LMFDB - Embedded newform 300.5.f.a.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(199,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.592240896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$1.99426 - 1.15139i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.5.f.a.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25647 + 3.30278i) q^{2} +5.19615 q^{3} +(-5.81665 + 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882 q^{7} +(-62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(2.25647 + 3.30278i) q^{2} +5.19615 q^{3} +(-5.81665 + 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882 q^{7} +(-62.3538 + 14.4222i) q^{8} +27.0000 q^{9} -134.561i q^{11} +(-30.2242 + 77.4500i) q^{12} -247.066i q^{13} +(-128.367 - 187.889i) q^{14} +(-188.333 - 173.397i) q^{16} -92.3112i q^{17} +(60.9248 + 89.1749i) q^{18} -29.5600i q^{19} -295.600 q^{21} +(444.425 - 303.633i) q^{22} +571.038 q^{23} +(-324.000 + 74.9400i) q^{24} +(816.005 - 557.499i) q^{26} +140.296 q^{27} +(330.899 - 847.933i) q^{28} -20.0891 q^{29} +474.736i q^{31} +(147.724 - 1013.29i) q^{32} -699.199i q^{33} +(304.883 - 208.298i) q^{34} +(-157.050 + 402.442i) q^{36} -755.867i q^{37} +(97.6300 - 66.7013i) q^{38} -1283.79i q^{39} +541.822 q^{41} +(-667.013 - 976.299i) q^{42} -3097.06 q^{43} +(2005.67 + 782.695i) q^{44} +(1288.53 + 1886.01i) q^{46} -1050.16 q^{47} +(-978.607 - 900.999i) q^{48} +835.266 q^{49} -479.663i q^{51} +(3682.59 + 1437.10i) q^{52} -1768.35i q^{53} +(316.574 + 463.367i) q^{54} +(3547.20 - 820.453i) q^{56} -153.598i q^{57} +(-45.3306 - 66.3499i) q^{58} -2582.98i q^{59} -2403.33 q^{61} +(-1567.95 + 1071.23i) q^{62} -1535.98 q^{63} +(3680.00 - 1798.56i) q^{64} +(2309.30 - 1577.72i) q^{66} -379.816 q^{67} +(1375.92 + 536.942i) q^{68} +2967.20 q^{69} -702.517i q^{71} +(-1683.55 + 389.400i) q^{72} -9824.92i q^{73} +(2496.46 - 1705.59i) q^{74} +(440.599 + 171.940i) q^{76} +7654.93i q^{77} +(4240.09 - 2896.85i) q^{78} +3756.40i q^{79} +729.000 q^{81} +(1222.61 + 1789.52i) q^{82} -10433.6 q^{83} +(1719.40 - 4405.99i) q^{84} +(-6988.43 - 10228.9i) q^{86} -104.386 q^{87} +(1940.67 + 8390.39i) q^{88} +11923.5 q^{89} +14055.2i q^{91} +(-3321.53 + 8511.46i) q^{92} +2466.80i q^{93} +(-2369.66 - 3468.45i) q^{94} +(767.597 - 5265.20i) q^{96} -2199.06i q^{97} +(1884.76 + 2758.70i) q^{98} -3633.15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9}+O(q^{10}) $ 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9	$ 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9} - 1200 q^{14} + 224 q^{16} - 288 q^{21} - 2592 q^{24} + 3384 q^{26} - 1776 q^{29} + 968 q^{34} + 1080 q^{36} + 1104 q^{41} + 7392 q^{44} - 768 q^{46} + 1144 q^{49} - 972 q^{54} + 3456 q^{56} + 8464 q^{61} + 29440 q^{64} + 9648 q^{66} + 19584 q^{69} + 8232 q^{74} - 3744 q^{76} + 5832 q^{81} + 21024 q^{84} - 39120 q^{86} + 50160 q^{89} + 10464 q^{94} - 16704 q^{96}+O(q^{100}) $ 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9 - 1200 * q^14 + 224 * q^16 - 288 * q^21 - 2592 * q^24 + 3384 * q^26 - 1776 * q^29 + 968 * q^34 + 1080 * q^36 + 1104 * q^41 + 7392 * q^44 - 768 * q^46 + 1144 * q^49 - 972 * q^54 + 3456 * q^56 + 8464 * q^61 + 29440 * q^64 + 9648 * q^66 + 19584 * q^69 + 8232 * q^74 - 3744 * q^76 + 5832 * q^81 + 21024 * q^84 - 39120 * q^86 + 50160 * q^89 + 10464 * q^94 - 16704 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	2.25647	+	3.30278i	0.564118	+	0.825694i
$2$	2.25647	+	3.30278i	0.564118	+	0.825694i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−5.81665	+	14.9053i	−0.363541	+	0.931578i
$5$		0			0
$5$		0			0
$6$	11.7250	+	17.1617i	0.325694	+	0.476715i
$7$	−56.8882			−1.16098			−0.580492	−	0.814266i	$-0.697140\pi$
$7$	−56.8882			−1.16098			−0.580492	+	0.814266i	$0.697140\pi$
$8$	−62.3538	+	14.4222i	−0.974279	+	0.225347i
$9$	27.0000			0.333333
$10$		0			0
$11$		−	134.561i		−	1.11207i	−0.831157	−	0.556037i	$-0.812321\pi$
$11$		−	134.561i		−	1.11207i	0.831157	−	0.556037i	$-0.187679\pi$
$12$	−30.2242	+	77.4500i	−0.209890	+	0.537847i
$13$		−	247.066i		−	1.46193i	−0.682414	−	0.730966i	$-0.739070\pi$
$13$		−	247.066i		−	1.46193i	0.682414	−	0.730966i	$-0.260930\pi$
$14$	−128.367	−	187.889i	−0.654932	−	0.958617i
$15$		0			0
$16$	−188.333	−	173.397i	−0.735676	−	0.677334i
$17$		−	92.3112i		−	0.319416i	−0.987164	−	0.159708i	$-0.948945\pi$
$17$		−	92.3112i		−	0.319416i	0.987164	−	0.159708i	$-0.0510552\pi$
$18$	60.9248	+	89.1749i	0.188039	+	0.275231i
$19$		−	29.5600i		−	0.0818836i	−0.999162	−	0.0409418i	$-0.986964\pi$
$19$		−	29.5600i		−	0.0818836i	0.999162	−	0.0409418i	$-0.0130358\pi$
$20$		0			0
$21$	−295.600			−0.670294
$22$	444.425	−	303.633i	0.918233	−	0.627342i
$23$	571.038			1.07947			0.539733	−	0.841836i	$-0.318525\pi$
$23$	571.038			1.07947			0.539733	+	0.841836i	$0.318525\pi$
$24$	−324.000	+	74.9400i	−0.562500	+	0.130104i
$25$		0			0
$26$	816.005	−	557.499i	1.20711	−	0.824703i
$27$	140.296			0.192450
$28$	330.899	−	847.933i	0.422065	−	1.08155i
$29$	−20.0891			−0.0238872			−0.0119436	−	0.999929i	$-0.503802\pi$
$29$	−20.0891			−0.0238872			−0.0119436	+	0.999929i	$0.503802\pi$
$30$		0			0
$31$			474.736i			0.494002i	0.969015	+	0.247001i	$0.0794452\pi$
$31$			474.736i			0.494002i	−0.969015	+	0.247001i	$0.920555\pi$
$32$	147.724	−	1013.29i	0.144262	−	0.989540i
$33$		−	699.199i		−	0.642056i
$34$	304.883	−	208.298i	0.263740	−	0.180188i
$35$		0			0
$36$	−157.050	+	402.442i	−0.121180	+	0.310526i
$37$		−	755.867i		−	0.552131i	−0.961139	−	0.276065i	$-0.910969\pi$
$37$		−	755.867i		−	0.552131i	0.961139	−	0.276065i	$-0.0890306\pi$
$38$	97.6300	−	66.7013i	0.0676108	−	0.0461920i
$39$		−	1283.79i		−	0.844047i
$40$		0			0
$41$	541.822			0.322321			0.161161	−	0.986928i	$-0.448476\pi$
$41$	541.822			0.322321			0.161161	+	0.986928i	$0.448476\pi$
$42$	−667.013	−	976.299i	−0.378125	−	0.553458i
$43$	−3097.06			−1.67499			−0.837496	−	0.546444i	$-0.815981\pi$
$43$	−3097.06			−1.67499			−0.837496	+	0.546444i	$0.815981\pi$
$44$	2005.67	+	782.695i	1.03598	+	0.404284i
$45$		0			0
$46$	1288.53	+	1886.01i	0.608947	+	0.891309i
$47$	−1050.16			−0.475401			−0.237701	−	0.971338i	$-0.576394\pi$
$47$	−1050.16			−0.475401			−0.237701	+	0.971338i	$0.576394\pi$
$48$	−978.607	−	900.999i	−0.424743	−	0.391059i
$49$	835.266			0.347882
$50$		0			0
$51$		−	479.663i		−	0.184415i
$52$	3682.59	+	1437.10i	1.36190	+	0.531472i
$53$		−	1768.35i		−	0.629532i	−0.949169	−	0.314766i	$-0.898074\pi$
$53$		−	1768.35i		−	0.629532i	0.949169	−	0.314766i	$-0.101926\pi$
$54$	316.574	+	463.367i	0.108565	+	0.158905i
$55$		0			0
$56$	3547.20	−	820.453i	1.13112	−	0.261624i
$57$		−	153.598i		−	0.0472755i
$58$	−45.3306	−	66.3499i	−0.0134752	−	0.0197235i
$59$		−	2582.98i		−	0.742024i	−0.928628	−	0.371012i	$-0.879011\pi$
$59$		−	2582.98i		−	0.742024i	0.928628	−	0.371012i	$-0.120989\pi$
$60$		0			0
$61$	−2403.33			−0.645883			−0.322941	−	0.946419i	$-0.604672\pi$
$61$	−2403.33			−0.645883			−0.322941	+	0.946419i	$0.604672\pi$
$62$	−1567.95	+	1071.23i	−0.407895	+	0.278676i
$63$	−1535.98			−0.386994
$64$	3680.00	−	1798.56i	0.898438	−	0.439101i
$65$		0			0
$66$	2309.30	−	1577.72i	0.530142	−	0.362196i
$67$	−379.816			−0.0846104			−0.0423052	−	0.999105i	$-0.513470\pi$
$67$	−379.816			−0.0846104			−0.0423052	+	0.999105i	$0.513470\pi$
