LMFDB - Embedded newform 9282.2.a.ce.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.a (trivial)

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:	yes
Analytic conductor:	$74.1171431562$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 23x^{5} + 70x^{4} + 115x^{3} - 422x^{2} + 118x + 208 $ x^7 - 3x^6 - 23x^5 + 70x^4 + 115x^3 - 422x^2 + 118x + 208
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.555964$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.555964 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.555964 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.555964 q^{10} +1.39751 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -0.555964 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -8.27840 q^{19} -0.555964 q^{20} -1.00000 q^{21} +1.39751 q^{22} +3.50413 q^{23} +1.00000 q^{24} -4.69090 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +8.96134 q^{29} -0.555964 q^{30} +5.16647 q^{31} +1.00000 q^{32} +1.39751 q^{33} +1.00000 q^{34} +0.555964 q^{35} +1.00000 q^{36} -8.03658 q^{37} -8.27840 q^{38} -1.00000 q^{39} -0.555964 q^{40} +1.96847 q^{41} -1.00000 q^{42} +8.77427 q^{43} +1.39751 q^{44} -0.555964 q^{45} +3.50413 q^{46} +12.8862 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.69090 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.97925 q^{53} +1.00000 q^{54} -0.776964 q^{55} -1.00000 q^{56} -8.27840 q^{57} +8.96134 q^{58} -2.01078 q^{59} -0.555964 q^{60} -8.17984 q^{61} +5.16647 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.555964 q^{65} +1.39751 q^{66} +8.56373 q^{67} +1.00000 q^{68} +3.50413 q^{69} +0.555964 q^{70} +9.45730 q^{71} +1.00000 q^{72} -9.45028 q^{73} -8.03658 q^{74} -4.69090 q^{75} -8.27840 q^{76} -1.39751 q^{77} -1.00000 q^{78} -4.13514 q^{79} -0.555964 q^{80} +1.00000 q^{81} +1.96847 q^{82} +2.72956 q^{83} -1.00000 q^{84} -0.555964 q^{85} +8.77427 q^{86} +8.96134 q^{87} +1.39751 q^{88} -3.42879 q^{89} -0.555964 q^{90} +1.00000 q^{91} +3.50413 q^{92} +5.16647 q^{93} +12.8862 q^{94} +4.60249 q^{95} +1.00000 q^{96} +4.98184 q^{97} +1.00000 q^{98} +1.39751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.555964	−0.248635	−0.124317	−	0.992243i	$-0.539674\pi$
$5$	−0.555964	−0.248635	−0.124317	+	0.992243i	$0.539674\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.555964	−0.175811
$11$	1.39751	0.421365	0.210682	−	0.977555i	$-0.432431\pi$
$11$	1.39751	0.421365	0.210682	+	0.977555i	$0.432431\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	−0.555964	−0.143549
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−8.27840	−1.89920	−0.949598	−	0.313472i	$-0.898508\pi$
$19$	−8.27840	−1.89920	−0.949598	+	0.313472i	$0.898508\pi$
$20$	−0.555964	−0.124317
$21$	−1.00000	−0.218218
$22$	1.39751	0.297950
$23$	3.50413	0.730662	0.365331	−	0.930878i	$-0.380956\pi$
$23$	3.50413	0.730662	0.365331	+	0.930878i	$0.380956\pi$
$24$	1.00000	0.204124
$25$	−4.69090	−0.938181
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	8.96134	1.66408	0.832040	−	0.554716i	$-0.187173\pi$
$29$	8.96134	1.66408	0.832040	+	0.554716i	$0.187173\pi$
$30$	−0.555964	−0.101505
$31$	5.16647	0.927926	0.463963	−	0.885855i	$-0.346427\pi$
$31$	5.16647	0.927926	0.463963	+	0.885855i	$0.346427\pi$
$32$	1.00000	0.176777
$33$	1.39751	0.243275
$34$	1.00000	0.171499
$35$	0.555964	0.0939751
$36$	1.00000	0.166667
$37$	−8.03658	−1.32121	−0.660603	−	0.750736i	$-0.729699\pi$
$37$	−8.03658	−1.32121	−0.660603	+	0.750736i	$0.729699\pi$
$38$	−8.27840	−1.34293
$39$	−1.00000	−0.160128
$40$	−0.555964	−0.0879056
$41$	1.96847	0.307423	0.153712	−	0.988116i	$-0.450877\pi$
$41$	1.96847	0.307423	0.153712	+	0.988116i	$0.450877\pi$
$42$	−1.00000	−0.154303
$43$	8.77427	1.33806	0.669032	−	0.743234i	$-0.266709\pi$
$43$	8.77427	1.33806	0.669032	+	0.743234i	$0.266709\pi$
$44$	1.39751	0.210682
$45$	−0.555964	−0.0828782
$46$	3.50413	0.516656
$47$	12.8862	1.87964	0.939822	−	0.341664i	$-0.110990\pi$
$47$	12.8862	1.87964	0.939822	+	0.341664i	$0.110990\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−4.69090	−0.663394
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	7.97925	1.09603	0.548017	−	0.836467i	$-0.315383\pi$
$53$	7.97925	1.09603	0.548017	+	0.836467i	$0.315383\pi$
$54$	1.00000	0.136083
$55$	−0.776964	−0.104766
$56$	−1.00000	−0.133631
$57$	−8.27840	−1.09650
$58$	8.96134	1.17668
$59$	−2.01078	−0.261781	−0.130891	−	0.991397i	$-0.541784\pi$
$59$	−2.01078	−0.261781	−0.130891	+	0.991397i	$0.541784\pi$
$60$	−0.555964	−0.0717746
$61$	−8.17984	−1.04732	−0.523661	−	0.851927i	$-0.675434\pi$
$61$	−8.17984	−1.04732	−0.523661	+	0.851927i	$0.675434\pi$
$62$	5.16647	0.656143
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0.555964	0.0689588
$66$	1.39751	0.172021
$67$	8.56373	1.04623	0.523113	−	0.852263i	$-0.324771\pi$
$67$	8.56373	1.04623	0.523113	+	0.852263i	$0.324771\pi$
$68$	1.00000	0.121268
$69$	3.50413	0.421848
$70$	0.555964	0.0664504
$71$	9.45730	1.12238	0.561188	−	0.827689i	$-0.310345\pi$
$71$	9.45730	1.12238	0.561188	+	0.827689i	$0.310345\pi$
$72$	1.00000	0.117851
$73$	−9.45028	−1.10607	−0.553036	−	0.833157i	$-0.686531\pi$
$73$	−9.45028	−1.10607	−0.553036	+	0.833157i	$0.686531\pi$
$74$	−8.03658	−0.934234
$75$	−4.69090	−0.541659
$76$	−8.27840	−0.949598
$77$	−1.39751	−0.159261
$78$	−1.00000	−0.113228
$79$	−4.13514	−0.465239	−0.232620	−	0.972568i	$-0.574730\pi$
$79$	−4.13514	−0.465239	−0.232620	+	0.972568i	$0.574730\pi$
$80$	−0.555964	−0.0621587
$81$	1.00000	0.111111
$82$	1.96847	0.217381
$83$	2.72956	0.299608	0.149804	−	0.988716i	$-0.452136\pi$
$83$	2.72956	0.299608	0.149804	+	0.988716i	$0.452136\pi$
$84$	−1.00000	−0.109109
$85$	−0.555964	−0.0603028
$86$	8.77427	0.946154
$87$	8.96134	0.960757
$88$	1.39751	0.148975
$89$	−3.42879	−0.363451	−0.181725	−	0.983349i	$-0.558168\pi$
