LMFDB - Embedded newform 37.4.b.a.36.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,4,Mod(36,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

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("37.36");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	37.b (of order $2$, degree $1$, 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:	$2.18307067021$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 58x^{5} + 197x^{4} + 26x^{3} + 2x^{2} + 28x + 196 $ x^8 - 4x^7 + 8x^6 + 58x^5 + 197x^4 + 26x^3 + 2x^2 + 28*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			36.4
Root			$3.85207 - 3.85207i$ of defining polynomial
Character	$\chi$	$=$	37.36
Dual form			37.4.b.a.36.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.835079i q^{2} -3.65228 q^{3} +7.30264 q^{4} -18.7560i q^{5} +3.04994i q^{6} +17.3131 q^{7} -12.7789i q^{8} -13.6608 q^{9} +O(q^{10})$	\(q-0.835079i q^{2} -3.65228 q^{3} +7.30264 q^{4} -18.7560i q^{5} +3.04994i q^{6} +17.3131 q^{7} -12.7789i q^{8} -13.6608 q^{9} -15.6628 q^{10} +7.36011 q^{11} -26.6713 q^{12} +59.6068i q^{13} -14.4578i q^{14} +68.5023i q^{15} +47.7497 q^{16} +12.1114i q^{17} +11.4079i q^{18} +11.2676i q^{19} -136.968i q^{20} -63.2324 q^{21} -6.14628i q^{22} +85.0106i q^{23} +46.6722i q^{24} -226.788 q^{25} +49.7764 q^{26} +148.505 q^{27} +126.432 q^{28} +125.545i q^{29} +57.2048 q^{30} -306.143i q^{31} -142.106i q^{32} -26.8812 q^{33} +10.1140 q^{34} -324.725i q^{35} -99.7602 q^{36} +(89.1136 + 206.668i) q^{37} +9.40933 q^{38} -217.701i q^{39} -239.682 q^{40} +401.583 q^{41} +52.8041i q^{42} +419.921i q^{43} +53.7483 q^{44} +256.223i q^{45} +70.9906 q^{46} -219.489 q^{47} -174.395 q^{48} -43.2559 q^{49} +189.386i q^{50} -44.2343i q^{51} +435.287i q^{52} -466.895 q^{53} -124.013i q^{54} -138.046i q^{55} -221.243i q^{56} -41.1524i q^{57} +104.840 q^{58} -517.302i q^{59} +500.247i q^{60} +212.798i q^{61} -255.653 q^{62} -236.512 q^{63} +263.328 q^{64} +1117.99 q^{65} +22.4479i q^{66} +348.617 q^{67} +88.4454i q^{68} -310.483i q^{69} -271.171 q^{70} -606.558 q^{71} +174.571i q^{72} -847.941 q^{73} +(172.584 - 74.4169i) q^{74} +828.294 q^{75} +82.2832i q^{76} +127.427 q^{77} -181.797 q^{78} -705.862i q^{79} -895.595i q^{80} -173.539 q^{81} -335.354i q^{82} +798.628 q^{83} -461.764 q^{84} +227.162 q^{85} +350.667 q^{86} -458.527i q^{87} -94.0543i q^{88} -705.030i q^{89} +213.966 q^{90} +1031.98i q^{91} +620.802i q^{92} +1118.12i q^{93} +183.291i q^{94} +211.335 q^{95} +519.012i q^{96} -1121.27i q^{97} +36.1221i q^{98} -100.545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 - 36 * q^4 + 4 * q^7 + 2 * q^9	$ 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9} - 62 q^{10} + 90 q^{11} - 62 q^{12} + 276 q^{16} + 232 q^{21} + 138 q^{25} - 750 q^{26} - 288 q^{27} - 184 q^{28} - 64 q^{30} + 132 q^{33} + 404 q^{34} + 246 q^{36} - 372 q^{37} - 276 q^{38} + 774 q^{40} + 690 q^{41} - 2310 q^{44} + 1642 q^{46} - 1392 q^{47} + 1502 q^{48} - 388 q^{49} + 768 q^{53} + 1190 q^{58} + 1338 q^{62} - 2588 q^{63} - 3044 q^{64} + 1692 q^{65} + 1102 q^{67} - 2316 q^{70} - 12 q^{71} - 1442 q^{73} + 1464 q^{74} + 1312 q^{75} + 2496 q^{77} + 3078 q^{78} - 2848 q^{81} + 1692 q^{83} - 5140 q^{84} + 1240 q^{85} - 3936 q^{86} + 2380 q^{90} - 1788 q^{95} - 2628 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 36 * q^4 + 4 * q^7 + 2 * q^9 - 62 * q^10 + 90 * q^11 - 62 * q^12 + 276 * q^16 + 232 * q^21 + 138 * q^25 - 750 * q^26 - 288 * q^27 - 184 * q^28 - 64 * q^30 + 132 * q^33 + 404 * q^34 + 246 * q^36 - 372 * q^37 - 276 * q^38 + 774 * q^40 + 690 * q^41 - 2310 * q^44 + 1642 * q^46 - 1392 * q^47 + 1502 * q^48 - 388 * q^49 + 768 * q^53 + 1190 * q^58 + 1338 * q^62 - 2588 * q^63 - 3044 * q^64 + 1692 * q^65 + 1102 * q^67 - 2316 * q^70 - 12 * q^71 - 1442 * q^73 + 1464 * q^74 + 1312 * q^75 + 2496 * q^77 + 3078 * q^78 - 2848 * q^81 + 1692 * q^83 - 5140 * q^84 + 1240 * q^85 - 3936 * q^86 + 2380 * q^90 - 1788 * q^95 - 2628 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	0.835079i		−	0.295245i	−0.989044	−	0.147623i	$-0.952838\pi$
$2$		−	0.835079i		−	0.295245i	0.989044	−	0.147623i	$-0.0471621\pi$
$3$	−3.65228			−0.702882			−0.351441	−	0.936210i	$-0.614308\pi$
$3$	−3.65228			−0.702882			−0.351441	+	0.936210i	$0.614308\pi$
$4$	7.30264			0.912830
$5$		−	18.7560i		−	1.67759i	−0.544448	−	0.838794i	$-0.683261\pi$
$5$		−	18.7560i		−	1.67759i	0.544448	−	0.838794i	$-0.316739\pi$
$6$			3.04994i			0.207522i
$7$	17.3131			0.934820			0.467410	−	0.884041i	$-0.345187\pi$
$7$	17.3131			0.934820			0.467410	+	0.884041i	$0.345187\pi$
$8$		−	12.7789i		−	0.564754i
$9$	−13.6608			−0.505957
$10$	−15.6628			−0.495300
$11$	7.36011			0.201742			0.100871	−	0.994900i	$-0.467837\pi$
$11$	7.36011			0.201742			0.100871	+	0.994900i	$0.467837\pi$
$12$	−26.6713			−0.641612
$13$			59.6068i			1.27169i	0.771818	+	0.635844i	$0.219348\pi$
$13$			59.6068i			1.27169i	−0.771818	+	0.635844i	$0.780652\pi$
$14$		−	14.4578i		−	0.276001i
$15$			68.5023i			1.17915i
$16$	47.7497			0.746090
$17$			12.1114i			0.172791i	0.996261	+	0.0863956i	$0.0275349\pi$
$17$			12.1114i			0.172791i	−0.996261	+	0.0863956i	$0.972465\pi$
$18$			11.4079i			0.149381i
$19$			11.2676i			0.136051i	0.997684	+	0.0680253i	$0.0216699\pi$
$19$			11.2676i			0.136051i	−0.997684	+	0.0680253i	$0.978330\pi$
$20$		−	136.968i		−	1.53135i
$21$	−63.2324			−0.657069
$22$		−	6.14628i		−	0.0595632i
$23$			85.0106i			0.770693i	0.922772	+	0.385346i	$0.125918\pi$
$23$			85.0106i			0.770693i	−0.922772	+	0.385346i	$0.874082\pi$
$24$			46.6722i			0.396955i
$25$	−226.788			−1.81430
$26$	49.7764			0.375460
$27$	148.505			1.05851
$28$	126.432			0.853333
$29$			125.545i			0.803902i	0.915661	+	0.401951i	$0.131668\pi$
$29$			125.545i			0.803902i	−0.915661	+	0.401951i	$0.868332\pi$
$30$	57.2048			0.348137
$31$		−	306.143i		−	1.77370i	−0.462053	−	0.886852i	$-0.652887\pi$
$31$		−	306.143i		−	1.77370i	0.462053	−	0.886852i	$-0.347113\pi$
$32$		−	142.106i		−	0.785033i
$33$	−26.8812			−0.141801
$34$	10.1140			0.0510157
$35$		−	324.725i		−	1.56824i
$36$	−99.7602			−0.461853
$37$	89.1136	+	206.668i	0.395951	+	0.918272i
$37$	89.1136	+	206.668i	0.395951	+	0.918272i
$38$	9.40933			0.0401683
$39$		−	217.701i		−	0.893846i
$40$	−239.682			−0.947425
$41$	401.583			1.52968			0.764839	−	0.644221i	$-0.222819\pi$
$41$	401.583			1.52968			0.764839	+	0.644221i	$0.222819\pi$
$42$			52.8041i			0.193996i
$43$			419.921i			1.48924i	0.667488	+	0.744620i	$0.267370\pi$
$43$			419.921i			1.48924i	−0.667488	+	0.744620i	$0.732630\pi$
$44$	53.7483			0.184156
$45$			256.223i			0.848788i
$46$	70.9906			0.227543
$47$	−219.489			−0.681186			−0.340593	−	0.940211i	$-0.610628\pi$
$47$	−219.489			−0.681186			−0.340593	+	0.940211i	$0.610628\pi$
