LMFDB - Embedded newform 250.4.d.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(51,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.d (of order $5$, 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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 135 x^{14} + 7296 x^{12} + 200295 x^{10} + 2912021 x^{8} + 20937420 x^{6} + 57578496 x^{4} + \cdots + 952576 $ x^16 + 135x^14 + 7296x^12 + 200295x^10 + 2912021x^8 + 20937420x^6 + 57578496x^4 + 16724160*x^2 + 952576
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.2
Root			$-2.36461i$ of defining polynomial
Character	$\chi$	$=$	250.101
Dual form			250.4.d.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.618034 + 1.90211i) q^{2} +(-3.55790 - 2.58496i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(7.11579 - 5.16993i) q^{6} -32.4633 q^{7} +(6.47214 - 4.70228i) q^{8} +(-2.36687 - 7.28447i) q^{9} +(-13.6751 + 42.0875i) q^{11} +(5.43598 + 16.7302i) q^{12} +(6.12486 + 18.8504i) q^{13} +(20.0634 - 61.7488i) q^{14} +(4.94427 + 15.2169i) q^{16} +(66.6454 - 48.4207i) q^{17} +15.3187 q^{18} +(-8.36319 + 6.07621i) q^{19} +(115.501 + 83.9163i) q^{21} +(-71.6036 - 52.0231i) q^{22} +(60.0803 - 184.908i) q^{23} -35.1824 q^{24} -39.6409 q^{26} +(-47.1019 + 144.965i) q^{27} +(105.053 + 76.3257i) q^{28} +(159.317 + 115.751i) q^{29} +(68.1740 - 49.5313i) q^{31} -32.0000 q^{32} +(157.449 - 114.394i) q^{33} +(50.9126 + 156.693i) q^{34} +(-9.46747 + 29.1379i) q^{36} +(70.9588 + 218.389i) q^{37} +(-6.38891 - 19.6630i) q^{38} +(26.9359 - 82.9003i) q^{39} +(-6.39296 - 19.6755i) q^{41} +(-231.002 + 167.833i) q^{42} +36.8678 q^{43} +(143.207 - 104.046i) q^{44} +(314.584 + 228.559i) q^{46} +(343.561 + 249.612i) q^{47} +(21.7439 - 66.9209i) q^{48} +710.864 q^{49} -362.283 q^{51} +(24.4995 - 75.4016i) q^{52} +(-4.23242 - 3.07504i) q^{53} +(-246.629 - 179.186i) q^{54} +(-210.107 + 152.651i) q^{56} +45.4621 q^{57} +(-318.635 + 231.502i) q^{58} +(16.0299 + 49.3350i) q^{59} +(-38.3804 + 118.123i) q^{61} +(52.0803 + 160.287i) q^{62} +(76.8363 + 236.478i) q^{63} +(19.7771 - 60.8676i) q^{64} +(120.280 + 370.185i) q^{66} +(-630.360 + 457.984i) q^{67} -329.513 q^{68} +(-691.740 + 502.578i) q^{69} +(-496.268 - 360.560i) q^{71} +(-49.5723 - 36.0164i) q^{72} +(280.603 - 863.608i) q^{73} -459.255 q^{74} +41.3499 q^{76} +(443.937 - 1366.30i) q^{77} +(141.038 + 102.470i) q^{78} +(500.100 + 363.344i) q^{79} +(375.005 - 272.457i) q^{81} +41.3761 q^{82} +(-365.730 + 265.719i) q^{83} +(-176.470 - 543.118i) q^{84} +(-22.7855 + 70.1266i) q^{86} +(-267.623 - 823.659i) q^{87} +(109.401 + 336.700i) q^{88} +(266.987 - 821.703i) q^{89} +(-198.833 - 611.945i) q^{91} +(-629.169 + 457.118i) q^{92} -370.592 q^{93} +(-687.123 + 499.224i) q^{94} +(113.853 + 82.7188i) q^{96} +(528.660 + 384.094i) q^{97} +(-439.338 + 1352.14i) q^{98} +338.953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 7 q^{3} - 16 q^{4} + 14 q^{6} + 54 q^{7} + 32 q^{8} - 83 q^{9} + 152 q^{11} + 12 q^{12} - 77 q^{13} + 52 q^{14} - 64 q^{16} - 76 q^{17} - 304 q^{18} - 20 q^{19} + 257 q^{21} + 226 q^{22}+ \cdots - 1786 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 7 * q^3 - 16 * q^4 + 14 * q^6 + 54 * q^7 + 32 * q^8 - 83 * q^9 + 152 * q^11 + 12 * q^12 - 77 * q^13 + 52 * q^14 - 64 * q^16 - 76 * q^17 - 304 * q^18 - 20 * q^19 + 257 * q^21 + 226 * q^22 + 383 * q^23 - 64 * q^24 - 716 * q^26 - 415 * q^27 - 4 * q^28 + 105 * q^29 + 177 * q^31 - 512 * q^32 - 64 * q^33 + 342 * q^34 - 332 * q^36 - 446 * q^37 - 90 * q^38 - 146 * q^39 + 462 * q^41 - 514 * q^42 + 1058 * q^43 - 452 * q^44 + 1124 * q^46 + 1114 * q^47 + 48 * q^48 + 1698 * q^49 - 3608 * q^51 - 308 * q^52 - 567 * q^53 + 390 * q^54 + 8 * q^56 + 1520 * q^57 - 210 * q^58 + 1275 * q^59 + 252 * q^61 + 176 * q^62 - 5402 * q^63 - 256 * q^64 + 998 * q^66 - 3296 * q^67 + 1976 * q^68 - 5491 * q^69 + 3712 * q^71 - 56 * q^72 + 1688 * q^73 - 1148 * q^74 - 200 * q^76 + 5453 * q^77 + 1152 * q^78 + 1750 * q^79 + 4106 * q^81 + 1576 * q^82 + 2153 * q^83 - 612 * q^84 + 1074 * q^86 + 1255 * q^87 - 1216 * q^88 + 5660 * q^89 - 493 * q^91 - 2248 * q^92 + 256 * q^93 - 2228 * q^94 + 224 * q^96 + 429 * q^97 + 674 * q^98 - 1786 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.618034	+	1.90211i	−0.218508	+	0.672499i
$2$	−0.618034	+	1.90211i	−0.218508	+	0.672499i
$3$	−3.55790	−	2.58496i	−0.684717	−	0.497476i	0.190202	−	0.981745i	$-0.439086\pi$
$3$	−3.55790	−	2.58496i	−0.684717	−	0.497476i	−0.874919	+	0.484269i	$0.839086\pi$
$4$	−3.23607	−	2.35114i	−0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	7.11579	−	5.16993i	0.484168	−	0.351769i
$7$	−32.4633			−1.75285			−0.876426	−	0.481537i	$-0.840079\pi$
$7$	−32.4633			−1.75285			−0.876426	+	0.481537i	$0.840079\pi$
$8$	6.47214	−	4.70228i	0.286031	−	0.207813i
$9$	−2.36687	−	7.28447i	−0.0876618	−	0.269795i
$10$		0			0
$11$	−13.6751	+	42.0875i	−0.374835	+	1.15362i	0.568754	+	0.822507i	$0.307425\pi$
$11$	−13.6751	+	42.0875i	−0.374835	+	1.15362i	−0.943590	+	0.331117i	$0.892575\pi$
$12$	5.43598	+	16.7302i	0.130769	+	0.402467i
$13$	6.12486	+	18.8504i	0.130672	+	0.402166i	0.994892	−	0.100948i	$-0.0321876\pi$
$13$	6.12486	+	18.8504i	0.130672	+	0.402166i	−0.864220	+	0.503114i	$0.832188\pi$
$14$	20.0634	−	61.7488i	0.383012	−	1.17879i
$15$		0			0
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	66.6454	−	48.4207i	0.950817	−	0.690809i	−0.000182954	−	1.00000i	$-0.500058\pi$
$17$	66.6454	−	48.4207i	0.950817	−	0.690809i	0.951000	+	0.309191i	$0.100058\pi$
$18$	15.3187			0.200592
$19$	−8.36319	+	6.07621i	−0.100981	+	0.0733673i	−0.637130	−	0.770756i	$-0.719879\pi$
$19$	−8.36319	+	6.07621i	−0.100981	+	0.0733673i	0.536149	+	0.844124i	$0.319879\pi$
$20$		0			0
$21$	115.501	+	83.9163i	1.20021	+	0.872002i
$22$	−71.6036	−	52.0231i	−0.693906	−	0.504152i
$23$	60.0803	−	184.908i	0.544678	−	1.67635i	−0.177075	−	0.984197i	$-0.556663\pi$
$23$	60.0803	−	184.908i	0.544678	−	1.67635i	0.721753	−	0.692151i	$-0.243337\pi$
$24$	−35.1824			−0.299232
$25$		0			0
$26$	−39.6409			−0.299009
$27$	−47.1019	+	144.965i	−0.335732	+	1.03328i
$28$	105.053	+	76.3257i	0.709043	+	0.515150i
$29$	159.317	+	115.751i	1.02016	+	0.741186i	0.966315	−	0.257363i	$-0.0828538\pi$
$29$	159.317	+	115.751i	1.02016	+	0.741186i	0.0538405	+	0.998550i	$0.482854\pi$
$30$		0			0
$31$	68.1740	−	49.5313i	0.394981	−	0.286970i	−0.372513	−	0.928027i	$-0.621504\pi$
$31$	68.1740	−	49.5313i	0.394981	−	0.286970i	0.767493	+	0.641057i	$0.221504\pi$
$32$	−32.0000			−0.176777
$33$	157.449	−	114.394i	0.830557	−	0.603435i
$34$	50.9126	+	156.693i	0.256807	+	0.790370i
$35$		0			0
$36$	−9.46747	+	29.1379i	−0.0438309	+	0.134898i
$37$	70.9588	+	218.389i	0.315285	+	0.970348i	0.975637	+	0.219391i	$0.0704072\pi$
$37$	70.9588	+	218.389i	0.315285	+	0.970348i	−0.660352	+	0.750956i	$0.729593\pi$
$38$	−6.38891	−	19.6630i	−0.0272741	−	0.0839412i
$39$	26.9359	−	82.9003i	0.110595	−	0.340376i
$40$		0			0
$41$	−6.39296	−	19.6755i	−0.0243515	−	0.0749463i	0.938142	−	0.346250i	$-0.112545\pi$
$41$	−6.39296	−	19.6755i	−0.0243515	−	0.0749463i	−0.962494	+	0.271304i	$0.912545\pi$
$42$	−231.002	+	167.833i	−0.848675	+	0.616599i
$43$	36.8678			0.130751			0.0653753	−	0.997861i	$-0.479176\pi$
$43$	36.8678			0.130751			0.0653753	+	0.997861i	$0.479176\pi$
$44$	143.207	−	104.046i	0.490666	−	0.356490i
$45$		0			0
$46$	314.584	+	228.559i	1.00832	+	0.732591i
$47$	343.561	+	249.612i	1.06625	+	0.774673i	0.975234	−	0.221177i	$-0.0709898\pi$
$47$	343.561	+	249.612i	1.06625	+	0.774673i	0.0910123	+	0.995850i	$0.470990\pi$
$48$	21.7439	−	66.9209i	0.0653847	−	0.201233i
$49$	710.864			2.07249
$50$		0			0
$51$	−362.283			−0.994702
$52$	24.4995	−	75.4016i	0.0653358	−	0.201083i
$53$	−4.23242	−	3.07504i	−0.0109692	−	0.00796960i	0.582287	−	0.812983i	$-0.302158\pi$
$53$	−4.23242	−	3.07504i	−0.0109692	−	0.00796960i	−0.593256	+	0.805014i	$0.702158\pi$
$54$	−246.629	−	179.186i	−0.621517	−	0.451558i
$55$		0			0
$56$	−210.107	+	152.651i	−0.501369	+	0.364266i
$57$	45.4621			0.105642
$58$	−318.635	+	231.502i	−0.721359	+	0.524098i
$59$	16.0299	+	49.3350i	0.0353715	+	0.108862i	0.967183	−	0.254079i	$-0.0817724\pi$
$59$	16.0299	+	49.3350i	0.0353715	+	0.108862i	−0.931812	+	0.362942i	$0.881772\pi$
$60$		0			0
