LMFDB - Embedded newform 300.5.c.d.151.6

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			151.6
Root			$-1.85197 + 2.13780i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28004 + 3.78966i) q^{2} -5.19615i q^{3} +(-12.7230 - 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} +89.0673i q^{7} +(53.0524 - 35.7972i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-1.28004 + 3.78966i) q^{2} -5.19615i q^{3} +(-12.7230 - 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} +89.0673i q^{7} +(53.0524 - 35.7972i) q^{8} -27.0000 q^{9} -174.486i q^{11} +(-50.4120 + 66.1107i) q^{12} +22.9919 q^{13} +(-337.534 - 114.009i) q^{14} +(67.7503 + 246.872i) q^{16} -69.2339 q^{17} +(34.5610 - 102.321i) q^{18} +341.023i q^{19} +462.807 q^{21} +(661.242 + 223.348i) q^{22} +319.580i q^{23} +(-186.008 - 275.668i) q^{24} +(-29.4305 + 87.1316i) q^{26} +140.296i q^{27} +(864.112 - 1133.20i) q^{28} +679.276 q^{29} +72.5397i q^{31} +(-1022.28 - 59.2548i) q^{32} -906.656 q^{33} +(88.6218 - 262.373i) q^{34} +(343.521 + 261.948i) q^{36} -2373.44 q^{37} +(-1292.36 - 436.521i) q^{38} -119.470i q^{39} -762.724 q^{41} +(-592.410 + 1753.88i) q^{42} -3111.55i q^{43} +(-1692.83 + 2219.99i) q^{44} +(-1211.10 - 409.073i) q^{46} -315.636i q^{47} +(1282.79 - 352.041i) q^{48} -5531.98 q^{49} +359.750i q^{51} +(-292.527 - 223.063i) q^{52} -3385.94 q^{53} +(-531.674 - 179.584i) q^{54} +(3188.36 + 4725.23i) q^{56} +1772.01 q^{57} +(-869.498 + 2574.22i) q^{58} -6683.46i q^{59} -5316.04 q^{61} +(-274.901 - 92.8534i) q^{62} -2404.82i q^{63} +(1533.12 - 3798.26i) q^{64} +(1160.55 - 3435.92i) q^{66} -4015.09i q^{67} +(880.863 + 671.693i) q^{68} +1660.58 q^{69} +2954.05i q^{71} +(-1432.41 + 966.525i) q^{72} -5741.92 q^{73} +(3038.09 - 8994.54i) q^{74} +(3308.53 - 4338.84i) q^{76} +15541.0 q^{77} +(452.749 + 152.925i) q^{78} +414.704i q^{79} +729.000 q^{81} +(976.314 - 2890.46i) q^{82} +9738.88i q^{83} +(-5888.30 - 4490.06i) q^{84} +(11791.7 + 3982.90i) q^{86} -3529.62i q^{87} +(-6246.12 - 9256.90i) q^{88} -8192.42 q^{89} +2047.83i q^{91} +(3100.50 - 4066.02i) q^{92} +376.927 q^{93} +(1196.15 + 404.025i) q^{94} +(-307.897 + 5311.94i) q^{96} -9564.24 q^{97} +(7081.13 - 20964.3i) q^{98} +4711.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.28004	+	3.78966i	−0.320009	+	0.947415i
$2$	−1.28004	+	3.78966i	−0.320009	+	0.947415i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−12.7230	−	9.70180i	−0.795189	−	0.606362i
$5$		0			0
$5$		0			0
$6$	19.6916	+	6.65126i	0.546990	+	0.184757i
$7$			89.0673i			1.81770i	0.417124	+	0.908850i	$0.363038\pi$
$7$			89.0673i			1.81770i	−0.417124	+	0.908850i	$0.636962\pi$
$8$	53.0524	−	35.7972i	0.828944	−	0.559332i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	174.486i		−	1.44203i	−0.692918	−	0.721017i	$-0.743675\pi$
$11$		−	174.486i		−	1.44203i	0.692918	−	0.721017i	$-0.256325\pi$
$12$	−50.4120	+	66.1107i	−0.350083	+	0.459102i
$13$	22.9919			0.136047			0.0680235	−	0.997684i	$-0.478331\pi$
$13$	22.9919			0.136047			0.0680235	+	0.997684i	$0.478331\pi$
$14$	−337.534	−	114.009i	−1.72211	−	0.581680i
$15$		0			0
$16$	67.7503	+	246.872i	0.264650	+	0.964345i
$17$	−69.2339			−0.239563			−0.119782	−	0.992800i	$-0.538219\pi$
$17$	−69.2339			−0.239563			−0.119782	+	0.992800i	$0.538219\pi$
$18$	34.5610	−	102.321i	0.106670	−	0.315805i
$19$			341.023i			0.944662i	0.881421	+	0.472331i	$0.156587\pi$
$19$			341.023i			0.944662i	−0.881421	+	0.472331i	$0.843413\pi$
$20$		0			0
$21$	462.807			1.04945
$22$	661.242	+	223.348i	1.36620	+	0.461464i
$23$			319.580i			0.604120i	0.953289	+	0.302060i	$0.0976743\pi$
$23$			319.580i			0.604120i	−0.953289	+	0.302060i	$0.902326\pi$
$24$	−186.008	−	275.668i	−0.322930	−	0.478591i
$25$		0			0
$26$	−29.4305	+	87.1316i	−0.0435362	+	0.128893i
$27$			140.296i			0.192450i
$28$	864.112	−	1133.20i	1.10218	−	1.44541i
$29$	679.276			0.807701			0.403850	−	0.914825i	$-0.367672\pi$
$29$	679.276			0.807701			0.403850	+	0.914825i	$0.367672\pi$
$30$		0			0
$31$			72.5397i			0.0754835i	0.999288	+	0.0377418i	$0.0120164\pi$
$31$			72.5397i			0.0754835i	−0.999288	+	0.0377418i	$0.987984\pi$
$32$	−1022.28	−	59.2548i	−0.998324	−	0.0578660i
$33$	−906.656			−0.832558
$34$	88.6218	−	262.373i	0.0766625	−	0.226966i
$35$		0			0
$36$	343.521	+	261.948i	0.265063	+	0.202121i
$37$	−2373.44			−1.73371			−0.866853	−	0.498564i	$-0.833861\pi$
$37$	−2373.44			−1.73371			−0.866853	+	0.498564i	$0.833861\pi$
$38$	−1292.36	−	436.521i	−0.894986	−	0.302300i
$39$		−	119.470i		−	0.0785467i
$40$		0			0
$41$	−762.724			−0.453732			−0.226866	−	0.973926i	$-0.572848\pi$
$41$	−762.724			−0.453732			−0.226866	+	0.973926i	$0.572848\pi$
$42$	−592.410	+	1753.88i	−0.335833	+	0.994263i
$43$		−	3111.55i		−	1.68283i	−0.540390	−	0.841415i	$-0.681723\pi$
$43$		−	3111.55i		−	1.68283i	0.540390	−	0.841415i	$-0.318277\pi$
$44$	−1692.83	+	2219.99i	−0.874395	+	1.14669i
$45$		0			0
$46$	−1211.10	−	409.073i	−0.572352	−	0.193324i
$47$		−	315.636i		−	0.142886i	−0.997445	−	0.0714432i	$-0.977240\pi$
$47$		−	315.636i		−	0.142886i	0.997445	−	0.0714432i	$-0.0227605\pi$
$48$	1282.79	−	352.041i	0.556765	−	0.152796i
$49$	−5531.98			−2.30403
$50$		0			0
$51$			359.750i			0.138312i
$52$	−292.527	−	223.063i	−0.108183	−	0.0824937i
$53$	−3385.94			−1.20539			−0.602695	−	0.797972i	$-0.705906\pi$
$53$	−3385.94			−1.20539			−0.602695	+	0.797972i	$0.705906\pi$
$54$	−531.674	−	179.584i	−0.182330	−	0.0615858i
$55$		0			0
$56$	3188.36	+	4725.23i	1.01670	+	1.50677i
$57$	1772.01			0.545401
$58$	−869.498	+	2574.22i	−0.258471	+	0.765227i
$59$		−	6683.46i		−	1.91998i	−0.280032	−	0.959991i	$-0.590345\pi$
$59$		−	6683.46i		−	1.91998i	0.280032	−	0.959991i	$-0.409655\pi$
$60$		0			0
$61$	−5316.04			−1.42866			−0.714330	−	0.699809i	$-0.753268\pi$
$61$	−5316.04			−1.42866			−0.714330	+	0.699809i	$0.753268\pi$
$62$	−274.901	−	92.8534i	−0.0715142	−	0.0241554i
$63$		−	2404.82i		−	0.605900i
$64$	1533.12	−	3798.26i	0.374296	−	0.927309i
$65$		0			0
$66$	1160.55	−	3435.92i	0.266426	−	0.788778i
$67$		−	4015.09i		−	0.894429i	−0.894427	−	0.447215i	$-0.852416\pi$
$67$		−	4015.09i		−	0.894429i	0.894427	−	0.447215i	$-0.147584\pi$
$68$	880.863	+	671.693i	0.190498	+	0.145262i
$69$	1660.58			0.348789
$70$		0			0
$71$			2954.05i			0.586005i	0.956112	+	0.293002i	$0.0946544\pi$
$71$			2954.05i			0.586005i	−0.956112	+	0.293002i	$0.905346\pi$
$72$	−1432.41	+	966.525i	−0.276315	+	0.186444i
$73$	−5741.92			−1.07749			−0.538743	−	0.842470i	$-0.681101\pi$
$73$	−5741.92			−1.07749			−0.538743	+	0.842470i	$0.681101\pi$
$74$	3038.09	−	8994.54i	0.554801	−	1.64254i
$75$		0			0
$76$	3308.53	−	4338.84i	0.572807	−	0.751184i
$77$	15541.0			2.62118
$78$	452.749	+	152.925i	0.0744163	+	0.0251357i
$79$			414.704i			0.0664484i	0.999448	+	0.0332242i	$0.0105775\pi$
$79$			414.704i			0.0664484i	−0.999448	+	0.0332242i	$0.989422\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	976.314	−	2890.46i	0.145198	−	0.429873i
