LMFDB - Embedded newform 289.4.b.a.288.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(288,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.a.288.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000 q^{2} -8.00000i q^{3} +1.00000 q^{4} +6.00000i q^{5} -24.0000i q^{6} +28.0000i q^{7} -21.0000 q^{8} -37.0000 q^{9} +O(q^{10})$	\(q+3.00000 q^{2} -8.00000i q^{3} +1.00000 q^{4} +6.00000i q^{5} -24.0000i q^{6} +28.0000i q^{7} -21.0000 q^{8} -37.0000 q^{9} +18.0000i q^{10} +24.0000i q^{11} -8.00000i q^{12} -58.0000 q^{13} +84.0000i q^{14} +48.0000 q^{15} -71.0000 q^{16} -111.000 q^{18} -116.000 q^{19} +6.00000i q^{20} +224.000 q^{21} +72.0000i q^{22} +60.0000i q^{23} +168.000i q^{24} +89.0000 q^{25} -174.000 q^{26} +80.0000i q^{27} +28.0000i q^{28} +30.0000i q^{29} +144.000 q^{30} -172.000i q^{31} -45.0000 q^{32} +192.000 q^{33} -168.000 q^{35} -37.0000 q^{36} -58.0000i q^{37} -348.000 q^{38} +464.000i q^{39} -126.000i q^{40} +342.000i q^{41} +672.000 q^{42} +148.000 q^{43} +24.0000i q^{44} -222.000i q^{45} +180.000i q^{46} +288.000 q^{47} +568.000i q^{48} -441.000 q^{49} +267.000 q^{50} -58.0000 q^{52} -318.000 q^{53} +240.000i q^{54} -144.000 q^{55} -588.000i q^{56} +928.000i q^{57} +90.0000i q^{58} -252.000 q^{59} +48.0000 q^{60} -110.000i q^{61} -516.000i q^{62} -1036.00i q^{63} +433.000 q^{64} -348.000i q^{65} +576.000 q^{66} -484.000 q^{67} +480.000 q^{69} -504.000 q^{70} -708.000i q^{71} +777.000 q^{72} +362.000i q^{73} -174.000i q^{74} -712.000i q^{75} -116.000 q^{76} -672.000 q^{77} +1392.00i q^{78} +484.000i q^{79} -426.000i q^{80} -359.000 q^{81} +1026.00i q^{82} -756.000 q^{83} +224.000 q^{84} +444.000 q^{86} +240.000 q^{87} -504.000i q^{88} -774.000 q^{89} -666.000i q^{90} -1624.00i q^{91} +60.0000i q^{92} -1376.00 q^{93} +864.000 q^{94} -696.000i q^{95} +360.000i q^{96} -382.000i q^{97} -1323.00 q^{98} -888.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 2 q^{4} - 42 q^{8} - 74 q^{9}+O(q^{10}) $ 2 * q + 6 * q^2 + 2 * q^4 - 42 * q^8 - 74 * q^9	$ 2 q + 6 q^{2} + 2 q^{4} - 42 q^{8} - 74 q^{9} - 116 q^{13} + 96 q^{15} - 142 q^{16} - 222 q^{18} - 232 q^{19} + 448 q^{21} + 178 q^{25} - 348 q^{26} + 288 q^{30} - 90 q^{32} + 384 q^{33} - 336 q^{35} - 74 q^{36} - 696 q^{38} + 1344 q^{42} + 296 q^{43} + 576 q^{47} - 882 q^{49} + 534 q^{50} - 116 q^{52} - 636 q^{53} - 288 q^{55} - 504 q^{59} + 96 q^{60} + 866 q^{64} + 1152 q^{66} - 968 q^{67} + 960 q^{69} - 1008 q^{70} + 1554 q^{72} - 232 q^{76} - 1344 q^{77} - 718 q^{81} - 1512 q^{83} + 448 q^{84} + 888 q^{86} + 480 q^{87} - 1548 q^{89} - 2752 q^{93} + 1728 q^{94} - 2646 q^{98}+O(q^{100}) $ 2 * q + 6 * q^2 + 2 * q^4 - 42 * q^8 - 74 * q^9 - 116 * q^13 + 96 * q^15 - 142 * q^16 - 222 * q^18 - 232 * q^19 + 448 * q^21 + 178 * q^25 - 348 * q^26 + 288 * q^30 - 90 * q^32 + 384 * q^33 - 336 * q^35 - 74 * q^36 - 696 * q^38 + 1344 * q^42 + 296 * q^43 + 576 * q^47 - 882 * q^49 + 534 * q^50 - 116 * q^52 - 636 * q^53 - 288 * q^55 - 504 * q^59 + 96 * q^60 + 866 * q^64 + 1152 * q^66 - 968 * q^67 + 960 * q^69 - 1008 * q^70 + 1554 * q^72 - 232 * q^76 - 1344 * q^77 - 718 * q^81 - 1512 * q^83 + 448 * q^84 + 888 * q^86 + 480 * q^87 - 1548 * q^89 - 2752 * q^93 + 1728 * q^94 - 2646 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	3.00000	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$2$	3.00000	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$3$	− 8.00000i	− 1.53960i	−0.638285	−	0.769800i	$-0.720356\pi$
$3$	− 8.00000i	− 1.53960i	0.638285	−	0.769800i	$-0.279644\pi$
$4$	1.00000	0.125000
$5$	6.00000i	0.536656i	0.963328	+	0.268328i	$0.0864711\pi$
$5$	6.00000i	0.536656i	−0.963328	+	0.268328i	$0.913529\pi$
$6$	− 24.0000i	− 1.63299i
$7$	28.0000i	1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$	28.0000i	1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	−21.0000	−0.928078
$9$	−37.0000	−1.37037
$10$	18.0000i	0.569210i
$11$	24.0000i	0.657843i	0.944357	+	0.328921i	$0.106685\pi$
$11$	24.0000i	0.657843i	−0.944357	+	0.328921i	$0.893315\pi$
$12$	− 8.00000i	− 0.192450i
$13$	−58.0000	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$13$	−58.0000	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$14$	84.0000i	1.60357i
$15$	48.0000	0.826236
$16$	−71.0000	−1.10938
$17$	0	0
$17$	0	0
$18$	−111.000	−1.45350
$19$	−116.000	−1.40064	−0.700322	−	0.713827i	$-0.746960\pi$
$19$	−116.000	−1.40064	−0.700322	+	0.713827i	$0.746960\pi$
$20$	6.00000i	0.0670820i
$21$	224.000	2.32766
$22$	72.0000i	0.697748i
$23$	60.0000i	0.543951i	0.962304	+	0.271975i	$0.0876769\pi$
$23$	60.0000i	0.543951i	−0.962304	+	0.271975i	$0.912323\pi$
$24$	168.000i	1.42887i
$25$	89.0000	0.712000
$26$	−174.000	−1.31247
$27$	80.0000i	0.570222i
$28$	28.0000i	0.188982i
$29$	30.0000i	0.192099i	0.995377	+	0.0960493i	$0.0306207\pi$
$29$	30.0000i	0.192099i	−0.995377	+	0.0960493i	$0.969379\pi$
$30$	144.000	0.876356
$31$	− 172.000i	− 0.996520i	−0.867028	−	0.498260i	$-0.833973\pi$
$31$	− 172.000i	− 0.996520i	0.867028	−	0.498260i	$-0.166027\pi$
$32$	−45.0000	−0.248592
$33$	192.000	1.01282
$34$	0	0
$35$	−168.000	−0.811348
$36$	−37.0000	−0.171296
$37$	− 58.0000i	− 0.257707i	−0.991664	−	0.128853i	$-0.958870\pi$
$37$	− 58.0000i	− 0.257707i	0.991664	−	0.128853i	$-0.0411296\pi$
$38$	−348.000	−1.48561
$39$	464.000i	1.90511i
$40$	− 126.000i	− 0.498059i
$41$	342.000i	1.30272i	0.758770	+	0.651359i	$0.225801\pi$
$41$	342.000i	1.30272i	−0.758770	+	0.651359i	$0.774199\pi$
$42$	672.000	2.46885
$43$	148.000	0.524879	0.262439	−	0.964948i	$-0.415473\pi$
$43$	148.000	0.524879	0.262439	+	0.964948i	$0.415473\pi$
$44$	24.0000i	0.0822304i
$45$	− 222.000i	− 0.735418i
$46$	180.000i	0.576947i
$47$	288.000	0.893811	0.446906	−	0.894581i	$-0.352526\pi$
$47$	288.000	0.893811	0.446906	+	0.894581i	$0.352526\pi$
$48$	568.000i	1.70799i
$49$	−441.000	−1.28571
$50$	267.000	0.755190
$51$	0	0
$52$	−58.0000	−0.154676
$53$	−318.000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−318.000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	240.000i	0.604812i
$55$	−144.000	−0.353036
$56$	− 588.000i	− 1.40312i
