LMFDB - Embedded newform 200.6.d.e.101.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.21
Character	$\chi$	$=$	200.101
Dual form			200.6.d.e.101.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.41648 - 3.53479i) q^{2} +21.4357i q^{3} +(7.01055 - 31.2226i) q^{4} +(75.7708 + 94.6704i) q^{6} -39.9262 q^{7} +(-79.4034 - 162.675i) q^{8} -216.491 q^{9} +O(q^{10})$	\(q+(4.41648 - 3.53479i) q^{2} +21.4357i q^{3} +(7.01055 - 31.2226i) q^{4} +(75.7708 + 94.6704i) q^{6} -39.9262 q^{7} +(-79.4034 - 162.675i) q^{8} -216.491 q^{9} -141.626i q^{11} +(669.280 + 150.276i) q^{12} -700.139i q^{13} +(-176.333 + 141.131i) q^{14} +(-925.704 - 437.776i) q^{16} +960.152 q^{17} +(-956.126 + 765.249i) q^{18} -2202.13i q^{19} -855.847i q^{21} +(-500.618 - 625.488i) q^{22} +4492.21 q^{23} +(3487.05 - 1702.07i) q^{24} +(-2474.84 - 3092.15i) q^{26} +568.247i q^{27} +(-279.905 + 1246.60i) q^{28} +4834.96i q^{29} -1122.17 q^{31} +(-5635.80 + 1338.74i) q^{32} +3035.86 q^{33} +(4240.49 - 3393.93i) q^{34} +(-1517.72 + 6759.41i) q^{36} -8779.50i q^{37} +(-7784.07 - 9725.67i) q^{38} +15008.0 q^{39} +11522.4 q^{41} +(-3025.24 - 3779.83i) q^{42} -17358.0i q^{43} +(-4421.94 - 992.877i) q^{44} +(19839.7 - 15879.0i) q^{46} +15167.7 q^{47} +(9384.04 - 19843.2i) q^{48} -15212.9 q^{49} +20581.6i q^{51} +(-21860.2 - 4908.36i) q^{52} -7119.05i q^{53} +(2008.63 + 2509.65i) q^{54} +(3170.28 + 6494.99i) q^{56} +47204.3 q^{57} +(17090.6 + 21353.5i) q^{58} -41761.3i q^{59} +20347.5i q^{61} +(-4956.04 + 3966.64i) q^{62} +8643.65 q^{63} +(-20158.2 + 25833.9i) q^{64} +(13407.8 - 10731.1i) q^{66} -23764.7i q^{67} +(6731.19 - 29978.4i) q^{68} +96293.7i q^{69} +881.677 q^{71} +(17190.1 + 35217.6i) q^{72} +7051.66 q^{73} +(-31033.7 - 38774.5i) q^{74} +(-68756.4 - 15438.2i) q^{76} +5654.59i q^{77} +(66282.5 - 53050.1i) q^{78} +47780.1 q^{79} -64788.0 q^{81} +(50888.6 - 40729.4i) q^{82} -51692.3i q^{83} +(-26721.8 - 5999.96i) q^{84} +(-61356.8 - 76661.1i) q^{86} -103641. q^{87} +(-23039.0 + 11245.6i) q^{88} -122761. q^{89} +27953.9i q^{91} +(31492.8 - 140258. i) q^{92} -24054.6i q^{93} +(66987.8 - 53614.6i) q^{94} +(-28696.9 - 120807. i) q^{96} -155549. q^{97} +(-67187.4 + 53774.4i) q^{98} +30660.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 12 q^{4} - 156 q^{6} - 1940 q^{9}+O(q^{10}) $ 28 * q + 12 * q^4 - 156 * q^6 - 1940 * q^9	$ 28 q + 12 q^{4} - 156 q^{6} - 1940 q^{9} + 692 q^{14} + 1560 q^{16} + 2224 q^{24} - 9976 q^{26} + 4368 q^{31} - 13016 q^{34} - 34116 q^{36} - 23360 q^{39} - 2480 q^{41} - 10712 q^{44} + 58372 q^{46} + 38420 q^{49} + 3568 q^{54} + 110944 q^{56} + 46944 q^{64} - 136120 q^{66} - 69232 q^{71} - 34176 q^{74} - 13944 q^{76} + 35984 q^{79} + 122596 q^{81} + 165688 q^{84} - 73676 q^{86} + 178744 q^{89} - 314740 q^{94} - 236176 q^{96}+O(q^{100}) $ 28 * q + 12 * q^4 - 156 * q^6 - 1940 * q^9 + 692 * q^14 + 1560 * q^16 + 2224 * q^24 - 9976 * q^26 + 4368 * q^31 - 13016 * q^34 - 34116 * q^36 - 23360 * q^39 - 2480 * q^41 - 10712 * q^44 + 58372 * q^46 + 38420 * q^49 + 3568 * q^54 + 110944 * q^56 + 46944 * q^64 - 136120 * q^66 - 69232 * q^71 - 34176 * q^74 - 13944 * q^76 + 35984 * q^79 + 122596 * q^81 + 165688 * q^84 - 73676 * q^86 + 178744 * q^89 - 314740 * q^94 - 236176 * 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 $

$2$	4.41648	−	3.53479i	0.780730	−	0.624868i
$2$	4.41648	−	3.53479i	0.780730	−	0.624868i
$3$			21.4357i			1.37510i	0.726136	+	0.687551i	$0.241314\pi$
$3$			21.4357i			1.37510i	−0.726136	+	0.687551i	$0.758686\pi$
$4$	7.01055	−	31.2226i	0.219080	−	0.975707i
$5$		0			0
$5$		0			0
$6$	75.7708	+	94.6704i	0.859258	+	1.07358i
$7$	−39.9262			−0.307973			−0.153987	−	0.988073i	$-0.549211\pi$
$7$	−39.9262			−0.307973			−0.153987	+	0.988073i	$0.549211\pi$
$8$	−79.4034	−	162.675i	−0.438646	−	0.898660i
$9$	−216.491			−0.890908
$10$		0			0
$11$		−	141.626i		−	0.352908i	−0.984309	−	0.176454i	$-0.943537\pi$
$11$		−	141.626i		−	0.352908i	0.984309	−	0.176454i	$-0.0564627\pi$
$12$	669.280	+	150.276i	1.34170	+	0.301257i
$13$		−	700.139i		−	1.14902i	−0.818499	−	0.574508i	$-0.805194\pi$
$13$		−	700.139i		−	1.14902i	0.818499	−	0.574508i	$-0.194806\pi$
$14$	−176.333	+	141.131i	−0.240444	+	0.192443i
$15$		0			0
$16$	−925.704	−	437.776i	−0.904008	−	0.427515i
$17$	960.152			0.805782			0.402891	−	0.915248i	$-0.368005\pi$
$17$	960.152			0.805782			0.402891	+	0.915248i	$0.368005\pi$
$18$	−956.126	+	765.249i	−0.695559	+	0.556700i
$19$		−	2202.13i		−	1.39946i	−0.714409	−	0.699728i	$-0.753304\pi$
$19$		−	2202.13i		−	1.39946i	0.714409	−	0.699728i	$-0.246696\pi$
$20$		0			0
$21$		−	855.847i		−	0.423495i
$22$	−500.618	−	625.488i	−0.220521	−	0.275526i
$23$	4492.21			1.77068			0.885340	−	0.464944i	$-0.153926\pi$
$23$	4492.21			1.77068			0.885340	+	0.464944i	$0.153926\pi$
$24$	3487.05	−	1702.07i	1.23575	−	0.603183i
$25$		0			0
$26$	−2474.84	−	3092.15i	−0.717983	−	0.897071i
$27$			568.247i			0.150012i
$28$	−279.905	+	1246.60i	−0.0674707	+	0.300492i
$29$			4834.96i			1.06757i	0.845619	+	0.533787i	$0.179232\pi$
$29$			4834.96i			1.06757i	−0.845619	+	0.533787i	$0.820768\pi$
$30$		0			0
$31$	−1122.17			−0.209727			−0.104864	−	0.994487i	$-0.533441\pi$
$31$	−1122.17			−0.209727			−0.104864	+	0.994487i	$0.533441\pi$
$32$	−5635.80	+	1338.74i	−0.972927	+	0.231112i
$33$	3035.86			0.485285
$34$	4240.49	−	3393.93i	0.629098	−	0.503507i
$35$		0			0
$36$	−1517.72	+	6759.41i	−0.195180	+	0.869265i
$37$		−	8779.50i		−	1.05430i	−0.849771	−	0.527152i	$-0.823260\pi$
$37$		−	8779.50i		−	1.05430i	0.849771	−	0.527152i	$-0.176740\pi$
$38$	−7784.07	−	9725.67i	−0.874476	−	1.09260i
$39$	15008.0			1.58001
$40$		0			0
$41$	11522.4			1.07050			0.535248	−	0.844695i	$-0.320218\pi$
$41$	11522.4			1.07050			0.535248	+	0.844695i	$0.320218\pi$
$42$	−3025.24	−	3779.83i	−0.264628	−	0.330635i
$43$		−	17358.0i		−	1.43162i	−0.698295	−	0.715811i	$-0.746057\pi$
$43$		−	17358.0i		−	1.43162i	0.698295	−	0.715811i	$-0.253943\pi$
$44$	−4421.94	−	992.877i	−0.344335	−	0.0773150i
$45$		0			0
$46$	19839.7	−	15879.0i	1.38242	−	1.10644i
$47$	15167.7			1.00156			0.500778	−	0.865576i	$-0.333047\pi$
$47$	15167.7			1.00156			0.500778	+	0.865576i	$0.333047\pi$
$48$	9384.04	−	19843.2i	0.587877	−	1.24310i
$49$	−15212.9			−0.905153
$50$		0			0
$51$			20581.6i			1.10803i
$52$	−21860.2	−	4908.36i	−1.12110	−	0.251726i
$53$		−	7119.05i		−	0.348123i	−0.984735	−	0.174061i	$-0.944311\pi$
$53$		−	7119.05i		−	0.348123i	0.984735	−	0.174061i	$-0.0556891\pi$
$54$	2008.63	+	2509.65i	0.0937380	+	0.117119i
$55$		0			0
$56$	3170.28	+	6494.99i	0.135091	+	0.276763i
$57$	47204.3			1.92440
$58$	17090.6	+	21353.5i	0.667093	+	0.833488i
$59$		−	41761.3i		−	1.56187i	−0.624614	−	0.780934i	$-0.714744\pi$
$59$		−	41761.3i		−	1.56187i	0.624614	−	0.780934i	$-0.285256\pi$
$60$		0			0
$61$			20347.5i			0.700143i	0.936723	+	0.350072i	$0.113843\pi$
$61$			20347.5i			0.700143i	−0.936723	+	0.350072i	$0.886157\pi$
$62$	−4956.04	+	3966.64i	−0.163740	+	0.131052i
$63$	8643.65			0.274376
$64$	−20158.2	+	25833.9i	−0.615179	+	0.788387i
$65$		0			0
$66$	13407.8	−	10731.1i	0.378877	−	0.303239i
$67$		−	23764.7i		−	0.646762i	−0.946269	−	0.323381i	$-0.895180\pi$
$67$		−	23764.7i		−	0.646762i	0.946269	−	0.323381i	$-0.104820\pi$
$68$	6731.19	−	29978.4i	0.176530	−	0.786207i
$69$			96293.7i			2.43487i
$70$		0			0
$71$	881.677			0.0207570			0.0103785	−	0.999946i	$-0.496696\pi$
$71$	881.677			0.0207570			0.0103785	+	0.999946i	$0.496696\pi$
