347			0.287448
$293$	−193.444	−	193.444i	−0.660219	−	0.660219i	0.295212	−	0.955432i	$-0.404610\pi$
$293$	−193.444	−	193.444i	−0.660219	−	0.660219i	−0.955432	+	0.295212i	$0.904610\pi$
$294$	44.5149	+	31.5326i	0.151411	+	0.107254i
$295$		−	3.59671i		−	0.0121922i
$296$		−	79.6781i		−	0.269183i
$297$			81.3477i			0.273898i
$298$	73.1077	+	73.1077i	0.245328	+	0.245328i
$299$	183.734	−	183.734i	0.614496	−	0.614496i
$300$	−23.9449	+	23.9449i	−0.0798163	+	0.0798163i
$301$	23.4381	+	276.578i	0.0778673	+	0.918863i
$302$	507.094	−	507.094i	1.67912	−	1.67912i
$303$	10.3215			0.0340642
$304$	218.799	+	218.799i	0.719732	+	0.719732i
$305$	11.4292			0.0374729
$306$	343.347	+	343.347i	1.12205	+	1.12205i
$307$	74.7932			0.243626			0.121813	−	0.992553i	$-0.461129\pi$
$307$	74.7932			0.243626			0.121813	+	0.992553i	$0.461129\pi$
$308$	−194.441	−	164.061i	−0.631303	−	0.532664i
$309$	18.2531	−	18.2531i	0.0590716	−	0.0590716i
$310$	−13.0758			−0.0421800
$311$	257.635	+	257.635i	0.828409	+	0.828409i	0.987297	−	0.158888i	$-0.0507908\pi$
$311$	257.635	+	257.635i	0.828409	+	0.828409i	−0.158888	+	0.987297i	$0.550791\pi$
$312$	−10.8052			−0.0346320
$313$	−58.4466	−	58.4466i	−0.186730	−	0.186730i	0.607551	−	0.794281i	$-0.292152\pi$
$313$	−58.4466	−	58.4466i	−0.186730	−	0.186730i	−0.794281	+	0.607551i	$0.792152\pi$
$314$	−71.5147	−	71.5147i	−0.227754	−	0.227754i
$315$	0.567578	+	6.69763i	0.00180184	+	0.0212623i
$316$	206.606	+	206.606i	0.653815	+	0.653815i
$317$	−13.2816	−	13.2816i	−0.0418977	−	0.0418977i	0.685848	−	0.727745i	$-0.259432\pi$
$317$	−13.2816	−	13.2816i	−0.0418977	−	0.0418977i	−0.727745	+	0.685848i	$0.759432\pi$
$318$			17.9178i			0.0563452i
$319$		−	145.388i		−	0.455762i
$320$	−4.29144			−0.0134108
$321$	−29.7543	+	29.7543i	−0.0926926	+	0.0926926i
$322$	−30.5148	−	360.086i	−0.0947664	−	1.11828i
$323$		−	343.597i		−	1.06377i
$324$	251.137			0.775113
$325$	240.047	−	240.047i	0.738605	−	0.738605i
$326$		−	392.932i		−	1.20531i
$327$			10.9284i			0.0334200i
$328$	−71.0080	−	34.7629i	−0.216488	−	0.105984i
$329$	426.850	+	360.157i	1.29742	+	1.09470i
$330$			1.33922i			0.00405824i
$331$	−376.040	−	376.040i	−1.13607	−	1.13607i	−0.989148	−	0.146925i	$-0.953062\pi$
$331$	−376.040	−	376.040i	−1.13607	−	1.13607i	−0.146925	−	0.989148i	$-0.546938\pi$
$332$		−	388.708i		−	1.17081i
$333$			364.852i			1.09565i
$334$	−22.1488	−	22.1488i	−0.0663139	−	0.0663139i
$335$	−5.48471	+	5.48471i	−0.0163723	+	0.0163723i
$336$	−34.1603	+	40.4861i	−0.101668	+	0.120494i
$337$			434.379i			1.28896i	0.764621	+	0.644480i	$0.222926\pi$
$337$			434.379i			1.28896i	−0.764621	+	0.644480i	$0.777074\pi$
$338$	−42.0161			−0.124308
$339$	46.8815	−	46.8815i	0.138294	−	0.138294i
$340$	5.14733	+	5.14733i	0.0151392	+	0.0151392i
$341$	348.430	−	348.430i	1.02179	−	1.02179i
$342$	−284.224	−	284.224i	−0.831065	−	0.831065i
$343$	−332.027	+	86.0632i	−0.968010	+	0.250913i
$344$	−76.4627			−0.222275
$345$	−0.606618	+	0.606618i	−0.00175831	+	0.00175831i
$346$		−	585.652i		−	1.69264i
$347$	−99.4907	+	99.4907i	−0.286717	+	0.286717i	−0.835780	−	0.549064i	$-0.814984\pi$
$347$	−99.4907	+	99.4907i	−0.286717	+	0.286717i	0.549064	+	0.835780i	$0.314984\pi$
$348$	17.8116			0.0511829
$349$	11.6679			0.0334324			0.0167162	−	0.999860i	$-0.494679\pi$
$349$	11.6679			0.0334324			0.0167162	+	0.999860i	$0.494679\pi$
$350$	−39.8672	−	470.448i	−0.113906	−	1.34414i
$351$	99.9088			0.284640
$352$	327.022	−	327.022i	0.929039	−	0.929039i
$353$			502.771i			1.42428i	0.702037	+	0.712141i	$0.252274\pi$
$353$			502.771i			1.42428i	−0.702037	+	0.712141i	$0.747726\pi$
$354$	−26.0363	+	26.0363i	−0.0735489	+	0.0735489i
$355$	2.21347	+	2.21347i	0.00623513	+	0.00623513i
$356$	196.803	−	196.803i	0.552817	−	0.552817i
$357$	58.6117	−	4.96693i	0.164178	−	0.0139130i
$358$	613.725	+	613.725i	1.71432	+	1.71432i
$359$	−44.6222			−0.124296			−0.0621480	−	0.998067i	$-0.519795\pi$
$359$	−44.6222			−0.124296			−0.0621480	+	0.998067i	$0.519795\pi$
$360$	−1.85163			−0.00514341
$361$		−	76.5686i		−	0.212102i
$362$	561.502	−	561.502i	1.55111	−	1.55111i
$363$	−0.396372	−	0.396372i	−0.00109193	−	0.00109193i
$364$	−201.494	+	238.807i	−0.553555	+	0.656062i
$365$	2.77811			0.00761127
$366$	−82.7355	−	82.7355i	−0.226053	−	0.226053i
$367$	25.4849			0.0694410			0.0347205	−	0.999397i	$-0.488946\pi$
$367$	25.4849			0.0694410			0.0347205	+	0.999397i	$0.488946\pi$
$368$	350.913			0.953569
$369$	325.151	+	159.182i	0.881168	+	0.431387i
$370$			12.1288i			0.0327805i
$371$	−86.1050	−	72.6515i	−0.232089	−	0.195826i
$372$	42.6866	+	42.6866i	0.114749	+	0.114749i
$373$	−349.736			−0.937629			−0.468814	−	0.883297i	$-0.655319\pi$
$373$	−349.736			−0.937629			−0.468814	+	0.883297i	$0.655319\pi$
$374$	−608.291			−1.62645
$375$	−1.58545	+	1.58545i	−0.00422788	+	0.00422788i
$376$	−108.788	+	108.788i	−0.289330	+	0.289330i
$377$	−178.561			−0.473637
$378$	89.6050	−	106.198i	0.237050	−	0.280947i
$379$	295.857			0.780625			0.390312	−	0.920682i	$-0.372367\pi$
$379$	295.857			0.780625			0.390312	+	0.920682i	$0.372367\pi$
$380$	−4.26099	−	4.26099i	−0.0112131	−	0.0112131i
$381$	−35.1575	+	35.1575i	−0.0922769	+	0.0922769i
$382$	3.78277	+	3.78277i	0.00990255	+	0.00990255i
$383$	10.2233	+	10.2233i	0.0266927	+	0.0266927i	0.720327	−	0.693634i	$-0.243992\pi$
$383$	10.2233	+	10.2233i	0.0266927	+	0.0266927i	−0.693634	+	0.720327i	$0.743992\pi$
$384$	−17.7096	−	17.7096i	−0.0461187	−	0.0461187i
$385$	−6.43571	−	5.43016i	−0.0167161	−	0.0141043i
