LMFDB - Embedded newform 950.3.c.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,3,Mod(151,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("950.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	950.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.8856251142$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 68x^{10} + 1670x^{8} + 18282x^{6} + 91461x^{4} + 207270x^{2} + 172225 $ x^12 + 68x^10 + 1670x^8 + 18282x^6 + 91461x^4 + 207270*x^2 + 172225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.2
Root			$-3.53663i$ of defining polynomial
Character	$\chi$	$=$	950.151
Dual form			950.3.c.c.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} -0.146462 q^{7} +2.82843i q^{8} -3.50774 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} -0.146462 q^{7} +2.82843i q^{8} -3.50774 q^{9} +15.8960 q^{11} +7.07326i q^{12} -16.9258i q^{13} +0.207129i q^{14} +4.00000 q^{16} -27.0986 q^{17} +4.96069i q^{18} +(11.5499 - 15.0864i) q^{19} +0.517983i q^{21} -22.4804i q^{22} -20.1654 q^{23} +10.0031 q^{24} -23.9366 q^{26} -19.4241i q^{27} +0.292925 q^{28} +5.45043i q^{29} -9.15415i q^{31} -5.65685i q^{32} -56.2183i q^{33} +38.3232i q^{34} +7.01547 q^{36} +7.37605i q^{37} +(-21.3354 - 16.3340i) q^{38} -59.8601 q^{39} -24.0093i q^{41} +0.732538 q^{42} +40.3144 q^{43} -31.7920 q^{44} +28.5181i q^{46} -85.7192 q^{47} -14.1465i q^{48} -48.9785 q^{49} +95.8376i q^{51} +33.8515i q^{52} -59.0413i q^{53} -27.4698 q^{54} -0.414258i q^{56} +(-53.3550 - 40.8477i) q^{57} +7.70807 q^{58} +86.4540i q^{59} -15.3251 q^{61} -12.9459 q^{62} +0.513751 q^{63} -8.00000 q^{64} -79.5047 q^{66} +100.455i q^{67} +54.1971 q^{68} +71.3174i q^{69} -93.5509i q^{71} -9.92138i q^{72} +4.45910 q^{73} +10.4313 q^{74} +(-23.0998 + 30.1728i) q^{76} -2.32817 q^{77} +84.6550i q^{78} +15.2517i q^{79} -100.265 q^{81} -33.9543 q^{82} +145.028 q^{83} -1.03597i q^{84} -57.0132i q^{86} +19.2761 q^{87} +44.9607i q^{88} +24.1281i q^{89} +2.47899i q^{91} +40.3308 q^{92} -32.3748 q^{93} +121.225i q^{94} -20.0062 q^{96} +3.08788i q^{97} +69.2661i q^{98} -55.7591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{4} - 8 q^{6} + 24 q^{7} - 28 q^{9}+O(q^{10}) $ 12 * q - 24 * q^4 - 8 * q^6 + 24 * q^7 - 28 * q^9	$ 12 q - 24 q^{4} - 8 q^{6} + 24 q^{7} - 28 q^{9} + 4 q^{11} + 48 q^{16} - 12 q^{19} - 32 q^{23} + 16 q^{24} - 16 q^{26} - 48 q^{28} + 56 q^{36} + 8 q^{38} + 100 q^{39} - 72 q^{42} - 188 q^{43} - 8 q^{44} - 180 q^{47} - 108 q^{49} + 112 q^{54} + 92 q^{57} + 120 q^{58} - 76 q^{61} - 64 q^{62} - 84 q^{63} - 96 q^{64} + 8 q^{66} - 124 q^{73} + 72 q^{74} + 24 q^{76} + 184 q^{77} - 132 q^{81} + 96 q^{82} + 500 q^{83} + 432 q^{87} + 64 q^{92} + 452 q^{93} - 32 q^{96} + 128 q^{99}+O(q^{100}) $ 12 * q - 24 * q^4 - 8 * q^6 + 24 * q^7 - 28 * q^9 + 4 * q^11 + 48 * q^16 - 12 * q^19 - 32 * q^23 + 16 * q^24 - 16 * q^26 - 48 * q^28 + 56 * q^36 + 8 * q^38 + 100 * q^39 - 72 * q^42 - 188 * q^43 - 8 * q^44 - 180 * q^47 - 108 * q^49 + 112 * q^54 + 92 * q^57 + 120 * q^58 - 76 * q^61 - 64 * q^62 - 84 * q^63 - 96 * q^64 + 8 * q^66 - 124 * q^73 + 72 * q^74 + 24 * q^76 + 184 * q^77 - 132 * q^81 + 96 * q^82 + 500 * q^83 + 432 * q^87 + 64 * q^92 + 452 * q^93 - 32 * q^96 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	3.53663i		−	1.17888i	−0.807814	−	0.589438i	$-0.799349\pi$
$3$		−	3.53663i		−	1.17888i	0.807814	−	0.589438i	$-0.200651\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−5.00155			−0.833591
$7$	−0.146462			−0.0209232			−0.0104616	−	0.999945i	$-0.503330\pi$
$7$	−0.146462			−0.0209232			−0.0104616	+	0.999945i	$0.503330\pi$
$8$			2.82843i			0.353553i
$9$	−3.50774			−0.389749
$10$		0			0
$11$	15.8960			1.44509			0.722546	−	0.691322i	$-0.242972\pi$
$11$	15.8960			1.44509			0.722546	+	0.691322i	$0.242972\pi$
$12$			7.07326i			0.589438i
$13$		−	16.9258i		−	1.30198i	−0.759086	−	0.650991i	$-0.774354\pi$
$13$		−	16.9258i		−	1.30198i	0.759086	−	0.650991i	$-0.225646\pi$
$14$			0.207129i			0.0147949i
$15$		0			0
$16$	4.00000			0.250000
$17$	−27.0986			−1.59403			−0.797017	−	0.603957i	$-0.793590\pi$
$17$	−27.0986			−1.59403			−0.797017	+	0.603957i	$0.793590\pi$
$18$			4.96069i			0.275594i
$19$	11.5499	−	15.0864i	0.607889	−	0.794022i
$19$	11.5499	−	15.0864i	0.607889	−	0.794022i
$20$		0			0
$21$			0.517983i			0.0246658i
$22$		−	22.4804i		−	1.02183i
$23$	−20.1654			−0.876755			−0.438378	−	0.898791i	$-0.644447\pi$
$23$	−20.1654			−0.876755			−0.438378	+	0.898791i	$0.644447\pi$
$24$	10.0031			0.416796
$25$		0			0
$26$	−23.9366			−0.920640
$27$		−	19.4241i		−	0.719411i
$28$	0.292925			0.0104616
$29$			5.45043i			0.187946i	0.995575	+	0.0939730i	$0.0299567\pi$
$29$			5.45043i			0.187946i	−0.995575	+	0.0939730i	$0.970043\pi$
$30$		0			0
$31$		−	9.15415i		−	0.295295i	−0.989040	−	0.147648i	$-0.952830\pi$
$31$		−	9.15415i		−	0.295295i	0.989040	−	0.147648i	$-0.0471701\pi$
$32$		−	5.65685i		−	0.176777i
$33$		−	56.2183i		−	1.70359i
$34$			38.3232i			1.12715i
$35$		0			0
$36$	7.01547			0.194874
$37$			7.37605i			0.199353i	0.995020	+	0.0996764i	$0.0317808\pi$
$37$			7.37605i			0.199353i	−0.995020	+	0.0996764i	$0.968219\pi$
$38$	−21.3354	−	16.3340i	−0.561458	−	0.429843i
$39$	−59.8601			−1.53487
$40$		0			0
$41$		−	24.0093i		−	0.585593i	−0.956175	−	0.292797i	$-0.905414\pi$
$41$		−	24.0093i		−	0.585593i	0.956175	−	0.292797i	$-0.0945859\pi$
$42$	0.732538			0.0174414
$43$	40.3144			0.937544			0.468772	−	0.883319i	$-0.344697\pi$
$43$	40.3144			0.937544			0.468772	+	0.883319i	$0.344697\pi$
$44$	−31.7920			−0.722546
$45$		0			0
$46$			28.5181i			0.619960i
$47$	−85.7192			−1.82381			−0.911906	−	0.410398i	$-0.865390\pi$
$47$	−85.7192			−1.82381			−0.911906	+	0.410398i	$0.865390\pi$
$48$		−	14.1465i		−	0.294719i
$49$	−48.9785			−0.999562
$50$		0			0
$51$			95.8376i			1.87917i
$52$			33.8515i			0.650991i
$53$		−	59.0413i		−	1.11399i	−0.830517	−	0.556994i	$-0.811955\pi$
$53$		−	59.0413i		−	1.11399i	0.830517	−	0.556994i	$-0.188045\pi$
$54$	−27.4698			−0.508700
$55$		0			0
$56$		−	0.414258i		−	0.00739747i
$57$	−53.3550	−	40.8477i	−0.936053	−	0.716626i
$58$	7.70807			0.132898
$59$			86.4540i			1.46532i	0.680593	+	0.732661i	$0.261722\pi$
$59$			86.4540i			1.46532i	−0.680593	+	0.732661i	$0.738278\pi$
