LMFDB - Embedded newform 315.4.d.b.64.6

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			64.6
Root			$-0.329739i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.b.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.428319i q^{2} +7.81654 q^{4} +(1.76884 - 11.0395i) q^{5} +7.00000i q^{7} +6.77452i q^{8} +O(q^{10})$	\(q+0.428319i q^{2} +7.81654 q^{4} +(1.76884 - 11.0395i) q^{5} +7.00000i q^{7} +6.77452i q^{8} +(4.72844 + 0.757628i) q^{10} +27.4721 q^{11} +46.5524i q^{13} -2.99823 q^{14} +59.6307 q^{16} -5.20546i q^{17} +91.0007 q^{19} +(13.8262 - 86.2910i) q^{20} +11.7668i q^{22} -111.563i q^{23} +(-118.742 - 39.0544i) q^{25} -19.9393 q^{26} +54.7158i q^{28} +0.0763413 q^{29} +201.784 q^{31} +79.7371i q^{32} +2.22960 q^{34} +(77.2767 + 12.3819i) q^{35} -312.859i q^{37} +38.9773i q^{38} +(74.7876 + 11.9831i) q^{40} -102.432 q^{41} -257.280i q^{43} +214.737 q^{44} +47.7847 q^{46} +350.994i q^{47} -49.0000 q^{49} +(16.7277 - 50.8596i) q^{50} +363.879i q^{52} +196.260i q^{53} +(48.5938 - 303.279i) q^{55} -47.4217 q^{56} +0.0326984i q^{58} +881.060 q^{59} +737.897 q^{61} +86.4280i q^{62} +442.893 q^{64} +(513.917 + 82.3439i) q^{65} +365.021i q^{67} -40.6887i q^{68} +(-5.30340 + 33.0991i) q^{70} -1112.53 q^{71} -261.995i q^{73} +134.004 q^{74} +711.311 q^{76} +192.305i q^{77} -273.829 q^{79} +(105.477 - 658.295i) q^{80} -43.8735i q^{82} -87.1353i q^{83} +(-57.4658 - 9.20763i) q^{85} +110.198 q^{86} +186.110i q^{88} -1090.99 q^{89} -325.867 q^{91} -872.039i q^{92} -150.337 q^{94} +(160.966 - 1004.61i) q^{95} +228.830i q^{97} -20.9876i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.428319i			0.151434i	0.997129	+	0.0757168i	$0.0241245\pi$
$2$			0.428319i			0.151434i	−0.997129	+	0.0757168i	$0.975876\pi$
$3$		0			0
$3$		0			0
$4$	7.81654			0.977068
$5$	1.76884	−	11.0395i	0.158210	−	0.987405i
$5$	1.76884	−	11.0395i	0.158210	−	0.987405i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			6.77452i			0.299394i
$9$		0			0
$10$	4.72844	+	0.757628i	0.149526	+	0.0239583i
$11$	27.4721			0.753013			0.376507	−	0.926414i	$-0.377125\pi$
$11$	27.4721			0.753013			0.376507	+	0.926414i	$0.377125\pi$
$12$		0			0
$13$			46.5524i			0.993179i	0.867986	+	0.496589i	$0.165414\pi$
$13$			46.5524i			0.993179i	−0.867986	+	0.496589i	$0.834586\pi$
$14$	−2.99823			−0.0572365
$15$		0			0
$16$	59.6307			0.931729
$17$		−	5.20546i		−	0.0742653i	−0.999310	−	0.0371326i	$-0.988178\pi$
$17$		−	5.20546i		−	0.0742653i	0.999310	−	0.0371326i	$-0.0118224\pi$
$18$		0			0
$19$	91.0007			1.09879			0.549395	−	0.835563i	$-0.314858\pi$
$19$	91.0007			1.09879			0.549395	+	0.835563i	$0.314858\pi$
$20$	13.8262	−	86.2910i	0.154582	−	0.964762i
$21$		0			0
$22$			11.7668i			0.114032i
$23$		−	111.563i		−	1.01142i	−0.862705	−	0.505708i	$-0.831231\pi$
$23$		−	111.563i		−	1.01142i	0.862705	−	0.505708i	$-0.168769\pi$
$24$		0			0
$25$	−118.742	−	39.0544i	−0.949939	−	0.312435i
$26$	−19.9393			−0.150401
$27$		0			0
$28$			54.7158i			0.369297i
$29$	0.0763413			0.000488835			0.000244418	−	1.00000i	$-0.499922\pi$
$29$	0.0763413			0.000488835			0.000244418		1.00000i	$0.499922\pi$
$30$		0			0
$31$	201.784			1.16908			0.584541	−	0.811364i	$-0.301275\pi$
$31$	201.784			1.16908			0.584541	+	0.811364i	$0.301275\pi$
$32$			79.7371i			0.440490i
$33$		0			0
$34$	2.22960			0.0112463
$35$	77.2767	+	12.3819i	0.373204	+	0.0597978i
$36$		0			0
$37$		−	312.859i		−	1.39010i	−0.718960	−	0.695051i	$-0.755382\pi$
$37$		−	312.859i		−	1.39010i	0.718960	−	0.695051i	$-0.244618\pi$
$38$			38.9773i			0.166394i
$39$		0			0
$40$	74.7876	+	11.9831i	0.295624	+	0.0473672i
$41$	−102.432			−0.390175			−0.195087	−	0.980786i	$-0.562499\pi$
$41$	−102.432			−0.390175			−0.195087	+	0.980786i	$0.562499\pi$
$42$		0			0
$43$		−	257.280i		−	0.912439i	−0.889867	−	0.456219i	$-0.849203\pi$
$43$		−	257.280i		−	0.912439i	0.889867	−	0.456219i	$-0.150797\pi$
$44$	214.737			0.735745
$45$		0			0
$46$	47.7847			0.153162
$47$			350.994i			1.08931i	0.838659	+	0.544657i	$0.183340\pi$
$47$			350.994i			1.08931i	−0.838659	+	0.544657i	$0.816660\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	16.7277	−	50.8596i	0.0473131	−	0.143853i
$51$		0			0
$52$			363.879i			0.970403i
$53$			196.260i			0.508649i	0.967119	+	0.254324i	$0.0818531\pi$
$53$			196.260i			0.508649i	−0.967119	+	0.254324i	$0.918147\pi$
$54$		0			0
$55$	48.5938	−	303.279i	0.119134	−	0.743530i
$56$	−47.4217			−0.113160
$57$		0			0
$58$			0.0326984i			7.40261e-5i
$59$	881.060			1.94414			0.972070	−	0.234692i	$-0.0754082\pi$
$59$	881.060			1.94414			0.972070	+	0.234692i	$0.0754082\pi$
$60$		0			0
$61$	737.897			1.54882			0.774410	−	0.632684i	$-0.218047\pi$
$61$	737.897			1.54882			0.774410	+	0.632684i	$0.218047\pi$
$62$			86.4280i			0.177038i
$63$		0			0
$64$	442.893			0.865025
$65$	513.917	+	82.3439i	0.980670	+	0.157131i
$66$		0			0
$67$			365.021i			0.665589i	0.942999	+	0.332794i	$0.107991\pi$
$67$			365.021i			0.665589i	−0.942999	+	0.332794i	$0.892009\pi$
$68$		−	40.6887i		−	0.0725622i
$69$		0			0
$70$	−5.30340	+	33.0991i	−0.00905539	+	0.0565157i
$71$	−1112.53			−1.85962			−0.929809	−	0.368042i	$-0.880028\pi$
$71$	−1112.53			−1.85962			−0.929809	+	0.368042i	$0.880028\pi$
$72$		0			0
$73$		−	261.995i		−	0.420057i	−0.977695	−	0.210029i	$-0.932644\pi$
$73$		−	261.995i		−	0.420057i	0.977695	−	0.210029i	$-0.0673558\pi$
$74$	134.004			0.210508
$75$		0			0
$76$	711.311			1.07359
$77$			192.305i			0.284612i
$78$		0			0
$79$	−273.829			−0.389977			−0.194988	−	0.980806i	$-0.562467\pi$
$79$	−273.829			−0.389977			−0.194988	+	0.980806i	$0.562467\pi$
$80$	105.477	−	658.295i	0.147409	−	0.919995i
$81$		0			0
$82$		−	43.8735i		−	0.0590856i
$83$		−	87.1353i		−	0.115233i	−0.998339	−	0.0576165i	$-0.981650\pi$
$83$		−	87.1353i		−	0.115233i	0.998339	−	0.0576165i	$-0.0183501\pi$
$84$		0			0
$85$	−57.4658	−	9.20763i	−0.0733299	−	0.0117495i
