LMFDB - Embedded newform 841.2.b.b.840.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(840,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("841.840");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			840.3
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	841.840
Dual form			841.2.b.b.840.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034i q^{2} -0.618034i q^{3} +1.61803 q^{4} -3.85410 q^{5} +0.381966 q^{6} -2.23607 q^{7} +2.23607i q^{8} +2.61803 q^{9} +O(q^{10})$	\(q+0.618034i q^{2} -0.618034i q^{3} +1.61803 q^{4} -3.85410 q^{5} +0.381966 q^{6} -2.23607 q^{7} +2.23607i q^{8} +2.61803 q^{9} -2.38197i q^{10} -1.38197i q^{11} -1.00000i q^{12} +0.236068 q^{13} -1.38197i q^{14} +2.38197i q^{15} +1.85410 q^{16} -4.38197i q^{17} +1.61803i q^{18} -4.85410i q^{19} -6.23607 q^{20} +1.38197i q^{21} +0.854102 q^{22} -1.23607 q^{23} +1.38197 q^{24} +9.85410 q^{25} +0.145898i q^{26} -3.47214i q^{27} -3.61803 q^{28} -1.47214 q^{30} -10.0902i q^{31} +5.61803i q^{32} -0.854102 q^{33} +2.70820 q^{34} +8.61803 q^{35} +4.23607 q^{36} -4.70820i q^{37} +3.00000 q^{38} -0.145898i q^{39} -8.61803i q^{40} -3.85410i q^{41} -0.854102 q^{42} -7.23607i q^{43} -2.23607i q^{44} -10.0902 q^{45} -0.763932i q^{46} +7.00000i q^{47} -1.14590i q^{48} -2.00000 q^{49} +6.09017i q^{50} -2.70820 q^{51} +0.381966 q^{52} -2.00000 q^{53} +2.14590 q^{54} +5.32624i q^{55} -5.00000i q^{56} -3.00000 q^{57} +6.09017 q^{59} +3.85410i q^{60} -0.618034i q^{61} +6.23607 q^{62} -5.85410 q^{63} +0.236068 q^{64} -0.909830 q^{65} -0.527864i q^{66} +1.52786 q^{67} -7.09017i q^{68} +0.763932i q^{69} +5.32624i q^{70} -10.4721 q^{71} +5.85410i q^{72} +13.7082i q^{73} +2.90983 q^{74} -6.09017i q^{75} -7.85410i q^{76} +3.09017i q^{77} +0.0901699 q^{78} -6.09017i q^{79} -7.14590 q^{80} +5.70820 q^{81} +2.38197 q^{82} -9.94427 q^{83} +2.23607i q^{84} +16.8885i q^{85} +4.47214 q^{86} +3.09017 q^{88} +4.70820i q^{89} -6.23607i q^{90} -0.527864 q^{91} -2.00000 q^{92} -6.23607 q^{93} -4.32624 q^{94} +18.7082i q^{95} +3.47214 q^{96} -3.56231i q^{97} -1.23607i q^{98} -3.61803i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{5} + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^5 + 6 * q^6 + 6 * q^9	$ 4 q + 2 q^{4} - 2 q^{5} + 6 q^{6} + 6 q^{9} - 8 q^{13} - 6 q^{16} - 16 q^{20} - 10 q^{22} + 4 q^{23} + 10 q^{24} + 26 q^{25} - 10 q^{28} + 12 q^{30} + 10 q^{33} - 16 q^{34} + 30 q^{35} + 8 q^{36} + 12 q^{38} + 10 q^{42} - 18 q^{45} - 8 q^{49} + 16 q^{51} + 6 q^{52} - 8 q^{53} + 22 q^{54} - 12 q^{57} + 2 q^{59} + 16 q^{62} - 10 q^{63} - 8 q^{64} - 26 q^{65} + 24 q^{67} - 24 q^{71} + 34 q^{74} - 22 q^{78} - 42 q^{80} - 4 q^{81} + 14 q^{82} - 4 q^{83} - 10 q^{88} - 20 q^{91} - 8 q^{92} - 16 q^{93} + 14 q^{94} - 4 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^5 + 6 * q^6 + 6 * q^9 - 8 * q^13 - 6 * q^16 - 16 * q^20 - 10 * q^22 + 4 * q^23 + 10 * q^24 + 26 * q^25 - 10 * q^28 + 12 * q^30 + 10 * q^33 - 16 * q^34 + 30 * q^35 + 8 * q^36 + 12 * q^38 + 10 * q^42 - 18 * q^45 - 8 * q^49 + 16 * q^51 + 6 * q^52 - 8 * q^53 + 22 * q^54 - 12 * q^57 + 2 * q^59 + 16 * q^62 - 10 * q^63 - 8 * q^64 - 26 * q^65 + 24 * q^67 - 24 * q^71 + 34 * q^74 - 22 * q^78 - 42 * q^80 - 4 * q^81 + 14 * q^82 - 4 * q^83 - 10 * q^88 - 20 * q^91 - 8 * q^92 - 16 * q^93 + 14 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	0.618034i	0.437016i	0.975835	+	0.218508i	$0.0701190\pi$
$2$	0.618034i	0.437016i	−0.975835	+	0.218508i	$0.929881\pi$
$3$	− 0.618034i	− 0.356822i	−0.983956	−	0.178411i	$-0.942904\pi$
$3$	− 0.618034i	− 0.356822i	0.983956	−	0.178411i	$-0.0570957\pi$
$4$	1.61803	0.809017
$5$	−3.85410	−1.72361	−0.861803	−	0.507242i	$-0.830665\pi$
$5$	−3.85410	−1.72361	−0.861803	+	0.507242i	$0.830665\pi$
$6$	0.381966	0.155937
$7$	−2.23607	−0.845154	−0.422577	−	0.906327i	$-0.638874\pi$
$7$	−2.23607	−0.845154	−0.422577	+	0.906327i	$0.638874\pi$
$8$	2.23607i	0.790569i
$9$	2.61803	0.872678
$10$	− 2.38197i	− 0.753244i
$11$	− 1.38197i	− 0.416678i	−0.978057	−	0.208339i	$-0.933194\pi$
$11$	− 1.38197i	− 0.416678i	0.978057	−	0.208339i	$-0.0668058\pi$
$12$	− 1.00000i	− 0.288675i
$13$	0.236068	0.0654735	0.0327367	−	0.999464i	$-0.489578\pi$
$13$	0.236068	0.0654735	0.0327367	+	0.999464i	$0.489578\pi$
$14$	− 1.38197i	− 0.369346i
$15$	2.38197i	0.615021i
$16$	1.85410	0.463525
$17$	− 4.38197i	− 1.06278i	−0.847126	−	0.531391i	$-0.821669\pi$
$17$	− 4.38197i	− 1.06278i	0.847126	−	0.531391i	$-0.178331\pi$
$18$	1.61803i	0.381374i
$19$	− 4.85410i	− 1.11361i	−0.830644	−	0.556804i	$-0.812028\pi$
$19$	− 4.85410i	− 1.11361i	0.830644	−	0.556804i	$-0.187972\pi$
$20$	−6.23607	−1.39443
$21$	1.38197i	0.301570i
$22$	0.854102	0.182095
$23$	−1.23607	−0.257738	−0.128869	−	0.991662i	$-0.541135\pi$
$23$	−1.23607	−0.257738	−0.128869	+	0.991662i	$0.541135\pi$
$24$	1.38197	0.282093
$25$	9.85410	1.97082
$26$	0.145898i	0.0286130i
$27$	− 3.47214i	− 0.668213i
$28$	−3.61803	−0.683744
$29$	0	0
$29$	0	0
$30$	−1.47214	−0.268774
$31$	− 10.0902i	− 1.81225i	−0.423012	−	0.906124i	$-0.639027\pi$
$31$	− 10.0902i	− 1.81225i	0.423012	−	0.906124i	$-0.360973\pi$
$32$	5.61803i	0.993137i
$33$	−0.854102	−0.148680
$34$	2.70820	0.464453
$35$	8.61803	1.45671
$36$	4.23607	0.706011
$37$	− 4.70820i	− 0.774024i	−0.922075	−	0.387012i	$-0.873507\pi$
$37$	− 4.70820i	− 0.774024i	0.922075	−	0.387012i	$-0.126493\pi$
$38$	3.00000	0.486664
$39$	− 0.145898i	− 0.0233624i
$40$	− 8.61803i	− 1.36263i
$41$	− 3.85410i	− 0.601910i	−0.953638	−	0.300955i	$-0.902695\pi$
$41$	− 3.85410i	− 0.601910i	0.953638	−	0.300955i	$-0.0973053\pi$
$42$	−0.854102	−0.131791
$43$	− 7.23607i	− 1.10349i	−0.834013	−	0.551745i	$-0.813962\pi$
$43$	− 7.23607i	− 1.10349i	0.834013	−	0.551745i	$-0.186038\pi$
$44$	− 2.23607i	− 0.337100i
$45$	−10.0902	−1.50415
$46$	− 0.763932i	− 0.112636i
$47$	7.00000i	1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$	7.00000i	1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	− 1.14590i	− 0.165396i
$49$	−2.00000	−0.285714
$50$	6.09017i	0.861280i
$51$	−2.70820	−0.379224
$52$	0.381966	0.0529692
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	2.14590	0.292020
$55$	5.32624i	0.718190i
$56$	− 5.00000i	− 0.668153i
$57$	−3.00000	−0.397360
$58$	0	0
$59$	6.09017	0.792873	0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017	0.792873	0.396436	+	0.918062i	$0.370247\pi$