$61$	−38.3804	+	118.123i	−0.0805592	+	0.247936i	−0.983222	−	0.182413i	$-0.941609\pi$
$61$	−38.3804	+	118.123i	−0.0805592	+	0.247936i	0.902663	+	0.430348i	$0.141609\pi$
$62$	52.0803	+	160.287i	0.106681	+	0.328329i
$63$	76.8363	+	236.478i	0.153658	+	0.472911i
$64$	19.7771	−	60.8676i	0.0386271	−	0.118882i
$65$		0			0
$66$	120.280	+	370.185i	0.224326	+	0.690404i
$67$	−630.360	+	457.984i	−1.14941	+	0.835098i	−0.988403	−	0.151854i	$-0.951476\pi$
$67$	−630.360	+	457.984i	−1.14941	+	0.835098i	−0.161011	+	0.986953i	$0.551476\pi$
$68$	−329.513			−0.587637
$69$	−691.740	+	502.578i	−1.20689	+	0.876860i
$70$		0			0
$71$	−496.268	−	360.560i	−0.829523	−	0.602684i	0.0899013	−	0.995951i	$-0.471345\pi$
$71$	−496.268	−	360.560i	−0.829523	−	0.602684i	−0.919424	+	0.393267i	$0.871345\pi$
$72$	−49.5723	−	36.0164i	−0.0811411	−	0.0589524i
$73$	280.603	−	863.608i	0.449892	−	1.38463i	−0.427136	−	0.904187i	$-0.640477\pi$
$73$	280.603	−	863.608i	0.449892	−	1.38463i	0.877028	−	0.480439i	$-0.159523\pi$
$74$	−459.255			−0.721450
$75$		0			0
$76$	41.3499			0.0624099
$77$	443.937	−	1366.30i	0.657031	−	2.02213i
$78$	141.038	+	102.470i	0.204737	+	0.148750i
$79$	500.100	+	363.344i	0.712224	+	0.517461i	0.883890	−	0.467694i	$-0.154915\pi$
$79$	500.100	+	363.344i	0.712224	+	0.517461i	−0.171667	+	0.985155i	$0.554915\pi$
$80$		0			0
$81$	375.005	−	272.457i	0.514411	−	0.373741i
$82$	41.3761			0.0557223
$83$	−365.730	+	265.719i	−0.483664	+	0.351403i	−0.802743	−	0.596326i	$-0.796627\pi$
$83$	−365.730	+	265.719i	−0.483664	+	0.351403i	0.319078	+	0.947728i	$0.396627\pi$
$84$	−176.470	−	543.118i	−0.229219	−	0.705465i
$85$		0			0
$86$	−22.7855	+	70.1266i	−0.0285701	+	0.0879296i
$87$	−267.623	−	823.659i	−0.329795	−	1.01501i
$88$	109.401	+	336.700i	0.132524	+	0.407868i
$89$	266.987	−	821.703i	0.317984	−	0.978656i	−0.656524	−	0.754305i	$-0.727974\pi$
$89$	266.987	−	821.703i	0.317984	−	0.978656i	0.974509	−	0.224350i	$-0.0720260\pi$
$90$		0			0
$91$	−198.833	−	611.945i	−0.229048	−	0.704937i
$92$	−629.169	+	457.118i	−0.712993	+	0.518020i
$93$	−370.592			−0.413211
$94$	−687.123	+	499.224i	−0.753950	+	0.547777i
$95$		0			0
$96$	113.853	+	82.7188i	0.121042	+	0.0879422i
$97$	528.660	+	384.094i	0.553374	+	0.402050i	0.829028	−	0.559207i	$-0.188894\pi$
$97$	528.660	+	384.094i	0.553374	+	0.402050i	−0.275654	+	0.961257i	$0.588894\pi$
$98$	−439.338	+	1352.14i	−0.452856	+	1.39375i
$99$	338.953			0.344101
$100$		0			0
$101$	684.563			0.674421			0.337211	−	0.941429i	$-0.390517\pi$
$101$	684.563			0.674421			0.337211	+	0.941429i	$0.390517\pi$
$102$	223.903	−	689.104i	0.217350	−	0.668936i
$103$	3.12140	+	2.26783i	0.00298603	+	0.00216948i	0.589277	−	0.807931i	$-0.299413\pi$
$103$	3.12140	+	2.26783i	0.00298603	+	0.00216948i	−0.586291	+	0.810100i	$0.699413\pi$
$104$	128.281	+	93.2015i	0.120952	+	0.0878765i
$105$		0			0
$106$	8.46485	−	6.15007i	0.00775640	−	0.00563536i
$107$	1045.89			0.944951			0.472476	−	0.881344i	$-0.343360\pi$
$107$	1045.89			0.944951			0.472476	+	0.881344i	$0.343360\pi$
$108$	493.257	−	358.372i	0.439479	−	0.319300i
$109$	−356.163	−	1096.16i	−0.312974	−	0.963236i	−0.976580	−	0.215153i	$-0.930975\pi$
$109$	−356.163	−	1096.16i	−0.312974	−	0.963236i	0.663606	−	0.748082i	$-0.269025\pi$
$110$		0			0
$111$	312.063	−	960.430i	0.266844	−	0.821261i
$112$	−160.507	−	493.990i	−0.135415	−	0.416765i
$113$	−41.9853	−	129.218i	−0.0349526	−	0.107573i	0.932058	−	0.362309i	$-0.118011\pi$
$113$	−41.9853	−	129.218i	−0.0349526	−	0.107573i	−0.967011	+	0.254736i	$0.918011\pi$
$114$	−28.0971	+	86.4741i	−0.0230837	+	0.0710442i
$115$		0			0
$116$	−243.415	−	749.155i	−0.194832	−	0.599632i
$117$	122.818	−	89.2328i	0.0970476	−	0.0705092i
$118$	−103.748			−0.0809387
$119$	−2163.53	+	1571.90i	−1.66664	+	1.21089i
$120$		0			0
$121$	−507.551	−	368.758i	−0.381331	−	0.277053i
$122$	−200.963	−	146.008i	−0.149134	−	0.108352i
$123$	−28.1150	+	86.5290i	−0.0206101	+	0.0634314i
$124$	−337.071			−0.244112
$125$		0			0
$126$	−497.295			−0.351608
$127$	505.692	−	1556.36i	0.353330	−	1.08744i	−0.603641	−	0.797256i	$-0.706284\pi$
$127$	505.692	−	1556.36i	0.353330	−	1.08744i	0.956971	−	0.290182i	$-0.0937159\pi$
$128$	103.554	+	75.2365i	0.0715077	+	0.0519534i
$129$	−131.172	−	95.3018i	−0.0895273	−	0.0650454i
$130$		0			0
$131$	874.934	−	635.677i	0.583537	−	0.423964i	−0.256461	−	0.966555i	$-0.582556\pi$
$131$	874.934	−	635.677i	0.583537	−	0.423964i	0.839997	+	0.542590i	$0.182556\pi$
$132$	−778.471			−0.513312
$133$	271.496	−	197.254i	0.177005	−	0.128602i
$134$	−481.552	−	1482.07i	−0.310446	−	0.955455i
$135$		0			0
$136$	203.650	−	626.771i	0.128403	−	0.395185i
$137$	716.275	+	2204.47i	0.446683	+	1.37475i	0.880628	+	0.473809i	$0.157121\pi$
$137$	716.275	+	2204.47i	0.446683	+	1.37475i	−0.433945	+	0.900939i	$0.642879\pi$
$138$	−528.442	−	1626.38i	−0.325971	−	1.00324i
$139$	−327.762	+	1008.75i	−0.200003	+	0.615546i	0.799879	+	0.600162i	$0.204897\pi$
$139$	−327.762	+	1008.75i	−0.200003	+	0.615546i	−0.999882	+	0.0153844i	$0.995103\pi$
$140$		0			0
$141$	−577.118	−	1776.19i	−0.344696	−	1.06086i
$142$	992.535	−	721.119i	0.586561	−	0.426162i
$143$	−877.124			−0.512929
$144$	99.1447	−	72.0328i	0.0573754	−	0.0416857i
$145$		0			0
$146$	1469.26	+	1067.48i	0.832854	+	0.605104i
$147$	−2529.18	−	1837.56i	−1.41907	−	1.03101i
$148$	283.835	−	873.554i	0.157643	−	0.485174i
$149$	−1830.45			−1.00642			−0.503209	−	0.864165i	$-0.667848\pi$
$149$	−1830.45			−1.00642			−0.503209	+	0.864165i	$0.667848\pi$
$150$		0			0
$151$	−1585.52			−0.854491			−0.427246	−	0.904136i	$-0.640516\pi$
$151$	−1585.52			−0.854491			−0.427246	+	0.904136i	$0.640516\pi$
$152$	−25.5556	+	78.6521i	−0.0136371	+	0.0419706i
$153$	−510.460	−	370.871i	−0.269727	−	0.195968i
$154$	2324.49	+	1688.84i	1.21631	+	0.883704i
$155$		0			0
$156$	−282.077	+	204.941i	−0.144771	+	0.105182i
$157$	1535.51			0.780554			0.390277	−	0.920698i	$-0.372379\pi$
$157$	1535.51			0.780554			0.390277	+	0.920698i	$0.372379\pi$
$158$	−1000.20	+	726.688i	−0.503618	+	0.365900i
$159$	7.10967	+	21.8813i	0.00354612	+	0.0109138i
$160$		0			0
$161$	−1950.40	+	6002.72i	−0.954741	+	2.93839i
$162$	286.479	+	881.690i	0.138938	+	0.427606i
$163$	517.820	+	1593.69i	0.248827	+	0.765811i	0.994983	+	0.100040i	$0.0318972\pi$
$163$	517.820	+	1593.69i	0.248827	+	0.765811i	−0.746156	+	0.665771i	$0.768103\pi$
$164$	−25.5719	+	78.7021i	−0.0121758	+	0.0374732i
$165$		0			0
$166$	−279.393	−	859.884i	−0.130633	−	0.402048i
$167$	−1664.99	+	1209.69i	−0.771503	+	0.560530i	−0.902417	−	0.430864i	$-0.858209\pi$
$167$	−1664.99	+	1209.69i	−0.771503	+	0.560530i	0.130914	+	0.991394i	$0.458209\pi$
$168$	1142.14			0.524510
$169$	1459.59	−	1060.45i	0.664355	−	0.482682i
$170$		0			0
$171$	64.0566	+	46.5398i	0.0286464	+	0.0208128i
$172$	−119.307	−	86.6813i	−0.0528898	−	0.0384267i
$173$	−1331.88	+	4099.10i	−0.585323	+	1.80144i	0.0126483	+	0.999920i	$0.495974\pi$
$173$	−1331.88	+	4099.10i	−0.585323	+	1.80144i	−0.597971	+	0.801518i	$0.704026\pi$
$174$	1732.09			0.754653
$175$		0			0
$176$	−708.055			−0.303248
$177$	70.4964	−	216.966i	0.0299369	−	0.0921364i
$178$	1397.96	+	1015.68i	0.588662	+	0.427688i
$179$	2202.60	+	1600.28i	0.919719	+	0.668215i	0.943454	−	0.331503i	$-0.107556\pi$
$179$	2202.60	+	1600.28i	0.919719	+	0.668215i	−0.0237350	+	0.999718i	$0.507556\pi$
$180$		0			0
$181$	1056.07	−	767.281i	0.433686	−	0.315091i	−0.349435	−	0.936961i	$-0.613626\pi$
$181$	1056.07	−	767.281i	0.433686	−	0.315091i	0.783121	+	0.621869i	$0.213626\pi$
$182$	1286.87			0.524118
$183$	441.897	−	321.057i	0.178502	−	0.129690i
$184$	−480.642	−	1479.26i	−0.192573	−	0.592679i
$185$		0			0
$186$	229.039	−	704.909i	0.0902900	−	0.277884i
$187$	1126.53	+	3467.10i	0.440534	+	1.35583i
$188$	−524.915	−	1615.52i	−0.203635	−	0.626724i
$189$	1529.08	−	4706.03i	0.588488	−	1.81118i
$190$		0			0
$191$	1225.39	+	3771.37i	0.464221	+	1.42872i	0.859960	+	0.510362i	$0.170489\pi$
$191$	1225.39	+	3771.37i	0.464221	+	1.42872i	−0.395739	+	0.918363i	$0.629511\pi$
$192$	−227.705	+	165.438i	−0.0855897	+	0.0621845i
$193$	1941.18			0.723986			0.361993	−	0.932181i	$-0.382096\pi$
$193$	1941.18			0.723986			0.361993	+	0.932181i	$0.382096\pi$
$194$	−1057.32	+	768.188i	−0.391295	+	0.284292i
$195$		0			0
