LMFDB - Embedded newform 196.6.d.c.195.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.18
Character	$\chi$	$=$	196.195
Dual form			196.6.d.c.195.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.84200 - 5.34855i) q^{2} +13.3457 q^{3} +(-25.2141 + 19.7041i) q^{4} +89.8785i q^{5} +(-24.5829 - 71.3804i) q^{6} +(151.833 + 98.5639i) q^{8} -64.8912 q^{9} +(480.720 - 165.556i) q^{10} +90.1372i q^{11} +(-336.500 + 262.966i) q^{12} -273.804i q^{13} +1199.50i q^{15} +(247.498 - 993.640i) q^{16} -692.565i q^{17} +(119.530 + 347.074i) q^{18} +1797.49 q^{19} +(-1770.97 - 2266.20i) q^{20} +(482.104 - 166.033i) q^{22} +4029.93i q^{23} +(2026.32 + 1315.41i) q^{24} -4953.14 q^{25} +(-1464.45 + 504.347i) q^{26} -4109.04 q^{27} -8236.85 q^{29} +(6415.56 - 2209.47i) q^{30} -8618.34 q^{31} +(-5770.43 + 506.528i) q^{32} +1202.95i q^{33} +(-3704.22 + 1275.71i) q^{34} +(1636.17 - 1278.62i) q^{36} +9457.54 q^{37} +(-3310.97 - 9613.96i) q^{38} -3654.11i q^{39} +(-8858.77 + 13646.5i) q^{40} +10538.0i q^{41} -6505.37i q^{43} +(-1776.07 - 2272.72i) q^{44} -5832.33i q^{45} +(21554.3 - 7423.13i) q^{46} -27987.0 q^{47} +(3303.05 - 13260.9i) q^{48} +(9123.69 + 26492.2i) q^{50} -9242.79i q^{51} +(5395.05 + 6903.70i) q^{52} -20667.5 q^{53} +(7568.85 + 21977.4i) q^{54} -8101.39 q^{55} +23988.8 q^{57} +(15172.3 + 44055.2i) q^{58} +12442.9 q^{59} +(-23634.9 - 30244.1i) q^{60} +10511.9i q^{61} +(15875.0 + 46095.6i) q^{62} +(13338.3 + 29930.4i) q^{64} +24609.1 q^{65} +(6434.03 - 2215.83i) q^{66} -6641.50i q^{67} +(13646.4 + 17462.4i) q^{68} +53782.4i q^{69} -57508.8i q^{71} +(-9852.61 - 6395.93i) q^{72} +20558.7i q^{73} +(-17420.8 - 50584.1i) q^{74} -66103.4 q^{75} +(-45322.0 + 35417.8i) q^{76} +(-19544.2 + 6730.88i) q^{78} +78140.5i q^{79} +(89306.9 + 22244.8i) q^{80} -39069.6 q^{81} +(56363.0 - 19411.0i) q^{82} -4248.11 q^{83} +62246.7 q^{85} +(-34794.3 + 11982.9i) q^{86} -109927. q^{87} +(-8884.27 + 13685.8i) q^{88} +44187.1i q^{89} +(-31194.5 + 10743.1i) q^{90} +(-79406.0 - 101611. i) q^{92} -115018. q^{93} +(51552.0 + 149690. i) q^{94} +161556. i q^{95} +(-77010.7 + 6759.99i) q^{96} -80366.9i q^{97} -5849.11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} - 172 q^{4} - 356 q^{8} + 5832 q^{9} + 84 q^{16} + 1620 q^{18} - 17616 q^{22} - 25000 q^{25} - 16288 q^{29} - 32440 q^{30} - 6556 q^{32} + 44444 q^{36} + 42592 q^{37} + 17784 q^{44} - 25560 q^{46}+ \cdots + 3168 q^{93}+O(q^{100}) $ 56 * q + 4 * q^2 - 172 * q^4 - 356 * q^8 + 5832 * q^9 + 84 * q^16 + 1620 * q^18 - 17616 * q^22 - 25000 * q^25 - 16288 * q^29 - 32440 * q^30 - 6556 * q^32 + 44444 * q^36 + 42592 * q^37 + 17784 * q^44 - 25560 * q^46 + 13932 * q^50 - 259888 * q^53 + 82592 * q^57 + 140792 * q^58 + 240488 * q^60 - 264340 * q^64 - 189440 * q^65 + 244444 * q^72 - 273608 * q^74 + 350936 * q^78 + 405112 * q^81 - 407344 * q^85 - 243776 * q^86 + 181248 * q^88 - 262696 * q^92 + 3168 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.84200	−	5.34855i	−0.325623	−	0.945500i
$2$	−1.84200	−	5.34855i	−0.325623	−	0.945500i
$3$	13.3457			0.856130			0.428065	−	0.903748i	$-0.359195\pi$
$3$	13.3457			0.856130			0.428065	+	0.903748i	$0.359195\pi$
$4$	−25.2141	+	19.7041i	−0.787940	+	0.615753i
$5$			89.8785i			1.60780i	0.594768	+	0.803898i	$0.297244\pi$
$5$			89.8785i			1.60780i	−0.594768	+	0.803898i	$0.702756\pi$
$6$	−24.5829	−	71.3804i	−0.278775	−	0.809470i
$7$		0			0
$7$		0			0
$8$	151.833	+	98.5639i	0.838765	+	0.544494i
$9$	−64.8912			−0.267042
$10$	480.720	−	165.556i	1.52017	−	0.523535i
$11$			90.1372i			0.224606i	0.993674	+	0.112303i	$0.0358228\pi$
$11$			90.1372i			0.224606i	−0.993674	+	0.112303i	$0.964177\pi$
$12$	−336.500	+	262.966i	−0.674578	+	0.527164i
$13$		−	273.804i		−	0.449346i	−0.974434	−	0.224673i	$-0.927869\pi$
$13$		−	273.804i		−	0.449346i	0.974434	−	0.224673i	$-0.0721314\pi$
$14$		0			0
$15$			1199.50i			1.37648i
$16$	247.498	−	993.640i	0.241698	−	0.970352i
$17$		−	692.565i		−	0.581217i	−0.956842	−	0.290608i	$-0.906142\pi$
$17$		−	692.565i		−	0.581217i	0.956842	−	0.290608i	$-0.0938577\pi$
$18$	119.530	+	347.074i	0.0869550	+	0.252488i
$19$	1797.49			1.14230			0.571152	−	0.820844i	$-0.306497\pi$
$19$	1797.49			1.14230			0.571152	+	0.820844i	$0.306497\pi$
$20$	−1770.97	−	2266.20i	−0.990004	−	1.26685i
$21$		0			0
$22$	482.104	−	166.033i	0.212365	−	0.0731370i
$23$			4029.93i			1.58847i	0.607614	+	0.794233i	$0.292127\pi$
$23$			4029.93i			1.58847i	−0.607614	+	0.794233i	$0.707873\pi$
$24$	2026.32	+	1315.41i	0.718092	+	0.466157i
$25$	−4953.14			−1.58501
$26$	−1464.45	+	504.347i	−0.424857	+	0.146317i
$27$	−4109.04			−1.08475
$28$		0			0
$29$	−8236.85			−1.81872			−0.909360	−	0.416009i	$-0.863428\pi$
$29$	−8236.85			−1.81872			−0.909360	+	0.416009i	$0.863428\pi$
$30$	6415.56	−	2209.47i	1.30146	−	0.448214i
$31$	−8618.34			−1.61072			−0.805358	−	0.592788i	$-0.798027\pi$
$31$	−8618.34			−1.61072			−0.805358	+	0.592788i	$0.798027\pi$
$32$	−5770.43	+	506.528i	−0.996169	+	0.0874437i
$33$			1202.95i			0.192292i
$34$	−3704.22	+	1275.71i	−0.549540	+	0.189257i
$35$		0			0
$36$	1636.17	−	1278.62i	0.210413	−	0.164432i
$37$	9457.54			1.13573			0.567863	−	0.823123i	$-0.307770\pi$
$37$	9457.54			1.13573			0.567863	+	0.823123i	$0.307770\pi$
$38$	−3310.97	−	9613.96i	−0.371960	−	1.08005i
$39$		−	3654.11i		−	0.384698i
$40$	−8858.77	+	13646.5i	−0.875434	+	1.34856i
$41$			10538.0i			0.979035i	0.871994	+	0.489517i	$0.162827\pi$
$41$			10538.0i			0.979035i	−0.871994	+	0.489517i	$0.837173\pi$
$42$		0			0
$43$		−	6505.37i		−	0.536538i	−0.963344	−	0.268269i	$-0.913548\pi$
$43$		−	6505.37i		−	0.536538i	0.963344	−	0.268269i	$-0.0864516\pi$
$44$	−1776.07	−	2272.72i	−0.138302	−	0.176976i
$45$		−	5832.33i		−	0.429349i
$46$	21554.3	−	7423.13i	1.50189	−	0.517241i
$47$	−27987.0			−1.84804			−0.924019	−	0.382346i	$-0.875116\pi$
$47$	−27987.0			−1.84804			−0.924019	+	0.382346i	$0.875116\pi$
$48$	3303.05	−	13260.9i	0.206924	−	0.830747i
$49$		0			0
$50$	9123.69	+	26492.2i	0.516114	+	1.49862i
$51$		−	9242.79i		−	0.497597i
$52$	5395.05	+	6903.70i	0.276686	+	0.354057i
$53$	−20667.5			−1.01064			−0.505322	−	0.862931i	$-0.668626\pi$
$53$	−20667.5			−1.01064			−0.505322	+	0.862931i	$0.668626\pi$
$54$	7568.85	+	21977.4i	0.353220	+	1.02563i
$55$	−8101.39			−0.361121
$56$		0			0
$57$	23988.8			0.977961
$58$	15172.3	+	44055.2i	0.592217	+	1.71960i
$59$	12442.9			0.465363			0.232682	−	0.972553i	$-0.425250\pi$
$59$	12442.9			0.465363			0.232682	+	0.972553i	$0.425250\pi$
$60$	−23634.9	−	30244.1i	−0.847572	−	1.08458i
$61$			10511.9i			0.361706i	0.983510	+	0.180853i	$0.0578859\pi$
$61$			10511.9i			0.361706i	−0.983510	+	0.180853i	$0.942114\pi$
$62$	15875.0	+	46095.6i	0.524486	+	1.52293i
$63$		0			0
$64$	13338.3	+	29930.4i	0.407053	+	0.913404i
$65$	24609.1			0.722456
$66$	6434.03	−	2215.83i	0.181812	−	0.0626147i
$67$		−	6641.50i		−	0.180750i	−0.995908	−	0.0903752i	$-0.971193\pi$
$67$		−	6641.50i		−	0.180750i	0.995908	−	0.0903752i	$-0.0288066\pi$
$68$	13646.4	+	17462.4i	0.357886	+	0.457964i
$69$			53782.4i			1.35993i
$70$		0			0
$71$		−	57508.8i		−	1.35391i	−0.736026	−	0.676953i	$-0.763300\pi$
$71$		−	57508.8i		−	1.35391i	0.736026	−	0.676953i	$-0.236700\pi$
$72$	−9852.61	−	6395.93i	−0.223986	−	0.145403i
$73$			20558.7i			0.451531i	0.974182	+	0.225766i	$0.0724884\pi$
$73$			20558.7i			0.451531i	−0.974182	+	0.225766i	$0.927512\pi$
$74$	−17420.8	−	50584.1i	−0.369818	−	1.07383i
$75$	−66103.4			−1.35697