$86$	110.198			0.138174
$87$		0			0
$88$			186.110i			0.225448i
$89$	−1090.99			−1.29938			−0.649690	−	0.760199i	$-0.725101\pi$
$89$	−1090.99			−1.29938			−0.649690	+	0.760199i	$0.725101\pi$
$90$		0			0
$91$	−325.867			−0.375386
$92$		−	872.039i		−	0.988221i
$93$		0			0
$94$	−150.337			−0.164959
$95$	160.966	−	1004.61i	0.173839	−	1.08495i
$96$		0			0
$97$			228.830i			0.239527i	0.992802	+	0.119764i	$0.0382137\pi$
$97$			228.830i			0.239527i	−0.992802	+	0.119764i	$0.961786\pi$
$98$		−	20.9876i		−	0.0216334i
$99$		0			0
$100$	−928.155	−	305.270i	−0.928155	−	0.305270i
$101$	590.728			0.581976			0.290988	−	0.956727i	$-0.406016\pi$
$101$	590.728			0.581976			0.290988	+	0.956727i	$0.406016\pi$
$102$		0			0
$103$			1471.06i			1.40726i	0.710568	+	0.703629i	$0.248438\pi$
$103$			1471.06i			1.40726i	−0.710568	+	0.703629i	$0.751562\pi$
$104$	−315.371			−0.297352
$105$		0			0
$106$	−84.0619			−0.0770265
$107$		−	1223.29i		−	1.10523i	−0.833435	−	0.552617i	$-0.813629\pi$
$107$		−	1223.29i		−	1.10523i	0.833435	−	0.552617i	$-0.186371\pi$
$108$		0			0
$109$	−1280.64			−1.12535			−0.562674	−	0.826679i	$-0.690227\pi$
$109$	−1280.64			−1.12535			−0.562674	+	0.826679i	$0.690227\pi$
$110$	129.900	+	20.8136i	0.112595	+	0.0180409i
$111$		0			0
$112$			417.415i			0.352161i
$113$			1805.38i			1.50297i	0.659748	+	0.751487i	$0.270663\pi$
$113$			1805.38i			1.50297i	−0.659748	+	0.751487i	$0.729337\pi$
$114$		0			0
$115$	−1231.61	−	197.338i	−0.998677	−	0.160016i
$116$	0.596725			0.000477625
$117$		0			0
$118$			377.375i			0.294408i
$119$	36.4382			0.0280696
$120$		0			0
$121$	−576.284			−0.432971
$122$			316.055i			0.234543i
$123$		0			0
$124$	1577.26			1.14227
$125$	−641.178	+	1241.78i	−0.458790	+	0.888545i
$126$		0			0
$127$		−	1642.42i		−	1.14757i	−0.819005	−	0.573786i	$-0.805474\pi$
$127$		−	1642.42i		−	1.14757i	0.819005	−	0.573786i	$-0.194526\pi$
$128$			827.596i			0.571483i
$129$		0			0
$130$	−35.2694	+	220.120i	−0.0237949	+	0.148506i
$131$	−2371.85			−1.58190			−0.790951	−	0.611879i	$-0.790414\pi$
$131$	−2371.85			−1.58190			−0.790951	+	0.611879i	$0.790414\pi$
$132$		0			0
$133$			637.005i			0.415303i
$134$	−156.345			−0.100792
$135$		0			0
$136$	35.2645			0.0222346
$137$			762.828i			0.475714i	0.971300	+	0.237857i	$0.0764450\pi$
$137$			762.828i			0.475714i	−0.971300	+	0.237857i	$0.923555\pi$
$138$		0			0
$139$	−2025.84			−1.23618			−0.618092	−	0.786105i	$-0.712094\pi$
$139$	−2025.84			−1.23618			−0.618092	+	0.786105i	$0.712094\pi$
$140$	604.037	+	96.7836i	0.364646	+	0.0584265i
$141$		0			0
$142$		−	476.517i		−	0.281609i
$143$			1278.89i			0.747877i
$144$		0			0
$145$	0.135036	−	0.842772i	7.73386e−5	−	0.000482679i
$146$	112.217			0.0636108
$147$		0			0
$148$		−	2445.48i		−	1.35822i
$149$	−10.7903			−0.00593272			−0.00296636	−	0.999996i	$-0.500944\pi$
$149$	−10.7903			−0.00593272			−0.00296636	+	0.999996i	$0.500944\pi$
$150$		0			0
$151$	−2404.48			−1.29585			−0.647925	−	0.761704i	$-0.724363\pi$
$151$	−2404.48			−1.29585			−0.647925	+	0.761704i	$0.724363\pi$
$152$			616.487i			0.328972i
$153$		0			0
$154$	−82.3677			−0.0430999
$155$	356.924	−	2227.60i	0.184960	−	1.15436i
$156$		0			0
$157$		−	396.624i		−	0.201618i	−0.994906	−	0.100809i	$-0.967857\pi$
$157$		−	396.624i		−	0.201618i	0.994906	−	0.100809i	$-0.0321431\pi$
$158$		−	117.286i		−	0.0590556i
$159$		0			0
$160$	880.260	+	141.042i	0.434942	+	0.0696899i
$161$	780.943			0.382279
$162$		0			0
$163$			2751.69i			1.32226i	0.750270	+	0.661132i	$0.229923\pi$
$163$			2751.69i			1.32226i	−0.750270	+	0.661132i	$0.770077\pi$
$164$	−800.663			−0.381227
$165$		0			0
$166$	37.3217			0.0174501
$167$		−	2079.43i		−	0.963541i	−0.876297	−	0.481771i	$-0.839994\pi$
$167$		−	2079.43i		−	0.963541i	0.876297	−	0.481771i	$-0.160006\pi$
$168$		0			0
$169$	29.8706			0.0135961
$170$	3.94380	−	24.6137i	0.00177927	−	0.0111046i
$171$		0			0
$172$		−	2011.04i		−	0.891515i
$173$			1929.59i			0.848000i	0.905662	+	0.424000i	$0.139374\pi$
$173$			1929.59i			0.848000i	−0.905662	+	0.424000i	$0.860626\pi$
$174$		0			0
$175$	273.380	−	831.197i	0.118089	−	0.359043i
$176$	1638.18			0.701605
$177$		0			0
$178$		−	467.292i		−	0.196770i
$179$	1638.15			0.684027			0.342014	−	0.939695i	$-0.388891\pi$
$179$	1638.15			0.684027			0.342014	+	0.939695i	$0.388891\pi$
$180$		0			0
$181$	−36.6604			−0.0150550			−0.00752749	−	0.999972i	$-0.502396\pi$
$181$	−36.6604			−0.0150550			−0.00752749	+	0.999972i	$0.502396\pi$
$182$		−	139.575i		−	0.0568461i
$183$		0			0
$184$	755.788			0.302812
$185$	−3453.82	−	553.399i	−1.37259	−	0.219928i
$186$		0			0
$187$		−	143.005i		−	0.0559227i
$188$			2743.56i			1.06433i
$189$		0			0
$190$	430.291	+	68.9447i	0.164298	+	0.0263251i
$191$	−1054.82			−0.399603			−0.199801	−	0.979836i	$-0.564030\pi$
$191$	−1054.82			−0.399603			−0.199801	+	0.979836i	$0.564030\pi$
$192$		0			0
$193$		−	213.661i		−	0.0796873i	−0.999206	−	0.0398436i	$-0.987314\pi$
$193$		−	213.661i		−	0.0796873i	0.999206	−	0.0398436i	$-0.0126860\pi$
$194$	−98.0121			−0.0362725
$195$		0			0
$196$	−383.011			−0.139581
$197$		−	3953.62i		−	1.42987i	−0.699193	−	0.714933i	$-0.746457\pi$
$197$		−	3953.62i		−	1.42987i	0.699193	−	0.714933i	$-0.253543\pi$
$198$		0			0
$199$	−929.168			−0.330990			−0.165495	−	0.986211i	$-0.552922\pi$
$199$	−929.168			−0.330990			−0.165495	+	0.986211i	$0.552922\pi$
$200$	264.575	−	804.423i	0.0935413	−	0.284407i
$201$		0			0
$202$			253.020i			0.0881308i
$203$			0.534389i			0.000184762i
$204$		0			0
$205$	−181.186	+	1130.80i	−0.0617295	+	0.385261i
$206$	−630.081			−0.213106
$207$		0			0
$208$			2775.95i			0.925374i
$209$	2499.98			0.827403
$210$		0			0
$211$	−926.806			−0.302388			−0.151194	−	0.988504i	$-0.548312\pi$
$211$	−926.806			−0.302388			−0.151194	+	0.988504i	$0.548312\pi$
$212$			1534.07i			0.496984i
$213$		0			0
$214$	523.959			0.167370
$215$	−2840.25	−	455.088i	−0.900947	−	0.144357i
