LMFDB - Embedded newform 850.2.g.d.149.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(149,850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(850, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("850.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.g (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,0,2,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	850.149
Dual form			850.2.g.d.599.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +3.00000i q^{9} +(-4.00000 + 4.00000i) q^{11} +4.00000i q^{13} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} +3.00000i q^{18} -4.00000i q^{19} +(-4.00000 + 4.00000i) q^{22} +(4.00000 + 4.00000i) q^{23} +4.00000i q^{26} +(3.00000 + 3.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +1.00000 q^{32} +(4.00000 + 1.00000i) q^{34} +3.00000i q^{36} +(3.00000 - 3.00000i) q^{37} -4.00000i q^{38} +(1.00000 - 1.00000i) q^{41} +4.00000 q^{43} +(-4.00000 + 4.00000i) q^{44} +(4.00000 + 4.00000i) q^{46} -8.00000i q^{47} -7.00000i q^{49} +4.00000i q^{52} +4.00000 q^{53} +(3.00000 + 3.00000i) q^{58} -4.00000i q^{59} +(-9.00000 + 9.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +1.00000 q^{64} +12.0000i q^{67} +(4.00000 + 1.00000i) q^{68} +(-4.00000 - 4.00000i) q^{71} +3.00000i q^{72} +(-5.00000 + 5.00000i) q^{73} +(3.00000 - 3.00000i) q^{74} -4.00000i q^{76} +(-8.00000 + 8.00000i) q^{79} -9.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +4.00000 q^{83} +4.00000 q^{86} +(-4.00000 + 4.00000i) q^{88} +(4.00000 + 4.00000i) q^{92} -8.00000i q^{94} +(3.00000 - 3.00000i) q^{97} -7.00000i q^{98} +(-12.0000 - 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 8 q^{11} + 2 q^{16} + 8 q^{17} - 8 q^{22} + 8 q^{23} + 6 q^{29} - 8 q^{31} + 2 q^{32} + 8 q^{34} + 6 q^{37} + 2 q^{41} + 8 q^{43} - 8 q^{44} + 8 q^{46} + 8 q^{53} + 6 q^{58}+ \cdots - 24 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 8 * q^11 + 2 * q^16 + 8 * q^17 - 8 * q^22 + 8 * q^23 + 6 * q^29 - 8 * q^31 + 2 * q^32 + 8 * q^34 + 6 * q^37 + 2 * q^41 + 8 * q^43 - 8 * q^44 + 8 * q^46 + 8 * q^53 + 6 * q^58 - 18 * q^61 - 8 * q^62 + 2 * q^64 + 8 * q^68 - 8 * q^71 - 10 * q^73 + 6 * q^74 - 16 * q^79 - 18 * q^81 + 2 * q^82 + 8 * q^83 + 8 * q^86 - 8 * q^88 + 8 * q^92 + 6 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$		0			0
$11$	−4.00000	+	4.00000i	−1.20605	+	1.20605i	−0.233748	+	0.972297i	$0.575099\pi$
$11$	−4.00000	+	4.00000i	−1.20605	+	1.20605i	−0.972297	+	0.233748i	$0.924901\pi$
$12$		0			0
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$18$			3.00000i			0.707107i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		0			0
$22$	−4.00000	+	4.00000i	−0.852803	+	0.852803i
$23$	4.00000	+	4.00000i	0.834058	+	0.834058i	0.988069	−	0.154011i	$-0.0492193\pi$
$23$	4.00000	+	4.00000i	0.834058	+	0.834058i	−0.154011	+	0.988069i	$0.549219\pi$
$24$		0			0
$25$		0			0
$26$			4.00000i			0.784465i
$27$		0			0
$28$		0			0
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	0.928477	−	0.371391i	$-0.121119\pi$
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	0.249861	−	0.968282i	$-0.419615\pi$
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	−0.968282	+	0.249861i	$0.919615\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	4.00000	+	1.00000i	0.685994	+	0.171499i
$35$		0			0
$36$			3.00000i			0.500000i
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$		−	4.00000i		−	0.648886i
$39$		0			0
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−4.00000	+	4.00000i	−0.603023	+	0.603023i
$45$		0			0
$46$	4.00000	+	4.00000i	0.589768	+	0.589768i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$		0			0
$51$		0			0
$52$			4.00000i			0.554700i
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	3.00000	+	3.00000i	0.393919	+	0.393919i
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.166248	+	0.986084i	$0.553165\pi$
$61$	−9.00000	+	9.00000i	−1.15233	+	1.15233i	−0.986084	+	0.166248i	$0.946835\pi$
$62$	−4.00000	−	4.00000i	−0.508001	−	0.508001i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	4.00000	+	1.00000i	0.485071	+	0.121268i
$69$		0			0
$70$		0			0
$71$	−4.00000	−	4.00000i	−0.474713	−	0.474713i	0.428723	−	0.903436i	$-0.358964\pi$
$71$	−4.00000	−	4.00000i	−0.474713	−	0.474713i	−0.903436	+	0.428723i	$0.858964\pi$
$72$			3.00000i			0.353553i
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$	3.00000	−	3.00000i	0.348743	−	0.348743i
$75$		0			0
$76$		−	4.00000i		−	0.458831i
$77$		0			0
$78$		0			0
$79$	−8.00000	+	8.00000i	−0.900070	+	0.900070i	−0.995442	−	0.0953714i	$-0.969596\pi$
$79$	−8.00000	+	8.00000i	−0.900070	+	0.900070i	0.0953714	+	0.995442i	$0.469596\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	1.00000	−	1.00000i	0.110432	−	0.110432i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$		0			0
$86$	4.00000			0.431331
$87$		0			0
$88$	−4.00000	+	4.00000i	−0.426401	+	0.426401i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$		0			0
$92$	4.00000	+	4.00000i	0.417029	+	0.417029i
$93$		0			0
$94$		−	8.00000i		−	0.825137i
$95$		0			0
$96$		0			0
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$		−	7.00000i		−	0.707107i
$99$	−12.0000	−	12.0000i	−1.20605	−	1.20605i
$100$		0			0
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$		0			0
$103$		−	16.0000i		−	1.57653i	−0.615338	−	0.788263i	$-0.710980\pi$
$103$		−	16.0000i		−	1.57653i	0.615338	−	0.788263i	$-0.289020\pi$