$89$	−3.42879	−0.363451	−0.181725	+	0.983349i	$0.558168\pi$
$90$	−0.555964	−0.0586037
$91$	1.00000	0.104828
$92$	3.50413	0.365331
$93$	5.16647	0.535738
$94$	12.8862	1.32911
$95$	4.60249	0.472206
$96$	1.00000	0.102062
$97$	4.98184	0.505829	0.252915	−	0.967489i	$-0.418611\pi$
$97$	4.98184	0.505829	0.252915	+	0.967489i	$0.418611\pi$
$98$	1.00000	0.101015
$99$	1.39751	0.140455
$100$	−4.69090	−0.469090
$101$	6.67041	0.663731	0.331865	−	0.943327i	$-0.392322\pi$
$101$	6.67041	0.663731	0.331865	+	0.943327i	$0.392322\pi$
$102$	1.00000	0.0990148
$103$	7.15663	0.705164	0.352582	−	0.935781i	$-0.385304\pi$
$103$	7.15663	0.705164	0.352582	+	0.935781i	$0.385304\pi$
$104$	−1.00000	−0.0980581
$105$	0.555964	0.0542565
$106$	7.97925	0.775013
$107$	0.836437	0.0808614	0.0404307	−	0.999182i	$-0.487127\pi$
$107$	0.836437	0.0808614	0.0404307	+	0.999182i	$0.487127\pi$
$108$	1.00000	0.0962250
$109$	16.8890	1.61767	0.808834	−	0.588037i	$-0.200099\pi$
$109$	16.8890	1.61767	0.808834	+	0.588037i	$0.200099\pi$
$110$	−0.776964	−0.0740807
$111$	−8.03658	−0.762798
$112$	−1.00000	−0.0944911
$113$	7.90144	0.743305	0.371653	−	0.928372i	$-0.378791\pi$
$113$	7.90144	0.743305	0.371653	+	0.928372i	$0.378791\pi$
$114$	−8.27840	−0.775343
$115$	−1.94817	−0.181668
$116$	8.96134	0.832040
$117$	−1.00000	−0.0924500
$118$	−2.01078	−0.185107
$119$	−1.00000	−0.0916698
$120$	−0.555964	−0.0507523
$121$	−9.04697	−0.822452
$122$	−8.17984	−0.740568
$123$	1.96847	0.177491
$124$	5.16647	0.463963
$125$	5.38779	0.481899
$126$	−1.00000	−0.0890871
$127$	2.21861	0.196870	0.0984348	−	0.995144i	$-0.468616\pi$
$127$	2.21861	0.196870	0.0984348	+	0.995144i	$0.468616\pi$
$128$	1.00000	0.0883883
$129$	8.77427	0.772531
$130$	0.555964	0.0487613
$131$	4.80737	0.420022	0.210011	−	0.977699i	$-0.432650\pi$
$131$	4.80737	0.420022	0.210011	+	0.977699i	$0.432650\pi$
$132$	1.39751	0.121638
$133$	8.27840	0.717828
$134$	8.56373	0.739793
$135$	−0.555964	−0.0478498
$136$	1.00000	0.0857493
$137$	6.84670	0.584953	0.292477	−	0.956273i	$-0.405521\pi$
$137$	6.84670	0.584953	0.292477	+	0.956273i	$0.405521\pi$
$138$	3.50413	0.298291
$139$	4.28381	0.363348	0.181674	−	0.983359i	$-0.441848\pi$
$139$	4.28381	0.363348	0.181674	+	0.983359i	$0.441848\pi$
$140$	0.555964	0.0469875
$141$	12.8862	1.08521
$142$	9.45730	0.793639
$143$	−1.39751	−0.116866
$144$	1.00000	0.0833333
$145$	−4.98218	−0.413748
$146$	−9.45028	−0.782111
$147$	1.00000	0.0824786
$148$	−8.03658	−0.660603
$149$	1.01362	0.0830393	0.0415197	−	0.999138i	$-0.486780\pi$
$149$	1.01362	0.0830393	0.0415197	+	0.999138i	$0.486780\pi$
$150$	−4.69090	−0.383011
$151$	16.2969	1.32623	0.663113	−	0.748520i	$-0.269235\pi$
$151$	16.2969	1.32623	0.663113	+	0.748520i	$0.269235\pi$
$152$	−8.27840	−0.671467
$153$	1.00000	0.0808452
$154$	−1.39751	−0.112614
$155$	−2.87237	−0.230714
$156$	−1.00000	−0.0800641
$157$	3.56118	0.284213	0.142106	−	0.989851i	$-0.454612\pi$
$157$	3.56118	0.284213	0.142106	+	0.989851i	$0.454612\pi$
$158$	−4.13514	−0.328974
$159$	7.97925	0.632796
$160$	−0.555964	−0.0439528
$161$	−3.50413	−0.276164
$162$	1.00000	0.0785674
$163$	−15.0760	−1.18084	−0.590421	−	0.807095i	$-0.701038\pi$
$163$	−15.0760	−1.18084	−0.590421	+	0.807095i	$0.701038\pi$
$164$	1.96847	0.153712
$165$	−0.776964	−0.0604866
$166$	2.72956	0.211855
$167$	4.57250	0.353831	0.176915	−	0.984226i	$-0.443388\pi$
$167$	4.57250	0.353831	0.176915	+	0.984226i	$0.443388\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−0.555964	−0.0426405
$171$	−8.27840	−0.633065
$172$	8.77427	0.669032
$173$	7.83977	0.596047	0.298023	−	0.954559i	$-0.403673\pi$
$173$	7.83977	0.596047	0.298023	+	0.954559i	$0.403673\pi$
$174$	8.96134	0.679358
$175$	4.69090	0.354599
$176$	1.39751	0.105341
$177$	−2.01078	−0.151140
$178$	−3.42879	−0.256998
$179$	10.0501	0.751183	0.375592	−	0.926785i	$-0.377440\pi$
$179$	10.0501	0.751183	0.375592	+	0.926785i	$0.377440\pi$
$180$	−0.555964	−0.0414391
$181$	−6.03619	−0.448666	−0.224333	−	0.974513i	$-0.572020\pi$
$181$	−6.03619	−0.448666	−0.224333	+	0.974513i	$0.572020\pi$
$182$	1.00000	0.0741249
$183$	−8.17984	−0.604671
$184$	3.50413	0.258328
$185$	4.46805	0.328497
$186$	5.16647	0.378824
$187$	1.39751	0.102196
$188$	12.8862	0.939822
$189$	−1.00000	−0.0727393
$190$	4.60249	0.333900
$191$	−9.20014	−0.665699	−0.332850	−	0.942980i	$-0.608010\pi$
$191$	−9.20014	−0.665699	−0.332850	+	0.942980i	$0.608010\pi$
$192$	1.00000	0.0721688
$193$	−23.6997	−1.70594	−0.852970	−	0.521961i	$-0.825201\pi$
$193$	−23.6997	−1.70594	−0.852970	+	0.521961i	$0.825201\pi$
$194$	4.98184	0.357675
$195$	0.555964	0.0398134
$196$	1.00000	0.0714286
$197$	−18.7284	−1.33435	−0.667173	−	0.744903i	$-0.732496\pi$
$197$	−18.7284	−1.33435	−0.667173	+	0.744903i	$0.732496\pi$
$198$	1.39751	0.0993166
$199$	−7.82675	−0.554823	−0.277412	−	0.960751i	$-0.589477\pi$
$199$	−7.82675	−0.554823	−0.277412	+	0.960751i	$0.589477\pi$
$200$	−4.69090	−0.331697
$201$	8.56373	0.604039
$202$	6.67041	0.469328
$203$	−8.96134	−0.628963
$204$	1.00000	0.0700140
$205$	−1.09440	−0.0764360
$206$	7.15663	0.498626
$207$	3.50413	0.243554
$208$	−1.00000	−0.0693375
$209$	−11.5691	−0.800254
$210$	0.555964	0.0383652
$211$	20.3462	1.40069	0.700344	−	0.713805i	$-0.253030\pi$
$211$	20.3462	1.40069	0.700344	+	0.713805i	$0.253030\pi$
$212$	7.97925	0.548017
$213$	9.45730	0.648004
$214$	0.836437	0.0571776
$215$	−4.87818	−0.332689
$216$	1.00000	0.0680414
$217$	−5.16647	−0.350723
$218$	16.8890	1.14386
$219$	−9.45028	−0.638591
$220$	−0.776964	−0.0523829
$221$	−1.00000	−0.0672673
$222$	−8.03658	−0.539380
$223$	3.27579	0.219363	0.109682	−	0.993967i	$-0.465017\pi$
$223$	3.27579	0.219363	0.109682	+	0.993967i	$0.465017\pi$
$224$	−1.00000	−0.0668153
$225$	−4.69090	−0.312727
$226$	7.90144	0.525596
$227$	−25.9702	−1.72370	−0.861851	−	0.507161i	$-0.830695\pi$
