LMFDB - Embedded newform 37.4.b.a.36.8

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			36.8
Root			$-0.759936 - 0.759936i$ of defining polynomial
Character	$\chi$	$=$	37.36
Dual form			37.4.b.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.39603i q^{2} +2.81527 q^{3} -21.1172 q^{4} +6.77552i q^{5} +15.1913i q^{6} +16.2590 q^{7} -70.7808i q^{8} -19.0743 q^{9} +O(q^{10})$	\(q+5.39603i q^{2} +2.81527 q^{3} -21.1172 q^{4} +6.77552i q^{5} +15.1913i q^{6} +16.2590 q^{7} -70.7808i q^{8} -19.0743 q^{9} -36.5609 q^{10} +56.6781 q^{11} -59.4505 q^{12} +41.6559i q^{13} +87.7342i q^{14} +19.0749i q^{15} +212.998 q^{16} -68.5374i q^{17} -102.925i q^{18} +84.5816i q^{19} -143.080i q^{20} +45.7734 q^{21} +305.837i q^{22} -70.4909i q^{23} -199.267i q^{24} +79.0923 q^{25} -224.776 q^{26} -129.711 q^{27} -343.345 q^{28} -111.643i q^{29} -102.929 q^{30} -322.350i q^{31} +583.099i q^{32} +159.564 q^{33} +369.830 q^{34} +110.163i q^{35} +402.795 q^{36} +(-206.337 - 89.8770i) q^{37} -456.405 q^{38} +117.272i q^{39} +479.577 q^{40} +131.601 q^{41} +246.995i q^{42} +112.203i q^{43} -1196.88 q^{44} -129.238i q^{45} +380.371 q^{46} -98.6542 q^{47} +599.646 q^{48} -78.6444 q^{49} +426.785i q^{50} -192.951i q^{51} -879.655i q^{52} +215.067 q^{53} -699.927i q^{54} +384.024i q^{55} -1150.83i q^{56} +238.120i q^{57} +602.432 q^{58} +40.1133i q^{59} -402.808i q^{60} +720.884i q^{61} +1739.41 q^{62} -310.129 q^{63} -1442.44 q^{64} -282.240 q^{65} +861.013i q^{66} -476.142 q^{67} +1447.32i q^{68} -198.450i q^{69} -594.445 q^{70} -664.816 q^{71} +1350.09i q^{72} +281.792 q^{73} +(484.979 - 1113.40i) q^{74} +222.666 q^{75} -1786.13i q^{76} +921.531 q^{77} -632.805 q^{78} +706.968i q^{79} +1443.17i q^{80} +149.834 q^{81} +710.121i q^{82} -370.053 q^{83} -966.607 q^{84} +464.377 q^{85} -605.449 q^{86} -314.306i q^{87} -4011.72i q^{88} -818.069i q^{89} +697.374 q^{90} +677.283i q^{91} +1488.57i q^{92} -907.502i q^{93} -532.341i q^{94} -573.084 q^{95} +1641.58i q^{96} -63.4075i q^{97} -424.368i q^{98} -1081.09 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			5.39603i			1.90779i	0.300146	+	0.953893i	$0.402965\pi$
$2$			5.39603i			1.90779i	−0.300146	+	0.953893i	$0.597035\pi$
$3$	2.81527			0.541798			0.270899	−	0.962608i	$-0.412679\pi$
$3$	2.81527			0.541798			0.270899	+	0.962608i	$0.412679\pi$
$4$	−21.1172			−2.63965
$5$			6.77552i			0.606021i	0.952987	+	0.303010i	$0.0979917\pi$
$5$			6.77552i			0.606021i	−0.952987	+	0.303010i	$0.902008\pi$
$6$			15.1913i			1.03363i
$7$	16.2590			0.877904			0.438952	−	0.898510i	$-0.355350\pi$
$7$	16.2590			0.877904			0.438952	+	0.898510i	$0.355350\pi$
$8$		−	70.7808i		−	3.12810i
$9$	−19.0743			−0.706455
$10$	−36.5609			−1.15616
$11$	56.6781			1.55355			0.776777	−	0.629775i	$-0.216853\pi$
$11$	56.6781			1.55355			0.776777	+	0.629775i	$0.216853\pi$
$12$	−59.4505			−1.43016
$13$			41.6559i			0.888712i	0.895850	+	0.444356i	$0.146567\pi$
$13$			41.6559i			0.888712i	−0.895850	+	0.444356i	$0.853433\pi$
$14$			87.7342i			1.67485i
$15$			19.0749i			0.328341i
$16$	212.998			3.32810
$17$		−	68.5374i		−	0.977810i	−0.872337	−	0.488905i	$-0.837396\pi$
$17$		−	68.5374i		−	0.977810i	0.872337	−	0.488905i	$-0.162604\pi$
$18$		−	102.925i		−	1.34777i
$19$			84.5816i			1.02128i	0.859794	+	0.510641i	$0.170592\pi$
$19$			84.5816i			1.02128i	−0.859794	+	0.510641i	$0.829408\pi$
$20$		−	143.080i		−	1.59968i
$21$	45.7734			0.475647
$22$			305.837i			2.96385i
$23$		−	70.4909i		−	0.639059i	−0.947576	−	0.319530i	$-0.896475\pi$
$23$		−	70.4909i		−	0.639059i	0.947576	−	0.319530i	$-0.103525\pi$
$24$		−	199.267i		−	1.69480i
$25$	79.0923			0.632739
$26$	−224.776			−1.69547
$27$	−129.711			−0.924554
$28$	−343.345			−2.31736
$29$		−	111.643i		−	0.714885i	−0.933935	−	0.357442i	$-0.883649\pi$
$29$		−	111.643i		−	0.714885i	0.933935	−	0.357442i	$-0.116351\pi$
$30$	−102.929			−0.626404
$31$		−	322.350i		−	1.86761i	−0.357786	−	0.933804i	$-0.616468\pi$
$31$		−	322.350i		−	1.86761i	0.357786	−	0.933804i	$-0.383532\pi$
$32$			583.099i			3.22120i
$33$	159.564			0.841713
$34$	369.830			1.86545
$35$			110.163i			0.532028i
$36$	402.795			1.86479
$37$	−206.337	−	89.8770i	−0.916802	−	0.399343i
$37$	−206.337	−	89.8770i	−0.916802	−	0.399343i
$38$	−456.405			−1.94839
$39$			117.272i			0.481502i
$40$	479.577			1.89569
$41$	131.601			0.501282			0.250641	−	0.968080i	$-0.419359\pi$
$41$	131.601			0.501282			0.250641	+	0.968080i	$0.419359\pi$
$42$			246.995i			0.907433i
$43$			112.203i			0.397924i	0.980007	+	0.198962i	$0.0637571\pi$
$43$			112.203i			0.397924i	−0.980007	+	0.198962i	$0.936243\pi$
$44$	−1196.88			−4.10084
$45$		−	129.238i		−	0.428126i
$46$	380.371			1.21919
$47$	−98.6542			−0.306174			−0.153087	−	0.988213i	$-0.548922\pi$
$47$	−98.6542			−0.306174			−0.153087	+	0.988213i	$0.548922\pi$
$48$	599.646			1.80316
$49$	−78.6444			−0.229284
$50$			426.785i			1.20713i
$51$		−	192.951i		−	0.529775i
$52$		−	879.655i		−	2.34589i
$53$	215.067			0.557390			0.278695	−	0.960380i	$-0.410098\pi$
$53$	215.067			0.557390			0.278695	+	0.960380i	$0.410098\pi$
$54$		−	699.927i		−	1.76385i
$55$			384.024i			0.941487i
$56$		−	1150.83i		−	2.74617i
$57$			238.120i			0.553328i
$58$	602.432			1.36385
$59$			40.1133i			0.0885136i	0.999020	+	0.0442568i	$0.0140920\pi$
$59$			40.1133i			0.0885136i	−0.999020	+	0.0442568i	$0.985908\pi$
$60$		−	402.808i		−	0.866705i
$61$			720.884i			1.51311i	0.653930	+	0.756555i	$0.273119\pi$
$61$			720.884i			1.51311i	−0.653930	+	0.756555i	$0.726881\pi$
$62$	1739.41			3.56300
$63$	−310.129			−0.620200
$64$	−1442.44			−2.81726
$65$	−282.240			−0.538578
$66$			861.013i			1.60581i
$67$	−476.142			−0.868209			−0.434105	−	0.900862i	$-0.642935\pi$
$67$	−476.142			−0.868209			−0.434105	+	0.900862i	$0.642935\pi$
$68$			1447.32i			2.58107i
$69$		−	198.450i		−	0.346241i
$70$	−594.445			−1.01500
$71$	−664.816			−1.11126			−0.555628	−	0.831431i	$-0.687522\pi$
$71$	−664.816			−1.11126			−0.555628	+	0.831431i	$0.687522\pi$
$72$			1350.09i			2.20986i
$73$	281.792			0.451798			0.225899	−	0.974151i	$-0.427468\pi$
$73$	281.792			0.451798			0.225899	+	0.974151i	$0.427468\pi$
$74$	484.979	−	1113.40i	0.761861	−	1.74906i
$75$	222.666			0.342817
$76$		−	1786.13i		−	2.69582i
$77$	921.531			1.36387
$78$	−632.805			−0.918604
$79$			706.968i			1.00684i	0.864043	+	0.503419i	$0.167925\pi$