$48$	−174.395			−0.524413
$49$	−43.2559			−0.126111
$50$			189.386i			0.535664i
$51$		−	44.2343i		−	0.121452i
$52$			435.287i			1.16084i
$53$	−466.895			−1.21006			−0.605028	−	0.796204i	$-0.706838\pi$
$53$	−466.895			−1.21006			−0.605028	+	0.796204i	$0.706838\pi$
$54$		−	124.013i		−	0.312520i
$55$		−	138.046i		−	0.338440i
$56$		−	221.243i		−	0.527943i
$57$		−	41.1524i		−	0.0956276i
$58$	104.840			0.237348
$59$		−	517.302i		−	1.14147i	−0.821133	−	0.570737i	$-0.806657\pi$
$59$		−	517.302i		−	1.14147i	0.821133	−	0.570737i	$-0.193343\pi$
$60$			500.247i			1.07636i
$61$			212.798i			0.446656i	0.974743	+	0.223328i	$0.0716921\pi$
$61$			212.798i			0.446656i	−0.974743	+	0.223328i	$0.928308\pi$
$62$	−255.653			−0.523677
$63$	−236.512			−0.472979
$64$	263.328			0.514312
$65$	1117.99			2.13337
$66$			22.4479i			0.0418659i
$67$	348.617			0.635678			0.317839	−	0.948145i	$-0.397043\pi$
$67$	348.617			0.635678			0.317839	+	0.948145i	$0.397043\pi$
$68$			88.4454i			0.157729i
$69$		−	310.483i		−	0.541706i
$70$	−271.171			−0.463016
$71$	−606.558			−1.01388			−0.506938	−	0.861983i	$-0.669223\pi$
$71$	−606.558			−1.01388			−0.506938	+	0.861983i	$0.669223\pi$
$72$			174.571i			0.285741i
$73$	−847.941			−1.35951			−0.679753	−	0.733441i	$-0.737913\pi$
$73$	−847.941			−1.35951			−0.679753	+	0.733441i	$0.737913\pi$
$74$	172.584	−	74.4169i	0.271115	−	0.116903i
$75$	828.294			1.27524
$76$			82.2832i			0.124191i
$77$	127.427			0.188592
$78$	−181.797			−0.263904
$79$		−	705.862i		−	1.00526i	−0.864501	−	0.502631i	$-0.832365\pi$
$79$		−	705.862i		−	1.00526i	0.864501	−	0.502631i	$-0.167635\pi$
$80$		−	895.595i		−	1.25163i
$81$	−173.539			−0.238051
$82$		−	335.354i		−	0.451630i
$83$	798.628			1.05615			0.528077	−	0.849196i	$-0.322913\pi$
$83$	798.628			1.05615			0.528077	+	0.849196i	$0.322913\pi$
$84$	−461.764			−0.599792
$85$	227.162			0.289873
$86$	350.667			0.439691
$87$		−	458.527i		−	0.565049i
$88$		−	94.0543i		−	0.113934i
$89$		−	705.030i		−	0.839696i	−0.907594	−	0.419848i	$-0.862083\pi$
$89$		−	705.030i		−	0.839696i	0.907594	−	0.419848i	$-0.137917\pi$
$90$	213.966			0.250600
$91$			1031.98i			1.18880i
$92$			620.802i			0.703512i
$93$			1118.12i			1.24670i
$94$			183.291i			0.201117i
$95$	211.335			0.228237
$96$			519.012i			0.551786i
$97$		−	1121.27i		−	1.17368i	−0.809702	−	0.586841i	$-0.800371\pi$
$97$		−	1121.27i		−	1.17368i	0.809702	−	0.586841i	$-0.199629\pi$
$98$			36.1221i			0.0372335i
$99$	−100.545			−0.102073
$100$	−1656.15			−1.65615
$101$	−1677.55			−1.65270			−0.826350	−	0.563157i	$-0.809587\pi$
$101$	−1677.55			−1.65270			−0.826350	+	0.563157i	$0.809587\pi$
$102$	−36.9392			−0.0358581
$103$		−	202.371i		−	0.193595i	−0.995304	−	0.0967974i	$-0.969140\pi$
$103$		−	202.371i		−	0.193595i	0.995304	−	0.0967974i	$-0.0308599\pi$
$104$	761.710			0.718190
$105$			1185.99i			1.10229i
$106$			389.894i			0.357263i
$107$	−502.032			−0.453582			−0.226791	−	0.973943i	$-0.572823\pi$
$107$	−502.032			−0.453582			−0.226791	+	0.973943i	$0.572823\pi$
$108$	1084.48			0.966240
$109$			490.221i			0.430777i	0.976528	+	0.215388i	$0.0691017\pi$
$109$			490.221i			0.430777i	−0.976528	+	0.215388i	$0.930898\pi$
$110$	−115.280			−0.0999226
$111$	−325.468	−	754.811i	−0.278307	−	0.645437i
$112$	826.697			0.697460
$113$			1869.43i			1.55630i	0.628081	+	0.778148i	$0.283840\pi$
$113$			1869.43i			1.55630i	−0.628081	+	0.778148i	$0.716160\pi$
$114$	−34.3655			−0.0282336
$115$	1594.46			1.29291
$116$			916.812i			0.733826i
$117$		−	814.278i		−	0.643419i
$118$	−431.988			−0.337015
$119$			209.686i			0.161529i
$120$	875.385			0.665928
$121$	−1276.83			−0.959300
$122$	177.703			0.131873
$123$	−1466.70			−1.07518
$124$		−	2235.65i		−	1.61909i
$125$			1909.14i			1.36607i
$126$			197.506i			0.139645i
$127$	775.931			0.542147			0.271074	−	0.962559i	$-0.412621\pi$
$127$	775.931			0.542147			0.271074	+	0.962559i	$0.412621\pi$
$128$		−	1356.75i		−	0.936881i
$129$		−	1533.67i		−	1.04676i
$130$		−	933.606i		−	0.629867i
$131$			2195.99i			1.46462i	0.680974	+	0.732308i	$0.261557\pi$
$131$			2195.99i			1.46462i	−0.680974	+	0.732308i	$0.738443\pi$
$132$	−196.304			−0.129440
$133$			195.077i			0.127183i
$134$		−	291.123i		−	0.187681i
$135$		−	2785.36i		−	1.77574i
$136$	154.771			0.0975845
$137$	−1564.32			−0.975539			−0.487770	−	0.872972i	$-0.662189\pi$
$137$	−1564.32			−0.975539			−0.487770	+	0.872972i	$0.662189\pi$
$138$	−259.278			−0.159936
$139$	912.136			0.556593			0.278296	−	0.960495i	$-0.410230\pi$
$139$	912.136			0.556593			0.278296	+	0.960495i	$0.410230\pi$
$140$		−	2371.35i		−	1.43154i
$141$	801.636			0.478794
$142$			506.524i			0.299342i
$143$			438.713i			0.256552i
$144$	−652.301			−0.377489
$145$	2354.73			1.34862
$146$			708.098i			0.401388i
$147$	157.983			0.0886409
$148$	650.765	+	1509.22i	0.361436	+	0.838226i
$149$	−133.411			−0.0733521			−0.0366760	−	0.999327i	$-0.511677\pi$
$149$	−133.411			−0.0733521			−0.0366760	+	0.999327i	$0.511677\pi$
$150$		−	691.691i		−	0.376509i
$151$	3558.83			1.91797			0.958986	−	0.283454i	$-0.0914805\pi$
$151$	3558.83			1.91797			0.958986	+	0.283454i	$0.0914805\pi$
$152$	143.988			0.0768351
$153$		−	165.452i		−	0.0874249i
$154$		−	106.411i		−	0.0556809i
$155$	−5742.01			−2.97555
$156$		−	1589.79i		−	0.815930i
$157$	569.434			0.289464			0.144732	−	0.989471i	$-0.453768\pi$
$157$	569.434			0.289464			0.144732	+	0.989471i	$0.453768\pi$
$158$	−589.451			−0.296799
$159$	1705.23			0.850526
$160$	−2665.35			−1.31696
$161$			1471.80i			0.720459i
$162$			144.919i			0.0702833i
$163$		−	1937.74i		−	0.931138i	−0.885012	−	0.465569i	$-0.845850\pi$
$163$		−	1937.74i		−	0.931138i	0.885012	−	0.465569i	$-0.154150\pi$
$164$	2932.62			1.39634
$165$			504.184i			0.237883i
$166$		−	666.918i		−	0.311825i
$167$			2055.33i			0.952372i	0.879345	+	0.476186i	$0.157981\pi$
$167$			2055.33i			0.952372i	−0.879345	+	0.476186i	$0.842019\pi$
$168$			808.042i			0.371082i
$169$	−1355.97			−0.617189
$170$		−	189.698i		−	0.0855835i
$171$		−	153.925i		−	0.0688358i
$172$			3066.53i			1.35942i
$173$	1690.85			0.743083			0.371541	−	0.928416i	$-0.378829\pi$
$173$	1690.85			0.743083			0.371541	+	0.928416i	$0.378829\pi$
$174$	−382.906			−0.166828
$175$	−3926.41			−1.69605
$176$	351.443			0.150517
$177$			1889.33i			0.802322i
$178$	−588.755			−0.247916
$179$		−	1631.08i		−	0.681075i	−0.940231	−	0.340538i	$-0.889391\pi$
$179$		−	1631.08i		−	0.681075i	0.940231	−	0.340538i	$-0.110609\pi$
$180$			1871.10i			0.774799i
$181$	−1738.81			−0.714061			−0.357030	−	0.934093i	$-0.616211\pi$
$181$	−1738.81			−0.714061			−0.357030	+	0.934093i	$0.616211\pi$
$182$	861.784			0.350987
$183$		−	777.199i		−	0.313946i
$184$	1086.34			0.435252
$185$	3876.27	−	1671.42i	1.54048	−	0.664243i
$186$	933.718			0.368083
$187$			89.1414i			0.0348592i