$72$	17190.1	+	35217.6i	0.390793	+	0.800623i
$73$	7051.66			0.154876			0.0774381	−	0.996997i	$-0.475326\pi$
$73$	7051.66			0.154876			0.0774381	+	0.996997i	$0.475326\pi$
$74$	−31033.7	−	38774.5i	−0.658800	−	0.823126i
$75$		0			0
$76$	−68756.4	−	15438.2i	−1.36546	−	0.306593i
$77$			5654.59i			0.108686i
$78$	66282.5	−	53050.1i	1.23357	−	0.987301i
$79$	47780.1			0.861350			0.430675	−	0.902507i	$-0.358276\pi$
$79$	47780.1			0.861350			0.430675	+	0.902507i	$0.358276\pi$
$80$		0			0
$81$	−64788.0			−1.09719
$82$	50888.6	−	40729.4i	0.835768	−	0.668919i
$83$		−	51692.3i		−	0.823628i	−0.911268	−	0.411814i	$-0.864895\pi$
$83$		−	51692.3i		−	0.823628i	0.911268	−	0.411814i	$-0.135105\pi$
$84$	−26721.8	−	5999.96i	−0.413207	−	0.0927791i
$85$		0			0
$86$	−61356.8	−	76661.1i	−0.894574	−	1.11771i
$87$	−103641.			−1.46802
$88$	−23039.0	+	11245.6i	−0.317144	+	0.154802i
$89$	−122761.			−1.64281			−0.821404	−	0.570347i	$-0.806809\pi$
$89$	−122761.			−1.64281			−0.821404	+	0.570347i	$0.806809\pi$
$90$		0			0
$91$			27953.9i			0.353866i
$92$	31492.8	−	140258.i	0.387920	−	1.72766i
$93$		−	24054.6i		−	0.288397i
$94$	66987.8	−	53614.6i	0.781945	−	0.625840i
$95$		0			0
$96$	−28696.9	−	120807.i	−0.317803	−	1.33788i
$97$	−155549.			−1.67856			−0.839282	−	0.543696i	$-0.817024\pi$
$97$	−155549.			−1.67856			−0.839282	+	0.543696i	$0.817024\pi$
$98$	−67187.4	+	53774.4i	−0.706680	+	0.565601i
$99$			30660.7i			0.314409i
$100$		0			0
$101$			195692.i			1.90884i	0.298466	+	0.954420i	$0.403525\pi$
$101$			195692.i			1.90884i	−0.298466	+	0.954420i	$0.596475\pi$
$102$	72751.4	+	90898.0i	0.692374	+	0.865075i
$103$	−60625.8			−0.563073			−0.281536	−	0.959551i	$-0.590844\pi$
$103$	−60625.8			−0.563073			−0.281536	+	0.959551i	$0.590844\pi$
$104$	−113895.	+	55593.4i	−1.03257	+	0.504011i
$105$		0			0
$106$	−25164.3	−	31441.1i	−0.217531	−	0.271790i
$107$			10924.2i			0.0922422i	0.998936	+	0.0461211i	$0.0146860\pi$
$107$			10924.2i			0.0922422i	−0.998936	+	0.0461211i	$0.985314\pi$
$108$	17742.1	+	3983.72i	0.146368	+	0.0328647i
$109$		−	11344.4i		−	0.0914569i	−0.998954	−	0.0457285i	$-0.985439\pi$
$109$		−	11344.4i		−	0.0914569i	0.998954	−	0.0457285i	$-0.0145609\pi$
$110$		0			0
$111$	188195.			1.44978
$112$	36959.9	+	17478.7i	0.278410	+	0.131663i
$113$	66586.5			0.490557			0.245279	−	0.969453i	$-0.421121\pi$
$113$	66586.5			0.490557			0.245279	+	0.969453i	$0.421121\pi$
$114$	208477.	−	166857.i	1.50244	−	1.20249i
$115$		0			0
$116$	150960.	+	33895.8i	1.04164	+	0.233884i
$117$			151574.i			1.02367i
$118$	−147617.	−	184438.i	−0.975961	−	1.21940i
$119$	−38335.2			−0.248159
$120$		0			0
$121$	140993.			0.875456
$122$	71924.2	+	89864.4i	0.437497	+	0.546623i
$123$			246992.i			1.47204i
$124$	−7867.04	+	35037.1i	−0.0459470	+	0.204632i
$125$		0			0
$126$	38174.5	−	30553.5i	0.214214	−	0.171449i
$127$	−88813.9			−0.488621			−0.244310	−	0.969697i	$-0.578562\pi$
$127$	−88813.9			−0.488621			−0.244310	+	0.969697i	$0.578562\pi$
$128$	2289.02	+	185350.i	0.0123488	+	0.999924i
$129$	372081.			1.96863
$130$		0			0
$131$			83967.1i			0.427495i	0.976889	+	0.213748i	$0.0685670\pi$
$131$			83967.1i			0.427495i	−0.976889	+	0.213748i	$0.931433\pi$
$132$	21283.0	−	94787.5i	0.106316	−	0.473496i
$133$			87922.8i			0.430995i
$134$	−84003.0	−	104956.i	−0.404141	−	0.504947i
$135$		0			0
$136$	−76239.3	−	156192.i	−0.353453	−	0.724124i
$137$	275285.			1.25309			0.626543	−	0.779387i	$-0.284469\pi$
$137$	275285.			1.25309			0.626543	+	0.779387i	$0.284469\pi$
$138$	340378.	+	425279.i	1.52147	+	1.90097i
$139$			153603.i			0.674317i	0.941448	+	0.337158i	$0.109466\pi$
$139$			153603.i			0.674317i	−0.941448	+	0.337158i	$0.890534\pi$
$140$		0			0
$141$			325131.i			1.37724i
$142$	3893.91	−	3116.54i	0.0162056	−	0.0129704i
$143$	−99157.9			−0.405497
$144$	200406.	+	94774.3i	0.805388	+	0.380877i
$145$		0			0
$146$	31143.5	−	24926.1i	0.120916	−	0.0967772i
$147$		−	326100.i		−	1.24468i
$148$	−274119.	−	61549.1i	−1.02869	−	0.230976i
$149$		−	30715.3i		−	0.113342i	−0.998393	−	0.0566708i	$-0.981951\pi$
$149$		−	30715.3i		−	0.113342i	0.998393	−	0.0566708i	$-0.0180486\pi$
$150$		0			0
$151$	−25896.6			−0.0924272			−0.0462136	−	0.998932i	$-0.514715\pi$
$151$	−25896.6			−0.0924272			−0.0462136	+	0.998932i	$0.514715\pi$
$152$	−358232.	+	174857.i	−1.25764	+	0.613866i
$153$	−207864.			−0.717878
$154$	19987.8	+	24973.4i	0.0679145	+	0.0848546i
$155$		0			0
$156$	105214.	−	468589.i	0.346149	−	1.54163i
$157$			334928.i			1.08443i	0.840239	+	0.542216i	$0.182415\pi$
$157$			334928.i			1.08443i	−0.840239	+	0.542216i	$0.817585\pi$
$158$	211020.	−	168893.i	0.672482	−	0.538230i
$159$	152602.			0.478704
$160$		0			0
$161$	−179357.			−0.545322
$162$	−286135.	+	229012.i	−0.856610	+	0.685600i
$163$		−	203546.i		−	0.600057i	−0.953930	−	0.300029i	$-0.903004\pi$
$163$		−	203546.i		−	0.600057i	0.953930	−	0.300029i	$-0.0969962\pi$
$164$	80778.7	−	359761.i	0.234524	−	1.04449i
$165$		0			0
$166$	−182721.	−	228298.i	−0.514659	−	0.643031i
$167$	52221.5			0.144897			0.0724483	−	0.997372i	$-0.476919\pi$
$167$	52221.5			0.144897			0.0724483	+	0.997372i	$0.476919\pi$
$168$	−139225.	+	67957.2i	−0.380578	+	0.185764i
$169$	−118902.			−0.320236
$170$		0			0
$171$			476741.i			1.24679i
$172$	−541962.	−	121689.i	−1.39684	−	0.313639i
$173$			503329.i			1.27861i	0.768955	+	0.639303i	$0.220777\pi$
$173$			503329.i			1.27861i	−0.768955	+	0.639303i	$0.779223\pi$
$174$	−457728.	+	366349.i	−1.14613	+	0.917322i
$175$		0			0
$176$	−62000.4	+	131104.i	−0.150873	+	0.319032i
$177$	895185.			2.14773
$178$	−542173.	+	433935.i	−1.28259	+	1.02654i
$179$			249706.i			0.582501i	0.956647	+	0.291251i	$0.0940713\pi$
$179$			249706.i			0.582501i	−0.956647	+	0.291251i	$0.905929\pi$
$180$		0			0
$181$		−	341157.i		−	0.774031i	−0.922073	−	0.387015i	$-0.873506\pi$
$181$		−	341157.i		−	0.774031i	0.922073	−	0.387015i	$-0.126494\pi$
$182$	98811.1	+	123458.i	0.221120	+	0.276274i
$183$	−436164.			−0.962769
$184$	−356696.	−	730769.i	−0.776702	−	1.59124i
$185$		0			0
$186$	−85027.8	−	106236.i	−0.180210	−	0.225160i
$187$		−	135982.i		−	0.284367i
$188$	106334.	−	473575.i	0.219420	−	0.977225i
$189$		−	22687.9i		−	0.0461998i
$190$		0			0
$191$	−592636.			−1.17545			−0.587726	−	0.809060i	$-0.699977\pi$
$191$	−592636.			−1.17545			−0.587726	+	0.809060i	$0.699977\pi$
$192$	−553768.	−	432106.i	−1.08411	−	0.845935i
$193$	771725.			1.49131			0.745657	−	0.666330i	$-0.232136\pi$
$193$	771725.			1.49131			0.745657	+	0.666330i	$0.232136\pi$
$194$	−686979.	+	549833.i	−1.31051	+	1.04888i
$195$		0			0
$196$	−106651.	+	474987.i	−0.198301	+	0.883164i
$197$		−	190213.i		−	0.349200i	−0.984639	−	0.174600i	$-0.944137\pi$
$197$		−	190213.i		−	0.349200i	0.984639	−	0.174600i	$-0.0558633\pi$
$198$	108379.	+	135412.i	0.196464	+	0.245468i
$199$	−949154.			−1.69904			−0.849521	−	0.527555i	$-0.823109\pi$
$199$	−949154.			−1.69904			−0.849521	+	0.527555i	$0.823109\pi$
$200$		0			0
$201$	509413.			0.889364
$202$	691730.	+	864269.i	1.19277	+	1.49029i
$203$		−	193042.i		−	0.328784i
$204$	642610.	+	144288.i	1.08112	+	0.242748i
$205$		0			0
$206$	−267753.	+	214299.i	−0.439608	+	0.351846i
$207$	−972521.			−1.57751
$208$	−306504.	+	648122.i	−0.491222	+	1.03872i
$209$	−311879.			−0.493879
$210$		0			0
$211$			47751.4i			0.0738380i	0.999318	+	0.0369190i	$0.0117544\pi$
$211$			47751.4i			0.0738380i	−0.999318	+	0.0369190i	$0.988246\pi$
$212$	−222275.	−	49908.4i	−0.339666	−	0.0762666i
