LMFDB - Embedded newform 108.6.b.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{3}, \sqrt{-29})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 13x^{2} + 64 $ x^4 + 13*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.3
Root			$0.866025 + 2.69258i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.a.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 5.38516i) q^{2} +(-26.0000 - 18.6548i) q^{4} -91.5478i q^{5} -158.565i q^{7} +(-145.492 + 107.703i) q^{8} +O(q^{10})$	\(q+(1.73205 - 5.38516i) q^{2} +(-26.0000 - 18.6548i) q^{4} -91.5478i q^{5} -158.565i q^{7} +(-145.492 + 107.703i) q^{8} +(-493.000 - 158.565i) q^{10} +580.237 q^{11} -166.000 q^{13} +(-853.901 - 274.643i) q^{14} +(328.000 + 970.047i) q^{16} +829.315i q^{17} -671.571i q^{19} +(-1707.80 + 2380.24i) q^{20} +(1005.00 - 3124.67i) q^{22} -3859.01 q^{23} -5256.00 q^{25} +(-287.520 + 893.937i) q^{26} +(-2958.00 + 4122.70i) q^{28} +3414.19i q^{29} -6333.29i q^{31} +(5791.98 - 86.1626i) q^{32} +(4466.00 + 1436.42i) q^{34} -14516.3 q^{35} +15332.0 q^{37} +(-3616.52 - 1163.20i) q^{38} +(9860.00 + 13319.5i) q^{40} +10102.6i q^{41} +3003.42i q^{43} +(-15086.2 - 10824.2i) q^{44} +(-6684.00 + 20781.4i) q^{46} +7070.23 q^{47} -8336.00 q^{49} +(-9103.66 + 28304.4i) q^{50} +(4316.00 + 3096.69i) q^{52} -17281.0i q^{53} -53119.4i q^{55} +(17078.0 + 23070.0i) q^{56} +(18386.0 + 5913.56i) q^{58} +28429.9 q^{59} -53188.0 q^{61} +(-34105.8 - 10969.6i) q^{62} +(9568.00 - 31340.0i) q^{64} +15196.9i q^{65} -41059.1i q^{67} +(15470.7 - 21562.2i) q^{68} +(-25143.0 + 78172.8i) q^{70} +26822.5 q^{71} -30739.0 q^{73} +(26555.8 - 82565.3i) q^{74} +(-12528.0 + 17460.9i) q^{76} -92005.5i q^{77} -70197.9i q^{79} +(88805.7 - 30027.7i) q^{80} +(54404.0 + 17498.2i) q^{82} -11402.1 q^{83} +75922.0 q^{85} +(16173.9 + 5202.07i) q^{86} +(-84420.0 + 62493.4i) q^{88} +68682.4i q^{89} +26321.9i q^{91} +(100334. + 71988.9i) q^{92} +(12246.0 - 38074.4i) q^{94} -61480.9 q^{95} -13717.0 q^{97} +(-14438.4 + 44890.7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 104 q^{4}+O(q^{10}) $ 4 * q - 104 * q^4	$ 4 q - 104 q^{4} - 1972 q^{10} - 664 q^{13} + 1312 q^{16} + 4020 q^{22} - 21024 q^{25} - 11832 q^{28} + 17864 q^{34} + 61328 q^{37} + 39440 q^{40} - 26736 q^{46} - 33344 q^{49} + 17264 q^{52} + 73544 q^{58} - 212752 q^{61} + 38272 q^{64} - 100572 q^{70} - 122956 q^{73} - 50112 q^{76} + 217616 q^{82} + 303688 q^{85} - 337680 q^{88} + 48984 q^{94} - 54868 q^{97}+O(q^{100}) $ 4 * q - 104 * q^4 - 1972 * q^10 - 664 * q^13 + 1312 * q^16 + 4020 * q^22 - 21024 * q^25 - 11832 * q^28 + 17864 * q^34 + 61328 * q^37 + 39440 * q^40 - 26736 * q^46 - 33344 * q^49 + 17264 * q^52 + 73544 * q^58 - 212752 * q^61 + 38272 * q^64 - 100572 * q^70 - 122956 * q^73 - 50112 * q^76 + 217616 * q^82 + 303688 * q^85 - 337680 * q^88 + 48984 * q^94 - 54868 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.73205	−	5.38516i	0.306186	−	0.951972i
$2$	1.73205	−	5.38516i	0.306186	−	0.951972i
$3$		0			0
$3$		0			0
$4$	−26.0000	−	18.6548i	−0.812500	−	0.582961i
$5$		−	91.5478i		−	1.63766i	−0.574038	−	0.818828i	$-0.694624\pi$
$5$		−	91.5478i		−	1.63766i	0.574038	−	0.818828i	$-0.305376\pi$
$6$		0			0
$7$		−	158.565i		−	1.22310i	−0.791204	−	0.611552i	$-0.790545\pi$
$7$		−	158.565i		−	1.22310i	0.791204	−	0.611552i	$-0.209455\pi$
$8$	−145.492	+	107.703i	−0.803739	+	0.594982i
$9$		0			0
$10$	−493.000	−	158.565i	−1.55900	−	0.501428i
$11$	580.237			1.44585			0.722926	−	0.690926i	$-0.242797\pi$
$11$	580.237			1.44585			0.722926	+	0.690926i	$0.242797\pi$
$12$		0			0
$13$	−166.000			−0.272427			−0.136213	−	0.990680i	$-0.543493\pi$
$13$	−166.000			−0.272427			−0.136213	+	0.990680i	$0.543493\pi$
$14$	−853.901	−	274.643i	−1.16436	−	0.374498i
$15$		0			0
$16$	328.000	+	970.047i	0.320312	+	0.947312i
$17$			829.315i			0.695981i	0.937498	+	0.347991i	$0.113136\pi$
$17$			829.315i			0.695981i	−0.937498	+	0.347991i	$0.886864\pi$
$18$		0			0
$19$		−	671.571i		−	0.426784i	−0.976967	−	0.213392i	$-0.931549\pi$
$19$		−	671.571i		−	0.426784i	0.976967	−	0.213392i	$-0.0684511\pi$
$20$	−1707.80	+	2380.24i	−0.954690	+	1.33060i
$21$		0			0
$22$	1005.00	−	3124.67i	0.442700	−	1.37641i
$23$	−3859.01			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$23$	−3859.01			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$24$		0			0
$25$	−5256.00			−1.68192
$26$	−287.520	+	893.937i	−0.0834133	+	0.259343i
$27$		0			0
$28$	−2958.00	+	4122.70i	−0.713022	+	0.993772i
$29$			3414.19i			0.753864i	0.926241	+	0.376932i	$0.123021\pi$
$29$			3414.19i			0.753864i	−0.926241	+	0.376932i	$0.876979\pi$
$30$		0			0
$31$		−	6333.29i		−	1.18366i	−0.806065	−	0.591828i	$-0.798407\pi$
$31$		−	6333.29i		−	1.18366i	0.806065	−	0.591828i	$-0.201593\pi$
$32$	5791.98	−	86.1626i	0.999889	−	0.0148746i
$33$		0			0
$34$	4466.00	+	1436.42i	0.662554	+	0.213100i
$35$	−14516.3			−2.00302
$36$		0			0
$37$	15332.0			1.84117			0.920586	−	0.390539i	$-0.127711\pi$
$37$	15332.0			1.84117			0.920586	+	0.390539i	$0.127711\pi$
$38$	−3616.52	−	1163.20i	−0.406286	−	0.130675i
$39$		0			0
$40$	9860.00	+	13319.5i	0.974377	+	1.31625i
$41$			10102.6i			0.938582i	0.883044	+	0.469291i	$0.155490\pi$
$41$			10102.6i			0.938582i	−0.883044	+	0.469291i	$0.844510\pi$
$42$		0			0
$43$			3003.42i			0.247710i	0.992300	+	0.123855i	$0.0395258\pi$
$43$			3003.42i			0.247710i	−0.992300	+	0.123855i	$0.960474\pi$
$44$	−15086.2	−	10824.2i	−1.17475	−	0.842875i
$45$		0			0
$46$	−6684.00	+	20781.4i	−0.465738	+	1.44804i
$47$	7070.23			0.466862			0.233431	−	0.972373i	$-0.425005\pi$
$47$	7070.23			0.466862			0.233431	+	0.972373i	$0.425005\pi$
$48$		0			0
$49$	−8336.00			−0.495984
$50$	−9103.66	+	28304.4i	−0.514981	+	1.60114i
$51$		0			0
$52$	4316.00	+	3096.69i	0.221347	+	0.158814i
$53$		−	17281.0i		−	0.845043i	−0.906353	−	0.422522i	$-0.861145\pi$
$53$		−	17281.0i		−	0.845043i	0.906353	−	0.422522i	$-0.138855\pi$
$54$		0			0
$55$		−	53119.4i		−	2.36781i
$56$	17078.0	+	23070.0i	0.727725	+	0.983056i
$57$		0			0
$58$	18386.0	+	5913.56i	0.717658	+	0.230823i
$59$	28429.9			1.06327			0.531637	−	0.846972i	$-0.321577\pi$
$59$	28429.9			1.06327			0.531637	+	0.846972i	$0.321577\pi$
$60$		0			0
$61$	−53188.0			−1.83016			−0.915080	−	0.403272i	$-0.867873\pi$
$61$	−53188.0			−1.83016			−0.915080	+	0.403272i	$0.867873\pi$
$62$	−34105.8	−	10969.6i	−1.12681	−	0.362419i
$63$		0			0
$64$	9568.00	−	31340.0i	0.291992	−	0.956421i
$65$			15196.9i			0.446141i
$66$		0			0
$67$		−	41059.1i		−	1.11744i	−0.829358	−	0.558718i	$-0.811293\pi$
$67$		−	41059.1i		−	1.11744i	0.829358	−	0.558718i	$-0.188707\pi$
$68$	15470.7	−	21562.2i	0.405730	−	0.565485i
$69$		0			0
$70$	−25143.0	+	78172.8i	−0.613299	+	1.90682i
$71$	26822.5			0.631472			0.315736	−	0.948847i	$-0.397749\pi$