$386$	233.498	−	233.498i	0.604917	−	0.604917i
$387$	350.129			0.904725
$388$	242.459	+	242.459i	0.624895	+	0.624895i
$389$			158.854i			0.408365i	0.978933	+	0.204183i	$0.0654536\pi$
$389$			158.854i			0.408365i	−0.978933	+	0.204183i	$0.934546\pi$
$390$	1.64479			0.00421741
$391$	−275.534	−	275.534i	−0.704690	−	0.704690i
$392$	−15.9001	−	93.1397i	−0.0405614	−	0.237601i
$393$	23.7821	−	23.7821i	0.0605142	−	0.0605142i
$394$	1022.29			2.59465
$395$	6.83833	+	6.83833i	0.0173122	+	0.0173122i
$396$	−226.920	+	226.920i	−0.573029	+	0.573029i
$397$	94.5647	−	94.5647i	0.238198	−	0.238198i	−0.577905	−	0.816104i	$-0.696130\pi$
$397$	94.5647	−	94.5647i	0.238198	−	0.238198i	0.816104	+	0.577905i	$0.196130\pi$
$398$	−655.090	+	655.090i	−1.64596	+	1.64596i
$399$	−48.5190	+	4.11165i	−0.121602	+	0.0103049i
$400$	458.464			1.14616
$401$			536.013i			1.33669i	0.743852	+	0.668345i	$0.232997\pi$
$401$			536.013i			1.33669i	−0.743852	+	0.668345i	$0.767003\pi$
$402$	79.4069			0.197529
$403$	−427.931	−	427.931i	−1.06186	−	1.06186i
$404$	58.1382	+	58.1382i	0.143906	+	0.143906i
$405$	8.31225			0.0205241
$406$	−160.146	+	189.801i	−0.394448	+	0.467491i
$407$	−323.196	−	323.196i	−0.794092	−	0.794092i
$408$			16.2038i			0.0397151i
$409$		−	48.9559i		−	0.119697i	−0.998207	−	0.0598483i	$-0.980938\pi$
$409$		−	48.9559i		−	0.119697i	0.998207	−	0.0598483i	$-0.0190617\pi$
$410$	10.8090	+	5.29168i	0.0263634	+	0.0129065i
$411$			95.4454i			0.232227i
$412$	205.631			0.499103
$413$	−19.5493	−	230.689i	−0.0473349	−	0.558569i
$414$	−455.844			−1.10107
$415$		−	12.8656i		−	0.0310015i
$416$	−401.638	−	401.638i	−0.965476	−	0.965476i
$417$	62.5381	+	62.5381i	0.149972	+	0.149972i
$418$	503.546			1.20466
$419$	−496.300			−1.18449			−0.592243	−	0.805759i	$-0.701758\pi$
$419$	−496.300			−1.18449			−0.592243	+	0.805759i	$0.701758\pi$
$420$	0.665254	−	0.788445i	0.00158394	−	0.00187725i
$421$	−556.492	−	556.492i	−1.32183	−	1.32183i	−0.912291	−	0.409543i	$-0.865688\pi$
$421$	−556.492	−	556.492i	−1.32183	−	1.32183i	−0.409543	−	0.912291i	$-0.634312\pi$
$422$	139.219	+	139.219i	0.329902	+	0.329902i
$423$	498.149	−	498.149i	1.17766	−	1.17766i
$424$	21.9449	−	21.9449i	0.0517569	−	0.0517569i
$425$	−359.982	−	359.982i	−0.847016	−	0.847016i
$426$		−	32.0463i		−	0.0752261i
$427$	733.060	−	62.1218i	1.71677	−	0.145484i
$428$	−335.197			−0.783171
$429$	−43.8287	+	43.8287i	−0.102165	+	0.102165i
$430$	11.6393			0.0270682
$431$		−	158.464i		−	0.367665i	−0.982958	−	0.183833i	$-0.941150\pi$
$431$		−	158.464i		−	0.367665i	0.982958	−	0.183833i	$-0.0588504\pi$
$432$	95.4077	+	95.4077i	0.220851	+	0.220851i
$433$			32.1706i			0.0742970i	0.999310	+	0.0371485i	$0.0118274\pi$
$433$			32.1706i			0.0742970i	−0.999310	+	0.0371485i	$0.988173\pi$
$434$	−838.667	+	71.0713i	−1.93241	+	0.163759i
$435$	0.589538			0.00135526
$436$	−61.5566	+	61.5566i	−0.141185	+	0.141185i
$437$	228.088	+	228.088i	0.521941	+	0.521941i
$438$	−20.1106	−	20.1106i	−0.0459145	−	0.0459145i
$439$	−330.128	+	330.128i	−0.752000	+	0.752000i	−0.974852	−	0.222852i	$-0.928463\pi$
$439$	−330.128	+	330.128i	−0.752000	+	0.752000i	0.222852	+	0.974852i	$0.428463\pi$
$440$	1.64022	−	1.64022i	0.00372777	−	0.00372777i
$441$	72.8077	+	426.494i	0.165097	+	0.967107i
$442$			747.084i			1.69024i
$443$		−	79.2409i		−	0.178873i	−0.995993	−	0.0894367i	$-0.971493\pi$
$443$		−	79.2409i		−	0.178873i	0.995993	−	0.0894367i	$-0.0285067\pi$
$444$	39.5950	−	39.5950i	0.0891779	−	0.0891779i
$445$	6.51388	−	6.51388i	0.0146379	−	0.0146379i
$446$	826.451			1.85303
$447$		−	15.7988i		−	0.0353441i
$448$	−275.249	+	23.3254i	−0.614395	+	0.0520657i
$449$			49.0577i			0.109260i	0.998507	+	0.0546300i	$0.0173979\pi$
$449$			49.0577i			0.109260i	−0.998507	+	0.0546300i	$0.982602\pi$
$450$	−595.555			−1.32346
$451$	−429.035	+	147.020i	−0.951296	+	0.325986i
$452$	528.143			1.16846
$453$	−109.585			−0.241909
$454$	625.618	−	625.618i	1.37801	−	1.37801i
$455$	−6.66915	+	7.90414i	−0.0146575	+	0.0173717i
$456$		−	13.4136i		−	0.0294157i
$457$	−65.0091	+	65.0091i	−0.142252	+	0.142252i	−0.774646	−	0.632395i	$-0.782072\pi$
$457$	−65.0091	+	65.0091i	−0.142252	+	0.142252i	0.632395	+	0.774646i	$0.282072\pi$
$458$	−205.542	+	205.542i	−0.448782	+	0.448782i
$459$		−	149.826i		−	0.326419i
$460$	−6.83385			−0.0148562
$461$			679.358i			1.47366i	0.676077	+	0.736831i	$0.263679\pi$
$461$			679.358i			1.47366i	−0.676077	+	0.736831i	$0.736321\pi$
$462$	7.27911	+	85.8962i	0.0157556	+	0.185922i
$463$	−113.244	−	113.244i	−0.244587	−	0.244587i	0.574158	−	0.818745i	$-0.305330\pi$
$463$	−113.244	−	113.244i	−0.244587	−	0.244587i	−0.818745	+	0.574158i	$0.805330\pi$
$464$	−170.517	−	170.517i	−0.367492	−	0.367492i
$465$	1.41286	+	1.41286i	0.00303841	+	0.00303841i
$466$	−450.255	+	450.255i	−0.966212	+	0.966212i
$467$		−	125.593i		−	0.268935i	−0.990918	−	0.134467i	$-0.957068\pi$
$467$		−	125.593i		−	0.268935i	0.990918	−	0.134467i	$-0.0429324\pi$
$468$	278.696	+	278.696i	0.595503	+	0.595503i
$469$	−321.972	+	381.595i	−0.686508	+	0.813635i
$470$	16.5600	−	16.5600i	0.0352340	−	0.0352340i
$471$			15.4546i			0.0328123i
$472$	63.7763			0.135119
$473$	−310.153	+	310.153i	−0.655715	+	0.655715i
$474$		−	99.0044i		−	0.208870i
$475$	297.995	+	297.995i	0.627357	+	0.627357i
$476$	358.122	+	302.167i	0.752357	+	0.634805i
$477$	−100.488	+	100.488i	−0.210666	+	0.210666i
$478$	−152.673	+	152.673i	−0.319399	+	0.319399i
$479$	307.603	−	307.603i	0.642178	−	0.642178i	−0.308912	−	0.951091i	$-0.599965\pi$
