LMFDB - Embedded newform 287.3.g.a.132.10

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			132.10
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69918i q^{2} +(0.291651 - 0.291651i) q^{3} -3.28560 q^{4} +0.108748 q^{5} +(-0.787221 - 0.787221i) q^{6} +(0.591083 - 6.97500i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +O(q^{10})$	\(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} +(0.591083 - 6.97500i) 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} +(-18.8268 - 1.59544i) 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} +(-1.94206 + 22.9170i) 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} +(0.0642793 - 0.758519i) 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} +(-13.4500 - 1.13979i) 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} +(61.5884 + 5.21919i) 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} +(-2.04738 - 0.173502i) 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	−0.656825	−	0.754043i	$-0.728101\pi$
$3$	0.291651	−	0.291651i	0.0972171	−	0.0972171i	0.754043	+	0.656825i	$0.228101\pi$
$4$	−3.28560			−0.821399
$5$	0.108748			0.0217497			0.0108748	−	0.999941i	$-0.496538\pi$
$5$	0.108748			0.0217497			0.0108748	+	0.999941i	$0.496538\pi$
$6$	−0.787221	−	0.787221i	−0.131203	−	0.131203i
$7$	0.591083	−	6.97500i	0.0844404	−	0.996429i
$7$	0.591083	−	6.97500i	0.0844404	−	0.996429i
$8$		−	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	−0.233421	−	0.972376i	$-0.574992\pi$
$13$	9.60641	−	9.60641i	0.738955	−	0.738955i	0.972376	+	0.233421i	$0.0749921\pi$
$14$	−18.8268	−	1.59544i	−1.34477	−	0.113960i
$15$	0.0317166	−	0.0317166i	0.00211444	−	0.00211444i
$16$	−18.3472			−1.14670
$17$	−14.4061	−	14.4061i	−0.847416	−	0.847416i	0.142394	−	0.989810i	$-0.454520\pi$
$17$	−14.4061	−	14.4061i	−0.847416	−	0.847416i	−0.989810	+	0.142394i	$0.954520\pi$
$18$	23.8335			1.32408
$19$	11.9254	+	11.9254i	0.627654	+	0.627654i	0.947477	−	0.319823i	$-0.103624\pi$
$19$	11.9254	+	11.9254i	0.627654	+	0.627654i	−0.319823	+	0.947477i	$0.603624\pi$
$20$	−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
$28$	−1.94206	+	22.9170i	−0.0693593	+	0.818465i
$29$	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	$-0.744833\pi$
$31$		−	44.5464i		−	1.43698i	0.695536	−	0.718491i	$-0.255167\pi$
$32$			41.8094i			1.30654i
$33$	−4.56244			−0.138256
$34$	−38.8847	+	38.8847i	−1.14367	+	1.14367i
$35$	0.0642793	−	0.758519i	0.00183655	−	0.0216720i
$36$		−	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	$0.0726581\pi$
$47$	56.4163	+	56.4163i	1.20035	+	1.20035i	0.226285	+	0.974061i	$0.427342\pi$
$48$	−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
$56$	−13.4500	−	1.13979i	−0.240178	−	0.0203534i
$57$	6.95613			0.122037
$58$	25.0858	−	25.0858i	0.432514	−	0.432514i
$59$		−	33.0737i		−	0.560571i	−0.959917	−	0.280286i	$-0.909571\pi$
$59$		−	33.0737i		−	0.560571i	0.959917	−	0.280286i	$-0.0904292\pi$
$60$	−0.104208	+	0.104208i	−0.00173680	+	0.00173680i
$61$	105.098			1.72292			0.861461	−	0.507824i	$-0.169550\pi$
$61$	105.098			1.72292			0.861461	+	0.507824i	$0.169550\pi$
$62$	−120.239			−1.93934
$63$	61.5884	+	5.21919i	0.977594	+	0.0828443i
$64$	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
$70$	−2.04738	−	0.173502i	−0.0292483	−	0.00247859i
$71$	−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	$-0.444016\pi$
