LMFDB - Embedded newform 950.3.c.b.151.11

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} +0.146462 q^{7} -2.82843i q^{8} -3.50774 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +3.53663i q^{3} -2.00000 q^{4} -5.00155 q^{6} +0.146462 q^{7} -2.82843i q^{8} -3.50774 q^{9} +15.8960 q^{11} -7.07326i q^{12} +16.9258i q^{13} +0.207129i q^{14} +4.00000 q^{16} +27.0986 q^{17} -4.96069i q^{18} +(11.5499 - 15.0864i) q^{19} +0.517983i q^{21} +22.4804i q^{22} +20.1654 q^{23} +10.0031 q^{24} -23.9366 q^{26} +19.4241i q^{27} -0.292925 q^{28} +5.45043i q^{29} -9.15415i q^{31} +5.65685i q^{32} +56.2183i q^{33} +38.3232i q^{34} +7.01547 q^{36} -7.37605i q^{37} +(21.3354 + 16.3340i) q^{38} -59.8601 q^{39} -24.0093i q^{41} -0.732538 q^{42} -40.3144 q^{43} -31.7920 q^{44} +28.5181i q^{46} +85.7192 q^{47} +14.1465i q^{48} -48.9785 q^{49} +95.8376i q^{51} -33.8515i q^{52} +59.0413i q^{53} -27.4698 q^{54} -0.414258i q^{56} +(53.3550 + 40.8477i) q^{57} -7.70807 q^{58} +86.4540i q^{59} -15.3251 q^{61} +12.9459 q^{62} -0.513751 q^{63} -8.00000 q^{64} -79.5047 q^{66} -100.455i q^{67} -54.1971 q^{68} +71.3174i q^{69} -93.5509i q^{71} +9.92138i q^{72} -4.45910 q^{73} +10.4313 q^{74} +(-23.0998 + 30.1728i) q^{76} +2.32817 q^{77} -84.6550i q^{78} +15.2517i q^{79} -100.265 q^{81} +33.9543 q^{82} -145.028 q^{83} -1.03597i q^{84} -57.0132i q^{86} -19.2761 q^{87} -44.9607i q^{88} +24.1281i q^{89} +2.47899i q^{91} -40.3308 q^{92} +32.3748 q^{93} +121.225i q^{94} -20.0062 q^{96} -3.08788i q^{97} -69.2661i q^{98} -55.7591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.200651\pi$
$3$			3.53663i			1.17888i	−0.807814	+	0.589438i	$0.799349\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−5.00155			−0.833591
$7$	0.146462			0.0209232			0.0104616	−	0.999945i	$-0.496670\pi$
$7$	0.146462			0.0209232			0.0104616	+	0.999945i	$0.496670\pi$
$8$		−	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	$0.225646\pi$
$13$			16.9258i			1.30198i	−0.759086	+	0.650991i	$0.774354\pi$
$14$			0.207129i			0.0147949i
$15$		0			0
$16$	4.00000			0.250000
$17$	27.0986			1.59403			0.797017	−	0.603957i	$-0.206410\pi$
$17$	27.0986			1.59403			0.797017	+	0.603957i	$0.206410\pi$
$18$		−	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	$-0.355553\pi$
$23$	20.1654			0.876755			0.438378	+	0.898791i	$0.355553\pi$
$24$	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	$-0.968219\pi$
$37$		−	7.37605i		−	0.199353i	0.995020	−	0.0996764i	$-0.0317808\pi$
$38$	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	$-0.655303\pi$
$43$	−40.3144			−0.937544			−0.468772	+	0.883319i	$0.655303\pi$
$44$	−31.7920			−0.722546
$45$		0			0
$46$			28.5181i			0.619960i
$47$	85.7192			1.82381			0.911906	−	0.410398i	$-0.134610\pi$
$47$	85.7192			1.82381			0.911906	+	0.410398i	$0.134610\pi$
$48$			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	$0.188045\pi$
$53$			59.0413i			1.11399i	−0.830517	+	0.556994i	$0.811955\pi$
$54$	−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	$-0.730215\pi$
$67$		−	100.455i		−	1.49933i	0.661818	−	0.749665i	$-0.269785\pi$
$68$	−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	$-0.509723\pi$
$73$	−4.45910			−0.0610836			−0.0305418	+	0.999533i	$0.509723\pi$
$74$	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	$-0.838261\pi$
$83$	−145.028			−1.74732			−0.873661	+	0.486535i	$0.838261\pi$
$84$		−	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	$-0.994933\pi$
$97$		−	3.08788i		−	0.0318338i	0.999873	−	0.0159169i	$-0.00506673\pi$
$98$		−	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	$0.210698\pi$
$103$			126.615i			1.22927i	−0.788810	+	0.614637i	$0.789302\pi$
$104$	47.8733			0.460320
$105$		0			0
$106$	−83.4970			−0.787708
$107$		−	22.0909i		−	0.206457i	−0.994658	−	0.103228i	$-0.967083\pi$
