LMFDB - Embedded newform 125.3.f.c.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,3,Mod(7,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

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

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

chi := DirichletCharacter("125.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	125.f (of order $20$, degree $8$, not 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:	$3.40600330450$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.3
Character	$\chi$	$=$	125.118
Dual form			125.3.f.c.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395527 + 0.776265i) q^{2} +(0.296456 + 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(-1.33572 + 0.970456i) q^{6} +(5.60844 - 5.60844i) q^{7} +(6.23083 + 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +O(q^{10})$	\(q+(0.395527 + 0.776265i) q^{2} +(0.296456 + 1.87175i) q^{3} +(1.90500 - 2.62200i) q^{4} +(-1.33572 + 0.970456i) q^{6} +(5.60844 - 5.60844i) q^{7} +(6.23083 + 0.986866i) q^{8} +(5.14394 - 1.67137i) q^{9} +(-4.46912 + 13.7545i) q^{11} +(5.47248 + 2.78837i) q^{12} +(-5.52703 + 10.8474i) q^{13} +(6.57192 + 2.13535i) q^{14} +(-2.30767 - 7.10228i) q^{16} +(-0.147755 + 0.932886i) q^{17} +(3.33199 + 3.33199i) q^{18} +(-11.5466 - 15.8926i) q^{19} +(12.1603 + 8.83494i) q^{21} +(-12.4448 + 1.97107i) q^{22} +(4.69757 - 2.39353i) q^{23} +11.9551i q^{24} -10.6066 q^{26} +(12.3965 + 24.3295i) q^{27} +(-4.02128 - 25.3894i) q^{28} +(-7.87983 + 10.8457i) q^{29} +(12.1549 - 8.83105i) q^{31} +(22.4436 - 22.4436i) q^{32} +(-27.0700 - 4.28747i) q^{33} +(-0.782608 + 0.254285i) q^{34} +(5.41686 - 16.6714i) q^{36} +(-57.7042 - 29.4017i) q^{37} +(7.76985 - 15.2492i) q^{38} +(-21.9422 - 7.12944i) q^{39} +(-16.7764 - 51.6323i) q^{41} +(-2.04855 + 12.9340i) q^{42} +(-3.47098 - 3.47098i) q^{43} +(27.5508 + 37.9204i) q^{44} +(3.71603 + 2.69985i) q^{46} +(-65.5638 + 10.3843i) q^{47} +(12.6096 - 6.42490i) q^{48} -13.9091i q^{49} -1.78993 q^{51} +(17.9129 + 35.1561i) q^{52} +(6.61077 + 41.7387i) q^{53} +(-13.9830 + 19.2459i) q^{54} +(40.4800 - 29.4104i) q^{56} +(26.3239 - 26.3239i) q^{57} +(-11.5358 - 1.82709i) q^{58} +(-35.6563 + 11.5854i) q^{59} +(-32.4776 + 99.9557i) q^{61} +(11.6628 + 5.94250i) q^{62} +(19.4757 - 38.2232i) q^{63} +(-2.10987 - 0.685539i) q^{64} +(-7.37870 - 22.7093i) q^{66} +(7.05644 - 44.5526i) q^{67} +(2.16456 + 2.16456i) q^{68} +(5.87272 + 8.08310i) q^{69} +(36.5810 + 26.5777i) q^{71} +(33.7004 - 5.33762i) q^{72} +(-47.8210 + 24.3660i) q^{73} -56.4229i q^{74} -63.6667 q^{76} +(52.0767 + 102.206i) q^{77} +(-3.14438 - 19.8528i) q^{78} +(70.5878 - 97.1558i) q^{79} +(-2.48243 + 1.80359i) q^{81} +(33.4449 - 33.4449i) q^{82} +(60.5919 + 9.59682i) q^{83} +(46.3305 - 15.0537i) q^{84} +(1.32153 - 4.06726i) q^{86} +(-22.6364 - 11.5338i) q^{87} +(-41.4202 + 81.2918i) q^{88} +(48.8275 + 15.8650i) q^{89} +(29.8390 + 91.8350i) q^{91} +(2.67300 - 16.8767i) q^{92} +(20.1329 + 20.1329i) q^{93} +(-33.9932 - 46.7876i) q^{94} +(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} - 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 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9	$ 32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9} - 6 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 2 q^{16} - 60 q^{17} - 140 q^{18} + 90 q^{19} - 6 q^{21} - 70 q^{22} - 10 q^{23} + 4 q^{26} + 100 q^{27} + 250 q^{28} - 110 q^{29} - 6 q^{31} + 290 q^{32} + 190 q^{33} - 260 q^{34} - 58 q^{36} - 50 q^{37} - 320 q^{38} + 390 q^{39} - 86 q^{41} - 690 q^{42} - 230 q^{43} + 340 q^{44} - 6 q^{46} - 70 q^{47} - 160 q^{48} - 16 q^{51} + 320 q^{52} + 190 q^{53} - 660 q^{54} - 70 q^{56} + 650 q^{57} + 640 q^{58} - 260 q^{59} + 114 q^{61} - 60 q^{62} + 20 q^{63} + 340 q^{64} + 138 q^{66} - 270 q^{67} - 710 q^{68} + 340 q^{69} - 66 q^{71} - 360 q^{72} - 30 q^{73} - 80 q^{76} + 250 q^{77} + 500 q^{78} - 210 q^{79} + 62 q^{81} - 30 q^{82} - 10 q^{84} - 6 q^{86} - 300 q^{87} - 190 q^{88} - 10 q^{89} - 6 q^{91} + 30 q^{92} - 520 q^{93} + 790 q^{94} + 174 q^{96} - 270 q^{97} - 170 q^{98}+O(q^{100}) $ 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9 - 6 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 2 * q^16 - 60 * q^17 - 140 * q^18 + 90 * q^19 - 6 * q^21 - 70 * q^22 - 10 * q^23 + 4 * q^26 + 100 * q^27 + 250 * q^28 - 110 * q^29 - 6 * q^31 + 290 * q^32 + 190 * q^33 - 260 * q^34 - 58 * q^36 - 50 * q^37 - 320 * q^38 + 390 * q^39 - 86 * q^41 - 690 * q^42 - 230 * q^43 + 340 * q^44 - 6 * q^46 - 70 * q^47 - 160 * q^48 - 16 * q^51 + 320 * q^52 + 190 * q^53 - 660 * q^54 - 70 * q^56 + 650 * q^57 + 640 * q^58 - 260 * q^59 + 114 * q^61 - 60 * q^62 + 20 * q^63 + 340 * q^64 + 138 * q^66 - 270 * q^67 - 710 * q^68 + 340 * q^69 - 66 * q^71 - 360 * q^72 - 30 * q^73 - 80 * q^76 + 250 * q^77 + 500 * q^78 - 210 * q^79 + 62 * q^81 - 30 * q^82 - 10 * q^84 - 6 * q^86 - 300 * q^87 - 190 * q^88 - 10 * q^89 - 6 * q^91 + 30 * q^92 - 520 * q^93 + 790 * q^94 + 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 $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

