LMFDB - Embedded newform 1005.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1005,2,Mod(1,1005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1005 = 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1005.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:	$8.02496540314$
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} - 6x^{5} + 15x^{4} + 14x^{3} - 15x^{2} - 6x + 4 $ x^7 - 3x^6 - 6x^5 + 15x^4 + 14x^3 - 15x^2 - 6x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.67802$ of defining polynomial
Character	$\chi$	$=$	1005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.67802 q^{2} +1.00000 q^{3} +5.17182 q^{4} +1.00000 q^{5} +2.67802 q^{6} -2.93755 q^{7} +8.49420 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67802 q^{2} +1.00000 q^{3} +5.17182 q^{4} +1.00000 q^{5} +2.67802 q^{6} -2.93755 q^{7} +8.49420 q^{8} +1.00000 q^{9} +2.67802 q^{10} -1.71548 q^{11} +5.17182 q^{12} -3.32239 q^{13} -7.86684 q^{14} +1.00000 q^{15} +12.4041 q^{16} +4.08812 q^{17} +2.67802 q^{18} +3.94442 q^{19} +5.17182 q^{20} -2.93755 q^{21} -4.59411 q^{22} -1.28493 q^{23} +8.49420 q^{24} +1.00000 q^{25} -8.89743 q^{26} +1.00000 q^{27} -15.1925 q^{28} -6.22248 q^{29} +2.67802 q^{30} -1.65693 q^{31} +16.2300 q^{32} -1.71548 q^{33} +10.9481 q^{34} -2.93755 q^{35} +5.17182 q^{36} +0.816404 q^{37} +10.5633 q^{38} -3.32239 q^{39} +8.49420 q^{40} -4.01555 q^{41} -7.86684 q^{42} +4.24766 q^{43} -8.87216 q^{44} +1.00000 q^{45} -3.44107 q^{46} -7.68857 q^{47} +12.4041 q^{48} +1.62923 q^{49} +2.67802 q^{50} +4.08812 q^{51} -17.1828 q^{52} -12.5579 q^{53} +2.67802 q^{54} -1.71548 q^{55} -24.9522 q^{56} +3.94442 q^{57} -16.6640 q^{58} +2.41729 q^{59} +5.17182 q^{60} -13.8271 q^{61} -4.43730 q^{62} -2.93755 q^{63} +18.6561 q^{64} -3.32239 q^{65} -4.59411 q^{66} +1.00000 q^{67} +21.1430 q^{68} -1.28493 q^{69} -7.86684 q^{70} +7.62533 q^{71} +8.49420 q^{72} +15.6054 q^{73} +2.18635 q^{74} +1.00000 q^{75} +20.3998 q^{76} +5.03933 q^{77} -8.89743 q^{78} -13.5024 q^{79} +12.4041 q^{80} +1.00000 q^{81} -10.7537 q^{82} +9.15183 q^{83} -15.1925 q^{84} +4.08812 q^{85} +11.3753 q^{86} -6.22248 q^{87} -14.5717 q^{88} -4.23914 q^{89} +2.67802 q^{90} +9.75969 q^{91} -6.64541 q^{92} -1.65693 q^{93} -20.5902 q^{94} +3.94442 q^{95} +16.2300 q^{96} -7.19034 q^{97} +4.36311 q^{98} -1.71548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9} + 4 q^{10} + 5 q^{11} + 8 q^{12} - q^{13} - 4 q^{14} + 7 q^{15} + 6 q^{16} + 11 q^{17} + 4 q^{18} + 8 q^{19} + 8 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} + 9 q^{24} + 7 q^{25} - 5 q^{26} + 7 q^{27} - 17 q^{28} + 4 q^{30} - 3 q^{31} + 22 q^{32} + 5 q^{33} + 4 q^{34} + 3 q^{35} + 8 q^{36} - 5 q^{37} - q^{39} + 9 q^{40} + q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 7 q^{45} - 12 q^{46} + 10 q^{47} + 6 q^{48} - 4 q^{49} + 4 q^{50} + 11 q^{51} - 6 q^{52} + 3 q^{53} + 4 q^{54} + 5 q^{55} - 12 q^{56} + 8 q^{57} - 24 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} + 20 q^{62} + 3 q^{63} - 3 q^{64} - q^{65} - 3 q^{66} + 7 q^{67} - 3 q^{68} + 11 q^{69} - 4 q^{70} + 6 q^{71} + 9 q^{72} - 9 q^{73} + 2 q^{74} + 7 q^{75} + 2 q^{76} + 17 q^{77} - 5 q^{78} - 11 q^{79} + 6 q^{80} + 7 q^{81} - 16 q^{82} + 30 q^{83} - 17 q^{84} + 11 q^{85} - 11 q^{86} - 25 q^{88} + 13 q^{89} + 4 q^{90} - 5 q^{91} + 10 q^{92} - 3 q^{93} - 25 q^{94} + 8 q^{95} + 22 q^{96} - 7 q^{97} - 10 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9 + 4 * q^10 + 5 * q^11 + 8 * q^12 - q^13 - 4 * q^14 + 7 * q^15 + 6 * q^16 + 11 * q^17 + 4 * q^18 + 8 * q^19 + 8 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 + 9 * q^24 + 7 * q^25 - 5 * q^26 + 7 * q^27 - 17 * q^28 + 4 * q^30 - 3 * q^31 + 22 * q^32 + 5 * q^33 + 4 * q^34 + 3 * q^35 + 8 * q^36 - 5 * q^37 - q^39 + 9 * q^40 + q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 7 * q^45 - 12 * q^46 + 10 * q^47 + 6 * q^48 - 4 * q^49 + 4 * q^50 + 11 * q^51 - 6 * q^52 + 3 * q^53 + 4 * q^54 + 5 * q^55 - 12 * q^56 + 8 * q^57 - 24 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 + 20 * q^62 + 3 * q^63 - 3 * q^64 - q^65 - 3 * q^66 + 7 * q^67 - 3 * q^68 + 11 * q^69 - 4 * q^70 + 6 * q^71 + 9 * q^72 - 9 * q^73 + 2 * q^74 + 7 * q^75 + 2 * q^76 + 17 * q^77 - 5 * q^78 - 11 * q^79 + 6 * q^80 + 7 * q^81 - 16 * q^82 + 30 * q^83 - 17 * q^84 + 11 * q^85 - 11 * q^86 - 25 * q^88 + 13 * q^89 + 4 * q^90 - 5 * q^91 + 10 * q^92 - 3 * q^93 - 25 * q^94 + 8 * q^95 + 22 * q^96 - 7 * q^97 - 10 * q^98 + 5 * 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 $

$2$	2.67802	1.89365	0.946825	−	0.321750i	$-0.104271\pi$
$2$	2.67802	1.89365	0.946825	+	0.321750i	$0.104271\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.17182	2.58591
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.67802	1.09330
$7$	−2.93755	−1.11029	−0.555146	−	0.831753i	$-0.687337\pi$
$7$	−2.93755	−1.11029	−0.555146	+	0.831753i	$0.687337\pi$
$8$	8.49420	3.00315
$9$	1.00000	0.333333
$10$	2.67802	0.846866
$11$	−1.71548	−0.517238	−0.258619	−	0.965979i	$-0.583267\pi$
$11$	−1.71548	−0.517238	−0.258619	+	0.965979i	$0.583267\pi$
$12$	5.17182	1.49297
$13$	−3.32239	−0.921464	−0.460732	−	0.887539i	$-0.652413\pi$
$13$	−3.32239	−0.921464	−0.460732	+	0.887539i	$0.652413\pi$
$14$	−7.86684	−2.10250
$15$	1.00000	0.258199
$16$	12.4041	3.10101
$17$	4.08812	0.991516	0.495758	−	0.868461i	$-0.334890\pi$
$17$	4.08812	0.991516	0.495758	+	0.868461i	$0.334890\pi$
$18$	2.67802	0.631216
$19$	3.94442	0.904913	0.452457	−	0.891786i	$-0.350548\pi$
$19$	3.94442	0.904913	0.452457	+	0.891786i	$0.350548\pi$
$20$	5.17182	1.15645
$21$	−2.93755	−0.641027
$22$	−4.59411	−0.979467
$23$	−1.28493	−0.267926	−0.133963	−	0.990986i	$-0.542770\pi$
$23$	−1.28493	−0.267926	−0.133963	+	0.990986i	$0.542770\pi$
$24$	8.49420	1.73387
$25$	1.00000	0.200000
$26$	−8.89743	−1.74493
$27$	1.00000	0.192450
$28$	−15.1925	−2.87111
$29$	−6.22248	−1.15549	−0.577743	−	0.816219i	$-0.696066\pi$
$29$	−6.22248	−1.15549	−0.577743	+	0.816219i	$0.696066\pi$
$30$	2.67802	0.488938
$31$	−1.65693	−0.297594	−0.148797	−	0.988868i	$-0.547540\pi$
$31$	−1.65693	−0.297594	−0.148797	+	0.988868i	$0.547540\pi$