$60$	3.85410i	0.497562i
$61$	− 0.618034i	− 0.0791311i	−0.999217	−	0.0395656i	$-0.987403\pi$
$61$	− 0.618034i	− 0.0791311i	0.999217	−	0.0395656i	$-0.0125974\pi$
$62$	6.23607	0.791981
$63$	−5.85410	−0.737548
$64$	0.236068	0.0295085
$65$	−0.909830	−0.112851
$66$	− 0.527864i	− 0.0649756i
$67$	1.52786	0.186658	0.0933292	−	0.995635i	$-0.470249\pi$
$67$	1.52786	0.186658	0.0933292	+	0.995635i	$0.470249\pi$
$68$	− 7.09017i	− 0.859809i
$69$	0.763932i	0.0919666i
$70$	5.32624i	0.636607i
$71$	−10.4721	−1.24281	−0.621407	−	0.783488i	$-0.713439\pi$
$71$	−10.4721	−1.24281	−0.621407	+	0.783488i	$0.713439\pi$
$72$	5.85410i	0.689913i
$73$	13.7082i	1.60442i	0.597039	+	0.802212i	$0.296344\pi$
$73$	13.7082i	1.60442i	−0.597039	+	0.802212i	$0.703656\pi$
$74$	2.90983	0.338261
$75$	− 6.09017i	− 0.703232i
$76$	− 7.85410i	− 0.900927i
$77$	3.09017i	0.352158i
$78$	0.0901699	0.0102097
$79$	− 6.09017i	− 0.685198i	−0.939482	−	0.342599i	$-0.888693\pi$
$79$	− 6.09017i	− 0.685198i	0.939482	−	0.342599i	$-0.111307\pi$
$80$	−7.14590	−0.798936
$81$	5.70820	0.634245
$82$	2.38197	0.263044
$83$	−9.94427	−1.09153	−0.545763	−	0.837940i	$-0.683760\pi$
$83$	−9.94427	−1.09153	−0.545763	+	0.837940i	$0.683760\pi$
$84$	2.23607i	0.243975i
$85$	16.8885i	1.83182i
$86$	4.47214	0.482243
$87$	0	0
$88$	3.09017	0.329413
$89$	4.70820i	0.499069i	0.968366	+	0.249534i	$0.0802775\pi$
$89$	4.70820i	0.499069i	−0.968366	+	0.249534i	$0.919722\pi$
$90$	− 6.23607i	− 0.657339i
$91$	−0.527864	−0.0553352
$92$	−2.00000	−0.208514
$93$	−6.23607	−0.646650
$94$	−4.32624	−0.446217
$95$	18.7082i	1.91942i
$96$	3.47214	0.354373
$97$	− 3.56231i	− 0.361697i	−0.983511	−	0.180849i	$-0.942116\pi$
$97$	− 3.56231i	− 0.361697i	0.983511	−	0.180849i	$-0.0578844\pi$
$98$	− 1.23607i	− 0.124862i
$99$	− 3.61803i	− 0.363626i
$100$	15.9443	1.59443
$101$	− 0.618034i	− 0.0614967i	−0.999527	−	0.0307483i	$-0.990211\pi$
$101$	− 0.618034i	− 0.0614967i	0.999527	−	0.0307483i	$-0.00978904\pi$
$102$	− 1.67376i	− 0.165727i
$103$	9.18034	0.904566	0.452283	−	0.891875i	$-0.350610\pi$
$103$	9.18034	0.904566	0.452283	+	0.891875i	$0.350610\pi$
$104$	0.527864i	0.0517613i
$105$	− 5.32624i	− 0.519788i
$106$	− 1.23607i	− 0.120058i
$107$	6.76393	0.653894	0.326947	−	0.945043i	$-0.393980\pi$
$107$	6.76393	0.653894	0.326947	+	0.945043i	$0.393980\pi$
$108$	− 5.61803i	− 0.540596i
$109$	14.3820	1.37754	0.688771	−	0.724979i	$-0.258150\pi$
$109$	14.3820	1.37754	0.688771	+	0.724979i	$0.258150\pi$
$110$	−3.29180	−0.313860
$111$	−2.90983	−0.276189
$112$	−4.14590	−0.391751
$113$	− 7.94427i	− 0.747334i	−0.927563	−	0.373667i	$-0.878100\pi$
$113$	− 7.94427i	− 0.747334i	0.927563	−	0.373667i	$-0.121900\pi$
$114$	− 1.85410i	− 0.173653i
$115$	4.76393	0.444239
$116$	0	0
$117$	0.618034	0.0571373
$118$	3.76393i	0.346498i
$119$	9.79837i	0.898215i
$120$	−5.32624	−0.486217
$121$	9.09017	0.826379
$122$	0.381966	0.0345816
$123$	−2.38197	−0.214775
$124$	− 16.3262i	− 1.46614i
$125$	−18.7082	−1.67331
$126$	− 3.61803i	− 0.322320i
$127$	15.9443i	1.41483i	0.706801	+	0.707413i	$0.250138\pi$
$127$	15.9443i	1.41483i	−0.706801	+	0.707413i	$0.749862\pi$
$128$	11.3820i	1.00603i
$129$	−4.47214	−0.393750
$130$	− 0.562306i	− 0.0493175i
$131$	− 14.3262i	− 1.25169i	−0.779948	−	0.625845i	$-0.784754\pi$
$131$	− 14.3262i	− 1.25169i	0.779948	−	0.625845i	$-0.215246\pi$
$132$	−1.38197	−0.120285
$133$	10.8541i	0.941170i
$134$	0.944272i	0.0815727i
$135$	13.3820i	1.15174i
$136$	9.79837	0.840204
$137$	7.14590i	0.610515i	0.952270	+	0.305258i	$0.0987426\pi$
$137$	7.14590i	0.610515i	−0.952270	+	0.305258i	$0.901257\pi$
$138$	−0.472136	−0.0401909
$139$	1.29180	0.109569	0.0547844	−	0.998498i	$-0.482553\pi$
$139$	1.29180	0.109569	0.0547844	+	0.998498i	$0.482553\pi$
$140$	13.9443	1.17851
$141$	4.32624	0.364335
$142$	− 6.47214i	− 0.543130i
$143$	− 0.326238i	− 0.0272814i
$144$	4.85410	0.404508
$145$	0	0
$146$	−8.47214	−0.701159
$147$	1.23607i	0.101949i
$148$	− 7.61803i	− 0.626199i
$149$	−9.61803	−0.787940	−0.393970	−	0.919123i	$-0.628899\pi$
$149$	−9.61803	−0.787940	−0.393970	+	0.919123i	$0.628899\pi$
$150$	3.76393	0.307324
$151$	−2.67376	−0.217588	−0.108794	−	0.994064i	$-0.534699\pi$
$151$	−2.67376	−0.217588	−0.108794	+	0.994064i	$0.534699\pi$
$152$	10.8541	0.880384
$153$	− 11.4721i	− 0.927467i
$154$	−1.90983	−0.153898
$155$	38.8885i	3.12360i
$156$	− 0.236068i	− 0.0189006i
$157$	− 14.5623i	− 1.16220i	−0.813833	−	0.581099i	$-0.802623\pi$
$157$	− 14.5623i	− 1.16220i	0.813833	−	0.581099i	$-0.197377\pi$
$158$	3.76393	0.299442
$159$	1.23607i	0.0980266i
$160$	− 21.6525i	− 1.71178i
$161$	2.76393	0.217828
$162$	3.52786i	0.277175i
$163$	6.03444i	0.472654i	0.971674	+	0.236327i	$0.0759436\pi$
$163$	6.03444i	0.472654i	−0.971674	+	0.236327i	$0.924056\pi$
$164$	− 6.23607i	− 0.486955i
$165$	3.29180	0.256266
$166$	− 6.14590i	− 0.477014i
$167$	−10.5279	−0.814671	−0.407335	−	0.913279i	$-0.633542\pi$
$167$	−10.5279	−0.814671	−0.407335	+	0.913279i	$0.633542\pi$
$168$	−3.09017	−0.238412
$169$	−12.9443	−0.995713
$170$	−10.4377	−0.800535
$171$	− 12.7082i	− 0.971821i
$172$	− 11.7082i	− 0.892742i
$173$	−4.09017	−0.310970	−0.155485	−	0.987838i	$-0.549694\pi$
$173$	−4.09017	−0.310970	−0.155485	+	0.987838i	$0.549694\pi$
$174$	0	0
$175$	−22.0344	−1.66565
$176$	− 2.56231i	− 0.193141i
$177$	− 3.76393i	− 0.282914i
$178$	−2.90983	−0.218101
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	−16.3262	−1.21689
$181$	5.94427	0.441834	0.220917	−	0.975293i	$-0.429095\pi$
$181$	5.94427	0.441834	0.220917	+	0.975293i	$0.429095\pi$
$182$	− 0.326238i	− 0.0241824i
$183$	−0.381966	−0.0282357
$184$	− 2.76393i	− 0.203760i
$185$	18.1459i	1.33411i
$186$	− 3.85410i	− 0.282596i
$187$	−6.05573	−0.442839
$188$	11.3262i	0.826051i
$189$	7.76393i	0.564743i
$190$	−11.5623	−0.838818
$191$	17.0344i	1.23257i	0.787524	+	0.616284i	$0.211363\pi$
$191$	17.0344i	1.23257i	−0.787524	+	0.616284i	$0.788637\pi$
$192$	− 0.145898i	− 0.0105293i
$193$	12.4721i	0.897764i	0.893591	+	0.448882i	$0.148178\pi$
$193$	12.4721i	0.897764i	−0.893591	+	0.448882i	$0.851822\pi$
$194$	2.20163	0.158068
$195$	0.562306i	0.0402676i
$196$	−3.23607	−0.231148
$197$	−6.29180	−0.448272	−0.224136	−	0.974558i	$-0.571956\pi$
$197$	−6.29180	−0.448272	−0.224136	+	0.974558i	$0.571956\pi$
$198$	2.23607	0.158910
