LMFDB - Embedded newform 200.6.f.a.149.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12220785438976.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 116x^{4} + 320x^{2} + 4096 $ x^8 + 5x^6 + 116x^4 + 320*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.7
Root			$-2.10784 - 1.88600i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.a.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.21569 - 3.77200i) q^{2} +3.25452 q^{3} +(3.54400 - 31.8031i) q^{4} +(13.7200 - 12.2760i) q^{6} +112.704i q^{7} +(-105.021 - 147.440i) q^{8} -232.408 q^{9} +O(q^{10})$	\(q+(4.21569 - 3.77200i) q^{2} +3.25452 q^{3} +(3.54400 - 31.8031i) q^{4} +(13.7200 - 12.2760i) q^{6} +112.704i q^{7} +(-105.021 - 147.440i) q^{8} -232.408 q^{9} +575.407i q^{11} +(11.5340 - 103.504i) q^{12} +117.735 q^{13} +(425.120 + 475.125i) q^{14} +(-998.880 - 225.421i) q^{16} +223.408i q^{17} +(-979.759 + 876.644i) q^{18} +1752.26i q^{19} +366.797i q^{21} +(2170.44 + 2425.74i) q^{22} +2361.15i q^{23} +(-341.793 - 479.846i) q^{24} +(496.336 - 444.098i) q^{26} -1547.22 q^{27} +(3584.34 + 399.424i) q^{28} -3865.52i q^{29} -1591.55 q^{31} +(-5061.25 + 2817.47i) q^{32} +1872.67i q^{33} +(842.696 + 941.818i) q^{34} +(-823.655 + 7391.31i) q^{36} -4736.44 q^{37} +(6609.52 + 7386.97i) q^{38} +383.172 q^{39} +8153.88 q^{41} +(1383.56 + 1546.30i) q^{42} +4920.23 q^{43} +(18299.8 + 2039.25i) q^{44} +(8906.27 + 9953.88i) q^{46} +21062.0i q^{47} +(-3250.87 - 733.636i) q^{48} +4104.79 q^{49} +727.085i q^{51} +(417.255 - 3744.36i) q^{52} -12709.0 q^{53} +(-6522.61 + 5836.13i) q^{54} +(16617.1 - 11836.3i) q^{56} +5702.75i q^{57} +(-14580.7 - 16295.8i) q^{58} -14111.1i q^{59} +42030.6i q^{61} +(-6709.48 + 6003.33i) q^{62} -26193.3i q^{63} +(-10709.1 + 30968.6i) q^{64} +(7063.73 + 7894.60i) q^{66} -54153.4 q^{67} +(7105.08 + 791.759i) q^{68} +7684.41i q^{69} +43879.9 q^{71} +(24407.8 + 34266.3i) q^{72} -31290.6i q^{73} +(-19967.4 + 17865.9i) q^{74} +(55727.3 + 6210.01i) q^{76} -64850.7 q^{77} +(1615.33 - 1445.33i) q^{78} +50211.5 q^{79} +51439.7 q^{81} +(34374.2 - 30756.4i) q^{82} -43707.0 q^{83} +(11665.3 + 1299.93i) q^{84} +(20742.1 - 18559.1i) q^{86} -12580.4i q^{87} +(84838.1 - 60429.9i) q^{88} -64418.7 q^{89} +13269.3i q^{91} +(75092.1 + 8367.93i) q^{92} -5179.73 q^{93} +(79446.0 + 88790.8i) q^{94} +(-16471.9 + 9169.52i) q^{96} +62350.9i q^{97} +(17304.5 - 15483.3i) q^{98} -133729. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 40 q^{4} - 232 q^{6} + 328 q^{9}+O(q^{10}) $ 8 * q - 40 * q^4 - 232 * q^6 + 328 * q^9	$ 8 q - 40 q^{4} - 232 q^{6} + 328 q^{9} + 4768 q^{14} - 6624 q^{16} + 15584 q^{24} + 11216 q^{26} - 25856 q^{31} + 9544 q^{34} - 20328 q^{36} - 70208 q^{39} - 9136 q^{41} + 58224 q^{44} + 58400 q^{46} - 19656 q^{49} - 46576 q^{54} + 81536 q^{56} + 83840 q^{64} + 86448 q^{66} + 413376 q^{71} - 34928 q^{74} + 199888 q^{76} + 495744 q^{79} + 59368 q^{81} - 393344 q^{84} - 37000 q^{86} + 169264 q^{89} + 197568 q^{94} - 231296 q^{96}+O(q^{100}) $ 8 * q - 40 * q^4 - 232 * q^6 + 328 * q^9 + 4768 * q^14 - 6624 * q^16 + 15584 * q^24 + 11216 * q^26 - 25856 * q^31 + 9544 * q^34 - 20328 * q^36 - 70208 * q^39 - 9136 * q^41 + 58224 * q^44 + 58400 * q^46 - 19656 * q^49 - 46576 * q^54 + 81536 * q^56 + 83840 * q^64 + 86448 * q^66 + 413376 * q^71 - 34928 * q^74 + 199888 * q^76 + 495744 * q^79 + 59368 * q^81 - 393344 * q^84 - 37000 * q^86 + 169264 * q^89 + 197568 * q^94 - 231296 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	4.21569	−	3.77200i	0.745235	−	0.666802i
$2$	4.21569	−	3.77200i	0.745235	−	0.666802i
$3$	3.25452			0.208777			0.104389	−	0.994537i	$-0.466711\pi$
$3$	3.25452			0.208777			0.104389	+	0.994537i	$0.466711\pi$
$4$	3.54400	−	31.8031i	0.110750	−	0.993848i
$5$		0			0
$5$		0			0
$6$	13.7200	−	12.2760i	0.155588	−	0.139213i
$7$			112.704i			0.869350i	0.900587	+	0.434675i	$0.143137\pi$
$7$			112.704i			0.869350i	−0.900587	+	0.434675i	$0.856863\pi$
$8$	−105.021	−	147.440i	−0.580165	−	0.814499i
$9$	−232.408			−0.956412
$10$		0			0
$11$			575.407i			1.43382i	0.697167	+	0.716909i	$0.254443\pi$
$11$			575.407i			1.43382i	−0.697167	+	0.716909i	$0.745557\pi$
$12$	11.5340	−	103.504i	0.0231221	−	0.207493i
$13$	117.735			0.193219			0.0966093	−	0.995322i	$-0.469200\pi$
$13$	117.735			0.193219			0.0966093	+	0.995322i	$0.469200\pi$
$14$	425.120	+	475.125i	0.579684	+	0.647870i
$15$		0			0
$16$	−998.880	−	225.421i	−0.975469	−	0.220138i
$17$			223.408i			0.187489i	0.995596	+	0.0937447i	$0.0298837\pi$
$17$			223.408i			0.187489i	−0.995596	+	0.0937447i	$0.970116\pi$
$18$	−979.759	+	876.644i	−0.712752	+	0.637737i
$19$			1752.26i			1.11356i	0.830660	+	0.556781i	$0.187964\pi$
$19$			1752.26i			1.11356i	−0.830660	+	0.556781i	$0.812036\pi$
$20$		0			0
$21$			366.797i			0.181501i
$22$	2170.44	+	2425.74i	0.956072	+	1.06853i
$23$			2361.15i			0.930689i	0.885130	+	0.465344i	$0.154070\pi$
$23$			2361.15i			0.930689i	−0.885130	+	0.465344i	$0.845930\pi$
$24$	−341.793	−	479.846i	−0.121125	−	0.170049i
$25$		0			0
$26$	496.336	−	444.098i	0.143993	−	0.128839i
$27$	−1547.22			−0.408455
$28$	3584.34	+	399.424i	0.864002	+	0.0962806i
$29$		−	3865.52i		−	0.853518i	−0.904365	−	0.426759i	$-0.859655\pi$
$29$		−	3865.52i		−	0.853518i	0.904365	−	0.426759i	$-0.140345\pi$
$30$		0			0
$31$	−1591.55			−0.297452			−0.148726	−	0.988878i	$-0.547517\pi$
$31$	−1591.55			−0.297452			−0.148726	+	0.988878i	$0.547517\pi$
$32$	−5061.25	+	2817.47i	−0.873742	+	0.486390i
$33$			1872.67i			0.299349i
$34$	842.696	+	941.818i	0.125018	+	0.139724i
$35$		0			0
$36$	−823.655	+	7391.31i	−0.105923	+	0.950528i
$37$	−4736.44			−0.568785			−0.284392	−	0.958708i	$-0.591792\pi$
$37$	−4736.44			−0.568785			−0.284392	+	0.958708i	$0.591792\pi$
$38$	6609.52	+	7386.97i	0.742525	+	0.829865i
$39$	383.172			0.0403397
$40$		0			0
$41$	8153.88			0.757538			0.378769	−	0.925491i	$-0.376347\pi$
$41$	8153.88			0.757538			0.378769	+	0.925491i	$0.376347\pi$
$42$	1383.56	+	1546.30i	0.121025	+	0.135261i
$43$	4920.23			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$43$	4920.23			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$44$	18299.8	+	2039.25i	1.42500	+	0.158795i
$45$		0			0
$46$	8906.27	+	9953.88i	0.620585	+	0.693582i
$47$			21062.0i			1.39077i	0.718637	+	0.695385i	$0.244766\pi$
$47$			21062.0i			1.39077i	−0.718637	+	0.695385i	$0.755234\pi$
$48$	−3250.87	−	733.636i	−0.203656	−	0.0459598i
$49$	4104.79			0.244231
$50$		0			0
$51$			727.085i			0.0391435i
$52$	417.255	−	3744.36i	0.0213990	−	0.192030i
$53$	−12709.0			−0.621470			−0.310735	−	0.950497i	$-0.600575\pi$
$53$	−12709.0			−0.621470			−0.310735	+	0.950497i	$0.600575\pi$
$54$	−6522.61	+	5836.13i	−0.304395	+	0.272358i
$55$		0			0
$56$	16617.1	−	11836.3i	0.708084	−	0.504366i
$57$			5702.75i			0.232486i
$58$	−14580.7	−	16295.8i	−0.569127	−	0.636071i
$59$		−	14111.1i		−	0.527752i	−0.964557	−	0.263876i	$-0.914999\pi$
$59$		−	14111.1i		−	0.527752i	0.964557	−	0.263876i	$-0.0850010\pi$
$60$		0			0
$61$			42030.6i			1.44624i	0.690721	+	0.723121i	$0.257293\pi$
$61$			42030.6i			1.44624i	−0.690721	+	0.723121i	$0.742707\pi$
$62$	−6709.48	+	6003.33i	−0.221671	+	0.198341i
$63$		−	26193.3i		−	0.831456i
$64$	−10709.1	+	30968.6i	−0.326817	+	0.945088i
$65$		0			0
$66$	7063.73	+	7894.60i	0.199606	+	0.223085i
$67$	−54153.4			−1.47380			−0.736901	−	0.676001i	$-0.763711\pi$
$67$	−54153.4			−1.47380			−0.736901	+	0.676001i	$0.763711\pi$
$68$	7105.08	+	791.759i	0.186336	+	0.0207645i
$69$			7684.41i			0.194307i
$70$		0			0
