LMFDB - Embedded newform 125.4.e.b.74.14

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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.14
Character	$\chi$	$=$	125.74
Dual form			125.4.e.b.49.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.12208 + 4.29718i) q^{2} +(5.96393 + 1.93780i) q^{3} +(-6.24620 + 19.2238i) q^{4} +(10.2928 + 31.6780i) q^{6} -9.63602i q^{7} +(-61.6963 + 20.0464i) q^{8} +(9.96993 + 7.24358i) q^{9} +O(q^{10})$	\(q+(3.12208 + 4.29718i) q^{2} +(5.96393 + 1.93780i) q^{3} +(-6.24620 + 19.2238i) q^{4} +(10.2928 + 31.6780i) q^{6} -9.63602i q^{7} +(-61.6963 + 20.0464i) q^{8} +(9.96993 + 7.24358i) q^{9} +(19.6877 - 14.3039i) q^{11} +(-74.5038 + 102.546i) q^{12} +(25.9791 - 35.7572i) q^{13} +(41.4077 - 30.0844i) q^{14} +(-147.942 - 107.486i) q^{16} +(-1.75088 + 0.568894i) q^{17} +65.4576i q^{18} +(22.1878 + 68.2870i) q^{19} +(18.6727 - 57.4685i) q^{21} +(122.933 + 39.9434i) q^{22} +(41.2202 + 56.7348i) q^{23} -406.798 q^{24} +234.764 q^{26} +(-54.0962 - 74.4571i) q^{27} +(185.241 + 60.1885i) q^{28} +(31.0824 - 95.6617i) q^{29} +(-51.1943 - 157.560i) q^{31} -452.340i q^{32} +(145.134 - 47.1569i) q^{33} +(-7.91102 - 5.74769i) q^{34} +(-201.524 + 146.415i) q^{36} +(-229.974 + 316.532i) q^{37} +(-224.169 + 308.542i) q^{38} +(224.228 - 162.911i) q^{39} +(-2.89600 - 2.10407i) q^{41} +(305.250 - 99.1818i) q^{42} -9.64426i q^{43} +(152.003 + 467.818i) q^{44} +(-115.107 + 354.261i) q^{46} +(-515.027 - 167.342i) q^{47} +(-674.027 - 927.719i) q^{48} +250.147 q^{49} -11.5445 q^{51} +(525.119 + 722.765i) q^{52} +(-154.735 - 50.2766i) q^{53} +(151.062 - 464.922i) q^{54} +(193.167 + 594.507i) q^{56} +450.254i q^{57} +(508.117 - 165.097i) q^{58} +(134.417 + 97.6599i) q^{59} +(692.078 - 502.824i) q^{61} +(517.230 - 711.905i) q^{62} +(69.7993 - 96.0704i) q^{63} +(760.253 - 552.356i) q^{64} +(655.762 + 476.439i) q^{66} +(671.926 - 218.322i) q^{67} -37.2120i q^{68} +(135.894 + 418.239i) q^{69} +(-209.430 + 644.559i) q^{71} +(-760.316 - 247.041i) q^{72} +(-28.4306 - 39.1313i) q^{73} -2078.19 q^{74} -1451.33 q^{76} +(-137.833 - 189.711i) q^{77} +(1400.12 + 454.925i) q^{78} +(-145.637 + 448.225i) q^{79} +(-281.164 - 865.334i) q^{81} -19.0137i q^{82} +(-572.410 + 185.987i) q^{83} +(988.132 + 717.920i) q^{84} +(41.4431 - 30.1102i) q^{86} +(370.746 - 510.288i) q^{87} +(-927.915 + 1277.17i) q^{88} +(558.915 - 406.075i) q^{89} +(-344.557 - 250.335i) q^{91} +(-1348.13 + 438.034i) q^{92} -1038.88i q^{93} +(-888.856 - 2735.62i) q^{94} +(876.544 - 2697.72i) q^{96} +(-585.617 - 190.279i) q^{97} +(780.980 + 1074.93i) q^{98} +299.896 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9}+O(q^{10}) $ 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9	$ 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9} - 178 q^{11} + 34 q^{14} - 414 q^{16} + 230 q^{19} - 288 q^{21} - 1560 q^{24} + 1172 q^{26} + 10 q^{29} - 1278 q^{31} + 1554 q^{34} + 1346 q^{36} + 2266 q^{39} + 682 q^{41} - 1096 q^{44} - 2478 q^{46} - 2688 q^{49} + 4012 q^{51} - 3230 q^{54} - 5820 q^{56} + 3810 q^{59} + 2782 q^{61} + 7192 q^{64} + 7264 q^{66} - 5374 q^{69} - 7438 q^{71} - 9696 q^{74} + 7040 q^{76} - 1550 q^{79} - 7424 q^{81} + 15224 q^{84} + 7782 q^{86} + 10150 q^{89} + 752 q^{91} - 7146 q^{94} - 15508 q^{96} - 13144 q^{99}+O(q^{100}) $ 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9 - 178 * q^11 + 34 * q^14 - 414 * q^16 + 230 * q^19 - 288 * q^21 - 1560 * q^24 + 1172 * q^26 + 10 * q^29 - 1278 * q^31 + 1554 * q^34 + 1346 * q^36 + 2266 * q^39 + 682 * q^41 - 1096 * q^44 - 2478 * q^46 - 2688 * q^49 + 4012 * q^51 - 3230 * q^54 - 5820 * q^56 + 3810 * q^59 + 2782 * q^61 + 7192 * q^64 + 7264 * q^66 - 5374 * q^69 - 7438 * q^71 - 9696 * q^74 + 7040 * q^76 - 1550 * q^79 - 7424 * q^81 + 15224 * q^84 + 7782 * q^86 + 10150 * q^89 + 752 * q^91 - 7146 * q^94 - 15508 * q^96 - 13144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	3.12208	+	4.29718i	1.10382	+	1.51928i	0.830217	+	0.557440i	$0.188216\pi$
$2$	3.12208	+	4.29718i	1.10382	+	1.51928i	0.273606	+	0.961842i	$0.411784\pi$
$3$	5.96393	+	1.93780i	1.14776	+	0.372929i	0.820299	−	0.571936i	$-0.193807\pi$
$3$	5.96393	+	1.93780i	1.14776	+	0.372929i	0.327460	+	0.944865i	$0.393807\pi$
$4$	−6.24620	+	19.2238i	−0.780775	+	2.40298i
$5$		0			0
$5$		0			0
$6$	10.2928	+	31.6780i	0.700337	+	2.15542i
$7$		−	9.63602i		−	0.520296i	−0.965569	−	0.260148i	$-0.916229\pi$
$7$		−	9.63602i		−	0.520296i	0.965569	−	0.260148i	$-0.0837714\pi$
$8$	−61.6963	+	20.0464i	−2.72662	+	0.885932i
$9$	9.96993	+	7.24358i	0.369257	+	0.268281i
$10$		0			0
$11$	19.6877	−	14.3039i	0.539641	−	0.392072i	−0.284311	−	0.958732i	$-0.591765\pi$
$11$	19.6877	−	14.3039i	0.539641	−	0.392072i	0.823952	+	0.566660i	$0.191765\pi$
$12$	−74.5038	+	102.546i	−1.79228	+	2.46687i
$13$	25.9791	−	35.7572i	0.554255	−	0.762866i	−0.436327	−	0.899788i	$-0.643721\pi$
$13$	25.9791	−	35.7572i	0.554255	−	0.762866i	0.990582	+	0.136922i	$0.0437210\pi$
$14$	41.4077	−	30.0844i	0.790476	−	0.574315i
$15$		0			0
$16$	−147.942	−	107.486i	−2.31159	−	1.67947i
$17$	−1.75088	+	0.568894i	−0.0249794	+	0.00811630i	−0.321480	−	0.946916i	$-0.604180\pi$
$17$	−1.75088	+	0.568894i	−0.0249794	+	0.00811630i	0.296501	+	0.955033i	$0.404180\pi$
$18$			65.4576i			0.857139i
$19$	22.1878	+	68.2870i	0.267907	+	0.824532i	0.991010	+	0.133791i	$0.0427152\pi$
$19$	22.1878	+	68.2870i	0.267907	+	0.824532i	−0.723103	+	0.690740i	$0.757285\pi$
$20$		0			0
$21$	18.6727	−	57.4685i	0.194034	−	0.597174i
$22$	122.933	+	39.9434i	1.19134	+	0.387089i
$23$	41.2202	+	56.7348i	0.373696	+	0.514349i	0.953901	−	0.300122i	$-0.0970274\pi$
$23$	41.2202	+	56.7348i	0.373696	+	0.514349i	−0.580205	+	0.814471i	$0.697027\pi$
$24$	−406.798			−3.45989
$25$		0			0
$26$	234.764			1.77081
$27$	−54.0962	−	74.4571i	−0.385586	−	0.530714i
$28$	185.241	+	60.1885i	1.25026	+	0.406234i
$29$	31.0824	−	95.6617i	0.199029	−	0.612549i	−0.800877	−	0.598830i	$-0.795633\pi$
$29$	31.0824	−	95.6617i	0.199029	−	0.612549i	0.999906	−	0.0137199i	$-0.00436731\pi$
$30$		0			0
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	−0.982678	−	0.185324i	$-0.940667\pi$
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	0.686072	−	0.727533i	$-0.259333\pi$
$32$		−	452.340i		−	2.49885i
$33$	145.134	−	47.1569i	0.765593	−	0.248756i
$34$	−7.91102	−	5.74769i	−0.0399038	−	0.0289918i
$35$		0			0
$36$	−201.524	+	146.415i	−0.932980	+	0.677849i
$37$	−229.974	+	316.532i	−1.02182	+	1.40642i	−0.110906	+	0.993831i	$0.535375\pi$
$37$	−229.974	+	316.532i	−1.02182	+	1.40642i	−0.910918	+	0.412588i	$0.864625\pi$
$38$	−224.169	+	308.542i	−0.956975	+	1.31716i
$39$	224.228	−	162.911i	0.920646	−	0.668888i
$40$		0			0
$41$	−2.89600	−	2.10407i	−0.0110312	−	0.00801463i	0.582256	−	0.813006i	$-0.302170\pi$
$41$	−2.89600	−	2.10407i	−0.0110312	−	0.00801463i	−0.593287	+	0.804991i	$0.702170\pi$
$42$	305.250	−	99.1818i	1.12145	−	0.364383i
$43$		−	9.64426i		−	0.0342032i	−0.999854	−	0.0171016i	$-0.994556\pi$
$43$		−	9.64426i		−	0.0342032i	0.999854	−	0.0171016i	$-0.00544387\pi$
$44$	152.003	+	467.818i	0.520803	+	1.60287i
$45$		0			0
$46$	−115.107	+	354.261i	−0.368946	+	1.13550i
$47$	−515.027	−	167.342i	−1.59839	−	0.519349i	−0.631682	−	0.775228i	$-0.717635\pi$
$47$	−515.027	−	167.342i	−1.59839	−	0.519349i	−0.966709	+	0.255879i	$0.917635\pi$
$48$	−674.027	−	927.719i	−2.02682	−	2.78968i
$49$	250.147			0.729292
$50$		0			0
$51$	−11.5445			−0.0316971
$52$	525.119	+	722.765i	1.40040	+	1.92749i
$53$	−154.735	−	50.2766i	−0.401029	−	0.130302i	0.101556	−	0.994830i	$-0.467618\pi$
$53$	−154.735	−	50.2766i	−0.401029	−	0.130302i	−0.502585	+	0.864528i	$0.667618\pi$
$54$	151.062	−	464.922i	0.380685	−	1.17163i
$55$		0			0
$56$	193.167	+	594.507i	0.460947	+	1.41865i
$57$			450.254i			1.04627i
$58$	508.117	−	165.097i	1.15033	−	0.373764i
$59$	134.417	+	97.6599i	0.296604	+	0.215496i	0.726127	−	0.687560i	$-0.241318\pi$
$59$	134.417	+	97.6599i	0.296604	+	0.215496i	−0.429523	+	0.903056i	$0.641318\pi$
$60$		0			0
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.467444	−	0.884023i	$-0.345175\pi$
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.985204	−	0.171387i	$-0.0548250\pi$
$62$	517.230	−	711.905i	1.05949	−	1.45826i
$63$	69.7993	−	96.0704i	0.139585	−	0.192123i
