LMFDB - Embedded newform 300.5.c.d.151.16

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} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.16
Root			$2.44021 + 1.43016i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.95975 + 0.566024i) q^{2} -5.19615i q^{3} +(15.3592 + 4.48263i) q^{4} +(2.94115 - 20.5755i) q^{6} +24.1355i q^{7} +(58.2814 + 26.4438i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(3.95975 + 0.566024i) q^{2} -5.19615i q^{3} +(15.3592 + 4.48263i) q^{4} +(2.94115 - 20.5755i) q^{6} +24.1355i q^{7} +(58.2814 + 26.4438i) q^{8} -27.0000 q^{9} +227.128i q^{11} +(23.2924 - 79.8089i) q^{12} -285.216 q^{13} +(-13.6613 + 95.5705i) q^{14} +(215.812 + 137.699i) q^{16} +301.510 q^{17} +(-106.913 - 15.2827i) q^{18} +674.273i q^{19} +125.412 q^{21} +(-128.560 + 899.370i) q^{22} -459.987i q^{23} +(137.406 - 302.839i) q^{24} +(-1129.38 - 161.439i) q^{26} +140.296i q^{27} +(-108.190 + 370.703i) q^{28} +146.681 q^{29} -702.116i q^{31} +(776.621 + 667.410i) q^{32} +1180.19 q^{33} +(1193.91 + 170.662i) q^{34} +(-414.699 - 121.031i) q^{36} +100.291 q^{37} +(-381.655 + 2669.95i) q^{38} +1482.03i q^{39} +1100.61 q^{41} +(496.599 + 70.9861i) q^{42} +811.156i q^{43} +(-1018.13 + 3488.51i) q^{44} +(260.364 - 1821.43i) q^{46} +1190.37i q^{47} +(715.507 - 1121.39i) q^{48} +1818.48 q^{49} -1566.69i q^{51} +(-4380.70 - 1278.52i) q^{52} -2293.09 q^{53} +(-79.4110 + 555.537i) q^{54} +(-638.234 + 1406.65i) q^{56} +3503.62 q^{57} +(580.819 + 83.0248i) q^{58} +3143.51i q^{59} -2026.98 q^{61} +(397.415 - 2780.20i) q^{62} -651.658i q^{63} +(2697.45 + 3082.36i) q^{64} +(4673.26 + 668.017i) q^{66} +2697.71i q^{67} +(4630.97 + 1351.56i) q^{68} -2390.16 q^{69} -8362.76i q^{71} +(-1573.60 - 713.982i) q^{72} +6721.01 q^{73} +(397.129 + 56.7674i) q^{74} +(-3022.51 + 10356.3i) q^{76} -5481.85 q^{77} +(-838.863 + 5868.45i) q^{78} -2839.66i q^{79} +729.000 q^{81} +(4358.13 + 622.970i) q^{82} +4621.51i q^{83} +(1926.23 + 562.174i) q^{84} +(-459.134 + 3211.97i) q^{86} -762.175i q^{87} +(-6006.12 + 13237.3i) q^{88} -245.915 q^{89} -6883.83i q^{91} +(2061.95 - 7065.05i) q^{92} -3648.30 q^{93} +(-673.779 + 4713.57i) q^{94} +(3467.97 - 4035.44i) q^{96} -1571.13 q^{97} +(7200.72 + 1029.30i) q^{98} -6132.46i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * 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 $

$2$	3.95975	+	0.566024i	0.989937	+	0.141506i
$2$	3.95975	+	0.566024i	0.989937	+	0.141506i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	15.3592	+	4.48263i	0.959952	+	0.280164i
$5$		0			0
$5$		0			0
$6$	2.94115	−	20.5755i	0.0816986	−	0.571541i
$7$			24.1355i			0.492561i	0.969199	+	0.246281i	$0.0792085\pi$
$7$			24.1355i			0.492561i	−0.969199	+	0.246281i	$0.920792\pi$
$8$	58.2814	+	26.4438i	0.910648	+	0.413184i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			227.128i			1.87709i	0.345155	+	0.938546i	$0.387826\pi$
$11$			227.128i			1.87709i	−0.345155	+	0.938546i	$0.612174\pi$
$12$	23.2924	−	79.8089i	0.161753	−	0.554229i
$13$	−285.216			−1.68767			−0.843835	−	0.536603i	$-0.819707\pi$
$13$	−285.216			−1.68767			−0.843835	+	0.536603i	$0.819707\pi$
$14$	−13.6613	+	95.5705i	−0.0697004	+	0.487605i
$15$		0			0
$16$	215.812	+	137.699i	0.843016	+	0.537889i
$17$	301.510			1.04329			0.521644	−	0.853163i	$-0.325319\pi$
$17$	301.510			1.04329			0.521644	+	0.853163i	$0.325319\pi$
$18$	−106.913	−	15.2827i	−0.329979	−	0.0471687i
$19$			674.273i			1.86779i	0.357545	+	0.933896i	$0.383614\pi$
$19$			674.273i			1.86779i	−0.357545	+	0.933896i	$0.616386\pi$
$20$		0			0
$21$	125.412			0.284380
$22$	−128.560	+	899.370i	−0.265620	+	1.85820i
$23$		−	459.987i		−	0.869541i	−0.900541	−	0.434770i	$-0.856830\pi$
$23$		−	459.987i		−	0.869541i	0.900541	−	0.434770i	$-0.143170\pi$
$24$	137.406	−	302.839i	0.238552	−	0.525763i
$25$		0			0
$26$	−1129.38	−	161.439i	−1.67069	−	0.238815i
$27$			140.296i			0.192450i
$28$	−108.190	+	370.703i	−0.137998	+	0.472835i
$29$	146.681			0.174412			0.0872061	−	0.996190i	$-0.472206\pi$
$29$	146.681			0.174412			0.0872061	+	0.996190i	$0.472206\pi$
$30$		0			0
$31$		−	702.116i		−	0.730610i	−0.930888	−	0.365305i	$-0.880965\pi$
$31$		−	702.116i		−	0.730610i	0.930888	−	0.365305i	$-0.119035\pi$
$32$	776.621	+	667.410i	0.758419	+	0.651768i
$33$	1180.19			1.08374
$34$	1193.91	+	170.662i	1.03279	+	0.147632i
$35$		0			0
$36$	−414.699	−	121.031i	−0.319984	−	0.0933881i
$37$	100.291			0.0732589			0.0366295	−	0.999329i	$-0.488338\pi$
$37$	100.291			0.0732589			0.0366295	+	0.999329i	$0.488338\pi$
$38$	−381.655	+	2669.95i	−0.264304	+	1.84900i
$39$			1482.03i			0.974376i
$40$		0			0
$41$	1100.61			0.654733			0.327367	−	0.944897i	$-0.393839\pi$
$41$	1100.61			0.654733			0.327367	+	0.944897i	$0.393839\pi$
$42$	496.599	+	70.9861i	0.281519	+	0.0402415i
$43$			811.156i			0.438700i	0.975646	+	0.219350i	$0.0703936\pi$
$43$			811.156i			0.438700i	−0.975646	+	0.219350i	$0.929606\pi$
$44$	−1018.13	+	3488.51i	−0.525894	+	1.80192i
$45$		0			0
$46$	260.364	−	1821.43i	0.123045	−	0.860791i
$47$			1190.37i			0.538874i	0.963018	+	0.269437i	$0.0868375\pi$
$47$			1190.37i			0.538874i	−0.963018	+	0.269437i	$0.913162\pi$
$48$	715.507	−	1121.39i	0.310550	−	0.486715i
$49$	1818.48			0.757384
$50$		0			0
$51$		−	1566.69i		−	0.602343i
$52$	−4380.70	−	1278.52i	−1.62008	−	0.472825i
$53$	−2293.09			−0.816337			−0.408168	−	0.912907i	$-0.633832\pi$
$53$	−2293.09			−0.816337			−0.408168	+	0.912907i	$0.633832\pi$
$54$	−79.4110	+	555.537i	−0.0272329	+	0.190514i
$55$		0			0
$56$	−638.234	+	1406.65i	−0.203518	+	0.448550i
$57$	3503.62			1.07837
$58$	580.819	+	83.0248i	0.172657	+	0.0246804i
$59$			3143.51i			0.903047i	0.892259	+	0.451523i	$0.149119\pi$
$59$			3143.51i			0.903047i	−0.892259	+	0.451523i	$0.850881\pi$
$60$		0			0
$61$	−2026.98			−0.544741			−0.272370	−	0.962193i	$-0.587808\pi$
$61$	−2026.98			−0.544741			−0.272370	+	0.962193i	$0.587808\pi$
$62$	397.415	−	2780.20i	0.103386	−	0.723258i
$63$		−	651.658i		−	0.164187i
$64$	2697.45	+	3082.36i	0.658558	+	0.752530i
$65$		0			0
$66$	4673.26	+	668.017i	1.07283	+	0.153356i
$67$			2697.71i			0.600959i	0.953788	+	0.300480i	$0.0971468\pi$
$67$			2697.71i			0.600959i	−0.953788	+	0.300480i	$0.902853\pi$
$68$	4630.97	+	1351.56i	1.00151	+	0.292292i
$69$	−2390.16			−0.502029
$70$		0			0
$71$		−	8362.76i		−	1.65895i	−0.558545	−	0.829474i	$-0.688640\pi$
$71$		−	8362.76i		−	1.65895i	0.558545	−	0.829474i	$-0.311360\pi$
$72$	−1573.60	−	713.982i	−0.303549	−	0.137728i
$73$	6721.01			1.26121			0.630607	−	0.776102i	$-0.282806\pi$
$73$	6721.01			1.26121			0.630607	+	0.776102i	$0.282806\pi$
$74$	397.129	+	56.7674i	0.0725217	+	0.0103666i
$75$		0			0
$76$	−3022.51	+	10356.3i	−0.523288	+	1.79299i
$77$	−5481.85			−0.924582
$78$	−838.863	+	5868.45i	−0.137880	+	0.964571i
$79$		−	2839.66i		−	0.455000i	−0.973778	−	0.227500i	$-0.926945\pi$
$79$		−	2839.66i		−	0.455000i	0.973778	−	0.227500i	$-0.0730552\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	4358.13	+	622.970i	0.648145	+	0.0926487i