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

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	0.968497	−	0.249025i	$-0.0801101\pi$
$2$	0.395527	+	0.776265i	0.197763	+	0.388132i	−0.770734	+	0.637157i	$0.780110\pi$
$3$	0.296456	+	1.87175i	0.0988188	+	0.623917i	0.986538	+	0.163532i	$0.0522887\pi$
$3$	0.296456	+	1.87175i	0.0988188	+	0.623917i	−0.887719	+	0.460385i	$0.847711\pi$
$4$	1.90500	−	2.62200i	0.476249	−	0.655500i
$5$		0			0
$5$		0			0
$6$	−1.33572	+	0.970456i	−0.222620	+	0.161743i
$7$	5.60844	−	5.60844i	0.801205	−	0.801205i	−0.182079	−	0.983284i	$-0.558283\pi$
$7$	5.60844	−	5.60844i	0.801205	−	0.801205i	0.983284	+	0.182079i	$0.0582826\pi$
$8$	6.23083	+	0.986866i	0.778854	+	0.123358i
$9$	5.14394	−	1.67137i	0.571549	−	0.185708i
$10$		0			0
$11$	−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	$0.305113\pi$
$13$	−5.52703	+	10.8474i	−0.425156	+	0.834416i	−0.999871	+	0.0160623i	$0.994887\pi$
$14$	6.57192	+	2.13535i	0.469423	+	0.152525i
$15$		0			0
$16$	−2.30767	−	7.10228i	−0.144229	−	0.443893i
$17$	−0.147755	+	0.932886i	−0.00869145	+	0.0548757i	−0.991653	−	0.128936i	$-0.958844\pi$
$17$	−0.147755	+	0.932886i	−0.00869145	+	0.0548757i	0.982961	+	0.183812i	$0.0588437\pi$
$18$	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	$0.972935\pi$
$20$		0			0
$21$	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	$-0.613437\pi$
$23$	4.69757	−	2.39353i	0.204242	−	0.104067i	0.553120	+	0.833102i	$0.313437\pi$
$24$			11.9551i			0.498130i
$25$		0			0
$26$	−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	$0.274245\pi$
$30$		0			0
$31$	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
$35$		0			0
$36$	5.41686	−	16.6714i	0.150468	−	0.463094i
$37$	−57.7042	−	29.4017i	−1.55957	−	0.794642i	−0.560142	−	0.828396i	$-0.689254\pi$
$37$	−57.7042	−	29.4017i	−1.55957	−	0.794642i	−0.999430	+	0.0337547i	$0.989254\pi$
$38$	7.76985	−	15.2492i	0.204470	−	0.401295i
$39$	−21.9422	−	7.12944i	−0.562620	−	0.182806i
$40$		0			0
$41$	−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	0.665594	−	0.746314i	$-0.268178\pi$
$43$	−3.47098	−	3.47098i	−0.0807204	−	0.0807204i	−0.746314	+	0.665594i	$0.768178\pi$
$44$	27.5508	+	37.9204i	0.626154	+	0.861827i
$45$		0			0
$46$	3.71603	+	2.69985i	0.0807832	+	0.0586924i
$47$	−65.5638	+	10.3843i	−1.39498	+	0.220942i	−0.808248	−	0.588842i	$-0.799584\pi$
$47$	−65.5638	+	10.3843i	−1.39498	+	0.220942i	−0.586727	+	0.809785i	$0.699584\pi$
$48$	12.6096	−	6.42490i	0.262700	−	0.133852i
$49$		−	13.9091i		−	0.283860i
$50$		0			0
$51$	−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	$0.0805281\pi$
$53$	6.61077	+	41.7387i	0.124731	+	0.787523i	−0.843438	+	0.537227i	$0.819472\pi$
$54$	−13.9830	+	19.2459i	−0.258944	+	0.356406i
$55$		0			0
$56$	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	$0.502918\pi$
$60$		0			0
$61$	−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
$65$		0			0
$66$	−7.37870	−	22.7093i	−0.111798	−	0.344080i
$67$	7.05644	−	44.5526i	0.105320	−	0.664965i	−0.877385	−	0.479787i	$-0.840714\pi$
$67$	7.05644	−	44.5526i	0.105320	−	0.664965i	0.982705	−	0.185178i	$-0.0592861\pi$
$68$	2.16456	+	2.16456i	0.0318317	+	0.0318317i
$69$	5.87272	+	8.08310i	0.0851118	+	0.117146i
$70$		0			0
$71$	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	−0.749744	−	0.661728i	$-0.769823\pi$
$73$	−47.8210	+	24.3660i	−0.655082	+	0.333781i	0.0946613	+	0.995510i	$0.469823\pi$
$74$		−	56.4229i		−	0.762472i
$75$		0			0
$76$	−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	$-0.0748356\pi$
$80$		0			0
$81$	−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	$-0.329508\pi$
$83$	60.5919	+	9.59682i	0.730023	+	0.115624i	0.219652	+	0.975578i	$0.429508\pi$
$84$	46.3305	−	15.0537i	0.551553	−	0.179210i
$85$		0			0
$86$	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	$0.506867\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	48.6625	+	35.3553i	0.506901	+	0.368285i
$97$	36.3164	−	5.75195i	0.374395	−	0.0592984i	0.0335987	−	0.999435i	$-0.489303\pi$
$97$	36.3164	−	5.75195i	0.374395	−	0.0592984i	0.340797	+	0.940137i	$0.389303\pi$
$98$	10.7972	−	5.50143i	0.110175	−	0.0561371i