$64$	760.253	−	552.356i	1.48487	−	1.07882i
$65$		0			0
$66$	655.762	+	476.439i	1.22301	+	0.888569i
$67$	671.926	−	218.322i	1.22521	−	0.398094i	0.376231	−	0.926526i	$-0.377220\pi$
$67$	671.926	−	218.322i	1.22521	−	0.398094i	0.848975	+	0.528432i	$0.177220\pi$
$68$		−	37.2120i		−	0.0663620i
$69$	135.894	+	418.239i	0.237097	+	0.729711i
$70$		0			0
$71$	−209.430	+	644.559i	−0.350067	+	1.07740i	0.608748	+	0.793364i	$0.291672\pi$
$71$	−209.430	+	644.559i	−0.350067	+	1.07740i	−0.958815	+	0.284032i	$0.908328\pi$
$72$	−760.316	−	247.041i	−1.24450	−	0.404363i
$73$	−28.4306	−	39.1313i	−0.0455829	−	0.0627394i	0.785617	−	0.618713i	$-0.212346\pi$
$73$	−28.4306	−	39.1313i	−0.0455829	−	0.0627394i	−0.831200	+	0.555974i	$0.812346\pi$
$74$	−2078.19			−3.26466
$75$		0			0
$76$	−1451.33			−2.19051
$77$	−137.833	−	189.711i	−0.203994	−	0.280773i
$78$	1400.12	+	454.925i	2.03246	+	0.660386i
$79$	−145.637	+	448.225i	−0.207411	+	0.638345i	0.792195	+	0.610268i	$0.208938\pi$
$79$	−145.637	+	448.225i	−0.207411	+	0.638345i	−0.999606	+	0.0280766i	$0.991062\pi$
$80$		0			0
$81$	−281.164	−	865.334i	−0.385685	−	1.18701i
$82$		−	19.0137i		−	0.0256062i
$83$	−572.410	+	185.987i	−0.756989	+	0.245961i	−0.661986	−	0.749516i	$-0.730286\pi$
$83$	−572.410	+	185.987i	−0.756989	+	0.245961i	−0.0950033	+	0.995477i	$0.530286\pi$
$84$	988.132	+	717.920i	1.28350	+	0.932518i
$85$		0			0
$86$	41.4431	−	30.1102i	0.0519643	−	0.0377542i
$87$	370.746	−	510.288i	0.456875	−	0.628835i
$88$	−927.915	+	1277.17i	−1.12405	+	1.54712i
$89$	558.915	−	406.075i	0.665672	−	0.483639i	−0.202902	−	0.979199i	$-0.565037\pi$
$89$	558.915	−	406.075i	0.665672	−	0.483639i	0.868574	+	0.495560i	$0.165037\pi$
$90$		0			0
$91$	−344.557	−	250.335i	−0.396916	−	0.288376i
$92$	−1348.13	+	438.034i	−1.52774	+	0.496394i
$93$		−	1038.88i		−	1.15835i
$94$	−888.856	−	2735.62i	−0.975303	−	3.00168i
$95$		0			0
$96$	876.544	−	2697.72i	0.931895	−	2.86808i
$97$	−585.617	−	190.279i	−0.612994	−	0.199174i	−0.0139669	−	0.999902i	$-0.504446\pi$
$97$	−585.617	−	190.279i	−0.612994	−	0.199174i	−0.599027	+	0.800729i	$0.704446\pi$
$98$	780.980	+	1074.93i	0.805009	+	1.10800i
$99$	299.896			0.304452
$100$		0			0
$101$	626.998			0.617709			0.308855	−	0.951109i	$-0.400054\pi$
$101$	626.998			0.617709			0.308855	+	0.951109i	$0.400054\pi$
$102$	−36.0429	−	49.6088i	−0.0349880	−	0.0481569i
$103$	−1448.36	−	470.599i	−1.38554	−	0.450189i	−0.481054	−	0.876691i	$-0.659746\pi$
$103$	−1448.36	−	470.599i	−1.38554	−	0.450189i	−0.904487	+	0.426502i	$0.859746\pi$
$104$	−886.015	+	2726.87i	−0.835393	+	2.57108i
$105$		0			0
$106$	−267.049	−	821.893i	−0.244699	−	0.753107i
$107$		−	435.652i		−	0.393608i	−0.980443	−	0.196804i	$-0.936944\pi$
$107$		−	435.652i		−	0.393608i	0.980443	−	0.196804i	$-0.0630563\pi$
$108$	1769.25	−	574.863i	1.57635	−	0.512187i
$109$	−1426.54	−	1036.44i	−1.25356	−	0.910764i	−0.255136	−	0.966905i	$-0.582120\pi$
$109$	−1426.54	−	1036.44i	−1.25356	−	0.910764i	−0.998423	+	0.0561410i	$0.982120\pi$
$110$		0			0
$111$	−1984.92	+	1442.13i	−1.69730	+	1.23316i
$112$	−1035.74	+	1425.57i	−0.873820	+	1.20271i
$113$	−540.754	+	744.284i	−0.450176	+	0.619614i	−0.972435	−	0.233173i	$-0.925089\pi$
$113$	−540.754	+	744.284i	−0.450176	+	0.619614i	0.522260	+	0.852786i	$0.325089\pi$
$114$	−1934.82	+	1405.73i	−1.58958	+	1.15490i
$115$		0			0
$116$	1644.84	+	1195.04i	1.31655	+	0.956527i
$117$	518.020	−	168.315i	0.409324	−	0.132998i
$118$			882.517i			0.688494i
$119$	5.48187	+	16.8715i	0.00422288	+	0.0129967i
$120$		0			0
$121$	−228.300	+	702.635i	−0.171525	+	0.527900i
$122$	4321.45	+	1404.12i	3.20693	+	1.04200i
$123$	−13.1943	−	18.1604i	−0.00967226	−	0.0133127i
$124$	3348.67			2.42516
$125$		0			0
$126$	630.751			0.445966
$127$	−605.495	−	833.392i	−0.423063	−	0.582296i	0.543281	−	0.839551i	$-0.317182\pi$
$127$	−605.495	−	833.392i	−0.423063	−	0.582296i	−0.966344	+	0.257255i	$0.917182\pi$
$128$	1305.54	+	424.196i	0.901520	+	0.292922i
$129$	18.6886	−	57.5177i	0.0127554	−	0.0392570i
$130$		0			0
$131$	94.1854	+	289.873i	0.0628169	+	0.193331i	0.977540	−	0.210751i	$-0.0675911\pi$
$131$	94.1854	+	289.873i	0.0628169	+	0.193331i	−0.914723	+	0.404082i	$0.867591\pi$
$132$			3084.58i			2.03393i
$133$	658.014	−	213.802i	0.429001	−	0.139391i
$134$	3035.98	+	2205.77i	1.95723	+	1.42201i
$135$		0			0
$136$	96.6184	−	70.1974i	0.0609188	−	0.0442601i
$137$	−1065.68	+	1466.78i	−0.664577	+	0.914712i	−0.999622	−	0.0274903i	$-0.991248\pi$
$137$	−1065.68	+	1466.78i	−0.664577	+	0.914712i	0.335045	+	0.942202i	$0.391248\pi$
$138$	−1372.97	+	1889.74i	−0.846923	+	1.16569i
$139$	−579.242	+	420.844i	−0.353458	+	0.256802i	−0.750318	−	0.661077i	$-0.770100\pi$
$139$	−579.242	+	420.844i	−0.353458	+	0.256802i	0.396860	+	0.917879i	$0.370100\pi$
$140$		0			0
$141$	−2747.31	−	1996.04i	−1.64089	−	1.19217i
$142$	−3423.64	+	1112.41i	−2.02328	+	0.657404i
$143$		−	1075.58i		−	0.628982i
$144$	−696.385	−	2143.25i	−0.403001	−	1.24031i
$145$		0			0
$146$	79.3917	−	244.343i	0.0450035	−	0.138506i
$147$	1491.86	+	484.735i	0.837051	+	0.271974i
$148$	−4648.49	−	6398.10i	−2.58178	−	3.55352i
$149$	−725.618			−0.398959			−0.199480	−	0.979902i	$-0.563925\pi$
$149$	−725.618			−0.398959			−0.199480	+	0.979902i	$0.563925\pi$
$150$		0			0
$151$	3051.31			1.64445			0.822227	−	0.569160i	$-0.192732\pi$
$151$	3051.31			1.64445			0.822227	+	0.569160i	$0.192732\pi$
$152$	−2737.81	−	3768.27i	−1.46096	−	2.01084i
$153$	−21.5769	−	7.01077i	−0.0114013	−	0.00370449i
$154$	384.895	−	1184.58i	0.201401	−	0.619848i
$155$		0			0
$156$	1731.20	+	5328.09i	0.888507	+	2.73454i
$157$		−	2166.76i		−	1.10144i	−0.834689	−	0.550722i	$-0.814353\pi$
$157$		−	2166.76i		−	1.10144i	0.834689	−	0.550722i	$-0.185647\pi$
$158$	−2380.79	+	773.566i	−1.19877	+	0.389504i
$159$	−825.405	−	599.692i	−0.411691	−	0.299111i
$160$		0			0
$161$	546.698	−	397.199i	0.267614	−	0.194433i
$162$	2840.68	−	3909.86i	1.37768	−	1.89622i
$163$	45.7313	−	62.9438i	0.0219752	−	0.0302463i	−0.797888	−	0.602806i	$-0.794049\pi$
$163$	45.7313	−	62.9438i	0.0219752	−	0.0302463i	0.819863	+	0.572559i	$0.194049\pi$
$164$	58.5372	−	42.5298i	0.0278719	−	0.0202501i
$165$		0			0
$166$	−2586.33	−	1879.08i	−1.20927	−	0.878583i
$167$	120.203	−	39.0563i	0.0556981	−	0.0180974i	−0.281035	−	0.959697i	$-0.590678\pi$
$167$	120.203	−	39.0563i	0.0556981	−	0.0180974i	0.336734	+	0.941600i	$0.390678\pi$
$168$			3919.92i			1.80017i
$169$	75.2487	+	231.592i	0.0342506	+	0.105413i
$170$		0			0
$171$	−273.431	+	841.535i	−0.122280	+	0.376338i
$172$	185.400	+	60.2400i	0.0821895	+	0.0267050i
$173$	1903.87	+	2620.45i	0.836697	+	1.15161i	0.986639	+	0.162919i	$0.0520910\pi$
$173$	1903.87	+	2620.45i	0.836697	+	1.15161i	−0.149943	+	0.988695i	$0.547909\pi$
$174$	3350.30			1.45969
$175$		0			0
$176$	−4450.09			−1.90590
$177$	612.410	+	842.910i	0.260065	+	0.357949i
$178$	3489.95	+	1133.96i	1.46957	+	0.477492i
$179$	−438.802	+	1350.49i	−0.183227	+	0.563914i	−0.999913	−	0.0131674i	$-0.995809\pi$
$179$	−438.802	+	1350.49i	−0.183227	+	0.563914i	0.816686	+	0.577082i	$0.195809\pi$
$180$		0			0
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	0.920383	−	0.391018i	$-0.127877\pi$
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	−0.974440	+	0.224648i	$0.927877\pi$
$182$		−	2262.19i		−	0.921344i
$183$	5101.88	−	1657.70i	2.06088	−	0.669621i
$184$	−3680.46	−	2674.01i	−1.47461	−	1.07136i
$185$		0			0
$186$	4464.25	−	3243.47i	1.75986	−	1.27862i
$187$	−26.3332	+	36.2446i	−0.0102977	+	0.0141736i
$188$	6433.92	−	8855.54i	2.49597	−	3.43541i
$189$	−717.470	+	521.272i	−0.276128	+	0.200619i
$190$		0			0
$191$	1193.36	+	867.030i	0.452088	+	0.328461i	0.790420	−	0.612566i	$-0.209862\pi$
$191$	1193.36	+	867.030i	0.452088	+	0.328461i	−0.338331	+	0.941027i	$0.609862\pi$
$192$	5604.45	−	1821.00i	2.10660	−	0.684475i
$193$			1535.93i			0.572841i	0.958104	+	0.286421i	$0.0924655\pi$
$193$			1535.93i			0.572841i	−0.958104	+	0.286421i	$0.907535\pi$
$194$	−1010.68	−	3110.57i	−0.374036	−	1.15116i
$195$		0			0
$196$	−1562.47	+	4808.79i	−0.569413	+	1.75247i
$197$	−296.613	−	96.3752i	−0.107273	−	0.0348551i	0.254889	−	0.966970i	$-0.417961\pi$
$197$	−296.613	−	96.3752i	−0.107273	−	0.0348551i	−0.362162	+	0.932115i	$0.617961\pi$
$198$	936.301	+	1288.71i	0.336061	+	0.462548i
