LMFDB - Embedded newform 435.4.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("435.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$1$
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} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 $ x^7 - x^6 - 35x^5 + 18x^4 + 329x^3 - 167x^2 - 767*x + 638
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.26184$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26184 q^{2} +3.00000 q^{3} -6.40776 q^{4} -5.00000 q^{5} -3.78552 q^{6} -13.4311 q^{7} +18.1803 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.26184 q^{2} +3.00000 q^{3} -6.40776 q^{4} -5.00000 q^{5} -3.78552 q^{6} -13.4311 q^{7} +18.1803 q^{8} +9.00000 q^{9} +6.30920 q^{10} -1.30869 q^{11} -19.2233 q^{12} +85.6641 q^{13} +16.9479 q^{14} -15.0000 q^{15} +28.3214 q^{16} +67.9685 q^{17} -11.3566 q^{18} -63.3429 q^{19} +32.0388 q^{20} -40.2934 q^{21} +1.65136 q^{22} -139.990 q^{23} +54.5409 q^{24} +25.0000 q^{25} -108.094 q^{26} +27.0000 q^{27} +86.0634 q^{28} -29.0000 q^{29} +18.9276 q^{30} -170.385 q^{31} -181.179 q^{32} -3.92607 q^{33} -85.7654 q^{34} +67.1557 q^{35} -57.6698 q^{36} -405.970 q^{37} +79.9286 q^{38} +256.992 q^{39} -90.9015 q^{40} -447.863 q^{41} +50.8438 q^{42} +407.779 q^{43} +8.38576 q^{44} -45.0000 q^{45} +176.645 q^{46} -178.857 q^{47} +84.9643 q^{48} -162.605 q^{49} -31.5460 q^{50} +203.905 q^{51} -548.915 q^{52} +93.3357 q^{53} -34.0697 q^{54} +6.54344 q^{55} -244.182 q^{56} -190.029 q^{57} +36.5934 q^{58} +279.796 q^{59} +96.1164 q^{60} -793.549 q^{61} +214.999 q^{62} -120.880 q^{63} +2.04805 q^{64} -428.321 q^{65} +4.95407 q^{66} +460.471 q^{67} -435.526 q^{68} -419.971 q^{69} -84.7397 q^{70} +803.153 q^{71} +163.623 q^{72} -150.833 q^{73} +512.269 q^{74} +75.0000 q^{75} +405.886 q^{76} +17.5772 q^{77} -324.283 q^{78} -313.814 q^{79} -141.607 q^{80} +81.0000 q^{81} +565.132 q^{82} +250.514 q^{83} +258.190 q^{84} -339.842 q^{85} -514.552 q^{86} -87.0000 q^{87} -23.7923 q^{88} -97.2972 q^{89} +56.7828 q^{90} -1150.57 q^{91} +897.024 q^{92} -511.156 q^{93} +225.689 q^{94} +316.714 q^{95} -543.538 q^{96} -1342.23 q^{97} +205.181 q^{98} -11.7782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19} - 75 q^{20} - 111 q^{21} - 369 q^{22} - 68 q^{23} - 108 q^{24} + 175 q^{25} + 181 q^{26} + 189 q^{27} - 637 q^{28} - 203 q^{29} + 15 q^{30} - 480 q^{31} - 779 q^{32} - 33 q^{33} - 897 q^{34} + 185 q^{35} + 135 q^{36} - 1032 q^{37} - 194 q^{38} - 399 q^{39} + 180 q^{40} - 638 q^{41} - 225 q^{42} - 512 q^{43} + 625 q^{44} - 315 q^{45} + 16 q^{46} - 111 q^{47} - 159 q^{48} + 178 q^{49} - 25 q^{50} + 63 q^{51} - 1263 q^{52} + 410 q^{53} - 27 q^{54} + 55 q^{55} + 1174 q^{56} - 510 q^{57} + 29 q^{58} - 426 q^{59} - 225 q^{60} - 1192 q^{61} + 460 q^{62} - 333 q^{63} + 390 q^{64} + 665 q^{65} - 1107 q^{66} - 1671 q^{67} + 1509 q^{68} - 204 q^{69} + 375 q^{70} - 1324 q^{71} - 324 q^{72} - 852 q^{73} + 1780 q^{74} + 525 q^{75} - 564 q^{76} - 2107 q^{77} + 543 q^{78} + 366 q^{79} + 265 q^{80} + 567 q^{81} - 318 q^{82} + 470 q^{83} - 1911 q^{84} - 105 q^{85} - 2196 q^{86} - 609 q^{87} - 2518 q^{88} + 51 q^{89} + 45 q^{90} - 1297 q^{91} - 684 q^{92} - 1440 q^{93} - 1837 q^{94} + 850 q^{95} - 2337 q^{96} - 3322 q^{97} + 1068 q^{98} - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * 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 $

$2$	−1.26184	−0.446128	−0.223064	−	0.974804i	$-0.571606\pi$
$2$	−1.26184	−0.446128	−0.223064	+	0.974804i	$0.571606\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−6.40776	−0.800970
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−3.78552	−0.257572
$7$	−13.4311	−0.725213	−0.362606	−	0.931942i	$-0.618113\pi$
$7$	−13.4311	−0.725213	−0.362606	+	0.931942i	$0.618113\pi$
$8$	18.1803	0.803463
$9$	9.00000	0.333333
$10$	6.30920	0.199514
$11$	−1.30869	−0.0358713	−0.0179357	−	0.999839i	$-0.505709\pi$
$11$	−1.30869	−0.0358713	−0.0179357	+	0.999839i	$0.505709\pi$
$12$	−19.2233	−0.462440
$13$	85.6641	1.82761	0.913806	−	0.406151i	$-0.133129\pi$
$13$	85.6641	1.82761	0.913806	+	0.406151i	$0.133129\pi$
$14$	16.9479	0.323538
$15$	−15.0000	−0.258199
$16$	28.3214	0.442523
$17$	67.9685	0.969693	0.484846	−	0.874599i	$-0.338876\pi$
$17$	67.9685	0.969693	0.484846	+	0.874599i	$0.338876\pi$
$18$	−11.3566	−0.148709
$19$	−63.3429	−0.764834	−0.382417	−	0.923990i	$-0.624908\pi$
$19$	−63.3429	−0.764834	−0.382417	+	0.923990i	$0.624908\pi$
$20$	32.0388	0.358205
$21$	−40.2934	−0.418702
$22$	1.65136	0.0160032
$23$	−139.990	−1.26913	−0.634565	−	0.772870i	$-0.718821\pi$
$23$	−139.990	−1.26913	−0.634565	+	0.772870i	$0.718821\pi$
$24$	54.5409	0.463880
$25$	25.0000	0.200000
$26$	−108.094	−0.815349
$27$	27.0000	0.192450
$28$	86.0634	0.580874
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	18.9276	0.115190
$31$	−170.385	−0.987164	−0.493582	−	0.869699i	$-0.664313\pi$
$31$	−170.385	−0.987164	−0.493582	+	0.869699i	$0.664313\pi$
$32$	−181.179	−1.00088
$33$	−3.92607	−0.0207103
$34$	−85.7654	−0.432607
$35$	67.1557	0.324325
$36$	−57.6698	−0.266990
$37$	−405.970	−1.80381	−0.901905	−	0.431934i	$-0.857831\pi$
$37$	−405.970	−1.80381	−0.901905	+	0.431934i	$0.857831\pi$
$38$	79.9286	0.341214
$39$	256.992	1.05517
$40$	−90.9015	−0.359320
$41$	−447.863	−1.70596	−0.852982	−	0.521940i	$-0.825208\pi$
$41$	−447.863	−1.70596	−0.852982	+	0.521940i	$0.825208\pi$
$42$	50.8438	0.186795
$43$	407.779	1.44618	0.723090	−	0.690754i	$-0.242721\pi$
$43$	407.779	1.44618	0.723090	+	0.690754i	$0.242721\pi$
$44$	8.38576	0.0287318
$45$	−45.0000	−0.149071
$46$	176.645	0.566194
$47$	−178.857	−0.555086	−0.277543	−	0.960713i	$-0.589520\pi$
$47$	−178.857	−0.555086	−0.277543	+	0.960713i	$0.589520\pi$
$48$	84.9643	0.255491
$49$	−162.605	−0.474066
$50$	−31.5460	−0.0892256
$51$	203.905	0.559852
$52$	−548.915	−1.46386
$53$	93.3357	0.241899	0.120949	−	0.992659i	$-0.461406\pi$
