LMFDB - Embedded newform 2850.2.a.bm.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.a (trivial)

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:	yes
Analytic conductor:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.07838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.07838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +6.34017 q^{11} -1.00000 q^{12} -3.41855 q^{13} +1.07838 q^{14} +1.00000 q^{16} +5.41855 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.07838 q^{21} +6.34017 q^{22} -6.34017 q^{23} -1.00000 q^{24} -3.41855 q^{26} -1.00000 q^{27} +1.07838 q^{28} -0.340173 q^{29} +1.07838 q^{31} +1.00000 q^{32} -6.34017 q^{33} +5.41855 q^{34} +1.00000 q^{36} -3.41855 q^{37} +1.00000 q^{38} +3.41855 q^{39} +7.60197 q^{41} -1.07838 q^{42} +11.1773 q^{43} +6.34017 q^{44} -6.34017 q^{46} +6.34017 q^{47} -1.00000 q^{48} -5.83710 q^{49} -5.41855 q^{51} -3.41855 q^{52} -6.00000 q^{53} -1.00000 q^{54} +1.07838 q^{56} -1.00000 q^{57} -0.340173 q^{58} +0.738205 q^{59} -2.68035 q^{61} +1.07838 q^{62} +1.07838 q^{63} +1.00000 q^{64} -6.34017 q^{66} -2.83710 q^{67} +5.41855 q^{68} +6.34017 q^{69} -2.83710 q^{71} +1.00000 q^{72} -6.83710 q^{73} -3.41855 q^{74} +1.00000 q^{76} +6.83710 q^{77} +3.41855 q^{78} -1.07838 q^{79} +1.00000 q^{81} +7.60197 q^{82} -0.894960 q^{83} -1.07838 q^{84} +11.1773 q^{86} +0.340173 q^{87} +6.34017 q^{88} +6.92162 q^{89} -3.68649 q^{91} -6.34017 q^{92} -1.07838 q^{93} +6.34017 q^{94} -1.00000 q^{96} +3.65983 q^{97} -5.83710 q^{98} +6.34017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 8 q^{11} - 3 q^{12} + 4 q^{13} + 3 q^{16} + 2 q^{17} + 3 q^{18} + 3 q^{19} + 8 q^{22} - 8 q^{23} - 3 q^{24} + 4 q^{26} - 3 q^{27} + 10 q^{29} + 3 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{36} + 4 q^{37} + 3 q^{38} - 4 q^{39} + 4 q^{41} - 6 q^{43} + 8 q^{44} - 8 q^{46} + 8 q^{47} - 3 q^{48} + 11 q^{49} - 2 q^{51} + 4 q^{52} - 18 q^{53} - 3 q^{54} - 3 q^{57} + 10 q^{58} + 10 q^{59} + 14 q^{61} + 3 q^{64} - 8 q^{66} + 20 q^{67} + 2 q^{68} + 8 q^{69} + 20 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} + 3 q^{76} - 8 q^{77} - 4 q^{78} + 3 q^{81} + 4 q^{82} - 4 q^{83} - 6 q^{86} - 10 q^{87} + 8 q^{88} + 24 q^{89} - 24 q^{91} - 8 q^{92} + 8 q^{94} - 3 q^{96} + 22 q^{97} + 11 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 8 * q^11 - 3 * q^12 + 4 * q^13 + 3 * q^16 + 2 * q^17 + 3 * q^18 + 3 * q^19 + 8 * q^22 - 8 * q^23 - 3 * q^24 + 4 * q^26 - 3 * q^27 + 10 * q^29 + 3 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^36 + 4 * q^37 + 3 * q^38 - 4 * q^39 + 4 * q^41 - 6 * q^43 + 8 * q^44 - 8 * q^46 + 8 * q^47 - 3 * q^48 + 11 * q^49 - 2 * q^51 + 4 * q^52 - 18 * q^53 - 3 * q^54 - 3 * q^57 + 10 * q^58 + 10 * q^59 + 14 * q^61 + 3 * q^64 - 8 * q^66 + 20 * q^67 + 2 * q^68 + 8 * q^69 + 20 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 + 3 * q^76 - 8 * q^77 - 4 * q^78 + 3 * q^81 + 4 * q^82 - 4 * q^83 - 6 * q^86 - 10 * q^87 + 8 * q^88 + 24 * q^89 - 24 * q^91 - 8 * q^92 + 8 * q^94 - 3 * q^96 + 22 * q^97 + 11 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	1.07838	0.407588	0.203794	−	0.979014i	$-0.434673\pi$
$7$	1.07838	0.407588	0.203794	+	0.979014i	$0.434673\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	6.34017	1.91163	0.955817	−	0.293962i	$-0.0949740\pi$
$11$	6.34017	1.91163	0.955817	+	0.293962i	$0.0949740\pi$
$12$	−1.00000	−0.288675
$13$	−3.41855	−0.948135	−0.474068	−	0.880488i	$-0.657215\pi$
$13$	−3.41855	−0.948135	−0.474068	+	0.880488i	$0.657215\pi$
$14$	1.07838	0.288209
$15$	0	0
$16$	1.00000	0.250000
$17$	5.41855	1.31419	0.657096	−	0.753807i	$-0.271785\pi$
$17$	5.41855	1.31419	0.657096	+	0.753807i	$0.271785\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−1.07838	−0.235321
$22$	6.34017	1.35173
$23$	−6.34017	−1.32202	−0.661009	−	0.750378i	$-0.729871\pi$
$23$	−6.34017	−1.32202	−0.661009	+	0.750378i	$0.729871\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−3.41855	−0.670433
$27$	−1.00000	−0.192450
$28$	1.07838	0.203794
$29$	−0.340173	−0.0631685	−0.0315843	−	0.999501i	$-0.510055\pi$
$29$	−0.340173	−0.0631685	−0.0315843	+	0.999501i	$0.510055\pi$
$30$	0	0
$31$	1.07838	0.193682	0.0968412	−	0.995300i	$-0.469126\pi$
$31$	1.07838	0.193682	0.0968412	+	0.995300i	$0.469126\pi$
$32$	1.00000	0.176777
$33$	−6.34017	−1.10368
$34$	5.41855	0.929274
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.41855	−0.562006	−0.281003	−	0.959707i	$-0.590667\pi$
$37$	−3.41855	−0.562006	−0.281003	+	0.959707i	$0.590667\pi$
$38$	1.00000	0.162221
$39$	3.41855	0.547406
$40$	0	0
$41$	7.60197	1.18723	0.593614	−	0.804750i	$-0.297701\pi$
$41$	7.60197	1.18723	0.593614	+	0.804750i	$0.297701\pi$
$42$	−1.07838	−0.166397
$43$	11.1773	1.70452	0.852259	−	0.523120i	$-0.175232\pi$
$43$	11.1773	1.70452	0.852259	+	0.523120i	$0.175232\pi$
$44$	6.34017	0.955817
$45$	0	0
$46$	−6.34017	−0.934808
$47$	6.34017	0.924809	0.462405	−	0.886669i	$-0.346987\pi$
$47$	6.34017	0.924809	0.462405	+	0.886669i	$0.346987\pi$
$48$	−1.00000	−0.144338
$49$	−5.83710	−0.833872
$50$	0	0
$51$	−5.41855	−0.758749
$52$	−3.41855	−0.474068
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.07838	0.144104
$57$	−1.00000	−0.132453
$58$	−0.340173	−0.0446669
$59$	0.738205	0.0961061	0.0480530	−	0.998845i	$-0.484698\pi$
$59$	0.738205	0.0961061	0.0480530	+	0.998845i	$0.484698\pi$
$60$	0	0
$61$	−2.68035	−0.343183	−0.171592	−	0.985168i	$-0.554891\pi$
$61$	−2.68035	−0.343183	−0.171592	+	0.985168i	$0.554891\pi$