$199$	1453.74			0.517855			0.258927	−	0.965897i	$-0.416631\pi$
$199$	1453.74			0.517855			0.258927	+	0.965897i	$0.416631\pi$
$200$		0			0
$201$	4430.38			1.55470
$202$	1957.54	+	2694.32i	0.681842	+	0.938474i
$203$	−921.798	−	299.510i	−0.318707	−	0.103554i
$204$	72.1093	−	221.930i	0.0247483	−	0.0761676i
$205$		0			0
$206$	−2499.64	−	7693.09i	−0.845427	−	2.60196i
$207$			864.224i			0.290182i
$208$	−7686.78	+	2497.59i	−2.56242	+	0.832579i
$209$	1413.60	+	1027.04i	0.467849	+	0.339912i
$210$		0			0
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	−0.878437	−	0.477858i	$-0.841413\pi$
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	0.183018	+	0.983110i	$0.441413\pi$
$212$	1933.02	−	2660.57i	0.626227	−	0.861928i
$213$	−2498.05	+	3438.27i	−0.803585	+	1.10604i
$214$	1872.07	−	1360.14i	0.598001	−	0.434473i
$215$		0			0
$216$	4830.13	+	3509.30i	1.52152	+	1.10545i
$217$	−1518.25	+	493.309i	−0.474956	+	0.154323i
$218$		−	9365.97i		−	2.90983i
$219$	−93.7294	−	288.469i	−0.0289207	−	0.0890089i
$220$		0			0
$221$	−25.1442	+	77.3858i	−0.00765330	+	0.0235544i
$222$	−12394.2	−	4027.11i	−3.74704	−	1.21749i
$223$	2055.08	+	2828.58i	0.617123	+	0.849396i	0.997140	−	0.0755831i	$-0.0240818\pi$
$223$	2055.08	+	2828.58i	0.617123	+	0.849396i	−0.380017	+	0.924980i	$0.624082\pi$
$224$	−4358.76			−1.30014
$225$		0			0
$226$	−4886.60			−1.43828
$227$	3159.23	+	4348.31i	0.923724	+	1.27140i	0.962258	+	0.272140i	$0.0877314\pi$
$227$	3159.23	+	4348.31i	0.923724	+	1.27140i	−0.0385335	+	0.999257i	$0.512269\pi$
$228$	−8655.61	−	2812.38i	−2.51417	−	0.816905i
$229$	207.178	−	637.627i	0.0597846	−	0.183998i	−0.916704	−	0.399567i	$-0.869161\pi$
$229$	207.178	−	637.627i	0.0597846	−	0.183998i	0.976489	+	0.215569i	$0.0691605\pi$
$230$		0			0
$231$	−454.404	−	1398.51i	−0.129427	−	0.398335i
$232$			6525.06i			1.84651i
$233$	−4438.46	+	1442.14i	−1.24795	+	0.405485i	−0.857187	−	0.515005i	$-0.827790\pi$
$233$	−4438.46	+	1442.14i	−1.24795	+	0.405485i	−0.390767	+	0.920490i	$0.627790\pi$
$234$	2340.58	+	1700.53i	0.653883	+	0.475073i
$235$		0			0
$236$	−2717.00	+	1974.01i	−0.749413	+	0.544480i
$237$	−1737.14	+	2390.97i	−0.476115	+	0.655316i
$238$	−55.3849	+	76.2307i	−0.0150843	+	0.0207618i
$239$	5138.90	−	3733.63i	1.39083	−	1.01050i	0.395054	−	0.918658i	$-0.370726\pi$
$239$	5138.90	−	3733.63i	1.39083	−	1.01050i	0.995774	−	0.0918383i	$-0.0292743\pi$
$240$		0			0
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	0.447938	−	0.894064i	$-0.352158\pi$
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	−0.711885	+	0.702296i	$0.752158\pi$
$242$	−3732.12	+	1212.64i	−0.991362	+	0.322113i
$243$		−	3220.71i		−	0.850242i
$244$	5343.35	+	16445.1i	1.40194	+	4.31472i
$245$		0			0
$246$	36.8447	−	113.396i	0.00954932	−	0.0293898i
$247$	3018.17	+	980.662i	0.777496	+	0.252624i
$248$	6317.00	+	8694.60i	1.61746	+	2.22624i
$249$	−3774.22			−0.960567
$250$		0			0
$251$	5225.08			1.31396			0.656980	−	0.753908i	$-0.271834\pi$
$251$	5225.08			1.31396			0.656980	+	0.753908i	$0.271834\pi$
$252$	1410.86	+	1941.89i	0.352682	+	0.485426i
$253$	1623.06	+	527.364i	0.403324	+	0.131048i
$254$	1690.83	−	5203.84i	0.417685	−	1.28550i
$255$		0			0
$256$	−69.9686	−	215.341i	−0.0170822	−	0.0525735i
$257$			5648.44i			1.37097i	0.728085	+	0.685487i	$0.240411\pi$
$257$			5648.44i			1.37097i	−0.728085	+	0.685487i	$0.759589\pi$
$258$	305.511	−	99.2666i	0.0737221	−	0.0239538i
$259$	3050.11	+	2216.03i	0.731754	+	0.531651i
$260$		0			0
$261$	1002.82	−	728.593i	0.237828	−	0.172792i
$262$	−951.580	+	1309.74i	−0.224385	+	0.308839i
$263$	−156.694	+	215.671i	−0.0367383	+	0.0505660i	−0.826991	−	0.562215i	$-0.809949\pi$
$263$	−156.694	+	215.671i	−0.0367383	+	0.0505660i	0.790253	+	0.612781i	$0.209949\pi$
$264$	−8008.91	+	5818.81i	−1.86710	+	1.35653i
$265$		0			0
$266$	2973.12	+	2160.10i	0.685314	+	0.497910i
$267$	4120.22	−	1338.74i	0.944394	−	0.306852i
$268$			14280.7i			3.25497i
$269$	20.8315	+	64.1126i	0.00472162	+	0.0145317i	0.953390	−	0.301742i	$-0.0975682\pi$
$269$	20.8315	+	64.1126i	0.00472162	+	0.0145317i	−0.948668	+	0.316274i	$0.897568\pi$
$270$		0			0
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	0.689810	+	0.723990i	$0.257694\pi$
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	−0.983619	+	0.180260i	$0.942306\pi$
$272$	320.175	+	104.031i	0.0713731	+	0.0231905i
$273$	−1569.81	−	2160.66i	−0.348020	−	0.479008i
$274$	−9630.15			−2.12328
$275$		0			0
$276$	−8888.98			−1.93860
$277$	−5134.61	−	7067.18i	−1.11375	−	1.53295i	−0.815773	−	0.578373i	$-0.803688\pi$
$277$	−5134.61	−	7067.18i	−1.11375	−	1.53295i	−0.297977	−	0.954573i	$-0.596312\pi$
$278$	−3616.88	−	1175.20i	−0.780310	−	0.253538i
$279$	630.893	−	1941.69i	0.135378	−	0.416652i
$280$		0			0
$281$	2157.19	+	6639.13i	0.457960	+	1.40946i	0.867624	+	0.497221i	$0.165646\pi$
$281$	2157.19	+	6639.13i	0.457960	+	1.40946i	−0.409664	+	0.912237i	$0.634354\pi$
$282$		−	18037.5i		−	3.80892i
$283$	6344.42	−	2061.43i	1.33264	−	0.433000i	0.445821	−	0.895122i	$-0.352912\pi$
$283$	6344.42	−	2061.43i	1.33264	−	0.433000i	0.886817	+	0.462122i	$0.152912\pi$
$284$	−11082.8	−	8052.10i	−2.31564	−	1.68241i
$285$		0			0
$286$	4621.95	−	3358.04i	0.955600	−	0.694284i
$287$	−20.2748	+	27.9059i	−0.00416998	+	0.00573949i
$288$	3276.56	−	4509.80i	0.670393	−	0.922717i
$289$	−3971.96	+	2885.80i	−0.808459	+	0.587380i
$290$		0			0
$291$	−3123.86	−	2269.62i	−0.629292	−	0.457207i
$292$	929.838	−	302.123i	0.186351	−	0.0605493i
$293$			4204.23i			0.838272i	0.907923	+	0.419136i	$0.137667\pi$
$293$			4204.23i			0.838272i	−0.907923	+	0.419136i	$0.862333\pi$
$294$	2574.72	+	7924.17i	0.510750	+	1.57193i
$295$		0			0
$296$	7843.23	−	24139.0i	1.54013	−	4.74003i
$297$	−2130.06	−	692.097i	−0.416156	−	0.135217i
$298$	−2265.44	−	3118.11i	−0.440380	−	0.606132i
$299$	3099.54			0.599502
$300$		0			0
$301$	−92.9323			−0.0177958
$302$	9526.46	+	13112.0i	1.81519	+	2.49839i
$303$	3739.37	+	1215.00i	0.708981	+	0.230362i
$304$	4057.39	−	12487.4i	0.765484	−	2.35592i
$305$		0			0
$306$	−37.2385	−	114.608i	−0.00695680	−	0.0214108i
$307$			1361.03i			0.253024i	0.991965	+	0.126512i	$0.0403782\pi$
$307$			1361.03i			0.253024i	−0.991965	+	0.126512i	$0.959622\pi$
$308$	4507.90	−	1464.70i	0.833965	−	0.270972i
$309$	−7725.96	−	5613.24i	−1.42238	−	1.03342i
$310$		0			0
$311$	−1990.40	+	1446.11i	−0.362911	+	0.263670i	−0.754265	−	0.656570i	$-0.772007\pi$
$311$	−1990.40	+	1446.11i	−0.362911	+	0.263670i	0.391354	+	0.920240i	$0.372007\pi$
$312$	−10568.3	+	14546.0i	−1.91766	+	2.63943i
$313$	1695.11	−	2333.11i	0.306112	−	0.421327i	−0.628052	−	0.778171i	$-0.716147\pi$
$313$	1695.11	−	2333.11i	0.306112	−	0.421327i	0.934164	+	0.356845i	$0.116147\pi$
$314$	9310.97	−	6764.82i	1.67340	−	1.21580i
$315$		0			0
$316$	−7706.92	−	5599.40i	−1.37199	−	0.996807i
$317$	7137.47	−	2319.10i	1.26461	−	0.410896i	0.401473	−	0.915871i	$-0.368498\pi$
$317$	7137.47	−	2319.10i	1.26461	−	0.410896i	0.863134	+	0.504975i	$0.168498\pi$
$318$		−	5419.20i		−	0.955641i
$319$	−756.398	−	2327.96i	−0.132759	−	0.408591i
$320$		0			0
$321$	844.205	−	2598.20i	0.146788	−	0.451767i
$322$	3413.67	+	1109.17i	0.590796	+	0.191961i
$323$	−77.6961	−	106.939i	−0.0133843	−	0.0184219i
$324$	18391.2			3.15351
$325$		0			0
$326$	413.258			0.0702093
$327$	−6499.38	−	8945.63i	−1.09913	−	1.51283i
$328$	220.851	+	71.7589i	0.0371783	+	0.0120800i
$329$	−1612.51	+	4962.81i	−0.270215	+	0.831636i
$330$		0			0
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	0.920960	−	0.389658i	$-0.127407\pi$
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	−0.974107	+	0.226087i	$0.927407\pi$
$332$		−	12165.6i		−	2.01107i
$333$	−4585.65	+	1489.97i	−0.754630	+	0.245194i
$334$	543.116	+	394.597i	0.0889760	+	0.0646448i
$335$		0			0
$336$	−8939.52	+	6494.94i	−1.45146	+	1.05455i
$337$	768.117	−	1057.22i	0.124160	−	0.170892i	−0.742412	−	0.669944i	$-0.766318\pi$
$337$	768.117	−	1057.22i	0.124160	−	0.170892i	0.866572	+	0.499052i	$0.166318\pi$
$338$	−760.258	+	1046.40i	−0.122345	+	0.168393i
$339$	−4667.29	+	3390.98i	−0.747765	+	0.543283i
$340$		0			0
$341$	−3261.62	−	2369.70i	−0.517966	−	0.376325i
$342$	−4469.90	+	1452.36i	−0.706739	+	0.229633i
$343$		−	5715.58i		−	0.899744i
$344$	193.332	+	595.016i	0.0303017	+	0.0932590i