$479$	307.603	−	307.603i	0.642178	−	0.642178i	0.951091	+	0.308912i	$0.0999649\pi$
$480$	1.32605	+	1.32605i	0.00276260	+	0.00276260i
$481$	−396.939	+	396.939i	−0.825236	+	0.825236i
$482$			155.406i			0.322420i
$483$	−35.6107	+	42.2050i	−0.0737281	+	0.0873810i
$484$		−	4.46533i		−	0.00922589i
$485$	8.02503	+	8.02503i	0.0165465	+	0.0165465i
$486$	−186.496	−	186.496i	−0.383737	−	0.383737i
$487$			514.832i			1.05715i	0.848887	+	0.528575i	$0.177274\pi$
$487$			514.832i			1.05715i	−0.848887	+	0.528575i	$0.822726\pi$
$488$			202.662i			0.415291i
$489$	−42.4570	+	42.4570i	−0.0868241	+	0.0868241i
$490$	2.42035	+	14.1779i	0.00493948	+	0.0289346i
$491$	180.051			0.366702			0.183351	−	0.983048i	$-0.441306\pi$
$491$	180.051			0.366702			0.183351	+	0.983048i	$0.441306\pi$
$492$	−18.0115	−	52.5615i	−0.0366088	−	0.106832i
$493$			267.776i			0.543156i
$494$		−	618.440i		−	1.25190i
$495$	−7.51070	+	7.51070i	−0.0151731	+	0.0151731i
$496$		−	817.304i		−	1.64779i
$497$	154.001	+	129.939i	0.309860	+	0.261446i
$498$	−93.1334	+	93.1334i	−0.187015	+	0.187015i
$499$	−533.464	−	533.464i	−1.06907	−	1.06907i	−0.997431	−	0.0716359i	$-0.977178\pi$
$499$	−533.464	−	533.464i	−1.06907	−	1.06907i	−0.0716359	−	0.997431i	$-0.522822\pi$
$500$	−17.8609			−0.0357218
$501$			4.78644i			0.00955377i
$502$			1278.47i			2.54674i
$503$	326.712	−	326.712i	0.649528	−	0.649528i	−0.303351	−	0.952879i	$-0.598106\pi$
$503$	326.712	−	326.712i	0.649528	−	0.649528i	0.952879	+	0.303351i	$0.0981055\pi$
$504$	−118.761	+	10.0642i	−0.235638	+	0.0199687i
$505$	1.92429	+	1.92429i	0.00381047	+	0.00381047i
$506$	403.799	−	403.799i	0.798021	−	0.798021i
$507$	4.53991	+	4.53991i	0.00895447	+	0.00895447i
$508$	−396.066			−0.779658
$509$	36.4860	+	36.4860i	0.0716818	+	0.0716818i	0.742039	−	0.670357i	$-0.233859\pi$
$509$	36.4860	+	36.4860i	0.0716818	+	0.0716818i	−0.670357	+	0.742039i	$0.733859\pi$
$510$		−	2.46658i		−	0.00483643i
$511$	178.185	−	15.1000i	0.348699	−	0.0295498i
$512$		−	625.570i		−	1.22182i
$513$			124.027i			0.241768i
$514$	−855.403	−	855.403i	−1.66421	−	1.66421i
$515$	6.80606			0.0132157
$516$	−37.9972	−	37.9972i	−0.0736379	−	0.0736379i
$517$			882.546i			1.70705i
$518$	65.9240	+	777.927i	0.127266	+	1.50179i
$519$	−63.2807	+	63.2807i	−0.121928	+	0.121928i
$520$	−2.01447	−	2.01447i	−0.00387397	−	0.00387397i
$521$	106.430	−	106.430i	0.204281	−	0.204281i	−0.597551	−	0.801831i	$-0.703859\pi$
$521$	106.430	−	106.430i	0.204281	−	0.204281i	0.801831	+	0.597551i	$0.203859\pi$
$522$	221.505	+	221.505i	0.424338	+	0.424338i
$523$			60.6104i			0.115890i	0.998320	+	0.0579449i	$0.0184548\pi$
$523$			60.6104i			0.115890i	−0.998320	+	0.0579449i	$0.981545\pi$
$524$	267.917			0.511291
$525$	−46.5249	+	55.1404i	−0.0886189	+	0.105029i
$526$	−475.906	−	475.906i	−0.904764	−	0.904764i
$527$	−641.739	+	641.739i	−1.21772	+	1.21772i
$528$	−83.7082			−0.158538
$529$	−163.188			−0.308483
$530$	−3.34051	+	3.34051i	−0.00630284	+	0.00630284i
$531$	−292.037			−0.549975
$532$	−296.455	−	250.135i	−0.557246	−	0.470179i
$533$	180.565	+	526.927i	0.338771	+	0.988606i
$534$	−94.3070			−0.176605
$535$	−11.0945			−0.0207374
$536$	−97.2541	−	97.2541i	−0.181444	−	0.181444i
$537$		−	132.628i		−	0.246979i
$538$	838.223			1.55803
$539$	−442.294	−	313.305i	−0.820583	−	0.581270i
$540$	−1.85801	−	1.85801i	−0.00344077	−	0.00344077i
$541$			419.862i			0.776085i	0.921642	+	0.388042i	$0.126849\pi$
$541$			419.862i			0.776085i	−0.921642	+	0.388042i	$0.873151\pi$
$542$	495.477			0.914164
$543$	−121.342			−0.223467
$544$	−602.309	+	602.309i	−1.10719	+	1.10719i
$545$	−2.03743	+	2.03743i	−0.00373841	+	0.00373841i
$546$	105.495	−	8.93997i	0.193214	−	0.0163736i
$547$	−306.417	+	306.417i	−0.560177	+	0.560177i	−0.929358	−	0.369180i	$-0.879638\pi$
$547$	−306.417	+	306.417i	−0.560177	+	0.560177i	0.369180	+	0.929358i	$0.379638\pi$
$548$	−537.620	+	537.620i	−0.981058	+	0.981058i
$549$		−	928.005i		−	1.69035i
$550$	527.558	−	527.558i	0.959196	−	0.959196i
$551$		−	221.666i		−	0.402298i
$552$	−10.7565	−	10.7565i	−0.0194864	−	0.0194864i
$553$	475.772	+	401.435i	0.860348	+	0.725922i
$554$			249.381i			0.450146i
$555$	1.31053	−	1.31053i	0.00236132	−	0.00236132i
$556$			704.523i			1.26713i
$557$	6.47782	−	6.47782i	0.0116298	−	0.0116298i	−0.701268	−	0.712898i	$-0.747382\pi$
$557$	6.47782	−	6.47782i	0.0116298	−	0.0116298i	0.712898	+	0.701268i	$0.247382\pi$
$558$			1061.70i			1.90268i
$559$	380.920	+	380.920i	0.681432	+	0.681432i
$560$	−13.9167	+	1.17935i	−0.0248513	+	0.00210598i
$561$	65.7269	+	65.7269i	0.117160	+	0.117160i
$562$	586.796	+	586.796i	1.04412	+	1.04412i
$563$	171.925	−	171.925i	0.305374	−	0.305374i	−0.537738	−	0.843112i	$-0.680721\pi$
$563$	171.925	−	171.925i	0.305374	−	0.305374i	0.843112	+	0.537738i	$0.180721\pi$
$564$	−108.122			−0.191705
$565$	17.4807			0.0309394
$566$	−400.592			−0.707760
$567$	533.139	−	45.1798i	0.940280	−	0.0796822i
$568$	−39.2489	+	39.2489i	−0.0691002	+	0.0691002i
$569$		−	1058.85i		−	1.86089i	−0.366431	−	0.930445i	$-0.619420\pi$
$569$		−	1058.85i		−	1.86089i	0.366431	−	0.930445i	$-0.380580\pi$
$570$			2.04184i			0.00358218i
$571$	277.503	+	277.503i	0.485995	+	0.485995i	0.907040	−	0.421045i	$-0.138336\pi$
$571$	277.503	+	277.503i	0.485995	+	0.485995i	−0.421045	+	0.907040i	$0.638336\pi$
$572$	−493.751			−0.863202
$573$		−	0.817470i		−	0.00142665i
$574$	722.040	+	280.652i	1.25791	+	0.488942i
$575$	477.929			0.831182