$68$	1375.92	+	536.942i	0.297561	+	0.116121i
$69$	2967.20			0.623230
$70$		0			0
$71$		−	702.517i		−	0.139361i	−0.997569	−	0.0696803i	$-0.977802\pi$
$71$		−	702.517i		−	0.139361i	0.997569	−	0.0696803i	$-0.0221979\pi$
$72$	−1683.55	+	389.400i	−0.324760	+	0.0751157i
$73$		−	9824.92i		−	1.84367i	−0.387581	−	0.921836i	$-0.626689\pi$
$73$		−	9824.92i		−	1.84367i	0.387581	−	0.921836i	$-0.373311\pi$
$74$	2496.46	−	1705.59i	0.455891	−	0.311467i
$75$		0			0
$76$	440.599	+	171.940i	0.0762810	+	0.0297680i
$77$			7654.93i			1.29110i
$78$	4240.09	−	2896.85i	0.696924	−	0.476142i
$79$			3756.40i			0.601890i	0.953641	+	0.300945i	$0.0973021\pi$
$79$			3756.40i			0.601890i	−0.953641	+	0.300945i	$0.902698\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	1222.61	+	1789.52i	0.181827	+	0.266139i
$83$	−10433.6			−1.51452			−0.757262	−	0.653111i	$-0.773463\pi$
$83$	−10433.6			−1.51452			−0.757262	+	0.653111i	$0.773463\pi$
$84$	1719.40	−	4405.99i	0.243679	−	0.624431i
$85$		0			0
$86$	−6988.43	−	10228.9i	−0.944893	−	1.38303i
$87$	−104.386			−0.0137913
$88$	1940.67	+	8390.39i	0.250603	+	1.08347i
$89$	11923.5			1.50530			0.752651	−	0.658419i	$-0.228775\pi$
$89$	11923.5			1.50530			0.752651	+	0.658419i	$0.228775\pi$
$90$		0			0
$91$			14055.2i			1.69728i
$92$	−3321.53	+	8511.46i	−0.392430	+	1.00561i
$93$			2466.80i			0.285212i
$94$	−2369.66	−	3468.45i	−0.268183	−	0.392536i
$95$		0			0
$96$	767.597	−	5265.20i	0.0832896	−	0.571311i
$97$		−	2199.06i		−	0.233718i	−0.993148	−	0.116859i	$-0.962717\pi$
$97$		−	2199.06i		−	0.233718i	0.993148	−	0.116859i	$-0.0372826\pi$
$98$	1884.76	+	2758.70i	0.196247	+	0.287244i
$99$		−	3633.15i		−	0.370691i
$100$		0			0
$101$	−874.835			−0.0857597			−0.0428799	−	0.999080i	$-0.513653\pi$
$101$	−874.835			−0.0857597			−0.0428799	+	0.999080i	$0.513653\pi$
$102$	1584.22	−	1082.35i	0.152270	−	0.104032i
$103$	−3036.94			−0.286260			−0.143130	−	0.989704i	$-0.545717\pi$
$103$	−3036.94			−0.286260			−0.143130	+	0.989704i	$0.545717\pi$
$104$	3563.24	+	15405.5i	0.329442	+	1.42433i
$105$		0			0
$106$	5840.48	−	3990.25i	0.519801	−	0.355131i
$107$	−19057.6			−1.66457			−0.832284	−	0.554350i	$-0.812967\pi$
$107$	−19057.6			−1.66457			−0.832284	+	0.554350i	$0.812967\pi$
$108$	−816.054	+	2091.15i	−0.0699635	+	0.179282i
$109$	13132.7			1.10535			0.552675	−	0.833397i	$-0.313607\pi$
$109$	13132.7			1.10535			0.552675	+	0.833397i	$0.313607\pi$
$110$		0			0
$111$		−	3927.60i		−	0.318773i
$112$	10713.9	+	9864.26i	0.854108	+	0.786373i
$113$		−	14541.5i		−	1.13882i	−0.822055	−	0.569408i	$-0.807173\pi$
$113$		−	14541.5i		−	1.13882i	0.822055	−	0.569408i	$-0.192827\pi$
$114$	507.300	−	346.590i	0.0390351	−	0.0266690i
$115$		0			0
$116$	116.852	−	299.434i	0.00868397	−	0.0222528i
$117$		−	6670.79i		−	0.487311i
$118$	8531.02	−	5828.44i	0.612685	−	0.418589i
$119$			5251.42i			0.370836i
$120$		0			0
$121$	−3465.66			−0.236709
$122$	−5423.05	−	7937.66i	−0.364354	−	0.533301i
$123$	2815.39			0.186092
$124$	−7076.06	−	2761.38i	−0.460202	−	0.179590i
$125$		0			0
$126$	−3465.90	−	5073.00i	−0.218311	−	0.319539i
$127$	25959.7			1.60951			0.804753	−	0.593609i	$-0.202298\pi$
$127$	25959.7			1.60951			0.804753	+	0.593609i	$0.202298\pi$
$128$	14244.1	+	8095.81i	0.869388	+	0.494129i
$129$	−16092.8			−0.967057
$130$		0			0
$131$			16440.3i			0.958003i	0.877814	+	0.479002i	$0.159001\pi$
$131$			16440.3i			0.958003i	−0.877814	+	0.479002i	$0.840999\pi$
$132$	10421.7	+	4067.00i	0.598126	+	0.233414i
$133$			1681.61i			0.0950655i
$134$	−857.045	−	1254.45i	−0.0477303	−	0.0698623i
$135$		0			0
$136$	1331.33	+	5755.96i	0.0719794	+	0.311200i
$137$		−	31618.7i		−	1.68462i	−0.538990	−	0.842312i	$-0.681194\pi$
$137$		−	31618.7i		−	1.68462i	0.538990	−	0.842312i	$-0.318806\pi$
$138$	6695.41	+	9799.99i	0.351576	+	0.514597i
$139$		−	12895.9i		−	0.667453i	−0.942670	−	0.333726i	$-0.891694\pi$
$139$		−	12895.9i		−	0.667453i	0.942670	−	0.333726i	$-0.108306\pi$
$140$		0			0
$141$	−5456.80			−0.274473
$142$	2320.25	−	1585.21i	0.115069	−	0.0786159i
$143$	−33245.5			−1.62578
$144$	−5084.99	−	4681.73i	−0.245225	−	0.225778i
$145$		0			0
$146$	32449.5	−	22169.7i	1.52231	−	1.04005i
$147$	4340.17			0.200850
$148$	11266.4	+	4396.62i	0.514353	+	0.200722i
$149$	−31474.8			−1.41772			−0.708859	−	0.705350i	$-0.750790\pi$
$149$	−31474.8			−1.41772			−0.708859	+	0.705350i	$0.750790\pi$
$150$		0			0
$151$			39479.3i			1.73147i	0.500502	+	0.865735i	$0.333149\pi$
$151$			39479.3i			1.73147i	−0.500502	+	0.865735i	$0.666851\pi$
$152$	426.320	+	1843.18i	0.0184522	+	0.0797774i
$153$		−	2492.40i		−	0.106472i
$154$	−25282.5	+	17273.1i	−1.06605	+	0.728333i
$155$		0			0
$156$	19135.3	+	7467.39i	0.786296	+	0.306845i
$157$			2619.07i			0.106255i	0.998588	+	0.0531273i	$0.0169189\pi$
$157$			2619.07i			0.106255i	−0.998588	+	0.0531273i	$0.983081\pi$
$158$	−12406.5	+	8476.21i	−0.496977	+	0.339537i
$159$		−	9188.64i		−	0.363460i
$160$		0			0
$161$	−32485.3			−1.25324
$162$	1644.97	+	2407.72i	0.0626798	+	0.0917438i
$163$	−7123.14			−0.268100			−0.134050	−	0.990975i	$-0.542798\pi$
$163$	−7123.14			−0.268100			−0.134050	+	0.990975i	$0.542798\pi$
$164$	−3151.59	+	8075.99i	−0.117177	+	0.300267i
$165$		0			0
$166$	−23543.0	−	34459.7i	−0.854371	−	1.25053i
$167$	−48670.8			−1.74516			−0.872580	−	0.488472i	$-0.837555\pi$
$167$	−48670.8			−1.74516			−0.872580	+	0.488472i	$0.837555\pi$
$168$	18431.8	−	4263.20i	0.653053	−	0.151049i
$169$	−32480.8			−1.13724
$170$		0			0
$171$		−	798.119i		−	0.0272945i
$172$	18014.5	−	46162.4i	0.608928	−	1.56039i
$173$			27575.9i			0.921377i	0.887562	+	0.460689i	$0.152397\pi$
$173$			27575.9i			0.921377i	−0.887562	+	0.460689i	$0.847603\pi$
$174$	−235.545	−	344.764i	−0.00777991	−	0.0113874i
$175$		0			0
$176$	−23332.5	+	25342.3i	−0.753245	+	0.818126i
$177$		−	13421.6i		−	0.428408i
$178$	26905.1	+	39380.7i	0.849169	+	1.24292i
$179$			42280.0i			1.31956i	0.751459	+	0.659780i	$0.229351\pi$
$179$			42280.0i			1.31956i	−0.751459	+	0.659780i	$0.770649\pi$
$180$		0			0
$181$	−1006.79			−0.0307313			−0.0153657	−	0.999882i	$-0.504891\pi$
$181$	−1006.79			−0.0307313			−0.0153657	+	0.999882i	$0.504891\pi$
$182$	−46421.1	+	31715.1i	−1.40143	+	0.957466i
$183$	−12488.1			−0.372901
$184$	−35606.4	+	8235.62i	−1.05170	+	0.243254i
$185$		0			0
$186$	−8147.29	+	5566.27i	−0.235498	+	0.160894i
$187$	−12421.5			−0.355214
$188$	6108.43	−	15652.9i	0.172828	−	0.442874i
$189$	−7981.19			−0.223431
$190$		0			0
$191$		−	6906.62i		−	0.189321i	−0.995510	−	0.0946605i	$-0.969823\pi$
$191$		−	6906.62i		−	0.189321i	0.995510	−	0.0946605i	$-0.0301766\pi$
$192$	19121.8	−	9345.59i	0.518713	−	0.253515i
$193$		−	28207.8i		−	0.757278i	−0.925545	−	0.378639i	$-0.876392\pi$
$193$		−	28207.8i		−	0.757278i	0.925545	−	0.378639i	$-0.123608\pi$
$194$	7262.99	−	4962.11i	0.192980	−	0.131845i
$195$		0			0
$196$	−4858.45	+	12449.8i	−0.126469	+	0.324080i
$197$			38453.6i			0.990843i	0.868653	+	0.495422i	$0.164986\pi$
$197$			38453.6i			0.990843i	−0.868653	+	0.495422i	$0.835014\pi$
$198$	11999.5	−	8198.10i	0.306078	−	0.209114i
$199$			5490.10i			0.138635i	0.997595	+	0.0693176i	$0.0220822\pi$
$199$			5490.10i			0.138635i	−0.997595	+	0.0693176i	$0.977918\pi$
$200$		0			0
$201$	−1973.58			−0.0488498
$202$	−1974.04	−	2889.38i	−0.0483787	−	0.0708113i