$345$		0			0
$346$	−5316.51	+	16362.5i	−0.826061	+	2.54236i
$347$	3177.49	+	1032.43i	0.491576	+	0.159723i	0.544307	−	0.838886i	$-0.316793\pi$
$347$	3177.49	+	1032.43i	0.491576	+	0.159723i	−0.0527312	+	0.998609i	$0.516793\pi$
$348$	7493.94	+	10314.5i	1.15436	+	1.58884i
$349$	−10728.2			−1.64546			−0.822732	−	0.568429i	$-0.807551\pi$
$349$	−10728.2			−1.64546			−0.822732	+	0.568429i	$0.807551\pi$
$350$		0			0
$351$	−4067.75			−0.618576
$352$	−6470.24	−	8905.52i	−0.979730	−	1.34848i
$353$	−7940.38	−	2579.99i	−1.19723	−	0.389005i	−0.358491	−	0.933533i	$-0.616709\pi$
$353$	−7940.38	−	2579.99i	−1.19723	−	0.389005i	−0.838743	+	0.544528i	$0.816709\pi$
$354$	−1710.14	+	5263.27i	−0.256760	+	0.790225i
$355$		0			0
$356$	4315.23	+	13280.9i	0.642435	+	1.97721i
$357$			111.243i			0.0164919i
$358$	−7173.29	+	2330.74i	−1.05899	+	0.344088i
$359$	8253.90	+	5996.81i	1.21344	+	0.881614i	0.995538	−	0.0943571i	$-0.0300795\pi$
$359$	8253.90	+	5996.81i	1.21344	+	0.881614i	0.217899	+	0.975971i	$0.430080\pi$
$360$		0			0
$361$	1378.24	−	1001.35i	0.200939	−	0.145990i
$362$	1329.94	−	1830.50i	0.193094	−	0.265771i
$363$	−2723.13	+	3748.06i	−0.393739	+	0.541935i
$364$	6964.57	−	5060.06i	1.00287	−	0.728624i
$365$		0			0
$366$	23051.9	+	16748.2i	3.29219	+	2.39192i
$367$	7102.49	−	2307.74i	1.01021	−	0.328237i	0.243272	−	0.969958i	$-0.421779\pi$
$367$	7102.49	−	2307.74i	1.01021	−	0.328237i	0.766938	+	0.641721i	$0.221779\pi$
$368$		−	12824.0i		−	1.81657i
$369$	−13.6319	−	41.9548i	−0.00192317	−	0.00591891i
$370$		0			0
$371$	−484.466	+	1491.03i	−0.0677958	+	0.208654i
$372$	19971.2	+	6489.05i	2.78350	+	0.904413i
$373$	−3396.77	−	4675.25i	−0.471523	−	0.648995i	0.505326	−	0.862929i	$-0.331372\pi$
$373$	−3396.77	−	4675.25i	−0.471523	−	0.648995i	−0.976848	+	0.213934i	$0.931372\pi$
$374$	−237.964			−0.0329006
$375$		0			0
$376$	35129.9			4.81831
$377$	−2613.10	−	3596.62i	−0.356980	−	0.491341i
$378$	−4480.00	−	1455.64i	−0.609593	−	0.198069i
$379$	2500.18	−	7694.77i	0.338854	−	1.04289i	−0.625938	−	0.779873i	$-0.715284\pi$
$379$	2500.18	−	7694.77i	0.338854	−	1.04289i	0.964792	−	0.263013i	$-0.0847162\pi$
$380$		0			0
$381$	−1996.18	−	6143.62i	−0.268419	−	0.826108i
$382$			7835.04i			1.04941i
$383$	2012.35	−	653.851i	0.268475	−	0.0872330i	−0.171686	−	0.985152i	$-0.554921\pi$
$383$	2012.35	−	653.851i	0.268475	−	0.0872330i	0.440161	+	0.897919i	$0.354921\pi$
$384$	6964.14	+	5059.75i	0.925488	+	0.672406i
$385$		0			0
$386$	−6600.15	+	4795.29i	−0.870307	+	0.632315i
$387$	69.8590	−	96.1526i	0.00917605	−	0.0126298i
$388$	7315.77	−	10069.3i	0.957222	−	1.31750i
$389$	−5428.83	+	3944.27i	−0.707590	+	0.514094i	−0.882395	−	0.470509i	$-0.844070\pi$
$389$	−5428.83	+	3944.27i	−0.707590	+	0.514094i	0.174805	+	0.984603i	$0.444070\pi$
$390$		0			0
$391$	−104.448	−	75.8857i	−0.0135093	−	0.00981510i
$392$	−15433.2	+	5014.54i	−1.98850	+	0.646103i
$393$			1911.29i			0.245323i
$394$	−511.907	−	1575.49i	−0.0654556	−	0.201452i
$395$		0			0
$396$	−1873.21	+	5765.16i	−0.237708	+	0.731591i
$397$	−6245.42	−	2029.26i	−0.789544	−	0.256538i	−0.113634	−	0.993523i	$-0.536249\pi$
$397$	−6245.42	−	2029.26i	−0.789544	−	0.256538i	−0.675910	+	0.736984i	$0.736249\pi$
$398$	4538.70	+	6246.99i	0.571620	+	0.786767i
$399$	4338.66			0.544372
$400$		0			0
$401$	−10290.4			−1.28149			−0.640744	−	0.767754i	$-0.721374\pi$
$401$	−10290.4			−1.28149			−0.640744	+	0.767754i	$0.721374\pi$
$402$	13832.0	+	19038.1i	1.71612	+	2.36203i
$403$	−6963.87	−	2262.70i	−0.860782	−	0.279685i
$404$	−3916.36	+	12053.3i	−0.482292	+	1.48434i
$405$		0			0
$406$	−1590.88	−	4896.23i	−0.194468	−	0.598511i
$407$			9521.30i			1.15959i
$408$	712.253	−	231.425i	0.0864260	−	0.0280815i
$409$	5384.48	+	3912.06i	0.650967	+	0.472955i	0.863600	−	0.504177i	$-0.168204\pi$
$409$	5384.48	+	3912.06i	0.650967	+	0.472955i	−0.212633	+	0.977132i	$0.568204\pi$
$410$		0			0
$411$	−9197.96	+	6682.71i	−1.10390	+	0.802028i
$412$	18093.4	−	24903.5i	2.16359	−	2.97793i
$413$	941.053	−	1295.25i	0.112121	−	0.154322i
$414$	−3713.73	+	2698.18i	−0.440869	+	0.320310i
$415$		0			0
$416$	−16174.4	−	11751.4i	−1.90629	−	1.38500i
$417$	−4270.07	+	1387.43i	−0.501454	+	0.162932i
$418$			9280.97i			1.08600i
$419$	−1348.17	−	4149.23i	−0.157189	−	0.483778i	0.841187	−	0.540744i	$-0.181857\pi$
$419$	−1348.17	−	4149.23i	−0.157189	−	0.483778i	−0.998376	+	0.0569662i	$0.981857\pi$
$420$		0			0
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	−0.678395	−	0.734697i	$-0.737324\pi$
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	0.980677	−	0.195632i	$-0.0626757\pi$
$422$	−13309.0	−	4324.35i	−1.53524	−	0.498830i
$423$	−3922.62	−	5399.03i	−0.450885	−	0.620590i
$424$	10554.5			1.20889
$425$		0			0
$426$	−22574.0			−2.56740
$427$	−4845.22	−	6668.88i	−0.549126	−	0.755807i
$428$	8374.90	+	2721.17i	0.945832	+	0.307319i
$429$	2084.25	−	6414.67i	0.234566	−	0.721919i
$430$		0			0
$431$	−123.883	−	381.273i	−0.0138451	−	0.0426109i	0.943895	−	0.330245i	$-0.107131\pi$
$431$	−123.883	−	381.273i	−0.0138451	−	0.0426109i	−0.957740	+	0.287634i	$0.907131\pi$
$432$			16829.9i			1.87437i
$433$	−12301.0	+	3996.84i	−1.36524	+	0.443594i	−0.897789	−	0.440425i	$-0.854828\pi$
$433$	−12301.0	+	3996.84i	−1.36524	+	0.443594i	−0.467451	+	0.884019i	$0.654828\pi$
$434$	−6859.93	−	4984.03i	−0.758727	−	0.551247i
$435$		0			0
$436$	28834.9	−	20949.8i	3.16730	−	2.30118i
$437$	−2959.66	+	4073.62i	−0.323981	+	0.445922i
$438$	946.973	−	1303.40i	0.103306	−	0.142189i
$439$	4561.58	−	3314.18i	0.495928	−	0.360313i	−0.311531	−	0.950236i	$-0.600842\pi$
$439$	4561.58	−	3314.18i	0.495928	−	0.360313i	0.807460	+	0.589923i	$0.200842\pi$
$440$		0			0
$441$	2493.95	+	1811.96i	0.269296	+	0.195655i
$442$	−411.042	+	133.556i	−0.0442337	+	0.0143724i
$443$			2827.26i			0.303221i	0.988440	+	0.151611i	$0.0484460\pi$
$443$			2827.26i			0.303221i	−0.988440	+	0.151611i	$0.951554\pi$
$444$	−15325.1	−	47165.7i	−1.63805	−	5.04140i
$445$		0			0
$446$	−5738.76	+	17662.1i	−0.609278	+	1.87517i
$447$	−4327.53	−	1406.10i	−0.457909	−	0.148784i
$448$	−5322.52	−	7325.82i	−0.561306	−	0.772572i
$449$	14913.8			1.56754			0.783769	−	0.621052i	$-0.213294\pi$
$449$	14913.8			1.56754			0.783769	+	0.621052i	$0.213294\pi$
$450$		0			0
$451$	−87.1118			−0.00909520
$452$	−10930.3	−	15044.3i	−1.13743	−	1.56554i
$453$	18197.8	+	5912.83i	1.88744	+	0.613265i
$454$	−8822.07	+	27151.5i	−0.911983	+	2.80679i
$455$		0			0
$456$	−9025.95	−	27779.0i	−0.926927	−	2.85279i
$457$			6570.60i			0.672559i	0.941762	+	0.336280i	$0.109169\pi$
$457$			6570.60i			0.672559i	−0.941762	+	0.336280i	$0.890831\pi$
$458$	3386.82	−	1100.45i	0.345537	−	0.112272i
$459$	137.074	+	99.5901i	0.0139391	+	0.0101274i
$460$		0			0
$461$	11261.5	−	8181.99i	1.13775	−	0.826623i	0.150945	−	0.988542i	$-0.451768\pi$
$461$	11261.5	−	8181.99i	1.13775	−	0.826623i	0.986804	+	0.161919i	$0.0517683\pi$
$462$	4590.97	−	6318.93i	0.462319	−	0.636327i
$463$	6827.02	−	9396.58i	0.685266	−	0.943188i	−0.314716	−	0.949186i	$-0.601909\pi$
$463$	6827.02	−	9396.58i	0.685266	−	0.943188i	0.999982	+	0.00599770i	$0.00190914\pi$
$464$	−14880.7	+	10811.4i	−1.48883	+	1.08170i
$465$		0			0
$466$	−20054.4	−	14570.4i	−1.99357	−	1.44841i
$467$	5393.52	−	1752.46i	0.534437	−	0.173649i	−0.0293500	−	0.999569i	$-0.509344\pi$
$467$	5393.52	−	1752.46i	0.534437	−	0.173649i	0.563787	+	0.825920i	$0.309344\pi$
$468$			11009.7i			1.08744i
$469$	−2103.75	−	6474.69i	−0.207127	−	0.637470i
$470$		0			0
$471$	4198.75	−	12922.4i	0.410761	−	1.26419i
$472$	−10250.8	−	3330.68i	−0.999641	−	0.324803i
$473$	−137.951	−	189.873i	−0.0134101	−	0.0184574i
$474$	−15697.9			−1.52116
$475$		0			0
$476$	−358.575			−0.0345279
$477$	−1178.52	−	1622.09i	−0.113125	−	0.155703i
$478$	32088.2	+	10426.1i	3.07046	+	0.997652i
$479$	−2337.30	+	7193.47i	−0.222952	+	0.686175i	0.775541	+	0.631297i	$0.217477\pi$
$479$	−2337.30	+	7193.47i	−0.222952	+	0.686175i	−0.998493	+	0.0548782i	$0.982523\pi$
$480$		0			0
$481$	5343.77	+	16446.4i	0.506559	+	1.55903i
$482$		−	6483.51i		−	0.612688i
$483$	4030.16	−	1309.48i	0.379666	−	0.123361i
$484$	−12081.3	−	8777.60i	−1.13461	−	0.824342i
$485$		0			0
$486$	13840.0	−	10055.3i	1.29176	−	0.938516i
$487$	2719.55	−	3743.14i	0.253049	−	0.348291i	−0.663527	−	0.748152i	$-0.730941\pi$