$99$			78.2221i			0.790123i
$100$		0			0
$101$	−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	$0.0713957\pi$
$103$	11.9943	+	75.7288i	0.116449	+	0.735231i	−0.858502	+	0.512811i	$0.828604\pi$
$104$	−45.1429	+	62.1339i	−0.434067	+	0.597441i
$105$		0			0
$106$	−29.7856	+	21.6405i	−0.280996	+	0.204156i
$107$	36.9784	−	36.9784i	0.345593	−	0.345593i	−0.512872	−	0.858465i	$-0.671419\pi$
$107$	36.9784	−	36.9784i	0.345593	−	0.345593i	0.858465	+	0.512872i	$0.171419\pi$
$108$	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	$0.442527\pi$
$110$		0			0
$111$	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	$-0.854856\pi$
$113$	−1.56513	+	3.07175i	−0.0138507	+	0.0271836i	0.883977	+	0.467529i	$0.154856\pi$
$114$	30.8461	+	10.0225i	0.270580	+	0.0879168i
$115$		0			0
$116$	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
$120$		0			0
$121$	−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
$125$		0			0
$126$	37.3745			0.296623
$127$	−72.0197	−	141.347i	−0.567084	−	1.11297i	−0.979401	−	0.201925i	$-0.935280\pi$
$127$	−72.0197	−	141.347i	−0.567084	−	1.11297i	0.412317	−	0.911041i	$-0.364720\pi$
$128$	−20.1633	−	127.306i	−0.157526	−	0.994580i
$129$	5.46781	−	7.52580i	0.0423862	−	0.0583395i
$130$		0			0
$131$	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
$135$		0			0
$136$	−1.84127	+	5.66684i	−0.0135387	+	0.0416679i
$137$	161.447	+	82.2613i	1.17844	+	0.600448i	0.929771	−	0.368139i	$-0.120005\pi$
$137$	161.447	+	82.2613i	1.17844	+	0.600448i	0.248674	+	0.968587i	$0.420005\pi$
$138$	−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	$0.680696\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	$0.817935\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−60.4931	+	43.9508i	−0.387777	+	0.281736i
$157$	−148.102	+	148.102i	−0.943325	+	0.943325i	−0.998478	−	0.0551526i	$-0.982435\pi$
$157$	−148.102	+	148.102i	−0.943325	+	0.943325i	0.0551526	+	0.998478i	$0.482435\pi$
$158$	103.338	+	16.3671i	0.654038	+	0.103589i
$159$	−76.1647	+	24.7474i	−0.479023	+	0.155644i
$160$		0			0
$161$	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	$-0.457264\pi$
$163$	139.677	−	274.131i	0.856914	−	1.68179i	0.723058	−	0.690787i	$-0.242736\pi$
$164$	−167.339	−	54.3717i	−1.02036	−	0.331535i
$165$		0			0
$166$	16.5160	+	50.8312i	0.0994943	+	0.306212i
$167$	−0.0999015	+	0.630753i	−0.000598213	+	0.00377697i	−0.987986	−	0.154546i	$-0.950609\pi$
$167$	−0.0999015	+	0.630753i	−0.000598213	+	0.00377697i	0.987387	+	0.158323i	$0.0506086\pi$
$168$	67.0496	+	67.0496i	0.399105	+	0.399105i
$169$	12.2175	+	16.8160i	0.0722929	+	0.0995027i
$170$		0			0
$171$	−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	$-0.521383\pi$
$173$	121.206	−	61.7573i	0.700610	−	0.356979i	0.767736	+	0.640766i	$0.221383\pi$
$174$		−	22.1338i		−	0.127206i
$175$		0			0
$176$	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	$0.238054\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	−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
$190$		0			0
$191$	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	0.978369	−	0.206867i	$-0.0663266\pi$
$193$	148.900	+	148.900i	0.771503	+	0.771503i	−0.206867	+	0.978369i	$0.566327\pi$
$194$	18.8291	+	25.9161i	0.0970573	+	0.133588i
$195$		0			0
$196$	−36.4698	−	26.4968i	−0.186070	−	0.135188i
$197$	277.234	−	43.9096i	1.40728	−	0.222891i	0.593860	−	0.804568i	$-0.297603\pi$
$197$	277.234	−	43.9096i	1.40728	−	0.222891i	0.813420	+	0.581677i	$0.197603\pi$
$198$	−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	$-0.0995524\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−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
$210$		0			0
$211$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	$-0.512726\pi$
$223$	166.115	−	84.6396i	0.744908	−	0.379550i	0.784877	+	0.619651i	$0.212726\pi$
$224$		−	251.747i		−	1.12387i
$225$		0			0
$226$	−3.00354			−0.0132900
$227$	−38.6087	−	75.7738i	−0.170082	−	0.333805i	0.790194	−	0.612857i	$-0.209980\pi$
$227$	−38.6087	−	75.7738i	−0.170082	−	0.333805i	−0.960276	+	0.279052i	$0.909980\pi$
$228$	−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	$0.0377509\pi$
$230$		0			0
$231$	−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	$-0.492551\pi$
$233$	−61.3442	−	9.71596i	−0.263280	−	0.0416994i	−0.286679	+	0.958027i	$0.592551\pi$
$234$	−54.5595	+	17.7274i	−0.233160	+	0.0757583i
$235$		0			0
$236$	−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	$0.625629\pi$
$240$		0			0
$241$	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
$245$		0			0
$246$	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
$250$		0			0