$71$	43879.9			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$71$	43879.9			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$72$	24407.8	+	34266.3i	0.554877	+	0.778996i
$73$		−	31290.6i		−	0.687238i	−0.939109	−	0.343619i	$-0.888347\pi$
$73$		−	31290.6i		−	0.687238i	0.939109	−	0.343619i	$-0.111653\pi$
$74$	−19967.4	+	17865.9i	−0.423878	+	0.379267i
$75$		0			0
$76$	55727.3	+	6210.01i	1.10671	+	0.123327i
$77$	−64850.7			−1.24649
$78$	1615.33	−	1445.33i	0.0300625	−	0.0268986i
$79$	50211.5			0.905180			0.452590	−	0.891719i	$-0.350500\pi$
$79$	50211.5			0.905180			0.452590	+	0.891719i	$0.350500\pi$
$80$		0			0
$81$	51439.7			0.871136
$82$	34374.2	−	30756.4i	0.564544	−	0.505128i
$83$	−43707.0			−0.696395			−0.348197	−	0.937421i	$-0.613206\pi$
$83$	−43707.0			−0.696395			−0.348197	+	0.937421i	$0.613206\pi$
$84$	11665.3	+	1299.93i	0.180384	+	0.0201012i
$85$		0			0
$86$	20742.1	−	18559.1i	0.302418	−	0.270590i
$87$		−	12580.4i		−	0.178195i
$88$	84838.1	−	60429.9i	1.16784	−	0.831851i
$89$	−64418.7			−0.862059			−0.431030	−	0.902338i	$-0.641850\pi$
$89$	−64418.7			−0.862059			−0.431030	+	0.902338i	$0.641850\pi$
$90$		0			0
$91$			13269.3i			0.167974i
$92$	75092.1	+	8367.93i	0.924963	+	0.103074i
$93$	−5179.73			−0.0621012
$94$	79446.0	+	88790.8i	0.927368	+	1.03645i
$95$		0			0
$96$	−16471.9	+	9169.52i	−0.182417	+	0.101547i
$97$			62350.9i			0.672843i	0.941712	+	0.336421i	$0.109217\pi$
$97$			62350.9i			0.672843i	−0.941712	+	0.336421i	$0.890783\pi$
$98$	17304.5	−	15483.3i	0.182010	−	0.162854i
$99$		−	133729.i		−	1.37132i
$100$		0			0
$101$		−	49960.5i		−	0.487330i	−0.969859	−	0.243665i	$-0.921650\pi$
$101$		−	49960.5i		−	0.487330i	0.969859	−	0.243665i	$-0.0783497\pi$
$102$	2742.57	+	3065.16i	0.0261010	+	0.0291711i
$103$			159260.i			1.47915i	0.673072	+	0.739577i	$0.264974\pi$
$103$			159260.i			1.47915i	−0.673072	+	0.739577i	$0.735026\pi$
$104$	−12364.7	−	17358.9i	−0.112099	−	0.157376i
$105$		0			0
$106$	−53576.9	+	47938.2i	−0.463141	+	0.414397i
$107$	−135565.			−1.14469			−0.572346	−	0.820012i	$-0.693967\pi$
$107$	−135565.			−1.14469			−0.572346	+	0.820012i	$0.693967\pi$
$108$	−5483.37	+	49206.6i	−0.0452364	+	0.405942i
$109$		−	115137.i		−	0.928218i	−0.885778	−	0.464109i	$-0.846375\pi$
$109$		−	115137.i		−	0.928218i	0.885778	−	0.464109i	$-0.153625\pi$
$110$		0			0
$111$	−15414.8			−0.118749
$112$	25405.9	−	112578.i	0.191377	−	0.848023i
$113$		−	19192.0i		−	0.141392i	−0.997498	−	0.0706960i	$-0.977478\pi$
$113$		−	19192.0i		−	0.141392i	0.997498	−	0.0706960i	$-0.0225220\pi$
$114$	21510.8	+	24041.0i	0.155022	+	0.173257i
$115$		0			0
$116$	−122936.	−	13699.4i	−0.848267	−	0.0945272i
$117$	−27362.7			−0.184797
$118$	−53227.0	−	59487.9i	−0.351906	−	0.393299i
$119$	−25179.0			−0.162994
$120$		0			0
$121$	−170043.			−1.05583
$122$	158540.	+	177188.i	0.964357	+	1.07779i
$123$	26536.9			0.158157
$124$	−5640.46	+	50616.3i	−0.0329428	+	0.295622i
$125$		0			0
$126$	−98801.3	−	110423.i	−0.554417	−	0.619630i
$127$		−	102000.i		−	0.561163i	−0.959830	−	0.280582i	$-0.909473\pi$
$127$		−	102000.i		−	0.561163i	0.959830	−	0.280582i	$-0.0905274\pi$
$128$	71667.4	+	170949.i	0.386631	+	0.922234i
$129$	16013.0			0.0847223
$130$		0			0
$131$		−	11296.1i		−	0.0575111i	−0.999586	−	0.0287556i	$-0.990846\pi$
$131$		−	11296.1i		−	0.0575111i	0.999586	−	0.0287556i	$-0.00915444\pi$
$132$	59556.9	+	6636.76i	0.297507	+	0.0331529i
$133$	−197487.			−0.968074
$134$	−228294.	+	204267.i	−1.09833	+	0.982734i
$135$		0			0
$136$	32939.3	−	23462.6i	0.152710	−	0.108775i
$137$		−	102753.i		−	0.467727i	−0.972269	−	0.233863i	$-0.924863\pi$
$137$		−	102753.i		−	0.467727i	0.972269	−	0.233863i	$-0.0751369\pi$
$138$	28985.6	+	32395.1i	0.129564	+	0.144804i
$139$		−	343928.i		−	1.50984i	−0.655818	−	0.754919i	$-0.727676\pi$
$139$		−	343928.i		−	1.50984i	0.655818	−	0.754919i	$-0.272324\pi$
$140$		0			0
$141$			68546.7i			0.290361i
$142$	184984.	−	165515.i	0.769862	−	0.688837i
$143$			67745.8i			0.277040i
$144$	232148.	+	52389.7i	0.932950	+	0.210542i
$145$		0			0
$146$	−118028.	−	131911.i	−0.458252	−	0.512154i
$147$	13359.1			0.0509900
$148$	−16786.0	+	150634.i	−0.0629930	+	0.565286i
$149$			186446.i			0.687998i	0.938970	+	0.343999i	$0.111782\pi$
$149$			186446.i			0.687998i	−0.938970	+	0.343999i	$0.888218\pi$
$150$		0			0
$151$	−285769.			−1.01994			−0.509968	−	0.860194i	$-0.670343\pi$
$151$	−285769.			−1.01994			−0.509968	+	0.860194i	$0.670343\pi$
$152$	258353.	−	184024.i	0.906994	−	0.646050i
$153$		−	51921.9i		−	0.179317i
$154$	−273390.	+	244617.i	−0.928927	+	0.831161i
$155$		0			0
$156$	1357.96	−	12186.1i	0.00446762	−	0.0400915i
$157$	−480654.			−1.55626			−0.778132	−	0.628101i	$-0.783833\pi$
$157$	−480654.			−1.55626			−0.778132	+	0.628101i	$0.783833\pi$
$158$	211676.	−	189398.i	0.674572	−	0.603576i
$159$	−41361.5			−0.129749
$160$		0			0
$161$	−266112.			−0.809094
$162$	216854.	−	194031.i	0.649201	−	0.580875i
$163$	176613.			0.520659			0.260329	−	0.965520i	$-0.416169\pi$
$163$	176613.			0.520659			0.260329	+	0.965520i	$0.416169\pi$
$164$	28897.4	−	259319.i	0.0838974	−	0.752878i
$165$		0			0
$166$	−184255.	+	164863.i	−0.518978	+	0.464358i
$167$			218853.i			0.607240i	0.952793	+	0.303620i	$0.0981954\pi$
$167$			218853.i			0.607240i	−0.952793	+	0.303620i	$0.901805\pi$
$168$	54080.6	−	38521.5i	0.147832	−	0.105300i
$169$	−357431.			−0.962667
$170$		0			0
$171$		−	407239.i		−	1.06502i
$172$	17437.3	−	156479.i	0.0449426	−	0.403306i
$173$	−522746.			−1.32793			−0.663965	−	0.747764i	$-0.731128\pi$
$173$	−522746.			−1.32793			−0.663965	+	0.747764i	$0.731128\pi$
$174$	−47453.2	−	53035.0i	−0.118821	−	0.132797i
$175$		0			0
$176$	129709.	−	574763.i	0.315637	−	1.39864i
$177$		−	45924.7i		−	0.110183i
$178$	−271569.	+	242988.i	−0.642437	+	0.574823i
$179$		−	411059.i		−	0.958897i	−0.877570	−	0.479449i	$-0.840837\pi$
$179$		−	411059.i		−	0.958897i	0.877570	−	0.479449i	$-0.159163\pi$
$180$		0			0
$181$			133094.i			0.301970i	0.988536	+	0.150985i	$0.0482445\pi$
$181$			133094.i			0.301970i	−0.988536	+	0.150985i	$0.951755\pi$
$182$	50051.7	+	55939.0i	0.112006	+	0.125180i
$183$			136789.i			0.301943i
$184$	348128.	−	247971.i	0.758045	−	0.539953i
$185$		0			0
$186$	−21836.1	+	19538.0i	−0.0462800	+	0.0414092i
$187$	−128551.			−0.268825
$188$	669838.	+	74643.9i	1.38221	+	0.154028i
$189$		−	174378.i		−	0.355090i
$190$		0			0
$191$	833447.			1.65308			0.826541	−	0.562877i	$-0.190305\pi$
$191$	833447.			1.65308			0.826541	+	0.562877i	$0.190305\pi$
$192$	−34853.0	+	100788.i	−0.0682319	+	0.197313i
$193$		−	597550.i		−	1.15473i	−0.816486	−	0.577366i	$-0.804081\pi$
$193$		−	597550.i		−	1.15473i	0.816486	−	0.577366i	$-0.195919\pi$
$194$	235188.	+	262852.i	0.448653	+	0.501426i
$195$		0			0
$196$	14547.4	−	130545.i	0.0270486	−	0.242729i
$197$	688179.			1.26339			0.631693	−	0.775219i	$-0.282360\pi$
$197$	688179.			1.26339			0.631693	+	0.775219i	$0.282360\pi$
$198$	−504427.	−	563761.i	−0.914399	−	1.02196i
$199$	977514.			1.74981			0.874904	−	0.484296i	$-0.160924\pi$
$199$	977514.			1.74981			0.874904	+	0.484296i	$0.160924\pi$
$200$		0			0
$201$	−176243.			−0.307696
$202$	−188451.	−	210618.i	−0.324952	−	0.363175i
$203$	435659.			0.742005
$204$	23123.6	+	2576.79i	0.0389027	+	0.00433515i
$205$		0			0
$206$	600729.	+	671390.i	0.986303	+	1.10232i
$207$		−	548751.i		−	0.890122i
$208$	−117604.	−	26540.0i	−0.188479	−	0.0425347i
$209$	−1.00826e6			−1.59664
$210$		0			0
$211$			44234.7i			0.0684001i	0.999415	+	0.0342000i	$0.0108883\pi$