$216$		0			0
$217$			1412.49i			0.441871i
$218$		−	548.521i		−	0.170415i
$219$		0			0
$220$	379.835	−	2370.59i	0.116402	−	0.726479i
$221$	242.327			0.0737587
$222$		0			0
$223$			5351.73i			1.60708i	0.595253	+	0.803538i	$0.297052\pi$
$223$			5351.73i			1.60708i	−0.595253	+	0.803538i	$0.702948\pi$
$224$	−558.160			−0.166489
$225$		0			0
$226$	−773.279			−0.227601
$227$		−	6016.48i		−	1.75915i	−0.475758	−	0.879576i	$-0.657826\pi$
$227$		−	6016.48i		−	1.75915i	0.475758	−	0.879576i	$-0.342174\pi$
$228$		0			0
$229$	−1210.84			−0.349408			−0.174704	−	0.984621i	$-0.555897\pi$
$229$	−1210.84			−0.349408			−0.174704	+	0.984621i	$0.555897\pi$
$230$	84.5235	−	527.520i	0.0242318	−	0.151233i
$231$		0			0
$232$			0.517176i			0.000146355i
$233$			3517.31i			0.988957i	0.869190	+	0.494478i	$0.164641\pi$
$233$			3517.31i			0.988957i	−0.869190	+	0.494478i	$0.835359\pi$
$234$		0			0
$235$	3874.81	+	620.853i	1.07559	+	0.172340i
$236$	6886.84			1.89956
$237$		0			0
$238$			15.6072i			0.00425068i
$239$	−6715.89			−1.81764			−0.908818	−	0.417194i	$-0.863014\pi$
$239$	−6715.89			−1.81764			−0.908818	+	0.417194i	$0.863014\pi$
$240$		0			0
$241$	−1715.70			−0.458582			−0.229291	−	0.973358i	$-0.573641\pi$
$241$	−1715.70			−0.458582			−0.229291	+	0.973358i	$0.573641\pi$
$242$		−	246.833i		−	0.0655663i
$243$		0			0
$244$	5767.80			1.51330
$245$	−86.6732	+	540.937i	−0.0226014	+	0.141058i
$246$		0			0
$247$			4236.31i			1.09129i
$248$			1366.99i			0.350017i
$249$		0			0
$250$	−531.877	−	274.629i	−0.134556	−	0.0694762i
$251$	2464.48			0.619748			0.309874	−	0.950778i	$-0.399713\pi$
$251$	2464.48			0.619748			0.309874	+	0.950778i	$0.399713\pi$
$252$		0			0
$253$		−	3064.88i		−	0.761609i
$254$	703.482			0.173781
$255$		0			0
$256$	3188.67			0.778483
$257$			1873.99i			0.454850i	0.973796	+	0.227425i	$0.0730307\pi$
$257$			1873.99i			0.454850i	−0.973796	+	0.227425i	$0.926969\pi$
$258$		0			0
$259$	2190.02			0.525409
$260$	4017.05	+	643.644i	0.958181	+	0.153527i
$261$		0			0
$262$		−	1015.91i		−	0.239553i
$263$			2064.39i			0.484013i	0.970275	+	0.242007i	$0.0778056\pi$
$263$			2064.39i			0.484013i	−0.970275	+	0.242007i	$0.922194\pi$
$264$		0			0
$265$	2166.62	+	347.153i	0.502243	+	0.0804733i
$266$	−272.841			−0.0628909
$267$		0			0
$268$			2853.20i			0.650325i
$269$	5649.86			1.28059			0.640294	−	0.768130i	$-0.278812\pi$
$269$	5649.86			1.28059			0.640294	+	0.768130i	$0.278812\pi$
$270$		0			0
$271$	−3094.93			−0.693739			−0.346870	−	0.937913i	$-0.612755\pi$
$271$	−3094.93			−0.693739			−0.346870	+	0.937913i	$0.612755\pi$
$272$		−	310.405i		−	0.0691951i
$273$		0			0
$274$	−326.734			−0.0720391
$275$	−3262.10	−	1072.90i	−0.715317	−	0.235268i
$276$		0			0
$277$		−	8962.93i		−	1.94415i	−0.234665	−	0.972076i	$-0.575399\pi$
$277$		−	8962.93i		−	1.94415i	0.234665	−	0.972076i	$-0.424601\pi$
$278$		−	867.706i		−	0.187200i
$279$		0			0
$280$	−83.8814	+	523.513i	−0.0179031	+	0.111735i
$281$	5858.94			1.24383			0.621913	−	0.783086i	$-0.286356\pi$
$281$	5858.94			1.24383			0.621913	+	0.783086i	$0.286356\pi$
$282$		0			0
$283$		−	5819.46i		−	1.22237i	−0.791487	−	0.611186i	$-0.790693\pi$
$283$		−	5819.46i		−	1.22237i	0.791487	−	0.611186i	$-0.209307\pi$
$284$	−8696.13			−1.81697
$285$		0			0
$286$	−547.774			−0.113254
$287$		−	717.023i		−	0.147472i
$288$		0			0
$289$	4885.90			0.994485
$290$	0.360975	+	0.0578383i	7.30938e−5	+	1.17117e-5i
$291$		0			0
$292$		−	2047.90i		−	0.410425i
$293$			5678.78i			1.13228i	0.824310	+	0.566139i	$0.191564\pi$
$293$			5678.78i			1.13228i	−0.824310	+	0.566139i	$0.808436\pi$
$294$		0			0
$295$	1558.46	−	9726.49i	0.307582	−	1.91965i
$296$	2119.47			0.416189
$297$		0			0
$298$		−	4.62169i		−	0.000898413i
$299$	5193.54			1.00452
$300$		0			0
$301$	1800.96			0.344869
$302$		−	1029.88i		−	0.196235i
$303$		0			0
$304$	5426.44			1.02377
$305$	1305.22	−	8146.04i	0.245039	−	1.52931i
$306$		0			0
$307$			9184.53i			1.70745i	0.520720	+	0.853727i	$0.325663\pi$
$307$			9184.53i			1.70745i	−0.520720	+	0.853727i	$0.674337\pi$
$308$			1503.16i			0.278086i
$309$		0			0
$310$	954.125	+	152.877i	0.174808	+	0.0280092i
$311$	−4410.22			−0.804119			−0.402059	−	0.915614i	$-0.631705\pi$
$311$	−4410.22			−0.804119			−0.402059	+	0.915614i	$0.631705\pi$
$312$		0			0
$313$			4405.28i			0.795530i	0.917487	+	0.397765i	$0.130214\pi$
$313$			4405.28i			0.795530i	−0.917487	+	0.397765i	$0.869786\pi$
$314$	169.882			0.0305318
$315$		0			0
$316$	−2140.40			−0.381034
$317$			7486.86i			1.32651i	0.748393	+	0.663256i	$0.230826\pi$
$317$			7486.86i			1.32651i	−0.748393	+	0.663256i	$0.769174\pi$
$318$		0			0
$319$	2.09726			0.000368100
$320$	783.407	−	4889.33i	0.136856	−	0.854130i
$321$		0			0
$322$			334.493i			0.0578899i
$323$		−	473.701i		−	0.0816019i
$324$		0			0
$325$	1818.08	−	5527.75i	0.310304	−	0.943459i
$326$	−1178.60			−0.200235
$327$		0			0
$328$		−	693.927i		−	0.116816i
$329$	−2456.96			−0.411722
$330$		0			0
$331$	8860.56			1.47136			0.735680	−	0.677329i	$-0.236863\pi$
$331$	8860.56			1.47136			0.735680	+	0.677329i	$0.236863\pi$
$332$		−	681.097i		−	0.112590i
$333$		0			0
$334$	890.660			0.145912
$335$	4029.66	+	645.665i	0.657206	+	0.105303i
$336$		0			0
$337$		−	8742.01i		−	1.41308i	−0.707674	−	0.706539i	$-0.750255\pi$
$337$		−	8742.01i		−	1.41308i	0.707674	−	0.706539i	$-0.249745\pi$
$338$			12.7942i			0.00205891i
$339$		0			0
$340$	−449.184	−	71.9719i	−0.0716483	−	0.0114801i
$341$	5543.44			0.880334
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	1742.95			0.273179
$345$		0			0
$346$	−826.480			−0.128416
$347$			7285.82i			1.12716i	0.826063	+	0.563579i	$0.190576\pi$
$347$			7285.82i			1.12716i	−0.826063	+	0.563579i	$0.809424\pi$
$348$		0			0
$349$	−12610.9			−1.93423			−0.967117	−	0.254330i	$-0.918145\pi$
$349$	−12610.9			−1.93423			−0.967117	+	0.254330i	$0.918145\pi$
$350$	356.017	+	117.094i	0.0543712	+	0.0178827i