$83$			9738.88i			1.41368i	0.707371	+	0.706842i	$0.249881\pi$
$83$			9738.88i			1.41368i	−0.707371	+	0.706842i	$0.750119\pi$
$84$	−5888.30	−	4490.06i	−0.834510	−	0.636346i
$85$		0			0
$86$	11791.7	+	3982.90i	1.59434	+	0.538521i
$87$		−	3529.62i		−	0.466326i
$88$	−6246.12	−	9256.90i	−0.806575	−	1.19536i
$89$	−8192.42			−1.03427			−0.517133	−	0.855905i	$-0.673001\pi$
$89$	−8192.42			−1.03427			−0.517133	+	0.855905i	$0.673001\pi$
$90$		0			0
$91$			2047.83i			0.247292i
$92$	3100.50	−	4066.02i	0.366316	−	0.480389i
$93$	376.927			0.0435804
$94$	1196.15	+	404.025i	0.135373	+	0.0457249i
$95$		0			0
$96$	−307.897	+	5311.94i	−0.0334089	+	0.576383i
$97$	−9564.24			−1.01650			−0.508250	−	0.861210i	$-0.669707\pi$
$97$	−9564.24			−1.01650			−0.508250	+	0.861210i	$0.669707\pi$
$98$	7081.13	−	20964.3i	0.737310	−	2.18287i
$99$			4711.12i			0.480678i
$100$		0			0
$101$	−1386.95			−0.135962			−0.0679809	−	0.997687i	$-0.521656\pi$
$101$	−1386.95			−0.135962			−0.0679809	+	0.997687i	$0.521656\pi$
$102$	−1363.33	−	460.492i	−0.131039	−	0.0442611i
$103$		−	627.330i		−	0.0591318i	−0.999563	−	0.0295659i	$-0.990588\pi$
$103$		−	627.330i		−	0.0591318i	0.999563	−	0.0295659i	$-0.00941250\pi$
$104$	1219.78	−	823.048i	0.112775	−	0.0760954i
$105$		0			0
$106$	4334.12	−	12831.5i	0.385735	−	1.14200i
$107$			2988.95i			0.261067i	0.991444	+	0.130533i	$0.0416689\pi$
$107$			2988.95i			0.261067i	−0.991444	+	0.130533i	$0.958331\pi$
$108$	1361.12	−	1784.99i	0.116694	−	0.153034i
$109$	15704.4			1.32181			0.660905	−	0.750469i	$-0.270173\pi$
$109$	15704.4			1.32181			0.660905	+	0.750469i	$0.270173\pi$
$110$		0			0
$111$			12332.8i			1.00096i
$112$	−21988.2	+	6034.33i	−1.75289	+	0.481053i
$113$	−19067.1			−1.49323			−0.746616	−	0.665255i	$-0.768323\pi$
$113$	−19067.1			−1.49323			−0.746616	+	0.665255i	$0.768323\pi$
$114$	−2268.23	+	6715.30i	−0.174533	+	0.516720i
$115$		0			0
$116$	−8642.44	−	6590.20i	−0.642274	−	0.489759i
$117$	−620.782			−0.0453490
$118$	25328.0	+	8555.06i	1.81902	+	0.614411i
$119$		−	6166.47i		−	0.435454i
$120$		0			0
$121$	−15804.4			−1.07946
$122$	6804.72	−	20146.0i	0.457184	−	1.35353i
$123$			3963.23i			0.261962i
$124$	703.765	−	922.924i	0.0457704	−	0.0600237i
$125$		0			0
$126$	9113.43	+	3078.25i	0.574038	+	0.193893i
$127$		−	375.889i		−	0.0233052i	−0.999932	−	0.0116526i	$-0.996291\pi$
$127$		−	375.889i		−	0.0233052i	0.999932	−	0.0116526i	$-0.00370922\pi$
$128$	12431.7	+	10671.9i	0.758768	+	0.651361i
$129$	−16168.1			−0.971582
$130$		0			0
$131$		−	11766.3i		−	0.685639i	−0.939401	−	0.342820i	$-0.888618\pi$
$131$		−	11766.3i		−	0.685639i	0.939401	−	0.342820i	$-0.111382\pi$
$132$	11535.4	+	8796.19i	0.662041	+	0.504832i
$133$	−30374.0			−1.71711
$134$	15215.8	+	5139.46i	0.847395	+	0.286225i
$135$		0			0
$136$	−3673.02	+	2478.38i	−0.198585	+	0.133995i
$137$	−1889.31			−0.100661			−0.0503306	−	0.998733i	$-0.516027\pi$
$137$	−1889.31			−0.100661			−0.0503306	+	0.998733i	$0.516027\pi$
$138$	−2125.61	+	6293.04i	−0.111616	+	0.330448i
$139$		−	15093.1i		−	0.781174i	−0.920566	−	0.390587i	$-0.872272\pi$
$139$		−	15093.1i		−	0.781174i	0.920566	−	0.390587i	$-0.127728\pi$
$140$		0			0
$141$	−1640.09			−0.0824955
$142$	−11194.8	−	3781.29i	−0.555189	−	0.187527i
$143$		−	4011.77i		−	0.196184i
$144$	−1829.26	−	6665.55i	−0.0882166	−	0.321448i
$145$		0			0
$146$	7349.87	−	21759.9i	0.344805	−	1.02083i
$147$			28745.0i			1.33023i
$148$	30197.3	+	23026.7i	1.37862	+	1.05125i
$149$	29887.1			1.34621			0.673103	−	0.739549i	$-0.264961\pi$
$149$	29887.1			1.34621			0.673103	+	0.739549i	$0.264961\pi$
$150$		0			0
$151$			15818.0i			0.693741i	0.937913	+	0.346871i	$0.112756\pi$
$151$			15818.0i			0.693741i	−0.937913	+	0.346871i	$0.887244\pi$
$152$	12207.7	+	18092.1i	0.528379	+	0.783071i
$153$	1869.31			0.0798545
$154$	−19893.0	+	58895.0i	−0.838802	+	2.48335i
$155$		0			0
$156$	−1159.07	+	1520.01i	−0.0476278	+	0.0624595i
$157$	32589.5			1.32214			0.661071	−	0.750324i	$-0.270102\pi$
$157$	32589.5			1.32214			0.661071	+	0.750324i	$0.270102\pi$
$158$	−1571.59	−	530.836i	−0.0629541	−	0.0212641i
$159$			17593.9i			0.695932i
$160$		0			0
$161$	−28464.1			−1.09811
$162$	−933.146	+	2762.66i	−0.0355565	+	0.105268i
$163$			19528.4i			0.735008i	0.930022	+	0.367504i	$0.119788\pi$
$163$			19528.4i			0.735008i	−0.930022	+	0.367504i	$0.880212\pi$
$164$	9704.15	+	7399.79i	0.360803	+	0.275126i
$165$		0			0
$166$	−36907.0	−	12466.1i	−1.33935	−	0.452392i
$167$		−	20882.0i		−	0.748755i	−0.927276	−	0.374377i	$-0.877856\pi$
$167$		−	20882.0i		−	0.748755i	0.927276	−	0.374377i	$-0.122144\pi$
$168$	24553.0	−	16567.2i	0.869934	−	0.586990i
$169$	−28032.4			−0.981491
$170$		0			0
$171$		−	9207.62i		−	0.314887i
$172$	−30187.6	+	39588.3i	−1.02040	+	1.33817i
$173$	5278.82			0.176378			0.0881891	−	0.996104i	$-0.471892\pi$
$173$	5278.82			0.176378			0.0881891	+	0.996104i	$0.471892\pi$
$174$	13376.1	+	4518.04i	0.441804	+	0.149229i
$175$		0			0
$176$	43075.8	−	11821.5i	1.39062	−	0.381634i
$177$	−34728.3			−1.10850
$178$	10486.6	−	31046.5i	0.330974	−	0.979878i
$179$			47041.6i			1.46817i	0.679058	+	0.734084i	$0.262388\pi$
$179$			47041.6i			1.46817i	−0.679058	+	0.734084i	$0.737612\pi$
$180$		0			0
$181$	−16396.0			−0.500472			−0.250236	−	0.968185i	$-0.580508\pi$
$181$	−16396.0			−0.500472			−0.250236	+	0.968185i	$0.580508\pi$
$182$	−7760.57	−	2621.29i	−0.234288	−	0.0791358i
$183$			27623.0i			0.824837i
$184$	11440.1	+	16954.5i	0.337904	+	0.500782i
$185$		0			0
$186$	−482.480	+	1428.43i	−0.0139461	+	0.0412887i
$187$			12080.3i			0.345459i
$188$	−3062.23	+	4015.84i	−0.0866409	+	0.113622i
$189$	−12495.8			−0.349816
$190$		0			0
$191$			32485.2i			0.890469i	0.895414	+	0.445235i	$0.146880\pi$
$191$			32485.2i			0.890469i	−0.895414	+	0.445235i	$0.853120\pi$
$192$	−19736.3	−	7966.30i	−0.535382	−	0.216100i
$193$	10400.5			0.279215			0.139607	−	0.990207i	$-0.455416\pi$
$193$	10400.5			0.279215			0.139607	+	0.990207i	$0.455416\pi$
$194$	12242.6	−	36245.2i	0.325289	−	0.963046i
$195$		0			0
$196$	70383.4	+	53670.1i	1.83214	+	1.39708i
$197$	47175.4			1.21558			0.607790	−	0.794098i	$-0.292056\pi$
$197$	47175.4			1.21558			0.607790	+	0.794098i	$0.292056\pi$
$198$	−17853.5	−	6030.41i	−0.455401	−	0.153821i
$199$			57145.1i			1.44302i	0.692403	+	0.721511i	$0.256552\pi$
$199$			57145.1i			1.44302i	−0.692403	+	0.721511i	$0.743448\pi$
$200$		0			0
$201$	−20863.0			−0.516399
$202$	1775.34	−	5256.05i	0.0435090	−	0.128812i
$203$			60501.3i			1.46816i
$204$	3490.22	−	4577.10i	0.0838672	−	0.109984i
$205$		0			0
$206$	2377.36	+	803.004i	0.0560224	+	0.0189227i
$207$		−	8628.65i		−	0.201373i
$208$	1557.71	+	5676.07i	0.0360048	+	0.131196i
$209$	59503.7			1.36223
$210$		0			0
$211$		−	24560.7i		−	0.551666i	−0.961206	−	0.275833i	$-0.911046\pi$
$211$		−	24560.7i		−	0.551666i	0.961206	−	0.275833i	$-0.0889536\pi$
$212$	43079.3	+	32849.7i	0.958512	+	0.730902i
$213$	15349.7			0.338330
$214$	−11327.1	−	3825.96i	−0.247338	−	0.0835436i
$215$		0			0
