LMFDB - Embedded newform 25.3.f.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

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

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

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, 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:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	25.3
Dual form			25.3.f.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395527 - 0.776265i) q^{2} +(-0.296456 - 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(1.22928 + 4.84653i) q^{5} +(-1.33572 + 0.970456i) q^{6} +(-5.60844 + 5.60844i) q^{7} +(-6.23083 - 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +O(q^{10})$	\(q+(-0.395527 - 0.776265i) q^{2} +(-0.296456 - 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(1.22928 + 4.84653i) q^{5} +(-1.33572 + 0.970456i) q^{6} +(-5.60844 + 5.60844i) q^{7} +(-6.23083 - 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +(3.27598 - 2.87118i) q^{10} +(-4.46912 + 13.7545i) q^{11} +(-5.47248 - 2.78837i) q^{12} +(5.52703 - 10.8474i) q^{13} +(6.57192 + 2.13535i) q^{14} +(8.70708 - 3.73769i) q^{15} +(-2.30767 - 7.10228i) q^{16} +(0.147755 - 0.932886i) q^{17} +(-3.33199 - 3.33199i) q^{18} +(-11.5466 - 15.8926i) q^{19} +(15.0494 + 6.00945i) q^{20} +(12.1603 + 8.83494i) q^{21} +(12.4448 - 1.97107i) q^{22} +(-4.69757 + 2.39353i) q^{23} +11.9551i q^{24} +(-21.9777 + 11.9155i) q^{25} -10.6066 q^{26} +(-12.3965 - 24.3295i) q^{27} +(4.02128 + 25.3894i) q^{28} +(-7.87983 + 10.8457i) q^{29} +(-6.34532 - 5.28064i) q^{30} +(12.1549 - 8.83105i) q^{31} +(-22.4436 + 22.4436i) q^{32} +(27.0700 + 4.28747i) q^{33} +(-0.782608 + 0.254285i) q^{34} +(-34.0758 - 20.2871i) q^{35} +(5.41686 - 16.6714i) q^{36} +(57.7042 + 29.4017i) q^{37} +(-7.76985 + 15.2492i) q^{38} +(-21.9422 - 7.12944i) q^{39} +(-2.87655 - 31.4110i) q^{40} +(-16.7764 - 51.6323i) q^{41} +(2.04855 - 12.9340i) q^{42} +(3.47098 + 3.47098i) q^{43} +(27.5508 + 37.9204i) q^{44} +(14.4237 + 22.8757i) q^{45} +(3.71603 + 2.69985i) q^{46} +(65.5638 - 10.3843i) q^{47} +(-12.6096 + 6.42490i) q^{48} -13.9091i q^{49} +(17.9424 + 12.3477i) q^{50} -1.78993 q^{51} +(-17.9129 - 35.1561i) q^{52} +(-6.61077 - 41.7387i) q^{53} +(-13.9830 + 19.2459i) q^{54} +(-72.1557 - 4.75157i) q^{55} +(40.4800 - 29.4104i) q^{56} +(-26.3239 + 26.3239i) q^{57} +(11.5358 + 1.82709i) q^{58} +(-35.6563 + 11.5854i) q^{59} +(6.78671 - 29.9502i) q^{60} +(-32.4776 + 99.9557i) q^{61} +(-11.6628 - 5.94250i) q^{62} +(-19.4757 + 38.2232i) q^{63} +(-2.10987 - 0.685539i) q^{64} +(59.3666 + 13.4524i) q^{65} +(-7.37870 - 22.7093i) q^{66} +(-7.05644 + 44.5526i) q^{67} +(-2.16456 - 2.16456i) q^{68} +(5.87272 + 8.08310i) q^{69} +(-2.27030 + 34.4760i) q^{70} +(36.5810 + 26.5777i) q^{71} +(-33.7004 + 5.33762i) q^{72} +(47.8210 - 24.3660i) q^{73} -56.4229i q^{74} +(28.8183 + 37.6045i) q^{75} -63.6667 q^{76} +(-52.0767 - 102.206i) q^{77} +(3.14438 + 19.8528i) q^{78} +(70.5878 - 97.1558i) q^{79} +(31.5847 - 19.9149i) q^{80} +(-2.48243 + 1.80359i) q^{81} +(-33.4449 + 33.4449i) q^{82} +(-60.5919 - 9.59682i) q^{83} +(46.3305 - 15.0537i) q^{84} +(4.70289 - 0.430680i) q^{85} +(1.32153 - 4.06726i) q^{86} +(22.6364 + 11.5338i) q^{87} +(41.4202 - 81.2918i) q^{88} +(48.8275 + 15.8650i) q^{89} +(12.0527 - 20.2445i) q^{90} +(29.8390 + 91.8350i) q^{91} +(-2.67300 + 16.8767i) q^{92} +(-20.1329 - 20.1329i) q^{93} +(-33.9932 - 46.7876i) q^{94} +(62.8299 - 75.4976i) q^{95} +(48.6625 + 35.3553i) q^{96} +(-36.3164 + 5.75195i) q^{97} +(-10.7972 + 5.50143i) q^{98} +78.2221i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.395527	−	0.776265i	−0.197763	−	0.388132i	0.770734	−	0.637157i	$-0.219890\pi$
$2$	−0.395527	−	0.776265i	−0.197763	−	0.388132i	−0.968497	+	0.249025i	$0.919890\pi$
$3$	−0.296456	−	1.87175i	−0.0988188	−	0.623917i	−0.986538	−	0.163532i	$-0.947711\pi$
$3$	−0.296456	−	1.87175i	−0.0988188	−	0.623917i	0.887719	−	0.460385i	$-0.152289\pi$
$4$	1.90500	−	2.62200i	0.476249	−	0.655500i
$5$	1.22928	+	4.84653i	0.245856	+	0.969306i
$5$	1.22928	+	4.84653i	0.245856	+	0.969306i
$6$	−1.33572	+	0.970456i	−0.222620	+	0.161743i
$7$	−5.60844	+	5.60844i	−0.801205	+	0.801205i	−0.983284	−	0.182079i	$-0.941717\pi$
$7$	−5.60844	+	5.60844i	−0.801205	+	0.801205i	0.182079	+	0.983284i	$0.441717\pi$
$8$	−6.23083	−	0.986866i	−0.778854	−	0.123358i
$9$	5.14394	−	1.67137i	0.571549	−	0.185708i
$10$	3.27598	−	2.87118i	0.327598	−	0.287118i
$11$	−4.46912	+	13.7545i	−0.406284	+	1.25041i	0.513534	+	0.858069i	$0.328336\pi$
$11$	−4.46912	+	13.7545i	−0.406284	+	1.25041i	−0.919818	+	0.392345i	$0.871664\pi$
$12$	−5.47248	−	2.78837i	−0.456040	−	0.232364i
$13$	5.52703	−	10.8474i	0.425156	−	0.834416i	−0.574715	−	0.818354i	$-0.694887\pi$
$13$	5.52703	−	10.8474i	0.425156	−	0.834416i	0.999871	−	0.0160623i	$-0.00511299\pi$
$14$	6.57192	+	2.13535i	0.469423	+	0.152525i
$15$	8.70708	−	3.73769i	0.580472	−	0.249179i
$16$	−2.30767	−	7.10228i	−0.144229	−	0.443893i
$17$	0.147755	−	0.932886i	0.00869145	−	0.0548757i	−0.982961	−	0.183812i	$-0.941156\pi$
$17$	0.147755	−	0.932886i	0.00869145	−	0.0548757i	0.991653	+	0.128936i	$0.0411563\pi$
$18$	−3.33199	−	3.33199i	−0.185111	−	0.185111i
$19$	−11.5466	−	15.8926i	−0.607718	−	0.836452i	0.388669	−	0.921377i	$-0.372935\pi$
$19$	−11.5466	−	15.8926i	−0.607718	−	0.836452i	−0.996387	+	0.0849253i	$0.972935\pi$
$20$	15.0494	+	6.00945i	0.752469	+	0.300472i
$21$	12.1603	+	8.83494i	0.579060	+	0.420712i
$22$	12.4448	−	1.97107i	0.565674	−	0.0895940i
$23$	−4.69757	+	2.39353i	−0.204242	+	0.104067i	−0.553120	−	0.833102i	$-0.686563\pi$
$23$	−4.69757	+	2.39353i	−0.204242	+	0.104067i	0.348878	+	0.937168i	$0.386563\pi$
$24$			11.9551i			0.498130i
$25$	−21.9777	+	11.9155i	−0.879110	+	0.476619i
$26$	−10.6066			−0.407944
$27$	−12.3965	−	24.3295i	−0.459129	−	0.901092i
$28$	4.02128	+	25.3894i	0.143617	+	0.906763i
$29$	−7.87983	+	10.8457i	−0.271718	+	0.373988i	−0.922969	−	0.384875i	$-0.874245\pi$
$29$	−7.87983	+	10.8457i	−0.271718	+	0.373988i	0.651251	+	0.758863i	$0.274245\pi$
$30$	−6.34532	−	5.28064i	−0.211511	−	0.176021i
$31$	12.1549	−	8.83105i	0.392093	−	0.284873i	−0.374219	−	0.927340i	$-0.622089\pi$
$31$	12.1549	−	8.83105i	0.392093	−	0.284873i	0.766313	+	0.642468i	$0.222089\pi$
$32$	−22.4436	+	22.4436i	−0.701363	+	0.701363i
$33$	27.0700	+	4.28747i	0.820303	+	0.129923i
$34$	−0.782608	+	0.254285i	−0.0230179	+	0.00747896i
$35$	−34.0758	−	20.2871i	−0.973594	−	0.579632i
$36$	5.41686	−	16.6714i	0.150468	−	0.463094i
$37$	57.7042	+	29.4017i	1.55957	+	0.794642i	0.999430	−	0.0337547i	$-0.0107465\pi$
$37$	57.7042	+	29.4017i	1.55957	+	0.794642i	0.560142	+	0.828396i	$0.310746\pi$
$38$	−7.76985	+	15.2492i	−0.204470	+	0.401295i
$39$	−21.9422	−	7.12944i	−0.562620	−	0.182806i
$40$	−2.87655	−	31.4110i	−0.0719137	−	0.785276i
$41$	−16.7764	−	51.6323i	−0.409180	−	1.25933i	−0.917355	−	0.398071i	$-0.869680\pi$
$41$	−16.7764	−	51.6323i	−0.409180	−	1.25933i	0.508175	−	0.861254i	$-0.330320\pi$
$42$	2.04855	−	12.9340i	0.0487750	−	0.307953i
$43$	3.47098	+	3.47098i	0.0807204	+	0.0807204i	0.746314	−	0.665594i	$-0.231822\pi$
$43$	3.47098	+	3.47098i	0.0807204	+	0.0807204i	−0.665594	+	0.746314i	$0.731822\pi$
$44$	27.5508	+	37.9204i	0.626154	+	0.861827i
$45$	14.4237	+	22.8757i	0.320526	+	0.508349i
$46$	3.71603	+	2.69985i	0.0807832	+	0.0586924i
$47$	65.5638	−	10.3843i	1.39498	−	0.220942i	0.586727	−	0.809785i	$-0.300416\pi$
$47$	65.5638	−	10.3843i	1.39498	−	0.220942i	0.808248	+	0.588842i	$0.200416\pi$
$48$	−12.6096	+	6.42490i	−0.262700	+	0.133852i
$49$		−	13.9091i		−	0.283860i
$50$	17.9424	+	12.3477i	0.358847	+	0.246953i
$51$	−1.78993			−0.0350967
$52$	−17.9129	−	35.1561i	−0.344480	−	0.676080i
$53$	−6.61077	−	41.7387i	−0.124731	−	0.787523i	−0.968169	−	0.250296i	$-0.919472\pi$
$53$	−6.61077	−	41.7387i	−0.124731	−	0.787523i	0.843438	−	0.537227i	$-0.180528\pi$
$54$	−13.9830	+	19.2459i	−0.258944	+	0.356406i
$55$	−72.1557	−	4.75157i	−1.31192	−	0.0863923i
$56$	40.4800	−	29.4104i	0.722857	−	0.525186i
$57$	−26.3239	+	26.3239i	−0.461823	+	0.461823i
$58$	11.5358	+	1.82709i	0.198893	+	0.0315015i
$59$	−35.6563	+	11.5854i	−0.604345	+	0.196363i	−0.595177	−	0.803595i	$-0.702918\pi$
$59$	−35.6563	+	11.5854i	−0.604345	+	0.196363i	−0.00916740	+	0.999958i	$0.502918\pi$
$60$	6.78671	−	29.9502i	0.113112	−	0.499171i
$61$	−32.4776	+	99.9557i	−0.532419	+	1.63862i	0.216742	+	0.976229i	$0.430457\pi$
$61$	−32.4776	+	99.9557i	−0.532419	+	1.63862i	−0.749161	+	0.662388i	$0.769543\pi$
$62$	−11.6628	−	5.94250i	−0.188110	−	0.0958468i
$63$	−19.4757	+	38.2232i	−0.309138	+	0.606718i
$64$	−2.10987	−	0.685539i	−0.0329668	−	0.0107116i
$65$	59.3666	+	13.4524i	0.913332	+	0.206961i
$66$	−7.37870	−	22.7093i	−0.111798	−	0.344080i
$67$	−7.05644	+	44.5526i	−0.105320	+	0.664965i	0.877385	+	0.479787i	$0.159286\pi$
$67$	−7.05644	+	44.5526i	−0.105320	+	0.664965i	−0.982705	+	0.185178i	$0.940714\pi$
$68$	−2.16456	−	2.16456i	−0.0318317	−	0.0318317i
$69$	5.87272	+	8.08310i	0.0851118	+	0.117146i
$70$	−2.27030	+	34.4760i	−0.0324329	+	0.492514i
$71$	36.5810	+	26.5777i	0.515226	+	0.374333i	0.814802	−	0.579739i	$-0.196845\pi$
$71$	36.5810	+	26.5777i	0.515226	+	0.374333i	−0.299577	+	0.954072i	$0.596845\pi$
$72$	−33.7004	+	5.33762i	−0.468062	+	0.0741337i
$73$	47.8210	−	24.3660i	0.655082	−	0.333781i	−0.0946613	−	0.995510i	$-0.530177\pi$
