LMFDB - Embedded newform 300.5.c.a.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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, 0]))

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (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:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.2
Root			$1.15139 + 1.99426i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30278 + 2.25647i) q^{2} -5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.30278 + 2.25647i) q^{2} -5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} -134.561i q^{11} +(-77.4500 - 30.2242i) q^{12} -247.066 q^{13} +(128.367 + 187.889i) q^{14} +(-188.333 - 173.397i) q^{16} +92.3112 q^{17} +(89.1749 - 60.9248i) q^{18} +29.5600i q^{19} -295.600 q^{21} +(303.633 + 444.425i) q^{22} -571.038i q^{23} +(324.000 - 74.9400i) q^{24} +(816.005 - 557.499i) q^{26} +140.296i q^{27} +(-847.933 - 330.899i) q^{28} +20.0891 q^{29} +474.736i q^{31} +(1013.29 + 147.724i) q^{32} -699.199 q^{33} +(-304.883 + 208.298i) q^{34} +(-157.050 + 402.442i) q^{36} +755.867 q^{37} +(-66.7013 - 97.6300i) q^{38} +1283.79i q^{39} +541.822 q^{41} +(976.299 - 667.013i) q^{42} +3097.06i q^{43} +(-2005.67 - 782.695i) q^{44} +(1288.53 + 1886.01i) q^{46} -1050.16i q^{47} +(-900.999 + 978.607i) q^{48} -835.266 q^{49} -479.663i q^{51} +(-1437.10 + 3682.59i) q^{52} -1768.35 q^{53} +(-316.574 - 463.367i) q^{54} +(3547.20 - 820.453i) q^{56} +153.598 q^{57} +(-66.3499 + 45.3306i) q^{58} +2582.98i q^{59} -2403.33 q^{61} +(-1071.23 - 1567.95i) q^{62} +1535.98i q^{63} +(-3680.00 + 1798.56i) q^{64} +(2309.30 - 1577.72i) q^{66} -379.816i q^{67} +(536.942 - 1375.92i) q^{68} -2967.20 q^{69} -702.517i q^{71} +(-389.400 - 1683.55i) q^{72} -9824.92 q^{73} +(-2496.46 + 1705.59i) q^{74} +(440.599 + 171.940i) q^{76} -7654.93 q^{77} +(-2896.85 - 4240.09i) q^{78} -3756.40i q^{79} +729.000 q^{81} +(-1789.52 + 1222.61i) q^{82} +10433.6i q^{83} +(-1719.40 + 4405.99i) q^{84} +(-6988.43 - 10228.9i) q^{86} -104.386i q^{87} +(8390.39 - 1940.67i) q^{88} -11923.5 q^{89} +14055.2i q^{91} +(-8511.46 - 3321.53i) q^{92} +2466.80 q^{93} +(2369.66 + 3468.45i) q^{94} +(767.597 - 5265.20i) q^{96} +2199.06 q^{97} +(2758.70 - 1884.76i) q^{98} +3633.15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 20 q^{4} - 18 q^{6} - 108 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 - 20 * q^4 - 18 * q^6 - 108 * q^9	$ 4 q - 6 q^{2} - 20 q^{4} - 18 q^{6} - 108 q^{9} - 180 q^{12} - 296 q^{13} + 600 q^{14} + 112 q^{16} + 600 q^{17} + 162 q^{18} - 144 q^{21} + 1128 q^{22} + 1296 q^{24} + 1692 q^{26} - 1488 q^{28} + 888 q^{29} + 2784 q^{32} - 720 q^{33} - 484 q^{34} + 540 q^{36} + 4408 q^{37} - 4680 q^{38} + 552 q^{41} + 2088 q^{42} - 3696 q^{44} - 384 q^{46} - 1008 q^{48} - 572 q^{49} - 6008 q^{52} - 5112 q^{53} + 486 q^{54} + 1728 q^{56} - 5616 q^{57} + 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 4824 q^{66} - 5496 q^{68} - 9792 q^{69} - 8840 q^{73} - 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 9900 q^{78} + 2916 q^{81} - 3740 q^{82} - 10512 q^{84} - 19560 q^{86} + 8640 q^{88} - 25080 q^{89} - 18816 q^{92} + 17136 q^{93} - 5232 q^{94} - 8352 q^{96} - 23048 q^{97} + 5850 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 20 * q^4 - 18 * q^6 - 108 * q^9 - 180 * q^12 - 296 * q^13 + 600 * q^14 + 112 * q^16 + 600 * q^17 + 162 * q^18 - 144 * q^21 + 1128 * q^22 + 1296 * q^24 + 1692 * q^26 - 1488 * q^28 + 888 * q^29 + 2784 * q^32 - 720 * q^33 - 484 * q^34 + 540 * q^36 + 4408 * q^37 - 4680 * q^38 + 552 * q^41 + 2088 * q^42 - 3696 * q^44 - 384 * q^46 - 1008 * q^48 - 572 * q^49 - 6008 * q^52 - 5112 * q^53 + 486 * q^54 + 1728 * q^56 - 5616 * q^57 + 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 4824 * q^66 - 5496 * q^68 - 9792 * q^69 - 8840 * q^73 - 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 9900 * q^78 + 2916 * q^81 - 3740 * q^82 - 10512 * q^84 - 19560 * q^86 + 8640 * q^88 - 25080 * q^89 - 18816 * q^92 + 17136 * q^93 - 5232 * q^94 - 8352 * q^96 - 23048 * q^97 + 5850 * q^98

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 $

$2$	−3.30278	+	2.25647i	−0.825694	+	0.564118i
$2$	−3.30278	+	2.25647i	−0.825694	+	0.564118i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	5.81665	−	14.9053i	0.363541	−	0.931578i
$5$		0			0
$5$		0			0
$6$	11.7250	+	17.1617i	0.325694	+	0.476715i
$7$		−	56.8882i		−	1.16098i	−0.814266	−	0.580492i	$-0.802860\pi$
$7$		−	56.8882i		−	1.16098i	0.814266	−	0.580492i	$-0.197140\pi$
$8$	14.4222	+	62.3538i	0.225347	+	0.974279i
$9$	−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	$-0.187679\pi$
$12$	−77.4500	−	30.2242i	−0.537847	−	0.209890i
$13$	−247.066			−1.46193			−0.730966	−	0.682414i	$-0.760930\pi$
$13$	−247.066			−1.46193			−0.730966	+	0.682414i	$0.760930\pi$
$14$	128.367	+	187.889i	0.654932	+	0.958617i
$15$		0			0
$16$	−188.333	−	173.397i	−0.735676	−	0.677334i
$17$	92.3112			0.319416			0.159708	−	0.987164i	$-0.448945\pi$
$17$	92.3112			0.319416			0.159708	+	0.987164i	$0.448945\pi$
$18$	89.1749	−	60.9248i	0.275231	−	0.188039i
$19$			29.5600i			0.0818836i	0.999162	+	0.0409418i	$0.0130358\pi$
$19$			29.5600i			0.0818836i	−0.999162	+	0.0409418i	$0.986964\pi$
$20$		0			0
$21$	−295.600			−0.670294
$22$	303.633	+	444.425i	0.627342	+	0.918233i
$23$		−	571.038i		−	1.07947i	−0.841836	−	0.539733i	$-0.818525\pi$
$23$		−	571.038i		−	1.07947i	0.841836	−	0.539733i	$-0.181475\pi$
$24$	324.000	−	74.9400i	0.562500	−	0.130104i
$25$		0			0
$26$	816.005	−	557.499i	1.20711	−	0.824703i
$27$			140.296i			0.192450i
$28$	−847.933	−	330.899i	−1.08155	−	0.422065i
$29$	20.0891			0.0238872			0.0119436	−	0.999929i	$-0.496198\pi$
$29$	20.0891			0.0238872			0.0119436	+	0.999929i	$0.496198\pi$
$30$		0			0
$31$			474.736i			0.494002i	0.969015	+	0.247001i	$0.0794452\pi$
$31$			474.736i			0.494002i	−0.969015	+	0.247001i	$0.920555\pi$
$32$	1013.29	+	147.724i	0.989540	+	0.144262i
$33$	−699.199			−0.642056
$34$	−304.883	+	208.298i	−0.263740	+	0.180188i
$35$		0			0
$36$	−157.050	+	402.442i	−0.121180	+	0.310526i
$37$	755.867			0.552131			0.276065	−	0.961139i	$-0.410969\pi$
$37$	755.867			0.552131			0.276065	+	0.961139i	$0.410969\pi$
$38$	−66.7013	−	97.6300i	−0.0461920	−	0.0676108i
$39$			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	$0.448476\pi$
$42$	976.299	−	667.013i	0.553458	−	0.378125i
$43$			3097.06i			1.67499i	0.546444	+	0.837496i	$0.315981\pi$
$43$			3097.06i			1.67499i	−0.546444	+	0.837496i	$0.684019\pi$
$44$	−2005.67	−	782.695i	−1.03598	−	0.404284i
$45$		0			0
$46$	1288.53	+	1886.01i	0.608947	+	0.891309i
$47$		−	1050.16i		−	0.475401i	−0.971338	−	0.237701i	$-0.923606\pi$
$47$		−	1050.16i		−	0.475401i	0.971338	−	0.237701i	$-0.0763937\pi$
$48$	−900.999	+	978.607i	−0.391059	+	0.424743i
$49$	−835.266			−0.347882
$50$		0			0
$51$		−	479.663i		−	0.184415i
$52$	−1437.10	+	3682.59i	−0.531472	+	1.36190i
$53$	−1768.35			−0.629532			−0.314766	−	0.949169i	$-0.601926\pi$
$53$	−1768.35			−0.629532			−0.314766	+	0.949169i	$0.601926\pi$
$54$	−316.574	−	463.367i	−0.108565	−	0.158905i
$55$		0			0