$216$	5022.21	+	7443.05i	0.107643	+	0.159530i
$217$	−6460.91			−0.137206
$218$	−20102.2	+	59514.4i	−0.422991	+	1.25230i
$219$			29835.9i			0.622087i
$220$		0			0
$221$	−1591.82			−0.0325919
$222$	−46737.0	−	15786.4i	−0.948319	−	0.320315i
$223$		−	71260.5i		−	1.43298i	−0.697599	−	0.716489i	$-0.745748\pi$
$223$		−	71260.5i		−	1.43298i	0.697599	−	0.716489i	$-0.254252\pi$
$224$	5277.66	−	91052.0i	0.105183	−	1.81465i
$225$		0			0
$226$	24406.6	−	72257.7i	0.477848	−	1.41471i
$227$		−	73287.1i		−	1.42225i	−0.703066	−	0.711125i	$-0.748186\pi$
$227$		−	73287.1i		−	1.42225i	0.703066	−	0.711125i	$-0.251814\pi$
$228$	−22545.3	−	17191.6i	−0.433696	−	0.330710i
$229$	−37103.1			−0.707520			−0.353760	−	0.935336i	$-0.615097\pi$
$229$	−37103.1			−0.707520			−0.353760	+	0.935336i	$0.615097\pi$
$230$		0			0
$231$		−	80753.4i		−	1.51334i
$232$	36037.2	−	24316.2i	0.669538	−	0.451773i
$233$	−21001.4			−0.386844			−0.193422	−	0.981116i	$-0.561959\pi$
$233$	−21001.4			−0.386844			−0.193422	+	0.981116i	$0.561959\pi$
$234$	794.623	−	2352.55i	0.0145121	−	0.0429643i
$235$		0			0
$236$	−64841.5	+	85033.7i	−1.16420	+	1.52675i
$237$	2154.87			0.0383640
$238$	23368.8	+	7893.30i	0.412556	+	0.139349i
$239$		−	8886.00i		−	0.155565i	−0.996970	−	0.0777823i	$-0.975216\pi$
$239$		−	8886.00i		−	0.155565i	0.996970	−	0.0777823i	$-0.0247839\pi$
$240$		0			0
$241$	−11033.8			−0.189973			−0.0949864	−	0.995479i	$-0.530281\pi$
$241$	−11033.8			−0.189973			−0.0949864	+	0.995479i	$0.530281\pi$
$242$	20230.2	−	59893.2i	0.345437	−	1.02270i
$243$		−	3788.00i		−	0.0641500i
$244$	67636.1	+	51575.1i	1.13605	+	0.866285i
$245$		0			0
$246$	−15019.3	−	5073.08i	−0.248187	−	0.0838303i
$247$			7840.77i			0.128518i
$248$	2596.72	+	3848.41i	0.0422204	+	0.0625716i
$249$	50604.7			0.816191
$250$		0			0
$251$		−	51472.3i		−	0.817008i	−0.912756	−	0.408504i	$-0.866051\pi$
$251$		−	51472.3i		−	0.817008i	0.912756	−	0.408504i	$-0.133949\pi$
$252$	−23331.0	+	30596.5i	−0.367395	+	0.481804i
$253$	55762.2			0.871161
$254$	1424.49	+	481.152i	0.0220797	+	0.00745787i
$255$		0			0
$256$	−56355.8	+	33451.3i	−0.859921	+	0.510427i
$257$	42550.6			0.644227			0.322114	−	0.946701i	$-0.395607\pi$
$257$	42550.6			0.644227			0.322114	+	0.946701i	$0.395607\pi$
$258$	20695.7	−	61271.6i	0.310915	−	0.920491i
$259$		−	211396.i		−	3.15135i
$260$		0			0
$261$	−18340.5			−0.269234
$262$	44590.1	+	15061.2i	0.649585	+	0.219411i
$263$		−	5761.02i		−	0.0832891i	−0.999132	−	0.0416445i	$-0.986740\pi$
$263$		−	5761.02i		−	0.0832891i	0.999132	−	0.0416445i	$-0.0132597\pi$
$264$	−48100.3	+	32455.8i	−0.690144	+	0.465676i
$265$		0			0
$266$	38879.8	−	115107.i	0.549491	−	1.62682i
$267$			42569.0i			0.597133i
$268$	−38953.6	+	51084.1i	−0.542348	+	0.711240i
$269$	19772.4			0.273247			0.136623	−	0.990623i	$-0.456375\pi$
$269$	19772.4			0.273247			0.136623	+	0.990623i	$0.456375\pi$
$270$		0			0
$271$			60381.3i			0.822174i	0.911596	+	0.411087i	$0.134851\pi$
$271$			60381.3i			0.822174i	−0.911596	+	0.411087i	$0.865149\pi$
$272$	−4690.62	−	17091.9i	−0.0634004	−	0.231022i
$273$	10640.8			0.142774
$274$	2418.38	−	7159.84i	0.0322125	−	0.0953679i
$275$		0			0
$276$	−21127.6	−	16110.6i	−0.277353	−	0.211492i
$277$	−137089.			−1.78666			−0.893332	−	0.449398i	$-0.851638\pi$
$277$	−137089.			−1.78666			−0.893332	+	0.449398i	$0.851638\pi$
$278$	57197.5	+	19319.6i	0.740095	+	0.249983i
$279$		−	1958.57i		−	0.0251612i
$280$		0			0
$281$	68276.4			0.864685			0.432343	−	0.901709i	$-0.357687\pi$
$281$	68276.4			0.864685			0.432343	+	0.901709i	$0.357687\pi$
$282$	2099.38	−	6215.39i	0.0263993	−	0.0781574i
$283$		−	46455.4i		−	0.580047i	−0.957019	−	0.290024i	$-0.906337\pi$
$283$		−	46455.4i		−	0.580047i	0.957019	−	0.290024i	$-0.0936632\pi$
$284$	28659.6	−	37584.4i	0.355331	−	0.465984i
$285$		0			0
$286$	15203.2	+	5135.21i	0.185868	+	0.0627807i
$287$		−	67933.7i		−	0.824749i
$288$	27601.7	+	1599.88i	0.332775	+	0.0192887i
$289$	−78727.7			−0.942609
$290$		0			0
$291$			49697.3i			0.586876i
$292$	73054.6	+	55707.0i	0.856805	+	0.653347i
$293$	−75824.8			−0.883234			−0.441617	−	0.897204i	$-0.645595\pi$
$293$	−75824.8			−0.883234			−0.441617	+	0.897204i	$0.645595\pi$
$294$	−108934.	−	36794.6i	−1.26028	−	0.425686i
$295$		0			0
$296$	−125917.	+	84962.7i	−1.43714	+	0.969717i
$297$	24479.7			0.277519
$298$	−38256.6	+	113262.i	−0.430798	+	1.27542i
$299$			7347.75i			0.0821887i
$300$		0			0
$301$	277137.			3.05888
$302$	−59944.8	−	20247.6i	−0.657261	−	0.222003i
$303$			7206.79i			0.0784976i
$304$	−84189.1	+	23104.4i	−0.910979	+	0.250004i
$305$		0			0
$306$	−2392.79	+	7084.06i	−0.0255542	+	0.0756553i
$307$			115095.i			1.22118i	0.791947	+	0.610590i	$0.209068\pi$
$307$			115095.i			1.22118i	−0.791947	+	0.610590i	$0.790932\pi$
$308$	−197728.	−	150776.i	−2.08433	−	1.58939i
$309$	−3259.70			−0.0341398
$310$		0			0
$311$			45164.1i			0.466953i	0.972362	+	0.233476i	$0.0750102\pi$
$311$			45164.1i			0.466953i	−0.972362	+	0.233476i	$0.924990\pi$
$312$	−4276.68	−	6338.15i	−0.0439337	−	0.0651108i
$313$	−27892.1			−0.284704			−0.142352	−	0.989816i	$-0.545466\pi$
$313$	−27892.1			−0.284704			−0.142352	+	0.989816i	$0.545466\pi$
$314$	−41715.7	+	123503.i	−0.423097	+	1.25262i
$315$		0			0
$316$	4023.38	−	5276.29i	0.0402918	−	0.0528390i
$317$	−90168.8			−0.897300			−0.448650	−	0.893708i	$-0.648095\pi$
$317$	−90168.8			−0.897300			−0.448650	+	0.893708i	$0.648095\pi$
$318$	−66674.7	−	22520.8i	−0.659336	−	0.222704i
$319$		−	118524.i		−	1.16473i
$320$		0			0
$321$	15531.0			0.150727
$322$	36435.0	−	107869.i	0.351405	−	1.04036i
$323$		−	23610.3i		−	0.226306i
$324$	−9275.08	−	7072.61i	−0.0883543	−	0.0673736i
$325$		0			0
$326$	−74006.1	−	24997.1i	−0.696357	−	0.235209i
$327$		−	81602.6i		−	0.763148i
$328$	−40464.3	+	27303.4i	−0.376119	+	0.253787i
$329$	28112.8			0.259724
$330$		0			0
$331$			135944.i			1.24081i	0.784283	+	0.620403i	$0.213031\pi$
$331$			135944.i			1.24081i	−0.784283	+	0.620403i	$0.786969\pi$
$332$	94484.6	−	123908.i	0.857205	−	1.12415i
$333$	64082.9			0.577902
$334$	79135.7	+	26729.7i	0.709381	+	0.239608i
$335$		0			0
$336$	31355.3	+	114254.i	0.277736	+	1.01203i
$337$	83154.4			0.732193			0.366096	−	0.930577i	$-0.380694\pi$
$337$	83154.4			0.732193			0.366096	+	0.930577i	$0.380694\pi$
$338$	35882.4	−	106233.i	0.314086	−	0.929879i
$339$			99075.5i			0.862118i
$340$		0			0
$341$	12657.2			0.108850
$342$	34893.7	+	11786.1i	0.298329	+	0.100767i
$343$		−	278867.i		−	2.37033i
$344$	−111385.	−	165075.i	−0.941260	−	1.39497i
$345$		0			0
$346$	−6757.08	+	20004.9i	−0.0564426	+	0.167103i
$347$			119011.i			0.988391i	0.869351	+	0.494195i	$0.164537\pi$
$347$			119011.i			0.988391i	−0.869351	+	0.494195i	$0.835463\pi$
$348$	−34243.7	+	44907.5i	−0.282763	+	0.370817i
$349$	−101177.			−0.830673			−0.415337	−	0.909668i	$-0.636336\pi$
$349$	−101177.			−0.830673			−0.415337	+	0.909668i	$0.636336\pi$
$350$		0			0
$351$			3225.68i			0.0261822i
$352$	−10339.1	+	178374.i	−0.0834447	+	1.43962i
