LMFDB - Embedded newform 252.6.b.d.55.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,6,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	252.b (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:	$40.4167225929$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 674 x^{14} + 3404 x^{13} + 173721 x^{12} - 919512 x^{11} - 21981508 x^{10} + \cdots + 224266997486896 $ x^16 - 4x^15 - 674x^14 + 3404x^13 + 173721x^12 - 919512x^11 - 21981508x^10 + 94817024x^9 + 1652635052x^8 - 4373672096x^7 - 73339451096x^6 + 61523648112x^5 + 1688776741892x^4 + 257949039296x^3 - 14815785541168x^2 + 39188323305792*x + 224266997486896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.12
Root			$2.37022 - 2.69664i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.6.b.d.55.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70662 + 5.39328i) q^{2} +(-26.1749 + 18.4085i) q^{4} +76.3023i q^{5} +(-120.438 - 47.9752i) q^{7} +(-143.953 - 109.752i) q^{8} +O(q^{10})$	\(q+(1.70662 + 5.39328i) q^{2} +(-26.1749 + 18.4085i) q^{4} +76.3023i q^{5} +(-120.438 - 47.9752i) q^{7} +(-143.953 - 109.752i) q^{8} +(-411.519 + 130.219i) q^{10} -334.774i q^{11} -912.099i q^{13} +(53.2015 - 731.433i) q^{14} +(346.251 - 963.684i) q^{16} +478.534i q^{17} +2651.10 q^{19} +(-1404.61 - 1997.20i) q^{20} +(1805.53 - 571.331i) q^{22} +1420.85i q^{23} -2697.03 q^{25} +(4919.20 - 1556.61i) q^{26} +(4035.61 - 961.346i) q^{28} -6813.64 q^{29} +513.105 q^{31} +(5788.33 + 222.787i) q^{32} +(-2580.87 + 816.675i) q^{34} +(3660.62 - 9189.71i) q^{35} -5370.81 q^{37} +(4524.42 + 14298.1i) q^{38} +(8374.34 - 10983.9i) q^{40} +697.095i q^{41} +527.614i q^{43} +(6162.70 + 8762.67i) q^{44} +(-7663.06 + 2424.86i) q^{46} +11640.9 q^{47} +(12203.8 + 11556.1i) q^{49} +(-4602.81 - 14545.9i) q^{50} +(16790.4 + 23874.1i) q^{52} -4929.75 q^{53} +25544.0 q^{55} +(12072.1 + 20124.5i) q^{56} +(-11628.3 - 36747.9i) q^{58} +10780.3 q^{59} -17440.4i q^{61} +(875.675 + 2767.32i) q^{62} +(8676.93 + 31598.3i) q^{64} +69595.2 q^{65} -49231.3i q^{67} +(-8809.11 - 12525.6i) q^{68} +(55810.0 + 4059.39i) q^{70} -40989.1i q^{71} -59368.9i q^{73} +(-9165.93 - 28966.3i) q^{74} +(-69392.3 + 48802.9i) q^{76} +(-16060.8 + 40319.6i) q^{77} +12641.7i q^{79} +(73531.2 + 26419.7i) q^{80} +(-3759.63 + 1189.68i) q^{82} +49569.1 q^{83} -36513.2 q^{85} +(-2845.57 + 900.437i) q^{86} +(-36742.1 + 48191.7i) q^{88} -13219.8i q^{89} +(-43758.1 + 109852. i) q^{91} +(-26155.8 - 37190.7i) q^{92} +(19866.5 + 62782.4i) q^{94} +202285. i q^{95} +57155.4i q^{97} +(-41498.1 + 85540.1i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8	$ 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8} - 1176 q^{14} - 3008 q^{16} + 1552 q^{22} - 9776 q^{25} - 14672 q^{28} - 26592 q^{29} - 11648 q^{32} - 26272 q^{37} + 12256 q^{44} + 20208 q^{46} + 8848 q^{49} - 5992 q^{50} + 41888 q^{53} - 38304 q^{56} - 144400 q^{58} + 45312 q^{64} - 66688 q^{65} + 79296 q^{70} - 348464 q^{74} - 320992 q^{77} + 78080 q^{85} + 78448 q^{86} - 66112 q^{88} - 446944 q^{92} - 224840 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8 - 1176 * q^14 - 3008 * q^16 + 1552 * q^22 - 9776 * q^25 - 14672 * q^28 - 26592 * q^29 - 11648 * q^32 - 26272 * q^37 + 12256 * q^44 + 20208 * q^46 + 8848 * q^49 - 5992 * q^50 + 41888 * q^53 - 38304 * q^56 - 144400 * q^58 + 45312 * q^64 - 66688 * q^65 + 79296 * q^70 - 348464 * q^74 - 320992 * q^77 + 78080 * q^85 + 78448 * q^86 - 66112 * q^88 - 446944 * q^92 - 224840 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.70662	+	5.39328i	0.301691	+	0.953406i
$2$	1.70662	+	5.39328i	0.301691	+	0.953406i
$3$		0			0
$3$		0			0
$4$	−26.1749	+	18.4085i	−0.817966	+	0.575267i
$5$			76.3023i			1.36494i	0.730915	+	0.682468i	$0.239093\pi$
$5$			76.3023i			1.36494i	−0.730915	+	0.682468i	$0.760907\pi$
$6$		0			0
$7$	−120.438	−	47.9752i	−0.929008	−	0.370060i
$7$	−120.438	−	47.9752i	−0.929008	−	0.370060i
$8$	−143.953	−	109.752i	−0.795235	−	0.606301i
$9$		0			0
$10$	−411.519	+	130.219i	−1.30134	+	0.411788i
$11$		−	334.774i		−	0.834199i	−0.908861	−	0.417099i	$-0.863047\pi$
$11$		−	334.774i		−	0.834199i	0.908861	−	0.417099i	$-0.136953\pi$
$12$		0			0
$13$		−	912.099i		−	1.49687i	−0.663209	−	0.748434i	$-0.730806\pi$
$13$		−	912.099i		−	1.49687i	0.663209	−	0.748434i	$-0.269194\pi$
$14$	53.2015	−	731.433i	0.0725444	−	0.997365i
$15$		0			0
$16$	346.251	−	963.684i	0.338136	−	0.941097i
$17$			478.534i			0.401597i	0.979633	+	0.200798i	$0.0643536\pi$
$17$			478.534i			0.401597i	−0.979633	+	0.200798i	$0.935646\pi$
$18$		0			0
$19$	2651.10			1.68478			0.842388	−	0.538872i	$-0.181149\pi$
$19$	2651.10			1.68478			0.842388	+	0.538872i	$0.181149\pi$
$20$	−1404.61	−	1997.20i	−0.785203	−	1.11647i
$21$		0			0
$22$	1805.53	−	571.331i	0.795330	−	0.251670i
$23$			1420.85i			0.560054i	0.959992	+	0.280027i	$0.0903434\pi$
$23$			1420.85i			0.560054i	−0.959992	+	0.280027i	$0.909657\pi$
$24$		0			0
$25$	−2697.03			−0.863051
$26$	4919.20	−	1556.61i	1.42712	−	0.451591i
$27$		0			0
$28$	4035.61	−	961.346i	0.972780	−	0.231731i
$29$	−6813.64			−1.50447			−0.752236	−	0.658894i	$-0.771025\pi$
$29$	−6813.64			−1.50447			−0.752236	+	0.658894i	$0.771025\pi$
$30$		0			0
$31$	513.105			0.0958963			0.0479482	−	0.998850i	$-0.484732\pi$
$31$	513.105			0.0958963			0.0479482	+	0.998850i	$0.484732\pi$
$32$	5788.33	+	222.787i	0.999260	+	0.0384604i
$33$		0			0
$34$	−2580.87	+	816.675i	−0.382885	+	0.121158i
$35$	3660.62	−	9189.71i	0.505108	−	1.26804i
$36$		0			0
$37$	−5370.81			−0.644964			−0.322482	−	0.946576i	$-0.604517\pi$
$37$	−5370.81			−0.644964			−0.322482	+	0.946576i	$0.604517\pi$
$38$	4524.42	+	14298.1i	0.508281	+	1.60627i
$39$		0			0
$40$	8374.34	−	10983.9i	0.827562	−	1.08545i
$41$			697.095i			0.0647638i	0.999476	+	0.0323819i	$0.0103093\pi$
$41$			697.095i			0.0647638i	−0.999476	+	0.0323819i	$0.989691\pi$
$42$		0			0
$43$			527.614i			0.0435156i	0.999763	+	0.0217578i	$0.00692628\pi$
$43$			527.614i			0.0435156i	−0.999763	+	0.0217578i	$0.993074\pi$
$44$	6162.70	+	8762.67i	0.479887	+	0.682346i
$45$		0			0
$46$	−7663.06	+	2424.86i	−0.533958	+	0.168963i
$47$	11640.9			0.768670			0.384335	−	0.923194i	$-0.374431\pi$
$47$	11640.9			0.768670			0.384335	+	0.923194i	$0.374431\pi$
$48$		0			0
$49$	12203.8	+	11556.1i	0.726111	+	0.687577i
$50$	−4602.81	−	14545.9i	−0.260374	−	0.822838i
$51$		0			0
$52$	16790.4	+	23874.1i	0.861099	+	1.22439i
$53$	−4929.75			−0.241066			−0.120533	−	0.992709i	$-0.538460\pi$
$53$	−4929.75			−0.241066			−0.120533	+	0.992709i	$0.538460\pi$
$54$		0			0
$55$	25544.0			1.13863
$56$	12072.1	+	20124.5i	0.514412	+	0.857543i
$57$		0			0
$58$	−11628.3	−	36747.9i	−0.453885	−	1.43437i
$59$	10780.3			0.403181			0.201591	−	0.979470i	$-0.435389\pi$
$59$	10780.3			0.403181			0.201591	+	0.979470i	$0.435389\pi$
$60$		0			0
$61$		−	17440.4i		−	0.600112i	−0.953922	−	0.300056i	$-0.902995\pi$
$61$		−	17440.4i		−	0.600112i	0.953922	−	0.300056i	$-0.0970053\pi$
$62$	875.675	+	2767.32i	0.0289310	+	0.0914281i
$63$		0			0
$64$	8676.93	+	31598.3i	0.264799	+	0.964304i
