LMFDB - Embedded newform 525.4.d.c.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.9760027530$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.c.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +9.00000 q^{6} -7.00000i q^{7} +21.0000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +9.00000 q^{6} -7.00000i q^{7} +21.0000i q^{8} -9.00000 q^{9} -36.0000 q^{11} +3.00000i q^{12} -34.0000i q^{13} +21.0000 q^{14} -71.0000 q^{16} -42.0000i q^{17} -27.0000i q^{18} +124.000 q^{19} -21.0000 q^{21} -108.000i q^{22} +63.0000 q^{24} +102.000 q^{26} +27.0000i q^{27} +7.00000i q^{28} -102.000 q^{29} -160.000 q^{31} -45.0000i q^{32} +108.000i q^{33} +126.000 q^{34} +9.00000 q^{36} -398.000i q^{37} +372.000i q^{38} -102.000 q^{39} -318.000 q^{41} -63.0000i q^{42} -268.000i q^{43} +36.0000 q^{44} -240.000i q^{47} +213.000i q^{48} -49.0000 q^{49} -126.000 q^{51} +34.0000i q^{52} -498.000i q^{53} -81.0000 q^{54} +147.000 q^{56} -372.000i q^{57} -306.000i q^{58} +132.000 q^{59} +398.000 q^{61} -480.000i q^{62} +63.0000i q^{63} -433.000 q^{64} -324.000 q^{66} -92.0000i q^{67} +42.0000i q^{68} -720.000 q^{71} -189.000i q^{72} -502.000i q^{73} +1194.00 q^{74} -124.000 q^{76} +252.000i q^{77} -306.000i q^{78} +1024.00 q^{79} +81.0000 q^{81} -954.000i q^{82} -204.000i q^{83} +21.0000 q^{84} +804.000 q^{86} +306.000i q^{87} -756.000i q^{88} -354.000 q^{89} -238.000 q^{91} +480.000i q^{93} +720.000 q^{94} -135.000 q^{96} +286.000i q^{97} -147.000i q^{98} +324.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 18 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 18 * q^6 - 18 * q^9	$ 2 q - 2 q^{4} + 18 q^{6} - 18 q^{9} - 72 q^{11} + 42 q^{14} - 142 q^{16} + 248 q^{19} - 42 q^{21} + 126 q^{24} + 204 q^{26} - 204 q^{29} - 320 q^{31} + 252 q^{34} + 18 q^{36} - 204 q^{39} - 636 q^{41} + 72 q^{44} - 98 q^{49} - 252 q^{51} - 162 q^{54} + 294 q^{56} + 264 q^{59} + 796 q^{61} - 866 q^{64} - 648 q^{66} - 1440 q^{71} + 2388 q^{74} - 248 q^{76} + 2048 q^{79} + 162 q^{81} + 42 q^{84} + 1608 q^{86} - 708 q^{89} - 476 q^{91} + 1440 q^{94} - 270 q^{96} + 648 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 18 * q^6 - 18 * q^9 - 72 * q^11 + 42 * q^14 - 142 * q^16 + 248 * q^19 - 42 * q^21 + 126 * q^24 + 204 * q^26 - 204 * q^29 - 320 * q^31 + 252 * q^34 + 18 * q^36 - 204 * q^39 - 636 * q^41 + 72 * q^44 - 98 * q^49 - 252 * q^51 - 162 * q^54 + 294 * q^56 + 264 * q^59 + 796 * q^61 - 866 * q^64 - 648 * q^66 - 1440 * q^71 + 2388 * q^74 - 248 * q^76 + 2048 * q^79 + 162 * q^81 + 42 * q^84 + 1608 * q^86 - 708 * q^89 - 476 * q^91 + 1440 * q^94 - 270 * q^96 + 648 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	3.00000i	1.06066i	0.847791	+	0.530330i	$0.177932\pi$
