LMFDB - Embedded newform 175.6.b.b.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,6,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	175.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:	$28.0671684673$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.6.b.b.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000i q^{2} -1.00000i q^{3} -32.0000 q^{4} -8.00000 q^{6} +49.0000i q^{7} +242.000 q^{9} +O(q^{10})$	\(q-8.00000i q^{2} -1.00000i q^{3} -32.0000 q^{4} -8.00000 q^{6} +49.0000i q^{7} +242.000 q^{9} -453.000 q^{11} +32.0000i q^{12} +969.000i q^{13} +392.000 q^{14} -1024.00 q^{16} +1637.00i q^{17} -1936.00i q^{18} +1550.00 q^{19} +49.0000 q^{21} +3624.00i q^{22} +1654.00i q^{23} +7752.00 q^{26} -485.000i q^{27} -1568.00i q^{28} +4985.00 q^{29} +1192.00 q^{31} +8192.00i q^{32} +453.000i q^{33} +13096.0 q^{34} -7744.00 q^{36} -11018.0i q^{37} -12400.0i q^{38} +969.000 q^{39} -1728.00 q^{41} -392.000i q^{42} +10814.0i q^{43} +14496.0 q^{44} +13232.0 q^{46} +26237.0i q^{47} +1024.00i q^{48} -2401.00 q^{49} +1637.00 q^{51} -31008.0i q^{52} -25936.0i q^{53} -3880.00 q^{54} -1550.00i q^{57} -39880.0i q^{58} +4580.00 q^{59} -12488.0 q^{61} -9536.00i q^{62} +11858.0i q^{63} +32768.0 q^{64} +3624.00 q^{66} -15848.0i q^{67} -52384.0i q^{68} +1654.00 q^{69} +51792.0 q^{71} -4846.00i q^{73} -88144.0 q^{74} -49600.0 q^{76} -22197.0i q^{77} -7752.00i q^{78} -62765.0 q^{79} +58321.0 q^{81} +13824.0i q^{82} +23644.0i q^{83} -1568.00 q^{84} +86512.0 q^{86} -4985.00i q^{87} +147300. q^{89} -47481.0 q^{91} -52928.0i q^{92} -1192.00i q^{93} +209896. q^{94} +8192.00 q^{96} -8343.00i q^{97} +19208.0i q^{98} -109626. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 64 q^{4} - 16 q^{6} + 484 q^{9}+O(q^{10}) $ 2 * q - 64 * q^4 - 16 * q^6 + 484 * q^9	$ 2 q - 64 q^{4} - 16 q^{6} + 484 q^{9} - 906 q^{11} + 784 q^{14} - 2048 q^{16} + 3100 q^{19} + 98 q^{21} + 15504 q^{26} + 9970 q^{29} + 2384 q^{31} + 26192 q^{34} - 15488 q^{36} + 1938 q^{39} - 3456 q^{41} + 28992 q^{44} + 26464 q^{46} - 4802 q^{49} + 3274 q^{51} - 7760 q^{54} + 9160 q^{59} - 24976 q^{61} + 65536 q^{64} + 7248 q^{66} + 3308 q^{69} + 103584 q^{71} - 176288 q^{74} - 99200 q^{76} - 125530 q^{79} + 116642 q^{81} - 3136 q^{84} + 173024 q^{86} + 294600 q^{89} - 94962 q^{91} + 419792 q^{94} + 16384 q^{96} - 219252 q^{99}+O(q^{100}) $ 2 * q - 64 * q^4 - 16 * q^6 + 484 * q^9 - 906 * q^11 + 784 * q^14 - 2048 * q^16 + 3100 * q^19 + 98 * q^21 + 15504 * q^26 + 9970 * q^29 + 2384 * q^31 + 26192 * q^34 - 15488 * q^36 + 1938 * q^39 - 3456 * q^41 + 28992 * q^44 + 26464 * q^46 - 4802 * q^49 + 3274 * q^51 - 7760 * q^54 + 9160 * q^59 - 24976 * q^61 + 65536 * q^64 + 7248 * q^66 + 3308 * q^69 + 103584 * q^71 - 176288 * q^74 - 99200 * q^76 - 125530 * q^79 + 116642 * q^81 - 3136 * q^84 + 173024 * q^86 + 294600 * q^89 - 94962 * q^91 + 419792 * q^94 + 16384 * q^96 - 219252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 8.00000i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	− 8.00000i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$3$	− 1.00000i	− 0.0641500i	−0.999485	−	0.0320750i	$-0.989788\pi$
$3$	− 1.00000i	− 0.0641500i	0.999485	−	0.0320750i	$-0.0102115\pi$
$4$	−32.0000	−1.00000
$5$	0	0
$5$	0	0
$6$	−8.00000	−0.0907218
$7$	49.0000i	0.377964i
$7$	49.0000i	0.377964i
$8$	0	0
$9$	242.000	0.995885
$10$	0	0
$11$	−453.000	−1.12880	−0.564399	−	0.825502i	$-0.690892\pi$
$11$	−453.000	−1.12880	−0.564399	+	0.825502i	$0.690892\pi$
$12$	32.0000i	0.0641500i
$13$	969.000i	1.59025i	0.606446	+	0.795125i	$0.292595\pi$
$13$	969.000i	1.59025i	−0.606446	+	0.795125i	$0.707405\pi$
$14$	392.000	0.534522
$15$	0	0
$16$	−1024.00	−1.00000
$17$	1637.00i	1.37381i	0.726748	+	0.686905i	$0.241031\pi$
$17$	1637.00i	1.37381i	−0.726748	+	0.686905i	$0.758969\pi$
$18$	− 1936.00i	− 1.40839i
$19$	1550.00	0.985026	0.492513	−	0.870305i	$-0.336078\pi$
$19$	1550.00	0.985026	0.492513	+	0.870305i	$0.336078\pi$
$20$	0	0
$21$	49.0000	0.0242464
$22$	3624.00i	1.59636i
$23$	1654.00i	0.651952i	0.945378	+	0.325976i	$0.105693\pi$
$23$	1654.00i	0.651952i	−0.945378	+	0.325976i	$0.894307\pi$
$24$	0	0
$25$	0	0
$26$	7752.00	2.24895
$27$	− 485.000i	− 0.128036i
$28$	− 1568.00i	− 0.377964i
$29$	4985.00	1.10070	0.550352	−	0.834933i	$-0.314494\pi$
$29$	4985.00	1.10070	0.550352	+	0.834933i	$0.314494\pi$
$30$	0	0
$31$	1192.00	0.222778	0.111389	−	0.993777i	$-0.464470\pi$
$31$	1192.00	0.222778	0.111389	+	0.993777i	$0.464470\pi$
$32$	8192.00i	1.41421i
$33$	453.000i	0.0724125i
$34$	13096.0	1.94286
$35$	0	0
$36$	−7744.00	−0.995885
$37$	− 11018.0i	− 1.32312i	−0.749893	−	0.661559i	$-0.769895\pi$
$37$	− 11018.0i	− 1.32312i	0.749893	−	0.661559i	$-0.230105\pi$
$38$	− 12400.0i	− 1.39304i
$39$	969.000	0.102015
$40$	0	0
$41$	−1728.00	−0.160540	−0.0802702	−	0.996773i	$-0.525578\pi$
$41$	−1728.00	−0.160540	−0.0802702	+	0.996773i	$0.525578\pi$
$42$	− 392.000i	− 0.0342896i
$43$	10814.0i	0.891898i	0.895058	+	0.445949i	$0.147134\pi$
$43$	10814.0i	0.891898i	−0.895058	+	0.445949i	$0.852866\pi$
$44$	14496.0	1.12880
$45$	0	0
$46$	13232.0	0.922000
$47$	26237.0i	1.73249i	0.499624	+	0.866243i	$0.333472\pi$
$47$	26237.0i	1.73249i	−0.499624	+	0.866243i	$0.666528\pi$
$48$	1024.00i	0.0641500i
$49$	−2401.00	−0.142857
$50$	0	0
$51$	1637.00	0.0881299
$52$	− 31008.0i	− 1.59025i
$53$	− 25936.0i	− 1.26827i	−0.773220	−	0.634137i	$-0.781355\pi$
$53$	− 25936.0i	− 1.26827i	0.773220	−	0.634137i	$-0.218645\pi$
$54$	−3880.00	−0.181070
$55$	0	0
$56$	0	0
$57$	− 1550.00i	− 0.0631894i
$58$	− 39880.0i	− 1.55663i
$59$	4580.00	0.171291	0.0856457	−	0.996326i	$-0.472705\pi$
$59$	4580.00	0.171291	0.0856457	+	0.996326i	$0.472705\pi$
$60$	0	0