$73$	25.5463			0.349949			0.174974	+	0.984573i	$0.444016\pi$
$74$		−	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	$-0.747476\pi$
$83$		−	118.307i		−	1.42538i	0.701479	−	0.712691i	$-0.252524\pi$
$84$	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	−0.285392	−	0.958411i	$-0.592124\pi$
$89$	59.8987	−	59.8987i	0.673019	−	0.673019i	0.958411	+	0.285392i	$0.0921238\pi$
$90$	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	0.976461	−	0.215693i	$-0.0692009\pi$
$97$	73.7946	+	73.7946i	0.760769	+	0.760769i	−0.215693	+	0.976461i	$0.569201\pi$
$98$	−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	0.789258	−	0.614062i	$-0.210465\pi$
$101$	17.6949	+	17.6949i	0.175197	+	0.175197i	−0.614062	+	0.789258i	$0.710465\pi$
$102$			22.6815i			0.222368i
$103$	62.5855			0.607626			0.303813	−	0.952732i	$-0.401740\pi$
$103$	62.5855			0.607626			0.303813	+	0.952732i	$0.401740\pi$
$104$	−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
$112$	−10.8447	+	127.972i	−0.0968281	+	1.14261i
$113$	−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
$126$	14.0876	−	166.238i	0.111806	−	1.31935i
$127$	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	$-0.399258\pi$
$131$	81.5428			0.622464			0.311232	+	0.950334i	$0.399258\pi$
$132$	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	$0.280405\pi$
$139$			214.428i			1.54265i	−0.636444	+	0.771323i	$0.719595\pi$
$140$	−0.211196	+	2.49219i	−0.00150854	+	0.0178013i
$141$	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
$147$	−16.4920	+	11.6823i	−0.112190	+	0.0794713i
$148$	−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	−0.786433	−	0.617676i	$-0.788075\pi$
$157$	−26.4949	+	26.4949i	−0.168758	+	0.168758i	0.617676	+	0.786433i	$0.288075\pi$
$158$	−169.731	+	169.731i	−1.07425	+	1.07425i
$159$	6.63822			0.0417498
$160$			4.54670i			0.0284168i
$161$	−11.3052	+	133.405i	−0.0702185	+	0.828605i
$162$			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	−0.731248	−	0.682112i	$-0.761062\pi$
$167$	−8.20575	+	8.20575i	−0.0491362	+	0.0491362i	0.682112	+	0.731248i	$0.261062\pi$
$168$	−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	$-0.715755\pi$
$173$	−216.974			−1.25418			−0.627092	+	0.778946i	$0.715755\pi$
$174$		−	14.6326i		−	0.0840955i
$175$	−14.7701	+	174.293i	−0.0844005	+	0.995957i
$176$	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	$-0.948002\pi$
$181$	−208.026	−	208.026i	−1.14932	−	1.14932i	−0.162630	−	0.986687i	$-0.551998\pi$
$182$	−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	$0.0810295\pi$
$199$	242.699	+	242.699i	1.21959	+	1.21959i	0.251821	+	0.967774i	$0.418971\pi$
$200$			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
$217$	−310.711	−	26.3306i	−1.43185	−	0.121339i
$218$	−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	$-0.759140\pi$
$223$		−	306.185i		−	1.37303i	0.727116	−	0.686515i	$-0.240860\pi$
$224$	291.620	+	24.7128i	1.30188	+	0.110325i
$225$		−	220.643i		−	0.980634i
$226$			433.880i			1.91982i
$227$	−231.780	−	231.780i	−1.02106	−	1.02106i	−0.999773	−	0.0212854i	$-0.993224\pi$
$227$	−231.780	−	231.780i	−1.02106	−	1.02106i	−0.0212854	−	0.999773i	$-0.506776\pi$
$228$	−22.8550			−0.100241
$229$	76.1497	+	76.1497i	0.332532	+	0.332532i	0.853547	−	0.521016i	$-0.174447\pi$
$229$	76.1497	+	76.1497i	0.332532	+	0.332532i	−0.521016	+	0.853547i	$0.674447\pi$
