LMFDB - Embedded newform 630.2.g.g.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(379,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("630.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.g (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.2.g.g.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.22474 - 0.224745i) q^{5} +1.00000i q^{7} +1.00000i q^{8} +(-0.224745 + 2.22474i) q^{10} +4.89898 q^{11} +4.44949i q^{13} +1.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} -1.55051 q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} -2.89898i q^{23} +(4.89898 + 1.00000i) q^{25} +4.44949 q^{26} -1.00000i q^{28} +6.89898 q^{29} +8.89898 q^{31} -1.00000i q^{32} +2.00000 q^{34} +(0.224745 - 2.22474i) q^{35} -2.00000i q^{37} +1.55051i q^{38} +(0.224745 - 2.22474i) q^{40} +1.10102 q^{41} -0.898979i q^{43} -4.89898 q^{44} -2.89898 q^{46} +8.89898i q^{47} -1.00000 q^{49} +(1.00000 - 4.89898i) q^{50} -4.44949i q^{52} +10.8990i q^{53} +(-10.8990 - 1.10102i) q^{55} -1.00000 q^{56} -6.89898i q^{58} -1.55051 q^{59} +3.55051 q^{61} -8.89898i q^{62} -1.00000 q^{64} +(1.00000 - 9.89898i) q^{65} +8.00000i q^{67} -2.00000i q^{68} +(-2.22474 - 0.224745i) q^{70} +1.10102 q^{71} +2.89898i q^{73} -2.00000 q^{74} +1.55051 q^{76} +4.89898i q^{77} -6.89898 q^{79} +(-2.22474 - 0.224745i) q^{80} -1.10102i q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} -0.898979 q^{86} +4.89898i q^{88} -10.0000 q^{89} -4.44949 q^{91} +2.89898i q^{92} +8.89898 q^{94} +(3.44949 + 0.348469i) q^{95} -15.7980i q^{97} +1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5} + 4 q^{10} + 4 q^{14} + 4 q^{16} - 16 q^{19} + 4 q^{20} + 8 q^{26} + 8 q^{29} + 16 q^{31} + 8 q^{34} - 4 q^{35} - 4 q^{40} + 24 q^{41} + 8 q^{46} - 4 q^{49} + 4 q^{50} - 24 q^{55}+ \cdots + 4 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 + 4 * q^10 + 4 * q^14 + 4 * q^16 - 16 * q^19 + 4 * q^20 + 8 * q^26 + 8 * q^29 + 16 * q^31 + 8 * q^34 - 4 * q^35 - 4 * q^40 + 24 * q^41 + 8 * q^46 - 4 * q^49 + 4 * q^50 - 24 * q^55 - 4 * q^56 - 16 * q^59 + 24 * q^61 - 4 * q^64 + 4 * q^65 - 4 * q^70 + 24 * q^71 - 8 * q^74 + 16 * q^76 - 8 * q^79 - 4 * q^80 - 8 * q^85 + 16 * q^86 - 40 * q^89 - 8 * q^91 + 16 * q^94 + 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.22474	−	0.224745i	−0.994936	−	0.100509i
$5$	−2.22474	−	0.224745i	−0.994936	−	0.100509i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.224745	+	2.22474i	−0.0710706	+	0.703526i
$11$	4.89898			1.47710			0.738549	−	0.674200i	$-0.235511\pi$
$11$	4.89898			1.47710			0.738549	+	0.674200i	$0.235511\pi$
$12$		0			0
$13$			4.44949i			1.23407i	0.786937	+	0.617033i	$0.211666\pi$
$13$			4.44949i			1.23407i	−0.786937	+	0.617033i	$0.788334\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	−1.55051			−0.355711			−0.177856	−	0.984057i	$-0.556916\pi$
$19$	−1.55051			−0.355711			−0.177856	+	0.984057i	$0.556916\pi$
$20$	2.22474	+	0.224745i	0.497468	+	0.0502545i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$		−	2.89898i		−	0.604479i	−0.953232	−	0.302240i	$-0.902266\pi$
$23$		−	2.89898i		−	0.604479i	0.953232	−	0.302240i	$-0.0977342\pi$
$24$		0			0
$25$	4.89898	+	1.00000i	0.979796	+	0.200000i
$26$	4.44949			0.872617
$27$		0			0
$28$		−	1.00000i		−	0.188982i
$29$	6.89898			1.28111			0.640554	−	0.767913i	$-0.278705\pi$
$29$	6.89898			1.28111			0.640554	+	0.767913i	$0.278705\pi$
$30$		0			0
$31$	8.89898			1.59830			0.799152	−	0.601129i	$-0.205282\pi$
$31$	8.89898			1.59830			0.799152	+	0.601129i	$0.205282\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	2.00000			0.342997
$35$	0.224745	−	2.22474i	0.0379888	−	0.376051i
$36$		0			0
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$			1.55051i			0.251526i
$39$		0			0
$40$	0.224745	−	2.22474i	0.0355353	−	0.351763i
$41$	1.10102			0.171951			0.0859753	−	0.996297i	$-0.472599\pi$
$41$	1.10102			0.171951			0.0859753	+	0.996297i	$0.472599\pi$
$42$		0			0
$43$		−	0.898979i		−	0.137093i	−0.997648	−	0.0685465i	$-0.978164\pi$
$43$		−	0.898979i		−	0.137093i	0.997648	−	0.0685465i	$-0.0218362\pi$
$44$	−4.89898			−0.738549
$45$		0			0
$46$	−2.89898			−0.427431
$47$			8.89898i			1.29805i	0.760767	+	0.649025i	$0.224823\pi$
$47$			8.89898i			1.29805i	−0.760767	+	0.649025i	$0.775177\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	1.00000	−	4.89898i	0.141421	−	0.692820i
$51$		0			0
$52$		−	4.44949i		−	0.617033i
$53$			10.8990i			1.49709i	0.663084	+	0.748545i	$0.269247\pi$
$53$			10.8990i			1.49709i	−0.663084	+	0.748545i	$0.730753\pi$
$54$		0			0
$55$	−10.8990	−	1.10102i	−1.46962	−	0.148462i
$56$	−1.00000			−0.133631
$57$		0			0
$58$		−	6.89898i		−	0.905880i
$59$	−1.55051			−0.201859			−0.100930	−	0.994894i	$-0.532182\pi$
$59$	−1.55051			−0.201859			−0.100930	+	0.994894i	$0.532182\pi$
$60$		0			0
$61$	3.55051			0.454596			0.227298	−	0.973825i	$-0.427011\pi$
$61$	3.55051			0.454596			0.227298	+	0.973825i	$0.427011\pi$
$62$		−	8.89898i		−	1.13017i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.00000	−	9.89898i	0.124035	−	1.22782i
$66$		0			0
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		−	2.00000i		−	0.242536i
$69$		0			0
$70$	−2.22474	−	0.224745i	−0.265908	−	0.0268622i
$71$	1.10102			0.130667			0.0653335	−	0.997863i	$-0.479189\pi$
$71$	1.10102			0.130667			0.0653335	+	0.997863i	$0.479189\pi$
$72$		0			0
$73$			2.89898i			0.339300i	0.985504	+	0.169650i	$0.0542637\pi$
$73$			2.89898i			0.339300i	−0.985504	+	0.169650i	$0.945736\pi$
$74$	−2.00000			−0.232495
$75$		0			0
$76$	1.55051			0.177856
$77$			4.89898i			0.558291i
$78$		0			0
$79$	−6.89898			−0.776196			−0.388098	−	0.921618i	$-0.626868\pi$
$79$	−6.89898			−0.776196			−0.388098	+	0.921618i	$0.626868\pi$
$80$	−2.22474	−	0.224745i	−0.248734	−	0.0251272i
$81$		0			0
$82$		−	1.10102i		−	0.121587i
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$		0			0
$85$	0.449490	−	4.44949i	0.0487540	−	0.482615i
$86$	−0.898979			−0.0969395
$87$		0			0
$88$			4.89898i			0.522233i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−4.44949			−0.466433