$32$	16.2300	2.86908
$33$	−1.71548	−0.298627
$34$	10.9481	1.87758
$35$	−2.93755	−0.496537
$36$	5.17182	0.861969
$37$	0.816404	0.134216	0.0671080	−	0.997746i	$-0.478623\pi$
$37$	0.816404	0.134216	0.0671080	+	0.997746i	$0.478623\pi$
$38$	10.5633	1.71359
$39$	−3.32239	−0.532008
$40$	8.49420	1.34305
$41$	−4.01555	−0.627123	−0.313561	−	0.949568i	$-0.601522\pi$
$41$	−4.01555	−0.627123	−0.313561	+	0.949568i	$0.601522\pi$
$42$	−7.86684	−1.21388
$43$	4.24766	0.647762	0.323881	−	0.946098i	$-0.395012\pi$
$43$	4.24766	0.647762	0.323881	+	0.946098i	$0.395012\pi$
$44$	−8.87216	−1.33753
$45$	1.00000	0.149071
$46$	−3.44107	−0.507358
$47$	−7.68857	−1.12149	−0.560746	−	0.827988i	$-0.689486\pi$
$47$	−7.68857	−1.12149	−0.560746	+	0.827988i	$0.689486\pi$
$48$	12.4041	1.79037
$49$	1.62923	0.232747
$50$	2.67802	0.378730
$51$	4.08812	0.572452
$52$	−17.1828	−2.38282
$53$	−12.5579	−1.72496	−0.862479	−	0.506093i	$-0.831089\pi$
$53$	−12.5579	−1.72496	−0.862479	+	0.506093i	$0.831089\pi$
$54$	2.67802	0.364433
$55$	−1.71548	−0.231316
$56$	−24.9522	−3.33438
$57$	3.94442	0.522452
$58$	−16.6640	−2.18809
$59$	2.41729	0.314704	0.157352	−	0.987543i	$-0.449704\pi$
$59$	2.41729	0.314704	0.157352	+	0.987543i	$0.449704\pi$
$60$	5.17182	0.667679
$61$	−13.8271	−1.77038	−0.885189	−	0.465231i	$-0.845971\pi$
$61$	−13.8271	−1.77038	−0.885189	+	0.465231i	$0.845971\pi$
$62$	−4.43730	−0.563538
$63$	−2.93755	−0.370097
$64$	18.6561	2.33201
$65$	−3.32239	−0.412091
$66$	−4.59411	−0.565495
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	21.1430	2.56397
$69$	−1.28493	−0.154687
$70$	−7.86684	−0.940268
$71$	7.62533	0.904960	0.452480	−	0.891774i	$-0.350539\pi$
$71$	7.62533	0.904960	0.452480	+	0.891774i	$0.350539\pi$
$72$	8.49420	1.00105
$73$	15.6054	1.82648	0.913239	−	0.407424i	$-0.133573\pi$
$73$	15.6054	1.82648	0.913239	+	0.407424i	$0.133573\pi$
$74$	2.18635	0.254158
$75$	1.00000	0.115470
$76$	20.3998	2.34002
$77$	5.03933	0.574284
$78$	−8.89743	−1.00744
$79$	−13.5024	−1.51914	−0.759570	−	0.650426i	$-0.774590\pi$
$79$	−13.5024	−1.51914	−0.759570	+	0.650426i	$0.774590\pi$
$80$	12.4041	1.38682
$81$	1.00000	0.111111
$82$	−10.7537	−1.18755
$83$	9.15183	1.00454	0.502272	−	0.864710i	$-0.332498\pi$
$83$	9.15183	1.00454	0.502272	+	0.864710i	$0.332498\pi$
$84$	−15.1925	−1.65764
$85$	4.08812	0.443419
$86$	11.3753	1.22663
$87$	−6.22248	−0.667120
$88$	−14.5717	−1.55334
$89$	−4.23914	−0.449348	−0.224674	−	0.974434i	$-0.572132\pi$
$89$	−4.23914	−0.449348	−0.224674	+	0.974434i	$0.572132\pi$
$90$	2.67802	0.282289
$91$	9.75969	1.02309
$92$	−6.64541	−0.692832
$93$	−1.65693	−0.171816
$94$	−20.5902	−2.12371
$95$	3.94442	0.404689
$96$	16.2300	1.65646
$97$	−7.19034	−0.730069	−0.365034	−	0.930994i	$-0.618943\pi$
$97$	−7.19034	−0.730069	−0.365034	+	0.930994i	$0.618943\pi$
$98$	4.36311	0.440740
$99$	−1.71548	−0.172413
$100$	5.17182	0.517182
$101$	6.22093	0.619006	0.309503	−	0.950898i	$-0.399837\pi$
$101$	6.22093	0.619006	0.309503	+	0.950898i	$0.399837\pi$
$102$	10.9481	1.08402
$103$	12.3039	1.21234	0.606169	−	0.795336i	$-0.292705\pi$
$103$	12.3039	1.21234	0.606169	+	0.795336i	$0.292705\pi$
$104$	−28.2210	−2.76730
$105$	−2.93755	−0.286676
$106$	−33.6303	−3.26647
$107$	18.6337	1.80139	0.900694	−	0.434453i	$-0.143058\pi$
$107$	18.6337	1.80139	0.900694	+	0.434453i	$0.143058\pi$
$108$	5.17182	0.497658
$109$	−3.12201	−0.299035	−0.149517	−	0.988759i	$-0.547772\pi$
$109$	−3.12201	−0.299035	−0.149517	+	0.988759i	$0.547772\pi$
$110$	−4.59411	−0.438031
$111$	0.816404	0.0774896
$112$	−36.4376	−3.44303
$113$	14.9635	1.40765	0.703825	−	0.710374i	$-0.251474\pi$
$113$	14.9635	1.40765	0.703825	+	0.710374i	$0.251474\pi$
$114$	10.5633	0.989340
$115$	−1.28493	−0.119820
$116$	−32.1815	−2.98798
$117$	−3.32239	−0.307155
$118$	6.47355	0.595939
$119$	−12.0091	−1.10087
$120$	8.49420	0.775411
$121$	−8.05712	−0.732465
$122$	−37.0293	−3.35248
$123$	−4.01555	−0.362070
$124$	−8.56935	−0.769550
$125$	1.00000	0.0894427
$126$	−7.86684	−0.700834
$127$	8.49151	0.753499	0.376750	−	0.926315i	$-0.377042\pi$
$127$	8.49151	0.753499	0.376750	+	0.926315i	$0.377042\pi$
$128$	17.5016	1.54694
$129$	4.24766	0.373985
$130$	−8.89743	−0.780356
$131$	17.3874	1.51914	0.759572	−	0.650424i	$-0.225409\pi$
$131$	17.3874	1.51914	0.759572	+	0.650424i	$0.225409\pi$
$132$	−8.87216	−0.772223
$133$	−11.5870	−1.00472
$134$	2.67802	0.231346
$135$	1.00000	0.0860663
$136$	34.7254	2.97767
$137$	−10.4138	−0.889711	−0.444856	−	0.895602i	$-0.646745\pi$
$137$	−10.4138	−0.889711	−0.444856	+	0.895602i	$0.646745\pi$
$138$	−3.44107	−0.292923
$139$	−1.76685	−0.149862	−0.0749310	−	0.997189i	$-0.523874\pi$
$139$	−1.76685	−0.149862	−0.0749310	+	0.997189i	$0.523874\pi$
$140$	−15.1925	−1.28400
$141$	−7.68857	−0.647494
$142$	20.4208	1.71368
$143$	5.69950	0.476616
$144$	12.4041	1.03367
$145$	−6.22248	−0.516749
$146$	41.7918	3.45871
$147$	1.62923	0.134376
$148$	4.22229	0.347070
$149$	−8.58033	−0.702928	−0.351464	−	0.936201i	$-0.614316\pi$
$149$	−8.58033	−0.702928	−0.351464	+	0.936201i	$0.614316\pi$
$150$	2.67802	0.218660
$151$	16.7257	1.36112	0.680561	−	0.732692i	$-0.261736\pi$
$151$	16.7257	1.36112	0.680561	+	0.732692i	$0.261736\pi$
$152$	33.5047	2.71759
$153$	4.08812	0.330505
$154$	13.4954	1.08749
$155$	−1.65693	−0.133088
$156$	−17.1828	−1.37572
$157$	23.5429	1.87893	0.939465	−	0.342644i	$-0.111323\pi$
$157$	23.5429	1.87893	0.939465	+	0.342644i	$0.111323\pi$
$158$	−36.1598	−2.87672
$159$	−12.5579	−0.995905
$160$	16.2300	1.28309
$161$	3.77454	0.297476
$162$	2.67802	0.210405
$163$	−2.44795	−0.191738	−0.0958691	−	0.995394i	$-0.530563\pi$
$163$	−2.44795	−0.191738	−0.0958691	+	0.995394i	$0.530563\pi$
$164$	−20.7677	−1.62168
$165$	−1.71548	−0.133550
$166$	24.5088	1.90225
$167$	−3.27391	−0.253342	−0.126671	−	0.991945i	$-0.540429\pi$
$167$	−3.27391	−0.253342	−0.126671	+	0.991945i	$0.540429\pi$
$168$	−24.9522	−1.92510
$169$	−1.96175	−0.150904
$170$	10.9481	0.839681
$171$	3.94442	0.301638
$172$	21.9681	1.67505
$173$	8.10304	0.616063	0.308032	−	0.951376i	$-0.400330\pi$
$173$	8.10304	0.616063	0.308032	+	0.951376i	$0.400330\pi$
$174$	−16.6640	−1.26329
$175$	−2.93755	−0.222058