$199$	−5.85410	−0.414986	−0.207493	−	0.978236i	$-0.566530\pi$
$199$	−5.85410	−0.414986	−0.207493	+	0.978236i	$0.566530\pi$
$200$	22.0344i	1.55807i
$201$	− 0.944272i	− 0.0666038i
$202$	0.381966	0.0268750
$203$	0	0
$204$	−4.38197	−0.306799
$205$	14.8541i	1.03746i
$206$	5.67376i	0.395310i
$207$	−3.23607	−0.224922
$208$	0.437694	0.0303486
$209$	−6.70820	−0.464016
$210$	3.29180	0.227156
$211$	11.6525i	0.802190i	0.916037	+	0.401095i	$0.131370\pi$
$211$	11.6525i	0.802190i	−0.916037	+	0.401095i	$0.868630\pi$
$212$	−3.23607	−0.222254
$213$	6.47214i	0.443463i
$214$	4.18034i	0.285762i
$215$	27.8885i	1.90198i
$216$	7.76393	0.528269
$217$	22.5623i	1.53163i
$218$	8.88854i	0.602008i
$219$	8.47214	0.572494
$220$	8.61803i	0.581028i
$221$	− 1.03444i	− 0.0695841i
$222$	− 1.79837i	− 0.120699i
$223$	2.67376	0.179048	0.0895242	−	0.995985i	$-0.471465\pi$
$223$	2.67376	0.179048	0.0895242	+	0.995985i	$0.471465\pi$
$224$	− 12.5623i	− 0.839354i
$225$	25.7984	1.71989
$226$	4.90983	0.326597
$227$	−20.8885	−1.38642	−0.693211	−	0.720735i	$-0.743804\pi$
$227$	−20.8885	−1.38642	−0.693211	+	0.720735i	$0.743804\pi$
$228$	−4.85410	−0.321471
$229$	− 2.29180i	− 0.151446i	−0.997129	−	0.0757231i	$-0.975874\pi$
$229$	− 2.29180i	− 0.151446i	0.997129	−	0.0757231i	$-0.0241265\pi$
$230$	2.94427i	0.194140i
$231$	1.90983	0.125658
$232$	0	0
$233$	15.2361	0.998148	0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361	0.998148	0.499074	+	0.866559i	$0.333674\pi$
$234$	0.381966i	0.0249699i
$235$	− 26.9787i	− 1.75990i
$236$	9.85410	0.641447
$237$	−3.76393	−0.244494
$238$	−6.05573	−0.392535
$239$	−27.7426	−1.79452	−0.897261	−	0.441500i	$-0.854447\pi$
$239$	−27.7426	−1.79452	−0.897261	+	0.441500i	$0.854447\pi$
$240$	4.41641i	0.285078i
$241$	4.65248	0.299692	0.149846	−	0.988709i	$-0.452122\pi$
$241$	4.65248	0.299692	0.149846	+	0.988709i	$0.452122\pi$
$242$	5.61803i	0.361141i
$243$	− 13.9443i	− 0.894525i
$244$	− 1.00000i	− 0.0640184i
$245$	7.70820	0.492459
$246$	− 1.47214i	− 0.0938600i
$247$	− 1.14590i	− 0.0729117i
$248$	22.5623	1.43271
$249$	6.14590i	0.389480i
$250$	− 11.5623i	− 0.731264i
$251$	− 19.6525i	− 1.24045i	−0.784423	−	0.620227i	$-0.787041\pi$
$251$	− 19.6525i	− 1.24045i	0.784423	−	0.620227i	$-0.212959\pi$
$252$	−9.47214	−0.596688
$253$	1.70820i	0.107394i
$254$	−9.85410	−0.618301
$255$	10.4377	0.653634
$256$	−6.56231	−0.410144
$257$	−23.1803	−1.44595	−0.722975	−	0.690874i	$-0.757226\pi$
$257$	−23.1803	−1.44595	−0.722975	+	0.690874i	$0.757226\pi$
$258$	− 2.76393i	− 0.172075i
$259$	10.5279i	0.654170i
$260$	−1.47214	−0.0912980
$261$	0	0
$262$	8.85410	0.547008
$263$	− 16.7082i	− 1.03027i	−0.857108	−	0.515136i	$-0.827741\pi$
$263$	− 16.7082i	− 1.03027i	0.857108	−	0.515136i	$-0.172259\pi$
$264$	− 1.90983i	− 0.117542i
$265$	7.70820	0.473511
$266$	−6.70820	−0.411306
$267$	2.90983	0.178079
$268$	2.47214	0.151010
$269$	6.00000i	0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$	6.00000i	0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$	−8.27051	−0.503327
$271$	− 10.1803i	− 0.618412i	−0.950995	−	0.309206i	$-0.899937\pi$
$271$	− 10.1803i	− 0.618412i	0.950995	−	0.309206i	$-0.100063\pi$
$272$	− 8.12461i	− 0.492627i
$273$	0.326238i	0.0197448i
$274$	−4.41641	−0.266805
$275$	− 13.6180i	− 0.821198i
$276$	1.23607i	0.0744025i
$277$	−21.3820	−1.28472	−0.642359	−	0.766404i	$-0.722044\pi$
$277$	−21.3820	−1.28472	−0.642359	+	0.766404i	$0.722044\pi$
$278$	0.798374i	0.0478833i
$279$	− 26.4164i	− 1.58151i
$280$	19.2705i	1.15163i
$281$	23.1246	1.37950	0.689749	−	0.724048i	$-0.257721\pi$
$281$	23.1246	1.37950	0.689749	+	0.724048i	$0.257721\pi$
$282$	2.67376i	0.159220i
$283$	5.23607	0.311252	0.155626	−	0.987816i	$-0.450261\pi$
$283$	5.23607	0.311252	0.155626	+	0.987816i	$0.450261\pi$
$284$	−16.9443	−1.00546
$285$	11.5623	0.684892
$286$	0.201626	0.0119224
$287$	8.61803i	0.508706i
$288$	14.7082i	0.866689i
$289$	−2.20163	−0.129507
$290$	0	0
$291$	−2.20163	−0.129062
$292$	22.1803i	1.29801i
$293$	8.52786i	0.498203i	0.968477	+	0.249102i	$0.0801353\pi$
$293$	8.52786i	0.498203i	−0.968477	+	0.249102i	$0.919865\pi$
$294$	−0.763932	−0.0445534
$295$	−23.4721	−1.36660
$296$	10.5279	0.611920
$297$	−4.79837	−0.278430
$298$	− 5.94427i	− 0.344342i
$299$	−0.291796	−0.0168750
$300$	− 9.85410i	− 0.568927i
$301$	16.1803i	0.932619i
$302$	− 1.65248i	− 0.0950893i
$303$	−0.381966	−0.0219434
$304$	− 9.00000i	− 0.516185i
$305$	2.38197i	0.136391i
$306$	7.09017	0.405318
$307$	− 19.1803i	− 1.09468i	−0.836910	−	0.547340i	$-0.815640\pi$
$307$	− 19.1803i	− 1.09468i	0.836910	−	0.547340i	$-0.184360\pi$
$308$	5.00000i	0.284901i
$309$	− 5.67376i	− 0.322769i
$310$	−24.0344	−1.36506
$311$	2.09017i	0.118523i	0.998243	+	0.0592613i	$0.0188745\pi$
$311$	2.09017i	0.118523i	−0.998243	+	0.0592613i	$0.981125\pi$
$312$	0.326238	0.0184696
$313$	−12.9098	−0.729707	−0.364853	−	0.931065i	$-0.618881\pi$
$313$	−12.9098	−0.729707	−0.364853	+	0.931065i	$0.618881\pi$
$314$	9.00000	0.507899
$315$	22.5623	1.27124
$316$	− 9.85410i	− 0.554337i
$317$	− 27.7082i	− 1.55625i	−0.628111	−	0.778124i	$-0.716172\pi$
$317$	− 27.7082i	− 1.55625i	0.628111	−	0.778124i	$-0.283828\pi$
$318$	−0.763932	−0.0428392
$319$	0	0
$320$	−0.909830	−0.0508610
$321$	− 4.18034i	− 0.233324i
$322$	1.70820i	0.0951945i
$323$	−21.2705	−1.18352
$324$	9.23607	0.513115
$325$	2.32624	0.129036
$326$	−3.72949	−0.206557
$327$	− 8.88854i	− 0.491538i
$328$	8.61803	0.475851
$329$	− 15.6525i	− 0.862949i
$330$	2.03444i	0.111992i
$331$	− 21.1803i	− 1.16418i	−0.813126	−	0.582088i	$-0.802236\pi$
$331$	− 21.1803i	− 1.16418i	0.813126	−	0.582088i	$-0.197764\pi$
$332$	−16.0902	−0.883063
$333$	− 12.3262i	− 0.675474i
$334$	− 6.50658i	− 0.356024i
$335$	−5.88854	−0.321726
$336$	2.56231i	0.139785i
$337$	34.0689i	1.85585i	0.372767	+	0.927925i	$0.378409\pi$
$337$	34.0689i	1.85585i	−0.372767	+	0.927925i	$0.621591\pi$
$338$	− 8.00000i	− 0.435143i
$339$	−4.90983	−0.266665
$340$	27.3262i	1.48197i
$341$	−13.9443	−0.755125
$342$	7.85410	0.424701
$343$	20.1246	1.08663
$344$	16.1803	0.872385
$345$	− 2.94427i	− 0.158514i
$346$	− 2.52786i	− 0.135899i
$347$	32.1246	1.72454	0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246	1.72454	0.862270	+	0.506449i	$0.169042\pi$
$348$	0	0
$349$	4.52786	0.242371	0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786	0.242371	0.121186	+	0.992630i	$0.461330\pi$
