LMFDB - Embedded newform 342.7.m.a.145.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,7,Mod(145,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("342.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	342.m (of order $6$, degree $2$, 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:	$78.6784965980$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 112 x^{19} + 116318 x^{18} + 1860432 x^{17} + 7532794771 x^{16} - 134305195660 x^{15} + \cdots + 10\!\cdots\!00 $ x^20 + 112x^19 + 116318x^18 + 1860432x^17 + 7532794771x^16 - 134305195660x^15 + 325182969245950x^14 - 19621760698865500x^13 + 9854002942286640625x^12 - 752050813940425462500x^11 + 212794421230351962687500x^10 - 19467496958800837319375000x^9 + 3089015887674989183171875000x^8 - 240050227854521311206750000000x^7 + 26278540191235238896725234375000x^6 - 1898563409956855640839492968750000x^5 + 144527031746751528323803406250000000x^4 - 6976605219260725504558647773437500000x^3 + 285081093706204578571098816796875000000x^2 - 6332329314761369487290216894531250000000*x + 105481874512885036706585939025878906250000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.10
Root			$85.1965 + 147.565i$ of defining polynomial
Character	$\chi$	$=$	342.145
Dual form			342.7.m.a.217.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(85.1965 + 147.565i) q^{5} +473.710 q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(85.1965 + 147.565i) q^{5} +473.710 q^{7} -181.019i q^{8} +(834.752 + 481.944i) q^{10} +2118.68 q^{11} +(2401.07 + 1386.26i) q^{13} +(2320.70 - 1339.85i) q^{14} +(-512.000 - 886.810i) q^{16} +(-4199.48 - 7273.71i) q^{17} +(6819.60 - 734.105i) q^{19} +5452.58 q^{20} +(10379.4 - 5992.52i) q^{22} +(-3495.35 + 6054.13i) q^{23} +(-6704.40 + 11612.4i) q^{25} +15683.7 q^{26} +(7579.36 - 13127.8i) q^{28} +(-25424.0 - 14678.6i) q^{29} +38548.2i q^{31} +(-5016.55 - 2896.31i) q^{32} +(-41146.3 - 23755.8i) q^{34} +(40358.4 + 69902.9i) q^{35} -49167.4i q^{37} +(31332.7 - 22885.1i) q^{38} +(26712.1 - 15422.2i) q^{40} +(-39559.5 + 22839.7i) q^{41} +(34060.1 + 58993.9i) q^{43} +(33898.8 - 58714.5i) q^{44} +39545.4i q^{46} +(79086.9 - 136983. i) q^{47} +106752. q^{49} +75851.6i q^{50} +(76834.3 - 44360.3i) q^{52} +(-60725.2 - 35059.7i) q^{53} +(180504. + 312642. i) q^{55} -85750.7i q^{56} -166069. q^{58} +(-214108. + 123615. i) q^{59} +(25917.8 - 44891.0i) q^{61} +(109031. + 188847. i) q^{62} -32768.0 q^{64} +472418. i q^{65} +(-144770. - 83583.2i) q^{67} -268767. q^{68} +(395430. + 228302. i) q^{70} +(-2281.45 + 1317.20i) q^{71} +(115884. + 200716. i) q^{73} +(-139066. - 240870. i) q^{74} +(88769.5 - 200736. i) q^{76} +1.00364e6 q^{77} +(-376948. + 217631. i) q^{79} +(87241.2 - 151106. i) q^{80} +(-129201. + 223782. i) q^{82} +553204. q^{83} +(715562. - 1.23939e6i) q^{85} +(333720. + 192673. i) q^{86} -383522. i q^{88} +(-324464. - 187330. i) q^{89} +(1.13741e6 + 656685. i) q^{91} +(111851. + 193732. i) q^{92} -894766. i q^{94} +(689334. + 943789. i) q^{95} +(274550. - 158512. i) q^{97} +(522976. - 301940. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 320 q^{4} - 112 q^{5} - 208 q^{7}+O(q^{10}) $ 20 * q + 320 * q^4 - 112 * q^5 - 208 * q^7	$ 20 q + 320 q^{4} - 112 q^{5} - 208 q^{7} + 284 q^{11} + 10500 q^{13} - 1248 q^{14} - 10240 q^{16} + 11684 q^{17} + 12862 q^{19} - 7168 q^{20} + 52704 q^{22} - 8488 q^{23} - 63842 q^{25} + 43968 q^{26} - 3328 q^{28} - 137760 q^{29} + 70560 q^{34} + 6916 q^{35} + 77232 q^{38} - 109206 q^{41} + 35572 q^{43} + 4544 q^{44} + 361184 q^{47} + 259740 q^{49} + 336000 q^{52} + 236172 q^{53} + 56760 q^{55} - 225600 q^{58} - 1310610 q^{59} + 83552 q^{61} - 225792 q^{62} - 655360 q^{64} + 806646 q^{67} + 747776 q^{68} - 245664 q^{70} + 869220 q^{71} - 207422 q^{73} - 1460832 q^{74} - 140096 q^{76} + 3988336 q^{77} - 1706808 q^{79} - 114688 q^{80} + 887712 q^{82} - 3527548 q^{83} - 5604 q^{85} - 195792 q^{86} - 708432 q^{89} - 1914384 q^{91} + 271616 q^{92} + 2820356 q^{95} + 5113242 q^{97} + 612480 q^{98}+O(q^{100}) $ 20 * q + 320 * q^4 - 112 * q^5 - 208 * q^7 + 284 * q^11 + 10500 * q^13 - 1248 * q^14 - 10240 * q^16 + 11684 * q^17 + 12862 * q^19 - 7168 * q^20 + 52704 * q^22 - 8488 * q^23 - 63842 * q^25 + 43968 * q^26 - 3328 * q^28 - 137760 * q^29 + 70560 * q^34 + 6916 * q^35 + 77232 * q^38 - 109206 * q^41 + 35572 * q^43 + 4544 * q^44 + 361184 * q^47 + 259740 * q^49 + 336000 * q^52 + 236172 * q^53 + 56760 * q^55 - 225600 * q^58 - 1310610 * q^59 + 83552 * q^61 - 225792 * q^62 - 655360 * q^64 + 806646 * q^67 + 747776 * q^68 - 245664 * q^70 + 869220 * q^71 - 207422 * q^73 - 1460832 * q^74 - 140096 * q^76 + 3988336 * q^77 - 1706808 * q^79 - 114688 * q^80 + 887712 * q^82 - 3527548 * q^83 - 5604 * q^85 - 195792 * q^86 - 708432 * q^89 - 1914384 * q^91 + 271616 * q^92 + 2820356 * q^95 + 5113242 * q^97 + 612480 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	85.1965	+	147.565i	0.681572	+	1.18052i	0.974501	+	0.224383i	$0.0720368\pi$
$5$	85.1965	+	147.565i	0.681572	+	1.18052i	−0.292929	+	0.956134i	$0.594630\pi$
$6$		0			0
$7$	473.710			1.38108			0.690539	−	0.723295i	$-0.257373\pi$
$7$	473.710			1.38108			0.690539	+	0.723295i	$0.257373\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	834.752	+	481.944i	0.834752	+	0.481944i
$11$	2118.68			1.59179			0.795897	−	0.605432i	$-0.207000\pi$
$11$	2118.68			1.59179			0.795897	+	0.605432i	$0.207000\pi$
$12$		0			0
$13$	2401.07	+	1386.26i	1.09289	+	0.630978i	0.934344	−	0.356374i	$-0.115987\pi$
$13$	2401.07	+	1386.26i	1.09289	+	0.630978i	0.158543	+	0.987352i	$0.449320\pi$
$14$	2320.70	−	1339.85i	0.845734	−	0.488285i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$	−4199.48	−	7273.71i	−0.854769	−	1.48050i	−0.876859	−	0.480747i	$-0.840365\pi$
$17$	−4199.48	−	7273.71i	−0.854769	−	1.48050i	0.0220902	−	0.999756i	$-0.492968\pi$
$18$		0			0
$19$	6819.60	−	734.105i	0.994256	−	0.107028i
$19$	6819.60	−	734.105i	0.994256	−	0.107028i
$20$	5452.58			0.681572
$21$		0			0
$22$	10379.4	−	5992.52i	0.974771	−	0.562784i
$23$	−3495.35	+	6054.13i	−0.287282	+	0.497586i	−0.973160	−	0.230130i	$-0.926085\pi$
$23$	−3495.35	+	6054.13i	−0.287282	+	0.497586i	0.685878	+	0.727716i	$0.259418\pi$
$24$		0			0
$25$	−6704.40	+	11612.4i	−0.429081	+	0.743191i
$26$	15683.7			0.892338
$27$		0			0
$28$	7579.36	−	13127.8i	0.345270	−	0.598025i
$29$	−25424.0	−	14678.6i	−1.04244	−	0.601853i	−0.121916	−	0.992540i	$-0.538904\pi$
$29$	−25424.0	−	14678.6i	−1.04244	−	0.601853i	−0.920523	+	0.390688i	$0.872237\pi$
$30$		0			0
$31$			38548.2i			1.29395i	0.762509	+	0.646977i	$0.223967\pi$
$31$			38548.2i			1.29395i	−0.762509	+	0.646977i	$0.776033\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−41146.3	−	23755.8i	−1.04687	−	0.604413i
$35$	40358.4	+	69902.9i	0.941305	+	1.63039i
$36$		0			0
$37$		−	49167.4i		−	0.970671i	−0.874328	−	0.485335i	$-0.838698\pi$
$37$		−	49167.4i		−	0.970671i	0.874328	−	0.485335i	$-0.161302\pi$
$38$	31332.7	−	22885.1i	0.571015	−	0.417064i
$39$		0			0
$40$	26712.1	−	15422.2i	0.417376	−	0.240972i
$41$	−39559.5	+	22839.7i	−0.573983	+	0.331389i	−0.758739	−	0.651395i	$-0.774184\pi$
$41$	−39559.5	+	22839.7i	−0.573983	+	0.331389i	0.184756	+	0.982785i	$0.440851\pi$
$42$		0			0
$43$	34060.1	+	58993.9i	0.428392	+	0.741996i	0.996730	−	0.0807986i	$-0.0257471\pi$
$43$	34060.1	+	58993.9i	0.428392	+	0.741996i	−0.568339	+	0.822795i	$0.692414\pi$
$44$	33898.8	−	58714.5i	0.397948	−	0.689267i
$45$		0			0
$46$			39545.4i			0.406277i
$47$	79086.9	−	136983.i	0.761748	−	1.31939i	−0.180201	−	0.983630i	$-0.557675\pi$
$47$	79086.9	−	136983.i	0.761748	−	1.31939i	0.941949	−	0.335756i	$-0.108992\pi$
$48$		0			0
$49$	106752.			0.907378
$50$			75851.6i			0.606813i
$51$		0			0
$52$	76834.3	−	44360.3i	0.546443	−	0.315489i