$79$			706.968i			1.00684i	−0.864043	+	0.503419i	$0.832075\pi$
$80$			1443.17i			2.01690i
$81$	149.834			0.205533
$82$			710.121i			0.956339i
$83$	−370.053			−0.489381			−0.244690	−	0.969601i	$-0.578686\pi$
$83$	−370.053			−0.489381			−0.244690	+	0.969601i	$0.578686\pi$
$84$	−966.607			−1.25554
$85$	464.377			0.592573
$86$	−605.449			−0.759154
$87$		−	314.306i		−	0.387323i
$88$		−	4011.72i		−	4.85967i
$89$		−	818.069i		−	0.974327i	−0.873311	−	0.487164i	$-0.838032\pi$
$89$		−	818.069i		−	0.974327i	0.873311	−	0.487164i	$-0.161968\pi$
$90$	697.374			0.816774
$91$			677.283i			0.780204i
$92$			1488.57i			1.68689i
$93$		−	907.502i		−	1.01187i
$94$		−	532.341i		−	0.584115i
$95$	−573.084			−0.618918
$96$			1641.58i			1.74524i
$97$		−	63.4075i		−	0.0663717i	−0.999449	−	0.0331859i	$-0.989435\pi$
$97$		−	63.4075i		−	0.0663717i	0.999449	−	0.0331859i	$-0.0105653\pi$
$98$		−	424.368i		−	0.437425i
$99$	−1081.09			−1.09752
$100$	−1670.21			−1.67021
$101$	−199.047			−0.196098			−0.0980492	−	0.995182i	$-0.531260\pi$
$101$	−199.047			−0.196098			−0.0980492	+	0.995182i	$0.531260\pi$
$102$	1041.17			1.01070
$103$			597.256i			0.571353i	0.958326	+	0.285677i	$0.0922183\pi$
$103$			597.256i			0.571353i	−0.958326	+	0.285677i	$0.907782\pi$
$104$	2948.44			2.77998
$105$			310.139i			0.288252i
$106$			1160.51i			1.06338i
$107$	973.289			0.879359			0.439679	−	0.898155i	$-0.355092\pi$
$107$	973.289			0.879359			0.439679	+	0.898155i	$0.355092\pi$
$108$	2739.14			2.44050
$109$		−	1023.51i		−	0.899397i	−0.893181	−	0.449698i	$-0.851532\pi$
$109$		−	1023.51i		−	0.899397i	0.893181	−	0.449698i	$-0.148468\pi$
$110$	−2072.21			−1.79616
$111$	−580.895	−	253.027i	−0.496721	−	0.216363i
$112$	3463.14			2.92175
$113$		−	1428.78i		−	1.18945i	−0.803929	−	0.594726i	$-0.797261\pi$
$113$		−	1428.78i		−	1.18945i	0.803929	−	0.594726i	$-0.202739\pi$
$114$	−1284.90			−1.05563
$115$	477.612			0.387283
$116$			2357.60i			1.88705i
$117$		−	794.556i		−	0.627835i
$118$	−216.452			−0.168865
$119$		−	1114.35i		−	0.858424i
$120$	1350.14			1.02708
$121$	1881.41			1.41353
$122$	−3889.91			−2.88669
$123$	370.491			0.271594
$124$			6807.13i			4.92983i
$125$			1382.83i			0.989474i
$126$		−	1673.47i		−	1.18321i
$127$	−1310.38			−0.915570			−0.457785	−	0.889063i	$-0.651357\pi$
$127$	−1310.38			−0.915570			−0.457785	+	0.889063i	$0.651357\pi$
$128$		−	3118.65i		−	2.15354i
$129$			315.880i			0.215595i
$130$		−	1522.98i		−	1.02749i
$131$		−	961.110i		−	0.641012i	−0.947247	−	0.320506i	$-0.896147\pi$
$131$		−	961.110i		−	0.641012i	0.947247	−	0.320506i	$-0.103853\pi$
$132$	−3369.54			−2.22183
$133$			1375.21i			0.896587i
$134$		−	2569.28i		−	1.65636i
$135$		−	878.862i		−	0.560299i
$136$	−4851.14			−3.05869
$137$	1310.93			0.817521			0.408761	−	0.912642i	$-0.365961\pi$
$137$	1310.93			0.817521			0.408761	+	0.912642i	$0.365961\pi$
$138$	1070.85			0.660554
$139$	1537.86			0.938416			0.469208	−	0.883088i	$-0.344540\pi$
$139$	1537.86			0.938416			0.469208	+	0.883088i	$0.344540\pi$
$140$		−	2326.34i		−	1.40437i
$141$	−277.738			−0.165885
$142$		−	3587.37i		−	2.12004i
$143$			2360.98i			1.38066i
$144$	−4062.79			−2.35115
$145$	756.442			0.433235
$146$			1520.56i			0.861935i
$147$	−221.405			−0.124226
$148$	4357.27	+	1897.95i	2.42003	+	1.05412i
$149$	30.2413			0.0166273			0.00831363	−	0.999965i	$-0.497354\pi$
$149$	30.2413			0.0166273			0.00831363	+	0.999965i	$0.497354\pi$
$150$			1201.51i			0.654021i
$151$	−1908.44			−1.02852			−0.514262	−	0.857633i	$-0.671934\pi$
$151$	−1908.44			−1.02852			−0.514262	+	0.857633i	$0.671934\pi$
$152$	5986.75			3.19467
$153$			1307.30i			0.690779i
$154$			4972.61i			2.60198i
$155$	2184.09			1.13181
$156$		−	2476.46i		−	1.27100i
$157$	−1280.88			−0.651116			−0.325558	−	0.945522i	$-0.605552\pi$
$157$	−1280.88			−0.651116			−0.325558	+	0.945522i	$0.605552\pi$
$158$	−3814.83			−1.92083
$159$	605.469			0.301993
$160$	−3950.80			−1.95211
$161$		−	1146.11i		−	0.561033i
$162$			808.509i			0.392114i
$163$			3921.25i			1.88427i	0.335234	+	0.942135i	$0.391185\pi$
$163$			3921.25i			1.88427i	−0.335234	+	0.942135i	$0.608815\pi$
$164$	−2779.04			−1.32321
$165$			1081.13i			0.510096i
$166$		−	1996.82i		−	0.933634i
$167$			402.648i			0.186574i	0.995639	+	0.0932870i	$0.0297374\pi$
$167$			402.648i			0.186574i	−0.995639	+	0.0932870i	$0.970263\pi$
$168$		−	3239.88i		−	1.48787i
$169$	461.789			0.210191
$170$			2505.79i			1.13050i
$171$		−	1613.33i		−	0.721489i
$172$		−	2369.40i		−	1.05038i
$173$	975.927			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$173$	975.927			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$174$	1696.01			0.738930
$175$	1285.96			0.555484
$176$	12072.3			5.17038
$177$			112.929i			0.0479565i
$178$	4414.33			1.85881
$179$		−	1963.02i		−	0.819682i	−0.912157	−	0.409841i	$-0.865584\pi$
$179$		−	1963.02i		−	0.819682i	0.912157	−	0.409841i	$-0.134416\pi$
$180$			2729.15i			1.13010i
$181$	−3578.38			−1.46950			−0.734749	−	0.678339i	$-0.762700\pi$
$181$	−3578.38			−1.46950			−0.734749	+	0.678339i	$0.762700\pi$
$182$	−3654.64			−1.48846
$183$			2029.48i			0.819800i
$184$	−4989.40			−1.99904
$185$	608.963	−	1398.04i	0.242010	−	0.555601i
$186$	4896.91			1.93042
$187$		−	3884.57i		−	1.51908i
$188$	2083.30			0.808193
$189$	−2108.98			−0.811670
$190$		−	3092.38i		−	1.18076i
$191$		−	3061.45i		−	1.15978i	−0.814694	−	0.579892i	$-0.803095\pi$
$191$		−	3061.45i		−	1.15978i	0.814694	−	0.579892i	$-0.196905\pi$
$192$	−4060.85			−1.52639
$193$			1963.06i			0.732144i	0.930586	+	0.366072i	$0.119298\pi$
$193$			1963.06i			0.732144i	−0.930586	+	0.366072i	$0.880702\pi$
$194$	342.149			0.126623
$195$	−794.581			−0.291801
$196$	1660.75			0.605229
$197$	−1697.56			−0.613940			−0.306970	−	0.951719i	$-0.599315\pi$
$197$	−1697.56			−0.613940			−0.306970	+	0.951719i	$0.599315\pi$
$198$		−	5833.62i		−	2.09383i
$199$			1024.90i			0.365092i	0.983197	+	0.182546i	$0.0584338\pi$
$199$			1024.90i			0.365092i	−0.983197	+	0.182546i	$0.941566\pi$
$200$		−	5598.22i		−	1.97927i
$201$	−1340.47			−0.470394
$202$		−	1074.07i		−	0.374114i
$203$		−	1815.21i		−	0.627601i
$204$			4074.58i			1.39842i
$205$			891.663i			0.303787i
$206$	−3222.81			−1.09002
$207$			1344.56i			0.451467i
$208$			8872.62i			2.95772i
$209$			4793.93i			1.58662i
$210$	−1673.52			−0.549923
