LMFDB - Embedded newform 200.6.f.a.149.3

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			149.3
Root			$1.51888 - 2.38600i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.a.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.03776 - 4.77200i) q^{2} +23.6095 q^{3} +(-13.5440 + 28.9924i) q^{4} +(-71.7200 - 112.665i) q^{6} +160.704i q^{7} +(179.495 - 23.4400i) q^{8} +314.408 q^{9} +O(q^{10})$	\(q+(-3.03776 - 4.77200i) q^{2} +23.6095 q^{3} +(-13.5440 + 28.9924i) q^{4} +(-71.7200 - 112.665i) q^{6} +160.704i q^{7} +(179.495 - 23.4400i) q^{8} +314.408 q^{9} +129.129i q^{11} +(-319.767 + 684.496i) q^{12} -759.659 q^{13} +(766.880 - 488.181i) q^{14} +(-657.120 - 785.347i) q^{16} +323.408i q^{17} +(-955.097 - 1500.36i) q^{18} +198.511i q^{19} +3794.14i q^{21} +(616.204 - 392.264i) q^{22} +1193.15i q^{23} +(4237.79 - 553.407i) q^{24} +(2307.66 + 3625.10i) q^{26} +1685.91 q^{27} +(-4659.20 - 2176.58i) q^{28} +5987.24i q^{29} -4872.45 q^{31} +(-1751.50 + 5521.47i) q^{32} +3048.67i q^{33} +(1543.30 - 982.437i) q^{34} +(-4258.34 + 9115.45i) q^{36} -3698.56 q^{37} +(947.297 - 603.031i) q^{38} -17935.2 q^{39} -10437.9 q^{41} +(18105.6 - 11525.7i) q^{42} +9873.11 q^{43} +(-3743.76 - 1748.93i) q^{44} +(5693.73 - 3624.51i) q^{46} -6297.98i q^{47} +(-15514.3 - 18541.6i) q^{48} -9018.79 q^{49} +7635.50i q^{51} +(10288.8 - 22024.4i) q^{52} -21728.1 q^{53} +(-5121.39 - 8045.16i) q^{54} +(3766.91 + 28845.6i) q^{56} +4686.75i q^{57} +(28571.1 - 18187.8i) q^{58} +33513.4i q^{59} +48506.8i q^{61} +(14801.3 + 23251.3i) q^{62} +50526.7i q^{63} +(31669.1 - 8414.75i) q^{64} +(14548.3 - 9261.14i) q^{66} +33182.4 q^{67} +(-9376.38 - 4380.24i) q^{68} +28169.7i q^{69} +59464.1 q^{71} +(56434.8 - 7369.74i) q^{72} -51278.6i q^{73} +(11235.4 + 17649.5i) q^{74} +(-5755.33 - 2688.64i) q^{76} -20751.6 q^{77} +(54482.8 + 85586.7i) q^{78} +73724.5 q^{79} -36597.7 q^{81} +(31707.8 + 49809.6i) q^{82} +61628.0 q^{83} +(-110001. - 51387.9i) q^{84} +(-29992.1 - 47114.5i) q^{86} +141356. i q^{87} +(3026.79 + 23178.1i) q^{88} +106735. q^{89} -122080. i q^{91} +(-34592.4 - 16160.1i) q^{92} -115036. q^{93} +(-30054.0 + 19131.8i) q^{94} +(-41352.1 + 130359. i) q^{96} +12562.9i q^{97} +(27397.0 + 43037.7i) q^{98} +40599.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.03776	−	4.77200i	−0.537006	−	0.843579i
$2$	−3.03776	−	4.77200i	−0.537006	−	0.843579i
$3$	23.6095			1.51455			0.757275	−	0.653096i	$-0.226530\pi$
$3$	23.6095			1.51455			0.757275	+	0.653096i	$0.226530\pi$
$4$	−13.5440	+	28.9924i	−0.423250	+	0.906013i
$5$		0			0
$5$		0			0
$6$	−71.7200	−	112.665i	−0.813322	−	1.27764i
$7$			160.704i			1.23960i	0.784760	+	0.619800i	$0.212786\pi$
$7$			160.704i			1.23960i	−0.784760	+	0.619800i	$0.787214\pi$
$8$	179.495	−	23.4400i	0.991581	−	0.129489i
$9$	314.408			1.29386
$10$		0			0
$11$			129.129i			0.321768i	0.986973	+	0.160884i	$0.0514345\pi$
$11$			129.129i			0.321768i	−0.986973	+	0.160884i	$0.948566\pi$
$12$	−319.767	+	684.496i	−0.641033	+	1.37220i
$13$	−759.659			−1.24670			−0.623348	−	0.781945i	$-0.714228\pi$
$13$	−759.659			−1.24670			−0.623348	+	0.781945i	$0.714228\pi$
$14$	766.880	−	488.181i	1.04570	−	0.665672i
$15$		0			0
$16$	−657.120	−	785.347i	−0.641719	−	0.766940i
$17$			323.408i			0.271412i	0.990749	+	0.135706i	$0.0433302\pi$
$17$			323.408i			0.271412i	−0.990749	+	0.135706i	$0.956670\pi$
$18$	−955.097	−	1500.36i	−0.694810	−	1.09147i
$19$			198.511i			0.126154i	0.998009	+	0.0630771i	$0.0200914\pi$
$19$			198.511i			0.126154i	−0.998009	+	0.0630771i	$0.979909\pi$
$20$		0			0
$21$			3794.14i			1.87744i
$22$	616.204	−	392.264i	0.271436	−	0.172791i
$23$			1193.15i			0.470302i	0.971959	+	0.235151i	$0.0755584\pi$
$23$			1193.15i			0.470302i	−0.971959	+	0.235151i	$0.924442\pi$
$24$	4237.79	−	553.407i	1.50180	−	0.196118i
$25$		0			0
$26$	2307.66	+	3625.10i	0.669483	+	1.05169i
$27$	1685.91			0.445066
$28$	−4659.20	−	2176.58i	−1.12309	−	0.524661i
$29$			5987.24i			1.32200i	0.750386	+	0.661000i	$0.229868\pi$
$29$			5987.24i			1.32200i	−0.750386	+	0.661000i	$0.770132\pi$
$30$		0			0
$31$	−4872.45			−0.910632			−0.455316	−	0.890330i	$-0.650474\pi$
$31$	−4872.45			−0.910632			−0.455316	+	0.890330i	$0.650474\pi$
$32$	−1751.50	+	5521.47i	−0.302368	+	0.953191i
$33$			3048.67i			0.487333i
$34$	1543.30	−	982.437i	0.228957	−	0.145750i
$35$		0			0
$36$	−4258.34	+	9115.45i	−0.547627	+	1.17225i
$37$	−3698.56			−0.444149			−0.222074	−	0.975030i	$-0.571283\pi$
$37$	−3698.56			−0.444149			−0.222074	+	0.975030i	$0.571283\pi$
$38$	947.297	−	603.031i	0.106421	−	0.0677455i
$39$	−17935.2			−1.88818
$40$		0			0
$41$	−10437.9			−0.969734			−0.484867	−	0.874588i	$-0.661132\pi$
$41$	−10437.9			−0.969734			−0.484867	+	0.874588i	$0.661132\pi$
$42$	18105.6	−	11525.7i	1.58377	−	1.00819i
$43$	9873.11			0.814297			0.407148	−	0.913362i	$-0.366523\pi$
$43$	9873.11			0.814297			0.407148	+	0.913362i	$0.366523\pi$
$44$	−3743.76	−	1748.93i	−0.291526	−	0.136188i
$45$		0			0
$46$	5693.73	−	3624.51i	0.396736	−	0.252555i
$47$		−	6297.98i		−	0.415869i	−0.978143	−	0.207935i	$-0.933326\pi$
$47$		−	6297.98i		−	0.415869i	0.978143	−	0.207935i	$-0.0666741\pi$
$48$	−15514.3	−	18541.6i	−0.971915	−	1.16157i
$49$	−9018.79			−0.536609
$50$		0			0
$51$			7635.50i			0.411067i
$52$	10288.8	−	22024.4i	0.527664	−	1.12952i
$53$	−21728.1			−1.06251			−0.531255	−	0.847212i	$-0.678279\pi$
$53$	−21728.1			−1.06251			−0.531255	+	0.847212i	$0.678279\pi$
$54$	−5121.39	−	8045.16i	−0.239003	−	0.375449i
$55$		0			0
$56$	3766.91	+	28845.6i	0.160515	+	1.22916i
$57$			4686.75i			0.191067i
$58$	28571.1	−	18187.8i	1.11521	−	0.709921i
$59$			33513.4i			1.25340i	0.779261	+	0.626699i	$0.215594\pi$
$59$			33513.4i			1.25340i	−0.779261	+	0.626699i	$0.784406\pi$
$60$		0			0
$61$			48506.8i			1.66908i	0.550944	+	0.834542i	$0.314268\pi$
$61$			48506.8i			1.66908i	−0.550944	+	0.834542i	$0.685732\pi$
$62$	14801.3	+	23251.3i	0.489015	+	0.768190i
$63$			50526.7i			1.60387i
$64$	31669.1	−	8414.75i	0.966465	−	0.256798i
$65$		0			0
$66$	14548.3	−	9261.14i	0.411104	−	0.261701i
$67$	33182.4			0.903068			0.451534	−	0.892254i	$-0.350877\pi$
$67$	33182.4			0.903068			0.451534	+	0.892254i	$0.350877\pi$
$68$	−9376.38	−	4380.24i	−0.245903	−	0.114875i
$69$			28169.7i			0.712295i
$70$		0			0
$71$	59464.1			1.39994			0.699970	−	0.714173i	$-0.253197\pi$
$71$	59464.1			1.39994			0.699970	+	0.714173i	$0.253197\pi$
$72$	56434.8	−	7369.74i	1.28297	−	0.167541i
$73$		−	51278.6i		−	1.12624i	−0.826377	−	0.563118i	$-0.809602\pi$
$73$		−	51278.6i		−	1.12624i	0.826377	−	0.563118i	$-0.190398\pi$
$74$	11235.4	+	17649.5i	0.238510	+	0.374675i
$75$		0			0
$76$	−5755.33	−	2688.64i	−0.114297	−	0.0533948i
$77$	−20751.6			−0.398863
$78$	54482.8	+	85586.7i	1.01396	+	1.59283i
$79$	73724.5			1.32906			0.664530	−	0.747262i	$-0.268632\pi$
$79$	73724.5			1.32906			0.664530	+	0.747262i	$0.268632\pi$
$80$		0			0
$81$	−36597.7			−0.619785
$82$	31707.8	+	49809.6i	0.520752	+	0.818047i
$83$	61628.0			0.981935			0.490967	−	0.871178i	$-0.336643\pi$
$83$	61628.0			0.981935			0.490967	+	0.871178i	$0.336643\pi$
$84$	−110001.	−	51387.9i	−1.70098	−	0.794625i
$85$		0			0
$86$	−29992.1	−	47114.5i	−0.437282	−	0.686923i
$87$			141356.i			2.00223i