$351$		0			0
$352$			2190.55i			0.331695i
$353$		−	1202.59i		−	0.181325i	−0.995882	−	0.0906623i	$-0.971102\pi$
$353$		−	1202.59i		−	0.181325i	0.995882	−	0.0906623i	$-0.0288984\pi$
$354$		0			0
$355$	−1967.89	+	12281.8i	−0.294210	+	1.83620i
$356$	−8527.78			−1.26958
$357$		0			0
$358$			701.649i			0.103585i
$359$	3216.35			0.472848			0.236424	−	0.971650i	$-0.424025\pi$
$359$	3216.35			0.472848			0.236424	+	0.971650i	$0.424025\pi$
$360$		0			0
$361$	1422.14			0.207339
$362$		−	15.7024i		−	0.00227983i
$363$		0			0
$364$	−2547.15			−0.366778
$365$	−2892.30	−	463.428i	−0.414767	−	0.0664573i
$366$		0			0
$367$		−	1259.66i		−	0.179165i	−0.995979	−	0.0895824i	$-0.971447\pi$
$367$		−	1259.66i		−	0.179165i	0.995979	−	0.0895824i	$-0.0285532\pi$
$368$		−	6652.59i		−	0.942365i
$369$		0			0
$370$	237.031	−	1479.34i	0.0333045	−	0.207857i
$371$	−1373.82			−0.192251
$372$		0			0
$373$			386.230i			0.0536145i	0.999641	+	0.0268073i	$0.00853404\pi$
$373$			386.230i			0.0536145i	−0.999641	+	0.0268073i	$0.991466\pi$
$374$	61.2517			0.00846858
$375$		0			0
$376$	−2377.82			−0.326135
$377$			3.55387i			0.000485501i
$378$		0			0
$379$	−14246.0			−1.93079			−0.965395	−	0.260794i	$-0.916016\pi$
$379$	−14246.0			−1.93079			−0.965395	+	0.260794i	$0.916016\pi$
$380$	1258.20	−	7852.54i	0.169853	−	1.06007i
$381$		0			0
$382$		−	451.800i		−	0.0605133i
$383$			9298.85i			1.24060i	0.784365	+	0.620299i	$0.212989\pi$
$383$			9298.85i			1.24060i	−0.784365	+	0.620299i	$0.787011\pi$
$384$		0			0
$385$	2122.95	+	340.156i	0.281028	+	0.0450285i
$386$	91.5150			0.0120673
$387$		0			0
$388$			1788.66i			0.234034i
$389$	−1043.80			−0.136049			−0.0680244	−	0.997684i	$-0.521670\pi$
$389$	−1043.80			−0.136049			−0.0680244	+	0.997684i	$0.521670\pi$
$390$		0			0
$391$	−580.738			−0.0751130
$392$		−	331.952i		−	0.0427706i
$393$		0			0
$394$	1693.41			0.216530
$395$	−484.360	+	3022.94i	−0.0616982	+	0.385065i
$396$		0			0
$397$			4482.04i			0.566617i	0.959029	+	0.283309i	$0.0914321\pi$
$397$			4482.04i			0.566617i	−0.959029	+	0.283309i	$0.908568\pi$
$398$		−	397.980i		−	0.0501230i
$399$		0			0
$400$	−7080.69	−	2328.84i	−0.885086	−	0.291105i
$401$	−12686.2			−1.57984			−0.789921	−	0.613209i	$-0.789878\pi$
$401$	−12686.2			−1.57984			−0.789921	+	0.613209i	$0.789878\pi$
$402$		0			0
$403$			9393.55i			1.16111i
$404$	4617.45			0.568630
$405$		0			0
$406$	−0.228889			−2.79792e−5
$407$		−	8594.90i		−	1.04677i
$408$		0			0
$409$	6836.54			0.826516			0.413258	−	0.910614i	$-0.364391\pi$
$409$	6836.54			0.826516			0.413258	+	0.910614i	$0.364391\pi$
$410$	−484.343	−	77.6052i	−0.0583414	−	0.00934793i
$411$		0			0
$412$			11498.6i			1.37499i
$413$			6167.42i			0.734816i
$414$		0			0
$415$	−961.932	−	154.128i	−0.113782	−	0.0182310i
$416$	−3711.96			−0.437485
$417$		0			0
$418$			1070.79i			0.125297i
$419$	−5091.64			−0.593659			−0.296829	−	0.954930i	$-0.595929\pi$
$419$	−5091.64			−0.593659			−0.296829	+	0.954930i	$0.595929\pi$
$420$		0			0
$421$	8373.48			0.969355			0.484677	−	0.874693i	$-0.338937\pi$
$421$	8373.48			0.969355			0.484677	+	0.874693i	$0.338937\pi$
$422$		−	396.968i		−	0.0457918i
$423$		0			0
$424$	−1329.57			−0.152287
$425$	−203.296	+	618.109i	−0.0232031	+	0.0705475i
$426$		0			0
$427$			5165.28i			0.585399i
$428$		−	9561.91i		−	1.07989i
$429$		0			0
$430$	194.923	−	1216.53i	0.0218605	−	0.136434i
$431$	−6027.75			−0.673657			−0.336829	−	0.941566i	$-0.609354\pi$
$431$	−6027.75			−0.673657			−0.336829	+	0.941566i	$0.609354\pi$
$432$		0			0
$433$		−	11927.5i		−	1.32379i	−0.749597	−	0.661894i	$-0.769753\pi$
$433$		−	11927.5i		−	1.32379i	0.749597	−	0.661894i	$-0.230247\pi$
$434$	−604.996			−0.0669141
$435$		0			0
$436$	−10010.2			−1.09954
$437$		−	10152.3i		−	1.11133i
$438$		0			0
$439$	−7914.93			−0.860499			−0.430250	−	0.902710i	$-0.641574\pi$
$439$	−7914.93			−0.860499			−0.430250	+	0.902710i	$0.641574\pi$
$440$	2054.57	+	329.200i	0.222609	+	0.0356681i
$441$		0			0
$442$			103.793i			0.0111695i
$443$		−	2522.71i		−	0.270559i	−0.990807	−	0.135279i	$-0.956807\pi$
$443$		−	2522.71i		−	0.270559i	0.990807	−	0.135279i	$-0.0431932\pi$
$444$		0			0
$445$	−1929.79	+	12044.0i	−0.205575	+	1.28302i
$446$	−2292.24			−0.243365
$447$		0			0
$448$			3100.25i			0.326949i
$449$	−5339.89			−0.561258			−0.280629	−	0.959816i	$-0.590543\pi$
$449$	−5339.89			−0.561258			−0.280629	+	0.959816i	$0.590543\pi$
$450$		0			0
$451$	−2814.02			−0.293807
$452$			14111.8i			1.46851i
$453$		0			0
$454$	2576.97			0.266395
$455$	−576.407	+	3597.42i	−0.0593899	+	0.370658i
$456$		0			0
$457$		−	13765.8i		−	1.40905i	−0.709679	−	0.704526i	$-0.751160\pi$
$457$		−	13765.8i		−	1.40905i	0.709679	−	0.704526i	$-0.248840\pi$
$458$		−	518.625i		−	0.0529122i
$459$		0			0
$460$	−9626.90	−	1542.50i	−0.975775	−	0.156346i
$461$	12501.1			1.26298			0.631489	−	0.775384i	$-0.282444\pi$
$461$	12501.1			1.26298			0.631489	+	0.775384i	$0.282444\pi$
$462$		0			0
$463$		−	3566.32i		−	0.357972i	−0.983852	−	0.178986i	$-0.942718\pi$
$463$		−	3566.32i		−	0.357972i	0.983852	−	0.178986i	$-0.0572817\pi$
$464$	4.55229			0.000455462
$465$		0			0
$466$	−1506.53			−0.149761
$467$			4078.17i			0.404101i	0.979375	+	0.202050i	$0.0647605\pi$
$467$			4078.17i			0.404101i	−0.979375	+	0.202050i	$0.935240\pi$
$468$		0			0
$469$	−2555.15			−0.251569
$470$	−265.923	+	1659.65i	−0.0260981	+	0.162881i
$471$		0			0
$472$			5968.76i			0.582065i
$473$		−	7068.03i		−	0.687079i
$474$		0			0
$475$	−10805.6	−	3553.98i	−1.04378	−	0.343300i
$476$	284.821			0.0274259
$477$		0			0
$478$		−	2876.54i		−	0.275251i
$479$	19078.0			1.81982			0.909911	−	0.414803i	$-0.136150\pi$
$479$	19078.0			1.81982			0.909911	+	0.414803i	$0.136150\pi$
$480$		0			0
$481$	14564.4			1.38062
$482$		−	734.868i		−	0.0694447i
$483$		0			0
$484$	−4504.55			−0.423042
$485$	2526.17	+	404.764i	0.236511	+	0.0378956i
$486$		0			0