$2$	3.00000i	1.06066i	−0.847791	+	0.530330i	$0.822068\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−1.00000	−0.125000
$5$	0	0
$5$	0	0
$6$	9.00000	0.612372
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	21.0000i	0.928078i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−36.0000	−0.986764	−0.493382	−	0.869813i	$-0.664240\pi$
$11$	−36.0000	−0.986764	−0.493382	+	0.869813i	$0.664240\pi$
$12$	3.00000i	0.0721688i
$13$	− 34.0000i	− 0.725377i	−0.931910	−	0.362689i	$-0.881859\pi$
$13$	− 34.0000i	− 0.725377i	0.931910	−	0.362689i	$-0.118141\pi$
$14$	21.0000	0.400892
$15$	0	0
$16$	−71.0000	−1.10938
$17$	− 42.0000i	− 0.599206i	−0.954064	−	0.299603i	$-0.903146\pi$
$17$	− 42.0000i	− 0.599206i	0.954064	−	0.299603i	$-0.0968542\pi$
$18$	− 27.0000i	− 0.353553i
$19$	124.000	1.49724	0.748620	−	0.663000i	$-0.230717\pi$
$19$	124.000	1.49724	0.748620	+	0.663000i	$0.230717\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	− 108.000i	− 1.04662i
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	63.0000	0.535826
$25$	0	0
$26$	102.000	0.769379
$27$	27.0000i	0.192450i
$28$	7.00000i	0.0472456i
$29$	−102.000	−0.653135	−0.326568	−	0.945174i	$-0.605892\pi$
$29$	−102.000	−0.653135	−0.326568	+	0.945174i	$0.605892\pi$
$30$	0	0
$31$	−160.000	−0.926995	−0.463498	−	0.886098i	$-0.653406\pi$
$31$	−160.000	−0.926995	−0.463498	+	0.886098i	$0.653406\pi$
$32$	− 45.0000i	− 0.248592i
$33$	108.000i	0.569709i
$34$	126.000	0.635554
$35$	0	0
$36$	9.00000	0.0416667
$37$	− 398.000i	− 1.76840i	−0.467109	−	0.884200i	$-0.654704\pi$
$37$	− 398.000i	− 1.76840i	0.467109	−	0.884200i	$-0.345296\pi$
$38$	372.000i	1.58806i
$39$	−102.000	−0.418797
$40$	0	0
$41$	−318.000	−1.21130	−0.605649	−	0.795732i	$-0.707087\pi$
$41$	−318.000	−1.21130	−0.605649	+	0.795732i	$0.707087\pi$
$42$	− 63.0000i	− 0.231455i
$43$	− 268.000i	− 0.950456i	−0.879863	−	0.475228i	$-0.842366\pi$
$43$	− 268.000i	− 0.950456i	0.879863	−	0.475228i	$-0.157634\pi$
$44$	36.0000	0.123346
$45$	0	0
$46$	0	0
$47$	− 240.000i	− 0.744843i	−0.928064	−	0.372421i	$-0.878528\pi$
$47$	− 240.000i	− 0.744843i	0.928064	−	0.372421i	$-0.121472\pi$
$48$	213.000i	0.640498i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−126.000	−0.345952
$52$	34.0000i	0.0906721i
$53$	− 498.000i	− 1.29067i	−0.763899	−	0.645335i	$-0.776718\pi$
$53$	− 498.000i	− 1.29067i	0.763899	−	0.645335i	$-0.223282\pi$
$54$	−81.0000	−0.204124
$55$	0	0
$56$	147.000	0.350780
$57$	− 372.000i	− 0.864432i
$58$	− 306.000i	− 0.692755i
$59$	132.000	0.291270	0.145635	−	0.989338i	$-0.453477\pi$
$59$	132.000	0.291270	0.145635	+	0.989338i	$0.453477\pi$
$60$	0	0
$61$	398.000	0.835388	0.417694	−	0.908588i	$-0.362838\pi$
$61$	398.000	0.835388	0.417694	+	0.908588i	$0.362838\pi$
$62$	− 480.000i	− 0.983227i
$63$	63.0000i	0.125988i
$64$	−433.000	−0.845703
$65$	0	0
$66$	−324.000	−0.604267
