LMFDB - Embedded newform 1200.3.bg.k.1057.1

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.1
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1200.1057
Dual form			1200.3.bg.k.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(3.44949 + 3.44949i) q^{7} -3.00000i q^{9} -11.3485 q^{11} +(5.55051 - 5.55051i) q^{13} +(17.3485 + 17.3485i) q^{17} -8.69694i q^{19} -8.44949 q^{21} +(11.5505 - 11.5505i) q^{23} +(3.67423 + 3.67423i) q^{27} +35.1464i q^{29} -10.6969 q^{31} +(13.8990 - 13.8990i) q^{33} +(6.04541 + 6.04541i) q^{37} +13.5959i q^{39} +0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +(44.2474 + 44.2474i) q^{47} -25.2020i q^{49} -42.4949 q^{51} +(0.696938 - 0.696938i) q^{53} +(10.6515 + 10.6515i) q^{57} +39.9342i q^{59} +5.90918 q^{61} +(10.3485 - 10.3485i) q^{63} +(-45.1010 - 45.1010i) q^{67} +28.2929i q^{69} +68.0000 q^{71} +(-77.7878 + 77.7878i) q^{73} +(-39.1464 - 39.1464i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(13.1464 - 13.1464i) q^{83} +(-43.0454 - 43.0454i) q^{87} +82.1816i q^{89} +38.2929 q^{91} +(13.1010 - 13.1010i) q^{93} +(24.5959 + 24.5959i) q^{97} +34.0454i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{7} - 16 q^{11} + 32 q^{13} + 40 q^{17} - 24 q^{21} + 56 q^{23} + 16 q^{31} + 36 q^{33} - 64 q^{37} - 56 q^{41} - 8 q^{43} + 128 q^{47} - 72 q^{51} - 56 q^{53} + 72 q^{57} + 200 q^{61} + 12 q^{63}+ \cdots + 20 q^{97}+O(q^{100}) $ 4 * q + 4 * q^7 - 16 * q^11 + 32 * q^13 + 40 * q^17 - 24 * q^21 + 56 * q^23 + 16 * q^31 + 36 * q^33 - 64 * q^37 - 56 * q^41 - 8 * q^43 + 128 * q^47 - 72 * q^51 - 56 * q^53 + 72 * q^57 + 200 * q^61 + 12 * q^63 - 200 * q^67 + 272 * q^71 - 76 * q^73 - 88 * q^77 - 36 * q^81 - 16 * q^83 - 84 * q^87 + 16 * q^91 + 72 * q^93 + 20 * q^97

Character values

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

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

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
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	0.909182	−	0.416398i	$-0.136708\pi$
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	−0.416398	+	0.909182i	$0.636708\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−11.3485			−1.03168			−0.515840	−	0.856685i	$-0.672520\pi$
$11$	−11.3485			−1.03168			−0.515840	+	0.856685i	$0.672520\pi$
$12$		0			0
$13$	5.55051	−	5.55051i	0.426962	−	0.426962i	−0.460630	−	0.887592i	$-0.652376\pi$
$13$	5.55051	−	5.55051i	0.426962	−	0.426962i	0.887592	+	0.460630i	$0.152376\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	17.3485	+	17.3485i	1.02050	+	1.02050i	0.999785	+	0.0207127i	$0.00659354\pi$
$17$	17.3485	+	17.3485i	1.02050	+	1.02050i	0.0207127	+	0.999785i	$0.493406\pi$
$18$		0			0
$19$		−	8.69694i		−	0.457734i	−0.973458	−	0.228867i	$-0.926498\pi$
$19$		−	8.69694i		−	0.457734i	0.973458	−	0.228867i	$-0.0735020\pi$
$20$		0			0
$21$	−8.44949			−0.402357
$22$		0			0
$23$	11.5505	−	11.5505i	0.502196	−	0.502196i	−0.409924	−	0.912120i	$-0.634445\pi$
$23$	11.5505	−	11.5505i	0.502196	−	0.502196i	0.912120	+	0.409924i	$0.134445\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$			35.1464i			1.21195i	0.795485	+	0.605973i	$0.207216\pi$
$29$			35.1464i			1.21195i	−0.795485	+	0.605973i	$0.792784\pi$
$30$		0			0
$31$	−10.6969			−0.345063			−0.172531	−	0.985004i	$-0.555195\pi$
$31$	−10.6969			−0.345063			−0.172531	+	0.985004i	$0.555195\pi$
$32$		0			0
$33$	13.8990	−	13.8990i	0.421181	−	0.421181i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.04541	+	6.04541i	0.163389	+	0.163389i	0.784066	−	0.620677i	$-0.213142\pi$
$37$	6.04541	+	6.04541i	0.163389	+	0.163389i	−0.620677	+	0.784066i	$0.713142\pi$
$38$		0			0
$39$			13.5959i			0.348613i
$40$		0			0
$41$	0.696938			0.0169985			0.00849925	−	0.999964i	$-0.497295\pi$
$41$	0.696938			0.0169985			0.00849925	+	0.999964i	$0.497295\pi$
$42$		0			0
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	−0.944544	−	0.328384i	$-0.893496\pi$
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	0.328384	+	0.944544i	$0.393496\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	44.2474	+	44.2474i	0.941435	+	0.941435i	0.998377	−	0.0569424i	$-0.0181351\pi$
$47$	44.2474	+	44.2474i	0.941435	+	0.941435i	−0.0569424	+	0.998377i	$0.518135\pi$
$48$		0			0
$49$		−	25.2020i		−	0.514327i
$50$		0			0
$51$	−42.4949			−0.833233
$52$		0			0
$53$	0.696938	−	0.696938i	0.0131498	−	0.0131498i	−0.700501	−	0.713651i	$-0.747040\pi$
$53$	0.696938	−	0.696938i	0.0131498	−	0.0131498i	0.713651	+	0.700501i	$0.247040\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	10.6515	+	10.6515i	0.186869	+	0.186869i
$58$		0			0
$59$			39.9342i			0.676851i	0.940993	+	0.338425i	$0.109894\pi$
$59$			39.9342i			0.676851i	−0.940993	+	0.338425i	$0.890106\pi$
$60$		0			0
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$		0			0
$63$	10.3485	−	10.3485i	0.164261	−	0.164261i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	0.285291	−	0.958441i	$-0.407910\pi$
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	−0.958441	+	0.285291i	$0.907910\pi$
$68$		0			0
$69$			28.2929i			0.410041i
$70$		0			0
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	−77.7878	+	77.7878i	−1.06559	+	1.06559i	−0.0678931	+	0.997693i	$0.521628\pi$
$73$	−77.7878	+	77.7878i	−1.06559	+	1.06559i	−0.997693	+	0.0678931i	$0.978372\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−39.1464	−	39.1464i	−0.508395	−	0.508395i
$78$		0			0
$79$			24.4949i			0.310062i	0.987910	+	0.155031i	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	13.1464	−	13.1464i	0.158391	−	0.158391i	−0.623463	−	0.781853i	$-0.714275\pi$
$83$	13.1464	−	13.1464i	0.158391	−	0.158391i	0.781853	+	0.623463i	$0.214275\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−43.0454	−	43.0454i	−0.494775	−	0.494775i
