LMFDB - Embedded newform 1200.3.bg.e.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,3,Mod(193,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))

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

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

chi := DirichletCharacter("1200.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1200.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.6976317232$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1200.193
Dual form			1200.3.bg.e.1057.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +O(q^{10})$	$q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +1.55051 q^{11} +(-9.55051 - 9.55051i) q^{13} +(-11.1464 + 11.1464i) q^{17} -12.6969i q^{19} -1.34847 q^{21} +(-21.3485 - 21.3485i) q^{23} +(-3.67423 + 3.67423i) q^{27} -44.0454i q^{29} +44.4949 q^{31} +(1.89898 + 1.89898i) q^{33} +(-20.6515 + 20.6515i) q^{37} -23.3939i q^{39} -48.2929 q^{41} +(-36.2929 - 36.2929i) q^{43} +(42.5403 - 42.5403i) q^{47} +48.3939i q^{49} -27.3031 q^{51} +(54.4949 + 54.4949i) q^{53} +(15.5505 - 15.5505i) q^{57} -47.4393i q^{59} -59.8888 q^{61} +(-1.65153 - 1.65153i) q^{63} +(81.2827 - 81.2827i) q^{67} -52.2929i q^{69} -87.5959 q^{71} +(-75.9898 - 75.9898i) q^{73} +(-0.853572 + 0.853572i) q^{77} -97.3031i q^{79} -9.00000 q^{81} +(41.0556 + 41.0556i) q^{83} +(53.9444 - 53.9444i) q^{87} +52.2020i q^{89} +10.5153 q^{91} +(54.4949 + 54.4949i) q^{93} +(37.0000 - 37.0000i) q^{97} +4.65153i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{7}+O(q^{10}) $ 4 * q - 12 * q^7	$ 4 q - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{17} + 24 q^{21} - 56 q^{23} + 80 q^{31} - 12 q^{33} - 112 q^{37} - 56 q^{41} - 8 q^{43} - 16 q^{47} - 168 q^{51} + 120 q^{53} + 72 q^{57} - 24 q^{61} - 36 q^{63} - 8 q^{67} - 272 q^{71} - 108 q^{73} - 72 q^{77} - 36 q^{81} + 272 q^{83} + 108 q^{87} + 336 q^{91} + 120 q^{93} + 148 q^{97}+O(q^{100}) $ 4 * q - 12 * q^7 + 16 * q^11 - 48 * q^13 + 24 * q^17 + 24 * q^21 - 56 * q^23 + 80 * q^31 - 12 * q^33 - 112 * q^37 - 56 * q^41 - 8 * q^43 - 16 * q^47 - 168 * q^51 + 120 * q^53 + 72 * q^57 - 24 * q^61 - 36 * q^63 - 8 * q^67 - 272 * q^71 - 108 * q^73 - 72 * q^77 - 36 * q^81 + 272 * q^83 + 108 * q^87 + 336 * q^91 + 120 * q^93 + 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.550510	+	0.550510i	−0.0786443	+	0.0786443i	−0.745335	−	0.666690i	$-0.767710\pi$
$7$	−0.550510	+	0.550510i	−0.0786443	+	0.0786443i	0.666690	+	0.745335i	$0.267710\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	1.55051			0.140955			0.0704777	−	0.997513i	$-0.477548\pi$
$11$	1.55051			0.140955			0.0704777	+	0.997513i	$0.477548\pi$
$12$		0			0
$13$	−9.55051	−	9.55051i	−0.734655	−	0.734655i	0.236883	−	0.971538i	$-0.423874\pi$
$13$	−9.55051	−	9.55051i	−0.734655	−	0.734655i	−0.971538	+	0.236883i	$0.923874\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−11.1464	+	11.1464i	−0.655672	+	0.655672i	−0.954353	−	0.298681i	$-0.903453\pi$
$17$	−11.1464	+	11.1464i	−0.655672	+	0.655672i	0.298681	+	0.954353i	$0.403453\pi$
$18$		0			0
$19$		−	12.6969i		−	0.668260i	−0.942527	−	0.334130i	$-0.891558\pi$
$19$		−	12.6969i		−	0.668260i	0.942527	−	0.334130i	$-0.108442\pi$
$20$		0			0
$21$	−1.34847			−0.0642128
$22$		0			0
$23$	−21.3485	−	21.3485i	−0.928194	−	0.928194i	0.0693950	−	0.997589i	$-0.477893\pi$
$23$	−21.3485	−	21.3485i	−0.928194	−	0.928194i	−0.997589	+	0.0693950i	$0.977893\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	44.0454i		−	1.51881i	−0.650620	−	0.759404i	$-0.725491\pi$
$29$		−	44.0454i		−	1.51881i	0.650620	−	0.759404i	$-0.274509\pi$
$30$		0			0
$31$	44.4949			1.43532			0.717660	−	0.696394i	$-0.245213\pi$
$31$	44.4949			1.43532			0.717660	+	0.696394i	$0.245213\pi$
$32$		0			0
$33$	1.89898	+	1.89898i	0.0575448	+	0.0575448i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−20.6515	+	20.6515i	−0.558149	+	0.558149i	−0.928780	−	0.370631i	$-0.879142\pi$
$37$	−20.6515	+	20.6515i	−0.558149	+	0.558149i	0.370631	+	0.928780i	$0.379142\pi$
$38$		0			0
$39$		−	23.3939i		−	0.599843i
$40$		0			0
$41$	−48.2929			−1.17787			−0.588937	−	0.808179i	$-0.700454\pi$
$41$	−48.2929			−1.17787			−0.588937	+	0.808179i	$0.700454\pi$
$42$		0			0
$43$	−36.2929	−	36.2929i	−0.844020	−	0.844020i	0.145359	−	0.989379i	$-0.453566\pi$
$43$	−36.2929	−	36.2929i	−0.844020	−	0.844020i	−0.989379	+	0.145359i	$0.953566\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	42.5403	−	42.5403i	0.905113	−	0.905113i	−0.0907599	−	0.995873i	$-0.528930\pi$
$47$	42.5403	−	42.5403i	0.905113	−	0.905113i	0.995873	+	0.0907599i	$0.0289296\pi$
$48$		0			0
$49$			48.3939i			0.987630i
$50$		0			0
$51$	−27.3031			−0.535354
$52$		0			0
$53$	54.4949	+	54.4949i	1.02821	+	1.02821i	0.999591	+	0.0286151i	$0.00910972\pi$
$53$	54.4949	+	54.4949i	1.02821	+	1.02821i	0.0286151	+	0.999591i	$0.490890\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	15.5505	−	15.5505i	0.272816	−	0.272816i
$58$		0			0
$59$		−	47.4393i		−	0.804056i	−0.915627	−	0.402028i	$-0.868306\pi$
$59$		−	47.4393i		−	0.804056i	0.915627	−	0.402028i	$-0.131694\pi$
$60$		0			0
$61$	−59.8888			−0.981783			−0.490892	−	0.871221i	$-0.663329\pi$
$61$	−59.8888			−0.981783			−0.490892	+	0.871221i	$0.663329\pi$
$62$		0			0
$63$	−1.65153	−	1.65153i	−0.0262148	−	0.0262148i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	81.2827	−	81.2827i	1.21317	−	1.21317i	0.243197	−	0.969977i	$-0.421804\pi$
$67$	81.2827	−	81.2827i	1.21317	−	1.21317i	0.969977	−	0.243197i	$-0.0781961\pi$
$68$		0			0
$69$		−	52.2929i		−	0.757867i
$70$		0			0
$71$	−87.5959			−1.23375			−0.616873	−	0.787063i	$-0.711601\pi$
$71$	−87.5959			−1.23375			−0.616873	+	0.787063i	$0.711601\pi$
$72$		0			0
$73$	−75.9898	−	75.9898i	−1.04096	−	1.04096i	−0.999125	−	0.0418314i	$-0.986681\pi$
$73$	−75.9898	−	75.9898i	−1.04096	−	1.04096i	−0.0418314	−	0.999125i	$-0.513319\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.853572	+	0.853572i	−0.0110853	+	0.0110853i