$57$	928.000i	2.15643i
$58$	90.0000i	0.203751i
$59$	−252.000	−0.556061	−0.278031	−	0.960572i	$-0.589682\pi$
$59$	−252.000	−0.556061	−0.278031	+	0.960572i	$0.589682\pi$
$60$	48.0000	0.103280
$61$	− 110.000i	− 0.230886i	−0.993314	−	0.115443i	$-0.963171\pi$
$61$	− 110.000i	− 0.230886i	0.993314	−	0.115443i	$-0.0368288\pi$
$62$	− 516.000i	− 1.05697i
$63$	− 1036.00i	− 2.07181i
$64$	433.000	0.845703
$65$	− 348.000i	− 0.664063i
$66$	576.000	1.07425
$67$	−484.000	−0.882537	−0.441269	−	0.897375i	$-0.645471\pi$
$67$	−484.000	−0.882537	−0.441269	+	0.897375i	$0.645471\pi$
$68$	0	0
$69$	480.000	0.837467
$70$	−504.000	−0.860565
$71$	− 708.000i	− 1.18344i	−0.806144	−	0.591719i	$-0.798449\pi$
$71$	− 708.000i	− 1.18344i	0.806144	−	0.591719i	$-0.201551\pi$
$72$	777.000	1.27181
$73$	362.000i	0.580396i	0.956967	+	0.290198i	$0.0937211\pi$
$73$	362.000i	0.580396i	−0.956967	+	0.290198i	$0.906279\pi$
$74$	− 174.000i	− 0.273339i
$75$	− 712.000i	− 1.09620i
$76$	−116.000	−0.175080
$77$	−672.000	−0.994565
$78$	1392.00i	2.02068i
$79$	484.000i	0.689294i	0.938732	+	0.344647i	$0.112001\pi$
$79$	484.000i	0.689294i	−0.938732	+	0.344647i	$0.887999\pi$
$80$	− 426.000i	− 0.595353i
$81$	−359.000	−0.492455
$82$	1026.00i	1.38174i
$83$	−756.000	−0.999780	−0.499890	−	0.866089i	$-0.666626\pi$
$83$	−756.000	−0.999780	−0.499890	+	0.866089i	$0.666626\pi$
$84$	224.000	0.290957
$85$	0	0
$86$	444.000	0.556718
$87$	240.000	0.295755
$88$	− 504.000i	− 0.610529i
$89$	−774.000	−0.921841	−0.460920	−	0.887441i	$-0.652481\pi$
$89$	−774.000	−0.921841	−0.460920	+	0.887441i	$0.652481\pi$
$90$	− 666.000i	− 0.780028i
$91$	− 1624.00i	− 1.87079i
$92$	60.0000i	0.0679938i
$93$	−1376.00	−1.53424
$94$	864.000	0.948030
$95$	− 696.000i	− 0.751664i
$96$	360.000i	0.382733i
$97$	− 382.000i	− 0.399858i	−0.979810	−	0.199929i	$-0.935929\pi$
$97$	− 382.000i	− 0.399858i	0.979810	−	0.199929i	$-0.0640711\pi$
$98$	−1323.00	−1.36371
$99$	− 888.000i	− 0.901488i
$100$	89.0000	0.0890000
$101$	−210.000	−0.206889	−0.103444	−	0.994635i	$-0.532986\pi$
$101$	−210.000	−0.206889	−0.103444	+	0.994635i	$0.532986\pi$
$102$	0	0
$103$	−232.000	−0.221938	−0.110969	−	0.993824i	$-0.535395\pi$
$103$	−232.000	−0.221938	−0.110969	+	0.993824i	$0.535395\pi$
$104$	1218.00	1.14841
$105$	1344.00i	1.24915i
$106$	−954.000	−0.874157
$107$	432.000i	0.390309i	0.980773	+	0.195154i	$0.0625208\pi$
$107$	432.000i	0.390309i	−0.980773	+	0.195154i	$0.937479\pi$
$108$	80.0000i	0.0712778i
$109$	1186.00i	1.04219i	0.853500	+	0.521093i	$0.174475\pi$
$109$	1186.00i	1.04219i	−0.853500	+	0.521093i	$0.825525\pi$
$110$	−432.000	−0.374451
$111$	−464.000	−0.396765
$112$	− 1988.00i	− 1.67722i
$113$	366.000i	0.304694i	0.988327	+	0.152347i	$0.0486831\pi$
$113$	366.000i	0.304694i	−0.988327	+	0.152347i	$0.951317\pi$
$114$	2784.00i	2.28724i
$115$	−360.000	−0.291915
$116$	30.0000i	0.0240123i
$117$	2146.00	1.69571
$118$	−756.000	−0.589792
$119$	0	0
$120$	−1008.00	−0.766812
$121$	755.000	0.567243
$122$	− 330.000i	− 0.244892i
$123$	2736.00	2.00567
$124$	− 172.000i	− 0.124565i
$125$	1284.00i	0.918756i
$126$	− 3108.00i	− 2.19748i
$127$	472.000	0.329789	0.164895	−	0.986311i	$-0.447272\pi$
$127$	472.000	0.329789	0.164895	+	0.986311i	$0.447272\pi$
$128$	1659.00	1.14560
$129$	− 1184.00i	− 0.808104i
$130$	− 1044.00i	− 0.704345i
$131$	2760.00i	1.84078i	0.391000	+	0.920391i	$0.372129\pi$
$131$	2760.00i	1.84078i	−0.391000	+	0.920391i	$0.627871\pi$
$132$	192.000	0.126602
$133$	− 3248.00i	− 2.11757i
$134$	−1452.00	−0.936072
$135$	−480.000	−0.306013
$136$	0	0
$137$	1098.00	0.684733	0.342367	−	0.939566i	$-0.388771\pi$
$137$	1098.00	0.684733	0.342367	+	0.939566i	$0.388771\pi$
$138$	1440.00	0.888268
$139$	2528.00i	1.54261i	0.636468	+	0.771303i	$0.280395\pi$
$139$	2528.00i	1.54261i	−0.636468	+	0.771303i	$0.719605\pi$
$140$	−168.000	−0.101419
$141$	− 2304.00i	− 1.37611i
$142$	− 2124.00i	− 1.25523i
$143$	− 1392.00i	− 0.814020i
$144$	2627.00	1.52025
$145$	−180.000	−0.103091
$146$	1086.00i	0.615603i
$147$	3528.00i	1.97949i
$148$	− 58.0000i	− 0.0322133i
$149$	1614.00	0.887410	0.443705	−	0.896173i	$-0.353664\pi$
$149$	1614.00	0.887410	0.443705	+	0.896173i	$0.353664\pi$
$150$	− 2136.00i	− 1.16269i
$151$	3328.00	1.79357	0.896784	−	0.442468i	$-0.145897\pi$
$151$	3328.00	1.79357	0.896784	+	0.442468i	$0.145897\pi$
$152$	2436.00	1.29991
$153$	0	0
$154$	−2016.00	−1.05490
$155$	1032.00	0.534789
$156$	464.000i	0.238139i
$157$	−2458.00	−1.24949	−0.624744	−	0.780829i	$-0.714797\pi$
$157$	−2458.00	−1.24949	−0.624744	+	0.780829i	$0.714797\pi$
$158$	1452.00i	0.731107i
$159$	2544.00i	1.26888i
$160$	− 270.000i	− 0.133409i
$161$	−1680.00	−0.822376
$162$	−1077.00	−0.522328
$163$	− 272.000i	− 0.130704i	−0.997862	−	0.0653518i	$-0.979183\pi$
$163$	− 272.000i	− 0.130704i	0.997862	−	0.0653518i	$-0.0208170\pi$
$164$	342.000i	0.162840i
$165$	1152.00i	0.543534i
$166$	−2268.00	−1.06043
$167$	3516.00i	1.62920i	0.580024	+	0.814600i	$0.303043\pi$
$167$	3516.00i	1.62920i	−0.580024	+	0.814600i	$0.696957\pi$
$168$	−4704.00	−2.16025
$169$	1167.00	0.531179
$170$	0	0
$171$	4292.00	1.91940
$172$	148.000	0.0656099
$173$	− 1842.00i	− 0.809507i	−0.914426	−	0.404753i	$-0.867357\pi$
$173$	− 1842.00i	− 0.809507i	0.914426	−	0.404753i	$-0.132643\pi$
$174$	720.000	0.313696
$175$	2492.00i	1.07644i
$176$	− 1704.00i	− 0.729795i
$177$	2016.00i	0.856112i
$178$	−2322.00	−0.977760
$179$	3516.00	1.46815	0.734073	−	0.679070i	$-0.237617\pi$
$179$	3516.00	1.46815	0.734073	+	0.679070i	$0.237617\pi$
$180$	− 222.000i	− 0.0919272i
$181$	− 3398.00i	− 1.39542i	−0.716379	−	0.697711i	$-0.754202\pi$
$181$	− 3398.00i	− 1.39542i	0.716379	−	0.697711i	$-0.245798\pi$
$182$	− 4872.00i	− 1.98427i
$183$	−880.000	−0.355473
$184$	− 1260.00i	− 0.504828i
$185$	348.000	0.138300
$186$	−4128.00	−1.62731
$187$	0	0
$188$	288.000	0.111726
$189$	−2240.00	−0.862095
$190$	− 2088.00i	− 0.797260i
$191$	−2640.00	−1.00012	−0.500062	−	0.865990i	$-0.666689\pi$
$191$	−2640.00	−1.00012	−0.500062	+	0.865990i	$0.666689\pi$
$192$	− 3464.00i	− 1.30205i
$193$	− 2882.00i	− 1.07488i	−0.843304	−	0.537438i	$-0.819392\pi$