$71$	26822.5			0.631472			0.315736	+	0.948847i	$0.397749\pi$
$72$		0			0
$73$	−30739.0			−0.675123			−0.337561	−	0.941304i	$-0.609602\pi$
$73$	−30739.0			−0.675123			−0.337561	+	0.941304i	$0.609602\pi$
$74$	26555.8	−	82565.3i	0.563742	−	1.75274i
$75$		0			0
$76$	−12528.0	+	17460.9i	−0.248799	+	0.346762i
$77$		−	92005.5i		−	1.76843i
$78$		0			0
$79$		−	70197.9i		−	1.26548i	−0.774363	−	0.632741i	$-0.781930\pi$
$79$		−	70197.9i		−	1.26548i	0.774363	−	0.632741i	$-0.218070\pi$
$80$	88805.7	−	30027.7i	1.55137	−	0.524562i
$81$		0			0
$82$	54404.0	+	17498.2i	0.893503	+	0.287381i
$83$	−11402.1			−0.181673			−0.0908363	−	0.995866i	$-0.528954\pi$
$83$	−11402.1			−0.181673			−0.0908363	+	0.995866i	$0.528954\pi$
$84$		0			0
$85$	75922.0			1.13978
$86$	16173.9	+	5202.07i	0.235813	+	0.0758455i
$87$		0			0
$88$	−84420.0	+	62493.4i	−1.16209	+	0.860256i
$89$			68682.4i			0.919116i	0.888148	+	0.459558i	$0.151992\pi$
$89$			68682.4i			0.919116i	−0.888148	+	0.459558i	$0.848008\pi$
$90$		0			0
$91$			26321.9i			0.333206i
$92$	100334.	+	71988.9i	1.23589	+	0.886739i
$93$		0			0
$94$	12246.0	−	38074.4i	0.142947	−	0.444440i
$95$	−61480.9			−0.698926
$96$		0			0
$97$	−13717.0			−0.148023			−0.0740116	−	0.997257i	$-0.523580\pi$
$97$	−13717.0			−0.148023			−0.0740116	+	0.997257i	$0.523580\pi$
$98$	−14438.4	+	44890.7i	−0.151863	+	0.472163i
$99$		0			0
$100$	136656.	+	98049.4i	1.36656	+	0.980494i
$101$		−	8492.40i		−	0.0828376i	−0.999142	−	0.0414188i	$-0.986812\pi$
$101$		−	8492.40i		−	0.0828376i	0.999142	−	0.0414188i	$-0.0131878\pi$
$102$		0			0
$103$		−	167986.i		−	1.56020i	−0.625655	−	0.780100i	$-0.715168\pi$
$103$		−	167986.i		−	1.56020i	0.625655	−	0.780100i	$-0.284832\pi$
$104$	24151.7	−	17878.7i	0.218960	−	0.162089i
$105$		0			0
$106$	−93061.0	−	29931.6i	−0.804457	−	0.258741i
$107$	108875.			0.919324			0.459662	−	0.888094i	$-0.347971\pi$
$107$	108875.			0.919324			0.459662	+	0.888094i	$0.347971\pi$
$108$		0			0
$109$	−87628.0			−0.706442			−0.353221	−	0.935540i	$-0.614914\pi$
$109$	−87628.0			−0.706442			−0.353221	+	0.935540i	$0.614914\pi$
$110$	−286057.	−	92005.5i	−2.25409	−	0.724990i
$111$		0			0
$112$	153816.	−	52009.5i	1.15866	−	0.391776i
$113$		−	98139.2i		−	0.723014i	−0.932369	−	0.361507i	$-0.882262\pi$
$113$		−	98139.2i		−	0.723014i	0.932369	−	0.361507i	$-0.117738\pi$
$114$		0			0
$115$			353284.i			2.49103i
$116$	63691.0	−	88769.1i	0.439474	−	0.612515i
$117$		0			0
$118$	49242.0	−	153100.i	0.325560	−	1.01221i
$119$	131501.			0.851257
$120$		0			0
$121$	175624.			1.09049
$122$	−92124.3	+	286426.i	−0.560370	+	1.74226i
$123$		0			0
$124$	−118146.	+	164666.i	−0.690025	+	0.961720i
$125$			195088.i			1.11675i
$126$		0			0
$127$			6240.02i			0.0343302i	0.999853	+	0.0171651i	$0.00546409\pi$
$127$			6240.02i			0.0343302i	−0.999853	+	0.0171651i	$0.994536\pi$
$128$	−152199.	−	105808.i	−0.821081	−	0.570811i
$129$		0			0
$130$	81838.0	+	26321.9i	0.424714	+	0.136602i
$131$	−177727.			−0.904849			−0.452425	−	0.891803i	$-0.649441\pi$
$131$	−177727.			−0.904849			−0.452425	+	0.891803i	$0.649441\pi$
$132$		0			0
$133$	−106488.			−0.522001
$134$	−221110.	−	71116.5i	−1.06377	−	0.342144i
$135$		0			0
$136$	−89320.0	−	120659.i	−0.414096	−	0.559387i
$137$		−	23339.3i		−	0.106240i	−0.998588	−	0.0531198i	$-0.983083\pi$
$137$		−	23339.3i		−	0.106240i	0.998588	−	0.0531198i	$-0.0169165\pi$
$138$		0			0
$139$			209717.i			0.920653i	0.887750	+	0.460327i	$0.152268\pi$
$139$			209717.i			0.920653i	−0.887750	+	0.460327i	$0.847732\pi$
$140$	377424.	+	270798.i	1.62746	+	1.16769i
$141$		0			0
$142$	46458.0	−	144444.i	0.193348	−	0.601143i
$143$	−96319.3			−0.393889
$144$		0			0
$145$	312562.			1.23457
$146$	−53241.5	+	165535.i	−0.206713	+	0.642697i
$147$		0			0
$148$	−398632.	−	286015.i	−1.49595	−	1.07333i
$149$		−	186591.i		−	0.688532i	−0.938872	−	0.344266i	$-0.888128\pi$
$149$		−	186591.i		−	0.688532i	0.938872	−	0.344266i	$-0.111872\pi$
$150$		0			0
$151$		−	145890.i		−	0.520693i	−0.965515	−	0.260347i	$-0.916163\pi$
$151$		−	145890.i		−	0.520693i	0.965515	−	0.260347i	$-0.0838368\pi$
$152$	72330.4	+	97708.4i	0.253929	+	0.343023i
$153$		0			0
$154$	−495465.	−	159358.i	−1.68349	−	0.541468i
$155$	−579799.			−1.93842
$156$		0			0
$157$	−223132.			−0.722458			−0.361229	−	0.932477i	$-0.617643\pi$
$157$	−223132.			−0.722458			−0.361229	+	0.932477i	$0.617643\pi$
$158$	−378027.	−	121586.i	−1.20470	−	0.387473i
$159$		0			0
$160$	−7888.00	−	530243.i	−0.0243594	−	1.63748i
$161$			611906.i			1.86046i
$162$		0			0
$163$			88927.2i			0.262160i	0.991372	+	0.131080i	$0.0418444\pi$
$163$			88927.2i			0.262160i	−0.991372	+	0.131080i	$0.958156\pi$
$164$	188461.	−	262667.i	0.547157	−	0.762598i
$165$		0			0
$166$	−19749.0	+	61402.1i	−0.0556256	+	0.172947i
$167$	−309029.			−0.857449			−0.428724	−	0.903435i	$-0.641037\pi$
$167$	−309029.			−0.857449			−0.428724	+	0.903435i	$0.641037\pi$
$168$		0			0
$169$	−343737.			−0.925784
$170$	131501.	−	408852.i	0.348984	−	1.08504i
$171$		0			0
$172$	56028.0	−	78088.8i	0.144406	−	0.201265i
$173$			772238.i			1.96172i	0.194727	+	0.980858i	$0.437618\pi$
$173$			772238.i			1.96172i	−0.194727	+	0.980858i	$0.562382\pi$
$174$		0			0
$175$			833420.i			2.05716i
$176$	190318.	+	562857.i	0.463124	+	1.36967i
$177$		0			0
$178$	369866.	+	118961.i	0.874973	+	0.281421i
$179$	302910.			0.706611			0.353306	−	0.935508i	$-0.385058\pi$
$179$	302910.			0.706611			0.353306	+	0.935508i	$0.385058\pi$
$180$		0			0
$181$	719552.			1.63255			0.816274	−	0.577665i	$-0.196036\pi$
$181$	719552.			1.63255			0.816274	+	0.577665i	$0.196036\pi$
$182$	141748.	+	45590.8i	0.317203	+	0.102023i
$183$		0			0
$184$	561456.	−	415628.i	1.22256	−	0.905024i
$185$		−	1.40361e6i		−	3.01521i
$186$		0			0
$187$			481199.i			1.00629i
$188$	−183826.	−	131893.i	−0.379326	−	0.272163i
$189$		0			0
$190$	−106488.	+	331085.i	−0.214001	+	0.665357i
$191$	970416.			1.92475			0.962376	−	0.271723i	$-0.0875934\pi$
$191$	970416.			1.92475			0.962376	+	0.271723i	$0.0875934\pi$
$192$		0			0
$193$	−100561.			−0.194328			−0.0971642	−	0.995268i	$-0.530977\pi$
$193$	−100561.			−0.194328			−0.0971642	+	0.995268i	$0.530977\pi$
$194$	−23758.5	+	73868.3i	−0.0453227	+	0.140914i
$195$		0			0
$196$	216736.	+	155506.i	0.402987	+	0.289139i
$197$		−	453932.i		−	0.833345i	−0.909057	−	0.416673i	$-0.863196\pi$
$197$		−	453932.i		−	0.833345i	0.909057	−	0.416673i	$-0.136804\pi$
$198$		0			0
$199$			529674.i			0.948147i	0.880485	+	0.474074i	$0.157217\pi$
$199$			529674.i			0.948147i	−0.880485	+	0.474074i	$0.842783\pi$
$200$	764707.	−	566089.i	1.35182	−	1.00071i
$201$		0			0
$202$	−45733.0	−	14709.3i	−0.0788590	−	0.0253637i
$203$	541373.			0.922055
$204$		0			0
$205$	924868.			1.53708
$206$	−904633.	−	290960.i	−1.48527	−	0.477712i
$207$		0			0