$213$			18899.4i			0.0285430i
$214$	38614.7	+	48246.4i	0.0576392	+	0.0720163i
$215$		0			0
$216$	92439.4	−	45120.7i	0.134810	−	0.0658024i
$217$	44804.0			0.0645904
$218$	−40100.2	−	50102.4i	−0.0571485	−	0.0714032i
$219$			151158.i			0.212971i
$220$		0			0
$221$		−	672239.i		−	0.925856i
$222$	831159.	−	665229.i	1.13188	−	0.905918i
$223$	648287.			0.872982			0.436491	−	0.899709i	$-0.356221\pi$
$223$	648287.			0.872982			0.436491	+	0.899709i	$0.356221\pi$
$224$	225016.	−	53450.9i	0.299635	−	0.0711762i
$225$		0			0
$226$	294078.	−	235369.i	0.382993	−	0.306534i
$227$			17476.8i			0.0225111i	0.999937	+	0.0112556i	$0.00358283\pi$
$227$			17476.8i			0.0225111i	−0.999937	+	0.0112556i	$0.996417\pi$
$228$	330928.	−	1.47384e6i	0.421596	−	1.87765i
$229$		−	735371.i		−	0.926655i	−0.886187	−	0.463327i	$-0.846655\pi$
$229$		−	735371.i		−	0.926655i	0.886187	−	0.463327i	$-0.153345\pi$
$230$		0			0
$231$	−121210.			−0.149455
$232$	786527.	−	383913.i	0.959386	−	0.468287i
$233$	−70875.0			−0.0855270			−0.0427635	−	0.999085i	$-0.513616\pi$
$233$	−70875.0			−0.0855270			−0.0427635	+	0.999085i	$0.513616\pi$
$234$	535780.	+	669421.i	0.639657	+	0.799208i
$235$		0			0
$236$	−1.30390e6	−	292770.i	−1.52392	−	0.342173i
$237$			1.02420e6i			1.18445i
$238$	−169307.	+	135507.i	−0.193745	+	0.155067i
$239$	516369.			0.584743			0.292372	−	0.956305i	$-0.405556\pi$
$239$	516369.			0.584743			0.292372	+	0.956305i	$0.405556\pi$
$240$		0			0
$241$	609937.			0.676460			0.338230	−	0.941064i	$-0.390172\pi$
$241$	609937.			0.676460			0.338230	+	0.941064i	$0.390172\pi$
$242$	622693.	−	498381.i	0.683495	−	0.547045i
$243$		−	1.25069e6i		−	1.35874i
$244$	635303.	+	142647.i	0.683135	+	0.153387i
$245$		0			0
$246$	873064.	+	1.09083e6i	0.919832	+	1.14927i
$247$	−1.54180e6			−1.60800
$248$	89104.2	+	182549.i	0.0919960	+	0.188474i
$249$	1.10806e6			1.13257
$250$		0			0
$251$			327106.i			0.327721i	0.986484	+	0.163860i	$0.0523947\pi$
$251$			327106.i			0.327721i	−0.986484	+	0.163860i	$0.947605\pi$
$252$	60596.7	−	269877.i	0.0601102	−	0.267710i
$253$		−	636213.i		−	0.624887i
$254$	−392245.	+	313938.i	−0.381481	+	0.305323i
$255$		0			0
$256$	665281.	+	810501.i	0.634462	+	0.772954i
$257$	882853.			0.833788			0.416894	−	0.908955i	$-0.363119\pi$
$257$	882853.			0.833788			0.416894	+	0.908955i	$0.363119\pi$
$258$	1.64329e6	−	1.31523e6i	1.53697	−	1.23013i
$259$			350532.i			0.324697i
$260$		0			0
$261$		−	1.04672e6i		−	0.951111i
$262$	296806.	+	370839.i	0.267128	+	0.333758i
$263$	454062.			0.404786			0.202393	−	0.979304i	$-0.435128\pi$
$263$	454062.			0.404786			0.202393	+	0.979304i	$0.435128\pi$
$264$	−241058.	−	493858.i	−0.212868	−	0.436106i
$265$		0			0
$266$	310788.	+	388309.i	0.269315	+	0.336491i
$267$		−	2.63148e6i		−	2.25903i
$268$	−741995.	−	166603.i	−0.631050	−	0.141692i
$269$			384748.i			0.324187i	0.986775	+	0.162093i	$0.0518246\pi$
$269$			384748.i			0.324187i	−0.986775	+	0.162093i	$0.948175\pi$
$270$		0			0
$271$	1.36818e6			1.13167			0.565837	−	0.824517i	$-0.308553\pi$
$271$	1.36818e6			1.13167			0.565837	+	0.824517i	$0.308553\pi$
$272$	−888816.	−	420331.i	−0.728433	−	0.344484i
$273$	−599212.			−0.486602
$274$	1.21579e6	−	973073.i	0.978322	−	0.783013i
$275$		0			0
$276$	3.00654e6	+	675072.i	2.37572	+	0.533430i
$277$			567739.i			0.444579i	0.974981	+	0.222290i	$0.0713530\pi$
$277$			567739.i			0.444579i	−0.974981	+	0.222290i	$0.928647\pi$
$278$	542955.	+	678386.i	0.421359	+	0.526459i
$279$	242940.			0.186848
$280$		0			0
$281$	−1.90809e6			−1.44156			−0.720779	−	0.693165i	$-0.756216\pi$
$281$	−1.90809e6			−1.44156			−0.720779	+	0.693165i	$0.756216\pi$
$282$	1.14927e6	+	1.43593e6i	0.860594	+	1.07525i
$283$			873157.i			0.648077i	0.946044	+	0.324038i	$0.105041\pi$
$283$			873157.i			0.648077i	−0.946044	+	0.324038i	$0.894959\pi$
$284$	6181.04	−	27528.3i	0.00454743	−	0.0202527i
$285$		0			0
$286$	−437929.	+	350502.i	−0.316584	+	0.253382i
$287$	−460047.			−0.329684
$288$	1.22010e6	−	289825.i	0.866789	−	0.205899i
$289$	−497966.			−0.350716
$290$		0			0
$291$		−	3.33431e6i		−	2.30820i
$292$	49436.0	−	220171.i	0.0339302	−	0.151114i
$293$		−	422723.i		−	0.287665i	−0.989602	−	0.143832i	$-0.954057\pi$
$293$		−	422723.i		−	0.287665i	0.989602	−	0.143832i	$-0.0459426\pi$
$294$	−1.15269e6	−	1.44021e6i	−0.777760	−	0.971758i
$295$		0			0
$296$	−1.42820e6	+	697122.i	−0.947460	+	0.462466i
$297$	80478.5			0.0529406
$298$	−108572.	−	135654.i	−0.0708236	−	0.0884893i
$299$		−	3.14517e6i		−	2.03454i
$300$		0			0
$301$			693038.i			0.440901i
$302$	−114372.	+	91538.9i	−0.0721608	+	0.0577548i
$303$	−4.19480e6			−2.62485
$304$	−964040.	+	2.03852e6i	−0.598289	+	1.26512i
$305$		0			0
$306$	−918026.	+	734755.i	−0.560469	+	0.448579i
$307$			1.38323e6i			0.837624i	0.908073	+	0.418812i	$0.137553\pi$
$307$			1.38323e6i			0.837624i	−0.908073	+	0.418812i	$0.862447\pi$
$308$	176551.	+	39641.8i	0.106046	+	0.0238109i
$309$		−	1.29956e6i		−	0.774283i
$310$		0			0
$311$	−1.96775e6			−1.15363			−0.576817	−	0.816873i	$-0.695706\pi$
$311$	−1.96775e6			−1.15363			−0.576817	+	0.816873i	$0.695706\pi$
$312$	−1.19169e6	−	2.44142e6i	−0.693067	−	1.41990i
$313$	2.42724e6			1.40040			0.700199	−	0.713948i	$-0.253095\pi$
$313$	2.42724e6			1.40040			0.700199	+	0.713948i	$0.253095\pi$
$314$	1.18390e6	+	1.47920e6i	0.677627	+	0.846650i
$315$		0			0
$316$	334965.	−	1.49182e6i	0.188704	−	0.840425i
$317$			1.28631e6i			0.718951i	0.933155	+	0.359475i	$0.117044\pi$
$317$			1.28631e6i			0.718951i	−0.933155	+	0.359475i	$0.882956\pi$
$318$	673963.	−	539416.i	0.373739	−	0.299127i
$319$	684757.			0.376756
$320$		0			0
$321$	−234168.			−0.126843
$322$	−792125.	+	633988.i	−0.425749	+	0.340754i
$323$		−	2.11438e6i		−	1.12766i
$324$	−454200.	+	2.02285e6i	−0.240372	+	1.07054i
$325$		0			0
$326$	−719491.	−	898955.i	−0.374957	−	0.468483i
$327$	243176.			0.125763
$328$	−914921.	−	1.87441e6i	−0.469569	−	0.962012i
$329$	−605588.			−0.308452
$330$		0			0
$331$		−	3.07996e6i		−	1.54517i	−0.634913	−	0.772584i	$-0.718964\pi$
$331$		−	3.07996e6i		−	1.54517i	0.634913	−	0.772584i	$-0.281036\pi$
$332$	−1.61397e6	−	362392.i	−0.803619	−	0.180440i
$333$			1.90068e6i			0.939287i
$334$	230635.	−	184592.i	0.113125	−	0.0905413i
$335$		0			0
$336$	−374669.	+	792262.i	−0.181050	+	0.382843i
$337$	1.51034e6			0.724437			0.362218	−	0.932093i	$-0.382019\pi$
$337$	1.51034e6			0.724437			0.362218	+	0.932093i	$0.382019\pi$
$338$	−525126.	+	420292.i	−0.250018	+	0.200105i
$339$			1.42733e6i			0.674567i
$340$		0			0
$341$			158929.i			0.0740144i
$342$	1.68518e6	+	2.10552e6i	0.779078	+	0.973405i
$343$	1.27843e6			0.586736
$344$	−2.82371e6	+	1.37828e6i	−1.28654	+	0.627975i
$345$		0			0
$346$	1.77916e6	+	2.22294e6i	0.798960	+	0.998246i
$347$		−	4.01257e6i		−	1.78895i	−0.447113	−	0.894477i	$-0.647548\pi$
$347$		−	4.01257e6i		−	1.78895i	0.447113	−	0.894477i	$-0.352452\pi$
$348$	−726580.	+	3.23594e6i	−0.321614	+	1.43236i
$349$			595449.i			0.261686i	0.991403	+	0.130843i	$0.0417684\pi$
$349$			595449.i			0.261686i	−0.991403	+	0.130843i	$0.958232\pi$
$350$		0			0
$351$	397852.			0.172367
$352$	189601.	+	798176.i	0.0815612	+	0.343354i
$353$	1.05328e6			0.449890			0.224945	−	0.974371i	$-0.427780\pi$
$353$	1.05328e6			0.449890			0.224945	+	0.974371i	$0.427780\pi$
$354$	3.95356e6	−	3.16429e6i	1.67680	−	1.34205i
$355$		0			0
$356$	−860624.	+	3.83293e6i	−0.359906	+	1.60290i
$357$		−	821743.i		−	0.341244i