$60$		0			0
$61$	−15.3251			−0.251231			−0.125615	−	0.992079i	$-0.540091\pi$
$61$	−15.3251			−0.251231			−0.125615	+	0.992079i	$0.540091\pi$
$62$	−12.9459			−0.208805
$63$	0.513751			0.00815478
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−79.5047			−1.20462
$67$			100.455i			1.49933i	0.661818	+	0.749665i	$0.269785\pi$
$67$			100.455i			1.49933i	−0.661818	+	0.749665i	$0.730215\pi$
$68$	54.1971			0.797017
$69$			71.3174i			1.03359i
$70$		0			0
$71$		−	93.5509i		−	1.31762i	−0.752310	−	0.658809i	$-0.771060\pi$
$71$		−	93.5509i		−	1.31762i	0.752310	−	0.658809i	$-0.228940\pi$
$72$		−	9.92138i		−	0.137797i
$73$	4.45910			0.0610836			0.0305418	−	0.999533i	$-0.490277\pi$
$73$	4.45910			0.0610836			0.0305418	+	0.999533i	$0.490277\pi$
$74$	10.4313			0.140964
$75$		0			0
$76$	−23.0998	+	30.1728i	−0.303945	+	0.397011i
$77$	−2.32817			−0.0302360
$78$			84.6550i			1.08532i
$79$			15.2517i			0.193059i	0.995330	+	0.0965295i	$0.0307742\pi$
$79$			15.2517i			0.193059i	−0.995330	+	0.0965295i	$0.969226\pi$
$80$		0			0
$81$	−100.265			−1.23784
$82$	−33.9543			−0.414077
$83$	145.028			1.74732			0.873661	−	0.486535i	$-0.161739\pi$
$83$	145.028			1.74732			0.873661	+	0.486535i	$0.161739\pi$
$84$		−	1.03597i		−	0.0123329i
$85$		0			0
$86$		−	57.0132i		−	0.662944i
$87$	19.2761			0.221565
$88$			44.9607i			0.510917i
$89$			24.1281i			0.271102i	0.990770	+	0.135551i	$0.0432804\pi$
$89$			24.1281i			0.271102i	−0.990770	+	0.135551i	$0.956720\pi$
$90$		0			0
$91$			2.47899i			0.0272416i
$92$	40.3308			0.438378
$93$	−32.3748			−0.348116
$94$			121.225i			1.28963i
$95$		0			0
$96$	−20.0062			−0.208398
$97$			3.08788i			0.0318338i	0.999873	+	0.0159169i	$0.00506673\pi$
$97$			3.08788i			0.0318338i	−0.999873	+	0.0159169i	$0.994933\pi$
$98$			69.2661i			0.706797i
$99$	−55.7591			−0.563223
$100$		0			0
$101$	103.059			1.02039			0.510193	−	0.860060i	$-0.329574\pi$
$101$	103.059			1.02039			0.510193	+	0.860060i	$0.329574\pi$
$102$	135.535			1.32877
$103$		−	126.615i		−	1.22927i	−0.788810	−	0.614637i	$-0.789302\pi$
$103$		−	126.615i		−	1.22927i	0.788810	−	0.614637i	$-0.210698\pi$
$104$	47.8733			0.460320
$105$		0			0
$106$	−83.4970			−0.787708
$107$			22.0909i			0.206457i	0.994658	+	0.103228i	$0.0329173\pi$
$107$			22.0909i			0.206457i	−0.994658	+	0.103228i	$0.967083\pi$
$108$			38.8482i			0.359705i
$109$		−	91.1256i		−	0.836015i	−0.908444	−	0.418007i	$-0.862729\pi$
$109$		−	91.1256i		−	0.836015i	0.908444	−	0.418007i	$-0.137271\pi$
$110$		0			0
$111$	26.0864			0.235012
$112$	−0.585849			−0.00523080
$113$			170.895i			1.51234i	0.654373	+	0.756172i	$0.272933\pi$
$113$			170.895i			1.51234i	−0.654373	+	0.756172i	$0.727067\pi$
$114$	−57.7674	+	75.4554i	−0.506731	+	0.661889i
$115$		0			0
$116$		−	10.9009i		−	0.0939730i
$117$			59.3711i			0.507445i
$118$	122.264			1.03614
$119$	3.96892			0.0333523
$120$		0			0
$121$	131.683			1.08829
$122$			21.6729i			0.177647i
$123$	−84.9120			−0.690342
$124$			18.3083i			0.147648i
$125$		0			0
$126$		−	0.726554i		−	0.00576630i
$127$		−	64.0896i		−	0.504643i	−0.967644	−	0.252321i	$-0.918806\pi$
$127$		−	64.0896i		−	0.504643i	0.967644	−	0.252321i	$-0.0811940\pi$
$128$			11.3137i			0.0883883i
$129$		−	142.577i		−	1.10525i
$130$		0			0
$131$	−141.977			−1.08380			−0.541898	−	0.840444i	$-0.682294\pi$
$131$	−141.977			−1.08380			−0.541898	+	0.840444i	$0.682294\pi$
$132$			112.437i			0.851793i
$133$	−1.69163	+	2.20959i	−0.0127190	+	0.0166135i
$134$	142.065			1.06019
$135$		0			0
$136$		−	76.6463i		−	0.563576i
$137$	−96.3583			−0.703345			−0.351673	−	0.936123i	$-0.614387\pi$
$137$	−96.3583			−0.703345			−0.351673	+	0.936123i	$0.614387\pi$
$138$	100.858			0.730856
$139$	−182.574			−1.31348			−0.656739	−	0.754118i	$-0.728065\pi$
$139$	−182.574			−1.31348			−0.656739	+	0.754118i	$0.728065\pi$
$140$		0			0
$141$			303.157i			2.15005i
$142$	−132.301			−0.931697
$143$		−	269.052i		−	1.88148i
$144$	−14.0309			−0.0974371
$145$		0			0
$146$		−	6.30612i		−	0.0431926i
$147$			173.219i			1.17836i
$148$		−	14.7521i		−	0.0996764i
$149$	−15.4418			−0.103636			−0.0518182	−	0.998657i	$-0.516502\pi$
$149$	−15.4418			−0.103636			−0.0518182	+	0.998657i	$0.516502\pi$
$150$		0			0
$151$			185.156i			1.22620i	0.790006	+	0.613099i	$0.210077\pi$
$151$			185.156i			1.22620i	−0.790006	+	0.613099i	$0.789923\pi$
$152$	42.6708	+	32.6680i	0.280729	+	0.214921i
$153$	95.0547			0.621272
$154$			3.29253i			0.0213800i
$155$		0			0
$156$	119.720			0.767437
$157$	29.2193			0.186110			0.0930552	−	0.995661i	$-0.470337\pi$
$157$	29.2193			0.186110			0.0930552	+	0.995661i	$0.470337\pi$
$158$	21.5691			0.136513
$159$	−208.807			−1.31325
$160$		0			0
$161$	2.95347			0.0183445
$162$			141.797i			0.875288i
$163$	−94.1505			−0.577611			−0.288805	−	0.957388i	$-0.593258\pi$
$163$	−94.1505			−0.577611			−0.288805	+	0.957388i	$0.593258\pi$
$164$			48.0186i			0.292797i
$165$		0			0
$166$		−	205.100i		−	1.23554i
$167$		−	56.3258i		−	0.337280i	−0.985678	−	0.168640i	$-0.946062\pi$
$167$		−	56.3258i		−	0.337280i	0.985678	−	0.168640i	$-0.0539376\pi$
$168$	−1.46508			−0.00872069
$169$	−117.481			−0.695156
$170$		0			0
$171$	−40.5140	+	52.9192i	−0.236924	+	0.309469i
$172$	−80.6288			−0.468772
$173$			45.4392i			0.262654i	0.991339	+	0.131327i	$0.0419238\pi$
$173$			45.4392i			0.262654i	−0.991339	+	0.131327i	$0.958076\pi$
$174$		−	27.2606i		−	0.156670i
$175$		0			0
$176$	63.5841			0.361273
$177$	305.756			1.72743
$178$	34.1222			0.191698
$179$			147.183i			0.822252i	0.911579	+	0.411126i	$0.134864\pi$
$179$			147.183i			0.822252i	−0.911579	+	0.411126i	$0.865136\pi$
$180$		0			0
$181$		−	243.383i		−	1.34466i	−0.740254	−	0.672328i	$-0.765295\pi$
$181$		−	243.383i		−	1.34466i	0.740254	−	0.672328i	$-0.234705\pi$
$182$	3.50582			0.0192627
$183$			54.1991i			0.296170i
$184$		−	57.0363i		−	0.309980i
$185$		0			0
$186$			45.7849i			0.246155i
$187$	−430.759			−2.30353
$188$	171.438			0.911906
$189$			2.84490i			0.0150524i
$190$		0			0
$191$	−73.8128			−0.386454			−0.193227	−	0.981154i	$-0.561895\pi$
$191$	−73.8128			−0.386454			−0.193227	+	0.981154i	$0.561895\pi$
$192$			28.2930i			0.147359i
$193$		−	99.7983i		−	0.517089i	−0.965999	−	0.258545i	$-0.916757\pi$
$193$		−	99.7983i		−	0.517089i	0.965999	−	0.258545i	$-0.0832429\pi$