$53$	−60725.2	−	35059.7i	−0.407888	−	0.235494i	0.281994	−	0.959416i	$-0.409004\pi$
$53$	−60725.2	−	35059.7i	−0.407888	−	0.235494i	−0.689882	+	0.723922i	$0.742338\pi$
$54$		0			0
$55$	180504.	+	312642.i	1.08492	+	1.87914i
$56$		−	85750.7i		−	0.488285i
$57$		0			0
$58$	−166069.			−0.851148
$59$	−214108.	+	123615.i	−1.04250	+	0.601887i	−0.920540	−	0.390648i	$-0.872251\pi$
$59$	−214108.	+	123615.i	−1.04250	+	0.601887i	−0.121959	+	0.992535i	$0.538918\pi$
$60$		0			0
$61$	25917.8	−	44891.0i	0.114185	−	0.197774i	−0.803269	−	0.595617i	$-0.796908\pi$
$61$	25917.8	−	44891.0i	0.114185	−	0.197774i	0.917454	+	0.397843i	$0.130241\pi$
$62$	109031.	+	188847.i	0.457482	+	0.792382i
$63$		0			0
$64$	−32768.0			−0.125000
$65$			472418.i			1.72023i
$66$		0			0
$67$	−144770.	−	83583.2i	−0.481344	−	0.277904i	0.239633	−	0.970864i	$-0.422973\pi$
$67$	−144770.	−	83583.2i	−0.481344	−	0.277904i	−0.720976	+	0.692960i	$0.756306\pi$
$68$	−268767.			−0.854769
$69$		0			0
$70$	395430.	+	228302.i	1.15286	+	0.665603i
$71$	−2281.45	+	1317.20i	−0.00637435	+	0.00368023i	−0.503184	−	0.864179i	$-0.667838\pi$
$71$	−2281.45	+	1317.20i	−0.00637435	+	0.00368023i	0.496809	+	0.867860i	$0.334505\pi$
$72$		0			0
$73$	115884.	+	200716.i	0.297889	+	0.515958i	0.975653	−	0.219321i	$-0.0703843\pi$
$73$	115884.	+	200716.i	0.297889	+	0.515958i	−0.677764	+	0.735279i	$0.737051\pi$
$74$	−139066.	−	240870.i	−0.343184	−	0.594412i
$75$		0			0
$76$	88769.5	−	200736.i	0.202220	−	0.457282i
$77$	1.00364e6			2.19839
$78$		0			0
$79$	−376948.	+	217631.i	−0.764540	+	0.441408i	−0.830924	−	0.556387i	$-0.812187\pi$
$79$	−376948.	+	217631.i	−0.764540	+	0.441408i	0.0663831	+	0.997794i	$0.478854\pi$
$80$	87241.2	−	151106.i	0.170393	−	0.295129i
$81$		0			0
$82$	−129201.	+	223782.i	−0.234328	+	0.405867i
$83$	553204.			0.967500			0.483750	−	0.875206i	$-0.339274\pi$
$83$	553204.			0.967500			0.483750	+	0.875206i	$0.339274\pi$
$84$		0			0
$85$	715562.	−	1.23939e6i	1.16517	−	2.01814i
$86$	333720.	+	192673.i	0.524670	+	0.302919i
$87$		0			0
$88$		−	383522.i		−	0.562784i
$89$	−324464.	−	187330.i	−0.460254	−	0.265727i	0.251897	−	0.967754i	$-0.418945\pi$
$89$	−324464.	−	187330.i	−0.460254	−	0.265727i	−0.712151	+	0.702026i	$0.752279\pi$
$90$		0			0
$91$	1.13741e6	+	656685.i	1.50936	+	0.871431i
$92$	111851.	+	193732.i	0.143641	+	0.248793i
$93$		0			0
$94$		−	894766.i		−	1.07727i
$95$	689334.	+	943789.i	0.804006	+	1.10079i
$96$		0			0
$97$	274550.	−	158512.i	0.300820	−	0.173678i	−0.341991	−	0.939703i	$-0.611101\pi$
$97$	274550.	−	158512.i	0.300820	−	0.173678i	0.642811	+	0.766025i	$0.277768\pi$
$98$	522976.	−	301940.i	0.555653	−	0.320806i
$99$		0			0
$100$	214541.	+	371595.i	0.214541	+	0.371595i
$101$	−56161.6	+	97274.8i	−0.0545099	+	0.0944139i	−0.891993	−	0.452050i	$-0.850693\pi$
$101$	−56161.6	+	97274.8i	−0.0545099	+	0.0944139i	0.837483	+	0.546464i	$0.184026\pi$
$102$		0			0
$103$		−	736462.i		−	0.673967i	−0.941511	−	0.336983i	$-0.890593\pi$
$103$		−	736462.i		−	0.673967i	0.941511	−	0.336983i	$-0.109407\pi$
$104$	250940.	−	434640.i	0.223085	−	0.386394i
$105$		0			0
$106$	−396655.			−0.333039
$107$		−	110276.i		−	0.0900184i	−0.998987	−	0.0450092i	$-0.985668\pi$
$107$		−	110276.i		−	0.0900184i	0.998987	−	0.0450092i	$-0.0143317\pi$
$108$		0			0
$109$	−628454.	+	362838.i	−0.485282	+	0.280177i	−0.722615	−	0.691251i	$-0.757060\pi$
$109$	−628454.	+	362838.i	−0.485282	+	0.280177i	0.237333	+	0.971428i	$0.423727\pi$
$110$	1.76857e6	+	1.02108e6i	1.32875	+	0.767156i
$111$		0			0
$112$	−242539.	−	420091.i	−0.172635	−	0.299012i
$113$		−	1.72474e6i		−	1.19533i	−0.801746	−	0.597665i	$-0.796095\pi$
$113$		−	1.72474e6i		−	1.19533i	0.801746	−	0.597665i	$-0.203905\pi$
$114$		0			0
$115$	−1.19117e6			−0.783212
$116$	−813570.	+	469715.i	−0.521220	+	0.300926i
$117$		0			0
$118$	−699272.	+	1.21118e6i	−0.425599	+	0.737159i
$119$	−1.98934e6	−	3.44563e6i	−1.18050	−	2.04469i
$120$		0			0
$121$	2.71723e6			1.53381
$122$		−	293227.i		−	0.161482i
$123$		0			0
$124$	1.06828e6	+	616771.i	0.560299	+	0.323489i
$125$	377626.			0.193345
$126$		0			0
$127$	1.48410e6	+	856846.i	0.724523	+	0.418304i	0.816415	−	0.577465i	$-0.195958\pi$
$127$	1.48410e6	+	856846.i	0.724523	+	0.418304i	−0.0918919	+	0.995769i	$0.529291\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.33620e6	+	2.31437e6i	0.608193	+	1.05342i
$131$	363251.	+	629170.i	0.161582	+	0.279868i	0.935436	−	0.353495i	$-0.115007\pi$
$131$	363251.	+	629170.i	0.161582	+	0.279868i	−0.773854	+	0.633364i	$0.781674\pi$
$132$		0			0
$133$	3.23051e6	−	347753.i	1.37315	−	0.147814i
$134$	−945636.			−0.393015
$135$		0			0
$136$	−1.31668e6	+	760187.i	−0.523437	+	0.302206i
$137$	−1.24733e6	+	2.16044e6i	−0.485088	+	0.840197i	−0.999853	−	0.0171344i	$-0.994546\pi$
$137$	−1.24733e6	+	2.16044e6i	−0.485088	+	0.840197i	0.514765	+	0.857331i	$0.327879\pi$
$138$		0			0
$139$	76133.2	−	131867.i	0.0283485	−	0.0491010i	−0.851503	−	0.524350i	$-0.824309\pi$
$139$	76133.2	−	131867.i	0.0283485	−	0.0491010i	0.879852	+	0.475249i	$0.157642\pi$
$140$	2.58294e6			0.941305
$141$		0			0
$142$	−7451.18	+	12905.8i	−0.00260232	+	0.00450734i
$143$	5.08710e6	+	2.93704e6i	1.73965	+	1.00439i
$144$		0			0
$145$		−	5.00226e6i		−	1.64082i
$146$	1.13542e6	+	655537.i	0.364837	+	0.210639i
$147$		0			0
$148$	−1.36257e6	−	786678.i	−0.420313	−	0.242668i
$149$	−2.11509e6	−	3.66345e6i	−0.639397	−	1.10747i	−0.985565	−	0.169295i	$-0.945851\pi$
$149$	−2.11509e6	−	3.66345e6i	−0.639397	−	1.10747i	0.346169	−	0.938172i	$-0.387482\pi$
$150$		0			0
$151$			1.23909e6i			0.359891i	0.983677	+	0.179946i	$0.0575922\pi$
$151$			1.23909e6i			0.359891i	−0.983677	+	0.179946i	$0.942408\pi$
$152$	−132887.	−	1.23448e6i	−0.0378401	−	0.351523i
$153$		0			0
$154$	4.91680e6	−	2.83872e6i	1.34623	−	0.777249i
$155$	−5.68835e6	+	3.28417e6i	−1.52754	+	0.881923i
$156$		0			0
$157$	2.26593e6	+	3.92470e6i	0.585527	+	1.01416i	0.994809	+	0.101755i	$0.0324458\pi$
$157$	2.26593e6	+	3.92470e6i	0.585527	+	1.01416i	−0.409282	+	0.912408i	$0.634221\pi$
$158$	−1.23111e6	+	2.13234e6i	−0.312122	+	0.540612i
$159$		0			0
$160$		−	987022.i		−	0.240972i
$161$	−1.65578e6	+	2.86790e6i	−0.396758	+	0.687206i
$162$		0			0
$163$	−3.81695e6			−0.881361			−0.440681	−	0.897664i	$-0.645263\pi$
$163$	−3.81695e6			−0.881361			−0.440681	+	0.897664i	$0.645263\pi$
$164$			1.46174e6i			0.331389i
$165$		0			0
$166$	2.71013e6	−	1.56470e6i	0.592470	−	0.342063i
$167$	4.57438e6	+	2.64102e6i	0.982161	+	0.567051i	0.902922	−	0.429805i	$-0.141418\pi$
$167$	4.57438e6	+	2.64102e6i	0.982161	+	0.567051i	0.0792390	+	0.996856i	$0.474751\pi$
$168$		0			0
$169$	1.43003e6	+	2.47688e6i	0.296267	+	0.513150i
$170$		−	8.09566e6i		−	1.64780i
$171$		0			0
$172$	2.17985e6			0.428392
$173$	−3.18607e6	+	1.83948e6i	−0.615342	+	0.355268i	−0.775053	−	0.631896i	$-0.782277\pi$
$173$	−3.18607e6	+	1.83948e6i	−0.615342	+	0.355268i	0.159711	+	0.987164i	$0.448944\pi$
$174$		0			0
$175$	−3.17594e6	+	5.50089e6i	−0.592595	+	1.02640i
$176$	−1.08476e6	−	1.87886e6i	−0.198974	−	0.344633i
$177$		0			0
$178$	−2.11939e6			−0.375795
$179$		−	580056.i		−	0.101137i	−0.998721	−	0.0505686i	$-0.983897\pi$
$179$		−	580056.i		−	0.101137i	0.998721	−	0.0505686i	$-0.0161033\pi$
$180$		0			0
$181$	7.93034e6	+	4.57858e6i	1.33738	+	0.772139i	0.986419	−	0.164250i	$-0.0525204\pi$
$181$	7.93034e6	+	4.57858e6i	1.33738	+	0.772139i	0.350965	+	0.936389i	$0.385854\pi$
$182$	7.42954e6			1.23239
$183$		0			0
$184$	1.09591e6	+	632727.i	0.175923	+	0.101569i
$185$	7.25537e6	−	4.18889e6i	1.14589	−	0.661582i
$186$		0			0
$187$	−8.89734e6	−	1.54107e7i	−1.36062	−	2.35666i
$188$	−2.53078e6	−	4.38344e6i	−0.380874	−	0.659693i
$189$		0			0
$190$	6.04647e6	+	2.67387e6i	0.881539	+	0.389834i
$191$	−2.51336e6			−0.360706			−0.180353	−	0.983602i	$-0.557724\pi$
$191$	−2.51336e6			−0.360706			−0.180353	+	0.983602i	$0.557724\pi$