$350$	− 13.6180i	− 0.727915i
$351$	− 0.819660i	− 0.0437502i
$352$	7.76393	0.413819
$353$	19.1246	1.01790	0.508950	−	0.860796i	$-0.330034\pi$
$353$	19.1246	1.01790	0.508950	+	0.860796i	$0.330034\pi$
$354$	2.32624	0.123638
$355$	40.3607	2.14212
$356$	7.61803i	0.403755i
$357$	6.05573	0.320503
$358$	9.88854i	0.522626i
$359$	− 23.7639i	− 1.25421i	−0.778934	−	0.627106i	$-0.784239\pi$
$359$	− 23.7639i	− 1.25421i	0.778934	−	0.627106i	$-0.215761\pi$
$360$	− 22.5623i	− 1.18914i
$361$	−4.56231	−0.240121
$362$	3.67376i	0.193089i
$363$	− 5.61803i	− 0.294870i
$364$	−0.854102	−0.0447671
$365$	− 52.8328i	− 2.76540i
$366$	− 0.236068i	− 0.0123395i
$367$	27.2705i	1.42351i	0.702428	+	0.711755i	$0.252099\pi$
$367$	27.2705i	1.42351i	−0.702428	+	0.711755i	$0.747901\pi$
$368$	−2.29180	−0.119468
$369$	− 10.0902i	− 0.525273i
$370$	−11.2148	−0.583029
$371$	4.47214	0.232182
$372$	−10.0902	−0.523151
$373$	20.6180	1.06756	0.533781	−	0.845623i	$-0.320771\pi$
$373$	20.6180	1.06756	0.533781	+	0.845623i	$0.320771\pi$
$374$	− 3.74265i	− 0.193528i
$375$	11.5623i	0.597075i
$376$	−15.6525	−0.807215
$377$	0	0
$378$	−4.79837	−0.246802
$379$	− 24.2918i	− 1.24779i	−0.781510	−	0.623893i	$-0.785550\pi$
$379$	− 24.2918i	− 1.24779i	0.781510	−	0.623893i	$-0.214450\pi$
$380$	30.2705i	1.55284i
$381$	9.85410	0.504841
$382$	−10.5279	−0.538652
$383$	28.8541	1.47438	0.737188	−	0.675688i	$-0.236153\pi$
$383$	28.8541	1.47438	0.737188	+	0.675688i	$0.236153\pi$
$384$	7.03444	0.358975
$385$	− 11.9098i	− 0.606981i
$386$	−7.70820	−0.392337
$387$	− 18.9443i	− 0.962991i
$388$	− 5.76393i	− 0.292619i
$389$	19.1246i	0.969656i	0.874609	+	0.484828i	$0.161118\pi$
$389$	19.1246i	0.969656i	−0.874609	+	0.484828i	$0.838882\pi$
$390$	−0.347524	−0.0175976
$391$	5.41641i	0.273920i
$392$	− 4.47214i	− 0.225877i
$393$	−8.85410	−0.446630
$394$	− 3.88854i	− 0.195902i
$395$	23.4721i	1.18101i
$396$	− 5.85410i	− 0.294180i
$397$	−14.0557	−0.705437	−0.352718	−	0.935730i	$-0.614743\pi$
$397$	−14.0557	−0.705437	−0.352718	+	0.935730i	$0.614743\pi$
$398$	− 3.61803i	− 0.181356i
$399$	6.70820	0.335830
$400$	18.2705	0.913525
$401$	25.0689	1.25188	0.625940	−	0.779871i	$-0.284715\pi$
$401$	25.0689	1.25188	0.625940	+	0.779871i	$0.284715\pi$
$402$	0.583592	0.0291069
$403$	− 2.38197i	− 0.118654i
$404$	− 1.00000i	− 0.0497519i
$405$	−22.0000	−1.09319
$406$	0	0
$407$	−6.50658	−0.322519
$408$	− 6.05573i	− 0.299803i
$409$	27.4164i	1.35565i	0.735221	+	0.677827i	$0.237078\pi$
$409$	27.4164i	1.35565i	−0.735221	+	0.677827i	$0.762922\pi$
$410$	−9.18034	−0.453385
$411$	4.41641	0.217845
$412$	14.8541	0.731809
$413$	−13.6180	−0.670100
$414$	− 2.00000i	− 0.0982946i
$415$	38.3262	1.88136
$416$	1.32624i	0.0650242i
$417$	− 0.798374i	− 0.0390965i
$418$	− 4.14590i	− 0.202783i
$419$	17.5623	0.857975	0.428987	−	0.903310i	$-0.358870\pi$
$419$	17.5623	0.857975	0.428987	+	0.903310i	$0.358870\pi$
$420$	− 8.61803i	− 0.420517i
$421$	31.0344i	1.51253i	0.654268	+	0.756263i	$0.272977\pi$
$421$	31.0344i	1.51253i	−0.654268	+	0.756263i	$0.727023\pi$
$422$	−7.20163	−0.350570
$423$	18.3262i	0.891052i
$424$	− 4.47214i	− 0.217186i
$425$	− 43.1803i	− 2.09455i
$426$	−4.00000	−0.193801
$427$	1.38197i	0.0668780i
$428$	10.9443	0.529011
$429$	−0.201626	−0.00973460
$430$	−17.2361	−0.831197
$431$	14.5967	0.703101	0.351550	−	0.936169i	$-0.385655\pi$
$431$	14.5967	0.703101	0.351550	+	0.936169i	$0.385655\pi$
$432$	− 6.43769i	− 0.309734i
$433$	− 10.3820i	− 0.498925i	−0.968384	−	0.249463i	$-0.919746\pi$
$433$	− 10.3820i	− 0.498925i	0.968384	−	0.249463i	$-0.0802540\pi$
$434$	−13.9443	−0.669346
$435$	0	0
$436$	23.2705	1.11446
$437$	6.00000i	0.287019i
$438$	5.23607i	0.250189i
$439$	20.9443	0.999616	0.499808	−	0.866136i	$-0.333404\pi$
$439$	20.9443	0.999616	0.499808	+	0.866136i	$0.333404\pi$
$440$	−11.9098	−0.567779
$441$	−5.23607	−0.249337
$442$	0.639320	0.0304094
$443$	1.90983i	0.0907388i	0.998970	+	0.0453694i	$0.0144465\pi$
$443$	1.90983i	0.0907388i	−0.998970	+	0.0453694i	$0.985554\pi$
$444$	−4.70820	−0.223441
$445$	− 18.1459i	− 0.860198i
$446$	1.65248i	0.0782470i
$447$	5.94427i	0.281154i
$448$	−0.527864	−0.0249392
$449$	− 26.1246i	− 1.23290i	−0.787395	−	0.616448i	$-0.788571\pi$
$449$	− 26.1246i	− 1.23290i	0.787395	−	0.616448i	$-0.211429\pi$
$450$	15.9443i	0.751620i
$451$	−5.32624	−0.250803
$452$	− 12.8541i	− 0.604606i
$453$	1.65248i	0.0776401i
$454$	− 12.9098i	− 0.605888i
$455$	2.03444	0.0953761
$456$	− 6.70820i	− 0.314140i
$457$	−18.7082	−0.875133	−0.437566	−	0.899186i	$-0.644160\pi$
$457$	−18.7082	−0.875133	−0.437566	+	0.899186i	$0.644160\pi$
$458$	1.41641	0.0661844
$459$	−15.2148	−0.710165
$460$	7.70820	0.359397
$461$	38.9787i	1.81542i	0.419598	+	0.907710i	$0.362171\pi$
$461$	38.9787i	1.81542i	−0.419598	+	0.907710i	$0.637829\pi$
$462$	1.18034i	0.0549144i
$463$	−10.7082	−0.497652	−0.248826	−	0.968548i	$-0.580045\pi$
$463$	−10.7082	−0.497652	−0.248826	+	0.968548i	$0.580045\pi$
$464$	0	0
$465$	24.0344	1.11457
$466$	9.41641i	0.436207i
$467$	− 17.9443i	− 0.830362i	−0.909739	−	0.415181i	$-0.863718\pi$
$467$	− 17.9443i	− 0.830362i	0.909739	−	0.415181i	$-0.136282\pi$
$468$	1.00000	0.0462250
$469$	−3.41641	−0.157755
$470$	16.6738	0.769103
$471$	−9.00000	−0.414698
$472$	13.6180i	0.626821i
$473$	−10.0000	−0.459800
$474$	− 2.32624i	− 0.106848i
$475$	− 47.8328i	− 2.19472i
$476$	15.8541i	0.726672i
$477$	−5.23607	−0.239743
$478$	− 17.1459i	− 0.784235i
$479$	11.1803i	0.510843i	0.966830	+	0.255421i	$0.0822142\pi$
$479$	11.1803i	0.510843i	−0.966830	+	0.255421i	$0.917786\pi$
$480$	−13.3820	−0.610800
$481$	− 1.11146i	− 0.0506780i
$482$	2.87539i	0.130970i
$483$	− 1.70820i	− 0.0777260i
$484$	14.7082	0.668555
$485$	13.7295i	0.623424i
$486$	8.61803	0.390922
$487$	42.5623	1.92868	0.964341	−	0.264663i	$-0.0852606\pi$
$487$	42.5623	1.92868	0.964341	+	0.264663i	$0.0852606\pi$
$488$	1.38197	0.0625587
$489$	3.72949	0.168653
$490$	4.76393i	0.215213i
$491$	15.1246i	0.682564i	0.939961	+	0.341282i	$0.110861\pi$
$491$	15.1246i	0.682564i	−0.939961	+	0.341282i	$0.889139\pi$
$492$	−3.85410	−0.173756
$493$	0	0
$494$	0.708204	0.0318636
$495$	13.9443i	0.626748i
$496$	− 18.7082i	− 0.840023i
$497$	23.4164	1.05037
$498$	−3.79837	−0.170209
$499$	−24.6869	−1.10514	−0.552569	−	0.833467i	$-0.686352\pi$
