LMFDB - Embedded newform 350.4.c.g.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(99,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.c (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:	$20.6506685020$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.4.c.g.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} -4.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} -4.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +48.0000 q^{11} +8.00000i q^{12} +56.0000i q^{13} -14.0000 q^{14} +16.0000 q^{16} +114.000i q^{17} -46.0000i q^{18} -2.00000 q^{19} -14.0000 q^{21} -96.0000i q^{22} -120.000i q^{23} +16.0000 q^{24} +112.000 q^{26} -100.000i q^{27} +28.0000i q^{28} +54.0000 q^{29} +236.000 q^{31} -32.0000i q^{32} -96.0000i q^{33} +228.000 q^{34} -92.0000 q^{36} -146.000i q^{37} +4.00000i q^{38} +112.000 q^{39} +126.000 q^{41} +28.0000i q^{42} -376.000i q^{43} -192.000 q^{44} -240.000 q^{46} +12.0000i q^{47} -32.0000i q^{48} -49.0000 q^{49} +228.000 q^{51} -224.000i q^{52} +174.000i q^{53} -200.000 q^{54} +56.0000 q^{56} +4.00000i q^{57} -108.000i q^{58} -138.000 q^{59} +380.000 q^{61} -472.000i q^{62} -161.000i q^{63} -64.0000 q^{64} -192.000 q^{66} +484.000i q^{67} -456.000i q^{68} -240.000 q^{69} +576.000 q^{71} +184.000i q^{72} -1150.00i q^{73} -292.000 q^{74} +8.00000 q^{76} -336.000i q^{77} -224.000i q^{78} -776.000 q^{79} +421.000 q^{81} -252.000i q^{82} +378.000i q^{83} +56.0000 q^{84} -752.000 q^{86} -108.000i q^{87} +384.000i q^{88} +390.000 q^{89} +392.000 q^{91} +480.000i q^{92} -472.000i q^{93} +24.0000 q^{94} -64.0000 q^{96} +1330.00i q^{97} +98.0000i q^{98} +1104.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} - 8 q^{6} + 46 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 - 8 * q^6 + 46 * q^9	$ 2 q - 8 q^{4} - 8 q^{6} + 46 q^{9} + 96 q^{11} - 28 q^{14} + 32 q^{16} - 4 q^{19} - 28 q^{21} + 32 q^{24} + 224 q^{26} + 108 q^{29} + 472 q^{31} + 456 q^{34} - 184 q^{36} + 224 q^{39} + 252 q^{41} - 384 q^{44} - 480 q^{46} - 98 q^{49} + 456 q^{51} - 400 q^{54} + 112 q^{56} - 276 q^{59} + 760 q^{61} - 128 q^{64} - 384 q^{66} - 480 q^{69} + 1152 q^{71} - 584 q^{74} + 16 q^{76} - 1552 q^{79} + 842 q^{81} + 112 q^{84} - 1504 q^{86} + 780 q^{89} + 784 q^{91} + 48 q^{94} - 128 q^{96} + 2208 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 - 8 * q^6 + 46 * q^9 + 96 * q^11 - 28 * q^14 + 32 * q^16 - 4 * q^19 - 28 * q^21 + 32 * q^24 + 224 * q^26 + 108 * q^29 + 472 * q^31 + 456 * q^34 - 184 * q^36 + 224 * q^39 + 252 * q^41 - 384 * q^44 - 480 * q^46 - 98 * q^49 + 456 * q^51 - 400 * q^54 + 112 * q^56 - 276 * q^59 + 760 * q^61 - 128 * q^64 - 384 * q^66 - 480 * q^69 + 1152 * q^71 - 584 * q^74 + 16 * q^76 - 1552 * q^79 + 842 * q^81 + 112 * q^84 - 1504 * q^86 + 780 * q^89 + 784 * q^91 + 48 * q^94 - 128 * q^96 + 2208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	− 2.00000i	− 0.384900i	−0.981307	−	0.192450i	$-0.938357\pi$
$3$	− 2.00000i	− 0.384900i	0.981307	−	0.192450i	$-0.0616434\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−4.00000	−0.272166
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	8.00000i	0.353553i
$9$	23.0000	0.851852
$10$	0	0
$11$	48.0000	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$11$	48.0000	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$12$	8.00000i	0.192450i
$13$	56.0000i	1.19474i	0.801966	+	0.597369i	$0.203787\pi$
$13$	56.0000i	1.19474i	−0.801966	+	0.597369i	$0.796213\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	114.000i	1.62642i	0.581974	+	0.813208i	$0.302281\pi$
$17$	114.000i	1.62642i	−0.581974	+	0.813208i	$0.697719\pi$
$18$	− 46.0000i	− 0.602350i
$19$	−2.00000	−0.0241490	−0.0120745	−	0.999927i	$-0.503844\pi$
$19$	−2.00000	−0.0241490	−0.0120745	+	0.999927i	$0.503844\pi$
$20$	0	0
$21$	−14.0000	−0.145479
$22$	− 96.0000i	− 0.930330i
$23$	− 120.000i	− 1.08790i	−0.839117	−	0.543951i	$-0.816928\pi$
$23$	− 120.000i	− 1.08790i	0.839117	−	0.543951i	$-0.183072\pi$
$24$	16.0000	0.136083
$25$	0	0
$26$	112.000	0.844808
$27$	− 100.000i	− 0.712778i
$28$	28.0000i	0.188982i
$29$	54.0000	0.345778	0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000	0.345778	0.172889	+	0.984941i	$0.444690\pi$
$30$	0	0
$31$	236.000	1.36732	0.683659	−	0.729802i	$-0.260388\pi$
$31$	236.000	1.36732	0.683659	+	0.729802i	$0.260388\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 96.0000i	− 0.506408i
$34$	228.000	1.15005
$35$	0	0
$36$	−92.0000	−0.425926
$37$	− 146.000i	− 0.648710i	−0.945936	−	0.324355i	$-0.894853\pi$
$37$	− 146.000i	− 0.648710i	0.945936	−	0.324355i	$-0.105147\pi$
$38$	4.00000i	0.0170759i
$39$	112.000	0.459855
$40$	0	0
$41$	126.000	0.479949	0.239974	−	0.970779i	$-0.422861\pi$
$41$	126.000	0.479949	0.239974	+	0.970779i	$0.422861\pi$
$42$	28.0000i	0.102869i
$43$	− 376.000i	− 1.33348i	−0.745292	−	0.666738i	$-0.767690\pi$
$43$	− 376.000i	− 1.33348i	0.745292	−	0.666738i	$-0.232310\pi$
$44$	−192.000	−0.657843
$45$	0	0
$46$	−240.000	−0.769262
$47$	12.0000i	0.0372421i	0.999827	+	0.0186211i	$0.00592761\pi$
$47$	12.0000i	0.0372421i	−0.999827	+	0.0186211i	$0.994072\pi$
$48$	− 32.0000i	− 0.0962250i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	228.000	0.626008
$52$	− 224.000i	− 0.597369i
$53$	174.000i	0.450957i	0.974248	+	0.225479i	$0.0723946\pi$
$53$	174.000i	0.450957i	−0.974248	+	0.225479i	$0.927605\pi$
$54$	−200.000	−0.504010
$55$	0	0
$56$	56.0000	0.133631
$57$	4.00000i	0.00929496i
$58$	− 108.000i	− 0.244502i
$59$	−138.000	−0.304510	−0.152255	−	0.988341i	$-0.548653\pi$
$59$	−138.000	−0.304510	−0.152255	+	0.988341i	$0.548653\pi$
$60$	0	0
$61$	380.000	0.797607	0.398803	−	0.917036i	$-0.369426\pi$
$61$	380.000	0.797607	0.398803	+	0.917036i	$0.369426\pi$
$62$	− 472.000i	− 0.966840i