$211$	1652.01			0.539000			0.269500	−	0.963000i	$-0.413142\pi$
$211$	1652.01			0.539000			0.269500	+	0.963000i	$0.413142\pi$
$212$	−4541.60			−1.47131
$213$	−1871.63			−0.602076
$214$			5251.90i			1.67763i
$215$	−760.231			−0.241150
$216$			9181.07i			2.89210i
$217$		−	5241.10i		−	1.63958i
$218$	5522.88			1.71586
$219$	793.320			0.244783
$220$		−	8109.51i		−	2.48519i
$221$	2854.99			0.868991
$222$	1365.35	−	3134.53i	0.412775	−	0.947638i
$223$	−1857.71			−0.557855			−0.278928	−	0.960312i	$-0.589979\pi$
$223$	−1857.71			−0.557855			−0.278928	+	0.960312i	$0.589979\pi$
$224$			9480.62i			2.82790i
$225$	−1508.63			−0.447001
$226$	7709.73			2.26922
$227$		−	564.595i		−	0.165081i	−0.996588	−	0.0825407i	$-0.973697\pi$
$227$		−	564.595i		−	0.165081i	0.996588	−	0.0825407i	$-0.0263034\pi$
$228$		−	5028.42i		−	1.46059i
$229$	−2685.42			−0.774922			−0.387461	−	0.921886i	$-0.626648\pi$
$229$	−2685.42			−0.774922			−0.387461	+	0.921886i	$0.626648\pi$
$230$			2577.21i			0.738854i
$231$	2594.35			0.738943
$232$	−7902.21			−2.23623
$233$	−3226.02			−0.907055			−0.453527	−	0.891242i	$-0.649835\pi$
$233$	−3226.02			−0.907055			−0.453527	+	0.891242i	$0.649835\pi$
$234$	4287.45			1.19778
$235$		−	668.434i		−	0.185548i
$236$		−	847.079i		−	0.233645i
$237$			1990.30i			0.545503i
$238$	6013.08			1.63769
$239$			2063.21i			0.558400i	0.960233	+	0.279200i	$0.0900693\pi$
$239$			2063.21i			0.558400i	−0.960233	+	0.279200i	$0.909931\pi$
$240$			4062.92i			1.09275i
$241$		−	5678.71i		−	1.51783i	−0.651187	−	0.758917i	$-0.725729\pi$
$241$		−	5678.71i		−	1.51783i	0.651187	−	0.758917i	$-0.274271\pi$
$242$			10152.2i			2.69672i
$243$	3924.03			1.03591
$244$		−	15223.0i		−	3.99408i
$245$		−	532.856i		−	0.138951i
$246$			1999.18i			0.518143i
$247$	−3523.32			−0.907625
$248$	−22816.2			−5.84206
$249$	−1041.80			−0.265146
$250$	−7461.81			−1.88770
$251$			1378.62i			0.346684i	0.984862	+	0.173342i	$0.0554566\pi$
$251$			1378.62i			0.346684i	−0.984862	+	0.173342i	$0.944543\pi$
$252$	6549.06			1.63711
$253$		−	3995.29i		−	0.992813i
$254$		−	7070.86i		−	1.74671i
$255$	1307.34			0.321055
$256$	5288.85			1.29122
$257$			7615.70i			1.84846i	0.381836	+	0.924230i	$0.375292\pi$
$257$			7615.70i			1.84846i	−0.381836	+	0.924230i	$0.624708\pi$
$258$	−1704.50			−0.411308
$259$	−3354.84	−	1461.31i	−0.804864	−	0.350585i
$260$	5960.12			1.42166
$261$			2129.52i			0.505034i
$262$	5186.18			1.22291
$263$	−3536.77			−0.829226			−0.414613	−	0.909998i	$-0.636083\pi$
$263$	−3536.77			−0.829226			−0.414613	+	0.909998i	$0.636083\pi$
$264$		−	11294.1i		−	2.63296i
$265$			1457.19i			0.337790i
$266$	−7420.70			−1.71050
$267$		−	2303.08i		−	0.527889i
$268$	10054.8			2.29177
$269$	6106.13			1.38400			0.692002	−	0.721896i	$-0.256729\pi$
$269$	6106.13			1.38400			0.692002	+	0.721896i	$0.256729\pi$
$270$	4742.37			1.06893
$271$	3088.62			0.692325			0.346162	−	0.938175i	$-0.387485\pi$
$271$	3088.62			0.692325			0.346162	+	0.938175i	$0.387485\pi$
$272$		−	14598.4i		−	3.25425i
$273$			1906.73i			0.422713i
$274$			7073.83i			1.55966i
$275$	4482.81			0.982994
$276$			4190.72i			0.913955i
$277$		−	753.598i		−	0.163463i	−0.996654	−	0.0817316i	$-0.973955\pi$
$277$		−	753.598i		−	0.163463i	0.996654	−	0.0817316i	$-0.0260450\pi$
$278$			8298.36i			1.79030i
$279$			6148.60i			1.31938i
$280$	7797.45			1.66424
$281$		−	5418.05i		−	1.15023i	−0.818074	−	0.575113i	$-0.804958\pi$
$281$		−	5418.05i		−	1.15023i	0.818074	−	0.575113i	$-0.195042\pi$
$282$		−	1498.68i		−	0.316472i
$283$			3197.10i			0.671548i	0.941943	+	0.335774i	$0.108998\pi$
$283$			3197.10i			0.671548i	−0.941943	+	0.335774i	$0.891002\pi$
$284$	14039.1			2.93333
$285$	−1613.38			−0.335328
$286$	−12739.9			−2.63401
$287$	2139.70			0.440078
$288$		−	11122.2i		−	2.27563i
$289$	215.621			0.0438878
$290$			4081.79i			0.826520i
$291$		−	178.509i		−	0.0359601i
$292$	−5950.66			−1.19259
$293$	8317.45			1.65840			0.829199	−	0.558953i	$-0.188797\pi$
$293$	8317.45			1.65840			0.829199	+	0.558953i	$0.188797\pi$
$294$		−	1194.71i		−	0.236996i
$295$	−271.788			−0.0536411
$296$	−6361.57	+	14604.7i	−1.24918	+	2.86785i
$297$	−7351.80			−1.43634
$298$			163.183i			0.0317212i
$299$	2936.36			0.567940
$300$	−4702.08			−0.904915
$301$			1824.30i			0.349339i
$302$		−	10298.0i		−	1.96220i
$303$	−560.371			−0.106246
$304$			18015.7i			3.39892i
$305$	−4884.36			−0.916977
$306$	−7054.25			−1.31786
$307$	10604.0			1.97135			0.985676	−	0.168650i	$-0.0539408\pi$
$307$	10604.0			1.97135			0.985676	+	0.168650i	$0.0539408\pi$
$308$	−19460.1			−3.60014
$309$			1681.43i			0.309558i
$310$			11785.4i			2.15925i
$311$			3623.18i			0.660617i	0.943873	+	0.330308i	$0.107153\pi$
$311$			3623.18i			0.660617i	−0.943873	+	0.330308i	$0.892847\pi$
$312$	8300.63			1.50619
$313$			7589.71i			1.37059i	0.728264	+	0.685297i	$0.240328\pi$
$313$			7589.71i			1.37059i	−0.728264	+	0.685297i	$0.759672\pi$
$314$		−	6911.66i		−	1.24219i
$315$		−	2101.29i		−	0.375854i
$316$		−	14929.2i		−	2.65770i
$317$	2035.56			0.360658			0.180329	−	0.983606i	$-0.442284\pi$
$317$	2035.56			0.360658			0.180329	+	0.983606i	$0.442284\pi$
$318$			3267.13i			0.576137i
$319$		−	6327.74i		−	1.11061i
$320$		−	9773.27i		−	1.70732i
$321$	2740.07			0.476435
$322$	6184.46			1.07033
$323$	5797.00			0.998619
$324$	−3164.07			−0.542536
$325$			3294.66i			0.562322i
$326$	−21159.2			−3.59478
$327$		−	2881.44i		−	0.487291i
$328$		−	9314.80i		−	1.56806i
$329$	−1604.02			−0.268792
$330$	−5833.81			−0.973153
$331$		−	10591.8i		−	1.75884i	−0.476043	−	0.879422i	$-0.657929\pi$
$331$		−	10591.8i		−	1.75884i	0.476043	−	0.879422i	$-0.342071\pi$
$332$	7814.48			1.29179
$333$	3935.74	+	1714.34i	0.647679	+	0.282118i
$334$	−2172.71			−0.355944
$335$		−	3226.11i		−	0.526153i
$336$	9749.66			1.58300
$337$	−7720.67			−1.24799			−0.623993	−	0.781430i	$-0.714491\pi$
$337$	−7720.67			−1.24799			−0.623993	+	0.781430i	$0.714491\pi$
$338$			2491.83i			0.400999i
$339$		−	4022.39i		−	0.644443i
$340$	−9806.33			−1.56419
$341$		−	18270.2i		−	2.90143i
$342$	8705.60			1.37645
$343$	−6855.52			−1.07919
$344$	7941.79			1.24475
$345$	1344.61			0.209829
$346$			5266.14i			0.818235i
$347$			10529.2i			1.62892i	0.580218	+	0.814461i	$0.302967\pi$
$347$			10529.2i			1.62892i	−0.580218	+	0.814461i	$0.697033\pi$
$348$			6637.26i			1.02240i