$193$	− 2882.00i	− 1.07488i	0.843304	−	0.537438i	$-0.180608\pi$
$194$	− 1146.00i	− 0.424113i
$195$	−2784.00	−1.02239
$196$	−441.000	−0.160714
$197$	42.0000i	0.0151897i	0.999971	+	0.00759486i	$0.00241754\pi$
$197$	42.0000i	0.0151897i	−0.999971	+	0.00759486i	$0.997582\pi$
$198$	− 2664.00i	− 0.956173i
$199$	− 3220.00i	− 1.14703i	−0.819194	−	0.573517i	$-0.805579\pi$
$199$	− 3220.00i	− 1.14703i	0.819194	−	0.573517i	$-0.194421\pi$
$200$	−1869.00	−0.660791
$201$	3872.00i	1.35876i
$202$	−630.000	−0.219439
$203$	−840.000	−0.290426
$204$	0	0
$205$	−2052.00	−0.699112
$206$	−696.000	−0.235401
$207$	− 2220.00i	− 0.745414i
$208$	4118.00	1.37275
$209$	− 2784.00i	− 0.921403i
$210$	4032.00i	1.32493i
$211$	2080.00i	0.678640i	0.940671	+	0.339320i	$0.110197\pi$
$211$	2080.00i	0.678640i	−0.940671	+	0.339320i	$0.889803\pi$
$212$	−318.000	−0.103020
$213$	−5664.00	−1.82202
$214$	1296.00i	0.413985i
$215$	888.000i	0.281680i
$216$	− 1680.00i	− 0.529211i
$217$	4816.00	1.50660
$218$	3558.00i	1.10540i
$219$	2896.00	0.893578
$220$	−144.000	−0.0441294
$221$	0	0
$222$	−1392.00	−0.420833
$223$	−4664.00	−1.40056	−0.700279	−	0.713869i	$-0.746941\pi$
$223$	−4664.00	−1.40056	−0.700279	+	0.713869i	$0.746941\pi$
$224$	− 1260.00i	− 0.375836i
$225$	−3293.00	−0.975704
$226$	1098.00i	0.323176i
$227$	1440.00i	0.421040i	0.977590	+	0.210520i	$0.0675158\pi$
$227$	1440.00i	0.421040i	−0.977590	+	0.210520i	$0.932484\pi$
$228$	928.000i	0.269554i
$229$	1186.00	0.342241	0.171120	−	0.985250i	$-0.445261\pi$
$229$	1186.00	0.342241	0.171120	+	0.985250i	$0.445261\pi$
$230$	−1080.00	−0.309622
$231$	5376.00i	1.53123i
$232$	− 630.000i	− 0.178282i
$233$	− 5334.00i	− 1.49975i	−0.661579	−	0.749875i	$-0.730113\pi$
$233$	− 5334.00i	− 1.49975i	0.661579	−	0.749875i	$-0.269887\pi$
$234$	6438.00	1.79857
$235$	1728.00i	0.479669i
$236$	−252.000	−0.0695076
$237$	3872.00	1.06124
$238$	0	0
$239$	5328.00	1.44201	0.721003	−	0.692931i	$-0.243681\pi$
$239$	5328.00	1.44201	0.721003	+	0.692931i	$0.243681\pi$
$240$	−3408.00	−0.916606
$241$	5618.00i	1.50161i	0.660526	+	0.750803i	$0.270333\pi$
$241$	5618.00i	1.50161i	−0.660526	+	0.750803i	$0.729667\pi$
$242$	2265.00	0.601652
$243$	5032.00i	1.32841i
$244$	− 110.000i	− 0.0288608i
$245$	− 2646.00i	− 0.689987i
$246$	8208.00	2.12733
$247$	6728.00	1.73317
$248$	3612.00i	0.924848i
$249$	6048.00i	1.53926i
$250$	3852.00i	0.974487i
$251$	−2028.00	−0.509985	−0.254992	−	0.966943i	$-0.582073\pi$
$251$	−2028.00	−0.509985	−0.254992	+	0.966943i	$0.582073\pi$
$252$	− 1036.00i	− 0.258976i
$253$	−1440.00	−0.357834
$254$	1416.00	0.349794
$255$	0	0
$256$	1513.00	0.369385
$257$	1902.00	0.461648	0.230824	−	0.972996i	$-0.425858\pi$
$257$	1902.00	0.461648	0.230824	+	0.972996i	$0.425858\pi$
$258$	− 3552.00i	− 0.857123i
$259$	1624.00	0.389616
$260$	− 348.000i	− 0.0830079i
$261$	− 1110.00i	− 0.263246i
$262$	8280.00i	1.95244i
$263$	5472.00	1.28296	0.641479	−	0.767141i	$-0.278321\pi$
$263$	5472.00	1.28296	0.641479	+	0.767141i	$0.278321\pi$
$264$	−4032.00	−0.939971
$265$	− 1908.00i	− 0.442292i
$266$	− 9744.00i	− 2.24603i
$267$	6192.00i	1.41927i
$268$	−484.000	−0.110317
$269$	− 3570.00i	− 0.809170i	−0.914500	−	0.404585i	$-0.867416\pi$
$269$	− 3570.00i	− 0.809170i	0.914500	−	0.404585i	$-0.132584\pi$
$270$	−1440.00	−0.324576
$271$	272.000	0.0609698	0.0304849	−	0.999535i	$-0.490295\pi$
$271$	272.000	0.0609698	0.0304849	+	0.999535i	$0.490295\pi$
$272$	0	0
$273$	−12992.0	−2.88026
$274$	3294.00	0.726269
$275$	2136.00i	0.468384i
$276$	480.000	0.104683
$277$	3830.00i	0.830767i	0.909646	+	0.415383i	$0.136353\pi$
$277$	3830.00i	0.830767i	−0.909646	+	0.415383i	$0.863647\pi$
$278$	7584.00i	1.63618i
$279$	6364.00i	1.36560i
$280$	3528.00	0.752994
$281$	−8874.00	−1.88391	−0.941955	−	0.335740i	$-0.891014\pi$
$281$	−8874.00	−1.88391	−0.941955	+	0.335740i	$0.891014\pi$
$282$	− 6912.00i	− 1.45959i
$283$	2632.00i	0.552849i	0.961036	+	0.276424i	$0.0891495\pi$
$283$	2632.00i	0.552849i	−0.961036	+	0.276424i	$0.910850\pi$
$284$	− 708.000i	− 0.147930i
$285$	−5568.00	−1.15726
$286$	− 4176.00i	− 0.863399i
$287$	−9576.00	−1.96952
$288$	1665.00	0.340663
$289$	0	0
$290$	−540.000	−0.109344
$291$	−3056.00	−0.615622
$292$	362.000i	0.0725495i
$293$	−6402.00	−1.27648	−0.638240	−	0.769837i	$-0.720337\pi$
$293$	−6402.00	−1.27648	−0.638240	+	0.769837i	$0.720337\pi$
$294$	10584.0i	2.09956i
$295$	− 1512.00i	− 0.298414i
$296$	1218.00i	0.239172i
$297$	−1920.00	−0.375117
$298$	4842.00	0.941240
$299$	− 3480.00i	− 0.673089i
$300$	− 712.000i	− 0.137024i
$301$	4144.00i	0.793542i
$302$	9984.00	1.90237
$303$	1680.00i	0.318526i
$304$	8236.00	1.55384
$305$	660.000	0.123907
$306$	0	0
$307$	−8980.00	−1.66943	−0.834716	−	0.550681i	$-0.814368\pi$
$307$	−8980.00	−1.66943	−0.834716	+	0.550681i	$0.814368\pi$
$308$	−672.000	−0.124321
$309$	1856.00i	0.341696i
$310$	3096.00	0.567229
$311$	− 3972.00i	− 0.724217i	−0.932136	−	0.362108i	$-0.882057\pi$
$311$	− 3972.00i	− 0.724217i	0.932136	−	0.362108i	$-0.117943\pi$
$312$	− 9744.00i	− 1.76809i
$313$	− 4730.00i	− 0.854171i	−0.904211	−	0.427085i	$-0.859540\pi$
$313$	− 4730.00i	− 0.854171i	0.904211	−	0.427085i	$-0.140460\pi$
$314$	−7374.00	−1.32528
$315$	6216.00	1.11185
$316$	484.000i	0.0861618i
$317$	2898.00i	0.513463i	0.966483	+	0.256732i	$0.0826457\pi$
$317$	2898.00i	0.513463i	−0.966483	+	0.256732i	$0.917354\pi$
$318$	7632.00i	1.34585i
$319$	−720.000	−0.126371
$320$	2598.00i	0.453852i
$321$	3456.00	0.600919
$322$	−5040.00	−0.872262
$323$	0	0
$324$	−359.000	−0.0615569
$325$	−5162.00	−0.881035
$326$	− 816.000i	− 0.138632i
$327$	9488.00	1.60455
$328$	− 7182.00i	− 1.20902i
$329$	8064.00i	1.35132i
$330$	3456.00i	0.576505i
$331$	4564.00	0.757886	0.378943	−	0.925420i	$-0.376288\pi$
$331$	4564.00	0.757886	0.378943	+	0.925420i	$0.376288\pi$
$332$	−756.000	−0.124973
$333$	2146.00i	0.353153i
$334$	10548.0i	1.72803i
$335$	− 2904.00i	− 0.473619i
$336$	−15904.0	−2.58225
$337$	722.000i	0.116706i	0.998296	+	0.0583529i	$0.0185849\pi$
$337$	722.000i	0.116706i	−0.998296	+	0.0583529i	$0.981415\pi$
$338$	3501.00	0.563400
$339$	2928.00	0.469107
$340$	0	0
$341$	4128.00	0.655553