$104$			4.00000i			0.392232i
$105$		0			0
$106$	4.00000			0.388514
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	−0.205308	−	0.978697i	$-0.565820\pi$
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	0.978697	+	0.205308i	$0.0658197\pi$
$108$		0			0
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	−0.836031	−	0.548683i	$-0.815129\pi$
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	0.548683	+	0.836031i	$0.315129\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	0.658505	−	0.752577i	$-0.271189\pi$
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	+	3.00000i	0.278543	+	0.278543i
$117$	−12.0000			−1.10940
$118$		−	4.00000i		−	0.368230i
$119$		0			0
$120$		0			0
$121$		−	21.0000i		−	1.90909i
$122$	−9.00000	+	9.00000i	−0.814822	+	0.814822i
$123$		0			0
$124$	−4.00000	−	4.00000i	−0.359211	−	0.359211i
$125$		0			0
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$		0			0
$131$	−4.00000	−	4.00000i	−0.349482	−	0.349482i	0.510435	−	0.859916i	$-0.329484\pi$
$131$	−4.00000	−	4.00000i	−0.349482	−	0.349482i	−0.859916	+	0.510435i	$0.829484\pi$
$132$		0			0
$133$		0			0
$134$			12.0000i			1.03664i
$135$		0			0
$136$	4.00000	+	1.00000i	0.342997	+	0.0857493i
$137$		−	8.00000i		−	0.683486i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$		−	8.00000i		−	0.683486i	0.939793	−	0.341743i	$-0.111017\pi$
$138$		0			0
$139$	8.00000	+	8.00000i	0.678551	+	0.678551i	0.959672	−	0.281121i	$-0.0907063\pi$
$139$	8.00000	+	8.00000i	0.678551	+	0.678551i	−0.281121	+	0.959672i	$0.590706\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	−	4.00000i	−0.335673	−	0.335673i
$143$	−16.0000	−	16.0000i	−1.33799	−	1.33799i
$144$			3.00000i			0.250000i
$145$		0			0
$146$	−5.00000	+	5.00000i	−0.413803	+	0.413803i
$147$		0			0
$148$	3.00000	−	3.00000i	0.246598	−	0.246598i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		−	4.00000i		−	0.324443i
$153$	−3.00000	+	12.0000i	−0.242536	+	0.970143i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	−8.00000	+	8.00000i	−0.636446	+	0.636446i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−9.00000			−0.707107
$163$	4.00000	+	4.00000i	0.313304	+	0.313304i	0.846188	−	0.532884i	$-0.178892\pi$
$163$	4.00000	+	4.00000i	0.313304	+	0.313304i	−0.532884	+	0.846188i	$0.678892\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$	4.00000			0.310460
$167$	8.00000	−	8.00000i	0.619059	−	0.619059i	−0.326231	−	0.945290i	$-0.605779\pi$
$167$	8.00000	−	8.00000i	0.619059	−	0.619059i	0.945290	+	0.326231i	$0.105779\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$	12.0000			0.917663
$172$	4.00000			0.304997
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	−0.871154	−	0.491011i	$-0.836628\pi$
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	0.491011	+	0.871154i	$0.336628\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000	+	4.00000i	−0.301511	+	0.301511i
$177$		0			0
$178$		0			0
$179$		−	4.00000i		−	0.298974i	−0.988764	−	0.149487i	$-0.952238\pi$
$179$		−	4.00000i		−	0.298974i	0.988764	−	0.149487i	$-0.0477622\pi$
$180$		0			0
$181$	11.0000	−	11.0000i	0.817624	−	0.817624i	−0.168140	−	0.985763i	$-0.553776\pi$
$181$	11.0000	−	11.0000i	0.817624	−	0.817624i	0.985763	+	0.168140i	$0.0537759\pi$
$182$		0			0
$183$		0			0
$184$	4.00000	+	4.00000i	0.294884	+	0.294884i
$185$		0			0
$186$		0			0
$187$	−20.0000	+	12.0000i	−1.46254	+	0.877527i
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	−11.0000	−	11.0000i	−0.791797	−	0.791797i	0.189989	−	0.981786i	$-0.439155\pi$
$193$	−11.0000	−	11.0000i	−0.791797	−	0.791797i	−0.981786	+	0.189989i	$0.939155\pi$
$194$	3.00000	−	3.00000i	0.215387	−	0.215387i
$195$		0			0
$196$		−	7.00000i		−	0.500000i
$197$	−5.00000	−	5.00000i	−0.356235	−	0.356235i	0.506188	−	0.862423i	$-0.331054\pi$
$197$	−5.00000	−	5.00000i	−0.356235	−	0.356235i	−0.862423	+	0.506188i	$0.831054\pi$
$198$	−12.0000	−	12.0000i	−0.852803	−	0.852803i
$199$	−12.0000	−	12.0000i	−0.850657	−	0.850657i	0.139557	−	0.990214i	$-0.455432\pi$
$199$	−12.0000	−	12.0000i	−0.850657	−	0.850657i	−0.990214	+	0.139557i	$0.955432\pi$
$200$		0			0
$201$		0			0
$202$	12.0000			0.844317
$203$		0			0
$204$		0			0
$205$		0			0
$206$		−	16.0000i		−	1.11477i
$207$	−12.0000	+	12.0000i	−0.834058	+	0.834058i
$208$			4.00000i			0.277350i
$209$	16.0000	+	16.0000i	1.10674	+	1.10674i
$210$		0			0
$211$	16.0000	−	16.0000i	1.10149	−	1.10149i	0.107254	−	0.994232i	$-0.465794\pi$
$211$	16.0000	−	16.0000i	1.10149	−	1.10149i	0.994232	−	0.107254i	$-0.0342057\pi$
$212$	4.00000			0.274721
$213$		0			0
$214$	8.00000	−	8.00000i	0.546869	−	0.546869i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−3.00000	+	3.00000i	−0.203186	+	0.203186i
$219$		0			0
$220$		0			0
$221$	−4.00000	+	16.0000i	−0.269069	+	1.07628i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$		0			0
$226$	−1.00000	−	1.00000i	−0.0665190	−	0.0665190i
$227$	−20.0000	−	20.0000i	−1.32745	−	1.32745i	−0.907591	−	0.419856i	$-0.862081\pi$
$227$	−20.0000	−	20.0000i	−1.32745	−	1.32745i	−0.419856	−	0.907591i	$-0.637919\pi$
$228$		0			0
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	+	3.00000i	0.196960	+	0.196960i
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	0.851658	+	0.524097i	$0.175597\pi$
$234$	−12.0000			−0.784465
$235$		0			0
$236$		−	4.00000i		−	0.260378i
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	21.0000	+	21.0000i	1.35273	+	1.35273i	0.882595	+	0.470134i	$0.155794\pi$