$53$	93.3357	0.241899	0.120949	+	0.992659i	$0.461406\pi$
$54$	−34.0697	−0.0858574
$55$	6.54344	0.0160421
$56$	−244.182	−0.582682
$57$	−190.029	−0.441577
$58$	36.5934	0.0828439
$59$	279.796	0.617396	0.308698	−	0.951160i	$-0.400107\pi$
$59$	279.796	0.617396	0.308698	+	0.951160i	$0.400107\pi$
$60$	96.1164	0.206810
$61$	−793.549	−1.66563	−0.832816	−	0.553550i	$-0.813273\pi$
$61$	−793.549	−1.66563	−0.832816	+	0.553550i	$0.813273\pi$
$62$	214.999	0.440402
$63$	−120.880	−0.241738
$64$	2.04805	0.00400010
$65$	−428.321	−0.817333
$66$	4.95407	0.00923945
$67$	460.471	0.839635	0.419818	−	0.907609i	$-0.362094\pi$
$67$	460.471	0.839635	0.419818	+	0.907609i	$0.362094\pi$
$68$	−435.526	−0.776695
$69$	−419.971	−0.732732
$70$	−84.7397	−0.144690
$71$	803.153	1.34249	0.671244	−	0.741236i	$-0.265760\pi$
$71$	803.153	1.34249	0.671244	+	0.741236i	$0.265760\pi$
$72$	163.623	0.267821
$73$	−150.833	−0.241832	−0.120916	−	0.992663i	$-0.538583\pi$
$73$	−150.833	−0.241832	−0.120916	+	0.992663i	$0.538583\pi$
$74$	512.269	0.804730
$75$	75.0000	0.115470
$76$	405.886	0.612609
$77$	17.5772	0.0260143
$78$	−324.283	−0.470742
$79$	−313.814	−0.446922	−0.223461	−	0.974713i	$-0.571735\pi$
$79$	−313.814	−0.446922	−0.223461	+	0.974713i	$0.571735\pi$
$80$	−141.607	−0.197902
$81$	81.0000	0.111111
$82$	565.132	0.761078
$83$	250.514	0.331295	0.165648	−	0.986185i	$-0.447029\pi$
$83$	250.514	0.331295	0.165648	+	0.986185i	$0.447029\pi$
$84$	258.190	0.335368
$85$	−339.842	−0.433660
$86$	−514.552	−0.645181
$87$	−87.0000	−0.107211
$88$	−23.7923	−0.0288213
$89$	−97.2972	−0.115882	−0.0579409	−	0.998320i	$-0.518453\pi$
$89$	−97.2972	−0.115882	−0.0579409	+	0.998320i	$0.518453\pi$
$90$	56.7828	0.0665048
$91$	−1150.57	−1.32541
$92$	897.024	1.01653
$93$	−511.156	−0.569940
$94$	225.689	0.247639
$95$	316.714	0.342044
$96$	−543.538	−0.577861
$97$	−1342.23	−1.40497	−0.702487	−	0.711697i	$-0.747927\pi$
$97$	−1342.23	−1.40497	−0.702487	+	0.711697i	$0.747927\pi$
$98$	205.181	0.211494
$99$	−11.7782	−0.0119571
$100$	−160.194	−0.160194
$101$	73.7087	0.0726167	0.0363084	−	0.999341i	$-0.488440\pi$
$101$	73.7087	0.0726167	0.0363084	+	0.999341i	$0.488440\pi$
$102$	−257.296	−0.249766
$103$	−1307.09	−1.25040	−0.625199	−	0.780465i	$-0.714982\pi$
$103$	−1307.09	−1.25040	−0.625199	+	0.780465i	$0.714982\pi$
$104$	1557.40	1.46842
$105$	201.467	0.187249
$106$	−117.775	−0.107918
$107$	845.454	0.763861	0.381930	−	0.924191i	$-0.375259\pi$
$107$	845.454	0.763861	0.381930	+	0.924191i	$0.375259\pi$
$108$	−173.009	−0.154147
$109$	−1502.99	−1.32074	−0.660370	−	0.750941i	$-0.729600\pi$
$109$	−1502.99	−1.32074	−0.660370	+	0.750941i	$0.729600\pi$
$110$	−8.25678	−0.00715685
$111$	−1217.91	−1.04143
$112$	−380.389	−0.320923
$113$	−317.218	−0.264083	−0.132042	−	0.991244i	$-0.542153\pi$
$113$	−317.218	−0.264083	−0.132042	+	0.991244i	$0.542153\pi$
$114$	239.786	0.197000
$115$	699.951	0.567572
$116$	185.825	0.148736
$117$	770.977	0.609204
$118$	−353.058	−0.275438
$119$	−912.893	−0.703234
$120$	−272.704	−0.207453
$121$	−1329.29	−0.998713
$122$	1001.33	0.743085
$123$	−1343.59	−0.984939
$124$	1091.79	0.790689
$125$	−125.000	−0.0894427
$126$	152.531	0.107846
$127$	−1936.01	−1.35270	−0.676349	−	0.736581i	$-0.736439\pi$
$127$	−1936.01	−1.35270	−0.676349	+	0.736581i	$0.736439\pi$
$128$	1446.85	0.999100
$129$	1223.34	0.834952
$130$	540.472	0.364635
$131$	−1234.54	−0.823379	−0.411689	−	0.911324i	$-0.635061\pi$
$131$	−1234.54	−0.823379	−0.411689	+	0.911324i	$0.635061\pi$
$132$	25.1573	0.0165883
$133$	850.767	0.554668
$134$	−581.042	−0.374585
$135$	−135.000	−0.0860663
$136$	1235.69	0.779112
$137$	−886.190	−0.552645	−0.276322	−	0.961065i	$-0.589116\pi$
$137$	−886.190	−0.552645	−0.276322	+	0.961065i	$0.589116\pi$
$138$	529.936	0.326892
$139$	1582.12	0.965421	0.482711	−	0.875780i	$-0.339652\pi$
$139$	1582.12	0.965421	0.482711	+	0.875780i	$0.339652\pi$
$140$	−430.317	−0.259775
$141$	−536.572	−0.320479
$142$	−1013.45	−0.598922
$143$	−112.108	−0.0655588
$144$	254.893	0.147508
$145$	145.000	0.0830455
$146$	190.328	0.107888
$147$	−487.814	−0.273702
$148$	2601.36	1.44480
$149$	−1649.57	−0.906969	−0.453485	−	0.891264i	$-0.649819\pi$
$149$	−1649.57	−0.906969	−0.453485	+	0.891264i	$0.649819\pi$
$150$	−94.6380	−0.0515144
$151$	343.852	0.185313	0.0926565	−	0.995698i	$-0.470464\pi$
$151$	343.852	0.185313	0.0926565	+	0.995698i	$0.470464\pi$
$152$	−1151.59	−0.614516
$153$	611.716	0.323231
$154$	−22.1796	−0.0116057
$155$	851.926	0.441473
$156$	−1646.75	−0.845161
$157$	2493.83	1.26770	0.633851	−	0.773455i	$-0.281473\pi$
$157$	2493.83	1.26770	0.633851	+	0.773455i	$0.281473\pi$
$158$	395.983	0.199384
$159$	280.007	0.139660
$160$	905.897	0.447609
$161$	1880.23	0.920389
$162$	−102.209	−0.0495698
$163$	−1915.12	−0.920270	−0.460135	−	0.887849i	$-0.652199\pi$
$163$	−1915.12	−0.920270	−0.460135	+	0.887849i	$0.652199\pi$
$164$	2869.80	1.36643
$165$	19.6303	0.00926194
$166$	−316.109	−0.147800
$167$	99.5806	0.0461424	0.0230712	−	0.999734i	$-0.492656\pi$
$167$	99.5806	0.0461424	0.0230712	+	0.999734i	$0.492656\pi$
$168$	−732.546	−0.336411
$169$	5141.34	2.34016
$170$	428.827	0.193468
$171$	−570.086	−0.254945
$172$	−2612.95	−1.15835
$173$	2139.30	0.940160	0.470080	−	0.882624i	$-0.344225\pi$
$173$	2139.30	0.940160	0.470080	+	0.882624i	$0.344225\pi$
$174$	109.780	0.0478299
$175$	−335.778	−0.145043
$176$	−37.0640	−0.0158739
$177$	839.389	0.356454
$178$	122.773	0.0516981
$179$	1863.54	0.778142	0.389071	−	0.921208i	$-0.372796\pi$
$179$	1863.54	0.778142	0.389071	+	0.921208i	$0.372796\pi$
$180$	288.349	0.119402
$181$	−3008.76	−1.23558	−0.617788	−	0.786345i	$-0.711971\pi$
$181$	−3008.76	−1.23558	−0.617788	+	0.786345i	$0.711971\pi$
$182$	1451.83	0.591301
$183$	−2380.65	−0.961653
$184$	−2545.06	−1.01970
$185$	2029.85	0.806689
$186$	644.997	0.254266
$187$	−88.9496	−0.0347842
$188$	1146.07	0.444607
$189$	−362.641	−0.139567
$190$	−399.643	−0.152596