$62$	1.07838	0.136954
$63$	1.07838	0.135863
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.34017	−0.780421
$67$	−2.83710	−0.346607	−0.173304	−	0.984868i	$-0.555444\pi$
$67$	−2.83710	−0.346607	−0.173304	+	0.984868i	$0.555444\pi$
$68$	5.41855	0.657096
$69$	6.34017	0.763267
$70$	0	0
$71$	−2.83710	−0.336702	−0.168351	−	0.985727i	$-0.553844\pi$
$71$	−2.83710	−0.336702	−0.168351	+	0.985727i	$0.553844\pi$
$72$	1.00000	0.117851
$73$	−6.83710	−0.800222	−0.400111	−	0.916467i	$-0.631028\pi$
$73$	−6.83710	−0.800222	−0.400111	+	0.916467i	$0.631028\pi$
$74$	−3.41855	−0.397398
$75$	0	0
$76$	1.00000	0.114708
$77$	6.83710	0.779160
$78$	3.41855	0.387075
$79$	−1.07838	−0.121327	−0.0606635	−	0.998158i	$-0.519322\pi$
$79$	−1.07838	−0.121327	−0.0606635	+	0.998158i	$0.519322\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	7.60197	0.839497
$83$	−0.894960	−0.0982347	−0.0491173	−	0.998793i	$-0.515641\pi$
$83$	−0.894960	−0.0982347	−0.0491173	+	0.998793i	$0.515641\pi$
$84$	−1.07838	−0.117661
$85$	0	0
$86$	11.1773	1.20528
$87$	0.340173	0.0364704
$88$	6.34017	0.675865
$89$	6.92162	0.733690	0.366845	−	0.930282i	$-0.380438\pi$
$89$	6.92162	0.733690	0.366845	+	0.930282i	$0.380438\pi$
$90$	0	0
$91$	−3.68649	−0.386449
$92$	−6.34017	−0.661009
$93$	−1.07838	−0.111823
$94$	6.34017	0.653939
$95$	0	0
$96$	−1.00000	−0.102062
$97$	3.65983	0.371599	0.185800	−	0.982588i	$-0.440512\pi$
$97$	3.65983	0.371599	0.185800	+	0.982588i	$0.440512\pi$
$98$	−5.83710	−0.589636
$99$	6.34017	0.637211
$100$	0	0
$101$	19.6020	1.95047	0.975234	−	0.221174i	$-0.0709889\pi$
$101$	19.6020	1.95047	0.975234	+	0.221174i	$0.0709889\pi$
$102$	−5.41855	−0.536516
$103$	11.7587	1.15862	0.579311	−	0.815107i	$-0.303322\pi$
$103$	11.7587	1.15862	0.579311	+	0.815107i	$0.303322\pi$
$104$	−3.41855	−0.335216
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−6.15676	−0.595196	−0.297598	−	0.954691i	$-0.596186\pi$
$107$	−6.15676	−0.595196	−0.297598	+	0.954691i	$0.596186\pi$
$108$	−1.00000	−0.0962250
$109$	17.9155	1.71599	0.857996	−	0.513657i	$-0.171709\pi$
$109$	17.9155	1.71599	0.857996	+	0.513657i	$0.171709\pi$
$110$	0	0
$111$	3.41855	0.324474
$112$	1.07838	0.101897
$113$	13.2039	1.24212	0.621061	−	0.783762i	$-0.286702\pi$
$113$	13.2039	1.24212	0.621061	+	0.783762i	$0.286702\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−0.340173	−0.0315843
$117$	−3.41855	−0.316045
$118$	0.738205	0.0679573
$119$	5.84324	0.535649
$120$	0	0
$121$	29.1978	2.65434
$122$	−2.68035	−0.242667
$123$	−7.60197	−0.685446
$124$	1.07838	0.0968412
$125$	0	0
$126$	1.07838	0.0960695
$127$	0.921622	0.0817808	0.0408904	−	0.999164i	$-0.486981\pi$
$127$	0.921622	0.0817808	0.0408904	+	0.999164i	$0.486981\pi$
$128$	1.00000	0.0883883
$129$	−11.1773	−0.984104
$130$	0	0
$131$	10.6537	0.930817	0.465408	−	0.885096i	$-0.345907\pi$
$131$	10.6537	0.930817	0.465408	+	0.885096i	$0.345907\pi$
$132$	−6.34017	−0.551841
$133$	1.07838	0.0935072
$134$	−2.83710	−0.245088
$135$	0	0
$136$	5.41855	0.464637
$137$	−20.6225	−1.76190	−0.880949	−	0.473211i	$-0.843095\pi$
$137$	−20.6225	−1.76190	−0.880949	+	0.473211i	$0.843095\pi$
$138$	6.34017	0.539711
$139$	18.8371	1.59774	0.798871	−	0.601502i	$-0.205431\pi$
$139$	18.8371	1.59774	0.798871	+	0.601502i	$0.205431\pi$
$140$	0	0
$141$	−6.34017	−0.533939
$142$	−2.83710	−0.238084
$143$	−21.6742	−1.81249
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.83710	−0.565843
$147$	5.83710	0.481436
$148$	−3.41855	−0.281003
$149$	−5.44521	−0.446089	−0.223045	−	0.974808i	$-0.571600\pi$
$149$	−5.44521	−0.446089	−0.223045	+	0.974808i	$0.571600\pi$
$150$	0	0
$151$	−23.1194	−1.88143	−0.940716	−	0.339196i	$-0.889845\pi$
$151$	−23.1194	−1.88143	−0.940716	+	0.339196i	$0.889845\pi$
$152$	1.00000	0.0811107
$153$	5.41855	0.438064
$154$	6.83710	0.550949
$155$	0	0
$156$	3.41855	0.273703
$157$	9.73206	0.776703	0.388352	−	0.921511i	$-0.373045\pi$
$157$	9.73206	0.776703	0.388352	+	0.921511i	$0.373045\pi$
$158$	−1.07838	−0.0857911
$159$	6.00000	0.475831
$160$	0	0
$161$	−6.83710	−0.538839
$162$	1.00000	0.0785674
$163$	6.49693	0.508879	0.254439	−	0.967089i	$-0.418109\pi$
$163$	6.49693	0.508879	0.254439	+	0.967089i	$0.418109\pi$
$164$	7.60197	0.593614
$165$	0	0
$166$	−0.894960	−0.0694624
$167$	−20.9939	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$167$	−20.9939	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$168$	−1.07838	−0.0831986
$169$	−1.31351	−0.101039
$170$	0	0
$171$	1.00000	0.0764719
$172$	11.1773	0.852259
$173$	6.99386	0.531733	0.265867	−	0.964010i	$-0.414342\pi$
$173$	6.99386	0.531733	0.265867	+	0.964010i	$0.414342\pi$
$174$	0.340173	0.0257884
$175$	0	0
$176$	6.34017	0.477909
$177$	−0.738205	−0.0554869
$178$	6.92162	0.518798
$179$	−4.73820	−0.354150	−0.177075	−	0.984197i	$-0.556664\pi$
$179$	−4.73820	−0.354150	−0.177075	+	0.984197i	$0.556664\pi$
$180$	0	0
$181$	−12.0722	−0.897322	−0.448661	−	0.893702i	$-0.648099\pi$
$181$	−12.0722	−0.897322	−0.448661	+	0.893702i	$0.648099\pi$
$182$	−3.68649	−0.273261
$183$	2.68035	0.198137
$184$	−6.34017	−0.467404
$185$	0	0
$186$	−1.07838	−0.0790705
$187$	34.3545	2.51225
$188$	6.34017	0.462405
$189$	−1.07838	−0.0784404
$190$	0	0
$191$	−7.26180	−0.525445	−0.262723	−	0.964871i	$-0.584620\pi$
$191$	−7.26180	−0.525445	−0.262723	+	0.964871i	$0.584620\pi$
$192$	−1.00000	−0.0721688
$193$	18.8638	1.35784	0.678922	−	0.734211i	$-0.262448\pi$
$193$	18.8638	1.35784	0.678922	+	0.734211i	$0.262448\pi$
$194$	3.65983	0.262760
$195$	0	0
$196$	−5.83710	−0.416936