$576$			348.446i			0.604942i
$577$	456.658	−	456.658i	0.791435	−	0.791435i	−0.190292	−	0.981728i	$-0.560944\pi$
$577$	456.658	−	456.658i	0.791435	−	0.791435i	0.981728	+	0.190292i	$0.0609435\pi$
$578$	340.287			0.588731
$579$	−50.4597			−0.0871497
$580$	3.32072	+	3.32072i	0.00572538	+	0.00572538i
$581$	−69.9290	−	825.189i	−0.120360	−	1.42029i
$582$		−	116.185i		−	0.199631i
$583$		−	178.029i		−	0.305367i
$584$			49.2611i			0.0843512i
$585$	9.22440	+	9.22440i	0.0157682	+	0.0157682i
$586$	−522.142	+	522.142i	−0.891027	+	0.891027i
$587$	−114.306	+	114.306i	−0.194730	+	0.194730i	−0.797736	−	0.603007i	$-0.793969\pi$
$587$	−114.306	+	114.306i	−0.194730	+	0.194730i	0.603007	+	0.797736i	$0.293969\pi$
$588$	38.3833	−	54.1859i	0.0652776	−	0.0921530i
$589$	531.235	−	531.235i	0.901927	−	0.901927i
$590$	−9.70818			−0.0164545
$591$	−110.460	−	110.460i	−0.186904	−	0.186904i
$592$	−758.111			−1.28059
$593$	−431.026	−	431.026i	−0.726857	−	0.726857i	0.243135	−	0.969992i	$-0.421824\pi$
$593$	−431.026	−	431.026i	−0.726857	−	0.726857i	−0.969992	+	0.243135i	$0.921824\pi$
$594$	219.573			0.369651
$595$	11.8533	+	10.0013i	0.0199215	+	0.0168089i
$596$	88.9907	−	88.9907i	0.149313	−	0.149313i
$597$	141.567			0.237131
$598$	−495.933	−	495.933i	−0.829319	−	0.829319i
$599$	1149.74			1.91943			0.959717	−	0.280969i	$-0.0906557\pi$
$599$	1149.74			1.91943			0.959717	+	0.280969i	$0.0906557\pi$
$600$	−14.0532	−	14.0532i	−0.0234220	−	0.0234220i
$601$	−582.676	−	582.676i	−0.969512	−	0.969512i	0.0300372	−	0.999549i	$-0.490437\pi$
$601$	−582.676	−	582.676i	−0.969512	−	0.969512i	−0.999549	+	0.0300372i	$0.990437\pi$
$602$	746.534	−	63.2636i	1.24009	−	0.105089i
$603$	445.334	+	445.334i	0.738531	+	0.738531i
$604$	−617.263	−	617.263i	−1.02196	−	1.02196i
$605$		−	0.147796i		−	0.000244290i
$606$		−	27.8595i		−	0.0459728i
$607$	−546.783			−0.900796			−0.450398	−	0.892828i	$-0.648718\pi$
$607$	−546.783			−0.900796			−0.450398	+	0.892828i	$0.648718\pi$
$608$	498.594	−	498.594i	0.820056	−	0.820056i
$609$	37.8124	−	3.20434i	0.0620893	−	0.00526164i
$610$		−	30.8496i		−	0.0505732i
$611$	1083.92			1.77400
$612$	417.941	−	417.941i	0.682910	−	0.682910i
$613$			143.590i			0.234241i	0.993118	+	0.117120i	$0.0373663\pi$
$613$			143.590i			0.234241i	−0.993118	+	0.117120i	$0.962634\pi$
$614$		−	201.881i		−	0.328796i
$615$	−0.596155	−	1.73971i	−0.000969358	−	0.00282879i
$616$	96.2868	−	114.117i	0.156310	−	0.185255i
$617$		−	93.2530i		−	0.151139i	−0.997141	−	0.0755697i	$-0.975922\pi$
$617$		−	93.2530i		−	0.151139i	0.997141	−	0.0755697i	$-0.0240775\pi$
$618$	−49.2686	−	49.2686i	−0.0797226	−	0.0797226i
$619$		−	957.768i		−	1.54728i	−0.633623	−	0.773642i	$-0.718433\pi$
$619$		−	957.768i		−	1.54728i	0.633623	−	0.773642i	$-0.281567\pi$
$620$			15.9166i			0.0256719i
$621$	99.4584	+	99.4584i	0.160159	+	0.160159i
$622$	695.405	−	695.405i	1.11801	−	1.11801i
$623$	382.388	−	453.198i	0.613785	−	0.727445i
$624$			102.808i			0.164756i
$625$	624.113			0.998581
$626$	−157.758	+	157.758i	−0.252010	+	0.252010i
$627$	−54.4090	−	54.4090i	−0.0867767	−	0.0867767i
$628$	−87.0517	+	87.0517i	−0.138617	+	0.138617i
$629$	595.262	+	595.262i	0.946362	+	0.946362i
$630$	18.0781	−	1.53200i	0.0286955	−	0.00243174i
$631$	−542.974			−0.860498			−0.430249	−	0.902710i	$-0.641574\pi$
$631$	−542.974			−0.860498			−0.430249	+	0.902710i	$0.641574\pi$
$632$	−121.256	+	121.256i	−0.191861	+	0.191861i
$633$		−	30.0857i		−	0.0475287i
$634$	−35.8494	+	35.8494i	−0.0565448	+	0.0565448i
$635$	−13.1092			−0.0206444
$636$	21.8105			0.0342932
$637$	−384.791	+	543.212i	−0.604067	+	0.852766i
$638$	−392.429			−0.615093
$639$	179.724	−	179.724i	0.281258	−	0.281258i
$640$		−	6.60338i		−	0.0103178i
$641$	−32.6463	+	32.6463i	−0.0509303	+	0.0509303i	−0.732113	−	0.681183i	$-0.761466\pi$
$641$	−32.6463	+	32.6463i	−0.0509303	+	0.0509303i	0.681183	+	0.732113i	$0.261466\pi$
$642$	80.3124	+	80.3124i	0.125097	+	0.125097i
$643$	−434.684	+	434.684i	−0.676025	+	0.676025i	−0.959098	−	0.283074i	$-0.908646\pi$
$643$	−434.684	+	434.684i	−0.676025	+	0.676025i	0.283074	+	0.959098i	$0.408646\pi$
$644$	−438.316	+	37.1443i	−0.680615	+	0.0576774i
$645$	−1.25765	−	1.25765i	−0.00194984	−	0.00194984i
$646$	−927.432			−1.43565
$647$	−633.926			−0.979793			−0.489896	−	0.871781i	$-0.662965\pi$
$647$	−633.926			−0.979793			−0.489896	+	0.871781i	$0.662965\pi$
$648$			147.392i			0.227456i
$649$	258.694	−	258.694i	0.398604	−	0.398604i
$650$	−647.930	−	647.930i	−0.996816	−	0.996816i
$651$	98.2988	+	82.9400i	0.150997	+	0.127404i
$652$	−478.299			−0.733587
$653$	372.602	+	372.602i	0.570601	+	0.570601i	0.932296	−	0.361696i	$-0.117802\pi$
$653$	372.602	+	372.602i	0.570601	+	0.570601i	−0.361696	+	0.932296i	$0.617802\pi$
$654$	29.4976			0.0451034
$655$	8.86764			0.0135384
$656$	−330.758	+	675.618i	−0.504204	+	1.02991i
$657$		−	225.570i		−	0.343334i
$658$	972.130	−	1152.15i	1.47740	−	1.75098i
$659$	750.613	+	750.613i	1.13902	+	1.13902i	0.988627	+	0.150391i	$0.0480533\pi$
$659$	750.613	+	750.613i	1.13902	+	1.13902i	0.150391	+	0.988627i	$0.451947\pi$
$660$	1.63017			0.00246996
$661$	216.172			0.327039			0.163519	−	0.986540i	$-0.447715\pi$
$661$	216.172			0.327039			0.163519	+	0.986540i	$0.447715\pi$
$662$	−1015.00	+	1015.00i	−1.53323	+	1.53323i
$663$	80.7237	−	80.7237i	0.121755	−	0.121755i
$664$	228.132			0.343572
$665$	−9.81222	−	8.27910i	−0.0147552	−	0.0124498i
$666$	984.803			1.47868
$667$	−177.756	−	177.756i	−0.266501	−	0.266501i