$83$			4621.51i			0.670853i	0.942066	+	0.335427i	$0.108880\pi$
$83$			4621.51i			0.670853i	−0.942066	+	0.335427i	$0.891120\pi$
$84$	1926.23	+	562.174i	0.272991	+	0.0796732i
$85$		0			0
$86$	−459.134	+	3211.97i	−0.0620787	+	0.434285i
$87$		−	762.175i		−	0.100697i
$88$	−6006.12	+	13237.3i	−0.775584	+	1.70937i
$89$	−245.915			−0.0310460			−0.0155230	−	0.999880i	$-0.504941\pi$
$89$	−245.915			−0.0310460			−0.0155230	+	0.999880i	$0.504941\pi$
$90$		0			0
$91$		−	6883.83i		−	0.831280i
$92$	2061.95	−	7065.05i	0.243614	−	0.834717i
$93$	−3648.30			−0.421818
$94$	−673.779	+	4713.57i	−0.0762539	+	0.533451i
$95$		0			0
$96$	3467.97	−	4035.44i	0.376298	−	0.437873i
$97$	−1571.13			−0.166982			−0.0834908	−	0.996509i	$-0.526607\pi$
$97$	−1571.13			−0.166982			−0.0834908	+	0.996509i	$0.526607\pi$
$98$	7200.72	+	1029.30i	0.749762	+	0.107174i
$99$		−	6132.46i		−	0.625697i
$100$		0			0
$101$	5857.49			0.574208			0.287104	−	0.957899i	$-0.407308\pi$
$101$	5857.49			0.574208			0.287104	+	0.957899i	$0.407308\pi$
$102$	886.787	−	6203.72i	0.0852352	−	0.596282i
$103$		−	13444.3i		−	1.26726i	−0.773638	−	0.633628i	$-0.781565\pi$
$103$		−	13444.3i		−	1.26726i	0.773638	−	0.633628i	$-0.218435\pi$
$104$	−16622.8	−	7542.19i	−1.53687	−	0.697318i
$105$		0			0
$106$	−9080.06	−	1297.94i	−0.808122	−	0.115517i
$107$			5130.98i			0.448160i	0.974571	+	0.224080i	$0.0719377\pi$
$107$			5130.98i			0.448160i	−0.974571	+	0.224080i	$0.928062\pi$
$108$	−628.895	+	2154.84i	−0.0539176	+	0.184743i
$109$	2448.93			0.206122			0.103061	−	0.994675i	$-0.467136\pi$
$109$	2448.93			0.206122			0.103061	+	0.994675i	$0.467136\pi$
$110$		0			0
$111$		−	521.130i		−	0.0422961i
$112$	−3323.45	+	5208.73i	−0.264943	+	0.415237i
$113$	−4654.07			−0.364482			−0.182241	−	0.983254i	$-0.558335\pi$
$113$	−4654.07			−0.364482			−0.182241	+	0.983254i	$0.558335\pi$
$114$	13873.5	+	1983.14i	1.06752	+	0.152596i
$115$		0			0
$116$	2252.90	+	657.515i	0.167427	+	0.0488641i
$117$	7700.83			0.562556
$118$	−1779.30	+	12447.5i	−0.127787	+	0.893960i
$119$			7277.10i			0.513883i
$120$		0			0
$121$	−36946.1			−2.52347
$122$	−8026.33	−	1147.32i	−0.539259	−	0.0770841i
$123$		−	5718.92i		−	0.378010i
$124$	3147.32	−	10784.0i	0.204691	−	0.701350i
$125$		0			0
$126$	368.854	−	2580.40i	0.0232335	−	0.162535i
$127$		−	2926.08i		−	0.181417i	−0.995877	−	0.0907086i	$-0.971087\pi$
$127$		−	2926.08i		−	0.181417i	0.995877	−	0.0907086i	$-0.0289132\pi$
$128$	8936.54	+	13732.2i	0.545443	+	0.838148i
$129$	4214.89			0.253283
$130$		0			0
$131$		−	16684.4i		−	0.972229i	−0.873895	−	0.486114i	$-0.838414\pi$
$131$		−	16684.4i		−	0.972229i	0.873895	−	0.486114i	$-0.161586\pi$
$132$	18126.8	+	5290.36i	1.04034	+	0.303625i
$133$	−16273.9			−0.920002
$134$	−1526.97	+	10682.2i	−0.0850394	+	0.594912i
$135$		0			0
$136$	17572.5	+	7973.08i	0.950068	+	0.431070i
$137$	−25513.0			−1.35932			−0.679659	−	0.733529i	$-0.737872\pi$
$137$	−25513.0			−1.35932			−0.679659	+	0.733529i	$0.737872\pi$
$138$	−9464.44	−	1352.89i	−0.496978	−	0.0710402i
$139$			1316.26i			0.0681261i	0.999420	+	0.0340630i	$0.0108447\pi$
$139$			1316.26i			0.0681261i	−0.999420	+	0.0340630i	$0.989155\pi$
$140$		0			0
$141$	6185.35			0.311119
$142$	4733.52	−	33114.4i	0.234751	−	1.64225i
$143$		−	64780.6i		−	3.16791i
$144$	−5826.93	−	3717.89i	−0.281005	−	0.179296i
$145$		0			0
$146$	26613.5	+	3804.26i	1.24852	+	0.178470i
$147$		−	9449.09i		−	0.437276i
$148$	1540.40	+	449.569i	0.0703251	+	0.0205245i
$149$	−20604.9			−0.928107			−0.464054	−	0.885807i	$-0.653606\pi$
$149$	−20604.9			−0.928107			−0.464054	+	0.885807i	$0.653606\pi$
$150$		0			0
$151$			9781.71i			0.429004i	0.976724	+	0.214502i	$0.0688128\pi$
$151$			9781.71i			0.429004i	−0.976724	+	0.214502i	$0.931187\pi$
$152$	−17830.3	+	39297.6i	−0.771742	+	1.70090i
$153$	−8140.78			−0.347763
$154$	−21706.7	−	3102.86i	−0.915278	−	0.130834i
$155$		0			0
$156$	−6643.37	+	22762.8i	−0.272985	+	0.935354i
$157$	20309.0			0.823929			0.411964	−	0.911200i	$-0.364843\pi$
$157$	20309.0			0.823929			0.411964	+	0.911200i	$0.364843\pi$
$158$	1607.31	−	11244.3i	0.0643853	−	0.450422i
$159$			11915.2i			0.471312i
$160$		0			0
$161$	11102.0			0.428302
$162$	2886.66	+	412.632i	0.109993	+	0.0157229i
$163$		−	34880.4i		−	1.31282i	−0.754402	−	0.656412i	$-0.772073\pi$
$163$		−	34880.4i		−	1.31282i	0.754402	−	0.656412i	$-0.227927\pi$
$164$	16904.5	+	4933.61i	0.628512	+	0.183433i
$165$		0			0
$166$	−2615.89	+	18300.0i	−0.0949298	+	0.664103i
$167$			26021.4i			0.933036i	0.884512	+	0.466518i	$0.154492\pi$
$167$			26021.4i			0.933036i	−0.884512	+	0.466518i	$0.845508\pi$
$168$	7309.18	+	3316.36i	0.258970	+	0.117501i
$169$	52787.2			1.84823
$170$		0			0
$171$		−	18205.4i		−	0.622597i
$172$	−3636.11	+	12458.7i	−0.122908	+	0.421131i
$173$	41594.8			1.38978			0.694891	−	0.719115i	$-0.255453\pi$
$173$	41594.8			1.38978			0.694891	+	0.719115i	$0.255453\pi$
$174$	431.410	−	3018.02i	0.0142492	−	0.0996837i
$175$		0			0
$176$	−31275.4	+	49017.0i	−1.00967	+	1.58242i
$177$	16334.1			0.521374
$178$	−973.764	−	139.194i	−0.0307336	−	0.00439320i
$179$		−	52061.3i		−	1.62483i	−0.583078	−	0.812416i	$-0.698152\pi$
$179$		−	52061.3i		−	1.62483i	0.583078	−	0.812416i	$-0.301848\pi$
$180$		0			0
$181$	48399.0			1.47734			0.738668	−	0.674070i	$-0.235455\pi$
$181$	48399.0			1.47734			0.738668	+	0.674070i	$0.235455\pi$
$182$	3896.42	−	27258.2i	0.117631	−	0.822915i
$183$			10532.5i			0.314506i
$184$	12163.8	−	26808.7i	0.359280	−	0.791845i
$185$		0			0
$186$	−14446.4	−	2065.03i	−0.417573	−	0.0596897i
$187$			68481.5i			1.95835i
$188$	−5336.00	+	18283.2i	−0.150973	+	0.517293i
$189$	−3386.12			−0.0947934
$190$		0			0
$191$			14536.0i			0.398453i	0.979953	+	0.199227i	$0.0638430\pi$
$191$			14536.0i			0.398453i	−0.979953	+	0.199227i	$0.936157\pi$
$192$	16016.4	−	14016.4i	0.434474	−	0.380218i
$193$	494.150			0.0132661			0.00663306	−	0.999978i	$-0.497889\pi$
$193$	494.150			0.0132661			0.00663306	+	0.999978i	$0.497889\pi$
$194$	−6221.28	−	889.297i	−0.165301	−	0.0236289i
$195$		0			0
$196$	27930.4	+	8151.56i	0.727052	+	0.212192i
$197$	3087.98			0.0795686			0.0397843	−	0.999208i	$-0.487333\pi$
$197$	3087.98			0.0795686			0.0397843	+	0.999208i	$0.487333\pi$
$198$	3471.12	−	24283.0i	0.0885399	−	0.619401i
$199$		−	48825.3i		−	1.23293i	−0.787382	−	0.616465i	$-0.788564\pi$
$199$		−	48825.3i		−	1.23293i	0.787382	−	0.616465i	$-0.211436\pi$
$200$		0			0
$201$	14017.7			0.346964
$202$	23194.2	+	3315.48i	0.568430	+	0.0812538i
$203$			3540.21i			0.0859087i
$204$	7022.91	−	24063.2i	0.168755	−	0.578220i
$205$		0			0
$206$	7609.81	−	53236.2i	0.179325	−	1.25450i
$207$			12419.6i			0.289847i
$208$	−61553.1	−	39274.1i	−1.42273	−	0.907778i
$209$	−153146.			−3.50601
$210$		0			0
$211$		−	68422.2i		−	1.53685i	−0.639938	−	0.768427i	$-0.721040\pi$
$211$		−	68422.2i		−	1.53685i	0.639938	−	0.768427i	$-0.278960\pi$
$212$	−35220.1	−	10279.1i	−0.783644	−	0.228708i
$213$	−43454.2			−0.957794