$78$		0			0
$79$		−	97.3031i		−	1.23168i	−0.787870	−	0.615842i	$-0.788816\pi$
$79$		−	97.3031i		−	1.23168i	0.787870	−	0.615842i	$-0.211184\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	41.0556	+	41.0556i	0.494646	+	0.494646i	0.909766	−	0.415120i	$-0.136261\pi$
$83$	41.0556	+	41.0556i	0.494646	+	0.494646i	−0.415120	+	0.909766i	$0.636261\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	53.9444	−	53.9444i	0.620050	−	0.620050i
$88$		0			0
$89$			52.2020i			0.586540i	0.956030	+	0.293270i	$0.0947435\pi$
$89$			52.2020i			0.586540i	−0.956030	+	0.293270i	$0.905257\pi$
$90$		0			0
$91$	10.5153			0.115553
$92$		0			0
$93$	54.4949	+	54.4949i	0.585967	+	0.585967i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	37.0000	−	37.0000i	0.381443	−	0.381443i	−0.490179	−	0.871622i	$-0.663068\pi$
$97$	37.0000	−	37.0000i	0.381443	−	0.381443i	0.871622	+	0.490179i	$0.163068\pi$
$98$		0			0
$99$			4.65153i			0.0469852i
$100$		0			0
$101$	−18.3383			−0.181567			−0.0907835	−	0.995871i	$-0.528937\pi$
$101$	−18.3383			−0.181567			−0.0907835	+	0.995871i	$0.528937\pi$
$102$		0			0
$103$	−10.6413	−	10.6413i	−0.103314	−	0.103314i	0.653560	−	0.756874i	$-0.273275\pi$
$103$	−10.6413	−	10.6413i	−0.103314	−	0.103314i	−0.756874	+	0.653560i	$0.773275\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−66.9444	+	66.9444i	−0.625648	+	0.625648i	−0.946970	−	0.321322i	$-0.895873\pi$
$107$	−66.9444	+	66.9444i	−0.625648	+	0.625648i	0.321322	+	0.946970i	$0.395873\pi$
$108$		0			0
$109$		−	97.2827i		−	0.892501i	−0.894908	−	0.446251i	$-0.852759\pi$
$109$		−	97.2827i		−	0.892501i	0.894908	−	0.446251i	$-0.147241\pi$
$110$		0			0
$111$	−50.5857			−0.455727
$112$		0			0
$113$	−30.1362	−	30.1362i	−0.266692	−	0.266692i	0.561074	−	0.827766i	$-0.310388\pi$
$113$	−30.1362	−	30.1362i	−0.266692	−	0.266692i	−0.827766	+	0.561074i	$0.810388\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	28.6515	−	28.6515i	0.244885	−	0.244885i
$118$		0			0
$119$		−	12.2724i		−	0.103130i
$120$		0			0
$121$	−118.596			−0.980132
$122$		0			0
$123$	−59.1464	−	59.1464i	−0.480865	−	0.480865i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	66.0556	−	66.0556i	0.520123	−	0.520123i	−0.397486	−	0.917608i	$-0.630117\pi$
$127$	66.0556	−	66.0556i	0.520123	−	0.520123i	0.917608	+	0.397486i	$0.130117\pi$
$128$		0			0
$129$		−	88.8990i		−	0.689139i
$130$		0			0
$131$	−86.8536			−0.663004			−0.331502	−	0.943454i	$-0.607555\pi$
$131$	−86.8536			−0.663004			−0.331502	+	0.943454i	$0.607555\pi$
$132$		0			0
$133$	6.98979	+	6.98979i	0.0525548	+	0.0525548i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	71.5301	−	71.5301i	0.522118	−	0.522118i	−0.396093	−	0.918210i	$-0.629634\pi$
$137$	71.5301	−	71.5301i	0.522118	−	0.522118i	0.918210	+	0.396093i	$0.129634\pi$
$138$		0			0
$139$			23.2122i			0.166995i	0.996508	+	0.0834973i	$0.0266090\pi$
$139$			23.2122i			0.166995i	−0.996508	+	0.0834973i	$0.973391\pi$
$140$		0			0
$141$	104.202			0.739022
$142$		0			0
$143$	−14.8082	−	14.8082i	−0.103554	−	0.103554i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−59.2702	+	59.2702i	−0.403198	+	0.403198i
$148$		0			0
$149$		−	137.530i		−	0.923021i	−0.887135	−	0.461510i	$-0.847308\pi$
$149$		−	137.530i		−	0.923021i	0.887135	−	0.461510i	$-0.152692\pi$
$150$		0			0
$151$	291.394			1.92976			0.964880	−	0.262690i	$-0.0846095\pi$
$151$	291.394			1.92976			0.964880	+	0.262690i	$0.0846095\pi$
$152$		0			0
$153$	−33.4393	−	33.4393i	−0.218557	−	0.218557i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	52.6311	−	52.6311i	0.335230	−	0.335230i	−0.519339	−	0.854569i	$-0.673822\pi$
$157$	52.6311	−	52.6311i	0.335230	−	0.335230i	0.854569	+	0.519339i	$0.173822\pi$
$158$		0			0
$159$			133.485i			0.839526i
$160$		0			0
$161$	23.5051			0.145994
$162$		0			0
$163$	117.576	+	117.576i	0.721322	+	0.721322i	0.968875	−	0.247552i	$-0.0796262\pi$
$163$	117.576	+	117.576i	0.721322	+	0.721322i	−0.247552	+	0.968875i	$0.579626\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−146.338	+	146.338i	−0.876277	+	0.876277i	−0.993147	−	0.116870i	$-0.962714\pi$
$167$	−146.338	+	146.338i	−0.876277	+	0.876277i	0.116870	+	0.993147i	$0.462714\pi$
$168$		0			0
$169$			13.4245i			0.0794349i
$170$		0			0
$171$	38.0908			0.222753
$172$		0			0
$173$	−3.75255	−	3.75255i	−0.0216910	−	0.0216910i	0.696178	−	0.717869i	$-0.254882\pi$
$173$	−3.75255	−	3.75255i	−0.0216910	−	0.0216910i	−0.717869	+	0.696178i	$0.754882\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	58.1010	−	58.1010i	0.328254	−	0.328254i
$178$		0			0
$179$			77.2372i			0.431493i	0.976449	+	0.215746i	$0.0692185\pi$
$179$			77.2372i			0.431493i	−0.976449	+	0.215746i	$0.930782\pi$
$180$		0			0
$181$	160.656			0.887603			0.443801	−	0.896125i	$-0.353630\pi$
$181$	160.656			0.887603			0.443801	+	0.896125i	$0.353630\pi$
$182$		0			0
$183$	−73.3485	−	73.3485i	−0.400811	−	0.400811i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−17.2827	+	17.2827i	−0.0924206	+	0.0924206i
$188$		0			0
$189$		−	4.04541i		−	0.0214043i
$190$		0			0
$191$	−251.868			−1.31868			−0.659341	−	0.751844i	$-0.729165\pi$
$191$	−251.868			−1.31868			−0.659341	+	0.751844i	$0.729165\pi$
$192$		0			0
$193$	−173.384	−	173.384i	−0.898361	−	0.898361i	0.0969302	−	0.995291i	$-0.469098\pi$
$193$	−173.384	−	173.384i	−0.898361	−	0.898361i	−0.995291	+	0.0969302i	$0.969098\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.09082	−	2.09082i	0.0106133	−	0.0106133i	−0.701780	−	0.712394i	$-0.747611\pi$
$197$	2.09082	−	2.09082i	0.0106133	−	0.0106133i	0.712394	+	0.701780i	$0.247611\pi$
$198$		0			0
$199$		−	304.565i		−	1.53048i	−0.643746	−	0.765239i	$-0.722621\pi$
$199$		−	304.565i		−	1.53048i	0.643746	−	0.765239i	$-0.277379\pi$
$200$		0			0
$201$	199.101			0.990552
$202$		0			0
$203$	24.2474	+	24.2474i	0.119446	+	0.119446i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	64.0454	−	64.0454i	0.309398	−	0.309398i
$208$		0			0
$209$		−	19.6867i		−	0.0941949i