$88$	3026.79	+	23178.1i	0.0416654	+	0.319059i
$89$	106735.			1.42834			0.714169	−	0.699974i	$-0.246805\pi$
$89$	106735.			1.42834			0.714169	+	0.699974i	$0.246805\pi$
$90$		0			0
$91$		−	122080.i		−	1.54540i
$92$	−34592.4	−	16160.1i	−0.426099	−	0.199055i
$93$	−115036.			−1.37920
$94$	−30054.0	+	19131.8i	−0.350818	+	0.223324i
$95$		0			0
$96$	−41352.1	+	130359.i	−0.457951	+	1.44366i
$97$			12562.9i			0.135569i	0.997700	+	0.0677846i	$0.0215931\pi$
$97$			12562.9i			0.135569i	−0.997700	+	0.0677846i	$0.978407\pi$
$98$	27397.0	+	43037.7i	0.288162	+	0.452672i
$99$			40599.2i			0.416323i
$100$		0			0
$101$			64962.8i			0.633667i	0.948481	+	0.316834i	$0.102620\pi$
$101$			64962.8i			0.633667i	−0.948481	+	0.316834i	$0.897380\pi$
$102$	36436.6	−	23194.8i	0.346767	−	0.220745i
$103$			69035.9i			0.641183i	0.947218	+	0.320591i	$0.103882\pi$
$103$			69035.9i			0.641183i	−0.947218	+	0.320591i	$0.896118\pi$
$104$	−136355.	+	17806.4i	−1.23620	+	0.161434i
$105$		0			0
$106$	66004.9	+	103687.i	0.570574	+	0.896311i
$107$	−187322.			−1.58172			−0.790858	−	0.612000i	$-0.790365\pi$
$107$	−187322.			−1.58172			−0.790858	+	0.612000i	$0.790365\pi$
$108$	−22834.0	+	48878.6i	−0.188374	+	0.403236i
$109$			49350.5i			0.397855i	0.980014	+	0.198928i	$0.0637459\pi$
$109$			49350.5i			0.397855i	−0.980014	+	0.198928i	$0.936254\pi$
$110$		0			0
$111$	−87321.2			−0.672686
$112$	126208.	−	105602.i	0.950699	−	0.795475i
$113$		−	171100.i		−	1.26053i	−0.776379	−	0.630266i	$-0.782946\pi$
$113$		−	171100.i		−	1.26053i	0.776379	−	0.630266i	$-0.217054\pi$
$114$	22365.2	−	14237.2i	0.161180	−	0.102604i
$115$		0			0
$116$	−173584.	−	81091.2i	−1.19775	−	0.559537i
$117$	−238843.			−1.61305
$118$	159926.	−	101806.i	1.05734	−	0.673082i
$119$	−51973.0			−0.336442
$120$		0			0
$121$	144377.			0.896466
$122$	231475.	−	147352.i	1.40800	−	0.896307i
$123$	−246433.			−1.46871
$124$	65992.5	−	141264.i	0.385425	−	0.825045i
$125$		0			0
$126$	241113.	−	153488.i	1.35299	−	0.861287i
$127$		−	90479.7i		−	0.497785i	−0.968531	−	0.248892i	$-0.919933\pi$
$127$		−	90479.7i		−	0.497785i	0.968531	−	0.248892i	$-0.0800666\pi$
$128$	−136358.	−	125563.i	−0.735626	−	0.677388i
$129$	233099.			1.23329
$130$		0			0
$131$		−	94491.0i		−	0.481074i	−0.970640	−	0.240537i	$-0.922676\pi$
$131$		−	94491.0i		−	0.481074i	0.970640	−	0.240537i	$-0.0773236\pi$
$132$	−88388.4	−	41291.2i	−0.441530	−	0.206264i
$133$	−31901.6			−0.156381
$134$	−100800.	−	158346.i	−0.484953	−	0.761809i
$135$		0			0
$136$	7580.70	+	58050.2i	0.0351449	+	0.269127i
$137$		−	5516.81i		−	0.0251123i	−0.999921	−	0.0125561i	$-0.996003\pi$
$137$		−	5516.81i		−	0.0251123i	0.999921	−	0.0125561i	$-0.00399685\pi$
$138$	134426.	−	85572.9i	0.600877	−	0.382506i
$139$		−	164489.i		−	0.722104i	−0.932546	−	0.361052i	$-0.882418\pi$
$139$		−	164489.i		−	0.722104i	0.932546	−	0.361052i	$-0.117582\pi$
$140$		0			0
$141$		−	148692.i		−	0.629854i
$142$	−180638.	−	283763.i	−0.751775	−	1.18096i
$143$		−	98094.2i		−	0.401147i
$144$	−206604.	−	246919.i	−0.830294	−	0.992314i
$145$		0			0
$146$	−244702.	+	155772.i	−0.950068	+	0.604795i
$147$	−212929.			−0.812722
$148$	50093.3	−	107230.i	0.187986	−	0.402405i
$149$			423122.i			1.56135i	0.624939	+	0.780674i	$0.285124\pi$
$149$			423122.i			1.56135i	−0.624939	+	0.780674i	$0.714876\pi$
$150$		0			0
$151$	−39975.1			−0.142675			−0.0713373	−	0.997452i	$-0.522727\pi$
$151$	−39975.1			−0.142675			−0.0713373	+	0.997452i	$0.522727\pi$
$152$	4653.12	+	35631.9i	0.0163356	+	0.125092i
$153$			101682.i			0.351169i
$154$	63038.3	+	99026.6i	0.214192	+	0.336473i
$155$		0			0
$156$	242914.	−	519984.i	0.799174	−	1.71072i
$157$	−367453.			−1.18974			−0.594870	−	0.803822i	$-0.702797\pi$
$157$	−367453.			−1.18974			−0.594870	+	0.803822i	$0.702797\pi$
$158$	−223958.	−	351814.i	−0.713712	−	1.12117i
$159$	−512991.			−1.60922
$160$		0			0
$161$	−191744.			−0.582986
$162$	111175.	+	174644.i	0.332828	+	0.522838i
$163$	16030.9			0.0472596			0.0236298	−	0.999721i	$-0.492478\pi$
$163$	16030.9			0.0472596			0.0236298	+	0.999721i	$0.492478\pi$
$164$	141371.	−	302619.i	0.410440	−	0.878591i
$165$		0			0
$166$	−187211.	−	294089.i	−0.527304	−	0.828339i
$167$		−	248107.i		−	0.688412i	−0.938894	−	0.344206i	$-0.888148\pi$
$167$		−	248107.i		−	0.688412i	0.938894	−	0.344206i	$-0.111852\pi$
$168$	88934.8	+	681031.i	0.243108	+	1.86163i
$169$	205789.			0.554251
$170$		0			0
$171$			62413.6i			0.163226i
$172$	−133721.	+	286245.i	−0.344651	+	0.737763i
$173$	574094.			1.45837			0.729185	−	0.684317i	$-0.239899\pi$
$173$	574094.			1.45837			0.729185	+	0.684317i	$0.239899\pi$
$174$	674549.	−	429405.i	1.68904	−	1.07521i
$175$		0			0
$176$	101411.	−	84853.3i	0.246777	−	0.206484i
$177$			791235.i			1.89833i
$178$	−324235.	−	509338.i	−0.767025	−	1.20491i
$179$			305296.i			0.712177i	0.934452	+	0.356088i	$0.115890\pi$
$179$			305296.i			0.712177i	−0.934452	+	0.356088i	$0.884110\pi$
$180$		0			0
$181$		−	421682.i		−	0.956728i	−0.878162	−	0.478364i	$-0.841230\pi$
$181$		−	421682.i		−	0.956728i	0.878162	−	0.478364i	$-0.158770\pi$
$182$	−582568.	+	370851.i	−1.30367	+	0.829891i
$183$			1.14522e6i			2.52791i
$184$	27967.5	+	214165.i	0.0608989	+	0.466342i
$185$		0			0
$186$	349452.	+	548952.i	0.740637	+	1.16346i
$187$	−41761.4			−0.0873315
$188$	182594.	+	85299.9i	0.376783	+	0.176017i
$189$			270932.i			0.551705i
$190$		0			0
$191$	−424231.			−0.841431			−0.420716	−	0.907193i	$-0.638221\pi$
$191$	−424231.			−0.841431			−0.420716	+	0.907193i	$0.638221\pi$
$192$	747692.	−	198668.i	1.46376	−	0.388933i
$193$			373902.i			0.722545i	0.932460	+	0.361272i	$0.117658\pi$
$193$			373902.i			0.722545i	−0.932460	+	0.361272i	$0.882342\pi$
$194$	59950.2	−	38163.1i	0.114363	−	0.0728014i
$195$		0			0
$196$	122151.	−	261477.i	0.227120	−	0.486175i
$197$	112848.			0.207171			0.103586	−	0.994621i	$-0.466968\pi$
$197$	112848.			0.207171			0.103586	+	0.994621i	$0.466968\pi$
$198$	193740.	−	123331.i	0.351201	−	0.223568i
$199$	−262938.			−0.470675			−0.235338	−	0.971914i	$-0.575620\pi$
$199$	−262938.			−0.470675			−0.235338	+	0.971914i	$0.575620\pi$
$200$		0			0
$201$	783419.			1.36774
$202$	310003.	−	197342.i	0.534548	−	0.340283i
$203$	−962173.			−1.63875
$204$	−221372.	−	103415.i	−0.372432	−	0.173984i
$205$		0			0
$206$	329439.	−	209715.i	0.540888	−	0.344319i
$207$			375137.i			0.608505i
$208$	499187.	+	596596.i	0.800028	+	0.956141i
$209$	−25633.6			−0.0405923
$210$		0			0
$211$			272968.i			0.422090i	0.977476	+	0.211045i	$0.0676866\pi$
$211$			272968.i			0.422090i	−0.977476	+	0.211045i	$0.932313\pi$
$212$	294286.	−	629951.i	0.449707	−	0.962648i
$213$	1.40392e6			2.12028
$214$	569039.	+	893899.i	0.849390	+	1.33430i
$215$		0			0
$216$	302613.	−	39517.8i	0.441319	−	0.0576313i
$217$		−	783022.i		−	1.12882i
$218$	235501.	−	149915.i	0.335622	−	0.213650i
$219$		−	1.21066e6i		−	1.70574i
$220$		0			0
$221$		−	245680.i		−	0.338368i
$222$	265261.	+	416697.i	0.361236	+	0.567463i
$223$		−	1.00553e6i		−	1.35405i	−0.735962	−	0.677023i	$-0.763270\pi$
$223$		−	1.00553e6i		−	1.35405i	0.735962	−	0.677023i	$-0.236730\pi$
$224$	−887323.	−	281473.i	−1.18158	−	0.374815i
$225$		0			0
$226$	−816490.	+	519761.i	−1.06336	+	0.676913i
$227$	−554991.			−0.714861			−0.357430	−	0.933940i	$-0.616347\pi$