$176$	−21.2789	−1.60396
$177$	2.41729	0.181694
$178$	−11.3525	−0.850908
$179$	−6.23102	−0.465729	−0.232864	−	0.972509i	$-0.574810\pi$
$179$	−6.23102	−0.465729	−0.232864	+	0.972509i	$0.574810\pi$
$180$	5.17182	0.385484
$181$	17.9465	1.33396	0.666978	−	0.745077i	$-0.267587\pi$
$181$	17.9465	1.33396	0.666978	+	0.745077i	$0.267587\pi$
$182$	26.1367	1.93738
$183$	−13.8271	−1.02213
$184$	−10.9144	−0.804623
$185$	0.816404	0.0600232
$186$	−4.43730	−0.325359
$187$	−7.01311	−0.512849
$188$	−39.7639	−2.90008
$189$	−2.93755	−0.213676
$190$	10.5633	0.766340
$191$	25.9356	1.87664	0.938318	−	0.345775i	$-0.112384\pi$
$191$	25.9356	1.87664	0.938318	+	0.345775i	$0.112384\pi$
$192$	18.6561	1.34639
$193$	−21.1578	−1.52297	−0.761485	−	0.648182i	$-0.775530\pi$
$193$	−21.1578	−1.52297	−0.761485	+	0.648182i	$0.775530\pi$
$194$	−19.2559	−1.38249
$195$	−3.32239	−0.237921
$196$	8.42606	0.601861
$197$	−16.2849	−1.16025	−0.580125	−	0.814527i	$-0.696996\pi$
$197$	−16.2849	−1.16025	−0.580125	+	0.814527i	$0.696996\pi$
$198$	−4.59411	−0.326489
$199$	−10.8832	−0.771489	−0.385744	−	0.922606i	$-0.626055\pi$
$199$	−10.8832	−0.771489	−0.385744	+	0.922606i	$0.626055\pi$
$200$	8.49420	0.600631
$201$	1.00000	0.0705346
$202$	16.6598	1.17218
$203$	18.2789	1.28293
$204$	21.1430	1.48031
$205$	−4.01555	−0.280458
$206$	32.9501	2.29574
$207$	−1.28493	−0.0893086
$208$	−41.2110	−2.85747
$209$	−6.76659	−0.468055
$210$	−7.86684	−0.542864
$211$	−14.1129	−0.971571	−0.485785	−	0.874078i	$-0.661466\pi$
$211$	−14.1129	−0.971571	−0.485785	+	0.874078i	$0.661466\pi$
$212$	−64.9471	−4.46058
$213$	7.62533	0.522479
$214$	49.9015	3.41120
$215$	4.24766	0.289688
$216$	8.49420	0.577957
$217$	4.86733	0.330416
$218$	−8.36083	−0.566267
$219$	15.6054	1.05452
$220$	−8.87216	−0.598161
$221$	−13.5823	−0.913646
$222$	2.18635	0.146738
$223$	−8.30108	−0.555881	−0.277941	−	0.960598i	$-0.589652\pi$
$223$	−8.30108	−0.555881	−0.277941	+	0.960598i	$0.589652\pi$
$224$	−47.6764	−3.18551
$225$	1.00000	0.0666667
$226$	40.0727	2.66559
$227$	4.80453	0.318888	0.159444	−	0.987207i	$-0.449030\pi$
$227$	4.80453	0.318888	0.159444	+	0.987207i	$0.449030\pi$
$228$	20.3998	1.35101
$229$	15.0700	0.995852	0.497926	−	0.867220i	$-0.334095\pi$
$229$	15.0700	0.995852	0.497926	+	0.867220i	$0.334095\pi$
$230$	−3.44107	−0.226897
$231$	5.03933	0.331563
$232$	−52.8550	−3.47010
$233$	22.5918	1.48004	0.740019	−	0.672586i	$-0.234816\pi$
$233$	22.5918	1.48004	0.740019	+	0.672586i	$0.234816\pi$
$234$	−8.89743	−0.581643
$235$	−7.68857	−0.501547
$236$	12.5018	0.813795
$237$	−13.5024	−0.877076
$238$	−32.1606	−2.08466
$239$	−5.34326	−0.345626	−0.172813	−	0.984955i	$-0.555286\pi$
$239$	−5.34326	−0.345626	−0.172813	+	0.984955i	$0.555286\pi$
$240$	12.4041	0.800678
$241$	−3.95333	−0.254656	−0.127328	−	0.991861i	$-0.540640\pi$
$241$	−3.95333	−0.254656	−0.127328	+	0.991861i	$0.540640\pi$
$242$	−21.5772	−1.38703
$243$	1.00000	0.0641500
$244$	−71.5112	−4.57804
$245$	1.62923	0.104087
$246$	−10.7537	−0.685633
$247$	−13.1049	−0.833845
$248$	−14.0743	−0.893720
$249$	9.15183	0.579974
$250$	2.67802	0.169373
$251$	10.0497	0.634333	0.317166	−	0.948370i	$-0.397269\pi$
$251$	10.0497	0.634333	0.317166	+	0.948370i	$0.397269\pi$
$252$	−15.1925	−0.957037
$253$	2.20427	0.138581
$254$	22.7405	1.42686
$255$	4.08812	0.256008
$256$	9.55753	0.597346
$257$	−12.8152	−0.799392	−0.399696	−	0.916648i	$-0.630884\pi$
$257$	−12.8152	−0.799392	−0.399696	+	0.916648i	$0.630884\pi$
$258$	11.3753	0.708197
$259$	−2.39823	−0.149019
$260$	−17.1828	−1.06563
$261$	−6.22248	−0.385162
$262$	46.5639	2.87673
$263$	8.19776	0.505495	0.252748	−	0.967532i	$-0.418666\pi$
$263$	8.19776	0.505495	0.252748	+	0.967532i	$0.418666\pi$
$264$	−14.5717	−0.896824
$265$	−12.5579	−0.771425
$266$	−31.0302	−1.90258
$267$	−4.23914	−0.259431
$268$	5.17182	0.315919
$269$	−4.69407	−0.286203	−0.143101	−	0.989708i	$-0.545707\pi$
$269$	−4.69407	−0.286203	−0.143101	+	0.989708i	$0.545707\pi$
$270$	2.67802	0.162979
$271$	30.8826	1.87598	0.937991	−	0.346659i	$-0.112684\pi$
$271$	30.8826	1.87598	0.937991	+	0.346659i	$0.112684\pi$
$272$	50.7093	3.07470
$273$	9.75969	0.590683
$274$	−27.8884	−1.68480
$275$	−1.71548	−0.103448
$276$	−6.64541	−0.400007
$277$	−28.9141	−1.73728	−0.868639	−	0.495446i	$-0.835005\pi$
$277$	−28.9141	−1.73728	−0.868639	+	0.495446i	$0.835005\pi$
$278$	−4.73166	−0.283786
$279$	−1.65693	−0.0991979
$280$	−24.9522	−1.49118
$281$	8.20399	0.489409	0.244704	−	0.969598i	$-0.421309\pi$
$281$	8.20399	0.489409	0.244704	+	0.969598i	$0.421309\pi$
$282$	−20.5902	−1.22613
$283$	5.78294	0.343760	0.171880	−	0.985118i	$-0.445016\pi$
$283$	5.78294	0.343760	0.171880	+	0.985118i	$0.445016\pi$
$284$	39.4368	2.34014
$285$	3.94442	0.233648
$286$	15.2634	0.902543
$287$	11.7959	0.696289
$288$	16.2300	0.956359
$289$	−0.287241	−0.0168965
$290$	−16.6640	−0.978541
$291$	−7.19034	−0.421505
$292$	80.7085	4.72311
$293$	26.8384	1.56791	0.783957	−	0.620815i	$-0.213198\pi$
$293$	26.8384	1.56791	0.783957	+	0.620815i	$0.213198\pi$
$294$	4.36311	0.254462
$295$	2.41729	0.140740
$296$	6.93470	0.403071
$297$	−1.71548	−0.0995424
$298$	−22.9783	−1.33110
$299$	4.26903	0.246884
$300$	5.17182	0.298595
$301$	−12.4777	−0.719204
$302$	44.7919	2.57749
$303$	6.22093	0.357383
$304$	48.9268	2.80615
$305$	−13.8271	−0.791737
$306$	10.9481	0.625861
$307$	1.37245	0.0783301	0.0391650	−	0.999233i	$-0.487530\pi$
$307$	1.37245	0.0783301	0.0391650	+	0.999233i	$0.487530\pi$
$308$	26.0625	1.48505
$309$	12.3039	0.699944
$310$	−4.43730	−0.252022
$311$	−26.5753	−1.50695	−0.753474	−	0.657478i	$-0.771623\pi$
$311$	−26.5753	−1.50695	−0.753474	+	0.657478i	$0.771623\pi$
$312$	−28.2210	−1.59770
$313$	−23.9168	−1.35186	−0.675929	−	0.736967i	$-0.736257\pi$
$313$	−23.9168	−1.35186	−0.675929	+	0.736967i	$0.736257\pi$
$314$	63.0486	3.55804
$315$	−2.93755	−0.165512
$316$	−69.8320	−3.92835
$317$	12.0685	0.677836	0.338918	−	0.940816i	$-0.389939\pi$
$317$	12.0685	0.677836	0.338918	+	0.940816i	$0.389939\pi$
$318$	−33.6303	−1.88589
$319$	10.6746	0.597661
$320$	18.6561	1.04291
$321$	18.6337	1.04003
$322$	10.1083	0.563315
$323$	16.1253	0.897235
$324$	5.17182	0.287323
$325$	−3.32239	−0.184293