$241$	21.0000	+	21.0000i	1.35273	+	1.35273i	0.470134	+	0.882595i	$0.344206\pi$
$242$		−	21.0000i		−	1.34993i
$243$		0			0
$244$	−9.00000	+	9.00000i	−0.576166	+	0.576166i
$245$		0			0
$246$		0			0
$247$	16.0000			1.01806
$248$	−4.00000	−	4.00000i	−0.254000	−	0.254000i
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$	8.00000			0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.00000	+	9.00000i	−0.557086	+	0.557086i
$262$	−4.00000	−	4.00000i	−0.247121	−	0.247121i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$			12.0000i			0.733017i
$269$	13.0000	+	13.0000i	0.792624	+	0.792624i	0.981920	−	0.189296i	$-0.0606206\pi$
$269$	13.0000	+	13.0000i	0.792624	+	0.792624i	−0.189296	+	0.981920i	$0.560621\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	4.00000	+	1.00000i	0.242536	+	0.0606339i
$273$		0			0
$274$		−	8.00000i		−	0.483298i
$275$		0			0
$276$		0			0
$277$	−7.00000	+	7.00000i	−0.420589	+	0.420589i	−0.885407	−	0.464817i	$-0.846120\pi$
$277$	−7.00000	+	7.00000i	−0.420589	+	0.420589i	0.464817	+	0.885407i	$0.346120\pi$
$278$	8.00000	+	8.00000i	0.479808	+	0.479808i
$279$	12.0000	−	12.0000i	0.718421	−	0.718421i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$	4.00000	+	4.00000i	0.237775	+	0.237775i	0.815928	−	0.578153i	$-0.196226\pi$
$283$	4.00000	+	4.00000i	0.237775	+	0.237775i	−0.578153	+	0.815928i	$0.696226\pi$
$284$	−4.00000	−	4.00000i	−0.237356	−	0.237356i
$285$		0			0
$286$	−16.0000	−	16.0000i	−0.946100	−	0.946100i
$287$		0			0
$288$			3.00000i			0.176777i
$289$	15.0000	+	8.00000i	0.882353	+	0.470588i
$290$		0			0
$291$		0			0
$292$	−5.00000	+	5.00000i	−0.292603	+	0.292603i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$	3.00000	−	3.00000i	0.174371	−	0.174371i
$297$		0			0
$298$	10.0000			0.579284
$299$	−16.0000	+	16.0000i	−0.925304	+	0.925304i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$		0			0
$306$	−3.00000	+	12.0000i	−0.171499	+	0.685994i
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−24.0000	−	24.0000i	−1.36092	−	1.36092i	−0.872753	−	0.488162i	$-0.837667\pi$
$311$	−24.0000	−	24.0000i	−1.36092	−	1.36092i	−0.488162	−	0.872753i	$-0.662333\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$			2.00000i			0.112867i
$315$		0			0
$316$	−8.00000	+	8.00000i	−0.450035	+	0.450035i
$317$	15.0000	+	15.0000i	0.842484	+	0.842484i	0.989181	−	0.146697i	$-0.0468644\pi$
$317$	15.0000	+	15.0000i	0.842484	+	0.842484i	−0.146697	+	0.989181i	$0.546864\pi$
$318$		0			0
$319$	−24.0000			−1.34374
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.00000	−	16.0000i	0.222566	−	0.890264i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	4.00000	+	4.00000i	0.221540	+	0.221540i
$327$		0			0
$328$	1.00000	−	1.00000i	0.0552158	−	0.0552158i
$329$		0			0
$330$		0			0
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$	4.00000			0.219529
$333$	9.00000	+	9.00000i	0.493197	+	0.493197i
$334$	8.00000	−	8.00000i	0.437741	−	0.437741i
$335$		0			0
$336$		0			0
$337$	−7.00000	+	7.00000i	−0.381314	+	0.381314i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−7.00000	+	7.00000i	−0.381314	+	0.381314i	0.490261	+	0.871576i	$0.336901\pi$
$338$	−3.00000			−0.163178
$339$		0			0
$340$		0			0
$341$	32.0000			1.73290
$342$	12.0000			0.648886
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−5.00000	+	5.00000i	−0.268802	+	0.268802i
$347$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$347$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$348$		0			0
$349$		−	4.00000i		−	0.214115i	−0.994253	−	0.107058i	$-0.965857\pi$
$349$		−	4.00000i		−	0.214115i	0.994253	−	0.107058i	$-0.0341429\pi$
$350$		0			0
$351$		0			0
$352$	−4.00000	+	4.00000i	−0.213201	+	0.213201i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		−	4.00000i		−	0.211407i
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	11.0000	−	11.0000i	0.578147	−	0.578147i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$367$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$368$	4.00000	+	4.00000i	0.208514	+	0.208514i
$369$	3.00000	+	3.00000i	0.156174	+	0.156174i
$370$		0			0
$371$		0			0
$372$		0			0
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$	−20.0000	+	12.0000i	−1.03418	+	0.620505i
$375$		0			0
$376$		−	8.00000i		−	0.412568i
$377$	−12.0000	+	12.0000i	−0.618031	+	0.618031i
$378$		0			0
$379$	−12.0000	−	12.0000i	−0.616399	−	0.616399i	0.328207	−	0.944606i	$-0.393556\pi$
$379$	−12.0000	−	12.0000i	−0.616399	−	0.616399i	−0.944606	+	0.328207i	$0.893556\pi$
$380$		0			0
$381$		0			0
$382$	−8.00000			−0.409316
$383$	24.0000			1.22634			0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000			1.22634			0.613171	+	0.789950i	$0.289894\pi$
$384$		0			0
$385$		0			0
$386$	−11.0000	−	11.0000i	−0.559885	−	0.559885i
$387$			12.0000i			0.609994i
$388$	3.00000	−	3.00000i	0.152302	−	0.152302i
$389$			6.00000i			0.304212i	0.988364	+	0.152106i	$0.0486055\pi$
$389$			6.00000i			0.304212i	−0.988364	+	0.152106i	$0.951394\pi$
$390$		0			0
$391$	12.0000	+	20.0000i	0.606866	+	1.01144i
$392$		−	7.00000i		−	0.353553i
$393$		0			0
$394$	−5.00000	−	5.00000i	−0.251896	−	0.251896i
$395$		0			0
$396$	−12.0000	−	12.0000i	−0.603023	−	0.603023i
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	0.222178	−	0.975006i	$-0.428683\pi$
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	−0.975006	+	0.222178i	$0.928683\pi$