$73$	47.8210	−	24.3660i	0.655082	−	0.333781i	0.749744	+	0.661728i	$0.230177\pi$
$74$		−	56.4229i		−	0.762472i
$75$	28.8183	+	37.6045i	0.384243	+	0.501393i
$76$	−63.6667			−0.837719
$77$	−52.0767	−	102.206i	−0.676321	−	1.32735i
$78$	3.14438	+	19.8528i	0.0403125	+	0.254523i
$79$	70.5878	−	97.1558i	0.893516	−	1.22982i	−0.0789740	−	0.996877i	$-0.525164\pi$
$79$	70.5878	−	97.1558i	0.893516	−	1.22982i	0.972490	−	0.232943i	$-0.0748356\pi$
$80$	31.5847	−	19.9149i	0.394808	−	0.248936i
$81$	−2.48243	+	1.80359i	−0.0306472	+	0.0222665i
$82$	−33.4449	+	33.4449i	−0.407864	+	0.407864i
$83$	−60.5919	−	9.59682i	−0.730023	−	0.115624i	−0.219652	−	0.975578i	$-0.570492\pi$
$83$	−60.5919	−	9.59682i	−0.730023	−	0.115624i	−0.510371	+	0.859954i	$0.670492\pi$
$84$	46.3305	−	15.0537i	0.551553	−	0.179210i
$85$	4.70289	−	0.430680i	0.0553282	−	0.00506682i
$86$	1.32153	−	4.06726i	0.0153667	−	0.0472937i
$87$	22.6364	+	11.5338i	0.260189	+	0.132573i
$88$	41.4202	−	81.2918i	0.470685	−	0.923771i
$89$	48.8275	+	15.8650i	0.548623	+	0.178258i	0.570196	−	0.821509i	$-0.306867\pi$
$89$	48.8275	+	15.8650i	0.548623	+	0.178258i	−0.0215727	+	0.999767i	$0.506867\pi$
$90$	12.0527	−	20.2445i	0.133918	−	0.224939i
$91$	29.8390	+	91.8350i	0.327901	+	1.00918i
$92$	−2.67300	+	16.8767i	−0.0290544	+	0.183442i
$93$	−20.1329	−	20.1329i	−0.216483	−	0.216483i
$94$	−33.9932	−	46.7876i	−0.361630	−	0.497741i
$95$	62.8299	−	75.4976i	0.661367	−	0.794711i
$96$	48.6625	+	35.3553i	0.506901	+	0.368285i
$97$	−36.3164	+	5.75195i	−0.374395	+	0.0592984i	−0.340797	−	0.940137i	$-0.610697\pi$
$97$	−36.3164	+	5.75195i	−0.374395	+	0.0592984i	−0.0335987	+	0.999435i	$0.510697\pi$
$98$	−10.7972	+	5.50143i	−0.110175	+	0.0561371i
$99$			78.2221i			0.790123i
$100$	−10.6251	+	80.3246i	−0.106251	+	0.803246i
$101$	−76.5209			−0.757632			−0.378816	−	0.925472i	$-0.623669\pi$
$101$	−76.5209			−0.757632			−0.378816	+	0.925472i	$0.623669\pi$
$102$	0.707967	+	1.38946i	0.00694085	+	0.0136222i
$103$	−11.9943	−	75.7288i	−0.116449	−	0.735231i	−0.974951	−	0.222420i	$-0.928604\pi$
$103$	−11.9943	−	75.7288i	−0.116449	−	0.735231i	0.858502	−	0.512811i	$-0.171396\pi$
$104$	−45.1429	+	62.1339i	−0.434067	+	0.597441i
$105$	−27.8705	+	69.7957i	−0.265433	+	0.664721i
$106$	−29.7856	+	21.6405i	−0.280996	+	0.204156i
$107$	−36.9784	+	36.9784i	−0.345593	+	0.345593i	−0.858465	−	0.512872i	$-0.828581\pi$
$107$	−36.9784	+	36.9784i	−0.345593	+	0.345593i	0.512872	+	0.858465i	$0.328581\pi$
$108$	−87.4072	−	13.8439i	−0.809325	−	0.128185i
$109$	−27.6176	+	8.97352i	−0.253373	+	0.0823258i	−0.432950	−	0.901418i	$-0.642527\pi$
$109$	−27.6176	+	8.97352i	−0.253373	+	0.0823258i	0.179577	+	0.983744i	$0.442527\pi$
$110$	24.8510	+	57.8913i	0.225918	+	0.526284i
$111$	37.9260	−	116.724i	0.341676	−	1.05157i
$112$	52.7751	+	26.8903i	0.471207	+	0.240092i
$113$	1.56513	−	3.07175i	0.0138507	−	0.0271836i	−0.883977	−	0.467529i	$-0.845144\pi$
$113$	1.56513	−	3.07175i	0.0138507	−	0.0271836i	0.897828	+	0.440346i	$0.145144\pi$
$114$	30.8461	+	10.0225i	0.270580	+	0.0879168i
$115$	−17.3749	−	19.8246i	−0.151086	−	0.172388i
$116$	13.4263	+	41.3219i	0.115744	+	0.356223i
$117$	10.3007	−	65.0361i	0.0880403	−	0.555864i
$118$	23.0964	+	23.0964i	0.195732	+	0.195732i
$119$	4.40336	+	6.06071i	0.0370030	+	0.0509303i
$120$	−57.9409	+	14.6962i	−0.482841	+	0.122468i
$121$	−71.3235	−	51.8196i	−0.589450	−	0.428261i
$122$	90.4378	−	14.3239i	0.741293	−	0.117409i
$123$	−91.6694	+	46.7079i	−0.745280	+	0.379739i
$124$		−	48.6933i		−	0.392688i
$125$	−84.7655	−	91.8684i	−0.678124	−	0.734947i
$126$	37.3745			0.296623
$127$	72.0197	+	141.347i	0.567084	+	1.11297i	0.979401	+	0.201925i	$0.0647197\pi$
$127$	72.0197	+	141.347i	0.567084	+	1.11297i	−0.412317	+	0.911041i	$0.635280\pi$
$128$	20.1633	+	127.306i	0.157526	+	0.994580i
$129$	5.46781	−	7.52580i	0.0423862	−	0.0583395i
$130$	−13.0384	−	51.4050i	−0.100295	−	0.395423i
$131$	94.7333	−	68.8278i	0.723155	−	0.525403i	−0.164236	−	0.986421i	$-0.552516\pi$
$131$	94.7333	−	68.8278i	0.723155	−	0.525403i	0.887391	+	0.461018i	$0.152516\pi$
$132$	62.8100	−	62.8100i	0.475833	−	0.475833i
$133$	153.891	+	24.3740i	1.15708	+	0.183263i
$134$	37.3757	−	12.1441i	0.278923	−	0.0906275i
$135$	102.675	−	89.9877i	0.760554	−	0.666575i
$136$	−1.84127	+	5.66684i	−0.0135387	+	0.0416679i
$137$	−161.447	−	82.2613i	−1.17844	−	0.600448i	−0.248674	−	0.968587i	$-0.579995\pi$
$137$	−161.447	−	82.2613i	−1.17844	−	0.600448i	−0.929771	+	0.368139i	$0.879995\pi$
$138$	3.95181	−	7.75587i	0.0286363	−	0.0562019i
$139$	−66.3122	−	21.5461i	−0.477066	−	0.155008i	0.0606066	−	0.998162i	$-0.480696\pi$
$139$	−66.3122	−	21.5461i	−0.477066	−	0.155008i	−0.537673	+	0.843153i	$0.680696\pi$
$140$	−118.107	+	50.6999i	−0.843622	+	0.362142i
$141$	−38.8736	−	119.641i	−0.275699	−	0.848516i
$142$	6.16254	−	38.9088i	0.0433982	−	0.274005i
$143$	124.500	+	124.500i	0.870631	+	0.870631i
$144$	−23.7411	−	32.6768i	−0.164868	−	0.226922i
$145$	−62.2503	−	24.8575i	−0.429313	−	0.171431i
$146$	−37.8290	−	27.4844i	−0.259103	−	0.188249i
$147$	−26.0344	+	4.12345i	−0.177105	+	0.0280507i
$148$	187.018	−	95.2902i	1.26363	−	0.643853i
$149$			161.305i			1.08259i	0.840834	+	0.541293i	$0.182065\pi$
$149$			161.305i			1.08259i	−0.840834	+	0.541293i	$0.817935\pi$
$150$	17.7926	−	37.2442i	0.118618	−	0.248294i
$151$	133.490			0.884041			0.442020	−	0.897005i	$-0.354262\pi$
$151$	133.490			0.884041			0.442020	+	0.897005i	$0.354262\pi$
$152$	56.2613	+	110.419i	0.370140	+	0.726441i
$153$	−0.799155	−	5.04566i	−0.00522323	−	0.0329782i
$154$	−58.7414	+	80.8507i	−0.381438	+	0.525004i
$155$	57.7417	+	48.0533i	0.372527	+	0.310021i
$156$	−60.4931	+	43.9508i	−0.387777	+	0.281736i
$157$	148.102	−	148.102i	0.943325	−	0.943325i	−0.0551526	−	0.998478i	$-0.517565\pi$
$157$	148.102	−	148.102i	0.943325	−	0.943325i	0.998478	+	0.0551526i	$0.0175645\pi$
$158$	−103.338	−	16.3671i	−0.654038	−	0.103589i
$159$	−76.1647	+	24.7474i	−0.479023	+	0.155644i
$160$	−136.363	−	81.1843i	−0.852270	−	0.507402i
$161$	12.9220	−	39.7700i	0.0802612	−	0.247018i
$162$	2.38193	+	1.21365i	0.0147033	+	0.00749169i
$163$	−139.677	+	274.131i	−0.856914	+	1.68179i	−0.133855	+	0.991001i	$0.542736\pi$
$163$	−139.677	+	274.131i	−0.856914	+	1.68179i	−0.723058	+	0.690787i	$0.757264\pi$
$164$	−167.339	−	54.3717i	−1.02036	−	0.331535i
$165$	12.4972	+	136.466i	0.0757408	+	0.827067i
$166$	16.5160	+	50.8312i	0.0994943	+	0.306212i
$167$	0.0999015	−	0.630753i	0.000598213	−	0.00377697i	−0.987387	−	0.158323i	$-0.949391\pi$
$167$	0.0999015	−	0.630753i	0.000598213	−	0.00377697i	0.987986	+	0.154546i	$0.0493914\pi$
$168$	−67.0496	−	67.0496i	−0.399105	−	0.399105i
$169$	12.2175	+	16.8160i	0.0722929	+	0.0995027i
$170$	−2.19444	−	3.48035i	−0.0129085	−	0.0204726i
$171$	−85.9576	−	62.4519i	−0.502676	−	0.365216i
$172$	15.7131	−	2.48871i	0.0913552	−	0.0144692i
$173$	−121.206	+	61.7573i	−0.700610	+	0.356979i	−0.767736	−	0.640766i	$-0.778617\pi$
$173$	−121.206	+	61.7573i	−0.700610	+	0.356979i	0.0671264	+	0.997744i	$0.478617\pi$
$174$		−	22.1338i		−	0.127206i
$175$	56.4336	−	190.088i	0.322478	−	1.08622i
$176$	108.002			0.613648
$177$	32.2556	+	63.3052i	0.182235	+	0.357657i
$178$	−6.99712	−	44.1781i	−0.0393097	−	0.248191i
$179$	−25.0966	+	34.5426i	−0.140205	+	0.192975i	−0.873345	−	0.487102i	$-0.838054\pi$
$179$	−25.0966	+	34.5426i	−0.140205	+	0.192975i	0.733140	+	0.680078i	$0.238054\pi$
$180$	87.4571	+	5.75920i	0.485873	+	0.0319956i
$181$	−146.810	+	106.664i	−0.811107	+	0.589304i	−0.914151	−	0.405373i	$-0.867142\pi$
$181$	−146.810	+	106.664i	−0.811107	+	0.589304i	0.103044	+	0.994677i	$0.467142\pi$
$182$	59.4862	−	59.4862i	0.326847	−	0.326847i
$183$	196.720	+	31.1574i	1.07497	+	0.170259i
$184$	31.6318	−	10.2778i	0.171912	−	0.0558576i
$185$	−71.5620	+	315.808i	−0.386822	+	1.70707i
$186$	−7.66537	+	23.5916i	−0.0412117	+	0.126837i
$187$	12.1711	+	6.20148i	0.0650861	+	0.0331630i
$188$	97.6712	−	191.690i	0.519528	−	1.01963i
$189$	205.975	+	66.9254i	1.08982	+	0.354103i
$190$	−83.4570	−	18.9113i	−0.439248	−	0.0995333i
$191$	17.3757	+	53.4768i	0.0909721	+	0.279983i	0.986183	−	0.165659i	$-0.0529752\pi$
$191$	17.3757	+	53.4768i	0.0909721	+	0.279983i	−0.895211	+	0.445643i	$0.852975\pi$
$192$	−0.657674	+	4.15239i	−0.00342539	+	0.0216270i
$193$	−148.900	−	148.900i	−0.771503	−	0.771503i	0.206867	−	0.978369i	$-0.433673\pi$
$193$	−148.900	−	148.900i	−0.771503	−	0.771503i	−0.978369	+	0.206867i	$0.933673\pi$
$194$	18.8291	+	25.9161i	0.0970573	+	0.133588i
$195$	7.58003	−	115.108i	0.0388719	−	0.590295i
$196$	−36.4698	−	26.4968i	−0.186070	−	0.135188i
$197$	−277.234	+	43.9096i	−1.40728	+	0.222891i	−0.813420	−	0.581677i	$-0.802397\pi$
$197$	−277.234	+	43.9096i	−1.40728	+	0.222891i	−0.593860	+	0.804568i	$0.702397\pi$
$198$	60.7211	−	30.9389i	0.306672	−	0.156257i
$199$		−	122.456i		−	0.615359i	−0.951490	−	0.307679i	$-0.900448\pi$
$199$		−	122.456i		−	0.615359i	0.951490	−	0.307679i	$-0.0995524\pi$
$200$	148.699	−	52.5542i	0.743493	−	0.262771i
$201$	85.4834			0.425290
$202$	30.2660	+	59.4005i	0.149832	+	0.294062i
$203$	−16.6336	−	105.021i	−0.0819392	−	0.517343i
$204$	−3.40982	+	4.69321i	−0.0167148	+	0.0230059i
$205$	229.615	−	144.778i	1.12007	−	0.706233i
$206$	−54.0415	+	39.2635i	−0.262338	+	0.190599i
$207$	−20.1635	+	20.1635i	−0.0974084	+	0.0974084i