$194$	4.36693			0.0225099
$195$		0			0
$196$	97.9571			0.499781
$197$	333.125			1.69099			0.845494	−	0.533985i	$-0.179306\pi$
$197$	333.125			1.69099			0.845494	+	0.533985i	$0.179306\pi$
$198$			78.8552i			0.398259i
$199$	80.1431			0.402729			0.201365	−	0.979516i	$-0.435462\pi$
$199$	80.1431			0.402729			0.201365	+	0.979516i	$0.435462\pi$
$200$		0			0
$201$	355.272			1.76752
$202$		−	145.747i		−	0.721522i
$203$		−	0.798283i		−	0.00393243i
$204$		−	191.675i		−	0.939584i
$205$		0			0
$206$	−179.061			−0.869229
$207$	70.7348			0.341714
$208$		−	67.7030i		−	0.325495i
$209$	183.597	−	239.814i	0.878457	−	1.14744i
$210$		0			0
$211$		−	72.6207i		−	0.344174i	−0.985082	−	0.172087i	$-0.944949\pi$
$211$		−	72.6207i		−	0.344174i	0.985082	−	0.172087i	$-0.0550510\pi$
$212$			118.083i			0.556994i
$213$	−330.855			−1.55331
$214$	31.2412			0.145987
$215$		0			0
$216$	54.9396			0.254350
$217$			1.34074i			0.00617852i
$218$	−128.871			−0.591152
$219$		−	15.7702i		−	0.0720100i
$220$		0			0
$221$			458.664i			2.07540i
$222$		−	36.8917i		−	0.166179i
$223$		−	323.793i		−	1.45199i	−0.687702	−	0.725993i	$-0.741380\pi$
$223$		−	323.793i		−	1.45199i	0.687702	−	0.725993i	$-0.258620\pi$
$224$			0.828516i			0.00369873i
$225$		0			0
$226$	241.682			1.06939
$227$		−	433.568i		−	1.90999i	−0.296618	−	0.954996i	$-0.595859\pi$
$227$		−	433.568i		−	1.90999i	0.296618	−	0.954996i	$-0.404141\pi$
$228$	106.710	+	81.6954i	0.468027	+	0.358313i
$229$	206.994			0.903904			0.451952	−	0.892042i	$-0.350728\pi$
$229$	206.994			0.903904			0.451952	+	0.892042i	$0.350728\pi$
$230$		0			0
$231$			8.23387i			0.0356444i
$232$	−15.4161			−0.0664489
$233$	−290.836			−1.24822			−0.624112	−	0.781335i	$-0.714539\pi$
$233$	−290.836			−1.24822			−0.624112	+	0.781335i	$0.714539\pi$
$234$	83.9634			0.358818
$235$		0			0
$236$		−	172.908i		−	0.732661i
$237$	53.9395			0.227593
$238$		−	5.61290i		−	0.0235836i
$239$	−90.0708			−0.376865			−0.188433	−	0.982086i	$-0.560341\pi$
$239$	−90.0708			−0.376865			−0.188433	+	0.982086i	$0.560341\pi$
$240$		0			0
$241$			85.6209i			0.355273i	0.984096	+	0.177637i	$0.0568452\pi$
$241$			85.6209i			0.355273i	−0.984096	+	0.177637i	$0.943155\pi$
$242$		−	186.229i		−	0.769540i
$243$			179.785i			0.739854i
$244$	30.6501			0.125615
$245$		0			0
$246$			120.084i			0.488145i
$247$	−255.349	−	195.491i	−1.03380	−	0.791461i
$248$	25.8918			0.104403
$249$		−	512.909i		−	2.05988i
$250$		0			0
$251$	−418.090			−1.66570			−0.832849	−	0.553500i	$-0.813292\pi$
$251$	−418.090			−1.66570			−0.832849	+	0.553500i	$0.813292\pi$
$252$	−1.02750			−0.00407739
$253$	−320.549			−1.26699
$254$	−90.6364			−0.356836
$255$		0			0
$256$	16.0000			0.0625000
$257$			81.0271i			0.315281i	0.987497	+	0.157640i	$0.0503886\pi$
$257$			81.0271i			0.315281i	−0.987497	+	0.157640i	$0.949611\pi$
$258$	−201.634			−0.781528
$259$		−	1.08031i		−	0.00417110i
$260$		0			0
$261$		−	19.1187i		−	0.0732516i
$262$			200.786i			0.766360i
$263$	−281.473			−1.07024			−0.535120	−	0.844776i	$-0.679733\pi$
$263$	−281.473			−1.07024			−0.535120	+	0.844776i	$0.679733\pi$
$264$	159.009			0.602308
$265$		0			0
$266$	3.12483	+	2.39232i	0.0117475	+	0.00899368i
$267$	85.3320			0.319596
$268$		−	200.910i		−	0.749665i
$269$		−	392.714i		−	1.45990i	−0.683499	−	0.729951i	$-0.739543\pi$
$269$		−	392.714i		−	1.45990i	0.683499	−	0.729951i	$-0.260457\pi$
$270$		0			0
$271$	435.861			1.60834			0.804172	−	0.594397i	$-0.202609\pi$
$271$	435.861			1.60834			0.804172	+	0.594397i	$0.202609\pi$
$272$	−108.394			−0.398508
$273$	8.76725			0.0321145
$274$			136.271i			0.497340i
$275$		0			0
$276$		−	142.635i		−	0.516793i
$277$	306.929			1.10805			0.554024	−	0.832501i	$-0.313092\pi$
$277$	306.929			1.10805			0.554024	+	0.832501i	$0.313092\pi$
$278$			258.198i			0.928770i
$279$			32.1103i			0.115091i
$280$		0			0
$281$		−	158.309i		−	0.563376i	−0.959506	−	0.281688i	$-0.909106\pi$
$281$		−	158.309i		−	0.563376i	0.959506	−	0.281688i	$-0.0908944\pi$
$282$	428.729			1.52031
$283$	109.390			0.386539			0.193269	−	0.981146i	$-0.438091\pi$
$283$	109.390			0.386539			0.193269	+	0.981146i	$0.438091\pi$
$284$			187.102i			0.658809i
$285$		0			0
$286$	−380.497			−1.33041
$287$			3.51646i			0.0122525i
$288$			19.8428i			0.0688985i
$289$	445.333			1.54094
$290$		0			0
$291$	10.9207			0.0375282
$292$	−8.91820			−0.0305418
$293$			332.451i			1.13464i	0.823496	+	0.567322i	$0.192020\pi$
$293$			332.451i			1.13464i	−0.823496	+	0.567322i	$0.807980\pi$
$294$	244.969			0.833226
$295$		0			0
$296$	−20.8626			−0.0704818
$297$		−	308.766i		−	1.03962i
$298$			21.8380i			0.0732819i
$299$			341.314i			1.14152i
$300$		0			0
$301$	−5.90454			−0.0196164
$302$	261.850			0.867053
$303$		−	364.481i		−	1.20291i
$304$	46.1996	−	60.3456i	0.151972	−	0.198505i
$305$		0			0
$306$		−	134.428i		−	0.439306i
$307$		−	469.296i		−	1.52865i	−0.644830	−	0.764326i	$-0.723072\pi$
$307$		−	469.296i		−	1.52865i	0.644830	−	0.764326i	$-0.276928\pi$
$308$	4.65634			0.0151180
$309$	−447.791			−1.44916
$310$		0			0
$311$	50.0531			0.160942			0.0804712	−	0.996757i	$-0.474357\pi$
$311$	50.0531			0.160942			0.0804712	+	0.996757i	$0.474357\pi$
$312$		−	169.310i		−	0.542660i
$313$	214.496			0.685290			0.342645	−	0.939465i	$-0.388677\pi$
$313$	214.496			0.685290			0.342645	+	0.939465i	$0.388677\pi$
$314$		−	41.3224i		−	0.131600i
$315$		0			0
$316$		−	30.5033i		−	0.0965295i
$317$		−	119.302i		−	0.376348i	−0.982136	−	0.188174i	$-0.939743\pi$
$317$		−	119.302i		−	0.376348i	0.982136	−	0.188174i	$-0.0602568\pi$
$318$			295.298i			0.928610i
$319$			86.6402i			0.271599i
$320$		0			0
$321$	78.1272			0.243387
$322$		−	4.17683i		−	0.0129715i
$323$	−312.986	+	408.820i	−0.968996	+	1.26570i
$324$	200.531			0.618922
$325$		0			0
$326$			133.149i			0.408432i
$327$	−322.277			−0.985557
$328$	67.9086			0.207038
$329$	12.5546			0.0381600
$330$		0			0
$331$		−	474.154i		−	1.43249i	−0.697849	−	0.716245i	$-0.745859\pi$
$331$		−	474.154i		−	1.43249i	0.697849	−	0.716245i	$-0.254141\pi$
$332$	−290.056			−0.873661
$333$		−	25.8733i		−	0.0776975i
$334$	−79.6567			−0.238493
$335$		0			0
$336$			2.07193i			0.00616646i
$337$			237.394i			0.704433i	0.935919	+	0.352216i	$0.114572\pi$
