LMFDB - Embedded newform 2850.2.d.v.799.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(799,2850)]

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, 1, 0]))

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

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

chi := DirichletCharacter("2850.799");

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.d (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:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.3
Root			$-1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	2850.799
Dual form			2850.2.d.v.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.16228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.16228i q^{7} -1.00000i q^{8} -1.00000 q^{9} -2.16228 q^{11} -1.00000i q^{12} +1.16228i q^{13} +3.16228 q^{14} +1.00000 q^{16} +7.16228i q^{17} -1.00000i q^{18} +1.00000 q^{19} +3.16228 q^{21} -2.16228i q^{22} -7.32456i q^{23} +1.00000 q^{24} -1.16228 q^{26} -1.00000i q^{27} +3.16228i q^{28} +10.1623 q^{29} -7.32456 q^{31} +1.00000i q^{32} -2.16228i q^{33} -7.16228 q^{34} +1.00000 q^{36} +10.0000i q^{37} +1.00000i q^{38} -1.16228 q^{39} +6.32456 q^{41} +3.16228i q^{42} +2.83772i q^{43} +2.16228 q^{44} +7.32456 q^{46} +6.00000i q^{47} +1.00000i q^{48} -3.00000 q^{49} -7.16228 q^{51} -1.16228i q^{52} -8.16228i q^{53} +1.00000 q^{54} -3.16228 q^{56} +1.00000i q^{57} +10.1623i q^{58} -11.4868 q^{59} +2.16228 q^{61} -7.32456i q^{62} +3.16228i q^{63} -1.00000 q^{64} +2.16228 q^{66} +12.4868i q^{67} -7.16228i q^{68} +7.32456 q^{69} -5.16228 q^{71} +1.00000i q^{72} +1.00000i q^{73} -10.0000 q^{74} -1.00000 q^{76} +6.83772i q^{77} -1.16228i q^{78} -7.32456 q^{79} +1.00000 q^{81} +6.32456i q^{82} +12.4868i q^{83} -3.16228 q^{84} -2.83772 q^{86} +10.1623i q^{87} +2.16228i q^{88} -5.32456 q^{89} +3.67544 q^{91} +7.32456i q^{92} -7.32456i q^{93} -6.00000 q^{94} -1.00000 q^{96} +19.4868i q^{97} -3.00000i q^{98} +2.16228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{16} + 4 q^{19} + 4 q^{24} + 8 q^{26} + 28 q^{29} - 4 q^{31} - 16 q^{34} + 4 q^{36} + 8 q^{39} - 4 q^{44} + 4 q^{46} - 12 q^{49} - 16 q^{51} + 4 q^{54} - 8 q^{59} - 4 q^{61} - 4 q^{64} - 4 q^{66} + 4 q^{69} - 8 q^{71} - 40 q^{74} - 4 q^{76} - 4 q^{79} + 4 q^{81} - 24 q^{86} + 4 q^{89} + 40 q^{91} - 24 q^{94} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^16 + 4 * q^19 + 4 * q^24 + 8 * q^26 + 28 * q^29 - 4 * q^31 - 16 * q^34 + 4 * q^36 + 8 * q^39 - 4 * q^44 + 4 * q^46 - 12 * q^49 - 16 * q^51 + 4 * q^54 - 8 * q^59 - 4 * q^61 - 4 * q^64 - 4 * q^66 + 4 * q^69 - 8 * q^71 - 40 * q^74 - 4 * q^76 - 4 * q^79 + 4 * q^81 - 24 * q^86 + 4 * q^89 + 40 * q^91 - 24 * q^94 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times$.

$n$	$1027$	$1351$	$1901$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 3.16228i	− 1.19523i	−0.801784	−	0.597614i	$-0.796115\pi$
$7$	− 3.16228i	− 1.19523i	0.801784	−	0.597614i	$-0.203885\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−2.16228	−0.651951	−0.325976	−	0.945378i	$-0.605693\pi$
$11$	−2.16228	−0.651951	−0.325976	+	0.945378i	$0.605693\pi$
$12$	− 1.00000i	− 0.288675i
$13$	1.16228i	0.322358i	0.986925	+	0.161179i	$0.0515296\pi$
$13$	1.16228i	0.322358i	−0.986925	+	0.161179i	$0.948470\pi$
$14$	3.16228	0.845154
$15$	0	0
$16$	1.00000	0.250000
$17$	7.16228i	1.73711i	0.495595	+	0.868554i	$0.334950\pi$
$17$	7.16228i	1.73711i	−0.495595	+	0.868554i	$0.665050\pi$
$18$	− 1.00000i	− 0.235702i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	3.16228	0.690066
$22$	− 2.16228i	− 0.460999i
$23$	− 7.32456i	− 1.52728i	−0.645645	−	0.763638i	$-0.723411\pi$
$23$	− 7.32456i	− 1.52728i	0.645645	−	0.763638i	$-0.276589\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.16228	−0.227941
$27$	− 1.00000i	− 0.192450i
$28$	3.16228i	0.597614i
$29$	10.1623	1.88709	0.943544	−	0.331248i	$-0.107470\pi$
$29$	10.1623	1.88709	0.943544	+	0.331248i	$0.107470\pi$
$30$	0	0
$31$	−7.32456	−1.31553	−0.657764	−	0.753224i	$-0.728498\pi$
$31$	−7.32456	−1.31553	−0.657764	+	0.753224i	$0.728498\pi$
$32$	1.00000i	0.176777i
$33$	− 2.16228i	− 0.376404i
$34$	−7.16228	−1.22832
$35$	0	0
$36$	1.00000	0.166667
$37$	10.0000i	1.64399i	0.569495	+	0.821995i	$0.307139\pi$
$37$	10.0000i	1.64399i	−0.569495	+	0.821995i	$0.692861\pi$
$38$	1.00000i	0.162221i
$39$	−1.16228	−0.186113
$40$	0	0
$41$	6.32456	0.987730	0.493865	−	0.869539i	$-0.335584\pi$
$41$	6.32456	0.987730	0.493865	+	0.869539i	$0.335584\pi$
$42$	3.16228i	0.487950i
$43$	2.83772i	0.432749i	0.976310	+	0.216374i	$0.0694231\pi$
$43$	2.83772i	0.432749i	−0.976310	+	0.216374i	$0.930577\pi$
$44$	2.16228	0.325976
$45$	0	0
$46$	7.32456	1.07995
$47$	6.00000i	0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$	6.00000i	0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	1.00000i	0.144338i
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−7.16228	−1.00292
$52$	− 1.16228i	− 0.161179i
$53$	− 8.16228i	− 1.12118i	−0.828095	−	0.560588i	$-0.810575\pi$
$53$	− 8.16228i	− 1.12118i	0.828095	−	0.560588i	$-0.189425\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−3.16228	−0.422577
$57$	1.00000i	0.132453i
$58$	10.1623i	1.33437i
$59$	−11.4868	−1.49546	−0.747729	−	0.664004i	$-0.768856\pi$
$59$	−11.4868	−1.49546	−0.747729	+	0.664004i	$0.768856\pi$
$60$	0	0
$61$	2.16228	0.276851	0.138426	−	0.990373i	$-0.455796\pi$
$61$	2.16228	0.276851	0.138426	+	0.990373i	$0.455796\pi$
$62$	− 7.32456i	− 0.930219i
$63$	3.16228i	0.398410i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.16228	0.266158