$358$	882659.	+	1.10282e6i	0.363986	+	0.454776i
$359$	−549662.			−0.225092			−0.112546	−	0.993647i	$-0.535901\pi$
$359$	−549662.			−0.225092			−0.112546	+	0.993647i	$0.535901\pi$
$360$		0			0
$361$	−2.37329e6			−0.958480
$362$	−1.20592e6	−	1.50671e6i	−0.483667	−	0.604309i
$363$			3.02229e6i			1.20384i
$364$	872794.	+	195972.i	0.345269	+	0.0775248i
$365$		0			0
$366$	−1.92631e6	+	1.54175e6i	−0.751663	+	0.601604i
$367$	313163.			0.121368			0.0606842	−	0.998157i	$-0.480672\pi$
$367$	313163.			0.121368			0.0606842	+	0.998157i	$0.480672\pi$
$368$	−4.15845e6	−	1.96658e6i	−1.60071	−	0.756993i
$369$	−2.49450e6			−0.953713
$370$		0			0
$371$			284236.i			0.107212i
$372$	−751047.	−	168636.i	−0.281391	−	0.0631818i
$373$		−	251757.i		−	0.0936935i	−0.998902	−	0.0468468i	$-0.985083\pi$
$373$		−	251757.i		−	0.0936935i	0.998902	−	0.0468468i	$-0.0149172\pi$
$374$	−480669.	−	600564.i	−0.177692	−	0.222014i
$375$		0			0
$376$	−1.20437e6	−	2.46740e6i	−0.439328	−	0.900058i
$377$	3.38515e6			1.22666
$378$	−80197.0	−	100201.i	−0.0288688	−	0.0360696i
$379$		−	862618.i		−	0.308476i	−0.988034	−	0.154238i	$-0.950708\pi$
$379$		−	862618.i		−	0.308476i	0.988034	−	0.154238i	$-0.0492922\pi$
$380$		0			0
$381$		−	1.90379e6i		−	0.671904i
$382$	−2.61736e6	+	2.09484e6i	−0.917711	+	0.734502i
$383$	4.09103e6			1.42507			0.712534	−	0.701638i	$-0.247547\pi$
$383$	4.09103e6			1.42507			0.712534	+	0.701638i	$0.247547\pi$
$384$	−3.97311e6	+	49066.9i	−1.37500	+	0.0169809i
$385$		0			0
$386$	3.40831e6	−	2.72788e6i	1.16431	−	0.931875i
$387$			3.75784e6i			1.27544i
$388$	−1.09048e6	+	4.85665e6i	−0.367739	+	1.63779i
$389$			5.39187e6i			1.80661i	0.428995	+	0.903307i	$0.358868\pi$
$389$			5.39187e6i			1.80661i	−0.428995	+	0.903307i	$0.641132\pi$
$390$		0			0
$391$	4.31320e6			1.42678
$392$	1.20796e6	+	2.47476e6i	0.397042	+	0.813424i
$393$	−1.79990e6			−0.587850
$394$	−672363.	−	840072.i	−0.218204	−	0.272631i
$395$		0			0
$396$	957308.	+	214949.i	0.306771	+	0.0688805i
$397$			5.41902e6i			1.72562i	0.505529	+	0.862809i	$0.331297\pi$
$397$			5.41902e6i			1.72562i	−0.505529	+	0.862809i	$0.668703\pi$
$398$	−4.19192e6	+	3.35506e6i	−1.32649	+	1.06168i
$399$	−1.88469e6			−0.592663
$400$		0			0
$401$	3.22720e6			1.00222			0.501112	−	0.865383i	$-0.332925\pi$
$401$	3.22720e6			1.00222			0.501112	+	0.865383i	$0.332925\pi$
$402$	2.24981e6	−	1.80067e6i	0.694354	−	0.555735i
$403$			785676.i			0.240980i
$404$	6.11002e6	+	1.37191e6i	1.86247	+	0.418188i
$405$		0			0
$406$	−682361.	−	852564.i	−0.205447	−	0.256692i
$407$	−1.24341e6			−0.372072
$408$	3.34810e6	−	1.63425e6i	0.995745	−	0.486034i
$409$	−523436.			−0.154723			−0.0773616	−	0.997003i	$-0.524650\pi$
$409$	−523436.			−0.154723			−0.0773616	+	0.997003i	$0.524650\pi$
$410$		0			0
$411$			5.90093e6i			1.72312i
$412$	−425020.	+	1.89290e6i	−0.123358	+	0.549394i
$413$			1.66737e6i			0.481013i
$414$	−4.29512e6	+	3.43765e6i	−1.23161	+	0.985738i
$415$		0			0
$416$	937306.	+	3.94584e6i	0.265551	+	1.11791i
$417$	−3.29260e6			−0.927255
$418$	−1.37741e6	+	1.10243e6i	−0.385587	+	0.308610i
$419$		−	3.66116e6i		−	1.01879i	−0.860534	−	0.509393i	$-0.829870\pi$
$419$		−	3.66116e6i		−	1.01879i	0.860534	−	0.509393i	$-0.170130\pi$
$420$		0			0
$421$			3.15337e6i			0.867101i	0.901129	+	0.433550i	$0.142739\pi$
$421$			3.15337e6i			0.867101i	−0.901129	+	0.433550i	$0.857261\pi$
$422$	168791.	+	210893.i	0.0461390	+	0.0576476i
$423$	−3.28366e6			−0.892294
$424$	−1.15809e6	+	565277.i	−0.312844	+	0.152703i
$425$		0			0
$426$	66805.4	+	83468.8i	0.0178356	+	0.0222844i
$427$		−	812399.i		−	0.215625i
$428$	341082.	+	76584.6i	0.0900014	+	0.0202084i
$429$		−	2.12552e6i		−	0.557600i
$430$		0			0
$431$	−1.92170e6			−0.498301			−0.249151	−	0.968465i	$-0.580151\pi$
$431$	−1.92170e6			−0.498301			−0.249151	+	0.968465i	$0.580151\pi$
$432$	248764.	−	526028.i	0.0641326	−	0.135613i
$433$	−3.16413e6			−0.811025			−0.405513	−	0.914089i	$-0.632907\pi$
$433$	−3.16413e6			−0.811025			−0.405513	+	0.914089i	$0.632907\pi$
$434$	197876.	−	158373.i	0.0504277	−	0.0403605i
$435$		0			0
$436$	−354203.	−	79530.7i	−0.0892352	−	0.0200364i
$437$		−	9.89244e6i		−	2.47799i
$438$	534310.	+	667584.i	0.133079	+	0.166273i
$439$	7.05163e6			1.74634			0.873169	−	0.487417i	$-0.162061\pi$
$439$	7.05163e6			1.74634			0.873169	+	0.487417i	$0.162061\pi$
$440$		0			0
$441$	3.29345e6			0.806408
$442$	−2.37622e6	−	2.96893e6i	−0.578538	−	0.722844i
$443$			722258.i			0.174857i	0.996171	+	0.0874285i	$0.0278649\pi$
$443$			722258.i			0.174857i	−0.996171	+	0.0874285i	$0.972135\pi$
$444$	1.31935e6	−	5.87594e6i	0.317616	−	1.41456i
$445$		0			0
$446$	2.86314e6	−	2.29156e6i	0.681563	−	0.545498i
$447$	658406.			0.155856
$448$	804840.	−	1.03145e6i	0.189459	−	0.242802i
$449$	−1.24334e6			−0.291055			−0.145528	−	0.989354i	$-0.546488\pi$
$449$	−1.24334e6			−0.291055			−0.145528	+	0.989354i	$0.546488\pi$
$450$		0			0
$451$		−	1.63188e6i		−	0.377786i
$452$	466808.	−	2.07900e6i	0.107471	−	0.478640i
$453$		−	555112.i		−	0.127097i
$454$	61776.8	+	77185.9i	0.0140665	+	0.0175751i
$455$		0			0
$456$	−3.74819e6	−	7.67896e6i	−0.844129	−	1.72938i
$457$	−4.26434e6			−0.955127			−0.477564	−	0.878597i	$-0.658480\pi$
$457$	−4.26434e6			−0.955127			−0.477564	+	0.878597i	$0.658480\pi$
$458$	−2.59938e6	−	3.24775e6i	−0.579037	−	0.723467i
$459$			545603.i			0.120877i
$460$		0			0
$461$		−	3.17128e6i		−	0.694997i	−0.937681	−	0.347498i	$-0.887031\pi$
$461$		−	3.17128e6i		−	0.694997i	0.937681	−	0.347498i	$-0.112969\pi$
$462$	−535323.	+	428453.i	−0.116684	+	0.0933895i
$463$	−605017.			−0.131164			−0.0655821	−	0.997847i	$-0.520890\pi$
$463$	−605017.			−0.131164			−0.0655821	+	0.997847i	$0.520890\pi$
$464$	2.11663e6	−	4.47575e6i	0.456404	−	0.965096i
$465$		0			0
$466$	−313018.	+	250528.i	−0.0667735	+	0.0534431i
$467$			7.35248e6i			1.56006i	0.625741	+	0.780031i	$0.284797\pi$
$467$			7.35248e6i			1.56006i	−0.625741	+	0.780031i	$0.715203\pi$
$468$	4.73252e6	+	1.06261e6i	0.998799	+	0.224265i
$469$			948832.i			0.199185i
$470$		0			0
$471$	−7.17943e6			−1.49121
$472$	−6.79352e6	+	3.31599e6i	−1.40359	+	0.685107i
$473$	−2.45834e6			−0.505230
$474$	3.62034e6	+	4.52337e6i	0.740122	+	0.924732i
$475$		0			0
$476$	−268751.	+	1.19693e6i	−0.0543666	+	0.242131i
$477$			1.54121e6i			0.310145i
$478$	2.28053e6	−	1.82525e6i	0.456527	−	0.365388i
$479$	3.01150e6			0.599714			0.299857	−	0.953984i	$-0.403061\pi$
$479$	3.01150e6			0.599714			0.299857	+	0.953984i	$0.403061\pi$
$480$		0			0
$481$	−6.14687e6			−1.21141
$482$	2.69377e6	−	2.15600e6i	0.528133	−	0.422698i
$483$		−	3.84464e6i		−	0.749874i
$484$	988439.	−	4.40217e6i	0.191795	−	0.854189i
$485$		0			0
$486$	−4.42094e6	−	5.52367e6i	−0.849032	−	1.06081i
$487$	3.76217e6			0.718813			0.359407	−	0.933181i	$-0.382979\pi$
$487$	3.76217e6			0.718813			0.359407	+	0.933181i	$0.382979\pi$
$488$	3.31003e6	−	1.61566e6i	0.629191	−	0.307115i
$489$	4.36315e6			0.825141
$490$		0			0
$491$			5.68936e6i			1.06502i	0.846422	+	0.532512i	$0.178752\pi$
$491$			5.68936e6i			1.06502i	−0.846422	+	0.532512i	$0.821248\pi$
$492$	7.71174e6	+	1.73155e6i	1.43628	+	0.322494i
$493$			4.64230e6i			0.860232i
$494$	−6.80932e6	+	5.44993e6i	−1.25541	+	1.00479i
$495$		0			0
$496$	1.03880e6	+	491259.i	0.189595	+	0.0896616i
$497$	−35202.0			−0.00639259
$498$	4.89374e6	−	3.91677e6i	0.884234	−	0.707709i
$499$			8.16772e6i			1.46842i	0.678924	+	0.734208i	$0.262447\pi$
$499$			8.16772e6i			1.46842i	−0.678924	+	0.734208i	$0.737553\pi$