$196$	−2300.40	−	1671.34i	−0.838340	−	0.609089i
$197$	−1633.01	−	1186.45i	−0.590595	−	0.429092i	0.251933	−	0.967745i	$-0.418934\pi$
$197$	−1633.01	−	1186.45i	−0.590595	−	0.429092i	−0.842528	+	0.538652i	$0.818934\pi$
$198$	−209.484	+	644.726i	−0.0751889	+	0.231408i
$199$	985.509			0.351060			0.175530	−	0.984474i	$-0.443836\pi$
$199$	985.509			0.351060			0.175530	+	0.984474i	$0.443836\pi$
$200$		0			0
$201$	3426.63			1.20247
$202$	−423.083	+	1302.12i	−0.147366	+	0.453547i
$203$	−5171.96	−	3757.65i	−1.78818	−	1.29919i
$204$	1172.37	+	851.779i	0.402365	+	0.292336i
$205$		0			0
$206$	−6.24281	+	4.53567i	−0.00211144	+	0.00153405i
$207$	−1489.16			−0.500018
$208$	−256.562	+	186.403i	−0.0855257	+	0.0621381i
$209$	−141.366	−	435.079i	−0.0467869	−	0.143995i
$210$		0			0
$211$	1338.94	−	4120.84i	0.436856	−	1.34450i	−0.454317	−	0.890840i	$-0.650116\pi$
$211$	1338.94	−	4120.84i	0.436856	−	1.34450i	0.891173	−	0.453664i	$-0.149884\pi$
$212$	6.46657	+	19.9021i	0.00209493	+	0.00644754i
$213$	833.636	+	2565.67i	0.268168	+	0.825336i
$214$	−646.394	+	1989.40i	−0.206479	+	0.635478i
$215$		0			0
$216$	376.815	+	1159.72i	0.118699	+	0.365318i
$217$	−2213.15	+	1607.95i	−0.692343	+	0.503017i
$218$	2305.13			0.716162
$219$	−3230.75	+	2347.28i	−0.996868	+	0.724267i
$220$		0			0
$221$	1320.94	+	959.722i	0.402065	+	0.292117i
$222$	1633.98	+	1187.16i	0.493989	+	0.358904i
$223$	1606.36	−	4943.88i	0.482377	−	1.48460i	−0.353367	−	0.935485i	$-0.614963\pi$
$223$	1606.36	−	4943.88i	0.482377	−	1.48460i	0.835744	−	0.549119i	$-0.185037\pi$
$224$	1038.82			0.309863
$225$		0			0
$226$	271.735			0.0799802
$227$	−1157.17	+	3561.42i	−0.338345	+	1.04132i	0.626705	+	0.779256i	$0.284403\pi$
$227$	−1157.17	+	3561.42i	−0.338345	+	1.04132i	−0.965051	+	0.262064i	$0.915597\pi$
$228$	−147.119	−	106.888i	−0.0427332	−	0.0310475i
$229$	3401.89	+	2471.62i	0.981673	+	0.713227i	0.958082	−	0.286494i	$-0.0924900\pi$
$229$	3401.89	+	2471.62i	0.981673	+	0.713227i	0.0235912	+	0.999722i	$0.492490\pi$
$230$		0			0
$231$	−5111.31	+	3713.59i	−1.45584	+	1.05773i
$232$	1575.42			0.445824
$233$	5028.05	−	3653.09i	1.41373	−	1.02713i	0.420961	−	0.907079i	$-0.361693\pi$
$233$	5028.05	−	3653.09i	1.41373	−	1.02713i	0.992767	−	0.120055i	$-0.0383072\pi$
$234$	93.8249	+	288.763i	0.0262116	+	0.0806712i
$235$		0			0
$236$	64.1197	−	197.340i	0.0176857	−	0.0544311i
$237$	−840.073	−	2585.48i	−0.230247	−	0.708629i
$238$	−1652.79	−	5086.76i	−0.450144	−	1.38540i
$239$	262.864	−	809.011i	0.0711432	−	0.218956i	−0.909163	−	0.416441i	$-0.863277\pi$
$239$	262.864	−	809.011i	0.0711432	−	0.218956i	0.980306	+	0.197485i	$0.0632773\pi$
$240$		0			0
$241$	1457.32	+	4485.16i	0.389518	+	1.19881i	0.933149	+	0.359490i	$0.117049\pi$
$241$	1457.32	+	4485.16i	0.389518	+	1.19881i	−0.543631	+	0.839325i	$0.682951\pi$
$242$	1015.10	−	737.515i	0.269642	−	0.195906i
$243$	2076.95			0.548298
$244$	401.925	−	292.016i	0.105453	−	0.0766164i
$245$		0			0
$246$	−147.212	−	106.956i	−0.0381540	−	0.0277205i
$247$	−165.762	−	120.433i	−0.0427012	−	0.0310243i
$248$	208.321	−	641.146i	0.0533403	−	0.164165i
$249$	1988.10			0.505988
$250$		0			0
$251$	619.865			0.155879			0.0779393	−	0.996958i	$-0.475166\pi$
$251$	619.865			0.155879			0.0779393	+	0.996958i	$0.475166\pi$
$252$	307.345	−	945.911i	0.0768291	−	0.236456i
$253$	6960.72	+	5057.26i	1.72971	+	1.25671i
$254$	2647.84	+	1923.77i	0.654095	+	0.475228i
$255$		0			0
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$	3006.52			0.729733			0.364867	−	0.931060i	$-0.381115\pi$
$257$	3006.52			0.729733			0.364867	+	0.931060i	$0.381115\pi$
$258$	262.343	−	190.604i	0.0633053	−	0.0459940i
$259$	−2303.55	−	7089.61i	−0.552648	−	1.70088i
$260$		0			0
$261$	466.101	−	1434.51i	0.110540	−	0.340207i
$262$	668.390	+	2057.09i	0.157608	+	0.485067i
$263$	−149.072	−	458.796i	−0.0349512	−	0.107569i	0.932059	−	0.362307i	$-0.118011\pi$
$263$	−149.072	−	458.796i	−0.0349512	−	0.107569i	−0.967010	+	0.254738i	$0.918011\pi$
$264$	481.122	−	1480.74i	0.112163	−	0.345202i
$265$		0			0
$266$	207.405	+	638.326i	0.0478075	+	0.147136i
$267$	−3073.99	+	2233.38i	−0.704587	+	0.511913i
$268$	3116.67			0.710377
$269$	−4209.63	+	3058.48i	−0.954148	+	0.693229i	−0.951784	−	0.306768i	$-0.900752\pi$
$269$	−4209.63	+	3058.48i	−0.954148	+	0.693229i	−0.00236368	+	0.999997i	$0.500752\pi$
$270$		0			0
$271$	1750.36	+	1271.71i	0.392351	+	0.285059i	0.766418	−	0.642342i	$-0.222037\pi$
$271$	1750.36	+	1271.71i	0.392351	+	0.285059i	−0.374067	+	0.927402i	$0.622037\pi$
$272$	1066.33	+	774.732i	0.237704	+	0.172702i
$273$	−874.428	+	2691.21i	−0.193856	+	0.596629i
$274$	−4635.83			−1.02212
$275$		0			0
$276$	3420.15			0.745902
$277$	1542.39	−	4746.99i	0.334561	−	1.02967i	−0.632377	−	0.774660i	$-0.717921\pi$
$277$	1542.39	−	4746.99i	0.334561	−	1.02967i	0.966938	−	0.255011i	$-0.0820792\pi$
$278$	−1716.19	−	1246.88i	−0.370252	−	0.269004i
$279$	−522.168	−	379.377i	−0.112048	−	0.0814076i
$280$		0			0
$281$	−355.968	+	258.626i	−0.0755704	+	0.0549051i	−0.624929	−	0.780682i	$-0.714872\pi$
$281$	−355.968	+	258.626i	−0.0755704	+	0.0549051i	0.549359	+	0.835587i	$0.314872\pi$
$282$	3735.19			0.788748
$283$	−2941.14	+	2136.86i	−0.617783	+	0.448845i	−0.852146	−	0.523304i	$-0.824699\pi$
$283$	−2941.14	+	2136.86i	−0.617783	+	0.448845i	0.234364	+	0.972149i	$0.424699\pi$
$284$	758.229	+	2333.59i	0.158425	+	0.487581i
$285$		0			0
$286$	542.093	−	1668.39i	0.112079	−	0.344944i
$287$	207.537	+	638.732i	0.0426846	+	0.131370i
$288$	75.7398	+	233.103i	0.0154966	+	0.0476935i
$289$	578.844	−	1781.50i	0.117819	−	0.362609i
$290$		0			0
$291$	−888.049	−	2733.13i	−0.178895	−	0.550581i
$292$	−2938.52	+	2134.96i	−0.588917	+	0.427873i
$293$	−7040.42			−1.40377			−0.701887	−	0.712288i	$-0.747659\pi$
$293$	−7040.42			−1.40377			−0.701887	+	0.712288i	$0.747659\pi$
$294$	5058.36	−	3675.11i	1.00343	−	0.729037i
$295$		0			0
$296$	1486.18	+	1079.77i	0.291833	+	0.212029i
$297$	−5457.09	−	3964.80i	−1.06617	−	0.774617i
$298$	1131.28	−	3481.72i	0.219911	−	0.676815i
$299$	3853.57			0.745344
$300$		0			0
$301$	−1196.85			−0.229187
$302$	979.908	−	3015.85i	0.186713	−	0.574644i
$303$	−2435.60	−	1769.57i	−0.461788	−	0.335509i
$304$	−133.811	−	97.2194i	−0.0252454	−	0.0183418i
$305$		0			0
$306$	1020.92	−	741.742i	0.190726	−	0.138571i
$307$	−3985.50			−0.740927			−0.370463	−	0.928847i	$-0.620801\pi$
$307$	−3985.50			−0.740927			−0.370463	+	0.928847i	$0.620801\pi$
$308$	−4648.97	+	3377.68i	−0.860064	+	0.624873i
$309$	−5.24337	−	16.1374i	−0.000965323	−	0.00297096i
$310$		0			0
$311$	1984.51	−	6107.70i	0.361837	−	1.11362i	−0.590101	−	0.807329i	$-0.700912\pi$
$311$	1984.51	−	6107.70i	0.361837	−	1.11362i	0.951938	−	0.306290i	$-0.0990878\pi$
$312$	−215.487	−	663.202i	−0.0391012	−	0.120341i
$313$	2142.09	+	6592.67i	0.386831	+	1.19054i	0.935143	+	0.354269i	$0.115270\pi$
$313$	2142.09	+	6592.67i	0.386831	+	1.19054i	−0.548313	+	0.836273i	$0.684730\pi$
$314$	−948.996	+	2920.71i	−0.170557	+	0.524921i
$315$		0			0
$316$	−764.085	−	2351.61i	−0.136023	−	0.418634i
$317$	5346.35	−	3884.35i	0.947258	−	0.688223i	−0.00289895	−	0.999996i	$-0.500923\pi$
$317$	5346.35	−	3884.35i	0.947258	−	0.688223i	0.950157	+	0.311773i	$0.100923\pi$
$318$	−46.0148			−0.00811440
$319$	−7050.35	+	5122.38i	−1.23744	+	0.899053i
$320$		0			0
$321$	−3721.16	−	2703.58i	−0.647024	−	0.470091i
$322$	−10212.4	−	7419.77i	−1.76744	−	1.28412i
$323$	−263.154	+	809.903i	−0.0453321	+	0.139518i
$324$	−1854.13			−0.317923
$325$		0			0
$326$	−3351.40			−0.569378
$327$	−1566.33	+	4820.68i	−0.264888	+	0.815241i
$328$	−133.896	−	97.2811i	−0.0225401	−	0.0163764i
$329$	−11153.1	−	8103.22i	−1.86897	−	1.35789i
$330$		0			0
$331$	3033.15	−	2203.71i	0.503676	−	0.365942i	−0.306743	−	0.951792i	$-0.599239\pi$
$331$	3033.15	−	2203.71i	0.503676	−	0.365942i	0.810420	+	0.585850i	$0.199239\pi$
$332$	1808.27			0.298921
$333$	1422.90	−	1033.79i	0.234157	−	0.170125i
$334$	−1271.94	−	3914.63i	−0.208376	−	0.641315i
$335$		0			0
$336$	−705.879	+	2172.47i	−0.114610	+	0.352732i
$337$	−97.7299	−	300.782i	−0.0157973	−	0.0486191i	0.942847	−	0.333226i	$-0.108137\pi$
$337$	−97.7299	−	300.782i	−0.0157973	−	0.0486191i	−0.958644	+	0.284606i	$0.908137\pi$
$338$	1115.03	+	3431.70i	0.179436	+	0.552247i