$353$	204510.			1.64121			0.820606	−	0.571495i	$-0.193636\pi$
$353$	204510.			1.64121			0.820606	+	0.571495i	$0.193636\pi$
$354$	44453.4	−	131608.i	0.354730	−	1.05021i
$355$		0			0
$356$	104232.	+	79481.2i	0.822436	+	0.627140i
$357$	−32041.9			−0.251410
$358$	−178272.	−	60214.9i	−1.39096	−	0.469827i
$359$		−	45291.4i		−	0.351420i	−0.984442	−	0.175710i	$-0.943778\pi$
$359$		−	45291.4i		−	0.351420i	0.984442	−	0.175710i	$-0.0562222\pi$
$360$		0			0
$361$	14024.4			0.107615
$362$	20987.4	−	62135.1i	0.160155	−	0.474154i
$363$			82122.0i			0.623227i
$364$	19867.6	−	26054.6i	0.149949	−	0.196644i
$365$		0			0
$366$	−104682.	−	35358.4i	−0.781462	−	0.263955i
$367$			17522.8i			0.130098i	0.997882	+	0.0650490i	$0.0207204\pi$
$367$			17522.8i			0.130098i	−0.997882	+	0.0650490i	$0.979280\pi$
$368$	−78895.3	+	21651.6i	−0.582580	+	0.159880i
$369$	20593.5			0.151244
$370$		0			0
$371$		−	301576.i		−	2.19103i
$372$	−4795.65	−	3656.87i	−0.0346547	−	0.0264255i
$373$	16535.7			0.118852			0.0594258	−	0.998233i	$-0.481073\pi$
$373$	16535.7			0.118852			0.0594258	+	0.998233i	$0.481073\pi$
$374$	−45780.4	−	15463.3i	−0.327292	−	0.110550i
$375$		0			0
$376$	−11298.9	−	16745.2i	−0.0799209	−	0.118445i
$377$	15617.9			0.109885
$378$	15995.1	−	47354.8i	0.111944	−	0.331421i
$379$			63835.5i			0.444410i	0.975000	+	0.222205i	$0.0713255\pi$
$379$			63835.5i			0.444410i	−0.975000	+	0.222205i	$0.928675\pi$
$380$		0			0
$381$	−1953.18			−0.0134553
$382$	−123108.	−	41582.2i	−0.843643	−	0.284958i
$383$			79806.3i			0.544051i	0.962290	+	0.272025i	$0.0876935\pi$
$383$			79806.3i			0.544051i	−0.962290	+	0.272025i	$0.912307\pi$
$384$	55452.8	−	64596.8i	0.376063	−	0.438075i
$385$		0			0
$386$	−13313.0	+	39414.2i	−0.0893512	+	0.264532i
$387$			84011.9i			0.560943i
$388$	121686.	+	92790.3i	0.808309	+	0.616367i
$389$	−159539.			−1.05431			−0.527153	−	0.849770i	$-0.676741\pi$
$389$	−159539.			−1.05431			−0.527153	+	0.849770i	$0.676741\pi$
$390$		0			0
$391$		−	22125.7i		−	0.144725i
$392$	−293485.	+	198029.i	−1.90991	+	1.28872i
$393$	−61139.3			−0.395854
$394$	−60386.2	+	178779.i	−0.388996	+	1.15166i
$395$		0			0
$396$	45706.4	−	59939.7i	0.291465	−	0.382229i
$397$	−147558.			−0.936231			−0.468115	−	0.883667i	$-0.655067\pi$
$397$	−147558.			−0.936231			−0.468115	+	0.883667i	$0.655067\pi$
$398$	−216561.	−	73147.8i	−1.36714	−	0.461780i
$399$			157828.i			0.991374i
$400$		0			0
$401$	−47897.3			−0.297867			−0.148934	−	0.988847i	$-0.547584\pi$
$401$	−47897.3			−0.297867			−0.148934	+	0.988847i	$0.547584\pi$
$402$	26705.4	−	79063.8i	0.165252	−	0.489244i
$403$			1667.83i			0.0102693i
$404$	17646.2	+	13455.9i	0.108115	+	0.0824421i
$405$		0			0
$406$	−229279.	−	77443.8i	−1.39095	−	0.469823i
$407$			414133.i			2.50006i
$408$	12878.0	+	19085.6i	0.0773623	+	0.114653i
$409$	25189.0			0.150579			0.0752894	−	0.997162i	$-0.476012\pi$
$409$	25189.0			0.150579			0.0752894	+	0.997162i	$0.476012\pi$
$410$		0			0
$411$			9817.14i			0.0581168i
$412$	−6086.22	+	7981.53i	−0.0358553	+	0.0470210i
$413$	595277.			3.48995
$414$	32699.6	+	11045.0i	0.190784	+	0.0644413i
$415$		0			0
$416$	−23504.3	−	1362.38i	−0.135819	−	0.00787249i
$417$	−78425.8			−0.451011
$418$	−76166.9	+	225499.i	−0.435927	+	1.29060i
$419$			180642.i			1.02894i	0.857508	+	0.514470i	$0.172011\pi$
$419$			180642.i			1.02894i	−0.857508	+	0.514470i	$0.827989\pi$
$420$		0			0
$421$	−139551.			−0.787354			−0.393677	−	0.919249i	$-0.628797\pi$
$421$	−139551.			−0.787354			−0.393677	+	0.919249i	$0.628797\pi$
$422$	93076.7	+	31438.6i	0.522656	+	0.176538i
$423$			8522.17i			0.0476288i
$424$	−179632.	+	121207.i	−0.999200	+	0.674213i
$425$		0			0
$426$	−19648.2	+	58170.1i	−0.108269	+	0.320539i
$427$		−	473485.i		−	2.59687i
$428$	28998.2	−	38028.5i	0.158301	−	0.207597i
$429$	−20845.8			−0.113267
$430$		0			0
$431$			165053.i			0.888523i	0.895897	+	0.444261i	$0.146534\pi$
$431$			165053.i			0.888523i	−0.895897	+	0.444261i	$0.853466\pi$
$432$	−34635.2	+	9505.11i	−0.185588	+	0.0509319i
$433$	−26213.4			−0.139813			−0.0699065	−	0.997554i	$-0.522270\pi$
$433$	−26213.4			−0.139813			−0.0699065	+	0.997554i	$0.522270\pi$
$434$	8270.20	−	24484.6i	0.0439073	−	0.129991i
$435$		0			0
$436$	−199808.	−	152361.i	−1.05109	−	0.801496i
$437$	−108984.			−0.570689
$438$	−113068.	−	38191.0i	−0.589374	−	0.199073i
$439$		−	355921.i		−	1.84682i	−0.383813	−	0.923411i	$-0.625389\pi$
$439$		−	355921.i		−	1.84682i	0.383813	−	0.923411i	$-0.374611\pi$
$440$		0			0
$441$	149363.			0.768010
$442$	2037.59	−	6032.45i	0.0104297	−	0.0308780i
$443$		−	114260.i		−	0.582220i	−0.956690	−	0.291110i	$-0.905975\pi$
$443$		−	114260.i		−	0.582220i	0.956690	−	0.291110i	$-0.0940246\pi$
$444$	119650.	−	156910.i	0.606941	−	0.795948i
$445$		0			0
$446$	270053.	+	91216.0i	1.35762	+	0.458566i
$447$		−	155298.i		−	0.777232i
$448$	338301.	+	136550.i	1.68557	+	0.680357i
$449$	85579.1			0.424497			0.212249	−	0.977216i	$-0.431921\pi$
$449$	85579.1			0.424497			0.212249	+	0.977216i	$0.431921\pi$
$450$		0			0
$451$			133085.i			0.654297i
$452$	242591.	+	184985.i	1.18740	+	0.905440i
$453$	82192.7			0.400532
$454$	277733.	+	93810.1i	1.34746	+	0.455133i
$455$		0			0
$456$	94009.2	−	63432.9i	0.452106	−	0.305060i
$457$	388386.			1.85965			0.929826	−	0.368000i	$-0.119958\pi$
$457$	388386.			1.85965			0.929826	+	0.368000i	$0.119958\pi$
$458$	47493.3	−	140608.i	0.226413	−	0.670315i
$459$		−	9713.24i		−	0.0461040i
$460$		0			0
$461$	322691.			1.51840			0.759198	−	0.650860i	$-0.225591\pi$
$461$	322691.			1.51840			0.759198	+	0.650860i	$0.225591\pi$
$462$	306028.	+	103367.i	1.43376	+	0.484283i
$463$		−	186325.i		−	0.869181i	−0.900628	−	0.434591i	$-0.856893\pi$
$463$		−	186325.i		−	0.869181i	0.900628	−	0.434591i	$-0.143107\pi$
$464$	46021.2	+	167694.i	0.213758	+	0.778902i
$465$		0			0
$466$	26882.5	−	79588.0i	0.123793	−	0.366501i
$467$		−	119419.i		−	0.547572i	−0.961791	−	0.273786i	$-0.911724\pi$
$467$		−	119419.i		−	0.547572i	0.961791	−	0.273786i	$-0.0882760\pi$
$468$	7898.22	+	6022.70i	0.0360610	+	0.0274979i
$469$	357613.			1.62580
$470$		0			0
$471$		−	169340.i		−	0.763339i
$472$	−239249.	−	354573.i	−1.07391	−	1.59156i
$473$	−542922.			−2.42670
$474$	−2758.31	+	8166.21i	−0.0122768	+	0.0363466i
$475$		0			0
$476$	−59825.8	+	78456.1i	−0.264043	+	0.346268i
$477$	91420.3			0.401796
$478$	33674.9	+	11374.4i	0.147384	+	0.0497820i
$479$		−	91602.7i		−	0.399243i	−0.979873	−	0.199622i	$-0.936029\pi$
$479$		−	91602.7i		−	0.399243i	0.979873	−	0.199622i	$-0.0639713\pi$
$480$		0			0
$481$	−54570.0			−0.235865
$482$	14123.7	−	41814.4i	0.0607930	−	0.179983i
$483$			147904.i			0.633993i
$484$	201079.	+	153331.i	0.858375	+	0.654544i
$485$		0			0
$486$	14355.2	+	4848.77i	0.0607767	+	0.0205286i
$487$		−	204150.i		−	0.860778i	−0.902644	−	0.430389i	$-0.858376\pi$
$487$		−	204150.i		−	0.860778i	0.902644	−	0.430389i	$-0.141624\pi$
$488$	−282029.	+	190300.i	−1.18428	+	0.799095i
$489$	101473.			0.424357
$490$		0			0
$491$		−	191987.i		−	0.796360i	−0.917307	−	0.398180i	$-0.869642\pi$