$88$		0			0
$89$			82.1816i			0.923389i	0.887039	+	0.461695i	$0.152758\pi$
$89$			82.1816i			0.923389i	−0.887039	+	0.461695i	$0.847242\pi$
$90$		0			0
$91$	38.2929			0.420801
$92$		0			0
$93$	13.1010	−	13.1010i	0.140871	−	0.140871i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	24.5959	+	24.5959i	0.253566	+	0.253566i	0.822431	−	0.568865i	$-0.192617\pi$
$97$	24.5959	+	24.5959i	0.253566	+	0.253566i	−0.568865	+	0.822431i	$0.692617\pi$
$98$		0			0
$99$			34.0454i			0.343893i
$100$		0			0
$101$	−105.621			−1.04575			−0.522876	−	0.852409i	$-0.675141\pi$
$101$	−105.621			−1.04575			−0.522876	+	0.852409i	$0.675141\pi$
$102$		0			0
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	−0.992081	−	0.125601i	$-0.959914\pi$
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	0.125601	+	0.992081i	$0.459914\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	0.951158	−	0.308706i	$-0.0998958\pi$
$107$	68.7423	+	68.7423i	0.642452	+	0.642452i	−0.308706	+	0.951158i	$0.599896\pi$
$108$		0			0
$109$			68.6969i			0.630247i	0.949051	+	0.315124i	$0.102046\pi$
$109$			68.6969i			0.630247i	−0.949051	+	0.315124i	$0.897954\pi$
$110$		0			0
$111$	−14.8082			−0.133407
$112$		0			0
$113$	−97.6413	+	97.6413i	−0.864083	+	0.864083i	−0.991809	−	0.127727i	$-0.959232\pi$
$113$	−97.6413	+	97.6413i	−0.864083	+	0.864083i	0.127727	+	0.991809i	$0.459232\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−16.6515	−	16.6515i	−0.142321	−	0.142321i
$118$		0			0
$119$			119.687i			1.00577i
$120$		0			0
$121$	7.78775			0.0643616
$122$		0			0
$123$	−0.853572	+	0.853572i	−0.00693961	+	0.00693961i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.930865	+	0.365362i	$0.119055\pi$
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.365362	+	0.930865i	$0.380945\pi$
$128$		0			0
$129$		−	64.8990i		−	0.503093i
$130$		0			0
$131$	−106.136			−0.810200			−0.405100	−	0.914272i	$-0.632763\pi$
$131$	−106.136			−0.810200			−0.405100	+	0.914272i	$0.632763\pi$
$132$		0			0
$133$	30.0000	−	30.0000i	0.225564	−	0.225564i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	166.631	+	166.631i	1.21629	+	1.21629i	0.968923	+	0.247363i	$0.0795639\pi$
$137$	166.631	+	166.631i	1.21629	+	1.21629i	0.247363	+	0.968923i	$0.420436\pi$
$138$		0			0
$139$			191.171i			1.37533i	0.726026	+	0.687667i	$0.241365\pi$
$139$			191.171i			1.37533i	−0.726026	+	0.687667i	$0.758635\pi$
$140$		0			0
$141$	−108.384			−0.768679
$142$		0			0
$143$	−62.9898	+	62.9898i	−0.440488	+	0.440488i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	30.8661	+	30.8661i	0.209973	+	0.209973i
$148$		0			0
$149$			84.8536i			0.569487i	0.958604	+	0.284744i	$0.0919084\pi$
$149$			84.8536i			0.569487i	−0.958604	+	0.284744i	$0.908092\pi$
$150$		0			0
$151$	−148.969			−0.986552			−0.493276	−	0.869873i	$-0.664201\pi$
$151$	−148.969			−0.986552			−0.493276	+	0.869873i	$0.664201\pi$
$152$		0			0
$153$	52.0454	−	52.0454i	0.340166	−	0.340166i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−16.8536	−	16.8536i	−0.107348	−	0.107348i	0.651393	−	0.758741i	$-0.274185\pi$
$157$	−16.8536	−	16.8536i	−0.107348	−	0.107348i	−0.758741	+	0.651393i	$0.774185\pi$
$158$		0			0
$159$			1.70714i			0.0107368i
$160$		0			0
$161$	79.6867			0.494949
$162$		0			0
$163$	130.606	−	130.606i	0.801265	−	0.801265i	−0.182029	−	0.983293i	$-0.558266\pi$
$163$	130.606	−	130.606i	0.801265	−	0.801265i	0.983293	+	0.182029i	$0.0582664\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−45.0352	−	45.0352i	−0.269672	−	0.269672i	0.559296	−	0.828968i	$-0.311071\pi$
$167$	−45.0352	−	45.0352i	−0.269672	−	0.269672i	−0.828968	+	0.559296i	$0.811071\pi$
$168$		0			0
$169$			107.384i			0.635406i
$170$		0			0
$171$	−26.0908			−0.152578
$172$		0			0
$173$	−146.631	+	146.631i	−0.847579	+	0.847579i	−0.989831	−	0.142252i	$-0.954566\pi$
$173$	−146.631	+	146.631i	−0.847579	+	0.847579i	0.142252	+	0.989831i	$0.454566\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−48.9092	−	48.9092i	−0.276323	−	0.276323i
$178$		0			0
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$		0			0
$183$	−7.23724	+	7.23724i	−0.0395478	+	0.0395478i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−196.879	−	196.879i	−1.05283	−	1.05283i
$188$		0			0
$189$			25.3485i			0.134119i
$190$		0			0
$191$	−48.0908			−0.251784			−0.125892	−	0.992044i	$-0.540179\pi$
$191$	−48.0908			−0.251784			−0.125892	+	0.992044i	$0.540179\pi$
$192$		0			0
$193$	255.565	−	255.565i	1.32417	−	1.32417i	0.413809	−	0.910364i	$-0.364198\pi$
$193$	255.565	−	255.565i	1.32417	−	1.32417i	0.910364	−	0.413809i	$-0.135802\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	96.6969	+	96.6969i	0.490847	+	0.490847i	0.908573	−	0.417726i	$-0.137173\pi$
$197$	96.6969	+	96.6969i	0.490847	+	0.490847i	−0.417726	+	0.908573i	$0.637173\pi$
$198$		0			0
$199$		−	192.606i		−	0.967870i	−0.875104	−	0.483935i	$-0.839207\pi$
$199$		−	192.606i		−	0.967870i	0.875104	−	0.483935i	$-0.160793\pi$
$200$		0			0
$201$	110.474			0.549624
$202$		0			0
$203$	−121.237	+	121.237i	−0.597228	+	0.597228i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−34.6515	−	34.6515i	−0.167399	−	0.167399i
$208$		0			0
$209$			98.6969i			0.472234i
$210$		0			0
$211$	−147.212			−0.697688			−0.348844	−	0.937181i	$-0.613426\pi$
$211$	−147.212			−0.697688			−0.348844	+	0.937181i	$0.613426\pi$
$212$		0			0
$213$	−83.2827	+	83.2827i	−0.390998	+	0.390998i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−36.8990	−	36.8990i	−0.170041	−	0.170041i
$218$		0			0
$219$		−	190.540i		−	0.870047i
$220$		0			0
$221$	192.586			0.871429
$222$		0			0
$223$	167.429	−	167.429i	0.750803	−	0.750803i	−0.223826	−	0.974629i	$-0.571855\pi$