$668$	−26.9608	+	26.9608i	−0.0403605	+	0.0403605i
$669$	−89.2994	−	89.2994i	−0.133482	−	0.133482i
$670$	14.8042	+	14.8042i	0.0220959	+	0.0220959i
$671$	822.050	+	822.050i	1.22511	+	1.22511i
$672$	92.2590	+	77.8439i	0.137290	+	0.115839i
$673$	−185.814	+	185.814i	−0.276098	+	0.276098i	−0.831549	−	0.555451i	$-0.812546\pi$
$673$	−185.814	+	185.814i	−0.276098	+	0.276098i	0.555451	+	0.831549i	$0.312546\pi$
$674$	1172.47			1.73957
$675$	129.941	+	129.941i	0.192506	+	0.192506i
$676$			51.1444i			0.0756573i
$677$	335.221			0.495156			0.247578	−	0.968868i	$-0.420365\pi$
$677$	335.221			0.495156			0.247578	+	0.968868i	$0.420365\pi$
$678$	−126.542	−	126.542i	−0.186640	−	0.186640i
$679$	558.336	+	471.098i	0.822291	+	0.693812i
$680$	−3.02096	+	3.02096i	−0.00444258	+	0.00444258i
$681$	−135.198			−0.198529
$682$	−940.478	−	940.478i	−1.37900	−	1.37900i
$683$	249.948	−	249.948i	0.365957	−	0.365957i	−0.500044	−	0.866000i	$-0.666683\pi$
$683$	249.948	−	249.948i	0.365957	−	0.365957i	0.866000	+	0.500044i	$0.166683\pi$
$684$	−345.973	+	345.973i	−0.505809	+	0.505809i
$685$	−17.7944	+	17.7944i	−0.0259772	+	0.0259772i
$686$	232.300	+	896.203i	0.338630	+	1.30642i
$687$	44.4183			0.0646555
$688$			727.518i			1.05744i
$689$	−218.650			−0.317343
$690$	1.63737	+	1.63737i	0.00237301	+	0.00237301i
$691$	−736.420	−	736.420i	−1.06573	−	1.06573i	−0.997682	−	0.0680483i	$-0.978323\pi$
$691$	−736.420	−	736.420i	−1.06573	−	1.06573i	−0.0680483	−	0.997682i	$-0.521677\pi$
$692$	−712.888			−1.03018
$693$	−440.905	+	522.551i	−0.636227	+	0.754042i
$694$	268.544	+	268.544i	0.386951	+	0.386951i
$695$			23.3186i			0.0335520i
$696$			10.4536i			0.0150195i
$697$	790.197	−	270.781i	1.13371	−	0.388495i
$698$		−	31.4938i		−	0.0451201i
$699$	97.3015			0.139201
$700$	−572.655	+	48.5285i	−0.818078	+	0.0693265i
$701$	−730.761			−1.04246			−0.521228	−	0.853418i	$-0.674526\pi$
$701$	−730.761			−1.04246			−0.521228	+	0.853418i	$0.674526\pi$
$702$		−	269.672i		−	0.384148i
$703$	−492.761	−	492.761i	−0.700940	−	0.700940i
$704$	−308.663	−	308.663i	−0.438441	−	0.438441i
$705$	−3.57866			−0.00507612
$706$	1357.07			1.92220
$707$	133.881	+	112.963i	0.189365	+	0.159777i
$708$	31.6928	+	31.6928i	0.0447639	+	0.0447639i
$709$	276.372	+	276.372i	0.389806	+	0.389806i	0.874618	−	0.484812i	$-0.161112\pi$
$709$	276.372	+	276.372i	0.389806	+	0.389806i	−0.484812	+	0.874618i	$0.661112\pi$
$710$	5.97457	−	5.97457i	0.00841488	−	0.00841488i
$711$	555.243	−	555.243i	0.780932	−	0.780932i
$712$	115.503	+	115.503i	0.162224	+	0.162224i
$713$		−	852.005i		−	1.19496i
$714$	−13.4067	−	158.204i	−0.0187768	−	0.221574i
$715$	−16.3424			−0.0228565
$716$	747.060	−	747.060i	1.04338	−	1.04338i
$717$	32.9931			0.0460155
$718$			120.444i			0.167749i
$719$	−526.229	−	526.229i	−0.731890	−	0.731890i	0.239104	−	0.970994i	$-0.423146\pi$
$719$	−526.229	−	526.229i	−0.731890	−	0.731890i	−0.970994	+	0.239104i	$0.923146\pi$
$720$			17.6176i			0.0244690i
$721$	436.534	−	36.9932i	0.605456	−	0.0513082i
$722$	−206.673			−0.286251
$723$	16.7919	−	16.7919i	0.0232254	−	0.0232254i
$724$	−683.491	−	683.491i	−0.944048	−	0.944048i
$725$	−232.236	−	232.236i	−0.320326	−	0.320326i
$726$	−1.06988	+	1.06988i	−0.00147367	+	0.00147367i
$727$	−420.446	+	420.446i	−0.578331	+	0.578331i	−0.934443	−	0.356113i	$-0.884102\pi$
$727$	−420.446	+	420.446i	−0.578331	+	0.578331i	0.356113	+	0.934443i	$0.384102\pi$
$728$	−140.155	−	118.256i	−0.192521	−	0.162440i
$729$		−	647.619i		−	0.888366i
$730$		−	7.49864i		−	0.0102721i
$731$	571.240	−	571.240i	0.781450	−	0.781450i
$732$	−100.710	+	100.710i	−0.137582	+	0.137582i
$733$	−403.056			−0.549872			−0.274936	−	0.961462i	$-0.588657\pi$
$733$	−403.056			−0.549872			−0.274936	+	0.961462i	$0.588657\pi$
$734$		−	68.7883i		−	0.0937171i
$735$	1.27043	−	1.79347i	0.00172847	−	0.00244010i
$736$		−	799.655i		−	1.08649i
$737$	−788.977			−1.07053
$738$	429.661	−	877.643i	0.582197	−	1.18922i
$739$	−555.307			−0.751431			−0.375715	−	0.926735i	$-0.622603\pi$
$739$	−555.307			−0.751431			−0.375715	+	0.926735i	$0.622603\pi$
$740$	14.7638			0.0199511
$741$	−66.8235	+	66.8235i	−0.0901801	+	0.0901801i
$742$	−196.100	+	232.413i	−0.264286	+	0.313226i
$743$		−	178.224i		−	0.239871i	−0.992782	−	0.119935i	$-0.961731\pi$
$743$		−	178.224i		−	0.239871i	0.992782	−	0.119935i	$-0.0382687\pi$
$744$	−25.0526	+	25.0526i	−0.0336729	+	0.0336729i
$745$	2.94546	−	2.94546i	0.00395364	−	0.00395364i
$746$			944.001i			1.26542i
$747$	−1044.63			−1.39844
$748$			740.445i			0.989900i
$749$	−711.591	+	60.3024i	−0.950055	+	0.0805106i
$750$	4.27943	+	4.27943i	0.00570591	+	0.00570591i
$751$	−213.649	−	213.649i	−0.284486	−	0.284486i	0.550409	−	0.834895i	$-0.314472\pi$
$751$	−213.649	−	213.649i	−0.284486	−	0.284486i	−0.834895	+	0.550409i	$0.814472\pi$
$752$	1035.08	+	1035.08i	1.37644	+	1.37644i
$753$	138.140	−	138.140i	0.183453	−	0.183453i
$754$			481.969i			0.639216i
$755$	−20.4305	−	20.4305i	−0.0270602	−	0.0270602i
$756$	−129.270	−	109.072i	−0.170992	−	0.144275i
$757$	340.949	−	340.949i	0.450394	−	0.450394i	−0.445091	−	0.895485i	$-0.646829\pi$
$757$	340.949	−	340.949i	0.450394	−	0.450394i	0.895485	+	0.445091i	$0.146829\pi$
$758$		−	798.572i		−	1.05353i
$759$	−87.2622			−0.114970
$760$	2.50076	−	2.50076i	0.00329048	−	0.00329048i
$761$			763.653i			1.00349i	0.865017	+	0.501743i	$0.167308\pi$
$761$			763.653i			1.00349i	−0.865017	+	0.501743i	$0.832692\pi$
$762$	94.8965	+	94.8965i	0.124536	+	0.124536i