$192$		0			0
$193$	5.97892e6	−	3.45193e6i	0.831670	−	0.480165i	−0.0227540	−	0.999741i	$-0.507243\pi$
$193$	5.97892e6	−	3.45193e6i	0.831670	−	0.480165i	0.854424	+	0.519576i	$0.173910\pi$
$194$	896677.	−	1.55309e6i	0.122809	−	0.212712i
$195$		0			0
$196$	1.70803e6	−	2.95840e6i	0.226844	−	0.392906i
$197$	−9.83753e6			−1.28673			−0.643365	−	0.765560i	$-0.722462\pi$
$197$	−9.83753e6			−1.28673			−0.643365	+	0.765560i	$0.722462\pi$
$198$		0			0
$199$	−747801.	+	1.29523e6i	−0.0948914	+	0.164357i	−0.909563	−	0.415565i	$-0.863584\pi$
$199$	−747801.	+	1.29523e6i	−0.0948914	+	0.164357i	0.814672	+	0.579922i	$0.196917\pi$
$200$	2.10206e6	+	1.21363e6i	0.262758	+	0.151703i
$201$		0			0
$202$			635396.i			0.0770887i
$203$	−1.20436e7	−	6.95339e6i	−1.43969	−	0.831206i
$204$		0			0
$205$	−6.74066e6	−	3.89172e6i	−0.782422	−	0.451731i
$206$	−2.08303e6	−	3.60791e6i	−0.238283	−	0.412719i
$207$		0			0
$208$		−	2.83906e6i		−	0.315489i
$209$	1.44485e7	−	1.55533e6i	1.58265	−	0.170366i
$210$		0			0
$211$	−1.21782e6	+	703106.i	−0.129639	+	0.0748469i	−0.563417	−	0.826173i	$-0.690513\pi$
$211$	−1.21782e6	+	703106.i	−0.129639	+	0.0748469i	0.433778	+	0.901020i	$0.357180\pi$
$212$	−1.94321e6	+	1.12191e6i	−0.203944	+	0.117747i
$213$		0			0
$214$	−311909.	−	540242.i	−0.0318263	−	0.0551248i
$215$	−5.80361e6	+	1.00521e7i	−0.583960	+	1.01145i
$216$		0			0
$217$			1.82607e7i			1.78705i
$218$	−2.05252e6	+	3.55507e6i	−0.198115	+	0.343146i
$219$		0			0
$220$	1.15523e7			1.08492
$221$		−	2.32863e7i		−	2.15736i
$222$		0			0
$223$	−6.31963e6	+	3.64864e6i	−0.569872	+	0.329016i	−0.757098	−	0.653301i	$-0.773384\pi$
$223$	−6.31963e6	+	3.64864e6i	−0.569872	+	0.329016i	0.187226	+	0.982317i	$0.440050\pi$
$224$	−2.37639e6	−	1.37201e6i	−0.211434	−	0.122071i
$225$		0			0
$226$	−4.87829e6	−	8.44945e6i	−0.422613	−	0.731987i
$227$			9.97093e6i			0.852429i	0.904622	+	0.426214i	$0.140153\pi$
$227$			9.97093e6i			0.852429i	−0.904622	+	0.426214i	$0.859847\pi$
$228$		0			0
$229$	−1.78273e7			−1.48450			−0.742250	−	0.670123i	$-0.766241\pi$
$229$	−1.78273e7			−1.48450			−0.742250	+	0.670123i	$0.766241\pi$
$230$	−5.83551e6	+	3.36913e6i	−0.479618	+	0.276907i
$231$		0			0
$232$	−2.65711e6	+	4.60224e6i	−0.212787	+	0.368558i
$233$	4.52526e6	+	7.83799e6i	0.357747	+	0.619636i	0.987584	−	0.157091i	$-0.0502117\pi$
$233$	4.52526e6	+	7.83799e6i	0.357747	+	0.619636i	−0.629837	+	0.776727i	$0.716878\pi$
$234$		0			0
$235$	2.69517e7			2.07674
$236$			7.91136e6i			0.601887i
$237$		0			0
$238$	−1.94914e7	−	1.12534e7i	−1.44582	−	0.834742i
$239$	1.07087e7			0.784407			0.392204	−	0.919878i	$-0.371713\pi$
$239$	1.07087e7			0.784407			0.392204	+	0.919878i	$0.371713\pi$
$240$		0			0
$241$	−1.09983e6	−	634985.i	−0.0785730	−	0.0453641i	0.460199	−	0.887816i	$-0.347778\pi$
$241$	−1.09983e6	−	634985.i	−0.0785730	−	0.0453641i	−0.538772	+	0.842452i	$0.681111\pi$
$242$	1.33117e7	−	7.68550e6i	0.939261	−	0.542283i
$243$		0			0
$244$	−829370.	−	1.43651e6i	−0.0570925	−	0.0988871i
$245$	9.09491e6	+	1.57528e7i	0.618443	+	1.07118i
$246$		0			0
$247$	1.73920e7	+	7.69110e6i	1.15414	+	0.510385i
$248$	6.97797e6			0.457482
$249$		0			0
$250$	1.84998e6	−	1.06809e6i	0.118399	−	0.0683577i
$251$	7.66607e6	−	1.32780e7i	0.484788	−	0.839677i	−0.515060	−	0.857154i	$-0.672230\pi$
$251$	7.66607e6	−	1.32780e7i	0.484788	−	0.839677i	0.999847	+	0.0174776i	$0.00556356\pi$
$252$		0			0
$253$	−7.40553e6	+	1.28268e7i	−0.457293	+	0.792055i
$254$	9.69411e6			0.591571
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	6.98740e6	+	4.03418e6i	0.411639	+	0.237660i	0.691494	−	0.722383i	$-0.256953\pi$
$257$	6.98740e6	+	4.03418e6i	0.411639	+	0.237660i	−0.279855	+	0.960042i	$0.590286\pi$
$258$		0			0
$259$		−	2.32911e7i		−	1.34057i
$260$	1.30920e7	+	7.55869e6i	0.744881	+	0.430057i
$261$		0			0
$262$	3.55912e6	+	2.05486e6i	0.197897	+	0.114256i
$263$	−319023.	−	552564.i	−0.0175370	−	0.0303749i	0.857124	−	0.515111i	$-0.172249\pi$
$263$	−319023.	−	552564.i	−0.0175370	−	0.0303749i	−0.874661	+	0.484736i	$0.838916\pi$
$264$		0			0
$265$		−	1.19479e7i		−	0.642026i
$266$	1.48426e7	−	1.08409e7i	0.788616	−	0.575997i
$267$		0			0
$268$	−4.63265e6	+	2.67466e6i	−0.240672	+	0.138952i
$269$	−2.20327e7	+	1.27206e7i	−1.13191	+	0.653507i	−0.944414	−	0.328759i	$-0.893370\pi$
$269$	−2.20327e7	+	1.27206e7i	−1.13191	+	0.653507i	−0.187493	+	0.982266i	$0.560036\pi$
$270$		0			0
$271$	3.57904e6	+	6.19908e6i	0.179829	+	0.311472i	0.941822	−	0.336113i	$-0.109112\pi$
$271$	3.57904e6	+	6.19908e6i	0.179829	+	0.311472i	−0.761993	+	0.647585i	$0.775779\pi$
$272$	−4.30027e6	+	7.44828e6i	−0.213692	+	0.370126i
$273$		0			0
$274$			1.41119e7i			0.686018i
$275$	−1.42045e7	+	2.46028e7i	−0.683009	+	1.18301i
$276$		0			0
$277$	−2.13300e7			−1.00358			−0.501788	−	0.864990i	$-0.667324\pi$
$277$	−2.13300e7			−1.00358			−0.501788	+	0.864990i	$0.667324\pi$
$278$		−	861349.i		−	0.0400908i
$279$		0			0
$280$	1.26538e7	−	7.30566e6i	0.576429	−	0.332801i
$281$	−8.37820e6	−	4.83716e6i	−0.377600	−	0.218007i	0.299174	−	0.954199i	$-0.403289\pi$
$281$	−8.37820e6	−	4.83716e6i	−0.377600	−	0.218007i	−0.676773	+	0.736191i	$0.736622\pi$
$282$		0			0
$283$	−3.92776e6	−	6.80308e6i	−0.173295	−	0.300155i	0.766275	−	0.642513i	$-0.222108\pi$
$283$	−3.92776e6	−	6.80308e6i	−0.173295	−	0.300155i	−0.939570	+	0.342357i	$0.888775\pi$
$284$			84300.5i			0.00368023i
$285$		0			0
$286$	3.32288e7			1.42042
$287$	−1.87397e7	+	1.08194e7i	−0.792716	+	0.457675i
$288$		0			0
$289$	−2.32025e7	+	4.01879e7i	−0.961260	+	1.66495i
$290$	−1.41485e7	−	2.45060e7i	−0.580119	−	1.00480i
$291$		0			0
$292$	7.41656e6			0.297889
$293$			4.56689e7i			1.81559i	0.419415	+	0.907795i	$0.362235\pi$
$293$			4.56689e7i			1.81559i	−0.419415	+	0.907795i	$0.637765\pi$
$294$		0			0
$295$	−3.64824e7	−	2.10631e7i	−1.42108	−	0.820460i
$296$	−8.90025e6			−0.343184
$297$		0			0
$298$	−2.07236e7	−	1.19648e7i	−0.783098	−	0.452122i
$299$	−1.67852e7	+	9.69094e6i	−0.627932	+	0.362537i
$300$		0			0
$301$	1.61346e7	+	2.79460e7i	0.591642	+	1.02475i
$302$	3.50467e6	+	6.07027e6i	0.127241	+	0.220388i
$303$		0			0
$304$	−4.14265e6	−	5.67183e6i	−0.147454	−	0.201884i
$305$	8.83243e6			0.311301
$306$		0			0
$307$	−3.95527e7	+	2.28357e7i	−1.36698	+	0.789223i	−0.990541	−	0.137220i	$-0.956183\pi$
$307$	−3.95527e7	+	2.28357e7i	−1.36698	+	0.789223i	−0.376435	+	0.926443i	$0.622850\pi$
$308$	1.60582e7	−	2.78136e7i	0.549598	−	0.951932i
$309$		0			0
$310$	−1.85781e7	+	3.21782e7i	−0.623614	+	1.08013i
$311$	−5.28277e7			−1.75623			−0.878113	−	0.478453i	$-0.841198\pi$
$311$	−5.28277e7			−1.75623			−0.878113	+	0.478453i	$0.841198\pi$
$312$		0			0
$313$	1.97271e7	−	3.41683e7i	0.643324	−	1.11427i	−0.341361	−	0.939932i	$-0.610888\pi$
$313$	1.97271e7	−	3.41683e7i	0.643324	−	1.11427i	0.984686	−	0.174338i	$-0.0557787\pi$
$314$	2.22015e7	+	1.28180e7i	0.717121	+	0.414030i
$315$		0			0
$316$			1.39284e7i			0.441408i
$317$	−2.25973e7	−	1.30466e7i	−0.709381	−	0.409561i	0.101451	−	0.994841i	$-0.467652\pi$
$317$	−2.25973e7	−	1.30466e7i	−0.709381	−	0.409561i	−0.810832	+	0.585279i	$0.800985\pi$
$318$		0			0
$319$	−5.38654e7	−	3.10992e7i	−1.65935	−	0.958025i
$320$	−2.79172e6	−	4.83540e6i	−0.0851965	−	0.147565i
$321$		0			0
$322$			1.87331e7i			0.561101i
$323$	−3.39784e7	−	4.65210e7i	−1.00831	−	1.38052i
$324$		0			0
$325$	−3.21955e7	+	1.85881e7i	−0.937875	+	0.541482i
$326$	−1.86992e7	+	1.07960e7i	−0.539721	+	0.311608i
$327$		0			0
$328$	4.13442e6	+	7.16103e6i	0.117164	+	0.202934i
$329$	3.74643e7	−	6.48900e7i	1.05203	−	1.82218i
$330$		0			0
$331$		−	2.71670e7i		−	0.749130i	−0.927201	−	0.374565i	$-0.877792\pi$
$331$		−	2.71670e7i		−	0.749130i	0.927201	−	0.374565i	$-0.122208\pi$
$332$	8.85126e6	−	1.53308e7i	0.241875	−	0.418940i
$333$		0			0
$334$	2.98797e7			0.801931