$191$	5175.24	1.96056	0.980280	−	0.197611i	$-0.0633184\pi$
$191$	5175.24	1.96056	0.980280	+	0.197611i	$0.0633184\pi$
$192$	6.14415	0.00230946
$193$	−3407.89	−1.27101	−0.635505	−	0.772097i	$-0.719208\pi$
$193$	−3407.89	−1.27101	−0.635505	+	0.772097i	$0.719208\pi$
$194$	1693.68	0.626798
$195$	−1284.96	−0.471887
$196$	1041.93	0.379713
$197$	−2662.23	−0.962823	−0.481412	−	0.876495i	$-0.659876\pi$
$197$	−2662.23	−0.962823	−0.481412	+	0.876495i	$0.659876\pi$
$198$	14.8622	0.00533440
$199$	1124.12	0.400437	0.200218	−	0.979751i	$-0.435835\pi$
$199$	1124.12	0.400437	0.200218	+	0.979751i	$0.435835\pi$
$200$	454.507	0.160693
$201$	1381.41	0.484764
$202$	−93.0086	−0.0323964
$203$	389.503	0.134669
$204$	−1306.58	−0.448425
$205$	2239.32	0.762930
$206$	1649.33	0.557837
$207$	−1259.91	−0.423043
$208$	2426.13	0.808759
$209$	82.8961	0.0274356
$210$	−254.219	−0.0835371
$211$	109.248	0.0356442	0.0178221	−	0.999841i	$-0.494327\pi$
$211$	109.248	0.0356442	0.0178221	+	0.999841i	$0.494327\pi$
$212$	−598.072	−0.193754
$213$	2409.46	0.775086
$214$	−1066.83	−0.340780
$215$	−2038.89	−0.646751
$216$	490.868	0.154627
$217$	2288.47	0.715904
$218$	1896.54	0.589219
$219$	−452.500	−0.139622
$220$	−41.9288	−0.0128493
$221$	5822.46	1.77222
$222$	1536.81	0.464611
$223$	−4655.65	−1.39805	−0.699026	−	0.715097i	$-0.746383\pi$
$223$	−4655.65	−1.39805	−0.699026	+	0.715097i	$0.746383\pi$
$224$	2433.45	0.725854
$225$	225.000	0.0666667
$226$	400.279	0.117815
$227$	3715.56	1.08639	0.543195	−	0.839606i	$-0.317214\pi$
$227$	3715.56	1.08639	0.543195	+	0.839606i	$0.317214\pi$
$228$	1217.66	0.353690
$229$	2437.74	0.703451	0.351726	−	0.936103i	$-0.385595\pi$
$229$	2437.74	0.703451	0.351726	+	0.936103i	$0.385595\pi$
$230$	−883.227	−0.253210
$231$	52.7315	0.0150194
$232$	−527.228	−0.149199
$233$	−2704.29	−0.760360	−0.380180	−	0.924912i	$-0.624138\pi$
$233$	−2704.29	−0.760360	−0.380180	+	0.924912i	$0.624138\pi$
$234$	−972.850	−0.271783
$235$	894.287	0.248242
$236$	−1792.87	−0.494516
$237$	−941.441	−0.258030
$238$	1151.93	0.313732
$239$	6018.67	1.62893	0.814467	−	0.580210i	$-0.197030\pi$
$239$	6018.67	1.62893	0.814467	+	0.580210i	$0.197030\pi$
$240$	−424.822	−0.114259
$241$	−1244.90	−0.332743	−0.166372	−	0.986063i	$-0.553205\pi$
$241$	−1244.90	−0.332743	−0.166372	+	0.986063i	$0.553205\pi$
$242$	1677.35	0.445554
$243$	243.000	0.0641500
$244$	5084.87	1.33412
$245$	813.024	0.212009
$246$	1695.40	0.439409
$247$	−5426.21	−1.39782
$248$	−3097.65	−0.793150
$249$	751.543	0.191273
$250$	157.730	0.0399029
$251$	2477.48	0.623016	0.311508	−	0.950244i	$-0.399166\pi$
$251$	2477.48	0.623016	0.311508	+	0.950244i	$0.399166\pi$
$252$	774.571	0.193625
$253$	183.204	0.0455254
$254$	2442.93	0.603477
$255$	−1019.53	−0.250374
$256$	−1842.08	−0.449727
$257$	−4778.08	−1.15972	−0.579860	−	0.814716i	$-0.696893\pi$
$257$	−4778.08	−1.15972	−0.579860	+	0.814716i	$0.696893\pi$
$258$	−1543.66	−0.372495
$259$	5452.63	1.30815
$260$	2744.58	0.654659
$261$	−261.000	−0.0618984
$262$	1557.80	0.367332
$263$	−1571.56	−0.368467	−0.184233	−	0.982883i	$-0.558980\pi$
$263$	−1571.56	−0.368467	−0.184233	+	0.982883i	$0.558980\pi$
$264$	−71.3770	−0.0166400
$265$	−466.678	−0.108180
$266$	−1073.53	−0.247453
$267$	−291.892	−0.0669044
$268$	−2950.59	−0.672522
$269$	4946.58	1.12118	0.560591	−	0.828093i	$-0.310574\pi$
$269$	4946.58	1.12118	0.560591	+	0.828093i	$0.310574\pi$
$270$	170.348	0.0383966
$271$	−914.942	−0.205088	−0.102544	−	0.994728i	$-0.532698\pi$
$271$	−914.942	−0.205088	−0.102544	+	0.994728i	$0.532698\pi$
$272$	1924.97	0.429111
$273$	−3451.70	−0.765224
$274$	1118.23	0.246550
$275$	−32.7172	−0.00717426
$276$	2691.07	0.586896
$277$	−2441.56	−0.529599	−0.264799	−	0.964304i	$-0.585306\pi$
$277$	−2441.56	−0.529599	−0.264799	+	0.964304i	$0.585306\pi$
$278$	−1996.38	−0.430701
$279$	−1533.47	−0.329055
$280$	1220.91	0.260583
$281$	−5311.04	−1.12751	−0.563755	−	0.825942i	$-0.690644\pi$
$281$	−5311.04	−1.12751	−0.563755	+	0.825942i	$0.690644\pi$
$282$	677.068	0.142975
$283$	669.167	0.140558	0.0702789	−	0.997527i	$-0.477611\pi$
$283$	669.167	0.140558	0.0702789	+	0.997527i	$0.477611\pi$
$284$	−5146.41	−1.07529
$285$	950.143	0.197479
$286$	141.462	0.0292476
$287$	6015.31	1.23719
$288$	−1630.62	−0.333628
$289$	−293.286	−0.0596960
$290$	−182.967	−0.0370489
$291$	−4026.68	−0.811162
$292$	966.504	0.193700
$293$	−7468.02	−1.48903	−0.744516	−	0.667604i	$-0.767320\pi$
$293$	−7468.02	−1.48903	−0.744516	+	0.667604i	$0.767320\pi$
$294$	615.544	0.122106
$295$	−1398.98	−0.276108
$296$	−7380.65	−1.44930
$297$	−35.3346	−0.00690344
$298$	2081.50	0.404624
$299$	−11992.1	−2.31948
$300$	−480.582	−0.0924880
$301$	−5476.93	−1.04879
$302$	−433.886	−0.0826733
$303$	221.126	0.0419253
$304$	−1793.96	−0.338456
$305$	3967.74	0.744893
$306$	−771.888	−0.144202
$307$	−9927.63	−1.84560	−0.922801	−	0.385278i	$-0.874106\pi$
$307$	−9927.63	−1.84560	−0.922801	+	0.385278i	$0.874106\pi$
$308$	−112.630	−0.0208367
$309$	−3921.26	−0.721918
$310$	−1075.00	−0.196954
$311$	3131.42	0.570953	0.285477	−	0.958386i	$-0.407848\pi$
$311$	3131.42	0.570953	0.285477	+	0.958386i	$0.407848\pi$
$312$	4672.20	0.847792
$313$	8434.75	1.52320	0.761598	−	0.648050i	$-0.224415\pi$
$313$	8434.75	1.52320	0.761598	+	0.648050i	$0.224415\pi$
$314$	−3146.82	−0.565558
$315$	604.401	0.108108
$316$	2010.84	0.357971
$317$	−9162.80	−1.62345	−0.811725	−	0.584039i	$-0.801471\pi$
$317$	−9162.80	−1.62345	−0.811725	+	0.584039i	$0.801471\pi$
$318$	−353.324	−0.0623064
$319$	37.9520	0.00666114
$320$	−10.2403	−0.00178890
$321$	2536.36	0.441015
$322$	−2372.55	−0.410611
$323$	−4305.32	−0.741654
$324$	−519.028	−0.0889966
$325$	2141.60	0.365522
$326$	2416.58	0.410558
$327$	−4508.98	−0.762529
$328$	−8142.29	−1.37068
$329$	2402.26	0.402555
$330$	−24.7703	−0.00413201
$331$	5194.87	0.862647	0.431323	−	0.902197i	$-0.358047\pi$
$331$	5194.87	0.862647	0.431323	+	0.902197i	$0.358047\pi$
$332$	−1605.23	−0.265357