$208$	−54448.0	−	161028.i	−0.0872617	−	0.258073i
$209$		−	389671.i		−	0.617066i
$210$		0			0
$211$		−	823831.i		−	1.27389i	−0.770909	−	0.636945i	$-0.780198\pi$
$211$		−	823831.i		−	1.27389i	0.770909	−	0.636945i	$-0.219802\pi$
$212$	−322373.	+	449306.i	−0.492628	+	0.686598i
$213$		0			0
$214$	188577.	−	586310.i	0.281484	−	0.875170i
$215$	274956.			0.405665
$216$		0			0
$217$	−1.00424e6			−1.44773
$218$	−151776.	+	471891.i	−0.216303	+	0.672513i
$219$		0			0
$220$	−990930.	+	1.38111e6i	−1.38034	+	1.92384i
$221$		−	137666.i		−	0.189604i
$222$		0			0
$223$		−	278385.i		−	0.374873i	−0.982277	−	0.187436i	$-0.939982\pi$
$223$		−	278385.i		−	0.374873i	0.982277	−	0.187436i	$-0.0600178\pi$
$224$	−13662.4	−	918408.i	−0.0181931	−	1.22297i
$225$		0			0
$226$	−528496.	−	169982.i	−0.688289	−	0.221377i
$227$	309112.			0.398154			0.199077	−	0.979984i	$-0.436206\pi$
$227$	309112.			0.398154			0.199077	+	0.979984i	$0.436206\pi$
$228$		0			0
$229$	140882.			0.177528			0.0887640	−	0.996053i	$-0.471708\pi$
$229$	140882.			0.177528			0.0887640	+	0.996053i	$0.471708\pi$
$230$	1.90249e6	+	611906.i	2.37139	+	0.762719i
$231$		0			0
$232$	−367720.	−	496739.i	−0.448536	−	0.605910i
$233$			886021.i			1.06919i	0.845109	+	0.534594i	$0.179536\pi$
$233$			886021.i			1.06919i	−0.845109	+	0.534594i	$0.820464\pi$
$234$		0			0
$235$		−	647264.i		−	0.764561i
$236$	−739177.	−	530353.i	−0.863910	−	0.619847i
$237$		0			0
$238$	227766.	−	708153.i	0.260643	−	0.810373i
$239$	210368.			0.238224			0.119112	−	0.992881i	$-0.461995\pi$
$239$	210368.			0.238224			0.119112	+	0.992881i	$0.461995\pi$
$240$		0			0
$241$	1.40339e6			1.55645			0.778226	−	0.627984i	$-0.216120\pi$
$241$	1.40339e6			1.55645			0.778226	+	0.627984i	$0.216120\pi$
$242$	304190.	−	945764.i	0.333892	−	1.03811i
$243$		0			0
$244$	1.38289e6	+	992209.i	1.48701	+	1.06691i
$245$			763142.i			0.812251i
$246$		0			0
$247$			111481.i			0.116267i
$248$	682116.	+	921445.i	0.704254	+	0.951350i
$249$		0			0
$250$	1.05058e6	+	337903.i	1.06312	+	0.341934i
$251$	−1.37851e6			−1.38110			−0.690550	−	0.723285i	$-0.742631\pi$
$251$	−1.37851e6			−1.38110			−0.690550	+	0.723285i	$0.742631\pi$
$252$		0			0
$253$	−2.23914e6			−2.19928
$254$	33603.5	+	10808.0i	0.0326814	+	0.0105114i
$255$		0			0
$256$	−833408.	+	636351.i	−0.794800	+	0.606872i
$257$		−	466581.i		−	0.440651i	−0.975426	−	0.220325i	$-0.929288\pi$
$257$		−	466581.i		−	0.440651i	0.975426	−	0.220325i	$-0.0707119\pi$
$258$		0			0
$259$		−	2.43113e6i		−	2.25195i
$260$	283495.	−	395120.i	0.260083	−	0.362490i
$261$		0			0
$262$	−307833.	+	957092.i	−0.277052	+	0.861391i
$263$	−209308.			−0.186593			−0.0932967	−	0.995638i	$-0.529741\pi$
$263$	−209308.			−0.186593			−0.0932967	+	0.995638i	$0.529741\pi$
$264$		0			0
$265$	−1.58204e6			−1.38389
$266$	−184443.	+	573455.i	−0.159830	+	0.496930i
$267$		0			0
$268$	−765948.	+	1.06754e6i	−0.651422	+	0.907917i
$269$		−	566035.i		−	0.476938i	−0.971150	−	0.238469i	$-0.923354\pi$
$269$		−	566035.i		−	0.476938i	0.971150	−	0.238469i	$-0.0766456\pi$
$270$		0			0
$271$			909503.i			0.752283i	0.926562	+	0.376141i	$0.122749\pi$
$271$			909503.i			0.752283i	−0.926562	+	0.376141i	$0.877251\pi$
$272$	−804475.	+	272015.i	−0.659311	+	0.222931i
$273$		0			0
$274$	−125686.	−	40424.9i	−0.101137	−	0.0325291i
$275$	−3.04973e6			−2.43181
$276$		0			0
$277$	−808732.			−0.633294			−0.316647	−	0.948543i	$-0.602557\pi$
$277$	−808732.			−0.633294			−0.316647	+	0.948543i	$0.602557\pi$
$278$	1.12936e6	+	363240.i	0.876436	+	0.281891i
$279$		0			0
$280$	2.11201e6	−	1.56346e6i	1.60991	−	1.19176i
$281$		−	370359.i		−	0.279806i	−0.990165	−	0.139903i	$-0.955321\pi$
$281$		−	370359.i		−	0.279806i	0.990165	−	0.139903i	$-0.0446791\pi$
$282$		0			0
$283$		−	866028.i		−	0.642786i	−0.946946	−	0.321393i	$-0.895849\pi$
$283$		−	866028.i		−	0.642786i	0.946946	−	0.321393i	$-0.104151\pi$
$284$	−697386.	−	500368.i	−0.513071	−	0.368124i
$285$		0			0
$286$	−166830.	+	518696.i	−0.120603	+	0.374971i
$287$	1.60192e6			1.14798
$288$		0			0
$289$	732093.			0.515610
$290$	541373.	−	1.68320e6i	0.378009	−	1.17528i
$291$		0			0
$292$	799214.	+	573429.i	0.548537	+	0.393570i
$293$		−	965980.i		−	0.657354i	−0.944442	−	0.328677i	$-0.893397\pi$
$293$		−	965980.i		−	0.657354i	0.944442	−	0.328677i	$-0.106603\pi$
$294$		0			0
$295$		−	2.60269e6i		−	1.74128i
$296$	−2.23069e6	+	1.65131e6i	−1.47982	+	1.09547i
$297$		0			0
$298$	−1.00482e6	−	323184.i	−0.655463	−	0.210819i
$299$	640596.			0.414387
$300$		0			0
$301$	476238.			0.302976
$302$	−785639.	−	252688.i	−0.495685	−	0.159429i
$303$		0			0
$304$	651456.	−	220275.i	0.404298	−	0.136704i
$305$			4.86924e6i			2.99717i
$306$		0			0
$307$		−	2.39913e6i		−	1.45281i	−0.687268	−	0.726404i	$-0.741190\pi$
$307$		−	2.39913e6i		−	1.45281i	0.687268	−	0.726404i	$-0.258810\pi$
$308$	−1.71634e6	+	2.39214e6i	−1.03092	+	1.43685i
$309$		0			0
$310$	−1.00424e6	+	3.12231e6i	−0.593518	+	1.84532i
$311$	1.35847e6			0.796432			0.398216	−	0.917292i	$-0.369630\pi$
$311$	1.35847e6			0.796432			0.398216	+	0.917292i	$0.369630\pi$
$312$		0			0
$313$	1.55076e6			0.894716			0.447358	−	0.894355i	$-0.352365\pi$
$313$	1.55076e6			0.894716			0.447358	+	0.894355i	$0.352365\pi$
$314$	−386476.	+	1.20160e6i	−0.221207	+	0.687760i
$315$		0			0
$316$	−1.30952e6	+	1.82514e6i	−0.737727	+	1.02820i
$317$			1.13244e6i			0.632947i	0.948601	+	0.316474i	$0.102499\pi$
$317$			1.13244e6i			0.632947i	−0.948601	+	0.316474i	$0.897501\pi$
$318$		0			0
$319$			1.98104e6i			1.08998i
$320$	−2.86911e6	−	875929.i	−1.56629	−	0.478183i
$321$		0			0
$322$	3.29521e6	+	1.05985e6i	1.77110	+	0.569646i
$323$	556944.			0.297034
$324$		0			0
$325$	872496.			0.458200
$326$	478888.	+	154026.i	0.249569	+	0.0802697i
$327$		0			0
$328$	−1.08808e6	−	1.46985e6i	−0.558440	−	0.754375i
$329$		−	1.12109e6i		−	0.571021i
$330$		0			0
$331$			3.69262e6i			1.85253i	0.376878	+	0.926263i	$0.376997\pi$
$331$			3.69262e6i			1.85253i	−0.376878	+	0.926263i	$0.623003\pi$
$332$	296454.	+	212703.i	0.147609	+	0.105908i
$333$		0			0
$334$	−535254.	+	1.66417e6i	−0.262539	+	0.816267i
$335$	−3.75887e6			−1.82998
$336$		0			0
$337$	498854.			0.239276			0.119638	−	0.992818i	$-0.461827\pi$
$337$	498854.			0.239276			0.119638	+	0.992818i	$0.461827\pi$
$338$	−595370.	+	1.85108e6i	−0.283462	+	0.881320i
$339$		0			0
$340$	−1.97397e6	−	1.41631e6i	−0.926070	−	0.664446i
$341$		−	3.67481e6i		−	1.71139i
$342$		0			0
$343$		−	1.34321e6i		−	0.616464i
$344$	−323478.	−	436974.i	−0.147383	−	0.199095i
$345$		0			0
$346$	4.15863e6	+	1.33756e6i	1.86750	+	0.600650i
$347$	−547933.			−0.244289			−0.122144	−	0.992512i	$-0.538977\pi$
$347$	−547933.			−0.244289			−0.122144	+	0.992512i	$0.538977\pi$
$348$		0			0
$349$	−1.64807e6			−0.724290			−0.362145	−	0.932122i	$-0.617956\pi$