$499$	−24.6869	−1.10514	−0.552569	+	0.833467i	$0.686352\pi$
$500$	−30.2705	−1.35374
$501$	6.50658i	0.290692i
$502$	12.1459	0.542098
$503$	− 14.2705i	− 0.636291i	−0.948042	−	0.318145i	$-0.896940\pi$
$503$	− 14.2705i	− 0.636291i	0.948042	−	0.318145i	$-0.103060\pi$
$504$	− 13.0902i	− 0.583083i
$505$	2.38197i	0.105996i
$506$	−1.05573	−0.0469328
$507$	8.00000i	0.355292i
$508$	25.7984i	1.14462i
$509$	31.5623	1.39897	0.699487	−	0.714645i	$-0.253412\pi$
$509$	31.5623	1.39897	0.699487	+	0.714645i	$0.253412\pi$
$510$	6.45085i	0.285648i
$511$	− 30.6525i	− 1.35599i
$512$	18.7082i	0.826794i
$513$	−16.8541	−0.744127
$514$	− 14.3262i	− 0.631903i
$515$	−35.3820	−1.55912
$516$	−7.23607	−0.318550
$517$	9.67376	0.425452
$518$	−6.50658	−0.285883
$519$	2.52786i	0.110961i
$520$	− 2.03444i	− 0.0892162i
$521$	−4.09017	−0.179194	−0.0895968	−	0.995978i	$-0.528558\pi$
$521$	−4.09017	−0.179194	−0.0895968	+	0.995978i	$0.528558\pi$
$522$	0	0
$523$	−20.3820	−0.891241	−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820	−0.891241	−0.445621	+	0.895222i	$0.647017\pi$
$524$	− 23.1803i	− 1.01264i
$525$	13.6180i	0.594340i
$526$	10.3262	0.450245
$527$	−44.2148	−1.92603
$528$	−1.58359	−0.0689170
$529$	−21.4721	−0.933571
$530$	4.76393i	0.206932i
$531$	15.9443	0.691922
$532$	17.5623i	0.761423i
$533$	− 0.909830i	− 0.0394091i
$534$	1.79837i	0.0778232i
$535$	−26.0689	−1.12706
$536$	3.41641i	0.147566i
$537$	− 9.88854i	− 0.426722i
$538$	−3.70820	−0.159872
$539$	2.76393i	0.119051i
$540$	21.6525i	0.931774i
$541$	− 14.5967i	− 0.627563i	−0.949495	−	0.313782i	$-0.898404\pi$
$541$	− 14.5967i	− 0.627563i	0.949495	−	0.313782i	$-0.101596\pi$
$542$	6.29180	0.270256
$543$	− 3.67376i	− 0.157656i
$544$	24.6180	1.05549
$545$	−55.4296	−2.37434
$546$	−0.201626	−0.00862880
$547$	7.38197	0.315630	0.157815	−	0.987469i	$-0.449555\pi$
$547$	7.38197	0.315630	0.157815	+	0.987469i	$0.449555\pi$
$548$	11.5623i	0.493917i
$549$	− 1.61803i	− 0.0690560i
$550$	8.41641	0.358877
$551$	0	0
$552$	−1.70820	−0.0727060
$553$	13.6180i	0.579098i
$554$	− 13.2148i	− 0.561442i
$555$	11.2148	0.476041
$556$	2.09017	0.0886430
$557$	5.50658	0.233321	0.116661	−	0.993172i	$-0.462781\pi$
$557$	5.50658	0.233321	0.116661	+	0.993172i	$0.462781\pi$
$558$	16.3262	0.691145
$559$	− 1.70820i	− 0.0722493i
$560$	15.9787	0.675224
$561$	3.74265i	0.158015i
$562$	14.2918i	0.602863i
$563$	− 28.3951i	− 1.19671i	−0.801230	−	0.598356i	$-0.795821\pi$
$563$	− 28.3951i	− 1.19671i	0.801230	−	0.598356i	$-0.204179\pi$
$564$	7.00000	0.294753
$565$	30.6180i	1.28811i
$566$	3.23607i	0.136022i
$567$	−12.7639	−0.536035
$568$	− 23.4164i	− 0.982531i
$569$	1.94427i	0.0815081i	0.999169	+	0.0407541i	$0.0129760\pi$
$569$	1.94427i	0.0815081i	−0.999169	+	0.0407541i	$0.987024\pi$
$570$	7.14590i	0.299309i
$571$	−34.5066	−1.44406	−0.722028	−	0.691864i	$-0.756790\pi$
$571$	−34.5066	−1.44406	−0.722028	+	0.691864i	$0.756790\pi$
$572$	− 0.527864i	− 0.0220711i
$573$	10.5279	0.439808
$574$	−5.32624	−0.222313
$575$	−12.1803	−0.507955
$576$	0.618034	0.0257514
$577$	2.76393i	0.115064i	0.998344	+	0.0575320i	$0.0183231\pi$
$577$	2.76393i	0.115064i	−0.998344	+	0.0575320i	$0.981677\pi$
$578$	− 1.36068i	− 0.0565968i
$579$	7.70820	0.320342
$580$	0	0
$581$	22.2361	0.922508
$582$	− 1.36068i	− 0.0564020i
$583$	2.76393i	0.114470i
$584$	−30.6525	−1.26841
$585$	−2.38197	−0.0984822
$586$	−5.27051	−0.217723
$587$	46.6180	1.92413	0.962066	−	0.272816i	$-0.0879552\pi$
$587$	46.6180	1.92413	0.962066	+	0.272816i	$0.0879552\pi$
$588$	2.00000i	0.0824786i
$589$	−48.9787	−2.01813
$590$	− 14.5066i	− 0.597226i
$591$	3.88854i	0.159953i
$592$	− 8.72949i	− 0.358780i
$593$	14.4377	0.592885	0.296443	−	0.955051i	$-0.404200\pi$
$593$	14.4377	0.592885	0.296443	+	0.955051i	$0.404200\pi$
$594$	− 2.96556i	− 0.121678i
$595$	− 37.7639i	− 1.54817i
$596$	−15.5623	−0.637457
$597$	3.61803i	0.148076i
$598$	− 0.180340i	− 0.00737465i
$599$	13.0689i	0.533980i	0.963699	+	0.266990i	$0.0860291\pi$
$599$	13.0689i	0.533980i	−0.963699	+	0.266990i	$0.913971\pi$
$600$	13.6180	0.555954
$601$	29.1591i	1.18942i	0.803939	+	0.594711i	$0.202734\pi$
$601$	29.1591i	1.18942i	−0.803939	+	0.594711i	$0.797266\pi$
$602$	−10.0000	−0.407570
$603$	4.00000	0.162893
$604$	−4.32624	−0.176032
$605$	−35.0344	−1.42435
$606$	− 0.236068i	− 0.00958961i
$607$	− 10.9787i	− 0.445612i	−0.974863	−	0.222806i	$-0.928478\pi$
$607$	− 10.9787i	− 0.445612i	0.974863	−	0.222806i	$-0.0715217\pi$
$608$	27.2705	1.10597
$609$	0	0
$610$	−1.47214	−0.0596050
$611$	1.65248i	0.0668520i
$612$	− 18.5623i	− 0.750337i
$613$	−27.5410	−1.11237	−0.556186	−	0.831058i	$-0.687736\pi$
$613$	−27.5410	−1.11237	−0.556186	+	0.831058i	$0.687736\pi$
$614$	11.8541	0.478393
$615$	9.18034	0.370187
$616$	−6.90983	−0.278405
$617$	14.1803i	0.570879i	0.958397	+	0.285439i	$0.0921396\pi$
$617$	14.1803i	0.570879i	−0.958397	+	0.285439i	$0.907860\pi$
$618$	3.50658	0.141055
$619$	− 7.05573i	− 0.283594i	−0.989896	−	0.141797i	$-0.954712\pi$
$619$	− 7.05573i	− 0.283594i	0.989896	−	0.141797i	$-0.0452880\pi$
$620$	62.9230i	2.52705i
$621$	4.29180i	0.172224i
$622$	−1.29180	−0.0517963
$623$	− 10.5279i	− 0.421790i
$624$	− 0.270510i	− 0.0108291i
$625$	22.8328	0.913313
$626$	− 7.97871i	− 0.318894i
$627$	4.14590i	0.165571i
$628$	− 23.5623i	− 0.940238i
$629$	−20.6312	−0.822619
$630$	13.9443i	0.555553i
$631$	28.2148	1.12321	0.561606	−	0.827405i	$-0.310184\pi$
$631$	28.2148	1.12321	0.561606	+	0.827405i	$0.310184\pi$
$632$	13.6180	0.541696
$633$	7.20163	0.286239
$634$	17.1246	0.680105
$635$	− 61.4508i	− 2.43860i
$636$	2.00000i	0.0793052i
$637$	−0.472136	−0.0187067
$638$	0	0
$639$	−27.4164	−1.08458
$640$	− 43.8673i	− 1.73401i
$641$	11.0557i	0.436675i	0.975873	+	0.218338i	$0.0700634\pi$
$641$	11.0557i	0.436675i	−0.975873	+	0.218338i	$0.929937\pi$
$642$	2.58359	0.101966
$643$	37.4164	1.47556	0.737780	−	0.675042i	$-0.235874\pi$
$643$	37.4164	1.47556	0.737780	+	0.675042i	$0.235874\pi$
$644$	4.47214	0.176227
$645$	17.2361	0.678670
$646$	− 13.1459i	− 0.517218i
$647$	30.5279	1.20017	0.600087	−	0.799935i	$-0.295133\pi$
$647$	30.5279	1.20017	0.600087	+	0.799935i	$0.295133\pi$
$648$	12.7639i	0.501415i
$649$	− 8.41641i	− 0.330373i
$650$	1.43769i	0.0563910i
$651$	13.9443	0.546519
$652$	9.76393i	0.382385i
$653$	− 48.0132i	− 1.87890i	−0.342686	−	0.939450i	$-0.611337\pi$
