LMFDB - Embedded newform 300.5.c.c.151.9

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.9
Root			$3.97720 + 0.426493i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.c.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61924 - 3.65760i) q^{2} +5.19615i q^{3} +(-10.7561 - 11.8451i) q^{4} +(19.0055 + 8.41384i) q^{6} +95.1090i q^{7} +(-60.7414 + 20.1614i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(1.61924 - 3.65760i) q^{2} +5.19615i q^{3} +(-10.7561 - 11.8451i) q^{4} +(19.0055 + 8.41384i) q^{6} +95.1090i q^{7} +(-60.7414 + 20.1614i) q^{8} -27.0000 q^{9} -115.814i q^{11} +(61.5490 - 55.8903i) q^{12} -171.055 q^{13} +(347.871 + 154.005i) q^{14} +(-24.6130 + 254.814i) q^{16} +228.789 q^{17} +(-43.7196 + 98.7552i) q^{18} -659.627i q^{19} -494.201 q^{21} +(-423.602 - 187.531i) q^{22} -968.886i q^{23} +(-104.762 - 315.622i) q^{24} +(-276.980 + 625.651i) q^{26} -140.296i q^{27} +(1126.58 - 1023.00i) q^{28} +588.178 q^{29} -515.636i q^{31} +(892.154 + 502.631i) q^{32} +601.788 q^{33} +(370.465 - 836.819i) q^{34} +(290.414 + 319.818i) q^{36} +135.534 q^{37} +(-2412.65 - 1068.10i) q^{38} -888.827i q^{39} -559.656 q^{41} +(-800.232 + 1807.59i) q^{42} +754.185i q^{43} +(-1371.83 + 1245.71i) q^{44} +(-3543.80 - 1568.86i) q^{46} -2164.84i q^{47} +(-1324.05 - 127.893i) q^{48} -6644.72 q^{49} +1188.82i q^{51} +(1839.88 + 2026.16i) q^{52} +1178.44 q^{53} +(-513.147 - 227.174i) q^{54} +(-1917.53 - 5777.06i) q^{56} +3427.52 q^{57} +(952.404 - 2151.32i) q^{58} +183.192i q^{59} -438.111 q^{61} +(-1885.99 - 834.942i) q^{62} -2567.94i q^{63} +(3283.04 - 2449.26i) q^{64} +(974.441 - 2201.10i) q^{66} +709.589i q^{67} +(-2460.87 - 2710.03i) q^{68} +5034.48 q^{69} -8724.78i q^{71} +(1640.02 - 544.357i) q^{72} -5208.61 q^{73} +(219.462 - 495.728i) q^{74} +(-7813.35 + 7095.01i) q^{76} +11015.0 q^{77} +(-3250.98 - 1439.23i) q^{78} +957.643i q^{79} +729.000 q^{81} +(-906.220 + 2047.00i) q^{82} +2603.89i q^{83} +(5315.67 + 5853.86i) q^{84} +(2758.51 + 1221.21i) q^{86} +3056.26i q^{87} +(2334.97 + 7034.71i) q^{88} -10133.8 q^{89} -16268.9i q^{91} +(-11476.6 + 10421.4i) q^{92} +2679.33 q^{93} +(-7918.11 - 3505.40i) q^{94} +(-2611.75 + 4635.77i) q^{96} +8539.24 q^{97} +(-10759.4 + 24303.8i) q^{98} +3126.98i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * 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 $

$2$	1.61924	−	3.65760i	0.404811	−	0.914400i
$2$	1.61924	−	3.65760i	0.404811	−	0.914400i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−10.7561	−	11.8451i	−0.672256	−	0.740319i
$5$		0			0
$5$		0			0
$6$	19.0055	+	8.41384i	0.527929	+	0.233718i
$7$			95.1090i			1.94100i	0.241101	+	0.970500i	$0.422492\pi$
$7$			95.1090i			1.94100i	−0.241101	+	0.970500i	$0.577508\pi$
$8$	−60.7414	+	20.1614i	−0.949085	+	0.315021i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	115.814i		−	0.957141i	−0.878049	−	0.478571i	$-0.841155\pi$
$11$		−	115.814i		−	0.957141i	0.878049	−	0.478571i	$-0.158845\pi$
$12$	61.5490	−	55.8903i	0.427423	−	0.388127i
$13$	−171.055			−1.01216			−0.506080	−	0.862487i	$-0.668906\pi$
$13$	−171.055			−1.01216			−0.506080	+	0.862487i	$0.668906\pi$
$14$	347.871	+	154.005i	1.77485	+	0.785739i
$15$		0			0
$16$	−24.6130	+	254.814i	−0.0961444	+	0.995367i
$17$	228.789			0.791657			0.395829	−	0.918324i	$-0.370457\pi$
$17$	228.789			0.791657			0.395829	+	0.918324i	$0.370457\pi$
$18$	−43.7196	+	98.7552i	−0.134937	+	0.304800i
$19$		−	659.627i		−	1.82722i	−0.406589	−	0.913611i	$-0.633282\pi$
$19$		−	659.627i		−	1.82722i	0.406589	−	0.913611i	$-0.366718\pi$
$20$		0			0
$21$	−494.201			−1.12064
$22$	−423.602	−	187.531i	−0.875210	−	0.387461i
$23$		−	968.886i		−	1.83154i	−0.401700	−	0.915771i	$-0.631580\pi$
$23$		−	968.886i		−	1.83154i	0.401700	−	0.915771i	$-0.368420\pi$
$24$	−104.762	−	315.622i	−0.181878	−	0.547954i
$25$		0			0
$26$	−276.980	+	625.651i	−0.409733	+	0.925519i
$27$		−	140.296i		−	0.192450i
$28$	1126.58	−	1023.00i	1.43696	−	1.30485i
$29$	588.178			0.699379			0.349690	−	0.936866i	$-0.386287\pi$
$29$	588.178			0.699379			0.349690	+	0.936866i	$0.386287\pi$
$30$		0			0
$31$		−	515.636i		−	0.536562i	−0.963341	−	0.268281i	$-0.913544\pi$
$31$		−	515.636i		−	0.536562i	0.963341	−	0.268281i	$-0.0864556\pi$
$32$	892.154	+	502.631i	0.871244	+	0.490850i
$33$	601.788			0.552606
$34$	370.465	−	836.819i	0.320472	−	0.723892i
$35$		0			0
$36$	290.414	+	319.818i	0.224085	+	0.246773i
$37$	135.534			0.0990019			0.0495010	−	0.998774i	$-0.484237\pi$
$37$	135.534			0.0990019			0.0495010	+	0.998774i	$0.484237\pi$
$38$	−2412.65	−	1068.10i	−1.67081	−	0.739680i
$39$		−	888.827i		−	0.584370i
$40$		0			0
$41$	−559.656			−0.332930			−0.166465	−	0.986047i	$-0.553235\pi$
$41$	−559.656			−0.332930			−0.166465	+	0.986047i	$0.553235\pi$
$42$	−800.232	+	1807.59i	−0.453646	+	1.02471i
$43$			754.185i			0.407888i	0.978983	+	0.203944i	$0.0653760\pi$
$43$			754.185i			0.407888i	−0.978983	+	0.203944i	$0.934624\pi$
$44$	−1371.83	+	1245.71i	−0.708590	+	0.643444i
$45$		0			0
$46$	−3543.80	−	1568.86i	−1.67476	−	0.741429i
$47$		−	2164.84i		−	0.980007i	−0.871720	−	0.490004i	$-0.836995\pi$
$47$		−	2164.84i		−	0.980007i	0.871720	−	0.490004i	$-0.163005\pi$
$48$	−1324.05	−	127.893i	−0.574676	−	0.0555090i
$49$	−6644.72			−2.76748
$50$		0			0
$51$			1188.82i			0.457063i
$52$	1839.88	+	2026.16i	0.680430	+	0.749321i
$53$	1178.44			0.419523			0.209762	−	0.977753i	$-0.432731\pi$
$53$	1178.44			0.419523			0.209762	+	0.977753i	$0.432731\pi$
$54$	−513.147	−	227.174i	−0.175976	−	0.0779060i
$55$		0			0
$56$	−1917.53	−	5777.06i	−0.611457	−	1.84217i
$57$	3427.52			1.05495
$58$	952.404	−	2151.32i	0.283117	−	0.639513i
$59$			183.192i			0.0526264i	0.999654	+	0.0263132i	$0.00837671\pi$
$59$			183.192i			0.0526264i	−0.999654	+	0.0263132i	$0.991623\pi$
$60$		0			0
$61$	−438.111			−0.117740			−0.0588701	−	0.998266i	$-0.518750\pi$
$61$	−438.111			−0.117740			−0.0588701	+	0.998266i	$0.518750\pi$
$62$	−1885.99	−	834.942i	−0.490633	−	0.217206i
$63$		−	2567.94i		−	0.647000i
$64$	3283.04	−	2449.26i	0.801523	−	0.597964i
$65$		0			0
$66$	974.441	−	2201.10i	0.223701	−	0.505303i
$67$			709.589i			0.158073i	0.996872	+	0.0790365i	$0.0251844\pi$
$67$			709.589i			0.158073i	−0.996872	+	0.0790365i	$0.974816\pi$
$68$	−2460.87	−	2710.03i	−0.532196	−	0.586079i
$69$	5034.48			1.05744
$70$		0			0
$71$		−	8724.78i		−	1.73076i	−0.501113	−	0.865382i	$-0.667076\pi$
$71$		−	8724.78i		−	1.73076i	0.501113	−	0.865382i	$-0.332924\pi$
$72$	1640.02	−	544.357i	0.316362	−	0.105007i
$73$	−5208.61			−0.977408			−0.488704	−	0.872450i	$-0.662530\pi$
$73$	−5208.61			−0.977408			−0.488704	+	0.872450i	$0.662530\pi$
$74$	219.462	−	495.728i	0.0400771	−	0.0905274i
$75$		0			0
$76$	−7813.35	+	7095.01i	−1.35273	+	1.22836i
$77$	11015.0			1.85781
$78$	−3250.98	−	1439.23i	−0.534348	−	0.236560i
$79$			957.643i			0.153444i	0.997053	+	0.0767219i	$0.0244454\pi$