$230$			5.61415i			0.0244094i
$231$	−2.69678	+	31.8230i	−0.0116744	+	0.137762i
$232$	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	$-0.461887\pi$
$241$	57.5754			0.238902			0.119451	+	0.992840i	$0.461887\pi$
$242$	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	$-0.107489\pi$
$251$	473.649			1.88705			0.943523	+	0.331306i	$0.107489\pi$
$252$	−202.355	−	17.1482i	−0.802994	−	0.0680482i
$253$	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	$0.587143\pi$
$257$	−316.912	+	316.912i	−1.23312	+	1.23312i	−0.962759	+	0.270360i	$0.912857\pi$
$258$	−31.2154	+	31.2154i	−0.120990	+	0.120990i
$259$	24.4237	−	288.208i	0.0942998	−	1.11277i
$260$	−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	$-0.804136\pi$
$269$		−	310.547i		−	1.15445i	0.816586	−	0.577224i	$-0.195864\pi$
$270$	1.52640	−	1.52640i	0.00565332	−	0.00565332i
$271$		−	183.565i		−	0.677363i	−0.940901	−	0.338681i	$-0.890019\pi$
$271$		−	183.565i		−	0.677363i	0.940901	−	0.338681i	$-0.109981\pi$
$272$	264.312	+	264.312i	0.971735	+	0.971735i
$273$	−39.0840	−	3.31210i	−0.143165	−	0.0121322i
$274$	−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
$280$	−1.46266	−	0.123950i	−0.00522378	−	0.000442679i
$281$	−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	$0.0844521\pi$
$283$			148.412i			0.524425i	−0.965010	+	0.262212i	$0.915548\pi$
$284$	66.8753	+	66.8753i	0.235476	+	0.235476i
$285$	0.756467			0.00265427
$286$			405.627i			1.41828i
$287$	246.191	+	147.509i	0.857809	+	0.513968i
$288$	−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	0.955432	−	0.295212i	$-0.0953904\pi$
$293$	193.444	+	193.444i	0.660219	+	0.660219i	−0.295212	+	0.955432i	$0.595390\pi$
$294$	31.5326	+	44.5149i	0.107254	+	0.151411i
$295$		−	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
$301$	−276.578	−	23.4381i	−0.918863	−	0.0778673i
$302$	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	$-0.538871\pi$
$307$	−74.7932			−0.243626			−0.121813	+	0.992553i	$0.538871\pi$
$308$	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	0.158888	−	0.987297i	$-0.449209\pi$
$311$	−257.635	−	257.635i	−0.828409	−	0.828409i	−0.987297	+	0.158888i	$0.949209\pi$
$312$	−10.8052			−0.0346320
$313$	58.4466	+	58.4466i	0.186730	+	0.186730i	0.794281	−	0.607551i	$-0.207848\pi$
$313$	58.4466	+	58.4466i	0.186730	+	0.186730i	−0.607551	+	0.794281i	$0.707848\pi$
$314$	71.5147	+	71.5147i	0.227754	+	0.227754i
$315$	6.69763	+	0.567578i	0.0212623	+	0.00180184i
$316$	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
$322$	360.086	+	30.5148i	1.11828	+	0.0947664i
$323$		−	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
$343$	−86.0632	+	332.027i	−0.250913	+	0.968010i
$344$	−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	$-0.505321\pi$
$349$	−11.6679			−0.0334324			−0.0167162	+	0.999860i	$0.505321\pi$
$350$	470.448	+	39.8672i	1.34414	+	0.113906i
$351$	99.9088			0.284640
$352$	327.022	−	327.022i	0.929039	−	0.929039i
$353$		−	502.771i		−	1.42428i	−0.702037	−	0.712141i	$-0.747726\pi$
$353$		−	502.771i		−	1.42428i	0.702037	−	0.712141i	$-0.252274\pi$
$354$	−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
$357$	−4.96693	+	58.6117i	−0.0139130	+	0.164178i
$358$	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	$-0.511054\pi$
$367$	−25.4849			−0.0694410			−0.0347205	+	0.999397i	$0.511054\pi$