$398$	−12.0000	−	12.0000i	−0.601506	−	0.601506i
$399$		0			0
$400$		0			0
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	−0.998752	−	0.0499376i	$-0.984098\pi$
$401$	−19.0000	+	19.0000i	−0.948815	+	0.948815i	0.0499376	+	0.998752i	$0.484098\pi$
$402$		0			0
$403$	16.0000	−	16.0000i	0.797017	−	0.797017i
$404$	12.0000			0.597022
$405$		0			0
$406$		0			0
$407$			24.0000i			1.18964i
$408$		0			0
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$		−	16.0000i		−	0.788263i
$413$		0			0
$414$	−12.0000	+	12.0000i	−0.589768	+	0.589768i
$415$		0			0
$416$			4.00000i			0.196116i
$417$		0			0
$418$	16.0000	+	16.0000i	0.782586	+	0.782586i
$419$	12.0000	−	12.0000i	0.586238	−	0.586238i	−0.350372	−	0.936611i	$-0.613945\pi$
$419$	12.0000	−	12.0000i	0.586238	−	0.586238i	0.936611	+	0.350372i	$0.113945\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	16.0000	−	16.0000i	0.778868	−	0.778868i
$423$	24.0000			1.16692
$424$	4.00000			0.194257
$425$		0			0
$426$		0			0
$427$		0			0
$428$	8.00000	−	8.00000i	0.386695	−	0.386695i
$429$		0			0
$430$		0			0
$431$	−24.0000	+	24.0000i	−1.15604	+	1.15604i	−0.170720	+	0.985320i	$0.554609\pi$
$431$	−24.0000	+	24.0000i	−1.15604	+	1.15604i	−0.985320	+	0.170720i	$0.945391\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$	−3.00000	+	3.00000i	−0.143674	+	0.143674i
$437$	16.0000	−	16.0000i	0.765384	−	0.765384i
$438$		0			0
$439$	−12.0000	−	12.0000i	−0.572729	−	0.572729i	0.360161	−	0.932890i	$-0.382722\pi$
$439$	−12.0000	−	12.0000i	−0.572729	−	0.572729i	−0.932890	+	0.360161i	$0.882722\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$	−4.00000	+	16.0000i	−0.190261	+	0.761042i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$		0			0
$446$	−16.0000			−0.757622
$447$		0			0
$448$		0			0
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	−0.774344	−	0.632765i	$-0.781920\pi$
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	0.632765	+	0.774344i	$0.281920\pi$
$450$		0			0
$451$			8.00000i			0.376705i
$452$	−1.00000	−	1.00000i	−0.0470360	−	0.0470360i
$453$		0			0
$454$	−20.0000	−	20.0000i	−0.938647	−	0.938647i
$455$		0			0
$456$		0			0
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$			6.00000i			0.280362i
$459$		0			0
$460$		0			0
$461$		−	20.0000i		−	0.931493i	−0.884918	−	0.465746i	$-0.845786\pi$
$461$		−	20.0000i		−	0.931493i	0.884918	−	0.465746i	$-0.154214\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	3.00000	+	3.00000i	0.139272	+	0.139272i
$465$		0			0
$466$	5.00000	−	5.00000i	0.231621	−	0.231621i
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$	−12.0000			−0.554700
$469$		0			0
$470$		0			0
$471$		0			0
$472$		−	4.00000i		−	0.184115i
$473$	−16.0000	+	16.0000i	−0.735681	+	0.735681i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			12.0000i			0.549442i
$478$		0			0
$479$	8.00000	+	8.00000i	0.365529	+	0.365529i	0.865844	−	0.500314i	$-0.166782\pi$
$479$	8.00000	+	8.00000i	0.365529	+	0.365529i	−0.500314	+	0.865844i	$0.666782\pi$
$480$		0			0
$481$	12.0000	+	12.0000i	0.547153	+	0.547153i
$482$	21.0000	+	21.0000i	0.956524	+	0.956524i
$483$		0			0
$484$		−	21.0000i		−	0.954545i
$485$		0			0
$486$		0			0
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	0.0896838	−	0.995970i	$-0.471414\pi$
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	−0.995970	+	0.0896838i	$0.971414\pi$
$488$	−9.00000	+	9.00000i	−0.407411	+	0.407411i
$489$		0			0
$490$		0			0
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$		0			0
$493$	9.00000	+	15.0000i	0.405340	+	0.675566i
$494$	16.0000			0.719874
$495$		0			0
$496$	−4.00000	−	4.00000i	−0.179605	−	0.179605i
$497$		0			0
$498$		0			0
$499$	−8.00000	+	8.00000i	−0.358129	+	0.358129i	−0.863123	−	0.504994i	$-0.831495\pi$
$499$	−8.00000	+	8.00000i	−0.358129	+	0.358129i	0.504994	+	0.863123i	$0.331495\pi$
$500$		0			0
$501$		0			0
$502$	12.0000			0.535586
$503$	4.00000	+	4.00000i	0.178351	+	0.178351i	0.790637	−	0.612286i	$-0.209750\pi$
$503$	4.00000	+	4.00000i	0.178351	+	0.178351i	−0.612286	+	0.790637i	$0.709750\pi$
$504$		0			0
$505$		0			0
$506$	−32.0000			−1.42257
$507$		0			0
$508$	8.00000			0.354943
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.0000			0.793946
$515$		0			0
$516$		0			0
$517$	32.0000	+	32.0000i	1.40736	+	1.40736i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.00000	−	1.00000i	0.0438108	−	0.0438108i	−0.684862	−	0.728673i	$-0.740138\pi$
$521$	1.00000	−	1.00000i	0.0438108	−	0.0438108i	0.728673	+	0.684862i	$0.240138\pi$
$522$	−9.00000	+	9.00000i	−0.393919	+	0.393919i
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	−4.00000	−	4.00000i	−0.174741	−	0.174741i
$525$		0			0
$526$	24.0000			1.04645
$527$	−12.0000	−	20.0000i	−0.522728	−	0.871214i
$528$		0			0
$529$			9.00000i			0.391304i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	4.00000	+	4.00000i	0.173259	+	0.173259i
$534$		0			0
$535$		0			0
$536$			12.0000i			0.518321i
$537$		0			0
$538$	13.0000	+	13.0000i	0.560470	+	0.560470i
$539$	28.0000	+	28.0000i	1.20605	+	1.20605i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−8.00000			−0.343629
$543$		0			0
$544$	4.00000	+	1.00000i	0.171499	+	0.0428746i
$545$		0			0
$546$		0			0
$547$	−12.0000	+	12.0000i	−0.513083	+	0.513083i	−0.915470	−	0.402387i	$-0.868181\pi$
$547$	−12.0000	+	12.0000i	−0.513083	+	0.513083i	0.402387	+	0.915470i	$0.368181\pi$
$548$		−	8.00000i		−	0.341743i