$79$			957.643i			0.153444i	−0.997053	+	0.0767219i	$0.975555\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−906.220	+	2047.00i	−0.134774	+	0.304432i
$83$			2603.89i			0.377978i	0.981979	+	0.188989i	$0.0605211\pi$
$83$			2603.89i			0.377978i	−0.981979	+	0.188989i	$0.939479\pi$
$84$	5315.67	+	5853.86i	0.753355	+	0.829629i
$85$		0			0
$86$	2758.51	+	1221.21i	0.372973	+	0.165118i
$87$			3056.26i			0.403787i
$88$	2334.97	+	7034.71i	0.301520	+	0.908408i
$89$	−10133.8			−1.27936			−0.639678	−	0.768643i	$-0.720932\pi$
$89$	−10133.8			−1.27936			−0.639678	+	0.768643i	$0.720932\pi$
$90$		0			0
$91$		−	16268.9i		−	1.96460i
$92$	−11476.6	+	10421.4i	−1.35593	+	1.23127i
$93$	2679.33			0.309784
$94$	−7918.11	−	3505.40i	−0.896119	−	0.396718i
$95$		0			0
$96$	−2611.75	+	4635.77i	−0.283393	+	0.503013i
$97$	8539.24			0.907561			0.453780	−	0.891114i	$-0.350075\pi$
$97$	8539.24			0.907561			0.453780	+	0.891114i	$0.350075\pi$
$98$	−10759.4	+	24303.8i	−1.12031	+	2.53059i
$99$			3126.98i			0.319047i
$100$		0			0
$101$	5132.89			0.503175			0.251588	−	0.967835i	$-0.419047\pi$
$101$	5132.89			0.503175			0.251588	+	0.967835i	$0.419047\pi$
$102$	4348.24	+	1924.99i	0.417939	+	0.185024i
$103$		−	9488.29i		−	0.894363i	−0.894443	−	0.447181i	$-0.852428\pi$
$103$		−	9488.29i		−	0.894363i	0.894443	−	0.447181i	$-0.147572\pi$
$104$	10390.1	−	3448.70i	0.960625	−	0.318852i
$105$		0			0
$106$	1908.19	−	4310.27i	0.169828	−	0.383612i
$107$			10036.7i			0.876645i	0.898818	+	0.438322i	$0.144427\pi$
$107$			10036.7i			0.876645i	−0.898818	+	0.438322i	$0.855573\pi$
$108$	−1661.82	+	1509.04i	−0.142474	+	0.129376i
$109$	−10512.1			−0.884785			−0.442393	−	0.896822i	$-0.645870\pi$
$109$	−10512.1			−0.884785			−0.442393	+	0.896822i	$0.645870\pi$
$110$		0			0
$111$			704.253i			0.0571588i
$112$	−24235.1	−	2340.92i	−1.93201	−	0.186616i
$113$	−18605.5			−1.45708			−0.728541	−	0.685002i	$-0.759801\pi$
$113$	−18605.5			−1.45708			−0.728541	+	0.685002i	$0.759801\pi$
$114$	5550.00	−	12536.5i	0.427054	−	0.964644i
$115$		0			0
$116$	−6326.50	−	6967.03i	−0.470162	−	0.517764i
$117$	4618.48			0.337386
$118$	670.045	+	296.633i	0.0481216	+	0.0213037i
$119$			21759.9i			1.53661i
$120$		0			0
$121$	1228.10			0.0838810
$122$	−709.410	+	1602.44i	−0.0476626	+	0.107662i
$123$		−	2908.06i		−	0.192217i
$124$	−6107.77	+	5546.23i	−0.397227	+	0.360707i
$125$		0			0
$126$	−9392.51	−	4158.13i	−0.591617	−	0.261913i
$127$		−	13799.8i		−	0.855586i	−0.903877	−	0.427793i	$-0.859291\pi$
$127$		−	13799.8i		−	0.855586i	0.903877	−	0.427793i	$-0.140709\pi$
$128$	−3642.37	−	15974.0i	−0.222313	−	0.974975i
$129$	−3918.86			−0.235494
$130$		0			0
$131$			20145.1i			1.17389i	0.809628	+	0.586943i	$0.199669\pi$
$131$			20145.1i			1.17389i	−0.809628	+	0.586943i	$0.800331\pi$
$132$	−6472.88	−	7128.24i	−0.371492	−	0.409104i
$133$	62736.5			3.54664
$134$	2595.40	+	1149.00i	0.144542	+	0.0639897i
$135$		0			0
$136$	−13897.0	+	4612.70i	−0.751350	+	0.249389i
$137$	11087.5			0.590734			0.295367	−	0.955384i	$-0.404558\pi$
$137$	11087.5			0.590734			0.295367	+	0.955384i	$0.404558\pi$
$138$	8152.06	−	18414.1i	0.428064	−	0.966925i
$139$		−	9763.23i		−	0.505317i	−0.967556	−	0.252659i	$-0.918695\pi$
$139$		−	9763.23i		−	0.505317i	0.967556	−	0.252659i	$-0.0813049\pi$
$140$		0			0
$141$	11248.8			0.565807
$142$	−31911.8	−	14127.6i	−1.58261	−	0.700633i
$143$			19810.6i			0.968779i
$144$	664.550	−	6879.98i	0.0320481	−	0.331789i
$145$		0			0
$146$	−8434.01	+	19051.0i	−0.395666	+	0.893742i
$147$		−	34527.0i		−	1.59781i
$148$	−1457.81	−	1605.41i	−0.0665546	−	0.0732930i
$149$	1558.71			0.0702092			0.0351046	−	0.999384i	$-0.488824\pi$
$149$	1558.71			0.0702092			0.0351046	+	0.999384i	$0.488824\pi$
$150$		0			0
$151$			32018.5i			1.40426i	0.712049	+	0.702129i	$0.247767\pi$
$151$			32018.5i			1.40426i	−0.712049	+	0.702129i	$0.752233\pi$
$152$	13299.0	+	40066.7i	0.575614	+	1.73419i
$153$	−6177.30			−0.263886
$154$	17835.9	−	40288.3i	0.752063	−	1.69878i
$155$		0			0
$156$	−10528.3	+	9560.31i	−0.432621	+	0.392846i
$157$	30661.9			1.24394			0.621971	−	0.783041i	$-0.286332\pi$
$157$	30661.9			1.24394			0.621971	+	0.783041i	$0.286332\pi$
$158$	3502.67	+	1550.66i	0.140309	+	0.0621158i
$159$			6123.36i			0.242212i
$160$		0			0
$161$	92149.8			3.55503
$162$	1180.43	−	2666.39i	0.0449790	−	0.101600i
$163$		−	36638.2i		−	1.37898i	−0.724293	−	0.689492i	$-0.757834\pi$
$163$		−	36638.2i		−	1.37898i	0.724293	−	0.689492i	$-0.242166\pi$
$164$	6019.71	+	6629.18i	0.223814	+	0.246475i
$165$		0			0
$166$	9524.01	+	4216.34i	0.345624	+	0.153010i
$167$		−	26157.8i		−	0.937926i	−0.883218	−	0.468963i	$-0.844628\pi$
$167$		−	26157.8i		−	0.937926i	0.883218	−	0.468963i	$-0.155372\pi$
$168$	30018.5	−	9963.77i	1.06358	−	0.353025i
$169$	698.786			0.0244664
$170$		0			0
$171$			17809.9i			0.609074i
$172$	8933.40	−	8112.08i	0.301967	−	0.274205i
$173$	4778.24			0.159652			0.0798262	−	0.996809i	$-0.474563\pi$
$173$	4778.24			0.159652			0.0798262	+	0.996809i	$0.474563\pi$
$174$	11178.6	+	4948.84i	0.369223	+	0.163457i
$175$		0			0
$176$	29511.1	+	2850.53i	0.952707	+	0.0920238i
$177$	−951.896			−0.0303838
$178$	−16409.1	+	37065.3i	−0.517898	+	1.16984i
$179$			27576.7i			0.860670i	0.902669	+	0.430335i	$0.141605\pi$
$179$			27576.7i			0.860670i	−0.902669	+	0.430335i	$0.858395\pi$
$180$		0			0
$181$	−25195.3			−0.769064			−0.384532	−	0.923112i	$-0.625637\pi$
$181$	−25195.3			−0.769064			−0.384532	+	0.923112i	$0.625637\pi$
$182$	−59505.0	−	26343.3i	−1.79643	−	0.795293i
$183$		−	2276.49i		−	0.0679773i
$184$	19534.1	+	58851.5i	0.576975	+	1.73829i
$185$		0			0
$186$	4338.48	−	9799.90i	0.125404	−	0.283267i
$187$		−	26497.0i		−	0.757728i
$188$	−25642.7	+	23285.2i	−0.725518	+	0.658815i
$189$	13343.4			0.373546
$190$		0			0
$191$		−	51407.2i		−	1.40915i	−0.709630	−	0.704574i	$-0.751138\pi$
$191$		−	51407.2i		−	1.40915i	0.709630	−	0.704574i	$-0.248862\pi$
$192$	12726.7	+	17059.2i	0.345235	+	0.462760i
$193$	−8968.09			−0.240760			−0.120380	−	0.992728i	$-0.538411\pi$
$193$	−8968.09			−0.240760			−0.120380	+	0.992728i	$0.538411\pi$
$194$	13827.1	−	31233.1i	0.367391	−	0.829874i
$195$		0			0
$196$	71471.3	+	78707.4i	1.86046	+	2.04882i
$197$	−28331.3			−0.730018			−0.365009	−	0.931004i	$-0.618934\pi$
$197$	−28331.3			−0.730018			−0.365009	+	0.931004i	$0.618934\pi$
$198$	11437.2	+	5063.35i	0.291737	+	0.129154i
$199$		−	25527.9i		−	0.644629i	−0.946633	−	0.322314i	$-0.895539\pi$
$199$		−	25527.9i		−	0.644629i	0.946633	−	0.322314i	$-0.104461\pi$
$200$		0			0
$201$	−3687.14			−0.0912635
$202$	8311.41	−	18774.1i	0.203691	−	0.460103i
$203$			55941.0i			1.35750i
$204$	14081.7	−	12787.1i	0.338373	−	0.307264i
$205$		0			0
$206$	−34704.4	−	15363.9i	−0.817806	−	0.362048i
$207$			26159.9i			0.610514i
$208$	4210.17	−	43587.2i	0.0973135	−	1.00747i
$209$	−76394.1			−1.74891
$210$		0			0
$211$		−	56431.4i		−	1.26752i	−0.773528	−	0.633762i	$-0.781510\pi$
$211$		−	56431.4i		−	1.26752i	0.773528	−	0.633762i	$-0.218490\pi$
