LMFDB - Embedded newform 261.3.f.a.244.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(46,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("261.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.f (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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			244.2
Root			$-1.35225i$ of defining polynomial
Character	$\chi$	$=$	261.244
Dual form			261.3.f.a.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909588 - 0.909588i) q^{2} -2.34530i q^{4} -4.16447i q^{5} -9.68815 q^{7} +(-5.77161 + 5.77161i) q^{8} +O(q^{10})$	\(q+(-0.909588 - 0.909588i) q^{2} -2.34530i q^{4} -4.16447i q^{5} -9.68815 q^{7} +(-5.77161 + 5.77161i) q^{8} +(-3.78796 + 3.78796i) q^{10} +(0.334930 + 0.334930i) q^{11} +12.2282i q^{13} +(8.81223 + 8.81223i) q^{14} +1.11839 q^{16} +(-6.80978 - 6.80978i) q^{17} +(14.6673 + 14.6673i) q^{19} -9.76693 q^{20} -0.609296i q^{22} +10.0844 q^{23} +7.65715 q^{25} +(11.1226 - 11.1226i) q^{26} +22.7216i q^{28} +(-28.1041 + 7.15263i) q^{29} +(-37.3099 - 37.3099i) q^{31} +(22.0692 + 22.0692i) q^{32} +12.3882i q^{34} +40.3460i q^{35} +(-45.0215 + 45.0215i) q^{37} -26.6824i q^{38} +(24.0357 + 24.0357i) q^{40} +(-22.8142 + 22.8142i) q^{41} +(-17.5030 - 17.5030i) q^{43} +(0.785510 - 0.785510i) q^{44} +(-9.17268 - 9.17268i) q^{46} +(-2.20999 + 2.20999i) q^{47} +44.8602 q^{49} +(-6.96485 - 6.96485i) q^{50} +28.6787 q^{52} -90.1375 q^{53} +(1.39481 - 1.39481i) q^{55} +(55.9162 - 55.9162i) q^{56} +(32.0691 + 19.0572i) q^{58} +90.4223 q^{59} +(-29.4354 - 29.4354i) q^{61} +67.8734i q^{62} -44.6213i q^{64} +50.9239 q^{65} -31.5543i q^{67} +(-15.9710 + 15.9710i) q^{68} +(36.6983 - 36.6983i) q^{70} -99.8673i q^{71} +(-3.96285 + 3.96285i) q^{73} +81.9020 q^{74} +(34.3992 - 34.3992i) q^{76} +(-3.24485 - 3.24485i) q^{77} +(-40.3117 - 40.3117i) q^{79} -4.65749i q^{80} +41.5030 q^{82} -137.714 q^{83} +(-28.3592 + 28.3592i) q^{85} +31.8411i q^{86} -3.86616 q^{88} +(-83.1506 - 83.1506i) q^{89} -118.468i q^{91} -23.6510i q^{92} +4.02036 q^{94} +(61.0816 - 61.0816i) q^{95} +(-79.9850 + 79.9850i) q^{97} +(-40.8043 - 40.8043i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{7} + 42 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^7 + 42 * q^8	$ 8 q - 2 q^{2} - 4 q^{7} + 42 q^{8} + 6 q^{10} + 6 q^{11} + 40 q^{14} - 32 q^{16} - 12 q^{17} - 16 q^{19} - 108 q^{20} + 104 q^{25} + 54 q^{26} - 128 q^{29} - 10 q^{31} + 106 q^{32} - 84 q^{37} + 226 q^{40} - 20 q^{41} - 190 q^{43} - 42 q^{44} + 12 q^{46} - 58 q^{47} - 72 q^{49} + 60 q^{50} - 144 q^{52} - 252 q^{53} - 74 q^{55} + 192 q^{56} + 326 q^{58} + 40 q^{59} - 208 q^{61} - 36 q^{65} + 296 q^{68} + 44 q^{70} - 188 q^{73} + 64 q^{74} + 592 q^{76} - 180 q^{77} - 382 q^{79} + 228 q^{82} - 280 q^{83} + 32 q^{85} + 20 q^{88} + 64 q^{89} - 460 q^{94} + 380 q^{95} - 44 q^{97} + 66 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^7 + 42 * q^8 + 6 * q^10 + 6 * q^11 + 40 * q^14 - 32 * q^16 - 12 * q^17 - 16 * q^19 - 108 * q^20 + 104 * q^25 + 54 * q^26 - 128 * q^29 - 10 * q^31 + 106 * q^32 - 84 * q^37 + 226 * q^40 - 20 * q^41 - 190 * q^43 - 42 * q^44 + 12 * q^46 - 58 * q^47 - 72 * q^49 + 60 * q^50 - 144 * q^52 - 252 * q^53 - 74 * q^55 + 192 * q^56 + 326 * q^58 + 40 * q^59 - 208 * q^61 - 36 * q^65 + 296 * q^68 + 44 * q^70 - 188 * q^73 + 64 * q^74 + 592 * q^76 - 180 * q^77 - 382 * q^79 + 228 * q^82 - 280 * q^83 + 32 * q^85 + 20 * q^88 + 64 * q^89 - 460 * q^94 + 380 * q^95 - 44 * q^97 + 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.909588	−	0.909588i	−0.454794	−	0.454794i	0.442148	−	0.896942i	$-0.354217\pi$
$2$	−0.909588	−	0.909588i	−0.454794	−	0.454794i	−0.896942	+	0.442148i	$0.854217\pi$
$3$		0			0
$3$		0			0
$4$		−	2.34530i		−	0.586324i
$5$		−	4.16447i		−	0.832895i	−0.909160	−	0.416447i	$-0.863275\pi$
$5$		−	4.16447i		−	0.832895i	0.909160	−	0.416447i	$-0.136725\pi$
$6$		0			0
$7$	−9.68815			−1.38402			−0.692011	−	0.721887i	$-0.743275\pi$
$7$	−9.68815			−1.38402			−0.692011	+	0.721887i	$0.743275\pi$
$8$	−5.77161	+	5.77161i	−0.721451	+	0.721451i
$9$		0			0
$10$	−3.78796	+	3.78796i	−0.378796	+	0.378796i
$11$	0.334930	+	0.334930i	0.0304481	+	0.0304481i	0.722167	−	0.691719i	$-0.243146\pi$
$11$	0.334930	+	0.334930i	0.0304481	+	0.0304481i	−0.691719	+	0.722167i	$0.743146\pi$
$12$		0			0
$13$			12.2282i			0.940628i	0.882499	+	0.470314i	$0.155859\pi$
$13$			12.2282i			0.940628i	−0.882499	+	0.470314i	$0.844141\pi$
$14$	8.81223	+	8.81223i	0.629445	+	0.629445i
$15$		0			0
$16$	1.11839			0.0698991
$17$	−6.80978	−	6.80978i	−0.400575	−	0.400575i	0.477861	−	0.878436i	$-0.341412\pi$
$17$	−6.80978	−	6.80978i	−0.400575	−	0.400575i	−0.878436	+	0.477861i	$0.841412\pi$
$18$		0			0
$19$	14.6673	+	14.6673i	0.771963	+	0.771963i	0.978449	−	0.206486i	$-0.0662029\pi$
$19$	14.6673	+	14.6673i	0.771963	+	0.771963i	−0.206486	+	0.978449i	$0.566203\pi$
$20$	−9.76693			−0.488347
$21$		0			0
$22$		−	0.609296i		−	0.0276953i
$23$	10.0844			0.438454			0.219227	−	0.975674i	$-0.429647\pi$
$23$	10.0844			0.438454			0.219227	+	0.975674i	$0.429647\pi$
$24$		0			0
$25$	7.65715			0.306286
$26$	11.1226	−	11.1226i	0.427792	−	0.427792i
$27$		0			0
$28$			22.7216i			0.811485i
$29$	−28.1041	+	7.15263i	−0.969107	+	0.246642i
$29$	−28.1041	+	7.15263i	−0.969107	+	0.246642i
$30$		0			0
$31$	−37.3099	−	37.3099i	−1.20355	−	1.20355i	−0.973080	−	0.230466i	$-0.925975\pi$
$31$	−37.3099	−	37.3099i	−1.20355	−	1.20355i	−0.230466	−	0.973080i	$-0.574025\pi$
$32$	22.0692	+	22.0692i	0.689661	+	0.689661i
$33$		0			0
$34$			12.3882i			0.364359i
$35$			40.3460i			1.15274i
$36$		0			0
$37$	−45.0215	+	45.0215i	−1.21680	+	1.21680i	−0.248050	+	0.968747i	$0.579790\pi$
$37$	−45.0215	+	45.0215i	−1.21680	+	1.21680i	−0.968747	+	0.248050i	$0.920210\pi$
$38$		−	26.6824i		−	0.702169i
$39$		0			0
$40$	24.0357	+	24.0357i	0.600893	+	0.600893i
$41$	−22.8142	+	22.8142i	−0.556443	+	0.556443i	−0.928293	−	0.371850i	$-0.878724\pi$
$41$	−22.8142	+	22.8142i	−0.556443	+	0.556443i	0.371850	+	0.928293i	$0.378724\pi$
$42$		0			0
$43$	−17.5030	−	17.5030i	−0.407048	−	0.407048i	0.473660	−	0.880708i	$-0.342933\pi$
$43$	−17.5030	−	17.5030i	−0.407048	−	0.407048i	−0.880708	+	0.473660i	$0.842933\pi$
$44$	0.785510	−	0.785510i	0.0178525	−	0.0178525i
$45$		0			0
$46$	−9.17268	−	9.17268i	−0.199406	−	0.199406i
$47$	−2.20999	+	2.20999i	−0.0470210	+	0.0470210i	−0.730226	−	0.683205i	$-0.760585\pi$
$47$	−2.20999	+	2.20999i	−0.0470210	+	0.0470210i	0.683205	+	0.730226i	$0.260585\pi$
$48$		0			0
$49$	44.8602			0.915514
$50$	−6.96485	−	6.96485i	−0.139297	−	0.139297i
$51$		0			0
$52$	28.6787			0.551513
$53$	−90.1375			−1.70071			−0.850354	−	0.526212i	$-0.823612\pi$
$53$	−90.1375			−1.70071			−0.850354	+	0.526212i	$0.823612\pi$
$54$		0			0
$55$	1.39481	−	1.39481i	0.0253601	−	0.0253601i
$56$	55.9162	−	55.9162i	0.998504	−	0.998504i
$57$		0			0
$58$	32.0691	+	19.0572i	0.552916	+	0.328573i
$59$	90.4223			1.53258			0.766291	−	0.642494i	$-0.222100\pi$
$59$	90.4223			1.53258			0.766291	+	0.642494i	$0.222100\pi$