$76$	−45322.0	+	35417.8i	−0.900067	+	0.703377i
$77$		0			0
$78$	−19544.2	+	6730.88i	−0.363732	+	0.125267i
$79$			78140.5i			1.40867i	0.709869	+	0.704333i	$0.248754\pi$
$79$			78140.5i			1.40867i	−0.709869	+	0.704333i	$0.751246\pi$
$80$	89306.9	+	22244.8i	1.56013	+	0.388600i
$81$	−39069.6			−0.661646
$82$	56363.0	−	19411.0i	0.925677	−	0.318796i
$83$	−4248.11			−0.0676862			−0.0338431	−	0.999427i	$-0.510775\pi$
$83$	−4248.11			−0.0676862			−0.0338431	+	0.999427i	$0.510775\pi$
$84$		0			0
$85$	62246.7			0.934478
$86$	−34794.3	+	11982.9i	−0.507297	+	0.174709i
$87$	−109927.			−1.55706
$88$	−8884.27	+	13685.8i	−0.122297	+	0.188392i
$89$			44187.1i			0.591317i	0.955294	+	0.295659i	$0.0955391\pi$
$89$			44187.1i			0.591317i	−0.955294	+	0.295659i	$0.904461\pi$
$90$	−31194.5	+	10743.1i	−0.405949	+	0.139806i
$91$		0			0
$92$	−79406.0	−	101611.i	−0.978102	−	1.25161i
$93$	−115018.			−1.37898
$94$	51552.0	+	149690.i	0.601764	+	1.74732i
$95$			161556.i			1.83659i
$96$	−77010.7	+	6759.99i	−0.852850	+	0.0748631i
$97$		−	80366.9i		−	0.867257i	−0.901092	−	0.433628i	$-0.857233\pi$
$97$		−	80366.9i		−	0.867257i	0.901092	−	0.433628i	$-0.142767\pi$
$98$		0			0
$99$		−	5849.11i		−	0.0599794i
$100$	124889.	−	97597.1i	1.24889	−	0.975971i
$101$		−	144438.i		−	1.40889i	−0.709758	−	0.704445i	$-0.751196\pi$
$101$		−	144438.i		−	1.40889i	0.709758	−	0.704445i	$-0.248804\pi$
$102$	−49435.6	+	17025.2i	−0.470478	+	0.162029i
$103$	−63973.0			−0.594160			−0.297080	−	0.954853i	$-0.596013\pi$
$103$	−63973.0			−0.594160			−0.297080	+	0.954853i	$0.596013\pi$
$104$	26987.1	−	41572.3i	0.244666	−	0.376896i
$105$		0			0
$106$	38069.6	+	110541.i	0.329089	+	0.955564i
$107$			136518.i			1.15273i	0.817191	+	0.576367i	$0.195530\pi$
$107$			136518.i			1.15273i	−0.817191	+	0.576367i	$0.804470\pi$
$108$	103606.	−	80964.8i	0.854719	−	0.667939i
$109$	105980.			0.854389			0.427195	−	0.904160i	$-0.359502\pi$
$109$	105980.			0.854389			0.427195	+	0.904160i	$0.359502\pi$
$110$	14922.8	+	43330.7i	0.117589	+	0.341440i
$111$	126218.			0.972329
$112$		0			0
$113$	113230.			0.834192			0.417096	−	0.908862i	$-0.363048\pi$
$113$	113230.			0.834192			0.417096	+	0.908862i	$0.363048\pi$
$114$	−44187.4	−	128305.i	−0.318446	−	0.924662i
$115$	−362204.			−2.55393
$116$	207684.	−	162300.i	1.43304	−	1.11988i
$117$			17767.5i			0.119994i
$118$	−22919.8	−	66551.6i	−0.151533	−	0.440001i
$119$		0			0
$120$	−118227.	+	182123.i	−0.749485	+	1.15454i
$121$	152926.			0.949552
$122$	56223.4	−	19362.9i	0.341993	−	0.117780i
$123$			140637.i			0.838181i
$124$	217303.	−	169816.i	1.26915	−	0.991803i
$125$		−	164311.i		−	0.940570i
$126$		0			0
$127$		−	51441.6i		−	0.283012i	−0.989937	−	0.141506i	$-0.954806\pi$
$127$		−	51441.6i		−	0.283012i	0.989937	−	0.141506i	$-0.0451945\pi$
$128$	135515.	−	126473.i	0.731078	−	0.682294i
$129$		−	86818.9i		−	0.459346i
$130$	−45329.9	−	131623.i	−0.235248	−	0.683082i
$131$	30369.8			0.154619			0.0773097	−	0.997007i	$-0.475367\pi$
$131$	30369.8			0.154619			0.0773097	+	0.997007i	$0.475367\pi$
$132$	−23703.0	−	30331.2i	−0.118404	−	0.151515i
$133$		0			0
$134$	−35522.4	+	12233.7i	−0.170899	+	0.0588565i
$135$		−	369314.i		−	1.74406i
$136$	68261.9	−	105154.i	0.316469	−	0.487504i
$137$	−69557.4			−0.316623			−0.158311	−	0.987389i	$-0.550605\pi$
$137$	−69557.4			−0.316623			−0.158311	+	0.987389i	$0.550605\pi$
$138$	287658.	−	99067.2i	1.28582	−	0.442825i
$139$	−69683.1			−0.305908			−0.152954	−	0.988233i	$-0.548879\pi$
$139$	−69683.1			−0.305908			−0.152954	+	0.988233i	$0.548879\pi$
$140$		0			0
$141$	−373507.			−1.58216
$142$	−307589.	+	105931.i	−1.28012	+	0.440863i
$143$	24679.9			0.100926
$144$	−16060.5	+	64478.5i	−0.0645434	+	0.259125i
$145$		−	740315.i		−	2.92413i
$146$	109959.	−	37869.1i	0.426923	−	0.147029i
$147$		0			0
$148$	−238463.	+	186352.i	−0.894884	+	0.699326i
$149$	−302553.			−1.11644			−0.558221	−	0.829692i	$-0.688516\pi$
$149$	−302553.			−1.11644			−0.558221	+	0.829692i	$0.688516\pi$
$150$	121762.	+	353557.i	0.441861	+	1.28302i
$151$			111408.i			0.397626i	0.980037	+	0.198813i	$0.0637086\pi$
$151$			111408.i			0.397626i	−0.980037	+	0.198813i	$0.936291\pi$
$152$	272917.	+	177167.i	0.958125	+	0.621978i
$153$			44941.4i			0.155209i
$154$		0			0
$155$		−	774603.i		−	2.58970i
$156$	72000.9	+	92135.0i	0.236879	+	0.303119i
$157$		−	111682.i		−	0.361605i	−0.983519	−	0.180802i	$-0.942131\pi$
$157$		−	111682.i		−	0.361605i	0.983519	−	0.180802i	$-0.0578695\pi$
$158$	417938.	−	143935.i	1.33189	−	0.458694i
$159$	−275823.			−0.865243
$160$	−45526.0	−	518638.i	−0.140592	−	1.60164i
$161$		0			0
$162$	71966.2	+	208966.i	0.215447	+	0.625587i
$163$		−	202294.i		−	0.596367i	−0.954509	−	0.298183i	$-0.903619\pi$
$163$		−	202294.i		−	0.596367i	0.954509	−	0.298183i	$-0.0963807\pi$
$164$	−207641.	−	265706.i	−0.602843	−	0.771420i
$165$	−108119.			−0.309167
$166$	7825.02	+	22721.2i	0.0220402	+	0.0639973i
$167$	−16381.5			−0.0454531			−0.0227266	−	0.999742i	$-0.507235\pi$
$167$	−16381.5			−0.0454531			−0.0227266	+	0.999742i	$0.507235\pi$
$168$		0			0
$169$	296325.			0.798088
$170$	−114658.	−	332930.i	−0.304287	−	0.883548i
$171$	−116641.			−0.305043
$172$	128182.	+	164027.i	0.330375	+	0.422760i
$173$			137145.i			0.348390i	0.984711	+	0.174195i	$0.0557323\pi$
$173$			137145.i			0.348390i	−0.984711	+	0.174195i	$0.944268\pi$
$174$	202485.	+	587950.i	0.507015	+	1.47220i
$175$		0			0
$176$	89563.9	+	22308.8i	0.217947	+	0.0542868i
$177$	166060.			0.398411
$178$	236337.	−	81392.7i	0.559090	−	0.192546i
$179$			603009.i			1.40667i	0.710860	+	0.703334i	$0.248306\pi$
$179$			603009.i			1.40667i	−0.710860	+	0.703334i	$0.751694\pi$
$180$	114921.	+	147057.i	0.264373	+	0.338301i
$181$			165698.i			0.375942i	0.982175	+	0.187971i	$0.0601911\pi$
$181$			165698.i			0.375942i	−0.982175	+	0.187971i	$0.939809\pi$
$182$		0			0
$183$			140289.i			0.309668i
$184$	−397205.	+	611875.i	−0.864909	+	1.33235i
$185$			850029.i			1.82602i
$186$	211863.	+	615180.i	0.449028	+	1.30383i
$187$	62425.8			0.130545
$188$	705665.	−	551457.i	1.45614	−	1.13793i
$189$		0			0
$190$	864088.	−	297585.i	1.73650	−	0.598036i
$191$			837537.i			1.66119i	0.556873	+	0.830597i	$0.312001\pi$
$191$			837537.i			1.66119i	−0.556873	+	0.830597i	$0.687999\pi$
$192$	178010.	+	399444.i	0.348491	+	0.781993i
$193$	119344.			0.230626			0.115313	−	0.993329i	$-0.463213\pi$
$193$	119344.			0.230626			0.115313	+	0.993329i	$0.463213\pi$
$194$	−429846.	+	148036.i	−0.819991	+	0.282399i
$195$	328426.			0.618516
$196$		0			0
$197$	−230198.			−0.422606			−0.211303	−	0.977421i	$-0.567771\pi$
$197$	−230198.			−0.422606			−0.211303	+	0.977421i	$0.567771\pi$
$198$	−31284.3	+	10774.1i	−0.0567105	+	0.0195306i
$199$	−168443.			−0.301522			−0.150761	−	0.988570i	$-0.548172\pi$
$199$	−168443.			−0.301522			−0.150761	+	0.988570i	$0.548172\pi$
$200$	−752049.	−	488201.i	−1.32945	−	0.863026i
$201$		−	88635.8i		−	0.154746i
$202$	−772533.	+	266054.i	−1.33211	+	0.458767i
$203$		0			0
$204$	182121.	+	233048.i	0.306397	+	0.392076i
$205$	−947139.			−1.57409
$206$	117838.	+	342163.i	0.193472	+	0.561778i
$207$		−	261507.i		−	0.424187i
$208$	−272062.	−	67765.9i	−0.436024	−	0.108606i
$209$			162020.i			0.256569i
$210$		0			0
$211$			285910.i			0.442103i	0.975262	+	0.221051i	$0.0709488\pi$
$211$			285910.i			0.442103i	−0.975262	+	0.221051i	$0.929051\pi$
$212$	521112.	−	407234.i	0.796327	−	0.622307i
$213$		−	767498.i		−	1.15912i
