LMFDB - Embedded newform 21.7.b.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(8,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 $ x^12 + 642x^10 + 155265x^8 + 17813036x^6 + 1003321428x^4 + 26369892864*x^2 + 256461520896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.1
Root			$-15.2632i$ of defining polynomial
Character	$\chi$	$=$	21.8
Dual form			21.7.b.a.8.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.2632i q^{2} +(26.9946 + 0.538759i) q^{3} -168.965 q^{4} -118.492i q^{5} +(8.22319 - 412.025i) q^{6} -129.642 q^{7} +1602.11i q^{8} +(728.419 + 29.0872i) q^{9} +O(q^{10})$	\(q-15.2632i q^{2} +(26.9946 + 0.538759i) q^{3} -168.965 q^{4} -118.492i q^{5} +(8.22319 - 412.025i) q^{6} -129.642 q^{7} +1602.11i q^{8} +(728.419 + 29.0872i) q^{9} -1808.56 q^{10} -356.410i q^{11} +(-4561.16 - 91.0317i) q^{12} +2041.21 q^{13} +1978.75i q^{14} +(63.8385 - 3198.64i) q^{15} +13639.5 q^{16} -4813.47i q^{17} +(443.964 - 11118.0i) q^{18} -1518.92 q^{19} +20021.0i q^{20} +(-3499.63 - 69.8457i) q^{21} -5439.96 q^{22} -13874.1i q^{23} +(-863.151 + 43248.3i) q^{24} +1584.72 q^{25} -31155.4i q^{26} +(19647.7 + 1177.64i) q^{27} +21905.0 q^{28} +42346.6i q^{29} +(-48821.5 - 974.380i) q^{30} +15583.3 q^{31} -105648. i q^{32} +(192.019 - 9621.15i) q^{33} -73469.0 q^{34} +15361.5i q^{35} +(-123078. - 4914.73i) q^{36} -7620.26 q^{37} +23183.6i q^{38} +(55101.8 + 1099.72i) q^{39} +189837. q^{40} +55431.0i q^{41} +(-1066.07 + 53415.6i) q^{42} +60273.7 q^{43} +60221.0i q^{44} +(3446.59 - 86311.7i) q^{45} -211763. q^{46} +129201. i q^{47} +(368194. + 7348.43i) q^{48} +16807.0 q^{49} -24187.8i q^{50} +(2593.30 - 129938. i) q^{51} -344894. q^{52} +60972.9i q^{53} +(17974.6 - 299887. i) q^{54} -42231.6 q^{55} -207700. i q^{56} +(-41002.7 - 818.332i) q^{57} +646346. q^{58} +40355.4i q^{59} +(-10786.5 + 540459. i) q^{60} -118768. q^{61} -237852. i q^{62} +(-94433.6 - 3770.92i) q^{63} -739597. q^{64} -241867. i q^{65} +(-146850. - 2930.83i) q^{66} -133205. q^{67} +813311. i q^{68} +(7474.81 - 374527. i) q^{69} +234465. q^{70} -195618. i q^{71} +(-46600.9 + 1.16701e6i) q^{72} +144743. q^{73} +116310. i q^{74} +(42778.8 + 853.780i) q^{75} +256645. q^{76} +46205.6i q^{77} +(16785.3 - 841029. i) q^{78} -894049. q^{79} -1.61617e6i q^{80} +(529749. + 42375.4i) q^{81} +846055. q^{82} -287164. i q^{83} +(591317. + 11801.5i) q^{84} -570357. q^{85} -919971. i q^{86} +(-22814.7 + 1.14313e6i) q^{87} +571008. q^{88} +799391. i q^{89} +(-1.31739e6 - 52606.1i) q^{90} -264626. q^{91} +2.34425e6i q^{92} +(420666. + 8395.67i) q^{93} +1.97203e6 q^{94} +179979. i q^{95} +(56918.9 - 2.85193e6i) q^{96} +1.17586e6 q^{97} -256529. i q^{98} +(10367.0 - 259616. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	15.2632i		−	1.90790i	−0.299965	−	0.953950i	$-0.596975\pi$
$2$		−	15.2632i		−	1.90790i	0.299965	−	0.953950i	$-0.403025\pi$
$3$	26.9946	+	0.538759i	0.999801	+	0.0199540i
$3$	26.9946	+	0.538759i	0.999801	+	0.0199540i
$4$	−168.965			−2.64009
$5$		−	118.492i		−	0.947934i	−0.880543	−	0.473967i	$-0.842822\pi$
$5$		−	118.492i		−	0.947934i	0.880543	−	0.473967i	$-0.157178\pi$
$6$	8.22319	−	412.025i	0.0380703	−	1.90752i
$7$	−129.642			−0.377964
$7$	−129.642			−0.377964
$8$			1602.11i			3.12912i
$9$	728.419	+	29.0872i	0.999204	+	0.0399002i
$10$	−1808.56			−1.80856
$11$		−	356.410i		−	0.267776i	−0.990996	−	0.133888i	$-0.957254\pi$
$11$		−	356.410i		−	0.267776i	0.990996	−	0.133888i	$-0.0427462\pi$
$12$	−4561.16	−	91.0317i	−2.63956	−	0.0526804i
$13$	2041.21			0.929091			0.464545	−	0.885549i	$-0.346218\pi$
$13$	2041.21			0.929091			0.464545	+	0.885549i	$0.346218\pi$
$14$			1978.75i			0.721119i
$15$	63.8385	−	3198.64i	0.0189151	−	0.947745i
$16$	13639.5			3.32996
$17$		−	4813.47i		−	0.979742i	−0.871795	−	0.489871i	$-0.837044\pi$
$17$		−	4813.47i		−	0.979742i	0.871795	−	0.489871i	$-0.162956\pi$
$18$	443.964	−	11118.0i	0.0761255	−	1.90638i
$19$	−1518.92			−0.221449			−0.110725	−	0.993851i	$-0.535317\pi$
$19$	−1518.92			−0.221449			−0.110725	+	0.993851i	$0.535317\pi$
$20$			20021.0i			2.50263i
$21$	−3499.63	−	69.8457i	−0.377889	−	0.00754192i
$22$	−5439.96			−0.510890
$23$		−	13874.1i		−	1.14031i	−0.821538	−	0.570154i	$-0.806884\pi$
$23$		−	13874.1i		−	1.14031i	0.821538	−	0.570154i	$-0.193116\pi$
$24$	−863.151	+	43248.3i	−0.0624386	+	3.12850i
$25$	1584.72			0.101422
$26$		−	31155.4i		−	1.77261i
$27$	19647.7	+	1177.64i	0.998209	+	0.0598304i
$28$	21905.0			0.997858
$29$			42346.6i			1.73630i	0.496301	+	0.868151i	$0.334691\pi$
$29$			42346.6i			1.73630i	−0.496301	+	0.868151i	$0.665309\pi$
$30$	−48821.5	−	974.380i	−1.80820	−	0.0360882i
$31$	15583.3			0.523089			0.261544	−	0.965191i	$-0.415768\pi$
$31$	15583.3			0.523089			0.261544	+	0.965191i	$0.415768\pi$
$32$		−	105648.i		−	3.22412i
$33$	192.019	−	9621.15i	0.00534322	−	0.267723i
$34$	−73469.0			−1.86925
$35$			15361.5i			0.358285i
$36$	−123078.	−	4914.73i	−2.63798	−	0.105340i
$37$	−7620.26			−0.150440			−0.0752202	−	0.997167i	$-0.523966\pi$
$37$	−7620.26			−0.150440			−0.0752202	+	0.997167i	$0.523966\pi$
$38$			23183.6i			0.422503i
$39$	55101.8	+	1099.72i	0.928906	+	0.0185391i
$40$	189837.			2.96620
$41$			55431.0i			0.804269i	0.915581	+	0.402134i	$0.131732\pi$
$41$			55431.0i			0.804269i	−0.915581	+	0.402134i	$0.868268\pi$
$42$	−1066.07	+	53415.6i	−0.0143892	+	0.720975i
$43$	60273.7			0.758094			0.379047	−	0.925378i	$-0.376252\pi$
$43$	60273.7			0.758094			0.379047	+	0.925378i	$0.376252\pi$
$44$			60221.0i			0.706951i
$45$	3446.59	−	86311.7i	0.0378227	−	0.947179i
$46$	−211763.			−2.17559
$47$			129201.i			1.24444i	0.782843	+	0.622219i	$0.213769\pi$
$47$			129201.i			1.24444i	−0.782843	+	0.622219i	$0.786231\pi$
$48$	368194.	+	7348.43i	3.32930	+	0.0664463i
$49$	16807.0			0.142857
$50$		−	24187.8i		−	0.193503i
$51$	2593.30	−	129938.i	0.0195498	−	0.979547i
$52$	−344894.			−2.45288
$53$			60972.9i			0.409552i	0.978809	+	0.204776i	$0.0656466\pi$
$53$			60972.9i			0.409552i	−0.978809	+	0.204776i	$0.934353\pi$
$54$	17974.6	−	299887.i	0.114150	−	1.90448i
$55$	−42231.6			−0.253834
$56$		−	207700.i		−	1.18270i
$57$	−41002.7	−	818.332i	−0.221405	−	0.00441881i
$58$	646346.			3.31269
$59$			40355.4i			0.196492i	0.995162	+	0.0982462i	$0.0313233\pi$
$59$			40355.4i			0.196492i	−0.995162	+	0.0982462i	$0.968677\pi$
$60$	−10786.5	+	540459.i	−0.0499375	+	2.50213i
$61$	−118768.			−0.523252			−0.261626	−	0.965169i	$-0.584259\pi$
$61$	−118768.			−0.523252			−0.261626	+	0.965169i	$0.584259\pi$
$62$		−	237852.i		−	0.998001i
$63$	−94433.6	−	3770.92i	−0.377663	−	0.0150808i
$64$	−739597.			−2.82134
$65$		−	241867.i		−	0.880716i
$66$	−146850.	−	2930.83i	−0.510788	−	0.0101943i
$67$	−133205.			−0.442890			−0.221445	−	0.975173i	$-0.571077\pi$
$67$	−133205.			−0.442890			−0.221445	+	0.975173i	$0.571077\pi$
$68$			813311.i			2.58660i
$69$	7474.81	−	374527.i	0.0227537	−	1.14008i
$70$	234465.			0.683573
$71$		−	195618.i		−	0.546556i	−0.961935	−	0.273278i	$-0.911892\pi$
$71$		−	195618.i		−	0.546556i	0.961935	−	0.273278i	$-0.0881079\pi$
$72$	−46600.9	+	1.16701e6i	−0.124852	+	3.12663i
$73$	144743.			0.372075			0.186037	−	0.982543i	$-0.440435\pi$
$73$	144743.			0.372075			0.186037	+	0.982543i	$0.440435\pi$
$74$			116310.i			0.287025i
$75$	42778.8	+	853.780i	0.101402	+	0.00202378i
$76$	256645.			0.584644
$77$			46205.6i			0.101210i
$78$	16785.3	−	841029.i	0.0353708	−	1.77226i
$79$	−894049.			−1.81334			−0.906672	−	0.421837i	$-0.861385\pi$
$79$	−894049.			−1.81334			−0.906672	+	0.421837i	$0.861385\pi$