$188$	−1602.85			−0.621808
$189$	2571.08			0.989517
$190$		−	176.482i		−	0.0673859i
$191$			1001.25i			0.379310i	0.981851	+	0.189655i	$0.0607369\pi$
$191$			1001.25i			0.379310i	−0.981851	+	0.189655i	$0.939263\pi$
$192$	−961.748			−0.361501
$193$			2515.29i			0.938107i	0.883170	+	0.469054i	$0.155405\pi$
$193$			2515.29i			0.938107i	−0.883170	+	0.469054i	$0.844595\pi$
$194$	−936.345			−0.346524
$195$	−4083.20			−1.49951
$196$	−315.883			−0.115118
$197$	−1841.44			−0.665976			−0.332988	−	0.942931i	$-0.608057\pi$
$197$	−1841.44			−0.665976			−0.332988	+	0.942931i	$0.608057\pi$
$198$			83.9633i			0.0301364i
$199$		−	854.101i		−	0.304249i	−0.988361	−	0.152125i	$-0.951388\pi$
$199$		−	854.101i		−	0.304249i	0.988361	−	0.152125i	$-0.0486115\pi$
$200$			2898.11i			1.02464i
$201$	−1273.25			−0.446806
$202$			1400.89i			0.487952i
$203$			2173.58i			0.751504i
$204$		−	323.027i		−	0.110865i
$205$		−	7532.10i		−	2.56617i
$206$	−168.996			−0.0571579
$207$		−	1161.32i		−	0.389937i
$208$			2846.21i			0.948793i
$209$			82.9308i			0.0274471i
$210$	990.394			0.325446
$211$	−1296.91			−0.423143			−0.211571	−	0.977363i	$-0.567858\pi$
$211$	−1296.91			−0.423143			−0.211571	+	0.977363i	$0.567858\pi$
$212$	−3409.57			−1.10458
$213$	2215.32			0.712635
$214$			419.237i			0.133918i
$215$	7876.05			2.49833
$216$		−	1897.73i		−	0.597797i
$217$		−	5300.28i		−	1.65810i
$218$	409.373			0.127185
$219$	3096.92			0.955573
$220$		−	1008.10i		−	0.308938i
$221$	−721.922			−0.219736
$222$	−630.327	+	271.792i	−0.190562	+	0.0821687i
$223$	3686.31			1.10697			0.553484	−	0.832860i	$-0.313298\pi$
$223$	3686.31			1.10697			0.553484	+	0.832860i	$0.313298\pi$
$224$		−	2460.30i		−	0.733865i
$225$	3098.11			0.917960
$226$	1561.12			0.459489
$227$		−	2426.26i		−	0.709412i	−0.934978	−	0.354706i	$-0.884581\pi$
$227$		−	2426.26i		−	0.709412i	0.934978	−	0.354706i	$-0.115419\pi$
$228$		−	300.521i		−	0.0872917i
$229$	−3655.45			−1.05484			−0.527421	−	0.849604i	$-0.676841\pi$
$229$	−3655.45			−1.05484			−0.527421	+	0.849604i	$0.676841\pi$
$230$		−	1331.50i		−	0.381724i
$231$	−465.398			−0.132558
$232$	1604.33			0.454007
$233$	−2528.17			−0.710842			−0.355421	−	0.934706i	$-0.615662\pi$
$233$	−2528.17			−0.710842			−0.355421	+	0.934706i	$0.615662\pi$
$234$	−679.987			−0.189966
$235$			4116.74i			1.14275i
$236$		−	3777.67i		−	1.04197i
$237$			2578.01i			0.706580i
$238$	175.105			0.0476906
$239$		−	1601.35i		−	0.433400i	−0.976238	−	0.216700i	$-0.930471\pi$
$239$		−	1601.35i		−	0.433400i	0.976238	−	0.216700i	$-0.0695293\pi$
$240$			3270.96i			0.879749i
$241$		−	5564.30i		−	1.48725i	−0.668595	−	0.743626i	$-0.733104\pi$
$241$		−	5564.30i		−	1.48725i	0.668595	−	0.743626i	$-0.266896\pi$
$242$			1066.25i			0.283229i
$243$	−3375.82			−0.891188
$244$			1553.99i			0.407721i
$245$			811.309i			0.211562i
$246$			1224.81i			0.317443i
$247$	−671.625			−0.173014
$248$	−3912.17			−1.00171
$249$	−2916.82			−0.742352
$250$	1594.28			0.403325
$251$			5857.17i			1.47291i	0.676485	+	0.736456i	$0.263502\pi$
$251$			5857.17i			1.47291i	−0.676485	+	0.736456i	$0.736498\pi$
$252$	−1727.16			−0.431749
$253$			625.688i			0.155481i
$254$		−	647.963i		−	0.160066i
$255$	−829.659			−0.203746
$256$	973.631			0.237703
$257$		−	3658.09i		−	0.887880i	−0.896056	−	0.443940i	$-0.853580\pi$
$257$		−	3658.09i		−	0.887880i	0.896056	−	0.443940i	$-0.146420\pi$
$258$	−1280.74			−0.309051
$259$	1542.83	+	3578.07i	0.370143	+	0.858419i
$260$	8164.25			1.94740
$261$		−	1715.05i		−	0.406740i
$262$	1833.83			0.432421
$263$	−4188.44			−0.982017			−0.491008	−	0.871155i	$-0.663372\pi$
$263$	−4188.44			−0.982017			−0.491008	+	0.871155i	$0.663372\pi$
$264$			343.513i			0.0800824i
$265$			8757.09i			2.02998i
$266$	162.905			0.0375501
$267$			2574.97i			0.590207i
$268$	2545.83			0.580266
$269$	870.480			0.197302			0.0986508	−	0.995122i	$-0.468547\pi$
$269$	870.480			0.197302			0.0986508	+	0.995122i	$0.468547\pi$
$270$	−2326.00			−0.524280
$271$	−714.832			−0.160232			−0.0801161	−	0.996786i	$-0.525529\pi$
$271$	−714.832			−0.160232			−0.0801161	+	0.996786i	$0.525529\pi$
$272$			578.317i			0.128918i
$273$		−	3769.08i		−	0.835586i
$274$			1306.33i			0.288023i
$275$	−1669.19			−0.366021
$276$		−	2267.34i		−	0.494486i
$277$		−	5003.16i		−	1.08524i	−0.839979	−	0.542619i	$-0.817433\pi$
$277$		−	5003.16i		−	1.08524i	0.839979	−	0.542619i	$-0.182567\pi$
$278$		−	761.706i		−	0.164331i
$279$			4182.16i			0.897418i
$280$	−4149.64			−0.885672
$281$		−	2771.50i		−	0.588377i	−0.955747	−	0.294188i	$-0.904951\pi$
$281$		−	2771.50i		−	0.588377i	0.955747	−	0.294188i	$-0.0950493\pi$
$282$		−	669.429i		−	0.141361i
$283$			2172.96i			0.456427i	0.973611	+	0.228214i	$0.0732885\pi$
$283$			2172.96i			0.456427i	−0.973611	+	0.228214i	$0.926712\pi$
$284$	−4429.48			−0.925496
$285$	−771.855			−0.160424
$286$	366.360			0.0757458
$287$	6952.66			1.42997
$288$			1941.29i			0.397193i
$289$	4766.31			0.970143
$290$		−	1966.38i		−	0.398173i
$291$			4095.18i			0.824960i
$292$	−6192.21			−1.24100
$293$	1837.50			0.366375			0.183188	−	0.983078i	$-0.441358\pi$
$293$	1837.50			0.366375			0.183188	+	0.983078i	$0.441358\pi$
$294$		−	131.928i		−	0.0261708i
$295$	−9702.53			−1.91493
$296$	2641.00	−	1138.78i	0.518597	−	0.223615i
$297$	1093.01			0.213546
$298$			111.409i			0.0216568i
$299$	−5067.20			−0.980080
$300$	6048.74			1.16408
$301$			7270.14i			1.39217i
$302$		−	2971.91i		−	0.566272i
$303$	6126.90			1.16165
$304$			538.024i			0.101506i
$305$	3991.25			0.749305
$306$	−138.166			−0.0258118
$307$	−1993.17			−0.370542			−0.185271	−	0.982687i	$-0.559316\pi$
$307$	−1993.17			−0.370542			−0.185271	+	0.982687i	$0.559316\pi$
$308$	930.550			0.172153
$309$			739.118i			0.136074i
$310$			4795.04i			0.878515i
$311$		−	6240.50i		−	1.13783i	−0.822395	−	0.568917i	$-0.807362\pi$
$311$		−	6240.50i		−	1.13783i	0.822395	−	0.568917i	$-0.192638\pi$
$312$	−2781.98			−0.504803
$313$			1131.64i			0.204357i	0.994766	+	0.102179i	$0.0325813\pi$
$313$			1131.64i			0.204357i	−0.994766	+	0.102179i	$0.967419\pi$
$314$		−	475.522i		−	0.0854627i
$315$			4436.02i			0.793464i
$316$		−	5154.66i		−	0.917634i
$317$	4461.56			0.790492			0.395246	−	0.918575i	$-0.370659\pi$
$317$	4461.56			0.790492			0.395246	+	0.918575i	$0.370659\pi$
$318$		−	1424.00i		−	0.251114i
$319$			924.027i			0.162181i
$320$		−	4938.98i		−	0.862805i
$321$	1833.56			0.318815
$322$	1229.07			0.212712
$323$	−136.466			−0.0235084
$324$	−1267.29			−0.217300
$325$		−	13518.1i		−	2.30723i
$326$	−1618.17			−0.274914
$327$		−	1790.43i		−	0.302785i
$328$		−	5131.80i		−	0.863891i
$329$	−3800.04			−0.636787
$330$	421.034			0.0702338
$331$			6263.31i			1.04007i	0.854145	+	0.520034i	$0.174081\pi$
$331$			6263.31i			1.04007i	−0.854145	+	0.520034i	$0.825919\pi$