$763$	−119.605	+	141.753i	−0.156756	+	0.185784i
$764$	4.60460	−	4.60460i	0.00602696	−	0.00602696i
$765$	13.8332	−	13.8332i	0.0180826	−	0.0180826i
$766$	27.5946	−	27.5946i	0.0360243	−	0.0360243i
$767$	−317.720	−	317.720i	−0.414237	−	0.414237i
$768$	−93.8382	+	93.8382i	−0.122185	+	0.122185i
$769$		−	1127.26i		−	1.46588i	−0.680295	−	0.732939i	$-0.738148\pi$
$769$		−	1127.26i		−	1.46588i	0.680295	−	0.732939i	$-0.261852\pi$
$770$	−14.6570	+	17.3712i	−0.0190351	+	0.0225600i
$771$			184.855i			0.239761i
$772$	−284.226	−	284.226i	−0.368169	−	0.368169i
$773$	567.816	+	567.816i	0.734562	+	0.734562i	0.971520	−	0.236958i	$-0.0761504\pi$
$773$	567.816	+	567.816i	0.734562	+	0.734562i	−0.236958	+	0.971520i	$0.576150\pi$
$774$		−	945.062i		−	1.22101i
$775$		−	1113.13i		−	1.43630i
$776$	−142.299	+	142.299i	−0.183375	+	0.183375i
$777$	76.9331	−	91.1795i	0.0990131	−	0.117348i
$778$	428.776			0.551126
$779$	−654.128	+	224.154i	−0.839703	+	0.287746i
$780$		−	2.00213i		−	0.00256683i
$781$			318.408i			0.407693i
$782$	−743.717	+	743.717i	−0.951044	+	0.951044i
$783$		−	96.6581i		−	0.123446i
$784$	−886.195	+	151.284i	−1.13035	+	0.192965i
$785$	−2.88128	+	2.88128i	−0.00367042	+	0.00367042i
$786$	−64.1922	−	64.1922i	−0.0816695	−	0.0816695i
$787$	−1069.34			−1.35876			−0.679380	−	0.733786i	$-0.737751\pi$
$787$	−1069.34			−1.35876			−0.679380	+	0.733786i	$0.737751\pi$
$788$		−	1244.39i		−	1.57918i
$789$			102.845i			0.130348i
$790$	18.4579	−	18.4579i	0.0233645	−	0.0233645i
$791$	1121.20	−	95.0137i	1.41744	−	0.120118i
$792$	−133.179	−	133.179i	−0.168155	−	0.168155i
$793$	1009.62	−	1009.62i	1.27316	−	1.27316i
$794$	−255.248	−	255.248i	−0.321470	−	0.321470i
$795$	0.721895			0.000908044
$796$	797.412	+	797.412i	1.00177	+	1.00177i
$797$		−	1045.16i		−	1.31137i	−0.755035	−	0.655684i	$-0.772380\pi$
$797$		−	1045.16i		−	1.31137i	0.755035	−	0.655684i	$-0.227620\pi$
$798$	11.0981	+	130.962i	0.0139074	+	0.164112i
$799$		−	1625.47i		−	2.03439i
$800$		−	1044.74i		−	1.30592i
$801$	−528.898	−	528.898i	−0.660297	−	0.660297i
$802$	1446.80			1.80399
$803$	199.816	+	199.816i	0.248837	+	0.248837i
$804$		−	96.6584i		−	0.120222i
$805$	−14.5076	+	1.22942i	−0.0180219	+	0.00152723i
$806$	−1155.07	+	1155.07i	−1.43308	+	1.43308i
$807$	−90.5714	−	90.5714i	−0.112232	−	0.112232i
$808$	−34.1211	+	34.1211i	−0.0422291	+	0.0422291i
$809$	447.264	+	447.264i	0.552860	+	0.552860i	0.927265	−	0.374405i	$-0.122153\pi$
$809$	447.264	+	447.264i	0.552860	+	0.552860i	−0.374405	+	0.927265i	$0.622153\pi$
$810$		−	22.4363i		−	0.0276991i
$811$	−139.682			−0.172234			−0.0861171	−	0.996285i	$-0.527446\pi$
$811$	−139.682			−0.172234			−0.0861171	+	0.996285i	$0.527446\pi$
$812$	231.037	+	194.938i	0.284528	+	0.240072i
$813$	−53.5371	−	53.5371i	−0.0658513	−	0.0658513i
$814$	−872.364	+	872.364i	−1.07170	+	1.07170i
$815$	−15.8310			−0.0194245
$816$	154.174			0.188939
$817$	−472.875	+	472.875i	−0.578795	+	0.578795i
$818$	−132.141			−0.161542
$819$	641.781	+	541.506i	0.783616	+	0.661179i
$820$	6.44133	−	13.1573i	0.00785528	−	0.0160455i
$821$	−99.3292			−0.120986			−0.0604928	−	0.998169i	$-0.519267\pi$
$821$	−99.3292			−0.120986			−0.0604928	+	0.998169i	$0.519267\pi$
$822$	257.625			0.313412
$823$	−775.819	−	775.819i	−0.942672	−	0.942672i	0.0557716	−	0.998444i	$-0.482238\pi$
$823$	−775.819	−	775.819i	−0.942672	−	0.942672i	−0.998444	+	0.0557716i	$0.982238\pi$
$824$			120.684i			0.146461i
$825$	−114.007			−0.138190
$826$	−622.673	+	52.7672i	−0.753841	+	0.0638828i
$827$	58.5991	+	58.5991i	0.0708574	+	0.0708574i	0.741647	−	0.670790i	$-0.234045\pi$
$827$	58.5991	+	58.5991i	0.0708574	+	0.0708574i	−0.670790	+	0.741647i	$0.734045\pi$
$828$			554.879i			0.670143i
$829$	−1644.00			−1.98312			−0.991558	−	0.129665i	$-0.958610\pi$
$829$	−1644.00			−1.98312			−0.991558	+	0.129665i	$0.958610\pi$
$830$	−34.7267			−0.0418394
$831$	26.9460	−	26.9460i	0.0324260	−	0.0324260i
$832$	−379.090	+	379.090i	−0.455637	+	0.455637i
$833$	814.618	+	577.045i	0.977933	+	0.692731i
$834$	168.802	−	168.802i	0.202400	−	0.202400i
$835$	−0.892361	+	0.892361i	−0.00106870	+	0.00106870i
$836$		−	612.944i		−	0.733187i
$837$	231.646	−	231.646i	0.276758	−	0.276758i
$838$			1339.61i			1.59857i
$839$	665.103	+	665.103i	0.792734	+	0.792734i	0.981938	−	0.189204i	$-0.0605908\pi$
$839$	665.103	+	665.103i	0.792734	+	0.792734i	−0.189204	+	0.981938i	$0.560591\pi$
$840$	0.462737	+	0.390436i	0.000550877	+	0.000464805i
$841$		−	668.249i		−	0.794588i
$842$	−1502.07	+	1502.07i	−1.78394	+	1.78394i
$843$		−	126.809i		−	0.150425i
$844$	169.465	−	169.465i	0.200788	−	0.200788i
$845$			1.69280i			0.00200332i
$846$	−1344.60	−	1344.60i	−1.58936	−	1.58936i
$847$	−0.803319	−	9.47946i	−0.000948428	−	0.0111918i
$848$	−208.799	−	208.799i	−0.246225	−	0.246225i
$849$	43.2846	+	43.2846i	0.0509831	+	0.0509831i
$850$	−971.657	+	971.657i	−1.14313	+	1.14313i
$851$	−790.299			−0.928671
$852$	−39.0085			−0.0457847
$853$	820.815			0.962269			0.481134	−	0.876647i	$-0.340225\pi$
$853$	820.815			0.962269			0.481134	+	0.876647i	$0.340225\pi$
$854$	−167.678	−	1978.66i	−0.196344	−	2.31694i
$855$	−11.4512	+	11.4512i	−0.0133932	+	0.0133932i
$856$		−	196.726i		−	0.229821i
$857$			817.231i			0.953595i	0.879013	+	0.476797i	$0.158202\pi$
$857$			817.231i			0.953595i	−0.879013	+	0.476797i	$0.841798\pi$
$858$	118.302	+	118.302i	0.137881	+	0.137881i
$859$	1295.26			1.50787			0.753937	−	0.656947i	$-0.228152\pi$
$859$	1295.26			1.50787			0.753937	+	0.656947i	$0.228152\pi$