$491$		−	191987.i		−	0.796360i	0.917307	−	0.398180i	$-0.130358\pi$
$492$	38450.5	−	50424.2i	0.158844	−	0.208310i
$493$	−47028.9			−0.193496
$494$	−29713.9	−	10036.5i	−0.121760	−	0.0411270i
$495$		0			0
$496$	−17908.0	+	4914.59i	−0.0727922	+	0.0199767i
$497$	−263109.			−1.06518
$498$	−64775.8	+	191774.i	−0.261189	+	0.773272i
$499$		−	86859.0i		−	0.348830i	−0.984672	−	0.174415i	$-0.944197\pi$
$499$		−	86859.0i		−	0.348830i	0.984672	−	0.174415i	$-0.0558034\pi$
$500$		0			0
$501$	−108506.			−0.432294
$502$	195063.	+	65886.4i	0.774046	+	0.261450i
$503$			351571.i			1.38956i	0.719222	+	0.694780i	$0.244498\pi$
$503$			351571.i			1.38956i	−0.719222	+	0.694780i	$0.755502\pi$
$504$	−86085.8	−	127581.i	−0.338899	−	0.502257i
$505$		0			0
$506$	−71377.6	+	211320.i	−0.278779	+	0.825351i
$507$			145660.i			0.566664i
$508$	−3646.80	+	4782.45i	−0.0141314	+	0.0185320i
$509$	−50040.2			−0.193145			−0.0965725	−	0.995326i	$-0.530788\pi$
$509$	−50040.2			−0.193145			−0.0965725	+	0.995326i	$0.530788\pi$
$510$		0			0
$511$		−	511417.i		−	1.95855i
$512$	−54631.7	−	256388.i	−0.208403	−	0.978043i
$513$	−47844.2			−0.181800
$514$	−54466.3	+	161252.i	−0.206159	+	0.610350i
$515$		0			0
$516$	205707.	+	156860.i	0.772591	+	0.589131i
$517$	−55074.1			−0.206047
$518$	801119.	+	270594.i	2.98564	+	1.00846i
$519$		−	27429.6i		−	0.101832i
$520$		0			0
$521$	−149074.			−0.549195			−0.274598	−	0.961559i	$-0.588545\pi$
$521$	−149074.			−0.549195			−0.274598	+	0.961559i	$0.588545\pi$
$522$	23476.4	−	69504.1i	0.0861571	−	0.255076i
$523$		−	109372.i		−	0.399854i	−0.979811	−	0.199927i	$-0.935930\pi$
$523$		−	109372.i		−	0.399854i	0.979811	−	0.199927i	$-0.0640705\pi$
$524$	−114154.	+	149702.i	−0.415746	+	0.545213i
$525$		0			0
$526$	21832.3	+	7374.31i	0.0789093	+	0.0266532i
$527$		−	5022.20i		−	0.0180831i
$528$	−61426.2	−	223828.i	−0.220336	−	0.802873i
$529$	177710.			0.635039
$530$		0			0
$531$			180453.i			0.639994i
$532$	386448.	+	294682.i	1.36543	+	1.04119i
$533$	−17536.5			−0.0617289
$534$	−161322.	−	54489.9i	−0.565733	−	0.191088i
$535$		0			0
$536$	−143729.	−	213010.i	−0.500283	−	0.741432i
$537$	244435.			0.847648
$538$	−25309.4	+	74930.7i	−0.0874414	+	0.258878i
$539$			965252.i			3.32249i
$540$		0			0
$541$	102538.			0.350340			0.175170	−	0.984538i	$-0.443953\pi$
$541$	102538.			0.350340			0.175170	+	0.984538i	$0.443953\pi$
$542$	−228825.	−	77290.2i	−0.778940	−	0.263103i
$543$			85195.9i			0.288947i
$544$	70776.7	+	4102.43i	0.239162	+	0.0138626i
$545$		0			0
$546$	−13620.6	+	40325.1i	−0.0456891	+	0.135266i
$547$			388547.i			1.29858i	0.760541	+	0.649290i	$0.224934\pi$
$547$			388547.i			1.29858i	−0.760541	+	0.649290i	$0.775066\pi$
$548$	24037.7	+	18329.7i	0.0800446	+	0.0610371i
$549$	143533.			0.476220
$550$		0			0
$551$			231649.i			0.763004i
$552$	88098.0	−	59444.3i	0.289126	−	0.195089i
$553$	−36936.6			−0.120783
$554$	175479.	−	519520.i	0.571748	−	1.69271i
$555$		0			0
$556$	−146430.	+	192029.i	−0.473674	+	0.621180i
$557$	24464.5			0.0788544			0.0394272	−	0.999222i	$-0.487447\pi$
$557$	24464.5			0.0788544			0.0394272	+	0.999222i	$0.487447\pi$
$558$	7422.32	+	2507.04i	0.0238381	+	0.00805180i
$559$		−	71540.6i		−	0.228944i
$560$		0			0
$561$	62771.3			0.199451
$562$	−87396.3	+	258744.i	−0.276707	+	0.819216i
$563$			534256.i			1.68551i	0.538294	+	0.842757i	$0.319069\pi$
$563$			534256.i			1.68551i	−0.538294	+	0.842757i	$0.680931\pi$
$564$	20866.9	+	15911.8i	0.0655994	+	0.0500221i
$565$		0			0
$566$	176050.	+	59464.6i	0.549545	+	0.185620i
$567$			64930.0i			0.201967i
$568$	105747.	+	156719.i	0.327771	+	0.485765i
$569$	−264769.			−0.817792			−0.408896	−	0.912581i	$-0.634086\pi$
$569$	−264769.			−0.817792			−0.408896	+	0.912581i	$0.634086\pi$
$570$		0			0
$571$			159329.i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$571$			159329.i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$572$	−38921.4	+	51041.8i	−0.118959	+	0.156003i
$573$	168798.			0.514113
$574$	257446.	+	86957.6i	0.781379	+	0.263927i
$575$		0			0
$576$	−41394.1	+	102553.i	−0.124765	+	0.309103i
$577$	−244978.			−0.735827			−0.367913	−	0.929860i	$-0.619928\pi$
$577$	−244978.			−0.735827			−0.367913	+	0.929860i	$0.619928\pi$
$578$	100774.	−	298351.i	0.301643	−	0.893042i
$579$		−	54042.4i		−	0.161205i
$580$		0			0
$581$	−867415.			−2.56965
$582$	−188336.	−	63614.3i	−0.556015	−	0.187806i
$583$			590799.i			1.73821i
$584$	−304623.	+	205545.i	−0.893176	+	0.602672i
$585$		0			0
$586$	97058.4	−	287350.i	0.282643	−	0.836789i
$587$		−	415608.i		−	1.20617i	−0.797678	−	0.603084i	$-0.793938\pi$
$587$		−	415608.i		−	1.20617i	0.797678	−	0.603084i	$-0.206062\pi$
$588$	278878.	−	365723.i	0.806603	−	1.05779i
$589$	−24737.7			−0.0713064
$590$		0			0
$591$		−	245131.i		−	0.701815i
$592$	−160801.	−	585937.i	−0.458825	−	1.67189i
$593$	149847.			0.426128			0.213064	−	0.977038i	$-0.431656\pi$
$593$	149847.			0.426128			0.213064	+	0.977038i	$0.431656\pi$
$594$	−31334.9	+	92769.7i	−0.0888087	+	0.262926i
$595$		0			0
$596$	−380254.	−	289959.i	−1.07049	−	0.816289i
$597$	296935.			0.833129
$598$	−27845.5	−	9405.38i	−0.0778668	−	0.0263011i
$599$			34050.6i			0.0949011i	0.998874	+	0.0474505i	$0.0151096\pi$
$599$			34050.6i			0.0949011i	−0.998874	+	0.0474505i	$0.984890\pi$
$600$		0			0
$601$	−618647.			−1.71275			−0.856375	−	0.516355i	$-0.827288\pi$
$601$	−618647.			−1.71275			−0.856375	+	0.516355i	$0.827288\pi$
$602$	−354746.	+	1.05026e6i	−0.978868	+	2.89803i
$603$			108408.i			0.298143i
$604$	153463.	−	201253.i	0.420659	−	0.551655i
$605$		0			0
$606$	−27311.3	−	9224.95i	−0.0743698	−	0.0251199i
$607$			35350.6i			0.0959444i	0.998849	+	0.0479722i	$0.0152759\pi$
$607$			35350.6i			0.0959444i	−0.998849	+	0.0479722i	$0.984724\pi$
$608$	20207.2	−	348622.i	0.0546638	−	0.943079i
$609$	314374.			0.847641
$610$		0			0
$611$		−	7257.08i		−	0.0194392i
$612$	−23783.3	−	18135.7i	−0.0634994	−	0.0484208i
$613$	−690354.			−1.83718			−0.918588	−	0.395215i	$-0.870670\pi$
$613$	−690354.			−1.83718			−0.918588	+	0.395215i	$0.870670\pi$
$614$	−436171.	−	147326.i	−1.15696	−	0.390789i
$615$		0			0
$616$	824487.	−	556325.i	2.17281	−	1.46611i
$617$	94309.0			0.247732			0.123866	−	0.992299i	$-0.460471\pi$
$617$	94309.0			0.247732			0.123866	+	0.992299i	$0.460471\pi$
$618$	4172.53	−	12353.2i	0.0109250	−	0.0323445i
$619$			107669.i			0.281002i	0.990081	+	0.140501i	$0.0448713\pi$
$619$			107669.i			0.281002i	−0.990081	+	0.140501i	$0.955129\pi$
$620$		0			0
$621$	−44835.8			−0.116263
$622$	−171157.	−	57811.7i	−0.442398	−	0.149429i
$623$		−	729676.i		−	1.87998i
$624$	29493.7	−	8094.10i	0.0757461	−	0.0207874i
$625$		0			0
$626$	35702.9	−	105702.i	0.0911077	−	0.269732i
$627$		−	309190.i		−	0.786486i
$628$	−414636.	−	316176.i	−1.05135	−	0.801697i
$629$	164323.			0.415332
$630$		0			0
$631$			489941.i			1.23051i	0.788329	+	0.615254i	$0.210947\pi$
$631$			489941.i			1.23051i	−0.788329	+	0.615254i	$0.789053\pi$