$223$	167.429	−	167.429i	0.750803	−	0.750803i	0.974629	+	0.223826i	$0.0718548\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	253.171	+	253.171i	1.11529	+	1.11529i	0.992423	+	0.122870i	$0.0392098\pi$
$227$	253.171	+	253.171i	1.11529	+	1.11529i	0.122870	+	0.992423i	$0.460790\pi$
$228$		0			0
$229$		−	224.202i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$229$		−	224.202i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$230$		0			0
$231$	95.8888			0.415103
$232$		0			0
$233$	205.712	−	205.712i	0.882883	−	0.882883i	−0.110944	−	0.993827i	$-0.535387\pi$
$233$	205.712	−	205.712i	0.882883	−	0.882883i	0.993827	+	0.110944i	$0.0353873\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−30.0000	−	30.0000i	−0.126582	−	0.126582i
$238$		0			0
$239$			345.798i			1.44685i	0.690401	+	0.723427i	$0.257434\pi$
$239$			345.798i			1.44685i	−0.690401	+	0.723427i	$0.742566\pi$
$240$		0			0
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−48.2724	−	48.2724i	−0.195435	−	0.195435i
$248$		0			0
$249$			32.2020i			0.129325i
$250$		0			0
$251$	331.258			1.31975			0.659876	−	0.751375i	$-0.270609\pi$
$251$	331.258			1.31975			0.659876	+	0.751375i	$0.270609\pi$
$252$		0			0
$253$	−131.081	+	131.081i	−0.518105	+	0.518105i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−33.2372	−	33.2372i	−0.129328	−	0.129328i	0.639480	−	0.768808i	$-0.279150\pi$
$257$	−33.2372	−	33.2372i	−0.129328	−	0.129328i	−0.768808	+	0.639480i	$0.779150\pi$
$258$		0			0
$259$			41.7071i			0.161031i
$260$		0			0
$261$	105.439			0.403982
$262$		0			0
$263$	−278.157	+	278.157i	−1.05763	+	1.05763i	−0.0593952	+	0.998235i	$0.518917\pi$
$263$	−278.157	+	278.157i	−1.05763	+	1.05763i	−0.998235	+	0.0593952i	$0.981083\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−100.652	−	100.652i	−0.376972	−	0.376972i
$268$		0			0
$269$		−	488.499i		−	1.81598i	−0.418988	−	0.907992i	$-0.637615\pi$
$269$		−	488.499i		−	1.81598i	0.418988	−	0.907992i	$-0.362385\pi$
$270$		0			0
$271$	−131.576			−0.485518			−0.242759	−	0.970087i	$-0.578053\pi$
$271$	−131.576			−0.485518			−0.242759	+	0.970087i	$0.578053\pi$
$272$		0			0
$273$	−46.8990	+	46.8990i	−0.171791	+	0.171791i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−101.510	−	101.510i	−0.366461	−	0.366461i	0.499724	−	0.866185i	$-0.333435\pi$
$277$	−101.510	−	101.510i	−0.366461	−	0.366461i	−0.866185	+	0.499724i	$0.833435\pi$
$278$		0			0
$279$			32.0908i			0.115021i
$280$		0			0
$281$	343.303			1.22172			0.610860	−	0.791739i	$-0.290824\pi$
$281$	343.303			1.22172			0.610860	+	0.791739i	$0.290824\pi$
$282$		0			0
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	−0.704998	−	0.709209i	$-0.749052\pi$
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	0.709209	+	0.704998i	$0.249052\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.40408	+	2.40408i	0.00837659	+	0.00837659i
$288$		0			0
$289$			312.939i			1.08283i
$290$		0			0
$291$	−60.2474			−0.207036
$292$		0			0
$293$	−96.5653	+	96.5653i	−0.329574	+	0.329574i	−0.852425	−	0.522850i	$-0.824869\pi$
$293$	−96.5653	+	96.5653i	−0.329574	+	0.329574i	0.522850	+	0.852425i	$0.324869\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−41.6969	−	41.6969i	−0.140394	−	0.140394i
$298$		0			0
$299$		−	128.222i		−	0.428838i
$300$		0			0
$301$	−182.788			−0.607268
$302$		0			0
$303$	129.359	−	129.359i	0.426926	−	0.426926i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	0.473648	−	0.880714i	$-0.342937\pi$
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	−0.880714	+	0.473648i	$0.842937\pi$
$308$		0			0
$309$		−	218.611i		−	0.707478i
$310$		0			0
$311$	586.302			1.88522			0.942608	−	0.333902i	$-0.108365\pi$
$311$	586.302			1.88522			0.942608	+	0.333902i	$0.108365\pi$
$312$		0			0
$313$	102.373	−	102.373i	0.327072	−	0.327072i	−0.524400	−	0.851472i	$-0.675710\pi$
$313$	102.373	−	102.373i	0.327072	−	0.327072i	0.851472	+	0.524400i	$0.175710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	108.783	+	108.783i	0.343165	+	0.343165i	0.857556	−	0.514391i	$-0.171982\pi$
$317$	108.783	+	108.783i	0.343165	+	0.343165i	−0.514391	+	0.857556i	$0.671982\pi$
$318$		0			0
$319$		−	398.858i		−	1.25034i
$320$		0			0
$321$	−168.384			−0.524560
$322$		0			0
$323$	150.879	−	150.879i	0.467116	−	0.467116i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−84.1362	−	84.1362i	−0.257297	−	0.257297i
$328$		0			0
$329$			305.262i			0.927849i
$330$		0			0
$331$	245.423			0.741461			0.370730	−	0.928741i	$-0.379107\pi$
$331$	245.423			0.741461			0.370730	+	0.928741i	$0.379107\pi$
$332$		0			0
$333$	18.1362	−	18.1362i	0.0544631	−	0.0544631i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−213.808	−	213.808i	−0.634446	−	0.634446i	0.314734	−	0.949180i	$-0.398085\pi$
$337$	−213.808	−	213.808i	−0.634446	−	0.634446i	−0.949180	+	0.314734i	$0.898085\pi$
$338$		0			0
$339$		−	239.171i		−	0.705520i
$340$		0			0
$341$	121.394			0.355994
$342$		0			0
$343$	255.959	−	255.959i	0.746237	−	0.746237i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−160.050	−	160.050i	−0.461239	−	0.461239i	0.437822	−	0.899062i	$-0.355750\pi$
$347$	−160.050	−	160.050i	−0.461239	−	0.461239i	−0.899062	+	0.437822i	$0.855750\pi$
$348$		0			0
$349$		−	298.009i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$349$		−	298.009i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$350$		0			0
$351$	40.7878			0.116204
$352$		0			0
$353$	22.5199	−	22.5199i	0.0637957	−	0.0637957i	−0.674489	−	0.738285i	$-0.735636\pi$
$353$	22.5199	−	22.5199i	0.0637957	−	0.0637957i	0.738285	+	0.674489i	$0.235636\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−146.586	−	146.586i	−0.410604	−	0.410604i
$358$		0			0
$359$		−	48.2724i		−	0.134464i	−0.997737	−	0.0672318i	$-0.978583\pi$
$359$		−	48.2724i		−	0.134464i	0.997737	−	0.0672318i	$-0.0214167\pi$