$333$	−3653.73	−0.601270
$334$	−125.655	−0.0205854
$335$	−2302.36	−0.375496
$336$	−1141.17	−0.185285
$337$	−3217.15	−0.520027	−0.260014	−	0.965605i	$-0.583727\pi$
$337$	−3217.15	−0.520027	−0.260014	+	0.965605i	$0.583727\pi$
$338$	−6487.55	−1.04401
$339$	−951.655	−0.152468
$340$	2177.63	0.347348
$341$	222.981	0.0354109
$342$	719.358	0.113738
$343$	6790.84	1.06901
$344$	7413.54	1.16195
$345$	2099.85	0.327688
$346$	−2699.45	−0.419432
$347$	−609.761	−0.0943334	−0.0471667	−	0.998887i	$-0.515019\pi$
$347$	−609.761	−0.0943334	−0.0471667	+	0.998887i	$0.515019\pi$
$348$	557.475	0.0858730
$349$	4406.40	0.675843	0.337921	−	0.941174i	$-0.390276\pi$
$349$	4406.40	0.675843	0.337921	+	0.941174i	$0.390276\pi$
$350$	423.699	0.0647075
$351$	2312.93	0.351724
$352$	237.108	0.0359031
$353$	2480.09	0.373943	0.186971	−	0.982365i	$-0.440133\pi$
$353$	2480.09	0.373943	0.186971	+	0.982365i	$0.440133\pi$
$354$	−1059.18	−0.159024
$355$	−4015.76	−0.600379
$356$	623.457	0.0928178
$357$	−2738.68	−0.406012
$358$	−2351.49	−0.347151
$359$	6578.82	0.967177	0.483589	−	0.875295i	$-0.339333\pi$
$359$	6578.82	0.967177	0.483589	+	0.875295i	$0.339333\pi$
$360$	−818.113	−0.119773
$361$	−2846.68	−0.415028
$362$	3796.57	0.551225
$363$	−3987.86	−0.576607
$364$	7372.55	1.06161
$365$	754.167	0.108150
$366$	3004.00	0.429020
$367$	−731.114	−0.103989	−0.0519943	−	0.998647i	$-0.516558\pi$
$367$	−731.114	−0.103989	−0.0519943	+	0.998647i	$0.516558\pi$
$368$	−3964.72	−0.561618
$369$	−4030.77	−0.568655
$370$	−2561.34	−0.359886
$371$	−1253.60	−0.175428
$372$	3275.36	0.456504
$373$	−1673.03	−0.232242	−0.116121	−	0.993235i	$-0.537046\pi$
$373$	−1673.03	−0.232242	−0.116121	+	0.993235i	$0.537046\pi$
$374$	112.240	0.0155182
$375$	−375.000	−0.0516398
$376$	−3251.68	−0.445991
$377$	−2484.26	−0.339379
$378$	457.594	0.0622649
$379$	3760.44	0.509659	0.254830	−	0.966986i	$-0.417981\pi$
$379$	3760.44	0.509659	0.254830	+	0.966986i	$0.417981\pi$
$380$	−2029.43	−0.273967
$381$	−5808.02	−0.780981
$382$	−6530.33	−0.874661
$383$	−12540.8	−1.67312	−0.836562	−	0.547872i	$-0.815438\pi$
$383$	−12540.8	−1.67312	−0.836562	+	0.547872i	$0.815438\pi$
$384$	4340.55	0.576831
$385$	−87.8859	−0.0116340
$386$	4300.21	0.567033
$387$	3670.01	0.482060
$388$	8600.66	1.12534
$389$	5779.21	0.753259	0.376629	−	0.926364i	$-0.377083\pi$
$389$	5779.21	0.753259	0.376629	+	0.926364i	$0.377083\pi$
$390$	1621.42	0.210522
$391$	−9514.92	−1.23067
$392$	−2956.20	−0.380895
$393$	−3703.63	−0.475378
$394$	3359.31	0.429542
$395$	1569.07	0.199869
$396$	75.4719	0.00957728
$397$	14394.6	1.81976	0.909881	−	0.414869i	$-0.136173\pi$
$397$	14394.6	1.81976	0.909881	+	0.414869i	$0.136173\pi$
$398$	−1418.46	−0.178646
$399$	2552.30	0.320238
$400$	708.036	0.0885045
$401$	8620.31	1.07351	0.536756	−	0.843738i	$-0.319650\pi$
$401$	8620.31	1.07351	0.536756	+	0.843738i	$0.319650\pi$
$402$	−1743.12	−0.216267
$403$	−14595.9	−1.80415
$404$	−472.308	−0.0581638
$405$	−405.000	−0.0496904
$406$	−491.490	−0.0600795
$407$	531.288	0.0647051
$408$	3707.06	0.449821
$409$	−14058.0	−1.69957	−0.849783	−	0.527133i	$-0.823267\pi$
$409$	−14058.0	−1.69957	−0.849783	+	0.527133i	$0.823267\pi$
$410$	−2825.66	−0.340365
$411$	−2658.57	−0.319070
$412$	8375.49	1.00153
$413$	−3757.98	−0.447744
$414$	1589.81	0.188731
$415$	−1252.57	−0.148160
$416$	−15520.6	−1.82923
$417$	4746.36	0.557386
$418$	−104.602	−0.0122398
$419$	−308.722	−0.0359954	−0.0179977	−	0.999838i	$-0.505729\pi$
$419$	−308.722	−0.0359954	−0.0179977	+	0.999838i	$0.505729\pi$
$420$	−1290.95	−0.149981
$421$	7341.48	0.849886	0.424943	−	0.905220i	$-0.360294\pi$
$421$	7341.48	0.849886	0.424943	+	0.905220i	$0.360294\pi$
$422$	−137.853	−0.0159019
$423$	−1609.72	−0.185029
$424$	1696.87	0.194357
$425$	1699.21	0.193939
$426$	−3040.35	−0.345788
$427$	10658.3	1.20794
$428$	−5417.47	−0.611830
$429$	−336.323	−0.0378504
$430$	2572.76	0.288534
$431$	−16660.8	−1.86201	−0.931003	−	0.365013i	$-0.881065\pi$
$431$	−16660.8	−1.86201	−0.931003	+	0.365013i	$0.881065\pi$
$432$	764.679	0.0851635
$433$	10091.5	1.12001	0.560006	−	0.828488i	$-0.310799\pi$
$433$	10091.5	1.12001	0.560006	+	0.828488i	$0.310799\pi$
$434$	−2887.68	−0.319385
$435$	435.000	0.0479463
$436$	9630.82	1.05787
$437$	8867.38	0.970674
$438$	570.983	0.0622891
$439$	5149.74	0.559871	0.279936	−	0.960019i	$-0.409687\pi$
$439$	5149.74	0.559871	0.279936	+	0.960019i	$0.409687\pi$
$440$	118.962	0.0128893
$441$	−1463.44	−0.158022
$442$	−7347.02	−0.790638
$443$	15820.5	1.69674	0.848371	−	0.529402i	$-0.177584\pi$
$443$	15820.5	1.69674	0.848371	+	0.529402i	$0.177584\pi$
$444$	7804.07	0.834154
$445$	486.486	0.0518239
$446$	5874.69	0.623710
$447$	−4948.72	−0.523639
$448$	−27.5076	−0.00290092
$449$	−13903.0	−1.46130	−0.730651	−	0.682751i	$-0.760783\pi$
$449$	−13903.0	−1.46130	−0.730651	+	0.682751i	$0.760783\pi$
$450$	−283.914	−0.0297419
$451$	586.114	0.0611952
$452$	2032.66	0.211523
$453$	1031.55	0.106990
$454$	−4688.45	−0.484669
$455$	5752.83	0.592740
$456$	−3454.78	−0.354791
$457$	4315.24	0.441704	0.220852	−	0.975307i	$-0.429116\pi$
$457$	4315.24	0.441704	0.220852	+	0.975307i	$0.429116\pi$
$458$	−3076.04	−0.313829
$459$	1835.15	0.186617
$460$	−4485.12	−0.454608
$461$	5936.08	0.599720	0.299860	−	0.953983i	$-0.403060\pi$
$461$	5936.08	0.599720	0.299860	+	0.953983i	$0.403060\pi$
$462$	−66.5388	−0.00670057
$463$	−12894.4	−1.29428	−0.647141	−	0.762370i	$-0.724036\pi$
$463$	−12894.4	−1.29428	−0.647141	+	0.762370i	$0.724036\pi$
$464$	−821.322	−0.0821744
$465$	2555.78	0.254885
$466$	3412.38	0.339218
$467$	12653.8	1.25385	0.626924	−	0.779081i	$-0.284314\pi$
$467$	12653.8	1.25385	0.626924	+	0.779081i	$0.284314\pi$
$468$	−4940.24	−0.487954
$469$	−6184.65	−0.608914
$470$	−1128.45	−0.110748
$471$	7481.49	0.731909
$472$	5086.78	0.496055
$473$	−533.656	−0.0518764
$474$	1187.95	0.115115
$475$	−1583.57	−0.152967
$476$	5849.60	0.563269
$477$	840.021	0.0806330
