LMFDB - Embedded newform 150.4.c.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(49,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("150.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.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:	$8.85028650086$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.4.c.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} -16.0000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} -16.0000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +12.0000 q^{11} -12.0000i q^{12} -38.0000i q^{13} -32.0000 q^{14} +16.0000 q^{16} -126.000i q^{17} +18.0000i q^{18} -20.0000 q^{19} +48.0000 q^{21} -24.0000i q^{22} -168.000i q^{23} -24.0000 q^{24} -76.0000 q^{26} -27.0000i q^{27} +64.0000i q^{28} -30.0000 q^{29} -88.0000 q^{31} -32.0000i q^{32} +36.0000i q^{33} -252.000 q^{34} +36.0000 q^{36} +254.000i q^{37} +40.0000i q^{38} +114.000 q^{39} +42.0000 q^{41} -96.0000i q^{42} +52.0000i q^{43} -48.0000 q^{44} -336.000 q^{46} -96.0000i q^{47} +48.0000i q^{48} +87.0000 q^{49} +378.000 q^{51} +152.000i q^{52} -198.000i q^{53} -54.0000 q^{54} +128.000 q^{56} -60.0000i q^{57} +60.0000i q^{58} +660.000 q^{59} -538.000 q^{61} +176.000i q^{62} +144.000i q^{63} -64.0000 q^{64} +72.0000 q^{66} +884.000i q^{67} +504.000i q^{68} +504.000 q^{69} +792.000 q^{71} -72.0000i q^{72} -218.000i q^{73} +508.000 q^{74} +80.0000 q^{76} -192.000i q^{77} -228.000i q^{78} +520.000 q^{79} +81.0000 q^{81} -84.0000i q^{82} +492.000i q^{83} -192.000 q^{84} +104.000 q^{86} -90.0000i q^{87} +96.0000i q^{88} -810.000 q^{89} -608.000 q^{91} +672.000i q^{92} -264.000i q^{93} -192.000 q^{94} +96.0000 q^{96} +1154.00i q^{97} -174.000i q^{98} -108.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9	$ 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} + 24 q^{11} - 64 q^{14} + 32 q^{16} - 40 q^{19} + 96 q^{21} - 48 q^{24} - 152 q^{26} - 60 q^{29} - 176 q^{31} - 504 q^{34} + 72 q^{36} + 228 q^{39} + 84 q^{41} - 96 q^{44} - 672 q^{46} + 174 q^{49} + 756 q^{51} - 108 q^{54} + 256 q^{56} + 1320 q^{59} - 1076 q^{61} - 128 q^{64} + 144 q^{66} + 1008 q^{69} + 1584 q^{71} + 1016 q^{74} + 160 q^{76} + 1040 q^{79} + 162 q^{81} - 384 q^{84} + 208 q^{86} - 1620 q^{89} - 1216 q^{91} - 384 q^{94} + 192 q^{96} - 216 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 + 24 * q^11 - 64 * q^14 + 32 * q^16 - 40 * q^19 + 96 * q^21 - 48 * q^24 - 152 * q^26 - 60 * q^29 - 176 * q^31 - 504 * q^34 + 72 * q^36 + 228 * q^39 + 84 * q^41 - 96 * q^44 - 672 * q^46 + 174 * q^49 + 756 * q^51 - 108 * q^54 + 256 * q^56 + 1320 * q^59 - 1076 * q^61 - 128 * q^64 + 144 * q^66 + 1008 * q^69 + 1584 * q^71 + 1016 * q^74 + 160 * q^76 + 1040 * q^79 + 162 * q^81 - 384 * q^84 + 208 * q^86 - 1620 * q^89 - 1216 * q^91 - 384 * q^94 + 192 * q^96 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	− 16.0000i	− 0.863919i	−0.901893	−	0.431959i	$-0.857822\pi$
$7$	− 16.0000i	− 0.863919i	0.901893	−	0.431959i	$-0.142178\pi$
$8$	8.00000i	0.353553i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	− 12.0000i	− 0.288675i
$13$	− 38.0000i	− 0.810716i	−0.914158	−	0.405358i	$-0.867147\pi$
$13$	− 38.0000i	− 0.810716i	0.914158	−	0.405358i	$-0.132853\pi$
$14$	−32.0000	−0.610883
$15$	0	0
$16$	16.0000	0.250000
$17$	− 126.000i	− 1.79762i	−0.438342	−	0.898808i	$-0.644434\pi$
$17$	− 126.000i	− 1.79762i	0.438342	−	0.898808i	$-0.355566\pi$
$18$	18.0000i	0.235702i
$19$	−20.0000	−0.241490	−0.120745	−	0.992684i	$-0.538528\pi$
$19$	−20.0000	−0.241490	−0.120745	+	0.992684i	$0.538528\pi$
$20$	0	0
$21$	48.0000	0.498784
$22$	− 24.0000i	− 0.232583i
$23$	− 168.000i	− 1.52306i	−0.648129	−	0.761531i	$-0.724448\pi$
$23$	− 168.000i	− 1.52306i	0.648129	−	0.761531i	$-0.275552\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	−76.0000	−0.573263
$27$	− 27.0000i	− 0.192450i
$28$	64.0000i	0.431959i
$29$	−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
$31$	−88.0000	−0.509847	−0.254924	−	0.966961i	$-0.582050\pi$
$31$	−88.0000	−0.509847	−0.254924	+	0.966961i	$0.582050\pi$
$32$	− 32.0000i	− 0.176777i
$33$	36.0000i	0.189903i
$34$	−252.000	−1.27111
$35$	0	0
$36$	36.0000	0.166667
$37$	254.000i	1.12858i	0.825578	+	0.564288i	$0.190849\pi$
$37$	254.000i	1.12858i	−0.825578	+	0.564288i	$0.809151\pi$
$38$	40.0000i	0.170759i
$39$	114.000	0.468067
$40$	0	0
$41$	42.0000	0.159983	0.0799914	−	0.996796i	$-0.474511\pi$
$41$	42.0000	0.159983	0.0799914	+	0.996796i	$0.474511\pi$
$42$	− 96.0000i	− 0.352693i
$43$	52.0000i	0.184417i	0.995740	+	0.0922084i	$0.0293926\pi$
$43$	52.0000i	0.184417i	−0.995740	+	0.0922084i	$0.970607\pi$
$44$	−48.0000	−0.164461
$45$	0	0
$46$	−336.000	−1.07697
$47$	− 96.0000i	− 0.297937i	−0.988842	−	0.148969i	$-0.952405\pi$
$47$	− 96.0000i	− 0.297937i	0.988842	−	0.148969i	$-0.0475953\pi$
$48$	48.0000i	0.144338i
$49$	87.0000	0.253644
$50$	0	0
$51$	378.000	1.03785
$52$	152.000i	0.405358i
$53$	− 198.000i	− 0.513158i	−0.966523	−	0.256579i	$-0.917405\pi$
$53$	− 198.000i	− 0.513158i	0.966523	−	0.256579i	$-0.0825954\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	128.000	0.305441
$57$	− 60.0000i	− 0.139424i
$58$	60.0000i	0.135834i
$59$	660.000	1.45635	0.728175	−	0.685391i	$-0.240369\pi$
$59$	660.000	1.45635	0.728175	+	0.685391i	$0.240369\pi$
$60$	0	0
$61$	−538.000	−1.12924	−0.564622	−	0.825350i	$-0.690978\pi$
$61$	−538.000	−1.12924	−0.564622	+	0.825350i	$0.690978\pi$
$62$	176.000i	0.360516i
$63$	144.000i	0.287973i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	72.0000	0.134282
$67$	884.000i	1.61191i	0.591979	+	0.805954i	$0.298347\pi$
$67$	884.000i	1.61191i	−0.591979	+	0.805954i	$0.701653\pi$
$68$	504.000i	0.898808i
$69$	504.000	0.879340
$70$	0	0
$71$	792.000	1.32385	0.661923	−	0.749572i	$-0.269740\pi$
$71$	792.000	1.32385	0.661923	+	0.749572i	$0.269740\pi$
$72$	− 72.0000i	− 0.117851i
$73$	− 218.000i	− 0.349520i	−0.984611	−	0.174760i	$-0.944085\pi$