$63$	− 161.000i	− 0.321970i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−192.000	−0.358084
$67$	484.000i	0.882537i	0.897375	+	0.441269i	$0.145471\pi$
$67$	484.000i	0.882537i	−0.897375	+	0.441269i	$0.854529\pi$
$68$	− 456.000i	− 0.813208i
$69$	−240.000	−0.418733
$70$	0	0
$71$	576.000	0.962798	0.481399	−	0.876502i	$-0.340129\pi$
$71$	576.000	0.962798	0.481399	+	0.876502i	$0.340129\pi$
$72$	184.000i	0.301175i
$73$	− 1150.00i	− 1.84380i	−0.387429	−	0.921899i	$-0.626637\pi$
$73$	− 1150.00i	− 1.84380i	0.387429	−	0.921899i	$-0.373363\pi$
$74$	−292.000	−0.458707
$75$	0	0
$76$	8.00000	0.0120745
$77$	− 336.000i	− 0.497283i
$78$	− 224.000i	− 0.325167i
$79$	−776.000	−1.10515	−0.552575	−	0.833463i	$-0.686355\pi$
$79$	−776.000	−1.10515	−0.552575	+	0.833463i	$0.686355\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	− 252.000i	− 0.339375i
$83$	378.000i	0.499890i	0.968260	+	0.249945i	$0.0804126\pi$
$83$	378.000i	0.499890i	−0.968260	+	0.249945i	$0.919587\pi$
$84$	56.0000	0.0727393
$85$	0	0
$86$	−752.000	−0.942910
$87$	− 108.000i	− 0.133090i
$88$	384.000i	0.465165i
$89$	390.000	0.464493	0.232247	−	0.972657i	$-0.425392\pi$
$89$	390.000	0.464493	0.232247	+	0.972657i	$0.425392\pi$
$90$	0	0
$91$	392.000	0.451569
$92$	480.000i	0.543951i
$93$	− 472.000i	− 0.526281i
$94$	24.0000	0.0263342
$95$	0	0
$96$	−64.0000	−0.0680414
$97$	1330.00i	1.39218i	0.717957	+	0.696088i	$0.245078\pi$
$97$	1330.00i	1.39218i	−0.717957	+	0.696088i	$0.754922\pi$
$98$	98.0000i	0.101015i
$99$	1104.00	1.12077
$100$	0	0
$101$	−1500.00	−1.47778	−0.738889	−	0.673827i	$-0.764649\pi$
$101$	−1500.00	−1.47778	−0.738889	+	0.673827i	$0.764649\pi$
$102$	− 456.000i	− 0.442654i
$103$	380.000i	0.363520i	0.983343	+	0.181760i	$0.0581793\pi$
$103$	380.000i	0.363520i	−0.983343	+	0.181760i	$0.941821\pi$
$104$	−448.000	−0.422404
$105$	0	0
$106$	348.000	0.318875
$107$	− 636.000i	− 0.574621i	−0.957838	−	0.287310i	$-0.907239\pi$
$107$	− 636.000i	− 0.574621i	0.957838	−	0.287310i	$-0.0927611\pi$
$108$	400.000i	0.356389i
$109$	−146.000	−0.128296	−0.0641480	−	0.997940i	$-0.520433\pi$
$109$	−146.000	−0.128296	−0.0641480	+	0.997940i	$0.520433\pi$
$110$	0	0
$111$	−292.000	−0.249688
$112$	− 112.000i	− 0.0944911i
$113$	198.000i	0.164834i	0.996598	+	0.0824171i	$0.0262640\pi$
$113$	198.000i	0.164834i	−0.996598	+	0.0824171i	$0.973736\pi$
$114$	8.00000	0.00657253
$115$	0	0
$116$	−216.000	−0.172889
$117$	1288.00i	1.01774i
$118$	276.000i	0.215321i
$119$	798.000	0.614727
$120$	0	0
$121$	973.000	0.731029
$122$	− 760.000i	− 0.563993i
$123$	− 252.000i	− 0.184732i
$124$	−944.000	−0.683659
$125$	0	0
$126$	−322.000	−0.227667
$127$	376.000i	0.262713i	0.991335	+	0.131357i	$0.0419333\pi$
$127$	376.000i	0.262713i	−0.991335	+	0.131357i	$0.958067\pi$
$128$	128.000i	0.0883883i
$129$	−752.000	−0.513255
$130$	0	0
$131$	2130.00	1.42060	0.710301	−	0.703898i	$-0.248559\pi$
$131$	2130.00	1.42060	0.710301	+	0.703898i	$0.248559\pi$
$132$	384.000i	0.253204i
$133$	14.0000i	0.00912747i
$134$	968.000	0.624048
$135$	0	0
$136$	−912.000	−0.575025
$137$	78.0000i	0.0486423i	0.999704	+	0.0243211i	$0.00774242\pi$
$137$	78.0000i	0.0486423i	−0.999704	+	0.0243211i	$0.992258\pi$
$138$	480.000i	0.296089i
$139$	2338.00	1.42667	0.713333	−	0.700825i	$-0.247185\pi$
$139$	2338.00	1.42667	0.713333	+	0.700825i	$0.247185\pi$
$140$	0	0
$141$	24.0000	0.0143345
$142$	− 1152.00i	− 0.680801i
$143$	2688.00i	1.57190i
$144$	368.000	0.212963
$145$	0	0
$146$	−2300.00	−1.30376
$147$	98.0000i	0.0549857i
$148$	584.000i	0.324355i
$149$	1002.00	0.550920	0.275460	−	0.961313i	$-0.411170\pi$
$149$	1002.00	0.550920	0.275460	+	0.961313i	$0.411170\pi$
$150$	0	0
$151$	−2752.00	−1.48314	−0.741571	−	0.670874i	$-0.765919\pi$
$151$	−2752.00	−1.48314	−0.741571	+	0.670874i	$0.765919\pi$
$152$	− 16.0000i	− 0.00853797i
$153$	2622.00i	1.38546i
$154$	−672.000	−0.351632
$155$	0	0
$156$	−448.000	−0.229928
$157$	520.000i	0.264335i	0.991227	+	0.132167i	$0.0421936\pi$
$157$	520.000i	0.264335i	−0.991227	+	0.132167i	$0.957806\pi$
$158$	1552.00i	0.781459i
$159$	348.000	0.173574
$160$	0	0
$161$	−840.000	−0.411188
$162$	− 842.000i	− 0.408357i
$163$	1280.00i	0.615076i	0.951536	+	0.307538i	$0.0995051\pi$
$163$	1280.00i	0.615076i	−0.951536	+	0.307538i	$0.900495\pi$
$164$	−504.000	−0.239974
$165$	0	0
$166$	756.000	0.353476
$167$	− 1764.00i	− 0.817380i	−0.912673	−	0.408690i	$-0.865986\pi$
$167$	− 1764.00i	− 0.817380i	0.912673	−	0.408690i	$-0.134014\pi$
$168$	− 112.000i	− 0.0514344i
$169$	−939.000	−0.427401
$170$	0	0
$171$	−46.0000	−0.0205714
$172$	1504.00i	0.666738i
$173$	− 768.000i	− 0.337514i	−0.985658	−	0.168757i	$-0.946025\pi$
$173$	− 768.000i	− 0.337514i	0.985658	−	0.168757i	$-0.0539753\pi$
$174$	−216.000	−0.0941087
$175$	0	0
$176$	768.000	0.328921
$177$	276.000i	0.117206i
$178$	− 780.000i	− 0.328446i
$179$	−1812.00	−0.756621	−0.378311	−	0.925679i	$-0.623495\pi$
$179$	−1812.00	−0.756621	−0.378311	+	0.925679i	$0.623495\pi$
$180$	0	0
$181$	−448.000	−0.183976	−0.0919878	−	0.995760i	$-0.529322\pi$
$181$	−448.000	−0.183976	−0.0919878	+	0.995760i	$0.529322\pi$
$182$	− 784.000i	− 0.319307i
$183$	− 760.000i	− 0.306999i
$184$	960.000	0.384631
$185$	0	0
$186$	−944.000	−0.372137
$187$	5472.00i	2.13985i
$188$	− 48.0000i	− 0.0186211i
$189$	−700.000	−0.269405
$190$	0	0
$191$	−2136.00	−0.809191	−0.404596	−	0.914496i	$-0.632588\pi$
$191$	−2136.00	−0.809191	−0.404596	+	0.914496i	$0.632588\pi$
$192$	128.000i	0.0481125i
$193$	4430.00i	1.65222i	0.563509	+	0.826110i	$0.309451\pi$
$193$	4430.00i	1.65222i	−0.563509	+	0.826110i	$0.690549\pi$
$194$	2660.00	0.984417
$195$	0	0
$196$	196.000	0.0714286
$197$	− 198.000i	− 0.0716087i	−0.999359	−	0.0358044i	$-0.988601\pi$
$197$	− 198.000i	− 0.0716087i	0.999359	−	0.0358044i	$-0.0113993\pi$
$198$	− 2208.00i	− 0.792504i
$199$	2284.00	0.813610	0.406805	−	0.913515i	$-0.366643\pi$
