LMFDB - Embedded newform 315.4.d.b.64.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(64,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("315.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 $ x^10 + 37x^8 + 398x^6 + 1149x^4 + 1040x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.10
Root			$-3.71490i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.18660i q^{2} -18.9008 q^{4} +(4.24321 - 10.3438i) q^{5} -7.00000i q^{7} -56.5383i q^{8} +O(q^{10})$	\(q+5.18660i q^{2} -18.9008 q^{4} +(4.24321 - 10.3438i) q^{5} -7.00000i q^{7} -56.5383i q^{8} +(53.6494 + 22.0078i) q^{10} +35.9555 q^{11} +45.2622i q^{13} +36.3062 q^{14} +142.035 q^{16} +113.154i q^{17} -61.5906 q^{19} +(-80.2001 + 195.507i) q^{20} +186.487i q^{22} +30.6108i q^{23} +(-88.9904 - 87.7822i) q^{25} -234.757 q^{26} +132.306i q^{28} +214.989 q^{29} +164.206 q^{31} +284.372i q^{32} -586.882 q^{34} +(-72.4069 - 29.7024i) q^{35} +410.533i q^{37} -319.446i q^{38} +(-584.823 - 239.904i) q^{40} +309.310 q^{41} -29.9519i q^{43} -679.589 q^{44} -158.766 q^{46} +483.790i q^{47} -49.0000 q^{49} +(455.291 - 461.558i) q^{50} -855.493i q^{52} +295.582i q^{53} +(152.567 - 371.918i) q^{55} -395.768 q^{56} +1115.06i q^{58} +416.191 q^{59} -151.196 q^{61} +851.670i q^{62} -338.644 q^{64} +(468.185 + 192.057i) q^{65} -89.5253i q^{67} -2138.70i q^{68} +(154.055 - 375.546i) q^{70} -714.265 q^{71} -1135.58i q^{73} -2129.27 q^{74} +1164.11 q^{76} -251.688i q^{77} +323.347 q^{79} +(602.683 - 1469.19i) q^{80} +1604.27i q^{82} -297.898i q^{83} +(1170.44 + 480.134i) q^{85} +155.348 q^{86} -2032.86i q^{88} -90.2097 q^{89} +316.835 q^{91} -578.570i q^{92} -2509.23 q^{94} +(-261.342 + 637.084i) q^{95} +492.101i q^{97} -254.143i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) $ 10 * q - 54 * q^4 + 14 * q^5	$ 10 q - 54 q^{4} + 14 q^{5} + 92 q^{10} - 132 q^{11} + 14 q^{14} + 310 q^{16} - 348 q^{19} - 366 q^{20} - 374 q^{25} - 892 q^{26} + 740 q^{29} + 684 q^{31} - 224 q^{34} - 2156 q^{40} - 1604 q^{41} + 580 q^{44} + 1280 q^{46} - 490 q^{49} + 2504 q^{50} - 452 q^{55} - 462 q^{56} + 1408 q^{59} + 1300 q^{61} - 150 q^{64} + 3296 q^{65} - 882 q^{70} - 2940 q^{71} - 2624 q^{74} + 8740 q^{76} + 1640 q^{79} + 4126 q^{80} - 1704 q^{85} - 1664 q^{86} + 572 q^{89} - 28 q^{91} - 5080 q^{94} - 1268 q^{95}+O(q^{100}) $ 10 * q - 54 * q^4 + 14 * q^5 + 92 * q^10 - 132 * q^11 + 14 * q^14 + 310 * q^16 - 348 * q^19 - 366 * q^20 - 374 * q^25 - 892 * q^26 + 740 * q^29 + 684 * q^31 - 224 * q^34 - 2156 * q^40 - 1604 * q^41 + 580 * q^44 + 1280 * q^46 - 490 * q^49 + 2504 * q^50 - 452 * q^55 - 462 * q^56 + 1408 * q^59 + 1300 * q^61 - 150 * q^64 + 3296 * q^65 - 882 * q^70 - 2940 * q^71 - 2624 * q^74 + 8740 * q^76 + 1640 * q^79 + 4126 * q^80 - 1704 * q^85 - 1664 * q^86 + 572 * q^89 - 28 * q^91 - 5080 * q^94 - 1268 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			5.18660i			1.83374i	0.399185	+	0.916870i	$0.369293\pi$
$2$			5.18660i			1.83374i	−0.399185	+	0.916870i	$0.630707\pi$
$3$		0			0
$3$		0			0
$4$	−18.9008			−2.36260
$5$	4.24321	−	10.3438i	0.379524	−	0.925182i
$5$	4.24321	−	10.3438i	0.379524	−	0.925182i
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	56.5383i		−	2.49866i
$9$		0			0
$10$	53.6494	+	22.0078i	1.69654	+	0.695948i
$11$	35.9555			0.985545			0.492772	−	0.870158i	$-0.335984\pi$
$11$	35.9555			0.985545			0.492772	+	0.870158i	$0.335984\pi$
$12$		0			0
$13$			45.2622i			0.965652i	0.875716	+	0.482826i	$0.160390\pi$
$13$			45.2622i			0.965652i	−0.875716	+	0.482826i	$0.839610\pi$
$14$	36.3062			0.693089
$15$		0			0
$16$	142.035			2.21929
$17$			113.154i			1.61434i	0.590319	+	0.807170i	$0.299002\pi$
$17$			113.154i			1.61434i	−0.590319	+	0.807170i	$0.700998\pi$
$18$		0			0
$19$	−61.5906			−0.743677			−0.371838	−	0.928297i	$-0.621272\pi$
$19$	−61.5906			−0.743677			−0.371838	+	0.928297i	$0.621272\pi$
$20$	−80.2001	+	195.507i	−0.896665	+	2.18584i
$21$		0			0
$22$			186.487i			1.80723i
$23$			30.6108i			0.277513i	0.990327	+	0.138756i	$0.0443105\pi$
$23$			30.6108i			0.277513i	−0.990327	+	0.138756i	$0.955690\pi$
$24$		0			0
$25$	−88.9904	−	87.7822i	−0.711923	−	0.702257i
$26$	−234.757			−1.77075
$27$		0			0
$28$			132.306i			0.892980i
$29$	214.989			1.37663			0.688317	−	0.725410i	$-0.258350\pi$
$29$	214.989			1.37663			0.688317	+	0.725410i	$0.258350\pi$
$30$		0			0
$31$	164.206			0.951362			0.475681	−	0.879618i	$-0.342202\pi$
$31$	164.206			0.951362			0.475681	+	0.879618i	$0.342202\pi$
$32$			284.372i			1.57095i
$33$		0			0
$34$	−586.882			−2.96028
$35$	−72.4069	−	29.7024i	−0.349686	−	0.143447i
$36$		0			0
$37$			410.533i			1.82409i	0.410095	+	0.912043i	$0.365496\pi$
$37$			410.533i			1.82409i	−0.410095	+	0.912043i	$0.634504\pi$
$38$		−	319.446i		−	1.36371i
$39$		0			0
$40$	−584.823	−	239.904i	−2.31172	−	0.948302i
$41$	309.310			1.17820			0.589100	−	0.808060i	$-0.299483\pi$
$41$	309.310			1.17820			0.589100	+	0.808060i	$0.299483\pi$
$42$		0			0
$43$		−	29.9519i		−	0.106224i	−0.998589	−	0.0531118i	$-0.983086\pi$
$43$		−	29.9519i		−	0.106224i	0.998589	−	0.0531118i	$-0.0169140\pi$
$44$	−679.589			−2.32845
$45$		0			0
$46$	−158.766			−0.508886
$47$			483.790i			1.50145i	0.660616	+	0.750724i	$0.270295\pi$
$47$			483.790i			1.50145i	−0.660616	+	0.750724i	$0.729705\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	455.291	−	461.558i	1.28776	−	1.30548i
$51$		0			0
$52$		−	855.493i		−	2.28145i
$53$			295.582i			0.766063i	0.923735	+	0.383031i	$0.125120\pi$
$53$			295.582i			0.766063i	−0.923735	+	0.383031i	$0.874880\pi$
$54$		0			0
$55$	152.567	−	371.918i	0.374038	−	0.911808i
$56$	−395.768			−0.944405
$57$		0			0
$58$			1115.06i			2.52439i
$59$	416.191			0.918364			0.459182	−	0.888342i	$-0.348143\pi$
$59$	416.191			0.918364			0.459182	+	0.888342i	$0.348143\pi$
$60$		0			0
$61$	−151.196			−0.317355			−0.158677	−	0.987330i	$-0.550723\pi$
$61$	−151.196			−0.317355			−0.158677	+	0.987330i	$0.550723\pi$
$62$			851.670i			1.74455i
$63$		0			0
$64$	−338.644			−0.661415
$65$	468.185	+	192.057i	0.893403	+	0.366488i
$66$		0			0