$214$	730172.	−	251466.i	1.08991	−	0.375357i
$215$	584693.			0.862644
$216$	−623886.	−	405002.i	−0.909852	−	0.590641i
$217$		0			0
$218$	−195214.	−	566837.i	−0.278209	−	0.807825i
$219$			274371.i			0.386569i
$220$	204269.	−	159631.i	0.284542	−	0.222361i
$221$	−189627.			−0.261167
$222$	−232493.	−	675083.i	−0.316612	−	0.919337i
$223$	204184.			0.274954			0.137477	−	0.990505i	$-0.456101\pi$
$223$	204184.			0.274954			0.137477	+	0.990505i	$0.456101\pi$
$224$		0			0
$225$	321416.			0.423263
$226$	−208570.	−	605618.i	−0.271632	−	0.788729i
$227$	417704.			0.538027			0.269014	−	0.963136i	$-0.413302\pi$
$227$	417704.			0.538027			0.269014	+	0.963136i	$0.413302\pi$
$228$	−604855.	+	472677.i	−0.770574	+	0.602182i
$229$			913450.i			1.15105i	0.817783	+	0.575527i	$0.195203\pi$
$229$			913450.i			1.15105i	−0.817783	+	0.575527i	$0.804797\pi$
$230$	667180.	+	1.93727e6i	0.831617	+	2.41474i
$231$		0			0
$232$	−1.25062e6	−	811856.i	−1.52548	−	0.990282i
$233$	1.40328e6			1.69337			0.846687	−	0.532091i	$-0.178594\pi$
$233$	1.40328e6			1.69337			0.846687	+	0.532091i	$0.178594\pi$
$234$	95030.2	−	32727.7i	0.113455	−	0.0390729i
$235$		−	2.51543e6i		−	2.97127i
$236$	−313736.	+	245176.i	−0.366678	+	0.286549i
$237$			1.04284e6i			1.20600i
$238$		0			0
$239$			1.43599e6i			1.62614i	0.582166	+	0.813070i	$0.302205\pi$
$239$			1.43599e6i			1.62614i	−0.582166	+	0.813070i	$0.697795\pi$
$240$	1.19187e6	+	296873.i	1.33567	+	0.332692i
$241$		−	287115.i		−	0.318429i	−0.987244	−	0.159214i	$-0.949104\pi$
$241$		−	287115.i		−	0.318429i	0.987244	−	0.159214i	$-0.0508961\pi$
$242$	−281690.	−	817935.i	−0.309196	−	0.897801i
$243$	477084.			0.518297
$244$	−207127.	−	265047.i	−0.222722	−	0.285003i
$245$		0			0
$246$	752206.	−	259054.i	0.792500	−	0.272931i
$247$		−	492159.i		−	0.513290i
$248$	−1.30855e6	−	849457.i	−1.35101	−	0.877025i
$249$	−56694.1			−0.0579482
$250$	−878825.	+	302661.i	−0.889308	+	0.306271i
$251$	−1.45529e6			−1.45803			−0.729015	−	0.684498i	$-0.760022\pi$
$251$	−1.45529e6			−1.45803			−0.729015	+	0.684498i	$0.760022\pi$
$252$		0			0
$253$	−363246.			−0.356780
$254$	−275138.	+	94755.4i	−0.267588	+	0.0921552i
$255$	830728.			0.800034
$256$	−926065.	−	491848.i	−0.883165	−	0.469063i
$257$			1.06667e6i			1.00739i	0.863881	+	0.503695i	$0.168027\pi$
$257$			1.06667e6i			1.00739i	−0.863881	+	0.503695i	$0.831973\pi$
$258$	−464356.	+	159921.i	−0.434312	+	0.149574i
$259$		0			0
$260$	−620494.	+	484899.i	−0.569252	+	0.444854i
$261$	534499.			0.485675
$262$	−55941.3	−	162435.i	−0.0503476	−	0.146193i
$263$			1.15036e6i			1.02552i	0.858531	+	0.512762i	$0.171378\pi$
$263$			1.15036e6i			1.02552i	−0.858531	+	0.512762i	$0.828622\pi$
$264$	−118567.	+	182647.i	−0.104702	+	0.161288i
$265$		−	1.85756e6i		−	1.62491i
$266$		0			0
$267$			589710.i			0.506244i
$268$	130865.	+	167459.i	0.111298	+	0.142420i
$269$			877595.i			0.739458i	0.929140	+	0.369729i	$0.120549\pi$
$269$			877595.i			0.739458i	−0.929140	+	0.369729i	$0.879451\pi$
$270$	−1.97530e6	+	680277.i	−1.64901	+	0.567906i
$271$	−2.05833e6			−1.70252			−0.851260	−	0.524744i	$-0.824161\pi$
$271$	−2.05833e6			−1.70252			−0.851260	+	0.524744i	$0.824161\pi$
$272$	−688160.	−	171409.i	−0.563985	−	0.140479i
$273$		0			0
$274$	128125.	+	372032.i	0.103100	+	0.299367i
$275$		−	446462.i		−	0.356003i
$276$	−1.05973e6	−	1.35607e6i	−0.837382	−	1.07154i
$277$	1.08549e6			0.850012			0.425006	−	0.905191i	$-0.360272\pi$
$277$	1.08549e6			0.850012			0.425006	+	0.905191i	$0.360272\pi$
$278$	128356.	+	372704.i	0.0996105	+	0.289236i
$279$	559254.			0.430129
$280$		0			0
$281$	1.33676e6			1.00992			0.504960	−	0.863143i	$-0.331507\pi$
$281$	1.33676e6			1.00992			0.504960	+	0.863143i	$0.331507\pi$
$282$	688000.	+	1.99772e6i	0.515188	+	1.49593i
$283$	1.77321e6			1.31612			0.658058	−	0.752967i	$-0.271378\pi$
$283$	1.77321e6			1.31612			0.658058	+	0.752967i	$0.271378\pi$
$284$	1.13316e6	+	1.45003e6i	0.833672	+	1.06680i
$285$			2.15608e6i			1.57236i
$286$	−45460.4	−	132002.i	−0.0328638	−	0.0954255i
$287$		0			0
$288$	374450.	−	32869.2i	0.266019	−	0.0233511i
$289$	940211.			0.662187
$290$	−3.95962e6	+	1.36366e6i	−2.76477	+	0.952164i
$291$		−	1.07256e6i		−	0.742484i
$292$	−405090.	−	518368.i	−0.278032	−	0.355779i
$293$		−	1.08511e6i		−	0.738424i	−0.929345	−	0.369212i	$-0.879628\pi$
$293$		−	1.08511e6i		−	0.738424i	0.929345	−	0.369212i	$-0.120372\pi$
$294$		0			0
$295$			1.11835e6i			0.748209i
$296$	1.43596e6	+	932171.i	0.952607	+	0.618396i
$297$		−	370377.i		−	0.243642i
$298$	557303.	+	1.61822e6i	0.363539	+	1.05560i
$299$	1.10341e6			0.713771
$300$	1.66673e6	−	1.30251e6i	1.06921	−	0.835558i
$301$		0			0
$302$	595872.	−	205214.i	0.375955	−	0.129476i
$303$		−	1.92763e6i		−	1.20619i
$304$	444875.	−	1.78606e6i	0.276092	−	1.10844i
$305$	−944793.			−0.581550
$306$	240371.	−	82782.1i	0.146750	−	0.0505397i
$307$	−1.85493e6			−1.12327			−0.561633	−	0.827386i	$-0.689827\pi$
$307$	−1.85493e6			−1.12327			−0.561633	+	0.827386i	$0.689827\pi$
$308$		0			0
$309$	−853767.			−0.508678
$310$	−4.14301e6	+	1.42682e6i	−2.44856	+	0.843266i
$311$	1.86803e6			1.09517			0.547587	−	0.836749i	$-0.315546\pi$
$311$	1.86803e6			1.09517			0.547587	+	0.836749i	$0.315546\pi$
$312$	360163.	−	554814.i	0.209466	−	0.322672i
$313$		−	2.08823e6i		−	1.20481i	−0.798191	−	0.602404i	$-0.794210\pi$
$313$		−	2.08823e6i		−	1.20481i	0.798191	−	0.602404i	$-0.205790\pi$
$314$	−597338.	+	205718.i	−0.341897	+	0.117747i
$315$		0			0
$316$	−1.53969e6	−	1.97024e6i	−0.867390	−	1.10994i
$317$	1.10686e6			0.618647			0.309324	−	0.950957i	$-0.399897\pi$
$317$	1.10686e6			0.618647			0.309324	+	0.950957i	$0.399897\pi$
$318$	508067.	+	1.47526e6i	0.281743	+	0.818087i
$319$		−	742446.i		−	0.408496i
$320$	−2.69010e6	+	1.19883e6i	−1.46857	+	0.654459i
$321$			1.82193e6i			0.986890i
$322$		0			0
$323$		−	1.24488e6i		−	0.663927i
$324$	985103.	−	769830.i	0.521337	−	0.407411i
$325$			1.35619e6i			0.712216i
$326$	−1.08198e6	+	372625.i	−0.563864	+	0.194191i
$327$	1.41438e6			0.731468
$328$	−1.03867e6	+	1.60001e6i	−0.533078	+	0.821180i
$329$		0			0
$330$	199155.	+	578281.i	0.100672	+	0.292317i
$331$			559286.i			0.280585i	0.990110	+	0.140292i	$0.0448043\pi$
$331$			559286.i			0.280585i	−0.990110	+	0.140292i	$0.955196\pi$
$332$	107112.	−	83705.1i	0.0533327	−	0.0416780i
$333$	−613711.			−0.303287
$334$	30174.8	+	87617.6i	0.0148006	+	0.0429759i
$335$	596928.			0.290610
$336$		0			0
$337$	−2.12539e6			−1.01944			−0.509722	−	0.860339i	$-0.670252\pi$
$337$	−2.12539e6			−1.01944			−0.509722	+	0.860339i	$0.670252\pi$
$338$	−545830.	−	1.58491e6i	−0.259876	−	0.754592i
$339$	1.51114e6			0.714177
$340$	−1.56949e6	+	1.22651e6i	−0.736312	+	0.575407i
$341$		−	776832.i		−	0.361777i
$342$	214853.	+	623862.i	0.0993291	+	0.288418i
$343$		0			0
$344$	641194.	−	987727.i	0.292142	−	0.450030i
$345$	−4.83388e6			−2.18649
$346$	733529.	−	252622.i	0.329403	−	0.113444i
$347$		−	756361.i		−	0.337214i	−0.985683	−	0.168607i	$-0.946073\pi$
$347$		−	756361.i		−	0.337214i	0.985683	−	0.168607i	$-0.0539268\pi$
$348$	2.77170e6	−	2.16601e6i	1.22687	−	0.958764i
$349$			1.06274e6i			0.467052i	0.972351	+	0.233526i	$0.0750264\pi$
$349$			1.06274e6i			0.467052i	−0.972351	+	0.233526i	$0.924974\pi$
$350$		0			0
$351$			1.12507e6i			0.487429i
$352$	−45657.0	−	520130.i	−0.0196404	−	0.223746i
$353$			2.41039e6i			1.02956i	0.857323	+	0.514779i	$0.172126\pi$
$353$			2.41039e6i			1.02956i	−0.857323	+	0.514779i	$0.827874\pi$