$487$	2719.55	−	3743.14i	0.253049	−	0.348291i	0.916576	+	0.399860i	$0.130941\pi$
$488$	−32618.9	+	44896.0i	−3.02579	+	4.16465i
$489$	394.711	−	286.774i	0.0365019	−	0.0265202i
$490$		0			0
$491$	14224.2	+	10334.5i	1.30739	+	0.949874i	0.999999	−	0.00170911i	$-0.000544026\pi$
$491$	14224.2	+	10334.5i	1.30739	+	0.949874i	0.307391	+	0.951583i	$0.400544\pi$
$492$	431.526	−	140.211i	0.0395421	−	0.0128480i
$493$			185.174i			0.0169165i
$494$	5208.89	+	16031.3i	0.474411	+	1.46009i
$495$		0			0
$496$	−9361.68	+	28812.3i	−0.847484	+	2.60829i
$497$	6210.99	+	2018.07i	0.560565	+	0.182139i
$498$	−11783.4	−	16218.5i	−1.06030	−	1.45937i
$499$	2983.65			0.267669			0.133834	−	0.991004i	$-0.457271\pi$
$499$	2983.65			0.267669			0.133834	+	0.991004i	$0.457271\pi$
$500$		0			0
$501$	792.566			0.0706771
$502$	16313.1	+	22453.1i	1.45038	+	1.99628i
$503$	−5406.72	−	1756.75i	−0.479272	−	0.155725i	0.0594106	−	0.998234i	$-0.481078\pi$
$503$	−5406.72	−	1756.75i	−0.479272	−	0.155725i	−0.538683	+	0.842509i	$0.681078\pi$
$504$	−2380.50	+	7326.41i	−0.210388	+	0.647509i
$505$		0			0
$506$	2801.15	+	8621.05i	0.246099	+	0.757416i
$507$			1527.01i			0.133761i
$508$	19803.0	−	6434.40i	1.72956	−	0.561969i
$509$	4078.11	+	2962.92i	0.355126	+	0.258014i	0.751016	−	0.660284i	$-0.229564\pi$
$509$	4078.11	+	2962.92i	0.355126	+	0.258014i	−0.395890	+	0.918298i	$0.629564\pi$
$510$		0			0
$511$	−377.070	+	273.958i	−0.0326431	+	0.0237166i
$512$	7161.86	−	9857.45i	0.618188	−	0.850863i
$513$	3884.17	−	5346.10i	0.334289	−	0.460110i
$514$	−24272.4	+	17634.9i	−2.08290	+	1.51331i
$515$		0			0
$516$	988.978	+	718.535i	0.0843747	+	0.0613018i
$517$	−12533.3	+	4072.32i	−1.06618	+	0.346423i
$518$			20025.5i			1.69859i
$519$	6276.64	+	19317.5i	0.530855	+	1.63380i
$520$		0			0
$521$	5057.33	−	15564.9i	0.425270	−	1.30885i	−0.477466	−	0.878650i	$-0.658445\pi$
$521$	5057.33	−	15564.9i	0.425270	−	1.30885i	0.902736	−	0.430196i	$-0.141555\pi$
$522$	6261.79	+	2034.58i	0.525040	+	0.170596i
$523$	1549.52	+	2132.73i	0.129552	+	0.178313i	0.868865	−	0.495048i	$-0.164850\pi$
$523$	1549.52	+	2132.73i	0.129552	+	0.178313i	−0.739313	+	0.673362i	$0.764850\pi$
$524$	−6160.77			−0.513615
$525$		0			0
$526$	−1415.99			−0.117377
$527$	179.270	+	246.743i	0.0148180	+	0.0203953i
$528$	−26540.0	−	8623.38i	−2.18751	−	0.710766i
$529$	2240.08	−	6894.26i	0.184111	−	0.566636i
$530$		0			0
$531$	632.724	+	1947.33i	0.0517098	+	0.159146i
$532$			13985.0i			1.13971i
$533$	−150.471	+	48.8910i	−0.0122282	+	0.00397318i
$534$	18616.5	+	13525.7i	1.50864	+	1.09609i
$535$		0			0
$536$	−37078.8	+	26939.3i	−2.98799	+	2.17090i
$537$	−5233.97	+	7203.94i	−0.420600	+	0.578907i
$538$	−210.466	+	289.681i	−0.0168658	+	0.0232138i
$539$	4924.81	−	3578.09i	0.393556	−	0.285935i
$540$		0			0
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	0.149573	−	0.988751i	$-0.452210\pi$
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	−0.894137	+	0.447793i	$0.852210\pi$
$542$	−21427.3	+	6962.16i	−1.69812	+	0.551754i
$543$		−	2671.24i		−	0.211112i
$544$	257.334	+	791.992i	0.0202814	+	0.0624198i
$545$		0			0
$546$	4383.67	−	13491.5i	0.343596	−	1.05748i
$547$	5392.13	+	1752.01i	0.421483	+	0.136948i	0.512076	−	0.858940i	$-0.328876\pi$
$547$	5392.13	+	1752.01i	0.421483	+	0.136948i	−0.0905938	+	0.995888i	$0.528876\pi$
$548$	−21540.7	−	29648.2i	−1.67915	−	2.31115i
$549$	10542.2			0.819546
$550$		0			0
$551$	7222.10			0.558388
$552$	−16768.3	−	23079.6i	−1.29295	−	1.77959i
$553$	4319.10	+	1403.36i	0.332128	+	0.107915i
$554$	14338.3	−	44128.7i	1.09959	−	3.38420i
$555$		0			0
$556$	−4472.17	−	13763.9i	−0.341119	−	1.04986i
$557$		−	4968.53i		−	0.377959i	−0.981981	−	0.188980i	$-0.939482\pi$
$557$		−	4968.53i		−	0.377959i	0.981981	−	0.188980i	$-0.0605180\pi$
$558$	10313.5	−	3351.06i	0.782446	−	0.254232i
$559$	−344.852	−	250.549i	−0.0260924	−	0.0189573i
$560$		0			0
$561$	−227.284	+	165.132i	−0.0171051	+	0.0124276i
$562$	−21794.6	+	29997.7i	−1.63586	+	2.25156i
$563$	−6343.47	+	8731.04i	−0.474859	+	0.653587i	−0.977507	−	0.210904i	$-0.932359\pi$
$563$	−6343.47	+	8731.04i	−0.474859	+	0.653587i	0.502648	+	0.864491i	$0.332359\pi$
$564$	55531.7	−	40346.1i	4.14593	−	3.01220i
$565$		0			0
$566$	28666.1	+	20827.1i	2.12885	+	1.54670i
$567$	−8338.37	+	2709.30i	−0.617599	+	0.200670i
$568$		−	43965.3i		−	3.24778i
$569$	876.580	+	2697.84i	0.0645838	+	0.198768i	0.978141	−	0.207941i	$-0.0666762\pi$
$569$	876.580	+	2697.84i	0.0645838	+	0.198768i	−0.913558	+	0.406709i	$0.866676\pi$
$570$		0			0
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	−0.849258	−	0.527978i	$-0.822950\pi$
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	0.997402	+	0.0720377i	$0.0229502\pi$
$572$	20676.7	+	6718.28i	1.51143	+	0.491093i
$573$	5437.01	+	7483.41i	0.396395	+	0.545591i
$574$	−183.216			−0.0133228
$575$		0			0
$576$	11580.7			0.837725
$577$	3188.69	+	4388.86i	0.230064	+	0.316656i	0.908405	−	0.418091i	$-0.137301\pi$
$577$	3188.69	+	4388.86i	0.230064	+	0.316656i	−0.678341	+	0.734747i	$0.737301\pi$
$578$	−24801.6	−	8058.52i	−1.78479	−	0.579914i
$579$	−2976.31	+	9160.15i	−0.213629	+	0.657484i
$580$		0			0
$581$	1792.18	+	5515.75i	0.127972	+	0.393859i
$582$		−	20509.7i		−	1.46075i
$583$	−3765.53	+	1223.50i	−0.267500	+	0.0869159i
$584$	2538.50	+	1844.33i	0.179870	+	0.130683i
$585$		0			0
$586$	−18066.3	+	13126.0i	−1.27357	+	0.925304i
$587$	−12249.4	+	16859.9i	−0.861310	+	1.18549i	0.119946	+	0.992780i	$0.461728\pi$
$587$	−12249.4	+	16859.9i	−0.861310	+	1.18549i	−0.981256	+	0.192711i	$0.938272\pi$
$588$	−18636.9	+	25651.5i	−1.30710	+	1.79907i
$589$	9623.39	−	6991.80i	0.673217	−	0.489121i
$590$		0			0
$591$	−1582.22	−	1149.55i	−0.110125	−	0.0800105i
$592$	68045.4	−	22109.3i	4.72407	−	1.53494i
$593$			8301.64i			0.574886i	0.957798	+	0.287443i	$0.0928052\pi$
$593$			8301.64i			0.574886i	−0.957798	+	0.287443i	$0.907195\pi$
$594$	−3676.15	−	11314.0i	−0.253929	−	0.781515i
$595$		0			0
$596$	4532.36	−	13949.2i	0.311498	−	0.958691i
$597$	8670.02	+	2817.06i	0.594372	+	0.193123i
$598$	9677.03	+	13319.3i	0.661744	+	0.910813i
$599$	−22052.7			−1.50426			−0.752129	−	0.659016i	$-0.770973\pi$
$599$	−22052.7			−1.50426			−0.752129	+	0.659016i	$0.770973\pi$
$600$		0			0
$601$	−4849.47			−0.329141			−0.164571	−	0.986365i	$-0.552624\pi$
$601$	−4849.47			−0.329141			−0.164571	+	0.986365i	$0.552624\pi$
$602$	−290.142	−	399.347i	−0.0196434	−	0.0270368i
$603$	8280.49	+	2690.49i	0.559217	+	0.181700i
$604$	−19059.1	+	58658.0i	−1.28395	+	3.95159i
$605$		0			0
$606$	6453.57	+	19862.1i	0.432605	+	1.33142i
$607$		−	23938.2i		−	1.60070i	−0.599536	−	0.800348i	$-0.704648\pi$
$607$		−	23938.2i		−	1.60070i	0.599536	−	0.800348i	$-0.295352\pi$
$608$	30888.9	−	10036.4i	2.06038	−	0.669458i
$609$	−4917.15	−	3572.52i	−0.327180	−	0.237710i
$610$		0			0
$611$	−19363.6	+	14068.5i	−1.28211	+	0.931507i
$612$	269.548	−	371.001i	0.0178036	−	0.0245046i
$613$	13997.5	−	19265.9i	0.922275	−	1.26940i	−0.0405223	−	0.999179i	$-0.512902\pi$
$613$	13997.5	−	19265.9i	0.922275	−	1.26940i	0.962797	−	0.270224i	$-0.0870978\pi$
$614$	−5848.60	+	4249.26i	−0.384414	+	0.279293i
$615$		0			0
$616$	12306.8	+	8941.40i	0.804959	+	0.584837i
$617$	−26.2199	+	8.51935i	−0.00171081	+	0.000555877i	−0.309872	−	0.950778i	$-0.600286\pi$
$617$	−26.2199	+	8.51935i	−0.00171081	+	0.000555877i	0.308161	+	0.951334i	$0.400286\pi$
$618$		−	50724.8i		−	3.30170i
$619$	−7240.90	−	22285.2i	−0.470172	−	1.44704i	−0.852360	−	0.522956i	$-0.824829\pi$
$619$	−7240.90	−	22285.2i	−0.470172	−	1.44704i	0.382188	−	0.924085i	$-0.375171\pi$
$620$		0			0
$621$	1994.45	−	6138.28i	0.128880	−	0.396651i
$622$	−12428.4	−	4038.23i	−0.801179	−	0.260319i
$623$	−3912.95	−	5385.71i	−0.251636	−	0.346347i
$624$	−50683.2			−3.25153
$625$		0			0
$626$	15318.1			0.978007
$627$	6440.40	+	8864.45i	0.410215	+	0.564612i
$628$	41653.5	+	13534.0i	2.64675	+	0.859980i
$629$	222.583	−	685.039i	0.0141096	−	0.0434249i
$630$		0			0
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	0.969774	−	0.244005i	$-0.0784614\pi$
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	−0.927986	+	0.372614i	$0.878461\pi$
$632$		−	30573.3i		−	1.92427i
$633$	−15712.5	+	5105.30i	−0.986597	+	0.320565i
$634$	32249.4	+	23430.5i	2.02017	+	1.46774i
$635$		0			0