$80$		−	1.61617e6i		−	3.15659i
$81$	529749.	+	42375.4i	0.996816	+	0.0797368i
$82$	846055.			1.53446
$83$		−	287164.i		−	0.502223i	−0.967958	−	0.251111i	$-0.919204\pi$
$83$		−	287164.i		−	0.502223i	0.967958	−	0.251111i	$-0.0807960\pi$
$84$	591317.	+	11801.5i	0.997660	+	0.0199113i
$85$	−570357.			−0.928731
$86$		−	919971.i		−	1.44637i
$87$	−22814.7	+	1.14313e6i	−0.0346462	+	1.73596i
$88$	571008.			0.837903
$89$			799391.i			1.13394i	0.823739	+	0.566969i	$0.191884\pi$
$89$			799391.i			1.13394i	−0.823739	+	0.566969i	$0.808116\pi$
$90$	−1.31739e6	−	52606.1i	−1.80712	−	0.0721620i
$91$	−264626.			−0.351163
$92$			2.34425e6i			3.01051i
$93$	420666.	+	8395.67i	0.522985	+	0.0104377i
$94$	1.97203e6			2.37426
$95$			179979.i			0.209919i
$96$	56918.9	−	2.85193e6i	0.0643343	−	3.22348i
$97$	1.17586e6			1.28837			0.644184	−	0.764870i	$-0.277197\pi$
$97$	1.17586e6			1.28837			0.644184	+	0.764870i	$0.277197\pi$
$98$		−	256529.i		−	0.272557i
$99$	10367.0	−	259616.i	0.0106843	−	0.267563i
$100$	−267762.			−0.267762
$101$			1.40394e6i			1.36265i	0.731981	+	0.681325i	$0.238596\pi$
$101$			1.40394e6i			1.36265i	−0.731981	+	0.681325i	$0.761404\pi$
$102$	−1.98327e6	−	39582.1i	−1.86888	−	0.0372991i
$103$	−1.19969e6			−1.09788			−0.548942	−	0.835861i	$-0.684969\pi$
$103$	−1.19969e6			−1.09788			−0.548942	+	0.835861i	$0.684969\pi$
$104$			3.27024e6i			2.90724i
$105$	−8276.14	+	414677.i	−0.00714924	+	0.358214i
$106$	930642.			0.781385
$107$		−	1.82547e6i		−	1.49013i	−0.666994	−	0.745063i	$-0.732419\pi$
$107$		−	1.82547e6i		−	1.49013i	0.666994	−	0.745063i	$-0.267581\pi$
$108$	−3.31979e6	−	198981.i	−2.63536	−	0.157957i
$109$	698011.			0.538993			0.269496	−	0.963001i	$-0.413143\pi$
$109$	698011.			0.538993			0.269496	+	0.963001i	$0.413143\pi$
$110$			644590.i			0.484290i
$111$	−205706.	−	4105.49i	−0.150411	−	0.00300190i
$112$	−1.76825e6			−1.25861
$113$		−	1.85528e6i		−	1.28580i	−0.765948	−	0.642902i	$-0.777730\pi$
$113$		−	1.85528e6i		−	1.28580i	0.765948	−	0.642902i	$-0.222270\pi$
$114$	−12490.4	+	625832.i	−0.00843064	+	0.422419i
$115$	−1.64397e6			−1.08094
$116$		−	7.15512e6i		−	4.58398i
$117$	1.48686e6	+	59373.2i	0.928351	+	0.0370709i
$118$	615953.			0.374888
$119$			624027.i			0.370308i
$120$	5.12457e6	+	102276.i	2.96561	+	0.0591877i
$121$	1.64453e6			0.928296
$122$			1.81278e6i			0.998313i
$123$	−29864.0	+	1.49634e6i	−0.0160484	+	0.804108i
$124$	−2.63305e6			−1.38100
$125$		−	2.03921e6i		−	1.04407i
$126$	−57556.3	+	1.44136e6i	−0.0287727	+	0.720544i
$127$	−327129.			−0.159701			−0.0798504	−	0.996807i	$-0.525444\pi$
$127$	−327129.			−0.159701			−0.0798504	+	0.996807i	$0.525444\pi$
$128$			4.52715e6i			2.15871i
$129$	1.62707e6	+	32473.0i	0.757943	+	0.0151270i
$130$	−3.69166e6			−1.68032
$131$			70499.3i			0.0313596i	0.999877	+	0.0156798i	$0.00499124\pi$
$131$			70499.3i			0.0313596i	−0.999877	+	0.0156798i	$0.995009\pi$
$132$	−32444.6	+	1.62564e6i	−0.0141065	+	0.706811i
$133$	196915.			0.0836999
$134$			2.03313e6i			0.844990i
$135$	139541.	−	2.32809e6i	0.0567152	−	0.946235i
$136$	7.71171e6			3.06573
$137$			645599.i			0.251074i	0.992089	+	0.125537i	$0.0400653\pi$
$137$			645599.i			0.251074i	−0.992089	+	0.125537i	$0.959935\pi$
$138$	−5.71648e6	−	114090.i	−2.17516	−	0.0434119i
$139$	−3.56997e6			−1.32929			−0.664645	−	0.747159i	$-0.731417\pi$
$139$	−3.56997e6			−1.32929			−0.664645	+	0.747159i	$0.731417\pi$
$140$		−	2.59556e6i		−	0.945904i
$141$	−69608.4	+	3.48774e6i	−0.0248316	+	1.24419i
$142$	−2.98576e6			−1.04277
$143$		−	727508.i		−	0.248788i
$144$	9.93530e6	+	396736.i	3.32731	+	0.132866i
$145$	5.01773e6			1.64590
$146$		−	2.20925e6i		−	0.709882i
$147$	453699.	+	9054.93i	0.142829	+	0.00285058i
$148$	1.28756e6			0.397176
$149$		−	4.81531e6i		−	1.45568i	−0.685748	−	0.727839i	$-0.740525\pi$
$149$		−	4.81531e6i		−	1.45568i	0.685748	−	0.727839i	$-0.259475\pi$
$150$	13031.4	−	652942.i	0.00386116	−	0.193464i
$151$	3.45321e6			1.00298			0.501490	−	0.865164i	$-0.332785\pi$
$151$	3.45321e6			1.00298			0.501490	+	0.865164i	$0.332785\pi$
$152$		−	2.43347e6i		−	0.692941i
$153$	140011.	−	3.50623e6i	0.0390919	−	0.978962i
$154$	705246.			0.193098
$155$		−	1.84650e6i		−	0.495853i
$156$	−9.31029e6	−	185815.i	−2.45239	−	0.0489449i
$157$	−1.96644e6			−0.508137			−0.254068	−	0.967186i	$-0.581769\pi$
$157$	−1.96644e6			−0.508137			−0.254068	+	0.967186i	$0.581769\pi$
$158$			1.36461e7i			3.45968i
$159$	−32849.7	+	1.64594e6i	−0.00817222	+	0.409470i
$160$	−1.25184e7			−3.05625
$161$			1.79867e6i			0.430996i
$162$	646784.	−	8.08567e6i	0.152130	−	1.90183i
$163$	−281420.			−0.0649819			−0.0324910	−	0.999472i	$-0.510344\pi$
$163$	−281420.			−0.0649819			−0.0324910	+	0.999472i	$0.510344\pi$
$164$		−	9.36592e6i		−	2.12334i
$165$	−1.14003e6	−	22752.7i	−0.253783	−	0.00506501i
$166$	−4.38305e6			−0.958191
$167$			8.16717e6i			1.75357i	0.480885	+	0.876783i	$0.340315\pi$
$167$			8.16717e6i			1.75357i	−0.480885	+	0.876783i	$0.659685\pi$
$168$	111900.	−	5.60679e6i	0.0235996	−	1.18246i
$169$	−660262.			−0.136791
$170$			8.70547e6i			1.77193i
$171$	−1.10641e6	−	44181.1i	−0.221273	−	0.00883585i
$172$	−1.01842e7			−2.00143
$173$			5.14129e6i			0.992965i	0.868047	+	0.496482i	$0.165375\pi$
$173$			5.14129e6i			0.992965i	−0.868047	+	0.496482i	$0.834625\pi$
$174$	1.74479e7	+	348225.i	3.31203	+	0.0661016i
$175$	−205445.			−0.0383338
$176$		−	4.86126e6i		−	0.891685i
$177$	−21741.8	+	1.08938e6i	−0.00392082	+	0.196453i
$178$	1.22013e7			2.16344
$179$			5.56327e6i			0.969999i	0.874514	+	0.485000i	$0.161180\pi$
$179$			5.56327e6i			0.969999i	−0.874514	+	0.485000i	$0.838820\pi$
$180$	−582355.	+	1.45837e7i	−0.0998551	+	2.50063i
$181$	−6.72940e6			−1.13486			−0.567428	−	0.823423i	$-0.692062\pi$
$181$	−6.72940e6			−1.13486			−0.567428	+	0.823423i	$0.692062\pi$
$182$			4.03905e6i			0.669985i
$183$	−3.20610e6	−	63987.5i	−0.523148	−	0.0104410i
$184$	2.22278e7			3.56816
$185$			902938.i			0.142608i
$186$	128145.	−	6.42072e6i	0.0199142	−	0.997803i
$187$	−1.71557e6			−0.262351
$188$		−	2.18305e7i		−	3.28542i
$189$	−2.54717e6	−	152672.i	−0.377287	−	0.0226138i
$190$	2.74706e6			0.400505
$191$			599009.i			0.0859673i	0.999076	+	0.0429836i	$0.0136863\pi$
$191$			599009.i			0.0859673i	−0.999076	+	0.0429836i	$0.986314\pi$
$192$	−1.99651e7	−	398465.i	−2.82078	−	0.0562971i
$193$	5.95379e6			0.828174			0.414087	−	0.910237i	$-0.364101\pi$
$193$	5.95379e6			0.828174			0.414087	+	0.910237i	$0.364101\pi$
$194$		−	1.79474e7i		−	2.45808i
$195$	130308.	−	6.52910e6i	0.0175739	−	0.880541i
$196$	−2.83980e6			−0.377155
$197$			2.64933e6i			0.346527i	0.984875	+	0.173264i	$0.0554313\pi$
$197$			2.64933e6i			0.346527i	−0.984875	+	0.173264i	$0.944569\pi$
$198$	−3.96257e6	−	158233.i	−0.510483	−	0.0203846i
$199$	−1.29359e7			−1.64148			−0.820741	−	0.571300i	$-0.806439\pi$
$199$	−1.29359e7			−1.64148			−0.820741	+	0.571300i	$0.806439\pi$
$200$			2.53889e6i			0.317361i
$201$	−3.59582e6	−	71765.4i	−0.442802	−	0.00883745i
$202$	2.14286e7			2.59980
$203$		−	5.48990e6i		−	0.656260i
$204$	−438179.	+	2.19550e7i	−0.0516132	+	2.58609i
$205$	6.56811e6			0.762393
$206$			1.83111e7i			2.09465i
$207$	403559.	−	1.01062e7i	0.0454984	−	1.13940i
$208$	2.78412e7			3.09384
$209$			541358.i			0.0592988i
$210$	6.32931e6	+	126320.i	0.683437	+	0.0136400i
$211$	3.92825e6			0.418169			0.209084	−	0.977898i	$-0.432952\pi$
$211$	3.92825e6			0.418169			0.209084	+	0.977898i	$0.432952\pi$
$212$		−	1.03023e7i		−	1.08125i
$213$	105391.	−	5.28065e6i	0.0109060	−	0.546447i
$214$	−2.78625e7			−2.84301