$210$		0			0
$211$	−273.151			−1.29455			−0.647277	−	0.762255i	$-0.724092\pi$
$211$	−273.151			−1.29455			−0.647277	+	0.762255i	$0.724092\pi$
$212$		0			0
$213$	−107.283	−	107.283i	−0.503674	−	0.503674i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−24.4949	+	24.4949i	−0.112880	+	0.112880i
$218$		0			0
$219$		−	186.136i		−	0.849937i
$220$		0			0
$221$	212.908			0.963385
$222$		0			0
$223$	174.662	+	174.662i	0.783236	+	0.783236i	0.980376	−	0.197139i	$-0.0631650\pi$
$223$	174.662	+	174.662i	0.783236	+	0.783236i	−0.197139	+	0.980376i	$0.563165\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−77.6163	+	77.6163i	−0.341922	+	0.341922i	−0.857090	−	0.515167i	$-0.827730\pi$
$227$	−77.6163	+	77.6163i	−0.341922	+	0.341922i	0.515167	+	0.857090i	$0.327730\pi$
$228$		0			0
$229$		−	8.96938i		−	0.0391676i	−0.999808	−	0.0195838i	$-0.993766\pi$
$229$		−	8.96938i		−	0.0391676i	0.999808	−	0.0195838i	$-0.00623412\pi$
$230$		0			0
$231$	−2.09082			−0.00905115
$232$		0			0
$233$	50.4699	+	50.4699i	0.216609	+	0.216609i	0.807068	−	0.590459i	$-0.201053\pi$
$233$	50.4699	+	50.4699i	0.216609	+	0.216609i	−0.590459	+	0.807068i	$0.701053\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	119.171	−	119.171i	0.502833	−	0.502833i
$238$		0			0
$239$			279.737i			1.17045i	0.810872	+	0.585223i	$0.198993\pi$
$239$			279.737i			1.17045i	−0.810872	+	0.585223i	$0.801007\pi$
$240$		0			0
$241$	−397.131			−1.64784			−0.823922	−	0.566703i	$-0.808219\pi$
$241$	−397.131			−1.64784			−0.823922	+	0.566703i	$0.808219\pi$
$242$		0			0
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−121.262	+	121.262i	−0.490940	+	0.490940i
$248$		0			0
$249$			100.565i			0.403877i
$250$		0			0
$251$	−53.8638			−0.214597			−0.107298	−	0.994227i	$-0.534220\pi$
$251$	−53.8638			−0.214597			−0.107298	+	0.994227i	$0.534220\pi$
$252$		0			0
$253$	−33.1010	−	33.1010i	−0.130834	−	0.130834i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−309.732	+	309.732i	−1.20518	+	1.20518i	−0.232614	+	0.972569i	$0.574728\pi$
$257$	−309.732	+	309.732i	−1.20518	+	1.20518i	−0.972569	+	0.232614i	$0.925272\pi$
$258$		0			0
$259$		−	22.7378i		−	0.0877906i
$260$		0			0
$261$	132.136			0.506269
$262$		0			0
$263$	−128.854	−	128.854i	−0.489938	−	0.489938i	0.418349	−	0.908286i	$-0.362609\pi$
$263$	−128.854	−	128.854i	−0.489938	−	0.489938i	−0.908286	+	0.418349i	$0.862609\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−63.9342	+	63.9342i	−0.239454	+	0.239454i
$268$		0			0
$269$			112.227i			0.417201i	0.978001	+	0.208600i	$0.0668908\pi$
$269$			112.227i			0.417201i	−0.978001	+	0.208600i	$0.933109\pi$
$270$		0			0
$271$	−167.616			−0.618510			−0.309255	−	0.950979i	$-0.600080\pi$
$271$	−167.616			−0.618510			−0.309255	+	0.950979i	$0.600080\pi$
$272$		0			0
$273$	12.8786	+	12.8786i	0.0471742	+	0.0471742i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	298.136	−	298.136i	1.07630	−	1.07630i	0.0794665	−	0.996838i	$-0.474678\pi$
$277$	298.136	−	298.136i	1.07630	−	1.07630i	0.996838	−	0.0794665i	$-0.0253217\pi$
$278$		0			0
$279$			133.485i			0.478440i
$280$		0			0
$281$	−336.434			−1.19727			−0.598636	−	0.801021i	$-0.704291\pi$
$281$	−336.434			−1.19727			−0.598636	+	0.801021i	$0.704291\pi$
$282$		0			0
$283$	20.1612	+	20.1612i	0.0712411	+	0.0712411i	0.741830	−	0.670588i	$-0.233958\pi$
$283$	20.1612	+	20.1612i	0.0712411	+	0.0712411i	−0.670588	+	0.741830i	$0.733958\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	26.5857	−	26.5857i	0.0926331	−	0.0926331i
$288$		0			0
$289$			40.5143i			0.140188i
$290$		0			0
$291$	90.6311			0.311447
$292$		0			0
$293$	246.586	+	246.586i	0.841589	+	0.841589i	0.989066	−	0.147476i	$-0.0471150\pi$
$293$	246.586	+	246.586i	0.841589	+	0.841589i	−0.147476	+	0.989066i	$0.547115\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.69694	+	5.69694i	−0.0191816	+	0.0191816i
$298$		0			0
$299$			407.778i			1.36380i
$300$		0			0
$301$	39.9592			0.132755
$302$		0			0
$303$	−22.4597	−	22.4597i	−0.0741244	−	0.0741244i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	365.373	−	365.373i	1.19014	−	1.19014i	0.213114	−	0.977027i	$-0.431639\pi$
$307$	365.373	−	365.373i	1.19014	−	1.19014i	0.977027	−	0.213114i	$-0.0683607\pi$
$308$		0			0
$309$		−	26.0658i		−	0.0843554i
$310$		0			0
$311$	154.384			0.496411			0.248205	−	0.968707i	$-0.420159\pi$
$311$	154.384			0.496411			0.248205	+	0.968707i	$0.420159\pi$
$312$		0			0
$313$	258.959	+	258.959i	0.827346	+	0.827346i	0.987149	−	0.159803i	$-0.0510860\pi$
$313$	258.959	+	258.959i	0.827346	+	0.827346i	−0.159803	+	0.987149i	$0.551086\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.85357	−	2.85357i	0.00900180	−	0.00900180i	−0.702592	−	0.711593i	$-0.747974\pi$
$317$	2.85357	−	2.85357i	0.00900180	−	0.00900180i	0.711593	+	0.702592i	$0.247974\pi$
$318$		0			0
$319$		−	68.2929i		−	0.214084i
$320$		0			0
$321$	−163.980			−0.510840
$322$		0			0
$323$	141.526	+	141.526i	0.438159	+	0.438159i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	119.146	−	119.146i	0.364362	−	0.364362i
$328$		0			0
$329$			46.8377i			0.142364i
$330$		0			0
$331$	497.646			1.50346			0.751731	−	0.659470i	$-0.229219\pi$
$331$	497.646			1.50346			0.751731	+	0.659470i	$0.229219\pi$
$332$		0			0
$333$	−61.9546	−	61.9546i	−0.186050	−	0.186050i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−274.757	+	274.757i	−0.815303	+	0.815303i	−0.985423	−	0.170120i	$-0.945584\pi$
$337$	−274.757	+	274.757i	−0.815303	+	0.815303i	0.170120	+	0.985423i	$0.445584\pi$
$338$		0			0
$339$		−	73.8184i		−	0.217753i
$340$		0			0
$341$	68.9898			0.202316
$342$		0			0
$343$	−53.6163	−	53.6163i	−0.156316	−	0.156316i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−465.848	+	465.848i	−1.34250	+	1.34250i	−0.448939	+	0.893563i	$0.648198\pi$
$347$	−465.848	+	465.848i	−1.34250	+	1.34250i	−0.893563	+	0.448939i	$0.851802\pi$
$348$		0			0
$349$			74.7173i			0.214090i	0.994254	+	0.107045i	$0.0341389\pi$
