LMFDB - Embedded newform 125.4.e.a.24.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,4,Mod(24,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("125.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, degree $4$, 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:	$7.37523875072$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.4
Character	$\chi$	$=$	125.24
Dual form			125.4.e.a.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48841 + 0.483614i) q^{2} +(4.16357 - 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(8.96855 - 6.51603i) q^{6} -1.18261i q^{7} +(-12.4652 - 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +O(q^{10})$	\(q+(1.48841 + 0.483614i) q^{2} +(4.16357 - 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(8.96855 - 6.51603i) q^{6} -1.18261i q^{7} +(-12.4652 - 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +(7.19826 - 22.1540i) q^{11} +(-37.3943 + 12.1501i) q^{12} +(34.0413 - 11.0607i) q^{13} +(0.571929 - 1.76022i) q^{14} +(3.46617 + 10.6678i) q^{16} +(-76.1834 - 104.857i) q^{17} -36.2705i q^{18} +(-85.6642 + 62.2387i) q^{19} +(-6.77717 - 4.92390i) q^{21} +(21.4280 - 29.4931i) q^{22} +(71.8250 + 23.3374i) q^{23} -150.220 q^{24} +56.0166 q^{26} +(25.7621 + 8.37062i) q^{27} +(-3.85845 + 5.31070i) q^{28} +(216.865 + 157.562i) q^{29} +(192.656 - 139.973i) q^{31} +187.211i q^{32} +(-96.9866 - 133.491i) q^{33} +(-62.6817 - 192.914i) q^{34} +(-39.7531 + 122.347i) q^{36} +(166.220 - 54.0080i) q^{37} +(-157.603 + 51.2084i) q^{38} +(78.3483 - 241.131i) q^{39} +(6.36260 + 19.5821i) q^{41} +(-7.70595 - 10.6063i) q^{42} +131.925i q^{43} +(-104.605 + 76.0003i) q^{44} +(95.6189 + 69.4712i) q^{46} +(101.704 - 139.984i) q^{47} +(75.5651 + 24.5526i) q^{48} +341.601 q^{49} -918.098 q^{51} +(-188.955 - 61.3951i) q^{52} +(19.3553 - 26.6403i) q^{53} +(34.2965 + 24.9179i) q^{54} +(-20.2899 + 14.7415i) q^{56} +750.049i q^{57} +(246.586 + 339.396i) q^{58} +(148.786 + 457.918i) q^{59} +(-174.560 + 537.239i) q^{61} +(354.445 - 115.166i) q^{62} +(-26.0667 + 8.46959i) q^{63} +(-62.8084 + 193.304i) q^{64} +(-79.7980 - 245.593i) q^{66} +(-198.345 - 272.998i) q^{67} +719.437i q^{68} +(432.787 - 314.438i) q^{69} +(-170.875 - 124.148i) q^{71} +(-288.892 + 397.626i) q^{72} +(-452.871 - 147.147i) q^{73} +273.522 q^{74} +587.751 q^{76} +(-26.1996 - 8.51277i) q^{77} +(233.229 - 321.013i) q^{78} +(-792.426 - 575.731i) q^{79} +(661.474 - 480.589i) q^{81} +32.2232i q^{82} +(-126.573 - 174.213i) q^{83} +(14.3689 + 44.2230i) q^{84} +(-63.8008 + 196.359i) q^{86} +(1805.87 - 586.763i) q^{87} +(-469.820 + 152.654i) q^{88} +(-120.001 + 369.326i) q^{89} +(-13.0805 - 40.2577i) q^{91} +(-246.399 - 339.139i) q^{92} -1686.84i q^{93} +(219.076 - 159.168i) q^{94} +(1072.84 + 779.466i) q^{96} +(-325.030 + 447.366i) q^{97} +(508.444 + 165.203i) q^{98} -539.861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} + 5 q^{3} + 13 q^{4} - 7 q^{6} + 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q + 5 * q^2 + 5 * q^3 + 13 * q^4 - 7 * q^6 + 110 * q^8 + 47 * q^9	$ 24 q + 5 q^{2} + 5 q^{3} + 13 q^{4} - 7 q^{6} + 110 q^{8} + 47 q^{9} + 83 q^{11} + 165 q^{12} + 5 q^{13} + 31 q^{14} + 89 q^{16} + 165 q^{17} - 115 q^{19} + 138 q^{21} - 30 q^{22} - 75 q^{23} + 640 q^{24} - 822 q^{26} - 595 q^{27} - 675 q^{28} + 125 q^{29} + 633 q^{31} + 1285 q^{33} - 779 q^{34} - 531 q^{36} + 1510 q^{37} - 255 q^{38} - 1241 q^{39} - 117 q^{41} - 1745 q^{42} + 516 q^{44} + 1233 q^{46} + 95 q^{47} - 1410 q^{48} + 1148 q^{49} - 2022 q^{51} - 1740 q^{52} - 2580 q^{53} + 1745 q^{54} + 3160 q^{56} + 4230 q^{58} - 1905 q^{59} - 567 q^{61} + 6880 q^{62} + 1950 q^{63} - 3612 q^{64} - 2774 q^{66} - 4195 q^{67} + 539 q^{69} + 2473 q^{71} - 215 q^{72} + 845 q^{73} + 3596 q^{74} - 3280 q^{76} - 3870 q^{77} - 9295 q^{78} + 775 q^{79} + 3309 q^{81} + 4625 q^{83} - 5694 q^{84} - 3897 q^{86} + 8485 q^{87} + 1650 q^{88} - 2410 q^{89} - 382 q^{91} - 4090 q^{92} + 5401 q^{94} + 6488 q^{96} - 5185 q^{97} - 5180 q^{98} + 6024 q^{99}+O(q^{100}) $ 24 * q + 5 * q^2 + 5 * q^3 + 13 * q^4 - 7 * q^6 + 110 * q^8 + 47 * q^9 + 83 * q^11 + 165 * q^12 + 5 * q^13 + 31 * q^14 + 89 * q^16 + 165 * q^17 - 115 * q^19 + 138 * q^21 - 30 * q^22 - 75 * q^23 + 640 * q^24 - 822 * q^26 - 595 * q^27 - 675 * q^28 + 125 * q^29 + 633 * q^31 + 1285 * q^33 - 779 * q^34 - 531 * q^36 + 1510 * q^37 - 255 * q^38 - 1241 * q^39 - 117 * q^41 - 1745 * q^42 + 516 * q^44 + 1233 * q^46 + 95 * q^47 - 1410 * q^48 + 1148 * q^49 - 2022 * q^51 - 1740 * q^52 - 2580 * q^53 + 1745 * q^54 + 3160 * q^56 + 4230 * q^58 - 1905 * q^59 - 567 * q^61 + 6880 * q^62 + 1950 * q^63 - 3612 * q^64 - 2774 * q^66 - 4195 * q^67 + 539 * q^69 + 2473 * q^71 - 215 * q^72 + 845 * q^73 + 3596 * q^74 - 3280 * q^76 - 3870 * q^77 - 9295 * q^78 + 775 * q^79 + 3309 * q^81 + 4625 * q^83 - 5694 * q^84 - 3897 * q^86 + 8485 * q^87 + 1650 * q^88 - 2410 * q^89 - 382 * q^91 - 4090 * q^92 + 5401 * q^94 + 6488 * q^96 - 5185 * q^97 - 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.48841	+	0.483614i	0.526233	+	0.170984i	0.560072	−	0.828444i	$-0.310773\pi$
$2$	1.48841	+	0.483614i	0.526233	+	0.170984i	−0.0338391	+	0.999427i	$0.510773\pi$
$3$	4.16357	−	5.73067i	0.801280	−	1.10287i	−0.191330	−	0.981526i	$-0.561280\pi$
$3$	4.16357	−	5.73067i	0.801280	−	1.10287i	0.992611	−	0.121342i	$-0.0387198\pi$
$4$	−4.49065	−	3.26265i	−0.561331	−	0.407831i
$5$		0			0
$5$		0			0
$6$	8.96855	−	6.51603i	0.610232	−	0.443360i
$7$		−	1.18261i		−	0.0638552i	−0.999490	−	0.0319276i	$-0.989835\pi$
$7$		−	1.18261i		−	0.0638552i	0.999490	−	0.0319276i	$-0.0101646\pi$
$8$	−12.4652	−	17.1569i	−0.550889	−	0.758233i
$9$	−7.16175	−	22.0416i	−0.265250	−	0.816356i
$10$		0			0
$11$	7.19826	−	22.1540i	0.197305	−	0.607243i	−0.802637	−	0.596468i	$-0.796570\pi$
$11$	7.19826	−	22.1540i	0.197305	−	0.607243i	0.999942	−	0.0107749i	$-0.00342983\pi$
$12$	−37.3943	+	12.1501i	−0.899567	+	0.292287i
$13$	34.0413	−	11.0607i	0.726258	−	0.235976i	0.0775239	−	0.996990i	$-0.475299\pi$
$13$	34.0413	−	11.0607i	0.726258	−	0.235976i	0.648734	+	0.761015i	$0.275299\pi$
$14$	0.571929	−	1.76022i	0.0109182	−	0.0336027i
$15$		0			0
$16$	3.46617	+	10.6678i	0.0541589	+	0.166684i
$17$	−76.1834	−	104.857i	−1.08689	−	1.49598i	−0.851699	−	0.524032i	$-0.824427\pi$
$17$	−76.1834	−	104.857i	−1.08689	−	1.49598i	−0.235194	−	0.971948i	$-0.575573\pi$
$18$		−	36.2705i		−	0.474947i
$19$	−85.6642	+	62.2387i	−1.03435	+	0.751502i	−0.969175	−	0.246372i	$-0.920762\pi$
$19$	−85.6642	+	62.2387i	−1.03435	+	0.751502i	−0.0651781	+	0.997874i	$0.520762\pi$
$20$		0			0
$21$	−6.77717	−	4.92390i	−0.0704238	−	0.0511659i
$22$	21.4280	−	29.4931i	0.207657	−	0.285816i
$23$	71.8250	+	23.3374i	0.651154	+	0.211573i	0.615923	−	0.787806i	$-0.288783\pi$
$23$	71.8250	+	23.3374i	0.651154	+	0.211573i	0.0352312	+	0.999379i	$0.488783\pi$
$24$	−150.220			−1.27765
$25$		0			0
$26$	56.0166			0.422529
$27$	25.7621	+	8.37062i	0.183627	+	0.0596640i
$28$	−3.85845	+	5.31070i	−0.0260421	+	0.0358439i
$29$	216.865	+	157.562i	1.38865	+	1.00891i	0.996012	+	0.0892210i	$0.0284377\pi$
$29$	216.865	+	157.562i	1.38865	+	1.00891i	0.392639	+	0.919693i	$0.371562\pi$
$30$		0			0
$31$	192.656	−	139.973i	1.11620	−	0.810964i	0.132568	−	0.991174i	$-0.457678\pi$
$31$	192.656	−	139.973i	1.11620	−	0.810964i	0.983628	+	0.180210i	$0.0576776\pi$
$32$			187.211i			1.03420i
$33$	−96.9866	−	133.491i	−0.511612	−	0.704174i
$34$	−62.6817	−	192.914i	−0.316171	−	0.973075i
$35$		0			0
$36$	−39.7531	+	122.347i	−0.184042	+	0.566423i
$37$	166.220	−	54.0080i	0.738550	−	0.239969i	0.0845026	−	0.996423i	$-0.473070\pi$
$37$	166.220	−	54.0080i	0.738550	−	0.239969i	0.654047	+	0.756454i	$0.273070\pi$
$38$	−157.603	+	51.2084i	−0.672806	+	0.218608i
$39$	78.3483	−	241.131i	0.321687	−	0.990049i
$40$		0			0
$41$	6.36260	+	19.5821i	0.0242359	+	0.0745903i	0.962443	−	0.271484i	$-0.0875144\pi$
$41$	6.36260	+	19.5821i	0.0242359	+	0.0745903i	−0.938207	+	0.346074i	$0.887514\pi$
$42$	−7.70595	−	10.6063i	−0.0283108	−	0.0389665i
$43$			131.925i			0.467869i	0.972252	+	0.233934i	$0.0751601\pi$
$43$			131.925i			0.467869i	−0.972252	+	0.233934i	$0.924840\pi$
$44$	−104.605	+	76.0003i	−0.358406	+	0.260397i
$45$		0			0
$46$	95.6189	+	69.4712i	0.306483	+	0.222673i
$47$	101.704	−	139.984i	0.315640	−	0.434441i	−0.621490	−	0.783422i	$-0.713472\pi$
$47$	101.704	−	139.984i	0.315640	−	0.434441i	0.937130	+	0.348981i	$0.113472\pi$
$48$	75.5651	+	24.5526i	0.227227	+	0.0738304i
$49$	341.601			0.995923
$50$		0			0
$51$	−918.098			−2.52077