$197$	−17.7009	−1.26113	−0.630567	−	0.776135i	$-0.717178\pi$
$197$	−17.7009	−1.26113	−0.630567	+	0.776135i	$0.717178\pi$
$198$	6.34017	0.450576
$199$	−0.313511	−0.0222242	−0.0111121	−	0.999938i	$-0.503537\pi$
$199$	−0.313511	−0.0222242	−0.0111121	+	0.999938i	$0.503537\pi$
$200$	0	0
$201$	2.83710	0.200114
$202$	19.6020	1.37919
$203$	−0.366835	−0.0257468
$204$	−5.41855	−0.379374
$205$	0	0
$206$	11.7587	0.819269
$207$	−6.34017	−0.440672
$208$	−3.41855	−0.237034
$209$	6.34017	0.438559
$210$	0	0
$211$	14.8371	1.02143	0.510714	−	0.859751i	$-0.329381\pi$
$211$	14.8371	1.02143	0.510714	+	0.859751i	$0.329381\pi$
$212$	−6.00000	−0.412082
$213$	2.83710	0.194395
$214$	−6.15676	−0.420867
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	1.16290	0.0789427
$218$	17.9155	1.21339
$219$	6.83710	0.462009
$220$	0	0
$221$	−18.5236	−1.24603
$222$	3.41855	0.229438
$223$	−1.28846	−0.0862815	−0.0431407	−	0.999069i	$-0.513736\pi$
$223$	−1.28846	−0.0862815	−0.0431407	+	0.999069i	$0.513736\pi$
$224$	1.07838	0.0720521
$225$	0	0
$226$	13.2039	0.878313
$227$	−20.9939	−1.39341	−0.696706	−	0.717357i	$-0.745352\pi$
$227$	−20.9939	−1.39341	−0.696706	+	0.717357i	$0.745352\pi$
$228$	−1.00000	−0.0662266
$229$	−2.36683	−0.156405	−0.0782024	−	0.996938i	$-0.524918\pi$
$229$	−2.36683	−0.156405	−0.0782024	+	0.996938i	$0.524918\pi$
$230$	0	0
$231$	−6.83710	−0.449848
$232$	−0.340173	−0.0223334
$233$	−5.10504	−0.334442	−0.167221	−	0.985919i	$-0.553479\pi$
$233$	−5.10504	−0.334442	−0.167221	+	0.985919i	$0.553479\pi$
$234$	−3.41855	−0.223478
$235$	0	0
$236$	0.738205	0.0480530
$237$	1.07838	0.0700482
$238$	5.84324	0.378761
$239$	10.4124	0.673523	0.336761	−	0.941590i	$-0.390668\pi$
$239$	10.4124	0.673523	0.336761	+	0.941590i	$0.390668\pi$
$240$	0	0
$241$	3.36069	0.216481	0.108241	−	0.994125i	$-0.465478\pi$
$241$	3.36069	0.216481	0.108241	+	0.994125i	$0.465478\pi$
$242$	29.1978	1.87691
$243$	−1.00000	−0.0641500
$244$	−2.68035	−0.171592
$245$	0	0
$246$	−7.60197	−0.484684
$247$	−3.41855	−0.217517
$248$	1.07838	0.0684771
$249$	0.894960	0.0567158
$250$	0	0
$251$	21.8576	1.37964	0.689820	−	0.723981i	$-0.257689\pi$
$251$	21.8576	1.37964	0.689820	+	0.723981i	$0.257689\pi$
$252$	1.07838	0.0679314
$253$	−40.1978	−2.52721
$254$	0.921622	0.0578277
$255$	0	0
$256$	1.00000	0.0625000
$257$	26.8781	1.67661	0.838306	−	0.545200i	$-0.183546\pi$
$257$	26.8781	1.67661	0.838306	+	0.545200i	$0.183546\pi$
$258$	−11.1773	−0.695867
$259$	−3.68649	−0.229067
$260$	0	0
$261$	−0.340173	−0.0210562
$262$	10.6537	0.658187
$263$	−22.3402	−1.37755	−0.688777	−	0.724973i	$-0.741852\pi$
$263$	−22.3402	−1.37755	−0.688777	+	0.724973i	$0.741852\pi$
$264$	−6.34017	−0.390211
$265$	0	0
$266$	1.07838	0.0661196
$267$	−6.92162	−0.423596
$268$	−2.83710	−0.173304
$269$	−17.3340	−1.05687	−0.528437	−	0.848972i	$-0.677222\pi$
$269$	−17.3340	−1.05687	−0.528437	+	0.848972i	$0.677222\pi$
$270$	0	0
$271$	−13.3607	−0.811604	−0.405802	−	0.913961i	$-0.633008\pi$
$271$	−13.3607	−0.811604	−0.405802	+	0.913961i	$0.633008\pi$
$272$	5.41855	0.328548
$273$	3.68649	0.223116
$274$	−20.6225	−1.24585
$275$	0	0
$276$	6.34017	0.381634
$277$	−0.738205	−0.0443544	−0.0221772	−	0.999754i	$-0.507060\pi$
$277$	−0.738205	−0.0443544	−0.0221772	+	0.999754i	$0.507060\pi$
$278$	18.8371	1.12977
$279$	1.07838	0.0645608
$280$	0	0
$281$	−31.7998	−1.89701	−0.948507	−	0.316755i	$-0.897407\pi$
$281$	−31.7998	−1.89701	−0.948507	+	0.316755i	$0.897407\pi$
$282$	−6.34017	−0.377552
$283$	4.70701	0.279803	0.139901	−	0.990165i	$-0.455321\pi$
$283$	4.70701	0.279803	0.139901	+	0.990165i	$0.455321\pi$
$284$	−2.83710	−0.168351
$285$	0	0
$286$	−21.6742	−1.28162
$287$	8.19779	0.483900
$288$	1.00000	0.0589256
$289$	12.3607	0.727100
$290$	0	0
$291$	−3.65983	−0.214543
$292$	−6.83710	−0.400111
$293$	−26.1978	−1.53049	−0.765246	−	0.643738i	$-0.777383\pi$
$293$	−26.1978	−1.53049	−0.765246	+	0.643738i	$0.777383\pi$
$294$	5.83710	0.340427
$295$	0	0
$296$	−3.41855	−0.198699
$297$	−6.34017	−0.367894
$298$	−5.44521	−0.315433
$299$	21.6742	1.25345
$300$	0	0
$301$	12.0533	0.694742
$302$	−23.1194	−1.33037
$303$	−19.6020	−1.12610
$304$	1.00000	0.0573539
$305$	0	0
$306$	5.41855	0.309758
$307$	−32.1978	−1.83763	−0.918813	−	0.394694i	$-0.870851\pi$
$307$	−32.1978	−1.83763	−0.918813	+	0.394694i	$0.870851\pi$
$308$	6.83710	0.389580
$309$	−11.7587	−0.668930
$310$	0	0
$311$	16.7382	0.949137	0.474568	−	0.880219i	$-0.342604\pi$
$311$	16.7382	0.949137	0.474568	+	0.880219i	$0.342604\pi$
$312$	3.41855	0.193537
$313$	14.1568	0.800187	0.400094	−	0.916474i	$-0.368978\pi$
$313$	14.1568	0.800187	0.400094	+	0.916474i	$0.368978\pi$
$314$	9.73206	0.549212
$315$	0	0
$316$	−1.07838	−0.0606635
$317$	21.8843	1.22914	0.614572	−	0.788861i	$-0.289329\pi$
$317$	21.8843	1.22914	0.614572	+	0.788861i	$0.289329\pi$
$318$	6.00000	0.336463
$319$	−2.15676	−0.120755
$320$	0	0
$321$	6.15676	0.343637
$322$	−6.83710	−0.381017
$323$	5.41855	0.301496
$324$	1.00000	0.0555556
$325$	0	0
$326$	6.49693	0.359832
$327$	−17.9155	−0.990728
$328$	7.60197	0.419748
$329$	6.83710	0.376942
$330$	0	0
$331$	−26.1568	−1.43771	−0.718853	−	0.695162i	$-0.755332\pi$
$331$	−26.1568	−1.43771	−0.718853	+	0.695162i	$0.755332\pi$
$332$	−0.894960	−0.0491173
$333$	−3.41855	−0.187335
$334$	−20.9939	−1.14873
$335$	0	0
$336$	−1.07838	−0.0588303
$337$	29.7009	1.61791	0.808955	−	0.587871i	$-0.200034\pi$
$337$	29.7009	1.61791	0.808955	+	0.587871i	$0.200034\pi$
$338$	−1.31351	−0.0714456
$339$	−13.2039	−0.717139
$340$	0	0
$341$	6.83710	0.370250