$67$	− 92.0000i	− 0.167755i	−0.996476	−	0.0838775i	$-0.973270\pi$
$67$	− 92.0000i	− 0.167755i	0.996476	−	0.0838775i	$-0.0267305\pi$
$68$	42.0000i	0.0749007i
$69$	0	0
$70$	0	0
$71$	−720.000	−1.20350	−0.601748	−	0.798686i	$-0.705529\pi$
$71$	−720.000	−1.20350	−0.601748	+	0.798686i	$0.705529\pi$
$72$	− 189.000i	− 0.309359i
$73$	− 502.000i	− 0.804858i	−0.915451	−	0.402429i	$-0.868166\pi$
$73$	− 502.000i	− 0.804858i	0.915451	−	0.402429i	$-0.131834\pi$
$74$	1194.00	1.87567
$75$	0	0
$76$	−124.000	−0.187155
$77$	252.000i	0.372962i
$78$	− 306.000i	− 0.444201i
$79$	1024.00	1.45834	0.729171	−	0.684332i	$-0.239906\pi$
$79$	1024.00	1.45834	0.729171	+	0.684332i	$0.239906\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 954.000i	− 1.28478i
$83$	− 204.000i	− 0.269782i	−0.990860	−	0.134891i	$-0.956932\pi$
$83$	− 204.000i	− 0.269782i	0.990860	−	0.134891i	$-0.0430684\pi$
$84$	21.0000	0.0272772
$85$	0	0
$86$	804.000	1.00811
$87$	306.000i	0.377088i
$88$	− 756.000i	− 0.915794i
$89$	−354.000	−0.421617	−0.210809	−	0.977527i	$-0.567610\pi$
$89$	−354.000	−0.421617	−0.210809	+	0.977527i	$0.567610\pi$
$90$	0	0
$91$	−238.000	−0.274167
$92$	0	0
$93$	480.000i	0.535201i
$94$	720.000	0.790025
$95$	0	0
$96$	−135.000	−0.143525
$97$	286.000i	0.299370i	0.988734	+	0.149685i	$0.0478260\pi$
$97$	286.000i	0.299370i	−0.988734	+	0.149685i	$0.952174\pi$
$98$	− 147.000i	− 0.151523i
$99$	324.000	0.328921
$100$	0	0
$101$	414.000	0.407867	0.203933	−	0.978985i	$-0.434627\pi$
$101$	414.000	0.407867	0.203933	+	0.978985i	$0.434627\pi$
$102$	− 378.000i	− 0.366937i
$103$	56.0000i	0.0535713i	0.999641	+	0.0267857i	$0.00852716\pi$
$103$	56.0000i	0.0535713i	−0.999641	+	0.0267857i	$0.991473\pi$
$104$	714.000	0.673206
$105$	0	0
$106$	1494.00	1.36896
$107$	− 12.0000i	− 0.0108419i	−0.999985	−	0.00542095i	$-0.998274\pi$
$107$	− 12.0000i	− 0.0108419i	0.999985	−	0.00542095i	$-0.00172555\pi$
$108$	− 27.0000i	− 0.0240563i
$109$	−1478.00	−1.29878	−0.649389	−	0.760457i	$-0.724975\pi$
$109$	−1478.00	−1.29878	−0.649389	+	0.760457i	$0.724975\pi$
$110$	0	0
$111$	−1194.00	−1.02099
$112$	497.000i	0.419304i
$113$	402.000i	0.334664i	0.985901	+	0.167332i	$0.0535151\pi$
$113$	402.000i	0.334664i	−0.985901	+	0.167332i	$0.946485\pi$
$114$	1116.00	0.916868
$115$	0	0
$116$	102.000	0.0816419
$117$	306.000i	0.241792i
$118$	396.000i	0.308939i
$119$	−294.000	−0.226478
$120$	0	0
$121$	−35.0000	−0.0262960
$122$	1194.00i	0.886063i
$123$	954.000i	0.699344i
$124$	160.000	0.115874
$125$	0	0
$126$	−189.000	−0.133631
$127$	− 1280.00i	− 0.894344i	−0.894448	−	0.447172i	$-0.852431\pi$
$127$	− 1280.00i	− 0.894344i	0.894448	−	0.447172i	$-0.147569\pi$
$128$	− 1659.00i	− 1.14560i
$129$	−804.000	−0.548746
$130$	0	0
$131$	1764.00	1.17650	0.588250	−	0.808679i	$-0.299817\pi$
$131$	1764.00	1.17650	0.588250	+	0.808679i	$0.299817\pi$