$368$	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	0.693634	−	0.720327i	$-0.256008\pi$
$383$	−10.2233	−	10.2233i	−0.0266927	−	0.0266927i	−0.720327	+	0.693634i	$0.756008\pi$
$384$	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	−0.816104	−	0.577905i	$-0.803870\pi$
$397$	−94.5647	+	94.5647i	−0.238198	+	0.238198i	0.577905	+	0.816104i	$0.303870\pi$
$398$	655.090	−	655.090i	1.64596	−	1.64596i
$399$	4.11165	−	48.5190i	0.0103049	−	0.121602i
$400$	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	$0.0190617\pi$
$409$			48.9559i			0.119697i	−0.998207	+	0.0598483i	$0.980938\pi$
$410$	10.8090	+	5.29168i	0.0263634	+	0.0129065i
$411$		−	95.4454i		−	0.232227i
$412$	−205.631			−0.499103
$413$	−230.689	−	19.5493i	−0.558569	−	0.0473349i
$414$	−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	$-0.298242\pi$
$419$	496.300			1.18449			0.592243	+	0.805759i	$0.298242\pi$
$420$	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
$427$	62.1218	−	733.060i	0.145484	−	1.71677i
$428$	−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	$-0.988173\pi$
$433$		−	32.1706i		−	0.0742970i	0.999310	−	0.0371485i	$-0.0118274\pi$
$434$	−71.0713	+	838.667i	−0.163759	+	1.93241i
$435$	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	−0.222852	−	0.974852i	$-0.571537\pi$
$439$	330.128	−	330.128i	0.752000	−	0.752000i	0.974852	+	0.222852i	$0.0715368\pi$
$440$	−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
$448$	23.3254	−	275.249i	0.0520657	−	0.614395i
$449$			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	$-0.736321\pi$
$461$		−	679.358i		−	1.47366i	0.676077	−	0.736831i	$-0.263679\pi$
$462$	85.8962	+	7.27911i	0.185922	+	0.0157556i
$463$	−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	$0.0429324\pi$
$467$			125.593i			0.268935i	−0.990918	+	0.134467i	$0.957068\pi$
$468$	−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	−0.951091	−	0.308912i	$-0.900035\pi$
$479$	−307.603	+	307.603i	−0.642178	+	0.642178i	0.308912	+	0.951091i	$0.400035\pi$
$480$	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	−0.952879	−	0.303351i	$-0.901894\pi$
$503$	−326.712	+	326.712i	−0.649528	+	0.649528i	0.303351	+	0.952879i	$0.401894\pi$
$504$	10.0642	−	118.761i	0.0199687	−	0.235638i
$505$	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	0.670357	−	0.742039i	$-0.266141\pi$
$509$	−36.4860	−	36.4860i	−0.0716818	−	0.0716818i	−0.742039	+	0.670357i	$0.766141\pi$
$510$			2.46658i			0.00483643i
$511$	15.1000	−	178.185i	0.0295498	−	0.348699i
$512$		−	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
$518$	−777.927	−	65.9240i	−1.50179	−	0.127266i
$519$	−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	−0.801831	−	0.597551i	$-0.796141\pi$
$521$	−106.430	+	106.430i	−0.204281	+	0.204281i	0.597551	+	0.801831i	$0.296141\pi$
$522$	221.505	+	221.505i	0.424338	+	0.424338i
$523$		−	60.6104i		−	0.115890i	−0.998320	−	0.0579449i	$-0.981545\pi$
$523$		−	60.6104i		−	0.115890i	0.998320	−	0.0579449i	$-0.0184548\pi$
$524$	−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
$539$	313.305	+	442.294i	0.581270	+	0.820583i
$540$	−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
$546$	−8.93997	+	105.495i	−0.0163736	+	0.193214i
$547$	−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
$560$	−1.17935	+	13.9167i	−0.00210598	+	0.0248513i
$561$	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	−0.843112	−	0.537738i	$-0.819279\pi$