$332$	5832.10			0.964090
$333$	−1217.37	−	2823.26i	−0.200334	−	0.464606i
$334$	1716.36			0.281183
$335$		−	6538.67i		−	1.06641i
$336$	−3019.33			−0.490232
$337$	1635.88			0.264427			0.132214	−	0.991221i	$-0.457792\pi$
$337$	1635.88			0.264427			0.132214	+	0.991221i	$0.457792\pi$
$338$			1132.34i			0.182222i
$339$		−	6827.69i		−	1.09389i
$340$	1658.88			0.264604
$341$		−	2253.24i		−	0.357830i
$342$	−128.539			−0.0203234
$343$	−6687.29			−1.05271
$344$	5366.14			0.841054
$345$	−5823.42			−0.908760
$346$		−	1412.00i		−	0.219392i
$347$			733.411i			0.113463i	0.998389	+	0.0567314i	$0.0180679\pi$
$347$			733.411i			0.113463i	−0.998389	+	0.0567314i	$0.981932\pi$
$348$		−	3348.46i		−	0.515793i
$349$	−1237.20			−0.189759			−0.0948796	−	0.995489i	$-0.530247\pi$
$349$	−1237.20			−0.189759			−0.0948796	+	0.995489i	$0.530247\pi$
$350$			3278.86i			0.500750i
$351$			8851.89i			1.34609i
$352$		−	1045.92i		−	0.158374i
$353$			3500.83i			0.527848i	0.964543	+	0.263924i	$0.0850168\pi$
$353$			3500.83i			0.527848i	−0.964543	+	0.263924i	$0.914983\pi$
$354$	1577.74			0.236882
$355$			11376.6i			1.70087i
$356$		−	5148.58i		−	0.766500i
$357$		−	765.834i		−	0.113536i
$358$	−1362.08			−0.201084
$359$	2282.34			0.335535			0.167768	−	0.985827i	$-0.446344\pi$
$359$	2282.34			0.335535			0.167768	+	0.985827i	$0.446344\pi$
$360$	3274.25			0.479356
$361$	6732.04			0.981490
$362$			1452.05i			0.210823i
$363$	4663.34			0.674275
$364$			7536.17i			1.08517i
$365$			15904.0i			2.28069i
$366$	−649.023			−0.0926911
$367$	−1857.18			−0.264153			−0.132076	−	0.991240i	$-0.542164\pi$
$367$	−1857.18			−0.264153			−0.132076	+	0.991240i	$0.542164\pi$
$368$			4059.23i			0.575006i
$369$	−5485.97			−0.773951
$370$	−1395.76	−	3236.99i	−0.196114	−	0.454820i
$371$	−8083.41			−1.13118
$372$			8165.22i			1.13803i
$373$	7259.11			1.00767			0.503837	−	0.863799i	$-0.331921\pi$
$373$	7259.11			1.00767			0.503837	+	0.863799i	$0.331921\pi$
$374$	74.4401			0.0102920
$375$		−	6972.71i		−	0.960185i
$376$			2804.83i			0.384703i
$377$	−7483.35			−1.02231
$378$		−	2147.06i		−	0.292150i
$379$	−3664.42			−0.496646			−0.248323	−	0.968677i	$-0.579879\pi$
$379$	−3664.42			−0.496646			−0.248323	+	0.968677i	$0.579879\pi$
$380$	1543.30			0.208342
$381$	−2833.92			−0.381066
$382$	836.126			0.111989
$383$		−	6831.81i		−	0.911461i	−0.890118	−	0.455730i	$-0.849378\pi$
$383$		−	6831.81i		−	0.911461i	0.890118	−	0.455730i	$-0.150622\pi$
$384$			4955.23i			0.658517i
$385$		−	2390.01i		−	0.316380i
$386$	2100.47			0.276972
$387$		−	5736.47i		−	0.753492i
$388$		−	8188.20i		−	1.07137i
$389$			5170.53i			0.673924i	0.941518	+	0.336962i	$0.109399\pi$
$389$			5170.53i			0.673924i	−0.941518	+	0.336962i	$0.890601\pi$
$390$			3409.79i			0.442722i
$391$	−1029.60			−0.133169
$392$			552.764i			0.0712215i
$393$		−	8020.38i		−	1.02945i
$394$			1537.75i			0.196626i
$395$	−13239.2			−1.68642
$396$	−734.247			−0.0931749
$397$	13328.4			1.68498			0.842488	−	0.538715i	$-0.181090\pi$
$397$	13328.4			1.68498			0.842488	+	0.538715i	$0.181090\pi$
$398$	−713.242			−0.0898281
$399$		−	712.477i		−	0.0893946i
$400$	−10829.1			−1.35363
$401$			10719.6i			1.33494i	0.744638	+	0.667469i	$0.232622\pi$
$401$			10719.6i			1.33494i	−0.744638	+	0.667469i	$0.767378\pi$
$402$			1063.26i			0.131917i
$403$	18248.2			2.25560
$404$	−12250.6			−1.50864
$405$			3254.90i			0.399351i
$406$	1815.11			0.221878
$407$	655.886	+	1521.10i	0.0798798	+	0.185254i
$408$	−565.267			−0.0685904
$409$			15428.1i			1.86520i	0.360907	+	0.932602i	$0.382467\pi$
$409$			15428.1i			1.86520i	−0.360907	+	0.932602i	$0.617533\pi$
$410$	−6289.90			−0.757649
$411$	5713.34			0.685689
$412$		−	1477.85i		−	0.176719i
$413$		−	8956.11i		−	1.06707i
$414$	−969.790			−0.115127
$415$		−	14979.1i		−	1.77179i
$416$	8470.49			0.998317
$417$	−3331.38			−0.391219
$418$	69.2538			0.00810362
$419$	13100.4			1.52744			0.763722	−	0.645546i	$-0.223370\pi$
$419$	13100.4			1.52744			0.763722	+	0.645546i	$0.223370\pi$
$420$			8660.84i			1.00620i
$421$		−	5452.09i		−	0.631160i	−0.948899	−	0.315580i	$-0.897801\pi$
$421$		−	5452.09i		−	0.631160i	0.948899	−	0.315580i	$-0.102199\pi$
$422$			1083.02i			0.124931i
$423$	2998.40			0.344651
$424$			5966.41i			0.683383i
$425$		−	2746.73i		−	0.313496i
$426$		−	1849.97i		−	0.210402i
$427$			3684.20i			0.417543i
$428$	−3666.16			−0.414044
$429$		−	1602.30i		−	0.180326i
$430$		−	6577.12i		−	0.737621i
$431$		−	11201.7i		−	1.25189i	−0.779866	−	0.625946i	$-0.784713\pi$
$431$		−	11201.7i		−	1.25189i	0.779866	−	0.625946i	$-0.215287\pi$
$432$	7091.07			0.789743
$433$	−6162.98			−0.684004			−0.342002	−	0.939699i	$-0.611105\pi$
$433$	−6162.98			−0.684004			−0.342002	+	0.939699i	$0.611105\pi$
$434$	−4426.16			−0.489544
$435$	−8600.13			−0.947919
$436$			3579.91i			0.393226i
$437$	−957.864			−0.104853
$438$		−	2586.17i		−	0.282128i
$439$		−	10605.2i		−	1.15298i	−0.817103	−	0.576492i	$-0.804421\pi$
$439$		−	10605.2i		−	1.15298i	0.817103	−	0.576492i	$-0.195579\pi$
$440$	−1764.08			−0.191135
$441$	590.912			0.0638065
$442$			602.862i			0.0648761i
$443$	7731.28			0.829174			0.414587	−	0.910010i	$-0.363926\pi$
$443$	7731.28			0.829174			0.414587	+	0.910010i	$0.363926\pi$
$444$	−2376.78	−	5512.11i	−0.254047	−	0.589174i
$445$	−13223.5			−1.40867
$446$		−	3078.36i		−	0.326827i
$447$	487.255			0.0515579
$448$	4559.03			0.480790
$449$			6856.41i			0.720654i	0.932826	+	0.360327i	$0.117335\pi$
$449$			6856.41i			0.720654i	−0.932826	+	0.360327i	$0.882665\pi$
$450$		−	2587.17i		−	0.271023i
$451$	2955.70			0.308600
$452$			13651.8i			1.42063i
$453$	−12997.9			−1.34811
$454$	−2026.12			−0.209450
$455$	19355.8			1.99432
$456$	−525.883			−0.0540060
$457$		−	17959.1i		−	1.83828i	−0.393933	−	0.919139i	$-0.628886\pi$
$457$		−	17959.1i		−	1.83828i	0.393933	−	0.919139i	$-0.371114\pi$
$458$			3052.59i			0.311437i
$459$			1798.60i			0.182901i
$460$	11643.8			1.18020
$461$		−	9795.05i		−	0.989590i	−0.869010	−	0.494795i	$-0.835243\pi$
$461$		−	9795.05i		−	0.989590i	0.869010	−	0.494795i	$-0.164757\pi$
$462$			388.644i			0.0391371i
$463$		−	14185.6i		−	1.42389i	−0.702237	−	0.711943i	$-0.747815\pi$
$463$		−	14185.6i		−	1.42389i	0.702237	−	0.711943i	$-0.252185\pi$
$464$			5994.75i			0.599783i
$465$	20971.5			2.09146
$466$			2111.22i			0.209873i
$467$			15060.8i			1.49236i	0.665746	+	0.746179i	$0.268114\pi$
$467$			15060.8i			1.49236i	−0.665746	+	0.746179i	$0.731886\pi$
$468$		−	5946.38i		−	0.587332i
$469$	6035.66			0.594245
$470$	3437.80			0.337391
$471$	−2079.73			−0.203459
$472$	−6610.56			−0.644652
$473$			3090.67i			0.300442i
$474$	2152.84			0.208614
$475$		−	2555.36i		−	0.246837i
$476$			1531.26i			0.147448i
$477$	6378.17			0.612236
$478$	−1337.25			−0.127959
$479$		−	462.686i		−	0.0441350i	−0.999756	−	0.0220675i	$-0.992975\pi$