$339$	−184.643	+	568.273i	−0.0295824	+	0.0910453i
$340$		0			0
$341$	1152.37	+	3546.62i	0.183003	+	0.563226i
$342$	−128.113	+	93.0796i	−0.0202560	+	0.0147169i
$343$	−11942.1			−1.87992
$344$	238.613	−	173.363i	0.0373987	−	0.0271718i
$345$		0			0
$346$	−6973.80	−	5066.77i	−1.08357	−	0.787257i
$347$	4798.35	+	3486.20i	0.742331	+	0.539335i	0.893440	−	0.449182i	$-0.148285\pi$
$347$	4798.35	+	3486.20i	0.742331	+	0.539335i	−0.151109	+	0.988517i	$0.548285\pi$
$348$	−1070.49	+	3294.64i	−0.164898	+	0.507503i
$349$	8313.16			1.27505			0.637526	−	0.770429i	$-0.279958\pi$
$349$	8313.16			1.27505			0.637526	+	0.770429i	$0.279958\pi$
$350$		0			0
$351$	−3021.13			−0.459419
$352$	437.602	−	1346.80i	0.0662621	−	0.203934i
$353$	−2915.82	−	2118.46i	−0.439641	−	0.319418i	0.345851	−	0.938289i	$-0.387590\pi$
$353$	−2915.82	−	2118.46i	−0.439641	−	0.319418i	−0.785492	+	0.618872i	$0.787590\pi$
$354$	369.124	+	268.184i	0.0554201	+	0.0402651i
$355$		0			0
$356$	−2795.93	+	2031.36i	−0.416247	+	0.302421i
$357$	11760.9			1.74357
$358$	−4405.19	+	3200.56i	−0.650340	+	0.472499i
$359$	2483.37	+	7643.04i	0.365090	+	1.12363i	0.949924	+	0.312480i	$0.101160\pi$
$359$	2483.37	+	7643.04i	0.365090	+	1.12363i	−0.584834	+	0.811153i	$0.698840\pi$
$360$		0			0
$361$	−2086.53	+	6421.66i	−0.304203	+	0.936239i
$362$	806.767	+	2482.97i	0.117135	+	0.360503i
$363$	852.590	+	2624.00i	0.123277	+	0.379406i
$364$	−795.332	+	2447.78i	−0.114524	+	0.352469i
$365$		0			0
$366$	337.579	+	1038.96i	0.0482119	+	0.148381i
$367$	10517.3	−	7641.29i	1.49591	−	1.08684i	0.523940	−	0.851755i	$-0.324462\pi$
$367$	10517.3	−	7641.29i	1.49591	−	1.08684i	0.971974	−	0.235090i	$-0.0755384\pi$
$368$	3110.78			0.440654
$369$	−128.194	+	93.1387i	−0.0180855	+	0.0131399i
$370$		0			0
$371$	137.398	+	99.8257i	0.0192274	+	0.0139695i
$372$	1199.26	+	871.315i	0.167147	+	0.121440i
$373$	2157.81	−	6641.04i	0.299536	−	0.921877i	−0.682124	−	0.731237i	$-0.738944\pi$
$373$	2157.81	−	6641.04i	0.299536	−	0.921877i	0.981660	−	0.190641i	$-0.0610565\pi$
$374$	−7291.05			−1.00805
$375$		0			0
$376$	3397.32			0.465967
$377$	−1206.15	+	3712.15i	−0.164774	+	0.507124i
$378$	8006.37	+	5816.97i	1.08943	+	0.791515i
$379$	741.524	+	538.749i	0.100500	+	0.0730176i	0.636900	−	0.770946i	$-0.280216\pi$
$379$	741.524	+	538.749i	0.100500	+	0.0730176i	−0.536400	+	0.843964i	$0.680216\pi$
$380$		0			0
$381$	−5822.33	+	4230.17i	−0.782906	+	0.568814i
$382$	−7930.90			−1.06225
$383$	453.273	−	329.322i	0.0604730	−	0.0439362i	−0.557138	−	0.830420i	$-0.688101\pi$
$383$	453.273	−	329.322i	0.0604730	−	0.0439362i	0.617611	+	0.786484i	$0.288101\pi$
$384$	−173.951	−	535.367i	−0.0231170	−	0.0711467i
$385$		0			0
$386$	−1199.72	+	3692.35i	−0.158197	+	0.486880i
$387$	−87.2611	−	268.562i	−0.0114618	−	0.0352759i
$388$	−807.721	−	2485.91i	−0.105685	−	0.325265i
$389$	−917.355	+	2823.33i	−0.119567	+	0.367991i	−0.992872	−	0.119183i	$-0.961972\pi$
$389$	−917.355	+	2823.33i	−0.119567	+	0.367991i	0.873305	+	0.487174i	$0.161972\pi$
$390$		0			0
$391$	−4949.31	−	15232.4i	−0.640147	−	1.97017i
$392$	4600.81	−	3342.68i	0.592796	−	0.430691i
$393$	−4756.12			−0.610470
$394$	3266.02	−	2372.90i	0.417613	−	0.303414i
$395$		0			0
$396$	−1096.87	−	796.925i	−0.139192	−	0.101129i
$397$	−5115.40	−	3716.55i	−0.646686	−	0.469845i	0.215455	−	0.976514i	$-0.430877\pi$
$397$	−5115.40	−	3716.55i	−0.646686	−	0.469845i	−0.862141	+	0.506669i	$0.830877\pi$
$398$	−609.078	+	1874.55i	−0.0767094	+	0.236087i
$399$	−1475.85			−0.185175
$400$		0			0
$401$	−3008.68			−0.374679			−0.187339	−	0.982295i	$-0.559986\pi$
$401$	−3008.68			−0.374679			−0.187339	+	0.982295i	$0.559986\pi$
$402$	−2117.77	+	6517.83i	−0.262748	+	0.808656i
$403$	1351.24	+	981.734i	0.167023	+	0.121349i
$404$	−2215.29	−	1609.50i	−0.272809	−	0.198207i
$405$		0			0
$406$	10343.9	−	7515.30i	1.26443	−	0.918666i
$407$	−10161.8			−1.23760
$408$	−2344.75	+	1703.56i	−0.284515	+	0.206712i
$409$	3472.20	+	10686.3i	0.419778	+	1.29194i	0.907907	+	0.419172i	$0.137680\pi$
$409$	3472.20	+	10686.3i	0.419778	+	1.29194i	−0.488129	+	0.872771i	$0.662320\pi$
$410$		0			0
$411$	3150.04	−	9694.82i	0.378053	−	1.16353i
$412$	−4.76908	−	14.6777i	−0.000570281	−	0.00175514i
$413$	−520.384	−	1601.58i	−0.0620010	−	0.190819i
$414$	920.352	−	2832.55i	0.109258	−	0.336262i
$415$		0			0
$416$	−195.996	−	603.212i	−0.0230997	−	0.0710936i
$417$	3773.72	−	2741.77i	0.443165	−	0.321978i
$418$	914.937			0.107060
$419$	−3609.66	+	2622.57i	−0.420867	+	0.305778i	−0.777987	−	0.628281i	$-0.783759\pi$
$419$	−3609.66	+	2622.57i	−0.420867	+	0.305778i	0.357119	+	0.934059i	$0.383759\pi$
$420$		0			0
$421$	4617.41	+	3354.74i	0.534534	+	0.388361i	0.822051	−	0.569414i	$-0.192830\pi$
$421$	4617.41	+	3354.74i	0.534534	+	0.388361i	−0.287517	+	0.957775i	$0.592830\pi$
$422$	7010.80	+	5093.64i	0.808721	+	0.587570i
$423$	1005.13	−	3093.46i	0.115534	−	0.355577i
$424$	−41.8525			−0.00479372
$425$		0			0
$426$	−5395.40			−0.613634
$427$	1245.95	−	3834.65i	0.141208	−	0.434595i
$428$	−3384.56	−	2459.03i	−0.382241	−	0.277714i
$429$	3120.72	+	2267.33i	0.351211	+	0.255170i
$430$		0			0
$431$	6487.97	−	4713.79i	0.725092	−	0.526810i	−0.162915	−	0.986640i	$-0.552090\pi$
$431$	6487.97	−	4713.79i	0.725092	−	0.526810i	0.888007	+	0.459830i	$0.152090\pi$
$432$	−2438.80			−0.271613
$433$	4678.75	−	3399.31i	0.519276	−	0.377276i	−0.297055	−	0.954860i	$-0.596005\pi$
$433$	4678.75	−	3399.31i	0.519276	−	0.377276i	0.816331	+	0.577584i	$0.196005\pi$
$434$	−1690.70	−	5203.43i	−0.186995	−	0.575513i
$435$		0			0
$436$	−1424.65	+	4384.62i	−0.156487	+	0.481618i
$437$	621.078	+	1911.48i	0.0679867	+	0.209242i
$438$	−2468.08	−	7595.95i	−0.269245	−	0.828650i
$439$	3630.68	−	11174.1i	0.394721	−	1.21483i	−0.534457	−	0.845196i	$-0.679484\pi$
$439$	3630.68	−	11174.1i	0.394721	−	1.21483i	0.929178	−	0.369632i	$-0.120516\pi$
$440$		0			0
$441$	−1682.52	−	5178.27i	−0.181678	−	0.559148i
$442$	−2641.89	+	1919.44i	−0.284303	+	0.206558i
$443$	−3568.50			−0.382719			−0.191360	−	0.981520i	$-0.561290\pi$
$443$	−3568.50			−0.382719			−0.191360	+	0.981520i	$0.561290\pi$
$444$	−3267.96	+	2374.31i	−0.349303	+	0.253784i
$445$		0			0
$446$	8411.03	+	6110.97i	0.892990	+	0.648795i
$447$	6512.55	+	4731.65i	0.689112	+	0.500669i
$448$	−642.029	+	1975.96i	−0.0677076	+	0.208383i
$449$	−14369.1			−1.51029			−0.755145	−	0.655558i	$-0.772434\pi$
$449$	−14369.1			−1.51029			−0.755145	+	0.655558i	$0.772434\pi$
$450$		0			0
$451$	915.518			0.0955878
$452$	−167.941	+	516.870i	−0.0174763	+	0.0537866i
$453$	5641.13	+	4098.52i	0.585085	+	0.425089i
$454$	−6059.05	−	4402.15i	−0.626355	−	0.455073i
$455$		0			0
$456$	294.237	−	213.776i	0.0302169	−	0.0219539i
$457$	402.073			0.0411558			0.0205779	−	0.999788i	$-0.493449\pi$
$457$	402.073			0.0411558			0.0205779	+	0.999788i	$0.493449\pi$
$458$	−6803.78	+	4943.23i	−0.694148	+	0.504328i
$459$	3880.17	+	11941.9i	0.394577	+	1.21438i
$460$		0			0
$461$	2232.00	−	6869.38i	0.225498	−	0.694010i	−0.772743	−	0.634719i	$-0.781116\pi$
$461$	2232.00	−	6869.38i	0.225498	−	0.694010i	0.998241	−	0.0592914i	$-0.0188841\pi$
$462$	−3904.70	−	12017.4i	−0.393210	−	1.21018i
$463$	1012.67	+	3116.67i	0.101647	+	0.312838i	0.988929	−	0.148390i	$-0.0474090\pi$
$463$	1012.67	+	3116.67i	0.101647	+	0.312838i	−0.887282	+	0.461228i	$0.847409\pi$
$464$	−973.661	+	2996.62i	−0.0974162	+	0.299816i
$465$		0			0
$466$	3841.09	+	11821.7i	0.381835	+	1.17517i
$467$	−4679.36	+	3399.75i	−0.463672	+	0.336877i	−0.794970	−	0.606649i	$-0.792513\pi$
$467$	−4679.36	+	3399.75i	−0.463672	+	0.336877i	0.331298	+	0.943526i	$0.392513\pi$
$468$	−607.248			−0.0599787
$469$	20463.6	−	14867.6i	2.01475	−	1.46380i
$470$		0			0
$471$	−5463.18	−	3969.23i	−0.534459	−	0.388307i
$472$	335.735	+	243.926i	0.0327404	+	0.0237873i
$473$	−504.169	+	1551.67i	−0.0490100	+	0.150837i
$474$	5437.07			0.526863
$475$		0			0
$476$	10697.1			1.03004
$477$	−12.3824	+	38.1092i	−0.00118858	+	0.00365807i
$478$	1376.37	+	999.992i	0.131702	+	0.0956874i
$479$	−1896.17	−	1377.64i	−0.180873	−	0.131412i	0.493665	−	0.869652i	$-0.335657\pi$
$479$	−1896.17	−	1377.64i	−0.180873	−	0.131412i	−0.674538	+	0.738241i	$0.735657\pi$
$480$		0			0
$481$	−3682.10	+	2675.20i	−0.349042	+	0.253594i
$482$	−9431.94			−0.891314