$335$		−	2.84840e7i		−	0.757646i
$336$		0			0
$337$	−774580.	+	447204.i	−0.0202384	+	0.0116847i	−0.510085	−	0.860124i	$-0.670386\pi$
$337$	−774580.	+	447204.i	−0.0202384	+	0.0116847i	0.489847	+	0.871809i	$0.337053\pi$
$338$	1.40113e7	+	8.08945e6i	0.362852	+	0.209493i
$339$		0			0
$340$	−2.28980e7	−	3.96605e7i	−0.582587	−	1.00907i
$341$			8.16712e7i			2.05971i
$342$		0			0
$343$	−5.16198e6			−0.127919
$344$	1.06790e7	−	6.16554e6i	0.262335	−	0.151459i
$345$		0			0
$346$	−1.04056e7	+	1.80231e7i	−0.251212	+	0.435112i
$347$	1.55261e6	+	2.68920e6i	0.0371599	+	0.0643628i	0.884007	−	0.467473i	$-0.154836\pi$
$347$	1.55261e6	+	2.68920e6i	0.0371599	+	0.0643628i	−0.846847	+	0.531836i	$0.821502\pi$
$348$		0			0
$349$	−5.85298e7			−1.37690			−0.688448	−	0.725286i	$-0.741708\pi$
$349$	−5.85298e7			−1.37690			−0.688448	+	0.725286i	$0.741708\pi$
$350$			3.59316e7i			0.838056i
$351$		0			0
$352$	−1.06285e7	−	6.13635e6i	−0.243693	−	0.140696i
$353$	1.20882e7			0.274814			0.137407	−	0.990515i	$-0.456123\pi$
$353$	1.20882e7			0.274814			0.137407	+	0.990515i	$0.456123\pi$
$354$		0			0
$355$	−388743.	−	224441.i	−0.00868916	−	0.00501669i
$356$	−1.03829e7	+	5.99455e6i	−0.230127	+	0.132864i
$357$		0			0
$358$	−1.64065e6	−	2.84168e6i	−0.0357574	−	0.0619336i
$359$	1.11371e7	+	1.92901e7i	0.240708	+	0.416918i	0.960916	−	0.276840i	$-0.0892871\pi$
$359$	1.11371e7	+	1.92901e7i	0.240708	+	0.416918i	−0.720208	+	0.693758i	$0.755954\pi$
$360$		0			0
$361$	4.59681e7	−	1.00126e7i	0.977090	−	0.212826i
$362$	5.18007e7			1.09197
$363$		0			0
$364$	3.63972e7	−	2.10139e7i	0.754681	−	0.435715i
$365$	−1.97458e7	+	3.42007e7i	−0.406065	+	0.703325i
$366$		0			0
$367$	4.10044e7	−	7.10217e7i	0.829530	−	1.43679i	−0.0688770	−	0.997625i	$-0.521942\pi$
$367$	4.10044e7	−	7.10217e7i	0.829530	−	1.43679i	0.898407	−	0.439163i	$-0.144725\pi$
$368$	7.15849e6			0.143641
$369$		0			0
$370$	2.36959e7	−	4.10426e7i	0.467809	−	0.810269i
$371$	−2.87661e7	−	1.66081e7i	−0.563326	−	0.325236i
$372$		0			0
$373$		−	3.36821e7i		−	0.649041i	−0.945879	−	0.324521i	$-0.894797\pi$
$373$		−	3.36821e7i		−	0.649041i	0.945879	−	0.324521i	$-0.105203\pi$
$374$	−8.71758e7	−	5.03310e7i	−1.66641	−	0.962101i
$375$		0			0
$376$	−2.47965e7	−	1.43163e7i	−0.466473	−	0.269318i
$377$	−4.06966e7	−	7.04887e7i	−0.759512	−	1.31551i
$378$		0			0
$379$			6.05239e6i			0.111175i	0.998454	+	0.0555877i	$0.0177033\pi$
$379$			6.05239e6i			0.111175i	−0.998454	+	0.0555877i	$0.982297\pi$
$380$	3.71844e7	−	4.00276e6i	0.677657	−	0.0729473i
$381$		0			0
$382$	−1.23129e7	+	7.10885e6i	−0.220887	+	0.127529i
$383$	6.43303e6	−	3.71411e6i	0.114504	−	0.0661087i	−0.441654	−	0.897185i	$-0.645608\pi$
$383$	6.43303e6	−	3.71411e6i	0.114504	−	0.0661087i	0.556158	+	0.831077i	$0.312275\pi$
$384$		0			0
$385$	8.55065e7	+	1.48102e8i	1.49836	+	2.59524i
$386$	1.95271e7	−	3.38219e7i	0.339528	−	0.588080i
$387$		0			0
$388$		−	1.01447e7i		−	0.173678i
$389$	3.11660e7	−	5.39811e7i	0.529459	−	0.917049i	−0.469951	−	0.882693i	$-0.655728\pi$
$389$	3.11660e7	−	5.39811e7i	0.529459	−	0.917049i	0.999410	−	0.0343568i	$-0.0109383\pi$
$390$		0			0
$391$	5.87147e7			0.982237
$392$		−	1.93242e7i		−	0.320806i
$393$		0			0
$394$	−4.81938e7	+	2.78247e7i	−0.787958	+	0.454928i
$395$	−6.42294e7	−	3.70828e7i	−1.04218	−	0.601702i
$396$		0			0
$397$	−5.89353e7	−	1.02079e8i	−0.941898	−	1.63141i	−0.761846	−	0.647758i	$-0.775707\pi$
$397$	−5.89353e7	−	1.02079e8i	−0.941898	−	1.63141i	−0.180051	−	0.983657i	$-0.557626\pi$
$398$			8.46040e6i			0.134197i
$399$		0			0
$400$	1.37306e7			0.214541
$401$	−1.07712e8	+	6.21876e7i	−1.67044	+	0.964430i	−0.703052	+	0.711138i	$0.748180\pi$
$401$	−1.07712e8	+	6.21876e7i	−1.67044	+	0.964430i	−0.967390	+	0.253292i	$0.918487\pi$
$402$		0			0
$403$	−5.34378e7	+	9.25570e7i	−0.816457	+	1.41415i
$404$	1.79717e6	+	3.11279e6i	0.0272550	+	0.0472070i
$405$		0			0
$406$	−7.86686e7			−1.17550
$407$		−	1.04170e8i		−	1.54511i
$408$		0			0
$409$	−2.42654e6	−	1.40096e6i	−0.0354664	−	0.0204765i	0.482162	−	0.876082i	$-0.339852\pi$
$409$	−2.42654e6	−	1.40096e6i	−0.0354664	−	0.0204765i	−0.517628	+	0.855606i	$0.673185\pi$
$410$	−4.40298e7			−0.638845
$411$		0			0
$412$	−2.04094e7	−	1.17834e7i	−0.291836	−	0.168492i
$413$	−1.01425e8	+	5.85577e7i	−1.43977	+	0.831254i
$414$		0			0
$415$	4.71310e7	+	8.16334e7i	0.659421	+	1.14215i
$416$	−8.03007e6	−	1.39085e7i	−0.111542	−	0.193197i
$417$		0			0
$418$	6.63839e7	−	4.84862e7i	0.908938	−	0.663879i
$419$	7.84560e7			1.06656			0.533278	−	0.845940i	$-0.320960\pi$
$419$	7.84560e7			1.06656			0.533278	+	0.845940i	$0.320960\pi$
$420$		0			0
$421$	−3.89553e7	+	2.24909e7i	−0.522060	+	0.301412i	−0.737777	−	0.675044i	$-0.764125\pi$
$421$	−3.89553e7	+	2.24909e7i	−0.522060	+	0.301412i	0.215717	+	0.976456i	$0.430791\pi$
$422$	−3.97737e6	+	6.88901e6i	−0.0529247	+	0.0916683i
$423$		0			0
$424$	−6.34648e6	+	1.09924e7i	−0.0832599	+	0.144210i
$425$	1.12620e8			1.46706
$426$		0			0
$427$	1.22775e7	−	2.12653e7i	0.157698	−	0.273142i
$428$	−3.05607e6	−	1.76442e6i	−0.0389791	−	0.0225046i
$429$		0			0
$430$			6.56603e7i			0.825844i
$431$	2.65195e7	+	1.53110e7i	0.331233	+	0.191237i	0.656388	−	0.754423i	$-0.272083\pi$
$431$	2.65195e7	+	1.53110e7i	0.331233	+	0.191237i	−0.325155	+	0.945661i	$0.605417\pi$
$432$		0			0
$433$	5.86645e7	+	3.38700e7i	0.722623	+	0.417207i	0.815717	−	0.578451i	$-0.196342\pi$
$433$	5.86645e7	+	3.38700e7i	0.722623	+	0.417207i	−0.0930943	+	0.995657i	$0.529676\pi$
$434$	5.16489e7	+	8.94586e7i	0.631818	+	1.09434i
$435$		0			0
$436$			2.32216e7i			0.280177i
$437$	−1.93926e7	+	4.38527e7i	−0.232376	+	0.525475i
$438$		0			0
$439$	1.04174e7	−	6.01448e6i	0.123130	−	0.0710893i	−0.437170	−	0.899379i	$-0.644019\pi$
$439$	1.04174e7	−	6.01448e6i	0.123130	−	0.0710893i	0.560300	+	0.828290i	$0.310686\pi$
$440$	5.65943e7	−	3.26747e7i	0.664377	−	0.383578i
$441$		0			0
$442$	−6.58635e7	−	1.14079e8i	−0.762743	−	1.32111i
$443$	−4.34937e7	+	7.53334e7i	−0.500283	+	0.866515i	0.499717	+	0.866189i	$0.333437\pi$
$443$	−4.34937e7	+	7.53334e7i	−0.500283	+	0.866515i	−1.00000		0.000326534i	$0.999896\pi$
$444$		0			0
$445$		−	6.38393e7i		−	0.724450i
$446$	−2.06398e7	+	3.57492e7i	−0.232649	+	0.402960i
$447$		0			0
$448$	−1.55225e7			−0.172635
$449$		−	1.35990e8i		−	1.50234i	−0.660109	−	0.751170i	$-0.729490\pi$
$449$		−	1.35990e8i		−	1.50234i	0.660109	−	0.751170i	$-0.270510\pi$
$450$		0			0
$451$	−8.38138e7	+	4.83899e7i	−0.913663	+	0.527503i
$452$	−4.77973e7	−	2.75958e7i	−0.517593	−	0.298832i
$453$		0			0
$454$	2.82020e7	+	4.88474e7i	0.301379	+	0.522004i
$455$			2.23789e8i			2.37577i
$456$		0			0
$457$	−1.41239e8			−1.47981			−0.739907	−	0.672709i	$-0.765131\pi$
$457$	−1.41239e8			−1.47981			−0.739907	+	0.672709i	$0.765131\pi$
$458$	−8.73358e7	+	5.04233e7i	−0.909067	+	0.524850i
$459$		0			0
$460$	−1.90587e7	+	3.30106e7i	−0.195803	+	0.339141i
$461$	−2.15628e7	−	3.73479e7i	−0.220091	−	0.381209i	0.734744	−	0.678344i	$-0.237302\pi$
$461$	−2.15628e7	−	3.73479e7i	−0.220091	−	0.381209i	−0.954835	+	0.297135i	$0.903969\pi$
$462$		0			0
$463$	1.48353e8			1.49470			0.747350	−	0.664431i	$-0.231326\pi$
$463$	1.48353e8			1.49470			0.747350	+	0.664431i	$0.231326\pi$
$464$			3.00617e7i			0.300926i
$465$		0			0
$466$	4.43383e7	+	2.55988e7i	0.438149	+	0.252965i
$467$	1.76094e8			1.72900			0.864500	−	0.502634i	$-0.167636\pi$
$467$	1.76094e8			1.72900			0.864500	+	0.502634i	$0.167636\pi$
$468$		0			0
$469$	−6.85791e7	−	3.95942e7i	−0.664773	−	0.383807i
$470$	1.32036e8	−	7.62310e7i	1.27174	−	0.734240i
$471$		0			0
$472$	2.23767e7	+	3.87576e7i	0.212799	+	0.368579i
$473$	7.21624e7	+	1.24989e8i	0.681911	+	1.18110i
$474$		0			0
$475$	−3.71966e7	+	8.41134e7i	−0.347075	+	0.784846i
$476$	−1.27317e8			−1.18050
$477$		0			0
$478$	5.24615e7	−	3.02887e7i	0.480349	−	0.277330i