$479$		−	462.686i		−	0.0441350i	0.999756	−	0.0220675i	$-0.00702488\pi$
$480$	9734.59			0.925669
$481$	−12318.8	+	5311.77i	−1.16775	+	0.503526i
$482$	−4646.63			−0.439104
$483$		−	5375.42i		−	0.506398i
$484$	−9324.22			−0.875678
$485$	−21030.5			−1.96896
$486$			2819.07i			0.263119i
$487$			4062.43i			0.378001i	0.981977	+	0.189000i	$0.0605247\pi$
$487$			4062.43i			0.378001i	−0.981977	+	0.189000i	$0.939475\pi$
$488$	2719.33			0.252251
$489$			7077.17i			0.654480i
$490$	677.507			0.0624626
$491$	6595.37			0.606202			0.303101	−	0.952958i	$-0.401978\pi$
$491$	6595.37			0.606202			0.303101	+	0.952958i	$0.401978\pi$
$492$	−10710.8			−0.981460
$493$	−1520.53			−0.138907
$494$			560.860i			0.0510815i
$495$			1885.83i			0.171236i
$496$		−	14618.2i		−	1.32334i
$497$	−10501.4			−0.947792
$498$			2435.77i			0.219176i
$499$			8920.55i			0.800278i	0.916454	+	0.400139i	$0.131038\pi$
$499$			8920.55i			0.800278i	−0.916454	+	0.400139i	$0.868962\pi$
$500$			13941.8i			1.24699i
$501$		−	7506.64i		−	0.669405i
$502$	4891.20			0.434870
$503$		−	1322.33i		−	0.117216i	−0.998281	−	0.0586079i	$-0.981334\pi$
$503$		−	1322.33i		−	0.117216i	0.998281	−	0.0586079i	$-0.0186662\pi$
$504$			3022.36i			0.267117i
$505$			31464.2i			2.77255i
$506$	522.499			0.0459049
$507$	4952.37			0.433811
$508$	5666.34			0.494888
$509$	−12912.0			−1.12439			−0.562193	−	0.827006i	$-0.690042\pi$
$509$	−12912.0			−1.12439			−0.562193	+	0.827006i	$0.690042\pi$
$510$			692.831i			0.0601551i
$511$	−14680.5			−1.27089
$512$		−	11667.1i		−	1.00706i
$513$			1673.29i			0.144011i
$514$	−3054.79			−0.262142
$515$	−3795.68			−0.324772
$516$		−	11199.8i		−	0.955515i
$517$	−1615.46			−0.137424
$518$	2987.97	−	1288.39i	0.253444	−	0.109283i
$519$	−6175.48			−0.522299
$520$		−	14286.6i		−	1.20483i
$521$	8160.28			0.686196			0.343098	−	0.939300i	$-0.388524\pi$
$521$	8160.28			0.686196			0.343098	+	0.939300i	$0.388524\pi$
$522$	−1432.21			−0.120088
$523$		−	3618.62i		−	0.302545i	−0.988492	−	0.151273i	$-0.951663\pi$
$523$		−	3618.62i		−	0.302545i	0.988492	−	0.151273i	$-0.0483372\pi$
$524$			16036.5i			1.33695i
$525$	14340.4			1.19212
$526$			3497.68i			0.289936i
$527$	3707.82			0.306480
$528$	−1283.57			−0.105796
$529$	4940.20			0.406033
$530$	7312.86			0.599340
$531$			7066.78i			0.577537i
$532$			1424.58i			0.116096i
$533$			23937.1i			1.94527i
$534$	2150.30			0.174256
$535$			9416.12i			0.760924i
$536$		−	4454.95i		−	0.359001i
$537$			5957.16i			0.478716i
$538$		−	726.920i		−	0.0582523i
$539$	−318.369			−0.0254418
$540$		−	20340.5i		−	1.62095i
$541$			7607.67i			0.604583i	0.953216	+	0.302291i	$0.0977516\pi$
$541$			7607.67i			0.604583i	−0.953216	+	0.302291i	$0.902248\pi$
$542$			596.941i			0.0473078i
$543$	6350.64			0.501900
$544$	1721.11			0.135647
$545$	9194.59			0.722666
$546$	−3147.48			−0.246703
$547$		−	9466.90i		−	0.739992i	−0.929033	−	0.369996i	$-0.879359\pi$
$547$		−	9466.90i		−	0.739992i	0.929033	−	0.369996i	$-0.120641\pi$
$548$	−11423.7			−0.890502
$549$		−	2907.00i		−	0.225989i
$550$			1393.90i			0.108066i
$551$	−1414.59			−0.109371
$552$	−3967.63			−0.305930
$553$		−	12220.7i		−	0.939739i
$554$	−4178.04			−0.320411
$555$	−14157.2	+	6104.48i	−1.08278	+	0.466884i
$556$	6661.00			0.508075
$557$		−	3463.24i		−	0.263451i	−0.991286	−	0.131726i	$-0.957948\pi$
$557$		−	3463.24i		−	0.263451i	0.991286	−	0.131726i	$-0.0420518\pi$
$558$	3492.44			0.264958
$559$	−25030.1			−1.89385
$560$		−	15505.5i		−	1.17005i
$561$		−	325.570i		−	0.0245019i
$562$	−2314.42			−0.173715
$563$			3993.51i			0.298946i	0.988766	+	0.149473i	$0.0477576\pi$
$563$			3993.51i			0.298946i	−0.988766	+	0.149473i	$0.952242\pi$
$564$	5854.06			0.437057
$565$	35063.1			2.61082
$566$	1814.59			0.134758
$567$	−3004.50			−0.222535
$568$			7751.15i			0.572590i
$569$		−	10066.4i		−	0.741664i	−0.928700	−	0.370832i	$-0.879073\pi$
$569$		−	10066.4i		−	0.741664i	0.928700	−	0.370832i	$-0.120927\pi$
$570$			644.560i			0.0473643i
$571$	−2733.41			−0.200332			−0.100166	−	0.994971i	$-0.531937\pi$
$571$	−2733.41			−0.200332			−0.100166	+	0.994971i	$0.531937\pi$
$572$			3203.76i			0.234189i
$573$		−	3656.86i		−	0.266610i
$574$		−	5806.02i		−	0.422193i
$575$		−	19279.4i		−	1.39827i
$576$	−3597.28			−0.260220
$577$		−	9604.68i		−	0.692977i	−0.938054	−	0.346489i	$-0.887374\pi$
$577$		−	9604.68i		−	0.692977i	0.938054	−	0.346489i	$-0.112626\pi$
$578$		−	3980.25i		−	0.286430i
$579$		−	9186.56i		−	0.659379i
$580$	17195.7			1.23106
$581$	13826.7			0.987315
$582$	3419.80			0.243566
$583$	−3436.40			−0.244119
$584$			10835.8i			0.767787i
$585$	−15272.6			−1.07939
$586$		−	1534.46i		−	0.108170i
$587$		−	25228.8i		−	1.77394i	−0.461824	−	0.886972i	$-0.652805\pi$
$587$		−	25228.8i		−	1.77394i	0.461824	−	0.886972i	$-0.347195\pi$
$588$	1153.69			0.0809141
$589$	3449.49			0.241314
$590$			8102.38i			0.565372i
$591$	6725.46			0.468102
$592$	4255.15	+	9868.35i	0.295415	+	0.685113i
$593$	−19783.9			−1.37003			−0.685015	−	0.728529i	$-0.740204\pi$
$593$	−19783.9			−1.37003			−0.685015	+	0.728529i	$0.740204\pi$
$594$		−	912.752i		−	0.0630483i
$595$	3932.88			0.270979
$596$	−974.253			−0.0669580
$597$			3119.42i			0.213851i
$598$			4231.52i			0.289364i
$599$	15249.0			1.04016			0.520082	−	0.854117i	$-0.325902\pi$
$599$	15249.0			1.04016			0.520082	+	0.854117i	$0.325902\pi$
$600$		−	10584.7i		−	0.720198i
$601$	−14562.8			−0.988403			−0.494202	−	0.869347i	$-0.664540\pi$
$601$	−14562.8			−0.988403			−0.494202	+	0.869347i	$0.664540\pi$
$602$	6071.14			0.411032
$603$	−4762.41			−0.321626
$604$	25988.9			1.75078
$605$			23948.2i			1.60931i
$606$		−	5116.44i		−	0.342972i
$607$			12587.9i			0.841722i	0.907125	+	0.420861i	$0.138272\pi$
$607$			12587.9i			0.841722i	−0.907125	+	0.420861i	$0.861728\pi$
$608$	1601.19			0.106804
$609$		−	7938.53i		−	0.528219i
$610$		−	3333.01i		−	0.221229i
$611$		−	13083.0i		−	0.866256i
$612$		−	1208.24i		−	0.0798041i
$613$	−7464.95			−0.491854			−0.245927	−	0.969288i	$-0.579092\pi$
$613$	−7464.95			−0.491854			−0.245927	+	0.969288i	$0.579092\pi$
$614$			1664.46i			0.109401i
$615$			27509.4i			1.80372i
$616$		−	1628.37i		−	0.106508i
$617$	2408.67			0.157163			0.0785814	−	0.996908i	$-0.474961\pi$
$617$	2408.67			0.157163			0.0785814	+	0.996908i	$0.474961\pi$
$618$	617.222			0.0401753
$619$	−11840.8			−0.768859			−0.384429	−	0.923154i	$-0.625602\pi$
$619$	−11840.8			−0.768859			−0.384429	+	0.923154i	$0.625602\pi$
$620$	−41931.9			−2.71617
$621$			12624.5i			0.815786i
$622$	−5211.31			−0.335940
$623$		−	12206.3i		−	0.784965i
$624$		−	10395.1i		−	0.666889i
$625$	7459.32			0.477396
$626$	945.006			0.0603355
$627$		−	302.887i		−	0.0192921i
$628$	4158.37			0.264231
$629$	−2503.05	+	1079.29i	−0.158669	+	0.0684168i
$630$	3704.42			0.234266