$199$	2284.00	0.813610	0.406805	+	0.913515i	$0.366643\pi$
$200$	0	0
$201$	968.000	0.339689
$202$	3000.00i	1.04495i
$203$	− 378.000i	− 0.130692i
$204$	−912.000	−0.313004
$205$	0	0
$206$	760.000	0.257047
$207$	− 2760.00i	− 0.926731i
$208$	896.000i	0.298685i
$209$	−96.0000	−0.0317725
$210$	0	0
$211$	4412.00	1.43950	0.719750	−	0.694233i	$-0.244256\pi$
$211$	4412.00	1.43950	0.719750	+	0.694233i	$0.244256\pi$
$212$	− 696.000i	− 0.225479i
$213$	− 1152.00i	− 0.370581i
$214$	−1272.00	−0.406318
$215$	0	0
$216$	800.000	0.252005
$217$	− 1652.00i	− 0.516798i
$218$	292.000i	0.0907190i
$219$	−2300.00	−0.709679
$220$	0	0
$221$	−6384.00	−1.94314
$222$	584.000i	0.176556i
$223$	2072.00i	0.622204i	0.950377	+	0.311102i	$0.100698\pi$
$223$	2072.00i	0.622204i	−0.950377	+	0.311102i	$0.899302\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	396.000	0.116555
$227$	366.000i	0.107014i	0.998567	+	0.0535072i	$0.0170400\pi$
$227$	366.000i	0.107014i	−0.998567	+	0.0535072i	$0.982960\pi$
$228$	− 16.0000i	− 0.00464748i
$229$	376.000	0.108501	0.0542506	−	0.998527i	$-0.482723\pi$
$229$	376.000	0.108501	0.0542506	+	0.998527i	$0.482723\pi$
$230$	0	0
$231$	−672.000	−0.191404
$232$	432.000i	0.122251i
$233$	− 2262.00i	− 0.636002i	−0.948090	−	0.318001i	$-0.896988\pi$
$233$	− 2262.00i	− 0.636002i	0.948090	−	0.318001i	$-0.103012\pi$
$234$	2576.00	0.719651
$235$	0	0
$236$	552.000	0.152255
$237$	1552.00i	0.425372i
$238$	− 1596.00i	− 0.434678i
$239$	−2592.00	−0.701517	−0.350758	−	0.936466i	$-0.614076\pi$
$239$	−2592.00	−0.701517	−0.350758	+	0.936466i	$0.614076\pi$
$240$	0	0
$241$	110.000	0.0294013	0.0147007	−	0.999892i	$-0.495320\pi$
$241$	110.000	0.0294013	0.0147007	+	0.999892i	$0.495320\pi$
$242$	− 1946.00i	− 0.516916i
$243$	− 3542.00i	− 0.935059i
$244$	−1520.00	−0.398803
$245$	0	0
$246$	−504.000	−0.130625
$247$	− 112.000i	− 0.0288518i
$248$	1888.00i	0.483420i
$249$	756.000	0.192408
$250$	0	0
$251$	−1890.00	−0.475282	−0.237641	−	0.971353i	$-0.576374\pi$
$251$	−1890.00	−0.475282	−0.237641	+	0.971353i	$0.576374\pi$
$252$	644.000i	0.160985i
$253$	− 5760.00i	− 1.43134i
$254$	752.000	0.185766
$255$	0	0
$256$	256.000	0.0625000
$257$	− 2130.00i	− 0.516987i	−0.966013	−	0.258494i	$-0.916774\pi$
$257$	− 2130.00i	− 0.516987i	0.966013	−	0.258494i	$-0.0832261\pi$
$258$	1504.00i	0.362926i
$259$	−1022.00	−0.245189
$260$	0	0
$261$	1242.00	0.294551
$262$	− 4260.00i	− 1.00452i
$263$	− 4992.00i	− 1.17042i	−0.810883	−	0.585209i	$-0.801012\pi$
$263$	− 4992.00i	− 1.17042i	0.810883	−	0.585209i	$-0.198988\pi$
$264$	768.000	0.179042
$265$	0	0
$266$	28.0000	0.00645410
$267$	− 780.000i	− 0.178784i
$268$	− 1936.00i	− 0.441269i
$269$	−6816.00	−1.54490	−0.772451	−	0.635074i	$-0.780970\pi$
$269$	−6816.00	−1.54490	−0.772451	+	0.635074i	$0.780970\pi$
$270$	0	0
$271$	8192.00	1.83627	0.918134	−	0.396270i	$-0.129696\pi$
$271$	8192.00	1.83627	0.918134	+	0.396270i	$0.129696\pi$
$272$	1824.00i	0.406604i
$273$	− 784.000i	− 0.173809i
$274$	156.000	0.0343953
$275$	0	0
$276$	960.000	0.209367
$277$	− 2414.00i	− 0.523622i	−0.965119	−	0.261811i	$-0.915680\pi$
$277$	− 2414.00i	− 0.523622i	0.965119	−	0.261811i	$-0.0843197\pi$
$278$	− 4676.00i	− 1.00881i
$279$	5428.00	1.16475
$280$	0	0
$281$	1962.00	0.416524	0.208262	−	0.978073i	$-0.433219\pi$
$281$	1962.00	0.416524	0.208262	+	0.978073i	$0.433219\pi$
$282$	− 48.0000i	− 0.0101360i
$283$	5402.00i	1.13468i	0.823482	+	0.567342i	$0.192028\pi$
$283$	5402.00i	1.13468i	−0.823482	+	0.567342i	$0.807972\pi$
$284$	−2304.00	−0.481399
$285$	0	0
$286$	5376.00	1.11150
$287$	− 882.000i	− 0.181404i
$288$	− 736.000i	− 0.150588i
$289$	−8083.00	−1.64523
$290$	0	0
$291$	2660.00	0.535849
$292$	4600.00i	0.921899i
$293$	− 4788.00i	− 0.954669i	−0.878722	−	0.477334i	$-0.841603\pi$
$293$	− 4788.00i	− 0.954669i	0.878722	−	0.477334i	$-0.158397\pi$
$294$	196.000	0.0388808
$295$	0	0
$296$	1168.00	0.229353
$297$	− 4800.00i	− 0.937792i
$298$	− 2004.00i	− 0.389559i
$299$	6720.00	1.29976
$300$	0	0
$301$	−2632.00	−0.504007
$302$	5504.00i	1.04874i
$303$	3000.00i	0.568797i
$304$	−32.0000	−0.00603726
$305$	0	0
$306$	5244.00	0.979672
$307$	574.000i	0.106710i	0.998576	+	0.0533549i	$0.0169915\pi$
$307$	574.000i	0.106710i	−0.998576	+	0.0533549i	$0.983009\pi$
$308$	1344.00i	0.248641i
$309$	760.000	0.139919
$310$	0	0
$311$	−8808.00	−1.60597	−0.802984	−	0.596001i	$-0.796755\pi$
$311$	−8808.00	−1.60597	−0.802984	+	0.596001i	$0.796755\pi$
$312$	896.000i	0.162583i
$313$	− 2770.00i	− 0.500223i	−0.968217	−	0.250111i	$-0.919533\pi$
$313$	− 2770.00i	− 0.500223i	0.968217	−	0.250111i	$-0.0804672\pi$
$314$	1040.00	0.186913
$315$	0	0
$316$	3104.00	0.552575
$317$	− 7566.00i	− 1.34053i	−0.742121	−	0.670266i	$-0.766180\pi$
$317$	− 7566.00i	− 1.34053i	0.742121	−	0.670266i	$-0.233820\pi$
$318$	− 696.000i	− 0.122735i
$319$	2592.00	0.454935
$320$	0	0
$321$	−1272.00	−0.221172
$322$	1680.00i	0.290754i
$323$	− 228.000i	− 0.0392763i
$324$	−1684.00	−0.288752
$325$	0	0
$326$	2560.00	0.434924
$327$	292.000i	0.0493812i
$328$	1008.00i	0.169687i
$329$	84.0000	0.0140762
$330$	0	0
$331$	−11320.0	−1.87977	−0.939884	−	0.341493i	$-0.889068\pi$
$331$	−11320.0	−1.87977	−0.939884	+	0.341493i	$0.889068\pi$
$332$	− 1512.00i	− 0.249945i
$333$	− 3358.00i	− 0.552604i
$334$	−3528.00	−0.577975
$335$	0	0
$336$	−224.000	−0.0363696
$337$	4786.00i	0.773620i	0.922159	+	0.386810i	$0.126423\pi$
$337$	4786.00i	0.773620i	−0.922159	+	0.386810i	$0.873577\pi$
$338$	1878.00i	0.302218i
$339$	396.000	0.0634447
$340$	0	0
$341$	11328.0	1.79896
$342$	92.0000i	0.0145462i
$343$	343.000i	0.0539949i
$344$	3008.00	0.471455
$345$	0	0
$346$	−1536.00	−0.238659
$347$	− 12648.0i	− 1.95672i	−0.206921	−	0.978358i	$-0.566344\pi$
$347$	− 12648.0i	− 1.95672i	0.206921	−	0.978358i	$-0.433656\pi$
$348$	432.000i	0.0665449i