$227$	−554991.			−0.714861			−0.357430	+	0.933940i	$0.616347\pi$
$228$	−135880.	−	63477.4i	−0.173109	−	0.0808690i
$229$			476013.i			0.599832i	0.953966	+	0.299916i	$0.0969587\pi$
$229$			476013.i			0.599832i	−0.953966	+	0.299916i	$0.903041\pi$
$230$		0			0
$231$	−489934.			−0.604098
$232$	140341.	+	1.07468e6i	0.171185	+	1.31087i
$233$		−	914141.i		−	1.10312i	−0.834135	−	0.551561i	$-0.814032\pi$
$233$		−	914141.i		−	1.10312i	0.834135	−	0.551561i	$-0.185968\pi$
$234$	725548.	+	1.13976e6i	0.866217	+	1.36074i
$235$		0			0
$236$	−971635.	−	453906.i	−1.13559	−	0.530501i
$237$	1.74060e6			2.01293
$238$	157882.	+	248015.i	0.180671	+	0.283815i
$239$	−375827.			−0.425592			−0.212796	−	0.977097i	$-0.568257\pi$
$239$	−375827.			−0.425592			−0.212796	+	0.977097i	$0.568257\pi$
$240$		0			0
$241$	612110.			0.678870			0.339435	−	0.940629i	$-0.389764\pi$
$241$	612110.			0.678870			0.339435	+	0.940629i	$0.389764\pi$
$242$	−438582.	−	688966.i	−0.481407	−	0.756239i
$243$	−1.27373e6			−1.38376
$244$	−1.40633e6	−	656977.i	−1.51221	−	0.706440i
$245$		0			0
$246$	748605.	+	1.17598e6i	0.788705	+	1.23897i
$247$		−	150801.i		−	0.157276i
$248$	−874582.	+	114210.i	−0.902966	+	0.117917i
$249$	1.45501e6			1.48719
$250$		0			0
$251$			462623.i			0.463493i	0.972776	+	0.231746i	$0.0744440\pi$
$251$			462623.i			0.463493i	−0.972776	+	0.231746i	$0.925556\pi$
$252$	−1.46489e6	−	684333.i	−1.45313	−	0.678838i
$253$	−154071.			−0.151328
$254$	−431769.	+	274856.i	−0.419921	+	0.267313i
$255$		0			0
$256$	−184963.	+	1.03213e6i	−0.176394	+	0.984320i
$257$		−	583345.i		−	0.550925i	−0.961312	−	0.275463i	$-0.911169\pi$
$257$		−	583345.i		−	0.550925i	0.961312	−	0.275463i	$-0.0888310\pi$
$258$	−708099.	−	1.11235e6i	−0.662285	−	1.04038i
$259$		−	594374.i		−	0.550567i
$260$		0			0
$261$			1.88244e6i			1.71048i
$262$	−450911.	+	287041.i	−0.405824	+	0.258339i
$263$			411975.i			0.367267i	0.982995	+	0.183633i	$0.0587859\pi$
$263$			411975.i			0.367267i	−0.982995	+	0.183633i	$0.941214\pi$
$264$	71461.0	+	547223.i	0.0631044	+	0.483230i
$265$		0			0
$266$	96909.5	+	152234.i	0.0839773	+	0.131919i
$267$	2.51995e6			2.16329
$268$	−449422.	+	962037.i	−0.382224	+	0.818191i
$269$		−	1.14460e6i		−	0.964436i	−0.876051	−	0.482218i	$-0.839831\pi$
$269$		−	1.14460e6i		−	0.964436i	0.876051	−	0.482218i	$-0.160169\pi$
$270$		0			0
$271$	−1.21607e6			−1.00586			−0.502928	−	0.864329i	$-0.667744\pi$
$271$	−1.21607e6			−1.00586			−0.502928	+	0.864329i	$0.667744\pi$
$272$	253987.	−	212518.i	0.208157	−	0.174170i
$273$		−	2.88225e6i		−	2.34059i
$274$	−26326.2	+	16758.7i	−0.0211842	+	0.0134854i
$275$		0			0
$276$	−816708.	−	381531.i	−0.645349	−	0.301479i
$277$	806054.			0.631196			0.315598	−	0.948893i	$-0.397795\pi$
$277$	806054.			0.631196			0.315598	+	0.948893i	$0.397795\pi$
$278$	−784942.	+	499679.i	−0.609152	+	0.387774i
$279$	−1.53194e6			−1.17823
$280$		0			0
$281$	1.19824e6			0.905272			0.452636	−	0.891695i	$-0.350484\pi$
$281$	1.19824e6			0.905272			0.452636	+	0.891695i	$0.350484\pi$
$282$	−709559.	+	451691.i	−0.531332	+	0.338235i
$283$	1.46287e6			1.08578			0.542888	−	0.839805i	$-0.317331\pi$
$283$	1.46287e6			1.08578			0.542888	+	0.839805i	$0.317331\pi$
$284$	−805382.	+	1.72401e6i	−0.592524	+	1.26836i
$285$		0			0
$286$	−468105.	+	297987.i	−0.338399	+	0.215418i
$287$		−	1.67741e6i		−	1.20208i
$288$	−550686.	+	1.73600e6i	−0.391222	+	1.23330i
$289$	1.31526e6			0.926336
$290$		0			0
$291$			296604.i			0.205326i
$292$	1.48669e6	+	694518.i	1.02038	+	0.476679i
$293$	−750723.			−0.510870			−0.255435	−	0.966826i	$-0.582219\pi$
$293$	−750723.			−0.510870			−0.255435	+	0.966826i	$0.582219\pi$
$294$	646828.	+	1.01610e6i	0.436436	+	0.685595i
$295$		0			0
$296$	−663874.	+	86694.4i	−0.440410	+	0.0575125i
$297$			217700.i			0.143208i
$298$	2.01914e6	−	1.28534e6i	1.31712	−	0.838452i
$299$		−	906390.i		−	0.586323i
$300$		0			0
$301$			1.58665e6i			1.00940i
$302$	121435.	+	190761.i	0.0766170	+	0.120357i
$303$			1.53374e6i			0.959721i
$304$	155900.	−	130446.i	0.0967527	−	0.0809555i
$305$		0			0
$306$	485227.	−	308886.i	0.296239	−	0.188580i
$307$	2.06754e6			1.25201			0.626005	−	0.779819i	$-0.284689\pi$
$307$	2.06754e6			1.25201			0.626005	+	0.779819i	$0.284689\pi$
$308$	281059.	−	601638.i	0.168819	−	0.361375i
$309$			1.62990e6i			0.971103i
$310$		0			0
$311$	3.06896e6			1.79924			0.899621	−	0.436671i	$-0.143843\pi$
$311$	3.06896e6			1.79924			0.899621	+	0.436671i	$0.143843\pi$
$312$	−3.21928e6	+	420401.i	−1.87229	+	0.244499i
$313$			115148.i			0.0664345i	0.999448	+	0.0332173i	$0.0105753\pi$
$313$			115148.i			0.0664345i	−0.999448	+	0.0332173i	$0.989425\pi$
$314$	1.11623e6	+	1.75348e6i	0.638897	+	1.00364i
$315$		0			0
$316$	−998526.	+	2.13745e6i	−0.562525	+	1.20414i
$317$	−1.29930e6			−0.726210			−0.363105	−	0.931748i	$-0.618283\pi$
$317$	−1.29930e6			−0.726210			−0.363105	+	0.931748i	$0.618283\pi$
$318$	1.55834e6	+	2.44799e6i	0.864162	+	1.35751i
$319$	−773127.			−0.425377
$320$		0			0
$321$	−4.42257e6			−2.39559
$322$	582474.	+	915005.i	0.313067	+	0.491795i
$323$	−64200.2			−0.0342397
$324$	495679.	−	1.06106e6i	0.262324	−	0.561534i
$325$		0			0
$326$	−48698.2	−	76499.7i	−0.0253787	−	0.0398672i
$327$			1.16514e6i			0.602571i
$328$	−1.87355e6	+	244664.i	−0.961569	+	0.125570i
$329$	1.01211e6			0.515512
$330$		0			0
$331$		−	2.02113e6i		−	1.01397i	−0.861955	−	0.506985i	$-0.830760\pi$
$331$		−	2.02113e6i		−	1.01397i	0.861955	−	0.506985i	$-0.169240\pi$
$332$	−834689.	+	1.78674e6i	−0.415604	+	0.889646i
$333$	−1.16286e6			−0.574667
$334$	−1.18397e6	+	753691.i	−0.580730	+	0.369681i
$335$		0			0
$336$	2.97972e6	−	2.49321e6i	1.43988	−	1.20479i
$337$			2.88553e6i			1.38405i	0.721875	+	0.692023i	$0.243281\pi$
$337$			2.88553e6i			1.38405i	−0.721875	+	0.692023i	$0.756719\pi$
$338$	−625139.	−	982027.i	−0.297636	−	0.467554i
$339$		−	4.03958e6i		−	1.90914i
$340$		0			0
$341$		−	629175.i		−	0.293012i
$342$	297838.	−	189598.i	0.137694	−	0.0876532i
$343$			1.25160e6i			0.574419i
$344$	1.77218e6	−	231426.i	0.807441	−	0.105443i
$345$		0			0
$346$	−1.74396e6	−	2.73958e6i	−0.783153	−	1.23025i
$347$	−1.01894e6			−0.454281			−0.227141	−	0.973862i	$-0.572938\pi$
$347$	−1.01894e6			−0.454281			−0.227141	+	0.973862i	$0.572938\pi$
$348$	−4.09824e6	−	1.91452e6i	−1.81405	−	0.847446i
$349$		−	1.53786e6i		−	0.675854i	−0.941172	−	0.337927i	$-0.890274\pi$
$349$		−	1.53786e6i		−	0.675854i	0.941172	−	0.337927i	$-0.109726\pi$
$350$		0			0
$351$	−1.28072e6			−0.554862
$352$	−712983.	−	226170.i	−0.306706	−	0.0972922i
$353$			490388.i			0.209461i	0.994501	+	0.104731i	$0.0333980\pi$
$353$			490388.i			0.209461i	−0.994501	+	0.104731i	$0.966602\pi$
$354$	3.77578e6	−	2.40358e6i	1.60139	−	1.01942i
$355$		0			0
$356$	−1.44562e6	+	3.09450e6i	−0.604544	+	1.29409i
$357$	−1.22706e6			−0.509558
$358$	1.45687e6	−	927415.i	0.600777	−	0.382443i
$359$	−3.19930e6			−1.31014			−0.655072	−	0.755567i	$-0.727362\pi$
$359$	−3.19930e6			−1.31014			−0.655072	+	0.755567i	$0.727362\pi$
$360$		0			0
$361$	2.43669e6			0.984085
$362$	−2.01227e6	+	1.28097e6i	−0.807075	+	0.513768i
$363$	3.40866e6			1.35774
$364$	3.53940e6	+	1.65346e6i	1.40016	+	0.654093i
$365$		0			0
$366$	5.46500e6	−	3.47891e6i	2.13249	−	1.35750i
$367$		−	2.06745e6i		−	0.801252i	−0.916242	−	0.400626i	$-0.868793\pi$