$487$		−	15616.4i		−	1.45307i	−0.687128	−	0.726537i	$-0.741129\pi$
$487$		−	15616.4i		−	1.45307i	0.687128	−	0.726537i	$-0.258871\pi$
$488$			4998.90i			0.463708i
$489$		0			0
$490$	−231.693	−	37.1238i	−0.0213609	−	0.00342262i
$491$	−7547.46			−0.693711			−0.346856	−	0.937919i	$-0.612751\pi$
$491$	−7547.46			−0.693711			−0.346856	+	0.937919i	$0.612751\pi$
$492$		0			0
$493$		−	0.397392i		−	3.63035e-5i
$494$	−1814.49			−0.165259
$495$		0			0
$496$	12032.5			1.08927
$497$		−	7787.70i		−	0.702870i
$498$		0			0
$499$	−3288.10			−0.294982			−0.147491	−	0.989063i	$-0.547120\pi$
$499$	−3288.10			−0.294982			−0.147491	+	0.989063i	$0.547120\pi$
$500$	−5011.80	+	9706.42i	−0.448269	+	0.868169i
$501$		0			0
$502$			1055.58i			0.0938506i
$503$			1044.67i			0.0926032i	0.998928	+	0.0463016i	$0.0147435\pi$
$503$			1044.67i			0.0926032i	−0.998928	+	0.0463016i	$0.985256\pi$
$504$		0			0
$505$	1044.90	−	6521.36i	0.0920745	−	0.574647i
$506$	1312.74			0.115333
$507$		0			0
$508$		−	12838.1i		−	1.12126i
$509$	−8783.91			−0.764912			−0.382456	−	0.923974i	$-0.624922\pi$
$509$	−8783.91			−0.764912			−0.382456	+	0.923974i	$0.624922\pi$
$510$		0			0
$511$	1833.97			0.158767
$512$			7986.54i			0.689372i
$513$		0			0
$514$	−802.666			−0.0688796
$515$	16239.8	+	2602.07i	1.38953	+	0.222642i
$516$		0			0
$517$			9642.54i			0.820268i
$518$			938.025i			0.0795646i
$519$		0			0
$520$	−557.841	+	3481.54i	−0.0470441	+	0.293607i
$521$	−9983.79			−0.839535			−0.419767	−	0.907632i	$-0.637888\pi$
$521$	−9983.79			−0.839535			−0.419767	+	0.907632i	$0.637888\pi$
$522$		0			0
$523$			8177.52i			0.683706i	0.939754	+	0.341853i	$0.111054\pi$
$523$			8177.52i			0.683706i	−0.939754	+	0.341853i	$0.888946\pi$
$524$	−18539.6			−1.54563
$525$		0			0
$526$	−884.215			−0.0732958
$527$		−	1050.38i		−	0.0868221i
$528$		0			0
$529$	−279.364			−0.0229608
$530$	−148.692	+	928.003i	−0.0121864	+	0.0760564i
$531$		0			0
$532$			4979.18i			0.405780i
$533$		−	4768.45i		−	0.387513i
$534$		0			0
$535$	−13504.6	−	2163.81i	−1.09131	−	0.174859i
$536$	−2472.85			−0.199274
$537$		0			0
$538$			2419.94i			0.193924i
$539$	−1346.13			−0.107573
$540$		0			0
$541$	−3425.16			−0.272198			−0.136099	−	0.990695i	$-0.543457\pi$
$541$	−3425.16			−0.272198			−0.136099	+	0.990695i	$0.543457\pi$
$542$		−	1325.61i		−	0.105055i
$543$		0			0
$544$	415.068			0.0327131
$545$	−2265.24	+	14137.6i	−0.178041	+	1.11117i
$546$		0			0
$547$		−	5955.72i		−	0.465536i	−0.972532	−	0.232768i	$-0.925222\pi$
$547$		−	5955.72i		−	0.465536i	0.972532	−	0.232768i	$-0.0747783\pi$
$548$			5962.68i			0.464805i
$549$		0			0
$550$	459.545	−	1397.22i	0.0356274	−	0.108323i
$551$	6.94712			0.000537127
$552$		0			0
$553$		−	1916.80i		−	0.147397i
$554$	3838.99			0.294410
$555$		0			0
$556$	−15835.1			−1.20784
$557$			2506.35i			0.190660i	0.995446	+	0.0953298i	$0.0303906\pi$
$557$			2506.35i			0.190660i	−0.995446	+	0.0953298i	$0.969609\pi$
$558$		0			0
$559$	11977.0			0.906215
$560$	4608.06	+	738.341i	0.347725	+	0.0557153i
$561$		0			0
$562$			2509.50i			0.188357i
$563$			3460.79i			0.259068i	0.991575	+	0.129534i	$0.0413481\pi$
$563$			3460.79i			0.259068i	−0.991575	+	0.129534i	$0.958652\pi$
$564$		0			0
$565$	19930.6	+	3193.43i	1.48404	+	0.237786i
$566$	2492.59			0.185108
$567$		0			0
$568$		−	7536.86i		−	0.556760i
$569$	22561.2			1.66224			0.831119	−	0.556095i	$-0.187701\pi$
$569$	22561.2			1.66224			0.831119	+	0.556095i	$0.187701\pi$
$570$		0			0
$571$	−992.585			−0.0727467			−0.0363734	−	0.999338i	$-0.511581\pi$
$571$	−992.585			−0.0727467			−0.0363734	+	0.999338i	$0.511581\pi$
$572$			9996.52i			0.730726i
$573$		0			0
$574$	307.114			0.0223322
$575$	−4357.03	+	13247.3i	−0.316001	+	0.960783i
$576$		0			0
$577$			9202.70i			0.663975i	0.943284	+	0.331987i	$0.107719\pi$
$577$			9202.70i			0.663975i	−0.943284	+	0.331987i	$0.892281\pi$
$578$			2092.72i			0.150598i
$579$		0			0
$580$	1.05551	−	6.58756i	7.55651e−5	−	0.000471610i
$581$	609.947			0.0435540
$582$		0			0
$583$			5391.67i			0.383019i
$584$	1774.89			0.125763
$585$		0			0
$586$	−2432.33			−0.171465
$587$		−	27046.3i		−	1.90174i	−0.309593	−	0.950869i	$-0.600193\pi$
$587$		−	27046.3i		−	1.90174i	0.309593	−	0.950869i	$-0.399807\pi$
$588$		0			0
$589$	18362.5			1.28457
$590$	4166.04	+	667.516i	0.290700	+	0.0465783i
$591$		0			0
$592$		−	18656.0i		−	1.29520i
$593$		−	26364.0i		−	1.82570i	−0.408298	−	0.912849i	$-0.633877\pi$
$593$		−	26364.0i		−	1.82570i	0.408298	−	0.912849i	$-0.366123\pi$
$594$		0			0
$595$	64.4534	−	402.261i	0.00444090	−	0.0277161i
$596$	−84.3428			−0.00579667
$597$		0			0
$598$			2224.49i			0.152117i
$599$	6624.09			0.451841			0.225921	−	0.974146i	$-0.427461\pi$
$599$	6624.09			0.451841			0.225921	+	0.974146i	$0.427461\pi$
$600$		0			0
$601$	−3984.03			−0.270403			−0.135201	−	0.990818i	$-0.543168\pi$
$601$	−3984.03			−0.270403			−0.135201	+	0.990818i	$0.543168\pi$
$602$			771.386i			0.0522248i
$603$		0			0
$604$	−18794.7			−1.26613
$605$	−1019.36	+	6361.91i	−0.0685003	+	0.427518i
$606$		0			0
$607$		−	8605.79i		−	0.575450i	−0.957713	−	0.287725i	$-0.907101\pi$
$607$		−	8605.79i		−	0.575450i	0.957713	−	0.287725i	$-0.0928990\pi$
$608$			7256.14i			0.484005i
$609$		0			0
$610$	3489.10	+	559.052i	0.231589	+	0.0371071i
$611$	−16339.6			−1.08188
$612$		0			0
$613$			22070.4i			1.45418i	0.686541	+	0.727091i	$0.259128\pi$
$613$			22070.4i			1.45418i	−0.686541	+	0.727091i	$0.740872\pi$
$614$	−3933.91			−0.258566
$615$		0			0
$616$	−1302.77			−0.0852114
$617$		−	17328.8i		−	1.13068i	−0.824858	−	0.565340i	$-0.808745\pi$
$617$		−	17328.8i		−	1.13068i	0.824858	−	0.565340i	$-0.191255\pi$
$618$		0			0
$619$	−1240.99			−0.0805808			−0.0402904	−	0.999188i	$-0.512828\pi$
$619$	−1240.99			−0.0805808			−0.0402904	+	0.999188i	$0.512828\pi$
$620$	2789.91	−	17412.2i	0.180719	−	1.12789i
$621$		0			0
$622$		−	1888.98i		−	0.121771i
$623$		−	7636.94i		−	0.491119i