$52$	−188.955	−	61.3951i	−0.503909	−	0.163730i
$53$	19.3553	−	26.6403i	0.0501633	−	0.0690438i	−0.783198	−	0.621772i	$-0.786413\pi$
$53$	19.3553	−	26.6403i	0.0501633	−	0.0690438i	0.833362	+	0.552728i	$0.186413\pi$
$54$	34.2965	+	24.9179i	0.0864290	+	0.0627943i
$55$		0			0
$56$	−20.2899	+	14.7415i	−0.0484171	+	0.0351771i
$57$			750.049i			1.74292i
$58$	246.586	+	339.396i	0.558246	+	0.768360i
$59$	148.786	+	457.918i	0.328311	+	1.01044i	0.969924	+	0.243409i	$0.0782656\pi$
$59$	148.786	+	457.918i	0.328311	+	1.01044i	−0.641613	+	0.767029i	$0.721734\pi$
$60$		0			0
$61$	−174.560	+	537.239i	−0.366395	+	1.12765i	0.582709	+	0.812681i	$0.301993\pi$
$61$	−174.560	+	537.239i	−0.366395	+	1.12765i	−0.949103	+	0.314965i	$0.898007\pi$
$62$	354.445	−	115.166i	0.726041	−	0.235905i
$63$	−26.0667	+	8.46959i	−0.0521285	+	0.0169376i
$64$	−62.8084	+	193.304i	−0.122673	+	0.377548i
$65$		0			0
$66$	−79.7980	−	245.593i	−0.148825	−	0.458037i
$67$	−198.345	−	272.998i	−0.361667	−	0.497791i	0.588946	−	0.808173i	$-0.299543\pi$
$67$	−198.345	−	272.998i	−0.361667	−	0.497791i	−0.950612	+	0.310381i	$0.899543\pi$
$68$			719.437i			1.28301i
$69$	432.787	−	314.438i	0.755094	−	0.548608i
$70$		0			0
$71$	−170.875	−	124.148i	−0.285622	−	0.207517i	0.435744	−	0.900071i	$-0.356485\pi$
$71$	−170.875	−	124.148i	−0.285622	−	0.207517i	−0.721366	+	0.692554i	$0.756485\pi$
$72$	−288.892	+	397.626i	−0.472865	+	0.650842i
$73$	−452.871	−	147.147i	−0.726090	−	0.235921i	−0.0774284	−	0.996998i	$-0.524671\pi$
$73$	−452.871	−	147.147i	−0.726090	−	0.235921i	−0.648662	+	0.761077i	$0.724671\pi$
$74$	273.522			0.429680
$75$		0			0
$76$	587.751			0.887100
$77$	−26.1996	−	8.51277i	−0.0387756	−	0.0125990i
$78$	233.229	−	321.013i	0.338564	−	0.465994i
$79$	−792.426	−	575.731i	−1.12854	−	0.819934i	−0.143060	−	0.989714i	$-0.545694\pi$
$79$	−792.426	−	575.731i	−1.12854	−	0.819934i	−0.985482	+	0.169780i	$0.945694\pi$
$80$		0			0
$81$	661.474	−	480.589i	0.907372	−	0.659244i
$82$			32.2232i			0.0433958i
$83$	−126.573	−	174.213i	−0.167388	−	0.230389i	0.717080	−	0.696991i	$-0.245478\pi$
$83$	−126.573	−	174.213i	−0.167388	−	0.230389i	−0.884468	+	0.466602i	$0.845478\pi$
$84$	14.3689	+	44.2230i	0.0186640	+	0.0574420i
$85$		0			0
$86$	−63.8008	+	196.359i	−0.0799978	+	0.246208i
$87$	1805.87	−	586.763i	2.22540	−	0.723075i
$88$	−469.820	+	152.654i	−0.569125	+	0.184920i
$89$	−120.001	+	369.326i	−0.142922	+	0.439870i	−0.996738	−	0.0807057i	$-0.974283\pi$
$89$	−120.001	+	369.326i	−0.142922	+	0.439870i	0.853816	+	0.520576i	$0.174283\pi$
$90$		0			0
$91$	−13.0805	−	40.2577i	−0.0150683	−	0.0463753i
$92$	−246.399	−	339.139i	−0.279227	−	0.384323i
$93$		−	1686.84i		−	1.88083i
$94$	219.076	−	159.168i	0.240382	−	0.174648i
$95$		0			0
$96$	1072.84	+	779.466i	1.14059	+	0.828686i
$97$	−325.030	+	447.366i	−0.340225	+	0.468280i	−0.944507	−	0.328491i	$-0.893460\pi$
$97$	−325.030	+	447.366i	−0.340225	+	0.468280i	0.604282	+	0.796770i	$0.293460\pi$
$98$	508.444	+	165.203i	0.524087	+	0.170286i
$99$	−539.861			−0.548062
$100$		0			0
$101$	−637.953			−0.628502			−0.314251	−	0.949340i	$-0.601753\pi$
$101$	−637.953			−0.628502			−0.314251	+	0.949340i	$0.601753\pi$
$102$	−1366.51	−	444.006i	−1.32651	−	0.431011i
$103$	−328.881	+	452.666i	−0.314618	+	0.433034i	−0.936814	−	0.349827i	$-0.886240\pi$
$103$	−328.881	+	452.666i	−0.314618	+	0.433034i	0.622197	+	0.782861i	$0.286240\pi$
$104$	−614.098	−	446.168i	−0.579012	−	0.420677i
$105$		0			0
$106$	41.6922	−	30.2912i	0.0382029	−	0.0277560i
$107$		−	347.014i		−	0.313524i	−0.987636	−	0.156762i	$-0.949894\pi$
$107$		−	347.014i		−	0.313524i	0.987636	−	0.156762i	$-0.0501056\pi$
$108$	−88.3783	−	121.642i	−0.0787426	−	0.108380i
$109$	44.4432	+	136.782i	0.0390540	+	0.120196i	0.968683	−	0.248301i	$-0.0798724\pi$
$109$	44.4432	+	136.782i	0.0390540	+	0.120196i	−0.929629	+	0.368497i	$0.879872\pi$
$110$		0			0
$111$	382.566	−	1177.42i	0.327131	−	1.00681i
$112$	12.6159	−	4.09914i	0.0106436	−	0.00345832i
$113$	1243.62	−	404.077i	1.03531	−	0.336393i	0.258423	−	0.966032i	$-0.416797\pi$
$113$	1243.62	−	404.077i	1.03531	−	0.336393i	0.776888	+	0.629639i	$0.216797\pi$
$114$	−362.734	+	1116.38i	−0.298010	+	0.917182i
$115$		0			0
$116$	−459.797	−	1415.11i	−0.368027	−	1.13267i
$117$	−487.591	−	671.111i	−0.385280	−	0.530293i
$118$			753.525i			0.587861i
$119$	−124.006	+	90.0955i	−0.0955260	+	0.0694037i
$120$		0			0
$121$	637.818	+	463.402i	0.479202	+	0.348161i
$122$	−519.633	+	715.214i	−0.385618	+	0.530758i
$123$	138.709	+	45.0694i	0.101683	+	0.0330388i
$124$	−1321.83			−0.957292
$125$		0			0
$126$	−42.8940			−0.0303278
$127$	−1927.43	−	626.261i	−1.34671	−	0.437572i	−0.455125	−	0.890427i	$-0.650406\pi$
$127$	−1927.43	−	626.261i	−1.34671	−	0.437572i	−0.891584	+	0.452855i	$0.850406\pi$
$128$	693.348	−	954.311i	0.478780	−	0.658984i
$129$	756.018	+	549.279i	0.515997	+	0.374894i
$130$		0			0
$131$	546.263	−	396.883i	0.364330	−	0.264701i	−0.390526	−	0.920592i	$-0.627707\pi$
$131$	546.263	−	396.883i	0.364330	−	0.264701i	0.754856	+	0.655891i	$0.227707\pi$
$132$			915.892i			0.603926i
$133$	73.6043	+	101.308i	0.0479873	+	0.0660488i
$134$	−163.193	−	502.256i	−0.105207	−	0.323793i
$135$		0			0
$136$	−849.384	+	2614.13i	−0.535545	+	1.64824i
$137$	94.5956	−	30.7360i	0.0589916	−	0.0191675i	−0.279373	−	0.960183i	$-0.590126\pi$
$137$	94.5956	−	30.7360i	0.0589916	−	0.0191675i	0.338364	+	0.941015i	$0.390126\pi$
$138$	796.233	−	258.712i	0.491158	−	0.159587i
$139$	550.842	−	1695.32i	0.336128	−	1.03450i	−0.630035	−	0.776566i	$-0.716960\pi$
$139$	550.842	−	1695.32i	0.336128	−	1.03450i	0.966164	−	0.257930i	$-0.0830403\pi$
$140$		0			0
$141$	−378.748	−	1165.67i	−0.226215	−	0.696218i
$142$	−194.293	−	267.421i	−0.114822	−	0.158039i
$143$		−	833.768i		−	0.487575i
$144$	210.311	−	152.800i	0.121708	−	0.0884258i
$145$		0			0
$146$	−602.897	−	438.030i	−0.341754	−	0.248299i
$147$	1422.28	−	1957.60i	0.798013	−	1.09837i
$148$	−922.643	−	299.785i	−0.512438	−	0.166501i
$149$	918.569			0.505048			0.252524	−	0.967591i	$-0.418739\pi$
$149$	918.569			0.505048			0.252524	+	0.967591i	$0.418739\pi$
$150$		0			0
$151$	96.9677			0.0522591			0.0261295	−	0.999659i	$-0.491682\pi$
$151$	96.9677			0.0522591			0.0261295	+	0.999659i	$0.491682\pi$
$152$	2135.64	+	693.912i	1.13963	+	0.370287i
$153$	−1765.62	+	2430.17i	−0.932953	+	1.28410i
$154$	−34.8789	−	25.3410i	−0.0182508	−	0.0132600i
$155$		0			0
$156$	−1138.56	+	827.213i	−0.584345	+	0.424552i
$157$			3116.13i			1.58404i	0.610497	+	0.792019i	$0.290970\pi$
$157$			3116.13i			1.58404i	−0.610497	+	0.792019i	$0.709030\pi$
$158$	−901.024	−	1240.15i	−0.453681	−	0.624439i
$159$	−72.0793	−	221.837i	−0.0359513	−	0.110647i
$160$		0			0
$161$	27.5991	−	84.9412i	0.0135100	−	0.0415796i
$162$	1216.97	−	395.416i	0.590209	−	0.191770i
$163$	−708.216	+	230.113i	−0.340317	+	0.110576i	−0.474190	−	0.880423i	$-0.657259\pi$
$163$	−708.216	+	230.113i	−0.340317	+	0.110576i	0.133872	+	0.990999i	$0.457259\pi$
$164$	35.3172	−	108.695i	0.0168159	−	0.0517540i
$165$		0			0
$166$	−104.141	−	320.513i	−0.0486922	−	0.149859i
$167$	−127.395	−	175.344i	−0.0590307	−	0.0812488i	0.778481	−	0.627668i	$-0.215991\pi$
$167$	−127.395	−	175.344i	−0.0590307	−	0.0812488i	−0.837512	+	0.546419i	$0.815991\pi$
$168$			177.652i			0.0815843i
$169$	−740.939	+	538.324i	−0.337250	+	0.245027i
$170$		0			0
$171$	1985.35	+	1442.44i	0.887855	+	0.645064i
$172$	430.424	−	592.428i	0.190811	−	0.262629i
$173$	16.8682	+	5.48081i	0.00741309	+	0.00240866i	0.312721	−	0.949845i	$-0.398759\pi$
$173$	16.8682	+	5.48081i	0.00741309	+	0.00240866i	−0.305308	+	0.952254i	$0.598759\pi$
$174$	2971.64			1.29471
$175$		0			0
$176$	261.284			0.111903
$177$	3243.66	+	1053.93i	1.37745	+	0.447560i
$178$	−357.222	+	491.674i	−0.150421	+	0.207037i
$179$	2206.88	+	1603.39i	0.921509	+	0.669515i	0.943899	−	0.330234i	$-0.107128\pi$
$179$	2206.88	+	1603.39i	0.921509	+	0.669515i	−0.0223903	+	0.999749i	$0.507128\pi$
$180$		0			0
$181$	−1252.23	+	909.799i	−0.514241	+	0.373618i	−0.814430	−	0.580262i	$-0.802950\pi$
$181$	−1252.23	+	909.799i	−0.514241	+	0.373618i	0.300189	+	0.953880i	$0.402950\pi$
$182$		−	66.2460i		−	0.0269807i
$183$	2351.95	+	3237.18i	0.950060	+	1.30765i
$184$	−494.916	−	1523.20i	−0.198292	−	0.610280i
$185$		0			0
$186$	815.779	−	2510.71i	0.321590	−	0.989753i
$187$	−2871.40	+	932.973i	−1.12287	+	0.364844i
$188$	−913.435	+	296.793i	−0.354357	+	0.115138i
$189$	9.89922	−	30.4667i	0.00380985	−	0.0117255i
$190$		0			0
$191$	994.375	+	3060.37i	0.376704	+	1.15938i	0.942322	+	0.334708i	$0.108638\pi$
