LMFDB - Embedded newform 25.3.f.a.17.2

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			17.2
Character	$\chi$	$=$	25.17
Dual form			25.3.f.a.3.2

$q$-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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{20}\right)$

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	−0.968497	−	0.249025i	$-0.919890\pi$
$2$	−0.395527	+	0.776265i	−0.197763	+	0.388132i	0.770734	+	0.637157i	$0.219890\pi$
$3$	−0.296456	+	1.87175i	−0.0988188	+	0.623917i	0.887719	+	0.460385i	$0.152289\pi$
$3$	−0.296456	+	1.87175i	−0.0988188	+	0.623917i	−0.986538	+	0.163532i	$0.947711\pi$
$4$	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	0.182079	−	0.983284i	$-0.441717\pi$
$7$	−5.60844	−	5.60844i	−0.801205	−	0.801205i	−0.983284	+	0.182079i	$0.941717\pi$
$8$	−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	−0.919818	−	0.392345i	$-0.871664\pi$
$11$	−4.46912	−	13.7545i	−0.406284	−	1.25041i	0.513534	−	0.858069i	$-0.328336\pi$
$12$	−5.47248	+	2.78837i	−0.456040	+	0.232364i
$13$	5.52703	+	10.8474i	0.425156	+	0.834416i	0.999871	+	0.0160623i	$0.00511299\pi$
$13$	5.52703	+	10.8474i	0.425156	+	0.834416i	−0.574715	+	0.818354i	$0.694887\pi$
$14$	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	0.991653	−	0.128936i	$-0.0411563\pi$
$17$	0.147755	+	0.932886i	0.00869145	+	0.0548757i	−0.982961	+	0.183812i	$0.941156\pi$
$18$	−3.33199	+	3.33199i	−0.185111	+	0.185111i
$19$	−11.5466	+	15.8926i	−0.607718	+	0.836452i	−0.996387	−	0.0849253i	$-0.972935\pi$
$19$	−11.5466	+	15.8926i	−0.607718	+	0.836452i	0.388669	+	0.921377i	$0.372935\pi$
$20$	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	0.348878	−	0.937168i	$-0.386563\pi$
$23$	−4.69757	−	2.39353i	−0.204242	−	0.104067i	−0.553120	+	0.833102i	$0.686563\pi$
$24$		−	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	0.651251	−	0.758863i	$-0.274245\pi$
$29$	−7.87983	−	10.8457i	−0.271718	−	0.373988i	−0.922969	+	0.384875i	$0.874245\pi$
$30$	−6.34532	+	5.28064i	−0.211511	+	0.176021i
$31$	12.1549	+	8.83105i	0.392093	+	0.284873i	0.766313	−	0.642468i	$-0.222089\pi$
$31$	12.1549	+	8.83105i	0.392093	+	0.284873i	−0.374219	+	0.927340i	$0.622089\pi$
$32$	−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	0.560142	−	0.828396i	$-0.310746\pi$
$37$	57.7042	−	29.4017i	1.55957	−	0.794642i	0.999430	+	0.0337547i	$0.0107465\pi$
$38$	−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	0.508175	+	0.861254i	$0.330320\pi$
$41$	−16.7764	+	51.6323i	−0.409180	+	1.25933i	−0.917355	+	0.398071i	$0.869680\pi$
$42$	2.04855	+	12.9340i	0.0487750	+	0.307953i
$43$	3.47098	−	3.47098i	0.0807204	−	0.0807204i	−0.665594	−	0.746314i	$-0.731822\pi$
$43$	3.47098	−	3.47098i	0.0807204	−	0.0807204i	0.746314	+	0.665594i	$0.231822\pi$
$44$	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	0.808248	−	0.588842i	$-0.200416\pi$
$47$	65.5638	+	10.3843i	1.39498	+	0.220942i	0.586727	+	0.809785i	$0.300416\pi$
$48$	−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	0.843438	+	0.537227i	$0.180528\pi$
$53$	−6.61077	+	41.7387i	−0.124731	+	0.787523i	−0.968169	+	0.250296i	$0.919472\pi$
$54$	−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	−0.00916740	−	0.999958i	$-0.502918\pi$
$59$	−35.6563	−	11.5854i	−0.604345	−	0.196363i	−0.595177	+	0.803595i	$0.702918\pi$
$60$	6.78671	+	29.9502i	0.113112	+	0.499171i
$61$	−32.4776	−	99.9557i	−0.532419	−	1.63862i	−0.749161	−	0.662388i	$-0.769543\pi$
$61$	−32.4776	−	99.9557i	−0.532419	−	1.63862i	0.216742	−	0.976229i	$-0.430457\pi$
$62$	−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	−0.982705	−	0.185178i	$-0.940714\pi$
$67$	−7.05644	−	44.5526i	−0.105320	−	0.664965i	0.877385	−	0.479787i	$-0.159286\pi$
$68$	−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	−0.299577	−	0.954072i	$-0.596845\pi$
$71$	36.5810	−	26.5777i	0.515226	−	0.374333i	0.814802	+	0.579739i	$0.196845\pi$
$72$	−33.7004	−	5.33762i	−0.468062	−	0.0741337i