$215$		−	7.14194e6i		−	0.718622i
$216$	−1.88671e6	+	3.14778e7i	−0.187216	+	3.12351i
$217$	−2.02025e6			−0.197709
$218$		−	1.06539e7i		−	1.02834i
$219$	3.90729e6	+	77981.9i	0.372001	+	0.00742440i
$220$	7.13568e6			0.670143
$221$		−	9.82532e6i		−	0.910269i
$222$	−62662.9	+	3.13973e6i	−0.00572732	+	0.286968i
$223$	−4.07259e6			−0.367245			−0.183623	−	0.982997i	$-0.558782\pi$
$223$	−4.07259e6			−0.367245			−0.183623	+	0.982997i	$0.558782\pi$
$224$			1.36964e7i			1.21860i
$225$	1.15434e6	+	46095.0i	0.101341	+	0.00404675i
$226$	−2.83176e7			−2.45319
$227$			1.04706e7i			0.895147i	0.894247	+	0.447573i	$0.147712\pi$
$227$			1.04706e7i			0.895147i	−0.894247	+	0.447573i	$0.852288\pi$
$228$	6.92803e6	+	138270.i	0.584528	+	0.0116660i
$229$	7.40529e6			0.616646			0.308323	−	0.951282i	$-0.400232\pi$
$229$	7.40529e6			0.616646			0.308323	+	0.951282i	$0.400232\pi$
$230$			2.50922e7i			2.06232i
$231$	−24893.7	+	1.24730e6i	−0.00201955	+	0.101190i
$232$	−6.78440e7			−5.43309
$233$			1.82011e7i			1.43889i	0.694547	+	0.719447i	$0.255605\pi$
$233$			1.82011e7i			1.43889i	−0.694547	+	0.719447i	$0.744395\pi$
$234$	906225.	−	2.26942e7i	0.0707275	−	1.77120i
$235$	1.53093e7			1.17964
$236$		−	6.81867e6i		−	0.518757i
$237$	−2.41345e7	−	481677.i	−1.81298	−	0.0361835i
$238$	9.52466e6			0.706510
$239$		−	1.67405e7i		−	1.22624i	−0.789991	−	0.613118i	$-0.789915\pi$
$239$		−	1.67405e7i		−	1.22624i	0.789991	−	0.613118i	$-0.210085\pi$
$240$	870728.	−	4.36279e7i	0.0629867	−	3.15596i
$241$	2.01770e7			1.44147			0.720735	−	0.693210i	$-0.243804\pi$
$241$	2.01770e7			1.44147			0.720735	+	0.693210i	$0.243804\pi$
$242$		−	2.51008e7i		−	1.77110i
$243$	1.42775e7	+	1.42931e6i	0.995026	+	0.0996114i
$244$	2.00677e7			1.38143
$245$		−	1.99149e6i		−	0.135419i
$246$	2.28389e7	+	455820.i	1.53416	+	0.0306188i
$247$	−3.10044e6			−0.205746
$248$			2.49662e7i			1.63681i
$249$	154713.	−	7.75190e6i	0.0100214	−	0.502123i
$250$	−3.11249e7			−1.99199
$251$			1.62774e7i			1.02935i	0.857384	+	0.514677i	$0.172088\pi$
$251$			1.62774e7i			1.02935i	−0.857384	+	0.514677i	$0.827912\pi$
$252$	1.59560e7	+	637155.i	0.997064	+	0.0398147i
$253$	−4.94487e6			−0.305347
$254$			4.99303e6i			0.304693i
$255$	−1.53966e7	−	307285.i	−0.928546	−	0.0185319i
$256$	2.17646e7			1.29727
$257$		−	2.44722e7i		−	1.44170i	−0.693093	−	0.720848i	$-0.743753\pi$
$257$		−	2.44722e7i		−	1.44170i	0.693093	−	0.720848i	$-0.256247\pi$
$258$	495643.	−	2.48343e7i	0.0288609	−	1.44608i
$259$	987904.			0.0568612
$260$			4.08671e7i			2.32517i
$261$	−1.23175e6	+	3.08461e7i	−0.0692787	+	1.73492i
$262$	1.07604e6			0.0598310
$263$			1.09689e7i			0.602972i	0.953471	+	0.301486i	$0.0974827\pi$
$263$			1.09689e7i			0.602972i	−0.953471	+	0.301486i	$0.902517\pi$
$264$	1.54141e7	+	307636.i	0.837736	+	0.0167196i
$265$	7.22478e6			0.388228
$266$		−	3.00556e6i		−	0.159691i
$267$	−430679.	+	2.15793e7i	−0.0226267	+	1.13371i
$268$	2.25070e7			1.16927
$269$		−	2.20170e7i		−	1.13110i	−0.824714	−	0.565549i	$-0.808664\pi$
$269$		−	2.20170e7i		−	1.13110i	0.824714	−	0.565549i	$-0.191336\pi$
$270$	−3.55342e7	−	2.12984e6i	−1.80532	−	0.108207i
$271$	243322.			0.0122257			0.00611286	−	0.999981i	$-0.498054\pi$
$271$	243322.			0.0122257			0.00611286	+	0.999981i	$0.498054\pi$
$272$		−	6.56535e7i		−	3.26251i
$273$	−7.14349e6	−	142570.i	−0.351093	−	0.00700713i
$274$	9.85392e6			0.479024
$275$		−	564808.i		−	0.0271583i
$276$	−1.26298e6	+	6.32820e7i	−0.0600718	+	3.00991i
$277$	1.63929e7			0.771289			0.385644	−	0.922648i	$-0.373979\pi$
$277$	1.63929e7			0.771289			0.385644	+	0.922648i	$0.373979\pi$
$278$			5.44891e7i			2.53615i
$279$	1.13512e7	+	453276.i	0.522672	+	0.0208713i
$280$	−2.46108e7			−1.12112
$281$			1.20421e7i			0.542731i	0.962476	+	0.271366i	$0.0874752\pi$
$281$			1.20421e7i			0.542731i	−0.962476	+	0.271366i	$0.912525\pi$
$282$	5.32341e7	+	1.06245e6i	2.37379	+	0.0473762i
$283$	−1.54181e7			−0.680257			−0.340128	−	0.940379i	$-0.610471\pi$
$283$	−1.54181e7			−0.680257			−0.340128	+	0.940379i	$0.610471\pi$
$284$			3.30528e7i			1.44295i
$285$	−96965.5	+	4.85847e6i	−0.00418873	+	0.209877i
$286$	−1.11041e7			−0.474663
$287$		−	7.18617e6i		−	0.303985i
$288$	3.07301e6	−	7.69561e7i	0.128643	−	3.22155i
$289$	968044.			0.0401053
$290$		−	7.65866e7i		−	3.14021i
$291$	3.17419e7	+	633505.i	1.28811	+	0.0257082i
$292$	−2.44566e7			−0.982309
$293$			3.13748e7i			1.24732i	0.781696	+	0.623659i	$0.214355\pi$
$293$			3.13748e7i			1.24732i	−0.781696	+	0.623659i	$0.785645\pi$
$294$	138207.	−	6.92490e6i	0.00543862	−	0.272503i
$295$	4.78178e6			0.186262
$296$		−	1.22085e7i		−	0.470746i
$297$	419723.	−	7.00265e6i	0.0160211	−	0.267296i
$298$	−7.34971e7			−2.77729
$299$		−	2.83200e7i		−	1.05945i
$300$	−7.22814e6	−	144259.i	−0.267709	−	0.00534294i
$301$	−7.81400e6			−0.286532
$302$		−	5.27071e7i		−	1.91359i
$303$	−756386.	+	3.78988e7i	−0.0271904	+	1.36238i
$304$	−2.07173e7			−0.737418
$305$			1.40730e7i			0.496008i
$306$	−5.35163e7	−	2.13701e6i	−1.86776	−	0.0745834i
$307$	3.26210e7			1.12741			0.563705	−	0.825976i	$-0.309375\pi$
$307$	3.26210e7			1.12741			0.563705	+	0.825976i	$0.309375\pi$
$308$		−	7.80715e6i		−	0.267203i
$309$	−3.23851e7	−	646343.i	−1.09766	−	0.0219072i
$310$	−2.81835e7			−0.946039
$311$		−	3.80992e7i		−	1.26659i	−0.773912	−	0.633293i	$-0.781703\pi$
$311$		−	3.80992e7i		−	1.26659i	0.773912	−	0.633293i	$-0.218297\pi$
$312$	−1.76187e6	+	8.82790e7i	−0.0580111	+	2.90666i
$313$	−1.64482e7			−0.536395			−0.268197	−	0.963364i	$-0.586428\pi$
$313$	−1.64482e7			−0.536395			−0.268197	+	0.963364i	$0.586428\pi$
$314$			3.00141e7i			0.969475i
$315$	−446823.	+	1.11896e7i	−0.0142956	+	0.358000i
$316$	1.51063e8			4.78738
$317$		−	3.18719e7i		−	1.00053i	−0.865872	−	0.500266i	$-0.833236\pi$
$317$		−	3.18719e7i		−	1.00053i	0.865872	−	0.500266i	$-0.166764\pi$
$318$	2.51223e7	+	501392.i	0.781229	+	0.0155918i
$319$	1.50928e7			0.464940
$320$			8.76361e7i			2.67444i
$321$	983489.	−	4.92779e7i	0.0297341	−	1.48983i
$322$	2.74534e7			0.822297
$323$			7.31128e6i			0.216963i
$324$	−8.95093e7	−	7.15998e6i	−2.63168	−	0.210512i
$325$	3.23474e6			0.0942300
$326$			4.29538e6i			0.123979i
$327$	1.88425e7	+	376060.i	0.538885	+	0.0107551i
$328$	−8.88065e7			−2.51665
$329$		−	1.67499e7i		−	0.470353i
$330$	−347279.	+	1.74005e7i	−0.00966354	+	0.484193i
$331$	5.26170e6			0.145092			0.0725458	−	0.997365i	$-0.476888\pi$
$331$	5.26170e6			0.145092			0.0725458	+	0.997365i	$0.476888\pi$
$332$			4.85209e7i			1.32591i
$333$	−5.55075e6	−	221652.i	−0.150321	−	0.00600260i
$334$	1.24657e8			3.34563
$335$			1.57837e7i			0.419830i
$336$	−4.77333e7	−	952663.i	−1.25836	−	0.0251143i
$337$	−7.23973e7			−1.89161			−0.945807	−	0.324729i	$-0.894727\pi$
$337$	−7.23973e7			−1.89161			−0.945807	+	0.324729i	$0.894727\pi$
$338$			1.00777e7i			0.260983i
$339$	999551.	−	5.00827e7i	0.0256570	−	1.28555i
$340$	9.63706e7			2.45193
$341$		−	5.55406e6i		−	0.140071i
$342$	−674346.	+	1.68874e7i	−0.0168579	+	0.422166i
$343$	−2.17889e6			−0.0539949
$344$			9.65651e7i			2.37217i
$345$	−4.43783e7	−	885703.i	−1.08072	−	0.0215690i
$346$	7.84726e7			1.89448
$347$		−	2.29798e7i		−	0.549994i	−0.961445	−	0.274997i	$-0.911323\pi$
$347$		−	2.29798e7i		−	0.549994i	0.961445	−	0.274997i	$-0.0886769\pi$
$348$	3.85489e6	−	1.93150e8i	0.0914690	−	4.58307i
$349$	−6.12628e7			−1.44119			−0.720594	−	0.693357i	$-0.756131\pi$
$349$	−6.12628e7			−1.44119			−0.720594	+	0.693357i	$0.756131\pi$
$350$			3.13576e6i			0.0731372i
$351$	4.01052e7	+	2.40382e6i	0.927426	+	0.0555878i
$352$	−3.76540e7			−0.863342