$203$	1142.83			0.0277326
$204$	7149.50	+	2790.03i	0.171797	+	0.0670423i
$205$		0			0
$206$	−6852.77	−	10030.3i	−0.161485	−	0.236363i
$207$	15418.0			0.359822
$208$	−42840.7	+	46530.8i	−0.990215	+	1.07551i
$209$	−3977.62			−0.0910606
$210$		0			0
$211$		−	46471.5i		−	1.04381i	−0.853004	−	0.521905i	$-0.825222\pi$
$211$		−	46471.5i		−	1.04381i	0.853004	−	0.521905i	$-0.174778\pi$
$212$	26357.8	+	10285.9i	0.586458	+	0.228861i
$213$		−	3650.38i		−	0.0804599i
$214$	−43003.0	−	62943.1i	−0.939013	−	1.37442i
$215$		0			0
$216$	−8748.00	+	2023.38i	−0.187500	+	0.0433680i
$217$		−	27006.9i		−	0.573529i
$218$	29633.5	+	43374.2i	0.623548	+	0.912681i
$219$		−	51051.8i		−	1.06444i
$220$		0			0
$221$	−22807.0			−0.466964
$222$	12972.0	−	8862.53i	0.263209	−	0.179826i
$223$	48307.2			0.971409			0.485704	−	0.874123i	$-0.338563\pi$
$223$	48307.2			0.971409			0.485704	+	0.874123i	$0.338563\pi$
$224$	−8403.75	+	57644.1i	−0.167486	+	1.14884i
$225$		0			0
$226$	48027.4	−	32812.6i	0.940313	−	0.642427i
$227$	19108.6			0.370832			0.185416	−	0.982660i	$-0.440637\pi$
$227$	19108.6			0.370832			0.185416	+	0.982660i	$0.440637\pi$
$228$	2289.42	+	893.427i	0.0440408	+	0.0171866i
$229$	73378.5			1.39926			0.699629	−	0.714506i	$-0.253349\pi$
$229$	73378.5			1.39926			0.699629	+	0.714506i	$0.253349\pi$
$230$		0			0
$231$			39776.2i			0.745417i
$232$	1252.63	−	289.730i	0.0232728	−	0.00538291i
$233$			34041.9i			0.627049i	0.949580	+	0.313524i	$0.101510\pi$
$233$			34041.9i			0.627049i	−0.949580	+	0.313524i	$0.898490\pi$
$234$	22032.1	−	15052.5i	0.402369	−	0.274901i
$235$		0			0
$236$	38500.0	+	15024.3i	0.691253	+	0.269756i
$237$			19518.8i			0.347501i
$238$	−17344.2	+	11849.7i	−0.306197	+	0.209196i
$239$			35114.3i			0.614735i	0.951591	+	0.307368i	$0.0994482\pi$
$239$			35114.3i			0.614735i	−0.951591	+	0.307368i	$0.900552\pi$
$240$		0			0
$241$	−19621.0			−0.337821			−0.168910	−	0.985631i	$-0.554025\pi$
$241$	−19621.0			−0.337821			−0.168910	+	0.985631i	$0.554025\pi$
$242$	−7820.17	−	11446.3i	−0.133532	−	0.195449i
$243$	3788.00			0.0641500
$244$	13979.3	−	35822.2i	0.234805	−	0.601690i
$245$		0			0
$246$	6352.85	+	9298.60i	0.104978	+	0.153655i
$247$	−7303.28			−0.119708
$248$	−6846.74	−	29601.6i	−0.111322	−	0.481296i
$249$	−54214.3			−0.874411
$250$		0			0
$251$			560.729i			0.00890032i	0.999990	+	0.00445016i	$0.00141654\pi$
$251$			560.729i			0.00890032i	−0.999990	+	0.00445016i	$0.998583\pi$
$252$	8934.27	−	22894.2i	0.140688	−	0.360516i
$253$		−	76839.4i		−	1.20045i
$254$	58577.5	+	85739.2i	0.907952	+	1.32896i
$255$		0			0
$256$	5402.70	+	65312.9i	0.0824386	+	0.996596i
$257$			80511.1i			1.21896i	0.792801	+	0.609480i	$0.208622\pi$
$257$			80511.1i			1.21896i	−0.792801	+	0.609480i	$0.791378\pi$
$258$	−36313.0	−	53150.9i	−0.545534	−	0.798493i
$259$			42999.9i			0.641015i
$260$		0			0
$261$	−542.406			−0.00796240
$262$	−54298.6	+	37097.1i	−0.791017	+	0.540427i
$263$	−34821.7			−0.503430			−0.251715	−	0.967801i	$-0.580995\pi$
$263$	−34821.7			−0.503430			−0.251715	+	0.967801i	$0.580995\pi$
$264$	10084.0	+	43597.8i	0.144685	+	0.625542i
$265$		0			0
$266$	−5553.99	+	3794.52i	−0.0784950	+	0.0536282i
$267$	61956.3			0.869087
$268$	2209.26	−	5661.26i	0.0307593	−	0.0788212i
$269$	28469.5			0.393438			0.196719	−	0.980460i	$-0.436971\pi$
$269$	28469.5			0.393438			0.196719	+	0.980460i	$0.436971\pi$
$270$		0			0
$271$		−	37653.7i		−	0.512706i	−0.966583	−	0.256353i	$-0.917479\pi$
$271$		−	37653.7i		−	0.512706i	0.966583	−	0.256353i	$-0.0825210\pi$
$272$	−16006.5	+	17385.2i	−0.216351	+	0.234987i
$273$			73032.8i			0.979924i
$274$	104429.	−	71346.8i	1.39098	−	0.950327i
$275$		0			0
$276$	−17259.2	+	44226.9i	−0.226570	+	0.580588i
$277$			25920.1i			0.337814i	0.985632	+	0.168907i	$0.0540237\pi$
$277$			25920.1i			0.337814i	−0.985632	+	0.168907i	$0.945976\pi$
$278$	42592.1	−	29099.2i	0.551112	−	0.376522i
$279$			12817.9i			0.164667i
$280$		0			0
$281$	49815.6			0.630889			0.315444	−	0.948944i	$-0.397846\pi$
$281$	49815.6			0.630889			0.315444	+	0.948944i	$0.397846\pi$
$282$	−12313.1	−	18022.6i	−0.154835	−	0.226631i
$283$	73403.9			0.916530			0.458265	−	0.888816i	$-0.348471\pi$
$283$	73403.9			0.916530			0.458265	+	0.888816i	$0.348471\pi$
$284$	10471.2	+	4086.30i	0.129825	+	0.0506633i
$285$		0			0
$286$	−75017.6	−	109802.i	−0.917131	−	1.34239i
$287$	−30823.3			−0.374209
$288$	3988.55	−	27358.8i	0.0480873	−	0.329847i
$289$	74999.6			0.897974
$290$		0			0
$291$		−	11426.6i		−	0.134937i
$292$	146443.	+	57148.2i	1.71752	+	0.670250i
$293$			130683.i			1.52224i	0.648611	+	0.761120i	$0.275350\pi$
$293$			130683.i			1.52224i	−0.648611	+	0.761120i	$0.724650\pi$
$294$	9793.48	+	14334.6i	0.113303	+	0.165841i
$295$		0			0
$296$	10901.3	+	47131.2i	0.124421	+	0.537929i
$297$		−	18878.4i		−	0.214019i
$298$	−71022.0	−	103954.i	−0.799761	−	1.17060i
$299$		−	141084.i		−	1.57811i
$300$		0			0
$301$	176186.			1.94464
$302$	−130391.	+	89083.9i	−1.42966	+	0.976754i
$303$	−4545.78			−0.0495134
$304$	−5125.62	+	5567.12i	−0.0554625	+	0.0602398i
$305$		0			0
$306$	8231.84	−	5624.04i	0.0879132	−	0.0600628i
$307$	−139512.			−1.48025			−0.740126	−	0.672469i	$-0.765234\pi$
$307$	−139512.			−1.48025			−0.740126	+	0.672469i	$0.765234\pi$
$308$	−114099.	−	44526.1i	−1.20276	−	0.469368i
$309$	−15780.4			−0.165273
$310$		0			0
$311$		−	132034.i		−	1.36510i	−0.730837	−	0.682552i	$-0.760870\pi$
$311$		−	132034.i		−	1.36510i	0.730837	−	0.682552i	$-0.239130\pi$
$312$	18515.2	+	80049.5i	0.190203	+	0.822337i
$313$		−	39526.3i		−	0.403458i	−0.979441	−	0.201729i	$-0.935344\pi$
$313$		−	39526.3i		−	0.403458i	0.979441	−	0.201729i	$-0.0646560\pi$
$314$	−8650.20	+	5909.86i	−0.0877338	+	0.0599402i
$315$		0			0
$316$	−55990.0	−	21849.7i	−0.560708	−	0.218812i
$317$		−	91959.1i		−	0.915116i	−0.889180	−	0.457558i	$-0.848724\pi$
$317$		−	91959.1i		−	0.915116i	0.889180	−	0.457558i	$-0.151276\pi$
$318$	30348.0	−	20733.9i	0.300107	−	0.205035i
$319$			2703.21i			0.0265643i
$320$		0			0
$321$	−99026.4			−0.961039
$322$	−73302.2	−	107292.i	−0.706977	−	1.03479i
$323$	−2728.72			−0.0261549
$324$	−4240.34	+	10865.9i	−0.0403934	+	0.103509i
$325$		0			0
$326$	−16073.2	−	23526.1i	−0.151240	−	0.221368i
$327$	68239.3			0.638174
$328$	−33784.7	+	7814.26i	−0.314031	+	0.0726341i
$329$	59741.8			0.551933
$330$		0			0
$331$			3244.08i			0.0296098i	0.999890	+	0.0148049i	$0.00471272\pi$
$331$			3244.08i			0.0296098i	−0.999890	+	0.0148049i	$0.995287\pi$
$332$	60688.4	−	155515.i	0.550591	−	1.41090i
$333$		−	20408.4i		−	0.184044i
$334$	−109824.	−	160749.i	−0.984477	−	1.44097i
$335$		0			0
$336$	55671.2	+	51256.2i	0.493119	+	0.454013i
$337$			5591.21i			0.0492318i	0.999697	+	0.0246159i	$0.00783628\pi$
$337$			5591.21i			0.0492318i	−0.999697	+	0.0246159i	$0.992164\pi$
$338$	−73292.1	−	107277.i	−0.641540	−	0.939016i
$339$		−	75560.0i		−	0.657495i
$340$		0			0
$341$	63881.0			0.549367
$342$	2636.01	−	1800.94i	0.0225369	−	0.0153973i
$343$	89071.8			0.757098
$344$	193113.	−	44666.4i	1.63191	−	0.377454i
$345$		0			0
$346$	−91077.0	+	62224.3i	−0.760775	+	0.519766i
$347$	170630.			1.41708			0.708542	−	0.705668i	$-0.249353\pi$
$347$	170630.			1.41708			0.708542	+	0.705668i	$0.249353\pi$
$348$	607.178	−	1555.90i	0.00501369	−	0.0128477i
