LMFDB - Embedded newform 425.4.b.c.324.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(324,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("425.324");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$25.0758117524$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	425.324
Dual form			425.4.b.c.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.00000i q^{2} +8.00000i q^{3} -1.00000 q^{4} +24.0000 q^{6} -28.0000i q^{7} -21.0000i q^{8} -37.0000 q^{9} +O(q^{10})$	\(q-3.00000i q^{2} +8.00000i q^{3} -1.00000 q^{4} +24.0000 q^{6} -28.0000i q^{7} -21.0000i q^{8} -37.0000 q^{9} -24.0000 q^{11} -8.00000i q^{12} +58.0000i q^{13} -84.0000 q^{14} -71.0000 q^{16} +17.0000i q^{17} +111.000i q^{18} -116.000 q^{19} +224.000 q^{21} +72.0000i q^{22} +60.0000i q^{23} +168.000 q^{24} +174.000 q^{26} -80.0000i q^{27} +28.0000i q^{28} -30.0000 q^{29} -172.000 q^{31} +45.0000i q^{32} -192.000i q^{33} +51.0000 q^{34} +37.0000 q^{36} -58.0000i q^{37} +348.000i q^{38} -464.000 q^{39} -342.000 q^{41} -672.000i q^{42} +148.000i q^{43} +24.0000 q^{44} +180.000 q^{46} +288.000i q^{47} -568.000i q^{48} -441.000 q^{49} -136.000 q^{51} -58.0000i q^{52} -318.000i q^{53} -240.000 q^{54} -588.000 q^{56} -928.000i q^{57} +90.0000i q^{58} -252.000 q^{59} +110.000 q^{61} +516.000i q^{62} +1036.00i q^{63} -433.000 q^{64} -576.000 q^{66} -484.000i q^{67} -17.0000i q^{68} -480.000 q^{69} -708.000 q^{71} +777.000i q^{72} -362.000i q^{73} -174.000 q^{74} +116.000 q^{76} +672.000i q^{77} +1392.00i q^{78} +484.000 q^{79} -359.000 q^{81} +1026.00i q^{82} -756.000i q^{83} -224.000 q^{84} +444.000 q^{86} -240.000i q^{87} +504.000i q^{88} +774.000 q^{89} +1624.00 q^{91} -60.0000i q^{92} -1376.00i q^{93} +864.000 q^{94} -360.000 q^{96} -382.000i q^{97} +1323.00i q^{98} +888.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 48 q^{6} - 74 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 48 * q^6 - 74 * q^9	$ 2 q - 2 q^{4} + 48 q^{6} - 74 q^{9} - 48 q^{11} - 168 q^{14} - 142 q^{16} - 232 q^{19} + 448 q^{21} + 336 q^{24} + 348 q^{26} - 60 q^{29} - 344 q^{31} + 102 q^{34} + 74 q^{36} - 928 q^{39} - 684 q^{41} + 48 q^{44} + 360 q^{46} - 882 q^{49} - 272 q^{51} - 480 q^{54} - 1176 q^{56} - 504 q^{59} + 220 q^{61} - 866 q^{64} - 1152 q^{66} - 960 q^{69} - 1416 q^{71} - 348 q^{74} + 232 q^{76} + 968 q^{79} - 718 q^{81} - 448 q^{84} + 888 q^{86} + 1548 q^{89} + 3248 q^{91} + 1728 q^{94} - 720 q^{96} + 1776 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 48 * q^6 - 74 * q^9 - 48 * q^11 - 168 * q^14 - 142 * q^16 - 232 * q^19 + 448 * q^21 + 336 * q^24 + 348 * q^26 - 60 * q^29 - 344 * q^31 + 102 * q^34 + 74 * q^36 - 928 * q^39 - 684 * q^41 + 48 * q^44 + 360 * q^46 - 882 * q^49 - 272 * q^51 - 480 * q^54 - 1176 * q^56 - 504 * q^59 + 220 * q^61 - 866 * q^64 - 1152 * q^66 - 960 * q^69 - 1416 * q^71 - 348 * q^74 + 232 * q^76 + 968 * q^79 - 718 * q^81 - 448 * q^84 + 888 * q^86 + 1548 * q^89 + 3248 * q^91 + 1728 * q^94 - 720 * q^96 + 1776 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 3.00000i	− 1.06066i	−0.847791	−	0.530330i	$-0.822068\pi$
$2$	− 3.00000i	− 1.06066i	0.847791	−	0.530330i	$-0.177932\pi$
$3$	8.00000i	1.53960i	0.638285	+	0.769800i	$0.279644\pi$
$3$	8.00000i	1.53960i	−0.638285	+	0.769800i	$0.720356\pi$
$4$	−1.00000	−0.125000
$5$	0	0
$5$	0	0
$6$	24.0000	1.63299
$7$	− 28.0000i	− 1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	− 28.0000i	− 1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$	− 21.0000i	− 0.928078i
$9$	−37.0000	−1.37037
$10$	0	0
$11$	−24.0000	−0.657843	−0.328921	−	0.944357i	$-0.606685\pi$
$11$	−24.0000	−0.657843	−0.328921	+	0.944357i	$0.606685\pi$
$12$	− 8.00000i	− 0.192450i
$13$	58.0000i	1.23741i	0.785624	+	0.618704i	$0.212342\pi$
$13$	58.0000i	1.23741i	−0.785624	+	0.618704i	$0.787658\pi$
$14$	−84.0000	−1.60357
$15$	0	0
$16$	−71.0000	−1.10938
$17$	17.0000i	0.242536i
$17$	17.0000i	0.242536i
$18$	111.000i	1.45350i
$19$	−116.000	−1.40064	−0.700322	−	0.713827i	$-0.746960\pi$
$19$	−116.000	−1.40064	−0.700322	+	0.713827i	$0.746960\pi$
$20$	0	0
$21$	224.000	2.32766
$22$	72.0000i	0.697748i
$23$	60.0000i	0.543951i	0.962304	+	0.271975i	$0.0876769\pi$
$23$	60.0000i	0.543951i	−0.962304	+	0.271975i	$0.912323\pi$
$24$	168.000	1.42887
$25$	0	0
$26$	174.000	1.31247
$27$	− 80.0000i	− 0.570222i
$28$	28.0000i	0.188982i
$29$	−30.0000	−0.192099	−0.0960493	−	0.995377i	$-0.530621\pi$
$29$	−30.0000	−0.192099	−0.0960493	+	0.995377i	$0.530621\pi$
$30$	0	0
$31$	−172.000	−0.996520	−0.498260	−	0.867028i	$-0.666027\pi$
$31$	−172.000	−0.996520	−0.498260	+	0.867028i	$0.666027\pi$
$32$	45.0000i	0.248592i
$33$	− 192.000i	− 1.01282i
$34$	51.0000	0.257248
$35$	0	0
$36$	37.0000	0.171296
$37$	− 58.0000i	− 0.257707i	−0.991664	−	0.128853i	$-0.958870\pi$
$37$	− 58.0000i	− 0.257707i	0.991664	−	0.128853i	$-0.0411296\pi$
$38$	348.000i	1.48561i
$39$	−464.000	−1.90511
$40$	0	0
$41$	−342.000	−1.30272	−0.651359	−	0.758770i	$-0.725801\pi$
$41$	−342.000	−1.30272	−0.651359	+	0.758770i	$0.725801\pi$
$42$	− 672.000i	− 2.46885i
$43$	148.000i	0.524879i	0.964948	+	0.262439i	$0.0845270\pi$
$43$	148.000i	0.524879i	−0.964948	+	0.262439i	$0.915473\pi$
$44$	24.0000	0.0822304
$45$	0	0
$46$	180.000	0.576947
$47$	288.000i	0.893811i	0.894581	+	0.446906i	$0.147474\pi$
$47$	288.000i	0.893811i	−0.894581	+	0.446906i	$0.852526\pi$
$48$	− 568.000i	− 1.70799i
$49$	−441.000	−1.28571
$50$	0	0
$51$	−136.000	−0.373408
$52$	− 58.0000i	− 0.154676i
$53$	− 318.000i	− 0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$	− 318.000i	− 0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−240.000	−0.604812
$55$	0	0
$56$	−588.000	−1.40312
$57$	− 928.000i	− 2.15643i
$58$	90.0000i	0.203751i