$353$			5.32886e7i			1.21146i	0.795669	+	0.605732i	$0.207119\pi$
$353$			5.32886e7i			1.21146i	−0.795669	+	0.605732i	$0.792881\pi$
$354$	1.66274e7	+	331850.i	0.374813	+	0.00748053i
$355$	−2.31792e7			−0.518099
$356$		−	1.35069e8i		−	2.99369i
$357$	−336201.	+	1.68454e7i	−0.00738914	+	0.370234i
$358$	8.49134e7			1.85066
$359$		−	6.23374e6i		−	0.134730i	−0.997728	−	0.0673651i	$-0.978541\pi$
$359$		−	6.23374e6i		−	0.134730i	0.997728	−	0.0673651i	$-0.0214592\pi$
$360$	1.38281e8	+	5.52182e6i	2.96384	+	0.118352i
$361$	−4.47388e7			−0.950960
$362$			1.02712e8i			2.16519i
$363$	4.43936e7	+	886008.i	0.928111	+	0.0185233i
$364$	4.47127e7			0.927101
$365$		−	1.71509e7i		−	0.352702i
$366$	−976654.	+	4.89354e7i	−0.0199204	+	0.998114i
$367$	−5.29535e7			−1.07126			−0.535632	−	0.844452i	$-0.679927\pi$
$367$	−5.29535e7			−1.07126			−0.535632	+	0.844452i	$0.679927\pi$
$368$		−	1.89236e8i		−	3.79718i
$369$	−1.61233e6	+	4.03770e7i	−0.0320904	+	0.803628i
$370$	1.37817e7			0.272081
$371$		−	7.90463e6i		−	0.154796i
$372$	−7.10781e7	−	1.41858e6i	−1.38072	−	0.0275565i
$373$	4.67074e7			0.900034			0.450017	−	0.893020i	$-0.351418\pi$
$373$	4.67074e7			0.900034			0.450017	+	0.893020i	$0.351418\pi$
$374$			2.61851e7i			0.500541i
$375$	1.09864e6	−	5.50477e7i	0.0208335	−	1.04387i
$376$	−2.06994e8			−3.89399
$377$			8.64385e7i			1.61318i
$378$	−2.33026e6	+	3.88780e7i	−0.0431448	+	0.719827i
$379$	2.19924e7			0.403975			0.201988	−	0.979388i	$-0.435260\pi$
$379$	2.19924e7			0.403975			0.201988	+	0.979388i	$0.435260\pi$
$380$		−	3.04103e7i		−	0.554204i
$381$	−8.83071e6	−	176244.i	−0.159669	−	0.00318668i
$382$	9.14280e6			0.164017
$383$			4.96363e7i			0.883494i	0.897140	+	0.441747i	$0.145641\pi$
$383$			4.96363e7i			0.883494i	−0.897140	+	0.441747i	$0.854359\pi$
$384$	−2.43905e6	+	1.22209e8i	−0.0430751	+	2.15828i
$385$	5.47498e6			0.0959402
$386$		−	9.08740e7i		−	1.58007i
$387$	4.39046e7	+	1.75320e6i	0.757490	+	0.0302481i
$388$	−1.98680e8			−3.40140
$389$			2.09851e7i			0.356502i	0.983985	+	0.178251i	$0.0570439\pi$
$389$			2.09851e7i			0.356502i	−0.983985	+	0.178251i	$0.942956\pi$
$390$	−9.96550e7	−	1.98892e6i	−1.67998	−	0.0335292i
$391$	−6.67827e7			−1.11721
$392$			2.69266e7i			0.447017i
$393$	−37982.1	+	1.90310e6i	−0.000625751	+	0.0313534i
$394$	4.04373e7			0.661140
$395$			1.05937e8i			1.71893i
$396$	−1.75166e6	+	4.38661e7i	−0.0282075	+	0.706388i
$397$	8.86430e7			1.41668			0.708342	−	0.705869i	$-0.249443\pi$
$397$	8.86430e7			1.41668			0.708342	+	0.705869i	$0.249443\pi$
$398$			1.97443e8i			3.13179i
$399$	5.31566e6	+	106090.i	0.0836832	+	0.00167015i
$400$	2.16148e7			0.337731
$401$		−	5.86359e7i		−	0.909349i	−0.890658	−	0.454675i	$-0.849756\pi$
$401$		−	5.86359e7i		−	0.909349i	0.890658	−	0.454675i	$-0.150244\pi$
$402$	−1.09537e6	+	5.48837e7i	−0.0168610	+	0.844822i
$403$	3.18089e7			0.485997
$404$		−	2.37217e8i		−	3.59751i
$405$	5.02113e6	−	6.27708e7i	0.0755852	−	0.944915i
$406$	−8.37934e7			−1.25208
$407$			2.71594e6i			0.0402843i
$408$	2.08175e8	+	4.15476e6i	3.06512	+	0.0611737i
$409$	8.09388e7			1.18301			0.591503	−	0.806303i	$-0.298535\pi$
$409$	8.09388e7			1.18301			0.591503	+	0.806303i	$0.298535\pi$
$410$		−	1.00250e8i		−	1.45457i
$411$	−347823.	+	1.74277e7i	−0.00500994	+	0.251024i
$412$	2.02706e8			2.89851
$413$		−	5.23175e6i		−	0.0742671i
$414$	−1.54253e8	−	6.15961e6i	−2.17386	−	0.0868065i
$415$	−3.40266e7			−0.476074
$416$		−	2.15650e8i		−	2.99550i
$417$	−9.63699e7	−	1.92335e6i	−1.32903	−	0.0265247i
$418$	8.26286e6			0.113136
$419$		−	1.01481e8i		−	1.37957i	−0.724015	−	0.689785i	$-0.757705\pi$
$419$		−	1.01481e8i		−	1.37957i	0.724015	−	0.689785i	$-0.242295\pi$
$420$	1.39838e6	−	7.00661e7i	0.0188746	−	0.945715i
$421$	2.35310e7			0.315350			0.157675	−	0.987491i	$-0.449600\pi$
$421$	2.35310e7			0.315350			0.157675	+	0.987491i	$0.449600\pi$
$422$		−	5.99576e7i		−	0.797824i
$423$	−3.75810e6	+	9.41127e7i	−0.0496532	+	1.24345i
$424$	−9.76852e7			−1.28154
$425$		−	7.62799e6i		−	0.0993672i
$426$	−8.05996e7	−	1.60861e6i	−1.04257	−	0.0208076i
$427$	1.53973e7			0.197771
$428$			3.08441e8i			3.93406i
$429$	391952.	−	1.96388e7i	0.00496433	−	0.248739i
$430$	−1.09009e8			−1.37106
$431$			1.30255e8i			1.62691i	0.581629	+	0.813454i	$0.302415\pi$
$431$			1.30255e8i			1.62691i	−0.581629	+	0.813454i	$0.697585\pi$
$432$	2.67986e8	+	1.60625e7i	3.32400	+	0.199233i
$433$	3.94140e7			0.485497			0.242748	−	0.970089i	$-0.421951\pi$
$433$	3.94140e7			0.485497			0.242748	+	0.970089i	$0.421951\pi$
$434$			3.08355e7i			0.377209i
$435$	1.35452e8	+	2.70335e6i	1.64557	+	0.0328423i
$436$	−1.17940e8			−1.42299
$437$			2.10737e7i			0.252520i
$438$	1.19025e6	−	5.96378e7i	0.0141650	−	0.709740i
$439$	−1.61575e8			−1.90977			−0.954884	−	0.296978i	$-0.904021\pi$
$439$	−1.61575e8			−1.90977			−0.954884	+	0.296978i	$0.904021\pi$
$440$		−	6.76597e7i		−	0.794277i
$441$	1.22425e7	+	488869.i	0.142743	+	0.00570002i
$442$	−1.49966e8			−1.73670
$443$		−	8.00677e7i		−	0.920971i	−0.887667	−	0.460486i	$-0.847675\pi$
$443$		−	8.00677e7i		−	0.920971i	0.887667	−	0.460486i	$-0.152325\pi$
$444$	3.47572e7	+	693685.i	0.397097	+	0.00792526i
$445$	9.47212e7			1.07490
$446$			6.21608e7i			0.700667i
$447$	2.59429e6	−	1.29988e8i	0.0290467	−	1.45539i
$448$	9.58827e7			1.06637
$449$		−	1.32122e8i		−	1.45961i	−0.683655	−	0.729805i	$-0.739611\pi$
$449$		−	1.32122e8i		−	1.45961i	0.683655	−	0.729805i	$-0.260389\pi$
$450$	703557.	−	1.76189e7i	0.00772079	−	0.193349i
$451$	1.97562e7			0.215364
$452$			3.13479e8i			3.39463i
$453$	9.32181e7	+	1.86045e6i	1.00278	+	0.0200135i
$454$	1.59815e8			1.70785
$455$			3.13560e7i			0.332879i
$456$	1.31106e6	−	6.56907e7i	0.0138270	−	0.692803i
$457$	−3.56971e7			−0.374010			−0.187005	−	0.982359i	$-0.559878\pi$
$457$	−3.56971e7			−0.374010			−0.187005	+	0.982359i	$0.559878\pi$
$458$		−	1.13029e8i		−	1.17650i
$459$	5.66854e6	−	9.45739e7i	0.0586183	−	0.977987i
$460$	2.77774e8			2.85376
$461$			8.85096e7i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$461$			8.85096e7i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$462$	1.90378e7	+	379958.i	0.193060	+	0.00385309i
$463$	−9.87878e7			−0.995315			−0.497657	−	0.867374i	$-0.665806\pi$
$463$	−9.87878e7			−0.995315			−0.497657	+	0.867374i	$0.665806\pi$
$464$			5.77589e8i			5.78182i
$465$	994817.	−	4.98455e7i	0.00989428	−	0.495755i
$466$	2.77806e8			2.74527
$467$			8.53806e7i			0.838318i	0.907913	+	0.419159i	$0.137675\pi$
$467$			8.53806e7i			0.838318i	−0.907913	+	0.419159i	$0.862325\pi$
$468$	−2.51228e8	−	1.00320e7i	−2.45092	−	0.0978702i
$469$	1.72689e7			0.167397
$470$		−	2.33669e8i		−	2.25064i
$471$	−5.30832e7	−	1.05944e6i	−0.508036	−	0.0101394i
$472$	−6.46538e7			−0.614848
$473$		−	2.14822e7i		−	0.202999i
$474$	−7.35194e6	+	3.68370e8i	−0.0690346	+	3.45899i
$475$	−2.40706e6			−0.0224598
$476$		−	1.05439e8i		−	0.977644i
$477$	−1.77353e6	+	4.44138e7i	−0.0163412	+	0.409226i
$478$	−2.55513e8			−2.33954
$479$		−	8.18328e7i		−	0.744597i	−0.928113	−	0.372298i	$-0.878570\pi$
$479$		−	8.18328e7i		−	0.744597i	0.928113	−	0.372298i	$-0.121430\pi$
$480$	−3.37930e8	−	6.74441e6i	−3.05564	−	0.0609846i
$481$	−1.55546e7			−0.139773
$482$		−	3.07966e8i		−	2.75018i
$483$	−969048.	+	4.85543e7i	−0.00860011	+	0.430910i
$484$	−2.77869e8			−2.45078
$485$		−	1.39330e8i		−	1.22129i
$486$	2.18159e7	−	2.17921e8i	0.190049	−	1.89841i
$487$	−2.20121e8			−1.90579			−0.952894	−	0.303303i	$-0.901911\pi$
$487$	−2.20121e8			−1.90579			−0.952894	+	0.303303i	$0.901911\pi$
$488$		−	1.90280e8i		−	1.63732i