$349$	96101.4			0.789003			0.394502	−	0.918895i	$-0.370917\pi$
$349$	96101.4			0.789003			0.394502	+	0.918895i	$0.370917\pi$
$350$		0			0
$351$		−	34662.5i		−	0.281349i
$352$	−136349.	−	19877.9i	−1.10044	−	0.160430i
$353$		−	205914.i		−	1.65248i	−0.563316	−	0.826242i	$-0.690474\pi$
$353$		−	205914.i		−	1.65248i	0.563316	−	0.826242i	$-0.309526\pi$
$354$	44328.5	−	30285.4i	0.353734	−	0.241673i
$355$		0			0
$356$	−69354.9	+	177723.i	−0.547239	+	1.40231i
$357$			27287.2i			0.214103i
$358$	−139641.	+	95403.8i	−1.08955	+	0.744388i
$359$			78435.2i			0.608586i	0.952578	+	0.304293i	$0.0984202\pi$
$359$			78435.2i			0.608586i	−0.952578	+	0.304293i	$0.901580\pi$
$360$		0			0
$361$	129447.			0.993295
$362$	−2271.79	−	3325.20i	−0.0173361	−	0.0253747i
$363$	−18008.1			−0.136664
$364$	−209496.	−	81754.0i	−1.58115	−	0.617030i
$365$		0			0
$366$	−28179.0	−	41245.3i	−0.210360	−	0.307902i
$367$	221785.			1.64664			0.823322	−	0.567574i	$-0.192118\pi$
$367$	221785.			1.64664			0.823322	+	0.567574i	$0.192118\pi$
$368$	−107545.	−	99016.5i	−0.794138	−	0.731159i
$369$	14629.2			0.107440
$370$		0			0
$371$			100599.i			0.730876i
$372$	−36768.3	−	14348.5i	−0.265698	−	0.103686i
$373$			25883.8i			0.186042i	0.995664	+	0.0930208i	$0.0296523\pi$
$373$			25883.8i			0.186042i	−0.995664	+	0.0930208i	$0.970348\pi$
$374$	−28028.7	−	41025.4i	−0.200383	−	0.293298i
$375$		0			0
$376$	65481.6	−	15145.6i	0.463173	−	0.107130i
$377$			4963.35i			0.0349214i
$378$	−18009.3	−	26360.1i	−0.126042	−	0.184486i
$379$			147801.i			1.02896i	0.857503	+	0.514479i	$0.172015\pi$
$379$			147801.i			1.02896i	−0.857503	+	0.514479i	$0.827985\pi$
$380$		0			0
$381$	134891.			0.929249
$382$	22811.0	−	15584.6i	0.156321	−	0.106800i
$383$	226231.			1.54225			0.771126	−	0.636683i	$-0.219694\pi$
$383$	226231.			1.54225			0.771126	+	0.636683i	$0.219694\pi$
$384$	74014.3	+	42067.1i	0.501942	+	0.285286i
$385$		0			0
$386$	93164.2	−	63650.2i	0.625280	−	0.427194i
$387$	−83620.6			−0.558330
$388$	32777.5	+	12791.2i	0.217727	+	0.0849662i
$389$	−256419.			−1.69453			−0.847267	−	0.531167i	$-0.821754\pi$
$389$	−256419.			−1.69453			−0.847267	+	0.531167i	$0.821754\pi$
$390$		0			0
$391$		−	52713.2i		−	0.344799i
$392$	−52082.0	+	12046.4i	−0.338934	+	0.0783943i
$393$			85426.3i			0.553103i
$394$	−127004.	+	86769.6i	−0.818133	+	0.558953i
$395$		0			0
$396$	54153.0	+	21132.8i	0.345328	+	0.134761i
$397$		−	56667.7i		−	0.359546i	−0.983708	−	0.179773i	$-0.942464\pi$
$397$		−	56667.7i		−	0.359546i	0.983708	−	0.179773i	$-0.0575364\pi$
$398$	−18132.6	+	12388.3i	−0.114470	+	0.0782067i
$399$			8737.92i			0.0548861i
$400$		0			0
$401$	10912.0			0.0678605			0.0339302	−	0.999424i	$-0.489198\pi$
$401$	10912.0			0.0678605			0.0339302	+	0.999424i	$0.489198\pi$
$402$	−4453.34	−	6518.30i	−0.0275571	−	0.0403350i
$403$	117291.			0.722198
$404$	5088.61	−	13039.6i	0.0311772	−	0.0798919i
$405$		0			0
$406$	2578.77	+	3774.52i	0.0156445	+	0.0228987i
$407$	−101710.			−0.614010
$408$	6917.80	+	29908.8i	0.0415573	+	0.179671i
$409$	289576.			1.73108			0.865538	−	0.500844i	$-0.166977\pi$
$409$	289576.			1.73108			0.865538	+	0.500844i	$0.166977\pi$
$410$		0			0
$411$		−	164296.i		−	0.972618i
$412$	17664.8	−	45266.3i	0.104067	−	0.266674i
$413$			146941.i			0.861477i
$414$	34790.4	+	50922.3i	0.202982	+	0.297103i
$415$		0			0
$416$	−250350.	−	36497.7i	−1.44664	−	0.210901i
$417$		−	67008.8i		−	0.385354i
$418$	−8975.39	−	13137.2i	−0.0513690	−	0.0751882i
$419$		−	69837.9i		−	0.397798i	−0.980020	−	0.198899i	$-0.936263\pi$
$419$		−	69837.9i		−	0.397798i	0.980020	−	0.198899i	$-0.0637366\pi$
$420$		0			0
$421$	16207.0			0.0914405			0.0457203	−	0.998954i	$-0.485442\pi$
$421$	16207.0			0.0914405			0.0457203	+	0.998954i	$0.485442\pi$
$422$	153485.	−	104862.i	0.861867	−	0.588832i
$423$	−28354.4			−0.158467
$424$	25503.6	+	110264.i	0.141863	+	0.613339i
$425$		0			0
$426$	12056.4	−	8236.99i	0.0664352	−	0.0453889i
$427$	136721.			0.749859
$428$	110852.	−	284059.i	0.605138	−	1.55067i
$429$	−172749.			−0.938643
$430$		0			0
$431$		−	105264.i		−	0.566662i	−0.959022	−	0.283331i	$-0.908560\pi$
$431$		−	105264.i		−	0.566662i	0.959022	−	0.283331i	$-0.0914395\pi$
$432$	−26422.4	−	24327.0i	−0.141581	−	0.130353i
$433$		−	131799.i		−	0.702970i	−0.936193	−	0.351485i	$-0.885677\pi$
$433$		−	131799.i		−	0.702970i	0.936193	−	0.351485i	$-0.114323\pi$
$434$	89197.7	−	60940.3i	0.473559	−	0.323538i
$435$		0			0
$436$	−76388.1	+	195746.i	−0.401840	+	1.02972i
$437$		−	16879.9i		−	0.0883906i
$438$	168613.	−	115197.i	0.878905	−	0.600473i
$439$			149053.i			0.773414i	0.922203	+	0.386707i	$0.126388\pi$
$439$			149053.i			0.773414i	−0.922203	+	0.386707i	$0.873612\pi$
$440$		0			0
$441$	22552.2			0.115961
$442$	−51463.4	−	75326.4i	−0.263423	−	0.385569i
$443$	−248933.			−1.26845			−0.634227	−	0.773147i	$-0.718682\pi$
$443$	−248933.			−1.26845			−0.634227	+	0.773147i	$0.718682\pi$
$444$	58541.9	+	22845.5i	0.296962	+	0.115887i
$445$		0			0
$446$	109004.	+	159548.i	0.547990	+	0.802086i
$447$	−163548.			−0.818520
$448$	−209349.	+	102317.i	−1.04307	+	0.509789i
$449$	−243749.			−1.20906			−0.604532	−	0.796581i	$-0.706640\pi$
$449$	−243749.			−1.20906			−0.604532	+	0.796581i	$0.706640\pi$
$450$		0			0
$451$		−	72908.1i		−	0.358445i
$452$	216745.	+	84583.1i	1.06090	+	0.414006i
$453$			205140.i			0.999665i
$454$	43118.1	+	63111.5i	0.209193	+	0.306194i
$455$		0			0
$456$	2215.22	+	9577.43i	0.0106534	+	0.0460595i
$457$			343278.i			1.64367i	0.569729	+	0.821833i	$0.307048\pi$
$457$			343278.i			1.64367i	−0.569729	+	0.821833i	$0.692952\pi$
$458$	165577.	+	242353.i	0.789347	+	1.15536i
$459$		−	12950.9i		−	0.0614716i
$460$		0			0
$461$	−155524.			−0.731804			−0.365902	−	0.930653i	$-0.619239\pi$
$461$	−155524.			−0.731804			−0.365902	+	0.930653i	$0.619239\pi$
$462$	−131372.	+	89753.9i	−0.615486	+	0.420503i
$463$	321457.			1.49955			0.749774	−	0.661694i	$-0.230162\pi$
$463$	321457.			1.49955			0.749774	+	0.661694i	$0.230162\pi$
$464$	3783.45	+	3483.40i	0.0175732	+	0.0161796i
$465$		0			0
$466$	−112433.	+	76814.6i	−0.517750	+	0.353730i
$467$	81219.7			0.372415			0.186208	−	0.982510i	$-0.440380\pi$
$467$	81219.7			0.372415			0.186208	+	0.982510i	$0.440380\pi$
$468$	99429.9	+	38801.7i	0.453968	+	0.177157i
$469$	21607.1			0.0982313
$470$		0			0
$471$			13609.1i			0.0613461i
$472$	37252.3	+	161059.i	0.167213	+	0.722938i
$473$			416743.i			1.86271i
$474$	−64466.3	+	44043.7i	−0.286930	+	0.196032i
$475$		0			0
$476$	−78273.7	−	30545.7i	−0.345463	−	0.134814i
$477$		−	47745.6i		−	0.209844i
$478$	−115975.	+	79234.5i	−0.507583	+	0.346784i
$479$		−	346051.i		−	1.50824i	−0.656738	−	0.754119i	$-0.728064\pi$
$479$		−	346051.i		−	1.50824i	0.656738	−	0.754119i	$-0.271936\pi$
$480$		0			0
$481$	−186749.			−0.807178
$482$	−44274.2	−	64803.6i	−0.190571	−	0.278936i
$483$	−168799.			−0.723560
$484$	20158.5	−	51656.5i	0.0860534	−	0.220513i
$485$		0			0
$486$	8547.51	+	12510.9i	0.0361882	+	0.0529683i
$487$	−94439.7			−0.398196			−0.199098	−	0.979980i	$-0.563801\pi$
$487$	−94439.7			−0.398196			−0.199098	+	0.979980i	$0.563801\pi$
$488$	149857.	−	34661.3i	0.629270	−	0.145548i
$489$	−37012.9			−0.154787
$490$		0			0
$491$		−	175728.i		−	0.728915i	−0.931220	−	0.364458i	$-0.881254\pi$
$491$		−	175728.i		−	0.728915i	0.931220	−	0.364458i	$-0.118746\pi$