$56$	3547.20	−	820.453i	1.13112	−	0.261624i
$57$	153.598			0.0472755
$58$	−66.3499	+	45.3306i	−0.0197235	+	0.0134752i
$59$			2582.98i			0.742024i	0.928628	+	0.371012i	$0.120989\pi$
$59$			2582.98i			0.742024i	−0.928628	+	0.371012i	$0.879011\pi$
$60$		0			0
$61$	−2403.33			−0.645883			−0.322941	−	0.946419i	$-0.604672\pi$
$61$	−2403.33			−0.645883			−0.322941	+	0.946419i	$0.604672\pi$
$62$	−1071.23	−	1567.95i	−0.278676	−	0.407895i
$63$			1535.98i			0.386994i
$64$	−3680.00	+	1798.56i	−0.898438	+	0.439101i
$65$		0			0
$66$	2309.30	−	1577.72i	0.530142	−	0.362196i
$67$		−	379.816i		−	0.0846104i	−0.999105	−	0.0423052i	$-0.986530\pi$
$67$		−	379.816i		−	0.0846104i	0.999105	−	0.0423052i	$-0.0134702\pi$
$68$	536.942	−	1375.92i	0.116121	−	0.297561i
$69$	−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	$-0.0221979\pi$
$72$	−389.400	−	1683.55i	−0.0751157	−	0.324760i
$73$	−9824.92			−1.84367			−0.921836	−	0.387581i	$-0.873311\pi$
$73$	−9824.92			−1.84367			−0.921836	+	0.387581i	$0.873311\pi$
$74$	−2496.46	+	1705.59i	−0.455891	+	0.311467i
$75$		0			0
$76$	440.599	+	171.940i	0.0762810	+	0.0297680i
$77$	−7654.93			−1.29110
$78$	−2896.85	−	4240.09i	−0.476142	−	0.696924i
$79$		−	3756.40i		−	0.601890i	−0.953641	−	0.300945i	$-0.902698\pi$
$79$		−	3756.40i		−	0.601890i	0.953641	−	0.300945i	$-0.0973021\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−1789.52	+	1222.61i	−0.266139	+	0.181827i
$83$			10433.6i			1.51452i	0.653111	+	0.757262i	$0.273463\pi$
$83$			10433.6i			1.51452i	−0.653111	+	0.757262i	$0.726537\pi$
$84$	−1719.40	+	4405.99i	−0.243679	+	0.624431i
$85$		0			0
$86$	−6988.43	−	10228.9i	−0.944893	−	1.38303i
$87$		−	104.386i		−	0.0137913i
$88$	8390.39	−	1940.67i	1.08347	−	0.250603i
$89$	−11923.5			−1.50530			−0.752651	−	0.658419i	$-0.771225\pi$
$89$	−11923.5			−1.50530			−0.752651	+	0.658419i	$0.771225\pi$
$90$		0			0
$91$			14055.2i			1.69728i
$92$	−8511.46	−	3321.53i	−1.00561	−	0.392430i
$93$	2466.80			0.285212
$94$	2369.66	+	3468.45i	0.268183	+	0.392536i
$95$		0			0
$96$	767.597	−	5265.20i	0.0832896	−	0.571311i
$97$	2199.06			0.233718			0.116859	−	0.993148i	$-0.462717\pi$
$97$	2199.06			0.233718			0.116859	+	0.993148i	$0.462717\pi$
$98$	2758.70	−	1884.76i	0.287244	−	0.196247i
$99$			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	$0.513653\pi$
$102$	1082.35	+	1584.22i	0.104032	+	0.152270i
$103$			3036.94i			0.286260i	0.989704	+	0.143130i	$0.0457168\pi$
$103$			3036.94i			0.286260i	−0.989704	+	0.143130i	$0.954283\pi$
$104$	−3563.24	−	15405.5i	−0.329442	−	1.42433i
$105$		0			0
$106$	5840.48	−	3990.25i	0.519801	−	0.355131i
$107$		−	19057.6i		−	1.66457i	−0.554350	−	0.832284i	$-0.687033\pi$
$107$		−	19057.6i		−	1.66457i	0.554350	−	0.832284i	$-0.312967\pi$
$108$	2091.15	+	816.054i	0.179282	+	0.0699635i
$109$	−13132.7			−1.10535			−0.552675	−	0.833397i	$-0.686393\pi$
$109$	−13132.7			−1.10535			−0.552675	+	0.833397i	$0.686393\pi$
$110$		0			0
$111$		−	3927.60i		−	0.318773i
$112$	−9864.26	+	10713.9i	−0.786373	+	0.854108i
$113$	−14541.5			−1.13882			−0.569408	−	0.822055i	$-0.692827\pi$
$113$	−14541.5			−1.13882			−0.569408	+	0.822055i	$0.692827\pi$
$114$	−507.300	+	346.590i	−0.0390351	+	0.0266690i
$115$		0			0
$116$	116.852	−	299.434i	0.00868397	−	0.0222528i
$117$	6670.79			0.487311
$118$	−5828.44	−	8531.02i	−0.418589	−	0.612685i
$119$		−	5251.42i		−	0.370836i
$120$		0			0
$121$	−3465.66			−0.236709
$122$	7937.66	−	5423.05i	0.533301	−	0.364354i
$123$		−	2815.39i		−	0.186092i
$124$	7076.06	+	2761.38i	0.460202	+	0.179590i
$125$		0			0
$126$	−3465.90	−	5073.00i	−0.218311	−	0.319539i
$127$			25959.7i			1.60951i	0.593609	+	0.804753i	$0.297702\pi$
$127$			25959.7i			1.60951i	−0.593609	+	0.804753i	$0.702298\pi$
$128$	8095.81	−	14244.1i	0.494129	−	0.869388i
$129$	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	$0.840999\pi$
$132$	−4067.00	+	10421.7i	−0.233414	+	0.598126i
$133$	1681.61			0.0950655
$134$	857.045	+	1254.45i	0.0477303	+	0.0698623i
$135$		0			0
$136$	1331.33	+	5755.96i	0.0719794	+	0.311200i
$137$	31618.7			1.68462			0.842312	−	0.538990i	$-0.181194\pi$
$137$	31618.7			1.68462			0.842312	+	0.538990i	$0.181194\pi$
$138$	9799.99	−	6695.41i	0.514597	−	0.351576i
$139$			12895.9i			0.667453i	0.942670	+	0.333726i	$0.108306\pi$
$139$			12895.9i			0.667453i	−0.942670	+	0.333726i	$0.891694\pi$
$140$		0			0
$141$	−5456.80			−0.274473
$142$	1585.21	+	2320.25i	0.0786159	+	0.115069i
$143$			33245.5i			1.62578i
$144$	5084.99	+	4681.73i	0.245225	+	0.225778i
$145$		0			0
$146$	32449.5	−	22169.7i	1.52231	−	1.04005i
$147$			4340.17i			0.200850i
$148$	4396.62	−	11266.4i	0.200722	−	0.514353i
$149$	31474.8			1.41772			0.708859	−	0.705350i	$-0.249210\pi$
$149$	31474.8			1.41772			0.708859	+	0.705350i	$0.249210\pi$
$150$		0			0
$151$			39479.3i			1.73147i	0.500502	+	0.865735i	$0.333149\pi$
$151$			39479.3i			1.73147i	−0.500502	+	0.865735i	$0.666851\pi$
$152$	−1843.18	+	426.320i	−0.0797774	+	0.0184522i
$153$	−2492.40			−0.106472
$154$	25282.5	−	17273.1i	1.06605	−	0.728333i
$155$		0			0
$156$	19135.3	+	7467.39i	0.786296	+	0.306845i
$157$	−2619.07			−0.106255			−0.0531273	−	0.998588i	$-0.516919\pi$
$157$	−2619.07			−0.106255			−0.0531273	+	0.998588i	$0.516919\pi$
$158$	8476.21	+	12406.5i	0.339537	+	0.496977i
$159$			9188.64i			0.363460i
$160$		0			0
$161$	−32485.3			−1.25324
$162$	−2407.72	+	1644.97i	−0.0917438	+	0.0626798i
$163$			7123.14i			0.268100i	0.990975	+	0.134050i	$0.0427982\pi$
$163$			7123.14i			0.268100i	−0.990975	+	0.134050i	$0.957202\pi$
$164$	3151.59	−	8075.99i	0.117177	−	0.300267i
$165$		0			0
$166$	−23543.0	−	34459.7i	−0.854371	−	1.25053i
$167$		−	48670.8i		−	1.74516i	−0.488472	−	0.872580i	$-0.662445\pi$
$167$		−	48670.8i		−	1.74516i	0.488472	−	0.872580i	$-0.337555\pi$
$168$	−4263.20	−	18431.8i	−0.151049	−	0.653053i
$169$	32480.8			1.13724
$170$		0			0
$171$		−	798.119i		−	0.0272945i
$172$	46162.4	+	18014.5i	1.56039	+	0.608928i
$173$	27575.9			0.921377			0.460689	−	0.887562i	$-0.347603\pi$
$173$	27575.9			0.921377			0.460689	+	0.887562i	$0.347603\pi$
$174$	235.545	+	344.764i	0.00777991	+	0.0113874i
$175$		0			0
$176$	−23332.5	+	25342.3i	−0.753245	+	0.818126i
$177$	13421.6			0.428408
$178$	39380.7	−	26905.1i	1.24292	−	0.849169i
$179$		−	42280.0i		−	1.31956i	−0.751459	−	0.659780i	$-0.770649\pi$
$179$		−	42280.0i		−	1.31956i	0.751459	−	0.659780i	$-0.229351\pi$
$180$		0			0
$181$	−1006.79			−0.0307313			−0.0153657	−	0.999882i	$-0.504891\pi$
$181$	−1006.79			−0.0307313			−0.0153657	+	0.999882i	$0.504891\pi$
$182$	−31715.1	−	46421.1i	−0.957466	−	1.40143i
$183$			12488.1i			0.372901i
$184$	35606.4	−	8235.62i	1.05170	−	0.243254i
$185$		0			0
$186$	−8147.29	+	5566.27i	−0.235498	+	0.160894i
$187$		−	12421.5i		−	0.355214i
$188$	−15652.9	−	6108.43i	−0.442874	−	0.172828i
$189$	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	$-0.0301766\pi$
$192$	9345.59	+	19121.8i	0.253515	+	0.518713i
$193$	−28207.8			−0.757278			−0.378639	−	0.925545i	$-0.623608\pi$
$193$	−28207.8			−0.757278			−0.378639	+	0.925545i	$0.623608\pi$
$194$	−7262.99	+	4962.11i	−0.192980	+	0.131845i
$195$		0			0