$478$	−7594.60	−0.726713
$479$	8991.57	0.857694	0.428847	−	0.903377i	$-0.358920\pi$
$479$	8991.57	0.857694	0.428847	+	0.903377i	$0.358920\pi$
$480$	2717.69	0.258427
$481$	−34777.0	−3.29667
$482$	1570.87	0.148446
$483$	5640.68	0.531387
$484$	8517.75	0.799939
$485$	6711.13	0.628323
$486$	−306.627	−0.0286191
$487$	7671.39	0.713806	0.356903	−	0.934141i	$-0.383833\pi$
$487$	7671.39	0.713806	0.356903	+	0.934141i	$0.383833\pi$
$488$	−14426.9	−1.33827
$489$	−5745.37	−0.531318
$490$	−1025.91	−0.0945831
$491$	10322.9	0.948809	0.474405	−	0.880307i	$-0.342663\pi$
$491$	10322.9	0.948809	0.474405	+	0.880307i	$0.342663\pi$
$492$	8609.40	0.788906
$493$	−1971.09	−0.180067
$494$	6847.01	0.623607
$495$	58.8910	0.00534738
$496$	−4825.56	−0.436843
$497$	−10787.3	−0.973590
$498$	−948.327	−0.0853324
$499$	−4385.18	−0.393402	−0.196701	−	0.980464i	$-0.563023\pi$
$499$	−4385.18	−0.393402	−0.196701	+	0.980464i	$0.563023\pi$
$500$	800.970	0.0716409
$501$	298.742	0.0266403
$502$	−3126.18	−0.277945
$503$	8327.07	0.738143	0.369071	−	0.929401i	$-0.379676\pi$
$503$	8327.07	0.738143	0.369071	+	0.929401i	$0.379676\pi$
$504$	−2197.64	−0.194227
$505$	−368.544	−0.0324752
$506$	−231.174	−0.0203101
$507$	15424.0	1.35109
$508$	12405.5	1.08347
$509$	−20580.8	−1.79220	−0.896098	−	0.443856i	$-0.853610\pi$
$509$	−20580.8	−1.79220	−0.896098	+	0.443856i	$0.853610\pi$
$510$	1286.48	0.111699
$511$	2025.86	0.175379
$512$	−9250.40	−0.798465
$513$	−1710.26	−0.147192
$514$	6029.17	0.517384
$515$	6535.43	0.559195
$516$	−7838.85	−0.668771
$517$	234.069	0.0199117
$518$	−6880.35	−0.583601
$519$	6417.89	0.542802
$520$	−7786.99	−0.656697
$521$	−15109.3	−1.27054	−0.635270	−	0.772290i	$-0.719111\pi$
$521$	−15109.3	−1.27054	−0.635270	+	0.772290i	$0.719111\pi$
$522$	329.340	0.0276146
$523$	−507.100	−0.0423976	−0.0211988	−	0.999775i	$-0.506748\pi$
$523$	−507.100	−0.0423976	−0.0211988	+	0.999775i	$0.506748\pi$
$524$	7910.66	0.659502
$525$	−1007.33	−0.0837404
$526$	1983.06	0.164383
$527$	−11580.8	−0.957246
$528$	−111.192	−0.00916478
$529$	7430.26	0.610690
$530$	588.874	0.0482623
$531$	2518.17	0.205799
$532$	−5451.51	−0.444272
$533$	−38365.8	−3.11784
$534$	368.320	0.0298479
$535$	−4227.27	−0.341609
$536$	8371.51	0.674616
$537$	5590.61	0.449260
$538$	−6241.79	−0.500191
$539$	212.799	0.0170054
$540$	865.047	0.0689365
$541$	8249.02	0.655551	0.327776	−	0.944756i	$-0.393701\pi$
$541$	8249.02	0.655551	0.327776	+	0.944756i	$0.393701\pi$
$542$	1154.51	0.0914954
$543$	−9026.27	−0.713360
$544$	−12314.5	−0.970551
$545$	7514.96	0.590653
$546$	4355.49	0.341388
$547$	−19432.6	−1.51897	−0.759486	−	0.650524i	$-0.774550\pi$
$547$	−19432.6	−1.51897	−0.759486	+	0.650524i	$0.774550\pi$
$548$	5678.49	0.442652
$549$	−7141.94	−0.555210
$550$	41.2839	0.00320064
$551$	1836.94	0.142026
$552$	−7635.19	−0.588723
$553$	4214.87	0.324113
$554$	3080.85	0.236269
$555$	6089.54	0.465742
$556$	−10137.8	−0.773273
$557$	18807.6	1.43071	0.715354	−	0.698762i	$-0.246265\pi$
$557$	18807.6	1.43071	0.715354	+	0.698762i	$0.246265\pi$
$558$	1934.99	0.146801
$559$	34932.0	2.64305
$560$	1901.94	0.143521
$561$	−266.849	−0.0200826
$562$	6701.69	0.503013
$563$	7337.15	0.549243	0.274622	−	0.961552i	$-0.411447\pi$
$563$	7337.15	0.549243	0.274622	+	0.961552i	$0.411447\pi$
$564$	3438.22	0.256694
$565$	1586.09	0.118102
$566$	−844.382	−0.0627068
$567$	−1087.92	−0.0805792
$568$	14601.6	1.07864
$569$	5459.12	0.402211	0.201106	−	0.979570i	$-0.435547\pi$
$569$	5459.12	0.402211	0.201106	+	0.979570i	$0.435547\pi$
$570$	−1198.93	−0.0881011
$571$	5306.93	0.388946	0.194473	−	0.980908i	$-0.437700\pi$
$571$	5306.93	0.388946	0.194473	+	0.980908i	$0.437700\pi$
$572$	718.359	0.0525107
$573$	15525.7	1.13193
$574$	−7590.36	−0.551944
$575$	−3499.76	−0.253826
$576$	18.4325	0.00133337
$577$	16127.1	1.16357	0.581785	−	0.813343i	$-0.302355\pi$
$577$	16127.1	1.16357	0.581785	+	0.813343i	$0.302355\pi$
$578$	370.081	0.0266320
$579$	−10223.7	−0.733818
$580$	−929.125	−0.0665169
$581$	−3364.69	−0.240260
$582$	5081.03	0.361882
$583$	−122.147	−0.00867723
$584$	−2742.19	−0.194303
$585$	−3854.89	−0.272444
$586$	9423.45	0.664299
$587$	9109.13	0.640501	0.320250	−	0.947333i	$-0.396233\pi$
$587$	9109.13	0.640501	0.320250	+	0.947333i	$0.396233\pi$
$588$	3125.80	0.219227
$589$	10792.7	0.755017
$590$	1765.29	0.123180
$591$	−7986.69	−0.555886
$592$	−11497.6	−0.798227
$593$	28352.1	1.96337	0.981687	−	0.190500i	$-0.0610110\pi$
$593$	28352.1	1.96337	0.981687	+	0.190500i	$0.0610110\pi$
$594$	44.5866	0.00307982
$595$	4564.47	0.314496
$596$	10570.1	0.726455
$597$	3372.37	0.231192
$598$	15132.2	1.03478
$599$	−15496.1	−1.05702	−0.528508	−	0.848928i	$-0.677248\pi$
$599$	−15496.1	−1.05702	−0.528508	+	0.848928i	$0.677248\pi$
$600$	1363.52	0.0927759
$601$	7637.92	0.518398	0.259199	−	0.965824i	$-0.416541\pi$
$601$	7637.92	0.518398	0.259199	+	0.965824i	$0.416541\pi$
$602$	6911.01	0.467894
$603$	4144.24	0.279878
$604$	−2203.32	−0.148430
$605$	6646.44	0.446638
$606$	−279.026	−0.0187040
$607$	−12012.8	−0.803268	−0.401634	−	0.915800i	$-0.631558\pi$
$607$	−12012.8	−0.803268	−0.401634	+	0.915800i	$0.631558\pi$
$608$	11476.4	0.765511
$609$	1168.51	0.0777510
$610$	−5006.66	−0.332318
$611$	−15321.7	−1.01448
$612$	−3919.73	−0.258898
$613$	−6113.47	−0.402807	−0.201404	−	0.979508i	$-0.564550\pi$
$613$	−6113.47	−0.402807	−0.201404	+	0.979508i	$0.564550\pi$
$614$	12527.1	0.823374
$615$	6717.95	0.440478
$616$	319.558	0.0209016
$617$	−28775.9	−1.87759	−0.938797	−	0.344472i	$-0.888058\pi$
$617$	−28775.9	−1.87759	−0.938797	+	0.344472i	$0.888058\pi$
$618$	4948.00	0.322068
$619$	−7092.81	−0.460556	−0.230278	−	0.973125i	$-0.573964\pi$
$619$	−7092.81	−0.460556	−0.230278	+	0.973125i	$0.573964\pi$
$620$	−5458.94	−0.353607
$621$	−3779.74	−0.244244
$622$	−3951.35	−0.254718
$623$	1306.81	0.0840390
$624$	7278.39	0.466937
$625$	625.000	0.0400000
$626$	−10643.3	−0.679540
$627$	248.688	0.0158400