$349$	−864.634			−0.132615			−0.0663077	−	0.997799i	$-0.521122\pi$
$349$	−864.634			−0.132615			−0.0663077	+	0.997799i	$0.521122\pi$
$350$			6939.10i			1.05974i
$351$		−	5403.24i		−	0.821662i
$352$			33049.0i			5.00431i
$353$			7032.15i			1.06029i	0.847906	+	0.530147i	$0.177863\pi$
$353$			7032.15i			1.06029i	−0.847906	+	0.530147i	$0.822137\pi$
$354$	−609.371			−0.0914907
$355$		−	4504.48i		−	0.673445i
$356$			17275.3i			2.57188i
$357$		−	3137.19i		−	0.465092i
$358$	10592.5			1.56378
$359$	−10296.2			−1.51368			−0.756839	−	0.653602i	$-0.773257\pi$
$359$	−10296.2			−1.51368			−0.756839	+	0.653602i	$0.773257\pi$
$360$	−9147.58			−1.33922
$361$	−295.043			−0.0430155
$362$		−	19309.1i		−	2.80349i
$363$	5296.67			0.765849
$364$		−	14302.3i		−	2.05947i
$365$			1909.29i			0.273799i
$366$	−10951.1			−1.56400
$367$	−2445.36			−0.347812			−0.173906	−	0.984762i	$-0.555639\pi$
$367$	−2445.36			−0.347812			−0.173906	+	0.984762i	$0.555639\pi$
$368$		−	15014.4i		−	2.12685i
$369$	−2510.19			−0.354133
$370$	7543.89	+	3285.99i	1.05997	+	0.461704i
$371$	3496.77			0.489335
$372$			19163.9i			2.67097i
$373$	−1453.10			−0.201712			−0.100856	−	0.994901i	$-0.532158\pi$
$373$	−1453.10			−0.201712			−0.100856	+	0.994901i	$0.532158\pi$
$374$	20961.3			2.89808
$375$			3893.04i			0.536095i
$376$			6982.82i			0.957744i
$377$	4650.60			0.635327
$378$		−	11380.1i		−	1.54849i
$379$	−356.951			−0.0483782			−0.0241891	−	0.999707i	$-0.507700\pi$
$379$	−356.951			−0.0483782			−0.0241891	+	0.999707i	$0.507700\pi$
$380$	12101.9			1.63373
$381$	−3689.07			−0.496054
$382$	16519.7			2.21262
$383$			8260.99i			1.10213i	0.834461	+	0.551067i	$0.185779\pi$
$383$			8260.99i			1.10213i	−0.834461	+	0.551067i	$0.814221\pi$
$384$		−	8779.83i		−	1.16678i
$385$			6243.85i			0.826535i
$386$	−10592.7			−1.39677
$387$		−	2140.18i		−	0.281116i
$388$			1338.99i			0.175198i
$389$		−	5751.61i		−	0.749661i	−0.927093	−	0.374831i	$-0.877701\pi$
$389$		−	5751.61i		−	0.749661i	0.927093	−	0.374831i	$-0.122299\pi$
$390$		−	4287.59i		−	0.556693i
$391$	−4831.26			−0.624878
$392$			5566.51i			0.717223i
$393$		−	2705.78i		−	0.347299i
$394$		−	9160.09i		−	1.17127i
$395$	−4790.08			−0.610165
$396$	22829.7			2.89706
$397$	−6861.12			−0.867380			−0.433690	−	0.901062i	$-0.642789\pi$
$397$	−6861.12			−0.867380			−0.433690	+	0.901062i	$0.642789\pi$
$398$	−5530.40			−0.696517
$399$			3871.59i			0.485769i
$400$	16846.5			2.10582
$401$			1404.27i			0.174878i	0.996170	+	0.0874388i	$0.0278682\pi$
$401$			1404.27i			0.174878i	−0.996170	+	0.0874388i	$0.972132\pi$
$402$		−	7233.20i		−	0.897411i
$403$	13427.8			1.65977
$404$	4203.32			0.517631
$405$			1015.20i			0.124558i
$406$	9794.95			1.19733
$407$	−11694.8	−	5094.06i	−1.42430	−	0.620401i
$408$	−13657.2			−1.65719
$409$		−	9142.35i		−	1.10528i	−0.833420	−	0.552641i	$-0.813620\pi$
$409$		−	9142.35i		−	1.10528i	0.833420	−	0.552641i	$-0.186380\pi$
$410$	−4811.44			−0.579561
$411$	3690.62			0.442932
$412$		−	12612.4i		−	1.50817i
$413$			652.202i			0.0777065i
$414$	−7255.31			−0.861302
$415$		−	2507.30i		−	0.296575i
$416$	−24289.5			−2.86272
$417$	4329.49			0.508432
$418$	−25868.2			−3.02692
$419$	−10074.7			−1.17465			−0.587327	−	0.809350i	$-0.699820\pi$
$419$	−10074.7			−1.17465			−0.587327	+	0.809350i	$0.699820\pi$
$420$		−	6549.26i		−	0.760884i
$421$			12798.1i			1.48158i	0.671739	+	0.740788i	$0.265548\pi$
$421$			12798.1i			1.48158i	−0.671739	+	0.740788i	$0.734452\pi$
$422$			8914.30i			1.02830i
$423$	1881.76			0.216298
$424$		−	15222.6i		−	1.74357i
$425$		−	5420.78i		−	0.618698i
$426$		−	10099.4i		−	1.14863i
$427$			11720.9i			1.32837i
$428$	−20553.1			−2.32120
$429$			6646.77i			0.748040i
$430$		−	4102.23i		−	0.460063i
$431$			11612.1i			1.29777i	0.760888	+	0.648883i	$0.224764\pi$
$431$			11612.1i			1.29777i	−0.760888	+	0.648883i	$0.775236\pi$
$432$	−27628.3			−3.07701
$433$	6856.28			0.760951			0.380476	−	0.924791i	$-0.375760\pi$
$433$	6856.28			0.760951			0.380476	+	0.924791i	$0.375760\pi$
$434$	28281.2			3.12797
$435$	2129.59			0.234726
$436$			21613.6i			2.37409i
$437$	5962.23			0.652659
$438$			4280.78i			0.466995i
$439$			254.645i			0.0276846i	0.999904	+	0.0138423i	$0.00440627\pi$
$439$			254.645i			0.0276846i	−0.999904	+	0.0138423i	$0.995594\pi$
$440$	27181.5			2.94506
$441$	1500.08			0.161979
$442$			15405.6i			1.65785i
$443$	−5451.49			−0.584669			−0.292334	−	0.956316i	$-0.594432\pi$
$443$	−5451.49			−0.584669			−0.292334	+	0.956316i	$0.594432\pi$
$444$	12266.9	+	5343.23i	1.31117	+	0.571123i
$445$	5542.84			0.590463
$446$		−	10024.3i		−	1.06427i
$447$	85.1372			0.00900861
$448$	−23452.6			−2.47329
$449$		−	12024.0i		−	1.26380i	−0.775050	−	0.631900i	$-0.782275\pi$
$449$		−	12024.0i		−	1.26380i	0.775050	−	0.631900i	$-0.217725\pi$
$450$		−	8140.62i		−	0.852783i
$451$	7458.88			0.778769
$452$			30171.8i			3.13974i
$453$	−5372.78			−0.557252
$454$	3046.57			0.314940
$455$	−4588.95			−0.472820
$456$	16854.3			1.73087
$457$		−	2235.58i		−	0.228831i	−0.993433	−	0.114416i	$-0.963500\pi$
$457$		−	2235.58i		−	0.228831i	0.993433	−	0.114416i	$-0.0364995\pi$
$458$		−	14490.6i		−	1.47839i
$459$			8890.08i			0.904038i
$460$	−10085.8			−1.02229
$461$			9012.14i			0.910493i	0.890366	+	0.455246i	$0.150449\pi$
$461$			9012.14i			0.910493i	−0.890366	+	0.455246i	$0.849551\pi$
$462$			13999.2i			1.40975i
$463$		−	11294.9i		−	1.13373i	−0.823811	−	0.566865i	$-0.808156\pi$
$463$		−	11294.9i		−	1.13373i	0.823811	−	0.566865i	$-0.191844\pi$
$464$		−	23779.9i		−	2.37921i
$465$	6148.80			0.613212
$466$		−	17407.7i		−	1.73047i
$467$		−	7336.43i		−	0.726959i	−0.931602	−	0.363479i	$-0.881589\pi$
$467$		−	7336.43i		−	0.726959i	0.931602	−	0.363479i	$-0.118411\pi$
$468$			16778.8i			1.65726i
$469$	−7741.60			−0.762205
$470$	3606.89			0.353986
$471$	−3606.01			−0.352773
$472$	2839.25			0.276879
$473$			6359.44i			0.618197i
$474$	−10739.7			−1.04070
$475$			6689.75i			0.646204i
$476$			23532.0i			2.26594i
$477$	−4102.24			−0.393771
$478$	−11133.1			−1.06531
$479$			14290.6i			1.36316i	0.731743	+	0.681580i	$0.238707\pi$
$479$			14290.6i			1.36316i	−0.731743	+	0.681580i	$0.761293\pi$
$480$	−11122.6			−1.05765
$481$	3743.90	−	8595.16i	0.354901	−	0.814773i
$482$	30642.5			2.89570
$483$		−	3226.61i		−	0.303967i
$484$	−39730.1			−3.73123
$485$	429.619			0.0402226
$486$			21174.2i			1.97630i