$631$			9731.02i			0.613924i	0.951722	+	0.306962i	$0.0993124\pi$
$631$			9731.02i			0.613924i	−0.951722	+	0.306962i	$0.900688\pi$
$632$	−9020.15			−0.567725
$633$	4736.69			0.297419
$634$		−	3725.75i		−	0.233389i
$635$		−	14553.4i		−	0.909500i
$636$	12452.7			0.776386
$637$		−	2578.35i		−	0.160373i
$638$	771.636			0.0478830
$639$	8286.09			0.512977
$640$	−25447.2			−1.57170
$641$	−105.888			−0.00652471			−0.00326235	−	0.999995i	$-0.501038\pi$
$641$	−105.888			−0.00652471			−0.00326235	+	0.999995i	$0.501038\pi$
$642$		−	1531.17i		−	0.0941285i
$643$			8839.82i			0.542160i	0.962557	+	0.271080i	$0.0873807\pi$
$643$			8839.82i			0.542160i	−0.962557	+	0.271080i	$0.912619\pi$
$644$			10748.0i			0.657657i
$645$	−28765.5			−1.75603
$646$			113.960i			0.00694073i
$647$			11824.0i			0.718469i	0.933247	+	0.359234i	$0.116962\pi$
$647$			11824.0i			0.718469i	−0.933247	+	0.359234i	$0.883038\pi$
$648$			2217.64i			0.134440i
$649$		−	3807.40i		−	0.230283i
$650$	−11288.7			−0.681198
$651$			19358.1i			1.16545i
$652$		−	14150.6i		−	0.849971i
$653$			1268.69i			0.0760299i	0.999277	+	0.0380150i	$0.0121035\pi$
$653$			1268.69i			0.0760299i	−0.999277	+	0.0380150i	$0.987897\pi$
$654$	−1495.15			−0.0893958
$655$	41188.0			2.45702
$656$	19175.5			1.14128
$657$	11583.6			0.687852
$658$			3173.33i			0.188008i
$659$	32720.3			1.93414			0.967072	−	0.254502i	$-0.0819116\pi$
$659$	32720.3			1.93414			0.967072	+	0.254502i	$0.0819116\pi$
$660$			3681.88i			0.217147i
$661$			15138.5i			0.890801i	0.895331	+	0.445400i	$0.146939\pi$
$661$			15138.5i			0.890801i	−0.895331	+	0.445400i	$0.853061\pi$
$662$	5230.36			0.307075
$663$	2636.66			0.154449
$664$		−	10205.6i		−	0.596467i
$665$	3658.87			0.213361
$666$	−2357.65	+	1016.60i	−0.137173	+	0.0591477i
$667$	−10672.7			−0.619562
$668$			15009.3i			0.869354i
$669$	−13463.5			−0.778067
$670$	−5460.31			−0.314851
$671$			1566.22i			0.0901091i
$672$			8985.71i			0.515820i
$673$	13344.1			0.764305			0.382153	−	0.924099i	$-0.375183\pi$
$673$	13344.1			0.764305			0.382153	+	0.924099i	$0.375183\pi$
$674$		−	1366.09i		−	0.0780708i
$675$	−33679.1			−1.92046
$676$	−9902.13			−0.563389
$677$	−836.145			−0.0474678			−0.0237339	−	0.999718i	$-0.507555\pi$
$677$	−836.145			−0.0474678			−0.0237339	+	0.999718i	$0.507555\pi$
$678$	−5701.66			−0.322966
$679$		−	19412.6i		−	1.09718i
$680$		−	2902.88i		−	0.163707i
$681$			8861.38i			0.498633i
$682$	−1881.64			−0.105648
$683$			8896.46i			0.498409i	0.968451	+	0.249205i	$0.0801692\pi$
$683$			8896.46i			0.498409i	−0.968451	+	0.249205i	$0.919831\pi$
$684$		−	1124.06i		−	0.0628354i
$685$			29340.4i			1.63655i
$686$			5584.42i			0.310808i
$687$	13350.7			0.741429
$688$			20051.1i			1.11111i
$689$		−	27830.1i		−	1.53881i
$690$			4863.01i			0.268307i
$691$	−28586.6			−1.57378			−0.786892	−	0.617090i	$-0.788311\pi$
$691$	−28586.6			−1.57378			−0.786892	+	0.617090i	$0.788311\pi$
$692$	12347.7			0.678308
$693$	−1740.75			−0.0954195
$694$	612.457			0.0334993
$695$		−	17108.0i		−	0.933734i
$696$	−5859.48			−0.319113
$697$			4863.74i			0.264315i
$698$			1033.16i			0.0560255i
$699$	9233.60			0.499638
$700$	−28673.2			−1.54821
$701$		−	25044.0i		−	1.34935i	−0.738113	−	0.674677i	$-0.764283\pi$
$701$		−	25044.0i		−	1.34935i	0.738113	−	0.674677i	$-0.235717\pi$
$702$	7392.03			0.397428
$703$	−2328.65	+	1004.10i	−0.124931	+	0.0538694i
$704$	1938.12			0.103758
$705$		−	15035.5i		−	0.803219i
$706$	2923.47			0.155844
$707$	−29043.7			−1.54498
$708$			13797.1i			0.732384i
$709$		−	12389.8i		−	0.656290i	−0.944627	−	0.328145i	$-0.893577\pi$
$709$		−	12389.8i		−	0.656290i	0.944627	−	0.328145i	$-0.106423\pi$
$710$	9500.37			0.502172
$711$			9642.67i			0.508619i
$712$	−9009.51			−0.474222
$713$	26025.4			1.36698
$714$	−639.532			−0.0335208
$715$	8228.50			0.430389
$716$		−	11911.2i		−	0.621706i
$717$			5848.57i			0.304629i
$718$		−	1905.93i		−	0.0990651i
$719$	11339.0			0.588140			0.294070	−	0.955784i	$-0.404990\pi$
$719$	11339.0			0.588140			0.294070	+	0.955784i	$0.404990\pi$
$720$			12234.6i			0.633272i
$721$		−	3503.68i		−	0.180976i
$722$		−	5621.79i		−	0.289780i
$723$			20322.4i			1.04536i
$724$	−12697.9			−0.651816
$725$		−	28472.2i		−	1.45852i
$726$		−	3894.26i		−	0.199076i
$727$		−	29893.0i		−	1.52499i	−0.646992	−	0.762497i	$-0.723973\pi$
$727$		−	29893.0i		−	1.52499i	0.646992	−	0.762497i	$-0.276027\pi$
$728$	13187.6			0.671379
$729$	17015.0			0.864451
$730$	13281.1			0.673364
$731$	−5085.84			−0.257328
$732$		−	5675.61i		−	0.286580i
$733$	−25981.2			−1.30919			−0.654595	−	0.755980i	$-0.727161\pi$
$733$	−25981.2			−1.30919			−0.654595	+	0.755980i	$0.727161\pi$
$734$			1550.89i			0.0779898i
$735$		−	2963.13i		−	0.148703i
$736$	12080.5			0.605019
$737$	2565.86			0.128243
$738$			4581.22i			0.228505i
$739$	16564.6			0.824545			0.412273	−	0.911061i	$-0.364735\pi$
$739$	16564.6			0.824545			0.412273	+	0.911061i	$0.364735\pi$
$740$	28307.0	−	12205.8i	1.40620	−	0.606341i
$741$	2452.96			0.121608
$742$			6750.28i			0.333977i
$743$	5488.93			0.271022			0.135511	−	0.990776i	$-0.456732\pi$
$743$	5488.93			0.271022			0.135511	+	0.990776i	$0.456732\pi$
$744$	14288.4			0.704081
$745$			2502.26i			0.123055i
$746$		−	6061.93i		−	0.297511i
$747$	−10909.9			−0.534369
$748$			650.968i			0.0318205i
$749$	−8691.74			−0.424018
$750$	−5822.77			−0.283490
$751$	6361.78			0.309114			0.154557	−	0.987984i	$-0.450605\pi$
$751$	6361.78			0.309114			0.154557	+	0.987984i	$0.450605\pi$
$752$	−10480.5			−0.508226
$753$		−	21392.0i		−	1.03528i
$754$			6249.19i			0.301833i
$755$		−	66749.5i		−	3.21757i
$756$	18775.7			0.903261
$757$		−	16846.3i		−	0.808837i	−0.914574	−	0.404418i	$-0.867474\pi$
$757$		−	16846.3i		−	0.808837i	0.914574	−	0.404418i	$-0.132526\pi$
$758$			3060.08i			0.146632i
$759$		−	2285.19i		−	0.109285i
$760$		−	2700.63i		−	0.128898i
$761$	−26209.9			−1.24850			−0.624250	−	0.781224i	$-0.714596\pi$
$761$	−26209.9			−1.24850			−0.624250	+	0.781224i	$0.714596\pi$
$762$			2366.55i			0.112508i
$763$			8487.25i			0.402699i
$764$			7311.80i			0.346245i
$765$	−3103.22			−0.146663
$766$	−5705.11			−0.269104
$767$	30834.7			1.45160
$768$	−3555.97			−0.167077
$769$		−	14273.5i		−	0.669332i	−0.942337	−	0.334666i	$-0.891376\pi$
$769$		−	14273.5i		−	0.669332i	0.942337	−	0.334666i	$-0.108624\pi$
$770$	−1995.85			−0.0934097
$771$			13360.4i			0.624075i
$772$			18368.3i			0.856333i
$773$	−926.584			−0.0431137			−0.0215569	−	0.999768i	$-0.506862\pi$
$773$	−926.584			−0.0431137			−0.0215569	+	0.999768i	$0.506862\pi$
$774$	−4790.41			−0.222465
$775$			69429.5i			3.21804i
$776$	−14328.6			−0.662842
$777$	−5634.87	−	13068.1i	−0.260167	−	0.603367i
$778$	4317.80			0.198973
$779$			4524.88i			0.208114i
$780$	−29818.1			−1.36880
$781$	−4464.34			−0.204541