$367$		−	2.06745e6i		−	0.801252i	0.916242	−	0.400626i	$-0.131207\pi$
$368$	937039.	−	784044.i	0.360693	−	0.301801i
$369$	−3.28175e6			−1.25470
$370$		0			0
$371$		−	3.49180e6i		−	1.31709i
$372$	1.55805e6	−	3.33517e6i	0.583746	−	1.24957i
$373$	4.93913e6			1.83814			0.919070	−	0.394095i	$-0.128942\pi$
$373$	4.93913e6			1.83814			0.919070	+	0.394095i	$0.128942\pi$
$374$	126861.	+	199286.i	0.0468975	+	0.0736710i
$375$		0			0
$376$	−147625.	−	1.13046e6i	−0.0538505	−	0.412368i
$377$		−	4.54826e6i		−	1.64813i
$378$	1.29289e6	−	823028.i	0.465406	−	0.296268i
$379$			5.21670e6i			1.86551i	0.360510	+	0.932755i	$0.382603\pi$
$379$			5.21670e6i			1.86551i	−0.360510	+	0.932755i	$0.617397\pi$
$380$		0			0
$381$		−	2.13618e6i		−	0.753920i
$382$	1.28871e6	+	2.02443e6i	0.451853	+	0.709814i
$383$			4.22327e6i			1.47113i	0.677453	+	0.735566i	$0.263084\pi$
$383$			4.22327e6i			1.47113i	−0.677453	+	0.735566i	$0.736916\pi$
$384$	−3.21935e6	−	2.96448e6i	−1.11414	−	1.02594i
$385$		0			0
$386$	1.78426e6	−	1.13583e6i	0.609523	−	0.388010i
$387$	3.10418e6			1.05359
$388$	−364229.	−	170152.i	−0.122827	−	0.0573797i
$389$			615402.i			0.206198i	0.994671	+	0.103099i	$0.0328759\pi$
$389$			615402.i			0.206198i	−0.994671	+	0.103099i	$0.967124\pi$
$390$		0			0
$391$	−385875.			−0.127645
$392$	−1.61883e6	+	211401.i	−0.532092	+	0.0694851i
$393$		−	2.23088e6i		−	0.728611i
$394$	−342807.	−	538513.i	−0.111252	−	0.174765i
$395$		0			0
$396$	−1.17707e6	−	549876.i	−0.377194	−	0.176209i
$397$	1.60554e6			0.511263			0.255632	−	0.966774i	$-0.417717\pi$
$397$	1.60554e6			0.511263			0.255632	+	0.966774i	$0.417717\pi$
$398$	798744.	+	1.25474e6i	0.252755	+	0.397051i
$399$	−753180.			−0.236846
$400$		0			0
$401$	1.47973e6			0.459539			0.229769	−	0.973245i	$-0.426203\pi$
$401$	1.47973e6			0.459539			0.229769	+	0.973245i	$0.426203\pi$
$402$	−2.37984e6	−	3.73848e6i	−0.734485	−	1.15380i
$403$	3.70140e6			1.13528
$404$	−1.88343e6	−	879856.i	−0.574111	−	0.268200i
$405$		0			0
$406$	2.92285e6	+	4.59149e6i	0.880019	+	1.38242i
$407$		−	477592.i		−	0.142913i
$408$	178976.	+	1.37054e6i	0.0532287	+	0.407606i
$409$	−1.15560e6			−0.341584			−0.170792	−	0.985307i	$-0.554633\pi$
$409$	−1.15560e6			−0.341584			−0.170792	+	0.985307i	$0.554633\pi$
$410$		0			0
$411$		−	130249.i		−	0.0380338i
$412$	−2.00152e6	−	935022.i	−0.580920	−	0.271381i
$413$	−5.38575e6			−1.55371
$414$	1.79015e6	−	1.13958e6i	0.513322	−	0.326770i
$415$		0			0
$416$	1.33054e6	−	4.19444e6i	0.376961	−	1.18834i
$417$		−	3.88350e6i		−	1.09366i
$418$	77868.8	+	122324.i	0.0217983	+	0.0342428i
$419$		−	1.84397e6i		−	0.513121i	−0.966528	−	0.256560i	$-0.917411\pi$
$419$		−	1.84397e6i		−	0.513121i	0.966528	−	0.256560i	$-0.0825893\pi$
$420$		0			0
$421$			4.13061e6i			1.13582i	0.823091	+	0.567909i	$0.192248\pi$
$421$			4.13061e6i			1.13582i	−0.823091	+	0.567909i	$0.807752\pi$
$422$	1.30260e6	−	829211.i	0.356066	−	0.226665i
$423$		−	1.98014e6i		−	0.538077i
$424$	−3.90010e6	+	509309.i	−1.05356	+	0.137583i
$425$		0			0
$426$	−4.26477e6	−	6.69950e6i	−1.13860	−	1.78862i
$427$	−7.79524e6			−2.06900
$428$	2.53708e6	−	5.43091e6i	0.669461	−	1.43305i
$429$		−	2.31595e6i		−	0.607556i
$430$		0			0
$431$	3.44366e6			0.892950			0.446475	−	0.894796i	$-0.352679\pi$
$431$	3.44366e6			0.892950			0.446475	+	0.894796i	$0.352679\pi$
$432$	−1.10784e6	−	1.32402e6i	−0.285607	−	0.341339i
$433$			2.41696e6i			0.619511i	0.950816	+	0.309755i	$0.100247\pi$
$433$			2.41696e6i			0.619511i	−0.950816	+	0.309755i	$0.899753\pi$
$434$	−3.73658e6	+	2.37864e6i	−0.952249	+	0.606183i
$435$		0			0
$436$	−1.43079e6	−	668403.i	−0.360462	−	0.168392i
$437$	−236854.			−0.0593305
$438$	−5.77728e6	+	3.67770e6i	−1.43893	+	0.915992i
$439$	3.22639e6			0.799015			0.399507	−	0.916730i	$-0.369181\pi$
$439$	3.22639e6			0.799015			0.399507	+	0.916730i	$0.369181\pi$
$440$		0			0
$441$	−2.83558e6			−0.694298
$442$	−1.17239e6	+	746317.i	−0.285440	+	0.181705i
$443$	−6.44624e6			−1.56062			−0.780310	−	0.625393i	$-0.784939\pi$
$443$	−6.44624e6			−1.56062			−0.780310	+	0.625393i	$0.784939\pi$
$444$	1.18268e6	−	2.53165e6i	0.284714	−	0.609462i
$445$		0			0
$446$	−4.79840e6	+	3.05457e6i	−1.14224	+	0.727130i
$447$			9.98969e6i			2.36474i
$448$	1.35229e6	+	5.08936e6i	0.318327	+	1.19803i
$449$	1.82600e6			0.427450			0.213725	−	0.976894i	$-0.431440\pi$
$449$	1.82600e6			0.427450			0.213725	+	0.976894i	$0.431440\pi$
$450$		0			0
$451$		−	1.34783e6i		−	0.312029i
$452$	4.96060e6	+	2.31738e6i	1.14206	+	0.533520i
$453$	−943791.			−0.216088
$454$	1.68593e6	+	2.64842e6i	0.383884	+	0.603041i
$455$		0			0
$456$	109858.	+	841250.i	0.0247411	+	0.189458i
$457$			2.26865e6i			0.508132i	0.967187	+	0.254066i	$0.0817680\pi$
$457$			2.26865e6i			0.508132i	−0.967187	+	0.254066i	$0.918232\pi$
$458$	2.27153e6	−	1.44601e6i	0.506006	−	0.322113i
$459$			545237.i			0.120796i
$460$		0			0
$461$		−	2.82378e6i		−	0.618840i	−0.950925	−	0.309420i	$-0.899865\pi$
$461$		−	2.82378e6i		−	0.618840i	0.950925	−	0.309420i	$-0.100135\pi$
$462$	1.48830e6	+	2.33797e6i	0.324404	+	0.509605i
$463$		−	3.05836e6i		−	0.663035i	−0.943449	−	0.331517i	$-0.892439\pi$
$463$		−	3.05836e6i		−	0.663035i	0.943449	−	0.331517i	$-0.107561\pi$
$464$	4.70206e6	−	3.93433e6i	1.01389	−	0.848352i
$465$		0			0
$466$	−4.36228e6	+	2.77694e6i	−0.930570	+	0.592383i
$467$	−5.19478e6			−1.10224			−0.551119	−	0.834427i	$-0.685799\pi$
$467$	−5.19478e6			−1.10224			−0.551119	+	0.834427i	$0.685799\pi$
$468$	3.23489e6	−	6.92464e6i	0.682724	−	1.46144i
$469$			5.33254e6i			1.11944i
$470$		0			0
$471$	−8.67537e6			−1.80192
$472$	785556.	+	6.01550e6i	0.162301	+	1.24285i
$473$			1.27491e6i			0.262014i
$474$	−5.28753e6	−	8.30614e6i	−1.08095	−	1.69806i
$475$		0			0
$476$	703922.	−	1.50682e6i	0.142399	−	0.304821i
$477$	−6.83151e6			−1.37474
$478$	1.14167e6	+	1.79345e6i	0.228545	+	0.359020i
$479$	8.27094e6			1.64708			0.823542	−	0.567255i	$-0.191994\pi$
$479$	8.27094e6			1.64708			0.823542	+	0.567255i	$0.191994\pi$
$480$		0			0
$481$	2.80965e6			0.553719
$482$	−1.85944e6	−	2.92099e6i	−0.364557	−	0.572680i
$483$	−4.52699e6			−0.882961
$484$	−1.95544e6	+	4.18583e6i	−0.379429	+	0.812209i
$485$		0			0
$486$	3.86929e6	+	6.07824e6i	0.743088	+	1.16731i
$487$		−	4.95663e6i		−	0.947031i	−0.880786	−	0.473515i	$-0.842985\pi$
$487$		−	4.95663e6i		−	0.947031i	0.880786	−	0.473515i	$-0.157015\pi$
$488$	1.13700e6	+	8.70675e6i	0.216128	+	1.65503i
$489$	378482.			0.0715770
$490$		0			0
$491$			6.01801e6i			1.12655i	0.826271	+	0.563273i	$0.190458\pi$
$491$			6.01801e6i			1.12655i	−0.826271	+	0.563273i	$0.809542\pi$
$492$	3.33769e6	−	7.14469e6i	0.621632	−	1.33067i
$493$	−1.93632e6			−0.358806
$494$	−719623.	+	458098.i	−0.132675	+	0.0844580i
$495$		0			0
$496$	3.20178e6	+	3.82656e6i	0.584370	+	0.698400i
$497$			9.55613e6i			1.73537i
$498$	−4.41996e6	−	6.94329e6i	−0.798629	−	1.25456i
$499$			7.87834e6i			1.41639i	0.706016	+	0.708196i	$0.250491\pi$
$499$			7.87834e6i			1.41639i	−0.706016	+	0.708196i	$0.749509\pi$
$500$		0			0
$501$		−	5.85769e6i		−	1.04263i
$502$	2.20764e6	−	1.40534e6i	0.390993	−	0.248898i
$503$		−	9.09472e6i		−	1.60276i	−0.598153	−	0.801382i	$-0.704099\pi$
$503$		−	9.09472e6i		−	1.60276i	0.598153	−	0.801382i	$-0.295901\pi$