$196$	−4858.45	+	12449.8i	−0.126469	+	0.324080i
$197$	−38453.6			−0.990843			−0.495422	−	0.868653i	$-0.664986\pi$
$197$	−38453.6			−0.990843			−0.495422	+	0.868653i	$0.664986\pi$
$198$	−8198.10	−	11999.5i	−0.209114	−	0.306078i
$199$		−	5490.10i		−	0.138635i	−0.997595	−	0.0693176i	$-0.977918\pi$
$199$		−	5490.10i		−	0.138635i	0.997595	−	0.0693176i	$-0.0220822\pi$
$200$		0			0
$201$	−1973.58			−0.0488498
$202$	2889.38	−	1974.04i	0.0708113	−	0.0483787i
$203$		−	1142.83i		−	0.0277326i
$204$	−7149.50	−	2790.03i	−0.171797	−	0.0670423i
$205$		0			0
$206$	−6852.77	−	10030.3i	−0.161485	−	0.236363i
$207$			15418.0i			0.359822i
$208$	46530.8	+	42840.7i	1.07551	+	0.990215i
$209$	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	$-0.174778\pi$
$212$	−10285.9	+	26357.8i	−0.228861	+	0.586458i
$213$	−3650.38			−0.0804599
$214$	43003.0	+	62943.1i	0.939013	+	1.37442i
$215$		0			0
$216$	−8748.00	+	2023.38i	−0.187500	+	0.0433680i
$217$	27006.9			0.573529
$218$	43374.2	−	29633.5i	0.912681	−	0.623548i
$219$			51051.8i			1.06444i
$220$		0			0
$221$	−22807.0			−0.466964
$222$	8862.53	+	12972.0i	0.179826	+	0.263209i
$223$		−	48307.2i		−	0.971409i	−0.874123	−	0.485704i	$-0.838563\pi$
$223$		−	48307.2i		−	0.971409i	0.874123	−	0.485704i	$-0.161437\pi$
$224$	8403.75	−	57644.1i	0.167486	−	1.14884i
$225$		0			0
$226$	48027.4	−	32812.6i	0.940313	−	0.642427i
$227$			19108.6i			0.370832i	0.982660	+	0.185416i	$0.0593633\pi$
$227$			19108.6i			0.370832i	−0.982660	+	0.185416i	$0.940637\pi$
$228$	893.427	−	2289.42i	0.0171866	−	0.0440408i
$229$	−73378.5			−1.39926			−0.699629	−	0.714506i	$-0.746651\pi$
$229$	−73378.5			−1.39926			−0.699629	+	0.714506i	$0.746651\pi$
$230$		0			0
$231$			39776.2i			0.745417i
$232$	289.730	+	1252.63i	0.00538291	+	0.0232728i
$233$	34041.9			0.627049			0.313524	−	0.949580i	$-0.398490\pi$
$233$	34041.9			0.627049			0.313524	+	0.949580i	$0.398490\pi$
$234$	−22032.1	+	15052.5i	−0.402369	+	0.274901i
$235$		0			0
$236$	38500.0	+	15024.3i	0.691253	+	0.269756i
$237$	−19518.8			−0.347501
$238$	11849.7	+	17344.2i	0.209196	+	0.306197i
$239$		−	35114.3i		−	0.614735i	−0.951591	−	0.307368i	$-0.900552\pi$
$239$		−	35114.3i		−	0.614735i	0.951591	−	0.307368i	$-0.0994482\pi$
$240$		0			0
$241$	−19621.0			−0.337821			−0.168910	−	0.985631i	$-0.554025\pi$
$241$	−19621.0			−0.337821			−0.168910	+	0.985631i	$0.554025\pi$
$242$	11446.3	−	7820.17i	0.195449	−	0.133532i
$243$		−	3788.00i		−	0.0641500i
$244$	−13979.3	+	35822.2i	−0.234805	+	0.601690i
$245$		0			0
$246$	6352.85	+	9298.60i	0.104978	+	0.153655i
$247$		−	7303.28i		−	0.119708i
$248$	−29601.6	+	6846.74i	−0.481296	+	0.111322i
$249$	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	$0.998583\pi$
$252$	22894.2	+	8934.27i	0.360516	+	0.140688i
$253$	−76839.4			−1.20045
$254$	−58577.5	−	85739.2i	−0.907952	−	1.32896i
$255$		0			0
$256$	5402.70	+	65312.9i	0.0824386	+	0.996596i
$257$	−80511.1			−1.21896			−0.609480	−	0.792801i	$-0.708622\pi$
$257$	−80511.1			−1.21896			−0.609480	+	0.792801i	$0.708622\pi$
$258$	−53150.9	+	36313.0i	−0.798493	+	0.545534i
$259$		−	42999.9i		−	0.641015i
$260$		0			0
$261$	−542.406			−0.00796240
$262$	−37097.1	−	54298.6i	−0.540427	−	0.791017i
$263$			34821.7i			0.503430i	0.967801	+	0.251715i	$0.0809945\pi$
$263$			34821.7i			0.503430i	−0.967801	+	0.251715i	$0.919005\pi$
$264$	−10084.0	−	43597.8i	−0.144685	−	0.625542i
$265$		0			0
$266$	−5553.99	+	3794.52i	−0.0784950	+	0.0536282i
$267$			61956.3i			0.869087i
$268$	−5661.26	−	2209.26i	−0.0788212	−	0.0307593i
$269$	−28469.5			−0.393438			−0.196719	−	0.980460i	$-0.563029\pi$
$269$	−28469.5			−0.393438			−0.196719	+	0.980460i	$0.563029\pi$
$270$		0			0
$271$		−	37653.7i		−	0.512706i	−0.966583	−	0.256353i	$-0.917479\pi$
$271$		−	37653.7i		−	0.512706i	0.966583	−	0.256353i	$-0.0825210\pi$
$272$	−17385.2	−	16006.5i	−0.234987	−	0.216351i
$273$	73032.8			0.979924
$274$	−104429.	+	71346.8i	−1.39098	+	0.950327i
$275$		0			0
$276$	−17259.2	+	44226.9i	−0.226570	+	0.580588i
$277$	−25920.1			−0.337814			−0.168907	−	0.985632i	$-0.554024\pi$
$277$	−25920.1			−0.337814			−0.168907	+	0.985632i	$0.554024\pi$
$278$	−29099.2	−	42592.1i	−0.376522	−	0.551112i
$279$		−	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	$0.397846\pi$
$282$	18022.6	−	12313.1i	0.226631	−	0.154835i
$283$		−	73403.9i		−	0.916530i	−0.888816	−	0.458265i	$-0.848471\pi$
$283$		−	73403.9i		−	0.916530i	0.888816	−	0.458265i	$-0.151529\pi$
$284$	−10471.2	−	4086.30i	−0.129825	−	0.0506633i
$285$		0			0
$286$	−75017.6	−	109802.i	−0.917131	−	1.34239i
$287$		−	30823.3i		−	0.374209i
$288$	−27358.8	−	3988.55i	−0.329847	−	0.0480873i
$289$	−74999.6			−0.897974
$290$		0			0
$291$		−	11426.6i		−	0.134937i
$292$	−57148.2	+	146443.i	−0.670250	+	1.71752i
$293$	130683.			1.52224			0.761120	−	0.648611i	$-0.224650\pi$
$293$	130683.			1.52224			0.761120	+	0.648611i	$0.224650\pi$
$294$	−9793.48	−	14334.6i	−0.113303	−	0.165841i
$295$		0			0
$296$	10901.3	+	47131.2i	0.124421	+	0.537929i
$297$	18878.4			0.214019
$298$	−103954.	+	71022.0i	−1.17060	+	0.799761i
$299$			141084.i			1.57811i
$300$		0			0
$301$	176186.			1.94464
$302$	−89083.9	−	130391.i	−0.976754	−	1.42966i
$303$			4545.78i			0.0495134i
$304$	5125.62	−	5567.12i	0.0554625	−	0.0602398i
$305$		0			0
$306$	8231.84	−	5624.04i	0.0879132	−	0.0600628i
$307$		−	139512.i		−	1.48025i	−0.672469	−	0.740126i	$-0.734766\pi$
$307$		−	139512.i		−	1.48025i	0.672469	−	0.740126i	$-0.265234\pi$
$308$	−44526.1	+	114099.i	−0.469368	+	1.20276i
$309$	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	$-0.239130\pi$
$312$	−80049.5	+	18515.2i	−0.822337	+	0.190203i
$313$	−39526.3			−0.403458			−0.201729	−	0.979441i	$-0.564656\pi$
$313$	−39526.3			−0.403458			−0.201729	+	0.979441i	$0.564656\pi$
$314$	8650.20	−	5909.86i	0.0877338	−	0.0599402i
$315$		0			0
$316$	−55990.0	−	21849.7i	−0.560708	−	0.218812i
$317$	91959.1			0.915116			0.457558	−	0.889180i	$-0.348724\pi$
$317$	91959.1			0.915116			0.457558	+	0.889180i	$0.348724\pi$
$318$	−20733.9	−	30348.0i	−0.205035	−	0.300107i
$319$		−	2703.21i		−	0.0265643i
$320$		0			0
$321$	−99026.4			−0.961039
$322$	107292.	−	73302.2i	1.03479	−	0.706977i
$323$			2728.72i			0.0261549i
$324$	4240.34	−	10865.9i	0.0403934	−	0.103509i
$325$		0			0
$326$	−16073.2	−	23526.1i	−0.151240	−	0.221368i
$327$			68239.3i			0.638174i
$328$	7814.26	+	33784.7i	0.0726341	+	0.314031i
$329$	−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	$0.995287\pi$
$332$	155515.	+	60688.4i	1.41090	+	0.550591i
$333$	−20408.4			−0.184044
$334$	109824.	+	160749.i	0.984477	+	1.44097i
$335$		0			0
$336$	55671.2	+	51256.2i	0.493119	+	0.454013i
$337$	−5591.21			−0.0492318			−0.0246159	−	0.999697i	$-0.507836\pi$
$337$	−5591.21			−0.0492318			−0.0246159	+	0.999697i	$0.507836\pi$
$338$	−107277.	+	73292.1i	−0.939016	+	0.641540i
$339$			75560.0i			0.657495i
$340$		0			0
$341$	63881.0			0.549367
$342$	1800.94	+	2636.01i	0.0153973	+	0.0225369i
$343$		−	89071.8i		−	0.757098i
$344$	−193113.	+	44666.4i	−1.63191	+	0.377454i
$345$		0			0
$346$	−91077.0	+	62224.3i	−0.760775	+	0.519766i