$65$	69595.2			2.04313
$66$		0			0
$67$		−	49231.3i		−	1.33984i	−0.742432	−	0.669922i	$-0.766328\pi$
$67$		−	49231.3i		−	1.33984i	0.742432	−	0.669922i	$-0.233672\pi$
$68$	−8809.11	−	12525.6i	−0.231025	−	0.328492i
$69$		0			0
$70$	55810.0	+	4059.39i	1.36134	+	0.0990185i
$71$		−	40989.1i		−	0.964990i	−0.875899	−	0.482495i	$-0.839731\pi$
$71$		−	40989.1i		−	0.964990i	0.875899	−	0.482495i	$-0.160269\pi$
$72$		0			0
$73$		−	59368.9i		−	1.30392i	−0.758252	−	0.651962i	$-0.773946\pi$
$73$		−	59368.9i		−	1.30392i	0.758252	−	0.651962i	$-0.226054\pi$
$74$	−9165.93	−	28966.3i	−0.194580	−	0.614913i
$75$		0			0
$76$	−69392.3	+	48802.9i	−1.37809	+	0.969196i
$77$	−16060.8	+	40319.6i	−0.308703	+	0.774977i
$78$		0			0
$79$			12641.7i			0.227896i	0.993487	+	0.113948i	$0.0363498\pi$
$79$			12641.7i			0.227896i	−0.993487	+	0.113948i	$0.963650\pi$
$80$	73531.2	+	26419.7i	1.28454	+	0.461534i
$81$		0			0
$82$	−3759.63	+	1189.68i	−0.0617462	+	0.0195386i
$83$	49569.1			0.789798			0.394899	−	0.918725i	$-0.370780\pi$
$83$	49569.1			0.789798			0.394899	+	0.918725i	$0.370780\pi$
$84$		0			0
$85$	−36513.2			−0.548154
$86$	−2845.57	+	900.437i	−0.0414881	+	0.0131283i
$87$		0			0
$88$	−36742.1	+	48191.7i	−0.505775	+	0.663384i
$89$		−	13219.8i		−	0.176909i	−0.996080	−	0.0884547i	$-0.971807\pi$
$89$		−	13219.8i		−	0.176909i	0.996080	−	0.0884547i	$-0.0281928\pi$
$90$		0			0
$91$	−43758.1	+	109852.i	−0.553931	+	1.39060i
$92$	−26155.8	−	37190.7i	−0.322180	−	0.458105i
$93$		0			0
$94$	19866.5	+	62782.4i	0.231901	+	0.732855i
$95$			202285.i			2.29961i
$96$		0			0
$97$			57155.4i			0.616777i	0.951261	+	0.308388i	$0.0997896\pi$
$97$			57155.4i			0.616777i	−0.951261	+	0.308388i	$0.900210\pi$
$98$	−41498.1	+	85540.1i	−0.436479	+	0.899714i
$99$		0			0
$100$	70594.6	−	49648.5i	0.705946	−	0.496485i
$101$		−	77288.8i		−	0.753899i	−0.926234	−	0.376949i	$-0.876973\pi$
$101$		−	77288.8i		−	0.753899i	0.926234	−	0.376949i	$-0.123027\pi$
$102$		0			0
$103$	180104.			1.67275			0.836374	−	0.548160i	$-0.184671\pi$
$103$	180104.			1.67275			0.836374	+	0.548160i	$0.184671\pi$
$104$	−100105.	+	131299.i	−0.907552	+	1.19036i
$105$		0			0
$106$	−8413.21	−	26587.5i	−0.0727273	−	0.229834i
$107$		−	214915.i		−	1.81471i	−0.420366	−	0.907354i	$-0.638098\pi$
$107$		−	214915.i		−	1.81471i	0.420366	−	0.907354i	$-0.361902\pi$
$108$		0			0
$109$	62569.2			0.504422			0.252211	−	0.967672i	$-0.418842\pi$
$109$	62569.2			0.504422			0.252211	+	0.967672i	$0.418842\pi$
$110$	43593.9	+	137766.i	0.343513	+	1.08557i
$111$		0			0
$112$	−87934.8	+	99452.9i	−0.662393	+	0.749156i
$113$	−126905.			−0.934939			−0.467469	−	0.884009i	$-0.654834\pi$
$113$	−126905.			−0.934939			−0.467469	+	0.884009i	$0.654834\pi$
$114$		0			0
$115$	−108414.			−0.764438
$116$	178346.	−	125429.i	1.23061	−	0.865473i
$117$		0			0
$118$	18397.8	+	58141.1i	0.121636	+	0.384395i
$119$	22957.8	−	57633.8i	0.148615	−	0.373087i
$120$		0			0
$121$	48977.6			0.304113
$122$	94061.0	−	29764.1i	0.572150	−	0.181048i
$123$		0			0
$124$	−13430.5	+	9445.51i	−0.0784399	+	0.0551660i
$125$			32654.7i			0.186927i
$126$		0			0
$127$		−	252336.i		−	1.38825i	−0.719852	−	0.694127i	$-0.755790\pi$
$127$		−	252336.i		−	1.38825i	0.719852	−	0.694127i	$-0.244210\pi$
$128$	−155610.	+	100723.i	−0.839485	+	0.543382i
$129$		0			0
$130$	118772.	+	375346.i	0.616393	+	1.94793i
$131$	309045.			1.57342			0.786708	−	0.617326i	$-0.211784\pi$
$131$	309045.			1.57342			0.786708	+	0.617326i	$0.211784\pi$
$132$		0			0
$133$	−319294.	−	127187.i	−1.56517	−	0.623468i
$134$	265518.	−	84019.0i	1.27741	−	0.404218i
$135$		0			0
$136$	52520.1	−	68886.4i	0.243488	−	0.319364i
$137$	−18629.7			−0.0848018			−0.0424009	−	0.999101i	$-0.513501\pi$
$137$	−18629.7			−0.0848018			−0.0424009	+	0.999101i	$0.513501\pi$
$138$		0			0
$139$	34562.3			0.151728			0.0758639	−	0.997118i	$-0.475829\pi$
$139$	34562.3			0.151728			0.0758639	+	0.997118i	$0.475829\pi$
$140$	73352.9	+	307926.i	0.316299	+	1.32778i
$141$		0			0
$142$	221066.	−	69952.9i	0.920027	−	0.291128i
$143$	−305347.			−1.24869
$144$		0			0
$145$		−	519896.i		−	2.05351i
$146$	320193.	−	101320.i	1.24317	−	0.393381i
$147$		0			0
$148$	140580.	−	98868.8i	0.527558	−	0.371027i
$149$	−226557.			−0.836010			−0.418005	−	0.908445i	$-0.637271\pi$
$149$	−226557.			−0.836010			−0.418005	+	0.908445i	$0.637271\pi$
$150$		0			0
$151$		−	292164.i		−	1.04276i	−0.853325	−	0.521380i	$-0.825418\pi$
$151$		−	292164.i		−	1.04276i	0.853325	−	0.521380i	$-0.174582\pi$
$152$	−381634.	−	290964.i	−1.33979	−	1.02148i
$153$		0			0
$154$	−244864.	−	17810.5i	−0.832001	−	0.0605164i
$155$			39151.1i			0.130892i
$156$		0			0
$157$		−	244229.i		−	0.790767i	−0.918516	−	0.395384i	$-0.870612\pi$
$157$		−	244229.i		−	0.790767i	0.918516	−	0.395384i	$-0.129388\pi$
$158$	−68180.1	+	21574.5i	−0.217278	+	0.0687541i
$159$		0			0
$160$	−16999.1	+	441663.i	−0.0524960	+	1.36393i
$161$	68165.8	−	171125.i	0.207253	−	0.520294i
$162$		0			0
$163$			218907.i			0.645342i	0.946511	+	0.322671i	$0.104581\pi$
$163$			218907.i			0.645342i	−0.946511	+	0.322671i	$0.895419\pi$
$164$	−12832.5	−	18246.4i	−0.0372565	−	0.0529745i
$165$		0			0
$166$	84595.6	+	267340.i	0.238275	+	0.752998i
$167$	−441969.			−1.22631			−0.613155	−	0.789962i	$-0.710100\pi$
$167$	−441969.			−1.22631			−0.613155	+	0.789962i	$0.710100\pi$
$168$		0			0
$169$	−460631.			−1.24061
$170$	−62314.2	−	196926.i	−0.165373	−	0.522613i
$171$		0			0
$172$	−9712.61	−	13810.2i	−0.0250331	−	0.0355943i
$173$		−	447193.i		−	1.13600i	−0.823028	−	0.568001i	$-0.807717\pi$
$173$		−	447193.i		−	1.13600i	0.823028	−	0.568001i	$-0.192283\pi$
$174$		0			0
$175$	324826.	+	129391.i	0.801781	+	0.319381i
$176$	−322616.	−	115916.i	−0.785062	−	0.282072i
$177$		0			0
$178$	71298.2	−	22561.2i	0.168666	−	0.0533719i
$179$			435778.i			1.01656i	0.861192	+	0.508280i	$0.169718\pi$
$179$			435778.i			1.01656i	−0.861192	+	0.508280i	$0.830282\pi$
$180$		0			0
$181$		−	715186.i		−	1.62264i	−0.584601	−	0.811321i	$-0.698749\pi$
$181$		−	715186.i		−	1.62264i	0.584601	−	0.811321i	$-0.301251\pi$
$182$	−667139.	−	48525.0i	−1.49292	−	0.108589i
$183$		0			0
$184$	155942.	−	204536.i	0.339561	−	0.445375i
$185$		−	409805.i		−	0.880335i
$186$		0			0
$187$	160201.			0.335012
$188$	−304698.	+	214291.i	−0.628746	+	0.442191i
$189$		0			0
$190$	−1.09098e6	+	345223.i	−2.19246	+	0.693771i
$191$		−	350615.i		−	0.695420i	−0.937602	−	0.347710i	$-0.886959\pi$
$191$		−	350615.i		−	0.695420i	0.937602	−	0.347710i	$-0.113041\pi$
$192$		0			0
$193$	337927.			0.653024			0.326512	−	0.945193i	$-0.394127\pi$
$193$	337927.			0.653024			0.326512	+	0.945193i	$0.394127\pi$
$194$	−308255.	+	97542.5i	−0.588039	+	0.186076i
$195$		0			0
$196$	−532163.	−	77826.6i	−0.989475	−	0.144706i
$197$	−31816.8			−0.0584105			−0.0292052	−	0.999573i	$-0.509298\pi$
$197$	−31816.8			−0.0584105			−0.0292052	+	0.999573i	$0.509298\pi$
$198$		0			0
$199$	31190.2			0.0558323			0.0279162	−	0.999610i	$-0.491113\pi$
$199$	31190.2			0.0558323			0.0279162	+	0.999610i	$0.491113\pi$
$200$	388246.	+	296005.i	0.686329	+	0.523268i