$483$	22456.1	−	16315.3i	2.11551	−	1.53701i
$484$	775.469	+	2386.65i	0.0728277	+	0.224141i
$485$		0			0
$486$	−1283.63	+	3950.60i	−0.119808	+	0.368730i
$487$	−3635.26	−	11188.2i	−0.338253	−	1.04104i	−0.965097	−	0.261892i	$-0.915654\pi$
$487$	−3635.26	−	11188.2i	−0.338253	−	1.04104i	0.626844	−	0.779145i	$-0.284346\pi$
$488$	307.044	+	944.983i	0.0284820	+	0.0876585i
$489$	2277.27	−	7008.72i	0.210597	−	0.648150i
$490$		0			0
$491$	3398.57	+	10459.7i	0.312374	+	0.961387i	0.976822	+	0.214053i	$0.0686666\pi$
$491$	3398.57	+	10459.7i	0.312374	+	0.961387i	−0.664448	+	0.747334i	$0.731333\pi$
$492$	294.424	−	213.912i	0.0269790	−	0.0196014i
$493$	16222.5			1.48200
$494$	331.525	−	240.867i	0.0301943	−	0.0219375i
$495$		0			0
$496$	1090.78	+	792.501i	0.0987452	+	0.0717426i
$497$	16110.5	+	11704.9i	1.45403	+	1.05642i
$498$	−1228.72	+	3781.60i	−0.110562	+	0.340276i
$499$	12608.1			1.13109			0.565545	−	0.824717i	$-0.308666\pi$
$499$	12608.1			1.13109			0.565545	+	0.824717i	$0.308666\pi$
$500$		0			0
$501$	9050.87			0.807112
$502$	−383.098	+	1179.05i	−0.0340607	+	0.104828i
$503$	−2621.20	−	1904.41i	−0.232353	−	0.168814i	0.465517	−	0.885039i	$-0.345869\pi$
$503$	−2621.20	−	1904.41i	−0.232353	−	0.168814i	−0.697870	+	0.716225i	$0.745869\pi$
$504$	1609.28	+	1169.21i	0.142228	+	0.103335i
$505$		0			0
$506$	−13921.4	+	10114.5i	−1.22309	+	0.888627i
$507$	−7934.29			−0.695018
$508$	−5295.68	+	3847.53i	−0.462515	+	0.336037i
$509$	1458.15	+	4487.74i	0.126977	+	0.390797i	0.994256	−	0.107026i	$-0.0341329\pi$
$509$	1458.15	+	4487.74i	0.126977	+	0.390797i	−0.867279	+	0.497823i	$0.834133\pi$
$510$		0			0
$511$	−9109.30	+	28035.6i	−0.788595	+	2.42704i
$512$	−158.217	−	486.941i	−0.0136568	−	0.0420312i
$513$	−486.914	−	1498.57i	−0.0419060	−	0.128973i
$514$	−1858.13	+	5718.74i	−0.159453	+	0.490744i
$515$		0			0
$516$	200.412	+	616.806i	0.0170982	+	0.0526228i
$517$	−15203.8	+	11046.2i	−1.29335	+	0.939673i
$518$	14908.9			1.26459
$519$	15334.7	−	11141.3i	1.29695	−	0.942292i
$520$		0			0
$521$	7016.16	+	5097.54i	0.589987	+	0.428651i	0.842311	−	0.538992i	$-0.181195\pi$
$521$	7016.16	+	5097.54i	0.589987	+	0.428651i	−0.252324	+	0.967643i	$0.581195\pi$
$522$	2440.53	+	1773.15i	0.204635	+	0.148676i
$523$	−1447.19	+	4454.00i	−0.120997	+	0.372390i	−0.993150	−	0.116842i	$-0.962723\pi$
$523$	−1447.19	+	4454.00i	−0.120997	+	0.372390i	0.872154	+	0.489232i	$0.162723\pi$
$524$	−4325.91			−0.360646
$525$		0			0
$526$	964.814			0.0799769
$527$	2145.14	−	6602.07i	0.177313	−	0.545713i
$528$	2519.19	+	1830.30i	0.207639	+	0.150859i
$529$	−20738.1	−	15067.1i	−1.70445	−	1.23836i
$530$		0			0
$531$	321.439	−	233.539i	0.0262698	−	0.0190861i
$532$	−1342.35			−0.109395
$533$	331.735	−	241.020i	0.0269588	−	0.0195867i
$534$	−2348.32	−	7227.37i	−0.190303	−	0.585691i
$535$		0			0
$536$	−1926.21	+	5928.26i	−0.155223	+	0.477728i
$537$	−3699.94	−	11387.3i	−0.297327	−	0.915077i
$538$	−3215.87	−	9897.44i	−0.257707	−	0.793139i
$539$	−9721.11	+	29918.5i	−0.776842	+	2.39087i
$540$		0			0
$541$	1143.80	+	3520.25i	0.0908980	+	0.279755i	0.986163	−	0.165779i	$-0.0530138\pi$
$541$	1143.80	+	3520.25i	0.0908980	+	0.279755i	−0.895265	+	0.445534i	$0.853014\pi$
$542$	−3500.73	+	2543.43i	−0.277434	+	0.201567i
$543$	−5740.78			−0.453703
$544$	−2132.65	+	1549.46i	−0.168082	+	0.122119i
$545$		0			0
$546$	−4578.57	−	3326.52i	−0.358873	−	0.260736i
$547$	15680.7	+	11392.7i	1.22570	+	0.890524i	0.996560	−	0.0828689i	$-0.0264083\pi$
$547$	15680.7	+	11392.7i	1.22570	+	0.890524i	0.229141	+	0.973393i	$0.426408\pi$
$548$	2865.10	−	8817.88i	0.223341	−	0.687374i
$549$	951.304			0.0739539
$550$		0			0
$551$	−2035.73			−0.157396
$552$	−2113.77	+	6505.51i	−0.162985	+	0.501618i
$553$	−16234.9	−	11795.3i	−1.24842	−	0.907032i
$554$	8076.06	+	5867.60i	0.619348	+	0.449983i
$555$		0			0
$556$	3432.37	−	2493.76i	0.261807	−	0.190214i
$557$	4428.74			0.336897			0.168448	−	0.985710i	$-0.446124\pi$
$557$	4428.74			0.336897			0.168448	+	0.985710i	$0.446124\pi$
$558$	1044.34	−	758.755i	0.0792299	−	0.0575639i
$559$	225.810	+	694.972i	0.0170854	+	0.0525835i
$560$		0			0
$561$	4954.25	−	15247.6i	0.372849	−	1.14751i
$562$	−271.936	−	836.932i	−0.0204109	−	0.0628182i
$563$	−3421.90	−	10531.5i	−0.256156	−	0.788367i	−0.993600	−	0.112959i	$-0.963967\pi$
$563$	−3421.90	−	10531.5i	−0.256156	−	0.788367i	0.737444	−	0.675409i	$-0.236033\pi$
$564$	−2308.47	+	7104.74i	−0.172348	+	0.530432i
$565$		0			0
$566$	−2246.83	−	6915.03i	−0.166857	−	0.513534i
$567$	−12173.9	+	8844.85i	−0.901685	+	0.655113i
$568$	−4907.36			−0.362515
$569$	21829.5	−	15860.1i	1.60833	−	1.16852i	0.739903	−	0.672714i	$-0.234872\pi$
$569$	21829.5	−	15860.1i	1.60833	−	1.16852i	0.868432	−	0.495809i	$-0.165128\pi$
$570$		0			0
$571$	−10821.3	−	7862.17i	−0.793099	−	0.576220i	0.115783	−	0.993275i	$-0.463062\pi$
$571$	−10821.3	−	7862.17i	−0.793099	−	0.576220i	−0.908881	+	0.417055i	$0.863062\pi$
$572$	2838.43	+	2062.24i	0.207484	+	0.150746i
$573$	5389.03	−	16585.7i	0.392897	−	1.20921i
$574$	−1343.20			−0.0976730
$575$		0			0
$576$	−490.198			−0.0354599
$577$	−3221.69	+	9915.34i	−0.232445	+	0.715391i	0.765005	+	0.644024i	$0.222736\pi$
$577$	−3221.69	+	9915.34i	−0.232445	+	0.715391i	−0.997450	+	0.0713674i	$0.977264\pi$
$578$	3030.87	+	2202.05i	0.218110	+	0.158466i
$579$	−6906.52	−	5017.88i	−0.495726	−	0.360166i
$580$		0			0
$581$	11872.8	−	8626.10i	0.847792	−	0.615957i
$582$	5747.57			0.409355
$583$	187.299	−	136.081i	0.0133056	−	0.00966706i
$584$	−2244.83	−	6908.87i	−0.159061	−	0.489539i
$585$		0			0
$586$	4351.22	−	13391.7i	0.306736	−	0.944036i
$587$	4132.00	+	12717.0i	0.290538	+	0.894184i	0.984684	+	0.174350i	$0.0557823\pi$
$587$	4132.00	+	12717.0i	0.290538	+	0.894184i	−0.694146	+	0.719835i	$0.744218\pi$
$588$	3864.24	+	11892.9i	0.271018	+	0.834108i
$589$	−269.189	+	828.479i	−0.0188315	+	0.0579573i
$590$		0			0
$591$	2743.15	+	8442.54i	0.190927	+	0.587614i
$592$	−2972.36	+	2159.55i	−0.206357	+	0.149927i
$593$	2768.13			0.191693			0.0958463	−	0.995396i	$-0.469444\pi$
$593$	2768.13			0.191693			0.0958463	+	0.995396i	$0.469444\pi$
$594$	10914.2	−	7929.61i	0.753895	−	0.547737i
$595$		0			0
$596$	5923.46	+	4303.65i	0.407105	+	0.295779i
$597$	−3506.34	−	2547.50i	−0.240377	−	0.174644i
$598$	−2381.64	+	7329.93i	−0.162864	+	0.501243i
$599$	4098.71			0.279580			0.139790	−	0.990181i	$-0.455357\pi$
$599$	4098.71			0.279580			0.139790	+	0.990181i	$0.455357\pi$
$600$		0			0
$601$	−17523.5			−1.18935			−0.594673	−	0.803968i	$-0.702718\pi$
$601$	−17523.5			−1.18935			−0.594673	+	0.803968i	$0.702718\pi$
$602$	739.693	−	2276.54i	0.0500791	−	0.154128i
$603$	4828.15	+	3507.85i	0.326065	+	0.236900i
$604$	5130.87	+	3727.79i	0.345649	+	0.251129i
$605$		0			0
$606$	4871.21	−	3539.14i	0.326533	−	0.237240i
$607$	−14982.0			−1.00182			−0.500908	−	0.865501i	$-0.667000\pi$
$607$	−14982.0			−1.00182			−0.500908	+	0.865501i	$0.667000\pi$
$608$	267.622	−	194.439i	0.0178512	−	0.0129696i
$609$	8687.92	+	26738.7i	0.578083	+	1.77916i
$610$		0			0
$611$	−2601.02	+	8005.10i	−0.172219	+	0.530036i
$612$	779.914	+	2400.33i	0.0515133	+	0.158542i
$613$	9223.52	+	28387.1i	0.607723	+	1.87038i	0.476859	+	0.878980i	$0.341775\pi$
$613$	9223.52	+	28387.1i	0.607723	+	1.87038i	0.130864	+	0.991400i	$0.458225\pi$
$614$	2463.17	−	7580.87i	0.161898	−	0.498272i
$615$		0			0
$616$	−3551.50	−	10930.4i	−0.232295	−	0.714932i
$617$	15515.7	−	11272.8i	1.01238	−	0.735538i	0.0476742	−	0.998863i	$-0.484819\pi$
$617$	15515.7	−	11272.8i	1.01238	−	0.735538i	0.964707	+	0.263325i	$0.0848191\pi$
$618$	33.9358			0.00220890
$619$	−12120.6	+	8806.12i	−0.787023	+	0.571806i	−0.907079	−	0.420961i	$-0.861693\pi$
$619$	−12120.6	+	8806.12i	−0.787023	+	0.571806i	0.120055	+	0.992767i	$0.461693\pi$
$620$		0			0
$621$	23975.3	+	17419.0i	1.54927	+	1.12561i
$622$	10391.0	+	7549.53i	0.669843	+	0.486670i
$623$	−8667.29	+	26675.2i	−0.557380	+	1.71544i
$624$	1394.66			0.0894731
$625$		0			0
$626$	−13863.9			−0.885164
$627$	−621.698	+	1913.39i	−0.0395984	+	0.121871i
$628$	−4969.01	−	3610.20i	−0.315741	−	0.229399i
$629$	15303.6	+	11118.7i	0.970103	+	0.704821i
$630$		0			0
$631$	−15151.7	+	11008.3i	−0.955908	+	0.694508i	−0.952197	−	0.305485i	$-0.901181\pi$