$487$			11788.6i			1.09690i	0.836182	+	0.548452i	$0.184783\pi$
$487$			11788.6i			1.09690i	−0.836182	+	0.548452i	$0.815217\pi$
$488$	51024.8			4.73316
$489$			11039.4i			1.02089i
$490$	2875.31			0.265088
$491$	−5302.95			−0.487411			−0.243706	−	0.969849i	$-0.578363\pi$
$491$	−5302.95			−0.487411			−0.243706	+	0.969849i	$0.578363\pi$
$492$	−7823.72			−0.716912
$493$	−7651.75			−0.699022
$494$		−	19011.9i		−	1.73155i
$495$		−	7324.98i		−	0.665118i
$496$		−	68660.1i		−	6.21558i
$497$	−10809.3			−0.975577
$498$		−	5621.58i		−	0.505841i
$499$		−	6326.67i		−	0.567576i	−0.958887	−	0.283788i	$-0.908409\pi$
$499$		−	6326.67i		−	0.567576i	0.958887	−	0.283788i	$-0.0915912\pi$
$500$		−	29201.5i		−	2.61186i
$501$			1133.56i			0.101085i
$502$	−7439.08			−0.661399
$503$		−	7696.81i		−	0.682274i	−0.940014	−	0.341137i	$-0.889188\pi$
$503$		−	7696.81i		−	0.682274i	0.940014	−	0.341137i	$-0.110812\pi$
$504$			21951.2i			1.94005i
$505$		−	1348.65i		−	0.118840i
$506$	21558.7			1.89408
$507$	1300.06			0.113881
$508$	27671.5			2.41678
$509$	17475.7			1.52180			0.760902	−	0.648867i	$-0.224757\pi$
$509$	17475.7			1.52180			0.760902	+	0.648867i	$0.224757\pi$
$510$			7054.47i			0.612504i
$511$	4581.66			0.396636
$512$			3589.61i			0.309843i
$513$		−	10971.2i		−	0.944230i
$514$	−41094.6			−3.52647
$515$	−4046.72			−0.346252
$516$		−	6670.50i		−	0.569094i
$517$	−5591.54			−0.475659
$518$	7885.29	−	18102.9i	0.668841	−	1.53551i
$519$	2747.49			0.232373
$520$			19977.2i			1.68473i
$521$	19380.0			1.62966			0.814832	−	0.579697i	$-0.196829\pi$
$521$	19380.0			1.62966			0.814832	+	0.579697i	$0.196829\pi$
$522$	−11491.0			−0.963497
$523$		−	4938.48i		−	0.412896i	−0.978458	−	0.206448i	$-0.933810\pi$
$523$		−	4938.48i		−	0.412896i	0.978458	−	0.206448i	$-0.0661904\pi$
$524$			20295.9i			1.69205i
$525$	3620.33			0.300960
$526$		−	19084.5i		−	1.58199i
$527$	−22093.1			−1.82617
$528$	33986.8			2.80130
$529$	7198.04			0.591603
$530$	−7863.03			−0.644431
$531$		−	765.131i		−	0.0625308i
$532$		−	29040.6i		−	2.36668i
$533$			5481.94i			0.445495i
$534$	12427.5			1.00710
$535$			6594.54i			0.532910i
$536$			33701.7i			2.71584i
$537$		−	5526.42i		−	0.444102i
$538$			32948.9i			2.64038i
$539$	−4457.42			−0.356205
$540$			18559.1i			1.47899i
$541$		−	17881.1i		−	1.42101i	−0.703691	−	0.710506i	$-0.748466\pi$
$541$		−	17881.1i		−	1.42101i	0.703691	−	0.710506i	$-0.251534\pi$
$542$			16666.3i			1.32081i
$543$	−10074.1			−0.796171
$544$	39964.1			3.14972
$545$	6934.80			0.545053
$546$	−10288.8			−0.806446
$547$			817.257i			0.0638819i	0.999490	+	0.0319409i	$0.0101688\pi$
$547$			817.257i			0.0638819i	−0.999490	+	0.0319409i	$0.989831\pi$
$548$	−27683.2			−2.15797
$549$		−	13750.3i		−	1.06894i
$550$			24189.4i			1.87534i
$551$	9442.98			0.730099
$552$	−14046.5			−1.08308
$553$			11494.6i			0.883907i
$554$	4066.44			0.311853
$555$	1714.39	−	3935.86i	0.131121	−	0.301024i
$556$	−32475.3			−2.47709
$557$		−	19213.5i		−	1.46158i	−0.682601	−	0.730791i	$-0.739151\pi$
$557$		−	19213.5i		−	1.46158i	0.682601	−	0.730791i	$-0.260849\pi$
$558$	−33178.1			−2.51710
$559$	−4673.90			−0.353640
$560$			23464.6i			1.77064i
$561$		−	10936.1i		−	0.823035i
$562$	29236.0			2.19439
$563$		−	1.52747i		−	0.000114343i	−1.00000		5.71715e-5i	$-0.999982\pi$
$563$		−	1.52747i		−	0.000114343i	1.00000		5.71715e-5i	$-1.81983e-5\pi$
$564$	5865.04			0.437877
$565$	9680.71			0.720833
$566$	−17251.7			−1.28117
$567$	2436.15			0.180439
$568$			47056.2i			3.47612i
$569$		−	1123.19i		−	0.0827533i	−0.999144	−	0.0413767i	$-0.986826\pi$
$569$		−	1123.19i		−	0.0827533i	0.999144	−	0.0413767i	$-0.0131744\pi$
$570$		−	8705.88i		−	0.639735i
$571$	−10827.8			−0.793574			−0.396787	−	0.917911i	$-0.629875\pi$
$571$	−10827.8			−0.793574			−0.396787	+	0.917911i	$0.629875\pi$
$572$		−	49857.2i		−	3.64446i
$573$		−	8618.79i		−	0.628368i
$574$			11545.9i			0.839574i
$575$		−	5575.29i		−	0.404357i
$576$	27513.5			1.99027
$577$			19564.6i			1.41159i	0.708417	+	0.705794i	$0.249410\pi$
$577$			19564.6i			1.41159i	−0.708417	+	0.705794i	$0.750590\pi$
$578$			1163.50i			0.0837285i
$579$			5526.52i			0.396674i
$580$	−15973.9			−1.14359
$581$	−6016.70			−0.429630
$582$	963.240			0.0686041
$583$	12189.6			0.865935
$584$		−	19945.5i		−	1.41327i
$585$	5383.53			0.380481
$586$			44881.3i			3.16387i
$587$		−	6952.71i		−	0.488874i	−0.969665	−	0.244437i	$-0.921397\pi$
$587$		−	6952.71i		−	0.488874i	0.969665	−	0.244437i	$-0.0786032\pi$
$588$	4675.45			0.327912
$589$	27264.9			1.90735
$590$		−	1466.58i		−	0.102336i
$591$	−4779.08			−0.332631
$592$	−43949.5	−	19143.6i	−3.05121	−	1.32905i
$593$	−18925.1			−1.31055			−0.655277	−	0.755388i	$-0.727448\pi$
$593$	−18925.1			−1.31055			−0.655277	+	0.755388i	$0.727448\pi$
$594$		−	39670.5i		−	2.74024i
$595$	7550.31			0.520223
$596$	−638.611			−0.0438901
$597$			2885.37i			0.197806i
$598$			15844.7i			1.08351i
$599$	−19111.5			−1.30363			−0.651817	−	0.758376i	$-0.725993\pi$
$599$	−19111.5			−1.30363			−0.651817	+	0.758376i	$0.725993\pi$
$600$		−	15760.5i		−	1.07236i
$601$	18224.7			1.23694			0.618471	−	0.785808i	$-0.287753\pi$
$601$	18224.7			1.23694			0.618471	+	0.785808i	$0.287753\pi$
$602$	−9844.01			−0.666465
$603$	9082.07			0.613351
$604$	40301.0			2.71494
$605$			12747.5i			0.856630i
$606$		−	3023.78i		−	0.202694i
$607$			2790.32i			0.186583i	0.995639	+	0.0932914i	$0.0297388\pi$
$607$			2790.32i			0.186583i	−0.995639	+	0.0932914i	$0.970261\pi$
$608$	−49319.5			−3.28975
$609$		−	5110.30i		−	0.340033i
$610$		−	26356.2i		−	1.74940i
$611$		−	4109.53i		−	0.272101i
$612$		−	27606.6i		−	1.82341i
$613$	8454.58			0.557059			0.278530	−	0.960428i	$-0.410153\pi$
$613$	8454.58			0.557059			0.278530	+	0.960428i	$0.410153\pi$
$614$			57219.8i			3.76092i
$615$			2510.27i			0.164591i
$616$		−	65226.7i		−	4.26633i
$617$	4510.28			0.294290			0.147145	−	0.989115i	$-0.452992\pi$
$617$	4510.28			0.294290			0.147145	+	0.989115i	$0.452992\pi$
$618$	−9073.08			−0.590571
$619$	−10525.8			−0.683470			−0.341735	−	0.939796i	$-0.611015\pi$
$619$	−10525.8			−0.683470			−0.341735	+	0.939796i	$0.611015\pi$
$620$	−46121.9			−2.98758
$621$			9143.46i			0.590845i
$622$	−19550.8			−1.26032
$623$		−	13301.0i		−	0.855366i
$624$			24978.8i			1.60249i
$625$	517.136			0.0330967
$626$	−40954.3			−2.61480
$627$			13496.2i			0.859626i