$208$	−89.7959	−	14.2223i	−0.431711	−	0.0683763i
$209$	270.199	−	87.7929i	1.29282	−	0.420062i
$210$	65.2035	−	5.97117i	0.310493	−	0.0284342i
$211$	57.5357	−	177.077i	0.272681	−	0.839227i	−0.717142	−	0.696927i	$-0.754550\pi$
$211$	57.5357	−	177.077i	0.272681	−	0.839227i	0.989824	−	0.142300i	$-0.0454497\pi$
$212$	−122.032	−	62.1786i	−0.575625	−	0.293296i
$213$	38.9021	−	76.3497i	0.182639	−	0.358449i
$214$	43.3310	+	14.0791i	0.202481	+	0.0657902i
$215$	−12.5554	+	21.0890i	−0.0583972	+	0.0980884i
$216$	53.2304	+	163.826i	0.246437	+	0.758456i
$217$	−18.6416	+	117.698i	−0.0859059	+	0.542389i
$218$	17.8893	+	17.8893i	0.0820612	+	0.0820612i
$219$	−59.7840	−	82.2856i	−0.272986	−	0.375733i
$220$	−149.915	+	180.140i	−0.681431	+	0.818820i
$221$	−9.30275	−	6.75885i	−0.0420939	−	0.0305830i
$222$	−105.610	+	16.7269i	−0.475719	+	0.0753465i
$223$	−166.115	+	84.6396i	−0.744908	+	0.379550i	−0.784877	−	0.619651i	$-0.787274\pi$
$223$	−166.115	+	84.6396i	−0.744908	+	0.379550i	0.0399691	+	0.999201i	$0.487274\pi$
$224$		−	251.747i		−	1.12387i
$225$	−93.1371	+	98.0254i	−0.413943	+	0.435669i
$226$	−3.00354			−0.0132900
$227$	38.6087	+	75.7738i	0.170082	+	0.333805i	0.960276	−	0.279052i	$-0.0900202\pi$
$227$	38.6087	+	75.7738i	0.170082	+	0.333805i	−0.790194	+	0.612857i	$0.790020\pi$
$228$	18.8744	+	119.168i	0.0827824	+	0.522668i
$229$	131.354	−	180.794i	0.573600	−	0.789493i	−0.419376	−	0.907813i	$-0.637751\pi$
$229$	131.354	−	180.794i	0.573600	−	0.789493i	0.992975	+	0.118320i	$0.0377509\pi$
$230$	−8.51688	+	21.3287i	−0.0370299	+	0.0927335i
$231$	−175.866	+	127.774i	−0.761326	+	0.553136i
$232$	59.8011	−	59.8011i	0.257763	−	0.257763i
$233$	61.3442	+	9.71596i	0.263280	+	0.0416994i	0.286679	−	0.958027i	$-0.407449\pi$
$233$	61.3442	+	9.71596i	0.263280	+	0.0416994i	−0.0233990	+	0.999726i	$0.507449\pi$
$234$	−54.5595	+	17.7274i	−0.233160	+	0.0757583i
$235$	130.924	+	304.992i	0.557124	+	1.29784i
$236$	−37.5481	+	115.561i	−0.159102	+	0.489666i
$237$	−202.778	−	103.320i	−0.855602	−	0.435951i
$238$	2.96307	−	5.81535i	0.0124499	−	0.0244342i
$239$	−36.5637	−	11.8803i	−0.152986	−	0.0497082i	0.231523	−	0.972829i	$-0.425629\pi$
$239$	−36.5637	−	11.8803i	−0.152986	−	0.0497082i	−0.384509	+	0.923121i	$0.625629\pi$
$240$	−46.6392	−	53.2148i	−0.194330	−	0.221728i
$241$	30.6594	+	94.3598i	0.127217	+	0.391535i	0.994299	−	0.106632i	$-0.0340067\pi$
$241$	30.6594	+	94.3598i	0.127217	+	0.391535i	−0.867081	+	0.498167i	$0.834007\pi$
$242$	−12.0154	+	75.8619i	−0.0496502	+	0.313479i
$243$	−169.660	−	169.660i	−0.698189	−	0.698189i
$244$	200.214	+	275.571i	0.820550	+	1.12939i
$245$	67.4110	−	17.0982i	0.275147	−	0.0697886i
$246$	72.5154	+	52.6855i	0.294778	+	0.214169i
$247$	−236.212	+	37.4123i	−0.956324	+	0.151467i
$248$	−84.4501	+	43.0295i	−0.340525	+	0.173506i
$249$			116.258i			0.466900i
$250$	−37.7872	+	102.137i	−0.151149	+	0.408548i
$251$	65.3291			0.260275			0.130138	−	0.991496i	$-0.458458\pi$
$251$	65.3291			0.260275			0.130138	+	0.991496i	$0.458458\pi$
$252$	63.1202	+	123.880i	0.250477	+	0.491589i
$253$	−11.9279	−	75.3099i	−0.0471459	−	0.297668i
$254$	81.2367	−	111.813i	0.319830	−	0.440208i
$255$	−2.20033	−	8.67497i	−0.00862874	−	0.0340195i
$256$	83.6692	−	60.7892i	0.326833	−	0.237458i
$257$	293.197	−	293.197i	1.14084	−	1.14084i	0.152547	−	0.988296i	$-0.451252\pi$
$257$	293.197	−	293.197i	1.14084	−	1.14084i	0.988296	−	0.152547i	$-0.0487475\pi$
$258$	−8.00468	−	1.26782i	−0.0310259	−	0.00491402i
$259$	−488.528	+	158.732i	−1.88621	+	0.612866i
$260$	148.365	−	130.032i	0.570636	−	0.500125i
$261$	−22.4063	+	68.9595i	−0.0858479	+	0.264213i
$262$	−90.8981	−	46.3149i	−0.346939	−	0.176774i
$263$	113.098	−	221.967i	0.430030	−	0.843981i	−0.569725	−	0.821836i	$-0.692950\pi$
$263$	113.098	−	221.967i	0.430030	−	0.843981i	0.999755	−	0.0221457i	$-0.00704979\pi$
$264$	−164.437	−	53.4289i	−0.622869	−	0.202382i
$265$	194.162	−	83.3478i	0.732685	−	0.314520i
$266$	−41.9474	−	129.101i	−0.157697	−	0.485342i
$267$	15.2201	−	96.0961i	0.0570042	−	0.359911i
$268$	103.375	+	103.375i	0.385726	+	0.385726i
$269$	−75.5099	−	103.931i	−0.280706	−	0.386359i	0.645262	−	0.763962i	$-0.276748\pi$
$269$	−75.5099	−	103.931i	−0.280706	−	0.386359i	−0.925968	+	0.377603i	$0.876748\pi$
$270$	−110.465	−	44.1103i	−0.409129	−	0.163372i
$271$	13.2869	+	9.65352i	0.0490293	+	0.0356219i	0.612030	−	0.790835i	$-0.290353\pi$
$271$	13.2869	+	9.65352i	0.0490293	+	0.0356219i	−0.563001	+	0.826456i	$0.690353\pi$
$272$	−6.96659	+	1.10340i	−0.0256125	+	0.00405662i
$273$	163.046	−	83.0763i	0.597239	−	0.304309i
$274$			157.862i			0.576139i
$275$	−65.6708	−	355.546i	−0.238803	−	1.29289i
$276$	32.3814			0.117324
$277$	−2.24494	−	4.40595i	−0.00810448	−	0.0159059i	0.886919	−	0.461925i	$-0.152841\pi$
$277$	−2.24494	−	4.40595i	−0.00810448	−	0.0159059i	−0.895023	+	0.446019i	$0.852841\pi$
$278$	9.50274	+	59.9979i	0.0341825	+	0.215820i
$279$	47.7641	−	65.7417i	0.171198	−	0.235633i
$280$	192.300	+	160.034i	0.686785	+	0.571550i
$281$	−60.1858	+	43.7275i	−0.214184	+	0.155614i	−0.689705	−	0.724091i	$-0.742260\pi$
$281$	−60.1858	+	43.7275i	−0.214184	+	0.155614i	0.475521	+	0.879705i	$0.342260\pi$
$282$	−77.4973	+	77.4973i	−0.274813	+	0.274813i
$283$	−120.915	−	19.1510i	−0.427260	−	0.0676714i	−0.0608988	−	0.998144i	$-0.519397\pi$
$283$	−120.915	−	19.1510i	−0.427260	−	0.0676714i	−0.366362	+	0.930473i	$0.619397\pi$
$284$	139.373	−	45.2852i	0.490751	−	0.159455i
$285$	−159.939	−	95.2202i	−0.561190	−	0.334106i
$286$	47.4020	−	145.888i	0.165741	−	0.510099i
$287$	383.666	+	195.487i	1.33681	+	0.681141i
$288$	−77.9372	+	152.960i	−0.270615	+	0.531112i
$289$	274.007	+	89.0302i	0.948121	+	0.308063i
$290$	5.32565	+	58.1546i	0.0183643	+	0.200533i
$291$	21.5324	+	66.2700i	0.0739946	+	0.227732i
$292$	27.2111	−	171.804i	0.0931886	−	0.588369i
$293$	365.947	+	365.947i	1.24897	+	1.24897i	0.956177	+	0.292788i	$0.0945831\pi$
$293$	365.947	+	365.947i	1.24897	+	1.24897i	0.292788	+	0.956177i	$0.405417\pi$
$294$	13.4982	+	18.5787i	0.0459123	+	0.0631928i
$295$	−99.9808	−	158.568i	−0.338918	−	0.537518i
$296$	−330.529	−	240.144i	−1.11665	−	0.811296i
$297$	390.042	−	61.7766i	1.31327	−	0.208002i
$298$	125.216	−	63.8005i	0.420187	−	0.214096i
$299$			64.1855i			0.214667i
$300$	153.498	−	3.92518i	0.511659	−	0.0130839i
$301$	−38.9335			−0.129347
$302$	−52.7989	−	103.624i	−0.174831	−	0.343125i
$303$	22.6851	+	143.228i	0.0748683	+	0.472700i
$304$	−86.2278	+	118.682i	−0.283644	+	0.390403i
$305$	−524.362	−	34.5302i	−1.71922	−	0.113214i
$306$	−3.60069	+	2.61605i	−0.0117669	+	0.00854919i
$307$	−127.024	+	127.024i	−0.413759	+	0.413759i	−0.883046	−	0.469287i	$-0.844511\pi$
$307$	−127.024	+	127.024i	−0.413759	+	0.413759i	0.469287	+	0.883046i	$0.344511\pi$
$308$	−367.191	−	58.1573i	−1.19218	−	0.188823i
$309$	−138.190	+	44.9005i	−0.447216	+	0.145309i
$310$	14.4637	−	63.8292i	0.0466570	−	0.205901i
$311$	3.65978	−	11.2636i	0.0117678	−	0.0362175i	−0.945000	−	0.327070i	$-0.893939\pi$
$311$	3.65978	−	11.2636i	0.0117678	−	0.0362175i	0.956768	+	0.290852i	$0.0939388\pi$
$312$	129.682	+	66.0763i	0.415648	+	0.211783i
$313$	−77.8591	+	152.807i	−0.248751	+	0.488201i	−0.981293	−	0.192521i	$-0.938334\pi$
$313$	−77.8591	+	152.807i	−0.248751	+	0.488201i	0.732542	+	0.680722i	$0.238334\pi$
$314$	−173.545	−	56.3881i	−0.552690	−	0.179580i
$315$	−209.191	−	47.4026i	−0.664099	−	0.150485i
$316$	−120.273	−	370.163i	−0.380611	−	1.17140i
$317$	−11.8851	+	75.0397i	−0.0374925	+	0.236718i	−0.999317	−	0.0369480i	$-0.988236\pi$
$317$	−11.8851	+	75.0397i	−0.0374925	+	0.236718i	0.961825	+	0.273666i	$0.0882364\pi$
$318$	49.3357	+	49.3357i	0.155144	+	0.155144i
$319$	−113.961	−	156.854i	−0.357245	−	0.491706i
$320$	0.728866	−	11.0683i	0.00227771	−	0.0345884i
$321$	80.1769	+	58.2519i	0.249772	+	0.181470i
$322$	−35.9830	+	5.69915i	−0.111749	+	0.0176992i
$323$	−16.5320	+	8.42350i	−0.0511828	+	0.0260789i
$324$			9.94475i			0.0306937i
$325$	7.78040	+	304.259i	0.0239397	+	0.936181i
$326$	268.045			0.822223
$327$	24.9836	+	49.0331i	0.0764025	+	0.149948i
$328$	53.5764	+	338.268i	0.163343	+	1.03131i
$329$	−309.471	+	425.950i	−0.940641	+	1.29468i
$330$	100.991	−	63.6771i	0.306033	−	0.192961i
$331$	343.246	−	249.383i	1.03700	−	0.753423i	0.0673003	−	0.997733i	$-0.478561\pi$
$331$	343.246	−	249.383i	1.03700	−	0.753423i	0.969697	+	0.244310i	$0.0785614\pi$
$332$	−140.590	+	140.590i	−0.423464	+	0.423464i
$333$	345.968	+	54.7960i	1.03894	+	0.164552i
$334$	−0.529145	+	0.171930i	−0.00158427	+	0.000514760i
$335$	−224.600	+	20.5683i	−0.670448	+	0.0613980i
$336$	34.6864	−	106.754i	0.103233	−	0.317719i
$337$	−124.280	−	63.3239i	−0.368784	−	0.187905i	0.259771	−	0.965670i	$-0.416353\pi$
$337$	−124.280	−	63.3239i	−0.368784	−	0.187905i	−0.628554	+	0.777766i	$0.716353\pi$
$338$	8.22128	−	16.1352i	0.0243233	−	0.0477372i
$339$	−6.21354	−	2.01890i	−0.0183290	−	0.00595547i
$340$	7.82975	−	13.1514i	0.0230287	−	0.0386807i
$341$	67.1454	+	206.652i	0.196907	+	0.606018i
$342$	−14.4807	+	91.4273i	−0.0423411	+	0.267331i
$343$	−196.805	−	196.805i	−0.573775	−	0.573775i
$344$	−18.2017	−	25.0525i	−0.0529118	−	0.0728269i
$345$	−31.9558	+	38.3987i	−0.0926255	+	0.111301i
$346$	95.8800	+	69.6609i	0.277110	+	0.201332i
$347$	443.450	−	70.2356i	1.27795	−	0.202408i	0.519690	−	0.854355i	$-0.326048\pi$
$347$	443.450	−	70.2356i	1.27795	−	0.202408i	0.758265	+	0.651947i	$0.226048\pi$