$624$		0			0
$625$	12574.5	+	9274.82i	0.804769	+	0.593588i
$626$	−1886.86			−0.120470
$627$		0			0
$628$		−	3100.23i		−	0.196995i
$629$	−1628.58			−0.103236
$630$		0			0
$631$	10004.0			0.631143			0.315572	−	0.948902i	$-0.397804\pi$
$631$	10004.0			0.631143			0.315572	+	0.948902i	$0.397804\pi$
$632$		−	1855.06i		−	0.116757i
$633$		0			0
$634$	−3206.76			−0.200878
$635$	−18131.6	−	2905.19i	−1.13312	−	0.181557i
$636$		0			0
$637$		−	2281.07i		−	0.141883i
$638$			0.898294i			5.57426e-5i
$639$		0			0
$640$	9136.27	+	1463.89i	0.564286	+	0.0904144i
$641$	23107.3			1.42384			0.711921	−	0.702260i	$-0.247826\pi$
$641$	23107.3			1.42384			0.711921	+	0.702260i	$0.247826\pi$
$642$		0			0
$643$		−	11629.9i		−	0.713281i	−0.934242	−	0.356641i	$-0.883922\pi$
$643$		−	11629.9i		−	0.713281i	0.934242	−	0.356641i	$-0.116078\pi$
$644$	6104.27			0.373513
$645$		0			0
$646$	202.895			0.0123573
$647$		−	6371.50i		−	0.387156i	−0.981085	−	0.193578i	$-0.937991\pi$
$647$		−	6371.50i		−	0.387156i	0.981085	−	0.193578i	$-0.0620092\pi$
$648$		0			0
$649$	24204.6			1.46396
$650$	2367.64	+	778.716i	0.142871	+	0.0469904i
$651$		0			0
$652$			21508.7i			1.29194i
$653$		−	20264.5i		−	1.21441i	−0.794544	−	0.607207i	$-0.792290\pi$
$653$		−	20264.5i		−	1.21441i	0.794544	−	0.607207i	$-0.207710\pi$
$654$		0			0
$655$	−4195.42	+	26184.1i	−0.250273	+	1.56198i
$656$	−6108.08			−0.363537
$657$		0			0
$658$		−	1052.36i		−	0.0623485i
$659$	−7132.74			−0.421627			−0.210813	−	0.977526i	$-0.567611\pi$
$659$	−7132.74			−0.421627			−0.210813	+	0.977526i	$0.567611\pi$
$660$		0			0
$661$	10555.8			0.621140			0.310570	−	0.950550i	$-0.399480\pi$
$661$	10555.8			0.621140			0.310570	+	0.950550i	$0.399480\pi$
$662$			3795.14i			0.222813i
$663$		0			0
$664$	590.300			0.0345001
$665$	7032.24	+	1126.76i	0.410073	+	0.0657052i
$666$		0			0
$667$		−	8.51689i		−	0.000494416i
$668$		−	16254.0i		−	0.941445i
$669$		0			0
$670$	−276.550	+	1725.98i	−0.0159464	+	0.0995231i
$671$	20271.6			1.16628
$672$		0			0
$673$		−	3828.08i		−	0.219259i	−0.993973	−	0.109630i	$-0.965034\pi$
$673$		−	3828.08i		−	0.219259i	0.993973	−	0.109630i	$-0.0349665\pi$
$674$	3744.37			0.213988
$675$		0			0
$676$	233.485			0.0132843
$677$			24660.6i			1.39998i	0.714154	+	0.699989i	$0.246812\pi$
$677$			24660.6i			1.39998i	−0.714154	+	0.699989i	$0.753188\pi$
$678$		0			0
$679$	−1601.81			−0.0905328
$680$	62.3773	−	389.304i	0.00351774	−	0.0219546i
$681$		0			0
$682$			2374.36i			0.133312i
$683$		−	18562.2i		−	1.03992i	−0.854192	−	0.519958i	$-0.825948\pi$
$683$		−	18562.2i		−	1.03992i	0.854192	−	0.519958i	$-0.174052\pi$
$684$		0			0
$685$	8421.26	+	1349.32i	0.469723	+	0.0752627i
$686$	146.913			0.00817665
$687$		0			0
$688$		−	15341.8i		−	0.850146i
$689$	−9136.38			−0.505179
$690$		0			0
$691$	27335.9			1.50493			0.752465	−	0.658632i	$-0.228865\pi$
$691$	27335.9			1.50493			0.752465	+	0.658632i	$0.228865\pi$
$692$			15082.7i			0.828554i
$693$		0			0
$694$	−3120.66			−0.170689
$695$	−3583.39	+	22364.3i	−0.195577	+	1.22062i
$696$		0			0
$697$			533.205i			0.0289764i
$698$		−	5401.50i		−	0.292908i
$699$		0			0
$700$	2136.89	−	6497.09i	0.115381	−	0.350810i
$701$	30924.1			1.66617			0.833087	−	0.553142i	$-0.186571\pi$
$701$	30924.1			1.66617			0.833087	+	0.553142i	$0.186571\pi$
$702$		0			0
$703$		−	28470.4i		−	1.52743i
$704$	12167.2			0.651375
$705$		0			0
$706$	515.093			0.0274586
$707$			4135.09i			0.219966i
$708$		0			0
$709$	28329.0			1.50059			0.750295	−	0.661103i	$-0.229912\pi$
$709$	28329.0			1.50059			0.750295	+	0.661103i	$0.229912\pi$
$710$	−5260.53	−	842.883i	−0.278062	−	0.0445533i
$711$		0			0
$712$		−	7390.95i		−	0.389027i
$713$		−	22511.7i		−	1.18243i
$714$		0			0
$715$	14118.4	+	2262.16i	0.738458	+	0.118322i
$716$	12804.6			0.668341
$717$		0			0
$718$			1377.62i			0.0716051i
$719$	−12563.4			−0.651651			−0.325825	−	0.945430i	$-0.605642\pi$
$719$	−12563.4			−0.651651			−0.325825	+	0.945430i	$0.605642\pi$
$720$		0			0
$721$	−10297.4			−0.531893
$722$			609.127i			0.0313980i
$723$		0			0
$724$	−286.558			−0.0147097
$725$	−9.06495	−	2.98146i	−0.000464364	−	0.000152729i
$726$		0			0
$727$		−	13523.2i		−	0.689888i	−0.938623	−	0.344944i	$-0.887898\pi$
$727$		−	13523.2i		−	0.689888i	0.938623	−	0.344944i	$-0.112102\pi$
$728$		−	2207.59i		−	0.112389i
$729$		0			0
$730$	198.495	−	1238.83i	0.0100639	−	0.0628097i
$731$	−1339.26			−0.0677625
$732$		0			0
$733$		−	21325.0i		−	1.07457i	−0.843402	−	0.537284i	$-0.819450\pi$
$733$		−	21325.0i		−	1.07457i	0.843402	−	0.537284i	$-0.180550\pi$
$734$	539.534			0.0271316
$735$		0			0
$736$	8895.74			0.445518
$737$			10027.9i			0.501197i
$738$		0			0
$739$	7403.75			0.368540			0.184270	−	0.982876i	$-0.441008\pi$
$739$	7403.75			0.368540			0.184270	+	0.982876i	$0.441008\pi$
$740$	−26996.9	−	4325.67i	−1.34112	−	0.214885i
$741$		0			0
$742$		−	588.433i		−	0.0291133i
$743$			27131.6i			1.33965i	0.742519	+	0.669825i	$0.233631\pi$
$743$			27131.6i			1.33965i	−0.742519	+	0.669825i	$0.766369\pi$
$744$		0			0
$745$	−19.0863	+	119.120i	−0.000938616	+	0.00585800i
$746$	−165.430			−0.00811904
$747$		0			0
$748$		−	1117.80i		−	0.0546403i
$749$	8563.04			0.417739
$750$		0			0
$751$	−29393.3			−1.42820			−0.714098	−	0.700046i	$-0.753163\pi$
$751$	−29393.3			−1.42820			−0.714098	+	0.700046i	$0.753163\pi$
$752$			20930.0i			1.01495i
$753$		0			0
$754$	−1.52219			−7.35211e−5
$755$	−4253.14	+	26544.3i	−0.205017	+	1.27953i
$756$		0			0
$757$			37648.5i			1.80761i	0.427946	+	0.903804i	$0.359237\pi$
$757$			37648.5i			1.80761i	−0.427946	+	0.903804i	$0.640763\pi$
$758$		−	6101.84i		−	0.292386i
$759$		0			0
$760$	6805.72	+	1090.47i	0.324828	+	0.0520466i
$761$	35633.2			1.69738			0.848688	−	0.528894i	$-0.177393\pi$
$761$	35633.2			1.69738			0.848688	+	0.528894i	$0.177393\pi$
$762$		0			0
$763$		−	8964.46i		−	0.425341i
$764$	−8245.05			−0.390439
$765$		0			0