$489$	−7.59684e6	−	151618.i	−0.0649690	−	0.00129665i
$490$	−3.03965e7			−0.258366
$491$		−	1.16286e8i		−	0.982384i	−0.871051	−	0.491192i	$-0.836561\pi$
$491$		−	1.16286e8i		−	0.982384i	0.871051	−	0.491192i	$-0.163439\pi$
$492$	5.04598e6	−	2.52830e8i	0.0423692	−	2.12291i
$493$	2.03834e8			1.70113
$494$			4.73226e7i			0.392543i
$495$	−3.07623e7	−	1.22840e6i	−0.253632	−	0.0101280i
$496$	2.12549e8			1.74187
$497$			2.53603e7i			0.206579i
$498$	−1.18319e8	−	2.36141e6i	−0.958000	−	0.0191198i
$499$	1.25472e8			1.00982			0.504911	−	0.863171i	$-0.331525\pi$
$499$	1.25472e8			1.00982			0.504911	+	0.863171i	$0.331525\pi$
$500$			3.44556e8i			2.75645i
$501$	−4.40014e6	+	2.20470e8i	−0.0349908	+	1.75322i
$502$	2.48446e8			1.96391
$503$			3.36217e7i			0.264190i	0.991237	+	0.132095i	$0.0421704\pi$
$503$			3.36217e7i			0.264190i	−0.991237	+	0.132095i	$0.957830\pi$
$504$	6.04142e6	−	1.51293e8i	0.0471898	−	1.18175i
$505$	1.66355e8			1.29170
$506$			7.54746e7i			0.582572i
$507$	−1.78235e7	−	355723.i	−0.136763	−	0.00272953i
$508$	5.52734e7			0.421624
$509$		−	1.55599e8i		−	1.17992i	−0.807431	−	0.589962i	$-0.799143\pi$
$509$		−	1.55599e8i		−	1.17992i	0.807431	−	0.589962i	$-0.200857\pi$
$510$	−4.69015e6	+	2.35001e8i	−0.0353571	+	1.77157i
$511$	−1.87648e7			−0.140631
$512$		−	4.24602e7i		−	0.316353i
$513$	−2.98433e7	−	1.78874e6i	−0.221052	−	0.0132494i
$514$	−3.73524e8			−2.75061
$515$			1.42153e8i			1.04072i
$516$	−2.74918e8	−	5.48682e6i	−2.00103	−	0.0399367i
$517$	4.60486e7			0.333231
$518$		−	1.50786e7i		−	0.108485i
$519$	−2.76992e6	+	1.38787e8i	−0.0198137	+	0.992767i
$520$	3.87497e8			2.75587
$521$			1.60889e8i			1.13766i	0.822454	+	0.568832i	$0.192605\pi$
$521$			1.60889e8i			1.13766i	−0.822454	+	0.568832i	$0.807395\pi$
$522$	4.70811e8	+	1.88004e7i	3.31005	+	0.132177i
$523$	−8.06025e7			−0.563435			−0.281717	−	0.959497i	$-0.590904\pi$
$523$	−8.06025e7			−0.563435			−0.281717	+	0.959497i	$0.590904\pi$
$524$		−	1.19119e7i		−	0.0827921i
$525$	−5.54592e6	−	110686.i	−0.0383262	−	0.000764915i
$526$	1.67421e8			1.15041
$527$		−	7.50100e7i		−	0.512492i
$528$	2.61905e6	−	1.31228e8i	0.0177927	−	0.891507i
$529$	−4.44552e7			−0.300300
$530$		−	1.10273e8i		−	0.740701i
$531$	−1.17383e6	+	2.93957e7i	−0.00784007	+	0.196336i
$532$	−3.32719e7			−0.220975
$533$			1.13146e8i			0.747238i
$534$	3.29369e8	+	6.57355e6i	2.16301	+	0.0431694i
$535$	−2.16303e8			−1.41254
$536$		−	2.13409e8i		−	1.38586i
$537$	−2.99727e6	+	1.50178e8i	−0.0193554	+	0.969806i
$538$	−3.36049e8			−2.15802
$539$		−	5.99018e6i		−	0.0382537i
$540$	−2.35776e7	+	3.93367e8i	−0.149733	+	2.49814i
$541$	−563602.			−0.00355943			−0.00177972	−	0.999998i	$-0.500567\pi$
$541$	−563602.			−0.00355943			−0.00177972	+	0.999998i	$0.500567\pi$
$542$		−	3.71388e6i		−	0.0233255i
$543$	−1.81658e8	−	3.62553e6i	−1.13463	−	0.0226450i
$544$	−5.08534e8			−3.15881
$545$		−	8.27085e7i		−	0.510929i
$546$	−2.17607e6	+	1.09033e8i	−0.0133689	+	0.669851i
$547$	3.12342e7			0.190840			0.0954198	−	0.995437i	$-0.469581\pi$
$547$	3.12342e7			0.190840			0.0954198	+	0.995437i	$0.469581\pi$
$548$		−	1.09084e8i		−	0.662856i
$549$	−8.65131e7	−	3.45464e6i	−0.522835	−	0.0208778i
$550$	−8.62079e6			−0.0518154
$551$		−	6.43211e7i		−	0.384502i
$552$	6.00032e8	+	1.19755e7i	3.56745	+	0.0711992i
$553$	1.15906e8			0.685379
$554$		−	2.50208e8i		−	1.47154i
$555$	−486466.	+	2.43745e7i	−0.00284560	+	0.142579i
$556$	6.03201e8			3.50944
$557$		−	8.81896e7i		−	0.510331i	−0.966897	−	0.255165i	$-0.917870\pi$
$557$		−	8.81896e7i		−	0.510331i	0.966897	−	0.255165i	$-0.0821299\pi$
$558$	6.91844e6	−	1.73256e8i	0.0398204	−	0.997207i
$559$	1.23031e8			0.704338
$560$			2.09523e8i			1.19308i
$561$	−4.63112e7	−	924279.i	−0.262299	−	0.00523497i
$562$	1.83802e8			1.03548
$563$		−	1.70614e8i		−	0.956067i	−0.878342	−	0.478034i	$-0.841350\pi$
$563$		−	1.70614e8i		−	0.956067i	0.878342	−	0.478034i	$-0.158650\pi$
$564$	1.17614e7	−	5.89307e8i	0.0655575	−	3.28477i
$565$	−2.19836e8			−1.21886
$566$			2.35330e8i			1.29786i
$567$	−6.86776e7	−	5.49362e6i	−0.376761	−	0.0301377i
$568$	3.13402e8			1.71024
$569$			1.22459e8i			0.664744i	0.943148	+	0.332372i	$0.107849\pi$
$569$			1.22459e8i			0.664744i	−0.943148	+	0.332372i	$0.892151\pi$
$570$	7.41559e7	+	1.48001e6i	0.400425	+	0.00799169i
$571$	−1.61790e8			−0.869050			−0.434525	−	0.900660i	$-0.643084\pi$
$571$	−1.61790e8			−0.869050			−0.434525	+	0.900660i	$0.643084\pi$
$572$			1.22924e8i			0.656822i
$573$	−322722.	+	1.61700e7i	−0.00171540	+	0.0859502i
$574$	−1.09684e8			−0.579973
$575$		−	2.19865e7i		−	0.115652i
$576$	−5.38737e8	−	2.15128e7i	−2.81909	−	0.112572i
$577$	2.12745e8			1.10747			0.553736	−	0.832692i	$-0.313202\pi$
$577$	2.12745e8			1.10747			0.553736	+	0.832692i	$0.313202\pi$
$578$		−	1.47754e7i		−	0.0765169i
$579$	1.60720e8	+	3.20766e6i	0.828010	+	0.0165254i
$580$	−8.47822e8			−4.34531
$581$			3.72285e7i			0.189822i
$582$	9.66932e6	−	4.84483e8i	0.0490486	−	2.45759i
$583$	2.17313e7			0.109668
$584$			2.31895e8i			1.16427i
$585$	7.03523e6	−	1.76180e8i	0.0351407	−	0.880015i
$586$	4.78879e8			2.37976
$587$			1.05054e8i			0.519397i	0.965690	+	0.259698i	$0.0836231\pi$
$587$			1.05054e8i			0.519397i	−0.965690	+	0.259698i	$0.916377\pi$
$588$	−7.66594e7	−	1.52997e6i	−0.377080	−	0.00752577i
$589$	−2.36698e7			−0.115838
$590$		−	7.29853e7i		−	0.355369i
$591$	−1.42735e6	+	7.15177e7i	−0.00691462	+	0.346458i
$592$	−1.03937e8			−0.500961
$593$			1.28998e8i			0.618614i	0.950962	+	0.309307i	$0.100097\pi$
$593$			1.28998e8i			0.618614i	−0.950962	+	0.309307i	$0.899903\pi$
$594$	−1.06883e8	−	6.40632e6i	−0.509975	−	0.0305667i
$595$	7.39421e7			0.351027
$596$			8.13621e8i			3.84312i
$597$	−3.49199e8	−	6.96932e6i	−1.64116	−	0.0327542i
$598$	−4.32254e8			−2.02132
$599$		−	2.22645e8i		−	1.03594i	−0.855400	−	0.517968i	$-0.826689\pi$
$599$		−	2.22645e8i		−	1.03594i	0.855400	−	0.517968i	$-0.173311\pi$
$600$	−1.36785e6	+	6.85363e7i	−0.00633264	+	0.317298i
$601$	−1.77397e7			−0.0817191			−0.0408596	−	0.999165i	$-0.513010\pi$
$601$	−1.77397e7			−0.0817191			−0.0408596	+	0.999165i	$0.513010\pi$
$602$			1.19267e8i			0.546675i
$603$	−9.70291e7	−	3.87456e6i	−0.442537	−	0.0176714i
$604$	−5.83473e8			−2.64795
$605$		−	1.94864e8i		−	0.879963i
$606$	5.78457e8	+	1.15449e7i	2.59928	+	0.0518765i
$607$	−2.74443e7			−0.122712			−0.0613559	−	0.998116i	$-0.519542\pi$
$607$	−2.74443e7			−0.122712			−0.0613559	+	0.998116i	$0.519542\pi$
$608$			1.60471e8i			0.713979i
$609$	2.95773e6	−	1.48198e8i	0.0130950	−	0.656129i
$610$	2.14800e8			0.946334
$611$			2.63727e8i			1.15620i
$612$	−2.36569e7	+	5.92431e8i	−0.103206	+	2.58454i
$613$	2.44566e8			1.06173			0.530867	−	0.847455i	$-0.321867\pi$
$613$	2.44566e8			1.06173			0.530867	+	0.847455i	$0.321867\pi$
$614$		−	4.97901e8i		−	2.15099i
$615$	1.77304e8	+	3.53863e6i	0.762241	+	0.0152128i
$616$	−7.40265e7			−0.316698
$617$		−	6.37471e7i		−	0.271397i	−0.990750	−	0.135699i	$-0.956672\pi$
$617$		−	6.37471e7i		−	0.271397i	0.990750	−	0.135699i	$-0.0433279\pi$
$618$	−9.86526e6	+	4.94300e8i	−0.0417968	+	2.09424i
$619$	2.88252e8			1.21535			0.607674	−	0.794187i	$-0.292103\pi$
$619$	2.88252e8			1.21535			0.607674	+	0.794187i	$0.292103\pi$
$620$			3.11994e8i			1.30910i
$621$	1.63387e7	−	2.72595e8i	0.0682250	−	1.13826i
$622$	−5.81516e8			−2.41652
$623$		−	1.03635e8i		−	0.428588i
$624$	7.51562e8	+	1.49997e7i	3.09322	+	0.0617346i
$625$	−2.16868e8			−0.888292
$626$			2.51052e8i			1.02339i
$627$	−291662.	+	1.46138e7i	−0.00118325	+	0.0592869i
$628$	3.32260e8			1.34152