$492$	−16376.1	+	41964.1i	−0.0676521	+	0.173359i
$493$			1854.45i			0.00762995i
$494$	−16479.7	−	24121.1i	−0.0675296	−	0.0988424i
$495$		0			0
$496$	82318.0	−	89408.5i	0.334604	−	0.363426i
$497$			39964.9i			0.161795i
$498$	−122333.	−	179058.i	−0.493271	−	0.721996i
$499$			37294.6i			0.149777i	0.997192	+	0.0748885i	$0.0238601\pi$
$499$			37294.6i			0.149777i	−0.997192	+	0.0748885i	$0.976140\pi$
$500$		0			0
$501$	−252901.			−1.00757
$502$	−1851.96	+	1265.27i	−0.00734894	+	0.00502084i
$503$	250727.			0.990979			0.495489	−	0.868614i	$-0.334989\pi$
$503$	250727.			0.990979			0.495489	+	0.868614i	$0.334989\pi$
$504$	95774.3	−	22152.2i	0.377040	−	0.0872080i
$505$		0			0
$506$	253783.	−	173386.i	0.991202	−	0.677194i
$507$	−168775.			−0.656588
$508$	−150999.	+	386936.i	−0.585121	+	1.49938i
$509$	−151144.			−0.583383			−0.291692	−	0.956512i	$-0.594218\pi$
$509$	−151144.			−0.583383			−0.291692	+	0.956512i	$0.594218\pi$
$510$		0			0
$511$			558922.i			2.14047i
$512$	−203523.	+	165221.i	−0.776378	+	0.630267i
$513$		−	4147.15i		−	0.0157585i
$514$	−265910.	+	181671.i	−1.00649	+	0.687638i
$515$		0			0
$516$	93606.2	−	239867.i	0.351565	−	0.900889i
$517$			141311.i			0.528682i
$518$	−142019.	+	97028.2i	−0.529282	+	0.361608i
$519$			143289.i			0.531957i
$520$		0			0
$521$	−179715.			−0.662079			−0.331039	−	0.943617i	$-0.607399\pi$
$521$	−179715.			−0.662079			−0.331039	+	0.943617i	$0.607399\pi$
$522$	−1223.93	−	1791.45i	−0.00449173	−	0.00657450i
$523$	−305226.			−1.11588			−0.557941	−	0.829881i	$-0.688408\pi$
$523$	−305226.			−1.11588			−0.557941	+	0.829881i	$0.688408\pi$
$524$	−245047.	−	95627.5i	−0.892455	−	0.348273i
$525$		0			0
$526$	−78574.3	−	115008.i	−0.283994	−	0.415679i
$527$	43823.5			0.157792
$528$	−121239.	+	131682.i	−0.434886	+	0.472346i
$529$	46243.2			0.165248
$530$		0			0
$531$		−	69740.6i		−	0.247341i
$532$	−25064.9	−	9781.36i	−0.0885609	−	0.0345602i
$533$		−	133866.i		−	0.471211i
$534$	139803.	+	204628.i	0.490268	+	0.717600i
$535$		0			0
$536$	23683.0	−	5477.79i	0.0824341	−	0.0190667i
$537$			219694.i			0.761849i
$538$	64240.8	+	94028.5i	0.221945	+	0.324859i
$539$		−	112394.i		−	0.386871i
$540$		0			0
$541$	−282083.			−0.963789			−0.481895	−	0.876229i	$-0.660051\pi$
$541$	−282083.			−0.963789			−0.481895	+	0.876229i	$0.660051\pi$
$542$	124362.	−	84964.5i	0.423338	−	0.289227i
$543$	−5231.43			−0.0177427
$544$	−93537.9	−	13636.6i	−0.316075	−	0.0460795i
$545$		0			0
$546$	−241211.	+	164797.i	−0.809117	+	0.552793i
$547$	−296270.			−0.990176			−0.495088	−	0.868843i	$-0.664864\pi$
$547$	−296270.			−0.990176			−0.495088	+	0.868843i	$0.664864\pi$
$548$	471285.	+	183915.i	1.56936	+	0.612430i
$549$	−64889.9			−0.215294
$550$		0			0
$551$			593.834i			0.00195597i
$552$	−185016.	+	42793.6i	−0.607200	+	0.140443i
$553$		−	213695.i		−	0.698785i
$554$	−85608.4	+	58488.1i	−0.278931	+	0.190567i
$555$		0			0
$556$	192216.	+	75010.7i	0.621785	+	0.242646i
$557$		−	116573.i		−	0.375739i	−0.982194	−	0.187869i	$-0.939842\pi$
$557$		−	116573.i		−	0.375739i	0.982194	−	0.187869i	$-0.0601582\pi$
$558$	−42334.6	+	28923.2i	−0.135965	+	0.0928919i
$559$			765179.i			2.44872i
$560$		0			0
$561$	−64543.9			−0.205083
$562$	112408.	+	164530.i	0.355896	+	0.520921i
$563$	117383.			0.370329			0.185164	−	0.982708i	$-0.440718\pi$
$563$	117383.			0.370329			0.185164	+	0.982708i	$0.440718\pi$
$564$	31740.3	−	81335.0i	0.0997822	−	0.255693i
$565$		0			0
$566$	165634.	+	242437.i	0.517031	+	0.756773i
$567$	−41471.5			−0.128998
$568$	10131.8	+	43804.6i	0.0314045	+	0.135776i
$569$	222193.			0.686288			0.343144	−	0.939283i	$-0.388508\pi$
$569$	222193.			0.686288			0.343144	+	0.939283i	$0.388508\pi$
$570$		0			0
$571$			117091.i			0.359131i	0.983746	+	0.179565i	$0.0574691\pi$
$571$			117091.i			0.359131i	−0.983746	+	0.179565i	$0.942531\pi$
$572$	193378.	−	495533.i	0.591036	−	1.51454i
$573$		−	35887.9i		−	0.109305i
$574$	−69551.9	−	101802.i	−0.211098	−	0.308982i
$575$		0			0
$576$	99360.0	−	48561.1i	0.299479	−	0.146367i
$577$		−	335932.i		−	1.00902i	−0.863406	−	0.504510i	$-0.831673\pi$
$577$		−	335932.i		−	1.00902i	0.863406	−	0.504510i	$-0.168327\pi$
$578$	169235.	+	247707.i	0.506563	+	0.741451i
$579$		−	146572.i		−	0.437214i
$580$		0			0
$581$	593546.			1.75834
$582$	37739.6	−	25783.9i	0.111417	−	0.0761207i
$583$	−237952.			−0.700086
$584$	141697.	+	612622.i	0.415466	+	1.79625i
$585$		0			0
$586$	−431616.	+	294882.i	−1.25690	+	0.858723i
$587$	396842.			1.15170			0.575852	−	0.817554i	$-0.304670\pi$
$587$	396842.			1.15170			0.575852	+	0.817554i	$0.304670\pi$
$588$	−25245.3	+	64691.3i	−0.0730172	+	0.187108i
$589$	14033.2			0.0404507
$590$		0			0
$591$			199811.i			0.572064i
$592$	−131065.	+	142355.i	−0.373977	+	0.406189i
$593$		−	13679.6i		−	0.0389012i	−0.999811	−	0.0194506i	$-0.993808\pi$
$593$		−	13679.6i		−	0.0389012i	0.999811	−	0.0194506i	$-0.00619171\pi$
$594$	62351.1	−	42598.6i	0.176714	−	0.120732i
$595$		0			0
$596$	183078.	−	469139.i	0.515399	−	1.32072i
$597$			28527.4i			0.0800411i
$598$	465970.	−	318353.i	1.30303	−	0.890239i
$599$		−	124021.i		−	0.345654i	−0.984952	−	0.172827i	$-0.944710\pi$
$599$		−	124021.i		−	0.345654i	0.984952	−	0.172827i	$-0.0552902\pi$
$600$		0			0
$601$	484678.			1.34185			0.670926	−	0.741525i	$-0.265897\pi$
$601$	484678.			1.34185			0.670926	+	0.741525i	$0.265897\pi$
$602$	397559.	+	581903.i	1.09701	+	1.60567i
$603$	−10255.0			−0.0282035
$604$	−588448.	−	229637.i	−1.61300	−	0.629460i
$605$		0			0
$606$	−10257.4	−	15013.7i	−0.0279314	−	0.0408829i
$607$	−298924.			−0.811303			−0.405651	−	0.914028i	$-0.632955\pi$
$607$	−298924.			−0.811303			−0.405651	+	0.914028i	$0.632955\pi$
$608$	−29952.8	−	4366.72i	−0.0810271	−	0.0118127i
$609$	5938.34			0.0160114
$610$		0			0
$611$			259460.i			0.695004i
$612$	37149.9	+	14497.4i	0.0991870	+	0.0387069i
$613$			155694.i			0.414334i	0.978306	+	0.207167i	$0.0664243\pi$
$613$			155694.i			0.414334i	−0.978306	+	0.207167i	$0.933576\pi$
$614$	−314806.	−	460777.i	−0.835037	−	1.22223i
$615$		0			0
$616$	−110401.	−	477314.i	−0.290945	−	1.25789i
$617$		−	625050.i		−	1.64189i	−0.571007	−	0.820946i	$-0.693447\pi$
$617$		−	625050.i		−	1.64189i	0.571007	−	0.820946i	$-0.306553\pi$
$618$	−35608.0	−	52119.1i	−0.0932333	−	0.136465i
$619$		−	368822.i		−	0.962576i	−0.876563	−	0.481288i	$-0.840169\pi$
$619$		−	368822.i		−	0.962576i	0.876563	−	0.481288i	$-0.159831\pi$
$620$		0			0
$621$	80114.4			0.207743
$622$	436079.	−	297932.i	1.12716	−	0.770080i
$623$	−678307.			−1.74763
$624$	−222607.	+	241781.i	−0.571701	+	0.620945i
$625$		0			0
$626$	130547.	−	89190.1i	0.333133	−	0.227598i
$627$	−20668.3			−0.0525739
$628$	−39037.9	−	15234.2i	−0.0989845	−	0.0386279i
$629$	−69775.0			−0.176359
$630$		0			0
$631$			457172.i			1.14821i	0.818782	+	0.574105i	$0.194650\pi$
$631$			457172.i			1.14821i	−0.818782	+	0.574105i	$0.805350\pi$
$632$	−54175.5	−	234226.i	−0.135634	−	0.586409i
$633$		−	241473.i		−	0.602644i
$634$	303720.	−	207503.i	0.755606	−	0.516234i
$635$		0			0
$636$	136959.	+	53447.1i	0.338592	+	0.132133i
$637$		−	206366.i		−	0.508580i
$638$	−8928.11	+	6099.73i	−0.0219340	+	0.0149854i
$639$		−	18967.9i		−	0.0464535i
$640$		0			0
$641$	−728866.			−1.77391			−0.886955	−	0.461855i	$-0.847184\pi$