$92$			2.89898i			0.302240i
$93$		0			0
$94$	8.89898			0.917860
$95$	3.44949	+	0.348469i	0.353910	+	0.0357522i
$96$		0			0
$97$		−	15.7980i		−	1.60404i	−0.597297	−	0.802020i	$-0.703759\pi$
$97$		−	15.7980i		−	1.60404i	0.597297	−	0.802020i	$-0.296241\pi$
$98$			1.00000i			0.101015i
$99$		0			0
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$	−3.55051			−0.353289			−0.176644	−	0.984275i	$-0.556524\pi$
$101$	−3.55051			−0.353289			−0.176644	+	0.984275i	$0.556524\pi$
$102$		0			0
$103$			12.8990i			1.27097i	0.772111	+	0.635487i	$0.219201\pi$
$103$			12.8990i			1.27097i	−0.772111	+	0.635487i	$0.780799\pi$
$104$	−4.44949			−0.436308
$105$		0			0
$106$	10.8990			1.05860
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$		0			0
$109$	−6.89898			−0.660802			−0.330401	−	0.943841i	$-0.607184\pi$
$109$	−6.89898			−0.660802			−0.330401	+	0.943841i	$0.607184\pi$
$110$	−1.10102	+	10.8990i	−0.104978	+	1.03918i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$		−	19.7980i		−	1.86244i	−0.364464	−	0.931218i	$-0.618748\pi$
$113$		−	19.7980i		−	1.86244i	0.364464	−	0.931218i	$-0.381252\pi$
$114$		0			0
$115$	−0.651531	+	6.44949i	−0.0607556	+	0.601418i
$116$	−6.89898			−0.640554
$117$		0			0
$118$			1.55051i			0.142736i
$119$	−2.00000			−0.183340
$120$		0			0
$121$	13.0000			1.18182
$122$		−	3.55051i		−	0.321448i
$123$		0			0
$124$	−8.89898			−0.799152
$125$	−10.6742	−	3.32577i	−0.954733	−	0.297465i
$126$		0			0
$127$			14.8990i			1.32207i	0.750355	+	0.661035i	$0.229883\pi$
$127$			14.8990i			1.32207i	−0.750355	+	0.661035i	$0.770117\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−9.89898	−	1.00000i	−0.868198	−	0.0877058i
$131$	6.44949			0.563495			0.281747	−	0.959489i	$-0.409086\pi$
$131$	6.44949			0.563495			0.281747	+	0.959489i	$0.409086\pi$
$132$		0			0
$133$		−	1.55051i		−	0.134446i
$134$	8.00000			0.691095
$135$		0			0
$136$	−2.00000			−0.171499
$137$		−	1.79796i		−	0.153610i	−0.997046	−	0.0768050i	$-0.975528\pi$
$137$		−	1.79796i		−	0.153610i	0.997046	−	0.0768050i	$-0.0244719\pi$
$138$		0			0
$139$	−1.55051			−0.131513			−0.0657563	−	0.997836i	$-0.520946\pi$
$139$	−1.55051			−0.131513			−0.0657563	+	0.997836i	$0.520946\pi$
$140$	−0.224745	+	2.22474i	−0.0189944	+	0.188025i
$141$		0			0
$142$		−	1.10102i		−	0.0923956i
$143$			21.7980i			1.82284i
$144$		0			0
$145$	−15.3485	−	1.55051i	−1.27462	−	0.128763i
$146$	2.89898			0.239921
$147$		0			0
$148$			2.00000i			0.164399i
$149$	−3.79796			−0.311141			−0.155570	−	0.987825i	$-0.549722\pi$
$149$	−3.79796			−0.311141			−0.155570	+	0.987825i	$0.549722\pi$
$150$		0			0
$151$	19.5959			1.59469			0.797347	−	0.603522i	$-0.206236\pi$
$151$	19.5959			1.59469			0.797347	+	0.603522i	$0.206236\pi$
$152$		−	1.55051i		−	0.125763i
$153$		0			0
$154$	4.89898			0.394771
$155$	−19.7980	−	2.00000i	−1.59021	−	0.160644i
$156$		0			0
$157$		−	3.55051i		−	0.283362i	−0.989912	−	0.141681i	$-0.954749\pi$
$157$		−	3.55051i		−	0.283362i	0.989912	−	0.141681i	$-0.0452507\pi$
$158$			6.89898i			0.548853i
$159$		0			0
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$	2.89898			0.228472
$162$		0			0
$163$		−	7.10102i		−	0.556195i	−0.960553	−	0.278097i	$-0.910296\pi$
$163$		−	7.10102i		−	0.556195i	0.960553	−	0.278097i	$-0.0897038\pi$
$164$	−1.10102			−0.0859753
$165$		0			0
$166$	2.44949			0.190117
$167$		−	4.89898i		−	0.379094i	−0.981872	−	0.189547i	$-0.939298\pi$
$167$		−	4.89898i		−	0.379094i	0.981872	−	0.189547i	$-0.0607020\pi$
$168$		0			0
$169$	−6.79796			−0.522920
$170$	−4.44949	−	0.449490i	−0.341260	−	0.0344743i
$171$		0			0
$172$			0.898979i			0.0685465i
$173$			6.24745i			0.474985i	0.971389	+	0.237492i	$0.0763255\pi$
$173$			6.24745i			0.474985i	−0.971389	+	0.237492i	$0.923675\pi$
$174$		0			0
$175$	−1.00000	+	4.89898i	−0.0755929	+	0.370328i
$176$	4.89898			0.369274
$177$		0			0
$178$			10.0000i			0.749532i
$179$	13.7980			1.03131			0.515654	−	0.856797i	$-0.327549\pi$
$179$	13.7980			1.03131			0.515654	+	0.856797i	$0.327549\pi$
$180$		0			0
$181$	−10.2474			−0.761687			−0.380843	−	0.924640i	$-0.624366\pi$
$181$	−10.2474			−0.761687			−0.380843	+	0.924640i	$0.624366\pi$
$182$			4.44949i			0.329818i
$183$		0			0
$184$	2.89898			0.213716
$185$	−0.449490	+	4.44949i	−0.0330471	+	0.327133i
$186$		0			0
$187$			9.79796i			0.716498i
$188$		−	8.89898i		−	0.649025i
$189$		0			0
$190$	0.348469	−	3.44949i	0.0252806	−	0.250252i
$191$	−12.6969			−0.918718			−0.459359	−	0.888251i	$-0.651921\pi$
$191$	−12.6969			−0.918718			−0.459359	+	0.888251i	$0.651921\pi$
$192$		0			0
$193$		−	21.5959i		−	1.55451i	−0.629187	−	0.777254i	$-0.716612\pi$
$193$		−	21.5959i		−	1.55451i	0.629187	−	0.777254i	$-0.283388\pi$
$194$	−15.7980			−1.13423
$195$		0			0
$196$	1.00000			0.0714286
$197$			18.8990i			1.34650i	0.739417	+	0.673248i	$0.235101\pi$
$197$			18.8990i			1.34650i	−0.739417	+	0.673248i	$0.764899\pi$
$198$		0			0
$199$	−16.8990			−1.19794			−0.598968	−	0.800773i	$-0.704423\pi$
$199$	−16.8990			−1.19794			−0.598968	+	0.800773i	$0.704423\pi$
$200$	−1.00000	+	4.89898i	−0.0707107	+	0.346410i
$201$		0			0
$202$			3.55051i			0.249813i
$203$			6.89898i			0.484213i
$204$		0			0
$205$	−2.44949	−	0.247449i	−0.171080	−	0.0172826i
$206$	12.8990			0.898714
$207$		0			0
$208$			4.44949i			0.308517i
$209$	−7.59592			−0.525421
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$		−	10.8990i		−	0.748545i
$213$		0			0
$214$	−8.00000			−0.546869
$215$	−0.202041	+	2.00000i	−0.0137791	+	0.136399i
$216$		0			0
$217$			8.89898i			0.604102i
$218$			6.89898i			0.467258i
$219$		0			0
$220$	10.8990	+	1.10102i	0.734809	+	0.0742308i
$221$	−8.89898			−0.598610
$222$		0			0
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−19.7980			−1.31694
$227$			7.34847i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$227$			7.34847i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$228$		0			0
$229$	19.1464			1.26523			0.632616	−	0.774466i	$-0.281981\pi$