$628$	27048.6			1.71872
$629$	−6159.94	+	14141.8i	−0.390481	+	0.896458i
$630$	11338.6			0.717049
$631$			9440.57i			0.595599i	0.954628	+	0.297800i	$0.0962527\pi$
$631$			9440.57i			0.595599i	−0.954628	+	0.297800i	$0.903747\pi$
$632$	50039.8			3.14949
$633$	4650.85			0.292029
$634$			10984.0i			0.688059i
$635$		−	8878.51i		−	0.554855i
$636$	−12785.8			−0.797155
$637$		−	3276.00i		−	0.203767i
$638$	34144.7			2.11881
$639$	12680.9			0.785052
$640$	21130.5			1.30509
$641$	7473.20			0.460489			0.230245	−	0.973133i	$-0.426047\pi$
$641$	7473.20			0.460489			0.230245	+	0.973133i	$0.426047\pi$
$642$			14785.5i			0.908936i
$643$			13277.8i			0.814346i	0.913351	+	0.407173i	$0.133485\pi$
$643$			13277.8i			0.814346i	−0.913351	+	0.407173i	$0.866515\pi$
$644$			24202.7i			1.48093i
$645$	−2140.25			−0.130655
$646$			31280.8i			1.90515i
$647$			1006.02i			0.0611296i	0.999533	+	0.0305648i	$0.00973059\pi$
$647$			1006.02i			0.0611296i	−0.999533	+	0.0305648i	$0.990269\pi$
$648$		−	10605.4i		−	0.642929i
$649$			2273.54i			0.137511i
$650$	−17778.1			−1.07279
$651$		−	14755.1i		−	0.888322i
$652$		−	82805.8i		−	4.97381i
$653$		−	17776.7i		−	1.06532i	−0.846328	−	0.532662i	$-0.821192\pi$
$653$		−	17776.7i		−	1.06532i	0.846328	−	0.532662i	$-0.178808\pi$
$654$	15548.4			0.929648
$655$	6512.02			0.388467
$656$	28030.7			1.66832
$657$	−5374.98			−0.319175
$658$		−	8655.35i		−	0.512797i
$659$	3178.94			0.187912			0.0939559	−	0.995576i	$-0.470049\pi$
$659$	3178.94			0.187912			0.0939559	+	0.995576i	$0.470049\pi$
$660$		−	22830.4i		−	1.34647i
$661$			30502.9i			1.79490i	0.441121	+	0.897448i	$0.354581\pi$
$661$			30502.9i			1.79490i	−0.441121	+	0.897448i	$0.645419\pi$
$662$	57153.7			3.35550
$663$	8037.54			0.470818
$664$			26192.7i			1.53083i
$665$	−9317.79			−0.543351
$666$	−9250.63	+	21237.4i	−0.538220	+	1.23563i
$667$	−7869.84			−0.456854
$668$		−	8502.80i		−	0.492490i
$669$	−5229.96			−0.302245
$670$	17408.2			1.00379
$671$			40858.4i			2.35070i
$672$			26690.5i			1.53215i
$673$	−27578.6			−1.57961			−0.789804	−	0.613360i	$-0.789818\pi$
$673$	−27578.6			−1.57961			−0.789804	+	0.613360i	$0.789818\pi$
$674$		−	41661.0i		−	2.38089i
$675$	−10259.2			−0.585001
$676$	−9751.69			−0.554830
$677$	11517.1			0.653821			0.326910	−	0.945055i	$-0.393992\pi$
$677$	11517.1			0.653821			0.326910	+	0.945055i	$0.393992\pi$
$678$	21704.9			1.22946
$679$		−	1030.94i		−	0.0582680i
$680$		−	32869.0i		−	1.85363i
$681$		−	1589.48i		−	0.0894408i
$682$	98586.7			5.53531
$683$			16518.0i			0.925394i	0.886517	+	0.462697i	$0.153118\pi$
$683$			16518.0i			0.925394i	−0.886517	+	0.462697i	$0.846882\pi$
$684$			34069.1i			1.90448i
$685$			8882.24i			0.495435i
$686$		−	36992.6i		−	2.05887i
$687$	−7560.16			−0.419851
$688$			23899.0i			1.32433i
$689$			8958.78i			0.495359i
$690$			7255.54i			0.400310i
$691$	11900.6			0.655164			0.327582	−	0.944823i	$-0.393766\pi$
$691$	11900.6			0.655164			0.327582	+	0.944823i	$0.393766\pi$
$692$	−20608.8			−1.13213
$693$	−17577.5			−0.963514
$694$	−56815.8			−3.10764
$695$			10419.8i			0.568700i
$696$	−22246.8			−1.21159
$697$		−	9019.57i		−	0.490159i
$698$		−	4665.59i		−	0.253002i
$699$	−9082.11			−0.491440
$700$	−27155.9			−1.46628
$701$		−	22713.7i		−	1.22380i	−0.790935	−	0.611901i	$-0.790405\pi$
$701$		−	22713.7i		−	1.22380i	0.790935	−	0.611901i	$-0.209595\pi$
$702$	29156.1			1.56756
$703$	7601.94	−	17452.3i	0.407841	−	0.936312i
$704$	−81754.7			−4.37677
$705$		−	1881.82i		−	0.100530i
$706$	−37945.7			−2.02281
$707$	−3236.31			−0.172156
$708$		−	2384.75i		−	0.126588i
$709$		−	10384.1i		−	0.550046i	−0.961438	−	0.275023i	$-0.911315\pi$
$709$		−	10384.1i		−	0.550046i	0.961438	−	0.275023i	$-0.0886855\pi$
$710$	24306.3			1.28479
$711$		−	13484.9i		−	0.711285i
$712$	−57903.6			−3.04779
$713$	−22722.8			−1.19351
$714$	16928.4			0.887297
$715$	−15996.8			−0.836711
$716$			41453.5i			2.16367i
$717$			5808.47i			0.302540i
$718$		−	55558.4i		−	2.88777i
$719$	−9083.51			−0.471151			−0.235576	−	0.971856i	$-0.575698\pi$
$719$	−9083.51			−0.471151			−0.235576	+	0.971856i	$0.575698\pi$
$720$		−	27527.5i		−	1.42485i
$721$			9710.80i			0.501594i
$722$		−	1592.06i		−	0.0820644i
$723$		−	15987.1i		−	0.822360i
$724$	75565.4			3.87896
$725$		−	8830.14i		−	0.452335i
$726$			28581.0i			1.46108i
$727$			4180.93i			0.213290i	0.994297	+	0.106645i	$0.0340109\pi$
$727$			4180.93i			0.213290i	−0.994297	+	0.106645i	$0.965989\pi$
$728$	47938.7			2.44056
$729$	7001.66			0.355721
$730$	−10302.6			−0.522351
$731$	7690.08			0.389094
$732$		−	42856.9i		−	2.16398i
$733$	1270.23			0.0640070			0.0320035	−	0.999488i	$-0.489811\pi$
$733$	1270.23			0.0640070			0.0320035	+	0.999488i	$0.489811\pi$
$734$		−	13195.3i		−	0.663550i
$735$		−	1500.13i		−	0.0752833i
$736$	41103.2			2.05854
$737$	−26986.8			−1.34881
$738$		−	13545.1i		−	0.675610i
$739$	6403.06			0.318729			0.159364	−	0.987220i	$-0.449056\pi$
$739$	6403.06			0.318729			0.159364	+	0.987220i	$0.449056\pi$
$740$	−12859.6	+	29522.7i	−0.638822	+	1.46659i
$741$	−9919.08			−0.491749
$742$			18868.7i			0.933546i
$743$	32423.7			1.60095			0.800477	−	0.599363i	$-0.204580\pi$
$743$	32423.7			1.60095			0.800477	+	0.599363i	$0.204580\pi$
$744$	−64233.7			−3.16522
$745$			204.900i			0.0100765i
$746$		−	7840.98i		−	0.384824i
$747$	7058.50			0.345725
$748$			82031.3i			4.00984i
$749$	15824.7			0.771993
$750$	−21007.0			−1.02275
$751$	13484.1			0.655185			0.327592	−	0.944819i	$-0.393763\pi$
$751$	13484.1			0.655185			0.327592	+	0.944819i	$0.393763\pi$
$752$	−21013.2			−1.01898
$753$			3881.18i			0.187833i
$754$			25094.8i			1.21207i
$755$		−	12930.7i		−	0.623307i
$756$	44535.7			2.14252
$757$			5500.92i			0.264114i	0.991242	+	0.132057i	$0.0421582\pi$
$757$			5500.92i			0.264114i	−0.991242	+	0.132057i	$0.957842\pi$
$758$		−	1926.12i		−	0.0922953i
$759$		−	11247.8i		−	0.537904i
$760$			40563.4i			1.93604i
$761$	41822.3			1.99219			0.996096	−	0.0882810i	$-0.0281373\pi$
$761$	41822.3			1.99219			0.996096	+	0.0882810i	$0.0281373\pi$
$762$		−	19906.3i		−	0.946365i
$763$		−	16641.2i		−	0.789584i
$764$			64649.2i			3.06142i
$765$	−8857.65			−0.418626
$766$	−44576.6			−2.10264
$767$	−1670.95			−0.0786631
$768$	14889.5			0.699582
$769$		−	9397.23i		−	0.440667i	−0.975425	−	0.220333i	$-0.929285\pi$