$214$	−2904.26	+	20317.4i	−0.0634173	+	0.443650i
$215$		0			0
$216$	−3709.96	+	8176.66i	−0.0795173	+	0.175254i
$217$	16945.9			0.359870
$218$	9697.15	+	1386.15i	0.204047	+	0.0291674i
$219$		−	34923.4i		−	0.728163i
$220$		0			0
$221$	−85995.6			−1.76073
$222$	294.972	−	2063.54i	0.00598515	−	0.0418704i
$223$			1815.89i			0.0365157i	0.999833	+	0.0182578i	$0.00581197\pi$
$223$			1815.89i			0.0365157i	−0.999833	+	0.0182578i	$0.994188\pi$
$224$	−16108.3	+	18744.1i	−0.321036	+	0.373568i
$225$		0			0
$226$	−18429.0	−	2634.32i	−0.360815	−	0.0515764i
$227$		−	25286.9i		−	0.490731i	−0.969431	−	0.245366i	$-0.921092\pi$
$227$		−	25286.9i		−	0.490731i	0.969431	−	0.245366i	$-0.0789080\pi$
$228$	53813.0	+	15705.4i	1.03518	+	0.302121i
$229$	61533.5			1.17338			0.586692	−	0.809810i	$-0.300430\pi$
$229$	61533.5			1.17338			0.586692	+	0.809810i	$0.300430\pi$
$230$		0			0
$231$			28484.5i			0.533808i
$232$	8548.76	+	3878.79i	0.158828	+	0.0720644i
$233$	−78964.4			−1.45452			−0.727260	−	0.686362i	$-0.759207\pi$
$233$	−78964.4			−1.45452			−0.727260	+	0.686362i	$0.759207\pi$
$234$	30493.4	+	4358.86i	0.556896	+	0.0796051i
$235$		0			0
$236$	−14091.2	+	48281.8i	−0.253001	+	0.866882i
$237$	−14755.3			−0.262694
$238$	−4119.02	+	28815.5i	−0.0727176	+	0.508712i
$239$			60958.7i			1.06719i	0.845742	+	0.533593i	$0.179159\pi$
$239$			60958.7i			1.06719i	−0.845742	+	0.533593i	$0.820841\pi$
$240$		0			0
$241$	43359.9			0.746541			0.373271	−	0.927723i	$-0.378236\pi$
$241$	43359.9			0.746541			0.373271	+	0.927723i	$0.378236\pi$
$242$	−146297.	−	20912.4i	−2.49808	−	0.357086i
$243$		−	3788.00i		−	0.0641500i
$244$	−31132.9	−	9086.20i	−0.522925	−	0.152617i
$245$		0			0
$246$	3237.05	−	22645.5i	0.0534908	−	0.374207i
$247$		−	192313.i		−	3.15221i
$248$	18566.6	−	40920.3i	0.301876	−	0.665328i
$249$	24014.1			0.387317
$250$		0			0
$251$			4036.99i			0.0640783i	0.999487	+	0.0320391i	$0.0102001\pi$
$251$			4036.99i			0.0640783i	−0.999487	+	0.0320391i	$0.989800\pi$
$252$	2921.14	−	10009.0i	0.0459993	−	0.157612i
$253$	104476.			1.63221
$254$	1656.23	−	11586.5i	0.0256716	−	0.179592i
$255$		0			0
$256$	27613.7	+	59434.4i	0.421352	+	0.906897i
$257$	−21219.0			−0.321261			−0.160631	−	0.987015i	$-0.551353\pi$
$257$	−21219.0			−0.321261			−0.160631	+	0.987015i	$0.551353\pi$
$258$	16689.9	+	2385.73i	0.250735	+	0.0358411i
$259$			2420.58i			0.0360845i
$260$		0			0
$261$	−3960.38			−0.0581374
$262$	9443.79	−	66066.1i	0.137576	−	0.962446i
$263$			65565.0i			0.947895i	0.880553	+	0.473948i	$0.157171\pi$
$263$			65565.0i			0.947895i	−0.880553	+	0.473948i	$0.842829\pi$
$264$	68783.3	+	31208.7i	0.986904	+	0.447784i
$265$		0			0
$266$	−64440.6	−	9211.43i	−0.910744	−	0.130186i
$267$			1277.81i			0.0179244i
$268$	−12092.8	+	41434.7i	−0.168367	+	0.576892i
$269$	71452.1			0.987439			0.493720	−	0.869621i	$-0.335637\pi$
$269$	71452.1			0.987439			0.493720	+	0.869621i	$0.335637\pi$
$270$		0			0
$271$			51926.3i			0.707048i	0.935426	+	0.353524i	$0.115017\pi$
$271$			51926.3i			0.707048i	−0.935426	+	0.353524i	$0.884983\pi$
$272$	65069.6	+	41517.8i	0.879509	+	0.561173i
$273$	−35769.4			−0.479940
$274$	−101025.	−	14441.0i	−1.34564	−	0.192352i
$275$		0			0
$276$	−36711.1	−	10714.2i	−0.481924	−	0.140651i
$277$	21894.1			0.285344			0.142672	−	0.989770i	$-0.454431\pi$
$277$	21894.1			0.285344			0.142672	+	0.989770i	$0.454431\pi$
$278$	−745.037	+	5212.08i	−0.00964025	+	0.0674406i
$279$			18957.1i			0.243537i
$280$		0			0
$281$	8050.35			0.101954			0.0509768	−	0.998700i	$-0.483767\pi$
$281$	8050.35			0.101954			0.0509768	+	0.998700i	$0.483767\pi$
$282$	24492.5	+	3501.06i	0.307988	+	0.0440252i
$283$			55028.7i			0.687094i	0.939136	+	0.343547i	$0.111628\pi$
$283$			55028.7i			0.687094i	−0.939136	+	0.343547i	$0.888372\pi$
$284$	37487.1	−	128446.i	0.464778	−	1.59251i
$285$		0			0
$286$	36667.4	−	256515.i	0.448278	−	3.13603i
$287$			26563.7i			0.322496i
$288$	−20968.8	−	18020.1i	−0.252806	−	0.217256i
$289$	7387.52			0.0884510
$290$		0			0
$291$			8163.83i			0.0964068i
$292$	103230.	+	30127.8i	1.21071	+	0.353347i
$293$	84067.6			0.979249			0.489625	−	0.871933i	$-0.337134\pi$
$293$	84067.6			0.979249			0.489625	+	0.871933i	$0.337134\pi$
$294$	5348.41	−	37416.0i	0.0618771	−	0.432875i
$295$		0			0
$296$	5845.13	+	2652.09i	0.0667131	+	0.0302694i
$297$	−31865.2			−0.361246
$298$	−81590.3	−	11662.9i	−0.918768	−	0.131333i
$299$			131196.i			1.46750i
$300$		0			0
$301$	−19577.7			−0.216086
$302$	−5536.68	+	38733.1i	−0.0607066	+	0.424687i
$303$		−	30436.4i		−	0.331519i
$304$	−92847.0	+	145516.i	−1.00466	+	1.57458i
$305$		0			0
$306$	−32235.5	−	4607.88i	−0.344263	−	0.0492106i
$307$			77747.6i			0.824917i	0.910976	+	0.412458i	$0.135330\pi$
$307$			77747.6i			0.824917i	−0.910976	+	0.412458i	$0.864670\pi$
$308$	−84197.0	−	24573.1i	−0.887555	−	0.259035i
$309$	−69858.8			−0.731651
$310$		0			0
$311$			94365.6i			0.975648i	0.872942	+	0.487824i	$0.162209\pi$
$311$			94365.6i			0.975648i	−0.872942	+	0.487824i	$0.837791\pi$
$312$	−39190.4	+	86374.6i	−0.402597	+	0.887313i
$313$	95720.9			0.977053			0.488527	−	0.872549i	$-0.337535\pi$
$313$	95720.9			0.977053			0.488527	+	0.872549i	$0.337535\pi$
$314$	80418.7	+	11495.4i	0.815638	+	0.116591i
$315$		0			0
$316$	12729.1	−	43614.9i	0.127475	−	0.436778i
$317$	−164258.			−1.63459			−0.817295	−	0.576220i	$-0.804527\pi$
$317$	−164258.			−1.63459			−0.817295	+	0.576220i	$0.804527\pi$
$318$	−6744.32	+	47181.4i	−0.0666935	+	0.466570i
$319$			33315.3i			0.327388i
$320$		0			0
$321$	26661.4			0.258745
$322$	43961.2	+	6284.01i	0.423992	+	0.0606073i
$323$			203300.i			1.94865i
$324$	11196.9	+	3267.84i	0.106661	+	0.0311294i
$325$		0			0
$326$	19743.2	−	138118.i	0.185773	−	1.29961i
$327$		−	12725.0i		−	0.119004i
$328$	64144.9	+	29104.2i	0.596231	+	0.270525i
$329$	−28730.2			−0.265428
$330$		0			0
$331$			155573.i			1.41997i	0.704218	+	0.709984i	$0.251298\pi$
$331$			155573.i			1.41997i	−0.704218	+	0.709984i	$0.748702\pi$
$332$	−20716.5	+	70982.8i	−0.187949	+	0.643987i
$333$	−2707.87			−0.0244196
$334$	−14728.8	+	103038.i	−0.132030	+	0.923647i
$335$		0			0
$336$	27065.4	+	17269.1i	0.239737	+	0.152965i
$337$	203622.			1.79294			0.896469	−	0.443106i	$-0.146124\pi$
$337$	203622.			1.79294			0.896469	+	0.443106i	$0.146124\pi$
$338$	209024.	+	29878.8i	1.82963	+	0.261535i
$339$			24183.3i			0.210434i
$340$		0			0
$341$	159470.			1.37142
$342$	10304.7	−	72088.7i	0.0881013	−	0.616332i
$343$			101839.i			0.865619i
$344$	−21450.0	+	47275.3i	−0.181264	+	0.399501i
$345$		0			0
$346$	164705.	+	23543.7i	1.37580	+	0.196663i
$347$		−	545.776i		−	0.00453269i	−0.999997	−	0.00226634i	$-0.999279\pi$
$347$		−	545.776i		−	0.00453269i	0.999997	−	0.00226634i	$-0.000721400\pi$
$348$	3416.55	−	11706.4i	0.0282117	−	0.0966642i
$349$	218943.			1.79755			0.898774	−	0.438413i	$-0.144459\pi$
$349$	218943.			1.79755			0.898774	+	0.438413i	$0.144459\pi$
$350$		0			0
$351$		−	40014.7i		−	0.324792i
$352$	−151588.	+	176392.i	−1.22343	+	1.42362i