$479$	−5.49533e7	+	9.51819e7i	−0.500020	+	0.866060i	0.499980	+	0.866037i	$0.333341\pi$
$479$	−5.49533e7	+	9.51819e7i	−0.500020	+	0.866060i	−1.00000		2.30769e-5i	$0.999993\pi$
$480$		0			0
$481$	6.81587e7	−	1.18054e8i	0.612472	−	1.06083i
$482$	−7.18404e6			−0.0641546
$483$		0			0
$484$	4.34757e7	−	7.53022e7i	0.383452	−	0.664158i
$485$	4.67815e7	+	2.70093e7i	0.410061	+	0.236749i
$486$		0			0
$487$		−	1.17186e8i		−	1.01458i	−0.861775	−	0.507291i	$-0.830647\pi$
$487$		−	1.17186e8i		−	1.01458i	0.861775	−	0.507291i	$-0.169353\pi$
$488$	−8.12614e6	−	4.69163e6i	−0.0699237	−	0.0403705i
$489$		0			0
$490$	8.91115e7	+	5.14486e7i	0.757435	+	0.437306i
$491$	5.26780e7	+	9.12410e7i	0.445026	+	0.770807i	0.998054	−	0.0623553i	$-0.0198612\pi$
$491$	5.26780e7	+	9.12410e7i	0.445026	+	0.770807i	−0.553028	+	0.833162i	$0.686528\pi$
$492$		0			0
$493$			2.46570e8i			2.05778i
$494$	1.06957e8	−	1.15135e7i	0.887213	−	0.0955051i
$495$		0			0
$496$	3.41849e7	−	1.97367e7i	0.280149	−	0.161744i
$497$	−1.08075e6	+	623968.i	−0.00880347	+	0.00508269i
$498$		0			0
$499$	−9.68864e7	−	1.67812e8i	−0.779761	−	1.35059i	−0.932080	−	0.362254i	$-0.882007\pi$
$499$	−9.68864e7	−	1.67812e8i	−0.779761	−	1.35059i	0.152319	−	0.988331i	$-0.451326\pi$
$500$	6.04202e6	−	1.04651e7i	0.0483362	−	0.0837207i
$501$		0			0
$502$		−	8.67317e7i		−	0.685593i
$503$	1.02650e8	−	1.77795e8i	0.806595	−	1.39706i	−0.108614	−	0.994084i	$-0.534641\pi$
$503$	1.02650e8	−	1.77795e8i	0.806595	−	1.39706i	0.915209	−	0.402980i	$-0.132026\pi$
$504$		0			0
$505$	−1.91391e7			−0.148610
$506$			8.37840e7i			0.646710i
$507$		0			0
$508$	4.74912e7	−	2.74191e7i	0.362262	−	0.209152i
$509$	−4.03451e6	−	2.32933e6i	−0.0305941	−	0.0176635i	0.484625	−	0.874722i	$-0.338956\pi$
$509$	−4.03451e6	−	2.32933e6i	−0.0305941	−	0.0176635i	−0.515219	+	0.857059i	$0.672289\pi$
$510$		0			0
$511$	5.48953e7	+	9.50814e7i	0.411407	+	0.712579i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	4.56415e7			0.336101
$515$	1.08676e8	−	6.27440e7i	0.795630	−	0.459357i
$516$		0			0
$517$	1.67560e8	−	2.90222e8i	1.21255	−	2.10019i
$518$	−6.58771e7	−	1.14102e8i	−0.473964	−	0.820929i
$519$		0			0
$520$	8.55168e7			0.608193
$521$		−	1.51264e8i		−	1.06960i	−0.844978	−	0.534801i	$-0.820387\pi$
$521$		−	1.51264e8i		−	1.06960i	0.844978	−	0.534801i	$-0.179613\pi$
$522$		0			0
$523$	1.89523e8	+	1.09421e8i	1.32482	+	0.764883i	0.984493	−	0.175425i	$-0.0561300\pi$
$523$	1.89523e8	+	1.09421e8i	1.32482	+	0.764883i	0.340324	+	0.940308i	$0.389463\pi$
$524$	2.32481e7			0.161582
$525$		0			0
$526$	−3.12577e6	−	1.80467e6i	−0.0214783	−	0.0124005i
$527$	2.80388e8	−	1.61882e8i	1.91570	−	1.10603i
$528$		0			0
$529$	4.95829e7	+	8.58802e7i	0.334939	+	0.580131i
$530$	−3.37937e7	−	5.85323e7i	−0.226990	−	0.393159i
$531$		0			0
$532$	4.20510e7	−	9.50906e7i	0.279281	−	0.631543i
$533$	−1.26647e8			−0.836398
$534$		0			0
$535$	1.62729e7	−	9.39517e6i	0.106268	−	0.0613540i
$536$	−1.51302e7	+	2.62062e7i	−0.0982538	+	0.170181i
$537$		0			0
$538$	−7.19585e7	+	1.24636e8i	−0.462099	+	0.800379i
$539$	2.26173e8			1.44436
$540$		0			0
$541$	6.56754e7	−	1.13753e8i	0.414773	−	0.718409i	−0.580631	−	0.814167i	$-0.697194\pi$
$541$	6.56754e7	−	1.13753e8i	0.414773	−	0.718409i	0.995405	+	0.0957581i	$0.0305275\pi$
$542$	3.50673e7	+	2.02461e7i	0.220244	+	0.127158i
$543$		0			0
$544$			4.86520e7i			0.302206i
$545$	−1.07084e8	−	6.18251e7i	−0.661509	−	0.381922i
$546$		0			0
$547$	1.10784e8	+	6.39611e7i	0.676885	+	0.390800i	0.798680	−	0.601756i	$-0.205532\pi$
$547$	1.10784e8	+	6.39611e7i	0.676885	+	0.390800i	−0.121796	+	0.992555i	$0.538865\pi$
$548$	3.99146e7	+	6.91341e7i	0.242544	+	0.420098i
$549$		0			0
$550$			1.60705e8i			0.965921i
$551$	−1.84158e8	−	8.14382e7i	−1.10087	−	0.486825i
$552$		0			0
$553$	−1.78564e8	+	1.03094e8i	−1.05589	+	0.609619i
$554$	−1.04495e8	+	6.03302e7i	−0.614563	+	0.354818i
$555$		0			0
$556$	−2.43626e6	−	4.21973e6i	−0.0141742	−	0.0245505i
$557$	5.21712e7	−	9.03632e7i	0.301902	−	0.522909i	−0.674665	−	0.738124i	$-0.735712\pi$
$557$	5.21712e7	−	9.03632e7i	0.301902	−	0.522909i	0.976567	+	0.215215i	$0.0690453\pi$
$558$		0			0
$559$			1.88865e8i			1.08122i
$560$	4.13270e7	−	7.15805e7i	0.235326	−	0.407597i
$561$		0			0
$562$	−5.47262e7			−0.308309
$563$			2.08088e8i			1.16606i	0.812450	+	0.583030i	$0.198133\pi$
$563$			2.08088e8i			1.16606i	−0.812450	+	0.583030i	$0.801867\pi$
$564$		0			0
$565$	2.54510e8	−	1.46942e8i	1.41111	−	0.814704i
$566$	−3.84840e7	−	2.22188e7i	−0.212242	−	0.122538i
$567$		0			0
$568$	238438.	+	412986.i	0.00130116	+	0.00225367i
$569$			1.74234e8i			0.945792i	0.881118	+	0.472896i	$0.156791\pi$
$569$			1.74234e8i			0.945792i	−0.881118	+	0.472896i	$0.843209\pi$
$570$		0			0
$571$	2.87430e8			1.54392			0.771958	−	0.635674i	$-0.219278\pi$
$571$	2.87430e8			1.54392			0.771958	+	0.635674i	$0.219278\pi$
$572$	1.62787e8	−	9.39852e7i	0.869825	−	0.502194i
$573$		0			0
$574$	−6.12037e7	+	1.06008e8i	−0.323625	+	0.560535i
$575$	−4.68685e7	−	8.11786e7i	−0.246534	−	0.427010i
$576$		0			0
$577$	−7.22861e6			−0.0376294			−0.0188147	−	0.999823i	$-0.505989\pi$
$577$	−7.22861e6			−0.0376294			−0.0188147	+	0.999823i	$0.505989\pi$
$578$			2.62506e8i			1.35943i
$579$		0			0
$580$	−1.38627e8	−	8.00361e7i	−0.710498	−	0.410206i
$581$	2.62058e8			1.33619
$582$		0			0
$583$	−1.28657e8	−	7.42802e7i	−0.649274	−	0.374859i
$584$	3.63336e7	−	2.09772e7i	0.182419	−	0.105319i
$585$		0			0
$586$	1.29171e8	+	2.23731e8i	0.641908	+	1.11182i
$587$	−2.51761e7	−	4.36062e7i	−0.124473	−	0.215593i	0.797054	−	0.603908i	$-0.206391\pi$
$587$	−2.51761e7	−	4.36062e7i	−0.124473	−	0.215593i	−0.921527	+	0.388315i	$0.873057\pi$
$588$		0			0
$589$	2.82984e7	+	2.62883e8i	0.138489	+	1.28652i
$590$	−2.38302e8			−1.16031
$591$		0			0
$592$	−4.36021e7	+	2.51737e7i	−0.210156	+	0.121334i
$593$	1.83196e8	−	3.17304e8i	0.878520	−	1.52164i	0.0255541	−	0.999673i	$-0.491865\pi$
$593$	1.83196e8	−	3.17304e8i	0.878520	−	1.52164i	0.852966	−	0.521967i	$-0.174802\pi$
$594$		0			0
$595$	3.38969e8	−	5.87111e8i	1.60920	−	2.78721i
$596$	−1.35366e8			−0.639397
$597$		0			0
$598$	−5.48202e7	+	9.49514e7i	−0.256352	+	0.444015i
$599$	−1.99548e8	−	1.15209e8i	−0.928466	−	0.536050i	−0.0421401	−	0.999112i	$-0.513418\pi$
$599$	−1.99548e8	−	1.15209e8i	−0.928466	−	0.536050i	−0.886326	+	0.463061i	$0.846751\pi$
$600$		0			0
$601$		−	2.68476e8i		−	1.23675i	−0.785884	−	0.618374i	$-0.787792\pi$
$601$		−	2.68476e8i		−	1.23675i	0.785884	−	0.618374i	$-0.212208\pi$
$602$	1.58086e8	+	9.12712e7i	0.724611	+	0.418354i
$603$		0			0
$604$	3.43386e7	+	1.98254e7i	0.155838	+	0.0899728i
$605$	2.31499e8	+	4.00968e8i	1.04540	+	1.81069i
$606$		0			0
$607$		−	9.66029e7i		−	0.431941i	−0.976400	−	0.215970i	$-0.930709\pi$
$607$		−	9.66029e7i		−	0.431941i	0.976400	−	0.215970i	$-0.0692915\pi$
$608$	−3.63371e7	−	1.60690e7i	−0.161674	−	0.0714954i
$609$		0			0
$610$	4.32699e7	−	2.49819e7i	0.190632	−	0.110062i
$611$	3.79787e8	−	2.19270e8i	1.66501	−	0.961293i
$612$		0			0
$613$	−4.38546e7	−	7.59583e7i	−0.190385	−	0.329757i	0.754993	−	0.655733i	$-0.227640\pi$
$613$	−4.38546e7	−	7.59583e7i	−0.190385	−	0.329757i	−0.945378	+	0.325976i	$0.894307\pi$
$614$	−1.29178e8	+	2.23744e8i	−0.558065	+	0.966597i
$615$		0			0
$616$		−	1.81678e8i		−	0.777249i
$617$	5.96747e7	−	1.03360e8i	0.254059	−	0.440043i	−0.710580	−	0.703616i	$-0.751568\pi$
$617$	5.96747e7	−	1.03360e8i	0.254059	−	0.440043i	0.964640	+	0.263573i	$0.0849009\pi$
$618$		0			0
$619$	−3.57227e7			−0.150617			−0.0753083	−	0.997160i	$-0.523994\pi$
$619$	−3.57227e7			−0.150617			−0.0753083	+	0.997160i	$0.523994\pi$
$620$			2.10187e8i			0.881923i
$621$		0			0
$622$	−2.58802e8	+	1.49419e8i	−1.07546	+	0.620920i
$623$	−1.53702e8	−	8.87399e7i	−0.635646	−	0.366991i
$624$		0			0
$625$	1.36929e8	+	2.37167e8i	0.560860	+	0.971438i