$349$	−1.64807e6			−0.724290			−0.362145	+	0.932122i	$0.617956\pi$
$350$	4.48810e6	+	1.44353e6i	1.95836	+	0.629875i
$351$		0			0
$352$	3.36072e6	−	49994.8i	1.44569	−	0.0215064i
$353$		−	1.17939e6i		−	0.503758i	−0.967759	−	0.251879i	$-0.918951\pi$
$353$		−	1.17939e6i		−	0.503758i	0.967759	−	0.251879i	$-0.0810485\pi$
$354$		0			0
$355$		−	2.45554e6i		−	1.03413i
$356$	1.28125e6	−	1.78574e6i	0.535809	−	0.746782i
$357$		0			0
$358$	524655.	−	1.63122e6i	0.216355	−	0.672674i
$359$	2.81312e6			1.15200			0.576000	−	0.817449i	$-0.304613\pi$
$359$	2.81312e6			1.15200			0.576000	+	0.817449i	$0.304613\pi$
$360$		0			0
$361$	2.02509e6			0.817855
$362$	1.24630e6	−	3.87491e6i	0.499863	−	1.55414i
$363$		0			0
$364$	491028.	−	684368.i	0.194246	−	0.270730i
$365$			2.81409e6i			1.10562i
$366$		0			0
$367$			2.94104e6i			1.13982i	0.821707	+	0.569910i	$0.193022\pi$
$367$			2.94104e6i			1.13982i	−0.821707	+	0.569910i	$0.806978\pi$
$368$	−1.26576e6	−	3.74342e6i	−0.487226	−	1.44095i
$369$		0			0
$370$	−7.55868e6	−	2.43113e6i	−2.87039	−	0.923215i
$371$	−2.74017e6			−1.03358
$372$		0			0
$373$	−2.11698e6			−0.787851			−0.393926	−	0.919142i	$-0.628883\pi$
$373$	−2.11698e6			−0.787851			−0.393926	+	0.919142i	$0.628883\pi$
$374$	2.59134e6	+	833462.i	0.957955	+	0.308111i
$375$		0			0
$376$	−1.02866e6	+	761487.i	−0.375236	+	0.277775i
$377$		−	566756.i		−	0.205373i
$378$		0			0
$379$			2.75613e6i			0.985602i	0.870142	+	0.492801i	$0.164027\pi$
$379$			2.75613e6i			0.985602i	−0.870142	+	0.492801i	$0.835973\pi$
$380$	1.59850e6	+	1.14691e6i	0.567877	+	0.407447i
$381$		0			0
$382$	1.68081e6	−	5.22585e6i	0.589332	−	1.83231i
$383$	4.51402e6			1.57241			0.786206	−	0.617964i	$-0.212042\pi$
$383$	4.51402e6			1.57241			0.786206	+	0.617964i	$0.212042\pi$
$384$		0			0
$385$	−8.42290e6			−2.89608
$386$	−174177.	+	541538.i	−0.0595007	+	0.184995i
$387$		0			0
$388$	356642.	+	255887.i	0.120269	+	0.0862918i
$389$		−	1.56097e6i		−	0.523023i	−0.965200	−	0.261511i	$-0.915779\pi$
$389$		−	1.56097e6i		−	0.523023i	0.965200	−	0.261511i	$-0.0842209\pi$
$390$		0			0
$391$		−	3.20034e6i		−	1.05865i
$392$	1.21282e6	−	897815.i	0.398641	−	0.295102i
$393$		0			0
$394$	−2.44450e6	−	786233.i	−0.793321	−	0.255159i
$395$	−6.42646e6			−2.07243
$396$		0			0
$397$	3.93330e6			1.25251			0.626255	−	0.779618i	$-0.284587\pi$
$397$	3.93330e6			1.25251			0.626255	+	0.779618i	$0.284587\pi$
$398$	2.85238e6	+	917422.i	0.902609	+	0.290310i
$399$		0			0
$400$	−1.72397e6	−	5.09857e6i	−0.538740	−	1.59330i
$401$			4.10604e6i			1.27515i	0.770387	+	0.637576i	$0.220063\pi$
$401$			4.10604e6i			1.27515i	−0.770387	+	0.637576i	$0.779937\pi$
$402$		0			0
$403$			1.05133e6i			0.322459i
$404$	−158424.	+	220803.i	−0.0482911	+	0.0673055i
$405$		0			0
$406$	937686.	−	2.91538e6i	0.282320	−	0.877770i
$407$	8.89619e6			2.66206
$408$		0			0
$409$	4.42833e6			1.30898			0.654488	−	0.756072i	$-0.272884\pi$
$409$	4.42833e6			1.30898			0.654488	+	0.756072i	$0.272884\pi$
$410$	1.60192e6	−	4.98057e6i	0.470631	−	1.46325i
$411$		0			0
$412$	−3.13374e6	+	4.36764e6i	−0.909536	+	1.26766i
$413$		−	4.50800e6i		−	1.30049i
$414$		0			0
$415$			1.04384e6i			0.297517i
$416$	−961468.	+	14303.0i	−0.272397	+	0.00405223i
$417$		0			0
$418$	−2.09844e6	−	674929.i	−0.587430	−	0.188937i
$419$	−585360.			−0.162888			−0.0814439	−	0.996678i	$-0.525953\pi$
$419$	−585360.			−0.162888			−0.0814439	+	0.996678i	$0.525953\pi$
$420$		0			0
$421$	3.61291e6			0.993463			0.496731	−	0.867904i	$-0.334533\pi$
$421$	3.61291e6			0.993463			0.496731	+	0.867904i	$0.334533\pi$
$422$	−4.43647e6	−	1.42692e6i	−1.21271	−	0.390048i
$423$		0			0
$424$	1.86122e6	+	2.51425e6i	0.502786	+	0.679194i
$425$		−	4.35888e6i		−	1.17058i
$426$		0			0
$427$			8.43378e6i			2.23848i
$428$	−2.83075e6	−	2.03104e6i	−0.746951	−	0.535930i
$429$		0			0
$430$	476238.	−	1.48068e6i	0.124209	−	0.386181i
$431$	1.66336e6			0.431314			0.215657	−	0.976469i	$-0.430811\pi$
$431$	1.66336e6			0.431314			0.215657	+	0.976469i	$0.430811\pi$
$432$		0			0
$433$	−783805.			−0.200904			−0.100452	−	0.994942i	$-0.532029\pi$
$433$	−783805.			−0.200904			−0.100452	+	0.994942i	$0.532029\pi$
$434$	−1.73940e6	+	5.40800e6i	−0.443276	+	1.37820i
$435$		0			0
$436$	2.27833e6	+	1.63468e6i	0.573984	+	0.411828i
$437$			2.59160e6i			0.649179i
$438$		0			0
$439$			1.91382e6i			0.473958i	0.971515	+	0.236979i	$0.0761572\pi$
$439$			1.91382e6i			0.473958i	−0.971515	+	0.236979i	$0.923843\pi$
$440$	5.72114e6	+	7.72847e6i	1.40880	+	1.90310i
$441$		0			0
$442$	−741356.	−	238445.i	−0.180497	−	0.0580541i
$443$	2.53916e6			0.614724			0.307362	−	0.951593i	$-0.400554\pi$
$443$	2.53916e6			0.614724			0.307362	+	0.951593i	$0.400554\pi$
$444$		0			0
$445$	6.28772e6			1.50520
$446$	−1.49915e6	−	482177.i	−0.356868	−	0.114781i
$447$		0			0
$448$	−4.96944e6	−	1.51715e6i	−1.16980	−	0.357137i
$449$		−	6.05887e6i		−	1.41833i	−0.705045	−	0.709163i	$-0.749073\pi$
$449$		−	6.05887e6i		−	1.41833i	0.705045	−	0.709163i	$-0.250927\pi$
$450$		0			0
$451$			5.86188e6i			1.35705i
$452$	−1.83076e6	+	2.55162e6i	−0.421489	+	0.587449i
$453$		0			0
$454$	535398.	−	1.66462e6i	0.121909	−	0.379032i
$455$	2.40971e6			0.545678
$456$		0			0
$457$	3.29032e6			0.736967			0.368483	−	0.929634i	$-0.379877\pi$
$457$	3.29032e6			0.736967			0.368483	+	0.929634i	$0.379877\pi$
$458$	244015.	−	758673.i	0.0543566	−	0.169002i
$459$		0			0
$460$	6.59042e6	−	9.18538e6i	1.45217	−	2.02396i
$461$			6.41710e6i			1.40633i	0.711028	+	0.703163i	$0.248230\pi$
$461$			6.41710e6i			1.40633i	−0.711028	+	0.703163i	$0.751770\pi$
$462$		0			0
$463$		−	1.34410e6i		−	0.291394i	−0.989329	−	0.145697i	$-0.953458\pi$
$463$		−	1.34410e6i		−	0.291394i	0.989329	−	0.145697i	$-0.0465424\pi$
$464$	−3.31193e6	+	1.11986e6i	−0.714145	+	0.241472i
$465$		0			0
$466$	4.77137e6	+	1.53463e6i	1.01784	+	0.327371i
$467$	−256155.			−0.0543513			−0.0271757	−	0.999631i	$-0.508651\pi$
$467$	−256155.			−0.0543513			−0.0271757	+	0.999631i	$0.508651\pi$
$468$		0			0
$469$	−6.51056e6			−1.36674
$470$	−3.48562e6	−	1.12109e6i	−0.727840	−	0.234098i
$471$		0			0
$472$	−4.13633e6	+	3.06199e6i	−0.854594	+	0.632629i
$473$			1.74269e6i			0.358153i
$474$		0			0
$475$			3.52978e6i			0.717817i
$476$	−3.41902e6	−	2.45311e6i	−0.691647	−	0.496250i
$477$		0			0
$478$	364368.	−	1.13287e6i	0.0729408	−	0.226782i
$479$	−9661.38			−0.00192398			−0.000961990	−	1.00000i	$-0.500306\pi$
$479$	−9661.38			−0.00192398			−0.000961990		1.00000i	$0.500306\pi$
$480$		0			0
$481$	−2.54511e6			−0.501585
$482$	2.43074e6	−	7.55749e6i	0.476564	−	1.48170i
$483$		0			0
$484$	−4.56622e6	−	3.27622e6i	−0.886021	−	0.635712i
$485$			1.25576e6i			0.242411i
$486$		0			0
$487$		−	7.37413e6i		−	1.40893i	−0.709740	−	0.704464i	$-0.751188\pi$
$487$		−	7.37413e6i		−	1.40893i	0.709740	−	0.704464i	$-0.248812\pi$