$201$		0			0
$202$	416840.	−	131902.i	0.718771	−	0.227444i
$203$	820623.	+	326886.i	1.39767	+	0.556745i
$204$		0			0
$205$	−53189.9			−0.0883984
$206$	307369.	+	971351.i	0.504652	+	1.59481i
$207$		0			0
$208$	−878975.	−	315815.i	−1.40870	−	0.506144i
$209$		−	887518.i		−	1.40544i
$210$		0			0
$211$			723348.i			1.11851i	0.828994	+	0.559257i	$0.188913\pi$
$211$			723348.i			1.11851i	−0.828994	+	0.559257i	$0.811087\pi$
$212$	129036.	−	90749.6i	0.197184	−	0.138677i
$213$		0			0
$214$	1.15910e6	−	366778.i	1.73015	−	0.547480i
$215$	−40258.2			−0.0593961
$216$		0			0
$217$	−61797.5	−	24616.3i	−0.0890884	−	0.0354874i
$218$	106782.	+	337453.i	0.152179	+	0.480919i
$219$		0			0
$220$	−668611.	+	470228.i	−0.931359	+	0.655015i
$221$	436470.			0.601137
$222$		0			0
$223$	−728622.			−0.981161			−0.490580	−	0.871396i	$-0.663215\pi$
$223$	−728622.			−0.981161			−0.490580	+	0.871396i	$0.663215\pi$
$224$	−686449.	−	304529.i	−0.914088	−	0.405516i
$225$		0			0
$226$	−216579.	−	684435.i	−0.282062	−	0.891376i
$227$	−874014.			−1.12578			−0.562890	−	0.826532i	$-0.690311\pi$
$227$	−874014.			−1.12578			−0.562890	+	0.826532i	$0.690311\pi$
$228$		0			0
$229$			1.15837e6i			1.45968i	0.683618	+	0.729840i	$0.260405\pi$
$229$			1.15837e6i			1.45968i	−0.683618	+	0.729840i	$0.739595\pi$
$230$	−185022.	−	584709.i	−0.230624	−	0.728819i
$231$		0			0
$232$	980844.	+	747812.i	1.19641	+	0.912163i
$233$	277974.			0.335440			0.167720	−	0.985835i	$-0.446360\pi$
$233$	277974.			0.335440			0.167720	+	0.985835i	$0.446360\pi$
$234$		0			0
$235$			888223.i			1.04919i
$236$	−282173.	+	198449.i	−0.329788	+	0.231937i
$237$		0			0
$238$	350015.	+	25458.7i	0.400539	+	0.0291336i
$239$		−	88758.8i		−	0.100512i	−0.998736	−	0.0502558i	$-0.983996\pi$
$239$		−	88758.8i		−	0.100512i	0.998736	−	0.0502558i	$-0.0160037\pi$
$240$		0			0
$241$		−	748467.i		−	0.830099i	−0.909799	−	0.415050i	$-0.863764\pi$
$241$		−	748467.i		−	0.830099i	0.909799	−	0.415050i	$-0.136236\pi$
$242$	83586.2	+	264150.i	0.0917479	+	0.289943i
$243$		0			0
$244$	321052.	+	456501.i	0.345224	+	0.490871i
$245$	−881757.	+	931174.i	−0.938499	+	0.991096i
$246$		0			0
$247$		−	2.41806e6i		−	2.52189i
$248$	−73863.0	−	56314.4i	−0.0762601	−	0.0581420i
$249$		0			0
$250$	−176116.	+	55729.2i	−0.178217	+	0.0563940i
$251$	−768117.			−0.769561			−0.384781	−	0.923008i	$-0.625723\pi$
$251$	−768117.			−0.769561			−0.384781	+	0.923008i	$0.625723\pi$
$252$		0			0
$253$	475664.			0.467196
$254$	1.36092e6	−	430641.i	1.32357	−	0.418823i
$255$		0			0
$256$	−808797.	−	667353.i	−0.771329	−	0.636437i
$257$			1.22830e6i			1.16003i	0.814604	+	0.580017i	$0.196954\pi$
$257$			1.22830e6i			1.16003i	−0.814604	+	0.580017i	$0.803046\pi$
$258$		0			0
$259$	646851.	+	257666.i	0.599177	+	0.238675i
$260$	−1.82165e6	+	1.28115e6i	−1.67121	+	1.17534i
$261$		0			0
$262$	527422.	+	1.66677e6i	0.474684	+	1.50010i
$263$		−	1.41313e6i		−	1.25978i	−0.776686	−	0.629888i	$-0.783101\pi$
$263$		−	1.41313e6i		−	1.25978i	0.776686	−	0.629888i	$-0.216899\pi$
$264$		0			0
$265$		−	376151.i		−	0.329039i
$266$	141042.	−	1.93910e6i	0.122221	−	1.68034i
$267$		0			0
$268$	906276.	+	1.28862e6i	0.770768	+	1.09595i
$269$			103713.i			0.0873878i	0.999045	+	0.0436939i	$0.0139126\pi$
$269$			103713.i			0.0873878i	−0.999045	+	0.0436939i	$0.986087\pi$
$270$		0			0
$271$	−1.31141e6			−1.08471			−0.542355	−	0.840149i	$-0.682467\pi$
$271$	−1.31141e6			−1.08471			−0.542355	+	0.840149i	$0.682467\pi$
$272$	461155.	+	165693.i	0.377942	+	0.135794i
$273$		0			0
$274$	−31793.9	−	100475.i	−0.0255839	−	0.0808506i
$275$			902896.i			0.719956i
$276$		0			0
$277$	−1.50328e6			−1.17717			−0.588587	−	0.808434i	$-0.700315\pi$
$277$	−1.50328e6			−1.17717			−0.588587	+	0.808434i	$0.700315\pi$
$278$	58984.7	+	186404.i	0.0457749	+	0.144658i
$279$		0			0
$280$	−1.53555e6	+	921126.i	−1.17049	+	0.702140i
$281$	−335270.			−0.253297			−0.126648	−	0.991948i	$-0.540422\pi$
$281$	−335270.			−0.253297			−0.126648	+	0.991948i	$0.540422\pi$
$282$		0			0
$283$	−933526.			−0.692884			−0.346442	−	0.938071i	$-0.612610\pi$
$283$	−933526.			−0.692884			−0.346442	+	0.938071i	$0.612610\pi$
$284$	754550.	+	1.07289e6i	0.555127	+	0.789329i
$285$		0			0
$286$	−521110.	−	1.64682e6i	−0.376716	−	1.19050i
$287$	33443.3	−	83956.9i	0.0239665	−	0.0601661i
$288$		0			0
$289$	1.19086e6			0.838720
$290$	2.80394e6	−	887265.i	1.95783	−	0.619524i
$291$		0			0
$292$	1.09290e6	+	1.55398e6i	0.750104	+	1.06656i
$293$			563086.i			0.383183i	0.981475	+	0.191591i	$0.0613648\pi$
$293$			563086.i			0.383183i	−0.981475	+	0.191591i	$0.938635\pi$
$294$		0			0
$295$			822560.i			0.550317i
$296$	773144.	+	589458.i	0.512898	+	0.391042i
$297$		0			0
$298$	−386646.	−	1.22188e6i	−0.252216	−	0.797057i
$299$	1.29596e6			0.838326
$300$		0			0
$301$	25312.4	−	63544.9i	0.0161034	−	0.0404264i
$302$	1.57572e6	−	498613.i	0.994173	−	0.314591i
$303$		0			0
$304$	917946.	−	2.55482e6i	0.569683	−	1.58554i
$305$	1.33074e6			0.819114
$306$		0			0
$307$	2.49384e6			1.51016			0.755079	−	0.655633i	$-0.227598\pi$
$307$	2.49384e6			1.51016			0.755079	+	0.655633i	$0.227598\pi$
$308$	−321833.	−	1.35102e6i	−0.193310	−	0.811492i
$309$		0			0
$310$	−211153.	+	66816.0i	−0.124794	+	0.0394890i
$311$	−198558.			−0.116409			−0.0582046	−	0.998305i	$-0.518538\pi$
$311$	−198558.			−0.116409			−0.0582046	+	0.998305i	$0.518538\pi$
$312$		0			0
$313$			2.40632e6i			1.38833i	0.719817	+	0.694164i	$0.244226\pi$
$313$			2.40632e6i			1.38833i	−0.719817	+	0.694164i	$0.755774\pi$
$314$	1.31720e6	−	416806.i	0.753922	−	0.238567i
$315$		0			0
$316$	−232715.	−	330895.i	−0.131101	−	0.186411i
$317$	−841749.			−0.470473			−0.235236	−	0.971938i	$-0.575586\pi$
$317$	−841749.			−0.470473			−0.235236	+	0.971938i	$0.575586\pi$
$318$		0			0
$319$			2.28103e6i			1.25503i
$320$	−2.41102e6	+	662069.i	−1.31621	+	0.361434i
$321$		0			0
$322$	1.03926e6	+	75591.5i	0.558578	+	0.0406287i
$323$			1.26864e6i			0.676601i
$324$		0			0
$325$			2.45996e6i			1.29187i
$326$	−1.18062e6	+	373590.i	−0.615273	+	0.194693i
$327$		0			0
$328$	76507.6	−	100349.i	0.0392663	−	0.0515024i
$329$	−1.40200e6	−	558473.i	−0.714101	−	0.284454i
$330$		0			0
$331$		−	1.95105e6i		−	0.978811i	−0.872056	−	0.489405i	$-0.837214\pi$
$331$		−	1.95105e6i		−	0.978811i	0.872056	−	0.489405i	$-0.162786\pi$
$332$	−1.29747e6	+	912495.i	−0.646028	+	0.454345i
$333$		0			0
$334$	−754272.	−	2.38366e6i	−0.369966	−	1.16917i
$335$	3.75646e6			1.82880
$336$		0			0
$337$	−1.26826e6			−0.608322			−0.304161	−	0.952621i	$-0.598376\pi$
$337$	−1.26826e6			−0.608322			−0.304161	+	0.952621i	$0.598376\pi$
$338$	−786122.	−	2.48431e6i	−0.374281	−	1.18281i
$339$		0			0
$340$	955730.	−	672155.i	0.448371	−	0.315335i
$341$		−	171774.i		−	0.0799966i
$342$		0			0
$343$	−915392.	−	1.97728e6i	−0.420119	−	0.907469i
$344$	57906.8	−	75951.6i	0.0263836	−	0.0346052i
$345$		0			0
$346$	2.41183e6	−	763187.i	1.08307	−	0.342721i
$347$		−	1.44829e6i		−	0.645703i	−0.946450	−	0.322852i	$-0.895359\pi$
$347$		−	1.44829e6i		−	0.645703i	0.946450	−	0.322852i	$-0.104641\pi$
$348$		0			0