$212$	−12675.4	−	13958.8i	−0.282027	−	0.310581i
$213$	45335.3			0.999257
$214$	36710.3	+	16251.9i	0.801604	+	0.354876i
$215$		0			0
$216$	2828.56	+	8521.78i	0.0606259	+	0.182651i
$217$	49041.7			1.04147
$218$	−17021.7	+	38449.2i	−0.358171	+	0.809048i
$219$		−	27064.7i		−	0.564307i
$220$		0			0
$221$	−39135.5			−0.801283
$222$	2575.88	+	1140.36i	0.0522660	+	0.0231385i
$223$		−	40609.4i		−	0.816615i	−0.912845	−	0.408307i	$-0.866119\pi$
$223$		−	40609.4i		−	0.816615i	0.912845	−	0.408307i	$-0.133881\pi$
$224$	−47804.7	+	84851.9i	−0.952741	+	1.69108i
$225$		0			0
$226$	−30126.8	+	68051.5i	−0.589843	+	1.33236i
$227$		−	12054.3i		−	0.233932i	−0.993136	−	0.116966i	$-0.962683\pi$
$227$		−	12054.3i		−	0.233932i	0.993136	−	0.116966i	$-0.0373168\pi$
$228$	−36866.8	−	40599.4i	−0.709194	−	0.780997i
$229$	60489.3			1.15347			0.576737	−	0.816930i	$-0.304326\pi$
$229$	60489.3			1.15347			0.576737	+	0.816930i	$0.304326\pi$
$230$		0			0
$231$			57235.4i			1.07261i
$232$	−35726.8	+	11858.5i	−0.663770	+	0.220319i
$233$	27750.5			0.511163			0.255582	−	0.966787i	$-0.417733\pi$
$233$	27750.5			0.511163			0.255582	+	0.966787i	$0.417733\pi$
$234$	7478.45	−	16892.6i	0.136578	−	0.308506i
$235$		0			0
$236$	2169.93	−	1970.43i	0.0389603	−	0.0353784i
$237$	−4976.06			−0.0885908
$238$	79589.0	+	35234.6i	1.40507	+	0.622036i
$239$		−	29154.5i		−	0.510399i	−0.966888	−	0.255200i	$-0.917859\pi$
$239$		−	29154.5i		−	0.510399i	0.966888	−	0.255200i	$-0.0821412\pi$
$240$		0			0
$241$	44625.6			0.768334			0.384167	−	0.923264i	$-0.374489\pi$
$241$	44625.6			0.768334			0.384167	+	0.923264i	$0.374489\pi$
$242$	1988.60	−	4491.91i	0.0339560	−	0.0767009i
$243$			3788.00i			0.0641500i
$244$	4712.37	+	5189.47i	0.0791515	+	0.0871653i
$245$		0			0
$246$	−10636.5	−	4708.86i	−0.175764	−	0.0778118i
$247$			112832.i			1.84944i
$248$	10395.9	+	31320.5i	0.169029	+	0.509243i
$249$	−13530.2			−0.218226
$250$		0			0
$251$			56303.7i			0.893696i	0.894610	+	0.446848i	$0.147454\pi$
$251$			56303.7i			0.893696i	−0.894610	+	0.446848i	$0.852546\pi$
$252$	−30417.6	+	27621.0i	−0.478986	+	0.434950i
$253$	−112211.			−1.75304
$254$	−50474.0	−	22345.2i	−0.782348	−	0.346351i
$255$		0			0
$256$	−64324.4	−	12543.5i	−0.981512	−	0.191398i
$257$	−88714.4			−1.34316			−0.671580	−	0.740932i	$-0.734384\pi$
$257$	−88714.4			−1.34316			−0.671580	+	0.740932i	$0.734384\pi$
$258$	−6345.59	+	14333.6i	−0.0953307	+	0.215336i
$259$			12890.5i			0.192163i
$260$		0			0
$261$	−15880.8			−0.233126
$262$	73682.6	+	32619.8i	1.07340	+	0.475202i
$263$			103470.i			1.49591i	0.663751	+	0.747953i	$0.268963\pi$
$263$			103470.i			1.49591i	−0.663751	+	0.747953i	$0.731037\pi$
$264$	−36553.4	+	12132.9i	−0.524469	+	0.174083i
$265$		0			0
$266$	101586.	−	229465.i	1.43572	−	3.24305i
$267$		−	52656.7i		−	0.738637i
$268$	8405.16	−	7632.41i	0.117024	−	0.106265i
$269$	3553.14			0.0491029			0.0245515	−	0.999699i	$-0.492184\pi$
$269$	3553.14			0.0491029			0.0245515	+	0.999699i	$0.492184\pi$
$270$		0			0
$271$		−	99010.4i		−	1.34816i	−0.738657	−	0.674081i	$-0.764540\pi$
$271$		−	99010.4i		−	1.34816i	0.738657	−	0.674081i	$-0.235460\pi$
$272$	−5631.18	+	58298.6i	−0.0761134	+	0.787990i
$273$	84535.5			1.13426
$274$	17953.3	−	40553.6i	0.239136	−	0.540167i
$275$		0			0
$276$	−54151.3	−	59633.9i	−0.710871	−	0.782844i
$277$	−100046.			−1.30389			−0.651943	−	0.758268i	$-0.726046\pi$
$277$	−100046.			−1.30389			−0.651943	+	0.758268i	$0.726046\pi$
$278$	−35710.0	−	15809.1i	−0.462062	−	0.204558i
$279$			13922.2i			0.178854i
$280$		0			0
$281$	−42287.1			−0.535545			−0.267772	−	0.963482i	$-0.586287\pi$
$281$	−42287.1			−0.535545			−0.267772	+	0.963482i	$0.586287\pi$
$282$	18214.6	−	41143.7i	0.229045	−	0.517374i
$283$			81612.9i			1.01903i	0.860463	+	0.509514i	$0.170175\pi$
$283$			81612.9i			1.01903i	−0.860463	+	0.509514i	$0.829825\pi$
$284$	−103346.	+	93844.5i	−1.28132	+	1.16352i
$285$		0			0
$286$	72459.1	+	32078.2i	0.885852	+	0.392173i
$287$		−	53228.3i		−	0.646218i
$288$	−24088.2	−	13571.0i	−0.290415	−	0.163617i
$289$	−31176.6			−0.373279
$290$		0			0
$291$			44371.2i			0.523980i
$292$	56024.3	+	61696.5i	0.657068	+	0.723594i
$293$	−138795.			−1.61673			−0.808366	−	0.588680i	$-0.799648\pi$
$293$	−138795.			−1.61673			−0.808366	+	0.588680i	$0.799648\pi$
$294$	−126286.	−	55907.7i	−1.46103	−	0.646810i
$295$		0			0
$296$	−8232.50	+	2732.54i	−0.0939612	+	0.0311877i
$297$	−16248.3			−0.184202
$298$	2523.94	−	5701.15i	0.0284215	−	0.0641993i
$299$			165733.i			1.85381i
$300$		0			0
$301$	−71729.8			−0.791710
$302$	117111.	+	51845.8i	1.28405	+	0.568460i
$303$			26671.3i			0.290508i
$304$	168082.	+	16235.4i	1.81876	+	0.175677i
$305$		0			0
$306$	−10002.6	+	22594.1i	−0.106824	+	0.241297i
$307$			123644.i			1.31188i	0.754812	+	0.655941i	$0.227728\pi$
$307$			123644.i			1.31188i	−0.754812	+	0.655941i	$0.772272\pi$
$308$	−118478.	−	130473.i	−1.24892	−	1.37537i
$309$	49302.6			0.516361
$310$		0			0
$311$			13560.3i			0.140201i	0.997540	+	0.0701003i	$0.0223319\pi$
$311$			13560.3i			0.140201i	−0.997540	+	0.0701003i	$0.977668\pi$
$312$	17920.0	+	53988.6i	0.184089	+	0.554617i
$313$	−97614.2			−0.996378			−0.498189	−	0.867068i	$-0.666001\pi$
$313$	−97614.2			−0.996378			−0.498189	+	0.867068i	$0.666001\pi$
$314$	49649.1	−	112149.i	0.503561	−	1.13746i
$315$		0			0
$316$	11343.4	−	10300.5i	0.113597	−	0.103153i
$317$	74431.9			0.740697			0.370348	−	0.928893i	$-0.379238\pi$
$317$	74431.9			0.740697			0.370348	+	0.928893i	$0.379238\pi$
$318$	22396.8	+	9915.22i	0.221479	+	0.0980501i
$319$		−	68119.3i		−	0.669405i
$320$		0			0
$321$	−52152.3			−0.506131
$322$	149213.	−	337047.i	1.43911	−	3.25072i
$323$		−	150915.i		−	1.44653i
$324$	−7841.19	−	8635.08i	−0.0746951	−	0.0822577i
$325$		0			0
$326$	−134008.	−	59326.3i	−1.26094	−	0.558228i
$327$		−	54622.6i		−	0.510831i
$328$	33994.3	−	11283.4i	0.315979	−	0.104880i
$329$	205895.			1.90219
$330$		0			0
$331$		−	76357.2i		−	0.696937i	−0.937320	−	0.348469i	$-0.886702\pi$
$331$		−	76357.2i		−	0.696937i	0.937320	−	0.348469i	$-0.113298\pi$
$332$	30843.4	−	28007.7i	0.279825	−	0.254098i
$333$	−3659.41			−0.0330006
$334$	−95674.9	−	42355.9i	−0.857640	−	0.379683i
$335$		0			0
$336$	12163.8	−	125929.i	0.107743	−	1.11545i
$337$	101465.			0.893418			0.446709	−	0.894679i	$-0.352596\pi$
$337$	101465.			0.893418			0.446709	+	0.894679i	$0.352596\pi$
$338$	1131.50	−	2555.88i	0.00990428	−	0.0223721i
$339$		−	96676.9i		−	0.841247i
$340$		0			0
$341$	−59718.0			−0.513566
$342$	65141.6	+	28838.6i	0.556937	+	0.246560i
$343$		−	403616.i		−	3.43068i
$344$	−15205.4	−	45810.2i	−0.128493	−	0.387120i
$345$		0			0
$346$	7737.14	−	17476.9i	0.0646291	−	0.145986i
$347$			208562.i			1.73212i	0.499944	+	0.866058i	$0.333354\pi$
$347$			208562.i			1.73212i	−0.499944	+	0.866058i	$0.666646\pi$
$348$	36201.7	−	32873.4i	0.298931	−	0.271448i
$349$	−3917.08			−0.0321596			−0.0160798	−	0.999871i	$-0.505119\pi$
$349$	−3917.08			−0.0321596			−0.0160798	+	0.999871i	$0.505119\pi$