$73$	− 218.000i	− 0.349520i	0.984611	−	0.174760i	$-0.0559150\pi$
$74$	508.000	0.798024
$75$	0	0
$76$	80.0000	0.120745
$77$	− 192.000i	− 0.284161i
$78$	− 228.000i	− 0.330973i
$79$	520.000	0.740564	0.370282	−	0.928919i	$-0.379261\pi$
$79$	520.000	0.740564	0.370282	+	0.928919i	$0.379261\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 84.0000i	− 0.113125i
$83$	492.000i	0.650651i	0.945602	+	0.325325i	$0.105474\pi$
$83$	492.000i	0.650651i	−0.945602	+	0.325325i	$0.894526\pi$
$84$	−192.000	−0.249392
$85$	0	0
$86$	104.000	0.130402
$87$	− 90.0000i	− 0.110908i
$88$	96.0000i	0.116291i
$89$	−810.000	−0.964717	−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000	−0.964717	−0.482359	+	0.875974i	$0.660220\pi$
$90$	0	0
$91$	−608.000	−0.700393
$92$	672.000i	0.761531i
$93$	− 264.000i	− 0.294360i
$94$	−192.000	−0.210673
$95$	0	0
$96$	96.0000	0.102062
$97$	1154.00i	1.20795i	0.797004	+	0.603974i	$0.206417\pi$
$97$	1154.00i	1.20795i	−0.797004	+	0.603974i	$0.793583\pi$
$98$	− 174.000i	− 0.179354i
$99$	−108.000	−0.109640
$100$	0	0
$101$	−618.000	−0.608845	−0.304422	−	0.952537i	$-0.598463\pi$
$101$	−618.000	−0.608845	−0.304422	+	0.952537i	$0.598463\pi$
$102$	− 756.000i	− 0.733874i
$103$	− 128.000i	− 0.122449i	−0.998124	−	0.0612243i	$-0.980499\pi$
$103$	− 128.000i	− 0.122449i	0.998124	−	0.0612243i	$-0.0195005\pi$
$104$	304.000	0.286631
$105$	0	0
$106$	−396.000	−0.362858
$107$	− 1476.00i	− 1.33355i	−0.745257	−	0.666777i	$-0.767673\pi$
$107$	− 1476.00i	− 1.33355i	0.745257	−	0.666777i	$-0.232327\pi$
$108$	108.000i	0.0962250i
$109$	−1190.00	−1.04570	−0.522850	−	0.852425i	$-0.675131\pi$
$109$	−1190.00	−1.04570	−0.522850	+	0.852425i	$0.675131\pi$
$110$	0	0
$111$	−762.000	−0.651584
$112$	− 256.000i	− 0.215980i
$113$	462.000i	0.384613i	0.981335	+	0.192307i	$0.0615968\pi$
$113$	462.000i	0.384613i	−0.981335	+	0.192307i	$0.938403\pi$
$114$	−120.000	−0.0985880
$115$	0	0
$116$	120.000	0.0960493
$117$	342.000i	0.270239i
$118$	− 1320.00i	− 1.02980i
$119$	−2016.00	−1.55300
$120$	0	0
$121$	−1187.00	−0.891811
$122$	1076.00i	0.798496i
$123$	126.000i	0.0923662i
$124$	352.000	0.254924
$125$	0	0
$126$	288.000	0.203628
$127$	− 2536.00i	− 1.77192i	−0.463763	−	0.885959i	$-0.653501\pi$
$127$	− 2536.00i	− 1.77192i	0.463763	−	0.885959i	$-0.346499\pi$
$128$	128.000i	0.0883883i
$129$	−156.000	−0.106473
$130$	0	0
$131$	2292.00	1.52865	0.764324	−	0.644832i	$-0.223073\pi$
$131$	2292.00	1.52865	0.764324	+	0.644832i	$0.223073\pi$
$132$	− 144.000i	− 0.0949514i
$133$	320.000i	0.208628i
$134$	1768.00	1.13979
$135$	0	0
$136$	1008.00	0.635554
$137$	− 726.000i	− 0.452747i	−0.974041	−	0.226374i	$-0.927313\pi$
$137$	− 726.000i	− 0.452747i	0.974041	−	0.226374i	$-0.0726870\pi$
$138$	− 1008.00i	− 0.621787i
$139$	−380.000	−0.231879	−0.115939	−	0.993256i	$-0.536988\pi$
$139$	−380.000	−0.231879	−0.115939	+	0.993256i	$0.536988\pi$
$140$	0	0
$141$	288.000	0.172014
$142$	− 1584.00i	− 0.936101i
$143$	− 456.000i	− 0.266662i
$144$	−144.000	−0.0833333
$145$	0	0
$146$	−436.000	−0.247148
$147$	261.000i	0.146442i
$148$	− 1016.00i	− 0.564288i
$149$	−1590.00	−0.874214	−0.437107	−	0.899410i	$-0.643997\pi$
$149$	−1590.00	−0.874214	−0.437107	+	0.899410i	$0.643997\pi$
$150$	0	0
$151$	2432.00	1.31068	0.655342	−	0.755332i	$-0.272524\pi$
$151$	2432.00	1.31068	0.655342	+	0.755332i	$0.272524\pi$
$152$	− 160.000i	− 0.0853797i
$153$	1134.00i	0.599206i
$154$	−384.000	−0.200932
$155$	0	0
$156$	−456.000	−0.234033
$157$	614.000i	0.312118i	0.987748	+	0.156059i	$0.0498790\pi$
$157$	614.000i	0.312118i	−0.987748	+	0.156059i	$0.950121\pi$
$158$	− 1040.00i	− 0.523658i
$159$	594.000	0.296272
$160$	0	0
$161$	−2688.00	−1.31580
$162$	− 162.000i	− 0.0785674i
$163$	1852.00i	0.889938i	0.895546	+	0.444969i	$0.146785\pi$
$163$	1852.00i	0.889938i	−0.895546	+	0.444969i	$0.853215\pi$
$164$	−168.000	−0.0799914
$165$	0	0
$166$	984.000	0.460080
$167$	− 2136.00i	− 0.989752i	−0.868964	−	0.494876i	$-0.835213\pi$
$167$	− 2136.00i	− 0.989752i	0.868964	−	0.494876i	$-0.164787\pi$
$168$	384.000i	0.176347i
$169$	753.000	0.342740
$170$	0	0
$171$	180.000	0.0804967
$172$	− 208.000i	− 0.0922084i
$173$	− 1758.00i	− 0.772591i	−0.922375	−	0.386296i	$-0.873754\pi$
$173$	− 1758.00i	− 0.772591i	0.922375	−	0.386296i	$-0.126246\pi$
$174$	−180.000	−0.0784239
$175$	0	0
$176$	192.000	0.0822304
$177$	1980.00i	0.840824i
$178$	1620.00i	0.682158i
$179$	540.000	0.225483	0.112742	−	0.993624i	$-0.464037\pi$
$179$	540.000	0.225483	0.112742	+	0.993624i	$0.464037\pi$
$180$	0	0
$181$	1982.00	0.813928	0.406964	−	0.913444i	$-0.366588\pi$
$181$	1982.00	0.813928	0.406964	+	0.913444i	$0.366588\pi$
$182$	1216.00i	0.495252i
$183$	− 1614.00i	− 0.651969i
$184$	1344.00	0.538484
$185$	0	0
$186$	−528.000	−0.208144
$187$	− 1512.00i	− 0.591275i
$188$	384.000i	0.148969i
$189$	−432.000	−0.166261
$190$	0	0
$191$	−2688.00	−1.01831	−0.509154	−	0.860675i	$-0.670042\pi$
$191$	−2688.00	−1.01831	−0.509154	+	0.860675i	$0.670042\pi$
$192$	− 192.000i	− 0.0721688i
$193$	2302.00i	0.858557i	0.903172	+	0.429279i	$0.141232\pi$
$193$	2302.00i	0.858557i	−0.903172	+	0.429279i	$0.858768\pi$
$194$	2308.00	0.854148
$195$	0	0
$196$	−348.000	−0.126822
$197$	4374.00i	1.58190i	0.611880	+	0.790951i	$0.290414\pi$
$197$	4374.00i	1.58190i	−0.611880	+	0.790951i	$0.709586\pi$
$198$	216.000i	0.0775275i
$199$	1600.00	0.569955	0.284977	−	0.958534i	$-0.408014\pi$
$199$	1600.00	0.569955	0.284977	+	0.958534i	$0.408014\pi$
$200$	0	0
$201$	−2652.00	−0.930635
$202$	1236.00i	0.430518i
$203$	480.000i	0.165958i
$204$	−1512.00	−0.518927
$205$	0	0
$206$	−256.000	−0.0865843
$207$	1512.00i	0.507687i
$208$	− 608.000i	− 0.202679i
$209$	−240.000	−0.0794313
$210$	0	0
$211$	3332.00	1.08713	0.543565	−	0.839367i	$-0.317074\pi$
$211$	3332.00	1.08713	0.543565	+	0.839367i	$0.317074\pi$
$212$	792.000i	0.256579i
$213$	2376.00i	0.764323i
$214$	−2952.00	−0.942965
$215$	0	0