$353$	−139457.			−1.11915			−0.559577	−	0.828778i	$-0.689037\pi$
$353$	−139457.			−1.11915			−0.559577	+	0.828778i	$0.689037\pi$
$354$	64679.1	+	9245.52i	0.516128	+	0.0737776i
$355$		0			0
$356$	−3777.07	−	1102.35i	−0.0298027	−	0.00869798i
$357$	37812.9			0.296691
$358$	29467.9	−	206150.i	0.229924	−	1.60848i
$359$		−	24598.3i		−	0.190861i	−0.995436	−	0.0954303i	$-0.969577\pi$
$359$		−	24598.3i		−	0.190861i	0.995436	−	0.0954303i	$-0.0304227\pi$
$360$		0			0
$361$	−324323.			−2.48865
$362$	191648.	+	27395.0i	1.46247	+	0.209052i
$363$			191978.i			1.45693i
$364$	30857.7	−	105730.i	0.232895	−	0.797989i
$365$		0			0
$366$	−5961.65	+	41706.0i	−0.0445045	+	0.311341i
$367$			9837.44i			0.0730382i	0.999333	+	0.0365191i	$0.0116270\pi$
$367$			9837.44i			0.0730382i	−0.999333	+	0.0365191i	$0.988373\pi$
$368$	63340.0	−	99270.7i	0.467716	−	0.733037i
$369$	−29716.4			−0.218244
$370$		0			0
$371$		−	55344.9i		−	0.402096i
$372$	−56035.1	−	16354.0i	−0.404925	−	0.118178i
$373$	45612.8			0.327845			0.163923	−	0.986473i	$-0.447585\pi$
$373$	45612.8			0.327845			0.163923	+	0.986473i	$0.447585\pi$
$374$	−38762.2	+	271169.i	−0.277118	+	1.93864i
$375$		0			0
$376$	−31477.9	+	69376.6i	−0.222654	+	0.490724i
$377$	−41835.7			−0.294350
$378$	−13408.2	−	1916.62i	−0.0938396	−	0.0134138i
$379$			215578.i			1.50081i	0.660978	+	0.750405i	$0.270142\pi$
$379$			215578.i			1.50081i	−0.660978	+	0.750405i	$0.729858\pi$
$380$		0			0
$381$	−15204.4			−0.104741
$382$	−8227.72	+	57558.8i	−0.0563836	+	0.394444i
$383$		−	59498.4i		−	0.405609i	−0.979219	−	0.202805i	$-0.934994\pi$
$383$		−	59498.4i		−	0.405609i	0.979219	−	0.202805i	$-0.0650056\pi$
$384$	71354.7	−	46435.6i	0.483905	−	0.314912i
$385$		0			0
$386$	1956.71	+	279.701i	0.0131326	+	0.00187724i
$387$		−	21901.2i		−	0.146233i
$388$	−24131.3	−	7042.79i	−0.160294	−	0.0467823i
$389$	−111361.			−0.735925			−0.367963	−	0.929841i	$-0.619945\pi$
$389$	−111361.			−0.735925			−0.367963	+	0.929841i	$0.619945\pi$
$390$		0			0
$391$		−	138691.i		−	0.907182i
$392$	105984.	+	48087.4i	0.689709	+	0.312939i
$393$	−86694.8			−0.561317
$394$	12227.6	+	1747.87i	0.0787679	+	0.0112594i
$395$		0			0
$396$	27489.5	−	94189.8i	0.175298	−	0.600639i
$397$	−202511.			−1.28489			−0.642446	−	0.766331i	$-0.722080\pi$
$397$	−202511.			−1.28489			−0.642446	+	0.766331i	$0.722080\pi$
$398$	27636.3	−	193336.i	0.174467	−	1.22052i
$399$			84561.7i			0.531163i
$400$		0			0
$401$	54865.9			0.341204			0.170602	−	0.985340i	$-0.445429\pi$
$401$	54865.9			0.341204			0.170602	+	0.985340i	$0.445429\pi$
$402$	55506.6	+	7934.36i	0.343473	+	0.0490975i
$403$			200255.i			1.23303i
$404$	89966.6	+	26257.0i	0.551212	+	0.160872i
$405$		0			0
$406$	−2003.85	+	14018.3i	−0.0121566	+	0.0850442i
$407$			22779.0i			0.137514i
$408$	41429.3	−	91309.2i	0.248879	−	0.548522i
$409$	194691.			1.16385			0.581927	−	0.813241i	$-0.302299\pi$
$409$	194691.			1.16385			0.581927	+	0.813241i	$0.302299\pi$
$410$		0			0
$411$			132570.i			0.784802i
$412$	60265.9	−	206495.i	0.355040	−	1.21651i
$413$	−75870.1			−0.444806
$414$	−7029.82	+	49178.7i	−0.0410151	+	0.286930i
$415$		0			0
$416$	−221505.	−	190356.i	−1.27996	−	1.09997i
$417$	6839.51			0.0393326
$418$	−606421.	−	86684.5i	−3.47074	−	0.496122i
$419$		−	138559.i		−	0.789234i	−0.918846	−	0.394617i	$-0.870877\pi$
$419$		−	138559.i		−	0.789234i	0.918846	−	0.394617i	$-0.129123\pi$
$420$		0			0
$421$	127025.			0.716682			0.358341	−	0.933591i	$-0.383343\pi$
$421$	127025.			0.716682			0.358341	+	0.933591i	$0.383343\pi$
$422$	38728.6	−	270935.i	0.217474	−	1.52139i
$423$		−	32140.0i		−	0.179625i
$424$	−133645.	−	60638.0i	−0.743395	−	0.337297i
$425$		0			0
$426$	−172068.	−	24596.1i	−0.948156	−	0.135534i
$427$		−	48922.2i		−	0.268318i
$428$	−23000.3	+	78808.0i	−0.125558	+	0.430212i
$429$	−336610.			−1.82899
$430$		0			0
$431$			139485.i			0.750884i	0.926846	+	0.375442i	$0.122509\pi$
$431$			139485.i			0.750884i	−0.926846	+	0.375442i	$0.877491\pi$
$432$	−19318.7	+	30277.6i	−0.103517	+	0.162238i
$433$	334231.			1.78267			0.891334	−	0.453348i	$-0.149770\pi$
$433$	334231.			1.78267			0.891334	+	0.453348i	$0.149770\pi$
$434$	67101.6	+	9591.80i	0.356249	+	0.0509238i
$435$		0			0
$436$	37613.7	+	10977.6i	0.197867	+	0.0577479i
$437$	310157.			1.62412
$438$	19767.5	−	138288.i	0.103039	−	0.720835i
$439$		−	290388.i		−	1.50678i	−0.657575	−	0.753389i	$-0.728418\pi$
$439$		−	290388.i		−	1.50678i	0.657575	−	0.753389i	$-0.271582\pi$
$440$		0			0
$441$	−49098.9			−0.252461
$442$	−340521.	−	48675.6i	−1.74301	−	0.249153i
$443$		−	31499.4i		−	0.160507i	−0.996774	−	0.0802537i	$-0.974427\pi$
$443$		−	31499.4i		−	0.160507i	0.996774	−	0.0802537i	$-0.0255731\pi$
$444$	2336.03	−	8004.15i	0.0118498	−	0.0406022i
$445$		0			0
$446$	−1027.84	+	7190.46i	−0.00516719	+	0.0361482i
$447$			107066.i			0.535843i
$448$	−74394.4	+	65104.4i	−0.370667	+	0.324380i
$449$	304272.			1.50928			0.754640	−	0.656139i	$-0.227812\pi$
$449$	304272.			1.50928			0.754640	+	0.656139i	$0.227812\pi$
$450$		0			0
$451$			249979.i			1.22899i
$452$	−71483.0	−	20862.5i	−0.349885	−	0.102115i
$453$	50827.3			0.247685
$454$	14313.0	−	100130.i	0.0694414	−	0.485793i
$455$		0			0
$456$	204196.	+	92649.1i	0.982015	+	0.445565i
$457$	−152004.			−0.727816			−0.363908	−	0.931435i	$-0.618558\pi$
$457$	−152004.			−0.727816			−0.363908	+	0.931435i	$0.618558\pi$
$458$	243657.	+	34829.4i	1.16158	+	0.166041i
$459$			42300.7i			0.200781i
$460$		0			0
$461$	161303.			0.758998			0.379499	−	0.925192i	$-0.376096\pi$
$461$	161303.			0.758998			0.379499	+	0.925192i	$0.376096\pi$
$462$	−16122.9	+	112792.i	−0.0755370	+	0.528436i
$463$		−	144022.i		−	0.671842i	−0.941890	−	0.335921i	$-0.890952\pi$
$463$		−	144022.i		−	0.671842i	0.941890	−	0.335921i	$-0.109048\pi$
$464$	31655.5	+	20197.9i	0.147032	+	0.0938143i
$465$		0			0
$466$	−312679.	−	44695.8i	−1.43988	−	0.205823i
$467$		−	286324.i		−	1.31288i	−0.754380	−	0.656438i	$-0.772062\pi$
$467$		−	286324.i		−	1.31288i	0.754380	−	0.656438i	$-0.227938\pi$
$468$	118279.	+	34520.0i	0.540027	+	0.157608i
$469$	−65110.5			−0.296009
$470$		0			0
$471$		−	105529.i		−	0.475696i
$472$	−83126.2	+	183208.i	−0.373125	+	0.822357i
$473$	−184236.			−0.823479
$474$	−58427.2	−	8351.85i	−0.260051	−	0.0371728i
$475$		0			0
$476$	−32620.5	+	111771.i	−0.143972	+	0.493303i
$477$	61913.4			0.272112
$478$	−34504.1	+	241381.i	−0.151013	+	1.05645i
$479$		−	261356.i		−	1.13910i	−0.821957	−	0.569550i	$-0.807117\pi$
$479$		−	261356.i		−	1.13910i	0.821957	−	0.569550i	$-0.192883\pi$
$480$		0			0
$481$	−28604.7			−0.123637
$482$	171694.	+	24542.7i	0.739029	+	0.105640i
$483$		−	57687.8i		−	0.247280i
$484$	−567464.	−	165616.i	−2.42241	−	0.706986i
$485$		0			0
$486$	2144.10	−	14999.5i	0.00907762	−	0.0635045i
$487$			176611.i			0.744662i	0.928100	+	0.372331i	$0.121441\pi$
$487$			176611.i			0.744662i	−0.928100	+	0.372331i	$0.878559\pi$
$488$	−118135.	−	53601.0i	−0.496067	−	0.225078i
$489$	−181244.			−0.757959