$67$		−	89.5253i		−	0.163243i	−0.996663	−	0.0816213i	$-0.973990\pi$
$67$		−	89.5253i		−	0.163243i	0.996663	−	0.0816213i	$-0.0260098\pi$
$68$		−	2138.70i		−	3.81404i
$69$		0			0
$70$	154.055	−	375.546i	0.263044	−	0.641233i
$71$	−714.265			−1.19391			−0.596955	−	0.802274i	$-0.703623\pi$
$71$	−714.265			−1.19391			−0.596955	+	0.802274i	$0.703623\pi$
$72$		0			0
$73$		−	1135.58i		−	1.82068i	−0.413861	−	0.910340i	$-0.635820\pi$
$73$		−	1135.58i		−	1.82068i	0.413861	−	0.910340i	$-0.364180\pi$
$74$	−2129.27			−3.34490
$75$		0			0
$76$	1164.11			1.75701
$77$		−	251.688i		−	0.372501i
$78$		0			0
$79$	323.347			0.460498			0.230249	−	0.973132i	$-0.426046\pi$
$79$	323.347			0.460498			0.230249	+	0.973132i	$0.426046\pi$
$80$	602.683	−	1469.19i	0.842275	−	2.05325i
$81$		0			0
$82$			1604.27i			2.16051i
$83$		−	297.898i		−	0.393959i	−0.980408	−	0.196979i	$-0.936887\pi$
$83$		−	297.898i		−	0.393959i	0.980408	−	0.196979i	$-0.0631132\pi$
$84$		0			0
$85$	1170.44	+	480.134i	1.49356	+	0.612680i
$86$	155.348			0.194787
$87$		0			0
$88$		−	2032.86i		−	2.46254i
$89$	−90.2097			−0.107441			−0.0537203	−	0.998556i	$-0.517108\pi$
$89$	−90.2097			−0.107441			−0.0537203	+	0.998556i	$0.517108\pi$
$90$		0			0
$91$	316.835			0.364982
$92$		−	578.570i		−	0.655653i
$93$		0			0
$94$	−2509.23			−2.75326
$95$	−261.342	+	637.084i	−0.282243	+	0.688036i
$96$		0			0
$97$			492.101i			0.515106i	0.966264	+	0.257553i	$0.0829162\pi$
$97$			492.101i			0.515106i	−0.966264	+	0.257553i	$0.917084\pi$
$98$		−	254.143i		−	0.261963i
$99$		0			0
$100$	1681.99	+	1659.16i	1.68199	+	1.65916i
$101$	272.636			0.268597			0.134299	−	0.990941i	$-0.457122\pi$
$101$	272.636			0.268597			0.134299	+	0.990941i	$0.457122\pi$
$102$		0			0
$103$		−	628.179i		−	0.600936i	−0.953792	−	0.300468i	$-0.902857\pi$
$103$		−	628.179i		−	0.600936i	0.953792	−	0.300468i	$-0.0971428\pi$
$104$	2559.05			2.41284
$105$		0			0
$106$	−1533.07			−1.40476
$107$			908.469i			0.820794i	0.911907	+	0.410397i	$0.134610\pi$
$107$			908.469i			0.820794i	−0.911907	+	0.410397i	$0.865390\pi$
$108$		0			0
$109$	−984.306			−0.864948			−0.432474	−	0.901646i	$-0.642359\pi$
$109$	−984.306			−0.864948			−0.432474	+	0.901646i	$0.642359\pi$
$110$	1928.99	+	791.302i	1.67202	+	0.685888i
$111$		0			0
$112$		−	994.244i		−	0.838814i
$113$			2228.79i			1.85546i	0.373251	+	0.927730i	$0.378243\pi$
$113$			2228.79i			1.85546i	−0.373251	+	0.927730i	$0.621757\pi$
$114$		0			0
$115$	316.633	+	129.888i	0.256750	+	0.105323i
$116$	−4063.47			−3.25244
$117$		0			0
$118$			2158.62i			1.68404i
$119$	792.075			0.610163
$120$		0			0
$121$	−38.2023			−0.0287019
$122$		−	784.193i		−	0.581946i
$123$		0			0
$124$	−3103.63			−2.24769
$125$	−1285.61	+	548.025i	−0.919908	+	0.392135i
$126$		0			0
$127$			2860.78i			1.99885i	0.0339770	+	0.999423i	$0.489183\pi$
$127$			2860.78i			1.99885i	−0.0339770	+	0.999423i	$0.510817\pi$
$128$			518.561i			0.358084i
$129$		0			0
$130$	−996.122	+	2428.29i	−0.672044	+	1.63827i
$131$	524.971			0.350130			0.175065	−	0.984557i	$-0.443987\pi$
$131$	524.971			0.350130			0.175065	+	0.984557i	$0.443987\pi$
$132$		0			0
$133$			431.134i			0.281083i
$134$	464.332			0.299344
$135$		0			0
$136$	6397.51			4.03369
$137$		−	2149.03i		−	1.34017i	−0.742282	−	0.670087i	$-0.766257\pi$
$137$		−	2149.03i		−	1.34017i	0.742282	−	0.670087i	$-0.233743\pi$
$138$		0			0
$139$	1507.78			0.920060			0.460030	−	0.887903i	$-0.347839\pi$
$139$	1507.78			0.920060			0.460030	+	0.887903i	$0.347839\pi$
$140$	1368.55	+	561.401i	0.826169	+	0.338907i
$141$		0			0
$142$		−	3704.61i		−	2.18932i
$143$			1627.42i			0.951693i
$144$		0			0
$145$	912.242	−	2223.81i	0.522466	−	1.27364i
$146$	5889.80			3.33865
$147$		0			0
$148$		−	7759.41i		−	4.30959i
$149$	−1013.61			−0.557304			−0.278652	−	0.960392i	$-0.589888\pi$
$149$	−1013.61			−0.557304			−0.278652	+	0.960392i	$0.589888\pi$
$150$		0			0
$151$	1663.70			0.896623			0.448312	−	0.893877i	$-0.352025\pi$
$151$	1663.70			0.896623			0.448312	+	0.893877i	$0.352025\pi$
$152$			3482.23i			1.85820i
$153$		0			0
$154$	1305.41			0.683070
$155$	696.759	−	1698.52i	0.361065	−	0.880183i
$156$		0			0
$157$		−	2399.48i		−	1.21974i	−0.792500	−	0.609872i	$-0.791221\pi$
$157$		−	2399.48i		−	1.21974i	0.792500	−	0.609872i	$-0.208779\pi$
$158$			1677.07i			0.844434i
$159$		0			0
$160$	2941.50	+	1206.65i	1.45341	+	0.596212i
$161$	214.276			0.104890
$162$		0			0
$163$			1415.81i			0.680337i	0.940365	+	0.340168i	$0.110484\pi$
$163$			1415.81i			0.680337i	−0.940365	+	0.340168i	$0.889516\pi$
$164$	−5846.22			−2.78362
$165$		0			0
$166$	1545.08			0.722418
$167$		−	3543.86i		−	1.64211i	−0.570850	−	0.821055i	$-0.693386\pi$
$167$		−	3543.86i		−	1.64211i	0.570850	−	0.821055i	$-0.306614\pi$
$168$		0			0
$169$	148.335			0.0675170
$170$	−2490.26	+	6070.62i	−1.12350	+	2.73880i
$171$		0			0
$172$			566.115i			0.250964i
$173$			95.6649i			0.0420420i	0.999779	+	0.0210210i	$0.00669169\pi$
$173$			95.6649i			0.0420420i	−0.999779	+	0.0210210i	$0.993308\pi$
$174$		0			0
$175$	−614.475	+	622.933i	−0.265428	+	0.269082i
$176$	5106.93			2.18721
$177$		0			0
$178$		−	467.882i		−	0.197018i
$179$	2166.13			0.904491			0.452245	−	0.891894i	$-0.350623\pi$
$179$	2166.13			0.904491			0.452245	+	0.891894i	$0.350623\pi$
$180$		0			0
$181$	−1859.24			−0.763514			−0.381757	−	0.924263i	$-0.624681\pi$
$181$	−1859.24			−0.763514			−0.381757	+	0.924263i	$0.624681\pi$
$182$			1643.30i			0.669282i
$183$		0			0
$184$	1730.68			0.693411
$185$	4246.49	+	1741.98i	1.68761	+	0.692284i
$186$		0			0
$187$			4068.49i			1.59100i
$188$		−	9144.03i		−	3.54733i
$189$		0			0
$190$	−3304.30	−	1355.48i	−1.26168	−	0.517561i
$191$	2661.60			1.00831			0.504154	−	0.863614i	$-0.331805\pi$
$191$	2661.60			1.00831			0.504154	+	0.863614i	$0.331805\pi$
$192$		0			0
$193$			1952.03i			0.728033i	0.931393	+	0.364016i	$0.118595\pi$
$193$			1952.03i			0.728033i	−0.931393	+	0.364016i	$0.881405\pi$
$194$	−2552.33			−0.944570
$195$		0			0
$196$	926.141			0.337515
$197$		−	3587.80i		−	1.29757i	−0.760974	−	0.648783i	$-0.775278\pi$
$197$		−	3587.80i		−	1.29757i	0.760974	−	0.648783i	$-0.224722\pi$