$216$	216.000	0.0680414
$217$	1408.00i	0.440467i
$218$	2380.00i	0.739422i
$219$	654.000	0.201796
$220$	0	0
$221$	−4788.00	−1.45736
$222$	1524.00i	0.460740i
$223$	− 2648.00i	− 0.795171i	−0.917565	−	0.397586i	$-0.869848\pi$
$223$	− 2648.00i	− 0.795171i	0.917565	−	0.397586i	$-0.130152\pi$
$224$	−512.000	−0.152721
$225$	0	0
$226$	924.000	0.271963
$227$	2244.00i	0.656121i	0.944657	+	0.328061i	$0.106395\pi$
$227$	2244.00i	0.656121i	−0.944657	+	0.328061i	$0.893605\pi$
$228$	240.000i	0.0697122i
$229$	5650.00	1.63040	0.815202	−	0.579177i	$-0.196626\pi$
$229$	5650.00	1.63040	0.815202	+	0.579177i	$0.196626\pi$
$230$	0	0
$231$	576.000	0.164061
$232$	− 240.000i	− 0.0679171i
$233$	− 4698.00i	− 1.32093i	−0.750858	−	0.660464i	$-0.770360\pi$
$233$	− 4698.00i	− 1.32093i	0.750858	−	0.660464i	$-0.229640\pi$
$234$	684.000	0.191088
$235$	0	0
$236$	−2640.00	−0.728175
$237$	1560.00i	0.427565i
$238$	4032.00i	1.09813i
$239$	1200.00	0.324776	0.162388	−	0.986727i	$-0.448080\pi$
$239$	1200.00	0.324776	0.162388	+	0.986727i	$0.448080\pi$
$240$	0	0
$241$	−718.000	−0.191911	−0.0959553	−	0.995386i	$-0.530591\pi$
$241$	−718.000	−0.191911	−0.0959553	+	0.995386i	$0.530591\pi$
$242$	2374.00i	0.630605i
$243$	243.000i	0.0641500i
$244$	2152.00	0.564622
$245$	0	0
$246$	252.000	0.0653127
$247$	760.000i	0.195780i
$248$	− 704.000i	− 0.180258i
$249$	−1476.00	−0.375653
$250$	0	0
$251$	6012.00	1.51185	0.755924	−	0.654659i	$-0.227188\pi$
$251$	6012.00	1.51185	0.755924	+	0.654659i	$0.227188\pi$
$252$	− 576.000i	− 0.143986i
$253$	− 2016.00i	− 0.500968i
$254$	−5072.00	−1.25294
$255$	0	0
$256$	256.000	0.0625000
$257$	− 2046.00i	− 0.496599i	−0.968683	−	0.248300i	$-0.920128\pi$
$257$	− 2046.00i	− 0.496599i	0.968683	−	0.248300i	$-0.0798717\pi$
$258$	312.000i	0.0752879i
$259$	4064.00	0.974999
$260$	0	0
$261$	270.000	0.0640329
$262$	− 4584.00i	− 1.08092i
$263$	6072.00i	1.42363i	0.702365	+	0.711817i	$0.252127\pi$
$263$	6072.00i	1.42363i	−0.702365	+	0.711817i	$0.747873\pi$
$264$	−288.000	−0.0671408
$265$	0	0
$266$	640.000	0.147522
$267$	− 2430.00i	− 0.556980i
$268$	− 3536.00i	− 0.805954i
$269$	6930.00	1.57074	0.785371	−	0.619025i	$-0.212472\pi$
$269$	6930.00	1.57074	0.785371	+	0.619025i	$0.212472\pi$
$270$	0	0
$271$	1352.00	0.303056	0.151528	−	0.988453i	$-0.451581\pi$
$271$	1352.00	0.303056	0.151528	+	0.988453i	$0.451581\pi$
$272$	− 2016.00i	− 0.449404i
$273$	− 1824.00i	− 0.404372i
$274$	−1452.00	−0.320141
$275$	0	0
$276$	−2016.00	−0.439670
$277$	− 1186.00i	− 0.257256i	−0.991693	−	0.128628i	$-0.958943\pi$
$277$	− 1186.00i	− 0.257256i	0.991693	−	0.128628i	$-0.0410573\pi$
$278$	760.000i	0.163963i
$279$	792.000	0.169949
$280$	0	0
$281$	2442.00	0.518425	0.259213	−	0.965820i	$-0.416537\pi$
$281$	2442.00	0.518425	0.259213	+	0.965820i	$0.416537\pi$
$282$	− 576.000i	− 0.121632i
$283$	− 2828.00i	− 0.594018i	−0.954875	−	0.297009i	$-0.904011\pi$
$283$	− 2828.00i	− 0.594018i	0.954875	−	0.297009i	$-0.0959892\pi$
$284$	−3168.00	−0.661923
$285$	0	0
$286$	−912.000	−0.188558
$287$	− 672.000i	− 0.138212i
$288$	288.000i	0.0589256i
$289$	−10963.0	−2.23143
$290$	0	0
$291$	−3462.00	−0.697409
$292$	872.000i	0.174760i
$293$	− 4758.00i	− 0.948687i	−0.880340	−	0.474344i	$-0.842685\pi$
$293$	− 4758.00i	− 0.948687i	0.880340	−	0.474344i	$-0.157315\pi$
$294$	522.000	0.103550
$295$	0	0
$296$	−2032.00	−0.399012
$297$	− 324.000i	− 0.0633010i
$298$	3180.00i	0.618163i
$299$	−6384.00	−1.23477
$300$	0	0
$301$	832.000	0.159321
$302$	− 4864.00i	− 0.926794i
$303$	− 1854.00i	− 0.351517i
$304$	−320.000	−0.0603726
$305$	0	0
$306$	2268.00	0.423702
$307$	− 8476.00i	− 1.57574i	−0.615844	−	0.787868i	$-0.711185\pi$
$307$	− 8476.00i	− 1.57574i	0.615844	−	0.787868i	$-0.288815\pi$
$308$	768.000i	0.142081i
$309$	384.000	0.0706958
$310$	0	0
$311$	4632.00	0.844555	0.422278	−	0.906467i	$-0.361231\pi$
$311$	4632.00	0.844555	0.422278	+	0.906467i	$0.361231\pi$
$312$	912.000i	0.165487i
$313$	4822.00i	0.870785i	0.900241	+	0.435392i	$0.143390\pi$
$313$	4822.00i	0.870785i	−0.900241	+	0.435392i	$0.856610\pi$
$314$	1228.00	0.220701
$315$	0	0
$316$	−2080.00	−0.370282
$317$	− 3426.00i	− 0.607014i	−0.952829	−	0.303507i	$-0.901842\pi$
$317$	− 3426.00i	− 0.607014i	0.952829	−	0.303507i	$-0.0981575\pi$
$318$	− 1188.00i	− 0.209496i
$319$	−360.000	−0.0631854
$320$	0	0
$321$	4428.00	0.769928
$322$	5376.00i	0.930412i
$323$	2520.00i	0.434107i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	3704.00	0.629281
$327$	− 3570.00i	− 0.603735i
$328$	336.000i	0.0565625i
$329$	−1536.00	−0.257393
$330$	0	0
$331$	−2788.00	−0.462968	−0.231484	−	0.972839i	$-0.574358\pi$
$331$	−2788.00	−0.462968	−0.231484	+	0.972839i	$0.574358\pi$
$332$	− 1968.00i	− 0.325325i
$333$	− 2286.00i	− 0.376192i
$334$	−4272.00	−0.699861
$335$	0	0
$336$	768.000	0.124696
$337$	434.000i	0.0701528i	0.999385	+	0.0350764i	$0.0111675\pi$
$337$	434.000i	0.0701528i	−0.999385	+	0.0350764i	$0.988833\pi$
$338$	− 1506.00i	− 0.242354i
$339$	−1386.00	−0.222057
$340$	0	0
$341$	−1056.00	−0.167700
$342$	− 360.000i	− 0.0569198i
$343$	− 6880.00i	− 1.08305i
$344$	−416.000	−0.0652012
$345$	0	0
$346$	−3516.00	−0.546304
$347$	6684.00i	1.03405i	0.855970	+	0.517026i	$0.172961\pi$
$347$	6684.00i	1.03405i	−0.855970	+	0.517026i	$0.827039\pi$
$348$	360.000i	0.0554541i
$349$	−2630.00	−0.403383	−0.201692	−	0.979449i	$-0.564644\pi$
$349$	−2630.00	−0.403383	−0.201692	+	0.979449i	$0.564644\pi$
$350$	0	0
$351$	−1026.00	−0.156022
$352$	− 384.000i	− 0.0581456i
$353$	7422.00i	1.11907i	0.828805	+	0.559537i	$0.189021\pi$
$353$	7422.00i	1.11907i	−0.828805	+	0.559537i	$0.810979\pi$
$354$	3960.00	0.594553
$355$	0	0
$356$	3240.00	0.482359
$357$	− 6048.00i	− 0.896622i
$358$	− 1080.00i	− 0.159441i
$359$	10440.0	1.53482	0.767412	−	0.641154i	$-0.221544\pi$
$359$	10440.0	1.53482	0.767412	+	0.641154i	$0.221544\pi$
$360$	0	0
$361$	−6459.00	−0.941682
$362$	− 3964.00i	− 0.575534i
$363$	− 3561.00i	− 0.514887i