$349$			2.38877e6i			1.04981i	0.851161	+	0.524905i	$0.175899\pi$
$349$			2.38877e6i			1.04981i	−0.851161	+	0.524905i	$0.824101\pi$
$350$	−143486.	+	1.97270e6i	−0.0626095	+	0.860777i
$351$		0			0
$352$	74583.0	−	1.93778e6i	0.0320836	−	0.833582i
$353$			126904.i			0.0542051i	0.999633	+	0.0271025i	$0.00862806\pi$
$353$			126904.i			0.0542051i	−0.999633	+	0.0271025i	$0.991372\pi$
$354$		0			0
$355$	3.12756e6			1.31715
$356$	243358.	+	346028.i	0.101770	+	0.144706i
$357$		0			0
$358$	−2.35027e6	+	743707.i	−0.969194	+	0.306686i
$359$		−	1.17972e6i		−	0.483105i	−0.970388	−	0.241552i	$-0.922343\pi$
$359$		−	1.17972e6i		−	0.483105i	0.970388	−	0.241552i	$-0.0776565\pi$
$360$		0			0
$361$	4.55223e6			1.83847
$362$	3.85720e6	−	1.22055e6i	1.54704	−	0.489536i
$363$		0			0
$364$	−876843.	−	3.68088e6i	−0.346871	−	1.45612i
$365$	4.52998e6			1.77977
$366$		0			0
$367$	−1.38080e6			−0.535136			−0.267568	−	0.963539i	$-0.586220\pi$
$367$	−1.38080e6			−0.535136			−0.267568	+	0.963539i	$0.586220\pi$
$368$	1.36925e6	+	491972.i	0.527065	+	0.189374i
$369$		0			0
$370$	2.21019e6	−	699381.i	0.839316	−	0.265589i
$371$	593731.	+	236506.i	0.223952	+	0.0892088i
$372$		0			0
$373$	3.90118e6			1.45186			0.725929	−	0.687770i	$-0.241410\pi$
$373$	3.90118e6			1.45186			0.725929	+	0.687770i	$0.241410\pi$
$374$	273401.	+	864006.i	0.101070	+	0.319402i
$375$		0			0
$376$	−1.67574e6	−	1.27761e6i	−0.611274	−	0.466045i
$377$			6.21471e6i			2.25200i
$378$		0			0
$379$		−	249613.i		−	0.0892627i	−0.999004	−	0.0446313i	$-0.985789\pi$
$379$		−	249613.i		−	0.0892627i	0.999004	−	0.0446313i	$-0.0142113\pi$
$380$	−3.72377e6	−	5.29479e6i	−1.32289	−	1.88100i
$381$		0			0
$382$	1.89097e6	−	598367.i	0.663018	−	0.209802i
$383$	49441.0			0.0172223			0.00861114	−	0.999963i	$-0.497259\pi$
$383$	49441.0			0.0172223			0.00861114	+	0.999963i	$0.497259\pi$
$384$		0			0
$385$	−3.07647e6	−	1.22548e6i	−1.05779	−	0.421361i
$386$	576713.	+	1.82253e6i	0.197011	+	0.622597i
$387$		0			0
$388$	−1.05215e6	−	1.49604e6i	−0.354811	−	0.504502i
$389$	3.79873e6			1.27281			0.636406	−	0.771355i	$-0.280420\pi$
$389$	3.79873e6			1.27281			0.636406	+	0.771355i	$0.280420\pi$
$390$		0			0
$391$	−679926.			−0.224916
$392$	−488459.	−	3.00292e6i	−0.160551	−	0.987028i
$393$		0			0
$394$	−54299.2	−	171597.i	−0.0176219	−	0.0556889i
$395$	−964589.			−0.311064
$396$		0			0
$397$		−	3.11906e6i		−	0.993225i	−0.867972	−	0.496613i	$-0.834577\pi$
$397$		−	3.11906e6i		−	0.993225i	0.867972	−	0.496613i	$-0.165423\pi$
$398$	53229.8	+	168218.i	0.0168441	+	0.0532309i
$399$		0			0
$400$	−933851.	+	2.59909e6i	−0.291828	+	0.812215i
$401$	108330.			0.0336424			0.0168212	−	0.999859i	$-0.494645\pi$
$401$	108330.			0.0336424			0.0168212	+	0.999859i	$0.494645\pi$
$402$		0			0
$403$		−	468002.i		−	0.143544i
$404$	1.42277e6	+	2.02303e6i	0.433693	+	0.616663i
$405$		0			0
$406$	−362496.	+	4.98372e6i	−0.109141	+	1.50051i
$407$			1.79801e6i			0.538028i
$408$		0			0
$409$			3.40094e6i			1.00529i	0.864494	+	0.502644i	$0.167639\pi$
$409$			3.40094e6i			1.00529i	−0.864494	+	0.502644i	$0.832361\pi$
$410$	−90774.9	−	286868.i	−0.0266690	−	0.0842796i
$411$		0			0
$412$	−4.71420e6	+	3.31545e6i	−1.36825	+	0.962276i
$413$	−1.29836e6	−	517187.i	−0.374559	−	0.149201i
$414$		0			0
$415$			3.78224e6i			1.07802i
$416$	203203.	−	5.27953e6i	0.0575702	−	1.49576i
$417$		0			0
$418$	4.78663e6	−	1.51466e6i	1.33995	−	0.424007i
$419$	−3.64283e6			−1.01369			−0.506843	−	0.862038i	$-0.669188\pi$
$419$	−3.64283e6			−1.01369			−0.506843	+	0.862038i	$0.669188\pi$
$420$		0			0
$421$	1.38888e6			0.381908			0.190954	−	0.981599i	$-0.438842\pi$
$421$	1.38888e6			0.381908			0.190954	+	0.981599i	$0.438842\pi$
$422$	−3.90122e6	+	1.23448e6i	−1.06640	+	0.337445i
$423$		0			0
$424$	709653.	+	541051.i	0.191704	+	0.146158i
$425$		−	1.29062e6i		−	0.346599i
$426$		0			0
$427$	−836707.	+	2.10049e6i	−0.222077	+	0.557508i
$428$	3.95627e6	+	5.62537e6i	1.04394	+	1.48437i
$429$		0			0
$430$	−68705.3	−	217123.i	−0.0179192	−	0.0566286i
$431$			7.38713e6i			1.91550i	0.287600	+	0.957751i	$0.407143\pi$
$431$			7.38713e6i			1.91550i	−0.287600	+	0.957751i	$0.592857\pi$
$432$		0			0
$433$			2.84317e6i			0.728759i	0.931251	+	0.364379i	$0.118719\pi$
$433$			2.84317e6i			0.728759i	−0.931251	+	0.364379i	$0.881281\pi$
$434$	27298.0	−	375302.i	0.00695674	−	0.0956436i
$435$		0			0
$436$	−1.63774e6	+	1.15181e6i	−0.412600	+	0.290177i
$437$			3.76682e6i			0.943565i
$438$		0			0
$439$	−3.25165e6			−0.805272			−0.402636	−	0.915360i	$-0.631906\pi$
$439$	−3.25165e6			−0.805272			−0.402636	+	0.915360i	$0.631906\pi$
$440$	−3.67713e6	−	2.80351e6i	−0.905477	−	0.690351i
$441$		0			0
$442$	744888.	+	2.35400e6i	0.181357	+	0.573128i
$443$		−	5.79357e6i		−	1.40261i	−0.712861	−	0.701305i	$-0.752601\pi$
$443$		−	5.79357e6i		−	1.40261i	0.712861	−	0.701305i	$-0.247399\pi$
$444$		0			0
$445$	1.00870e6			0.241470
$446$	−1.24348e6	−	3.92966e6i	−0.296007	−	0.935444i
$447$		0			0
$448$	470901.	−	4.22192e6i	0.110850	−	0.993837i
$449$	−5.24967e6			−1.22890			−0.614450	−	0.788956i	$-0.710622\pi$
$449$	−5.24967e6			−1.22890			−0.614450	+	0.788956i	$0.710622\pi$
$450$		0			0
$451$	233369.			0.0540259
$452$	3.32173e6	−	2.33614e6i	0.764748	−	0.537839i
$453$		0			0
$454$	−1.49161e6	−	4.71380e6i	−0.339637	−	1.07333i
$455$	−8.38192e6	−	3.33885e6i	−1.89808	−	0.756080i
$456$		0			0
$457$	−4.80494e6			−1.07621			−0.538105	−	0.842878i	$-0.680860\pi$
$457$	−4.80494e6			−1.07621			−0.538105	+	0.842878i	$0.680860\pi$
$458$	−6.24740e6	+	1.97689e6i	−1.39167	+	0.440372i
$459$		0			0
$460$	2.83773e6	−	1.99575e6i	0.625284	−	0.439756i
$461$		−	7.81325e6i		−	1.71230i	−0.516729	−	0.856149i	$-0.672851\pi$
$461$		−	7.81325e6i		−	1.71230i	0.516729	−	0.856149i	$-0.327149\pi$
$462$		0			0
$463$		−	4.81625e6i		−	1.04413i	−0.852904	−	0.522067i	$-0.825161\pi$
$463$		−	4.81625e6i		−	1.04413i	0.852904	−	0.522067i	$-0.174839\pi$
$464$	−2.35923e6	+	6.56619e6i	−0.508716	+	1.41585i
$465$		0			0
$466$	474397.	+	1.49919e6i	0.101199	+	0.319811i
$467$	−1.24144e6			−0.263411			−0.131705	−	0.991289i	$-0.542045\pi$
$467$	−1.24144e6			−0.263411			−0.131705	+	0.991289i	$0.542045\pi$
$468$		0			0
$469$	−2.36188e6	+	5.92933e6i	−0.495822	+	1.24472i
$470$	−4.79044e6	+	1.51586e6i	−1.00030	+	0.316529i
$471$		0			0
$472$	−1.55185e6	−	1.18316e6i	−0.320624	−	0.244449i
$473$	176631.			0.0363007
$474$		0			0
$475$	−7.15011e6			−1.45405
$476$	460037.	+	1.93118e6i	0.0930626	+	0.390665i
$477$		0			0
$478$	478701.	−	151477.i	0.0958284	−	0.0303234i
$479$	7.73156e6			1.53967			0.769836	−	0.638242i	$-0.220338\pi$
$479$	7.73156e6			1.53967			0.769836	+	0.638242i	$0.220338\pi$
$480$		0			0
$481$			4.89871e6i			0.965426i
$482$	4.03669e6	−	1.27735e6i	0.791421	−	0.250433i
$483$		0			0
$484$	−1.28198e6	+	901607.i	−0.248754	+	0.174946i
$485$	−4.36109e6			−0.841861
$486$		0			0
$487$			2.72935e6i			0.521479i	0.965409	+	0.260739i	$0.0839663\pi$
$487$			2.72935e6i			0.521479i	−0.965409	+	0.260739i	$0.916034\pi$
$488$	−1.91412e6	+	2.51060e6i	−0.363848	+	0.477230i
$489$		0			0