$342$	12876.0	2.03583
$343$	− 2744.00i	− 0.431959i
$344$	−3108.00	−0.487128
$345$	2880.00i	0.449432i
$346$	− 5526.00i	− 0.858612i
$347$	− 5544.00i	− 0.857687i	−0.903379	−	0.428844i	$-0.858921\pi$
$347$	− 5544.00i	− 0.857687i	0.903379	−	0.428844i	$-0.141079\pi$
$348$	240.000	0.0369694
$349$	−11126.0	−1.70648	−0.853239	−	0.521519i	$-0.825365\pi$
$349$	−11126.0	−1.70648	−0.853239	+	0.521519i	$0.825365\pi$
$350$	7476.00i	1.14174i
$351$	− 4640.00i	− 0.705598i
$352$	− 1080.00i	− 0.163535i
$353$	7842.00	1.18240	0.591200	−	0.806525i	$-0.298654\pi$
$353$	7842.00	1.18240	0.591200	+	0.806525i	$0.298654\pi$
$354$	6048.00i	0.908044i
$355$	4248.00	0.635100
$356$	−774.000	−0.115230
$357$	0	0
$358$	10548.0	1.55720
$359$	−5040.00	−0.740950	−0.370475	−	0.928842i	$-0.620805\pi$
$359$	−5040.00	−0.740950	−0.370475	+	0.928842i	$0.620805\pi$
$360$	4662.00i	0.682525i
$361$	6597.00	0.961802
$362$	− 10194.0i	− 1.48007i
$363$	− 6040.00i	− 0.873327i
$364$	− 1624.00i	− 0.233848i
$365$	−2172.00	−0.311473
$366$	−2640.00	−0.377036
$367$	8404.00i	1.19533i	0.801747	+	0.597664i	$0.203904\pi$
$367$	8404.00i	1.19533i	−0.801747	+	0.597664i	$0.796096\pi$
$368$	− 4260.00i	− 0.603445i
$369$	− 12654.0i	− 1.78521i
$370$	1044.00	0.146689
$371$	− 8904.00i	− 1.24602i
$372$	−1376.00	−0.191780
$373$	−8098.00	−1.12412	−0.562062	−	0.827095i	$-0.689992\pi$
$373$	−8098.00	−1.12412	−0.562062	+	0.827095i	$0.689992\pi$
$374$	0	0
$375$	10272.0	1.41452
$376$	−6048.00	−0.829526
$377$	− 1740.00i	− 0.237704i
$378$	−6720.00	−0.914390
$379$	320.000i	0.0433702i	0.999765	+	0.0216851i	$0.00690312\pi$
$379$	320.000i	0.0433702i	−0.999765	+	0.0216851i	$0.993097\pi$
$380$	− 696.000i	− 0.0939580i
$381$	− 3776.00i	− 0.507744i
$382$	−7920.00	−1.06079
$383$	10872.0	1.45048	0.725239	−	0.688497i	$-0.241729\pi$
$383$	10872.0	1.45048	0.725239	+	0.688497i	$0.241729\pi$
$384$	− 13272.0i	− 1.76376i
$385$	− 4032.00i	− 0.533740i
$386$	− 8646.00i	− 1.14008i
$387$	−5476.00	−0.719278
$388$	− 382.000i	− 0.0499822i
$389$	−1374.00	−0.179086	−0.0895431	−	0.995983i	$-0.528541\pi$
$389$	−1374.00	−0.179086	−0.0895431	+	0.995983i	$0.528541\pi$
$390$	−8352.00	−1.08441
$391$	0	0
$392$	9261.00	1.19324
$393$	22080.0	2.83407
$394$	126.000i	0.0161111i
$395$	−2904.00	−0.369914
$396$	− 888.000i	− 0.112686i
$397$	7522.00i	0.950928i	0.879735	+	0.475464i	$0.157720\pi$
$397$	7522.00i	0.950928i	−0.879735	+	0.475464i	$0.842280\pi$
$398$	− 9660.00i	− 1.21661i
$399$	−25984.0	−3.26022
$400$	−6319.00	−0.789875
$401$	− 2706.00i	− 0.336986i	−0.985703	−	0.168493i	$-0.946110\pi$
$401$	− 2706.00i	− 0.336986i	0.985703	−	0.168493i	$-0.0538900\pi$
$402$	11616.0i	1.44118i
$403$	9976.00i	1.23310i
$404$	−210.000	−0.0258611
$405$	− 2154.00i	− 0.264279i
$406$	−2520.00	−0.308043
$407$	1392.00	0.169530
$408$	0	0
$409$	266.000	0.0321586	0.0160793	−	0.999871i	$-0.494882\pi$
$409$	266.000	0.0321586	0.0160793	+	0.999871i	$0.494882\pi$
$410$	−6156.00	−0.741520
$411$	− 8784.00i	− 1.05422i
$412$	−232.000	−0.0277423
$413$	− 7056.00i	− 0.840685i
$414$	− 6660.00i	− 0.790631i
$415$	− 4536.00i	− 0.536539i
$416$	2610.00	0.307610
$417$	20224.0	2.37500
$418$	− 8352.00i	− 0.977296i
$419$	− 2688.00i	− 0.313407i	−0.987646	−	0.156703i	$-0.949913\pi$
$419$	− 2688.00i	− 0.313407i	0.987646	−	0.156703i	$-0.0500867\pi$
$420$	1344.00i	0.156144i
$421$	−13810.0	−1.59871	−0.799357	−	0.600857i	$-0.794826\pi$
$421$	−13810.0	−1.59871	−0.799357	+	0.600857i	$0.794826\pi$
$422$	6240.00i	0.719807i
$423$	−10656.0	−1.22485
$424$	6678.00	0.764888
$425$	0	0
$426$	−16992.0	−1.93255
$427$	3080.00	0.349067
$428$	432.000i	0.0487886i
$429$	−11136.0	−1.25327
$430$	2664.00i	0.298766i
$431$	− 3036.00i	− 0.339302i	−0.985504	−	0.169651i	$-0.945736\pi$
$431$	− 3036.00i	− 0.339302i	0.985504	−	0.169651i	$-0.0542640\pi$
$432$	− 5680.00i	− 0.632591i
$433$	11422.0	1.26768	0.633841	−	0.773463i	$-0.281477\pi$
$433$	11422.0	1.26768	0.633841	+	0.773463i	$0.281477\pi$
$434$	14448.0	1.59799
$435$	1440.00i	0.158719i
$436$	1186.00i	0.130273i
$437$	− 6960.00i	− 0.761881i
$438$	8688.00	0.947782
$439$	− 52.0000i	− 0.00565336i	−0.999996	−	0.00282668i	$-0.999100\pi$
$439$	− 52.0000i	− 0.00565336i	0.999996	−	0.00282668i	$-0.000899761\pi$
$440$	3024.00	0.327644
$441$	16317.0	1.76190
$442$	0	0
$443$	3108.00	0.333331	0.166665	−	0.986014i	$-0.446700\pi$
$443$	3108.00	0.333331	0.166665	+	0.986014i	$0.446700\pi$
$444$	−464.000	−0.0495956
$445$	− 4644.00i	− 0.494712i
$446$	−13992.0	−1.48552
$447$	− 12912.0i	− 1.36626i
$448$	12124.0i	1.27858i
$449$	− 6114.00i	− 0.642622i	−0.946974	−	0.321311i	$-0.895876\pi$
$449$	− 6114.00i	− 0.642622i	0.946974	−	0.321311i	$-0.104124\pi$
$450$	−9879.00	−1.03489
$451$	−8208.00	−0.856984
$452$	366.000i	0.0380867i
$453$	− 26624.0i	− 2.76138i
$454$	4320.00i	0.446581i
$455$	9744.00	1.00397
$456$	− 19488.0i	− 2.00134i
$457$	−4106.00	−0.420286	−0.210143	−	0.977671i	$-0.567393\pi$
$457$	−4106.00	−0.420286	−0.210143	+	0.977671i	$0.567393\pi$
$458$	3558.00	0.363001
$459$	0	0
$460$	−360.000	−0.0364893
$461$	−3366.00	−0.340066	−0.170033	−	0.985438i	$-0.554387\pi$
$461$	−3366.00	−0.340066	−0.170033	+	0.985438i	$0.554387\pi$
$462$	16128.0i	1.62412i
$463$	896.000	0.0899366	0.0449683	−	0.998988i	$-0.485681\pi$
$463$	896.000	0.0899366	0.0449683	+	0.998988i	$0.485681\pi$
$464$	− 2130.00i	− 0.213109i
$465$	− 8256.00i	− 0.823361i
$466$	− 16002.0i	− 1.59073i
$467$	10236.0	1.01427	0.507137	−	0.861866i	$-0.330704\pi$
$467$	10236.0	1.01427	0.507137	+	0.861866i	$0.330704\pi$
$468$	2146.00	0.211963
$469$	− 13552.0i	− 1.33427i
$470$	5184.00i	0.508766i
$471$	19664.0i	1.92371i
$472$	5292.00	0.516068
$473$	3552.00i	0.345288i
$474$	11616.0	1.12561
$475$	−10324.0	−0.997258
$476$	0	0
$477$	11766.0	1.12941
$478$	15984.0	1.52948
$479$	5172.00i	0.493350i	0.969098	+	0.246675i	$0.0793380\pi$
$479$	5172.00i	0.493350i	−0.969098	+	0.246675i	$0.920662\pi$
$480$	−2160.00	−0.205396
$481$	3364.00i	0.318888i
$482$	16854.0i	1.59269i
$483$	13440.0i	1.26613i
$484$	755.000	0.0709053
$485$	2292.00	0.214586
$486$	15096.0i	1.40899i
$487$	15052.0i	1.40056i	0.713870	+	0.700278i	$0.246941\pi$