$61$	−12488.0	−0.429703	−0.214851	−	0.976647i	$-0.568927\pi$
$61$	−12488.0	−0.429703	−0.214851	+	0.976647i	$0.568927\pi$
$62$	− 9536.00i	− 0.315055i
$63$	11858.0i	0.376409i
$64$	32768.0	1.00000
$65$	0	0
$66$	3624.00	0.102407
$67$	− 15848.0i	− 0.431308i	−0.976470	−	0.215654i	$-0.930812\pi$
$67$	− 15848.0i	− 0.431308i	0.976470	−	0.215654i	$-0.0691883\pi$
$68$	− 52384.0i	− 1.37381i
$69$	1654.00	0.0418228
$70$	0	0
$71$	51792.0	1.21932	0.609659	−	0.792664i	$-0.291306\pi$
$71$	51792.0	1.21932	0.609659	+	0.792664i	$0.291306\pi$
$72$	0	0
$73$	− 4846.00i	− 0.106433i	−0.998583	−	0.0532165i	$-0.983053\pi$
$73$	− 4846.00i	− 0.106433i	0.998583	−	0.0532165i	$-0.0169473\pi$
$74$	−88144.0	−1.87117
$75$	0	0
$76$	−49600.0	−0.985026
$77$	− 22197.0i	− 0.426646i
$78$	− 7752.00i	− 0.144270i
$79$	−62765.0	−1.13149	−0.565744	−	0.824581i	$-0.691411\pi$
$79$	−62765.0	−1.13149	−0.565744	+	0.824581i	$0.691411\pi$
$80$	0	0
$81$	58321.0	0.987671
$82$	13824.0i	0.227038i
$83$	23644.0i	0.376726i	0.982099	+	0.188363i	$0.0603182\pi$
$83$	23644.0i	0.376726i	−0.982099	+	0.188363i	$0.939682\pi$
$84$	−1568.00	−0.0242464
$85$	0	0
$86$	86512.0	1.26133
$87$	− 4985.00i	− 0.0706101i
$88$	0	0
$89$	147300.	1.97119	0.985593	−	0.169133i	$-0.0540967\pi$
$89$	147300.	1.97119	0.985593	+	0.169133i	$0.0540967\pi$
$90$	0	0
$91$	−47481.0	−0.601058
$92$	− 52928.0i	− 0.651952i
$93$	− 1192.00i	− 0.0142912i
$94$	209896.	2.45010
$95$	0	0
$96$	8192.00	0.0907218
$97$	− 8343.00i	− 0.0900312i	−0.998986	−	0.0450156i	$-0.985666\pi$
$97$	− 8343.00i	− 0.0900312i	0.998986	−	0.0450156i	$-0.0143337\pi$
$98$	19208.0i	0.202031i
$99$	−109626.	−1.12415
$100$	0	0
$101$	−11878.0	−0.115862	−0.0579308	−	0.998321i	$-0.518450\pi$
$101$	−11878.0	−0.115862	−0.0579308	+	0.998321i	$0.518450\pi$
$102$	− 13096.0i	− 0.124634i
$103$	132439.i	1.23005i	0.788508	+	0.615025i	$0.210854\pi$
$103$	132439.i	1.23005i	−0.788508	+	0.615025i	$0.789146\pi$
$104$	0	0
$105$	0	0
$106$	−207488.	−1.79361
$107$	136842.i	1.15547i	0.816223	+	0.577737i	$0.196064\pi$
$107$	136842.i	1.15547i	−0.816223	+	0.577737i	$0.803936\pi$
$108$	15520.0i	0.128036i
$109$	−109485.	−0.882650	−0.441325	−	0.897347i	$-0.645491\pi$
$109$	−109485.	−0.882650	−0.441325	+	0.897347i	$0.645491\pi$
$110$	0	0
$111$	−11018.0	−0.0848780
$112$	− 50176.0i	− 0.377964i
$113$	200934.i	1.48033i	0.672428	+	0.740163i	$0.265252\pi$
$113$	200934.i	1.48033i	−0.672428	+	0.740163i	$0.734748\pi$
$114$	−12400.0	−0.0893634
$115$	0	0
$116$	−159520.	−1.10070
$117$	234498.i	1.58371i
$118$	− 36640.0i	− 0.242243i
$119$	−80213.0	−0.519251
$120$	0	0
$121$	44158.0	0.274186
$122$	99904.0i	0.607692i
$123$	1728.00i	0.0102987i
$124$	−38144.0	−0.222778
$125$	0	0
$126$	94864.0	0.532323
$127$	330692.i	1.81934i	0.415329	+	0.909671i	$0.363666\pi$
$127$	330692.i	1.81934i	−0.415329	+	0.909671i	$0.636334\pi$
$128$	0	0
$129$	10814.0	0.0572153
$130$	0	0
$131$	43982.0	0.223922	0.111961	−	0.993713i	$-0.464287\pi$
$131$	43982.0	0.223922	0.111961	+	0.993713i	$0.464287\pi$
$132$	− 14496.0i	− 0.0724125i
$133$	75950.0i	0.372305i
$134$	−126784.	−0.609962
$135$	0	0
$136$	0	0
$137$	− 99748.0i	− 0.454049i	−0.973889	−	0.227025i	$-0.927100\pi$
$137$	− 99748.0i	− 0.454049i	0.973889	−	0.227025i	$-0.0728998\pi$
$138$	− 13232.0i	− 0.0591463i
$139$	−258930.	−1.13670	−0.568349	−	0.822787i	$-0.692418\pi$
$139$	−258930.	−1.13670	−0.568349	+	0.822787i	$0.692418\pi$
$140$	0	0
$141$	26237.0	0.111139
$142$	− 414336.i	− 1.72438i
$143$	− 438957.i	− 1.79507i
$144$	−247808.	−0.995885
$145$	0	0
$146$	−38768.0	−0.150519
$147$	2401.00i	0.00916429i
$148$	352576.i	1.32312i
$149$	498430.	1.83924	0.919620	−	0.392809i	$-0.128497\pi$
$149$	498430.	1.83924	0.919620	+	0.392809i	$0.128497\pi$
$150$	0	0
$151$	−245803.	−0.877293	−0.438647	−	0.898660i	$-0.644542\pi$
$151$	−245803.	−0.877293	−0.438647	+	0.898660i	$0.644542\pi$
$152$	0	0
$153$	396154.i	1.36816i
$154$	−177576.	−0.603368
$155$	0	0
$156$	−31008.0	−0.102015
$157$	− 85478.0i	− 0.276761i	−0.990379	−	0.138381i	$-0.955810\pi$
$157$	− 85478.0i	− 0.276761i	0.990379	−	0.138381i	$-0.0441897\pi$
$158$	502120.i	1.60017i
$159$	−25936.0	−0.0813599
$160$	0	0
$161$	−81046.0	−0.246415
$162$	− 466568.i	− 1.39678i
$163$	− 193026.i	− 0.569045i	−0.958669	−	0.284523i	$-0.908165\pi$
$163$	− 193026.i	− 0.569045i	0.958669	−	0.284523i	$-0.0918351\pi$
$164$	55296.0	0.160540
$165$	0	0
$166$	189152.	0.532771
$167$	− 157783.i	− 0.437793i	−0.975748	−	0.218897i	$-0.929754\pi$
$167$	− 157783.i	− 0.437793i	0.975748	−	0.218897i	$-0.0702457\pi$
$168$	0	0
$169$	−567668.	−1.52889
$170$	0	0
$171$	375100.	0.980972
$172$	− 346048.i	− 0.891898i
$173$	265659.i	0.674853i	0.941352	+	0.337427i	$0.109556\pi$
$173$	265659.i	0.674853i	−0.941352	+	0.337427i	$0.890444\pi$
$174$	−39880.0	−0.0998578
$175$	0	0
$176$	463872.	1.12880
$177$	− 4580.00i	− 0.0109883i
$178$	− 1.17840e6i	− 2.78768i
$179$	−183660.	−0.428432	−0.214216	−	0.976786i	$-0.568720\pi$
$179$	−183660.	−0.428432	−0.214216	+	0.976786i	$0.568720\pi$
$180$	0	0
$181$	−635048.	−1.44082	−0.720411	−	0.693548i	$-0.756047\pi$
$181$	−635048.	−1.44082	−0.720411	+	0.693548i	$0.756047\pi$
$182$	379848.i	0.850024i
$183$	12488.0i	0.0275655i
$184$	0	0
$185$	0	0
$186$	−9536.00	−0.0202108
$187$	− 741561.i	− 1.55075i
$188$	− 839584.i	− 1.73249i
$189$	23765.0	0.0483931
$190$	0	0
$191$	−226613.	−0.449471	−0.224735	−	0.974420i	$-0.572152\pi$
$191$	−226613.	−0.449471	−0.224735	+	0.974420i	$0.572152\pi$
$192$	− 32768.0i	− 0.0641500i
$193$	− 46476.0i	− 0.0898122i	−0.998991	−	0.0449061i	$-0.985701\pi$
$193$	− 46476.0i	− 0.0898122i	0.998991	−	0.0449061i	$-0.0142989\pi$
$194$	−66744.0	−0.127323
$195$	0	0
$196$	76832.0	0.142857
$197$	204972.i	0.376295i	0.982141	+	0.188148i	$0.0602484\pi$