$326$	−6.55567	−0.363085
$327$	−3.12201	−0.172648
$328$	−34.1089	−1.88335
$329$	22.5856	1.24518
$330$	−4.59411	−0.252897
$331$	−20.4573	−1.12444	−0.562218	−	0.826989i	$-0.690052\pi$
$331$	−20.4573	−1.12444	−0.562218	+	0.826989i	$0.690052\pi$
$332$	47.3316	2.59766
$333$	0.816404	0.0447386
$334$	−8.76760	−0.479742
$335$	1.00000	0.0546358
$336$	−36.4376	−1.98783
$337$	−16.9672	−0.924261	−0.462131	−	0.886812i	$-0.652915\pi$
$337$	−16.9672	−0.924261	−0.462131	+	0.886812i	$0.652915\pi$
$338$	−5.25362	−0.285759
$339$	14.9635	0.812707
$340$	21.1430	1.14664
$341$	2.84244	0.153927
$342$	10.5633	0.571196
$343$	15.7769	0.851875
$344$	36.0805	1.94533
$345$	−1.28493	−0.0691782
$346$	21.7002	1.16661
$347$	−1.93074	−0.103648	−0.0518238	−	0.998656i	$-0.516503\pi$
$347$	−1.93074	−0.103648	−0.0518238	+	0.998656i	$0.516503\pi$
$348$	−32.1815	−1.72511
$349$	−5.47085	−0.292848	−0.146424	−	0.989222i	$-0.546776\pi$
$349$	−5.47085	−0.292848	−0.146424	+	0.989222i	$0.546776\pi$
$350$	−7.86684	−0.420500
$351$	−3.32239	−0.177336
$352$	−27.8422	−1.48399
$353$	14.9217	0.794200	0.397100	−	0.917775i	$-0.370017\pi$
$353$	14.9217	0.794200	0.397100	+	0.917775i	$0.370017\pi$
$354$	6.47355	0.344066
$355$	7.62533	0.404711
$356$	−21.9241	−1.16197
$357$	−12.0091	−0.635588
$358$	−16.6868	−0.881927
$359$	−27.5188	−1.45239	−0.726193	−	0.687491i	$-0.758712\pi$
$359$	−27.5188	−1.45239	−0.726193	+	0.687491i	$0.758712\pi$
$360$	8.49420	0.447684
$361$	−3.44152	−0.181132
$362$	48.0613	2.52605
$363$	−8.05712	−0.422889
$364$	50.4753	2.64563
$365$	15.6054	0.816826
$366$	−37.0293	−1.93555
$367$	−24.7563	−1.29227	−0.646135	−	0.763223i	$-0.723616\pi$
$367$	−24.7563	−1.29227	−0.646135	+	0.763223i	$0.723616\pi$
$368$	−15.9383	−0.830842
$369$	−4.01555	−0.209041
$370$	2.18635	0.113663
$371$	36.8895	1.91521
$372$	−8.56935	−0.444300
$373$	−23.3059	−1.20673	−0.603366	−	0.797465i	$-0.706174\pi$
$373$	−23.3059	−1.20673	−0.603366	+	0.797465i	$0.706174\pi$
$374$	−18.7813	−0.971157
$375$	1.00000	0.0516398
$376$	−65.3082	−3.36802
$377$	20.6735	1.06474
$378$	−7.86684	−0.404627
$379$	−29.5945	−1.52017	−0.760085	−	0.649824i	$-0.774843\pi$
$379$	−29.5945	−1.52017	−0.760085	+	0.649824i	$0.774843\pi$
$380$	20.3998	1.04649
$381$	8.49151	0.435033
$382$	69.4562	3.55369
$383$	20.1023	1.02718	0.513590	−	0.858036i	$-0.328315\pi$
$383$	20.1023	1.02718	0.513590	+	0.858036i	$0.328315\pi$
$384$	17.5016	0.893125
$385$	5.03933	0.256828
$386$	−56.6611	−2.88397
$387$	4.24766	0.215921
$388$	−37.1871	−1.88789
$389$	38.9487	1.97478	0.987388	−	0.158321i	$-0.0506081\pi$
$389$	38.9487	1.97478	0.987388	+	0.158321i	$0.0506081\pi$
$390$	−8.89743	−0.450539
$391$	−5.25294	−0.265653
$392$	13.8390	0.698974
$393$	17.3874	0.877078
$394$	−43.6113	−2.19711
$395$	−13.5024	−0.679380
$396$	−8.87216	−0.445843
$397$	−7.23673	−0.363201	−0.181601	−	0.983372i	$-0.558128\pi$
$397$	−7.23673	−0.363201	−0.181601	+	0.983372i	$0.558128\pi$
$398$	−29.1454	−1.46093
$399$	−11.5870	−0.580074
$400$	12.4041	0.620203
$401$	16.1117	0.804578	0.402289	−	0.915513i	$-0.368215\pi$
$401$	16.1117	0.804578	0.402289	+	0.915513i	$0.368215\pi$
$402$	2.67802	0.133568
$403$	5.50497	0.274222
$404$	32.1735	1.60069
$405$	1.00000	0.0496904
$406$	48.9513	2.42941
$407$	−1.40053	−0.0694215
$408$	34.7254	1.71916
$409$	−6.12555	−0.302889	−0.151445	−	0.988466i	$-0.548393\pi$
$409$	−6.12555	−0.302889	−0.151445	+	0.988466i	$0.548393\pi$
$410$	−10.7537	−0.531089
$411$	−10.4138	−0.513675
$412$	63.6335	3.13500
$413$	−7.10091	−0.349413
$414$	−3.44107	−0.169119
$415$	9.15183	0.449246
$416$	−53.9222	−2.64375
$417$	−1.76685	−0.0865228
$418$	−18.1211	−0.886332
$419$	19.7767	0.966156	0.483078	−	0.875577i	$-0.339519\pi$
$419$	19.7767	0.966156	0.483078	+	0.875577i	$0.339519\pi$
$420$	−15.1925	−0.741318
$421$	3.09670	0.150924	0.0754619	−	0.997149i	$-0.475957\pi$
$421$	3.09670	0.150924	0.0754619	+	0.997149i	$0.475957\pi$
$422$	−37.7946	−1.83981
$423$	−7.68857	−0.373831
$424$	−106.669	−5.18031
$425$	4.08812	0.198303
$426$	20.4208	0.989392
$427$	40.6179	1.96564
$428$	96.3701	4.65823
$429$	5.69950	0.275174
$430$	11.3753	0.548567
$431$	−14.2396	−0.685896	−0.342948	−	0.939354i	$-0.611425\pi$
$431$	−14.2396	−0.685896	−0.342948	+	0.939354i	$0.611425\pi$
$432$	12.4041	0.596790
$433$	33.0204	1.58686	0.793428	−	0.608664i	$-0.208294\pi$
$433$	33.0204	1.58686	0.793428	+	0.608664i	$0.208294\pi$
$434$	13.0348	0.625691
$435$	−6.22248	−0.298345
$436$	−16.1465	−0.773276
$437$	−5.06830	−0.242450
$438$	41.7918	1.99689
$439$	26.7281	1.27566	0.637832	−	0.770175i	$-0.279831\pi$
$439$	26.7281	1.27566	0.637832	+	0.770175i	$0.279831\pi$
$440$	−14.5717	−0.694677
$441$	1.62923	0.0775822
$442$	−36.3738	−1.73013
$443$	−3.44565	−0.163708	−0.0818539	−	0.996644i	$-0.526084\pi$
$443$	−3.44565	−0.163708	−0.0818539	+	0.996644i	$0.526084\pi$
$444$	4.22229	0.200381
$445$	−4.23914	−0.200955
$446$	−22.2305	−1.05264
$447$	−8.58033	−0.405836
$448$	−54.8033	−2.58921
$449$	6.75694	0.318880	0.159440	−	0.987208i	$-0.449031\pi$
$449$	6.75694	0.318880	0.159440	+	0.987208i	$0.449031\pi$
$450$	2.67802	0.126243
$451$	6.88860	0.324372
$452$	77.3886	3.64005
$453$	16.7257	0.785844
$454$	12.8667	0.603862
$455$	9.75969	0.457541
$456$	33.5047	1.56900
$457$	27.6885	1.29522	0.647608	−	0.761974i	$-0.275770\pi$
$457$	27.6885	1.29522	0.647608	+	0.761974i	$0.275770\pi$
$458$	40.3578	1.88579
$459$	4.08812	0.190817
$460$	−6.64541	−0.309844
$461$	15.0380	0.700389	0.350194	−	0.936677i	$-0.386115\pi$
$461$	15.0380	0.700389	0.350194	+	0.936677i	$0.386115\pi$
$462$	13.4954	0.627865
$463$	−13.2650	−0.616476	−0.308238	−	0.951309i	$-0.599739\pi$
$463$	−13.2650	−0.616476	−0.308238	+	0.951309i	$0.599739\pi$
$464$	−77.1840	−3.58318
$465$	−1.65693	−0.0768384
$466$	60.5014	2.80267
$467$	−17.4982	−0.809718	−0.404859	−	0.914379i	$-0.632679\pi$
$467$	−17.4982	−0.809718	−0.404859	+	0.914379i	$0.632679\pi$
$468$	−17.1828	−0.794274
$469$	−2.93755	−0.135644
$470$	−20.5902	−0.949754
$471$	23.5429	1.08480
$472$	20.5329	0.945104
$473$	−7.28678	−0.335047
$474$	−36.1598	−1.66087
$475$	3.94442	0.180983
$476$	−62.1088	−2.84675
$477$	−12.5579	−0.574986
$478$	−14.3094	−0.654495