$67$	12.4868i	1.52551i	0.646688	+	0.762755i	$0.276154\pi$
$67$	12.4868i	1.52551i	−0.646688	+	0.762755i	$0.723846\pi$
$68$	− 7.16228i	− 0.868554i
$69$	7.32456	0.881773
$70$	0	0
$71$	−5.16228	−0.612650	−0.306325	−	0.951927i	$-0.599099\pi$
$71$	−5.16228	−0.612650	−0.306325	+	0.951927i	$0.599099\pi$
$72$	1.00000i	0.117851i
$73$	1.00000i	0.117041i	0.998286	+	0.0585206i	$0.0186383\pi$
$73$	1.00000i	0.117041i	−0.998286	+	0.0585206i	$0.981362\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−1.00000	−0.114708
$77$	6.83772i	0.779231i
$78$	− 1.16228i	− 0.131602i
$79$	−7.32456	−0.824077	−0.412038	−	0.911166i	$-0.635183\pi$
$79$	−7.32456	−0.824077	−0.412038	+	0.911166i	$0.635183\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	6.32456i	0.698430i
$83$	12.4868i	1.37061i	0.728257	+	0.685304i	$0.240331\pi$
$83$	12.4868i	1.37061i	−0.728257	+	0.685304i	$0.759669\pi$
$84$	−3.16228	−0.345033
$85$	0	0
$86$	−2.83772	−0.305999
$87$	10.1623i	1.08951i
$88$	2.16228i	0.230500i
$89$	−5.32456	−0.564402	−0.282201	−	0.959355i	$-0.591064\pi$
$89$	−5.32456	−0.564402	−0.282201	+	0.959355i	$0.591064\pi$
$90$	0	0
$91$	3.67544	0.385291
$92$	7.32456i	0.763638i
$93$	− 7.32456i	− 0.759521i
$94$	−6.00000	−0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	19.4868i	1.97859i	0.145936	+	0.989294i	$0.453381\pi$
$97$	19.4868i	1.97859i	−0.145936	+	0.989294i	$0.546619\pi$
$98$	− 3.00000i	− 0.303046i
$99$	2.16228	0.217317
$100$	0	0
$101$	17.8114	1.77230	0.886150	−	0.463399i	$-0.153370\pi$
$101$	17.8114	1.77230	0.886150	+	0.463399i	$0.153370\pi$
$102$	− 7.16228i	− 0.709171i
$103$	9.64911i	0.950755i	0.879782	+	0.475378i	$0.157689\pi$
$103$	9.64911i	0.950755i	−0.879782	+	0.475378i	$0.842311\pi$
$104$	1.16228	0.113971
$105$	0	0
$106$	8.16228	0.792790
$107$	19.1623i	1.85249i	0.376925	+	0.926244i	$0.376981\pi$
$107$	19.1623i	1.85249i	−0.376925	+	0.926244i	$0.623019\pi$
$108$	1.00000i	0.0962250i
$109$	−20.3246	−1.94674	−0.973370	−	0.229241i	$-0.926376\pi$
$109$	−20.3246	−1.94674	−0.973370	+	0.229241i	$0.926376\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	− 3.16228i	− 0.298807i
$113$	15.6491i	1.47214i	0.676903	+	0.736072i	$0.263322\pi$
$113$	15.6491i	1.47214i	−0.676903	+	0.736072i	$0.736678\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−10.1623	−0.943544
$117$	− 1.16228i	− 0.107453i
$118$	− 11.4868i	− 1.05745i
$119$	22.6491	2.07624
$120$	0	0
$121$	−6.32456	−0.574960
$122$	2.16228i	0.195763i
$123$	6.32456i	0.570266i
$124$	7.32456	0.657764
$125$	0	0
$126$	−3.16228	−0.281718
$127$	− 9.64911i	− 0.856220i	−0.903727	−	0.428110i	$-0.859180\pi$
$127$	− 9.64911i	− 0.856220i	0.903727	−	0.428110i	$-0.140820\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−2.83772	−0.249848
$130$	0	0
$131$	6.48683	0.566757	0.283379	−	0.959008i	$-0.408545\pi$
$131$	6.48683	0.566757	0.283379	+	0.959008i	$0.408545\pi$
$132$	2.16228i	0.188202i
$133$	− 3.16228i	− 0.274204i
$134$	−12.4868	−1.07870
$135$	0	0
$136$	7.16228	0.614160
$137$	− 10.3246i	− 0.882086i	−0.897486	−	0.441043i	$-0.854609\pi$
$137$	− 10.3246i	− 0.882086i	0.897486	−	0.441043i	$-0.145391\pi$
$138$	7.32456i	0.623508i
$139$	−2.51317	−0.213164	−0.106582	−	0.994304i	$-0.533991\pi$
$139$	−2.51317	−0.213164	−0.106582	+	0.994304i	$0.533991\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	− 5.16228i	− 0.433209i
$143$	− 2.51317i	− 0.210162i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−1.00000	−0.0827606
$147$	− 3.00000i	− 0.247436i
$148$	− 10.0000i	− 0.821995i
$149$	8.64911	0.708563	0.354281	−	0.935139i	$-0.384726\pi$
$149$	8.64911	0.708563	0.354281	+	0.935139i	$0.384726\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	− 7.16228i	− 0.579036i
$154$	−6.83772	−0.550999
$155$	0	0
$156$	1.16228	0.0930567
$157$	5.67544i	0.452950i	0.974017	+	0.226475i	$0.0727201\pi$
$157$	5.67544i	0.452950i	−0.974017	+	0.226475i	$0.927280\pi$
$158$	− 7.32456i	− 0.582710i
$159$	8.16228	0.647311
$160$	0	0
$161$	−23.1623	−1.82544
$162$	1.00000i	0.0785674i
$163$	− 2.64911i	− 0.207494i	−0.994604	−	0.103747i	$-0.966917\pi$
$163$	− 2.64911i	− 0.207494i	0.994604	−	0.103747i	$-0.0330833\pi$
$164$	−6.32456	−0.493865
$165$	0	0
$166$	−12.4868	−0.969166
$167$	− 22.6491i	− 1.75264i	−0.481729	−	0.876320i	$-0.659991\pi$
$167$	− 22.6491i	− 1.75264i	0.481729	−	0.876320i	$-0.340009\pi$
$168$	− 3.16228i	− 0.243975i
$169$	11.6491	0.896085
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	− 2.83772i	− 0.216374i
$173$	− 4.16228i	− 0.316452i	−0.987403	−	0.158226i	$-0.949423\pi$
$173$	− 4.16228i	− 0.316452i	0.987403	−	0.158226i	$-0.0505775\pi$
$174$	−10.1623	−0.770400
$175$	0	0
$176$	−2.16228	−0.162988
$177$	− 11.4868i	− 0.863403i
$178$	− 5.32456i	− 0.399092i
$179$	−4.64911	−0.347491	−0.173745	−	0.984791i	$-0.555587\pi$
$179$	−4.64911	−0.347491	−0.173745	+	0.984791i	$0.555587\pi$
$180$	0	0
$181$	2.83772	0.210926	0.105463	−	0.994423i	$-0.466368\pi$
$181$	2.83772	0.210926	0.105463	+	0.994423i	$0.466368\pi$
$182$	3.67544i	0.272442i
$183$	2.16228i	0.159840i
$184$	−7.32456	−0.539973
$185$	0	0
$186$	7.32456	0.537062
$187$	− 15.4868i	− 1.13251i
$188$	− 6.00000i	− 0.437595i
$189$	−3.16228	−0.230022
$190$	0	0
$191$	−3.64911	−0.264040	−0.132020	−	0.991247i	$-0.542146\pi$
$191$	−3.64911	−0.264040	−0.132020	+	0.991247i	$0.542146\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	2.83772i	0.204264i	0.994771	+	0.102132i	$0.0325664\pi$
$193$	2.83772i	0.204264i	−0.994771	+	0.102132i	$0.967434\pi$
$194$	−19.4868	−1.39907
$195$	0	0
$196$	3.00000	0.214286