$229$	19.1464			1.26523			0.632616	+	0.774466i	$0.281981\pi$
$230$	6.44949	+	0.651531i	0.425267	+	0.0429607i
$231$		0			0
$232$			6.89898i			0.452940i
$233$		−	29.7980i		−	1.95213i	−0.217481	−	0.976065i	$-0.569784\pi$
$233$		−	29.7980i		−	1.95213i	0.217481	−	0.976065i	$-0.430216\pi$
$234$		0			0
$235$	2.00000	−	19.7980i	0.130466	−	1.29148i
$236$	1.55051			0.100930
$237$		0			0
$238$			2.00000i			0.129641i
$239$	−6.20204			−0.401177			−0.200588	−	0.979676i	$-0.564285\pi$
$239$	−6.20204			−0.401177			−0.200588	+	0.979676i	$0.564285\pi$
$240$		0			0
$241$	−8.69694			−0.560219			−0.280110	−	0.959968i	$-0.590371\pi$
$241$	−8.69694			−0.560219			−0.280110	+	0.959968i	$0.590371\pi$
$242$		−	13.0000i		−	0.835672i
$243$		0			0
$244$	−3.55051			−0.227298
$245$	2.22474	+	0.224745i	0.142134	+	0.0143584i
$246$		0			0
$247$		−	6.89898i		−	0.438972i
$248$			8.89898i			0.565086i
$249$		0			0
$250$	−3.32577	+	10.6742i	−0.210340	+	0.675098i
$251$	6.44949			0.407088			0.203544	−	0.979066i	$-0.434754\pi$
$251$	6.44949			0.407088			0.203544	+	0.979066i	$0.434754\pi$
$252$		0			0
$253$		−	14.2020i		−	0.892875i
$254$	14.8990			0.934845
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	8.69694i		−	0.542500i	−0.962509	−	0.271250i	$-0.912563\pi$
$257$		−	8.69694i		−	0.542500i	0.962509	−	0.271250i	$-0.0874370\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	−1.00000	+	9.89898i	−0.0620174	+	0.613909i
$261$		0			0
$262$		−	6.44949i		−	0.398451i
$263$		−	9.79796i		−	0.604168i	−0.953281	−	0.302084i	$-0.902318\pi$
$263$		−	9.79796i		−	0.604168i	0.953281	−	0.302084i	$-0.0976823\pi$
$264$		0			0
$265$	2.44949	−	24.2474i	0.150471	−	1.48951i
$266$	−1.55051			−0.0950679
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$	19.1464			1.16738			0.583689	−	0.811977i	$-0.301609\pi$
$269$	19.1464			1.16738			0.583689	+	0.811977i	$0.301609\pi$
$270$		0			0
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−1.79796			−0.108619
$275$	24.0000	+	4.89898i	1.44725	+	0.295420i
$276$		0			0
$277$			14.8990i			0.895193i	0.894236	+	0.447596i	$0.147720\pi$
$277$			14.8990i			0.895193i	−0.894236	+	0.447596i	$0.852280\pi$
$278$			1.55051i			0.0929934i
$279$		0			0
$280$	2.22474	+	0.224745i	0.132954	+	0.0134311i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$			3.75255i			0.223066i	0.993761	+	0.111533i	$0.0355761\pi$
$283$			3.75255i			0.223066i	−0.993761	+	0.111533i	$0.964424\pi$
$284$	−1.10102			−0.0653335
$285$		0			0
$286$	21.7980			1.28894
$287$			1.10102i			0.0649912i
$288$		0			0
$289$	13.0000			0.764706
$290$	−1.55051	+	15.3485i	−0.0910491	+	0.901293i
$291$		0			0
$292$		−	2.89898i		−	0.169650i
$293$		−	18.2474i		−	1.06603i	−0.846107	−	0.533014i	$-0.821059\pi$
$293$		−	18.2474i		−	1.06603i	0.846107	−	0.533014i	$-0.178941\pi$
$294$		0			0
$295$	3.44949	+	0.348469i	0.200837	+	0.0202887i
$296$	2.00000			0.116248
$297$		0			0
$298$			3.79796i			0.220010i
$299$	12.8990			0.745967
$300$		0			0
$301$	0.898979			0.0518163
$302$		−	19.5959i		−	1.12762i
$303$		0			0
$304$	−1.55051			−0.0889279
$305$	−7.89898	−	0.797959i	−0.452294	−	0.0456910i
$306$		0			0
$307$			20.2474i			1.15558i	0.816184	+	0.577791i	$0.196085\pi$
$307$			20.2474i			1.15558i	−0.816184	+	0.577791i	$0.803915\pi$
$308$		−	4.89898i		−	0.279145i
$309$		0			0
$310$	−2.00000	+	19.7980i	−0.113592	+	1.12445i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$		−	21.5959i		−	1.22067i	−0.792142	−	0.610337i	$-0.791034\pi$
$313$		−	21.5959i		−	1.22067i	0.792142	−	0.610337i	$-0.208966\pi$
$314$	−3.55051			−0.200367
$315$		0			0
$316$	6.89898			0.388098
$317$		−	22.4949i		−	1.26344i	−0.775197	−	0.631720i	$-0.782349\pi$
$317$		−	22.4949i		−	1.26344i	0.775197	−	0.631720i	$-0.217651\pi$
$318$		0			0
$319$	33.7980			1.89232
$320$	2.22474	+	0.224745i	0.124367	+	0.0125636i
$321$		0			0
$322$		−	2.89898i		−	0.161554i
$323$		−	3.10102i		−	0.172545i
$324$		0			0
$325$	−4.44949	+	21.7980i	−0.246813	+	1.20913i
$326$	−7.10102			−0.393289
$327$		0			0
$328$			1.10102i			0.0607937i
$329$	−8.89898			−0.490617
$330$		0			0
$331$	−18.6969			−1.02768			−0.513838	−	0.857887i	$-0.671777\pi$
$331$	−18.6969			−1.02768			−0.513838	+	0.857887i	$0.671777\pi$
$332$		−	2.44949i		−	0.134433i
$333$		0			0
$334$	−4.89898			−0.268060
$335$	1.79796	−	17.7980i	0.0982330	−	0.972406i
$336$		0			0
$337$		−	9.59592i		−	0.522723i	−0.965241	−	0.261361i	$-0.915829\pi$
$337$		−	9.59592i		−	0.522723i	0.965241	−	0.261361i	$-0.0841715\pi$
$338$			6.79796i			0.369760i
$339$		0			0
$340$	−0.449490	+	4.44949i	−0.0243770	+	0.241307i
$341$	43.5959			2.36085
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	0.898979			0.0484697
$345$		0			0
$346$	6.24745			0.335865
$347$			28.8990i			1.55138i	0.631115	+	0.775689i	$0.282598\pi$
$347$			28.8990i			1.55138i	−0.631115	+	0.775689i	$0.717402\pi$
$348$		0			0
$349$	8.44949			0.452291			0.226145	−	0.974094i	$-0.427388\pi$
$349$	8.44949			0.452291			0.226145	+	0.974094i	$0.427388\pi$
$350$	4.89898	+	1.00000i	0.261861	+	0.0534522i
$351$		0			0
$352$		−	4.89898i		−	0.261116i
$353$		−	22.8990i		−	1.21879i	−0.792867	−	0.609395i	$-0.791412\pi$
$353$		−	22.8990i		−	1.21879i	0.792867	−	0.609395i	$-0.208588\pi$
$354$		0			0
$355$	−2.44949	−	0.247449i	−0.130005	−	0.0131332i
$356$	10.0000			0.529999
$357$		0			0
$358$		−	13.7980i		−	0.729245i
$359$	−27.5959			−1.45646			−0.728228	−	0.685334i	$-0.759656\pi$
$359$	−27.5959			−1.45646			−0.728228	+	0.685334i	$0.759656\pi$
$360$		0			0
$361$	−16.5959			−0.873469
$362$			10.2474i			0.538594i
$363$		0			0
$364$	4.44949			0.233217
$365$	0.651531	−	6.44949i	0.0341027	−	0.337582i
$366$		0			0
$367$		−	32.0000i		−	1.67039i	−0.549957	−	0.835193i	$-0.685356\pi$
$367$		−	32.0000i		−	1.67039i	0.549957	−	0.835193i	$-0.314644\pi$
$368$		−	2.89898i		−	0.151120i
$369$		0			0
$370$	4.44949	+	0.449490i	0.231318	+	0.0233679i
$371$	−10.8990			−0.565847
$372$		0			0
$373$		−	4.69694i		−	0.243198i	−0.992579	−	0.121599i	$-0.961198\pi$
$373$		−	4.69694i		−	0.243198i	0.992579	−	0.121599i	$-0.0388022\pi$