$364$	2432.00	0.350196
$365$	0	0
$366$	−3228.00	−0.461012
$367$	10424.0i	1.48264i	0.671153	+	0.741319i	$0.265800\pi$
$367$	10424.0i	1.48264i	−0.671153	+	0.741319i	$0.734200\pi$
$368$	− 2688.00i	− 0.380765i
$369$	−378.000	−0.0533276
$370$	0	0
$371$	−3168.00	−0.443327
$372$	1056.00i	0.147180i
$373$	− 3278.00i	− 0.455036i	−0.973774	−	0.227518i	$-0.926939\pi$
$373$	− 3278.00i	− 0.455036i	0.973774	−	0.227518i	$-0.0730610\pi$
$374$	−3024.00	−0.418094
$375$	0	0
$376$	768.000	0.105337
$377$	1140.00i	0.155737i
$378$	864.000i	0.117564i
$379$	−6140.00	−0.832165	−0.416083	−	0.909327i	$-0.636597\pi$
$379$	−6140.00	−0.832165	−0.416083	+	0.909327i	$0.636597\pi$
$380$	0	0
$381$	7608.00	1.02302
$382$	5376.00i	0.720053i
$383$	3072.00i	0.409848i	0.978778	+	0.204924i	$0.0656948\pi$
$383$	3072.00i	0.409848i	−0.978778	+	0.204924i	$0.934305\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	4604.00	0.607092
$387$	− 468.000i	− 0.0614723i
$388$	− 4616.00i	− 0.603974i
$389$	−6150.00	−0.801587	−0.400794	−	0.916168i	$-0.631266\pi$
$389$	−6150.00	−0.801587	−0.400794	+	0.916168i	$0.631266\pi$
$390$	0	0
$391$	−21168.0	−2.73788
$392$	696.000i	0.0896768i
$393$	6876.00i	0.882566i
$394$	8748.00	1.11857
$395$	0	0
$396$	432.000	0.0548202
$397$	− 106.000i	− 0.0134005i	−0.999978	−	0.00670024i	$-0.997867\pi$
$397$	− 106.000i	− 0.0134005i	0.999978	−	0.00670024i	$-0.00213277\pi$
$398$	− 3200.00i	− 0.403019i
$399$	−960.000	−0.120451
$400$	0	0
$401$	−1758.00	−0.218929	−0.109464	−	0.993991i	$-0.534914\pi$
$401$	−1758.00	−0.218929	−0.109464	+	0.993991i	$0.534914\pi$
$402$	5304.00i	0.658058i
$403$	3344.00i	0.413341i
$404$	2472.00	0.304422
$405$	0	0
$406$	960.000	0.117350
$407$	3048.00i	0.371213i
$408$	3024.00i	0.366937i
$409$	3670.00	0.443691	0.221846	−	0.975082i	$-0.428792\pi$
$409$	3670.00	0.443691	0.221846	+	0.975082i	$0.428792\pi$
$410$	0	0
$411$	2178.00	0.261394
$412$	512.000i	0.0612243i
$413$	− 10560.0i	− 1.25817i
$414$	3024.00	0.358989
$415$	0	0
$416$	−1216.00	−0.143316
$417$	− 1140.00i	− 0.133875i
$418$	480.000i	0.0561664i
$419$	9660.00	1.12631	0.563153	−	0.826353i	$-0.309588\pi$
$419$	9660.00	1.12631	0.563153	+	0.826353i	$0.309588\pi$
$420$	0	0
$421$	8462.00	0.979602	0.489801	−	0.871834i	$-0.337069\pi$
$421$	8462.00	0.979602	0.489801	+	0.871834i	$0.337069\pi$
$422$	− 6664.00i	− 0.768717i
$423$	864.000i	0.0993123i
$424$	1584.00	0.181429
$425$	0	0
$426$	4752.00	0.540458
$427$	8608.00i	0.975575i
$428$	5904.00i	0.666777i
$429$	1368.00	0.153957
$430$	0	0
$431$	9792.00	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$432$	− 432.000i	− 0.0481125i
$433$	7342.00i	0.814859i	0.913237	+	0.407430i	$0.133575\pi$
$433$	7342.00i	0.814859i	−0.913237	+	0.407430i	$0.866425\pi$
$434$	2816.00	0.311457
$435$	0	0
$436$	4760.00	0.522850
$437$	3360.00i	0.367805i
$438$	− 1308.00i	− 0.142691i
$439$	−10640.0	−1.15676	−0.578382	−	0.815766i	$-0.696316\pi$
$439$	−10640.0	−1.15676	−0.578382	+	0.815766i	$0.696316\pi$
$440$	0	0
$441$	−783.000	−0.0845481
$442$	9576.00i	1.03051i
$443$	17412.0i	1.86742i	0.358024	+	0.933712i	$0.383451\pi$
$443$	17412.0i	1.86742i	−0.358024	+	0.933712i	$0.616549\pi$
$444$	3048.00	0.325792
$445$	0	0
$446$	−5296.00	−0.562271
$447$	− 4770.00i	− 0.504728i
$448$	1024.00i	0.107990i
$449$	1710.00	0.179732	0.0898662	−	0.995954i	$-0.471356\pi$
$449$	1710.00	0.179732	0.0898662	+	0.995954i	$0.471356\pi$
$450$	0	0
$451$	504.000	0.0526218
$452$	− 1848.00i	− 0.192307i
$453$	7296.00i	0.756724i
$454$	4488.00	0.463948
$455$	0	0
$456$	480.000	0.0492940
$457$	− 646.000i	− 0.0661239i	−0.999453	−	0.0330619i	$-0.989474\pi$
$457$	− 646.000i	− 0.0661239i	0.999453	−	0.0330619i	$-0.0105259\pi$
$458$	− 11300.0i	− 1.15287i
$459$	−3402.00	−0.345952
$460$	0	0
$461$	−6018.00	−0.607996	−0.303998	−	0.952673i	$-0.598322\pi$
$461$	−6018.00	−0.607996	−0.303998	+	0.952673i	$0.598322\pi$
$462$	− 1152.00i	− 0.116008i
$463$	6712.00i	0.673722i	0.941554	+	0.336861i	$0.109365\pi$
$463$	6712.00i	0.673722i	−0.941554	+	0.336861i	$0.890635\pi$
$464$	−480.000	−0.0480247
$465$	0	0
$466$	−9396.00	−0.934037
$467$	5364.00i	0.531512i	0.964040	+	0.265756i	$0.0856216\pi$
$467$	5364.00i	0.531512i	−0.964040	+	0.265756i	$0.914378\pi$
$468$	− 1368.00i	− 0.135119i
$469$	14144.0	1.39256
$470$	0	0
$471$	−1842.00	−0.180201
$472$	5280.00i	0.514898i
$473$	624.000i	0.0606587i
$474$	3120.00	0.302334
$475$	0	0
$476$	8064.00	0.776498
$477$	1782.00i	0.171053i
$478$	− 2400.00i	− 0.229652i
$479$	−9840.00	−0.938624	−0.469312	−	0.883032i	$-0.655498\pi$
$479$	−9840.00	−0.938624	−0.469312	+	0.883032i	$0.655498\pi$
$480$	0	0
$481$	9652.00	0.914955
$482$	1436.00i	0.135701i
$483$	− 8064.00i	− 0.759678i
$484$	4748.00	0.445905
$485$	0	0
$486$	486.000	0.0453609
$487$	1424.00i	0.132500i	0.997803	+	0.0662501i	$0.0211035\pi$
$487$	1424.00i	0.132500i	−0.997803	+	0.0662501i	$0.978896\pi$
$488$	− 4304.00i	− 0.399248i
$489$	−5556.00	−0.513806
$490$	0	0
$491$	−4548.00	−0.418021	−0.209011	−	0.977913i	$-0.567024\pi$
$491$	−4548.00	−0.418021	−0.209011	+	0.977913i	$0.567024\pi$
$492$	− 504.000i	− 0.0461831i
$493$	3780.00i	0.345320i
$494$	1520.00	0.138437
$495$	0	0
$496$	−1408.00	−0.127462
$497$	− 12672.0i	− 1.14370i
$498$	2952.00i	0.265627i
$499$	−6500.00	−0.583126	−0.291563	−	0.956552i	$-0.594175\pi$
$499$	−6500.00	−0.583126	−0.291563	+	0.956552i	$0.594175\pi$
$500$	0	0
$501$	6408.00	0.571434
$502$	− 12024.0i	− 1.06904i
$503$	− 12168.0i	− 1.07862i	−0.842108	−	0.539308i	$-0.818686\pi$
$503$	− 12168.0i	− 1.07862i	0.842108	−	0.539308i	$-0.181314\pi$
$504$	−1152.00	−0.101814
$505$	0	0
$506$	−4032.00	−0.354238
$507$	2259.00i	0.197881i
$508$	10144.0i	0.885959i
$509$	21090.0	1.83654	0.918269	−	0.395957i	$-0.129587\pi$
$509$	21090.0	1.83654	0.918269	+	0.395957i	$0.129587\pi$
$510$	0	0
$511$	−3488.00	−0.301957
$512$	− 512.000i	− 0.0441942i
$513$	540.000i	0.0464748i
$514$	−4092.00	−0.351149
$515$	0	0