$227$	−25.9702	−1.72370	−0.861851	+	0.507161i	$0.830695\pi$
$228$	−8.27840	−0.548250
$229$	1.31161	0.0866733	0.0433367	−	0.999061i	$-0.486201\pi$
$229$	1.31161	0.0866733	0.0433367	+	0.999061i	$0.486201\pi$
$230$	−1.94817	−0.128459
$231$	−1.39751	−0.0919493
$232$	8.96134	0.588341
$233$	14.4214	0.944775	0.472387	−	0.881391i	$-0.343392\pi$
$233$	14.4214	0.944775	0.472387	+	0.881391i	$0.343392\pi$
$234$	−1.00000	−0.0653720
$235$	−7.16426	−0.467345
$236$	−2.01078	−0.130891
$237$	−4.13514	−0.268606
$238$	−1.00000	−0.0648204
$239$	0.821048	0.0531092	0.0265546	−	0.999647i	$-0.491546\pi$
$239$	0.821048	0.0531092	0.0265546	+	0.999647i	$0.491546\pi$
$240$	−0.555964	−0.0358873
$241$	20.8247	1.34144	0.670720	−	0.741711i	$-0.265985\pi$
$241$	20.8247	1.34144	0.670720	+	0.741711i	$0.265985\pi$
$242$	−9.04697	−0.581561
$243$	1.00000	0.0641500
$244$	−8.17984	−0.523661
$245$	−0.555964	−0.0355192
$246$	1.96847	0.125505
$247$	8.27840	0.526742
$248$	5.16647	0.328071
$249$	2.72956	0.172979
$250$	5.38779	0.340754
$251$	20.2117	1.27575	0.637875	−	0.770140i	$-0.279813\pi$
$251$	20.2117	1.27575	0.637875	+	0.770140i	$0.279813\pi$
$252$	−1.00000	−0.0629941
$253$	4.89705	0.307875
$254$	2.21861	0.139208
$255$	−0.555964	−0.0348158
$256$	1.00000	0.0625000
$257$	−2.18495	−0.136294	−0.0681468	−	0.997675i	$-0.521709\pi$
$257$	−2.18495	−0.136294	−0.0681468	+	0.997675i	$0.521709\pi$
$258$	8.77427	0.546262
$259$	8.03658	0.499369
$260$	0.555964	0.0344794
$261$	8.96134	0.554693
$262$	4.80737	0.297000
$263$	−11.9490	−0.736807	−0.368404	−	0.929666i	$-0.620096\pi$
$263$	−11.9490	−0.736807	−0.368404	+	0.929666i	$0.620096\pi$
$264$	1.39751	0.0860107
$265$	−4.43617	−0.272512
$266$	8.27840	0.507581
$267$	−3.42879	−0.209838
$268$	8.56373	0.523113
$269$	−31.1706	−1.90050	−0.950252	−	0.311481i	$-0.899175\pi$
$269$	−31.1706	−1.90050	−0.950252	+	0.311481i	$0.899175\pi$
$270$	−0.555964	−0.0338349
$271$	−17.2790	−1.04963	−0.524813	−	0.851218i	$-0.675865\pi$
$271$	−17.2790	−1.04963	−0.524813	+	0.851218i	$0.675865\pi$
$272$	1.00000	0.0606339
$273$	1.00000	0.0605228
$274$	6.84670	0.413624
$275$	−6.55558	−0.395316
$276$	3.50413	0.210924
$277$	11.3154	0.679877	0.339938	−	0.940448i	$-0.389594\pi$
$277$	11.3154	0.679877	0.339938	+	0.940448i	$0.389594\pi$
$278$	4.28381	0.256926
$279$	5.16647	0.309309
$280$	0.555964	0.0332252
$281$	18.9409	1.12992	0.564959	−	0.825119i	$-0.308892\pi$
$281$	18.9409	1.12992	0.564959	+	0.825119i	$0.308892\pi$
$282$	12.8862	0.767362
$283$	−2.09810	−0.124719	−0.0623597	−	0.998054i	$-0.519863\pi$
$283$	−2.09810	−0.124719	−0.0623597	+	0.998054i	$0.519863\pi$
$284$	9.45730	0.561188
$285$	4.60249	0.272628
$286$	−1.39751	−0.0826364
$287$	−1.96847	−0.116195
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−4.98218	−0.292564
$291$	4.98184	0.292041
$292$	−9.45028	−0.553036
$293$	9.71937	0.567812	0.283906	−	0.958852i	$-0.408370\pi$
$293$	9.71937	0.567812	0.283906	+	0.958852i	$0.408370\pi$
$294$	1.00000	0.0583212
$295$	1.11792	0.0650879
$296$	−8.03658	−0.467117
$297$	1.39751	0.0810917
$298$	1.01362	0.0587177
$299$	−3.50413	−0.202649
$300$	−4.69090	−0.270829
$301$	−8.77427	−0.505740
$302$	16.2969	0.937783
$303$	6.67041	0.383205
$304$	−8.27840	−0.474799
$305$	4.54770	0.260400
$306$	1.00000	0.0571662
$307$	−14.3152	−0.817011	−0.408505	−	0.912756i	$-0.633950\pi$
$307$	−14.3152	−0.817011	−0.408505	+	0.912756i	$0.633950\pi$
$308$	−1.39751	−0.0796305
$309$	7.15663	0.407127
$310$	−2.87237	−0.163140
$311$	−23.2866	−1.32046	−0.660231	−	0.751062i	$-0.729542\pi$
$311$	−23.2866	−1.32046	−0.660231	+	0.751062i	$0.729542\pi$
$312$	−1.00000	−0.0566139
$313$	27.2065	1.53780	0.768901	−	0.639368i	$-0.220804\pi$
$313$	27.2065	1.53780	0.768901	+	0.639368i	$0.220804\pi$
$314$	3.56118	0.200969
$315$	0.555964	0.0313250
$316$	−4.13514	−0.232620
$317$	6.80426	0.382165	0.191083	−	0.981574i	$-0.438800\pi$
$317$	6.80426	0.382165	0.191083	+	0.981574i	$0.438800\pi$
$318$	7.97925	0.447454
$319$	12.5236	0.701185
$320$	−0.555964	−0.0310793
$321$	0.836437	0.0466853
$322$	−3.50413	−0.195278
$323$	−8.27840	−0.460622
$324$	1.00000	0.0555556
$325$	4.69090	0.260205
$326$	−15.0760	−0.834981
$327$	16.8890	0.933961
$328$	1.96847	0.108690
$329$	−12.8862	−0.710439
$330$	−0.776964	−0.0427705
$331$	−30.6819	−1.68643	−0.843215	−	0.537577i	$-0.819340\pi$
$331$	−30.6819	−1.68643	−0.843215	+	0.537577i	$0.819340\pi$
$332$	2.72956	0.149804
$333$	−8.03658	−0.440402
$334$	4.57250	0.250196
$335$	−4.76112	−0.260128
$336$	−1.00000	−0.0545545
$337$	25.4632	1.38707	0.693536	−	0.720422i	$-0.256052\pi$
$337$	25.4632	1.38707	0.693536	+	0.720422i	$0.256052\pi$
$338$	1.00000	0.0543928
$339$	7.90144	0.429148
$340$	−0.555964	−0.0301514
$341$	7.22019	0.390995
$342$	−8.27840	−0.447645
$343$	−1.00000	−0.0539949
$344$	8.77427	0.473077
$345$	−1.94817	−0.104886
$346$	7.83977	0.421469
$347$	−13.9072	−0.746578	−0.373289	−	0.927715i	$-0.621770\pi$
$347$	−13.9072	−0.746578	−0.373289	+	0.927715i	$0.621770\pi$
$348$	8.96134	0.480378
$349$	0.803175	0.0429930	0.0214965	−	0.999769i	$-0.493157\pi$
$349$	0.803175	0.0429930	0.0214965	+	0.999769i	$0.493157\pi$
$350$	4.69090	0.250739
$351$	−1.00000	−0.0533761
$352$	1.39751	0.0744875
$353$	−31.1000	−1.65529	−0.827643	−	0.561254i	$-0.810319\pi$
$353$	−31.1000	−1.65529	−0.827643	+	0.561254i	$0.810319\pi$
$354$	−2.01078	−0.106872
$355$	−5.25792	−0.279061
$356$	−3.42879	−0.181725
$357$	−1.00000	−0.0529256
$358$	10.0501	0.531167
$359$	−12.8782	−0.679684	−0.339842	−	0.940483i	$-0.610374\pi$
$359$	−12.8782	−0.679684	−0.339842	+	0.940483i	$0.610374\pi$
$360$	−0.555964	−0.0293019
$361$	49.5319	2.60694
$362$	−6.03619	−0.317255
$363$	−9.04697	−0.474843
$364$	1.00000	0.0524142
$365$	5.25402	0.275008
$366$	−8.17984	−0.427567
$367$	−12.6895	−0.662387	−0.331193	−	0.943563i	$-0.607451\pi$