$490$	−6.52690e6	−	3.16640e6i	−1.22805	−	0.595766i
$491$		−	4.78104e6i		−	0.894991i	−0.894286	−	0.447496i	$-0.852316\pi$
$491$		−	4.78104e6i		−	0.894991i	0.894286	−	0.447496i	$-0.147684\pi$
$492$		0			0
$493$		−	3.26056e6i		−	0.604191i
$494$	1.30413e7	−	4.12671e6i	2.40438	−	0.760829i
$495$		0			0
$496$	177663.	−	494471.i	0.0324260	−	0.0902478i
$497$	−1.96646e6	+	4.93666e6i	−0.357104	+	0.896484i
$498$		0			0
$499$		−	1.43655e6i		−	0.258267i	−0.991627	−	0.129134i	$-0.958780\pi$
$499$		−	1.43655e6i		−	0.258267i	0.991627	−	0.129134i	$-0.0412196\pi$
$500$	−601126.	−	854735.i	−0.107533	−	0.152900i
$501$		0			0
$502$	−1.31088e6	−	4.14267e6i	−0.232169	−	0.733704i
$503$	−4.30022e6			−0.757828			−0.378914	−	0.925432i	$-0.623702\pi$
$503$	−4.30022e6			−0.757828			−0.378914	+	0.925432i	$0.623702\pi$
$504$		0			0
$505$	5.89731e6			1.02902
$506$	811778.	+	2.56539e6i	0.140949	+	0.445427i
$507$		0			0
$508$	4.64513e6	+	6.60486e6i	0.798617	+	1.13554i
$509$		−	2.38009e6i		−	0.407192i	−0.979055	−	0.203596i	$-0.934737\pi$
$509$		−	2.38009e6i		−	0.407192i	0.979055	−	0.203596i	$-0.0652629\pi$
$510$		0			0
$511$	−2.84824e6	+	7.15029e6i	−0.482530	+	1.21136i
$512$	2.21891e6	−	5.50098e6i	0.374080	−	0.927396i
$513$		0			0
$514$	−6.62455e6	+	2.09624e6i	−1.10598	+	0.349971i
$515$			1.37423e7i			2.28319i
$516$		0			0
$517$		−	3.89705e6i		−	0.641224i
$518$	−285735.	+	3.92839e6i	−0.0467885	+	0.643265i
$519$		0			0
$520$	−1.00184e7	−	7.63822e6i	−1.62477	−	1.23875i
$521$		−	6.45172e6i		−	1.04131i	−0.853766	−	0.520657i	$-0.825687\pi$
$521$		−	6.45172e6i		−	1.04131i	0.853766	−	0.520657i	$-0.174313\pi$
$522$		0			0
$523$	−5.18760e6			−0.829302			−0.414651	−	0.909981i	$-0.636096\pi$
$523$	−5.18760e6			−0.829302			−0.414651	+	0.909981i	$0.636096\pi$
$524$	−8.08922e6	+	5.68907e6i	−1.28700	+	0.905134i
$525$		0			0
$526$	7.62141e6	−	2.41168e6i	1.20108	−	0.380062i
$527$			245538.i			0.0385117i
$528$		0			0
$529$	4.41752e6			0.686340
$530$	2.02869e6	−	641947.i	0.313708	−	0.0992681i
$531$		0			0
$532$	1.06988e7	−	2.54862e6i	1.63892	−	0.390415i
$533$	635819.			0.0969428
$534$		0			0
$535$	1.63985e7			2.47696
$536$	−5.40324e6	+	7.08699e6i	−0.812348	+	1.06549i
$537$		0			0
$538$	−559351.	+	176998.i	−0.0833160	+	0.0263641i
$539$	3.86868e6	−	4.08549e6i	0.573576	−	0.605721i
$540$		0			0
$541$	−1.02776e7			−1.50973			−0.754863	−	0.655882i	$-0.772297\pi$
$541$	−1.02776e7			−1.50973			−0.754863	+	0.655882i	$0.772297\pi$
$542$	−2.23807e6	−	7.07278e6i	−0.327247	−	1.03417i
$543$		0			0
$544$	−106611.	+	2.76991e6i	−0.0154456	+	0.401300i
$545$			4.77417e6i			0.688504i
$546$		0			0
$547$		−	3.13504e6i		−	0.447997i	−0.974590	−	0.223998i	$-0.928089\pi$
$547$		−	3.13504e6i		−	0.447997i	0.974590	−	0.223998i	$-0.0719110\pi$
$548$	487631.	−	342946.i	0.0693650	−	0.0487837i
$549$		0			0
$550$	−4.86957e6	+	1.54090e6i	−0.686410	+	0.217204i
$551$	−1.80636e7			−2.53470
$552$		0			0
$553$	606488.	−	1.52254e6i	0.0843352	−	0.211717i
$554$	−2.56553e6	−	8.10761e6i	−0.355142	−	1.12232i
$555$		0			0
$556$	−904664.	+	636241.i	−0.124108	+	0.0872841i
$557$	1.08742e7			1.48511			0.742554	−	0.669787i	$-0.233614\pi$
$557$	1.08742e7			1.48511			0.742554	+	0.669787i	$0.233614\pi$
$558$		0			0
$559$	481236.			0.0651372
$560$	−7.58848e6	−	6.70962e6i	−1.02255	−	0.904124i
$561$		0			0
$562$	−572179.	−	1.80821e6i	−0.0764172	−	0.241494i
$563$	4.81281e6			0.639923			0.319961	−	0.947431i	$-0.396330\pi$
$563$	4.81281e6			0.639923			0.319961	+	0.947431i	$0.396330\pi$
$564$		0			0
$565$		−	9.68315e6i		−	1.27613i
$566$	−1.59317e6	−	5.03477e6i	−0.209037	−	0.660600i
$567$		0			0
$568$	−4.49865e6	+	5.90051e6i	−0.585074	+	0.767394i
$569$	830234.			0.107503			0.0537514	−	0.998554i	$-0.482882\pi$
$569$	830234.			0.107503			0.0537514	+	0.998554i	$0.482882\pi$
$570$		0			0
$571$		−	4.35081e6i		−	0.558444i	−0.960227	−	0.279222i	$-0.909923\pi$
$571$		−	4.35081e6i		−	0.558444i	0.960227	−	0.279222i	$-0.0900766\pi$
$572$	7.99242e6	−	5.62099e6i	1.02138	−	0.718327i
$573$		0			0
$574$	509878.	+	37086.5i	0.0645931	+	0.00469825i
$575$		−	3.83209e6i		−	0.483355i
$576$		0			0
$577$		−	9.01602e6i		−	1.12739i	−0.825982	−	0.563697i	$-0.809379\pi$
$577$		−	9.01602e6i		−	1.12739i	0.825982	−	0.563697i	$-0.190621\pi$
$578$	2.03235e6	+	6.42265e6i	0.253034	+	0.799641i
$579$		0			0
$580$	9.57053e6	+	1.36082e7i	1.18132	+	1.67970i
$581$	−5.97002e6	−	2.37809e6i	−0.733728	−	0.292272i
$582$		0			0
$583$			1.65035e6i			0.201097i
$584$	−6.51587e6	+	8.54634e6i	−0.790570	+	1.03693i
$585$		0			0
$586$	−3.03688e6	+	960974.i	−0.365329	+	0.115603i
$587$	1.16822e7			1.39936			0.699679	−	0.714457i	$-0.253326\pi$
$587$	1.16822e7			1.39936			0.699679	+	0.714457i	$0.253326\pi$
$588$		0			0
$589$	1.36029e6			0.161564
$590$	−4.43630e6	+	1.40380e6i	−0.524675	+	0.166025i
$591$		0			0
$592$	−1.85965e6	+	5.17576e6i	−0.218085	+	0.606974i
$593$		−	7.34176e6i		−	0.857361i	−0.903456	−	0.428680i	$-0.858979\pi$
$593$		−	7.34176e6i		−	0.857361i	0.903456	−	0.428680i	$-0.141021\pi$
$594$		0			0
$595$	4.39759e6	+	1.75173e6i	0.509240	+	0.202850i
$596$	5.93011e6	−	4.17058e6i	0.683828	−	0.480929i
$597$		0			0
$598$	2.21171e6	+	6.98946e6i	0.252915	+	0.799265i
$599$			1.39805e7i			1.59204i	0.605268	+	0.796022i	$0.293066\pi$
$599$			1.39805e7i			1.59204i	−0.605268	+	0.796022i	$0.706934\pi$
$600$		0			0
$601$		−	9.66115e6i		−	1.09105i	−0.838096	−	0.545523i	$-0.816331\pi$
$601$		−	9.66115e6i		−	1.09105i	0.838096	−	0.545523i	$-0.183669\pi$
$602$	385914.	+	28069.9i	0.0434010	+	0.00315682i
$603$		0			0
$604$	5.37831e6	+	7.64736e6i	0.599865	+	0.852942i
$605$			3.73710e6i			0.415094i
$606$		0			0
$607$	3.62733e6			0.399591			0.199795	−	0.979838i	$-0.435972\pi$
$607$	3.62733e6			0.399591			0.199795	+	0.979838i	$0.435972\pi$
$608$	1.53454e7	+	590629.i	1.68353	+	0.0647972i
$609$		0			0
$610$	2.27107e6	+	7.17706e6i	0.247119	+	0.780948i
$611$		−	1.06176e7i		−	1.15060i
$612$		0			0
$613$	−9.03872e6			−0.971529			−0.485764	−	0.874090i	$-0.661459\pi$
$613$	−9.03872e6			−0.971529			−0.485764	+	0.874090i	$0.661459\pi$
$614$	4.25603e6	+	1.34500e7i	0.455601	+	1.43979i
$615$		0			0
$616$	6.73716e6	−	4.04141e6i	0.715361	−	0.429122i
$617$	1.23771e7			1.30890			0.654448	−	0.756107i	$-0.272901\pi$
$617$	1.23771e7			1.30890			0.654448	+	0.756107i	$0.272901\pi$
$618$		0			0
$619$	−5.58961e6			−0.586348			−0.293174	−	0.956059i	$-0.594711\pi$
$619$	−5.58961e6			−0.586348			−0.293174	+	0.956059i	$0.594711\pi$
$620$	−720714.	−	1.02478e6i	−0.0752981	−	0.107065i
$621$		0			0
$622$	−338864.	−	1.07088e6i	−0.0351195	−	0.110985i
$623$	−634224.	+	1.59217e6i	−0.0654670	+	0.164350i
$624$		0			0
$625$	−1.09199e7			−1.11819
$626$	−1.29779e7	+	4.10667e6i	−1.32364	+	0.418845i
$627$		0			0
$628$	4.49591e6	+	6.39268e6i	0.454902	+	0.646820i
$629$		−	2.57011e6i		−	0.259016i
$630$		0			0
$631$		−	1.92095e7i		−	1.92062i	−0.278931	−	0.960311i	$-0.589980\pi$
$631$		−	1.92095e7i		−	1.92062i	0.278931	−	0.960311i	$-0.410020\pi$
$632$	1.38745e6	−	1.81981e6i	0.138174	−	0.181231i
$633$		0			0
$634$	−1.43655e6	−	4.53979e6i	−0.141937	−	0.448552i