$766$	−3982.87			−0.187868
$767$			41015.5i			1.93088i
$768$		0			0
$769$	3571.28			0.167469			0.0837345	−	0.996488i	$-0.473315\pi$
$769$	3571.28			0.167469			0.0837345	+	0.996488i	$0.473315\pi$
$770$	−145.695	+	909.301i	−0.00681883	+	0.0425570i
$771$		0			0
$772$		−	1670.09i		−	0.0778599i
$773$			16250.3i			0.756122i	0.925781	+	0.378061i	$0.123409\pi$
$773$			16250.3i			0.756122i	−0.925781	+	0.378061i	$0.876591\pi$
$774$		0			0
$775$	−23960.3	−	7880.55i	−1.11056	−	0.365262i
$776$	−1550.21			−0.0717131
$777$		0			0
$778$		−	447.081i		−	0.0206024i
$779$	−9321.37			−0.428720
$780$		0			0
$781$	−30563.5			−1.40032
$782$		−	248.741i		−	0.0113746i
$783$		0			0
$784$	−2921.90			−0.133104
$785$	−4378.54	−	701.565i	−0.199079	−	0.0318980i
$786$		0			0
$787$			13156.5i			0.595906i	0.954581	+	0.297953i	$0.0963038\pi$
$787$			13156.5i			0.595906i	−0.954581	+	0.297953i	$0.903696\pi$
$788$		−	30903.6i		−	1.39708i
$789$		0			0
$790$	−1294.78	−	207.461i	−0.0583118	−	0.00934319i
$791$	−12637.7			−0.568071
$792$		0			0
$793$			34350.9i			1.53826i
$794$	−1919.74			−0.0858049
$795$		0			0
$796$	−7262.88			−0.323399
$797$		−	13868.8i		−	0.616385i	−0.951324	−	0.308192i	$-0.900276\pi$
$797$		−	13868.8i		−	0.616385i	0.951324	−	0.308192i	$-0.0997240\pi$
$798$		0			0
$799$	1827.09			0.0808982
$800$	3114.08	−	9468.18i	0.137624	−	0.418438i
$801$		0			0
$802$		−	5433.72i		−	0.239241i
$803$		−	7197.55i		−	0.316309i
$804$		0			0
$805$	1381.36	−	8621.24i	0.0604804	−	0.377464i
$806$	−4023.43			−0.175831
$807$		0			0
$808$			4001.90i			0.174240i
$809$	−7042.67			−0.306066			−0.153033	−	0.988221i	$-0.548904\pi$
$809$	−7042.67			−0.306066			−0.153033	+	0.988221i	$0.548904\pi$
$810$		0			0
$811$	−8985.64			−0.389061			−0.194531	−	0.980896i	$-0.562318\pi$
$811$	−8985.64			−0.389061			−0.194531	+	0.980896i	$0.562318\pi$
$812$			4.17708i			0.000180525i
$813$		0			0
$814$	3681.36			0.158515
$815$	30377.3	+	4867.30i	1.30561	+	0.209195i
$816$		0			0
$817$		−	23412.7i		−	1.00258i
$818$			2928.22i			0.125162i
$819$		0			0
$820$	−1416.25	+	8838.94i	−0.0603140	+	0.376426i
$821$	1293.90			0.0550031			0.0275016	−	0.999622i	$-0.491245\pi$
$821$	1293.90			0.0550031			0.0275016	+	0.999622i	$0.491245\pi$
$822$		0			0
$823$		−	28480.7i		−	1.20629i	−0.797632	−	0.603144i	$-0.793914\pi$
$823$		−	28480.7i		−	1.20629i	0.797632	−	0.603144i	$-0.206086\pi$
$824$	−9965.71			−0.421325
$825$		0			0
$826$	−2641.62			−0.111276
$827$			8825.09i			0.371074i	0.982637	+	0.185537i	$0.0594025\pi$
$827$			8825.09i			0.371074i	−0.982637	+	0.185537i	$0.940597\pi$
$828$		0			0
$829$	6673.08			0.279572			0.139786	−	0.990182i	$-0.455358\pi$
$829$	6673.08			0.279572			0.139786	+	0.990182i	$0.455358\pi$
$830$	66.0161	−	412.014i	0.00276079	−	0.0172304i
$831$		0			0
$832$			20617.7i			0.859124i
$833$			255.068i			0.0106093i
$834$		0			0
$835$	−22956.0	−	3678.19i	−0.951406	−	0.152442i
$836$	19541.2			0.808429
$837$		0			0
$838$		−	2180.85i		−	0.0898999i
$839$	−7026.24			−0.289121			−0.144561	−	0.989496i	$-0.546177\pi$
$839$	−7026.24			−0.289121			−0.144561	+	0.989496i	$0.546177\pi$
$840$		0			0
$841$	−24389.0			−1.00000
$842$			3586.52i			0.146793i
$843$		0			0
$844$	−7244.42			−0.295454
$845$	52.8364	−	329.758i	0.00215104	−	0.0134249i
$846$		0			0
$847$		−	4033.99i		−	0.163648i
$848$			11703.1i			0.473923i
$849$		0			0
$850$	−264.748	−	87.0754i	−0.0106833	−	0.00351372i
$851$	−34903.6			−1.40597
$852$		0			0
$853$		−	7181.30i		−	0.288257i	−0.989559	−	0.144128i	$-0.953962\pi$
$853$		−	7181.30i		−	0.288257i	0.989559	−	0.144128i	$-0.0460378\pi$
$854$	−2212.39			−0.0886491
$855$		0			0
$856$	8287.21			0.330901
$857$		−	23061.9i		−	0.919228i	−0.888119	−	0.459614i	$-0.847988\pi$
$857$		−	23061.9i		−	0.919228i	0.888119	−	0.459614i	$-0.152012\pi$
$858$		0			0
$859$	−32264.0			−1.28153			−0.640764	−	0.767738i	$-0.721382\pi$
$859$	−32264.0			−1.28153			−0.640764	+	0.767738i	$0.721382\pi$
$860$	−22201.0	−	3557.21i	−0.880286	−	0.141047i
$861$		0			0
$862$		−	2581.80i		−	0.102014i
$863$			2831.11i			0.111671i	0.998440	+	0.0558354i	$0.0177822\pi$
$863$			2831.11i			0.111671i	−0.998440	+	0.0558354i	$0.982218\pi$
$864$		0			0
$865$	21301.8	+	3413.14i	0.837320	+	0.134162i
$866$	5108.79			0.200466
$867$		0			0
$868$			11040.8i			0.431738i
$869$	−7522.66			−0.293658
$870$		0			0
$871$	−16992.6			−0.661048
$872$		−	8675.71i		−	0.336923i
$873$		0			0
$874$	4348.44			0.168293
$875$	−8692.45	−	4488.25i	−0.335838	−	0.173406i
$876$		0			0
$877$		−	17952.1i		−	0.691218i	−0.938379	−	0.345609i	$-0.887672\pi$
$877$		−	17952.1i		−	0.691218i	0.938379	−	0.345609i	$-0.112328\pi$
$878$		−	3390.12i		−	0.130309i
$879$		0			0
$880$	2897.68	−	18084.7i	0.111001	−	0.692768i
$881$	−25983.2			−0.993641			−0.496821	−	0.867853i	$-0.665499\pi$
$881$	−25983.2			−0.993641			−0.496821	+	0.867853i	$0.665499\pi$
$882$		0			0
$883$			10296.7i			0.392424i	0.980562	+	0.196212i	$0.0628641\pi$
$883$			10296.7i			0.392424i	−0.980562	+	0.196212i	$0.937136\pi$
$884$	1894.16			0.0720672
$885$		0			0
$886$	1080.52			0.0409717
$887$		−	14925.6i		−	0.564996i	−0.959268	−	0.282498i	$-0.908837\pi$
$887$		−	14925.6i		−	0.564996i	0.959268	−	0.282498i	$-0.0911631\pi$
$888$		0			0
$889$	11497.0			0.433741
$890$	−5158.68	−	826.566i	−0.194292	−	0.0311309i
$891$		0			0
$892$			41832.0i			1.57022i
$893$			31940.7i			1.19693i
$894$		0			0
$895$	2897.62	−	18084.4i	0.108220	−	0.675412i
$896$	−5793.17			−0.216000
$897$		0			0
$898$		−	2287.17i		−	0.0849933i
$899$	15.4045			0.000571488
$900$		0			0
$901$	1021.62			0.0377749
$902$		−	1205.30i		−	0.0444922i
$903$		0			0
$904$	−12230.6			−0.449982
$905$	−64.8465	+	404.714i	−0.00238185	+	0.0148654i
$906$		0			0
$907$			24744.9i			0.905889i	0.891539	+	0.452944i	$0.149626\pi$
$907$			24744.9i			0.905889i	−0.891539	+	0.452944i	$0.850374\pi$
$908$		−	47028.0i		−	1.71881i
$909$		0			0