$198$		0			0
$199$	767.691			0.273468			0.136734	−	0.990608i	$-0.456339\pi$
$199$	767.691			0.273468			0.136734	+	0.990608i	$0.456339\pi$
$200$	−4963.05	+	5031.36i	−1.75470	+	1.77886i
$201$		0			0
$202$			1414.06i			0.492538i
$203$		−	1504.92i		−	0.520319i
$204$		0			0
$205$	1312.47	−	3199.46i	0.447155	−	1.09005i
$206$	3258.12			1.10196
$207$		0			0
$208$			6428.81i			2.14306i
$209$	−2214.52			−0.732927
$210$		0			0
$211$	−1199.84			−0.391472			−0.195736	−	0.980657i	$-0.562710\pi$
$211$	−1199.84			−0.391472			−0.195736	+	0.980657i	$0.562710\pi$
$212$		−	5586.75i		−	1.80990i
$213$		0			0
$214$	−4711.87			−1.50512
$215$	−309.818	−	127.092i	−0.0982762	−	0.0403144i
$216$		0			0
$217$		−	1149.44i		−	0.359581i
$218$		−	5105.20i		−	1.58609i
$219$		0			0
$220$	−2883.64	+	7029.56i	−0.883703	+	2.15424i
$221$	−5121.58			−1.55889
$222$		0			0
$223$		−	2917.84i		−	0.876203i	−0.898926	−	0.438101i	$-0.855651\pi$
$223$		−	2917.84i		−	0.876203i	0.898926	−	0.438101i	$-0.144349\pi$
$224$	1990.60			0.593762
$225$		0			0
$226$	−11559.9			−3.40243
$227$		−	612.679i		−	0.179141i	−0.995981	−	0.0895703i	$-0.971451\pi$
$227$		−	612.679i		−	0.179141i	0.995981	−	0.0895703i	$-0.0285494\pi$
$228$		0			0
$229$	−2641.51			−0.762253			−0.381126	−	0.924523i	$-0.624464\pi$
$229$	−2641.51			−0.762253			−0.381126	+	0.924523i	$0.624464\pi$
$230$	−673.677	+	1642.25i	−0.193135	+	0.470812i
$231$		0			0
$232$		−	12155.1i		−	3.43974i
$233$		−	2322.87i		−	0.653117i	−0.945177	−	0.326558i	$-0.894111\pi$
$233$		−	2322.87i		−	0.653117i	0.945177	−	0.326558i	$-0.105889\pi$
$234$		0			0
$235$	5004.25	+	2052.82i	1.38911	+	0.569835i
$236$	−7866.36			−2.16973
$237$		0			0
$238$			4108.18i			1.11888i
$239$	5372.54			1.45406			0.727030	−	0.686605i	$-0.240900\pi$
$239$	5372.54			1.45406			0.727030	+	0.686605i	$0.240900\pi$
$240$		0			0
$241$	−1412.33			−0.377494			−0.188747	−	0.982026i	$-0.560443\pi$
$241$	−1412.33			−0.377494			−0.188747	+	0.982026i	$0.560443\pi$
$242$		−	198.140i		−	0.0526319i
$243$		0			0
$244$	2857.73			0.749784
$245$	−207.917	+	506.849i	−0.0542177	+	0.132169i
$246$		0			0
$247$		−	2787.73i		−	0.718133i
$248$		−	9283.91i		−	2.37713i
$249$		0			0
$250$	−2842.39	−	6667.95i	−0.719074	−	1.68687i
$251$	−5676.06			−1.42737			−0.713684	−	0.700467i	$-0.752975\pi$
$251$	−5676.06			−1.42737			−0.713684	+	0.700467i	$0.752975\pi$
$252$		0			0
$253$			1100.63i			0.273501i
$254$	−14837.7			−3.66536
$255$		0			0
$256$	−5398.72			−1.31805
$257$			3939.60i			0.956207i	0.878303	+	0.478104i	$0.158676\pi$
$257$			3939.60i			0.956207i	−0.878303	+	0.478104i	$0.841324\pi$
$258$		0			0
$259$	2873.73			0.689440
$260$	−8849.09	−	3630.03i	−2.11076	−	0.865866i
$261$		0			0
$262$			2722.82i			0.642047i
$263$		−	5397.68i		−	1.26553i	−0.774343	−	0.632766i	$-0.781919\pi$
$263$		−	5397.68i		−	1.26553i	0.774343	−	0.632766i	$-0.218081\pi$
$264$		0			0
$265$	3057.46	+	1254.22i	0.708747	+	0.290739i
$266$	−2236.12			−0.515434
$267$		0			0
$268$			1692.10i			0.385678i
$269$	4973.60			1.12731			0.563654	−	0.826011i	$-0.309395\pi$
$269$	4973.60			1.12731			0.563654	+	0.826011i	$0.309395\pi$
$270$		0			0
$271$	4147.48			0.929672			0.464836	−	0.885397i	$-0.346113\pi$
$271$	4147.48			0.929672			0.464836	+	0.885397i	$0.346113\pi$
$272$			16071.7i			3.58269i
$273$		0			0
$274$	11146.2			2.45753
$275$	−3199.69	−	3156.25i	−0.701632	−	0.692106i
$276$		0			0
$277$		−	2616.79i		−	0.567609i	−0.958882	−	0.283805i	$-0.908403\pi$
$277$		−	2616.79i		−	0.567609i	0.958882	−	0.283805i	$-0.0915968\pi$
$278$			7820.26i			1.68715i
$279$		0			0
$280$	−1679.32	+	4093.76i	−0.358424	+	0.873747i
$281$	−2866.89			−0.608628			−0.304314	−	0.952572i	$-0.598427\pi$
$281$	−2866.89			−0.608628			−0.304314	+	0.952572i	$0.598427\pi$
$282$		0			0
$283$		−	3015.40i		−	0.633381i	−0.948529	−	0.316691i	$-0.897428\pi$
$283$		−	3015.40i		−	0.633381i	0.948529	−	0.316691i	$-0.102572\pi$
$284$	13500.2			2.82074
$285$		0			0
$286$	−8440.80			−1.74516
$287$		−	2165.17i		−	0.445318i
$288$		0			0
$289$	−7890.73			−1.60609
$290$	11534.0	+	4731.43i	2.33552	+	0.958067i
$291$		0			0
$292$			21463.4i			4.30155i
$293$			3580.41i			0.713890i	0.934125	+	0.356945i	$0.116182\pi$
$293$			3580.41i			0.713890i	−0.934125	+	0.356945i	$0.883818\pi$
$294$		0			0
$295$	1765.98	−	4305.02i	0.348541	−	0.849653i
$296$	23210.8			4.55777
$297$		0			0
$298$		−	5257.20i		−	1.02195i
$299$	−1385.51			−0.267981
$300$		0			0
$301$	−209.663			−0.0401488
$302$			8628.96i			1.64417i
$303$		0			0
$304$	−8748.01			−1.65044
$305$	−641.555	+	1563.95i	−0.120444	+	0.293611i
$306$		0			0
$307$		−	1432.92i		−	0.266389i	−0.991090	−	0.133194i	$-0.957477\pi$
$307$		−	1432.92i		−	0.266389i	0.991090	−	0.133194i	$-0.0425234\pi$
$308$			4757.12i			0.880072i
$309$		0			0
$310$	8809.54	+	3613.81i	1.61403	+	0.662099i
$311$	−5488.33			−1.00069			−0.500345	−	0.865826i	$-0.666794\pi$
$311$	−5488.33			−1.00069			−0.500345	+	0.865826i	$0.666794\pi$
$312$		0			0
$313$		−	2461.68i		−	0.444545i	−0.974985	−	0.222272i	$-0.928653\pi$
$313$		−	2461.68i		−	0.444545i	0.974985	−	0.222272i	$-0.0713474\pi$
$314$	12445.2			2.23669
$315$		0			0
$316$	−6111.53			−1.08798
$317$			3113.12i			0.551579i	0.961218	+	0.275789i	$0.0889393\pi$
$317$			3113.12i			0.551579i	−0.961218	+	0.275789i	$0.911061\pi$
$318$		0			0
$319$	7730.03			1.35673
$320$	−1436.94	+	3502.88i	−0.251023	+	0.611929i
$321$		0			0
$322$			1111.36i			0.192341i
$323$		−	6969.20i		−	1.20055i
$324$		0			0
$325$	3973.21	−	4027.90i	0.678136	−	0.687470i
$326$	−7343.25			−1.24756
$327$		0			0
$328$		−	17487.9i		−	2.94392i
$329$	3386.53			0.567494
$330$		0			0
$331$	−6364.21			−1.05682			−0.528411	−	0.848988i	$-0.677212\pi$
$331$	−6364.21			−1.05682			−0.528411	+	0.848988i	$0.677212\pi$
$332$			5630.52i			0.930768i
$333$		0			0
$334$	18380.6			3.01120
$335$	−926.036	−	379.874i	−0.151029	−	0.0619545i
$336$		0			0
$337$			5163.25i			0.834600i	0.908769	+	0.417300i	$0.137024\pi$
$337$			5163.25i			0.834600i	−0.908769	+	0.417300i	$0.862976\pi$
$338$			769.353i			0.123809i
$339$		0			0
$340$	−22122.4	−	9074.93i	−3.52869	−	1.44752i