$487$	15052.0i	1.40056i	−0.713870	+	0.700278i	$0.753059\pi$
$488$	2310.00i	0.214280i
$489$	−2176.00	−0.201231
$490$	− 7938.00i	− 0.731841i
$491$	−8700.00	−0.799645	−0.399822	−	0.916593i	$-0.630928\pi$
$491$	−8700.00	−0.799645	−0.399822	+	0.916593i	$0.630928\pi$
$492$	2736.00	0.250708
$493$	0	0
$494$	20184.0	1.83830
$495$	5328.00	0.483789
$496$	12212.0i	1.10551i
$497$	19824.0	1.78919
$498$	18144.0i	1.63263i
$499$	1168.00i	0.104783i	0.998627	+	0.0523916i	$0.0166844\pi$
$499$	1168.00i	0.104783i	−0.998627	+	0.0523916i	$0.983316\pi$
$500$	1284.00i	0.114844i
$501$	28128.0	2.50832
$502$	−6084.00	−0.540921
$503$	1740.00i	0.154240i	0.997022	+	0.0771200i	$0.0245725\pi$
$503$	1740.00i	0.154240i	−0.997022	+	0.0771200i	$0.975428\pi$
$504$	21756.0i	1.92280i
$505$	− 1260.00i	− 0.111028i
$506$	−4320.00	−0.379540
$507$	− 9336.00i	− 0.817803i
$508$	472.000	0.0412236
$509$	−12570.0	−1.09461	−0.547304	−	0.836934i	$-0.684346\pi$
$509$	−12570.0	−1.09461	−0.547304	+	0.836934i	$0.684346\pi$
$510$	0	0
$511$	−10136.0	−0.877476
$512$	−8733.00	−0.753804
$513$	− 9280.00i	− 0.798678i
$514$	5706.00	0.489651
$515$	− 1392.00i	− 0.119105i
$516$	− 1184.00i	− 0.101013i
$517$	6912.00i	0.587987i
$518$	4872.00	0.413250
$519$	−14736.0	−1.24632
$520$	7308.00i	0.616302i
$521$	− 11658.0i	− 0.980319i	−0.871633	−	0.490160i	$-0.836939\pi$
$521$	− 11658.0i	− 0.980319i	0.871633	−	0.490160i	$-0.163061\pi$
$522$	− 3330.00i	− 0.279215i
$523$	13700.0	1.14543	0.572714	−	0.819755i	$-0.305890\pi$
$523$	13700.0	1.14543	0.572714	+	0.819755i	$0.305890\pi$
$524$	2760.00i	0.230098i
$525$	19936.0	1.65729
$526$	16416.0	1.36078
$527$	0	0
$528$	−13632.0	−1.12359
$529$	8567.00	0.704118
$530$	− 5724.00i	− 0.469122i
$531$	9324.00	0.762010
$532$	− 3248.00i	− 0.264697i
$533$	− 19836.0i	− 1.61199i
$534$	18576.0i	1.50536i
$535$	−2592.00	−0.209462
$536$	10164.0	0.819063
$537$	− 28128.0i	− 2.26036i
$538$	− 10710.0i	− 0.858254i
$539$	− 10584.0i	− 0.845798i
$540$	−480.000	−0.0382517
$541$	17822.0i	1.41632i	0.706053	+	0.708159i	$0.250474\pi$
$541$	17822.0i	1.41632i	−0.706053	+	0.708159i	$0.749526\pi$
$542$	816.000	0.0646683
$543$	−27184.0	−2.14839
$544$	0	0
$545$	−7116.00	−0.559295
$546$	−38976.0	−3.05498
$547$	3800.00i	0.297032i	0.988910	+	0.148516i	$0.0474496\pi$
$547$	3800.00i	0.297032i	−0.988910	+	0.148516i	$0.952550\pi$
$548$	1098.00	0.0855917
$549$	4070.00i	0.316400i
$550$	6408.00i	0.496796i
$551$	− 3480.00i	− 0.269062i
$552$	−10080.0	−0.777234
$553$	−13552.0	−1.04212
$554$	11490.0i	0.881161i
$555$	− 2784.00i	− 0.212927i
$556$	2528.00i	0.192826i
$557$	−10074.0	−0.766336	−0.383168	−	0.923679i	$-0.625167\pi$
$557$	−10074.0	−0.766336	−0.383168	+	0.923679i	$0.625167\pi$
$558$	19092.0i	1.44844i
$559$	−8584.00	−0.649489
$560$	11928.0	0.900089
$561$	0	0
$562$	−26622.0	−1.99819
$563$	15948.0	1.19383	0.596917	−	0.802303i	$-0.296392\pi$
$563$	15948.0	1.19383	0.596917	+	0.802303i	$0.296392\pi$
$564$	− 2304.00i	− 0.172014i
$565$	−2196.00	−0.163516
$566$	7896.00i	0.586385i
$567$	− 10052.0i	− 0.744523i
$568$	14868.0i	1.09832i
$569$	−21834.0	−1.60866	−0.804331	−	0.594181i	$-0.797476\pi$
$569$	−21834.0	−1.60866	−0.804331	+	0.594181i	$0.797476\pi$
$570$	−16704.0	−1.22746
$571$	21208.0i	1.55434i	0.629292	+	0.777169i	$0.283345\pi$
$571$	21208.0i	1.55434i	−0.629292	+	0.777169i	$0.716655\pi$
$572$	− 1392.00i	− 0.101753i
$573$	21120.0i	1.53979i
$574$	−28728.0	−2.08900
$575$	5340.00i	0.387293i
$576$	−16021.0	−1.15893
$577$	12530.0	0.904039	0.452020	−	0.892008i	$-0.350704\pi$
$577$	12530.0	0.904039	0.452020	+	0.892008i	$0.350704\pi$
$578$	0	0
$579$	−23056.0	−1.65488
$580$	−180.000	−0.0128864
$581$	− 21168.0i	− 1.51153i
$582$	−9168.00	−0.652965
$583$	− 7632.00i	− 0.542170i
$584$	− 7602.00i	− 0.538652i
$585$	12876.0i	0.910012i
$586$	−19206.0	−1.35391
$587$	−2220.00	−0.156097	−0.0780487	−	0.996950i	$-0.524869\pi$
$587$	−2220.00	−0.156097	−0.0780487	+	0.996950i	$0.524869\pi$
$588$	3528.00i	0.247436i
$589$	19952.0i	1.39577i
$590$	− 4536.00i	− 0.316516i
$591$	336.000	0.0233861
$592$	4118.00i	0.285893i
$593$	25038.0	1.73387	0.866937	−	0.498418i	$-0.166085\pi$
$593$	25038.0	1.73387	0.866937	+	0.498418i	$0.166085\pi$
$594$	−5760.00	−0.397871
$595$	0	0
$596$	1614.00	0.110926
$597$	−25760.0	−1.76597
$598$	− 10440.0i	− 0.713919i
$599$	5784.00	0.394537	0.197269	−	0.980349i	$-0.436793\pi$
$599$	5784.00	0.394537	0.197269	+	0.980349i	$0.436793\pi$
$600$	14952.0i	1.01735i
$601$	4198.00i	0.284925i	0.989800	+	0.142463i	$0.0455020\pi$
$601$	4198.00i	0.284925i	−0.989800	+	0.142463i	$0.954498\pi$
$602$	12432.0i	0.841679i
$603$	17908.0	1.20940
$604$	3328.00	0.224196
$605$	4530.00i	0.304414i
$606$	5040.00i	0.337848i
$607$	− 12124.0i	− 0.810705i	−0.914160	−	0.405353i	$-0.867149\pi$
$607$	− 12124.0i	− 0.810705i	0.914160	−	0.405353i	$-0.132851\pi$
$608$	5220.00	0.348189
$609$	6720.00i	0.447140i
$610$	1980.00	0.131423
$611$	−16704.0	−1.10601
$612$	0	0
$613$	7454.00	0.491133	0.245566	−	0.969380i	$-0.421026\pi$
$613$	7454.00	0.491133	0.245566	+	0.969380i	$0.421026\pi$
$614$	−26940.0	−1.77070
$615$	16416.0i	1.07635i
$616$	14112.0	0.923034
$617$	28842.0i	1.88190i	0.338539	+	0.940952i	$0.390067\pi$
$617$	28842.0i	1.88190i	−0.338539	+	0.940952i	$0.609933\pi$
$618$	5568.00i	0.362424i
$619$	17224.0i	1.11840i	0.829032	+	0.559201i	$0.188892\pi$
$619$	17224.0i	1.11840i	−0.829032	+	0.559201i	$0.811108\pi$
$620$	1032.00	0.0668486
$621$	−4800.00	−0.310173
$622$	− 11916.0i	− 0.768148i
$623$	− 21672.0i	− 1.39369i
$624$	− 32944.0i	− 2.11349i
$625$	3421.00	0.218944
$626$	− 14190.0i	− 0.905985i
$627$	−22272.0	−1.41859
$628$	−2458.00	−0.156186
$629$	0	0
$630$	18648.0	1.17929
$631$	12448.0	0.785336	0.392668	−	0.919680i	$-0.371552\pi$
$631$	12448.0	0.785336	0.392668	+	0.919680i	$0.371552\pi$
$632$	− 10164.0i	− 0.639719i
$633$	16640.0	1.04484
$634$	8694.00i	0.544610i
$635$	2832.00i	0.176983i
$636$	2544.00i	0.158610i
$637$	25578.0	1.59095
$638$	−2160.00	−0.134036
$639$	26196.0i	1.62175i
$640$	9954.00i	0.614791i
$641$	− 25182.0i	− 1.55168i	−0.630927	−	0.775842i	$-0.717325\pi$