$635$	1.92538e7			1.89488
$636$		0			0
$637$	1.05403e7	−	1.11310e7i	1.02921	−	1.08689i
$638$	−1.23022e7	+	3.89284e6i	−1.19655	+	0.378630i
$639$		0			0
$640$	−7.68542e6	−	1.18734e7i	−0.741682	−	1.14584i
$641$	−1.00426e7			−0.965388			−0.482694	−	0.875789i	$-0.660342\pi$
$641$	−1.00426e7			−0.965388			−0.482694	+	0.875789i	$0.660342\pi$
$642$		0			0
$643$	1.06242e7			1.01337			0.506686	−	0.862131i	$-0.330870\pi$
$643$	1.06242e7			1.01337			0.506686	+	0.862131i	$0.330870\pi$
$644$	1.36593e6	+	5.73402e6i	0.129782	+	0.544809i
$645$		0			0
$646$	−6.84213e6	+	2.16509e6i	−0.645075	+	0.204124i
$647$	1.78505e6			0.167644			0.0838222	−	0.996481i	$-0.473287\pi$
$647$	1.78505e6			0.167644			0.0838222	+	0.996481i	$0.473287\pi$
$648$		0			0
$649$		−	3.60896e6i		−	0.336333i
$650$	−1.32673e7	+	4.19822e6i	−1.23168	+	0.389746i
$651$		0			0
$652$	−4.02975e6	−	5.72986e6i	−0.371244	−	0.527867i
$653$	−2.00432e7			−1.83943			−0.919715	−	0.392586i	$-0.871581\pi$
$653$	−2.00432e7			−1.83943			−0.919715	+	0.392586i	$0.871581\pi$
$654$		0			0
$655$			2.35808e7i			2.14761i
$656$	671779.	+	241370.i	0.0609490	+	0.0218989i
$657$		0			0
$658$	619311.	−	8.51450e6i	0.0557627	−	0.766645i
$659$		−	1.04062e7i		−	0.933419i	−0.884411	−	0.466710i	$-0.845439\pi$
$659$		−	1.04062e7i		−	0.933419i	0.884411	−	0.466710i	$-0.154561\pi$
$660$		0			0
$661$			1.60791e7i			1.43139i	0.698411	+	0.715697i	$0.253891\pi$
$661$			1.60791e7i			1.43139i	−0.698411	+	0.715697i	$0.746109\pi$
$662$	1.05226e7	−	3.32970e6i	0.933204	−	0.295298i
$663$		0			0
$664$	−7.13562e6	−	5.44032e6i	−0.628075	−	0.478855i
$665$	9.70466e6	−	2.43628e7i	0.850994	−	2.13636i
$666$		0			0
$667$		−	9.68118e6i		−	0.842585i
$668$	1.15685e7	−	8.13600e6i	1.00308	−	0.705456i
$669$		0			0
$670$	6.41084e6	+	2.02596e7i	0.551732	+	1.74359i
$671$	−5.83859e6			−0.500612
$672$		0			0
$673$	1.22652e7			1.04384			0.521922	−	0.852993i	$-0.325215\pi$
$673$	1.22652e7			1.04384			0.521922	+	0.852993i	$0.325215\pi$
$674$	−2.16444e6	−	6.84008e6i	−0.183525	−	0.579978i
$675$		0			0
$676$	1.20570e7	−	8.47955e6i	1.01478	−	0.713684i
$677$			3.04232e6i			0.255113i	0.991831	+	0.127557i	$0.0407134\pi$
$677$			3.04232e6i			0.255113i	−0.991831	+	0.127557i	$0.959287\pi$
$678$		0			0
$679$	2.74204e6	−	6.88370e6i	0.228244	−	0.572990i
$680$	5.25619e6	+	4.00740e6i	0.435912	+	0.332346i
$681$		0			0
$682$	926425.	−	293153.i	0.0762692	−	0.0241342i
$683$		−	7.90467e6i		−	0.648384i	−0.945991	−	0.324192i	$-0.894908\pi$
$683$		−	7.90467e6i		−	0.648384i	0.945991	−	0.324192i	$-0.105092\pi$
$684$		0			0
$685$		−	1.42149e6i		−	0.115749i
$686$	9.10177e6	−	8.31142e6i	0.738441	−	0.674318i
$687$		0			0
$688$	508453.	+	182687.i	0.0409525	+	0.0147142i
$689$			4.49642e6i			0.360844i
$690$		0			0
$691$	1.21588e6			0.0968717			0.0484359	−	0.998826i	$-0.484576\pi$
$691$	1.21588e6			0.0968717			0.0484359	+	0.998826i	$0.484576\pi$
$692$	8.23216e6	+	1.17052e7i	0.653505	+	0.929211i
$693$		0			0
$694$	7.81105e6	−	2.47169e6i	0.615617	−	0.194802i
$695$			2.63718e6i			0.207099i
$696$		0			0
$697$	−333583.			−0.0260089
$698$	−1.28833e7	+	4.07672e6i	−1.00090	+	0.316718i
$699$		0			0
$700$	−1.08842e7	+	2.59278e6i	−0.839559	+	0.199996i
$701$	15658.1			0.00120350			0.000601748	−	1.00000i	$-0.499808\pi$
$701$	15658.1			0.00120350			0.000601748		1.00000i	$0.499808\pi$
$702$		0			0
$703$	−1.42386e7			−1.08662
$704$	1.05783e7	−	2.90481e6i	0.804421	−	0.220895i
$705$		0			0
$706$	−684431.	+	216577.i	−0.0516794	+	0.0163532i
$707$	−3.70795e6	+	9.30853e6i	−0.278988	+	0.700378i
$708$		0			0
$709$	8.85478e6			0.661550			0.330775	−	0.943710i	$-0.392690\pi$
$709$	8.85478e6			0.661550			0.330775	+	0.943710i	$0.392690\pi$
$710$	5.33756e6	+	1.68678e7i	0.397372	+	1.25578i
$711$		0			0
$712$	−1.45090e6	+	1.90303e6i	−0.107260	+	0.140685i
$713$			729047.i			0.0537071i
$714$		0			0
$715$		−	2.32986e7i		−	1.70438i
$716$	−8.02204e6	−	1.14064e7i	−0.584793	−	0.831511i
$717$		0			0
$718$	6.36254e6	−	2.01333e6i	0.460595	−	0.145748i
$719$	3.64275e6			0.262789			0.131394	−	0.991330i	$-0.458055\pi$
$719$	3.64275e6			0.262789			0.131394	+	0.991330i	$0.458055\pi$
$720$		0			0
$721$	−2.16914e7	−	8.64053e6i	−1.55400	−	0.619017i
$722$	7.76892e6	+	2.45514e7i	0.554648	+	1.75281i
$723$		0			0
$724$	1.31655e7	+	1.87199e7i	0.933452	+	1.32726i
$725$	1.83766e7			1.29844
$726$		0			0
$727$	1.57332e7			1.10403			0.552015	−	0.833834i	$-0.313859\pi$
$727$	1.57332e7			1.10403			0.552015	+	0.833834i	$0.313859\pi$
$728$	1.83556e7	−	1.10109e7i	1.28363	−	0.770008i
$729$		0			0
$730$	7.73096e6	+	2.44315e7i	0.536941	+	1.69685i
$731$	−252481.			−0.0174757
$732$		0			0
$733$			8.40149e6i			0.577559i	0.957396	+	0.288780i	$0.0932495\pi$
$733$			8.40149e6i			0.577559i	−0.957396	+	0.288780i	$0.906751\pi$
$734$	−2.35649e6	−	7.44701e6i	−0.161445	−	0.510202i
$735$		0			0
$736$	−316547.	+	8.22437e6i	−0.0215399	+	0.559639i
$737$	−1.64813e7			−1.11770
$738$		0			0
$739$			2.67625e7i			1.80267i	0.433125	+	0.901334i	$0.357411\pi$
$739$			2.67625e7i			1.80267i	−0.433125	+	0.901334i	$0.642589\pi$
$740$	7.54391e6	+	1.07266e7i	0.506428	+	0.720084i
$741$		0			0
$742$	−262270.	+	3.60578e6i	−0.0174880	+	0.240431i
$743$		−	4.36420e6i		−	0.290023i	−0.989430	−	0.145011i	$-0.953678\pi$
$743$		−	4.36420e6i		−	0.290023i	0.989430	−	0.145011i	$-0.0463219\pi$
$744$		0			0
$745$		−	1.72868e7i		−	1.14110i
$746$	6.65783e6	+	2.10402e7i	0.438012	+	1.38421i
$747$		0			0
$748$	−4.19323e6	+	2.94906e6i	−0.274028	+	0.192721i
$749$	−1.03106e7	+	2.58840e7i	−0.671551	+	1.68588i
$750$		0			0
$751$			1.22583e7i			0.793106i	0.918012	+	0.396553i	$0.129794\pi$
$751$			1.22583e7i			0.793106i	−0.918012	+	0.396553i	$0.870206\pi$
$752$	4.03066e6	−	1.12181e7i	0.259915	−	0.723394i
$753$		0			0
$754$	−3.35177e7	+	1.06061e7i	−2.14707	+	0.679406i
$755$	2.22928e7			1.42330
$756$		0			0
$757$	−1.29285e7			−0.819991			−0.409995	−	0.912088i	$-0.634470\pi$
$757$	−1.29285e7			−0.819991			−0.409995	+	0.912088i	$0.634470\pi$
$758$	1.34623e6	−	425995.i	0.0851036	−	0.0269297i
$759$		0			0
$760$	2.22012e7	−	2.91195e7i	1.39426	−	1.82873i
$761$			2.91943e7i			1.82741i	0.406375	+	0.913707i	$0.366793\pi$
$761$			2.91943e7i			1.82741i	−0.406375	+	0.913707i	$0.633207\pi$
$762$		0			0
$763$	−7.53572e6	−	3.00177e6i	−0.468612	−	0.186666i
$764$	6.45432e6	+	9.17732e6i	0.400052	+	0.568830i
$765$		0			0
$766$	84377.0	+	266649.i	0.00519580	+	0.0164198i
$767$		−	9.83269e6i		−	0.603509i
$768$		0			0
$769$			1.48516e7i			0.905645i	0.891601	+	0.452823i	$0.149583\pi$
$769$			1.48516e7i			0.905645i	−0.891601	+	0.452823i	$0.850417\pi$
$770$	1.35898e6	−	1.86837e7i	0.0826011	−	1.13563i
$771$		0			0
$772$	−8.84520e6	+	6.22074e6i	−0.534152	+	0.375663i
$773$			6.86539e6i			0.413254i	0.978420	+	0.206627i	$0.0662486\pi$
$773$			6.86539e6i			0.413254i	−0.978420	+	0.206627i	$0.933751\pi$
$774$		0			0
$775$	−1.38386e6			−0.0827634
$776$	6.27293e6	−	8.22769e6i	0.373952	−	0.490483i
$777$		0			0
$778$	6.48298e6	+	2.04876e7i	0.383995	+	1.21351i
$779$			1.84807e6i			0.109112i
$780$		0			0
$781$	−1.37221e7			−0.804994