$490$		0			0
$491$		−	143358.i		−	0.594646i	−0.954777	−	0.297323i	$-0.903906\pi$
$491$		−	143358.i		−	0.594646i	0.954777	−	0.297323i	$-0.0960938\pi$
$492$	25635.8	−	87838.2i	0.105905	−	0.362872i
$493$	44225.7			0.181962
$494$	108854.	−	761513.i	0.446057	−	3.12049i
$495$		0			0
$496$	96681.0	−	151525.i	0.392987	−	0.615915i
$497$	201839.			0.817133
$498$	95089.7	+	13592.5i	0.383420	+	0.0548078i
$499$		−	104729.i		−	0.420595i	−0.977637	−	0.210298i	$-0.932557\pi$
$499$		−	104729.i		−	0.420595i	0.977637	−	0.210298i	$-0.0674433\pi$
$500$		0			0
$501$	135211.			0.538689
$502$	−2285.04	+	15985.5i	−0.00906746	+	0.0634335i
$503$			187746.i			0.742053i	0.928622	+	0.371026i	$0.120994\pi$
$503$			187746.i			0.742053i	−0.928622	+	0.371026i	$0.879006\pi$
$504$	17232.3	−	37979.6i	0.0678395	−	0.149517i
$505$		0			0
$506$	413698.	+	59135.9i	1.61578	+	0.230967i
$507$		−	274290.i		−	1.06707i
$508$	13116.5	−	44942.3i	0.0508266	−	0.174152i
$509$	−358820.			−1.38497			−0.692486	−	0.721432i	$-0.743484\pi$
$509$	−358820.			−1.38497			−0.692486	+	0.721432i	$0.743484\pi$
$510$		0			0
$511$			162215.i			0.621225i
$512$	75702.1	+	250975.i	0.288780	+	0.957395i
$513$	−94597.8			−0.359457
$514$	−84021.9	−	12010.5i	−0.318029	−	0.0454604i
$515$		0			0
$516$	64737.5	+	18893.8i	0.243140	+	0.0709610i
$517$	−270367.			−1.01151
$518$	−1370.11	+	9584.91i	−0.00510618	+	0.0357214i
$519$		−	216133.i		−	0.802391i
$520$		0			0
$521$	62111.6			0.228822			0.114411	−	0.993434i	$-0.463502\pi$
$521$	62111.6			0.228822			0.114411	+	0.993434i	$0.463502\pi$
$522$	−15682.1	−	2241.67i	−0.0575524	−	0.00822680i
$523$		−	439230.i		−	1.60579i	−0.596122	−	0.802894i	$-0.703293\pi$
$523$		−	439230.i		−	1.60579i	0.596122	−	0.802894i	$-0.296707\pi$
$524$	74790.1	−	256260.i	0.272384	−	0.933293i
$525$		0			0
$526$	−37111.4	+	259621.i	−0.134133	+	0.938357i
$527$		−	211695.i		−	0.762237i
$528$	254700.	+	162512.i	0.913609	+	0.582931i
$529$	68253.0			0.243899
$530$		0			0
$531$		−	84874.6i		−	0.301016i
$532$	−249955.	−	72949.9i	−0.883157	−	0.257752i
$533$	−313911.			−1.10497
$534$	−723.274	+	5059.82i	−0.00253641	+	0.0177441i
$535$		0			0
$536$	−71337.6	+	157226.i	−0.248307	+	0.547262i
$537$	−270518.			−0.938098
$538$	282932.	+	40443.6i	0.977503	+	0.139729i
$539$			413027.i			1.42168i
$540$		0			0
$541$	−268086.			−0.915966			−0.457983	−	0.888961i	$-0.651428\pi$
$541$	−268086.			−0.915966			−0.457983	+	0.888961i	$0.651428\pi$
$542$	−29391.5	+	205615.i	−0.100052	+	0.699933i
$543$		−	251489.i		−	0.852940i
$544$	234159.	+	201231.i	0.791249	+	0.679982i
$545$		0			0
$546$	−141638.	−	20246.4i	−0.475110	−	0.0679144i
$547$		−	86050.0i		−	0.287592i	−0.989607	−	0.143796i	$-0.954069\pi$
$547$		−	86050.0i		−	0.287592i	0.989607	−	0.143796i	$-0.0459309\pi$
$548$	−391860.	−	114365.i	−1.30488	−	0.380832i
$549$	54728.5			0.181580
$550$		0			0
$551$			98902.8i			0.325766i
$552$	−139302.	−	63204.9i	−0.457172	−	0.207431i
$553$	68536.5			0.224115
$554$	86695.3	+	12392.6i	0.282472	+	0.0403778i
$555$		0			0
$556$	−5900.32	+	20216.8i	−0.0190865	+	0.0653978i
$557$	246565.			0.794734			0.397367	−	0.917660i	$-0.369924\pi$
$557$	246565.			0.794734			0.397367	+	0.917660i	$0.369924\pi$
$558$	−10730.2	+	75065.5i	−0.0344619	+	0.241086i
$559$		−	231355.i		−	0.740380i
$560$		0			0
$561$	355840.			1.13065
$562$	31877.4	+	4556.70i	0.100928	+	0.0144270i
$563$		−	368835.i		−	1.16363i	−0.813321	−	0.581816i	$-0.802343\pi$
$563$		−	368835.i		−	1.16363i	0.813321	−	0.581816i	$-0.197657\pi$
$564$	95002.3	+	27726.6i	0.298659	+	0.0871644i
$565$		0			0
$566$	−31147.6	+	217900.i	−0.0972279	+	0.680180i
$567$			17594.8i			0.0547290i
$568$	221143.	−	487394.i	0.685451	−	1.51072i
$569$	−56443.8			−0.174338			−0.0871689	−	0.996194i	$-0.527782\pi$
$569$	−56443.8			−0.174338			−0.0871689	+	0.996194i	$0.527782\pi$
$570$		0			0
$571$		−	143219.i		−	0.439265i	−0.975583	−	0.219633i	$-0.929514\pi$
$571$		−	143219.i		−	0.439265i	0.975583	−	0.219633i	$-0.0704859\pi$
$572$	290387.	−	994980.i	0.887535	−	3.04104i
$573$	75531.2			0.230047
$574$	−15035.7	+	105186.i	−0.0456352	+	0.319251i
$575$		0			0
$576$	−72831.2	−	83223.8i	−0.219519	−	0.250843i
$577$	347057.			1.04244			0.521218	−	0.853423i	$-0.325478\pi$
$577$	347057.			1.04244			0.521218	+	0.853423i	$0.325478\pi$
$578$	29252.7	+	4181.51i	0.0875609	+	0.0125164i
$579$		−	2567.68i		−	0.00765920i
$580$		0			0
$581$	−111542.			−0.330436
$582$	−4620.92	+	32326.7i	−0.0136422	+	0.0954367i
$583$		−	520825.i		−	1.53234i
$584$	391710.	+	177729.i	1.14852	+	0.521114i
$585$		0			0
$586$	332887.	+	47584.3i	0.969396	+	0.138570i
$587$			217679.i			0.631743i	0.948802	+	0.315872i	$0.102297\pi$
$587$			217679.i			0.631743i	−0.948802	+	0.315872i	$0.897703\pi$
$588$	42356.8	−	145131.i	0.122509	−	0.419764i
$589$	473418.			1.36463
$590$		0			0
$591$		−	16045.6i		−	0.0459389i
$592$	21644.1	+	13810.1i	0.0617584	+	0.0394051i
$593$	287874.			0.818640			0.409320	−	0.912391i	$-0.365766\pi$
$593$	287874.			0.818640			0.409320	+	0.912391i	$0.365766\pi$
$594$	−126178.	−	18036.5i	−0.357611	−	0.0511185i
$595$		0			0
$596$	−316476.	−	92364.2i	−0.890939	−	0.260023i
$597$	−253704.			−0.711833
$598$	−74259.9	+	519502.i	−0.207660	+	1.45273i
$599$		−	311200.i		−	0.867332i	−0.901074	−	0.433666i	$-0.857220\pi$
$599$		−	311200.i		−	0.867332i	0.901074	−	0.433666i	$-0.142780\pi$
$600$		0			0
$601$	−111234.			−0.307957			−0.153978	−	0.988074i	$-0.549209\pi$
$601$	−111234.			−0.307957			−0.153978	+	0.988074i	$0.549209\pi$
$602$	−77522.6	−	11081.4i	−0.213912	−	0.0305775i
$603$		−	72838.1i		−	0.200320i
$604$	−43847.8	+	150240.i	−0.120191	+	0.411823i
$605$		0			0
$606$	17227.7	−	120521.i	0.0469119	−	0.328183i
$607$			162372.i			0.440690i	0.975422	+	0.220345i	$0.0707183\pi$
$607$			162372.i			0.440690i	−0.975422	+	0.220345i	$0.929282\pi$
$608$	−450017.	+	523654.i	−1.21737	+	1.41657i
$609$	18395.5			0.0495994
$610$		0			0
$611$		−	339513.i		−	0.909440i
$612$	−125036.	−	36492.1i	−0.333836	−	0.0974307i
$613$	48840.5			0.129975			0.0649874	−	0.997886i	$-0.479299\pi$
$613$	48840.5			0.129975			0.0649874	+	0.997886i	$0.479299\pi$
$614$	−44007.0	+	307861.i	−0.116731	+	0.816616i
$615$		0			0
$616$	−319490.	−	144961.i	−0.841968	−	0.382023i
$617$	75750.5			0.198983			0.0994913	−	0.995038i	$-0.468278\pi$
$617$	75750.5			0.198983			0.0994913	+	0.995038i	$0.468278\pi$
$618$	−276623.	−	39541.8i	−0.724289	−	0.103533i
$619$			156219.i			0.407711i	0.979001	+	0.203856i	$0.0653473\pi$
$619$			156219.i			0.407711i	−0.979001	+	0.203856i	$0.934653\pi$
$620$		0			0
$621$	64534.4			0.167343
$622$	−53413.2	+	373664.i	−0.138060	+	0.965830i
$623$		−	5935.29i		−	0.0152921i
$624$	−204074.	+	319839.i	−0.524106	+	0.821415i
$625$		0			0
$626$	379031.	+	54180.4i	0.967221	+	0.138259i
$627$			795771.i			2.02420i
$628$	311931.	+	91037.8i	0.790932	+	0.230835i
$629$	30238.9			0.0764302
$630$		0			0
$631$		−	505064.i		−	1.26849i	−0.773131	−	0.634246i	$-0.781310\pi$