$348$	73.3639	−	37.3808i	0.210816	−	0.107416i
$349$			127.497i			0.365320i	0.983176	+	0.182660i	$0.0584708\pi$
$349$			127.497i			0.365320i	−0.983176	+	0.182660i	$0.941529\pi$
$350$	−169.880	+	31.3775i	−0.485370	+	0.0896499i
$351$	−332.428			−0.947087
$352$	−208.399	−	409.005i	−0.592042	−	1.16195i
$353$	−74.6432	−	471.279i	−0.211454	−	1.33507i	−0.833688	−	0.552236i	$-0.813775\pi$
$353$	−74.6432	−	471.279i	−0.211454	−	1.33507i	0.622234	−	0.782831i	$-0.286225\pi$
$354$	36.3836	−	50.0778i	0.102779	−	0.141463i
$355$	−83.8413	+	209.963i	−0.236173	+	0.591444i
$356$	134.614	−	97.8029i	0.378130	−	0.274727i
$357$	10.0387	−	10.0387i	0.0281197	−	0.0281197i
$358$	36.7406	+	5.81914i	0.102627	+	0.0162546i
$359$	389.162	−	126.446i	1.08402	−	0.352218i	0.288085	−	0.957605i	$-0.406982\pi$
$359$	389.162	−	126.446i	1.08402	−	0.352218i	0.795931	+	0.605387i	$0.206982\pi$
$360$	−67.2962	−	156.769i	−0.186934	−	0.435469i
$361$	−7.69430	+	23.6806i	−0.0213138	+	0.0655973i
$362$	140.867	+	71.7753i	0.389135	+	0.198274i
$363$	−75.8490	+	148.862i	−0.208950	+	0.410088i
$364$	297.635	+	96.7074i	0.817678	+	0.265680i
$365$	176.876	+	201.813i	0.484592	+	0.552913i
$366$	−53.6217	−	165.031i	−0.146507	−	0.450903i
$367$	18.6772	−	117.923i	0.0508916	−	0.321317i	−0.949088	−	0.315010i	$-0.897992\pi$
$367$	18.6772	−	117.923i	0.0508916	−	0.321317i	0.999980	−	0.00630745i	$-0.00200774\pi$
$368$	27.8400	+	27.8400i	0.0756521	+	0.0756521i
$369$	−172.593	−	237.554i	−0.467732	−	0.643778i
$370$	273.455	−	69.3595i	0.739069	−	0.187458i
$371$	271.165	+	197.013i	0.730903	+	0.531032i
$372$	−91.1417	+	14.4354i	−0.245005	+	0.0388049i
$373$	−228.816	+	116.587i	−0.613446	+	0.312567i	−0.732966	−	0.680265i	$-0.761865\pi$
$373$	−228.816	+	116.587i	−0.613446	+	0.312567i	0.119520	+	0.992832i	$0.461865\pi$
$374$		−	11.9008i		−	0.0318204i
$375$	−146.826	+	185.895i	−0.391535	+	0.495720i
$376$	−418.765			−1.11374
$377$	74.0952	+	145.420i	0.196539	+	0.385730i
$378$	−29.5169	−	186.362i	−0.0780869	−	0.493021i
$379$	145.323	−	200.020i	0.383438	−	0.527757i	−0.573053	−	0.819518i	$-0.694241\pi$
$379$	145.323	−	200.020i	0.383438	−	0.527757i	0.956491	+	0.291761i	$0.0942413\pi$
$380$	−78.2641	−	308.563i	−0.205958	−	0.812007i
$381$	243.215	−	176.706i	0.638360	−	0.463795i
$382$	34.6396	−	34.6396i	0.0906797	−	0.0906797i
$383$	254.126	+	40.2496i	0.663515	+	0.105090i	0.479103	−	0.877759i	$-0.340962\pi$
$383$	254.126	+	40.2496i	0.663515	+	0.105090i	0.184412	+	0.982849i	$0.440962\pi$
$384$	232.308	−	75.4815i	0.604969	−	0.196566i
$385$	431.329	−	378.032i	1.12034	−	0.981900i
$386$	−56.6919	+	174.480i	−0.146870	+	0.452020i
$387$	23.6558	+	12.0532i	0.0611261	+	0.0311453i
$388$	−54.1009	+	106.179i	−0.139435	+	0.273657i
$389$	−508.333	−	165.168i	−1.30677	−	0.424595i	−0.428838	−	0.903381i	$-0.641077\pi$
$389$	−508.333	−	165.168i	−1.30677	−	0.424595i	−0.877931	+	0.478786i	$0.841077\pi$
$390$	−92.3520	+	39.6440i	−0.236800	+	0.101651i
$391$	1.53880	+	4.73595i	0.00393556	+	0.0121124i
$392$	−13.7265	+	86.6654i	−0.0350165	+	0.221085i
$393$	−156.913	−	156.913i	−0.399269	−	0.399269i
$394$	143.739	+	197.840i	0.364820	+	0.502131i
$395$	557.641	+	222.674i	1.41175	+	0.563733i
$396$	205.099	+	149.013i	0.517926	+	0.376295i
$397$	128.831	−	20.4049i	0.324512	−	0.0513976i	0.00794678	−	0.999968i	$-0.497470\pi$
$397$	128.831	−	20.4049i	0.324512	−	0.0513976i	0.316565	+	0.948571i	$0.397470\pi$
$398$	−95.0586	+	48.4348i	−0.238841	+	0.121695i
$399$		−	295.272i		−	0.740030i
$400$	135.345	+	128.595i	0.338361	+	0.321488i
$401$	−791.621			−1.97412			−0.987059	−	0.160358i	$-0.948735\pi$
$401$	−791.621			−1.97412			−0.987059	+	0.160358i	$0.948735\pi$
$402$	−33.8110	−	66.3577i	−0.0841069	−	0.165069i
$403$	−28.6135	−	180.659i	−0.0710013	−	0.448284i
$404$	−145.772	+	200.638i	−0.360821	+	0.496628i
$405$	−11.7927	−	9.81405i	−0.0291179	−	0.0242322i
$406$	−74.9448	+	54.4506i	−0.184593	+	0.134115i
$407$	−662.295	+	662.295i	−1.62726	+	1.62726i
$408$	11.1528	+	1.76643i	0.0273352	+	0.00432947i
$409$	15.0598	−	4.89323i	0.0368210	−	0.0119639i	−0.290549	−	0.956860i	$-0.593838\pi$
$409$	15.0598	−	4.89323i	0.0368210	−	0.0119639i	0.327370	+	0.944896i	$0.393838\pi$
$410$	−203.205	−	120.979i	−0.495621	−	0.295070i
$411$	−106.111	+	326.575i	−0.258177	+	0.794588i
$412$	−221.410	−	112.814i	−0.537403	−	0.273820i
$413$	135.000	−	264.952i	0.326877	−	0.641531i
$414$	23.6275	+	7.67703i	0.0570712	+	0.0185436i
$415$	−27.9731	−	305.458i	−0.0674050	−	0.736043i
$416$	119.409	+	367.502i	0.287040	+	0.883418i
$417$	−20.6704	+	130.507i	−0.0495692	+	0.312968i
$418$	−175.021	−	175.021i	−0.418711	−	0.418711i
$419$	322.442	+	443.803i	0.769551	+	1.05920i	0.996359	+	0.0852562i	$0.0271709\pi$
$419$	322.442	+	443.803i	0.769551	+	1.05920i	−0.226808	+	0.973939i	$0.572829\pi$
$420$	129.911	+	206.037i	0.309312	+	0.490564i
$421$	195.688	+	142.176i	0.464818	+	0.337710i	0.795418	−	0.606061i	$-0.207251\pi$
$421$	195.688	+	142.176i	0.464818	+	0.337710i	−0.330601	+	0.943771i	$0.607251\pi$
$422$	−160.215	+	25.3756i	−0.379657	+	0.0601318i
$423$	319.901	−	162.998i	0.756266	−	0.385337i
$424$			266.591i			0.628752i
$425$	7.86847	+	22.2633i	0.0185141	+	0.0523842i
$426$	−74.6544			−0.175245
$427$	−378.447	−	742.743i	−0.886292	−	1.73945i
$428$	26.5138	+	167.401i	0.0619480	+	0.391124i
$429$	196.125	−	269.942i	0.457167	−	0.629236i
$430$	21.3367	+	1.40506i	0.0496201	+	0.00326757i
$431$	−515.262	+	374.360i	−1.19550	+	0.868585i	−0.993835	−	0.110869i	$-0.964637\pi$
$431$	−515.262	+	374.360i	−1.19550	+	0.868585i	−0.201669	+	0.979454i	$0.564637\pi$
$432$	−144.188	+	144.188i	−0.333768	+	0.333768i
$433$	−270.426	−	42.8313i	−0.624540	−	0.0989175i	−0.163860	−	0.986484i	$-0.552395\pi$
$433$	−270.426	−	42.8313i	−0.624540	−	0.0989175i	−0.460680	+	0.887566i	$0.652395\pi$
$434$	98.7383	−	32.0820i	0.227508	−	0.0739217i
$435$	−28.0726	+	123.886i	−0.0645347	+	0.284796i
$436$	−29.0829	+	89.5080i	−0.0667039	+	0.205294i
$437$	92.2805	+	47.0193i	0.211168	+	0.107596i
$438$	−40.2292	+	78.9543i	−0.0918476	+	0.180261i
$439$	27.3685	+	8.89257i	0.0623429	+	0.0202564i	0.340022	−	0.940417i	$-0.389565\pi$
$439$	27.3685	+	8.89257i	0.0623429	+	0.0202564i	−0.277680	+	0.960674i	$0.589565\pi$
$440$	444.900	+	100.814i	1.01114	+	0.229123i
$441$	−23.2473	−	71.5478i	−0.0527149	−	0.162240i
$442$	−1.56717	+	9.89470i	−0.00354563	+	0.0223862i
$443$	176.930	+	176.930i	0.399390	+	0.399390i	0.878018	−	0.478628i	$-0.158866\pi$
$443$	176.930	+	176.930i	0.399390	+	0.399390i	−0.478628	+	0.878018i	$0.658866\pi$
$444$	−233.802	−	321.801i	−0.526581	−	0.724777i
$445$	−16.8677	+	256.146i	−0.0379049	+	0.575610i
$446$	131.405	+	95.4717i	0.294631	+	0.214062i
$447$	301.923	−	47.8199i	0.675444	−	0.106980i
$448$	15.6779	−	7.98829i	0.0349953	−	0.0178310i
$449$		−	715.203i		−	1.59288i	−0.604717	−	0.796440i	$-0.706714\pi$
$449$		−	715.203i		−	1.59288i	0.604717	−	0.796440i	$-0.293286\pi$
$450$	112.932	+	33.5274i	0.250960	+	0.0745053i
$451$	785.155			1.74092
$452$	−5.07256	−	9.95545i	−0.0112225	−	0.0220253i
$453$	−39.5740	−	249.860i	−0.0873598	−	0.551568i
$454$	43.5497	−	59.9411i	0.0959246	−	0.132029i
$455$	−408.401	+	257.507i	−0.897584	+	0.565948i
$456$	189.998	−	138.042i	0.416662	−	0.302723i
$457$	−368.956	+	368.956i	−0.807343	+	0.807343i	−0.984231	−	0.176888i	$-0.943397\pi$
$457$	−368.956	+	368.956i	−0.807343	+	0.807343i	0.176888	+	0.984231i	$0.443397\pi$
$458$	−192.298	−	30.4570i	−0.419865	−	0.0665000i
$459$	−24.5283	+	7.96972i	−0.0534385	+	0.0173632i
$460$	−85.0793	+	7.79135i	−0.184955	+	0.0169377i
$461$	−11.9458	+	36.7653i	−0.0259127	+	0.0797512i	−0.963177	−	0.268870i	$-0.913350\pi$
$461$	−11.9458	+	36.7653i	−0.0259127	+	0.0797512i	0.937264	+	0.348621i	$0.113350\pi$
$462$	168.747	+	85.9807i	0.365252	+	0.186105i
$463$	−103.445	+	203.022i	−0.223423	+	0.438492i	−0.975322	−	0.220786i	$-0.929138\pi$
$463$	−103.445	+	203.022i	−0.223423	+	0.438492i	0.751900	+	0.659278i	$0.229138\pi$
$464$	95.2130	+	30.9366i	0.205200	+	0.0666737i
$465$	72.8259	−	122.324i	0.156615	−	0.263062i
$466$	−16.7211	−	51.4622i	−0.0358822	−	0.110434i
$467$	134.672	−	850.285i	0.288377	−	1.82074i	−0.238899	−	0.971044i	$-0.576787\pi$
$467$	134.672	−	850.285i	0.288377	−	1.82074i	0.527276	−	0.849694i	$-0.323213\pi$
$468$	−150.902	−	150.902i	−0.322440	−	0.322440i
$469$	−210.295	−	289.446i	−0.448390	−	0.617156i
$470$	184.971	−	222.264i	0.393555	−	0.472903i
$471$	−321.116	−	233.304i	−0.681775	−	0.495339i
$472$	233.602	−	36.9989i	0.494919	−	0.0783875i
$473$	−63.2540	+	32.2295i	−0.133729	+	0.0681385i
$474$			198.275i			0.418302i
$475$	443.137	+	211.700i	0.932920	+	0.445683i
$476$	24.2796			0.0510075
$477$	−103.766	−	203.653i	−0.217539	−	0.426945i
$478$	5.23968	+	33.0820i	0.0109617	+	0.0692093i
$479$	54.7418	−	75.3456i	0.114284	−	0.157298i	−0.748043	−	0.663650i	$-0.769006\pi$
$479$	54.7418	−	75.3456i	0.114284	−	0.157298i	0.862327	+	0.506352i	$0.169006\pi$
$480$	−111.531	+	279.306i	−0.232356	+	0.581887i
$481$	637.866	−	463.436i	1.32612	−	0.963485i
$482$	61.1216	−	61.1216i	0.126808	−	0.126808i
$483$	−78.2703	−	12.3968i	−0.162050	−	0.0256663i
$484$	−271.742	+	88.2943i	−0.561450	+	0.182426i
$485$	−72.5199	−	168.938i	−0.149526	−	0.348325i
$486$	−64.5960	+	198.806i	−0.132914	+	0.409066i
$487$	356.586	+	181.689i	0.732209	+	0.373079i	0.780001	−	0.625778i	$-0.215219\pi$