$629$			3.66799e7i			0.147393i
$630$	1.70789e8	+	6.81995e6i	0.683028	+	0.0272747i
$631$	−2.57686e8			−1.02566			−0.512830	−	0.858490i	$-0.671403\pi$
$631$	−2.57686e8			−1.02566			−0.512830	+	0.858490i	$0.671403\pi$
$632$		−	1.43236e9i		−	5.67417i
$633$	1.06042e8	+	2.11638e6i	0.418085	+	0.00834416i
$634$	−4.86468e8			−1.90891
$635$			3.87620e7i			0.151386i
$636$	5.55047e6	−	2.78107e8i	0.0215754	−	1.08104i
$637$	3.43067e7			0.132727
$638$		−	2.30364e8i		−	0.887059i
$639$	5.69000e6	−	1.42492e8i	0.0218077	−	0.546121i
$640$	5.36430e8			2.04632
$641$		−	2.04007e8i		−	0.774588i	−0.921956	−	0.387294i	$-0.873410\pi$
$641$		−	2.04007e8i		−	0.774588i	0.921956	−	0.387294i	$-0.126590\pi$
$642$	−7.52138e8	−	1.50112e7i	−2.84245	−	0.0567296i
$643$	4.66132e8			1.75338			0.876690	−	0.481055i	$-0.159746\pi$
$643$	4.66132e8			1.75338			0.876690	+	0.481055i	$0.159746\pi$
$644$		−	3.03912e8i		−	1.13786i
$645$	3.84779e6	−	1.92794e8i	0.0143394	−	0.718479i
$646$	1.11594e8			0.413944
$647$			7.13431e7i			0.263414i	0.991289	+	0.131707i	$0.0420458\pi$
$647$			7.13431e7i			0.263414i	−0.991289	+	0.131707i	$0.957954\pi$
$648$	−6.78900e7	+	8.48716e8i	−0.249506	+	3.11916i
$649$	1.43831e7			0.0526159
$650$		−	4.93725e7i		−	0.179782i
$651$	−5.45359e7	−	1.08843e6i	−0.197670	−	0.00394509i
$652$	4.75503e7			0.171558
$653$			3.40530e8i			1.22297i	0.791255	+	0.611486i	$0.209428\pi$
$653$			3.40530e8i			1.22297i	−0.791255	+	0.611486i	$0.790572\pi$
$654$	5.73988e6	−	2.87598e8i	0.0205196	−	1.02814i
$655$	8.35358e6			0.0297268
$656$			7.56053e8i			2.67819i
$657$	1.05434e8	+	4.21018e6i	0.371778	+	0.0148458i
$658$	−2.55657e8			−0.897387
$659$			1.33221e8i			0.465495i	0.972537	+	0.232748i	$0.0747716\pi$
$659$			1.33221e8i			0.465495i	−0.972537	+	0.232748i	$0.925228\pi$
$660$	1.92625e8	+	3.84442e6i	0.670010	+	0.0133721i
$661$	−1.15163e8			−0.398758			−0.199379	−	0.979922i	$-0.563892\pi$
$661$	−1.15163e8			−0.398758			−0.199379	+	0.979922i	$0.563892\pi$
$662$		−	8.03104e7i		−	0.276820i
$663$	5.29348e6	−	2.65231e8i	0.0181636	−	0.910088i
$664$	4.60069e8			1.57152
$665$		−	2.33328e7i		−	0.0793419i
$666$	−3.38312e6	+	8.47222e7i	−0.0114524	+	0.286797i
$667$	5.87522e8			1.97992
$668$		−	1.37997e9i		−	4.62957i
$669$	−1.09938e8	−	2.19415e6i	−0.367172	−	0.00732803i
$670$	2.40910e8			0.800995
$671$			4.23302e7i			0.140114i
$672$	−7.37906e6	+	3.69729e8i	−0.0243161	+	1.21836i
$673$	1.27548e8			0.418436			0.209218	−	0.977869i	$-0.432908\pi$
$673$	1.27548e8			0.418436			0.209218	+	0.977869i	$0.432908\pi$
$674$			1.10501e9i			3.60901i
$675$	3.11361e7	+	1.86623e6i	0.101240	+	0.00606810i
$676$	1.11562e8			0.361139
$677$			3.13042e8i			1.00887i	0.863448	+	0.504437i	$0.168300\pi$
$677$			3.13042e8i			1.00887i	−0.863448	+	0.504437i	$0.831700\pi$
$678$	−7.64422e8	−	1.52563e7i	−2.45270	−	0.0489510i
$679$	−1.52441e8			−0.486958
$680$		−	9.13774e8i		−	2.90611i
$681$	−5.64114e6	+	2.82650e8i	−0.0178618	+	0.894968i
$682$	−8.47727e7			−0.267241
$683$			3.04900e7i			0.0956964i	0.998855	+	0.0478482i	$0.0152364\pi$
$683$			3.04900e7i			0.0956964i	−0.998855	+	0.0478482i	$0.984764\pi$
$684$	1.86945e8	+	7.46508e6i	0.584179	+	0.0233274i
$685$	7.64982e7			0.238001
$686$			3.32568e7i			0.103017i
$687$	1.99903e8	+	3.98967e6i	0.616523	+	0.0123046i
$688$	8.22106e8			2.52442
$689$			1.24459e8i			0.380511i
$690$	−1.35187e7	+	6.77355e8i	−0.0411516	+	2.06191i
$691$	−4.93596e8			−1.49602			−0.748010	−	0.663688i	$-0.768990\pi$
$691$	−4.93596e8			−1.49602			−0.748010	+	0.663688i	$0.768990\pi$
$692$		−	8.68701e8i		−	2.62151i
$693$	−1.34399e6	+	3.36571e7i	−0.00403829	+	0.101129i
$694$	−3.50745e8			−1.04933
$695$			4.23011e8i			1.26008i
$696$	−1.83142e9	−	3.65516e7i	−5.43201	−	0.108412i
$697$	2.66816e8			0.787976
$698$			9.35067e8i			2.74965i
$699$	−9.80599e6	+	4.91331e8i	−0.0287118	+	1.43861i
$700$	3.47132e7			0.101205
$701$			4.50780e8i			1.30861i	0.756230	+	0.654306i	$0.227039\pi$
$701$			4.50780e8i			1.30861i	−0.756230	+	0.654306i	$0.772961\pi$
$702$	3.66899e7	−	6.12134e8i	0.106056	−	1.76944i
$703$	1.15746e7			0.0333149
$704$			2.63600e8i			0.755487i
$705$	4.13268e8	+	8.24801e6i	1.17941	+	0.0235387i
$706$	8.13355e8			2.31135
$707$		−	1.82009e8i		−	0.515033i
$708$	3.67362e6	−	1.84067e8i	0.0103513	−	0.518653i
$709$	−5.70371e8			−1.60036			−0.800182	−	0.599757i	$-0.795264\pi$
$709$	−5.70371e8			−1.60036			−0.800182	+	0.599757i	$0.795264\pi$
$710$			3.53788e8i			0.988481i
$711$	−6.51243e8	−	2.60054e7i	−1.81190	−	0.0723527i
$712$	−1.28071e9			−3.54823
$713$		−	2.16205e8i		−	0.596482i
$714$	2.57115e8	+	5.13150e6i	0.706370	+	0.0140977i
$715$	−8.62037e7			−0.235835
$716$		−	9.40001e8i		−	2.56088i
$717$	9.01909e6	−	4.51903e8i	0.0244684	−	1.22599i
$718$	−9.51468e7			−0.257052
$719$		−	1.28727e8i		−	0.346325i	−0.984893	−	0.173163i	$-0.944601\pi$
$719$		−	1.28727e8i		−	0.346325i	0.984893	−	0.173163i	$-0.0553986\pi$
$720$	4.70099e7	−	1.17725e9i	0.125948	−	3.15407i
$721$	1.55530e8			0.414961
$722$			6.82857e8i			1.81434i
$723$	5.44671e8	+	1.08706e7i	1.44118	+	0.0287632i
$724$	1.13704e9			2.99612
$725$			6.71074e7i			0.176099i
$726$	1.35233e7	−	6.77588e8i	0.0353405	−	1.77074i
$727$	−5.00584e8			−1.30279			−0.651394	−	0.758740i	$-0.725815\pi$
$727$	−5.00584e8			−1.30279			−0.651394	+	0.758740i	$0.725815\pi$
$728$		−	4.23960e8i		−	1.09883i
$729$	3.84647e8	+	4.62760e7i	0.992841	+	0.119446i
$730$	−2.61778e8			−0.672921
$731$		−	2.90126e8i		−	0.742736i
$732$	5.41721e8	+	1.08117e7i	1.38115	+	0.0275651i
$733$	5.86354e7			0.148884			0.0744420	−	0.997225i	$-0.476282\pi$
$733$	5.86354e7			0.148884			0.0744420	+	0.997225i	$0.476282\pi$
$734$			8.08240e8i			2.04387i
$735$	1.07293e6	−	5.37595e7i	0.00270216	−	0.135392i
$736$	−1.46577e9			−3.67649
$737$			4.74756e7i			0.118595i
$738$	6.16283e8	+	2.46094e7i	1.53324	+	0.0612254i
$739$	4.44555e8			1.10152			0.550760	−	0.834664i	$-0.314338\pi$
$739$	4.44555e8			1.10152			0.550760	+	0.834664i	$0.314338\pi$
$740$		−	1.52565e8i		−	0.376496i
$741$	−8.36951e7	−	1.67039e6i	−0.205705	−	0.00410547i
$742$	−1.20650e8			−0.295336
$743$		−	8.35867e6i		−	0.0203784i	−0.999948	−	0.0101892i	$-0.996757\pi$
$743$		−	8.35867e6i		−	0.0203784i	0.999948	−	0.0101892i	$-0.00324339\pi$
$744$	−1.34508e7	+	6.73953e8i	−0.0326609	+	1.63648i
$745$	−5.70574e8			−1.37989
$746$		−	7.12904e8i		−	1.71718i
$747$	8.35281e6	−	2.09176e8i	0.0200388	−	0.501823i
$748$	2.89872e8			0.692630
$749$			2.36657e8i			0.563215i
$750$	−8.40204e8	−	1.67688e7i	−1.99159	−	0.0397483i
$751$	2.94347e8			0.694929			0.347464	−	0.937693i	$-0.387043\pi$
$751$	2.94347e8			0.694929			0.347464	+	0.937693i	$0.387043\pi$
$752$			1.76224e9i			4.14393i
$753$	−8.76962e6	+	4.39403e8i	−0.0205398	+	1.02915i
$754$	1.31933e9			3.07779
$755$		−	4.09177e8i		−	0.950758i
$756$	4.30383e8	+	2.57962e7i	0.996071	+	0.0597022i
$757$	−2.95864e8			−0.682031			−0.341016	−	0.940058i	$-0.610771\pi$
$757$	−2.95864e8			−0.682031			−0.341016	+	0.940058i	$0.610771\pi$
$758$		−	3.35674e8i		−	0.770745i
$759$	−1.33485e8	−	2.66410e6i	−0.305286	−	0.00609291i
$760$	−2.88347e8			−0.656862
$761$		−	7.57657e8i		−	1.71917i	−0.510993	−	0.859585i	$-0.670722\pi$
$761$		−	7.57657e8i		−	1.71917i	0.510993	−	0.859585i	$-0.329278\pi$
$762$	−2.69004e6	+	1.34785e8i	−0.00607987	+	0.304633i
$763$	−9.04914e7			−0.203720
$764$		−	1.01212e8i		−	0.226961i
$765$	−4.15459e8	−	1.65901e7i	−0.927991	−	0.0370565i
$766$	7.57610e8			1.68562
$767$			8.23739e7i			0.182559i
$768$	5.87528e8	+	1.17259e7i	1.29701	+	0.0258858i
$769$	−8.35758e8			−1.83781			−0.918907	−	0.394475i	$-0.870927\pi$