$374$	9.79796			0.506640
$375$		0			0
$376$	−8.89898			−0.458930
$377$			30.6969i			1.58097i
$378$		0			0
$379$	−30.6969			−1.57680			−0.788398	−	0.615166i	$-0.789089\pi$
$379$	−30.6969			−1.57680			−0.788398	+	0.615166i	$0.789089\pi$
$380$	−3.44949	−	0.348469i	−0.176955	−	0.0178761i
$381$		0			0
$382$			12.6969i			0.649632i
$383$			7.10102i			0.362845i	0.983405	+	0.181423i	$0.0580702\pi$
$383$			7.10102i			0.362845i	−0.983405	+	0.181423i	$0.941930\pi$
$384$		0			0
$385$	1.10102	−	10.8990i	0.0561132	−	0.555463i
$386$	−21.5959			−1.09920
$387$		0			0
$388$			15.7980i			0.802020i
$389$	13.1010			0.664248			0.332124	−	0.943236i	$-0.392235\pi$
$389$	13.1010			0.664248			0.332124	+	0.943236i	$0.392235\pi$
$390$		0			0
$391$	5.79796			0.293215
$392$		−	1.00000i		−	0.0505076i
$393$		0			0
$394$	18.8990			0.952117
$395$	15.3485	+	1.55051i	0.772265	+	0.0780146i
$396$		0			0
$397$			2.65153i			0.133077i	0.997784	+	0.0665383i	$0.0211954\pi$
$397$			2.65153i			0.133077i	−0.997784	+	0.0665383i	$0.978805\pi$
$398$			16.8990i			0.847069i
$399$		0			0
$400$	4.89898	+	1.00000i	0.244949	+	0.0500000i
$401$	29.3939			1.46786			0.733930	−	0.679225i	$-0.237684\pi$
$401$	29.3939			1.46786			0.733930	+	0.679225i	$0.237684\pi$
$402$		0			0
$403$			39.5959i			1.97241i
$404$	3.55051			0.176644
$405$		0			0
$406$	6.89898			0.342391
$407$		−	9.79796i		−	0.485667i
$408$		0			0
$409$	−34.4949			−1.70566			−0.852831	−	0.522186i	$-0.825117\pi$
$409$	−34.4949			−1.70566			−0.852831	+	0.522186i	$0.825117\pi$
$410$	−0.247449	+	2.44949i	−0.0122206	+	0.120972i
$411$		0			0
$412$		−	12.8990i		−	0.635487i
$413$		−	1.55051i		−	0.0762956i
$414$		0			0
$415$	0.550510	−	5.44949i	0.0270235	−	0.267505i
$416$	4.44949			0.218154
$417$		0			0
$418$			7.59592i			0.371528i
$419$	−1.55051			−0.0757474			−0.0378737	−	0.999283i	$-0.512058\pi$
$419$	−1.55051			−0.0757474			−0.0378737	+	0.999283i	$0.512058\pi$
$420$		0			0
$421$	−4.20204			−0.204795			−0.102397	−	0.994744i	$-0.532651\pi$
$421$	−4.20204			−0.204795			−0.102397	+	0.994744i	$0.532651\pi$
$422$		−	12.0000i		−	0.584151i
$423$		0			0
$424$	−10.8990			−0.529301
$425$	−2.00000	+	9.79796i	−0.0970143	+	0.475271i
$426$		0			0
$427$			3.55051i			0.171821i
$428$			8.00000i			0.386695i
$429$		0			0
$430$	2.00000	+	0.202041i	0.0964486	+	0.00974328i
$431$	1.79796			0.0866046			0.0433023	−	0.999062i	$-0.486212\pi$
$431$	1.79796			0.0866046			0.0433023	+	0.999062i	$0.486212\pi$
$432$		0			0
$433$		−	0.202041i		−	0.00970947i	−0.999988	−	0.00485474i	$-0.998455\pi$
$433$		−	0.202041i		−	0.00970947i	0.999988	−	0.00485474i	$-0.00154532\pi$
$434$	8.89898			0.427165
$435$		0			0
$436$	6.89898			0.330401
$437$			4.49490i			0.215020i
$438$		0			0
$439$	21.3939			1.02107			0.510537	−	0.859856i	$-0.329447\pi$
$439$	21.3939			1.02107			0.510537	+	0.859856i	$0.329447\pi$
$440$	1.10102	−	10.8990i	0.0524891	−	0.519588i
$441$		0			0
$442$			8.89898i			0.423281i
$443$		−	9.79796i		−	0.465515i	−0.972535	−	0.232758i	$-0.925225\pi$
$443$		−	9.79796i		−	0.465515i	0.972535	−	0.232758i	$-0.0747749\pi$
$444$		0			0
$445$	22.2474	+	2.24745i	1.05463	+	0.106539i
$446$	−4.00000			−0.189405
$447$		0			0
$448$		−	1.00000i		−	0.0472456i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$		0			0
$451$	5.39388			0.253988
$452$			19.7980i			0.931218i
$453$		0			0
$454$	7.34847			0.344881
$455$	9.89898	+	1.00000i	0.464071	+	0.0468807i
$456$		0			0
$457$		−	29.5959i		−	1.38444i	−0.721687	−	0.692219i	$-0.756633\pi$
$457$		−	29.5959i		−	1.38444i	0.721687	−	0.692219i	$-0.243367\pi$
$458$		−	19.1464i		−	0.894654i
$459$		0			0
$460$	0.651531	−	6.44949i	0.0303778	−	0.300709i
$461$	−17.3485			−0.807999			−0.403999	−	0.914759i	$-0.632380\pi$
$461$	−17.3485			−0.807999			−0.403999	+	0.914759i	$0.632380\pi$
$462$		0			0
$463$			3.59592i			0.167116i	0.996503	+	0.0835582i	$0.0266285\pi$
$463$			3.59592i			0.167116i	−0.996503	+	0.0835582i	$0.973372\pi$
$464$	6.89898			0.320277
$465$		0			0
$466$	−29.7980			−1.38036
$467$			10.4495i			0.483545i	0.970333	+	0.241772i	$0.0777287\pi$
$467$			10.4495i			0.483545i	−0.970333	+	0.241772i	$0.922271\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$	−19.7980	−	2.00000i	−0.913212	−	0.0922531i
$471$		0			0
$472$		−	1.55051i		−	0.0713680i
$473$		−	4.40408i		−	0.202500i
$474$		0			0
$475$	−7.59592	−	1.55051i	−0.348525	−	0.0711423i
$476$	2.00000			0.0916698
$477$		0			0
$478$			6.20204i			0.283675i
$479$	9.30306			0.425068			0.212534	−	0.977154i	$-0.431828\pi$
$479$	9.30306			0.425068			0.212534	+	0.977154i	$0.431828\pi$
$480$		0			0
$481$	8.89898			0.405759
$482$			8.69694i			0.396135i
$483$		0			0
$484$	−13.0000			−0.590909
$485$	−3.55051	+	35.1464i	−0.161220	+	1.59592i
$486$		0			0
$487$			7.30306i			0.330933i	0.986215	+	0.165467i	$0.0529130\pi$
$487$			7.30306i			0.330933i	−0.986215	+	0.165467i	$0.947087\pi$
$488$			3.55051i			0.160724i
$489$		0			0
$490$	0.224745	−	2.22474i	0.0101529	−	0.100504i
$491$	−19.5959			−0.884351			−0.442176	−	0.896928i	$-0.645793\pi$
$491$	−19.5959			−0.884351			−0.442176	+	0.896928i	$0.645793\pi$
$492$		0			0
$493$			13.7980i			0.621429i
$494$	−6.89898			−0.310400
$495$		0			0
$496$	8.89898			0.399576
$497$			1.10102i			0.0493875i
$498$		0			0
$499$	−6.20204			−0.277641			−0.138821	−	0.990318i	$-0.544331\pi$
$499$	−6.20204			−0.277641			−0.138821	+	0.990318i	$0.544331\pi$
$500$	10.6742	+	3.32577i	0.477366	+	0.148733i
$501$		0			0
$502$		−	6.44949i		−	0.287855i
$503$			4.00000i			0.178351i	0.996016	+	0.0891756i	$0.0284232\pi$
$503$			4.00000i			0.178351i	−0.996016	+	0.0891756i	$0.971577\pi$
$504$		0			0
$505$	7.89898	+	0.797959i	0.351500	+	0.0355087i
$506$	−14.2020			−0.631358
$507$		0			0
$508$		−	14.8990i		−	0.661035i
$509$	−31.5505			−1.39845			−0.699226	−	0.714901i	$-0.746472\pi$
$509$	−31.5505			−1.39845			−0.699226	+	0.714901i	$0.746472\pi$
$510$		0			0
$511$	−2.89898			−0.128243
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−8.69694			−0.383606