$360$		0			0
$361$	285.363			0.790480
$362$		0			0
$363$	−9.53801	+	9.53801i	−0.0262755	+	0.0262755i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	146.510	+	146.510i	0.399209	+	0.399209i	0.877954	−	0.478745i	$-0.158908\pi$
$367$	146.510	+	146.510i	0.399209	+	0.399209i	−0.478745	+	0.877954i	$0.658908\pi$
$368$		0			0
$369$		−	2.09082i		−	0.00566617i
$370$		0			0
$371$	4.80816			0.0129600
$372$		0			0
$373$	−86.2066	+	86.2066i	−0.231117	+	0.231117i	−0.813159	−	0.582042i	$-0.802254\pi$
$373$	−86.2066	+	86.2066i	−0.231117	+	0.231117i	0.582042	+	0.813159i	$0.302254\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	195.081	+	195.081i	0.517455	+	0.517455i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$	−403.237			−1.05837
$382$		0			0
$383$	−10.6311	+	10.6311i	−0.0277575	+	0.0277575i	−0.720849	−	0.693092i	$-0.756248\pi$
$383$	−10.6311	+	10.6311i	−0.0277575	+	0.0277575i	0.693092	+	0.720849i	$0.256248\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	79.4847	+	79.4847i	0.205387	+	0.205387i
$388$		0			0
$389$		−	535.337i		−	1.37619i	−0.725621	−	0.688094i	$-0.758448\pi$
$389$		−	535.337i		−	1.37619i	0.725621	−	0.688094i	$-0.241552\pi$
$390$		0			0
$391$	400.767			1.02498
$392$		0			0
$393$	129.990	−	129.990i	0.330763	−	0.330763i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−118.742	−	118.742i	−0.299099	−	0.299099i	0.541562	−	0.840661i	$-0.317833\pi$
$397$	−118.742	−	118.742i	−0.299099	−	0.299099i	−0.840661	+	0.541562i	$0.817833\pi$
$398$		0			0
$399$			73.4847i			0.184172i
$400$		0			0
$401$	420.302			1.04813			0.524067	−	0.851677i	$-0.324414\pi$
$401$	420.302			1.04813			0.524067	+	0.851677i	$0.324414\pi$
$402$		0			0
$403$	−59.3735	+	59.3735i	−0.147329	+	0.147329i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−68.6061	−	68.6061i	−0.168565	−	0.168565i
$408$		0			0
$409$		−	515.110i		−	1.25944i	−0.776823	−	0.629719i	$-0.783170\pi$
$409$		−	515.110i		−	1.25944i	0.776823	−	0.629719i	$-0.216830\pi$
$410$		0			0
$411$	−408.161			−0.993093
$412$		0			0
$413$	−137.753	+	137.753i	−0.333541	+	0.333541i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−234.136	−	234.136i	−0.561478	−	0.561478i
$418$		0			0
$419$			88.6015i			0.211460i	0.994395	+	0.105730i	$0.0337178\pi$
$419$			88.6015i			0.211460i	−0.994395	+	0.105730i	$0.966282\pi$
$420$		0			0
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$		0			0
$423$	132.742	−	132.742i	0.313812	−	0.313812i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	20.3837	+	20.3837i	0.0477369	+	0.0477369i
$428$		0			0
$429$		−	154.293i		−	0.359657i
$430$		0			0
$431$	−804.636			−1.86690			−0.933452	−	0.358702i	$-0.883219\pi$
$431$	−804.636			−1.86690			−0.933452	+	0.358702i	$0.883219\pi$
$432$		0			0
$433$	344.848	−	344.848i	0.796416	−	0.796416i	−0.186113	−	0.982528i	$-0.559589\pi$
$433$	344.848	−	344.848i	0.796416	−	0.796416i	0.982528	+	0.186113i	$0.0595890\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−100.454	−	100.454i	−0.229872	−	0.229872i
$438$		0			0
$439$		−	432.929i		−	0.986170i	−0.869981	−	0.493085i	$-0.835869\pi$
$439$		−	432.929i		−	0.986170i	0.869981	−	0.493085i	$-0.164131\pi$
$440$		0			0
$441$	−75.6061			−0.171442
$442$		0			0
$443$	245.131	−	245.131i	0.553342	−	0.553342i	−0.374062	−	0.927404i	$-0.622035\pi$
$443$	245.131	−	245.131i	0.553342	−	0.553342i	0.927404	+	0.374062i	$0.122035\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−103.924	−	103.924i	−0.232492	−	0.232492i
$448$		0			0
$449$			386.091i			0.859890i	0.902855	+	0.429945i	$0.141467\pi$
$449$			386.091i			0.859890i	−0.902855	+	0.429945i	$0.858533\pi$
$450$		0			0
$451$	−7.90918			−0.0175370
$452$		0			0
$453$	182.449	−	182.449i	0.402758	−	0.402758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	223.747	+	223.747i	0.489599	+	0.489599i	0.908180	−	0.418580i	$-0.137472\pi$
$457$	223.747	+	223.747i	0.489599	+	0.489599i	−0.418580	+	0.908180i	$0.637472\pi$
$458$		0			0
$459$			127.485i			0.277744i
$460$		0			0
$461$	−722.620			−1.56751			−0.783753	−	0.621073i	$-0.786697\pi$
$461$	−722.620			−1.56751			−0.783753	+	0.621073i	$0.786697\pi$
$462$		0			0
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	−0.833162	−	0.553029i	$-0.813472\pi$
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	0.553029	+	0.833162i	$0.313472\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	415.258	+	415.258i	0.889203	+	0.889203i	0.994446	−	0.105244i	$-0.0335623\pi$
$467$	415.258	+	415.258i	0.889203	+	0.889203i	−0.105244	+	0.994446i	$0.533562\pi$
$468$		0			0
$469$		−	311.151i		−	0.663435i
$470$		0			0
$471$	41.2827			0.0876489
$472$		0			0
$473$	300.677	−	300.677i	0.635680	−	0.635680i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.09082	−	2.09082i	−0.00438326	−	0.00438326i
$478$		0			0
$479$		−	304.949i		−	0.636637i	−0.947984	−	0.318318i	$-0.896882\pi$
$479$		−	304.949i		−	0.636637i	0.947984	−	0.318318i	$-0.103118\pi$
$480$		0			0
$481$	67.1102			0.139522
$482$		0			0
$483$	−97.5959	+	97.5959i	−0.202062	+	0.202062i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	0.112137	−	0.993693i	$-0.464231\pi$
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	−0.993693	+	0.112137i	$0.964231\pi$
$488$		0			0
$489$			319.918i			0.654230i
$490$		0			0
$491$	414.318			0.843825			0.421912	−	0.906637i	$-0.361359\pi$
$491$	414.318			0.843825			0.421912	+	0.906637i	$0.361359\pi$
$492$		0			0
$493$	−609.737	+	609.737i	−1.23679	+	1.23679i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	234.565	+	234.565i	0.471962	+	0.471962i
$498$		0			0
$499$		−	367.585i		−	0.736643i	−0.929699	−	0.368321i	$-0.879933\pi$
$499$		−	367.585i		−	0.736643i	0.929699	−	0.368321i	$-0.120067\pi$
$500$		0			0
$501$	110.313			0.220186
$502$		0			0