$479$	0.729119	0.0333143	0.0166572	−	0.999861i	$-0.494698\pi$
$479$	0.729119	0.0333143	0.0166572	+	0.999861i	$0.494698\pi$
$480$	16.2300	0.740792
$481$	−2.71241	−0.123675
$482$	−10.5871	−0.482229
$483$	3.77454	0.171748
$484$	−41.6699	−1.89409
$485$	−7.19034	−0.326497
$486$	2.67802	0.121478
$487$	22.0260	0.998096	0.499048	−	0.866574i	$-0.333683\pi$
$487$	22.0260	0.998096	0.499048	+	0.866574i	$0.333683\pi$
$488$	−117.450	−5.31672
$489$	−2.44795	−0.110700
$490$	4.36311	0.197105
$491$	−4.03954	−0.182302	−0.0911509	−	0.995837i	$-0.529055\pi$
$491$	−4.03954	−0.182302	−0.0911509	+	0.995837i	$0.529055\pi$
$492$	−20.7677	−0.936279
$493$	−25.4383	−1.14568
$494$	−35.0952	−1.57901
$495$	−1.71548	−0.0771052
$496$	−20.5527	−0.922842
$497$	−22.3998	−1.00477
$498$	24.5088	1.09827
$499$	−39.9303	−1.78752	−0.893762	−	0.448542i	$-0.851944\pi$
$499$	−39.9303	−1.78752	−0.893762	+	0.448542i	$0.851944\pi$
$500$	5.17182	0.231291
$501$	−3.27391	−0.146267
$502$	26.9134	1.20120
$503$	−12.7228	−0.567281	−0.283640	−	0.958931i	$-0.591542\pi$
$503$	−12.7228	−0.567281	−0.283640	+	0.958931i	$0.591542\pi$
$504$	−24.9522	−1.11146
$505$	6.22093	0.276828
$506$	5.90309	0.262425
$507$	−1.96175	−0.0871244
$508$	43.9165	1.94848
$509$	−33.4517	−1.48272	−0.741360	−	0.671107i	$-0.765819\pi$
$509$	−33.4517	−1.48272	−0.741360	+	0.671107i	$0.765819\pi$
$510$	10.9481	0.484790
$511$	−45.8418	−2.02792
$512$	−9.40791	−0.415775
$513$	3.94442	0.174151
$514$	−34.3195	−1.51377
$515$	12.3039	0.542174
$516$	21.9681	0.967092
$517$	13.1896	0.580078
$518$	−6.42252	−0.282189
$519$	8.10304	0.355684
$520$	−28.2210	−1.23757
$521$	−10.5574	−0.462527	−0.231264	−	0.972891i	$-0.574286\pi$
$521$	−10.5574	−0.462527	−0.231264	+	0.972891i	$0.574286\pi$
$522$	−16.6640	−0.729362
$523$	−1.26165	−0.0551680	−0.0275840	−	0.999619i	$-0.508781\pi$
$523$	−1.26165	−0.0551680	−0.0275840	+	0.999619i	$0.508781\pi$
$524$	89.9244	3.92837
$525$	−2.93755	−0.128205
$526$	21.9538	0.957231
$527$	−6.77374	−0.295069
$528$	−21.2789	−0.926047
$529$	−21.3490	−0.928216
$530$	−33.6303	−1.46081
$531$	2.41729	0.104901
$532$	−59.9256	−2.59811
$533$	13.3412	0.577871
$534$	−11.3525	−0.491272
$535$	18.6337	0.805606
$536$	8.49420	0.366894
$537$	−6.23102	−0.268888
$538$	−12.5708	−0.541968
$539$	−2.79491	−0.120385
$540$	5.17182	0.222560
$541$	−29.1980	−1.25532	−0.627660	−	0.778488i	$-0.715987\pi$
$541$	−29.1980	−1.25532	−0.627660	+	0.778488i	$0.715987\pi$
$542$	82.7043	3.55245
$543$	17.9465	0.770160
$544$	66.3501	2.84473
$545$	−3.12201	−0.133732
$546$	26.1367	1.11855
$547$	32.1623	1.37516	0.687580	−	0.726109i	$-0.258673\pi$
$547$	32.1623	1.37516	0.687580	+	0.726109i	$0.258673\pi$
$548$	−53.8583	−2.30071
$549$	−13.8271	−0.590126
$550$	−4.59411	−0.195893
$551$	−24.5441	−1.04561
$552$	−10.9144	−0.464549
$553$	39.6641	1.68669
$554$	−77.4326	−3.28979
$555$	0.816404	0.0346544
$556$	−9.13780	−0.387529
$557$	34.1182	1.44564	0.722818	−	0.691039i	$-0.242847\pi$
$557$	34.1182	1.44564	0.722818	+	0.691039i	$0.242847\pi$
$558$	−4.43730	−0.187846
$559$	−14.1124	−0.596889
$560$	−36.4376	−1.53977
$561$	−7.01311	−0.296094
$562$	21.9705	0.926769
$563$	39.6874	1.67262	0.836312	−	0.548253i	$-0.184707\pi$
$563$	39.6874	1.67262	0.836312	+	0.548253i	$0.184707\pi$
$564$	−39.7639	−1.67436
$565$	14.9635	0.629520
$566$	15.4868	0.650961
$567$	−2.93755	−0.123366
$568$	64.7711	2.71774
$569$	−3.65190	−0.153096	−0.0765479	−	0.997066i	$-0.524390\pi$
$569$	−3.65190	−0.153096	−0.0765479	+	0.997066i	$0.524390\pi$
$570$	10.5633	0.442447
$571$	−8.83791	−0.369855	−0.184927	−	0.982752i	$-0.559205\pi$
$571$	−8.83791	−0.369855	−0.184927	+	0.982752i	$0.559205\pi$
$572$	29.4768	1.23248
$573$	25.9356	1.08348
$574$	31.5897	1.31853
$575$	−1.28493	−0.0535852
$576$	18.6561	0.777338
$577$	−4.88707	−0.203451	−0.101726	−	0.994812i	$-0.532436\pi$
$577$	−4.88707	−0.203451	−0.101726	+	0.994812i	$0.532436\pi$
$578$	−0.769239	−0.0319961
$579$	−21.1578	−0.879288
$580$	−32.1815	−1.33627
$581$	−26.8840	−1.11534
$582$	−19.2559	−0.798184
$583$	21.5428	0.892213
$584$	132.556	5.48520
$585$	−3.32239	−0.137364
$586$	71.8738	2.96908
$587$	−40.3399	−1.66500	−0.832502	−	0.554022i	$-0.813092\pi$
$587$	−40.3399	−1.66500	−0.832502	+	0.554022i	$0.813092\pi$
$588$	8.42606	0.347485
$589$	−6.53564	−0.269296
$590$	6.47355	0.266512
$591$	−16.2849	−0.669871
$592$	10.1267	0.416205
$593$	0.00336085	0.000138014 0	6.90068e−5	−	1.00000i	$-0.499978\pi$
$593$	0.00336085	0.000138014 0	6.90068e−5		1.00000i	$0.499978\pi$
$594$	−4.59411	−0.188498
$595$	−12.0091	−0.492325
$596$	−44.3759	−1.81771
$597$	−10.8832	−0.445419
$598$	11.4326	0.467512
$599$	−14.4315	−0.589654	−0.294827	−	0.955551i	$-0.595262\pi$
$599$	−14.4315	−0.589654	−0.294827	+	0.955551i	$0.595262\pi$
$600$	8.49420	0.346774
$601$	−13.0069	−0.530564	−0.265282	−	0.964171i	$-0.585465\pi$
$601$	−13.0069	−0.530564	−0.265282	+	0.964171i	$0.585465\pi$
$602$	−33.4156	−1.36192
$603$	1.00000	0.0407231
$604$	86.5025	3.51973
$605$	−8.05712	−0.327568
$606$	16.6598	0.676759
$607$	5.78556	0.234829	0.117414	−	0.993083i	$-0.462539\pi$
$607$	5.78556	0.234829	0.117414	+	0.993083i	$0.462539\pi$
$608$	64.0178	2.59627
$609$	18.2789	0.740698
$610$	−37.0293	−1.49927
$611$	25.5444	1.03342
$612$	21.1430	0.854656
$613$	−38.7419	−1.56477	−0.782386	−	0.622794i	$-0.785998\pi$
$613$	−38.7419	−1.56477	−0.782386	+	0.622794i	$0.785998\pi$
$614$	3.67546	0.148330
$615$	−4.01555	−0.161922
$616$	42.8050	1.72466
$617$	28.7393	1.15700	0.578501	−	0.815682i	$-0.303638\pi$
$617$	28.7393	1.15700	0.578501	+	0.815682i	$0.303638\pi$
$618$	32.9501	1.32545
$619$	−39.0204	−1.56836	−0.784181	−	0.620533i	$-0.786916\pi$
$619$	−39.0204	−1.56836	−0.784181	+	0.620533i	$0.786916\pi$
$620$	−8.56935	−0.344153
$621$	−1.28493	−0.0515624
$622$	−71.1694	−2.85363
$623$	12.4527	0.498907
$624$	−41.2110	−1.64976
$625$	1.00000	0.0400000
$626$	−64.0498	−2.55994
$627$	−6.76659	−0.270232
$628$	121.760	4.85874
$629$	3.33756	0.133077
$630$	−7.86684	−0.313423
$631$	21.3961	0.851764	0.425882	−	0.904779i	$-0.359964\pi$
$631$	21.3961	0.851764	0.425882	+	0.904779i	$0.359964\pi$
$632$	−114.692	−4.56221
$633$	−14.1129	−0.560937