$60$		0			0
$61$	−29.4354	−	29.4354i	−0.482548	−	0.482548i	0.423397	−	0.905944i	$-0.360838\pi$
$61$	−29.4354	−	29.4354i	−0.482548	−	0.482548i	−0.905944	+	0.423397i	$0.860838\pi$
$62$			67.8734i			1.09473i
$63$		0			0
$64$		−	44.6213i		−	0.697207i
$65$	50.9239			0.783445
$66$		0			0
$67$		−	31.5543i		−	0.470960i	−0.971879	−	0.235480i	$-0.924334\pi$
$67$		−	31.5543i		−	0.470960i	0.971879	−	0.235480i	$-0.0756662\pi$
$68$	−15.9710	+	15.9710i	−0.234867	+	0.234867i
$69$		0			0
$70$	36.6983	−	36.6983i	0.524261	−	0.524261i
$71$		−	99.8673i		−	1.40658i	−0.710902	−	0.703291i	$-0.751713\pi$
$71$		−	99.8673i		−	1.40658i	0.710902	−	0.703291i	$-0.248287\pi$
$72$		0			0
$73$	−3.96285	+	3.96285i	−0.0542856	+	0.0542856i	−0.733728	−	0.679443i	$-0.762222\pi$
$73$	−3.96285	+	3.96285i	−0.0542856	+	0.0542856i	0.679443	+	0.733728i	$0.262222\pi$
$74$	81.9020			1.10678
$75$		0			0
$76$	34.3992	−	34.3992i	0.452621	−	0.452621i
$77$	−3.24485	−	3.24485i	−0.0421409	−	0.0421409i
$78$		0			0
$79$	−40.3117	−	40.3117i	−0.510275	−	0.510275i	0.404335	−	0.914611i	$-0.367503\pi$
$79$	−40.3117	−	40.3117i	−0.510275	−	0.510275i	−0.914611	+	0.404335i	$0.867503\pi$
$80$		−	4.65749i		−	0.0582186i
$81$		0			0
$82$	41.5030			0.506134
$83$	−137.714			−1.65921			−0.829604	−	0.558352i	$-0.811434\pi$
$83$	−137.714			−1.65921			−0.829604	+	0.558352i	$0.811434\pi$
$84$		0			0
$85$	−28.3592	+	28.3592i	−0.333637	+	0.333637i
$86$			31.8411i			0.370246i
$87$		0			0
$88$	−3.86616			−0.0439337
$89$	−83.1506	−	83.1506i	−0.934276	−	0.934276i	0.0636936	−	0.997969i	$-0.479712\pi$
$89$	−83.1506	−	83.1506i	−0.934276	−	0.934276i	−0.997969	+	0.0636936i	$0.979712\pi$
$90$		0			0
$91$		−	118.468i		−	1.30185i
$92$		−	23.6510i		−	0.257076i
$93$		0			0
$94$	4.02036			0.0427698
$95$	61.0816	−	61.0816i	0.642964	−	0.642964i
$96$		0			0
$97$	−79.9850	+	79.9850i	−0.824588	+	0.824588i	−0.986762	−	0.162174i	$-0.948149\pi$
$97$	−79.9850	+	79.9850i	−0.824588	+	0.824588i	0.162174	+	0.986762i	$0.448149\pi$
$98$	−40.8043	−	40.8043i	−0.416371	−	0.416371i
$99$		0			0
$100$		−	17.9583i		−	0.179583i
$101$	52.1216	+	52.1216i	0.516055	+	0.516055i	0.916375	−	0.400320i	$-0.131101\pi$
$101$	52.1216	+	52.1216i	0.516055	+	0.516055i	−0.400320	+	0.916375i	$0.631101\pi$
$102$		0			0
$103$	139.377			1.35318			0.676588	−	0.736361i	$-0.263458\pi$
$103$	139.377			1.35318			0.676588	+	0.736361i	$0.263458\pi$
$104$	−70.5762	−	70.5762i	−0.678617	−	0.678617i
$105$		0			0
$106$	81.9880	+	81.9880i	0.773472	+	0.773472i
$107$	14.9646			0.139856			0.0699282	−	0.997552i	$-0.477723\pi$
$107$	14.9646			0.139856			0.0699282	+	0.997552i	$0.477723\pi$
$108$		0			0
$109$		−	38.6223i		−	0.354333i	−0.984181	−	0.177167i	$-0.943307\pi$
$109$		−	38.6223i		−	0.354333i	0.984181	−	0.177167i	$-0.0566931\pi$
$110$	−2.53740			−0.0230673
$111$		0			0
$112$	−10.8351			−0.0967418
$113$	20.2695	−	20.2695i	0.179376	−	0.179376i	−0.611708	−	0.791084i	$-0.709517\pi$
$113$	20.2695	−	20.2695i	0.179376	−	0.179376i	0.791084	+	0.611708i	$0.209517\pi$
$114$		0			0
$115$		−	41.9964i		−	0.365186i
$116$	16.7750	+	65.9125i	0.144612	+	0.568211i
$117$		0			0
$118$	−82.2471	−	82.2471i	−0.697009	−	0.697009i
$119$	65.9741	+	65.9741i	0.554405	+	0.554405i
$120$		0			0
$121$		−	120.776i		−	0.998146i
$122$			53.5482i			0.438920i
$123$		0			0
$124$	−87.5029	+	87.5029i	−0.705669	+	0.705669i
$125$		−	136.000i		−	1.08800i
$126$		0			0
$127$	52.2215	+	52.2215i	0.411193	+	0.411193i	0.882154	−	0.470961i	$-0.156093\pi$
$127$	52.2215	+	52.2215i	0.411193	+	0.411193i	−0.470961	+	0.882154i	$0.656093\pi$
$128$	47.6897	−	47.6897i	0.372576	−	0.372576i
$129$		0			0
$130$	−46.3198	−	46.3198i	−0.356306	−	0.356306i
$131$	−25.3821	+	25.3821i	−0.193756	+	0.193756i	−0.797317	−	0.603561i	$-0.793748\pi$
$131$	−25.3821	+	25.3821i	−0.193756	+	0.193756i	0.603561	+	0.797317i	$0.293748\pi$
$132$		0			0
$133$	−142.099	−	142.099i	−1.06841	−	1.06841i
$134$	−28.7014	+	28.7014i	−0.214190	+	0.214190i
$135$		0			0
$136$	78.6068			0.577991
$137$	117.179	+	117.179i	0.855320	+	0.855320i	0.990782	−	0.135462i	$-0.0432520\pi$
$137$	117.179	+	117.179i	0.855320	+	0.855320i	−0.135462	+	0.990782i	$0.543252\pi$
$138$		0			0
$139$	62.2884			0.448118			0.224059	−	0.974576i	$-0.428069\pi$
$139$	62.2884			0.448118			0.224059	+	0.974576i	$0.428069\pi$
$140$	94.6235			0.675882
$141$		0			0
$142$	−90.8381	+	90.8381i	−0.639705	+	0.639705i
$143$	−4.09558	+	4.09558i	−0.0286404	+	0.0286404i
$144$		0			0
$145$	29.7869	+	117.039i	0.205427	+	0.807164i
$146$	7.20912			0.0493776
$147$		0			0
$148$	105.589	+	105.589i	0.713438	+	0.713438i
$149$			140.996i			0.946284i	0.880986	+	0.473142i	$0.156880\pi$
$149$			140.996i			0.946284i	−0.880986	+	0.473142i	$0.843120\pi$
$150$		0			0
$151$			269.100i			1.78212i	0.453889	+	0.891058i	$0.350036\pi$
$151$			269.100i			1.78212i	−0.453889	+	0.891058i	$0.649964\pi$
$152$	−169.308			−1.11387
$153$		0			0
$154$			5.90295i			0.0383308i
$155$	−155.376	+	155.376i	−1.00243	+	1.00243i
$156$		0			0
$157$	−82.6681	+	82.6681i	−0.526549	+	0.526549i	−0.919541	−	0.392993i	$-0.871440\pi$
$157$	−82.6681	+	82.6681i	−0.526549	+	0.526549i	0.392993	+	0.919541i	$0.371440\pi$
$158$			73.3342i			0.464140i
$159$		0			0
$160$	91.9065	−	91.9065i	0.574416	−	0.574416i
$161$	−97.6995			−0.606829
$162$		0			0
$163$	16.1649	−	16.1649i	0.0991711	−	0.0991711i	−0.655780	−	0.754952i	$-0.727660\pi$
$163$	16.1649	−	16.1649i	0.0991711	−	0.0991711i	0.754952	+	0.655780i	$0.227660\pi$
$164$	53.5060	+	53.5060i	0.326256	+	0.326256i
$165$		0			0
$166$	125.263	+	125.263i	0.754598	+	0.754598i
$167$		−	134.528i		−	0.805558i	−0.915297	−	0.402779i	$-0.868044\pi$
$167$		−	134.528i		−	0.805558i	0.915297	−	0.402779i	$-0.131956\pi$
$168$		0			0
$169$	19.4719			0.115218
$170$	51.5903			0.303472
$171$		0			0
$172$	−41.0499	+	41.0499i	−0.238662	+	0.238662i
$173$		−	94.1756i		−	0.544368i	−0.962245	−	0.272184i	$-0.912254\pi$
$173$		−	94.1756i		−	0.544368i	0.962245	−	0.272184i	$-0.0877459\pi$
$174$		0			0
$175$	−74.1836			−0.423906
$176$	0.374580	+	0.374580i	0.00212830	+	0.00212830i
$177$		0			0
$178$			151.266i			0.849806i
$179$		−	55.6892i		−	0.311113i	−0.987827	−	0.155557i	$-0.950283\pi$
$179$		−	55.6892i		−	0.311113i	0.987827	−	0.155557i	$-0.0497171\pi$
$180$		0			0
$181$	−131.878			−0.728610			−0.364305	−	0.931280i	$-0.618693\pi$
$181$	−131.878			−0.728610			−0.364305	+	0.931280i	$0.618693\pi$
$182$	−107.757	+	107.757i	−0.592074	+	0.592074i
$183$		0			0
$184$	−58.2034	+	58.2034i	−0.316323	+	0.316323i
$185$	187.491	+	187.491i	1.01346	+	1.01346i
$186$		0			0
$187$		−	4.56159i		−	0.0243935i
$188$	5.18308	+	5.18308i	0.0275696	+	0.0275696i
$189$		0			0
$190$	−111.118			−0.584833
$191$	−122.543	−	122.543i	−0.641588	−	0.641588i	0.309358	−	0.950946i	$-0.399886\pi$
$191$	−122.543	−	122.543i	−0.641588	−	0.641588i	−0.950946	+	0.309358i	$0.899886\pi$
$192$		0			0
$193$	−175.959	−	175.959i	−0.911702	−	0.911702i	0.0847039	−	0.996406i	$-0.473006\pi$