$487$	356.586	+	181.689i	0.732209	+	0.373079i	−0.0477923	+	0.998857i	$0.515219\pi$
$488$	301.005	−	590.756i	0.616813	−	1.21056i
$489$	554.514	+	180.173i	1.13398	+	0.368451i
$490$	−39.9356	−	45.5660i	−0.0815012	−	0.0929919i
$491$	−204.267	−	628.670i	−0.416023	−	1.28039i	−0.911333	−	0.411671i	$-0.864945\pi$
$491$	−204.267	−	628.670i	−0.416023	−	1.28039i	0.495310	−	0.868716i	$-0.335055\pi$
$492$	−52.1616	+	329.336i	−0.106020	+	0.669381i
$493$	8.95348	+	8.95348i	0.0181612	+	0.0181612i
$494$	122.470	+	168.566i	0.247915	+	0.341226i
$495$	−379.106	+	96.1568i	−0.765871	+	0.194256i
$496$	−90.7701	−	65.9484i	−0.183004	−	0.132960i
$497$	−354.222	+	56.1032i	−0.712720	+	0.112884i
$498$	90.2470	−	45.9832i	0.181219	−	0.0923356i
$499$			608.633i			1.21971i	0.792514	+	0.609853i	$0.208772\pi$
$499$			608.633i			1.21971i	−0.792514	+	0.609853i	$0.791228\pi$
$500$	−402.357	+	47.2464i	−0.804714	+	0.0944929i
$501$	−1.21023			−0.00241563
$502$	−25.8394	−	50.7127i	−0.0514729	−	0.101021i
$503$	71.0647	+	448.685i	0.141282	+	0.892018i	0.951892	+	0.306432i	$0.0991353\pi$
$503$	71.0647	+	448.685i	0.141282	+	0.892018i	−0.810611	+	0.585585i	$0.800865\pi$
$504$	159.071	−	218.943i	0.315617	−	0.434410i
$505$	−94.0655	−	370.861i	−0.186268	−	0.734378i
$506$	−53.7426	+	39.0463i	−0.106211	+	0.0771666i
$507$	27.8533	−	27.8533i	0.0549375	−	0.0549375i
$508$	507.808	+	80.4289i	0.999622	+	0.158325i
$509$	−466.349	+	151.526i	−0.916207	+	0.297694i	−0.728910	−	0.684610i	$-0.759973\pi$
$509$	−466.349	+	151.526i	−0.916207	+	0.297694i	−0.187297	+	0.982303i	$0.559973\pi$
$510$	−5.86379	+	5.13922i	−0.0114976	+	0.0100769i
$511$	−131.546	+	404.856i	−0.257428	+	0.792283i
$512$	379.097	+	193.159i	0.740423	+	0.377264i
$513$	−243.521	+	477.936i	−0.474699	+	0.931649i
$514$	−343.565	−	111.631i	−0.668415	−	0.217181i
$515$	352.278	−	151.222i	0.684034	−	0.293636i
$516$	−9.31650	−	28.6732i	−0.0180552	−	0.0555683i
$517$	−150.182	+	948.210i	−0.290487	+	1.83406i
$518$	316.444	+	316.444i	0.610896	+	0.610896i
$519$	151.526	+	208.558i	0.291958	+	0.401846i
$520$	−356.627	−	142.407i	−0.685822	−	0.273859i
$521$	232.370	+	168.827i	0.446008	+	0.324044i	0.788018	−	0.615653i	$-0.211108\pi$
$521$	232.370	+	168.827i	0.446008	+	0.324044i	−0.342009	+	0.939696i	$0.611108\pi$
$522$	62.3932	−	9.88210i	0.119527	−	0.0189312i
$523$	45.9244	−	23.3997i	0.0878096	−	0.0447412i	−0.409534	−	0.912295i	$-0.634309\pi$
$523$	45.9244	−	23.3997i	0.0878096	−	0.0447412i	0.497344	+	0.867554i	$0.334309\pi$
$524$		−	379.507i		−	0.724251i
$525$	−372.528	−	49.2769i	−0.709576	−	0.0938607i
$526$	−217.038			−0.412621
$527$	−6.44242	−	12.6440i	−0.0122247	−	0.0239923i
$528$	−32.0179	−	202.153i	−0.0606399	−	0.382865i
$529$	−294.600	+	405.482i	−0.556900	+	0.766507i
$530$	−141.496	−	117.755i	−0.266974	−	0.222178i
$531$	−164.051	+	119.190i	−0.308946	+	0.224463i
$532$	357.071	−	357.071i	0.671185	−	0.671185i
$533$	−652.800	−	103.393i	−1.22477	−	0.193984i
$534$	−80.6160	+	26.1937i	−0.150966	+	0.0490519i
$535$	−224.674	−	133.760i	−0.419951	−	0.250019i
$536$	87.9350	−	270.636i	0.164058	−	0.504918i
$537$	72.0952	+	36.7343i	0.134255	+	0.0684066i
$538$	−50.8114	+	99.7230i	−0.0944450	+	0.185359i
$539$	191.314	+	62.1616i	0.354942	+	0.115328i
$540$	−40.3527	−	440.640i	−0.0747272	−	0.815999i
$541$	−306.990	−	944.819i	−0.567450	−	1.74643i	−0.660559	−	0.750775i	$-0.729680\pi$
$541$	−306.990	−	944.819i	−0.567450	−	1.74643i	0.0931088	−	0.995656i	$-0.470320\pi$
$542$	2.23835	−	14.1324i	0.00412980	−	0.0260746i
$543$	243.171	+	243.171i	0.447829	+	0.447829i
$544$	17.6212	+	24.2535i	0.0323919	+	0.0445836i
$545$	−77.4402	−	122.819i	−0.142092	−	0.225356i
$546$	−128.978	−	93.7083i	−0.236224	−	0.171627i
$547$	120.296	−	19.0530i	0.219919	−	0.0348318i	−0.0455024	−	0.998964i	$-0.514489\pi$
$547$	120.296	−	19.0530i	0.219919	−	0.0348318i	0.265422	+	0.964132i	$0.414489\pi$
$548$	−523.245	+	266.607i	−0.954827	+	0.486508i
$549$			568.448i			1.03542i
$550$	−250.023	+	191.606i	−0.454588	+	0.348374i
$551$	263.351			0.477951
$552$	−28.6150	−	56.1600i	−0.0518387	−	0.101739i
$553$	149.005	+	940.779i	0.269448	+	1.70123i
$554$	−2.53225	+	3.48534i	−0.00457084	+	0.00629122i
$555$	612.329	+	40.3229i	1.10330	+	0.0726539i
$556$	−182.818	+	132.825i	−0.328810	+	0.238895i
$557$	576.978	−	576.978i	1.03587	−	1.03587i	0.0365353	−	0.999332i	$-0.488368\pi$
$557$	576.978	−	576.978i	1.03587	−	1.03587i	0.999332	−	0.0365353i	$-0.0116321\pi$
$558$	−69.9250	−	11.0750i	−0.125314	−	0.0198477i
$559$	56.8353	−	18.4669i	0.101673	−	0.0330356i
$560$	−65.4492	+	288.832i	−0.116874	+	0.515771i
$561$	7.99944	−	24.6197i	0.0142592	−	0.0438854i
$562$	57.7493	+	29.4247i	0.102757	+	0.0523571i
$563$	447.785	−	878.827i	0.795355	−	1.56097i	−0.0321302	−	0.999484i	$-0.510229\pi$
$563$	447.785	−	878.827i	0.795355	−	1.56097i	0.827485	−	0.561488i	$-0.189771\pi$
$564$	−387.752	−	125.988i	−0.687504	−	0.223384i
$565$	16.8113	+	3.80944i	0.0297545	+	0.00674237i
$566$	32.9587	+	101.437i	0.0582310	+	0.179217i
$567$	3.80722	−	24.0378i	0.00671467	−	0.0423948i
$568$	−201.702	−	201.702i	−0.355108	−	0.355108i
$569$	176.314	+	242.675i	0.309866	+	0.426495i	0.935340	−	0.353751i	$-0.115094\pi$
$569$	176.314	+	242.675i	0.309866	+	0.426495i	−0.625473	+	0.780246i	$0.715094\pi$
$570$	−10.6559	+	161.817i	−0.0186946	+	0.283890i
$571$	−212.912	−	154.690i	−0.372876	−	0.270910i	0.385527	−	0.922697i	$-0.374020\pi$
$571$	−212.912	−	154.690i	−0.372876	−	0.270910i	−0.758402	+	0.651787i	$0.774020\pi$
$572$	563.612	−	89.2674i	0.985336	−	0.156062i
$573$	94.9442	−	48.3765i	0.165697	−	0.0844267i
$574$		−	375.147i		−	0.653566i
$575$	74.7219	−	108.578i	0.129951	−	0.188832i
$576$	−11.9989			−0.0208313
$577$	205.720	+	403.749i	0.356535	+	0.699739i	0.997709	−	0.0676569i	$-0.0215523\pi$
$577$	205.720	+	403.749i	0.356535	+	0.699739i	−0.641174	+	0.767396i	$0.721552\pi$
$578$	−39.2660	−	247.916i	−0.0679343	−	0.428920i
$579$	−234.561	+	322.846i	−0.405115	+	0.557593i
$580$	−183.763	+	115.867i	−0.316833	+	0.199771i
$581$	393.649	−	286.003i	0.677537	−	0.492259i
$582$	42.9264	−	42.9264i	0.0737567	−	0.0737567i
$583$	603.642	+	95.6075i	1.03541	+	0.163992i
$584$	−322.011	+	104.628i	−0.551388	+	0.179157i
$585$	327.862	−	30.0248i	0.560448	−	0.0513245i
$586$	139.330	−	428.813i	0.237764	−	0.731764i
$587$	−542.594	−	276.465i	−0.924351	−	0.470980i	−0.0740364	−	0.997256i	$-0.523588\pi$
$587$	−542.594	−	276.465i	−0.924351	−	0.470980i	−0.850314	+	0.526275i	$0.823588\pi$
$588$	−38.7838	+	76.1175i	−0.0659588	+	0.129451i
$589$	−280.696	−	91.2038i	−0.476564	−	0.154845i
$590$	−83.5455	+	140.329i	−0.141603	+	0.237846i
$591$	164.376	+	505.896i	0.278131	+	0.856000i
$592$	75.6572	−	477.681i	0.127799	−	0.806893i
$593$	173.944	+	173.944i	0.293329	+	0.293329i	0.838394	−	0.545065i	$-0.183495\pi$
$593$	173.944	+	173.944i	0.293329	+	0.293329i	−0.545065	+	0.838394i	$0.683495\pi$
$594$	−202.227	−	278.342i	−0.340450	−	0.468589i
$595$	−23.9604	+	28.7913i	−0.0402697	+	0.0483888i
$596$	422.942	+	307.286i	0.709635	+	0.515580i
$597$	−229.208	+	36.3030i	−0.383933	+	0.0608090i
$598$	49.8250	−	25.3871i	0.0833194	−	0.0424533i
$599$		−	46.7267i		−	0.0780079i	−0.999239	−	0.0390039i	$-0.987582\pi$
$599$		−	46.7267i		−	0.0780079i	0.999239	−	0.0390039i	$-0.0124185\pi$
$600$	−142.451	−	262.747i	−0.237418	−	0.437911i
$601$	−76.3417			−0.127025			−0.0635123	−	0.997981i	$-0.520230\pi$
$601$	−76.3417			−0.127025			−0.0635123	+	0.997981i	$0.520230\pi$
$602$	15.3992	+	30.2227i	0.0255801	+	0.0502039i
$603$	38.1659	+	240.970i	0.0632934	+	0.399619i
$604$	254.298	−	350.011i	0.421023	−	0.579489i
$605$	163.469	−	409.372i	0.270196	−	0.676648i
$606$	102.210	−	74.2602i	0.168664	−	0.122542i
$607$	−126.996	+	126.996i	−0.209220	+	0.209220i	−0.803936	−	0.594716i	$-0.797264\pi$
$607$	−126.996	+	126.996i	−0.209220	+	0.209220i	0.594716	+	0.803936i	$0.297264\pi$
$608$	615.836	+	97.5388i	1.01289	+	0.160426i
$609$	−191.642	+	62.2681i	−0.314682	+	0.102246i
$610$	180.595	+	420.702i	0.296057	+	0.689675i
$611$	249.731	−	768.592i	0.408725	−	1.25792i
$612$	−14.7521	−	7.51658i	−0.0241048	−	0.0122820i
$613$	−160.158	+	314.328i	−0.261269	+	0.512770i	−0.983957	−	0.178405i	$-0.942906\pi$
$613$	−160.158	+	314.328i	−0.261269	+	0.512770i	0.722688	+	0.691175i	$0.242906\pi$
$614$	148.846	+	48.3628i	0.242419	+	0.0787668i
$615$	−339.059	−	386.862i	−0.551315	−	0.629044i
$616$	223.617	+	688.223i	0.363015	+	1.11724i
$617$	41.9822	−	265.065i	0.0680425	−	0.429603i	−0.930027	−	0.367492i	$-0.880217\pi$
$617$	41.9822	−	265.065i	0.0680425	−	0.429603i	0.998069	−	0.0621114i	$-0.0197834\pi$
$618$	89.5124	+	89.5124i	0.144842	+	0.144842i
$619$	−15.8671	−	21.8392i	−0.0256335	−	0.0352815i	0.796008	−	0.605286i	$-0.206941\pi$
$619$	−15.8671	−	21.8392i	−0.0256335	−	0.0352815i	−0.821641	+	0.570005i	$0.806941\pi$
$620$	235.993	−	59.8576i	0.380635	−	0.0965445i
$621$	116.467	+	84.6180i	0.187547	+	0.136261i
$622$	−10.1911	+	1.61411i	−0.0163844	+	0.00259504i
$623$	−362.824	+	184.868i	−0.582381	+	0.296738i
$624$			172.292i			0.276109i
$625$	341.043	−	523.751i	0.545668	−	0.838001i
$626$	149.414			0.238681
$627$	−244.429	−	479.718i	−0.389838	−	0.765101i
$628$	−106.190	−	670.458i	−0.169092	−	1.06761i
$629$	35.9545	−	49.4872i	0.0571614	−	0.0786760i
$630$	45.9437	+	181.137i	0.0729265	+	0.287519i