$769$		−	9397.23i		−	0.440667i	0.975425	−	0.220333i	$-0.0707145\pi$
$770$	−33692.0			−1.57685
$771$			21440.2i			1.00149i
$772$		−	41454.2i		−	1.93260i
$773$	−35322.7			−1.64356			−0.821779	−	0.569807i	$-0.807018\pi$
$773$	−35322.7			−1.64356			−0.821779	+	0.569807i	$0.807018\pi$
$774$	11548.5			0.536308
$775$		−	25495.4i		−	1.18171i
$776$	−4488.03			−0.207617
$777$	−9444.77	−	4113.98i	−0.436074	−	0.189946i
$778$	31035.9			1.43019
$779$			11131.0i			0.511950i
$780$	16779.3			0.770251
$781$	−37680.6			−1.72640
$782$		−	26069.7i		−	1.19213i
$783$			14481.4i			0.660950i
$784$	−16751.1			−0.763079
$785$		−	8678.62i		−	0.394590i
$786$	14600.5			0.662572
$787$	−7480.97			−0.338841			−0.169420	−	0.985544i	$-0.554190\pi$
$787$	−7480.97			−0.338841			−0.169420	+	0.985544i	$0.554190\pi$
$788$	35847.7			1.62059
$789$	−9956.93			−0.449273
$790$		−	25847.4i		−	1.16406i
$791$		−	23230.5i		−	1.04422i
$792$			76520.8i			3.43314i
$793$	−30029.0			−1.34472
$794$		−	37022.9i		−	1.65478i
$795$			4102.37i			0.183014i
$796$		−	21643.0i		−	0.963714i
$797$			26995.5i			1.19979i	0.800080	+	0.599893i	$0.204790\pi$
$797$			26995.5i			1.19979i	−0.800080	+	0.599893i	$0.795210\pi$
$798$	−20891.2			−0.926744
$799$			6761.51i			0.299380i
$800$			46118.7i			2.03818i
$801$			15604.1i			0.688318i
$802$	−7577.49			−0.333629
$803$	15971.5			0.701893
$804$	28306.9			1.24168
$805$	7765.51			0.339998
$806$			72456.8i			3.16648i
$807$	17190.4			0.749851
$808$			14088.7i			0.613415i
$809$		−	16765.1i		−	0.728592i	−0.931283	−	0.364296i	$-0.881310\pi$
$809$		−	16765.1i		−	0.728592i	0.931283	−	0.364296i	$-0.118690\pi$
$810$	−5478.07			−0.237629
$811$	37839.3			1.63837			0.819186	−	0.573528i	$-0.194426\pi$
$811$	37839.3			1.63837			0.819186	+	0.573528i	$0.194426\pi$
$812$			38332.2i			1.65665i
$813$	8695.27			0.375100
$814$	27487.7	−	63105.7i	1.18359	−	2.71726i
$815$	−26568.5			−1.14191
$816$		−	41098.2i		−	1.76314i
$817$	−9490.28			−0.406393
$818$	49332.4			2.10864
$819$		−	12918.7i		−	0.551179i
$820$		−	18829.4i		−	0.801892i
$821$	−9497.30			−0.403725			−0.201862	−	0.979414i	$-0.564699\pi$
$821$	−9497.30			−0.403725			−0.201862	+	0.979414i	$0.564699\pi$
$822$			19914.7i			0.845019i
$823$	−14347.2			−0.607669			−0.303835	−	0.952725i	$-0.598267\pi$
$823$	−14347.2			−0.607669			−0.303835	+	0.952725i	$0.598267\pi$
$824$	42274.3			1.78725
$825$	12620.3			0.532584
$826$	−3519.30			−0.148247
$827$		−	38052.7i		−	1.60003i	−0.599982	−	0.800014i	$-0.704825\pi$
$827$		−	38052.7i		−	1.60003i	0.599982	−	0.800014i	$-0.295175\pi$
$828$		−	28393.4i		−	1.19171i
$829$		−	31374.8i		−	1.31446i	−0.753688	−	0.657232i	$-0.771727\pi$
$829$		−	31374.8i		−	1.31446i	0.753688	−	0.657232i	$-0.228273\pi$
$830$	13529.5			0.565802
$831$		−	2121.58i		−	0.0885641i
$832$		−	60086.0i		−	2.50374i
$833$			5390.08i			0.224196i
$834$			23362.1i			0.969979i
$835$	−2728.15			−0.113068
$836$		−	101234.i		−	4.18811i
$837$			41812.5i			1.72670i
$838$		−	54363.2i		−	2.24099i
$839$	4964.39			0.204279			0.102139	−	0.994770i	$-0.467431\pi$
$839$	4964.39			0.204279			0.102139	+	0.994770i	$0.467431\pi$
$840$	21951.9			0.901681
$841$	11924.7			0.488939
$842$	−69059.3			−2.82653
$843$		−	15253.2i		−	0.623190i
$844$	−34885.8			−1.42277
$845$			3128.86i			0.127380i
$846$			10154.0i			0.412651i
$847$	30589.9			1.24095
$848$	45808.8			1.85505
$849$			9000.69i			0.363843i
$850$	29250.7			1.18034
$851$	−6335.51	+	14544.9i	−0.255204	+	0.585891i
$852$	39523.7			1.58927
$853$			1052.83i			0.0422606i	0.999777	+	0.0211303i	$0.00672648\pi$
$853$			1052.83i			0.0422606i	−0.999777	+	0.0211303i	$0.993274\pi$
$854$	−63246.2			−2.53424
$855$	10931.2			0.437238
$856$		−	68890.2i		−	2.75072i
$857$			17715.6i			0.706128i	0.935599	+	0.353064i	$0.114860\pi$
$857$			17715.6i			0.706128i	−0.935599	+	0.353064i	$0.885140\pi$
$858$	−35866.2			−1.42710
$859$			24512.7i			0.973648i	0.873500	+	0.486824i	$0.161845\pi$
$859$			24512.7i			0.973648i	−0.873500	+	0.486824i	$0.838155\pi$
$860$	16053.9			0.636552
$861$	6023.81			0.238433
$862$	−62659.6			−2.47586
$863$	−86.4617			−0.00341042			−0.00170521	−	0.999999i	$-0.500543\pi$
$863$	−86.4617			−0.00341042			−0.00170521	+	0.999999i	$0.500543\pi$
$864$		−	75634.6i		−	2.97817i
$865$			6612.41i			0.259918i
$866$			36996.7i			1.45173i
$867$	607.030			0.0237783
$868$			110677.i			4.32792i
$869$			40069.7i			1.56418i
$870$			11491.3i			0.447807i
$871$		−	19834.1i		−	0.771588i
$872$	−72444.7			−2.81340
$873$			1209.45i			0.0468886i
$874$			32172.4i			1.24513i
$875$			22483.5i			0.868663i
$876$	−16752.7			−0.646142
$877$	−3881.39			−0.149447			−0.0747236	−	0.997204i	$-0.523807\pi$
$877$	−3881.39			−0.149447			−0.0747236	+	0.997204i	$0.523807\pi$
$878$	−1374.07			−0.0528162
$879$	23415.8			0.898517
$880$			81796.4i			3.13336i
$881$	48985.9			1.87330			0.936649	−	0.350270i	$-0.113910\pi$
$881$	48985.9			1.87330			0.936649	+	0.350270i	$0.113910\pi$
$882$			8094.51i			0.309021i
$883$		−	11751.2i		−	0.447858i	−0.974605	−	0.223929i	$-0.928112\pi$
$883$		−	11751.2i		−	0.447858i	0.974605	−	0.223929i	$-0.0718883\pi$
$884$	−60289.3			−2.29383
$885$	−765.156			−0.0290626
$886$		−	29416.4i		−	1.11542i
$887$	11678.4			0.442076			0.221038	−	0.975265i	$-0.429056\pi$
$887$	11678.4			0.442076			0.221038	+	0.975265i	$0.429056\pi$
$888$	−17909.5	+	41116.2i	−0.676805	+	1.55379i
$889$	−21305.5			−0.803783
$890$			29909.4i			1.12648i
$891$	8492.30			0.319307
$892$	39229.7			1.47254
$893$		−	8344.33i		−	0.312690i
$894$			459.403i			0.0171865i
$895$	13300.5			0.496744
$896$		−	50706.2i		−	1.89060i
$897$	8266.63			0.307709
$898$	64881.8			2.41106
$899$	−35988.3			−1.33512
$900$	31858.0			1.17993
$901$		−	14740.1i		−	0.545021i
$902$			40248.4i			1.48572i
$903$			5135.90i			0.189271i
$904$	−101130.			−3.72072
$905$		−	24245.4i		−	0.890546i
$906$		−	28991.7i		−	1.06312i
$907$			43196.8i			1.58139i	0.612207	+	0.790697i	$0.290282\pi$
$907$			43196.8i			1.58139i	−0.612207	+	0.790697i	$0.709718\pi$
$908$			11922.7i			0.435757i
$909$	3796.68			0.138535
$910$		−	24762.1i		−	0.902040i
$911$			1508.36i			0.0548563i	0.999624	+	0.0274282i	$0.00873175\pi$
$911$			1508.36i			0.0548563i	−0.999624	+	0.0274282i	$0.991268\pi$
$912$			50719.0i			1.84153i
$913$	−20973.9			−0.760280
$914$	12063.2			0.436561
$915$	−13750.8			−0.496816
$916$	56708.4			2.04552