$653$	− 48.0132i	− 1.87890i	0.342686	−	0.939450i	$-0.388663\pi$
$654$	5.49342	0.214810
$655$	55.2148i	2.15742i
$656$	− 7.14590i	− 0.279000i
$657$	35.8885i	1.40015i
$658$	9.67376	0.377123
$659$	− 7.05573i	− 0.274852i	−0.990512	−	0.137426i	$-0.956117\pi$
$659$	− 7.05573i	− 0.274852i	0.990512	−	0.137426i	$-0.0438830\pi$
$660$	5.32624	0.207324
$661$	−37.4508	−1.45667	−0.728335	−	0.685222i	$-0.759705\pi$
$661$	−37.4508	−1.45667	−0.728335	+	0.685222i	$0.759705\pi$
$662$	13.0902	0.508764
$663$	−0.639320	−0.0248291
$664$	− 22.2361i	− 0.862927i
$665$	− 41.8328i	− 1.62221i
$666$	7.61803	0.295193
$667$	0	0
$668$	−17.0344	−0.659082
$669$	− 1.65248i	− 0.0638884i
$670$	− 3.63932i	− 0.140599i
$671$	−0.854102	−0.0329722
$672$	−7.76393	−0.299500
$673$	6.47214	0.249483	0.124741	−	0.992189i	$-0.460190\pi$
$673$	6.47214	0.249483	0.124741	+	0.992189i	$0.460190\pi$
$674$	−21.0557	−0.811036
$675$	− 34.2148i	− 1.31693i
$676$	−20.9443	−0.805549
$677$	40.8328i	1.56933i	0.619918	+	0.784666i	$0.287166\pi$
$677$	40.8328i	1.56933i	−0.619918	+	0.784666i	$0.712834\pi$
$678$	− 3.03444i	− 0.116537i
$679$	7.96556i	0.305690i
$680$	−37.7639	−1.44818
$681$	12.9098i	0.494706i
$682$	− 8.61803i	− 0.330002i
$683$	20.8541	0.797960	0.398980	−	0.916960i	$-0.369364\pi$
$683$	20.8541	0.797960	0.398980	+	0.916960i	$0.369364\pi$
$684$	− 20.5623i	− 0.786219i
$685$	− 27.5410i	− 1.05229i
$686$	12.4377i	0.474873i
$687$	−1.41641	−0.0540393
$688$	− 13.4164i	− 0.511496i
$689$	−0.472136	−0.0179869
$690$	1.81966	0.0692733
$691$	11.8328	0.450142	0.225071	−	0.974342i	$-0.427739\pi$
$691$	11.8328	0.450142	0.225071	+	0.974342i	$0.427739\pi$
$692$	−6.61803	−0.251580
$693$	8.09017i	0.307320i
$694$	19.8541i	0.753651i
$695$	−4.97871	−0.188853
$696$	0	0
$697$	−16.8885	−0.639699
$698$	2.79837i	0.105920i
$699$	− 9.41641i	− 0.356161i
$700$	−35.6525	−1.34754
$701$	21.0557	0.795264	0.397632	−	0.917545i	$-0.369832\pi$
$701$	21.0557	0.795264	0.397632	+	0.917545i	$0.369832\pi$
$702$	0.506578	0.0191195
$703$	−22.8541	−0.861959
$704$	− 0.326238i	− 0.0122956i
$705$	−16.6738	−0.627970
$706$	11.8197i	0.444839i
$707$	1.38197i	0.0519742i
$708$	− 6.09017i	− 0.228883i
$709$	41.5066	1.55881	0.779406	−	0.626519i	$-0.215521\pi$
$709$	41.5066	1.55881	0.779406	+	0.626519i	$0.215521\pi$
$710$	24.9443i	0.936142i
$711$	− 15.9443i	− 0.597957i
$712$	−10.5279	−0.394548
$713$	12.4721i	0.467085i
$714$	3.74265i	0.140065i
$715$	1.25735i	0.0470224i
$716$	25.8885	0.967500
$717$	17.1459i	0.640325i
$718$	14.6869	0.548111
$719$	8.50658	0.317242	0.158621	−	0.987340i	$-0.449295\pi$
$719$	8.50658	0.317242	0.158621	+	0.987340i	$0.449295\pi$
$720$	−18.7082	−0.697214
$721$	−20.5279	−0.764498
$722$	− 2.81966i	− 0.104937i
$723$	− 2.87539i	− 0.106937i
$724$	9.61803	0.357451
$725$	0	0
$726$	3.47214	0.128863
$727$	28.0557i	1.04053i	0.854005	+	0.520265i	$0.174167\pi$
$727$	28.0557i	1.04053i	−0.854005	+	0.520265i	$0.825833\pi$
$728$	− 1.18034i	− 0.0437463i
$729$	8.50658	0.315058
$730$	32.6525	1.20852
$731$	−31.7082	−1.17277
$732$	−0.618034	−0.0228432
$733$	− 14.8197i	− 0.547377i	−0.961818	−	0.273688i	$-0.911756\pi$
$733$	− 14.8197i	− 0.547377i	0.961818	−	0.273688i	$-0.0882437\pi$
$734$	−16.8541	−0.622096
$735$	− 4.76393i	− 0.175720i
$736$	− 6.94427i	− 0.255969i
$737$	− 2.11146i	− 0.0777765i
$738$	6.23607	0.229553
$739$	− 50.0689i	− 1.84181i	−0.389783	−	0.920907i	$-0.627450\pi$
$739$	− 50.0689i	− 1.84181i	0.389783	−	0.920907i	$-0.372550\pi$
$740$	29.3607i	1.07932i
$741$	−0.708204	−0.0260165
$742$	2.76393i	0.101467i
$743$	− 35.2361i	− 1.29269i	−0.763047	−	0.646343i	$-0.776298\pi$
$743$	− 35.2361i	− 1.29269i	0.763047	−	0.646343i	$-0.223702\pi$
$744$	− 13.9443i	− 0.511222i
$745$	37.0689	1.35810
$746$	12.7426i	0.466541i
$747$	−26.0344	−0.952550
$748$	−9.79837	−0.358264
$749$	−15.1246	−0.552641
$750$	−7.14590	−0.260931
$751$	18.5279i	0.676091i	0.941130	+	0.338046i	$0.109766\pi$
$751$	18.5279i	0.676091i	−0.941130	+	0.338046i	$0.890234\pi$
$752$	12.9787i	0.473285i
$753$	−12.1459	−0.442621
$754$	0	0
$755$	10.3050	0.375036
$756$	12.5623i	0.456887i
$757$	− 0.0212862i	0 0.000773661i	−1.00000		0.000386831i	$-0.999877\pi$
$757$	− 0.0212862i	0 0.000773661i	1.00000		0.000386831i	$-0.000123132\pi$
$758$	15.0132	0.545302
$759$	1.05573	0.0383205
$760$	−41.8328	−1.51744
$761$	25.2016	0.913558	0.456779	−	0.889580i	$-0.349003\pi$
$761$	25.2016	0.913558	0.456779	+	0.889580i	$0.349003\pi$
$762$	6.09017i	0.220624i
$763$	−32.1591	−1.16424
$764$	27.5623i	0.997169i
$765$	44.2148i	1.59859i
$766$	17.8328i	0.644326i
$767$	1.43769	0.0519121
$768$	4.05573i	0.146348i
$769$	19.3607i	0.698164i	0.937092	+	0.349082i	$0.113507\pi$
$769$	19.3607i	0.698164i	−0.937092	+	0.349082i	$0.886493\pi$
$770$	7.36068	0.265260
$771$	14.3262i	0.515947i
$772$	20.1803i	0.726306i
$773$	− 14.0000i	− 0.503545i	−0.967786	−	0.251773i	$-0.918987\pi$
$773$	− 14.0000i	− 0.503545i	0.967786	−	0.251773i	$-0.0810135\pi$
$774$	11.7082	0.420843
$775$	− 99.4296i	− 3.57162i
$776$	7.96556	0.285947
$777$	6.50658	0.233422
$778$	−11.8197	−0.423755
$779$	−18.7082	−0.670291
$780$	0.909830i	0.0325771i
$781$	14.4721i	0.517854i
$782$	−3.34752	−0.119707
$783$	0	0
$784$	−3.70820	−0.132436
$785$	56.1246i	2.00317i
$786$	− 5.47214i	− 0.195185i
$787$	−19.3607	−0.690134	−0.345067	−	0.938578i	$-0.612144\pi$
$787$	−19.3607	−0.690134	−0.345067	+	0.938578i	$0.612144\pi$
$788$	−10.1803	−0.362660
$789$	−10.3262	−0.367624
$790$	−14.5066	−0.516121
$791$	17.7639i	0.631613i
$792$	8.09017	0.287472
$793$	− 0.145898i	− 0.00518099i
$794$	− 8.68692i	− 0.308287i
$795$	− 4.76393i	− 0.168959i
$796$	−9.47214	−0.335731
$797$	43.1803i	1.52953i	0.644312	+	0.764763i	$0.277144\pi$
$797$	43.1803i	1.52953i	−0.644312	+	0.764763i	$0.722856\pi$
$798$	4.14590i	0.146763i
$799$	30.6738	1.08516
$800$	55.3607i	1.95730i
$801$	12.3262i	0.435526i
$802$	15.4934i	0.547092i
$803$	18.9443	0.668529
$804$	− 1.52786i	− 0.0538836i
$805$	−10.6525	−0.375450
$806$	1.47214	0.0518538
$807$	3.70820	0.130535
$808$	1.38197	0.0486174
$809$	43.0689i	1.51422i	0.653287	+	0.757111i	$0.273390\pi$
$809$	43.0689i	1.51422i	−0.653287	+	0.757111i	$0.726610\pi$
$810$	− 13.5967i	− 0.477741i
$811$	−5.65248	−0.198485	−0.0992426	−	0.995063i	$-0.531642\pi$
$811$	−5.65248	−0.198485	−0.0992426	+	0.995063i	$0.531642\pi$
$812$	0	0
$813$	−6.29180	−0.220663