$631$		−	505064.i		−	1.26849i	0.773131	−	0.634246i	$-0.218690\pi$
$632$	75091.2	−	165499.i	0.187999	−	0.414345i
$633$	−355532.			−0.887303
$634$	−650421.	−	92974.1i	−1.61814	−	0.231304i
$635$		0			0
$636$	−53411.6	+	183009.i	−0.132045	+	0.452437i
$637$	−518659.			−1.27821
$638$	−18857.3	+	131920.i	−0.0463273	+	0.324093i
$639$			225794.i			0.552983i
$640$		0			0
$641$	−277583.			−0.675579			−0.337790	−	0.941222i	$-0.609679\pi$
$641$	−277583.			−0.675579			−0.337790	+	0.941222i	$0.609679\pi$
$642$	105572.	+	15091.0i	0.256142	+	0.0366140i
$643$			444328.i			1.07469i	0.843363	+	0.537344i	$0.180572\pi$
$643$			444328.i			1.07469i	−0.843363	+	0.537344i	$0.819428\pi$
$644$	170518.	+	49766.2i	0.411149	+	0.119995i
$645$		0			0
$646$	−115073.	+	805018.i	−0.275745	+	1.92904i
$647$			676912.i			1.61705i	0.588462	+	0.808525i	$0.299734\pi$
$647$			676912.i			1.61705i	−0.588462	+	0.808525i	$0.700266\pi$
$648$	42487.2	+	19277.5i	0.101183	+	0.0459093i
$649$	−713978.			−1.69510
$650$		0			0
$651$		−	88053.5i		−	0.207771i
$652$	156356.	−	535737.i	0.367806	−	1.26025i
$653$	−5432.36			−0.0127398			−0.00636989	−	0.999980i	$-0.502028\pi$
$653$	−5432.36			−0.0127398			−0.00636989	+	0.999980i	$0.502028\pi$
$654$	7202.67	−	50387.9i	0.0168398	−	0.117807i
$655$		0			0
$656$	237524.	+	151553.i	0.551950	+	0.352173i
$657$	−181467.			−0.420405
$658$	−113764.	−	16262.0i	−0.262757	−	0.0375597i
$659$			400476.i			0.922159i	0.887359	+	0.461079i	$0.152538\pi$
$659$			400476.i			0.922159i	−0.887359	+	0.461079i	$0.847462\pi$
$660$		0			0
$661$	−293134.			−0.670909			−0.335455	−	0.942056i	$-0.608890\pi$
$661$	−293134.			−0.670909			−0.335455	+	0.942056i	$0.608890\pi$
$662$	−88058.2	+	616031.i	−0.200934	+	1.40568i
$663$			446846.i			1.01656i
$664$	−122210.	+	269348.i	−0.277186	+	0.610911i
$665$		0			0
$666$	−10722.5	−	1532.72i	−0.0241739	−	0.00345553i
$667$		−	67471.2i		−	0.151658i
$668$	−116644.	+	399669.i	−0.261403	+	0.895670i
$669$	9435.63			0.0210823
$670$		0			0
$671$		−	460384.i		−	1.02253i
$672$	97397.3	+	83701.1i	0.215679	+	0.185350i
$673$	−200122.			−0.441839			−0.220920	−	0.975292i	$-0.570906\pi$
$673$	−200122.			−0.441839			−0.220920	+	0.975292i	$0.570906\pi$
$674$	806293.	+	115255.i	1.77490	+	0.253712i
$675$		0			0
$676$	810771.	+	236625.i	1.77421	+	0.517807i
$677$	631369.			1.37755			0.688773	−	0.724977i	$-0.258150\pi$
$677$	631369.			1.37755			0.688773	+	0.724977i	$0.258150\pi$
$678$	−13688.3	+	95759.7i	−0.0297777	+	0.208316i
$679$		−	37920.0i		−	0.0822486i
$680$		0			0
$681$	−131395.			−0.283324
$682$	631462.	+	90264.0i	1.35762	+	0.194064i
$683$		−	489626.i		−	1.04960i	−0.851226	−	0.524799i	$-0.824140\pi$
$683$		−	489626.i		−	1.04960i	0.851226	−	0.524799i	$-0.175860\pi$
$684$	81607.9	−	279620.i	0.174429	−	0.597663i
$685$		0			0
$686$	−57643.5	+	403258.i	−0.122490	+	0.856908i
$687$		−	319737.i		−	0.677454i
$688$	−111696.	+	175057.i	−0.235972	+	0.369831i
$689$	654026.			1.37771
$690$		0			0
$691$		−	901400.i		−	1.88782i	−0.330197	−	0.943912i	$-0.607115\pi$
$691$		−	901400.i		−	1.88782i	0.330197	−	0.943912i	$-0.392885\pi$
$692$	638864.	+	186454.i	1.33412	+	0.389367i
$693$	148010.			0.308194
$694$	308.923	−	2161.14i	0.000641403	−	0.00448708i
$695$		0			0
$696$	20154.8	−	44420.7i	0.0416064	−	0.0916994i
$697$	331844.			0.683076
$698$	866960.	+	123927.i	1.77946	+	0.254364i
$699$			410311.i			0.839767i
$700$		0			0
$701$	−547685.			−1.11454			−0.557269	−	0.830332i	$-0.688151\pi$
$701$	−547685.			−1.11454			−0.557269	+	0.830332i	$0.688151\pi$
$702$	22649.3	−	158448.i	0.0459600	−	0.321524i
$703$			67623.8i			0.136832i
$704$	−700091.	+	612667.i	−1.41257	+	1.23617i
$705$		0			0
$706$	−552214.	−	78935.9i	−1.10789	−	0.158367i
$707$			141373.i			0.282832i
$708$	250880.	+	73219.9i	0.500494	+	0.146070i
$709$	861198.			1.71321			0.856604	−	0.515974i	$-0.172570\pi$
$709$	861198.			1.71321			0.856604	+	0.515974i	$0.172570\pi$
$710$		0			0
$711$			76670.7i			0.151667i
$712$	−14332.3	−	6502.94i	−0.0282720	−	0.0128277i
$713$	−322964.			−0.635295
$714$	149730.	+	21403.0i	0.293705	+	0.0419835i
$715$		0			0
$716$	233371.	−	799621.i	0.455220	−	1.55976i
$717$	316751.			0.616140
$718$	13923.2	−	97403.2i	0.0270079	−	0.188940i
$719$		−	865354.i		−	1.67393i	−0.547260	−	0.836963i	$-0.684329\pi$
$719$		−	865354.i		−	1.67393i	0.547260	−	0.836963i	$-0.315671\pi$
$720$		0			0
$721$	324485.			0.624201
$722$	−1.28424e6	−	183575.i	−2.46360	−	0.352158i
$723$		−	225304.i		−	0.431016i
$724$	743371.	+	216955.i	1.41817	+	0.413897i
$725$		0			0
$726$	−108664.	+	760184.i	−0.206164	+	1.44227i
$727$			525474.i			0.994220i	0.867687	+	0.497110i	$0.165606\pi$
$727$			525474.i			0.994220i	−0.867687	+	0.497110i	$0.834394\pi$
$728$	182035.	−	401200.i	0.343472	−	0.757003i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			244572.i			0.457690i
$732$	−47213.3	+	161771.i	−0.0881134	+	0.301911i
$733$	−160865.			−0.299401			−0.149700	−	0.988731i	$-0.547831\pi$
$733$	−160865.			−0.299401			−0.149700	+	0.988731i	$0.547831\pi$
$734$	−5568.23	+	38953.8i	−0.0103354	+	0.0723033i
$735$		0			0
$736$	307000.	−	357235.i	0.566739	−	0.659476i
$737$	−612725.			−1.12806
$738$	−117669.	−	16820.2i	−0.216048	−	0.0308829i
$739$			859197.i			1.57327i	0.617417	+	0.786636i	$0.288179\pi$
$739$			859197.i			1.57327i	−0.617417	+	0.786636i	$0.711821\pi$
$740$		0			0
$741$	−999290.			−1.81993
$742$	31326.5	−	219152.i	0.0568990	−	0.398050i
$743$		−	647679.i		−	1.17323i	−0.809867	−	0.586614i	$-0.800461\pi$
$743$		−	647679.i		−	1.17323i	0.809867	−	0.586614i	$-0.199539\pi$
$744$	−212628.	−	96474.9i	−0.384127	−	0.174288i
$745$		0			0
$746$	180615.	+	25817.9i	0.324546	+	0.0463921i
$747$		−	124781.i		−	0.223618i
$748$	−306977.	+	1.05182e6i	−0.548659	+	1.87992i
$749$	−123839.			−0.220746
$750$		0			0
$751$			990728.i			1.75661i	0.478104	+	0.878303i	$0.341324\pi$
$751$			990728.i			1.75661i	−0.478104	+	0.878303i	$0.658676\pi$
$752$	−163914.	+	256897.i	−0.289854	+	0.454279i
$753$	20976.8			0.0369956
$754$	−165659.	−	23680.0i	−0.291388	−	0.0416523i
$755$		0			0
$756$	−52008.2	−	15178.7i	−0.0909972	−	0.0265577i
$757$	410201.			0.715823			0.357911	−	0.933756i	$-0.383489\pi$
$757$	410201.			0.715823			0.357911	+	0.933756i	$0.383489\pi$
$758$	−122022.	+	853634.i	−0.212374	+	1.48571i
$759$		−	542873.i		−	0.942355i
$760$		0			0
$761$	383591.			0.662367			0.331184	−	0.943566i	$-0.392552\pi$
$761$	383591.			0.662367			0.331184	+	0.943566i	$0.392552\pi$
$762$	−60205.4	−	8606.03i	−0.103687	−	0.0148215i
$763$			59106.1i			0.101527i
$764$	−65159.4	+	223261.i	−0.111632	+	0.382496i
$765$		0			0
$766$	33677.5	−	235599.i	0.0573961	−	0.401528i
$767$		−	896578.i		−	1.52404i
$768$	308830.	−	143485.i	0.523597	−	0.243268i
$769$	−880209.			−1.48845			−0.744223	−	0.667932i	$-0.767180\pi$
$769$	−880209.			−1.48845			−0.744223	+	0.667932i	$0.767180\pi$
$770$		0			0
$771$			110257.i			0.185480i
$772$	7589.76	+	2215.09i	0.0127348	+	0.00371669i
$773$	657589.			1.10051			0.550257	−	0.834995i	$-0.314530\pi$