$350$		0			0
$351$			23998.3i			0.194790i
$352$	58211.7	−	103324.i	0.469813	−	0.833903i
$353$	102995.			0.826548			0.413274	−	0.910607i	$-0.364385\pi$
$353$	102995.			0.826548			0.413274	+	0.910607i	$0.364385\pi$
$354$	−1541.35	+	3481.65i	−0.0122997	+	0.0277830i
$355$		0			0
$356$	109000.	+	120036.i	0.860055	+	0.947132i
$357$	−113068.			−0.887160
$358$	100865.	+	44653.5i	0.786997	+	0.348409i
$359$		−	236871.i		−	1.83790i	−0.394371	−	0.918951i	$-0.629038\pi$
$359$		−	236871.i		−	1.83790i	0.394371	−	0.918951i	$-0.370962\pi$
$360$		0			0
$361$	−304787.			−2.33874
$362$	−40797.4	+	92154.4i	−0.311326	+	0.703233i
$363$			6381.41i			0.0484287i
$364$	−192706.	+	174989.i	−1.45443	+	1.32071i
$365$		0			0
$366$	−8326.50	−	3686.20i	−0.0621585	−	0.0275180i
$367$			165846.i			1.23133i	0.788009	+	0.615664i	$0.211112\pi$
$367$			165846.i			1.23133i	−0.788009	+	0.615664i	$0.788888\pi$
$368$	246886.	+	23847.2i	1.82306	+	0.176093i
$369$	15110.7			0.110977
$370$		0			0
$371$			112080.i			0.814295i
$372$	−28819.1	−	31736.9i	−0.208254	−	0.229339i
$373$	−170798.			−1.22762			−0.613812	−	0.789452i	$-0.710365\pi$
$373$	−170798.			−1.22762			−0.613812	+	0.789452i	$0.710365\pi$
$374$	−96915.4	−	42905.1i	−0.692866	−	0.306737i
$375$		0			0
$376$	43646.1	+	131495.i	0.308723	+	0.930110i
$377$	−100611.			−0.707883
$378$	21606.3	−	48804.9i	0.151215	−	0.341570i
$379$		−	207834.i		−	1.44690i	−0.690378	−	0.723449i	$-0.742556\pi$
$379$		−	207834.i		−	1.44690i	0.690378	−	0.723449i	$-0.257444\pi$
$380$		0			0
$381$	71705.6			0.493973
$382$	−188027.	−	83240.8i	−1.28853	−	0.570439i
$383$			145912.i			0.994706i	0.867548	+	0.497353i	$0.165695\pi$
$383$			145912.i			0.994706i	−0.867548	+	0.497353i	$0.834305\pi$
$384$	83003.3	−	18926.3i	0.562902	−	0.128352i
$385$		0			0
$386$	−14521.5	+	32801.7i	−0.0974625	+	0.220151i
$387$		−	20363.0i		−	0.135963i
$388$	−91848.8	−	101148.i	−0.610113	−	0.671884i
$389$	−100959.			−0.667183			−0.333591	−	0.942718i	$-0.608261\pi$
$389$	−100959.			−0.667183			−0.333591	+	0.942718i	$0.608261\pi$
$390$		0			0
$391$		−	221670.i		−	1.44995i
$392$	403610.	−	133967.i	2.62657	−	0.871816i
$393$	−104677.			−0.677743
$394$	−45875.3	+	103625.i	−0.295520	+	0.667529i
$395$		0			0
$396$	37039.4	−	33634.1i	0.236197	−	0.214481i
$397$	−38963.5			−0.247216			−0.123608	−	0.992331i	$-0.539447\pi$
$397$	−38963.5			−0.247216			−0.123608	+	0.992331i	$0.539447\pi$
$398$	−93371.0	−	41336.0i	−0.589449	−	0.260953i
$399$			325988.i			2.04765i
$400$		0			0
$401$	−63269.6			−0.393465			−0.196732	−	0.980457i	$-0.563033\pi$
$401$	−63269.6			−0.393465			−0.196732	+	0.980457i	$0.563033\pi$
$402$	−5970.37	+	13486.1i	−0.0369445	+	0.0834513i
$403$			88202.2i			0.543087i
$404$	−55209.8	−	60799.6i	−0.338262	−	0.372510i
$405$		0			0
$406$	204610.	+	90582.2i	1.24129	+	0.549529i
$407$		−	15696.7i		−	0.0947588i
$408$	−23968.3	−	72210.7i	−0.143985	−	0.433792i
$409$	188419.			1.12636			0.563181	−	0.826333i	$-0.309577\pi$
$409$	188419.			1.12636			0.563181	+	0.826333i	$0.309577\pi$
$410$		0			0
$411$			57612.2i			0.341060i
$412$	−112390.	+	102057.i	−0.662114	+	0.601240i
$413$	−17423.2			−0.102148
$414$	95682.6	+	42359.3i	0.558254	+	0.247143i
$415$		0			0
$416$	−152607.	−	85977.5i	−0.881838	−	0.496819i
$417$	50731.2			0.291745
$418$	−123701.	+	279419.i	−0.707978	+	1.59920i
$419$			31463.3i			0.179216i	0.995977	+	0.0896080i	$0.0285614\pi$
$419$			31463.3i			0.179216i	−0.995977	+	0.0896080i	$0.971439\pi$
$420$		0			0
$421$	−146901.			−0.828822			−0.414411	−	0.910090i	$-0.636012\pi$
$421$	−146901.			−0.828822			−0.414411	+	0.910090i	$0.636012\pi$
$422$	−206404.	−	91376.3i	−1.15902	−	0.513108i
$423$			58450.6i			0.326669i
$424$	−71580.2	+	23759.0i	−0.398163	+	0.132159i
$425$		0			0
$426$	73408.9	−	165818.i	0.404510	−	0.913721i
$427$		−	41668.3i		−	0.228534i
$428$	118886.	−	107956.i	0.648997	−	0.589330i
$429$	−102939.			−0.559325
$430$		0			0
$431$			184568.i			0.993578i	0.867871	+	0.496789i	$0.165488\pi$
$431$			184568.i			0.993578i	−0.867871	+	0.496789i	$0.834512\pi$
$432$	35749.4	+	3453.10i	0.191559	+	0.0185030i
$433$	313272.			1.67088			0.835440	−	0.549582i	$-0.185213\pi$
$433$	313272.			1.67088			0.835440	+	0.549582i	$0.185213\pi$
$434$	79410.5	−	179375.i	0.421598	−	0.952318i
$435$		0			0
$436$	113069.	+	124517.i	0.594802	+	0.655023i
$437$	−639104.			−3.34664
$438$	−98991.9	−	43824.4i	−0.516002	−	0.228438i
$439$			104426.i			0.541851i	0.962600	+	0.270925i	$0.0873297\pi$
$439$			104426.i			0.541851i	−0.962600	+	0.270925i	$0.912670\pi$
$440$		0			0
$441$	179408.			0.922494
$442$	−63369.9	+	143142.i	−0.324368	+	0.732694i
$443$		−	23106.0i		−	0.117738i	−0.998266	−	0.0588691i	$-0.981251\pi$
$443$		−	23106.0i		−	0.117738i	0.998266	−	0.0588691i	$-0.0187495\pi$
$444$	8341.95	−	7575.01i	0.0423157	−	0.0384253i
$445$		0			0
$446$	−148533.	−	65756.6i	−0.746713	−	0.330575i
$447$			8099.32i			0.0405353i
$448$	232947.	+	312247.i	1.16065	+	1.55576i
$449$	63670.0			0.315822			0.157911	−	0.987453i	$-0.449524\pi$
$449$	63670.0			0.315822			0.157911	+	0.987453i	$0.449524\pi$
$450$		0			0
$451$			64816.0i			0.318661i
$452$	200122.	+	220384.i	0.979532	+	1.07871i
$453$	−166373.			−0.810749
$454$	−44089.7	−	19518.8i	−0.213907	−	0.0946982i
$455$		0			0
$456$	−208193.	+	69103.6i	−1.00123	+	0.332331i
$457$	−113519.			−0.543544			−0.271772	−	0.962362i	$-0.587610\pi$
$457$	−113519.			−0.543544			−0.271772	+	0.962362i	$0.587610\pi$
$458$	97947.0	−	221246.i	0.466939	−	1.05474i
$459$		−	32098.2i		−	0.152354i
$460$		0			0
$461$	279353.			1.31447			0.657235	−	0.753685i	$-0.271726\pi$
$461$	279353.			1.31447			0.657235	+	0.753685i	$0.271726\pi$
$462$	209344.	+	92678.2i	0.980793	+	0.434204i
$463$			47283.9i			0.220572i	0.993900	+	0.110286i	$0.0351767\pi$
$463$			47283.9i			0.220572i	−0.993900	+	0.110286i	$0.964823\pi$
$464$	−14476.8	+	149876.i	−0.0672414	+	0.696139i
$465$		0			0
$466$	44934.9	−	101500.i	0.206925	−	0.467408i
$467$		−	355616.i		−	1.63060i	−0.579039	−	0.815300i	$-0.696572\pi$
$467$		−	355616.i		−	1.63060i	0.579039	−	0.815300i	$-0.303428\pi$
$468$	−49676.8	−	54706.4i	−0.226810	−	0.249774i
$469$	−67488.4			−0.306820
$470$		0			0
$471$			159324.i			0.718190i
$472$	−3693.41	−	11127.4i	−0.0165784	−	0.0499469i
$473$	87345.2			0.390406
$474$	−8057.45	+	18200.4i	−0.0358626	+	0.0810075i
$475$		0			0
$476$	257748.	−	234051.i	1.13758	−	1.03299i
$477$	−31817.9			−0.139841
$478$	−106636.	−	47208.3i	−0.466709	−	0.206615i
$479$		−	217649.i		−	0.948605i	−0.880362	−	0.474302i	$-0.842700\pi$
$479$		−	217649.i		−	0.948605i	0.880362	−	0.474302i	$-0.157300\pi$
$480$		0			0
$481$	−23183.7			−0.100206
$482$	72259.8	−	163223.i	0.311030	−	0.702565i
$483$			478824.i			2.05249i
$484$	−13209.6	−	14547.0i	−0.0563895	−	0.0620987i
$485$		0			0
$486$	13855.0	+	6133.69i	0.0586588	+	0.0259687i
$487$			26631.0i			0.112287i	0.998423	+	0.0561435i	$0.0178804\pi$