$59$	−252.000	−0.556061	−0.278031	−	0.960572i	$-0.589682\pi$
$59$	−252.000	−0.556061	−0.278031	+	0.960572i	$0.589682\pi$
$60$	0	0
$61$	110.000	0.230886	0.115443	−	0.993314i	$-0.463171\pi$
$61$	110.000	0.230886	0.115443	+	0.993314i	$0.463171\pi$
$62$	516.000i	1.05697i
$63$	1036.00i	2.07181i
$64$	−433.000	−0.845703
$65$	0	0
$66$	−576.000	−1.07425
$67$	− 484.000i	− 0.882537i	−0.897375	−	0.441269i	$-0.854529\pi$
$67$	− 484.000i	− 0.882537i	0.897375	−	0.441269i	$-0.145471\pi$
$68$	− 17.0000i	− 0.0303170i
$69$	−480.000	−0.837467
$70$	0	0
$71$	−708.000	−1.18344	−0.591719	−	0.806144i	$-0.701551\pi$
$71$	−708.000	−1.18344	−0.591719	+	0.806144i	$0.701551\pi$
$72$	777.000i	1.27181i
$73$	− 362.000i	− 0.580396i	−0.956967	−	0.290198i	$-0.906279\pi$
$73$	− 362.000i	− 0.580396i	0.956967	−	0.290198i	$-0.0937211\pi$
$74$	−174.000	−0.273339
$75$	0	0
$76$	116.000	0.175080
$77$	672.000i	0.994565i
$78$	1392.00i	2.02068i
$79$	484.000	0.689294	0.344647	−	0.938732i	$-0.387999\pi$
$79$	484.000	0.689294	0.344647	+	0.938732i	$0.387999\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	1026.00i	1.38174i
$83$	− 756.000i	− 0.999780i	−0.866089	−	0.499890i	$-0.833374\pi$
$83$	− 756.000i	− 0.999780i	0.866089	−	0.499890i	$-0.166626\pi$
$84$	−224.000	−0.290957
$85$	0	0
$86$	444.000	0.556718
$87$	− 240.000i	− 0.295755i
$88$	504.000i	0.610529i
$89$	774.000	0.921841	0.460920	−	0.887441i	$-0.347519\pi$
$89$	774.000	0.921841	0.460920	+	0.887441i	$0.347519\pi$
$90$	0	0
$91$	1624.00	1.87079
$92$	− 60.0000i	− 0.0679938i
$93$	− 1376.00i	− 1.53424i
$94$	864.000	0.948030
$95$	0	0
$96$	−360.000	−0.382733
$97$	− 382.000i	− 0.399858i	−0.979810	−	0.199929i	$-0.935929\pi$
$97$	− 382.000i	− 0.399858i	0.979810	−	0.199929i	$-0.0640711\pi$
$98$	1323.00i	1.36371i
$99$	888.000	0.901488
$100$	0	0
$101$	−210.000	−0.206889	−0.103444	−	0.994635i	$-0.532986\pi$
$101$	−210.000	−0.206889	−0.103444	+	0.994635i	$0.532986\pi$
$102$	408.000i	0.396059i
$103$	232.000i	0.221938i	0.993824	+	0.110969i	$0.0353955\pi$
$103$	232.000i	0.221938i	−0.993824	+	0.110969i	$0.964605\pi$
$104$	1218.00	1.14841
$105$	0	0
$106$	−954.000	−0.874157
$107$	432.000i	0.390309i	0.980773	+	0.195154i	$0.0625208\pi$
$107$	432.000i	0.390309i	−0.980773	+	0.195154i	$0.937479\pi$
$108$	80.0000i	0.0712778i
$109$	1186.00	1.04219	0.521093	−	0.853500i	$-0.325525\pi$
$109$	1186.00	1.04219	0.521093	+	0.853500i	$0.325525\pi$
$110$	0	0
$111$	464.000	0.396765
$112$	1988.00i	1.67722i
$113$	366.000i	0.304694i	0.988327	+	0.152347i	$0.0486831\pi$
$113$	366.000i	0.304694i	−0.988327	+	0.152347i	$0.951317\pi$
$114$	−2784.00	−2.28724
$115$	0	0
$116$	30.0000	0.0240123
$117$	− 2146.00i	− 1.69571i
$118$	756.000i	0.589792i
$119$	476.000	0.366679
$120$	0	0
$121$	−755.000	−0.567243
$122$	− 330.000i	− 0.244892i
$123$	− 2736.00i	− 2.00567i
$124$	172.000	0.124565
$125$	0	0
$126$	3108.00	2.19748
$127$	− 472.000i	− 0.329789i	−0.986311	−	0.164895i	$-0.947272\pi$
$127$	− 472.000i	− 0.329789i	0.986311	−	0.164895i	$-0.0527284\pi$
$128$	1659.00i	1.14560i
$129$	−1184.00	−0.808104
$130$	0	0
$131$	2760.00	1.84078	0.920391	−	0.391000i	$-0.127871\pi$
$131$	2760.00	1.84078	0.920391	+	0.391000i	$0.127871\pi$
$132$	192.000i	0.126602i
$133$	3248.00i	2.11757i
$134$	−1452.00	−0.936072
$135$	0	0
$136$	357.000	0.225092
$137$	1098.00i	0.684733i	0.939566	+	0.342367i	$0.111229\pi$
$137$	1098.00i	0.684733i	−0.939566	+	0.342367i	$0.888771\pi$
$138$	1440.00i	0.888268i
$139$	−2528.00	−1.54261	−0.771303	−	0.636468i	$-0.780395\pi$
$139$	−2528.00	−1.54261	−0.771303	+	0.636468i	$0.780395\pi$
$140$	0	0
$141$	−2304.00	−1.37611
$142$	2124.00i	1.25523i
$143$	− 1392.00i	− 0.814020i
$144$	2627.00	1.52025
$145$	0	0
$146$	−1086.00	−0.615603
$147$	− 3528.00i	− 1.97949i
$148$	58.0000i	0.0322133i
$149$	−1614.00	−0.887410	−0.443705	−	0.896173i	$-0.646336\pi$
$149$	−1614.00	−0.887410	−0.443705	+	0.896173i	$0.646336\pi$
$150$	0	0
$151$	−3328.00	−1.79357	−0.896784	−	0.442468i	$-0.854103\pi$
$151$	−3328.00	−1.79357	−0.896784	+	0.442468i	$0.854103\pi$
$152$	2436.00i	1.29991i
$153$	− 629.000i	− 0.332364i
$154$	2016.00	1.05490
$155$	0	0
$156$	464.000	0.238139
$157$	− 2458.00i	− 1.24949i	−0.780829	−	0.624744i	$-0.785203\pi$
$157$	− 2458.00i	− 1.24949i	0.780829	−	0.624744i	$-0.214797\pi$
$158$	− 1452.00i	− 0.731107i
$159$	2544.00	1.26888
$160$	0	0
$161$	1680.00	0.822376
$162$	1077.00i	0.522328i
$163$	− 272.000i	− 0.130704i	−0.997862	−	0.0653518i	$-0.979183\pi$
$163$	− 272.000i	− 0.130704i	0.997862	−	0.0653518i	$-0.0208170\pi$
$164$	342.000	0.162840
$165$	0	0
$166$	−2268.00	−1.06043
$167$	3516.00i	1.62920i	0.580024	+	0.814600i	$0.303043\pi$
$167$	3516.00i	1.62920i	−0.580024	+	0.814600i	$0.696957\pi$
$168$	− 4704.00i	− 2.16025i
$169$	−1167.00	−0.531179
$170$	0	0
$171$	4292.00	1.91940
$172$	− 148.000i	− 0.0656099i
$173$	1842.00i	0.809507i	0.914426	+	0.404753i	$0.132643\pi$
$173$	1842.00i	0.809507i	−0.914426	+	0.404753i	$0.867357\pi$
$174$	−720.000	−0.313696
$175$	0	0
$176$	1704.00	0.729795
$177$	− 2016.00i	− 0.856112i
$178$	− 2322.00i	− 0.977760i
$179$	3516.00	1.46815	0.734073	−	0.679070i	$-0.237617\pi$
$179$	3516.00	1.46815	0.734073	+	0.679070i	$0.237617\pi$
$180$	0	0
$181$	3398.00	1.39542	0.697711	−	0.716379i	$-0.254202\pi$
$181$	3398.00	1.39542	0.697711	+	0.716379i	$0.254202\pi$
$182$	− 4872.00i	− 1.98427i
$183$	880.000i	0.355473i
$184$	1260.00	0.504828
$185$	0	0
$186$	−4128.00	−1.62731
$187$	− 408.000i	− 0.159550i
$188$	− 288.000i	− 0.111726i
$189$	−2240.00	−0.862095
$190$	0	0
$191$	−2640.00	−1.00012	−0.500062	−	0.865990i	$-0.666689\pi$
$191$	−2640.00	−1.00012	−0.500062	+	0.865990i	$0.666689\pi$
$192$	− 3464.00i	− 1.30205i
$193$	− 2882.00i	− 1.07488i	−0.843304	−	0.537438i	$-0.819392\pi$