$632$	14845.3	+	22001.1i	0.0371667	+	0.0550820i
$633$	−127621.			−0.318504
$634$	115419.	−	341709.i	0.287144	−	0.850115i
$635$		0			0
$636$	170692.	−	223847.i	0.421987	−	0.553397i
$637$	−127191.			−0.313456
$638$	449166.	+	151715.i	1.10348	+	0.372724i
$639$		−	79759.3i		−	0.195335i
$640$		0			0
$641$	593431.			1.44429			0.722145	−	0.691742i	$-0.243156\pi$
$641$	593431.			1.44429			0.722145	+	0.691742i	$0.243156\pi$
$642$	−19880.3	+	58857.3i	−0.0482339	+	0.142801i
$643$		−	263108.i		−	0.636372i	−0.948028	−	0.318186i	$-0.896926\pi$
$643$		−	263108.i		−	0.636372i	0.948028	−	0.318186i	$-0.103074\pi$
$644$	362149.	+	276153.i	0.873203	+	0.665851i
$645$		0			0
$646$	89475.1	+	30222.1i	0.214406	+	0.0724201i
$647$			640998.i			1.53126i	0.643282	+	0.765629i	$0.277572\pi$
$647$			640998.i			1.53126i	−0.643282	+	0.765629i	$0.722428\pi$
$648$	38675.2	−	26096.2i	0.0921049	−	0.0621480i
$649$	−1.16617e6			−2.76868
$650$		0			0
$651$			33571.9i			0.0792161i
$652$	189461.	−	248461.i	0.445681	−	0.584470i
$653$	−453024.			−1.06242			−0.531208	−	0.847241i	$-0.678262\pi$
$653$	−453024.			−1.06242			−0.531208	+	0.847241i	$0.678262\pi$
$654$	309246.	+	104454.i	0.723017	+	0.244214i
$655$		0			0
$656$	−51674.8	−	188295.i	−0.120080	−	0.437554i
$657$	155032.			0.359162
$658$	−35985.4	+	106538.i	−0.0831141	+	0.246067i
$659$			16332.5i			0.0376081i	0.999823	+	0.0188040i	$0.00598586\pi$
$659$			16332.5i			0.0376081i	−0.999823	+	0.0188040i	$0.994014\pi$
$660$		0			0
$661$	143631.			0.328735			0.164367	−	0.986399i	$-0.447442\pi$
$661$	143631.			0.328735			0.164367	+	0.986399i	$0.447442\pi$
$662$	−515181.	−	174013.i	−1.17556	−	0.397069i
$663$			8271.34i			0.0188169i
$664$	348625.	+	516671.i	0.790719	+	1.17187i
$665$		0			0
$666$	−82028.5	+	242852.i	−0.184934	+	0.547513i
$667$			217083.i			0.487948i
$668$	−202593.	+	265682.i	−0.454017	+	0.595401i
$669$	−370281.			−0.827330
$670$		0			0
$671$			927575.i			2.06017i
$672$	−473120.	−	27423.5i	−1.04769	−	0.0607274i
$673$	331571.			0.732058			0.366029	−	0.930603i	$-0.380717\pi$
$673$	331571.			0.732058			0.366029	+	0.930603i	$0.380717\pi$
$674$	−106441.	+	315127.i	−0.234308	+	0.693690i
$675$		0			0
$676$	356656.	+	271964.i	0.780471	+	0.595139i
$677$	495629.			1.08138			0.540691	−	0.841221i	$-0.318163\pi$
$677$	495629.			1.08138			0.540691	+	0.841221i	$0.318163\pi$
$678$	−375462.	−	126820.i	−0.816783	−	0.275886i
$679$		−	851861.i		−	1.84769i
$680$		0			0
$681$	−380811.			−0.821136
$682$	−16201.6	+	47966.3i	−0.0348329	+	0.103126i
$683$		−	490413.i		−	1.05128i	−0.850706	−	0.525642i	$-0.823825\pi$
$683$		−	490413.i		−	1.05128i	0.850706	−	0.525642i	$-0.176175\pi$
$684$	−89330.4	+	117149.i	−0.190936	+	0.250395i
$685$		0			0
$686$	1.05681e6	+	356960.i	2.24569	+	0.758528i
$687$			192793.i			0.408487i
$688$	768156.	−	210809.i	1.62283	−	0.445360i
$689$	−77849.3			−0.163990
$690$		0			0
$691$		−	157915.i		−	0.330725i	−0.986233	−	0.165363i	$-0.947121\pi$
$691$		−	157915.i		−	0.330725i	0.986233	−	0.165363i	$-0.0528794\pi$
$692$	−67162.6	−	51214.1i	−0.140254	−	0.106949i
$693$	−419607.			−0.873728
$694$	−451012.	−	152339.i	−0.936416	−	0.316294i
$695$		0			0
$696$	−126351.	−	187255.i	−0.260831	−	0.386558i
$697$	52806.3			0.108698
$698$	129510.	−	383425.i	0.265823	−	0.786992i
$699$			109126.i			0.223344i
$700$		0			0
$701$	−125021.			−0.254418			−0.127209	−	0.991876i	$-0.540602\pi$
$701$	−125021.			−0.254418			−0.127209	+	0.991876i	$0.540602\pi$
$702$	−12224.2	−	4128.98i	−0.0248054	−	0.00837855i
$703$		−	809398.i		−	1.63776i
$704$	−662743.	−	267507.i	−1.33721	−	0.539747i
$705$		0			0
$706$	−261780.	+	775022.i	−0.525202	+	1.55491i
$707$		−	123532.i		−	0.247138i
$708$	441848.	+	336926.i	0.881468	+	0.672154i
$709$	−223380.			−0.444377			−0.222189	−	0.975004i	$-0.571320\pi$
$709$	−223380.			−0.444377			−0.222189	+	0.975004i	$0.571320\pi$
$710$		0			0
$711$		−	11197.0i		−	0.0221495i
$712$	−434627.	+	293266.i	−0.857348	+	0.578498i
$713$	−23182.2			−0.0456011
$714$	41014.8	−	121428.i	0.0804533	−	0.238189i
$715$		0			0
$716$	456388.	−	598511.i	0.890242	−	1.16747i
$717$	−46173.0			−0.0898152
$718$	171639.	+	57974.6i	0.332941	+	0.112458i
$719$		−	839679.i		−	1.62426i	−0.583477	−	0.812130i	$-0.698308\pi$
$719$		−	839679.i		−	1.62426i	0.583477	−	0.812130i	$-0.301692\pi$
$720$		0			0
$721$	55874.5			0.107484
$722$	−17951.8	+	53147.8i	−0.0344376	+	0.101956i
$723$			57333.4i			0.109681i
$724$	208606.	+	159070.i	0.397969	+	0.303467i
$725$		0			0
$726$	−311214.	−	105119.i	−0.590454	−	0.199438i
$727$		−	244897.i		−	0.463355i	−0.972793	−	0.231678i	$-0.925579\pi$
$727$		−	244897.i		−	0.463355i	0.972793	−	0.231678i	$-0.0744214\pi$
$728$	73306.6	+	108642.i	0.138319	+	0.204991i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			215425.i			0.403145i
$732$	267992.	−	351447.i	0.500150	−	0.655901i
$733$	−370157.			−0.688935			−0.344467	−	0.938798i	$-0.611940\pi$
$733$	−370157.			−0.688935			−0.344467	+	0.938798i	$0.611940\pi$
$734$	−66405.3	−	22429.8i	−0.123257	−	0.0416325i
$735$		0			0
$736$	18936.6	−	326701.i	0.0349580	−	0.603108i
$737$	−700578.			−1.28980
$738$	−26360.5	+	78042.5i	−0.0483995	+	0.143291i
$739$			555878.i			1.01787i	0.860806	+	0.508933i	$0.169960\pi$
$739$			555878.i			1.01787i	−0.860806	+	0.508933i	$0.830040\pi$
$740$		0			0
$741$	40741.9			0.0742001
$742$	1.14287e6	+	386028.i	2.07582	+	0.701151i
$743$		−	282516.i		−	0.511759i	−0.966709	−	0.255880i	$-0.917635\pi$
$743$		−	282516.i		−	0.511759i	0.966709	−	0.255880i	$-0.0823650\pi$
$744$	19996.9	−	13493.0i	0.0361257	−	0.0243759i
$745$		0			0
$746$	−21166.3	+	62664.7i	−0.0380336	+	0.112602i
$747$		−	262950.i		−	0.471228i
$748$	117201.	−	153698.i	0.209473	−	0.274705i
$749$	−266218.			−0.474540
$750$		0			0
$751$			406925.i			0.721498i	0.932663	+	0.360749i	$0.117479\pi$
$751$			406925.i			0.721498i	−0.932663	+	0.360749i	$0.882521\pi$
$752$	77921.7	−	21384.4i	0.137792	−	0.0378148i
$753$	−267458.			−0.471700
$754$	−19991.4	+	59186.4i	−0.0351642	+	0.104107i
$755$		0			0
$756$	158984.	+	121232.i	0.278170	+	0.212115i
$757$	973008.			1.69795			0.848974	−	0.528434i	$-0.177221\pi$
$757$	973008.			1.69795			0.848974	+	0.528434i	$0.177221\pi$
$758$	−241915.	−	81711.8i	−0.421041	−	0.142215i
$759$		−	289749.i		−	0.502965i
$760$		0			0
$761$	−457654.			−0.790255			−0.395128	−	0.918626i	$-0.629300\pi$
$761$	−457654.			−0.790255			−0.395128	+	0.918626i	$0.629300\pi$
$762$	2500.14	−	7401.88i	0.00430580	−	0.0127477i
$763$			1.39875e6i			2.40265i
$764$	315165.	−	413310.i	0.539947	−	0.708091i
$765$		0			0
$766$	−302439.	−	102155.i	−0.515442	−	0.174101i
$767$		−	153666.i		−	0.261208i
$768$	173818.	+	292833.i	0.294695	+	0.496476i
$769$	449424.			0.759982			0.379991	−	0.924990i	$-0.375927\pi$
$769$	449424.			0.759982			0.379991	+	0.924990i	$0.375927\pi$
$770$		0			0
$771$		−	221099.i		−	0.371945i
$772$	−132325.	−	100903.i	−0.222028	−	0.169305i
$773$	−842657.			−1.41024			−0.705118	−	0.709090i	$-0.749106\pi$