$488$	7.73844e6	−	5.72852e6i	1.47097	−	1.08891i
$489$		0			0
$490$	4.10965e6	+	1.32180e6i	0.773240	+	0.248700i
$491$	−4.96250e6			−0.928960			−0.464480	−	0.885584i	$-0.653759\pi$
$491$	−4.96250e6			−0.928960			−0.464480	+	0.885584i	$0.653759\pi$
$492$		0			0
$493$	−2.83144e6			−0.524675
$494$	600343.	+	193090.i	0.110683	+	0.0355995i
$495$		0			0
$496$	6.14359e6	−	2.07732e6i	1.12129	−	0.379140i
$497$		−	4.25313e6i		−	0.772356i
$498$		0			0
$499$			2.22135e6i			0.399361i	0.979861	+	0.199681i	$0.0639905\pi$
$499$			2.22135e6i			0.399361i	−0.979861	+	0.199681i	$0.936010\pi$
$500$	3.63933e6	−	5.07230e6i	0.651022	−	0.907360i
$501$		0			0
$502$	−2.38765e6	+	7.42349e6i	−0.422874	+	1.31477i
$503$	−1.01231e7			−1.78400			−0.891999	−	0.452037i	$-0.850698\pi$
$503$	−1.01231e7			−1.78400			−0.891999	+	0.452037i	$0.850698\pi$
$504$		0			0
$505$	−777461.			−0.135659
$506$	−3.87830e6	+	1.20581e7i	−0.673388	+	2.09365i
$507$		0			0
$508$	116406.	−	162240.i	0.0200132	−	0.0278933i
$509$			1.04816e7i			1.79322i	0.442819	+	0.896611i	$0.353979\pi$
$509$			1.04816e7i			1.79322i	−0.442819	+	0.896611i	$0.646021\pi$
$510$		0			0
$511$			4.87414e6i			0.825745i
$512$	1.98335e6	+	5.59023e6i	0.334368	+	0.942443i
$513$		0			0
$514$	−2.51262e6	−	808143.i	−0.419487	−	0.134921i
$515$	−1.53788e7			−2.55507
$516$		0			0
$517$	4.10241e6			0.675014
$518$	−1.30920e7	−	4.21083e6i	−2.14379	−	0.689515i
$519$		0			0
$520$	−1.63676e6	−	2.21104e6i	−0.265446	−	0.358581i
$521$			1.59021e6i			0.256661i	0.991731	+	0.128330i	$0.0409618\pi$
$521$			1.59021e6i			0.256661i	−0.991731	+	0.128330i	$0.959038\pi$
$522$		0			0
$523$			2.90818e6i			0.464909i	0.972607	+	0.232454i	$0.0746756\pi$
$523$			2.90818e6i			0.464909i	−0.972607	+	0.232454i	$0.925324\pi$
$524$	4.62091e6	+	3.31546e6i	0.735190	+	0.527492i
$525$		0			0
$526$	−362532.	+	1.12716e6i	−0.0571323	+	0.177632i
$527$	5.25230e6			0.823802
$528$		0			0
$529$	8.45561e6			1.31373
$530$	−2.74017e6	+	8.51953e6i	−0.423728	+	1.31743i
$531$		0			0
$532$	2.76869e6	+	1.98651e6i	0.424126	+	0.304306i
$533$		−	1.67703e6i		−	0.255695i
$534$		0			0
$535$		−	9.96727e6i		−	1.50554i
$536$	4.42220e6	+	5.97378e6i	0.664855	+	0.898127i
$537$		0			0
$538$	−3.04819e6	−	980401.i	−0.454032	−	0.146032i
$539$	−4.83686e6			−0.717119
$540$		0			0
$541$	1.04918e6			0.154119			0.0770596	−	0.997026i	$-0.475447\pi$
$541$	1.04918e6			0.154119			0.0770596	+	0.997026i	$0.475447\pi$
$542$	4.89783e6	+	1.57531e6i	0.716152	+	0.230339i
$543$		0			0
$544$	71456.0	+	4.80338e6i	0.0103524	+	0.695904i
$545$			8.02215e6i			1.15691i
$546$		0			0
$547$		−	1.32733e7i		−	1.89675i	−0.317150	−	0.948375i	$-0.602726\pi$
$547$		−	1.32733e7i		−	1.89675i	0.317150	−	0.948375i	$-0.397274\pi$
$548$	−435389.	+	606822.i	−0.0619336	+	0.0863197i
$549$		0			0
$550$	−5.28228e6	+	1.64233e7i	−0.744586	+	2.31501i
$551$	2.29288e6			0.321737
$552$		0			0
$553$	−1.11310e7			−1.54782
$554$	−1.40076e6	+	4.35516e6i	−0.193906	+	0.602878i
$555$		0			0
$556$	3.91222e6	−	5.45264e6i	0.536705	−	0.748031i
$557$		−	7.30021e6i		−	0.997005i	−0.866888	−	0.498503i	$-0.833883\pi$
$557$		−	7.30021e6i		−	0.997005i	0.866888	−	0.498503i	$-0.166117\pi$
$558$		0			0
$559$		−	498567.i		−	0.0674830i
$560$	−4.76135e6	−	1.40815e7i	−0.641594	−	1.89749i
$561$		0			0
$562$	−1.99445e6	−	641481.i	−0.266368	−	0.0856728i
$563$	−262653.			−0.0349230			−0.0174615	−	0.999848i	$-0.505558\pi$
$563$	−262653.			−0.0349230			−0.0174615	+	0.999848i	$0.505558\pi$
$564$		0			0
$565$	−8.98443e6			−1.18405
$566$	−4.66371e6	−	1.50001e6i	−0.611914	−	0.196812i
$567$		0			0
$568$	−3.90247e6	+	2.88888e6i	−0.507538	+	0.375715i
$569$			4.86509e6i			0.629956i	0.949099	+	0.314978i	$0.101997\pi$
$569$			4.86509e6i			0.629956i	−0.949099	+	0.314978i	$0.898003\pi$
$570$		0			0
$571$		−	3.80253e6i		−	0.488070i	−0.969766	−	0.244035i	$-0.921529\pi$
$571$		−	3.80253e6i		−	0.488070i	0.969766	−	0.244035i	$-0.0784712\pi$
$572$	2.50430e6	+	1.79681e6i	0.320035	+	0.229622i
$573$		0			0
$574$	2.77460e6	−	8.62659e6i	0.351497	−	1.09285i
$575$	2.02830e7			2.55836
$576$		0			0
$577$	−123970.			−0.0155016			−0.00775081	−	0.999970i	$-0.502467\pi$
$577$	−123970.			−0.0155016			−0.00775081	+	0.999970i	$0.502467\pi$
$578$	1.26802e6	−	3.94244e6i	0.157873	−	0.490846i
$579$		0			0
$580$	−8.12661e6	−	5.83077e6i	−1.00309	−	0.719707i
$581$			1.80798e6i			0.222204i
$582$		0			0
$583$		−	1.00271e7i		−	1.22181i
$584$	4.47229e6	−	3.31069e6i	0.542622	−	0.401686i
$585$		0			0
$586$	−5.20196e6	−	1.67313e6i	−0.625782	−	0.201273i
$587$	−5.68744e6			−0.681274			−0.340637	−	0.940195i	$-0.610643\pi$
$587$	−5.68744e6			−0.681274			−0.340637	+	0.940195i	$0.610643\pi$
$588$		0			0
$589$	−4.25326e6			−0.505165
$590$	−1.40159e7	−	4.50800e6i	−1.65765	−	0.533155i
$591$		0			0
$592$	5.02890e6	+	1.48728e7i	0.589751	+	1.74416i
$593$		−	8.77471e6i		−	1.02470i	−0.858777	−	0.512349i	$-0.828775\pi$
$593$		−	8.77471e6i		−	1.02470i	0.858777	−	0.512349i	$-0.171225\pi$
$594$		0			0
$595$		−	1.20386e7i		−	1.39407i
$596$	−3.48080e6	+	4.85135e6i	−0.401387	+	0.559432i
$597$		0			0
$598$	1.10954e6	−	3.44971e6i	0.126880	−	0.394484i
$599$	1.28831e7			1.46707			0.733537	−	0.679649i	$-0.237868\pi$
$599$	1.28831e7			1.46707			0.733537	+	0.679649i	$0.237868\pi$
$600$		0			0
$601$	−2.62470e6			−0.296410			−0.148205	−	0.988957i	$-0.547350\pi$
$601$	−2.62470e6			−0.296410			−0.148205	+	0.988957i	$0.547350\pi$
$602$	824868.	−	2.56462e6i	0.0927670	−	0.288424i
$603$		0			0
$604$	−2.72153e6	+	3.79313e6i	−0.303544	+	0.423063i
$605$		−	1.60780e7i		−	1.78584i
$606$		0			0
$607$			5.78348e6i			0.637114i	0.947904	+	0.318557i	$0.103198\pi$
$607$			5.78348e6i			0.637114i	−0.947904	+	0.318557i	$0.896802\pi$
$608$	−57864.4	−	3.88973e6i	−0.00634822	−	0.426737i
$609$		0			0
$610$	2.62217e7	+	8.43378e6i	2.85322	+	0.917693i
$611$	−1.17366e6			−0.127186
$612$		0			0
$613$	−1.67367e6			−0.179895			−0.0899476	−	0.995946i	$-0.528670\pi$
$613$	−1.67367e6			−0.179895			−0.0899476	+	0.995946i	$0.528670\pi$
$614$	−1.29197e7	−	4.15542e6i	−1.38303	−	0.444830i
$615$		0			0
$616$	9.90930e6	+	1.33861e7i	1.05218	+	1.42135i
$617$		−	8.52976e6i		−	0.902036i	−0.892515	−	0.451018i	$-0.851061\pi$
$617$		−	8.52976e6i		−	0.902036i	0.892515	−	0.451018i	$-0.148939\pi$
$618$		0			0
$619$		−	9.46604e6i		−	0.992983i	−0.868042	−	0.496491i	$-0.834621\pi$
$619$		−	9.46604e6i		−	0.992983i	0.868042	−	0.496491i	$-0.165379\pi$
$620$	1.50748e7	+	1.08160e7i	1.57497	+	1.13002i
$621$		0			0
$622$	2.35294e6	−	7.31558e6i	0.243856	−	0.758180i
$623$	1.08907e7			1.12417
$624$		0			0
$625$	1.43491e6			0.146935
$626$	2.68600e6	−	8.35113e6i	0.273950	−	0.851744i
$627$		0			0
$628$	5.80143e6	+	4.16247e6i	0.586997	+	0.421165i
$629$			1.27151e7i			1.28142i
$630$		0			0
$631$			1.04052e7i			1.04035i	0.854060	+	0.520174i	$0.174133\pi$