$193$	− 2882.00i	− 1.07488i	0.843304	−	0.537438i	$-0.180608\pi$
$194$	−1146.00	−0.424113
$195$	0	0
$196$	441.000	0.160714
$197$	− 42.0000i	− 0.0151897i	−0.999971	−	0.00759486i	$-0.997582\pi$
$197$	− 42.0000i	− 0.0151897i	0.999971	−	0.00759486i	$-0.00241754\pi$
$198$	− 2664.00i	− 0.956173i
$199$	3220.00	1.14703	0.573517	−	0.819194i	$-0.305579\pi$
$199$	3220.00	1.14703	0.573517	+	0.819194i	$0.305579\pi$
$200$	0	0
$201$	3872.00	1.35876
$202$	630.000i	0.219439i
$203$	840.000i	0.290426i
$204$	136.000	0.0466760
$205$	0	0
$206$	696.000	0.235401
$207$	− 2220.00i	− 0.745414i
$208$	− 4118.00i	− 1.37275i
$209$	2784.00	0.921403
$210$	0	0
$211$	−2080.00	−0.678640	−0.339320	−	0.940671i	$-0.610197\pi$
$211$	−2080.00	−0.678640	−0.339320	+	0.940671i	$0.610197\pi$
$212$	318.000i	0.103020i
$213$	− 5664.00i	− 1.82202i
$214$	1296.00	0.413985
$215$	0	0
$216$	−1680.00	−0.529211
$217$	4816.00i	1.50660i
$218$	− 3558.00i	− 1.10540i
$219$	2896.00	0.893578
$220$	0	0
$221$	−986.000	−0.300116
$222$	− 1392.00i	− 0.420833i
$223$	− 4664.00i	− 1.40056i	−0.713869	−	0.700279i	$-0.753059\pi$
$223$	− 4664.00i	− 1.40056i	0.713869	−	0.700279i	$-0.246941\pi$
$224$	1260.00	0.375836
$225$	0	0
$226$	1098.00	0.323176
$227$	− 1440.00i	− 0.421040i	−0.977590	−	0.210520i	$-0.932484\pi$
$227$	− 1440.00i	− 0.421040i	0.977590	−	0.210520i	$-0.0675158\pi$
$228$	928.000i	0.269554i
$229$	1186.00	0.342241	0.171120	−	0.985250i	$-0.445261\pi$
$229$	1186.00	0.342241	0.171120	+	0.985250i	$0.445261\pi$
$230$	0	0
$231$	−5376.00	−1.53123
$232$	630.000i	0.178282i
$233$	5334.00i	1.49975i	0.661579	+	0.749875i	$0.269887\pi$
$233$	5334.00i	1.49975i	−0.661579	+	0.749875i	$0.730113\pi$
$234$	−6438.00	−1.79857
$235$	0	0
$236$	252.000	0.0695076
$237$	3872.00i	1.06124i
$238$	− 1428.00i	− 0.388922i
$239$	−5328.00	−1.44201	−0.721003	−	0.692931i	$-0.756319\pi$
$239$	−5328.00	−1.44201	−0.721003	+	0.692931i	$0.756319\pi$
$240$	0	0
$241$	5618.00	1.50161	0.750803	−	0.660526i	$-0.229667\pi$
$241$	5618.00	1.50161	0.750803	+	0.660526i	$0.229667\pi$
$242$	2265.00i	0.601652i
$243$	− 5032.00i	− 1.32841i
$244$	−110.000	−0.0288608
$245$	0	0
$246$	−8208.00	−2.12733
$247$	− 6728.00i	− 1.73317i
$248$	3612.00i	0.924848i
$249$	6048.00	1.53926
$250$	0	0
$251$	−2028.00	−0.509985	−0.254992	−	0.966943i	$-0.582073\pi$
$251$	−2028.00	−0.509985	−0.254992	+	0.966943i	$0.582073\pi$
$252$	− 1036.00i	− 0.258976i
$253$	− 1440.00i	− 0.357834i
$254$	−1416.00	−0.349794
$255$	0	0
$256$	1513.00	0.369385
$257$	− 1902.00i	− 0.461648i	−0.972996	−	0.230824i	$-0.925858\pi$
$257$	− 1902.00i	− 0.461648i	0.972996	−	0.230824i	$-0.0741421\pi$
$258$	3552.00i	0.857123i
$259$	−1624.00	−0.389616
$260$	0	0
$261$	1110.00	0.263246
$262$	− 8280.00i	− 1.95244i
$263$	5472.00i	1.28296i	0.767141	+	0.641479i	$0.221679\pi$
$263$	5472.00i	1.28296i	−0.767141	+	0.641479i	$0.778321\pi$
$264$	−4032.00	−0.939971
$265$	0	0
$266$	9744.00	2.24603
$267$	6192.00i	1.41927i
$268$	484.000i	0.110317i
$269$	3570.00	0.809170	0.404585	−	0.914500i	$-0.367416\pi$
$269$	3570.00	0.809170	0.404585	+	0.914500i	$0.367416\pi$
$270$	0	0
$271$	272.000	0.0609698	0.0304849	−	0.999535i	$-0.490295\pi$
$271$	272.000	0.0609698	0.0304849	+	0.999535i	$0.490295\pi$
$272$	− 1207.00i	− 0.269063i
$273$	12992.0i	2.88026i
$274$	3294.00	0.726269
$275$	0	0
$276$	480.000	0.104683
$277$	3830.00i	0.830767i	0.909646	+	0.415383i	$0.136353\pi$
$277$	3830.00i	0.830767i	−0.909646	+	0.415383i	$0.863647\pi$
$278$	7584.00i	1.63618i
$279$	6364.00	1.36560
$280$	0	0
$281$	8874.00	1.88391	0.941955	−	0.335740i	$-0.108986\pi$
$281$	8874.00	1.88391	0.941955	+	0.335740i	$0.108986\pi$
$282$	6912.00i	1.45959i
$283$	2632.00i	0.552849i	0.961036	+	0.276424i	$0.0891495\pi$
$283$	2632.00i	0.552849i	−0.961036	+	0.276424i	$0.910850\pi$
$284$	708.000	0.147930
$285$	0	0
$286$	−4176.00	−0.863399
$287$	9576.00i	1.96952i
$288$	− 1665.00i	− 0.340663i
$289$	−289.000	−0.0588235
$290$	0	0
$291$	3056.00	0.615622
$292$	362.000i	0.0725495i
$293$	6402.00i	1.27648i	0.769837	+	0.638240i	$0.220337\pi$
$293$	6402.00i	1.27648i	−0.769837	+	0.638240i	$0.779663\pi$
$294$	−10584.0	−2.09956
$295$	0	0
$296$	−1218.00	−0.239172
$297$	1920.00i	0.375117i
$298$	4842.00i	0.941240i
$299$	−3480.00	−0.673089
$300$	0	0
$301$	4144.00	0.793542
$302$	9984.00i	1.90237i
$303$	− 1680.00i	− 0.318526i
$304$	8236.00	1.55384
$305$	0	0
$306$	−1887.00	−0.352525
$307$	− 8980.00i	− 1.66943i	−0.550681	−	0.834716i	$-0.685632\pi$
$307$	− 8980.00i	− 1.66943i	0.550681	−	0.834716i	$-0.314368\pi$
$308$	− 672.000i	− 0.124321i
$309$	−1856.00	−0.341696
$310$	0	0
$311$	−3972.00	−0.724217	−0.362108	−	0.932136i	$-0.617943\pi$
$311$	−3972.00	−0.724217	−0.362108	+	0.932136i	$0.617943\pi$
$312$	9744.00i	1.76809i
$313$	− 4730.00i	− 0.854171i	−0.904211	−	0.427085i	$-0.859540\pi$
$313$	− 4730.00i	− 0.854171i	0.904211	−	0.427085i	$-0.140460\pi$
$314$	−7374.00	−1.32528
$315$	0	0
$316$	−484.000	−0.0861618
$317$	− 2898.00i	− 0.513463i	−0.966483	−	0.256732i	$-0.917354\pi$
$317$	− 2898.00i	− 0.513463i	0.966483	−	0.256732i	$-0.0826457\pi$
$318$	− 7632.00i	− 1.34585i
$319$	720.000	0.126371
$320$	0	0
$321$	−3456.00	−0.600919
$322$	− 5040.00i	− 0.872262i
$323$	− 1972.00i	− 0.339706i
$324$	359.000	0.0615569
$325$	0	0
$326$	−816.000	−0.138632
$327$	9488.00i	1.60455i
$328$	7182.00i	1.20902i
$329$	8064.00	1.35132
$330$	0	0
$331$	−4564.00	−0.757886	−0.378943	−	0.925420i	$-0.623712\pi$
$331$	−4564.00	−0.757886	−0.378943	+	0.925420i	$0.623712\pi$
$332$	756.000i	0.124973i
$333$	2146.00i	0.353153i
$334$	10548.0	1.72803
$335$	0	0
$336$	−15904.0	−2.58225
$337$	722.000i	0.116706i	0.998296	+	0.0583529i	$0.0185849\pi$
$337$	722.000i	0.116706i	−0.998296	+	0.0583529i	$0.981415\pi$
$338$	3501.00i	0.563400i