$193$	−175.959	−	175.959i	−0.911702	−	0.911702i	−0.996406	+	0.0847039i	$0.973006\pi$
$194$	145.507			0.750036
$195$		0			0
$196$		−	105.211i		−	0.536789i
$197$	−42.7699			−0.217106			−0.108553	−	0.994091i	$-0.534622\pi$
$197$	−42.7699			−0.217106			−0.108553	+	0.994091i	$0.534622\pi$
$198$		0			0
$199$	−101.732			−0.511216			−0.255608	−	0.966781i	$-0.582276\pi$
$199$	−101.732			−0.511216			−0.255608	+	0.966781i	$0.582276\pi$
$200$	−44.1941	+	44.1941i	−0.220970	+	0.220970i
$201$		0			0
$202$		−	94.8184i		−	0.469398i
$203$	272.277	−	69.2957i	1.34126	−	0.341358i
$204$		0			0
$205$	95.0090	+	95.0090i	0.463459	+	0.463459i
$206$	−126.776	−	126.776i	−0.615417	−	0.615417i
$207$		0			0
$208$			13.6758i			0.0657491i
$209$			9.82502i			0.0470097i
$210$		0			0
$211$	84.0454	−	84.0454i	0.398319	−	0.398319i	−0.479321	−	0.877640i	$-0.659117\pi$
$211$	84.0454	−	84.0454i	0.398319	−	0.398319i	0.877640	+	0.479321i	$0.159117\pi$
$212$			211.399i			0.997166i
$213$		0			0
$214$	−13.6117	−	13.6117i	−0.0636058	−	0.0636058i
$215$	−72.8910	+	72.8910i	−0.339028	+	0.339028i
$216$		0			0
$217$	361.464	+	361.464i	1.66573	+	1.66573i
$218$	−35.1304	+	35.1304i	−0.161149	+	0.161149i
$219$		0			0
$220$	−3.27123	−	3.27123i	−0.0148692	−	0.0148692i
$221$	83.2711	−	83.2711i	0.376792	−	0.376792i
$222$		0			0
$223$	−306.140			−1.37283			−0.686413	−	0.727212i	$-0.740816\pi$
$223$	−306.140			−1.37283			−0.686413	+	0.727212i	$0.740816\pi$
$224$	−213.809	−	213.809i	−0.954506	−	0.954506i
$225$		0			0
$226$	−36.8739			−0.163159
$227$	−19.8257			−0.0873379			−0.0436689	−	0.999046i	$-0.513905\pi$
$227$	−19.8257			−0.0873379			−0.0436689	+	0.999046i	$0.513905\pi$
$228$		0			0
$229$	150.087	−	150.087i	0.655402	−	0.655402i	−0.298887	−	0.954289i	$-0.596615\pi$
$229$	150.087	−	150.087i	0.655402	−	0.655402i	0.954289	+	0.298887i	$0.0966153\pi$
$230$	−38.1994	+	38.1994i	−0.166084	+	0.166084i
$231$		0			0
$232$	120.924	−	203.488i	0.521223	−	0.877103i
$233$	−132.431			−0.568375			−0.284187	−	0.958769i	$-0.591724\pi$
$233$	−132.431			−0.568375			−0.284187	+	0.958769i	$0.591724\pi$
$234$		0			0
$235$	9.20344	+	9.20344i	0.0391636	+	0.0391636i
$236$		−	212.067i		−	0.898590i
$237$		0			0
$238$		−	120.019i		−	0.504280i
$239$	−176.690			−0.739288			−0.369644	−	0.929173i	$-0.620520\pi$
$239$	−176.690			−0.739288			−0.369644	+	0.929173i	$0.620520\pi$
$240$		0			0
$241$			161.010i			0.668093i	0.942557	+	0.334046i	$0.108414\pi$
$241$			161.010i			0.668093i	−0.942557	+	0.334046i	$0.891586\pi$
$242$	−109.856	+	109.856i	−0.453951	+	0.453951i
$243$		0			0
$244$	−69.0348	+	69.0348i	−0.282930	+	0.282930i
$245$		−	186.819i		−	0.762527i
$246$		0			0
$247$	−179.354	+	179.354i	−0.726130	+	0.726130i
$248$	430.677			1.73660
$249$		0			0
$250$	−123.704	+	123.704i	−0.494816	+	0.494816i
$251$	−136.621	−	136.621i	−0.544306	−	0.544306i	0.380482	−	0.924788i	$-0.375758\pi$
$251$	−136.621	−	136.621i	−0.544306	−	0.544306i	−0.924788	+	0.380482i	$0.875758\pi$
$252$		0			0
$253$	3.37757	+	3.37757i	0.0133501	+	0.0133501i
$254$		−	95.0001i		−	0.374016i
$255$		0			0
$256$	−265.241			−1.03610
$257$	275.616			1.07244			0.536218	−	0.844079i	$-0.319852\pi$
$257$	275.616			1.07244			0.536218	+	0.844079i	$0.319852\pi$
$258$		0			0
$259$	436.175	−	436.175i	1.68407	−	1.68407i
$260$		−	119.432i		−	0.459353i
$261$		0			0
$262$	46.1744			0.176238
$263$	242.820	+	242.820i	0.923269	+	0.923269i	0.997259	−	0.0739900i	$-0.0235733\pi$
$263$	242.820	+	242.820i	0.923269	+	0.923269i	−0.0739900	+	0.997259i	$0.523573\pi$
$264$		0			0
$265$			375.375i			1.41651i
$266$			258.503i			0.971816i
$267$		0			0
$268$	−74.0042			−0.276135
$269$	−167.754	+	167.754i	−0.623620	+	0.623620i	−0.946455	−	0.322836i	$-0.895364\pi$
$269$	−167.754	+	167.754i	−0.623620	+	0.623620i	0.322836	+	0.946455i	$0.395364\pi$
$270$		0			0
$271$	282.361	−	282.361i	1.04192	−	1.04192i	0.0428420	−	0.999082i	$-0.486359\pi$
$271$	282.361	−	282.361i	1.04192	−	1.04192i	0.999082	−	0.0428420i	$-0.0136412\pi$
$272$	−7.61596	−	7.61596i	−0.0279998	−	0.0279998i
$273$		0			0
$274$		−	213.169i		−	0.777989i
$275$	2.56461	+	2.56461i	0.00932584	+	0.00932584i
$276$		0			0
$277$	30.5322			0.110224			0.0551122	−	0.998480i	$-0.482448\pi$
$277$	30.5322			0.110224			0.0551122	+	0.998480i	$0.482448\pi$
$278$	−56.6568	−	56.6568i	−0.203802	−	0.203802i
$279$		0			0
$280$	−232.862	−	232.862i	−0.831649	−	0.831649i
$281$	2.92201			0.0103986			0.00519931	−	0.999986i	$-0.498345\pi$
$281$	2.92201			0.0103986			0.00519931	+	0.999986i	$0.498345\pi$
$282$		0			0
$283$			26.9414i			0.0951993i	0.998866	+	0.0475997i	$0.0151572\pi$
$283$			26.9414i			0.0951993i	−0.998866	+	0.0475997i	$0.984843\pi$
$284$	−234.219			−0.824713
$285$		0			0
$286$	7.45058			0.0260510
$287$	221.027	−	221.027i	0.770129	−	0.770129i
$288$		0			0
$289$		−	196.254i		−	0.679079i
$290$	79.3633	−	133.551i	0.273666	−	0.460521i
$291$		0			0
$292$	9.29406	+	9.29406i	0.0318290	+	0.0318290i
$293$	255.770	+	255.770i	0.872934	+	0.872934i	0.992791	−	0.119857i	$-0.0382436\pi$
$293$	255.770	+	255.770i	0.872934	+	0.872934i	−0.119857	+	0.992791i	$0.538244\pi$
$294$		0			0
$295$		−	376.561i		−	1.27648i
$296$		−	519.693i		−	1.75572i
$297$		0			0
$298$	128.249	−	128.249i	0.430364	−	0.430364i
$299$			123.314i			0.412422i
$300$		0			0
$301$	169.572	+	169.572i	0.563362	+	0.563362i
$302$	244.770	−	244.770i	0.810496	−	0.810496i
$303$		0			0
$304$	16.4037	+	16.4037i	0.0539595	+	0.0539595i
$305$	−122.583	+	122.583i	−0.401912	+	0.401912i
$306$		0			0
$307$	−9.20371	−	9.20371i	−0.0299795	−	0.0299795i	0.691958	−	0.721938i	$-0.256748\pi$
$307$	−9.20371	−	9.20371i	−0.0299795	−	0.0299795i	−0.721938	+	0.691958i	$0.756748\pi$
$308$	−7.61013	+	7.61013i	−0.0247082	+	0.0247082i
$309$		0			0
$310$	282.657			0.911796
$311$	−94.0902	−	94.0902i	−0.302541	−	0.302541i	0.539466	−	0.842007i	$-0.318626\pi$
$311$	−94.0902	−	94.0902i	−0.302541	−	0.302541i	−0.842007	+	0.539466i	$0.818626\pi$
$312$		0			0
$313$	133.762			0.427356			0.213678	−	0.976904i	$-0.431456\pi$
$313$	133.762			0.427356			0.213678	+	0.976904i	$0.431456\pi$
$314$	150.388			0.478942
$315$		0			0
$316$	−94.5431	+	94.5431i	−0.299187	+	0.299187i
$317$	−405.329	+	405.329i	−1.27864	+	1.27864i	−0.337213	+	0.941428i	$0.609484\pi$
$317$	−405.329	+	405.329i	−1.27864	+	1.27864i	−0.941428	+	0.337213i	$0.890516\pi$
$318$		0			0
$319$	−11.8085	−	7.01726i	−0.0370173	−	0.0219977i
$320$	−185.824			−0.580700
$321$		0			0
$322$	88.8663	+	88.8663i	0.275982	+	0.275982i
$323$		−	199.762i		−	0.618458i
$324$		0			0
$325$			93.6329i			0.288101i
$326$	−29.4068			−0.0902049
$327$		0			0
$328$		−	263.349i		−	0.802893i
$329$	21.4107	−	21.4107i	0.0650781	−	0.0650781i
$330$		0			0
$331$	185.108	−	185.108i	0.559238	−	0.559238i	−0.369853	−	0.929090i	$-0.620592\pi$
$331$	185.108	−	185.108i	0.559238	−	0.559238i	0.929090	+	0.369853i	$0.120592\pi$
$332$			322.981i			0.972834i
$333$		0			0
$334$	−122.365	+	122.365i	−0.366363	+	0.366363i
$335$	−131.407			−0.392260
$336$		0			0