$349$	−9632.00	−1.47733	−0.738666	−	0.674071i	$-0.764544\pi$
$349$	−9632.00	−1.47733	−0.738666	+	0.674071i	$0.764544\pi$
$350$	0	0
$351$	5600.00	0.851584
$352$	− 1536.00i	− 0.232583i
$353$	− 3390.00i	− 0.511137i	−0.966791	−	0.255569i	$-0.917737\pi$
$353$	− 3390.00i	− 0.511137i	0.966791	−	0.255569i	$-0.0822627\pi$
$354$	552.000	0.0828770
$355$	0	0
$356$	−1560.00	−0.232247
$357$	− 1596.00i	− 0.236609i
$358$	3624.00i	0.535012i
$359$	10704.0	1.57364	0.786818	−	0.617185i	$-0.211727\pi$
$359$	10704.0	1.57364	0.786818	+	0.617185i	$0.211727\pi$
$360$	0	0
$361$	−6855.00	−0.999417
$362$	896.000i	0.130090i
$363$	− 1946.00i	− 0.281373i
$364$	−1568.00	−0.225784
$365$	0	0
$366$	−1520.00	−0.217081
$367$	8584.00i	1.22093i	0.792043	+	0.610465i	$0.209017\pi$
$367$	8584.00i	1.22093i	−0.792043	+	0.610465i	$0.790983\pi$
$368$	− 1920.00i	− 0.271975i
$369$	2898.00	0.408845
$370$	0	0
$371$	1218.00	0.170446
$372$	1888.00i	0.263140i
$373$	− 2122.00i	− 0.294566i	−0.989094	−	0.147283i	$-0.952947\pi$
$373$	− 2122.00i	− 0.294566i	0.989094	−	0.147283i	$-0.0470528\pi$
$374$	10944.0	1.51310
$375$	0	0
$376$	−96.0000	−0.0131671
$377$	3024.00i	0.413114i
$378$	1400.00i	0.190498i
$379$	4912.00	0.665732	0.332866	−	0.942974i	$-0.391984\pi$
$379$	4912.00	0.665732	0.332866	+	0.942974i	$0.391984\pi$
$380$	0	0
$381$	752.000	0.101118
$382$	4272.00i	0.572185i
$383$	9060.00i	1.20873i	0.796707	+	0.604366i	$0.206574\pi$
$383$	9060.00i	1.20873i	−0.796707	+	0.604366i	$0.793426\pi$
$384$	256.000	0.0340207
$385$	0	0
$386$	8860.00	1.16830
$387$	− 8648.00i	− 1.13592i
$388$	− 5320.00i	− 0.696088i
$389$	−8994.00	−1.17227	−0.586136	−	0.810213i	$-0.699352\pi$
$389$	−8994.00	−1.17227	−0.586136	+	0.810213i	$0.699352\pi$
$390$	0	0
$391$	13680.0	1.76938
$392$	− 392.000i	− 0.0505076i
$393$	− 4260.00i	− 0.546790i
$394$	−396.000	−0.0506350
$395$	0	0
$396$	−4416.00	−0.560385
$397$	12976.0i	1.64042i	0.572062	+	0.820210i	$0.306143\pi$
$397$	12976.0i	1.64042i	−0.572062	+	0.820210i	$0.693857\pi$
$398$	− 4568.00i	− 0.575309i
$399$	28.0000	0.00351317
$400$	0	0
$401$	−3522.00	−0.438604	−0.219302	−	0.975657i	$-0.570378\pi$
$401$	−3522.00	−0.438604	−0.219302	+	0.975657i	$0.570378\pi$
$402$	− 1936.00i	− 0.240196i
$403$	13216.0i	1.63359i
$404$	6000.00	0.738889
$405$	0	0
$406$	−756.000	−0.0924129
$407$	− 7008.00i	− 0.853498i
$408$	1824.00i	0.221327i
$409$	−12710.0	−1.53660	−0.768300	−	0.640090i	$-0.778897\pi$
$409$	−12710.0	−1.53660	−0.768300	+	0.640090i	$0.778897\pi$
$410$	0	0
$411$	156.000	0.0187224
$412$	− 1520.00i	− 0.181760i
$413$	966.000i	0.115094i
$414$	−5520.00	−0.655298
$415$	0	0
$416$	1792.00	0.211202
$417$	− 4676.00i	− 0.549124i
$418$	192.000i	0.0224666i
$419$	−1638.00	−0.190982	−0.0954911	−	0.995430i	$-0.530442\pi$
$419$	−1638.00	−0.190982	−0.0954911	+	0.995430i	$0.530442\pi$
$420$	0	0
$421$	−12850.0	−1.48758	−0.743789	−	0.668414i	$-0.766973\pi$
$421$	−12850.0	−1.48758	−0.743789	+	0.668414i	$0.766973\pi$
$422$	− 8824.00i	− 1.01788i
$423$	276.000i	0.0317248i
$424$	−1392.00	−0.159437
$425$	0	0
$426$	−2304.00	−0.262040
$427$	− 2660.00i	− 0.301467i
$428$	2544.00i	0.287310i
$429$	5376.00	0.605025
$430$	0	0
$431$	−8016.00	−0.895863	−0.447932	−	0.894068i	$-0.647839\pi$
$431$	−8016.00	−0.895863	−0.447932	+	0.894068i	$0.647839\pi$
$432$	− 1600.00i	− 0.178195i
$433$	2198.00i	0.243947i	0.992533	+	0.121974i	$0.0389223\pi$
$433$	2198.00i	0.243947i	−0.992533	+	0.121974i	$0.961078\pi$
$434$	−3304.00	−0.365431
$435$	0	0
$436$	584.000	0.0641480
$437$	240.000i	0.0262718i
$438$	4600.00i	0.501818i
$439$	376.000	0.0408781	0.0204391	−	0.999791i	$-0.493494\pi$
$439$	376.000	0.0408781	0.0204391	+	0.999791i	$0.493494\pi$
$440$	0	0
$441$	−1127.00	−0.121693
$442$	12768.0i	1.37401i
$443$	7188.00i	0.770908i	0.922727	+	0.385454i	$0.125955\pi$
$443$	7188.00i	0.770908i	−0.922727	+	0.385454i	$0.874045\pi$
$444$	1168.00	0.124844
$445$	0	0
$446$	4144.00	0.439964
$447$	− 2004.00i	− 0.212049i
$448$	448.000i	0.0472456i
$449$	14670.0	1.54192	0.770958	−	0.636886i	$-0.219778\pi$
$449$	14670.0	1.54192	0.770958	+	0.636886i	$0.219778\pi$
$450$	0	0
$451$	6048.00	0.631462
$452$	− 792.000i	− 0.0824171i
$453$	5504.00i	0.570862i
$454$	732.000	0.0756706
$455$	0	0
$456$	−32.0000	−0.00328627
$457$	5146.00i	0.526739i	0.964695	+	0.263370i	$0.0848338\pi$
$457$	5146.00i	0.526739i	−0.964695	+	0.263370i	$0.915166\pi$
$458$	− 752.000i	− 0.0767219i
$459$	11400.0	1.15927
$460$	0	0
$461$	−1512.00	−0.152757	−0.0763784	−	0.997079i	$-0.524336\pi$
$461$	−1512.00	−0.152757	−0.0763784	+	0.997079i	$0.524336\pi$
$462$	1344.00i	0.135343i
$463$	7184.00i	0.721099i	0.932740	+	0.360549i	$0.117411\pi$
$463$	7184.00i	0.721099i	−0.932740	+	0.360549i	$0.882589\pi$
$464$	864.000	0.0864444
$465$	0	0
$466$	−4524.00	−0.449722
$467$	16518.0i	1.63675i	0.574685	+	0.818375i	$0.305125\pi$
$467$	16518.0i	1.63675i	−0.574685	+	0.818375i	$0.694875\pi$
$468$	− 5152.00i	− 0.508870i
$469$	3388.00	0.333568
$470$	0	0
$471$	1040.00	0.101742
$472$	− 1104.00i	− 0.107660i
$473$	− 18048.0i	− 1.75444i
$474$	3104.00	0.300784
$475$	0	0
$476$	−3192.00	−0.307364
$477$	4002.00i	0.384149i
$478$	5184.00i	0.496047i
$479$	−10092.0	−0.962662	−0.481331	−	0.876539i	$-0.659847\pi$
$479$	−10092.0	−0.962662	−0.481331	+	0.876539i	$0.659847\pi$
$480$	0	0
$481$	8176.00	0.775038
$482$	− 220.000i	− 0.0207899i
$483$	1680.00i	0.158266i
$484$	−3892.00	−0.365515
$485$	0	0
$486$	−7084.00	−0.661187
$487$	− 7832.00i	− 0.728751i	−0.931252	−	0.364376i	$-0.881282\pi$
$487$	− 7832.00i	− 0.728751i	0.931252	−	0.364376i	$-0.118718\pi$
$488$	3040.00i	0.281997i
$489$	2560.00	0.236743
$490$	0	0
$491$	−6732.00	−0.618759	−0.309380	−	0.950939i	$-0.600121\pi$
$491$	−6732.00	−0.618759	−0.309380	+	0.950939i	$0.600121\pi$
$492$	1008.00i	0.0923662i
$493$	6156.00i	0.562378i
$494$	−224.000	−0.0204013