$516$	624.000	0.0532366
$517$	− 1152.00i	− 0.0979979i
$518$	− 8128.00i	− 0.689428i
$519$	5274.00	0.446056
$520$	0	0
$521$	−5238.00	−0.440462	−0.220231	−	0.975448i	$-0.570681\pi$
$521$	−5238.00	−0.440462	−0.220231	+	0.975448i	$0.570681\pi$
$522$	− 540.000i	− 0.0452781i
$523$	− 8588.00i	− 0.718025i	−0.933333	−	0.359012i	$-0.883114\pi$
$523$	− 8588.00i	− 0.718025i	0.933333	−	0.359012i	$-0.116886\pi$
$524$	−9168.00	−0.764324
$525$	0	0
$526$	12144.0	1.00666
$527$	11088.0i	0.916510i
$528$	576.000i	0.0474757i
$529$	−16057.0	−1.31972
$530$	0	0
$531$	−5940.00	−0.485450
$532$	− 1280.00i	− 0.104314i
$533$	− 1596.00i	− 0.129701i
$534$	−4860.00	−0.393844
$535$	0	0
$536$	−7072.00	−0.569895
$537$	1620.00i	0.130183i
$538$	− 13860.0i	− 1.11068i
$539$	1044.00	0.0834291
$540$	0	0
$541$	3062.00	0.243338	0.121669	−	0.992571i	$-0.461175\pi$
$541$	3062.00	0.243338	0.121669	+	0.992571i	$0.461175\pi$
$542$	− 2704.00i	− 0.214293i
$543$	5946.00i	0.469921i
$544$	−4032.00	−0.317777
$545$	0	0
$546$	−3648.00	−0.285934
$547$	− 8476.00i	− 0.662537i	−0.943537	−	0.331268i	$-0.892523\pi$
$547$	− 8476.00i	− 0.662537i	0.943537	−	0.331268i	$-0.107477\pi$
$548$	2904.00i	0.226374i
$549$	4842.00	0.376414
$550$	0	0
$551$	600.000	0.0463899
$552$	4032.00i	0.310894i
$553$	− 8320.00i	− 0.639787i
$554$	−2372.00	−0.181907
$555$	0	0
$556$	1520.00	0.115939
$557$	− 12546.0i	− 0.954383i	−0.878799	−	0.477191i	$-0.841655\pi$
$557$	− 12546.0i	− 0.954383i	0.878799	−	0.477191i	$-0.158345\pi$
$558$	− 1584.00i	− 0.120172i
$559$	1976.00	0.149510
$560$	0	0
$561$	4536.00	0.341373
$562$	− 4884.00i	− 0.366582i
$563$	12.0000i	0 0.000898294i	1.00000		0.000449147i	$0.000142968\pi$
$563$	12.0000i	0 0.000898294i	−1.00000		0.000449147i	$0.999857\pi$
$564$	−1152.00	−0.0860070
$565$	0	0
$566$	−5656.00	−0.420034
$567$	− 1296.00i	− 0.0959910i
$568$	6336.00i	0.468050i
$569$	−19290.0	−1.42123	−0.710614	−	0.703582i	$-0.751583\pi$
$569$	−19290.0	−1.42123	−0.710614	+	0.703582i	$0.751583\pi$
$570$	0	0
$571$	−12148.0	−0.890329	−0.445165	−	0.895449i	$-0.646855\pi$
$571$	−12148.0	−0.890329	−0.445165	+	0.895449i	$0.646855\pi$
$572$	1824.00i	0.133331i
$573$	− 8064.00i	− 0.587920i
$574$	−1344.00	−0.0977308
$575$	0	0
$576$	576.000	0.0416667
$577$	− 10366.0i	− 0.747907i	−0.927447	−	0.373953i	$-0.878002\pi$
$577$	− 10366.0i	− 0.747907i	0.927447	−	0.373953i	$-0.121998\pi$
$578$	21926.0i	1.57786i
$579$	−6906.00	−0.495688
$580$	0	0
$581$	7872.00	0.562109
$582$	6924.00i	0.493143i
$583$	− 2376.00i	− 0.168789i
$584$	1744.00	0.123574
$585$	0	0
$586$	−9516.00	−0.670823
$587$	7644.00i	0.537482i	0.963213	+	0.268741i	$0.0866075\pi$
$587$	7644.00i	0.537482i	−0.963213	+	0.268741i	$0.913393\pi$
$588$	− 1044.00i	− 0.0732208i
$589$	1760.00	0.123123
$590$	0	0
$591$	−13122.0	−0.913311
$592$	4064.00i	0.282144i
$593$	− 8658.00i	− 0.599564i	−0.954008	−	0.299782i	$-0.903086\pi$
$593$	− 8658.00i	− 0.599564i	0.954008	−	0.299782i	$-0.0969139\pi$
$594$	−648.000	−0.0447605
$595$	0	0
$596$	6360.00	0.437107
$597$	4800.00i	0.329064i
$598$	12768.0i	0.873114i
$599$	−25800.0	−1.75987	−0.879933	−	0.475098i	$-0.842413\pi$
$599$	−25800.0	−1.75987	−0.879933	+	0.475098i	$0.842413\pi$
$600$	0	0
$601$	16202.0	1.09966	0.549828	−	0.835278i	$-0.314693\pi$
$601$	16202.0	1.09966	0.549828	+	0.835278i	$0.314693\pi$
$602$	− 1664.00i	− 0.112657i
$603$	− 7956.00i	− 0.537302i
$604$	−9728.00	−0.655342
$605$	0	0
$606$	−3708.00	−0.248560
$607$	− 24136.0i	− 1.61392i	−0.590605	−	0.806960i	$-0.701111\pi$
$607$	− 24136.0i	− 1.61392i	0.590605	−	0.806960i	$-0.298889\pi$
$608$	640.000i	0.0426898i
$609$	−1440.00	−0.0958157
$610$	0	0
$611$	−3648.00	−0.241542
$612$	− 4536.00i	− 0.299603i
$613$	4642.00i	0.305854i	0.988237	+	0.152927i	$0.0488700\pi$
$613$	4642.00i	0.305854i	−0.988237	+	0.152927i	$0.951130\pi$
$614$	−16952.0	−1.11421
$615$	0	0
$616$	1536.00	0.100466
$617$	− 6726.00i	− 0.438863i	−0.975628	−	0.219432i	$-0.929580\pi$
$617$	− 6726.00i	− 0.438863i	0.975628	−	0.219432i	$-0.0704203\pi$
$618$	− 768.000i	− 0.0499895i
$619$	21220.0	1.37787	0.688937	−	0.724821i	$-0.258078\pi$
$619$	21220.0	1.37787	0.688937	+	0.724821i	$0.258078\pi$
$620$	0	0
$621$	−4536.00	−0.293113
$622$	− 9264.00i	− 0.597191i
$623$	12960.0i	0.833437i
$624$	1824.00	0.117017
$625$	0	0
$626$	9644.00	0.615738
$627$	− 720.000i	− 0.0458597i
$628$	− 2456.00i	− 0.156059i
$629$	32004.0	2.02875
$630$	0	0
$631$	29792.0	1.87956	0.939779	−	0.341783i	$-0.111031\pi$
$631$	29792.0	1.87956	0.939779	+	0.341783i	$0.111031\pi$
$632$	4160.00i	0.261829i
$633$	9996.00i	0.627655i
$634$	−6852.00	−0.429223
$635$	0	0
$636$	−2376.00	−0.148136
$637$	− 3306.00i	− 0.205633i
$638$	720.000i	0.0446788i
$639$	−7128.00	−0.441282
$640$	0	0
$641$	−10158.0	−0.625923	−0.312962	−	0.949766i	$-0.601321\pi$
$641$	−10158.0	−0.625923	−0.312962	+	0.949766i	$0.601321\pi$
$642$	− 8856.00i	− 0.544421i
$643$	− 29828.0i	− 1.82940i	−0.404138	−	0.914698i	$-0.632429\pi$
$643$	− 29828.0i	− 1.82940i	0.404138	−	0.914698i	$-0.367571\pi$
$644$	10752.0	0.657901
$645$	0	0
$646$	5040.00	0.306960
$647$	1944.00i	0.118124i	0.998254	+	0.0590622i	$0.0188110\pi$
$647$	1944.00i	0.118124i	−0.998254	+	0.0590622i	$0.981189\pi$
$648$	648.000i	0.0392837i
$649$	7920.00	0.479025
$650$	0	0
$651$	−4224.00	−0.254304
$652$	− 7408.00i	− 0.444969i
$653$	− 26718.0i	− 1.60116i	−0.599227	−	0.800579i	$-0.704525\pi$
$653$	− 26718.0i	− 1.60116i	0.599227	−	0.800579i	$-0.295475\pi$
$654$	−7140.00	−0.426905
$655$	0	0
$656$	672.000	0.0399957
$657$	1962.00i	0.116507i
$658$	3072.00i	0.182005i
$659$	−4260.00	−0.251815	−0.125907	−	0.992042i	$-0.540184\pi$
$659$	−4260.00	−0.251815	−0.125907	+	0.992042i	$0.540184\pi$
$660$	0	0
$661$	22862.0	1.34528	0.672639	−	0.739971i	$-0.265161\pi$
$661$	22862.0	1.34528	0.672639	+	0.739971i	$0.265161\pi$
$662$	5576.00i	0.327368i
$663$	− 14364.0i	− 0.841405i
$664$	−3936.00	−0.230040
$665$	0	0
$666$	−4572.00	−0.266008