$73$	47.8210	+	24.3660i	0.655082	+	0.333781i	0.749744	−	0.661728i	$-0.230177\pi$
$73$	47.8210	+	24.3660i	0.655082	+	0.333781i	−0.0946613	+	0.995510i	$0.530177\pi$
$74$			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	0.972490	+	0.232943i	$0.0748356\pi$
$79$	70.5878	+	97.1558i	0.893516	+	1.22982i	−0.0789740	+	0.996877i	$0.525164\pi$
$80$	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	−0.510371	−	0.859954i	$-0.670492\pi$
$83$	−60.5919	+	9.59682i	−0.730023	+	0.115624i	−0.219652	+	0.975578i	$0.570492\pi$
$84$	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	−0.0215727	−	0.999767i	$-0.506867\pi$
$89$	48.8275	−	15.8650i	0.548623	−	0.178258i	0.570196	+	0.821509i	$0.306867\pi$
$90$	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	−0.0335987	−	0.999435i	$-0.510697\pi$
$97$	−36.3164	−	5.75195i	−0.374395	−	0.0592984i	−0.340797	+	0.940137i	$0.610697\pi$
$98$	−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	0.858502	+	0.512811i	$0.171396\pi$
$103$	−11.9943	+	75.7288i	−0.116449	+	0.735231i	−0.974951	+	0.222420i	$0.928604\pi$
$104$	−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	0.512872	−	0.858465i	$-0.328581\pi$
$107$	−36.9784	−	36.9784i	−0.345593	−	0.345593i	−0.858465	+	0.512872i	$0.828581\pi$
$108$	−87.4072	+	13.8439i	−0.809325	+	0.128185i
$109$	−27.6176	−	8.97352i	−0.253373	−	0.0823258i	0.179577	−	0.983744i	$-0.442527\pi$
$109$	−27.6176	−	8.97352i	−0.253373	−	0.0823258i	−0.432950	+	0.901418i	$0.642527\pi$
$110$	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	0.897828	−	0.440346i	$-0.145144\pi$
$113$	1.56513	+	3.07175i	0.0138507	+	0.0271836i	−0.883977	+	0.467529i	$0.845144\pi$
$114$	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	−0.412317	−	0.911041i	$-0.635280\pi$
$127$	72.0197	−	141.347i	0.567084	−	1.11297i	0.979401	−	0.201925i	$-0.0647197\pi$
$128$	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	0.887391	−	0.461018i	$-0.152516\pi$
$131$	94.7333	+	68.8278i	0.723155	+	0.525403i	−0.164236	+	0.986421i	$0.552516\pi$
$132$	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	−0.929771	−	0.368139i	$-0.879995\pi$
$137$	−161.447	+	82.2613i	−1.17844	+	0.600448i	−0.248674	+	0.968587i	$0.579995\pi$
$138$	3.95181	+	7.75587i	0.0286363	+	0.0562019i
$139$	−66.3122	+	21.5461i	−0.477066	+	0.155008i	−0.537673	−	0.843153i	$-0.680696\pi$
$139$	−66.3122	+	21.5461i	−0.477066	+	0.155008i	0.0606066	+	0.998162i	$0.480696\pi$
$140$	−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	$-0.817935\pi$
$149$		−	161.305i		−	1.08259i	0.840834	−	0.541293i	$-0.182065\pi$
$150$	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	0.998478	−	0.0551526i	$-0.0175645\pi$
$157$	148.102	+	148.102i	0.943325	+	0.943325i	−0.0551526	+	0.998478i	$0.517565\pi$
$158$	−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	−0.723058	−	0.690787i	$-0.757264\pi$
$163$	−139.677	−	274.131i	−0.856914	−	1.68179i	−0.133855	−	0.991001i	$-0.542736\pi$
$164$	−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	0.987986	−	0.154546i	$-0.0493914\pi$
$167$	0.0999015	+	0.630753i	0.000598213	+	0.00377697i	−0.987387	+	0.158323i	$0.949391\pi$
$168$	−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	0.0671264	−	0.997744i	$-0.478617\pi$
$173$	−121.206	−	61.7573i	−0.700610	−	0.356979i	−0.767736	+	0.640766i	$0.778617\pi$
$174$			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	0.733140	−	0.680078i	$-0.238054\pi$
$179$	−25.0966	−	34.5426i	−0.140205	−	0.192975i	−0.873345	+	0.487102i	$0.838054\pi$
$180$	87.4571	−	5.75920i	0.485873	−	0.0319956i
$181$	−146.810	−	106.664i	−0.811107	−	0.589304i	0.103044	−	0.994677i	$-0.467142\pi$
$181$	−146.810	−	106.664i	−0.811107	−	0.589304i	−0.914151	+	0.405373i	$0.867142\pi$
$182$	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	−0.895211	−	0.445643i	$-0.852975\pi$
$191$	17.3757	−	53.4768i	0.0909721	−	0.279983i	0.986183	+	0.165659i	$0.0529752\pi$