$197$	204972.i	0.376295i	−0.982141	+	0.188148i	$0.939752\pi$
$198$	877008.i	1.58979i
$199$	953020.	1.70596	0.852981	−	0.521942i	$-0.174792\pi$
$199$	953020.	1.70596	0.852981	+	0.521942i	$0.174792\pi$
$200$	0	0
$201$	−15848.0	−0.0276684
$202$	95024.0i	0.163853i
$203$	244265.i	0.416027i
$204$	−52384.0	−0.0881299
$205$	0	0
$206$	1.05951e6	1.73955
$207$	400268.i	0.649270i
$208$	− 992256.i	− 1.59025i
$209$	−702150.	−1.11190
$210$	0	0
$211$	−223523.	−0.345634	−0.172817	−	0.984954i	$-0.555287\pi$
$211$	−223523.	−0.345634	−0.172817	+	0.984954i	$0.555287\pi$
$212$	829952.i	1.26827i
$213$	− 51792.0i	− 0.0782193i
$214$	1.09474e6	1.63409
$215$	0	0
$216$	0	0
$217$	58408.0i	0.0842021i
$218$	875880.i	1.24826i
$219$	−4846.00	−0.00682768
$220$	0	0
$221$	−1.58625e6	−2.18470
$222$	88144.0i	0.120036i
$223$	− 1.01480e6i	− 1.36653i	−0.730171	−	0.683264i	$-0.760560\pi$
$223$	− 1.01480e6i	− 1.36653i	0.730171	−	0.683264i	$-0.239440\pi$
$224$	−401408.	−0.534522
$225$	0	0
$226$	1.60747e6	2.09350
$227$	999797.i	1.28780i	0.765111	+	0.643898i	$0.222684\pi$
$227$	999797.i	1.28780i	−0.765111	+	0.643898i	$0.777316\pi$
$228$	49600.0i	0.0631894i
$229$	851120.	1.07251	0.536256	−	0.844055i	$-0.319838\pi$
$229$	851120.	1.07251	0.536256	+	0.844055i	$0.319838\pi$
$230$	0	0
$231$	−22197.0	−0.0273693
$232$	0	0
$233$	− 1.09270e6i	− 1.31859i	−0.751885	−	0.659295i	$-0.770855\pi$
$233$	− 1.09270e6i	− 1.31859i	0.751885	−	0.659295i	$-0.229145\pi$
$234$	1.87598e6	2.23970
$235$	0	0
$236$	−146560.	−0.171291
$237$	62765.0i	0.0725850i
$238$	641704.i	0.734332i
$239$	−765905.	−0.867322	−0.433661	−	0.901076i	$-0.642778\pi$
$239$	−765905.	−0.867322	−0.433661	+	0.901076i	$0.642778\pi$
$240$	0	0
$241$	−1.21094e6	−1.34301	−0.671505	−	0.741000i	$-0.734352\pi$
$241$	−1.21094e6	−1.34301	−0.671505	+	0.741000i	$0.734352\pi$
$242$	− 353264.i	− 0.387758i
$243$	− 176176.i	− 0.191395i
$244$	399616.	0.429703
$245$	0	0
$246$	13824.0	0.0145645
$247$	1.50195e6i	1.56644i
$248$	0	0
$249$	23644.0	0.0241670
$250$	0	0
$251$	278262.	0.278785	0.139393	−	0.990237i	$-0.455485\pi$
$251$	278262.	0.278785	0.139393	+	0.990237i	$0.455485\pi$
$252$	− 379456.i	− 0.376409i
$253$	− 749262.i	− 0.735923i
$254$	2.64554e6	2.57294
$255$	0	0
$256$	1.04858e6	1.00000
$257$	− 352998.i	− 0.333380i	−0.986009	−	0.166690i	$-0.946692\pi$
$257$	− 352998.i	− 0.333380i	0.986009	−	0.166690i	$-0.0533079\pi$
$258$	− 86512.0i	− 0.0809146i
$259$	539882.	0.500091
$260$	0	0
$261$	1.20637e6	1.09617
$262$	− 351856.i	− 0.316674i
$263$	1.55809e6i	1.38901i	0.719490	+	0.694503i	$0.244376\pi$
$263$	1.55809e6i	1.38901i	−0.719490	+	0.694503i	$0.755624\pi$
$264$	0	0
$265$	0	0
$266$	607600.	0.526519
$267$	− 147300.i	− 0.126452i
$268$	507136.i	0.431308i
$269$	1.21963e6	1.02766	0.513828	−	0.857893i	$-0.328227\pi$
$269$	1.21963e6	1.02766	0.513828	+	0.857893i	$0.328227\pi$
$270$	0	0
$271$	405792.	0.335645	0.167823	−	0.985817i	$-0.446326\pi$
$271$	405792.	0.335645	0.167823	+	0.985817i	$0.446326\pi$
$272$	− 1.67629e6i	− 1.37381i
$273$	47481.0i	0.0385579i
$274$	−797984.	−0.642122
$275$	0	0
$276$	−52928.0	−0.0418228
$277$	652442.i	0.510908i	0.966821	+	0.255454i	$0.0822249\pi$
$277$	652442.i	0.510908i	−0.966821	+	0.255454i	$0.917775\pi$
$278$	2.07144e6i	1.60753i
$279$	288464.	0.221861
$280$	0	0
$281$	118827.	0.0897737	0.0448869	−	0.998992i	$-0.485707\pi$
$281$	118827.	0.0897737	0.0448869	+	0.998992i	$0.485707\pi$
$282$	− 209896.i	− 0.157174i
$283$	− 1.48801e6i	− 1.10443i	−0.833700	−	0.552217i	$-0.813782\pi$
$283$	− 1.48801e6i	− 1.10443i	0.833700	−	0.552217i	$-0.186218\pi$
$284$	−1.65734e6	−1.21932
$285$	0	0
$286$	−3.51166e6	−2.53862
$287$	− 84672.0i	− 0.0606785i
$288$	1.98246e6i	1.40839i
$289$	−1.25991e6	−0.887351
$290$	0	0
$291$	−8343.00	−0.00577550
$292$	155072.i	0.106433i
$293$	− 1.89580e6i	− 1.29010i	−0.764140	−	0.645050i	$-0.776836\pi$
$293$	− 1.89580e6i	− 1.29010i	0.764140	−	0.645050i	$-0.223164\pi$
$294$	19208.0	0.0129603
$295$	0	0
$296$	0	0
$297$	219705.i	0.144527i
$298$	− 3.98744e6i	− 2.60108i
$299$	−1.60273e6	−1.03677
$300$	0	0
$301$	−529886.	−0.337106
$302$	1.96642e6i	1.24068i
$303$	11878.0i	0.00743253i
$304$	−1.58720e6	−0.985026
$305$	0	0
$306$	3.16923e6	1.93486
$307$	− 821853.i	− 0.497678i	−0.968545	−	0.248839i	$-0.919951\pi$
$307$	− 821853.i	− 0.497678i	0.968545	−	0.248839i	$-0.0800490\pi$
$308$	710304.i	0.426646i
$309$	132439.	0.0789078
$310$	0	0
$311$	−2.09600e6	−1.22882	−0.614412	−	0.788985i	$-0.710607\pi$
$311$	−2.09600e6	−1.22882	−0.614412	+	0.788985i	$0.710607\pi$
$312$	0	0
$313$	− 394571.i	− 0.227648i	−0.993501	−	0.113824i	$-0.963690\pi$
$313$	− 394571.i	− 0.227648i	0.993501	−	0.113824i	$-0.0363100\pi$
$314$	−683824.	−0.391399
$315$	0	0
$316$	2.00848e6	1.13149
$317$	321422.i	0.179650i	0.995958	+	0.0898250i	$0.0286308\pi$
$317$	321422.i	0.179650i	−0.995958	+	0.0898250i	$0.971369\pi$
$318$	207488.i	0.115060i
$319$	−2.25820e6	−1.24247
$320$	0	0
$321$	136842.	0.0741237
$322$	648368.i	0.348483i
$323$	2.53735e6i	1.35324i
$324$	−1.86627e6	−0.987671
$325$	0	0
$326$	−1.54421e6	−0.804752
$327$	109485.i	0.0566220i
$328$	0	0
$329$	−1.28561e6	−0.654818
$330$	0	0
$331$	−2.23259e6	−1.12005	−0.560027	−	0.828475i	$-0.689209\pi$
$331$	−2.23259e6	−1.12005	−0.560027	+	0.828475i	$0.689209\pi$
$332$	− 756608.i	− 0.376726i
$333$	− 2.66636e6i	− 1.31767i
$334$	−1.26226e6	−0.619133
$335$	0	0
$336$	−50176.0	−0.0242464
$337$	− 3.65656e6i	− 1.75387i	−0.480608	−	0.876936i	$-0.659584\pi$
$337$	− 3.65656e6i	− 1.75387i	0.480608	−	0.876936i	$-0.340416\pi$
$338$	4.54134e6i	2.16218i
$339$	200934.	0.0949629
$340$	0	0
$341$	−539976.	−0.251471
$342$	− 3.00080e6i	− 1.38730i
$343$	− 117649.i	− 0.0539949i
$344$	0	0
$345$	0	0
$346$	2.12527e6	0.954386