$132$	− 108.000i	− 0.0712136i
$133$	− 868.000i	− 0.565903i
$134$	276.000	0.177931
$135$	0	0
$136$	882.000	0.556109
$137$	2358.00i	1.47049i	0.677800	+	0.735246i	$0.262934\pi$
$137$	2358.00i	1.47049i	−0.677800	+	0.735246i	$0.737066\pi$
$138$	0	0
$139$	52.0000	0.0317308	0.0158654	−	0.999874i	$-0.494950\pi$
$139$	52.0000	0.0317308	0.0158654	+	0.999874i	$0.494950\pi$
$140$	0	0
$141$	−720.000	−0.430035
$142$	− 2160.00i	− 1.27650i
$143$	1224.00i	0.715776i
$144$	639.000	0.369792
$145$	0	0
$146$	1506.00	0.853681
$147$	147.000i	0.0824786i
$148$	398.000i	0.221050i
$149$	1746.00	0.959986	0.479993	−	0.877272i	$-0.340639\pi$
$149$	1746.00	0.959986	0.479993	+	0.877272i	$0.340639\pi$
$150$	0	0
$151$	−232.000	−0.125032	−0.0625162	−	0.998044i	$-0.519913\pi$
$151$	−232.000	−0.125032	−0.0625162	+	0.998044i	$0.519913\pi$
$152$	2604.00i	1.38955i
$153$	378.000i	0.199735i
$154$	−756.000	−0.395586
$155$	0	0
$156$	102.000	0.0523496
$157$	− 1694.00i	− 0.861120i	−0.902562	−	0.430560i	$-0.858316\pi$
$157$	− 1694.00i	− 0.861120i	0.902562	−	0.430560i	$-0.141684\pi$
$158$	3072.00i	1.54681i
$159$	−1494.00	−0.745169
$160$	0	0
$161$	0	0
$162$	243.000i	0.117851i
$163$	− 2932.00i	− 1.40891i	−0.709750	−	0.704454i	$-0.751192\pi$
$163$	− 2932.00i	− 1.40891i	0.709750	−	0.704454i	$-0.248808\pi$
$164$	318.000	0.151412
$165$	0	0
$166$	612.000	0.286147
$167$	− 1176.00i	− 0.544920i	−0.962167	−	0.272460i	$-0.912163\pi$
$167$	− 1176.00i	− 0.544920i	0.962167	−	0.272460i	$-0.0878372\pi$
$168$	− 441.000i	− 0.202523i
$169$	1041.00	0.473828
$170$	0	0
$171$	−1116.00	−0.499080
$172$	268.000i	0.118807i
$173$	870.000i	0.382340i	0.981557	+	0.191170i	$0.0612282\pi$
$173$	870.000i	0.382340i	−0.981557	+	0.191170i	$0.938772\pi$
$174$	−918.000	−0.399962
$175$	0	0
$176$	2556.00	1.09469
$177$	− 396.000i	− 0.168165i
$178$	− 1062.00i	− 0.447193i
$179$	2316.00	0.967072	0.483536	−	0.875324i	$-0.339352\pi$
$179$	2316.00	0.967072	0.483536	+	0.875324i	$0.339352\pi$
$180$	0	0
$181$	−106.000	−0.0435299	−0.0217650	−	0.999763i	$-0.506929\pi$
$181$	−106.000	−0.0435299	−0.0217650	+	0.999763i	$0.506929\pi$
$182$	− 714.000i	− 0.290798i
$183$	− 1194.00i	− 0.482312i
$184$	0	0
$185$	0	0
$186$	−1440.00	−0.567666
$187$	1512.00i	0.591275i
$188$	240.000i	0.0931053i
$189$	189.000	0.0727393
$190$	0	0
$191$	−1128.00	−0.427326	−0.213663	−	0.976907i	$-0.568539\pi$
$191$	−1128.00	−0.427326	−0.213663	+	0.976907i	$0.568539\pi$
$192$	1299.00i	0.488267i
$193$	4034.00i	1.50453i	0.658862	+	0.752263i	$0.271038\pi$
$193$	4034.00i	1.50453i	−0.658862	+	0.752263i	$0.728962\pi$
$194$	−858.000	−0.317530
$195$	0	0
$196$	49.0000	0.0178571
$197$	1314.00i	0.475221i	0.971360	+	0.237611i	$0.0763643\pi$
$197$	1314.00i	0.475221i	−0.971360	+	0.237611i	$0.923636\pi$
$198$	972.000i	0.348874i