$500$		0			0
$501$			1.11941e6i			0.199248i
$502$	1.15625e6	+	1.44466e6i	0.204782	+	0.255862i
$503$	−207353.			−0.0365419			−0.0182709	−	0.999833i	$-0.505816\pi$
$503$	−207353.			−0.0365419			−0.0182709	+	0.999833i	$0.505816\pi$
$504$	−686335.	−	1.40610e6i	−0.120354	−	0.246571i
$505$		0			0
$506$	−2.24888e6	−	2.80982e6i	−0.390472	−	0.487868i
$507$		−	2.54874e6i		−	0.440358i
$508$	−622635.	+	2.77300e6i	−0.107047	+	0.476751i
$509$		−	4.43777e6i		−	0.759224i	−0.925146	−	0.379612i	$-0.876057\pi$
$509$		−	4.43777e6i		−	0.759224i	0.925146	−	0.379612i	$-0.123943\pi$
$510$		0			0
$511$	−281546.			−0.0476977
$512$	5.80315e6	+	1.22793e6i	0.978338	+	0.207014i
$513$	1.25135e6			0.209936
$514$	3.89910e6	−	3.12070e6i	0.650963	−	0.521007i
$515$		0			0
$516$	2.60849e6	−	1.16173e7i	0.431286	−	1.92080i
$517$		−	2.14814e6i		−	0.353457i
$518$	1.23906e6	+	1.54812e6i	0.202893	+	0.253501i
$519$	−1.07892e7			−1.75821
$520$		0			0
$521$	8.59405e6			1.38709			0.693543	−	0.720415i	$-0.256049\pi$
$521$	8.59405e6			1.38709			0.693543	+	0.720415i	$0.256049\pi$
$522$	−3.69995e6	−	4.62284e6i	−0.594319	−	0.742561i
$523$			4.23189e6i			0.676519i	0.941053	+	0.338259i	$0.109838\pi$
$523$			4.23189e6i			0.676519i	−0.941053	+	0.338259i	$0.890162\pi$
$524$	2.62167e6	+	588656.i	0.417110	+	0.0936555i
$525$		0			0
$526$	2.00535e6	−	1.60501e6i	0.316029	−	0.252938i
$527$	−1.07745e6			−0.168994
$528$	−2.81031e6	−	1.32902e6i	−0.438701	−	0.207467i
$529$	1.37436e7			2.13531
$530$		0			0
$531$			9.04094e6i			1.39148i
$532$	2.74518e6	+	616387.i	0.420525	+	0.0944223i
$533$		−	8.06731e6i		−	1.23002i
$534$	−9.30172e6	−	1.16219e7i	−1.41160	−	1.76369i
$535$		0			0
$536$	−3.86591e6	+	1.88699e6i	−0.581219	+	0.283700i
$537$	−5.35264e6			−0.800999
$538$	1.36000e6	+	1.69923e6i	0.202574	+	0.253103i
$539$			2.15454e6i			0.319436i
$540$		0			0
$541$			1.04071e7i			1.52875i	0.644770	+	0.764377i	$0.276953\pi$
$541$			1.04071e7i			1.52875i	−0.644770	+	0.764377i	$0.723047\pi$
$542$	6.04255e6	−	4.83624e6i	0.883532	−	0.707147i
$543$	7.31296e6			1.06437
$544$	−5.41122e6	+	1.28540e6i	−0.783967	+	0.186226i
$545$		0			0
$546$	−2.64641e6	+	2.11809e6i	−0.379905	+	0.304062i
$547$			2.44104e6i			0.348825i	0.984673	+	0.174412i	$0.0558026\pi$
$547$			2.44104e6i			0.348825i	−0.984673	+	0.174412i	$0.944197\pi$
$548$	1.92990e6	−	8.59511e6i	0.274526	−	1.22264i
$549$		−	4.40505e6i		−	0.623763i
$550$		0			0
$551$	1.06472e7			1.49402
$552$	1.56646e7	−	7.64605e6i	2.18812	−	1.06804i
$553$	−1.90768e6			−0.265273
$554$	2.00684e6	+	2.50740e6i	0.277803	+	0.347096i
$555$		0			0
$556$	4.79590e6	+	1.07684e6i	0.657935	+	0.147729i
$557$			2.55398e6i			0.348803i	0.984675	+	0.174402i	$0.0557991\pi$
$557$			2.55398e6i			0.348803i	−0.984675	+	0.174402i	$0.944201\pi$
$558$	1.07294e6	−	858740.i	0.145878	−	0.116755i
$559$	−1.21530e7			−1.64495
$560$		0			0
$561$	2.91488e6			0.391034
$562$	−8.42702e6	+	6.74468e6i	−1.12547	+	0.900784i
$563$		−	6.75752e6i		−	0.898496i	−0.893407	−	0.449248i	$-0.851692\pi$
$563$		−	6.75752e6i		−	0.898496i	0.893407	−	0.449248i	$-0.148308\pi$
$564$	1.01514e7	+	2.27934e6i	1.34378	+	0.301726i
$565$		0			0
$566$	3.08643e6	+	3.85628e6i	0.404963	+	0.505973i
$567$	2.58674e6			0.337905
$568$	−70008.2	−	143427.i	−0.00910496	−	0.0186535i
$569$	−9.34676e6			−1.21027			−0.605133	−	0.796125i	$-0.706880\pi$
$569$	−9.34676e6			−1.21027			−0.605133	+	0.796125i	$0.706880\pi$
$570$		0			0
$571$			1.78748e6i			0.229431i	0.993398	+	0.114715i	$0.0365956\pi$
$571$			1.78748e6i			0.229431i	−0.993398	+	0.114715i	$0.963404\pi$
$572$	−695152.	+	3.09597e6i	−0.0888361	+	0.395646i
$573$		−	1.27036e7i		−	1.61637i
$574$	−2.03179e6	+	1.62617e6i	−0.257394	+	0.206009i
$575$		0			0
$576$	4.36406e6	−	5.59279e6i	0.548068	−	0.702381i
$577$	−8.09579e6			−1.01232			−0.506162	−	0.862438i	$-0.668936\pi$
$577$	−8.09579e6			−1.01232			−0.506162	+	0.862438i	$0.668936\pi$
$578$	−2.19926e6	+	1.76020e6i	−0.273814	+	0.219151i
$579$			1.65425e7i			2.05071i
$580$		0			0
$581$			2.06388e6i			0.253655i
$582$	−1.17861e7	−	1.47259e7i	−1.44232	−	1.80208i
$583$	−1.00824e6			−0.122855
$584$	−559926.	−	1.14713e6i	−0.0679358	−	0.139181i
$585$		0			0
$586$	−1.49424e6	−	1.86695e6i	−0.179753	−	0.224589i
$587$			3.38443e6i			0.405407i	0.979240	+	0.202703i	$0.0649727\pi$
$587$			3.38443e6i			0.405407i	−0.979240	+	0.202703i	$0.935027\pi$
$588$	−1.01817e7	−	2.28614e6i	−1.21444	−	0.272684i
$589$			2.47117e6i			0.293504i
$590$		0			0
$591$	4.07736e6			0.480186
$592$	−3.84345e6	+	8.12722e6i	−0.450731	+	0.953099i
$593$	1.19814e7			1.39917			0.699585	−	0.714549i	$-0.253368\pi$
$593$	1.19814e7			1.39917			0.699585	+	0.714549i	$0.253368\pi$
$594$	355432.	−	284475.i	0.0413323	−	0.0330809i
$595$		0			0
$596$	−959013.	−	215331.i	−0.110588	−	0.0248309i
$597$		−	2.03458e7i		−	2.33636i
$598$	−1.11175e7	−	1.38906e7i	−1.27132	−	1.58843i
$599$	5.66907e6			0.645572			0.322786	−	0.946472i	$-0.395381\pi$
$599$	5.66907e6			0.645572			0.322786	+	0.946472i	$0.395381\pi$
$600$		0			0
$601$	−2.59514e6			−0.293072			−0.146536	−	0.989205i	$-0.546812\pi$
$601$	−2.59514e6			−0.293072			−0.146536	+	0.989205i	$0.546812\pi$
$602$	2.44974e6	+	3.06079e6i	0.275505	+	0.344225i
$603$			5.14483e6i			0.576206i
$604$	−181549.	+	808559.i	−0.0202489	+	0.0901819i
$605$		0			0
$606$	−1.85262e7	+	1.48277e7i	−2.04930	+	1.64019i
$607$	1.37152e7			1.51089			0.755443	−	0.655214i	$-0.227422\pi$
$607$	1.37152e7			1.51089			0.755443	+	0.655214i	$0.227422\pi$
$608$	2.94809e6	+	1.24108e7i	0.323431	+	1.36157i
$609$	4.13799e6			0.452112
$610$		0			0
$611$		−	1.06195e7i		−	1.15080i
$612$	−1.45724e6	+	6.49006e6i	−0.157272	+	0.700438i
$613$		−	8.09513e6i		−	0.870107i	−0.900405	−	0.435054i	$-0.856729\pi$
$613$		−	8.09513e6i		−	0.870107i	0.900405	−	0.435054i	$-0.143271\pi$
$614$	4.88943e6	+	6.10902e6i	0.523405	+	0.653959i
$615$		0			0
$616$	919859.	−	448994.i	0.0976719	−	0.0476748i
$617$	−5.98284e6			−0.632695			−0.316347	−	0.948643i	$-0.602457\pi$
$617$	−5.98284e6			−0.632695			−0.316347	+	0.948643i	$0.602457\pi$
$618$	−4.59366e6	−	5.73947e6i	−0.483825	−	0.604506i
$619$			719050.i			0.0754280i	0.999289	+	0.0377140i	$0.0120076\pi$
$619$			719050.i			0.0754280i	−0.999289	+	0.0377140i	$0.987992\pi$
$620$		0			0
$621$			2.55268e6i			0.265624i
$622$	−8.69051e6	+	6.95557e6i	−0.900678	+	0.720870i
$623$	4.90139e6			0.505940
$624$	−1.38930e7	−	6.57013e6i	−1.42835	−	0.675480i
$625$		0			0
$626$	1.07198e7	−	8.57977e6i	1.09333	−	0.875064i
$627$		−	6.68536e6i		−	0.679135i
$628$	1.04573e7	+	2.34803e6i	1.05809	+	0.237577i
$629$		−	8.42965e6i		−	0.849538i
$630$		0			0
$631$	−8.84500e6			−0.884350			−0.442175	−	0.896929i	$-0.645793\pi$
$631$	−8.84500e6			−0.884350			−0.442175	+	0.896929i	$0.645793\pi$
$632$	−3.79391e6	−	7.77263e6i	−0.377828	−	0.774061i
$633$	−1.02359e6			−0.101535
$634$	4.54685e6	+	5.68098e6i	0.449249	+	0.561307i
$635$		0			0
$636$	1.06982e6	−	4.76463e6i	0.104874	−	0.467075i
$637$			1.06511e7i			1.04003i
$638$	3.02421e6	−	2.42047e6i	0.294144	−	0.235423i
$639$	−190875.			−0.0184925
$640$		0			0
$641$	−1.09511e7			−1.05272			−0.526360	−	0.850262i	$-0.676443\pi$
$641$	−1.09511e7			−1.05272			−0.526360	+	0.850262i	$0.676443\pi$
$642$	−1.03420e6	+	827734.i	−0.0990298	+	0.0792599i
$643$			3.55893e6i			0.339462i	0.985490	+	0.169731i	$0.0542899\pi$
$643$			3.55893e6i			0.339462i	−0.985490	+	0.169731i	$0.945710\pi$
$644$	−1.25739e6	+	5.59999e6i	−0.119469	+	0.532074i