$515$	2.89898	−	28.6969i	0.127744	−	1.26454i
$516$		0			0
$517$			43.5959i			1.91735i
$518$		−	2.00000i		−	0.0878750i
$519$		0			0
$520$	9.89898	+	1.00000i	0.434099	+	0.0438529i
$521$	−32.6969			−1.43248			−0.716239	−	0.697855i	$-0.754138\pi$
$521$	−32.6969			−1.43248			−0.716239	+	0.697855i	$0.754138\pi$
$522$		0			0
$523$		−	33.1464i		−	1.44939i	−0.689069	−	0.724696i	$-0.741980\pi$
$523$		−	33.1464i		−	1.44939i	0.689069	−	0.724696i	$-0.258020\pi$
$524$	−6.44949			−0.281747
$525$		0			0
$526$	−9.79796			−0.427211
$527$			17.7980i			0.775291i
$528$		0			0
$529$	14.5959			0.634605
$530$	−24.2474	−	2.44949i	−1.05324	−	0.106399i
$531$		0			0
$532$			1.55051i			0.0672231i
$533$			4.89898i			0.212198i
$534$		0			0
$535$	−1.79796	+	17.7980i	−0.0777325	+	0.769473i
$536$	−8.00000			−0.345547
$537$		0			0
$538$		−	19.1464i		−	0.825461i
$539$	−4.89898			−0.211014
$540$		0			0
$541$	9.59592			0.412561			0.206280	−	0.978493i	$-0.433864\pi$
$541$	9.59592			0.412561			0.206280	+	0.978493i	$0.433864\pi$
$542$		−	12.0000i		−	0.515444i
$543$		0			0
$544$	2.00000			0.0857493
$545$	15.3485	+	1.55051i	0.657456	+	0.0664166i
$546$		0			0
$547$			18.6969i			0.799423i	0.916641	+	0.399712i	$0.130890\pi$
$547$			18.6969i			0.799423i	−0.916641	+	0.399712i	$0.869110\pi$
$548$			1.79796i			0.0768050i
$549$		0			0
$550$	4.89898	−	24.0000i	0.208893	−	1.02336i
$551$	−10.6969			−0.455705
$552$		0			0
$553$		−	6.89898i		−	0.293374i
$554$	14.8990			0.632997
$555$		0			0
$556$	1.55051			0.0657563
$557$			12.6969i			0.537987i	0.963142	+	0.268993i	$0.0866909\pi$
$557$			12.6969i			0.537987i	−0.963142	+	0.268993i	$0.913309\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	0.224745	−	2.22474i	0.00949720	−	0.0940126i
$561$		0			0
$562$		−	18.0000i		−	0.759284i
$563$			30.0454i			1.26626i	0.774044	+	0.633131i	$0.218231\pi$
$563$			30.0454i			1.26626i	−0.774044	+	0.633131i	$0.781769\pi$
$564$		0			0
$565$	−4.44949	+	44.0454i	−0.187191	+	1.85300i
$566$	3.75255			0.157731
$567$		0			0
$568$			1.10102i			0.0461978i
$569$	33.7980			1.41688			0.708442	−	0.705769i	$-0.249398\pi$
$569$	33.7980			1.41688			0.708442	+	0.705769i	$0.249398\pi$
$570$		0			0
$571$	−11.1010			−0.464563			−0.232282	−	0.972649i	$-0.574619\pi$
$571$	−11.1010			−0.464563			−0.232282	+	0.972649i	$0.574619\pi$
$572$		−	21.7980i		−	0.911418i
$573$		0			0
$574$	1.10102			0.0459557
$575$	2.89898	−	14.2020i	0.120896	−	0.592266i
$576$		0			0
$577$			2.49490i			0.103864i	0.998651	+	0.0519320i	$0.0165379\pi$
$577$			2.49490i			0.103864i	−0.998651	+	0.0519320i	$0.983462\pi$
$578$		−	13.0000i		−	0.540729i
$579$		0			0
$580$	15.3485	+	1.55051i	0.637310	+	0.0643814i
$581$	−2.44949			−0.101622
$582$		0			0
$583$			53.3939i			2.21135i
$584$	−2.89898			−0.119961
$585$		0			0
$586$	−18.2474			−0.753795
$587$			1.14643i			0.0473182i	0.999720	+	0.0236591i	$0.00753162\pi$
$587$			1.14643i			0.0473182i	−0.999720	+	0.0236591i	$0.992468\pi$
$588$		0			0
$589$	−13.7980			−0.568535
$590$	0.348469	−	3.44949i	0.0143463	−	0.142013i
$591$		0			0
$592$		−	2.00000i		−	0.0821995i
$593$			10.8990i			0.447567i	0.974639	+	0.223784i	$0.0718409\pi$
$593$			10.8990i			0.447567i	−0.974639	+	0.223784i	$0.928159\pi$
$594$		0			0
$595$	4.44949	+	0.449490i	0.182411	+	0.0184273i
$596$	3.79796			0.155570
$597$		0			0
$598$		−	12.8990i		−	0.527478i
$599$	−13.1010			−0.535293			−0.267647	−	0.963517i	$-0.586246\pi$
$599$	−13.1010			−0.535293			−0.267647	+	0.963517i	$0.586246\pi$
$600$		0			0
$601$	−39.3939			−1.60691			−0.803455	−	0.595366i	$-0.797007\pi$
$601$	−39.3939			−1.60691			−0.803455	+	0.595366i	$0.797007\pi$
$602$		−	0.898979i		−	0.0366397i
$603$		0			0
$604$	−19.5959			−0.797347
$605$	−28.9217	−	2.92168i	−1.17583	−	0.118783i
$606$		0			0
$607$		−	33.3939i		−	1.35542i	−0.735331	−	0.677708i	$-0.762973\pi$
$607$		−	33.3939i		−	1.35542i	0.735331	−	0.677708i	$-0.237027\pi$
$608$			1.55051i			0.0628815i
$609$		0			0
$610$	−0.797959	+	7.89898i	−0.0323084	+	0.319820i
$611$	−39.5959			−1.60188
$612$		0			0
$613$		−	27.7980i		−	1.12275i	−0.827562	−	0.561374i	$-0.810273\pi$
$613$		−	27.7980i		−	1.12275i	0.827562	−	0.561374i	$-0.189727\pi$
$614$	20.2474			0.817121
$615$		0			0
$616$	−4.89898			−0.197386
$617$			29.5959i			1.19149i	0.803175	+	0.595743i	$0.203142\pi$
$617$			29.5959i			1.19149i	−0.803175	+	0.595743i	$0.796858\pi$
$618$		0			0
$619$	41.5505			1.67006			0.835028	−	0.550207i	$-0.185451\pi$
$619$	41.5505			1.67006			0.835028	+	0.550207i	$0.185451\pi$
$620$	19.7980	+	2.00000i	0.795105	+	0.0803219i
$621$		0			0
$622$			12.0000i			0.481156i
$623$		−	10.0000i		−	0.400642i
$624$		0			0
$625$	23.0000	+	9.79796i	0.920000	+	0.391918i
$626$	−21.5959			−0.863146
$627$		0			0
$628$			3.55051i			0.141681i
$629$	4.00000			0.159490
$630$		0			0
$631$	−42.4949			−1.69170			−0.845848	−	0.533425i	$-0.820905\pi$
$631$	−42.4949			−1.69170			−0.845848	+	0.533425i	$0.820905\pi$
$632$		−	6.89898i		−	0.274427i
$633$		0			0
$634$	−22.4949			−0.893387
$635$	3.34847	−	33.1464i	0.132880	−	1.31538i
$636$		0			0
$637$		−	4.44949i		−	0.176295i
$638$		−	33.7980i		−	1.33807i
$639$		0			0
$640$	0.224745	−	2.22474i	0.00888382	−	0.0879408i
$641$	−25.7980			−1.01896			−0.509479	−	0.860483i	$-0.670162\pi$
$641$	−25.7980			−1.01896			−0.509479	+	0.860483i	$0.670162\pi$
$642$		0			0
$643$			25.1464i			0.991678i	0.868414	+	0.495839i	$0.165139\pi$
$643$			25.1464i			0.991678i	−0.868414	+	0.495839i	$0.834861\pi$
$644$	−2.89898			−0.114236
$645$		0			0
$646$	−3.10102			−0.122008
$647$		−	46.2929i		−	1.81996i	−0.414652	−	0.909980i	$-0.636097\pi$
$647$		−	46.2929i		−	1.81996i	0.414652	−	0.909980i	$-0.363903\pi$
$648$		0			0
$649$	−7.59592			−0.298166
$650$	21.7980	+	4.44949i	0.854986	+	0.174523i
$651$		0			0
$652$			7.10102i			0.278097i
$653$			20.2020i			0.790567i	0.918559	+	0.395283i	$0.129354\pi$
$653$			20.2020i			0.790567i	−0.918559	+	0.395283i	$0.870646\pi$
$654$		0			0
$655$	−14.3485	−	1.44949i	−0.560641	−	0.0566363i
$656$	1.10102			0.0429876
$657$		0			0