$495$	0	0
$496$	3776.00	0.341829
$497$	− 4032.00i	− 0.363903i
$498$	− 1512.00i	− 0.136053i
$499$	−18668.0	−1.67474	−0.837369	−	0.546638i	$-0.815907\pi$
$499$	−18668.0	−1.67474	−0.837369	+	0.546638i	$0.815907\pi$
$500$	0	0
$501$	−3528.00	−0.314610
$502$	3780.00i	0.336075i
$503$	− 6048.00i	− 0.536117i	−0.963403	−	0.268059i	$-0.913618\pi$
$503$	− 6048.00i	− 0.536117i	0.963403	−	0.268059i	$-0.0863821\pi$
$504$	1288.00	0.113833
$505$	0	0
$506$	−11520.0	−1.01211
$507$	1878.00i	0.164507i
$508$	− 1504.00i	− 0.131357i
$509$	−11328.0	−0.986453	−0.493227	−	0.869901i	$-0.664183\pi$
$509$	−11328.0	−0.986453	−0.493227	+	0.869901i	$0.664183\pi$
$510$	0	0
$511$	−8050.00	−0.696890
$512$	− 512.000i	− 0.0441942i
$513$	200.000i	0.0172129i
$514$	−4260.00	−0.365565
$515$	0	0
$516$	3008.00	0.256628
$517$	576.000i	0.0489989i
$518$	2044.00i	0.173375i
$519$	−1536.00	−0.129909
$520$	0	0
$521$	−4146.00	−0.348636	−0.174318	−	0.984689i	$-0.555772\pi$
$521$	−4146.00	−0.348636	−0.174318	+	0.984689i	$0.555772\pi$
$522$	− 2484.00i	− 0.208279i
$523$	− 1006.00i	− 0.0841096i	−0.999115	−	0.0420548i	$-0.986610\pi$
$523$	− 1006.00i	− 0.0841096i	0.999115	−	0.0420548i	$-0.0133904\pi$
$524$	−8520.00	−0.710301
$525$	0	0
$526$	−9984.00	−0.827610
$527$	26904.0i	2.22383i
$528$	− 1536.00i	− 0.126602i
$529$	−2233.00	−0.183529
$530$	0	0
$531$	−3174.00	−0.259397
$532$	− 56.0000i	− 0.00456374i
$533$	7056.00i	0.573413i
$534$	−1560.00	−0.126419
$535$	0	0
$536$	−3872.00	−0.312024
$537$	3624.00i	0.291224i
$538$	13632.0i	1.09241i
$539$	−2352.00	−0.187955
$540$	0	0
$541$	−14722.0	−1.16996	−0.584980	−	0.811048i	$-0.698898\pi$
$541$	−14722.0	−1.16996	−0.584980	+	0.811048i	$0.698898\pi$
$542$	− 16384.0i	− 1.29844i
$543$	896.000i	0.0708122i
$544$	3648.00	0.287512
$545$	0	0
$546$	−1568.00	−0.122901
$547$	13480.0i	1.05368i	0.849964	+	0.526840i	$0.176623\pi$
$547$	13480.0i	1.05368i	−0.849964	+	0.526840i	$0.823377\pi$
$548$	− 312.000i	− 0.0243211i
$549$	8740.00	0.679443
$550$	0	0
$551$	−108.000	−0.00835019
$552$	− 1920.00i	− 0.148045i
$553$	5432.00i	0.417707i
$554$	−4828.00	−0.370256
$555$	0	0
$556$	−9352.00	−0.713333
$557$	− 6222.00i	− 0.473312i	−0.971594	−	0.236656i	$-0.923949\pi$
$557$	− 6222.00i	− 0.473312i	0.971594	−	0.236656i	$-0.0760514\pi$
$558$	− 10856.0i	− 0.823604i
$559$	21056.0	1.59316
$560$	0	0
$561$	10944.0	0.823629
$562$	− 3924.00i	− 0.294527i
$563$	4926.00i	0.368750i	0.982856	+	0.184375i	$0.0590261\pi$
$563$	4926.00i	0.368750i	−0.982856	+	0.184375i	$0.940974\pi$
$564$	−96.0000	−0.00716725
$565$	0	0
$566$	10804.0	0.802343
$567$	− 2947.00i	− 0.218276i
$568$	4608.00i	0.340400i
$569$	−22182.0	−1.63430	−0.817151	−	0.576424i	$-0.804448\pi$
$569$	−22182.0	−1.63430	−0.817151	+	0.576424i	$0.804448\pi$
$570$	0	0
$571$	3296.00	0.241564	0.120782	−	0.992679i	$-0.461460\pi$
$571$	3296.00	0.241564	0.120782	+	0.992679i	$0.461460\pi$
$572$	− 10752.0i	− 0.785951i
$573$	4272.00i	0.311458i
$574$	−1764.00	−0.128272
$575$	0	0
$576$	−1472.00	−0.106481
$577$	24334.0i	1.75570i	0.478938	+	0.877849i	$0.341022\pi$
$577$	24334.0i	1.75570i	−0.478938	+	0.877849i	$0.658978\pi$
$578$	16166.0i	1.16335i
$579$	8860.00	0.635940
$580$	0	0
$581$	2646.00	0.188941
$582$	− 5320.00i	− 0.378902i
$583$	8352.00i	0.593318i
$584$	9200.00	0.651881
$585$	0	0
$586$	−9576.00	−0.675053
$587$	− 1638.00i	− 0.115175i	−0.998340	−	0.0575873i	$-0.981659\pi$
$587$	− 1638.00i	− 0.115175i	0.998340	−	0.0575873i	$-0.0183408\pi$
$588$	− 392.000i	− 0.0274929i
$589$	−472.000	−0.0330194
$590$	0	0
$591$	−396.000	−0.0275622
$592$	− 2336.00i	− 0.162177i
$593$	− 7446.00i	− 0.515633i	−0.966194	−	0.257817i	$-0.916997\pi$
$593$	− 7446.00i	− 0.515633i	0.966194	−	0.257817i	$-0.0830031\pi$
$594$	−9600.00	−0.663119
$595$	0	0
$596$	−4008.00	−0.275460
$597$	− 4568.00i	− 0.313159i
$598$	− 13440.0i	− 0.919068i
$599$	6504.00	0.443650	0.221825	−	0.975087i	$-0.428799\pi$
$599$	6504.00	0.443650	0.221825	+	0.975087i	$0.428799\pi$
$600$	0	0
$601$	16058.0	1.08988	0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0	1.08988	0.544941	+	0.838474i	$0.316552\pi$
$602$	5264.00i	0.356386i
$603$	11132.0i	0.751791i
$604$	11008.0	0.741571
$605$	0	0
$606$	6000.00	0.402200
$607$	− 10208.0i	− 0.682586i	−0.939957	−	0.341293i	$-0.889135\pi$
$607$	− 10208.0i	− 0.682586i	0.939957	−	0.341293i	$-0.110865\pi$
$608$	64.0000i	0.00426898i
$609$	−756.000	−0.0503032
$610$	0	0
$611$	−672.000	−0.0444946
$612$	− 10488.0i	− 0.692732i
$613$	− 14974.0i	− 0.986614i	−0.869855	−	0.493307i	$-0.835788\pi$
$613$	− 14974.0i	− 0.986614i	0.869855	−	0.493307i	$-0.164212\pi$
$614$	1148.00	0.0754552
$615$	0	0
$616$	2688.00	0.175816
$617$	− 7254.00i	− 0.473314i	−0.971593	−	0.236657i	$-0.923948\pi$
$617$	− 7254.00i	− 0.473314i	0.971593	−	0.236657i	$-0.0760518\pi$
$618$	− 1520.00i	− 0.0989375i
$619$	−12458.0	−0.808933	−0.404466	−	0.914553i	$-0.632543\pi$
$619$	−12458.0	−0.808933	−0.404466	+	0.914553i	$0.632543\pi$
$620$	0	0
$621$	−12000.0	−0.775432
$622$	17616.0i	1.13559i
$623$	− 2730.00i	− 0.175562i
$624$	1792.00	0.114964
$625$	0	0
$626$	−5540.00	−0.353711
$627$	192.000i	0.0122293i
$628$	− 2080.00i	− 0.132167i
$629$	16644.0	1.05507
$630$	0	0
$631$	28352.0	1.78871	0.894354	−	0.447359i	$-0.147635\pi$
$631$	28352.0	1.78871	0.894354	+	0.447359i	$0.147635\pi$
$632$	− 6208.00i	− 0.390729i
$633$	− 8824.00i	− 0.554064i
$634$	−15132.0	−0.947900
$635$	0	0
$636$	−1392.00	−0.0867868
$637$	− 2744.00i	− 0.170677i
$638$	− 5184.00i	− 0.321687i
$639$	13248.0	0.820161
$640$	0	0
$641$	27390.0	1.68774	0.843869	−	0.536549i	$-0.180272\pi$
$641$	27390.0	1.68774	0.843869	+	0.536549i	$0.180272\pi$
$642$	2544.00i	0.156392i
$643$	− 21490.0i	− 1.31801i	−0.752137	−	0.659007i	$-0.770977\pi$
$643$	− 21490.0i	− 1.31801i	0.752137	−	0.659007i	$-0.229023\pi$
$644$	3360.00	0.205594
$645$	0	0