$339$	−2928.00	−0.469107
$340$	0	0
$341$	4128.00	0.655553
$342$	− 12876.0i	− 2.03583i
$343$	2744.00i	0.431959i
$344$	3108.00	0.487128
$345$	0	0
$346$	5526.00	0.858612
$347$	5544.00i	0.857687i	0.903379	+	0.428844i	$0.141079\pi$
$347$	5544.00i	0.857687i	−0.903379	+	0.428844i	$0.858921\pi$
$348$	240.000i	0.0369694i
$349$	−11126.0	−1.70648	−0.853239	−	0.521519i	$-0.825365\pi$
$349$	−11126.0	−1.70648	−0.853239	+	0.521519i	$0.825365\pi$
$350$	0	0
$351$	4640.00	0.705598
$352$	− 1080.00i	− 0.163535i
$353$	− 7842.00i	− 1.18240i	−0.806525	−	0.591200i	$-0.798654\pi$
$353$	− 7842.00i	− 1.18240i	0.806525	−	0.591200i	$-0.201346\pi$
$354$	−6048.00	−0.908044
$355$	0	0
$356$	−774.000	−0.115230
$357$	3808.00i	0.564540i
$358$	− 10548.0i	− 1.55720i
$359$	−5040.00	−0.740950	−0.370475	−	0.928842i	$-0.620805\pi$
$359$	−5040.00	−0.740950	−0.370475	+	0.928842i	$0.620805\pi$
$360$	0	0
$361$	6597.00	0.961802
$362$	− 10194.0i	− 1.48007i
$363$	− 6040.00i	− 0.873327i
$364$	−1624.00	−0.233848
$365$	0	0
$366$	2640.00	0.377036
$367$	− 8404.00i	− 1.19533i	−0.801747	−	0.597664i	$-0.796096\pi$
$367$	− 8404.00i	− 1.19533i	0.801747	−	0.597664i	$-0.203904\pi$
$368$	− 4260.00i	− 0.603445i
$369$	12654.0	1.78521
$370$	0	0
$371$	−8904.00	−1.24602
$372$	1376.00i	0.191780i
$373$	8098.00i	1.12412i	0.827095	+	0.562062i	$0.189992\pi$
$373$	8098.00i	1.12412i	−0.827095	+	0.562062i	$0.810008\pi$
$374$	−1224.00	−0.169229
$375$	0	0
$376$	6048.00	0.829526
$377$	− 1740.00i	− 0.237704i
$378$	6720.00i	0.914390i
$379$	−320.000	−0.0433702	−0.0216851	−	0.999765i	$-0.506903\pi$
$379$	−320.000	−0.0433702	−0.0216851	+	0.999765i	$0.506903\pi$
$380$	0	0
$381$	3776.00	0.507744
$382$	7920.00i	1.06079i
$383$	10872.0i	1.45048i	0.688497	+	0.725239i	$0.258271\pi$
$383$	10872.0i	1.45048i	−0.688497	+	0.725239i	$0.741729\pi$
$384$	−13272.0	−1.76376
$385$	0	0
$386$	−8646.00	−1.14008
$387$	− 5476.00i	− 0.719278i
$388$	382.000i	0.0499822i
$389$	−1374.00	−0.179086	−0.0895431	−	0.995983i	$-0.528541\pi$
$389$	−1374.00	−0.179086	−0.0895431	+	0.995983i	$0.528541\pi$
$390$	0	0
$391$	−1020.00	−0.131927
$392$	9261.00i	1.19324i
$393$	22080.0i	2.83407i
$394$	−126.000	−0.0161111
$395$	0	0
$396$	−888.000	−0.112686
$397$	− 7522.00i	− 0.950928i	−0.879735	−	0.475464i	$-0.842280\pi$
$397$	− 7522.00i	− 0.950928i	0.879735	−	0.475464i	$-0.157720\pi$
$398$	− 9660.00i	− 1.21661i
$399$	−25984.0	−3.26022
$400$	0	0
$401$	2706.00	0.336986	0.168493	−	0.985703i	$-0.446110\pi$
$401$	2706.00	0.336986	0.168493	+	0.985703i	$0.446110\pi$
$402$	− 11616.0i	− 1.44118i
$403$	− 9976.00i	− 1.23310i
$404$	210.000	0.0258611
$405$	0	0
$406$	2520.00	0.308043
$407$	1392.00i	0.169530i
$408$	2856.00i	0.346552i
$409$	−266.000	−0.0321586	−0.0160793	−	0.999871i	$-0.505118\pi$
$409$	−266.000	−0.0321586	−0.0160793	+	0.999871i	$0.505118\pi$
$410$	0	0
$411$	−8784.00	−1.05422
$412$	− 232.000i	− 0.0277423i
$413$	7056.00i	0.840685i
$414$	−6660.00	−0.790631
$415$	0	0
$416$	−2610.00	−0.307610
$417$	− 20224.0i	− 2.37500i
$418$	− 8352.00i	− 0.977296i
$419$	−2688.00	−0.313407	−0.156703	−	0.987646i	$-0.550087\pi$
$419$	−2688.00	−0.313407	−0.156703	+	0.987646i	$0.550087\pi$
$420$	0	0
$421$	−13810.0	−1.59871	−0.799357	−	0.600857i	$-0.794826\pi$
$421$	−13810.0	−1.59871	−0.799357	+	0.600857i	$0.794826\pi$
$422$	6240.00i	0.719807i
$423$	− 10656.0i	− 1.22485i
$424$	−6678.00	−0.764888
$425$	0	0
$426$	−16992.0	−1.93255
$427$	− 3080.00i	− 0.349067i
$428$	− 432.000i	− 0.0487886i
$429$	11136.0	1.25327
$430$	0	0
$431$	3036.00	0.339302	0.169651	−	0.985504i	$-0.445736\pi$
$431$	3036.00	0.339302	0.169651	+	0.985504i	$0.445736\pi$
$432$	5680.00i	0.632591i
$433$	11422.0i	1.26768i	0.773463	+	0.633841i	$0.218523\pi$
$433$	11422.0i	1.26768i	−0.773463	+	0.633841i	$0.781477\pi$
$434$	14448.0	1.59799
$435$	0	0
$436$	−1186.00	−0.130273
$437$	− 6960.00i	− 0.761881i
$438$	− 8688.00i	− 0.947782i
$439$	52.0000	0.00565336	0.00282668	−	0.999996i	$-0.499100\pi$
$439$	52.0000	0.00565336	0.00282668	+	0.999996i	$0.499100\pi$
$440$	0	0
$441$	16317.0	1.76190
$442$	2958.00i	0.318321i
$443$	− 3108.00i	− 0.333331i	−0.986014	−	0.166665i	$-0.946700\pi$
$443$	− 3108.00i	− 0.333331i	0.986014	−	0.166665i	$-0.0533000\pi$
$444$	−464.000	−0.0495956
$445$	0	0
$446$	−13992.0	−1.48552
$447$	− 12912.0i	− 1.36626i
$448$	12124.0i	1.27858i
$449$	−6114.00	−0.642622	−0.321311	−	0.946974i	$-0.604124\pi$
$449$	−6114.00	−0.642622	−0.321311	+	0.946974i	$0.604124\pi$
$450$	0	0
$451$	8208.00	0.856984
$452$	− 366.000i	− 0.0380867i
$453$	− 26624.0i	− 2.76138i
$454$	−4320.00	−0.446581
$455$	0	0
$456$	−19488.0	−2.00134
$457$	4106.00i	0.420286i	0.977671	+	0.210143i	$0.0673929\pi$
$457$	4106.00i	0.420286i	−0.977671	+	0.210143i	$0.932607\pi$
$458$	− 3558.00i	− 0.363001i
$459$	1360.00	0.138299
$460$	0	0
$461$	3366.00	0.340066	0.170033	−	0.985438i	$-0.445613\pi$
$461$	3366.00	0.340066	0.170033	+	0.985438i	$0.445613\pi$
$462$	16128.0i	1.62412i
$463$	− 896.000i	− 0.0899366i	−0.998988	−	0.0449683i	$-0.985681\pi$
$463$	− 896.000i	− 0.0899366i	0.998988	−	0.0449683i	$-0.0143187\pi$
$464$	2130.00	0.213109
$465$	0	0
$466$	16002.0	1.59073
$467$	− 10236.0i	− 1.01427i	−0.861866	−	0.507137i	$-0.830704\pi$
$467$	− 10236.0i	− 1.01427i	0.861866	−	0.507137i	$-0.169296\pi$
$468$	2146.00i	0.211963i
$469$	−13552.0	−1.33427
$470$	0	0
$471$	19664.0	1.92371
$472$	5292.00i	0.516068i
$473$	− 3552.00i	− 0.345288i
$474$	11616.0	1.12561
$475$	0	0
$476$	−476.000	−0.0458349
$477$	11766.0i	1.12941i
$478$	15984.0i	1.52948i
$479$	−5172.00	−0.493350	−0.246675	−	0.969098i	$-0.579338\pi$
$479$	−5172.00	−0.493350	−0.246675	+	0.969098i	$0.579338\pi$
$480$	0	0
$481$	3364.00	0.318888
$482$	− 16854.0i	− 1.59269i
$483$	13440.0i	1.26613i
$484$	755.000	0.0709053