$199$	−5096.00	−1.81531	−0.907653	−	0.419722i	$-0.862128\pi$
$199$	−5096.00	−1.81531	−0.907653	+	0.419722i	$0.862128\pi$
$200$	0	0
$201$	−276.000	−0.0968534
$202$	1242.00i	0.432608i
$203$	714.000i	0.246862i
$204$	126.000	0.0432439
$205$	0	0
$206$	−168.000	−0.0568209
$207$	0	0
$208$	2414.00i	0.804715i
$209$	−4464.00	−1.47742
$210$	0	0
$211$	−3076.00	−1.00360	−0.501802	−	0.864982i	$-0.667330\pi$
$211$	−3076.00	−1.00360	−0.501802	+	0.864982i	$0.667330\pi$
$212$	498.000i	0.161334i
$213$	2160.00i	0.694839i
$214$	36.0000	0.0114996
$215$	0	0
$216$	−567.000	−0.178609
$217$	1120.00i	0.350371i
$218$	− 4434.00i	− 1.37756i
$219$	−1506.00	−0.464685
$220$	0	0
$221$	−1428.00	−0.434650
$222$	− 3582.00i	− 1.08292i
$223$	− 1888.00i	− 0.566950i	−0.958980	−	0.283475i	$-0.908513\pi$
$223$	− 1888.00i	− 0.566950i	0.958980	−	0.283475i	$-0.0914873\pi$
$224$	−315.000	−0.0939590
$225$	0	0
$226$	−1206.00	−0.354964
$227$	4716.00i	1.37891i	0.724330	+	0.689454i	$0.242149\pi$
$227$	4716.00i	1.37891i	−0.724330	+	0.689454i	$0.757851\pi$
$228$	372.000i	0.108054i
$229$	1690.00	0.487678	0.243839	−	0.969816i	$-0.421593\pi$
$229$	1690.00	0.487678	0.243839	+	0.969816i	$0.421593\pi$
$230$	0	0
$231$	756.000	0.215330
$232$	− 2142.00i	− 0.606160i
$233$	138.000i	0.0388012i	0.999812	+	0.0194006i	$0.00617579\pi$
$233$	138.000i	0.0388012i	−0.999812	+	0.0194006i	$0.993824\pi$
$234$	−918.000	−0.256460
$235$	0	0
$236$	−132.000	−0.0364088
$237$	− 3072.00i	− 0.841974i
$238$	− 882.000i	− 0.240217i
$239$	−1896.00	−0.513147	−0.256573	−	0.966525i	$-0.582594\pi$
$239$	−1896.00	−0.513147	−0.256573	+	0.966525i	$0.582594\pi$
$240$	0	0
$241$	−3598.00	−0.961691	−0.480846	−	0.876805i	$-0.659670\pi$
$241$	−3598.00	−0.961691	−0.480846	+	0.876805i	$0.659670\pi$
$242$	− 105.000i	− 0.0278911i
$243$	− 243.000i	− 0.0641500i
$244$	−398.000	−0.104424
$245$	0	0
$246$	−2862.00	−0.741766
$247$	− 4216.00i	− 1.08606i
$248$	− 3360.00i	− 0.860323i
$249$	−612.000	−0.155759
$250$	0	0
$251$	−3060.00	−0.769504	−0.384752	−	0.923020i	$-0.625713\pi$
$251$	−3060.00	−0.769504	−0.384752	+	0.923020i	$0.625713\pi$
$252$	− 63.0000i	− 0.0157485i
$253$	0	0
$254$	3840.00	0.948595
$255$	0	0
$256$	1513.00	0.369385
$257$	6822.00i	1.65582i	0.560864	+	0.827908i	$0.310469\pi$
$257$	6822.00i	1.65582i	−0.560864	+	0.827908i	$0.689531\pi$
$258$	− 2412.00i	− 0.582033i
$259$	−2786.00	−0.668392
$260$	0	0
$261$	918.000	0.217712
$262$	5292.00i	1.24787i
$263$	2592.00i	0.607717i	0.952717	+	0.303858i	$0.0982750\pi$
$263$	2592.00i	0.607717i	−0.952717	+	0.303858i	$0.901725\pi$
$264$	−2268.00	−0.528734
$265$	0	0
$266$	2604.00	0.600231
$267$	1062.00i	0.243421i
$268$	92.0000i	0.0209694i
$269$	−8214.00	−1.86177	−0.930886	−	0.365311i	$-0.880963\pi$
$269$	−8214.00	−1.86177	−0.930886	+	0.365311i	$0.880963\pi$
$270$	0	0