$347$			170630.i			1.41708i	0.705668	+	0.708542i	$0.250647\pi$
$347$			170630.i			1.41708i	−0.705668	+	0.708542i	$0.749353\pi$
$348$	−1555.90	−	607.178i	−0.0128477	−	0.00501369i
$349$	−96101.4			−0.789003			−0.394502	−	0.918895i	$-0.629083\pi$
$349$	−96101.4			−0.789003			−0.394502	+	0.918895i	$0.629083\pi$
$350$		0			0
$351$		−	34662.5i		−	0.281349i
$352$	19877.9	−	136349.i	0.160430	−	1.10044i
$353$	−205914.			−1.65248			−0.826242	−	0.563316i	$-0.809526\pi$
$353$	−205914.			−1.65248			−0.826242	+	0.563316i	$0.809526\pi$
$354$	−44328.5	+	30285.4i	−0.353734	+	0.241673i
$355$		0			0
$356$	−69354.9	+	177723.i	−0.547239	+	1.40231i
$357$	−27287.2			−0.214103
$358$	95403.8	+	139641.i	0.744388	+	1.08955i
$359$		−	78435.2i		−	0.608586i	−0.952578	−	0.304293i	$-0.901580\pi$
$359$		−	78435.2i		−	0.608586i	0.952578	−	0.304293i	$-0.0984202\pi$
$360$		0			0
$361$	129447.			0.993295
$362$	3325.20	−	2271.79i	0.0253747	−	0.0173361i
$363$			18008.1i			0.136664i
$364$	209496.	+	81754.0i	1.58115	+	0.617030i
$365$		0			0
$366$	−28179.0	−	41245.3i	−0.210360	−	0.307902i
$367$			221785.i			1.64664i	0.567574	+	0.823322i	$0.307882\pi$
$367$			221785.i			1.64664i	−0.567574	+	0.823322i	$0.692118\pi$
$368$	−99016.5	+	107545.i	−0.731159	+	0.794138i
$369$	−14629.2			−0.107440
$370$		0			0
$371$			100599.i			0.730876i
$372$	14348.5	−	36768.3i	0.103686	−	0.265698i
$373$	25883.8			0.186042			0.0930208	−	0.995664i	$-0.470348\pi$
$373$	25883.8			0.186042			0.0930208	+	0.995664i	$0.470348\pi$
$374$	28028.7	+	41025.4i	0.200383	+	0.293298i
$375$		0			0
$376$	65481.6	−	15145.6i	0.463173	−	0.107130i
$377$	−4963.35			−0.0349214
$378$	−26360.1	+	18009.3i	−0.184486	+	0.126042i
$379$		−	147801.i		−	1.02896i	−0.857503	−	0.514479i	$-0.827985\pi$
$379$		−	147801.i		−	1.02896i	0.857503	−	0.514479i	$-0.172015\pi$
$380$		0			0
$381$	134891.			0.929249
$382$	15584.6	+	22811.0i	0.106800	+	0.156321i
$383$		−	226231.i		−	1.54225i	−0.636683	−	0.771126i	$-0.719694\pi$
$383$		−	226231.i		−	1.54225i	0.636683	−	0.771126i	$-0.280306\pi$
$384$	−74014.3	−	42067.1i	−0.501942	−	0.285286i
$385$		0			0
$386$	93164.2	−	63650.2i	0.625280	−	0.427194i
$387$		−	83620.6i		−	0.558330i
$388$	12791.2	−	32777.5i	0.0849662	−	0.217727i
$389$	256419.			1.69453			0.847267	−	0.531167i	$-0.178246\pi$
$389$	256419.			1.69453			0.847267	+	0.531167i	$0.178246\pi$
$390$		0			0
$391$		−	52713.2i		−	0.344799i
$392$	−12046.4	−	52082.0i	−0.0783943	−	0.338934i
$393$	85426.3			0.553103
$394$	127004.	−	86769.6i	0.818133	−	0.558953i
$395$		0			0
$396$	54153.0	+	21132.8i	0.345328	+	0.134761i
$397$	56667.7			0.359546			0.179773	−	0.983708i	$-0.442464\pi$
$397$	56667.7			0.359546			0.179773	+	0.983708i	$0.442464\pi$
$398$	12388.3	+	18132.6i	0.0782067	+	0.114470i
$399$		−	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	$0.489198\pi$
$402$	6518.30	−	4453.34i	0.0403350	−	0.0275571i
$403$		−	117291.i		−	0.722198i
$404$	−5088.61	+	13039.6i	−0.0311772	+	0.0798919i
$405$		0			0
$406$	2578.77	+	3774.52i	0.0156445	+	0.0228987i
$407$		−	101710.i		−	0.614010i
$408$	29908.8	−	6917.80i	0.179671	−	0.0415573i
$409$	−289576.			−1.73108			−0.865538	−	0.500844i	$-0.833023\pi$
$409$	−289576.			−1.73108			−0.865538	+	0.500844i	$0.833023\pi$
$410$		0			0
$411$		−	164296.i		−	0.972618i
$412$	45266.3	+	17664.8i	0.266674	+	0.104067i
$413$	146941.			0.861477
$414$	−34790.4	−	50922.3i	−0.202982	−	0.297103i
$415$		0			0
$416$	−250350.	−	36497.7i	−1.44664	−	0.210901i
$417$	67008.8			0.385354
$418$	−13137.2	+	8975.39i	−0.0751882	+	0.0513690i
$419$			69837.9i			0.397798i	0.980020	+	0.198899i	$0.0637366\pi$
$419$			69837.9i			0.397798i	−0.980020	+	0.198899i	$0.936263\pi$
$420$		0			0
$421$	16207.0			0.0914405			0.0457203	−	0.998954i	$-0.485442\pi$
$421$	16207.0			0.0914405			0.0457203	+	0.998954i	$0.485442\pi$
$422$	104862.	+	153485.i	0.588832	+	0.861867i
$423$			28354.4i			0.158467i
$424$	−25503.6	−	110264.i	−0.141863	−	0.613339i
$425$		0			0
$426$	12056.4	−	8236.99i	0.0664352	−	0.0453889i
$427$			136721.i			0.749859i
$428$	−284059.	−	110852.i	−1.55067	−	0.605138i
$429$	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	$-0.0914395\pi$
$432$	24327.0	−	26422.4i	0.130353	−	0.141581i
$433$	−131799.			−0.702970			−0.351485	−	0.936193i	$-0.614323\pi$
$433$	−131799.			−0.702970			−0.351485	+	0.936193i	$0.614323\pi$
$434$	−89197.7	+	60940.3i	−0.473559	+	0.323538i
$435$		0			0
$436$	−76388.1	+	195746.i	−0.401840	+	1.02972i
$437$	16879.9			0.0883906
$438$	−115197.	−	168613.i	−0.600473	−	0.878905i
$439$		−	149053.i		−	0.773414i	−0.922203	−	0.386707i	$-0.873612\pi$
$439$		−	149053.i		−	0.773414i	0.922203	−	0.386707i	$-0.126388\pi$
$440$		0			0
$441$	22552.2			0.115961
$442$	75326.4	−	51463.4i	0.385569	−	0.263423i
$443$			248933.i			1.26845i	0.773147	+	0.634227i	$0.218682\pi$
$443$			248933.i			1.26845i	−0.773147	+	0.634227i	$0.781318\pi$
$444$	−58541.9	−	22845.5i	−0.296962	−	0.115887i
$445$		0			0
$446$	109004.	+	159548.i	0.547990	+	0.802086i
$447$		−	163548.i		−	0.818520i
$448$	102317.	+	209349.i	0.509789	+	1.04307i
$449$	243749.			1.20906			0.604532	−	0.796581i	$-0.293360\pi$
$449$	243749.			1.20906			0.604532	+	0.796581i	$0.293360\pi$
$450$		0			0
$451$		−	72908.1i		−	0.358445i
$452$	−84583.1	+	216745.i	−0.414006	+	1.06090i
$453$	205140.			0.999665
$454$	−43118.1	−	63111.5i	−0.209193	−	0.306194i
$455$		0			0
$456$	2215.22	+	9577.43i	0.0106534	+	0.0460595i
$457$	−343278.			−1.64367			−0.821833	−	0.569729i	$-0.807048\pi$
$457$	−343278.			−1.64367			−0.821833	+	0.569729i	$0.807048\pi$
$458$	242353.	−	165577.i	1.15536	−	0.789347i
$459$			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	$0.619239\pi$
$462$	−89753.9	−	131372.i	−0.420503	−	0.615486i
$463$		−	321457.i		−	1.49955i	−0.661694	−	0.749774i	$-0.730162\pi$
$463$		−	321457.i		−	1.49955i	0.661694	−	0.749774i	$-0.269838\pi$
$464$	−3783.45	−	3483.40i	−0.0175732	−	0.0161796i
$465$		0			0
$466$	−112433.	+	76814.6i	−0.517750	+	0.353730i
$467$			81219.7i			0.372415i	0.982510	+	0.186208i	$0.0596197\pi$
$467$			81219.7i			0.372415i	−0.982510	+	0.186208i	$0.940380\pi$
$468$	38801.7	−	99429.9i	0.177157	−	0.453968i
$469$	−21607.1			−0.0982313
$470$		0			0
$471$			13609.1i			0.0613461i
$472$	−161059.	+	37252.3i	−0.722938	+	0.167213i
$473$	416743.			1.86271
$474$	64466.3	−	44043.7i	0.286930	−	0.196032i
$475$		0			0
$476$	−78273.7	−	30545.7i	−0.345463	−	0.134814i
$477$	47745.6			0.209844
$478$	79234.5	+	115975.i	0.346784	+	0.507583i
$479$			346051.i			1.50824i	0.656738	+	0.754119i	$0.271936\pi$
$479$			346051.i			1.50824i	−0.656738	+	0.754119i	$0.728064\pi$
$480$		0			0
$481$	−186749.			−0.807178
$482$	64803.6	−	44274.2i	0.278936	−	0.190571i
$483$			168799.i			0.723560i
$484$	−20158.5	+	51656.5i	−0.0860534	+	0.220513i
$485$		0			0
$486$	8547.51	+	12510.9i	0.0361882	+	0.0529683i
$487$		−	94439.7i		−	0.398196i	−0.979980	−	0.199098i	$-0.936199\pi$
$487$		−	94439.7i		−	0.398196i	0.979980	−	0.199098i	$-0.0638012\pi$
$488$	−34661.3	−	149857.i	−0.145548	−	0.629270i
$489$	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	$-0.118746\pi$