$191$	994.375	+	3060.37i	0.376704	+	1.15938i	−0.565618	+	0.824667i	$0.691362\pi$
$192$	846.256	+	1164.77i	0.318090	+	0.437813i
$193$			2386.85i			0.890205i	0.895480	+	0.445102i	$0.146833\pi$
$193$			2386.85i			0.890205i	−0.895480	+	0.445102i	$0.853167\pi$
$194$	−700.132	+	508.676i	−0.259106	+	0.188251i
$195$		0			0
$196$	−1534.01	−	1114.52i	−0.559042	−	0.406168i
$197$	−726.915	+	1000.51i	−0.262896	+	0.361846i	−0.919976	−	0.391976i	$-0.871792\pi$
$197$	−726.915	+	1000.51i	−0.262896	+	0.361846i	0.657079	+	0.753822i	$0.271792\pi$
$198$	−803.536	−	261.085i	−0.288408	−	0.0937095i
$199$	−2580.97			−0.919396			−0.459698	−	0.888075i	$-0.652042\pi$
$199$	−2580.97			−0.919396			−0.459698	+	0.888075i	$0.652042\pi$
$200$		0			0
$201$	−2390.28			−0.838794
$202$	−949.537	−	308.523i	−0.330738	−	0.107463i
$203$	186.335	−	256.468i	0.0644243	−	0.0886725i
$204$	4122.86	+	2995.43i	1.41499	+	1.02805i
$205$		0			0
$206$	−708.427	+	514.702i	−0.239604	+	0.174083i
$207$		−	1750.27i		−	0.587693i
$208$	235.986	+	324.807i	0.0786667	+	0.108275i
$209$	762.201	+	2345.81i	0.252261	+	0.776379i
$210$		0			0
$211$	−888.596	+	2734.82i	−0.289922	+	0.892287i	0.694958	+	0.719050i	$0.255423\pi$
$211$	−888.596	+	2734.82i	−0.289922	+	0.892287i	−0.984880	+	0.173237i	$0.944577\pi$
$212$	−173.836	+	56.4826i	−0.0563164	+	0.0182983i
$213$	−1422.90	+	462.330i	−0.457727	+	0.148724i
$214$	167.821	−	516.500i	0.0536075	−	0.164987i
$215$		0			0
$216$	−177.516	−	546.338i	−0.0559187	−	0.172100i
$217$	−165.534	−	227.838i	−0.0517843	−	0.0712749i
$218$			225.082i			0.0699287i
$219$	−2728.81	+	1982.60i	−0.841991	+	0.611742i
$220$		0			0
$221$	−3753.18	−	2726.84i	−1.14238	−	0.829988i
$222$	1138.83	−	1567.47i	0.344294	−	0.473880i
$223$	3938.36	+	1279.65i	1.18266	+	0.384268i	0.833353	−	0.552742i	$-0.186418\pi$
$223$	3938.36	+	1279.65i	1.18266	+	0.384268i	0.349303	+	0.937010i	$0.386418\pi$
$224$	221.398			0.0660392
$225$		0			0
$226$	2046.44			0.602332
$227$	2216.13	+	720.064i	0.647972	+	0.210539i	0.614520	−	0.788901i	$-0.289350\pi$
$227$	2216.13	+	720.064i	0.647972	+	0.210539i	0.0334522	+	0.999440i	$0.489350\pi$
$228$	2447.14	−	3368.20i	0.710816	−	0.978354i
$229$	−4250.24	−	3087.98i	−1.22648	−	0.891088i	−0.229857	−	0.973224i	$-0.573826\pi$
$229$	−4250.24	−	3087.98i	−1.22648	−	0.891088i	−0.996621	+	0.0821360i	$0.973826\pi$
$230$		0			0
$231$	−157.868	+	114.698i	−0.0449651	+	0.0326691i
$232$		−	5684.76i		−	1.60872i
$233$	−2231.74	−	3071.72i	−0.627493	−	0.863671i	0.370378	−	0.928881i	$-0.379228\pi$
$233$	−2231.74	−	3071.72i	−0.627493	−	0.863671i	−0.997872	+	0.0652105i	$0.979228\pi$
$234$	−401.177	−	1234.70i	−0.112076	−	0.344934i
$235$		0			0
$236$	825.876	−	2541.78i	0.227796	−	0.701085i
$237$	−6598.65	+	2144.03i	−1.80856	+	0.587636i
$238$	−228.143	+	74.1283i	−0.0621359	+	0.0201892i
$239$	2008.57	−	6181.73i	0.543613	−	1.67307i	−0.180653	−	0.983547i	$-0.557821\pi$
$239$	2008.57	−	6181.73i	0.543613	−	1.67307i	0.724266	−	0.689521i	$-0.242179\pi$
$240$		0			0
$241$	952.246	+	2930.71i	0.254521	+	0.783335i	0.993924	+	0.110071i	$0.0351080\pi$
$241$	952.246	+	2930.71i	0.254521	+	0.783335i	−0.739403	+	0.673263i	$0.764892\pi$
$242$	725.228	+	998.191i	0.192642	+	0.265149i
$243$		−	5060.28i		−	1.33587i
$244$	2536.71	−	1843.03i	0.665558	−	0.483556i
$245$		0			0
$246$	184.661	+	134.164i	0.0478599	+	0.0347722i
$247$	−2227.72	+	3066.19i	−0.573872	+	0.789867i
$248$	−4802.99	−	1560.59i	−1.22980	−	0.399586i
$249$	−1525.35			−0.388213
$250$		0			0
$251$	7819.56			1.96640			0.983199	−	0.182536i	$-0.0584305\pi$
$251$	7819.56			1.96640			0.983199	+	0.182536i	$0.0584305\pi$
$252$	144.690	+	47.0125i	0.0361690	+	0.0117520i
$253$	1034.03	−	1423.22i	0.256952	−	0.353664i
$254$	−2565.95	−	1864.27i	−0.633866	−	0.460530i
$255$		0			0
$256$	2808.98	−	2040.85i	0.685787	−	0.498253i
$257$		−	2384.26i		−	0.578700i	−0.957223	−	0.289350i	$-0.906561\pi$
$257$		−	2384.26i		−	0.578700i	0.957223	−	0.289350i	$-0.0934392\pi$
$258$	859.627	+	1183.17i	0.207434	+	0.285509i
$259$	−63.8706	−	196.574i	−0.0153233	−	0.0471602i
$260$		0			0
$261$	1919.78	−	5908.48i	0.455293	−	1.40125i
$262$	1005.00	−	326.545i	0.236982	−	0.0770001i
$263$	2942.84	−	956.186i	0.689974	−	0.224186i	0.0570172	−	0.998373i	$-0.481841\pi$
$263$	2942.84	−	956.186i	0.689974	−	0.224186i	0.632957	+	0.774187i	$0.281841\pi$
$264$	−1081.32	+	3327.97i	−0.252086	+	0.775842i
$265$		0			0
$266$	60.5597	+	186.384i	0.0139592	+	0.0429621i
$267$	1616.85	+	2225.40i	0.370597	+	0.510084i
$268$			1873.07i			0.426924i
$269$	−1193.33	+	867.006i	−0.270478	+	0.196514i	−0.714754	−	0.699376i	$-0.753461\pi$
$269$	−1193.33	+	867.006i	−0.270478	+	0.196514i	0.444275	+	0.895890i	$0.353461\pi$
$270$		0			0
$271$	245.587	+	178.429i	0.0550492	+	0.0399956i	0.614970	−	0.788551i	$-0.289168\pi$
$271$	245.587	+	178.429i	0.0550492	+	0.0399956i	−0.559920	+	0.828546i	$0.689168\pi$
$272$	854.530	−	1176.16i	0.190491	−	0.262188i
$273$	−285.165	−	92.6559i	−0.0632198	−	0.0205413i
$274$	155.662			0.0343206
$275$		0			0
$276$	−2969.40			−0.647597
$277$	−4610.31	−	1497.98i	−1.00002	−	0.324927i	−0.237148	−	0.971473i	$-0.576213\pi$
$277$	−4610.31	−	1497.98i	−1.00002	−	0.324927i	−0.762875	+	0.646546i	$0.776213\pi$
$278$	1639.76	−	2256.94i	0.353764	−	0.486914i
$279$	−4464.99	−	3244.00i	−0.958107	−	0.696105i
$280$		0			0
$281$	1203.90	−	874.687i	0.255583	−	0.185692i	−0.452614	−	0.891706i	$-0.649509\pi$
$281$	1203.90	−	874.687i	0.255583	−	0.185692i	0.708198	+	0.706014i	$0.249509\pi$
$282$		−	1918.16i		−	0.405052i
$283$	−1574.63	−	2167.29i	−0.330749	−	0.455237i	0.610962	−	0.791660i	$-0.290783\pi$
$283$	−1574.63	−	2167.29i	−0.330749	−	0.455237i	−0.941711	+	0.336423i	$0.890783\pi$
$284$	362.289	+	1115.01i	0.0756969	+	0.232971i
$285$		0			0
$286$	403.222	−	1240.99i	0.0833672	−	0.256578i
$287$	23.1580	−	7.52450i	0.00476298	−	0.00154759i
$288$	4126.42	−	1340.76i	0.844277	−	0.274322i
$289$	−3672.97	+	11304.2i	−0.747603	+	2.30088i
$290$		0			0
$291$	1210.42	+	3725.28i	0.243835	+	0.750447i
$292$	1553.60	+	2138.34i	0.311361	+	0.428552i
$293$			3929.37i			0.783468i	0.920078	+	0.391734i	$0.128125\pi$
$293$			3929.37i			0.783468i	−0.920078	+	0.391734i	$0.871875\pi$
$294$	3063.67	−	2225.89i	0.607744	−	0.441552i
$295$		0			0
$296$	−2998.57	−	2178.59i	−0.588811	−	0.427796i
$297$	370.885	−	510.480i	0.0724611	−	0.0997341i
$298$	1367.21	+	444.233i	0.265773	+	0.0863549i
$299$	2703.14			0.522832
$300$		0			0
$301$	156.016			0.0298758
$302$	144.328	+	46.8950i	0.0275005	+	0.00893544i
$303$	−2656.16	+	3655.90i	−0.503606	+	0.693154i
$304$	−960.875	−	698.116i	−0.181283	−	0.131710i
$305$		0			0
$306$	−3803.23	+	2763.21i	−0.710511	+	0.516216i
$307$		−	8263.41i		−	1.53621i	−0.640322	−	0.768107i	$-0.721199\pi$
$307$		−	8263.41i		−	1.53621i	0.640322	−	0.768107i	$-0.278801\pi$
$308$	89.8790	+	123.708i	0.0166277	+	0.0228861i
$309$	1224.76	+	3769.42i	0.225483	+	0.693964i
$310$		0			0
$311$	−1483.86	+	4566.84i	−0.270552	+	0.832675i	0.719810	+	0.694172i	$0.244229\pi$
$311$	−1483.86	+	4566.84i	−0.270552	+	0.832675i	−0.990362	+	0.138503i	$0.955771\pi$
$312$	−5113.68	+	1661.54i	−0.927902	+	0.301494i
$313$	−9805.98	+	3186.15i	−1.77082	+	0.575374i	−0.998227	−	0.0595277i	$-0.981041\pi$
$313$	−9805.98	+	3186.15i	−1.77082	+	0.575374i	−0.772593	+	0.634902i	$0.781041\pi$
$314$	−1507.00	+	4638.08i	−0.270844	+	0.833573i
$315$		0			0
$316$	1680.10	+	5170.81i	0.299091	+	0.920509i
$317$	1928.95	+	2654.97i	0.341768	+	0.470403i	0.944957	−	0.327195i	$-0.106104\pi$
$317$	1928.95	+	2654.97i	0.341768	+	0.470403i	−0.603189	+	0.797598i	$0.706104\pi$
$318$		−	365.044i		−	0.0643731i
$319$	5051.67	−	3670.26i	0.886644	−	0.644185i
$320$		0			0
$321$	−1988.62	−	1444.82i	−0.345776	−	0.251221i
$322$	82.1576	−	113.080i	0.0142188	−	0.0195705i
$323$	13052.4	+	4240.97i	2.24846	+	0.730570i
$324$	−4538.44			−0.778196
$325$		0			0
$326$	−1165.40			−0.197993
$327$	968.896	+	314.813i	0.163853	+	0.0532392i
$328$	256.656	−	353.256i	0.0432056	−	0.0594674i
$329$	−165.547	−	120.277i	−0.0277413	−	0.0201552i
$330$		0			0
$331$	290.415	−	210.999i	0.0482255	−	0.0350379i	−0.563411	−	0.826177i	$-0.690511\pi$
$331$	290.415	−	210.999i	0.0482255	−	0.0350379i	0.611637	+	0.791139i	$0.290511\pi$
$332$			1195.29i			0.197591i
$333$	−2380.85	−	3276.95i	−0.391801	−	0.539267i
$334$	−104.817	−	322.595i	−0.0171717	−	0.0528491i
$335$		0			0
$336$	29.0362	−	89.3644i	0.00471445	−	0.0145096i
$337$	1246.37	−	404.970i	0.201466	−	0.0654603i	−0.206546	−	0.978437i	$-0.566222\pi$
$337$	1246.37	−	404.970i	0.201466	−	0.0654603i	0.408012	+	0.912977i	$0.366222\pi$