$549$	−27.0000	−	27.0000i	−1.15233	−	1.15233i
$550$		0			0
$551$	12.0000	−	12.0000i	0.511217	−	0.511217i
$552$		0			0
$553$		0			0
$554$	−7.00000	+	7.00000i	−0.297402	+	0.297402i
$555$		0			0
$556$	8.00000	+	8.00000i	0.339276	+	0.339276i
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$	12.0000	−	12.0000i	0.508001	−	0.508001i
$559$			16.0000i			0.676728i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$		0			0
$565$		0			0
$566$	4.00000	+	4.00000i	0.168133	+	0.168133i
$567$		0			0
$568$	−4.00000	−	4.00000i	−0.167836	−	0.167836i
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$		0			0
$571$	−24.0000	+	24.0000i	−1.00437	+	1.00437i	−0.00437833	+	0.999990i	$0.501394\pi$
$571$	−24.0000	+	24.0000i	−1.00437	+	1.00437i	−0.999990	+	0.00437833i	$0.998606\pi$
$572$	−16.0000	−	16.0000i	−0.668994	−	0.668994i
$573$		0			0
$574$		0			0
$575$		0			0
$576$			3.00000i			0.125000i
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$	15.0000	+	8.00000i	0.623918	+	0.332756i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−16.0000	+	16.0000i	−0.662652	+	0.662652i
$584$	−5.00000	+	5.00000i	−0.206901	+	0.206901i
$585$		0			0
$586$		−	6.00000i		−	0.247858i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−16.0000	+	16.0000i	−0.659269	+	0.659269i
$590$		0			0
$591$		0			0
$592$	3.00000	−	3.00000i	0.123299	−	0.123299i
$593$	−16.0000			−0.657041			−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000			−0.657041			−0.328521	+	0.944497i	$0.606550\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	−16.0000	+	16.0000i	−0.654289	+	0.654289i
$599$	−40.0000			−1.63436			−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000			−1.63436			−0.817178	+	0.576386i	$0.804463\pi$
$600$		0			0
$601$	−19.0000	+	19.0000i	−0.775026	+	0.775026i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−19.0000	+	19.0000i	−0.775026	+	0.775026i	0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−36.0000			−1.46603
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.0000	−	28.0000i	1.13648	−	1.13648i	0.147409	−	0.989076i	$-0.452907\pi$
$607$	28.0000	−	28.0000i	1.13648	−	1.13648i	0.989076	−	0.147409i	$-0.0470935\pi$
$608$		−	4.00000i		−	0.162221i
$609$		0			0
$610$		0			0
$611$	32.0000			1.29458
$612$	−3.00000	+	12.0000i	−0.121268	+	0.485071i
$613$		−	26.0000i		−	1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$613$		−	26.0000i		−	1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$614$			12.0000i			0.484281i
$615$		0			0
$616$		0			0
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−8.00000	+	8.00000i	−0.321547	+	0.321547i	−0.849360	−	0.527813i	$-0.823012\pi$
$619$	−8.00000	+	8.00000i	−0.321547	+	0.321547i	0.527813	+	0.849360i	$0.323012\pi$
$620$		0			0
$621$		0			0
$622$	−24.0000	−	24.0000i	−0.962312	−	0.962312i
$623$		0			0
$624$		0			0
$625$		0			0
$626$	9.00000	+	9.00000i	0.359712	+	0.359712i
$627$		0			0
$628$			2.00000i			0.0798087i
$629$	15.0000	−	9.00000i	0.598089	−	0.358854i
$630$		0			0
$631$		−	40.0000i		−	1.59237i	−0.605050	−	0.796187i	$-0.706847\pi$
$631$		−	40.0000i		−	1.59237i	0.605050	−	0.796187i	$-0.293153\pi$
$632$	−8.00000	+	8.00000i	−0.318223	+	0.318223i
$633$		0			0
$634$	15.0000	+	15.0000i	0.595726	+	0.595726i
$635$		0			0
$636$		0			0
$637$	28.0000			1.10940
$638$	−24.0000			−0.950169
$639$	12.0000	−	12.0000i	0.474713	−	0.474713i
$640$		0			0
$641$	11.0000	+	11.0000i	0.434474	+	0.434474i	0.890147	−	0.455673i	$-0.150601\pi$
$641$	11.0000	+	11.0000i	0.434474	+	0.434474i	−0.455673	+	0.890147i	$0.650601\pi$
$642$		0			0
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$	4.00000	−	16.0000i	0.157378	−	0.629512i
$647$			32.0000i			1.25805i	0.777385	+	0.629025i	$0.216546\pi$
$647$			32.0000i			1.25805i	−0.777385	+	0.629025i	$0.783454\pi$
$648$	−9.00000			−0.353553
$649$	16.0000	+	16.0000i	0.628055	+	0.628055i
$650$		0			0
$651$		0			0
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	29.0000	+	29.0000i	1.13486	+	1.13486i	0.989358	+	0.145499i	$0.0464789\pi$
$653$	29.0000	+	29.0000i	1.13486	+	1.13486i	0.145499	+	0.989358i	$0.453521\pi$
$654$		0			0
$655$		0			0
$656$	1.00000	−	1.00000i	0.0390434	−	0.0390434i
$657$	−15.0000	−	15.0000i	−0.585206	−	0.585206i
$658$		0			0
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$		−	20.0000i		−	0.777910i	−0.921257	−	0.388955i	$-0.872836\pi$
$661$		−	20.0000i		−	0.777910i	0.921257	−	0.388955i	$-0.127164\pi$
$662$			20.0000i			0.777322i
$663$		0			0
$664$	4.00000			0.155230
$665$		0			0
$666$	9.00000	+	9.00000i	0.348743	+	0.348743i
$667$			24.0000i			0.929284i
$668$	8.00000	−	8.00000i	0.309529	−	0.309529i
$669$		0			0
$670$		0			0
$671$		−	72.0000i		−	2.77953i
$672$		0			0
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	0.971094	−	0.238698i	$-0.0767205\pi$
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	−0.238698	+	0.971094i	$0.576721\pi$
$674$	−7.00000	+	7.00000i	−0.269630	+	0.269630i
$675$		0			0
$676$	−3.00000			−0.115385
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	−0.411692	−	0.911323i	$-0.635062\pi$
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	0.911323	+	0.411692i	$0.135062\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	32.0000			1.22534
$683$	−20.0000	+	20.0000i	−0.765279	+	0.765279i	−0.977271	−	0.211993i	$-0.932005\pi$
$683$	−20.0000	+	20.0000i	−0.765279	+	0.765279i	0.211993	+	0.977271i	$0.432005\pi$