$492$	−41964.1	−	16376.1i	−0.173359	−	0.0676521i
$493$	1854.45			0.00762995
$494$	16479.7	+	24121.1i	0.0675296	+	0.0988424i
$495$		0			0
$496$	82318.0	−	89408.5i	0.334604	−	0.363426i
$497$	−39964.9			−0.161795
$498$	−179058.	+	122333.i	−0.721996	+	0.493271i
$499$		−	37294.6i		−	0.149777i	−0.997192	−	0.0748885i	$-0.976140\pi$
$499$		−	37294.6i		−	0.149777i	0.997192	−	0.0748885i	$-0.0238601\pi$
$500$		0			0
$501$	−252901.			−1.00757
$502$	−1265.27	−	1851.96i	−0.00502084	−	0.00734894i
$503$		−	250727.i		−	0.990979i	−0.868614	−	0.495489i	$-0.834989\pi$
$503$		−	250727.i		−	0.990979i	0.868614	−	0.495489i	$-0.165011\pi$
$504$	−95774.3	+	22152.2i	−0.377040	+	0.0872080i
$505$		0			0
$506$	253783.	−	173386.i	0.991202	−	0.677194i
$507$		−	168775.i		−	0.656588i
$508$	386936.	+	150999.i	1.49938	+	0.585121i
$509$	151144.			0.583383			0.291692	−	0.956512i	$-0.405782\pi$
$509$	151144.			0.583383			0.291692	+	0.956512i	$0.405782\pi$
$510$		0			0
$511$			558922.i			2.14047i
$512$	−165221.	−	203523.i	−0.630267	−	0.776378i
$513$	−4147.15			−0.0157585
$514$	265910.	−	181671.i	1.00649	−	0.687638i
$515$		0			0
$516$	93606.2	−	239867.i	0.351565	−	0.900889i
$517$	−141311.			−0.528682
$518$	97028.2	+	142019.i	0.361608	+	0.529282i
$519$		−	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	$0.607399\pi$
$522$	1791.45	−	1223.93i	0.00657450	−	0.00449173i
$523$			305226.i			1.11588i	0.829881	+	0.557941i	$0.188408\pi$
$523$			305226.i			1.11588i	−0.829881	+	0.557941i	$0.811592\pi$
$524$	245047.	+	95627.5i	0.892455	+	0.348273i
$525$		0			0
$526$	−78574.3	−	115008.i	−0.283994	−	0.415679i
$527$			43823.5i			0.157792i
$528$	131682.	+	121239.i	0.472346	+	0.434886i
$529$	−46243.2			−0.165248
$530$		0			0
$531$		−	69740.6i		−	0.247341i
$532$	9781.36	−	25064.9i	0.0345602	−	0.0885609i
$533$	−133866.			−0.471211
$534$	−139803.	−	204628.i	−0.490268	−	0.717600i
$535$		0			0
$536$	23683.0	−	5477.79i	0.0824341	−	0.0190667i
$537$	−219694.			−0.761849
$538$	94028.5	−	64240.8i	0.324859	−	0.221945i
$539$			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	$0.660051\pi$
$542$	84964.5	+	124362.i	0.289227	+	0.423338i
$543$			5231.43i			0.0177427i
$544$	93537.9	+	13636.6i	0.316075	+	0.0460795i
$545$		0			0
$546$	−241211.	+	164797.i	−0.809117	+	0.552793i
$547$		−	296270.i		−	0.990176i	−0.868843	−	0.495088i	$-0.835136\pi$
$547$		−	296270.i		−	0.990176i	0.868843	−	0.495088i	$-0.164864\pi$
$548$	183915.	−	471285.i	0.612430	−	1.56936i
$549$	64889.9			0.215294
$550$		0			0
$551$			593.834i			0.00195597i
$552$	−42793.6	−	185016.i	−0.140443	−	0.607200i
$553$	−213695.			−0.698785
$554$	85608.4	−	58488.1i	0.278931	−	0.190567i
$555$		0			0
$556$	192216.	+	75010.7i	0.621785	+	0.242646i
$557$	116573.			0.375739			0.187869	−	0.982194i	$-0.439842\pi$
$557$	116573.			0.375739			0.187869	+	0.982194i	$0.439842\pi$
$558$	28923.2	+	42334.6i	0.0928919	+	0.135965i
$559$		−	765179.i		−	2.44872i
$560$		0			0
$561$	−64543.9			−0.205083
$562$	−164530.	+	112408.i	−0.520921	+	0.355896i
$563$		−	117383.i		−	0.370329i	−0.982708	−	0.185164i	$-0.940718\pi$
$563$		−	117383.i		−	0.370329i	0.982708	−	0.185164i	$-0.0592817\pi$
$564$	−31740.3	+	81335.0i	−0.0997822	+	0.255693i
$565$		0			0
$566$	165634.	+	242437.i	0.517031	+	0.756773i
$567$		−	41471.5i		−	0.128998i
$568$	43804.6	−	10131.8i	0.135776	−	0.0314045i
$569$	−222193.			−0.686288			−0.343144	−	0.939283i	$-0.611492\pi$
$569$	−222193.			−0.686288			−0.343144	+	0.939283i	$0.611492\pi$
$570$		0			0
$571$			117091.i			0.359131i	0.983746	+	0.179565i	$0.0574691\pi$
$571$			117091.i			0.359131i	−0.983746	+	0.179565i	$0.942531\pi$
$572$	495533.	+	193378.i	1.51454	+	0.591036i
$573$	−35887.9			−0.109305
$574$	69551.9	+	101802.i	0.211098	+	0.308982i
$575$		0			0
$576$	99360.0	−	48561.1i	0.299479	−	0.146367i
$577$	335932.			1.00902			0.504510	−	0.863406i	$-0.331673\pi$
$577$	335932.			1.00902			0.504510	+	0.863406i	$0.331673\pi$
$578$	247707.	−	169235.i	0.741451	−	0.506563i
$579$			146572.i			0.437214i
$580$		0			0
$581$	593546.			1.75834
$582$	25783.9	+	37739.6i	0.0761207	+	0.111417i
$583$			237952.i			0.700086i
$584$	−141697.	−	612622.i	−0.415466	−	1.79625i
$585$		0			0
$586$	−431616.	+	294882.i	−1.25690	+	0.858723i
$587$			396842.i			1.15170i	0.817554	+	0.575852i	$0.195330\pi$
$587$			396842.i			1.15170i	−0.817554	+	0.575852i	$0.804670\pi$
$588$	64691.3	+	25245.3i	0.187108	+	0.0730172i
$589$	−14033.2			−0.0404507
$590$		0			0
$591$			199811.i			0.572064i
$592$	−142355.	−	131065.i	−0.406189	−	0.373977i
$593$	−13679.6			−0.0389012			−0.0194506	−	0.999811i	$-0.506192\pi$
$593$	−13679.6			−0.0389012			−0.0194506	+	0.999811i	$0.506192\pi$
$594$	−62351.1	+	42598.6i	−0.176714	+	0.120732i
$595$		0			0
$596$	183078.	−	469139.i	0.515399	−	1.32072i
$597$	−28527.4			−0.0800411
$598$	−318353.	−	465970.i	−0.890239	−	1.30303i
$599$			124021.i			0.345654i	0.984952	+	0.172827i	$0.0552902\pi$
$599$			124021.i			0.345654i	−0.984952	+	0.172827i	$0.944710\pi$
$600$		0			0
$601$	484678.			1.34185			0.670926	−	0.741525i	$-0.265897\pi$
$601$	484678.			1.34185			0.670926	+	0.741525i	$0.265897\pi$
$602$	−581903.	+	397559.i	−1.60567	+	1.09701i
$603$			10255.0i			0.0282035i
$604$	588448.	+	229637.i	1.61300	+	0.629460i
$605$		0			0
$606$	−10257.4	−	15013.7i	−0.0279314	−	0.0408829i
$607$		−	298924.i		−	0.811303i	−0.914028	−	0.405651i	$-0.867045\pi$
$607$		−	298924.i		−	0.811303i	0.914028	−	0.405651i	$-0.132955\pi$
$608$	−4366.72	+	29952.8i	−0.0118127	+	0.0810271i
$609$	−5938.34			−0.0160114
$610$		0			0
$611$			259460.i			0.695004i
$612$	−14497.4	+	37149.9i	−0.0387069	+	0.0991870i
$613$	155694.			0.414334			0.207167	−	0.978306i	$-0.433576\pi$
$613$	155694.			0.414334			0.207167	+	0.978306i	$0.433576\pi$
$614$	314806.	+	460777.i	0.835037	+	1.22223i
$615$		0			0
$616$	−110401.	−	477314.i	−0.290945	−	1.25789i
$617$	625050.			1.64189			0.820946	−	0.571007i	$-0.193447\pi$
$617$	625050.			1.64189			0.820946	+	0.571007i	$0.193447\pi$
$618$	−52119.1	+	35608.0i	−0.136465	+	0.0932333i
$619$			368822.i			0.962576i	0.876563	+	0.481288i	$0.159831\pi$
$619$			368822.i			0.962576i	−0.876563	+	0.481288i	$0.840169\pi$
$620$		0			0
$621$	80114.4			0.207743
$622$	297932.	+	436079.i	0.770080	+	1.12716i
$623$			678307.i			1.74763i
$624$	222607.	−	241781.i	0.571701	−	0.620945i
$625$		0			0
$626$	130547.	−	89190.1i	0.333133	−	0.227598i
$627$		−	20668.3i		−	0.0525739i
$628$	−15234.2	+	39037.9i	−0.0386279	+	0.0989845i
$629$	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	$0.805350\pi$
$632$	234226.	−	54175.5i	0.586409	−	0.135634i
$633$	−241473.			−0.602644
$634$	−303720.	+	207503.i	−0.755606	+	0.516234i
$635$		0			0
$636$	136959.	+	53447.1i	0.338592	+	0.132133i
$637$	206366.			0.508580
$638$	6099.73	+	8928.11i	0.0149854	+	0.0219340i
$639$			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	$0.847184\pi$
$642$	327062.	−	223450.i	0.793524	−	0.542140i
$643$			201261.i			0.486786i	0.969928	+	0.243393i	$0.0782604\pi$
$643$			201261.i			0.486786i	−0.969928	+	0.243393i	$0.921740\pi$
$644$	−188956.	+	484202.i	−0.455605	+	1.16749i
$645$		0			0