$107$		−	22.0909i		−	0.206457i	0.994658	−	0.103228i	$-0.0329173\pi$
$108$		−	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	$-0.727067\pi$
$113$		−	170.895i		−	1.51234i	0.654373	−	0.756172i	$-0.272933\pi$
$114$	−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	$0.0811940\pi$
$127$			64.0896i			0.504643i	−0.967644	+	0.252321i	$0.918806\pi$
$128$		−	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	$-0.385613\pi$
$137$	96.3583			0.703345			0.351673	+	0.936123i	$0.385613\pi$
$138$	−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	$-0.529663\pi$
$157$	−29.2193			−0.186110			−0.0930552	+	0.995661i	$0.529663\pi$
$158$	−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	$-0.406742\pi$
$163$	94.1505			0.577611			0.288805	+	0.957388i	$0.406742\pi$
$164$			48.0186i			0.292797i
$165$		0			0
$166$		−	205.100i		−	1.23554i
$167$			56.3258i			0.337280i	0.985678	+	0.168640i	$0.0539376\pi$
$167$			56.3258i			0.337280i	−0.985678	+	0.168640i	$0.946062\pi$
$168$	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	$-0.958076\pi$
$173$		−	45.4392i		−	0.262654i	0.991339	−	0.131327i	$-0.0419238\pi$
$174$		−	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	$0.0832429\pi$
$193$			99.7983i			0.517089i	−0.965999	+	0.258545i	$0.916757\pi$
$194$	4.36693			0.0225099
$195$		0			0
$196$	97.9571			0.499781
$197$	−333.125			−1.69099			−0.845494	−	0.533985i	$-0.820694\pi$
$197$	−333.125			−1.69099			−0.845494	+	0.533985i	$0.820694\pi$
$198$		−	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	$0.258620\pi$
$223$			323.793i			1.45199i	−0.687702	+	0.725993i	$0.741380\pi$
$224$			0.828516i			0.00369873i
$225$		0			0
$226$	241.682			1.06939
$227$			433.568i			1.90999i	0.296618	+	0.954996i	$0.404141\pi$
$227$			433.568i			1.90999i	−0.296618	+	0.954996i	$0.595859\pi$
$228$	−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	$-0.285461\pi$
$233$	290.836			1.24822			0.624112	+	0.781335i	$0.285461\pi$
$234$	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	$-0.949611\pi$
$257$		−	81.0271i		−	0.315281i	0.987497	−	0.157640i	$-0.0503886\pi$
$258$	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	$-0.320267\pi$
$263$	281.473			1.07024			0.535120	+	0.844776i	$0.320267\pi$
$264$	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	$-0.686908\pi$
$277$	−306.929			−1.10805			−0.554024	+	0.832501i	$0.686908\pi$
$278$		−	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	$-0.561909\pi$
$283$	−109.390			−0.386539			−0.193269	+	0.981146i	$0.561909\pi$
$284$			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	$-0.807980\pi$
$293$		−	332.451i		−	1.13464i	0.823496	−	0.567322i	$-0.192020\pi$
$294$	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	$0.276928\pi$
$307$			469.296i			1.52865i	−0.644830	+	0.764326i	$0.723072\pi$
$308$	−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	$-0.611323\pi$
$313$	−214.496			−0.685290			−0.342645	+	0.939465i	$0.611323\pi$
$314$		−	41.3224i		−	0.131600i
$315$		0			0
$316$		−	30.5033i		−	0.0965295i
$317$			119.302i			0.376348i	0.982136	+	0.188174i	$0.0602568\pi$
$317$			119.302i			0.376348i	−0.982136	+	0.188174i	$0.939743\pi$
$318$		−	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	$-0.885428\pi$
$337$		−	237.394i		−	0.704433i	0.935919	−	0.352216i	$-0.114572\pi$
$338$		−	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	$-0.844100\pi$
$347$	−612.413			−1.76488			−0.882440	+	0.470426i	$0.844100\pi$
$348$	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	$-0.600054\pi$
$353$	−218.281			−0.618359			−0.309179	+	0.951004i	$0.600054\pi$
$354$		−	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	$-0.195335\pi$
$367$	600.077			1.63509			0.817543	+	0.575867i	$0.195335\pi$
$368$	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	$-0.973983\pi$