$636$	16684.0	−	12121.7i	1.04020	−	0.755747i
$637$	6498.60	−	8944.56i	0.404213	−	0.556352i
$638$	7642.10	−	10518.4i	0.474222	−	0.652710i
$639$	−6756.92	+	4909.19i	−0.418309	+	0.303920i
$640$		0			0
$641$	−16852.6	−	12244.1i	−1.03844	−	0.754469i	−0.0684575	−	0.997654i	$-0.521808\pi$
$641$	−16852.6	−	12244.1i	−1.03844	−	0.754469i	−0.969980	+	0.243185i	$0.921808\pi$
$642$	13800.6	−	4484.08i	0.848389	−	0.275658i
$643$			29336.6i			1.79926i	0.436657	+	0.899628i	$0.356162\pi$
$643$			29336.6i			1.79926i	−0.436657	+	0.899628i	$0.643838\pi$
$644$	4220.91	+	12990.6i	0.258272	+	0.794879i
$645$		0			0
$646$	216.964	−	667.748i	0.0132142	−	0.0406690i
$647$	−7548.13	−	2452.54i	−0.458652	−	0.149025i	0.0705732	−	0.997507i	$-0.477517\pi$
$647$	−7548.13	−	2452.54i	−0.458652	−	0.149025i	−0.529225	+	0.848482i	$0.677517\pi$
$648$	34693.6	+	47751.6i	2.10323	+	2.89485i
$649$	4043.28			0.244550
$650$		0			0
$651$	−10010.7			−0.602686
$652$	924.374	+	1272.29i	0.0555234	+	0.0764215i
$653$	10350.8	+	3363.18i	0.620304	+	0.201549i	0.602275	−	0.798288i	$-0.294261\pi$
$653$	10350.8	+	3363.18i	0.620304	+	0.201549i	0.0180290	+	0.999837i	$0.494261\pi$
$654$	18149.4	−	55858.0i	1.08516	−	3.33979i
$655$		0			0
$656$	202.281	+	622.558i	0.0120393	+	0.0370530i
$657$		−	596.076i		−	0.0353960i
$658$	−26360.5	+	8565.03i	−1.56176	+	0.507447i
$659$	−23268.1	−	16905.3i	−1.37541	−	0.999295i	−0.997292	−	0.0735377i	$-0.976571\pi$
$659$	−23268.1	−	16905.3i	−1.37541	−	0.999295i	−0.378119	−	0.925757i	$-0.623429\pi$
$660$		0			0
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	−0.447823	−	0.894122i	$-0.647801\pi$
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	0.711976	+	0.702204i	$0.247801\pi$
$662$	3233.60	−	4450.67i	0.189845	−	0.261299i
$663$	−299.916	+	412.799i	−0.0175683	+	0.0241807i
$664$	31587.2	−	22949.4i	1.84612	−	1.34128i
$665$		0			0
$666$	−20719.4	−	15053.5i	−1.20550	−	0.875845i
$667$	6708.57	−	2179.75i	0.389441	−	0.126537i
$668$			2554.72i			0.147972i
$669$	6775.15	+	20851.8i	0.391543	+	1.20505i
$670$		0			0
$671$	6433.04	−	19798.9i	0.370111	−	1.13909i
$672$	−25995.3	−	8446.39i	−1.49225	−	0.484861i
$673$	−6476.14	−	8913.64i	−0.370931	−	0.510543i	0.582222	−	0.813030i	$-0.302183\pi$
$673$	−6476.14	−	8913.64i	−0.370931	−	0.510543i	−0.953154	+	0.302487i	$0.902183\pi$
$674$	6941.20			0.396684
$675$		0			0
$676$	−4922.10			−0.280047
$677$	2816.10	+	3876.03i	0.159869	+	0.220041i	0.881436	−	0.472304i	$-0.156578\pi$
$677$	2816.10	+	3876.03i	0.159869	+	0.220041i	−0.721566	+	0.692345i	$0.756578\pi$
$678$	−29143.3	−	9469.24i	−1.65080	−	0.536378i
$679$	−1833.53	+	5643.02i	−0.103629	+	0.318938i
$680$		0			0
$681$	10415.3	+	32054.9i	0.586071	+	1.80374i
$682$		−	21414.2i		−	1.20233i
$683$	10371.5	−	3369.89i	0.581044	−	0.188793i	−0.00372404	−	0.999993i	$-0.501185\pi$
$683$	10371.5	−	3369.89i	0.581044	−	0.188793i	0.584768	+	0.811200i	$0.301185\pi$
$684$	−14469.6	−	10512.8i	−0.808860	−	0.587671i
$685$		0			0
$686$	24560.9	−	17844.5i	1.36696	−	0.993158i
$687$	2471.19	−	3401.30i	0.137237	−	0.188890i
$688$	−1036.62	+	1426.79i	−0.0574431	+	0.0790636i
$689$	−5817.64	+	4226.76i	−0.321675	+	0.233711i
$690$		0			0
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.960029	−	0.279900i	$-0.0903012\pi$
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.0304648	+	0.999536i	$0.490301\pi$
$692$	−62267.1	+	20231.8i	−3.42058	+	1.11141i
$693$		−	2889.81i		−	0.158405i
$694$	5483.86	+	16877.6i	0.299949	+	0.923148i
$695$		0			0
$696$	−12644.3	+	38915.0i	−0.688620	+	2.11935i
$697$	6.26753	+	2.03644i	0.000340602	+	0.000110668i
$698$	−33494.3	−	46101.0i	−1.81630	−	2.49992i
$699$	−29265.2			−1.58357
$700$		0			0
$701$	−23186.1			−1.24925			−0.624626	−	0.780924i	$-0.714749\pi$
$701$	−23186.1			−1.24925			−0.624626	+	0.780924i	$0.714749\pi$
$702$	−12699.8	−	17479.8i	−0.682799	−	0.939792i
$703$	−26717.6	−	8681.07i	−1.43339	−	0.465737i
$704$	7066.75	−	21749.2i	0.378321	−	1.16435i
$705$		0			0
$706$	−13703.9	−	42176.1i	−0.730526	−	2.24833i
$707$		−	6041.76i		−	0.321392i
$708$	−20029.2	+	6507.88i	−1.06320	+	0.345454i
$709$	−6798.49	−	4939.39i	−0.360117	−	0.261640i	0.392984	−	0.919545i	$-0.371443\pi$
$709$	−6798.49	−	4939.39i	−0.360117	−	0.261640i	−0.753101	+	0.657905i	$0.771443\pi$
$710$		0			0
$711$	−4698.74	+	3413.84i	−0.247843	+	0.180069i
$712$	−26342.6	+	36257.5i	−1.38656	+	1.90844i
$713$	6828.88	−	9399.15i	0.358687	−	0.493690i
$714$	−478.031	+	347.310i	−0.0250558	+	0.0182041i
$715$		0			0
$716$	−23220.8	−	16870.9i	−1.21202	−	0.880581i
$717$	37883.1	−	12309.0i	1.97318	−	0.641125i
$718$			54191.0i			2.81670i
$719$	2318.10	+	7134.38i	0.120237	+	0.370052i	0.993003	−	0.118087i	$-0.0376760\pi$
$719$	2318.10	+	7134.38i	0.120237	+	0.370052i	−0.872766	+	0.488139i	$0.837676\pi$
$720$		0			0
$721$	−4534.70	+	13956.4i	−0.234232	+	0.720891i
$722$	8605.94	+	2796.24i	0.443601	+	0.144135i
$723$	−4499.14	−	6192.53i	−0.231431	−	0.318538i
$724$	8610.36			0.441991
$725$		0			0
$726$	−24607.9			−1.25797
$727$	−1475.79	−	2031.25i	−0.0752876	−	0.103624i	0.769712	−	0.638391i	$-0.220400\pi$
$727$	−1475.79	−	2031.25i	−0.0752876	−	0.103624i	−0.845000	+	0.534766i	$0.820400\pi$
$728$	26276.2	+	8537.65i	1.33772	+	0.434652i
$729$	−1350.34	+	4155.92i	−0.0686044	+	0.211143i
$730$		0			0
$731$	5.48656	+	16.8859i	0.000277603	+	0.000854375i
$732$			108432.i			5.47508i
$733$	−2117.61	+	688.054i	−0.106706	+	0.0346710i	−0.361884	−	0.932223i	$-0.617866\pi$
$733$	−2117.61	+	688.054i	−0.106706	+	0.0346710i	0.255177	+	0.966894i	$0.417866\pi$
$734$	32091.3	+	23315.7i	1.61378	+	1.17248i
$735$		0			0
$736$	25663.4	−	18645.6i	1.28528	−	0.933811i
$737$	10105.8	−	13909.4i	0.505090	−	0.695197i
$738$	137.727	−	189.565i	0.00686966	−	0.00945527i
$739$	−6654.13	+	4834.51i	−0.331226	+	0.240650i	−0.740951	−	0.671559i	$-0.765625\pi$
$739$	−6654.13	+	4834.51i	−0.331226	+	0.240650i	0.409724	+	0.912209i	$0.365625\pi$
$740$		0			0
$741$	16099.8	+	11697.2i	0.798167	+	0.579902i
$742$	−7919.78	+	2573.29i	−0.391839	+	0.127316i
$743$			449.577i			0.0221984i	0.999938	+	0.0110992i	$0.00353305\pi$
$743$			449.577i			0.0221984i	−0.999938	+	0.0110992i	$0.996467\pi$
$744$	20825.7	+	64095.0i	1.02622	+	3.15838i
$745$		0			0
$746$	9485.39	−	29193.0i	0.465529	−	1.43275i
$747$	−7054.10	−	2292.02i	−0.345510	−	0.112263i
$748$	−532.277	−	732.617i	−0.0260187	−	0.0358117i
$749$	−4197.95			−0.204793
$750$		0			0
$751$	4588.83			0.222968			0.111484	−	0.993766i	$-0.464440\pi$
$751$	4588.83			0.222968			0.111484	+	0.993766i	$0.464440\pi$
$752$	58206.9	+	80115.0i	2.82259	+	3.88496i
$753$	31162.0	+	10125.1i	1.50811	+	0.490014i
$754$	7297.02	−	22457.9i	0.352443	−	1.08471i
$755$		0			0
$756$	−5539.39	−	17048.5i	−0.266489	−	0.820169i
$757$			3857.39i			0.185204i	0.995703	+	0.0926019i	$0.0295184\pi$
$757$			3857.39i			0.185204i	−0.995703	+	0.0926019i	$0.970482\pi$
$758$	40871.6	−	13280.0i	1.95847	−	0.636346i
$759$	8657.89	+	6290.33i	0.414047	+	0.300823i
$760$		0			0
$761$	1652.00	−	1200.25i	0.0786924	−	0.0571734i	−0.547743	−	0.836646i	$-0.684513\pi$
$761$	1652.00	−	1200.25i	0.0786924	−	0.0571734i	0.626436	+	0.779473i	$0.284513\pi$
$762$	20168.0	−	27758.8i	0.958804	−	1.31968i
$763$	−9987.19	+	13746.2i	−0.473867	+	0.652222i
$764$	−24121.7	+	17525.4i	−1.14227	+	0.829904i
$765$		0			0
$766$	9092.43	+	6606.03i	0.428881	+	0.311600i
$767$	6984.08	−	2269.27i	0.328788	−	0.106830i
$768$		−	1419.86i		−	0.0667121i
$769$	−2316.48	−	7129.41i	−0.108628	−	0.334321i	0.881937	−	0.471367i	$-0.156239\pi$
$769$	−2316.48	−	7129.41i	−0.108628	−	0.334321i	−0.990565	+	0.137046i	$0.956239\pi$
$770$		0			0
$771$	−10945.5	+	33686.9i	−0.511276	+	1.57355i
$772$	−29526.4	−	9593.70i	−1.37653	−	0.447260i
$773$	6894.08	+	9488.89i	0.320780	+	0.441516i	0.938705	−	0.344721i	$-0.112027\pi$
$773$	6894.08	+	9488.89i	0.320780	+	0.441516i	−0.617925	+	0.786237i	$0.712027\pi$
$774$	631.291			0.0293169
$775$		0			0
$776$	39944.8			1.84786
$777$	13896.4	+	19126.7i	0.641609	+	0.883099i
$778$	−33898.5	−	11014.3i	−1.56211	−	0.507560i
$779$	79.4245	−	244.443i	0.00365299	−	0.0112427i
$780$		0			0
$781$	5096.54	+	15685.5i	0.233506	+	0.718659i
$782$		−	685.751i		−	0.0313586i
$783$	−8804.13	+	2860.63i	−0.401831	+	0.130563i
$784$	−37007.2	−	26887.3i	−1.68582	−	1.22482i