$485$	0	0
$486$	−15096.0	−1.40899
$487$	− 15052.0i	− 1.40056i	−0.713870	−	0.700278i	$-0.753059\pi$
$487$	− 15052.0i	− 1.40056i	0.713870	−	0.700278i	$-0.246941\pi$
$488$	− 2310.00i	− 0.214280i
$489$	2176.00	0.201231
$490$	0	0
$491$	8700.00	0.799645	0.399822	−	0.916593i	$-0.369072\pi$
$491$	8700.00	0.799645	0.399822	+	0.916593i	$0.369072\pi$
$492$	2736.00i	0.250708i
$493$	− 510.000i	− 0.0465908i
$494$	−20184.0	−1.83830
$495$	0	0
$496$	12212.0	1.10551
$497$	19824.0i	1.78919i
$498$	− 18144.0i	− 1.63263i
$499$	1168.00	0.104783	0.0523916	−	0.998627i	$-0.483316\pi$
$499$	1168.00	0.104783	0.0523916	+	0.998627i	$0.483316\pi$
$500$	0	0
$501$	−28128.0	−2.50832
$502$	6084.00i	0.540921i
$503$	1740.00i	0.154240i	0.997022	+	0.0771200i	$0.0245725\pi$
$503$	1740.00i	0.154240i	−0.997022	+	0.0771200i	$0.975428\pi$
$504$	21756.0	1.92280
$505$	0	0
$506$	−4320.00	−0.379540
$507$	− 9336.00i	− 0.817803i
$508$	472.000i	0.0412236i
$509$	12570.0	1.09461	0.547304	−	0.836934i	$-0.315654\pi$
$509$	12570.0	1.09461	0.547304	+	0.836934i	$0.315654\pi$
$510$	0	0
$511$	−10136.0	−0.877476
$512$	8733.00i	0.753804i
$513$	9280.00i	0.798678i
$514$	−5706.00	−0.489651
$515$	0	0
$516$	1184.00	0.101013
$517$	− 6912.00i	− 0.587987i
$518$	4872.00i	0.413250i
$519$	−14736.0	−1.24632
$520$	0	0
$521$	11658.0	0.980319	0.490160	−	0.871633i	$-0.336939\pi$
$521$	11658.0	0.980319	0.490160	+	0.871633i	$0.336939\pi$
$522$	− 3330.00i	− 0.279215i
$523$	− 13700.0i	− 1.14543i	−0.819755	−	0.572714i	$-0.805890\pi$
$523$	− 13700.0i	− 1.14543i	0.819755	−	0.572714i	$-0.194110\pi$
$524$	−2760.00	−0.230098
$525$	0	0
$526$	16416.0	1.36078
$527$	− 2924.00i	− 0.241692i
$528$	13632.0i	1.12359i
$529$	8567.00	0.704118
$530$	0	0
$531$	9324.00	0.762010
$532$	− 3248.00i	− 0.264697i
$533$	− 19836.0i	− 1.61199i
$534$	18576.0	1.50536
$535$	0	0
$536$	−10164.0	−0.819063
$537$	28128.0i	2.26036i
$538$	− 10710.0i	− 0.858254i
$539$	10584.0	0.845798
$540$	0	0
$541$	17822.0	1.41632	0.708159	−	0.706053i	$-0.249526\pi$
$541$	17822.0	1.41632	0.708159	+	0.706053i	$0.249526\pi$
$542$	− 816.000i	− 0.0646683i
$543$	27184.0i	2.14839i
$544$	−765.000	−0.0602925
$545$	0	0
$546$	38976.0	3.05498
$547$	3800.00i	0.297032i	0.988910	+	0.148516i	$0.0474496\pi$
$547$	3800.00i	0.297032i	−0.988910	+	0.148516i	$0.952550\pi$
$548$	− 1098.00i	− 0.0855917i
$549$	−4070.00	−0.316400
$550$	0	0
$551$	3480.00	0.269062
$552$	10080.0i	0.777234i
$553$	− 13552.0i	− 1.04212i
$554$	11490.0	0.881161
$555$	0	0
$556$	2528.00	0.192826
$557$	− 10074.0i	− 0.766336i	−0.923679	−	0.383168i	$-0.874833\pi$
$557$	− 10074.0i	− 0.766336i	0.923679	−	0.383168i	$-0.125167\pi$
$558$	− 19092.0i	− 1.44844i
$559$	−8584.00	−0.649489
$560$	0	0
$561$	3264.00	0.245644
$562$	− 26622.0i	− 1.99819i
$563$	15948.0i	1.19383i	0.802303	+	0.596917i	$0.203608\pi$
$563$	15948.0i	1.19383i	−0.802303	+	0.596917i	$0.796392\pi$
$564$	2304.00	0.172014
$565$	0	0
$566$	7896.00	0.586385
$567$	10052.0i	0.744523i
$568$	14868.0i	1.09832i
$569$	−21834.0	−1.60866	−0.804331	−	0.594181i	$-0.797476\pi$
$569$	−21834.0	−1.60866	−0.804331	+	0.594181i	$0.797476\pi$
$570$	0	0
$571$	−21208.0	−1.55434	−0.777169	−	0.629292i	$-0.783345\pi$
$571$	−21208.0	−1.55434	−0.777169	+	0.629292i	$0.783345\pi$
$572$	1392.00i	0.101753i
$573$	− 21120.0i	− 1.53979i
$574$	28728.0	2.08900
$575$	0	0
$576$	16021.0	1.15893
$577$	12530.0i	0.904039i	0.892008	+	0.452020i	$0.149296\pi$
$577$	12530.0i	0.904039i	−0.892008	+	0.452020i	$0.850704\pi$
$578$	867.000i	0.0623918i
$579$	23056.0	1.65488
$580$	0	0
$581$	−21168.0	−1.51153
$582$	− 9168.00i	− 0.652965i
$583$	7632.00i	0.542170i
$584$	−7602.00	−0.538652
$585$	0	0
$586$	19206.0	1.35391
$587$	2220.00i	0.156097i	0.996950	+	0.0780487i	$0.0248690\pi$
$587$	2220.00i	0.156097i	−0.996950	+	0.0780487i	$0.975131\pi$
$588$	3528.00i	0.247436i
$589$	19952.0	1.39577
$590$	0	0
$591$	336.000	0.0233861
$592$	4118.00i	0.285893i
$593$	25038.0i	1.73387i	0.498418	+	0.866937i	$0.333915\pi$
$593$	25038.0i	1.73387i	−0.498418	+	0.866937i	$0.666085\pi$
$594$	5760.00	0.397871
$595$	0	0
$596$	1614.00	0.110926
$597$	25760.0i	1.76597i
$598$	10440.0i	0.713919i
$599$	−5784.00	−0.394537	−0.197269	−	0.980349i	$-0.563207\pi$
$599$	−5784.00	−0.394537	−0.197269	+	0.980349i	$0.563207\pi$
$600$	0	0
$601$	−4198.00	−0.284925	−0.142463	−	0.989800i	$-0.545502\pi$
$601$	−4198.00	−0.284925	−0.142463	+	0.989800i	$0.545502\pi$
$602$	− 12432.0i	− 0.841679i
$603$	17908.0i	1.20940i
$604$	3328.00	0.224196
$605$	0	0
$606$	−5040.00	−0.337848
$607$	− 12124.0i	− 0.810705i	−0.914160	−	0.405353i	$-0.867149\pi$
$607$	− 12124.0i	− 0.810705i	0.914160	−	0.405353i	$-0.132851\pi$
$608$	− 5220.00i	− 0.348189i
$609$	−6720.00	−0.447140
$610$	0	0
$611$	−16704.0	−1.10601
$612$	629.000i	0.0415455i
$613$	− 7454.00i	− 0.491133i	−0.969380	−	0.245566i	$-0.921026\pi$
$613$	− 7454.00i	− 0.491133i	0.969380	−	0.245566i	$-0.0789739\pi$
$614$	−26940.0	−1.77070
$615$	0	0
$616$	14112.0	0.923034
$617$	28842.0i	1.88190i	0.338539	+	0.940952i	$0.390067\pi$
$617$	28842.0i	1.88190i	−0.338539	+	0.940952i	$0.609933\pi$
$618$	5568.00i	0.362424i
$619$	17224.0	1.11840	0.559201	−	0.829032i	$-0.311108\pi$
$619$	17224.0	1.11840	0.559201	+	0.829032i	$0.311108\pi$
$620$	0	0
$621$	4800.00	0.310173
$622$	11916.0i	0.768148i
$623$	− 21672.0i	− 1.39369i
$624$	32944.0	2.11349
$625$	0	0
$626$	−14190.0	−0.905985
$627$	22272.0i	1.41859i
$628$	2458.00i	0.156186i
$629$	986.000	0.0625030
$630$	0	0
$631$	−12448.0	−0.785336	−0.392668	−	0.919680i	$-0.628448\pi$
$631$	−12448.0	−0.785336	−0.392668	+	0.919680i	$0.628448\pi$
$632$	− 10164.0i	− 0.639719i
$633$	− 16640.0i	− 1.04484i
$634$	−8694.00	−0.544610
$635$	0	0
$636$	−2544.00	−0.158610
$637$	− 25578.0i	− 1.59095i
$638$	− 2160.00i	− 0.134036i