$631$			1.04052e7i			1.04035i	−0.854060	+	0.520174i	$0.825867\pi$
$632$	7.56054e6	+	1.02132e7i	0.752940	+	1.01712i
$633$		0			0
$634$	6.09838e6	+	1.96145e6i	0.602548	+	0.193800i
$635$	571260.			0.0562211
$636$		0			0
$637$	1.38378e6			0.135119
$638$	1.06682e7	+	3.43127e6i	1.03763	+	0.333736i
$639$		0			0
$640$	−9.68646e6	+	1.39335e7i	−0.934793	+	1.34465i
$641$		−	360957.i		−	0.0346985i	−0.999849	−	0.0173492i	$-0.994477\pi$
$641$		−	360957.i		−	0.0346985i	0.999849	−	0.0173492i	$-0.00552271\pi$
$642$		0			0
$643$		−	557777.i		−	0.0532027i	−0.999646	−	0.0266013i	$-0.991532\pi$
$643$		−	557777.i		−	0.0532027i	0.999646	−	0.0266013i	$-0.00846847\pi$
$644$	1.14149e7	−	1.59095e7i	1.08457	−	1.51162i
$645$		0			0
$646$	964656.	−	2.99924e6i	0.0909476	−	0.282768i
$647$	6.76712e6			0.635540			0.317770	−	0.948168i	$-0.397066\pi$
$647$	6.76712e6			0.635540			0.317770	+	0.948168i	$0.397066\pi$
$648$		0			0
$649$	1.64961e7			1.53734
$650$	1.51121e6	−	4.69853e6i	0.140295	−	0.436193i
$651$		0			0
$652$	1.65892e6	−	2.31211e6i	0.152829	−	0.213005i
$653$		−	9.16397e6i		−	0.841009i	−0.907290	−	0.420505i	$-0.861853\pi$
$653$		−	9.16397e6i		−	0.841009i	0.907290	−	0.420505i	$-0.138147\pi$
$654$		0			0
$655$			1.62706e7i			1.48183i
$656$	−9.79997e6	+	3.31364e6i	−0.889130	+	0.300640i
$657$		0			0
$658$	−6.03728e6	−	1.94179e6i	−0.543596	−	0.174839i
$659$	−3.33571e6			−0.299209			−0.149605	−	0.988746i	$-0.547800\pi$
$659$	−3.33571e6			−0.299209			−0.149605	+	0.988746i	$0.547800\pi$
$660$		0			0
$661$	−1.08460e7			−0.965528			−0.482764	−	0.875750i	$-0.660367\pi$
$661$	−1.08460e7			−0.965528			−0.482764	+	0.875750i	$0.660367\pi$
$662$	1.98853e7	+	6.39580e6i	1.76355	+	0.567218i
$663$		0			0
$664$	1.65892e6	−	1.22804e6i	0.146017	−	0.108092i
$665$			9.74874e6i			0.854859i
$666$		0			0
$667$		−	1.31754e7i		−	1.14670i
$668$	8.03476e6	+	5.76486e6i	0.696677	+	0.499859i
$669$		0			0
$670$	−6.51056e6	+	2.02421e7i	−0.560314	+	1.74209i
$671$	−3.08616e7			−2.64614
$672$		0			0
$673$	1.59743e7			1.35952			0.679759	−	0.733436i	$-0.262084\pi$
$673$	1.59743e7			1.35952			0.679759	+	0.733436i	$0.262084\pi$
$674$	864040.	−	2.68641e6i	0.0732629	−	0.227784i
$675$		0			0
$676$	8.93716e6	+	6.41233e6i	0.752199	+	0.539696i
$677$		−	587812.i		−	0.0492909i	−0.999696	−	0.0246455i	$-0.992154\pi$
$677$		−	587812.i		−	0.0492909i	0.999696	−	0.0246455i	$-0.00784569\pi$
$678$		0			0
$679$			2.17504e6i			0.181048i
$680$	−1.10461e7	+	8.17705e6i	−0.916084	+	0.678148i
$681$		0			0
$682$	−1.97895e7	−	6.36496e6i	−1.62919	−	0.524004i
$683$	−8.64998e6			−0.709518			−0.354759	−	0.934958i	$-0.615437\pi$
$683$	−8.64998e6			−0.709518			−0.354759	+	0.934958i	$0.615437\pi$
$684$		0			0
$685$	−2.13666e6			−0.173984
$686$	−7.23340e6	−	2.32650e6i	−0.586857	−	0.188753i
$687$		0			0
$688$	−2.91346e6	+	985120.i	−0.234659	+	0.0793448i
$689$			2.86864e6i			0.230212i
$690$		0			0
$691$		−	1.81129e7i		−	1.44309i	−0.692368	−	0.721545i	$-0.743432\pi$
$691$		−	1.81129e7i		−	1.44309i	0.692368	−	0.721545i	$-0.256568\pi$
$692$	1.44059e7	−	2.00782e7i	1.14360	−	1.59389i
$693$		0			0
$694$	−949047.	+	2.95071e6i	−0.0747978	+	0.232556i
$695$	1.91991e7			1.50771
$696$		0			0
$697$	−8.37822e6			−0.653235
$698$	−2.85454e6	+	8.87514e6i	−0.221768	+	0.689504i
$699$		0			0
$700$	1.55472e7	−	2.16689e7i	1.19925	−	1.67145i
$701$			3.00066e6i			0.230633i	0.993329	+	0.115317i	$0.0367883\pi$
$701$			3.00066e6i			0.230633i	−0.993329	+	0.115317i	$0.963212\pi$
$702$		0			0
$703$		−	1.02965e7i		−	0.785783i
$704$	5.55171e6	−	1.81846e7i	0.422177	−	1.38284i
$705$		0			0
$706$	−6.35123e6	−	2.04277e6i	−0.479564	−	0.154244i
$707$	−1.34660e6			−0.101319
$708$		0			0
$709$	1.58384e7			1.18330			0.591651	−	0.806194i	$-0.298476\pi$
$709$	1.58384e7			1.18330			0.591651	+	0.806194i	$0.298476\pi$
$710$	−1.32235e7	−	4.25313e6i	−0.984466	−	0.316638i
$711$		0			0
$712$	−7.39732e6	−	9.99276e6i	−0.546858	−	0.738729i
$713$			2.44402e7i			1.80045i
$714$		0			0
$715$			8.81782e6i			0.645054i
$716$	−7.87565e6	−	5.65071e6i	−0.574122	−	0.411927i
$717$		0			0
$718$	4.87247e6	−	1.51491e7i	0.352727	−	1.09667i
$719$	2.87578e6			0.207460			0.103730	−	0.994606i	$-0.466922\pi$
$719$	2.87578e6			0.207460			0.103730	+	0.994606i	$0.466922\pi$
$720$		0			0
$721$	−2.66368e7			−1.90829
$722$	3.50756e6	−	1.09054e7i	0.250416	−	0.778575i
$723$		0			0
$724$	−1.87084e7	−	1.34231e7i	−1.32644	−	0.951712i
$725$		−	1.79450e7i		−	1.26794i
$726$		0			0
$727$		−	2.80274e6i		−	0.196674i	−0.995153	−	0.0983369i	$-0.968648\pi$
$727$		−	2.80274e6i		−	0.196674i	0.995153	−	0.0983369i	$-0.0313523\pi$
$728$	−2.83495e6	−	3.82963e6i	−0.198252	−	0.267811i
$729$		0			0
$730$	1.51543e7	+	4.87414e6i	1.05252	+	0.338525i
$731$	−2.49078e6			−0.172402
$732$		0			0
$733$	1.04544e7			0.718685			0.359342	−	0.933206i	$-0.383001\pi$
$733$	1.04544e7			0.718685			0.359342	+	0.933206i	$0.383001\pi$
$734$	1.58380e7	+	5.09404e6i	1.08508	+	0.348997i
$735$		0			0
$736$	−2.23513e7	+	332502.i	−1.52093	+	0.0226256i
$737$		−	2.38240e7i		−	1.61565i
$738$		0			0
$739$			2.46827e7i			1.66257i	0.555844	+	0.831286i	$0.312395\pi$
$739$			2.46827e7i			1.66257i	−0.555844	+	0.831286i	$0.687605\pi$
$740$	−2.61840e7	+	3.64939e7i	−1.75775	+	2.44986i
$741$		0			0
$742$	−4.74611e6	+	1.47563e7i	−0.316467	+	0.983935i
$743$	2.00401e7			1.33177			0.665884	−	0.746056i	$-0.268055\pi$
$743$	2.00401e7			1.33177			0.665884	+	0.746056i	$0.268055\pi$
$744$		0			0
$745$	−1.70820e7			−1.12758
$746$	−3.66671e6	+	1.14003e7i	−0.241229	+	0.750012i
$747$		0			0
$748$	8.97666e6	−	1.25112e7i	0.586625	−	0.817607i
$749$		−	1.72638e7i		−	1.12443i
$750$		0			0
$751$			8.22982e6i			0.532464i	0.963909	+	0.266232i	$0.0857787\pi$
$751$			8.22982e6i			0.532464i	−0.963909	+	0.266232i	$0.914221\pi$
$752$	2.31904e6	+	6.85846e6i	0.149542	+	0.442264i
$753$		0			0
$754$	−3.05208e6	−	981651.i	−0.195509	−	0.0628823i
$755$	−1.33559e7			−0.852717
$756$		0			0
$757$	−5.34992e6			−0.339319			−0.169659	−	0.985503i	$-0.554267\pi$
$757$	−5.34992e6			−0.339319			−0.169659	+	0.985503i	$0.554267\pi$
$758$	1.48422e7	+	4.77375e6i	0.938265	+	0.301778i
$759$		0			0
$760$	8.94499e6	−	6.62169e6i	0.561754	−	0.415848i
$761$			1.17630e7i			0.736301i	0.929766	+	0.368150i	$0.120009\pi$
$761$			1.17630e7i			0.736301i	−0.929766	+	0.368150i	$0.879991\pi$
$762$		0			0
$763$			1.38948e7i			0.864052i
$764$	−2.52308e7	−	1.81029e7i	−1.56386	−	1.12206i
$765$		0			0
$766$	7.81851e6	−	2.43087e7i	0.481451	−	1.49689i
$767$	−4.71936e6			−0.289664
$768$		0			0
$769$	−1.34112e7			−0.817807			−0.408903	−	0.912578i	$-0.634089\pi$
$769$	−1.34112e7			−0.817807			−0.408903	+	0.912578i	$0.634089\pi$
$770$	−1.45889e7	+	4.53587e7i	−0.886739	+	2.75698i
$771$		0			0
$772$	2.61459e6	+	1.87594e6i	0.157892	+	0.113286i