$349$			74.7173i			0.214090i	−0.994254	+	0.107045i	$0.965861\pi$
$350$		0			0
$351$	70.1816			0.199948
$352$		0			0
$353$	34.8332	+	34.8332i	0.0986775	+	0.0986775i	0.754722	−	0.656045i	$-0.227772\pi$
$353$	34.8332	+	34.8332i	0.0986775	+	0.0986775i	−0.656045	+	0.754722i	$0.727772\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	15.0306	−	15.0306i	0.0421026	−	0.0421026i
$358$		0			0
$359$		−	129.889i		−	0.361807i	−0.983501	−	0.180904i	$-0.942098\pi$
$359$		−	129.889i		−	0.361807i	0.983501	−	0.180904i	$-0.0579022\pi$
$360$		0			0
$361$	199.788			0.553429
$362$		0			0
$363$	−145.250	−	145.250i	−0.400137	−	0.400137i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−160.056	+	160.056i	−0.436119	+	0.436119i	−0.890704	−	0.454585i	$-0.849788\pi$
$367$	−160.056	+	160.056i	−0.436119	+	0.436119i	0.454585	+	0.890704i	$0.349788\pi$
$368$		0			0
$369$		−	144.879i		−	0.392625i
$370$		0			0
$371$	−60.0000			−0.161725
$372$		0			0
$373$	30.0250	+	30.0250i	0.0804960	+	0.0804960i	0.746208	−	0.665712i	$-0.231872\pi$
$373$	30.0250	+	30.0250i	0.0804960	+	0.0804960i	−0.665712	+	0.746208i	$0.731872\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−420.656	+	420.656i	−1.11580	+	1.11580i
$378$		0			0
$379$			424.343i			1.11964i	0.828615	+	0.559819i	$0.189129\pi$
$379$			424.343i			1.11964i	−0.828615	+	0.559819i	$0.810871\pi$
$380$		0			0
$381$	161.803			0.424679
$382$		0			0
$383$	325.460	+	325.460i	0.849764	+	0.849764i	0.990103	−	0.140339i	$-0.0448193\pi$
$383$	325.460	+	325.460i	0.849764	+	0.849764i	−0.140339	+	0.990103i	$0.544819\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	108.879	−	108.879i	0.281340	−	0.281340i
$388$		0			0
$389$			698.116i			1.79464i	0.441378	+	0.897321i	$0.354490\pi$
$389$			698.116i			1.79464i	−0.441378	+	0.897321i	$0.645510\pi$
$390$		0			0
$391$	475.918			1.21718
$392$		0			0
$393$	−106.373	−	106.373i	−0.270670	−	0.270670i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−257.984	+	257.984i	−0.649834	+	0.649834i	−0.952953	−	0.303119i	$-0.901972\pi$
$397$	−257.984	+	257.984i	−0.649834	+	0.649834i	0.303119	+	0.952953i	$0.401972\pi$
$398$		0			0
$399$			17.1214i			0.0429109i
$400$		0			0
$401$	−357.151			−0.890651			−0.445325	−	0.895369i	$-0.646912\pi$
$401$	−357.151			−0.890651			−0.445325	+	0.895369i	$0.646912\pi$
$402$		0			0
$403$	−424.949	−	424.949i	−1.05446	−	1.05446i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−32.0204	+	32.0204i	−0.0786742	+	0.0786742i
$408$		0			0
$409$			66.3837i			0.162307i	0.996702	+	0.0811536i	$0.0258604\pi$
$409$			66.3837i			0.162307i	−0.996702	+	0.0811536i	$0.974140\pi$
$410$		0			0
$411$	175.212			0.426307
$412$		0			0
$413$	26.1158	+	26.1158i	0.0632344	+	0.0632344i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−28.4291	+	28.4291i	−0.0681753	+	0.0681753i
$418$		0			0
$419$		−	414.772i		−	0.989909i	−0.868919	−	0.494955i	$-0.835185\pi$
$419$		−	414.772i		−	0.989909i	0.868919	−	0.494955i	$-0.164815\pi$
$420$		0			0
$421$	762.727			1.81170			0.905851	−	0.423597i	$-0.139233\pi$
$421$	762.727			1.81170			0.905851	+	0.423597i	$0.139233\pi$
$422$		0			0
$423$	127.621	+	127.621i	0.301704	+	0.301704i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	32.9694	−	32.9694i	0.0772117	−	0.0772117i
$428$		0			0
$429$		−	36.2724i		−	0.0845512i
$430$		0			0
$431$	−21.3439			−0.0495218			−0.0247609	−	0.999693i	$-0.507882\pi$
$431$	−21.3439			−0.0495218			−0.0247609	+	0.999693i	$0.507882\pi$
$432$		0			0
$433$	−288.868	−	288.868i	−0.667132	−	0.667132i	0.289919	−	0.957051i	$-0.406372\pi$
$433$	−288.868	−	288.868i	−0.667132	−	0.667132i	−0.957051	+	0.289919i	$0.906372\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−271.060	+	271.060i	−0.620275	+	0.620275i
$438$		0			0
$439$			410.182i			0.934355i	0.884164	+	0.467177i	$0.154729\pi$
$439$			410.182i			0.934355i	−0.884164	+	0.467177i	$0.845271\pi$
$440$		0			0
$441$	−145.182			−0.329210
$442$		0			0
$443$	262.747	+	262.747i	0.593108	+	0.593108i	0.938470	−	0.345362i	$-0.112244\pi$
$443$	262.747	+	262.747i	0.593108	+	0.593108i	−0.345362	+	0.938470i	$0.612244\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	168.439	−	168.439i	0.376822	−	0.376822i
$448$		0			0
$449$			841.242i			1.87359i	0.349879	+	0.936795i	$0.386223\pi$
$449$			841.242i			1.87359i	−0.349879	+	0.936795i	$0.613777\pi$
$450$		0			0
$451$	−74.8786			−0.166028
$452$		0			0
$453$	356.883	+	356.883i	0.787822	+	0.787822i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	23.8286	−	23.8286i	0.0521413	−	0.0521413i	−0.680555	−	0.732697i	$-0.738261\pi$
$457$	23.8286	−	23.8286i	0.0521413	−	0.0521413i	0.732697	+	0.680555i	$0.238261\pi$
$458$		0			0
$459$		−	81.9092i		−	0.178451i
$460$		0			0
$461$	44.3179			0.0961342			0.0480671	−	0.998844i	$-0.484694\pi$
$461$	44.3179			0.0961342			0.0480671	+	0.998844i	$0.484694\pi$
$462$		0			0
$463$	−193.116	−	193.116i	−0.417097	−	0.417097i	0.467105	−	0.884202i	$-0.345297\pi$
$463$	−193.116	−	193.116i	−0.417097	−	0.417097i	−0.884202	+	0.467105i	$0.845297\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	377.369	−	377.369i	0.808070	−	0.808070i	−0.176271	−	0.984342i	$-0.556404\pi$
$467$	377.369	−	377.369i	0.808070	−	0.808070i	0.984342	+	0.176271i	$0.0564036\pi$
$468$		0			0
$469$			89.4939i			0.190818i
$470$		0			0
$471$	128.919			0.273714
$472$		0			0
$473$	−56.2724	−	56.2724i	−0.118969	−	0.118969i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−163.485	+	163.485i	−0.342735	+	0.342735i
$478$		0			0
$479$			112.141i			0.234114i	0.993125	+	0.117057i	$0.0373461\pi$
$479$			112.141i			0.234114i	−0.993125	+	0.117057i	$0.962654\pi$
$480$		0			0
$481$	394.465			0.820094
$482$		0			0
$483$	28.7878	+	28.7878i	0.0596020	+	0.0596020i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−41.9444	+	41.9444i	−0.0861281	+	0.0861281i	−0.748858	−	0.662730i	$-0.769398\pi$
$487$	−41.9444	+	41.9444i	−0.0861281	+	0.0861281i	0.662730	+	0.748858i	$0.269398\pi$
$488$		0			0