$337$			237.394i			0.704433i	−0.935919	+	0.352216i	$0.885428\pi$
$338$			166.144i			0.491549i
$339$	604.392			1.78287
$340$		0			0
$341$		−	145.515i		−	0.426729i
$342$	74.8390	+	57.2955i	0.218827	+	0.167531i
$343$	14.3502			0.0418372
$344$			114.026i			0.331472i
$345$		0			0
$346$	64.2607			0.185724
$347$	612.413			1.76488			0.882440	−	0.470426i	$-0.155900\pi$
$347$	612.413			1.76488			0.882440	+	0.470426i	$0.155900\pi$
$348$	−38.5523			−0.110782
$349$	625.895			1.79340			0.896698	−	0.442644i	$-0.145959\pi$
$349$	625.895			1.79340			0.896698	+	0.442644i	$0.145959\pi$
$350$		0			0
$351$	−328.767			−0.936659
$352$		−	89.9215i		−	0.255459i
$353$	218.281			0.618359			0.309179	−	0.951004i	$-0.399946\pi$
$353$	218.281			0.618359			0.309179	+	0.951004i	$0.399946\pi$
$354$		−	432.404i		−	1.22148i
$355$		0			0
$356$		−	48.2561i		−	0.135551i
$357$		−	14.0366i		−	0.0393182i
$358$	208.148			0.581420
$359$	316.232			0.880870			0.440435	−	0.897784i	$-0.354824\pi$
$359$	316.232			0.880870			0.440435	+	0.897784i	$0.354824\pi$
$360$		0			0
$361$	−94.1997	−	348.493i	−0.260941	−	0.965355i
$362$	−344.195			−0.950815
$363$		−	465.716i		−	1.28296i
$364$		−	4.95797i		−	0.0136208i
$365$		0			0
$366$	76.6491			0.209424
$367$	−600.077			−1.63509			−0.817543	−	0.575867i	$-0.804665\pi$
$367$	−600.077			−1.63509			−0.817543	+	0.575867i	$0.804665\pi$
$368$	−80.6615			−0.219189
$369$			84.2184i			0.228234i
$370$		0			0
$371$			8.64733i			0.0233082i
$372$	64.7496			0.174058
$373$			60.9072i			0.163290i	0.996661	+	0.0816451i	$0.0260174\pi$
$373$			60.9072i			0.163290i	−0.996661	+	0.0816451i	$0.973983\pi$
$374$			609.186i			1.62884i
$375$		0			0
$376$		−	242.450i		−	0.644815i
$377$	92.2527			0.244702
$378$	4.02329			0.0106436
$379$		−	162.907i		−	0.429835i	−0.976632	−	0.214917i	$-0.931052\pi$
$379$		−	162.907i		−	0.429835i	0.976632	−	0.214917i	$-0.0689482\pi$
$380$		0			0
$381$	−226.661			−0.594911
$382$			104.387i			0.273264i
$383$			638.343i			1.66669i	0.552752	+	0.833346i	$0.313578\pi$
$383$			638.343i			1.66669i	−0.552752	+	0.833346i	$0.686422\pi$
$384$	40.0124			0.104199
$385$		0			0
$386$	−141.136			−0.365637
$387$	−141.412			−0.365406
$388$		−	6.17577i		−	0.0159169i
$389$	175.089			0.450100			0.225050	−	0.974347i	$-0.427746\pi$
$389$	175.089			0.450100			0.225050	+	0.974347i	$0.427746\pi$
$390$		0			0
$391$	546.453			1.39758
$392$		−	138.532i		−	0.353399i
$393$			502.121i			1.27766i
$394$		−	471.109i		−	1.19571i
$395$		0			0
$396$	111.518			0.281611
$397$	725.042			1.82630			0.913151	−	0.407622i	$-0.133642\pi$
$397$	725.042			1.82630			0.913151	+	0.407622i	$0.133642\pi$
$398$		−	113.339i		−	0.284773i
$399$	7.81450	+	5.98265i	0.0195852	+	0.0149941i
$400$		0			0
$401$		−	566.987i		−	1.41393i	−0.707248	−	0.706966i	$-0.750063\pi$
$401$		−	566.987i		−	1.41393i	0.707248	−	0.706966i	$-0.249937\pi$
$402$		−	502.431i		−	1.24983i
$403$	−154.941			−0.384469
$404$	−206.118			−0.510193
$405$		0			0
$406$	−1.12894			−0.00278065
$407$			117.250i			0.288083i
$408$	−271.070			−0.664386
$409$			216.398i			0.529091i	0.964373	+	0.264545i	$0.0852219\pi$
$409$			216.398i			0.529091i	−0.964373	+	0.264545i	$0.914778\pi$
$410$		0			0
$411$			340.783i			0.829157i
$412$			253.231i			0.614637i
$413$		−	12.6623i		−	0.0306592i
$414$		−	100.034i		−	0.241628i
$415$		0			0
$416$	−95.7465			−0.230160
$417$			645.695i			1.54843i
$418$	−339.148	−	259.646i	−0.811359	−	0.621163i
$419$	484.914			1.15731			0.578656	−	0.815572i	$-0.303577\pi$
$419$	484.914			1.15731			0.578656	+	0.815572i	$0.303577\pi$
$420$		0			0
$421$			413.265i			0.981626i	0.871265	+	0.490813i	$0.163300\pi$
$421$			413.265i			0.981626i	−0.871265	+	0.490813i	$0.836700\pi$
$422$	−102.701			−0.243368
$423$	300.680			0.710828
$424$	166.994			0.393854
$425$		0			0
$426$			467.899i			1.09836i
$427$	2.24455			0.00525655
$428$		−	44.1818i		−	0.103228i
$429$	−951.538			−2.21804
$430$		0			0
$431$		−	450.677i		−	1.04565i	−0.852439	−	0.522827i	$-0.824877\pi$
$431$		−	450.677i		−	1.04565i	0.852439	−	0.522827i	$-0.175123\pi$
$432$		−	77.6964i		−	0.179853i
$433$			2.50133i			0.00577673i	0.999996	+	0.00288837i	$0.000919397\pi$
$433$			2.50133i			0.00577673i	−0.999996	+	0.00288837i	$0.999081\pi$
$434$	1.89609			0.00436887
$435$		0			0
$436$			182.251i			0.418007i
$437$	−232.908	+	304.223i	−0.532970	+	0.696163i
$438$	−22.3024			−0.0509187
$439$		−	491.152i		−	1.11880i	−0.828898	−	0.559399i	$-0.811032\pi$
$439$		−	491.152i		−	1.11880i	0.828898	−	0.559399i	$-0.188968\pi$
$440$		0			0
$441$	171.804			0.389578
$442$	648.649			1.46753
$443$	238.895			0.539267			0.269634	−	0.962963i	$-0.413097\pi$
$443$	238.895			0.539267			0.269634	+	0.962963i	$0.413097\pi$
$444$	−52.1727			−0.117506
$445$		0			0
$446$	−457.912			−1.02671
$447$			54.6119i			0.122174i
$448$	1.17170			0.00261540
$449$			452.733i			1.00832i	0.863612	+	0.504158i	$0.168197\pi$
$449$			452.733i			1.00832i	−0.863612	+	0.504158i	$0.831803\pi$
$450$		0			0
$451$		−	381.653i		−	0.846236i
$452$		−	341.790i		−	0.756172i
$453$	654.828			1.44554
$454$	−613.158			−1.35057
$455$		0			0
$456$	115.535	−	150.911i	0.253366	−	0.330945i
$457$	−697.754			−1.52681			−0.763407	−	0.645918i	$-0.776475\pi$
$457$	−697.754			−1.52681			−0.763407	+	0.645918i	$0.776475\pi$
$458$		−	292.734i		−	0.639156i
$459$			526.365i			1.14677i
$460$		0			0
$461$	420.342			0.911804			0.455902	−	0.890030i	$-0.349317\pi$
$461$	420.342			0.911804			0.455902	+	0.890030i	$0.349317\pi$
$462$	11.6444			0.0252044
$463$	480.580			1.03797			0.518985	−	0.854783i	$-0.326310\pi$
$463$	480.580			1.03797			0.518985	+	0.854783i	$0.326310\pi$
$464$			21.8017i			0.0469865i
$465$		0			0
$466$			411.304i			0.882627i
$467$	559.285			1.19761			0.598806	−	0.800894i	$-0.295642\pi$
$467$	559.285			1.19761			0.598806	+	0.800894i	$0.295642\pi$
$468$		−	118.742i		−	0.253723i
$469$		−	14.7129i		−	0.0313708i
$470$		0			0
$471$		−	103.338i		−	0.219401i
$472$	−244.529			−0.518070
$473$	640.838			1.35484
$474$		−	76.2819i		−	0.160932i
$475$		0			0
$476$	−7.93784			−0.0166761
$477$			207.101i			0.434175i
$478$			127.379i			0.266484i
$479$	246.678			0.514986			0.257493	−	0.966280i	$-0.417104\pi$
$479$	246.678			0.514986			0.257493	+	0.966280i	$0.417104\pi$