$487$			26631.0i			0.112287i	−0.998423	+	0.0561435i	$0.982120\pi$
$488$	26611.5	−	8832.93i	0.111745	−	0.0370907i
$489$	190378.			0.796157
$490$		0			0
$491$			464401.i			1.92633i	0.268912	+	0.963165i	$0.413336\pi$
$491$			464401.i			1.92633i	−0.268912	+	0.963165i	$0.586664\pi$
$492$	−34446.3	+	31279.3i	−0.142302	+	0.129219i
$493$	134569.			0.553669
$494$	412696.	+	182703.i	1.69113	+	0.748674i
$495$		0			0
$496$	131391.	+	12691.3i	0.534077	+	0.0515875i
$497$	829805.			3.35941
$498$	−21908.8	+	49488.2i	−0.0883403	+	0.199546i
$499$		−	94648.3i		−	0.380112i	−0.981773	−	0.190056i	$-0.939133\pi$
$499$		−	94648.3i		−	0.380112i	0.981773	−	0.190056i	$-0.0608670\pi$
$500$		0			0
$501$	135920.			0.541512
$502$	205937.	+	91169.6i	0.817196	+	0.361778i
$503$			276138.i			1.09141i	0.837976	+	0.545707i	$0.183739\pi$
$503$			276138.i			1.09141i	−0.837976	+	0.545707i	$0.816261\pi$
$504$	51773.3	+	155981.i	0.203819	+	0.614058i
$505$		0			0
$506$	−181697.	+	410422.i	−0.709652	+	1.60298i
$507$			3631.00i			0.0141257i
$508$	−163459.	+	148431.i	−0.633407	+	0.575173i
$509$	423966.			1.63642			0.818212	−	0.574917i	$-0.194966\pi$
$509$	423966.			1.63642			0.818212	+	0.574917i	$0.194966\pi$
$510$		0			0
$511$		−	495385.i		−	1.89715i
$512$	−150036.	+	214962.i	−0.572342	+	0.820015i
$513$	−92543.1			−0.351649
$514$	−143650.	+	324482.i	−0.543726	+	1.22819i
$515$		0			0
$516$	42151.6	+	46419.3i	0.158312	+	0.174341i
$517$	−250718.			−0.938005
$518$	47148.2	+	20872.8i	0.175714	+	0.0777896i
$519$			24828.5i			0.0921754i
$520$		0			0
$521$	101217.			0.372889			0.186444	−	0.982466i	$-0.440304\pi$
$521$	101217.			0.372889			0.186444	+	0.982466i	$0.440304\pi$
$522$	−25714.9	+	58085.6i	−0.0943722	+	0.213171i
$523$			161604.i			0.590813i	0.955372	+	0.295406i	$0.0954550\pi$
$523$			161604.i			0.590813i	−0.955372	+	0.295406i	$0.904545\pi$
$524$	238620.	−	216682.i	0.869050	−	0.789152i
$525$		0			0
$526$	378453.	+	167544.i	1.36786	+	0.605560i
$527$		−	117972.i		−	0.424773i
$528$	−14811.8	+	153344.i	−0.0531300	+	0.550046i
$529$	−658900.			−2.35455
$530$		0			0
$531$		−	4946.19i		−	0.0175421i
$532$	−674799.	−	743120.i	−2.38425	−	2.62564i
$533$	95731.9			0.336979
$534$	−192597.	−	85264.1i	−0.675410	−	0.299009i
$535$		0			0
$536$	−14306.3	−	43101.5i	−0.0497964	−	0.150025i
$537$	−143293.			−0.496908
$538$	5753.40	−	12996.0i	0.0198774	−	0.0448997i
$539$			769553.i			2.64887i
$540$		0			0
$541$	387943.			1.32548			0.662740	−	0.748850i	$-0.269394\pi$
$541$	387943.			1.32548			0.662740	+	0.748850i	$0.269394\pi$
$542$	−362141.	−	160322.i	−1.23276	−	0.545751i
$543$		−	130919.i		−	0.444020i
$544$	204115.	+	114996.i	0.689726	+	0.388585i
$545$		0			0
$546$	136884.	−	309197.i	0.459162	−	1.03717i
$547$			27433.2i			0.0916858i	0.998949	+	0.0458429i	$0.0145974\pi$
$547$			27433.2i			0.0916858i	−0.998949	+	0.0458429i	$0.985403\pi$
$548$	−119258.	−	131332.i	−0.397124	−	0.437331i
$549$	11829.0			0.0392467
$550$		0			0
$551$		−	387978.i		−	1.27792i
$552$	−305801.	+	101502.i	−1.00360	+	0.333117i
$553$	−91080.4			−0.297834
$554$	−161999.	+	365928.i	−0.527828	+	1.19227i
$555$		0			0
$556$	−115646.	+	105014.i	−0.374096	+	0.339702i
$557$	313521.			1.01055			0.505273	−	0.862959i	$-0.331392\pi$
$557$	313521.			1.01055			0.505273	+	0.862959i	$0.331392\pi$
$558$	50921.8	+	22543.4i	0.163544	+	0.0724022i
$559$		−	129007.i		−	0.412847i
$560$		0			0
$561$	137682.			0.437474
$562$	−68473.2	+	154669.i	−0.216794	+	0.489702i
$563$		−	437532.i		−	1.38036i	−0.723637	−	0.690181i	$-0.757531\pi$
$563$		−	437532.i		−	1.38036i	0.723637	−	0.690181i	$-0.242469\pi$
$564$	−120993.	−	133243.i	−0.380367	−	0.418878i
$565$		0			0
$566$	298507.	+	132151.i	0.931799	+	0.412514i
$567$			69334.5i			0.215667i
$568$	175904.	+	529956.i	0.545228	+	1.64264i
$569$	−86379.1			−0.266799			−0.133400	−	0.991062i	$-0.542589\pi$
$569$	−86379.1			−0.266799			−0.133400	+	0.991062i	$0.542589\pi$
$570$		0			0
$571$		−	204020.i		−	0.625748i	−0.949795	−	0.312874i	$-0.898708\pi$
$571$		−	204020.i		−	0.625748i	0.949795	−	0.312874i	$-0.101292\pi$
$572$	234658.	−	213084.i	0.717206	−	0.651267i
$573$	267119.			0.813572
$574$	−194688.	−	86189.7i	−0.590902	−	0.261596i
$575$		0			0
$576$	−88642.0	+	66130.0i	−0.267174	+	0.199321i
$577$	63845.4			0.191769			0.0958844	−	0.995392i	$-0.469432\pi$
$577$	63845.4			0.191769			0.0958844	+	0.995392i	$0.469432\pi$
$578$	−50482.6	+	114032.i	−0.151108	+	0.341326i
$579$		−	46599.5i		−	0.139003i
$580$		0			0
$581$	−247654.			−0.733656
$582$	162292.	+	71847.8i	0.479128	+	0.212113i
$583$		−	136480.i		−	0.401543i
$584$	316378.	−	105013.i	0.927643	−	0.307904i
$585$		0			0
$586$	−224743.	+	507656.i	−0.654471	+	1.47834i
$587$		−	490014.i		−	1.42211i	−0.703137	−	0.711054i	$-0.748218\pi$
$587$		−	490014.i		−	1.42211i	0.703137	−	0.711054i	$-0.251782\pi$
$588$	−408976.	+	371376.i	−1.18289	+	1.07413i
$589$	−340128.			−0.980419
$590$		0			0
$591$		−	147214.i		−	0.421476i
$592$	−3335.89	+	34535.9i	−0.00951848	+	0.0985433i
$593$	440204.			1.25183			0.625913	−	0.779893i	$-0.284726\pi$
$593$	440204.			1.25183			0.625913	+	0.779893i	$0.284726\pi$
$594$	−26309.9	+	59429.7i	−0.0745670	+	0.168434i
$595$		0			0
$596$	−16765.7	−	18463.1i	−0.0471985	−	0.0519772i
$597$	132647.			0.372177
$598$	606184.	+	268362.i	1.69513	+	0.750444i
$599$		−	363994.i		−	1.01447i	−0.861807	−	0.507236i	$-0.830667\pi$
$599$		−	363994.i		−	1.01447i	0.861807	−	0.507236i	$-0.169333\pi$
$600$		0			0
$601$	237926.			0.658707			0.329353	−	0.944207i	$-0.393169\pi$
$601$	237926.			0.658707			0.329353	+	0.944207i	$0.393169\pi$
$602$	−116148.	+	262359.i	−0.320493	+	0.723940i
$603$		−	19158.9i		−	0.0526910i
$604$	379262.	−	344394.i	1.03960	−	0.944021i
$605$		0			0
$606$	97552.9	+	43187.3i	0.265641	+	0.117601i
$607$			566612.i			1.53783i	0.639351	+	0.768915i	$0.279203\pi$
$607$			566612.i			1.53783i	−0.639351	+	0.768915i	$0.720797\pi$
$608$	331549.	−	588489.i	0.896893	−	1.59196i
$609$	−290678.			−0.783750
$610$		0			0
$611$			370306.i			0.991923i
$612$	66443.6	+	73170.8i	0.177399	+	0.195360i
$613$	−464259.			−1.23549			−0.617745	−	0.786378i	$-0.711954\pi$
$613$	−464259.			−1.23549			−0.617745	+	0.786378i	$0.711954\pi$
$614$	452239.	+	200209.i	1.19959	+	0.531064i
$615$		0			0
$616$	−669064.	+	222077.i	−1.76322	+	0.585250i
$617$	−460844.			−1.21055			−0.605277	−	0.796015i	$-0.706938\pi$
$617$	−460844.			−1.21055			−0.605277	+	0.796015i	$0.706938\pi$
$618$	79833.0	−	180329.i	0.209029	−	0.472160i
$619$		−	38455.6i		−	0.100364i	−0.998740	−	0.0501821i	$-0.984020\pi$
$619$		−	38455.6i		−	0.100364i	0.998740	−	0.0501821i	$-0.0159802\pi$
$620$		0			0
$621$	−135931.			−0.352481
$622$	49598.3	+	21957.5i	0.128199	+	0.0567548i
$623$		−	963814.i		−	2.48323i
$624$	226486.	+	21876.7i	0.581663	+	0.0561840i
$625$		0			0
$626$	−158061.	+	357034.i	−0.403345	+	0.911089i
$627$		−	396955.i		−	1.00973i
$628$	−329802.	−	363194.i	−0.836247	−	0.920913i
$629$	31008.6			0.0783756
$630$		0			0