$489$			288.000i			0.588957i
$490$		0			0
$491$	926.468			1.88690			0.943450	−	0.331515i	$-0.107560\pi$
$491$	926.468			1.88690			0.943450	+	0.331515i	$0.107560\pi$
$492$		0			0
$493$	490.949	+	490.949i	0.995840	+	0.995840i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	48.2225	−	48.2225i	0.0970271	−	0.0970271i
$498$		0			0
$499$			67.5255i			0.135322i	0.997708	+	0.0676608i	$0.0215536\pi$
$499$			67.5255i			0.135322i	−0.997708	+	0.0676608i	$0.978446\pi$
$500$		0			0
$501$	−358.454			−0.715477
$502$		0			0
$503$	−180.470	−	180.470i	−0.358787	−	0.358787i	0.504579	−	0.863366i	$-0.331648\pi$
$503$	−180.470	−	180.470i	−0.358787	−	0.358787i	−0.863366	+	0.504579i	$0.831648\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−16.4416	+	16.4416i	−0.0324291	+	0.0324291i
$508$		0			0
$509$		−	920.772i		−	1.80898i	−0.426493	−	0.904491i	$-0.640251\pi$
$509$		−	920.772i		−	1.80898i	0.426493	−	0.904491i	$-0.359749\pi$
$510$		0			0
$511$	83.6663			0.163731
$512$		0			0
$513$	46.6515	+	46.6515i	0.0909387	+	0.0909387i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	65.9592	−	65.9592i	0.127581	−	0.127581i
$518$		0			0
$519$		−	9.19184i		−	0.0177107i
$520$		0			0
$521$	−333.687			−0.640474			−0.320237	−	0.947338i	$-0.603762\pi$
$521$	−333.687			−0.640474			−0.320237	+	0.947338i	$0.603762\pi$
$522$		0			0
$523$	−380.474	−	380.474i	−0.727485	−	0.727485i	0.242633	−	0.970118i	$-0.421989\pi$
$523$	−380.474	−	380.474i	−0.727485	−	0.727485i	−0.970118	+	0.242633i	$0.921989\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−495.959	+	495.959i	−0.941099	+	0.941099i
$528$		0			0
$529$			382.514i			0.723089i
$530$		0			0
$531$	142.318			0.268019
$532$		0			0
$533$	461.221	+	461.221i	0.865331	+	0.865331i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−94.5959	+	94.5959i	−0.176156	+	0.176156i
$538$		0			0
$539$			75.0352i			0.139212i
$540$		0			0
$541$	156.515			0.289307			0.144654	−	0.989482i	$-0.453793\pi$
$541$	156.515			0.289307			0.144654	+	0.989482i	$0.453793\pi$
$542$		0			0
$543$	196.763	+	196.763i	0.362362	+	0.362362i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−12.6061	+	12.6061i	−0.0230459	+	0.0230459i	−0.718536	−	0.695490i	$-0.755187\pi$
$547$	−12.6061	+	12.6061i	−0.0230459	+	0.0230459i	0.695490	+	0.718536i	$0.255187\pi$
$548$		0			0
$549$		−	179.666i		−	0.327261i
$550$		0			0
$551$	−559.242			−1.01496
$552$		0			0
$553$	53.5663	+	53.5663i	0.0968650	+	0.0968650i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.0194	−	21.0194i	0.0377368	−	0.0377368i	−0.687987	−	0.725723i	$-0.741505\pi$
$557$	21.0194	−	21.0194i	0.0377368	−	0.0377368i	0.725723	+	0.687987i	$0.241505\pi$
$558$		0			0
$559$			693.231i			1.24013i
$560$		0			0
$561$	−42.3337			−0.0754611
$562$		0			0
$563$	360.536	+	360.536i	0.640383	+	0.640383i	0.950650	−	0.310266i	$-0.100418\pi$
$563$	360.536	+	360.536i	0.640383	+	0.640383i	−0.310266	+	0.950650i	$0.600418\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.95459	−	4.95459i	0.00873826	−	0.00873826i
$568$		0			0
$569$			486.504i			0.855016i	0.904012	+	0.427508i	$0.140608\pi$
$569$			486.504i			0.855016i	−0.904012	+	0.427508i	$0.859392\pi$
$570$		0			0
$571$	−447.040			−0.782907			−0.391453	−	0.920198i	$-0.628028\pi$
$571$	−447.040			−0.782907			−0.391453	+	0.920198i	$0.628028\pi$
$572$		0			0
$573$	−308.474	−	308.474i	−0.538350	−	0.538350i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	248.444	−	248.444i	0.430579	−	0.430579i	−0.458247	−	0.888825i	$-0.651522\pi$
$577$	248.444	−	248.444i	0.430579	−	0.430579i	0.888825	+	0.458247i	$0.151522\pi$
$578$		0			0
$579$		−	424.702i		−	0.733509i
$580$		0			0
$581$	−45.2031			−0.0778022
$582$		0			0
$583$	84.4949	+	84.4949i	0.144931	+	0.144931i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	547.712	−	547.712i	0.933069	−	0.933069i	−0.0648271	−	0.997897i	$-0.520650\pi$
$587$	547.712	−	547.712i	0.933069	−	0.933069i	0.997897	+	0.0648271i	$0.0206496\pi$
$588$		0			0
$589$		−	564.949i		−	0.959166i
$590$		0			0
$591$	5.12143			0.00866570
$592$		0			0
$593$	78.9444	+	78.9444i	0.133127	+	0.133127i	0.770530	−	0.637403i	$-0.219991\pi$
$593$	78.9444	+	78.9444i	0.133127	+	0.133127i	−0.637403	+	0.770530i	$0.719991\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	373.015	−	373.015i	0.624815	−	0.624815i
$598$		0			0
$599$		−	381.807i		−	0.637408i	−0.947854	−	0.318704i	$-0.896752\pi$
$599$		−	381.807i		−	0.637408i	0.947854	−	0.318704i	$-0.103248\pi$
$600$		0			0
$601$	−231.757			−0.385619			−0.192810	−	0.981236i	$-0.561760\pi$
$601$	−231.757			−0.385619			−0.192810	+	0.981236i	$0.561760\pi$
$602$		0			0
$603$	243.848	+	243.848i	0.404391	+	0.404391i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	96.8434	−	96.8434i	0.159544	−	0.159544i	−0.622821	−	0.782365i	$-0.714013\pi$
$607$	96.8434	−	96.8434i	0.159544	−	0.159544i	0.782365	+	0.622821i	$0.214013\pi$
$608$		0			0
$609$			59.3939i			0.0975269i
$610$		0			0
$611$	−812.563			−1.32989
$612$		0			0
$613$	−105.712	−	105.712i	−0.172450	−	0.172450i	0.615605	−	0.788055i	$-0.288912\pi$
$613$	−105.712	−	105.712i	−0.172450	−	0.172450i	−0.788055	+	0.615605i	$0.788912\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	41.9250	−	41.9250i	0.0679498	−	0.0679498i	−0.672315	−	0.740265i	$-0.734700\pi$
$617$	41.9250	−	41.9250i	0.0679498	−	0.0679498i	0.740265	+	0.672315i	$0.234700\pi$
$618$		0			0
$619$		−	434.363i		−	0.701718i	−0.936428	−	0.350859i	$-0.885890\pi$
$619$		−	434.363i		−	0.701718i	0.936428	−	0.350859i	$-0.114110\pi$
$620$		0			0
$621$	156.879			0.252622
$622$		0			0
$623$	−28.7378	−	28.7378i	−0.0461280	−	0.0461280i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	24.1112	−	24.1112i	0.0384549	−	0.0384549i
$628$		0			0
$629$		−	460.382i		−	0.731926i
$630$		0			0
$631$	−816.413			−1.29384			−0.646920	−	0.762558i	$-0.723943\pi$
$631$	−816.413			−1.29384			−0.646920	+	0.762558i	$0.723943\pi$
$632$		0			0