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	−0.716577	−	0.697508i	$-0.754292\pi$
$503$	−9.59133	+	9.59133i	−0.0190683	+	0.0190683i	0.697508	+	0.716577i	$0.254292\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−131.518	−	131.518i	−0.259404	−	0.259404i
$508$		0			0
$509$			777.489i			1.52748i	0.645522	+	0.763742i	$0.276640\pi$
$509$			777.489i			1.52748i	−0.645522	+	0.763742i	$0.723360\pi$
$510$		0			0
$511$	−536.656			−1.05021
$512$		0			0
$513$	31.9546	−	31.9546i	0.0622897	−	0.0622897i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−502.141	−	502.141i	−0.971259	−	0.971259i
$518$		0			0
$519$		−	359.171i		−	0.692045i
$520$		0			0
$521$	321.605			0.617284			0.308642	−	0.951178i	$-0.400125\pi$
$521$	321.605			0.617284			0.308642	+	0.951178i	$0.400125\pi$
$522$		0			0
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.121030	+	0.992649i	$0.538620\pi$
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.992649	+	0.121030i	$0.961380\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−185.576	−	185.576i	−0.352136	−	0.352136i
$528$		0			0
$529$			262.171i			0.495598i
$530$		0			0
$531$	119.803			0.225617
$532$		0			0
$533$	3.86836	−	3.86836i	0.00725772	−	0.00725772i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	225.000	+	225.000i	0.418994	+	0.418994i
$538$		0			0
$539$			286.005i			0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$		0			0
$543$	350.611	−	350.611i	0.645692	−	0.645692i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.971081	−	0.238750i	$-0.923262\pi$
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.238750	−	0.971081i	$-0.576738\pi$
$548$		0			0
$549$		−	17.7276i		−	0.0322906i
$550$		0			0
$551$	305.666			0.554748
$552$		0			0
$553$	−84.4949	+	84.4949i	−0.152794	+	0.152794i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−125.909	−	125.909i	−0.226049	−	0.226049i	0.584991	−	0.811040i	$-0.301098\pi$
$557$	−125.909	−	125.909i	−0.226049	−	0.226049i	−0.811040	+	0.584991i	$0.801098\pi$
$558$		0			0
$559$			294.120i			0.526155i
$560$		0			0
$561$	482.252			0.859629
$562$		0			0
$563$	−200.009	+	200.009i	−0.355256	+	0.355256i	−0.862061	−	0.506805i	$-0.830826\pi$
$563$	−200.009	+	200.009i	−0.355256	+	0.355256i	0.506805	+	0.862061i	$0.330826\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−31.0454	−	31.0454i	−0.0547538	−	0.0547538i
$568$		0			0
$569$		−	599.839i		−	1.05420i	−0.849804	−	0.527099i	$-0.823280\pi$
$569$		−	599.839i		−	1.05420i	0.849804	−	0.527099i	$-0.176720\pi$
$570$		0			0
$571$	247.970			0.434274			0.217137	−	0.976141i	$-0.430328\pi$
$571$	247.970			0.434274			0.217137	+	0.976141i	$0.430328\pi$
$572$		0			0
$573$	58.8990	−	58.8990i	0.102791	−	0.102791i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	292.121	+	292.121i	0.506276	+	0.506276i	0.913381	−	0.407105i	$-0.133462\pi$
$577$	292.121	+	292.121i	0.506276	+	0.506276i	−0.407105	+	0.913381i	$0.633462\pi$
$578$		0			0
$579$			626.005i			1.08118i
$580$		0			0
$581$	90.6969			0.156105
$582$		0			0
$583$	−7.90918	+	7.90918i	−0.0135664	+	0.0135664i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	611.217	+	611.217i	1.04126	+	1.04126i	0.999112	+	0.0421437i	$0.0134187\pi$
$587$	611.217	+	611.217i	1.04126	+	1.04126i	0.0421437	+	0.999112i	$0.486581\pi$
$588$		0			0
$589$			93.0306i			0.157947i
$590$		0			0
$591$	−236.858			−0.400775
$592$		0			0
$593$	−524.742	+	524.742i	−0.884894	+	0.884894i	−0.994027	−	0.109133i	$-0.965193\pi$
$593$	−524.742	+	524.742i	−0.884894	+	0.884894i	0.109133	+	0.994027i	$0.465193\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	235.893	+	235.893i	0.395131	+	0.395131i
$598$		0			0
$599$			368.858i			0.615790i	0.951420	+	0.307895i	$0.0996245\pi$
$599$			368.858i			0.615790i	−0.951420	+	0.307895i	$0.900375\pi$
$600$		0			0
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$		0			0
$603$	−135.303	+	135.303i	−0.224383	+	0.224383i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	513.611	+	513.611i	0.846146	+	0.846146i	0.989650	−	0.143504i	$-0.0458369\pi$
$607$	513.611	+	513.611i	0.846146	+	0.846146i	−0.143504	+	0.989650i	$0.545837\pi$
$608$		0			0
$609$		−	296.969i		−	0.487634i
$610$		0			0
$611$	491.192			0.803915
$612$		0			0
$613$	615.287	−	615.287i	1.00373	−	1.00373i	0.00373821	−	0.999993i	$-0.498810\pi$
$613$	615.287	−	615.287i	1.00373	−	1.00373i	0.999993	−	0.00373821i	$-0.00118991\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−546.752	−	546.752i	−0.886145	−	0.886145i	0.108005	−	0.994150i	$-0.465554\pi$
$617$	−546.752	−	546.752i	−0.886145	−	0.886145i	−0.994150	+	0.108005i	$0.965554\pi$
$618$		0			0
$619$		−	152.869i		−	0.246962i	−0.992347	−	0.123481i	$-0.960594\pi$
$619$		−	152.869i		−	0.246962i	0.992347	−	0.123481i	$-0.0394058\pi$
$620$		0			0
$621$	84.8786			0.136680
$622$		0			0
$623$	−283.485	+	283.485i	−0.455032	+	0.455032i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−120.879	−	120.879i	−0.192789	−	0.192789i
$628$		0			0
$629$			209.757i			0.333477i
$630$		0			0
$631$	41.4847			0.0657444			0.0328722	−	0.999460i	$-0.489535\pi$
$631$	41.4847			0.0657444			0.0328722	+	0.999460i	$0.489535\pi$
$632$		0			0
$633$	180.297	−	180.297i	0.284830	−	0.284830i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−139.884	−	139.884i	−0.219598	−	0.219598i
$638$		0			0
$639$		−	204.000i		−	0.319249i
$640$		0			0
$641$	47.2122			0.0736541			0.0368270	−	0.999322i	$-0.488275\pi$
$641$	47.2122			0.0736541			0.0368270	+	0.999322i	$0.488275\pi$
$642$		0			0
$643$	460.372	−	460.372i	0.715976	−	0.715976i	−0.251803	−	0.967779i	$-0.581023\pi$
$643$	460.372	−	460.372i	0.715976	−	0.715976i	0.967779	+	0.251803i	$0.0810234\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	0.455487	−	0.890243i	$-0.349465\pi$