$197$	20.1359i	1.43463i	0.696751	+	0.717313i	$0.254628\pi$
$197$	20.1359i	1.43463i	−0.696751	+	0.717313i	$0.745372\pi$
$198$	2.16228i	0.153666i
$199$	−6.64911	−0.471343	−0.235671	−	0.971833i	$-0.575729\pi$
$199$	−6.64911	−0.471343	−0.235671	+	0.971833i	$0.575729\pi$
$200$	0	0
$201$	−12.4868	−0.880753
$202$	17.8114i	1.25320i
$203$	− 32.1359i	− 2.25550i
$204$	7.16228	0.501460
$205$	0	0
$206$	−9.64911	−0.672285
$207$	7.32456i	0.509092i
$208$	1.16228i	0.0805895i
$209$	−2.16228	−0.149568
$210$	0	0
$211$	12.8114	0.881972	0.440986	−	0.897514i	$-0.354629\pi$
$211$	12.8114	0.881972	0.440986	+	0.897514i	$0.354629\pi$
$212$	8.16228i	0.560588i
$213$	− 5.16228i	− 0.353713i
$214$	−19.1623	−1.30991
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	23.1623i	1.57236i
$218$	− 20.3246i	− 1.37655i
$219$	−1.00000	−0.0675737
$220$	0	0
$221$	−8.32456	−0.559970
$222$	− 10.0000i	− 0.671156i
$223$	0.350889i	0.0234973i	0.999931	+	0.0117486i	$0.00373980\pi$
$223$	0.350889i	0.0234973i	−0.999931	+	0.0117486i	$0.996260\pi$
$224$	3.16228	0.211289
$225$	0	0
$226$	−15.6491	−1.04096
$227$	− 2.00000i	− 0.132745i	−0.997795	−	0.0663723i	$-0.978857\pi$
$227$	− 2.00000i	− 0.132745i	0.997795	−	0.0663723i	$-0.0211425\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	−1.83772	−0.121440	−0.0607201	−	0.998155i	$-0.519340\pi$
$229$	−1.83772	−0.121440	−0.0607201	+	0.998155i	$0.519340\pi$
$230$	0	0
$231$	−6.83772	−0.449889
$232$	− 10.1623i	− 0.667186i
$233$	− 19.8114i	− 1.29789i	−0.760837	−	0.648944i	$-0.775211\pi$
$233$	− 19.8114i	− 1.29789i	0.760837	−	0.648944i	$-0.224789\pi$
$234$	1.16228	0.0759805
$235$	0	0
$236$	11.4868	0.747729
$237$	− 7.32456i	− 0.475781i
$238$	22.6491i	1.46812i
$239$	11.6754	0.755222	0.377611	−	0.925964i	$-0.376746\pi$
$239$	11.6754	0.755222	0.377611	+	0.925964i	$0.376746\pi$
$240$	0	0
$241$	29.4868	1.89941	0.949707	−	0.313140i	$-0.101381\pi$
$241$	29.4868	1.89941	0.949707	+	0.313140i	$0.101381\pi$
$242$	− 6.32456i	− 0.406558i
$243$	1.00000i	0.0641500i
$244$	−2.16228	−0.138426
$245$	0	0
$246$	−6.32456	−0.403239
$247$	1.16228i	0.0739540i
$248$	7.32456i	0.465110i
$249$	−12.4868	−0.791321
$250$	0	0
$251$	14.6491	0.924644	0.462322	−	0.886712i	$-0.347016\pi$
$251$	14.6491	0.924644	0.462322	+	0.886712i	$0.347016\pi$
$252$	− 3.16228i	− 0.199205i
$253$	15.8377i	0.995709i
$254$	9.64911	0.605439
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 6.67544i	− 0.416403i	−0.978086	−	0.208201i	$-0.933239\pi$
$257$	− 6.67544i	− 0.416403i	0.978086	−	0.208201i	$-0.0667609\pi$
$258$	− 2.83772i	− 0.176669i
$259$	31.6228	1.96494
$260$	0	0
$261$	−10.1623	−0.629029
$262$	6.48683i	0.400758i
$263$	5.97367i	0.368352i	0.982893	+	0.184176i	$0.0589616\pi$
$263$	5.97367i	0.368352i	−0.982893	+	0.184176i	$0.941038\pi$
$264$	−2.16228	−0.133079
$265$	0	0
$266$	3.16228	0.193892
$267$	− 5.32456i	− 0.325857i
$268$	− 12.4868i	− 0.762755i
$269$	0.324555	0.0197885	0.00989424	−	0.999951i	$-0.496851\pi$
$269$	0.324555	0.0197885	0.00989424	+	0.999951i	$0.496851\pi$
$270$	0	0
$271$	5.16228	0.313586	0.156793	−	0.987631i	$-0.449884\pi$
$271$	5.16228	0.313586	0.156793	+	0.987631i	$0.449884\pi$
$272$	7.16228i	0.434277i
$273$	3.67544i	0.222448i
$274$	10.3246	0.623729
$275$	0	0
$276$	−7.32456	−0.440886
$277$	− 6.81139i	− 0.409257i	−0.978840	−	0.204628i	$-0.934401\pi$
$277$	− 6.81139i	− 0.409257i	0.978840	−	0.204628i	$-0.0655986\pi$
$278$	− 2.51317i	− 0.150730i
$279$	7.32456	0.438510
$280$	0	0
$281$	−17.6491	−1.05286	−0.526429	−	0.850219i	$-0.676469\pi$
$281$	−17.6491	−1.05286	−0.526429	+	0.850219i	$0.676469\pi$
$282$	− 6.00000i	− 0.357295i
$283$	0.649111i	0.0385856i	0.999814	+	0.0192928i	$0.00614147\pi$
$283$	0.649111i	0.0385856i	−0.999814	+	0.0192928i	$0.993859\pi$
$284$	5.16228	0.306325
$285$	0	0
$286$	2.51317	0.148607
$287$	− 20.0000i	− 1.18056i
$288$	− 1.00000i	− 0.0589256i
$289$	−34.2982	−2.01754
$290$	0	0
$291$	−19.4868	−1.14234
$292$	− 1.00000i	− 0.0585206i
$293$	2.48683i	0.145282i	0.997358	+	0.0726412i	$0.0231428\pi$
$293$	2.48683i	0.145282i	−0.997358	+	0.0726412i	$0.976857\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	10.0000	0.581238
$297$	2.16228i	0.125468i
$298$	8.64911i	0.501030i
$299$	8.51317	0.492329
$300$	0	0
$301$	8.97367	0.517234
$302$	− 10.0000i	− 0.575435i
$303$	17.8114i	1.02324i
$304$	1.00000	0.0573539
$305$	0	0
$306$	7.16228	0.409440
$307$	32.4868i	1.85412i	0.374911	+	0.927061i	$0.377673\pi$
$307$	32.4868i	1.85412i	−0.374911	+	0.927061i	$0.622327\pi$
$308$	− 6.83772i	− 0.389615i
$309$	−9.64911	−0.548919
$310$	0	0
$311$	−26.0000	−1.47432	−0.737162	−	0.675716i	$-0.763835\pi$
$311$	−26.0000	−1.47432	−0.737162	+	0.675716i	$0.763835\pi$
$312$	1.16228i	0.0658010i
$313$	23.3246i	1.31838i	0.751976	+	0.659191i	$0.229101\pi$
$313$	23.3246i	1.31838i	−0.751976	+	0.659191i	$0.770899\pi$
$314$	−5.67544	−0.320284
$315$	0	0
$316$	7.32456	0.412038
$317$	− 2.16228i	− 0.121446i	−0.998155	−	0.0607228i	$-0.980659\pi$
$317$	− 2.16228i	− 0.121446i	0.998155	−	0.0607228i	$-0.0193406\pi$
$318$	8.16228i	0.457718i
$319$	−21.9737	−1.23029
$320$	0	0
$321$	−19.1623	−1.06953
$322$	− 23.1623i	− 1.29078i
$323$	7.16228i	0.398520i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	2.64911	0.146721
$327$	− 20.3246i	− 1.12395i
$328$	− 6.32456i	− 0.349215i
$329$	18.9737	1.04605
$330$	0	0
$331$	−34.8114	−1.91341	−0.956703	−	0.291064i	$-0.905991\pi$
$331$	−34.8114	−1.91341	−0.956703	+	0.291064i	$0.905991\pi$
$332$	− 12.4868i	− 0.685304i
$333$	− 10.0000i	− 0.547997i
$334$	22.6491	1.23930
$335$	0	0