$347$	− 1.88962e6i	− 0.842462i	−0.906953	−	0.421231i	$-0.861598\pi$
$347$	− 1.88962e6i	− 0.842462i	0.906953	−	0.421231i	$-0.138402\pi$
$348$	159520.i	0.0706101i
$349$	2.69329e6	1.18364	0.591820	−	0.806070i	$-0.298410\pi$
$349$	2.69329e6	1.18364	0.591820	+	0.806070i	$0.298410\pi$
$350$	0	0
$351$	469965.	0.203609
$352$	− 3.71098e6i	− 1.59636i
$353$	1.57468e6i	0.672598i	0.941755	+	0.336299i	$0.109175\pi$
$353$	1.57468e6i	0.672598i	−0.941755	+	0.336299i	$0.890825\pi$
$354$	−36640.0	−0.0155399
$355$	0	0
$356$	−4.71360e6	−1.97119
$357$	80213.0i	0.0333100i
$358$	1.46928e6i	0.605894i
$359$	−4.05576e6	−1.66087	−0.830436	−	0.557114i	$-0.811909\pi$
$359$	−4.05576e6	−1.66087	−0.830436	+	0.557114i	$0.811909\pi$
$360$	0	0
$361$	−73599.0	−0.0297238
$362$	5.08038e6i	2.03763i
$363$	− 44158.0i	− 0.0175891i
$364$	1.51939e6	0.601058
$365$	0	0
$366$	99904.0	0.0389834
$367$	− 4.90628e6i	− 1.90146i	−0.310018	−	0.950731i	$-0.600335\pi$
$367$	− 4.90628e6i	− 1.90146i	0.310018	−	0.950731i	$-0.399665\pi$
$368$	− 1.69370e6i	− 0.651952i
$369$	−418176.	−0.159880
$370$	0	0
$371$	1.27086e6	0.479363
$372$	38144.0i	0.0142912i
$373$	3.45336e6i	1.28520i	0.766202	+	0.642599i	$0.222144\pi$
$373$	3.45336e6i	1.28520i	−0.766202	+	0.642599i	$0.777856\pi$
$374$	−5.93249e6	−2.19310
$375$	0	0
$376$	0	0
$377$	4.83046e6i	1.75039i
$378$	− 190120.i	− 0.0684382i
$379$	4.23466e6	1.51433	0.757165	−	0.653224i	$-0.226584\pi$
$379$	4.23466e6	1.51433	0.757165	+	0.653224i	$0.226584\pi$
$380$	0	0
$381$	330692.	0.116711
$382$	1.81290e6i	0.635648i
$383$	1.86460e6i	0.649516i	0.945797	+	0.324758i	$0.105283\pi$
$383$	1.86460e6i	0.649516i	−0.945797	+	0.324758i	$0.894717\pi$
$384$	0	0
$385$	0	0
$386$	−371808.	−0.127014
$387$	2.61699e6i	0.888228i
$388$	266976.i	0.0900312i
$389$	4.81502e6	1.61333	0.806666	−	0.591008i	$-0.201270\pi$
$389$	4.81502e6	1.61333	0.806666	+	0.591008i	$0.201270\pi$
$390$	0	0
$391$	−2.70760e6	−0.895658
$392$	0	0
$393$	− 43982.0i	− 0.0143646i
$394$	1.63978e6	0.532162
$395$	0	0
$396$	3.50803e6	1.12415
$397$	1.21376e6i	0.386505i	0.981149	+	0.193253i	$0.0619037\pi$
$397$	1.21376e6i	0.386505i	−0.981149	+	0.193253i	$0.938096\pi$
$398$	− 7.62416e6i	− 2.41259i
$399$	75950.0	0.0238834
$400$	0	0
$401$	5.90442e6	1.83365	0.916824	−	0.399291i	$-0.130744\pi$
$401$	5.90442e6	1.83365	0.916824	+	0.399291i	$0.130744\pi$
$402$	126784.i	0.0391291i
$403$	1.15505e6i	0.354272i
$404$	380096.	0.115862
$405$	0	0
$406$	1.95412e6	0.588351
$407$	4.99115e6i	1.49353i
$408$	0	0
$409$	−4.84289e6	−1.43152	−0.715758	−	0.698348i	$-0.753919\pi$
$409$	−4.84289e6	−1.43152	−0.715758	+	0.698348i	$0.753919\pi$
$410$	0	0
$411$	−99748.0	−0.0291273
$412$	− 4.23805e6i	− 1.23005i
$413$	224420.i	0.0647420i
$414$	3.20214e6	0.918206
$415$	0	0
$416$	−7.93805e6	−2.24895
$417$	258930.i	0.0729193i
$418$	5.61720e6i	1.57246i
$419$	−270360.	−0.0752328	−0.0376164	−	0.999292i	$-0.511977\pi$
$419$	−270360.	−0.0752328	−0.0376164	+	0.999292i	$0.511977\pi$
$420$	0	0
$421$	3.13648e6	0.862456	0.431228	−	0.902243i	$-0.358080\pi$
$421$	3.13648e6	0.862456	0.431228	+	0.902243i	$0.358080\pi$
$422$	1.78818e6i	0.488800i
$423$	6.34935e6i	1.72536i
$424$	0	0
$425$	0	0
$426$	−414336.	−0.110619
$427$	− 611912.i	− 0.162412i
$428$	− 4.37894e6i	− 1.15547i
$429$	−438957.	−0.115154
$430$	0	0
$431$	−1.87703e6	−0.486719	−0.243360	−	0.969936i	$-0.578250\pi$
$431$	−1.87703e6	−0.486719	−0.243360	+	0.969936i	$0.578250\pi$
$432$	496640.i	0.128036i
$433$	− 3.20357e6i	− 0.821134i	−0.911830	−	0.410567i	$-0.865331\pi$
$433$	− 3.20357e6i	− 0.821134i	0.911830	−	0.410567i	$-0.134669\pi$
$434$	467264.	0.119080
$435$	0	0
$436$	3.50352e6	0.882650
$437$	2.56370e6i	0.642190i
$438$	38768.0i	0.00965580i
$439$	6.27209e6	1.55328	0.776642	−	0.629942i	$-0.216921\pi$
$439$	6.27209e6	1.55328	0.776642	+	0.629942i	$0.216921\pi$
$440$	0	0
$441$	−581042.	−0.142269
$442$	1.26900e7i	3.08963i
$443$	− 724986.i	− 0.175517i	−0.996142	−	0.0877587i	$-0.972030\pi$
$443$	− 724986.i	− 0.175517i	0.996142	−	0.0877587i	$-0.0279705\pi$
$444$	352576.	0.0848780
$445$	0	0
$446$	−8.11841e6	−1.93256
$447$	− 498430.i	− 0.117987i
$448$	1.60563e6i	0.377964i
$449$	875985.	0.205060	0.102530	−	0.994730i	$-0.467306\pi$
$449$	875985.	0.205060	0.102530	+	0.994730i	$0.467306\pi$
$450$	0	0
$451$	782784.	0.181218
$452$	− 6.42989e6i	− 1.48033i
$453$	245803.i	0.0562784i
$454$	7.99838e6	1.82122
$455$	0	0
$456$	0	0
$457$	− 832668.i	− 0.186501i	−0.995643	−	0.0932505i	$-0.970274\pi$
$457$	− 832668.i	− 0.186501i	0.995643	−	0.0932505i	$-0.0297258\pi$
$458$	− 6.80896e6i	− 1.51676i
$459$	793945.	0.175897
$460$	0	0
$461$	5.92115e6	1.29764	0.648820	−	0.760942i	$-0.275263\pi$
$461$	5.92115e6	1.29764	0.648820	+	0.760942i	$0.275263\pi$
$462$	177576.i	0.0387061i
$463$	− 682776.i	− 0.148022i	−0.997257	−	0.0740109i	$-0.976420\pi$
$463$	− 682776.i	− 0.148022i	0.997257	−	0.0740109i	$-0.0235800\pi$
$464$	−5.10464e6	−1.10070
$465$	0	0
$466$	−8.74157e6	−1.86477
$467$	− 5.41667e6i	− 1.14932i	−0.818393	−	0.574659i	$-0.805135\pi$
$467$	− 5.41667e6i	− 1.14932i	0.818393	−	0.574659i	$-0.194865\pi$
$468$	− 7.50394e6i	− 1.58371i
$469$	776552.	0.163019
$470$	0	0
$471$	−85478.0	−0.0177542
$472$	0	0
$473$	− 4.89874e6i	− 1.00677i
$474$	502120.	0.102651
$475$	0	0
$476$	2.56682e6	0.519251
$477$	− 6.27651e6i	− 1.26306i
$478$	6.12724e6i	1.22658i
$479$	−1.98599e6	−0.395493	−0.197746	−	0.980253i	$-0.563362\pi$
$479$	−1.98599e6	−0.395493	−0.197746	+	0.980253i	$0.563362\pi$
$480$	0	0
$481$	1.06764e7	2.10409
$482$	9.68750e6i	1.89930i
$483$	81046.0i	0.0158075i
$484$	−1.41306e6	−0.274186
$485$	0	0
$486$	−1.40941e6	−0.270674
$487$	− 1.06974e6i	− 0.204388i	−0.994764	−	0.102194i	$-0.967414\pi$