$480$		0			0
$481$	124.845			0.259554
$482$	121.086			0.251216
$483$		−	10.4453i		−	0.0216259i
$484$	−263.367			−0.544147
$485$		0			0
$486$	254.254			0.523156
$487$		−	418.804i		−	0.859968i	−0.902837	−	0.429984i	$-0.858519\pi$
$487$		−	418.804i		−	0.859968i	0.902837	−	0.429984i	$-0.141481\pi$
$488$		−	43.3459i		−	0.0888235i
$489$			332.975i			0.680931i
$490$		0			0
$491$	−514.657			−1.04818			−0.524091	−	0.851662i	$-0.675595\pi$
$491$	−514.657			−1.04818			−0.524091	+	0.851662i	$0.675595\pi$
$492$	169.824			0.345171
$493$		−	147.699i		−	0.299592i
$494$	−276.466	+	361.118i	−0.559647	+	0.731008i
$495$		0			0
$496$		−	36.6166i		−	0.0738238i
$497$			13.7017i			0.0275688i
$498$	−725.363			−1.45655
$499$	−152.709			−0.306031			−0.153015	−	0.988224i	$-0.548898\pi$
$499$	−152.709			−0.306031			−0.153015	+	0.988224i	$0.548898\pi$
$500$		0			0
$501$	−199.203			−0.397612
$502$			591.269i			1.17783i
$503$	173.503			0.344937			0.172469	−	0.985015i	$-0.444826\pi$
$503$	173.503			0.344937			0.172469	+	0.985015i	$0.444826\pi$
$504$			1.45311i			0.00288315i
$505$		0			0
$506$			453.325i			0.895899i
$507$			415.488i			0.819502i
$508$			128.179i			0.252321i
$509$		−	856.653i		−	1.68301i	−0.540247	−	0.841506i	$-0.681669\pi$
$509$		−	856.653i		−	1.68301i	0.540247	−	0.841506i	$-0.318331\pi$
$510$		0			0
$511$	−0.653090			−0.00127806
$512$		−	22.6274i		−	0.0441942i
$513$	−293.040	−	224.346i	−0.571228	−	0.437322i
$514$	114.590			0.222937
$515$		0			0
$516$			285.154i			0.552624i
$517$	−1362.59			−2.63558
$518$	−1.52779			−0.00294941
$519$	160.701			0.309637
$520$		0			0
$521$			99.1018i			0.190215i	0.995467	+	0.0951073i	$0.0303194\pi$
$521$			99.1018i			0.190215i	−0.995467	+	0.0951073i	$0.969681\pi$
$522$	−27.0379			−0.0517967
$523$			56.3564i			0.107756i	0.998548	+	0.0538780i	$0.0171582\pi$
$523$			56.3564i			0.107756i	−0.998548	+	0.0538780i	$0.982842\pi$
$524$	283.955			0.541898
$525$		0			0
$526$			398.063i			0.756773i
$527$			248.064i			0.470710i
$528$		−	224.873i		−	0.425896i
$529$	−122.358			−0.231300
$530$		0			0
$531$		−	303.258i		−	0.571107i
$532$	3.38325	−	4.41918i	0.00635949	−	0.00830673i
$533$	−406.376			−0.762431
$534$		−	120.678i		−	0.225988i
$535$		0			0
$536$	−284.130			−0.530093
$537$	520.532			0.969333
$538$	−555.381			−1.03231
$539$	−778.564			−1.44446
$540$		0			0
$541$	909.463			1.68108			0.840538	−	0.541752i	$-0.182239\pi$
$541$	909.463			1.68108			0.840538	+	0.541752i	$0.182239\pi$
$542$		−	616.401i		−	1.13727i
$543$	−860.754			−1.58518
$544$			153.293i			0.281788i
$545$		0			0
$546$		−	12.3988i		−	0.0227084i
$547$		−	174.393i		−	0.318817i	−0.987213	−	0.159408i	$-0.949041\pi$
$547$		−	174.393i		−	0.318817i	0.987213	−	0.159408i	$-0.0509587\pi$
$548$	192.717			0.351673
$549$	53.7563			0.0979168
$550$		0			0
$551$	82.2275	+	62.9519i	0.149233	+	0.114250i
$552$	−201.716			−0.365428
$553$		−	2.23379i		−	0.00403941i
$554$		−	434.064i		−	0.783508i
$555$		0			0
$556$	365.147			0.656739
$557$	134.156			0.240854			0.120427	−	0.992722i	$-0.461574\pi$
$557$	134.156			0.240854			0.120427	+	0.992722i	$0.461574\pi$
$558$	45.4109			0.0813815
$559$		−	682.352i		−	1.22066i
$560$		0			0
$561$			1523.44i			2.71557i
$562$	−223.882			−0.398367
$563$			178.310i			0.316715i	0.987382	+	0.158357i	$0.0506198\pi$
$563$			178.310i			0.316715i	−0.987382	+	0.158357i	$0.949380\pi$
$564$		−	606.314i		−	1.07502i
$565$		0			0
$566$		−	154.702i		−	0.273324i
$567$	14.6851			0.0258997
$568$	264.602			0.465849
$569$		−	189.835i		−	0.333629i	−0.985988	−	0.166815i	$-0.946652\pi$
$569$		−	189.835i		−	0.333629i	0.985988	−	0.166815i	$-0.0533482\pi$
$570$		0			0
$571$	−604.730			−1.05907			−0.529536	−	0.848287i	$-0.677634\pi$
$571$	−604.730			−1.05907			−0.529536	+	0.848287i	$0.677634\pi$
$572$			538.104i			0.940742i
$573$			261.048i			0.455582i
$574$	4.97303			0.00866381
$575$		0			0
$576$	28.0619			0.0487186
$577$	1138.28			1.97276			0.986379	−	0.164488i	$-0.0525972\pi$
$577$	1138.28			1.97276			0.986379	+	0.164488i	$0.0525972\pi$
$578$		−	629.795i		−	1.08961i
$579$	−352.949			−0.609584
$580$		0			0
$581$	−21.2411			−0.0365596
$582$		−	15.4442i		−	0.0265364i
$583$		−	938.522i		−	1.60982i
$584$			12.6122i			0.0215963i
$585$		0			0
$586$	470.156			0.802314
$587$	103.008			0.175482			0.0877410	−	0.996143i	$-0.472035\pi$
$587$	103.008			0.175482			0.0877410	+	0.996143i	$0.472035\pi$
$588$		−	346.438i		−	0.589180i
$589$	−138.103	−	105.730i	−0.234471	−	0.179507i
$590$		0			0
$591$		−	1178.14i		−	1.99346i
$592$			29.5042i			0.0498382i
$593$	−354.332			−0.597525			−0.298763	−	0.954327i	$-0.596574\pi$
$593$	−354.332			−0.597525			−0.298763	+	0.954327i	$0.596574\pi$
$594$	−436.661			−0.735119
$595$		0			0
$596$	30.8836			0.0518182
$597$		−	283.436i		−	0.474768i
$598$	482.691			0.807176
$599$			1112.64i			1.85750i	0.370704	+	0.928751i	$0.379116\pi$
$599$			1112.64i			1.85750i	−0.370704	+	0.928751i	$0.620884\pi$
$600$		0			0
$601$		−	44.8624i		−	0.0746463i	−0.999303	−	0.0373231i	$-0.988117\pi$
$601$		−	44.8624i		−	0.0746463i	0.999303	−	0.0373231i	$-0.0118831\pi$
$602$			8.35028i			0.0138709i
$603$		−	352.370i		−	0.584361i
$604$		−	370.312i		−	0.613099i
$605$		0			0
$606$	−515.455			−0.850585
$607$			740.250i			1.21952i	0.792585	+	0.609762i	$0.208735\pi$
$607$			740.250i			1.21952i	−0.792585	+	0.609762i	$0.791265\pi$
$608$	−85.3416	−	65.3361i	−0.140365	−	0.107461i
$609$	−2.82323			−0.00463585
$610$		0			0
$611$			1450.86i			2.37457i
$612$	−190.109			−0.310636
$613$	758.605			1.23753			0.618764	−	0.785577i	$-0.287634\pi$
$613$	758.605			1.23753			0.618764	+	0.785577i	$0.287634\pi$
$614$	−663.685			−1.08092
$615$		0			0
$616$		−	6.58505i		−	0.0106900i
$617$	617.701			1.00114			0.500568	−	0.865697i	$-0.333125\pi$
$617$	617.701			1.00114			0.500568	+	0.865697i	$0.333125\pi$
$618$			633.272i			1.02471i
$619$	−434.677			−0.702224			−0.351112	−	0.936333i	$-0.614196\pi$
$619$	−434.677			−0.702224			−0.351112	+	0.936333i	$0.614196\pi$
$620$		0			0
$621$			391.694i			0.630747i
$622$		−	70.7858i		−	0.113803i
$623$		−	3.53385i		−	0.00567232i
$624$	−239.440			−0.383719
$625$		0			0
$626$		−	303.343i		−	0.484573i
$627$	−848.133	−	649.316i	−1.35268	−	1.03559i
$628$	−58.4387			−0.0930552