$342$	1.00000	0.0540738
$343$	−13.8432	−0.747465
$344$	11.1773	0.602638
$345$	0	0
$346$	6.99386	0.375992
$347$	−23.4186	−1.25717	−0.628587	−	0.777739i	$-0.716366\pi$
$347$	−23.4186	−1.25717	−0.628587	+	0.777739i	$0.716366\pi$
$348$	0.340173	0.0182352
$349$	6.48255	0.347003	0.173502	−	0.984834i	$-0.444492\pi$
$349$	6.48255	0.347003	0.173502	+	0.984834i	$0.444492\pi$
$350$	0	0
$351$	3.41855	0.182469
$352$	6.34017	0.337932
$353$	−2.58145	−0.137397	−0.0686983	−	0.997637i	$-0.521885\pi$
$353$	−2.58145	−0.137397	−0.0686983	+	0.997637i	$0.521885\pi$
$354$	−0.738205	−0.0392351
$355$	0	0
$356$	6.92162	0.366845
$357$	−5.84324	−0.309257
$358$	−4.73820	−0.250422
$359$	28.1399	1.48517	0.742584	−	0.669752i	$-0.233600\pi$
$359$	28.1399	1.48517	0.742584	+	0.669752i	$0.233600\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−12.0722	−0.634503
$363$	−29.1978	−1.53249
$364$	−3.68649	−0.193225
$365$	0	0
$366$	2.68035	0.140104
$367$	−10.5548	−0.550955	−0.275478	−	0.961307i	$-0.588836\pi$
$367$	−10.5548	−0.550955	−0.275478	+	0.961307i	$0.588836\pi$
$368$	−6.34017	−0.330504
$369$	7.60197	0.395743
$370$	0	0
$371$	−6.47027	−0.335919
$372$	−1.07838	−0.0559113
$373$	−17.8888	−0.926248	−0.463124	−	0.886294i	$-0.653272\pi$
$373$	−17.8888	−0.926248	−0.463124	+	0.886294i	$0.653272\pi$
$374$	34.3545	1.77643
$375$	0	0
$376$	6.34017	0.326969
$377$	1.16290	0.0598923
$378$	−1.07838	−0.0554658
$379$	4.36683	0.224309	0.112155	−	0.993691i	$-0.464225\pi$
$379$	4.36683	0.224309	0.112155	+	0.993691i	$0.464225\pi$
$380$	0	0
$381$	−0.921622	−0.0472161
$382$	−7.26180	−0.371546
$383$	−22.5236	−1.15090	−0.575451	−	0.817836i	$-0.695173\pi$
$383$	−22.5236	−1.15090	−0.575451	+	0.817836i	$0.695173\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	18.8638	0.960140
$387$	11.1773	0.568173
$388$	3.65983	0.185800
$389$	−9.07838	−0.460292	−0.230146	−	0.973156i	$-0.573920\pi$
$389$	−9.07838	−0.460292	−0.230146	+	0.973156i	$0.573920\pi$
$390$	0	0
$391$	−34.3545	−1.73738
$392$	−5.83710	−0.294818
$393$	−10.6537	−0.537407
$394$	−17.7009	−0.891757
$395$	0	0
$396$	6.34017	0.318606
$397$	3.74435	0.187923	0.0939617	−	0.995576i	$-0.470047\pi$
$397$	3.74435	0.187923	0.0939617	+	0.995576i	$0.470047\pi$
$398$	−0.313511	−0.0157149
$399$	−1.07838	−0.0539864
$400$	0	0
$401$	−11.9155	−0.595031	−0.297515	−	0.954717i	$-0.596158\pi$
$401$	−11.9155	−0.595031	−0.297515	+	0.954717i	$0.596158\pi$
$402$	2.83710	0.141502
$403$	−3.68649	−0.183637
$404$	19.6020	0.975234
$405$	0	0
$406$	−0.366835	−0.0182057
$407$	−21.6742	−1.07435
$408$	−5.41855	−0.268258
$409$	−2.99386	−0.148037	−0.0740183	−	0.997257i	$-0.523582\pi$
$409$	−2.99386	−0.148037	−0.0740183	+	0.997257i	$0.523582\pi$
$410$	0	0
$411$	20.6225	1.01723
$412$	11.7587	0.579311
$413$	0.796064	0.0391717
$414$	−6.34017	−0.311603
$415$	0	0
$416$	−3.41855	−0.167608
$417$	−18.8371	−0.922457
$418$	6.34017	0.310108
$419$	−33.5441	−1.63874	−0.819368	−	0.573267i	$-0.805676\pi$
$419$	−33.5441	−1.63874	−0.819368	+	0.573267i	$0.805676\pi$
$420$	0	0
$421$	31.5897	1.53959	0.769793	−	0.638293i	$-0.220359\pi$
$421$	31.5897	1.53959	0.769793	+	0.638293i	$0.220359\pi$
$422$	14.8371	0.722259
$423$	6.34017	0.308270
$424$	−6.00000	−0.291386
$425$	0	0
$426$	2.83710	0.137458
$427$	−2.89043	−0.139877
$428$	−6.15676	−0.297598
$429$	21.6742	1.04644
$430$	0	0
$431$	−40.5113	−1.95136	−0.975680	−	0.219198i	$-0.929656\pi$
$431$	−40.5113	−1.95136	−0.975680	+	0.219198i	$0.929656\pi$
$432$	−1.00000	−0.0481125
$433$	−5.13624	−0.246832	−0.123416	−	0.992355i	$-0.539385\pi$
$433$	−5.13624	−0.246832	−0.123416	+	0.992355i	$0.539385\pi$
$434$	1.16290	0.0558209
$435$	0	0
$436$	17.9155	0.857996
$437$	−6.34017	−0.303292
$438$	6.83710	0.326689
$439$	−17.7054	−0.845033	−0.422516	−	0.906355i	$-0.638853\pi$
$439$	−17.7054	−0.845033	−0.422516	+	0.906355i	$0.638853\pi$
$440$	0	0
$441$	−5.83710	−0.277957
$442$	−18.5236	−0.881077
$443$	−6.73820	−0.320142	−0.160071	−	0.987106i	$-0.551172\pi$
$443$	−6.73820	−0.320142	−0.160071	+	0.987106i	$0.551172\pi$
$444$	3.41855	0.162237
$445$	0	0
$446$	−1.28846	−0.0610102
$447$	5.44521	0.257550
$448$	1.07838	0.0509486
$449$	−36.2290	−1.70975	−0.854876	−	0.518833i	$-0.826367\pi$
$449$	−36.2290	−1.70975	−0.854876	+	0.518833i	$0.826367\pi$
$450$	0	0
$451$	48.1978	2.26955
$452$	13.2039	0.621061
$453$	23.1194	1.08624
$454$	−20.9939	−0.985291
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	−2.36683	−0.110595
$459$	−5.41855	−0.252916
$460$	0	0
$461$	35.7464	1.66488	0.832439	−	0.554117i	$-0.186944\pi$
$461$	35.7464	1.66488	0.832439	+	0.554117i	$0.186944\pi$
$462$	−6.83710	−0.318091
$463$	37.3295	1.73485	0.867424	−	0.497569i	$-0.165774\pi$
$463$	37.3295	1.73485	0.867424	+	0.497569i	$0.165774\pi$
$464$	−0.340173	−0.0157921
$465$	0	0
$466$	−5.10504	−0.236486
$467$	12.0989	0.559870	0.279935	−	0.960019i	$-0.409687\pi$
$467$	12.0989	0.559870	0.279935	+	0.960019i	$0.409687\pi$
$468$	−3.41855	−0.158023
$469$	−3.05947	−0.141273
$470$	0	0
$471$	−9.73206	−0.448430
$472$	0.738205	0.0339786
$473$	70.8659	3.25842
$474$	1.07838	0.0495315
$475$	0	0
$476$	5.84324	0.267825
$477$	−6.00000	−0.274721
$478$	10.4124	0.476252
$479$	−34.6102	−1.58138	−0.790690	−	0.612216i	$-0.790278\pi$
$479$	−34.6102	−1.58138	−0.790690	+	0.612216i	$0.790278\pi$
$480$	0	0
$481$	11.6865	0.532858
$482$	3.36069	0.153075
$483$	6.83710	0.311099
$484$	29.1978	1.32717
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−30.2823	−1.37222	−0.686111	−	0.727497i	$-0.740684\pi$