$487$	− 1.06974e6i	− 0.204388i	0.994764	−	0.102194i	$-0.0325862\pi$
$488$	0	0
$489$	−193026.	−0.0365043
$490$	0	0
$491$	4.59246e6	0.859689	0.429844	−	0.902903i	$-0.358568\pi$
$491$	4.59246e6	0.859689	0.429844	+	0.902903i	$0.358568\pi$
$492$	− 55296.0i	− 0.0102987i
$493$	8.16045e6i	1.51216i
$494$	1.20156e7	2.21528
$495$	0	0
$496$	−1.22061e6	−0.222778
$497$	2.53781e6i	0.460859i
$498$	− 189152.i	− 0.0341773i
$499$	−1.96066e6	−0.352492	−0.176246	−	0.984346i	$-0.556395\pi$
$499$	−1.96066e6	−0.352492	−0.176246	+	0.984346i	$0.556395\pi$
$500$	0	0
$501$	−157783.	−0.0280844
$502$	− 2.22610e6i	− 0.394262i
$503$	− 3.51483e6i	− 0.619419i	−0.950831	−	0.309709i	$-0.899768\pi$
$503$	− 3.51483e6i	− 0.619419i	0.950831	−	0.309709i	$-0.100232\pi$
$504$	0	0
$505$	0	0
$506$	−5.99410e6	−1.04075
$507$	567668.i	0.0980787i
$508$	− 1.05821e7i	− 1.81934i
$509$	1.45211e6	0.248431	0.124215	−	0.992255i	$-0.460359\pi$
$509$	1.45211e6	0.248431	0.124215	+	0.992255i	$0.460359\pi$
$510$	0	0
$511$	237454.	0.0402279
$512$	− 8.38861e6i	− 1.41421i
$513$	− 751750.i	− 0.126119i
$514$	−2.82398e6	−0.471470
$515$	0	0
$516$	−346048.	−0.0572153
$517$	− 1.18854e7i	− 1.95563i
$518$	− 4.31906e6i	− 0.707236i
$519$	265659.	0.0432918
$520$	0	0
$521$	−4.24240e6	−0.684726	−0.342363	−	0.939568i	$-0.611227\pi$
$521$	−4.24240e6	−0.684726	−0.342363	+	0.939568i	$0.611227\pi$
$522$	− 9.65096e6i	− 1.55022i
$523$	7.56012e6i	1.20858i	0.796765	+	0.604289i	$0.206543\pi$
$523$	7.56012e6i	1.20858i	−0.796765	+	0.604289i	$0.793457\pi$
$524$	−1.40742e6	−0.223922
$525$	0	0
$526$	1.24648e7	1.96435
$527$	1.95130e6i	0.306054i
$528$	− 463872.i	− 0.0724125i
$529$	3.70063e6	0.574958
$530$	0	0
$531$	1.10836e6	0.170586
$532$	− 2.43040e6i	− 0.372305i
$533$	− 1.67443e6i	− 0.255299i
$534$	−1.17840e6	−0.178830
$535$	0	0
$536$	0	0
$537$	183660.i	0.0274839i
$538$	− 9.75704e6i	− 1.45332i
$539$	1.08765e6	0.161257
$540$	0	0
$541$	1.24065e6	0.182245	0.0911224	−	0.995840i	$-0.470955\pi$
$541$	1.24065e6	0.182245	0.0911224	+	0.995840i	$0.470955\pi$
$542$	− 3.24634e6i	− 0.474674i
$543$	635048.i	0.0924287i
$544$	−1.34103e7	−1.94286
$545$	0	0
$546$	379848.	0.0545291
$547$	− 1.85057e6i	− 0.264446i	−0.991220	−	0.132223i	$-0.957789\pi$
$547$	− 1.85057e6i	− 0.264446i	0.991220	−	0.132223i	$-0.0422115\pi$
$548$	3.19194e6i	0.454049i
$549$	−3.02210e6	−0.427935
$550$	0	0
$551$	7.72675e6	1.08422
$552$	0	0
$553$	− 3.07548e6i	− 0.427662i
$554$	5.21954e6	0.722533
$555$	0	0
$556$	8.28576e6	1.13670
$557$	7.77555e6i	1.06192i	0.847396	+	0.530962i	$0.178169\pi$
$557$	7.77555e6i	1.06192i	−0.847396	+	0.530962i	$0.821831\pi$
$558$	− 2.30771e6i	− 0.313759i
$559$	−1.04788e7	−1.41834
$560$	0	0
$561$	−741561.	−0.0994809
$562$	− 950616.i	− 0.126959i
$563$	− 8.37716e6i	− 1.11385i	−0.830564	−	0.556924i	$-0.811982\pi$
$563$	− 8.37716e6i	− 1.11385i	0.830564	−	0.556924i	$-0.188018\pi$
$564$	−839584.	−0.111139
$565$	0	0
$566$	−1.19041e7	−1.56191
$567$	2.85773e6i	0.373305i
$568$	0	0
$569$	6.15591e6	0.797098	0.398549	−	0.917147i	$-0.369514\pi$
$569$	6.15591e6	0.797098	0.398549	+	0.917147i	$0.369514\pi$
$570$	0	0
$571$	7.21513e6	0.926092	0.463046	−	0.886334i	$-0.346757\pi$
$571$	7.21513e6	0.926092	0.463046	+	0.886334i	$0.346757\pi$
$572$	1.40466e7i	1.79507i
$573$	226613.i	0.0288336i
$574$	−677376.	−0.0858124
$575$	0	0
$576$	7.92986e6	0.995885
$577$	1.36699e7i	1.70933i	0.519177	+	0.854666i	$0.326238\pi$
$577$	1.36699e7i	1.70933i	−0.519177	+	0.854666i	$0.673762\pi$
$578$	1.00793e7i	1.25490i
$579$	−46476.0	−0.00576146
$580$	0	0
$581$	−1.15856e6	−0.142389
$582$	66744.0i	0.00816779i
$583$	1.17490e7i	1.43163i
$584$	0	0
$585$	0	0
$586$	−1.51664e7	−1.82448
$587$	− 1.00686e7i	− 1.20608i	−0.797711	−	0.603040i	$-0.793956\pi$
$587$	− 1.00686e7i	− 1.20608i	0.797711	−	0.603040i	$-0.206044\pi$
$588$	− 76832.0i	− 0.00916429i
$589$	1.84760e6	0.219442
$590$	0	0
$591$	204972.	0.0241394
$592$	1.12824e7i	1.32312i
$593$	− 9.80615e6i	− 1.14515i	−0.819853	−	0.572574i	$-0.805945\pi$
$593$	− 9.80615e6i	− 1.14515i	0.819853	−	0.572574i	$-0.194055\pi$
$594$	1.75764e6	0.204392
$595$	0	0
$596$	−1.59498e7	−1.83924
$597$	− 953020.i	− 0.109438i
$598$	1.28218e7i	1.46621i
$599$	−8.26257e6	−0.940911	−0.470455	−	0.882424i	$-0.655910\pi$
$599$	−8.26257e6	−0.940911	−0.470455	+	0.882424i	$0.655910\pi$
$600$	0	0
$601$	−3.59492e6	−0.405978	−0.202989	−	0.979181i	$-0.565066\pi$
$601$	−3.59492e6	−0.405978	−0.202989	+	0.979181i	$0.565066\pi$
$602$	4.23909e6i	0.476740i
$603$	− 3.83522e6i	− 0.429533i
$604$	7.86570e6	0.877293
$605$	0	0
$606$	95024.0	0.0105112
$607$	− 1.32969e7i	− 1.46480i	−0.680873	−	0.732401i	$-0.738400\pi$
$607$	− 1.32969e7i	− 1.46480i	0.680873	−	0.732401i	$-0.261600\pi$
$608$	1.26976e7i	1.39304i
$609$	244265.	0.0266881
$610$	0	0
$611$	−2.54237e7	−2.75508
$612$	− 1.26769e7i	− 1.36816i
$613$	− 2.50327e6i	− 0.269064i	−0.990909	−	0.134532i	$-0.957047\pi$
$613$	− 2.50327e6i	− 0.269064i	0.990909	−	0.134532i	$-0.0429531\pi$
$614$	−6.57482e6	−0.703823
$615$	0	0
$616$	0	0
$617$	1.88254e6i	0.199082i	0.995033	+	0.0995409i	$0.0317374\pi$
$617$	1.88254e6i	0.199082i	−0.995033	+	0.0995409i	$0.968263\pi$
$618$	− 1.05951e6i	− 0.111592i
$619$	−8.21487e6	−0.861736	−0.430868	−	0.902415i	$-0.641792\pi$
$619$	−8.21487e6	−0.861736	−0.430868	+	0.902415i	$0.641792\pi$
$620$	0	0
$621$	802190.	0.0834734
$622$	1.67680e7i	1.73782i
$623$	7.21770e6i	0.745038i
$624$	−992256.	−0.102015
$625$	0	0
$626$	−3.15657e6	−0.321943
$627$	702150.i	0.0713282i
$628$	2.73530e6i	0.276761i
$629$	1.80365e7	1.81771
$630$	0	0
$631$	1.61155e7	1.61128	0.805638	−	0.592408i	$-0.201823\pi$
$631$	1.61155e7	1.61128	0.805638	+	0.592408i	$0.201823\pi$
$632$	0	0
$633$	223523.i	0.0221724i
$634$	2.57138e6	0.254064
$635$	0	0
$636$	829952.	0.0813599