$354$	−305882.	−	888180.i	−0.129732	−	0.376698i
$355$	5.16881e6			2.17680
$356$	−870666.	−	1.11414e6i	−0.364105	−	0.465922i
$357$		0			0
$358$	3.22523e6	−	1.11074e6i	1.33000	−	0.458043i
$359$			1.79755e6i			0.736114i	0.929803	+	0.368057i	$0.119977\pi$
$359$			1.79755e6i			0.736114i	−0.929803	+	0.368057i	$0.880023\pi$
$360$	574857.	−	885538.i	0.233778	−	0.360123i
$361$	754864.			0.304860
$362$	886245.	−	305216.i	0.355453	−	0.122415i
$363$	2.04091e6			0.812940
$364$		0			0
$365$	−1.84778e6			−0.725970
$366$	750343.	−	258412.i	0.292791	−	0.100835i
$367$	502973.			0.194930			0.0974652	−	0.995239i	$-0.468927\pi$
$367$	502973.			0.194930			0.0974652	+	0.995239i	$0.468927\pi$
$368$	4.00430e6	+	997400.i	1.54137	+	0.383928i
$369$		−	683823.i		−	0.261443i
$370$	4.54643e6	−	1.56575e6i	1.72650	−	0.594592i
$371$		0			0
$372$	2.90007e6	−	2.26633e6i	1.08655	−	0.849112i
$373$	206010.			0.0766685			0.0383342	−	0.999265i	$-0.487795\pi$
$373$	206010.			0.0766685			0.0383342	+	0.999265i	$0.487795\pi$
$374$	−114988.	−	333888.i	−0.0425084	−	0.123430i
$375$		−	2.19285e6i		−	0.805250i
$376$	−4.24934e6	−	2.75850e6i	−1.55007	−	1.00625i
$377$			2.25528e6i			0.817235i
$378$		0			0
$379$			1.82620e6i			0.653056i	0.945188	+	0.326528i	$0.105879\pi$
$379$			1.82620e6i			0.653056i	−0.945188	+	0.326528i	$0.894121\pi$
$380$	−3.18330e6	−	4.07347e6i	−1.13089	−	1.44712i
$381$		−	686526.i		−	0.242295i
$382$	4.47961e6	−	1.54274e6i	1.57066	−	0.540923i
$383$	383118.			0.133455			0.0667277	−	0.997771i	$-0.478744\pi$
$383$	383118.			0.133455			0.0667277	+	0.997771i	$0.478744\pi$
$384$	1.80855e6	−	1.68787e6i	0.625897	−	0.584132i
$385$		0			0
$386$	−219832.	−	638319.i	−0.0750970	−	0.218057i
$387$			422141.i			0.143278i
$388$	1.58356e6	+	2.02638e6i	0.534016	+	0.683346i
$389$	4.92325e6			1.64960			0.824799	−	0.565427i	$-0.191288\pi$
$389$	4.92325e6			1.64960			0.824799	+	0.565427i	$0.191288\pi$
$390$	−604961.	−	1.75660e6i	−0.201403	−	0.584807i
$391$	2.79099e6			0.923243
$392$		0			0
$393$	405308.			0.132374
$394$	424025.	+	1.23123e6i	0.137610	+	0.399574i
$395$	−7.02315e6			−2.26485
$396$	115251.	+	147480.i	0.0369324	+	0.0472601i
$397$		−	6.06605e6i		−	1.93165i	−0.259186	−	0.965827i	$-0.583454\pi$
$397$		−	6.06605e6i		−	1.93165i	0.259186	−	0.965827i	$-0.416546\pi$
$398$	310272.	+	900925.i	0.0981826	+	0.285089i
$399$		0			0
$400$	−1.22589e6	+	4.92164e6i	−0.383092	+	1.53801i
$401$	−1.26119e6			−0.391670			−0.195835	−	0.980637i	$-0.562742\pi$
$401$	−1.26119e6			−0.391670			−0.195835	+	0.980637i	$0.562742\pi$
$402$	−474073.	+	163267.i	−0.146312	+	0.0503888i
$403$			2.35973e6i			0.723769i
$404$	2.84601e6	+	3.64186e6i	0.867528	+	1.11012i
$405$		−	3.51151e6i		−	1.06379i
$406$		0			0
$407$			852475.i			0.255091i
$408$	911005.	−	1.40336e6i	0.270938	−	0.417367i
$409$		−	4.93737e6i		−	1.45945i	−0.683743	−	0.729723i	$-0.739649\pi$
$409$		−	4.93737e6i		−	1.45945i	0.683743	−	0.729723i	$-0.260351\pi$
$410$	1.74463e6	+	5.06582e6i	0.512559	+	1.48830i
$411$	−928295.			−0.271070
$412$	1.61302e6	−	1.26053e6i	0.468162	−	0.365856i
$413$		0			0
$414$	−1.39868e6	+	481696.i	−0.401069	+	0.138125i
$415$		−	381814.i		−	0.108826i
$416$	138689.	+	1.57996e6i	0.0392925	+	0.447625i
$417$	−929972.			−0.261897
$418$	866575.	−	298442.i	0.242586	−	0.0835447i
$419$	2.05004e6			0.570462			0.285231	−	0.958459i	$-0.407930\pi$
$419$	2.05004e6			0.570462			0.285231	+	0.958459i	$0.407930\pi$
$420$		0			0
$421$	4.46712e6			1.22835			0.614176	−	0.789169i	$-0.289489\pi$
$421$	4.46712e6			1.22835			0.614176	+	0.789169i	$0.289489\pi$
$422$	1.52920e6	−	526646.i	0.418008	−	0.143959i
$423$	1.81611e6			0.493504
$424$	−3.13800e6	−	2.03707e6i	−0.847693	−	0.550290i
$425$			3.43037e6i			0.921232i
$426$	−4.10500e6	+	1.41373e6i	−1.09595	+	0.377436i
$427$		0			0
$428$	−2.68995e6	−	3.44216e6i	−0.709799	−	0.908285i
$429$	329371.			0.0864057
$430$	−1.07700e6	−	3.12726e6i	−0.280896	−	0.815629i
$431$			5.25792e6i			1.36339i	0.731636	+	0.681696i	$0.238757\pi$
$431$			5.25792e6i			1.36339i	−0.731636	+	0.681696i	$0.761243\pi$
$432$	−1.01698e6	+	4.08290e6i	−0.262182	+	1.05259i
$433$		−	2.50514e6i		−	0.642113i	−0.947060	−	0.321057i	$-0.895962\pi$
$433$		−	2.50514e6i		−	0.642113i	0.947060	−	0.321057i	$-0.104038\pi$
$434$		0			0
$435$		−	9.88006e6i		−	2.50344i
$436$	−2.67218e6	+	2.08823e6i	−0.673207	+	0.526092i
$437$			7.24375e6i			1.81451i
$438$	1.46749e6	−	505391.i	0.365501	−	0.125876i
$439$	−2.23442e6			−0.553353			−0.276677	−	0.960963i	$-0.589233\pi$
$439$	−2.23442e6			−0.553353			−0.276677	+	0.960963i	$0.589233\pi$
$440$	−1.23006e6	−	798505.i	−0.302896	−	0.196628i
$441$		0			0
$442$	349293.	+	1.01423e6i	0.0850421	+	0.246934i
$443$		−	5.06686e6i		−	1.22667i	−0.789821	−	0.613337i	$-0.789827\pi$
$443$		−	5.06686e6i		−	1.22667i	0.789821	−	0.613337i	$-0.210173\pi$
$444$	−3.18246e6	+	2.48701e6i	−0.766136	+	0.598714i
$445$	−3.97147e6			−0.950717
$446$	−376107.	−	1.09209e6i	−0.0895313	−	0.259969i
$447$	−4.03780e6			−0.955819
$448$		0			0
$449$	−5.80397e6			−1.35866			−0.679328	−	0.733835i	$-0.737728\pi$
$449$	−5.80397e6			−1.35866			−0.679328	+	0.733835i	$0.737728\pi$
$450$	−592048.	−	1.71911e6i	−0.137824	−	0.400195i
$451$	−949865.			−0.219898
$452$	−2.85499e6	+	2.23110e6i	−0.657293	+	0.513656i
$453$			1.48682e6i			0.340419i
$454$	−769412.	−	2.23411e6i	−0.175194	−	0.508705i
$455$		0			0
$456$	3.64228e6	+	2.36443e6i	0.820279	+	0.532493i
$457$	467087.			0.104618			0.0523092	−	0.998631i	$-0.483342\pi$
$457$	467087.			0.104618			0.0523092	+	0.998631i	$0.483342\pi$
$458$	4.88564e6	−	1.68258e6i	1.08832	−	0.374810i
$459$			2.84577e6i			0.630476i
$460$	9.13263e6	−	7.13690e6i	2.01234	−	1.57259i
$461$		−	1.16943e6i		−	0.256285i	−0.991756	−	0.128142i	$-0.959099\pi$
$461$		−	1.16943e6i		−	0.256285i	0.991756	−	0.128142i	$-0.0409015\pi$
$462$		0			0
$463$			1.26331e6i			0.273877i	0.990580	+	0.136939i	$0.0437263\pi$
$463$			1.26331e6i			0.273877i	−0.990580	+	0.136939i	$0.956274\pi$
$464$	−2.03861e6	+	8.18446e6i	−0.439580	+	1.76480i
$465$		−	1.03377e7i		−	2.21712i
$466$	−2.58483e6	−	7.50549e6i	−0.551401	−	1.60109i
$467$	−9.13929e6			−1.93919			−0.969595	−	0.244716i	$-0.921305\pi$
$467$	−9.13929e6			−1.93919			−0.969595	+	0.244716i	$0.921305\pi$
$468$	−350091.	−	447990.i	−0.0738868	−	0.0945482i
$469$		0			0
$470$	−1.34539e7	+	4.63342e6i	−2.80933	+	0.967513i
$471$		−	1.49048e6i		−	0.309581i
$472$	1.88924e6	+	1.22642e6i	0.390330	+	0.253387i
$473$	586375.			0.120510
$474$	5.57770e6	−	1.92092e6i	1.14027	−	0.392701i
$475$	−8.90322e6			−1.81056
$476$		0			0
$477$	1.34114e6			0.269885
$478$	7.68049e6	−	2.64510e6i	1.53751	−	0.529508i
$479$	−4.19007e6			−0.834415			−0.417208	−	0.908811i	$-0.636991\pi$
$479$	−4.19007e6			−0.834415			−0.417208	+	0.908811i	$0.636991\pi$
$480$	−607578.	−	6.92160e6i	−0.120365	−	1.37121i
$481$		−	2.58951e6i		−	0.510334i
$482$	−1.53565e6	+	528865.i	−0.301074	+	0.103688i
$483$		0			0
$484$	−3.85589e6	+	3.01327e6i	−0.748190	+	0.584689i
$485$	7.22325e6			1.39437
$486$	−878788.	−	2.55171e6i	−0.168769	−	0.490050i
$487$			5.03451e6i			0.961911i	0.876745	+	0.480956i	$0.159710\pi$
$487$			5.03451e6i			0.961911i	−0.876745	+	0.480956i	$0.840290\pi$
$488$	−1.03609e6	+	1.59605e6i	−0.196947	+	0.303387i
$489$		−	2.69976e6i		−	0.510567i
$490$		0			0
$491$		−	4.18235e6i		−	0.782919i	−0.920195	−	0.391460i	$-0.871970\pi$
$491$		−	4.18235e6i		−	0.782919i	0.920195	−	0.391460i	$-0.128030\pi$
$492$	−2.77113e6	−	3.54604e6i	−0.516112	−	0.660436i