$563$	−171.925	+	171.925i	−0.305374	+	0.305374i	0.537738	+	0.843112i	$0.319279\pi$
$564$	−108.122			−0.191705
$565$	−17.4807			−0.0309394
$566$	400.592			0.707760
$567$	−45.1798	+	533.139i	−0.0796822	+	0.940280i
$568$	−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
$574$	398.153	−	664.516i	0.693647	−	1.15769i
$575$	477.929			0.831182
$576$			348.446i			0.604942i
$577$	−456.658	+	456.658i	−0.791435	+	0.791435i	−0.981728	−	0.190292i	$-0.939056\pi$
$577$	−456.658	+	456.658i	−0.791435	+	0.791435i	0.190292	+	0.981728i	$0.439056\pi$
$578$	340.287			0.588731
$579$	50.4597			0.0871497
$580$	−3.32072	−	3.32072i	−0.00572538	−	0.00572538i
$581$	−825.189	−	69.9290i	−1.42029	−	0.120360i
$582$		−	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	−0.603007	−	0.797736i	$-0.706031\pi$
$587$	114.306	−	114.306i	0.194730	−	0.194730i	0.797736	+	0.603007i	$0.206031\pi$
$588$	54.1859	−	38.3833i	0.0921530	−	0.0652776i
$589$	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	0.969992	−	0.243135i	$-0.0781758\pi$
$593$	431.026	+	431.026i	0.726857	+	0.726857i	−0.243135	+	0.969992i	$0.578176\pi$
$594$	−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	0.999549	−	0.0300372i	$-0.00956257\pi$
$601$	582.676	+	582.676i	0.969512	+	0.969512i	−0.0300372	+	0.999549i	$0.509563\pi$
$602$	−63.2636	+	746.534i	−0.105089	+	1.24009i
$603$	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	$-0.351282\pi$
$607$	546.783			0.900796			0.450398	+	0.892828i	$0.351282\pi$
$608$	−498.594	+	498.594i	−0.820056	+	0.820056i
$609$	3.20434	−	37.8124i	0.00526164	−	0.0620893i
$610$		−	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	$0.281567\pi$
$619$			957.768i			1.54728i	−0.633623	+	0.773642i	$0.718433\pi$
$620$			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
$630$	1.53200	−	18.0781i	0.00243174	−	0.0286955i
$631$	−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
$637$	−543.212	+	384.791i	−0.852766	+	0.604067i
$638$	−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	−0.283074	−	0.959098i	$-0.591354\pi$
$643$	434.684	−	434.684i	0.676025	−	0.676025i	0.959098	+	0.283074i	$0.0913541\pi$
$644$	37.1443	−	438.316i	0.0576774	−	0.680615i
$645$	−1.25765	−	1.25765i	−0.00194984	−	0.00194984i
$646$	−927.432			−1.43565
$647$	633.926			0.979793			0.489896	−	0.871781i	$-0.337035\pi$
$647$	633.926			0.979793			0.489896	+	0.871781i	$0.337035\pi$
$648$			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	$-0.552285\pi$
$661$	−216.172			−0.327039			−0.163519	+	0.986540i	$0.552285\pi$
$662$	−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	$-0.579635\pi$
$677$	−335.221			−0.495156			−0.247578	+	0.968868i	$0.579635\pi$
$678$	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
$686$	896.203	+	232.300i	1.30642	+	0.338630i
$687$	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	$0.0216772\pi$
$691$	736.420	+	736.420i	1.06573	+	1.06573i	0.0680483	+	0.997682i	$0.478323\pi$
$692$	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
$700$	48.5285	−	572.655i	0.0693265	−	0.818078i
$701$	−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
$714$	158.204	+	13.4067i	0.221574	+	0.0187768i
$715$	−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	0.970994	−	0.239104i	$-0.0768537\pi$
$719$	526.229	+	526.229i	0.731890	+	0.731890i	−0.239104	+	0.970994i	$0.576854\pi$