$336$	3.16228	0.172516
$337$	34.9737i	1.90514i	0.304324	+	0.952568i	$0.401569\pi$
$337$	34.9737i	1.90514i	−0.304324	+	0.952568i	$0.598431\pi$
$338$	11.6491i	0.633628i
$339$	−15.6491	−0.849943
$340$	0	0
$341$	15.8377	0.857661
$342$	− 1.00000i	− 0.0540738i
$343$	− 12.6491i	− 0.682988i
$344$	2.83772	0.153000
$345$	0	0
$346$	4.16228	0.223765
$347$	− 20.0000i	− 1.07366i	−0.843692	−	0.536828i	$-0.819622\pi$
$347$	− 20.0000i	− 1.07366i	0.843692	−	0.536828i	$-0.180378\pi$
$348$	− 10.1623i	− 0.544755i
$349$	24.1623	1.29338	0.646689	−	0.762754i	$-0.276153\pi$
$349$	24.1623	1.29338	0.646689	+	0.762754i	$0.276153\pi$
$350$	0	0
$351$	1.16228	0.0620378
$352$	− 2.16228i	− 0.115250i
$353$	7.81139i	0.415758i	0.978155	+	0.207879i	$0.0666561\pi$
$353$	7.81139i	0.415758i	−0.978155	+	0.207879i	$0.933344\pi$
$354$	11.4868	0.610518
$355$	0	0
$356$	5.32456	0.282201
$357$	22.6491i	1.19872i
$358$	− 4.64911i	− 0.245713i
$359$	24.3246	1.28380	0.641900	−	0.766788i	$-0.278146\pi$
$359$	24.3246	1.28380	0.641900	+	0.766788i	$0.278146\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.83772i	0.149147i
$363$	− 6.32456i	− 0.331953i
$364$	−3.67544	−0.192646
$365$	0	0
$366$	−2.16228	−0.113024
$367$	11.4868i	0.599608i	0.954001	+	0.299804i	$0.0969213\pi$
$367$	11.4868i	0.599608i	−0.954001	+	0.299804i	$0.903079\pi$
$368$	− 7.32456i	− 0.381819i
$369$	−6.32456	−0.329243
$370$	0	0
$371$	−25.8114	−1.34006
$372$	7.32456i	0.379761i
$373$	− 28.1359i	− 1.45682i	−0.685139	−	0.728412i	$-0.740259\pi$
$373$	− 28.1359i	− 1.45682i	0.685139	−	0.728412i	$-0.259741\pi$
$374$	15.4868	0.800805
$375$	0	0
$376$	6.00000	0.309426
$377$	11.8114i	0.608317i
$378$	− 3.16228i	− 0.162650i
$379$	14.9737	0.769146	0.384573	−	0.923095i	$-0.374349\pi$
$379$	14.9737	0.769146	0.384573	+	0.923095i	$0.374349\pi$
$380$	0	0
$381$	9.64911	0.494339
$382$	− 3.64911i	− 0.186705i
$383$	− 15.4868i	− 0.791340i	−0.918393	−	0.395670i	$-0.870512\pi$
$383$	− 15.4868i	− 0.791340i	0.918393	−	0.395670i	$-0.129488\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−2.83772	−0.144436
$387$	− 2.83772i	− 0.144250i
$388$	− 19.4868i	− 0.989294i
$389$	9.35089	0.474109	0.237054	−	0.971496i	$-0.423818\pi$
$389$	9.35089	0.474109	0.237054	+	0.971496i	$0.423818\pi$
$390$	0	0
$391$	52.4605	2.65304
$392$	3.00000i	0.151523i
$393$	6.48683i	0.327217i
$394$	−20.1359	−1.01443
$395$	0	0
$396$	−2.16228	−0.108659
$397$	− 27.1359i	− 1.36191i	−0.732323	−	0.680957i	$-0.761564\pi$
$397$	− 27.1359i	− 1.36191i	0.732323	−	0.680957i	$-0.238436\pi$
$398$	− 6.64911i	− 0.333290i
$399$	3.16228	0.158312
$400$	0	0
$401$	−11.6491	−0.581729	−0.290864	−	0.956764i	$-0.593943\pi$
$401$	−11.6491	−0.581729	−0.290864	+	0.956764i	$0.593943\pi$
$402$	− 12.4868i	− 0.622787i
$403$	− 8.51317i	− 0.424071i
$404$	−17.8114	−0.886150
$405$	0	0
$406$	32.1359	1.59488
$407$	− 21.6228i	− 1.07180i
$408$	7.16228i	0.354586i
$409$	20.3246	1.00498	0.502492	−	0.864582i	$-0.332417\pi$
$409$	20.3246	1.00498	0.502492	+	0.864582i	$0.332417\pi$
$410$	0	0
$411$	10.3246	0.509273
$412$	− 9.64911i	− 0.475378i
$413$	36.3246i	1.78741i
$414$	−7.32456	−0.359982
$415$	0	0
$416$	−1.16228	−0.0569854
$417$	− 2.51317i	− 0.123070i
$418$	− 2.16228i	− 0.105760i
$419$	−8.00000	−0.390826	−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000	−0.390826	−0.195413	+	0.980721i	$0.562605\pi$
$420$	0	0
$421$	−6.64911	−0.324058	−0.162029	−	0.986786i	$-0.551804\pi$
$421$	−6.64911	−0.324058	−0.162029	+	0.986786i	$0.551804\pi$
$422$	12.8114i	0.623649i
$423$	− 6.00000i	− 0.291730i
$424$	−8.16228	−0.396395
$425$	0	0
$426$	5.16228	0.250113
$427$	− 6.83772i	− 0.330901i
$428$	− 19.1623i	− 0.926244i
$429$	2.51317	0.121337
$430$	0	0
$431$	12.3246	0.593653	0.296826	−	0.954931i	$-0.404072\pi$
$431$	12.3246	0.593653	0.296826	+	0.954931i	$0.404072\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	16.1359i	0.775444i	0.921776	+	0.387722i	$0.126738\pi$
$433$	16.1359i	0.775444i	−0.921776	+	0.387722i	$0.873262\pi$
$434$	−23.1623	−1.11182
$435$	0	0
$436$	20.3246	0.973370
$437$	− 7.32456i	− 0.350381i
$438$	− 1.00000i	− 0.0477818i
$439$	11.6491	0.555982	0.277991	−	0.960584i	$-0.410332\pi$
$439$	11.6491	0.555982	0.277991	+	0.960584i	$0.410332\pi$
$440$	0	0
$441$	3.00000	0.142857
$442$	− 8.32456i	− 0.395959i
$443$	18.1623i	0.862916i	0.902133	+	0.431458i	$0.142001\pi$
$443$	18.1623i	0.862916i	−0.902133	+	0.431458i	$0.857999\pi$
$444$	10.0000	0.474579
$445$	0	0
$446$	−0.350889	−0.0166151
$447$	8.64911i	0.409089i
$448$	3.16228i	0.149404i
$449$	11.0000	0.519122	0.259561	−	0.965727i	$-0.416422\pi$
$449$	11.0000	0.519122	0.259561	+	0.965727i	$0.416422\pi$
$450$	0	0
$451$	−13.6754	−0.643952
$452$	− 15.6491i	− 0.736072i
$453$	− 10.0000i	− 0.469841i
$454$	2.00000	0.0938647
$455$	0	0
$456$	1.00000	0.0468293
$457$	22.3246i	1.04430i	0.852854	+	0.522149i	$0.174870\pi$
$457$	22.3246i	1.04430i	−0.852854	+	0.522149i	$0.825130\pi$
$458$	− 1.83772i	− 0.0858711i
$459$	7.16228	0.334306
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	− 6.83772i	− 0.318120i
$463$	34.3246i	1.59520i	0.603188	+	0.797599i	$0.293897\pi$
$463$	34.3246i	1.59520i	−0.603188	+	0.797599i	$0.706103\pi$
$464$	10.1623	0.471772
$465$	0	0
$466$	19.8114	0.917745
$467$	7.13594i	0.330212i	0.986276	+	0.165106i	$0.0527966\pi$
$467$	7.13594i	0.330212i	−0.986276	+	0.165106i	$0.947203\pi$
$468$	1.16228i	0.0537263i
$469$	39.4868	1.82333
$470$	0	0
$471$	−5.67544	−0.261511
$472$	11.4868i	0.528724i
$473$	− 6.13594i	− 0.282131i
$474$	7.32456	0.336428
$475$	0	0
$476$	−22.6491	−1.03812
$477$	8.16228i	0.373725i