$373$		−	60.9072i		−	0.163290i	0.996661	−	0.0816451i	$-0.0260174\pi$
$374$			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	$-0.686422\pi$
$383$		−	638.343i		−	1.66669i	0.552752	−	0.833346i	$-0.313578\pi$
$384$	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	$-0.866358\pi$
$397$	−725.042			−1.82630			−0.913151	+	0.407622i	$0.866358\pi$
$398$			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	$-0.999081\pi$
$433$		−	2.50133i		−	0.00577673i	0.999996	−	0.00288837i	$-0.000919397\pi$
$434$	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	$-0.586903\pi$
$443$	−238.895			−0.539267			−0.269634	+	0.962963i	$0.586903\pi$
$444$	−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	$-0.223525\pi$
$457$	697.754			1.52681			0.763407	+	0.645918i	$0.223525\pi$
$458$			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	$-0.673690\pi$
$463$	−480.580			−1.03797			−0.518985	+	0.854783i	$0.673690\pi$
$464$			21.8017i			0.0469865i
$465$		0			0
$466$			411.304i			0.882627i
$467$	−559.285			−1.19761			−0.598806	−	0.800894i	$-0.704358\pi$
$467$	−559.285			−1.19761			−0.598806	+	0.800894i	$0.704358\pi$
$468$			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	$0.141481\pi$
$487$			418.804i			0.859968i	−0.902837	+	0.429984i	$0.858519\pi$
$488$			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	$-0.555174\pi$
$503$	−173.503			−0.344937			−0.172469	+	0.985015i	$0.555174\pi$
$504$			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	$-0.982842\pi$
$523$		−	56.3564i		−	0.107756i	0.998548	−	0.0538780i	$-0.0171582\pi$
$524$	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	$0.0509587\pi$
$547$			174.393i			0.318817i	−0.987213	+	0.159408i	$0.949041\pi$
$548$	−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	$-0.538426\pi$
$557$	−134.156			−0.240854			−0.120427	+	0.992722i	$0.538426\pi$
$558$	−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	$-0.949380\pi$
$563$		−	178.310i		−	0.316715i	0.987382	−	0.158357i	$-0.0506198\pi$
$564$		−	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	$-0.947403\pi$
$577$	−1138.28			−1.97276			−0.986379	+	0.164488i	$0.947403\pi$
$578$			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	$-0.527965\pi$
$587$	−103.008			−0.175482			−0.0877410	+	0.996143i	$0.527965\pi$
$588$			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	$-0.403426\pi$
$593$	354.332			0.597525			0.298763	+	0.954327i	$0.403426\pi$
$594$	−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	$-0.791265\pi$
$607$		−	740.250i		−	1.21952i	0.792585	−	0.609762i	$-0.208735\pi$
$608$	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	$-0.712366\pi$
$613$	−758.605			−1.23753			−0.618764	+	0.785577i	$0.712366\pi$
$614$	−663.685			−1.08092
$615$		0			0
$616$		−	6.58505i		−	0.0106900i
$617$	−617.701			−1.00114			−0.500568	−	0.865697i	$-0.666875\pi$
$617$	−617.701			−1.00114			−0.500568	+	0.865697i	$0.666875\pi$
$618$		−	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	$-0.270912\pi$
$643$	847.680			1.31832			0.659160	+	0.752003i	$0.270912\pi$
$644$	−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	$-0.308817\pi$
$647$	731.308			1.13031			0.565153	+	0.824986i	$0.308817\pi$
$648$			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	$-0.824094\pi$
$653$	−1111.60			−1.70230			−0.851150	+	0.524922i	$0.824094\pi$
$654$			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	$-0.935706\pi$
$673$		−	270.027i		−	0.401228i	0.979670	−	0.200614i	$-0.0642938\pi$
$674$	335.726			0.498109
$675$		0			0
$676$	234.963			0.347578
$677$		−	826.165i		−	1.22033i	−0.792274	−	0.610166i	$-0.791103\pi$
$677$		−	826.165i		−	1.22033i	0.792274	−	0.610166i	$-0.208897\pi$
$678$			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	$-0.781524\pi$
$683$		−	865.671i		−	1.26745i	0.773557	−	0.633727i	$-0.218476\pi$