$367$	−12.6895	−0.662387	−0.331193	+	0.943563i	$0.607451\pi$
$368$	3.50413	0.182665
$369$	1.96847	0.102474
$370$	4.46805	0.232283
$371$	−7.97925	−0.414262
$372$	5.16647	0.267869
$373$	13.5337	0.700750	0.350375	−	0.936609i	$-0.386054\pi$
$373$	13.5337	0.700750	0.350375	+	0.936609i	$0.386054\pi$
$374$	1.39751	0.0722635
$375$	5.38779	0.278224
$376$	12.8862	0.664555
$377$	−8.96134	−0.461533
$378$	−1.00000	−0.0514344
$379$	−15.1848	−0.779993	−0.389997	−	0.920816i	$-0.627524\pi$
$379$	−15.1848	−0.779993	−0.389997	+	0.920816i	$0.627524\pi$
$380$	4.60249	0.236103
$381$	2.21861	0.113663
$382$	−9.20014	−0.470720
$383$	−29.0741	−1.48562	−0.742809	−	0.669504i	$-0.766507\pi$
$383$	−29.0741	−1.48562	−0.742809	+	0.669504i	$0.766507\pi$
$384$	1.00000	0.0510310
$385$	0.776964	0.0395978
$386$	−23.6997	−1.20628
$387$	8.77427	0.446021
$388$	4.98184	0.252915
$389$	14.5250	0.736445	0.368222	−	0.929738i	$-0.379966\pi$
$389$	14.5250	0.736445	0.368222	+	0.929738i	$0.379966\pi$
$390$	0.555964	0.0281523
$391$	3.50413	0.177212
$392$	1.00000	0.0505076
$393$	4.80737	0.242500
$394$	−18.7284	−0.943524
$395$	2.29899	0.115675
$396$	1.39751	0.0702275
$397$	−12.1558	−0.610080	−0.305040	−	0.952340i	$-0.598670\pi$
$397$	−12.1558	−0.610080	−0.305040	+	0.952340i	$0.598670\pi$
$398$	−7.82675	−0.392319
$399$	8.27840	0.414438
$400$	−4.69090	−0.234545
$401$	7.25731	0.362413	0.181206	−	0.983445i	$-0.442000\pi$
$401$	7.25731	0.362413	0.181206	+	0.983445i	$0.442000\pi$
$402$	8.56373	0.427120
$403$	−5.16647	−0.257360
$404$	6.67041	0.331865
$405$	−0.555964	−0.0276261
$406$	−8.96134	−0.444744
$407$	−11.2312	−0.556710
$408$	1.00000	0.0495074
$409$	−22.3636	−1.10581	−0.552904	−	0.833245i	$-0.686481\pi$
$409$	−22.3636	−1.10581	−0.552904	+	0.833245i	$0.686481\pi$
$410$	−1.09440	−0.0540484
$411$	6.84670	0.337723
$412$	7.15663	0.352582
$413$	2.01078	0.0989441
$414$	3.50413	0.172219
$415$	−1.51754	−0.0744930
$416$	−1.00000	−0.0490290
$417$	4.28381	0.209779
$418$	−11.5691	−0.565865
$419$	1.73045	0.0845381	0.0422691	−	0.999106i	$-0.486541\pi$
$419$	1.73045	0.0845381	0.0422691	+	0.999106i	$0.486541\pi$
$420$	0.555964	0.0271283
$421$	26.9598	1.31394	0.656971	−	0.753916i	$-0.271838\pi$
$421$	26.9598	1.31394	0.656971	+	0.753916i	$0.271838\pi$
$422$	20.3462	0.990436
$423$	12.8862	0.626548
$424$	7.97925	0.387507
$425$	−4.69090	−0.227542
$426$	9.45730	0.458208
$427$	8.17984	0.395850
$428$	0.836437	0.0404307
$429$	−1.39751	−0.0674724
$430$	−4.87818	−0.235247
$431$	28.4045	1.36820	0.684099	−	0.729389i	$-0.260196\pi$
$431$	28.4045	1.36820	0.684099	+	0.729389i	$0.260196\pi$
$432$	1.00000	0.0481125
$433$	−13.4351	−0.645649	−0.322825	−	0.946459i	$-0.604632\pi$
$433$	−13.4351	−0.645649	−0.322825	+	0.946459i	$0.604632\pi$
$434$	−5.16647	−0.247999
$435$	−4.98218	−0.238877
$436$	16.8890	0.808834
$437$	−29.0086	−1.38767
$438$	−9.45028	−0.451552
$439$	28.6839	1.36901	0.684504	−	0.729009i	$-0.260019\pi$
$439$	28.6839	1.36901	0.684504	+	0.729009i	$0.260019\pi$
$440$	−0.776964	−0.0370403
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	−3.82304	−0.181638	−0.0908191	−	0.995867i	$-0.528949\pi$
$443$	−3.82304	−0.181638	−0.0908191	+	0.995867i	$0.528949\pi$
$444$	−8.03658	−0.381399
$445$	1.90628	0.0903664
$446$	3.27579	0.155113
$447$	1.01362	0.0479428
$448$	−1.00000	−0.0472456
$449$	−32.4276	−1.53036	−0.765178	−	0.643819i	$-0.777349\pi$
$449$	−32.4276	−1.53036	−0.765178	+	0.643819i	$0.777349\pi$
$450$	−4.69090	−0.221131
$451$	2.75095	0.129537
$452$	7.90144	0.371653
$453$	16.2969	0.765696
$454$	−25.9702	−1.21884
$455$	−0.555964	−0.0260640
$456$	−8.27840	−0.387672
$457$	−14.6627	−0.685893	−0.342946	−	0.939355i	$-0.611425\pi$
$457$	−14.6627	−0.685893	−0.342946	+	0.939355i	$0.611425\pi$
$458$	1.31161	0.0612873
$459$	1.00000	0.0466760
$460$	−1.94817	−0.0908339
$461$	37.9688	1.76838	0.884192	−	0.467123i	$-0.154709\pi$
$461$	37.9688	1.76838	0.884192	+	0.467123i	$0.154709\pi$
$462$	−1.39751	−0.0650180
$463$	−9.08891	−0.422397	−0.211199	−	0.977443i	$-0.567737\pi$
$463$	−9.08891	−0.422397	−0.211199	+	0.977443i	$0.567737\pi$
$464$	8.96134	0.416020
$465$	−2.87237	−0.133203
$466$	14.4214	0.668057
$467$	40.4413	1.87140	0.935700	−	0.352795i	$-0.114769\pi$
$467$	40.4413	1.87140	0.935700	+	0.352795i	$0.114769\pi$
$468$	−1.00000	−0.0462250
$469$	−8.56373	−0.395436
$470$	−7.16426	−0.330463
$471$	3.56118	0.164090
$472$	−2.01078	−0.0925537
$473$	12.2621	0.563813
$474$	−4.13514	−0.189933
$475$	38.8332	1.78179
$476$	−1.00000	−0.0458349
$477$	7.97925	0.365345
$478$	0.821048	0.0375538
$479$	25.6040	1.16988	0.584939	−	0.811077i	$-0.301118\pi$
$479$	25.6040	1.16988	0.584939	+	0.811077i	$0.301118\pi$
$480$	−0.555964	−0.0253762
$481$	8.03658	0.366437
$482$	20.8247	0.948541
$483$	−3.50413	−0.159444
$484$	−9.04697	−0.411226
$485$	−2.76972	−0.125767
$486$	1.00000	0.0453609
$487$	−25.8583	−1.17175	−0.585877	−	0.810400i	$-0.699250\pi$
$487$	−25.8583	−1.17175	−0.585877	+	0.810400i	$0.699250\pi$
$488$	−8.17984	−0.370284
$489$	−15.0760	−0.681759
$490$	−0.555964	−0.0251159
$491$	0.538253	0.0242910	0.0121455	−	0.999926i	$-0.496134\pi$
$491$	0.538253	0.0242910	0.0121455	+	0.999926i	$0.496134\pi$
$492$	1.96847	0.0887454
$493$	8.96134	0.403599
$494$	8.27840	0.372463
$495$	−0.776964	−0.0349220
$496$	5.16647	0.231981
$497$	−9.45730	−0.424218
$498$	2.72956	0.122315
$499$	41.3316	1.85026	0.925129	−	0.379652i	$-0.123956\pi$
$499$	41.3316	1.85026	0.925129	+	0.379652i	$0.123956\pi$
$500$	5.38779	0.240949
$501$	4.57250	0.204284
$502$	20.2117	0.902092
$503$	3.21091	0.143167	0.0715837	−	0.997435i	$-0.477195\pi$
$503$	3.21091	0.143167	0.0715837	+	0.997435i	$0.477195\pi$
$504$	−1.00000	−0.0445435
$505$	−3.70851	−0.165026
$506$	4.89705	0.217701
$507$	1.00000	0.0444116
$508$	2.21861	0.0984348
$509$	36.4834	1.61710	0.808550	−	0.588428i	$-0.200253\pi$