$337$	−71.8022	+	71.8022i	−0.213063	+	0.213063i	−0.805567	−	0.592504i	$-0.798139\pi$
$337$	−71.8022	+	71.8022i	−0.213063	+	0.213063i	0.592504	+	0.805567i	$0.298139\pi$
$338$	−17.7114	−	17.7114i	−0.0524006	−	0.0524006i
$339$		0			0
$340$	66.5107	+	66.5107i	0.195620	+	0.195620i
$341$		−	24.9924i		−	0.0732915i
$342$		0			0
$343$	40.1069			0.116930
$344$	202.041			0.587330
$345$		0			0
$346$	−85.6610	+	85.6610i	−0.247575	+	0.247575i
$347$		−	181.565i		−	0.523241i	−0.965171	−	0.261621i	$-0.915743\pi$
$347$		−	181.565i		−	0.523241i	0.965171	−	0.261621i	$-0.0842569\pi$
$348$		0			0
$349$	205.399			0.588536			0.294268	−	0.955723i	$-0.404924\pi$
$349$	205.399			0.588536			0.294268	+	0.955723i	$0.404924\pi$
$350$	67.4765	+	67.4765i	0.192790	+	0.192790i
$351$		0			0
$352$			14.7832i			0.0419978i
$353$		−	150.904i		−	0.427489i	−0.976890	−	0.213745i	$-0.931434\pi$
$353$		−	150.904i		−	0.427489i	0.976890	−	0.213745i	$-0.0685660\pi$
$354$		0			0
$355$	−415.895			−1.17153
$356$	−195.013	+	195.013i	−0.547789	+	0.547789i
$357$		0			0
$358$	−50.6543	+	50.6543i	−0.141492	+	0.141492i
$359$	366.501	+	366.501i	1.02089	+	1.02089i	0.999777	+	0.0211170i	$0.00672225\pi$
$359$	366.501	+	366.501i	1.02089	+	1.02089i	0.0211170	+	0.999777i	$0.493278\pi$
$360$		0			0
$361$			69.2592i			0.191854i
$362$	119.955	+	119.955i	0.331368	+	0.331368i
$363$		0			0
$364$	−277.843			−0.763306
$365$	16.5032	+	16.5032i	0.0452142	+	0.0452142i
$366$		0			0
$367$	−84.3213	−	84.3213i	−0.229758	−	0.229758i	0.582833	−	0.812592i	$-0.301944\pi$
$367$	−84.3213	−	84.3213i	−0.229758	−	0.229758i	−0.812592	+	0.582833i	$0.801944\pi$
$368$	11.2783			0.0306475
$369$		0			0
$370$		−	341.079i		−	0.921835i
$371$	873.265			2.35381
$372$		0			0
$373$	91.4080			0.245062			0.122531	−	0.992465i	$-0.460899\pi$
$373$	91.4080			0.245062			0.122531	+	0.992465i	$0.460899\pi$
$374$	−4.14917	+	4.14917i	−0.0110940	+	0.0110940i
$375$		0			0
$376$		−	25.5104i		−	0.0678468i
$377$	−87.4635	−	343.662i	−0.231999	−	0.911569i
$378$		0			0
$379$	178.021	+	178.021i	0.469713	+	0.469713i	0.901822	−	0.432108i	$-0.142230\pi$
$379$	178.021	+	178.021i	0.469713	+	0.469713i	−0.432108	+	0.901822i	$0.642230\pi$
$380$	−143.255	−	143.255i	−0.376986	−	0.376986i
$381$		0			0
$382$			222.928i			0.583581i
$383$		−	142.083i		−	0.370973i	−0.982647	−	0.185486i	$-0.940614\pi$
$383$		−	142.083i		−	0.370973i	0.982647	−	0.185486i	$-0.0593860\pi$
$384$		0			0
$385$	−13.5131	+	13.5131i	−0.0350989	+	0.0350989i
$386$			320.100i			0.829274i
$387$		0			0
$388$	187.589	+	187.589i	0.483476	+	0.483476i
$389$	339.694	−	339.694i	0.873250	−	0.873250i	−0.119575	−	0.992825i	$-0.538153\pi$
$389$	339.694	−	339.694i	0.873250	−	0.873250i	0.992825	+	0.119575i	$0.0381533\pi$
$390$		0			0
$391$	−68.6727	−	68.6727i	−0.175634	−	0.175634i
$392$	−258.916	+	258.916i	−0.660499	+	0.660499i
$393$		0			0
$394$	38.9030	+	38.9030i	0.0987386	+	0.0987386i
$395$	−167.877	+	167.877i	−0.425006	+	0.425006i
$396$		0			0
$397$	−657.787			−1.65689			−0.828447	−	0.560068i	$-0.810775\pi$
$397$	−657.787			−1.65689			−0.828447	+	0.560068i	$0.810775\pi$
$398$	92.5342	+	92.5342i	0.232498	+	0.232498i
$399$		0			0
$400$	8.56364			0.0214091
$401$	−343.872			−0.857537			−0.428768	−	0.903414i	$-0.641052\pi$
$401$	−343.872			−0.857537			−0.428768	+	0.903414i	$0.641052\pi$
$402$		0			0
$403$	456.232	−	456.232i	1.13209	−	1.13209i
$404$	122.241	−	122.241i	0.302576	−	0.302576i
$405$		0			0
$406$	−310.690	−	184.629i	−0.765247	−	0.454751i
$407$	−30.1581			−0.0740984
$408$		0			0
$409$	219.662	+	219.662i	0.537072	+	0.537072i	0.922668	−	0.385596i	$-0.126004\pi$
$409$	219.662	+	219.662i	0.537072	+	0.537072i	−0.385596	+	0.922668i	$0.626004\pi$
$410$		−	172.838i		−	0.421557i
$411$		0			0
$412$		−	326.881i		−	0.793401i
$413$	−876.024			−2.12112
$414$		0			0
$415$			573.508i			1.38195i
$416$	−269.866	+	269.866i	−0.648715	+	0.648715i
$417$		0			0
$418$	8.93673	−	8.93673i	0.0213797	−	0.0213797i
$419$		−	512.017i		−	1.22200i	−0.791631	−	0.610999i	$-0.790768\pi$
$419$		−	512.017i		−	1.22200i	0.791631	−	0.610999i	$-0.209232\pi$
$420$		0			0
$421$	−426.710	+	426.710i	−1.01356	+	1.01356i	−0.0136572	+	0.999907i	$0.504347\pi$
$421$	−426.710	+	426.710i	−1.01356	+	1.01356i	−0.999907	+	0.0136572i	$0.995653\pi$
$422$	−152.893			−0.362307
$423$		0			0
$424$	520.238	−	520.238i	1.22698	−	1.22698i
$425$	−52.1435	−	52.1435i	−0.122691	−	0.122691i
$426$		0			0
$427$	285.175	+	285.175i	0.667857	+	0.667857i
$428$		−	35.0965i		−	0.0820012i
$429$		0			0
$430$	132.602			0.308376
$431$	−596.638			−1.38431			−0.692156	−	0.721748i	$-0.743339\pi$
$431$	−596.638			−1.38431			−0.692156	+	0.721748i	$0.743339\pi$
$432$		0			0
$433$	−41.8737	+	41.8737i	−0.0967059	+	0.0967059i	−0.753805	−	0.657099i	$-0.771783\pi$
$433$	−41.8737	+	41.8737i	−0.0967059	+	0.0967059i	0.657099	+	0.753805i	$0.271783\pi$
$434$		−	657.567i		−	1.51513i
$435$		0			0
$436$	−90.5808			−0.207754
$437$	147.911	+	147.911i	0.338470	+	0.338470i
$438$		0			0
$439$		−	344.567i		−	0.784891i	−0.919775	−	0.392445i	$-0.871629\pi$
$439$		−	344.567i		−	0.784891i	0.919775	−	0.392445i	$-0.128371\pi$
$440$			16.1005i			0.0365922i
$441$		0			0
$442$	−151.485			−0.342726
$443$	124.564	−	124.564i	0.281184	−	0.281184i	−0.552397	−	0.833581i	$-0.686287\pi$
$443$	124.564	−	124.564i	0.281184	−	0.281184i	0.833581	+	0.552397i	$0.186287\pi$
$444$		0			0
$445$	−346.278	+	346.278i	−0.778154	+	0.778154i
$446$	278.462	+	278.462i	0.624353	+	0.624353i
$447$		0			0
$448$			432.297i			0.964949i
$449$	562.904	+	562.904i	1.25368	+	1.25368i	0.954056	+	0.299628i	$0.0968626\pi$
$449$	562.904	+	562.904i	1.25368	+	1.25368i	0.299628	+	0.954056i	$0.403137\pi$
$450$		0			0
$451$	−15.2823			−0.0338853
$452$	−47.5381	−	47.5381i	−0.105173	−	0.105173i
$453$		0			0
$454$	18.0332	+	18.0332i	0.0397208	+	0.0397208i
$455$	−493.358			−1.08430
$456$		0			0
$457$			377.138i			0.825247i	0.910902	+	0.412623i	$0.135387\pi$
$457$			377.138i			0.825247i	−0.910902	+	0.412623i	$0.864613\pi$
$458$	−273.035			−0.596146
$459$		0			0
$460$	−98.4940			−0.214117
$461$	40.0863	−	40.0863i	0.0869552	−	0.0869552i	−0.662291	−	0.749246i	$-0.730416\pi$
$461$	40.0863	−	40.0863i	0.0869552	−	0.0869552i	0.749246	+	0.662291i	$0.230416\pi$
$462$		0			0
$463$		−	410.934i		−	0.887546i	−0.896139	−	0.443773i	$-0.853640\pi$
$463$		−	410.934i		−	0.887546i	0.896139	−	0.443773i	$-0.146360\pi$
$464$	−31.4312	+	7.99939i	−0.0677397	+	0.0172401i
$465$		0			0
$466$	120.458	+	120.458i	0.258494	+	0.258494i
$467$	427.051	+	427.051i	0.914455	+	0.914455i	0.996619	−	0.0821634i	$-0.0261829\pi$
$467$	427.051	+	427.051i	0.914455	+	0.914455i	−0.0821634	+	0.996619i	$0.526183\pi$
$468$		0			0
$469$			305.703i			0.651818i
$470$		−	16.7427i		−	0.0356227i
$471$		0			0
$472$	−521.882	+	521.882i	−1.10568	+	1.10568i
$473$		−	11.7246i		−	0.0247877i
$474$		0			0
$475$	112.310	+	112.310i	0.236441	+	0.236441i
$476$	154.729	−	154.729i	0.325061	−	0.325061i
$477$		0			0
$478$	160.715	+	160.715i	0.336224	+	0.336224i