$631$	−945.873	+	687.217i	−1.49901	+	1.08909i	−0.528232	+	0.849100i	$0.677145\pi$
$631$	−945.873	+	687.217i	−1.49901	+	1.08909i	−0.970775	+	0.239992i	$0.922855\pi$
$632$	−535.700	+	535.700i	−0.847627	+	0.847627i
$633$	−348.501	−	55.1971i	−0.550554	−	0.0871992i
$634$	62.9516	−	20.4542i	0.0992927	−	0.0322621i
$635$	−596.509	+	522.800i	−0.939384	+	0.823307i
$636$	−80.2057	+	246.848i	−0.126110	+	0.388125i
$637$	−150.878	−	76.8762i	−0.236857	−	0.120685i
$638$	−76.6856	+	150.504i	−0.120197	+	0.235900i
$639$	232.592	+	75.5737i	0.363993	+	0.118269i
$640$	−592.207	+	254.217i	−0.925324	+	0.397214i
$641$	1.53254	+	4.71668i	0.00239086	+	0.00735831i	0.952245	−	0.305336i	$-0.0987686\pi$
$641$	1.53254	+	4.71668i	0.00239086	+	0.00735831i	−0.949854	+	0.312694i	$0.898769\pi$
$642$	13.5068	−	85.2787i	0.0210387	−	0.132833i
$643$	−750.489	−	750.489i	−1.16717	−	1.16717i	−0.982871	−	0.184297i	$-0.940999\pi$
$643$	−750.489	−	750.489i	−1.16717	−	1.16717i	−0.184297	−	0.982871i	$-0.559001\pi$
$644$	−79.6605	−	109.643i	−0.123696	−	0.170253i
$645$	43.1955	+	17.2486i	0.0669698	+	0.0267421i
$646$	13.0777	+	9.50153i	0.0202442	+	0.0147082i
$647$	−919.207	+	145.588i	−1.42072	+	0.225020i	−0.819049	−	0.573723i	$-0.805498\pi$
$647$	−919.207	+	145.588i	−1.42072	+	0.225020i	−0.601672	+	0.798743i	$0.705498\pi$
$648$	17.2475	−	8.78803i	0.0266165	−	0.0135618i
$649$		−	542.213i		−	0.835460i
$650$	233.108	−	126.382i	0.358628	−	0.194434i
$651$	225.828			0.346895
$652$	452.689	+	888.452i	0.694308	+	1.36266i
$653$	76.1349	+	480.697i	0.116592	+	0.736136i	0.974841	+	0.222901i	$0.0715528\pi$
$653$	76.1349	+	480.697i	0.116592	+	0.736136i	−0.858249	+	0.513234i	$0.828447\pi$
$654$	28.1810	−	38.7878i	0.0430902	−	0.0593086i
$655$	450.030	+	374.519i	0.687068	+	0.571785i
$656$	−327.993	+	238.301i	−0.499989	+	0.363264i
$657$	205.264	−	205.264i	0.312426	−	0.312426i
$658$	453.054	+	71.7568i	0.688532	+	0.109053i
$659$	1117.29	−	363.029i	1.69543	−	0.550879i	0.707628	−	0.706585i	$-0.249765\pi$
$659$	1117.29	−	363.029i	1.69543	−	0.550879i	0.987804	+	0.155705i	$0.0497651\pi$
$660$	381.621	+	227.200i	0.578214	+	0.344242i
$661$	−218.229	+	671.641i	−0.330150	+	1.01610i	0.638912	+	0.769280i	$0.279385\pi$
$661$	−218.229	+	671.641i	−0.330150	+	1.01610i	−0.969062	+	0.246818i	$0.920615\pi$
$662$	−329.350	−	167.812i	−0.497508	−	0.253493i
$663$	−9.89302	+	19.4161i	−0.0149216	+	0.0292853i
$664$	368.067	+	119.592i	0.554318	+	0.180109i
$665$	71.0460	+	775.801i	0.106836	+	1.16662i
$666$	−94.3034	−	290.236i	−0.141597	−	0.435790i
$667$	11.0566	−	69.8088i	0.0165767	−	0.104661i
$668$	−1.46352	−	1.46352i	−0.00219090	−	0.00219090i
$669$	207.670	+	285.833i	0.310418	+	0.427254i
$670$	104.802	+	166.214i	0.156421	+	0.248080i
$671$	−1229.70	−	893.428i	−1.83264	−	1.33149i
$672$	−471.208	+	74.6321i	−0.701203	+	0.111060i
$673$	576.463	−	293.723i	0.856558	−	0.436438i	0.0301736	−	0.999545i	$-0.490394\pi$
$673$	576.463	−	293.723i	0.856558	−	0.436438i	0.826384	+	0.563107i	$0.190394\pi$
$674$			121.521i			0.180298i
$675$	562.344	+	386.997i	0.833103	+	0.573329i
$676$	67.3657			0.0996535
$677$	442.948	+	869.334i	0.654280	+	1.28410i	0.944932	+	0.327268i	$0.106128\pi$
$677$	442.948	+	869.334i	0.654280	+	1.28410i	−0.290652	+	0.956829i	$0.593872\pi$
$678$	0.890419	+	5.62189i	0.00131330	+	0.00829187i
$679$	171.419	−	235.937i	0.252457	−	0.347478i
$680$	−29.7280	−	1.95764i	−0.0437176	−	0.00287888i
$681$	130.384	−	94.7294i	0.191459	−	0.139103i
$682$	133.859	−	133.859i	0.196274	−	0.196274i
$683$	−1038.24	−	164.442i	−1.52012	−	0.240764i	−0.660161	−	0.751124i	$-0.729512\pi$
$683$	−1038.24	−	164.442i	−1.52012	−	0.240764i	−0.859961	+	0.510360i	$0.829512\pi$
$684$	−327.498	+	106.410i	−0.478798	+	0.155571i
$685$	200.219	−	883.580i	0.292290	−	1.28990i
$686$	−74.9311	+	230.614i	−0.109229	+	0.336173i
$687$	−377.342	−	192.265i	−0.549260	−	0.279862i
$688$	16.6420	−	32.6617i	0.0241889	−	0.0474735i
$689$	−489.295	−	158.982i	−0.710152	−	0.230742i
$690$	42.4469	+	9.61846i	0.0615173	+	0.0139398i
$691$	299.045	+	920.367i	0.432772	+	1.33193i	0.895353	+	0.445358i	$0.146923\pi$
$691$	299.045	+	920.367i	0.432772	+	1.33193i	−0.462581	+	0.886577i	$0.653077\pi$
$692$	−68.9682	+	435.448i	−0.0996651	+	0.629261i
$693$	−438.704	−	438.704i	−0.633050	−	0.633050i
$694$	−229.918	−	316.455i	−0.331294	−	0.455987i
$695$	22.9079	−	347.871i	0.0329610	−	0.500533i
$696$	−129.661	−	94.2044i	−0.186295	−	0.135351i
$697$	−50.6459	+	8.02152i	−0.0726627	+	0.0115086i
$698$	98.9713	−	50.4284i	0.141793	−	0.0722470i
$699$		−	117.701i		−	0.168385i
$700$	−390.905	−	510.086i	−0.558436	−	0.728694i
$701$	802.003			1.14408			0.572042	−	0.820224i	$-0.306151\pi$
$701$	802.003			1.14408			0.572042	+	0.820224i	$0.306151\pi$
$702$	131.484	+	258.052i	0.187299	+	0.367595i
$703$	−199.020	−	1256.56i	−0.283100	−	1.78743i
$704$	18.8586	−	25.9566i	0.0267877	−	0.0368702i
$705$	532.056	−	335.474i	0.754690	−	0.475850i
$706$	−336.314	+	244.346i	−0.476365	+	0.346099i
$707$	429.162	−	429.162i	0.607019	−	0.607019i
$708$	227.433	+	36.0219i	0.321233	+	0.0508783i
$709$	1339.27	−	435.155i	1.88896	−	0.613759i	0.908193	−	0.418551i	$-0.137462\pi$
$709$	1339.27	−	435.155i	1.88896	−	0.613759i	0.980762	−	0.195208i	$-0.0625383\pi$
$710$	196.148	−	17.9628i	0.276265	−	0.0252997i
$711$	200.716	−	617.742i	0.282302	−	0.868835i
$712$	−288.579	−	147.038i	−0.405307	−	0.206514i
$713$	−35.9611	+	70.5776i	−0.0504363	+	0.0989868i
$714$	−11.7633	−	3.82213i	−0.0164752	−	0.00535312i
$715$	−450.349	+	756.440i	−0.629859	+	1.05796i
$716$	42.7617	+	131.607i	0.0597230	+	0.183808i
$717$	−11.3974	+	71.9601i	−0.0158959	+	0.100363i
$718$	−252.080	−	252.080i	−0.351086	−	0.351086i
$719$	87.1456	+	119.946i	0.121204	+	0.166823i	0.865308	−	0.501241i	$-0.167123\pi$
$719$	87.1456	+	119.946i	0.121204	+	0.166823i	−0.744104	+	0.668064i	$0.767123\pi$
$720$	129.185	−	155.231i	0.179423	−	0.215598i
$721$	491.989	+	357.451i	0.682370	+	0.495771i
$722$	21.4257	−	3.39350i	0.0296755	−	0.00470014i
$723$	167.529	−	85.3603i	0.231714	−	0.118064i
$724$			588.131i			0.812336i
$725$	43.9497	−	332.255i	0.0606203	−	0.458283i
$726$	145.557			0.200491
$727$	138.831	+	272.472i	0.190965	+	0.374789i	0.966560	−	0.256441i	$-0.0825501\pi$
$727$	138.831	+	272.472i	0.190965	+	0.374789i	−0.775595	+	0.631231i	$0.782550\pi$
$728$	−95.2928	−	601.655i	−0.130897	−	0.826450i
$729$	−283.497	+	390.200i	−0.388885	+	0.535254i
$730$	86.7015	−	217.125i	0.118769	−	0.297432i
$731$	3.75088	−	2.72517i	0.00513116	−	0.00372801i
$732$	456.446	−	456.446i	0.623560	−	0.623560i
$733$	−253.788	−	40.1961i	−0.346232	−	0.0548378i	−0.0191034	−	0.999818i	$-0.506081\pi$
$733$	−253.788	−	40.1961i	−0.346232	−	0.0548378i	−0.327129	+	0.944980i	$0.606081\pi$
$734$	−98.9271	+	32.1434i	−0.134778	+	0.0437920i
$735$	−51.9880	−	121.108i	−0.0707320	−	0.164773i
$736$	51.7110	−	159.150i	0.0702595	−	0.216236i
$737$	−581.265	−	296.169i	−0.788691	−	0.401858i
$738$	−116.140	+	227.937i	−0.157371	+	0.308858i
$739$	49.8443	+	16.1954i	0.0674483	+	0.0219153i	0.342547	−	0.939501i	$-0.388710\pi$
$739$	49.8443	+	16.1954i	0.0674483	+	0.0219153i	−0.275098	+	0.961416i	$0.588710\pi$
$740$	691.724	+	789.248i	0.934762	+	1.06655i
$741$	140.053	+	431.039i	0.189006	+	0.581699i
$742$	45.6812	−	288.420i	0.0615650	−	0.388706i
$743$	833.010	+	833.010i	1.12114	+	1.12114i	0.991570	+	0.129574i	$0.0413609\pi$
$743$	833.010	+	833.010i	1.12114	+	1.12114i	0.129574	+	0.991570i	$0.458639\pi$
$744$	105.576	+	145.313i	0.141904	+	0.195314i
$745$	−781.771	+	198.289i	−1.04936	+	0.266160i
$746$	181.005	+	131.508i	0.242634	+	0.176284i
$747$	−327.721	+	51.9059i	−0.438716	+	0.0694858i
$748$	39.4462	−	20.0988i	0.0527355	−	0.0268701i
$749$		−	414.782i		−	0.553782i
$750$	202.377	+	40.4491i	0.269836	+	0.0539321i
$751$	−635.244			−0.845865			−0.422932	−	0.906161i	$-0.638999\pi$
$751$	−635.244			−0.845865			−0.422932	+	0.906161i	$0.638999\pi$
$752$	−225.052	−	441.689i	−0.299271	−	0.587353i
$753$	−19.3672	−	122.280i	−0.0257201	−	0.162390i
$754$	83.5778	−	115.035i	0.110846	−	0.152566i
$755$	164.097	+	646.964i	0.217347	+	0.856906i
$756$	567.860	−	412.575i	0.751138	−	0.545734i
$757$	490.741	−	490.741i	0.648270	−	0.648270i	−0.304304	−	0.952575i	$-0.598424\pi$
$757$	490.741	−	490.741i	0.648270	−	0.648270i	0.952575	+	0.304304i	$0.0984240\pi$
$758$	−212.747	−	33.6959i	−0.280669	−	0.0444537i
$759$	−137.425	+	44.6522i	−0.181061	+	0.0588303i
$760$	−465.988	+	408.408i	−0.613143	+	0.537379i
$761$	−16.2710	+	50.0771i	−0.0213811	+	0.0658044i	−0.961178	−	0.275930i	$-0.911014\pi$
$761$	−16.2710	+	50.0771i	−0.0213811	+	0.0658044i	0.939797	+	0.341734i	$0.111014\pi$
$762$	−233.369	−	118.907i	−0.306258	−	0.156046i
$763$	104.564	−	205.219i	0.137044	−	0.268964i
$764$	173.317	+	56.3141i	0.226855	+	0.0737095i
$765$	23.4716	−	10.0757i	0.0306818	−	0.0131708i
$766$	−69.2693	−	213.189i	−0.0904299	−	0.278315i
$767$	−71.4016	+	450.812i	−0.0930920	+	0.587760i
$768$	−138.587	−	138.587i	−0.180451	−	0.180451i
$769$	−613.908	−	844.972i	−0.798320	−	1.09879i	−0.993022	−	0.117931i	$-0.962374\pi$
$769$	−613.908	−	844.972i	−0.798320	−	1.09879i	0.194702	−	0.980862i	$-0.437626\pi$
$770$	−464.055	−	185.304i	−0.602669	−	0.240655i
$771$	−635.711	−	461.871i	−0.824528	−	0.599055i
$772$	−674.070	+	106.762i	−0.873147	+	0.138293i