$504$	1.18435e6	+	9.06930e6i	0.207684	+	1.59037i
$505$		0			0
$506$	468030.	+	735226.i	0.0812639	+	0.127657i
$507$	4.85858e6			0.839440
$508$	2.62322e6	+	1.22546e6i	0.450999	+	0.210687i
$509$		−	1.07691e7i		−	1.84241i	−0.389076	−	0.921206i	$-0.627206\pi$
$509$		−	1.07691e7i		−	1.84241i	0.389076	−	0.921206i	$-0.372794\pi$
$510$		0			0
$511$	8.24068e6			1.39608
$512$	5.48722e6	−	2.25273e6i	0.925076	−	0.379783i
$513$			334672.i			0.0561470i
$514$	−2.78372e6	+	1.77206e6i	−0.464749	+	0.295850i
$515$		0			0
$516$	−3.15709e6	+	6.75810e6i	−0.521991	+	1.11738i
$517$	813253.			0.133813
$518$	−2.83635e6	+	1.80557e6i	−0.464447	+	0.295658i
$519$	1.35541e7			2.20877
$520$		0			0
$521$	−1.88429e6			−0.304126			−0.152063	−	0.988371i	$-0.548592\pi$
$521$	−1.88429e6			−0.304126			−0.152063	+	0.988371i	$0.548592\pi$
$522$	8.98299e6	−	5.71839e6i	1.44293	−	0.918539i
$523$	−2.14270e6			−0.342537			−0.171269	−	0.985224i	$-0.554787\pi$
$523$	−2.14270e6			−0.342537			−0.171269	+	0.985224i	$0.554787\pi$
$524$	2.73952e6	+	1.27979e6i	0.435859	+	0.203615i
$525$		0			0
$526$	1.96595e6	−	1.25148e6i	0.309818	−	0.197224i
$527$		−	1.57579e6i		−	0.247156i
$528$	2.39427e6	−	2.00334e6i	0.373755	−	0.312731i
$529$	5.01273e6			0.778816
$530$		0			0
$531$			1.05369e7i			1.62172i
$532$	432075.	−	924904.i	0.0661882	−	0.141683i
$533$	7.92923e6			1.20896
$534$	−7.65502e6	−	1.20252e7i	−1.16170	−	1.82490i
$535$		0			0
$536$	5.95608e6	−	777796.i	0.895465	−	0.116938i
$537$			7.20787e6i			1.07863i
$538$	−5.46204e6	+	3.47703e6i	−0.813578	+	0.517908i
$539$		−	1.16459e6i		−	0.172664i
$540$		0			0
$541$		−	9.23309e6i		−	1.35629i	−0.734926	−	0.678147i	$-0.762783\pi$
$541$		−	9.23309e6i		−	1.35629i	0.734926	−	0.678147i	$-0.237217\pi$
$542$	3.69413e6	+	5.80309e6i	0.540150	+	0.848518i
$543$		−	9.95569e6i		−	1.44901i
$544$	−1.78569e6	−	566450.i	−0.258707	−	0.0820662i
$545$		0			0
$546$	−1.37541e7	+	8.75560e6i	−1.97447	+	1.25691i
$547$	−6.30413e6			−0.900858			−0.450429	−	0.892812i	$-0.648729\pi$
$547$	−6.30413e6			−0.900858			−0.450429	+	0.892812i	$0.648729\pi$
$548$	159946.	+	74719.7i	0.0227521	+	0.0106288i
$549$			1.52509e7i			2.15956i
$550$		0			0
$551$	−1.18853e6			−0.166776
$552$	660300.	+	5.05633e6i	0.0922345	+	0.706298i
$553$			1.18478e7i			1.64750i
$554$	−2.44860e6	−	3.84649e6i	−0.338956	−	0.532464i
$555$		0			0
$556$	4.76893e6	+	2.22784e6i	0.654236	+	0.305631i
$557$	6.50282e6			0.888104			0.444052	−	0.896001i	$-0.353540\pi$
$557$	6.50282e6			0.888104			0.444052	+	0.896001i	$0.353540\pi$
$558$	4.65366e6	+	7.31041e6i	0.632717	+	0.993931i
$559$	−7.50020e6			−1.01518
$560$		0			0
$561$	−985966.			−0.132268
$562$	−3.63998e6	−	5.71802e6i	−0.486136	−	0.763668i
$563$	−6.06434e6			−0.806329			−0.403165	−	0.915127i	$-0.632090\pi$
$563$	−6.06434e6			−0.806329			−0.403165	+	0.915127i	$0.632090\pi$
$564$	4.31094e6	+	2.01389e6i	0.570656	+	0.266586i
$565$		0			0
$566$	−4.44385e6	−	6.98082e6i	−0.583067	−	0.915937i
$567$		−	5.88140e6i		−	0.768286i
$568$	1.06735e7	−	1.39384e6i	1.38815	−	0.181277i
$569$	−8.67931e6			−1.12384			−0.561920	−	0.827191i	$-0.689937\pi$
$569$	−8.67931e6			−1.12384			−0.561920	+	0.827191i	$0.689937\pi$
$570$		0			0
$571$			5.13091e6i			0.658573i	0.944230	+	0.329287i	$0.106808\pi$
$571$			5.13091e6i			0.658573i	−0.944230	+	0.329287i	$0.893192\pi$
$572$	2.84399e6	+	1.32859e6i	0.363444	+	0.169785i
$573$	−1.00159e7			−1.27439
$574$	−8.00460e6	+	5.09557e6i	−1.01405	+	0.645525i
$575$		0			0
$576$	9.95703e6	−	2.64567e6i	1.25047	−	0.332261i
$577$		−	1.05397e7i		−	1.31792i	−0.752176	−	0.658962i	$-0.770996\pi$
$577$		−	1.05397e7i		−	1.31792i	0.752176	−	0.658962i	$-0.229004\pi$
$578$	−3.99546e6	−	6.27644e6i	−0.497447	−	0.781437i
$579$			8.82764e6i			1.09433i
$580$		0			0
$581$			9.90387e6i			1.21721i
$582$	1.41539e6	−	901012.i	0.173209	−	0.110261i
$583$		−	2.80574e6i		−	0.341881i
$584$	−1.20197e6	−	9.20427e6i	−0.145835	−	1.11675i
$585$		0			0
$586$	2.28052e6	+	3.58245e6i	0.274340	+	0.430959i
$587$	5.07345e6			0.607727			0.303863	−	0.952716i	$-0.401723\pi$
$587$	5.07345e6			0.607727			0.303863	+	0.952716i	$0.401723\pi$
$588$	2.88391e6	−	6.17333e6i	0.343985	−	0.736336i
$589$		−	967237.i		−	0.114880i
$590$		0			0
$591$	2.66429e6			0.313771
$592$	2.43040e6	+	2.90465e6i	0.285019	+	0.340636i
$593$			1.41356e7i			1.65073i	0.564599	+	0.825366i	$0.309031\pi$
$593$			1.41356e7i			1.65073i	−0.564599	+	0.825366i	$0.690969\pi$
$594$	1.03886e6	−	661321.i	0.120807	−	0.0769035i
$595$		0			0
$596$	−1.22673e7	−	5.73076e6i	−1.41460	−	0.660841i
$597$	−6.20784e6			−0.712861
$598$	−4.32529e6	+	2.75340e6i	−0.494610	+	0.314859i
$599$	−7.17896e6			−0.817512			−0.408756	−	0.912644i	$-0.634037\pi$
$599$	−7.17896e6			−0.817512			−0.408756	+	0.912644i	$0.634037\pi$
$600$		0			0
$601$	−3.61001e6			−0.407683			−0.203841	−	0.979004i	$-0.565343\pi$
$601$	−3.61001e6			−0.407683			−0.203841	+	0.979004i	$0.565343\pi$
$602$	7.57149e6	−	4.81986e6i	0.851511	−	0.542055i
$603$	1.04328e7			1.16844
$604$	541422.	−	1.15897e6i	0.0603870	−	0.129265i
$605$		0			0
$606$	7.31900e6	−	4.65913e6i	0.809600	−	0.515375i
$607$			4.03263e6i			0.444239i	0.975020	+	0.222119i	$0.0712974\pi$
$607$			4.03263e6i			0.444239i	−0.975020	+	0.222119i	$0.928703\pi$
$608$	−1.09608e6	−	347693.i	−0.120249	−	0.0381450i
$609$	−2.27164e7			−2.48197
$610$		0			0
$611$			4.78432e6i			0.518462i
$612$	−2.94801e6	−	1.37718e6i	−0.318164	−	0.148632i
$613$	1.31815e7			1.41682			0.708410	−	0.705801i	$-0.249413\pi$
$613$	1.31815e7			1.41682			0.708410	+	0.705801i	$0.249413\pi$
$614$	−6.28069e6	−	9.86630e6i	−0.672336	−	1.05617i
$615$		0			0
$616$	−3.72481e6	+	486418.i	−0.395505	+	0.0516485i
$617$			7.04507e6i			0.745027i	0.928027	+	0.372514i	$0.121504\pi$
$617$			7.04507e6i			0.745027i	−0.928027	+	0.372514i	$0.878496\pi$
$618$	7.77790e6	−	4.95126e6i	0.819202	−	0.521488i
$619$			6.48539e6i			0.680314i	0.940369	+	0.340157i	$0.110480\pi$
$619$			6.48539e6i			0.680314i	−0.940369	+	0.340157i	$0.889520\pi$
$620$		0			0
$621$			2.01155e6i			0.209315i
$622$	−9.32276e6	−	1.46451e7i	−0.966203	−	1.51780i
$623$			1.71527e7i			1.77057i
$624$	1.17856e7	+	1.40853e7i	1.21168	+	1.44812i
$625$		0			0
$626$	549484.	−	349791.i	0.0560428	−	0.0356757i
$627$	−605196.			−0.0614791
$628$	4.97678e6	−	1.06533e7i	0.503558	−	1.07792i
$629$		−	1.19614e6i		−	0.120547i
$630$		0			0
$631$	−4.09103e6			−0.409034			−0.204517	−	0.978863i	$-0.565562\pi$
$631$	−4.09103e6			−0.409034			−0.204517	+	0.978863i	$0.565562\pi$
$632$	1.32332e7	−	1.72811e6i	1.31787	−	0.172099i
$633$			6.44463e6i			0.639276i
$634$	3.94698e6	+	6.20028e6i	0.389979	+	0.612616i
$635$		0			0
$636$	6.94795e6	−	1.48728e7i	0.681104	−	1.45798i
$637$	6.85121e6			0.668989
$638$	2.34857e6	+	3.68936e6i	0.228430	+	0.358839i
$639$	1.86960e7			1.81133
$640$		0			0
$641$	8.17877e6			0.786218			0.393109	−	0.919492i	$-0.371400\pi$
$641$	8.17877e6			0.786218			0.393109	+	0.919492i	$0.371400\pi$
$642$	1.34347e7	+	2.11045e7i	1.28644	+	2.02087i
$643$	1.41619e7			1.35081			0.675404	−	0.737448i	$-0.263969\pi$
$643$	1.41619e7			1.35081			0.675404	+	0.737448i	$0.263969\pi$
$644$	2.59699e6	−	5.55914e6i	0.246749	−	0.528193i
$645$		0			0
$646$	195025.	+	306364.i	0.0183869	+	0.0288839i