$814$	− 4.02129i	− 0.140946i
$815$	− 23.2574i	− 0.814670i
$816$	−5.02129	−0.175780
$817$	−35.1246	−1.22885
$818$	−16.9443	−0.592443
$819$	−1.38197	−0.0482898
$820$	24.0344i	0.839319i
$821$	−8.58359	−0.299569	−0.149785	−	0.988719i	$-0.547858\pi$
$821$	−8.58359	−0.299569	−0.149785	+	0.988719i	$0.547858\pi$
$822$	2.72949i	0.0952019i
$823$	− 5.47214i	− 0.190747i	−0.995442	−	0.0953733i	$-0.969596\pi$
$823$	− 5.47214i	− 0.190747i	0.995442	−	0.0953733i	$-0.0304045\pi$
$824$	20.5279i	0.715122i
$825$	−8.41641	−0.293022
$826$	− 8.41641i	− 0.292844i
$827$	− 26.9656i	− 0.937684i	−0.883282	−	0.468842i	$-0.844671\pi$
$827$	− 26.9656i	− 0.937684i	0.883282	−	0.468842i	$-0.155329\pi$
$828$	−5.23607	−0.181966
$829$	32.7984i	1.13913i	0.821945	+	0.569567i	$0.192889\pi$
$829$	32.7984i	1.13913i	−0.821945	+	0.569567i	$0.807111\pi$
$830$	23.6869i	0.822185i
$831$	13.2148i	0.458416i
$832$	0.0557281	0.00193202
$833$	8.76393i	0.303652i
$834$	0.493422	0.0170858
$835$	40.5755	1.40417
$836$	−10.8541	−0.375397
$837$	−35.0344	−1.21097
$838$	10.8541i	0.374949i
$839$	48.2148i	1.66456i	0.554356	+	0.832280i	$0.312965\pi$
$839$	48.2148i	1.66456i	−0.554356	+	0.832280i	$0.687035\pi$
$840$	11.9098	0.410928
$841$	0	0
$842$	−19.1803	−0.660998
$843$	− 14.2918i	− 0.492236i
$844$	18.8541i	0.648985i
$845$	49.8885	1.71622
$846$	−11.3262	−0.389404
$847$	−20.3262	−0.698418
$848$	−3.70820	−0.127340
$849$	− 3.23607i	− 0.111062i
$850$	26.6869	0.915354
$851$	5.81966i	0.199495i
$852$	10.4721i	0.358769i
$853$	45.0000i	1.54077i	0.637579	+	0.770385i	$0.279936\pi$
$853$	45.0000i	1.54077i	−0.637579	+	0.770385i	$0.720064\pi$
$854$	−0.854102	−0.0292268
$855$	48.9787i	1.67504i
$856$	15.1246i	0.516949i
$857$	−45.3262	−1.54831	−0.774157	−	0.632993i	$-0.781826\pi$
$857$	−45.3262	−1.54831	−0.774157	+	0.632993i	$0.781826\pi$
$858$	− 0.124612i	− 0.00425418i
$859$	− 32.7082i	− 1.11599i	−0.829844	−	0.557995i	$-0.811571\pi$
$859$	− 32.7082i	− 1.11599i	0.829844	−	0.557995i	$-0.188429\pi$
$860$	45.1246i	1.53874i
$861$	5.32624	0.181518
$862$	9.02129i	0.307266i
$863$	−17.7426	−0.603967	−0.301983	−	0.953313i	$-0.597649\pi$
$863$	−17.7426	−0.603967	−0.301983	+	0.953313i	$0.597649\pi$
$864$	19.5066	0.663627
$865$	15.7639	0.535990
$866$	6.41641	0.218038
$867$	1.36068i	0.0462111i
$868$	36.5066i	1.23911i
$869$	−8.41641	−0.285507
$870$	0	0
$871$	0.360680	0.0122212
$872$	32.1591i	1.08904i
$873$	− 9.32624i	− 0.315645i
$874$	−3.70820	−0.125432
$875$	41.8328	1.41421
$876$	13.7082	0.463157
$877$	4.38197	0.147968	0.0739842	−	0.997259i	$-0.476429\pi$
$877$	4.38197	0.147968	0.0739842	+	0.997259i	$0.476429\pi$
$878$	12.9443i	0.436848i
$879$	5.27051	0.177770
$880$	9.87539i	0.332899i
$881$	4.27051i	0.143877i	0.997409	+	0.0719386i	$0.0229186\pi$
$881$	4.27051i	0.143877i	−0.997409	+	0.0719386i	$0.977081\pi$
$882$	− 3.23607i	− 0.108964i
$883$	20.6869	0.696170	0.348085	−	0.937463i	$-0.386832\pi$
$883$	20.6869	0.696170	0.348085	+	0.937463i	$0.386832\pi$
$884$	− 1.67376i	− 0.0562947i
$885$	14.5066i	0.487633i
$886$	−1.18034	−0.0396543
$887$	− 38.0689i	− 1.27823i	−0.769112	−	0.639114i	$-0.779301\pi$
$887$	− 38.0689i	− 1.27823i	0.769112	−	0.639114i	$-0.220699\pi$
$888$	− 6.50658i	− 0.218346i
$889$	− 35.6525i	− 1.19575i
$890$	11.2148	0.375920
$891$	− 7.88854i	− 0.264276i
$892$	4.32624	0.144853
$893$	33.9787	1.13705
$894$	−3.67376	−0.122869
$895$	−61.6656	−2.06125
$896$	− 25.4508i	− 0.850253i
$897$	0.180340i	0.00602137i
$898$	16.1459	0.538796
$899$	0	0
$900$	41.7426	1.39142
$901$	8.76393i	0.291969i
$902$	− 3.29180i	− 0.109605i
$903$	10.0000	0.332779
$904$	17.7639	0.590820
$905$	−22.9098	−0.761549
$906$	−1.02129	−0.0339300
$907$	− 9.76393i	− 0.324206i	−0.986774	−	0.162103i	$-0.948172\pi$
$907$	− 9.76393i	− 0.324206i	0.986774	−	0.162103i	$-0.0518277\pi$
$908$	−33.7984	−1.12164
$909$	− 1.61803i	− 0.0536668i
$910$	1.25735i	0.0416809i
$911$	10.9443i	0.362600i	0.983428	+	0.181300i	$0.0580305\pi$
$911$	10.9443i	0.362600i	−0.983428	+	0.181300i	$0.941970\pi$
$912$	−5.56231	−0.184186
$913$	13.7426i	0.454815i
$914$	− 11.5623i	− 0.382447i
$915$	1.47214	0.0486673
$916$	− 3.70820i	− 0.122523i
$917$	32.0344i	1.05787i
$918$	− 9.40325i	− 0.310354i
$919$	31.3050	1.03266	0.516328	−	0.856391i	$-0.327299\pi$
$919$	31.3050	1.03266	0.516328	+	0.856391i	$0.327299\pi$
$920$	10.6525i	0.351202i
$921$	−11.8541	−0.390606
$922$	−24.0902	−0.793367
$923$	−2.47214	−0.0813713
$924$	3.09017	0.101659
$925$	− 46.3951i	− 1.52546i
$926$	− 6.61803i	− 0.217482i
$927$	24.0344	0.789395
$928$	0	0
$929$	−3.65248	−0.119834	−0.0599169	−	0.998203i	$-0.519084\pi$
$929$	−3.65248	−0.119834	−0.0599169	+	0.998203i	$0.519084\pi$
$930$	14.8541i	0.487085i
$931$	9.70820i	0.318174i
$932$	24.6525	0.807519
$933$	1.29180	0.0422915
$934$	11.0902	0.362881
$935$	23.3394	0.763280
$936$	1.38197i	0.0451710i
$937$	−6.65248	−0.217327	−0.108663	−	0.994079i	$-0.534657\pi$
$937$	−6.65248	−0.217327	−0.108663	+	0.994079i	$0.534657\pi$
$938$	− 2.11146i	− 0.0689415i
$939$	7.97871i	0.260375i
$940$	− 43.6525i	− 1.42379i
$941$	34.8885	1.13733	0.568667	−	0.822568i	$-0.307459\pi$
$941$	34.8885	1.13733	0.568667	+	0.822568i	$0.307459\pi$
$942$	− 5.56231i	− 0.181230i
$943$	4.76393i	0.155135i
$944$	11.2918	0.367517
$945$	− 29.9230i	− 0.973395i
$946$	− 6.18034i	− 0.200940i
$947$	43.0344i	1.39843i	0.714911	+	0.699216i	$0.246467\pi$
$947$	43.0344i	1.39843i	−0.714911	+	0.699216i	$0.753533\pi$
$948$	−6.09017	−0.197800
$949$	3.23607i	0.105047i
$950$	29.5623	0.959128
$951$	−17.1246	−0.555304
$952$	−21.9098	−0.710102
$953$	42.6312	1.38096	0.690480	−	0.723352i	$-0.257399\pi$
$953$	42.6312	1.38096	0.690480	+	0.723352i	$0.257399\pi$
$954$	− 3.23607i	− 0.104772i
$955$	− 65.6525i	− 2.12446i
$956$	−44.8885	−1.45180
$957$	0	0
$958$	−6.90983	−0.223246
$959$	− 15.9787i	− 0.515980i
$960$	0.562306i	0.0181483i
$961$	−70.8115	−2.28424
$962$	0.686918	0.0221471
$963$	17.7082	0.570639
$964$	7.52786	0.242456
$965$	− 48.0689i	− 1.54739i
$966$	1.05573	0.0339675
$967$	− 3.56231i	− 0.114556i	−0.998358	−	0.0572780i	$-0.981758\pi$
$967$	− 3.56231i	− 0.114556i	0.998358	−	0.0572780i	$-0.0182421\pi$
$968$	20.3262i	0.653310i
$969$	13.1459i	0.422307i
$970$	−8.48529	−0.272446
$971$	− 19.5066i	− 0.625996i	−0.949754	−	0.312998i	$-0.898667\pi$
$971$	− 19.5066i	− 0.625996i	0.949754	−	0.312998i	$-0.101333\pi$