$271$	−5344.00	−1.19788	−0.598939	−	0.800795i	$-0.704411\pi$
$271$	−5344.00	−1.19788	−0.598939	+	0.800795i	$0.704411\pi$
$272$	2982.00i	0.664744i
$273$	714.000i	0.158290i
$274$	−7074.00	−1.55969
$275$	0	0
$276$	0	0
$277$	6514.00i	1.41295i	0.707736	+	0.706477i	$0.249717\pi$
$277$	6514.00i	1.41295i	−0.707736	+	0.706477i	$0.750283\pi$
$278$	156.000i	0.0336556i
$279$	1440.00	0.308998
$280$	0	0
$281$	6618.00	1.40497	0.702485	−	0.711698i	$-0.252074\pi$
$281$	6618.00	1.40497	0.702485	+	0.711698i	$0.252074\pi$
$282$	− 2160.00i	− 0.456121i
$283$	3260.00i	0.684759i	0.939562	+	0.342380i	$0.111233\pi$
$283$	3260.00i	0.684759i	−0.939562	+	0.342380i	$0.888767\pi$
$284$	720.000	0.150437
$285$	0	0
$286$	−3672.00	−0.759195
$287$	2226.00i	0.457828i
$288$	405.000i	0.0828641i
$289$	3149.00	0.640953
$290$	0	0
$291$	858.000	0.172841
$292$	502.000i	0.100607i
$293$	5118.00i	1.02047i	0.860036	+	0.510233i	$0.170441\pi$
$293$	5118.00i	1.02047i	−0.860036	+	0.510233i	$0.829559\pi$
$294$	−441.000	−0.0874818
$295$	0	0
$296$	8358.00	1.64121
$297$	− 972.000i	− 0.189903i
$298$	5238.00i	1.01822i
$299$	0	0
$300$	0	0
$301$	−1876.00	−0.359239
$302$	− 696.000i	− 0.132617i
$303$	− 1242.00i	− 0.235482i
$304$	−8804.00	−1.66100
$305$	0	0
$306$	−1134.00	−0.211851
$307$	− 452.000i	− 0.0840293i	−0.999117	−	0.0420147i	$-0.986622\pi$
$307$	− 452.000i	− 0.0840293i	0.999117	−	0.0420147i	$-0.0133776\pi$
$308$	− 252.000i	− 0.0466202i
$309$	168.000	0.0309294
$310$	0	0
$311$	5016.00	0.914570	0.457285	−	0.889320i	$-0.348822\pi$
$311$	5016.00	0.914570	0.457285	+	0.889320i	$0.348822\pi$
$312$	− 2142.00i	− 0.388676i
$313$	5402.00i	0.975524i	0.872977	+	0.487762i	$0.162187\pi$
$313$	5402.00i	0.975524i	−0.872977	+	0.487762i	$0.837813\pi$
$314$	5082.00	0.913356
$315$	0	0
$316$	−1024.00	−0.182293
$317$	− 10086.0i	− 1.78702i	−0.449041	−	0.893511i	$-0.648234\pi$
$317$	− 10086.0i	− 1.78702i	0.449041	−	0.893511i	$-0.351766\pi$
$318$	− 4482.00i	− 0.790371i
$319$	3672.00	0.644491
$320$	0	0
$321$	−36.0000	−0.00625958
$322$	0	0
$323$	− 5208.00i	− 0.897154i
$324$	−81.0000	−0.0138889
$325$	0	0
$326$	8796.00	1.49437
$327$	4434.00i	0.749849i
$328$	− 6678.00i	− 1.12418i
$329$	−1680.00	−0.281524
$330$	0	0
$331$	−8044.00	−1.33577	−0.667883	−	0.744267i	$-0.732799\pi$
$331$	−8044.00	−1.33577	−0.667883	+	0.744267i	$0.732799\pi$
$332$	204.000i	0.0337228i
$333$	3582.00i	0.589467i
$334$	3528.00	0.577975
$335$	0	0
$336$	1491.00	0.242085
$337$	− 4178.00i	− 0.675342i	−0.941264	−	0.337671i	$-0.890361\pi$
$337$	− 4178.00i	− 0.675342i	0.941264	−	0.337671i	$-0.109639\pi$
$338$	3123.00i	0.502570i
$339$	1206.00	0.193218
$340$	0	0
$341$	5760.00	0.914726
$342$	− 3348.00i	− 0.529354i
$343$	343.000i	0.0539949i
$344$	5628.00	0.882097
$345$	0	0
$346$	−2610.00	−0.405533
$347$	− 156.000i	− 0.0241341i	−0.999927	−	0.0120670i	$-0.996159\pi$