$338$	−1363.16	+	442.919i	−0.219368	+	0.0712769i
$339$	2862.28	−	8809.19i	0.458577	−	1.41136i
$340$		0			0
$341$	−1714.17	−	5275.67i	−0.272221	−	0.837810i
$342$	2257.43	+	3107.09i	0.356923	+	0.491263i
$343$		−	809.619i		−	0.127450i
$344$	2263.42	−	1644.47i	0.354754	−	0.257744i
$345$		0			0
$346$	22.4562	+	16.3154i	0.00348917	+	0.00253503i
$347$	2278.45	−	3136.01i	0.352488	−	0.485158i	−0.595549	−	0.803319i	$-0.703065\pi$
$347$	2278.45	−	3136.01i	0.352488	−	0.485158i	0.948037	+	0.318161i	$0.103065\pi$
$348$	−10023.9	−	3256.97i	−1.54408	−	0.501701i
$349$	7122.39			1.09242			0.546208	−	0.837650i	$-0.316071\pi$
$349$	7122.39			1.09242			0.546208	+	0.837650i	$0.316071\pi$
$350$		0			0
$351$	969.561			0.147440
$352$	4147.46	+	1347.59i	0.628012	+	0.204054i
$353$	−6423.28	+	8840.89i	−0.968490	+	1.33301i	−0.0256839	+	0.999670i	$0.508176\pi$
$353$	−6423.28	+	8840.89i	−0.968490	+	1.33301i	−0.942806	+	0.333342i	$0.891824\pi$
$354$	4318.20	+	3137.36i	0.648333	+	0.471042i
$355$		0			0
$356$	1743.86	−	1266.99i	0.259619	−	0.188624i
$357$			1085.76i			0.160964i
$358$	2509.33	+	3453.79i	0.370452	+	0.509884i
$359$	−603.519	−	1857.44i	−0.0887256	−	0.273069i	0.896842	−	0.442351i	$-0.145855\pi$
$359$	−603.519	−	1857.44i	−0.0887256	−	0.273069i	−0.985568	+	0.169281i	$0.945855\pi$
$360$		0			0
$361$	1345.15	−	4139.96i	0.196115	−	0.603581i
$362$	−2303.83	+	748.559i	−0.334493	+	0.108683i
$363$	5311.21	−	1725.72i	0.767950	−	0.249522i
$364$	−72.6067	+	223.460i	−0.0104550	+	0.0321772i
$365$		0			0
$366$	1935.12	+	5955.69i	0.276367	+	0.850571i
$367$	6175.15	+	8499.37i	0.878312	+	1.20889i	0.976886	+	0.213763i	$0.0685719\pi$
$367$	6175.15	+	8499.37i	0.878312	+	1.20889i	−0.0985740	+	0.995130i	$0.531428\pi$
$368$			847.104i			0.119995i
$369$	386.053	−	280.484i	0.0544637	−	0.0395702i
$370$		0			0
$371$	−31.5051	−	22.8898i	−0.00440880	−	0.00320318i
$372$	−5503.56	+	7574.99i	−0.767059	+	1.05577i
$373$	859.018	+	279.112i	0.119245	+	0.0387450i	0.368032	−	0.929813i	$-0.380032\pi$
$373$	859.018	+	279.112i	0.119245	+	0.0387450i	−0.248787	+	0.968558i	$0.580032\pi$
$374$	−4725.02			−0.653275
$375$		0			0
$376$	−3669.44			−0.503290
$377$	9125.12	+	2964.93i	1.24660	+	0.405044i
$378$	29.4682	−	40.5595i	0.00400974	−	0.00551893i
$379$	7139.52	+	5187.17i	0.967632	+	0.703026i	0.954911	−	0.296893i	$-0.0959505\pi$
$379$	7139.52	+	5187.17i	0.967632	+	0.703026i	0.0127216	+	0.999919i	$0.495950\pi$
$380$		0			0
$381$	−11613.9	+	8438.00i	−1.56168	+	1.13462i
$382$			5035.99i			0.674512i
$383$	−3587.32	−	4937.52i	−0.478599	−	0.658734i	0.499636	−	0.866235i	$-0.333467\pi$
$383$	−3587.32	−	4937.52i	−0.478599	−	0.658734i	−0.978235	+	0.207501i	$0.933467\pi$
$384$	−2582.04	−	7946.69i	−0.343135	−	1.05606i
$385$		0			0
$386$	−1154.32	+	3552.62i	−0.152210	+	0.468455i
$387$	2907.84	−	944.813i	0.381947	−	0.124102i
$388$	2919.19	−	948.504i	0.381958	−	0.124106i
$389$	2180.80	−	6711.81i	0.284244	−	0.874812i	−0.702380	−	0.711802i	$-0.747879\pi$
$389$	2180.80	−	6711.81i	0.284244	−	0.874812i	0.986624	−	0.163011i	$-0.0521205\pi$
$390$		0			0
$391$	−3024.78	−	9309.30i	−0.391226	−	1.20407i
$392$	−4258.13	−	5860.81i	−0.548642	−	0.755141i
$393$		−	4782.90i		−	0.613907i
$394$	−1565.81	+	1137.63i	−0.200214	+	0.145464i
$395$		0			0
$396$	2424.33	+	1761.38i	0.307644	+	0.223516i
$397$	2498.77	−	3439.26i	0.315893	−	0.434789i	−0.621315	−	0.783561i	$-0.713401\pi$
$397$	2498.77	−	3439.26i	0.315893	−	0.434789i	0.937208	+	0.348772i	$0.113401\pi$
$398$	−3841.54	−	1248.19i	−0.483817	−	0.157202i
$399$	887.018			0.111294
$400$		0			0
$401$	7335.40			0.913497			0.456749	−	0.889596i	$-0.349014\pi$
$401$	7335.40			0.913497			0.456749	+	0.889596i	$0.349014\pi$
$402$	−3557.73	−	1155.98i	−0.441401	−	0.143420i
$403$	5010.07	−	6895.77i	0.619279	−	0.852365i
$404$	2864.82	+	2081.41i	0.352798	+	0.256322i
$405$		0			0
$406$	401.375	−	291.616i	0.0490638	−	0.0356469i
$407$		−	4071.19i		−	0.495826i
$408$	11444.3	+	15751.7i	1.38867	+	1.91133i
$409$	2850.25	+	8772.17i	0.344586	+	1.06053i	0.961805	+	0.273736i	$0.0882594\pi$
$409$	2850.25	+	8772.17i	0.344586	+	1.06053i	−0.617219	+	0.786792i	$0.711741\pi$
$410$		0			0
$411$	217.718	−	670.067i	0.0261295	−	0.0804185i
$412$	2953.78	−	959.742i	0.353210	−	0.114765i
$413$	541.540	−	175.957i	0.0645216	−	0.0209643i
$414$	846.458	−	2605.13i	0.100486	−	0.309264i
$415$		0			0
$416$	2070.68	+	6372.89i	0.244047	+	0.751098i
$417$	−7421.83	−	10215.3i	−0.871580	−	1.19963i
$418$			3860.15i			0.451689i
$419$	−13028.6	+	9465.86i	−1.51907	+	1.10367i	−0.557124	+	0.830429i	$0.688095\pi$
$419$	−13028.6	+	9465.86i	−1.51907	+	1.10367i	−0.961946	+	0.273240i	$0.911905\pi$
$420$		0			0
$421$	−7316.13	−	5315.48i	−0.846950	−	0.615346i	0.0773531	−	0.997004i	$-0.475353\pi$
$421$	−7316.13	−	5315.48i	−0.846950	−	0.615346i	−0.924304	+	0.381658i	$0.875353\pi$
$422$	−2645.19	+	3640.80i	−0.305133	+	0.419979i
$423$	−3813.84	−	1239.19i	−0.438382	−	0.142439i
$424$	−698.330			−0.0799857
$425$		0			0
$426$	−2341.46			−0.266300
$427$	635.347	+	206.437i	0.0720060	+	0.0233962i
$428$	−1132.18	+	1558.32i	−0.127865	+	0.175991i
$429$	−4778.05	−	3471.45i	−0.537730	−	0.390684i
$430$		0			0
$431$	−4692.76	+	3409.49i	−0.524460	+	0.381043i	−0.818282	−	0.574818i	$-0.805073\pi$
$431$	−4692.76	+	3409.49i	−0.524460	+	0.381043i	0.293821	+	0.955860i	$0.405073\pi$
$432$			303.838i			0.0338390i
$433$	−2478.33	−	3411.13i	−0.275060	−	0.378587i	0.649030	−	0.760763i	$-0.275175\pi$
$433$	−2478.33	−	3411.13i	−0.275060	−	0.378587i	−0.924090	+	0.382176i	$0.875175\pi$
$434$	−136.197	−	419.172i	−0.0150638	−	0.0463615i
$435$		0			0
$436$	246.693	−	759.243i	0.0270974	−	0.0833971i
$437$	−7605.32	+	2471.12i	−0.832521	+	0.270502i
$438$	−5020.41	+	1631.23i	−0.547681	+	0.177952i
$439$	1064.67	−	3276.71i	0.115749	−	0.356239i	−0.876354	−	0.481668i	$-0.840031\pi$
$439$	1064.67	−	3276.71i	0.115749	−	0.356239i	0.992102	+	0.125430i	$0.0400310\pi$
$440$		0			0
$441$	−2446.46	−	7529.44i	−0.264168	−	0.813027i
$442$	−4267.53	−	5873.76i	−0.459244	−	0.632095i
$443$			6083.40i			0.652441i	0.945294	+	0.326220i	$0.105775\pi$
$443$			6083.40i			0.652441i	−0.945294	+	0.326220i	$0.894225\pi$
$444$	−5559.46	+	4039.18i	−0.594235	+	0.431737i
$445$		0			0
$446$	5243.05	+	3809.30i	0.556649	+	0.404429i
$447$	3824.53	−	5264.02i	0.404685	−	0.557001i
$448$	228.605	+	74.2781i	0.0241084	+	0.00783328i
$449$	11313.0			1.18907			0.594534	−	0.804070i	$-0.297337\pi$
$449$	11313.0			1.18907			0.594534	+	0.804070i	$0.297337\pi$
$450$		0			0
$451$	479.620			0.0500763
$452$	−6903.03	−	2242.93i	−0.718343	−	0.233404i
$453$	403.732	−	555.690i	0.0418742	−	0.0576348i
$454$	2950.28	+	2143.50i	0.304986	+	0.221585i
$455$		0			0
$456$	12868.5	−	9349.50i	1.32154	−	0.960154i
$457$			16237.9i			1.66209i	0.556206	+	0.831045i	$0.312257\pi$
$457$			16237.9i			1.66209i	−0.556206	+	0.831045i	$0.687743\pi$
$458$	−4832.71	−	6651.66i	−0.493052	−	0.678628i
$459$	−1084.92	−	3339.05i	−0.110327	−	0.339550i
$460$		0			0
$461$	−1865.25	+	5740.66i	−0.188446	+	0.579976i	−0.999991	−	0.00431376i	$-0.998627\pi$
$461$	−1865.25	+	5740.66i	−0.188446	+	0.579976i	0.811545	+	0.584290i	$0.198627\pi$
$462$	−290.442	+	94.3703i	−0.0292480	+	0.00950325i
$463$	−978.735	+	318.010i	−0.0982412	+	0.0319205i	−0.357725	−	0.933827i	$-0.616448\pi$
$463$	−978.735	+	318.010i	−0.0982412	+	0.0319205i	0.259484	+	0.965747i	$0.416448\pi$
$464$	−929.142	+	2859.60i	−0.0929619	+	0.286107i
$465$		0			0
$466$	−1836.22	−	5651.29i	−0.182534	−	0.561783i
$467$	−4995.54	−	6875.76i	−0.495002	−	0.681311i	0.486299	−	0.873792i	$-0.338347\pi$
$467$	−4995.54	−	6875.76i	−0.495002	−	0.681311i	−0.981301	+	0.192481i	$0.938347\pi$
$468$			4604.56i			0.454799i
$469$	−322.851	+	234.565i	−0.0317865	+	0.0230943i
$470$		0			0
$471$	17857.5	+	12974.2i	1.74698	+	1.26926i
$472$	6001.78	−	8260.74i	0.585284	−	0.805575i
$473$	2922.66	+	949.630i	0.284110	+	0.0923130i
$474$	−10858.4			−1.05220
$475$		0			0
$476$	850.817			0.0819267
$477$	−725.812	−	235.831i	−0.0696701	−	0.0226372i
$478$	5979.15	−	8229.60i	0.572134	−	0.787475i
$479$	−2456.46	−	1784.72i	−0.234318	−	0.170242i	0.464430	−	0.885610i	$-0.346259\pi$
$479$	−2456.46	−	1784.72i	−0.234318	−	0.170242i	−0.698748	+	0.715368i	$0.746259\pi$
$480$		0			0
$481$	5060.97	−	3677.01i	0.479751	−	0.348559i
$482$			4822.62i			0.455736i
$483$	−371.859	−	511.820i	−0.0350314	−	0.0482166i
$484$	−1352.30	−	4161.95i	−0.127000	−	0.390867i
$485$		0			0
$486$	2447.23	−	7531.79i	0.228412	−	0.702981i