$509$	36.4834	1.61710	0.808550	+	0.588428i	$0.200253\pi$
$510$	−0.555964	−0.0246185
$511$	9.45028	0.418056
$512$	1.00000	0.0441942
$513$	−8.27840	−0.365500
$514$	−2.18495	−0.0963741
$515$	−3.97883	−0.175328
$516$	8.77427	0.386266
$517$	18.0086	0.792016
$518$	8.03658	0.353107
$519$	7.83977	0.344128
$520$	0.555964	0.0243806
$521$	−2.05721	−0.0901279	−0.0450640	−	0.998984i	$-0.514349\pi$
$521$	−2.05721	−0.0901279	−0.0450640	+	0.998984i	$0.514349\pi$
$522$	8.96134	0.392227
$523$	−8.73575	−0.381988	−0.190994	−	0.981591i	$-0.561171\pi$
$523$	−8.73575	−0.381988	−0.190994	+	0.981591i	$0.561171\pi$
$524$	4.80737	0.210011
$525$	4.69090	0.204728
$526$	−11.9490	−0.521001
$527$	5.16647	0.225055
$528$	1.39751	0.0608188
$529$	−10.7211	−0.466133
$530$	−4.43617	−0.192695
$531$	−2.01078	−0.0872605
$532$	8.27840	0.358914
$533$	−1.96847	−0.0852638
$534$	−3.42879	−0.148378
$535$	−0.465029	−0.0201049
$536$	8.56373	0.369897
$537$	10.0501	0.433696
$538$	−31.1706	−1.34386
$539$	1.39751	0.0601950
$540$	−0.555964	−0.0239249
$541$	−3.41727	−0.146920	−0.0734600	−	0.997298i	$-0.523404\pi$
$541$	−3.41727	−0.146920	−0.0734600	+	0.997298i	$0.523404\pi$
$542$	−17.2790	−0.742197
$543$	−6.03619	−0.259038
$544$	1.00000	0.0428746
$545$	−9.38965	−0.402208
$546$	1.00000	0.0427960
$547$	25.9640	1.11014	0.555071	−	0.831803i	$-0.312691\pi$
$547$	25.9640	1.11014	0.555071	+	0.831803i	$0.312691\pi$
$548$	6.84670	0.292477
$549$	−8.17984	−0.349107
$550$	−6.55558	−0.279531
$551$	−74.1856	−3.16041
$552$	3.50413	0.149146
$553$	4.13514	0.175844
$554$	11.3154	0.480746
$555$	4.46805	0.189658
$556$	4.28381	0.181674
$557$	−22.0865	−0.935835	−0.467918	−	0.883772i	$-0.654996\pi$
$557$	−22.0865	−0.935835	−0.467918	+	0.883772i	$0.654996\pi$
$558$	5.16647	0.218714
$559$	−8.77427	−0.371112
$560$	0.555964	0.0234938
$561$	1.39751	0.0590029
$562$	18.9409	0.798973
$563$	42.1589	1.77679	0.888393	−	0.459084i	$-0.151822\pi$
$563$	42.1589	1.77679	0.888393	+	0.459084i	$0.151822\pi$
$564$	12.8862	0.542607
$565$	−4.39292	−0.184811
$566$	−2.09810	−0.0881899
$567$	−1.00000	−0.0419961
$568$	9.45730	0.396820
$569$	0.109138	0.00457530	0.00228765	−	0.999997i	$-0.499272\pi$
$569$	0.109138	0.00457530	0.00228765	+	0.999997i	$0.499272\pi$
$570$	4.60249	0.192777
$571$	31.8544	1.33307	0.666533	−	0.745475i	$-0.267777\pi$
$571$	31.8544	1.33307	0.666533	+	0.745475i	$0.267777\pi$
$572$	−1.39751	−0.0584328
$573$	−9.20014	−0.384342
$574$	−1.96847	−0.0821623
$575$	−16.4375	−0.685493
$576$	1.00000	0.0416667
$577$	−3.79862	−0.158139	−0.0790693	−	0.996869i	$-0.525195\pi$
$577$	−3.79862	−0.158139	−0.0790693	+	0.996869i	$0.525195\pi$
$578$	1.00000	0.0415945
$579$	−23.6997	−0.984924
$580$	−4.98218	−0.206874
$581$	−2.72956	−0.113241
$582$	4.98184	0.206504
$583$	11.1511	0.461830
$584$	−9.45028	−0.391055
$585$	0.555964	0.0229863
$586$	9.71937	0.401503
$587$	32.4592	1.33974	0.669868	−	0.742481i	$-0.266351\pi$
$587$	32.4592	1.33974	0.669868	+	0.742481i	$0.266351\pi$
$588$	1.00000	0.0412393
$589$	−42.7701	−1.76231
$590$	1.11792	0.0460241
$591$	−18.7284	−0.770385
$592$	−8.03658	−0.330301
$593$	−27.5413	−1.13098	−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413	−1.13098	−0.565492	+	0.824754i	$0.691314\pi$
$594$	1.39751	0.0573405
$595$	0.555964	0.0227923
$596$	1.01362	0.0415197
$597$	−7.82675	−0.320327
$598$	−3.50413	−0.143295
$599$	−3.22887	−0.131928	−0.0659640	−	0.997822i	$-0.521012\pi$
$599$	−3.22887	−0.131928	−0.0659640	+	0.997822i	$0.521012\pi$
$600$	−4.69090	−0.191505
$601$	12.3547	0.503961	0.251980	−	0.967732i	$-0.418918\pi$
$601$	12.3547	0.503961	0.251980	+	0.967732i	$0.418918\pi$
$602$	−8.77427	−0.357612
$603$	8.56373	0.348742
$604$	16.2969	0.663113
$605$	5.02979	0.204490
$606$	6.67041	0.270967
$607$	−31.1309	−1.26357	−0.631783	−	0.775145i	$-0.717677\pi$
$607$	−31.1309	−1.26357	−0.631783	+	0.775145i	$0.717677\pi$
$608$	−8.27840	−0.335733
$609$	−8.96134	−0.363132
$610$	4.54770	0.184131
$611$	−12.8862	−0.521320
$612$	1.00000	0.0404226
$613$	−23.5029	−0.949271	−0.474636	−	0.880182i	$-0.657420\pi$
$613$	−23.5029	−0.949271	−0.474636	+	0.880182i	$0.657420\pi$
$614$	−14.3152	−0.577714
$615$	−1.09440	−0.0441304
$616$	−1.39751	−0.0563072
$617$	15.6099	0.628429	0.314215	−	0.949352i	$-0.398259\pi$
$617$	15.6099	0.628429	0.314215	+	0.949352i	$0.398259\pi$
$618$	7.15663	0.287882
$619$	−31.2423	−1.25573	−0.627867	−	0.778320i	$-0.716072\pi$
$619$	−31.2423	−1.25573	−0.627867	+	0.778320i	$0.716072\pi$
$620$	−2.87237	−0.115357
$621$	3.50413	0.140616
$622$	−23.2866	−0.933708
$623$	3.42879	0.137371
$624$	−1.00000	−0.0400320
$625$	20.4591	0.818364
$626$	27.2065	1.08739
$627$	−11.5691	−0.462027
$628$	3.56118	0.142106
$629$	−8.03658	−0.320439
$630$	0.555964	0.0221501
$631$	−32.5466	−1.29566	−0.647829	−	0.761785i	$-0.724323\pi$
$631$	−32.5466	−1.29566	−0.647829	+	0.761785i	$0.724323\pi$
$632$	−4.13514	−0.164487
$633$	20.3462	0.808688
$634$	6.80426	0.270232
$635$	−1.23347	−0.0489486
$636$	7.97925	0.316398
$637$	−1.00000	−0.0396214
$638$	12.5236	0.495812
$639$	9.45730	0.374125
$640$	−0.555964	−0.0219764
$641$	3.66918	0.144924	0.0724619	−	0.997371i	$-0.476914\pi$
$641$	3.66918	0.144924	0.0724619	+	0.997371i	$0.476914\pi$
$642$	0.836437	0.0330115
$643$	20.7240	0.817274	0.408637	−	0.912697i	$-0.366004\pi$
$643$	20.7240	0.817274	0.408637	+	0.912697i	$0.366004\pi$
$644$	−3.50413	−0.138082
$645$	−4.87818	−0.192078
$646$	−8.27840	−0.325709
$647$	−16.2860	−0.640268	−0.320134	−	0.947372i	$-0.603728\pi$
$647$	−16.2860	−0.640268	−0.320134	+	0.947372i	$0.603728\pi$
$648$	1.00000	0.0392837
$649$	−2.81008	−0.110305
$650$	4.69090	0.183992
$651$	−5.16647	−0.202490
$652$	−15.0760	−0.590421
$653$	−23.8296	−0.932526	−0.466263	−	0.884646i	$-0.654400\pi$
$653$	−23.8296	−0.932526	−0.466263	+	0.884646i	$0.654400\pi$