$785$		0			0
$786$	−8213.16	+	5967.21i	−0.372715	+	0.270793i
$787$	4846.71	−	6670.93i	0.219526	−	0.302151i	−0.685023	−	0.728521i	$-0.740208\pi$
$787$	4846.71	−	6670.93i	0.219526	−	0.302151i	0.904549	+	0.426370i	$0.140208\pi$
$788$	3705.40	−	5100.05i	0.167512	−	0.230561i
$789$	−1352.44	+	982.606i	−0.0610243	+	0.0443368i
$790$		0			0
$791$	7171.93	+	5210.71i	0.322382	+	0.234225i
$792$	−18502.5	+	6011.82i	−0.830123	+	0.269723i
$793$		−	37809.7i		−	1.69314i
$794$	−10778.6	−	33173.2i	−0.481762	−	1.48271i
$795$		0			0
$796$	−9080.37	+	27946.5i	−0.404328	+	1.24439i
$797$	−13095.1	−	4254.84i	−0.581996	−	0.189102i	0.00319879	−	0.999995i	$-0.498982\pi$
$797$	−13095.1	−	4254.84i	−0.581996	−	0.189102i	−0.585194	+	0.810893i	$0.698982\pi$
$798$	13545.6	+	18644.0i	0.600890	+	0.827055i
$799$	996.948			0.0441420
$800$		0			0
$801$	8513.78			0.375555
$802$	−32127.4	−	44219.6i	−1.41454	−	1.94694i
$803$	−1119.46	−	363.736i	−0.0491968	−	0.0159850i
$804$	−27673.1	+	85169.0i	−1.21387	+	3.73592i
$805$		0			0
$806$	−12018.6	−	36989.3i	−0.525231	−	1.61649i
$807$			422.730i			0.0184397i
$808$	−38683.5	+	12569.0i	−1.68426	+	0.547248i
$809$	−29901.2	−	21724.5i	−1.29947	−	0.944119i	−0.299518	−	0.954091i	$-0.596826\pi$
$809$	−29901.2	−	21724.5i	−1.29947	−	0.944119i	−0.999950	+	0.00997139i	$0.996826\pi$
$810$		0			0
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	−0.299562	−	0.954077i	$-0.596841\pi$
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	0.814811	+	0.579726i	$0.196841\pi$
$812$	11515.5	−	15849.7i	0.497677	−	0.684994i
$813$	−15634.4	+	21518.9i	−0.674443	+	0.928291i
$814$	−40914.7	+	29726.3i	−1.76174	+	1.27998i
$815$		0			0
$816$	1707.91	+	1240.87i	0.0732707	+	0.0532343i
$817$	658.577	−	213.985i	0.0282016	−	0.00916325i
$818$			35351.8i			1.51106i
$819$	−1621.89	−	4991.65i	−0.0691981	−	0.212970i
$820$		0			0
$821$	−11760.0	+	36193.6i	−0.499911	+	1.53857i	0.309249	+	0.950981i	$0.399922\pi$
$821$	−11760.0	+	36193.6i	−0.499911	+	1.53857i	−0.809160	+	0.587588i	$0.800078\pi$
$822$	−57433.6	−	18661.3i	−2.43701	−	0.791834i
$823$	−2414.36	−	3323.08i	−0.102259	−	0.140748i	0.754821	−	0.655931i	$-0.227724\pi$
$823$	−2414.36	−	3323.08i	−0.102259	−	0.140748i	−0.857080	+	0.515183i	$0.827724\pi$
$824$	98792.0			4.17668
$825$		0			0
$826$	8503.95			0.358221
$827$	9865.62	+	13578.9i	0.414826	+	0.570959i	0.964387	−	0.264494i	$-0.0852051\pi$
$827$	9865.62	+	13578.9i	0.414826	+	0.570959i	−0.549561	+	0.835453i	$0.685205\pi$
$828$	−16613.7	−	5398.12i	−0.697302	−	0.226567i
$829$	3997.64	−	12303.5i	0.167483	−	0.515461i	−0.831727	−	0.555184i	$-0.812648\pi$
$829$	3997.64	−	12303.5i	0.167483	−	0.515461i	0.999211	+	0.0397237i	$0.0126478\pi$
$830$		0			0
$831$	−16927.7	−	52098.0i	−0.706636	−	2.17480i
$832$		−	41534.3i		−	1.73070i
$833$	−437.977	+	142.307i	−0.0182173	+	0.00591915i
$834$	−19293.5	−	14017.6i	−0.801056	−	0.582001i
$835$		0			0
$836$	−28573.2	+	20759.7i	−1.18209	+	0.858837i
$837$	−8962.02	+	12335.2i	−0.370099	+	0.509397i
$838$	13620.9	−	18747.5i	0.561486	−	0.772819i
$839$	34205.0	−	24851.4i	1.40750	−	1.02261i	0.413815	−	0.910361i	$-0.364196\pi$
$839$	34205.0	−	24851.4i	1.40750	−	1.02261i	0.993681	−	0.112244i	$-0.0358040\pi$
$840$		0			0
$841$	11546.1	+	8388.71i	0.473413	+	0.343955i
$842$	42686.0	−	13869.5i	1.74710	−	0.567666i
$843$			43775.5i			1.78850i
$844$	−16456.2	−	50646.9i	−0.671144	−	2.06557i
$845$		0			0
$846$	10953.8	−	33712.4i	0.445154	−	1.37004i
$847$	6770.60	+	2199.90i	0.274664	+	0.0892438i
$848$	17487.8	+	24069.9i	0.708176	+	0.974720i
$849$	41832.3			1.69103
$850$		0			0
$851$	−27437.9			−1.10524
$852$	−50493.5	−	69498.3i	−2.03037	−	2.79457i
$853$	−27107.3	−	8807.70i	−1.08809	−	0.353540i	−0.290579	−	0.956851i	$-0.593848\pi$
$853$	−27107.3	−	8807.70i	−1.08809	−	0.353540i	−0.797506	+	0.603310i	$0.793848\pi$
$854$	13530.2	−	41641.6i	0.542146	−	1.66855i
$855$		0			0
$856$	8733.23	+	26878.1i	0.348710	+	1.07322i
$857$			4999.42i			0.199273i	0.995024	+	0.0996366i	$0.0317680\pi$
$857$			4999.42i			0.199273i	−0.995024	+	0.0996366i	$0.968232\pi$
$858$	34072.2	−	11070.7i	1.35572	−	0.440499i
$859$	20283.7	+	14737.0i	0.805669	+	0.585353i	0.912572	−	0.408916i	$-0.134093\pi$
$859$	20283.7	+	14737.0i	0.805669	+	0.585353i	−0.106902	+	0.994270i	$0.534093\pi$
$860$		0			0
$861$	−174.994	+	127.140i	−0.00692656	+	0.00503244i
$862$	1251.63	−	1722.72i	0.0494554	−	0.0680695i
$863$	−2647.71	+	3644.26i	−0.104437	+	0.143745i	−0.858037	−	0.513588i	$-0.828316\pi$
$863$	−2647.71	+	3644.26i	−0.104437	+	0.143745i	0.753600	+	0.657334i	$0.228316\pi$
$864$	−33679.9	+	24469.9i	−1.32617	+	0.963522i
$865$		0			0
$866$	−55579.9	−	40381.2i	−2.18093	−	1.58454i
$867$	−29280.6	+	9513.83i	−1.14697	+	0.372672i
$868$		−	32267.9i		−	1.26180i
$869$	3544.12	+	10907.7i	0.138350	+	0.425797i
$870$		0			0
$871$	9649.46	−	29698.0i	0.375384	−	1.15531i
$872$	108789.	+	35347.8i	4.22485	+	1.37274i
$873$	−4460.27	−	6139.03i	−0.172918	−	0.238001i
$874$	−26745.4			−1.03510
$875$		0			0
$876$	6130.94			0.236467
$877$	−5972.92	−	8221.02i	−0.229979	−	0.316538i	0.678395	−	0.734697i	$-0.262676\pi$
$877$	−5972.92	−	8221.02i	−0.229979	−	0.316538i	−0.908374	+	0.418159i	$0.862676\pi$
$878$	28483.3	+	9254.78i	1.09483	+	0.355733i
$879$	−8146.95	+	25073.7i	−0.312616	+	0.962134i
$880$		0			0
$881$	−10338.8	−	31819.5i	−0.395372	−	1.21683i	−0.928672	−	0.370903i	$-0.879048\pi$
$881$	−10338.8	−	31819.5i	−0.395372	−	1.21683i	0.533300	−	0.845926i	$-0.320952\pi$
$882$			16374.0i			0.625105i
$883$	14056.2	−	4567.13i	0.535706	−	0.174061i	−0.0286552	−	0.999589i	$-0.509122\pi$
$883$	14056.2	−	4567.13i	0.535706	−	0.174061i	0.564361	+	0.825528i	$0.309122\pi$
$884$	−1330.60	−	966.734i	−0.0506253	−	0.0367814i
$885$		0			0
$886$	−12149.2	+	8826.93i	−0.460678	+	0.334702i
$887$	−9066.41	+	12478.8i	−0.343202	+	0.472377i	−0.945373	−	0.325990i	$-0.894302\pi$
$887$	−9066.41	+	12478.8i	−0.343202	+	0.472377i	0.602171	+	0.798367i	$0.294302\pi$
$888$	93553.0	−	128765.i	3.53540	−	4.86606i
$889$	−8030.58	+	5834.56i	−0.302966	+	0.220118i
$890$		0			0
$891$	−17913.1	−	13014.7i	−0.673527	−	0.489346i
$892$	−67212.5	+	21838.7i	−2.52292	+	0.819745i
$893$		−	38882.6i		−	1.45706i
$894$	−7468.65	−	22986.2i	−0.279406	−	0.859924i
$895$		0			0
$896$	4087.56	−	12580.2i	0.152406	−	0.469057i
$897$	18485.4	+	6006.29i	0.688084	+	0.223572i
$898$	46562.1	+	64087.2i	1.73028	+	2.38153i
$899$	−16663.7			−0.618203
$900$		0			0
$901$	299.525			0.0110750
$902$	−271.970	−	374.335i	−0.0100395	−	0.0138182i
$903$	−554.242	−	180.084i	−0.0204253	−	0.00663657i
$904$	18442.3	−	56759.7i	0.678521	−	2.08827i
$905$		0			0
$906$	31406.6	+	96659.6i	1.15167	+	3.54448i
$907$			43594.8i			1.59596i	0.602681	+	0.797982i	$0.294099\pi$
$907$			43594.8i			1.59596i	−0.602681	+	0.797982i	$0.705901\pi$
$908$	−103324.	+	33572.1i	−3.77636	+	1.22701i
$909$	6251.13	+	4541.71i	0.228093	+	0.165719i
$910$		0			0
$911$	42130.2	−	30609.4i	1.53220	−	1.11321i	0.577205	−	0.816599i	$-0.304143\pi$
$911$	42130.2	−	30609.4i	1.53220	−	1.11321i	0.954998	−	0.296612i	$-0.0958568\pi$
$912$	48395.9	−	66611.3i	1.75718	−	2.41855i
$913$	−8609.06	+	11849.4i	−0.312068	+	0.429525i
$914$	−28235.0	+	20514.0i	−1.02181	+	0.742386i
$915$		0			0
$916$	10963.6	+	7965.50i	0.395466	+	0.287323i
$917$	2793.22	−	907.572i	0.100589	−	0.0326834i
$918$			899.960i			0.0323563i
$919$	−4485.22	−	13804.1i	−0.160994	−	0.495490i	0.837724	−	0.546093i	$-0.183886\pi$
$919$	−4485.22	−	13804.1i	−0.160994	−	0.495490i	−0.998719	+	0.0506033i	$0.983886\pi$
$920$		0			0
$921$	−2637.41	+	8117.11i	−0.0943600	+	0.290410i
$922$	70318.9	+	22848.0i	2.51175	+	0.816116i
$923$	17606.8	+	24233.7i	0.627882	+	0.864206i
$924$	29723.1			1.05824
$925$		0			0
$926$	61693.3			2.18938
$927$	−11031.2	−	15183.1i	−0.390843	−	0.537949i
$928$	−43271.6	−	14059.8i	−1.53067	−	0.497345i
$929$	−8814.66	+	27128.7i	−0.311302	+	0.958089i	0.665948	+	0.745998i	$0.268027\pi$
$929$	−8814.66	+	27128.7i	−0.311302	+	0.958089i	−0.977250	+	0.212091i	$0.931973\pi$
$930$		0			0
$931$	5550.21	+	17081.8i	0.195382	+	0.601324i
$932$		−	94332.2i		−	3.31540i
$933$	−14672.9	+	4767.51i	−0.514865	+	0.167290i
$934$	24369.6	+	17705.6i	0.853746	+	0.620283i
$935$		0			0
$936$	−28585.8	+	20768.8i	−0.998245	+	0.725267i