$628$	−15979.9	−1.01539
$629$	−27593.1	−1.74914
$630$	−762.657	−0.0482302
$631$	−2283.67	−0.144075	−0.0720377	−	0.997402i	$-0.522950\pi$
$631$	−2283.67	−0.144075	−0.0720377	+	0.997402i	$0.522950\pi$
$632$	−5705.23	−0.359085
$633$	327.743	0.0205792
$634$	11562.0	0.724267
$635$	9680.03	0.604945
$636$	−1794.22	−0.111864
$637$	−13929.4	−0.866409
$638$	−47.8893	−0.00297172
$639$	7228.38	0.447496
$640$	−7234.26	−0.446811
$641$	−17599.2	−1.08444	−0.542220	−	0.840236i	$-0.682416\pi$
$641$	−17599.2	−1.08444	−0.542220	+	0.840236i	$0.682416\pi$
$642$	−3200.48	−0.196749
$643$	9248.80	0.567242	0.283621	−	0.958936i	$-0.408464\pi$
$643$	9248.80	0.567242	0.283621	+	0.958936i	$0.408464\pi$
$644$	−12048.0	−0.737204
$645$	−6116.68	−0.373402
$646$	5432.63	0.330873
$647$	−12201.5	−0.741409	−0.370704	−	0.928751i	$-0.620884\pi$
$647$	−12201.5	−0.741409	−0.370704	+	0.928751i	$0.620884\pi$
$648$	1472.60	0.0892737
$649$	−366.166	−0.0221468
$650$	−2702.36	−0.163070
$651$	6865.40	0.413328
$652$	12271.6	0.737108
$653$	9769.75	0.585482	0.292741	−	0.956192i	$-0.405433\pi$
$653$	9769.75	0.585482	0.292741	+	0.956192i	$0.405433\pi$
$654$	5689.61	0.340186
$655$	6172.72	0.368226
$656$	−12684.1	−0.754927
$657$	−1357.50	−0.0806105
$658$	−3031.26	−0.179591
$659$	−15386.3	−0.909506	−0.454753	−	0.890618i	$-0.650272\pi$
$659$	−15386.3	−0.909506	−0.454753	+	0.890618i	$0.650272\pi$
$660$	−125.786	−0.00741853
$661$	16886.7	0.993671	0.496835	−	0.867845i	$-0.334495\pi$
$661$	16886.7	0.993671	0.496835	+	0.867845i	$0.334495\pi$
$662$	−6555.10	−0.384851
$663$	17467.4	1.02319
$664$	4554.42	0.266183
$665$	−4253.83	−0.248055
$666$	4610.42	0.268243
$667$	4059.72	0.235671
$668$	−638.089	−0.0369587
$669$	−13967.0	−0.807165
$670$	2905.21	0.167519
$671$	1038.51	0.0597484
$672$	7300.34	0.419072
$673$	26462.8	1.51570	0.757851	−	0.652428i	$-0.226249\pi$
$673$	26462.8	1.51570	0.757851	+	0.652428i	$0.226249\pi$
$674$	4059.53	0.231999
$675$	675.000	0.0384900
$676$	−32944.5	−1.87440
$677$	28533.1	1.61982	0.809908	−	0.586556i	$-0.199517\pi$
$677$	28533.1	1.61982	0.809908	+	0.586556i	$0.199517\pi$
$678$	1200.84	0.0680204
$679$	18027.6	1.01890
$680$	−6178.43	−0.348430
$681$	11146.7	0.627228
$682$	−281.367	−0.0157978
$683$	27990.7	1.56813	0.784066	−	0.620677i	$-0.213142\pi$
$683$	27990.7	1.56813	0.784066	+	0.620677i	$0.213142\pi$
$684$	3652.97	0.204203
$685$	4430.95	0.247150
$686$	−8568.96	−0.476916
$687$	7313.22	0.406138
$688$	11548.9	0.639967
$689$	7995.52	0.442097
$690$	−2649.68	−0.146191
$691$	9248.47	0.509158	0.254579	−	0.967052i	$-0.418063\pi$
$691$	9248.47	0.509158	0.254579	+	0.967052i	$0.418063\pi$
$692$	−13708.1	−0.753040
$693$	158.195	0.00867145
$694$	769.421	0.0420848
$695$	−7910.59	−0.431749
$696$	−1581.69	−0.0861403
$697$	−30440.6	−1.65426
$698$	−5560.17	−0.301512
$699$	−8112.87	−0.438994
$700$	2151.59	0.116175
$701$	16805.6	0.905474	0.452737	−	0.891644i	$-0.350448\pi$
$701$	16805.6	0.905474	0.452737	+	0.891644i	$0.350448\pi$
$702$	−2918.55	−0.156914
$703$	25715.3	1.37962
$704$	−2.68026	−0.000143489 0
$705$	2682.86	0.143322
$706$	−3129.48	−0.166826
$707$	−989.991	−0.0526626
$708$	−5378.60	−0.285509
$709$	28586.0	1.51421	0.757103	−	0.653296i	$-0.226614\pi$
$709$	28586.0	1.51421	0.757103	+	0.653296i	$0.226614\pi$
$710$	5067.25	0.267846
$711$	−2824.32	−0.148974
$712$	−1768.89	−0.0931067
$713$	23852.3	1.25284
$714$	3455.78	0.181133
$715$	560.538	0.0293188
$716$	−11941.1	−0.623268
$717$	18056.0	0.940465
$718$	−8301.42	−0.431485
$719$	−37753.6	−1.95824	−0.979119	−	0.203289i	$-0.934837\pi$
$719$	−37753.6	−1.95824	−0.979119	+	0.203289i	$0.934837\pi$
$720$	−1274.46	−0.0659674
$721$	17555.6	0.906805
$722$	3592.05	0.185156
$723$	−3734.70	−0.192109
$724$	19279.4	0.989659
$725$	−725.000	−0.0371391
$726$	5032.05	0.257241
$727$	−10769.6	−0.549412	−0.274706	−	0.961528i	$-0.588581\pi$
$727$	−10769.6	−0.549412	−0.274706	+	0.961528i	$0.588581\pi$
$728$	−20917.6	−1.06492
$729$	729.000	0.0370370
$730$	−951.638	−0.0482489
$731$	27716.1	1.40235
$732$	15254.6	0.770255
$733$	−29083.9	−1.46554	−0.732768	−	0.680479i	$-0.761772\pi$
$733$	−29083.9	−1.46554	−0.732768	+	0.680479i	$0.761772\pi$
$734$	922.549	0.0463923
$735$	2439.07	0.122403
$736$	25363.4	1.27025
$737$	−602.614	−0.0301188
$738$	5086.19	0.253693
$739$	5594.45	0.278478	0.139239	−	0.990259i	$-0.455534\pi$
$739$	5594.45	0.278478	0.139239	+	0.990259i	$0.455534\pi$
$740$	−13006.8	−0.646133
$741$	−16278.6	−0.807032
$742$	1581.85	0.0782634
$743$	8984.59	0.443624	0.221812	−	0.975089i	$-0.428803\pi$
$743$	8984.59	0.443624	0.221812	+	0.975089i	$0.428803\pi$
$744$	−9292.96	−0.457925
$745$	8247.87	0.405609
$746$	2111.10	0.103610
$747$	2254.63	0.110432
$748$	569.967	0.0278611
$749$	−11355.4	−0.553962
$750$	473.190	0.0230379
$751$	4621.64	0.224562	0.112281	−	0.993676i	$-0.464184\pi$
$751$	4621.64	0.224562	0.112281	+	0.993676i	$0.464184\pi$
$752$	−5065.50	−0.245638
$753$	7432.44	0.359699
$754$	3134.74	0.151406
$755$	−1719.26	−0.0828745
$756$	2323.71	0.111789
$757$	−5554.76	−0.266699	−0.133349	−	0.991069i	$-0.542573\pi$
$757$	−5554.76	−0.266699	−0.133349	+	0.991069i	$0.542573\pi$
$758$	−4745.07	−0.227373
$759$	549.611	0.0262841
$760$	5757.96	0.274820
$761$	28686.9	1.36649	0.683245	−	0.730189i	$-0.260568\pi$
$761$	28686.9	1.36649	0.683245	+	0.730189i	$0.260568\pi$
$762$	7328.79	0.348417
$763$	20186.9	0.957817
$764$	−33161.7	−1.57035
$765$	−3058.58	−0.144553
$766$	15824.5	0.746427
$767$	23968.5	1.12836
$768$	−5526.24	−0.259650
$769$	26311.7	1.23384	0.616921	−	0.787025i	$-0.288380\pi$
$769$	26311.7	1.23384	0.616921	+	0.787025i	$0.288380\pi$
$770$	110.898	0.00519024
$771$	−14334.2	−0.669565
$772$	21836.9	1.01804
$773$	−25176.4	−1.17145	−0.585727	−	0.810508i	$-0.699191\pi$
$773$	−25176.4	−1.17145	−0.585727	+	0.810508i	$0.699191\pi$
$774$	−4630.97	−0.215060
$775$	−4259.63	−0.197433
$776$	−24402.1	−1.12884
$777$	16357.9	0.755259