$773$	−842657.			−1.41024			−0.705118	+	0.709090i	$0.749106\pi$
$774$	−318376.	−	107538.i	−0.531446	−	0.179507i
$775$		0			0
$776$	−507406.	+	342373.i	−0.842621	+	0.568560i
$777$	−1.09845e6			−1.81944
$778$	204215.	−	604597.i	0.337387	−	0.998865i
$779$		−	260106.i		−	0.428623i
$780$		0			0
$781$	515440.			0.845038
$782$	83848.9	+	28321.7i	0.137115	+	0.0463133i
$783$			95299.8i			0.155442i
$784$	−374793.	−	1.36569e6i	−0.609761	−	2.22188i
$785$		0			0
$786$	78260.4	−	231697.i	0.126677	−	0.375038i
$787$			370408.i			0.598041i	0.954247	+	0.299021i	$0.0966600\pi$
$787$			370408.i			0.598041i	−0.954247	+	0.299021i	$0.903340\pi$
$788$	−600214.	−	457686.i	−0.966615	−	0.737081i
$789$	−29935.1			−0.0480870
$790$		0			0
$791$		−	1.69825e6i		−	2.71425i
$792$	168645.	+	249936.i	0.268858	+	0.398455i
$793$	−122226.			−0.194365
$794$	188880.	−	559196.i	0.299602	−	0.886999i
$795$		0			0
$796$	554410.	−	727058.i	0.874994	−	1.14747i
$797$	321175.			0.505621			0.252810	−	0.967516i	$-0.418645\pi$
$797$	321175.			0.505621			0.252810	+	0.967516i	$0.418645\pi$
$798$	−598113.	−	202025.i	−0.939242	−	0.317249i
$799$			21852.7i			0.0342303i
$800$		0			0
$801$	221195.			0.344755
$802$	61310.3	−	181514.i	0.0953201	−	0.282204i
$803$			1.00189e6i			1.55377i
$804$	265441.	+	202409.i	0.410635	+	0.313125i
$805$		0			0
$806$	−6320.50	−	2134.88i	−0.00972929	−	0.00328627i
$807$		−	102740.i		−	0.157759i
$808$	−73580.9	+	49648.9i	−0.112705	+	0.0760478i
$809$	596798.			0.911864			0.455932	−	0.890015i	$-0.349306\pi$
$809$	596798.			0.911864			0.455932	+	0.890015i	$0.349306\pi$
$810$		0			0
$811$			479347.i			0.728800i	0.931243	+	0.364400i	$0.118726\pi$
$811$			479347.i			0.728800i	−0.931243	+	0.364400i	$0.881274\pi$
$812$	586971.	−	769759.i	0.890235	−	1.16746i
$813$	313750.			0.474683
$814$	−1.56942e6	−	530105.i	−2.36859	−	0.800042i
$815$		0			0
$816$	−88812.2	+	24373.2i	−0.133380	+	0.0366042i
$817$	1.06111e6			1.58970
$818$	−32242.8	+	95457.7i	−0.0481866	+	0.142661i
$819$		−	55291.4i		−	0.0824308i
$820$		0			0
$821$	84958.2			0.126043			0.0630215	−	0.998012i	$-0.479926\pi$
$821$	84958.2			0.126043			0.0630215	+	0.998012i	$0.479926\pi$
$822$	−37203.6	−	12566.3i	−0.0550607	−	0.0185979i
$823$			67392.6i			0.0994975i	0.998762	+	0.0497488i	$0.0158421\pi$
$823$			67392.6i			0.0994975i	−0.998762	+	0.0497488i	$0.984158\pi$
$824$	−22456.7	−	33281.3i	−0.0330743	−	0.0490170i
$825$		0			0
$826$	−761976.	+	2.25590e6i	−1.11681	+	3.30643i
$827$		−	433061.i		−	0.633196i	−0.948560	−	0.316598i	$-0.897459\pi$
$827$		−	433061.i		−	0.633196i	0.948560	−	0.316598i	$-0.102541\pi$
$828$	−83713.4	+	109782.i	−0.122105	+	0.160130i
$829$	1.14798e6			1.67043			0.835213	−	0.549927i	$-0.185345\pi$
$829$	1.14798e6			1.67043			0.835213	+	0.549927i	$0.185345\pi$
$830$		0			0
$831$			712335.i			1.03153i
$832$	35249.3	−	87329.3i	0.0509218	−	0.126158i
$833$	383000.			0.551961
$834$	100388.	−	297207.i	0.144327	−	0.427294i
$835$		0			0
$836$	−757067.	−	577293.i	−1.08323	−	0.826007i
$837$	−10177.0			−0.0145268
$838$	−684570.	−	231228.i	−0.974832	−	0.329270i
$839$		−	499869.i		−	0.710121i	−0.934843	−	0.355060i	$-0.884460\pi$
$839$		−	499869.i		−	0.710121i	0.934843	−	0.355060i	$-0.115540\pi$
$840$		0			0
$841$	−245865.			−0.347620
$842$	178631.	−	528852.i	0.251960	−	0.745950i
$843$		−	354775.i		−	0.499226i
$844$	−238283.	+	312486.i	−0.334509	+	0.438678i
$845$		0			0
$846$	−32296.1	−	10908.7i	−0.0451242	−	0.0152416i
$847$		−	1.40765e6i		−	1.96213i
$848$	−229398.	−	835894.i	−0.319006	−	1.16241i
$849$	−241389.			−0.334890
$850$		0			0
$851$		−	758504.i		−	1.04737i
$852$	−195294.	−	148920.i	−0.269036	−	0.205151i
$853$	−490741.			−0.674457			−0.337228	−	0.941423i	$-0.609489\pi$
$853$	−490741.			−0.674457			−0.337228	+	0.941423i	$0.609489\pi$
$854$	1.79435e6	+	606078.i	2.46031	+	0.831022i
$855$		0			0
$856$	106996.	+	158571.i	0.146023	+	0.216410i
$857$	−920396.			−1.25318			−0.626590	−	0.779349i	$-0.715550\pi$
$857$	−920396.			−1.25318			−0.626590	+	0.779349i	$0.715550\pi$
$858$	26683.3	−	78998.4i	0.0362465	−	0.107311i
$859$			1.31521e6i			1.78242i	0.453595	+	0.891208i	$0.350141\pi$
$859$			1.31521e6i			1.78242i	−0.453595	+	0.891208i	$0.649859\pi$
$860$		0			0
$861$	−352994.			−0.476169
$862$	−625494.	−	211274.i	−0.841799	−	0.284335i
$863$			68287.4i			0.0916894i	0.998949	+	0.0458447i	$0.0145979\pi$
$863$			68287.4i			0.0916894i	−0.998949	+	0.0458447i	$0.985402\pi$
$864$	8313.21	−	143422.i	0.0111363	−	0.192128i
$865$		0			0
$866$	33554.1	−	99339.8i	0.0447414	−	0.132461i
$867$			409081.i			0.544216i
$868$	82202.3	+	62682.4i	0.109105	+	0.0831968i
$869$	72360.1			0.0958208
$870$		0			0
$871$		−	92314.8i		−	0.121684i
$872$	833158.	−	562175.i	1.09571	−	0.739331i
$873$	258235.			0.338833
$874$	139503.	−	413012.i	0.182626	−	0.540679i
$875$		0			0
$876$	289462.	−	379603.i	0.377210	−	0.494676i
$877$	−1.14924e6			−1.49421			−0.747104	−	0.664707i	$-0.768556\pi$
$877$	−1.14924e6			−1.49421			−0.747104	+	0.664707i	$0.768556\pi$
$878$	1.34882e6	+	455592.i	1.74971	+	0.591000i
$879$			393997.i			0.509935i
$880$		0			0
$881$	−79533.6			−0.102470			−0.0512352	−	0.998687i	$-0.516316\pi$
$881$	−79533.6			−0.102470			−0.0512352	+	0.998687i	$0.516316\pi$
$882$	−191190.	+	566036.i	−0.245770	+	0.727624i
$883$		−	226846.i		−	0.290945i	−0.989362	−	0.145472i	$-0.953530\pi$
$883$		−	226846.i		−	0.290945i	0.989362	−	0.145472i	$-0.0464702\pi$
$884$	20252.8	+	15443.5i	0.0259167	+	0.0197625i
$885$		0			0
$886$	433007.	+	146257.i	0.551604	+	0.186316i
$887$		−	421203.i		−	0.535358i	−0.963508	−	0.267679i	$-0.913743\pi$
$887$		−	421203.i		−	0.535358i	0.963508	−	0.267679i	$-0.0862567\pi$
$888$	441479.	+	654283.i	0.559866	+	0.829736i
$889$	33479.4			0.0423618
$890$		0			0
$891$		−	127200.i		−	0.160226i
$892$	−691355.	+	906649.i	−0.868904	+	1.13949i
$893$	107639.			0.134979
$894$	588526.	+	198787.i	0.736361	+	0.248721i
$895$		0			0
$896$	−950516.	+	1.10725e6i	−1.18398	+	1.37921i
$897$	38180.0			0.0474517
$898$	−109544.	+	324316.i	−0.135843	+	0.402175i
$899$			49274.5i			0.0609681i
$900$		0			0
$901$	234422.			0.288767
$902$	−504346.	−	170353.i	−0.619891	−	0.209381i
$903$		−	1.44005e6i		−	1.76604i
$904$	−1.01155e6	+	682549.i	−1.23781	+	0.835213i
$905$		0			0
$906$	−105210.	+	311482.i	−0.128174	+	0.379470i
$907$			743335.i			0.903587i	0.892123	+	0.451793i	$0.149216\pi$
$907$			743335.i			0.903587i	−0.892123	+	0.451793i	$0.850784\pi$
$908$	−711016.	+	932433.i	−0.862398	+	1.13096i
$909$	37447.6			0.0453206
$910$		0			0
$911$			460545.i			0.554927i	0.960736	+	0.277463i	$0.0894937\pi$
$911$			460545.i			0.554927i	−0.960736	+	0.277463i	$0.910506\pi$
$912$	120054.	+	437459.i	0.144340	+	0.525954i
$913$	1.69930e6			2.03858
$914$	−497148.	+	1.47185e6i	−0.595105	+	1.76186i
$915$		0			0
$916$	472063.	+	359966.i	0.562612	+	0.429014i
$917$	1.04799e6			1.24629
$918$	36809.9	+	12433.3i	0.0436796	+	0.0147537i
$919$		−	398036.i		−	0.471293i	−0.971839	−	0.235647i	$-0.924279\pi$