$487$	−30.2823	−1.37222	−0.686111	+	0.727497i	$0.740684\pi$
$488$	−2.68035	−0.121334
$489$	−6.49693	−0.293801
$490$	0	0
$491$	−27.0205	−1.21942	−0.609709	−	0.792625i	$-0.708714\pi$
$491$	−27.0205	−1.21942	−0.609709	+	0.792625i	$0.708714\pi$
$492$	−7.60197	−0.342723
$493$	−1.84324	−0.0830156
$494$	−3.41855	−0.153808
$495$	0	0
$496$	1.07838	0.0484206
$497$	−3.05947	−0.137236
$498$	0.894960	0.0401041
$499$	−35.0349	−1.56838	−0.784189	−	0.620522i	$-0.786921\pi$
$499$	−35.0349	−1.56838	−0.784189	+	0.620522i	$0.786921\pi$
$500$	0	0
$501$	20.9939	0.937936
$502$	21.8576	0.975553
$503$	29.5441	1.31731	0.658653	−	0.752447i	$-0.271126\pi$
$503$	29.5441	1.31731	0.658653	+	0.752447i	$0.271126\pi$
$504$	1.07838	0.0480348
$505$	0	0
$506$	−40.1978	−1.78701
$507$	1.31351	0.0583351
$508$	0.921622	0.0408904
$509$	29.2183	1.29508	0.647539	−	0.762032i	$-0.275798\pi$
$509$	29.2183	1.29508	0.647539	+	0.762032i	$0.275798\pi$
$510$	0	0
$511$	−7.37298	−0.326161
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	26.8781	1.18554
$515$	0	0
$516$	−11.1773	−0.492052
$517$	40.1978	1.76790
$518$	−3.68649	−0.161975
$519$	−6.99386	−0.306996
$520$	0	0
$521$	−16.3980	−0.718411	−0.359205	−	0.933259i	$-0.616952\pi$
$521$	−16.3980	−0.718411	−0.359205	+	0.933259i	$0.616952\pi$
$522$	−0.340173	−0.0148890
$523$	13.8432	0.605323	0.302661	−	0.953098i	$-0.402125\pi$
$523$	13.8432	0.605323	0.302661	+	0.953098i	$0.402125\pi$
$524$	10.6537	0.465408
$525$	0	0
$526$	−22.3402	−0.974078
$527$	5.84324	0.254536
$528$	−6.34017	−0.275921
$529$	17.1978	0.747730
$530$	0	0
$531$	0.738205	0.0320354
$532$	1.07838	0.0467536
$533$	−25.9877	−1.12565
$534$	−6.92162	−0.299528
$535$	0	0
$536$	−2.83710	−0.122544
$537$	4.73820	0.204469
$538$	−17.3340	−0.747323
$539$	−37.0082	−1.59406
$540$	0	0
$541$	−5.20394	−0.223735	−0.111867	−	0.993723i	$-0.535683\pi$
$541$	−5.20394	−0.223735	−0.111867	+	0.993723i	$0.535683\pi$
$542$	−13.3607	−0.573891
$543$	12.0722	0.518069
$544$	5.41855	0.232318
$545$	0	0
$546$	3.68649	0.157767
$547$	−19.8843	−0.850191	−0.425095	−	0.905149i	$-0.639759\pi$
$547$	−19.8843	−0.850191	−0.425095	+	0.905149i	$0.639759\pi$
$548$	−20.6225	−0.880949
$549$	−2.68035	−0.114394
$550$	0	0
$551$	−0.340173	−0.0144919
$552$	6.34017	0.269856
$553$	−1.16290	−0.0494515
$554$	−0.738205	−0.0313633
$555$	0	0
$556$	18.8371	0.798871
$557$	−17.0205	−0.721183	−0.360591	−	0.932724i	$-0.617425\pi$
$557$	−17.0205	−0.721183	−0.360591	+	0.932724i	$0.617425\pi$
$558$	1.07838	0.0456514
$559$	−38.2101	−1.61611
$560$	0	0
$561$	−34.3545	−1.45045
$562$	−31.7998	−1.34139
$563$	−12.6270	−0.532166	−0.266083	−	0.963950i	$-0.585729\pi$
$563$	−12.6270	−0.532166	−0.266083	+	0.963950i	$0.585729\pi$
$564$	−6.34017	−0.266969
$565$	0	0
$566$	4.70701	0.197850
$567$	1.07838	0.0452876
$568$	−2.83710	−0.119042
$569$	−31.9155	−1.33797	−0.668983	−	0.743277i	$-0.733270\pi$
$569$	−31.9155	−1.33797	−0.668983	+	0.743277i	$0.733270\pi$
$570$	0	0
$571$	24.5113	1.02577	0.512883	−	0.858458i	$-0.328577\pi$
$571$	24.5113	1.02577	0.512883	+	0.858458i	$0.328577\pi$
$572$	−21.6742	−0.906244
$573$	7.26180	0.303366
$574$	8.19779	0.342169
$575$	0	0
$576$	1.00000	0.0416667
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	12.3607	0.514137
$579$	−18.8638	−0.783951
$580$	0	0
$581$	−0.965105	−0.0400393
$582$	−3.65983	−0.151705
$583$	−38.0410	−1.57550
$584$	−6.83710	−0.282921
$585$	0	0
$586$	−26.1978	−1.08222
$587$	8.58145	0.354194	0.177097	−	0.984193i	$-0.443329\pi$
$587$	8.58145	0.354194	0.177097	+	0.984193i	$0.443329\pi$
$588$	5.83710	0.240718
$589$	1.07838	0.0444338
$590$	0	0
$591$	17.7009	0.728116
$592$	−3.41855	−0.140502
$593$	10.7792	0.442650	0.221325	−	0.975200i	$-0.428962\pi$
$593$	10.7792	0.442650	0.221325	+	0.975200i	$0.428962\pi$
$594$	−6.34017	−0.260140
$595$	0	0
$596$	−5.44521	−0.223045
$597$	0.313511	0.0128312
$598$	21.6742	0.886324
$599$	−18.2101	−0.744044	−0.372022	−	0.928224i	$-0.621335\pi$
$599$	−18.2101	−0.744044	−0.372022	+	0.928224i	$0.621335\pi$
$600$	0	0
$601$	−32.0410	−1.30698	−0.653491	−	0.756935i	$-0.726696\pi$
$601$	−32.0410	−1.30698	−0.653491	+	0.756935i	$0.726696\pi$
$602$	12.0533	0.491257
$603$	−2.83710	−0.115536
$604$	−23.1194	−0.940716
$605$	0	0
$606$	−19.6020	−0.796276
$607$	−11.5609	−0.469244	−0.234622	−	0.972087i	$-0.575385\pi$
$607$	−11.5609	−0.469244	−0.234622	+	0.972087i	$0.575385\pi$
$608$	1.00000	0.0405554
$609$	0.366835	0.0148649
$610$	0	0
$611$	−21.6742	−0.876844
$612$	5.41855	0.219032
$613$	2.58145	0.104264	0.0521319	−	0.998640i	$-0.483398\pi$
$613$	2.58145	0.104264	0.0521319	+	0.998640i	$0.483398\pi$
$614$	−32.1978	−1.29940
$615$	0	0
$616$	6.83710	0.275475
$617$	9.90110	0.398603	0.199302	−	0.979938i	$-0.436133\pi$
$617$	9.90110	0.398603	0.199302	+	0.979938i	$0.436133\pi$
$618$	−11.7587	−0.473005
$619$	11.2039	0.450324	0.225162	−	0.974321i	$-0.427709\pi$
$619$	11.2039	0.450324	0.225162	+	0.974321i	$0.427709\pi$
$620$	0	0
$621$	6.34017	0.254422
$622$	16.7382	0.671141
$623$	7.46412	0.299044
$624$	3.41855	0.136852
$625$	0	0
$626$	14.1568	0.565818
$627$	−6.34017	−0.253202
$628$	9.73206	0.388352
$629$	−18.5236	−0.738584
$630$	0	0
$631$	−23.3197	−0.928341	−0.464170	−	0.885746i	$-0.653647\pi$
$631$	−23.3197	−0.928341	−0.464170	+	0.885746i	$0.653647\pi$
$632$	−1.07838	−0.0428956
$633$	−14.8371	−0.589722
$634$	21.8843	0.869136
$635$	0	0
$636$	6.00000	0.237915
$637$	19.9544	0.790623
$638$	−2.15676	−0.0853868
$639$	−2.83710	−0.112234
$640$	0	0
$641$	−19.2885	−0.761848	−0.380924	−	0.924606i	$-0.624394\pi$