$629$		−	199.881i		−	0.317775i
$630$		0			0
$631$	−406.725			−0.644571			−0.322286	−	0.946642i	$-0.604451\pi$
$631$	−406.725			−0.644571			−0.322286	+	0.946642i	$0.604451\pi$
$632$	−43.1382			−0.0682567
$633$	−256.832			−0.405738
$634$	−168.719			−0.266118
$635$		0			0
$636$	417.614			0.656626
$637$			828.999i			1.30141i
$638$	122.528			0.192050
$639$			328.152i			0.513540i
$640$		0			0
$641$			994.339i			1.55123i	0.631206	+	0.775616i	$0.282560\pi$
$641$			994.339i			1.55123i	−0.631206	+	0.775616i	$0.717440\pi$
$642$		−	110.489i		−	0.172101i
$643$	−847.680			−1.31832			−0.659160	−	0.752003i	$-0.729088\pi$
$643$	−847.680			−1.31832			−0.659160	+	0.752003i	$0.729088\pi$
$644$	−5.90694			−0.00917226
$645$		0			0
$646$	578.159	+	442.629i	0.894983	+	0.685184i
$647$	−731.308			−1.13031			−0.565153	−	0.824986i	$-0.691183\pi$
$647$	−731.308			−1.13031			−0.565153	+	0.824986i	$0.691183\pi$
$648$		−	283.593i		−	0.437644i
$649$			1374.28i			2.11753i
$650$		0			0
$651$	4.74169			0.00728370
$652$	188.301			0.288805
$653$	1111.60			1.70230			0.851150	−	0.524922i	$-0.175906\pi$
$653$	1111.60			1.70230			0.851150	+	0.524922i	$0.175906\pi$
$654$			455.769i			0.696894i
$655$		0			0
$656$		−	96.0373i		−	0.146398i
$657$	−15.6414			−0.0238072
$658$		−	17.7549i		−	0.0269832i
$659$			363.690i			0.551881i	0.961175	+	0.275941i	$0.0889893\pi$
$659$			363.690i			0.551881i	−0.961175	+	0.275941i	$0.911011\pi$
$660$		0			0
$661$		−	1069.74i		−	1.61836i	−0.587560	−	0.809180i	$-0.699911\pi$
$661$		−	1069.74i		−	1.61836i	0.587560	−	0.809180i	$-0.300089\pi$
$662$	−670.555			−1.01292
$663$	1622.12			2.44664
$664$			410.200i			0.617772i
$665$		0			0
$666$	−36.5903			−0.0549404
$667$		−	109.910i		−	0.164783i
$668$			112.652i			0.168640i
$669$	−1145.14			−1.71171
$670$		0			0
$671$	−243.608			−0.363052
$672$	2.93015			0.00436035
$673$			270.027i			0.401228i	0.979670	+	0.200614i	$0.0642938\pi$
$673$			270.027i			0.401228i	−0.979670	+	0.200614i	$0.935706\pi$
$674$	335.726			0.498109
$675$		0			0
$676$	234.963			0.347578
$677$			826.165i			1.22033i	0.792274	+	0.610166i	$0.208897\pi$
$677$			826.165i			1.22033i	−0.792274	+	0.610166i	$0.791103\pi$
$678$		−	854.739i		−	1.26068i
$679$		−	0.452259i		−	0.000666066i
$680$		0			0
$681$	−1533.37			−2.25164
$682$	−205.789			−0.301743
$683$			865.671i			1.26745i	0.773557	+	0.633727i	$0.218476\pi$
$683$			865.671i			1.26745i	−0.773557	+	0.633727i	$0.781524\pi$
$684$	81.0280	−	105.838i	0.118462	−	0.154734i
$685$		0			0
$686$		−	20.2942i		−	0.0295834i
$687$		−	732.060i		−	1.06559i
$688$	161.258			0.234386
$689$	−999.319			−1.45039
$690$		0			0
$691$	28.2977			0.0409518			0.0204759	−	0.999790i	$-0.493482\pi$
$691$	28.2977			0.0409518			0.0204759	+	0.999790i	$0.493482\pi$
$692$		−	90.8783i		−	0.131327i
$693$	8.16660			0.0117844
$694$		−	866.083i		−	1.24796i
$695$		0			0
$696$			54.5212i			0.0783350i
$697$			650.618i			0.933455i
$698$		−	885.149i		−	1.26812i
$699$			1028.58i			1.47150i
$700$		0			0
$701$	134.912			0.192456			0.0962282	−	0.995359i	$-0.469322\pi$
$701$	134.912			0.192456			0.0962282	+	0.995359i	$0.469322\pi$
$702$			464.947i			0.662318i
$703$	111.278	+	85.1927i	0.158290	+	0.121184i
$704$	−127.168			−0.180637
$705$		0			0
$706$		−	308.695i		−	0.437246i
$707$	−15.0943			−0.0213497
$708$	−611.512			−0.863717
$709$	−328.768			−0.463707			−0.231853	−	0.972751i	$-0.574479\pi$
$709$	−328.768			−0.463707			−0.231853	+	0.972751i	$0.574479\pi$
$710$		0			0
$711$		−	53.4988i		−	0.0752445i
$712$	−68.2445			−0.0958490
$713$			184.597i			0.258902i
$714$	−19.8507			−0.0278022
$715$		0			0
$716$		−	294.366i		−	0.411126i
$717$			318.547i			0.444277i
$718$		−	447.220i		−	0.622869i
$719$	132.152			0.183799			0.0918997	−	0.995768i	$-0.470706\pi$
$719$	132.152			0.183799			0.0918997	+	0.995768i	$0.470706\pi$
$720$		0			0
$721$			18.5444i			0.0257204i
$722$	−492.844	+	133.218i	−0.682609	+	0.184513i
$723$	302.809			0.418823
$724$			486.765i			0.672328i
$725$		0			0
$726$	−658.621			−0.907192
$727$	−370.952			−0.510250			−0.255125	−	0.966908i	$-0.582117\pi$
$727$	−370.952			−0.510250			−0.255125	+	0.966908i	$0.582117\pi$
$728$	−7.01163			−0.00963136
$729$	−266.557			−0.365648
$730$		0			0
$731$	−1092.46			−1.49448
$732$		−	108.398i		−	0.148085i
$733$	778.543			1.06213			0.531066	−	0.847331i	$-0.321792\pi$
$733$	778.543			1.06213			0.531066	+	0.847331i	$0.321792\pi$
$734$			848.637i			1.15618i
$735$		0			0
$736$			114.073i			0.154990i
$737$			1596.84i			2.16667i
$738$	119.103			0.161386
$739$	686.378			0.928793			0.464396	−	0.885627i	$-0.346271\pi$
$739$	686.378			0.928793			0.464396	+	0.885627i	$0.346271\pi$
$740$		0			0
$741$	−691.378	+	903.074i	−0.933034	+	1.21872i
$742$	12.2292			0.0164814
$743$			944.989i			1.27186i	0.771748	+	0.635928i	$0.219383\pi$
$743$			944.989i			1.27186i	−0.771748	+	0.635928i	$0.780617\pi$
$744$		−	91.5698i		−	0.123078i
$745$		0			0
$746$	86.1358			0.115464
$747$	−508.719			−0.681016
$748$	861.519			1.15176
$749$		−	3.23548i		−	0.00431974i
$750$		0			0
$751$		−	372.272i		−	0.495701i	−0.968798	−	0.247851i	$-0.920276\pi$
$751$		−	372.272i		−	0.495701i	0.968798	−	0.247851i	$-0.0797243\pi$
$752$	−342.877			−0.455953
$753$			1478.63i			1.96365i
$754$		−	130.465i		−	0.173031i
$755$		0			0
$756$		−	5.68980i		−	0.00752618i
$757$	−65.8572			−0.0869977			−0.0434988	−	0.999053i	$-0.513850\pi$
$757$	−65.8572			−0.0869977			−0.0434988	+	0.999053i	$0.513850\pi$
$758$	−230.386			−0.303939
$759$			1133.66i			1.49363i
$760$		0			0
$761$	−1305.80			−1.71590			−0.857951	−	0.513732i	$-0.828263\pi$
$761$	−1305.80			−1.71590			−0.857951	+	0.513732i	$0.828263\pi$
$762$			320.547i			0.420666i
$763$			13.3465i			0.0174921i
$764$	147.626			0.193227
$765$		0			0
$766$	902.753			1.17853
$767$	1463.30			1.90782
$768$		−	56.5860i		−	0.0736797i
$769$	320.091			0.416244			0.208122	−	0.978103i	$-0.433265\pi$
$769$	320.091			0.416244			0.208122	+	0.978103i	$0.433265\pi$
$770$		0			0
$771$	286.563			0.371677
$772$			199.597i			0.258545i
$773$		−	892.160i		−	1.15415i	−0.816690	−	0.577076i	$-0.804194\pi$
$773$		−	892.160i		−	1.15415i	0.816690	−	0.577076i	$-0.195806\pi$
$774$			199.987i			0.258381i
$775$		0			0
$776$	−8.73385			−0.0112550