$645$		0			0
$646$	−7.47389e6	−	9.33812e6i	−0.704637	−	0.880396i
$647$	2.00678e7			1.88469			0.942343	−	0.334649i	$-0.108618\pi$
$647$	2.00678e7			1.88469			0.942343	+	0.334649i	$0.108618\pi$
$648$	5.14439e6	+	1.05394e7i	0.481278	+	0.986001i
$649$	−5.91449e6			−0.551195
$650$		0			0
$651$			960407.i			0.0888184i
$652$	−6.35523e6	−	1.42697e6i	−0.585480	−	0.131460i
$653$			1.67704e7i			1.53907i	0.638602	+	0.769537i	$0.279513\pi$
$653$			1.67704e7i			1.53907i	−0.638602	+	0.769537i	$0.720487\pi$
$654$	1.07398e6	−	859576.i	0.0981867	−	0.0785851i
$655$		0			0
$656$	−1.06664e7	−	5.04424e6i	−0.967737	−	0.457653i
$657$	−1.52662e6			−0.137980
$658$	−2.67457e6	+	2.14063e6i	−0.240818	+	0.192742i
$659$		−	1.99619e7i		−	1.79055i	−0.445510	−	0.895277i	$-0.646978\pi$
$659$		−	1.99619e7i		−	1.79055i	0.445510	−	0.895277i	$-0.353022\pi$
$660$		0			0
$661$			4.41003e6i			0.392589i	0.980545	+	0.196295i	$0.0628909\pi$
$661$			4.41003e6i			0.392589i	−0.980545	+	0.196295i	$0.937109\pi$
$662$	−1.08870e7	−	1.36026e7i	−0.965526	−	1.20636i
$663$	1.44099e7			1.27315
$664$	−8.40904e6	+	4.10455e6i	−0.740161	+	0.361281i
$665$		0			0
$666$	6.71850e6	+	8.39431e6i	0.586931	+	0.733330i
$667$			2.17197e7i			1.89033i
$668$	366102.	−	1.63049e6i	0.0317439	−	0.141377i
$669$			1.38965e7i			1.20044i
$670$		0			0
$671$	2.88174e6			0.247086
$672$	1.14576e6	+	4.82338e6i	0.0978747	+	0.412030i
$673$	−1.91274e7			−1.62787			−0.813933	−	0.580959i	$-0.802678\pi$
$673$	−1.91274e7			−1.62787			−0.813933	+	0.580959i	$0.802678\pi$
$674$	6.67039e6	−	5.33874e6i	0.565590	−	0.452677i
$675$		0			0
$676$	−833565.	+	3.71242e6i	−0.0701573	+	0.312457i
$677$		−	1.47330e7i		−	1.23544i	−0.786399	−	0.617718i	$-0.788057\pi$
$677$		−	1.47330e7i		−	1.23544i	0.786399	−	0.617718i	$-0.211943\pi$
$678$	5.04531e6	+	6.30377e6i	0.421515	+	0.526655i
$679$	6.21048e6			0.516953
$680$		0			0
$681$	−374628.			−0.0309551
$682$	561779.	+	701905.i	0.0462493	+	0.0577853i
$683$			2.53230e6i			0.207713i	0.994592	+	0.103856i	$0.0331182\pi$
$683$			2.53230e6i			0.207713i	−0.994592	+	0.103856i	$0.966882\pi$
$684$	1.48851e7	+	3.34222e6i	1.21650	+	0.273146i
$685$		0			0
$686$	5.64617e6	−	4.51899e6i	0.458082	−	0.366633i
$687$	1.57632e7			1.27425
$688$	−7.59890e6	+	1.60684e7i	−0.612040	+	1.29420i
$689$	−4.98432e6			−0.399998
$690$		0			0
$691$		−	2.97284e6i		−	0.236852i	−0.992963	−	0.118426i	$-0.962215\pi$
$691$		−	2.97284e6i		−	0.236852i	0.992963	−	0.118426i	$-0.0377848\pi$
$692$	1.57152e7	+	3.52861e6i	1.24754	+	0.280116i
$693$		−	1.22417e6i		−	0.0968294i
$694$	−1.41836e7	−	1.77214e7i	−1.11786	−	1.39669i
$695$		0			0
$696$	8.22945e6	+	1.68598e7i	0.643943	+	1.31926i
$697$	1.10633e7			0.862586
$698$	2.10479e6	+	2.62979e6i	0.163519	+	0.204306i
$699$		−	1.51926e6i		−	0.117608i
$700$		0			0
$701$		−	9.09229e6i		−	0.698841i	−0.936966	−	0.349420i	$-0.886379\pi$
$701$		−	9.09229e6i		−	0.698841i	0.936966	−	0.349420i	$-0.113621\pi$
$702$	1.75710e6	−	1.40632e6i	0.134572	−	0.107706i
$703$	−1.93336e7			−1.47545
$704$	3.65875e6	+	2.85493e6i	0.278228	+	0.217102i
$705$		0			0
$706$	4.65178e6	−	3.72312e6i	0.351243	−	0.281122i
$707$		−	7.81324e6i		−	0.587872i
$708$	6.27574e6	−	2.79500e7i	0.470524	−	2.09555i
$709$			3.91601e6i			0.292569i	0.989243	+	0.146284i	$0.0467315\pi$
$709$			3.91601e6i			0.292569i	−0.989243	+	0.146284i	$0.953269\pi$
$710$		0			0
$711$	−1.03440e7			−0.767384
$712$	9.74767e6	+	1.99702e7i	0.720611	+	1.47632i
$713$	−5.04103e6			−0.371360
$714$	−2.90469e6	−	3.62921e6i	−0.213233	−	0.266420i
$715$		0			0
$716$	7.79648e6	+	1.75058e6i	0.568350	+	0.127614i
$717$			1.10687e7i			0.804082i
$718$	−2.42757e6	+	1.94294e6i	−0.175736	+	0.140653i
$719$	1.30009e7			0.937890			0.468945	−	0.883227i	$-0.344634\pi$
$719$	1.30009e7			0.937890			0.468945	+	0.883227i	$0.344634\pi$
$720$		0			0
$721$	2.42056e6			0.173411
$722$	−1.04816e7	+	8.38908e6i	−0.748314	+	0.598924i
$723$			1.30744e7i			0.930202i
$724$	−1.06518e7	−	2.39170e6i	−0.755227	−	0.169574i
$725$		0			0
$726$	1.06832e7	+	1.33479e7i	0.752243	+	0.939876i
$727$	−2.08574e7			−1.46361			−0.731804	−	0.681515i	$-0.761321\pi$
$727$	−2.08574e7			−1.46361			−0.731804	+	0.681515i	$0.761321\pi$
$728$	4.54739e6	−	2.21963e6i	0.318005	−	0.155222i
$729$	1.10661e7			0.771214
$730$		0			0
$731$		−	1.66663e7i		−	1.15357i
$732$	−3.05775e6	+	1.36182e7i	−0.210923	+	0.939381i
$733$			2.35771e6i			0.162081i	0.996711	+	0.0810403i	$0.0258242\pi$
$733$			2.35771e6i			0.162081i	−0.996711	+	0.0810403i	$0.974176\pi$
$734$	1.38308e6	−	1.10697e6i	0.0947560	−	0.0758393i
$735$		0			0
$736$	−2.53172e7	+	6.01391e6i	−1.72274	+	0.409225i
$737$	−3.36569e6			−0.228247
$738$	−1.10169e7	+	8.81753e6i	−0.744593	+	0.595945i
$739$		−	1.75976e7i		−	1.18534i	−0.805445	−	0.592670i	$-0.798074\pi$
$739$		−	1.75976e7i		−	1.18534i	0.805445	−	0.592670i	$-0.201926\pi$
$740$		0			0
$741$		−	3.30496e7i		−	2.21116i
$742$	1.00472e6	+	1.25532e6i	0.0669936	+	0.0837040i
$743$	−2.71312e6			−0.180301			−0.0901504	−	0.995928i	$-0.528735\pi$
$743$	−2.71312e6			−0.180301			−0.0901504	+	0.995928i	$0.528735\pi$
$744$	−3.91307e6	+	1.91001e6i	−0.259170	+	0.126504i
$745$		0			0
$746$	−889908.	−	1.11188e6i	−0.0585461	−	0.0731494i
$747$			1.11909e7i			0.733777i
$748$	−4.24573e6	−	953312.i	−0.277459	−	0.0622990i
$749$		−	436161.i		−	0.0284081i
$750$		0			0
$751$	1.51201e7			0.978262			0.489131	−	0.872210i	$-0.337314\pi$
$751$	1.51201e7			0.978262			0.489131	+	0.872210i	$0.337314\pi$
$752$	−1.40408e7	−	6.64005e6i	−0.905414	−	0.428180i
$753$	−7.01176e6			−0.450650
$754$	1.49504e7	−	1.19658e7i	0.957690	−	0.766500i
$755$		0			0
$756$	−708377.	−	159055.i	−0.0450775	−	0.0101214i
$757$		−	1.87944e7i		−	1.19204i	−0.802971	−	0.596018i	$-0.796749\pi$
$757$		−	1.87944e7i		−	1.19204i	0.802971	−	0.596018i	$-0.203251\pi$
$758$	−3.04917e6	−	3.80974e6i	−0.192757	−	0.240836i
$759$	1.36377e7			0.859284
$760$		0			0
$761$	−1.06723e7			−0.668031			−0.334016	−	0.942567i	$-0.608404\pi$
$761$	−1.06723e7			−0.668031			−0.334016	+	0.942567i	$0.608404\pi$
$762$	−6.72950e6	−	8.40805e6i	−0.419851	−	0.524576i
$763$			452940.i			0.0281663i
$764$	−4.15471e6	+	1.85037e7i	−0.257518	+	1.14690i
$765$		0			0
$766$	1.80679e7	−	1.44609e7i	1.11259	−	0.890480i
$767$	−2.92387e7			−1.79461
$768$	−1.73737e7	+	1.42608e7i	−1.06289	+	0.872450i
$769$	−2.98430e7			−1.81981			−0.909905	−	0.414816i	$-0.863846\pi$
$769$	−2.98430e7			−1.81981			−0.909905	+	0.414816i	$0.863846\pi$
$770$		0			0
$771$			1.89246e7i			1.14654i
$772$	5.41022e6	−	2.40953e7i	0.326717	−	1.45509i
$773$			1.33577e6i			0.0804049i	0.999192	+	0.0402024i	$0.0128003\pi$
$773$			1.33577e6i			0.0804049i	−0.999192	+	0.0402024i	$0.987200\pi$
$774$	1.32832e7	+	1.65964e7i	0.796984	+	0.995777i
$775$		0			0
$776$	1.23511e7	+	2.53039e7i	0.736295	+	1.50846i
$777$	−7.51391e6			−0.446492
$778$	1.90591e7	+	2.38131e7i	1.12890	+	1.41048i
$779$		−	2.53740e7i		−	1.49811i
$780$		0			0
$781$		−	124868.i		−	0.00732530i
$782$	1.90491e7	−	1.52462e7i	1.11393	−	0.891550i
$783$	−2.74745e6			−0.160150
$784$	1.40826e7	+	6.65983e6i	0.818265	+	0.386966i
$785$		0			0
$786$	−7.94921e6	+	6.36226e6i	−0.458952	+	0.367329i
$787$			1.08897e7i			0.626729i	0.949633	+	0.313364i	$0.101456\pi$
$787$			1.08897e7i			0.626729i	−0.949633	+	0.313364i	$0.898544\pi$
$788$	−5.93895e6	−	1.33350e6i	−0.340717	−	0.0765027i
$789$			9.73315e6i			0.556623i
$790$		0			0
$791$	−2.65854e6			−0.151078