$641$	−19.2885	−0.761848	−0.380924	+	0.924606i	$0.624394\pi$
$642$	6.15676	0.242988
$643$	−31.3751	−1.23731	−0.618656	−	0.785662i	$-0.712323\pi$
$643$	−31.3751	−1.23731	−0.618656	+	0.785662i	$0.712323\pi$
$644$	−6.83710	−0.269420
$645$	0	0
$646$	5.41855	0.213190
$647$	−33.2306	−1.30643	−0.653215	−	0.757173i	$-0.726580\pi$
$647$	−33.2306	−1.30643	−0.653215	+	0.757173i	$0.726580\pi$
$648$	1.00000	0.0392837
$649$	4.68035	0.183720
$650$	0	0
$651$	−1.16290	−0.0455776
$652$	6.49693	0.254439
$653$	−7.85762	−0.307492	−0.153746	−	0.988110i	$-0.549134\pi$
$653$	−7.85762	−0.307492	−0.153746	+	0.988110i	$0.549134\pi$
$654$	−17.9155	−0.700551
$655$	0	0
$656$	7.60197	0.296807
$657$	−6.83710	−0.266741
$658$	6.83710	0.266538
$659$	−25.4186	−0.990166	−0.495083	−	0.868846i	$-0.664862\pi$
$659$	−25.4186	−0.990166	−0.495083	+	0.868846i	$0.664862\pi$
$660$	0	0
$661$	30.9093	1.20223	0.601117	−	0.799161i	$-0.294723\pi$
$661$	30.9093	1.20223	0.601117	+	0.799161i	$0.294723\pi$
$662$	−26.1568	−1.01661
$663$	18.5236	0.719397
$664$	−0.894960	−0.0347312
$665$	0	0
$666$	−3.41855	−0.132466
$667$	2.15676	0.0835099
$668$	−20.9939	−0.812277
$669$	1.28846	0.0498146
$670$	0	0
$671$	−16.9939	−0.656041
$672$	−1.07838	−0.0415993
$673$	27.9733	1.07829	0.539146	−	0.842212i	$-0.318747\pi$
$673$	27.9733	1.07829	0.539146	+	0.842212i	$0.318747\pi$
$674$	29.7009	1.14403
$675$	0	0
$676$	−1.31351	−0.0505197
$677$	4.15676	0.159757	0.0798785	−	0.996805i	$-0.474547\pi$
$677$	4.15676	0.159757	0.0798785	+	0.996805i	$0.474547\pi$
$678$	−13.2039	−0.507094
$679$	3.94668	0.151460
$680$	0	0
$681$	20.9939	0.804486
$682$	6.83710	0.261806
$683$	19.5708	0.748855	0.374427	−	0.927256i	$-0.377839\pi$
$683$	19.5708	0.748855	0.374427	+	0.927256i	$0.377839\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	−13.8432	−0.528538
$687$	2.36683	0.0903004
$688$	11.1773	0.426130
$689$	20.5113	0.781418
$690$	0	0
$691$	−10.8371	−0.412263	−0.206131	−	0.978524i	$-0.566087\pi$
$691$	−10.8371	−0.412263	−0.206131	+	0.978524i	$0.566087\pi$
$692$	6.99386	0.265867
$693$	6.83710	0.259720
$694$	−23.4186	−0.888956
$695$	0	0
$696$	0.340173	0.0128942
$697$	41.1917	1.56025
$698$	6.48255	0.245368
$699$	5.10504	0.193090
$700$	0	0
$701$	−42.0098	−1.58669	−0.793345	−	0.608772i	$-0.791662\pi$
$701$	−42.0098	−1.58669	−0.793345	+	0.608772i	$0.791662\pi$
$702$	3.41855	0.129025
$703$	−3.41855	−0.128933
$704$	6.34017	0.238954
$705$	0	0
$706$	−2.58145	−0.0971541
$707$	21.1383	0.794989
$708$	−0.738205	−0.0277434
$709$	23.6209	0.887101	0.443550	−	0.896249i	$-0.353719\pi$
$709$	23.6209	0.887101	0.443550	+	0.896249i	$0.353719\pi$
$710$	0	0
$711$	−1.07838	−0.0404423
$712$	6.92162	0.259399
$713$	−6.83710	−0.256051
$714$	−5.84324	−0.218678
$715$	0	0
$716$	−4.73820	−0.177075
$717$	−10.4124	−0.388858
$718$	28.1399	1.05017
$719$	30.9770	1.15525	0.577624	−	0.816303i	$-0.303980\pi$
$719$	30.9770	1.15525	0.577624	+	0.816303i	$0.303980\pi$
$720$	0	0
$721$	12.6803	0.472241
$722$	1.00000	0.0372161
$723$	−3.36069	−0.124985
$724$	−12.0722	−0.448661
$725$	0	0
$726$	−29.1978	−1.08363
$727$	−23.7464	−0.880707	−0.440353	−	0.897825i	$-0.645147\pi$
$727$	−23.7464	−0.880707	−0.440353	+	0.897825i	$0.645147\pi$
$728$	−3.68649	−0.136630
$729$	1.00000	0.0370370
$730$	0	0
$731$	60.5646	2.24006
$732$	2.68035	0.0990684
$733$	−41.9832	−1.55068	−0.775342	−	0.631542i	$-0.782423\pi$
$733$	−41.9832	−1.55068	−0.775342	+	0.631542i	$0.782423\pi$
$734$	−10.5548	−0.389584
$735$	0	0
$736$	−6.34017	−0.233702
$737$	−17.9877	−0.662586
$738$	7.60197	0.279832
$739$	−41.3074	−1.51952	−0.759758	−	0.650206i	$-0.774683\pi$
$739$	−41.3074	−1.51952	−0.759758	+	0.650206i	$0.774683\pi$
$740$	0	0
$741$	3.41855	0.125584
$742$	−6.47027	−0.237531
$743$	−28.3668	−1.04068	−0.520339	−	0.853960i	$-0.674194\pi$
$743$	−28.3668	−1.04068	−0.520339	+	0.853960i	$0.674194\pi$
$744$	−1.07838	−0.0395352
$745$	0	0
$746$	−17.8888	−0.654956
$747$	−0.894960	−0.0327449
$748$	34.3545	1.25613
$749$	−6.63931	−0.242595
$750$	0	0
$751$	5.75872	0.210139	0.105069	−	0.994465i	$-0.466494\pi$
$751$	5.75872	0.210139	0.105069	+	0.994465i	$0.466494\pi$
$752$	6.34017	0.231202
$753$	−21.8576	−0.796536
$754$	1.16290	0.0423503
$755$	0	0
$756$	−1.07838	−0.0392202
$757$	32.3090	1.17429	0.587145	−	0.809482i	$-0.300252\pi$
$757$	32.3090	1.17429	0.587145	+	0.809482i	$0.300252\pi$
$758$	4.36683	0.158611
$759$	40.1978	1.45909
$760$	0	0
$761$	33.5708	1.21694	0.608470	−	0.793577i	$-0.291784\pi$
$761$	33.5708	1.21694	0.608470	+	0.793577i	$0.291784\pi$
$762$	−0.921622	−0.0333869
$763$	19.3197	0.699418
$764$	−7.26180	−0.262723
$765$	0	0
$766$	−22.5236	−0.813810
$767$	−2.52359	−0.0911216
$768$	−1.00000	−0.0360844
$769$	−17.8843	−0.644924	−0.322462	−	0.946582i	$-0.604510\pi$
$769$	−17.8843	−0.644924	−0.322462	+	0.946582i	$0.604510\pi$
$770$	0	0
$771$	−26.8781	−0.967993
$772$	18.8638	0.678922
$773$	46.5113	1.67290	0.836448	−	0.548047i	$-0.184628\pi$
$773$	46.5113	1.67290	0.836448	+	0.548047i	$0.184628\pi$
$774$	11.1773	0.401759
$775$	0	0
$776$	3.65983	0.131380
$777$	3.68649	0.132252
$778$	−9.07838	−0.325476
$779$	7.60197	0.272369
$780$	0	0
$781$	−17.9877	−0.643651
$782$	−34.3545	−1.22852
$783$	0.340173	0.0121568
$784$	−5.83710	−0.208468
$785$	0	0
$786$	−10.6537	−0.380004
$787$	41.9877	1.49670	0.748350	−	0.663304i	$-0.230846\pi$
$787$	41.9877	1.49670	0.748350	+	0.663304i	$0.230846\pi$
$788$	−17.7009	−0.630567
$789$	22.3402	0.795331
$790$	0	0
$791$	14.2388	0.506275
$792$	6.34017	0.225288