$631$	−15151.7	+	11008.3i	−0.955908	+	0.694508i	−0.00371118	+	0.999993i	$0.501181\pi$
$632$	4945.26			0.311253
$633$	−15416.0	+	11200.4i	−0.967982	+	0.703280i
$634$	4084.24	+	12570.0i	0.255846	+	0.787412i
$635$		0			0
$636$	28.4387	−	87.5253i	0.00177306	−	0.00545692i
$637$	4353.94	+	13400.1i	0.270816	+	0.833485i
$638$	−5385.98	−	16576.4i	−0.334221	−	1.02863i
$639$	−1451.89	+	4468.44i	−0.0898837	+	0.276634i
$640$		0			0
$641$	−5889.14	−	18124.9i	−0.362881	−	1.11683i	−0.951297	−	0.308275i	$-0.900248\pi$
$641$	−5889.14	−	18124.9i	−0.362881	−	1.11683i	0.588416	−	0.808558i	$-0.299752\pi$
$642$	7442.32	−	5407.16i	0.457515	−	0.332404i
$643$	10953.1			0.671768			0.335884	−	0.941903i	$-0.390965\pi$
$643$	10953.1			0.671768			0.335884	+	0.941903i	$0.390965\pi$
$644$	20424.9	−	14839.5i	1.24977	−	0.908012i
$645$		0			0
$646$	−1377.89	−	1001.10i	−0.0839201	−	0.0609715i
$647$	−8682.80	−	6308.42i	−0.527598	−	0.383323i	0.291860	−	0.956461i	$-0.405726\pi$
$647$	−8682.80	−	6308.42i	−0.527598	−	0.383323i	−0.819459	+	0.573138i	$0.805726\pi$
$648$	1145.91	−	3526.76i	0.0694688	−	0.213803i
$649$	−2295.60			−0.138845
$650$		0			0
$651$	12030.6			0.724298
$652$	2071.28	−	6374.75i	0.124414	−	0.382906i
$653$	−6391.92	−	4644.00i	−0.383055	−	0.278306i	0.379548	−	0.925172i	$-0.376079\pi$
$653$	−6391.92	−	4644.00i	−0.383055	−	0.278306i	−0.762604	+	0.646866i	$0.776079\pi$
$654$	−8201.42	−	5958.68i	−0.490368	−	0.356274i
$655$		0			0
$656$	267.792	−	194.562i	0.0159383	−	0.0115798i
$657$	−6955.08			−0.413004
$658$	22306.2	−	16206.4i	1.32156	−	0.960171i
$659$	−4537.13	−	13963.8i	−0.268196	−	0.825423i	−0.990940	−	0.134307i	$-0.957119\pi$
$659$	−4537.13	−	13963.8i	−0.268196	−	0.825423i	0.722743	−	0.691116i	$-0.242881\pi$
$660$		0			0
$661$	−3412.01	+	10501.1i	−0.200774	+	0.617919i	0.799086	+	0.601216i	$0.205317\pi$
$661$	−3412.01	+	10501.1i	−0.200774	+	0.617919i	−0.999860	+	0.0167028i	$0.994683\pi$
$662$	2317.12	+	7131.36i	0.136038	+	0.418683i
$663$	−2218.94	−	6829.18i	−0.129979	−	0.400035i
$664$	−1117.57	+	3439.54i	−0.0653166	+	0.201024i
$665$		0			0
$666$	1087.00	+	3345.43i	0.0632436	+	0.194644i
$667$	30975.1	−	22504.7i	1.79814	−	1.30643i
$668$	8232.18			0.476815
$669$	−18495.0	+	13437.4i	−1.06885	+	0.776563i
$670$		0			0
$671$	−4446.64	−	3230.68i	−0.255828	−	0.185870i
$672$	−3696.03	−	2685.32i	−0.212169	−	0.154150i
$673$	−4257.81	+	13104.2i	−0.243873	+	0.750564i	0.751947	+	0.659224i	$0.229115\pi$
$673$	−4257.81	+	13104.2i	−0.243873	+	0.750564i	−0.995820	+	0.0913399i	$0.970885\pi$
$674$	632.521			0.0361481
$675$		0			0
$676$	−7216.60			−0.410594
$677$	−1996.34	+	6144.11i	−0.113332	+	0.348799i	−0.991595	−	0.129377i	$-0.958702\pi$
$677$	−1996.34	+	6144.11i	−0.113332	+	0.348799i	0.878264	+	0.478177i	$0.158702\pi$
$678$	−966.804	−	702.424i	−0.0547638	−	0.0397882i
$679$	−17162.0	−	12468.9i	−0.969983	−	0.704734i
$680$		0			0
$681$	13323.2	−	9679.90i	0.749703	−	0.544691i
$682$	−7458.27			−0.418756
$683$	−9137.33	+	6638.66i	−0.511904	+	0.371920i	−0.813545	−	0.581501i	$-0.802465\pi$
$683$	−9137.33	+	6638.66i	−0.511904	+	0.371920i	0.301641	+	0.953421i	$0.402465\pi$
$684$	−97.8697	−	301.212i	−0.00547097	−	0.0168379i
$685$		0			0
$686$	7380.60	−	22715.2i	0.410777	−	1.26424i
$687$	−5714.53	−	17587.5i	−0.317355	−	0.976718i
$688$	182.284	+	561.013i	0.0101010	+	0.0310878i
$689$	32.0426	−	98.6170i	0.00177174	−	0.00545284i
$690$		0			0
$691$	828.470	+	2549.77i	0.0456100	+	0.140373i	0.971268	−	0.237988i	$-0.0764878\pi$
$691$	828.470	+	2549.77i	0.0456100	+	0.140373i	−0.925658	+	0.378361i	$0.876488\pi$
$692$	13947.6	−	10133.5i	0.766197	−	0.556675i
$693$	−11003.5			−0.603158
$694$	−9596.70	+	6972.41i	−0.524907	+	0.381367i
$695$		0			0
$696$	−5605.17	−	4072.39i	−0.305264	−	0.221787i
$697$	−1378.76	−	1001.73i	−0.0749275	−	0.0544380i
$698$	−5137.82	+	15812.6i	−0.278609	+	0.857471i
$699$	−27332.4			−1.47898
$700$		0			0
$701$	−34520.6			−1.85995			−0.929976	−	0.367620i	$-0.880173\pi$
$701$	−34520.6			−1.85995			−0.929976	+	0.367620i	$0.880173\pi$
$702$	1867.16	−	5746.54i	0.100387	−	0.308959i
$703$	−1920.42	−	1395.26i	−0.103030	−	0.0748555i
$704$	2291.31	+	1664.74i	0.122666	+	0.0891224i
$705$		0			0
$706$	5831.63	−	4236.93i	0.310873	−	0.225862i
$707$	−22223.1			−1.18216
$708$	−738.248	+	536.369i	−0.0391879	+	0.0284717i
$709$	−6361.25	−	19577.9i	−0.336956	−	1.03704i	−0.965751	−	0.259472i	$-0.916451\pi$
$709$	−6361.25	−	19577.9i	−0.336956	−	1.03704i	0.628794	−	0.777572i	$-0.283549\pi$
$710$		0			0
$711$	1463.10	−	4502.95i	0.0771736	−	0.237516i
$712$	−2135.90	−	6573.62i	−0.112424	−	0.346007i
$713$	−5062.82	−	15581.8i	−0.265925	−	0.818432i
$714$	−7268.64	+	22370.6i	−0.380983	+	1.17255i
$715$		0			0
$716$	−3365.27	−	10357.2i	−0.175651	−	0.540597i
$717$	−3026.50	+	2198.88i	−0.157639	+	0.114531i
$718$	−16072.7			−0.835417
$719$	8049.33	−	5848.18i	0.417510	−	0.303339i	−0.359125	−	0.933289i	$-0.616925\pi$
$719$	8049.33	−	5848.18i	0.417510	−	0.303339i	0.776635	+	0.629951i	$0.216925\pi$
$720$		0			0
$721$	−101.331	−	73.6213i	−0.00523407	−	0.00380277i
$722$	−10925.2	−	7937.61i	−0.563149	−	0.409151i
$723$	6408.98	−	19724.8i	0.329672	−	1.01463i
$724$	−5221.50			−0.268033
$725$		0			0
$726$	−5518.08			−0.282087
$727$	2960.41	−	9111.21i	0.151026	−	0.464809i	−0.846711	−	0.532053i	$-0.821421\pi$
$727$	2960.41	−	9111.21i	0.151026	−	0.464809i	0.997737	+	0.0672442i	$0.0214206\pi$
$728$	−4164.41	−	3025.62i	−0.212010	−	0.154034i
$729$	−17514.7	−	12725.2i	−0.889840	−	0.646506i
$730$		0			0
$731$	2457.07	−	1785.16i	0.124320	−	0.0903238i
$732$	−2184.86			−0.110321
$733$	−25696.8	+	18669.8i	−1.29486	+	0.940772i	−0.999891	−	0.0147351i	$-0.995310\pi$
$733$	−25696.8	+	18669.8i	−1.29486	+	0.940772i	−0.294970	+	0.955507i	$0.595310\pi$
$734$	8034.53	+	24727.7i	0.404032	+	1.24348i
$735$		0			0
$736$	−1922.57	+	5917.06i	−0.0962865	+	0.296339i
$737$	−10655.2	−	32793.3i	−0.532549	−	1.63902i
$738$	−97.9319	−	301.403i	−0.00488472	−	0.0150336i
$739$	4249.28	−	13077.9i	0.211519	−	0.650987i	−0.787864	−	0.615849i	$-0.788813\pi$
$739$	4249.28	−	13077.9i	0.211519	−	0.650987i	0.999382	−	0.0351378i	$-0.0111870\pi$
$740$		0			0
$741$	278.449	+	856.979i	0.0138044	+	0.0424857i
$742$	−274.797	+	199.651i	−0.0135958	+	0.00987795i
$743$	6312.16			0.311670			0.155835	−	0.987783i	$-0.450193\pi$
$743$	6312.16			0.311670			0.155835	+	0.987783i	$0.450193\pi$
$744$	−2398.52	+	1742.63i	−0.118191	+	0.0858708i
$745$		0			0
$746$	11298.4	+	8208.78i	0.554510	+	0.402875i
$747$	2801.26	+	2035.23i	0.137206	+	0.0996857i
$748$	4506.11	−	13868.4i	0.220267	−	0.677913i
$749$	−33952.9			−1.65636
$750$		0			0
$751$	40114.6			1.94914			0.974569	−	0.224087i	$-0.0719400\pi$
$751$	40114.6			1.94914			0.974569	+	0.224087i	$0.0719400\pi$
$752$	−2099.66	+	6462.09i	−0.101817	+	0.313362i
$753$	−2205.42	−	1602.33i	−0.106733	−	0.0775459i
$754$	−6315.49	−	4588.47i	−0.305035	−	0.221621i
$755$		0			0
$756$	−16012.7	+	11633.9i	−0.770341	+	0.559686i
$757$	8151.37			0.391369			0.195685	−	0.980667i	$-0.437307\pi$
$757$	8151.37			0.391369			0.195685	+	0.980667i	$0.437307\pi$
$758$	−1483.05	+	1077.50i	−0.0710643	+	0.0516312i
$759$	−11692.7	−	35986.4i	−0.559181	−	1.72098i
$760$		0			0
$761$	−1730.96	+	5327.36i	−0.0824538	+	0.253767i	−0.983781	−	0.179371i	$-0.942594\pi$
$761$	−1730.96	+	5327.36i	−0.0824538	+	0.253767i	0.901328	+	0.433138i	$0.142594\pi$
$762$	−4447.87	−	13689.1i	−0.211456	−	0.650793i
$763$	11562.2	+	35584.8i	0.548597	+	1.68841i
$764$	4901.56	−	15085.5i	0.232110	−	0.714362i
$765$		0			0
$766$	346.270	+	1065.71i	0.0163332	+	0.0502684i
$767$	−831.804	+	604.341i	−0.0391587	+	0.0284504i
$768$	1125.84			0.0528973
$769$	−2973.61	+	2160.45i	−0.139442	+	0.101311i	−0.655320	−	0.755352i	$-0.727466\pi$
$769$	−2973.61	+	2160.45i	−0.139442	+	0.101311i	0.515877	+	0.856662i	$0.327466\pi$
$770$		0			0
$771$	−10696.9	−	7771.73i	−0.499661	−	0.363025i
$772$	−6281.80	−	4563.99i	−0.292859	−	0.212774i
$773$	2094.03	−	6444.75i	0.0974345	−	0.299873i	−0.890446	−	0.455089i	$-0.849607\pi$
$773$	2094.03	−	6444.75i	0.0974345	−	0.299873i	0.987881	+	0.155216i	$0.0496074\pi$
$774$	564.766			0.0262275
$775$		0			0
$776$	5227.68			0.241833
$777$	−10130.6	+	31178.7i	−0.467738	+	1.43955i
$778$	−4803.33	−	3489.83i	−0.221347	−	0.160818i