$478$	11.6754i	0.534022i
$479$	2.02633	0.0925856	0.0462928	−	0.998928i	$-0.485259\pi$
$479$	2.02633	0.0925856	0.0462928	+	0.998928i	$0.485259\pi$
$480$	0	0
$481$	−11.6228	−0.529953
$482$	29.4868i	1.34309i
$483$	− 23.1623i	− 1.05392i
$484$	6.32456	0.287480
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	− 3.35089i	− 0.151843i	−0.997114	−	0.0759216i	$-0.975810\pi$
$487$	− 3.35089i	− 0.151843i	0.997114	−	0.0759216i	$-0.0241899\pi$
$488$	− 2.16228i	− 0.0978817i
$489$	2.64911	0.119797
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	− 6.32456i	− 0.285133i
$493$	72.7851i	3.27807i
$494$	−1.16228	−0.0522933
$495$	0	0
$496$	−7.32456	−0.328882
$497$	16.3246i	0.732256i
$498$	− 12.4868i	− 0.559548i
$499$	−25.8114	−1.15548	−0.577738	−	0.816222i	$-0.696065\pi$
$499$	−25.8114	−1.15548	−0.577738	+	0.816222i	$0.696065\pi$
$500$	0	0
$501$	22.6491	1.01189
$502$	14.6491i	0.653822i
$503$	− 21.2982i	− 0.949641i	−0.880083	−	0.474820i	$-0.842513\pi$
$503$	− 21.2982i	− 0.949641i	0.880083	−	0.474820i	$-0.157487\pi$
$504$	3.16228	0.140859
$505$	0	0
$506$	−15.8377	−0.704073
$507$	11.6491i	0.517355i
$508$	9.64911i	0.428110i
$509$	14.8114	0.656503	0.328252	−	0.944590i	$-0.393541\pi$
$509$	14.8114	0.656503	0.328252	+	0.944590i	$0.393541\pi$
$510$	0	0
$511$	3.16228	0.139891
$512$	1.00000i	0.0441942i
$513$	− 1.00000i	− 0.0441511i
$514$	6.67544	0.294441
$515$	0	0
$516$	2.83772	0.124924
$517$	− 12.9737i	− 0.570581i
$518$	31.6228i	1.38943i
$519$	4.16228	0.182704
$520$	0	0
$521$	−17.9737	−0.787441	−0.393720	−	0.919230i	$-0.628812\pi$
$521$	−17.9737	−0.787441	−0.393720	+	0.919230i	$0.628812\pi$
$522$	− 10.1623i	− 0.444791i
$523$	− 8.64911i	− 0.378199i	−0.981958	−	0.189100i	$-0.939443\pi$
$523$	− 8.64911i	− 0.378199i	0.981958	−	0.189100i	$-0.0605569\pi$
$524$	−6.48683	−0.283379
$525$	0	0
$526$	−5.97367	−0.260464
$527$	− 52.4605i	− 2.28522i
$528$	− 2.16228i	− 0.0941011i
$529$	−30.6491	−1.33257
$530$	0	0
$531$	11.4868	0.498486
$532$	3.16228i	0.137102i
$533$	7.35089i	0.318402i
$534$	5.32456	0.230416
$535$	0	0
$536$	12.4868	0.539349
$537$	− 4.64911i	− 0.200624i
$538$	0.324555i	0.0139926i
$539$	6.48683	0.279408
$540$	0	0
$541$	6.16228	0.264937	0.132469	−	0.991187i	$-0.457710\pi$
$541$	6.16228	0.264937	0.132469	+	0.991187i	$0.457710\pi$
$542$	5.16228i	0.221739i
$543$	2.83772i	0.121778i
$544$	−7.16228	−0.307080
$545$	0	0
$546$	−3.67544	−0.157295
$547$	14.8114i	0.633289i	0.948544	+	0.316645i	$0.102556\pi$
$547$	14.8114i	0.633289i	−0.948544	+	0.316645i	$0.897444\pi$
$548$	10.3246i	0.441043i
$549$	−2.16228	−0.0922838
$550$	0	0
$551$	10.1623	0.432928
$552$	− 7.32456i	− 0.311754i
$553$	23.1623i	0.984960i
$554$	6.81139	0.289388
$555$	0	0
$556$	2.51317	0.106582
$557$	− 29.1623i	− 1.23565i	−0.786317	−	0.617823i	$-0.788015\pi$
$557$	− 29.1623i	− 1.23565i	0.786317	−	0.617823i	$-0.211985\pi$
$558$	7.32456i	0.310073i
$559$	−3.29822	−0.139500
$560$	0	0
$561$	15.4868	0.653855
$562$	− 17.6491i	− 0.744483i
$563$	− 24.8377i	− 1.04679i	−0.852092	−	0.523393i	$-0.824666\pi$
$563$	− 24.8377i	− 1.04679i	0.852092	−	0.523393i	$-0.175334\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	−0.649111	−0.0272842
$567$	− 3.16228i	− 0.132803i
$568$	5.16228i	0.216604i
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	15.8114	0.661686	0.330843	−	0.943686i	$-0.392667\pi$
$571$	15.8114	0.661686	0.330843	+	0.943686i	$0.392667\pi$
$572$	2.51317i	0.105081i
$573$	− 3.64911i	− 0.152444i
$574$	20.0000	0.834784
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 29.3246i	− 1.22080i	−0.792094	−	0.610399i	$-0.791009\pi$
$577$	− 29.3246i	− 1.22080i	0.792094	−	0.610399i	$-0.208991\pi$
$578$	− 34.2982i	− 1.42662i
$579$	−2.83772	−0.117932
$580$	0	0
$581$	39.4868	1.63819
$582$	− 19.4868i	− 0.807755i
$583$	17.6491i	0.730951i
$584$	1.00000	0.0413803
$585$	0	0
$586$	−2.48683	−0.102730
$587$	12.8114i	0.528783i	0.964415	+	0.264391i	$0.0851710\pi$
$587$	12.8114i	0.528783i	−0.964415	+	0.264391i	$0.914829\pi$
$588$	3.00000i	0.123718i
$589$	−7.32456	−0.301803
$590$	0	0
$591$	−20.1359	−0.828282
$592$	10.0000i	0.410997i
$593$	− 10.3246i	− 0.423979i	−0.977272	−	0.211989i	$-0.932006\pi$
$593$	− 10.3246i	− 0.423979i	0.977272	−	0.211989i	$-0.0679942\pi$
$594$	−2.16228	−0.0887193
$595$	0	0
$596$	−8.64911	−0.354281
$597$	− 6.64911i	− 0.272130i
$598$	8.51317i	0.348129i
$599$	35.8114	1.46321	0.731607	−	0.681727i	$-0.238771\pi$
$599$	35.8114	1.46321	0.731607	+	0.681727i	$0.238771\pi$
$600$	0	0
$601$	14.1886	0.578766	0.289383	−	0.957213i	$-0.406550\pi$
$601$	14.1886	0.578766	0.289383	+	0.957213i	$0.406550\pi$
$602$	8.97367i	0.365739i
$603$	− 12.4868i	− 0.508503i
$604$	10.0000	0.406894
$605$	0	0
$606$	−17.8114	−0.723538
$607$	39.9737i	1.62248i	0.584713	+	0.811241i	$0.301207\pi$
$607$	39.9737i	1.62248i	−0.584713	+	0.811241i	$0.698793\pi$
$608$	1.00000i	0.0405554i
$609$	32.1359	1.30221
$610$	0	0
$611$	−6.97367	−0.282124
$612$	7.16228i	0.289518i
$613$	− 23.2982i	− 0.941006i	−0.882398	−	0.470503i	$-0.844072\pi$
$613$	− 23.2982i	− 0.941006i	0.882398	−	0.470503i	$-0.155928\pi$
$614$	−32.4868	−1.31106
$615$	0	0
$616$	6.83772	0.275500
$617$	− 24.3246i	− 0.979270i	−0.871928	−	0.489635i	$-0.837130\pi$
$617$	− 24.3246i	− 0.979270i	0.871928	−	0.489635i	$-0.162870\pi$
$618$	− 9.64911i	− 0.388144i
$619$	−17.1623	−0.689810	−0.344905	−	0.938638i	$-0.612089\pi$
$619$	−17.1623	−0.689810	−0.344905	+	0.938638i	$0.612089\pi$
$620$	0	0
$621$	−7.32456	−0.293924
$622$	− 26.0000i	− 1.04251i
$623$	16.8377i	0.674589i
$624$	−1.16228	−0.0465283