$251$	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
$255$		0			0
$256$	83.6692	−	60.7892i	0.326833	−	0.237458i
$257$	−293.197	+	293.197i	−1.14084	+	1.14084i	−0.152547	+	0.988296i	$0.548748\pi$
$257$	−293.197	+	293.197i	−1.14084	+	1.14084i	−0.988296	+	0.152547i	$0.951252\pi$
$258$	8.00468	+	1.26782i	0.0310259	+	0.00491402i
$259$	−488.528	+	158.732i	−1.88621	+	0.612866i
$260$		0			0
$261$	−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	$0.307050\pi$
$263$	−113.098	+	221.967i	−0.430030	+	0.843981i	−0.999755	+	0.0221457i	$0.992950\pi$
$264$	−164.437	−	53.4289i	−0.622869	−	0.202382i
$265$		0			0
$266$	−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	$0.876748\pi$
$270$		0			0
$271$	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
$275$		0			0
$276$	32.3814			0.117324
$277$	2.24494	+	4.40595i	0.00810448	+	0.0159059i	0.895023	−	0.446019i	$-0.147159\pi$
$277$	2.24494	+	4.40595i	0.00810448	+	0.0159059i	−0.886919	+	0.461925i	$0.847159\pi$
$278$	−9.50274	−	59.9979i	−0.0341825	−	0.215820i
$279$	47.7641	−	65.7417i	0.171198	−	0.235633i
$280$		0			0
$281$	−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	0.366362	−	0.930473i	$-0.380603\pi$
$283$	120.915	+	19.1510i	0.427260	+	0.0676714i	0.0608988	+	0.998144i	$0.480603\pi$
$284$	139.373	−	45.2852i	0.490751	−	0.159455i
$285$		0			0
$286$	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
$290$		0			0
$291$	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	$-0.905417\pi$
$293$	−365.947	−	365.947i	−1.24897	−	1.24897i	−0.292788	−	0.956177i	$-0.594583\pi$
$294$	13.4982	+	18.5787i	0.0459123	+	0.0631928i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−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
$305$		0			0
$306$	−3.60069	+	2.61605i	−0.0117669	+	0.00854919i
$307$	127.024	−	127.024i	0.413759	−	0.413759i	−0.469287	−	0.883046i	$-0.655489\pi$
$307$	127.024	−	127.024i	0.413759	−	0.413759i	0.883046	+	0.469287i	$0.155489\pi$
$308$	367.191	+	58.1573i	1.19218	+	0.188823i
$309$	−138.190	+	44.9005i	−0.447216	+	0.145309i
$310$		0			0
$311$	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	−0.732542	−	0.680722i	$-0.761666\pi$
$313$	77.8591	−	152.807i	0.248751	−	0.488201i	0.981293	+	0.192521i	$0.0616662\pi$
$314$	−173.545	−	56.3881i	−0.552690	−	0.179580i
$315$		0			0
$316$	−120.273	−	370.163i	−0.380611	−	1.17140i
$317$	11.8851	−	75.0397i	0.0374925	−	0.236718i	−0.961825	−	0.273666i	$-0.911764\pi$
$317$	11.8851	−	75.0397i	0.0374925	−	0.236718i	0.999317	+	0.0369480i	$0.0117636\pi$
$318$	−49.3357	−	49.3357i	−0.155144	−	0.155144i
$319$	−113.961	−	156.854i	−0.357245	−	0.491706i
$320$		0			0
$321$	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
$325$		0			0
$326$	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
$330$		0			0
$331$	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
$335$		0			0
$336$	34.6864	−	106.754i	0.103233	−	0.317719i
$337$	124.280	+	63.3239i	0.368784	+	0.187905i	0.628554	−	0.777766i	$-0.283647\pi$
$337$	124.280	+	63.3239i	0.368784	+	0.187905i	−0.259771	+	0.965670i	$0.583647\pi$
$338$	−8.22128	+	16.1352i	−0.0243233	+	0.0477372i
$339$	−6.21354	−	2.01890i	−0.0183290	−	0.00595547i
$340$		0			0
$341$	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
$345$		0			0
$346$	95.8800	+	69.6609i	0.277110	+	0.201332i
$347$	−443.450	+	70.2356i	−1.27795	+	0.202408i	−0.758265	−	0.651947i	$-0.773952\pi$
$347$	−443.450	+	70.2356i	−1.27795	+	0.202408i	−0.519690	+	0.854355i	$0.673952\pi$
$348$	−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	$0.941529\pi$
$350$		0			0
$351$	−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	$0.186225\pi$
$353$	74.6432	+	471.279i	0.211454	+	1.33507i	−0.622234	+	0.782831i	$0.713775\pi$
$354$	36.3836	−	50.0778i	0.102779	−	0.141463i
$355$		0			0
$356$	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	$0.206982\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−53.6217	−	165.031i	−0.146507	−	0.450903i
$367$	−18.6772	+	117.923i	−0.0508916	+	0.321317i	0.949088	+	0.315010i	$0.102008\pi$
$367$	−18.6772	+	117.923i	−0.0508916	+	0.321317i	−0.999980	+	0.00630745i	$0.997992\pi$
$368$	−27.8400	−	27.8400i	−0.0756521	−	0.0756521i
$369$	−172.593	−	237.554i	−0.467732	−	0.643778i
$370$		0			0
$371$	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	$-0.538135\pi$
$373$	228.816	−	116.587i	0.613446	−	0.312567i	0.732966	+	0.680265i	$0.238135\pi$
$374$		−	11.9008i		−	0.0318204i
$375$		0			0
$376$	−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	$0.0942413\pi$
$380$		0			0
$381$	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	$-0.559038\pi$