$341$	5904.10			0.937610
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−1693.43			−0.265417
$345$		0			0
$346$	−496.176			−0.0770941
$347$			305.000i			0.0471851i	0.999722	+	0.0235926i	$0.00751044\pi$
$347$			305.000i			0.0471851i	−0.999722	+	0.0235926i	$0.992490\pi$
$348$		0			0
$349$	8233.50			1.26283			0.631417	−	0.775443i	$-0.282474\pi$
$349$	8233.50			1.26283			0.631417	+	0.775443i	$0.282474\pi$
$350$	−3230.90	−	3187.04i	−0.493426	−	0.486727i
$351$		0			0
$352$			10224.7i			1.54824i
$353$			1064.37i			0.160483i	0.996775	+	0.0802415i	$0.0255692\pi$
$353$			1064.37i			0.160483i	−0.996775	+	0.0802415i	$0.974431\pi$
$354$		0			0
$355$	−3030.77	+	7388.25i	−0.453118	+	1.10458i
$356$	1705.04			0.253839
$357$		0			0
$358$			11234.8i			1.65860i
$359$	−3915.59			−0.575646			−0.287823	−	0.957684i	$-0.592931\pi$
$359$	−3915.59			−0.575646			−0.287823	+	0.957684i	$0.592931\pi$
$360$		0			0
$361$	−3065.59			−0.446945
$362$		−	9643.13i		−	1.40009i
$363$		0			0
$364$	−5988.45			−0.862308
$365$	−11746.3	−	4818.50i	−1.68446	−	0.690992i
$366$		0			0
$367$		−	7430.70i		−	1.05689i	−0.848967	−	0.528446i	$-0.822775\pi$
$367$		−	7430.70i		−	1.05689i	0.848967	−	0.528446i	$-0.177225\pi$
$368$			4347.80i			0.615882i
$369$		0			0
$370$	−9034.93	+	22024.8i	−1.26947	+	3.09464i
$371$	2069.07			0.289544
$372$		0			0
$373$		−	3275.71i		−	0.454718i	−0.973811	−	0.227359i	$-0.926991\pi$
$373$		−	3275.71i		−	0.454718i	0.973811	−	0.227359i	$-0.0730090\pi$
$374$	−21101.6			−2.91749
$375$		0			0
$376$	27352.7			3.75161
$377$			9730.86i			1.32935i
$378$		0			0
$379$	−5745.18			−0.778655			−0.389327	−	0.921099i	$-0.627293\pi$
$379$	−5745.18			−0.778655			−0.389327	+	0.921099i	$0.627293\pi$
$380$	4939.58	−	12041.4i	0.666829	−	1.62556i
$381$		0			0
$382$			13804.7i			1.84897i
$383$		−	101.844i		−	0.0135874i	−0.999977	−	0.00679372i	$-0.997837\pi$
$383$		−	101.844i		−	0.0135874i	0.999977	−	0.00679372i	$-0.00216252\pi$
$384$		0			0
$385$	−2603.43	−	1067.97i	−0.344631	−	0.141373i
$386$	−10124.4			−1.33502
$387$		0			0
$388$		−	9301.11i		−	1.21699i
$389$	3047.72			0.397237			0.198619	−	0.980077i	$-0.436354\pi$
$389$	3047.72			0.397237			0.198619	+	0.980077i	$0.436354\pi$
$390$		0			0
$391$	−3463.72			−0.448000
$392$			2770.38i			0.356952i
$393$		0			0
$394$	18608.5			2.37940
$395$	1372.03	−	3344.65i	0.174770	−	0.426045i
$396$		0			0
$397$		−	9830.23i		−	1.24273i	−0.783520	−	0.621367i	$-0.786578\pi$
$397$		−	9830.23i		−	1.24273i	0.783520	−	0.621367i	$-0.213422\pi$
$398$			3981.71i			0.501470i
$399$		0			0
$400$	−12639.7	−	12468.1i	−1.57997	−	1.55852i
$401$	−3693.01			−0.459900			−0.229950	−	0.973202i	$-0.573856\pi$
$401$	−3693.01			−0.459900			−0.229950	+	0.973202i	$0.573856\pi$
$402$		0			0
$403$			7432.31i			0.918684i
$404$	−5153.06			−0.634589
$405$		0			0
$406$	7805.43			0.954130
$407$			14760.9i			1.79772i
$408$		0			0
$409$	−8815.07			−1.06571			−0.532857	−	0.846205i	$-0.678882\pi$
$409$	−8815.07			−1.06571			−0.532857	+	0.846205i	$0.678882\pi$
$410$	16594.3	+	6807.25i	1.99887	+	0.819966i
$411$		0			0
$412$			11873.1i			1.41977i
$413$		−	2913.34i		−	0.347109i
$414$		0			0
$415$	−3081.41	−	1264.04i	−0.364483	−	0.149517i
$416$	−12871.3			−1.51699
$417$		0			0
$418$		−	11485.8i		−	1.34400i
$419$	3746.84			0.436862			0.218431	−	0.975852i	$-0.429906\pi$
$419$	3746.84			0.436862			0.218431	+	0.975852i	$0.429906\pi$
$420$		0			0
$421$	−10554.5			−1.22184			−0.610922	−	0.791690i	$-0.709201\pi$
$421$	−10554.5			−1.22184			−0.610922	+	0.791690i	$0.709201\pi$
$422$		−	6223.10i		−	0.717858i
$423$		0			0
$424$	16711.7			1.91413
$425$	9932.87	−	10069.6i	1.13368	−	1.14929i
$426$		0			0
$427$			1058.37i			0.119949i
$428$		−	17170.8i		−	1.93921i
$429$		0			0
$430$	659.175	−	1606.90i	0.0739262	−	0.180213i
$431$	14029.9			1.56797			0.783986	−	0.620778i	$-0.213183\pi$
$431$	14029.9			1.56797			0.783986	+	0.620778i	$0.213183\pi$
$432$		0			0
$433$		−	9639.08i		−	1.06980i	−0.844915	−	0.534901i	$-0.820349\pi$
$433$		−	9639.08i		−	1.06980i	0.844915	−	0.534901i	$-0.179651\pi$
$434$	5961.69			0.659378
$435$		0			0
$436$	18604.2			2.04353
$437$		−	1885.34i		−	0.206380i
$438$		0			0
$439$	−3936.53			−0.427974			−0.213987	−	0.976837i	$-0.568645\pi$
$439$	−3936.53			−0.427974			−0.213987	+	0.976837i	$0.568645\pi$
$440$	−21027.6	−	8625.85i	−2.27830	−	0.934594i
$441$		0			0
$442$		−	26563.6i		−	2.85860i
$443$			10812.5i			1.15963i	0.814746	+	0.579817i	$0.196876\pi$
$443$			10812.5i			1.15963i	−0.814746	+	0.579817i	$0.803124\pi$
$444$		0			0
$445$	−382.778	+	933.115i	−0.0407762	+	0.0994020i
$446$	15133.7			1.60673
$447$		0			0
$448$			2370.51i			0.249991i
$449$	8154.86			0.857131			0.428565	−	0.903511i	$-0.359019\pi$
$449$	8154.86			0.857131			0.428565	+	0.903511i	$0.359019\pi$
$450$		0			0
$451$	11121.4			1.16117
$452$		−	42126.0i		−	4.38372i
$453$		0			0
$454$	3177.72			0.328497
$455$	1344.40	−	3277.30i	0.138519	−	0.337675i
$456$		0			0
$457$			17787.5i			1.82071i	0.413833	+	0.910353i	$0.364190\pi$
$457$			17787.5i			1.82071i	−0.413833	+	0.910353i	$0.635810\pi$
$458$		−	13700.5i		−	1.39777i
$459$		0			0
$460$	−5984.64	−	2454.99i	−0.606598	−	0.248836i
$461$	−13192.1			−1.33280			−0.666398	−	0.745596i	$-0.732165\pi$
$461$	−13192.1			−1.33280			−0.666398	+	0.745596i	$0.732165\pi$
$462$		0			0
$463$		−	542.568i		−	0.0544607i	−0.999629	−	0.0272303i	$-0.991331\pi$
$463$		−	542.568i		−	0.0544607i	0.999629	−	0.0272303i	$-0.00866876\pi$
$464$	30535.9			3.05516
$465$		0			0
$466$	12047.8			1.19765
$467$		−	5962.51i		−	0.590818i	−0.955371	−	0.295409i	$-0.904544\pi$
$467$		−	5962.51i		−	0.590818i	0.955371	−	0.295409i	$-0.0954559\pi$
$468$		0			0
$469$	−626.677			−0.0616999
$470$	−10647.2	+	25955.1i	−1.04493	+	2.54727i
$471$		0			0
$472$		−	23530.7i		−	2.29468i
$473$		−	1076.93i		−	0.104688i
$474$		0			0
$475$	5480.98	+	5406.56i	0.529441	+	0.522253i
$476$	−14970.9			−1.44157
$477$		0			0
$478$			27865.2i			2.66637i
$479$	−1317.66			−0.125690			−0.0628451	−	0.998023i	$-0.520017\pi$
$479$	−1317.66			−0.125690			−0.0628451	+	0.998023i	$0.520017\pi$