$778$	−7292.44	−0.336050
$779$	28369.0	1.30478
$780$	8233.73	0.377968
$781$	−1051.08	−0.0481568
$782$	12006.3	0.549034
$783$	−783.000	−0.0357371
$784$	−4605.20	−0.209785
$785$	−12469.2	−0.566934
$786$	4673.39	0.212079
$787$	−27651.8	−1.25245	−0.626226	−	0.779641i	$-0.715401\pi$
$787$	−27651.8	−1.25245	−0.626226	+	0.779641i	$0.715401\pi$
$788$	17058.9	0.771192
$789$	−4714.69	−0.212734
$790$	−1979.91	−0.0891673
$791$	4260.60	0.191516
$792$	−214.131	−0.00960709
$793$	−67978.7	−3.04413
$794$	−18163.7	−0.811847
$795$	−1400.03	−0.0624580
$796$	−7203.11	−0.320738
$797$	−35053.5	−1.55792	−0.778958	−	0.627076i	$-0.784252\pi$
$797$	−35053.5	−1.55792	−0.778958	+	0.627076i	$0.784252\pi$
$798$	−3220.59	−0.142867
$799$	−12156.7	−0.538262
$800$	−4529.49	−0.200177
$801$	−875.675	−0.0386273
$802$	−10877.5	−0.478923
$803$	197.394	0.00867482
$804$	−8851.77	−0.388281
$805$	−9401.13	−0.411610
$806$	18417.7	0.804883
$807$	14839.7	0.647315
$808$	1340.05	0.0583449
$809$	−23824.8	−1.03540	−0.517699	−	0.855563i	$-0.673211\pi$
$809$	−23824.8	−1.03540	−0.517699	+	0.855563i	$0.673211\pi$
$810$	511.045	0.0221683
$811$	19361.6	0.838322	0.419161	−	0.907912i	$-0.362324\pi$
$811$	19361.6	0.838322	0.419161	+	0.907912i	$0.362324\pi$
$812$	−2495.84	−0.107866
$813$	−2744.83	−0.118407
$814$	−670.401	−0.0288667
$815$	9575.61	0.411557
$816$	5774.90	0.247747
$817$	−25829.9	−1.10609
$818$	17738.9	0.758224
$819$	−10355.1	−0.441803
$820$	−14349.0	−0.611084
$821$	−14914.6	−0.634012	−0.317006	−	0.948424i	$-0.602678\pi$
$821$	−14914.6	−0.634012	−0.317006	+	0.948424i	$0.602678\pi$
$822$	3354.69	0.142346
$823$	7639.98	0.323588	0.161794	−	0.986825i	$-0.448272\pi$
$823$	7639.98	0.323588	0.161794	+	0.986825i	$0.448272\pi$
$824$	−23763.2	−1.00465
$825$	−98.1517	−0.00414206
$826$	4741.97	0.199751
$827$	12462.1	0.524003	0.262001	−	0.965068i	$-0.415618\pi$
$827$	12462.1	0.524003	0.262001	+	0.965068i	$0.415618\pi$
$828$	8073.21	0.338845
$829$	−26986.5	−1.13062	−0.565309	−	0.824880i	$-0.691243\pi$
$829$	−26986.5	−1.13062	−0.565309	+	0.824880i	$0.691243\pi$
$830$	1580.54	0.0660982
$831$	−7324.67	−0.305764
$832$	175.444	0.00731063
$833$	−11052.0	−0.459699
$834$	−5989.14	−0.248666
$835$	−497.903	−0.0206355
$836$	−531.178	−0.0219751
$837$	−4600.40	−0.189980
$838$	389.558	0.0160585
$839$	23448.1	0.964860	0.482430	−	0.875935i	$-0.339754\pi$
$839$	23448.1	0.964860	0.482430	+	0.875935i	$0.339754\pi$
$840$	3662.73	0.150448
$841$	841.000	0.0344828
$842$	−9263.78	−0.379158
$843$	−15933.1	−0.650968
$844$	−700.034	−0.0285499
$845$	−25706.7	−1.04655
$846$	2031.20	0.0825464
$847$	17853.8	0.724280
$848$	2643.40	0.107046
$849$	2007.50	0.0811511
$850$	−2144.13	−0.0865214
$851$	56831.8	2.28927
$852$	−15439.2	−0.620821
$853$	−30230.4	−1.21344	−0.606722	−	0.794914i	$-0.707516\pi$
$853$	−30230.4	−1.21344	−0.606722	+	0.794914i	$0.707516\pi$
$854$	−13449.0	−0.538895
$855$	2850.43	0.114015
$856$	15370.6	0.613734
$857$	32088.1	1.27900	0.639502	−	0.768789i	$-0.279140\pi$
$857$	32088.1	1.27900	0.639502	+	0.768789i	$0.279140\pi$
$858$	424.386	0.0168861
$859$	−43201.3	−1.71596	−0.857980	−	0.513683i	$-0.828281\pi$
$859$	−43201.3	−1.71596	−0.857980	+	0.513683i	$0.828281\pi$
$860$	13064.7	0.518028
$861$	18045.9	0.714290
$862$	21023.3	0.830692
$863$	−15650.5	−0.617323	−0.308662	−	0.951172i	$-0.599881\pi$
$863$	−15650.5	−0.617323	−0.308662	+	0.951172i	$0.599881\pi$
$864$	−4891.85	−0.192620
$865$	−10696.5	−0.420452
$866$	−12733.8	−0.499669
$867$	−879.859	−0.0344655
$868$	−14663.9	−0.573418
$869$	410.685	0.0160317
$870$	−548.901	−0.0213902
$871$	39445.9	1.53453
$872$	−27324.9	−1.06117
$873$	−12080.0	−0.468324
$874$	−11189.2	−0.433045
$875$	1678.89	0.0648650
$876$	2899.51	0.111833
$877$	−37921.1	−1.46010	−0.730049	−	0.683395i	$-0.760503\pi$
$877$	−37921.1	−1.46010	−0.730049	+	0.683395i	$0.760503\pi$
$878$	−6498.14	−0.249774
$879$	−22404.1	−0.859693
$880$	185.320	0.00709901
$881$	19844.4	0.758881	0.379441	−	0.925216i	$-0.376116\pi$
$881$	19844.4	0.758881	0.379441	+	0.925216i	$0.376116\pi$
$882$	1846.63	0.0704981
$883$	33386.5	1.27242	0.636210	−	0.771516i	$-0.280501\pi$
$883$	33386.5	1.27242	0.636210	+	0.771516i	$0.280501\pi$
$884$	−37308.9	−1.41950
$885$	−4196.95	−0.159411
$886$	−19963.0	−0.756964
$887$	−25988.8	−0.983788	−0.491894	−	0.870655i	$-0.663695\pi$
$887$	−25988.8	−0.983788	−0.491894	+	0.870655i	$0.663695\pi$
$888$	−22141.9	−0.836751
$889$	26002.7	0.980994
$890$	−613.867	−0.0231201
$891$	−106.004	−0.00398570
$892$	29832.3	1.11980
$893$	11329.3	0.424549
$894$	6244.50	0.233610
$895$	−9317.69	−0.347996
$896$	−19432.9	−0.724560
$897$	−35976.4	−1.33915
$898$	17543.4	0.651928
$899$	4941.17	0.183312
$900$	−1441.75	−0.0533980
$901$	6343.88	0.234568
$902$	−739.582	−0.0273009
$903$	−16430.8	−0.605518
$904$	−5767.12	−0.212181
$905$	15043.8	0.552566
$906$	−1301.66	−0.0477314
$907$	−26383.8	−0.965887	−0.482943	−	0.875652i	$-0.660432\pi$
$907$	−26383.8	−0.965887	−0.482943	+	0.875652i	$0.660432\pi$
$908$	−23808.4	−0.870166
$909$	663.378	0.0242056
$910$	−7259.15	−0.264438
$911$	−23448.5	−0.852779	−0.426390	−	0.904540i	$-0.640215\pi$
$911$	−23448.5	−0.852779	−0.426390	+	0.904540i	$0.640215\pi$
$912$	−5381.89	−0.195408
$913$	−327.845	−0.0118840
$914$	−5445.15	−0.197056
$915$	11903.2	0.430064
$916$	−15620.4	−0.563443
$917$	16581.3	0.597125
$918$	−2315.66	−0.0832553
$919$	−1649.45	−0.0592060	−0.0296030	−	0.999562i	$-0.509424\pi$
$919$	−1649.45	−0.0592060	−0.0296030	+	0.999562i	$0.509424\pi$
$920$	12725.3	0.456023
$921$	−29782.9	−1.06556
$922$	−7490.39	−0.267552
$923$	68801.4	2.45355
$924$	−337.891	−0.0120301
$925$	−10149.2	−0.360762
$926$	16270.7	0.577415
$927$	−11763.8	−0.416799
$928$	5254.20	0.185860
$929$	48039.5	1.69658	0.848291	−	0.529531i	$-0.177632\pi$
$929$	48039.5	1.69658	0.848291	+	0.529531i	$0.177632\pi$
$930$	−3224.99	−0.113711
$931$	10299.9	0.362582
$932$	17328.4	0.609026
$933$	9394.26	0.329640