$383$	−254.126	−	40.2496i	−0.663515	−	0.105090i	−0.479103	+	0.877759i	$0.659038\pi$
$384$	232.308	−	75.4815i	0.604969	−	0.196566i
$385$		0			0
$386$	−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	$0.841077\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	205.099	+	149.013i	0.517926	+	0.376295i
$397$	−128.831	+	20.4049i	−0.324512	+	0.0513976i	−0.316565	−	0.948571i	$-0.602530\pi$
$397$	−128.831	+	20.4049i	−0.324512	+	0.0513976i	−0.00794678	+	0.999968i	$0.502530\pi$
$398$	95.0586	−	48.4348i	0.238841	−	0.121695i
$399$		−	295.272i		−	0.740030i
$400$		0			0
$401$	−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
$405$		0			0
$406$	−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	$0.393838\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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	$0.572829\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−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	0.460680	−	0.887566i	$-0.347605\pi$
$433$	270.426	+	42.8313i	0.624540	+	0.0989175i	0.163860	+	0.986484i	$0.447605\pi$
$434$	98.7383	−	32.0820i	0.227508	−	0.0739217i
$435$		0			0
$436$	−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	$0.589565\pi$
$440$		0			0
$441$	−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	$-0.341134\pi$
$443$	−176.930	−	176.930i	−0.399390	−	0.399390i	−0.878018	+	0.478628i	$0.841134\pi$
$444$	−233.802	−	321.801i	−0.526581	−	0.724777i
$445$		0			0
$446$	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	$-0.293286\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	189.998	−	138.042i	0.416662	−	0.302723i
$457$	368.956	−	368.956i	0.807343	−	0.807343i	−0.176888	−	0.984231i	$-0.556603\pi$
$457$	368.956	−	368.956i	0.807343	−	0.807343i	0.984231	+	0.176888i	$0.0566030\pi$
$458$	192.298	+	30.4570i	0.419865	+	0.0665000i
$459$	−24.5283	+	7.96972i	−0.0534385	+	0.0173632i
$460$		0			0
$461$	−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	−0.751900	−	0.659278i	$-0.770862\pi$
$463$	103.445	−	203.022i	0.223423	−	0.438492i	0.975322	+	0.220786i	$0.0708622\pi$
$464$	95.2130	+	30.9366i	0.205200	+	0.0666737i
$465$		0			0
$466$	−16.7211	−	51.4622i	−0.0358822	−	0.110434i
$467$	−134.672	+	850.285i	−0.288377	+	1.82074i	0.238899	+	0.971044i	$0.423213\pi$
$467$	−134.672	+	850.285i	−0.288377	+	1.82074i	−0.527276	+	0.849694i	$0.676787\pi$
$468$	150.902	+	150.902i	0.322440	+	0.322440i
$469$	−210.295	−	289.446i	−0.448390	−	0.617156i
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	$0.169006\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−64.5960	+	198.806i	−0.132914	+	0.409066i
$487$	−356.586	−	181.689i	−0.732209	−	0.373079i	0.0477923	−	0.998857i	$-0.484781\pi$
$487$	−356.586	−	181.689i	−0.732209	−	0.373079i	−0.780001	+	0.625778i	$0.784781\pi$
$488$	−301.005	+	590.756i	−0.616813	+	1.21056i
$489$	554.514	+	180.173i	1.13398	+	0.368451i
$490$		0			0
$491$	−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
$495$		0			0
$496$	−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	$0.791228\pi$
$500$		0			0
$501$	−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	$-0.900865\pi$
$503$	−71.0647	−	448.685i	−0.141282	−	0.892018i	0.810611	−	0.585585i	$-0.199135\pi$
$504$	159.071	−	218.943i	0.315617	−	0.434410i
$505$		0			0
$506$	−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	$0.559973\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	−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
$520$		0			0
$521$	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	−0.497344	−	0.867554i	$-0.665691\pi$
$523$	−45.9244	+	23.3997i	−0.0878096	+	0.0447412i	0.409534	+	0.912295i	$0.365691\pi$
$524$		−	379.507i		−	0.724251i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		0			0
$541$	−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
$545$		0			0
$546$	−128.978	−	93.7083i	−0.236224	−	0.171627i
$547$	−120.296	+	19.0530i	−0.219919	+	0.0348318i	−0.265422	−	0.964132i	$-0.585511\pi$
$547$	−120.296	+	19.0530i	−0.219919	+	0.0348318i	0.0455024	+	0.998964i	$0.485511\pi$
$548$	523.245	−	266.607i	0.954827	−	0.486508i
$549$			568.448i			1.03542i
$550$		0			0
$551$	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
$555$		0			0
$556$	−182.818	+	132.825i	−0.328810	+	0.238895i
$557$	−576.978	+	576.978i	−1.03587	+	1.03587i	−0.0365353	+	0.999332i	$0.511632\pi$
$557$	−576.978	+	576.978i	−1.03587	+	1.03587i	−0.999332	+	0.0365353i	$0.988368\pi$
$558$	69.9250	+	11.0750i	0.125314	+	0.0198477i
$559$	56.8353	−	18.4669i	0.101673	−	0.0330356i
$560$		0			0
$561$	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	$0.489771\pi$
$563$	−447.785	+	878.827i	−0.795355	+	1.56097i	−0.827485	+	0.561488i	$0.810229\pi$