$625$	0	0
$626$	−23.3246	−0.932237
$627$	− 2.16228i	− 0.0863531i
$628$	− 5.67544i	− 0.226475i
$629$	−71.6228	−2.85579
$630$	0	0
$631$	−5.29822	−0.210919	−0.105459	−	0.994424i	$-0.533631\pi$
$631$	−5.29822	−0.210919	−0.105459	+	0.994424i	$0.533631\pi$
$632$	7.32456i	0.291355i
$633$	12.8114i	0.509207i
$634$	2.16228	0.0858750
$635$	0	0
$636$	−8.16228	−0.323655
$637$	− 3.48683i	− 0.138153i
$638$	− 21.9737i	− 0.869946i
$639$	5.16228	0.204217
$640$	0	0
$641$	13.2982	0.525248	0.262624	−	0.964898i	$-0.415412\pi$
$641$	13.2982	0.525248	0.262624	+	0.964898i	$0.415412\pi$
$642$	− 19.1623i	− 0.756275i
$643$	18.6491i	0.735449i	0.929935	+	0.367725i	$0.119863\pi$
$643$	18.6491i	0.735449i	−0.929935	+	0.367725i	$0.880137\pi$
$644$	23.1623	0.912722
$645$	0	0
$646$	−7.16228	−0.281796
$647$	− 9.00000i	− 0.353827i	−0.984226	−	0.176913i	$-0.943389\pi$
$647$	− 9.00000i	− 0.353827i	0.984226	−	0.176913i	$-0.0566112\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	24.8377	0.974966
$650$	0	0
$651$	−23.1623	−0.907801
$652$	2.64911i	0.103747i
$653$	30.9737i	1.21209i	0.795429	+	0.606047i	$0.207246\pi$
$653$	30.9737i	1.21209i	−0.795429	+	0.606047i	$0.792754\pi$
$654$	20.3246	0.794753
$655$	0	0
$656$	6.32456	0.246932
$657$	− 1.00000i	− 0.0390137i
$658$	18.9737i	0.739671i
$659$	18.1886	0.708528	0.354264	−	0.935146i	$-0.384731\pi$
$659$	18.1886	0.708528	0.354264	+	0.935146i	$0.384731\pi$
$660$	0	0
$661$	−13.2982	−0.517241	−0.258620	−	0.965979i	$-0.583268\pi$
$661$	−13.2982	−0.517241	−0.258620	+	0.965979i	$0.583268\pi$
$662$	− 34.8114i	− 1.35298i
$663$	− 8.32456i	− 0.323299i
$664$	12.4868	0.484583
$665$	0	0
$666$	10.0000	0.387492
$667$	− 74.4342i	− 2.88210i
$668$	22.6491i	0.876320i
$669$	−0.350889	−0.0135662
$670$	0	0
$671$	−4.67544	−0.180494
$672$	3.16228i	0.121988i
$673$	− 24.4605i	− 0.942883i	−0.881897	−	0.471441i	$-0.843734\pi$
$673$	− 24.4605i	− 0.942883i	0.881897	−	0.471441i	$-0.156266\pi$
$674$	−34.9737	−1.34714
$675$	0	0
$676$	−11.6491	−0.448043
$677$	− 0.486833i	− 0.0187105i	−0.999956	−	0.00935526i	$-0.997022\pi$
$677$	− 0.486833i	− 0.0187105i	0.999956	−	0.00935526i	$-0.00297791\pi$
$678$	− 15.6491i	− 0.601000i
$679$	61.6228	2.36487
$680$	0	0
$681$	2.00000	0.0766402
$682$	15.8377i	0.606458i
$683$	− 45.1096i	− 1.72607i	−0.505143	−	0.863036i	$-0.668560\pi$
$683$	− 45.1096i	− 1.72607i	0.505143	−	0.863036i	$-0.331440\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	12.6491	0.482945
$687$	− 1.83772i	− 0.0701135i
$688$	2.83772i	0.108187i
$689$	9.48683	0.361420
$690$	0	0
$691$	−5.48683	−0.208729	−0.104364	−	0.994539i	$-0.533281\pi$
$691$	−5.48683	−0.208729	−0.104364	+	0.994539i	$0.533281\pi$
$692$	4.16228i	0.158226i
$693$	− 6.83772i	− 0.259744i
$694$	20.0000	0.759190
$695$	0	0
$696$	10.1623	0.385200
$697$	45.2982i	1.71579i
$698$	24.1623i	0.914556i
$699$	19.8114	0.749336
$700$	0	0
$701$	6.97367	0.263392	0.131696	−	0.991290i	$-0.457958\pi$
$701$	6.97367	0.263392	0.131696	+	0.991290i	$0.457958\pi$
$702$	1.16228i	0.0438673i
$703$	10.0000i	0.377157i
$704$	2.16228	0.0814939
$705$	0	0
$706$	−7.81139	−0.293985
$707$	− 56.3246i	− 2.11830i
$708$	11.4868i	0.431702i
$709$	−42.4868	−1.59563	−0.797813	−	0.602905i	$-0.794010\pi$
$709$	−42.4868	−1.59563	−0.797813	+	0.602905i	$0.794010\pi$
$710$	0	0
$711$	7.32456	0.274692
$712$	5.32456i	0.199546i
$713$	53.6491i	2.00917i
$714$	−22.6491	−0.847622
$715$	0	0
$716$	4.64911	0.173745
$717$	11.6754i	0.436027i
$718$	24.3246i	0.907784i
$719$	−6.67544	−0.248952	−0.124476	−	0.992223i	$-0.539725\pi$
$719$	−6.67544	−0.248952	−0.124476	+	0.992223i	$0.539725\pi$
$720$	0	0
$721$	30.5132	1.13637
$722$	1.00000i	0.0372161i
$723$	29.4868i	1.09663i
$724$	−2.83772	−0.105463
$725$	0	0
$726$	6.32456	0.234726
$727$	13.6228i	0.505241i	0.967565	+	0.252620i	$0.0812924\pi$
$727$	13.6228i	0.505241i	−0.967565	+	0.252620i	$0.918708\pi$
$728$	− 3.67544i	− 0.136221i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−20.3246	−0.751731
$732$	− 2.16228i	− 0.0799201i
$733$	− 31.5132i	− 1.16397i	−0.813201	−	0.581983i	$-0.802277\pi$
$733$	− 31.5132i	− 1.16397i	0.813201	−	0.581983i	$-0.197723\pi$
$734$	−11.4868	−0.423987
$735$	0	0
$736$	7.32456	0.269987
$737$	− 27.0000i	− 0.994558i
$738$	− 6.32456i	− 0.232810i
$739$	6.32456	0.232653	0.116326	−	0.993211i	$-0.462888\pi$
$739$	6.32456	0.232653	0.116326	+	0.993211i	$0.462888\pi$
$740$	0	0
$741$	−1.16228	−0.0426973
$742$	− 25.8114i	− 0.947566i
$743$	20.6491i	0.757542i	0.925490	+	0.378771i	$0.123653\pi$
$743$	20.6491i	0.757542i	−0.925490	+	0.378771i	$0.876347\pi$
$744$	−7.32456	−0.268531
$745$	0	0
$746$	28.1359	1.03013
$747$	− 12.4868i	− 0.456869i
$748$	15.4868i	0.566255i
$749$	60.5964	2.21415
$750$	0	0
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	6.00000i	0.218797i
$753$	14.6491i	0.533843i
$754$	−11.8114	−0.430145
$755$	0	0
$756$	3.16228	0.115011
$757$	− 49.1359i	− 1.78588i	−0.450179	−	0.892938i	$-0.648640\pi$
$757$	− 49.1359i	− 1.78588i	0.450179	−	0.892938i	$-0.351360\pi$
$758$	14.9737i	0.543868i
$759$	−15.8377	−0.574873
$760$	0	0
$761$	−20.5132	−0.743602	−0.371801	−	0.928313i	$-0.621260\pi$
$761$	−20.5132	−0.743602	−0.371801	+	0.928313i	$0.621260\pi$
$762$	9.64911i	0.349550i
$763$	64.2719i	2.32680i
$764$	3.64911	0.132020
$765$	0	0
$766$	15.4868	0.559562
$767$	− 13.3509i	− 0.482073i
$768$	1.00000i	0.0360844i
$769$	−47.3246	−1.70657	−0.853284	−	0.521447i	$-0.825392\pi$
$769$	−47.3246	−1.70657	−0.853284	+	0.521447i	$0.825392\pi$
$770$	0	0
$771$	6.67544	0.240410
$772$	− 2.83772i	− 0.102132i