$777$	−3.82067			−0.00491721
$778$		−	247.613i		−	0.318269i
$779$	−362.214	−	277.305i	−0.464974	−	0.355976i
$780$		0			0
$781$		−	1487.09i		−	1.90408i
$782$		−	772.801i		−	0.988237i
$783$	105.870			0.135210
$784$	−195.914			−0.249891
$785$		0			0
$786$	710.107			0.903444
$787$		−	1088.23i		−	1.38276i	−0.722493	−	0.691378i	$-0.757004\pi$
$787$		−	1088.23i		−	1.38276i	0.722493	−	0.691378i	$-0.242996\pi$
$788$	−666.249			−0.845494
$789$			995.465i			1.26168i
$790$		0			0
$791$		−	25.0297i		−	0.0316431i
$792$		−	157.710i		−	0.199129i
$793$			259.388i			0.327098i
$794$		−	1025.36i		−	1.29139i
$795$		0			0
$796$	−160.286			−0.201365
$797$		−	1371.00i		−	1.72020i	−0.510123	−	0.860102i	$-0.670400\pi$
$797$		−	1371.00i		−	1.72020i	0.510123	−	0.860102i	$-0.329600\pi$
$798$	8.46074	−	11.0514i	0.0106024	−	0.0138488i
$799$	2322.87			2.90722
$800$		0			0
$801$		−	84.6349i		−	0.105662i
$802$	−801.840			−0.999801
$803$	70.8820			0.0882714
$804$	−710.544			−0.883762
$805$		0			0
$806$			219.120i			0.271860i
$807$	−1388.88			−1.72104
$808$			291.495i			0.360761i
$809$	−580.084			−0.717038			−0.358519	−	0.933522i	$-0.616718\pi$
$809$	−580.084			−0.717038			−0.358519	+	0.933522i	$0.616718\pi$
$810$		0			0
$811$		−	1339.70i		−	1.65191i	−0.563738	−	0.825954i	$-0.690637\pi$
$811$		−	1339.70i		−	1.65191i	0.563738	−	0.825954i	$-0.309363\pi$
$812$			1.59657i			0.00196621i
$813$		−	1541.48i		−	1.89604i
$814$	165.816			0.203706
$815$		0			0
$816$			383.350i			0.469792i
$817$	465.627	−	608.199i	0.569923	−	0.744430i
$818$	306.033			0.374124
$819$		−	8.69563i		−	0.0106174i
$820$		0			0
$821$	1526.64			1.85949			0.929747	−	0.368199i	$-0.120025\pi$
$821$	1526.64			1.85949			0.929747	+	0.368199i	$0.120025\pi$
$822$	481.941			0.586302
$823$	−238.601			−0.289916			−0.144958	−	0.989438i	$-0.546305\pi$
$823$	−238.601			−0.289916			−0.144958	+	0.989438i	$0.546305\pi$
$824$	358.122			0.434614
$825$		0			0
$826$	−17.9071			−0.0216793
$827$		−	1190.01i		−	1.43895i	−0.694521	−	0.719473i	$-0.744383\pi$
$827$		−	1190.01i		−	1.43895i	0.694521	−	0.719473i	$-0.255617\pi$
$828$	−141.470			−0.170857
$829$		−	1208.18i		−	1.45739i	−0.684838	−	0.728696i	$-0.740127\pi$
$829$		−	1208.18i		−	1.45739i	0.684838	−	0.728696i	$-0.259873\pi$
$830$		0			0
$831$		−	1085.49i		−	1.30625i
$832$			135.406i			0.162748i
$833$	1327.25			1.59334
$834$	913.150			1.09490
$835$		0			0
$836$	−367.195	+	479.628i	−0.439228	+	0.573718i
$837$	−177.811			−0.212439
$838$		−	685.771i		−	0.818343i
$839$			360.467i			0.429639i	0.976654	+	0.214819i	$0.0689163\pi$
$839$			360.467i			0.429639i	−0.976654	+	0.214819i	$0.931084\pi$
$840$		0			0
$841$	811.293			0.964676
$842$	584.444			0.694114
$843$	−559.879			−0.664151
$844$			145.241i			0.172087i
$845$		0			0
$846$		−	425.226i		−	0.502632i
$847$	−19.2867			−0.0227706
$848$		−	236.165i		−	0.278497i
$849$		−	386.873i		−	0.455681i
$850$		0			0
$851$		−	148.741i		−	0.174784i
$852$	661.710			0.776655
$853$	−625.741			−0.733577			−0.366788	−	0.930304i	$-0.619543\pi$
$853$	−625.741			−0.733577			−0.366788	+	0.930304i	$0.619543\pi$
$854$		−	3.17427i		−	0.00371694i
$855$		0			0
$856$	−62.4825			−0.0729935
$857$			1576.70i			1.83979i	0.392167	+	0.919894i	$0.371726\pi$
$857$			1576.70i			1.83979i	−0.392167	+	0.919894i	$0.628274\pi$
$858$			1345.68i			1.56839i
$859$	954.288			1.11093			0.555464	−	0.831540i	$-0.312540\pi$
$859$	954.288			1.11093			0.555464	+	0.831540i	$0.312540\pi$
$860$		0			0
$861$	12.4364			0.0144441
$862$	−637.353			−0.739389
$863$			363.759i			0.421505i	0.977539	+	0.210752i	$0.0675914\pi$
$863$			363.759i			0.421505i	−0.977539	+	0.210752i	$0.932409\pi$
$864$	−109.879			−0.127175
$865$		0			0
$866$	3.53741			0.00408477
$867$		−	1574.98i		−	1.81658i
$868$		−	2.68148i		−	0.00308926i
$869$			242.441i			0.278988i
$870$		0			0
$871$	1700.28			1.95210
$872$	257.742			0.295576
$873$		−	10.8315i		−	0.0124072i
$874$	430.237	+	329.382i	0.492261	+	0.376867i
$875$		0			0
$876$			31.5404i			0.0360050i
$877$			1186.98i			1.35346i	0.736231	+	0.676730i	$0.236604\pi$
$877$			1186.98i			1.35346i	−0.736231	+	0.676730i	$0.763396\pi$
$878$	−694.594			−0.791110
$879$	1175.75			1.33760
$880$		0			0
$881$	316.952			0.359764			0.179882	−	0.983688i	$-0.442428\pi$
$881$	316.952			0.359764			0.179882	+	0.983688i	$0.442428\pi$
$882$		−	242.967i		−	0.275473i
$883$	−846.927			−0.959148			−0.479574	−	0.877502i	$-0.659209\pi$
$883$	−846.927			−0.959148			−0.479574	+	0.877502i	$0.659209\pi$
$884$		−	917.328i		−	1.03770i
$885$		0			0
$886$		−	337.849i		−	0.381319i
$887$			443.640i			0.500157i	0.968226	+	0.250079i	$0.0804565\pi$
$887$			443.640i			0.500157i	−0.968226	+	0.250079i	$0.919544\pi$
$888$			73.7834i			0.0830894i
$889$			9.38671i			0.0105587i
$890$		0			0
$891$	−1593.82			−1.78880
$892$			647.586i			0.725993i
$893$	−990.048	+	1293.20i	−1.10868	+	1.44815i
$894$	77.2329			0.0863903
$895$		0			0
$896$		−	1.65703i		−	0.00184937i
$897$	1207.10			1.34571
$898$	640.262			0.712986
$899$	49.8941			0.0554995
$900$		0			0
$901$			1599.94i			1.77573i
$902$	−539.738			−0.598379
$903$			20.8822i			0.0231253i
$904$	−483.364			−0.534694
$905$		0			0
$906$		−	926.066i		−	1.02215i
$907$			5.46337i			0.00602356i	0.999995	+	0.00301178i	$0.000958681\pi$
$907$			5.46337i			0.00602356i	−0.999995	+	0.00301178i	$0.999041\pi$
$908$			867.137i			0.954996i
$909$	−361.504			−0.397694
$910$		0			0
$911$		−	1403.59i		−	1.54071i	−0.637614	−	0.770356i	$-0.720078\pi$
$911$		−	1403.59i		−	1.54071i	0.637614	−	0.770356i	$-0.279922\pi$
$912$	−213.420	−	163.391i	−0.234013	−	0.179157i
$913$	2305.36			2.52504
$914$			986.773i			1.07962i
$915$		0			0
$916$	−413.988			−0.451952
$917$	20.7943			0.0226765
$918$	744.393			0.810885
$919$	−357.449			−0.388954			−0.194477	−	0.980907i	$-0.562301\pi$
$919$	−357.449			−0.388954			−0.194477	+	0.980907i	$0.562301\pi$
$920$		0			0
$921$	−1659.73			−1.80209
$922$		−	594.453i		−	0.644743i
$923$	−1583.42			−1.71552
$924$		−	16.4677i		−	0.0178222i
$925$		0			0
$926$		−	679.643i		−	0.733956i
$927$			444.133i			0.479108i
$928$	30.8323			0.0332245
$929$	−261.924			−0.281942			−0.140971	−	0.990014i	$-0.545022\pi$
$929$	−261.924			−0.281942			−0.140971	+	0.990014i	$0.545022\pi$
$930$		0			0