$493$			5.70455e6i			1.05707i
$494$	−2.63234e6	+	906557.i	−0.485316	+	0.167139i
$495$	525709.			0.0964345
$496$	−2.13302e6	+	8.56352e6i	−0.389306	+	1.56296i
$497$		0			0
$498$	104431.	+	303232.i	0.0188693	+	0.0547900i
$499$			3.52981e6i			0.634600i	0.948325	+	0.317300i	$0.102776\pi$
$499$			3.52981e6i			0.634600i	−0.948325	+	0.317300i	$0.897224\pi$
$500$	3.23759e6	+	4.14294e6i	0.579158	+	0.741112i
$501$	−218624.			−0.0389138
$502$	2.68065e6	+	7.78372e6i	0.474768	+	1.37857i
$503$	7.88657e6			1.38985			0.694926	−	0.719082i	$-0.255437\pi$
$503$	7.88657e6			1.38985			0.694926	+	0.719082i	$0.255437\pi$
$504$		0			0
$505$	1.29818e7			2.26521
$506$	669100.	+	1.94284e6i	0.116176	+	0.337335i
$507$	3.95467e6			0.683267
$508$	1.01361e6	+	1.29705e6i	0.174265	+	0.222996i
$509$			1.39453e6i			0.238579i	0.992860	+	0.119289i	$0.0380616\pi$
$509$			1.39453e6i			0.238579i	−0.992860	+	0.119289i	$0.961938\pi$
$510$	−1.53020e6	−	4.44319e6i	−0.260509	−	0.756432i
$511$		0			0
$512$	−924865.	+	5.85910e6i	−0.155921	+	0.987770i
$513$	−7.38594e6			−1.23912
$514$	5.70515e6	−	1.96481e6i	0.952487	−	0.328029i
$515$		−	5.74979e6i		−	0.955288i
$516$	1.71069e6	+	2.18906e6i	0.282844	+	0.361937i
$517$		−	2.52267e6i		−	0.415081i
$518$		0			0
$519$			1.83031e6i			0.298267i
$520$	3.73646e6	+	2.42556e6i	0.605971	+	0.393373i
$521$		−	9.24415e6i		−	1.49201i	−0.665939	−	0.746007i	$-0.731969\pi$
$521$		−	9.24415e6i		−	1.49201i	0.665939	−	0.746007i	$-0.268031\pi$
$522$	−984548.	−	2.85880e6i	−0.158147	−	0.459206i
$523$	−1.84905e6			−0.295593			−0.147797	−	0.989018i	$-0.547218\pi$
$523$	−1.84905e6			−0.295593			−0.147797	+	0.989018i	$0.547218\pi$
$524$	−765747.	+	598410.i	−0.121831	+	0.0952073i
$525$		0			0
$526$	6.15279e6	−	2.11897e6i	0.969634	−	0.333934i
$527$			5.96876e6i			0.936176i
$528$	1.19530e6	+	297727.i	0.186591	+	0.0464766i
$529$	−9.80398e6			−1.52322
$530$	−9.93529e6	+	3.42164e6i	−1.53635	+	0.529108i
$531$	−807436.			−0.124272
$532$		0			0
$533$	2.88534e6			0.439925
$534$	3.15409e6	−	1.08625e6i	0.478654	−	0.164845i
$535$	−1.22700e7			−1.85336
$536$	654612.	−	1.00840e6i	0.0984174	−	0.151607i
$537$			8.04761e6i			1.20429i
$538$	4.69386e6	−	1.61653e6i	0.699157	−	0.240784i
$539$		0			0
$540$	7.27699e6	+	9.31191e6i	1.07391	+	1.37421i
$541$	7.61135e6			1.11807			0.559034	−	0.829145i	$-0.311172\pi$
$541$	7.61135e6			1.11807			0.559034	+	0.829145i	$0.311172\pi$
$542$	3.79145e6	+	1.10091e7i	0.554379	+	1.60973i
$543$			2.21136e6i			0.321855i
$544$	350803.	+	3.99640e6i	0.0508237	+	0.578990i
$545$			9.52528e6i			1.37368i
$546$		0			0
$547$			1.04808e7i			1.49771i	0.662735	+	0.748854i	$0.269396\pi$
$547$			1.04808e7i			1.49771i	−0.662735	+	0.748854i	$0.730604\pi$
$548$	1.75383e6	−	1.37057e6i	0.249480	−	0.194961i
$549$		−	682129.i		−	0.0965908i
$550$	−2.38793e6	+	822384.i	−0.336600	+	0.115923i
$551$	−1.48056e7			−2.07753
$552$	−5.30100e6	+	8.16592e6i	−0.740474	+	1.14066i
$553$		0			0
$554$	−1.99947e6	−	5.80578e6i	−0.276783	−	0.803686i
$555$			1.13443e7i			1.56331i
$556$	1.75699e6	−	1.37304e6i	0.241037	−	0.188363i
$557$	8.15600e6			1.11388			0.556941	−	0.830552i	$-0.311975\pi$
$557$	8.15600e6			1.11388			0.556941	+	0.830552i	$0.311975\pi$
$558$	−1.03015e6	−	2.99120e6i	−0.140060	−	0.406687i
$559$	−1.78119e6			−0.241091
$560$		0			0
$561$	833119.			0.111763
$562$	−2.46231e6	−	7.14973e6i	−0.328853	−	0.954880i
$563$	−1.10987e7			−1.47571			−0.737853	−	0.674962i	$-0.764160\pi$
$563$	−1.10987e7			−1.47571			−0.737853	+	0.674962i	$0.764160\pi$
$564$	9.41762e6	−	7.35961e6i	1.24665	−	0.974220i
$565$			1.01770e7i			1.34121i
$566$	−3.26626e6	−	9.48411e6i	−0.428558	−	1.24439i
$567$		0			0
$568$	5.66829e6	−	8.73172e6i	0.737193	−	1.13561i
$569$	−4.43267e6			−0.573964			−0.286982	−	0.957936i	$-0.592652\pi$
$569$	−4.43267e6			−0.573964			−0.286982	+	0.957936i	$0.592652\pi$
$570$	1.15319e7	−	3.97150e6i	1.48667	−	0.511997i
$571$			5.16366e6i			0.662777i	0.943494	+	0.331388i	$0.107517\pi$
$571$			5.16366e6i			0.662777i	−0.943494	+	0.331388i	$0.892483\pi$
$572$	−622280.	+	486295.i	−0.0795236	+	0.0621454i
$573$			1.11776e7i			1.42220i
$574$		0			0
$575$		−	1.99608e7i		−	2.51773i
$576$	−865540.	−	1.94222e6i	−0.108700	−	0.243917i
$577$		−	3.41650e6i		−	0.427211i	−0.976920	−	0.213605i	$-0.931479\pi$
$577$		−	3.41650e6i		−	0.427211i	0.976920	−	0.213605i	$-0.0685206\pi$
$578$	−1.73187e6	−	5.02877e6i	−0.215623	−	0.626098i
$579$	1.59274e6			0.197446
$580$	1.45872e7	+	1.86664e7i	1.80054	+	2.30404i
$581$		0			0
$582$	−5.73662e6	+	1.97565e6i	−0.702019	+	0.241770i
$583$		−	1.86291e6i		−	0.226997i
$584$	−2.02634e6	+	3.12148e6i	−0.245856	+	0.378729i
$585$	−1.59691e6			−0.192926
$586$	−5.80378e6	+	1.99878e6i	−0.698179	+	0.240448i
$587$	1.63173e7			1.95458			0.977292	−	0.211899i	$-0.0679649\pi$
$587$	1.63173e7			1.95458			0.977292	+	0.211899i	$0.0679649\pi$
$588$		0			0
$589$	−1.54914e7			−1.83993
$590$	5.98156e6	−	2.06000e6i	0.707431	−	0.243634i
$591$	−3.07216e6			−0.361805
$592$	2.34072e6	−	9.39739e6i	0.274502	−	1.10205i
$593$		−	1.02246e7i		−	1.19401i	−0.802236	−	0.597007i	$-0.796357\pi$
$593$		−	1.02246e7i		−	1.19401i	0.802236	−	0.597007i	$-0.203643\pi$
$594$	−1.98098e6	+	682234.i	−0.230364	+	0.0793355i
$595$		0			0
$596$	7.62860e6	−	5.96153e6i	0.879689	−	0.687452i
$597$	−2.24799e6			−0.258142
$598$	−2.03248e6	−	5.90164e6i	−0.232420	−	0.674870i
$599$		−	1.06888e7i		−	1.21720i	−0.793477	−	0.608601i	$-0.791731\pi$
$599$		−	1.06888e7i		−	1.21720i	0.793477	−	0.608601i	$-0.208269\pi$
$600$	−1.00367e7	−	6.51540e6i	−1.13818	−	0.738862i
$601$			9.61817e6i			1.08619i	0.839671	+	0.543096i	$0.182748\pi$
$601$			9.61817e6i			1.08619i	−0.839671	+	0.543096i	$0.817252\pi$
$602$		0			0
$603$			430975.i			0.0482680i
$604$	−2.19519e6	−	2.80905e6i	−0.244839	−	0.313305i
$605$			1.37448e7i			1.52669i
$606$	−1.03100e7	+	3.55069e6i	−1.14046	+	0.392764i
$607$	8.55600e6			0.942538			0.471269	−	0.881989i	$-0.343796\pi$
$607$	8.55600e6			0.942538			0.471269	+	0.881989i	$0.343796\pi$
$608$	−1.03723e7	+	910478.i	−1.13793	+	0.0998873i
$609$		0			0
$610$	1.74031e6	+	5.05328e6i	0.189366	+	0.549855i
$611$			7.66293e6i			0.830409i
$612$	−885529.	−	1.13316e6i	−0.0955706	−	0.122296i
$613$	−8.45419e6			−0.908700			−0.454350	−	0.890823i	$-0.650129\pi$
$613$	−8.45419e6			−0.908700			−0.454350	+	0.890823i	$0.650129\pi$
$614$	3.41679e6	+	9.92122e6i	0.365761	+	1.06205i
$615$	−1.26403e7			−1.34762
$616$		0			0
$617$	354693.			0.0375094			0.0187547	−	0.999824i	$-0.494030\pi$
$617$	354693.			0.0375094			0.0187547	+	0.999824i	$0.494030\pi$
$618$	1.57264e6	+	4.56642e6i	0.165637	+	0.480955i
$619$	3.08678e6			0.323802			0.161901	−	0.986807i	$-0.448238\pi$
$619$	3.08678e6			0.323802			0.161901	+	0.986807i	$0.448238\pi$
$620$	1.52628e7	+	1.95309e7i	1.59462	+	2.04053i
$621$		−	1.65591e7i		−	1.72309i
$622$	−3.44092e6	−	9.99127e6i	−0.356614	−	1.03549i
$623$		0			0
$624$	−3.63087e6	−	904387.i	−0.373293	−	0.0929807i
$625$	−710569.			−0.0727623
$626$	−1.11690e7	+	3.84653e6i	−1.13915	+	0.392313i
$627$			2.16228e6i			0.219656i
$628$	2.20059e6	+	2.81596e6i	0.222659	+	0.284923i
$629$		−	6.54996e6i		−	0.660103i
$630$		0			0
$631$		−	3.18364e6i		−	0.318310i	−0.987254	−	0.159155i	$-0.949123\pi$
$631$		−	3.18364e6i		−	0.318310i	0.987254	−	0.159155i	$-0.0508769\pi$
$632$	−7.70182e6	+	1.18643e7i	−0.767010	+	1.18154i
$633$			3.81568e6i			0.378497i
$634$	−2.03883e6	−	5.92008e6i	−0.201446	−	0.584931i