$637$	− 2.32657e6i	− 0.227179i
$638$	1.80656e7i	1.75712i
$639$	1.25337e7	1.21430
$640$	0	0
$641$	−8.50544e6	−0.817620	−0.408810	−	0.912619i	$-0.634056\pi$
$641$	−8.50544e6	−0.817620	−0.408810	+	0.912619i	$0.634056\pi$
$642$	− 1.09474e6i	− 0.104827i
$643$	1.32191e7i	1.26088i	0.776238	+	0.630440i	$0.217126\pi$
$643$	1.32191e7i	1.26088i	−0.776238	+	0.630440i	$0.782874\pi$
$644$	2.59347e6	0.246415
$645$	0	0
$646$	2.02988e7	1.91377
$647$	1.89115e6i	0.177609i	0.996049	+	0.0888047i	$0.0283047\pi$
$647$	1.89115e6i	0.177609i	−0.996049	+	0.0888047i	$0.971695\pi$
$648$	0	0
$649$	−2.07474e6	−0.193353
$650$	0	0
$651$	58408.0	0.00540157
$652$	6.17683e6i	0.569045i
$653$	− 4.90587e6i	− 0.450228i	−0.974332	−	0.225114i	$-0.927725\pi$
$653$	− 4.90587e6i	− 0.450228i	0.974332	−	0.225114i	$-0.0722755\pi$
$654$	875880.	0.0800756
$655$	0	0
$656$	1.76947e6	0.160540
$657$	− 1.17273e6i	− 0.105995i
$658$	1.02849e7i	0.926052i
$659$	−1.36367e7	−1.22319	−0.611597	−	0.791169i	$-0.709473\pi$
$659$	−1.36367e7	−1.22319	−0.611597	+	0.791169i	$0.709473\pi$
$660$	0	0
$661$	−2.22345e6	−0.197935	−0.0989677	−	0.995091i	$-0.531554\pi$
$661$	−2.22345e6	−0.197935	−0.0989677	+	0.995091i	$0.531554\pi$
$662$	1.78607e7i	1.58399i
$663$	1.58625e6i	0.140149i
$664$	0	0
$665$	0	0
$666$	−2.13308e7	−1.86347
$667$	8.24519e6i	0.717606i
$668$	5.04906e6i	0.437793i
$669$	−1.01480e6	−0.0876629
$670$	0	0
$671$	5.65706e6	0.485048
$672$	401408.i	0.0342896i
$673$	− 4.88484e6i	− 0.415731i	−0.978157	−	0.207865i	$-0.933348\pi$
$673$	− 4.88484e6i	− 0.415731i	0.978157	−	0.207865i	$-0.0666516\pi$
$674$	−2.92525e7	−2.48035
$675$	0	0
$676$	1.81654e7	1.52889
$677$	− 1.98785e7i	− 1.66691i	−0.552590	−	0.833453i	$-0.686360\pi$
$677$	− 1.98785e7i	− 1.66691i	0.552590	−	0.833453i	$-0.313640\pi$
$678$	− 1.60747e6i	− 0.134298i
$679$	408807.	0.0340286
$680$	0	0
$681$	999797.	0.0826122
$682$	4.31981e6i	0.355634i
$683$	− 4.27870e6i	− 0.350962i	−0.984483	−	0.175481i	$-0.943852\pi$
$683$	− 4.27870e6i	− 0.350962i	0.984483	−	0.175481i	$-0.0561480\pi$
$684$	−1.20032e7	−0.980972
$685$	0	0
$686$	−941192.	−0.0763604
$687$	− 851120.i	− 0.0688017i
$688$	− 1.10735e7i	− 0.891898i
$689$	2.51320e7	2.01687
$690$	0	0
$691$	9.48925e6	0.756026	0.378013	−	0.925800i	$-0.376607\pi$
$691$	9.48925e6	0.756026	0.378013	+	0.925800i	$0.376607\pi$
$692$	− 8.50109e6i	− 0.674853i
$693$	− 5.37167e6i	− 0.424890i
$694$	−1.51169e7	−1.19142
$695$	0	0
$696$	0	0
$697$	− 2.82874e6i	− 0.220552i
$698$	− 2.15463e7i	− 1.67392i
$699$	−1.09270e6	−0.0845875
$700$	0	0
$701$	−5.86385e6	−0.450700	−0.225350	−	0.974278i	$-0.572353\pi$
$701$	−5.86385e6	−0.450700	−0.225350	+	0.974278i	$0.572353\pi$
$702$	− 3.75972e6i	− 0.287947i
$703$	− 1.70779e7i	− 1.30331i
$704$	−1.48439e7	−1.12880
$705$	0	0
$706$	1.25974e7	0.951197
$707$	− 582022.i	− 0.0437916i
$708$	146560.i	0.0109883i
$709$	2.66670e6	0.199232	0.0996161	−	0.995026i	$-0.468239\pi$
$709$	2.66670e6	0.199232	0.0996161	+	0.995026i	$0.468239\pi$
$710$	0	0
$711$	−1.51891e7	−1.12683
$712$	0	0
$713$	1.97157e6i	0.145241i
$714$	641704.	0.0471074
$715$	0	0
$716$	5.87712e6	0.428432
$717$	765905.i	0.0556387i
$718$	3.24461e7i	2.34883i
$719$	4.46629e6	0.322199	0.161100	−	0.986938i	$-0.448496\pi$
$719$	4.46629e6	0.322199	0.161100	+	0.986938i	$0.448496\pi$
$720$	0	0
$721$	−6.48951e6	−0.464915
$722$	588792.i	0.0420358i
$723$	1.21094e6i	0.0861541i
$724$	2.03215e7	1.44082
$725$	0	0
$726$	−353264.	−0.0248747
$727$	− 7.47757e6i	− 0.524716i	−0.964971	−	0.262358i	$-0.915500\pi$
$727$	− 7.47757e6i	− 0.524716i	0.964971	−	0.262358i	$-0.0845001\pi$
$728$	0	0
$729$	1.39958e7	0.975393
$730$	0	0
$731$	−1.77025e7	−1.22530
$732$	− 399616.i	− 0.0275655i
$733$	4.39751e6i	0.302306i	0.988510	+	0.151153i	$0.0482986\pi$
$733$	4.39751e6i	0.302306i	−0.988510	+	0.151153i	$0.951701\pi$
$734$	−3.92503e7	−2.68907
$735$	0	0
$736$	−1.35496e7	−0.922000
$737$	7.17914e6i	0.486860i
$738$	3.34541e6i	0.226104i
$739$	−2.84036e7	−1.91321	−0.956603	−	0.291395i	$-0.905880\pi$
$739$	−2.84036e7	−1.91321	−0.956603	+	0.291395i	$0.905880\pi$
$740$	0	0
$741$	1.50195e6	0.100487
$742$	− 1.01669e7i	− 0.677921i
$743$	1.96012e7i	1.30260i	0.758821	+	0.651299i	$0.225776\pi$
$743$	1.96012e7i	1.30260i	−0.758821	+	0.651299i	$0.774224\pi$
$744$	0	0
$745$	0	0
$746$	2.76269e7	1.81755
$747$	5.72185e6i	0.375176i
$748$	2.37300e7i	1.55075i
$749$	−6.70526e6	−0.436728
$750$	0	0
$751$	−2.60344e6	−0.168441	−0.0842206	−	0.996447i	$-0.526840\pi$
$751$	−2.60344e6	−0.168441	−0.0842206	+	0.996447i	$0.526840\pi$
$752$	− 2.68667e7i	− 1.73249i
$753$	− 278262.i	− 0.0178841i
$754$	3.86437e7	2.47543
$755$	0	0
$756$	−760480.	−0.0483931
$757$	− 2.98869e7i	− 1.89558i	−0.318899	−	0.947789i	$-0.603313\pi$
$757$	− 2.98869e7i	− 1.89558i	0.318899	−	0.947789i	$-0.396687\pi$
$758$	− 3.38773e7i	− 2.14159i
$759$	−749262.	−0.0472095
$760$	0	0
$761$	1.21470e7	0.760338	0.380169	−	0.924917i	$-0.375866\pi$
$761$	1.21470e7	0.760338	0.380169	+	0.924917i	$0.375866\pi$
$762$	− 2.64554e6i	− 0.165054i
$763$	− 5.36476e6i	− 0.333610i
$764$	7.25162e6	0.449471
$765$	0	0
$766$	1.49168e7	0.918554
$767$	4.43802e6i	0.272396i
$768$	− 1.04858e6i	− 0.0641500i
$769$	−4.53845e6	−0.276753	−0.138376	−	0.990380i	$-0.544188\pi$
$769$	−4.53845e6	−0.276753	−0.138376	+	0.990380i	$0.544188\pi$
$770$	0	0
$771$	−352998.	−0.0213863
$772$	1.48723e6i	0.0898122i
$773$	− 1.93330e7i	− 1.16372i	−0.813288	−	0.581861i	$-0.802325\pi$
$773$	− 1.93330e7i	− 1.16372i	0.813288	−	0.581861i	$-0.197675\pi$
$774$	2.09359e7	1.25614
$775$	0	0
$776$	0	0
$777$	− 539882.i	− 0.0320809i
$778$	− 3.85201e7i	− 2.28160i
$779$	−2.67840e6	−0.158136
$780$	0	0
$781$	−2.34618e7	−1.37636
$782$	2.16608e7i	1.26665i
$783$	− 2.41772e6i	− 0.140930i