$192$	−0.657674	−	4.15239i	−0.00342539	−	0.0216270i
$193$	−148.900	+	148.900i	−0.771503	+	0.771503i	−0.978369	−	0.206867i	$-0.933673\pi$
$193$	−148.900	+	148.900i	−0.771503	+	0.771503i	0.206867	+	0.978369i	$0.433673\pi$
$194$	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	−0.593860	−	0.804568i	$-0.702397\pi$
$197$	−277.234	−	43.9096i	−1.40728	−	0.222891i	−0.813420	+	0.581677i	$0.802397\pi$
$198$	60.7211	+	30.9389i	0.306672	+	0.156257i
$199$			122.456i			0.615359i	0.951490	+	0.307679i	$0.0995524\pi$
$199$			122.456i			0.615359i	−0.951490	+	0.307679i	$0.900448\pi$
$200$	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	0.989824	+	0.142300i	$0.0454497\pi$
$211$	57.5357	+	177.077i	0.272681	+	0.839227i	−0.717142	+	0.696927i	$0.754550\pi$
$212$	−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	0.0399691	−	0.999201i	$-0.487274\pi$
$223$	−166.115	−	84.6396i	−0.744908	−	0.379550i	−0.784877	+	0.619651i	$0.787274\pi$
$224$			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	−0.790194	−	0.612857i	$-0.790020\pi$
$227$	38.6087	−	75.7738i	0.170082	−	0.333805i	0.960276	+	0.279052i	$0.0900202\pi$
$228$	18.8744	−	119.168i	0.0827824	−	0.522668i
$229$	131.354	+	180.794i	0.573600	+	0.789493i	0.992975	−	0.118320i	$-0.0377509\pi$
$229$	131.354	+	180.794i	0.573600	+	0.789493i	−0.419376	+	0.907813i	$0.637751\pi$
$230$	−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	−0.0233990	−	0.999726i	$-0.507449\pi$
$233$	61.3442	−	9.71596i	0.263280	−	0.0416994i	0.286679	+	0.958027i	$0.407449\pi$
$234$	−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	−0.384509	−	0.923121i	$-0.625629\pi$
$239$	−36.5637	+	11.8803i	−0.152986	+	0.0497082i	0.231523	+	0.972829i	$0.425629\pi$
$240$	−46.6392	+	53.2148i	−0.194330	+	0.221728i
$241$	30.6594	−	94.3598i	0.127217	−	0.391535i	−0.867081	−	0.498167i	$-0.834007\pi$
$241$	30.6594	−	94.3598i	0.127217	−	0.391535i	0.994299	+	0.106632i	$0.0340067\pi$
$242$	−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	0.988296	+	0.152547i	$0.0487475\pi$
$257$	293.197	+	293.197i	1.14084	+	1.14084i	0.152547	+	0.988296i	$0.451252\pi$
$258$	−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	0.999755	+	0.0221457i	$0.00704979\pi$
$263$	113.098	+	221.967i	0.430030	+	0.843981i	−0.569725	+	0.821836i	$0.692950\pi$
$264$	−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	−0.925968	−	0.377603i	$-0.876748\pi$
$269$	−75.5099	+	103.931i	−0.280706	+	0.386359i	0.645262	+	0.763962i	$0.276748\pi$
$270$	−110.465	+	44.1103i	−0.409129	+	0.163372i
$271$	13.2869	−	9.65352i	0.0490293	−	0.0356219i	−0.563001	−	0.826456i	$-0.690353\pi$
$271$	13.2869	−	9.65352i	0.0490293	−	0.0356219i	0.612030	+	0.790835i	$0.290353\pi$
$272$	−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	−0.895023	−	0.446019i	$-0.852841\pi$
$277$	−2.24494	+	4.40595i	−0.00810448	+	0.0159059i	0.886919	+	0.461925i	$0.152841\pi$
$278$	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	0.475521	−	0.879705i	$-0.342260\pi$
$281$	−60.1858	−	43.7275i	−0.214184	−	0.155614i	−0.689705	+	0.724091i	$0.742260\pi$
$282$	−77.4973	−	77.4973i	−0.274813	−	0.274813i
$283$	−120.915	+	19.1510i	−0.427260	+	0.0676714i	−0.366362	−	0.930473i	$-0.619397\pi$
$283$	−120.915	+	19.1510i	−0.427260	+	0.0676714i	−0.0608988	+	0.998144i	$0.519397\pi$
$284$	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	0.292788	−	0.956177i	$-0.405417\pi$
$293$	365.947	−	365.947i	1.24897	−	1.24897i	0.956177	−	0.292788i	$-0.0945831\pi$
$294$	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	0.469287	−	0.883046i	$-0.344511\pi$
$307$	−127.024	−	127.024i	−0.413759	−	0.413759i	−0.883046	+	0.469287i	$0.844511\pi$
$308$	−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	0.956768	−	0.290852i	$-0.0939388\pi$
$311$	3.65978	+	11.2636i	0.0117678	+	0.0362175i	−0.945000	+	0.327070i	$0.893939\pi$
$312$	129.682	−	66.0763i	0.415648	−	0.211783i