$211$			44234.7i			0.0684001i	−0.999415	+	0.0342000i	$0.989112\pi$
$212$	−45040.6	+	404185.i	−0.0688279	+	0.617647i
$213$	142808.			0.215677
$214$	−571501.	+	511352.i	−0.853065	+	0.763284i
$215$		0			0
$216$	162491.	+	228123.i	0.236971	+	0.332686i
$217$		−	179374.i		−	0.258589i
$218$	−434298.	−	485383.i	−0.618938	−	0.691741i
$219$		−	101836.i		−	0.143480i
$220$		0			0
$221$			26303.1i			0.0362264i
$222$	−64984.1	+	58144.8i	−0.0884962	+	0.0791823i
$223$		−	73883.6i		−	0.0994915i	−0.998762	−	0.0497458i	$-0.984159\pi$
$223$		−	73883.6i		−	0.0994915i	0.998762	−	0.0497458i	$-0.0158411\pi$
$224$	−317541.	−	570424.i	−0.422843	−	0.759587i
$225$		0			0
$226$	−72392.4	−	80907.5i	−0.0942804	−	0.105370i
$227$	−195146.			−0.251359			−0.125680	−	0.992071i	$-0.540111\pi$
$227$	−195146.			−0.251359			−0.125680	+	0.992071i	$0.540111\pi$
$228$	181366.	+	20210.6i	0.231056	+	0.0257479i
$229$			1.55451e6i			1.95886i	0.201779	+	0.979431i	$0.435328\pi$
$229$			1.55451e6i			1.95886i	−0.201779	+	0.979431i	$0.564672\pi$
$230$		0			0
$231$	−211058.			−0.260239
$232$	−569932.	+	405961.i	−0.695189	+	0.495181i
$233$		−	56457.4i		−	0.0681289i	−0.999420	−	0.0340644i	$-0.989155\pi$
$233$		−	56457.4i		−	0.0681289i	0.999420	−	0.0340644i	$-0.0108451\pi$
$234$	−115352.	+	103212.i	−0.137717	+	0.123223i
$235$		0			0
$236$	−448777.	−	50009.7i	−0.524506	−	0.0584486i
$237$	163414.			0.188981
$238$	−106147.	+	94975.2i	−0.121469	+	0.108685i
$239$	551027.			0.623990			0.311995	−	0.950084i	$-0.399003\pi$
$239$	551027.			0.623990			0.311995	+	0.950084i	$0.399003\pi$
$240$		0			0
$241$	1.31586e6			1.45938			0.729689	−	0.683779i	$-0.239665\pi$
$241$	1.31586e6			1.45938			0.729689	+	0.683779i	$0.239665\pi$
$242$	−716846.	+	641401.i	−0.786842	+	0.704030i
$243$	543387.			0.590328
$244$	1.33671e6	+	148957.i	1.43735	+	0.160172i
$245$		0			0
$246$	111871.	−	100097.i	0.117864	−	0.105459i
$247$			206303.i			0.215161i
$248$	167146.	+	234658.i	0.172571	+	0.242274i
$249$	−142245.			−0.145391
$250$		0			0
$251$			95208.0i			0.0953870i	0.998862	+	0.0476935i	$0.0151871\pi$
$251$			95208.0i			0.0953870i	−0.998862	+	0.0476935i	$0.984813\pi$
$252$	−833031.	−	92829.3i	−0.826342	−	0.0920839i
$253$	−1.35862e6			−1.33444
$254$	−384743.	−	429998.i	−0.374185	−	0.418199i
$255$		0			0
$256$	946947.	+	450337.i	0.903079	+	0.429475i
$257$			1.73166e6i			1.63542i	0.575630	+	0.817711i	$0.304757\pi$
$257$			1.73166e6i			1.63542i	−0.575630	+	0.817711i	$0.695243\pi$
$258$	67505.7	−	60401.0i	0.0631380	−	0.0564930i
$259$		−	533816.i		−	0.494473i
$260$		0			0
$261$			898377.i			0.816315i
$262$	−42609.1	−	47621.0i	−0.0383485	−	0.0428593i
$263$			1.51692e6i			1.35230i	0.736764	+	0.676150i	$0.236353\pi$
$263$			1.51692e6i			1.35230i	−0.736764	+	0.676150i	$0.763647\pi$
$264$	276107.	−	196670.i	0.243819	−	0.173672i
$265$		0			0
$266$	−832541.	+	744920.i	−0.721443	+	0.645514i
$267$	−209652.			−0.179978
$268$	−191920.	+	1.72225e6i	−0.163224	+	1.46473i
$269$			1.89610e6i			1.59765i	0.601565	+	0.798824i	$0.294544\pi$
$269$			1.89610e6i			1.59765i	−0.601565	+	0.798824i	$0.705456\pi$
$270$		0			0
$271$	476326.			0.393986			0.196993	−	0.980405i	$-0.436882\pi$
$271$	476326.			0.393986			0.196993	+	0.980405i	$0.436882\pi$
$272$	50360.9	−	223158.i	0.0412735	−	0.182890i
$273$			43185.0i			0.0350693i
$274$	−387584.	−	433173.i	−0.311881	−	0.348566i
$275$		0			0
$276$	244388.	+	27233.6i	0.193111	+	0.0215195i
$277$	842760.			0.659940			0.329970	−	0.943991i	$-0.392961\pi$
$277$	842760.			0.659940			0.329970	+	0.943991i	$0.392961\pi$
$278$	−1.29730e6	−	1.44989e6i	−1.00676	−	1.12518i
$279$	369889.			0.284486
$280$		0			0
$281$	−1.64465e6			−1.24254			−0.621268	−	0.783598i	$-0.713382\pi$
$281$	−1.64465e6			−1.24254			−0.621268	+	0.783598i	$0.713382\pi$
$282$	258558.	+	288971.i	0.193614	+	0.216387i
$283$	2.22864e6			1.65415			0.827074	−	0.562092i	$-0.190003\pi$
$283$	2.22864e6			1.65415			0.827074	+	0.562092i	$0.190003\pi$
$284$	155510.	−	1.39552e6i	0.114410	−	1.02669i
$285$		0			0
$286$	255537.	+	285595.i	0.184731	+	0.206460i
$287$			918975.i			0.658565i
$288$	1.17628e6	−	654804.i	0.835657	−	0.465190i
$289$	1.36995e6			0.964848
$290$		0			0
$291$			202922.i			0.140474i
$292$	−995140.	−	110894.i	−0.683010	−	0.0761117i
$293$	692080.			0.470964			0.235482	−	0.971879i	$-0.424333\pi$
$293$	692080.			0.470964			0.235482	+	0.971879i	$0.424333\pi$
$294$	56317.9	−	50390.6i	0.0379995	−	0.0340002i
$295$		0			0
$296$	497426.	+	698341.i	0.329989	+	0.463275i
$297$		−	890284.i		−	0.585649i
$298$	703274.	+	785997.i	0.458758	+	0.512720i
$299$			277991.i			0.179826i
$300$		0			0
$301$			554530.i			0.352784i
$302$	−1.20471e6	+	1.07792e6i	−0.760091	+	0.680095i
$303$		−	162597.i		−	0.101743i
$304$	394996.	−	1.75030e6i	0.245137	−	1.08624i
$305$		0			0
$306$	−195849.	−	218886.i	−0.119569	−	0.133633i
$307$	2.91707e6			1.76645			0.883223	−	0.468952i	$-0.155368\pi$
$307$	2.91707e6			1.76645			0.883223	+	0.468952i	$0.155368\pi$
$308$	−229831.	+	2.06246e6i	−0.138049	+	1.23882i
$309$			518314.i			0.308814i
$310$		0			0
$311$	1.10725e6			0.649151			0.324575	−	0.945860i	$-0.394779\pi$
$311$	1.10725e6			0.649151			0.324575	+	0.945860i	$0.394779\pi$
$312$	−40241.2	−	56494.9i	−0.0234037	−	0.0328566i
$313$		−	1.65389e6i		−	0.954213i	−0.878845	−	0.477107i	$-0.841686\pi$
$313$		−	1.65389e6i		−	0.954213i	0.878845	−	0.477107i	$-0.158314\pi$
$314$	−2.02629e6	+	1.81303e6i	−1.15978	+	1.03772i
$315$		0			0
$316$	177950.	−	1.59688e6i	0.100249	−	0.899612i
$317$	459259.			0.256691			0.128345	−	0.991730i	$-0.459033\pi$
$317$	459259.			0.256691			0.128345	+	0.991730i	$0.459033\pi$
$318$	−174367.	+	156016.i	−0.0966934	+	0.0865168i
$319$	2.22425e6			1.22379
$320$		0			0
$321$	−441199.			−0.238986
$322$	−1.12184e6	+	1.00377e6i	−0.602965	+	0.539505i
$323$	−391469.			−0.208781
$324$	182303.	−	1.63594e6i	0.0964784	−	0.865777i
$325$		0			0
$326$	744544.	−	666184.i	0.388013	−	0.347176i
$327$		−	374717.i		−	0.193791i
$328$	−856329.	−	1.20221e6i	−0.439497	−	0.617014i
$329$	−2.37378e6			−1.20907
$330$		0			0
$331$		−	1.55618e6i		−	0.780711i	−0.920664	−	0.390356i	$-0.872352\pi$
$331$		−	1.55618e6i		−	0.780711i	0.920664	−	0.390356i	$-0.127648\pi$
$332$	−154898.	+	1.39002e6i	−0.0771258	+	0.692111i
$333$	1.10079e6			0.543993
$334$	825513.	+	922614.i	0.404909	+	0.452537i
$335$		0			0
$336$	82683.8	−	366386.i	0.0399551	−	0.177048i
$337$		−	919178.i		−	0.440885i	−0.975400	−	0.220442i	$-0.929250\pi$
$337$		−	919178.i		−	0.440885i	0.975400	−	0.220442i	$-0.0707501\pi$
$338$	−1.50682e6	+	1.34823e6i	−0.717413	+	0.641908i
$339$		−	62460.8i		−	0.0295194i
$340$		0			0
$341$		−	915790.i		−	0.426491i
$342$	−1.53611e6	−	1.71679e6i	−0.710160	−	0.793693i
$343$			2.35684e6i			1.08167i
$344$	−516728.	−	725439.i	−0.235432	−	0.330525i
$345$		0			0
$346$	−2.20373e6	+	1.97180e6i	−0.989620	+	0.885466i
$347$	1.87289e6			0.835003			0.417502	−	0.908676i	$-0.362906\pi$
$347$	1.87289e6			0.835003			0.417502	+	0.908676i	$0.362906\pi$
$348$	−400096.	−	44584.9i	−0.177099	−	0.0197351i
$349$			2.41450e6i			1.06112i	0.847649	+	0.530558i	$0.178018\pi$
$349$			2.41450e6i			1.06112i	−0.847649	+	0.530558i	$0.821982\pi$
$350$		0			0
$351$	−182163.			−0.0789210
$352$	−1.62120e6	−	2.91228e6i	−0.697395	−	1.25279i
$353$		−	2.43268e6i		−	1.03908i	−0.854447	−	0.519539i	$-0.826104\pi$
$353$		−	2.43268e6i		−	1.03908i	0.854447	−	0.519539i	$-0.173896\pi$
$354$	−173228.	−	193604.i	−0.0734701	−	0.0821120i
$355$		0			0
$356$	−228300.	+	2.04872e6i	−0.0954732	+	0.856756i