$919$		−	398036.i		−	0.471293i	0.971839	−	0.235647i	$-0.0757208\pi$
$920$		0			0
$921$	598052.			0.705049
$922$	−413056.	+	1.22289e6i	−0.485900	+	1.43855i
$923$			67919.3i			0.0797241i
$924$	−783453.	+	1.02743e6i	−0.917633	+	1.20339i
$925$		0			0
$926$	706110.	+	238503.i	0.823475	+	0.278146i
$927$			16937.9i			0.0197106i
$928$	−694413.	−	40250.3i	−0.806347	−	0.0467384i
$929$	−1.29517e6			−1.50070			−0.750352	−	0.661039i	$-0.770116\pi$
$929$	−1.29517e6			−1.50070			−0.750352	+	0.661039i	$0.770116\pi$
$930$		0			0
$931$		−	1.88653e6i		−	2.17653i
$932$	267201.	+	203751.i	0.307614	+	0.234567i
$933$	234680.			0.269595
$934$	452559.	+	152861.i	0.518778	+	0.175228i
$935$		0			0
$936$	−32934.0	+	22222.3i	−0.0375918	+	0.0253651i
$937$	−567776.			−0.646693			−0.323347	−	0.946281i	$-0.604808\pi$
$937$	−567776.			−0.646693			−0.323347	+	0.946281i	$0.604808\pi$
$938$	−457758.	+	1.35523e6i	−0.520272	+	1.54031i
$939$			144932.i			0.164374i
$940$		0			0
$941$	595092.			0.672055			0.336027	−	0.941852i	$-0.390917\pi$
$941$	595092.			0.672055			0.336027	+	0.941852i	$0.390917\pi$
$942$	641740.	+	216761.i	0.723198	+	0.244275i
$943$		−	243751.i		−	0.274109i
$944$	1.64996e6	−	452806.i	1.85152	−	0.508122i
$945$		0			0
$946$	694960.	−	2.05749e6i	0.776565	−	2.29909i
$947$			847579.i			0.945105i	0.881303	+	0.472552i	$0.156667\pi$
$947$			847579.i			0.945105i	−0.881303	+	0.472552i	$0.843333\pi$
$948$	−27416.4	−	20906.1i	−0.0305066	−	0.0232625i
$949$	−132018.			−0.146589
$950$		0			0
$951$			468531.i			0.518056i
$952$	−220743.	−	327146.i	−0.243563	−	0.360967i
$953$	705705.			0.777030			0.388515	−	0.921442i	$-0.372988\pi$
$953$	705705.			0.777030			0.388515	+	0.921442i	$0.372988\pi$
$954$	−117021.	+	346452.i	−0.128578	+	0.380668i
$955$		0			0
$956$	−86210.2	+	113057.i	−0.0943285	+	0.123703i
$957$	−615870.			−0.672458
$958$	347143.	+	117255.i	0.378249	+	0.127761i
$959$		−	168276.i		−	0.182972i
$960$		0			0
$961$	918259.			0.994302
$962$	69851.6	−	206802.i	0.0754790	−	0.223462i
$963$		−	80701.7i		−	0.0870222i
$964$	140383.	+	107048.i	0.151064	+	0.115192i
$965$		0			0
$966$	−560504.	−	189322.i	−0.600654	−	0.202883i
$967$			1.51802e6i			1.62339i	0.584079	+	0.811697i	$0.301456\pi$
$967$			1.51802e6i			1.62339i	−0.584079	+	0.811697i	$0.698544\pi$
$968$	−838460.	+	565753.i	−0.894812	+	0.603777i
$969$	−122683.			−0.130658
$970$		0			0
$971$			697559.i			0.739848i	0.929062	+	0.369924i	$0.120616\pi$
$971$			697559.i			0.739848i	−0.929062	+	0.369924i	$0.879384\pi$
$972$	−36750.4	+	48194.7i	−0.0388982	+	0.0510114i
$973$	1.34430e6			1.41994
$974$	773658.	+	261319.i	0.815513	+	0.275457i
$975$		0			0
$976$	−360163.	−	1.31238e6i	−0.378094	−	1.37772i
$977$	1.31716e6			1.37990			0.689952	−	0.723856i	$-0.257632\pi$
$977$	1.31716e6			1.37990			0.689952	+	0.723856i	$0.257632\pi$
$978$	−129889.	+	384547.i	−0.135798	+	0.402042i
$979$			1.42946e6i			1.49145i
$980$		0			0
$981$	−424020.			−0.440603
$982$	727566.	+	245751.i	0.754483	+	0.254842i
$983$		−	1.38061e6i		−	1.42878i	−0.699749	−	0.714389i	$-0.746705\pi$
$983$		−	1.38061e6i		−	1.42878i	0.699749	−	0.714389i	$-0.253295\pi$
$984$	141873.	+	210259.i	0.146524	+	0.217152i
$985$		0			0
$986$	60198.7	−	178223.i	0.0619203	−	0.183321i
$987$		−	146078.i		−	0.149952i
$988$	76069.6	−	99758.3i	0.0779287	−	0.102196i
$989$	994388.			1.01663
$990$		0			0
$991$		−	183725.i		−	0.187077i	−0.995616	−	0.0935385i	$-0.970182\pi$
$991$		−	183725.i		−	0.187077i	0.995616	−	0.0935385i	$-0.0298178\pi$
$992$	4298.32	−	74156.2i	0.00436793	−	0.0753571i
$993$	706385.			0.716379
$994$	336789.	−	997093.i	0.340867	−	1.00917i
$995$		0			0
$996$	−643844.	−	490956.i	−0.649026	−	0.494908i
$997$	−547047.			−0.550344			−0.275172	−	0.961395i	$-0.588735\pi$
$997$	−547047.			−0.550344			−0.275172	+	0.961395i	$0.588735\pi$
$998$	329166.	+	111183.i	0.330486	+	0.111629i
$999$		−	332985.i		−	0.333652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.6		16
4.3	odd	2	inner	300.5.c.d.151.5		16
5.2	odd	4		300.5.f.b.199.3		32
5.3	odd	4		300.5.f.b.199.30		32
5.4	even	2		60.5.c.a.31.11	✓	16
15.14	odd	2		180.5.c.c.91.6		16
20.3	even	4		300.5.f.b.199.4		32
20.7	even	4		300.5.f.b.199.29		32
20.19	odd	2		60.5.c.a.31.12	yes	16
40.19	odd	2		960.5.e.f.511.12		16
40.29	even	2		960.5.e.f.511.1		16
60.59	even	2		180.5.c.c.91.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.11	✓	16	5.4	even	2
60.5.c.a.31.12	yes	16	20.19	odd	2
180.5.c.c.91.5		16	60.59	even	2
180.5.c.c.91.6		16	15.14	odd	2
300.5.c.d.151.5		16	4.3	odd	2	inner
300.5.c.d.151.6		16	1.1	even	1	trivial
300.5.f.b.199.3		32	5.2	odd	4
300.5.f.b.199.4		32	20.3	even	4
300.5.f.b.199.29		32	20.7	even	4
300.5.f.b.199.30		32	5.3	odd	4
960.5.e.f.511.1		16	40.29	even	2
960.5.e.f.511.12		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)

\(f(q)\)	\(=\)	\(q+(-1.28004 + 3.78966i) q^{2} -5.19615i q^{3} +(-12.7230 - 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} +89.0673i q^{7} +(53.0524 - 35.7972i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-1.28004 + 3.78966i) q^{2} -5.19615i q^{3} +(-12.7230 - 9.70180i) q^{4} +(19.6916 + 6.65126i) q^{6} +89.0673i q^{7} +(53.0524 - 35.7972i) q^{8} -27.0000 q^{9} -174.486i q^{11} +(-50.4120 + 66.1107i) q^{12} +22.9919 q^{13} +(-337.534 - 114.009i) q^{14} +(67.7503 + 246.872i) q^{16} -69.2339 q^{17} +(34.5610 - 102.321i) q^{18} +341.023i q^{19} +462.807 q^{21} +(661.242 + 223.348i) q^{22} +319.580i q^{23} +(-186.008 - 275.668i) q^{24} +(-29.4305 + 87.1316i) q^{26} +140.296i q^{27} +(864.112 - 1133.20i) q^{28} +679.276 q^{29} +72.5397i q^{31} +(-1022.28 - 59.2548i) q^{32} -906.656 q^{33} +(88.6218 - 262.373i) q^{34} +(343.521 + 261.948i) q^{36} -2373.44 q^{37} +(-1292.36 - 436.521i) q^{38} -119.470i q^{39} -762.724 q^{41} +(-592.410 + 1753.88i) q^{42} -3111.55i q^{43} +(-1692.83 + 2219.99i) q^{44} +(-1211.10 - 409.073i) q^{46} -315.636i q^{47} +(1282.79 - 352.041i) q^{48} -5531.98 q^{49} +359.750i q^{51} +(-292.527 - 223.063i) q^{52} -3385.94 q^{53} +(-531.674 - 179.584i) q^{54} +(3188.36 + 4725.23i) q^{56} +1772.01 q^{57} +(-869.498 + 2574.22i) q^{58} -6683.46i q^{59} -5316.04 q^{61} +(-274.901 - 92.8534i) q^{62} -2404.82i q^{63} +(1533.12 - 3798.26i) q^{64} +(1160.55 - 3435.92i) q^{66} -4015.09i q^{67} +(880.863 + 671.693i) q^{68} +1660.58 q^{69} +2954.05i q^{71} +(-1432.41 + 966.525i) q^{72} -5741.92 q^{73} +(3038.09 - 8994.54i) q^{74} +(3308.53 - 4338.84i) q^{76} +15541.0 q^{77} +(452.749 + 152.925i) q^{78} +414.704i q^{79} +729.000 q^{81} +(976.314 - 2890.46i) q^{82} +9738.88i q^{83} +(-5888.30 - 4490.06i) q^{84} +(11791.7 + 3982.90i) q^{86} -3529.62i q^{87} +(-6246.12 - 9256.90i) q^{88} -8192.42 q^{89} +2047.83i q^{91} +(3100.50 - 4066.02i) q^{92} +376.927 q^{93} +(1196.15 + 404.025i) q^{94} +(-307.897 + 5311.94i) q^{96} -9564.24 q^{97} +(7081.13 - 20964.3i) q^{98} +4711.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

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