$635$	4.62349e6			0.455026
$636$	6.95463e6	−	5.43484e6i	0.681759	−	0.532776i
$637$		0			0
$638$	−3.97101e6	+	1.36759e6i	−0.386233	+	0.133016i
$639$			3.73182e6i			0.361550i
$640$	1.13672e7	+	1.21799e7i	1.09699	+	1.17542i
$641$	−8.87135e6			−0.852795			−0.426397	−	0.904536i	$-0.640217\pi$
$641$	−8.87135e6			−0.852795			−0.426397	+	0.904536i	$0.640217\pi$
$642$	9.74468e6	−	3.35599e6i	0.933104	−	0.321354i
$643$	−1.13171e7			−1.07946			−0.539732	−	0.841837i	$-0.681474\pi$
$643$	−1.13171e7			−1.07946			−0.539732	+	0.841837i	$0.681474\pi$
$644$		0			0
$645$	7.80316e6			0.738535
$646$	−6.65829e6	+	2.29306e6i	−0.627743	+	0.216190i
$647$	7.45552e6			0.700192			0.350096	−	0.936714i	$-0.386149\pi$
$647$	7.45552e6			0.700192			0.350096	+	0.936714i	$0.386149\pi$
$648$	−5.93204e6	−	3.85085e6i	−0.554966	−	0.360262i
$649$			1.12157e6i			0.104524i
$650$	7.25365e6	−	2.49810e6i	0.673400	−	0.231914i
$651$		0			0
$652$	3.98601e6	+	5.10065e6i	0.367214	+	0.469901i
$653$	2.74051e6			0.251506			0.125753	−	0.992062i	$-0.459865\pi$
$653$	2.74051e6			0.251506			0.125753	+	0.992062i	$0.459865\pi$
$654$	−2.60528e6	−	7.56486e6i	−0.238183	−	0.691603i
$655$			2.72959e6i			0.248596i
$656$	1.04710e7	+	2.60813e6i	0.950008	+	0.236630i
$657$		−	1.33408e6i		−	0.120578i
$658$		0			0
$659$			3.98395e6i			0.357356i	0.983908	+	0.178678i	$0.0571820\pi$
$659$			3.98395e6i			0.357356i	−0.983908	+	0.178678i	$0.942818\pi$
$660$	2.72612e6	−	2.13039e6i	0.243605	−	0.190370i
$661$		−	1.24849e7i		−	1.11142i	−0.831375	−	0.555712i	$-0.812446\pi$
$661$		−	1.24849e7i		−	1.11142i	0.831375	−	0.555712i	$-0.187554\pi$
$662$	2.99137e6	−	1.03021e6i	0.265293	−	0.0913648i
$663$	−2.53071e6			−0.223593
$664$	−645002.	−	418710.i	−0.0567728	−	0.0368547i
$665$		0			0
$666$	1.13046e6	+	3.28247e6i	0.0987571	+	0.286757i
$667$		−	3.31939e7i		−	2.88898i
$668$	413045.	−	322783.i	0.0358143	−	0.0279879i
$669$	2.72499e6			0.235396
$670$	−1.09954e6	−	3.19270e6i	−0.0946291	−	0.274771i
$671$	−947512.			−0.0812416
$672$		0			0
$673$	−2.97264e6			−0.252991			−0.126495	−	0.991967i	$-0.540373\pi$
$673$	−2.97264e6			−0.252991			−0.126495	+	0.991967i	$0.540373\pi$
$674$	3.91497e6	+	1.13678e7i	0.331954	+	0.963885i
$675$	2.03526e7			1.71934
$676$	−7.47155e6	+	5.83880e6i	−0.628845	+	0.491425i
$677$			1.78476e7i			1.49661i	0.663354	+	0.748305i	$0.269132\pi$
$677$			1.78476e7i			1.49661i	−0.663354	+	0.748305i	$0.730868\pi$
$678$	−2.78352e6	−	8.08242e6i	−0.232552	−	0.675254i
$679$		0			0
$680$	9.45108e6	+	6.13527e6i	0.783807	+	0.508817i
$681$	5.57457e6			0.460621
$682$	−4.15493e6	+	1.43093e6i	−0.342060	+	0.117803i
$683$			859663.i			0.0705142i	0.999378	+	0.0352571i	$0.0112250\pi$
$683$			859663.i			0.0705142i	−0.999378	+	0.0352571i	$0.988775\pi$
$684$	2.94100e6	−	2.29831e6i	0.240356	−	0.187831i
$685$		−	6.25172e6i		−	0.509065i
$686$		0			0
$687$			1.21907e7i			0.985452i
$688$	−6.46399e6	−	1.61007e6i	−0.520631	−	0.129680i
$689$			5.65884e6i			0.454129i
$690$	8.90401e6	+	2.58543e7i	0.711972	+	2.06733i
$691$	607080.			0.0483672			0.0241836	−	0.999708i	$-0.492301\pi$
$691$	607080.			0.0483672			0.0241836	+	0.999708i	$0.492301\pi$
$692$	−2.70232e6	−	3.45799e6i	−0.214522	−	0.274510i
$693$		0			0
$694$	−4.04544e6	+	1.39322e6i	−0.318835	+	0.109804i
$695$		−	6.26301e6i		−	0.491837i
$696$	−1.66905e7	−	1.08348e7i	−1.30601	−	0.847810i
$697$	7.29824e6			0.569032
$698$	5.68415e6	−	1.95758e6i	0.441598	−	0.152083i
$699$	1.87277e7			1.44975
$700$		0			0
$701$	−2.09454e7			−1.60988			−0.804942	−	0.593354i	$-0.797804\pi$
$701$	−2.09454e7			−1.60988			−0.804942	+	0.593354i	$0.797804\pi$
$702$	6.01749e6	−	2.07238e6i	0.460864	−	0.158718i
$703$	1.69998e7			1.29735
$704$	−2.69784e6	+	1.20228e6i	−0.205156	+	0.0914268i
$705$		−	3.35702e7i		−	2.54379i
$706$	1.28921e7	−	4.43994e6i	0.973446	−	0.335247i
$707$		0			0
$708$	−4.18704e6	+	3.27206e6i	−0.313924	+	0.245323i
$709$	−6.73565e6			−0.503227			−0.251614	−	0.967828i	$-0.580961\pi$
$709$	−6.73565e6			−0.503227			−0.251614	+	0.967828i	$0.580961\pi$
$710$	−9.52095e6	−	2.76456e7i	−0.708817	−	2.05817i
$711$		−	5.07063e6i		−	0.376173i
$712$	−4.35525e6	+	6.70905e6i	−0.321968	+	0.495976i
$713$		−	3.47313e7i		−	2.55857i
$714$		0			0
$715$			2.21819e6i			0.162268i
$716$	−1.18817e7	−	1.52043e7i	−0.866159	−	1.10837i
$717$			1.91644e7i			1.39219i
$718$	9.61430e6	−	3.31109e6i	0.695996	−	0.239696i
$719$	1.33017e7			0.959585			0.479792	−	0.877382i	$-0.340712\pi$
$719$	1.33017e7			0.959585			0.479792	+	0.877382i	$0.340712\pi$
$720$	−5.79523e6	−	1.44349e6i	−0.416619	−	0.103773i
$721$		0			0
$722$	−1.39046e6	−	4.03743e6i	−0.0992694	−	0.288245i
$723$		−	3.83176e6i		−	0.272616i
$724$	−3.26493e6	−	4.17792e6i	−0.231487	−	0.296220i
$725$	4.07983e7			2.88268
$726$	−3.75937e6	−	1.09159e7i	−0.264712	−	0.768634i
$727$	−1.37948e7			−0.968012			−0.484006	−	0.875065i	$-0.660819\pi$
$727$	−1.37948e7			−0.968012			−0.484006	+	0.875065i	$0.660819\pi$
$728$		0			0
$729$	1.58609e7			1.10538
$730$	3.40362e6	+	9.88296e6i	0.236392	+	0.686404i
$731$	−4.50539e6			−0.311845
$732$	−2.76427e6	−	3.53726e6i	−0.190679	−	0.243999i
$733$			2.30159e7i			1.58222i	0.611673	+	0.791111i	$0.290497\pi$
$733$			2.30159e7i			1.58222i	−0.611673	+	0.791111i	$0.709503\pi$
$734$	−926476.	−	2.69018e6i	−0.0634738	−	0.184307i
$735$		0			0
$736$	−2.04127e6	−	2.32544e7i	−0.138901	−	1.58238i
$737$	598646.			0.0405977
$738$	−3.65746e6	+	1.25960e6i	−0.247195	+	0.0851320i
$739$			8.18624e6i			0.551408i	0.961243	+	0.275704i	$0.0889110\pi$
$739$			8.18624e6i			0.551408i	−0.961243	+	0.275704i	$0.911089\pi$
$740$	−1.67490e7	−	2.14327e7i	−1.12437	−	1.43879i
$741$		−	6.56822e6i		−	0.439443i
$742$		0			0
$743$		−	1.02915e6i		−	0.0683924i	−0.999415	−	0.0341962i	$-0.989113\pi$
$743$		−	1.02915e6i		−	0.0683924i	0.999415	−	0.0341962i	$-0.0108871\pi$
$744$	−1.74635e7	−	1.13366e7i	−1.15664	−	0.750847i
$745$		−	2.71930e7i		−	1.79501i
$746$	−379471.	−	1.10186e6i	−0.0249650	−	0.0724900i
$747$	275665.			0.0180751
$748$	−1.57401e6	+	1.23004e6i	−0.102862	+	0.0803834i
$749$		0			0
$750$	−1.17286e7	+	4.03923e6i	−0.761363	+	0.262208i
$751$		−	1.49274e7i		−	0.965792i	−0.875678	−	0.482896i	$-0.839585\pi$
$751$		−	1.49274e7i		−	0.965792i	0.875678	−	0.482896i	$-0.160415\pi$
$752$	−6.92672e6	+	2.78090e7i	−0.446666	+	1.79325i
$753$	−1.94220e7			−1.24826
$754$	1.20625e7	−	4.15423e6i	0.772695	−	0.266110i
$755$	−1.00132e7			−0.639301
$756$		0			0
$757$	−1.14616e7			−0.726949			−0.363474	−	0.931604i	$-0.618410\pi$
$757$	−1.14616e7			−0.726949			−0.363474	+	0.931604i	$0.618410\pi$
$758$	9.76753e6	−	3.36386e6i	0.617464	−	0.212650i
$759$	−4.84779e6			−0.305450
$760$	−1.59235e7	+	2.45294e7i	−1.00001	+	1.54047i
$761$		−	9.49769e6i		−	0.594506i	−0.954799	−	0.297253i	$-0.903929\pi$
$761$		−	9.49769e6i		−	0.594506i	0.954799	−	0.297253i	$-0.0960705\pi$
$762$	−3.67192e6	+	1.26458e6i	−0.229090	+	0.0788968i
$763$		0			0
$764$	−1.65029e7	−	2.11177e7i	−1.02289	−	1.30892i
$765$	−4.03926e6			−0.249545
$766$	−705705.	−	2.04913e6i	−0.0434561	−	0.126182i
$767$		−	3.40691e6i		−	0.209109i
$768$	−1.23590e7	−	6.56408e6i	−0.756103	−	0.401579i
$769$			5.58813e6i			0.340762i	0.985378	+	0.170381i	$0.0544998\pi$
$769$			5.58813e6i			0.340762i	−0.985378	+	0.170381i	$0.945500\pi$
$770$		0			0
$771$			1.42355e7i			0.862457i
$772$	−3.00915e6	+	2.35157e6i	−0.181719	+	0.142008i
$773$			1.38777e7i			0.835348i	0.908597	+	0.417674i	$0.137155\pi$
$773$			1.38777e7i			0.835348i	−0.908597	+	0.417674i	$0.862845\pi$