$684$	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	$-0.417883\pi$
$727$	370.952			0.510250			0.255125	+	0.966908i	$0.417883\pi$
$728$	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	$-0.678208\pi$
$733$	−778.543			−1.06213			−0.531066	+	0.847331i	$0.678208\pi$
$734$			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	$-0.780617\pi$
$743$		−	944.989i		−	1.27186i	0.771748	−	0.635928i	$-0.219383\pi$
$744$		−	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	$-0.486150\pi$
$757$	65.8572			0.0869977			0.0434988	+	0.999053i	$0.486150\pi$
$758$	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	$0.195806\pi$
$773$			892.160i			1.15415i	−0.816690	+	0.577076i	$0.804194\pi$
$774$			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	$0.242996\pi$
$787$			1088.23i			1.38276i	−0.722493	+	0.691378i	$0.757004\pi$
$788$	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	$0.329600\pi$
$797$			1371.00i			1.72020i	−0.510123	+	0.860102i	$0.670400\pi$
$798$	−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	$-0.453695\pi$
$823$	238.601			0.289916			0.144958	+	0.989438i	$0.453695\pi$
$824$	358.122			0.434614
$825$		0			0
$826$	−17.9071			−0.0216793
$827$			1190.01i			1.43895i	0.694521	+	0.719473i	$0.255617\pi$
$827$			1190.01i			1.43895i	−0.694521	+	0.719473i	$0.744383\pi$
$828$	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	$-0.380457\pi$
$853$	625.741			0.733577			0.366788	+	0.930304i	$0.380457\pi$
$854$		−	3.17427i		−	0.00371694i
$855$		0			0
$856$	−62.4825			−0.0729935
$857$		−	1576.70i		−	1.83979i	−0.392167	−	0.919894i	$-0.628274\pi$
$857$		−	1576.70i		−	1.83979i	0.392167	−	0.919894i	$-0.371726\pi$
$858$		−	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	$-0.932409\pi$
$863$		−	363.759i		−	0.421505i	0.977539	−	0.210752i	$-0.0675914\pi$
$864$	−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	$-0.763396\pi$
$877$		−	1186.98i		−	1.35346i	0.736231	−	0.676730i	$-0.236604\pi$
$878$	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	$-0.340791\pi$
$883$	846.927			0.959148			0.479574	+	0.877502i	$0.340791\pi$
$884$		−	917.328i		−	1.03770i
$885$		0			0
$886$		−	337.849i		−	0.381319i
$887$		−	443.640i		−	0.500157i	−0.968226	−	0.250079i	$-0.919544\pi$
$887$		−	443.640i		−	0.500157i	0.968226	−	0.250079i	$-0.0804565\pi$
$888$		−	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	$-0.999041\pi$
$907$		−	5.46337i		−	0.00602356i	0.999995	−	0.00301178i	$-0.000958681\pi$
$908$		−	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	$-0.259059\pi$
$937$	1286.88			1.37340			0.686700	+	0.726941i	$0.259059\pi$
$938$	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	$-0.685171\pi$
$947$	−1040.70			−1.09895			−0.549473	+	0.835512i	$0.685171\pi$
$948$	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	$0.0265067\pi$
$953$			158.536i			0.166354i	−0.996535	+	0.0831771i	$0.973493\pi$
$954$	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	$-0.423190\pi$
$967$	462.170			0.477942			0.238971	+	0.971027i	$0.423190\pi$
$968$		−	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	$0.189937\pi$
$977$			1097.99i			1.12384i	−0.827191	+	0.561921i	$0.810063\pi$
$978$	−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	$0.158415\pi$
$983$			938.538i			0.954769i	−0.878694	+	0.477385i	$0.841585\pi$
$984$		−	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	$-0.434627\pi$
$997$	406.644			0.407868			0.203934	+	0.978985i	$0.434627\pi$
$998$		−	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.b.151.11	yes	12
5.2	odd	4		950.3.d.b.949.5		24
5.3	odd	4		950.3.d.b.949.20		24
5.4	even	2		950.3.c.c.151.2	yes	12
19.18	odd	2	inner	950.3.c.b.151.2	✓	12
95.18	even	4		950.3.d.b.949.8		24
95.37	even	4		950.3.d.b.949.17		24
95.94	odd	2		950.3.c.c.151.11	yes	12

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