$782$			859.796i			0.0393175i
$783$			18644.1i			0.850939i
$784$	−2065.46			−0.0940898
$785$		−	10680.3i		−	0.485601i
$786$	−6697.65			−0.303941
$787$	15471.0			0.700738			0.350369	−	0.936612i	$-0.386056\pi$
$787$	15471.0			0.700738			0.350369	+	0.936612i	$0.386056\pi$
$788$	−13447.4			−0.607923
$789$	15297.4			0.690242
$790$			11055.7i			0.497906i
$791$			32365.7i			1.45486i
$792$			1284.86i			0.0576459i
$793$	−12684.2			−0.568007
$794$		−	11130.3i		−	0.497481i
$795$		−	31983.3i		−	1.42683i
$796$		−	6237.19i		−	0.277728i
$797$			26694.2i			1.18639i	0.805058	+	0.593197i	$0.202134\pi$
$797$			26694.2i			1.18639i	−0.805058	+	0.593197i	$0.797866\pi$
$798$	−594.974			−0.0263933
$799$		−	2658.32i		−	0.117703i
$800$			32228.0i			1.42429i
$801$			9631.29i			0.424850i
$802$	8951.70			0.394134
$803$	−6240.94			−0.274269
$804$	−9298.09			−0.407858
$805$	27605.1			1.20863
$806$		−	15238.7i		−	0.665954i
$807$	−3179.24			−0.138680
$808$			21437.3i			0.933369i
$809$			22896.4i			0.995050i	0.867450	+	0.497525i	$0.165758\pi$
$809$			22896.4i			0.995050i	−0.867450	+	0.497525i	$0.834242\pi$
$810$	2718.10			0.117907
$811$	20247.5			0.876677			0.438338	−	0.898810i	$-0.355567\pi$
$811$	20247.5			0.876677			0.438338	+	0.898810i	$0.355567\pi$
$812$			15872.9i			0.685996i
$813$	2610.77			0.112624
$814$	1270.24	−	547.717i	0.0546952	−	0.0235841i
$815$	−36344.3			−1.56207
$816$		−	2112.18i		−	0.0906139i
$817$	−4731.50			−0.202612
$818$	12883.6			0.550692
$819$		−	14097.7i		−	0.601481i
$820$		−	55004.3i		−	2.34248i
$821$	33370.0			1.41854			0.709269	−	0.704938i	$-0.249025\pi$
$821$	33370.0			1.41854			0.709269	+	0.704938i	$0.249025\pi$
$822$		−	4771.09i		−	0.202446i
$823$	−25717.4			−1.08925			−0.544625	−	0.838679i	$-0.683328\pi$
$823$	−25717.4			−1.08925			−0.544625	+	0.838679i	$0.683328\pi$
$824$	−2586.09			−0.109333
$825$	6096.34			0.257269
$826$	−7479.06			−0.315048
$827$			4944.75i			0.207915i	0.994582	+	0.103958i	$0.0331506\pi$
$827$			4944.75i			0.207915i	−0.994582	+	0.103958i	$0.966849\pi$
$828$		−	8480.67i		−	0.355947i
$829$			6084.42i			0.254910i	0.991844	+	0.127455i	$0.0406809\pi$
$829$			6084.42i			0.254910i	−0.991844	+	0.127455i	$0.959319\pi$
$830$	−12508.7			−0.523113
$831$			18273.0i			0.762794i
$832$			15696.1i			0.654045i
$833$		−	523.891i		−	0.0217908i
$834$			2781.96i			0.115505i
$835$	38549.8			1.59769
$836$			605.614i			0.0250545i
$837$		−	45463.7i		−	1.87748i
$838$		−	10939.9i		−	0.450970i
$839$	−43585.8			−1.79350			−0.896752	−	0.442534i	$-0.854080\pi$
$839$	−43585.8			−1.79350			−0.896752	+	0.442534i	$0.854080\pi$
$840$	15155.6			0.622523
$841$	8627.39			0.353741
$842$	−4552.93			−0.186347
$843$			10122.3i			0.413559i
$844$	−9470.89			−0.386258
$845$			25432.5i			1.03539i
$846$		−	2503.90i		−	0.101756i
$847$	−22105.9			−0.896774
$848$	−22294.1			−0.902810
$849$		−	7936.26i		−	0.320815i
$850$	−2293.73			−0.0925581
$851$	−17569.0	+	7575.60i	−0.707705	+	0.305156i
$852$	16177.7			0.650515
$853$			17271.6i			0.693282i	0.937998	+	0.346641i	$0.112678\pi$
$853$			17271.6i			0.693282i	−0.937998	+	0.346641i	$0.887322\pi$
$854$	3076.60			0.123278
$855$	−2887.01			−0.115478
$856$			6415.43i			0.256162i
$857$			26059.0i			1.03869i	0.854564	+	0.519345i	$0.173824\pi$
$857$			26059.0i			1.03869i	−0.854564	+	0.519345i	$0.826176\pi$
$858$	−1338.05			−0.0532404
$859$			5584.41i			0.221813i	0.993831	+	0.110907i	$0.0353755\pi$
$859$			5584.41i			0.221813i	−0.993831	+	0.110907i	$0.964625\pi$
$860$	57515.9			2.28056
$861$	−25393.1			−1.00510
$862$	−9354.28			−0.369615
$863$	−20657.8			−0.814834			−0.407417	−	0.913242i	$-0.633570\pi$
$863$	−20657.8			−0.814834			−0.407417	+	0.913242i	$0.633570\pi$
$864$		−	21103.5i		−	0.830965i
$865$		−	31713.7i		−	1.24659i
$866$			5146.57i			0.201949i
$867$	−17407.9			−0.681896
$868$		−	38706.1i		−	1.51356i
$869$		−	5195.23i		−	0.202803i
$870$			7181.79i			0.279868i
$871$			20780.0i			0.808383i
$872$	6264.49			0.243283
$873$			15317.4i			0.593833i
$874$			799.893i			0.0309574i
$875$			33053.1i			1.27703i
$876$	22615.7			0.872276
$877$	−34001.9			−1.30919			−0.654596	−	0.755979i	$-0.727161\pi$
$877$	−34001.9			−1.30919			−0.654596	+	0.755979i	$0.727161\pi$
$878$	−8856.21			−0.340413
$879$	−6711.07			−0.257519
$880$		−	6591.68i		−	0.252506i
$881$	19668.2			0.752142			0.376071	−	0.926591i	$-0.377275\pi$
$881$	19668.2			0.752142			0.376071	+	0.926591i	$0.377275\pi$
$882$		−	493.459i		−	0.0188386i
$883$			6477.54i			0.246871i	0.992353	+	0.123435i	$0.0393911\pi$
$883$			6477.54i			0.246871i	−0.992353	+	0.123435i	$0.960609\pi$
$884$	−5271.94			−0.200582
$885$	35436.4			1.34597
$886$		−	6456.23i		−	0.244809i
$887$	10299.9			0.389895			0.194948	−	0.980814i	$-0.437546\pi$
$887$	10299.9			0.389895			0.194948	+	0.980814i	$0.437546\pi$
$888$	−9645.66	+	4159.13i	−0.364513	+	0.157175i
$889$	13433.8			0.506810
$890$			11042.7i			0.415902i
$891$	−1277.27			−0.0480247
$892$	26919.8			1.01047
$893$		−	2473.11i		−	0.0926759i
$894$		−	406.896i		−	0.0152222i
$895$	−30592.5			−1.14256
$896$		−	23489.6i		−	0.875816i
$897$	18506.9			0.688881
$898$	5725.64			0.212770
$899$	38434.8			1.42589
$900$	22624.4			0.837942
$901$		−	5654.76i		−	0.209087i
$902$		−	2468.24i		−	0.0911126i
$903$		−	26552.6i		−	0.978533i
$904$	23889.3			0.878924
$905$			32613.2i			1.19790i
$906$			10854.2i			0.398022i
$907$		−	8248.07i		−	0.301954i	−0.988537	−	0.150977i	$-0.951758\pi$
$907$		−	8248.07i		−	0.301954i	0.988537	−	0.150977i	$-0.0482420\pi$
$908$		−	17718.1i		−	0.647572i
$909$	22916.8			0.836195
$910$		−	16163.6i		−	0.588812i
$911$		−	28146.8i		−	1.02365i	−0.859090	−	0.511825i	$-0.828970\pi$
$911$		−	28146.8i		−	1.02365i	0.859090	−	0.511825i	$-0.171030\pi$
$912$		−	1965.02i		−	0.0713467i
$913$	5878.00			0.213070
$914$	−14997.3			−0.542743
$915$	−14577.2			−0.526673
$916$	−26694.4			−0.962892
$917$			38019.5i			1.36915i
$918$	1501.98			0.0540007
$919$		−	34518.4i		−	1.23902i	−0.784990	−	0.619508i	$-0.787332\pi$
$919$		−	34518.4i		−	1.23902i	0.784990	−	0.619508i	$-0.212668\pi$
$920$		−	20375.5i		−	0.730173i
$921$	7279.63			0.260447
$922$	−8179.64			−0.292172
$923$		−	36154.9i		−	1.28933i
$924$	−3398.63			−0.121003
$925$	−20209.9	−	46869.9i	−0.718376	−	1.66602i
$926$	−11846.1			−0.420396
$927$			2764.56i			0.0979506i
$928$	17840.8			0.631090
$929$	−19113.5			−0.675021			−0.337511	−	0.941322i	$-0.609585\pi$
$929$	−19113.5			−0.675021			−0.337511	+	0.941322i	$0.609585\pi$
$930$		−	17512.8i		−	0.617493i
$931$		−	487.390i		−	0.0171574i
$932$	−18462.3			−0.648878
$933$			22792.1i			0.799763i
$934$	12577.0			0.440611
$935$	1671.94			0.0584794
$936$	−10405.6			−0.363373
$937$	8700.71			0.303351			0.151675	−	0.988430i	$-0.451533\pi$
$937$	8700.71			0.303351			0.151675	+	0.988430i	$0.451533\pi$