$773$	657589.			1.10051			0.550257	+	0.834995i	$0.314530\pi$
$774$	12396.6	−	86723.3i	0.0206929	−	0.144762i
$775$		0			0
$776$	−91567.7	−	41546.6i	−0.152061	−	0.0689941i
$777$	12577.7			0.0208334
$778$	−440962.	−	63033.0i	−0.728520	−	0.104138i
$779$			742109.i			1.22290i
$780$		0			0
$781$	1.89942e6			3.11400
$782$	78502.4	−	549181.i	0.128372	−	0.898053i
$783$			20578.7i			0.0335656i
$784$	392449.	+	250403.i	0.638486	+	0.407388i
$785$		0			0
$786$	−343290.	−	49071.4i	−0.555668	−	0.0794297i
$787$		−	97654.3i		−	0.157667i	−0.996888	−	0.0788337i	$-0.974880\pi$
$787$		−	97654.3i		−	0.157667i	0.996888	−	0.0788337i	$-0.0251196\pi$
$788$	47429.0	+	13842.3i	0.0763820	+	0.0222923i
$789$	340686.			0.547267
$790$		0			0
$791$		−	112328.i		−	0.179530i
$792$	162165.	−	357408.i	0.258528	−	0.569789i
$793$	578127.			0.919342
$794$	−801892.	−	114626.i	−1.27196	−	0.181820i
$795$		0			0
$796$	218866.	−	749919.i	0.345423	−	1.18355i
$797$	−911016.			−1.43420			−0.717099	−	0.696971i	$-0.754531\pi$
$797$	−911016.			−1.43420			−0.717099	+	0.696971i	$0.754531\pi$
$798$	−47864.0	+	334843.i	−0.0751628	+	0.525818i
$799$			358910.i			0.562201i
$800$		0			0
$801$	6639.72			0.0103487
$802$	217255.	+	31055.4i	0.337770	+	0.0482824i
$803$			1.52653e6i			2.36741i
$804$	215301.	+	62836.1i	0.333069	+	0.0972070i
$805$		0			0
$806$	−113349.	+	792958.i	−0.174481	+	1.22062i
$807$		−	371276.i		−	0.570098i
$808$	341383.	+	154894.i	0.522901	+	0.237253i
$809$	−535190.			−0.817733			−0.408866	−	0.912594i	$-0.634076\pi$
$809$	−535190.			−0.817733			−0.408866	+	0.912594i	$0.634076\pi$
$810$		0			0
$811$		−	441885.i		−	0.671842i	−0.941890	−	0.335921i	$-0.890952\pi$
$811$		−	441885.i		−	0.671842i	0.941890	−	0.335921i	$-0.109048\pi$
$812$	−15869.5	+	54374.9i	−0.0240685	+	0.0824682i
$813$	269817.			0.408214
$814$	−12893.5	+	90199.1i	−0.0194590	+	0.136130i
$815$		0			0
$816$	215733.	−	338111.i	0.323993	−	0.507785i
$817$	−546940.			−0.819400
$818$	770926.	+	110200.i	1.15214	+	0.164692i
$819$			185863.i			0.277093i
$820$		0			0
$821$	418246.			0.620505			0.310253	−	0.950654i	$-0.399586\pi$
$821$	418246.			0.620505			0.310253	+	0.950654i	$0.399586\pi$
$822$	−75037.6	+	524942.i	−0.111054	+	0.776905i
$823$		−	546065.i		−	0.806203i	−0.915155	−	0.403101i	$-0.867932\pi$
$823$		−	546065.i		−	0.806203i	0.915155	−	0.403101i	$-0.132068\pi$
$824$	355519.	−	783555.i	0.523610	−	1.15402i
$825$		0			0
$826$	−300426.	−	42944.3i	−0.440330	−	0.0629427i
$827$		−	170798.i		−	0.249731i	−0.992174	−	0.124865i	$-0.960150\pi$
$827$		−	170798.i		−	0.249731i	0.992174	−	0.124865i	$-0.0398499\pi$
$828$	−55672.7	+	190756.i	−0.0812047	+	0.278239i
$829$	−409275.			−0.595534			−0.297767	−	0.954639i	$-0.596242\pi$
$829$	−409275.			−0.595534			−0.297767	+	0.954639i	$0.596242\pi$
$830$		0			0
$831$		−	113765.i		−	0.164743i
$832$	−769357.	−	879140.i	−1.11143	−	1.27002i
$833$	548290.			0.790170
$834$	27082.7	+	3871.33i	0.0389368	+	0.00556580i
$835$		0			0
$836$	−2.35221e6	−	686498.i	−3.36561	−	0.982260i
$837$	98504.1			0.140606
$838$	78427.6	−	548658.i	0.111681	−	0.781293i
$839$			442416.i			0.628502i	0.949340	+	0.314251i	$0.101753\pi$
$839$			442416.i			0.628502i	−0.949340	+	0.314251i	$0.898247\pi$
$840$		0			0
$841$	−685766.			−0.969580
$842$	502989.	+	71899.4i	0.709470	+	0.101415i
$843$		−	41830.9i		−	0.0588629i
$844$	306711.	−	1.05091e6i	0.430571	−	1.47531i
$845$		0			0
$846$	18192.0	−	127267.i	0.0254180	−	0.177817i
$847$		−	891713.i		−	1.24296i
$848$	−494877.	−	315757.i	−0.688185	−	0.439098i
$849$	285937.			0.396694
$850$		0			0
$851$		−	46132.8i		−	0.0637016i
$852$	−667423.	−	194789.i	−0.919436	−	0.268340i
$853$	−1.02334e6			−1.40645			−0.703224	−	0.710969i	$-0.748257\pi$
$853$	−1.02334e6			−1.40645			−0.703224	+	0.710969i	$0.748257\pi$
$854$	27691.1	−	193720.i	0.0379686	−	0.265618i
$855$		0			0
$856$	−135683.	+	299041.i	−0.185173	+	0.408116i
$857$	−605173.			−0.823982			−0.411991	−	0.911188i	$-0.635167\pi$
$857$	−605173.			−0.823982			−0.411991	+	0.911188i	$0.635167\pi$
$858$	−1.33289e6	−	190529.i	−1.81059	−	0.258814i
$859$		−	607227.i		−	0.822933i	−0.911425	−	0.411467i	$-0.865017\pi$
$859$		−	607227.i		−	0.822933i	0.911425	−	0.411467i	$-0.134983\pi$
$860$		0			0
$861$	138029.			0.186193
$862$	−78951.8	+	552325.i	−0.106255	+	0.743328i
$863$		−	1.41500e6i		−	1.89992i	−0.312365	−	0.949962i	$-0.601121\pi$
$863$		−	1.41500e6i		−	1.89992i	0.312365	−	0.949962i	$-0.398879\pi$
$864$	−93635.1	+	108957.i	−0.125433	+	0.145958i
$865$		0			0
$866$	1.32347e6	+	189183.i	1.76473	+	0.252258i
$867$		−	38386.7i		−	0.0510672i
$868$	260276.	+	75962.2i	0.345458	+	0.100823i
$869$	644965.			0.854076
$870$		0			0
$871$		−	769429.i		−	1.01422i
$872$	142727.	+	64759.0i	0.187704	+	0.0851662i
$873$	42420.5			0.0556605
$874$	1.22814e6	+	175556.i	1.60778	+	0.229823i
$875$		0			0
$876$	156549.	−	536397.i	0.204005	−	0.699001i
$877$	1.26941e6			1.65045			0.825223	−	0.564807i	$-0.191049\pi$
$877$	1.26941e6			1.65045			0.825223	+	0.564807i	$0.191049\pi$
$878$	164367.	−	1.14986e6i	0.213218	−	1.49162i
$879$		−	436828.i		−	0.565370i
$880$		0			0
$881$	−175455.			−0.226055			−0.113027	−	0.993592i	$-0.536055\pi$
$881$	−175455.			−0.226055			−0.113027	+	0.993592i	$0.536055\pi$
$882$	−194419.	−	27791.2i	−0.249921	−	0.0357248i
$883$			1.00549e6i			1.28960i	0.764349	+	0.644802i	$0.223060\pi$
$883$			1.00549e6i			1.28960i	−0.764349	+	0.644802i	$0.776940\pi$
$884$	−1.32083e6	−	385486.i	−1.69021	−	0.493292i
$885$		0			0
$886$	17829.4	−	124730.i	0.0227128	−	0.158892i
$887$			796613.i			1.01251i	0.862383	+	0.506256i	$0.168971\pi$
$887$			796613.i			1.01251i	−0.862383	+	0.506256i	$0.831029\pi$
$888$	13780.6	−	30372.2i	0.0174761	−	0.0385168i
$889$	70622.4			0.0893591
$890$		0			0
$891$			165576.i			0.208566i
$892$	−8139.95	+	27890.6i	−0.0102304	+	0.0350533i
$893$	−802635.			−1.00650
$894$	−60602.1	+	423956.i	−0.0758250	+	0.530451i
$895$		0			0
$896$	−331434.	+	215688.i	−0.412839	+	0.268664i
$897$	681713.			0.847260
$898$	1.20484e6	+	172225.i	1.49409	+	0.213572i
$899$		−	102987.i		−	0.127427i
$900$		0			0
$901$	−691391.			−0.851675
$902$	−141494.	+	989852.i	−0.173910	+	1.21663i
$903$			101728.i			0.124758i
$904$	−271246.	−	123071.i	−0.331915	−	0.150598i
$905$		0			0
$906$	201263.	+	28769.5i	0.245193	+	0.0350490i
$907$		−	1.00997e6i		−	1.22770i	−0.789423	−	0.613850i	$-0.789620\pi$
$907$		−	1.00997e6i		−	1.22770i	0.789423	−	0.613850i	$-0.210380\pi$
$908$	113352.	−	388387.i	0.137485	−	0.471078i
$909$	−158152.			−0.191403
$910$		0			0
$911$			243711.i			0.293656i	0.989162	+	0.146828i	$0.0469063\pi$
$911$			243711.i			0.293656i	−0.989162	+	0.146828i	$0.953094\pi$
$912$	756124.	+	482447.i	0.909083	+	0.580043i
$913$	−1.04967e6			−1.25925
$914$	−601896.	−	86037.7i	−0.720492	−	0.102990i
$915$		0			0
$916$	945107.	+	275832.i	1.12639	+	0.328740i
$917$	402687.			0.478882
$918$	−23943.2	+	167500.i	−0.0284117	+	0.198761i