$647$			1.23662e7i			1.16138i	0.814124	+	0.580690i	$0.197217\pi$
$647$			1.23662e7i			1.16138i	−0.814124	+	0.580690i	$0.802783\pi$
$648$	−6.56912e6	+	857852.i	−0.614567	+	0.0802555i
$649$	−4.32756e6			−0.403303
$650$		0			0
$651$		−	1.84868e7i		−	1.70965i
$652$	−217123.	+	464776.i	−0.0200026	+	0.0428178i
$653$	−1.99967e7			−1.83517			−0.917584	−	0.397543i	$-0.869863\pi$
$653$	−1.99967e7			−1.83517			−0.917584	+	0.397543i	$0.869863\pi$
$654$	5.56005e6	−	3.53942e6i	0.508316	−	0.323584i
$655$		0			0
$656$	6.85894e6	+	8.19735e6i	0.622296	+	0.743728i
$657$		−	1.61224e7i		−	1.45719i
$658$	−3.07455e6	−	4.82980e6i	−0.276833	−	0.434875i
$659$			1.68566e7i			1.51202i	0.654562	+	0.756009i	$0.272853\pi$
$659$			1.68566e7i			1.51202i	−0.654562	+	0.756009i	$0.727147\pi$
$660$		0			0
$661$			1.65602e6i			0.147422i	0.997280	+	0.0737111i	$0.0234843\pi$
$661$			1.65602e6i			0.147422i	−0.997280	+	0.0737111i	$0.976516\pi$
$662$	−9.64485e6	+	6.13972e6i	−0.855363	+	0.544507i
$663$		−	5.80038e6i		−	0.512475i
$664$	1.10619e7	−	1.44456e6i	0.973668	−	0.127150i
$665$		0			0
$666$	3.53249e6	+	5.54916e6i	0.308599	+	0.484777i
$667$	−7.14369e6			−0.621739
$668$	7.19323e6	+	3.36037e6i	0.623710	+	0.291370i
$669$		−	2.37401e7i		−	2.05077i
$670$		0			0
$671$	−6.26364e6			−0.537057
$672$	−2.09493e7	−	6.64545e6i	−1.78956	−	0.567676i
$673$		−	1.37081e7i		−	1.16665i	−0.812240	−	0.583324i	$-0.801752\pi$
$673$		−	1.37081e7i		−	1.16665i	0.812240	−	0.583324i	$-0.198248\pi$
$674$	1.37698e7	−	8.76555e6i	1.16755	−	0.743241i
$675$		0			0
$676$	−2.78721e6	+	5.96633e6i	−0.234587	+	0.502158i
$677$	2.21494e6			0.185734			0.0928669	−	0.995679i	$-0.470397\pi$
$677$	2.21494e6			0.185734			0.0928669	+	0.995679i	$0.470397\pi$
$678$	−1.92769e7	+	1.22713e7i	−1.61051	+	1.02522i
$679$	−2.01891e6			−0.168052
$680$		0			0
$681$	−1.31031e7			−1.08269
$682$	−3.00242e6	+	1.91128e6i	−0.247179	+	0.157349i
$683$	532823.			0.0437050			0.0218525	−	0.999761i	$-0.493044\pi$
$683$	532823.			0.0437050			0.0218525	+	0.999761i	$0.493044\pi$
$684$	−1.80952e6	−	845330.i	−0.147885	−	0.0690854i
$685$		0			0
$686$	5.97262e6	−	3.80205e6i	0.484568	−	0.308466i
$687$			1.12384e7i			0.908476i
$688$	−6.48781e6	−	7.75381e6i	−0.522549	−	0.624517i
$689$	1.65060e7			1.32463
$690$		0			0
$691$		−	5.63330e6i		−	0.448816i	−0.974495	−	0.224408i	$-0.927955\pi$
$691$		−	5.63330e6i		−	0.448816i	0.974495	−	0.224408i	$-0.0720448\pi$
$692$	−7.77553e6	+	1.66444e7i	−0.617255	+	1.32130i
$693$	−6.52446e6			−0.516074
$694$	3.09530e6	+	4.86238e6i	0.243952	+	0.383222i
$695$		0			0
$696$	3.31338e6	+	2.53727e7i	0.259268	+	1.98538i
$697$		−	3.37569e6i		−	0.263197i
$698$	−7.33866e6	+	4.67165e6i	−0.570136	+	0.362937i
$699$		−	2.15824e7i		−	1.67073i
$700$		0			0
$701$		−	5.94926e6i		−	0.457265i	−0.973513	−	0.228633i	$-0.926575\pi$
$701$		−	5.94926e6i		−	0.457265i	0.973513	−	0.228633i	$-0.0734254\pi$
$702$	3.89051e6	+	6.11158e6i	0.297964	+	0.468070i
$703$		−	734207.i		−	0.0560312i
$704$	1.08659e6	+	4.08941e6i	0.0826293	+	0.310977i
$705$		0			0
$706$	2.34013e6	−	1.48968e6i	0.176697	−	0.112482i
$707$	−1.04398e7			−0.785494
$708$	−2.29398e7	−	1.07165e7i	−1.71991	−	0.803470i
$709$			8.89034e6i			0.664206i	0.943243	+	0.332103i	$0.107758\pi$
$709$			8.89034e6i			0.664206i	−0.943243	+	0.332103i	$0.892242\pi$
$710$		0			0
$711$	2.31796e7			1.71962
$712$	1.91584e7	−	2.50187e6i	1.41631	−	0.184954i
$713$		−	5.81358e6i		−	0.428272i
$714$	3.72750e6	+	5.85551e6i	0.273636	+	0.429853i
$715$		0			0
$716$	−8.85125e6	−	4.13492e6i	−0.645241	−	0.301429i
$717$	−8.87308e6			−0.644579
$718$	9.71871e6	+	1.52671e7i	0.703554	+	1.10521i
$719$	1.23030e7			0.887539			0.443769	−	0.896141i	$-0.353641\pi$
$719$	1.23030e7			0.887539			0.443769	+	0.896141i	$0.353641\pi$
$720$		0			0
$721$	−1.10943e7			−0.794811
$722$	−7.40209e6	−	1.16279e7i	−0.528459	−	0.830153i
$723$	1.44516e7			1.02818
$724$	1.22256e7	+	5.71126e6i	0.866807	+	0.404935i
$725$		0			0
$726$	−1.03547e7	−	1.62661e7i	−0.729115	−	1.14536i
$727$		−	4.81217e6i		−	0.337679i	−0.985644	−	0.168840i	$-0.945998\pi$
$727$		−	4.81217e6i		−	0.337679i	0.985644	−	0.168840i	$-0.0540020\pi$
$728$	−2.86157e6	−	2.19128e7i	−0.200113	−	1.53239i
$729$	−2.11789e7			−1.47599
$730$		0			0
$731$			3.19304e6i			0.221010i
$732$	−3.32027e7	−	1.55109e7i	−2.29032	−	1.06994i
$733$	2.11550e6			0.145430			0.0727148	−	0.997353i	$-0.476834\pi$
$733$	2.11550e6			0.145430			0.0727148	+	0.997353i	$0.476834\pi$
$734$	−9.86585e6	+	6.28041e6i	−0.675919	+	0.430277i
$735$		0			0
$736$	−6.58796e6	−	2.08981e6i	−0.448287	−	0.142204i
$737$			4.28481e6i			0.290578i
$738$	9.96918e6	+	1.56605e7i	0.673781	+	1.05844i
$739$		−	3.53365e6i		−	0.238019i	−0.992893	−	0.119010i	$-0.962028\pi$
$739$		−	3.53365e6i		−	0.238019i	0.992893	−	0.119010i	$-0.0379719\pi$
$740$		0			0
$741$		−	3.56034e6i		−	0.238202i
$742$	−1.66629e7	+	1.06073e7i	−1.11107	+	0.707283i
$743$		−	2.10515e7i		−	1.39898i	−0.714643	−	0.699489i	$-0.753411\pi$
$743$		−	2.10515e7i		−	1.39898i	0.714643	−	0.699489i	$-0.246589\pi$
$744$	−2.06484e7	+	2.69645e6i	−1.36759	+	0.178591i
$745$		0			0
$746$	−1.50039e7	−	2.35695e7i	−0.987091	−	1.55062i
$747$	1.93763e7			1.27049
$748$	565617.	−	1.21076e6i	0.0369631	−	0.0791235i
$749$		−	3.01033e7i		−	1.96070i
$750$		0			0
$751$	−9.76794e6			−0.631980			−0.315990	−	0.948763i	$-0.602337\pi$
$751$	−9.76794e6			−0.631980			−0.315990	+	0.948763i	$0.602337\pi$
$752$	−4.94610e6	+	4.13853e6i	−0.318947	+	0.266871i
$753$			1.09223e7i			0.701983i
$754$	−2.17043e7	+	1.38165e7i	−1.39033	+	0.885056i
$755$		0			0
$756$	−7.85499e6	−	3.66951e6i	−0.499851	−	0.233509i
$757$	−3.90009e6			−0.247363			−0.123682	−	0.992322i	$-0.539470\pi$
$757$	−3.90009e6			−0.247363			−0.123682	+	0.992322i	$0.539470\pi$
$758$	2.48941e7	−	1.58471e7i	1.57370	−	1.00179i
$759$	−3.63753e6			−0.229194
$760$		0			0
$761$	−1.28261e7			−0.802845			−0.401422	−	0.915893i	$-0.631484\pi$
$761$	−1.28261e7			−0.802845			−0.401422	+	0.915893i	$0.631484\pi$
$762$	−1.01938e7	+	6.48920e6i	−0.635991	+	0.404859i
$763$	−7.93082e6			−0.493181
$764$	5.74578e6	−	1.22995e7i	0.356136	−	0.762348i
$765$		0			0
$766$	2.01534e7	−	1.28293e7i	1.24102	−	0.790006i
$767$		−	2.54588e7i		−	1.56261i
$768$	−4.36688e6	+	2.43682e7i	−0.267158	+	1.49080i
$769$	−1.15731e7			−0.705724			−0.352862	−	0.935675i	$-0.614792\pi$
$769$	−1.15731e7			−0.705724			−0.352862	+	0.935675i	$0.614792\pi$
$770$		0			0
$771$		−	1.37725e7i		−	0.834404i
$772$	−1.08403e7	−	5.06413e6i	−0.654635	−	0.305817i
$773$	−3.69152e6			−0.222206			−0.111103	−	0.993809i	$-0.535438\pi$
$773$	−3.69152e6			−0.222206			−0.111103	+	0.993809i	$0.535438\pi$
$774$	−9.42977e6	−	1.48132e7i	−0.565782	−	0.888783i
$775$		0			0
$776$	294475.	+	2.25498e6i	0.0175547	+	0.134428i
$777$		−	1.40329e7i		−	0.833861i
$778$	2.93670e6	−	1.86944e6i	0.173944	−	0.110730i
$779$		−	2.07204e6i		−	0.122336i
$780$		0			0
$781$			7.67855e6i			0.450455i
$782$	1.17220e6	+	1.84140e6i	0.0685463	+	0.107679i
$783$			1.00939e7i			0.588378i
$784$	5.92643e6	+	7.08288e6i	0.344352	+	0.411547i
$785$		0			0
$786$	−1.06458e7	+	6.77689e6i	−0.614640	+	0.391268i
$787$	3.15075e7			1.81333			0.906665	−	0.421851i	$-0.138619\pi$
$787$	3.15075e7			1.81333			0.906665	+	0.421851i	$0.138619\pi$
$788$	−1.52842e6	+	3.27175e6i	−0.0876853	+	0.187700i