$667$	5040.00i	0.292578i
$668$	8544.00i	0.494876i
$669$	7944.00	0.459092
$670$	0	0
$671$	−6456.00	−0.371432
$672$	− 1536.00i	− 0.0881733i
$673$	32542.0i	1.86390i	0.362592	+	0.931948i	$0.381892\pi$
$673$	32542.0i	1.86390i	−0.362592	+	0.931948i	$0.618108\pi$
$674$	868.000	0.0496055
$675$	0	0
$676$	−3012.00	−0.171370
$677$	14214.0i	0.806925i	0.914996	+	0.403463i	$0.132193\pi$
$677$	14214.0i	0.806925i	−0.914996	+	0.403463i	$0.867807\pi$
$678$	2772.00i	0.157018i
$679$	18464.0	1.04357
$680$	0	0
$681$	−6732.00	−0.378812
$682$	2112.00i	0.118582i
$683$	7092.00i	0.397317i	0.980069	+	0.198659i	$0.0636585\pi$
$683$	7092.00i	0.397317i	−0.980069	+	0.198659i	$0.936341\pi$
$684$	−720.000	−0.0402484
$685$	0	0
$686$	−13760.0	−0.765830
$687$	16950.0i	0.941314i
$688$	832.000i	0.0461042i
$689$	−7524.00	−0.416026
$690$	0	0
$691$	−13228.0	−0.728244	−0.364122	−	0.931351i	$-0.618631\pi$
$691$	−13228.0	−0.728244	−0.364122	+	0.931351i	$0.618631\pi$
$692$	7032.00i	0.386296i
$693$	1728.00i	0.0947205i
$694$	13368.0	0.731185
$695$	0	0
$696$	720.000	0.0392120
$697$	− 5292.00i	− 0.287588i
$698$	5260.00i	0.285235i
$699$	14094.0	0.762638
$700$	0	0
$701$	28062.0	1.51196	0.755982	−	0.654592i	$-0.227160\pi$
$701$	28062.0	1.51196	0.755982	+	0.654592i	$0.227160\pi$
$702$	2052.00i	0.110324i
$703$	− 5080.00i	− 0.272540i
$704$	−768.000	−0.0411152
$705$	0	0
$706$	14844.0	0.791305
$707$	9888.00i	0.525992i
$708$	− 7920.00i	− 0.420412i
$709$	27250.0	1.44343	0.721717	−	0.692188i	$-0.243353\pi$
$709$	27250.0	1.44343	0.721717	+	0.692188i	$0.243353\pi$
$710$	0	0
$711$	−4680.00	−0.246855
$712$	− 6480.00i	− 0.341079i
$713$	14784.0i	0.776529i
$714$	−12096.0	−0.634008
$715$	0	0
$716$	−2160.00	−0.112742
$717$	3600.00i	0.187510i
$718$	− 20880.0i	− 1.08529i
$719$	14400.0	0.746912	0.373456	−	0.927648i	$-0.378173\pi$
$719$	14400.0	0.746912	0.373456	+	0.927648i	$0.378173\pi$
$720$	0	0
$721$	−2048.00	−0.105786
$722$	12918.0i	0.665870i
$723$	− 2154.00i	− 0.110800i
$724$	−7928.00	−0.406964
$725$	0	0
$726$	−7122.00	−0.364080
$727$	17984.0i	0.917455i	0.888577	+	0.458727i	$0.151695\pi$
$727$	17984.0i	0.917455i	−0.888577	+	0.458727i	$0.848305\pi$
$728$	− 4864.00i	− 0.247626i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	6552.00	0.331511
$732$	6456.00i	0.325984i
$733$	− 16598.0i	− 0.836373i	−0.908361	−	0.418186i	$-0.862666\pi$
$733$	− 16598.0i	− 0.836373i	0.908361	−	0.418186i	$-0.137334\pi$
$734$	20848.0	1.04838
$735$	0	0
$736$	−5376.00	−0.269242
$737$	10608.0i	0.530191i
$738$	756.000i	0.0377083i
$739$	−1460.00	−0.0726752	−0.0363376	−	0.999340i	$-0.511569\pi$
$739$	−1460.00	−0.0726752	−0.0363376	+	0.999340i	$0.511569\pi$
$740$	0	0
$741$	−2280.00	−0.113034
$742$	6336.00i	0.313480i
$743$	30072.0i	1.48484i	0.669936	+	0.742419i	$0.266322\pi$
$743$	30072.0i	1.48484i	−0.669936	+	0.742419i	$0.733678\pi$
$744$	2112.00	0.104072
$745$	0	0
$746$	−6556.00	−0.321759
$747$	− 4428.00i	− 0.216884i
$748$	6048.00i	0.295637i
$749$	−23616.0	−1.15208
$750$	0	0
$751$	−18088.0	−0.878882	−0.439441	−	0.898271i	$-0.644823\pi$
$751$	−18088.0	−0.878882	−0.439441	+	0.898271i	$0.644823\pi$
$752$	− 1536.00i	− 0.0744843i
$753$	18036.0i	0.872866i
$754$	2280.00	0.110123
$755$	0	0
$756$	1728.00	0.0831306
$757$	24734.0i	1.18755i	0.804633	+	0.593773i	$0.202362\pi$
$757$	24734.0i	1.18755i	−0.804633	+	0.593773i	$0.797638\pi$
$758$	12280.0i	0.588430i
$759$	6048.00	0.289234
$760$	0	0
$761$	−22278.0	−1.06120	−0.530602	−	0.847621i	$-0.678034\pi$
$761$	−22278.0	−1.06120	−0.530602	+	0.847621i	$0.678034\pi$
$762$	− 15216.0i	− 0.723383i
$763$	19040.0i	0.903400i
$764$	10752.0	0.509154
$765$	0	0
$766$	6144.00	0.289806
$767$	− 25080.0i	− 1.18069i
$768$	768.000i	0.0360844i
$769$	−16130.0	−0.756388	−0.378194	−	0.925726i	$-0.623455\pi$
$769$	−16130.0	−0.756388	−0.378194	+	0.925726i	$0.623455\pi$
$770$	0	0
$771$	6138.00	0.286712
$772$	− 9208.00i	− 0.429279i
$773$	− 29718.0i	− 1.38277i	−0.722486	−	0.691386i	$-0.757001\pi$
$773$	− 29718.0i	− 1.38277i	0.722486	−	0.691386i	$-0.242999\pi$
$774$	−936.000	−0.0434675
$775$	0	0
$776$	−9232.00	−0.427074
$777$	12192.0i	0.562916i
$778$	12300.0i	0.566808i
$779$	−840.000	−0.0386343
$780$	0	0
$781$	9504.00	0.435442
$782$	42336.0i	1.93597i
$783$	810.000i	0.0369694i
$784$	1392.00	0.0634111
$785$	0	0
$786$	13752.0	0.624068
$787$	9524.00i	0.431377i	0.976462	+	0.215689i	$0.0691996\pi$
$787$	9524.00i	0.431377i	−0.976462	+	0.215689i	$0.930800\pi$
$788$	− 17496.0i	− 0.790951i
$789$	−18216.0	−0.821935
$790$	0	0
$791$	7392.00	0.332275
$792$	− 864.000i	− 0.0387638i
$793$	20444.0i	0.915495i
$794$	−212.000	−0.00947556
$795$	0	0
$796$	−6400.00	−0.284977
$797$	− 33906.0i	− 1.50692i	−0.657496	−	0.753458i	$-0.728384\pi$
$797$	− 33906.0i	− 1.50692i	0.657496	−	0.753458i	$-0.271616\pi$
$798$	1920.00i	0.0851720i
$799$	−12096.0	−0.535577
$800$	0	0
$801$	7290.00	0.321572
$802$	3516.00i	0.154806i
$803$	− 2616.00i	− 0.114965i
$804$	10608.0	0.465318
$805$	0	0
$806$	6688.00	0.292276
$807$	20790.0i	0.906868i
$808$	− 4944.00i	− 0.215259i
$809$	630.000	0.0273790	0.0136895	−	0.999906i	$-0.495642\pi$
$809$	630.000	0.0273790	0.0136895	+	0.999906i	$0.495642\pi$
$810$	0	0
$811$	−20788.0	−0.900081	−0.450040	−	0.893008i	$-0.648590\pi$
$811$	−20788.0	−0.900081	−0.450040	+	0.893008i	$0.648590\pi$
$812$	− 1920.00i	− 0.0829788i
$813$	4056.00i	0.174969i
$814$	6096.00	0.262487
$815$	0	0
$816$	6048.00	0.259464
$817$	− 1040.00i	− 0.0445349i
$818$	− 7340.00i	− 0.313737i
$819$	5472.00	0.233464
$820$	0	0
$821$	−43098.0	−1.83207	−0.916036	−	0.401097i	$-0.868629\pi$
$821$	−43098.0	−1.83207	−0.916036	+	0.401097i	$0.868629\pi$
$822$	− 4356.00i	− 0.184833i
$823$	14272.0i	0.604484i	0.953231	+	0.302242i	$0.0977351\pi$
$823$	14272.0i	0.604484i	−0.953231	+	0.302242i	$0.902265\pi$
$824$	1024.00	0.0432921
$825$	0	0
$826$	−21120.0	−0.889660
$827$	13644.0i	0.573698i	0.957976	+	0.286849i	$0.0926078\pi$