$641$	−728866.			−1.77391			−0.886955	+	0.461855i	$0.847184\pi$
$642$	−223450.	−	327062.i	−0.542140	−	0.793524i
$643$	−201261.			−0.486786			−0.243393	−	0.969928i	$-0.578260\pi$
$643$	−201261.			−0.486786			−0.243393	+	0.969928i	$0.578260\pi$
$644$	188956.	−	484202.i	0.455605	−	1.16749i
$645$		0			0
$646$	−6157.28	−	9012.34i	−0.0147545	−	0.0215960i
$647$	284857.			0.680484			0.340242	−	0.940338i	$-0.389491\pi$
$647$	284857.			0.680484			0.340242	+	0.940338i	$0.389491\pi$
$648$	−45455.9	+	10513.8i	−0.108253	+	0.0250386i
$649$	−347569.			−0.825186
$650$		0			0
$651$		−	140332.i		−	0.331127i
$652$	41432.8	−	106172.i	0.0974652	−	0.249756i
$653$		−	639617.i		−	1.50001i	−0.661433	−	0.750005i	$-0.730051\pi$
$653$		−	639617.i		−	1.50001i	0.661433	−	0.750005i	$-0.269949\pi$
$654$	153980.	+	225379.i	0.360006	+	0.526936i
$655$		0			0
$656$	−102043.	−	93950.5i	−0.237124	−	0.218319i
$657$		−	265273.i		−	0.614557i
$658$	134806.	+	197314.i	0.311356	+	0.455728i
$659$		−	372398.i		−	0.857505i	−0.903422	−	0.428753i	$-0.858953\pi$
$659$		−	372398.i		−	0.857505i	0.903422	−	0.428753i	$-0.141047\pi$
$660$		0			0
$661$	−137125.			−0.313843			−0.156922	−	0.987611i	$-0.550157\pi$
$661$	−137125.			−0.313843			−0.156922	+	0.987611i	$0.550157\pi$
$662$	−10714.5	+	7320.19i	−0.0244487	+	0.0167035i
$663$	−118509.			−0.269602
$664$	650572.	−	150475.i	1.47557	−	0.341293i
$665$		0			0
$666$	67404.4	−	46051.0i	0.151964	−	0.103822i
$667$	−11471.7			−0.0257854
$668$	283101.	−	725450.i	0.634437	−	1.62575i
$669$	251011.			0.560843
$670$		0			0
$671$			323394.i			0.718269i
$672$	−43667.2	+	299528.i	−0.0966978	+	0.663283i
$673$		−	840931.i		−	1.85665i	−0.371770	−	0.928325i	$-0.621249\pi$
$673$		−	840931.i		−	1.85665i	0.371770	−	0.928325i	$-0.378751\pi$
$674$	−18466.5	+	12616.4i	−0.0406504	+	0.0277726i
$675$		0			0
$676$	188930.	−	484135.i	0.413435	−	1.05943i
$677$			207006.i			0.451653i	0.974168	+	0.225827i	$0.0725083\pi$
$677$			207006.i			0.451653i	−0.974168	+	0.225827i	$0.927492\pi$
$678$	249558.	−	170499.i	0.542890	−	0.370905i
$679$			125100.i			0.271343i
$680$		0			0
$681$	99291.3			0.214100
$682$	144146.	+	210985.i	0.309908	+	0.453609i
$683$	−241334.			−0.517341			−0.258670	−	0.965966i	$-0.583284\pi$
$683$	−241334.			−0.517341			−0.258670	+	0.965966i	$0.583284\pi$
$684$	11896.2	+	4642.38i	0.0254270	+	0.00992268i
$685$		0			0
$686$	200988.	+	294184.i	0.427093	+	0.625131i
$687$	381286.			0.807862
$688$	583279.	+	537022.i	1.23225	+	1.13453i
$689$	−436901.			−0.920333
$690$		0			0
$691$		−	628208.i		−	1.31567i	−0.753161	−	0.657836i	$-0.771472\pi$
$691$		−	628208.i		−	1.31567i	0.753161	−	0.657836i	$-0.228528\pi$
$692$	−411026.	−	160399.i	−0.858335	−	0.334958i
$693$			206683.i			0.430367i
$694$	385022.	+	563552.i	0.799404	+	1.17008i
$695$		0			0
$696$	6508.88	−	1505.48i	0.0134365	−	0.00310782i
$697$		−	50016.2i		−	0.102954i
$698$	216850.	+	317401.i	0.445091	+	0.651475i
$699$			176887.i			0.362027i
$700$		0			0
$701$	−470333.			−0.957127			−0.478563	−	0.878053i	$-0.658842\pi$
$701$	−470333.			−0.957127			−0.478563	+	0.878053i	$0.658842\pi$
$702$	114482.	−	78214.9i	0.232308	−	0.158714i
$703$	−22343.4			−0.0452105
$704$	−242016.	−	495184.i	−0.488313	−	0.999129i
$705$		0			0
$706$	680089.	−	464640.i	1.36445	−	0.932196i
$707$	49767.8			0.0995656
$708$	200052.	+	78068.7i	0.399095	+	0.155744i
$709$	666498.			1.32589			0.662944	−	0.748669i	$-0.269307\pi$
$709$	666498.			1.32589			0.662944	+	0.748669i	$0.269307\pi$
$710$		0			0
$711$			101423.i			0.200630i
$712$	−743476.	+	171963.i	−1.46658	+	0.339215i
$713$			271092.i			0.533259i
$714$	−90123.4	+	61572.7i	−0.176783	+	0.120779i
$715$		0			0
$716$	−630195.	−	245928.i	−1.22927	−	0.479714i
$717$			182459.i			0.354918i
$718$	−259054.	+	176987.i	−0.502506	+	0.343315i
$719$			551482.i			1.06678i	0.845870	+	0.533388i	$0.179082\pi$
$719$			551482.i			1.06678i	−0.845870	+	0.533388i	$0.820918\pi$
$720$		0			0
$721$	172766.			0.332344
$722$	292094.	+	427535.i	0.560336	+	0.820158i
$723$	−101953.			−0.195041
$724$	5856.14	−	15006.4i	0.0111721	−	0.0286286i
$725$		0			0
$726$	−40634.8	−	59476.7i	−0.0770947	−	0.112843i
$727$	−735388.			−1.39139			−0.695694	−	0.718339i	$-0.744903\pi$
$727$	−735388.			−1.39139			−0.695694	+	0.718339i	$0.744903\pi$
$728$	−202706.	−	876393.i	−0.382477	−	1.65362i
$729$	19683.0			0.0370370
$730$		0			0
$731$			285893.i			0.535019i
$732$	72638.8	−	186138.i	0.135565	−	0.347386i
$733$		−	372734.i		−	0.693731i	−0.937915	−	0.346866i	$-0.887246\pi$
$733$		−	372734.i		−	0.693731i	0.937915	−	0.346866i	$-0.112754\pi$
$734$	500452.	+	732506.i	0.928902	+	1.35962i
$735$		0			0
$736$	84356.0	−	578626.i	0.155726	−	1.06817i
$737$			51108.4i			0.0940931i
$738$	33010.4	+	48316.9i	0.0606091	+	0.0887129i
$739$		−	962125.i		−	1.76174i	−0.473356	−	0.880871i	$-0.656957\pi$
$739$		−	962125.i		−	1.76174i	0.473356	−	0.880871i	$-0.343043\pi$
$740$		0			0
$741$	−37949.0			−0.0691136
$742$	−332254.	+	226998.i	−0.603480	+	0.412301i
$743$	557423.			1.00973			0.504867	−	0.863197i	$-0.331541\pi$
$743$	557423.			1.00973			0.504867	+	0.863197i	$0.331541\pi$
$744$	−35576.7	−	153815.i	−0.0642717	−	0.277876i
$745$		0			0
$746$	−85488.3	+	58406.1i	−0.153613	+	0.104949i
$747$	−281706.			−0.504841
$748$	72251.5	−	185145.i	0.129135	−	0.330910i
$749$	1.08415e6			1.93254
$750$		0			0
$751$		−	619927.i		−	1.09916i	−0.835441	−	0.549580i	$-0.814788\pi$
$751$		−	619927.i		−	1.09916i	0.835441	−	0.549580i	$-0.185212\pi$
$752$	197780.	+	182095.i	0.349741	+	0.322005i
$753$			2913.64i			0.00513860i
$754$	−16392.8	+	11199.7i	−0.0288344	+	0.0196998i
$755$		0			0
$756$	46423.8	−	118962.i	0.0812264	−	0.208144i
$757$		−	66502.8i		−	0.116051i	−0.998315	−	0.0580254i	$-0.981520\pi$
$757$		−	66502.8i		−	0.116051i	0.998315	−	0.0580254i	$-0.0184804\pi$
$758$	−488152.	+	333508.i	−0.849604	+	0.580454i
$759$		−	399269.i		−	0.693078i
$760$		0			0
$761$	417057.			0.720156			0.360078	−	0.932922i	$-0.382750\pi$
$761$	417057.			0.720156			0.360078	+	0.932922i	$0.382750\pi$
$762$	304377.	+	445514.i	0.524207	+	0.767275i
$763$	−747093.			−1.28329
$764$	102945.	+	40173.4i	0.176367	+	0.0688260i
$765$		0			0
$766$	510485.	+	747192.i	0.870013	+	1.27343i
$767$	−638169.			−1.08479
$768$	28073.2	+	339376.i	0.0475959	+	0.575385i
$769$	284602.			0.481266			0.240633	−	0.970616i	$-0.422645\pi$
$769$	284602.			0.481266			0.240633	+	0.970616i	$0.422645\pi$
$770$		0			0
$771$			418348.i			0.703767i
$772$	420445.	+	164075.i	0.705463	+	0.275301i
$773$		−	690220.i		−	1.15512i	−0.816347	−	0.577562i	$-0.804004\pi$
$773$		−	690220.i		−	1.15512i	0.816347	−	0.577562i	$-0.195996\pi$
$774$	−188688.	−	276180.i	−0.314964	−	0.461010i
$775$		0			0
$776$	31715.3	+	137120.i	0.0526677	+	0.227707i
$777$			223434.i			0.370090i
$778$	−578602.	−	846893.i	−0.955918	−	1.39917i
$779$		−	16016.2i		−	0.0263928i
$780$		0			0
$781$	−94531.3			−0.154979
$782$	174100.	−	118946.i	0.284698	−	0.194507i
$783$	−2818.43			−0.00459709
$784$	−157308.	−	144833.i	−0.255929	−	0.235632i
$785$		0			0
$786$	−282144.	+	192762.i	−0.456694	+	0.312016i
$787$	855688.			1.38155			0.690774	−	0.723071i	$-0.257270\pi$
$787$	855688.			1.38155			0.690774	+	0.723071i	$0.257270\pi$
$788$	−573161.	−	223672.i	−0.923048	−	0.360212i
$789$	−180939.			−0.290655
$790$		0			0