$633$	−334.540	−	334.540i	−0.528500	−	0.528500i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	462.186	−	462.186i	0.725567	−	0.725567i
$638$		0			0
$639$		−	262.788i		−	0.411248i
$640$		0			0
$641$	−937.959			−1.46327			−0.731637	−	0.681694i	$-0.761244\pi$
$641$	−937.959			−1.46327			−0.731637	+	0.681694i	$0.761244\pi$
$642$		0			0
$643$	62.8786	+	62.8786i	0.0977894	+	0.0977894i	0.754309	−	0.656520i	$-0.227972\pi$
$643$	62.8786	+	62.8786i	0.0977894	+	0.0977894i	−0.656520	+	0.754309i	$0.727972\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−86.3087	+	86.3087i	−0.133398	+	0.133398i	−0.770653	−	0.637255i	$-0.780070\pi$
$647$	−86.3087	+	86.3087i	−0.133398	+	0.133398i	0.637255	+	0.770653i	$0.280070\pi$
$648$		0			0
$649$		−	73.5551i		−	0.113336i
$650$		0			0
$651$	−60.0000			−0.0921659
$652$		0			0
$653$	−294.904	−	294.904i	−0.451613	−	0.451613i	0.444276	−	0.895890i	$-0.353461\pi$
$653$	−294.904	−	294.904i	−0.451613	−	0.451613i	−0.895890	+	0.444276i	$0.853461\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	227.969	−	227.969i	0.346985	−	0.346985i
$658$		0			0
$659$			1156.80i			1.75539i	0.479220	+	0.877695i	$0.340919\pi$
$659$			1156.80i			1.75539i	−0.479220	+	0.877695i	$0.659081\pi$
$660$		0			0
$661$	908.838			1.37494			0.687472	−	0.726211i	$-0.258720\pi$
$661$	908.838			1.37494			0.687472	+	0.726211i	$0.258720\pi$
$662$		0			0
$663$	260.758	+	260.758i	0.393300	+	0.393300i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−940.302	+	940.302i	−1.40975	+	1.40975i
$668$		0			0
$669$			427.832i			0.639510i
$670$		0			0
$671$	−92.8582			−0.138388
$672$		0			0
$673$	−833.756	−	833.756i	−1.23886	−	1.23886i	−0.960465	−	0.278400i	$-0.910196\pi$
$673$	−833.756	−	833.756i	−1.23886	−	1.23886i	−0.278400	−	0.960465i	$-0.589804\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	200.257	−	200.257i	0.295800	−	0.295800i	−0.543566	−	0.839366i	$-0.682926\pi$
$677$	200.257	−	200.257i	0.295800	−	0.295800i	0.839366	+	0.543566i	$0.182926\pi$
$678$		0			0
$679$			40.7378i			0.0599967i
$680$		0			0
$681$	−190.120			−0.279178
$682$		0			0
$683$	156.025	+	156.025i	0.228441	+	0.228441i	0.812041	−	0.583600i	$-0.198357\pi$
$683$	156.025	+	156.025i	0.228441	+	0.228441i	−0.583600	+	0.812041i	$0.698357\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	10.9852	−	10.9852i	0.0159901	−	0.0159901i
$688$		0			0
$689$		−	1040.91i		−	1.51075i
$690$		0			0
$691$	−774.940			−1.12148			−0.560738	−	0.827993i	$-0.689482\pi$
$691$	−774.940			−1.12148			−0.560738	+	0.827993i	$0.689482\pi$
$692$		0			0
$693$	−2.56072	−	2.56072i	−0.00369512	−	0.00369512i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	538.293	−	538.293i	0.772300	−	0.772300i
$698$		0			0
$699$			123.626i			0.176861i
$700$		0			0
$701$	280.309			0.399870			0.199935	−	0.979809i	$-0.435927\pi$
$701$	280.309			0.399870			0.199935	+	0.979809i	$0.435927\pi$
$702$		0			0
$703$	262.211	+	262.211i	0.372989	+	0.372989i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.0954	−	10.0954i	0.0142792	−	0.0142792i
$708$		0			0
$709$		−	926.686i		−	1.30703i	−0.756913	−	0.653516i	$-0.773293\pi$
$709$		−	926.686i		−	1.30703i	0.756913	−	0.653516i	$-0.226707\pi$
$710$		0			0
$711$	291.909			0.410561
$712$		0			0
$713$	−949.898	−	949.898i	−1.33226	−	1.33226i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−342.606	+	342.606i	−0.477833	+	0.477833i
$718$		0			0
$719$		−	938.565i		−	1.30538i	−0.757627	−	0.652688i	$-0.773641\pi$
$719$		−	938.565i		−	1.30538i	0.757627	−	0.652688i	$-0.226359\pi$
$720$		0			0
$721$	11.7163			0.0162501
$722$		0			0
$723$	−486.384	−	486.384i	−0.672730	−	0.672730i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	404.803	−	404.803i	0.556812	−	0.556812i	−0.371586	−	0.928398i	$-0.621186\pi$
$727$	404.803	−	404.803i	0.556812	−	0.556812i	0.928398	+	0.371586i	$0.121186\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	809.071			1.10680
$732$		0			0
$733$	644.529	+	644.529i	0.879303	+	0.879303i	0.993462	−	0.114159i	$-0.0364175\pi$
$733$	644.529	+	644.529i	0.879303	+	0.879303i	−0.114159	+	0.993462i	$0.536417\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	126.030	−	126.030i	0.171004	−	0.171004i
$738$		0			0
$739$		−	1182.11i		−	1.59961i	−0.600262	−	0.799803i	$-0.704937\pi$
$739$		−	1182.11i		−	1.59961i	0.600262	−	0.799803i	$-0.295063\pi$
$740$		0			0
$741$	−297.031			−0.400851
$742$		0			0
$743$	−570.681	−	570.681i	−0.768077	−	0.768077i	0.209691	−	0.977768i	$-0.432754\pi$
$743$	−570.681	−	570.681i	−0.768077	−	0.768077i	−0.977768	+	0.209691i	$0.932754\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−123.167	+	123.167i	−0.164882	+	0.164882i
$748$		0			0
$749$		−	73.7071i		−	0.0984074i
$750$		0			0
$751$	−180.050			−0.239747			−0.119873	−	0.992789i	$-0.538249\pi$
$751$	−180.050			−0.239747			−0.119873	+	0.992789i	$0.538249\pi$
$752$		0			0
$753$	−65.9694	−	65.9694i	−0.0876087	−	0.0876087i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	187.176	−	187.176i	0.247260	−	0.247260i	−0.572585	−	0.819845i	$-0.694059\pi$
$757$	187.176	−	187.176i	0.247260	−	0.247260i	0.819845	+	0.572585i	$0.194059\pi$
$758$		0			0
$759$		−	81.0806i		−	0.106826i
$760$		0			0
$761$	912.130			1.19859			0.599297	−	0.800527i	$-0.295447\pi$
$761$	912.130			1.19859			0.599297	+	0.800527i	$0.295447\pi$
$762$		0			0
$763$	53.5551	+	53.5551i	0.0701902	+	0.0701902i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−453.069	+	453.069i	−0.590703	+	0.590703i
$768$		0			0
$769$		−	201.778i		−	0.262390i	−0.991357	−	0.131195i	$-0.958119\pi$
$769$		−	201.778i		−	0.262390i	0.991357	−	0.131195i	$-0.0418813\pi$
$770$		0			0
$771$	−758.686			−0.984028
$772$		0			0
$773$	147.793	+	147.793i	0.191195	+	0.191195i	0.796212	−	0.605018i	$-0.206834\pi$
$773$	147.793	+	147.793i	0.191195	+	0.191195i	−0.605018	+	0.796212i	$0.706834\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	27.8480	−	27.8480i	0.0358404	−	0.0358404i
$778$		0			0
$779$			613.171i			0.787126i
$780$		0			0