$789$			9.72652e6i			0.556244i
$790$		0			0
$791$	2.74965e7			1.56256
$792$	951648.	+	7.28737e6i	0.0539093	+	0.412818i
$793$		−	3.68487e7i		−	2.08084i
$794$	−4.87725e6	−	7.66164e6i	−0.274551	−	0.431291i
$795$		0			0
$796$	3.56124e6	−	7.62322e6i	0.199213	−	0.426438i
$797$	1.13115e7			0.630775			0.315387	−	0.948963i	$-0.397866\pi$
$797$	1.13115e7			0.630775			0.315387	+	0.948963i	$0.397866\pi$
$798$	2.28798e6	+	3.59418e6i	0.127188	+	0.199799i
$799$	2.03682e6			0.112872
$800$		0			0
$801$	3.35583e7			1.84807
$802$	−4.49507e6	−	7.06128e6i	−0.246775	−	0.387657i
$803$	6.62156e6			0.362386
$804$	−1.06106e7	+	2.27132e7i	−0.578897	+	1.23919i
$805$		0			0
$806$	−1.12440e7	−	1.76631e7i	−0.609652	−	0.957699i
$807$		−	2.70235e7i		−	1.46069i
$808$	1.52273e6	+	1.16605e7i	0.0820530	+	0.628332i
$809$	1.87371e7			1.00654			0.503271	−	0.864128i	$-0.332130\pi$
$809$	1.87371e7			1.00654			0.503271	+	0.864128i	$0.332130\pi$
$810$		0			0
$811$			1.04019e6i			0.0555341i	0.999614	+	0.0277671i	$0.00883967\pi$
$811$			1.04019e6i			0.0555341i	−0.999614	+	0.0277671i	$0.991160\pi$
$812$	1.30317e7	−	2.78957e7i	0.693602	−	1.48473i
$813$	−2.87108e7			−1.52342
$814$	−2.27907e6	+	1.45081e6i	−0.120558	+	0.0767450i
$815$		0			0
$816$	5.99652e6	−	5.01744e6i	0.315263	−	0.263789i
$817$			1.95992e6i			0.102727i
$818$	3.51043e6	+	5.51451e6i	0.183433	+	0.288153i
$819$		−	3.83831e7i		−	1.99954i
$820$		0			0
$821$			2.89521e7i			1.49907i	0.661965	+	0.749535i	$0.269723\pi$
$821$			2.89521e7i			1.49907i	−0.661965	+	0.749535i	$0.730277\pi$
$822$	−621549.	+	395666.i	−0.0320845	+	0.0204244i
$823$			1.73232e7i			0.891517i	0.895153	+	0.445758i	$0.147066\pi$
$823$			1.73232e7i			0.891517i	−0.895153	+	0.445758i	$0.852934\pi$
$824$	1.61820e6	+	1.23916e7i	0.0830262	+	0.635785i
$825$		0			0
$826$	1.63606e7	+	2.57008e7i	0.834352	+	1.31068i
$827$	−7.19436e6			−0.365787			−0.182893	−	0.983133i	$-0.558546\pi$
$827$	−7.19436e6			−0.365787			−0.182893	+	0.983133i	$0.558546\pi$
$828$	−1.08761e7	−	5.08086e6i	−0.551313	−	0.257550i
$829$		−	2.28187e7i		−	1.15320i	−0.817026	−	0.576600i	$-0.804379\pi$
$829$		−	2.28187e7i		−	1.15320i	0.817026	−	0.576600i	$-0.195621\pi$
$830$		0			0
$831$	1.90305e7			0.955978
$832$	−2.40578e7	+	6.39235e6i	−1.20489	+	0.320149i
$833$		−	2.91675e6i		−	0.145642i
$834$	−1.85321e7	+	1.17972e7i	−0.922591	+	0.587303i
$835$		0			0
$836$	347182.	−	743180.i	0.0171807	−	0.0367772i
$837$	−8.21451e6			−0.405292
$838$	−8.79945e6	+	5.60155e6i	−0.432858	+	0.275549i
$839$	−1.81694e7			−0.891121			−0.445560	−	0.895252i	$-0.646996\pi$
$839$	−1.81694e7			−0.891121			−0.445560	+	0.895252i	$0.646996\pi$
$840$		0			0
$841$	−1.53359e7			−0.747684
$842$	1.97113e7	−	1.25478e7i	0.958152	−	0.609941i
$843$	2.82899e7			1.37108
$844$	−7.91399e6	−	3.69707e6i	−0.382419	−	0.178650i
$845$		0			0
$846$	−9.44921e6	+	6.01518e6i	−0.453910	+	0.288950i
$847$			2.32019e7i			1.11126i
$848$	1.42780e7	+	1.70641e7i	0.681832	+	0.814882i
$849$	3.45376e7			1.64446
$850$		0			0
$851$		−	4.41295e6i		−	0.208884i
$852$	−1.90147e7	+	4.07030e7i	−0.897408	+	1.92100i
$853$	2.58313e7			1.21555			0.607776	−	0.794108i	$-0.292062\pi$
$853$	2.58313e7			1.21555			0.607776	+	0.794108i	$0.292062\pi$
$854$	2.36801e7	+	3.71989e7i	1.11106	+	1.74536i
$855$		0			0
$856$	−3.36234e7	+	4.39083e6i	−1.56840	+	0.204815i
$857$			1.83988e7i			0.855731i	0.903842	+	0.427866i	$0.140734\pi$
$857$			1.83988e7i			0.855731i	−0.903842	+	0.427866i	$0.859266\pi$
$858$	−1.10517e7	+	7.03531e6i	−0.512522	+	0.326261i
$859$			2.69993e7i			1.24845i	0.781246	+	0.624224i	$0.214585\pi$
$859$			2.69993e7i			1.24845i	−0.781246	+	0.624224i	$0.785415\pi$
$860$		0			0
$861$		−	3.96028e7i		−	1.82061i
$862$	−1.04610e7	−	1.64332e7i	−0.479519	−	0.753274i
$863$		−	3.05160e7i		−	1.39477i	−0.716699	−	0.697383i	$-0.754348\pi$
$863$		−	3.05160e7i		−	1.39477i	0.716699	−	0.697383i	$-0.245652\pi$
$864$	−2.95287e6	+	9.30870e6i	−0.134574	+	0.424233i
$865$		0			0
$866$	1.15337e7	−	7.34214e6i	0.522606	−	0.332681i
$867$	3.10527e7			1.40298
$868$	2.27017e7	+	1.06053e7i	1.02273	+	0.477773i
$869$			9.51999e6i			0.427648i
$870$		0			0
$871$	−2.52073e7			−1.12585
$872$	1.15678e6	+	8.85818e6i	0.0515179	+	0.394506i
$873$			3.94988e6i			0.175408i
$874$	719508.	+	1.13027e6i	0.0318608	+	0.0500499i
$875$		0			0
$876$	3.51000e7	+	1.63972e7i	1.54542	+	0.721954i
$877$	2.80238e7			1.23035			0.615174	−	0.788391i	$-0.289086\pi$
$877$	2.80238e7			1.23035			0.615174	+	0.788391i	$0.289086\pi$
$878$	−9.80099e6	−	1.53963e7i	−0.429075	−	0.674032i
$879$	−1.77242e7			−0.773738
$880$		0			0
$881$	−8.04971e6			−0.349414			−0.174707	−	0.984620i	$-0.555898\pi$
$881$	−8.04971e6			−0.349414			−0.174707	+	0.984620i	$0.555898\pi$
$882$	8.61382e6	+	1.35314e7i	0.372842	+	0.585695i
$883$	8.61922e6			0.372020			0.186010	−	0.982548i	$-0.440444\pi$
$883$	8.61922e6			0.372020			0.186010	+	0.982548i	$0.440444\pi$
$884$	7.12286e6	+	3.32749e6i	0.306566	+	0.143214i
$885$		0			0
$886$	1.95821e7	+	3.07615e7i	0.838061	+	1.31651i
$887$			6.77038e6i			0.288937i	0.989509	+	0.144469i	$0.0461473\pi$
$887$			6.77038e6i			0.288937i	−0.989509	+	0.144469i	$0.953853\pi$
$888$	−1.56737e7	+	2.04681e6i	−0.667022	+	0.0871055i
$889$	1.45404e7			0.617054
$890$		0			0
$891$		−	4.72583e6i		−	0.199427i
$892$	2.91528e7	+	1.36189e7i	1.22678	+	0.573100i
$893$	1.25022e6			0.0524636
$894$	4.76708e7	−	3.03463e7i	1.99484	−	1.26988i
$895$		0			0
$896$	2.01785e7	−	2.19134e7i	0.839690	−	0.911883i
$897$		−	2.13994e7i		−	0.888015i
$898$	−5.54696e6	−	8.71369e6i	−0.229543	−	0.360588i
$899$		−	2.91725e7i		−	1.20386i
$900$		0			0
$901$		−	7.02706e6i		−	0.288378i
$902$	−6.43187e6	+	4.09440e6i	−0.263221	+	0.167561i
$903$			3.74600e7i			1.52879i
$904$	−4.01059e6	−	3.07117e7i	−0.163225	−	1.24992i
$905$		0			0
$906$	2.86701e6	+	4.50377e6i	0.116040	+	0.182287i
$907$	−3.35760e7			−1.35522			−0.677611	−	0.735421i	$-0.736985\pi$
$907$	−3.35760e7			−1.35522			−0.677611	+	0.735421i	$0.736985\pi$
$908$	7.51680e6	−	1.60905e7i	0.302565	−	0.647673i
$909$			2.04248e7i			0.819877i
$910$		0			0
$911$	−3.92094e7			−1.56529			−0.782645	−	0.622469i	$-0.786130\pi$
$911$	−3.92094e7			−1.56529			−0.782645	+	0.622469i	$0.786130\pi$
$912$	3.68073e6	−	3.07976e6i	0.146537	−	0.122611i
$913$			7.95797e6i			0.315955i
$914$	1.08260e7	−	6.89161e6i	0.428649	−	0.272869i
$915$		0			0
$916$	−1.38008e7	−	6.44712e6i	−0.543456	−	0.253879i
$917$	1.51851e7			0.596340
$918$	2.60187e6	−	1.65630e6i	0.101901	−	0.0648683i
$919$	−1.65806e7			−0.647609			−0.323804	−	0.946124i	$-0.604962\pi$
$919$	−1.65806e7			−0.647609			−0.323804	+	0.946124i	$0.604962\pi$
$920$		0			0
$921$	4.88136e7			1.89623
$922$	−1.34751e7	+	8.57797e6i	−0.522040	+	0.332321i
$923$	−4.51725e7			−1.74530
$924$	6.63567e6	−	1.42044e7i	0.255685	−	0.547321i
$925$		0			0
$926$	−1.45945e7	+	9.29057e6i	−0.559322	+	0.356053i
$927$			2.17054e7i			0.829601i
$928$	−3.30584e7	−	1.04867e7i	−1.26012	−	0.399730i
$929$	−3.97202e7			−1.50998			−0.754992	−	0.655734i	$-0.772359\pi$
$929$	−3.97202e7			−1.50998			−0.754992	+	0.655734i	$0.772359\pi$
$930$		0			0
$931$		−	1.79033e6i		−	0.0676955i
$932$	2.65032e7	+	1.23811e7i	0.999443	+	0.466897i
$933$	7.24565e7			2.72504
$934$	1.57805e7	+	2.47895e7i	0.591907	+	0.929824i