$919$		−	997533.i		−	1.18113i	−0.806992	−	0.590563i	$-0.798906\pi$
$919$		−	997533.i		−	1.18113i	0.806992	−	0.590563i	$-0.201094\pi$
$920$		0			0
$921$	403988.			0.476266
$922$	638720.	+	91301.4i	0.751361	+	0.107403i
$923$			2.38519e6i			2.79976i
$924$	−127686.	+	437500.i	−0.149554	+	0.512430i
$925$		0			0
$926$	81520.0	−	570292.i	0.0950698	−	0.665082i
$927$			362997.i			0.422419i
$928$	113915.	+	97896.2i	0.132277	+	0.113676i
$929$	−101841.			−0.118003			−0.0590013	−	0.998258i	$-0.518792\pi$
$929$	−101841.			−0.118003			−0.0590013	+	0.998258i	$0.518792\pi$
$930$		0			0
$931$			1.22615e6i			1.41463i
$932$	−1.21283e6	−	353968.i	−1.39627	−	0.407505i
$933$	490338.			0.563291
$934$	162066.	−	1.13377e6i	0.185780	−	1.29966i
$935$		0			0
$936$	448816.	+	203639.i	0.512291	+	0.232439i
$937$	903469.			1.02904			0.514522	−	0.857477i	$-0.327969\pi$
$937$	903469.			1.02904			0.514522	+	0.857477i	$0.327969\pi$
$938$	−257821.	−	36854.1i	−0.293031	−	0.0418871i
$939$		−	497381.i		−	0.564102i
$940$		0			0
$941$	−489666.			−0.552995			−0.276497	−	0.961015i	$-0.589174\pi$
$941$	−489666.			−0.552995			−0.276497	+	0.961015i	$0.589174\pi$
$942$	59731.9	−	417868.i	0.0673138	−	0.470909i
$943$		−	506265.i		−	0.569317i
$944$	−432859.	+	678406.i	−0.485738	+	0.761283i
$945$		0			0
$946$	−729529.	−	104282.i	−0.815193	−	0.116527i
$947$			1.16141e6i			1.29504i	0.762047	+	0.647521i	$0.224194\pi$
$947$			1.16141e6i			1.29504i	−0.762047	+	0.647521i	$0.775806\pi$
$948$	−226630.	−	66142.4i	−0.252174	−	0.0735976i
$949$	−1.91694e6			−2.12851
$950$		0			0
$951$			853511.i			0.943730i
$952$	−192434.	+	424120.i	−0.212328	+	0.467967i
$953$	1.02846e6			1.13241			0.566204	−	0.824265i	$-0.308411\pi$
$953$	1.02846e6			1.13241			0.566204	+	0.824265i	$0.308411\pi$
$954$	245162.	+	35044.5i	0.269374	+	0.0385055i
$955$		0			0
$956$	−273255.	+	936279.i	−0.298987	+	1.02445i
$957$	173111.			0.189017
$958$	147934.	−	1.03491e6i	0.161190	−	1.12764i
$959$		−	615770.i		−	0.669547i
$960$		0			0
$961$	430554.			0.466210
$962$	−113268.	−	16191.0i	−0.122393	−	0.0174954i
$963$		−	138537.i		−	0.149387i
$964$	665974.	+	194366.i	0.716644	+	0.209154i
$965$		0			0
$966$	32652.7	−	228429.i	0.0349916	−	0.244792i
$967$			1.38968e6i			1.48615i	0.669210	+	0.743074i	$0.266633\pi$
$967$			1.38968e6i			1.48615i	−0.669210	+	0.743074i	$0.733367\pi$
$968$	−2.15327e6	−	976996.i	−2.29799	−	1.04266i
$969$	1.05638e6			1.12505
$970$		0			0
$971$			1.30092e6i			1.37979i	0.723911	+	0.689893i	$0.242342\pi$
$971$			1.30092e6i			1.37979i	−0.723911	+	0.689893i	$0.757658\pi$
$972$	16980.2	−	58180.7i	0.0179725	−	0.0615810i
$973$	−31768.7			−0.0335563
$974$	−99965.9	+	699334.i	−0.105374	+	0.737168i
$975$		0			0
$976$	−437447.	−	279114.i	−0.459225	−	0.293010i
$977$	−1.20079e6			−1.25799			−0.628994	−	0.777410i	$-0.716533\pi$
$977$	−1.20079e6			−1.25799			−0.628994	+	0.777410i	$0.716533\pi$
$978$	−717681.	−	102589.i	−0.750332	−	0.107256i
$979$		−	55854.3i		−	0.0582762i
$980$		0			0
$981$	−66121.1			−0.0687072
$982$	81144.0	−	567661.i	0.0841460	−	0.588662i
$983$		−	12695.6i		−	0.0131385i	−0.999978	−	0.00656923i	$-0.997909\pi$
$983$		−	12695.6i		−	0.0131385i	0.999978	−	0.00656923i	$-0.00209107\pi$
$984$	151230.	−	333307.i	0.156188	−	0.344234i
$985$		0			0
$986$	175123.	+	25032.8i	0.180131	+	0.0257488i
$987$			149287.i			0.153245i
$988$	862070.	−	2.95379e6i	0.883138	−	3.02597i
$989$	373121.			0.381467
$990$		0			0
$991$			1.57211e6i			1.60079i	0.599470	+	0.800397i	$0.295378\pi$
$991$			1.57211e6i			1.60079i	−0.599470	+	0.800397i	$0.704622\pi$
$992$	468599.	−	545278.i	0.476188	−	0.554108i
$993$	808382.			0.819819
$994$	799233.	+	114246.i	0.808911	+	0.115629i
$995$		0			0
$996$	368838.	+	107646.i	0.371806	+	0.108512i
$997$	−774236.			−0.778902			−0.389451	−	0.921047i	$-0.627335\pi$
$997$	−774236.			−0.778902			−0.389451	+	0.921047i	$0.627335\pi$
$998$	59278.9	−	414699.i	0.0595167	−	0.416363i
$999$			14070.5i			0.0140987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.16		16
4.3	odd	2	inner	300.5.c.d.151.15		16
5.2	odd	4		300.5.f.b.199.16		32
5.3	odd	4		300.5.f.b.199.17		32
5.4	even	2		60.5.c.a.31.1	✓	16
15.14	odd	2		180.5.c.c.91.16		16
20.3	even	4		300.5.f.b.199.15		32
20.7	even	4		300.5.f.b.199.18		32
20.19	odd	2		60.5.c.a.31.2	yes	16
40.19	odd	2		960.5.e.f.511.11		16
40.29	even	2		960.5.e.f.511.2		16
60.59	even	2		180.5.c.c.91.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.1	✓	16	5.4	even	2
60.5.c.a.31.2	yes	16	20.19	odd	2
180.5.c.c.91.15		16	60.59	even	2
180.5.c.c.91.16		16	15.14	odd	2
300.5.c.d.151.15		16	4.3	odd	2	inner
300.5.c.d.151.16		16	1.1	even	1	trivial
300.5.f.b.199.15		32	20.3	even	4
300.5.f.b.199.16		32	5.2	odd	4
300.5.f.b.199.17		32	5.3	odd	4
300.5.f.b.199.18		32	20.7	even	4
960.5.e.f.511.2		16	40.29	even	2
960.5.e.f.511.11		16	40.19	odd	2

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)

\(f(q)\)	\(=\)	\(q+(3.95975 + 0.566024i) q^{2} -5.19615i q^{3} +(15.3592 + 4.48263i) q^{4} +(2.94115 - 20.5755i) q^{6} +24.1355i q^{7} +(58.2814 + 26.4438i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(3.95975 + 0.566024i) q^{2} -5.19615i q^{3} +(15.3592 + 4.48263i) q^{4} +(2.94115 - 20.5755i) q^{6} +24.1355i q^{7} +(58.2814 + 26.4438i) q^{8} -27.0000 q^{9} +227.128i q^{11} +(23.2924 - 79.8089i) q^{12} -285.216 q^{13} +(-13.6613 + 95.5705i) q^{14} +(215.812 + 137.699i) q^{16} +301.510 q^{17} +(-106.913 - 15.2827i) q^{18} +674.273i q^{19} +125.412 q^{21} +(-128.560 + 899.370i) q^{22} -459.987i q^{23} +(137.406 - 302.839i) q^{24} +(-1129.38 - 161.439i) q^{26} +140.296i q^{27} +(-108.190 + 370.703i) q^{28} +146.681 q^{29} -702.116i q^{31} +(776.621 + 667.410i) q^{32} +1180.19 q^{33} +(1193.91 + 170.662i) q^{34} +(-414.699 - 121.031i) q^{36} +100.291 q^{37} +(-381.655 + 2669.95i) q^{38} +1482.03i q^{39} +1100.61 q^{41} +(496.599 + 70.9861i) q^{42} +811.156i q^{43} +(-1018.13 + 3488.51i) q^{44} +(260.364 - 1821.43i) q^{46} +1190.37i q^{47} +(715.507 - 1121.39i) q^{48} +1818.48 q^{49} -1566.69i q^{51} +(-4380.70 - 1278.52i) q^{52} -2293.09 q^{53} +(-79.4110 + 555.537i) q^{54} +(-638.234 + 1406.65i) q^{56} +3503.62 q^{57} +(580.819 + 83.0248i) q^{58} +3143.51i q^{59} -2026.98 q^{61} +(397.415 - 2780.20i) q^{62} -651.658i q^{63} +(2697.45 + 3082.36i) q^{64} +(4673.26 + 668.017i) q^{66} +2697.71i q^{67} +(4630.97 + 1351.56i) q^{68} -2390.16 q^{69} -8362.76i q^{71} +(-1573.60 - 713.982i) q^{72} +6721.01 q^{73} +(397.129 + 56.7674i) q^{74} +(-3022.51 + 10356.3i) q^{76} -5481.85 q^{77} +(-838.863 + 5868.45i) q^{78} -2839.66i q^{79} +729.000 q^{81} +(4358.13 + 622.970i) q^{82} +4621.51i q^{83} +(1926.23 + 562.174i) q^{84} +(-459.134 + 3211.97i) q^{86} -762.175i q^{87} +(-6006.12 + 13237.3i) q^{88} -245.915 q^{89} -6883.83i q^{91} +(2061.95 - 7065.05i) q^{92} -3648.30 q^{93} +(-673.779 + 4713.57i) q^{94} +(3467.97 - 4035.44i) q^{96} -1571.13 q^{97} +(7200.72 + 1029.30i) q^{98} -6132.46i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more