$938$		−	5040.25i		−	0.175448i
$939$		−	4133.05i		−	0.143639i
$940$			30063.1i			1.04314i
$941$	3369.59			0.116733			0.0583664	−	0.998295i	$-0.481411\pi$
$941$	3369.59			0.116733			0.0583664	+	0.998295i	$0.481411\pi$
$942$			1736.74i			0.0600702i
$943$			34138.8i			1.17891i
$944$		−	24701.0i		−	0.851642i
$945$		−	48223.2i		−	1.66000i
$946$	2580.95			0.0887040
$947$			53448.4i			1.83404i	0.398836	+	0.917022i	$0.369414\pi$
$947$			53448.4i			1.83404i	−0.398836	+	0.917022i	$0.630586\pi$
$948$			18826.3i			0.644988i
$949$		−	50543.0i		−	1.72887i
$950$	−2133.92			−0.0728775
$951$	−16294.9			−0.555623
$952$	2679.57			0.0912240
$953$	32565.9			1.10694			0.553470	−	0.832869i	$-0.313303\pi$
$953$	32565.9			1.10694			0.553470	+	0.832869i	$0.313303\pi$
$954$		−	5326.28i		−	0.180760i
$955$	18779.5			0.636326
$956$		−	11694.1i		−	0.395621i
$957$		−	3374.81i		−	0.113994i
$958$	−386.380			−0.0130307
$959$	−27083.3			−0.911954
$960$			18038.6i			0.606450i
$961$	−63932.3			−2.14603
$962$	4435.75	+	10287.2i	0.148664	+	0.344774i
$963$	6858.18			0.229493
$964$		−	40634.1i		−	1.35761i
$965$	47176.9			1.57376
$966$	−4488.90			−0.149511
$967$			14669.1i			0.487825i	0.969797	+	0.243912i	$0.0784309\pi$
$967$			14669.1i			0.487825i	−0.969797	+	0.243912i	$0.921569\pi$
$968$			16316.5i			0.541768i
$969$	498.414			0.0165236
$970$			17562.1i			0.581325i
$971$	51959.5			1.71726			0.858630	−	0.512596i	$-0.171316\pi$
$971$	51959.5			1.71726			0.858630	+	0.512596i	$0.171316\pi$
$972$	−24652.4			−0.813504
$973$	15791.9			0.520314
$974$	3392.45			0.111603
$975$			49371.9i			1.62171i
$976$			10161.1i			0.333245i
$977$			14022.2i			0.459171i	0.973289	+	0.229585i	$0.0737370\pi$
$977$			14022.2i			0.459171i	−0.973289	+	0.229585i	$0.926263\pi$
$978$	5910.00			0.193232
$979$		−	5189.10i		−	0.169402i
$980$			5924.70i			0.193120i
$981$		−	6696.83i		−	0.217954i
$982$		−	5507.66i		−	0.178978i
$983$	−28951.8			−0.939387			−0.469694	−	0.882829i	$-0.655636\pi$
$983$	−28951.8			−0.939387			−0.469694	+	0.882829i	$0.655636\pi$
$984$			18742.8i			0.607214i
$985$			34538.1i			1.11723i
$986$			1269.76i			0.0410117i
$987$	13878.8			0.447586
$988$	−4904.63			−0.157932
$989$	−35697.7			−1.14775
$990$	1574.82			0.0505565
$991$			57751.4i			1.85120i	0.378508	+	0.925598i	$0.376437\pi$
$991$			57751.4i			1.85120i	−0.378508	+	0.925598i	$0.623563\pi$
$992$	−43504.7			−1.39242
$993$		−	22875.4i		−	0.731045i
$994$			8769.51i			0.279831i
$995$	−16019.5			−0.510405
$996$	−21300.5			−0.677642
$997$		−	33740.0i		−	1.07177i	−0.844291	−	0.535886i	$-0.819978\pi$
$997$		−	33740.0i		−	1.07177i	0.844291	−	0.535886i	$-0.180022\pi$
$998$	7449.37			0.236278
$999$	13233.8	+	30691.2i	0.419118	+	0.972000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.4.b.a.36.4	✓	8
3.2	odd	2		333.4.c.d.73.5		8
4.3	odd	2		592.4.g.c.369.5		8
37.6	odd	4		1369.4.a.b.1.2		4
37.31	odd	4		1369.4.a.a.1.3		4
37.36	even	2	inner	37.4.b.a.36.5	yes	8
111.110	odd	2		333.4.c.d.73.4		8
148.147	odd	2		592.4.g.c.369.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.4.b.a.36.4	✓	8	1.1	even	1	trivial
37.4.b.a.36.5	yes	8	37.36	even	2	inner
333.4.c.d.73.4		8	111.110	odd	2
333.4.c.d.73.5		8	3.2	odd	2
592.4.g.c.369.5		8	4.3	odd	2
592.4.g.c.369.6		8	148.147	odd	2
1369.4.a.a.1.3		4	37.31	odd	4
1369.4.a.b.1.2		4	37.6	odd	4

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	37.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.835079i q^{2} -3.65228 q^{3} +7.30264 q^{4} -18.7560i q^{5} +3.04994i q^{6} +17.3131 q^{7} -12.7789i q^{8} -13.6608 q^{9} +O(q^{10})\)	\(q-0.835079i q^{2} -3.65228 q^{3} +7.30264 q^{4} -18.7560i q^{5} +3.04994i q^{6} +17.3131 q^{7} -12.7789i q^{8} -13.6608 q^{9} -15.6628 q^{10} +7.36011 q^{11} -26.6713 q^{12} +59.6068i q^{13} -14.4578i q^{14} +68.5023i q^{15} +47.7497 q^{16} +12.1114i q^{17} +11.4079i q^{18} +11.2676i q^{19} -136.968i q^{20} -63.2324 q^{21} -6.14628i q^{22} +85.0106i q^{23} +46.6722i q^{24} -226.788 q^{25} +49.7764 q^{26} +148.505 q^{27} +126.432 q^{28} +125.545i q^{29} +57.2048 q^{30} -306.143i q^{31} -142.106i q^{32} -26.8812 q^{33} +10.1140 q^{34} -324.725i q^{35} -99.7602 q^{36} +(89.1136 + 206.668i) q^{37} +9.40933 q^{38} -217.701i q^{39} -239.682 q^{40} +401.583 q^{41} +52.8041i q^{42} +419.921i q^{43} +53.7483 q^{44} +256.223i q^{45} +70.9906 q^{46} -219.489 q^{47} -174.395 q^{48} -43.2559 q^{49} +189.386i q^{50} -44.2343i q^{51} +435.287i q^{52} -466.895 q^{53} -124.013i q^{54} -138.046i q^{55} -221.243i q^{56} -41.1524i q^{57} +104.840 q^{58} -517.302i q^{59} +500.247i q^{60} +212.798i q^{61} -255.653 q^{62} -236.512 q^{63} +263.328 q^{64} +1117.99 q^{65} +22.4479i q^{66} +348.617 q^{67} +88.4454i q^{68} -310.483i q^{69} -271.171 q^{70} -606.558 q^{71} +174.571i q^{72} -847.941 q^{73} +(172.584 - 74.4169i) q^{74} +828.294 q^{75} +82.2832i q^{76} +127.427 q^{77} -181.797 q^{78} -705.862i q^{79} -895.595i q^{80} -173.539 q^{81} -335.354i q^{82} +798.628 q^{83} -461.764 q^{84} +227.162 q^{85} +350.667 q^{86} -458.527i q^{87} -94.0543i q^{88} -705.030i q^{89} +213.966 q^{90} +1031.98i q^{91} +620.802i q^{92} +1118.12i q^{93} +183.291i q^{94} +211.335 q^{95} +519.012i q^{96} -1121.27i q^{97} +36.1221i q^{98} -100.545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 - 36 * q^4 + 4 * q^7 + 2 * q^9	\( 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9} - 62 q^{10} + 90 q^{11} - 62 q^{12} + 276 q^{16} + 232 q^{21} + 138 q^{25} - 750 q^{26} - 288 q^{27} - 184 q^{28} - 64 q^{30} + 132 q^{33} + 404 q^{34} + 246 q^{36} - 372 q^{37} - 276 q^{38} + 774 q^{40} + 690 q^{41} - 2310 q^{44} + 1642 q^{46} - 1392 q^{47} + 1502 q^{48} - 388 q^{49} + 768 q^{53} + 1190 q^{58} + 1338 q^{62} - 2588 q^{63} - 3044 q^{64} + 1692 q^{65} + 1102 q^{67} - 2316 q^{70} - 12 q^{71} - 1442 q^{73} + 1464 q^{74} + 1312 q^{75} + 2496 q^{77} + 3078 q^{78} - 2848 q^{81} + 1692 q^{83} - 5140 q^{84} + 1240 q^{85} - 3936 q^{86} + 2380 q^{90} - 1788 q^{95} - 2628 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 36 * q^4 + 4 * q^7 + 2 * q^9 - 62 * q^10 + 90 * q^11 - 62 * q^12 + 276 * q^16 + 232 * q^21 + 138 * q^25 - 750 * q^26 - 288 * q^27 - 184 * q^28 - 64 * q^30 + 132 * q^33 + 404 * q^34 + 246 * q^36 - 372 * q^37 - 276 * q^38 + 774 * q^40 + 690 * q^41 - 2310 * q^44 + 1642 * q^46 - 1392 * q^47 + 1502 * q^48 - 388 * q^49 + 768 * q^53 + 1190 * q^58 + 1338 * q^62 - 2588 * q^63 - 3044 * q^64 + 1692 * q^65 + 1102 * q^67 - 2316 * q^70 - 12 * q^71 - 1442 * q^73 + 1464 * q^74 + 1312 * q^75 + 2496 * q^77 + 3078 * q^78 - 2848 * q^81 + 1692 * q^83 - 5140 * q^84 + 1240 * q^85 - 3936 * q^86 + 2380 * q^90 - 1788 * q^95 - 2628 * q^99

Introduction

L-functions

Modular forms

Varieties

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