$487$	12099.9	−	3931.48i	1.12587	−	0.365816i	0.313863	−	0.949468i	$-0.398377\pi$
$487$	12099.9	−	3931.48i	1.12587	−	0.365816i	0.812004	+	0.583652i	$0.198377\pi$
$488$	11393.3	−	3701.89i	1.05686	−	0.343395i
$489$	−1630.01	+	5016.64i	−0.150739	+	0.463927i
$490$		0			0
$491$	−2121.17	−	6528.30i	−0.194964	−	0.600037i	−0.999977	−	0.00678001i	$-0.997842\pi$
$491$	−2121.17	−	6528.30i	−0.194964	−	0.600037i	0.805013	−	0.593257i	$-0.202158\pi$
$492$	−475.850	−	654.951i	−0.0436036	−	0.0600152i
$493$		−	34743.5i		−	3.17398i
$494$	−4798.62	+	3486.40i	−0.437045	+	0.317531i
$495$		0			0
$496$	2160.98	+	1570.04i	0.195627	+	0.142131i
$497$	−146.819	+	202.080i	−0.0132510	+	0.0182384i
$498$	−2270.35	−	737.681i	−0.204291	−	0.0663781i
$499$	−10000.2			−0.897134			−0.448567	−	0.893749i	$-0.648065\pi$
$499$	−10000.2			−0.897134			−0.448567	+	0.893749i	$0.648065\pi$
$500$		0			0
$501$	−1535.26			−0.136907
$502$	11638.7	+	3781.65i	1.03478	+	0.336222i
$503$	−1995.92	+	2747.15i	−0.176926	+	0.243518i	−0.888265	−	0.459331i	$-0.848089\pi$
$503$	−1995.92	+	2747.15i	−0.176926	+	0.243518i	0.711339	+	0.702849i	$0.248089\pi$
$504$	470.238	+	341.648i	0.0415596	+	0.0301948i
$505$		0			0
$506$	2227.35	−	1618.27i	0.195688	−	0.142175i
$507$			6487.43i			0.568278i
$508$	6612.16	+	9100.86i	0.577494	+	0.794853i
$509$	−2003.56	−	6166.33i	−0.174472	−	0.536970i	0.825137	−	0.564933i	$-0.191098\pi$
$509$	−2003.56	−	6166.33i	−0.174472	−	0.536970i	−0.999609	+	0.0279631i	$0.991098\pi$
$510$		0			0
$511$	−174.018	+	535.572i	−0.0150648	+	0.0463646i
$512$	−3806.98	+	1236.96i	−0.328606	+	0.106770i
$513$	−2727.87	+	886.338i	−0.234773	+	0.0762822i
$514$	1153.06	−	3548.76i	0.0989482	−	0.304531i
$515$		0			0
$516$	−1602.91	−	4933.24i	−0.136752	−	0.420879i
$517$	−2369.10	−	3260.79i	−0.201534	−	0.277388i
$518$		−	323.471i		−	0.0274373i
$519$	101.641	−	73.8462i	0.00859639	−	0.00624565i
$520$		0			0
$521$	5997.28	+	4357.28i	0.504310	+	0.366403i	0.810661	−	0.585516i	$-0.199108\pi$
$521$	5997.28	+	4357.28i	0.504310	+	0.366403i	−0.306351	+	0.951919i	$0.599108\pi$
$522$	5714.85	−	7865.82i	0.479180	−	0.659535i
$523$	−8183.77	−	2659.07i	−0.684228	−	0.222319i	−0.0537826	−	0.998553i	$-0.517128\pi$
$523$	−8183.77	−	2659.07i	−0.684228	−	0.222319i	−0.630446	+	0.776233i	$0.717128\pi$
$524$	−3747.96			−0.312463
$525$		0			0
$526$	4842.58			0.401419
$527$	−29354.4	−	9537.83i	−2.42637	−	0.788376i
$528$	1087.87	−	1497.33i	0.0896661	−	0.123415i
$529$	−5229.11	−	3799.17i	−0.429778	−	0.312252i
$530$		0			0
$531$	9027.67	−	6558.98i	0.737792	−	0.536037i
$532$		−	695.082i		−	0.0566459i
$533$	433.182	+	596.224i	0.0352030	+	0.0484528i
$534$	1330.30	+	4094.25i	0.107805	+	0.331789i
$535$		0			0
$536$	−2211.38	+	6805.94i	−0.178204	+	0.548455i
$537$	18377.0	−	5971.06i	1.47677	−	0.479833i
$538$	−2195.47	+	713.350i	−0.175935	+	0.0571649i
$539$	2458.94	−	7567.83i	0.196501	−	0.604767i
$540$		0			0
$541$	−1851.10	−	5697.10i	−0.147107	−	0.452749i	0.850169	−	0.526510i	$-0.176500\pi$
$541$	−1851.10	−	5697.10i	−0.147107	−	0.452749i	−0.997276	+	0.0737611i	$0.976500\pi$
$542$	279.243	+	384.346i	0.0221301	+	0.0304595i
$543$			10964.1i			0.866512i
$544$	19630.4	−	14262.3i	1.54715	−	1.12407i
$545$		0			0
$546$	−379.634	−	275.820i	−0.0297561	−	0.0216191i
$547$	−12795.7	+	17611.8i	−1.00019	+	1.37665i	−0.0749850	+	0.997185i	$0.523891\pi$
$547$	−12795.7	+	17611.8i	−1.00019	+	1.37665i	−0.925207	+	0.379462i	$0.876109\pi$
$548$	−525.076	−	170.608i	−0.0409309	−	0.0132993i
$549$	13091.8			1.01775
$550$		0			0
$551$	−28384.0			−2.19456
$552$	−10789.5	−	3505.74i	−0.831945	−	0.270315i
$553$	−680.867	+	937.134i	−0.0523570	+	0.0720632i
$554$	−6137.59	−	4459.22i	−0.470688	−	0.341975i
$555$		0			0
$556$	−8004.86	+	5815.87i	−0.610579	+	0.443611i
$557$			10736.7i			0.816749i	0.912814	+	0.408375i	$0.133904\pi$
$557$			10736.7i			0.816749i	−0.912814	+	0.408375i	$0.866096\pi$
$558$	−5076.89	−	6987.74i	−0.385165	−	0.530134i
$559$	1459.18	+	4490.89i	0.110406	+	0.339794i
$560$		0			0
$561$	−6608.71	+	20339.5i	−0.497362	+	1.53072i
$562$	2214.92	−	719.670i	0.166247	−	0.0540168i
$563$	5145.09	−	1671.74i	0.385151	−	0.125143i	−0.110040	−	0.993927i	$-0.535098\pi$
$563$	5145.09	−	1671.74i	0.385151	−	0.125143i	0.495191	+	0.868784i	$0.335098\pi$
$564$	−2102.33	+	6470.31i	−0.156958	+	0.483066i
$565$		0			0
$566$	−1295.56	−	3987.34i	−0.0962131	−	0.296114i
$567$	−568.351	−	782.268i	−0.0420961	−	0.0579404i
$568$			4479.21i			0.330887i
$569$	3521.64	−	2558.62i	0.259464	−	0.188511i	−0.450447	−	0.892803i	$-0.648735\pi$
$569$	3521.64	−	2558.62i	0.259464	−	0.188511i	0.709911	+	0.704292i	$0.248735\pi$
$570$		0			0
$571$	−14846.9	−	10786.9i	−1.08813	−	0.790575i	−0.109050	−	0.994036i	$-0.534781\pi$
$571$	−14846.9	−	10786.9i	−1.08813	−	0.790575i	−0.979083	+	0.203461i	$0.934781\pi$
$572$	−2720.29	+	3744.16i	−0.198848	+	0.273691i
$573$	21678.1	+	7043.65i	1.58048	+	0.513530i
$574$	38.1076			0.00277105
$575$		0			0
$576$	4710.56			0.340752
$577$	−817.930	−	265.761i	−0.0590136	−	0.0191747i	0.279361	−	0.960186i	$-0.409877\pi$
$577$	−817.930	−	265.761i	−0.0590136	−	0.0191747i	−0.338375	+	0.941011i	$0.609877\pi$
$578$	−10933.8	+	15049.1i	−0.786827	+	1.08297i
$579$	13678.3	+	9937.84i	0.981778	+	0.713303i
$580$		0			0
$581$	−206.026	+	149.687i	−0.0147116	+	0.0106886i
$582$			6130.13i			0.436602i
$583$	−450.863	−	620.560i	−0.0320289	−	0.0440840i
$584$	3120.55	+	9604.06i	0.221112	+	0.680512i
$585$		0			0
$586$	−1900.30	+	5848.52i	−0.133960	+	0.412287i
$587$	19306.5	−	6273.05i	1.35752	−	0.441084i	0.462304	−	0.886721i	$-0.347023\pi$
$587$	19306.5	−	6273.05i	1.35752	−	0.441084i	0.895214	+	0.445637i	$0.147023\pi$
$588$	−12773.9	+	4150.51i	−0.895899	+	0.291095i
$589$	−7792.01	+	23981.4i	−0.545101	+	1.67765i
$590$		0			0
$591$	2707.04	+	8331.42i	0.188414	+	0.579880i
$592$	1152.29	+	1585.99i	0.0799980	+	0.110108i
$593$			20628.0i			1.42848i	0.699900	+	0.714241i	$0.253228\pi$
$593$			20628.0i			1.42848i	−0.699900	+	0.714241i	$0.746772\pi$
$594$	798.905	−	580.439i	0.0551843	−	0.0400937i
$595$		0			0
$596$	−4124.97	−	2996.97i	−0.283499	−	0.205974i
$597$	−10746.0	+	14790.7i	−0.736694	+	1.01397i
$598$	4023.39	+	1307.28i	0.275132	+	0.0893957i
$599$	2506.63			0.170982			0.0854909	−	0.996339i	$-0.472754\pi$
$599$	2506.63			0.170982			0.0854909	+	0.996339i	$0.472754\pi$
$600$		0			0
$601$	−1595.54			−0.108292			−0.0541459	−	0.998533i	$-0.517244\pi$
$601$	−1595.54			−0.108292			−0.0541459	+	0.998533i	$0.517244\pi$
$602$	232.216	+	75.4517i	0.0157217	+	0.00510827i
$603$	−4596.82	+	6326.98i	−0.310443	+	0.427288i
$604$	−435.448	−	316.371i	−0.0293346	−	0.0213129i
$605$		0			0
$606$	−5721.51	+	4156.92i	−0.383532	+	0.278652i
$607$		−	26119.6i		−	1.74656i	−0.487222	−	0.873278i	$-0.661990\pi$
$607$		−	26119.6i		−	1.74656i	0.487222	−	0.873278i	$-0.338010\pi$
$608$	−11651.7	−	16037.3i	−0.777205	−	1.06973i
$609$	−693.914	−	2135.65i	−0.0461721	−	0.142103i
$610$		0			0
$611$	1913.82	−	5890.15i	0.126719	−	0.390000i
$612$	15857.6	−	5152.43i	1.04739	−	0.340318i
$613$	6416.22	−	2084.75i	0.422754	−	0.137361i	−0.0899108	−	0.995950i	$-0.528658\pi$
$613$	6416.22	−	2084.75i	0.422754	−	0.137361i	0.512665	+	0.858589i	$0.328658\pi$
$614$	3996.30	−	12299.4i	0.262667	−	0.808406i
$615$		0			0
$616$	180.531	+	555.616i	0.0118081	+	0.0363416i
$617$	3731.74	+	5136.30i	0.243491	+	0.335137i	0.913219	−	0.407470i	$-0.133589\pi$
$617$	3731.74	+	5136.30i	0.243491	+	0.335137i	−0.669727	+	0.742607i	$0.733589\pi$
$618$			6202.76i			0.403741i
$619$	4852.37	−	3525.45i	0.315078	−	0.228918i	−0.418994	−	0.907989i	$-0.637617\pi$
$619$	4852.37	−	3525.45i	0.315078	−	0.228918i	0.734072	+	0.679071i	$0.237617\pi$
$620$		0			0
$621$	1655.02	+	1202.44i	0.106946	+	0.0777009i
$622$	−4417.18	+	6079.73i	−0.284747	+	0.391921i
$623$	436.770	+	141.915i	0.0280880	+	0.00912633i
$624$	2843.90			0.182448
$625$		0			0
$626$	−16136.2			−1.03024
$627$	16616.6	+	5399.05i	1.05838	+	0.343887i
$628$	10166.8	−	13993.4i	0.646019	−	0.889169i
$629$	−18326.3	−	13314.8i	−1.16171	−	0.844034i
$630$		0			0
$631$	14269.4	−	10367.4i	0.900250	−	0.654070i	−0.0382803	−	0.999267i	$-0.512188\pi$
$631$	14269.4	−	10367.4i	0.900250	−	0.654070i	0.938530	+	0.345197i	$0.112188\pi$
$632$			20772.1i			1.30739i
$633$	11972.6	+	16478.9i	0.751766	+	1.03472i
$634$	1587.09	+	4884.55i	0.0994184	+	0.305978i
$635$		0			0
$636$	−400.094	+	1231.36i	−0.0249446	+	0.0767716i
$637$	11628.6	−	3778.35i	0.723297	−	0.235013i
$638$	9293.96	−	3019.79i	0.576726	−	0.187390i
$639$	−1512.66	+	4655.48i	−0.0936461	+	0.288213i
$640$		0			0