$793$	9.16290	0.325384
$794$	3.74435	0.132882
$795$	0	0
$796$	−0.313511	−0.0111121
$797$	11.3074	0.400528	0.200264	−	0.979742i	$-0.435820\pi$
$797$	11.3074	0.400528	0.200264	+	0.979742i	$0.435820\pi$
$798$	−1.07838	−0.0381742
$799$	34.3545	1.21538
$800$	0	0
$801$	6.92162	0.244563
$802$	−11.9155	−0.420750
$803$	−43.3484	−1.52973
$804$	2.83710	0.100057
$805$	0	0
$806$	−3.68649	−0.129851
$807$	17.3340	0.610187
$808$	19.6020	0.689595
$809$	−48.5523	−1.70701	−0.853505	−	0.521085i	$-0.825527\pi$
$809$	−48.5523	−1.70701	−0.853505	+	0.521085i	$0.825527\pi$
$810$	0	0
$811$	−1.42309	−0.0499713	−0.0249856	−	0.999688i	$-0.507954\pi$
$811$	−1.42309	−0.0499713	−0.0249856	+	0.999688i	$0.507954\pi$
$812$	−0.366835	−0.0128734
$813$	13.3607	0.468580
$814$	−21.6742	−0.759680
$815$	0	0
$816$	−5.41855	−0.189687
$817$	11.1773	0.391043
$818$	−2.99386	−0.104678
$819$	−3.68649	−0.128816
$820$	0	0
$821$	−6.55479	−0.228764	−0.114382	−	0.993437i	$-0.536489\pi$
$821$	−6.55479	−0.228764	−0.114382	+	0.993437i	$0.536489\pi$
$822$	20.6225	0.719292
$823$	−0.0845208	−0.00294621	−0.00147311	−	0.999999i	$-0.500469\pi$
$823$	−0.0845208	−0.00294621	−0.00147311	+	0.999999i	$0.500469\pi$
$824$	11.7587	0.409635
$825$	0	0
$826$	0.796064	0.0276986
$827$	26.4703	0.920461	0.460231	−	0.887799i	$-0.347767\pi$
$827$	26.4703	0.920461	0.460231	+	0.887799i	$0.347767\pi$
$828$	−6.34017	−0.220336
$829$	−12.4924	−0.433879	−0.216939	−	0.976185i	$-0.569607\pi$
$829$	−12.4924	−0.433879	−0.216939	+	0.976185i	$0.569607\pi$
$830$	0	0
$831$	0.738205	0.0256080
$832$	−3.41855	−0.118517
$833$	−31.6286	−1.09587
$834$	−18.8371	−0.652275
$835$	0	0
$836$	6.34017	0.219279
$837$	−1.07838	−0.0372742
$838$	−33.5441	−1.15876
$839$	−17.5297	−0.605194	−0.302597	−	0.953119i	$-0.597854\pi$
$839$	−17.5297	−0.605194	−0.302597	+	0.953119i	$0.597854\pi$
$840$	0	0
$841$	−28.8843	−0.996010
$842$	31.5897	1.08865
$843$	31.7998	1.09524
$844$	14.8371	0.510714
$845$	0	0
$846$	6.34017	0.217980
$847$	31.4863	1.08188
$848$	−6.00000	−0.206041
$849$	−4.70701	−0.161544
$850$	0	0
$851$	21.6742	0.742982
$852$	2.83710	0.0971975
$853$	22.0456	0.754826	0.377413	−	0.926045i	$-0.376814\pi$
$853$	22.0456	0.754826	0.377413	+	0.926045i	$0.376814\pi$
$854$	−2.89043	−0.0989083
$855$	0	0
$856$	−6.15676	−0.210434
$857$	−13.1506	−0.449216	−0.224608	−	0.974449i	$-0.572110\pi$
$857$	−13.1506	−0.449216	−0.224608	+	0.974449i	$0.572110\pi$
$858$	21.6742	0.739945
$859$	5.42309	0.185033	0.0925166	−	0.995711i	$-0.470509\pi$
$859$	5.42309	0.185033	0.0925166	+	0.995711i	$0.470509\pi$
$860$	0	0
$861$	−8.19779	−0.279380
$862$	−40.5113	−1.37982
$863$	28.6803	0.976290	0.488145	−	0.872762i	$-0.337674\pi$
$863$	28.6803	0.976290	0.488145	+	0.872762i	$0.337674\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−5.13624	−0.174536
$867$	−12.3607	−0.419791
$868$	1.16290	0.0394713
$869$	−6.83710	−0.231933
$870$	0	0
$871$	9.69878	0.328630
$872$	17.9155	0.606695
$873$	3.65983	0.123866
$874$	−6.34017	−0.214460
$875$	0	0
$876$	6.83710	0.231004
$877$	24.4657	0.826149	0.413075	−	0.910697i	$-0.364455\pi$
$877$	24.4657	0.826149	0.413075	+	0.910697i	$0.364455\pi$
$878$	−17.7054	−0.597528
$879$	26.1978	0.883630
$880$	0	0
$881$	5.51745	0.185888	0.0929438	−	0.995671i	$-0.470372\pi$
$881$	5.51745	0.185888	0.0929438	+	0.995671i	$0.470372\pi$
$882$	−5.83710	−0.196545
$883$	7.23060	0.243329	0.121665	−	0.992571i	$-0.461177\pi$
$883$	7.23060	0.243329	0.121665	+	0.992571i	$0.461177\pi$
$884$	−18.5236	−0.623016
$885$	0	0
$886$	−6.73820	−0.226374
$887$	−18.1568	−0.609644	−0.304822	−	0.952409i	$-0.598597\pi$
$887$	−18.1568	−0.609644	−0.304822	+	0.952409i	$0.598597\pi$
$888$	3.41855	0.114719
$889$	0.993857	0.0333329
$890$	0	0
$891$	6.34017	0.212404
$892$	−1.28846	−0.0431407
$893$	6.34017	0.212166
$894$	5.44521	0.182115
$895$	0	0
$896$	1.07838	0.0360261
$897$	−21.6742	−0.723681
$898$	−36.2290	−1.20898
$899$	−0.366835	−0.0122346
$900$	0	0
$901$	−32.5113	−1.08311
$902$	48.1978	1.60481
$903$	−12.0533	−0.401110
$904$	13.2039	0.439156
$905$	0	0
$906$	23.1194	0.768091
$907$	19.2039	0.637656	0.318828	−	0.947813i	$-0.396711\pi$
$907$	19.2039	0.637656	0.318828	+	0.947813i	$0.396711\pi$
$908$	−20.9939	−0.696706
$909$	19.6020	0.650156
$910$	0	0
$911$	52.8781	1.75193	0.875965	−	0.482374i	$-0.160225\pi$
$911$	52.8781	1.75193	0.875965	+	0.482374i	$0.160225\pi$
$912$	−1.00000	−0.0331133
$913$	−5.67420	−0.187789
$914$	8.00000	0.264616
$915$	0	0
$916$	−2.36683	−0.0782024
$917$	11.4887	0.379390
$918$	−5.41855	−0.178839
$919$	10.0410	0.331223	0.165612	−	0.986191i	$-0.447040\pi$
$919$	10.0410	0.331223	0.165612	+	0.986191i	$0.447040\pi$
$920$	0	0
$921$	32.1978	1.06095
$922$	35.7464	1.17725
$923$	9.69878	0.319239
$924$	−6.83710	−0.224924
$925$	0	0
$926$	37.3295	1.22672
$927$	11.7587	0.386207
$928$	−0.340173	−0.0111667
$929$	11.3074	0.370983	0.185491	−	0.982646i	$-0.440612\pi$
$929$	11.3074	0.370983	0.185491	+	0.982646i	$0.440612\pi$
$930$	0	0
$931$	−5.83710	−0.191303
$932$	−5.10504	−0.167221
$933$	−16.7382	−0.547984
$934$	12.0989	0.395888
$935$	0	0
$936$	−3.41855	−0.111739
$937$	27.0349	0.883192	0.441596	−	0.897214i	$-0.354413\pi$
$937$	27.0349	0.883192	0.441596	+	0.897214i	$0.354413\pi$
$938$	−3.05947	−0.0998951
$939$	−14.1568	−0.461988
$940$	0	0
$941$	−19.9733	−0.651112	−0.325556	−	0.945523i	$-0.605551\pi$
$941$	−19.9733	−0.651112	−0.325556	+	0.945523i	$0.605551\pi$
$942$	−9.73206	−0.317088
$943$	−48.1978	−1.56954
$944$	0.738205	0.0240265
$945$	0	0
$946$	70.8659	2.30405