$626$		−	2.23187e8i		−	0.909798i
$627$		0			0
$628$	1.45019e8			0.585527
$629$	−3.57629e8	+	2.06477e8i	−1.43708	+	0.829699i
$630$		0			0
$631$	−1.05749e8	+	1.83162e8i	−0.420907	+	0.729032i	−0.996028	−	0.0890356i	$-0.971621\pi$
$631$	−1.05749e8	+	1.83162e8i	−0.420907	+	0.729032i	0.575121	+	0.818068i	$0.304955\pi$
$632$	3.93954e7	+	6.82349e7i	0.156061	+	0.270306i
$633$		0			0
$634$	−1.47605e8			−0.579207
$635$			2.92001e8i			1.14042i
$636$		0			0
$637$	2.56319e8	+	1.47986e8i	0.991661	+	0.572536i
$638$	−3.51847e8			−1.35485
$639$		0			0
$640$	−2.73532e7	−	1.57924e7i	−0.104344	−	0.0602430i
$641$	1.29393e7	−	7.47051e6i	0.0491289	−	0.0283646i	−0.475234	−	0.879859i	$-0.657637\pi$
$641$	1.29393e7	−	7.47051e6i	0.0491289	−	0.0283646i	0.524363	+	0.851495i	$0.324303\pi$
$642$		0			0
$643$	−9.07546e7	−	1.57192e8i	−0.341378	−	0.591284i	0.643311	−	0.765605i	$-0.277560\pi$
$643$	−9.07546e7	−	1.57192e8i	−0.341378	−	0.591284i	−0.984689	+	0.174321i	$0.944227\pi$
$644$	5.29851e7	+	9.17729e7i	0.198379	+	0.343603i
$645$		0			0
$646$	−2.98041e8	−	1.31800e8i	−1.10555	−	0.488896i
$647$	−4.57321e8			−1.68853			−0.844265	−	0.535927i	$-0.819962\pi$
$647$	−4.57321e8			−1.68853			−0.844265	+	0.535927i	$0.819962\pi$
$648$		0			0
$649$	−4.53625e8	+	2.61900e8i	−1.65944	+	0.958081i
$650$	−1.05150e8	+	1.82125e8i	−0.382886	+	0.663177i
$651$		0			0
$652$	−6.10712e7	+	1.05778e8i	−0.220340	+	0.381641i
$653$	2.28284e8			0.819852			0.409926	−	0.912119i	$-0.365555\pi$
$653$	2.28284e8			0.819852			0.409926	+	0.912119i	$0.365555\pi$
$654$		0			0
$655$	−6.18955e7	+	1.07206e8i	−0.220260	+	0.381501i
$656$	4.05089e7	+	2.33878e7i	0.143496	+	0.0828473i
$657$		0			0
$658$		−	4.23860e8i		−	1.48780i
$659$	−3.43814e8	−	1.98501e8i	−1.20134	−	0.693595i	−0.240489	−	0.970652i	$-0.577308\pi$
$659$	−3.43814e8	−	1.98501e8i	−1.20134	−	0.693595i	−0.960854	+	0.277057i	$0.910641\pi$
$660$		0			0
$661$	−1.88382e8	−	1.08763e8i	−0.652282	−	0.376595i	0.137048	−	0.990564i	$-0.456239\pi$
$661$	−1.88382e8	−	1.08763e8i	−0.652282	−	0.376595i	−0.789330	+	0.613969i	$0.789572\pi$
$662$	−7.68398e7	−	1.33090e8i	−0.264857	−	0.458746i
$663$		0			0
$664$		−	1.00141e8i		−	0.342063i
$665$	3.26545e8	+	4.47082e8i	1.11039	+	1.52028i
$666$		0			0
$667$	1.77732e8	−	1.02614e8i	0.598947	−	0.345802i
$668$	1.46380e8	−	8.45126e7i	0.491080	−	0.283525i
$669$		0			0
$670$	−8.05649e7	−	1.39542e8i	−0.267868	−	0.463962i
$671$	5.49115e7	−	9.51095e7i	0.181759	−	0.314816i
$672$		0			0
$673$			3.63099e8i			1.19119i	0.803286	+	0.595593i	$0.203083\pi$
$673$			3.63099e8i			1.19119i	−0.803286	+	0.595593i	$0.796917\pi$
$674$	−2.52977e6	+	4.38168e6i	−0.00826230	+	0.0143107i
$675$		0			0
$676$	9.15217e7			0.296267
$677$		−	2.31011e8i		−	0.744504i	−0.928132	−	0.372252i	$-0.878586\pi$
$677$		−	2.31011e8i		−	0.744504i	0.928132	−	0.372252i	$-0.121414\pi$
$678$		0			0
$679$	1.30057e8	−	7.50885e7i	0.415456	−	0.239864i
$680$	−2.24354e8	−	1.29531e8i	−0.713520	−	0.411951i
$681$		0			0
$682$	2.31001e8	+	4.00105e8i	0.728217	+	1.26131i
$683$		−	1.93486e8i		−	0.607276i	−0.952787	−	0.303638i	$-0.901799\pi$
$683$		−	1.93486e8i		−	0.607276i	0.952787	−	0.303638i	$-0.0982014\pi$
$684$		0			0
$685$	−4.25073e8			−1.32249
$686$	−2.52884e7	+	1.46003e7i	−0.0783339	+	0.0452261i
$687$		0			0
$688$	3.48776e7	−	6.04097e7i	0.107098	−	0.185499i
$689$	−9.72037e7	−	1.68362e8i	−0.297184	−	0.514737i
$690$		0			0
$691$	−1.56808e8			−0.475264			−0.237632	−	0.971355i	$-0.576371\pi$
$691$	−1.56808e8			−0.475264			−0.237632	+	0.971355i	$0.576371\pi$
$692$			1.17726e8i			0.355268i
$693$		0			0
$694$	1.52124e7	+	8.78290e6i	0.0455114	+	0.0262760i
$695$	2.59451e7			0.0772861
$696$		0			0
$697$	3.32259e8	+	1.91830e8i	0.981246	+	0.566523i
$698$	−2.86736e8	+	1.65547e8i	−0.843173	+	0.486806i
$699$		0			0
$700$	1.01630e8	+	1.76028e8i	0.296298	+	0.513202i
$701$	7.57926e7	+	1.31277e8i	0.220025	+	0.381095i	0.954815	−	0.297199i	$-0.0960526\pi$
$701$	7.57926e7	+	1.31277e8i	0.220025	+	0.381095i	−0.734790	+	0.678295i	$0.762719\pi$
$702$		0			0
$703$	−3.60940e7	−	3.35302e8i	−0.103889	−	0.965095i
$704$	−6.94248e7			−0.198974
$705$		0			0
$706$	5.92200e7	−	3.41907e7i	0.168289	−	0.0971614i
$707$	−2.66043e7	+	4.60800e7i	−0.0752825	+	0.130393i
$708$		0			0
$709$	−9.62778e7	+	1.66758e8i	−0.270139	+	0.467894i	−0.968897	−	0.247463i	$-0.920403\pi$
$709$	−9.62778e7	+	1.66758e8i	−0.270139	+	0.467894i	0.698758	+	0.715358i	$0.253736\pi$
$710$	−2.53926e6			−0.00709467
$711$		0			0
$712$	−3.39103e7	+	5.87343e7i	−0.0939489	+	0.162724i
$713$	−2.33376e8	−	1.34740e8i	−0.643854	−	0.371729i
$714$		0			0
$715$			1.00090e9i			2.73825i
$716$	−1.60750e7	−	9.28090e6i	−0.0437937	−	0.0252843i
$717$		0			0
$718$	1.09121e8	+	6.30012e7i	0.294806	+	0.170206i
$719$	3.07401e8	+	5.32434e8i	0.827024	+	1.43245i	0.900362	+	0.435141i	$0.143301\pi$
$719$	3.07401e8	+	5.32434e8i	0.827024	+	1.43245i	−0.0733379	+	0.997307i	$0.523365\pi$
$720$		0			0
$721$		−	3.48869e8i		−	0.930801i
$722$	1.96877e8	−	1.79069e8i	0.523098	−	0.475782i
$723$		0			0
$724$	2.53771e8	−	1.46515e8i	0.668692	−	0.386069i
$725$	3.40906e8	−	1.96822e8i	0.894582	−	0.516487i
$726$		0			0
$727$	−2.88645e8	−	4.99947e8i	−0.751208	−	1.30113i	−0.947238	−	0.320532i	$-0.896138\pi$
$727$	−2.88645e8	−	4.99947e8i	−0.751208	−	1.30113i	0.196030	−	0.980598i	$-0.437195\pi$
$728$	1.18873e8	−	2.05893e8i	0.308097	−	0.533640i
$729$		0			0
$730$			2.23398e8i			0.574263i
$731$	2.86070e8	−	4.95487e8i	0.732352	−	1.26847i
$732$		0			0
$733$	−1.47386e7			−0.0374236			−0.0187118	−	0.999825i	$-0.505956\pi$
$733$	−1.47386e7			−0.0374236			−0.0187118	+	0.999825i	$0.505956\pi$
$734$		−	4.63912e8i		−	1.17313i
$735$		0			0
$736$	3.50693e7	−	2.02473e7i	0.0879616	−	0.0507847i
$737$	−3.06722e8	−	1.77086e8i	−0.766200	−	0.442366i
$738$		0			0
$739$	6.64418e7	+	1.15081e8i	0.164630	+	0.285147i	0.936524	−	0.350604i	$-0.114024\pi$
$739$	6.64418e7	+	1.15081e8i	0.164630	+	0.285147i	−0.771894	+	0.635751i	$0.780690\pi$
$740$		−	2.68089e8i		−	0.661582i
$741$		0			0
$742$	−1.87900e8			−0.459954
$743$	3.69572e8	−	2.13372e8i	0.901016	−	0.520202i	0.0234864	−	0.999724i	$-0.492523\pi$
$743$	3.69572e8	−	2.13372e8i	0.901016	−	0.520202i	0.877530	+	0.479522i	$0.159190\pi$
$744$		0			0
$745$	3.60397e8	−	6.24226e8i	0.871590	−	1.50964i
$746$	−9.52673e7	−	1.65008e8i	−0.229471	−	0.397455i
$747$		0			0
$748$	−5.69430e8			−1.36062
$749$		−	5.22390e7i		−	0.124322i
$750$		0			0
$751$	7.55366e7	+	4.36111e7i	0.178335	+	0.102962i	0.586510	−	0.809942i	$-0.300501\pi$
$751$	7.55366e7	+	4.36111e7i	0.178335	+	0.102962i	−0.408175	+	0.912904i	$0.633835\pi$
$752$	−1.61970e8			−0.380874
$753$		0			0
$754$	−3.98744e8	−	2.30215e8i	−0.930208	−	0.537056i
$755$	−1.82846e8	+	1.05566e8i	−0.424858	+	0.245292i
$756$		0			0
$757$	−9.60655e7	−	1.66390e8i	−0.221452	−	0.383566i	0.733797	−	0.679369i	$-0.237746\pi$
$757$	−9.60655e7	−	1.66390e8i	−0.221452	−	0.383566i	−0.955249	+	0.295802i	$0.904413\pi$
$758$	1.71187e7	+	2.96505e7i	0.0393065	+	0.0680808i
$759$		0			0
$760$	1.70844e8	−	1.24783e8i	0.389188	−	0.284259i
$761$	−3.89947e8			−0.884814			−0.442407	−	0.896814i	$-0.645875\pi$
$761$	−3.89947e8			−0.884814			−0.442407	+	0.896814i	$0.645875\pi$
$762$		0			0
$763$	−2.97705e8	+	1.71880e8i	−0.670212	+	0.386947i
$764$	−4.02137e7	+	6.96522e7i	−0.0901766	+	0.156190i
$765$		0			0
$766$	2.10102e7	−	3.63907e7i	0.0467459	−	0.0809663i
$767$	−6.85450e8			−1.51911
$768$		0			0
$769$	1.28041e8	−	2.21774e8i	0.281560	−	0.487676i	−0.690209	−	0.723610i	$-0.742482\pi$
$769$	1.28041e8	−	2.21774e8i	0.281560	−	0.487676i	0.971769	+	0.235934i	$0.0758149\pi$
$770$	8.37789e8	+	4.83698e8i	1.83511	+	1.05950i
$771$		0			0
$772$		−	2.20924e8i		−	0.480165i
$773$	3.69690e7	+	2.13441e7i	0.0800385	+	0.0462103i	0.539485	−	0.841995i	$-0.318619\pi$