$784$	2.45862e6	0.142857
$785$	0	0
$786$	−351856.	−0.0203146
$787$	1.66392e7i	0.957627i	0.877917	+	0.478814i	$0.158933\pi$
$787$	1.66392e7i	0.957627i	−0.877917	+	0.478814i	$0.841067\pi$
$788$	− 6.55910e6i	− 0.376295i
$789$	1.55809e6	0.0891048
$790$	0	0
$791$	−9.84577e6	−0.559511
$792$	0	0
$793$	− 1.21009e7i	− 0.683335i
$794$	9.71006e6	0.546601
$795$	0	0
$796$	−3.04966e7	−1.70596
$797$	1.80409e7i	1.00603i	0.864276	+	0.503017i	$0.167777\pi$
$797$	1.80409e7i	1.00603i	−0.864276	+	0.503017i	$0.832223\pi$
$798$	− 607600.i	− 0.0337762i
$799$	−4.29500e7	−2.38010
$800$	0	0
$801$	3.56466e7	1.96307
$802$	− 4.72353e7i	− 2.59317i
$803$	2.19524e6i	0.120141i
$804$	507136.	0.0276684
$805$	0	0
$806$	9.24038e6	0.501017
$807$	− 1.21963e6i	− 0.0659241i
$808$	0	0
$809$	−2.33891e7	−1.25644	−0.628220	−	0.778036i	$-0.716216\pi$
$809$	−2.33891e7	−1.25644	−0.628220	+	0.778036i	$0.716216\pi$
$810$	0	0
$811$	−2.29037e7	−1.22279	−0.611397	−	0.791324i	$-0.709392\pi$
$811$	−2.29037e7	−1.22279	−0.611397	+	0.791324i	$0.709392\pi$
$812$	− 7.81648e6i	− 0.416027i
$813$	− 405792.i	− 0.0215316i
$814$	3.99292e7	2.11218
$815$	0	0
$816$	−1.67629e6	−0.0881299
$817$	1.67617e7i	0.878543i
$818$	3.87431e7i	2.02447i
$819$	−1.14904e7	−0.598585
$820$	0	0
$821$	−1.80745e7	−0.935853	−0.467926	−	0.883767i	$-0.654999\pi$
$821$	−1.80745e7	−0.935853	−0.467926	+	0.883767i	$0.654999\pi$
$822$	797984.i	0.0411922i
$823$	− 1.17989e7i	− 0.607216i	−0.952797	−	0.303608i	$-0.901809\pi$
$823$	− 1.17989e7i	− 0.607216i	0.952797	−	0.303608i	$-0.0981913\pi$
$824$	0	0
$825$	0	0
$826$	1.79536e6	0.0915591
$827$	2.57650e6i	0.130999i	0.997853	+	0.0654993i	$0.0208640\pi$
$827$	2.57650e6i	0.130999i	−0.997853	+	0.0654993i	$0.979136\pi$
$828$	− 1.28086e7i	− 0.649270i
$829$	3.84340e7	1.94236	0.971178	−	0.238356i	$-0.0766084\pi$
$829$	3.84340e7	1.94236	0.971178	+	0.238356i	$0.0766084\pi$
$830$	0	0
$831$	652442.	0.0327747
$832$	3.17522e7i	1.59025i
$833$	− 3.93044e6i	− 0.196258i
$834$	2.07144e6	0.103123
$835$	0	0
$836$	2.24688e7	1.11190
$837$	− 578120.i	− 0.0285236i
$838$	2.16288e6i	0.106395i
$839$	1.24222e7	0.609247	0.304623	−	0.952473i	$-0.401469\pi$
$839$	1.24222e7	0.609247	0.304623	+	0.952473i	$0.401469\pi$
$840$	0	0
$841$	4.33908e6	0.211547
$842$	− 2.50918e7i	− 1.21970i
$843$	− 118827.i	− 0.00575899i
$844$	7.15274e6	0.345634
$845$	0	0
$846$	5.07948e7	2.44002
$847$	2.16374e6i	0.103633i
$848$	2.65585e7i	1.26827i
$849$	−1.48801e6	−0.0708495
$850$	0	0
$851$	1.82238e7	0.862610
$852$	1.65734e6i	0.0782193i
$853$	− 7.92067e6i	− 0.372726i	−0.982481	−	0.186363i	$-0.940330\pi$
$853$	− 7.92067e6i	− 0.372726i	0.982481	−	0.186363i	$-0.0596700\pi$
$854$	−4.89530e6	−0.229686
$855$	0	0
$856$	0	0
$857$	1.48983e7i	0.692924i	0.938064	+	0.346462i	$0.112617\pi$
$857$	1.48983e7i	0.692924i	−0.938064	+	0.346462i	$0.887383\pi$
$858$	3.51166e6i	0.162852i
$859$	1.38740e7	0.641534	0.320767	−	0.947158i	$-0.396059\pi$
$859$	1.38740e7	0.641534	0.320767	+	0.947158i	$0.396059\pi$
$860$	0	0
$861$	−84672.0	−0.00389253
$862$	1.50163e7i	0.688325i
$863$	− 1.25500e7i	− 0.573610i	−0.957989	−	0.286805i	$-0.907407\pi$
$863$	− 1.25500e7i	− 0.573610i	0.957989	−	0.286805i	$-0.0925932\pi$
$864$	3.97312e6	0.181070
$865$	0	0
$866$	−2.56285e7	−1.16126
$867$	1.25991e6i	0.0569236i
$868$	− 1.86906e6i	− 0.0842021i
$869$	2.84325e7	1.27722
$870$	0	0
$871$	1.53567e7	0.685887
$872$	0	0
$873$	− 2.01901e6i	− 0.0896607i
$874$	2.05096e7	0.908194
$875$	0	0
$876$	155072.	0.00682768
$877$	− 2.86002e7i	− 1.25565i	−0.778353	−	0.627827i	$-0.783944\pi$
$877$	− 2.86002e7i	− 1.25565i	0.778353	−	0.627827i	$-0.216056\pi$
$878$	− 5.01767e7i	− 2.19668i
$879$	−1.89580e6	−0.0827600
$880$	0	0
$881$	4.09608e7	1.77799	0.888993	−	0.457922i	$-0.151406\pi$
$881$	4.09608e7	1.77799	0.888993	+	0.457922i	$0.151406\pi$
$882$	4.64834e6i	0.201199i
$883$	− 1.30504e7i	− 0.563279i	−0.959520	−	0.281639i	$-0.909122\pi$
$883$	− 1.30504e7i	− 0.563279i	0.959520	−	0.281639i	$-0.0908782\pi$
$884$	5.07601e7	2.18470
$885$	0	0
$886$	−5.79989e6	−0.248219
$887$	2.53595e7i	1.08226i	0.840939	+	0.541129i	$0.182003\pi$
$887$	2.53595e7i	1.08226i	−0.840939	+	0.541129i	$0.817997\pi$
$888$	0	0
$889$	−1.62039e7	−0.687647
$890$	0	0
$891$	−2.64194e7	−1.11488
$892$	3.24736e7i	1.36653i
$893$	4.06674e7i	1.70654i
$894$	−3.98744e6	−0.166859
$895$	0	0
$896$	0	0
$897$	1.60273e6i	0.0665087i
$898$	− 7.00788e6i	− 0.289999i
$899$	5.94212e6	0.245212
$900$	0	0
$901$	4.24572e7	1.74237
$902$	− 6.26227e6i	− 0.256281i
$903$	529886.i	0.0216253i
$904$	0	0
$905$	0	0
$906$	1.96642e6	0.0795897
$907$	1.98595e7i	0.801585i	0.916169	+	0.400793i	$0.131265\pi$
$907$	1.98595e7i	0.801585i	−0.916169	+	0.400793i	$0.868735\pi$
$908$	− 3.19935e7i	− 1.28780i
$909$	−2.87448e6	−0.115385
$910$	0	0
$911$	−1.99344e7	−0.795808	−0.397904	−	0.917427i	$-0.630262\pi$
$911$	−1.99344e7	−0.795808	−0.397904	+	0.917427i	$0.630262\pi$
$912$	1.58720e6i	0.0631894i
$913$	− 1.07107e7i	− 0.425248i
$914$	−6.66134e6	−0.263752
$915$	0	0
$916$	−2.72358e7	−1.07251
$917$	2.15512e6i	0.0846346i
$918$	− 6.35156e6i	− 0.248756i
$919$	1.10695e7	0.432355	0.216178	−	0.976354i	$-0.430641\pi$
$919$	1.10695e7	0.432355	0.216178	+	0.976354i	$0.430641\pi$
$920$	0	0
$921$	−821853.	−0.0319260
$922$	− 4.73692e7i	− 1.83514i
$923$	5.01864e7i	1.93902i
$924$	710304.	0.0273693
$925$	0	0
$926$	−5.46221e6	−0.209334
$927$	3.20502e7i	1.22499i
$928$	4.08371e7i	1.55663i
$929$	3.25682e7	1.23810	0.619048	−	0.785353i	$-0.287519\pi$
$929$	3.25682e7	1.23810	0.619048	+	0.785353i	$0.287519\pi$
$930$	0	0
$931$	−3.72155e6	−0.140718
$932$	3.49663e7i	1.31859i
$933$	2.09600e6i	0.0788291i
$934$	−4.33334e7	−1.62538
$935$	0	0
$936$	0	0
$937$	3.15690e7i	1.17466i	0.809348	+	0.587329i	$0.199821\pi$