$479$	−223.602	+	223.602i	−0.466811	+	0.466811i	−0.900880	−	0.434069i	$-0.857077\pi$
$479$	−223.602	+	223.602i	−0.466811	+	0.466811i	0.434069	+	0.900880i	$0.357077\pi$
$480$		0			0
$481$	−550.530	−	550.530i	−1.14455	−	1.14455i
$482$	146.453	−	146.453i	0.303845	−	0.303845i
$483$		0			0
$484$	−283.255			−0.585237
$485$	333.096	+	333.096i	0.686795	+	0.686795i
$486$		0			0
$487$	397.009			0.815214			0.407607	−	0.913157i	$-0.366363\pi$
$487$	397.009			0.815214			0.407607	+	0.913157i	$0.366363\pi$
$488$	339.780			0.696270
$489$		0			0
$490$	−169.929	+	169.929i	−0.346793	+	0.346793i
$491$	441.208	−	441.208i	0.898591	−	0.898591i	−0.0967208	−	0.995312i	$-0.530835\pi$
$491$	441.208	−	441.208i	0.898591	−	0.898591i	0.995312	+	0.0967208i	$0.0308354\pi$
$492$		0			0
$493$	240.090	+	142.675i	0.486999	+	0.289401i
$494$	326.277			0.660480
$495$		0			0
$496$	−41.7269	−	41.7269i	−0.0841268	−	0.0841268i
$497$			967.529i			1.94674i
$498$		0			0
$499$			94.9470i			0.190275i	0.995464	+	0.0951373i	$0.0303290\pi$
$499$			94.9470i			0.190275i	−0.995464	+	0.0951373i	$0.969671\pi$
$500$	−318.960			−0.637920
$501$		0			0
$502$			248.537i			0.495094i
$503$	35.4061	−	35.4061i	0.0703899	−	0.0703899i	−0.671035	−	0.741425i	$-0.734150\pi$
$503$	35.4061	−	35.4061i	0.0703899	−	0.0703899i	0.741425	+	0.671035i	$0.234150\pi$
$504$		0			0
$505$	217.059	−	217.059i	0.429820	−	0.429820i
$506$		−	6.14440i		−	0.0121431i
$507$		0			0
$508$	122.475	−	122.475i	0.241092	−	0.241092i
$509$	−215.741			−0.423852			−0.211926	−	0.977286i	$-0.567974\pi$
$509$	−215.741			−0.423852			−0.211926	+	0.977286i	$0.567974\pi$
$510$		0			0
$511$	38.3927	−	38.3927i	0.0751324	−	0.0751324i
$512$	50.5014	+	50.5014i	0.0986355	+	0.0986355i
$513$		0			0
$514$	−250.697	−	250.697i	−0.487738	−	0.487738i
$515$		−	580.433i		−	1.12705i
$516$		0			0
$517$	−1.48038			−0.00286341
$518$	−793.479			−1.53181
$519$		0			0
$520$	−293.913	+	293.913i	−0.565217	+	0.565217i
$521$			279.099i			0.535700i	0.963461	+	0.267850i	$0.0863131\pi$
$521$			279.099i			0.535700i	−0.963461	+	0.267850i	$0.913687\pi$
$522$		0			0
$523$	−135.622			−0.259316			−0.129658	−	0.991559i	$-0.541388\pi$
$523$	−135.622			−0.259316			−0.129658	+	0.991559i	$0.541388\pi$
$524$	59.5285	+	59.5285i	0.113604	+	0.113604i
$525$		0			0
$526$		−	441.732i		−	0.839795i
$527$			508.145i			0.964221i
$528$		0			0
$529$	−427.304			−0.807758
$530$	341.437	−	341.437i	0.644221	−	0.644221i
$531$		0			0
$532$	−333.264	+	333.264i	−0.626437	+	0.626437i
$533$	−278.975	−	278.975i	−0.523406	−	0.523406i
$534$		0			0
$535$		−	62.3198i		−	0.116486i
$536$	182.119	+	182.119i	0.339774	+	0.339774i
$537$		0			0
$538$	305.174			0.567237
$539$	15.0250	+	15.0250i	0.0278757	+	0.0278757i
$540$		0			0
$541$	381.445	+	381.445i	0.705074	+	0.705074i	0.965495	−	0.260421i	$-0.0838614\pi$
$541$	381.445	+	381.445i	0.705074	+	0.705074i	−0.260421	+	0.965495i	$0.583861\pi$
$542$	−513.665			−0.947722
$543$		0			0
$544$		−	300.572i		−	0.552523i
$545$	−160.842			−0.295122
$546$		0			0
$547$	104.335			0.190739			0.0953697	−	0.995442i	$-0.469597\pi$
$547$	104.335			0.190739			0.0953697	+	0.995442i	$0.469597\pi$
$548$	274.819	−	274.819i	0.501495	−	0.501495i
$549$		0			0
$550$		−	4.66547i		−	0.00848268i
$551$	−517.121	−	307.301i	−0.938513	−	0.557716i
$552$		0			0
$553$	390.546	+	390.546i	0.706232	+	0.706232i
$554$	−27.7717	−	27.7717i	−0.0501295	−	0.0501295i
$555$		0			0
$556$		−	146.085i		−	0.262743i
$557$			132.616i			0.238090i	0.992889	+	0.119045i	$0.0379833\pi$
$557$			132.616i			0.238090i	−0.992889	+	0.119045i	$0.962017\pi$
$558$		0			0
$559$	214.030	−	214.030i	0.382880	−	0.382880i
$560$			45.1224i			0.0805758i
$561$		0			0
$562$	−2.65783	−	2.65783i	−0.00472923	−	0.00472923i
$563$	−253.583	+	253.583i	−0.450413	+	0.450413i	−0.895492	−	0.445078i	$-0.853176\pi$
$563$	−253.583	+	253.583i	−0.450413	+	0.450413i	0.445078	+	0.895492i	$0.353176\pi$
$564$		0			0
$565$	−84.4120	−	84.4120i	−0.149402	−	0.149402i
$566$	24.5056	−	24.5056i	0.0432961	−	0.0432961i
$567$		0			0
$568$	576.395	+	576.395i	1.01478	+	1.01478i
$569$	−216.864	+	216.864i	−0.381133	+	0.381133i	−0.871510	−	0.490377i	$-0.836859\pi$
$569$	−216.864	+	216.864i	−0.381133	+	0.381133i	0.490377	+	0.871510i	$0.336859\pi$
$570$		0			0
$571$	398.256			0.697472			0.348736	−	0.937221i	$-0.386611\pi$
$571$	398.256			0.697472			0.348736	+	0.937221i	$0.386611\pi$
$572$	9.60534	+	9.60534i	0.0167926	+	0.0167926i
$573$		0			0
$574$	−402.087			−0.700500
$575$	77.2180			0.134292
$576$		0			0
$577$	−504.599	+	504.599i	−0.874521	+	0.874521i	−0.992961	−	0.118440i	$-0.962211\pi$
$577$	−504.599	+	504.599i	−0.874521	+	0.874521i	0.118440	+	0.992961i	$0.462211\pi$
$578$	−178.510	+	178.510i	−0.308841	+	0.308841i
$579$		0			0
$580$	274.491	−	69.8592i	0.473260	−	0.120447i
$581$	1334.20			2.29638
$582$		0			0
$583$	−30.1897	−	30.1897i	−0.0517834	−	0.0517834i
$584$		−	45.7440i		−	0.0783288i
$585$		0			0
$586$		−	465.290i		−	0.794011i
$587$	−110.932			−0.188982			−0.0944911	−	0.995526i	$-0.530122\pi$
$587$	−110.932			−0.188982			−0.0944911	+	0.995526i	$0.530122\pi$
$588$		0			0
$589$		−	1094.47i		−	1.85819i
$590$	−342.516	+	342.516i	−0.580535	+	0.580535i
$591$		0			0
$592$	−50.3514	+	50.3514i	−0.0850530	+	0.0850530i
$593$		−	988.969i		−	1.66774i	−0.551962	−	0.833870i	$-0.686121\pi$
$593$		−	988.969i		−	1.66774i	0.551962	−	0.833870i	$-0.313879\pi$
$594$		0			0
$595$	274.748	−	274.748i	0.461761	−	0.461761i
$596$	330.678			0.554829
$597$		0			0
$598$	112.165	−	112.165i	0.187567	−	0.187567i
$599$	−262.125	−	262.125i	−0.437604	−	0.437604i	0.453601	−	0.891205i	$-0.350139\pi$
$599$	−262.125	−	262.125i	−0.437604	−	0.437604i	−0.891205	+	0.453601i	$0.850139\pi$
$600$		0			0
$601$	−496.848	−	496.848i	−0.826702	−	0.826702i	0.160357	−	0.987059i	$-0.448735\pi$
$601$	−496.848	−	496.848i	−0.826702	−	0.826702i	−0.987059	+	0.160357i	$0.948735\pi$
$602$		−	308.482i		−	0.512428i
$603$		0			0
$604$	631.119			1.04490
$605$	−502.967			−0.831351
$606$		0			0
$607$	−466.144	+	466.144i	−0.767947	+	0.767947i	−0.977745	−	0.209798i	$-0.932719\pi$
$607$	−466.144	+	466.144i	−0.767947	+	0.767947i	0.209798	+	0.977745i	$0.432719\pi$
$608$			647.390i			1.06479i
$609$		0			0
$610$	223.000			0.365574
$611$	−27.0241	−	27.0241i	−0.0442293	−	0.0442293i
$612$		0			0
$613$		−	581.681i		−	0.948908i	−0.880280	−	0.474454i	$-0.842645\pi$
$613$		−	581.681i		−	0.948908i	0.880280	−	0.474454i	$-0.157355\pi$
$614$			16.7432i			0.0272690i
$615$		0			0
$616$	37.4560			0.0608052
$617$	546.898	−	546.898i	0.886383	−	0.886383i	−0.107791	−	0.994174i	$-0.534378\pi$
$617$	546.898	−	546.898i	0.886383	−	0.886383i	0.994174	+	0.107791i	$0.0343777\pi$
$618$		0			0
$619$	−650.477	+	650.477i	−1.05085	+	1.05085i	−0.0522157	+	0.998636i	$0.516628\pi$
$619$	−650.477	+	650.477i	−1.05085	+	1.05085i	−0.998636	+	0.0522157i	$0.983372\pi$
$620$	364.404	+	364.404i	0.587748	+	0.587748i
$621$		0			0
$622$			171.167i			0.275188i
$623$	805.575	+	805.575i	1.29306	+	1.29306i
$624$		0			0
$625$	−374.939			−0.599903