$634$	32.3198	1.28358
$635$	8.49151	0.336975
$636$	−64.9471	−2.57532
$637$	−5.41292	−0.214468
$638$	28.5867	1.13176
$639$	7.62533	0.301653
$640$	17.5016	0.691812
$641$	−39.7885	−1.57155	−0.785775	−	0.618513i	$-0.787736\pi$
$641$	−39.7885	−1.57155	−0.785775	+	0.618513i	$0.787736\pi$
$642$	49.9015	1.96946
$643$	36.8386	1.45277	0.726386	−	0.687287i	$-0.241198\pi$
$643$	36.8386	1.45277	0.726386	+	0.687287i	$0.241198\pi$
$644$	19.5213	0.769245
$645$	4.24766	0.167251
$646$	43.1839	1.69905
$647$	14.6683	0.576669	0.288334	−	0.957530i	$-0.406899\pi$
$647$	14.6683	0.576669	0.288334	+	0.957530i	$0.406899\pi$
$648$	8.49420	0.333684
$649$	−4.14682	−0.162777
$650$	−8.89743	−0.348986
$651$	4.86733	0.190766
$652$	−12.6603	−0.495817
$653$	−25.0074	−0.978616	−0.489308	−	0.872111i	$-0.662751\pi$
$653$	−25.0074	−0.978616	−0.489308	+	0.872111i	$0.662751\pi$
$654$	−8.36083	−0.326934
$655$	17.3874	0.679382
$656$	−49.8090	−1.94472
$657$	15.6054	0.608826
$658$	60.4848	2.35794
$659$	−20.9641	−0.816645	−0.408322	−	0.912838i	$-0.633886\pi$
$659$	−20.9641	−0.816645	−0.408322	+	0.912838i	$0.633886\pi$
$660$	−8.87216	−0.345349
$661$	−1.24040	−0.0482459	−0.0241229	−	0.999709i	$-0.507679\pi$
$661$	−1.24040	−0.0482459	−0.0241229	+	0.999709i	$0.507679\pi$
$662$	−54.7852	−2.12929
$663$	−13.5823	−0.527494
$664$	77.7375	3.01680
$665$	−11.5870	−0.449323
$666$	2.18635	0.0847193
$667$	7.99544	0.309585
$668$	−16.9320	−0.655120
$669$	−8.30108	−0.320938
$670$	2.67802	0.103461
$671$	23.7202	0.915707
$672$	−47.6764	−1.83916
$673$	−22.8502	−0.880809	−0.440405	−	0.897799i	$-0.645165\pi$
$673$	−22.8502	−0.880809	−0.440405	+	0.897799i	$0.645165\pi$
$674$	−45.4385	−1.75023
$675$	1.00000	0.0384900
$676$	−10.1458	−0.390224
$677$	35.4330	1.36180	0.680901	−	0.732376i	$-0.261589\pi$
$677$	35.4330	1.36180	0.680901	+	0.732376i	$0.261589\pi$
$678$	40.0727	1.53898
$679$	21.1220	0.810589
$680$	34.7254	1.33166
$681$	4.80453	0.184110
$682$	7.61212	0.291483
$683$	20.3470	0.778555	0.389278	−	0.921121i	$-0.372725\pi$
$683$	20.3470	0.778555	0.389278	+	0.921121i	$0.372725\pi$
$684$	20.3998	0.780007
$685$	−10.4138	−0.397891
$686$	42.2510	1.61315
$687$	15.0700	0.574955
$688$	52.6881	2.00872
$689$	41.7221	1.58949
$690$	−3.44107	−0.130999
$691$	36.2888	1.38049	0.690246	−	0.723575i	$-0.257502\pi$
$691$	36.2888	1.38049	0.690246	+	0.723575i	$0.257502\pi$
$692$	41.9075	1.59308
$693$	5.03933	0.191428
$694$	−5.17057	−0.196272
$695$	−1.76685	−0.0670203
$696$	−52.8550	−2.00346
$697$	−16.4161	−0.621802
$698$	−14.6511	−0.554551
$699$	22.5918	0.854500
$700$	−15.1925	−0.574222
$701$	34.7845	1.31379	0.656895	−	0.753982i	$-0.271869\pi$
$701$	34.7845	1.31379	0.656895	+	0.753982i	$0.271869\pi$
$702$	−8.89743	−0.335812
$703$	3.22024	0.121454
$704$	−32.0042	−1.20620
$705$	−7.68857	−0.289568
$706$	39.9606	1.50394
$707$	−18.2743	−0.687277
$708$	12.5018	0.469845
$709$	36.0123	1.35247	0.676236	−	0.736685i	$-0.263610\pi$
$709$	36.0123	1.35247	0.676236	+	0.736685i	$0.263610\pi$
$710$	20.4208	0.766380
$711$	−13.5024	−0.506380
$712$	−36.0081	−1.34946
$713$	2.12904	0.0797331
$714$	−32.1606	−1.20358
$715$	5.69950	0.213149
$716$	−32.2257	−1.20433
$717$	−5.34326	−0.199548
$718$	−73.6960	−2.75031
$719$	−24.9530	−0.930590	−0.465295	−	0.885156i	$-0.654052\pi$
$719$	−24.9530	−0.930590	−0.465295	+	0.885156i	$0.654052\pi$
$720$	12.4041	0.462272
$721$	−36.1433	−1.34605
$722$	−9.21647	−0.343001
$723$	−3.95333	−0.147026
$724$	92.8162	3.44949
$725$	−6.22248	−0.231097
$726$	−21.5772	−0.800803
$727$	21.6836	0.804201	0.402100	−	0.915596i	$-0.368280\pi$
$727$	21.6836	0.804201	0.402100	+	0.915596i	$0.368280\pi$
$728$	82.9008	3.07251
$729$	1.00000	0.0370370
$730$	41.7918	1.54678
$731$	17.3649	0.642266
$732$	−71.5112	−2.64313
$733$	24.4842	0.904345	0.452172	−	0.891931i	$-0.350649\pi$
$733$	24.4842	0.904345	0.452172	+	0.891931i	$0.350649\pi$
$734$	−66.2980	−2.44711
$735$	1.62923	0.0600949
$736$	−20.8543	−0.768700
$737$	−1.71548	−0.0631906
$738$	−10.7537	−0.395850
$739$	16.1989	0.595884	0.297942	−	0.954584i	$-0.403700\pi$
$739$	16.1989	0.595884	0.297942	+	0.954584i	$0.403700\pi$
$740$	4.22229	0.155214
$741$	−13.1049	−0.481421
$742$	98.7909	3.62673
$743$	41.1179	1.50847	0.754234	−	0.656605i	$-0.228008\pi$
$743$	41.1179	1.50847	0.754234	+	0.656605i	$0.228008\pi$
$744$	−14.0743	−0.515989
$745$	−8.58033	−0.314359
$746$	−62.4137	−2.28513
$747$	9.15183	0.334848
$748$	−36.2705	−1.32618
$749$	−54.7375	−2.00007
$750$	2.67802	0.0977876
$751$	−13.9897	−0.510492	−0.255246	−	0.966876i	$-0.582157\pi$
$751$	−13.9897	−0.510492	−0.255246	+	0.966876i	$0.582157\pi$
$752$	−95.3694	−3.47776
$753$	10.0497	0.366232
$754$	55.3641	2.01624
$755$	16.7257	0.608712
$756$	−15.1925	−0.552546
$757$	−31.9542	−1.16139	−0.580697	−	0.814120i	$-0.697220\pi$
$757$	−31.9542	−1.16139	−0.580697	+	0.814120i	$0.697220\pi$
$758$	−79.2549	−2.87867
$759$	2.20427	0.0800100
$760$	33.5047	1.21534
$761$	−41.5290	−1.50542	−0.752712	−	0.658349i	$-0.771255\pi$
$761$	−41.5290	−1.50542	−0.752712	+	0.658349i	$0.771255\pi$
$762$	22.7405	0.823800
$763$	9.17109	0.332016
$764$	134.134	4.85281
$765$	4.08812	0.147806
$766$	53.8345	1.94512
$767$	−8.03116	−0.289988
$768$	9.55753	0.344878
$769$	−16.3690	−0.590280	−0.295140	−	0.955454i	$-0.595366\pi$
$769$	−16.3690	−0.590280	−0.295140	+	0.955454i	$0.595366\pi$
$770$	13.4954	0.486342
$771$	−12.8152	−0.461529
$772$	−109.424	−3.93826
$773$	−31.3105	−1.12616	−0.563080	−	0.826402i	$-0.690384\pi$
$773$	−31.3105	−1.12616	−0.563080	+	0.826402i	$0.690384\pi$
$774$	11.3753	0.408878
$775$	−1.65693	−0.0595187
$776$	−61.0762	−2.19251
$777$	−2.39823	−0.0860360
$778$	104.305	3.73953
$779$	−15.8390	−0.567492
$780$	−17.1828	−0.615242
$781$	−13.0811	−0.468080
$782$	−14.0675	−0.503053
$783$	−6.22248	−0.222373
$784$	20.2090	0.721750
$785$	23.5429	0.840283
$786$	46.5639	1.66088
$787$	−9.52277	−0.339450	−0.169725	−	0.985491i	$-0.554288\pi$
$787$	−9.52277	−0.339450	−0.169725	+	0.985491i	$0.554288\pi$
$788$	−84.2224	−3.00030
$789$	8.19776	0.291848
$790$	−36.1598	−1.28651
$791$	−43.9561	−1.56290
$792$	−14.5717	−0.517781
$793$	45.9390	1.63134
$794$	−19.3802	−0.687776