$357$	−81945.5			−0.0340294
$358$	−1.55052e6	−	1.73290e6i	−0.639395	−	0.714604i
$359$	−2.14148e6			−0.876958			−0.438479	−	0.898741i	$-0.644483\pi$
$359$	−2.14148e6			−0.876958			−0.438479	+	0.898741i	$0.644483\pi$
$360$		0			0
$361$	−594310.			−0.240019
$362$	502033.	+	561085.i	0.201354	+	0.225039i
$363$	−553407.			−0.220434
$364$	422004.	+	47026.3i	0.166941	+	0.0186032i
$365$		0			0
$366$	515970.	+	576661.i	0.201336	+	0.225018i
$367$		−	1.43273e6i		−	0.555262i	−0.960688	−	0.277631i	$-0.910451\pi$
$367$		−	1.43273e6i		−	0.555262i	0.960688	−	0.277631i	$-0.0895492\pi$
$368$	532253.	−	2.35851e6i	0.204880	−	0.907858i
$369$	−1.89503e6			−0.724519
$370$		0			0
$371$		−	1.43235e6i		−	0.540275i
$372$	−18357.0	+	164732.i	−0.00687771	+	0.0617191i
$373$	−2.57608e6			−0.958711			−0.479356	−	0.877621i	$-0.659130\pi$
$373$	−2.57608e6			−0.958711			−0.479356	+	0.877621i	$0.659130\pi$
$374$	−541929.	+	484893.i	−0.200338	+	0.179253i
$375$		0			0
$376$	3.10538e6	−	2.21196e6i	1.13278	−	0.806876i
$377$		−	455108.i		−	0.164915i
$378$	−657756.	−	735124.i	−0.236775	−	0.264625i
$379$			1.88270e6i			0.673260i	0.941637	+	0.336630i	$0.109287\pi$
$379$			1.88270e6i			0.673260i	−0.941637	+	0.336630i	$0.890713\pi$
$380$		0			0
$381$		−	331960.i		−	0.117158i
$382$	3.51355e6	−	3.14376e6i	1.23193	−	1.10228i
$383$		−	929245.i		−	0.323693i	−0.986816	−	0.161847i	$-0.948255\pi$
$383$		−	929245.i		−	0.323693i	0.986816	−	0.161847i	$-0.0517450\pi$
$384$	233243.	+	556356.i	0.0807198	+	0.192542i
$385$		0			0
$386$	−2.25396e6	−	2.51908e6i	−0.769977	−	0.860546i
$387$	−1.14350e6			−0.388114
$388$	1.98296e6	+	220972.i	0.668703	+	0.0745174i
$389$		−	1.88218e6i		−	0.630647i	−0.948984	−	0.315324i	$-0.897887\pi$
$389$		−	1.88218e6i		−	0.630647i	0.948984	−	0.315324i	$-0.102113\pi$
$390$		0			0
$391$	−527501.			−0.174494
$392$	−431090.	−	605211.i	−0.141694	−	0.198926i
$393$		−	36763.5i		−	0.0120070i
$394$	2.90115e6	−	2.59581e6i	0.941519	−	0.842428i
$395$		0			0
$396$	−4.25301e6	−	473937.i	−1.36288	−	0.151874i
$397$	4.38186e6			1.39535			0.697673	−	0.716417i	$-0.254219\pi$
$397$	4.38186e6			1.39535			0.697673	+	0.716417i	$0.254219\pi$
$398$	4.12089e6	−	3.68719e6i	1.30402	−	1.16678i
$399$	−642724.			−0.202112
$400$		0			0
$401$	1.43544e6			0.445784			0.222892	−	0.974843i	$-0.428450\pi$
$401$	1.43544e6			0.445784			0.222892	+	0.974843i	$0.428450\pi$
$402$	−742986.	+	664790.i	−0.229306	+	0.205173i
$403$	−187382.			−0.0574732
$404$	−1.58890e6	−	177060.i	−0.484332	−	0.0539718i
$405$		0			0
$406$	1.83660e6	−	1.64331e6i	0.552968	−	0.494771i
$407$		−	2.72538e6i		−	0.815533i
$408$	107202.	−	76359.3i	0.0318824	−	0.0227097i
$409$	479384.			0.141702			0.0708509	−	0.997487i	$-0.477429\pi$
$409$	479384.			0.141702			0.0708509	+	0.997487i	$0.477429\pi$
$410$		0			0
$411$		−	334411.i		−	0.0976508i
$412$	5.06497e6	+	564418.i	1.47005	+	0.163816i
$413$	1.59038e6			0.458801
$414$	−2.06989e6	−	2.31336e6i	−0.593535	−	0.663350i
$415$		0			0
$416$	−595889.	+	331717.i	−0.168823	+	0.0939796i
$417$		−	1.11932e6i		−	0.315220i
$418$	−4.25052e6	+	3.80317e6i	−1.18987	+	1.06464i
$419$		−	4.82901e6i		−	1.34376i	−0.740658	−	0.671882i	$-0.765486\pi$
$419$		−	4.82901e6i		−	1.34376i	0.740658	−	0.671882i	$-0.234514\pi$
$420$		0			0
$421$		−	918869.i		−	0.252667i	−0.991988	−	0.126333i	$-0.959679\pi$
$421$		−	918869.i		−	0.252667i	0.991988	−	0.126333i	$-0.0403209\pi$
$422$	166853.	+	186479.i	0.0456093	+	0.0509741i
$423$		−	4.89498e6i		−	1.33015i
$424$	1.33471e6	+	1.87381e6i	0.360555	+	0.506186i
$425$		0			0
$426$	602033.	−	538671.i	0.160730	−	0.143814i
$427$	−4.73702e6			−1.25729
$428$	−480444.	+	4.31140e6i	−0.126775	+	1.13765i
$429$			220480.i			0.0578397i
$430$		0			0
$431$	−4.81272e6			−1.24795			−0.623975	−	0.781444i	$-0.714483\pi$
$431$	−4.81272e6			−1.24795			−0.623975	+	0.781444i	$0.714483\pi$
$432$	1.54549e6	+	348777.i	0.398435	+	0.0899162i
$433$			5.84598e6i			1.49843i	0.662324	+	0.749217i	$0.269570\pi$
$433$			5.84598e6i			1.49843i	−0.662324	+	0.749217i	$0.730430\pi$
$434$	−676600.	−	756186.i	−0.172428	−	0.192710i
$435$		0			0
$436$	−3.66173e6	−	408047.i	−0.922508	−	0.102800i
$437$	−4.13735e6			−1.03638
$438$	−384125.	−	429308.i	−0.0956726	−	0.106926i
$439$	2.28777e6			0.566568			0.283284	−	0.959036i	$-0.408576\pi$
$439$	2.28777e6			0.566568			0.283284	+	0.959036i	$0.408576\pi$
$440$		0			0
$441$	−953988.			−0.233586
$442$	99215.2	+	110885.i	0.0241559	+	0.0269972i
$443$	982970.			0.237975			0.118987	−	0.992896i	$-0.462035\pi$
$443$	982970.			0.237975			0.118987	+	0.992896i	$0.462035\pi$
$444$	−54630.2	+	490240.i	−0.0131515	+	0.118019i
$445$		0			0
$446$	−278689.	−	311470.i	−0.0663411	−	0.0741446i
$447$			606791.i			0.143638i
$448$	−3.49029e6	−	1.20696e6i	−0.821612	−	0.284118i
$449$	2.86769e6			0.671299			0.335650	−	0.941987i	$-0.391044\pi$
$449$	2.86769e6			0.671299			0.335650	+	0.941987i	$0.391044\pi$
$450$		0			0
$451$			4.69180e6i			1.08617i
$452$	−610367.	−	68016.6i	−0.140522	−	0.0156592i
$453$	−930040.			−0.212939
$454$	−822673.	+	736091.i	−0.187322	+	0.167607i
$455$		0			0
$456$	840814.	−	598910.i	0.189360	−	0.134881i
$457$			451218.i			0.101064i	0.998722	+	0.0505319i	$0.0160917\pi$
$457$			451218.i			0.101064i	−0.998722	+	0.0505319i	$0.983908\pi$
$458$	5.86360e6	+	6.55331e6i	1.30617	+	1.45981i
$459$		−	345662.i		−	0.0765809i
$460$		0			0
$461$		−	242143.i		−	0.0530665i	−0.999648	−	0.0265332i	$-0.991553\pi$
$461$		−	242143.i		−	0.0530665i	0.999648	−	0.0265332i	$-0.00844678\pi$
$462$	−889753.	+	796111.i	−0.193939	+	0.173528i
$463$			4.80106e6i			1.04084i	0.853910	+	0.520421i	$0.174225\pi$
$463$			4.80106e6i			1.04084i	−0.853910	+	0.520421i	$0.825775\pi$
$464$	−871368.	+	3.86119e6i	−0.187891	+	0.832580i
$465$		0			0
$466$	−212957.	−	238007.i	−0.0454285	−	0.0507720i
$467$	−306183.			−0.0649664			−0.0324832	−	0.999472i	$-0.510342\pi$
$467$	−306183.			−0.0649664			−0.0324832	+	0.999472i	$0.510342\pi$
$468$	−96973.4	+	870219.i	−0.0204662	+	0.183660i
$469$		−	6.10331e6i		−	1.28125i
$470$		0			0
$471$	−1.56430e6			−0.324913
$472$	−2.08054e6	+	1.48196e6i	−0.429854	+	0.306183i
$473$			2.83114e6i			0.581846i
$474$	688902.	−	616398.i	0.140835	−	0.126013i
$475$		0			0
$476$	−89234.5	+	800771.i	−0.0180516	+	0.161991i
$477$	2.95366e6			0.594381
$478$	2.32296e6	−	2.07847e6i	0.465019	−	0.416078i
$479$	−3.99196e6			−0.794964			−0.397482	−	0.917610i	$-0.630116\pi$
$479$	−3.99196e6			−0.794964			−0.397482	+	0.917610i	$0.630116\pi$
$480$		0			0
$481$	−557647.			−0.109900
$482$	5.54726e6	−	4.96343e6i	1.08758	−	0.973116i
$483$	−866064.			−0.168920
$484$	−602632.	+	5.40789e6i	−0.116933	+	1.04934i
$485$		0			0
$486$	2.29075e6	−	2.04966e6i	0.439933	−	0.393632i
$487$			6.45190e6i			1.23272i	0.787464	+	0.616361i	$0.211394\pi$
$487$			6.45190e6i			1.23272i	−0.787464	+	0.616361i	$0.788606\pi$
$488$	6.19700e6	−	4.41410e6i	1.17796	−	0.839060i
$489$	574790.			0.108702
$490$		0			0
$491$		−	4.37221e6i		−	0.818459i	−0.912432	−	0.409229i	$-0.865798\pi$
$491$		−	4.37221e6i		−	0.818459i	0.912432	−	0.409229i	$-0.134202\pi$
$492$	94047.0	−	843958.i	0.0175159	−	0.157184i
$493$	863588.			0.160025
$494$	778175.	+	869708.i	0.143470	+	0.160345i
$495$		0			0
$496$	1.58977e6	+	358769.i	0.290155	+	0.0654803i
$497$			4.94544e6i			0.898078i
$498$	−599661.	+	536549.i	−0.108351	+	0.0969473i
$499$			5.17114e6i			0.929683i	0.885394	+	0.464842i	$0.153889\pi$
$499$			5.17114e6i			0.929683i	−0.885394	+	0.464842i	$0.846111\pi$
$500$		0			0
$501$			712260.i			0.126778i