$641$	− 25182.0i	− 1.55168i	0.630927	−	0.775842i	$-0.282675\pi$
$642$	10368.0	0.637371
$643$	17048.0i	1.04558i	0.852462	+	0.522790i	$0.175109\pi$
$643$	17048.0i	1.04558i	−0.852462	+	0.522790i	$0.824891\pi$
$644$	−1680.00	−0.102797
$645$	7104.00	0.433674
$646$	0	0
$647$	7128.00	0.433123	0.216562	−	0.976269i	$-0.430516\pi$
$647$	7128.00	0.433123	0.216562	+	0.976269i	$0.430516\pi$
$648$	7539.00	0.457037
$649$	− 6048.00i	− 0.365801i
$650$	−15486.0	−0.934478
$651$	− 38528.0i	− 2.31956i
$652$	− 272.000i	− 0.0163379i
$653$	− 18462.0i	− 1.10639i	−0.833051	−	0.553196i	$-0.813408\pi$
$653$	− 18462.0i	− 1.10639i	0.833051	−	0.553196i	$-0.186592\pi$
$654$	28464.0	1.70188
$655$	−16560.0	−0.987867
$656$	− 24282.0i	− 1.44520i
$657$	− 13394.0i	− 0.795357i
$658$	24192.0i	1.43329i
$659$	28092.0	1.66056	0.830280	−	0.557347i	$-0.188181\pi$
$659$	28092.0	1.66056	0.830280	+	0.557347i	$0.188181\pi$
$660$	1152.00i	0.0679417i
$661$	−10910.0	−0.641982	−0.320991	−	0.947082i	$-0.604016\pi$
$661$	−10910.0	−0.641982	−0.320991	+	0.947082i	$0.604016\pi$
$662$	13692.0	0.803859
$663$	0	0
$664$	15876.0	0.927874
$665$	19488.0	1.13641
$666$	6438.00i	0.374576i
$667$	−1800.00	−0.104492
$668$	3516.00i	0.203650i
$669$	37312.0i	2.15630i
$670$	− 8712.00i	− 0.502349i
$671$	2640.00	0.151887
$672$	−10080.0	−0.578638
$673$	28414.0i	1.62746i	0.581244	+	0.813729i	$0.302566\pi$
$673$	28414.0i	1.62746i	−0.581244	+	0.813729i	$0.697434\pi$
$674$	2166.00i	0.123785i
$675$	7120.00i	0.405998i
$676$	1167.00	0.0663974
$677$	− 6042.00i	− 0.343003i	−0.985184	−	0.171501i	$-0.945138\pi$
$677$	− 6042.00i	− 0.343003i	0.985184	−	0.171501i	$-0.0548618\pi$
$678$	8784.00	0.497563
$679$	10696.0	0.604528
$680$	0	0
$681$	11520.0	0.648234
$682$	12384.0	0.695319
$683$	34752.0i	1.94692i	0.228851	+	0.973461i	$0.426503\pi$
$683$	34752.0i	1.94692i	−0.228851	+	0.973461i	$0.573497\pi$
$684$	4292.00	0.239925
$685$	6588.00i	0.367466i
$686$	− 8232.00i	− 0.458162i
$687$	− 9488.00i	− 0.526914i
$688$	−10508.0	−0.582287
$689$	18444.0	1.01983
$690$	8640.00i	0.476694i
$691$	− 18320.0i	− 1.00858i	−0.863536	−	0.504288i	$-0.831755\pi$
$691$	− 18320.0i	− 1.00858i	0.863536	−	0.504288i	$-0.168245\pi$
$692$	− 1842.00i	− 0.101188i
$693$	24864.0	1.36292
$694$	− 16632.0i	− 0.909715i
$695$	−15168.0	−0.827849
$696$	−5040.00	−0.274484
$697$	0	0
$698$	−33378.0	−1.80999
$699$	−42672.0	−2.30902
$700$	2492.00i	0.134555i
$701$	−22890.0	−1.23330	−0.616650	−	0.787237i	$-0.711511\pi$
$701$	−22890.0	−1.23330	−0.616650	+	0.787237i	$0.711511\pi$
$702$	− 13920.0i	− 0.748400i
$703$	6728.00i	0.360955i
$704$	10392.0i	0.556340i
$705$	13824.0	0.738499
$706$	23526.0	1.25413
$707$	− 5880.00i	− 0.312787i
$708$	2016.00i	0.107014i
$709$	22886.0i	1.21227i	0.795361	+	0.606137i	$0.207282\pi$
$709$	22886.0i	1.21227i	−0.795361	+	0.606137i	$0.792718\pi$
$710$	12744.0	0.673625
$711$	− 17908.0i	− 0.944589i
$712$	16254.0	0.855540
$713$	10320.0	0.542058
$714$	0	0
$715$	8352.00	0.436849
$716$	3516.00	0.183518
$717$	− 42624.0i	− 2.22011i
$718$	−15120.0	−0.785896
$719$	− 13452.0i	− 0.697740i	−0.937171	−	0.348870i	$-0.886565\pi$
$719$	− 13452.0i	− 0.697740i	0.937171	−	0.348870i	$-0.113435\pi$
$720$	15762.0i	0.815854i
$721$	− 6496.00i	− 0.335539i
$722$	19791.0	1.02015
$723$	44944.0	2.31187
$724$	− 3398.00i	− 0.174428i
$725$	2670.00i	0.136774i
$726$	− 18120.0i	− 0.926303i
$727$	−27304.0	−1.39292	−0.696458	−	0.717598i	$-0.745242\pi$
$727$	−27304.0	−1.39292	−0.696458	+	0.717598i	$0.745242\pi$
$728$	34104.0i	1.73623i
$729$	30563.0	1.55276
$730$	−6516.00	−0.330367
$731$	0	0
$732$	−880.000	−0.0444341
$733$	−24470.0	−1.23304	−0.616521	−	0.787338i	$-0.711459\pi$
$733$	−24470.0	−1.23304	−0.616521	+	0.787338i	$0.711459\pi$
$734$	25212.0i	1.26784i
$735$	−21168.0	−1.06230
$736$	− 2700.00i	− 0.135222i
$737$	− 11616.0i	− 0.580571i
$738$	− 37962.0i	− 1.89350i
$739$	−35252.0	−1.75476	−0.877379	−	0.479798i	$-0.840710\pi$
$739$	−35252.0	−1.75476	−0.877379	+	0.479798i	$0.840710\pi$
$740$	348.000	0.0172875
$741$	− 53824.0i	− 2.66839i
$742$	− 26712.0i	− 1.32160i
$743$	1548.00i	0.0764342i	0.999269	+	0.0382171i	$0.0121678\pi$
$743$	1548.00i	0.0764342i	−0.999269	+	0.0382171i	$0.987832\pi$
$744$	28896.0	1.42390
$745$	9684.00i	0.476234i
$746$	−24294.0	−1.19231
$747$	27972.0	1.37007
$748$	0	0
$749$	−12096.0	−0.590091
$750$	30816.0	1.50032
$751$	2948.00i	0.143241i	0.997432	+	0.0716205i	$0.0228171\pi$
$751$	2948.00i	0.143241i	−0.997432	+	0.0716205i	$0.977183\pi$
$752$	−20448.0	−0.991572
$753$	16224.0i	0.785173i
$754$	− 5220.00i	− 0.252124i
$755$	19968.0i	0.962530i
$756$	−2240.00	−0.107762
$757$	754.000	0.0362016	0.0181008	−	0.999836i	$-0.494238\pi$
$757$	754.000	0.0362016	0.0181008	+	0.999836i	$0.494238\pi$
$758$	960.000i	0.0460010i
$759$	11520.0i	0.550922i
$760$	14616.0i	0.697603i
$761$	−41574.0	−1.98036	−0.990182	−	0.139787i	$-0.955358\pi$
$761$	−41574.0	−1.98036	−0.990182	+	0.139787i	$0.955358\pi$
$762$	− 11328.0i	− 0.538543i
$763$	−33208.0	−1.57564
$764$	−2640.00	−0.125016
$765$	0	0
$766$	32616.0	1.53846
$767$	14616.0	0.688075
$768$	− 12104.0i	− 0.568705i
$769$	−15118.0	−0.708932	−0.354466	−	0.935069i	$-0.615337\pi$
$769$	−15118.0	−0.708932	−0.354466	+	0.935069i	$0.615337\pi$
$770$	− 12096.0i	− 0.566116i
$771$	− 15216.0i	− 0.710753i
$772$	− 2882.00i	− 0.134359i
$773$	−23550.0	−1.09578	−0.547888	−	0.836552i	$-0.684568\pi$
$773$	−23550.0	−1.09578	−0.547888	+	0.836552i	$0.684568\pi$
$774$	−16428.0	−0.762910
$775$	− 15308.0i	− 0.709522i
$776$	8022.00i	0.371099i
$777$	− 12992.0i	− 0.599853i
$778$	−4122.00	−0.189950
$779$	− 39672.0i	− 1.82464i
$780$	−2784.00	−0.127799
$781$	16992.0	0.778517
$782$	0	0
$783$	−2400.00	−0.109539
$784$	31311.0	1.42634
$785$	− 14748.0i	− 0.670546i
$786$	66240.0	3.00598
$787$	5240.00i	0.237339i	0.992934	+	0.118670i	$0.0378629\pi$
$787$	5240.00i	0.237339i	−0.992934	+	0.118670i	$0.962137\pi$
$788$	42.0000i	0.00189872i
$789$	− 43776.0i	− 1.97524i
$790$	−8712.00	−0.392353
$791$	−10248.0	−0.460654
$792$	18648.0i	0.836651i
$793$	6380.00i	0.285700i
$794$	22566.0i	1.00861i
$795$	−15264.0	−0.680954
$796$	− 3220.00i	− 0.143379i