$658$			8.89898i			0.346918i
$659$	16.8990			0.658291			0.329145	−	0.944279i	$-0.393239\pi$
$659$	16.8990			0.658291			0.329145	+	0.944279i	$0.393239\pi$
$660$		0			0
$661$	−40.9444			−1.59255			−0.796276	−	0.604933i	$-0.793200\pi$
$661$	−40.9444			−1.59255			−0.796276	+	0.604933i	$0.793200\pi$
$662$			18.6969i			0.726677i
$663$		0			0
$664$	−2.44949			−0.0950586
$665$	−0.348469	+	3.44949i	−0.0135131	+	0.133765i
$666$		0			0
$667$		−	20.0000i		−	0.774403i
$668$			4.89898i			0.189547i
$669$		0			0
$670$	−17.7980	−	1.79796i	−0.687595	−	0.0694612i
$671$	17.3939			0.671483
$672$		0			0
$673$		−	17.7980i		−	0.686061i	−0.939324	−	0.343030i	$-0.888547\pi$
$673$		−	17.7980i		−	0.686061i	0.939324	−	0.343030i	$-0.111453\pi$
$674$	−9.59592			−0.369621
$675$		0			0
$676$	6.79796			0.261460
$677$		−	36.4495i		−	1.40087i	−0.713717	−	0.700434i	$-0.752990\pi$
$677$		−	36.4495i		−	1.40087i	0.713717	−	0.700434i	$-0.247010\pi$
$678$		0			0
$679$	15.7980			0.606270
$680$	4.44949	+	0.449490i	0.170630	+	0.0172371i
$681$		0			0
$682$		−	43.5959i		−	1.66937i
$683$		−	3.59592i		−	0.137594i	−0.997631	−	0.0687970i	$-0.978084\pi$
$683$		−	3.59592i		−	0.137594i	0.997631	−	0.0687970i	$-0.0219161\pi$
$684$		0			0
$685$	−0.404082	+	4.00000i	−0.0154392	+	0.152832i
$686$	−1.00000			−0.0381802
$687$		0			0
$688$		−	0.898979i		−	0.0342733i
$689$	−48.4949			−1.84751
$690$		0			0
$691$	21.1464			0.804448			0.402224	−	0.915541i	$-0.368237\pi$
$691$	21.1464			0.804448			0.402224	+	0.915541i	$0.368237\pi$
$692$		−	6.24745i		−	0.237492i
$693$		0			0
$694$	28.8990			1.09699
$695$	3.44949	+	0.348469i	0.130847	+	0.0132182i
$696$		0			0
$697$			2.20204i			0.0834083i
$698$		−	8.44949i		−	0.319818i
$699$		0			0
$700$	1.00000	−	4.89898i	0.0377964	−	0.185164i
$701$	−11.3031			−0.426911			−0.213455	−	0.976953i	$-0.568472\pi$
$701$	−11.3031			−0.426911			−0.213455	+	0.976953i	$0.568472\pi$
$702$		0			0
$703$			3.10102i			0.116957i
$704$	−4.89898			−0.184637
$705$		0			0
$706$	−22.8990			−0.861814
$707$		−	3.55051i		−	0.133531i
$708$		0			0
$709$	28.2929			1.06256			0.531280	−	0.847196i	$-0.321711\pi$
$709$	28.2929			1.06256			0.531280	+	0.847196i	$0.321711\pi$
$710$	−0.247449	+	2.44949i	−0.00928658	+	0.0919277i
$711$		0			0
$712$		−	10.0000i		−	0.374766i
$713$		−	25.7980i		−	0.966141i
$714$		0			0
$715$	4.89898	−	48.4949i	0.183211	−	1.81361i
$716$	−13.7980			−0.515654
$717$		0			0
$718$			27.5959i			1.02987i
$719$	−4.49490			−0.167631			−0.0838157	−	0.996481i	$-0.526711\pi$
$719$	−4.49490			−0.167631			−0.0838157	+	0.996481i	$0.526711\pi$
$720$		0			0
$721$	−12.8990			−0.480383
$722$			16.5959i			0.617636i
$723$		0			0
$724$	10.2474			0.380843
$725$	33.7980	+	6.89898i	1.25522	+	0.256222i
$726$		0			0
$727$		−	22.6969i		−	0.841783i	−0.907111	−	0.420891i	$-0.861717\pi$
$727$		−	22.6969i		−	0.841783i	0.907111	−	0.420891i	$-0.138283\pi$
$728$		−	4.44949i		−	0.164909i
$729$		0			0
$730$	−6.44949	−	0.651531i	−0.238706	−	0.0241142i
$731$	1.79796			0.0664999
$732$		0			0
$733$			39.6413i			1.46419i	0.681205	+	0.732093i	$0.261456\pi$
$733$			39.6413i			1.46419i	−0.681205	+	0.732093i	$0.738544\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−2.89898			−0.106858
$737$			39.1918i			1.44365i
$738$		0			0
$739$	−4.49490			−0.165347			−0.0826737	−	0.996577i	$-0.526346\pi$
$739$	−4.49490			−0.165347			−0.0826737	+	0.996577i	$0.526346\pi$
$740$	0.449490	−	4.44949i	0.0165236	−	0.163566i
$741$		0			0
$742$			10.8990i			0.400114i
$743$			44.6969i			1.63977i	0.572527	+	0.819886i	$0.305963\pi$
$743$			44.6969i			1.63977i	−0.572527	+	0.819886i	$0.694037\pi$
$744$		0			0
$745$	8.44949	+	0.853572i	0.309565	+	0.0312725i
$746$	−4.69694			−0.171967
$747$		0			0
$748$		−	9.79796i		−	0.358249i
$749$	8.00000			0.292314
$750$		0			0
$751$	−41.7980			−1.52523			−0.762615	−	0.646853i	$-0.776085\pi$
$751$	−41.7980			−1.52523			−0.762615	+	0.646853i	$0.776085\pi$
$752$			8.89898i			0.324512i
$753$		0			0
$754$	30.6969			1.11792
$755$	−43.5959	−	4.40408i	−1.58662	−	0.160281i
$756$		0			0
$757$			51.7980i			1.88263i	0.337531	+	0.941314i	$0.390408\pi$
$757$			51.7980i			1.88263i	−0.337531	+	0.941314i	$0.609592\pi$
$758$			30.6969i			1.11496i
$759$		0			0
$760$	−0.348469	+	3.44949i	−0.0126403	+	0.125126i
$761$	21.1010			0.764911			0.382456	−	0.923974i	$-0.375078\pi$
$761$	21.1010			0.764911			0.382456	+	0.923974i	$0.375078\pi$
$762$		0			0
$763$		−	6.89898i		−	0.249760i
$764$	12.6969			0.459359
$765$		0			0
$766$	7.10102			0.256570
$767$		−	6.89898i		−	0.249108i
$768$		0			0
$769$	40.6969			1.46757			0.733785	−	0.679382i	$-0.237752\pi$
$769$	40.6969			1.46757			0.733785	+	0.679382i	$0.237752\pi$
$770$	−10.8990	−	1.10102i	−0.392772	−	0.0396780i
$771$		0			0
$772$			21.5959i			0.777254i
$773$		−	1.34847i		−	0.0485011i	−0.999706	−	0.0242505i	$-0.992280\pi$
$773$		−	1.34847i		−	0.0485011i	0.999706	−	0.0242505i	$-0.00771994\pi$
$774$		0			0
$775$	43.5959	+	8.89898i	1.56601	+	0.319661i
$776$	15.7980			0.567114
$777$		0			0
$778$		−	13.1010i		−	0.469694i
$779$	−1.70714			−0.0611648
$780$		0			0
$781$	5.39388			0.193008
$782$		−	5.79796i		−	0.207335i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	−0.797959	+	7.89898i	−0.0284804	+	0.281927i
$786$		0			0
$787$		−	50.4495i		−	1.79833i	−0.437610	−	0.899165i	$-0.644175\pi$
$787$		−	50.4495i		−	1.79833i	0.437610	−	0.899165i	$-0.355825\pi$
$788$		−	18.8990i		−	0.673248i
$789$		0			0
$790$	1.55051	−	15.3485i	0.0551647	−	0.546074i
$791$	19.7980			0.703934
$792$		0			0
$793$			15.7980i			0.561002i
$794$	2.65153			0.0940993
$795$		0			0
$796$	16.8990			0.598968
$797$		−	0.944387i		−	0.0334519i	−0.999860	−	0.0167260i	$-0.994676\pi$
$797$		−	0.944387i		−	0.0334519i	0.999860	−	0.0167260i	$-0.00532429\pi$
$798$		0			0
$799$	−17.7980			−0.629647
$800$	1.00000	−	4.89898i	0.0353553	−	0.173205i
$801$		0			0
$802$		−	29.3939i		−	1.03793i
$803$			14.2020i			0.501179i
$804$		0			0
$805$	−6.44949	−	0.651531i	−0.227315	−	0.0229634i
$806$	39.5959			1.39471