$782$	−1.16038e6	−	3.66703e6i	−0.0678550	−	0.214436i
$783$		0			0
$784$	1.53620e7	−	7.75925e6i	0.892601	−	0.450847i
$785$	1.86352e7			1.07935
$786$		0			0
$787$	1.71195e7			0.985268			0.492634	−	0.870237i	$-0.336034\pi$
$787$	1.71195e7			0.985268			0.492634	+	0.870237i	$0.336034\pi$
$788$	832802.	−	585701.i	0.0477778	−	0.0336016i
$789$		0			0
$790$	−1.64619e6	−	5.20230e6i	−0.0938450	−	0.296570i
$791$	1.52842e7	+	6.08830e6i	0.868565	+	0.345983i
$792$		0			0
$793$	−1.59074e7			−0.898288
$794$	1.68220e7	−	5.32305e6i	0.946947	−	0.299647i
$795$		0			0
$796$	−816401.	+	574167.i	−0.0456689	+	0.0321185i
$797$		−	9.93315e6i		−	0.553913i	−0.960883	−	0.276956i	$-0.910674\pi$
$797$		−	9.93315e6i		−	0.553913i	0.960883	−	0.276956i	$-0.0893257\pi$
$798$		0			0
$799$			5.57054e6i			0.308696i
$800$	−1.56113e7	−	600863.i	−0.862412	−	0.0331933i
$801$		0			0
$802$	184878.	+	584253.i	0.0101496	+	0.0320749i
$803$	−1.98752e7			−1.08773
$804$		0			0
$805$	1.30572e7	+	5.20120e6i	0.710169	+	0.282888i
$806$	2.52407e6	−	798702.i	0.136856	−	0.0433059i
$807$		0			0
$808$	−8.48261e6	+	1.11259e7i	−0.457089	+	0.599527i
$809$	−7.89984e6			−0.424372			−0.212186	−	0.977229i	$-0.568058\pi$
$809$	−7.89984e6			−0.424372			−0.212186	+	0.977229i	$0.568058\pi$
$810$		0			0
$811$	422897.			0.0225778			0.0112889	−	0.999936i	$-0.496407\pi$
$811$	422897.			0.0225778			0.0112889	+	0.999936i	$0.496407\pi$
$812$	−2.74972e7	+	6.55027e6i	−1.46352	+	0.348633i
$813$		0			0
$814$	−9.69714e6	+	3.06851e6i	−0.512959	+	0.162318i
$815$	−1.67031e7			−0.880850
$816$		0			0
$817$			1.39876e6i			0.0733141i
$818$	−1.83422e7	+	5.80410e6i	−0.958447	+	0.303286i
$819$		0			0
$820$	1.39224e6	−	979149.i	0.0723069	−	0.0508527i
$821$	−4.21022e6			−0.217995			−0.108998	−	0.994042i	$-0.534764\pi$
$821$	−4.21022e6			−0.217995			−0.108998	+	0.994042i	$0.534764\pi$
$822$		0			0
$823$			1.39124e7i			0.715984i	0.933725	+	0.357992i	$0.116539\pi$
$823$			1.39124e7i			0.715984i	−0.933725	+	0.357992i	$0.883461\pi$
$824$	−2.59265e7	−	1.97668e7i	−1.33023	−	1.01419i
$825$		0			0
$826$	573528.	−	7.88505e6i	0.0292485	−	0.402119i
$827$		−	7.78047e6i		−	0.395587i	−0.980244	−	0.197794i	$-0.936622\pi$
$827$		−	7.78047e6i		−	0.395587i	0.980244	−	0.197794i	$-0.0633776\pi$
$828$		0			0
$829$		−	2.12812e6i		−	0.107550i	−0.998553	−	0.0537748i	$-0.982875\pi$
$829$		−	2.12812e6i		−	0.107550i	0.998553	−	0.0537748i	$-0.0171253\pi$
$830$	−2.03986e7	+	6.45484e6i	−1.02779	+	0.325230i
$831$		0			0
$832$	2.88208e7	−	7.91422e6i	1.44344	−	0.396369i
$833$	−5.52999e6	+	5.83991e6i	−0.276129	+	0.291604i
$834$		0			0
$835$		−	3.37232e7i		−	1.67384i
$836$	1.63379e7	+	2.32307e7i	0.808502	+	1.14960i
$837$		0			0
$838$	−6.21692e6	−	1.96468e7i	−0.305820	−	0.966455i
$839$	−1.95328e7			−0.957988			−0.478994	−	0.877818i	$-0.658998\pi$
$839$	−1.95328e7			−0.957988			−0.478994	+	0.877818i	$0.658998\pi$
$840$		0			0
$841$	2.59145e7			1.26344
$842$	2.37029e6	+	7.49060e6i	0.115218	+	0.364113i
$843$		0			0
$844$	−1.33158e7	−	1.89336e7i	−0.643444	−	0.914906i
$845$		−	3.51472e7i		−	1.69336i
$846$		0			0
$847$	−5.89878e6	−	2.34971e6i	−0.282523	−	0.112540i
$848$	−1.70693e6	+	4.75072e6i	−0.0815129	+	0.226866i
$849$		0			0
$850$	6.96069e6	−	2.20260e6i	0.330449	−	0.104566i
$851$		−	7.63113e6i		−	0.361214i
$852$		0			0
$853$		−	1.65240e7i		−	0.777576i	−0.921327	−	0.388788i	$-0.872894\pi$
$853$		−	1.65240e7i		−	0.777576i	0.921327	−	0.388788i	$-0.127106\pi$
$854$	−1.27565e7	−	927856.i	−0.598530	−	0.0435347i
$855$		0			0
$856$	−2.35874e7	+	3.09376e7i	−1.10026	+	1.44312i
$857$		−	4.14446e7i		−	1.92760i	−0.266634	−	0.963798i	$-0.585912\pi$
$857$		−	4.14446e7i		−	1.92760i	0.266634	−	0.963798i	$-0.414088\pi$
$858$		0			0
$859$	1.64726e7			0.761691			0.380845	−	0.924639i	$-0.375633\pi$
$859$	1.64726e7			0.761691			0.380845	+	0.924639i	$0.375633\pi$
$860$	1.05375e6	−	741094.i	0.0485839	−	0.0341686i
$861$		0			0
$862$	−3.98408e7	+	1.26070e7i	−1.82625	+	0.577889i
$863$			2.56771e7i			1.17360i	0.809733	+	0.586798i	$0.199612\pi$
$863$			2.56771e7i			1.17360i	−0.809733	+	0.586798i	$0.800388\pi$
$864$		0			0
$865$	3.41218e7			1.55057
$866$	−1.53340e7	+	4.85222e6i	−0.694803	+	0.219860i
$867$		0			0
$868$	2.07069e6	−	493272.i	0.0932860	−	0.0222222i
$869$	4.23210e6			0.190111
$870$		0			0
$871$	−4.49038e7			−2.00557
$872$	−9.00702e6	−	6.86710e6i	−0.401134	−	0.305832i
$873$		0			0
$874$	−2.03155e7	+	6.42853e6i	−0.899600	+	0.284664i
$875$	1.56662e6	−	3.93288e6i	0.0691740	−	0.173656i
$876$		0			0
$877$	2.56342e7			1.12543			0.562717	−	0.826649i	$-0.309756\pi$
$877$	2.56342e7			1.12543			0.562717	+	0.826649i	$0.309756\pi$
$878$	−5.54933e6	−	1.75370e7i	−0.242943	−	0.767751i
$879$		0			0
$880$	8.84463e6	−	2.46163e7i	0.385011	−	1.07156i
$881$		−	2.41946e7i		−	1.05022i	−0.851036	−	0.525108i	$-0.824025\pi$
$881$		−	2.41946e7i		−	1.05022i	0.851036	−	0.525108i	$-0.175975\pi$
$882$		0			0
$883$			1.42568e6i			0.0615348i	0.999527	+	0.0307674i	$0.00979512\pi$
$883$			1.42568e6i			0.0615348i	−0.999527	+	0.0307674i	$0.990205\pi$
$884$	−1.14246e7	+	8.03478e6i	−0.491710	+	0.345815i
$885$		0			0
$886$	3.12463e7	−	9.88742e6i	1.33726	−	0.423154i
$887$	2.26183e7			0.965274			0.482637	−	0.875821i	$-0.339679\pi$
$887$	2.26183e7			0.965274			0.482637	+	0.875821i	$0.339679\pi$
$888$		0			0
$889$	−1.21059e7	+	3.03909e7i	−0.513737	+	1.28970i
$890$	1.72147e6	+	5.44021e6i	0.0728492	+	0.230219i
$891$		0			0
$892$	1.90716e7	−	1.34129e7i	0.802556	−	0.564429i
$893$	3.08611e7			1.29504
$894$		0			0
$895$	−3.32509e7			−1.38754
$896$	2.35737e7	−	4.66551e6i	0.980973	−	0.194146i
$897$		0			0
$898$	−8.95919e6	−	2.83129e7i	−0.370747	−	1.17164i
$899$	−3.49611e6			−0.144273
$900$		0			0
$901$		−	2.35905e6i		−	0.0968113i
$902$	398272.	+	1.25862e6i	0.0162991	+	0.0515086i
$903$		0			0
$904$	1.82684e7	+	1.39281e7i	0.743496	+	0.566854i
$905$	5.45703e7			2.21480
$906$		0			0
$907$			1.26676e7i			0.511301i	0.966769	+	0.255650i	$0.0822896\pi$
$907$			1.26676e7i			0.511301i	−0.966769	+	0.255650i	$0.917710\pi$
$908$	2.28772e7	−	1.60893e7i	0.920850	−	0.647624i
$909$		0			0
$910$	3.70257e6	−	5.09042e7i	0.148218	−	2.03775i
$911$			347737.i			0.0138821i	0.999976	+	0.00694105i	$0.00220942\pi$
$911$			347737.i			0.0138821i	−0.999976	+	0.00694105i	$0.997791\pi$
$912$		0			0
$913$		−	1.65944e7i		−	0.658848i
$914$	−8.20020e6	−	2.59144e7i	−0.324682	−	1.02607i
$915$		0			0
$916$	−2.13239e7	−	3.03202e7i	−0.839706	−	1.19397i
$917$	−3.72208e7	−	1.48265e7i	−1.46172	−	0.582258i
$918$		0			0
$919$		−	3.37846e6i		−	0.131956i	−0.997821	−	0.0659781i	$-0.978983\pi$
$919$		−	3.37846e6i		−	0.131956i	0.997821	−	0.0659781i	$-0.0210167\pi$
$920$	1.56066e7	+	1.18987e7i	0.607908	+	0.463479i
$921$		0			0
$922$	4.21390e7	−	1.33342e7i	1.63251	−	0.516584i
$923$	−3.73861e7			−1.44446
$924$		0			0
$925$	1.44853e7			0.556637
$926$	2.59754e7	−	8.21950e6i	0.995484	−	0.315005i
$927$		0			0
$928$	−3.94396e7	−	1.51799e6i	−1.50336	−	0.0578626i
$929$			3.30634e7i			1.25692i	0.777841	+	0.628461i	$0.216315\pi$
$929$			3.30634e7i			1.25692i	−0.777841	+	0.628461i	$0.783685\pi$