$647$	−281.287	−	281.287i	−0.434756	−	0.434756i	−0.890243	+	0.455487i	$0.849465\pi$
$648$		0			0
$649$		−	453.192i		−	0.698293i
$650$		0			0
$651$	90.3837			0.138838
$652$		0			0
$653$	−89.8230	+	89.8230i	−0.137554	+	0.137554i	−0.772531	−	0.634977i	$-0.781010\pi$
$653$	−89.8230	+	89.8230i	−0.137554	+	0.137554i	0.634977	+	0.772531i	$0.281010\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	233.363	+	233.363i	0.355195	+	0.355195i
$658$		0			0
$659$		−	1081.24i		−	1.64072i	−0.571844	−	0.820362i	$-0.693772\pi$
$659$		−	1081.24i		−	1.64072i	0.571844	−	0.820362i	$-0.306228\pi$
$660$		0			0
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$		0			0
$663$	−235.868	+	235.868i	−0.355759	+	0.355759i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	405.959	+	405.959i	0.608634	+	0.608634i
$668$		0			0
$669$			410.116i			0.613028i
$670$		0			0
$671$	−67.0602			−0.0999407
$672$		0			0
$673$	−233.293	+	233.293i	−0.346646	+	0.346646i	−0.858859	−	0.512213i	$-0.828826\pi$
$673$	−233.293	+	233.293i	−0.346646	+	0.346646i	0.512213	+	0.858859i	$0.328826\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	48.3883	+	48.3883i	0.0714745	+	0.0714745i	0.741940	−	0.670466i	$-0.233906\pi$
$677$	48.3883	+	48.3883i	0.0714745	+	0.0714745i	−0.670466	+	0.741940i	$0.733906\pi$
$678$		0			0
$679$			169.687i			0.249907i
$680$		0			0
$681$	−620.141			−0.910633
$682$		0			0
$683$	213.410	−	213.410i	0.312459	−	0.312459i	−0.533402	−	0.845862i	$-0.679087\pi$
$683$	213.410	−	213.410i	0.312459	−	0.312459i	0.845862	+	0.533402i	$0.179087\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	274.590	+	274.590i	0.399695	+	0.399695i
$688$		0			0
$689$		−	7.73673i		−	0.0112289i
$690$		0			0
$691$	−151.121			−0.218700			−0.109350	−	0.994003i	$-0.534877\pi$
$691$	−151.121			−0.218700			−0.109350	+	0.994003i	$0.534877\pi$
$692$		0			0
$693$	−117.439	+	117.439i	−0.169465	+	0.169465i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	12.0908	+	12.0908i	0.0173469	+	0.0173469i
$698$		0			0
$699$			503.889i			0.720871i
$700$		0			0
$701$	−745.680			−1.06374			−0.531869	−	0.846827i	$-0.678510\pi$
$701$	−745.680			−1.06374			−0.531869	+	0.846827i	$0.678510\pi$
$702$		0			0
$703$	52.5765	−	52.5765i	0.0747888	−	0.0747888i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−364.338	−	364.338i	−0.515330	−	0.515330i
$708$		0			0
$709$			719.049i			1.01417i	0.861895	+	0.507087i	$0.169278\pi$
$709$			719.049i			1.01417i	−0.861895	+	0.507087i	$0.830722\pi$
$710$		0			0
$711$	73.4847			0.103354
$712$		0			0
$713$	−123.555	+	123.555i	−0.173289	+	0.173289i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−423.514	−	423.514i	−0.590675	−	0.590675i
$718$		0			0
$719$			605.271i			0.841824i	0.907101	+	0.420912i	$0.138290\pi$
$719$			605.271i			0.841824i	−0.907101	+	0.420912i	$0.861710\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$		0			0
$723$	−124.404	+	124.404i	−0.172067	+	0.172067i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	0.517271	−	0.855821i	$-0.326948\pi$
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	−0.855821	+	0.517271i	$0.826948\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−919.292			−1.25758
$732$		0			0
$733$	270.763	−	270.763i	0.369390	−	0.369390i	−0.497865	−	0.867255i	$-0.665882\pi$
$733$	270.763	−	270.763i	0.369390	−	0.369390i	0.867255	+	0.497865i	$0.165882\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	511.828	+	511.828i	0.694474	+	0.694474i
$738$		0			0
$739$			515.666i			0.697789i	0.937162	+	0.348895i	$0.113443\pi$
$739$			515.666i			0.697789i	−0.937162	+	0.348895i	$0.886557\pi$
$740$		0			0
$741$	118.243			0.159572
$742$		0			0
$743$	420.702	−	420.702i	0.566220	−	0.566220i	−0.364847	−	0.931067i	$-0.618879\pi$
$743$	420.702	−	420.702i	0.566220	−	0.566220i	0.931067	+	0.364847i	$0.118879\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−39.4393	−	39.4393i	−0.0527969	−	0.0527969i
$748$		0			0
$749$			474.252i			0.633180i
$750$		0			0
$751$	859.787			1.14486			0.572428	−	0.819955i	$-0.306002\pi$
$751$	859.787			1.14486			0.572428	+	0.819955i	$0.306002\pi$
$752$		0			0
$753$	−405.706	+	405.706i	−0.538786	+	0.538786i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	956.075	+	956.075i	1.26298	+	1.26298i	0.949642	+	0.313337i	$0.101447\pi$
$757$	956.075	+	956.075i	1.26298	+	1.26298i	0.313337	+	0.949642i	$0.398553\pi$
$758$		0			0
$759$		−	321.081i		−	0.423031i
$760$		0			0
$761$	−322.758			−0.424124			−0.212062	−	0.977256i	$-0.568018\pi$
$761$	−322.758			−0.424124			−0.212062	+	0.977256i	$0.568018\pi$
$762$		0			0
$763$	−236.969	+	236.969i	−0.310576	+	0.310576i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	221.655	+	221.655i	0.288990	+	0.288990i
$768$		0			0
$769$			692.402i			0.900393i	0.892930	+	0.450196i	$0.148646\pi$
$769$			692.402i			0.900393i	−0.892930	+	0.450196i	$0.851354\pi$
$770$		0			0
$771$	81.4143			0.105596
$772$		0			0
$773$	−375.226	+	375.226i	−0.485415	+	0.485415i	−0.906856	−	0.421441i	$-0.861525\pi$
$773$	−375.226	+	375.226i	−0.485415	+	0.485415i	0.421441	+	0.906856i	$0.361525\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−51.0806	−	51.0806i	−0.0657408	−	0.0657408i
$778$		0			0
$779$		−	6.06123i		−	0.00778078i
$780$		0			0
$781$	−771.696			−0.988087
$782$		0			0
$783$	−129.136	+	129.136i	−0.164925	+	0.164925i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.985001	+	0.172546i	$0.0551993\pi$
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.172546	+	0.985001i	$0.444801\pi$
$788$		0			0
$789$		−	681.342i		−	0.863551i
$790$		0			0
$791$	−673.626			−0.851613
$792$		0			0
$793$	32.7990	−	32.7990i	0.0413606	−	0.0413606i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.21683	+	7.21683i	0.00905500	+	0.00905500i	0.711620	−	0.702565i	$-0.247962\pi$