$937$	3.15690e7i	1.17466i	−0.809348	+	0.587329i	$0.800179\pi$
$938$	− 6.21242e6i	− 0.230544i
$939$	−394571.	−0.0146036
$940$	0	0
$941$	−3.67997e7	−1.35479	−0.677393	−	0.735622i	$-0.736890\pi$
$941$	−3.67997e7	−1.35479	−0.677393	+	0.735622i	$0.736890\pi$
$942$	683824.i	0.0251083i
$943$	− 2.85811e6i	− 0.104665i
$944$	−4.68992e6	−0.171291
$945$	0	0
$946$	−3.91899e7	−1.42379
$947$	1.88453e7i	0.682853i	0.939909	+	0.341426i	$0.110910\pi$
$947$	1.88453e7i	0.682853i	−0.939909	+	0.341426i	$0.889090\pi$
$948$	− 2.00848e6i	− 0.0725850i
$949$	4.69577e6	0.169255
$950$	0	0
$951$	321422.	0.0115246
$952$	0	0
$953$	1.25120e7i	0.446265i	0.974788	+	0.223133i	$0.0716283\pi$
$953$	1.25120e7i	0.446265i	−0.974788	+	0.223133i	$0.928372\pi$
$954$	−5.02121e7	−1.78623
$955$	0	0
$956$	2.45090e7	0.867322
$957$	2.25820e6i	0.0797046i
$958$	1.58879e7i	0.559311i
$959$	4.88765e6	0.171614
$960$	0	0
$961$	−2.72083e7	−0.950370
$962$	− 8.54115e7i	− 2.97563i
$963$	3.31158e7i	1.15072i
$964$	3.87500e7	1.34301
$965$	0	0
$966$	648368.	0.0223552
$967$	− 3.42344e7i	− 1.17733i	−0.808379	−	0.588663i	$-0.799654\pi$
$967$	− 3.42344e7i	− 1.17733i	0.808379	−	0.588663i	$-0.200346\pi$
$968$	0	0
$969$	2.53735e6	0.0868102
$970$	0	0
$971$	−2.62027e7	−0.891864	−0.445932	−	0.895067i	$-0.647128\pi$
$971$	−2.62027e7	−0.891864	−0.445932	+	0.895067i	$0.647128\pi$
$972$	5.63763e6i	0.191395i
$973$	− 1.26876e7i	− 0.429632i
$974$	−8.55790e6	−0.289048
$975$	0	0
$976$	1.27877e7	0.429703
$977$	− 8.01114e6i	− 0.268508i	−0.990947	−	0.134254i	$-0.957136\pi$
$977$	− 8.01114e6i	− 0.268508i	0.990947	−	0.134254i	$-0.0428639\pi$
$978$	1.54421e6i	0.0516248i
$979$	−6.67269e7	−2.22507
$980$	0	0
$981$	−2.64954e7	−0.879017
$982$	− 3.67397e7i	− 1.21578i
$983$	4.60126e7i	1.51877i	0.650639	+	0.759387i	$0.274501\pi$
$983$	4.60126e7i	1.51877i	−0.650639	+	0.759387i	$0.725499\pi$
$984$	0	0
$985$	0	0
$986$	6.52836e7	2.13851
$987$	1.28561e6i	0.0420066i
$988$	− 4.80624e7i	− 1.56644i
$989$	−1.78864e7	−0.581475
$990$	0	0
$991$	−3.75828e7	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$991$	−3.75828e7	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$992$	9.76486e6i	0.315055i
$993$	2.23259e6i	0.0718514i
$994$	2.03025e7	0.651753
$995$	0	0
$996$	−756608.	−0.0241670
$997$	2.22066e7i	0.707529i	0.935334	+	0.353765i	$0.115099\pi$
$997$	2.22066e7i	0.707529i	−0.935334	+	0.353765i	$0.884901\pi$
$998$	1.56852e7i	0.498500i
$999$	−5.34373e6	−0.169407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.6.b.b.99.1		2
5.2	odd	4		175.6.a.a.1.1		1
5.3	odd	4		35.6.a.a.1.1	✓	1
5.4	even	2	inner	175.6.b.b.99.2		2
15.8	even	4		315.6.a.a.1.1		1
20.3	even	4		560.6.a.c.1.1		1
35.13	even	4		245.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.a.1.1	✓	1	5.3	odd	4
175.6.a.a.1.1		1	5.2	odd	4
175.6.b.b.99.1		2	1.1	even	1	trivial
175.6.b.b.99.2		2	5.4	even	2	inner
245.6.a.a.1.1		1	35.13	even	4
315.6.a.a.1.1		1	15.8	even	4
560.6.a.c.1.1		1	20.3	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-8.00000i q^{2} -1.00000i q^{3} -32.0000 q^{4} -8.00000 q^{6} +49.0000i q^{7} +242.000 q^{9} +O(q^{10})\)	\(q-8.00000i q^{2} -1.00000i q^{3} -32.0000 q^{4} -8.00000 q^{6} +49.0000i q^{7} +242.000 q^{9} -453.000 q^{11} +32.0000i q^{12} +969.000i q^{13} +392.000 q^{14} -1024.00 q^{16} +1637.00i q^{17} -1936.00i q^{18} +1550.00 q^{19} +49.0000 q^{21} +3624.00i q^{22} +1654.00i q^{23} +7752.00 q^{26} -485.000i q^{27} -1568.00i q^{28} +4985.00 q^{29} +1192.00 q^{31} +8192.00i q^{32} +453.000i q^{33} +13096.0 q^{34} -7744.00 q^{36} -11018.0i q^{37} -12400.0i q^{38} +969.000 q^{39} -1728.00 q^{41} -392.000i q^{42} +10814.0i q^{43} +14496.0 q^{44} +13232.0 q^{46} +26237.0i q^{47} +1024.00i q^{48} -2401.00 q^{49} +1637.00 q^{51} -31008.0i q^{52} -25936.0i q^{53} -3880.00 q^{54} -1550.00i q^{57} -39880.0i q^{58} +4580.00 q^{59} -12488.0 q^{61} -9536.00i q^{62} +11858.0i q^{63} +32768.0 q^{64} +3624.00 q^{66} -15848.0i q^{67} -52384.0i q^{68} +1654.00 q^{69} +51792.0 q^{71} -4846.00i q^{73} -88144.0 q^{74} -49600.0 q^{76} -22197.0i q^{77} -7752.00i q^{78} -62765.0 q^{79} +58321.0 q^{81} +13824.0i q^{82} +23644.0i q^{83} -1568.00 q^{84} +86512.0 q^{86} -4985.00i q^{87} +147300. q^{89} -47481.0 q^{91} -52928.0i q^{92} -1192.00i q^{93} +209896. q^{94} +8192.00 q^{96} -8343.00i q^{97} +19208.0i q^{98} -109626. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 64 q^{4} - 16 q^{6} + 484 q^{9}+O(q^{10}) \) 2 * q - 64 * q^4 - 16 * q^6 + 484 * q^9	\( 2 q - 64 q^{4} - 16 q^{6} + 484 q^{9} - 906 q^{11} + 784 q^{14} - 2048 q^{16} + 3100 q^{19} + 98 q^{21} + 15504 q^{26} + 9970 q^{29} + 2384 q^{31} + 26192 q^{34} - 15488 q^{36} + 1938 q^{39} - 3456 q^{41} + 28992 q^{44} + 26464 q^{46} - 4802 q^{49} + 3274 q^{51} - 7760 q^{54} + 9160 q^{59} - 24976 q^{61} + 65536 q^{64} + 7248 q^{66} + 3308 q^{69} + 103584 q^{71} - 176288 q^{74} - 99200 q^{76} - 125530 q^{79} + 116642 q^{81} - 3136 q^{84} + 173024 q^{86} + 294600 q^{89} - 94962 q^{91} + 419792 q^{94} + 16384 q^{96} - 219252 q^{99}+O(q^{100}) \) 2 * q - 64 * q^4 - 16 * q^6 + 484 * q^9 - 906 * q^11 + 784 * q^14 - 2048 * q^16 + 3100 * q^19 + 98 * q^21 + 15504 * q^26 + 9970 * q^29 + 2384 * q^31 + 26192 * q^34 - 15488 * q^36 + 1938 * q^39 - 3456 * q^41 + 28992 * q^44 + 26464 * q^46 - 4802 * q^49 + 3274 * q^51 - 7760 * q^54 + 9160 * q^59 - 24976 * q^61 + 65536 * q^64 + 7248 * q^66 + 3308 * q^69 + 103584 * q^71 - 176288 * q^74 - 99200 * q^76 - 125530 * q^79 + 116642 * q^81 - 3136 * q^84 + 173024 * q^86 + 294600 * q^89 - 94962 * q^91 + 419792 * q^94 + 16384 * q^96 - 219252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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