$934$	−15967.0	−0.559376
$935$	444.748	0.0155559
$936$	14016.6	0.489473
$937$	−28647.5	−0.998796	−0.499398	−	0.866373i	$-0.666445\pi$
$937$	−28647.5	−0.998796	−0.499398	+	0.866373i	$0.666445\pi$
$938$	7804.04	0.271654
$939$	25304.2	0.879417
$940$	−5730.37	−0.198834
$941$	9541.12	0.330533	0.165267	−	0.986249i	$-0.447152\pi$
$941$	9541.12	0.330533	0.165267	+	0.986249i	$0.447152\pi$
$942$	−9440.45	−0.326525
$943$	62696.5	2.16509
$944$	7924.24	0.273212
$945$	1813.20	0.0624164
$946$	673.388	0.0231435
$947$	44596.6	1.53030	0.765151	−	0.643851i	$-0.222664\pi$
$947$	44596.6	1.53030	0.765151	+	0.643851i	$0.222664\pi$
$948$	6032.53	0.206674
$949$	−12921.0	−0.441974
$950$	1998.22	0.0682428
$951$	−27488.4	−0.937300
$952$	−16596.7	−0.565022
$953$	437.931	0.0148856	0.00744279	−	0.999972i	$-0.497631\pi$
$953$	437.931	0.0148856	0.00744279	+	0.999972i	$0.497631\pi$
$954$	−1059.97	−0.0359726
$955$	−25876.2	−0.876790
$956$	−38566.2	−1.30473
$957$	113.856	0.00384581
$958$	−11345.9	−0.382641
$959$	11902.5	0.400785
$960$	−30.7208	−0.00103282
$961$	−759.861	−0.0255064
$962$	43883.1	1.47073
$963$	7609.09	0.254620
$964$	7977.02	0.266517
$965$	17039.4	0.568413
$966$	−7117.64	−0.237067
$967$	−37762.6	−1.25580	−0.627902	−	0.778292i	$-0.716086\pi$
$967$	−37762.6	−1.25580	−0.627902	+	0.778292i	$0.716086\pi$
$968$	−24166.8	−0.802429
$969$	−12916.0	−0.428194
$970$	−8468.38	−0.280313
$971$	16153.0	0.533858	0.266929	−	0.963716i	$-0.413991\pi$
$971$	16153.0	0.533858	0.266929	+	0.963716i	$0.413991\pi$
$972$	−1557.09	−0.0513822
$973$	−21249.6	−0.700136
$974$	−9680.07	−0.318449
$975$	6424.81	0.211034
$976$	−22474.4	−0.737079
$977$	33700.3	1.10355	0.551775	−	0.833993i	$-0.313951\pi$
$977$	33700.3	1.10355	0.551775	+	0.833993i	$0.313951\pi$
$978$	7249.74	0.237036
$979$	127.332	0.00415683
$980$	−5209.66	−0.169813
$981$	−13526.9	−0.440247
$982$	−13025.8	−0.423290
$983$	−7637.13	−0.247799	−0.123900	−	0.992295i	$-0.539540\pi$
$983$	−7637.13	−0.247799	−0.123900	+	0.992295i	$0.539540\pi$
$984$	−24426.9	−0.791362
$985$	13311.2	0.430588
$986$	2487.20	0.0803331
$987$	7206.77	0.232415
$988$	34769.9	1.11961
$989$	−57085.1	−1.83539
$990$	−74.3110	−0.00238562
$991$	9339.90	0.299386	0.149693	−	0.988733i	$-0.452171\pi$
$991$	9339.90	0.299386	0.149693	+	0.988733i	$0.452171\pi$
$992$	30870.3	0.988038
$993$	15584.6	0.498049
$994$	13611.8	0.434346
$995$	−5620.61	−0.179081
$996$	−4815.70	−0.153204
$997$	−11144.7	−0.354017	−0.177009	−	0.984209i	$-0.556642\pi$
$997$	−11144.7	−0.354017	−0.177009	+	0.984209i	$0.556642\pi$
$998$	5533.39	0.175508
$999$	−10961.2	−0.347144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.3	✓	7
3.2	odd	2		1305.4.a.m.1.5		7
5.4	even	2		2175.4.a.m.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.3	✓	7	1.1	even	1	trivial
1305.4.a.m.1.5		7	3.2	odd	2
2175.4.a.m.1.5		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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26184 q^{2} +3.00000 q^{3} -6.40776 q^{4} -5.00000 q^{5} -3.78552 q^{6} -13.4311 q^{7} +18.1803 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.26184 q^{2} +3.00000 q^{3} -6.40776 q^{4} -5.00000 q^{5} -3.78552 q^{6} -13.4311 q^{7} +18.1803 q^{8} +9.00000 q^{9} +6.30920 q^{10} -1.30869 q^{11} -19.2233 q^{12} +85.6641 q^{13} +16.9479 q^{14} -15.0000 q^{15} +28.3214 q^{16} +67.9685 q^{17} -11.3566 q^{18} -63.3429 q^{19} +32.0388 q^{20} -40.2934 q^{21} +1.65136 q^{22} -139.990 q^{23} +54.5409 q^{24} +25.0000 q^{25} -108.094 q^{26} +27.0000 q^{27} +86.0634 q^{28} -29.0000 q^{29} +18.9276 q^{30} -170.385 q^{31} -181.179 q^{32} -3.92607 q^{33} -85.7654 q^{34} +67.1557 q^{35} -57.6698 q^{36} -405.970 q^{37} +79.9286 q^{38} +256.992 q^{39} -90.9015 q^{40} -447.863 q^{41} +50.8438 q^{42} +407.779 q^{43} +8.38576 q^{44} -45.0000 q^{45} +176.645 q^{46} -178.857 q^{47} +84.9643 q^{48} -162.605 q^{49} -31.5460 q^{50} +203.905 q^{51} -548.915 q^{52} +93.3357 q^{53} -34.0697 q^{54} +6.54344 q^{55} -244.182 q^{56} -190.029 q^{57} +36.5934 q^{58} +279.796 q^{59} +96.1164 q^{60} -793.549 q^{61} +214.999 q^{62} -120.880 q^{63} +2.04805 q^{64} -428.321 q^{65} +4.95407 q^{66} +460.471 q^{67} -435.526 q^{68} -419.971 q^{69} -84.7397 q^{70} +803.153 q^{71} +163.623 q^{72} -150.833 q^{73} +512.269 q^{74} +75.0000 q^{75} +405.886 q^{76} +17.5772 q^{77} -324.283 q^{78} -313.814 q^{79} -141.607 q^{80} +81.0000 q^{81} +565.132 q^{82} +250.514 q^{83} +258.190 q^{84} -339.842 q^{85} -514.552 q^{86} -87.0000 q^{87} -23.7923 q^{88} -97.2972 q^{89} +56.7828 q^{90} -1150.57 q^{91} +897.024 q^{92} -511.156 q^{93} +225.689 q^{94} +316.714 q^{95} -543.538 q^{96} -1342.23 q^{97} +205.181 q^{98} -11.7782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19} - 75 q^{20} - 111 q^{21} - 369 q^{22} - 68 q^{23} - 108 q^{24} + 175 q^{25} + 181 q^{26} + 189 q^{27} - 637 q^{28} - 203 q^{29} + 15 q^{30} - 480 q^{31} - 779 q^{32} - 33 q^{33} - 897 q^{34} + 185 q^{35} + 135 q^{36} - 1032 q^{37} - 194 q^{38} - 399 q^{39} + 180 q^{40} - 638 q^{41} - 225 q^{42} - 512 q^{43} + 625 q^{44} - 315 q^{45} + 16 q^{46} - 111 q^{47} - 159 q^{48} + 178 q^{49} - 25 q^{50} + 63 q^{51} - 1263 q^{52} + 410 q^{53} - 27 q^{54} + 55 q^{55} + 1174 q^{56} - 510 q^{57} + 29 q^{58} - 426 q^{59} - 225 q^{60} - 1192 q^{61} + 460 q^{62} - 333 q^{63} + 390 q^{64} + 665 q^{65} - 1107 q^{66} - 1671 q^{67} + 1509 q^{68} - 204 q^{69} + 375 q^{70} - 1324 q^{71} - 324 q^{72} - 852 q^{73} + 1780 q^{74} + 525 q^{75} - 564 q^{76} - 2107 q^{77} + 543 q^{78} + 366 q^{79} + 265 q^{80} + 567 q^{81} - 318 q^{82} + 470 q^{83} - 1911 q^{84} - 105 q^{85} - 2196 q^{86} - 609 q^{87} - 2518 q^{88} + 51 q^{89} + 45 q^{90} - 1297 q^{91} - 684 q^{92} - 1440 q^{93} - 1837 q^{94} + 850 q^{95} - 2337 q^{96} - 3322 q^{97} + 1068 q^{98} - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

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