$795$	−12.5579	−0.445382
$796$	−56.2858	−1.99500
$797$	13.3603	0.473245	0.236622	−	0.971602i	$-0.423960\pi$
$797$	13.3603	0.473245	0.236622	+	0.971602i	$0.423960\pi$
$798$	−31.0302	−1.09846
$799$	−31.4318	−1.11198
$800$	16.2300	0.573815
$801$	−4.23914	−0.149783
$802$	43.1475	1.52359
$803$	−26.7709	−0.944723
$804$	5.17182	0.182396
$805$	3.77454	0.133035
$806$	14.7424	0.519280
$807$	−4.69407	−0.165239
$808$	52.8419	1.85897
$809$	50.0231	1.75872	0.879359	−	0.476159i	$-0.157971\pi$
$809$	50.0231	1.75872	0.879359	+	0.476159i	$0.157971\pi$
$810$	2.67802	0.0940962
$811$	−2.88647	−0.101358	−0.0506788	−	0.998715i	$-0.516138\pi$
$811$	−2.88647	−0.101358	−0.0506788	+	0.998715i	$0.516138\pi$
$812$	94.5350	3.31753
$813$	30.8826	1.08310
$814$	−3.75065	−0.131460
$815$	−2.44795	−0.0857479
$816$	50.7093	1.77518
$817$	16.7546	0.586168
$818$	−16.4044	−0.573566
$819$	9.75969	0.341031
$820$	−20.7677	−0.725238
$821$	30.6578	1.06996	0.534982	−	0.844863i	$-0.320318\pi$
$821$	30.6578	1.06996	0.534982	+	0.844863i	$0.320318\pi$
$822$	−27.8884	−0.972720
$823$	−31.9639	−1.11419	−0.557095	−	0.830449i	$-0.688084\pi$
$823$	−31.9639	−1.11419	−0.557095	+	0.830449i	$0.688084\pi$
$824$	104.512	3.64084
$825$	−1.71548	−0.0597255
$826$	−19.0164	−0.661666
$827$	−38.5687	−1.34117	−0.670583	−	0.741835i	$-0.733956\pi$
$827$	−38.5687	−1.34117	−0.670583	+	0.741835i	$0.733956\pi$
$828$	−6.64541	−0.230944
$829$	−3.09182	−0.107383	−0.0536917	−	0.998558i	$-0.517099\pi$
$829$	−3.09182	−0.107383	−0.0536917	+	0.998558i	$0.517099\pi$
$830$	24.5088	0.850714
$831$	−28.9141	−1.00302
$832$	−61.9828	−2.14887
$833$	6.66048	0.230772
$834$	−4.73166	−0.163844
$835$	−3.27391	−0.113298
$836$	−34.9956	−1.21035
$837$	−1.65693	−0.0572719
$838$	52.9626	1.82956
$839$	−18.0696	−0.623833	−0.311917	−	0.950109i	$-0.600971\pi$
$839$	−18.0696	−0.623833	−0.311917	+	0.950109i	$0.600971\pi$
$840$	−24.9522	−0.860932
$841$	9.71928	0.335148
$842$	8.29303	0.285797
$843$	8.20399	0.282560
$844$	−72.9892	−2.51239
$845$	−1.96175	−0.0674863
$846$	−20.5902	−0.707905
$847$	23.6682	0.813250
$848$	−155.769	−5.34912
$849$	5.78294	0.198470
$850$	10.9481	0.375517
$851$	−1.04902	−0.0359599
$852$	39.4368	1.35108
$853$	−41.1426	−1.40870	−0.704348	−	0.709855i	$-0.748760\pi$
$853$	−41.1426	−1.40870	−0.704348	+	0.709855i	$0.748760\pi$
$854$	108.776	3.72223
$855$	3.94442	0.134896
$856$	158.279	5.40985
$857$	34.8300	1.18977	0.594885	−	0.803811i	$-0.297197\pi$
$857$	34.8300	1.18977	0.594885	+	0.803811i	$0.297197\pi$
$858$	15.2634	0.521084
$859$	−9.22679	−0.314814	−0.157407	−	0.987534i	$-0.550313\pi$
$859$	−9.22679	−0.314814	−0.157407	+	0.987534i	$0.550313\pi$
$860$	21.9681	0.749106
$861$	11.7959	0.402003
$862$	−38.1339	−1.29885
$863$	36.3399	1.23703	0.618513	−	0.785774i	$-0.287735\pi$
$863$	36.3399	1.23703	0.618513	+	0.785774i	$0.287735\pi$
$864$	16.2300	0.552154
$865$	8.10304	0.275512
$866$	88.4293	3.00495
$867$	−0.287241	−0.00975522
$868$	25.1729	0.854425
$869$	23.1632	0.785756
$870$	−16.6640	−0.564961
$871$	−3.32239	−0.112575
$872$	−26.5190	−0.898047
$873$	−7.19034	−0.243356
$874$	−13.5730	−0.459115
$875$	−2.93755	−0.0993075
$876$	80.7085	2.72689
$877$	−33.7559	−1.13986	−0.569928	−	0.821695i	$-0.693029\pi$
$877$	−33.7559	−1.13986	−0.569928	+	0.821695i	$0.693029\pi$
$878$	71.5786	2.41566
$879$	26.8384	0.905236
$880$	−21.2789	−0.717313
$881$	2.19718	0.0740250	0.0370125	−	0.999315i	$-0.488216\pi$
$881$	2.19718	0.0740250	0.0370125	+	0.999315i	$0.488216\pi$
$882$	4.36311	0.146913
$883$	0.891116	0.0299884	0.0149942	−	0.999888i	$-0.495227\pi$
$883$	0.891116	0.0299884	0.0149942	+	0.999888i	$0.495227\pi$
$884$	−70.2453	−2.36260
$885$	2.41729	0.0812562
$886$	−9.22754	−0.310005
$887$	6.83153	0.229380	0.114690	−	0.993401i	$-0.463412\pi$
$887$	6.83153	0.229380	0.114690	+	0.993401i	$0.463412\pi$
$888$	6.93470	0.232713
$889$	−24.9443	−0.836604
$890$	−11.3525	−0.380538
$891$	−1.71548	−0.0574708
$892$	−42.9316	−1.43746
$893$	−30.3270	−1.01485
$894$	−22.9783	−0.768511
$895$	−6.23102	−0.208280
$896$	−51.4119	−1.71755
$897$	4.26903	0.142539
$898$	18.0953	0.603847
$899$	10.3102	0.343865
$900$	5.17182	0.172394
$901$	−51.3382	−1.71032
$902$	18.4478	0.614246
$903$	−12.4777	−0.415233
$904$	127.103	4.22739
$905$	17.9465	0.596563
$906$	44.7919	1.48811
$907$	−31.4180	−1.04322	−0.521609	−	0.853185i	$-0.674668\pi$
$907$	−31.4180	−1.04322	−0.521609	+	0.853185i	$0.674668\pi$
$908$	24.8482	0.824616
$909$	6.22093	0.206335
$910$	26.1367	0.866423
$911$	17.5160	0.580332	0.290166	−	0.956976i	$-0.406289\pi$
$911$	17.5160	0.580332	0.290166	+	0.956976i	$0.406289\pi$
$912$	48.9268	1.62013
$913$	−15.6998	−0.519588
$914$	74.1506	2.45268
$915$	−13.8271	−0.457110
$916$	77.9391	2.57518
$917$	−51.0764	−1.68669
$918$	10.9481	0.361341
$919$	5.51226	0.181833	0.0909164	−	0.995859i	$-0.471020\pi$
$919$	5.51226	0.181833	0.0909164	+	0.995859i	$0.471020\pi$
$920$	−10.9144	−0.359838
$921$	1.37245	0.0452239
$922$	40.2721	1.32629
$923$	−25.3343	−0.833889
$924$	26.0625	0.857392
$925$	0.816404	0.0268432
$926$	−35.5239	−1.16739
$927$	12.3039	0.404113
$928$	−100.991	−3.31518
$929$	−52.5559	−1.72430	−0.862151	−	0.506651i	$-0.830883\pi$
$929$	−52.5559	−1.72430	−0.862151	+	0.506651i	$0.830883\pi$
$930$	−4.43730	−0.145505
$931$	6.42636	0.210615
$932$	116.841	3.82724
$933$	−26.5753	−0.870037
$934$	−46.8605	−1.53332
$935$	−7.01311	−0.229353
$936$	−28.2210	−0.922433
$937$	−40.5829	−1.32578	−0.662892	−	0.748715i	$-0.730671\pi$
$937$	−40.5829	−1.32578	−0.662892	+	0.748715i	$0.730671\pi$
$938$	−7.86684	−0.256862
$939$	−23.9168	−0.780495
$940$	−39.7639	−1.29695
$941$	10.3401	0.337076	0.168538	−	0.985695i	$-0.446095\pi$
$941$	10.3401	0.337076	0.168538	+	0.985695i	$0.446095\pi$
$942$	63.0486	2.05423
$943$	5.15969	0.168022
$944$	29.9841	0.975901
$945$	−2.93755	−0.0955587
$946$	−19.5142	−0.634461
$947$	−8.99498	−0.292298	−0.146149	−	0.989263i	$-0.546688\pi$
$947$	−8.99498	−0.292298	−0.146149	+	0.989263i	$0.546688\pi$
$948$	−69.8320	−2.26804
$949$	−51.8473	−1.68303
$950$	10.5633	0.342718
$951$	12.0685	0.391349
$952$	−102.008	−3.30609
$953$	9.15335	0.296506	0.148253	−	0.988949i	$-0.452635\pi$