$313$	−77.8591	−	152.807i	−0.248751	−	0.488201i	0.732542	−	0.680722i	$-0.238334\pi$
$313$	−77.8591	−	152.807i	−0.248751	−	0.488201i	−0.981293	+	0.192521i	$0.938334\pi$
$314$	−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	0.961825	−	0.273666i	$-0.0882364\pi$
$317$	−11.8851	−	75.0397i	−0.0374925	−	0.236718i	−0.999317	+	0.0369480i	$0.988236\pi$
$318$	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	0.969697	−	0.244310i	$-0.0785614\pi$
$331$	343.246	+	249.383i	1.03700	+	0.753423i	0.0673003	+	0.997733i	$0.478561\pi$
$332$	−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	−0.628554	−	0.777766i	$-0.716353\pi$
$337$	−124.280	+	63.3239i	−0.368784	+	0.187905i	0.259771	+	0.965670i	$0.416353\pi$
$338$	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	0.758265	−	0.651947i	$-0.226048\pi$
$347$	443.450	+	70.2356i	1.27795	+	0.202408i	0.519690	+	0.854355i	$0.326048\pi$
$348$	73.3639	+	37.3808i	0.210816	+	0.107416i
$349$		−	127.497i		−	0.365320i	−0.983176	−	0.182660i	$-0.941529\pi$
$349$		−	127.497i		−	0.365320i	0.983176	−	0.182660i	$-0.0584708\pi$
$350$	−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	0.622234	+	0.782831i	$0.286225\pi$
$353$	−74.6432	+	471.279i	−0.211454	+	1.33507i	−0.833688	+	0.552236i	$0.813775\pi$
$354$	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	0.795931	−	0.605387i	$-0.206982\pi$
$359$	389.162	+	126.446i	1.08402	+	0.352218i	0.288085	+	0.957605i	$0.406982\pi$
$360$	−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	0.999980	+	0.00630745i	$0.00200774\pi$
$367$	18.6772	+	117.923i	0.0508916	+	0.321317i	−0.949088	+	0.315010i	$0.897992\pi$
$368$	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	0.119520	−	0.992832i	$-0.461865\pi$
$373$	−228.816	−	116.587i	−0.613446	−	0.312567i	−0.732966	+	0.680265i	$0.761865\pi$
$374$			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	0.956491	−	0.291761i	$-0.0942413\pi$
$379$	145.323	+	200.020i	0.383438	+	0.527757i	−0.573053	+	0.819518i	$0.694241\pi$
$380$	−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	0.184412	−	0.982849i	$-0.440962\pi$
$383$	254.126	−	40.2496i	0.663515	−	0.105090i	0.479103	+	0.877759i	$0.340962\pi$
$384$	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	−0.877931	−	0.478786i	$-0.841077\pi$
$389$	−508.333	+	165.168i	−1.30677	+	0.424595i	−0.428838	+	0.903381i	$0.641077\pi$
$390$	−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	0.316565	−	0.948571i	$-0.397470\pi$
$397$	128.831	+	20.4049i	0.324512	+	0.0513976i	0.00794678	+	0.999968i	$0.497470\pi$
$398$	−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	0.327370	−	0.944896i	$-0.393838\pi$
$409$	15.0598	+	4.89323i	0.0368210	+	0.0119639i	−0.290549	+	0.956860i	$0.593838\pi$
$410$	−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	−0.226808	−	0.973939i	$-0.572829\pi$
$419$	322.442	−	443.803i	0.769551	−	1.05920i	0.996359	−	0.0852562i	$-0.0271709\pi$
$420$	129.911	−	206.037i	0.309312	−	0.490564i
$421$	195.688	−	142.176i	0.464818	−	0.337710i	−0.330601	−	0.943771i	$-0.607251\pi$
$421$	195.688	−	142.176i	0.464818	−	0.337710i	0.795418	+	0.606061i	$0.207251\pi$
$422$	−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	−0.201669	−	0.979454i	$-0.564637\pi$
$431$	−515.262	−	374.360i	−1.19550	−	0.868585i	−0.993835	+	0.110869i	$0.964637\pi$
$432$	−144.188	−	144.188i	−0.333768	−	0.333768i
$433$	−270.426	+	42.8313i	−0.624540	+	0.0989175i	−0.460680	−	0.887566i	$-0.652395\pi$
$433$	−270.426	+	42.8313i	−0.624540	+	0.0989175i	−0.163860	+	0.986484i	$0.552395\pi$
$434$	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	−0.277680	−	0.960674i	$-0.589565\pi$
$439$	27.3685	−	8.89257i	0.0623429	−	0.0202564i	0.340022	+	0.940417i	$0.389565\pi$
$440$	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	−0.478628	−	0.878018i	$-0.658866\pi$
$443$	176.930	−	176.930i	0.399390	−	0.399390i	0.878018	+	0.478628i	$0.158866\pi$
$444$	−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	$0.293286\pi$