$860$		−	14.1680i		−	0.0164745i
$861$	−47.6926	−	108.343i	−0.0553921	−	0.125833i
$862$	−427.723			−0.496198
$863$			272.595i			0.315869i	0.987450	+	0.157934i	$0.0504834\pi$
$863$			272.595i			0.315869i	−0.987450	+	0.157934i	$0.949517\pi$
$864$	217.413	−	217.413i	0.251636	−	0.251636i
$865$	−23.5955			−0.0272780
$866$	86.8343			0.100271
$867$	−36.7686	−	36.7686i	−0.0424089	−	0.0424089i
$868$	86.5118	+	1020.87i	0.0996680	+	1.17612i
$869$			983.696i			1.13199i
$870$		−	1.59127i		−	0.00182905i
$871$			968.997i			1.11251i
$872$	−36.1274	−	36.1274i	−0.0414305	−	0.0414305i
$873$	651.597	−	651.597i	0.746388	−	0.746388i
$874$	615.652	−	615.652i	0.704408	−	0.704408i
$875$	−37.9170	+	3.21320i	−0.0433337	+	0.00367223i
$876$	−24.4797	+	24.4797i	−0.0279448	+	0.0279448i
$877$	931.069			1.06165			0.530826	−	0.847481i	$-0.321882\pi$
$877$	931.069			1.06165			0.530826	+	0.847481i	$0.321882\pi$
$878$	891.076	+	891.076i	1.01489	+	1.01489i
$879$	112.837			0.128369
$880$	−15.6062	−	15.6062i	−0.0177343	−	0.0177343i
$881$	−136.897			−0.155388			−0.0776940	−	0.996977i	$-0.524756\pi$
$881$	−136.897			−0.155388			−0.0776940	+	0.996977i	$0.524756\pi$
$882$	1151.19	−	196.521i	1.30520	−	0.222813i
$883$	−312.579	+	312.579i	−0.353996	+	0.353996i	−0.861594	−	0.507598i	$-0.830534\pi$
$883$	−312.579	+	312.579i	−0.353996	+	0.353996i	0.507598	+	0.861594i	$0.330534\pi$
$884$	909.392			1.02872
$885$	1.04899	+	1.04899i	0.00118529	+	0.00118529i
$886$	−213.886			−0.241406
$887$	−335.449	−	335.449i	−0.378184	−	0.378184i	0.492263	−	0.870447i	$-0.336170\pi$
$887$	−335.449	−	335.449i	−0.378184	−	0.378184i	−0.870447	+	0.492263i	$0.836170\pi$
$888$	23.2382	+	23.2382i	0.0261692	+	0.0261692i
$889$	−840.810	+	71.2528i	−0.945793	+	0.0801494i
$890$	−17.5822	−	17.5822i	−0.0197552	−	0.0197552i
$891$	597.860	+	597.860i	0.670998	+	0.670998i
$892$		−	1006.00i		−	1.12780i
$893$			1345.58i			1.50680i
$894$	−42.6439			−0.0477001
$895$	24.7265	−	24.7265i	0.0276274	−	0.0276274i
$896$	−35.8916	−	423.534i	−0.0400576	−	0.472694i
$897$			107.173i			0.119479i
$898$	132.416			0.147456
$899$	−414.008	+	414.008i	−0.460520	+	0.460520i
$900$			724.942i			0.805491i
$901$			327.894i			0.363922i
$902$	396.834	+	1158.04i	0.439949	+	1.28386i
$903$	−87.5000	−	73.8285i	−0.0968992	−	0.0817592i
$904$			309.966i			0.342883i
$905$	−22.6225	−	22.6225i	−0.0249972	−	0.0249972i
$906$			295.790i			0.326479i
$907$		−	487.246i		−	0.537207i	−0.963251	−	0.268603i	$-0.913438\pi$
$907$		−	487.246i		−	0.537207i	0.963251	−	0.268603i	$-0.0865621\pi$
$908$	−761.537	−	761.537i	−0.838697	−	0.838697i
$909$	156.243	−	156.243i	0.171885	−	0.171885i
$910$	21.3347	+	18.0013i	0.0234448	+	0.0197816i
$911$			1029.92i			1.13054i	0.824907	+	0.565269i	$0.191227\pi$
$911$			1029.92i			1.13054i	−0.824907	+	0.565269i	$0.808773\pi$
$912$	−127.626			−0.139941
$913$	925.363	−	925.363i	1.01354	−	1.01354i
$914$	175.472	+	175.472i	0.191982	+	0.191982i
$915$	−3.33336	+	3.33336i	−0.00364301	+	0.00364301i
$916$	250.197	+	250.197i	0.273141	+	0.273141i
$917$	568.761	−	48.1986i	0.620241	−	0.0525611i
$918$	−404.409			−0.440533
$919$	−162.214	+	162.214i	−0.176512	+	0.176512i	−0.789833	−	0.613322i	$-0.789833\pi$
$919$	−162.214	+	162.214i	−0.176512	+	0.176512i	0.613322	+	0.789833i	$0.289833\pi$
$920$		−	4.01077i		−	0.00435954i
$921$	−21.8135	+	21.8135i	−0.0236846	+	0.0236846i
$922$	1833.71			1.98884
$923$	391.059			0.423683
$924$	104.558	−	8.86053i	0.113158	−	0.00958932i
$925$	−1032.52			−1.11623
$926$	−305.666	+	305.666i	−0.330092	+	0.330092i
$927$		−	552.622i		−	0.596140i
$928$	−388.570	+	388.570i	−0.418718	+	0.418718i
$929$	−799.224	−	799.224i	−0.860305	−	0.860305i	0.131068	−	0.991373i	$-0.458159\pi$
$929$	−799.224	−	799.224i	−0.860305	−	0.860305i	−0.991373	+	0.131068i	$0.958159\pi$
$930$	3.81357	−	3.81357i	0.00410061	−	0.00410061i
$931$	−674.345	−	477.680i	−0.724323	−	0.513083i
$932$	548.075	+	548.075i	0.588063	+	0.588063i
$933$	−150.279			−0.161071
$934$	−338.997			−0.362952
$935$			24.5076i			0.0262114i
$936$	−163.566	+	163.566i	−0.174750	+	0.174750i
$937$	92.6222	+	92.6222i	0.0988498	+	0.0988498i	0.754802	−	0.655952i	$-0.227733\pi$
$937$	92.6222	+	92.6222i	0.0988498	+	0.0988498i	−0.655952	+	0.754802i	$0.727733\pi$
$938$	1029.99	+	869.063i	1.09808	+	0.926506i
$939$	34.0920			0.0363067
$940$	−20.1577	−	20.1577i	−0.0214444	−	0.0214444i
$941$	720.423			0.765593			0.382797	−	0.923833i	$-0.374961\pi$
$941$	720.423			0.765593			0.382797	+	0.923833i	$0.374961\pi$
$942$	41.7147			0.0442832
$943$	−344.801	+	704.303i	−0.365642	+	0.746875i
$944$		−	606.812i		−	0.642809i
$945$	−4.27864	−	3.61012i	−0.00452766	−	0.00382024i
$946$	837.160	+	837.160i	0.884947	+	0.884947i
$947$	792.897			0.837272			0.418636	−	0.908154i	$-0.362508\pi$
$947$	792.897			0.837272			0.418636	+	0.908154i	$0.362508\pi$
$948$	−120.514			−0.127124
$949$	245.408	−	245.408i	0.258596	−	0.258596i
$950$	804.342	−	804.342i	0.846676	−	0.846676i
$951$	7.74718			0.00814635
$952$	−177.341	+	210.181i	−0.186283	+	0.220778i
$953$	1126.03			1.18157			0.590784	−	0.806830i	$-0.298819\pi$
$953$	1126.03			1.18157			0.590784	+	0.806830i	$0.298819\pi$
$954$	271.234	+	271.234i	0.284313	+	0.284313i
$955$	0.152405	−	0.152405i	0.000159587	−	0.000159587i
$956$	185.842	+	185.842i	0.194395	+	0.194395i
$957$	42.4026	+	42.4026i	0.0443079	+	0.0443079i
$958$	−830.278	−	830.278i	−0.866679	−	0.866679i
$959$	−1044.60	+	1238.03i	−1.08926	+	1.29096i