$639$	26196.0	1.62175
$640$	0	0
$641$	−25182.0	−1.55168	−0.775842	−	0.630927i	$-0.782675\pi$
$641$	−25182.0	−1.55168	−0.775842	+	0.630927i	$0.782675\pi$
$642$	10368.0i	0.637371i
$643$	− 17048.0i	− 1.04558i	−0.852462	−	0.522790i	$-0.824891\pi$
$643$	− 17048.0i	− 1.04558i	0.852462	−	0.522790i	$-0.175109\pi$
$644$	−1680.00	−0.102797
$645$	0	0
$646$	−5916.00	−0.360313
$647$	7128.00i	0.433123i	0.976269	+	0.216562i	$0.0694842\pi$
$647$	7128.00i	0.433123i	−0.976269	+	0.216562i	$0.930516\pi$
$648$	7539.00i	0.457037i
$649$	6048.00	0.365801
$650$	0	0
$651$	−38528.0	−2.31956
$652$	272.000i	0.0163379i
$653$	− 18462.0i	− 1.10639i	−0.833051	−	0.553196i	$-0.813408\pi$
$653$	− 18462.0i	− 1.10639i	0.833051	−	0.553196i	$-0.186592\pi$
$654$	28464.0	1.70188
$655$	0	0
$656$	24282.0	1.44520
$657$	13394.0i	0.795357i
$658$	− 24192.0i	− 1.43329i
$659$	−28092.0	−1.66056	−0.830280	−	0.557347i	$-0.811819\pi$
$659$	−28092.0	−1.66056	−0.830280	+	0.557347i	$0.811819\pi$
$660$	0	0
$661$	10910.0	0.641982	0.320991	−	0.947082i	$-0.395984\pi$
$661$	10910.0	0.641982	0.320991	+	0.947082i	$0.395984\pi$
$662$	13692.0i	0.803859i
$663$	− 7888.00i	− 0.462058i
$664$	−15876.0	−0.927874
$665$	0	0
$666$	6438.00	0.374576
$667$	− 1800.00i	− 0.104492i
$668$	− 3516.00i	− 0.203650i
$669$	37312.0	2.15630
$670$	0	0
$671$	−2640.00	−0.151887
$672$	10080.0i	0.578638i
$673$	28414.0i	1.62746i	0.581244	+	0.813729i	$0.302566\pi$
$673$	28414.0i	1.62746i	−0.581244	+	0.813729i	$0.697434\pi$
$674$	2166.00	0.123785
$675$	0	0
$676$	1167.00	0.0663974
$677$	− 6042.00i	− 0.343003i	−0.985184	−	0.171501i	$-0.945138\pi$
$677$	− 6042.00i	− 0.343003i	0.985184	−	0.171501i	$-0.0548618\pi$
$678$	8784.00i	0.497563i
$679$	−10696.0	−0.604528
$680$	0	0
$681$	11520.0	0.648234
$682$	− 12384.0i	− 0.695319i
$683$	− 34752.0i	− 1.94692i	−0.228851	−	0.973461i	$-0.573497\pi$
$683$	− 34752.0i	− 1.94692i	0.228851	−	0.973461i	$-0.426503\pi$
$684$	−4292.00	−0.239925
$685$	0	0
$686$	8232.00	0.458162
$687$	9488.00i	0.526914i
$688$	− 10508.0i	− 0.582287i
$689$	18444.0	1.01983
$690$	0	0
$691$	18320.0	1.00858	0.504288	−	0.863536i	$-0.331755\pi$
$691$	18320.0	1.00858	0.504288	+	0.863536i	$0.331755\pi$
$692$	− 1842.00i	− 0.101188i
$693$	− 24864.0i	− 1.36292i
$694$	16632.0	0.909715
$695$	0	0
$696$	−5040.00	−0.274484
$697$	− 5814.00i	− 0.315955i
$698$	33378.0i	1.80999i
$699$	−42672.0	−2.30902
$700$	0	0
$701$	−22890.0	−1.23330	−0.616650	−	0.787237i	$-0.711511\pi$
$701$	−22890.0	−1.23330	−0.616650	+	0.787237i	$0.711511\pi$
$702$	− 13920.0i	− 0.748400i
$703$	6728.00i	0.360955i
$704$	10392.0	0.556340
$705$	0	0
$706$	−23526.0	−1.25413
$707$	5880.00i	0.312787i
$708$	2016.00i	0.107014i
$709$	−22886.0	−1.21227	−0.606137	−	0.795361i	$-0.707282\pi$
$709$	−22886.0	−1.21227	−0.606137	+	0.795361i	$0.707282\pi$
$710$	0	0
$711$	−17908.0	−0.944589
$712$	− 16254.0i	− 0.855540i
$713$	− 10320.0i	− 0.542058i
$714$	11424.0	0.598785
$715$	0	0
$716$	−3516.00	−0.183518
$717$	− 42624.0i	− 2.22011i
$718$	15120.0i	0.785896i
$719$	13452.0	0.697740	0.348870	−	0.937171i	$-0.386565\pi$
$719$	13452.0	0.697740	0.348870	+	0.937171i	$0.386565\pi$
$720$	0	0
$721$	6496.00	0.335539
$722$	− 19791.0i	− 1.02015i
$723$	44944.0i	2.31187i
$724$	−3398.00	−0.174428
$725$	0	0
$726$	−18120.0	−0.926303
$727$	− 27304.0i	− 1.39292i	−0.717598	−	0.696458i	$-0.754758\pi$
$727$	− 27304.0i	− 1.39292i	0.717598	−	0.696458i	$-0.245242\pi$
$728$	− 34104.0i	− 1.73623i
$729$	30563.0	1.55276
$730$	0	0
$731$	−2516.00	−0.127302
$732$	− 880.000i	− 0.0444341i
$733$	− 24470.0i	− 1.23304i	−0.787338	−	0.616521i	$-0.788541\pi$
$733$	− 24470.0i	− 1.23304i	0.787338	−	0.616521i	$-0.211459\pi$
$734$	−25212.0	−1.26784
$735$	0	0
$736$	−2700.00	−0.135222
$737$	11616.0i	0.580571i
$738$	− 37962.0i	− 1.89350i
$739$	−35252.0	−1.75476	−0.877379	−	0.479798i	$-0.840710\pi$
$739$	−35252.0	−1.75476	−0.877379	+	0.479798i	$0.840710\pi$
$740$	0	0
$741$	53824.0	2.66839
$742$	26712.0i	1.32160i
$743$	− 1548.00i	− 0.0764342i	−0.999269	−	0.0382171i	$-0.987832\pi$
$743$	− 1548.00i	− 0.0764342i	0.999269	−	0.0382171i	$-0.0121678\pi$
$744$	−28896.0	−1.42390
$745$	0	0
$746$	24294.0	1.19231
$747$	27972.0i	1.37007i
$748$	408.000i	0.0199438i
$749$	12096.0	0.590091
$750$	0	0
$751$	2948.00	0.143241	0.0716205	−	0.997432i	$-0.477183\pi$
$751$	2948.00	0.143241	0.0716205	+	0.997432i	$0.477183\pi$
$752$	− 20448.0i	− 0.991572i
$753$	− 16224.0i	− 0.785173i
$754$	−5220.00	−0.252124
$755$	0	0
$756$	2240.00	0.107762
$757$	− 754.000i	− 0.0362016i	−0.999836	−	0.0181008i	$-0.994238\pi$
$757$	− 754.000i	− 0.0362016i	0.999836	−	0.0181008i	$-0.00576198\pi$
$758$	960.000i	0.0460010i
$759$	11520.0	0.550922
$760$	0	0
$761$	−41574.0	−1.98036	−0.990182	−	0.139787i	$-0.955358\pi$
$761$	−41574.0	−1.98036	−0.990182	+	0.139787i	$0.955358\pi$
$762$	− 11328.0i	− 0.538543i
$763$	− 33208.0i	− 1.57564i
$764$	2640.00	0.125016
$765$	0	0
$766$	32616.0	1.53846
$767$	− 14616.0i	− 0.688075i
$768$	12104.0i	0.568705i
$769$	15118.0	0.708932	0.354466	−	0.935069i	$-0.384663\pi$
$769$	15118.0	0.708932	0.354466	+	0.935069i	$0.384663\pi$
$770$	0	0
$771$	15216.0	0.710753
$772$	2882.00i	0.134359i
$773$	− 23550.0i	− 1.09578i	−0.836552	−	0.547888i	$-0.815432\pi$
$773$	− 23550.0i	− 1.09578i	0.836552	−	0.547888i	$-0.184568\pi$
$774$	−16428.0	−0.762910
$775$	0	0
$776$	−8022.00	−0.371099
$777$	− 12992.0i	− 0.599853i
$778$	4122.00i	0.189950i
$779$	39672.0	1.82464
$780$	0	0
$781$	16992.0	0.778517
$782$	3060.00i	0.139930i
$783$	2400.00i	0.109539i
$784$	31311.0	1.42634
$785$	0	0
$786$	66240.0	3.00598
$787$	5240.00i	0.237339i	0.992934	+	0.118670i	$0.0378629\pi$
$787$	5240.00i	0.237339i	−0.992934	+	0.118670i	$0.962137\pi$
$788$	42.0000i	0.00189872i
$789$	−43776.0	−1.97524