$449$			715.203i			1.59288i	−0.604717	+	0.796440i	$0.706714\pi$
$450$	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	0.176888	−	0.984231i	$-0.443397\pi$
$457$	−368.956	−	368.956i	−0.807343	−	0.807343i	−0.984231	+	0.176888i	$0.943397\pi$
$458$	−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	0.937264	−	0.348621i	$-0.113350\pi$
$461$	−11.9458	−	36.7653i	−0.0259127	−	0.0797512i	−0.963177	+	0.268870i	$0.913350\pi$
$462$	168.747	−	85.9807i	0.365252	−	0.186105i
$463$	−103.445	−	203.022i	−0.223423	−	0.438492i	0.751900	−	0.659278i	$-0.229138\pi$
$463$	−103.445	−	203.022i	−0.223423	−	0.438492i	−0.975322	+	0.220786i	$0.929138\pi$
$464$	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	0.527276	+	0.849694i	$0.323213\pi$
$467$	134.672	+	850.285i	0.288377	+	1.82074i	−0.238899	+	0.971044i	$0.576787\pi$
$468$	−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	0.862327	−	0.506352i	$-0.169006\pi$
$479$	54.7418	+	75.3456i	0.114284	+	0.157298i	−0.748043	+	0.663650i	$0.769006\pi$
$480$	−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	−0.0477923	−	0.998857i	$-0.515219\pi$
$487$	356.586	−	181.689i	0.732209	−	0.373079i	0.780001	+	0.625778i	$0.215219\pi$
$488$	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	0.495310	+	0.868716i	$0.335055\pi$
$491$	−204.267	+	628.670i	−0.416023	+	1.28039i	−0.911333	+	0.411671i	$0.864945\pi$
$492$	−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	$-0.791228\pi$
$499$		−	608.633i		−	1.21971i	0.792514	−	0.609853i	$-0.208772\pi$
$500$	−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	−0.810611	−	0.585585i	$-0.800865\pi$
$503$	71.0647	−	448.685i	0.141282	−	0.892018i	0.951892	−	0.306432i	$-0.0991353\pi$
$504$	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	−0.187297	−	0.982303i	$-0.559973\pi$
$509$	−466.349	−	151.526i	−0.916207	−	0.297694i	−0.728910	+	0.684610i	$0.759973\pi$
$510$	−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	−0.342009	−	0.939696i	$-0.611108\pi$
$521$	232.370	−	168.827i	0.446008	−	0.324044i	0.788018	+	0.615653i	$0.211108\pi$
$522$	62.3932	+	9.88210i	0.119527	+	0.0189312i
$523$	45.9244	+	23.3997i	0.0878096	+	0.0447412i	0.497344	−	0.867554i	$-0.334309\pi$
$523$	45.9244	+	23.3997i	0.0878096	+	0.0447412i	−0.409534	+	0.912295i	$0.634309\pi$
$524$			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	0.0931088	+	0.995656i	$0.470320\pi$
$541$	−306.990	+	944.819i	−0.567450	+	1.74643i	−0.660559	+	0.750775i	$0.729680\pi$
$542$	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	0.265422	−	0.964132i	$-0.414489\pi$
$547$	120.296	+	19.0530i	0.219919	+	0.0348318i	−0.0455024	+	0.998964i	$0.514489\pi$
$548$	−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	0.999332	+	0.0365353i	$0.0116321\pi$
$557$	576.978	+	576.978i	1.03587	+	1.03587i	0.0365353	+	0.999332i	$0.488368\pi$
$558$	−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	0.827485	+	0.561488i	$0.189771\pi$
$563$	447.785	+	878.827i	0.795355	+	1.56097i	−0.0321302	+	0.999484i	$0.510229\pi$
$564$	−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	−0.625473	−	0.780246i	$-0.715094\pi$
$569$	176.314	−	242.675i	0.309866	−	0.426495i	0.935340	+	0.353751i	$0.115094\pi$
$570$	−10.6559	−	161.817i	−0.0186946	−	0.283890i
$571$	−212.912	+	154.690i	−0.372876	+	0.270910i	−0.758402	−	0.651787i	$-0.774020\pi$
$571$	−212.912	+	154.690i	−0.372876	+	0.270910i	0.385527	+	0.922697i	$0.374020\pi$
$572$	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	−0.641174	−	0.767396i	$-0.721552\pi$
$577$	205.720	−	403.749i	0.356535	−	0.699739i	0.997709	+	0.0676569i	$0.0215523\pi$
$578$	−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	−0.850314	−	0.526275i	$-0.823588\pi$
$587$	−542.594	+	276.465i	−0.924351	+	0.470980i	−0.0740364	+	0.997256i	$0.523588\pi$
$588$	−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	−0.545065	−	0.838394i	$-0.683495\pi$