$807$		0			0
$808$		−	3.55051i		−	0.124907i
$809$	47.5959			1.67338			0.836692	−	0.547674i	$-0.184487\pi$
$809$	47.5959			1.67338			0.836692	+	0.547674i	$0.184487\pi$
$810$		0			0
$811$	14.9444			0.524768			0.262384	−	0.964963i	$-0.415491\pi$
$811$	14.9444			0.524768			0.262384	+	0.964963i	$0.415491\pi$
$812$		−	6.89898i		−	0.242107i
$813$		0			0
$814$	−9.79796			−0.343418
$815$	−1.59592	+	15.7980i	−0.0559026	+	0.553378i
$816$		0			0
$817$			1.39388i			0.0487656i
$818$			34.4949i			1.20609i
$819$		0			0
$820$	2.44949	+	0.247449i	0.0855399	+	0.00864128i
$821$	−8.20204			−0.286253			−0.143127	−	0.989704i	$-0.545716\pi$
$821$	−8.20204			−0.286253			−0.143127	+	0.989704i	$0.545716\pi$
$822$		0			0
$823$		−	39.1918i		−	1.36614i	−0.730352	−	0.683071i	$-0.760644\pi$
$823$		−	39.1918i		−	1.36614i	0.730352	−	0.683071i	$-0.239356\pi$
$824$	−12.8990			−0.449357
$825$		0			0
$826$	−1.55051			−0.0539492
$827$		−	15.5959i		−	0.542323i	−0.962534	−	0.271162i	$-0.912592\pi$
$827$		−	15.5959i		−	0.542323i	0.962534	−	0.271162i	$-0.0874078\pi$
$828$		0			0
$829$	43.6413			1.51573			0.757863	−	0.652414i	$-0.226244\pi$
$829$	43.6413			1.51573			0.757863	+	0.652414i	$0.226244\pi$
$830$	−5.44949	−	0.550510i	−0.189155	−	0.0191085i
$831$		0			0
$832$		−	4.44949i		−	0.154258i
$833$		−	2.00000i		−	0.0692959i
$834$		0			0
$835$	−1.10102	+	10.8990i	−0.0381024	+	0.377175i
$836$	7.59592			0.262710
$837$		0			0
$838$			1.55051i			0.0535615i
$839$	36.8990			1.27389			0.636947	−	0.770907i	$-0.280197\pi$
$839$	36.8990			1.27389			0.636947	+	0.770907i	$0.280197\pi$
$840$		0			0
$841$	18.5959			0.641239
$842$			4.20204i			0.144812i
$843$		0			0
$844$	−12.0000			−0.413057
$845$	15.1237	+	1.52781i	0.520272	+	0.0525581i
$846$		0			0
$847$			13.0000i			0.446685i
$848$			10.8990i			0.374272i
$849$		0			0
$850$	9.79796	+	2.00000i	0.336067	+	0.0685994i
$851$	−5.79796			−0.198751
$852$		0			0
$853$		−	33.8434i		−	1.15877i	−0.815052	−	0.579387i	$-0.803292\pi$
$853$		−	33.8434i		−	1.15877i	0.815052	−	0.579387i	$-0.196708\pi$
$854$	3.55051			0.121496
$855$		0			0
$856$	8.00000			0.273434
$857$		−	53.1918i		−	1.81700i	−0.417886	−	0.908499i	$-0.637229\pi$
$857$		−	53.1918i		−	1.81700i	0.417886	−	0.908499i	$-0.362771\pi$
$858$		0			0
$859$	−53.6413			−1.83022			−0.915109	−	0.403206i	$-0.867896\pi$
$859$	−53.6413			−1.83022			−0.915109	+	0.403206i	$0.867896\pi$
$860$	0.202041	−	2.00000i	0.00688954	−	0.0681994i
$861$		0			0
$862$		−	1.79796i		−	0.0612387i
$863$			45.3939i			1.54523i	0.634878	+	0.772613i	$0.281051\pi$
$863$			45.3939i			1.54523i	−0.634878	+	0.772613i	$0.718949\pi$
$864$		0			0
$865$	1.40408	−	13.8990i	0.0477402	−	0.472579i
$866$	−0.202041			−0.00686563
$867$		0			0
$868$		−	8.89898i		−	0.302051i
$869$	−33.7980			−1.14652
$870$		0			0
$871$	−35.5959			−1.20612
$872$		−	6.89898i		−	0.233629i
$873$		0			0
$874$	4.49490			0.152042
$875$	3.32577	−	10.6742i	0.112431	−	0.360855i
$876$		0			0
$877$			39.3939i			1.33024i	0.746738	+	0.665118i	$0.231619\pi$
$877$			39.3939i			1.33024i	−0.746738	+	0.665118i	$0.768381\pi$
$878$		−	21.3939i		−	0.722008i
$879$		0			0
$880$	−10.8990	−	1.10102i	−0.367405	−	0.0371154i
$881$	−8.20204			−0.276334			−0.138167	−	0.990409i	$-0.544121\pi$
$881$	−8.20204			−0.276334			−0.138167	+	0.990409i	$0.544121\pi$
$882$		0			0
$883$			22.2020i			0.747158i	0.927598	+	0.373579i	$0.121870\pi$
$883$			22.2020i			0.747158i	−0.927598	+	0.373579i	$0.878130\pi$
$884$	8.89898			0.299305
$885$		0			0
$886$	−9.79796			−0.329169
$887$			2.69694i			0.0905543i	0.998974	+	0.0452772i	$0.0144171\pi$
$887$			2.69694i			0.0905543i	−0.998974	+	0.0452772i	$0.985583\pi$
$888$		0			0
$889$	−14.8990			−0.499696
$890$	2.24745	−	22.2474i	0.0753347	−	0.745736i
$891$		0			0
$892$			4.00000i			0.133930i
$893$		−	13.7980i		−	0.461731i
$894$		0			0
$895$	−30.6969	−	3.10102i	−1.02609	−	0.103656i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$			10.0000i			0.333704i
$899$	61.3939			2.04760
$900$		0			0
$901$	−21.7980			−0.726195
$902$		−	5.39388i		−	0.179596i
$903$		0			0
$904$	19.7980			0.658470
$905$	22.7980	+	2.30306i	0.757830	+	0.0765564i
$906$		0			0
$907$			41.7980i			1.38788i	0.720034	+	0.693939i	$0.244126\pi$
$907$			41.7980i			1.38788i	−0.720034	+	0.693939i	$0.755874\pi$
$908$		−	7.34847i		−	0.243868i
$909$		0			0
$910$	1.00000	−	9.89898i	0.0331497	−	0.328148i
$911$	35.5959			1.17935			0.589673	−	0.807642i	$-0.299257\pi$
$911$	35.5959			1.17935			0.589673	+	0.807642i	$0.299257\pi$
$912$		0			0
$913$			12.0000i			0.397142i
$914$	−29.5959			−0.978946
$915$		0			0
$916$	−19.1464			−0.632616
$917$			6.44949i			0.212981i
$918$		0			0
$919$	26.8990			0.887315			0.443658	−	0.896196i	$-0.353681\pi$
$919$	26.8990			0.887315			0.443658	+	0.896196i	$0.353681\pi$
$920$	−6.44949	−	0.651531i	−0.212633	−	0.0214803i
$921$		0			0
$922$			17.3485i			0.571341i
$923$			4.89898i			0.161252i
$924$		0			0
$925$	2.00000	−	9.79796i	0.0657596	−	0.322155i
$926$	3.59592			0.118169
$927$		0			0
$928$		−	6.89898i		−	0.226470i
$929$	−28.2929			−0.928259			−0.464129	−	0.885767i	$-0.653633\pi$
$929$	−28.2929			−0.928259			−0.464129	+	0.885767i	$0.653633\pi$
$930$		0			0
$931$	1.55051			0.0508159
$932$			29.7980i			0.976065i
$933$		0			0
$934$	10.4495			0.341918
$935$	2.20204	−	21.7980i	0.0720144	−	0.712869i
$936$		0			0
$937$			41.1010i			1.34271i	0.741135	+	0.671356i	$0.234288\pi$
$937$			41.1010i			1.34271i	−0.741135	+	0.671356i	$0.765712\pi$
$938$			8.00000i			0.261209i
$939$		0			0
$940$	−2.00000	+	19.7980i	−0.0652328	+	0.645738i
$941$	19.5505			0.637328			0.318664	−	0.947868i	$-0.396766\pi$
$941$	19.5505			0.637328			0.318664	+	0.947868i	$0.396766\pi$
$942$		0			0
$943$		−	3.19184i		−	0.103940i
$944$	−1.55051			−0.0504648
$945$		0			0
$946$	−4.40408			−0.143189
$947$			44.0908i			1.43276i	0.697711	+	0.716379i	$0.254202\pi$
$947$			44.0908i			1.43276i	−0.697711	+	0.716379i	$0.745798\pi$
$948$		0			0
$949$	−12.8990			−0.418719
$950$	−1.55051	+	7.59592i	−0.0503052	+	0.246444i