$947$	−12.5281	−0.407109	−0.203555	−	0.979064i	$-0.565249\pi$
$947$	−12.5281	−0.407109	−0.203555	+	0.979064i	$0.565249\pi$
$948$	1.07838	0.0350241
$949$	23.3730	0.758719
$950$	0	0
$951$	−21.8843	−0.709646
$952$	5.84324	0.189381
$953$	46.5113	1.50665	0.753324	−	0.657649i	$-0.228449\pi$
$953$	46.5113	1.50665	0.753324	+	0.657649i	$0.228449\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	10.4124	0.336761
$957$	2.15676	0.0697180
$958$	−34.6102	−1.11820
$959$	−22.2388	−0.718129
$960$	0	0
$961$	−29.8371	−0.962487
$962$	11.6865	0.376788
$963$	−6.15676	−0.198399
$964$	3.36069	0.108241
$965$	0	0
$966$	6.83710	0.219980
$967$	−37.2762	−1.19872	−0.599360	−	0.800479i	$-0.704578\pi$
$967$	−37.2762	−1.19872	−0.599360	+	0.800479i	$0.704578\pi$
$968$	29.1978	0.938453
$969$	−5.41855	−0.174069
$970$	0	0
$971$	−16.4534	−0.528016	−0.264008	−	0.964520i	$-0.585045\pi$
$971$	−16.4534	−0.528016	−0.264008	+	0.964520i	$0.585045\pi$
$972$	−1.00000	−0.0320750
$973$	20.3135	0.651221
$974$	−30.2823	−0.970308
$975$	0	0
$976$	−2.68035	−0.0857958
$977$	34.5646	1.10582	0.552910	−	0.833241i	$-0.313517\pi$
$977$	34.5646	1.10582	0.552910	+	0.833241i	$0.313517\pi$
$978$	−6.49693	−0.207749
$979$	43.8843	1.40255
$980$	0	0
$981$	17.9155	0.571997
$982$	−27.0205	−0.862259
$983$	40.1978	1.28211	0.641055	−	0.767495i	$-0.278497\pi$
$983$	40.1978	1.28211	0.641055	+	0.767495i	$0.278497\pi$
$984$	−7.60197	−0.242342
$985$	0	0
$986$	−1.84324	−0.0587009
$987$	−6.83710	−0.217627
$988$	−3.41855	−0.108759
$989$	−70.8659	−2.25340
$990$	0	0
$991$	−24.6491	−0.783006	−0.391503	−	0.920177i	$-0.628045\pi$
$991$	−24.6491	−0.783006	−0.391503	+	0.920177i	$0.628045\pi$
$992$	1.07838	0.0342385
$993$	26.1568	0.830060
$994$	−3.05947	−0.0970404
$995$	0	0
$996$	0.894960	0.0283579
$997$	−6.89496	−0.218366	−0.109183	−	0.994022i	$-0.534823\pi$
$997$	−6.89496	−0.218366	−0.109183	+	0.994022i	$0.534823\pi$
$998$	−35.0349	−1.10901
$999$	3.41855	0.108158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.bm.1.2		3
3.2	odd	2		8550.2.a.ce.1.2		3
5.2	odd	4		570.2.d.c.229.5	yes	6
5.3	odd	4		570.2.d.c.229.2	✓	6
5.4	even	2		2850.2.a.bl.1.2		3
15.2	even	4		1710.2.d.f.1369.2		6
15.8	even	4		1710.2.d.f.1369.5		6
15.14	odd	2		8550.2.a.cq.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.c.229.2	✓	6	5.3	odd	4
570.2.d.c.229.5	yes	6	5.2	odd	4
1710.2.d.f.1369.2		6	15.2	even	4
1710.2.d.f.1369.5		6	15.8	even	4
2850.2.a.bl.1.2		3	5.4	even	2
2850.2.a.bm.1.2		3	1.1	even	1	trivial
8550.2.a.ce.1.2		3	3.2	odd	2
8550.2.a.cq.1.2		3	15.14	odd	2

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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.07838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.07838 q^{7} +1.00000 q^{8} +1.00000 q^{9} +6.34017 q^{11} -1.00000 q^{12} -3.41855 q^{13} +1.07838 q^{14} +1.00000 q^{16} +5.41855 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.07838 q^{21} +6.34017 q^{22} -6.34017 q^{23} -1.00000 q^{24} -3.41855 q^{26} -1.00000 q^{27} +1.07838 q^{28} -0.340173 q^{29} +1.07838 q^{31} +1.00000 q^{32} -6.34017 q^{33} +5.41855 q^{34} +1.00000 q^{36} -3.41855 q^{37} +1.00000 q^{38} +3.41855 q^{39} +7.60197 q^{41} -1.07838 q^{42} +11.1773 q^{43} +6.34017 q^{44} -6.34017 q^{46} +6.34017 q^{47} -1.00000 q^{48} -5.83710 q^{49} -5.41855 q^{51} -3.41855 q^{52} -6.00000 q^{53} -1.00000 q^{54} +1.07838 q^{56} -1.00000 q^{57} -0.340173 q^{58} +0.738205 q^{59} -2.68035 q^{61} +1.07838 q^{62} +1.07838 q^{63} +1.00000 q^{64} -6.34017 q^{66} -2.83710 q^{67} +5.41855 q^{68} +6.34017 q^{69} -2.83710 q^{71} +1.00000 q^{72} -6.83710 q^{73} -3.41855 q^{74} +1.00000 q^{76} +6.83710 q^{77} +3.41855 q^{78} -1.07838 q^{79} +1.00000 q^{81} +7.60197 q^{82} -0.894960 q^{83} -1.07838 q^{84} +11.1773 q^{86} +0.340173 q^{87} +6.34017 q^{88} +6.92162 q^{89} -3.68649 q^{91} -6.34017 q^{92} -1.07838 q^{93} +6.34017 q^{94} -1.00000 q^{96} +3.65983 q^{97} -5.83710 q^{98} +6.34017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 8 q^{11} - 3 q^{12} + 4 q^{13} + 3 q^{16} + 2 q^{17} + 3 q^{18} + 3 q^{19} + 8 q^{22} - 8 q^{23} - 3 q^{24} + 4 q^{26} - 3 q^{27} + 10 q^{29} + 3 q^{32} - 8 q^{33} + 2 q^{34} + 3 q^{36} + 4 q^{37} + 3 q^{38} - 4 q^{39} + 4 q^{41} - 6 q^{43} + 8 q^{44} - 8 q^{46} + 8 q^{47} - 3 q^{48} + 11 q^{49} - 2 q^{51} + 4 q^{52} - 18 q^{53} - 3 q^{54} - 3 q^{57} + 10 q^{58} + 10 q^{59} + 14 q^{61} + 3 q^{64} - 8 q^{66} + 20 q^{67} + 2 q^{68} + 8 q^{69} + 20 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} + 3 q^{76} - 8 q^{77} - 4 q^{78} + 3 q^{81} + 4 q^{82} - 4 q^{83} - 6 q^{86} - 10 q^{87} + 8 q^{88} + 24 q^{89} - 24 q^{91} - 8 q^{92} + 8 q^{94} - 3 q^{96} + 22 q^{97} + 11 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 8 * q^11 - 3 * q^12 + 4 * q^13 + 3 * q^16 + 2 * q^17 + 3 * q^18 + 3 * q^19 + 8 * q^22 - 8 * q^23 - 3 * q^24 + 4 * q^26 - 3 * q^27 + 10 * q^29 + 3 * q^32 - 8 * q^33 + 2 * q^34 + 3 * q^36 + 4 * q^37 + 3 * q^38 - 4 * q^39 + 4 * q^41 - 6 * q^43 + 8 * q^44 - 8 * q^46 + 8 * q^47 - 3 * q^48 + 11 * q^49 - 2 * q^51 + 4 * q^52 - 18 * q^53 - 3 * q^54 - 3 * q^57 + 10 * q^58 + 10 * q^59 + 14 * q^61 + 3 * q^64 - 8 * q^66 + 20 * q^67 + 2 * q^68 + 8 * q^69 + 20 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 + 3 * q^76 - 8 * q^77 - 4 * q^78 + 3 * q^81 + 4 * q^82 - 4 * q^83 - 6 * q^86 - 10 * q^87 + 8 * q^88 + 24 * q^89 - 24 * q^91 - 8 * q^92 + 8 * q^94 - 3 * q^96 + 22 * q^97 + 11 * q^98 + 8 * q^99

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