$502$	359125.	+	401367.i	0.0636043	+	0.0710857i
$503$		−	4.16421e6i		−	0.733859i	−0.930249	−	0.366929i	$-0.880409\pi$
$503$		−	4.16421e6i		−	0.733859i	0.930249	−	0.366929i	$-0.119591\pi$
$504$	−3.86195e6	+	2.75085e6i	−0.677220	+	0.482382i
$505$		0			0
$506$	−5.72753e6	+	5.12474e6i	−0.994469	+	0.889806i
$507$	−1.16327e6			−0.200983
$508$	−3.24391e6	−	361487.i	−0.557711	−	0.0621489i
$509$		−	4.71340e6i		−	0.806381i	−0.915116	−	0.403190i	$-0.867901\pi$
$509$		−	4.71340e6i		−	0.806381i	0.915116	−	0.403190i	$-0.132099\pi$
$510$		0			0
$511$	3.52658e6			0.597450
$512$	5.69070e6	−	1.67341e6i	0.959381	−	0.282115i
$513$		−	2.71114e6i		−	0.454839i
$514$	6.53182e6	+	7.30013e6i	1.09050	+	1.21877i
$515$		0			0
$516$	56750.0	−	509263.i	0.00938301	−	0.0842011i
$517$	−1.21192e7			−1.99411
$518$	−2.01356e6	−	2.25040e6i	−0.329715	−	0.368498i
$519$	−1.70128e6			−0.277242
$520$		0			0
$521$	2.34479e6			0.378451			0.189225	−	0.981934i	$-0.439402\pi$
$521$	2.34479e6			0.378451			0.189225	+	0.981934i	$0.439402\pi$
$522$	3.38868e6	+	3.78728e6i	0.544320	+	0.608346i
$523$	−8.17020e6			−1.30611			−0.653053	−	0.757312i	$-0.726512\pi$
$523$	−8.17020e6			−1.30611			−0.653053	+	0.757312i	$0.726512\pi$
$524$	−359253.	−	40033.6i	−0.0571573	−	0.00636936i
$525$		0			0
$526$	5.72182e6	+	6.39485e6i	0.901716	+	1.00778i
$527$		−	355565.i		−	0.0557690i
$528$	422140.	−	1.87058e6i	0.0658979	−	0.292005i
$529$	861301.			0.133818
$530$		0			0
$531$			3.27953e6i			0.504749i
$532$	−699893.	+	6.28070e6i	−0.107214	+	0.962119i
$533$	960000.			0.146370
$534$	−883826.	+	790807.i	−0.134126	+	0.120010i
$535$		0			0
$536$	5.68725e6	+	7.98438e6i	0.855048	+	1.20041i
$537$		−	1.33780e6i		−	0.200196i
$538$	7.15210e6	+	7.99337e6i	1.06531	+	1.19062i
$539$			2.36193e6i			0.350183i
$540$		0			0
$541$			3.53355e6i			0.519060i	0.965735	+	0.259530i	$0.0835677\pi$
$541$			3.53355e6i			0.519060i	−0.965735	+	0.259530i	$0.916432\pi$
$542$	2.00804e6	−	1.79670e6i	0.293612	−	0.262711i
$543$			433158.i			0.0630445i
$544$	−629447.	−	1.13072e6i	−0.0911930	−	0.163817i
$545$		0			0
$546$	162894.	+	182055.i	0.0233843	+	0.0261348i
$547$	−657235.			−0.0939187			−0.0469594	−	0.998897i	$-0.514953\pi$
$547$	−657235.			−0.0939187			−0.0469594	+	0.998897i	$0.514953\pi$
$548$	−3.26786e6	−	364156.i	−0.464850	−	0.0518008i
$549$		−	9.76826e6i		−	1.38320i
$550$		0			0
$551$	6.77338e6			0.950444
$552$	1.13299e6	−	807026.i	0.158263	−	0.112730i
$553$			5.65903e6i			0.786918i
$554$	3.55281e6	−	3.17889e6i	0.491810	−	0.440049i
$555$		0			0
$556$	−1.09380e7	−	1.21888e6i	−1.50055	−	0.167215i
$557$	−1.35929e7			−1.85641			−0.928207	−	0.372065i	$-0.878650\pi$
$557$	−1.35929e7			−1.85641			−0.928207	+	0.372065i	$0.878650\pi$
$558$	1.55934e6	−	1.39522e6i	0.212009	−	0.189696i
$559$	579286.			0.0784085
$560$		0			0
$561$	−418370.			−0.0561247
$562$	−6.93335e6	+	6.20364e6i	−0.925981	+	0.828525i
$563$	−1.18702e7			−1.57829			−0.789146	−	0.614206i	$-0.789477\pi$
$563$	−1.18702e7			−1.57829			−0.789146	+	0.614206i	$0.789477\pi$
$564$	2.18000e6	+	242930.i	0.288575	+	0.0321575i
$565$		0			0
$566$	9.39526e6	−	8.40645e6i	1.23273	−	1.10299i
$567$			5.79746e6i			0.757322i
$568$	−4.60831e6	−	6.46965e6i	−0.599337	−	0.841414i
$569$	1.16590e7			1.50966			0.754831	−	0.655920i	$-0.227719\pi$
$569$	1.16590e7			1.50966			0.754831	+	0.655920i	$0.227719\pi$
$570$		0			0
$571$			1.14849e7i			1.47414i	0.675819	+	0.737068i	$0.263790\pi$
$571$			1.14849e7i			1.47414i	−0.675819	+	0.737068i	$0.736210\pi$
$572$	2.15453e6	+	240092.i	0.275336	+	0.0306822i
$573$	2.71247e6			0.345126
$574$	3.46638e6	+	3.87411e6i	0.439133	+	0.490786i
$575$		0			0
$576$	2.48889e6	−	7.19736e6i	0.312571	−	0.903893i
$577$		−	7.93609e6i		−	0.992355i	−0.868221	−	0.496178i	$-0.834736\pi$
$577$		−	7.93609e6i		−	0.992355i	0.868221	−	0.496178i	$-0.165264\pi$
$578$	5.77526e6	−	5.16744e6i	0.719038	−	0.643362i
$579$		−	1.94474e6i		−	0.241082i
$580$		0			0
$581$		−	4.92595e6i		−	0.605411i
$582$	765423.	+	855456.i	0.0936685	+	0.104686i
$583$		−	7.31282e6i		−	0.891074i
$584$	−4.61349e6	+	3.28618e6i	−0.559754	+	0.398712i
$585$		0			0
$586$	2.91759e6	−	2.61053e6i	0.350978	−	0.314039i
$587$	−7.16597e6			−0.858381			−0.429190	−	0.903214i	$-0.641201\pi$
$587$	−7.16597e6			−0.858381			−0.429190	+	0.903214i	$0.641201\pi$
$588$	47344.8	−	424862.i	0.00564714	−	0.0506763i
$589$		−	2.78881e6i		−	0.331231i
$590$		0			0
$591$	2.23969e6			0.263766
$592$	4.73114e6	+	1.06769e6i	0.554832	+	0.125211i
$593$		−	1.99624e6i		−	0.233118i	−0.993184	−	0.116559i	$-0.962814\pi$
$593$		−	1.99624e6i		−	0.233118i	0.993184	−	0.116559i	$-0.0371865\pi$
$594$	−3.35815e6	−	3.75316e6i	−0.390512	−	0.436446i
$595$		0			0
$596$	5.92957e6	+	660765.i	0.683766	+	0.0761958i
$597$	3.18134e6			0.365320
$598$	1.04858e6	+	1.17192e6i	0.119909	+	0.134013i
$599$	−1.20579e7			−1.37311			−0.686555	−	0.727078i	$-0.740878\pi$
$599$	−1.20579e7			−1.37311			−0.686555	+	0.727078i	$0.740878\pi$
$600$		0			0
$601$	1.50698e7			1.70185			0.850924	−	0.525289i	$-0.176043\pi$
$601$	1.50698e7			1.70185			0.850924	+	0.525289i	$0.176043\pi$
$602$	2.09169e6	+	2.33772e6i	0.235237	+	0.262907i
$603$	1.25857e7			1.40956
$604$	−1.01277e6	+	9.08835e6i	−0.112958	+	1.01366i
$605$		0			0
$606$	−613317.	−	685458.i	−0.0678427	−	0.0758227i
$607$		−	4.03809e6i		−	0.444841i	−0.974951	−	0.222420i	$-0.928604\pi$
$607$		−	4.03809e6i		−	0.444841i	0.974951	−	0.222420i	$-0.0713958\pi$
$608$	−4.93694e6	−	8.86862e6i	−0.541625	−	0.972965i
$609$	1.41786e6			0.154914
$610$		0			0
$611$			2.47975e6i			0.268723i
$612$	−1.65128e6	−	184011.i	−0.178214	−	0.0198594i
$613$	1.07407e7			1.15447			0.577236	−	0.816578i	$-0.304131\pi$
$613$	1.07407e7			1.15447			0.577236	+	0.816578i	$0.304131\pi$
$614$	1.22974e7	−	1.10032e7i	1.31642	−	1.17787i
$615$		0			0
$616$	6.81070e6	+	9.56160e6i	0.723169	+	1.01526i
$617$			9.37637e6i			0.991567i	0.868446	+	0.495783i	$0.165119\pi$
$617$			9.37637e6i			0.991567i	−0.868446	+	0.495783i	$0.834881\pi$
$618$	1.95508e6	+	2.18505e6i	0.205918	+	0.230139i
$619$			4.03378e6i			0.423141i	0.977363	+	0.211571i	$0.0678579\pi$
$619$			4.03378e6i			0.423141i	−0.977363	+	0.211571i	$0.932142\pi$
$620$		0			0
$621$		−	3.65323e6i		−	0.380144i
$622$	4.66783e6	−	4.17656e6i	0.483770	−	0.432855i
$623$		−	7.26025e6i		−	0.749431i
$624$	−382743.	−	86375.0i	−0.0393501	−	0.00888028i
$625$		0			0
$626$	−6.23847e6	−	6.97227e6i	−0.636271	−	0.711113i
$627$	−3.28141e6			−0.333343
$628$	−1.70344e6	+	1.52863e7i	−0.172356	+	1.54669i
$629$		−	1.05816e6i		−	0.106641i
$630$		0			0
$631$	3.01348e6			0.301297			0.150648	−	0.988587i	$-0.451864\pi$
$631$	3.01348e6			0.301297			0.150648	+	0.988587i	$0.451864\pi$
$632$	−5.27326e6	−	7.40318e6i	−0.525154	−	0.737268i
$633$			143962.i			0.0142804i
$634$	1.93609e6	−	1.73233e6i	0.191295	−	0.171162i
$635$		0			0
$636$	−146585.	+	1.31543e6i	−0.0143697	+	0.128951i
$637$	483280.			0.0471900
$638$	9.37672e6	−	8.38986e6i	0.912010	−	0.816024i
$639$	−1.01980e7			−0.988017
$640$		0			0
$641$	−2.09755e6			−0.201636			−0.100818	−	0.994905i	$-0.532146\pi$
$641$	−2.09755e6			−0.201636			−0.100818	+	0.994905i	$0.532146\pi$
$642$	−1.85996e6	+	1.66421e6i	−0.178101	+	0.159356i
$643$	−3.48456e6			−0.332369			−0.166185	−	0.986095i	$-0.553145\pi$
$643$	−3.48456e6			−0.332369			−0.166185	+	0.986095i	$0.553145\pi$
$644$	−943100.	+	8.46318e6i	−0.0896073	+	0.804117i
$645$		0			0
$646$	−1.65031e6	+	1.47662e6i	−0.155591	+	0.139216i
$647$		−	9.25999e6i		−	0.869660i	−0.900513	−	0.434830i	$-0.856808\pi$