$951$		0			0
$952$		−	2.00000i		−	0.0648204i
$953$		−	2.20204i		−	0.0713311i	−0.999364	−	0.0356656i	$-0.988645\pi$
$953$		−	2.20204i		−	0.0713311i	0.999364	−	0.0356656i	$-0.0113551\pi$
$954$		0			0
$955$	28.2474	+	2.85357i	0.914066	+	0.0923394i
$956$	6.20204			0.200588
$957$		0			0
$958$		−	9.30306i		−	0.300568i
$959$	1.79796			0.0580591
$960$		0			0
$961$	48.1918			1.55458
$962$		−	8.89898i		−	0.286915i
$963$		0			0
$964$	8.69694			0.280110
$965$	−4.85357	+	48.0454i	−0.156242	+	1.54664i
$966$		0			0
$967$			36.2929i			1.16710i	0.812077	+	0.583550i	$0.198337\pi$
$967$			36.2929i			1.16710i	−0.812077	+	0.583550i	$0.801663\pi$
$968$			13.0000i			0.417836i
$969$		0			0
$970$	35.1464	+	3.55051i	1.12848	+	0.114000i
$971$	9.55051			0.306490			0.153245	−	0.988188i	$-0.451028\pi$
$971$	9.55051			0.306490			0.153245	+	0.988188i	$0.451028\pi$
$972$		0			0
$973$		−	1.55051i		−	0.0497071i
$974$	7.30306			0.234005
$975$		0			0
$976$	3.55051			0.113649
$977$		−	29.3939i		−	0.940393i	−0.882562	−	0.470197i	$-0.844183\pi$
$977$		−	29.3939i		−	0.940393i	0.882562	−	0.470197i	$-0.155817\pi$
$978$		0			0
$979$	−48.9898			−1.56572
$980$	−2.22474	−	0.224745i	−0.0710669	−	0.00717921i
$981$		0			0
$982$			19.5959i			0.625331i
$983$			13.3031i			0.424302i	0.977237	+	0.212151i	$0.0680468\pi$
$983$			13.3031i			0.424302i	−0.977237	+	0.212151i	$0.931953\pi$
$984$		0			0
$985$	4.24745	−	42.0454i	0.135335	−	1.33968i
$986$	13.7980			0.439417
$987$		0			0
$988$			6.89898i			0.219486i
$989$	−2.60612			−0.0828699
$990$		0			0
$991$	31.3031			0.994375			0.497187	−	0.867643i	$-0.334366\pi$
$991$	31.3031			0.994375			0.497187	+	0.867643i	$0.334366\pi$
$992$		−	8.89898i		−	0.282543i
$993$		0			0
$994$	1.10102			0.0349223
$995$	37.5959	+	3.79796i	1.19187	+	0.120403i
$996$		0			0
$997$		−	57.3485i		−	1.81624i	−0.418705	−	0.908122i	$-0.637516\pi$
$997$		−	57.3485i		−	1.81624i	0.418705	−	0.908122i	$-0.362484\pi$
$998$			6.20204i			0.196322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.g.g.379.1		4
3.2	odd	2		70.2.c.a.29.3	yes	4
4.3	odd	2		5040.2.t.t.1009.1		4
5.2	odd	4		3150.2.a.bt.1.2		2
5.3	odd	4		3150.2.a.bs.1.2		2
5.4	even	2	inner	630.2.g.g.379.3		4
12.11	even	2		560.2.g.e.449.4		4
15.2	even	4		350.2.a.g.1.1		2
15.8	even	4		350.2.a.h.1.2		2
15.14	odd	2		70.2.c.a.29.2	✓	4
20.19	odd	2		5040.2.t.t.1009.2		4
21.2	odd	6		490.2.i.c.459.4		8
21.5	even	6		490.2.i.f.459.3		8
21.11	odd	6		490.2.i.c.79.1		8
21.17	even	6		490.2.i.f.79.2		8
21.20	even	2		490.2.c.e.99.4		4
24.5	odd	2		2240.2.g.j.449.3		4
24.11	even	2		2240.2.g.i.449.1		4
60.23	odd	4		2800.2.a.bl.1.1		2
60.47	odd	4		2800.2.a.bm.1.2		2
60.59	even	2		560.2.g.e.449.2		4
105.44	odd	6		490.2.i.c.459.1		8
105.59	even	6		490.2.i.f.79.3		8
105.62	odd	4		2450.2.a.bl.1.2		2
105.74	odd	6		490.2.i.c.79.4		8
105.83	odd	4		2450.2.a.bq.1.1		2
105.89	even	6		490.2.i.f.459.2		8
105.104	even	2		490.2.c.e.99.1		4
120.29	odd	2		2240.2.g.j.449.1		4
120.59	even	2		2240.2.g.i.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.c.a.29.2	✓	4	15.14	odd	2
70.2.c.a.29.3	yes	4	3.2	odd	2
350.2.a.g.1.1		2	15.2	even	4
350.2.a.h.1.2		2	15.8	even	4
490.2.c.e.99.1		4	105.104	even	2
490.2.c.e.99.4		4	21.20	even	2
490.2.i.c.79.1		8	21.11	odd	6
490.2.i.c.79.4		8	105.74	odd	6
490.2.i.c.459.1		8	105.44	odd	6
490.2.i.c.459.4		8	21.2	odd	6
490.2.i.f.79.2		8	21.17	even	6
490.2.i.f.79.3		8	105.59	even	6
490.2.i.f.459.2		8	105.89	even	6
490.2.i.f.459.3		8	21.5	even	6
560.2.g.e.449.2		4	60.59	even	2
560.2.g.e.449.4		4	12.11	even	2
630.2.g.g.379.1		4	1.1	even	1	trivial
630.2.g.g.379.3		4	5.4	even	2	inner
2240.2.g.i.449.1		4	24.11	even	2
2240.2.g.i.449.3		4	120.59	even	2
2240.2.g.j.449.1		4	120.29	odd	2
2240.2.g.j.449.3		4	24.5	odd	2
2450.2.a.bl.1.2		2	105.62	odd	4
2450.2.a.bq.1.1		2	105.83	odd	4
2800.2.a.bl.1.1		2	60.23	odd	4
2800.2.a.bm.1.2		2	60.47	odd	4
3150.2.a.bs.1.2		2	5.3	odd	4
3150.2.a.bt.1.2		2	5.2	odd	4
5040.2.t.t.1009.1		4	4.3	odd	2
5040.2.t.t.1009.2		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.22474 - 0.224745i) q^{5} +1.00000i q^{7} +1.00000i q^{8} +(-0.224745 + 2.22474i) q^{10} +4.89898 q^{11} +4.44949i q^{13} +1.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} -1.55051 q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} -2.89898i q^{23} +(4.89898 + 1.00000i) q^{25} +4.44949 q^{26} -1.00000i q^{28} +6.89898 q^{29} +8.89898 q^{31} -1.00000i q^{32} +2.00000 q^{34} +(0.224745 - 2.22474i) q^{35} -2.00000i q^{37} +1.55051i q^{38} +(0.224745 - 2.22474i) q^{40} +1.10102 q^{41} -0.898979i q^{43} -4.89898 q^{44} -2.89898 q^{46} +8.89898i q^{47} -1.00000 q^{49} +(1.00000 - 4.89898i) q^{50} -4.44949i q^{52} +10.8990i q^{53} +(-10.8990 - 1.10102i) q^{55} -1.00000 q^{56} -6.89898i q^{58} -1.55051 q^{59} +3.55051 q^{61} -8.89898i q^{62} -1.00000 q^{64} +(1.00000 - 9.89898i) q^{65} +8.00000i q^{67} -2.00000i q^{68} +(-2.22474 - 0.224745i) q^{70} +1.10102 q^{71} +2.89898i q^{73} -2.00000 q^{74} +1.55051 q^{76} +4.89898i q^{77} -6.89898 q^{79} +(-2.22474 - 0.224745i) q^{80} -1.10102i q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} -0.898979 q^{86} +4.89898i q^{88} -10.0000 q^{89} -4.44949 q^{91} +2.89898i q^{92} +8.89898 q^{94} +(3.44949 + 0.348469i) q^{95} -15.7980i q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5} + 4 q^{10} + 4 q^{14} + 4 q^{16} - 16 q^{19} + 4 q^{20} + 8 q^{26} + 8 q^{29} + 16 q^{31} + 8 q^{34} - 4 q^{35} - 4 q^{40} + 24 q^{41} + 8 q^{46} - 4 q^{49} + 4 q^{50} - 24 q^{55}+ \cdots + 4 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 + 4 * q^10 + 4 * q^14 + 4 * q^16 - 16 * q^19 + 4 * q^20 + 8 * q^26 + 8 * q^29 + 16 * q^31 + 8 * q^34 - 4 * q^35 - 4 * q^40 + 24 * q^41 + 8 * q^46 - 4 * q^49 + 4 * q^50 - 24 * q^55 - 4 * q^56 - 16 * q^59 + 24 * q^61 - 4 * q^64 + 4 * q^65 - 4 * q^70 + 24 * q^71 - 8 * q^74 + 16 * q^76 - 8 * q^79 - 4 * q^80 - 8 * q^85 + 16 * q^86 - 40 * q^89 - 8 * q^91 + 16 * q^94 + 4 * q^95

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