$773$			2.94018e7i			1.76980i	0.465779	+	0.884901i	$0.345774\pi$
$773$			2.94018e7i			1.76980i	−0.465779	+	0.884901i	$0.654226\pi$
$774$		0			0
$775$			3.32878e7i			1.99081i
$776$	1.99572e6	−	1.47737e6i	0.118972	−	0.0880712i
$777$		0			0
$778$	−8.40608e6	−	2.70368e6i	−0.497903	−	0.160142i
$779$	6.78460e6			0.400572
$780$		0			0
$781$	1.55634e7			0.913015
$782$	−1.72343e7	−	5.54314e6i	−1.00781	−	0.324145i
$783$		0			0
$784$	−2.73421e6	−	8.08632e6i	−0.158870	−	0.469851i
$785$			2.04272e7i			1.18314i
$786$		0			0
$787$		−	1.80678e7i		−	1.03984i	−0.854214	−	0.519921i	$-0.825961\pi$
$787$		−	1.80678e7i		−	1.03984i	0.854214	−	0.519921i	$-0.174039\pi$
$788$	−8.46799e6	+	1.18022e7i	−0.485808	+	0.677093i
$789$		0			0
$790$	−1.11310e7	+	3.46075e7i	−0.634548	+	1.97289i
$791$	−1.55615e7			−0.884321
$792$		0			0
$793$	8.82921e6			0.498585
$794$	6.81268e6	−	2.11815e7i	0.383501	−	1.19235i
$795$		0			0
$796$	9.88094e6	−	1.37715e7i	0.552733	−	0.770370i
$797$		−	1.32498e7i		−	0.738860i	−0.929259	−	0.369430i	$-0.879553\pi$
$797$		−	1.32498e7i		−	0.738860i	0.929259	−	0.369430i	$-0.120447\pi$
$798$		0			0
$799$			5.86345e6i			0.324927i
$800$	−3.04426e7	+	452871.i	−1.68173	+	0.0250178i
$801$		0			0
$802$	2.21117e7	+	7.11187e6i	1.21391	+	0.390434i
$803$	−1.78359e7			−0.976127
$804$		0			0
$805$	5.60186e7			3.04679
$806$	5.66156e6	+	1.82095e6i	0.306972	+	0.0987326i
$807$		0			0
$808$	914660.	+	1.23558e6i	0.0492869	+	0.0665798i
$809$		−	8.99804e6i		−	0.483367i	−0.970355	−	0.241683i	$-0.922301\pi$
$809$		−	8.99804e6i		−	0.483367i	0.970355	−	0.241683i	$-0.0776995\pi$
$810$		0			0
$811$		−	3.58015e6i		−	0.191139i	−0.995423	−	0.0955694i	$-0.969533\pi$
$811$		−	3.58015e6i		−	0.191139i	0.995423	−	0.0955694i	$-0.0304672\pi$
$812$	−1.40757e7	−	1.00992e7i	−0.749169	−	0.537522i
$813$		0			0
$814$	1.54087e7	−	4.79075e7i	0.815087	−	2.53421i
$815$	8.14109e6			0.429327
$816$		0			0
$817$	2.01701e6			0.105719
$818$	7.67009e6	−	2.38473e7i	0.400790	−	1.24611i
$819$		0			0
$820$	−2.40466e7	−	1.72532e7i	−1.24887	−	0.896055i
$821$			2.61319e7i			1.35305i	0.736421	+	0.676524i	$0.236514\pi$
$821$			2.61319e7i			1.35305i	−0.736421	+	0.676524i	$0.763486\pi$
$822$		0			0
$823$			3.26854e7i			1.68211i	0.540952	+	0.841054i	$0.318064\pi$
$823$			3.26854e7i			1.68211i	−0.540952	+	0.841054i	$0.681936\pi$
$824$	1.80927e7	+	2.44407e7i	0.928291	+	1.25399i
$825$		0			0
$826$	−2.42763e7	−	7.80808e6i	−1.23803	−	0.398193i
$827$	1.91029e7			0.971262			0.485631	−	0.874164i	$-0.338590\pi$
$827$	1.91029e7			0.971262			0.485631	+	0.874164i	$0.338590\pi$
$828$		0			0
$829$	−3.47493e7			−1.75614			−0.878072	−	0.478529i	$-0.841170\pi$
$829$	−3.47493e7			−1.75614			−0.878072	+	0.478529i	$0.841170\pi$
$830$	5.62123e6	+	1.80798e6i	0.283228	+	0.0910957i
$831$		0			0
$832$	−1.58829e6	+	5.20244e6i	−0.0795465	+	0.260555i
$833$		−	6.91317e6i		−	0.345195i
$834$		0			0
$835$			2.82909e7i			1.40421i
$836$	−7.26921e6	+	1.01314e7i	−0.359726	+	0.501366i
$837$		0			0
$838$	−1.01387e6	+	3.15226e6i	−0.0498740	+	0.155064i
$839$	−1.55294e7			−0.761641			−0.380821	−	0.924649i	$-0.624358\pi$
$839$	−1.55294e7			−0.761641			−0.380821	+	0.924649i	$0.624358\pi$
$840$		0			0
$841$	8.85442e6			0.431688
$842$	6.25774e6	−	1.94561e7i	0.304185	−	0.945749i
$843$		0			0
$844$	−1.53684e7	+	2.14196e7i	−0.742629	+	1.03504i
$845$			3.14684e7i			1.51612i
$846$		0			0
$847$		−	2.78479e7i		−	1.33378i
$848$	1.67634e7	−	5.66817e6i	0.800520	−	0.270678i
$849$		0			0
$850$	−2.34733e7	−	7.54980e6i	−1.11436	−	0.358417i
$851$	−5.91663e7			−2.80060
$852$		0			0
$853$	−1.34459e7			−0.632728			−0.316364	−	0.948638i	$-0.602462\pi$
$853$	−1.34459e7			−0.632728			−0.316364	+	0.948638i	$0.602462\pi$
$854$	4.54173e7	+	1.46077e7i	2.13097	+	0.685391i
$855$		0			0
$856$	−1.58405e7	+	1.17262e7i	−0.738896	+	0.546982i
$857$			5.67903e6i			0.264133i	0.991241	+	0.132066i	$0.0421612\pi$
$857$			5.67903e6i			0.264133i	−0.991241	+	0.132066i	$0.957839\pi$
$858$		0			0
$859$		−	6.68060e6i		−	0.308911i	−0.988000	−	0.154455i	$-0.950638\pi$
$859$		−	6.68060e6i		−	0.308911i	0.988000	−	0.154455i	$-0.0493623\pi$
$860$	−7.14886e6	−	5.12924e6i	−0.329603	−	0.236487i
$861$		0			0
$862$	2.88103e6	−	8.95747e6i	0.132062	−	0.410599i
$863$	−7.52289e6			−0.343841			−0.171920	−	0.985111i	$-0.554997\pi$
$863$	−7.52289e6			−0.343841			−0.171920	+	0.985111i	$0.554997\pi$
$864$		0			0
$865$	7.06967e7			3.21262
$866$	−1.35759e6	+	4.22092e6i	−0.0615140	+	0.191255i
$867$		0			0
$868$	2.61103e7	+	1.87339e7i	1.17628	+	0.843972i
$869$		−	4.07314e7i		−	1.82970i
$870$		0			0
$871$			6.81581e6i			0.304419i
$872$	1.27492e7	−	9.43782e6i	0.567795	−	0.420321i
$873$		0			0
$874$	1.39562e7	+	4.48878e6i	0.618000	+	0.198770i
$875$	3.09343e7			1.36590
$876$		0			0
$877$	−1.96365e7			−0.862117			−0.431058	−	0.902324i	$-0.641860\pi$
$877$	−1.96365e7			−0.862117			−0.431058	+	0.902324i	$0.641860\pi$
$878$	1.03062e7	+	3.31483e6i	0.451194	+	0.145119i
$879$		0			0
$880$	5.15284e7	−	1.74232e7i	2.24305	−	0.758439i
$881$			1.37695e6i			0.0597695i	0.999553	+	0.0298848i	$0.00951403\pi$
$881$			1.37695e6i			0.0597695i	−0.999553	+	0.0298848i	$0.990486\pi$
$882$		0			0
$883$			3.80009e7i			1.64018i	0.572234	+	0.820090i	$0.306077\pi$
$883$			3.80009e7i			1.64018i	−0.572234	+	0.820090i	$0.693923\pi$
$884$	−2.56813e6	+	3.57933e6i	−0.110532	+	0.154053i
$885$		0			0
$886$	4.39795e6	−	1.36738e7i	0.188220	−	0.585200i
$887$	8.46706e6			0.361346			0.180673	−	0.983543i	$-0.442172\pi$
$887$	8.46706e6			0.361346			0.180673	+	0.983543i	$0.442172\pi$
$888$		0			0
$889$	989451.			0.0419894
$890$	1.08907e7	−	3.38604e7i	0.460871	−	1.43290i
$891$		0			0
$892$	−5.19320e6	+	7.23801e6i	−0.218536	+	0.304584i
$893$		−	4.74816e6i		−	0.199249i
$894$		0			0
$895$		−	2.77307e7i		−	1.15719i
$896$	−1.67774e7	+	2.41335e7i	−0.698161	+	1.00427i
$897$		0			0
$898$	−3.26280e7	−	1.04943e7i	−1.35021	−	0.434272i
$899$	2.16231e7			0.892315
$900$		0			0
$901$	1.43314e7			0.588134
$902$	3.15672e7	+	1.01531e7i	1.29187	+	0.415510i
$903$		0			0
$904$	1.05699e7	+	1.42785e7i	0.430180	+	0.581114i
$905$		−	6.58734e7i		−	2.67355i
$906$		0			0
$907$			3.13826e7i			1.26669i	0.773870	+	0.633345i	$0.218318\pi$
$907$			3.13826e7i			1.26669i	−0.773870	+	0.633345i	$0.781682\pi$
$908$	−8.03692e6	−	5.76641e6i	−0.323500	−	0.232109i
$909$		0			0
$910$	4.17374e6	−	1.29767e7i	0.167079	−	0.519470i
$911$	4.53974e6			0.181232			0.0906160	−	0.995886i	$-0.471116\pi$
$911$	4.53974e6			0.181232			0.0906160	+	0.995886i	$0.471116\pi$
$912$		0			0
$913$	−6.61592e6			−0.262672
$914$	5.69900e6	−	1.77189e7i	0.225649	−	0.701571i
$915$		0			0
$916$	−3.66293e6	−	2.62812e6i	−0.144241	−	0.103492i
$917$			2.81814e7i			1.10673i
$918$		0			0
$919$			5.27164e6i			0.205900i	0.994687	+	0.102950i	$0.0328282\pi$