$684$	12.0000			0.458831
$685$		0			0
$686$		0			0
$687$		0			0
$688$	4.00000			0.152499
$689$			16.0000i			0.609551i
$690$		0			0
$691$	−24.0000	+	24.0000i	−0.913003	+	0.913003i	−0.996507	−	0.0835044i	$-0.973389\pi$
$691$	−24.0000	+	24.0000i	−0.913003	+	0.913003i	0.0835044	+	0.996507i	$0.473389\pi$
$692$	−5.00000	+	5.00000i	−0.190071	+	0.190071i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.00000	−	3.00000i	0.189389	−	0.113633i
$698$		−	4.00000i		−	0.151402i
$699$		0			0
$700$		0			0
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	−12.0000	−	12.0000i	−0.452589	−	0.452589i
$704$	−4.00000	+	4.00000i	−0.150756	+	0.150756i
$705$		0			0
$706$			14.0000i			0.526897i
$707$		0			0
$708$		0			0
$709$	23.0000	+	23.0000i	0.863783	+	0.863783i	0.991775	−	0.127992i	$-0.0408532\pi$
$709$	23.0000	+	23.0000i	0.863783	+	0.863783i	−0.127992	+	0.991775i	$0.540853\pi$
$710$		0			0
$711$	−24.0000	−	24.0000i	−0.900070	−	0.900070i
$712$		0			0
$713$		−	32.0000i		−	1.19841i
$714$		0			0
$715$		0			0
$716$		−	4.00000i		−	0.149487i
$717$		0			0
$718$		−	24.0000i		−	0.895672i
$719$	8.00000	+	8.00000i	0.298350	+	0.298350i	0.840367	−	0.542018i	$-0.182339\pi$
$719$	8.00000	+	8.00000i	0.298350	+	0.298350i	−0.542018	+	0.840367i	$0.682339\pi$
$720$		0			0
$721$		0			0
$722$	3.00000			0.111648
$723$		0			0
$724$	11.0000	−	11.0000i	0.408812	−	0.408812i
$725$		0			0
$726$		0			0
$727$		−	48.0000i		−	1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$		−	48.0000i		−	1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	16.0000	+	4.00000i	0.591781	+	0.147945i
$732$		0			0
$733$	−36.0000			−1.32969			−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000			−1.32969			−0.664845	+	0.746981i	$0.731502\pi$
$734$		0			0
$735$		0			0
$736$	4.00000	+	4.00000i	0.147442	+	0.147442i
$737$	−48.0000	−	48.0000i	−1.76810	−	1.76810i
$738$	3.00000	+	3.00000i	0.110432	+	0.110432i
$739$		−	4.00000i		−	0.147142i	−0.997290	−	0.0735712i	$-0.976560\pi$
$739$		−	4.00000i		−	0.147142i	0.997290	−	0.0735712i	$-0.0234396\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$		0			0
$745$		0			0
$746$			4.00000i			0.146450i
$747$			12.0000i			0.439057i
$748$	−20.0000	+	12.0000i	−0.731272	+	0.438763i
$749$		0			0
$750$		0			0
$751$	16.0000	+	16.0000i	0.583848	+	0.583848i	0.935959	−	0.352110i	$-0.114536\pi$
$751$	16.0000	+	16.0000i	0.583848	+	0.583848i	−0.352110	+	0.935959i	$0.614536\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	−12.0000	+	12.0000i	−0.437014	+	0.437014i
$755$		0			0
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−12.0000	−	12.0000i	−0.435860	−	0.435860i
$759$		0			0
$760$		0			0
$761$	−8.00000			−0.290000			−0.145000	−	0.989432i	$-0.546318\pi$
$761$	−8.00000			−0.290000			−0.145000	+	0.989432i	$0.546318\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$		0			0
$766$	24.0000			0.867155
$767$	16.0000			0.577727
$768$		0			0
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$		0			0
$772$	−11.0000	−	11.0000i	−0.395899	−	0.395899i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$			12.0000i			0.431331i
$775$		0			0
$776$	3.00000	−	3.00000i	0.107694	−	0.107694i
$777$		0			0
$778$			6.00000i			0.215110i
$779$	−4.00000	−	4.00000i	−0.143315	−	0.143315i
$780$		0			0
$781$	32.0000			1.14505
$782$	12.0000	+	20.0000i	0.429119	+	0.715199i
$783$		0			0
$784$		−	7.00000i		−	0.250000i
$785$		0			0
$786$		0			0
$787$	−12.0000	+	12.0000i	−0.427754	+	0.427754i	−0.887863	−	0.460109i	$-0.847810\pi$
$787$	−12.0000	+	12.0000i	−0.427754	+	0.427754i	0.460109	+	0.887863i	$0.347810\pi$
$788$	−5.00000	−	5.00000i	−0.178118	−	0.178118i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−12.0000	−	12.0000i	−0.426401	−	0.426401i
$793$	−36.0000	−	36.0000i	−1.27840	−	1.27840i
$794$	−15.0000	−	15.0000i	−0.532330	−	0.532330i
$795$		0			0
$796$	−12.0000	−	12.0000i	−0.425329	−	0.425329i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$	8.00000	−	32.0000i	0.283020	−	1.13208i
$800$		0			0
$801$		0			0
$802$	−19.0000	+	19.0000i	−0.670913	+	0.670913i
$803$		−	40.0000i		−	1.41157i
$804$		0			0
$805$		0			0
$806$	16.0000	−	16.0000i	0.563576	−	0.563576i
$807$		0			0
$808$	12.0000			0.422159
$809$	−23.0000	+	23.0000i	−0.808637	+	0.808637i	−0.984428	−	0.175791i	$-0.943752\pi$
$809$	−23.0000	+	23.0000i	−0.808637	+	0.808637i	0.175791	+	0.984428i	$0.443752\pi$
$810$		0			0
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	0.633381	−	0.773840i	$-0.281667\pi$
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	−0.773840	+	0.633381i	$0.781667\pi$
$812$		0			0
$813$		0			0
$814$			24.0000i			0.841200i
$815$		0			0
$816$		0			0
$817$		−	16.0000i		−	0.559769i
$818$	10.0000			0.349642
$819$		0			0
$820$		0			0
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$821$	−19.0000	−	19.0000i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$822$		0			0
$823$	−36.0000	−	36.0000i	−1.25488	−	1.25488i	−0.953506	−	0.301376i	$-0.902554\pi$
$823$	−36.0000	−	36.0000i	−1.25488	−	1.25488i	−0.301376	−	0.953506i	$-0.597446\pi$
$824$		−	16.0000i		−	0.557386i
$825$		0			0
$826$		0			0
$827$	20.0000	+	20.0000i	0.695468	+	0.695468i	0.963430	−	0.267961i	$-0.0863500\pi$
$827$	20.0000	+	20.0000i	0.695468	+	0.695468i	−0.267961	+	0.963430i	$0.586350\pi$
$828$	−12.0000	+	12.0000i	−0.417029	+	0.417029i
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$		0			0
$832$			4.00000i			0.138675i