$960$	1.25161	−	1.25161i	0.00130376	−	0.00130376i
$961$	−1023.38			−1.06492
$962$	1071.41	+	1071.41i	1.11373	+	1.11373i
$963$			900.826i			0.935437i
$964$	189.169			0.196234
$965$	−9.40747	−	9.40747i	−0.00974867	−	0.00974867i
$966$	113.919	+	96.1198i	0.117929	+	0.0995029i
$967$	363.918	−	363.918i	0.376337	−	0.376337i	−0.493442	−	0.869779i	$-0.664261\pi$
$967$	363.918	−	363.918i	0.376337	−	0.376337i	0.869779	+	0.493442i	$0.164261\pi$
$968$	2.62069			0.00270733
$969$	100.211	+	100.211i	0.103416	+	0.103416i
$970$	21.6610	−	21.6610i	0.0223310	−	0.0223310i
$971$	427.420	−	427.420i	0.440185	−	0.440185i	−0.451889	−	0.892074i	$-0.649250\pi$
$971$	427.420	−	427.420i	0.440185	−	0.440185i	0.892074	+	0.451889i	$0.149250\pi$
$972$	−227.013	+	227.013i	−0.233553	+	0.233553i
$973$	126.745	+	1495.63i	0.130262	+	1.53714i
$974$	1389.63			1.42672
$975$			140.020i			0.143610i
$976$	1928.26			1.97568
$977$	−497.841	−	497.841i	−0.509561	−	0.509561i	0.404831	−	0.914392i	$-0.367330\pi$
$977$	−497.841	−	497.841i	−0.509561	−	0.509561i	−0.914392	+	0.404831i	$0.867330\pi$
$978$	114.599	+	114.599i	0.117177	+	0.117177i
$979$	937.023			0.957123
$980$	17.2582	−	2.94618i	0.0176104	−	0.00300631i
$981$	165.430	+	165.430i	0.168634	+	0.168634i
$982$		−	485.990i		−	0.494898i
$983$		−	723.727i		−	0.736243i	−0.929778	−	0.368122i	$-0.880001\pi$
$983$		−	723.727i		−	0.736243i	0.929778	−	0.368122i	$-0.119999\pi$
$984$	30.8482	−	10.5709i	0.0313498	−	0.0107428i
$985$		−	41.1874i		−	0.0418147i
$986$	722.776			0.733039
$987$	−229.532	+	19.4512i	−0.232555	+	0.0197074i
$988$	−752.799			−0.761942
$989$			758.407i			0.766842i
$990$	20.2728	+	20.2728i	0.0204775	+	0.0204775i
$991$	−593.214	−	593.214i	−0.598602	−	0.598602i	0.341339	−	0.939940i	$-0.389120\pi$
$991$	−593.214	−	593.214i	−0.598602	−	0.598602i	−0.939940	+	0.341339i	$0.889120\pi$
$992$	−1862.46			−1.87748
$993$	219.345			0.220891
$994$	350.729	−	415.676i	0.352846	−	0.418185i
$995$	26.3931	+	26.3931i	0.0265258	+	0.0265258i
$996$	113.367	+	113.367i	0.113822	+	0.113822i
$997$	−1028.75	+	1028.75i	−1.03185	+	1.03185i	−0.0323714	+	0.999476i	$0.510306\pi$
$997$	−1028.75	+	1028.75i	−1.03185	+	1.03185i	−0.999476	+	0.0323714i	$0.989694\pi$
$998$	−1439.92	+	1439.92i	−1.44280	+	1.44280i
$999$	−214.869	−	214.869i	−0.215085	−	0.215085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.9	✓	108
7.6	odd	2	inner	287.3.g.a.132.10	yes	108
41.32	even	4	inner	287.3.g.a.237.46	yes	108
287.237	odd	4	inner	287.3.g.a.237.45	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.9	✓	108	1.1	even	1	trivial
287.3.g.a.132.10	yes	108	7.6	odd	2	inner
287.3.g.a.237.45	yes	108	287.237	odd	4	inner
287.3.g.a.237.46	yes	108	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.69918i q^{2} +(-0.291651 + 0.291651i) q^{3} -3.28560 q^{4} -0.108748 q^{5} +(0.787221 + 0.787221i) q^{6} +(-6.97500 + 0.591083i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +O(q^{10})\)	\(q-2.69918i q^{2} +(-0.291651 + 0.291651i) q^{3} -3.28560 q^{4} -0.108748 q^{5} +(0.787221 + 0.787221i) q^{6} +(-6.97500 + 0.591083i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +0.293532i q^{10} +(-7.82173 - 7.82173i) q^{11} +(0.958249 - 0.958249i) q^{12} +(-9.60641 + 9.60641i) q^{13} +(1.59544 + 18.8268i) q^{14} +(0.0317166 - 0.0317166i) q^{15} -18.3472 q^{16} +(14.4061 + 14.4061i) q^{17} +23.8335 q^{18} +(-11.9254 - 11.9254i) q^{19} +0.357303 q^{20} +(1.86188 - 2.20666i) q^{21} +(-21.1123 + 21.1123i) q^{22} -19.1262 q^{23} +(0.562394 + 0.562394i) q^{24} -24.9882 q^{25} +(25.9295 + 25.9295i) q^{26} +(-5.20011 - 5.20011i) q^{27} +(22.9170 - 1.94206i) q^{28} +(9.29385 + 9.29385i) q^{29} +(-0.0856089 - 0.0856089i) q^{30} +44.5464i q^{31} +41.8094i q^{32} +4.56244 q^{33} +(38.8847 - 38.8847i) q^{34} +(0.758519 - 0.0642793i) q^{35} -29.0114i q^{36} +41.3202 q^{37} +(-32.1889 + 32.1889i) q^{38} -5.60345i q^{39} +0.209700i q^{40} +(18.0276 - 36.8240i) q^{41} +(-5.95618 - 5.02555i) q^{42} -39.6527i q^{43} +(25.6991 + 25.6991i) q^{44} -0.960234i q^{45} +51.6252i q^{46} +(-56.4163 - 56.4163i) q^{47} +(5.35100 - 5.35100i) q^{48} +(48.3012 - 8.24561i) q^{49} +67.4477i q^{50} -8.40311 q^{51} +(31.5628 - 31.5628i) q^{52} +(11.3804 + 11.3804i) q^{53} +(-14.0361 + 14.0361i) q^{54} +(0.850600 + 0.850600i) q^{55} +(1.13979 + 13.4500i) q^{56} +6.95613 q^{57} +(25.0858 - 25.0858i) q^{58} +33.0737i q^{59} +(-0.104208 + 0.104208i) q^{60} -105.098 q^{61} +120.239 q^{62} +(-5.21919 - 61.5884i) q^{63} +39.4622 q^{64} +(1.04468 - 1.04468i) q^{65} -12.3149i q^{66} +(50.4349 - 50.4349i) q^{67} +(-47.3326 - 47.3326i) q^{68} +(5.57819 - 5.57819i) q^{69} +(-0.173502 - 2.04738i) q^{70} +(-20.3541 - 20.3541i) q^{71} +17.0267 q^{72} -25.5463 q^{73} -111.531i q^{74} +(7.28784 - 7.28784i) q^{75} +(39.1821 + 39.1821i) q^{76} +(59.1799 + 49.9333i) q^{77} -15.1247 q^{78} +(-62.8822 - 62.8822i) q^{79} +1.99523 q^{80} -76.4357 q^{81} +(-99.3947 - 48.6599i) q^{82} +118.307i q^{83} +(-6.11738 + 7.25019i) q^{84} +(-1.56664 - 1.56664i) q^{85} -107.030 q^{86} -5.42113 q^{87} +(-15.0827 + 15.0827i) q^{88} +(-59.8987 + 59.8987i) q^{89} -2.59185 q^{90} +(61.3265 - 72.6829i) q^{91} +62.8410 q^{92} +(-12.9920 - 12.9920i) q^{93} +(-152.278 + 152.278i) q^{94} +(1.29687 + 1.29687i) q^{95} +(-12.1938 - 12.1938i) q^{96} +(-73.7946 - 73.7946i) q^{97} +(-22.2564 - 130.374i) q^{98} +(69.0650 - 69.0650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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