$930$		0			0
$931$	3.23534e7	+	3.06364e7i	1.22333	+	1.15841i
$932$	−7.27595e6	+	5.11711e6i	−0.274379	+	0.192968i
$933$		0			0
$934$	−2.11866e6	−	6.69543e6i	−0.0794685	−	0.251137i
$935$			1.22237e7i			0.457270i
$936$		0			0
$937$			1.72186e7i			0.640692i	0.947301	+	0.320346i	$0.103799\pi$
$937$			1.72186e7i			0.640692i	−0.947301	+	0.320346i	$0.896201\pi$
$938$	−3.60093e7	−	2.61918e6i	−1.33631	−	0.0971981i
$939$		0			0
$940$	−1.63509e7	−	2.32492e7i	−0.603562	−	0.858198i
$941$			2.81758e7i			1.03729i	0.854989	+	0.518647i	$0.173564\pi$
$941$			2.81758e7i			1.03729i	−0.854989	+	0.518647i	$0.826436\pi$
$942$		0			0
$943$	−990469.			−0.0362712
$944$	3.73269e6	−	1.03888e7i	0.136330	−	0.379433i
$945$		0			0
$946$	301442.	+	952622.i	0.0109516	+	0.0346093i
$947$		−	2.79057e6i		−	0.101115i	−0.998721	−	0.0505577i	$-0.983900\pi$
$947$		−	2.79057e6i		−	0.101115i	0.998721	−	0.0505577i	$-0.0160999\pi$
$948$		0			0
$949$	−5.41503e7			−1.95180
$950$	−1.22025e7	−	3.85625e7i	−0.438672	−	1.38630i
$951$		0			0
$952$	−9.63027e6	+	5.77689e6i	−0.344387	+	0.206586i
$953$	−4.15030e7			−1.48029			−0.740146	−	0.672446i	$-0.765244\pi$
$953$	−4.15030e7			−1.48029			−0.740146	+	0.672446i	$0.765244\pi$
$954$		0			0
$955$	2.67527e7			0.949204
$956$	1.63392e6	+	2.32325e6i	0.0578211	+	0.0822151i
$957$		0			0
$958$	1.31948e7	+	4.16984e7i	0.464504	+	1.46793i
$959$	2.24373e6	+	893766.i	0.0787816	+	0.0313818i
$960$		0			0
$961$	−2.83659e7			−0.990804
$962$	−2.64201e7	+	8.36023e6i	−0.920443	+	0.291260i
$963$		0			0
$964$	1.37782e7	+	1.95910e7i	0.477529	+	0.678993i
$965$			2.57846e7i			0.891337i
$966$		0			0
$967$		−	5.78401e7i		−	1.98913i	−0.104121	−	0.994565i	$-0.533203\pi$
$967$		−	5.78401e7i		−	1.98913i	0.104121	−	0.994565i	$-0.466797\pi$
$968$	−7.05048e6	−	5.37540e6i	−0.241841	−	0.184384i
$969$		0			0
$970$	−7.44271e6	−	2.35206e7i	−0.253981	−	0.802635i
$971$	3.86875e7			1.31681			0.658405	−	0.752664i	$-0.271232\pi$
$971$	3.86875e7			1.31681			0.658405	+	0.752664i	$0.271232\pi$
$972$		0			0
$973$	−4.16262e6	−	1.65813e6i	−0.140956	−	0.0561484i
$974$	−1.47201e7	+	4.65796e6i	−0.497181	+	0.157325i
$975$		0			0
$976$	−1.68070e7	−	6.03876e6i	−0.564763	−	0.202919i
$977$	−3.97537e7			−1.33242			−0.666211	−	0.745764i	$-0.732085\pi$
$977$	−3.97537e7			−1.33242			−0.666211	+	0.745764i	$0.732085\pi$
$978$		0			0
$979$	−4.42565e6			−0.147578
$980$	5.93835e6	−	4.06053e7i	0.197515	−	1.35057i
$981$		0			0
$982$	2.57855e7	−	8.15942e6i	0.853290	−	0.270010i
$983$	−5.72858e7			−1.89088			−0.945439	−	0.325799i	$-0.894367\pi$
$983$	−5.72858e7			−1.89088			−0.945439	+	0.325799i	$0.894367\pi$
$984$		0			0
$985$		−	2.42769e6i		−	0.0797266i
$986$	1.75851e7	−	5.56453e6i	0.576040	−	0.182279i
$987$		0			0
$988$	4.45130e7	+	6.32926e7i	1.45076	+	2.06282i
$989$	−749662.			−0.0243711
$990$		0			0
$991$			4.14746e6i			0.134152i	0.997748	+	0.0670762i	$0.0213671\pi$
$991$			4.14746e6i			0.134152i	−0.997748	+	0.0670762i	$0.978633\pi$
$992$	2.97002e6	+	114313.i	0.0958254	+	0.00368821i
$993$		0			0
$994$	−2.99808e7	−	2.18068e6i	−0.962448	−	0.0700046i
$995$			2.37988e6i			0.0762076i
$996$		0			0
$997$			4.07956e7i			1.29980i	0.760021	+	0.649898i	$0.225189\pi$
$997$			4.07956e7i			1.29980i	−0.760021	+	0.649898i	$0.774811\pi$
$998$	7.74771e6	−	2.45164e6i	0.246233	−	0.0779167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.6.b.d.55.12		16
3.2	odd	2		28.6.d.b.27.6	yes	16
4.3	odd	2	inner	252.6.b.d.55.10		16
7.6	odd	2	inner	252.6.b.d.55.11		16
12.11	even	2		28.6.d.b.27.7	yes	16
21.20	even	2		28.6.d.b.27.5	✓	16
24.5	odd	2		448.6.f.d.447.8		16
24.11	even	2		448.6.f.d.447.10		16
28.27	even	2	inner	252.6.b.d.55.9		16
84.83	odd	2		28.6.d.b.27.8	yes	16
168.83	odd	2		448.6.f.d.447.7		16
168.125	even	2		448.6.f.d.447.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.d.b.27.5	✓	16	21.20	even	2
28.6.d.b.27.6	yes	16	3.2	odd	2
28.6.d.b.27.7	yes	16	12.11	even	2
28.6.d.b.27.8	yes	16	84.83	odd	2
252.6.b.d.55.9		16	28.27	even	2	inner
252.6.b.d.55.10		16	4.3	odd	2	inner
252.6.b.d.55.11		16	7.6	odd	2	inner
252.6.b.d.55.12		16	1.1	even	1	trivial
448.6.f.d.447.7		16	168.83	odd	2
448.6.f.d.447.8		16	24.5	odd	2
448.6.f.d.447.9		16	168.125	even	2
448.6.f.d.447.10		16	24.11	even	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70662 + 5.39328i) q^{2} +(-26.1749 + 18.4085i) q^{4} +76.3023i q^{5} +(-120.438 - 47.9752i) q^{7} +(-143.953 - 109.752i) q^{8} +O(q^{10})\)	\(q+(1.70662 + 5.39328i) q^{2} +(-26.1749 + 18.4085i) q^{4} +76.3023i q^{5} +(-120.438 - 47.9752i) q^{7} +(-143.953 - 109.752i) q^{8} +(-411.519 + 130.219i) q^{10} -334.774i q^{11} -912.099i q^{13} +(53.2015 - 731.433i) q^{14} +(346.251 - 963.684i) q^{16} +478.534i q^{17} +2651.10 q^{19} +(-1404.61 - 1997.20i) q^{20} +(1805.53 - 571.331i) q^{22} +1420.85i q^{23} -2697.03 q^{25} +(4919.20 - 1556.61i) q^{26} +(4035.61 - 961.346i) q^{28} -6813.64 q^{29} +513.105 q^{31} +(5788.33 + 222.787i) q^{32} +(-2580.87 + 816.675i) q^{34} +(3660.62 - 9189.71i) q^{35} -5370.81 q^{37} +(4524.42 + 14298.1i) q^{38} +(8374.34 - 10983.9i) q^{40} +697.095i q^{41} +527.614i q^{43} +(6162.70 + 8762.67i) q^{44} +(-7663.06 + 2424.86i) q^{46} +11640.9 q^{47} +(12203.8 + 11556.1i) q^{49} +(-4602.81 - 14545.9i) q^{50} +(16790.4 + 23874.1i) q^{52} -4929.75 q^{53} +25544.0 q^{55} +(12072.1 + 20124.5i) q^{56} +(-11628.3 - 36747.9i) q^{58} +10780.3 q^{59} -17440.4i q^{61} +(875.675 + 2767.32i) q^{62} +(8676.93 + 31598.3i) q^{64} +69595.2 q^{65} -49231.3i q^{67} +(-8809.11 - 12525.6i) q^{68} +(55810.0 + 4059.39i) q^{70} -40989.1i q^{71} -59368.9i q^{73} +(-9165.93 - 28966.3i) q^{74} +(-69392.3 + 48802.9i) q^{76} +(-16060.8 + 40319.6i) q^{77} +12641.7i q^{79} +(73531.2 + 26419.7i) q^{80} +(-3759.63 + 1189.68i) q^{82} +49569.1 q^{83} -36513.2 q^{85} +(-2845.57 + 900.437i) q^{86} +(-36742.1 + 48191.7i) q^{88} -13219.8i q^{89} +(-43758.1 + 109852. i) q^{91} +(-26155.8 - 37190.7i) q^{92} +(19866.5 + 62782.4i) q^{94} +202285. i q^{95} +57155.4i q^{97} +(-41498.1 + 85540.1i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8	\( 16 q - 8 q^{2} - 48 q^{4} - 608 q^{8} - 1176 q^{14} - 3008 q^{16} + 1552 q^{22} - 9776 q^{25} - 14672 q^{28} - 26592 q^{29} - 11648 q^{32} - 26272 q^{37} + 12256 q^{44} + 20208 q^{46} + 8848 q^{49} - 5992 q^{50} + 41888 q^{53} - 38304 q^{56} - 144400 q^{58} + 45312 q^{64} - 66688 q^{65} + 79296 q^{70} - 348464 q^{74} - 320992 q^{77} + 78080 q^{85} + 78448 q^{86} - 66112 q^{88} - 446944 q^{92} - 224840 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 48 * q^4 - 608 * q^8 - 1176 * q^14 - 3008 * q^16 + 1552 * q^22 - 9776 * q^25 - 14672 * q^28 - 26592 * q^29 - 11648 * q^32 - 26272 * q^37 + 12256 * q^44 + 20208 * q^46 + 8848 * q^49 - 5992 * q^50 + 41888 * q^53 - 38304 * q^56 - 144400 * q^58 + 45312 * q^64 - 66688 * q^65 + 79296 * q^70 - 348464 * q^74 - 320992 * q^77 + 78080 * q^85 + 78448 * q^86 - 66112 * q^88 - 446944 * q^92 - 224840 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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