$564$	−387.752	−	125.988i	−0.687504	−	0.223384i
$565$		0			0
$566$	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	$0.715094\pi$
$570$		0			0
$571$	−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
$575$		0			0
$576$	−11.9989			−0.0208313
$577$	−205.720	−	403.749i	−0.356535	−	0.699739i	0.641174	−	0.767396i	$-0.278448\pi$
$577$	−205.720	−	403.749i	−0.356535	−	0.699739i	−0.997709	+	0.0676569i	$0.978448\pi$
$578$	39.2660	+	247.916i	0.0679343	+	0.428920i
$579$	−234.561	+	322.846i	−0.405115	+	0.557593i
$580$		0			0
$581$	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
$585$		0			0
$586$	139.330	−	428.813i	0.237764	−	0.731764i
$587$	542.594	+	276.465i	0.924351	+	0.470980i	0.850314	−	0.526275i	$-0.176412\pi$
$587$	542.594	+	276.465i	0.924351	+	0.470980i	0.0740364	+	0.997256i	$0.476412\pi$
$588$	38.7838	−	76.1175i	0.0659588	−	0.129451i
$589$	−280.696	−	91.2038i	−0.476564	−	0.154845i
$590$		0			0
$591$	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	$-0.316505\pi$
$593$	−173.944	−	173.944i	−0.293329	−	0.293329i	−0.838394	+	0.545065i	$0.816505\pi$
$594$	−202.227	−	278.342i	−0.340450	−	0.468589i
$595$		0			0
$596$	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	$-0.0124185\pi$
$600$		0			0
$601$	−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
$605$		0			0
$606$	102.210	−	74.2602i	0.168664	−	0.122542i
$607$	126.996	−	126.996i	0.209220	−	0.209220i	−0.594716	−	0.803936i	$-0.702736\pi$
$607$	126.996	−	126.996i	0.209220	−	0.209220i	0.803936	+	0.594716i	$0.202736\pi$
$608$	−615.836	−	97.5388i	−1.01289	−	0.160426i
$609$	−191.642	+	62.2681i	−0.314682	+	0.102246i
$610$		0			0
$611$	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	$-0.757094\pi$
$613$	160.158	−	314.328i	0.261269	−	0.512770i	0.983957	+	0.178405i	$0.0570936\pi$
$614$	148.846	+	48.3628i	0.242419	+	0.0787668i
$615$		0			0
$616$	223.617	+	688.223i	0.363015	+	1.11724i
$617$	−41.9822	+	265.065i	−0.0680425	+	0.429603i	0.930027	+	0.367492i	$0.119783\pi$
$617$	−41.9822	+	265.065i	−0.0680425	+	0.429603i	−0.998069	+	0.0621114i	$0.980217\pi$
$618$	−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	$0.806941\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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
$630$		0			0
$631$	−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
$635$		0			0
$636$	−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
$640$		0			0
$641$	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	$0.0590007\pi$
$643$	750.489	+	750.489i	1.16717	+	1.16717i	0.184297	+	0.982871i	$0.440999\pi$
$644$	−79.6605	−	109.643i	−0.123696	−	0.170253i
$645$		0			0
$646$	13.0777	+	9.50153i	0.0202442	+	0.0147082i
$647$	919.207	−	145.588i	1.42072	−	0.225020i	0.601672	−	0.798743i	$-0.294502\pi$
$647$	919.207	−	145.588i	1.42072	−	0.225020i	0.819049	+	0.573723i	$0.194502\pi$
$648$	−17.2475	+	8.78803i	−0.0266165	+	0.0135618i
$649$		−	542.213i		−	0.835460i
$650$		0			0
$651$	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	$-0.928447\pi$
$653$	−76.1349	−	480.697i	−0.116592	−	0.736136i	0.858249	−	0.513234i	$-0.171553\pi$
$654$	28.1810	−	38.7878i	0.0430902	−	0.0593086i
$655$		0			0
$656$	−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	$0.0497651\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$	−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	$-0.809606\pi$
$673$	−576.463	+	293.723i	−0.856558	+	0.436438i	−0.0301736	+	0.999545i	$0.509606\pi$
$674$			121.521i			0.180298i
$675$		0			0
$676$	67.3657			0.0996535
$677$	−442.948	−	869.334i	−0.654280	−	1.28410i	−0.944932	−	0.327268i	$-0.893872\pi$
$677$	−442.948	−	869.334i	−0.654280	−	1.28410i	0.290652	−	0.956829i	$-0.406128\pi$
$678$	−0.890419	−	5.62189i	−0.00131330	−	0.00829187i
$679$	171.419	−	235.937i	0.252457	−	0.347478i
$680$		0			0
$681$	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	$-0.170488\pi$
$683$	1038.24	+	164.442i	1.52012	+	0.240764i	0.660161	+	0.751124i	$0.270488\pi$
$684$	−327.498	+	106.410i	−0.478798	+	0.155571i
$685$		0			0
$686$	−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
$690$		0			0
$691$	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
$695$		0			0
$696$	−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
$700$		0			0
$701$	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
$705$		0			0
$706$	−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	$-0.0625383\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	$0.767123\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	145.557			0.200491
$727$	−138.831	−	272.472i	−0.190965	−	0.374789i	0.775595	−	0.631231i	$-0.217450\pi$