$827$	13644.0i	0.573698i	−0.957976	+	0.286849i	$0.907392\pi$
$828$	− 6048.00i	− 0.253844i
$829$	2410.00	0.100968	0.0504842	−	0.998725i	$-0.483924\pi$
$829$	2410.00	0.100968	0.0504842	+	0.998725i	$0.483924\pi$
$830$	0	0
$831$	3558.00	0.148527
$832$	2432.00i	0.101339i
$833$	− 10962.0i	− 0.455955i
$834$	−2280.00	−0.0946642
$835$	0	0
$836$	960.000	0.0397157
$837$	2376.00i	0.0981202i
$838$	− 19320.0i	− 0.796418i
$839$	−23160.0	−0.953006	−0.476503	−	0.879173i	$-0.658096\pi$
$839$	−23160.0	−0.953006	−0.476503	+	0.879173i	$0.658096\pi$
$840$	0	0
$841$	−23489.0	−0.963098
$842$	− 16924.0i	− 0.692684i
$843$	7326.00i	0.299313i
$844$	−13328.0	−0.543565
$845$	0	0
$846$	1728.00	0.0702244
$847$	18992.0i	0.770452i
$848$	− 3168.00i	− 0.128290i
$849$	8484.00	0.342957
$850$	0	0
$851$	42672.0	1.71889
$852$	− 9504.00i	− 0.382162i
$853$	− 32078.0i	− 1.28761i	−0.765190	−	0.643804i	$-0.777355\pi$
$853$	− 32078.0i	− 1.28761i	0.765190	−	0.643804i	$-0.222645\pi$
$854$	17216.0	0.689835
$855$	0	0
$856$	11808.0	0.471483
$857$	− 14406.0i	− 0.574212i	−0.957899	−	0.287106i	$-0.907307\pi$
$857$	− 14406.0i	− 0.574212i	0.957899	−	0.287106i	$-0.0926932\pi$
$858$	− 2736.00i	− 0.108864i
$859$	−30620.0	−1.21623	−0.608115	−	0.793849i	$-0.708074\pi$
$859$	−30620.0	−1.21623	−0.608115	+	0.793849i	$0.708074\pi$
$860$	0	0
$861$	2016.00	0.0797969
$862$	− 19584.0i	− 0.773821i
$863$	− 17568.0i	− 0.692957i	−0.938058	−	0.346478i	$-0.887377\pi$
$863$	− 17568.0i	− 0.692957i	0.938058	−	0.346478i	$-0.112623\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	14684.0	0.576192
$867$	− 32889.0i	− 1.28831i
$868$	− 5632.00i	− 0.220233i
$869$	6240.00	0.243587
$870$	0	0
$871$	33592.0	1.30680
$872$	− 9520.00i	− 0.369711i
$873$	− 10386.0i	− 0.402649i
$874$	6720.00	0.260077
$875$	0	0
$876$	−2616.00	−0.100898
$877$	− 21706.0i	− 0.835758i	−0.908503	−	0.417879i	$-0.862774\pi$
$877$	− 21706.0i	− 0.835758i	0.908503	−	0.417879i	$-0.137226\pi$
$878$	21280.0i	0.817956i
$879$	14274.0	0.547725
$880$	0	0
$881$	−14958.0	−0.572018	−0.286009	−	0.958227i	$-0.592329\pi$
$881$	−14958.0	−0.572018	−0.286009	+	0.958227i	$0.592329\pi$
$882$	1566.00i	0.0597845i
$883$	32812.0i	1.25052i	0.780415	+	0.625261i	$0.215008\pi$
$883$	32812.0i	1.25052i	−0.780415	+	0.625261i	$0.784992\pi$
$884$	19152.0	0.728678
$885$	0	0
$886$	34824.0	1.32047
$887$	− 38856.0i	− 1.47086i	−0.677598	−	0.735432i	$-0.736979\pi$
$887$	− 38856.0i	− 1.47086i	0.677598	−	0.735432i	$-0.263021\pi$
$888$	− 6096.00i	− 0.230370i
$889$	−40576.0	−1.53079
$890$	0	0
$891$	972.000	0.0365468
$892$	10592.0i	0.397586i
$893$	1920.00i	0.0719489i
$894$	−9540.00	−0.356896
$895$	0	0
$896$	2048.00	0.0763604
$897$	− 19152.0i	− 0.712895i
$898$	− 3420.00i	− 0.127090i
$899$	2640.00	0.0979410
$900$	0	0
$901$	−24948.0	−0.922462
$902$	− 1008.00i	− 0.0372092i
$903$	2496.00i	0.0919841i
$904$	−3696.00	−0.135981
$905$	0	0
$906$	14592.0	0.535085
$907$	− 28276.0i	− 1.03516i	−0.855635	−	0.517579i	$-0.826833\pi$
$907$	− 28276.0i	− 1.03516i	0.855635	−	0.517579i	$-0.173167\pi$
$908$	− 8976.00i	− 0.328061i
$909$	5562.00	0.202948
$910$	0	0
$911$	8112.00	0.295019	0.147510	−	0.989061i	$-0.452874\pi$
$911$	8112.00	0.295019	0.147510	+	0.989061i	$0.452874\pi$
$912$	− 960.000i	− 0.0348561i
$913$	5904.00i	0.214013i
$914$	−1292.00	−0.0467566
$915$	0	0
$916$	−22600.0	−0.815202
$917$	− 36672.0i	− 1.32063i
$918$	6804.00i	0.244625i
$919$	26080.0	0.936126	0.468063	−	0.883695i	$-0.344952\pi$
$919$	26080.0	0.936126	0.468063	+	0.883695i	$0.344952\pi$
$920$	0	0
$921$	25428.0	0.909751
$922$	12036.0i	0.429918i
$923$	− 30096.0i	− 1.07326i
$924$	−2304.00	−0.0820303
$925$	0	0
$926$	13424.0	0.476393
$927$	1152.00i	0.0408162i
$928$	960.000i	0.0339586i
$929$	−49170.0	−1.73651	−0.868254	−	0.496120i	$-0.834757\pi$
$929$	−49170.0	−1.73651	−0.868254	+	0.496120i	$0.834757\pi$
$930$	0	0
$931$	−1740.00	−0.0612526
$932$	18792.0i	0.660464i
$933$	13896.0i	0.487604i
$934$	10728.0	0.375836
$935$	0	0
$936$	−2736.00	−0.0955438
$937$	48314.0i	1.68447i	0.539110	+	0.842236i	$0.318761\pi$
$937$	48314.0i	1.68447i	−0.539110	+	0.842236i	$0.681239\pi$
$938$	− 28288.0i	− 0.984687i
$939$	−14466.0	−0.502748
$940$	0	0
$941$	34782.0	1.20495	0.602477	−	0.798137i	$-0.294181\pi$
$941$	34782.0	1.20495	0.602477	+	0.798137i	$0.294181\pi$
$942$	3684.00i	0.127422i
$943$	− 7056.00i	− 0.243664i
$944$	10560.0	0.364088
$945$	0	0
$946$	1248.00	0.0428922
$947$	− 25116.0i	− 0.861838i	−0.902391	−	0.430919i	$-0.858190\pi$
$947$	− 25116.0i	− 0.861838i	0.902391	−	0.430919i	$-0.141810\pi$
$948$	− 6240.00i	− 0.213782i
$949$	−8284.00	−0.283361
$950$	0	0
$951$	10278.0	0.350460
$952$	− 16128.0i	− 0.549067i
$953$	15462.0i	0.525565i	0.964855	+	0.262782i	$0.0846401\pi$
$953$	15462.0i	0.525565i	−0.964855	+	0.262782i	$0.915360\pi$
$954$	3564.00	0.120953
$955$	0	0
$956$	−4800.00	−0.162388
$957$	− 1080.00i	− 0.0364801i
$958$	19680.0i	0.663708i
$959$	−11616.0	−0.391137
$960$	0	0
$961$	−22047.0	−0.740056
$962$	− 19304.0i	− 0.646971i
$963$	13284.0i	0.444518i
$964$	2872.00	0.0959553
$965$	0	0
$966$	−16128.0	−0.537174
$967$	− 736.000i	− 0.0244759i	−0.999925	−	0.0122379i	$-0.996104\pi$
$967$	− 736.000i	− 0.0244759i	0.999925	−	0.0122379i	$-0.00389555\pi$
$968$	− 9496.00i	− 0.315303i
$969$	−7560.00	−0.250632
$970$	0	0
$971$	−29268.0	−0.967307	−0.483653	−	0.875260i	$-0.660690\pi$
$971$	−29268.0	−0.967307	−0.483653	+	0.875260i	$0.660690\pi$
$972$	− 972.000i	− 0.0320750i
$973$	6080.00i	0.200325i
$974$	2848.00	0.0936918
$975$	0	0
$976$	−8608.00	−0.282311
$977$	16674.0i	0.546007i	0.962013	+	0.273003i	$0.0880170\pi$
$977$	16674.0i	0.546007i	−0.962013	+	0.273003i	$0.911983\pi$
$978$	11112.0i	0.363316i
$979$	−9720.00	−0.317316
$980$	0	0
$981$	10710.0	0.348567
$982$	9096.00i	0.295586i
$983$	31272.0i	1.01467i	0.861749	+	0.507336i	$0.169370\pi$
$983$	31272.0i	1.01467i	−0.861749	+	0.507336i	$0.830630\pi$
$984$	−1008.00	−0.0326564
$985$	0	0