$647$		−	9.25999e6i		−	0.869660i	0.900513	−	0.434830i	$-0.143192\pi$
$648$	−5.40226e6	−	7.58427e6i	−0.505403	−	0.709539i
$649$	8.11962e6			0.756700
$650$		0			0
$651$		−	583777.i		−	0.0539876i
$652$	625917.	−	5.61684e6i	0.0576630	−	0.517456i
$653$	−1.12475e7			−1.03222			−0.516109	−	0.856523i	$-0.672620\pi$
$653$	−1.12475e7			−1.03222			−0.516109	+	0.856523i	$0.672620\pi$
$654$	−1.41343e6	−	1.57969e6i	−0.129220	−	0.144420i
$655$		0			0
$656$	−8.14474e6	−	1.83805e6i	−0.738955	−	0.166763i
$657$			7.27220e6i			0.657283i
$658$	−1.00071e7	+	8.95388e6i	−0.901038	+	0.806207i
$659$			6.37278e6i			0.571630i	0.958285	+	0.285815i	$0.0922643\pi$
$659$			6.37278e6i			0.571630i	−0.958285	+	0.285815i	$0.907736\pi$
$660$		0			0
$661$			4.13736e6i			0.368315i	0.982897	+	0.184158i	$0.0589556\pi$
$661$			4.13736e6i			0.368315i	−0.982897	+	0.184158i	$0.941044\pi$
$662$	−5.86992e6	−	6.56037e6i	−0.520580	−	0.581813i
$663$			85603.7i			0.00756326i
$664$	4.59016e6	+	6.44416e6i	0.404024	+	0.567213i
$665$		0			0
$666$	4.64057e6	−	4.15217e6i	0.405402	−	0.362735i
$667$	9.12707e6			0.794359
$668$	6.96020e6	+	775615.i	0.603505	+	0.0672519i
$669$		−	240456.i		−	0.0207716i
$670$		0			0
$671$	−2.41847e7			−2.07365
$672$	−1.03344e6	−	1.85645e6i	−0.0882801	−	0.158585i
$673$			1.50812e7i			1.28350i	0.766913	+	0.641752i	$0.221792\pi$
$673$			1.50812e7i			1.28350i	−0.766913	+	0.641752i	$0.778208\pi$
$674$	−3.46714e6	−	3.87497e6i	−0.293983	−	0.328563i
$675$		0			0
$676$	−1.26674e6	+	1.13674e7i	−0.106615	+	0.956745i
$677$	1.85553e7			1.55595			0.777975	−	0.628295i	$-0.216247\pi$
$677$	1.85553e7			1.55595			0.777975	+	0.628295i	$0.216247\pi$
$678$	−235602.	−	263315.i	−0.0196836	−	0.0219989i
$679$	−7.02720e6			−0.584935
$680$		0			0
$681$	−635105.			−0.0524781
$682$	−3.45436e6	−	3.86068e6i	−0.284385	−	0.317836i
$683$	−2.31850e7			−1.90176			−0.950881	−	0.309558i	$-0.899819\pi$
$683$	−2.31850e7			−1.90176			−0.950881	+	0.309558i	$0.899819\pi$
$684$	−1.29515e7	−	1.44326e6i	−1.05847	−	0.117951i
$685$		0			0
$686$	8.89002e6	+	9.93571e6i	0.721261	+	0.806100i
$687$			5.05917e6i			0.408966i
$688$	−4.91472e6	−	1.10912e6i	−0.395847	−	0.0893323i
$689$	−1.49629e6			−0.120080
$690$		0			0
$691$		−	1.04315e7i		−	0.831099i	−0.909571	−	0.415549i	$-0.863589\pi$
$691$		−	1.04315e7i		−	0.831099i	0.909571	−	0.415549i	$-0.136411\pi$
$692$	−1.85261e6	+	1.66250e7i	−0.147068	+	1.31976i
$693$	1.50718e7			1.19216
$694$	7.89551e6	−	7.06454e6i	0.622273	−	0.556782i
$695$		0			0
$696$	−1.85485e6	+	1.32121e6i	−0.145140	+	0.103383i
$697$			1.82164e6i			0.142030i
$698$	9.10748e6	+	1.01788e7i	0.707554	+	0.790781i
$699$		−	183742.i		−	0.0142238i
$700$		0			0
$701$		−	1.93026e7i		−	1.48362i	−0.670613	−	0.741808i	$-0.733969\pi$
$701$		−	1.93026e7i		−	1.48362i	0.670613	−	0.741808i	$-0.266031\pi$
$702$	−767942.	+	687120.i	−0.0588147	+	0.0526247i
$703$		−	8.29947e6i		−	0.633377i
$704$	−1.78196e7	−	6.16211e6i	−1.35508	−	0.468595i
$705$		0			0
$706$	−9.17607e6	−	1.02554e7i	−0.692859	−	0.774357i
$707$	5.63075e6			0.423660
$708$	−1.46055e6	−	162757.i	−0.109505	−	0.0122027i
$709$			5.90966e6i			0.441517i	0.975329	+	0.220758i	$0.0708532\pi$
$709$			5.90966e6i			0.441517i	−0.975329	+	0.220758i	$0.929147\pi$
$710$		0			0
$711$	−1.16695e7			−0.865725
$712$	6.76533e6	+	9.49790e6i	0.500137	+	0.702146i
$713$		−	3.75790e6i		−	0.276835i
$714$	−345456.	+	309099.i	−0.0253599	+	0.0226909i
$715$		0			0
$716$	−1.30730e7	−	1.45680e6i	−0.952998	−	0.106198i
$717$	1.79333e6			0.130275
$718$	−9.02782e6	+	8.07768e6i	−0.653540	+	0.584757i
$719$	2.58536e7			1.86509			0.932543	−	0.361058i	$-0.117584\pi$
$719$	2.58536e7			1.86509			0.932543	+	0.361058i	$0.117584\pi$
$720$		0			0
$721$	−1.79492e7			−1.28590
$722$	−2.50542e6	+	2.24174e6i	−0.178870	+	0.160045i
$723$	4.28250e6			0.304685
$724$	4.23282e6	+	471687.i	0.300112	+	0.0334432i
$725$		0			0
$726$	−2.33299e6	+	2.08745e6i	−0.164275	+	0.146986i
$727$			497513.i			0.0349115i	0.999848	+	0.0174558i	$0.00555662\pi$
$727$			497513.i			0.0349115i	−0.999848	+	0.0174558i	$0.994443\pi$
$728$	1.95642e6	−	1.39355e6i	0.136815	−	0.0974530i
$729$	−1.07314e7			−0.747889
$730$		0			0
$731$			1.09922e6i			0.0760836i
$732$	4.35033e6	+	484782.i	0.300085	+	0.0334402i
$733$	9.66956e6			0.664732			0.332366	−	0.943150i	$-0.392153\pi$
$733$	9.66956e6			0.664732			0.332366	+	0.943150i	$0.392153\pi$
$734$	−5.40424e6	−	6.03992e6i	−0.370250	−	0.413800i
$735$		0			0
$736$	−6.65249e6	−	1.19504e7i	−0.452678	−	0.813182i
$737$		−	3.11603e7i		−	2.11316i
$738$	−7.98884e6	+	7.14805e6i	−0.539936	+	0.483110i
$739$			1.83759e7i			1.23776i	0.785485	+	0.618881i	$0.212414\pi$
$739$			1.83759e7i			1.23776i	−0.785485	+	0.618881i	$0.787586\pi$
$740$		0			0
$741$			671416.i			0.0449207i
$742$	−5.40283e6	−	6.03834e6i	−0.360256	−	0.402631i
$743$			1.51555e7i			1.00716i	0.863950	+	0.503578i	$0.167983\pi$
$743$			1.51555e7i			1.00716i	−0.863950	+	0.503578i	$0.832017\pi$
$744$	543981.	+	763700.i	0.0360289	+	0.0505813i
$745$		0			0
$746$	−1.08600e7	+	9.71699e6i	−0.714465	+	0.639271i
$747$	1.01579e7			0.666040
$748$	−455584.	+	4.08832e6i	−0.0297724	+	0.267172i
$749$		−	1.52788e7i		−	0.995138i
$750$		0			0
$751$	7.70448e6			0.498475			0.249238	−	0.968442i	$-0.419820\pi$
$751$	7.70448e6			0.498475			0.249238	+	0.968442i	$0.419820\pi$
$752$	4.74782e6	−	2.10384e7i	0.306161	−	1.35665i
$753$			309856.i			0.0199147i
$754$	−1.71667e6	−	1.91859e6i	−0.109966	−	0.122901i
$755$		0			0
$756$	−5.54578e6	−	617998.i	−0.352905	−	0.0393262i
$757$	1.96934e7			1.24905			0.624525	−	0.781005i	$-0.285293\pi$
$757$	1.96934e7			1.24905			0.624525	+	0.781005i	$0.285293\pi$
$758$	7.10154e6	+	7.93686e6i	0.448931	+	0.501737i
$759$	−4.42167e6			−0.278600
$760$		0			0
$761$	−6.73562e6			−0.421615			−0.210807	−	0.977528i	$-0.567609\pi$
$761$	−6.73562e6			−0.421615			−0.210807	+	0.977528i	$0.567609\pi$
$762$	−1.25215e6	−	1.39944e6i	−0.0781213	−	0.0873104i
$763$	1.29765e7			0.806946
$764$	2.95374e6	−	2.65062e7i	0.183079	−	1.64291i
$765$		0			0
$766$	−3.50512e6	−	3.91741e6i	−0.215839	−	0.241227i
$767$		−	1.66137e6i		−	0.101972i
$768$	3.08185e6	+	1.46563e6i	0.188542	+	0.0896646i
$769$	6.67796e6			0.407219			0.203609	−	0.979052i	$-0.434733\pi$
$769$	6.67796e6			0.407219			0.203609	+	0.979052i	$0.434733\pi$
$770$		0			0
$771$			5.63571e6i			0.341439i
$772$	−1.90040e7	−	2.11772e6i	−1.14763	−	0.127887i
$773$	2.85469e6			0.171835			0.0859173	−	0.996302i	$-0.472618\pi$
$773$	2.85469e6			0.171835			0.0859173	+	0.996302i	$0.472618\pi$
$774$	−4.82064e6	+	4.31329e6i	−0.289236	+	0.258795i
$775$		0			0
$776$	9.19302e6	−	6.54816e6i	0.548030	−	0.390360i
$777$		−	1.73731e6i		−	0.103235i
$778$	−7.09957e6	−	7.93466e6i	−0.420517	−	0.469980i
$779$			1.42877e7i			0.843565i
$780$		0			0
$781$			2.52488e7i			1.48120i
$782$	−2.22378e6	+	1.98973e6i	−0.130039	+	0.116353i
$783$			5.98082e6i			0.348623i
$784$	−4.10020e6	−	925307.i	−0.238240	−	0.0537645i
$785$		0			0
$786$	−138672.	−	154983.i	−0.00800630	−	0.00894805i
$787$	1.38785e7			0.798738			0.399369	−	0.916790i	$-0.369229\pi$
$787$	1.38785e7			0.798738			0.399369	+	0.916790i	$0.369229\pi$
$788$	2.43891e6	−	2.18863e7i	0.139920	−	1.25561i
$789$			4.93684e6i			0.282330i
$790$		0			0
$791$	2.16302e6			0.122919
$792$	−1.97171e7	+	1.40444e7i	−1.11694	+	0.795592i
$793$			4.94849e6i			0.279441i
$794$	1.84725e7	−	1.65284e7i	1.03986	−	0.930419i
$795$		0			0
$796$	3.46431e6	−	3.10880e7i	0.193791	−	1.73904i
$797$	−8.67764e6			−0.483900			−0.241950	−	0.970289i	$-0.577787\pi$