$626$	−121.669	−	121.669i	−0.194359	−	0.194359i
$627$		0			0
$628$	193.881	+	193.881i	0.308728	+	0.308728i
$629$	613.173			0.974837
$630$		0			0
$631$		−	1020.55i		−	1.61735i	−0.588253	−	0.808677i	$-0.700184\pi$
$631$		−	1020.55i		−	1.61735i	0.588253	−	0.808677i	$-0.299816\pi$
$632$	465.327			0.736277
$633$		0			0
$634$	737.366			1.16304
$635$	217.475	−	217.475i	0.342480	−	0.342480i
$636$		0			0
$637$			548.558i			0.861159i
$638$	4.35807	+	17.1237i	0.00683083	+	0.0268397i
$639$		0			0
$640$	−198.603	−	198.603i	−0.310316	−	0.310316i
$641$	−65.0163	−	65.0163i	−0.101430	−	0.101430i	0.654571	−	0.756001i	$-0.272849\pi$
$641$	−65.0163	−	65.0163i	−0.101430	−	0.101430i	−0.756001	+	0.654571i	$0.772849\pi$
$642$		0			0
$643$			590.198i			0.917882i	0.888467	+	0.458941i	$0.151771\pi$
$643$			590.198i			0.917882i	−0.888467	+	0.458941i	$0.848229\pi$
$644$			229.134i			0.355799i
$645$		0			0
$646$	−181.701	+	181.701i	−0.281271	+	0.281271i
$647$		−	96.4448i		−	0.149065i	−0.997219	−	0.0745323i	$-0.976254\pi$
$647$		−	96.4448i		−	0.149065i	0.997219	−	0.0745323i	$-0.0237464\pi$
$648$		0			0
$649$	30.2851	+	30.2851i	0.0466642	+	0.0466642i
$650$	85.1674	−	85.1674i	0.131027	−	0.131027i
$651$		0			0
$652$	−37.9115	−	37.9115i	−0.0581465	−	0.0581465i
$653$	185.978	−	185.978i	0.284806	−	0.284806i	−0.550216	−	0.835022i	$-0.685455\pi$
$653$	185.978	−	185.978i	0.284806	−	0.284806i	0.835022	+	0.550216i	$0.185455\pi$
$654$		0			0
$655$	105.703	+	105.703i	0.161379	+	0.161379i
$656$	−25.5150	+	25.5150i	−0.0388949	+	0.0388949i
$657$		0			0
$658$	−38.9498			−0.0591943
$659$	−811.110	−	811.110i	−1.23082	−	1.23082i	−0.963649	−	0.267170i	$-0.913911\pi$
$659$	−811.110	−	811.110i	−1.23082	−	1.23082i	−0.267170	−	0.963649i	$-0.586089\pi$
$660$		0			0
$661$	442.227			0.669027			0.334513	−	0.942391i	$-0.391428\pi$
$661$	442.227			0.669027			0.334513	+	0.942391i	$0.391428\pi$
$662$	−336.744			−0.508676
$663$		0			0
$664$	794.833	−	794.833i	1.19704	−	1.19704i
$665$	−591.767	+	591.767i	−0.889876	+	0.889876i
$666$		0			0
$667$	−283.414	+	72.1302i	−0.424908	+	0.108141i
$668$	−315.509			−0.472318
$669$		0			0
$670$	119.526	+	119.526i	0.178398	+	0.178398i
$671$		−	19.7176i		−	0.0293854i
$672$		0			0
$673$		−	725.102i		−	1.07742i	−0.842492	−	0.538708i	$-0.818912\pi$
$673$		−	725.102i		−	1.07742i	0.842492	−	0.538708i	$-0.181088\pi$
$674$	130.621			0.193799
$675$		0			0
$676$		−	45.6673i		−	0.0675552i
$677$	−650.790	+	650.790i	−0.961285	+	0.961285i	−0.999278	−	0.0379933i	$-0.987903\pi$
$677$	−650.790	+	650.790i	−0.961285	+	0.961285i	0.0379933	+	0.999278i	$0.487903\pi$
$678$		0			0
$679$	774.907	−	774.907i	1.14125	−	1.14125i
$680$		−	327.356i		−	0.481406i
$681$		0			0
$682$	−22.7328	+	22.7328i	−0.0333325	+	0.0333325i
$683$	791.357			1.15865			0.579324	−	0.815097i	$-0.303317\pi$
$683$	791.357			1.15865			0.579324	+	0.815097i	$0.303317\pi$
$684$		0			0
$685$	487.988	−	487.988i	0.712392	−	0.712392i
$686$	−36.4808	−	36.4808i	−0.0531790	−	0.0531790i
$687$		0			0
$688$	−19.5751	−	19.5751i	−0.0284522	−	0.0284522i
$689$		−	1102.22i		−	1.59973i
$690$		0			0
$691$	646.166			0.935118			0.467559	−	0.883962i	$-0.345134\pi$
$691$	646.166			0.935118			0.467559	+	0.883962i	$0.345134\pi$
$692$	−220.870			−0.319176
$693$		0			0
$694$	−165.149	+	165.149i	−0.237967	+	0.237967i
$695$		−	259.399i		−	0.373235i
$696$		0			0
$697$	310.719			0.445795
$698$	−186.829	−	186.829i	−0.267663	−	0.267663i
$699$		0			0
$700$			173.983i			0.248547i
$701$		−	738.399i		−	1.05335i	−0.850066	−	0.526676i	$-0.823438\pi$
$701$		−	738.399i		−	1.05335i	0.850066	−	0.526676i	$-0.176562\pi$
$702$		0			0
$703$	−1320.69			−1.87864
$704$	14.9450	−	14.9450i	0.0212287	−	0.0212287i
$705$		0			0
$706$	−137.260	+	137.260i	−0.194420	+	0.194420i
$707$	−504.962	−	504.962i	−0.714231	−	0.714231i
$708$		0			0
$709$		−	211.506i		−	0.298316i	−0.988813	−	0.149158i	$-0.952344\pi$
$709$		−	211.506i		−	0.298316i	0.988813	−	0.149158i	$-0.0476564\pi$
$710$	378.293	+	378.293i	0.532807	+	0.532807i
$711$		0			0
$712$	959.825			1.34807
$713$	−376.249	−	376.249i	−0.527699	−	0.527699i
$714$		0			0
$715$	17.0559	+	17.0559i	0.0238544	+	0.0238544i
$716$	−130.608			−0.182413
$717$		0			0
$718$		−	666.730i		−	0.928593i
$719$	479.844			0.667376			0.333688	−	0.942684i	$-0.391707\pi$
$719$	479.844			0.667376			0.333688	+	0.942684i	$0.391707\pi$
$720$		0			0
$721$	−1350.31			−1.87283
$722$	62.9974	−	62.9974i	0.0872540	−	0.0872540i
$723$		0			0
$724$			309.294i			0.427202i
$725$	−215.197	+	54.7687i	−0.296824	+	0.0755431i
$726$		0			0
$727$	−943.499	−	943.499i	−1.29780	−	1.29780i	−0.929844	−	0.367953i	$-0.880059\pi$
$727$	−943.499	−	943.499i	−1.29780	−	1.29780i	−0.367953	−	0.929844i	$-0.619941\pi$
$728$	683.753	+	683.753i	0.939221	+	0.939221i
$729$		0			0
$730$		−	30.0222i		−	0.0411263i
$731$			238.384i			0.326106i
$732$		0			0
$733$	256.074	−	256.074i	0.349350	−	0.349350i	−0.510517	−	0.859868i	$-0.670546\pi$
$733$	256.074	−	256.074i	0.349350	−	0.349350i	0.859868	+	0.510517i	$0.170546\pi$
$734$			153.395i			0.208986i
$735$		0			0
$736$	222.555	+	222.555i	0.302385	+	0.302385i
$737$	10.5685	−	10.5685i	0.0143398	−	0.0143398i
$738$		0			0
$739$	9.12101	+	9.12101i	0.0123424	+	0.0123424i	0.713251	−	0.700909i	$-0.247222\pi$
$739$	9.12101	+	9.12101i	0.0123424	+	0.0123424i	−0.700909	+	0.713251i	$0.747222\pi$
$740$	439.722	−	439.722i	0.594219	−	0.594219i
$741$		0			0
$742$	−794.312	−	794.312i	−1.07050	−	1.07050i
$743$	343.894	−	343.894i	0.462845	−	0.462845i	−0.436742	−	0.899587i	$-0.643868\pi$
$743$	343.894	−	343.894i	0.462845	−	0.462845i	0.899587	+	0.436742i	$0.143868\pi$
$744$		0			0
$745$	587.175			0.788155
$746$	−83.1437	−	83.1437i	−0.111453	−	0.111453i
$747$		0			0
$748$	−10.6983			−0.0143025
$749$	−144.980			−0.193564
$750$		0			0
$751$	485.159	−	485.159i	0.646017	−	0.646017i	−0.306011	−	0.952028i	$-0.598994\pi$
$751$	485.159	−	485.159i	0.646017	−	0.646017i	0.952028	+	0.306011i	$0.0989945\pi$
$752$	−2.47162	+	2.47162i	−0.00328673	+	0.00328673i
$753$		0			0
$754$	−233.035	+	392.146i	−0.309065	+	0.520088i
$755$	1120.66			1.48432
$756$		0			0
$757$	−158.090	−	158.090i	−0.208838	−	0.208838i	0.594936	−	0.803773i	$-0.297178\pi$
$757$	−158.090	−	158.090i	−0.208838	−	0.208838i	−0.803773	+	0.594936i	$0.797178\pi$
$758$		−	323.852i		−	0.427246i
$759$		0			0
$760$			705.078i			0.927734i
$761$	−1412.54			−1.85617			−0.928084	−	0.372371i	$-0.878545\pi$
$761$	−1412.54			−1.85617			−0.928084	+	0.372371i	$0.878545\pi$
$762$		0			0
$763$			374.179i			0.490405i
$764$	−287.400	+	287.400i	−0.376179	+	0.376179i
$765$		0			0
$766$	−129.237	+	129.237i	−0.168716	+	0.168716i
$767$			1105.70i			1.44159i
$768$		0			0
$769$	−137.717	+	137.717i	−0.179086	+	0.179086i	−0.790957	−	0.611871i	$-0.790417\pi$
$769$	−137.717	+	137.717i	−0.179086	+	0.179086i	0.611871	+	0.790957i	$0.290417\pi$
$770$	24.5827			0.0319256
$771$		0			0
$772$	−412.675	+	412.675i	−0.534553	+	0.534553i
$773$	349.001	+	349.001i	0.451489	+	0.451489i	0.895848	−	0.444360i	$-0.146569\pi$