$797$	7.21683	+	7.21683i	0.00905500	+	0.00905500i	−0.702565	+	0.711620i	$0.747962\pi$
$798$		0			0
$799$			1535.25i			1.92147i
$800$		0			0
$801$	246.545			0.307796
$802$		0			0
$803$	882.772	−	882.772i	1.09934	−	1.09934i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	598.287	+	598.287i	0.741372	+	0.741372i
$808$		0			0
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	−1336.85			−1.64839			−0.824197	−	0.566304i	$-0.808373\pi$
$811$	−1336.85			−1.64839			−0.824197	+	0.566304i	$0.808373\pi$
$812$		0			0
$813$	161.146	−	161.146i	0.198212	−	0.198212i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	230.424	+	230.424i	0.282037	+	0.282037i
$818$		0			0
$819$		−	114.879i		−	0.140267i
$820$		0			0
$821$	−33.8934			−0.0412830			−0.0206415	−	0.999787i	$-0.506571\pi$
$821$	−33.8934			−0.0412830			−0.0206415	+	0.999787i	$0.506571\pi$
$822$		0			0
$823$	481.631	−	481.631i	0.585214	−	0.585214i	−0.351117	−	0.936331i	$-0.614198\pi$
$823$	481.631	−	481.631i	0.585214	−	0.585214i	0.936331	+	0.351117i	$0.114198\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	350.756	+	350.756i	0.424131	+	0.424131i	0.886623	−	0.462492i	$-0.153045\pi$
$827$	350.756	+	350.756i	0.424131	+	0.424131i	−0.462492	+	0.886623i	$0.653045\pi$
$828$		0			0
$829$		−	697.423i		−	0.841283i	−0.907227	−	0.420641i	$-0.861805\pi$
$829$		−	697.423i		−	0.841283i	0.907227	−	0.420641i	$-0.138195\pi$
$830$		0			0
$831$	248.647			0.299214
$832$		0			0
$833$	437.217	−	437.217i	0.524870	−	0.524870i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−39.3031	−	39.3031i	−0.0469571	−	0.0469571i
$838$		0			0
$839$		−	72.3724i		−	0.0862604i	−0.999069	−	0.0431302i	$-0.986267\pi$
$839$		−	72.3724i		−	0.0862604i	0.999069	−	0.0431302i	$-0.0137330\pi$
$840$		0			0
$841$	−394.271			−0.468813
$842$		0			0
$843$	−420.459	+	420.459i	−0.498765	+	0.498765i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	26.8638	+	26.8638i	0.0317164	+	0.0317164i
$848$		0			0
$849$			2.91939i			0.00343862i
$850$		0			0
$851$	139.655			0.164107
$852$		0			0
$853$	74.5699	−	74.5699i	0.0874207	−	0.0874207i	−0.662044	−	0.749465i	$-0.730311\pi$
$853$	74.5699	−	74.5699i	0.0874207	−	0.0874207i	0.749465	+	0.662044i	$0.230311\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	293.176	+	293.176i	0.342096	+	0.342096i	0.857155	−	0.515059i	$-0.172230\pi$
$857$	293.176	+	293.176i	0.342096	+	0.342096i	−0.515059	+	0.857155i	$0.672230\pi$
$858$		0			0
$859$			786.867i			0.916027i	0.888945	+	0.458014i	$0.151439\pi$
$859$			786.867i			0.916027i	−0.888945	+	0.458014i	$0.848561\pi$
$860$		0			0
$861$	−5.88877			−0.00683946
$862$		0			0
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.284204	+	0.958764i	$0.591729\pi$
$863$	−1072.68	+	1072.68i	−1.24297	+	1.24297i	−0.958764	+	0.284204i	$0.908271\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−383.270	−	383.270i	−0.442065	−	0.442065i
$868$		0			0
$869$		−	277.980i		−	0.319884i
$870$		0			0
$871$	−500.667			−0.574819
$872$		0			0
$873$	73.7878	−	73.7878i	0.0845221	−	0.0845221i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−239.460	−	239.460i	−0.273044	−	0.273044i	0.557280	−	0.830324i	$-0.311845\pi$
$877$	−239.460	−	239.460i	−0.273044	−	0.273044i	−0.830324	+	0.557280i	$0.811845\pi$
$878$		0			0
$879$		−	236.536i		−	0.269096i
$880$		0			0
$881$	62.8490			0.0713382			0.0356691	−	0.999364i	$-0.488644\pi$
$881$	62.8490			0.0713382			0.0356691	+	0.999364i	$0.488644\pi$
$882$		0			0
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	−0.790922	−	0.611917i	$-0.790399\pi$
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	0.611917	+	0.790922i	$0.290399\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	30.2066	+	30.2066i	0.0340548	+	0.0340548i	0.723929	−	0.689874i	$-0.242334\pi$
$887$	30.2066	+	30.2066i	0.0340548	+	0.0340548i	−0.689874	+	0.723929i	$0.742334\pi$
$888$		0			0
$889$			1135.72i			1.27752i
$890$		0			0
$891$	102.136			0.114631
$892$		0			0
$893$	384.817	−	384.817i	0.430926	−	0.430926i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	157.040	+	157.040i	0.175072	+	0.175072i
$898$		0			0
$899$		−	375.959i		−	0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$		0			0
$903$	223.868	−	223.868i	0.247916	−	0.247916i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	571.342	+	571.342i	0.629925	+	0.629925i	0.948049	−	0.318124i	$-0.103053\pi$
$907$	571.342	+	571.342i	0.629925	+	0.629925i	−0.318124	+	0.948049i	$0.603053\pi$
$908$		0			0
$909$			316.863i			0.348584i
$910$		0			0
$911$	−173.362			−0.190299			−0.0951494	−	0.995463i	$-0.530333\pi$
$911$	−173.362			−0.190299			−0.0951494	+	0.995463i	$0.530333\pi$
$912$		0			0
$913$	−149.192	+	149.192i	−0.163408	+	0.163408i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−366.116	−	366.116i	−0.399254	−	0.399254i
$918$		0			0
$919$		−	1147.42i		−	1.24856i	−0.781202	−	0.624278i	$-0.785393\pi$
$919$		−	1147.42i		−	1.24856i	0.781202	−	0.624278i	$-0.214607\pi$
$920$		0			0
$921$	306.111			0.332368
$922$		0			0
$923$	377.435	−	377.435i	0.408922	−	0.408922i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	267.742	+	267.742i	0.288827	+	0.288827i
$928$		0			0
$929$		−	220.293i		−	0.237129i	−0.992946	−	0.118565i	$-0.962171\pi$
$929$		−	220.293i		−	0.237129i	0.992946	−	0.118565i	$-0.0378292\pi$
$930$		0			0
$931$	−219.181			−0.235425
$932$		0			0
$933$	−718.070	+	718.070i	−0.769636	+	0.769636i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	396.090	+	396.090i	0.422721	+	0.422721i	0.886140	−	0.463418i	$-0.153377\pi$
$937$	396.090	+	396.090i	0.422721	+	0.422721i	−0.463418	+	0.886140i	$0.653377\pi$
$938$		0			0
$939$			250.763i			0.267053i
$940$		0			0
$941$	185.771			0.197419			0.0987093	−	0.995116i	$-0.468529\pi$