$797$	−8.67764e6			−0.483900			−0.241950	+	0.970289i	$0.577787\pi$
$798$	−2.70952e6	+	2.42435e6i	−0.150621	+	0.134769i
$799$	−4.70543e6			−0.260755
$800$		0			0
$801$	1.49714e7			0.824484
$802$	6.05136e6	−	5.41448e6i	0.332214	−	0.297249i
$803$	1.80049e7			0.985373
$804$	−624607.	+	5.60509e6i	−0.0340774	+	0.305803i
$805$		0			0
$806$	−789944.	+	706805.i	−0.0428310	+	0.0383232i
$807$			6.17089e6i			0.333553i
$808$	−7.36617e6	+	5.24690e6i	−0.396930	+	0.282732i
$809$	−7.54612e6			−0.405371			−0.202685	−	0.979244i	$-0.564967\pi$
$809$	−7.54612e6			−0.405371			−0.202685	+	0.979244i	$0.564967\pi$
$810$		0			0
$811$		−	2.53731e7i		−	1.35463i	−0.735692	−	0.677316i	$-0.763143\pi$
$811$		−	2.53731e7i		−	1.35463i	0.735692	−	0.677316i	$-0.236857\pi$
$812$	1.54398e6	−	1.38553e7i	0.0821772	−	0.737441i
$813$	1.55021e6			0.0822554
$814$	−1.02802e7	−	1.14894e7i	−0.543799	−	0.607764i
$815$		0			0
$816$	163900.	−	726271.i	0.00861696	−	0.0381833i
$817$			8.62152e6i			0.451886i
$818$	2.02093e6	−	1.80824e6i	0.105601	−	0.0944871i
$819$		−	3.08388e6i		−	0.160653i
$820$		0			0
$821$		−	1.52925e7i		−	0.791812i	−0.918291	−	0.395906i	$-0.870431\pi$
$821$		−	1.52925e7i		−	0.791812i	0.918291	−	0.395906i	$-0.129569\pi$
$822$	−1.26140e6	−	1.40977e6i	−0.0651137	−	0.0727728i
$823$			4.47750e6i			0.230428i	0.993341	+	0.115214i	$0.0367554\pi$
$823$			4.47750e6i			0.230428i	−0.993341	+	0.115214i	$0.963245\pi$
$824$	2.34813e7	−	1.67257e7i	1.20477	−	0.858154i
$825$		0			0
$826$	6.70452e6	−	5.99890e6i	0.341915	−	0.305930i
$827$	8.21663e6			0.417763			0.208882	−	0.977941i	$-0.433018\pi$
$827$	8.21663e6			0.417763			0.208882	+	0.977941i	$0.433018\pi$
$828$	−1.74520e7	−	1.94478e6i	−0.884646	−	0.0985811i
$829$			1.58318e7i			0.800098i	0.916494	+	0.400049i	$0.131007\pi$
$829$			1.58318e7i			0.800098i	−0.916494	+	0.400049i	$0.868993\pi$
$830$		0			0
$831$	2.74278e6			0.137781
$832$	−1.26084e6	+	3.64611e6i	−0.0631471	+	0.182609i
$833$			917045.i			0.0457908i
$834$	−4.22207e6	−	4.71870e6i	−0.210189	−	0.234913i
$835$		0			0
$836$	−3.57329e6	+	3.20659e7i	−0.176828	+	1.58682i
$837$	2.46249e6			0.121495
$838$	−1.82150e7	−	2.03576e7i	−0.896024	−	1.00142i
$839$	−1.29263e7			−0.633970			−0.316985	−	0.948430i	$-0.602671\pi$
$839$	−1.29263e7			−0.633970			−0.316985	+	0.948430i	$0.602671\pi$
$840$		0			0
$841$	5.56893e6			0.271508
$842$	−3.46598e6	−	3.87366e6i	−0.168479	−	0.188296i
$843$	−5.35256e6			−0.259413
$844$	1.40680e6	+	156768.i	0.0679793	+	0.00757532i
$845$		0			0
$846$	−1.84639e7	−	2.06357e7i	−0.886946	−	0.991274i
$847$		−	1.91645e7i		−	0.917886i
$848$	1.26947e7	+	2.86486e6i	0.606224	+	0.136809i
$849$	7.25316e6			0.345349
$850$		0			0
$851$		−	1.11835e7i		−	0.529362i
$852$	506111.	−	4.54174e6i	0.0238862	−	0.214350i
$853$	−8.07995e6			−0.380221			−0.190110	−	0.981763i	$-0.560885\pi$
$853$	−8.07995e6			−0.380221			−0.190110	+	0.981763i	$0.560885\pi$
$854$	−1.99698e7	+	1.78681e7i	−0.936977	+	0.838364i
$855$		0			0
$856$	1.42372e7	+	1.99877e7i	0.664111	+	0.932351i
$857$		−	1.51474e7i		−	0.704510i	−0.935904	−	0.352255i	$-0.885415\pi$
$857$		−	1.51474e7i		−	0.704510i	0.935904	−	0.352255i	$-0.114585\pi$
$858$	831651.	+	929474.i	0.0385676	+	0.0431042i
$859$		−	1.27089e7i		−	0.587658i	−0.955858	−	0.293829i	$-0.905070\pi$
$859$		−	1.27089e7i		−	0.587658i	0.955858	−	0.293829i	$-0.0949297\pi$
$860$		0			0
$861$			2.99082e6i			0.137494i
$862$	−2.02889e7	+	1.81536e7i	−0.930016	+	0.832136i
$863$		−	3.10500e7i		−	1.41917i	−0.704620	−	0.709585i	$-0.748882\pi$
$863$		−	3.10500e7i		−	1.41917i	0.704620	−	0.709585i	$-0.251118\pi$
$864$	7.83089e6	−	4.35926e6i	0.356884	−	0.198668i
$865$		0			0
$866$	2.20511e7	+	2.46448e7i	0.999159	+	1.11669i
$867$	4.45851e6			0.201438
$868$	−5.70467e6	−	635703.i	−0.256999	−	0.0286388i
$869$			2.88920e7i			1.29786i
$870$		0			0
$871$	−6.37578e6			−0.284766
$872$	−1.69759e7	+	1.20919e7i	−0.756033	+	0.538520i
$873$		−	1.44909e7i		−	0.643515i
$874$	−1.74418e7	+	1.56061e7i	−0.772346	+	0.691060i
$875$		0			0
$876$	−3.23870e6	−	360907.i	−0.142597	−	0.0158904i
$877$	1.45850e7			0.640336			0.320168	−	0.947361i	$-0.396261\pi$
$877$	1.45850e7			0.640336			0.320168	+	0.947361i	$0.396261\pi$
$878$	9.64454e6	−	8.62949e6i	0.422226	−	0.377789i
$879$	2.25239e6			0.0983265
$880$		0			0
$881$	5.73224e6			0.248820			0.124410	−	0.992231i	$-0.460296\pi$
$881$	5.73224e6			0.248820			0.124410	+	0.992231i	$0.460296\pi$
$882$	−4.02171e6	+	3.59844e6i	−0.174076	+	0.155755i
$883$	−522077.			−0.0225337			−0.0112669	−	0.999937i	$-0.503586\pi$
$883$	−522077.			−0.0225337			−0.0112669	+	0.999937i	$0.503586\pi$
$884$	836520.	+	93218.1i	0.0360036	+	0.00401208i
$885$		0			0
$886$	4.14389e6	−	3.70776e6i	0.177347	−	0.158682i
$887$			2.52815e7i			1.07893i	0.842007	+	0.539466i	$0.181374\pi$
$887$			2.52815e7i			1.07893i	−0.842007	+	0.539466i	$0.818626\pi$
$888$	1.61888e6	+	2.27276e6i	0.0688943	+	0.0967212i
$889$	1.14958e7			0.487847
$890$		0			0
$891$			2.95988e7i			1.24905i
$892$	−2.34973e6	−	261844.i	−0.0988795	−	0.0110187i
$893$	−3.69061e7			−1.54871
$894$	2.28882e6	+	2.55804e6i	0.0957784	+	0.107044i
$895$		0			0
$896$	−1.92666e7	+	8.07721e6i	−0.801744	+	0.336118i
$897$			904728.i			0.0375437i
$898$	1.20893e7	−	1.08169e7i	0.500276	−	0.447624i
$899$			6.15217e6i			0.253880i
$900$		0			0
$901$		−	2.83928e6i		−	0.116519i
$902$	1.76975e7	+	1.97792e7i	0.724261	+	0.809453i
$903$			1.80473e6i			0.0736533i
$904$	−2.82967e6	+	2.01557e6i	−0.115164	+	0.0820307i
$905$		0			0
$906$	−3.92076e6	+	3.50811e6i	−0.158690	+	0.141988i
$907$	1.27692e7			0.515402			0.257701	−	0.966225i	$-0.417035\pi$
$907$	1.27692e7			0.515402			0.257701	+	0.966225i	$0.417035\pi$
$908$	−691598.	+	6.20625e6i	−0.0278381	+	0.249813i
$909$			1.16112e7i			0.466088i
$910$		0			0
$911$	3.33197e7			1.33017			0.665083	−	0.746770i	$-0.268396\pi$
$911$	3.33197e7			1.33017			0.665083	+	0.746770i	$0.268396\pi$
$912$	1.28552e6	−	5.69637e6i	0.0511790	−	0.226783i
$913$		−	2.51493e7i		−	0.998503i
$914$	1.70200e6	+	1.90219e6i	0.0673896	+	0.0753163i
$915$		0			0
$916$	4.94382e7	+	5.50918e6i	1.94681	+	0.216944i
$917$	1.27312e6			0.0499973
$918$	−1.30384e6	−	1.45720e6i	−0.0510643	−	0.0570707i
$919$	2.91253e7			1.13758			0.568789	−	0.822484i	$-0.307412\pi$
$919$	2.91253e7			1.13758			0.568789	+	0.822484i	$0.307412\pi$
$920$		0			0
$921$	9.49365e6			0.368794
$922$	−913365.	−	1.02080e6i	−0.0353848	−	0.0395470i
$923$	5.16622e6			0.199604
$924$	−747990.	+	6.71230e6i	−0.0288214	+	0.258638i
$925$		0			0
$926$	1.81096e7	+	2.02398e7i	0.694036	+	0.775672i
$927$		−	3.70133e7i		−	1.41468i
$928$	1.08910e7	+	1.95644e7i	0.415143	+	0.745754i
$929$	−1.84988e7			−0.703242			−0.351621	−	0.936143i	$-0.614369\pi$
$929$	−1.84988e7			−0.703242			−0.351621	+	0.936143i	$0.614369\pi$
$930$		0			0
$931$			7.19266e6i			0.271966i
$932$	−1.79552e6	−	200085.i	−0.0677098	−	0.00754528i
$933$	3.60357e6			0.135528
$934$	−1.29077e6	+	1.15492e6i	−0.0484152	+	0.0433197i
$935$		0			0
$936$	2.87366e6	+	4.03435e6i	0.107213	+	0.150517i
$937$			3.42891e7i			1.27587i	0.770089	+	0.637936i	$0.220212\pi$
$937$			3.42891e7i			1.27587i	−0.770089	+	0.637936i	$0.779788\pi$
$938$	−2.30217e7	−	2.57296e7i	−0.854339	−	0.954831i
$939$		−	5.38261e6i		−	0.199218i
$940$		0			0
$941$		−	1.23906e7i		−	0.456161i	−0.973642	−	0.228080i	$-0.926755\pi$
$941$		−	1.23906e7i		−	0.456161i	0.973642	−	0.228080i	$-0.0732449\pi$
$942$	−6.59458e6	+	5.90053e6i	−0.242136	+	0.216652i
$943$			1.92525e7i			0.705032i
$944$	−3.18093e6	+	1.40953e7i	−0.116178	+	0.514806i
$945$		0			0