$646$	−456.000	−0.0277726
$647$	− 17652.0i	− 1.07260i	−0.844028	−	0.536300i	$-0.819822\pi$
$647$	− 17652.0i	− 1.07260i	0.844028	−	0.536300i	$-0.180178\pi$
$648$	3368.00i	0.204178i
$649$	−6624.00	−0.400639
$650$	0	0
$651$	−3304.00	−0.198915
$652$	− 5120.00i	− 0.307538i
$653$	− 4782.00i	− 0.286576i	−0.989681	−	0.143288i	$-0.954232\pi$
$653$	− 4782.00i	− 0.286576i	0.989681	−	0.143288i	$-0.0457675\pi$
$654$	584.000	0.0349177
$655$	0	0
$656$	2016.00	0.119987
$657$	− 26450.0i	− 1.57064i
$658$	− 168.000i	− 0.00995338i
$659$	27144.0	1.60452	0.802261	−	0.596973i	$-0.203630\pi$
$659$	27144.0	1.60452	0.802261	+	0.596973i	$0.203630\pi$
$660$	0	0
$661$	−11860.0	−0.697883	−0.348941	−	0.937145i	$-0.613459\pi$
$661$	−11860.0	−0.697883	−0.348941	+	0.937145i	$0.613459\pi$
$662$	22640.0i	1.32920i
$663$	12768.0i	0.747916i
$664$	−3024.00	−0.176738
$665$	0	0
$666$	−6716.00	−0.390750
$667$	− 6480.00i	− 0.376172i
$668$	7056.00i	0.408690i
$669$	4144.00	0.239486
$670$	0	0
$671$	18240.0	1.04940
$672$	448.000i	0.0257172i
$673$	5546.00i	0.317656i	0.987306	+	0.158828i	$0.0507716\pi$
$673$	5546.00i	0.317656i	−0.987306	+	0.158828i	$0.949228\pi$
$674$	9572.00	0.547032
$675$	0	0
$676$	3756.00	0.213701
$677$	14880.0i	0.844734i	0.906425	+	0.422367i	$0.138801\pi$
$677$	14880.0i	0.844734i	−0.906425	+	0.422367i	$0.861199\pi$
$678$	− 792.000i	− 0.0448622i
$679$	9310.00	0.526193
$680$	0	0
$681$	732.000	0.0411899
$682$	− 22656.0i	− 1.27206i
$683$	20964.0i	1.17447i	0.809415	+	0.587237i	$0.199784\pi$
$683$	20964.0i	1.17447i	−0.809415	+	0.587237i	$0.800216\pi$
$684$	184.000	0.0102857
$685$	0	0
$686$	686.000	0.0381802
$687$	− 752.000i	− 0.0417621i
$688$	− 6016.00i	− 0.333369i
$689$	−9744.00	−0.538776
$690$	0	0
$691$	13106.0	0.721528	0.360764	−	0.932657i	$-0.382516\pi$
$691$	13106.0	0.721528	0.360764	+	0.932657i	$0.382516\pi$
$692$	3072.00i	0.168757i
$693$	− 7728.00i	− 0.423611i
$694$	−25296.0	−1.38361
$695$	0	0
$696$	864.000	0.0470544
$697$	14364.0i	0.780596i
$698$	19264.0i	1.04463i
$699$	−4524.00	−0.244797
$700$	0	0
$701$	−4590.00	−0.247307	−0.123653	−	0.992325i	$-0.539461\pi$
$701$	−4590.00	−0.247307	−0.123653	+	0.992325i	$0.539461\pi$
$702$	− 11200.0i	− 0.602161i
$703$	292.000i	0.0156657i
$704$	−3072.00	−0.164461
$705$	0	0
$706$	−6780.00	−0.361429
$707$	10500.0i	0.558548i
$708$	− 1104.00i	− 0.0586029i
$709$	862.000	0.0456602	0.0228301	−	0.999739i	$-0.492732\pi$
$709$	862.000	0.0456602	0.0228301	+	0.999739i	$0.492732\pi$
$710$	0	0
$711$	−17848.0	−0.941424
$712$	3120.00i	0.164223i
$713$	− 28320.0i	− 1.48751i
$714$	−3192.00	−0.167308
$715$	0	0
$716$	7248.00	0.378311
$717$	5184.00i	0.270014i
$718$	− 21408.0i	− 1.11273i
$719$	3540.00	0.183616	0.0918079	−	0.995777i	$-0.470735\pi$
$719$	3540.00	0.183616	0.0918079	+	0.995777i	$0.470735\pi$
$720$	0	0
$721$	2660.00	0.137397
$722$	13710.0i	0.706694i
$723$	− 220.000i	− 0.0113166i
$724$	1792.00	0.0919878
$725$	0	0
$726$	−3892.00	−0.198961
$727$	4228.00i	0.215692i	0.994168	+	0.107846i	$0.0343953\pi$
$727$	4228.00i	0.215692i	−0.994168	+	0.107846i	$0.965605\pi$
$728$	3136.00i	0.159654i
$729$	4283.00	0.217599
$730$	0	0
$731$	42864.0	2.16879
$732$	3040.00i	0.153499i
$733$	5420.00i	0.273114i	0.990632	+	0.136557i	$0.0436036\pi$
$733$	5420.00i	0.273114i	−0.990632	+	0.136557i	$0.956396\pi$
$734$	17168.0	0.863328
$735$	0	0
$736$	−3840.00	−0.192316
$737$	23232.0i	1.16114i
$738$	− 5796.00i	− 0.289097i
$739$	−1280.00	−0.0637152	−0.0318576	−	0.999492i	$-0.510142\pi$
$739$	−1280.00	−0.0637152	−0.0318576	+	0.999492i	$0.510142\pi$
$740$	0	0
$741$	−224.000	−0.0111051
$742$	− 2436.00i	− 0.120523i
$743$	− 35712.0i	− 1.76332i	−0.471886	−	0.881660i	$-0.656427\pi$
$743$	− 35712.0i	− 1.76332i	0.471886	−	0.881660i	$-0.343573\pi$
$744$	3776.00	0.186068
$745$	0	0
$746$	−4244.00	−0.208289
$747$	8694.00i	0.425832i
$748$	− 21888.0i	− 1.06993i
$749$	−4452.00	−0.217186
$750$	0	0
$751$	24464.0	1.18869	0.594344	−	0.804211i	$-0.297412\pi$
$751$	24464.0	1.18869	0.594344	+	0.804211i	$0.297412\pi$
$752$	192.000i	0.00931053i
$753$	3780.00i	0.182936i
$754$	6048.00	0.292116
$755$	0	0
$756$	2800.00	0.134702
$757$	− 30242.0i	− 1.45200i	−0.687695	−	0.726000i	$-0.741377\pi$
$757$	− 30242.0i	− 1.45200i	0.687695	−	0.726000i	$-0.258623\pi$
$758$	− 9824.00i	− 0.470744i
$759$	−11520.0	−0.550922
$760$	0	0
$761$	−2154.00	−0.102605	−0.0513025	−	0.998683i	$-0.516337\pi$
$761$	−2154.00	−0.102605	−0.0513025	+	0.998683i	$0.516337\pi$
$762$	− 1504.00i	− 0.0715015i
$763$	1022.00i	0.0484913i
$764$	8544.00	0.404596
$765$	0	0
$766$	18120.0	0.854703
$767$	− 7728.00i	− 0.363810i
$768$	− 512.000i	− 0.0240563i
$769$	−10262.0	−0.481219	−0.240609	−	0.970622i	$-0.577347\pi$
$769$	−10262.0	−0.481219	−0.240609	+	0.970622i	$0.577347\pi$
$770$	0	0
$771$	−4260.00	−0.198989
$772$	− 17720.0i	− 0.826110i
$773$	9084.00i	0.422676i	0.977413	+	0.211338i	$0.0677821\pi$
$773$	9084.00i	0.422676i	−0.977413	+	0.211338i	$0.932218\pi$
$774$	−17296.0	−0.803219
$775$	0	0
$776$	−10640.0	−0.492208
$777$	2044.00i	0.0943733i
$778$	17988.0i	0.828922i
$779$	−252.000	−0.0115903
$780$	0	0
$781$	27648.0	1.26674
$782$	− 27360.0i	− 1.25114i
$783$	− 5400.00i	− 0.246463i
$784$	−784.000	−0.0357143
$785$	0	0
$786$	−8520.00	−0.386639
$787$	19798.0i	0.896725i	0.893852	+	0.448362i	$0.147993\pi$
$787$	19798.0i	0.896725i	−0.893852	+	0.448362i	$0.852007\pi$
$788$	792.000i	0.0358044i
$789$	−9984.00	−0.450494
$790$	0	0
$791$	1386.00	0.0623015
$792$	8832.00i	0.396252i
$793$	21280.0i	0.952932i
$794$	25952.0	1.15995
$795$	0	0
$796$	−9136.00	−0.406805
$797$	− 30240.0i	− 1.34398i	−0.740558	−	0.671992i	$-0.765439\pi$
$797$	− 30240.0i	− 1.34398i	0.740558	−	0.671992i	$-0.234561\pi$
$798$	− 56.0000i	− 0.00248418i
$799$	−1368.00	−0.0605712
$800$	0	0
$801$	8970.00	0.395680
$802$	7044.00i	0.310140i