$790$	0	0
$791$	10248.0	0.460654
$792$	− 18648.0i	− 0.836651i
$793$	6380.00i	0.285700i
$794$	−22566.0	−1.00861
$795$	0	0
$796$	−3220.00	−0.143379
$797$	5526.00i	0.245597i	0.992432	+	0.122799i	$0.0391869\pi$
$797$	5526.00i	0.245597i	−0.992432	+	0.122799i	$0.960813\pi$
$798$	77952.0i	3.45798i
$799$	−4896.00	−0.216781
$800$	0	0
$801$	−28638.0	−1.26326
$802$	− 8118.00i	− 0.357427i
$803$	8688.00i	0.381809i
$804$	−3872.00	−0.169844
$805$	0	0
$806$	−29928.0	−1.30790
$807$	28560.0i	1.24580i
$808$	4410.00i	0.192009i
$809$	438.000	0.0190349	0.00951747	−	0.999955i	$-0.496970\pi$
$809$	438.000	0.0190349	0.00951747	+	0.999955i	$0.496970\pi$
$810$	0	0
$811$	−30448.0	−1.31834	−0.659170	−	0.751994i	$-0.729092\pi$
$811$	−30448.0	−1.31834	−0.659170	+	0.751994i	$0.729092\pi$
$812$	− 840.000i	− 0.0363032i
$813$	2176.00i	0.0938692i
$814$	4176.00	0.179814
$815$	0	0
$816$	9656.00	0.414250
$817$	− 17168.0i	− 0.735168i
$818$	798.000i	0.0341093i
$819$	−60088.0	−2.56367
$820$	0	0
$821$	−21930.0	−0.932232	−0.466116	−	0.884724i	$-0.654347\pi$
$821$	−21930.0	−0.932232	−0.466116	+	0.884724i	$0.654347\pi$
$822$	26352.0i	1.11816i
$823$	27436.0i	1.16204i	0.813889	+	0.581020i	$0.197346\pi$
$823$	27436.0i	1.16204i	−0.813889	+	0.581020i	$0.802654\pi$
$824$	4872.00	0.205976
$825$	0	0
$826$	21168.0	0.891681
$827$	− 17832.0i	− 0.749794i	−0.927067	−	0.374897i	$-0.877678\pi$
$827$	− 17832.0i	− 0.749794i	0.927067	−	0.374897i	$-0.122322\pi$
$828$	2220.00i	0.0931767i
$829$	4090.00	0.171353	0.0856765	−	0.996323i	$-0.472695\pi$
$829$	4090.00	0.171353	0.0856765	+	0.996323i	$0.472695\pi$
$830$	0	0
$831$	−30640.0	−1.27905
$832$	− 25114.0i	− 1.04648i
$833$	− 7497.00i	− 0.311832i
$834$	−60672.0	−2.51906
$835$	0	0
$836$	−2784.00	−0.115175
$837$	13760.0i	0.568238i
$838$	8064.00i	0.332418i
$839$	2508.00	0.103201	0.0516006	−	0.998668i	$-0.483568\pi$
$839$	2508.00	0.103201	0.0516006	+	0.998668i	$0.483568\pi$
$840$	0	0
$841$	−23489.0	−0.963098
$842$	41430.0i	1.69569i
$843$	70992.0i	2.90047i
$844$	2080.00	0.0848300
$845$	0	0
$846$	−31968.0	−1.29915
$847$	21140.0i	0.857590i
$848$	22578.0i	0.914306i
$849$	−21056.0	−0.851166
$850$	0	0
$851$	3480.00	0.140180
$852$	5664.00i	0.227753i
$853$	42442.0i	1.70362i	0.523852	+	0.851809i	$0.324494\pi$
$853$	42442.0i	1.70362i	−0.523852	+	0.851809i	$0.675506\pi$
$854$	−9240.00	−0.370242
$855$	0	0
$856$	9072.00	0.362237
$857$	32730.0i	1.30459i	0.757964	+	0.652296i	$0.226194\pi$
$857$	32730.0i	1.30459i	−0.757964	+	0.652296i	$0.773806\pi$
$858$	− 33408.0i	− 1.32929i
$859$	6148.00	0.244199	0.122100	−	0.992518i	$-0.461037\pi$
$859$	6148.00	0.244199	0.122100	+	0.992518i	$0.461037\pi$
$860$	0	0
$861$	−76608.0	−3.03228
$862$	− 9108.00i	− 0.359884i
$863$	22512.0i	0.887969i	0.896034	+	0.443985i	$0.146436\pi$
$863$	22512.0i	0.887969i	−0.896034	+	0.443985i	$0.853564\pi$
$864$	3600.00	0.141753
$865$	0	0
$866$	34266.0	1.34458
$867$	− 2312.00i	− 0.0905647i
$868$	− 4816.00i	− 0.188325i
$869$	−11616.0	−0.453447
$870$	0	0
$871$	28072.0	1.09206
$872$	− 24906.0i	− 0.967229i
$873$	14134.0i	0.547954i
$874$	−20880.0	−0.808097
$875$	0	0
$876$	−2896.00	−0.111697
$877$	9182.00i	0.353539i	0.984252	+	0.176770i	$0.0565648\pi$
$877$	9182.00i	0.353539i	−0.984252	+	0.176770i	$0.943435\pi$
$878$	− 156.000i	− 0.00599629i
$879$	−51216.0	−1.96527
$880$	0	0
$881$	28530.0	1.09103	0.545517	−	0.838100i	$-0.316334\pi$
$881$	28530.0	1.09103	0.545517	+	0.838100i	$0.316334\pi$
$882$	− 48951.0i	− 1.86878i
$883$	12436.0i	0.473958i	0.971515	+	0.236979i	$0.0761572\pi$
$883$	12436.0i	0.473958i	−0.971515	+	0.236979i	$0.923843\pi$
$884$	986.000	0.0375144
$885$	0	0
$886$	−9324.00	−0.353551
$887$	7404.00i	0.280273i	0.990132	+	0.140136i	$0.0447541\pi$
$887$	7404.00i	0.280273i	−0.990132	+	0.140136i	$0.955246\pi$
$888$	− 9744.00i	− 0.368229i
$889$	−13216.0	−0.498594
$890$	0	0
$891$	8616.00	0.323958
$892$	4664.00i	0.175070i
$893$	− 33408.0i	− 1.25191i
$894$	−38736.0	−1.44913
$895$	0	0
$896$	46452.0	1.73198
$897$	− 27840.0i	− 1.03629i
$898$	18342.0i	0.681604i
$899$	5160.00	0.191430
$900$	0	0
$901$	5406.00	0.199889
$902$	− 24624.0i	− 0.908968i
$903$	33152.0i	1.22174i
$904$	7686.00	0.282779
$905$	0	0
$906$	−79872.0	−2.92888
$907$	15368.0i	0.562609i	0.959619	+	0.281304i	$0.0907670\pi$
$907$	15368.0i	0.562609i	−0.959619	+	0.281304i	$0.909233\pi$
$908$	1440.00i	0.0526300i
$909$	7770.00	0.283514
$910$	0	0
$911$	27276.0	0.991980	0.495990	−	0.868328i	$-0.334805\pi$
$911$	27276.0	0.991980	0.495990	+	0.868328i	$0.334805\pi$
$912$	65888.0i	2.39229i
$913$	18144.0i	0.657699i
$914$	12318.0	0.445780
$915$	0	0
$916$	−1186.00	−0.0427801
$917$	− 77280.0i	− 2.78300i
$918$	− 4080.00i	− 0.146689i
$919$	46456.0	1.66751	0.833755	−	0.552134i	$-0.186186\pi$
$919$	46456.0	1.66751	0.833755	+	0.552134i	$0.186186\pi$
$920$	0	0
$921$	71840.0	2.57026
$922$	− 10098.0i	− 0.360694i
$923$	− 41064.0i	− 1.46440i
$924$	5376.00	0.191404
$925$	0	0
$926$	−2688.00	−0.0953922
$927$	− 8584.00i	− 0.304138i
$928$	− 1350.00i	− 0.0477542i
$929$	−13026.0	−0.460031	−0.230016	−	0.973187i	$-0.573878\pi$
$929$	−13026.0	−0.460031	−0.230016	+	0.973187i	$0.573878\pi$
$930$	0	0
$931$	51156.0	1.80083
$932$	− 5334.00i	− 0.187469i
$933$	− 31776.0i	− 1.11500i
$934$	−30708.0	−1.07580
$935$	0	0
$936$	−45066.0	−1.57375
$937$	26330.0i	0.917997i	0.888437	+	0.458999i	$0.151792\pi$
$937$	26330.0i	0.917997i	−0.888437	+	0.458999i	$0.848208\pi$
$938$	40656.0i	1.41521i
$939$	37840.0	1.31508
$940$	0	0
$941$	28254.0	0.978803	0.489402	−	0.872058i	$-0.337215\pi$
$941$	28254.0	0.978803	0.489402	+	0.872058i	$0.337215\pi$
$942$	− 58992.0i	− 2.04041i
$943$	− 20520.0i	− 0.708614i
$944$	17892.0	0.616880
$945$	0	0
$946$	−10656.0	−0.366233