$773$	−633.871	+	322.973i	−0.820014	+	0.417818i	−0.813076	−	0.582158i	$-0.802209\pi$
$773$	−633.871	+	322.973i	−0.820014	+	0.417818i	−0.00693843	+	0.999976i	$0.502209\pi$
$774$		−	23.1305i		−	0.0298844i
$775$	−161.911	+	338.918i	−0.208917	+	0.437314i
$776$	231.957			0.298914
$777$	441.935	+	867.346i	0.568771	+	1.11628i
$778$	72.8457	+	459.929i	0.0936320	+	0.591169i
$779$	−626.861	+	862.800i	−0.804699	+	1.10757i
$780$	−287.372	−	239.154i	−0.368426	−	0.306608i
$781$	−529.049	+	384.377i	−0.677400	+	0.492160i
$782$	3.06771	−	3.06771i	0.00392291	−	0.00392291i
$783$	361.551	+	57.2641i	0.461751	+	0.0731342i
$784$	−98.7866	+	32.0977i	−0.126003	+	0.0409409i
$785$	899.840	+	535.723i	1.14629	+	0.682449i
$786$	−59.7427	+	183.869i	−0.0760085	+	0.233930i
$787$	709.028	+	361.268i	0.900925	+	0.459044i	0.842160	−	0.539228i	$-0.181284\pi$
$787$	709.028	+	361.268i	0.900925	+	0.459044i	0.0587649	+	0.998272i	$0.481284\pi$
$788$	−412.999	+	810.556i	−0.524110	+	1.02862i
$789$	−448.996	−	145.888i	−0.569069	−	0.184902i
$790$	−47.7074	−	520.951i	−0.0603891	−	0.659431i
$791$	8.44975	+	26.0057i	0.0106824	+	0.0328770i
$792$	77.1948	−	487.389i	0.0974682	−	0.615390i
$793$	904.755	+	904.755i	1.14093	+	1.14093i
$794$	−66.7958	−	91.9365i	−0.0841256	−	0.115789i
$795$	−213.567	−	338.713i	−0.268638	−	0.426054i
$796$	−321.081	−	233.279i	−0.403368	−	0.293064i
$797$	180.384	−	28.5701i	0.226329	−	0.0358470i	−0.0422397	−	0.999108i	$-0.513449\pi$
$797$	180.384	−	28.5701i	0.226329	−	0.0358470i	0.268569	+	0.963260i	$0.413449\pi$
$798$	−229.209	+	116.788i	−0.287230	+	0.146351i
$799$		−	62.6979i		−	0.0784705i
$800$	225.834	−	760.687i	0.282292	−	0.950859i
$801$	277.682			0.346669
$802$	313.107	+	614.508i	0.390408	+	0.766219i
$803$	121.426	+	766.651i	0.151215	+	0.954734i
$804$	162.845	−	224.138i	0.202544	−	0.278778i
$805$	208.631	+	13.7387i	0.259169	+	0.0170667i
$806$	−128.922	+	93.6670i	−0.159952	+	0.116212i
$807$	−172.147	+	172.147i	−0.213317	+	0.213317i
$808$	476.788	+	75.5159i	0.590085	+	0.0934602i
$809$	−775.024	+	251.821i	−0.958003	+	0.311274i	−0.745963	−	0.665987i	$-0.768011\pi$
$809$	−775.024	+	251.821i	−0.958003	+	0.311274i	−0.212040	+	0.977261i	$0.568011\pi$
$810$	−2.95395	+	13.0360i	−0.00364686	+	0.0160938i
$811$	363.428	−	1118.52i	0.448123	−	1.37918i	−0.430899	−	0.902400i	$-0.641804\pi$
$811$	363.428	−	1118.52i	0.448123	−	1.37918i	0.879022	−	0.476781i	$-0.158196\pi$
$812$	−307.051	−	156.451i	−0.378142	−	0.192673i
$813$	14.1300	−	27.7317i	0.0173801	−	0.0341103i
$814$	776.072	+	252.161i	0.953405	+	0.309780i
$815$	−1500.29	−	339.965i	−1.84085	−	0.417135i
$816$	4.13058	+	12.7126i	0.00506198	+	0.0155792i
$817$	15.0847	−	95.2410i	0.0184635	−	0.116574i
$818$	−9.75499	−	9.75499i	−0.0119254	−	0.0119254i
$819$	306.980	+	422.522i	0.374823	+	0.515900i
$820$	57.8080	−	877.851i	0.0704976	−	1.07055i
$821$	353.666	+	256.954i	0.430775	+	0.312976i	0.781959	−	0.623330i	$-0.214221\pi$
$821$	353.666	+	256.954i	0.430775	+	0.312976i	−0.351184	+	0.936307i	$0.614221\pi$
$822$	295.479	−	46.7992i	0.359463	−	0.0569334i
$823$	1176.87	−	599.645i	1.42997	−	0.728609i	0.444082	−	0.895986i	$-0.353530\pi$
$823$	1176.87	−	599.645i	1.42997	−	0.728609i	0.985893	+	0.167377i	$0.0535299\pi$
$824$			483.690i			0.587002i
$825$	−646.025	+	228.323i	−0.783060	+	0.276755i
$826$	−259.069			−0.313643
$827$	−279.354	−	548.262i	−0.337792	−	0.662953i	0.658157	−	0.752881i	$-0.271336\pi$
$827$	−279.354	−	548.262i	−0.337792	−	0.662953i	−0.995948	+	0.0899277i	$0.971336\pi$
$828$	14.4574	+	91.2803i	0.0174606	+	0.110242i
$829$	263.753	−	363.024i	0.318158	−	0.437906i	−0.619746	−	0.784802i	$-0.712764\pi$
$829$	263.753	−	363.024i	0.318158	−	0.437906i	0.937904	+	0.346896i	$0.112764\pi$
$830$	−226.052	+	142.531i	−0.272352	+	0.171724i
$831$	−7.58131	+	5.50814i	−0.00912311	+	0.00662833i
$832$	−19.0977	+	19.0977i	−0.0229539	+	0.0229539i
$833$	−12.9756	−	2.05514i	−0.0155770	−	0.00246715i
$834$	109.484	−	35.5735i	0.131276	−	0.0426541i
$835$	3.17977	−	0.291196i	0.00380811	−	0.000348738i
$836$	284.534	−	875.706i	0.340352	−	1.04750i
$837$	−365.533	−	186.248i	−0.436718	−	0.222519i
$838$	216.974	−	425.836i	0.258919	−	0.508158i
$839$	−770.629	−	250.392i	−0.918509	−	0.298442i	−0.188654	−	0.982044i	$-0.560412\pi$
$839$	−770.629	−	250.392i	−0.918509	−	0.298442i	−0.729855	+	0.683602i	$0.760412\pi$
$840$	242.535	−	407.380i	0.288732	−	0.484977i
$841$	204.347	+	628.915i	0.242981	+	0.747818i
$842$	32.9662	−	208.140i	0.0391522	−	0.247197i
$843$	99.6896	+	99.6896i	0.118256	+	0.118256i
$844$	−354.690	−	488.189i	−0.420249	−	0.578423i
$845$	−66.4803	+	79.8840i	−0.0786750	+	0.0945373i
$846$	−253.058	−	183.858i	−0.299124	−	0.217326i
$847$	690.640	−	109.387i	0.815396	−	0.129146i
$848$	−281.185	+	143.271i	−0.331586	+	0.168951i
$849$			232.000i			0.273262i
$850$	14.1700	−	14.9138i	0.0166706	−	0.0175456i
$851$	−341.443			−0.401226
$852$	−126.081	−	247.447i	−0.147982	−	0.290431i
$853$	175.917	+	1110.70i	0.206234	+	1.30211i	0.845853	+	0.533417i	$0.179092\pi$
$853$	175.917	+	1110.70i	0.206234	+	1.30211i	−0.639619	+	0.768692i	$0.720908\pi$
$854$	−426.880	+	587.550i	−0.499859	+	0.687997i
$855$	197.009	−	493.367i	0.230420	−	0.577038i
$856$	266.899	−	193.914i	0.311798	−	0.226534i
$857$	870.435	−	870.435i	1.01568	−	1.01568i	0.0158015	−	0.999875i	$-0.494970\pi$
$857$	870.435	−	870.435i	1.01568	−	1.01568i	0.999875	−	0.0158015i	$-0.00503000\pi$
$858$	−287.119	−	45.4752i	−0.334638	−	0.0530014i
$859$	−1395.30	+	453.359i	−1.62433	+	0.527775i	−0.972957	−	0.230986i	$-0.925805\pi$
$859$	−1395.30	+	453.359i	−1.62433	+	0.527775i	−0.651369	+	0.758761i	$0.725805\pi$
$860$	31.3774	+	73.0947i	0.0364854	+	0.0849939i
$861$	252.164	−	776.081i	0.292873	−	0.901371i
$862$	494.403	+	251.911i	0.573553	+	0.292240i
$863$	503.210	−	987.606i	0.583094	−	1.14439i	−0.391452	−	0.920199i	$-0.628027\pi$
$863$	503.210	−	987.606i	0.583094	−	1.14439i	0.974546	−	0.224188i	$-0.0719730\pi$
$864$	824.264	+	267.820i	0.954009	+	0.309976i
$865$	−448.304	−	511.509i	−0.518271	−	0.591340i
$866$	73.7123	+	226.863i	0.0851181	+	0.261967i
$867$	85.4114	−	539.266i	0.0985137	−	0.621991i
$868$	273.093	+	273.093i	0.314623	+	0.314623i
$869$	1020.87	+	1405.10i	1.17476	+	1.61692i
$870$	107.272	−	27.2086i	0.123301	−	0.0312742i
$871$	444.279	+	322.788i	0.510080	+	0.370595i
$872$	180.936	−	28.6575i	0.207496	−	0.0328641i
$873$	−177.196	+	90.2857i	−0.202973	+	0.103420i
$874$		−	90.2315i		−	0.103240i
$875$	990.640	+	39.8360i	1.13216	+	0.0455268i
$876$	−329.641			−0.376303
$877$	375.480	+	736.921i	0.428141	+	0.840275i	0.999804	+	0.0197861i	$0.00629854\pi$
$877$	375.480	+	736.921i	0.428141	+	0.840275i	−0.571663	+	0.820489i	$0.693701\pi$
$878$	−3.92199	−	24.7625i	−0.00446696	−	0.0282033i
$879$	576.474	−	793.449i	0.655830	−	0.902672i
$880$	132.765	+	523.435i	0.150869	+	0.594812i
$881$	738.102	−	536.263i	0.837800	−	0.608698i	−0.0839550	−	0.996470i	$-0.526755\pi$
$881$	738.102	−	536.263i	0.837800	−	0.608698i	0.921755	+	0.387772i	$0.126755\pi$
$882$	−46.3451	+	46.3451i	−0.0525455	+	0.0525455i
$883$	−850.354	−	134.683i	−0.963029	−	0.152529i	−0.344929	−	0.938629i	$-0.612097\pi$
$883$	−850.354	−	134.683i	−0.963029	−	0.152529i	−0.618099	+	0.786100i	$0.712097\pi$
$884$	−35.4434	+	11.5163i	−0.0400943	+	0.0130274i
$885$	−267.160	+	234.148i	−0.301875	+	0.264574i
$886$	67.3640	−	207.325i	0.0760316	−	0.234001i
$887$	1248.92	+	636.358i	1.40803	+	0.717427i	0.982281	−	0.187414i	$-0.0600106\pi$
$887$	1248.92	+	636.358i	1.40803	+	0.717427i	0.425749	+	0.904841i	$0.360011\pi$
$888$	−351.502	+	689.861i	−0.395835	+	0.776870i
$889$	−1196.65	−	388.816i	−1.34606	−	0.437363i
$890$	205.509	−	88.2189i	0.230909	−	0.0991224i
$891$	−13.7133	−	42.2051i	−0.0153909	−	0.0473683i
$892$	−94.5223	+	596.790i	−0.105967	+	0.669048i
$893$	−922.075	−	922.075i	−1.03256	−	1.03256i
$894$	−156.540	−	215.458i	−0.175100	−	0.241005i
$895$	−198.262	−	79.1693i	−0.221522	−	0.0884573i
$896$	−827.074	−	600.904i	−0.923073	−	0.670652i
$897$	120.139	−	19.0282i	0.133935	−	0.0212132i
$898$	−555.187	+	282.882i	−0.618249	+	0.315013i
$899$			201.415i			0.224043i
$900$	79.5971	+	430.944i	0.0884412	+	0.478826i
$901$	−39.9143			−0.0443000
$902$	−310.550	−	609.488i	−0.344290	−	0.675708i
$903$	11.5421	+	72.8739i	0.0127819	+	0.0807020i
$904$	−12.7835	+	17.5950i	−0.0141410	+	0.0194635i
$905$	−697.421	−	580.401i	−0.770631	−	0.641328i
$906$	−178.305	+	129.546i	−0.196805	+	0.142987i
$907$	−338.384	+	338.384i	−0.373081	+	0.373081i	−0.868598	−	0.495517i	$-0.834979\pi$
$907$	−338.384	+	338.384i	−0.373081	+	0.373081i	0.495517	+	0.868598i	$0.334979\pi$
$908$	272.228	+	43.1167i	0.299811	+	0.0474854i
$909$	−393.619	+	127.895i	−0.433024	+	0.140698i
$910$	361.427	+	215.177i	0.397172	+	0.236458i
$911$	−433.886	+	1335.36i	−0.476274	+	1.46582i	0.367958	+	0.929842i	$0.380057\pi$
$911$	−433.886	+	1335.36i	−0.476274	+	1.46582i	−0.844232	+	0.535978i	$0.819943\pi$
$912$	247.707	+	126.213i	0.271608	+	0.138391i
$913$	402.793	−	790.525i	0.441175	−	0.865854i
$914$	432.339	+	140.476i	0.473019	+	0.153693i
$915$	90.8186	+	991.712i	0.0992553	+	1.08384i
$916$	−223.812	−	688.823i	−0.244336	−	0.751990i
$917$	−145.290	+	917.322i	−0.158440	+	1.00035i
$918$	15.8882	+	15.8882i	0.0173074	+	0.0173074i
$919$	−44.4183	−	61.1365i	−0.0483332	−	0.0665250i	0.784166	−	0.620551i	$-0.213091\pi$