$774$	2.25785e6	−	777585.i	0.135470	−	0.0466547i
$775$	4.26879e7			2.55300
$776$	7.92127e6	−	1.22023e7i	0.472216	−	0.727425i
$777$		0			0
$778$	−9.06863e6	−	2.63323e7i	−0.537146	−	1.55969i
$779$			1.89419e7i			1.11836i
$780$	−8.28096e6	+	6.47134e6i	−0.487353	+	0.380853i
$781$	5.18368e6			0.304096
$782$	−5.14100e6	−	1.49277e7i	−0.300629	−	0.872926i
$783$	3.38455e7			1.97286
$784$		0			0
$785$	1.00378e7			0.581387
$786$	−746577.	−	2.16781e6i	−0.0431041	−	0.125160i
$787$	−8.83903e6			−0.508707			−0.254353	−	0.967111i	$-0.581863\pi$
$787$	−8.83903e6			−0.508707			−0.254353	+	0.967111i	$0.581863\pi$
$788$	5.80422e6	−	4.53584e6i	0.332988	−	0.260221i
$789$			1.53525e7i			0.877982i
$790$	1.29366e7	+	3.75637e7i	0.737486	+	2.14141i
$791$		0			0
$792$	576511.	−	888086.i	0.0326584	−	0.0503086i
$793$	2.87819e6			0.162531
$794$	−3.24446e7	+	1.11737e7i	−1.82638	+	0.628991i
$795$		−	2.47906e7i		−	1.39113i
$796$	4.24713e6	−	3.31901e6i	0.237581	−	0.185663i
$797$			3.23169e7i			1.80212i	0.433692	+	0.901061i	$0.357211\pi$
$797$			3.23169e7i			1.80212i	−0.433692	+	0.901061i	$0.642789\pi$
$798$		0			0
$799$			1.93828e7i			1.07411i
$800$	2.85818e7	−	2.50891e6i	1.57893	−	0.138599i
$801$		−	2.86735e6i		−	0.157907i
$802$	2.32312e6	+	6.74555e6i	0.127537	+	0.370324i
$803$	−1.85310e6			−0.101417
$804$	1.74649e6	+	2.23487e6i	0.0952851	+	0.121930i
$805$		0			0
$806$	1.26212e7	−	4.34663e6i	0.684324	−	0.235676i
$807$			1.17122e7i			0.633072i
$808$	1.42363e7	−	2.19304e7i	0.767132	−	1.18173i
$809$	9.13479e6			0.490713			0.245356	−	0.969433i	$-0.421095\pi$
$809$	9.13479e6			0.490713			0.245356	+	0.969433i	$0.421095\pi$
$810$	−1.87815e7	+	6.46821e6i	−1.00582	+	0.346395i
$811$	5.46042e6			0.291524			0.145762	−	0.989320i	$-0.453437\pi$
$811$	5.46042e6			0.291524			0.145762	+	0.989320i	$0.453437\pi$
$812$		0			0
$813$	−2.74700e7			−1.45758
$814$	4.55951e6	−	1.57026e6i	0.241189	−	0.0830636i
$815$	1.81819e7			0.958835
$816$	−9.18401e6	−	2.28758e6i	−0.482844	−	0.120268i
$817$		−	1.16933e7i		−	0.612890i
$818$	−2.64078e7	+	9.09465e6i	−1.37990	+	0.475229i
$819$		0			0
$820$	2.38812e7	−	1.86625e7i	1.24029	−	0.969248i
$821$	−2.66517e7			−1.37996			−0.689982	−	0.723827i	$-0.742381\pi$
$821$	−2.66517e7			−1.37996			−0.689982	+	0.723827i	$0.742381\pi$
$822$	1.70992e6	+	4.96504e6i	0.0882666	+	0.256297i
$823$		−	3.60068e7i		−	1.85304i	−0.376246	−	0.926520i	$-0.622785\pi$
$823$		−	3.60068e7i		−	1.85304i	0.376246	−	0.926520i	$-0.377215\pi$
$824$	−9.71319e6	−	6.30542e6i	−0.498361	−	0.323516i
$825$		−	5.95837e6i		−	0.304784i
$826$		0			0
$827$			2.10722e7i			1.07139i	0.844412	+	0.535694i	$0.179950\pi$
$827$			2.10722e7i			1.07139i	−0.844412	+	0.535694i	$0.820050\pi$
$828$	5.15276e6	+	6.59365e6i	0.261194	+	0.334234i
$829$			7.66472e6i			0.387355i	0.981065	+	0.193678i	$0.0620416\pi$
$829$			7.66472e6i			0.387355i	−0.981065	+	0.193678i	$0.937958\pi$
$830$	−2.04215e6	+	703301.i	−0.102895	+	0.0354361i
$831$	1.44866e7			0.727720
$832$	8.19506e6	−	3.65208e6i	0.410435	−	0.182908i
$833$		0			0
$834$	1.71301e6	+	4.97401e6i	0.0852795	+	0.247623i
$835$		−	1.47235e6i		−	0.0730793i
$836$	−3.19246e6	−	4.08519e6i	−0.157983	−	0.202161i
$837$	3.54131e7			1.74723
$838$	−3.77617e6	−	1.09647e7i	−0.185755	−	0.539371i
$839$	−2.25202e6			−0.110450			−0.0552252	−	0.998474i	$-0.517588\pi$
$839$	−2.25202e6			−0.110450			−0.0552252	+	0.998474i	$0.517588\pi$
$840$		0			0
$841$	4.73345e7			2.30775
$842$	−8.22844e6	−	2.38926e7i	−0.399979	−	1.16141i
$843$	1.78400e7			0.864623
$844$	−5.63359e6	−	7.20895e6i	−0.272226	−	0.348350i
$845$			2.66332e7i			1.28316i
$846$	−3.34527e6	−	9.71355e6i	−0.160696	−	0.466608i
$847$		0			0
$848$	−5.11517e6	+	2.05361e7i	−0.244270	+	0.980681i
$849$	2.36648e7			1.12677
$850$	1.83475e7	−	6.31875e6i	0.871025	−	0.299974i
$851$			3.81132e7i			1.80406i
$852$	1.51228e7	+	1.93517e7i	0.713731	+	0.913316i
$853$		−	2.75023e7i		−	1.29418i	−0.762412	−	0.647092i	$-0.775985\pi$
$853$		−	2.75023e7i		−	1.29418i	0.762412	−	0.647092i	$-0.224015\pi$
$854$		0			0
$855$		−	1.04835e7i		−	0.490447i
$856$	−1.34557e7	+	2.07278e7i	−0.627656	+	0.966873i
$857$			1.03253e7i			0.480233i	0.970744	+	0.240116i	$0.0771856\pi$
$857$			1.03253e7i			0.480233i	−0.970744	+	0.240116i	$0.922814\pi$
$858$	−606702.	−	1.76166e6i	−0.0281357	−	0.0816966i
$859$	−2.10893e7			−0.975168			−0.487584	−	0.873076i	$-0.662122\pi$
$859$	−2.10893e7			−0.975168			−0.487584	+	0.873076i	$0.662122\pi$
$860$	−1.47425e7	+	1.15208e7i	−0.679711	+	0.531175i
$861$		0			0
$862$	2.81222e7	−	9.68508e6i	1.28909	−	0.443951i
$863$			1.49585e7i			0.683695i	0.939755	+	0.341847i	$0.111053\pi$
$863$			1.49585e7i			0.683695i	−0.939755	+	0.341847i	$0.888947\pi$
$864$	2.37109e7	−	2.08134e6i	1.08060	−	0.0948547i
$865$	−1.23264e7			−0.560140
$866$	−1.33989e7	+	4.61446e6i	−0.607118	+	0.209087i
$867$	1.25478e7			0.566918
$868$		0			0
$869$	−7.04336e6			−0.316396
$870$	−5.28440e7	+	1.81991e7i	−2.36700	+	0.815176i
$871$	−1.81847e6			−0.0812195
$872$	1.60912e7	+	1.04458e7i	0.716632	+	0.465209i
$873$			5.21510e6i			0.231594i
$874$	3.87436e7	−	1.33430e7i	1.71562	−	0.590846i
$875$		0			0
$876$	−5.40622e6	−	6.91800e6i	−0.238031	−	0.304593i
$877$	−4.29065e6			−0.188375			−0.0941876	−	0.995554i	$-0.530025\pi$
$877$	−4.29065e6			−0.188375			−0.0941876	+	0.995554i	$0.530025\pi$
$878$	4.11579e6	+	1.19509e7i	0.180184	+	0.523195i
$879$		−	1.44816e7i		−	0.632186i
$880$	−2.00508e6	+	8.04987e6i	−0.0872821	+	0.350415i
$881$			3.13278e7i			1.35985i	0.733282	+	0.679925i	$0.237987\pi$
$881$			3.13278e7i			1.35985i	−0.733282	+	0.679925i	$0.762013\pi$
$882$		0			0
$883$			2.34445e7i			1.01190i	0.862562	+	0.505952i	$0.168859\pi$
$883$			2.34445e7i			1.01190i	−0.862562	+	0.505952i	$0.831141\pi$
$884$	4.78126e6	−	3.73642e6i	0.205784	−	0.160815i
$885$			1.49252e7i			0.640564i
$886$	−2.71004e7	+	9.33316e6i	−1.15982	+	0.399433i
$887$	−2.55628e6			−0.109094			−0.0545468	−	0.998511i	$-0.517371\pi$
$887$	−2.55628e6			−0.109094			−0.0545468	+	0.998511i	$0.517371\pi$
$888$	1.91640e7	+	1.24405e7i	0.815555	+	0.529427i
$889$		0			0
$890$	7.31545e6	+	2.12416e7i	0.309575	+	0.898903i
$891$		−	3.52162e6i		−	0.148610i
$892$	−5.14831e6	+	4.02326e6i	−0.216647	+	0.169304i
$893$	−5.03062e7			−2.11102
$894$	7.43763e6	+	2.15964e7i	0.311236	+	0.903727i
$895$	−5.41976e7			−2.26163
$896$		0			0
$897$	1.47258e7			0.611080
$898$	1.06909e7	+	3.10428e7i	0.442409	+	1.28461i
$899$	7.09879e7			2.92944
$900$	−8.10419e6	+	6.33320e6i	−0.333506	+	0.260625i
$901$			1.43136e7i			0.587404i
$902$	1.74965e6	+	5.08040e6i	0.0716036	+	0.207913i
$903$		0			0
$904$	1.71920e7	+	1.11604e7i	0.699691	+	0.454212i
$905$	−1.48927e7			−0.604438
$906$	7.95236e6	−	2.73873e6i	0.321866	−	0.110848i
$907$		−	1.39379e7i		−	0.562574i	−0.959624	−	0.281287i	$-0.909239\pi$
$907$		−	1.39379e7i		−	0.562574i	0.959624	−	0.281287i	$-0.0907612\pi$
$908$	−1.05320e7	+	8.23048e6i	−0.423933	+	0.331292i
$909$			9.37274e6i			0.376233i
$910$		0			0
$911$		−	4.03701e7i		−	1.61162i	−0.592171	−	0.805812i	$-0.701729\pi$
$911$		−	4.03701e7i		−	1.61162i	0.592171	−	0.805812i	$-0.298271\pi$
$912$	5.93719e6	−	2.38362e7i	0.236371	−	0.948966i
$913$		−	382912.i		−	0.0152028i
$914$	−860376.	−	2.49824e6i	−0.0340661	−	0.0989166i
$915$	−1.26090e7			−0.497882
$916$	−1.79987e7	−	2.30318e7i	−0.708765	−	0.906961i
$917$		0			0
$918$	1.52208e7	−	5.24192e6i	0.596115	−	0.205297i
$919$		−	2.52684e7i		−	0.986938i	−0.869763	−	0.493469i	$-0.835729\pi$