$480$		0			0
$481$	−18581.6			−1.76143
$482$		−	7325.19i		−	0.692227i
$483$		0			0
$484$	722.054			0.0678113
$485$	5090.22	+	2088.08i	0.476567	+	0.195495i
$486$		0			0
$487$		−	5976.21i		−	0.556074i	−0.960570	−	0.278037i	$-0.910316\pi$
$487$		−	5976.21i		−	0.556074i	0.960570	−	0.278037i	$-0.0896837\pi$
$488$			8548.35i			0.792962i
$489$		0			0
$490$	−2628.82	−	1078.38i	−0.242363	−	0.0994212i
$491$	−10338.9			−0.950285			−0.475143	−	0.879909i	$-0.657604\pi$
$491$	−10338.9			−0.950285			−0.475143	+	0.879909i	$0.657604\pi$
$492$		0			0
$493$			24326.7i			2.22236i
$494$	14458.8			1.31687
$495$		0			0
$496$	23322.9			2.11135
$497$			4999.85i			0.451256i
$498$		0			0
$499$	4161.74			0.373357			0.186678	−	0.982421i	$-0.440228\pi$
$499$	4161.74			0.373357			0.186678	+	0.982421i	$0.440228\pi$
$500$	24299.1	−	10358.1i	2.17338	−	0.926460i
$501$		0			0
$502$		−	29439.4i		−	2.61742i
$503$		−	7556.24i		−	0.669813i	−0.942251	−	0.334907i	$-0.891295\pi$
$503$		−	7556.24i		−	0.669813i	0.942251	−	0.334907i	$-0.108705\pi$
$504$		0			0
$505$	1156.85	−	2820.11i	0.101939	−	0.248501i
$506$	−5708.51			−0.501530
$507$		0			0
$508$		−	54071.2i		−	4.72248i
$509$	7231.12			0.629693			0.314847	−	0.949143i	$-0.398047\pi$
$509$	7231.12			0.629693			0.314847	+	0.949143i	$0.398047\pi$
$510$		0			0
$511$	−7949.06			−0.688152
$512$		−	23852.5i		−	2.05887i
$513$		0			0
$514$	−20433.1			−1.75344
$515$	−6497.79	−	2665.50i	−0.555975	−	0.228069i
$516$		0			0
$517$			17394.9i			1.47974i
$518$			14904.9i			1.26425i
$519$		0			0
$520$	10858.6	−	26470.4i	0.915729	−	2.23231i
$521$	7378.54			0.620460			0.310230	−	0.950661i	$-0.399594\pi$
$521$	7378.54			0.620460			0.310230	+	0.950661i	$0.399594\pi$
$522$		0			0
$523$			2200.53i			0.183982i	0.995760	+	0.0919909i	$0.0293231\pi$
$523$			2200.53i			0.183982i	−0.995760	+	0.0919909i	$0.970677\pi$
$524$	−9922.40			−0.827217
$525$		0			0
$526$	27995.6			2.32066
$527$			18580.5i			1.53582i
$528$		0			0
$529$	11230.0			0.922987
$530$	−6505.12	+	15857.8i	−0.533140	+	1.29966i
$531$		0			0
$532$		−	8148.80i		−	0.664089i
$533$			14000.1i			1.13773i
$534$		0			0
$535$	9397.06	+	3854.82i	0.759384	+	0.311511i
$536$	−5061.60			−0.407888
$537$		0			0
$538$			25796.1i			2.06719i
$539$	−1761.82			−0.140792
$540$		0			0
$541$	−23797.3			−1.89118			−0.945588	−	0.325365i	$-0.894513\pi$
$541$	−23797.3			−1.89118			−0.945588	+	0.325365i	$0.894513\pi$
$542$			21511.3i			1.70478i
$543$		0			0
$544$	−32177.7			−2.53604
$545$	−4176.61	+	10181.5i	−0.328269	+	0.800235i
$546$		0			0
$547$		−	6586.46i		−	0.514839i	−0.966300	−	0.257419i	$-0.917128\pi$
$547$		−	6586.46i		−	0.514839i	0.966300	−	0.257419i	$-0.0828721\pi$
$548$			40618.4i			3.16630i
$549$		0			0
$550$	16370.2	−	16595.5i	1.26914	−	1.28661i
$551$	−13241.3			−1.02377
$552$		0			0
$553$		−	2263.43i		−	0.174052i
$554$	13572.3			1.04085
$555$		0			0
$556$	−28498.3			−2.17374
$557$			23522.6i			1.78938i	0.446686	+	0.894691i	$0.352604\pi$
$557$			23522.6i			1.78938i	−0.446686	+	0.894691i	$0.647396\pi$
$558$		0			0
$559$	1355.69			0.102575
$560$	−10284.3	−	4218.78i	−0.776056	−	0.318350i
$561$		0			0
$562$		−	14869.4i		−	1.11607i
$563$		−	17654.3i		−	1.32156i	−0.750578	−	0.660782i	$-0.770225\pi$
$563$		−	17654.3i		−	1.32156i	0.750578	−	0.660782i	$-0.229775\pi$
$564$		0			0
$565$	23054.3	+	9457.22i	1.71664	+	0.704192i
$566$	15639.7			1.16146
$567$		0			0
$568$			40383.3i			2.98318i
$569$	−13453.6			−0.991223			−0.495611	−	0.868544i	$-0.665056\pi$
$569$	−13453.6			−0.991223			−0.495611	+	0.868544i	$0.665056\pi$
$570$		0			0
$571$	9019.88			0.661069			0.330534	−	0.943794i	$-0.392771\pi$
$571$	9019.88			0.661069			0.330534	+	0.943794i	$0.392771\pi$
$572$		−	30759.7i		−	2.24847i
$573$		0			0
$574$	11229.9			0.816597
$575$	2687.08	−	2724.07i	0.194885	−	0.197568i
$576$		0			0
$577$		−	1328.73i		−	0.0958680i	−0.998851	−	0.0479340i	$-0.984736\pi$
$577$		−	1328.73i		−	0.0958680i	0.998851	−	0.0479340i	$-0.0152637\pi$
$578$		−	40926.1i		−	2.94516i
$579$		0			0
$580$	−17242.1	+	42031.9i	−1.23438	+	3.00910i
$581$	−2085.29			−0.148902
$582$		0			0
$583$			10627.8i			0.754989i
$584$	−64203.8			−4.54926
$585$		0			0
$586$	−18570.2			−1.30909
$587$			13927.3i			0.979283i	0.871924	+	0.489642i	$0.162872\pi$
$587$			13927.3i			0.979283i	−0.871924	+	0.489642i	$0.837128\pi$
$588$		0			0
$589$	−10113.5			−0.707506
$590$	22328.4	+	9159.46i	1.55804	+	0.639134i
$591$		0			0
$592$			58309.9i			4.04818i
$593$			5684.69i			0.393663i	0.980437	+	0.196831i	$0.0630652\pi$
$593$			5684.69i			0.393663i	−0.980437	+	0.196831i	$0.936935\pi$
$594$		0			0
$595$	3360.94	−	8193.10i	0.231571	−	0.564512i
$596$	19158.1			1.31669
$597$		0			0
$598$		−	7186.10i		−	0.491407i
$599$	27961.5			1.90730			0.953651	−	0.300914i	$-0.0972916\pi$
$599$	27961.5			1.90730			0.953651	+	0.300914i	$0.0972916\pi$
$600$		0			0
$601$	−12396.7			−0.841386			−0.420693	−	0.907203i	$-0.638213\pi$
$601$	−12396.7			−0.841386			−0.420693	+	0.907203i	$0.638213\pi$
$602$		−	1087.44i		−	0.0736224i
$603$		0			0
$604$	−31445.3			−2.11837
$605$	−162.100	+	395.158i	−0.0108931	+	0.0265545i
$606$		0			0
$607$		−	3124.52i		−	0.208930i	−0.994529	−	0.104465i	$-0.966687\pi$
$607$		−	3124.52i		−	0.208930i	0.994529	−	0.104465i	$-0.0333130\pi$
$608$		−	17514.6i		−	1.16828i
$609$		0			0
$610$	−8111.57	−	3327.49i	−0.538406	−	0.220863i
$611$	−21897.4			−1.44988
$612$		0			0
$613$		−	9531.29i		−	0.628002i	−0.949423	−	0.314001i	$-0.898330\pi$
$613$		−	9531.29i		−	0.628002i	0.949423	−	0.314001i	$-0.101670\pi$
$614$	7432.01			0.488488
$615$		0			0
$616$	−14230.0			−0.930754
$617$		−	5410.37i		−	0.353020i	−0.984299	−	0.176510i	$-0.943519\pi$
$617$		−	5410.37i		−	0.353020i	0.984299	−	0.176510i	$-0.0564808\pi$
$618$		0			0
$619$	10244.9			0.665228			0.332614	−	0.943063i	$-0.392069\pi$
$619$	10244.9			0.665228			0.332614	+	0.943063i	$0.392069\pi$
$620$	−13169.3	+	32103.4i	−0.853053	+	2.07952i
$621$		0			0
$622$		−	28465.8i		−	1.83501i
$623$			631.468i			0.0406087i
$624$		0			0
$625$	213.582	+	15623.5i	0.0136693	+	0.999907i
$626$	12767.8			0.815180