$919$			5.27164e6i			0.205900i	−0.994687	+	0.102950i	$0.967172\pi$
$920$	−3.80498e7	−	5.14001e7i	−1.48212	−	2.00214i
$921$		0			0
$922$	3.45571e7	+	1.11147e7i	1.33878	+	0.430598i
$923$	−4.45254e6			−0.172030
$924$		0			0
$925$	−8.05850e7			−3.09670
$926$	−7.23822e6	−	2.32806e6i	−0.277399	−	0.0892207i
$927$		0			0
$928$	294176.	+	1.97749e7i	0.0112134	+	0.753781i
$929$		−	4.33058e7i		−	1.64629i	−0.567831	−	0.823145i	$-0.692217\pi$
$929$		−	4.33058e7i		−	1.64629i	0.567831	−	0.823145i	$-0.307783\pi$
$930$		0			0
$931$			5.59822e6i			0.211678i
$932$	1.65285e7	−	2.30366e7i	0.623295	−	0.868716i
$933$		0			0
$934$	−443673.	+	1.37944e6i	−0.0166416	+	0.0517409i
$935$	4.40528e7			1.64795
$936$		0			0
$937$	−1.73741e7			−0.646476			−0.323238	−	0.946318i	$-0.604771\pi$
$937$	−1.73741e7			−0.646476			−0.323238	+	0.946318i	$0.604771\pi$
$938$	−1.12766e7	+	3.50604e7i	−0.418477	+	1.30110i
$939$		0			0
$940$	−1.20746e7	+	1.68289e7i	−0.445709	+	0.621205i
$941$			2.37767e7i			0.875341i	0.899135	+	0.437671i	$0.144196\pi$
$941$			2.37767e7i			0.875341i	−0.899135	+	0.437671i	$0.855804\pi$
$942$		0			0
$943$		−	3.89859e7i		−	1.42767i
$944$	9.32500e6	+	2.75783e7i	0.340580	+	1.00725i
$945$		0			0
$946$	9.38469e6	+	3.01843e6i	0.340951	+	0.109661i
$947$	4.87215e7			1.76541			0.882706	−	0.469926i	$-0.155719\pi$
$947$	4.87215e7			1.76541			0.882706	+	0.469926i	$0.155719\pi$
$948$		0			0
$949$	5.10267e6			0.183921
$950$	1.90084e7	+	6.11376e6i	0.683341	+	0.219786i
$951$		0			0
$952$	−1.91323e7	+	1.41631e7i	−0.684189	+	0.506483i
$953$			1.99112e7i			0.710173i	0.934833	+	0.355086i	$0.115549\pi$
$953$			1.99112e7i			0.710173i	−0.934833	+	0.355086i	$0.884451\pi$
$954$		0			0
$955$		−	8.88395e7i		−	3.15208i
$956$	−5.46957e6	−	3.92436e6i	−0.193557	−	0.138875i
$957$		0			0
$958$	−16734.0	+	52028.1i	−0.000589096	+	0.00183157i
$959$	−3.70081e6			−0.129942
$960$		0			0
$961$	−1.14814e7			−0.401039
$962$	−4.40826e6	+	1.37058e7i	−0.153578	+	0.477494i
$963$		0			0
$964$	−3.64881e7	−	2.61799e7i	−1.26462	−	0.907351i
$965$			9.20614e6i			0.318243i
$966$		0			0
$967$		−	4.49698e7i		−	1.54652i	−0.634091	−	0.773258i	$-0.718626\pi$
$967$		−	4.49698e7i		−	1.54652i	0.634091	−	0.773258i	$-0.281374\pi$
$968$	−2.55519e7	+	1.89153e7i	−0.876467	+	0.648820i
$969$		0			0
$970$	6.76248e6	+	2.17504e6i	0.230769	+	0.0742230i
$971$	1.00467e7			0.341959			0.170979	−	0.985275i	$-0.445307\pi$
$971$	1.00467e7			0.341959			0.170979	+	0.985275i	$0.445307\pi$
$972$		0			0
$973$	3.32538e7			1.12606
$974$	−3.97109e7	−	1.27724e7i	−1.34126	−	0.431394i
$975$		0			0
$976$	−1.74457e7	−	5.15949e7i	−0.586223	−	1.73373i
$977$			3.14663e7i			1.05465i	0.849663	+	0.527326i	$0.176805\pi$
$977$			3.14663e7i			1.05465i	−0.849663	+	0.527326i	$0.823195\pi$
$978$		0			0
$979$			3.98521e7i			1.32891i
$980$	1.42362e7	−	1.98417e7i	0.473511	−	0.659954i
$981$		0			0
$982$	−8.59530e6	+	2.67239e7i	−0.284435	+	0.884343i
$983$	−1.65935e7			−0.547714			−0.273857	−	0.961770i	$-0.588300\pi$
$983$	−1.65935e7			−0.547714			−0.273857	+	0.961770i	$0.588300\pi$
$984$		0			0
$985$	−4.15564e7			−1.36473
$986$	−4.90420e6	+	1.52478e7i	−0.160648	+	0.499476i
$987$		0			0
$988$	2.07965e6	−	2.89850e6i	0.0677794	−	0.0944672i
$989$		−	1.15902e7i		−	0.376791i
$990$		0			0
$991$		−	4.59454e7i		−	1.48613i	−0.669218	−	0.743066i	$-0.733371\pi$
$991$		−	4.59454e7i		−	1.48613i	0.669218	−	0.743066i	$-0.266629\pi$
$992$	−545693.	−	3.66823e7i	−0.0176063	−	1.18352i
$993$		0			0
$994$	−2.29038e7	−	7.36663e6i	−0.735261	−	0.236485i
$995$	4.84905e7			1.55274
$996$		0			0
$997$	−2.17918e7			−0.694312			−0.347156	−	0.937807i	$-0.612853\pi$
$997$	−2.17918e7			−0.694312			−0.347156	+	0.937807i	$0.612853\pi$
$998$	1.19624e7	+	3.84750e6i	0.380181	+	0.122279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.a.107.3	yes	4
3.2	odd	2	inner	108.6.b.a.107.2	yes	4
4.3	odd	2	inner	108.6.b.a.107.1	✓	4
12.11	even	2	inner	108.6.b.a.107.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.a.107.1	✓	4	4.3	odd	2	inner
108.6.b.a.107.2	yes	4	3.2	odd	2	inner
108.6.b.a.107.3	yes	4	1.1	even	1	trivial
108.6.b.a.107.4	yes	4	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 5.38516i) q^{2} +(-26.0000 - 18.6548i) q^{4} -91.5478i q^{5} -158.565i q^{7} +(-145.492 + 107.703i) q^{8} +O(q^{10})\)	\(q+(1.73205 - 5.38516i) q^{2} +(-26.0000 - 18.6548i) q^{4} -91.5478i q^{5} -158.565i q^{7} +(-145.492 + 107.703i) q^{8} +(-493.000 - 158.565i) q^{10} +580.237 q^{11} -166.000 q^{13} +(-853.901 - 274.643i) q^{14} +(328.000 + 970.047i) q^{16} +829.315i q^{17} -671.571i q^{19} +(-1707.80 + 2380.24i) q^{20} +(1005.00 - 3124.67i) q^{22} -3859.01 q^{23} -5256.00 q^{25} +(-287.520 + 893.937i) q^{26} +(-2958.00 + 4122.70i) q^{28} +3414.19i q^{29} -6333.29i q^{31} +(5791.98 - 86.1626i) q^{32} +(4466.00 + 1436.42i) q^{34} -14516.3 q^{35} +15332.0 q^{37} +(-3616.52 - 1163.20i) q^{38} +(9860.00 + 13319.5i) q^{40} +10102.6i q^{41} +3003.42i q^{43} +(-15086.2 - 10824.2i) q^{44} +(-6684.00 + 20781.4i) q^{46} +7070.23 q^{47} -8336.00 q^{49} +(-9103.66 + 28304.4i) q^{50} +(4316.00 + 3096.69i) q^{52} -17281.0i q^{53} -53119.4i q^{55} +(17078.0 + 23070.0i) q^{56} +(18386.0 + 5913.56i) q^{58} +28429.9 q^{59} -53188.0 q^{61} +(-34105.8 - 10969.6i) q^{62} +(9568.00 - 31340.0i) q^{64} +15196.9i q^{65} -41059.1i q^{67} +(15470.7 - 21562.2i) q^{68} +(-25143.0 + 78172.8i) q^{70} +26822.5 q^{71} -30739.0 q^{73} +(26555.8 - 82565.3i) q^{74} +(-12528.0 + 17460.9i) q^{76} -92005.5i q^{77} -70197.9i q^{79} +(88805.7 - 30027.7i) q^{80} +(54404.0 + 17498.2i) q^{82} -11402.1 q^{83} +75922.0 q^{85} +(16173.9 + 5202.07i) q^{86} +(-84420.0 + 62493.4i) q^{88} +68682.4i q^{89} +26321.9i q^{91} +(100334. + 71988.9i) q^{92} +(12246.0 - 38074.4i) q^{94} -61480.9 q^{95} -13717.0 q^{97} +(-14438.4 + 44890.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 104 q^{4}+O(q^{10}) \) 4 * q - 104 * q^4	\( 4 q - 104 q^{4} - 1972 q^{10} - 664 q^{13} + 1312 q^{16} + 4020 q^{22} - 21024 q^{25} - 11832 q^{28} + 17864 q^{34} + 61328 q^{37} + 39440 q^{40} - 26736 q^{46} - 33344 q^{49} + 17264 q^{52} + 73544 q^{58} - 212752 q^{61} + 38272 q^{64} - 100572 q^{70} - 122956 q^{73} - 50112 q^{76} + 217616 q^{82} + 303688 q^{85} - 337680 q^{88} + 48984 q^{94} - 54868 q^{97}+O(q^{100}) \) 4 * q - 104 * q^4 - 1972 * q^10 - 664 * q^13 + 1312 * q^16 + 4020 * q^22 - 21024 * q^25 - 11832 * q^28 + 17864 * q^34 + 61328 * q^37 + 39440 * q^40 - 26736 * q^46 - 33344 * q^49 + 17264 * q^52 + 73544 * q^58 - 212752 * q^61 + 38272 * q^64 - 100572 * q^70 - 122956 * q^73 - 50112 * q^76 + 217616 * q^82 + 303688 * q^85 - 337680 * q^88 + 48984 * q^94 - 54868 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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