$972$	− 22.5623i	− 0.723686i
$973$	−2.88854	−0.0926025
$974$	26.3050i	0.842865i
$975$	− 1.43769i	− 0.0460431i
$976$	− 1.14590i	− 0.0366793i
$977$	−45.2148	−1.44655	−0.723275	−	0.690561i	$-0.757364\pi$
$977$	−45.2148	−1.44655	−0.723275	+	0.690561i	$0.757364\pi$
$978$	2.30495i	0.0737042i
$979$	6.50658	0.207951
$980$	12.4721	0.398408
$981$	37.6525	1.20215
$982$	−9.34752	−0.298291
$983$	10.9443i	0.349068i	0.984651	+	0.174534i	$0.0558419\pi$
$983$	10.9443i	0.349068i	−0.984651	+	0.174534i	$0.944158\pi$
$984$	− 5.32624i	− 0.169794i
$985$	24.2492	0.772645
$986$	0	0
$987$	−9.67376	−0.307919
$988$	− 1.85410i	− 0.0589868i
$989$	8.94427i	0.284411i
$990$	−8.61803	−0.273899
$991$	−7.34752	−0.233402	−0.116701	−	0.993167i	$-0.537232\pi$
$991$	−7.34752	−0.233402	−0.116701	+	0.993167i	$0.537232\pi$
$992$	56.6869	1.79981
$993$	−13.0902	−0.415404
$994$	14.4721i	0.459028i
$995$	22.5623	0.715273
$996$	9.94427i	0.315096i
$997$	16.9098i	0.535540i	0.963483	+	0.267770i	$0.0862867\pi$
$997$	16.9098i	0.535540i	−0.963483	+	0.267770i	$0.913713\pi$
$998$	− 15.2574i	− 0.482963i
$999$	−16.3475	−0.517213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.b.b.840.3		4
29.2	odd	28		841.2.d.i.605.1		12
29.3	odd	28		841.2.d.i.571.1		12
29.4	even	14		841.2.e.j.651.2		24
29.5	even	14		841.2.e.j.236.3		24
29.6	even	14		841.2.e.j.196.2		24
29.7	even	7		841.2.e.j.270.2		24
29.8	odd	28		841.2.d.g.574.1		12
29.9	even	14		841.2.e.j.267.2		24
29.10	odd	28		841.2.d.g.190.2		12
29.11	odd	28		841.2.d.i.778.2		12
29.12	odd	4		841.2.a.c.1.1	yes	2
29.13	even	14		841.2.e.j.63.3		24
29.14	odd	28		841.2.d.i.645.1		12
29.15	odd	28		841.2.d.g.645.2		12
29.16	even	7		841.2.e.j.63.2		24
29.17	odd	4		841.2.a.a.1.2	✓	2
29.18	odd	28		841.2.d.g.778.1		12
29.19	odd	28		841.2.d.i.190.1		12
29.20	even	7		841.2.e.j.267.3		24
29.21	odd	28		841.2.d.i.574.2		12
29.22	even	14		841.2.e.j.270.3		24
29.23	even	7		841.2.e.j.196.3		24
29.24	even	7		841.2.e.j.236.2		24
29.25	even	7		841.2.e.j.651.3		24
29.26	odd	28		841.2.d.g.571.2		12
29.27	odd	28		841.2.d.g.605.2		12
29.28	even	2	inner	841.2.b.b.840.2		4
87.17	even	4		7569.2.a.l.1.1		2
87.41	even	4		7569.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.a.1.2	✓	2	29.17	odd	4
841.2.a.c.1.1	yes	2	29.12	odd	4
841.2.b.b.840.2		4	29.28	even	2	inner
841.2.b.b.840.3		4	1.1	even	1	trivial
841.2.d.g.190.2		12	29.10	odd	28
841.2.d.g.571.2		12	29.26	odd	28
841.2.d.g.574.1		12	29.8	odd	28
841.2.d.g.605.2		12	29.27	odd	28
841.2.d.g.645.2		12	29.15	odd	28
841.2.d.g.778.1		12	29.18	odd	28
841.2.d.i.190.1		12	29.19	odd	28
841.2.d.i.571.1		12	29.3	odd	28
841.2.d.i.574.2		12	29.21	odd	28
841.2.d.i.605.1		12	29.2	odd	28
841.2.d.i.645.1		12	29.14	odd	28
841.2.d.i.778.2		12	29.11	odd	28
841.2.e.j.63.2		24	29.16	even	7
841.2.e.j.63.3		24	29.13	even	14
841.2.e.j.196.2		24	29.6	even	14
841.2.e.j.196.3		24	29.23	even	7
841.2.e.j.236.2		24	29.24	even	7
841.2.e.j.236.3		24	29.5	even	14
841.2.e.j.267.2		24	29.9	even	14
841.2.e.j.267.3		24	29.20	even	7
841.2.e.j.270.2		24	29.7	even	7
841.2.e.j.270.3		24	29.22	even	14
841.2.e.j.651.2		24	29.4	even	14
841.2.e.j.651.3		24	29.25	even	7
7569.2.a.d.1.2		2	87.41	even	4
7569.2.a.l.1.1		2	87.17	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.618034i q^{2} -0.618034i q^{3} +1.61803 q^{4} -3.85410 q^{5} +0.381966 q^{6} -2.23607 q^{7} +2.23607i q^{8} +2.61803 q^{9} +O(q^{10})\)	\(q+0.618034i q^{2} -0.618034i q^{3} +1.61803 q^{4} -3.85410 q^{5} +0.381966 q^{6} -2.23607 q^{7} +2.23607i q^{8} +2.61803 q^{9} -2.38197i q^{10} -1.38197i q^{11} -1.00000i q^{12} +0.236068 q^{13} -1.38197i q^{14} +2.38197i q^{15} +1.85410 q^{16} -4.38197i q^{17} +1.61803i q^{18} -4.85410i q^{19} -6.23607 q^{20} +1.38197i q^{21} +0.854102 q^{22} -1.23607 q^{23} +1.38197 q^{24} +9.85410 q^{25} +0.145898i q^{26} -3.47214i q^{27} -3.61803 q^{28} -1.47214 q^{30} -10.0902i q^{31} +5.61803i q^{32} -0.854102 q^{33} +2.70820 q^{34} +8.61803 q^{35} +4.23607 q^{36} -4.70820i q^{37} +3.00000 q^{38} -0.145898i q^{39} -8.61803i q^{40} -3.85410i q^{41} -0.854102 q^{42} -7.23607i q^{43} -2.23607i q^{44} -10.0902 q^{45} -0.763932i q^{46} +7.00000i q^{47} -1.14590i q^{48} -2.00000 q^{49} +6.09017i q^{50} -2.70820 q^{51} +0.381966 q^{52} -2.00000 q^{53} +2.14590 q^{54} +5.32624i q^{55} -5.00000i q^{56} -3.00000 q^{57} +6.09017 q^{59} +3.85410i q^{60} -0.618034i q^{61} +6.23607 q^{62} -5.85410 q^{63} +0.236068 q^{64} -0.909830 q^{65} -0.527864i q^{66} +1.52786 q^{67} -7.09017i q^{68} +0.763932i q^{69} +5.32624i q^{70} -10.4721 q^{71} +5.85410i q^{72} +13.7082i q^{73} +2.90983 q^{74} -6.09017i q^{75} -7.85410i q^{76} +3.09017i q^{77} +0.0901699 q^{78} -6.09017i q^{79} -7.14590 q^{80} +5.70820 q^{81} +2.38197 q^{82} -9.94427 q^{83} +2.23607i q^{84} +16.8885i q^{85} +4.47214 q^{86} +3.09017 q^{88} +4.70820i q^{89} -6.23607i q^{90} -0.527864 q^{91} -2.00000 q^{92} -6.23607 q^{93} -4.32624 q^{94} +18.7082i q^{95} +3.47214 q^{96} -3.56231i q^{97} -1.23607i q^{98} -3.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{5} + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^5 + 6 * q^6 + 6 * q^9	\( 4 q + 2 q^{4} - 2 q^{5} + 6 q^{6} + 6 q^{9} - 8 q^{13} - 6 q^{16} - 16 q^{20} - 10 q^{22} + 4 q^{23} + 10 q^{24} + 26 q^{25} - 10 q^{28} + 12 q^{30} + 10 q^{33} - 16 q^{34} + 30 q^{35} + 8 q^{36} + 12 q^{38} + 10 q^{42} - 18 q^{45} - 8 q^{49} + 16 q^{51} + 6 q^{52} - 8 q^{53} + 22 q^{54} - 12 q^{57} + 2 q^{59} + 16 q^{62} - 10 q^{63} - 8 q^{64} - 26 q^{65} + 24 q^{67} - 24 q^{71} + 34 q^{74} - 22 q^{78} - 42 q^{80} - 4 q^{81} + 14 q^{82} - 4 q^{83} - 10 q^{88} - 20 q^{91} - 8 q^{92} - 16 q^{93} + 14 q^{94} - 4 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^5 + 6 * q^6 + 6 * q^9 - 8 * q^13 - 6 * q^16 - 16 * q^20 - 10 * q^22 + 4 * q^23 + 10 * q^24 + 26 * q^25 - 10 * q^28 + 12 * q^30 + 10 * q^33 - 16 * q^34 + 30 * q^35 + 8 * q^36 + 12 * q^38 + 10 * q^42 - 18 * q^45 - 8 * q^49 + 16 * q^51 + 6 * q^52 - 8 * q^53 + 22 * q^54 - 12 * q^57 + 2 * q^59 + 16 * q^62 - 10 * q^63 - 8 * q^64 - 26 * q^65 + 24 * q^67 - 24 * q^71 + 34 * q^74 - 22 * q^78 - 42 * q^80 - 4 * q^81 + 14 * q^82 - 4 * q^83 - 10 * q^88 - 20 * q^91 - 8 * q^92 - 16 * q^93 + 14 * q^94 - 4 * q^96

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