$791$			827242.i			1.32215i
$792$	52398.0	+	226541.i	0.0835342	+	0.361157i
$793$			593782.i			0.944236i
$794$	187161.	−	127869.i	0.296875	−	0.202827i
$795$		0			0
$796$	−81831.3	−	31934.0i	−0.129150	−	0.0503996i
$797$			579975.i			0.913046i	0.889712	+	0.456523i	$0.150905\pi$
$797$			579975.i			0.913046i	−0.889712	+	0.456523i	$0.849095\pi$
$798$	−28859.4	+	19716.9i	−0.0453191	+	0.0309623i
$799$			96941.7i			0.151851i
$800$		0			0
$801$	321935.			0.501768
$802$	24622.7	+	36040.0i	0.0382814	+	0.0560320i
$803$	−1.32205e6			−2.05030
$804$	11479.6	−	29416.7i	0.0177589	−	0.0455075i
$805$		0			0
$806$	264665.	+	387387.i	0.407405	+	0.596314i
$807$	147932.			0.227151
$808$	54549.3	−	12617.1i	0.0835539	−	0.0193257i
$809$	60860.6			0.0929907			0.0464953	−	0.998919i	$-0.485195\pi$
$809$	60860.6			0.0929907			0.0464953	+	0.998919i	$0.485195\pi$
$810$		0			0
$811$		−	103330.i		−	0.157103i	−0.996910	−	0.0785515i	$-0.974970\pi$
$811$		−	103330.i		−	0.157103i	0.996910	−	0.0785515i	$-0.0250295\pi$
$812$	−6647.47	+	17034.2i	−0.0100819	+	0.0258351i
$813$		−	195654.i		−	0.296011i
$814$	−229506.	−	335926.i	−0.346375	−	0.506985i
$815$		0			0
$816$	−83172.3	+	90336.4i	−0.124910	+	0.135670i
$817$			91549.0i			0.137154i
$818$	653421.	+	956404.i	0.976531	+	1.42934i
$819$			379489.i			0.565759i
$820$		0			0
$821$	533333.			0.791247			0.395623	−	0.918413i	$-0.370529\pi$
$821$	533333.			0.791247			0.395623	+	0.918413i	$0.370529\pi$
$822$	542632.	−	370729.i	0.803085	−	0.548672i
$823$	728807.			1.07600			0.538000	−	0.842945i	$-0.319180\pi$
$823$	728807.			1.07600			0.538000	+	0.842945i	$0.319180\pi$
$824$	189365.	−	43799.3i	0.278897	−	0.0645079i
$825$		0			0
$826$	−485314.	+	331569.i	−0.711317	+	0.485975i
$827$	−768434.			−1.12356			−0.561779	−	0.827287i	$-0.689883\pi$
$827$	−768434.			−1.12356			−0.561779	+	0.827287i	$0.689883\pi$
$828$	−89681.3	+	229809.i	−0.130810	+	0.335203i
$829$	401672.			0.584471			0.292235	−	0.956346i	$-0.405601\pi$
$829$	401672.			0.584471			0.292235	+	0.956346i	$0.405601\pi$
$830$		0			0
$831$			134685.i			0.195037i
$832$	−444364.	−	909205.i	−0.641936	−	1.31345i
$833$		−	77104.4i		−	0.111119i
$834$	221315.	−	151204.i	0.318185	−	0.217385i
$835$		0			0
$836$	23136.4	−	59287.4i	0.0331043	−	0.0848301i
$837$			66603.7i			0.0950708i
$838$	230659.	−	157587.i	0.328460	−	0.224405i
$839$			429703.i			0.610443i	0.952281	+	0.305221i	$0.0987305\pi$
$839$			429703.i			0.610443i	−0.952281	+	0.305221i	$0.901270\pi$
$840$		0			0
$841$	−706877.			−0.999429
$842$	36570.7	+	53528.1i	0.0515833	+	0.0755019i
$843$	258849.			0.364244
$844$	692669.	+	270308.i	0.972391	+	0.379468i
$845$		0			0
$846$	−63980.9	−	93648.1i	−0.0893942	−	0.130845i
$847$	197155.			0.274815
$848$	−306628.	+	333040.i	−0.426403	+	0.463132i
$849$	381418.			0.529159
$850$		0			0
$851$		−	431629.i		−	0.596007i
$852$	54409.9	+	21233.0i	0.0749547	+	0.0292504i
$853$			732176.i			1.00628i	0.864206	+	0.503138i	$0.167821\pi$
$853$			732176.i			1.00628i	−0.864206	+	0.503138i	$0.832179\pi$
$854$	308507.	+	451559.i	0.423009	+	0.619154i
$855$		0			0
$856$	1.18832e6	−	274853.i	1.62175	−	0.375105i
$857$			430159.i			0.585689i	0.956160	+	0.292844i	$0.0946018\pi$
$857$			430159.i			0.585689i	−0.956160	+	0.292844i	$0.905398\pi$
$858$	−389803.	−	570550.i	−0.529506	−	0.775031i
$859$		−	489975.i		−	0.664030i	−0.943274	−	0.332015i	$-0.892272\pi$
$859$		−	489975.i		−	0.664030i	0.943274	−	0.332015i	$-0.107728\pi$
$860$		0			0
$861$	−160162.			−0.216050
$862$	347662.	−	237525.i	0.467890	−	0.319665i
$863$	999093.			1.34148			0.670740	−	0.741692i	$-0.265977\pi$
$863$	999093.			1.34148			0.670740	+	0.741692i	$0.265977\pi$
$864$	20725.1	−	142160.i	0.0277632	−	0.190437i
$865$		0			0
$866$	435303.	−	297401.i	0.580438	−	0.396559i
$867$	389710.			0.518445
$868$	402544.	+	157090.i	0.534287	+	0.208501i
$869$	505464.			0.669347
$870$		0			0
$871$			93839.8i			0.123695i
$872$	−818872.	+	189402.i	−1.07692	+	0.249087i
$873$		−	59374.5i		−	0.0779062i
$874$	55750.4	−	38089.0i	0.0729836	−	0.0498628i
$875$		0			0
$876$	760940.	+	296951.i	0.991613	+	0.386969i
$877$			634599.i			0.825087i	0.910938	+	0.412544i	$0.135360\pi$
$877$			634599.i			0.825087i	−0.910938	+	0.412544i	$0.864640\pi$
$878$	−492289.	+	336334.i	−0.638603	+	0.436297i
$879$			679047.i			0.878865i
$880$		0			0
$881$	312649.			0.402815			0.201407	−	0.979508i	$-0.435448\pi$
$881$	312649.			0.402815			0.201407	+	0.979508i	$0.435448\pi$
$882$	50888.4	+	74484.8i	0.0654156	+	0.0957481i
$883$	209047.			0.268116			0.134058	−	0.990973i	$-0.457199\pi$
$883$	209047.			0.268116			0.134058	+	0.990973i	$0.457199\pi$
$884$	132660.	−	339944.i	0.169761	−	0.435014i
$885$		0			0
$886$	−561710.	−	822169.i	−0.715558	−	1.04735i
$887$	178008.			0.226252			0.113126	−	0.993581i	$-0.463914\pi$
$887$	178008.			0.226252			0.113126	+	0.993581i	$0.463914\pi$
$888$	56644.7	+	244901.i	0.0718345	+	0.310574i
$889$	−1.47680e6			−1.86861
$890$		0			0
$891$		−	98095.0i		−	0.123564i
$892$	−280986.	+	720031.i	−0.353147	+	0.904943i
$893$			31042.8i			0.0389276i
$894$	−369041.	−	540161.i	−0.461742	−	0.675847i
$895$		0			0
$896$	−810319.	−	460556.i	−1.00935	−	0.573676i
$897$		−	733095.i		−	0.911120i
$898$	−550012.	−	805047.i	−0.682055	−	0.998317i
$899$		−	9537.04i		−	0.0118003i
$900$		0			0
$901$	−163239.			−0.201082
$902$	240799.	−	164515.i	0.295966	−	0.202205i
$903$	915490.			1.12274
$904$	209721.	+	906720.i	0.256629	+	1.10952i
$905$		0			0
$906$	−677532.	+	462894.i	−0.825417	+	0.563929i
$907$	−62871.2			−0.0764253			−0.0382126	−	0.999270i	$-0.512166\pi$
$907$	−62871.2			−0.0764253			−0.0382126	+	0.999270i	$0.512166\pi$
$908$	−111148.	+	284819.i	−0.134813	+	0.345459i
$909$	−23620.5			−0.0285866
$910$		0			0
$911$		−	1.45791e6i		−	1.75669i	−0.478027	−	0.878345i	$-0.658648\pi$
$911$		−	1.45791e6i		−	1.75669i	0.478027	−	0.878345i	$-0.341352\pi$
$912$	−26633.5	+	28927.6i	−0.0320213	+	0.0347795i
$913$			1.40395e6i			1.68426i
$914$	−1.13377e6	+	774598.i	−1.35716	+	0.927222i
$915$		0			0
$916$	−426817.	+	1.09372e6i	−0.508687	+	1.30352i
$917$		−	935258.i		−	1.11223i
$918$	42773.9	−	29223.4i	0.0507567	−	0.0346773i
$919$		−	315989.i		−	0.374146i	−0.982346	−	0.187073i	$-0.940100\pi$
$919$		−	315989.i		−	0.374146i	0.982346	−	0.187073i	$-0.0599001\pi$
$920$		0			0
$921$	−724927.			−0.854623
$922$	−350935.	−	513660.i	−0.412824	−	0.604246i
$923$	−173568.			−0.203736
$924$	−592874.	−	231364.i	−0.694414	−	0.270989i
$925$		0			0
$926$	725358.	+	1.06170e6i	0.845923	+	1.23817i
$927$	−81997.3			−0.0954201
$928$	−2967.65	+	20356.1i	−0.00344601	+	0.0236373i
$929$	−122547.			−0.141994			−0.0709971	−	0.997477i	$-0.522618\pi$
$929$	−122547.			−0.141994			−0.0709971	+	0.997477i	$0.522618\pi$
$930$		0			0
$931$		−	24690.4i		−	0.0284859i
$932$	−507403.	−	198010.i	−0.584145	−	0.227958i
$933$		−	686070.i		−	0.788143i
$934$	183270.	+	268250.i	0.210086	+	0.307501i
$935$		0			0
$936$	96207.6	+	415950.i	0.109814	+	0.474776i
$937$			495399.i			0.564256i	0.959377	+	0.282128i	$0.0910402\pi$
$937$			495399.i			0.564256i	−0.959377	+	0.282128i	$0.908960\pi$
$938$	48755.7	+	71363.3i	0.0554141	+	0.0811090i
$939$		−	205385.i		−	0.232936i
$940$		0			0
$941$	−1.14226e6			−1.28999			−0.644994	−	0.764188i	$-0.723140\pi$