$627$		0			0
$628$			45352.3i			2.88177i
$629$	−46453.2			−2.94469
$630$		0			0
$631$	−10342.8			−0.652522			−0.326261	−	0.945280i	$-0.605789\pi$
$631$	−10342.8			−0.652522			−0.326261	+	0.945280i	$0.605789\pi$
$632$		−	18281.5i		−	1.15063i
$633$		0			0
$634$	−16146.5			−1.01145
$635$	29591.5	+	12138.9i	1.84930	+	0.758610i
$636$		0			0
$637$		−	2217.85i		−	0.137950i
$638$			40092.6i			2.48790i
$639$		0			0
$640$	5363.92	+	2200.36i	0.331293	+	0.135901i
$641$	981.309			0.0604671			0.0302335	−	0.999543i	$-0.490375\pi$
$641$	981.309			0.0604671			0.0302335	+	0.999543i	$0.490375\pi$
$642$		0			0
$643$		−	16289.5i		−	0.999062i	−0.866296	−	0.499531i	$-0.833506\pi$
$643$		−	16289.5i		−	0.999062i	0.866296	−	0.499531i	$-0.166494\pi$
$644$	−4049.99			−0.247813
$645$		0			0
$646$	36146.5			2.20149
$647$		−	11349.5i		−	0.689634i	−0.938670	−	0.344817i	$-0.887941\pi$
$647$		−	11349.5i		−	0.689634i	0.938670	−	0.344817i	$-0.112059\pi$
$648$		0			0
$649$	14964.4			0.905088
$650$	20891.1	+	20607.5i	1.26064	+	1.24353i
$651$		0			0
$652$		−	26760.0i		−	1.60737i
$653$		−	20510.7i		−	1.22917i	−0.788852	−	0.614583i	$-0.789324\pi$
$653$		−	20510.7i		−	1.22917i	0.788852	−	0.614583i	$-0.210676\pi$
$654$		0			0
$655$	2227.56	−	5430.22i	0.132883	−	0.323934i
$656$	43932.8			2.61477
$657$		0			0
$658$			17564.6i			1.04064i
$659$	15480.4			0.915070			0.457535	−	0.889191i	$-0.348732\pi$
$659$	15480.4			0.915070			0.457535	+	0.889191i	$0.348732\pi$
$660$		0			0
$661$	3720.51			0.218928			0.109464	−	0.993991i	$-0.465087\pi$
$661$	3720.51			0.218928			0.109464	+	0.993991i	$0.465087\pi$
$662$		−	33008.6i		−	1.93794i
$663$		0			0
$664$	−16842.6			−0.984369
$665$	4459.59	+	1829.39i	0.260053	+	0.106678i
$666$		0			0
$667$			6580.98i			0.382034i
$668$			66981.9i			3.87965i
$669$		0			0
$670$	1970.26	−	4802.98i	0.113608	−	0.276948i
$671$	−5436.32			−0.312767
$672$		0			0
$673$			17977.2i			1.02967i	0.857288	+	0.514837i	$0.172147\pi$
$673$			17977.2i			1.02967i	−0.857288	+	0.514837i	$0.827853\pi$
$674$	−26779.7			−1.53044
$675$		0			0
$676$	−2803.65			−0.159516
$677$		−	13079.2i		−	0.742505i	−0.928532	−	0.371253i	$-0.878928\pi$
$677$		−	13079.2i		−	0.742505i	0.928532	−	0.371253i	$-0.121072\pi$
$678$		0			0
$679$	3444.70			0.194692
$680$	27145.9	−	66174.8i	1.53088	−	3.73190i
$681$		0			0
$682$			30622.2i			1.71933i
$683$			22608.2i			1.26659i	0.773912	+	0.633293i	$0.218297\pi$
$683$			22608.2i			1.26659i	−0.773912	+	0.633293i	$0.781703\pi$
$684$		0			0
$685$	−22229.2	−	9118.77i	−1.23991	−	0.508628i
$686$	−1779.00			−0.0990127
$687$		0			0
$688$		−	4254.21i		−	0.235742i
$689$	−13378.7			−0.739749
$690$		0			0
$691$	26262.2			1.44582			0.722910	−	0.690942i	$-0.242804\pi$
$691$	26262.2			1.44582			0.722910	+	0.690942i	$0.242804\pi$
$692$		−	1808.15i		−	0.0993286i
$693$		0			0
$694$	−1581.91			−0.0865253
$695$	6397.83	−	15596.3i	0.349185	−	0.851223i
$696$		0			0
$697$			34999.6i			1.90201i
$698$			42703.9i			2.31571i
$699$		0			0
$700$	11614.1	−	11773.9i	0.627102	−	0.635733i
$701$	15831.3			0.852982			0.426491	−	0.904492i	$-0.359750\pi$
$701$	15831.3			0.852982			0.426491	+	0.904492i	$0.359750\pi$
$702$		0			0
$703$		−	25285.0i		−	1.35653i
$704$	−12176.1			−0.651853
$705$		0			0
$706$	−5520.44			−0.294284
$707$		−	1908.46i		−	0.101520i
$708$		0			0
$709$	874.284			0.0463109			0.0231554	−	0.999732i	$-0.492629\pi$
$709$	874.284			0.0463109			0.0231554	+	0.999732i	$0.492629\pi$
$710$	−38319.9	−	15719.4i	−2.02552	−	0.830900i
$711$		0			0
$712$			5100.30i			0.268458i
$713$			5026.47i			0.264015i
$714$		0			0
$715$	16833.8	+	6905.50i	0.880489	+	0.361190i
$716$	−40941.6			−2.13695
$717$		0			0
$718$		−	20308.6i		−	1.05559i
$719$	103.934			0.00539091			0.00269546	−	0.999996i	$-0.499142\pi$
$719$	103.934			0.00539091			0.00269546	+	0.999996i	$0.499142\pi$
$720$		0			0
$721$	−4397.26			−0.227132
$722$		−	15900.0i		−	0.819580i
$723$		0			0
$724$	35141.2			1.80388
$725$	−19131.9	−	18872.2i	−0.980058	−	0.966752i
$726$		0			0
$727$		−	20972.0i		−	1.06989i	−0.844887	−	0.534945i	$-0.820332\pi$
$727$		−	20972.0i		−	1.06989i	0.844887	−	0.534945i	$-0.179668\pi$
$728$		−	17913.3i		−	0.911967i
$729$		0			0
$730$	24991.7	−	60923.2i	1.26710	−	3.08886i
$731$	3389.16			0.171481
$732$		0			0
$733$			32298.2i			1.62750i	0.581213	+	0.813751i	$0.302578\pi$
$733$			32298.2i			1.62750i	−0.581213	+	0.813751i	$0.697422\pi$
$734$	38540.1			1.93807
$735$		0			0
$736$	−8704.85			−0.435958
$737$		−	3218.93i		−	0.160883i
$738$		0			0
$739$	−19402.4			−0.965804			−0.482902	−	0.875674i	$-0.660417\pi$
$739$	−19402.4			−0.965804			−0.482902	+	0.875674i	$0.660417\pi$
$740$	−80262.2	−	32924.8i	−3.98716	−	1.63559i
$741$		0			0
$742$			10731.5i			0.530949i
$743$			28784.0i			1.42124i	0.703575	+	0.710621i	$0.251586\pi$
$743$			28784.0i			1.42124i	−0.703575	+	0.710621i	$0.748414\pi$
$744$		0			0
$745$	−4300.97	+	10484.7i	−0.211510	+	0.515608i
$746$	16989.8			0.833834
$747$		0			0
$748$		−	76897.9i		−	3.75891i
$749$	6359.28			0.310231
$750$		0			0
$751$	4382.70			0.212952			0.106476	−	0.994315i	$-0.466043\pi$
$751$	4382.70			0.212952			0.106476	+	0.994315i	$0.466043\pi$
$752$			68715.0i			3.33215i
$753$		0			0
$754$	−50470.1			−2.43768
$755$	7059.43	−	17209.1i	0.340290	−	0.829540i
$756$		0			0
$757$		−	13669.8i		−	0.656326i	−0.944621	−	0.328163i	$-0.893570\pi$
$757$		−	13669.8i		−	0.656326i	0.944621	−	0.328163i	$-0.106430\pi$
$758$		−	29798.0i		−	1.42785i
$759$		0			0
$760$	36019.6	+	14775.8i	1.71917	+	0.705230i
$761$	25216.4			1.20117			0.600586	−	0.799560i	$-0.294934\pi$
$761$	25216.4			1.20117			0.600586	+	0.799560i	$0.294934\pi$
$762$		0			0
$763$			6890.14i			0.326920i
$764$	−50306.5			−2.38223
$765$		0			0
$766$	528.225			0.0249158
$767$			18837.7i			0.886819i
$768$		0			0
$769$	−15930.6			−0.747038			−0.373519	−	0.927622i	$-0.621849\pi$
$769$	−15930.6			−0.747038			−0.373519	+	0.927622i	$0.621849\pi$
$770$	5539.11	−	13502.9i	0.259241	−	0.631964i
$771$		0			0
$772$		−	36895.0i		−	1.72005i
$773$		−	28154.5i		−	1.31002i	−0.755618	−	0.655012i	$-0.772664\pi$