$773$	3.69690e7	+	2.13441e7i	0.0800385	+	0.0462103i	−0.459447	+	0.888205i	$0.651952\pi$
$774$		0			0
$775$	−4.47635e8	−	2.58442e8i	−0.961655	−	0.555212i
$776$	−2.86937e7	−	4.96989e7i	−0.0614046	−	0.106356i
$777$		0			0
$778$		−	3.52603e8i		−	0.748768i
$779$	−2.53013e8	+	1.84798e8i	−0.535218	+	0.390918i
$780$		0			0
$781$	−4.83365e6	+	2.79071e6i	−0.0101466	+	0.00585817i
$782$	2.87642e8	−	1.66070e8i	0.601495	−	0.347273i
$783$		0			0
$784$	−5.46571e7	−	9.46688e7i	−0.113422	−	0.196453i
$785$	−3.86098e8	+	6.68742e8i	−0.798158	+	1.38245i
$786$		0			0
$787$		−	6.52431e8i		−	1.33847i	−0.743049	−	0.669237i	$-0.766621\pi$
$787$		−	6.52431e8i		−	1.33847i	0.743049	−	0.669237i	$-0.233379\pi$
$788$	−1.57400e8	+	2.72625e8i	−0.321682	+	0.557170i
$789$		0			0
$790$	−4.19544e8			−0.850936
$791$		−	8.17025e8i		−	1.65084i
$792$		0			0
$793$	1.24461e8	−	7.18576e7i	0.249582	−	0.144097i
$794$	−5.77445e8	−	3.33388e8i	−1.15358	−	0.666022i
$795$		0			0
$796$	2.39296e7	+	4.14473e7i	0.0474457	+	0.0821784i
$797$			5.56853e8i			1.09993i	0.835187	+	0.549966i	$0.185359\pi$
$797$			5.56853e8i			1.09993i	−0.835187	+	0.549966i	$0.814641\pi$
$798$		0			0
$799$	−1.32850e9			−2.60447
$800$	6.72659e7	−	3.88360e7i	0.131379	−	0.0758516i
$801$		0			0
$802$	−3.51786e8	+	6.09312e8i	−0.681955	+	1.18118i
$803$	2.45520e8	+	4.25253e8i	0.474177	+	0.821299i
$804$		0			0
$805$	−5.64268e8			−1.08168
$806$			6.04580e8i			1.15464i
$807$		0			0
$808$	1.76086e7	+	1.01663e7i	0.0333804	+	0.0192722i
$809$	8.85849e8			1.67307			0.836535	−	0.547914i	$-0.184578\pi$
$809$	8.85849e8			1.67307			0.836535	+	0.547914i	$0.184578\pi$
$810$		0			0
$811$	−2.91933e8	−	1.68547e8i	−0.547294	−	0.315980i	0.200736	−	0.979645i	$-0.435667\pi$
$811$	−2.91933e8	−	1.68547e8i	−0.547294	−	0.315980i	−0.748030	+	0.663665i	$0.769000\pi$
$812$	−3.85396e8	+	2.22508e8i	−0.719845	+	0.415603i
$813$		0			0
$814$	−2.94637e8	−	5.10326e8i	−0.546278	−	0.946181i
$815$	−3.25191e8	−	5.63247e8i	−0.600711	−	1.04046i
$816$		0			0
$817$	2.75584e8	+	3.77311e8i	0.505345	+	0.691884i
$818$	−1.58501e7			−0.0289582
$819$		0			0
$820$	−2.15701e8	+	1.24535e8i	−0.391211	+	0.225866i
$821$	−3.08479e8	+	5.34300e8i	−0.557437	+	0.965508i	0.440273	+	0.897864i	$0.354882\pi$
$821$	−3.08479e8	+	5.34300e8i	−0.557437	+	0.965508i	−0.997709	+	0.0676445i	$0.978452\pi$
$822$		0			0
$823$	−1.86716e8	+	3.23401e8i	−0.334951	+	0.580153i	−0.983475	−	0.181041i	$-0.942053\pi$
$823$	−1.86716e8	+	3.23401e8i	−0.334951	+	0.580153i	0.648524	+	0.761194i	$0.275387\pi$
$824$	−1.33314e8			−0.238283
$825$		0			0
$826$	−3.31252e8	+	5.73746e8i	−0.587785	+	1.01807i
$827$	−2.92181e8	−	1.68691e8i	−0.516577	−	0.298246i	0.218956	−	0.975735i	$-0.429735\pi$
$827$	−2.92181e8	−	1.68691e8i	−0.516577	−	0.298246i	−0.735533	+	0.677489i	$0.763068\pi$
$828$		0			0
$829$			8.99748e8i			1.57927i	0.613575	+	0.789637i	$0.289731\pi$
$829$			8.99748e8i			1.57927i	−0.613575	+	0.789637i	$0.710269\pi$
$830$	4.61788e8	+	2.66613e8i	0.807623	+	0.466281i
$831$		0			0
$832$	−7.86783e7	−	4.54249e7i	−0.136611	−	0.0788723i
$833$	−4.48303e8	−	7.76484e8i	−0.775598	−	1.34338i
$834$		0			0
$835$			9.00022e8i			1.54594i
$836$	1.88074e8	−	4.25295e8i	0.321892	−	0.727899i
$837$		0			0
$838$	3.84354e8	−	2.21907e8i	0.653130	−	0.377085i
$839$	−2.08397e8	+	1.20318e8i	−0.352863	+	0.203726i	−0.665946	−	0.746000i	$-0.731972\pi$
$839$	−2.08397e8	+	1.20318e8i	−0.352863	+	0.203726i	0.313082	+	0.949726i	$0.398638\pi$
$840$		0			0
$841$	1.33510e8	+	2.31246e8i	0.224453	+	0.388764i
$842$	−1.27228e8	+	2.20365e8i	−0.213130	+	0.369152i
$843$		0			0
$844$			4.49988e7i			0.0748469i
$845$	−2.43667e8	+	4.22043e8i	−0.403855	+	0.699498i
$846$		0			0
$847$	1.28718e9			2.11831
$848$			7.18023e7i			0.117747i
$849$		0			0
$850$	5.51723e8	−	3.18537e8i	0.898388	−	0.518685i
$851$	2.97666e8	+	1.71857e8i	0.482992	+	0.278856i
$852$		0			0
$853$	−4.17202e8	−	7.22615e8i	−0.672201	−	1.16429i	−0.977278	−	0.211959i	$-0.932016\pi$
$853$	−4.17202e8	−	7.22615e8i	−0.672201	−	1.16429i	0.305077	−	0.952328i	$-0.401318\pi$
$854$		−	1.38904e8i		−	0.223019i
$855$		0			0
$856$	−1.99622e7			−0.0318263
$857$	3.04172e8	−	1.75614e8i	0.483255	−	0.279007i	−0.238517	−	0.971138i	$-0.576661\pi$
$857$	3.04172e8	−	1.75614e8i	0.483255	−	0.279007i	0.721772	+	0.692131i	$0.243328\pi$
$858$		0			0
$859$	4.57849e8	−	7.93018e8i	0.722342	−	1.25113i	−0.237716	−	0.971335i	$-0.576399\pi$
$859$	4.57849e8	−	7.93018e8i	0.722342	−	1.25113i	0.960059	−	0.279799i	$-0.0902678\pi$
$860$	1.85715e8	+	3.21669e8i	0.291980	+	0.505724i
$861$		0			0
$862$	1.73225e8			0.270451
$863$			1.32268e8i			0.205789i	0.994692	+	0.102895i	$0.0328104\pi$
$863$			1.32268e8i			0.205789i	−0.994692	+	0.102895i	$0.967190\pi$
$864$		0			0
$865$	−5.42883e8	−	3.13434e8i	−0.838800	−	0.484281i
$866$	3.83195e8			0.590019
$867$		0			0
$868$	5.06054e8	+	2.92171e8i	0.773816	+	0.446763i
$869$	−7.98632e8	+	4.61090e8i	−1.21699	+	0.702630i
$870$		0			0
$871$	−2.31736e8	−	4.01378e8i	−0.350703	−	0.607435i
$872$	6.56807e7	+	1.13762e8i	0.0990577	+	0.171573i
$873$		0			0
$874$	2.90305e7	+	2.69684e8i	0.0434830	+	0.403944i
$875$	1.78885e8			0.267024
$876$		0			0
$877$	−2.45547e8	+	1.41767e8i	−0.364029	+	0.210172i	−0.670847	−	0.741596i	$-0.734069\pi$
$877$	−2.45547e8	+	1.41767e8i	−0.364029	+	0.210172i	0.306818	+	0.951768i	$0.400736\pi$
$878$	3.40230e7	−	5.89296e7i	0.0502677	−	0.0870663i
$879$		0			0
$880$	1.84836e8	−	3.20145e8i	0.271231	−	0.469785i
$881$	2.29004e8			0.334901			0.167450	−	0.985881i	$-0.446447\pi$
$881$	2.29004e8			0.334901			0.167450	+	0.985881i	$0.446447\pi$
$882$		0			0
$883$	−8.94334e7	+	1.54903e8i	−0.129902	+	0.224998i	−0.923639	−	0.383265i	$-0.874800\pi$
$883$	−8.94334e7	+	1.54903e8i	−0.129902	+	0.224998i	0.793736	+	0.608262i	$0.208133\pi$
$884$	−6.45328e8	−	3.72580e8i	−0.934166	−	0.539341i
$885$		0			0
$886$			4.92075e8i			0.707507i
$887$	−1.25755e8	−	7.26046e7i	−0.180200	−	0.104038i	0.407187	−	0.913345i	$-0.366510\pi$
$887$	−1.25755e8	−	7.26046e7i	−0.180200	−	0.104038i	−0.587386	+	0.809307i	$0.699843\pi$
$888$		0			0
$889$	7.03034e8	+	4.05897e8i	1.00062	+	0.577710i
$890$	−1.80565e8	−	3.12748e8i	−0.256132	−	0.443633i
$891$		0			0
$892$			2.33513e8i			0.329016i
$893$	4.38782e8	−	9.92225e8i	0.616161	−	1.39334i
$894$		0			0
$895$	8.55958e7	−	4.94188e7i	0.119394	−	0.0689323i
$896$	−7.60445e7	+	4.39043e7i	−0.105717	+	0.0610356i
$897$		0			0
$898$	−3.84638e8	−	6.66213e8i	−0.531158	−	0.919992i
$899$	5.65833e8	−	9.80051e8i	0.778770	−	1.34887i
$900$		0			0
$901$			5.88930e8i			0.805173i
$902$	−2.73735e8	+	4.74122e8i	−0.373001	+	0.646057i
$903$		0			0
$904$	−3.12211e8			−0.422613
$905$			1.56032e9i			2.10507i
$906$		0			0
$907$	−1.02435e9	+	5.91408e8i	−1.37286	+	0.792621i	−0.991287	−	0.131718i	$-0.957951\pi$
$907$	−1.02435e9	+	5.91408e8i	−1.37286	+	0.792621i	−0.381573	+	0.924339i	$0.624617\pi$
$908$	2.76322e8	+	1.59535e8i	0.369112	+	0.213107i
$909$		0			0
$910$	6.32971e8	+	1.09634e9i	0.839962	+	1.45486i
$911$			1.07316e8i			0.141942i	0.997478	+	0.0709708i	$0.0226097\pi$
$911$			1.07316e8i			0.141942i	−0.997478	+	0.0709708i	$0.977390\pi$
$912$		0			0
$913$	1.17206e9			1.54006
$914$	−6.91929e8	+	3.99485e8i	−0.906198	+	0.523194i
$915$		0			0
$916$	−2.85237e8	+	4.94046e8i	−0.371125	+	0.642807i
$917$	1.72076e8	+	2.98044e8i	0.223158	+	0.386520i
$918$		0			0
$919$	8.67281e7			0.111741			0.0558706	−	0.998438i	$-0.482207\pi$
$919$	8.67281e7			0.111741			0.0558706	+	0.998438i	$0.482207\pi$
$920$			2.15624e8i			0.276907i
$921$		0			0
$922$	−2.11271e8	−	1.21978e8i	−0.269555	−	0.155628i
$923$	−7.30390e6			−0.00928859
$924$		0			0
$925$	5.70949e8	+	3.29638e8i	0.721393	+	0.416497i
$926$	7.26779e8	−	4.19606e8i	0.915313	−	0.528456i
$927$		0			0
$928$	8.50274e7	+	1.47272e8i	0.106393	+	0.184279i
$929$	5.27852e8	+	9.14267e8i	0.658362	+	1.14032i	0.981039	+	0.193808i	$0.0620839\pi$