$792$	4.98773e6	−	2.43457e6i	0.282546	−	0.137914i
$793$	1.42461e7			0.804476
$794$	1.91551e7	+	2.39330e7i	1.07828	+	1.34724i
$795$		0			0
$796$	−6.65409e6	+	2.96351e7i	−0.372226	+	1.65777i
$797$			1.87183e7i			1.04381i	0.853004	+	0.521904i	$0.174778\pi$
$797$			1.87183e7i			1.04381i	−0.853004	+	0.521904i	$0.825222\pi$
$798$	−8.32369e6	+	6.66198e6i	−0.462710	+	0.370336i
$799$	1.45633e7			0.807035
$800$		0			0
$801$	2.65767e7			1.46359
$802$	1.42528e7	−	1.14075e7i	0.782466	−	0.626258i
$803$		−	998699.i		−	0.0546570i
$804$	3.57126e6	−	1.59052e7i	0.194842	−	0.867759i
$805$		0			0
$806$	2.77720e6	+	3.46992e6i	0.150581	+	0.188140i
$807$	−8.24735e6			−0.445790
$808$	3.18342e7	−	1.55386e7i	1.71540	−	0.837305i
$809$	1.03428e6			0.0555608			0.0277804	−	0.999614i	$-0.491156\pi$
$809$	1.03428e6			0.0555608			0.0277804	+	0.999614i	$0.491156\pi$
$810$		0			0
$811$		−	2.15728e7i		−	1.15174i	−0.817542	−	0.575870i	$-0.804664\pi$
$811$		−	2.15728e7i		−	1.15174i	0.817542	−	0.575870i	$-0.195336\pi$
$812$	−6.02727e6	−	1.35333e6i	−0.320797	−	0.0720300i
$813$			2.93280e7i			1.55617i
$814$	−5.49147e6	+	4.39518e6i	−0.290488	+	0.232496i
$815$		0			0
$816$	9.01010e6	−	1.90524e7i	0.473701	−	1.00167i
$817$	−3.82246e7			−2.00349
$818$	−2.31174e6	+	1.85024e6i	−0.120797	+	0.0966816i
$819$		−	6.05176e6i		−	0.315262i
$820$		0			0
$821$			1.19912e7i			0.620874i	0.950594	+	0.310437i	$0.100475\pi$
$821$			1.19912e7i			0.620874i	−0.950594	+	0.310437i	$0.899525\pi$
$822$	2.08585e7	+	2.60613e7i	1.07672	+	1.34529i
$823$	1.47880e7			0.761045			0.380523	−	0.924772i	$-0.375744\pi$
$823$	1.47880e7			0.761045			0.380523	+	0.924772i	$0.375744\pi$
$824$	4.81390e6	+	9.86229e6i	0.246990	+	0.506011i
$825$		0			0
$826$	5.89380e6	+	7.36391e6i	0.300570	+	0.375542i
$827$		−	3.13464e6i		−	0.159376i	−0.996820	−	0.0796882i	$-0.974608\pi$
$827$		−	3.13464e6i		−	0.159376i	0.996820	−	0.0796882i	$-0.0253925\pi$
$828$	−6.81791e6	+	3.03647e7i	−0.345601	+	1.53919i
$829$			1.80218e7i			0.910777i	0.890293	+	0.455389i	$0.150500\pi$
$829$			1.80218e7i			0.910777i	−0.890293	+	0.455389i	$0.849500\pi$
$830$		0			0
$831$	−1.21699e7			−0.611342
$832$	1.80873e7	+	1.41135e7i	0.905869	+	0.706851i
$833$	−1.46067e7			−0.729355
$834$	−1.45417e7	+	1.16386e7i	−0.723936	+	0.579412i
$835$		0			0
$836$	−2.18645e6	+	9.73769e6i	−0.108199	+	0.481882i
$837$		−	637670.i		−	0.0314617i
$838$	−1.29414e7	−	1.61694e7i	−0.636607	−	0.795398i
$839$	−3.26760e7			−1.60260			−0.801298	−	0.598265i	$-0.795857\pi$
$839$	−3.26760e7			−1.60260			−0.801298	+	0.598265i	$0.795857\pi$
$840$		0			0
$841$	−2.86572e6			−0.139715
$842$	1.11465e7	+	1.39268e7i	0.541824	+	0.676972i
$843$		−	4.09012e7i		−	1.98229i
$844$	1.49092e6	+	334764.i	0.0720443	+	0.0161764i
$845$		0			0
$846$	−1.45022e7	+	1.16071e7i	−0.696641	+	0.557566i
$847$	−5.62932e6			−0.269617
$848$	−3.11654e6	+	6.59013e6i	−0.148828	+	0.314706i
$849$	−1.87168e7			−0.891172
$850$		0			0
$851$		−	3.94393e7i		−	1.86683i
$852$	590089.	+	132495.i	0.0278496	+	0.00625318i
$853$			3.87723e6i			0.182452i	0.995830	+	0.0912261i	$0.0290786\pi$
$853$			3.87723e6i			0.182452i	−0.995830	+	0.0912261i	$0.970921\pi$
$854$	−2.87166e6	−	3.58794e6i	−0.134737	−	0.168345i
$855$		0			0
$856$	1.77709e6	−	867418.i	0.0828944	−	0.0404617i
$857$	−3.53502e6			−0.164414			−0.0822071	−	0.996615i	$-0.526197\pi$
$857$	−3.53502e6			−0.164414			−0.0822071	+	0.996615i	$0.526197\pi$
$858$	−7.51327e6	−	9.38732e6i	−0.348426	−	0.435335i
$859$			2.22265e7i			1.02775i	0.857864	+	0.513877i	$0.171791\pi$
$859$			2.22265e7i			1.02775i	−0.857864	+	0.513877i	$0.828209\pi$
$860$		0			0
$861$		−	9.86145e6i		−	0.453349i
$862$	−8.48714e6	+	6.79279e6i	−0.389039	+	0.311373i
$863$	−1.10828e7			−0.506549			−0.253274	−	0.967394i	$-0.581508\pi$
$863$	−1.10828e7			−0.506549			−0.253274	+	0.967394i	$0.581508\pi$
$864$	−760736.	−	3.20252e6i	−0.0346697	−	0.145951i
$865$		0			0
$866$	−1.39743e7	+	1.11845e7i	−0.633192	+	0.506784i
$867$		−	1.06743e7i		−	0.482270i
$868$	314101.	−	1.39890e6i	0.0141504	−	0.0630213i
$869$		−	6.76691e6i		−	0.303977i
$870$		0			0
$871$	−1.66386e7			−0.743139
$872$	−1.84545e6	+	900787.i	−0.0821887	+	0.0401172i
$873$	3.36749e7			1.49545
$874$	−3.49677e7	−	4.36897e7i	−1.54842	−	1.93464i
$875$		0			0
$876$	4.71954e6	+	1.05970e6i	0.207797	+	0.0466575i
$877$			1.24789e7i			0.547869i	0.961748	+	0.273934i	$0.0883251\pi$
$877$			1.24789e7i			0.547869i	−0.961748	+	0.273934i	$0.911675\pi$
$878$	3.11434e7	−	2.49260e7i	1.36342	−	1.09123i
$879$	9.06137e6			0.395569
$880$		0			0
$881$	−5.51270e6			−0.239290			−0.119645	−	0.992817i	$-0.538176\pi$
$881$	−5.51270e6			−0.239290			−0.119645	+	0.992817i	$0.538176\pi$
$882$	1.45455e7	−	1.16417e7i	0.629587	−	0.503899i
$883$			3.28692e7i			1.41869i	0.704861	+	0.709346i	$0.251009\pi$
$883$			3.28692e7i			1.41869i	−0.704861	+	0.709346i	$0.748991\pi$
$884$	−2.09891e7	−	4.71277e6i	−0.903364	−	0.202836i
$885$		0			0
$886$	2.55303e6	+	3.18984e6i	0.109263	+	0.136516i
$887$	2.60618e7			1.11223			0.556115	−	0.831105i	$-0.312291\pi$
$887$	2.60618e7			1.11223			0.556115	+	0.831105i	$0.312291\pi$
$888$	−1.49433e7	−	3.06146e7i	−0.635938	−	1.30285i
$889$	3.54600e6			0.150482
$890$		0			0
$891$			9.17567e6i			0.387207i
$892$	4.54485e6	−	2.02412e7i	0.191253	−	0.851774i
$893$		−	3.34013e7i		−	1.40163i
$894$	2.90783e6	−	2.32732e6i	0.121682	−	0.0973897i
$895$		0			0
$896$	−91392.0	−	7.40031e6i	−0.00380311	−	0.307950i
$897$	6.74190e7			2.79770
$898$	−5.49120e6	+	4.39496e6i	−0.227236	+	0.181871i
$899$		−	5.42566e6i		−	0.223900i
$900$		0			0
$901$		−	6.83536e6i		−	0.280511i
$902$	−5.76834e6	−	7.20715e6i	−0.236067	−	0.294949i
$903$	−1.48558e7			−0.606284
$904$	−5.28719e6	−	1.08319e7i	−0.215181	−	0.440844i
$905$		0			0
$906$	−1.96220e6	−	2.45164e6i	−0.0794189	−	0.0992285i
$907$		−	1.70037e7i		−	0.686319i	−0.939277	−	0.343160i	$-0.888503\pi$
$907$		−	1.70037e7i		−	0.686319i	0.939277	−	0.343160i	$-0.111497\pi$
$908$	545672.	+	122522.i	0.0219643	+	0.00493173i
$909$		−	4.23655e7i		−	1.70060i
$910$		0			0
$911$	2.80920e7			1.12147			0.560734	−	0.827996i	$-0.310519\pi$
$911$	2.80920e7			1.12147			0.560734	+	0.827996i	$0.310519\pi$
$912$	−4.36973e7	−	2.06649e7i	−1.73967	−	0.822709i
$913$	−7.32098e6			−0.290665
$914$	−1.88334e7	+	1.50735e7i	−0.745697	+	0.596829i
$915$		0			0
$916$	−2.29602e7	−	5.15536e6i	−0.904143	−	0.203011i
$917$		−	3.35249e6i		−	0.131657i
$918$	1.92859e6	+	2.40964e6i	0.0755324	+	0.0943726i
$919$	−4.45468e7			−1.73992			−0.869958	−	0.493126i	$-0.835854\pi$
$919$	−4.45468e7			−1.73992			−0.869958	+	0.493126i	$0.835854\pi$
$920$		0			0
$921$	−2.96506e7			−1.15182
$922$	−1.12098e7	−	1.40059e7i	−0.434281	−	0.542605i
$923$		−	617297.i		−	0.0238501i
$924$	−849751.	+	3.78450e6i	−0.0327425	+	0.145824i
$925$		0			0
$926$	−2.67204e6	+	2.13861e6i	−0.102404	+	0.0819603i
$927$	1.31249e7			0.501646
$928$	−6.47277e6	−	2.72489e7i	−0.246729	−	1.03867i
$929$	2.74746e7			1.04446			0.522229	−	0.852805i	$-0.325100\pi$
$929$	2.74746e7			1.04446			0.522229	+	0.852805i	$0.325100\pi$
$930$		0			0
$931$			3.35008e7i			1.26672i
$932$	−496873.	+	2.21290e6i	−0.0187372	+	0.0834493i
$933$		−	4.21801e7i		−	1.58637i
$934$	2.59895e7	+	3.24721e7i	0.974833	+	1.21799i
$935$		0			0
$936$	2.46572e7	−	1.20355e7i	0.919929	−	0.449028i
$937$	2.68158e7			0.997795			0.498898	−	0.866661i	$-0.333738\pi$
$937$	2.68158e7			0.997795			0.498898	+	0.866661i	$0.333738\pi$
$938$	3.35392e6	+	4.19050e6i	0.124465	+	0.155510i