$773$		−	28154.5i		−	1.31002i	0.755618	−	0.655012i	$-0.227336\pi$
$774$		0			0
$775$	−14612.7	−	14414.3i	−0.677297	−	0.668101i
$776$	27822.5			1.28708
$777$		0			0
$778$			15807.3i			0.728430i
$779$	−19050.6			−0.876200
$780$		0			0
$781$	−25681.8			−1.17665
$782$		−	17964.9i		−	0.821515i
$783$		0			0
$784$	−6959.71			−0.317042
$785$	−24819.9	−	10181.5i	−1.12848	−	0.462922i
$786$		0			0
$787$			16392.1i			0.742461i	0.928541	+	0.371231i	$0.121064\pi$
$787$			16392.1i			0.742461i	−0.928541	+	0.371231i	$0.878936\pi$
$788$			67812.5i			3.06563i
$789$		0			0
$790$	17347.4	+	7116.16i	0.781255	+	0.320483i
$791$	15601.5			0.701298
$792$		0			0
$793$		−	6843.45i		−	0.306454i
$794$	50985.5			2.27885
$795$		0			0
$796$	−14510.0			−0.646097
$797$			2966.12i			0.131826i	0.997825	+	0.0659129i	$0.0209960\pi$
$797$			2966.12i			0.131826i	−0.997825	+	0.0659129i	$0.979004\pi$
$798$		0			0
$799$	−54742.6			−2.42385
$800$	24962.8	−	25306.4i	1.10321	−	1.11839i
$801$		0			0
$802$		−	19154.2i		−	0.843338i
$803$		−	40830.4i		−	1.79436i
$804$		0			0
$805$	909.216	−	2216.43i	0.0398082	−	0.0970423i
$806$	−38548.4			−1.68463
$807$		0			0
$808$		−	15414.4i		−	0.671134i
$809$	−14712.3			−0.639378			−0.319689	−	0.947523i	$-0.603578\pi$
$809$	−14712.3			−0.639378			−0.319689	+	0.947523i	$0.603578\pi$
$810$		0			0
$811$	5794.69			0.250899			0.125450	−	0.992100i	$-0.459963\pi$
$811$	5794.69			0.250899			0.125450	+	0.992100i	$0.459963\pi$
$812$			28444.3i			1.22931i
$813$		0			0
$814$	−76559.0			−3.29655
$815$	14644.9	+	6007.58i	0.629435	+	0.258204i
$816$		0			0
$817$			1844.75i			0.0789961i
$818$		−	45720.3i		−	1.95424i
$819$		0			0
$820$	−24806.7	+	60472.5i	−1.05645	+	2.57535i
$821$	−34345.7			−1.46002			−0.730009	−	0.683438i	$-0.760484\pi$
$821$	−34345.7			−1.46002			−0.730009	+	0.683438i	$0.760484\pi$
$822$		0			0
$823$		−	17454.4i		−	0.739274i	−0.929176	−	0.369637i	$-0.879482\pi$
$823$		−	17454.4i		−	0.739274i	0.929176	−	0.369637i	$-0.120518\pi$
$824$	−35516.2			−1.50153
$825$		0			0
$826$	15110.3			0.636508
$827$		−	1378.54i		−	0.0579645i	−0.999580	−	0.0289822i	$-0.990773\pi$
$827$		−	1378.54i		−	0.0579645i	0.999580	−	0.0289822i	$-0.00922663\pi$
$828$		0			0
$829$	−36714.7			−1.53818			−0.769092	−	0.639138i	$-0.779291\pi$
$829$	−36714.7			−1.53818			−0.769092	+	0.639138i	$0.779291\pi$
$830$	6556.09	−	15982.1i	0.274175	−	0.668368i
$831$		0			0
$832$		−	15327.8i		−	0.638696i
$833$		−	5544.52i		−	0.230620i
$834$		0			0
$835$	−36657.2	−	15037.3i	−1.51925	−	0.623220i
$836$	41856.3			1.73162
$837$		0			0
$838$			19433.4i			0.801091i
$839$	3191.34			0.131320			0.0656598	−	0.997842i	$-0.479085\pi$
$839$	3191.34			0.131320			0.0656598	+	0.997842i	$0.479085\pi$
$840$		0			0
$841$	21831.2			0.895123
$842$		−	54742.2i		−	2.24055i
$843$		0			0
$844$	22678.0			0.924893
$845$	629.415	−	1534.35i	0.0256243	−	0.0624655i
$846$		0			0
$847$			267.416i			0.0108483i
$848$			41982.9i			1.70012i
$849$		0			0
$850$	52226.9	+	51517.8i	2.10749	+	2.07888i
$851$	−12566.7			−0.506207
$852$		0			0
$853$		−	42221.5i		−	1.69477i	−0.530980	−	0.847384i	$-0.678176\pi$
$853$		−	42221.5i		−	1.69477i	0.530980	−	0.847384i	$-0.321824\pi$
$854$	−5489.35			−0.219955
$855$		0			0
$856$	51363.3			2.05089
$857$		−	5849.17i		−	0.233143i	−0.993182	−	0.116572i	$-0.962810\pi$
$857$		−	5849.17i		−	0.233143i	0.993182	−	0.116572i	$-0.0371904\pi$
$858$		0			0
$859$	45756.1			1.81744			0.908719	−	0.417409i	$-0.137062\pi$
$859$	45756.1			1.81744			0.908719	+	0.417409i	$0.137062\pi$
$860$	5855.81	+	2402.14i	0.232188	+	0.0952470i
$861$		0			0
$862$			72767.5i			2.87526i
$863$			33012.0i			1.30213i	0.759020	+	0.651067i	$0.225678\pi$
$863$			33012.0i			1.30213i	−0.759020	+	0.651067i	$0.774322\pi$
$864$		0			0
$865$	989.543	+	405.926i	0.0388965	+	0.0159559i
$866$	49994.1			1.96174
$867$		0			0
$868$			21725.4i			0.849548i
$869$	11626.1			0.453842
$870$		0			0
$871$	4052.11			0.157635
$872$			55650.9i			2.16121i
$873$		0			0
$874$	9778.50			0.378447
$875$	3836.18	+	8999.27i	0.148213	+	0.347692i
$876$		0			0
$877$			20709.9i			0.797404i	0.917080	+	0.398702i	$0.130539\pi$
$877$			20709.9i			0.797404i	−0.917080	+	0.398702i	$0.869461\pi$
$878$		−	20417.2i		−	0.784793i
$879$		0			0
$880$	21669.8	−	52825.3i	0.830100	−	2.02357i
$881$	13604.5			0.520258			0.260129	−	0.965574i	$-0.416235\pi$
$881$	13604.5			0.520258			0.260129	+	0.965574i	$0.416235\pi$
$882$		0			0
$883$		−	47582.7i		−	1.81346i	−0.421713	−	0.906729i	$-0.638571\pi$
$883$		−	47582.7i		−	1.81346i	0.421713	−	0.906729i	$-0.361429\pi$
$884$	96802.1			3.68304
$885$		0			0
$886$	−56080.2			−2.12647
$887$			25132.9i			0.951386i	0.879611	+	0.475693i	$0.157803\pi$
$887$			25132.9i			0.951386i	−0.879611	+	0.475693i	$0.842197\pi$
$888$		0			0
$889$	20025.5			0.755492
$890$	−4839.70	−	1985.32i	−0.182278	−	0.0747731i
$891$		0			0
$892$			55149.7i			2.07012i
$893$		−	29796.9i		−	1.11659i
$894$		0			0
$895$	9191.32	−	22406.1i	0.343276	−	0.836819i
$896$	3629.93			0.135343
$897$		0			0
$898$			42296.0i			1.57176i
$899$	35302.4			1.30968
$900$		0			0
$901$	−33446.2			−1.23668
$902$			57682.3i			2.12928i
$903$		0			0
$904$	126012.			4.63617
$905$	−7889.13	+	19231.7i	−0.289772	+	0.706390i
$906$		0			0
$907$			36233.4i			1.32647i	0.748411	+	0.663235i	$0.230817\pi$
$907$			36233.4i			1.32647i	−0.748411	+	0.663235i	$0.769183\pi$
$908$			11580.1i			0.423238i
$909$		0			0
$910$	16998.0	+	6972.85i	0.619208	+	0.254009i
$911$	−16912.4			−0.615076			−0.307538	−	0.951536i	$-0.599505\pi$
$911$	−16912.4			−0.615076			−0.307538	+	0.951536i	$0.599505\pi$
$912$		0			0
$913$		−	10711.1i		−	0.388264i
$914$	−92256.5			−3.33870
$915$		0			0
$916$	49926.7			1.80090
$917$		−	3674.80i		−	0.132337i
$918$		0			0
$919$	49589.9			1.78000			0.890001	−	0.455959i	$-0.150704\pi$
$919$	49589.9			1.78000			0.890001	+	0.455959i	$0.150704\pi$
$920$	7343.64	−	17901.9i	0.263166	−	0.641531i
$921$		0			0
$922$		−	68422.4i		−	2.44400i
$923$		−	32329.2i		−	1.15290i
$924$		0			0
$925$	36037.5	−	36533.5i	1.28098	−	1.29861i
$926$	2814.09			0.0998668
$927$		0			0
$928$			61136.7i			2.16262i