$769$	−8.35758e8			−1.83781			−0.918907	+	0.394475i	$0.870927\pi$
$770$		−	8.35658e7i		−	0.183044i
$771$	1.31846e7	−	6.60618e8i	0.0287677	−	1.44141i
$772$	−1.00599e9			−2.18645
$773$		−	6.51151e8i		−	1.40975i	−0.709329	−	0.704877i	$-0.751002\pi$
$773$		−	6.51151e8i		−	1.40975i	0.709329	−	0.704877i	$-0.248998\pi$
$774$	2.67594e7	−	6.70124e8i	0.0577103	−	1.44522i
$775$	2.46952e7			0.0530526
$776$			1.88385e9i			4.03146i
$777$	2.66681e7	+	532243.i	0.0568498	+	0.00113461i
$778$	3.20300e8			0.680171
$779$		−	8.41952e7i		−	0.178105i
$780$	−2.20175e7	+	1.10319e9i	−0.0463965	+	2.32470i
$781$	−6.97203e7			−0.146355
$782$			1.01932e9i			2.13152i
$783$	−4.98692e7	+	8.32016e8i	−0.103884	+	1.73319i
$784$	2.29240e8			0.475709
$785$			2.33006e8i			0.481680i
$786$	2.90474e7	+	579729.i	0.0598191	+	0.00119387i
$787$	2.96849e8			0.608991			0.304495	−	0.952514i	$-0.401512\pi$
$787$	2.96849e8			0.608991			0.304495	+	0.952514i	$0.401512\pi$
$788$		−	4.47645e8i		−	0.914862i
$789$	−5.90962e6	+	2.96102e8i	−0.0120317	+	0.602852i
$790$	1.61694e9			3.27955
$791$			2.40522e8i			0.485988i
$792$	4.15933e8	+	1.66090e7i	0.837236	+	0.0334325i
$793$	−2.42431e8			−0.486148
$794$		−	1.35298e9i		−	2.70289i
$795$	1.95030e8	+	3.89242e6i	0.388151	+	0.00774672i
$796$	2.18571e9			4.33365
$797$		−	2.57514e7i		−	0.0508659i	−0.999677	−	0.0254329i	$-0.991904\pi$
$797$		−	2.57514e7i		−	0.0508659i	0.999677	−	0.0254329i	$-0.00809643\pi$
$798$	1.61927e6	−	8.11340e7i	0.00318648	−	0.159659i
$799$	6.21907e8			1.21923
$800$		−	1.67422e8i		−	0.326996i
$801$	−2.32521e7	+	5.82292e8i	−0.0452443	+	1.13303i
$802$	−8.94972e8			−1.73495
$803$		−	5.15880e7i		−	0.0996327i
$804$	6.07569e8	+	1.21259e7i	1.16903	+	0.0233316i
$805$	2.13127e8			0.408555
$806$		−	4.85506e8i		−	0.927234i
$807$	1.18618e7	−	5.94340e8i	0.0225700	−	1.13087i
$808$	−2.24926e9			−4.26389
$809$		−	6.07452e8i		−	1.14727i	−0.819110	−	0.573636i	$-0.805532\pi$
$809$		−	6.07452e8i		−	1.14727i	0.819110	−	0.573636i	$-0.194468\pi$
$810$	−9.58084e8	−	7.66386e7i	−1.80280	−	0.144209i
$811$	−1.78071e8			−0.333835			−0.166917	−	0.985971i	$-0.553381\pi$
$811$	−1.78071e8			−0.333835			−0.166917	+	0.985971i	$0.553381\pi$
$812$			9.27603e8i			1.73258i
$813$	6.56840e6	+	131092.i	0.0122233	+	0.000243953i
$814$	4.14539e7			0.0768585
$815$			3.33460e7i			0.0615986i
$816$	3.53715e7	−	1.77229e9i	0.0651002	−	3.26186i
$817$	−9.15510e7			−0.167879
$818$		−	1.23539e9i		−	2.25706i
$819$	−1.92759e8	−	7.69725e6i	−0.350884	−	0.0140115i
$820$	−1.10978e9			−2.01278
$821$		−	3.25560e8i		−	0.588304i	−0.955759	−	0.294152i	$-0.904963\pi$
$821$		−	3.25560e8i		−	0.588304i	0.955759	−	0.294152i	$-0.0950372\pi$
$822$	2.66003e8	+	5.30889e6i	0.478928	+	0.00955847i
$823$	−3.15464e7			−0.0565914			−0.0282957	−	0.999600i	$-0.509008\pi$
$823$	−3.15464e7			−0.0565914			−0.0282957	+	0.999600i	$0.509008\pi$
$824$		−	1.92203e9i		−	3.43541i
$825$	304296.	−	1.52468e7i	0.000541919	−	0.0271529i
$826$	−7.98532e7			−0.141694
$827$			3.83741e8i			0.678456i	0.940704	+	0.339228i	$0.110166\pi$
$827$			3.83741e8i			0.678456i	−0.940704	+	0.339228i	$0.889834\pi$
$828$	−6.81876e7	+	1.70759e9i	−0.120120	+	3.00811i
$829$	−7.83129e7			−0.137458			−0.0687289	−	0.997635i	$-0.521894\pi$
$829$	−7.83129e7			−0.137458			−0.0687289	+	0.997635i	$0.521894\pi$
$830$			5.19355e8i			0.908302i
$831$	4.42521e8	+	8.83184e6i	0.771135	+	0.0153903i
$832$	−1.50967e9			−2.62128
$833$		−	8.09000e7i		−	0.139963i
$834$	−2.93565e7	+	1.47091e9i	−0.0506065	+	2.53565i
$835$	9.67742e8			1.66227
$836$		−	9.14708e7i		−	0.156554i
$837$	3.06177e8	+	1.83516e7i	0.522152	+	0.0312966i
$838$	−1.54893e9			−2.63208
$839$		−	5.38101e8i		−	0.911125i	−0.890204	−	0.455562i	$-0.849438\pi$
$839$		−	5.38101e8i		−	0.911125i	0.890204	−	0.455562i	$-0.150562\pi$
$840$	−6.64358e8	−	1.32593e7i	−1.12089	−	0.0223708i
$841$	−1.19842e9			−2.01474
$842$		−	3.59158e8i		−	0.601657i
$843$	−6.48782e6	+	3.25073e8i	−0.0108297	+	0.542623i
$844$	−6.63738e8			−1.10400
$845$			7.82356e7i			0.129668i
$846$	1.43646e9	+	5.73607e7i	2.37237	+	0.0947335i
$847$	−2.13200e8			−0.350863
$848$			8.31642e8i			1.36379i
$849$	−4.16207e8	−	8.30667e6i	−0.680121	−	0.0135739i
$850$	−1.16428e8			−0.189583
$851$			1.05724e8i			0.171548i
$852$	−1.78075e7	+	8.92247e8i	−0.0287928	+	1.44267i
$853$	−4.26618e8			−0.687372			−0.343686	−	0.939085i	$-0.611676\pi$
$853$	−4.26618e8			−0.687372			−0.343686	+	0.939085i	$0.611676\pi$
$854$		−	2.35013e8i		−	0.377327i
$855$	−5.23510e6	+	1.31100e8i	−0.00837580	+	0.209752i
$856$	2.92460e9			4.66278
$857$			5.94150e8i			0.943960i	0.881609	+	0.471980i	$0.156461\pi$
$857$			5.94150e8i			0.943960i	−0.881609	+	0.471980i	$0.843539\pi$
$858$	−2.99751e8	−	5.98244e6i	−0.474569	−	0.00947145i
$859$	−7.06773e8			−1.11507			−0.557533	−	0.830155i	$-0.688252\pi$
$859$	−7.06773e8			−1.11507			−0.557533	+	0.830155i	$0.688252\pi$
$860$			1.20674e9i			1.89722i
$861$	3.87162e6	−	1.93988e8i	0.00606573	−	0.303924i
$862$	1.98811e9			3.10398
$863$		−	2.61287e8i		−	0.406523i	−0.979124	−	0.203262i	$-0.934846\pi$
$863$		−	2.61287e8i		−	0.406523i	0.979124	−	0.203262i	$-0.0651542\pi$
$864$	1.24415e8	−	2.07574e9i	0.192900	−	3.21835i
$865$	6.09200e8			0.941265
$866$		−	6.01583e8i		−	0.926280i
$867$	2.61320e7	+	521542.i	0.0400973	+	0.000800262i
$868$	3.41353e8			0.521969
$869$			3.18648e8i			0.485570i
$870$	4.12617e7	−	2.06743e9i	0.0626599	−	3.13959i
$871$	−2.71900e8			−0.411485
$872$			1.11829e9i			1.68657i
$873$	8.56519e8	+	3.42025e7i	1.28734	+	0.0514061i
$874$	3.21652e8			0.481783
$875$			2.64367e8i			0.394623i
$876$	−6.60198e8	−	1.31762e7i	−0.982113	−	0.0196010i
$877$	−3.73441e8			−0.553634			−0.276817	−	0.960923i	$-0.589280\pi$
$877$	−3.73441e8			−0.553634			−0.276817	+	0.960923i	$0.589280\pi$
$878$			2.46615e9i			3.64365i
$879$	−1.69034e7	+	8.46950e8i	−0.0248891	+	1.24707i
$880$	−5.76019e8			−0.845258
$881$		−	9.23680e8i		−	1.35081i	−0.737447	−	0.675405i	$-0.763969\pi$
$881$		−	9.23680e8i		−	1.35081i	0.737447	−	0.675405i	$-0.236031\pi$
$882$	7.46170e6	−	1.86860e8i	0.0108751	−	0.272340i
$883$	3.97760e8			0.577749			0.288875	−	0.957367i	$-0.406719\pi$
$883$	3.97760e8			0.577749			0.288875	+	0.957367i	$0.406719\pi$
$884$			1.66014e9i			2.40319i
$885$	1.29082e8	+	2.57623e6i	0.186225	+	0.00371668i
$886$	−1.22209e9			−1.75712
$887$			1.35041e9i			1.93506i	0.252758	+	0.967530i	$0.418662\pi$
$887$			1.35041e9i			1.93506i	−0.252758	+	0.967530i	$0.581338\pi$
$888$	6.57744e6	−	3.29564e8i	0.00939329	−	0.470652i
$889$	4.24095e7			0.0603613
$890$		−	1.44575e9i		−	2.05080i
$891$	1.51030e7	−	1.88808e8i	0.0213516	−	0.266923i
$892$	6.88127e8			0.969559
$893$		−	1.96246e8i		−	0.275580i
$894$	−1.98403e9	−	3.95972e7i	−2.77674	−	0.0554182i
$895$	6.59202e8			0.919495
$896$		−	5.86908e8i		−	0.815917i
$897$	1.52577e7	−	7.64488e8i	0.0211403	−	1.05924i
$898$	−2.01661e9			−2.78479
$899$			6.59902e8i			0.908240i
$900$	−1.95043e8	−	7.78846e6i	−0.267549	−	0.0106838i
$901$	2.93491e8			0.401255
$902$		−	3.01542e8i		−	0.410893i
$903$	−2.10936e8	−	4.20986e6i	−0.286475	−	0.00571748i
$904$	2.97237e9			4.02343
$905$			7.97379e8i			1.07577i
$906$	2.83964e7	−	1.42281e9i	0.0381838	−	1.91320i
$907$	−8.88661e7			−0.119101			−0.0595504	−	0.998225i	$-0.518967\pi$
$907$	−8.88661e7			−0.119101			−0.0595504	+	0.998225i	$0.518967\pi$
$908$		−	1.76917e9i		−	2.36326i
$909$	−4.08367e7	+	1.02266e9i	−0.0543699	+	1.36156i
$910$	4.78594e8			0.635101
$911$		−	8.00546e8i		−	1.05884i	−0.848359	−	0.529421i	$-0.822409\pi$