$917$		−	15626.7i		−	0.562747i
$918$	−47971.2			−1.72471
$919$			13881.1i			0.498253i	0.968471	+	0.249127i	$0.0801436\pi$
$919$			13881.1i			0.498253i	−0.968471	+	0.249127i	$0.919856\pi$
$920$		−	33805.8i		−	1.21146i
$921$	29853.2			1.06807
$922$	−48629.8			−1.73703
$923$		−	27693.5i		−	0.987587i
$924$	−54785.5			−1.95055
$925$	−16319.7	−	7108.58i	−0.580096	−	0.252680i
$926$	60947.5			2.16292
$927$		−	11392.2i		−	0.403635i
$928$	65099.2			2.30279
$929$	−10665.2			−0.376657			−0.188329	−	0.982106i	$-0.560307\pi$
$929$	−10665.2			−0.376657			−0.188329	+	0.982106i	$0.560307\pi$
$930$			33179.1i			1.16988i
$931$		−	6651.86i		−	0.234163i
$932$	68124.5			2.39431
$933$			10200.2i			0.357921i
$934$	39587.7			1.38688
$935$	26320.0			0.920595
$936$	−56239.3			−1.96393
$937$	47774.6			1.66567			0.832833	−	0.553525i	$-0.186718\pi$
$937$	47774.6			1.66567			0.832833	+	0.553525i	$0.186718\pi$
$938$		−	41774.0i		−	1.45412i
$939$			21367.0i			0.742585i
$940$			14115.4i			0.489782i
$941$	8817.39			0.305461			0.152731	−	0.988268i	$-0.451193\pi$
$941$	8817.39			0.305461			0.152731	+	0.988268i	$0.451193\pi$
$942$		−	19458.2i		−	0.673016i
$943$		−	9276.64i		−	0.320349i
$944$			8544.05i			0.294582i
$945$		−	14289.4i		−	0.491889i
$946$	−34315.7			−1.17939
$947$			52689.9i			1.80802i	0.427516	+	0.904008i	$0.359389\pi$
$947$			52689.9i			1.80802i	−0.427516	+	0.904008i	$0.640611\pi$
$948$		−	42029.6i		−	1.43994i
$949$			11738.3i			0.401519i
$950$	−36098.1			−1.23282
$951$	5730.65			0.195404
$952$	−78874.7			−2.68523
$953$	35605.1			1.21025			0.605123	−	0.796132i	$-0.293124\pi$
$953$	35605.1			1.21025			0.605123	+	0.796132i	$0.293124\pi$
$954$		−	22135.8i		−	0.751230i
$955$	20742.9			0.702853
$956$		−	43569.1i		−	1.47398i
$957$		−	17814.3i		−	0.601728i
$958$	−77112.6			−2.60062
$959$	21314.5			0.717706
$960$		−	27514.3i		−	0.925023i
$961$	−74118.7			−2.48796
$962$	46379.8	+	20202.2i	1.55441	+	0.677075i
$963$	−18564.8			−0.621227
$964$			119918.i			4.00655i
$965$	−13300.7			−0.443695
$966$	17410.9			0.579903
$967$		−	40228.2i		−	1.33780i	−0.743352	−	0.668900i	$-0.766765\pi$
$967$		−	40228.2i		−	1.33780i	0.743352	−	0.668900i	$-0.233235\pi$
$968$		−	133168.i		−	4.42167i
$969$	16320.1			0.541050
$970$			2318.24i			0.0767362i
$971$	−51053.3			−1.68731			−0.843656	−	0.536884i	$-0.819601\pi$
$971$	−51053.3			−1.68731			−0.843656	+	0.536884i	$0.819601\pi$
$972$	−82864.4			−2.73444
$973$	25004.1			0.823839
$974$	−63611.6			−2.09266
$975$			9275.34i			0.304665i
$976$			153547.i			5.03578i
$977$			11131.9i			0.364526i	0.983250	+	0.182263i	$0.0583423\pi$
$977$			11131.9i			0.364526i	−0.983250	+	0.182263i	$0.941658\pi$
$978$	−59568.8			−1.94765
$979$		−	46366.6i		−	1.51367i
$980$			11252.4i			0.366781i
$981$			19522.7i			0.635383i
$982$		−	28614.9i		−	0.929877i
$983$	−23333.3			−0.757086			−0.378543	−	0.925584i	$-0.623575\pi$
$983$	−23333.3			−0.757086			−0.378543	+	0.925584i	$0.623575\pi$
$984$		−	26223.6i		−	0.849572i
$985$		−	11501.9i		−	0.372060i
$986$		−	41289.1i		−	1.33358i
$987$	−4515.74			−0.145631
$988$	74402.6			2.39581
$989$	7909.26			0.254297
$990$	39525.8			1.26890
$991$		−	41509.7i		−	1.33057i	−0.746587	−	0.665287i	$-0.768309\pi$
$991$		−	41509.7i		−	1.33057i	0.746587	−	0.665287i	$-0.231691\pi$
$992$	187962.			6.01594
$993$		−	29818.7i		−	0.952938i
$994$		−	58327.1i		−	1.86119i
$995$	−6944.24			−0.221253
$996$	21999.8			0.699891
$997$			6314.58i			0.200587i	0.994958	+	0.100293i	$0.0319781\pi$
$997$			6314.58i			0.200587i	−0.994958	+	0.100293i	$0.968022\pi$
$998$	34138.9			1.08281
$999$	26764.3	+	11658.1i	0.847633	+	0.369214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.4.b.a.36.8	yes	8
3.2	odd	2		333.4.c.d.73.1		8
4.3	odd	2		592.4.g.c.369.4		8
37.6	odd	4		1369.4.a.a.1.4		4
37.31	odd	4		1369.4.a.b.1.1		4
37.36	even	2	inner	37.4.b.a.36.1	✓	8
111.110	odd	2		333.4.c.d.73.8		8
148.147	odd	2		592.4.g.c.369.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.4.b.a.36.1	✓	8	37.36	even	2	inner
37.4.b.a.36.8	yes	8	1.1	even	1	trivial
333.4.c.d.73.1		8	3.2	odd	2
333.4.c.d.73.8		8	111.110	odd	2
592.4.g.c.369.3		8	148.147	odd	2
592.4.g.c.369.4		8	4.3	odd	2
1369.4.a.a.1.4		4	37.6	odd	4
1369.4.a.b.1.1		4	37.31	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)

\(f(q)\)	\(=\)	\(q+5.39603i q^{2} +2.81527 q^{3} -21.1172 q^{4} +6.77552i q^{5} +15.1913i q^{6} +16.2590 q^{7} -70.7808i q^{8} -19.0743 q^{9} +O(q^{10})\)	\(q+5.39603i q^{2} +2.81527 q^{3} -21.1172 q^{4} +6.77552i q^{5} +15.1913i q^{6} +16.2590 q^{7} -70.7808i q^{8} -19.0743 q^{9} -36.5609 q^{10} +56.6781 q^{11} -59.4505 q^{12} +41.6559i q^{13} +87.7342i q^{14} +19.0749i q^{15} +212.998 q^{16} -68.5374i q^{17} -102.925i q^{18} +84.5816i q^{19} -143.080i q^{20} +45.7734 q^{21} +305.837i q^{22} -70.4909i q^{23} -199.267i q^{24} +79.0923 q^{25} -224.776 q^{26} -129.711 q^{27} -343.345 q^{28} -111.643i q^{29} -102.929 q^{30} -322.350i q^{31} +583.099i q^{32} +159.564 q^{33} +369.830 q^{34} +110.163i q^{35} +402.795 q^{36} +(-206.337 - 89.8770i) q^{37} -456.405 q^{38} +117.272i q^{39} +479.577 q^{40} +131.601 q^{41} +246.995i q^{42} +112.203i q^{43} -1196.88 q^{44} -129.238i q^{45} +380.371 q^{46} -98.6542 q^{47} +599.646 q^{48} -78.6444 q^{49} +426.785i q^{50} -192.951i q^{51} -879.655i q^{52} +215.067 q^{53} -699.927i q^{54} +384.024i q^{55} -1150.83i q^{56} +238.120i q^{57} +602.432 q^{58} +40.1133i q^{59} -402.808i q^{60} +720.884i q^{61} +1739.41 q^{62} -310.129 q^{63} -1442.44 q^{64} -282.240 q^{65} +861.013i q^{66} -476.142 q^{67} +1447.32i q^{68} -198.450i q^{69} -594.445 q^{70} -664.816 q^{71} +1350.09i q^{72} +281.792 q^{73} +(484.979 - 1113.40i) q^{74} +222.666 q^{75} -1786.13i q^{76} +921.531 q^{77} -632.805 q^{78} +706.968i q^{79} +1443.17i q^{80} +149.834 q^{81} +710.121i q^{82} -370.053 q^{83} -966.607 q^{84} +464.377 q^{85} -605.449 q^{86} -314.306i q^{87} -4011.72i q^{88} -818.069i q^{89} +697.374 q^{90} +677.283i q^{91} +1488.57i q^{92} -907.502i q^{93} -532.341i q^{94} -573.084 q^{95} +1641.58i q^{96} -63.4075i q^{97} -424.368i q^{98} -1081.09 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 36 q^{4} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 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

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