$631$			237480.i			0.596443i	0.954497	+	0.298221i	$0.0963934\pi$
$631$			237480.i			0.596443i	−0.954497	+	0.298221i	$0.903607\pi$
$632$	−19307.4	−	58168.6i	−0.0483381	−	0.145631i
$633$	293226.			0.731805
$634$	120523.	−	272242.i	0.299842	−	0.677293i
$635$		0			0
$636$	72531.8	−	65863.4i	0.179314	−	0.162828i
$637$	1.13661e6			2.80113
$638$	−249153.	−	110302.i	−0.612104	−	0.270982i
$639$			235569.i			0.576921i
$640$		0			0
$641$	−182574.			−0.444348			−0.222174	−	0.975007i	$-0.571315\pi$
$641$	−182574.			−0.444348			−0.222174	+	0.975007i	$0.571315\pi$
$642$	−84447.3	+	190752.i	−0.204888	+	0.462806i
$643$			145787.i			0.352613i	0.984335	+	0.176306i	$0.0564149\pi$
$643$			145787.i			0.352613i	−0.984335	+	0.176306i	$0.943585\pi$
$644$	−991172.	−	1.09152e6i	−2.38989	−	2.63185i
$645$		0			0
$646$	−551988.	−	244369.i	−1.32271	−	0.585573i
$647$		−	25742.8i		−	0.0614959i	−0.999527	−	0.0307480i	$-0.990211\pi$
$647$		−	25742.8i		−	0.0614959i	0.999527	−	0.0307480i	$-0.00978892\pi$
$648$	−44280.5	+	14697.6i	−0.105454	+	0.0350024i
$649$	21216.3			0.0503709
$650$		0			0
$651$			254828.i			0.601292i
$652$	−433984.	+	394084.i	−1.02089	+	0.927030i
$653$	759303.			1.78069			0.890346	−	0.455285i	$-0.150463\pi$
$653$	759303.			1.78069			0.890346	+	0.455285i	$0.150463\pi$
$654$	−199788.	−	88447.4i	−0.467104	−	0.206790i
$655$		0			0
$656$	13774.8	−	142608.i	0.0320094	−	0.331388i
$657$	140632.			0.325803
$658$	333395.	−	753083.i	0.770030	−	1.73937i
$659$		−	206499.i		−	0.475497i	−0.971327	−	0.237748i	$-0.923591\pi$
$659$		−	206499.i		−	0.475497i	0.971327	−	0.237748i	$-0.0764094\pi$
$660$		0			0
$661$	−130969.			−0.299755			−0.149878	−	0.988705i	$-0.547888\pi$
$661$	−130969.			−0.299755			−0.149878	+	0.988705i	$0.547888\pi$
$662$	−279284.	−	123641.i	−0.637280	−	0.282128i
$663$		−	203354.i		−	0.462621i
$664$	−52498.1	−	158164.i	−0.119071	−	0.358734i
$665$		0			0
$666$	−5925.48	+	13384.7i	−0.0133590	+	0.0301758i
$667$		−	569877.i		−	1.28094i
$668$	−309842.	+	281356.i	−0.694365	+	0.630526i
$669$	211013.			0.471473
$670$		0			0
$671$			50739.5i			0.112694i
$672$	−440903.	−	248401.i	−0.976348	−	0.550065i
$673$	−703745.			−1.55376			−0.776882	−	0.629647i	$-0.783200\pi$
$673$	−703745.			−1.55376			−0.776882	+	0.629647i	$0.783200\pi$
$674$	164296.	−	371117.i	0.361666	−	0.816942i
$675$		0			0
$676$	−7516.20	−	8277.19i	−0.0164477	−	0.0181130i
$677$	840675.			1.83422			0.917108	−	0.398638i	$-0.130517\pi$
$677$	840675.			1.83422			0.917108	+	0.398638i	$0.130517\pi$
$678$	−353606.	−	156544.i	−0.769237	−	0.340546i
$679$			812158.i			1.76158i
$680$		0			0
$681$	62635.8			0.135061
$682$	−96698.0	+	218424.i	−0.207897	+	0.469605i
$683$			570663.i			1.22332i	0.791123	+	0.611658i	$0.209497\pi$
$683$			570663.i			1.22332i	−0.791123	+	0.611658i	$0.790503\pi$
$684$	210961.	−	191565.i	0.450909	−	0.409453i
$685$		0			0
$686$	−1.47627e6	−	653554.i	−3.13702	−	1.38878i
$687$			314312.i			0.665958i
$688$	−192177.	−	18562.7i	−0.405998	−	0.0392161i
$689$	−201578.			−0.424625
$690$		0			0
$691$		−	260946.i		−	0.546505i	−0.961942	−	0.273253i	$-0.911901\pi$
$691$		−	260946.i		−	0.546505i	0.961942	−	0.273253i	$-0.0880995\pi$
$692$	−51395.2	−	56598.7i	−0.107327	−	0.118194i
$693$	−297404.			−0.619270
$694$	762838.	+	337713.i	1.58385	+	0.701180i
$695$		0			0
$696$	−61618.4	−	185642.i	−0.127201	−	0.383228i
$697$	−128043.			−0.263567
$698$	−6342.71	+	14327.1i	−0.0130186	+	0.0294068i
$699$			144196.i			0.295120i
$700$		0			0
$701$	655810.			1.33457			0.667286	−	0.744801i	$-0.267456\pi$
$701$	655810.			1.33457			0.667286	+	0.744801i	$0.267456\pi$
$702$	87776.4	+	38859.2i	0.178116	+	0.0788532i
$703$		−	89401.6i		−	0.180898i
$704$	−283659.	−	380222.i	−0.572336	−	0.767171i
$705$		0			0
$706$	166775.	−	376716.i	0.334596	−	0.755796i
$707$			488184.i			0.976663i
$708$	10238.7	+	11275.3i	0.0204257	+	0.0224937i
$709$	502376.			0.999393			0.499696	−	0.866201i	$-0.333445\pi$
$709$	502376.			0.999393			0.499696	+	0.866201i	$0.333445\pi$
$710$		0			0
$711$		−	25856.4i		−	0.0511479i
$712$	615540.	−	204311.i	1.21422	−	0.403025i
$713$	−499593.			−0.982737
$714$	−183084.	+	413557.i	−0.359132	+	0.811220i
$715$		0			0
$716$	326649.	−	296618.i	0.637170	−	0.578590i
$717$	151491.			0.294679
$718$	−866379.	−	383552.i	−1.68058	−	0.744004i
$719$		−	666208.i		−	1.28870i	−0.764730	−	0.644350i	$-0.777128\pi$
$719$		−	666208.i		−	1.28870i	0.764730	−	0.644350i	$-0.222872\pi$
$720$		0			0
$721$	902422.			1.73596
$722$	−493525.	+	1.11479e6i	−0.946748	+	2.13854i
$723$			231881.i			0.443598i
$724$	271003.	+	298441.i	0.517008	+	0.569353i
$725$		0			0
$726$	23340.6	+	10333.1i	0.0442833	+	0.0196045i
$727$		−	86784.8i		−	0.164201i	−0.996624	−	0.0821003i	$-0.973837\pi$
$727$		−	86784.8i		−	0.164201i	0.996624	−	0.0821003i	$-0.0261628\pi$
$728$	328003.	+	988194.i	0.618891	+	1.86457i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			172549.i			0.322907i
$732$	−26965.3	+	24486.2i	−0.0503249	+	0.0456982i
$733$	499460.			0.929592			0.464796	−	0.885418i	$-0.346128\pi$
$733$	499460.			0.929592			0.464796	+	0.885418i	$0.346128\pi$
$734$	606600.	+	268546.i	1.12593	+	0.498456i
$735$		0			0
$736$	486992.	−	864395.i	0.899014	−	1.59572i
$737$	82180.4			0.151298
$738$	24467.9	−	55269.0i	0.0449247	−	0.101477i
$739$			457929.i			0.838512i	0.907868	+	0.419256i	$0.137709\pi$
$739$			457929.i			0.838512i	−0.907868	+	0.419256i	$0.862291\pi$
$740$		0			0
$741$	−586295.			−1.06777
$742$	409945.	+	181486.i	0.744592	+	0.329636i
$743$		−	92845.0i		−	0.168183i	−0.996458	−	0.0840913i	$-0.973201\pi$
$743$		−	92845.0i		−	0.168183i	0.996458	−	0.0840913i	$-0.0267987\pi$
$744$	−162746.	+	54018.9i	−0.294012	+	0.0975887i
$745$		0			0
$746$	−276564.	+	624711.i	−0.496956	+	1.12254i
$747$		−	70305.1i		−	0.125993i
$748$	−313859.	+	285004.i	−0.560960	+	0.509387i
$749$	−954581.			−1.70157
$750$		0			0
$751$		−	415086.i		−	0.735966i	−0.929832	−	0.367983i	$-0.880048\pi$
$751$		−	415086.i		−	0.735966i	0.929832	−	0.367983i	$-0.119952\pi$
$752$	551631.	+	53283.1i	0.975467	+	0.0942222i
$753$	−292563.			−0.515976
$754$	−162913.	+	367994.i	−0.286559	+	0.647289i
$755$		0			0
$756$	−143523.	−	158054.i	−0.251118	−	0.276543i
$757$	144592.			0.252321			0.126161	−	0.992010i	$-0.459735\pi$
$757$	144592.			0.252321			0.126161	+	0.992010i	$0.459735\pi$
$758$	−760173.	−	336534.i	−1.32304	−	0.585720i
$759$		−	583064.i		−	1.01212i
$760$		0			0
$761$	−345143.			−0.595977			−0.297989	−	0.954569i	$-0.596316\pi$
$761$	−345143.			−0.595977			−0.297989	+	0.954569i	$0.596316\pi$
$762$	116109.	−	262271.i	0.199966	−	0.451689i
$763$		−	999799.i		−	1.71737i
$764$	−608923.	+	552940.i	−1.04322	+	0.947308i
$765$		0			0
$766$	533689.	+	236268.i	0.909559	+	0.402668i
$767$		−	31336.0i		−	0.0532663i
$768$	65177.8	−	334239.i	0.110504	−	0.566677i
$769$	−10368.2			−0.0175328			−0.00876641	−	0.999962i	$-0.502790\pi$
$769$	−10368.2			−0.0175328			−0.00876641	+	0.999962i	$0.502790\pi$