$654$	16.8890	0.660410
$655$	−2.67272	−0.104432
$656$	1.96847	0.0768558
$657$	−9.45028	−0.368691
$658$	−12.8862	−0.502356
$659$	−18.2043	−0.709139	−0.354570	−	0.935030i	$-0.615373\pi$
$659$	−18.2043	−0.709139	−0.354570	+	0.935030i	$0.615373\pi$
$660$	−0.776964	−0.0302433
$661$	7.40101	0.287866	0.143933	−	0.989587i	$-0.454025\pi$
$661$	7.40101	0.287866	0.143933	+	0.989587i	$0.454025\pi$
$662$	−30.6819	−1.19249
$663$	−1.00000	−0.0388368
$664$	2.72956	0.105928
$665$	−4.60249	−0.178477
$666$	−8.03658	−0.311411
$667$	31.4017	1.21588
$668$	4.57250	0.176915
$669$	3.27579	0.126649
$670$	−4.76112	−0.183938
$671$	−11.4314	−0.441304
$672$	−1.00000	−0.0385758
$673$	−42.5713	−1.64100	−0.820501	−	0.571646i	$-0.806305\pi$
$673$	−42.5713	−1.64100	−0.820501	+	0.571646i	$0.806305\pi$
$674$	25.4632	0.980808
$675$	−4.69090	−0.180553
$676$	1.00000	0.0384615
$677$	35.1756	1.35191	0.675954	−	0.736944i	$-0.263732\pi$
$677$	35.1756	1.35191	0.675954	+	0.736944i	$0.263732\pi$
$678$	7.90144	0.303453
$679$	−4.98184	−0.191185
$680$	−0.555964	−0.0213202
$681$	−25.9702	−0.995180
$682$	7.22019	0.276475
$683$	27.9274	1.06861	0.534306	−	0.845291i	$-0.320573\pi$
$683$	27.9274	1.06861	0.534306	+	0.845291i	$0.320573\pi$
$684$	−8.27840	−0.316533
$685$	−3.80652	−0.145440
$686$	−1.00000	−0.0381802
$687$	1.31161	0.0500409
$688$	8.77427	0.334516
$689$	−7.97925	−0.303985
$690$	−1.94817	−0.0741656
$691$	−19.4212	−0.738816	−0.369408	−	0.929267i	$-0.620440\pi$
$691$	−19.4212	−0.738816	−0.369408	+	0.929267i	$0.620440\pi$
$692$	7.83977	0.298023
$693$	−1.39751	−0.0530870
$694$	−13.9072	−0.527910
$695$	−2.38164	−0.0903409
$696$	8.96134	0.339679
$697$	1.96847	0.0745611
$698$	0.803175	0.0304006
$699$	14.4214	0.545466
$700$	4.69090	0.177300
$701$	−31.5999	−1.19351	−0.596757	−	0.802422i	$-0.703544\pi$
$701$	−31.5999	−1.19351	−0.596757	+	0.802422i	$0.703544\pi$
$702$	−1.00000	−0.0377426
$703$	66.5300	2.50923
$704$	1.39751	0.0526706
$705$	−7.16426	−0.269822
$706$	−31.1000	−1.17046
$707$	−6.67041	−0.250867
$708$	−2.01078	−0.0755698
$709$	3.46703	0.130207	0.0651035	−	0.997879i	$-0.479262\pi$
$709$	3.46703	0.130207	0.0651035	+	0.997879i	$0.479262\pi$
$710$	−5.25792	−0.197326
$711$	−4.13514	−0.155080
$712$	−3.42879	−0.128499
$713$	18.1040	0.678000
$714$	−1.00000	−0.0374241
$715$	0.776964	0.0290568
$716$	10.0501	0.375592
$717$	0.821048	0.0306626
$718$	−12.8782	−0.480609
$719$	−11.0275	−0.411256	−0.205628	−	0.978630i	$-0.565924\pi$
$719$	−11.0275	−0.411256	−0.205628	+	0.978630i	$0.565924\pi$
$720$	−0.555964	−0.0207196
$721$	−7.15663	−0.266527
$722$	49.5319	1.84339
$723$	20.8247	0.774480
$724$	−6.03619	−0.224333
$725$	−42.0368	−1.56121
$726$	−9.04697	−0.335765
$727$	−31.9137	−1.18361	−0.591807	−	0.806080i	$-0.701585\pi$
$727$	−31.9137	−1.18361	−0.591807	+	0.806080i	$0.701585\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	5.25402	0.194460
$731$	8.77427	0.324528
$732$	−8.17984	−0.302336
$733$	52.4543	1.93744	0.968722	−	0.248148i	$-0.0798220\pi$
$733$	52.4543	1.93744	0.968722	+	0.248148i	$0.0798220\pi$
$734$	−12.6895	−0.468378
$735$	−0.555964	−0.0205070
$736$	3.50413	0.129164
$737$	11.9679	0.440843
$738$	1.96847	0.0724603
$739$	−25.4275	−0.935366	−0.467683	−	0.883896i	$-0.654911\pi$
$739$	−25.4275	−0.935366	−0.467683	+	0.883896i	$0.654911\pi$
$740$	4.46805	0.164249
$741$	8.27840	0.304115
$742$	−7.97925	−0.292927
$743$	21.8715	0.802386	0.401193	−	0.915994i	$-0.368596\pi$
$743$	21.8715	0.802386	0.401193	+	0.915994i	$0.368596\pi$
$744$	5.16647	0.189412
$745$	−0.563539	−0.0206465
$746$	13.5337	0.495505
$747$	2.72956	0.0998694
$748$	1.39751	0.0510980
$749$	−0.836437	−0.0305627
$750$	5.38779	0.196734
$751$	0.248568	0.00907036	0.00453518	−	0.999990i	$-0.498556\pi$
$751$	0.248568	0.00907036	0.00453518	+	0.999990i	$0.498556\pi$
$752$	12.8862	0.469911
$753$	20.2117	0.736555
$754$	−8.96134	−0.326353
$755$	−9.06050	−0.329745
$756$	−1.00000	−0.0363696
$757$	−9.77688	−0.355347	−0.177673	−	0.984090i	$-0.556857\pi$
$757$	−9.77688	−0.355347	−0.177673	+	0.984090i	$0.556857\pi$
$758$	−15.1848	−0.551538
$759$	4.89705	0.177752
$760$	4.60249	0.166950
$761$	−26.1850	−0.949207	−0.474603	−	0.880200i	$-0.657408\pi$
$761$	−26.1850	−0.949207	−0.474603	+	0.880200i	$0.657408\pi$
$762$	2.21861	0.0803716
$763$	−16.8890	−0.611421
$764$	−9.20014	−0.332850
$765$	−0.555964	−0.0201009
$766$	−29.0741	−1.05049
$767$	2.01078	0.0726051
$768$	1.00000	0.0360844
$769$	15.6416	0.564051	0.282025	−	0.959407i	$-0.408994\pi$
$769$	15.6416	0.564051	0.282025	+	0.959407i	$0.408994\pi$
$770$	0.776964	0.0279999
$771$	−2.18495	−0.0786891
$772$	−23.6997	−0.852970
$773$	−34.4453	−1.23891	−0.619455	−	0.785032i	$-0.712646\pi$
$773$	−34.4453	−1.23891	−0.619455	+	0.785032i	$0.712646\pi$
$774$	8.77427	0.315385
$775$	−24.2354	−0.870562
$776$	4.98184	0.178838
$777$	8.03658	0.288311
$778$	14.5250	0.520745
$779$	−16.2958	−0.583857
$780$	0.555964	0.0199067
$781$	13.2167	0.472929
$782$	3.50413	0.125307
$783$	8.96134	0.320252
$784$	1.00000	0.0357143
$785$	−1.97989	−0.0706652
$786$	4.80737	0.171473
$787$	−37.9038	−1.35112	−0.675562	−	0.737304i	$-0.736099\pi$
$787$	−37.9038	−1.35112	−0.675562	+	0.737304i	$0.736099\pi$
$788$	−18.7284	−0.667173
$789$	−11.9490	−0.425396
$790$	2.29899	0.0817943
$791$	−7.90144	−0.280943
$792$	1.39751	0.0496583
$793$	8.17984	0.290475
$794$	−12.1558	−0.431392
$795$	−4.43617	−0.157335
$796$	−7.82675	−0.277412
$797$	−42.3114	−1.49875	−0.749373	−	0.662148i	$-0.769645\pi$
$797$	−42.3114	−1.49875	−0.749373	+	0.662148i	$0.769645\pi$
$798$	8.27840	0.293052
$799$	12.8862	0.455881
$800$	−4.69090	−0.165849
$801$	−3.42879	−0.121150
$802$	7.25731	0.256265
$803$	−13.2069	−0.466060
$804$	8.56373	0.302019
$805$	1.94817	0.0686640
$806$	−5.16647	−0.181981
$807$	−31.1706	−1.09726
$808$	6.67041	0.234664