$779$	173.018	+	125.705i	0.00795766	+	0.00578158i
$780$		0			0
$781$	21961.6	−	15956.0i	1.00621	−	0.731051i
$782$	32032.6			1.46481
$783$	−24283.9	+	17643.3i	−1.10835	+	0.805263i
$784$	3514.70	+	10817.1i	0.160109	+	0.492764i
$785$		0			0
$786$	2939.45	−	9046.69i	0.133393	−	0.410540i
$787$	−1608.89	−	4951.65i	−0.0728725	−	0.224278i	0.907986	−	0.419001i	$-0.137619\pi$
$787$	−1608.89	−	4951.65i	−0.0728725	−	0.224278i	−0.980858	+	0.194722i	$0.937619\pi$
$788$	2495.02	+	7678.87i	0.112794	+	0.347143i
$789$	−655.588	+	2017.69i	−0.0295812	+	0.0910416i
$790$		0			0
$791$	1362.98	+	4194.82i	0.0612668	+	0.188560i
$792$	2193.75	−	1593.85i	0.0984235	−	0.0715089i
$793$	−2461.74			−0.110238
$794$	10230.8	−	7433.11i	0.457276	−	0.332231i
$795$		0			0
$796$	−3189.17	−	2317.07i	−0.142007	−	0.103174i
$797$	−26265.4	−	19082.9i	−1.16734	−	0.848121i	−0.176650	−	0.984274i	$-0.556526\pi$
$797$	−26265.4	−	19082.9i	−1.16734	−	0.848121i	−0.990688	+	0.136153i	$0.956526\pi$
$798$	912.125	−	2807.23i	0.0404623	−	0.124530i
$799$	34983.2			1.54896
$800$		0			0
$801$	−6617.60			−0.291912
$802$	1859.47	−	5722.85i	0.0818703	−	0.251971i
$803$	32509.9	+	23619.8i	1.42870	+	1.03801i
$804$	−11088.8	−	8056.48i	−0.486408	−	0.353396i
$805$		0			0
$806$	−2702.48	+	1963.47i	−0.118103	+	0.0858067i
$807$	22883.5			0.998187
$808$	4430.58	−	3219.01i	0.192905	−	0.140154i
$809$	4880.74	+	15021.4i	0.212111	+	0.652811i	0.999346	+	0.0361575i	$0.0115118\pi$
$809$	4880.74	+	15021.4i	0.212111	+	0.652811i	−0.787235	+	0.616653i	$0.788488\pi$
$810$		0			0
$811$	1468.40	−	4519.27i	0.0635789	−	0.195676i	−0.914221	−	0.405215i	$-0.867197\pi$
$811$	1468.40	−	4519.27i	0.0635789	−	0.195676i	0.977800	+	0.209540i	$0.0671965\pi$
$812$	7902.06	+	24320.0i	0.341512	+	1.05107i
$813$	−2940.28	−	9049.25i	−0.126839	−	0.390370i
$814$	6280.34	−	19328.9i	0.270425	−	0.832282i
$815$		0			0
$816$	−1791.23	−	5512.83i	−0.0768450	−	0.236504i
$817$	−308.332	+	224.016i	−0.0132034	+	0.00959282i
$818$	−22472.5			−0.960555
$819$	−3987.09	+	2896.79i	−0.170110	+	0.123592i
$820$		0			0
$821$	−33068.5	−	24025.6i	−1.40572	−	1.02132i	−0.993927	−	0.110039i	$-0.964902\pi$
$821$	−33068.5	−	24025.6i	−1.40572	−	1.02132i	−0.411794	−	0.911277i	$-0.635098\pi$
$822$	16493.8	+	11983.5i	0.699863	+	0.508480i
$823$	−4691.60	+	14439.2i	−0.198710	+	0.611568i	0.801203	+	0.598393i	$0.204194\pi$
$823$	−4691.60	+	14439.2i	−0.198710	+	0.611568i	−0.999913	+	0.0131750i	$0.995806\pi$
$824$	30.8661			0.00130494
$825$		0			0
$826$	3367.99			0.141874
$827$	4888.31	−	15044.7i	0.205542	−	0.632593i	−0.794149	−	0.607723i	$-0.792083\pi$
$827$	4888.31	−	15044.7i	0.205542	−	0.632593i	0.999691	−	0.0248693i	$-0.00791697\pi$
$828$	4819.02	+	3501.23i	0.202262	+	0.146952i
$829$	−1.67554	−	1.21735i	−7.01976e−5	−	5.10015e-5i	0.587750	−	0.809042i	$-0.300014\pi$
$829$	−1.67554	−	1.21735i	−7.01976e−5	−	5.10015e-5i	−0.587820	+	0.808991i	$0.700014\pi$
$830$		0			0
$831$	−17758.5	+	12902.3i	−0.741317	+	0.538598i
$832$	1268.51			0.0528578
$833$	47375.8	−	34420.6i	1.97056	−	1.43169i
$834$	2882.87	+	8872.55i	0.119695	+	0.368383i
$835$		0			0
$836$	−565.462	+	1740.31i	−0.0233935	+	0.0719976i
$837$	3969.17	+	12215.8i	0.163912	+	0.504470i
$838$	−2757.53	−	8486.82i	−0.113672	−	0.349848i
$839$	5938.00	−	18275.3i	0.244341	−	0.752005i	−0.751403	−	0.659844i	$-0.770622\pi$
$839$	5938.00	−	18275.3i	0.244341	−	0.752005i	0.995744	−	0.0921615i	$-0.0293776\pi$
$840$		0			0
$841$	4447.16	+	13686.9i	0.182343	+	0.561193i
$842$	−9234.81	+	6709.49i	−0.377972	+	0.274613i
$843$	1935.04			0.0790584
$844$	−14021.6	+	10187.3i	−0.571852	+	0.415475i
$845$		0			0
$846$	5262.91	+	3823.73i	0.213880	+	0.155393i
$847$	16476.8	+	11971.1i	0.668416	+	0.485633i
$848$	25.8663	−	79.6082i	0.00104747	−	0.00322377i
$849$	15988.0			0.646296
$850$		0			0
$851$	44645.0			1.79837
$852$	3334.54	−	10262.7i	0.134084	−	0.412668i
$853$	−20360.1	−	14792.5i	−0.817253	−	0.593769i	0.0986714	−	0.995120i	$-0.468541\pi$
$853$	−20360.1	−	14792.5i	−0.817253	−	0.593769i	−0.915924	+	0.401351i	$0.868541\pi$
$854$	6523.90	+	4739.89i	0.261409	+	0.189925i
$855$		0			0
$856$	6769.13	−	4918.06i	0.270285	−	0.196374i
$857$	−32539.4			−1.29699			−0.648497	−	0.761217i	$-0.724602\pi$
$857$	−32539.4			−1.29699			−0.648497	+	0.761217i	$0.724602\pi$
$858$	−6241.43	+	4534.67i	−0.248344	+	0.180432i
$859$	14076.7	+	43323.7i	0.559129	+	1.72082i	0.684783	+	0.728747i	$0.259897\pi$
$859$	14076.7	+	43323.7i	0.559129	+	1.72082i	−0.125654	+	0.992074i	$0.540103\pi$
$860$		0			0
$861$	912.704	−	2809.02i	0.0361265	−	0.111186i
$862$	4956.37	+	15254.1i	0.195841	+	0.602735i
$863$	−1234.72	−	3800.08i	−0.0487027	−	0.149892i	0.923748	−	0.383002i	$-0.125110\pi$
$863$	−1234.72	−	3800.08i	−0.0487027	−	0.149892i	−0.972450	+	0.233110i	$0.925110\pi$
$864$	1507.26	−	4638.87i	0.0593496	−	0.182659i
$865$		0			0
$866$	3574.25	+	11000.4i	0.140252	+	0.431650i
$867$	−6664.58	+	4842.10i	−0.261062	+	0.189673i
$868$	10942.4			0.427891
$869$	−22131.2	+	16079.2i	−0.863922	+	0.627676i
$870$		0			0
$871$	−12494.0	−	9077.45i	−0.486044	−	0.353132i
$872$	−7459.57	−	5419.69i	−0.289694	−	0.210475i
$873$	1546.65	−	4760.11i	0.0599614	−	0.184542i
$874$	−4019.70			−0.155570
$875$		0			0
$876$	15973.7			0.616098
$877$	757.438	−	2331.16i	0.0291641	−	0.0897577i	−0.935415	−	0.353552i	$-0.884974\pi$
$877$	757.438	−	2331.16i	0.0291641	−	0.0897577i	0.964579	+	0.263794i	$0.0849739\pi$
$878$	19010.5	+	13811.9i	0.730720	+	0.530899i
$879$	25049.1	+	18199.2i	0.961189	+	0.698345i
$880$		0			0
$881$	−28818.0	+	20937.5i	−1.10205	+	0.800684i	−0.981393	−	0.192011i	$-0.938499\pi$
$881$	−28818.0	+	20937.5i	−1.10205	+	0.800684i	−0.120654	+	0.992695i	$0.538499\pi$
$882$	10889.5			0.415724
$883$	16992.6	−	12345.8i	0.647617	−	0.470521i	−0.214842	−	0.976649i	$-0.568924\pi$
$883$	16992.6	−	12345.8i	0.647617	−	0.470521i	0.862459	+	0.506128i	$0.168924\pi$
$884$	−2018.22	−	6211.45i	−0.0767875	−	0.236328i
$885$		0			0
$886$	2205.45	−	6787.69i	0.0836272	−	0.257378i
$887$	−3762.96	−	11581.2i	−0.142444	−	0.438398i	0.854229	−	0.519896i	$-0.174029\pi$
$887$	−3762.96	−	11581.2i	−0.142444	−	0.438398i	−0.996673	+	0.0814984i	$0.974029\pi$
$888$	−2496.50	−	7683.44i	−0.0943435	−	0.290360i
$889$	−16416.4	+	50524.5i	−0.619335	+	1.90612i
$890$		0			0
$891$	6338.83	+	19508.9i	0.238338	+	0.733528i
$892$	−16822.1	+	12221.9i	−0.631440	+	0.458768i
$893$	−4389.96			−0.164507
$894$	−13025.1	+	9463.29i	−0.487276	+	0.354027i
$895$		0			0
$896$	−3361.71	−	2442.42i	−0.125342	−	0.0910666i
$897$	−13710.6	−	9961.34i	−0.510350	−	0.370791i
$898$	8880.60	−	27331.7i	0.330011	−	1.01567i
$899$	16594.6			0.615640
$900$		0			0
$901$	−430.967			−0.0159352
$902$	−565.821	+	1741.42i	−0.0208867	+	0.0642826i
$903$	4258.26	+	3093.81i	0.156928	+	0.114015i
$904$	−879.352	−	638.887i	−0.0323527	−	0.0235056i
$905$		0			0
$906$	−11282.3	+	8197.04i	−0.413718	+	0.300583i
$907$	33352.4			1.22100			0.610501	−	0.792015i	$-0.290968\pi$
$907$	33352.4			1.22100			0.610501	+	0.792015i	$0.290968\pi$
$908$	12118.1	−	8804.31i	0.442900	−	0.321786i
$909$	−1620.27	−	4986.68i	−0.0591210	−	0.181956i
$910$		0			0
$911$	5604.85	−	17249.9i	0.203839	−	0.627350i	−0.795921	−	0.605401i	$-0.793013\pi$
$911$	5604.85	−	17249.9i	0.203839	−	0.627350i	0.999759	−	0.0219494i	$-0.00698727\pi$
$912$	224.777	+	691.793i	0.00816131	+	0.0251179i
$913$	−6182.06	−	19026.4i	−0.224092	−	0.689685i
$914$	−248.495	+	764.789i	−0.00899287	+	0.0276772i
$915$		0			0
$916$	−5197.62	−	15996.6i	−0.187483	−	0.577013i
$917$	−28403.2	+	20636.1i	−1.02285	+	0.743147i
$918$	−25113.0			−0.902889
$919$	25633.4	−	18623.8i	0.920096	−	0.668489i	−0.0234522	−	0.999725i	$-0.507466\pi$
$919$	25633.4	−	18623.8i	0.920096	−	0.668489i	0.943548	+	0.331236i	$0.107466\pi$
$920$		0			0
$921$	14180.0	+	10302.4i	0.507325	+	0.368593i
$922$	11686.9	+	8491.02i	0.417448	+	0.303294i
$923$	3757.12	−	11563.2i	0.133984	−	0.412360i
$924$	25271.7			0.899761
$925$		0			0
$926$	−6554.13			−0.232594
$927$	9.13201	−	28.1054i	0.000323554	−	0.000995797i
$928$	−5098.16	−	3704.03i	−0.180340	−	0.131024i
$929$	22563.0	+	16393.0i	0.796844	+	0.578941i	0.909987	−	0.414638i	$-0.136092\pi$
$929$	22563.0	+	16393.0i	0.796844	+	0.578941i	−0.113143	+	0.993579i	$0.536092\pi$
$930$		0			0