$770$		0			0
$771$		−	460973.i		−	0.775474i
$772$	96461.6	+	106228.i	0.161853	+	0.178240i
$773$	304512.			0.509619			0.254809	−	0.966991i	$-0.417987\pi$
$773$	304512.			0.509619			0.254809	+	0.966991i	$0.417987\pi$
$774$	−74479.7	−	32972.7i	−0.124324	−	0.0550392i
$775$		0			0
$776$	−518685.	+	172163.i	−0.861352	+	0.285901i
$777$	−66980.8			−0.110945
$778$	−163477.	+	369267.i	−0.270083	+	0.610072i
$779$			369164.i			0.608338i
$780$		0			0
$781$	−1.01045e6			−1.65659
$782$	−810782.	−	358939.i	−1.32584	−	0.586958i
$783$		−	82519.1i		−	0.134596i
$784$	163546.	−	1.69317e6i	0.266078	−	2.75466i
$785$		0			0
$786$	−169497.	+	382866.i	−0.274358	+	0.619729i
$787$		−	103418.i		−	0.166974i	−0.996509	−	0.0834869i	$-0.973394\pi$
$787$		−	103418.i		−	0.166974i	0.996509	−	0.0834869i	$-0.0266057\pi$
$788$	304734.	+	335587.i	0.490759	+	0.540446i
$789$	−537648.			−0.863662
$790$		0			0
$791$		−	1.76955e6i		−	2.82820i
$792$	−63044.2	−	189937.i	−0.100507	−	0.302803i
$793$	74941.1			0.119172
$794$	−63091.4	+	142513.i	−0.100076	+	0.226054i
$795$		0			0
$796$	−302381.	+	274581.i	−0.477231	+	0.433355i
$797$	292136.			0.459905			0.229952	−	0.973202i	$-0.426143\pi$
$797$	292136.			0.459905			0.229952	+	0.973202i	$0.426143\pi$
$798$	1.19234e6	+	527855.i	1.87237	+	0.828913i
$799$		−	495290.i		−	0.775830i
$800$		0			0
$801$	273612.			0.426452
$802$	−102449.	+	231415.i	−0.159279	+	0.359785i
$803$			603230.i			0.935517i
$804$	39659.2	+	43674.5i	0.0613524	+	0.0675641i
$805$		0			0
$806$	322608.	+	142821.i	0.496599	+	0.219848i
$807$			18462.6i			0.0283496i
$808$	−311779.	+	103486.i	−0.477556	+	0.158511i
$809$	−303085.			−0.463092			−0.231546	−	0.972824i	$-0.574378\pi$
$809$	−303085.			−0.463092			−0.231546	+	0.972824i	$0.574378\pi$
$810$		0			0
$811$			451521.i			0.686493i	0.939245	+	0.343246i	$0.111527\pi$
$811$			451521.i			0.686493i	−0.939245	+	0.343246i	$0.888473\pi$
$812$	662627.	−	601707.i	1.00498	−	0.912584i
$813$	514473.			0.778362
$814$	−57412.3	−	25416.8i	−0.0866475	−	0.0383594i
$815$		0			0
$816$	−302929.	−	29260.4i	−0.454946	−	0.0439441i
$817$	497481.			0.745302
$818$	305097.	−	689162.i	0.455964	−	1.02995i
$819$			439259.i			0.654867i
$820$		0			0
$821$	−758512.			−1.12532			−0.562660	−	0.826689i	$-0.690222\pi$
$821$	−758512.			−1.12532			−0.562660	+	0.826689i	$0.690222\pi$
$822$	210723.	+	93288.3i	0.311866	+	0.138065i
$823$			246363.i			0.363727i	0.983324	+	0.181863i	$0.0582128\pi$
$823$			246363.i			0.363727i	−0.983324	+	0.181863i	$0.941787\pi$
$824$	191297.	+	576332.i	0.281743	+	0.848826i
$825$		0			0
$826$	−28212.5	+	63727.3i	−0.0413506	+	0.0934040i
$827$			726117.i			1.06168i	0.847471	+	0.530842i	$0.178124\pi$
$827$			726117.i			1.06168i	−0.847471	+	0.530842i	$0.821876\pi$
$828$	309867.	−	281379.i	0.451975	−	0.410422i
$829$	97639.2			0.142074			0.0710371	−	0.997474i	$-0.477369\pi$
$829$	97639.2			0.142074			0.0710371	+	0.997474i	$0.477369\pi$
$830$		0			0
$831$		−	519854.i		−	0.752799i
$832$	−561580.	+	418958.i	−0.811269	+	0.605235i
$833$	−1.52024e6			−2.19090
$834$	82146.3	−	185555.i	0.118102	−	0.266772i
$835$		0			0
$836$	821702.	+	904896.i	1.17571	+	1.29475i
$837$	−72341.8			−0.103261
$838$	115080.	+	50946.8i	0.163875	+	0.0725486i
$839$			716452.i			1.01780i	0.860825	+	0.508901i	$0.169948\pi$
$839$			716452.i			1.01780i	−0.860825	+	0.508901i	$0.830052\pi$
$840$		0			0
$841$	−361328.			−0.510869
$842$	−237869.	+	537306.i	−0.335517	+	0.757875i
$843$		−	219730.i		−	0.309197i
$844$	−668436.	+	606981.i	−0.938372	+	0.852100i
$845$		0			0
$846$	213789.	+	94645.8i	0.298706	+	0.132239i
$847$			116804.i			0.162813i
$848$	−29004.9	+	300283.i	−0.0403348	+	0.417580i
$849$	−424073.			−0.588336
$850$		0			0
$851$		−	131317.i		−	0.181326i
$852$	−487631.	−	537001.i	−0.671756	−	0.739769i
$853$	1.10240e6			1.51510			0.757552	−	0.652775i	$-0.226395\pi$
$853$	1.10240e6			1.51510			0.757552	+	0.652775i	$0.226395\pi$
$854$	−152406.	−	67471.2i	−0.208971	−	0.0925130i
$855$		0			0
$856$	−202354.	−	609644.i	−0.276162	−	0.832010i
$857$	−599509.			−0.816271			−0.408135	−	0.912921i	$-0.633821\pi$
$857$	−599509.			−0.816271			−0.408135	+	0.912921i	$0.633821\pi$
$858$	−166683.	+	376509.i	−0.226421	+	0.511447i
$859$		−	653569.i		−	0.885737i	−0.896586	−	0.442869i	$-0.853961\pi$
$859$		−	653569.i		−	0.885737i	0.896586	−	0.442869i	$-0.146039\pi$
$860$		0			0
$861$	276583.			0.373094
$862$	675076.	+	298861.i	0.908528	+	0.402212i
$863$		−	45308.8i		−	0.0608361i	−0.999537	−	0.0304181i	$-0.990316\pi$
$863$		−	45308.8i		−	0.0608361i	0.999537	−	0.0304181i	$-0.00968386\pi$
$864$	70517.1	−	125166.i	0.0944642	−	0.167671i
$865$		0			0
$866$	507263.	−	1.14582e6i	0.676391	−	1.52785i
$867$		−	161999.i		−	0.215513i
$868$	−527497.	−	580904.i	−0.700133	−	0.771018i
$869$	110908.			0.146867
$870$		0			0
$871$		−	121379.i		−	0.159995i
$872$	638522.	−	211939.i	0.839736	−	0.278726i
$873$	−230559.			−0.302520
$874$	−1.03487e6	+	2.33759e6i	−1.35476	+	3.06016i
$875$		0			0
$876$	−320584.	+	291111.i	−0.417767	+	0.379358i
$877$	−388906.			−0.505645			−0.252822	−	0.967513i	$-0.581359\pi$
$877$	−388906.			−0.505645			−0.252822	+	0.967513i	$0.581359\pi$
$878$	381949.	+	169091.i	0.495469	+	0.219347i
$879$		−	721199.i		−	0.933421i
$880$		0			0
$881$	944009.			1.21625			0.608127	−	0.793840i	$-0.291921\pi$
$881$	944009.			1.21625			0.608127	+	0.793840i	$0.291921\pi$
$882$	290505.	−	656201.i	0.373436	−	0.843529i
$883$			1.21479e6i			1.55804i	0.626997	+	0.779022i	$0.284284\pi$
$883$			1.21479e6i			1.55804i	−0.626997	+	0.779022i	$0.715716\pi$
$884$	420945.	+	463564.i	0.538667	+	0.593205i
$885$		0			0
$886$	−84512.6	−	37414.3i	−0.107660	−	0.0476618i
$887$			622178.i			0.790801i	0.918509	+	0.395400i	$0.129394\pi$
$887$			622178.i			0.790801i	−0.918509	+	0.395400i	$0.870606\pi$
$888$	−14198.7	−	42777.3i	−0.0180062	−	0.0542485i
$889$	1.31248e6			1.66069
$890$		0			0
$891$		−	84428.5i		−	0.106349i
$892$	−481023.	+	436799.i	−0.604555	+	0.548974i
$893$	−1.42798e6			−1.79069
$894$	29624.1	+	13114.8i	0.0370655	+	0.0164091i
$895$		0			0
$896$	1.51927e6	−	346423.i	1.89243	−	0.431509i
$897$	−861173.			−1.07030
$898$	103097.	−	232879.i	0.127848	−	0.288788i
$899$		−	303286.i		−	0.375261i
$900$		0			0
$901$	269614.			0.332119
$902$	237071.	+	104953.i	0.291384	+	0.128998i
$903$		−	372719.i		−	0.457094i
$904$	1.13012e6	−	375112.i	1.38289	−	0.459012i
$905$		0			0
$906$	−269399.	+	608526.i	−0.328200	+	0.741349i
$907$		−	1.50427e6i		−	1.82857i	−0.405071	−	0.914285i	$-0.632753\pi$
$907$		−	1.50427e6i		−	1.82857i	0.405071	−	0.914285i	$-0.367247\pi$
$908$	−142784.	+	129657.i	−0.173184	+	0.157262i
$909$	−138588.			−0.167725
$910$		0			0
$911$		−	201013.i		−	0.242207i	−0.992640	−	0.121104i	$-0.961357\pi$
$911$		−	201013.i		−	0.242207i	0.992640	−	0.121104i	$-0.0386433\pi$
$912$	−84361.5	+	873381.i	−0.101427	+	1.05006i
$913$	301568.			0.361779
$914$	−183814.	+	415206.i	−0.220033	+	0.497017i
$915$		0			0