$911$		−	8.00546e8i		−	1.05884i	0.848359	−	0.529421i	$-0.177591\pi$
$912$	−5.59257e8	−	1.11617e7i	−0.737271	−	0.0147145i
$913$	−1.02348e8			−0.134483
$914$			5.44851e8i			0.713575i
$915$	−7.58199e6	+	3.79897e8i	−0.00989737	+	0.495909i
$916$	−1.25124e9			−1.62800
$917$		−	9.13965e6i		−	0.0118528i
$918$	−1.44350e9	−	8.65202e7i	−1.86590	−	0.111838i
$919$	1.33761e9			1.72338			0.861691	−	0.507434i	$-0.169406\pi$
$919$	1.33761e9			1.72338			0.861691	+	0.507434i	$0.169406\pi$
$920$		−	2.63382e9i		−	3.38238i
$921$	8.80591e8	+	1.75749e7i	1.12719	+	0.0224964i
$922$	1.35094e9			1.72363
$923$		−	3.99299e8i		−	0.507800i
$924$	4.20618e6	−	2.10751e8i	0.00533177	−	0.267149i
$925$	−1.20759e7			−0.0152579
$926$			1.50782e9i			1.89896i
$927$	−8.73875e8	−	3.48956e7i	−1.09701	−	0.0438057i
$928$	4.47384e9			5.59805
$929$			1.17941e9i			1.47102i	0.677513	+	0.735511i	$0.263058\pi$
$929$			1.17941e9i			1.47102i	−0.677513	+	0.735511i	$0.736942\pi$
$930$	−7.60802e8	−	1.51841e7i	−0.945851	−	0.0188773i
$931$	−2.55285e7			−0.0316356
$932$		−	3.07535e9i		−	3.79880i
$933$	2.05263e7	−	1.02847e9i	0.0252735	−	1.26633i
$934$	1.30318e9			1.59943
$935$			2.03281e8i			0.248692i
$936$	−9.51223e7	+	2.38211e9i	−0.115999	+	2.90492i
$937$	−6.97854e8			−0.848293			−0.424147	−	0.905594i	$-0.639426\pi$
$937$	−6.97854e8			−0.848293			−0.424147	+	0.905594i	$0.639426\pi$
$938$		−	2.63579e8i		−	0.319376i
$939$	−4.44012e8	−	8.86161e6i	−0.536288	−	0.0107033i
$940$	−2.58674e9			−3.11436
$941$			6.81654e8i			0.818079i	0.912517	+	0.409040i	$0.134136\pi$
$941$			6.81654e8i			0.818079i	−0.912517	+	0.409040i	$0.865864\pi$
$942$	−1.61704e7	+	8.10219e8i	−0.0193449	+	0.969282i
$943$	7.69056e8			0.917113
$944$			5.50429e8i			0.654312i
$945$	−1.80903e7	+	3.01818e8i	−0.0214363	+	0.357643i
$946$	−3.27887e8			−0.387302
$947$		−	1.31995e9i		−	1.55420i	−0.629378	−	0.777099i	$-0.716690\pi$
$947$		−	1.31995e9i		−	1.55420i	0.629378	−	0.777099i	$-0.283310\pi$
$948$	4.07790e9	+	8.13868e7i	4.78643	+	0.0955276i
$949$	2.95452e8			0.345691
$950$			3.67394e7i			0.0428510i
$951$	1.71713e7	−	8.60371e8i	0.0199646	−	1.00033i
$952$	−9.99760e8			−1.15874
$953$		−	1.01893e9i		−	1.17724i	−0.808411	−	0.588618i	$-0.799672\pi$
$953$		−	1.01893e9i		−	1.17724i	0.808411	−	0.588618i	$-0.200328\pi$
$954$	6.77897e8	+	2.70698e7i	0.780762	+	0.0311774i
$955$	7.09776e7			0.0814913
$956$			2.82856e9i			3.23737i
$957$	4.07423e8	+	8.13137e6i	0.464847	+	0.00927743i
$958$	−1.24903e9			−1.42062
$959$		−	8.36967e7i		−	0.0948970i
$960$	−4.72148e7	+	2.36570e9i	−0.0533660	+	2.67391i
$961$	−6.44663e8			−0.726378
$962$			2.37413e8i			0.266673i
$963$	5.30978e7	−	1.32971e9i	0.0594563	−	1.48894i
$964$	−3.40922e9			−3.80561
$965$		−	7.05475e8i		−	0.785054i
$966$	7.41094e8	+	1.47908e7i	0.822133	+	0.0164082i
$967$	−7.83984e7			−0.0867018			−0.0433509	−	0.999060i	$-0.513803\pi$
$967$	−7.83984e7			−0.0867018			−0.0433509	+	0.999060i	$0.513803\pi$
$968$			2.63472e9i			2.90475i
$969$	−3.93902e6	+	1.97365e8i	−0.00432929	+	0.216920i
$970$	−2.12662e9			−2.33010
$971$		−	7.64016e8i		−	0.834535i	−0.908784	−	0.417267i	$-0.862988\pi$
$971$		−	7.64016e8i		−	0.834535i	0.908784	−	0.417267i	$-0.137012\pi$
$972$	−2.41241e9	−	2.41505e8i	−2.62695	−	0.262983i
$973$	4.62817e8			0.502424
$974$			3.35975e9i			3.63606i
$975$	8.73206e7	+	1.74275e6i	0.0942113	+	0.00188027i
$976$	−1.61994e9			−1.74241
$977$			3.22166e8i			0.345459i	0.984969	+	0.172729i	$0.0552586\pi$
$977$			3.22166e8i			0.345459i	−0.984969	+	0.172729i	$0.944741\pi$
$978$	−2.31417e6	+	1.15952e8i	−0.00247388	+	0.123954i
$979$	2.84911e8			0.303641
$980$			3.36493e8i			0.357518i
$981$	5.08445e8	+	2.03032e7i	0.538563	+	0.0215059i
$982$	−1.77489e9			−1.87429
$983$		−	1.94805e8i		−	0.205088i	−0.994728	−	0.102544i	$-0.967302\pi$
$983$		−	1.94805e8i		−	0.205088i	0.994728	−	0.102544i	$-0.0326982\pi$
$984$	−2.39730e9	−	4.78453e7i	−2.51615	−	0.0502174i
$985$	3.13924e8			0.328485
$986$		−	3.11117e9i		−	3.24558i
$987$	9.02416e6	−	4.52157e8i	0.00938545	−	0.470260i
$988$	5.23867e8			0.543188
$989$		−	8.36245e8i		−	0.864459i
$990$	−1.87493e7	+	4.69532e8i	−0.0193232	+	0.483904i
$991$	5.49963e8			0.565083			0.282542	−	0.959255i	$-0.408822\pi$
$991$	5.49963e8			0.565083			0.282542	+	0.959255i	$0.408822\pi$
$992$		−	1.64635e9i		−	1.68650i
$993$	1.42038e8	+	2.83479e6i	0.145063	+	0.00289516i
$994$	3.87080e8			0.394132
$995$			1.53279e9i			1.55602i
$996$	−2.61411e7	+	1.30980e9i	−0.0264573	+	1.32565i
$997$	1.45349e9			1.46665			0.733324	−	0.679879i	$-0.237968\pi$
$997$	1.45349e9			1.46665			0.733324	+	0.679879i	$0.237968\pi$
$998$		−	1.91510e9i		−	1.92664i
$999$	−1.49721e8	−	8.97393e6i	−0.150171	−	0.00900091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.b.a.8.1	✓	12
3.2	odd	2	inner	21.7.b.a.8.12	yes	12
4.3	odd	2		336.7.d.a.113.1		12
7.6	odd	2		147.7.b.b.50.1		12
12.11	even	2		336.7.d.a.113.2		12
21.20	even	2		147.7.b.b.50.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.b.a.8.1	✓	12	1.1	even	1	trivial
21.7.b.a.8.12	yes	12	3.2	odd	2	inner
147.7.b.b.50.1		12	7.6	odd	2
147.7.b.b.50.12		12	21.20	even	2
336.7.d.a.113.1		12	4.3	odd	2
336.7.d.a.113.2		12	12.11	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-15.2632i q^{2} +(26.9946 + 0.538759i) q^{3} -168.965 q^{4} -118.492i q^{5} +(8.22319 - 412.025i) q^{6} -129.642 q^{7} +1602.11i q^{8} +(728.419 + 29.0872i) q^{9} +O(q^{10})\)	\(q-15.2632i q^{2} +(26.9946 + 0.538759i) q^{3} -168.965 q^{4} -118.492i q^{5} +(8.22319 - 412.025i) q^{6} -129.642 q^{7} +1602.11i q^{8} +(728.419 + 29.0872i) q^{9} -1808.56 q^{10} -356.410i q^{11} +(-4561.16 - 91.0317i) q^{12} +2041.21 q^{13} +1978.75i q^{14} +(63.8385 - 3198.64i) q^{15} +13639.5 q^{16} -4813.47i q^{17} +(443.964 - 11118.0i) q^{18} -1518.92 q^{19} +20021.0i q^{20} +(-3499.63 - 69.8457i) q^{21} -5439.96 q^{22} -13874.1i q^{23} +(-863.151 + 43248.3i) q^{24} +1584.72 q^{25} -31155.4i q^{26} +(19647.7 + 1177.64i) q^{27} +21905.0 q^{28} +42346.6i q^{29} +(-48821.5 - 974.380i) q^{30} +15583.3 q^{31} -105648. i q^{32} +(192.019 - 9621.15i) q^{33} -73469.0 q^{34} +15361.5i q^{35} +(-123078. - 4914.73i) q^{36} -7620.26 q^{37} +23183.6i q^{38} +(55101.8 + 1099.72i) q^{39} +189837. q^{40} +55431.0i q^{41} +(-1066.07 + 53415.6i) q^{42} +60273.7 q^{43} +60221.0i q^{44} +(3446.59 - 86311.7i) q^{45} -211763. q^{46} +129201. i q^{47} +(368194. + 7348.43i) q^{48} +16807.0 q^{49} -24187.8i q^{50} +(2593.30 - 129938. i) q^{51} -344894. q^{52} +60972.9i q^{53} +(17974.6 - 299887. i) q^{54} -42231.6 q^{55} -207700. i q^{56} +(-41002.7 - 818.332i) q^{57} +646346. q^{58} +40355.4i q^{59} +(-10786.5 + 540459. i) q^{60} -118768. q^{61} -237852. i q^{62} +(-94433.6 - 3770.92i) q^{63} -739597. q^{64} -241867. i q^{65} +(-146850. - 2930.83i) q^{66} -133205. q^{67} +813311. i q^{68} +(7474.81 - 374527. i) q^{69} +234465. q^{70} -195618. i q^{71} +(-46600.9 + 1.16701e6i) q^{72} +144743. q^{73} +116310. i q^{74} +(42778.8 + 853.780i) q^{75} +256645. q^{76} +46205.6i q^{77} +(16785.3 - 841029. i) q^{78} -894049. q^{79} -1.61617e6i q^{80} +(529749. + 42375.4i) q^{81} +846055. q^{82} -287164. i q^{83} +(591317. + 11801.5i) q^{84} -570357. q^{85} -919971. i q^{86} +(-22814.7 + 1.14313e6i) q^{87} +571008. q^{88} +799391. i q^{89} +(-1.31739e6 - 52606.1i) q^{90} -264626. q^{91} +2.34425e6i q^{92} +(420666. + 8395.67i) q^{93} +1.97203e6 q^{94} +179979. i q^{95} +(56918.9 - 2.85193e6i) q^{96} +1.17586e6 q^{97} -256529. i q^{98} +(10367.0 - 259616. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more