$941$	185.771			0.197419			0.0987093	+	0.995116i	$0.468529\pi$
$942$		0			0
$943$	8.04999	−	8.04999i	0.00853658	−	0.00853658i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−845.190	−	845.190i	−0.892492	−	0.892492i	0.102265	−	0.994757i	$-0.467391\pi$
$947$	−845.190	−	845.190i	−0.892492	−	0.892492i	−0.994757	+	0.102265i	$0.967391\pi$
$948$		0			0
$949$			863.523i			0.909930i
$950$		0			0
$951$	−266.463			−0.280193
$952$		0			0
$953$	630.499	−	630.499i	0.661594	−	0.661594i	−0.294161	−	0.955756i	$-0.595040\pi$
$953$	630.499	−	630.499i	0.661594	−	0.661594i	0.955756	+	0.294161i	$0.0950403\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	488.499	+	488.499i	0.510449	+	0.510449i
$958$		0			0
$959$			1149.58i			1.19873i
$960$		0			0
$961$	−846.576			−0.880932
$962$		0			0
$963$	206.227	−	206.227i	0.214151	−	0.214151i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	0.481649	−	0.876364i	$-0.340038\pi$
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	−0.876364	+	0.481649i	$0.840038\pi$
$968$		0			0
$969$			369.576i			0.381399i
$970$		0			0
$971$	1000.44			1.03032			0.515159	−	0.857095i	$-0.327733\pi$
$971$	1000.44			1.03032			0.515159	+	0.857095i	$0.327733\pi$
$972$		0			0
$973$	−659.444	+	659.444i	−0.677743	+	0.677743i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−593.662	−	593.662i	−0.607637	−	0.607637i	0.334691	−	0.942328i	$-0.391368\pi$
$977$	−593.662	−	593.662i	−0.607637	−	0.607637i	−0.942328	+	0.334691i	$0.891368\pi$
$978$		0			0
$979$		−	932.636i		−	0.952641i
$980$		0			0
$981$	206.091			0.210082
$982$		0			0
$983$	−1217.34	+	1217.34i	−1.23839	+	1.23839i	−0.277731	+	0.960659i	$0.589582\pi$
$983$	−1217.34	+	1217.34i	−1.23839	+	1.23839i	−0.960659	+	0.277731i	$0.910418\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−373.868	−	373.868i	−0.378793	−	0.378793i
$988$		0			0
$989$			612.059i			0.618867i
$990$		0			0
$991$	544.061			0.549002			0.274501	−	0.961587i	$-0.411487\pi$
$991$	544.061			0.549002			0.274501	+	0.961587i	$0.411487\pi$
$992$		0			0
$993$	−300.581	+	300.581i	−0.302700	+	0.302700i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	316.733	+	316.733i	0.317686	+	0.317686i	0.847878	−	0.530192i	$-0.177880\pi$
$997$	316.733	+	316.733i	0.317686	+	0.317686i	−0.530192	+	0.847878i	$0.677880\pi$
$998$		0			0
$999$			44.4245i			0.0444690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.k.1057.1		4
4.3	odd	2		75.3.f.c.7.1		4
5.2	odd	4		240.3.bg.a.193.2		4
5.3	odd	4	inner	1200.3.bg.k.193.1		4
5.4	even	2		240.3.bg.a.97.2		4
12.11	even	2		225.3.g.a.82.2		4
15.2	even	4		720.3.bh.k.433.2		4
15.14	odd	2		720.3.bh.k.577.2		4
20.3	even	4		75.3.f.c.43.1		4
20.7	even	4		15.3.f.a.13.2	yes	4
20.19	odd	2		15.3.f.a.7.2	✓	4
40.19	odd	2		960.3.bg.i.577.2		4
40.27	even	4		960.3.bg.i.193.2		4
40.29	even	2		960.3.bg.h.577.1		4
40.37	odd	4		960.3.bg.h.193.1		4
60.23	odd	4		225.3.g.a.118.2		4
60.47	odd	4		45.3.g.b.28.1		4
60.59	even	2		45.3.g.b.37.1		4
180.7	even	12		405.3.l.h.28.1		8
180.47	odd	12		405.3.l.f.28.2		8
180.59	even	6		405.3.l.f.217.2		8
180.67	even	12		405.3.l.h.298.2		8
180.79	odd	6		405.3.l.h.352.2		8
180.119	even	6		405.3.l.f.352.1		8
180.139	odd	6		405.3.l.h.217.1		8
180.167	odd	12		405.3.l.f.298.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	20.19	odd	2
15.3.f.a.13.2	yes	4	20.7	even	4
45.3.g.b.28.1		4	60.47	odd	4
45.3.g.b.37.1		4	60.59	even	2
75.3.f.c.7.1		4	4.3	odd	2
75.3.f.c.43.1		4	20.3	even	4
225.3.g.a.82.2		4	12.11	even	2
225.3.g.a.118.2		4	60.23	odd	4
240.3.bg.a.97.2		4	5.4	even	2
240.3.bg.a.193.2		4	5.2	odd	4
405.3.l.f.28.2		8	180.47	odd	12
405.3.l.f.217.2		8	180.59	even	6
405.3.l.f.298.1		8	180.167	odd	12
405.3.l.f.352.1		8	180.119	even	6
405.3.l.h.28.1		8	180.7	even	12
405.3.l.h.217.1		8	180.139	odd	6
405.3.l.h.298.2		8	180.67	even	12
405.3.l.h.352.2		8	180.79	odd	6
720.3.bh.k.433.2		4	15.2	even	4
720.3.bh.k.577.2		4	15.14	odd	2
960.3.bg.h.193.1		4	40.37	odd	4
960.3.bg.h.577.1		4	40.29	even	2
960.3.bg.i.193.2		4	40.27	even	4
960.3.bg.i.577.2		4	40.19	odd	2
1200.3.bg.k.193.1		4	5.3	odd	4	inner
1200.3.bg.k.1057.1		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(3.44949 + 3.44949i) q^{7} -3.00000i q^{9} -11.3485 q^{11} +(5.55051 - 5.55051i) q^{13} +(17.3485 + 17.3485i) q^{17} -8.69694i q^{19} -8.44949 q^{21} +(11.5505 - 11.5505i) q^{23} +(3.67423 + 3.67423i) q^{27} +35.1464i q^{29} -10.6969 q^{31} +(13.8990 - 13.8990i) q^{33} +(6.04541 + 6.04541i) q^{37} +13.5959i q^{39} +0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +(44.2474 + 44.2474i) q^{47} -25.2020i q^{49} -42.4949 q^{51} +(0.696938 - 0.696938i) q^{53} +(10.6515 + 10.6515i) q^{57} +39.9342i q^{59} +5.90918 q^{61} +(10.3485 - 10.3485i) q^{63} +(-45.1010 - 45.1010i) q^{67} +28.2929i q^{69} +68.0000 q^{71} +(-77.7878 + 77.7878i) q^{73} +(-39.1464 - 39.1464i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(13.1464 - 13.1464i) q^{83} +(-43.0454 - 43.0454i) q^{87} +82.1816i q^{89} +38.2929 q^{91} +(13.1010 - 13.1010i) q^{93} +(24.5959 + 24.5959i) q^{97} +34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{7} - 16 q^{11} + 32 q^{13} + 40 q^{17} - 24 q^{21} + 56 q^{23} + 16 q^{31} + 36 q^{33} - 64 q^{37} - 56 q^{41} - 8 q^{43} + 128 q^{47} - 72 q^{51} - 56 q^{53} + 72 q^{57} + 200 q^{61} + 12 q^{63}+ \cdots + 20 q^{97}+O(q^{100}) \) 4 * q + 4 * q^7 - 16 * q^11 + 32 * q^13 + 40 * q^17 - 24 * q^21 + 56 * q^23 + 16 * q^31 + 36 * q^33 - 64 * q^37 - 56 * q^41 - 8 * q^43 + 128 * q^47 - 72 * q^51 - 56 * q^53 + 72 * q^57 + 200 * q^61 + 12 * q^63 - 200 * q^67 + 272 * q^71 - 76 * q^73 - 88 * q^77 - 36 * q^81 - 16 * q^83 - 84 * q^87 + 16 * q^91 + 72 * q^93 + 20 * q^97

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