$809$	−8.99644	−0.316298	−0.158149	−	0.987415i	$-0.550553\pi$
$809$	−8.99644	−0.316298	−0.158149	+	0.987415i	$0.550553\pi$
$810$	−0.555964	−0.0195346
$811$	11.3935	0.400081	0.200040	−	0.979788i	$-0.435893\pi$
$811$	11.3935	0.400081	0.200040	+	0.979788i	$0.435893\pi$
$812$	−8.96134	−0.314481
$813$	−17.2790	−0.606002
$814$	−11.2312	−0.393653
$815$	8.38170	0.293598
$816$	1.00000	0.0350070
$817$	−72.6369	−2.54124
$818$	−22.3636	−0.781925
$819$	1.00000	0.0349428
$820$	−1.09440	−0.0382180
$821$	−23.0586	−0.804752	−0.402376	−	0.915475i	$-0.631815\pi$
$821$	−23.0586	−0.804752	−0.402376	+	0.915475i	$0.631815\pi$
$822$	6.84670	0.238806
$823$	37.5345	1.30837	0.654184	−	0.756335i	$-0.273012\pi$
$823$	37.5345	1.30837	0.654184	+	0.756335i	$0.273012\pi$
$824$	7.15663	0.249313
$825$	−6.55558	−0.228236
$826$	2.01078	0.0699640
$827$	−1.15644	−0.0402135	−0.0201067	−	0.999798i	$-0.506401\pi$
$827$	−1.15644	−0.0402135	−0.0201067	+	0.999798i	$0.506401\pi$
$828$	3.50413	0.121777
$829$	−37.9688	−1.31871	−0.659355	−	0.751832i	$-0.729171\pi$
$829$	−37.9688	−1.31871	−0.659355	+	0.751832i	$0.729171\pi$
$830$	−1.51754	−0.0526745
$831$	11.3154	0.392527
$832$	−1.00000	−0.0346688
$833$	1.00000	0.0346479
$834$	4.28381	0.148336
$835$	−2.54214	−0.0879745
$836$	−11.5691	−0.400127
$837$	5.16647	0.178579
$838$	1.73045	0.0597775
$839$	−41.5235	−1.43355	−0.716775	−	0.697305i	$-0.754382\pi$
$839$	−41.5235	−1.43355	−0.716775	+	0.697305i	$0.754382\pi$
$840$	0.555964	0.0191826
$841$	51.3057	1.76916
$842$	26.9598	0.929097
$843$	18.9409	0.652358
$844$	20.3462	0.700344
$845$	−0.555964	−0.0191257
$846$	12.8862	0.443036
$847$	9.04697	0.310858
$848$	7.97925	0.274009
$849$	−2.09810	−0.0720067
$850$	−4.69090	−0.160897
$851$	−28.1612	−0.965355
$852$	9.45730	0.324002
$853$	28.5898	0.978896	0.489448	−	0.872032i	$-0.337198\pi$
$853$	28.5898	0.978896	0.489448	+	0.872032i	$0.337198\pi$
$854$	8.17984	0.279908
$855$	4.60249	0.157402
$856$	0.836437	0.0285888
$857$	21.6266	0.738751	0.369375	−	0.929280i	$-0.379572\pi$
$857$	21.6266	0.738751	0.369375	+	0.929280i	$0.379572\pi$
$858$	−1.39751	−0.0477102
$859$	−52.5190	−1.79192	−0.895962	−	0.444131i	$-0.853512\pi$
$859$	−52.5190	−1.79192	−0.895962	+	0.444131i	$0.853512\pi$
$860$	−4.87818	−0.166344
$861$	−1.96847	−0.0670852
$862$	28.4045	0.967462
$863$	−14.3763	−0.489374	−0.244687	−	0.969602i	$-0.578685\pi$
$863$	−14.3763	−0.489374	−0.244687	+	0.969602i	$0.578685\pi$
$864$	1.00000	0.0340207
$865$	−4.35863	−0.148198
$866$	−13.4351	−0.456543
$867$	1.00000	0.0339618
$868$	−5.16647	−0.175361
$869$	−5.77889	−0.196035
$870$	−4.98218	−0.168912
$871$	−8.56373	−0.290171
$872$	16.8890	0.571932
$873$	4.98184	0.168610
$874$	−29.0086	−0.981231
$875$	−5.38779	−0.182141
$876$	−9.45028	−0.319295
$877$	6.85965	0.231634	0.115817	−	0.993271i	$-0.463051\pi$
$877$	6.85965	0.231634	0.115817	+	0.993271i	$0.463051\pi$
$878$	28.6839	0.968035
$879$	9.71937	0.327826
$880$	−0.776964	−0.0261915
$881$	−36.6579	−1.23504	−0.617519	−	0.786556i	$-0.711862\pi$
$881$	−36.6579	−1.23504	−0.617519	+	0.786556i	$0.711862\pi$
$882$	1.00000	0.0336718
$883$	3.09629	0.104198	0.0520992	−	0.998642i	$-0.483409\pi$
$883$	3.09629	0.104198	0.0520992	+	0.998642i	$0.483409\pi$
$884$	−1.00000	−0.0336336
$885$	1.11792	0.0375785
$886$	−3.82304	−0.128438
$887$	19.4050	0.651556	0.325778	−	0.945446i	$-0.394374\pi$
$887$	19.4050	0.651556	0.325778	+	0.945446i	$0.394374\pi$
$888$	−8.03658	−0.269690
$889$	−2.21861	−0.0744097
$890$	1.90628	0.0638987
$891$	1.39751	0.0468183
$892$	3.27579	0.109682
$893$	−106.677	−3.56981
$894$	1.01362	0.0339007
$895$	−5.58752	−0.186770
$896$	−1.00000	−0.0334077
$897$	−3.50413	−0.117000
$898$	−32.4276	−1.08212
$899$	46.2985	1.54414
$900$	−4.69090	−0.156363
$901$	7.97925	0.265827
$902$	2.75095	0.0915967
$903$	−8.77427	−0.291989
$904$	7.90144	0.262798
$905$	3.35590	0.111554
$906$	16.2969	0.541429
$907$	−26.5614	−0.881958	−0.440979	−	0.897517i	$-0.645369\pi$
$907$	−26.5614	−0.881958	−0.440979	+	0.897517i	$0.645369\pi$
$908$	−25.9702	−0.861851
$909$	6.67041	0.221244
$910$	−0.555964	−0.0184300
$911$	11.3109	0.374748	0.187374	−	0.982289i	$-0.440002\pi$
$911$	11.3109	0.374748	0.187374	+	0.982289i	$0.440002\pi$
$912$	−8.27840	−0.274125
$913$	3.81459	0.126244
$914$	−14.6627	−0.484999
$915$	4.54770	0.150342
$916$	1.31161	0.0433367
$917$	−4.80737	−0.158753
$918$	1.00000	0.0330049
$919$	40.5295	1.33694	0.668472	−	0.743737i	$-0.266949\pi$
$919$	40.5295	1.33694	0.668472	+	0.743737i	$0.266949\pi$
$920$	−1.94817	−0.0642293
$921$	−14.3152	−0.471701
$922$	37.9688	1.25044
$923$	−9.45730	−0.311291
$924$	−1.39751	−0.0459747
$925$	37.6988	1.23953
$926$	−9.08891	−0.298680
$927$	7.15663	0.235055
$928$	8.96134	0.294170
$929$	30.3706	0.996428	0.498214	−	0.867054i	$-0.333989\pi$
$929$	30.3706	0.996428	0.498214	+	0.867054i	$0.333989\pi$
$930$	−2.87237	−0.0941888
$931$	−8.27840	−0.271314
$932$	14.4214	0.472387
$933$	−23.2866	−0.762369
$934$	40.4413	1.32328
$935$	−0.776964	−0.0254095
$936$	−1.00000	−0.0326860
$937$	35.9504	1.17445	0.587224	−	0.809424i	$-0.300221\pi$
$937$	35.9504	1.17445	0.587224	+	0.809424i	$0.300221\pi$
$938$	−8.56373	−0.279616
$939$	27.2065	0.887850
$940$	−7.16426	−0.233672
$941$	−2.98948	−0.0974542	−0.0487271	−	0.998812i	$-0.515516\pi$
$941$	−2.98948	−0.0974542	−0.0487271	+	0.998812i	$0.515516\pi$
$942$	3.56118	0.116029
$943$	6.89777	0.224622
$944$	−2.01078	−0.0654454
$945$	0.555964	0.0180855
$946$	12.2621	0.398676
$947$	−43.3956	−1.41017	−0.705084	−	0.709124i	$-0.749091\pi$
$947$	−43.3956	−1.41017	−0.705084	+	0.709124i	$0.749091\pi$
$948$	−4.13514	−0.134303
$949$	9.45028	0.306769
$950$	38.8332	1.25991
$951$	6.80426	0.220643
$952$	−1.00000	−0.0324102
$953$	28.6928	0.929450	0.464725	−	0.885455i	$-0.346153\pi$
$953$	28.6928	0.929450	0.464725	+	0.885455i	$0.346153\pi$