$919$	−44.4183	−	61.1365i	−0.0483332	−	0.0665250i	−0.832500	+	0.554026i	$0.813091\pi$
$920$	88.6961	+	140.670i	0.0964088	+	0.152903i
$921$	275.414	+	200.100i	0.299038	+	0.217264i
$922$	33.2645	−	5.26858i	0.0360786	−	0.00571429i
$923$	490.483	−	249.914i	0.531401	−	0.270763i
$924$			704.531i			0.762480i
$925$	−1618.54	+	41.3888i	−1.74978	+	0.0447447i
$926$	198.514			0.214378
$927$	−188.268	−	369.498i	−0.203094	−	0.398595i
$928$	−66.5639	−	420.268i	−0.0717283	−	0.452875i
$929$	832.874	−	1146.35i	0.896527	−	1.23396i	−0.0750356	−	0.997181i	$-0.523907\pi$
$929$	832.874	−	1146.35i	0.896527	−	1.23396i	0.971563	−	0.236783i	$-0.0760930\pi$
$930$	−123.760	−	8.14983i	−0.133076	−	0.00876326i
$931$	−221.052	+	160.604i	−0.237435	+	0.172507i
$932$	142.336	−	142.336i	0.152721	−	0.152721i
$933$	−22.1677	−	3.51102i	−0.0237596	−	0.00376315i
$934$	−713.313	+	231.769i	−0.763718	+	0.248147i
$935$	−15.0940	+	66.6110i	−0.0161433	+	0.0712417i
$936$	−128.364	+	395.064i	−0.137141	+	0.422077i
$937$	−1076.49	−	548.497i	−1.14886	−	0.585376i	−0.227386	−	0.973805i	$-0.573018\pi$
$937$	−1076.49	−	548.497i	−1.14886	−	0.585376i	−0.921479	+	0.388429i	$0.873018\pi$
$938$	−141.510	+	277.728i	−0.150863	+	0.296086i
$939$	309.099	+	100.432i	0.329178	+	0.106957i
$940$	1049.10	+	237.725i	1.11606	+	0.252899i
$941$	−286.084	−	880.476i	−0.304021	−	0.935681i	−0.980041	−	0.198797i	$-0.936296\pi$
$941$	−286.084	−	880.476i	−0.304021	−	0.935681i	0.676019	−	0.736884i	$-0.263704\pi$
$942$	−54.0961	+	341.549i	−0.0574268	+	0.362579i
$943$	202.392	+	202.392i	0.214625	+	0.214625i
$944$	164.566	+	226.506i	0.174329	+	0.239943i
$945$	−71.1551	+	1080.54i	−0.0752964	+	1.14342i
$946$	50.0373	+	36.3542i	0.0528935	+	0.0384294i
$947$	−877.188	+	138.933i	−0.926280	+	0.146708i	−0.601310	−	0.799016i	$-0.705354\pi$
$947$	−877.188	+	138.933i	−0.926280	+	0.146708i	−0.324970	+	0.945724i	$0.605354\pi$
$948$	−657.197	+	334.858i	−0.693245	+	0.353226i
$949$		−	653.406i		−	0.688520i
$950$	−10.9376	−	427.724i	−0.0115133	−	0.450236i
$951$	143.979			0.151398
$952$	−21.4555	−	42.1088i	−0.0225373	−	0.0442319i
$953$	−47.9001	−	302.429i	−0.0502625	−	0.317345i	−0.999991	−	0.00426975i	$-0.998641\pi$
$953$	−47.9001	−	302.429i	−0.0502625	−	0.317345i	0.949728	−	0.313075i	$-0.101359\pi$
$954$	−117.046	+	161.100i	−0.122690	+	0.168868i
$955$	−237.818	+	149.950i	−0.249024	+	0.157015i
$956$	−100.804	+	73.2381i	−0.105443	+	0.0766089i
$957$	−259.807	+	259.807i	−0.271481	+	0.271481i
$958$	−80.1400	−	12.6929i	−0.0836535	−	0.0132494i
$959$	1366.82	−	444.108i	1.42526	−	0.463094i
$960$	−20.9332	+	1.91701i	−0.0218054	+	0.00199688i
$961$	−227.211	+	699.284i	−0.236432	+	0.727663i
$962$	−612.042	−	311.851i	−0.636219	−	0.324170i
$963$	−128.410	+	252.019i	−0.133344	+	0.261702i
$964$	305.818	+	99.3661i	0.317238	+	0.103077i
$965$	538.609	−	904.688i	0.558144	−	0.937501i
$966$	21.3348	+	65.6618i	0.0220857	+	0.0679728i
$967$	94.6041	−	597.307i	0.0978326	−	0.617691i	−0.889243	−	0.457435i	$-0.848768\pi$
$967$	94.6041	−	597.307i	0.0978326	−	0.617691i	0.987076	−	0.160256i	$-0.0512318\pi$
$968$	393.265	+	393.265i	0.406266	+	0.406266i
$969$	20.6677	+	28.4467i	0.0213289	+	0.0293567i
$970$	−102.457	+	123.114i	−0.105626	+	0.126922i
$971$	1288.45	+	936.112i	1.32693	+	0.964070i	0.999818	+	0.0190840i	$0.00607498\pi$
$971$	1288.45	+	936.112i	1.32693	+	0.964070i	0.327111	+	0.944986i	$0.393925\pi$
$972$	−768.050	+	121.647i	−0.790175	+	0.125151i
$973$	492.748	−	251.068i	0.506422	−	0.258035i
$974$		−	348.668i		−	0.357975i
$975$	567.190	−	104.762i	0.581734	−	0.107449i
$976$	784.861			0.804161
$977$	−133.140	−	261.301i	−0.136274	−	0.267453i	0.812777	−	0.582575i	$-0.197955\pi$
$977$	−133.140	−	261.301i	−0.136274	−	0.267453i	−0.949051	+	0.315122i	$0.897955\pi$
$978$	−79.4635	−	501.713i	−0.0812510	−	0.512999i
$979$	−436.432	+	600.697i	−0.445794	+	0.613582i
$980$	83.5862	−	209.324i	0.0852921	−	0.213596i
$981$	−127.066	+	92.3185i	−0.129527	+	0.0941065i
$982$	−407.221	+	407.221i	−0.414686	+	0.414686i
$983$	−65.4417	−	10.3649i	−0.0665734	−	0.0105442i	0.123059	−	0.992399i	$-0.460730\pi$
$983$	−65.4417	−	10.3649i	−0.0665734	−	0.0105442i	−0.189632	+	0.981855i	$0.560730\pi$
$984$	617.271	−	200.563i	0.627308	−	0.203825i
$985$	−553.607	−	1289.65i	−0.562038	−	1.30929i
$986$	3.40893	−	10.4916i	0.00345734	−	0.0106406i
$987$	889.018	+	452.977i	0.900727	+	0.458943i
$988$	−351.888	+	690.618i	−0.356162	+	0.699007i
$989$	−24.6130	−	7.99726i	−0.0248868	−	0.00808621i
$990$	224.590	+	256.254i	0.226858	+	0.258843i
$991$	245.405	+	755.279i	0.247634	+	0.762138i	0.995192	+	0.0979420i	$0.0312260\pi$
$991$	245.405	+	755.279i	0.247634	+	0.762138i	−0.747558	+	0.664196i	$0.768774\pi$
$992$	−74.5992	+	471.001i	−0.0752008	+	0.474799i
$993$	−568.540	−	568.540i	−0.572548	−	0.572548i
$994$	183.655	+	252.780i	0.184764	+	0.254305i
$995$	593.489	−	150.533i	0.596471	−	0.151290i
$996$	304.829	+	221.471i	0.306053	+	0.222360i
$997$	236.698	−	37.4893i	0.237410	−	0.0376021i	−0.0365955	−	0.999330i	$-0.511651\pi$
$997$	236.698	−	37.4893i	0.237410	−	0.0376021i	0.274006	+	0.961728i	$0.411651\pi$
$998$	472.461	−	240.731i	0.473408	−	0.241213i
$999$		−	1768.39i		−	1.77016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.3.2	✓	32
3.2	odd	2		225.3.r.a.28.3		32
4.3	odd	2		400.3.bg.c.353.3		32
5.2	odd	4		125.3.f.a.7.3		32
5.3	odd	4		125.3.f.b.7.2		32
5.4	even	2		125.3.f.c.118.3		32
25.6	even	5		125.3.f.a.18.3		32
25.8	odd	20		125.3.f.c.107.3		32
25.17	odd	20	inner	25.3.f.a.17.2	yes	32
25.19	even	10		125.3.f.b.18.2		32
75.17	even	20		225.3.r.a.217.3		32
100.67	even	20		400.3.bg.c.17.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.3.2	✓	32	1.1	even	1	trivial
25.3.f.a.17.2	yes	32	25.17	odd	20	inner
125.3.f.a.7.3		32	5.2	odd	4
125.3.f.a.18.3		32	25.6	even	5
125.3.f.b.7.2		32	5.3	odd	4
125.3.f.b.18.2		32	25.19	even	10
125.3.f.c.107.3		32	25.8	odd	20
125.3.f.c.118.3		32	5.4	even	2
225.3.r.a.28.3		32	3.2	odd	2
225.3.r.a.217.3		32	75.17	even	20
400.3.bg.c.17.3		32	100.67	even	20
400.3.bg.c.353.3		32	4.3	odd	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395527 - 0.776265i) q^{2} +(-0.296456 - 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(1.22928 + 4.84653i) q^{5} +(-1.33572 + 0.970456i) q^{6} +(-5.60844 + 5.60844i) q^{7} +(-6.23083 - 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +O(q^{10})\)	\(q+(-0.395527 - 0.776265i) q^{2} +(-0.296456 - 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(1.22928 + 4.84653i) q^{5} +(-1.33572 + 0.970456i) q^{6} +(-5.60844 + 5.60844i) q^{7} +(-6.23083 - 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +(3.27598 - 2.87118i) q^{10} +(-4.46912 + 13.7545i) q^{11} +(-5.47248 - 2.78837i) q^{12} +(5.52703 - 10.8474i) q^{13} +(6.57192 + 2.13535i) q^{14} +(8.70708 - 3.73769i) q^{15} +(-2.30767 - 7.10228i) q^{16} +(0.147755 - 0.932886i) q^{17} +(-3.33199 - 3.33199i) q^{18} +(-11.5466 - 15.8926i) q^{19} +(15.0494 + 6.00945i) q^{20} +(12.1603 + 8.83494i) q^{21} +(12.4448 - 1.97107i) q^{22} +(-4.69757 + 2.39353i) q^{23} +11.9551i q^{24} +(-21.9777 + 11.9155i) q^{25} -10.6066 q^{26} +(-12.3965 - 24.3295i) q^{27} +(4.02128 + 25.3894i) q^{28} +(-7.87983 + 10.8457i) q^{29} +(-6.34532 - 5.28064i) q^{30} +(12.1549 - 8.83105i) q^{31} +(-22.4436 + 22.4436i) q^{32} +(27.0700 + 4.28747i) q^{33} +(-0.782608 + 0.254285i) q^{34} +(-34.0758 - 20.2871i) q^{35} +(5.41686 - 16.6714i) q^{36} +(57.7042 + 29.4017i) q^{37} +(-7.76985 + 15.2492i) q^{38} +(-21.9422 - 7.12944i) q^{39} +(-2.87655 - 31.4110i) q^{40} +(-16.7764 - 51.6323i) q^{41} +(2.04855 - 12.9340i) q^{42} +(3.47098 + 3.47098i) q^{43} +(27.5508 + 37.9204i) q^{44} +(14.4237 + 22.8757i) q^{45} +(3.71603 + 2.69985i) q^{46} +(65.5638 - 10.3843i) q^{47} +(-12.6096 + 6.42490i) q^{48} -13.9091i q^{49} +(17.9424 + 12.3477i) q^{50} -1.78993 q^{51} +(-17.9129 - 35.1561i) q^{52} +(-6.61077 - 41.7387i) q^{53} +(-13.9830 + 19.2459i) q^{54} +(-72.1557 - 4.75157i) q^{55} +(40.4800 - 29.4104i) q^{56} +(-26.3239 + 26.3239i) q^{57} +(11.5358 + 1.82709i) q^{58} +(-35.6563 + 11.5854i) q^{59} +(6.78671 - 29.9502i) q^{60} +(-32.4776 + 99.9557i) q^{61} +(-11.6628 - 5.94250i) q^{62} +(-19.4757 + 38.2232i) q^{63} +(-2.10987 - 0.685539i) q^{64} +(59.3666 + 13.4524i) q^{65} +(-7.37870 - 22.7093i) q^{66} +(-7.05644 + 44.5526i) q^{67} +(-2.16456 - 2.16456i) q^{68} +(5.87272 + 8.08310i) q^{69} +(-2.27030 + 34.4760i) q^{70} +(36.5810 + 26.5777i) q^{71} +(-33.7004 + 5.33762i) q^{72} +(47.8210 - 24.3660i) q^{73} -56.4229i q^{74} +(28.8183 + 37.6045i) q^{75} -63.6667 q^{76} +(-52.0767 - 102.206i) q^{77} +(3.14438 + 19.8528i) q^{78} +(70.5878 - 97.1558i) q^{79} +(31.5847 - 19.9149i) q^{80} +(-2.48243 + 1.80359i) q^{81} +(-33.4449 + 33.4449i) q^{82} +(-60.5919 - 9.59682i) q^{83} +(46.3305 - 15.0537i) q^{84} +(4.70289 - 0.430680i) q^{85} +(1.32153 - 4.06726i) q^{86} +(22.6364 + 11.5338i) q^{87} +(41.4202 - 81.2918i) q^{88} +(48.8275 + 15.8650i) q^{89} +(12.0527 - 20.2445i) q^{90} +(29.8390 + 91.8350i) q^{91} +(-2.67300 + 16.8767i) q^{92} +(-20.1329 - 20.1329i) q^{93} +(-33.9932 - 46.7876i) q^{94} +(62.8299 - 75.4976i) q^{95} +(48.6625 + 35.3553i) q^{96} +(-36.3164 + 5.75195i) q^{97} +(-10.7972 + 5.50143i) q^{98} +78.2221i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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