$781$	−135.818			−0.173903
$782$		0			0
$783$	161.833	+	161.833i	0.206683	+	0.206683i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−447.576	+	447.576i	−0.568711	+	0.568711i	−0.931767	−	0.363056i	$-0.881733\pi$
$787$	−447.576	+	447.576i	−0.568711	+	0.568711i	0.363056	+	0.931767i	$0.381733\pi$
$788$		0			0
$789$		−	315.626i		−	0.400032i
$790$		0			0
$791$	33.1806			0.0419477
$792$		0			0
$793$	571.968	+	571.968i	0.721272	+	0.721272i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	128.338	−	128.338i	0.161027	−	0.161027i	−0.621995	−	0.783021i	$-0.713677\pi$
$797$	128.338	−	128.338i	0.161027	−	0.161027i	0.783021	+	0.621995i	$0.213677\pi$
$798$		0			0
$799$			948.345i			1.18691i
$800$		0			0
$801$	−156.606			−0.195513
$802$		0			0
$803$	−117.823	−	117.823i	−0.146728	−	0.146728i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−137.449	+	137.449i	−0.170322	+	0.170322i
$808$		0			0
$809$			699.212i			0.864292i	0.901804	+	0.432146i	$0.142243\pi$
$809$			699.212i			0.864292i	−0.901804	+	0.432146i	$0.857757\pi$
$810$		0			0
$811$	90.5041			0.111596			0.0557978	−	0.998442i	$-0.482230\pi$
$811$	90.5041			0.111596			0.0557978	+	0.998442i	$0.482230\pi$
$812$		0			0
$813$	−205.287	−	205.287i	−0.252506	−	0.252506i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−460.808	+	460.808i	−0.564025	+	0.564025i
$818$		0			0
$819$			31.5459i			0.0385176i
$820$		0			0
$821$	250.783			0.305461			0.152730	−	0.988268i	$-0.451193\pi$
$821$	250.783			0.305461			0.152730	+	0.988268i	$0.451193\pi$
$822$		0			0
$823$	−27.0954	−	27.0954i	−0.0329227	−	0.0329227i	0.690454	−	0.723377i	$-0.257411\pi$
$823$	−27.0954	−	27.0954i	−0.0329227	−	0.0329227i	−0.723377	+	0.690454i	$0.757411\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	589.930	−	589.930i	0.713337	−	0.713337i	−0.253895	−	0.967232i	$-0.581712\pi$
$827$	589.930	−	589.930i	0.713337	−	0.713337i	0.967232	+	0.253895i	$0.0817117\pi$
$828$		0			0
$829$		−	1576.77i		−	1.90202i	−0.309160	−	0.951010i	$-0.600048\pi$
$829$		−	1576.77i		−	1.90202i	0.309160	−	0.951010i	$-0.399952\pi$
$830$		0			0
$831$	730.282			0.878799
$832$		0			0
$833$	−539.419	−	539.419i	−0.647562	−	0.647562i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−163.485	+	163.485i	−0.195322	+	0.195322i
$838$		0			0
$839$		−	963.523i		−	1.14842i	−0.818708	−	0.574209i	$-0.805310\pi$
$839$		−	963.523i		−	1.14842i	0.818708	−	0.574209i	$-0.194690\pi$
$840$		0			0
$841$	−1099.00			−1.30678
$842$		0			0
$843$	−412.045	−	412.045i	−0.488785	−	0.488785i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	65.2883	−	65.2883i	0.0770818	−	0.0770818i
$848$		0			0
$849$			49.3847i			0.0581681i
$850$		0			0
$851$	881.757			1.03614
$852$		0			0
$853$	−254.166	−	254.166i	−0.297967	−	0.297967i	0.542250	−	0.840217i	$-0.317573\pi$
$853$	−254.166	−	254.166i	−0.297967	−	0.297967i	−0.840217	+	0.542250i	$0.817573\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	699.206	−	699.206i	0.815876	−	0.815876i	−0.169632	−	0.985508i	$-0.554258\pi$
$857$	699.206	−	699.206i	0.815876	−	0.815876i	0.985508	+	0.169632i	$0.0542578\pi$
$858$		0			0
$859$		−	246.708i		−	0.287204i	−0.989636	−	0.143602i	$-0.954131\pi$
$859$		−	246.708i		−	0.287204i	0.989636	−	0.143602i	$-0.0458685\pi$
$860$		0			0
$861$	65.1214			0.0756346
$862$		0			0
$863$	−1051.01	−	1051.01i	−1.21786	−	1.21786i	−0.968379	−	0.249483i	$-0.919739\pi$
$863$	−1051.01	−	1051.01i	−1.21786	−	1.21786i	−0.249483	−	0.968379i	$-0.580261\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−49.6197	+	49.6197i	−0.0572314	+	0.0572314i
$868$		0			0
$869$		−	150.869i		−	0.173613i
$870$		0			0
$871$	−1552.58			−1.78253
$872$		0			0
$873$	111.000	+	111.000i	0.127148	+	0.127148i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−30.2974	+	30.2974i	−0.0345467	+	0.0345467i	−0.724169	−	0.689622i	$-0.757777\pi$
$877$	−30.2974	+	30.2974i	−0.0345467	+	0.0345467i	0.689622	+	0.724169i	$0.257777\pi$
$878$		0			0
$879$			604.009i			0.687155i
$880$		0			0
$881$	751.294			0.852774			0.426387	−	0.904541i	$-0.359786\pi$
$881$	751.294			0.852774			0.426387	+	0.904541i	$0.359786\pi$
$882$		0			0
$883$	−666.929	−	666.929i	−0.755298	−	0.755298i	0.220164	−	0.975463i	$-0.429341\pi$
$883$	−666.929	−	666.929i	−0.755298	−	0.755298i	−0.975463	+	0.220164i	$0.929341\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−269.662	+	269.662i	−0.304015	+	0.304015i	−0.842583	−	0.538567i	$-0.818966\pi$
$887$	−269.662	+	269.662i	−0.304015	+	0.304015i	0.538567	+	0.842583i	$0.318966\pi$
$888$		0			0
$889$			72.7286i			0.0818094i
$890$		0			0
$891$	−13.9546			−0.0156617
$892$		0			0
$893$	−540.132	−	540.132i	−0.604851	−	0.604851i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−499.423	+	499.423i	−0.556771	+	0.556771i
$898$		0			0
$899$		−	1959.80i		−	2.17997i
$900$		0			0
$901$	−1214.85			−1.34833
$902$		0			0
$903$	48.9398	+	48.9398i	0.0541969	+	0.0541969i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	578.515	−	578.515i	0.637834	−	0.637834i	−0.312187	−	0.950021i	$-0.601062\pi$
$907$	578.515	−	578.515i	0.637834	−	0.637834i	0.950021	+	0.312187i	$0.101062\pi$
$908$		0			0
$909$		−	55.0148i		−	0.0605223i
$910$		0			0
$911$	−90.4745			−0.0993134			−0.0496567	−	0.998766i	$-0.515813\pi$
$911$	−90.4745			−0.0993134			−0.0496567	+	0.998766i	$0.515813\pi$
$912$		0			0
$913$	63.6571	+	63.6571i	0.0697231	+	0.0697231i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	47.8138	−	47.8138i	0.0521415	−	0.0521415i
$918$		0			0
$919$		−	1467.08i		−	1.59639i	−0.602402	−	0.798193i	$-0.705790\pi$
$919$		−	1467.08i		−	1.59639i	0.602402	−	0.798193i	$-0.294210\pi$
$920$		0			0
$921$	894.979			0.971747
$922$		0			0
$923$	836.586	+	836.586i	0.906377	+	0.906377i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	31.9240	−	31.9240i	0.0344379	−	0.0344379i
$928$		0			0
$929$		−	907.444i		−	0.976796i	−0.872621	−	0.488398i	$-0.837581\pi$
$929$		−	907.444i		−	0.976796i	0.872621	−	0.488398i	$-0.162419\pi$