$939$			5.20296e7i			1.92569i
$940$		0			0
$941$			431928.i			0.0159015i	0.999968	+	0.00795074i	$0.00253083\pi$
$941$			431928.i			0.0159015i	−0.999968	+	0.00795074i	$0.997469\pi$
$942$	−3.17078e7	+	2.53778e7i	−1.16423	+	0.931807i
$943$	5.17612e7			1.89551
$944$	−1.82821e7	+	3.86586e7i	−0.667722	+	1.41194i
$945$		0			0
$946$	−1.08572e7	+	8.68972e6i	−0.394449	+	0.315702i
$947$		−	4.14162e7i		−	1.50070i	−0.661039	−	0.750352i	$-0.729884\pi$
$947$		−	4.14162e7i		−	1.50070i	0.661039	−	0.750352i	$-0.270116\pi$
$948$	3.19783e7	+	7.18022e6i	1.15567	+	0.259488i
$949$		−	4.93714e6i		−	0.177955i
$950$		0			0
$951$	−2.75731e7			−0.988631
$952$	3.04395e6	+	6.23617e6i	0.108854	+	0.223011i
$953$	−2.33270e7			−0.832006			−0.416003	−	0.909363i	$-0.636569\pi$
$953$	−2.33270e7			−0.832006			−0.416003	+	0.909363i	$0.636569\pi$
$954$	5.44784e6	+	6.80671e6i	0.193800	+	0.242140i
$955$		0			0
$956$	3.62003e6	−	1.61224e7i	0.128105	−	0.570538i
$957$			1.46783e7i			0.518078i
$958$	1.33002e7	−	1.06450e7i	0.468215	−	0.374742i
$959$	−1.09911e7			−0.385917
$960$		0			0
$961$	−2.73699e7			−0.956014
$962$	−2.71475e7	+	2.17279e7i	−0.945785	+	0.756972i
$963$		−	2.36498e6i		−	0.0821793i
$964$	4.27599e6	−	1.90438e7i	0.148199	−	0.660027i
$965$		0			0
$966$	−1.35900e7	−	1.69798e7i	−0.468572	−	0.585449i
$967$	−2.07177e7			−0.712485			−0.356243	−	0.934393i	$-0.615942\pi$
$967$	−2.07177e7			−0.712485			−0.356243	+	0.934393i	$0.615942\pi$
$968$	−1.11953e7	−	2.29360e7i	−0.384015	−	0.786737i
$969$	4.53233e7			1.55064
$970$		0			0
$971$		−	1.95292e7i		−	0.664716i	−0.943153	−	0.332358i	$-0.892156\pi$
$971$		−	1.95292e7i		−	0.664716i	0.943153	−	0.332358i	$-0.107844\pi$
$972$	−3.90500e7	−	8.76806e6i	−1.32573	−	0.297672i
$973$		−	6.13280e6i		−	0.207671i
$974$	1.66155e7	−	1.32985e7i	0.561199	−	0.449164i
$975$		0			0
$976$	8.90765e6	−	1.88358e7i	0.299322	−	0.632935i
$977$	3.94484e7			1.32219			0.661093	−	0.750304i	$-0.270093\pi$
$977$	3.94484e7			1.32219			0.661093	+	0.750304i	$0.270093\pi$
$978$	1.92698e7	−	1.54228e7i	0.644212	−	0.515604i
$979$			1.73862e7i			0.579760i
$980$		0			0
$981$			2.45596e6i			0.0814797i
$982$	2.01107e7	+	2.51269e7i	0.665500	+	0.831497i
$983$	−5.47261e7			−1.80639			−0.903194	−	0.429233i	$-0.858784\pi$
$983$	−5.47261e7			−1.80639			−0.903194	+	0.429233i	$0.858784\pi$
$984$	4.01794e7	−	1.96120e7i	1.32287	−	0.645705i
$985$		0			0
$986$	1.64095e7	+	2.05026e7i	0.537532	+	0.671609i
$987$		−	1.29812e7i		−	0.424153i
$988$	−1.08089e7	+	4.81390e7i	−0.352280	+	1.56893i
$989$		−	7.79756e7i		−	2.53494i
$990$		0			0
$991$	3.95278e7			1.27855			0.639276	−	0.768977i	$-0.279234\pi$
$991$	3.95278e7			1.27855			0.639276	+	0.768977i	$0.279234\pi$
$992$	6.32433e6	−	1.50230e6i	0.204049	−	0.0484705i
$993$	6.60213e7			2.12476
$994$	−155469.	+	124432.i	−0.00499089	+	0.00399452i
$995$		0			0
$996$	7.76813e6	−	3.45966e7i	0.248124	−	1.10506i
$997$			1.20027e7i			0.382421i	0.981549	+	0.191210i	$0.0612413\pi$
$997$			1.20027e7i			0.382421i	−0.981549	+	0.191210i	$0.938759\pi$
$998$	2.88711e7	+	3.60725e7i	0.917567	+	1.14644i
$999$	4.98892e6			0.158159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.e.101.21		28
4.3	odd	2		800.6.d.e.401.17		28
5.2	odd	4		40.6.f.a.29.22	yes	28
5.3	odd	4		40.6.f.a.29.7	✓	28
5.4	even	2	inner	200.6.d.e.101.8		28
8.3	odd	2		800.6.d.e.401.18		28
8.5	even	2	inner	200.6.d.e.101.22		28
20.3	even	4		160.6.f.a.49.23		28
20.7	even	4		160.6.f.a.49.6		28
20.19	odd	2		800.6.d.e.401.12		28
40.3	even	4		160.6.f.a.49.5		28
40.13	odd	4		40.6.f.a.29.21	yes	28
40.19	odd	2		800.6.d.e.401.11		28
40.27	even	4		160.6.f.a.49.24		28
40.29	even	2	inner	200.6.d.e.101.7		28
40.37	odd	4		40.6.f.a.29.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.7	✓	28	5.3	odd	4
40.6.f.a.29.8	yes	28	40.37	odd	4
40.6.f.a.29.21	yes	28	40.13	odd	4
40.6.f.a.29.22	yes	28	5.2	odd	4
160.6.f.a.49.5		28	40.3	even	4
160.6.f.a.49.6		28	20.7	even	4
160.6.f.a.49.23		28	20.3	even	4
160.6.f.a.49.24		28	40.27	even	4
200.6.d.e.101.7		28	40.29	even	2	inner
200.6.d.e.101.8		28	5.4	even	2	inner
200.6.d.e.101.21		28	1.1	even	1	trivial
200.6.d.e.101.22		28	8.5	even	2	inner
800.6.d.e.401.11		28	40.19	odd	2
800.6.d.e.401.12		28	20.19	odd	2
800.6.d.e.401.17		28	4.3	odd	2
800.6.d.e.401.18		28	8.3	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.41648 - 3.53479i) q^{2} +21.4357i q^{3} +(7.01055 - 31.2226i) q^{4} +(75.7708 + 94.6704i) q^{6} -39.9262 q^{7} +(-79.4034 - 162.675i) q^{8} -216.491 q^{9} +O(q^{10})\)	\(q+(4.41648 - 3.53479i) q^{2} +21.4357i q^{3} +(7.01055 - 31.2226i) q^{4} +(75.7708 + 94.6704i) q^{6} -39.9262 q^{7} +(-79.4034 - 162.675i) q^{8} -216.491 q^{9} -141.626i q^{11} +(669.280 + 150.276i) q^{12} -700.139i q^{13} +(-176.333 + 141.131i) q^{14} +(-925.704 - 437.776i) q^{16} +960.152 q^{17} +(-956.126 + 765.249i) q^{18} -2202.13i q^{19} -855.847i q^{21} +(-500.618 - 625.488i) q^{22} +4492.21 q^{23} +(3487.05 - 1702.07i) q^{24} +(-2474.84 - 3092.15i) q^{26} +568.247i q^{27} +(-279.905 + 1246.60i) q^{28} +4834.96i q^{29} -1122.17 q^{31} +(-5635.80 + 1338.74i) q^{32} +3035.86 q^{33} +(4240.49 - 3393.93i) q^{34} +(-1517.72 + 6759.41i) q^{36} -8779.50i q^{37} +(-7784.07 - 9725.67i) q^{38} +15008.0 q^{39} +11522.4 q^{41} +(-3025.24 - 3779.83i) q^{42} -17358.0i q^{43} +(-4421.94 - 992.877i) q^{44} +(19839.7 - 15879.0i) q^{46} +15167.7 q^{47} +(9384.04 - 19843.2i) q^{48} -15212.9 q^{49} +20581.6i q^{51} +(-21860.2 - 4908.36i) q^{52} -7119.05i q^{53} +(2008.63 + 2509.65i) q^{54} +(3170.28 + 6494.99i) q^{56} +47204.3 q^{57} +(17090.6 + 21353.5i) q^{58} -41761.3i q^{59} +20347.5i q^{61} +(-4956.04 + 3966.64i) q^{62} +8643.65 q^{63} +(-20158.2 + 25833.9i) q^{64} +(13407.8 - 10731.1i) q^{66} -23764.7i q^{67} +(6731.19 - 29978.4i) q^{68} +96293.7i q^{69} +881.677 q^{71} +(17190.1 + 35217.6i) q^{72} +7051.66 q^{73} +(-31033.7 - 38774.5i) q^{74} +(-68756.4 - 15438.2i) q^{76} +5654.59i q^{77} +(66282.5 - 53050.1i) q^{78} +47780.1 q^{79} -64788.0 q^{81} +(50888.6 - 40729.4i) q^{82} -51692.3i q^{83} +(-26721.8 - 5999.96i) q^{84} +(-61356.8 - 76661.1i) q^{86} -103641. q^{87} +(-23039.0 + 11245.6i) q^{88} -122761. q^{89} +27953.9i q^{91} +(31492.8 - 140258. i) q^{92} -24054.6i q^{93} +(66987.8 - 53614.6i) q^{94} +(-28696.9 - 120807. i) q^{96} -155549. q^{97} +(-67187.4 + 53774.4i) q^{98} +30660.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 12 q^{4} - 156 q^{6} - 1940 q^{9}+O(q^{10}) \) 28 * q + 12 * q^4 - 156 * q^6 - 1940 * q^9	\( 28 q + 12 q^{4} - 156 q^{6} - 1940 q^{9} + 692 q^{14} + 1560 q^{16} + 2224 q^{24} - 9976 q^{26} + 4368 q^{31} - 13016 q^{34} - 34116 q^{36} - 23360 q^{39} - 2480 q^{41} - 10712 q^{44} + 58372 q^{46} + 38420 q^{49} + 3568 q^{54} + 110944 q^{56} + 46944 q^{64} - 136120 q^{66} - 69232 q^{71} - 34176 q^{74} - 13944 q^{76} + 35984 q^{79} + 122596 q^{81} + 165688 q^{84} - 73676 q^{86} + 178744 q^{89} - 314740 q^{94} - 236176 q^{96}+O(q^{100}) \) 28 * q + 12 * q^4 - 156 * q^6 - 1940 * q^9 + 692 * q^14 + 1560 * q^16 + 2224 * q^24 - 9976 * q^26 + 4368 * q^31 - 13016 * q^34 - 34116 * q^36 - 23360 * q^39 - 2480 * q^41 - 10712 * q^44 + 58372 * q^46 + 38420 * q^49 + 3568 * q^54 + 110944 * q^56 + 46944 * q^64 - 136120 * q^66 - 69232 * q^71 - 34176 * q^74 - 13944 * q^76 + 35984 * q^79 + 122596 * q^81 + 165688 * q^84 - 73676 * q^86 + 178744 * q^89 - 314740 * q^94 - 236176 * q^96

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