$720$		−	17.6176i		−	0.0244690i
$721$	36.9932	−	436.534i	0.0513082	−	0.605456i
$722$	−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	−0.356113	−	0.934443i	$-0.615898\pi$
$727$	420.446	−	420.446i	0.578331	−	0.578331i	0.934443	+	0.356113i	$0.115898\pi$
$728$	−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	$-0.411343\pi$
$733$	403.056			0.549872			0.274936	+	0.961462i	$0.411343\pi$
$734$			68.7883i			0.0937171i
$735$	−1.79347	+	1.27043i	−0.00244010	+	0.00172847i
$736$		−	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
$749$	60.3024	−	711.591i	0.0805106	−	0.950055i
$750$	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	$-0.832692\pi$
$761$		−	763.653i		−	1.00349i	0.865017	−	0.501743i	$-0.167308\pi$
$762$	−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	$0.261852\pi$
$769$			1127.26i			1.46588i	−0.680295	+	0.732939i	$0.738148\pi$
$770$	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	0.236958	−	0.971520i	$-0.423850\pi$
$773$	−567.816	−	567.816i	−0.734562	−	0.734562i	−0.971520	+	0.236958i	$0.923850\pi$
$774$		−	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	$-0.262249\pi$
$787$	1069.34			1.35876			0.679380	+	0.733786i	$0.262249\pi$
$788$		−	1244.39i		−	1.57918i
$789$		−	102.845i		−	0.130348i
$790$	−18.4579	+	18.4579i	−0.0233645	+	0.0233645i
$791$	−95.0137	+	1121.20i	−0.120118	+	1.41744i
$792$	−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	$0.227620\pi$
$797$			1045.16i			1.31137i	−0.755035	+	0.655684i	$0.772380\pi$
$798$	−130.962	−	11.0981i	−0.164112	−	0.0139074i
$799$		−	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
$805$	−1.22942	+	14.5076i	−0.00152723	+	0.0180219i
$806$	−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	$-0.472554\pi$
$811$	139.682			0.172234			0.0861171	+	0.996285i	$0.472554\pi$
$812$	−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
$826$	−52.7672	+	622.673i	−0.0638828	+	0.753841i
$827$	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	$-0.0413903\pi$
$829$	1644.00			1.98312			0.991558	+	0.129665i	$0.0413903\pi$
$830$	−34.7267			−0.0418394
$831$	−26.9460	+	26.9460i	−0.0324260	+	0.0324260i
$832$	379.090	−	379.090i	0.455637	−	0.455637i
$833$	577.045	+	814.618i	0.692731	+	0.977933i
$834$	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	0.189204	−	0.981938i	$-0.439409\pi$
$839$	−665.103	−	665.103i	−0.792734	−	0.792734i	−0.981938	+	0.189204i	$0.939409\pi$
$840$	−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
$847$	9.47946	+	0.803319i	0.0111918	+	0.000948428i
$848$	−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	$-0.659775\pi$
$853$	−820.815			−0.962269			−0.481134	+	0.876647i	$0.659775\pi$
$854$	−1978.66	−	167.678i	−2.31694	−	0.196344i
$855$	−11.4512	+	11.4512i	−0.0133932	+	0.0133932i
$856$		−	196.726i		−	0.229821i
$857$		−	817.231i		−	0.953595i	−0.879013	−	0.476797i	$-0.841798\pi$
$857$		−	817.231i		−	0.953595i	0.879013	−	0.476797i	$-0.158202\pi$
$858$	118.302	+	118.302i	0.137881	+	0.137881i
$859$	−1295.26			−1.50787			−0.753937	−	0.656947i	$-0.771848\pi$
$859$	−1295.26			−1.50787			−0.753937	+	0.656947i	$0.771848\pi$
$860$			14.1680i			0.0164745i
$861$	114.823	−	28.7809i	0.133360	−	0.0334273i
$862$	−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
$868$	1020.87	+	86.5118i	1.17612	+	0.0996680i
$869$			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