$641$	8585.30	+	26422.8i	0.529015	+	1.62814i	0.756236	+	0.654299i	$0.227036\pi$
$641$	8585.30	+	26422.8i	0.529015	+	1.62814i	−0.227221	+	0.973843i	$0.572964\pi$
$642$	−2261.15	−	3112.21i	−0.139004	−	0.191323i
$643$		−	7215.33i		−	0.442527i	−0.975214	−	0.221263i	$-0.928982\pi$
$643$		−	7215.33i		−	0.442527i	0.975214	−	0.221263i	$-0.0710181\pi$
$644$	−401.071	+	291.395i	−0.0245410	+	0.0178301i
$645$		0			0
$646$	17376.3	+	12624.6i	1.05830	+	0.768900i
$647$	10027.9	−	13802.3i	0.609334	−	0.838676i	−0.387189	−	0.922001i	$-0.626554\pi$
$647$	10027.9	−	13802.3i	0.609334	−	0.838676i	0.996522	+	0.0833244i	$0.0265538\pi$
$648$	−16490.8	−	5358.18i	−0.999721	−	0.324829i
$649$	11215.7			0.678359
$650$		0			0
$651$	−1994.88			−0.120100
$652$	3931.13	+	1277.30i	0.236127	+	0.0767223i
$653$	−5562.33	+	7655.89i	−0.333340	+	0.458803i	−0.942481	−	0.334259i	$-0.891514\pi$
$653$	−5562.33	+	7655.89i	−0.333340	+	0.458803i	0.609142	+	0.793061i	$0.291514\pi$
$654$	1289.87	+	937.144i	0.0771221	+	0.0560325i
$655$		0			0
$656$	−186.843	+	135.749i	−0.0111204	+	0.00807946i
$657$			11035.8i			0.655326i
$658$	−188.234	−	259.082i	−0.0111522	−	0.0153497i
$659$	4965.73	+	15282.9i	0.293531	+	0.903397i	0.983711	+	0.179759i	$0.0575317\pi$
$659$	4965.73	+	15282.9i	0.293531	+	0.903397i	−0.690179	+	0.723638i	$0.742468\pi$
$660$		0			0
$661$	4844.24	−	14909.0i	0.285051	−	0.877298i	−0.701332	−	0.712835i	$-0.747411\pi$
$661$	4844.24	−	14909.0i	0.285051	−	0.877298i	0.986383	−	0.164463i	$-0.0525891\pi$
$662$	534.299	−	173.604i	0.0313688	−	0.0101923i
$663$	−31253.3	+	10154.8i	−1.83073	+	0.594841i
$664$	−1411.19	+	4343.19i	−0.0824769	+	0.253838i
$665$		0			0
$666$	−1958.90	−	6028.87i	−0.113973	−	0.350772i
$667$	11899.3	+	16377.9i	0.690767	+	0.950759i
$668$			1203.06i			0.0696821i
$669$	23730.9	−	17241.5i	1.37144	−	0.996406i
$670$		0			0
$671$	10645.5	+	7734.38i	0.612464	+	0.444981i
$672$	921.807	−	1268.76i	0.0529159	−	0.0728325i
$673$	−8548.51	−	2777.58i	−0.489630	−	0.159090i	0.0537886	−	0.998552i	$-0.482870\pi$
$673$	−8548.51	−	2777.58i	−0.489630	−	0.159090i	−0.543418	+	0.839462i	$0.682870\pi$
$674$	2050.96			0.117211
$675$		0			0
$676$	5083.66			0.289239
$677$	5438.99	+	1767.23i	0.308770	+	0.100325i	0.459303	−	0.888279i	$-0.348099\pi$
$677$	5438.99	+	1767.23i	0.308770	+	0.100325i	−0.150533	+	0.988605i	$0.548099\pi$
$678$	8520.50	−	11727.5i	0.482637	−	0.664293i
$679$	529.061	+	384.386i	0.0299021	+	0.0217251i
$680$		0			0
$681$	13353.5	−	9701.86i	0.751404	−	0.545927i
$682$		−	8681.36i		−	0.487429i
$683$	−4557.14	−	6272.37i	−0.255306	−	0.351399i	0.662054	−	0.749456i	$-0.269685\pi$
$683$	−4557.14	−	6272.37i	−0.255306	−	0.351399i	−0.917361	+	0.398057i	$0.869685\pi$
$684$	−4209.32	−	12955.0i	−0.235303	−	0.724189i
$685$		0			0
$686$	391.544	−	1205.05i	0.0217918	−	0.0670684i
$687$	−35392.3	+	11499.7i	−1.96551	+	0.638631i
$688$	−1407.34	+	457.274i	−0.0779862	+	0.0253392i
$689$	364.219	−	1120.95i	0.0201388	−	0.0619809i
$690$		0			0
$691$	−3235.80	−	9958.77i	−0.178141	−	0.548262i	0.821622	−	0.570033i	$-0.193070\pi$
$691$	−3235.80	−	9958.77i	−0.178141	−	0.548262i	−0.999763	+	0.0217707i	$0.993070\pi$
$692$	−57.8672	−	79.6473i	−0.00317887	−	0.00437534i
$693$			638.448i			0.0349966i
$694$	4907.89	−	3565.79i	0.268445	−	0.195037i
$695$		0			0
$696$	−32577.5	−	23668.9i	−1.77421	−	1.28904i
$697$	1568.60	−	2158.99i	0.0852439	−	0.117328i
$698$	10601.1	+	3444.49i	0.574865	+	0.186785i
$699$	−26895.0			−1.45531
$700$		0			0
$701$	8823.63			0.475412			0.237706	−	0.971337i	$-0.423605\pi$
$701$	8823.63			0.475412			0.237706	+	0.971337i	$0.423605\pi$
$702$	1443.11	+	468.894i	0.0775877	+	0.0252098i
$703$	−10877.7	+	14971.8i	−0.583584	+	0.803234i
$704$	3830.35	+	2782.91i	0.205059	+	0.148984i
$705$		0			0
$706$	−13836.1	+	10052.5i	−0.737575	+	0.535879i
$707$			754.452i			0.0401331i
$708$	−11127.5	−	15315.7i	−0.590675	−	0.812995i
$709$	−7039.37	−	21665.0i	−0.372876	−	1.14759i	−0.944900	−	0.327358i	$-0.893842\pi$
$709$	−7039.37	−	21665.0i	−0.372876	−	1.14759i	0.572024	−	0.820237i	$-0.306158\pi$
$710$		0			0
$711$	−7014.88	+	21589.6i	−0.370012	+	1.13878i
$712$	7832.30	−	2544.87i	0.412258	−	0.133951i
$713$	17104.1	−	5557.47i	0.898394	−	0.291906i
$714$	−525.087	+	1616.05i	−0.0275223	+	0.0847048i
$715$		0			0
$716$	−4679.02	−	14400.6i	−0.244222	−	0.751639i
$717$	−27062.7	−	37248.5i	−1.40959	−	1.94013i
$718$		−	3056.51i		−	0.158869i
$719$	−20157.2	+	14645.1i	−1.04553	+	0.759624i	−0.971358	−	0.237621i	$-0.923632\pi$
$719$	−20157.2	+	14645.1i	−1.04553	+	0.759624i	−0.0741754	+	0.997245i	$0.523632\pi$
$720$		0			0
$721$	535.330	+	388.940i	0.0276515	+	0.0200900i
$722$	4004.29	−	5511.43i	0.206405	−	0.284092i
$723$	20759.7	+	6745.23i	1.06786	+	0.346968i
$724$	8591.68			0.441032
$725$		0			0
$726$	8739.84			0.446785
$727$	−33574.1	−	10908.9i	−1.71278	−	0.556518i	−0.721992	−	0.691902i	$-0.756773\pi$
$727$	−33574.1	−	10908.9i	−1.71278	−	0.556518i	−0.990793	+	0.135384i	$0.956773\pi$
$728$	−527.645	+	726.241i	−0.0268624	+	0.0369729i
$729$	−11139.0	−	8092.96i	−0.565920	−	0.411165i
$730$		0			0
$731$	13833.3	−	10050.5i	0.699922	−	0.508523i
$732$		−	22210.6i		−	1.12149i
$733$	8613.37	+	11855.3i	0.434027	+	0.597388i	0.968872	−	0.247563i	$-0.0796297\pi$
$733$	8613.37	+	11855.3i	0.434027	+	0.597388i	−0.534844	+	0.844951i	$0.679630\pi$
$734$	5080.76	+	15637.0i	0.255496	+	0.786336i
$735$		0			0
$736$	−4369.00	+	13446.4i	−0.218809	+	0.673425i
$737$	−7475.73	+	2429.01i	−0.373639	+	0.121403i
$738$	710.251	−	230.775i	0.0354264	−	0.0115108i
$739$	−2051.60	+	6314.18i	−0.102124	+	0.314304i	−0.989045	−	0.147617i	$-0.952840\pi$
$739$	−2051.60	+	6314.18i	−0.102124	+	0.314304i	0.886921	+	0.461921i	$0.152840\pi$
$740$		0			0
$741$	8296.05	+	25532.6i	0.411286	+	1.26581i
$742$	−35.8228	−	49.3058i	−0.00177237	−	0.00243945i
$743$		−	15188.5i		−	0.749950i	−0.927035	−	0.374975i	$-0.877651\pi$
$743$		−	15188.5i		−	0.749950i	0.927035	−	0.374975i	$-0.122349\pi$
$744$	−28940.8	+	21026.7i	−1.42611	+	1.03613i
$745$		0			0
$746$	1143.59	+	830.867i	0.0561258	+	0.0407778i
$747$	−2933.44	+	4037.54i	−0.143680	+	0.197759i
$748$	15938.4	+	5178.70i	0.779098	+	0.253144i
$749$	−410.384			−0.0200201
$750$		0			0
$751$	−9087.13			−0.441537			−0.220768	−	0.975326i	$-0.570856\pi$
$751$	−9087.13			−0.441537			−0.220768	+	0.975326i	$0.570856\pi$
$752$	1845.84	+	599.749i	0.0895090	+	0.0290832i
$753$	32557.3	−	44811.3i	1.57564	−	2.16868i
$754$	12148.1	+	8826.08i	0.586745	+	0.426295i
$755$		0			0
$756$	−143.856	+	104.517i	−0.00692062	+	0.00502812i
$757$			13103.6i			0.629140i	0.949234	+	0.314570i	$0.101860\pi$
$757$			13103.6i			0.629140i	−0.949234	+	0.314570i	$0.898140\pi$
$758$	8117.96	+	11173.4i	0.388994	+	0.535405i
$759$	−3850.74	−	11851.4i	−0.184154	−	0.566769i
$760$		0			0
$761$	9148.33	−	28155.7i	0.435777	−	1.34119i	−0.456510	−	0.889718i	$-0.650901\pi$
$761$	9148.33	−	28155.7i	0.435777	−	1.34119i	0.892288	−	0.451467i	$-0.149099\pi$
$762$	−21367.0	+	6942.57i	−1.01581	+	0.330056i
$763$	161.760	−	52.5592i	0.00767513	−	0.00249380i
$764$	5519.52	−	16987.3i	0.261373	−	0.804425i
$765$		0			0
$766$	−2951.55	−	9083.94i	−0.139222	−	0.428480i
$767$	10129.8	+	13942.4i	0.476877	+	0.656365i
$768$		−	24594.6i		−	1.15557i
$769$	−29802.3	+	21652.6i	−1.39753	+	1.01536i	−0.402534	+	0.915405i	$0.631870\pi$
$769$	−29802.3	+	21652.6i	−1.39753	+	1.01536i	−0.994992	+	0.0999568i	$0.968130\pi$
$770$		0			0
$771$	−13663.4	−	9927.04i	−0.638230	−	0.463701i
$772$	7787.46	−	10718.5i	0.363053	−	0.499699i
$773$	−28237.4	−	9174.90i	−1.31388	−	0.426906i	−0.433492	−	0.901158i	$-0.642719\pi$
$773$	−28237.4	−	9174.90i	−1.31388	−	0.426906i	−0.880389	+	0.474252i	$0.842719\pi$
$774$	4784.98			0.222213
$775$		0			0
$776$	11727.0			0.542491
$777$	−1392.43	−	452.427i	−0.0642897	−	0.0208890i
$778$	6491.85	−	8935.27i	0.299157	−	0.411754i
$779$	−1763.81	−	1281.48i	−0.0811232	−	0.0589395i
$780$		0			0
$781$	−3980.38	+	2891.92i	−0.182368	+	0.132498i
$782$		−	15318.9i		−	0.700515i
$783$	4268.02	+	5874.42i	0.194798	+	0.268116i
$784$	1184.05	+	3644.13i	0.0539381	+	0.166004i
$785$		0			0
$786$	2313.08	−	7118.93i	0.104968	−	0.323058i
$787$	−28425.6	+	9236.05i	−1.28750	+	0.418335i	−0.871216	−	0.490899i	$-0.836668\pi$
$787$	−28425.6	+	9236.05i	−1.28750	+	0.418335i	−0.416286	+	0.909234i	$0.636668\pi$
$788$	6528.64	−	2121.28i	0.295144	−	0.0958980i
$789$	6773.14	−	20845.6i	0.305615	−	0.940586i
$790$		0			0
$791$	−477.867	−	1470.72i	−0.0214804	−	0.0661099i
$792$	6729.47	+	9262.32i	0.301921	+	0.415558i
$793$			20219.1i			0.905423i