$797$	−5526.00	−0.245597	−0.122799	−	0.992432i	$-0.539187\pi$
$797$	−5526.00	−0.245597	−0.122799	+	0.992432i	$0.539187\pi$
$798$	−77952.0	−3.45798
$799$	0	0
$800$	−4005.00	−0.176998
$801$	28638.0	1.26326
$802$	− 8118.00i	− 0.357427i
$803$	−8688.00	−0.381809
$804$	3872.00i	0.169844i
$805$	− 10080.0i	− 0.441333i
$806$	29928.0i	1.30790i
$807$	−28560.0	−1.24580
$808$	4410.00	0.192009
$809$	438.000i	0.0190349i	0.999955	+	0.00951747i	$0.00302955\pi$
$809$	438.000i	0.0190349i	−0.999955	+	0.00951747i	$0.996970\pi$
$810$	− 6462.00i	− 0.280311i
$811$	− 30448.0i	− 1.31834i	−0.751994	−	0.659170i	$-0.770908\pi$
$811$	− 30448.0i	− 1.31834i	0.751994	−	0.659170i	$-0.229092\pi$
$812$	−840.000	−0.0363032
$813$	− 2176.00i	− 0.0938692i
$814$	4176.00	0.179814
$815$	1632.00	0.0701429
$816$	0	0
$817$	−17168.0	−0.735168
$818$	798.000	0.0341093
$819$	60088.0i	2.56367i
$820$	−2052.00	−0.0873890
$821$	− 21930.0i	− 0.932232i	−0.884724	−	0.466116i	$-0.845653\pi$
$821$	− 21930.0i	− 0.932232i	0.884724	−	0.466116i	$-0.154347\pi$
$822$	− 26352.0i	− 1.11816i
$823$	27436.0i	1.16204i	0.813889	+	0.581020i	$0.197346\pi$
$823$	27436.0i	1.16204i	−0.813889	+	0.581020i	$0.802654\pi$
$824$	4872.00	0.205976
$825$	17088.0	0.721125
$826$	− 21168.0i	− 0.891681i
$827$	17832.0i	0.749794i	0.927067	+	0.374897i	$0.122322\pi$
$827$	17832.0i	0.749794i	−0.927067	+	0.374897i	$0.877678\pi$
$828$	− 2220.00i	− 0.0931767i
$829$	−4090.00	−0.171353	−0.0856765	−	0.996323i	$-0.527305\pi$
$829$	−4090.00	−0.171353	−0.0856765	+	0.996323i	$0.527305\pi$
$830$	− 13608.0i	− 0.569085i
$831$	30640.0	1.27905
$832$	−25114.0	−1.04648
$833$	0	0
$834$	60672.0	2.51906
$835$	−21096.0	−0.874320
$836$	− 2784.00i	− 0.115175i
$837$	13760.0	0.568238
$838$	− 8064.00i	− 0.332418i
$839$	2508.00i	0.103201i	0.998668	+	0.0516006i	$0.0164323\pi$
$839$	2508.00i	0.103201i	−0.998668	+	0.0516006i	$0.983568\pi$
$840$	− 28224.0i	− 1.15931i
$841$	23489.0	0.963098
$842$	−41430.0	−1.69569
$843$	70992.0i	2.90047i
$844$	2080.00i	0.0848300i
$845$	7002.00i	0.285061i
$846$	−31968.0	−1.29915
$847$	21140.0i	0.857590i
$848$	22578.0	0.914306
$849$	21056.0	0.851166
$850$	0	0
$851$	3480.00	0.140180
$852$	−5664.00	−0.227753
$853$	− 42442.0i	− 1.70362i	−0.523852	−	0.851809i	$-0.675506\pi$
$853$	− 42442.0i	− 1.70362i	0.523852	−	0.851809i	$-0.324494\pi$
$854$	9240.00	0.370242
$855$	25752.0i	1.03006i
$856$	− 9072.00i	− 0.362237i
$857$	− 32730.0i	− 1.30459i	−0.757964	−	0.652296i	$-0.773806\pi$
$857$	− 32730.0i	− 1.30459i	0.757964	−	0.652296i	$-0.226194\pi$
$858$	−33408.0	−1.32929
$859$	6148.00	0.244199	0.122100	−	0.992518i	$-0.461037\pi$
$859$	6148.00	0.244199	0.122100	+	0.992518i	$0.461037\pi$
$860$	888.000i	0.0352099i
$861$	76608.0i	3.03228i
$862$	− 9108.00i	− 0.359884i
$863$	−22512.0	−0.887969	−0.443985	−	0.896034i	$-0.646436\pi$
$863$	−22512.0	−0.887969	−0.443985	+	0.896034i	$0.646436\pi$
$864$	− 3600.00i	− 0.141753i
$865$	11052.0	0.434427
$866$	34266.0	1.34458
$867$	0	0
$868$	4816.00	0.188325
$869$	−11616.0	−0.453447
$870$	4320.00i	0.168347i
$871$	28072.0	1.09206
$872$	− 24906.0i	− 0.967229i
$873$	14134.0i	0.547954i
$874$	− 20880.0i	− 0.808097i
$875$	−35952.0	−1.38903
$876$	2896.00	0.111697
$877$	− 9182.00i	− 0.353539i	−0.984252	−	0.176770i	$-0.943435\pi$
$877$	− 9182.00i	− 0.353539i	0.984252	−	0.176770i	$-0.0565648\pi$
$878$	− 156.000i	− 0.00599629i
$879$	51216.0i	1.96527i
$880$	10224.0	0.391649
$881$	28530.0i	1.09103i	0.838100	+	0.545517i	$0.183666\pi$
$881$	28530.0i	1.09103i	−0.838100	+	0.545517i	$0.816334\pi$
$882$	48951.0	1.86878
$883$	−12436.0	−0.473958	−0.236979	−	0.971515i	$-0.576157\pi$
$883$	−12436.0	−0.473958	−0.236979	+	0.971515i	$0.576157\pi$
$884$	0	0
$885$	−12096.0	−0.459438
$886$	9324.00	0.353551
$887$	7404.00i	0.280273i	0.990132	+	0.140136i	$0.0447541\pi$
$887$	7404.00i	0.280273i	−0.990132	+	0.140136i	$0.955246\pi$
$888$	9744.00	0.368229
$889$	13216.0i	0.498594i
$890$	− 13932.0i	− 0.524721i
$891$	− 8616.00i	− 0.323958i
$892$	−4664.00	−0.175070
$893$	−33408.0	−1.25191
$894$	− 38736.0i	− 1.44913i
$895$	21096.0i	0.787890i
$896$	46452.0i	1.73198i
$897$	−27840.0	−1.03629
$898$	− 18342.0i	− 0.681604i
$899$	5160.00	0.191430
$900$	−3293.00	−0.121963
$901$	0	0
$902$	−24624.0	−0.908968
$903$	33152.0	1.22174
$904$	− 7686.00i	− 0.282779i
$905$	20388.0	0.748862
$906$	− 79872.0i	− 2.92888i
$907$	− 15368.0i	− 0.562609i	−0.959619	−	0.281304i	$-0.909233\pi$
$907$	− 15368.0i	− 0.562609i	0.959619	−	0.281304i	$-0.0907670\pi$
$908$	1440.00i	0.0526300i
$909$	7770.00	0.283514
$910$	29232.0	1.06487
$911$	− 27276.0i	− 0.991980i	−0.868328	−	0.495990i	$-0.834805\pi$
$911$	− 27276.0i	− 0.991980i	0.868328	−	0.495990i	$-0.165195\pi$
$912$	− 65888.0i	− 2.39229i
$913$	− 18144.0i	− 0.657699i
$914$	−12318.0	−0.445780
$915$	− 5280.00i	− 0.190767i
$916$	1186.00	0.0427801
$917$	−77280.0	−2.78300
$918$	0	0
$919$	−46456.0	−1.66751	−0.833755	−	0.552134i	$-0.813814\pi$
$919$	−46456.0	−1.66751	−0.833755	+	0.552134i	$0.813814\pi$
$920$	7560.00	0.270919
$921$	71840.0i	2.57026i
$922$	−10098.0	−0.360694
$923$	41064.0i	1.46440i
$924$	5376.00i	0.191404i
$925$	− 5162.00i	− 0.183487i
$926$	2688.00	0.0953922
$927$	8584.00	0.304138
$928$	− 1350.00i	− 0.0477542i
$929$	− 13026.0i	− 0.460031i	−0.973187	−	0.230016i	$-0.926122\pi$
$929$	− 13026.0i	− 0.460031i	0.973187	−	0.230016i	$-0.0738778\pi$
$930$	− 24768.0i	− 0.873306i
$931$	51156.0	1.80083
$932$	− 5334.00i	− 0.187469i
$933$	−31776.0	−1.11500
$934$	30708.0	1.07580
$935$	0	0
$936$	−45066.0	−1.57375
$937$	−26330.0	−0.917997	−0.458999	−	0.888437i	$-0.651792\pi$
$937$	−26330.0	−0.917997	−0.458999	+	0.888437i	$0.651792\pi$
$938$	− 40656.0i	− 1.41521i
$939$	−37840.0	−1.31508
$940$	1728.00i	0.0599587i
$941$	− 28254.0i	− 0.978803i	−0.872058	−	0.489402i	$-0.837215\pi$
$941$	− 28254.0i	− 0.978803i	0.872058	−	0.489402i	$-0.162785\pi$
$942$	58992.0i	2.04041i
$943$	−20520.0	−0.708614
$944$	17892.0	0.616880
$945$	− 13440.0i	− 0.462649i
$946$	10656.0i	0.366233i
$947$	49272.0i	1.69073i	0.534186	+	0.845367i	$0.320618\pi$
$947$	49272.0i	1.69073i	−0.534186	+	0.845367i	$0.679382\pi$