$930$		0			0
$931$	614.454			0.659994
$932$		0			0
$933$	189.081	+	189.081i	0.202659	+	0.202659i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−158.898	+	158.898i	−0.169582	+	0.169582i	−0.786795	−	0.617214i	$-0.788261\pi$
$937$	−158.898	+	158.898i	−0.169582	+	0.169582i	0.617214	+	0.786795i	$0.288261\pi$
$938$		0			0
$939$			634.318i			0.675525i
$940$		0			0
$941$	−666.497			−0.708286			−0.354143	−	0.935191i	$-0.615227\pi$
$941$	−666.497			−0.708286			−0.354143	+	0.935191i	$0.615227\pi$
$942$		0			0
$943$	1030.98	+	1030.98i	1.09330	+	1.09330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1038.08	−	1038.08i	1.09618	−	1.09618i	0.101323	−	0.994854i	$-0.467692\pi$
$947$	1038.08	−	1038.08i	1.09618	−	1.09618i	0.994854	−	0.101323i	$-0.0323077\pi$
$948$		0			0
$949$			1451.48i			1.52949i
$950$		0			0
$951$	6.98979			0.00734994
$952$		0			0
$953$	262.045	+	262.045i	0.274969	+	0.274969i	0.831097	−	0.556128i	$-0.187714\pi$
$953$	262.045	+	262.045i	0.274969	+	0.274969i	−0.556128	+	0.831097i	$0.687714\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	83.6413	−	83.6413i	0.0873995	−	0.0873995i
$958$		0			0
$959$			78.7561i			0.0821232i
$960$		0			0
$961$	1018.80			1.06014
$962$		0			0
$963$	−200.833	−	200.833i	−0.208549	−	0.208549i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1277.98	−	1277.98i	1.32160	−	1.32160i	0.409111	−	0.912484i	$-0.365839\pi$
$967$	1277.98	−	1277.98i	1.32160	−	1.32160i	0.912484	−	0.409111i	$-0.134161\pi$
$968$		0			0
$969$			346.665i			0.357756i
$970$		0			0
$971$	−1640.26			−1.68924			−0.844622	−	0.535363i	$-0.820175\pi$
$971$	−1640.26			−1.68924			−0.844622	+	0.535363i	$0.820175\pi$
$972$		0			0
$973$	−12.7786	−	12.7786i	−0.0131332	−	0.0131332i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	761.480	−	761.480i	0.779406	−	0.779406i	−0.200323	−	0.979730i	$-0.564199\pi$
$977$	761.480	−	761.480i	0.779406	−	0.779406i	0.979730	+	0.200323i	$0.0641993\pi$
$978$		0			0
$979$			80.9398i			0.0826760i
$980$		0			0
$981$	291.848			0.297500
$982$		0			0
$983$	215.035	+	215.035i	0.218754	+	0.218754i	0.807973	−	0.589219i	$-0.200565\pi$
$983$	215.035	+	215.035i	0.218754	+	0.218754i	−0.589219	+	0.807973i	$0.700565\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−57.3643	+	57.3643i	−0.0581199	+	0.0581199i
$988$		0			0
$989$			1549.59i			1.56683i
$990$		0			0
$991$	1240.62			1.25189			0.625946	−	0.779867i	$-0.284713\pi$
$991$	1240.62			1.25189			0.625946	+	0.779867i	$0.284713\pi$
$992$		0			0
$993$	609.489	+	609.489i	0.613786	+	0.613786i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−899.358	+	899.358i	−0.902064	+	0.902064i	−0.995615	−	0.0935507i	$-0.970178\pi$
$997$	−899.358	+	899.358i	−0.902064	+	0.902064i	0.0935507	+	0.995615i	$0.470178\pi$
$998$		0			0
$999$		−	151.757i		−	0.151909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.e.193.2		4
4.3	odd	2		600.3.u.e.193.1		4
5.2	odd	4	inner	1200.3.bg.e.1057.2		4
5.3	odd	4		240.3.bg.c.97.1		4
5.4	even	2		240.3.bg.c.193.1		4
12.11	even	2		1800.3.v.n.793.1		4
15.8	even	4		720.3.bh.g.577.1		4
15.14	odd	2		720.3.bh.g.433.1		4
20.3	even	4		120.3.u.a.97.2	yes	4
20.7	even	4		600.3.u.e.457.1		4
20.19	odd	2		120.3.u.a.73.2	✓	4
40.3	even	4		960.3.bg.c.577.1		4
40.13	odd	4		960.3.bg.d.577.2		4
40.19	odd	2		960.3.bg.c.193.1		4
40.29	even	2		960.3.bg.d.193.2		4
60.23	odd	4		360.3.v.b.217.1		4
60.47	odd	4		1800.3.v.n.1657.1		4
60.59	even	2		360.3.v.b.73.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.a.73.2	✓	4	20.19	odd	2
120.3.u.a.97.2	yes	4	20.3	even	4
240.3.bg.c.97.1		4	5.3	odd	4
240.3.bg.c.193.1		4	5.4	even	2
360.3.v.b.73.1		4	60.59	even	2
360.3.v.b.217.1		4	60.23	odd	4
600.3.u.e.193.1		4	4.3	odd	2
600.3.u.e.457.1		4	20.7	even	4
720.3.bh.g.433.1		4	15.14	odd	2
720.3.bh.g.577.1		4	15.8	even	4
960.3.bg.c.193.1		4	40.19	odd	2
960.3.bg.c.577.1		4	40.3	even	4
960.3.bg.d.193.2		4	40.29	even	2
960.3.bg.d.577.2		4	40.13	odd	4
1200.3.bg.e.193.2		4	1.1	even	1	trivial
1200.3.bg.e.1057.2		4	5.2	odd	4	inner
1800.3.v.n.793.1		4	12.11	even	2
1800.3.v.n.1657.1		4	60.47	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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.22474 + 1.22474i) q^{3} +(-0.550510 + 0.550510i) q^{7} +3.00000i q^{9} +1.55051 q^{11} +(-9.55051 - 9.55051i) q^{13} +(-11.1464 + 11.1464i) q^{17} -12.6969i q^{19} -1.34847 q^{21} +(-21.3485 - 21.3485i) q^{23} +(-3.67423 + 3.67423i) q^{27} -44.0454i q^{29} +44.4949 q^{31} +(1.89898 + 1.89898i) q^{33} +(-20.6515 + 20.6515i) q^{37} -23.3939i q^{39} -48.2929 q^{41} +(-36.2929 - 36.2929i) q^{43} +(42.5403 - 42.5403i) q^{47} +48.3939i q^{49} -27.3031 q^{51} +(54.4949 + 54.4949i) q^{53} +(15.5505 - 15.5505i) q^{57} -47.4393i q^{59} -59.8888 q^{61} +(-1.65153 - 1.65153i) q^{63} +(81.2827 - 81.2827i) q^{67} -52.2929i q^{69} -87.5959 q^{71} +(-75.9898 - 75.9898i) q^{73} +(-0.853572 + 0.853572i) q^{77} -97.3031i q^{79} -9.00000 q^{81} +(41.0556 + 41.0556i) q^{83} +(53.9444 - 53.9444i) q^{87} +52.2020i q^{89} +10.5153 q^{91} +(54.4949 + 54.4949i) q^{93} +(37.0000 - 37.0000i) q^{97} +4.65153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{7}+O(q^{10}) \) 4 * q - 12 * q^7	\( 4 q - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{17} + 24 q^{21} - 56 q^{23} + 80 q^{31} - 12 q^{33} - 112 q^{37} - 56 q^{41} - 8 q^{43} - 16 q^{47} - 168 q^{51} + 120 q^{53} + 72 q^{57} - 24 q^{61} - 36 q^{63} - 8 q^{67} - 272 q^{71} - 108 q^{73} - 72 q^{77} - 36 q^{81} + 272 q^{83} + 108 q^{87} + 336 q^{91} + 120 q^{93} + 148 q^{97}+O(q^{100}) \) 4 * q - 12 * q^7 + 16 * q^11 - 48 * q^13 + 24 * q^17 + 24 * q^21 - 56 * q^23 + 80 * q^31 - 12 * q^33 - 112 * q^37 - 56 * q^41 - 8 * q^43 - 16 * q^47 - 168 * q^51 + 120 * q^53 + 72 * q^57 - 24 * q^61 - 36 * q^63 - 8 * q^67 - 272 * q^71 - 108 * q^73 - 72 * q^77 - 36 * q^81 + 272 * q^83 + 108 * q^87 + 336 * q^91 + 120 * q^93 + 148 * q^97

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