$593$	173.944	−	173.944i	0.293329	−	0.293329i	0.838394	+	0.545065i	$0.183495\pi$
$594$	−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	$0.0124185\pi$
$599$			46.7267i			0.0780079i	−0.999239	+	0.0390039i	$0.987582\pi$
$600$	−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	0.594716	−	0.803936i	$-0.297264\pi$
$607$	−126.996	−	126.996i	−0.209220	−	0.209220i	−0.803936	+	0.594716i	$0.797264\pi$
$608$	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	0.722688	−	0.691175i	$-0.242906\pi$
$613$	−160.158	−	314.328i	−0.261269	−	0.512770i	−0.983957	+	0.178405i	$0.942906\pi$
$614$	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	0.998069	+	0.0621114i	$0.0197834\pi$
$617$	41.9822	+	265.065i	0.0680425	+	0.429603i	−0.930027	+	0.367492i	$0.880217\pi$
$618$	89.5124	−	89.5124i	0.144842	−	0.144842i
$619$	−15.8671	+	21.8392i	−0.0256335	+	0.0352815i	−0.821641	−	0.570005i	$-0.806941\pi$
$619$	−15.8671	+	21.8392i	−0.0256335	+	0.0352815i	0.796008	+	0.605286i	$0.206941\pi$
$620$	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	−0.970775	−	0.239992i	$-0.922855\pi$
$631$	−945.873	−	687.217i	−1.49901	−	1.08909i	−0.528232	−	0.849100i	$-0.677145\pi$
$632$	−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	−0.949854	−	0.312694i	$-0.898769\pi$
$641$	1.53254	−	4.71668i	0.00239086	−	0.00735831i	0.952245	+	0.305336i	$0.0987686\pi$
$642$	13.5068	+	85.2787i	0.0210387	+	0.132833i
$643$	−750.489	+	750.489i	−1.16717	+	1.16717i	−0.184297	+	0.982871i	$0.559001\pi$
$643$	−750.489	+	750.489i	−1.16717	+	1.16717i	−0.982871	+	0.184297i	$0.940999\pi$
$644$	−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	−0.601672	−	0.798743i	$-0.705498\pi$
$647$	−919.207	−	145.588i	−1.42072	−	0.225020i	−0.819049	+	0.573723i	$0.805498\pi$
$648$	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	−0.858249	−	0.513234i	$-0.828447\pi$
$653$	76.1349	−	480.697i	0.116592	−	0.736136i	0.974841	−	0.222901i	$-0.0715528\pi$
$654$	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	0.987804	−	0.155705i	$-0.0497651\pi$
$659$	1117.29	+	363.029i	1.69543	+	0.550879i	0.707628	+	0.706585i	$0.249765\pi$
$660$	381.621	−	227.200i	0.578214	−	0.344242i
$661$	−218.229	−	671.641i	−0.330150	−	1.01610i	−0.969062	−	0.246818i	$-0.920615\pi$
$661$	−218.229	−	671.641i	−0.330150	−	1.01610i	0.638912	−	0.769280i	$-0.279385\pi$
$662$	−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	0.826384	−	0.563107i	$-0.190394\pi$
$673$	576.463	+	293.723i	0.856558	+	0.436438i	0.0301736	+	0.999545i	$0.490394\pi$
$674$		−	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	−0.290652	−	0.956829i	$-0.593872\pi$
$677$	442.948	−	869.334i	0.654280	−	1.28410i	0.944932	−	0.327268i	$-0.106128\pi$
$678$	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	−0.859961	−	0.510360i	$-0.829512\pi$
$683$	−1038.24	+	164.442i	−1.52012	+	0.240764i	−0.660161	+	0.751124i	$0.729512\pi$
$684$	−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	−0.462581	−	0.886577i	$-0.653077\pi$
$691$	299.045	−	920.367i	0.432772	−	1.33193i	0.895353	−	0.445358i	$-0.146923\pi$
$692$	−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	0.980762	+	0.195208i	$0.0625383\pi$
$709$	1339.27	+	435.155i	1.88896	+	0.613759i	0.908193	+	0.418551i	$0.137462\pi$
$710$	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	−0.744104	−	0.668064i	$-0.767123\pi$
$719$	87.1456	−	119.946i	0.121204	−	0.166823i	0.865308	+	0.501241i	$0.167123\pi$
$720$	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	−0.775595	−	0.631231i	$-0.782550\pi$
$727$	138.831	−	272.472i	0.190965	−	0.374789i	0.966560	+	0.256441i	$0.0825501\pi$
$728$	−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	−0.327129	−	0.944980i	$-0.606081\pi$
$733$	−253.788	+	40.1961i	−0.346232	+	0.0548378i	−0.0191034	+	0.999818i	$0.506081\pi$
$734$	−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	−0.275098	−	0.961416i	$-0.588710\pi$