$727$	−138.831	−	272.472i	−0.190965	−	0.374789i	−0.966560	+	0.256441i	$0.917450\pi$
$728$	95.2928	+	601.655i	0.130897	+	0.826450i
$729$	−283.497	+	390.200i	−0.388885	+	0.535254i
$730$		0			0
$731$	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	$-0.393919\pi$
$733$	253.788	+	40.1961i	0.346232	+	0.0548378i	0.0191034	+	0.999818i	$0.493919\pi$
$734$	−98.9271	+	32.1434i	−0.134778	+	0.0437920i
$735$		0			0
$736$	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	$0.588710\pi$
$740$		0			0
$741$	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	$-0.958639\pi$
$743$	−833.010	−	833.010i	−1.12114	−	1.12114i	−0.129574	−	0.991570i	$-0.541361\pi$
$744$	105.576	+	145.313i	0.141904	+	0.195314i
$745$		0			0
$746$	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
$750$		0			0
$751$	−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
$755$		0			0
$756$	567.860	−	412.575i	0.751138	−	0.545734i
$757$	−490.741	+	490.741i	−0.648270	+	0.648270i	−0.952575	−	0.304304i	$-0.901576\pi$
$757$	−490.741	+	490.741i	−0.648270	+	0.648270i	0.304304	+	0.952575i	$0.401576\pi$
$758$	212.747	+	33.6959i	0.280669	+	0.0444537i
$759$	−137.425	+	44.6522i	−0.181061	+	0.0588303i
$760$		0			0
$761$	−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
$765$		0			0
$766$	−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	$-0.437626\pi$
$770$		0			0
$771$	−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	$-0.497791\pi$
$773$	633.871	−	322.973i	0.820014	−	0.417818i	0.813076	+	0.582158i	$0.197791\pi$
$774$		−	23.1305i		−	0.0298844i
$775$		0			0
$776$	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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−59.7427	+	183.869i	−0.0760085	+	0.233930i
$787$	−709.028	−	361.268i	−0.900925	−	0.459044i	−0.0587649	−	0.998272i	$-0.518716\pi$
$787$	−709.028	−	361.268i	−0.900925	−	0.459044i	−0.842160	+	0.539228i	$0.818716\pi$
$788$	412.999	−	810.556i	0.524110	−	1.02862i
$789$	−448.996	−	145.888i	−0.569069	−	0.184902i
$790$		0			0
$791$	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
$795$		0			0
$796$	−321.081	−	233.279i	−0.403368	−	0.293064i
$797$	−180.384	+	28.5701i	−0.226329	+	0.0358470i	−0.268569	−	0.963260i	$-0.586551\pi$
$797$	−180.384	+	28.5701i	−0.226329	+	0.0358470i	0.0422397	+	0.999108i	$0.486551\pi$
$798$	229.209	−	116.788i	0.287230	−	0.146351i
$799$		−	62.6979i		−	0.0784705i
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	$0.568011\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	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
$820$		0			0
$821$	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	−0.985893	−	0.167377i	$-0.946470\pi$
$823$	−1176.87	+	599.645i	−1.42997	+	0.728609i	−0.444082	+	0.895986i	$0.646470\pi$
$824$			483.690i			0.587002i
$825$		0			0
$826$	−259.069			−0.313643
$827$	279.354	+	548.262i	0.337792	+	0.662953i	0.995948	−	0.0899277i	$-0.0286636\pi$
$827$	279.354	+	548.262i	0.337792	+	0.662953i	−0.658157	+	0.752881i	$0.728664\pi$
$828$	−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	$0.112764\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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	$0.760412\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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
$850$		0			0
$851$	−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	$-0.820908\pi$
$853$	−175.917	−	1110.70i	−0.206234	−	1.30211i	0.639619	−	0.768692i	$-0.279092\pi$
$854$	−426.880	+	587.550i	−0.499859	+	0.687997i
$855$		0			0
$856$	266.899	−	193.914i	0.311798	−	0.226534i
$857$	−870.435	+	870.435i	−1.01568	+	1.01568i	−0.0158015	+	0.999875i	$0.505030\pi$
$857$	−870.435	+	870.435i	−1.01568	+	1.01568i	−0.999875	+	0.0158015i	$0.994970\pi$
$858$	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	$0.725805\pi$
$860$		0			0
$861$	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	$0.371973\pi$
$863$	−503.210	+	987.606i	−0.583094	+	1.14439i	−0.974546	+	0.224188i	$0.928027\pi$
$864$	824.264	+	267.820i	0.954009	+	0.309976i
$865$		0			0
$866$	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
$870$		0			0
$871$	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
$875$		0			0
$876$	−329.641			−0.376303
$877$	−375.480	−	736.921i	−0.428141	−	0.840275i	−0.999804	−	0.0197861i	$-0.993701\pi$
$877$	−375.480	−	736.921i	−0.428141	−	0.840275i	0.571663	−	0.820489i	$-0.306299\pi$
$878$	3.92199	+	24.7625i	0.00446696	+	0.0282033i
$879$	576.474	−	793.449i	0.655830	−	0.902672i
$880$		0			0
$881$	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	0.618099	−	0.786100i	$-0.287903\pi$