$833$	7.00000	−	28.0000i	0.242536	−	0.970143i
$834$		0			0
$835$		0			0
$836$	16.0000	+	16.0000i	0.553372	+	0.553372i
$837$		0			0
$838$	12.0000	−	12.0000i	0.414533	−	0.414533i
$839$	32.0000	−	32.0000i	1.10476	−	1.10476i	0.110935	−	0.993828i	$-0.464615\pi$
$839$	32.0000	−	32.0000i	1.10476	−	1.10476i	0.993828	−	0.110935i	$-0.0353845\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$	−28.0000			−0.964944
$843$		0			0
$844$	16.0000	−	16.0000i	0.550743	−	0.550743i
$845$		0			0
$846$	24.0000			0.825137
$847$		0			0
$848$	4.00000			0.137361
$849$		0			0
$850$		0			0
$851$	24.0000			0.822709
$852$		0			0
$853$	25.0000	−	25.0000i	0.855984	−	0.855984i	−0.134878	−	0.990862i	$-0.543064\pi$
$853$	25.0000	−	25.0000i	0.855984	−	0.855984i	0.990862	+	0.134878i	$0.0430644\pi$
$854$		0			0
$855$		0			0
$856$	8.00000	−	8.00000i	0.273434	−	0.273434i
$857$	15.0000	+	15.0000i	0.512390	+	0.512390i	0.915258	−	0.402868i	$-0.131987\pi$
$857$	15.0000	+	15.0000i	0.512390	+	0.512390i	−0.402868	+	0.915258i	$0.631987\pi$
$858$		0			0
$859$			36.0000i			1.22830i	0.789188	+	0.614152i	$0.210502\pi$
$859$			36.0000i			1.22830i	−0.789188	+	0.614152i	$0.789498\pi$
$860$		0			0
$861$		0			0
$862$	−24.0000	+	24.0000i	−0.817443	+	0.817443i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$		0			0
$866$	14.0000			0.475739
$867$		0			0
$868$		0			0
$869$		−	64.0000i		−	2.17105i
$870$		0			0
$871$	−48.0000			−1.62642
$872$	−3.00000	+	3.00000i	−0.101593	+	0.101593i
$873$	9.00000	+	9.00000i	0.304604	+	0.304604i
$874$	16.0000	−	16.0000i	0.541208	−	0.541208i
$875$		0			0
$876$		0			0
$877$	−35.0000	−	35.0000i	−1.18187	−	1.18187i	−0.979260	−	0.202606i	$-0.935059\pi$
$877$	−35.0000	−	35.0000i	−1.18187	−	1.18187i	−0.202606	−	0.979260i	$-0.564941\pi$
$878$	−12.0000	−	12.0000i	−0.404980	−	0.404980i
$879$		0			0
$880$		0			0
$881$	−39.0000	−	39.0000i	−1.31394	−	1.31394i	−0.918483	−	0.395460i	$-0.870585\pi$
$881$	−39.0000	−	39.0000i	−1.31394	−	1.31394i	−0.395460	−	0.918483i	$-0.629415\pi$
$882$	21.0000			0.707107
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$	−4.00000	+	16.0000i	−0.134535	+	0.538138i
$885$		0			0
$886$			4.00000i			0.134383i
$887$	28.0000	−	28.0000i	0.940148	−	0.940148i	−0.0581593	−	0.998307i	$-0.518523\pi$
$887$	28.0000	−	28.0000i	0.940148	−	0.940148i	0.998307	+	0.0581593i	$0.0185231\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	36.0000	−	36.0000i	1.20605	−	1.20605i
$892$	−16.0000			−0.535720
$893$	−32.0000			−1.07084
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		−	24.0000i		−	0.800445i
$900$		0			0
$901$	16.0000	+	4.00000i	0.533037	+	0.133259i
$902$			8.00000i			0.266371i
$903$		0			0
$904$	−1.00000	−	1.00000i	−0.0332595	−	0.0332595i
$905$		0			0
$906$		0			0
$907$	−20.0000	−	20.0000i	−0.664089	−	0.664089i	0.292252	−	0.956341i	$-0.405595\pi$
$907$	−20.0000	−	20.0000i	−0.664089	−	0.664089i	−0.956341	+	0.292252i	$0.905595\pi$
$908$	−20.0000	−	20.0000i	−0.663723	−	0.663723i
$909$			36.0000i			1.19404i
$910$		0			0
$911$	−4.00000	+	4.00000i	−0.132526	+	0.132526i	−0.770258	−	0.637732i	$-0.779873\pi$
$911$	−4.00000	+	4.00000i	−0.132526	+	0.132526i	0.637732	+	0.770258i	$0.279873\pi$
$912$		0			0
$913$	−16.0000	+	16.0000i	−0.529523	+	0.529523i
$914$	−22.0000			−0.727695
$915$		0			0
$916$			6.00000i			0.198246i
$917$		0			0
$918$		0			0
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$		0			0
$921$		0			0
$922$		−	20.0000i		−	0.658665i
$923$	16.0000	−	16.0000i	0.526646	−	0.526646i
$924$		0			0
$925$		0			0
$926$			24.0000i			0.788689i
$927$	48.0000			1.57653
$928$	3.00000	+	3.00000i	0.0984798	+	0.0984798i
$929$	−13.0000	+	13.0000i	−0.426516	+	0.426516i	−0.887440	−	0.460924i	$-0.847518\pi$
$929$	−13.0000	+	13.0000i	−0.426516	+	0.426516i	0.460924	+	0.887440i	$0.347518\pi$
$930$		0			0
$931$	−28.0000			−0.917663
$932$	5.00000	−	5.00000i	0.163780	−	0.163780i
$933$		0			0
$934$	28.0000			0.916188
$935$		0			0
$936$	−12.0000			−0.392232
$937$	48.0000			1.56809			0.784046	−	0.620703i	$-0.213153\pi$
$937$	48.0000			1.56809			0.784046	+	0.620703i	$0.213153\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.00000	−	1.00000i	0.0325991	−	0.0325991i	−0.690619	−	0.723218i	$-0.742662\pi$
$941$	1.00000	−	1.00000i	0.0325991	−	0.0325991i	0.723218	+	0.690619i	$0.242662\pi$
$942$		0			0
$943$	8.00000			0.260516
$944$		−	4.00000i		−	0.130189i
$945$		0			0
$946$	−16.0000	+	16.0000i	−0.520205	+	0.520205i
$947$	−12.0000	+	12.0000i	−0.389948	+	0.389948i	−0.874669	−	0.484721i	$-0.838921\pi$
$947$	−12.0000	+	12.0000i	−0.389948	+	0.389948i	0.484721	+	0.874669i	$0.338921\pi$
$948$		0			0
$949$	−20.0000	−	20.0000i	−0.649227	−	0.649227i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	8.00000	+	8.00000i	0.258468	+	0.258468i
$959$		0			0
$960$		0			0
$961$			1.00000i			0.0322581i
$962$	12.0000	+	12.0000i	0.386896	+	0.386896i
$963$	24.0000	+	24.0000i	0.773389	+	0.773389i
$964$	21.0000	+	21.0000i	0.676364	+	0.676364i
$965$		0			0
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		−	21.0000i		−	0.674966i
$969$		0			0
$970$		0			0
$971$		−	20.0000i		−	0.641831i	−0.947108	−	0.320915i	$-0.896010\pi$
$971$		−	20.0000i		−	0.641831i	0.947108	−	0.320915i	$-0.103990\pi$
$972$		0			0
$973$		0			0
$974$	−20.0000	−	20.0000i	−0.640841	−	0.640841i
$975$		0			0
$976$	−9.00000	+	9.00000i	−0.288083	+	0.288083i