$929$	5.27852e8	+	9.14267e8i	0.658362	+	1.14032i	−0.322677	+	0.946509i	$0.604583\pi$
$930$		0			0
$931$	7.28007e8	−	7.83672e7i	0.902166	−	0.0971148i
$932$	2.89617e8			0.357747
$933$		0			0
$934$	8.62683e8	−	4.98070e8i	1.05879	−	0.611293i
$935$	1.51605e9	−	2.62587e9i	1.85472	−	3.21246i
$936$		0			0
$937$	3.34198e8	−	5.78847e8i	0.406242	−	0.703632i	−0.588223	−	0.808699i	$-0.700172\pi$
$937$	3.34198e8	−	5.78847e8i	0.406242	−	0.703632i	0.994465	+	0.105067i	$0.0335057\pi$
$938$	−4.47957e8			−0.542785
$939$		0			0
$940$	4.31228e8	−	7.46908e8i	0.519186	−	0.899257i
$941$	−7.92814e8	−	4.57731e8i	−0.951486	−	0.549341i	−0.0579438	−	0.998320i	$-0.518454\pi$
$941$	−7.92814e8	−	4.57731e8i	−0.951486	−	0.549341i	−0.893542	+	0.448979i	$0.851788\pi$
$942$		0			0
$943$		−	3.19331e8i		−	0.380808i
$944$	2.19246e8	+	1.26582e8i	0.260625	+	0.150472i
$945$		0			0
$946$	7.07044e8	+	4.08212e8i	0.835167	+	0.482184i
$947$	−2.84686e8	−	4.93091e8i	−0.335209	−	0.580600i	0.648316	−	0.761372i	$-0.275474\pi$
$947$	−2.84686e8	−	4.93091e8i	−0.335209	−	0.580600i	−0.983525	+	0.180772i	$0.942140\pi$
$948$		0			0
$949$			6.42580e8i			0.751845i
$950$	5.56830e7	+	5.17278e8i	0.0649459	+	0.603327i
$951$		0			0
$952$	−6.23726e8	+	3.60108e8i	−0.722908	+	0.417371i
$953$	−1.37353e9	+	7.93011e8i	−1.58694	+	0.916221i	−0.593134	+	0.805104i	$0.702110\pi$
$953$	−1.37353e9	+	7.93011e8i	−1.58694	+	0.916221i	−0.993807	+	0.111118i	$0.964557\pi$
$954$		0			0
$955$	−2.14129e8	−	3.70883e8i	−0.245848	−	0.425820i
$956$	1.71339e8	−	2.96767e8i	0.196102	−	0.339658i
$957$		0			0
$958$			6.21726e8i			0.707135i
$959$	−5.90873e8	+	1.02342e9i	−0.669944	+	1.16038i
$960$		0			0
$961$	−5.98459e8			−0.674318
$962$		−	7.71128e8i		−	0.866166i
$963$		0			0
$964$	−3.51945e7	+	2.03195e7i	−0.0392865	+	0.0226821i
$965$	1.01877e9	+	5.88186e8i	1.13369	+	0.654534i
$966$		0			0
$967$	−1.43965e8	−	2.49354e8i	−0.159212	−	0.275763i	0.775373	−	0.631504i	$-0.217562\pi$
$967$	−1.43965e8	−	2.49354e8i	−0.159212	−	0.275763i	−0.934585	+	0.355740i	$0.884229\pi$
$968$		−	4.91872e8i		−	0.542283i
$969$		0			0
$970$	3.05575e8			0.334813
$971$	1.24333e9	−	7.17834e8i	1.35809	−	0.784091i	0.368720	−	0.929541i	$-0.379796\pi$
$971$	1.24333e9	−	7.17834e8i	1.35809	−	0.784091i	0.989366	+	0.145449i	$0.0464628\pi$
$972$		0			0
$973$	3.60650e7	−	6.24665e7i	0.0391515	−	0.0678123i
$974$	−3.31451e8	−	5.74090e8i	−0.358709	−	0.621302i
$975$		0			0
$976$	−5.30797e7			−0.0570925
$977$			1.35543e9i			1.45343i	0.686940	+	0.726715i	$0.258954\pi$
$977$			1.35543e9i			1.45343i	−0.686940	+	0.726715i	$0.741046\pi$
$978$		0			0
$979$	−6.87436e8	−	3.96891e8i	−0.732629	−	0.422983i
$980$	5.82074e8			0.618443
$981$		0			0
$982$	5.16137e8	+	2.97992e8i	0.545043	+	0.314681i
$983$	−4.46227e8	+	2.57629e8i	−0.469781	+	0.271228i	−0.716148	−	0.697948i	$-0.754096\pi$
$983$	−4.46227e8	+	2.57629e8i	−0.469781	+	0.271228i	0.246367	+	0.969177i	$0.420763\pi$
$984$		0			0
$985$	−8.38123e8	−	1.45167e9i	−0.876999	−	1.51901i
$986$	6.97404e8	+	1.20794e9i	0.727535	+	1.26013i
$987$		0			0
$988$	4.91414e8	−	3.58924e8i	0.509538	−	0.372162i
$989$	−4.76209e8			−0.492276
$990$		0			0
$991$	−2.51972e8	+	1.45476e8i	−0.258900	+	0.149476i	−0.623833	−	0.781558i	$-0.714425\pi$
$991$	−2.51972e8	+	1.45476e8i	−0.258900	+	0.149476i	0.364933	+	0.931034i	$0.381092\pi$
$992$	1.11647e8	−	1.93379e8i	0.114370	−	0.198095i
$993$		0			0
$994$	−3.52970e6	+	6.11362e6i	−0.00359400	+	0.00622500i
$995$	−2.54840e8			−0.258701
$996$		0			0
$997$	−8.07050e8	+	1.39785e9i	−0.814357	+	1.41051i	0.0954314	+	0.995436i	$0.469577\pi$
$997$	−8.07050e8	+	1.39785e9i	−0.814357	+	1.41051i	−0.909789	+	0.415072i	$0.863756\pi$
$998$	−9.49289e8	−	5.48072e8i	−0.955008	−	0.551374i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.7.m.a.145.10		20
3.2	odd	2		38.7.d.a.31.2	yes	20
19.8	odd	6	inner	342.7.m.a.217.10		20
57.8	even	6		38.7.d.a.27.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.2	✓	20	57.8	even	6
38.7.d.a.31.2	yes	20	3.2	odd	2
342.7.m.a.145.10		20	1.1	even	1	trivial
342.7.m.a.217.10		20	19.8	odd	6	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	342.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(85.1965 + 147.565i) q^{5} +473.710 q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(85.1965 + 147.565i) q^{5} +473.710 q^{7} -181.019i q^{8} +(834.752 + 481.944i) q^{10} +2118.68 q^{11} +(2401.07 + 1386.26i) q^{13} +(2320.70 - 1339.85i) q^{14} +(-512.000 - 886.810i) q^{16} +(-4199.48 - 7273.71i) q^{17} +(6819.60 - 734.105i) q^{19} +5452.58 q^{20} +(10379.4 - 5992.52i) q^{22} +(-3495.35 + 6054.13i) q^{23} +(-6704.40 + 11612.4i) q^{25} +15683.7 q^{26} +(7579.36 - 13127.8i) q^{28} +(-25424.0 - 14678.6i) q^{29} +38548.2i q^{31} +(-5016.55 - 2896.31i) q^{32} +(-41146.3 - 23755.8i) q^{34} +(40358.4 + 69902.9i) q^{35} -49167.4i q^{37} +(31332.7 - 22885.1i) q^{38} +(26712.1 - 15422.2i) q^{40} +(-39559.5 + 22839.7i) q^{41} +(34060.1 + 58993.9i) q^{43} +(33898.8 - 58714.5i) q^{44} +39545.4i q^{46} +(79086.9 - 136983. i) q^{47} +106752. q^{49} +75851.6i q^{50} +(76834.3 - 44360.3i) q^{52} +(-60725.2 - 35059.7i) q^{53} +(180504. + 312642. i) q^{55} -85750.7i q^{56} -166069. q^{58} +(-214108. + 123615. i) q^{59} +(25917.8 - 44891.0i) q^{61} +(109031. + 188847. i) q^{62} -32768.0 q^{64} +472418. i q^{65} +(-144770. - 83583.2i) q^{67} -268767. q^{68} +(395430. + 228302. i) q^{70} +(-2281.45 + 1317.20i) q^{71} +(115884. + 200716. i) q^{73} +(-139066. - 240870. i) q^{74} +(88769.5 - 200736. i) q^{76} +1.00364e6 q^{77} +(-376948. + 217631. i) q^{79} +(87241.2 - 151106. i) q^{80} +(-129201. + 223782. i) q^{82} +553204. q^{83} +(715562. - 1.23939e6i) q^{85} +(333720. + 192673. i) q^{86} -383522. i q^{88} +(-324464. - 187330. i) q^{89} +(1.13741e6 + 656685. i) q^{91} +(111851. + 193732. i) q^{92} -894766. i q^{94} +(689334. + 943789. i) q^{95} +(274550. - 158512. i) q^{97} +(522976. - 301940. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 320 q^{4} - 112 q^{5} - 208 q^{7}+O(q^{10}) \) 20 * q + 320 * q^4 - 112 * q^5 - 208 * q^7	\( 20 q + 320 q^{4} - 112 q^{5} - 208 q^{7} + 284 q^{11} + 10500 q^{13} - 1248 q^{14} - 10240 q^{16} + 11684 q^{17} + 12862 q^{19} - 7168 q^{20} + 52704 q^{22} - 8488 q^{23} - 63842 q^{25} + 43968 q^{26} - 3328 q^{28} - 137760 q^{29} + 70560 q^{34} + 6916 q^{35} + 77232 q^{38} - 109206 q^{41} + 35572 q^{43} + 4544 q^{44} + 361184 q^{47} + 259740 q^{49} + 336000 q^{52} + 236172 q^{53} + 56760 q^{55} - 225600 q^{58} - 1310610 q^{59} + 83552 q^{61} - 225792 q^{62} - 655360 q^{64} + 806646 q^{67} + 747776 q^{68} - 245664 q^{70} + 869220 q^{71} - 207422 q^{73} - 1460832 q^{74} - 140096 q^{76} + 3988336 q^{77} - 1706808 q^{79} - 114688 q^{80} + 887712 q^{82} - 3527548 q^{83} - 5604 q^{85} - 195792 q^{86} - 708432 q^{89} - 1914384 q^{91} + 271616 q^{92} + 2820356 q^{95} + 5113242 q^{97} + 612480 q^{98}+O(q^{100}) \) 20 * q + 320 * q^4 - 112 * q^5 - 208 * q^7 + 284 * q^11 + 10500 * q^13 - 1248 * q^14 - 10240 * q^16 + 11684 * q^17 + 12862 * q^19 - 7168 * q^20 + 52704 * q^22 - 8488 * q^23 - 63842 * q^25 + 43968 * q^26 - 3328 * q^28 - 137760 * q^29 + 70560 * q^34 + 6916 * q^35 + 77232 * q^38 - 109206 * q^41 + 35572 * q^43 + 4544 * q^44 + 361184 * q^47 + 259740 * q^49 + 336000 * q^52 + 236172 * q^53 + 56760 * q^55 - 225600 * q^58 - 1310610 * q^59 + 83552 * q^61 - 225792 * q^62 - 655360 * q^64 + 806646 * q^67 + 747776 * q^68 - 245664 * q^70 + 869220 * q^71 - 207422 * q^73 - 1460832 * q^74 - 140096 * q^76 + 3988336 * q^77 - 1706808 * q^79 - 114688 * q^80 + 887712 * q^82 - 3527548 * q^83 - 5604 * q^85 - 195792 * q^86 - 708432 * q^89 - 1914384 * q^91 + 271616 * q^92 + 2820356 * q^95 + 5113242 * q^97 + 612480 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more