$883$	850.354	+	134.683i	0.963029	+	0.152529i	0.344929	+	0.938629i	$0.387903\pi$
$884$	−35.4434	+	11.5163i	−0.0400943	+	0.0130274i
$885$		0			0
$886$	67.3640	−	207.325i	0.0760316	−	0.234001i
$887$	−1248.92	−	636.358i	−1.40803	−	0.717427i	−0.425749	−	0.904841i	$-0.639989\pi$
$887$	−1248.92	−	636.358i	−1.40803	−	0.717427i	−0.982281	+	0.187414i	$0.939989\pi$
$888$	351.502	−	689.861i	0.395835	−	0.776870i
$889$	−1196.65	−	388.816i	−1.34606	−	0.437363i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−178.305	+	129.546i	−0.196805	+	0.142987i
$907$	338.384	−	338.384i	0.373081	−	0.373081i	−0.495517	−	0.868598i	$-0.665021\pi$
$907$	338.384	−	338.384i	0.373081	−	0.373081i	0.868598	+	0.495517i	$0.165021\pi$
$908$	−272.228	−	43.1167i	−0.299811	−	0.0474854i
$909$	−393.619	+	127.895i	−0.433024	+	0.140698i
$910$		0			0
$911$	−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
$915$		0			0
$916$	−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	$0.813091\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	$-0.0760930\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−128.364	+	395.064i	−0.137141	+	0.422077i
$937$	1076.49	+	548.497i	1.14886	+	0.585376i	0.921479	−	0.388429i	$-0.126982\pi$
$937$	1076.49	+	548.497i	1.14886	+	0.585376i	0.227386	+	0.973805i	$0.426982\pi$
$938$	141.510	−	277.728i	0.150863	−	0.296086i
$939$	309.099	+	100.432i	0.329178	+	0.106957i
$940$		0			0
$941$	−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
$945$		0			0
$946$	50.0373	+	36.3542i	0.0528935	+	0.0384294i
$947$	877.188	−	138.933i	0.926280	−	0.146708i	0.324970	−	0.945724i	$-0.394646\pi$
$947$	877.188	−	138.933i	0.926280	−	0.146708i	0.601310	+	0.799016i	$0.294646\pi$
$948$	657.197	−	334.858i	0.693245	−	0.353226i
$949$		−	653.406i		−	0.688520i
$950$		0			0
$951$	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	$0.00135911\pi$
$953$	47.9001	+	302.429i	0.0502625	+	0.317345i	−0.949728	+	0.313075i	$0.898641\pi$
$954$	−117.046	+	161.100i	−0.122690	+	0.168868i
$955$		0			0
$956$	−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
$960$		0			0
$961$	−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
$965$		0			0
$966$	21.3348	+	65.6618i	0.0220857	+	0.0679728i
$967$	−94.6041	+	597.307i	−0.0978326	+	0.617691i	0.889243	+	0.457435i	$0.151232\pi$
$967$	−94.6041	+	597.307i	−0.0978326	+	0.617691i	−0.987076	+	0.160256i	$0.948768\pi$
$968$	−393.265	−	393.265i	−0.406266	−	0.406266i
$969$	20.6677	+	28.4467i	0.0213289	+	0.0293567i
$970$		0			0
$971$	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
$975$		0			0
$976$	784.861			0.804161
$977$	133.140	+	261.301i	0.136274	+	0.267453i	0.949051	−	0.315122i	$-0.102045\pi$
$977$	133.140	+	261.301i	0.136274	+	0.267453i	−0.812777	+	0.582575i	$0.802045\pi$
$978$	79.4635	+	501.713i	0.0812510	+	0.512999i
$979$	−436.432	+	600.697i	−0.445794	+	0.613582i
$980$		0			0
$981$	−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	$-0.439270\pi$
$983$	65.4417	+	10.3649i	0.0665734	+	0.0105442i	−0.123059	+	0.992399i	$0.539270\pi$
$984$	617.271	−	200.563i	0.627308	−	0.203825i
$985$		0			0
$986$	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
$990$		0			0
$991$	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
$995$		0			0
$996$	304.829	+	221.471i	0.306053	+	0.222360i
$997$	−236.698	+	37.4893i	−0.237410	+	0.0376021i	−0.274006	−	0.961728i	$-0.588349\pi$
$997$	−236.698	+	37.4893i	−0.237410	+	0.0376021i	0.0365955	+	0.999330i	$0.488349\pi$
$998$	−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	125.3.f.c.118.3		32
5.2	odd	4		125.3.f.b.7.2		32
5.3	odd	4		125.3.f.a.7.3		32
5.4	even	2		25.3.f.a.3.2	✓	32
15.14	odd	2		225.3.r.a.28.3		32
20.19	odd	2		400.3.bg.c.353.3		32
25.6	even	5		125.3.f.b.18.2		32
25.8	odd	20		25.3.f.a.17.2	yes	32
25.17	odd	20	inner	125.3.f.c.107.3		32
25.19	even	10		125.3.f.a.18.3		32
75.8	even	20		225.3.r.a.217.3		32
100.83	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	5.4	even	2
25.3.f.a.17.2	yes	32	25.8	odd	20
125.3.f.a.7.3		32	5.3	odd	4
125.3.f.a.18.3		32	25.19	even	10
125.3.f.b.7.2		32	5.2	odd	4
125.3.f.b.18.2		32	25.6	even	5
125.3.f.c.107.3		32	25.17	odd	20	inner
125.3.f.c.118.3		32	1.1	even	1	trivial
225.3.r.a.28.3		32	15.14	odd	2
225.3.r.a.217.3		32	75.8	even	20
400.3.bg.c.17.3		32	100.83	even	20
400.3.bg.c.353.3		32	20.19	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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	125.f (of order \(20\), degree \(8\), not minimal)

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

Introduction

L-functions

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