$977$	8.00000			0.255943			0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000			0.255943			0.127971	+	0.991778i	$0.459153\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−9.00000	−	9.00000i	−0.287348	−	0.287348i
$982$			20.0000i			0.638226i
$983$	20.0000	−	20.0000i	0.637901	−	0.637901i	−0.312136	−	0.950037i	$-0.601045\pi$
$983$	20.0000	−	20.0000i	0.637901	−	0.637901i	0.950037	+	0.312136i	$0.101045\pi$
$984$		0			0
$985$		0			0
$986$	9.00000	+	15.0000i	0.286618	+	0.477697i
$987$		0			0
$988$	16.0000			0.509028
$989$	16.0000	+	16.0000i	0.508770	+	0.508770i
$990$		0			0
$991$	−24.0000	−	24.0000i	−0.762385	−	0.762385i	0.214368	−	0.976753i	$-0.431231\pi$
$991$	−24.0000	−	24.0000i	−0.762385	−	0.762385i	−0.976753	+	0.214368i	$0.931231\pi$
$992$	−4.00000	−	4.00000i	−0.127000	−	0.127000i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	35.0000	+	35.0000i	1.10846	+	1.10846i	0.993353	+	0.115108i	$0.0367215\pi$
$997$	35.0000	+	35.0000i	1.10846	+	1.10846i	0.115108	+	0.993353i	$0.463279\pi$
$998$	−8.00000	+	8.00000i	−0.253236	+	0.253236i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.g.d.149.1		2
5.2	odd	4		34.2.c.b.13.1	✓	2
5.3	odd	4		850.2.h.c.251.1		2
5.4	even	2		850.2.g.a.149.1		2
15.2	even	4		306.2.g.d.217.1		2
17.4	even	4		850.2.g.a.599.1		2
20.7	even	4		272.2.o.c.81.1		2
40.27	even	4		1088.2.o.i.897.1		2
40.37	odd	4		1088.2.o.k.897.1		2
60.47	odd	4		2448.2.be.j.1441.1		2
85.2	odd	8		578.2.a.b.1.2		2
85.4	even	4	inner	850.2.g.d.599.1		2
85.7	even	16		578.2.d.f.399.2		8
85.12	even	16		578.2.d.f.155.1		8
85.22	even	16		578.2.d.f.155.2		8
85.27	even	16		578.2.d.f.399.1		8
85.32	odd	8		578.2.a.b.1.1		2
85.37	even	16		578.2.d.f.423.2		8
85.38	odd	4		850.2.h.c.701.1		2
85.42	odd	8		578.2.b.c.577.1		2
85.47	odd	4		578.2.c.b.327.1		2
85.57	even	16		578.2.d.f.179.1		8
85.62	even	16		578.2.d.f.179.2		8
85.67	odd	4		578.2.c.b.251.1		2
85.72	odd	4		34.2.c.b.21.1	yes	2
85.77	odd	8		578.2.b.c.577.2		2
85.82	even	16		578.2.d.f.423.1		8
255.2	even	8		5202.2.a.bb.1.1		2
255.32	even	8		5202.2.a.bb.1.2		2
255.242	even	4		306.2.g.d.55.1		2
340.87	even	8		4624.2.a.l.1.2		2
340.287	even	8		4624.2.a.l.1.1		2
340.327	even	4		272.2.o.c.225.1		2
680.157	odd	4		1088.2.o.k.769.1		2
680.667	even	4		1088.2.o.i.769.1		2
1020.1007	odd	4		2448.2.be.j.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.c.b.13.1	✓	2	5.2	odd	4
34.2.c.b.21.1	yes	2	85.72	odd	4
272.2.o.c.81.1		2	20.7	even	4
272.2.o.c.225.1		2	340.327	even	4
306.2.g.d.55.1		2	255.242	even	4
306.2.g.d.217.1		2	15.2	even	4
578.2.a.b.1.1		2	85.32	odd	8
578.2.a.b.1.2		2	85.2	odd	8
578.2.b.c.577.1		2	85.42	odd	8
578.2.b.c.577.2		2	85.77	odd	8
578.2.c.b.251.1		2	85.67	odd	4
578.2.c.b.327.1		2	85.47	odd	4
578.2.d.f.155.1		8	85.12	even	16
578.2.d.f.155.2		8	85.22	even	16
578.2.d.f.179.1		8	85.57	even	16
578.2.d.f.179.2		8	85.62	even	16
578.2.d.f.399.1		8	85.27	even	16
578.2.d.f.399.2		8	85.7	even	16
578.2.d.f.423.1		8	85.82	even	16
578.2.d.f.423.2		8	85.37	even	16
850.2.g.a.149.1		2	5.4	even	2
850.2.g.a.599.1		2	17.4	even	4
850.2.g.d.149.1		2	1.1	even	1	trivial
850.2.g.d.599.1		2	85.4	even	4	inner
850.2.h.c.251.1		2	5.3	odd	4
850.2.h.c.701.1		2	85.38	odd	4
1088.2.o.i.769.1		2	680.667	even	4
1088.2.o.i.897.1		2	40.27	even	4
1088.2.o.k.769.1		2	680.157	odd	4
1088.2.o.k.897.1		2	40.37	odd	4
2448.2.be.j.1441.1		2	60.47	odd	4
2448.2.be.j.1585.1		2	1020.1007	odd	4
4624.2.a.l.1.1		2	340.287	even	8
4624.2.a.l.1.2		2	340.87	even	8
5202.2.a.bb.1.1		2	255.2	even	8
5202.2.a.bb.1.2		2	255.32	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +3.00000i q^{9} +(-4.00000 + 4.00000i) q^{11} +4.00000i q^{13} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} +3.00000i q^{18} -4.00000i q^{19} +(-4.00000 + 4.00000i) q^{22} +(4.00000 + 4.00000i) q^{23} +4.00000i q^{26} +(3.00000 + 3.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +1.00000 q^{32} +(4.00000 + 1.00000i) q^{34} +3.00000i q^{36} +(3.00000 - 3.00000i) q^{37} -4.00000i q^{38} +(1.00000 - 1.00000i) q^{41} +4.00000 q^{43} +(-4.00000 + 4.00000i) q^{44} +(4.00000 + 4.00000i) q^{46} -8.00000i q^{47} -7.00000i q^{49} +4.00000i q^{52} +4.00000 q^{53} +(3.00000 + 3.00000i) q^{58} -4.00000i q^{59} +(-9.00000 + 9.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +1.00000 q^{64} +12.0000i q^{67} +(4.00000 + 1.00000i) q^{68} +(-4.00000 - 4.00000i) q^{71} +3.00000i q^{72} +(-5.00000 + 5.00000i) q^{73} +(3.00000 - 3.00000i) q^{74} -4.00000i q^{76} +(-8.00000 + 8.00000i) q^{79} -9.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +4.00000 q^{83} +4.00000 q^{86} +(-4.00000 + 4.00000i) q^{88} +(4.00000 + 4.00000i) q^{92} -8.00000i q^{94} +(3.00000 - 3.00000i) q^{97} -7.00000i q^{98} +(-12.0000 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 8 q^{11} + 2 q^{16} + 8 q^{17} - 8 q^{22} + 8 q^{23} + 6 q^{29} - 8 q^{31} + 2 q^{32} + 8 q^{34} + 6 q^{37} + 2 q^{41} + 8 q^{43} - 8 q^{44} + 8 q^{46} + 8 q^{53} + 6 q^{58}+ \cdots - 24 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 8 * q^11 + 2 * q^16 + 8 * q^17 - 8 * q^22 + 8 * q^23 + 6 * q^29 - 8 * q^31 + 2 * q^32 + 8 * q^34 + 6 * q^37 + 2 * q^41 + 8 * q^43 - 8 * q^44 + 8 * q^46 + 8 * q^53 + 6 * q^58 - 18 * q^61 - 8 * q^62 + 2 * q^64 + 8 * q^68 - 8 * q^71 - 10 * q^73 + 6 * q^74 - 16 * q^79 - 18 * q^81 + 2 * q^82 + 8 * q^83 + 8 * q^86 - 8 * q^88 + 8 * q^92 + 6 * q^97 - 24 * q^99

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