$803$	− 55200.0i	− 2.42586i
$804$	−3872.00	−0.169844
$805$	0	0
$806$	26432.0	1.15512
$807$	13632.0i	0.594633i
$808$	− 12000.0i	− 0.522473i
$809$	2346.00	0.101954	0.0509771	−	0.998700i	$-0.483766\pi$
$809$	2346.00	0.101954	0.0509771	+	0.998700i	$0.483766\pi$
$810$	0	0
$811$	−29806.0	−1.29054	−0.645271	−	0.763953i	$-0.723256\pi$
$811$	−29806.0	−1.29054	−0.645271	+	0.763953i	$0.723256\pi$
$812$	1512.00i	0.0653458i
$813$	− 16384.0i	− 0.706780i
$814$	−14016.0	−0.603514
$815$	0	0
$816$	3648.00	0.156502
$817$	752.000i	0.0322021i
$818$	25420.0i	1.08654i
$819$	9016.00	0.384670
$820$	0	0
$821$	−1506.00	−0.0640192	−0.0320096	−	0.999488i	$-0.510191\pi$
$821$	−1506.00	−0.0640192	−0.0320096	+	0.999488i	$0.510191\pi$
$822$	− 312.000i	− 0.0132387i
$823$	− 20392.0i	− 0.863694i	−0.901947	−	0.431847i	$-0.857862\pi$
$823$	− 20392.0i	− 0.863694i	0.901947	−	0.431847i	$-0.142138\pi$
$824$	−3040.00	−0.128524
$825$	0	0
$826$	1932.00	0.0813836
$827$	− 36108.0i	− 1.51826i	−0.650941	−	0.759128i	$-0.725626\pi$
$827$	− 36108.0i	− 1.51826i	0.650941	−	0.759128i	$-0.274374\pi$
$828$	11040.0i	0.463365i
$829$	13876.0	0.581343	0.290672	−	0.956823i	$-0.406121\pi$
$829$	13876.0	0.581343	0.290672	+	0.956823i	$0.406121\pi$
$830$	0	0
$831$	−4828.00	−0.201542
$832$	− 3584.00i	− 0.149342i
$833$	− 5586.00i	− 0.232345i
$834$	−9352.00	−0.388289
$835$	0	0
$836$	384.000	0.0158863
$837$	− 23600.0i	− 0.974594i
$838$	3276.00i	0.135045i
$839$	−23436.0	−0.964363	−0.482182	−	0.876071i	$-0.660155\pi$
$839$	−23436.0	−0.964363	−0.482182	+	0.876071i	$0.660155\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	25700.0i	1.05188i
$843$	− 3924.00i	− 0.160320i
$844$	−17648.0	−0.719750
$845$	0	0
$846$	552.000	0.0224328
$847$	− 6811.00i	− 0.276303i
$848$	2784.00i	0.112739i
$849$	10804.0	0.436740
$850$	0	0
$851$	−17520.0	−0.705732
$852$	4608.00i	0.185290i
$853$	8120.00i	0.325936i	0.986631	+	0.162968i	$0.0521068\pi$
$853$	8120.00i	0.325936i	−0.986631	+	0.162968i	$0.947893\pi$
$854$	−5320.00	−0.213169
$855$	0	0
$856$	5088.00	0.203159
$857$	50010.0i	1.99336i	0.0814218	+	0.996680i	$0.474054\pi$
$857$	50010.0i	1.99336i	−0.0814218	+	0.996680i	$0.525946\pi$
$858$	− 10752.0i	− 0.427817i
$859$	−34526.0	−1.37138	−0.685688	−	0.727896i	$-0.740499\pi$
$859$	−34526.0	−1.37138	−0.685688	+	0.727896i	$0.740499\pi$
$860$	0	0
$861$	−1764.00	−0.0698223
$862$	16032.0i	0.633471i
$863$	− 17256.0i	− 0.680650i	−0.940308	−	0.340325i	$-0.889463\pi$
$863$	− 17256.0i	− 0.680650i	0.940308	−	0.340325i	$-0.110537\pi$
$864$	−3200.00	−0.126003
$865$	0	0
$866$	4396.00	0.172497
$867$	16166.0i	0.633248i
$868$	6608.00i	0.258399i
$869$	−37248.0	−1.45403
$870$	0	0
$871$	−27104.0	−1.05440
$872$	− 1168.00i	− 0.0453595i
$873$	30590.0i	1.18593i
$874$	480.000	0.0185769
$875$	0	0
$876$	9200.00	0.354839
$877$	− 8714.00i	− 0.335520i	−0.985828	−	0.167760i	$-0.946347\pi$
$877$	− 8714.00i	− 0.335520i	0.985828	−	0.167760i	$-0.0536533\pi$
$878$	− 752.000i	− 0.0289052i
$879$	−9576.00	−0.367452
$880$	0	0
$881$	−22806.0	−0.872138	−0.436069	−	0.899913i	$-0.643630\pi$
$881$	−22806.0	−0.872138	−0.436069	+	0.899913i	$0.643630\pi$
$882$	2254.00i	0.0860500i
$883$	40196.0i	1.53194i	0.642876	+	0.765970i	$0.277741\pi$
$883$	40196.0i	1.53194i	−0.642876	+	0.765970i	$0.722259\pi$
$884$	25536.0	0.971571
$885$	0	0
$886$	14376.0	0.545114
$887$	− 40812.0i	− 1.54491i	−0.635071	−	0.772454i	$-0.719029\pi$
$887$	− 40812.0i	− 1.54491i	0.635071	−	0.772454i	$-0.280971\pi$
$888$	− 2336.00i	− 0.0882782i
$889$	2632.00	0.0992963
$890$	0	0
$891$	20208.0	0.759813
$892$	− 8288.00i	− 0.311102i
$893$	− 24.0000i	0 0.000899361i
$894$	−4008.00	−0.149941
$895$	0	0
$896$	896.000	0.0334077
$897$	− 13440.0i	− 0.500277i
$898$	− 29340.0i	− 1.09030i
$899$	12744.0	0.472788
$900$	0	0
$901$	−19836.0	−0.733444
$902$	− 12096.0i	− 0.446511i
$903$	5264.00i	0.193992i
$904$	−1584.00	−0.0582777
$905$	0	0
$906$	11008.0	0.403660
$907$	13588.0i	0.497444i	0.968575	+	0.248722i	$0.0800106\pi$
$907$	13588.0i	0.497444i	−0.968575	+	0.248722i	$0.919989\pi$
$908$	− 1464.00i	− 0.0535072i
$909$	−34500.0	−1.25885
$910$	0	0
$911$	−47304.0	−1.72036	−0.860182	−	0.509987i	$-0.829650\pi$
$911$	−47304.0	−1.72036	−0.860182	+	0.509987i	$0.829650\pi$
$912$	64.0000i	0.00232374i
$913$	18144.0i	0.657699i
$914$	10292.0	0.372461
$915$	0	0
$916$	−1504.00	−0.0542506
$917$	− 14910.0i	− 0.536937i
$918$	− 22800.0i	− 0.819730i
$919$	−1784.00	−0.0640356	−0.0320178	−	0.999487i	$-0.510193\pi$
$919$	−1784.00	−0.0640356	−0.0320178	+	0.999487i	$0.510193\pi$
$920$	0	0
$921$	1148.00	0.0410726
$922$	3024.00i	0.108015i
$923$	32256.0i	1.15029i
$924$	2688.00	0.0957021
$925$	0	0
$926$	14368.0	0.509894
$927$	8740.00i	0.309665i
$928$	− 1728.00i	− 0.0611254i
$929$	35922.0	1.26864	0.634318	−	0.773072i	$-0.281281\pi$
$929$	35922.0	1.26864	0.634318	+	0.773072i	$0.281281\pi$
$930$	0	0
$931$	98.0000	0.00344986
$932$	9048.00i	0.318001i
$933$	17616.0i	0.618137i
$934$	33036.0	1.15736
$935$	0	0
$936$	−10304.0	−0.359826
$937$	26782.0i	0.933756i	0.884322	+	0.466878i	$0.154621\pi$
$937$	26782.0i	0.933756i	−0.884322	+	0.466878i	$0.845379\pi$
$938$	− 6776.00i	− 0.235868i
$939$	−5540.00	−0.192536
$940$	0	0
$941$	4044.00	0.140096	0.0700482	−	0.997544i	$-0.477685\pi$
$941$	4044.00	0.140096	0.0700482	+	0.997544i	$0.477685\pi$
$942$	− 2080.00i	− 0.0719427i
$943$	− 15120.0i	− 0.522137i
$944$	−2208.00	−0.0761274
$945$	0	0
$946$	−36096.0	−1.24057
$947$	2136.00i	0.0732953i	0.999328	+	0.0366477i	$0.0116679\pi$
$947$	2136.00i	0.0732953i	−0.999328	+	0.0366477i	$0.988332\pi$
$948$	− 6208.00i	− 0.212686i
$949$	64400.0	2.20286
$950$	0	0
$951$	−15132.0	−0.515971
$952$	6384.00i	0.217339i
$953$	− 15174.0i	− 0.515776i	−0.966175	−	0.257888i	$-0.916974\pi$
$953$	− 15174.0i	− 0.515776i	0.966175	−	0.257888i	$-0.0830265\pi$
$954$	8004.00	0.271634