$910$	−1540.84	−	246.886i	−0.0561301	−	0.00899362i
$911$	−4378.72			−0.159246			−0.0796232	−	0.996825i	$-0.525372\pi$
$911$	−4378.72			−0.159246			−0.0796232	+	0.996825i	$0.525372\pi$
$912$		0			0
$913$		−	2393.79i		−	0.0867720i
$914$	5896.15			0.213378
$915$		0			0
$916$	−9464.58			−0.341396
$917$		−	16602.9i		−	0.597903i
$918$		0			0
$919$	−26026.1			−0.934192			−0.467096	−	0.884207i	$-0.654700\pi$
$919$	−26026.1			−0.934192			−0.467096	+	0.884207i	$0.654700\pi$
$920$	1336.87	−	8343.54i	0.0479079	−	0.298998i
$921$		0			0
$922$			5354.45i			0.191257i
$923$		−	51790.9i		−	1.84693i
$924$		0			0
$925$	−12218.5	+	37149.7i	−0.434316	+	1.32051i
$926$	1527.52			0.0542090
$927$		0			0
$928$			6.08724i			0.000215327i
$929$	4240.78			0.149769			0.0748846	−	0.997192i	$-0.476141\pi$
$929$	4240.78			0.149769			0.0748846	+	0.997192i	$0.476141\pi$
$930$		0			0
$931$	−4459.04			−0.156970
$932$			27493.2i			0.966278i
$933$		0			0
$934$	−1746.76			−0.0611944
$935$	−1578.71	−	252.953i	−0.0552184	−	0.00884753i
$936$		0			0
$937$		−	664.833i		−	0.0231794i	−0.999933	−	0.0115897i	$-0.996311\pi$
$937$		−	664.833i		−	0.0231794i	0.999933	−	0.0115897i	$-0.00368921\pi$
$938$		−	1094.42i		−	0.0380960i
$939$		0			0
$940$	30287.6	+	4852.92i	1.05093	+	0.168388i
$941$	−9520.60			−0.329822			−0.164911	−	0.986308i	$-0.552734\pi$
$941$	−9520.60			−0.329822			−0.164911	+	0.986308i	$0.552734\pi$
$942$		0			0
$943$			11427.6i			0.394629i
$944$	52538.2			1.81141
$945$		0			0
$946$	3027.37			0.104047
$947$		−	17066.3i		−	0.585618i	−0.956171	−	0.292809i	$-0.905410\pi$
$947$		−	17066.3i		−	0.585618i	0.956171	−	0.292809i	$-0.0945900\pi$
$948$		0			0
$949$	12196.5			0.417192
$950$	1522.23	−	4628.26i	0.0519872	−	0.158064i
$951$		0			0
$952$			246.852i			0.00840389i
$953$			6991.85i			0.237658i	0.992915	+	0.118829i	$0.0379140\pi$
$953$			6991.85i			0.237658i	−0.992915	+	0.118829i	$0.962086\pi$
$954$		0			0
$955$	−1865.81	+	11644.7i	−0.0632212	+	0.394570i
$956$	−52495.0			−1.77595
$957$		0			0
$958$			8171.46i			0.275582i
$959$	−5339.80			−0.179803
$960$		0			0
$961$	10925.9			0.366751
$962$			6238.20i			0.209072i
$963$		0			0
$964$	−13410.9			−0.448065
$965$	−2358.72	−	377.932i	−0.0786837	−	0.0126073i
$966$		0			0
$967$			18731.2i			0.622911i	0.950261	+	0.311455i	$0.100816\pi$
$967$			18731.2i			0.622911i	−0.950261	+	0.311455i	$0.899184\pi$
$968$		−	3904.05i		−	0.129629i
$969$		0			0
$970$	−173.368	+	1082.01i	−0.00573867	+	0.0358156i
$971$	45780.2			1.51303			0.756517	−	0.653974i	$-0.226900\pi$
$971$	45780.2			1.51303			0.756517	+	0.653974i	$0.226900\pi$
$972$		0			0
$973$		−	14180.9i		−	0.467234i
$974$	6688.80			0.220044
$975$		0			0
$976$	44001.3			1.44308
$977$			20137.9i			0.659436i	0.944080	+	0.329718i	$0.106954\pi$
$977$			20137.9i			0.659436i	−0.944080	+	0.329718i	$0.893046\pi$
$978$		0			0
$979$	−29971.8			−0.978451
$980$	−677.485	+	4228.26i	−0.0220831	+	0.137823i
$981$		0			0
$982$		−	3232.72i		−	0.105051i
$983$		−	6220.73i		−	0.201842i	−0.994894	−	0.100921i	$-0.967821\pi$
$983$		−	6220.73i		−	0.201842i	0.994894	−	0.100921i	$-0.0321789\pi$
$984$		0			0
$985$	−43646.1	−	6993.33i	−1.41186	−	0.226219i
$986$	0.170210			5.49757e−6
$987$		0			0
$988$			33113.3i			1.06627i
$989$	−28703.0			−0.922855
$990$		0			0
$991$	−10296.5			−0.330049			−0.165025	−	0.986289i	$-0.552770\pi$
$991$	−10296.5			−0.330049			−0.165025	+	0.986289i	$0.552770\pi$
$992$			16089.7i			0.514968i
$993$		0			0
$994$	3335.62			0.106438
$995$	−1643.55	+	10257.6i	−0.0523659	+	0.326821i
$996$		0			0
$997$		−	27392.6i		−	0.870144i	−0.900396	−	0.435072i	$-0.856723\pi$
$997$		−	27392.6i		−	0.870144i	0.900396	−	0.435072i	$-0.143277\pi$
$998$		−	1408.36i		−	0.0446701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.b.64.6		10
3.2	odd	2		105.4.d.b.64.5	✓	10
5.2	odd	4		1575.4.a.bp.1.3		5
5.3	odd	4		1575.4.a.bo.1.3		5
5.4	even	2	inner	315.4.d.b.64.5		10
15.2	even	4		525.4.a.w.1.3		5
15.8	even	4		525.4.a.x.1.3		5
15.14	odd	2		105.4.d.b.64.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.5	✓	10	3.2	odd	2
105.4.d.b.64.6	yes	10	15.14	odd	2
315.4.d.b.64.5		10	5.4	even	2	inner
315.4.d.b.64.6		10	1.1	even	1	trivial
525.4.a.w.1.3		5	15.2	even	4
525.4.a.x.1.3		5	15.8	even	4
1575.4.a.bo.1.3		5	5.3	odd	4
1575.4.a.bp.1.3		5	5.2	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)

\(f(q)\)	\(=\)	\(q+0.428319i q^{2} +7.81654 q^{4} +(1.76884 - 11.0395i) q^{5} +7.00000i q^{7} +6.77452i q^{8} +O(q^{10})\)	\(q+0.428319i q^{2} +7.81654 q^{4} +(1.76884 - 11.0395i) q^{5} +7.00000i q^{7} +6.77452i q^{8} +(4.72844 + 0.757628i) q^{10} +27.4721 q^{11} +46.5524i q^{13} -2.99823 q^{14} +59.6307 q^{16} -5.20546i q^{17} +91.0007 q^{19} +(13.8262 - 86.2910i) q^{20} +11.7668i q^{22} -111.563i q^{23} +(-118.742 - 39.0544i) q^{25} -19.9393 q^{26} +54.7158i q^{28} +0.0763413 q^{29} +201.784 q^{31} +79.7371i q^{32} +2.22960 q^{34} +(77.2767 + 12.3819i) q^{35} -312.859i q^{37} +38.9773i q^{38} +(74.7876 + 11.9831i) q^{40} -102.432 q^{41} -257.280i q^{43} +214.737 q^{44} +47.7847 q^{46} +350.994i q^{47} -49.0000 q^{49} +(16.7277 - 50.8596i) q^{50} +363.879i q^{52} +196.260i q^{53} +(48.5938 - 303.279i) q^{55} -47.4217 q^{56} +0.0326984i q^{58} +881.060 q^{59} +737.897 q^{61} +86.4280i q^{62} +442.893 q^{64} +(513.917 + 82.3439i) q^{65} +365.021i q^{67} -40.6887i q^{68} +(-5.30340 + 33.0991i) q^{70} -1112.53 q^{71} -261.995i q^{73} +134.004 q^{74} +711.311 q^{76} +192.305i q^{77} -273.829 q^{79} +(105.477 - 658.295i) q^{80} -43.8735i q^{82} -87.1353i q^{83} +(-57.4658 - 9.20763i) q^{85} +110.198 q^{86} +186.110i q^{88} -1090.99 q^{89} -325.867 q^{91} -872.039i q^{92} -150.337 q^{94} +(160.966 - 1004.61i) q^{95} +228.830i q^{97} -20.9876i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) \) 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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