$794$	5382.47	−	3910.59i	0.240575	−	0.174788i
$795$		0			0
$796$	11590.2	+	8420.78i	0.516086	+	0.374958i
$797$	6471.90	−	8907.81i	0.287637	−	0.395898i	−0.640608	−	0.767868i	$-0.721318\pi$
$797$	6471.90	−	8907.81i	0.287637	−	0.395898i	0.928245	+	0.371970i	$0.121318\pi$
$798$	1320.25	+	428.975i	0.0585668	+	0.0190295i
$799$	−22426.5			−0.992982
$800$		0			0
$801$	8999.95			0.397001
$802$	10918.1	+	3547.50i	0.480712	+	0.156193i
$803$	−6519.77	+	8973.70i	−0.286523	+	0.394365i
$804$	10733.9	+	7798.65i	0.470841	+	0.342086i
$805$		0			0
$806$	10792.0	−	7840.81i	0.471626	−	0.342656i
$807$			10448.4i			0.455765i
$808$	7952.20	+	10945.3i	0.346234	+	0.476551i
$809$	−2620.85	−	8066.15i	−0.113899	−	0.350545i	0.877817	−	0.478996i	$-0.158999\pi$
$809$	−2620.85	−	8066.15i	−0.113899	−	0.350545i	−0.991716	+	0.128452i	$0.958999\pi$
$810$		0			0
$811$	10024.8	−	30853.2i	0.434055	−	1.33588i	−0.459997	−	0.887921i	$-0.652149\pi$
$811$	10024.8	−	30853.2i	0.434055	−	1.33588i	0.894052	−	0.447964i	$-0.147851\pi$
$812$	−1673.53	+	543.762i	−0.0723268	+	0.0235004i
$813$	2045.04	−	664.473i	0.0882197	−	0.0286643i
$814$	1968.89	−	6059.61i	0.0847781	−	0.260920i
$815$		0			0
$816$	−3182.28	−	9794.06i	−0.136522	−	0.420172i
$817$	−8210.83	−	11301.2i	−0.351604	−	0.483942i
$818$			14435.0i			0.617003i
$819$	−793.665	+	576.632i	−0.0338619	+	0.0246021i
$820$		0			0
$821$	20550.8	+	14931.0i	0.873601	+	0.634709i	0.931551	−	0.363611i	$-0.118456\pi$
$821$	20550.8	+	14931.0i	0.873601	+	0.634709i	−0.0579495	+	0.998320i	$0.518456\pi$
$822$	648.108	−	892.045i	0.0275005	−	0.0378511i
$823$	−40857.0	−	13275.2i	−1.73048	−	0.562267i	−0.736962	−	0.675934i	$-0.763740\pi$
$823$	−40857.0	−	13275.2i	−1.73048	−	0.562267i	−0.993519	+	0.113667i	$0.963740\pi$
$824$	11865.9			0.501660
$825$		0			0
$826$	891.130			0.0375380
$827$	29110.9	+	9458.71i	1.22405	+	0.397717i	0.848554	−	0.529109i	$-0.177474\pi$
$827$	29110.9	+	9458.71i	1.22405	+	0.397717i	0.375492	+	0.926826i	$0.377474\pi$
$828$	−5710.53	+	7859.87i	−0.239679	+	0.329890i
$829$	17898.0	+	13003.6i	0.749846	+	0.544795i	0.895779	−	0.444499i	$-0.146618\pi$
$829$	17898.0	+	13003.6i	0.749846	+	0.544795i	−0.145933	+	0.989294i	$0.546618\pi$
$830$		0			0
$831$	−27779.8	+	20183.2i	−1.15965	+	0.842536i
$832$			7275.04i			0.303145i
$833$	−26024.4	−	35819.4i	−1.08246	−	1.48988i
$834$	−6106.49	−	18793.8i	−0.253538	−	0.780309i
$835$		0			0
$836$	4230.78	−	13021.0i	0.175030	−	0.538686i
$837$	6134.90	−	1993.35i	0.253349	−	0.0823181i
$838$	−23969.8	+	7788.26i	−0.988094	+	0.321051i
$839$	10771.3	−	33150.6i	0.443226	−	1.36411i	−0.441192	−	0.897413i	$-0.645444\pi$
$839$	10771.3	−	33150.6i	0.443226	−	1.36411i	0.884418	−	0.466696i	$-0.154556\pi$
$840$		0			0
$841$	14668.2	+	45144.1i	0.601427	+	1.85100i
$842$	−8318.77	−	11449.8i	−0.340479	−	0.468630i
$843$		−	10541.0i		−	0.430666i
$844$	12913.1	−	9381.93i	0.526644	−	0.382629i
$845$		0			0
$846$	−5077.28	−	3688.86i	−0.206336	−	0.149912i
$847$	548.026	−	754.293i	0.0222319	−	0.0305995i
$848$	351.281	+	114.138i	0.0142253	+	0.00462207i
$849$	−18976.1			−0.767089
$850$		0			0
$851$	13199.1			0.531681
$852$	7898.18	+	2566.27i	0.317591	+	0.103191i
$853$	−14739.6	+	20287.3i	−0.591646	+	0.814331i	−0.994912	−	0.100752i	$-0.967875\pi$
$853$	−14739.6	+	20287.3i	−0.591646	+	0.814331i	0.403265	+	0.915083i	$0.367875\pi$
$854$	845.822	+	614.526i	0.0338916	+	0.0246237i
$855$		0			0
$856$	−5953.67	+	4325.59i	−0.237725	+	0.172717i
$857$		−	45770.6i		−	1.82438i	−0.409767	−	0.912190i	$-0.634390\pi$
$857$		−	45770.6i		−	1.82438i	0.409767	−	0.912190i	$-0.365610\pi$
$858$	−5432.86	−	7477.69i	−0.216171	−	0.297534i
$859$	2248.85	+	6921.23i	0.0893243	+	0.274912i	0.985733	−	0.168316i	$-0.0538330\pi$
$859$	2248.85	+	6921.23i	0.0893243	+	0.274912i	−0.896409	+	0.443228i	$0.853833\pi$
$860$		0			0
$861$	53.2997	−	164.040i	0.00210970	−	0.00649298i
$862$	−8633.64	+	2805.24i	−0.341140	+	0.110843i
$863$	44371.3	−	14417.1i	1.75019	−	0.568672i	0.754081	−	0.656782i	$-0.228083\pi$
$863$	44371.3	−	14417.1i	1.75019	−	0.568672i	0.996111	+	0.0881101i	$0.0280827\pi$
$864$	−1567.07	+	4822.94i	−0.0617046	+	0.189907i
$865$		0			0
$866$	−2039.10	−	6275.72i	−0.0800133	−	0.246256i
$867$	49488.2	+	68114.7i	1.93853	+	2.66816i
$868$			1563.22i			0.0611280i
$869$	−18458.8	+	13411.1i	−0.720567	+	0.523522i
$870$		0			0
$871$	−9771.46	−	7099.38i	−0.380130	−	0.276181i
$872$	1792.76	−	2467.52i	0.0696221	−	0.0958266i
$873$	12188.5	+	3960.27i	0.472528	+	0.153534i
$874$	−12514.9			−0.484352
$875$		0			0
$876$	18722.7			0.722123
$877$	33210.6	+	10790.8i	1.27873	+	0.415484i	0.868132	−	0.496334i	$-0.165321\pi$
$877$	33210.6	+	10790.8i	1.27873	+	0.415484i	0.410595	+	0.911818i	$0.365321\pi$
$878$	3169.33	−	4362.20i	0.121822	−	0.167673i
$879$	22517.9	+	16360.2i	0.864062	+	0.627778i
$880$		0			0
$881$	−27671.6	+	20104.6i	−1.05821	+	0.768833i	−0.973756	−	0.227594i	$-0.926914\pi$
$881$	−27671.6	+	20104.6i	−1.05821	+	0.768833i	−0.0844522	+	0.996428i	$0.526914\pi$
$882$		−	12390.1i		−	0.473010i
$883$	27589.2	+	37973.3i	1.05147	+	1.44723i	0.887525	+	0.460760i	$0.152423\pi$
$883$	27589.2	+	37973.3i	1.05147	+	1.44723i	0.163948	+	0.986469i	$0.447577\pi$
$884$	7957.47	+	24490.6i	0.302759	+	0.931796i
$885$		0			0
$886$	−2942.02	+	9054.61i	−0.111557	+	0.343336i
$887$	−23565.0	+	7656.74i	−0.892036	+	0.289840i	−0.718946	−	0.695066i	$-0.755375\pi$
$887$	−23565.0	+	7656.74i	−0.892036	+	0.289840i	−0.173090	+	0.984906i	$0.555375\pi$
$888$	−24969.5	+	8113.08i	−0.943606	+	0.306596i
$889$	−740.625	+	2279.41i	−0.0279413	+	0.0859943i
$890$		0			0
$891$	−5885.49	−	18113.7i	−0.221292	−	0.681068i
$892$	−13510.7	−	18595.9i	−0.507145	−	0.698025i
$893$			18321.5i			0.686569i
$894$	8238.23	−	5985.43i	0.308197	−	0.223918i
$895$		0			0
$896$	−1128.58	−	819.963i	−0.0420795	−	0.0305726i
$897$	11254.7	−	15490.8i	0.418935	−	0.576615i
$898$	16838.3	+	5471.11i	0.625727	+	0.203311i
$899$	63834.9			2.36820
$900$		0			0
$901$	−4267.98			−0.157810
$902$	713.872	+	231.951i	0.0263518	+	0.00856223i
$903$	649.585	−	894.077i	0.0239389	−	0.0329491i
$904$	−22434.7	−	16299.7i	−0.825405	−	0.599692i
$905$		0			0
$906$	869.659	−	631.845i	0.0318902	−	0.0231696i
$907$		−	5545.03i		−	0.202999i	−0.994836	−	0.101499i	$-0.967636\pi$
$907$		−	5545.03i		−	0.202999i	0.994836	−	0.101499i	$-0.0323640\pi$
$908$	−7602.54	−	10464.0i	−0.277863	−	0.382445i
$909$	4568.86	+	14061.5i	0.166710	+	0.513081i
$910$		0			0
$911$	−11280.5	+	34717.8i	−0.410252	+	1.26263i	0.506177	+	0.862429i	$0.331058\pi$
$911$	−11280.5	+	34717.8i	−0.410252	+	1.26263i	−0.916429	+	0.400196i	$0.868942\pi$
$912$	−8001.35	+	2599.79i	−0.290516	+	0.0943945i
$913$	−4770.61	+	1550.06i	−0.172929	+	0.0561880i
$914$	−7852.86	+	24168.6i	−0.284190	+	0.874646i
$915$		0			0
$916$	9011.33	+	27734.0i	0.325047	+	1.00039i
$917$	−469.359	−	646.018i	−0.0169025	−	0.0232643i
$918$		−	5494.57i		−	0.197547i
$919$	11538.5	−	8383.20i	0.414167	−	0.300910i	−0.361120	−	0.932519i	$-0.617605\pi$
$919$	11538.5	−	8383.20i	0.414167	−	0.300910i	0.775287	+	0.631610i	$0.217605\pi$
$920$		0			0
$921$	−47354.8	−	34405.3i	−1.69424	−	1.23094i
$922$	−5552.53	+	7642.40i	−0.198333	+	0.272982i
$923$	−7189.98	−	2336.17i	−0.256404	−	0.0833108i
$924$	1083.15			0.0385638
$925$		0			0
$926$	−1610.56			−0.0571557
$927$	12332.9	+	4007.19i	0.436963	+	0.141978i
$928$	−29497.3	+	40599.5i	−1.04342	+	1.43615i
$929$	−2382.32	−	1730.86i	−0.0841350	−	0.0611276i	0.544923	−	0.838486i	$-0.316559\pi$
$929$	−2382.32	−	1730.86i	−0.0841350	−	0.0611276i	−0.629058	+	0.777359i	$0.716559\pi$
$930$		0			0
$931$	−29263.0	+	21260.8i	−1.03014	+	0.748438i
$932$			21075.4i			0.740716i
$933$	19992.9	+	27517.9i	0.701542	+	0.965589i
$934$	−4110.20	−	12649.9i	−0.143993	−	0.443166i
$935$		0			0
$936$	−5436.25	+	16731.0i	−0.189839	+	0.584264i
$937$	−27716.1	+	9005.50i	−0.966323	+	0.313978i	−0.749331	−	0.662196i	$-0.769625\pi$
$937$	−27716.1	+	9005.50i	−0.966323	+	0.313978i	−0.216993	+	0.976173i	$0.569625\pi$
$938$	−593.975	+	192.994i	−0.0206759	+	0.00671800i
$939$	−22569.1	+	69460.6i	−0.784361	+	2.41402i
$940$		0			0
$941$	−10416.1	−	32057.5i	−0.360845	−	1.11057i	−0.952542	−	0.304406i	$-0.901542\pi$
$941$	−10416.1	−	32057.5i	−0.360845	−	1.11057i	0.591697	−	0.806160i	$-0.298458\pi$
$942$	20304.8	+	27947.1i	0.702299	+	0.966631i
$943$			1554.97i			0.0536975i
$944$	−4369.24	+	3174.44i	−0.150643	+	0.109448i
$945$		0			0
$946$	3890.87	+	2826.88i	0.133724	+	0.0971563i
$947$	−14117.7	+	19431.3i	−0.484438	+	0.666772i	−0.979350	−	0.202171i	$-0.935200\pi$