$773$	349.001	+	349.001i	0.451489	+	0.451489i	−0.444360	+	0.895848i	$0.646569\pi$
$774$		0			0
$775$	−285.688	−	285.688i	−0.368629	−	0.368629i
$776$		−	923.285i		−	1.18980i
$777$		0			0
$778$	−617.964			−0.794298
$779$	−669.244			−0.859107
$780$		0			0
$781$	33.4485	−	33.4485i	0.0428278	−	0.0428278i
$782$			124.928i			0.159754i
$783$		0			0
$784$	50.1710			0.0639936
$785$	344.269	+	344.269i	0.438560	+	0.438560i
$786$		0			0
$787$			880.918i			1.11934i	0.828717	+	0.559668i	$0.189071\pi$
$787$			880.918i			1.11934i	−0.828717	+	0.559668i	$0.810929\pi$
$788$			100.308i			0.127295i
$789$		0			0
$790$	305.398			0.386580
$791$	−196.374	+	196.374i	−0.248261	+	0.248261i
$792$		0			0
$793$	359.941	−	359.941i	0.453898	−	0.453898i
$794$	598.315	+	598.315i	0.753545	+	0.753545i
$795$		0			0
$796$			238.592i			0.299738i
$797$	−634.695	−	634.695i	−0.796356	−	0.796356i	0.186163	−	0.982519i	$-0.440395\pi$
$797$	−634.695	−	634.695i	−0.796356	−	0.796356i	−0.982519	+	0.186163i	$0.940395\pi$
$798$		0			0
$799$	30.0991			0.0376709
$800$	168.987	+	168.987i	0.211234	+	0.211234i
$801$		0			0
$802$	312.782	+	312.782i	0.390003	+	0.390003i
$803$	−2.65455			−0.00330579
$804$		0			0
$805$			406.867i			0.505425i
$806$	−829.967			−1.02974
$807$		0			0
$808$	−601.651			−0.744617
$809$	768.799	−	768.799i	0.950308	−	0.950308i	−0.0485143	−	0.998822i	$-0.515449\pi$
$809$	768.799	−	768.799i	0.950308	−	0.950308i	0.998822	+	0.0485143i	$0.0154486\pi$
$810$		0			0
$811$			615.818i			0.759332i	0.925124	+	0.379666i	$0.123961\pi$
$811$			615.818i			0.759332i	−0.925124	+	0.379666i	$0.876039\pi$
$812$	−162.519	−	638.570i	−0.200147	−	0.786416i
$813$		0			0
$814$	27.4314	+	27.4314i	0.0336995	+	0.0336995i
$815$	−67.3183	−	67.3183i	−0.0825991	−	0.0825991i
$816$		0			0
$817$		−	513.445i		−	0.628451i
$818$		−	399.605i		−	0.488514i
$819$		0			0
$820$	222.824	−	222.824i	0.271737	−	0.271737i
$821$			998.934i			1.21673i	0.793658	+	0.608364i	$0.208174\pi$
$821$			998.934i			1.21673i	−0.793658	+	0.608364i	$0.791826\pi$
$822$		0			0
$823$	−117.268	−	117.268i	−0.142489	−	0.142489i	0.632264	−	0.774753i	$-0.282126\pi$
$823$	−117.268	−	117.268i	−0.142489	−	0.142489i	−0.774753	+	0.632264i	$0.782126\pi$
$824$	−804.431	+	804.431i	−0.976251	+	0.976251i
$825$		0			0
$826$	796.822	+	796.822i	0.964675	+	0.964675i
$827$	−1079.32	+	1079.32i	−1.30510	+	1.30510i	−0.380195	+	0.924906i	$0.624143\pi$
$827$	−1079.32	+	1079.32i	−1.30510	+	1.30510i	−0.924906	+	0.380195i	$0.875857\pi$
$828$		0			0
$829$	671.650	+	671.650i	0.810192	+	0.810192i	0.984662	−	0.174470i	$-0.0558212\pi$
$829$	671.650	+	671.650i	0.810192	+	0.810192i	−0.174470	+	0.984662i	$0.555821\pi$
$830$	521.656	−	521.656i	0.628501	−	0.628501i
$831$		0			0
$832$	545.636			0.655813
$833$	−305.488	−	305.488i	−0.366732	−	0.366732i
$834$		0			0
$835$	−560.239			−0.670945
$836$	23.0426			0.0275629
$837$		0			0
$838$	−465.725	+	465.725i	−0.555758	+	0.555758i
$839$	100.846	−	100.846i	0.120197	−	0.120197i	−0.644449	−	0.764647i	$-0.722913\pi$
$839$	100.846	−	100.846i	0.120197	−	0.120197i	0.764647	+	0.644449i	$0.222913\pi$
$840$		0			0
$841$	738.680	−	402.036i	0.878335	−	0.478045i
$842$	776.262			0.921926
$843$		0			0
$844$	−197.111	−	197.111i	−0.233544	−	0.233544i
$845$		−	81.0901i		−	0.0959646i
$846$		0			0
$847$			1170.09i			1.38145i
$848$	−100.808			−0.118878
$849$		0			0
$850$			94.8582i			0.111598i
$851$	−454.016	+	454.016i	−0.533509	+	0.533509i
$852$		0			0
$853$	−922.579	+	922.579i	−1.08157	+	1.08157i	−0.0852066	+	0.996363i	$0.527155\pi$
$853$	−922.579	+	922.579i	−1.08157	+	1.08157i	−0.996363	+	0.0852066i	$0.972845\pi$
$854$		−	518.783i		−	0.607475i
$855$		0			0
$856$	−86.3700	+	86.3700i	−0.100900	+	0.100900i
$857$	633.774			0.739527			0.369763	−	0.929126i	$-0.379439\pi$
$857$	633.774			0.739527			0.369763	+	0.929126i	$0.379439\pi$
$858$		0			0
$859$	−834.541	+	834.541i	−0.971526	+	0.971526i	−0.999606	−	0.0280796i	$-0.991061\pi$
$859$	−834.541	+	834.541i	−0.971526	+	0.971526i	0.0280796	+	0.999606i	$0.491061\pi$
$860$	170.951	+	170.951i	0.198780	+	0.198780i
$861$		0			0
$862$	542.695	+	542.695i	0.629577	+	0.629577i
$863$			805.408i			0.933265i	0.884451	+	0.466632i	$0.154533\pi$
$863$			805.408i			0.933265i	−0.884451	+	0.466632i	$0.845467\pi$
$864$		0			0
$865$	−392.192			−0.453401
$866$	76.1756			0.0879626
$867$		0			0
$868$	847.741	−	847.741i	0.976660	−	0.976660i
$869$		−	27.0032i		−	0.0310739i
$870$		0			0
$871$	385.851			0.442998
$872$	222.913	+	222.913i	0.255634	+	0.255634i
$873$		0			0
$874$		−	269.077i		−	0.307868i
$875$			1317.59i			1.50581i
$876$		0			0
$877$	427.725			0.487714			0.243857	−	0.969811i	$-0.421587\pi$
$877$	427.725			0.487714			0.243857	+	0.969811i	$0.421587\pi$
$878$	−313.414	+	313.414i	−0.356964	+	0.356964i
$879$		0			0
$880$	1.55993	−	1.55993i	0.00177265	−	0.00177265i
$881$	977.952	+	977.952i	1.11005	+	1.11005i	0.993143	+	0.116905i	$0.0372972\pi$
$881$	977.952	+	977.952i	1.11005	+	1.11005i	0.116905	+	0.993143i	$0.462703\pi$
$882$		0			0
$883$		−	1215.83i		−	1.37693i	−0.725270	−	0.688464i	$-0.758285\pi$
$883$		−	1215.83i		−	1.37693i	0.725270	−	0.688464i	$-0.241715\pi$
$884$	−195.296	−	195.296i	−0.220923	−	0.220923i
$885$		0			0
$886$	−226.604			−0.255761
$887$	−1221.32	−	1221.32i	−1.37691	−	1.37691i	−0.849790	−	0.527122i	$-0.823271\pi$
$887$	−1221.32	−	1221.32i	−1.37691	−	1.37691i	−0.527122	−	0.849790i	$-0.676729\pi$
$888$		0			0
$889$	−505.929	−	505.929i	−0.569099	−	0.569099i
$890$	629.942			0.707800
$891$		0			0
$892$			717.990i			0.804922i
$893$	−64.8291			−0.0725970
$894$		0			0
$895$	−231.916			−0.259124
$896$	−462.025	+	462.025i	−0.515653	+	0.515653i
$897$		0			0
$898$		−	1024.02i		−	1.14034i
$899$	1315.43	+	781.698i	1.46321	+	0.869519i
$900$		0			0
$901$	613.816	+	613.816i	0.681261	+	0.681261i
$902$	13.9006	+	13.9006i	0.0154108	+	0.0154108i
$903$		0			0
$904$			233.976i			0.258823i
$905$			549.204i			0.606856i
$906$		0			0
$907$	−236.820	+	236.820i	−0.261103	+	0.261103i	−0.825502	−	0.564399i	$-0.809108\pi$
$907$	−236.820	+	236.820i	−0.261103	+	0.261103i	0.564399	+	0.825502i	$0.309108\pi$
$908$			46.4972i			0.0512083i
$909$		0			0
$910$	448.753	+	448.753i	0.493135	+	0.493135i
$911$	807.445	−	807.445i	0.886328	−	0.886328i	−0.107840	−	0.994168i	$-0.534394\pi$
$911$	807.445	−	807.445i	0.886328	−	0.886328i	0.994168	+	0.107840i	$0.0343936\pi$
$912$		0			0
$913$	−46.1246	−	46.1246i	−0.0505198	−	0.0505198i
$914$	343.040	−	343.040i	0.375317	−	0.375317i
$915$		0			0
$916$	−351.999	−	351.999i	−0.384278	−	0.384278i
$917$	245.905	−	245.905i	0.268163	−	0.268163i
$918$		0			0
$919$	−791.267			−0.861009			−0.430504	−	0.902589i	$-0.641664\pi$
$919$	−791.267			−0.861009			−0.430504	+	0.902589i	$0.641664\pi$
$920$	242.387	+	242.387i	0.263464	+	0.263464i
$921$		0			0
$922$	−72.9241			−0.0790934
$923$	1221.19			1.32307
$924$		0			0
$925$	−344.736	+	344.736i	−0.372688	+	0.372688i
$926$	−373.781	+	373.781i	−0.403651	+	0.403651i
$927$		0			0