$875$	−3.21320	+	37.9170i	−0.00367223	+	0.0433337i
$876$	−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	$-0.475244\pi$
$881$	136.897			0.155388			0.0776940	+	0.996977i	$0.475244\pi$
$882$	−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	0.870447	−	0.492263i	$-0.163830\pi$
$887$	335.449	+	335.449i	0.378184	+	0.378184i	−0.492263	+	0.870447i	$0.663830\pi$
$888$	−23.2382	−	23.2382i	−0.0261692	−	0.0261692i
$889$	71.2528	−	840.810i	0.0801494	−	0.945793i
$890$	−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
$896$	423.534	+	35.8916i	0.472694	+	0.0400576i
$897$			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
$917$	48.1986	−	568.761i	0.0525611	−	0.620241i
$918$	−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
$924$	8.86053	−	104.558i	0.00958932	−	0.113158i
$925$	−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	0.991373	−	0.131068i	$-0.0418407\pi$
$929$	799.224	+	799.224i	0.860305	+	0.860305i	−0.131068	+	0.991373i	$0.541841\pi$
$930$	−3.81357	+	3.81357i	−0.00410061	+	0.00410061i
$931$	−477.680	−	674.345i	−0.513083	−	0.724323i
$932$	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	0.655952	−	0.754802i	$-0.272267\pi$
$937$	−92.6222	−	92.6222i	−0.0988498	−	0.0988498i	−0.754802	+	0.655952i	$0.772267\pi$
$938$	−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	$-0.625039\pi$
$941$	−720.423			−0.765593			−0.382797	+	0.923833i	$0.625039\pi$
$942$	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	−0.892074	−	0.451889i	$-0.850750\pi$
$971$	−427.420	+	427.420i	−0.440185	+	0.440185i	0.451889	+	0.892074i	$0.350750\pi$
$972$	227.013	−	227.013i	0.233553	−	0.233553i
$973$	1495.63	+	126.745i	1.53714	+	0.130262i
$974$	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	$0.119999\pi$
$983$			723.727i			0.736243i	−0.929778	+	0.368122i	$0.880001\pi$
$984$	30.8482	−	10.5709i	0.0313498	−	0.0107428i
$985$			41.1874i			0.0418147i
$986$	−722.776			−0.733039
$987$	19.4512	−	229.532i	0.0197074	−	0.232555i
$988$	−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	$-0.489694\pi$
$997$	1028.75	−	1028.75i	1.03185	−	1.03185i	0.999476	−	0.0323714i	$-0.0103059\pi$
$998$	−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.132.10	yes	108
7.6	odd	2	inner	287.3.g.a.132.9	✓	108
41.32	even	4	inner	287.3.g.a.237.45	yes	108
287.237	odd	4	inner	287.3.g.a.237.46	yes	108

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

\(f(q)\)	\(=\)	\(q-2.69918i q^{2} +(0.291651 - 0.291651i) q^{3} -3.28560 q^{4} +0.108748 q^{5} +(-0.787221 - 0.787221i) q^{6} +(0.591083 - 6.97500i) q^{7} -1.92831i q^{8} +8.82988i q^{9} +O(q^{10})\)	\(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} +(0.591083 - 6.97500i) 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} +(-18.8268 - 1.59544i) 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} +(-1.94206 + 22.9170i) 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} +(0.0642793 - 0.758519i) 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} +(-13.4500 - 1.13979i) 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} +(61.5884 + 5.21919i) 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} +(-2.04738 - 0.173502i) 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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Database

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