$947$	−14117.7	+	19431.3i	−0.484438	+	0.666772i	0.494912	+	0.868943i	$0.335200\pi$
$948$	36627.4	+	11901.0i	1.25486	+	0.407727i
$949$	−17043.9			−0.583000
$950$		0			0
$951$	23246.0			0.792644
$952$	3091.51	+	1004.49i	0.105248	+	0.0341973i
$953$	−21529.5	+	29632.9i	−0.731805	+	1.00724i	0.267244	+	0.963629i	$0.413887\pi$
$953$	−21529.5	+	29632.9i	−0.731805	+	1.00724i	−0.999048	+	0.0436139i	$0.986113\pi$
$954$	−966.256	−	702.026i	−0.0327921	−	0.0238249i
$955$		0			0
$956$	−29188.6	+	21206.7i	−0.987475	+	0.717443i
$957$		−	44230.9i		−	1.49402i
$958$	−2793.11	−	3844.38i	−0.0941975	−	0.129652i
$959$	−36.3488	−	111.870i	−0.00122395	−	0.00376692i
$960$		0			0
$961$	8318.09	−	25600.4i	0.279215	−	0.859335i
$962$	9311.06	−	3025.35i	0.312059	−	0.101394i
$963$	−7648.74	+	2485.23i	−0.255947	+	0.0831623i
$964$	5285.67	−	16267.6i	0.176598	−	0.543512i
$965$		0			0
$966$	−305.956	−	941.636i	−0.0101905	−	0.0313630i
$967$	−4694.17	−	6460.97i	−0.156106	−	0.214861i	0.723799	−	0.690010i	$-0.242394\pi$
$967$	−4694.17	−	6460.97i	−0.156106	−	0.214861i	−0.879905	+	0.475149i	$0.842394\pi$
$968$		−	16719.3i		−	0.555145i
$969$	78648.2	−	57141.2i	2.60737	−	1.89437i
$970$		0			0
$971$	−3656.19	−	2656.38i	−0.120837	−	0.0877932i	0.525725	−	0.850654i	$-0.323794\pi$
$971$	−3656.19	−	2656.38i	−0.120837	−	0.0877932i	−0.646562	+	0.762861i	$0.723794\pi$
$972$	−16509.9	+	22723.9i	−0.544810	+	0.749867i
$973$	−2004.91	−	651.434i	−0.0660579	−	0.0214635i
$974$	19910.9			0.655017
$975$		0			0
$976$	−6336.20			−0.207804
$977$	−1677.36	−	545.007i	−0.0549267	−	0.0178468i	0.281425	−	0.959583i	$-0.409193\pi$
$977$	−1677.36	−	545.007i	−0.0549267	−	0.0178468i	−0.336352	+	0.941737i	$0.609193\pi$
$978$	−4852.24	+	6678.54i	−0.158648	+	0.218360i
$979$	7318.23	+	5317.00i	0.238909	+	0.173577i
$980$		0			0
$981$	2696.61	−	1959.20i	0.0877635	−	0.0637639i
$982$		−	10742.6i		−	0.349095i
$983$	−18302.6	−	25191.3i	−0.593857	−	0.817374i	0.401271	−	0.915959i	$-0.368568\pi$
$983$	−18302.6	−	25191.3i	−0.593857	−	0.817374i	−0.995129	+	0.0985849i	$0.968568\pi$
$984$	−955.789	−	2941.62i	−0.0309649	−	0.0953001i
$985$		0			0
$986$	16802.5	−	51712.7i	0.542697	−	1.67025i
$987$	−1378.53	+	447.912i	−0.0444571	+	0.0144450i
$988$	20007.8	−	6500.93i	0.644264	−	0.209334i
$989$	−3078.78	+	9475.50i	−0.0989883	+	0.304655i
$990$		0			0
$991$	4516.20	+	13899.4i	0.144765	+	0.445540i	0.996981	−	0.0776501i	$-0.0247417\pi$
$991$	4516.20	+	13899.4i	0.144765	+	0.445540i	−0.852216	+	0.523190i	$0.824742\pi$
$992$	26204.4	+	36067.3i	0.838701	+	1.15437i
$993$		−	2542.78i		−	0.0812616i
$994$	−316.256	+	229.774i	−0.0100916	+	0.00733197i
$995$		0			0
$996$	6849.81	+	4976.68i	0.217916	+	0.158325i
$997$	−7437.62	+	10237.0i	−0.236261	+	0.325185i	−0.910640	−	0.413200i	$-0.864411\pi$
$997$	−7437.62	+	10237.0i	−0.236261	+	0.325185i	0.674380	+	0.738385i	$0.264411\pi$
$998$	−14884.4	−	4836.23i	−0.472102	−	0.153395i
$999$	4734.25			0.149935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.4.e.a.24.4		24
5.2	odd	4		125.4.d.b.101.5		48
5.3	odd	4		125.4.d.b.101.8		48
5.4	even	2		25.4.e.a.4.3	✓	24
15.14	odd	2		225.4.m.a.154.4		24
25.6	even	5		25.4.e.a.19.3	yes	24
25.8	odd	20		125.4.d.b.26.8		48
25.12	odd	20		625.4.a.g.1.9		24
25.13	odd	20		625.4.a.g.1.16		24
25.17	odd	20		125.4.d.b.26.5		48
25.19	even	10	inner	125.4.e.a.99.4		24
75.56	odd	10		225.4.m.a.19.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.4.3	✓	24	5.4	even	2
25.4.e.a.19.3	yes	24	25.6	even	5
125.4.d.b.26.5		48	25.17	odd	20
125.4.d.b.26.8		48	25.8	odd	20
125.4.d.b.101.5		48	5.2	odd	4
125.4.d.b.101.8		48	5.3	odd	4
125.4.e.a.24.4		24	1.1	even	1	trivial
125.4.e.a.99.4		24	25.19	even	10	inner
225.4.m.a.19.4		24	75.56	odd	10
225.4.m.a.154.4		24	15.14	odd	2
625.4.a.g.1.9		24	25.12	odd	20
625.4.a.g.1.16		24	25.13	odd	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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48841 + 0.483614i) q^{2} +(4.16357 - 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(8.96855 - 6.51603i) q^{6} -1.18261i q^{7} +(-12.4652 - 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +O(q^{10})\)	\(q+(1.48841 + 0.483614i) q^{2} +(4.16357 - 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(8.96855 - 6.51603i) q^{6} -1.18261i q^{7} +(-12.4652 - 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +(7.19826 - 22.1540i) q^{11} +(-37.3943 + 12.1501i) q^{12} +(34.0413 - 11.0607i) q^{13} +(0.571929 - 1.76022i) q^{14} +(3.46617 + 10.6678i) q^{16} +(-76.1834 - 104.857i) q^{17} -36.2705i q^{18} +(-85.6642 + 62.2387i) q^{19} +(-6.77717 - 4.92390i) q^{21} +(21.4280 - 29.4931i) q^{22} +(71.8250 + 23.3374i) q^{23} -150.220 q^{24} +56.0166 q^{26} +(25.7621 + 8.37062i) q^{27} +(-3.85845 + 5.31070i) q^{28} +(216.865 + 157.562i) q^{29} +(192.656 - 139.973i) q^{31} +187.211i q^{32} +(-96.9866 - 133.491i) q^{33} +(-62.6817 - 192.914i) q^{34} +(-39.7531 + 122.347i) q^{36} +(166.220 - 54.0080i) q^{37} +(-157.603 + 51.2084i) q^{38} +(78.3483 - 241.131i) q^{39} +(6.36260 + 19.5821i) q^{41} +(-7.70595 - 10.6063i) q^{42} +131.925i q^{43} +(-104.605 + 76.0003i) q^{44} +(95.6189 + 69.4712i) q^{46} +(101.704 - 139.984i) q^{47} +(75.5651 + 24.5526i) q^{48} +341.601 q^{49} -918.098 q^{51} +(-188.955 - 61.3951i) q^{52} +(19.3553 - 26.6403i) q^{53} +(34.2965 + 24.9179i) q^{54} +(-20.2899 + 14.7415i) q^{56} +750.049i q^{57} +(246.586 + 339.396i) q^{58} +(148.786 + 457.918i) q^{59} +(-174.560 + 537.239i) q^{61} +(354.445 - 115.166i) q^{62} +(-26.0667 + 8.46959i) q^{63} +(-62.8084 + 193.304i) q^{64} +(-79.7980 - 245.593i) q^{66} +(-198.345 - 272.998i) q^{67} +719.437i q^{68} +(432.787 - 314.438i) q^{69} +(-170.875 - 124.148i) q^{71} +(-288.892 + 397.626i) q^{72} +(-452.871 - 147.147i) q^{73} +273.522 q^{74} +587.751 q^{76} +(-26.1996 - 8.51277i) q^{77} +(233.229 - 321.013i) q^{78} +(-792.426 - 575.731i) q^{79} +(661.474 - 480.589i) q^{81} +32.2232i q^{82} +(-126.573 - 174.213i) q^{83} +(14.3689 + 44.2230i) q^{84} +(-63.8008 + 196.359i) q^{86} +(1805.87 - 586.763i) q^{87} +(-469.820 + 152.654i) q^{88} +(-120.001 + 369.326i) q^{89} +(-13.0805 - 40.2577i) q^{91} +(-246.399 - 339.139i) q^{92} -1686.84i q^{93} +(219.076 - 159.168i) q^{94} +(1072.84 + 779.466i) q^{96} +(-325.030 + 447.366i) q^{97} +(508.444 + 165.203i) q^{98} -539.861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} + 5 q^{3} + 13 q^{4} - 7 q^{6} + 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q + 5 * q^2 + 5 * q^3 + 13 * q^4 - 7 * q^6 + 110 * q^8 + 47 * q^9	\( 24 q + 5 q^{2} + 5 q^{3} + 13 q^{4} - 7 q^{6} + 110 q^{8} + 47 q^{9} + 83 q^{11} + 165 q^{12} + 5 q^{13} + 31 q^{14} + 89 q^{16} + 165 q^{17} - 115 q^{19} + 138 q^{21} - 30 q^{22} - 75 q^{23} + 640 q^{24} - 822 q^{26} - 595 q^{27} - 675 q^{28} + 125 q^{29} + 633 q^{31} + 1285 q^{33} - 779 q^{34} - 531 q^{36} + 1510 q^{37} - 255 q^{38} - 1241 q^{39} - 117 q^{41} - 1745 q^{42} + 516 q^{44} + 1233 q^{46} + 95 q^{47} - 1410 q^{48} + 1148 q^{49} - 2022 q^{51} - 1740 q^{52} - 2580 q^{53} + 1745 q^{54} + 3160 q^{56} + 4230 q^{58} - 1905 q^{59} - 567 q^{61} + 6880 q^{62} + 1950 q^{63} - 3612 q^{64} - 2774 q^{66} - 4195 q^{67} + 539 q^{69} + 2473 q^{71} - 215 q^{72} + 845 q^{73} + 3596 q^{74} - 3280 q^{76} - 3870 q^{77} - 9295 q^{78} + 775 q^{79} + 3309 q^{81} + 4625 q^{83} - 5694 q^{84} - 3897 q^{86} + 8485 q^{87} + 1650 q^{88} - 2410 q^{89} - 382 q^{91} - 4090 q^{92} + 5401 q^{94} + 6488 q^{96} - 5185 q^{97} - 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q + 5 * q^2 + 5 * q^3 + 13 * q^4 - 7 * q^6 + 110 * q^8 + 47 * q^9 + 83 * q^11 + 165 * q^12 + 5 * q^13 + 31 * q^14 + 89 * q^16 + 165 * q^17 - 115 * q^19 + 138 * q^21 - 30 * q^22 - 75 * q^23 + 640 * q^24 - 822 * q^26 - 595 * q^27 - 675 * q^28 + 125 * q^29 + 633 * q^31 + 1285 * q^33 - 779 * q^34 - 531 * q^36 + 1510 * q^37 - 255 * q^38 - 1241 * q^39 - 117 * q^41 - 1745 * q^42 + 516 * q^44 + 1233 * q^46 + 95 * q^47 - 1410 * q^48 + 1148 * q^49 - 2022 * q^51 - 1740 * q^52 - 2580 * q^53 + 1745 * q^54 + 3160 * q^56 + 4230 * q^58 - 1905 * q^59 - 567 * q^61 + 6880 * q^62 + 1950 * q^63 - 3612 * q^64 - 2774 * q^66 - 4195 * q^67 + 539 * q^69 + 2473 * q^71 - 215 * q^72 + 845 * q^73 + 3596 * q^74 - 3280 * q^76 - 3870 * q^77 - 9295 * q^78 + 775 * q^79 + 3309 * q^81 + 4625 * q^83 - 5694 * q^84 - 3897 * q^86 + 8485 * q^87 + 1650 * q^88 - 2410 * q^89 - 382 * q^91 - 4090 * q^92 + 5401 * q^94 + 6488 * q^96 - 5185 * q^97 - 5180 * q^98 + 6024 * q^99

Introduction

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