$955$	0	0
$956$	10368.0	0.350758
$957$	− 5184.00i	− 0.175104i
$958$	20184.0i	0.680705i
$959$	546.000	0.0183850
$960$	0	0
$961$	25905.0	0.869558
$962$	− 16352.0i	− 0.548035i
$963$	− 14628.0i	− 0.489492i
$964$	−440.000	−0.0147007
$965$	0	0
$966$	3360.00	0.111911
$967$	− 25832.0i	− 0.859050i	−0.903055	−	0.429525i	$-0.858681\pi$
$967$	− 25832.0i	− 0.859050i	0.903055	−	0.429525i	$-0.141319\pi$
$968$	7784.00i	0.258458i
$969$	−456.000	−0.0151175
$970$	0	0
$971$	−37686.0	−1.24552	−0.622761	−	0.782412i	$-0.713989\pi$
$971$	−37686.0	−1.24552	−0.622761	+	0.782412i	$0.713989\pi$
$972$	14168.0i	0.467530i
$973$	− 16366.0i	− 0.539229i
$974$	−15664.0	−0.515305
$975$	0	0
$976$	6080.00	0.199402
$977$	54006.0i	1.76848i	0.467033	+	0.884240i	$0.345323\pi$
$977$	54006.0i	1.76848i	−0.467033	+	0.884240i	$0.654677\pi$
$978$	− 5120.00i	− 0.167402i
$979$	18720.0	0.611127
$980$	0	0
$981$	−3358.00	−0.109289
$982$	13464.0i	0.437529i
$983$	33276.0i	1.07969i	0.841763	+	0.539847i	$0.181518\pi$
$983$	33276.0i	1.07969i	−0.841763	+	0.539847i	$0.818482\pi$
$984$	2016.00	0.0653127
$985$	0	0
$986$	12312.0	0.397661
$987$	− 168.000i	− 0.00541793i
$988$	448.000i	0.0144259i
$989$	−45120.0	−1.45069
$990$	0	0
$991$	−3760.00	−0.120525	−0.0602625	−	0.998183i	$-0.519194\pi$
$991$	−3760.00	−0.120525	−0.0602625	+	0.998183i	$0.519194\pi$
$992$	− 7552.00i	− 0.241710i
$993$	22640.0i	0.723523i
$994$	−8064.00	−0.257318
$995$	0	0
$996$	−3024.00	−0.0962039
$997$	− 36524.0i	− 1.16021i	−0.814543	−	0.580104i	$-0.803012\pi$
$997$	− 36524.0i	− 1.16021i	0.814543	−	0.580104i	$-0.196988\pi$
$998$	37336.0i	1.18422i
$999$	−14600.0	−0.462386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.c.g.99.1		2
5.2	odd	4		14.4.a.b.1.1	✓	1
5.3	odd	4		350.4.a.f.1.1		1
5.4	even	2	inner	350.4.c.g.99.2		2
15.2	even	4		126.4.a.d.1.1		1
20.7	even	4		112.4.a.e.1.1		1
35.2	odd	12		98.4.c.c.67.1		2
35.12	even	12		98.4.c.b.67.1		2
35.13	even	4		2450.4.a.i.1.1		1
35.17	even	12		98.4.c.b.79.1		2
35.27	even	4		98.4.a.e.1.1		1
35.32	odd	12		98.4.c.c.79.1		2
40.27	even	4		448.4.a.g.1.1		1
40.37	odd	4		448.4.a.k.1.1		1
55.32	even	4		1694.4.a.b.1.1		1
60.47	odd	4		1008.4.a.r.1.1		1
65.12	odd	4		2366.4.a.c.1.1		1
105.2	even	12		882.4.g.p.361.1		2
105.17	odd	12		882.4.g.v.667.1		2
105.32	even	12		882.4.g.p.667.1		2
105.47	odd	12		882.4.g.v.361.1		2
105.62	odd	4		882.4.a.b.1.1		1
140.27	odd	4		784.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.b.1.1	✓	1	5.2	odd	4
98.4.a.e.1.1		1	35.27	even	4
98.4.c.b.67.1		2	35.12	even	12
98.4.c.b.79.1		2	35.17	even	12
98.4.c.c.67.1		2	35.2	odd	12
98.4.c.c.79.1		2	35.32	odd	12
112.4.a.e.1.1		1	20.7	even	4
126.4.a.d.1.1		1	15.2	even	4
350.4.a.f.1.1		1	5.3	odd	4
350.4.c.g.99.1		2	1.1	even	1	trivial
350.4.c.g.99.2		2	5.4	even	2	inner
448.4.a.g.1.1		1	40.27	even	4
448.4.a.k.1.1		1	40.37	odd	4
784.4.a.h.1.1		1	140.27	odd	4
882.4.a.b.1.1		1	105.62	odd	4
882.4.g.p.361.1		2	105.2	even	12
882.4.g.p.667.1		2	105.32	even	12
882.4.g.v.361.1		2	105.47	odd	12
882.4.g.v.667.1		2	105.17	odd	12
1008.4.a.r.1.1		1	60.47	odd	4
1694.4.a.b.1.1		1	55.32	even	4
2366.4.a.c.1.1		1	65.12	odd	4
2450.4.a.i.1.1		1	35.13	even	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} -4.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} -4.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +48.0000 q^{11} +8.00000i q^{12} +56.0000i q^{13} -14.0000 q^{14} +16.0000 q^{16} +114.000i q^{17} -46.0000i q^{18} -2.00000 q^{19} -14.0000 q^{21} -96.0000i q^{22} -120.000i q^{23} +16.0000 q^{24} +112.000 q^{26} -100.000i q^{27} +28.0000i q^{28} +54.0000 q^{29} +236.000 q^{31} -32.0000i q^{32} -96.0000i q^{33} +228.000 q^{34} -92.0000 q^{36} -146.000i q^{37} +4.00000i q^{38} +112.000 q^{39} +126.000 q^{41} +28.0000i q^{42} -376.000i q^{43} -192.000 q^{44} -240.000 q^{46} +12.0000i q^{47} -32.0000i q^{48} -49.0000 q^{49} +228.000 q^{51} -224.000i q^{52} +174.000i q^{53} -200.000 q^{54} +56.0000 q^{56} +4.00000i q^{57} -108.000i q^{58} -138.000 q^{59} +380.000 q^{61} -472.000i q^{62} -161.000i q^{63} -64.0000 q^{64} -192.000 q^{66} +484.000i q^{67} -456.000i q^{68} -240.000 q^{69} +576.000 q^{71} +184.000i q^{72} -1150.00i q^{73} -292.000 q^{74} +8.00000 q^{76} -336.000i q^{77} -224.000i q^{78} -776.000 q^{79} +421.000 q^{81} -252.000i q^{82} +378.000i q^{83} +56.0000 q^{84} -752.000 q^{86} -108.000i q^{87} +384.000i q^{88} +390.000 q^{89} +392.000 q^{91} +480.000i q^{92} -472.000i q^{93} +24.0000 q^{94} -64.0000 q^{96} +1330.00i q^{97} +98.0000i q^{98} +1104.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} - 8 q^{6} + 46 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 - 8 * q^6 + 46 * q^9	\( 2 q - 8 q^{4} - 8 q^{6} + 46 q^{9} + 96 q^{11} - 28 q^{14} + 32 q^{16} - 4 q^{19} - 28 q^{21} + 32 q^{24} + 224 q^{26} + 108 q^{29} + 472 q^{31} + 456 q^{34} - 184 q^{36} + 224 q^{39} + 252 q^{41} - 384 q^{44} - 480 q^{46} - 98 q^{49} + 456 q^{51} - 400 q^{54} + 112 q^{56} - 276 q^{59} + 760 q^{61} - 128 q^{64} - 384 q^{66} - 480 q^{69} + 1152 q^{71} - 584 q^{74} + 16 q^{76} - 1552 q^{79} + 842 q^{81} + 112 q^{84} - 1504 q^{86} + 780 q^{89} + 784 q^{91} + 48 q^{94} - 128 q^{96} + 2208 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 - 8 * q^6 + 46 * q^9 + 96 * q^11 - 28 * q^14 + 32 * q^16 - 4 * q^19 - 28 * q^21 + 32 * q^24 + 224 * q^26 + 108 * q^29 + 472 * q^31 + 456 * q^34 - 184 * q^36 + 224 * q^39 + 252 * q^41 - 384 * q^44 - 480 * q^46 - 98 * q^49 + 456 * q^51 - 400 * q^54 + 112 * q^56 - 276 * q^59 + 760 * q^61 - 128 * q^64 - 384 * q^66 - 480 * q^69 + 1152 * q^71 - 584 * q^74 + 16 * q^76 - 1552 * q^79 + 842 * q^81 + 112 * q^84 - 1504 * q^86 + 780 * q^89 + 784 * q^91 + 48 * q^94 - 128 * q^96 + 2208 * q^99

Introduction

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