$646$	−6157.28	−	9012.34i	−0.0147545	−	0.0215960i
$647$			284857.i			0.680484i	0.940338	+	0.340242i	$0.110509\pi$
$647$			284857.i			0.680484i	−0.940338	+	0.340242i	$0.889491\pi$
$648$	10513.8	+	45455.9i	0.0250386	+	0.108253i
$649$	347569.			0.825186
$650$		0			0
$651$		−	140332.i		−	0.331127i
$652$	106172.	+	41432.8i	0.249756	+	0.0974652i
$653$	−639617.			−1.50001			−0.750005	−	0.661433i	$-0.769949\pi$
$653$	−639617.			−1.50001			−0.750005	+	0.661433i	$0.769949\pi$
$654$	−153980.	−	225379.i	−0.360006	−	0.526936i
$655$		0			0
$656$	−102043.	−	93950.5i	−0.237124	−	0.218319i
$657$	265273.			0.614557
$658$	197314.	−	134806.i	0.455728	−	0.311356i
$659$			372398.i			0.857505i	0.903422	+	0.428753i	$0.141047\pi$
$659$			372398.i			0.857505i	−0.903422	+	0.428753i	$0.858953\pi$
$660$		0			0
$661$	−137125.			−0.313843			−0.156922	−	0.987611i	$-0.550157\pi$
$661$	−137125.			−0.313843			−0.156922	+	0.987611i	$0.550157\pi$
$662$	−7320.19	−	10714.5i	−0.0167035	−	0.0244487i
$663$			118509.i			0.269602i
$664$	−650572.	+	150475.i	−1.47557	+	0.341293i
$665$		0			0
$666$	67404.4	−	46051.0i	0.151964	−	0.103822i
$667$		−	11471.7i		−	0.0257854i
$668$	−725450.	−	283101.i	−1.62575	−	0.634437i
$669$	−251011.			−0.560843
$670$		0			0
$671$			323394.i			0.718269i
$672$	−299528.	−	43667.2i	−0.663283	−	0.0966978i
$673$	−840931.			−1.85665			−0.928325	−	0.371770i	$-0.878751\pi$
$673$	−840931.			−1.85665			−0.928325	+	0.371770i	$0.878751\pi$
$674$	18466.5	−	12616.4i	0.0406504	−	0.0277726i
$675$		0			0
$676$	188930.	−	484135.i	0.413435	−	1.05943i
$677$	−207006.			−0.451653			−0.225827	−	0.974168i	$-0.572508\pi$
$677$	−207006.			−0.451653			−0.225827	+	0.974168i	$0.572508\pi$
$678$	−170499.	−	249558.i	−0.370905	−	0.542890i
$679$		−	125100.i		−	0.271343i
$680$		0			0
$681$	99291.3			0.214100
$682$	−210985.	+	144146.i	−0.453609	+	0.309908i
$683$			241334.i			0.517341i	0.965966	+	0.258670i	$0.0832844\pi$
$683$			241334.i			0.517341i	−0.965966	+	0.258670i	$0.916716\pi$
$684$	−11896.2	−	4642.38i	−0.0254270	−	0.00992268i
$685$		0			0
$686$	200988.	+	294184.i	0.427093	+	0.625131i
$687$			381286.i			0.807862i
$688$	537022.	−	583279.i	1.13453	−	1.23225i
$689$	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	$-0.228528\pi$
$692$	160399.	−	411026.i	0.334958	−	0.858335i
$693$	206683.			0.430367
$694$	−385022.	−	563552.i	−0.799404	−	1.17008i
$695$		0			0
$696$	6508.88	−	1505.48i	0.0134365	−	0.00310782i
$697$	50016.2			0.102954
$698$	317401.	−	216850.i	0.651475	−	0.445091i
$699$		−	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	$0.658842\pi$
$702$	78214.9	+	114482.i	0.158714	+	0.232308i
$703$			22343.4i			0.0452105i
$704$	242016.	+	495184.i	0.488313	+	0.999129i
$705$		0			0
$706$	680089.	−	464640.i	1.36445	−	0.932196i
$707$			49767.8i			0.0995656i
$708$	78068.7	−	200052.i	0.155744	−	0.399095i
$709$	−666498.			−1.32589			−0.662944	−	0.748669i	$-0.730693\pi$
$709$	−666498.			−1.32589			−0.662944	+	0.748669i	$0.730693\pi$
$710$		0			0
$711$			101423.i			0.200630i
$712$	−171963.	−	743476.i	−0.339215	−	1.46658i
$713$	271092.			0.533259
$714$	90123.4	−	61572.7i	0.176783	−	0.120779i
$715$		0			0
$716$	−630195.	−	245928.i	−1.22927	−	0.479714i
$717$	−182459.			−0.354918
$718$	176987.	+	259054.i	0.343315	+	0.502506i
$719$		−	551482.i		−	1.06678i	−0.845870	−	0.533388i	$-0.820918\pi$
$719$		−	551482.i		−	1.06678i	0.845870	−	0.533388i	$-0.179082\pi$
$720$		0			0
$721$	172766.			0.332344
$722$	−427535.	+	292094.i	−0.820158	+	0.560336i
$723$			101953.i			0.195041i
$724$	−5856.14	+	15006.4i	−0.0111721	+	0.0286286i
$725$		0			0
$726$	−40634.8	−	59476.7i	−0.0770947	−	0.112843i
$727$		−	735388.i		−	1.39139i	−0.718339	−	0.695694i	$-0.755097\pi$
$727$		−	735388.i		−	1.39139i	0.718339	−	0.695694i	$-0.244903\pi$
$728$	−876393.	+	202706.i	−1.65362	+	0.382477i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			285893.i			0.535019i
$732$	186138.	+	72638.8i	0.347386	+	0.135565i
$733$	−372734.			−0.693731			−0.346866	−	0.937915i	$-0.612754\pi$
$733$	−372734.			−0.693731			−0.346866	+	0.937915i	$0.612754\pi$
$734$	−500452.	−	732506.i	−0.928902	−	1.35962i
$735$		0			0
$736$	84356.0	−	578626.i	0.155726	−	1.06817i
$737$	−51108.4			−0.0940931
$738$	48316.9	−	33010.4i	0.0887129	−	0.0606091i
$739$			962125.i			1.76174i	0.473356	+	0.880871i	$0.343043\pi$
$739$			962125.i			1.76174i	−0.473356	+	0.880871i	$0.656957\pi$
$740$		0			0
$741$	−37949.0			−0.0691136
$742$	−226998.	−	332254.i	−0.412301	−	0.603480i
$743$		−	557423.i		−	1.00973i	−0.863197	−	0.504867i	$-0.831541\pi$
$743$		−	557423.i		−	1.00973i	0.863197	−	0.504867i	$-0.168459\pi$
$744$	35576.7	+	153815.i	0.0642717	+	0.277876i
$745$		0			0
$746$	−85488.3	+	58406.1i	−0.153613	+	0.104949i
$747$		−	281706.i		−	0.504841i
$748$	−185145.	−	72251.5i	−0.330910	−	0.129135i
$749$	−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	$-0.185212\pi$
$752$	−182095.	+	197780.i	−0.322005	+	0.349741i
$753$	2913.64			0.00513860
$754$	16392.8	−	11199.7i	0.0288344	−	0.0196998i
$755$		0			0
$756$	46423.8	−	118962.i	0.0812264	−	0.208144i
$757$	66502.8			0.116051			0.0580254	−	0.998315i	$-0.481520\pi$
$757$	66502.8			0.116051			0.0580254	+	0.998315i	$0.481520\pi$
$758$	333508.	+	488152.i	0.580454	+	0.849604i
$759$			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	$0.382750\pi$
$762$	−445514.	+	304377.i	−0.767275	+	0.524207i
$763$			747093.i			1.28329i
$764$	−102945.	−	40173.4i	−0.176367	−	0.0688260i
$765$		0			0
$766$	510485.	+	747192.i	0.870013	+	1.27343i
$767$		−	638169.i		−	1.08479i
$768$	339376.	−	28073.2i	0.575385	−	0.0475959i
$769$	−284602.			−0.481266			−0.240633	−	0.970616i	$-0.577355\pi$
$769$	−284602.			−0.481266			−0.240633	+	0.970616i	$0.577355\pi$
$770$		0			0
$771$			418348.i			0.703767i
$772$	−164075.	+	420445.i	−0.275301	+	0.705463i
$773$	−690220.			−1.15512			−0.577562	−	0.816347i	$-0.695996\pi$
$773$	−690220.			−1.15512			−0.577562	+	0.816347i	$0.695996\pi$
$774$	188688.	+	276180.i	0.314964	+	0.461010i
$775$		0			0
$776$	31715.3	+	137120.i	0.0526677	+	0.227707i
$777$	−223434.			−0.370090
$778$	−846893.	+	578602.i	−1.39917	+	0.955918i
$779$			16016.2i			0.0263928i
$780$		0			0
$781$	−94531.3			−0.154979
$782$	118946.	+	174100.i	0.194507	+	0.284698i
$783$			2818.43i			0.00459709i
$784$	157308.	+	144833.i	0.255929	+	0.235632i
$785$		0			0
$786$	−282144.	+	192762.i	−0.456694	+	0.312016i
$787$			855688.i			1.38155i	0.723071	+	0.690774i	$0.242730\pi$
$787$			855688.i			1.38155i	−0.723071	+	0.690774i	$0.757270\pi$
$788$	−223672.	+	573161.i	−0.360212	+	0.923048i
$789$	180939.			0.290655
$790$		0			0
$791$			827242.i			1.32215i
$792$	−226541.	+	52398.0i	−0.361157	+	0.0835342i
$793$	593782.			0.944236
$794$	−187161.	+	127869.i	−0.296875	+	0.202827i
$795$		0			0
$796$	−81831.3	−	31934.0i	−0.129150	−	0.0503996i
$797$	−579975.			−0.913046			−0.456523	−	0.889712i	$-0.650905\pi$
$797$	−579975.			−0.913046			−0.456523	+	0.889712i	$0.650905\pi$
$798$	19716.9	+	28859.4i	0.0309623	+	0.0453191i
$799$		−	96941.7i		−	0.151851i
$800$		0			0
$801$	321935.			0.501768