$937$	16214.1	−	22316.8i	0.565306	−	0.778077i	−0.426683	−	0.904401i	$-0.640318\pi$
$937$	16214.1	−	22316.8i	0.565306	−	0.778077i	0.991989	+	0.126324i	$0.0403179\pi$
$938$	21254.8	−	29254.7i	0.739866	−	1.01834i
$939$	14630.6	−	10629.7i	0.508468	−	0.369423i
$940$		0			0
$941$	2094.39	+	1521.66i	0.0725560	+	0.0527150i	0.623472	−	0.781846i	$-0.285722\pi$
$941$	2094.39	+	1521.66i	0.0725560	+	0.0527150i	−0.550916	+	0.834561i	$0.685722\pi$
$942$	68638.8	−	22302.1i	2.37407	−	0.771382i
$943$		−	251.034i		−	0.00866892i
$944$	−9388.85	−	28895.9i	−0.323709	−	0.996273i
$945$		0			0
$946$	385.224	−	1185.60i	0.0132397	−	0.0407475i
$947$	−22028.6	−	7157.52i	−0.755895	−	0.245605i	−0.0943789	−	0.995536i	$-0.530087\pi$
$947$	−22028.6	−	7157.52i	−0.755895	−	0.245605i	−0.661516	+	0.749931i	$0.730087\pi$
$948$	−35113.0	−	48328.9i	−1.20297	−	1.65575i
$949$	−2137.83			−0.0731263
$950$		0			0
$951$	47061.3			1.60470
$952$	−676.423	−	931.016i	−0.0230284	−	0.0316958i
$953$	40474.6	+	13151.0i	1.37576	+	0.447012i	0.901274	−	0.433250i	$-0.142633\pi$
$953$	40474.6	+	13151.0i	1.37576	+	0.447012i	0.474488	+	0.880262i	$0.342633\pi$
$954$	3290.99	−	10128.6i	0.111687	−	0.343738i
$955$		0			0
$956$	39676.1	+	122110.i	1.34228	+	4.13110i
$957$		−	15349.5i		−	0.518473i
$958$	−38208.8	+	12414.8i	−1.28859	+	0.418689i
$959$	14133.9	+	10268.9i	0.475921	+	0.345777i
$960$		0			0
$961$	1897.20	−	1378.40i	0.0636838	−	0.0462690i
$962$	−53989.6	+	74310.2i	−1.80945	+	2.49050i
$963$	3155.68	−	4343.42i	0.105597	−	0.145342i
$964$	19960.7	−	14502.3i	0.666899	−	0.484531i
$965$		0			0
$966$	18209.5	+	13230.0i	0.606503	+	0.440651i
$967$	−28547.0	+	9275.49i	−0.949339	+	0.308459i	−0.742447	−	0.669905i	$-0.766335\pi$
$967$	−28547.0	+	9275.49i	−0.949339	+	0.308459i	−0.206892	+	0.978364i	$0.566335\pi$
$968$		−	47926.6i		−	1.59134i
$969$	−256.147	−	788.339i	−0.00849187	−	0.0261353i
$970$		0			0
$971$	−2208.86	+	6798.18i	−0.0730028	+	0.224680i	−0.980900	−	0.194514i	$-0.937687\pi$
$971$	−2208.86	+	6798.18i	−0.0730028	+	0.224680i	0.907897	+	0.419193i	$0.137687\pi$
$972$	61914.4	+	20117.2i	2.04311	+	0.663848i
$973$	4055.26	+	5581.59i	0.133613	+	0.183903i
$974$	24575.6			0.808474
$975$		0			0
$976$	−156434.			−5.13045
$977$	−27565.5	−	37940.6i	−0.902658	−	1.24240i	−0.969612	−	0.244646i	$-0.921328\pi$
$977$	−27565.5	−	37940.6i	−0.902658	−	1.24240i	0.0669543	−	0.997756i	$-0.478672\pi$
$978$	2464.64	+	800.810i	0.0805833	+	0.0261831i
$979$	5195.25	−	15989.3i	0.169603	−	0.521983i
$980$		0			0
$981$	−6714.97	−	20666.5i	−0.218545	−	0.672612i
$982$			93388.9i			3.03479i
$983$	58296.8	−	18941.8i	1.89154	−	0.614597i	0.913225	−	0.407456i	$-0.133584\pi$
$983$	58296.8	−	18941.8i	1.89154	−	0.614597i	0.978311	−	0.207142i	$-0.0664161\pi$
$984$	1178.09	+	855.930i	0.0381667	+	0.0277297i
$985$		0			0
$986$	−795.727	+	578.130i	−0.0257009	+	0.0186728i
$987$	−19233.8	+	26473.1i	−0.620283	+	0.853747i
$988$	−37704.2	+	51895.3i	−1.21410	+	1.67106i
$989$	547.165	−	397.539i	0.0175924	−	0.0127816i
$990$		0			0
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	0.369441	−	0.929254i	$-0.379549\pi$
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	−0.769609	+	0.638515i	$0.779549\pi$
$992$	−71270.6	+	23157.2i	−2.28109	+	0.741172i
$993$		−	6494.83i		−	0.207560i
$994$	10719.2	+	32990.3i	0.342045	+	1.05270i
$995$		0			0
$996$	23574.5	−	72554.9i	0.749987	−	2.30822i
$997$	20453.7	+	6645.80i	0.649723	+	0.211108i	0.615292	−	0.788299i	$-0.289038\pi$
$997$	20453.7	+	6645.80i	0.649723	+	0.211108i	0.0344311	+	0.999407i	$0.489038\pi$
$998$	9315.21	+	12821.3i	0.295459	+	0.406664i
$999$	36008.7			1.14041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.4.e.b.74.14		56
5.2	odd	4		125.4.d.a.51.1		28
5.3	odd	4		25.4.d.a.11.7	✓	28
5.4	even	2	inner	125.4.e.b.74.1		56
15.8	even	4		225.4.h.b.136.1		28
25.3	odd	20		625.4.a.c.1.1		14
25.9	even	10	inner	125.4.e.b.49.14		56
25.12	odd	20		125.4.d.a.76.1		28
25.13	odd	20		25.4.d.a.16.7	yes	28
25.16	even	5	inner	125.4.e.b.49.1		56
25.22	odd	20		625.4.a.d.1.14		14
75.38	even	20		225.4.h.b.91.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.7	✓	28	5.3	odd	4
25.4.d.a.16.7	yes	28	25.13	odd	20
125.4.d.a.51.1		28	5.2	odd	4
125.4.d.a.76.1		28	25.12	odd	20
125.4.e.b.49.1		56	25.16	even	5	inner
125.4.e.b.49.14		56	25.9	even	10	inner
125.4.e.b.74.1		56	5.4	even	2	inner
125.4.e.b.74.14		56	1.1	even	1	trivial
225.4.h.b.91.1		28	75.38	even	20
225.4.h.b.136.1		28	15.8	even	4
625.4.a.c.1.1		14	25.3	odd	20
625.4.a.d.1.14		14	25.22	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)

\(f(q)\)	\(=\)	\(q+(3.12208 + 4.29718i) q^{2} +(5.96393 + 1.93780i) q^{3} +(-6.24620 + 19.2238i) q^{4} +(10.2928 + 31.6780i) q^{6} -9.63602i q^{7} +(-61.6963 + 20.0464i) q^{8} +(9.96993 + 7.24358i) q^{9} +O(q^{10})\)	\(q+(3.12208 + 4.29718i) q^{2} +(5.96393 + 1.93780i) q^{3} +(-6.24620 + 19.2238i) q^{4} +(10.2928 + 31.6780i) q^{6} -9.63602i q^{7} +(-61.6963 + 20.0464i) q^{8} +(9.96993 + 7.24358i) q^{9} +(19.6877 - 14.3039i) q^{11} +(-74.5038 + 102.546i) q^{12} +(25.9791 - 35.7572i) q^{13} +(41.4077 - 30.0844i) q^{14} +(-147.942 - 107.486i) q^{16} +(-1.75088 + 0.568894i) q^{17} +65.4576i q^{18} +(22.1878 + 68.2870i) q^{19} +(18.6727 - 57.4685i) q^{21} +(122.933 + 39.9434i) q^{22} +(41.2202 + 56.7348i) q^{23} -406.798 q^{24} +234.764 q^{26} +(-54.0962 - 74.4571i) q^{27} +(185.241 + 60.1885i) q^{28} +(31.0824 - 95.6617i) q^{29} +(-51.1943 - 157.560i) q^{31} -452.340i q^{32} +(145.134 - 47.1569i) q^{33} +(-7.91102 - 5.74769i) q^{34} +(-201.524 + 146.415i) q^{36} +(-229.974 + 316.532i) q^{37} +(-224.169 + 308.542i) q^{38} +(224.228 - 162.911i) q^{39} +(-2.89600 - 2.10407i) q^{41} +(305.250 - 99.1818i) q^{42} -9.64426i q^{43} +(152.003 + 467.818i) q^{44} +(-115.107 + 354.261i) q^{46} +(-515.027 - 167.342i) q^{47} +(-674.027 - 927.719i) q^{48} +250.147 q^{49} -11.5445 q^{51} +(525.119 + 722.765i) q^{52} +(-154.735 - 50.2766i) q^{53} +(151.062 - 464.922i) q^{54} +(193.167 + 594.507i) q^{56} +450.254i q^{57} +(508.117 - 165.097i) q^{58} +(134.417 + 97.6599i) q^{59} +(692.078 - 502.824i) q^{61} +(517.230 - 711.905i) q^{62} +(69.7993 - 96.0704i) q^{63} +(760.253 - 552.356i) q^{64} +(655.762 + 476.439i) q^{66} +(671.926 - 218.322i) q^{67} -37.2120i q^{68} +(135.894 + 418.239i) q^{69} +(-209.430 + 644.559i) q^{71} +(-760.316 - 247.041i) q^{72} +(-28.4306 - 39.1313i) q^{73} -2078.19 q^{74} -1451.33 q^{76} +(-137.833 - 189.711i) q^{77} +(1400.12 + 454.925i) q^{78} +(-145.637 + 448.225i) q^{79} +(-281.164 - 865.334i) q^{81} -19.0137i q^{82} +(-572.410 + 185.987i) q^{83} +(988.132 + 717.920i) q^{84} +(41.4431 - 30.1102i) q^{86} +(370.746 - 510.288i) q^{87} +(-927.915 + 1277.17i) q^{88} +(558.915 - 406.075i) q^{89} +(-344.557 - 250.335i) q^{91} +(-1348.13 + 438.034i) q^{92} -1038.88i q^{93} +(-888.856 - 2735.62i) q^{94} +(876.544 - 2697.72i) q^{96} +(-585.617 - 190.279i) q^{97} +(780.980 + 1074.93i) q^{98} +299.896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9}+O(q^{10}) \) 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9	\( 56 q + 62 q^{4} + 2 q^{6} + 68 q^{9} - 178 q^{11} + 34 q^{14} - 414 q^{16} + 230 q^{19} - 288 q^{21} - 1560 q^{24} + 1172 q^{26} + 10 q^{29} - 1278 q^{31} + 1554 q^{34} + 1346 q^{36} + 2266 q^{39} + 682 q^{41} - 1096 q^{44} - 2478 q^{46} - 2688 q^{49} + 4012 q^{51} - 3230 q^{54} - 5820 q^{56} + 3810 q^{59} + 2782 q^{61} + 7192 q^{64} + 7264 q^{66} - 5374 q^{69} - 7438 q^{71} - 9696 q^{74} + 7040 q^{76} - 1550 q^{79} - 7424 q^{81} + 15224 q^{84} + 7782 q^{86} + 10150 q^{89} + 752 q^{91} - 7146 q^{94} - 15508 q^{96} - 13144 q^{99}+O(q^{100}) \) 56 * q + 62 * q^4 + 2 * q^6 + 68 * q^9 - 178 * q^11 + 34 * q^14 - 414 * q^16 + 230 * q^19 - 288 * q^21 - 1560 * q^24 + 1172 * q^26 + 10 * q^29 - 1278 * q^31 + 1554 * q^34 + 1346 * q^36 + 2266 * q^39 + 682 * q^41 - 1096 * q^44 - 2478 * q^46 - 2688 * q^49 + 4012 * q^51 - 3230 * q^54 - 5820 * q^56 + 3810 * q^59 + 2782 * q^61 + 7192 * q^64 + 7264 * q^66 - 5374 * q^69 - 7438 * q^71 - 9696 * q^74 + 7040 * q^76 - 1550 * q^79 - 7424 * q^81 + 15224 * q^84 + 7782 * q^86 + 10150 * q^89 + 752 * q^91 - 7146 * q^94 - 15508 * q^96 - 13144 * q^99

Introduction

L-functions

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