$946$	1.06791e7	+	1.19352e7i	0.387976	+	0.433612i
$947$	−5.12809e7			−1.85815			−0.929074	−	0.369893i	$-0.879394\pi$
$947$	−5.12809e7			−1.85815			−0.929074	+	0.369893i	$0.879394\pi$
$948$	579140.	−	5.19708e6i	0.0209297	−	0.187819i
$949$		−	3.68402e6i		−	0.132787i
$950$		0			0
$951$	1.49467e6			0.0535912
$952$	2.64433e6	+	3.71239e6i	0.0945633	+	0.132758i
$953$		−	1.10363e7i		−	0.393634i	−0.980440	−	0.196817i	$-0.936940\pi$
$953$		−	1.10363e7i		−	0.393634i	0.980440	−	0.196817i	$-0.0630605\pi$
$954$	1.24517e7	−	1.11412e7i	0.442954	−	0.396335i
$955$		0			0
$956$	1.95284e6	−	1.75244e7i	0.0691070	−	0.620152i
$957$	7.23885e6			0.255499
$958$	−1.68289e7	+	1.50577e7i	−0.592435	+	0.530084i
$959$	1.15807e7			0.406618
$960$		0			0
$961$	−2.60961e7			−0.911523
$962$	−2.35087e6	+	2.10345e6i	−0.0819012	+	0.0732814i
$963$	3.15065e7			1.09480
$964$	4.66342e6	−	4.18486e7i	0.161626	−	1.45040i
$965$		0			0
$966$	−3.65105e6	+	3.26680e6i	−0.125885	+	0.112637i
$967$			4.54331e7i			1.56245i	0.624249	+	0.781225i	$0.285405\pi$
$967$			4.54331e7i			1.56245i	−0.624249	+	0.781225i	$0.714595\pi$
$968$	1.78581e7	+	2.50711e7i	0.612557	+	0.859973i
$969$	−1.27404e6			−0.0435887
$970$		0			0
$971$			6.77731e6i			0.230680i	0.993326	+	0.115340i	$0.0367957\pi$
$971$			6.77731e6i			0.230680i	−0.993326	+	0.115340i	$0.963204\pi$
$972$	1.92576e6	−	1.72814e7i	0.0653789	−	0.586696i
$973$	3.87621e7			1.31258
$974$	2.43366e7	+	2.71992e7i	0.821981	+	0.918667i
$975$		0			0
$976$	9.47458e6	−	4.19835e7i	0.318372	−	1.41076i
$977$			4.58953e7i			1.53827i	0.639087	+	0.769134i	$0.279312\pi$
$977$			4.58953e7i			1.53827i	−0.639087	+	0.769134i	$0.720688\pi$
$978$	2.42313e6	−	2.16811e6i	0.0810084	−	0.0724826i
$979$		−	3.70670e7i		−	1.23604i
$980$		0			0
$981$			2.67589e7i			0.887759i
$982$	−1.64920e7	−	1.84318e7i	−0.545750	−	0.609944i
$983$			4.96160e7i			1.63771i	0.573998	+	0.818857i	$0.305392\pi$
$983$			4.96160e7i			1.63771i	−0.573998	+	0.818857i	$0.694608\pi$
$984$	−2.78694e6	−	3.91261e6i	−0.0917571	−	0.128819i
$985$		0			0
$986$	3.64061e6	−	3.25745e6i	0.119257	−	0.106705i
$987$	−7.72549e6			−0.252425
$988$	6.56108e6	+	731138.i	0.213837	+	0.0238291i
$989$			1.16174e7i			0.377676i
$990$		0			0
$991$	2.24227e7			0.725276			0.362638	−	0.931930i	$-0.381876\pi$
$991$	2.24227e7			0.725276			0.362638	+	0.931930i	$0.381876\pi$
$992$	8.05524e6	−	4.48415e6i	0.259896	−	0.144678i
$993$		−	5.06462e6i		−	0.162995i
$994$	1.86542e7	+	2.08484e7i	0.598840	+	0.669279i
$995$		0			0
$996$	−504117.	+	4.52384e6i	−0.0161021	+	0.144497i
$997$	−5.13276e7			−1.63536			−0.817679	−	0.575675i	$-0.804740\pi$
$997$	−5.13276e7			−1.63536			−0.817679	+	0.575675i	$0.804740\pi$
$998$	1.95056e7	+	2.17999e7i	0.619915	+	0.692832i
$999$	7.32834e6			0.232323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.a.149.7		8
4.3	odd	2		800.6.f.a.49.3		8
5.2	odd	4		8.6.b.a.5.4	yes	4
5.3	odd	4		200.6.d.a.101.1		4
5.4	even	2	inner	200.6.f.a.149.2		8
8.3	odd	2		800.6.f.a.49.5		8
8.5	even	2	inner	200.6.f.a.149.1		8
15.2	even	4		72.6.d.b.37.1		4
20.3	even	4		800.6.d.a.401.2		4
20.7	even	4		32.6.b.a.17.3		4
20.19	odd	2		800.6.f.a.49.6		8
40.3	even	4		800.6.d.a.401.3		4
40.13	odd	4		200.6.d.a.101.2		4
40.19	odd	2		800.6.f.a.49.4		8
40.27	even	4		32.6.b.a.17.2		4
40.29	even	2	inner	200.6.f.a.149.8		8
40.37	odd	4		8.6.b.a.5.3	✓	4
60.47	odd	4		288.6.d.b.145.4		4
80.27	even	4		256.6.a.n.1.3		4
80.37	odd	4		256.6.a.k.1.2		4
80.67	even	4		256.6.a.n.1.2		4
80.77	odd	4		256.6.a.k.1.3		4
120.77	even	4		72.6.d.b.37.2		4
120.107	odd	4		288.6.d.b.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.6.b.a.5.3	✓	4	40.37	odd	4
8.6.b.a.5.4	yes	4	5.2	odd	4
32.6.b.a.17.2		4	40.27	even	4
32.6.b.a.17.3		4	20.7	even	4
72.6.d.b.37.1		4	15.2	even	4
72.6.d.b.37.2		4	120.77	even	4
200.6.d.a.101.1		4	5.3	odd	4
200.6.d.a.101.2		4	40.13	odd	4
200.6.f.a.149.1		8	8.5	even	2	inner
200.6.f.a.149.2		8	5.4	even	2	inner
200.6.f.a.149.7		8	1.1	even	1	trivial
200.6.f.a.149.8		8	40.29	even	2	inner
256.6.a.k.1.2		4	80.37	odd	4
256.6.a.k.1.3		4	80.77	odd	4
256.6.a.n.1.2		4	80.67	even	4
256.6.a.n.1.3		4	80.27	even	4
288.6.d.b.145.1		4	120.107	odd	4
288.6.d.b.145.4		4	60.47	odd	4
800.6.d.a.401.2		4	20.3	even	4
800.6.d.a.401.3		4	40.3	even	4
800.6.f.a.49.3		8	4.3	odd	2
800.6.f.a.49.4		8	40.19	odd	2
800.6.f.a.49.5		8	8.3	odd	2
800.6.f.a.49.6		8	20.19	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.21569 - 3.77200i) q^{2} +3.25452 q^{3} +(3.54400 - 31.8031i) q^{4} +(13.7200 - 12.2760i) q^{6} +112.704i q^{7} +(-105.021 - 147.440i) q^{8} -232.408 q^{9} +O(q^{10})\)	\(q+(4.21569 - 3.77200i) q^{2} +3.25452 q^{3} +(3.54400 - 31.8031i) q^{4} +(13.7200 - 12.2760i) q^{6} +112.704i q^{7} +(-105.021 - 147.440i) q^{8} -232.408 q^{9} +575.407i q^{11} +(11.5340 - 103.504i) q^{12} +117.735 q^{13} +(425.120 + 475.125i) q^{14} +(-998.880 - 225.421i) q^{16} +223.408i q^{17} +(-979.759 + 876.644i) q^{18} +1752.26i q^{19} +366.797i q^{21} +(2170.44 + 2425.74i) q^{22} +2361.15i q^{23} +(-341.793 - 479.846i) q^{24} +(496.336 - 444.098i) q^{26} -1547.22 q^{27} +(3584.34 + 399.424i) q^{28} -3865.52i q^{29} -1591.55 q^{31} +(-5061.25 + 2817.47i) q^{32} +1872.67i q^{33} +(842.696 + 941.818i) q^{34} +(-823.655 + 7391.31i) q^{36} -4736.44 q^{37} +(6609.52 + 7386.97i) q^{38} +383.172 q^{39} +8153.88 q^{41} +(1383.56 + 1546.30i) q^{42} +4920.23 q^{43} +(18299.8 + 2039.25i) q^{44} +(8906.27 + 9953.88i) q^{46} +21062.0i q^{47} +(-3250.87 - 733.636i) q^{48} +4104.79 q^{49} +727.085i q^{51} +(417.255 - 3744.36i) q^{52} -12709.0 q^{53} +(-6522.61 + 5836.13i) q^{54} +(16617.1 - 11836.3i) q^{56} +5702.75i q^{57} +(-14580.7 - 16295.8i) q^{58} -14111.1i q^{59} +42030.6i q^{61} +(-6709.48 + 6003.33i) q^{62} -26193.3i q^{63} +(-10709.1 + 30968.6i) q^{64} +(7063.73 + 7894.60i) q^{66} -54153.4 q^{67} +(7105.08 + 791.759i) q^{68} +7684.41i q^{69} +43879.9 q^{71} +(24407.8 + 34266.3i) q^{72} -31290.6i q^{73} +(-19967.4 + 17865.9i) q^{74} +(55727.3 + 6210.01i) q^{76} -64850.7 q^{77} +(1615.33 - 1445.33i) q^{78} +50211.5 q^{79} +51439.7 q^{81} +(34374.2 - 30756.4i) q^{82} -43707.0 q^{83} +(11665.3 + 1299.93i) q^{84} +(20742.1 - 18559.1i) q^{86} -12580.4i q^{87} +(84838.1 - 60429.9i) q^{88} -64418.7 q^{89} +13269.3i q^{91} +(75092.1 + 8367.93i) q^{92} -5179.73 q^{93} +(79446.0 + 88790.8i) q^{94} +(-16471.9 + 9169.52i) q^{96} +62350.9i q^{97} +(17304.5 - 15483.3i) q^{98} -133729. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 40 q^{4} - 232 q^{6} + 328 q^{9}+O(q^{10}) \) 8 * q - 40 * q^4 - 232 * q^6 + 328 * q^9	\( 8 q - 40 q^{4} - 232 q^{6} + 328 q^{9} + 4768 q^{14} - 6624 q^{16} + 15584 q^{24} + 11216 q^{26} - 25856 q^{31} + 9544 q^{34} - 20328 q^{36} - 70208 q^{39} - 9136 q^{41} + 58224 q^{44} + 58400 q^{46} - 19656 q^{49} - 46576 q^{54} + 81536 q^{56} + 83840 q^{64} + 86448 q^{66} + 413376 q^{71} - 34928 q^{74} + 199888 q^{76} + 495744 q^{79} + 59368 q^{81} - 393344 q^{84} - 37000 q^{86} + 169264 q^{89} + 197568 q^{94} - 231296 q^{96}+O(q^{100}) \) 8 * q - 40 * q^4 - 232 * q^6 + 328 * q^9 + 4768 * q^14 - 6624 * q^16 + 15584 * q^24 + 11216 * q^26 - 25856 * q^31 + 9544 * q^34 - 20328 * q^36 - 70208 * q^39 - 9136 * q^41 + 58224 * q^44 + 58400 * q^46 - 19656 * q^49 - 46576 * q^54 + 81536 * q^56 + 83840 * q^64 + 86448 * q^66 + 413376 * q^71 - 34928 * q^74 + 199888 * q^76 + 495744 * q^79 + 59368 * q^81 - 393344 * q^84 - 37000 * q^86 + 169264 * q^89 + 197568 * q^94 - 231296 * q^96

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