$947$	49272.0i	1.69073i	0.534186	+	0.845367i	$0.320618\pi$
$947$	49272.0i	1.69073i	−0.534186	+	0.845367i	$0.679382\pi$
$948$	− 3872.00i	− 0.132655i
$949$	20996.0	0.718187
$950$	0	0
$951$	23184.0	0.790529
$952$	− 9996.00i	− 0.340307i
$953$	− 32922.0i	− 1.11904i	−0.828816	−	0.559522i	$-0.810985\pi$
$953$	− 32922.0i	− 1.11904i	0.828816	−	0.559522i	$-0.189015\pi$
$954$	35298.0	1.19792
$955$	0	0
$956$	5328.00	0.180251
$957$	5760.00i	0.194560i
$958$	15516.0i	0.523277i
$959$	30744.0	1.03522
$960$	0	0
$961$	−207.000	−0.00694841
$962$	− 10092.0i	− 0.338232i
$963$	− 15984.0i	− 0.534867i
$964$	−5618.00	−0.187701
$965$	0	0
$966$	40320.0	1.34293
$967$	− 1168.00i	− 0.0388421i	−0.999811	−	0.0194211i	$-0.993818\pi$
$967$	− 1168.00i	− 0.0388421i	0.999811	−	0.0194211i	$-0.00618231\pi$
$968$	15855.0i	0.526445i
$969$	15776.0	0.523011
$970$	0	0
$971$	−19812.0	−0.654786	−0.327393	−	0.944888i	$-0.606170\pi$
$971$	−19812.0	−0.654786	−0.327393	+	0.944888i	$0.606170\pi$
$972$	5032.00i	0.166051i
$973$	70784.0i	2.33220i
$974$	−45156.0	−1.48551
$975$	0	0
$976$	−7810.00	−0.256139
$977$	− 28494.0i	− 0.933064i	−0.884504	−	0.466532i	$-0.845503\pi$
$977$	− 28494.0i	− 0.933064i	0.884504	−	0.466532i	$-0.154497\pi$
$978$	− 6528.00i	− 0.213438i
$979$	−18576.0	−0.606426
$980$	0	0
$981$	−43882.0	−1.42818
$982$	− 26100.0i	− 0.848151i
$983$	42708.0i	1.38573i	0.721067	+	0.692866i	$0.243652\pi$
$983$	42708.0i	1.38573i	−0.721067	+	0.692866i	$0.756348\pi$
$984$	−57456.0	−1.86141
$985$	0	0
$986$	−1530.00	−0.0494170
$987$	64512.0i	2.08049i
$988$	6728.00i	0.216646i
$989$	−8880.00	−0.285508
$990$	0	0
$991$	−29500.0	−0.945609	−0.472804	−	0.881167i	$-0.656758\pi$
$991$	−29500.0	−0.945609	−0.472804	+	0.881167i	$0.656758\pi$
$992$	− 7740.00i	− 0.247727i
$993$	− 36512.0i	− 1.16684i
$994$	59472.0	1.89772
$995$	0	0
$996$	−6048.00	−0.192408
$997$	− 9322.00i	− 0.296119i	−0.988978	−	0.148060i	$-0.952697\pi$
$997$	− 9322.00i	− 0.296119i	0.988978	−	0.148060i	$-0.0473027\pi$
$998$	− 3504.00i	− 0.111139i
$999$	−4640.00	−0.146950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.b.c.324.1		2
5.2	odd	4		425.4.a.d.1.1		1
5.3	odd	4		17.4.a.a.1.1	✓	1
5.4	even	2	inner	425.4.b.c.324.2		2
15.8	even	4		153.4.a.d.1.1		1
20.3	even	4		272.4.a.d.1.1		1
35.13	even	4		833.4.a.a.1.1		1
40.3	even	4		1088.4.a.a.1.1		1
40.13	odd	4		1088.4.a.l.1.1		1
55.43	even	4		2057.4.a.d.1.1		1
60.23	odd	4		2448.4.a.f.1.1		1
85.13	odd	4		289.4.b.a.288.1		2
85.33	odd	4		289.4.a.a.1.1		1
85.38	odd	4		289.4.b.a.288.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.a.1.1	✓	1	5.3	odd	4
153.4.a.d.1.1		1	15.8	even	4
272.4.a.d.1.1		1	20.3	even	4
289.4.a.a.1.1		1	85.33	odd	4
289.4.b.a.288.1		2	85.13	odd	4
289.4.b.a.288.2		2	85.38	odd	4
425.4.a.d.1.1		1	5.2	odd	4
425.4.b.c.324.1		2	1.1	even	1	trivial
425.4.b.c.324.2		2	5.4	even	2	inner
833.4.a.a.1.1		1	35.13	even	4
1088.4.a.a.1.1		1	40.3	even	4
1088.4.a.l.1.1		1	40.13	odd	4
2057.4.a.d.1.1		1	55.43	even	4
2448.4.a.f.1.1		1	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-3.00000i q^{2} +8.00000i q^{3} -1.00000 q^{4} +24.0000 q^{6} -28.0000i q^{7} -21.0000i q^{8} -37.0000 q^{9} +O(q^{10})\)	\(q-3.00000i q^{2} +8.00000i q^{3} -1.00000 q^{4} +24.0000 q^{6} -28.0000i q^{7} -21.0000i q^{8} -37.0000 q^{9} -24.0000 q^{11} -8.00000i q^{12} +58.0000i q^{13} -84.0000 q^{14} -71.0000 q^{16} +17.0000i q^{17} +111.000i q^{18} -116.000 q^{19} +224.000 q^{21} +72.0000i q^{22} +60.0000i q^{23} +168.000 q^{24} +174.000 q^{26} -80.0000i q^{27} +28.0000i q^{28} -30.0000 q^{29} -172.000 q^{31} +45.0000i q^{32} -192.000i q^{33} +51.0000 q^{34} +37.0000 q^{36} -58.0000i q^{37} +348.000i q^{38} -464.000 q^{39} -342.000 q^{41} -672.000i q^{42} +148.000i q^{43} +24.0000 q^{44} +180.000 q^{46} +288.000i q^{47} -568.000i q^{48} -441.000 q^{49} -136.000 q^{51} -58.0000i q^{52} -318.000i q^{53} -240.000 q^{54} -588.000 q^{56} -928.000i q^{57} +90.0000i q^{58} -252.000 q^{59} +110.000 q^{61} +516.000i q^{62} +1036.00i q^{63} -433.000 q^{64} -576.000 q^{66} -484.000i q^{67} -17.0000i q^{68} -480.000 q^{69} -708.000 q^{71} +777.000i q^{72} -362.000i q^{73} -174.000 q^{74} +116.000 q^{76} +672.000i q^{77} +1392.00i q^{78} +484.000 q^{79} -359.000 q^{81} +1026.00i q^{82} -756.000i q^{83} -224.000 q^{84} +444.000 q^{86} -240.000i q^{87} +504.000i q^{88} +774.000 q^{89} +1624.00 q^{91} -60.0000i q^{92} -1376.00i q^{93} +864.000 q^{94} -360.000 q^{96} -382.000i q^{97} +1323.00i q^{98} +888.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 48 q^{6} - 74 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 48 * q^6 - 74 * q^9	\( 2 q - 2 q^{4} + 48 q^{6} - 74 q^{9} - 48 q^{11} - 168 q^{14} - 142 q^{16} - 232 q^{19} + 448 q^{21} + 336 q^{24} + 348 q^{26} - 60 q^{29} - 344 q^{31} + 102 q^{34} + 74 q^{36} - 928 q^{39} - 684 q^{41} + 48 q^{44} + 360 q^{46} - 882 q^{49} - 272 q^{51} - 480 q^{54} - 1176 q^{56} - 504 q^{59} + 220 q^{61} - 866 q^{64} - 1152 q^{66} - 960 q^{69} - 1416 q^{71} - 348 q^{74} + 232 q^{76} + 968 q^{79} - 718 q^{81} - 448 q^{84} + 888 q^{86} + 1548 q^{89} + 3248 q^{91} + 1728 q^{94} - 720 q^{96} + 1776 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 48 * q^6 - 74 * q^9 - 48 * q^11 - 168 * q^14 - 142 * q^16 - 232 * q^19 + 448 * q^21 + 336 * q^24 + 348 * q^26 - 60 * q^29 - 344 * q^31 + 102 * q^34 + 74 * q^36 - 928 * q^39 - 684 * q^41 + 48 * q^44 + 360 * q^46 - 882 * q^49 - 272 * q^51 - 480 * q^54 - 1176 * q^56 - 504 * q^59 + 220 * q^61 - 866 * q^64 - 1152 * q^66 - 960 * q^69 - 1416 * q^71 - 348 * q^74 + 232 * q^76 + 968 * q^79 - 718 * q^81 - 448 * q^84 + 888 * q^86 + 1548 * q^89 + 3248 * q^91 + 1728 * q^94 - 720 * q^96 + 1776 * q^99

Introduction

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