$739$	49.8443	−	16.1954i	0.0674483	−	0.0219153i	0.342547	+	0.939501i	$0.388710\pi$
$740$	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	0.129574	−	0.991570i	$-0.458639\pi$
$743$	833.010	−	833.010i	1.12114	−	1.12114i	0.991570	−	0.129574i	$-0.0413609\pi$
$744$	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	0.952575	−	0.304304i	$-0.0984240\pi$
$757$	490.741	+	490.741i	0.648270	+	0.648270i	−0.304304	+	0.952575i	$0.598424\pi$
$758$	−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	0.939797	−	0.341734i	$-0.111014\pi$
$761$	−16.2710	−	50.0771i	−0.0213811	−	0.0658044i	−0.961178	+	0.275930i	$0.911014\pi$
$762$	−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	0.194702	+	0.980862i	$0.437626\pi$
$769$	−613.908	+	844.972i	−0.798320	+	1.09879i	−0.993022	+	0.117931i	$0.962374\pi$
$770$	−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	−0.00693843	−	0.999976i	$-0.502209\pi$
$773$	−633.871	−	322.973i	−0.820014	−	0.417818i	−0.813076	+	0.582158i	$0.802209\pi$
$774$			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	0.0587649	−	0.998272i	$-0.481284\pi$
$787$	709.028	−	361.268i	0.900925	−	0.459044i	0.842160	+	0.539228i	$0.181284\pi$
$788$	−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	0.268569	−	0.963260i	$-0.413449\pi$
$797$	180.384	+	28.5701i	0.226329	+	0.0358470i	−0.0422397	+	0.999108i	$0.513449\pi$
$798$	−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	−0.212040	−	0.977261i	$-0.568011\pi$
$809$	−775.024	−	251.821i	−0.958003	−	0.311274i	−0.745963	+	0.665987i	$0.768011\pi$
$810$	−2.95395	−	13.0360i	−0.00364686	−	0.0160938i
$811$	363.428	+	1118.52i	0.448123	+	1.37918i	0.879022	+	0.476781i	$0.158196\pi$
$811$	363.428	+	1118.52i	0.448123	+	1.37918i	−0.430899	+	0.902400i	$0.641804\pi$
$812$	−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	−0.351184	−	0.936307i	$-0.614221\pi$
$821$	353.666	−	256.954i	0.430775	−	0.312976i	0.781959	+	0.623330i	$0.214221\pi$
$822$	295.479	+	46.7992i	0.359463	+	0.0569334i
$823$	1176.87	+	599.645i	1.42997	+	0.728609i	0.985893	−	0.167377i	$-0.0535299\pi$
$823$	1176.87	+	599.645i	1.42997	+	0.728609i	0.444082	+	0.895986i	$0.353530\pi$
$824$		−	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	−0.995948	−	0.0899277i	$-0.971336\pi$
$827$	−279.354	+	548.262i	−0.337792	+	0.662953i	0.658157	+	0.752881i	$0.271336\pi$
$828$	14.4574	−	91.2803i	0.0174606	−	0.110242i
$829$	263.753	+	363.024i	0.318158	+	0.437906i	0.937904	−	0.346896i	$-0.112764\pi$
$829$	263.753	+	363.024i	0.318158	+	0.437906i	−0.619746	+	0.784802i	$0.712764\pi$
$830$	−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	−0.729855	−	0.683602i	$-0.760412\pi$
$839$	−770.629	+	250.392i	−0.918509	+	0.298442i	−0.188654	+	0.982044i	$0.560412\pi$
$840$	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	−0.639619	−	0.768692i	$-0.720908\pi$
$853$	175.917	−	1110.70i	0.206234	−	1.30211i	0.845853	−	0.533417i	$-0.179092\pi$
$854$	−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	0.999875	+	0.0158015i	$0.00503000\pi$
$857$	870.435	+	870.435i	1.01568	+	1.01568i	0.0158015	+	0.999875i	$0.494970\pi$
$858$	−287.119	+	45.4752i	−0.334638	+	0.0530014i
$859$	−1395.30	−	453.359i	−1.62433	−	0.527775i	−0.651369	−	0.758761i	$-0.725805\pi$
$859$	−1395.30	−	453.359i	−1.62433	−	0.527775i	−0.972957	+	0.230986i	$0.925805\pi$
$860$	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	0.974546	+	0.224188i	$0.0719730\pi$
$863$	503.210	+	987.606i	0.583094	+	1.14439i	−0.391452	+	0.920199i	$0.628027\pi$
$864$	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	−0.571663	−	0.820489i	$-0.693701\pi$
$877$	375.480	−	736.921i	0.428141	−	0.840275i	0.999804	−	0.0197861i	$-0.00629854\pi$
$878$	−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	0.921755	−	0.387772i	$-0.126755\pi$
$881$	738.102	+	536.263i	0.837800	+	0.608698i	−0.0839550	+	0.996470i	$0.526755\pi$
$882$	−46.3451	−	46.3451i	−0.0525455	−	0.0525455i