$935$		0			0
$936$	−4.28712e7	+	5.59849e6i	−1.59947	+	0.208873i
$937$			2.47490e7i			0.920891i	0.887688	+	0.460446i	$0.152310\pi$
$937$			2.47490e7i			0.920891i	−0.887688	+	0.460446i	$0.847690\pi$
$938$	2.54469e7	−	1.61990e7i	0.944339	−	0.601148i
$939$			2.71858e6i			0.100618i
$940$		0			0
$941$			3.63378e7i			1.33778i	0.743361	+	0.668890i	$0.233230\pi$
$941$			3.63378e7i			1.33778i	−0.743361	+	0.668890i	$0.766770\pi$
$942$	2.63537e7	+	4.13989e7i	0.967641	+	1.52006i
$943$		−	1.24540e7i		−	0.456067i
$944$	2.63197e7	−	2.20223e7i	0.961281	−	0.804329i
$945$		0			0
$946$	6.08385e6	−	3.87286e6i	0.221030	−	0.140703i
$947$	−5.78262e6			−0.209532			−0.104766	−	0.994497i	$-0.533409\pi$
$947$	−5.78262e6			−0.209532			−0.104766	+	0.994497i	$0.533409\pi$
$948$	−2.35747e7	+	5.04642e7i	−0.851971	+	1.82374i
$949$			3.89543e7i			1.40407i
$950$		0			0
$951$	−3.06759e7			−1.09988
$952$	−9.32891e6	+	1.21825e6i	−0.333610	+	0.0435656i
$953$			4.95180e7i			1.76616i	0.469220	+	0.883081i	$0.344535\pi$
$953$			4.95180e7i			1.76616i	−0.469220	+	0.883081i	$0.655465\pi$
$954$	2.07525e7	+	3.26000e7i	0.738243	+	1.15970i
$955$		0			0
$956$	5.09020e6	−	1.08961e7i	0.180132	−	0.385591i
$957$	−1.82531e7			−0.644254
$958$	−2.51251e7	−	3.94689e7i	−0.884494	−	1.38945i
$959$	886573.			0.0311292
$960$		0			0
$961$	−4.88839e6			−0.170749
$962$	−8.53504e6	−	1.34076e7i	−0.297350	−	0.467105i
$963$	−5.88954e7			−2.04652
$964$	−8.29042e6	+	1.77465e7i	−0.287332	+	0.615065i
$965$		0			0
$966$	1.37519e7	+	2.16028e7i	0.474155	+	0.744847i
$967$		−	1.73855e7i		−	0.597891i	−0.954270	−	0.298945i	$-0.903365\pi$
$967$		−	1.73855e7i		−	0.597891i	0.954270	−	0.298945i	$-0.0966348\pi$
$968$	2.59149e7	−	3.38419e6i	0.888918	−	0.116083i
$969$	−1.51573e6			−0.0518577
$970$		0			0
$971$			5.82121e7i			1.98137i	0.136186	+	0.990683i	$0.456516\pi$
$971$			5.82121e7i			1.98137i	−0.136186	+	0.990683i	$0.543484\pi$
$972$	1.72514e7	−	3.69285e7i	0.585677	−	1.25371i
$973$	2.64341e7			0.895121
$974$	−2.36530e7	+	1.50571e7i	−0.798895	+	0.508561i
$975$		0			0
$976$	3.80947e7	−	3.18748e7i	1.28009	−	1.07108i
$977$			2.03137e7i			0.680853i	0.940271	+	0.340426i	$0.110571\pi$
$977$			2.03137e7i			0.680853i	−0.940271	+	0.340426i	$0.889429\pi$
$978$	−1.14974e6	−	1.80612e6i	−0.0384373	−	0.0603809i
$979$			1.37826e7i			0.459593i
$980$		0			0
$981$			1.55162e7i			0.514769i
$982$	2.87180e7	−	1.82813e7i	0.950331	−	0.604962i
$983$			5.54003e7i			1.82864i	0.404991	+	0.914321i	$0.367275\pi$
$983$			5.54003e7i			1.82864i	−0.404991	+	0.914321i	$0.632725\pi$
$984$	−4.42336e7	+	5.77640e6i	−1.45634	+	0.190182i
$985$		0			0
$986$	5.88208e6	+	9.24013e6i	0.192681	+	0.302681i
$987$	2.38954e7			0.780768
$988$	4.37209e6	+	2.04245e6i	0.142494	+	0.0665670i
$989$			1.17801e7i			0.382965i
$990$		0			0
$991$	−9.26753e6			−0.299764			−0.149882	−	0.988704i	$-0.547889\pi$
$991$	−9.26753e6			−0.299764			−0.149882	+	0.988704i	$0.547889\pi$
$992$	8.53410e6	−	2.69031e7i	0.275346	−	0.868007i
$993$		−	4.77179e7i		−	1.53571i
$994$	4.56019e7	−	2.90292e7i	1.46392	−	0.931901i
$995$		0			0
$996$	−1.97066e7	+	4.21841e7i	−0.629453	+	1.34741i
$997$	5.53912e7			1.76483			0.882415	−	0.470471i	$-0.155916\pi$
$997$	5.53912e7			1.76483			0.882415	+	0.470471i	$0.155916\pi$
$998$	3.75955e7	−	2.39325e7i	1.19484	−	0.760611i
$999$	−6.23544e6			−0.197676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.a.149.3		8
4.3	odd	2		800.6.f.a.49.1		8
5.2	odd	4		200.6.d.a.101.3		4
5.3	odd	4		8.6.b.a.5.2	yes	4
5.4	even	2	inner	200.6.f.a.149.6		8
8.3	odd	2		800.6.f.a.49.7		8
8.5	even	2	inner	200.6.f.a.149.5		8
15.8	even	4		72.6.d.b.37.3		4
20.3	even	4		32.6.b.a.17.1		4
20.7	even	4		800.6.d.a.401.4		4
20.19	odd	2		800.6.f.a.49.8		8
40.3	even	4		32.6.b.a.17.4		4
40.13	odd	4		8.6.b.a.5.1	✓	4
40.19	odd	2		800.6.f.a.49.2		8
40.27	even	4		800.6.d.a.401.1		4
40.29	even	2	inner	200.6.f.a.149.4		8
40.37	odd	4		200.6.d.a.101.4		4
60.23	odd	4		288.6.d.b.145.3		4
80.3	even	4		256.6.a.n.1.4		4
80.13	odd	4		256.6.a.k.1.1		4
80.43	even	4		256.6.a.n.1.1		4
80.53	odd	4		256.6.a.k.1.4		4
120.53	even	4		72.6.d.b.37.4		4
120.83	odd	4		288.6.d.b.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.6.b.a.5.1	✓	4	40.13	odd	4
8.6.b.a.5.2	yes	4	5.3	odd	4
32.6.b.a.17.1		4	20.3	even	4
32.6.b.a.17.4		4	40.3	even	4
72.6.d.b.37.3		4	15.8	even	4
72.6.d.b.37.4		4	120.53	even	4
200.6.d.a.101.3		4	5.2	odd	4
200.6.d.a.101.4		4	40.37	odd	4
200.6.f.a.149.3		8	1.1	even	1	trivial
200.6.f.a.149.4		8	40.29	even	2	inner
200.6.f.a.149.5		8	8.5	even	2	inner
200.6.f.a.149.6		8	5.4	even	2	inner
256.6.a.k.1.1		4	80.13	odd	4
256.6.a.k.1.4		4	80.53	odd	4
256.6.a.n.1.1		4	80.43	even	4
256.6.a.n.1.4		4	80.3	even	4
288.6.d.b.145.2		4	120.83	odd	4
288.6.d.b.145.3		4	60.23	odd	4
800.6.d.a.401.1		4	40.27	even	4
800.6.d.a.401.4		4	20.7	even	4
800.6.f.a.49.1		8	4.3	odd	2
800.6.f.a.49.2		8	40.19	odd	2
800.6.f.a.49.7		8	8.3	odd	2
800.6.f.a.49.8		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)

\(f(q)\)	\(=\)	\(q+(-3.03776 - 4.77200i) q^{2} +23.6095 q^{3} +(-13.5440 + 28.9924i) q^{4} +(-71.7200 - 112.665i) q^{6} +160.704i q^{7} +(179.495 - 23.4400i) q^{8} +314.408 q^{9} +O(q^{10})\)	\(q+(-3.03776 - 4.77200i) q^{2} +23.6095 q^{3} +(-13.5440 + 28.9924i) q^{4} +(-71.7200 - 112.665i) q^{6} +160.704i q^{7} +(179.495 - 23.4400i) q^{8} +314.408 q^{9} +129.129i q^{11} +(-319.767 + 684.496i) q^{12} -759.659 q^{13} +(766.880 - 488.181i) q^{14} +(-657.120 - 785.347i) q^{16} +323.408i q^{17} +(-955.097 - 1500.36i) q^{18} +198.511i q^{19} +3794.14i q^{21} +(616.204 - 392.264i) q^{22} +1193.15i q^{23} +(4237.79 - 553.407i) q^{24} +(2307.66 + 3625.10i) q^{26} +1685.91 q^{27} +(-4659.20 - 2176.58i) q^{28} +5987.24i q^{29} -4872.45 q^{31} +(-1751.50 + 5521.47i) q^{32} +3048.67i q^{33} +(1543.30 - 982.437i) q^{34} +(-4258.34 + 9115.45i) q^{36} -3698.56 q^{37} +(947.297 - 603.031i) q^{38} -17935.2 q^{39} -10437.9 q^{41} +(18105.6 - 11525.7i) q^{42} +9873.11 q^{43} +(-3743.76 - 1748.93i) q^{44} +(5693.73 - 3624.51i) q^{46} -6297.98i q^{47} +(-15514.3 - 18541.6i) q^{48} -9018.79 q^{49} +7635.50i q^{51} +(10288.8 - 22024.4i) q^{52} -21728.1 q^{53} +(-5121.39 - 8045.16i) q^{54} +(3766.91 + 28845.6i) q^{56} +4686.75i q^{57} +(28571.1 - 18187.8i) q^{58} +33513.4i q^{59} +48506.8i q^{61} +(14801.3 + 23251.3i) q^{62} +50526.7i q^{63} +(31669.1 - 8414.75i) q^{64} +(14548.3 - 9261.14i) q^{66} +33182.4 q^{67} +(-9376.38 - 4380.24i) q^{68} +28169.7i q^{69} +59464.1 q^{71} +(56434.8 - 7369.74i) q^{72} -51278.6i q^{73} +(11235.4 + 17649.5i) q^{74} +(-5755.33 - 2688.64i) q^{76} -20751.6 q^{77} +(54482.8 + 85586.7i) q^{78} +73724.5 q^{79} -36597.7 q^{81} +(31707.8 + 49809.6i) q^{82} +61628.0 q^{83} +(-110001. - 51387.9i) q^{84} +(-29992.1 - 47114.5i) q^{86} +141356. i q^{87} +(3026.79 + 23178.1i) q^{88} +106735. q^{89} -122080. i q^{91} +(-34592.4 - 16160.1i) q^{92} -115036. q^{93} +(-30054.0 + 19131.8i) q^{94} +(-41352.1 + 130359. i) q^{96} +12562.9i q^{97} +(27397.0 + 43037.7i) q^{98} +40599.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 40 q^{4} - 232 q^{6} + 328 q^{9}+O(q^{10}) \) 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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