$929$	−40649.1			−1.43558			−0.717789	−	0.696261i	$-0.754846\pi$
$929$	−40649.1			−1.43558			−0.717789	+	0.696261i	$0.754846\pi$
$930$		0			0
$931$	3017.94			0.106240
$932$			43904.2i			1.54306i
$933$		0			0
$934$	30925.1			1.08341
$935$	42083.9	+	17263.5i	1.47197	+	0.603824i
$936$		0			0
$937$			3678.18i			0.128240i	0.997942	+	0.0641200i	$0.0204240\pi$
$937$			3678.18i			0.128240i	−0.997942	+	0.0641200i	$0.979576\pi$
$938$		−	3250.32i		−	0.113142i
$939$		0			0
$940$	−94584.5	−	38800.0i	−3.28192	−	1.34629i
$941$	4835.12			0.167503			0.0837516	−	0.996487i	$-0.473310\pi$
$941$	4835.12			0.167503			0.0837516	+	0.996487i	$0.473310\pi$
$942$		0			0
$943$			9468.24i			0.326965i
$944$	59113.6			2.03812
$945$		0			0
$946$	5585.63			0.191971
$947$		−	31497.4i		−	1.08081i	−0.841405	−	0.540405i	$-0.818271\pi$
$947$		−	31497.4i		−	1.08081i	0.841405	−	0.540405i	$-0.181729\pi$
$948$		0			0
$949$	51398.9			1.75814
$950$	−28041.7	+	28427.6i	−0.957676	+	0.970857i
$951$		0			0
$952$		−	44782.5i		−	1.52459i
$953$		−	26365.5i		−	0.896183i	−0.893988	−	0.448092i	$-0.852104\pi$
$953$		−	26365.5i		−	0.896183i	0.893988	−	0.448092i	$-0.147896\pi$
$954$		0			0
$955$	11293.7	−	27531.2i	0.382677	−	0.932868i
$956$	−101545.			−3.43537
$957$		0			0
$958$		−	6834.20i		−	0.230483i
$959$	−15043.2			−0.506538
$960$		0			0
$961$	−2827.48			−0.0949104
$962$		−	96375.4i		−	3.23001i
$963$		0			0
$964$	26694.2			0.891870
$965$	20191.5	+	8282.87i	0.673563	+	0.276306i
$966$		0			0
$967$			2307.07i			0.0767221i	0.999264	+	0.0383611i	$0.0122137\pi$
$967$			2307.07i			0.0767221i	−0.999264	+	0.0383611i	$0.987786\pi$
$968$			2159.89i			0.0717164i
$969$		0			0
$970$	−10830.1	+	26400.9i	−0.358487	+	0.873899i
$971$	48345.5			1.59782			0.798909	−	0.601452i	$-0.205411\pi$
$971$	48345.5			1.59782			0.798909	+	0.601452i	$0.205411\pi$
$972$		0			0
$973$		−	10554.5i		−	0.347750i
$974$	30996.2			1.01969
$975$		0			0
$976$	−21475.1			−0.704304
$977$			25534.5i			0.836153i	0.908412	+	0.418076i	$0.137296\pi$
$977$			25534.5i			0.836153i	−0.908412	+	0.418076i	$0.862704\pi$
$978$		0			0
$979$	−3243.53			−0.105887
$980$	3929.81	−	9579.86i	0.128095	−	0.312263i
$981$		0			0
$982$		−	53624.0i		−	1.74258i
$983$			41611.3i			1.35015i	0.737750	+	0.675074i	$0.235888\pi$
$983$			41611.3i			1.35015i	−0.737750	+	0.675074i	$0.764112\pi$
$984$		0			0
$985$	−37111.7	−	15223.8i	−1.20048	−	0.492457i
$986$	−126173.			−4.07522
$987$		0			0
$988$			52690.4i			1.69666i
$989$	916.851			0.0294784
$990$		0			0
$991$	9963.65			0.319380			0.159690	−	0.987167i	$-0.448950\pi$
$991$	9963.65			0.319380			0.159690	+	0.987167i	$0.448950\pi$
$992$			46695.5i			1.49454i
$993$		0			0
$994$	−25932.3			−0.827486
$995$	3257.47	−	7940.88i	0.103788	−	0.253008i
$996$		0			0
$997$		−	15960.8i		−	0.507005i	−0.967335	−	0.253502i	$-0.918417\pi$
$997$		−	15960.8i		−	0.507005i	0.967335	−	0.253502i	$-0.0815825\pi$
$998$			21585.3i			0.684639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.b.64.10		10
3.2	odd	2		105.4.d.b.64.1	✓	10
5.2	odd	4		1575.4.a.bo.1.1		5
5.3	odd	4		1575.4.a.bp.1.5		5
5.4	even	2	inner	315.4.d.b.64.1		10
15.2	even	4		525.4.a.x.1.5		5
15.8	even	4		525.4.a.w.1.1		5
15.14	odd	2		105.4.d.b.64.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.1	✓	10	3.2	odd	2
105.4.d.b.64.10	yes	10	15.14	odd	2
315.4.d.b.64.1		10	5.4	even	2	inner
315.4.d.b.64.10		10	1.1	even	1	trivial
525.4.a.w.1.1		5	15.8	even	4
525.4.a.x.1.5		5	15.2	even	4
1575.4.a.bo.1.1		5	5.2	odd	4
1575.4.a.bp.1.5		5	5.3	odd	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.18660i q^{2} -18.9008 q^{4} +(4.24321 - 10.3438i) q^{5} -7.00000i q^{7} -56.5383i q^{8} +O(q^{10})\)	\(q+5.18660i q^{2} -18.9008 q^{4} +(4.24321 - 10.3438i) q^{5} -7.00000i q^{7} -56.5383i q^{8} +(53.6494 + 22.0078i) q^{10} +35.9555 q^{11} +45.2622i q^{13} +36.3062 q^{14} +142.035 q^{16} +113.154i q^{17} -61.5906 q^{19} +(-80.2001 + 195.507i) q^{20} +186.487i q^{22} +30.6108i q^{23} +(-88.9904 - 87.7822i) q^{25} -234.757 q^{26} +132.306i q^{28} +214.989 q^{29} +164.206 q^{31} +284.372i q^{32} -586.882 q^{34} +(-72.4069 - 29.7024i) q^{35} +410.533i q^{37} -319.446i q^{38} +(-584.823 - 239.904i) q^{40} +309.310 q^{41} -29.9519i q^{43} -679.589 q^{44} -158.766 q^{46} +483.790i q^{47} -49.0000 q^{49} +(455.291 - 461.558i) q^{50} -855.493i q^{52} +295.582i q^{53} +(152.567 - 371.918i) q^{55} -395.768 q^{56} +1115.06i q^{58} +416.191 q^{59} -151.196 q^{61} +851.670i q^{62} -338.644 q^{64} +(468.185 + 192.057i) q^{65} -89.5253i q^{67} -2138.70i q^{68} +(154.055 - 375.546i) q^{70} -714.265 q^{71} -1135.58i q^{73} -2129.27 q^{74} +1164.11 q^{76} -251.688i q^{77} +323.347 q^{79} +(602.683 - 1469.19i) q^{80} +1604.27i q^{82} -297.898i q^{83} +(1170.44 + 480.134i) q^{85} +155.348 q^{86} -2032.86i q^{88} -90.2097 q^{89} +316.835 q^{91} -578.570i q^{92} -2509.23 q^{94} +(-261.342 + 637.084i) q^{95} +492.101i q^{97} -254.143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) \) 10 * q - 54 * q^4 + 14 * q^5	\( 10 q - 54 q^{4} + 14 q^{5} + 92 q^{10} - 132 q^{11} + 14 q^{14} + 310 q^{16} - 348 q^{19} - 366 q^{20} - 374 q^{25} - 892 q^{26} + 740 q^{29} + 684 q^{31} - 224 q^{34} - 2156 q^{40} - 1604 q^{41} + 580 q^{44} + 1280 q^{46} - 490 q^{49} + 2504 q^{50} - 452 q^{55} - 462 q^{56} + 1408 q^{59} + 1300 q^{61} - 150 q^{64} + 3296 q^{65} - 882 q^{70} - 2940 q^{71} - 2624 q^{74} + 8740 q^{76} + 1640 q^{79} + 4126 q^{80} - 1704 q^{85} - 1664 q^{86} + 572 q^{89} - 28 q^{91} - 5080 q^{94} - 1268 q^{95}+O(q^{100}) \) 10 * q - 54 * q^4 + 14 * q^5 + 92 * q^10 - 132 * q^11 + 14 * q^14 + 310 * q^16 - 348 * q^19 - 366 * q^20 - 374 * q^25 - 892 * q^26 + 740 * q^29 + 684 * q^31 - 224 * q^34 - 2156 * q^40 - 1604 * q^41 + 580 * q^44 + 1280 * q^46 - 490 * q^49 + 2504 * q^50 - 452 * q^55 - 462 * q^56 + 1408 * q^59 + 1300 * q^61 - 150 * q^64 + 3296 * q^65 - 882 * q^70 - 2940 * q^71 - 2624 * q^74 + 8740 * q^76 + 1640 * q^79 + 4126 * q^80 - 1704 * q^85 - 1664 * q^86 + 572 * q^89 - 28 * q^91 - 5080 * q^94 - 1268 * q^95

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