$773$	28.9737i	1.04211i	0.853523	+	0.521055i	$0.174461\pi$
$773$	28.9737i	1.04211i	−0.853523	+	0.521055i	$0.825539\pi$
$774$	2.83772	0.102000
$775$	0	0
$776$	19.4868	0.699537
$777$	31.6228i	1.13446i
$778$	9.35089i	0.335246i
$779$	6.32456	0.226601
$780$	0	0
$781$	11.1623	0.399418
$782$	52.4605i	1.87598i
$783$	− 10.1623i	− 0.363170i
$784$	−3.00000	−0.107143
$785$	0	0
$786$	−6.48683	−0.231378
$787$	15.5132i	0.552985i	0.961016	+	0.276492i	$0.0891720\pi$
$787$	15.5132i	0.552985i	−0.961016	+	0.276492i	$0.910828\pi$
$788$	− 20.1359i	− 0.717313i
$789$	−5.97367	−0.212668
$790$	0	0
$791$	49.4868	1.75955
$792$	− 2.16228i	− 0.0768332i
$793$	2.51317i	0.0892452i
$794$	27.1359	0.963019
$795$	0	0
$796$	6.64911	0.235671
$797$	− 15.6228i	− 0.553387i	−0.960958	−	0.276694i	$-0.910761\pi$
$797$	− 15.6228i	− 0.553387i	0.960958	−	0.276694i	$-0.0892387\pi$
$798$	3.16228i	0.111943i
$799$	−42.9737	−1.52030
$800$	0	0
$801$	5.32456	0.188134
$802$	− 11.6491i	− 0.411344i
$803$	− 2.16228i	− 0.0763051i
$804$	12.4868	0.440377
$805$	0	0
$806$	8.51317	0.299864
$807$	0.324555i	0.0114249i
$808$	− 17.8114i	− 0.626602i
$809$	16.8377	0.591983	0.295991	−	0.955191i	$-0.404350\pi$
$809$	16.8377	0.591983	0.295991	+	0.955191i	$0.404350\pi$
$810$	0	0
$811$	42.8114	1.50331	0.751656	−	0.659556i	$-0.229256\pi$
$811$	42.8114	1.50331	0.751656	+	0.659556i	$0.229256\pi$
$812$	32.1359i	1.12775i
$813$	5.16228i	0.181049i
$814$	21.6228	0.757878
$815$	0	0
$816$	−7.16228	−0.250730
$817$	2.83772i	0.0992793i
$818$	20.3246i	0.710631i
$819$	−3.67544	−0.128430
$820$	0	0
$821$	43.1623	1.50637	0.753187	−	0.657807i	$-0.228516\pi$
$821$	43.1623	1.50637	0.753187	+	0.657807i	$0.228516\pi$
$822$	10.3246i	0.360110i
$823$	− 23.2982i	− 0.812125i	−0.913845	−	0.406062i	$-0.866902\pi$
$823$	− 23.2982i	− 0.812125i	0.913845	−	0.406062i	$-0.133098\pi$
$824$	9.64911	0.336143
$825$	0	0
$826$	−36.3246	−1.26389
$827$	− 1.16228i	− 0.0404164i	−0.999796	−	0.0202082i	$-0.993567\pi$
$827$	− 1.16228i	− 0.0404164i	0.999796	−	0.0202082i	$-0.00643290\pi$
$828$	− 7.32456i	− 0.254546i
$829$	−46.7851	−1.62491	−0.812456	−	0.583022i	$-0.801870\pi$
$829$	−46.7851	−1.62491	−0.812456	+	0.583022i	$0.801870\pi$
$830$	0	0
$831$	6.81139	0.236284
$832$	− 1.16228i	− 0.0402947i
$833$	− 21.4868i	− 0.744475i
$834$	2.51317	0.0870239
$835$	0	0
$836$	2.16228	0.0747839
$837$	7.32456i	0.253174i
$838$	− 8.00000i	− 0.276355i
$839$	19.1623	0.661555	0.330778	−	0.943709i	$-0.392689\pi$
$839$	19.1623	0.661555	0.330778	+	0.943709i	$0.392689\pi$
$840$	0	0
$841$	74.2719	2.56110
$842$	− 6.64911i	− 0.229143i
$843$	− 17.6491i	− 0.607868i
$844$	−12.8114	−0.440986
$845$	0	0
$846$	6.00000	0.206284
$847$	20.0000i	0.687208i
$848$	− 8.16228i	− 0.280294i
$849$	−0.649111	−0.0222774
$850$	0	0
$851$	73.2456	2.51083
$852$	5.16228i	0.176857i
$853$	− 19.6754i	− 0.673674i	−0.941563	−	0.336837i	$-0.890643\pi$
$853$	− 19.6754i	− 0.673674i	0.941563	−	0.336837i	$-0.109357\pi$
$854$	6.83772	0.233982
$855$	0	0
$856$	19.1623	0.654953
$857$	38.3246i	1.30914i	0.756001	+	0.654571i	$0.227151\pi$
$857$	38.3246i	1.30914i	−0.756001	+	0.654571i	$0.772849\pi$
$858$	2.51317i	0.0857981i
$859$	30.6491	1.04573	0.522867	−	0.852414i	$-0.324862\pi$
$859$	30.6491	1.04573	0.522867	+	0.852414i	$0.324862\pi$
$860$	0	0
$861$	20.0000	0.681598
$862$	12.3246i	0.419776i
$863$	− 17.0263i	− 0.579583i	−0.957090	−	0.289792i	$-0.906414\pi$
$863$	− 17.0263i	− 0.579583i	0.957090	−	0.289792i	$-0.0935860\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−16.1359	−0.548322
$867$	− 34.2982i	− 1.16483i
$868$	− 23.1623i	− 0.786179i
$869$	15.8377	0.537258
$870$	0	0
$871$	−14.5132	−0.491760
$872$	20.3246i	0.688276i
$873$	− 19.4868i	− 0.659529i
$874$	7.32456	0.247757
$875$	0	0
$876$	1.00000	0.0337869
$877$	− 17.6228i	− 0.595079i	−0.954710	−	0.297539i	$-0.903834\pi$
$877$	− 17.6228i	− 0.595079i	0.954710	−	0.297539i	$-0.0961660\pi$
$878$	11.6491i	0.393138i
$879$	−2.48683	−0.0838788
$880$	0	0
$881$	1.67544	0.0564472	0.0282236	−	0.999602i	$-0.491015\pi$
$881$	1.67544	0.0564472	0.0282236	+	0.999602i	$0.491015\pi$
$882$	3.00000i	0.101015i
$883$	10.5132i	0.353796i	0.984229	+	0.176898i	$0.0566063\pi$
$883$	10.5132i	0.353796i	−0.984229	+	0.176898i	$0.943394\pi$
$884$	8.32456	0.279985
$885$	0	0
$886$	−18.1623	−0.610174
$887$	34.3246i	1.15251i	0.817271	+	0.576253i	$0.195486\pi$
$887$	34.3246i	1.15251i	−0.817271	+	0.576253i	$0.804514\pi$
$888$	10.0000i	0.335578i
$889$	−30.5132	−1.02338
$890$	0	0
$891$	−2.16228	−0.0724390
$892$	− 0.350889i	− 0.0117486i
$893$	6.00000i	0.200782i
$894$	−8.64911	−0.289270
$895$	0	0
$896$	−3.16228	−0.105644
$897$	8.51317i	0.284246i
$898$	11.0000i	0.367075i
$899$	−74.4342	−2.48252
$900$	0	0
$901$	58.4605	1.94760
$902$	− 13.6754i	− 0.455343i
$903$	8.97367i	0.298625i
$904$	15.6491	0.520482
$905$	0	0
$906$	10.0000	0.332228
$907$	− 13.3509i	− 0.443309i	−0.975125	−	0.221655i	$-0.928854\pi$
$907$	− 13.3509i	− 0.443309i	0.975125	−	0.221655i	$-0.0711457\pi$
$908$	2.00000i	0.0663723i
$909$	−17.8114	−0.590766
$910$	0	0
$911$	−44.9737	−1.49004	−0.745022	−	0.667040i	$-0.767561\pi$
$911$	−44.9737	−1.49004	−0.745022	+	0.667040i	$0.767561\pi$
$912$	1.00000i	0.0331133i
$913$	− 27.0000i	− 0.893570i
$914$	−22.3246	−0.738431
$915$	0	0
$916$	1.83772	0.0607201
$917$	− 20.5132i	− 0.677404i
$918$	7.16228i	0.236390i
$919$	25.1623	0.830027	0.415013	−	0.909815i	$-0.363777\pi$
$919$	25.1623	0.830027	0.415013	+	0.909815i	$0.363777\pi$
$920$	0	0
$921$	−32.4868	−1.07048
$922$	12.0000i	0.395199i
$923$	− 6.00000i	− 0.197492i
$924$	6.83772	0.224945