$928$	−778.086	−	462.381i	−0.838455	−	0.498256i
$929$	−1491.46			−1.60545			−0.802724	−	0.596351i	$-0.796617\pi$
$929$	−1491.46			−1.60545			−0.802724	+	0.596351i	$0.796617\pi$
$930$		0			0
$931$	657.978	+	657.978i	0.706743	+	0.706743i
$932$			310.591i			0.333252i
$933$		0			0
$934$		−	776.881i		−	0.831778i
$935$	−18.9966			−0.0203173
$936$		0			0
$937$			910.587i			0.971811i	0.874011	+	0.485905i	$0.161510\pi$
$937$			910.587i			0.971811i	−0.874011	+	0.485905i	$0.838490\pi$
$938$	278.064	−	278.064i	0.296443	−	0.296443i
$939$		0			0
$940$	21.5848	−	21.5848i	0.0229626	−	0.0229626i
$941$		−	1302.28i		−	1.38393i	−0.721929	−	0.691967i	$-0.756744\pi$
$941$		−	1302.28i		−	1.38393i	0.721929	−	0.691967i	$-0.243256\pi$
$942$		0			0
$943$	−230.068	+	230.068i	−0.243974	+	0.243974i
$944$	101.127			0.107126
$945$		0			0
$946$	−10.6645	+	10.6645i	−0.0112733	+	0.0112733i
$947$	455.078	+	455.078i	0.480547	+	0.480547i	0.905306	−	0.424759i	$-0.139641\pi$
$947$	455.078	+	455.078i	0.480547	+	0.480547i	−0.424759	+	0.905306i	$0.639641\pi$
$948$		0			0
$949$	−48.4584	−	48.4584i	−0.0510626	−	0.0510626i
$950$		−	204.311i		−	0.215064i
$951$		0			0
$952$	−761.554			−0.799952
$953$	−299.880			−0.314670			−0.157335	−	0.987545i	$-0.550290\pi$
$953$	−299.880			−0.314670			−0.157335	+	0.987545i	$0.550290\pi$
$954$		0			0
$955$	−510.328	+	510.328i	−0.534375	+	0.534375i
$956$			414.391i			0.433463i
$957$		0			0
$958$	406.772			0.424606
$959$	−1135.25	−	1135.25i	−1.18378	−	1.18378i
$960$		0			0
$961$			1823.06i			1.89705i
$962$			1001.51i			1.04107i
$963$		0			0
$964$	377.617			0.391719
$965$	−732.775	+	732.775i	−0.759352	+	0.759352i
$966$		0			0
$967$	136.707	−	136.707i	0.141372	−	0.141372i	−0.632879	−	0.774251i	$-0.718127\pi$
$967$	136.707	−	136.707i	0.141372	−	0.141372i	0.774251	+	0.632879i	$0.218127\pi$
$968$	697.070	+	697.070i	0.720113	+	0.720113i
$969$		0			0
$970$		−	605.960i		−	0.624701i
$971$	−225.421	−	225.421i	−0.232153	−	0.232153i	0.581438	−	0.813591i	$-0.302490\pi$
$971$	−225.421	−	225.421i	−0.232153	−	0.232153i	−0.813591	+	0.581438i	$0.802490\pi$
$972$		0			0
$973$	−603.459			−0.620205
$974$	−361.115	−	361.115i	−0.370755	−	0.370755i
$975$		0			0
$976$	−32.9201	−	32.9201i	−0.0337297	−	0.0337297i
$977$	−119.816			−0.122637			−0.0613186	−	0.998118i	$-0.519531\pi$
$977$	−119.816			−0.122637			−0.0613186	+	0.998118i	$0.519531\pi$
$978$		0			0
$979$		−	55.6992i		−	0.0568939i
$980$	−438.147			−0.447088
$981$		0			0
$982$	−802.635			−0.817348
$983$	−727.465	+	727.465i	−0.740046	+	0.740046i	−0.972587	−	0.232540i	$-0.925296\pi$
$983$	−727.465	+	727.465i	−0.740046	+	0.740046i	0.232540	+	0.972587i	$0.425296\pi$
$984$		0			0
$985$			178.114i			0.180827i
$986$	−88.6081	−	348.159i	−0.0898662	−	0.353102i
$987$		0			0
$988$	420.639	+	420.639i	0.425748	+	0.425748i
$989$	−176.508	−	176.508i	−0.178471	−	0.178471i
$990$		0			0
$991$			76.7646i			0.0774617i	0.999250	+	0.0387309i	$0.0123315\pi$
$991$			76.7646i			0.0774617i	−0.999250	+	0.0387309i	$0.987669\pi$
$992$		−	1646.80i		−	1.66008i
$993$		0			0
$994$	880.053	−	880.053i	0.885365	−	0.885365i
$995$			423.660i			0.425789i
$996$		0			0
$997$	−352.075	−	352.075i	−0.353135	−	0.353135i	0.508140	−	0.861275i	$-0.330333\pi$
$997$	−352.075	−	352.075i	−0.353135	−	0.353135i	−0.861275	+	0.508140i	$0.830333\pi$
$998$	86.3627	−	86.3627i	0.0865358	−	0.0865358i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.f.a.244.2		8
3.2	odd	2		29.3.c.a.12.3	✓	8
12.11	even	2		464.3.l.c.273.2		8
29.17	odd	4	inner	261.3.f.a.46.2		8
87.17	even	4		29.3.c.a.17.3	yes	8
348.191	odd	4		464.3.l.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.3	✓	8	3.2	odd	2
29.3.c.a.17.3	yes	8	87.17	even	4
261.3.f.a.46.2		8	29.17	odd	4	inner
261.3.f.a.244.2		8	1.1	even	1	trivial
464.3.l.c.17.2		8	348.191	odd	4
464.3.l.c.273.2		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909588 - 0.909588i) q^{2} -2.34530i q^{4} -4.16447i q^{5} -9.68815 q^{7} +(-5.77161 + 5.77161i) q^{8} +O(q^{10})\)	\(q+(-0.909588 - 0.909588i) q^{2} -2.34530i q^{4} -4.16447i q^{5} -9.68815 q^{7} +(-5.77161 + 5.77161i) q^{8} +(-3.78796 + 3.78796i) q^{10} +(0.334930 + 0.334930i) q^{11} +12.2282i q^{13} +(8.81223 + 8.81223i) q^{14} +1.11839 q^{16} +(-6.80978 - 6.80978i) q^{17} +(14.6673 + 14.6673i) q^{19} -9.76693 q^{20} -0.609296i q^{22} +10.0844 q^{23} +7.65715 q^{25} +(11.1226 - 11.1226i) q^{26} +22.7216i q^{28} +(-28.1041 + 7.15263i) q^{29} +(-37.3099 - 37.3099i) q^{31} +(22.0692 + 22.0692i) q^{32} +12.3882i q^{34} +40.3460i q^{35} +(-45.0215 + 45.0215i) q^{37} -26.6824i q^{38} +(24.0357 + 24.0357i) q^{40} +(-22.8142 + 22.8142i) q^{41} +(-17.5030 - 17.5030i) q^{43} +(0.785510 - 0.785510i) q^{44} +(-9.17268 - 9.17268i) q^{46} +(-2.20999 + 2.20999i) q^{47} +44.8602 q^{49} +(-6.96485 - 6.96485i) q^{50} +28.6787 q^{52} -90.1375 q^{53} +(1.39481 - 1.39481i) q^{55} +(55.9162 - 55.9162i) q^{56} +(32.0691 + 19.0572i) q^{58} +90.4223 q^{59} +(-29.4354 - 29.4354i) q^{61} +67.8734i q^{62} -44.6213i q^{64} +50.9239 q^{65} -31.5543i q^{67} +(-15.9710 + 15.9710i) q^{68} +(36.6983 - 36.6983i) q^{70} -99.8673i q^{71} +(-3.96285 + 3.96285i) q^{73} +81.9020 q^{74} +(34.3992 - 34.3992i) q^{76} +(-3.24485 - 3.24485i) q^{77} +(-40.3117 - 40.3117i) q^{79} -4.65749i q^{80} +41.5030 q^{82} -137.714 q^{83} +(-28.3592 + 28.3592i) q^{85} +31.8411i q^{86} -3.86616 q^{88} +(-83.1506 - 83.1506i) q^{89} -118.468i q^{91} -23.6510i q^{92} +4.02036 q^{94} +(61.0816 - 61.0816i) q^{95} +(-79.9850 + 79.9850i) q^{97} +(-40.8043 - 40.8043i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{7} + 42 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^7 + 42 * q^8	\( 8 q - 2 q^{2} - 4 q^{7} + 42 q^{8} + 6 q^{10} + 6 q^{11} + 40 q^{14} - 32 q^{16} - 12 q^{17} - 16 q^{19} - 108 q^{20} + 104 q^{25} + 54 q^{26} - 128 q^{29} - 10 q^{31} + 106 q^{32} - 84 q^{37} + 226 q^{40} - 20 q^{41} - 190 q^{43} - 42 q^{44} + 12 q^{46} - 58 q^{47} - 72 q^{49} + 60 q^{50} - 144 q^{52} - 252 q^{53} - 74 q^{55} + 192 q^{56} + 326 q^{58} + 40 q^{59} - 208 q^{61} - 36 q^{65} + 296 q^{68} + 44 q^{70} - 188 q^{73} + 64 q^{74} + 592 q^{76} - 180 q^{77} - 382 q^{79} + 228 q^{82} - 280 q^{83} + 32 q^{85} + 20 q^{88} + 64 q^{89} - 460 q^{94} + 380 q^{95} - 44 q^{97} + 66 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^7 + 42 * q^8 + 6 * q^10 + 6 * q^11 + 40 * q^14 - 32 * q^16 - 12 * q^17 - 16 * q^19 - 108 * q^20 + 104 * q^25 + 54 * q^26 - 128 * q^29 - 10 * q^31 + 106 * q^32 - 84 * q^37 + 226 * q^40 - 20 * q^41 - 190 * q^43 - 42 * q^44 + 12 * q^46 - 58 * q^47 - 72 * q^49 + 60 * q^50 - 144 * q^52 - 252 * q^53 - 74 * q^55 + 192 * q^56 + 326 * q^58 + 40 * q^59 - 208 * q^61 - 36 * q^65 + 296 * q^68 + 44 * q^70 - 188 * q^73 + 64 * q^74 + 592 * q^76 - 180 * q^77 - 382 * q^79 + 228 * q^82 - 280 * q^83 + 32 * q^85 + 20 * q^88 + 64 * q^89 - 460 * q^94 + 380 * q^95 - 44 * q^97 + 66 * q^98

Introduction

L-functions

Modular forms

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