$954$	7.97925	0.258338
$955$	5.11495	0.165516
$956$	0.821048	0.0265546
$957$	12.5236	0.404829
$958$	25.6040	0.827229
$959$	−6.84670	−0.221092
$960$	−0.555964	−0.0179437
$961$	−4.30757	−0.138954
$962$	8.03658	0.259110
$963$	0.836437	0.0269538
$964$	20.8247	0.670720
$965$	13.1762	0.424156
$966$	−3.50413	−0.112744
$967$	−33.2363	−1.06881	−0.534404	−	0.845229i	$-0.679464\pi$
$967$	−33.2363	−1.06881	−0.534404	+	0.845229i	$0.679464\pi$
$968$	−9.04697	−0.290781
$969$	−8.27840	−0.265941
$970$	−2.76972	−0.0889305
$971$	43.9614	1.41079	0.705394	−	0.708816i	$-0.250770\pi$
$971$	43.9614	1.41079	0.705394	+	0.708816i	$0.250770\pi$
$972$	1.00000	0.0320750
$973$	−4.28381	−0.137333
$974$	−25.8583	−0.828555
$975$	4.69090	0.150229
$976$	−8.17984	−0.261830
$977$	53.6195	1.71544	0.857720	−	0.514117i	$-0.171880\pi$
$977$	53.6195	1.71544	0.857720	+	0.514117i	$0.171880\pi$
$978$	−15.0760	−0.482077
$979$	−4.79176	−0.153145
$980$	−0.555964	−0.0177596
$981$	16.8890	0.539223
$982$	0.538253	0.0171764
$983$	50.6422	1.61524	0.807618	−	0.589706i	$-0.200756\pi$
$983$	50.6422	1.61524	0.807618	+	0.589706i	$0.200756\pi$
$984$	1.96847	0.0627525
$985$	10.4123	0.331764
$986$	8.96134	0.285387
$987$	−12.8862	−0.410172
$988$	8.27840	0.263371
$989$	30.7462	0.977672
$990$	−0.776964	−0.0246936
$991$	−52.7758	−1.67648	−0.838240	−	0.545302i	$-0.816415\pi$
$991$	−52.7758	−1.67648	−0.838240	+	0.545302i	$0.816415\pi$
$992$	5.16647	0.164036
$993$	−30.6819	−0.973661
$994$	−9.45730	−0.299967
$995$	4.35139	0.137948
$996$	2.72956	0.0864895
$997$	59.0267	1.86939	0.934697	−	0.355446i	$-0.115671\pi$
$997$	59.0267	1.86939	0.934697	+	0.355446i	$0.115671\pi$
$998$	41.3316	1.30833
$999$	−8.03658	−0.254266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.ce.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.ce.1.3	✓	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.555964 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.555964 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.555964 q^{10} +1.39751 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} -0.555964 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -8.27840 q^{19} -0.555964 q^{20} -1.00000 q^{21} +1.39751 q^{22} +3.50413 q^{23} +1.00000 q^{24} -4.69090 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +8.96134 q^{29} -0.555964 q^{30} +5.16647 q^{31} +1.00000 q^{32} +1.39751 q^{33} +1.00000 q^{34} +0.555964 q^{35} +1.00000 q^{36} -8.03658 q^{37} -8.27840 q^{38} -1.00000 q^{39} -0.555964 q^{40} +1.96847 q^{41} -1.00000 q^{42} +8.77427 q^{43} +1.39751 q^{44} -0.555964 q^{45} +3.50413 q^{46} +12.8862 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.69090 q^{50} +1.00000 q^{51} -1.00000 q^{52} +7.97925 q^{53} +1.00000 q^{54} -0.776964 q^{55} -1.00000 q^{56} -8.27840 q^{57} +8.96134 q^{58} -2.01078 q^{59} -0.555964 q^{60} -8.17984 q^{61} +5.16647 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.555964 q^{65} +1.39751 q^{66} +8.56373 q^{67} +1.00000 q^{68} +3.50413 q^{69} +0.555964 q^{70} +9.45730 q^{71} +1.00000 q^{72} -9.45028 q^{73} -8.03658 q^{74} -4.69090 q^{75} -8.27840 q^{76} -1.39751 q^{77} -1.00000 q^{78} -4.13514 q^{79} -0.555964 q^{80} +1.00000 q^{81} +1.96847 q^{82} +2.72956 q^{83} -1.00000 q^{84} -0.555964 q^{85} +8.77427 q^{86} +8.96134 q^{87} +1.39751 q^{88} -3.42879 q^{89} -0.555964 q^{90} +1.00000 q^{91} +3.50413 q^{92} +5.16647 q^{93} +12.8862 q^{94} +4.60249 q^{95} +1.00000 q^{96} +4.98184 q^{97} +1.00000 q^{98} +1.39751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 3 q^{5} + 7 q^{6} - 7 q^{7} + 7 q^{8} + 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 7 q^{13} - 7 q^{14} + 3 q^{15} + 7 q^{16} + 7 q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 7 q^{22} + 12 q^{23} + 7 q^{24} + 20 q^{25} - 7 q^{26} + 7 q^{27} - 7 q^{28} + 18 q^{29} + 3 q^{30} - 6 q^{31} + 7 q^{32} + 7 q^{33} + 7 q^{34} - 3 q^{35} + 7 q^{36} + 5 q^{37} - 2 q^{38} - 7 q^{39} + 3 q^{40} + 10 q^{41} - 7 q^{42} + 18 q^{43} + 7 q^{44} + 3 q^{45} + 12 q^{46} + 3 q^{47} + 7 q^{48} + 7 q^{49} + 20 q^{50} + 7 q^{51} - 7 q^{52} + 18 q^{53} + 7 q^{54} + 4 q^{55} - 7 q^{56} - 2 q^{57} + 18 q^{58} + 20 q^{59} + 3 q^{60} + 19 q^{61} - 6 q^{62} - 7 q^{63} + 7 q^{64} - 3 q^{65} + 7 q^{66} - 16 q^{67} + 7 q^{68} + 12 q^{69} - 3 q^{70} + 5 q^{71} + 7 q^{72} + 2 q^{73} + 5 q^{74} + 20 q^{75} - 2 q^{76} - 7 q^{77} - 7 q^{78} + 12 q^{79} + 3 q^{80} + 7 q^{81} + 10 q^{82} + 11 q^{83} - 7 q^{84} + 3 q^{85} + 18 q^{86} + 18 q^{87} + 7 q^{88} + 6 q^{89} + 3 q^{90} + 7 q^{91} + 12 q^{92} - 6 q^{93} + 3 q^{94} + 35 q^{95} + 7 q^{96} - 3 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 3 * q^5 + 7 * q^6 - 7 * q^7 + 7 * q^8 + 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 7 * q^13 - 7 * q^14 + 3 * q^15 + 7 * q^16 + 7 * q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 7 * q^22 + 12 * q^23 + 7 * q^24 + 20 * q^25 - 7 * q^26 + 7 * q^27 - 7 * q^28 + 18 * q^29 + 3 * q^30 - 6 * q^31 + 7 * q^32 + 7 * q^33 + 7 * q^34 - 3 * q^35 + 7 * q^36 + 5 * q^37 - 2 * q^38 - 7 * q^39 + 3 * q^40 + 10 * q^41 - 7 * q^42 + 18 * q^43 + 7 * q^44 + 3 * q^45 + 12 * q^46 + 3 * q^47 + 7 * q^48 + 7 * q^49 + 20 * q^50 + 7 * q^51 - 7 * q^52 + 18 * q^53 + 7 * q^54 + 4 * q^55 - 7 * q^56 - 2 * q^57 + 18 * q^58 + 20 * q^59 + 3 * q^60 + 19 * q^61 - 6 * q^62 - 7 * q^63 + 7 * q^64 - 3 * q^65 + 7 * q^66 - 16 * q^67 + 7 * q^68 + 12 * q^69 - 3 * q^70 + 5 * q^71 + 7 * q^72 + 2 * q^73 + 5 * q^74 + 20 * q^75 - 2 * q^76 - 7 * q^77 - 7 * q^78 + 12 * q^79 + 3 * q^80 + 7 * q^81 + 10 * q^82 + 11 * q^83 - 7 * q^84 + 3 * q^85 + 18 * q^86 + 18 * q^87 + 7 * q^88 + 6 * q^89 + 3 * q^90 + 7 * q^91 + 12 * q^92 - 6 * q^93 + 3 * q^94 + 35 * q^95 + 7 * q^96 - 3 * q^97 + 7 * q^98 + 7 * q^99

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