$925$	0	0
$926$	−34.3246	−1.12797
$927$	− 9.64911i	− 0.316918i
$928$	10.1623i	0.333593i
$929$	−13.2982	−0.436300	−0.218150	−	0.975915i	$-0.570002\pi$
$929$	−13.2982	−0.436300	−0.218150	+	0.975915i	$0.570002\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	19.8114i	0.648944i
$933$	− 26.0000i	− 0.851202i
$934$	−7.13594	−0.233495
$935$	0	0
$936$	−1.16228	−0.0379902
$937$	− 1.35089i	− 0.0441316i	−0.999757	−	0.0220658i	$-0.992976\pi$
$937$	− 1.35089i	− 0.0441316i	0.999757	−	0.0220658i	$-0.00702434\pi$
$938$	39.4868i	1.28929i
$939$	−23.3246	−0.761168
$940$	0	0
$941$	1.18861	0.0387476	0.0193738	−	0.999812i	$-0.493833\pi$
$941$	1.18861	0.0387476	0.0193738	+	0.999812i	$0.493833\pi$
$942$	− 5.67544i	− 0.184916i
$943$	− 46.3246i	− 1.50854i
$944$	−11.4868	−0.373865
$945$	0	0
$946$	6.13594	0.199497
$947$	− 48.0000i	− 1.55979i	−0.625910	−	0.779895i	$-0.715272\pi$
$947$	− 48.0000i	− 1.55979i	0.625910	−	0.779895i	$-0.284728\pi$
$948$	7.32456i	0.237890i
$949$	−1.16228	−0.0377291
$950$	0	0
$951$	2.16228	0.0701167
$952$	− 22.6491i	− 0.734062i
$953$	53.3246i	1.72735i	0.504048	+	0.863676i	$0.331844\pi$
$953$	53.3246i	1.72735i	−0.504048	+	0.863676i	$0.668156\pi$
$954$	−8.16228	−0.264263
$955$	0	0
$956$	−11.6754	−0.377611
$957$	− 21.9737i	− 0.710308i
$958$	2.02633i	0.0654679i
$959$	−32.6491	−1.05429
$960$	0	0
$961$	22.6491	0.730616
$962$	− 11.6228i	− 0.374733i
$963$	− 19.1623i	− 0.617496i
$964$	−29.4868	−0.949707
$965$	0	0
$966$	23.1623	0.745234
$967$	11.6754i	0.375457i	0.982221	+	0.187728i	$0.0601125\pi$
$967$	11.6754i	0.375457i	−0.982221	+	0.187728i	$0.939887\pi$
$968$	6.32456i	0.203279i
$969$	−7.16228	−0.230086
$970$	0	0
$971$	31.4868	1.01046	0.505230	−	0.862985i	$-0.331408\pi$
$971$	31.4868	1.01046	0.505230	+	0.862985i	$0.331408\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	7.94733i	0.254780i
$974$	3.35089	0.107369
$975$	0	0
$976$	2.16228	0.0692128
$977$	21.9473i	0.702157i	0.936346	+	0.351079i	$0.114185\pi$
$977$	21.9473i	0.702157i	−0.936346	+	0.351079i	$0.885815\pi$
$978$	2.64911i	0.0847092i
$979$	11.5132	0.367962
$980$	0	0
$981$	20.3246	0.648913
$982$	0	0
$983$	− 8.13594i	− 0.259496i	−0.991547	−	0.129748i	$-0.958583\pi$
$983$	− 8.13594i	− 0.259496i	0.991547	−	0.129748i	$-0.0414169\pi$
$984$	6.32456	0.201619
$985$	0	0
$986$	−72.7851	−2.31795
$987$	18.9737i	0.603938i
$988$	− 1.16228i	− 0.0369770i
$989$	20.7851	0.660926
$990$	0	0
$991$	−26.2982	−0.835391	−0.417695	−	0.908587i	$-0.637162\pi$
$991$	−26.2982	−0.835391	−0.417695	+	0.908587i	$0.637162\pi$
$992$	− 7.32456i	− 0.232555i
$993$	− 34.8114i	− 1.10471i
$994$	−16.3246	−0.517783
$995$	0	0
$996$	12.4868	0.395660
$997$	32.4868i	1.02887i	0.857530	+	0.514434i	$0.171998\pi$
$997$	32.4868i	1.02887i	−0.857530	+	0.514434i	$0.828002\pi$
$998$	− 25.8114i	− 0.817045i
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.d.v.799.3		4
5.2	odd	4		2850.2.a.bf.1.2	✓	2
5.3	odd	4		2850.2.a.bg.1.1	yes	2
5.4	even	2	inner	2850.2.d.v.799.2		4
15.2	even	4		8550.2.a.ca.1.2		2
15.8	even	4		8550.2.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bf.1.2	✓	2	5.2	odd	4
2850.2.a.bg.1.1	yes	2	5.3	odd	4
2850.2.d.v.799.2		4	5.4	even	2	inner
2850.2.d.v.799.3		4	1.1	even	1	trivial
8550.2.a.bq.1.1		2	15.8	even	4
8550.2.a.ca.1.2		2	15.2	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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.16228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.16228i q^{7} -1.00000i q^{8} -1.00000 q^{9} -2.16228 q^{11} -1.00000i q^{12} +1.16228i q^{13} +3.16228 q^{14} +1.00000 q^{16} +7.16228i q^{17} -1.00000i q^{18} +1.00000 q^{19} +3.16228 q^{21} -2.16228i q^{22} -7.32456i q^{23} +1.00000 q^{24} -1.16228 q^{26} -1.00000i q^{27} +3.16228i q^{28} +10.1623 q^{29} -7.32456 q^{31} +1.00000i q^{32} -2.16228i q^{33} -7.16228 q^{34} +1.00000 q^{36} +10.0000i q^{37} +1.00000i q^{38} -1.16228 q^{39} +6.32456 q^{41} +3.16228i q^{42} +2.83772i q^{43} +2.16228 q^{44} +7.32456 q^{46} +6.00000i q^{47} +1.00000i q^{48} -3.00000 q^{49} -7.16228 q^{51} -1.16228i q^{52} -8.16228i q^{53} +1.00000 q^{54} -3.16228 q^{56} +1.00000i q^{57} +10.1623i q^{58} -11.4868 q^{59} +2.16228 q^{61} -7.32456i q^{62} +3.16228i q^{63} -1.00000 q^{64} +2.16228 q^{66} +12.4868i q^{67} -7.16228i q^{68} +7.32456 q^{69} -5.16228 q^{71} +1.00000i q^{72} +1.00000i q^{73} -10.0000 q^{74} -1.00000 q^{76} +6.83772i q^{77} -1.16228i q^{78} -7.32456 q^{79} +1.00000 q^{81} +6.32456i q^{82} +12.4868i q^{83} -3.16228 q^{84} -2.83772 q^{86} +10.1623i q^{87} +2.16228i q^{88} -5.32456 q^{89} +3.67544 q^{91} +7.32456i q^{92} -7.32456i q^{93} -6.00000 q^{94} -1.00000 q^{96} +19.4868i q^{97} -3.00000i q^{98} +2.16228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{16} + 4 q^{19} + 4 q^{24} + 8 q^{26} + 28 q^{29} - 4 q^{31} - 16 q^{34} + 4 q^{36} + 8 q^{39} - 4 q^{44} + 4 q^{46} - 12 q^{49} - 16 q^{51} + 4 q^{54} - 8 q^{59} - 4 q^{61} - 4 q^{64} - 4 q^{66} + 4 q^{69} - 8 q^{71} - 40 q^{74} - 4 q^{76} - 4 q^{79} + 4 q^{81} - 24 q^{86} + 4 q^{89} + 40 q^{91} - 24 q^{94} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^16 + 4 * q^19 + 4 * q^24 + 8 * q^26 + 28 * q^29 - 4 * q^31 - 16 * q^34 + 4 * q^36 + 8 * q^39 - 4 * q^44 + 4 * q^46 - 12 * q^49 - 16 * q^51 + 4 * q^54 - 8 * q^59 - 4 * q^61 - 4 * q^64 - 4 * q^66 + 4 * q^69 - 8 * q^71 - 40 * q^74 - 4 * q^76 - 4 * q^79 + 4 * q^81 - 24 * q^86 + 4 * q^89 + 40 * q^91 - 24 * q^94 - 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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