$953$	9.15335	0.296506	0.148253	+	0.988949i	$0.452635\pi$
$954$	−33.6303	−1.08882
$955$	25.9356	0.839257
$956$	−27.6343	−0.893758
$957$	10.6746	0.345060
$958$	1.95260	0.0630856
$959$	30.5911	0.987839
$960$	18.6561	0.602123
$961$	−28.2546	−0.911438
$962$	−7.26390	−0.234197
$963$	18.6337	0.600463
$964$	−20.4459	−0.658517
$965$	−21.1578	−0.681093
$966$	10.1083	0.325230
$967$	28.3567	0.911889	0.455944	−	0.890008i	$-0.349302\pi$
$967$	28.3567	0.911889	0.455944	+	0.890008i	$0.349302\pi$
$968$	−68.4388	−2.19971
$969$	16.1253	0.518019
$970$	−19.2559	−0.618270
$971$	−45.6039	−1.46350	−0.731749	−	0.681575i	$-0.761296\pi$
$971$	−45.6039	−1.46350	−0.731749	+	0.681575i	$0.761296\pi$
$972$	5.17182	0.165886
$973$	5.19021	0.166390
$974$	58.9863	1.89004
$975$	−3.32239	−0.106402
$976$	−171.512	−5.48997
$977$	−11.7573	−0.376149	−0.188074	−	0.982155i	$-0.560225\pi$
$977$	−11.7573	−0.376149	−0.188074	+	0.982155i	$0.560225\pi$
$978$	−6.55567	−0.209627
$979$	7.27218	0.232420
$980$	8.42606	0.269160
$981$	−3.12201	−0.0996782
$982$	−10.8180	−0.345216
$983$	47.6788	1.52072	0.760359	−	0.649503i	$-0.225023\pi$
$983$	47.6788	1.52072	0.760359	+	0.649503i	$0.225023\pi$
$984$	−34.1089	−1.08735
$985$	−16.2849	−0.518880
$986$	−68.1243	−2.16952
$987$	22.5856	0.718907
$988$	−67.7761	−2.15625
$989$	−5.45793	−0.173552
$990$	−4.59411	−0.146010
$991$	15.9231	0.505812	0.252906	−	0.967491i	$-0.418614\pi$
$991$	15.9231	0.505812	0.252906	+	0.967491i	$0.418614\pi$
$992$	−26.8919	−0.853819
$993$	−20.4573	−0.649193
$994$	−59.9873	−1.90268
$995$	−10.8832	−0.345020
$996$	47.3316	1.49976
$997$	16.9132	0.535646	0.267823	−	0.963468i	$-0.413696\pi$
$997$	16.9132	0.535646	0.267823	+	0.963468i	$0.413696\pi$
$998$	−106.934	−3.38494
$999$	0.816404	0.0258299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1005.2.a.i.1.7	✓	7
3.2	odd	2		3015.2.a.l.1.1		7
5.4	even	2		5025.2.a.bb.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1005.2.a.i.1.7	✓	7	1.1	even	1	trivial
3015.2.a.l.1.1		7	3.2	odd	2
5025.2.a.bb.1.1		7	5.4	even	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:	\( N \)	\(=\)	\( 1005 = 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1005.a (trivial)

\(f(q)\)	\(=\)	\(q+2.67802 q^{2} +1.00000 q^{3} +5.17182 q^{4} +1.00000 q^{5} +2.67802 q^{6} -2.93755 q^{7} +8.49420 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67802 q^{2} +1.00000 q^{3} +5.17182 q^{4} +1.00000 q^{5} +2.67802 q^{6} -2.93755 q^{7} +8.49420 q^{8} +1.00000 q^{9} +2.67802 q^{10} -1.71548 q^{11} +5.17182 q^{12} -3.32239 q^{13} -7.86684 q^{14} +1.00000 q^{15} +12.4041 q^{16} +4.08812 q^{17} +2.67802 q^{18} +3.94442 q^{19} +5.17182 q^{20} -2.93755 q^{21} -4.59411 q^{22} -1.28493 q^{23} +8.49420 q^{24} +1.00000 q^{25} -8.89743 q^{26} +1.00000 q^{27} -15.1925 q^{28} -6.22248 q^{29} +2.67802 q^{30} -1.65693 q^{31} +16.2300 q^{32} -1.71548 q^{33} +10.9481 q^{34} -2.93755 q^{35} +5.17182 q^{36} +0.816404 q^{37} +10.5633 q^{38} -3.32239 q^{39} +8.49420 q^{40} -4.01555 q^{41} -7.86684 q^{42} +4.24766 q^{43} -8.87216 q^{44} +1.00000 q^{45} -3.44107 q^{46} -7.68857 q^{47} +12.4041 q^{48} +1.62923 q^{49} +2.67802 q^{50} +4.08812 q^{51} -17.1828 q^{52} -12.5579 q^{53} +2.67802 q^{54} -1.71548 q^{55} -24.9522 q^{56} +3.94442 q^{57} -16.6640 q^{58} +2.41729 q^{59} +5.17182 q^{60} -13.8271 q^{61} -4.43730 q^{62} -2.93755 q^{63} +18.6561 q^{64} -3.32239 q^{65} -4.59411 q^{66} +1.00000 q^{67} +21.1430 q^{68} -1.28493 q^{69} -7.86684 q^{70} +7.62533 q^{71} +8.49420 q^{72} +15.6054 q^{73} +2.18635 q^{74} +1.00000 q^{75} +20.3998 q^{76} +5.03933 q^{77} -8.89743 q^{78} -13.5024 q^{79} +12.4041 q^{80} +1.00000 q^{81} -10.7537 q^{82} +9.15183 q^{83} -15.1925 q^{84} +4.08812 q^{85} +11.3753 q^{86} -6.22248 q^{87} -14.5717 q^{88} -4.23914 q^{89} +2.67802 q^{90} +9.75969 q^{91} -6.64541 q^{92} -1.65693 q^{93} -20.5902 q^{94} +3.94442 q^{95} +16.2300 q^{96} -7.19034 q^{97} +4.36311 q^{98} -1.71548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9} + 4 q^{10} + 5 q^{11} + 8 q^{12} - q^{13} - 4 q^{14} + 7 q^{15} + 6 q^{16} + 11 q^{17} + 4 q^{18} + 8 q^{19} + 8 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} + 9 q^{24} + 7 q^{25} - 5 q^{26} + 7 q^{27} - 17 q^{28} + 4 q^{30} - 3 q^{31} + 22 q^{32} + 5 q^{33} + 4 q^{34} + 3 q^{35} + 8 q^{36} - 5 q^{37} - q^{39} + 9 q^{40} + q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 7 q^{45} - 12 q^{46} + 10 q^{47} + 6 q^{48} - 4 q^{49} + 4 q^{50} + 11 q^{51} - 6 q^{52} + 3 q^{53} + 4 q^{54} + 5 q^{55} - 12 q^{56} + 8 q^{57} - 24 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} + 20 q^{62} + 3 q^{63} - 3 q^{64} - q^{65} - 3 q^{66} + 7 q^{67} - 3 q^{68} + 11 q^{69} - 4 q^{70} + 6 q^{71} + 9 q^{72} - 9 q^{73} + 2 q^{74} + 7 q^{75} + 2 q^{76} + 17 q^{77} - 5 q^{78} - 11 q^{79} + 6 q^{80} + 7 q^{81} - 16 q^{82} + 30 q^{83} - 17 q^{84} + 11 q^{85} - 11 q^{86} - 25 q^{88} + 13 q^{89} + 4 q^{90} - 5 q^{91} + 10 q^{92} - 3 q^{93} - 25 q^{94} + 8 q^{95} + 22 q^{96} - 7 q^{97} - 10 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9 + 4 * q^10 + 5 * q^11 + 8 * q^12 - q^13 - 4 * q^14 + 7 * q^15 + 6 * q^16 + 11 * q^17 + 4 * q^18 + 8 * q^19 + 8 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 + 9 * q^24 + 7 * q^25 - 5 * q^26 + 7 * q^27 - 17 * q^28 + 4 * q^30 - 3 * q^31 + 22 * q^32 + 5 * q^33 + 4 * q^34 + 3 * q^35 + 8 * q^36 - 5 * q^37 - q^39 + 9 * q^40 + q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 7 * q^45 - 12 * q^46 + 10 * q^47 + 6 * q^48 - 4 * q^49 + 4 * q^50 + 11 * q^51 - 6 * q^52 + 3 * q^53 + 4 * q^54 + 5 * q^55 - 12 * q^56 + 8 * q^57 - 24 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 + 20 * q^62 + 3 * q^63 - 3 * q^64 - q^65 - 3 * q^66 + 7 * q^67 - 3 * q^68 + 11 * q^69 - 4 * q^70 + 6 * q^71 + 9 * q^72 - 9 * q^73 + 2 * q^74 + 7 * q^75 + 2 * q^76 + 17 * q^77 - 5 * q^78 - 11 * q^79 + 6 * q^80 + 7 * q^81 - 16 * q^82 + 30 * q^83 - 17 * q^84 + 11 * q^85 - 11 * q^86 - 25 * q^88 + 13 * q^89 + 4 * q^90 - 5 * q^91 + 10 * q^92 - 3 * q^93 - 25 * q^94 + 8 * q^95 + 22 * q^96 - 7 * q^97 - 10 * q^98 + 5 * q^99

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