$986$	7560.00	0.244178
$987$	− 4608.00i	− 0.148606i
$988$	− 3040.00i	− 0.0978900i
$989$	8736.00	0.280878
$990$	0	0
$991$	−15928.0	−0.510565	−0.255282	−	0.966867i	$-0.582168\pi$
$991$	−15928.0	−0.510565	−0.255282	+	0.966867i	$0.582168\pi$
$992$	2816.00i	0.0901291i
$993$	− 8364.00i	− 0.267295i
$994$	−25344.0	−0.808715
$995$	0	0
$996$	5904.00	0.187827
$997$	42014.0i	1.33460i	0.744789	+	0.667300i	$0.232550\pi$
$997$	42014.0i	1.33460i	−0.744789	+	0.667300i	$0.767450\pi$
$998$	13000.0i	0.412332i
$999$	6858.00	0.217195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.c.d.49.1		2
3.2	odd	2		450.4.c.e.199.2		2
4.3	odd	2		1200.4.f.j.49.1		2
5.2	odd	4		150.4.a.i.1.1		1
5.3	odd	4		6.4.a.a.1.1	✓	1
5.4	even	2	inner	150.4.c.d.49.2		2
15.2	even	4		450.4.a.h.1.1		1
15.8	even	4		18.4.a.a.1.1		1
15.14	odd	2		450.4.c.e.199.1		2
20.3	even	4		48.4.a.c.1.1		1
20.7	even	4		1200.4.a.b.1.1		1
20.19	odd	2		1200.4.f.j.49.2		2
35.3	even	12		294.4.e.g.79.1		2
35.13	even	4		294.4.a.e.1.1		1
35.18	odd	12		294.4.e.h.79.1		2
35.23	odd	12		294.4.e.h.67.1		2
35.33	even	12		294.4.e.g.67.1		2
40.3	even	4		192.4.a.c.1.1		1
40.13	odd	4		192.4.a.i.1.1		1
45.13	odd	12		162.4.c.f.55.1		2
45.23	even	12		162.4.c.c.55.1		2
45.38	even	12		162.4.c.c.109.1		2
45.43	odd	12		162.4.c.f.109.1		2
55.43	even	4		726.4.a.f.1.1		1
60.23	odd	4		144.4.a.c.1.1		1
65.8	even	4		1014.4.b.d.337.1		2
65.18	even	4		1014.4.b.d.337.2		2
65.38	odd	4		1014.4.a.g.1.1		1
80.3	even	4		768.4.d.c.385.2		2
80.13	odd	4		768.4.d.n.385.1		2
80.43	even	4		768.4.d.c.385.1		2
80.53	odd	4		768.4.d.n.385.2		2
85.33	odd	4		1734.4.a.d.1.1		1
95.18	even	4		2166.4.a.i.1.1		1
105.23	even	12		882.4.g.i.361.1		2
105.38	odd	12		882.4.g.f.667.1		2
105.53	even	12		882.4.g.i.667.1		2
105.68	odd	12		882.4.g.f.361.1		2
105.83	odd	4		882.4.a.n.1.1		1
120.53	even	4		576.4.a.q.1.1		1
120.83	odd	4		576.4.a.r.1.1		1
140.83	odd	4		2352.4.a.e.1.1		1
165.98	odd	4		2178.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.4.a.a.1.1	✓	1	5.3	odd	4
18.4.a.a.1.1		1	15.8	even	4
48.4.a.c.1.1		1	20.3	even	4
144.4.a.c.1.1		1	60.23	odd	4
150.4.a.i.1.1		1	5.2	odd	4
150.4.c.d.49.1		2	1.1	even	1	trivial
150.4.c.d.49.2		2	5.4	even	2	inner
162.4.c.c.55.1		2	45.23	even	12
162.4.c.c.109.1		2	45.38	even	12
162.4.c.f.55.1		2	45.13	odd	12
162.4.c.f.109.1		2	45.43	odd	12
192.4.a.c.1.1		1	40.3	even	4
192.4.a.i.1.1		1	40.13	odd	4
294.4.a.e.1.1		1	35.13	even	4
294.4.e.g.67.1		2	35.33	even	12
294.4.e.g.79.1		2	35.3	even	12
294.4.e.h.67.1		2	35.23	odd	12
294.4.e.h.79.1		2	35.18	odd	12
450.4.a.h.1.1		1	15.2	even	4
450.4.c.e.199.1		2	15.14	odd	2
450.4.c.e.199.2		2	3.2	odd	2
576.4.a.q.1.1		1	120.53	even	4
576.4.a.r.1.1		1	120.83	odd	4
726.4.a.f.1.1		1	55.43	even	4
768.4.d.c.385.1		2	80.43	even	4
768.4.d.c.385.2		2	80.3	even	4
768.4.d.n.385.1		2	80.13	odd	4
768.4.d.n.385.2		2	80.53	odd	4
882.4.a.n.1.1		1	105.83	odd	4
882.4.g.f.361.1		2	105.68	odd	12
882.4.g.f.667.1		2	105.38	odd	12
882.4.g.i.361.1		2	105.23	even	12
882.4.g.i.667.1		2	105.53	even	12
1014.4.a.g.1.1		1	65.38	odd	4
1014.4.b.d.337.1		2	65.8	even	4
1014.4.b.d.337.2		2	65.18	even	4
1200.4.a.b.1.1		1	20.7	even	4
1200.4.f.j.49.1		2	4.3	odd	2
1200.4.f.j.49.2		2	20.19	odd	2
1734.4.a.d.1.1		1	85.33	odd	4
2166.4.a.i.1.1		1	95.18	even	4
2178.4.a.e.1.1		1	165.98	odd	4
2352.4.a.e.1.1		1	140.83	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} -16.0000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} -16.0000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +12.0000 q^{11} -12.0000i q^{12} -38.0000i q^{13} -32.0000 q^{14} +16.0000 q^{16} -126.000i q^{17} +18.0000i q^{18} -20.0000 q^{19} +48.0000 q^{21} -24.0000i q^{22} -168.000i q^{23} -24.0000 q^{24} -76.0000 q^{26} -27.0000i q^{27} +64.0000i q^{28} -30.0000 q^{29} -88.0000 q^{31} -32.0000i q^{32} +36.0000i q^{33} -252.000 q^{34} +36.0000 q^{36} +254.000i q^{37} +40.0000i q^{38} +114.000 q^{39} +42.0000 q^{41} -96.0000i q^{42} +52.0000i q^{43} -48.0000 q^{44} -336.000 q^{46} -96.0000i q^{47} +48.0000i q^{48} +87.0000 q^{49} +378.000 q^{51} +152.000i q^{52} -198.000i q^{53} -54.0000 q^{54} +128.000 q^{56} -60.0000i q^{57} +60.0000i q^{58} +660.000 q^{59} -538.000 q^{61} +176.000i q^{62} +144.000i q^{63} -64.0000 q^{64} +72.0000 q^{66} +884.000i q^{67} +504.000i q^{68} +504.000 q^{69} +792.000 q^{71} -72.0000i q^{72} -218.000i q^{73} +508.000 q^{74} +80.0000 q^{76} -192.000i q^{77} -228.000i q^{78} +520.000 q^{79} +81.0000 q^{81} -84.0000i q^{82} +492.000i q^{83} -192.000 q^{84} +104.000 q^{86} -90.0000i q^{87} +96.0000i q^{88} -810.000 q^{89} -608.000 q^{91} +672.000i q^{92} -264.000i q^{93} -192.000 q^{94} +96.0000 q^{96} +1154.00i q^{97} -174.000i q^{98} -108.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9	\( 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} + 24 q^{11} - 64 q^{14} + 32 q^{16} - 40 q^{19} + 96 q^{21} - 48 q^{24} - 152 q^{26} - 60 q^{29} - 176 q^{31} - 504 q^{34} + 72 q^{36} + 228 q^{39} + 84 q^{41} - 96 q^{44} - 672 q^{46} + 174 q^{49} + 756 q^{51} - 108 q^{54} + 256 q^{56} + 1320 q^{59} - 1076 q^{61} - 128 q^{64} + 144 q^{66} + 1008 q^{69} + 1584 q^{71} + 1016 q^{74} + 160 q^{76} + 1040 q^{79} + 162 q^{81} - 384 q^{84} + 208 q^{86} - 1620 q^{89} - 1216 q^{91} - 384 q^{94} + 192 q^{96} - 216 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 + 24 * q^11 - 64 * q^14 + 32 * q^16 - 40 * q^19 + 96 * q^21 - 48 * q^24 - 152 * q^26 - 60 * q^29 - 176 * q^31 - 504 * q^34 + 72 * q^36 + 228 * q^39 + 84 * q^41 - 96 * q^44 - 672 * q^46 + 174 * q^49 + 756 * q^51 - 108 * q^54 + 256 * q^56 + 1320 * q^59 - 1076 * q^61 - 128 * q^64 + 144 * q^66 + 1008 * q^69 + 1584 * q^71 + 1016 * q^74 + 160 * q^76 + 1040 * q^79 + 162 * q^81 - 384 * q^84 + 208 * q^86 - 1620 * q^89 - 1216 * q^91 - 384 * q^94 + 192 * q^96 - 216 * q^99

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