$941$	−1.14226e6			−1.28999			−0.644994	+	0.764188i	$0.723140\pi$
$942$	−44947.8	+	30708.5i	−0.0506531	+	0.0346065i
$943$	309401.			0.347935
$944$	−447883.	+	486461.i	−0.502598	+	0.545889i
$945$		0			0
$946$	−1.37641e6	+	940370.i	−1.53803	+	1.05079i
$947$	−527337.			−0.588015			−0.294007	−	0.955803i	$-0.594989\pi$
$947$	−527337.			−0.588015			−0.294007	+	0.955803i	$0.594989\pi$
$948$	−290933.	−	113534.i	−0.323725	−	0.126331i
$949$	−2.42741e6			−2.69532
$950$		0			0
$951$		−	477833.i		−	0.528342i
$952$	−75737.0	−	327446.i	−0.0835669	−	0.361298i
$953$			259379.i			0.285594i	0.989752	+	0.142797i	$0.0456096\pi$
$953$			259379.i			0.285594i	−0.989752	+	0.142797i	$0.954390\pi$
$954$	157693.	−	107737.i	0.173267	−	0.118377i
$955$		0			0
$956$	−523387.	−	204248.i	−0.572674	−	0.223481i
$957$			14046.3i			0.0153369i
$958$	1.14293e6	−	780856.i	1.24534	−	0.850824i
$959$			1.79873e6i			1.95582i
$960$		0			0
$961$	698146.			0.755962
$962$	−421395.	−	616791.i	−0.455344	−	0.666482i
$963$	−514556.			−0.554856
$964$	114128.	−	292455.i	0.122812	−	0.314706i
$965$		0			0
$966$	−380890.	−	557504.i	−0.408174	−	0.597439i
$967$	1.03870e6			1.11081			0.555403	−	0.831581i	$-0.312564\pi$
$967$	1.03870e6			1.11081			0.555403	+	0.831581i	$0.312564\pi$
$968$	216097.	−	49982.4i	0.230621	−	0.0533417i
$969$	−14178.8			−0.0151005
$970$		0			0
$971$		−	1.15698e6i		−	1.22713i	−0.789646	−	0.613563i	$-0.789736\pi$
$971$		−	1.15698e6i		−	1.22713i	0.789646	−	0.613563i	$-0.210264\pi$
$972$	−22033.5	+	56461.0i	−0.0233212	+	0.0597608i
$973$			733622.i			0.774902i
$974$	−213101.	−	311913.i	−0.224630	−	0.328788i
$975$		0			0
$976$	452626.	+	416731.i	0.475160	+	0.437478i
$977$			1.09732e6i			1.14960i	0.818295	+	0.574799i	$0.194920\pi$
$977$			1.09732e6i			1.14960i	−0.818295	+	0.574799i	$0.805080\pi$
$978$	−83518.7	−	122245.i	−0.0873184	−	0.127807i
$979$		−	1.60444e6i		−	1.67401i
$980$		0			0
$981$	354582.			0.368450
$982$	580389.	−	396525.i	0.601861	−	0.411195i
$983$	1.71299e6			1.77276			0.886378	−	0.462963i	$-0.153214\pi$
$983$	1.71299e6			1.77276			0.886378	+	0.462963i	$0.153214\pi$
$984$	−175550.	+	40604.1i	−0.181306	+	0.0419353i
$985$		0			0
$986$	−6124.84	+	4184.52i	−0.00630000	+	0.00430419i
$987$	310427.			0.318659
$988$	42480.6	−	108857.i	0.0435188	−	0.111518i
$989$	−1.76854e6			−1.80810
$990$		0			0
$991$		−	1.03974e6i		−	1.05872i	−0.848399	−	0.529358i	$-0.822433\pi$
$991$		−	1.03974e6i		−	1.05872i	0.848399	−	0.529358i	$-0.177567\pi$
$992$	481045.	+	70130.0i	0.488835	+	0.0712657i
$993$			16856.8i			0.0170953i
$994$	−131995.	+	90179.7i	−0.133593	+	0.0912717i
$995$		0			0
$996$	315346.	−	808078.i	0.317884	−	0.814582i
$997$		−	1.11868e6i		−	1.12542i	−0.826655	−	0.562709i	$-0.809759\pi$
$997$		−	1.11868e6i		−	1.12542i	0.826655	−	0.562709i	$-0.190241\pi$
$998$	−123176.	+	84154.4i	−0.123670	+	0.0844920i
$999$		−	106045.i		−	0.106258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.f.a.199.6		8
4.3	odd	2	inner	300.5.f.a.199.4		8
5.2	odd	4		300.5.c.a.151.2		4
5.3	odd	4		12.5.d.a.7.3	✓	4
5.4	even	2	inner	300.5.f.a.199.3		8
15.8	even	4		36.5.d.b.19.2		4
20.3	even	4		12.5.d.a.7.4	yes	4
20.7	even	4		300.5.c.a.151.1		4
20.19	odd	2	inner	300.5.f.a.199.5		8
40.3	even	4		192.5.g.d.127.4		4
40.13	odd	4		192.5.g.d.127.2		4
60.23	odd	4		36.5.d.b.19.1		4
80.3	even	4		768.5.b.g.127.7		8
80.13	odd	4		768.5.b.g.127.3		8
80.43	even	4		768.5.b.g.127.2		8
80.53	odd	4		768.5.b.g.127.6		8
120.53	even	4		576.5.g.m.127.2		4
120.83	odd	4		576.5.g.m.127.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.3	✓	4	5.3	odd	4
12.5.d.a.7.4	yes	4	20.3	even	4
36.5.d.b.19.1		4	60.23	odd	4
36.5.d.b.19.2		4	15.8	even	4
192.5.g.d.127.2		4	40.13	odd	4
192.5.g.d.127.4		4	40.3	even	4
300.5.c.a.151.1		4	20.7	even	4
300.5.c.a.151.2		4	5.2	odd	4
300.5.f.a.199.3		8	5.4	even	2	inner
300.5.f.a.199.4		8	4.3	odd	2	inner
300.5.f.a.199.5		8	20.19	odd	2	inner
300.5.f.a.199.6		8	1.1	even	1	trivial
576.5.g.m.127.1		4	120.83	odd	4
576.5.g.m.127.2		4	120.53	even	4
768.5.b.g.127.2		8	80.43	even	4
768.5.b.g.127.3		8	80.13	odd	4
768.5.b.g.127.6		8	80.53	odd	4
768.5.b.g.127.7		8	80.3	even	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.25647 + 3.30278i) q^{2} +5.19615 q^{3} +(-5.81665 + 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882 q^{7} +(-62.3538 + 14.4222i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(2.25647 + 3.30278i) q^{2} +5.19615 q^{3} +(-5.81665 + 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882 q^{7} +(-62.3538 + 14.4222i) q^{8} +27.0000 q^{9} -134.561i q^{11} +(-30.2242 + 77.4500i) q^{12} -247.066i q^{13} +(-128.367 - 187.889i) q^{14} +(-188.333 - 173.397i) q^{16} -92.3112i q^{17} +(60.9248 + 89.1749i) q^{18} -29.5600i q^{19} -295.600 q^{21} +(444.425 - 303.633i) q^{22} +571.038 q^{23} +(-324.000 + 74.9400i) q^{24} +(816.005 - 557.499i) q^{26} +140.296 q^{27} +(330.899 - 847.933i) q^{28} -20.0891 q^{29} +474.736i q^{31} +(147.724 - 1013.29i) q^{32} -699.199i q^{33} +(304.883 - 208.298i) q^{34} +(-157.050 + 402.442i) q^{36} -755.867i q^{37} +(97.6300 - 66.7013i) q^{38} -1283.79i q^{39} +541.822 q^{41} +(-667.013 - 976.299i) q^{42} -3097.06 q^{43} +(2005.67 + 782.695i) q^{44} +(1288.53 + 1886.01i) q^{46} -1050.16 q^{47} +(-978.607 - 900.999i) q^{48} +835.266 q^{49} -479.663i q^{51} +(3682.59 + 1437.10i) q^{52} -1768.35i q^{53} +(316.574 + 463.367i) q^{54} +(3547.20 - 820.453i) q^{56} -153.598i q^{57} +(-45.3306 - 66.3499i) q^{58} -2582.98i q^{59} -2403.33 q^{61} +(-1567.95 + 1071.23i) q^{62} -1535.98 q^{63} +(3680.00 - 1798.56i) q^{64} +(2309.30 - 1577.72i) q^{66} -379.816 q^{67} +(1375.92 + 536.942i) q^{68} +2967.20 q^{69} -702.517i q^{71} +(-1683.55 + 389.400i) q^{72} -9824.92i q^{73} +(2496.46 - 1705.59i) q^{74} +(440.599 + 171.940i) q^{76} +7654.93i q^{77} +(4240.09 - 2896.85i) q^{78} +3756.40i q^{79} +729.000 q^{81} +(1222.61 + 1789.52i) q^{82} -10433.6 q^{83} +(1719.40 - 4405.99i) q^{84} +(-6988.43 - 10228.9i) q^{86} -104.386 q^{87} +(1940.67 + 8390.39i) q^{88} +11923.5 q^{89} +14055.2i q^{91} +(-3321.53 + 8511.46i) q^{92} +2466.80i q^{93} +(-2369.66 - 3468.45i) q^{94} +(767.597 - 5265.20i) q^{96} -2199.06i q^{97} +(1884.76 + 2758.70i) q^{98} -3633.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9}+O(q^{10}) \) 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9	\( 8 q + 40 q^{4} - 36 q^{6} + 216 q^{9} - 1200 q^{14} + 224 q^{16} - 288 q^{21} - 2592 q^{24} + 3384 q^{26} - 1776 q^{29} + 968 q^{34} + 1080 q^{36} + 1104 q^{41} + 7392 q^{44} - 768 q^{46} + 1144 q^{49} - 972 q^{54} + 3456 q^{56} + 8464 q^{61} + 29440 q^{64} + 9648 q^{66} + 19584 q^{69} + 8232 q^{74} - 3744 q^{76} + 5832 q^{81} + 21024 q^{84} - 39120 q^{86} + 50160 q^{89} + 10464 q^{94} - 16704 q^{96}+O(q^{100}) \) 8 * q + 40 * q^4 - 36 * q^6 + 216 * q^9 - 1200 * q^14 + 224 * q^16 - 288 * q^21 - 2592 * q^24 + 3384 * q^26 - 1776 * q^29 + 968 * q^34 + 1080 * q^36 + 1104 * q^41 + 7392 * q^44 - 768 * q^46 + 1144 * q^49 - 972 * q^54 + 3456 * q^56 + 8464 * q^61 + 29440 * q^64 + 9648 * q^66 + 19584 * q^69 + 8232 * q^74 - 3744 * q^76 + 5832 * q^81 + 21024 * q^84 - 39120 * q^86 + 50160 * q^89 + 10464 * q^94 - 16704 * q^96

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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