$948$	3872.00	0.132655
$949$	− 20996.0i	− 0.718187i
$950$	−30972.0	−1.05775
$951$	23184.0	0.790529
$952$	0	0
$953$	32922.0	1.11904	0.559522	−	0.828816i	$-0.310985\pi$
$953$	32922.0	1.11904	0.559522	+	0.828816i	$0.310985\pi$
$954$	35298.0	1.19792
$955$	− 15840.0i	− 0.536723i
$956$	5328.00	0.180251
$957$	5760.00i	0.194560i
$958$	15516.0i	0.523277i
$959$	30744.0i	1.03522i
$960$	20784.0	0.698751
$961$	207.000	0.00694841
$962$	10092.0i	0.338232i
$963$	− 15984.0i	− 0.534867i
$964$	5618.00i	0.187701i
$965$	17292.0	0.576839
$966$	40320.0i	1.34293i
$967$	1168.00	0.0388421	0.0194211	−	0.999811i	$-0.493818\pi$
$967$	1168.00	0.0388421	0.0194211	+	0.999811i	$0.493818\pi$
$968$	−15855.0	−0.526445
$969$	0	0
$970$	6876.00	0.227603
$971$	19812.0	0.654786	0.327393	−	0.944888i	$-0.393830\pi$
$971$	19812.0	0.654786	0.327393	+	0.944888i	$0.393830\pi$
$972$	5032.00i	0.166051i
$973$	−70784.0	−2.33220
$974$	45156.0i	1.48551i
$975$	41296.0i	1.35644i
$976$	7810.00i	0.256139i
$977$	28494.0	0.933064	0.466532	−	0.884504i	$-0.345503\pi$
$977$	28494.0	0.933064	0.466532	+	0.884504i	$0.345503\pi$
$978$	−6528.00	−0.213438
$979$	− 18576.0i	− 0.606426i
$980$	− 2646.00i	− 0.0862483i
$981$	− 43882.0i	− 1.42818i
$982$	−26100.0	−0.848151
$983$	− 42708.0i	− 1.38573i	−0.721067	−	0.692866i	$-0.756348\pi$
$983$	− 42708.0i	− 1.38573i	0.721067	−	0.692866i	$-0.243652\pi$
$984$	−57456.0	−1.86141
$985$	−252.000	−0.00815166
$986$	0	0
$987$	64512.0	2.08049
$988$	6728.00	0.216646
$989$	8880.00i	0.285508i
$990$	15984.0	0.513136
$991$	− 29500.0i	− 0.945609i	−0.881167	−	0.472804i	$-0.843242\pi$
$991$	− 29500.0i	− 0.945609i	0.881167	−	0.472804i	$-0.156758\pi$
$992$	7740.00i	0.247727i
$993$	− 36512.0i	− 1.16684i
$994$	59472.0	1.89772
$995$	19320.0	0.615563
$996$	6048.00i	0.192408i
$997$	9322.00i	0.296119i	0.988978	+	0.148060i	$0.0473027\pi$
$997$	9322.00i	0.296119i	−0.988978	+	0.148060i	$0.952697\pi$
$998$	3504.00i	0.111139i
$999$	4640.00	0.146950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.a.288.1		2
17.4	even	4		17.4.a.a.1.1	✓	1
17.13	even	4		289.4.a.a.1.1		1
17.16	even	2	inner	289.4.b.a.288.2		2
51.38	odd	4		153.4.a.d.1.1		1
68.55	odd	4		272.4.a.d.1.1		1
85.4	even	4		425.4.a.d.1.1		1
85.38	odd	4		425.4.b.c.324.2		2
85.72	odd	4		425.4.b.c.324.1		2
119.55	odd	4		833.4.a.a.1.1		1
136.21	even	4		1088.4.a.l.1.1		1
136.123	odd	4		1088.4.a.a.1.1		1
187.21	odd	4		2057.4.a.d.1.1		1
204.191	even	4		2448.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.a.1.1	✓	1	17.4	even	4
153.4.a.d.1.1		1	51.38	odd	4
272.4.a.d.1.1		1	68.55	odd	4
289.4.a.a.1.1		1	17.13	even	4
289.4.b.a.288.1		2	1.1	even	1	trivial
289.4.b.a.288.2		2	17.16	even	2	inner
425.4.a.d.1.1		1	85.4	even	4
425.4.b.c.324.1		2	85.72	odd	4
425.4.b.c.324.2		2	85.38	odd	4
833.4.a.a.1.1		1	119.55	odd	4
1088.4.a.a.1.1		1	136.123	odd	4
1088.4.a.l.1.1		1	136.21	even	4
2057.4.a.d.1.1		1	187.21	odd	4
2448.4.a.f.1.1		1	204.191	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.00000 q^{2} -8.00000i q^{3} +1.00000 q^{4} +6.00000i q^{5} -24.0000i q^{6} +28.0000i q^{7} -21.0000 q^{8} -37.0000 q^{9} +O(q^{10})\)	\(q+3.00000 q^{2} -8.00000i q^{3} +1.00000 q^{4} +6.00000i q^{5} -24.0000i q^{6} +28.0000i q^{7} -21.0000 q^{8} -37.0000 q^{9} +18.0000i q^{10} +24.0000i q^{11} -8.00000i q^{12} -58.0000 q^{13} +84.0000i q^{14} +48.0000 q^{15} -71.0000 q^{16} -111.000 q^{18} -116.000 q^{19} +6.00000i q^{20} +224.000 q^{21} +72.0000i q^{22} +60.0000i q^{23} +168.000i q^{24} +89.0000 q^{25} -174.000 q^{26} +80.0000i q^{27} +28.0000i q^{28} +30.0000i q^{29} +144.000 q^{30} -172.000i q^{31} -45.0000 q^{32} +192.000 q^{33} -168.000 q^{35} -37.0000 q^{36} -58.0000i q^{37} -348.000 q^{38} +464.000i q^{39} -126.000i q^{40} +342.000i q^{41} +672.000 q^{42} +148.000 q^{43} +24.0000i q^{44} -222.000i q^{45} +180.000i q^{46} +288.000 q^{47} +568.000i q^{48} -441.000 q^{49} +267.000 q^{50} -58.0000 q^{52} -318.000 q^{53} +240.000i q^{54} -144.000 q^{55} -588.000i q^{56} +928.000i q^{57} +90.0000i q^{58} -252.000 q^{59} +48.0000 q^{60} -110.000i q^{61} -516.000i q^{62} -1036.00i q^{63} +433.000 q^{64} -348.000i q^{65} +576.000 q^{66} -484.000 q^{67} +480.000 q^{69} -504.000 q^{70} -708.000i q^{71} +777.000 q^{72} +362.000i q^{73} -174.000i q^{74} -712.000i q^{75} -116.000 q^{76} -672.000 q^{77} +1392.00i q^{78} +484.000i q^{79} -426.000i q^{80} -359.000 q^{81} +1026.00i q^{82} -756.000 q^{83} +224.000 q^{84} +444.000 q^{86} +240.000 q^{87} -504.000i q^{88} -774.000 q^{89} -666.000i q^{90} -1624.00i q^{91} +60.0000i q^{92} -1376.00 q^{93} +864.000 q^{94} -696.000i q^{95} +360.000i q^{96} -382.000i q^{97} -1323.00 q^{98} -888.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 2 q^{4} - 42 q^{8} - 74 q^{9}+O(q^{10}) \) 2 * q + 6 * q^2 + 2 * q^4 - 42 * q^8 - 74 * q^9	\( 2 q + 6 q^{2} + 2 q^{4} - 42 q^{8} - 74 q^{9} - 116 q^{13} + 96 q^{15} - 142 q^{16} - 222 q^{18} - 232 q^{19} + 448 q^{21} + 178 q^{25} - 348 q^{26} + 288 q^{30} - 90 q^{32} + 384 q^{33} - 336 q^{35} - 74 q^{36} - 696 q^{38} + 1344 q^{42} + 296 q^{43} + 576 q^{47} - 882 q^{49} + 534 q^{50} - 116 q^{52} - 636 q^{53} - 288 q^{55} - 504 q^{59} + 96 q^{60} + 866 q^{64} + 1152 q^{66} - 968 q^{67} + 960 q^{69} - 1008 q^{70} + 1554 q^{72} - 232 q^{76} - 1344 q^{77} - 718 q^{81} - 1512 q^{83} + 448 q^{84} + 888 q^{86} + 480 q^{87} - 1548 q^{89} - 2752 q^{93} + 1728 q^{94} - 2646 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 + 2 * q^4 - 42 * q^8 - 74 * q^9 - 116 * q^13 + 96 * q^15 - 142 * q^16 - 222 * q^18 - 232 * q^19 + 448 * q^21 + 178 * q^25 - 348 * q^26 + 288 * q^30 - 90 * q^32 + 384 * q^33 - 336 * q^35 - 74 * q^36 - 696 * q^38 + 1344 * q^42 + 296 * q^43 + 576 * q^47 - 882 * q^49 + 534 * q^50 - 116 * q^52 - 636 * q^53 - 288 * q^55 - 504 * q^59 + 96 * q^60 + 866 * q^64 + 1152 * q^66 - 968 * q^67 + 960 * q^69 - 1008 * q^70 + 1554 * q^72 - 232 * q^76 - 1344 * q^77 - 718 * q^81 - 1512 * q^83 + 448 * q^84 + 888 * q^86 + 480 * q^87 - 1548 * q^89 - 2752 * q^93 + 1728 * q^94 - 2646 * q^98

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