$931$	−565.697	+	738.911i	−0.607623	+	0.793674i
$932$	581.672			0.624112
$933$		−	177.019i		−	0.189731i
$934$		−	790.948i		−	0.846839i
$935$		0			0
$936$	−167.927			−0.179409
$937$	−1286.88			−1.37340			−0.686700	−	0.726941i	$-0.740941\pi$
$937$	−1286.88			−1.37340			−0.686700	+	0.726941i	$0.740941\pi$
$938$	−20.8072			−0.0221825
$939$		−	758.592i		−	0.807872i
$940$		0			0
$941$			1118.46i			1.18858i	0.804249	+	0.594292i	$0.202568\pi$
$941$			1118.46i			1.18858i	−0.804249	+	0.594292i	$0.797432\pi$
$942$	−146.142			−0.155140
$943$			484.157i			0.513422i
$944$			345.816i			0.366331i
$945$		0			0
$946$		−	906.282i		−	0.958015i
$947$	1040.70			1.09895			0.549473	−	0.835512i	$-0.314829\pi$
$947$	1040.70			1.09895			0.549473	+	0.835512i	$0.314829\pi$
$948$	−107.879			−0.113796
$949$		−	75.4737i		−	0.0795297i
$950$		0			0
$951$	−421.928			−0.443667
$952$			11.2258i			0.0117918i
$953$		−	158.536i		−	0.166354i	−0.996535	−	0.0831771i	$-0.973493\pi$
$953$		−	158.536i		−	0.166354i	0.996535	−	0.0831771i	$-0.0265067\pi$
$954$	292.886			0.307008
$955$		0			0
$956$	180.142			0.188433
$957$	306.414			0.320182
$958$		−	348.856i		−	0.364150i
$959$	14.1129			0.0147162
$960$		0			0
$961$	877.202			0.912801
$962$		−	176.558i		−	0.183532i
$963$		−	77.4890i		−	0.0804663i
$964$		−	171.242i		−	0.177637i
$965$		0			0
$966$	−14.7719			−0.0152918
$967$	−462.170			−0.477942			−0.238971	−	0.971027i	$-0.576810\pi$
$967$	−462.170			−0.477942			−0.238971	+	0.971027i	$0.576810\pi$
$968$			372.457i			0.384770i
$969$	1445.85	+	1106.91i	1.49210	+	1.14233i
$970$		0			0
$971$			1501.52i			1.54636i	0.634184	+	0.773182i	$0.281336\pi$
$971$			1501.52i			1.54636i	−0.634184	+	0.773182i	$0.718664\pi$
$972$		−	359.569i		−	0.369927i
$973$	26.7401			0.0274822
$974$	−592.279			−0.608089
$975$		0			0
$976$	−61.3003			−0.0628077
$977$		−	1097.99i		−	1.12384i	−0.827191	−	0.561921i	$-0.810063\pi$
$977$		−	1097.99i		−	1.12384i	0.827191	−	0.561921i	$-0.189937\pi$
$978$	470.898			0.481491
$979$			383.540i			0.391767i
$980$		0			0
$981$			319.645i			0.325835i
$982$			727.835i			0.741176i
$983$		−	938.538i		−	0.954769i	−0.878694	−	0.477385i	$-0.841585\pi$
$983$		−	938.538i		−	0.954769i	0.878694	−	0.477385i	$-0.158415\pi$
$984$		−	240.167i		−	0.244073i
$985$		0			0
$986$	−208.878			−0.211844
$987$		−	44.4011i		−	0.0449859i
$988$	510.698	+	390.982i	0.516901	+	0.395730i
$989$	−812.955			−0.821997
$990$		0			0
$991$			540.016i			0.544920i	0.962167	+	0.272460i	$0.0878372\pi$
$991$			540.016i			0.544920i	−0.962167	+	0.272460i	$0.912163\pi$
$992$	−51.7837			−0.0522013
$993$	−1676.91			−1.68873
$994$	19.3771			0.0194941
$995$		0			0
$996$			1025.82i			1.02994i
$997$	−406.644			−0.407868			−0.203934	−	0.978985i	$-0.565373\pi$
$997$	−406.644			−0.407868			−0.203934	+	0.978985i	$0.565373\pi$
$998$			215.964i			0.216396i
$999$	143.273			0.143417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.3.c.c.151.2	yes	12
5.2	odd	4		950.3.d.b.949.20		24
5.3	odd	4		950.3.d.b.949.5		24
5.4	even	2		950.3.c.b.151.11	yes	12
19.18	odd	2	inner	950.3.c.c.151.11	yes	12
95.18	even	4		950.3.d.b.949.17		24
95.37	even	4		950.3.d.b.949.8		24
95.94	odd	2		950.3.c.b.151.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.3.c.b.151.2	✓	12	95.94	odd	2
950.3.c.b.151.11	yes	12	5.4	even	2
950.3.c.c.151.2	yes	12	1.1	even	1	trivial
950.3.c.c.151.11	yes	12	19.18	odd	2	inner
950.3.d.b.949.5		24	5.3	odd	4
950.3.d.b.949.8		24	95.37	even	4
950.3.d.b.949.17		24	95.18	even	4
950.3.d.b.949.20		24	5.2	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	950.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} -0.146462 q^{7} +2.82843i q^{8} -3.50774 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} -0.146462 q^{7} +2.82843i q^{8} -3.50774 q^{9} +15.8960 q^{11} +7.07326i q^{12} -16.9258i q^{13} +0.207129i q^{14} +4.00000 q^{16} -27.0986 q^{17} +4.96069i q^{18} +(11.5499 - 15.0864i) q^{19} +0.517983i q^{21} -22.4804i q^{22} -20.1654 q^{23} +10.0031 q^{24} -23.9366 q^{26} -19.4241i q^{27} +0.292925 q^{28} +5.45043i q^{29} -9.15415i q^{31} -5.65685i q^{32} -56.2183i q^{33} +38.3232i q^{34} +7.01547 q^{36} +7.37605i q^{37} +(-21.3354 - 16.3340i) q^{38} -59.8601 q^{39} -24.0093i q^{41} +0.732538 q^{42} +40.3144 q^{43} -31.7920 q^{44} +28.5181i q^{46} -85.7192 q^{47} -14.1465i q^{48} -48.9785 q^{49} +95.8376i q^{51} +33.8515i q^{52} -59.0413i q^{53} -27.4698 q^{54} -0.414258i q^{56} +(-53.3550 - 40.8477i) q^{57} +7.70807 q^{58} +86.4540i q^{59} -15.3251 q^{61} -12.9459 q^{62} +0.513751 q^{63} -8.00000 q^{64} -79.5047 q^{66} +100.455i q^{67} +54.1971 q^{68} +71.3174i q^{69} -93.5509i q^{71} -9.92138i q^{72} +4.45910 q^{73} +10.4313 q^{74} +(-23.0998 + 30.1728i) q^{76} -2.32817 q^{77} +84.6550i q^{78} +15.2517i q^{79} -100.265 q^{81} -33.9543 q^{82} +145.028 q^{83} -1.03597i q^{84} -57.0132i q^{86} +19.2761 q^{87} +44.9607i q^{88} +24.1281i q^{89} +2.47899i q^{91} +40.3308 q^{92} -32.3748 q^{93} +121.225i q^{94} -20.0062 q^{96} +3.08788i q^{97} +69.2661i q^{98} -55.7591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{4} - 8 q^{6} + 24 q^{7} - 28 q^{9}+O(q^{10}) \) 12 * q - 24 * q^4 - 8 * q^6 + 24 * q^7 - 28 * q^9	\( 12 q - 24 q^{4} - 8 q^{6} + 24 q^{7} - 28 q^{9} + 4 q^{11} + 48 q^{16} - 12 q^{19} - 32 q^{23} + 16 q^{24} - 16 q^{26} - 48 q^{28} + 56 q^{36} + 8 q^{38} + 100 q^{39} - 72 q^{42} - 188 q^{43} - 8 q^{44} - 180 q^{47} - 108 q^{49} + 112 q^{54} + 92 q^{57} + 120 q^{58} - 76 q^{61} - 64 q^{62} - 84 q^{63} - 96 q^{64} + 8 q^{66} - 124 q^{73} + 72 q^{74} + 24 q^{76} + 184 q^{77} - 132 q^{81} + 96 q^{82} + 500 q^{83} + 432 q^{87} + 64 q^{92} + 452 q^{93} - 32 q^{96} + 128 q^{99}+O(q^{100}) \) 12 * q - 24 * q^4 - 8 * q^6 + 24 * q^7 - 28 * q^9 + 4 * q^11 + 48 * q^16 - 12 * q^19 - 32 * q^23 + 16 * q^24 - 16 * q^26 - 48 * q^28 + 56 * q^36 + 8 * q^38 + 100 * q^39 - 72 * q^42 - 188 * q^43 - 8 * q^44 - 180 * q^47 - 108 * q^49 + 112 * q^54 + 92 * q^57 + 120 * q^58 - 76 * q^61 - 64 * q^62 - 84 * q^63 - 96 * q^64 + 8 * q^66 - 124 * q^73 + 72 * q^74 + 24 * q^76 + 184 * q^77 - 132 * q^81 + 96 * q^82 + 500 * q^83 + 432 * q^87 + 64 * q^92 + 452 * q^93 - 32 * q^96 + 128 * q^99

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