$916$	−650628.	−	716502.i	−0.775429	−	0.853938i
$917$	−1.91598e6			−2.27851
$918$	−117402.	−	51974.8i	−0.139313	−	0.0616748i
$919$		−	448820.i		−	0.531424i	−0.964052	−	0.265712i	$-0.914393\pi$
$919$		−	448820.i		−	0.531424i	0.964052	−	0.265712i	$-0.0856071\pi$
$920$		0			0
$921$	−642471.			−0.757415
$922$	452340.	−	1.02176e6i	0.532112	−	1.20195i
$923$			1.49242e6i			1.75181i
$924$	677959.	−	615629.i	0.794072	−	0.721067i
$925$		0			0
$926$	172946.	+	76564.2i	0.201691	+	0.0892902i
$927$			256184.i			0.298121i
$928$	524745.	+	295636.i	0.609330	+	0.343291i
$929$	162931.			0.188788			0.0943938	−	0.995535i	$-0.469909\pi$
$929$	162931.			0.188788			0.0943938	+	0.995535i	$0.469909\pi$
$930$		0			0
$931$			4.38304e6i			5.05680i
$932$	−298487.	−	328708.i	−0.343632	−	0.378424i
$933$	−70461.6			−0.0809449
$934$	−1.30070e6	−	575829.i	−1.49102	−	0.660085i
$935$		0			0
$936$	−280533.	+	93114.9i	−0.320208	+	0.106284i
$937$	−588705.			−0.670531			−0.335266	−	0.942124i	$-0.608826\pi$
$937$	−588705.			−0.670531			−0.335266	+	0.942124i	$0.608826\pi$
$938$	−109280.	+	246845.i	−0.124204	+	0.280556i
$939$		−	507218.i		−	0.575259i
$940$		0			0
$941$	564925.			0.637987			0.318994	−	0.947757i	$-0.396655\pi$
$941$	564925.			0.637987			0.318994	+	0.947757i	$0.396655\pi$
$942$	582744.	+	257985.i	0.656713	+	0.290731i
$943$			542243.i			0.609776i
$944$	−46680.0	−	4508.91i	−0.0523826	−	0.00505973i
$945$		0			0
$946$	141433.	−	319474.i	0.158041	−	0.356988i
$947$		−	563610.i		−	0.628461i	−0.949347	−	0.314231i	$-0.898253\pi$
$947$		−	563610.i		−	0.628461i	0.949347	−	0.314231i	$-0.101747\pi$
$948$	53522.9	+	58941.9i	0.0595557	+	0.0655855i
$949$	890958.			0.989293
$950$		0			0
$951$			386759.i			0.427641i
$952$	−438709.	−	1.32173e6i	−0.484064	−	1.45837i
$953$	1.47849e6			1.62791			0.813957	−	0.580925i	$-0.197309\pi$
$953$	1.47849e6			1.62791			0.813957	+	0.580925i	$0.197309\pi$
$954$	−51521.0	+	116377.i	−0.0566093	+	0.127871i
$955$		0			0
$956$	−345338.	+	313589.i	−0.377858	+	0.343119i
$957$	353958.			0.386481
$958$	−796072.	−	352427.i	−0.867404	−	0.384006i
$959$			1.05452e6i			1.14661i
$960$		0			0
$961$	657640.			0.712101
$962$	−37540.1	+	84796.7i	−0.0405644	+	0.0916281i
$963$		−	270991.i		−	0.292215i
$964$	−479997.	−	528595.i	−0.516517	−	0.568812i
$965$		0			0
$966$	1.75135e6	+	775334.i	1.87680	+	0.830873i
$967$			475196.i			0.508183i	0.967180	+	0.254091i	$0.0817764\pi$
$967$			475196.i			0.508183i	−0.967180	+	0.254091i	$0.918224\pi$
$968$	−74596.7	+	24760.2i	−0.0796102	+	0.0264243i
$969$	784179.			0.835156
$970$		0			0
$971$			1.36244e6i			1.44503i	0.691354	+	0.722516i	$0.257014\pi$
$971$			1.36244e6i			1.44503i	−0.691354	+	0.722516i	$0.742986\pi$
$972$	44869.2	−	40744.0i	0.0474915	−	0.0431252i
$973$	928571.			0.980820
$974$	97405.5	+	43122.1i	0.102675	+	0.0454550i
$975$		0			0
$976$	10783.2	−	111637.i	0.0113201	−	0.117195i
$977$	172640.			0.180865			0.0904323	−	0.995903i	$-0.471175\pi$
$977$	172640.			0.180865			0.0904323	+	0.995903i	$0.471175\pi$
$978$	308268.	−	696326.i	0.322293	−	0.728006i
$979$			1.17363e6i			1.22452i
$980$		0			0
$981$	283828.			0.294928
$982$	1.69860e6	+	751980.i	1.76144	+	0.779800i
$983$		−	1.11330e6i		−	1.15214i	−0.817400	−	0.576070i	$-0.804585\pi$
$983$		−	1.11330e6i		−	1.15214i	0.817400	−	0.576070i	$-0.195415\pi$
$984$	58630.4	+	176640.i	0.0605526	+	0.182431i
$985$		0			0
$986$	217900.	−	492198.i	0.224131	−	0.506275i
$987$			1.06986e6i			1.09823i
$988$	1.33651e6	−	1.21364e6i	1.36918	−	1.24330i
$989$	730719.			0.747064
$990$		0			0
$991$		−	174924.i		−	0.178115i	−0.996026	−	0.0890576i	$-0.971614\pi$
$991$		−	174924.i		−	0.178115i	0.996026	−	0.0890576i	$-0.0283855\pi$
$992$	259175.	−	460027.i	0.263372	−	0.467477i
$993$	396763.			0.402377
$994$	1.34366e6	−	3.03510e6i	1.35993	−	3.07185i
$995$		0			0
$996$	145532.	+	160267.i	0.146704	+	0.161557i
$997$	−1.21175e6			−1.21906			−0.609528	−	0.792764i	$-0.708641\pi$
$997$	−1.21175e6			−1.21906			−0.609528	+	0.792764i	$0.708641\pi$
$998$	−346186.	−	153259.i	−0.347574	−	0.153874i
$999$		−	19014.8i		−	0.0190529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.c.151.9	yes	16
4.3	odd	2	inner	300.5.c.c.151.10	yes	16
5.2	odd	4		300.5.f.c.199.30		32
5.3	odd	4		300.5.f.c.199.3		32
5.4	even	2		300.5.c.b.151.8	yes	16
20.3	even	4		300.5.f.c.199.29		32
20.7	even	4		300.5.f.c.199.4		32
20.19	odd	2		300.5.c.b.151.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.7	✓	16	20.19	odd	2
300.5.c.b.151.8	yes	16	5.4	even	2
300.5.c.c.151.9	yes	16	1.1	even	1	trivial
300.5.c.c.151.10	yes	16	4.3	odd	2	inner
300.5.f.c.199.3		32	5.3	odd	4
300.5.f.c.199.4		32	20.7	even	4
300.5.f.c.199.29		32	20.3	even	4
300.5.f.c.199.30		32	5.2	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)

\(f(q)\)	\(=\)	\(q+(1.61924 - 3.65760i) q^{2} +5.19615i q^{3} +(-10.7561 - 11.8451i) q^{4} +(19.0055 + 8.41384i) q^{6} +95.1090i q^{7} +(-60.7414 + 20.1614i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(1.61924 - 3.65760i) q^{2} +5.19615i q^{3} +(-10.7561 - 11.8451i) q^{4} +(19.0055 + 8.41384i) q^{6} +95.1090i q^{7} +(-60.7414 + 20.1614i) q^{8} -27.0000 q^{9} -115.814i q^{11} +(61.5490 - 55.8903i) q^{12} -171.055 q^{13} +(347.871 + 154.005i) q^{14} +(-24.6130 + 254.814i) q^{16} +228.789 q^{17} +(-43.7196 + 98.7552i) q^{18} -659.627i q^{19} -494.201 q^{21} +(-423.602 - 187.531i) q^{22} -968.886i q^{23} +(-104.762 - 315.622i) q^{24} +(-276.980 + 625.651i) q^{26} -140.296i q^{27} +(1126.58 - 1023.00i) q^{28} +588.178 q^{29} -515.636i q^{31} +(892.154 + 502.631i) q^{32} +601.788 q^{33} +(370.465 - 836.819i) q^{34} +(290.414 + 319.818i) q^{36} +135.534 q^{37} +(-2412.65 - 1068.10i) q^{38} -888.827i q^{39} -559.656 q^{41} +(-800.232 + 1807.59i) q^{42} +754.185i q^{43} +(-1371.83 + 1245.71i) q^{44} +(-3543.80 - 1568.86i) q^{46} -2164.84i q^{47} +(-1324.05 - 127.893i) q^{48} -6644.72 q^{49} +1188.82i q^{51} +(1839.88 + 2026.16i) q^{52} +1178.44 q^{53} +(-513.147 - 227.174i) q^{54} +(-1917.53 - 5777.06i) q^{56} +3427.52 q^{57} +(952.404 - 2151.32i) q^{58} +183.192i q^{59} -438.111 q^{61} +(-1885.99 - 834.942i) q^{62} -2567.94i q^{63} +(3283.04 - 2449.26i) q^{64} +(974.441 - 2201.10i) q^{66} +709.589i q^{67} +(-2460.87 - 2710.03i) q^{68} +5034.48 q^{69} -8724.78i q^{71} +(1640.02 - 544.357i) q^{72} -5208.61 q^{73} +(219.462 - 495.728i) q^{74} +(-7813.35 + 7095.01i) q^{76} +11015.0 q^{77} +(-3250.98 - 1439.23i) q^{78} +957.643i q^{79} +729.000 q^{81} +(-906.220 + 2047.00i) q^{82} +2603.89i q^{83} +(5315.67 + 5853.86i) q^{84} +(2758.51 + 1221.21i) q^{86} +3056.26i q^{87} +(2334.97 + 7034.71i) q^{88} -10133.8 q^{89} -16268.9i q^{91} +(-11476.6 + 10421.4i) q^{92} +2679.33 q^{93} +(-7918.11 - 3505.40i) q^{94} +(-2611.75 + 4635.77i) q^{96} +8539.24 q^{97} +(-10759.4 + 24303.8i) q^{98} +3126.98i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Introduction

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