$931$	−5945.09	+	4319.36i	−0.209283	+	0.152053i
$932$	−24860.1			−0.873732
$933$	−22848.8	+	16600.7i	−0.801755	+	0.582509i
$934$	−3574.71	−	11001.8i	−0.125234	−	0.385429i
$935$		0			0
$936$	375.300	−	1155.05i	0.0131058	−	0.0403356i
$937$	12599.7	+	38777.9i	0.439290	+	1.35200i	0.888626	+	0.458633i	$0.151661\pi$
$937$	12599.7	+	38777.9i	0.439290	+	1.35200i	−0.449336	+	0.893363i	$0.648339\pi$
$938$	15632.8	+	48112.7i	0.544166	+	1.67477i
$939$	9420.48	−	28993.3i	0.327397	−	1.00762i
$940$		0			0
$941$	−7635.56	−	23499.8i	−0.264519	−	0.814105i	−0.991804	−	0.127769i	$-0.959218\pi$
$941$	−7635.56	−	23499.8i	−0.264519	−	0.814105i	0.727285	−	0.686335i	$-0.240782\pi$
$942$	10926.4	−	7938.46i	0.377919	−	0.274574i
$943$	−4022.25			−0.138900
$944$	−671.470	+	487.852i	−0.0231509	+	0.0168201i
$945$		0			0
$946$	−2639.86	−	1917.97i	−0.0907287	−	0.0659183i
$947$	26803.1	+	19473.6i	0.919730	+	0.668223i	0.943457	−	0.331496i	$-0.107553\pi$
$947$	26803.1	+	19473.6i	0.919730	+	0.668223i	−0.0237270	+	0.999718i	$0.507553\pi$
$948$	−3360.29	+	10341.9i	−0.115124	+	0.354314i
$949$	17998.0			0.615638
$950$		0			0
$951$	−29062.6			−0.990978
$952$	−6611.15	+	20347.0i	−0.225072	+	0.692701i
$953$	26148.8	+	18998.2i	0.888816	+	0.645763i	0.935569	−	0.353144i	$-0.114887\pi$
$953$	26148.8	+	18998.2i	0.888816	+	0.645763i	−0.0467529	+	0.998906i	$0.514887\pi$
$954$	−64.8352	−	47.1055i	−0.00220033	−	0.00159864i
$955$		0			0
$956$	−2752.74	+	1999.98i	−0.0931277	+	0.0676612i
$957$	38325.5			1.29455
$958$	3792.33	−	2755.29i	0.127896	−	0.0929221i
$959$	−23252.6	−	71564.3i	−0.782969	−	2.40973i
$960$		0			0
$961$	−7011.58	+	21579.4i	−0.235359	+	0.724361i
$962$	−2812.87	−	8657.13i	−0.0942730	−	0.290143i
$963$	−2475.48	−	7618.74i	−0.0828361	−	0.254943i
$964$	5829.26	−	17940.6i	0.194759	−	0.599407i
$965$		0			0
$966$	17155.0	+	52797.6i	0.571379	+	1.75852i
$967$	10355.3	−	7523.54i	0.344367	−	0.250197i	−0.402135	−	0.915580i	$-0.631732\pi$
$967$	10355.3	−	7523.54i	0.344367	−	0.250197i	0.746502	+	0.665383i	$0.231732\pi$
$968$	−5018.94			−0.166648
$969$	3029.84	−	2201.31i	0.100446	−	0.0729786i
$970$		0			0
$971$	30611.3	+	22240.4i	1.01170	+	0.735046i	0.964566	−	0.263842i	$-0.0849898\pi$
$971$	30611.3	+	22240.4i	1.01170	+	0.735046i	0.0471385	+	0.998888i	$0.484990\pi$
$972$	−6721.15	−	4883.20i	−0.221791	−	0.161141i
$973$	10640.2	−	32747.3i	0.350576	−	1.07896i
$974$	23527.9			0.774006
$975$		0			0
$976$	−1987.23			−0.0651738
$977$	−9126.82	+	28089.5i	−0.298867	+	0.919817i	0.683028	+	0.730392i	$0.260663\pi$
$977$	−9126.82	+	28089.5i	−0.298867	+	0.919817i	−0.981895	+	0.189425i	$0.939337\pi$
$978$	11923.9	+	8663.25i	0.389863	+	0.283252i
$979$	30932.4	+	22473.7i	1.00981	+	0.733669i
$980$		0			0
$981$	−7141.93	+	5188.91i	−0.232441	+	0.168878i
$982$	−21996.0			−0.714788
$983$	−859.475	+	624.445i	−0.0278871	+	0.0202611i	−0.601641	−	0.798766i	$-0.705486\pi$
$983$	−859.475	+	624.445i	−0.0278871	+	0.0202611i	0.573754	+	0.819027i	$0.305486\pi$
$984$	224.920	+	692.232i	0.00728677	+	0.0224264i
$985$		0			0
$986$	−10026.1	+	30857.1i	−0.323829	+	0.996642i
$987$	18735.1	+	57660.8i	0.604200	+	1.85954i
$988$	253.262	+	779.461i	0.00815521	+	0.0250992i
$989$	2215.03	−	6817.15i	0.0712171	−	0.219184i
$990$		0			0
$991$	15803.1	+	48637.0i	0.506561	+	1.55904i	0.798130	+	0.602486i	$0.205823\pi$
$991$	15803.1	+	48637.0i	0.506561	+	1.55904i	−0.291568	+	0.956550i	$0.594177\pi$
$992$	−2181.57	+	1585.00i	−0.0698234	+	0.0507297i
$993$	−16488.1			−0.526924
$994$	−32220.9	+	23409.9i	−1.02816	+	0.746998i
$995$		0			0
$996$	−6433.64	−	4674.31i	−0.204676	−	0.148706i
$997$	−38107.1	−	27686.5i	−1.21050	−	0.879477i	−0.215221	−	0.976565i	$-0.569047\pi$
$997$	−38107.1	−	27686.5i	−1.21050	−	0.879477i	−0.995276	+	0.0970879i	$0.969047\pi$
$998$	−7792.21	+	23982.0i	−0.247152	+	0.760657i
$999$	−35000.9			−1.10849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.d.b.101.2		16
5.2	odd	4		250.4.e.c.149.2		32
5.3	odd	4		250.4.e.c.149.7		32
5.4	even	2		50.4.d.b.21.3	✓	16
25.6	even	5	inner	250.4.d.b.151.2		16
25.8	odd	20		250.4.e.c.99.2		32
25.9	even	10		1250.4.a.j.1.3		8
25.16	even	5		1250.4.a.g.1.6		8
25.17	odd	20		250.4.e.c.99.7		32
25.19	even	10		50.4.d.b.31.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.b.21.3	✓	16	5.4	even	2
50.4.d.b.31.3	yes	16	25.19	even	10
250.4.d.b.101.2		16	1.1	even	1	trivial
250.4.d.b.151.2		16	25.6	even	5	inner
250.4.e.c.99.2		32	25.8	odd	20
250.4.e.c.99.7		32	25.17	odd	20
250.4.e.c.149.2		32	5.2	odd	4
250.4.e.c.149.7		32	5.3	odd	4
1250.4.a.g.1.6		8	25.16	even	5
1250.4.a.j.1.3		8	25.9	even	10

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 + 1.90211i) q^{2} +(-3.55790 - 2.58496i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(7.11579 - 5.16993i) q^{6} -32.4633 q^{7} +(6.47214 - 4.70228i) q^{8} +(-2.36687 - 7.28447i) q^{9} +(-13.6751 + 42.0875i) q^{11} +(5.43598 + 16.7302i) q^{12} +(6.12486 + 18.8504i) q^{13} +(20.0634 - 61.7488i) q^{14} +(4.94427 + 15.2169i) q^{16} +(66.6454 - 48.4207i) q^{17} +15.3187 q^{18} +(-8.36319 + 6.07621i) q^{19} +(115.501 + 83.9163i) q^{21} +(-71.6036 - 52.0231i) q^{22} +(60.0803 - 184.908i) q^{23} -35.1824 q^{24} -39.6409 q^{26} +(-47.1019 + 144.965i) q^{27} +(105.053 + 76.3257i) q^{28} +(159.317 + 115.751i) q^{29} +(68.1740 - 49.5313i) q^{31} -32.0000 q^{32} +(157.449 - 114.394i) q^{33} +(50.9126 + 156.693i) q^{34} +(-9.46747 + 29.1379i) q^{36} +(70.9588 + 218.389i) q^{37} +(-6.38891 - 19.6630i) q^{38} +(26.9359 - 82.9003i) q^{39} +(-6.39296 - 19.6755i) q^{41} +(-231.002 + 167.833i) q^{42} +36.8678 q^{43} +(143.207 - 104.046i) q^{44} +(314.584 + 228.559i) q^{46} +(343.561 + 249.612i) q^{47} +(21.7439 - 66.9209i) q^{48} +710.864 q^{49} -362.283 q^{51} +(24.4995 - 75.4016i) q^{52} +(-4.23242 - 3.07504i) q^{53} +(-246.629 - 179.186i) q^{54} +(-210.107 + 152.651i) q^{56} +45.4621 q^{57} +(-318.635 + 231.502i) q^{58} +(16.0299 + 49.3350i) q^{59} +(-38.3804 + 118.123i) q^{61} +(52.0803 + 160.287i) q^{62} +(76.8363 + 236.478i) q^{63} +(19.7771 - 60.8676i) q^{64} +(120.280 + 370.185i) q^{66} +(-630.360 + 457.984i) q^{67} -329.513 q^{68} +(-691.740 + 502.578i) q^{69} +(-496.268 - 360.560i) q^{71} +(-49.5723 - 36.0164i) q^{72} +(280.603 - 863.608i) q^{73} -459.255 q^{74} +41.3499 q^{76} +(443.937 - 1366.30i) q^{77} +(141.038 + 102.470i) q^{78} +(500.100 + 363.344i) q^{79} +(375.005 - 272.457i) q^{81} +41.3761 q^{82} +(-365.730 + 265.719i) q^{83} +(-176.470 - 543.118i) q^{84} +(-22.7855 + 70.1266i) q^{86} +(-267.623 - 823.659i) q^{87} +(109.401 + 336.700i) q^{88} +(266.987 - 821.703i) q^{89} +(-198.833 - 611.945i) q^{91} +(-629.169 + 457.118i) q^{92} -370.592 q^{93} +(-687.123 + 499.224i) q^{94} +(113.853 + 82.7188i) q^{96} +(528.660 + 384.094i) q^{97} +(-439.338 + 1352.14i) q^{98} +338.953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 7 q^{3} - 16 q^{4} + 14 q^{6} + 54 q^{7} + 32 q^{8} - 83 q^{9} + 152 q^{11} + 12 q^{12} - 77 q^{13} + 52 q^{14} - 64 q^{16} - 76 q^{17} - 304 q^{18} - 20 q^{19} + 257 q^{21} + 226 q^{22}+ \cdots - 1786 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 7 * q^3 - 16 * q^4 + 14 * q^6 + 54 * q^7 + 32 * q^8 - 83 * q^9 + 152 * q^11 + 12 * q^12 - 77 * q^13 + 52 * q^14 - 64 * q^16 - 76 * q^17 - 304 * q^18 - 20 * q^19 + 257 * q^21 + 226 * q^22 + 383 * q^23 - 64 * q^24 - 716 * q^26 - 415 * q^27 - 4 * q^28 + 105 * q^29 + 177 * q^31 - 512 * q^32 - 64 * q^33 + 342 * q^34 - 332 * q^36 - 446 * q^37 - 90 * q^38 - 146 * q^39 + 462 * q^41 - 514 * q^42 + 1058 * q^43 - 452 * q^44 + 1124 * q^46 + 1114 * q^47 + 48 * q^48 + 1698 * q^49 - 3608 * q^51 - 308 * q^52 - 567 * q^53 + 390 * q^54 + 8 * q^56 + 1520 * q^57 - 210 * q^58 + 1275 * q^59 + 252 * q^61 + 176 * q^62 - 5402 * q^63 - 256 * q^64 + 998 * q^66 - 3296 * q^67 + 1976 * q^68 - 5491 * q^69 + 3712 * q^71 - 56 * q^72 + 1688 * q^73 - 1148 * q^74 - 200 * q^76 + 5453 * q^77 + 1152 * q^78 + 1750 * q^79 + 4106 * q^81 + 1576 * q^82 + 2153 * q^83 - 612 * q^84 + 1074 * q^86 + 1255 * q^87 - 1216 * q^88 + 5660 * q^89 - 493 * q^91 - 2248 * q^92 + 256 * q^93 - 2228 * q^94 + 224 * q^96 + 429 * q^97 + 674 * q^98 - 1786 * q^99

Introduction

L-functions

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