$919$		−	2.52684e7i		−	0.986938i	0.869763	−	0.493469i	$-0.164271\pi$
$920$	−5.49944e7	−	3.57002e7i	−2.14214	−	1.39060i
$921$	−2.47555e7			−0.961662
$922$	−6.25478e6	+	2.15410e6i	−0.242317	+	0.0834522i
$923$	−1.57461e7			−0.608373
$924$		0			0
$925$	−4.68445e7			−1.80013
$926$	6.75686e6	−	2.32701e6i	0.258951	−	0.0891807i
$927$	4.15128e6			0.158666
$928$	4.75302e7	−	4.17219e6i	1.81175	−	0.159036i
$929$		−	2.01196e7i		−	0.764856i	−0.923985	−	0.382428i	$-0.875088\pi$
$929$		−	2.01196e7i		−	0.764856i	0.923985	−	0.382428i	$-0.124912\pi$
$930$	−5.52915e7	+	1.90420e7i	−2.09629	+	0.721945i
$931$		0			0
$932$	−3.53823e7	+	2.76502e7i	−1.33428	+	1.04270i
$933$	2.49303e7			0.937611
$934$	1.68346e7	+	4.88820e7i	0.631444	+	1.83350i
$935$			5.61074e6i			0.209890i
$936$	−1.75123e6	+	2.69768e6i	−0.0653361	+	0.100647i
$937$			2.14075e7i			0.796556i	0.917265	+	0.398278i	$0.130392\pi$
$937$			2.14075e7i			0.796556i	−0.917265	+	0.398278i	$0.869608\pi$
$938$		0			0
$939$		−	2.78690e7i		−	1.03147i
$940$	4.95642e7	+	6.34241e7i	1.82957	+	2.34118i
$941$		−	1.34883e7i		−	0.496574i	−0.968687	−	0.248287i	$-0.920132\pi$
$941$		−	1.34883e7i		−	0.496574i	0.968687	−	0.248287i	$-0.0798676\pi$
$942$	−7.97191e6	+	2.74547e6i	−0.292708	+	0.100807i
$943$	−4.24673e7			−1.55516
$944$	3.07960e6	−	1.23638e7i	0.112477	−	0.451566i
$945$		0			0
$946$	−1.08010e6	−	3.13626e6i	−0.0392408	−	0.113942i
$947$		−	3.51268e6i		−	0.127281i	−0.997973	−	0.0636406i	$-0.979729\pi$
$947$		−	3.51268e6i		−	0.127281i	0.997973	−	0.0636406i	$-0.0202711\pi$
$948$	−2.05482e7	−	2.62943e7i	−0.742598	−	0.950256i
$949$	5.62904e6			0.202894
$950$	1.63997e7	+	4.76193e7i	0.589560	+	1.71188i
$951$	1.47718e7			0.529642
$952$		0			0
$953$	1.69346e7			0.604008			0.302004	−	0.953307i	$-0.402344\pi$
$953$	1.69346e7			0.604008			0.302004	+	0.953307i	$0.402344\pi$
$954$	−2.47038e6	−	7.17316e6i	−0.0878806	−	0.255176i
$955$	−7.52766e7			−2.67086
$956$	−2.82949e7	−	3.62073e7i	−1.00130	−	1.28130i
$957$		−	9.90849e6i		−	0.349726i
$958$	7.71811e6	+	2.24108e7i	0.271705	+	0.788939i
$959$		0			0
$960$	−3.59014e7	+	1.59993e7i	−1.25728	+	0.560301i
$961$	4.56466e7			1.59441
$962$	−1.38501e7	+	4.76988e6i	−0.482521	+	0.166176i
$963$		−	8.85879e6i		−	0.307829i
$964$	5.65733e6	+	7.23932e6i	0.196073	+	0.250903i
$965$			1.07265e7i			0.370799i
$966$		0			0
$967$		−	4.46651e6i		−	0.153604i	−0.997046	−	0.0768020i	$-0.975529\pi$
$967$		−	4.46651e6i		−	0.153604i	0.997046	−	0.0768020i	$-0.0244709\pi$
$968$	2.32192e7	+	1.50730e7i	0.796451	+	0.517025i
$969$		−	1.66138e7i		−	0.568407i
$970$	−1.33052e7	−	3.86340e7i	−0.454039	−	1.31838i
$971$	1.22197e7			0.415924			0.207962	−	0.978137i	$-0.433317\pi$
$971$	1.22197e7			0.415924			0.207962	+	0.978137i	$0.433317\pi$
$972$	−1.20292e7	+	9.40049e6i	−0.408387	+	0.319143i
$973$		0			0
$974$	2.69274e7	−	9.27358e6i	0.909487	−	0.313220i
$975$			1.80993e7i			0.609749i
$976$	1.04450e7	+	2.60167e6i	0.350982	+	0.0874236i
$977$	−3.37515e7			−1.13124			−0.565622	−	0.824664i	$-0.691364\pi$
$977$	−3.37515e7			−1.13124			−0.565622	+	0.824664i	$0.691364\pi$
$978$	−1.44398e7	+	4.97296e6i	−0.482741	+	0.166252i
$979$	−3.98290e6			−0.132814
$980$		0			0
$981$	−6.87714e6			−0.228158
$982$	−2.23695e7	+	7.70390e6i	−0.740250	+	0.254936i
$983$	−3.28416e7			−1.08403			−0.542015	−	0.840369i	$-0.682338\pi$
$983$	−3.28416e7			−1.08403			−0.542015	+	0.840369i	$0.682338\pi$
$984$	−1.38618e7	+	2.13533e7i	−0.456384	+	0.703037i
$985$		−	2.06898e7i		−	0.679464i
$986$	3.05111e7	−	1.05078e7i	0.999461	−	0.344207i
$987$		0			0
$988$	9.69754e6	+	1.24093e7i	0.316060	+	0.404442i
$989$	2.62162e7			0.852273
$990$	−968357.	−	2.81178e6i	−0.0314013	−	0.0911788i
$991$			3.67267e7i			1.18795i	0.804484	+	0.593974i	$0.202442\pi$
$991$			3.67267e7i			1.18795i	−0.804484	+	0.593974i	$0.797558\pi$
$992$	4.97315e7	−	4.36543e6i	1.60455	−	0.140847i
$993$			7.46409e6i			0.240217i
$994$		0			0
$995$		−	1.51394e7i		−	0.484786i
$996$	1.42949e6	−	1.11711e6i	0.0456597	−	0.0356817i
$997$			3.75177e7i			1.19536i	0.801735	+	0.597680i	$0.203911\pi$
$997$			3.75177e7i			1.19536i	−0.801735	+	0.597680i	$0.796089\pi$
$998$	1.88794e7	−	6.50191e6i	0.600014	−	0.206640i
$999$	−3.88614e7			−1.23198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.c.195.18	yes	56
4.3	odd	2	inner	196.6.d.c.195.19	yes	56
7.6	odd	2	inner	196.6.d.c.195.17	✓	56
28.27	even	2	inner	196.6.d.c.195.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.6.d.c.195.17	✓	56	7.6	odd	2	inner
196.6.d.c.195.18	yes	56	1.1	even	1	trivial
196.6.d.c.195.19	yes	56	4.3	odd	2	inner
196.6.d.c.195.20	yes	56	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84200 - 5.34855i) q^{2} +13.3457 q^{3} +(-25.2141 + 19.7041i) q^{4} +89.8785i q^{5} +(-24.5829 - 71.3804i) q^{6} +(151.833 + 98.5639i) q^{8} -64.8912 q^{9} +(480.720 - 165.556i) q^{10} +90.1372i q^{11} +(-336.500 + 262.966i) q^{12} -273.804i q^{13} +1199.50i q^{15} +(247.498 - 993.640i) q^{16} -692.565i q^{17} +(119.530 + 347.074i) q^{18} +1797.49 q^{19} +(-1770.97 - 2266.20i) q^{20} +(482.104 - 166.033i) q^{22} +4029.93i q^{23} +(2026.32 + 1315.41i) q^{24} -4953.14 q^{25} +(-1464.45 + 504.347i) q^{26} -4109.04 q^{27} -8236.85 q^{29} +(6415.56 - 2209.47i) q^{30} -8618.34 q^{31} +(-5770.43 + 506.528i) q^{32} +1202.95i q^{33} +(-3704.22 + 1275.71i) q^{34} +(1636.17 - 1278.62i) q^{36} +9457.54 q^{37} +(-3310.97 - 9613.96i) q^{38} -3654.11i q^{39} +(-8858.77 + 13646.5i) q^{40} +10538.0i q^{41} -6505.37i q^{43} +(-1776.07 - 2272.72i) q^{44} -5832.33i q^{45} +(21554.3 - 7423.13i) q^{46} -27987.0 q^{47} +(3303.05 - 13260.9i) q^{48} +(9123.69 + 26492.2i) q^{50} -9242.79i q^{51} +(5395.05 + 6903.70i) q^{52} -20667.5 q^{53} +(7568.85 + 21977.4i) q^{54} -8101.39 q^{55} +23988.8 q^{57} +(15172.3 + 44055.2i) q^{58} +12442.9 q^{59} +(-23634.9 - 30244.1i) q^{60} +10511.9i q^{61} +(15875.0 + 46095.6i) q^{62} +(13338.3 + 29930.4i) q^{64} +24609.1 q^{65} +(6434.03 - 2215.83i) q^{66} -6641.50i q^{67} +(13646.4 + 17462.4i) q^{68} +53782.4i q^{69} -57508.8i q^{71} +(-9852.61 - 6395.93i) q^{72} +20558.7i q^{73} +(-17420.8 - 50584.1i) q^{74} -66103.4 q^{75} +(-45322.0 + 35417.8i) q^{76} +(-19544.2 + 6730.88i) q^{78} +78140.5i q^{79} +(89306.9 + 22244.8i) q^{80} -39069.6 q^{81} +(56363.0 - 19411.0i) q^{82} -4248.11 q^{83} +62246.7 q^{85} +(-34794.3 + 11982.9i) q^{86} -109927. q^{87} +(-8884.27 + 13685.8i) q^{88} +44187.1i q^{89} +(-31194.5 + 10743.1i) q^{90} +(-79406.0 - 101611. i) q^{92} -115018. q^{93} +(51552.0 + 149690. i) q^{94} +161556. i q^{95} +(-77010.7 + 6759.99i) q^{96} -80366.9i q^{97} -5849.11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} - 172 q^{4} - 356 q^{8} + 5832 q^{9} + 84 q^{16} + 1620 q^{18} - 17616 q^{22} - 25000 q^{25} - 16288 q^{29} - 32440 q^{30} - 6556 q^{32} + 44444 q^{36} + 42592 q^{37} + 17784 q^{44} - 25560 q^{46}+ \cdots + 3168 q^{93}+O(q^{100}) \) 56 * q + 4 * q^2 - 172 * q^4 - 356 * q^8 + 5832 * q^9 + 84 * q^16 + 1620 * q^18 - 17616 * q^22 - 25000 * q^25 - 16288 * q^29 - 32440 * q^30 - 6556 * q^32 + 44444 * q^36 + 42592 * q^37 + 17784 * q^44 - 25560 * q^46 + 13932 * q^50 - 259888 * q^53 + 82592 * q^57 + 140792 * q^58 + 240488 * q^60 - 264340 * q^64 - 189440 * q^65 + 244444 * q^72 - 273608 * q^74 + 350936 * q^78 + 405112 * q^81 - 407344 * q^85 - 243776 * q^86 + 181248 * q^88 - 262696 * q^92 + 3168 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more