$802$	−36040.0	+	24622.7i	−0.0560320	+	0.0382814i
$803$			1.32205e6i			2.05030i
$804$	−11479.6	+	29416.7i	−0.0177589	+	0.0455075i
$805$		0			0
$806$	264665.	+	387387.i	0.407405	+	0.596314i
$807$			147932.i			0.227151i
$808$	−12617.1	−	54549.3i	−0.0193257	−	0.0835539i
$809$	−60860.6			−0.0929907			−0.0464953	−	0.998919i	$-0.514805\pi$
$809$	−60860.6			−0.0929907			−0.0464953	+	0.998919i	$0.514805\pi$
$810$		0			0
$811$		−	103330.i		−	0.157103i	−0.996910	−	0.0785515i	$-0.974970\pi$
$811$		−	103330.i		−	0.157103i	0.996910	−	0.0785515i	$-0.0250295\pi$
$812$	−17034.2	−	6647.47i	−0.0258351	−	0.0100819i
$813$	−195654.			−0.296011
$814$	229506.	+	335926.i	0.346375	+	0.506985i
$815$		0			0
$816$	−83172.3	+	90336.4i	−0.124910	+	0.135670i
$817$	−91549.0			−0.137154
$818$	956404.	−	653421.i	1.42934	−	0.976531i
$819$		−	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	$0.370529\pi$
$822$	370729.	+	542632.i	0.548672	+	0.803085i
$823$		−	728807.i		−	1.07600i	−0.842945	−	0.538000i	$-0.819180\pi$
$823$		−	728807.i		−	1.07600i	0.842945	−	0.538000i	$-0.180820\pi$
$824$	−189365.	+	43799.3i	−0.278897	+	0.0645079i
$825$		0			0
$826$	−485314.	+	331569.i	−0.711317	+	0.485975i
$827$		−	768434.i		−	1.12356i	−0.827287	−	0.561779i	$-0.810117\pi$
$827$		−	768434.i		−	1.12356i	0.827287	−	0.561779i	$-0.189883\pi$
$828$	229809.	+	89681.3i	0.335203	+	0.130810i
$829$	−401672.			−0.584471			−0.292235	−	0.956346i	$-0.594399\pi$
$829$	−401672.			−0.584471			−0.292235	+	0.956346i	$0.594399\pi$
$830$		0			0
$831$			134685.i			0.195037i
$832$	909205.	−	444364.i	1.31345	−	0.641936i
$833$	−77104.4			−0.111119
$834$	−221315.	+	151204.i	−0.318185	+	0.217385i
$835$		0			0
$836$	23136.4	−	59287.4i	0.0331043	−	0.0848301i
$837$	−66603.7			−0.0950708
$838$	−157587.	−	230659.i	−0.224405	−	0.328460i
$839$		−	429703.i		−	0.610443i	−0.952281	−	0.305221i	$-0.901270\pi$
$839$		−	429703.i		−	0.610443i	0.952281	−	0.305221i	$-0.0987305\pi$
$840$		0			0
$841$	−706877.			−0.999429
$842$	−53528.1	+	36570.7i	−0.0755019	+	0.0515833i
$843$		−	258849.i		−	0.364244i
$844$	−692669.	−	270308.i	−0.972391	−	0.379468i
$845$		0			0
$846$	−63980.9	−	93648.1i	−0.0893942	−	0.130845i
$847$			197155.i			0.274815i
$848$	333040.	+	306628.i	0.463132	+	0.426403i
$849$	−381418.			−0.529159
$850$		0			0
$851$		−	431629.i		−	0.596007i
$852$	−21233.0	+	54409.9i	−0.0292504	+	0.0749547i
$853$	732176.			1.00628			0.503138	−	0.864206i	$-0.332179\pi$
$853$	732176.			1.00628			0.503138	+	0.864206i	$0.332179\pi$
$854$	−308507.	−	451559.i	−0.423009	−	0.619154i
$855$		0			0
$856$	1.18832e6	−	274853.i	1.62175	−	0.375105i
$857$	−430159.			−0.585689			−0.292844	−	0.956160i	$-0.594602\pi$
$857$	−430159.			−0.585689			−0.292844	+	0.956160i	$0.594602\pi$
$858$	−570550.	+	389803.i	−0.775031	+	0.529506i
$859$			489975.i			0.664030i	0.943274	+	0.332015i	$0.107728\pi$
$859$			489975.i			0.664030i	−0.943274	+	0.332015i	$0.892272\pi$
$860$		0			0
$861$	−160162.			−0.216050
$862$	237525.	+	347662.i	0.319665	+	0.467890i
$863$		−	999093.i		−	1.34148i	−0.741692	−	0.670740i	$-0.765977\pi$
$863$		−	999093.i		−	1.34148i	0.741692	−	0.670740i	$-0.234023\pi$
$864$	−20725.1	+	142160.i	−0.0277632	+	0.190437i
$865$		0			0
$866$	435303.	−	297401.i	0.580438	−	0.396559i
$867$			389710.i			0.518445i
$868$	157090.	−	402544.i	0.208501	−	0.534287i
$869$	−505464.			−0.669347
$870$		0			0
$871$			93839.8i			0.123695i
$872$	−189402.	−	818872.i	−0.249087	−	1.07692i
$873$	−59374.5			−0.0779062
$874$	−55750.4	+	38089.0i	−0.0729836	+	0.0498628i
$875$		0			0
$876$	760940.	+	296951.i	0.991613	+	0.386969i
$877$	−634599.			−0.825087			−0.412544	−	0.910938i	$-0.635360\pi$
$877$	−634599.			−0.825087			−0.412544	+	0.910938i	$0.635360\pi$
$878$	336334.	+	492289.i	0.436297	+	0.638603i
$879$		−	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	$0.435448\pi$
$882$	−74484.8	+	50888.4i	−0.0957481	+	0.0654156i
$883$		−	209047.i		−	0.268116i	−0.990973	−	0.134058i	$-0.957199\pi$
$883$		−	209047.i		−	0.268116i	0.990973	−	0.134058i	$-0.0428008\pi$
$884$	−132660.	+	339944.i	−0.169761	+	0.435014i
$885$		0			0
$886$	−561710.	−	822169.i	−0.715558	−	1.04735i
$887$			178008.i			0.226252i	0.993581	+	0.113126i	$0.0360864\pi$
$887$			178008.i			0.226252i	−0.993581	+	0.113126i	$0.963914\pi$
$888$	244901.	−	56644.7i	0.310574	−	0.0718345i
$889$	1.47680e6			1.86861
$890$		0			0
$891$		−	98095.0i		−	0.123564i
$892$	−720031.	−	280986.i	−0.904943	−	0.353147i
$893$	31042.8			0.0389276
$894$	369041.	+	540161.i	0.461742	+	0.675847i
$895$		0			0
$896$	−810319.	−	460556.i	−1.00935	−	0.573676i
$897$	733095.			0.911120
$898$	−805047.	+	550012.i	−0.998317	+	0.682055i
$899$			9537.04i			0.0118003i
$900$		0			0
$901$	−163239.			−0.201082
$902$	164515.	+	240799.i	0.202205	+	0.295966i
$903$		−	915490.i		−	1.12274i
$904$	−209721.	−	906720.i	−0.256629	−	1.10952i
$905$		0			0
$906$	−677532.	+	462894.i	−0.825417	+	0.563929i
$907$		−	62871.2i		−	0.0764253i	−0.999270	−	0.0382126i	$-0.987834\pi$
$907$		−	62871.2i		−	0.0764253i	0.999270	−	0.0382126i	$-0.0121664\pi$
$908$	284819.	+	111148.i	0.345459	+	0.134813i
$909$	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	$-0.341352\pi$
$912$	−28927.6	−	26633.5i	−0.0347795	−	0.0320213i
$913$	1.40395e6			1.68426
$914$	1.13377e6	−	774598.i	1.35716	−	0.927222i
$915$		0			0
$916$	−426817.	+	1.09372e6i	−0.508687	+	1.30352i
$917$	935258.			1.11223
$918$	−29223.4	−	42773.9i	−0.0346773	−	0.0507567i
$919$			315989.i			0.374146i	0.982346	+	0.187073i	$0.0599001\pi$
$919$			315989.i			0.374146i	−0.982346	+	0.187073i	$0.940100\pi$
$920$		0			0
$921$	−724927.			−0.854623
$922$	513660.	−	350935.i	0.604246	−	0.412824i
$923$			173568.i			0.203736i
$924$	592874.	+	231364.i	0.694414	+	0.270989i
$925$		0			0
$926$	725358.	+	1.06170e6i	0.845923	+	1.23817i
$927$		−	81997.3i		−	0.0954201i
$928$	20356.1	+	2967.65i	0.0236373	+	0.00344601i
$929$	122547.			0.141994			0.0709971	−	0.997477i	$-0.477382\pi$
$929$	122547.			0.141994			0.0709971	+	0.997477i	$0.477382\pi$
$930$		0			0
$931$		−	24690.4i		−	0.0284859i
$932$	198010.	−	507403.i	0.227958	−	0.584145i
$933$	−686070.			−0.788143
$934$	−183270.	−	268250.i	−0.210086	−	0.307501i
$935$		0			0
$936$	96207.6	+	415950.i	0.109814	+	0.474776i
$937$	−495399.			−0.564256			−0.282128	−	0.959377i	$-0.591040\pi$
$937$	−495399.			−0.564256			−0.282128	+	0.959377i	$0.591040\pi$
$938$	71363.3	−	48755.7i	0.0811090	−	0.0554141i
$939$			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	$0.723140\pi$
$942$	−30708.5	−	44947.8i	−0.0346065	−	0.0506531i
$943$		−	309401.i		−	0.347935i
$944$	447883.	−	486461.i	0.502598	−	0.545889i
$945$		0			0
$946$	−1.37641e6	+	940370.i	−1.53803	+	1.05079i
$947$		−	527337.i		−	0.588015i	−0.955803	−	0.294007i	$-0.905011\pi$
$947$		−	527337.i		−	0.588015i	0.955803	−	0.294007i	$-0.0949890\pi$
$948$	−113534.	+	290933.i	−0.126331	+	0.323725i
$949$	2.42741e6			2.69532
$950$		0			0
$951$		−	477833.i		−	0.528342i
$952$	327446.	−	75737.0i	0.361298	−	0.0835669i
$953$	259379.			0.285594			0.142797	−	0.989752i	$-0.454390\pi$
$953$	259379.			0.285594			0.142797	+	0.989752i	$0.454390\pi$