$883$	−850.354	+	134.683i	−0.963029	+	0.152529i	−0.618099	−	0.786100i	$-0.712097\pi$
$883$	−850.354	+	134.683i	−0.963029	+	0.152529i	−0.344929	+	0.938629i	$0.612097\pi$
$884$	−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	0.425749	−	0.904841i	$-0.360011\pi$
$887$	1248.92	−	636.358i	1.40803	−	0.717427i	0.982281	+	0.187414i	$0.0600106\pi$
$888$	−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	0.495517	−	0.868598i	$-0.334979\pi$
$907$	−338.384	−	338.384i	−0.373081	−	0.373081i	−0.868598	+	0.495517i	$0.834979\pi$
$908$	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	−0.844232	−	0.535978i	$-0.819943\pi$
$911$	−433.886	−	1335.36i	−0.476274	−	1.46582i	0.367958	−	0.929842i	$-0.380057\pi$
$912$	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	−0.832500	−	0.554026i	$-0.813091\pi$
$919$	−44.4183	+	61.1365i	−0.0483332	+	0.0665250i	0.784166	+	0.620551i	$0.213091\pi$
$920$	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	0.971563	+	0.236783i	$0.0760930\pi$
$929$	832.874	+	1146.35i	0.896527	+	1.23396i	−0.0750356	+	0.997181i	$0.523907\pi$
$930$	−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	−0.921479	−	0.388429i	$-0.873018\pi$
$937$	−1076.49	+	548.497i	−1.14886	+	0.585376i	−0.227386	+	0.973805i	$0.573018\pi$
$938$	−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	0.676019	+	0.736884i	$0.263704\pi$
$941$	−286.084	+	880.476i	−0.304021	+	0.935681i	−0.980041	+	0.198797i	$0.936296\pi$
$942$	−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	−0.324970	−	0.945724i	$-0.605354\pi$
$947$	−877.188	−	138.933i	−0.926280	−	0.146708i	−0.601310	+	0.799016i	$0.705354\pi$
$948$	−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	0.949728	+	0.313075i	$0.101359\pi$
$953$	−47.9001	+	302.429i	−0.0502625	+	0.317345i	−0.999991	+	0.00426975i	$0.998641\pi$
$954$	−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	0.987076	+	0.160256i	$0.0512318\pi$
$967$	94.6041	+	597.307i	0.0978326	+	0.617691i	−0.889243	+	0.457435i	$0.848768\pi$
$968$	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	0.327111	−	0.944986i	$-0.393925\pi$
$971$	1288.45	−	936.112i	1.32693	−	0.964070i	0.999818	−	0.0190840i	$-0.00607498\pi$
$972$	−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	−0.949051	−	0.315122i	$-0.897955\pi$
$977$	−133.140	+	261.301i	−0.136274	+	0.267453i	0.812777	+	0.582575i	$0.197955\pi$
$978$	−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	−0.189632	−	0.981855i	$-0.560730\pi$
$983$	−65.4417	+	10.3649i	−0.0665734	+	0.0105442i	0.123059	+	0.992399i	$0.460730\pi$
$984$	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	−0.747558	−	0.664196i	$-0.768774\pi$
$991$	245.405	−	755.279i	0.247634	−	0.762138i	0.995192	−	0.0979420i	$-0.0312260\pi$
$992$	−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	0.274006	−	0.961728i	$-0.411651\pi$
$997$	236.698	+	37.4893i	0.237410	+	0.0376021i	−0.0365955	+	0.999330i	$0.511651\pi$
$998$	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.17.2	yes	32
3.2	odd	2		225.3.r.a.217.3		32
4.3	odd	2		400.3.bg.c.17.3		32
5.2	odd	4		125.3.f.b.18.2		32
5.3	odd	4		125.3.f.a.18.3		32
5.4	even	2		125.3.f.c.107.3		32
25.3	odd	20	inner	25.3.f.a.3.2	✓	32
25.4	even	10		125.3.f.b.7.2		32
25.21	even	5		125.3.f.a.7.3		32
25.22	odd	20		125.3.f.c.118.3		32
75.53	even	20		225.3.r.a.28.3		32
100.3	even	20		400.3.bg.c.353.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.3.2	✓	32	25.3	odd	20	inner
25.3.f.a.17.2	yes	32	1.1	even	1	trivial
125.3.f.a.7.3		32	25.21	even	5
125.3.f.a.18.3		32	5.3	odd	4
125.3.f.b.7.2		32	25.4	even	10
125.3.f.b.18.2		32	5.2	odd	4
125.3.f.c.107.3		32	5.4	even	2
125.3.f.c.118.3		32	25.22	odd	20
225.3.r.a.28.3		32	75.53	even	20
225.3.r.a.217.3		32	3.2	odd	2
400.3.bg.c.17.3		32	4.3	odd	2
400.3.bg.c.353.3		32	100.3	even	20

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

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