$954$	−157693.	+	107737.i	−0.173267	+	0.118377i
$955$		0			0
$956$	−523387.	−	204248.i	−0.572674	−	0.223481i
$957$	−14046.3			−0.0153369
$958$	−780856.	−	1.14293e6i	−0.850824	−	1.24534i
$959$		−	1.79873e6i		−	1.95582i
$960$		0			0
$961$	698146.			0.755962
$962$	616791.	−	421395.i	0.666482	−	0.455344i
$963$			514556.i			0.554856i
$964$	−114128.	+	292455.i	−0.122812	+	0.314706i
$965$		0			0
$966$	−380890.	−	557504.i	−0.408174	−	0.597439i
$967$			1.03870e6i			1.11081i	0.831581	+	0.555403i	$0.187436\pi$
$967$			1.03870e6i			1.11081i	−0.831581	+	0.555403i	$0.812564\pi$
$968$	−49982.4	−	216097.i	−0.0533417	−	0.230621i
$969$	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	$-0.210264\pi$
$972$	−56461.0	−	22033.5i	−0.0597608	−	0.0233212i
$973$	733622.			0.774902
$974$	213101.	+	311913.i	0.224630	+	0.328788i
$975$		0			0
$976$	452626.	+	416731.i	0.475160	+	0.437478i
$977$	−1.09732e6			−1.14960			−0.574799	−	0.818295i	$-0.694920\pi$
$977$	−1.09732e6			−1.14960			−0.574799	+	0.818295i	$0.694920\pi$
$978$	−122245.	+	83518.7i	−0.127807	+	0.0873184i
$979$			1.60444e6i			1.67401i
$980$		0			0
$981$	354582.			0.368450
$982$	396525.	+	580389.i	0.411195	+	0.601861i
$983$		−	1.71299e6i		−	1.77276i	−0.462963	−	0.886378i	$-0.653214\pi$
$983$		−	1.71299e6i		−	1.77276i	0.462963	−	0.886378i	$-0.346786\pi$
$984$	175550.	−	40604.1i	0.181306	−	0.0419353i
$985$		0			0
$986$	−6124.84	+	4184.52i	−0.00630000	+	0.00430419i
$987$			310427.i			0.318659i
$988$	−108857.	−	42480.6i	−0.111518	−	0.0435188i
$989$	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	$-0.177567\pi$
$992$	−70130.0	+	481045.i	−0.0712657	+	0.488835i
$993$	16856.8			0.0170953
$994$	131995.	−	90179.7i	0.133593	−	0.0912717i
$995$		0			0
$996$	315346.	−	808078.i	0.317884	−	0.814582i
$997$	1.11868e6			1.12542			0.562709	−	0.826655i	$-0.309759\pi$
$997$	1.11868e6			1.12542			0.562709	+	0.826655i	$0.309759\pi$
$998$	84154.4	+	123176.i	0.0844920	+	0.123670i
$999$			106045.i			0.106258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.a.151.2		4
4.3	odd	2	inner	300.5.c.a.151.1		4
5.2	odd	4		300.5.f.a.199.3		8
5.3	odd	4		300.5.f.a.199.6		8
5.4	even	2		12.5.d.a.7.3	✓	4
15.14	odd	2		36.5.d.b.19.2		4
20.3	even	4		300.5.f.a.199.4		8
20.7	even	4		300.5.f.a.199.5		8
20.19	odd	2		12.5.d.a.7.4	yes	4
40.19	odd	2		192.5.g.d.127.4		4
40.29	even	2		192.5.g.d.127.2		4
60.59	even	2		36.5.d.b.19.1		4
80.19	odd	4		768.5.b.g.127.7		8
80.29	even	4		768.5.b.g.127.3		8
80.59	odd	4		768.5.b.g.127.2		8
80.69	even	4		768.5.b.g.127.6		8
120.29	odd	2		576.5.g.m.127.2		4
120.59	even	2		576.5.g.m.127.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.3	✓	4	5.4	even	2
12.5.d.a.7.4	yes	4	20.19	odd	2
36.5.d.b.19.1		4	60.59	even	2
36.5.d.b.19.2		4	15.14	odd	2
192.5.g.d.127.2		4	40.29	even	2
192.5.g.d.127.4		4	40.19	odd	2
300.5.c.a.151.1		4	4.3	odd	2	inner
300.5.c.a.151.2		4	1.1	even	1	trivial
300.5.f.a.199.3		8	5.2	odd	4
300.5.f.a.199.4		8	20.3	even	4
300.5.f.a.199.5		8	20.7	even	4
300.5.f.a.199.6		8	5.3	odd	4
576.5.g.m.127.1		4	120.59	even	2
576.5.g.m.127.2		4	120.29	odd	2
768.5.b.g.127.2		8	80.59	odd	4
768.5.b.g.127.3		8	80.29	even	4
768.5.b.g.127.6		8	80.69	even	4
768.5.b.g.127.7		8	80.19	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.30278 + 2.25647i) q^{2} -5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.30278 + 2.25647i) q^{2} -5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} +(11.7250 + 17.1617i) q^{6} -56.8882i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} -134.561i q^{11} +(-77.4500 - 30.2242i) q^{12} -247.066 q^{13} +(128.367 + 187.889i) q^{14} +(-188.333 - 173.397i) q^{16} +92.3112 q^{17} +(89.1749 - 60.9248i) q^{18} +29.5600i q^{19} -295.600 q^{21} +(303.633 + 444.425i) q^{22} -571.038i q^{23} +(324.000 - 74.9400i) q^{24} +(816.005 - 557.499i) q^{26} +140.296i q^{27} +(-847.933 - 330.899i) q^{28} +20.0891 q^{29} +474.736i q^{31} +(1013.29 + 147.724i) q^{32} -699.199 q^{33} +(-304.883 + 208.298i) q^{34} +(-157.050 + 402.442i) q^{36} +755.867 q^{37} +(-66.7013 - 97.6300i) q^{38} +1283.79i q^{39} +541.822 q^{41} +(976.299 - 667.013i) q^{42} +3097.06i q^{43} +(-2005.67 - 782.695i) q^{44} +(1288.53 + 1886.01i) q^{46} -1050.16i q^{47} +(-900.999 + 978.607i) q^{48} -835.266 q^{49} -479.663i q^{51} +(-1437.10 + 3682.59i) q^{52} -1768.35 q^{53} +(-316.574 - 463.367i) q^{54} +(3547.20 - 820.453i) q^{56} +153.598 q^{57} +(-66.3499 + 45.3306i) q^{58} +2582.98i q^{59} -2403.33 q^{61} +(-1071.23 - 1567.95i) q^{62} +1535.98i q^{63} +(-3680.00 + 1798.56i) q^{64} +(2309.30 - 1577.72i) q^{66} -379.816i q^{67} +(536.942 - 1375.92i) q^{68} -2967.20 q^{69} -702.517i q^{71} +(-389.400 - 1683.55i) q^{72} -9824.92 q^{73} +(-2496.46 + 1705.59i) q^{74} +(440.599 + 171.940i) q^{76} -7654.93 q^{77} +(-2896.85 - 4240.09i) q^{78} -3756.40i q^{79} +729.000 q^{81} +(-1789.52 + 1222.61i) q^{82} +10433.6i q^{83} +(-1719.40 + 4405.99i) q^{84} +(-6988.43 - 10228.9i) q^{86} -104.386i q^{87} +(8390.39 - 1940.67i) q^{88} -11923.5 q^{89} +14055.2i q^{91} +(-8511.46 - 3321.53i) q^{92} +2466.80 q^{93} +(2369.66 + 3468.45i) q^{94} +(767.597 - 5265.20i) q^{96} +2199.06 q^{97} +(2758.70 - 1884.76i) q^{98} +3633.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 20 q^{4} - 18 q^{6} - 108 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 - 20 * q^4 - 18 * q^6 - 108 * q^9	\( 4 q - 6 q^{2} - 20 q^{4} - 18 q^{6} - 108 q^{9} - 180 q^{12} - 296 q^{13} + 600 q^{14} + 112 q^{16} + 600 q^{17} + 162 q^{18} - 144 q^{21} + 1128 q^{22} + 1296 q^{24} + 1692 q^{26} - 1488 q^{28} + 888 q^{29} + 2784 q^{32} - 720 q^{33} - 484 q^{34} + 540 q^{36} + 4408 q^{37} - 4680 q^{38} + 552 q^{41} + 2088 q^{42} - 3696 q^{44} - 384 q^{46} - 1008 q^{48} - 572 q^{49} - 6008 q^{52} - 5112 q^{53} + 486 q^{54} + 1728 q^{56} - 5616 q^{57} + 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 4824 q^{66} - 5496 q^{68} - 9792 q^{69} - 8840 q^{73} - 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 9900 q^{78} + 2916 q^{81} - 3740 q^{82} - 10512 q^{84} - 19560 q^{86} + 8640 q^{88} - 25080 q^{89} - 18816 q^{92} + 17136 q^{93} - 5232 q^{94} - 8352 q^{96} - 23048 q^{97} + 5850 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 20 * q^4 - 18 * q^6 - 108 * q^9 - 180 * q^12 - 296 * q^13 + 600 * q^14 + 112 * q^16 + 600 * q^17 + 162 * q^18 - 144 * q^21 + 1128 * q^22 + 1296 * q^24 + 1692 * q^26 - 1488 * q^28 + 888 * q^29 + 2784 * q^32 - 720 * q^33 - 484 * q^34 + 540 * q^36 + 4408 * q^37 - 4680 * q^38 + 552 * q^41 + 2088 * q^42 - 3696 * q^44 - 384 * q^46 - 1008 * q^48 - 572 * q^49 - 6008 * q^52 - 5112 * q^53 + 486 * q^54 + 1728 * q^56 - 5616 * q^57 + 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 4824 * q^66 - 5496 * q^68 - 9792 * q^69 - 8840 * q^73 - 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 9900 * q^78 + 2916 * q^81 - 3740 * q^82 - 10512 * q^84 - 19560 * q^86 + 8640 * q^88 - 25080 * q^89 - 18816 * q^92 + 17136 * q^93 - 5232 * q^94 - 8352 * q^96 - 23048 * q^97 + 5850 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more