$347$	− 156.000i	− 0.0241341i	0.999927	−	0.0120670i	$-0.00384115\pi$
$348$	− 306.000i	− 0.0471360i
$349$	12418.0	1.90464	0.952321	−	0.305097i	$-0.0986888\pi$
$349$	12418.0	1.90464	0.952321	+	0.305097i	$0.0986888\pi$
$350$	0	0
$351$	918.000	0.139599
$352$	1620.00i	0.245302i
$353$	− 7830.00i	− 1.18059i	−0.807187	−	0.590296i	$-0.799011\pi$
$353$	− 7830.00i	− 1.18059i	0.807187	−	0.590296i	$-0.200989\pi$
$354$	1188.00	0.178366
$355$	0	0
$356$	354.000	0.0527021
$357$	882.000i	0.130757i
$358$	6948.00i	1.02574i
$359$	9312.00	1.36899	0.684497	−	0.729016i	$-0.260022\pi$
$359$	9312.00	1.36899	0.684497	+	0.729016i	$0.260022\pi$
$360$	0	0
$361$	8517.00	1.24173
$362$	− 318.000i	− 0.0461705i
$363$	105.000i	0.0151820i
$364$	238.000	0.0342709
$365$	0	0
$366$	3582.00	0.511569
$367$	3760.00i	0.534797i	0.963586	+	0.267398i	$0.0861640\pi$
$367$	3760.00i	0.534797i	−0.963586	+	0.267398i	$0.913836\pi$
$368$	0	0
$369$	2862.00	0.403766
$370$	0	0
$371$	−3486.00	−0.487828
$372$	− 480.000i	− 0.0669001i
$373$	5870.00i	0.814845i	0.913240	+	0.407422i	$0.133572\pi$
$373$	5870.00i	0.814845i	−0.913240	+	0.407422i	$0.866428\pi$
$374$	−4536.00	−0.627142
$375$	0	0
$376$	5040.00	0.691272
$377$	3468.00i	0.473769i
$378$	567.000i	0.0771517i
$379$	1852.00	0.251005	0.125502	−	0.992093i	$-0.459946\pi$
$379$	1852.00	0.251005	0.125502	+	0.992093i	$0.459946\pi$
$380$	0	0
$381$	−3840.00	−0.516350
$382$	− 3384.00i	− 0.453247i
$383$	2160.00i	0.288175i	0.989565	+	0.144087i	$0.0460246\pi$
$383$	2160.00i	0.288175i	−0.989565	+	0.144087i	$0.953975\pi$
$384$	−4977.00	−0.661410
$385$	0	0
$386$	−12102.0	−1.59579
$387$	2412.00i	0.316819i
$388$	− 286.000i	− 0.0374213i
$389$	6786.00	0.884483	0.442241	−	0.896896i	$-0.354183\pi$
$389$	6786.00	0.884483	0.442241	+	0.896896i	$0.354183\pi$
$390$	0	0
$391$	0	0
$392$	− 1029.00i	− 0.132583i
$393$	− 5292.00i	− 0.679252i
$394$	−3942.00	−0.504048
$395$	0	0
$396$	−324.000	−0.0411152
$397$	6514.00i	0.823497i	0.911298	+	0.411748i	$0.135082\pi$
$397$	6514.00i	0.823497i	−0.911298	+	0.411748i	$0.864918\pi$
$398$	− 15288.0i	− 1.92542i
$399$	−2604.00	−0.326724
$400$	0	0
$401$	3330.00	0.414694	0.207347	−	0.978267i	$-0.433517\pi$
$401$	3330.00	0.414694	0.207347	+	0.978267i	$0.433517\pi$
$402$	− 828.000i	− 0.102729i
$403$	5440.00i	0.672421i
$404$	−414.000	−0.0509833
$405$	0	0
$406$	−2142.00	−0.261837
$407$	14328.0i	1.74499i
$408$	− 2646.00i	− 0.321070i
$409$	5398.00	0.652601	0.326301	−	0.945266i	$-0.394198\pi$
$409$	5398.00	0.652601	0.326301	+	0.945266i	$0.394198\pi$
$410$	0	0
$411$	7074.00	0.848990
$412$	− 56.0000i	− 0.00669641i
$413$	− 924.000i	− 0.110090i
$414$	0	0
$415$	0	0
$416$	−1530.00	−0.180323
$417$	− 156.000i	− 0.0183198i
$418$	− 13392.0i	− 1.56704i
$419$	−13092.0	−1.52646	−0.763229	−	0.646128i	$-0.776387\pi$
$419$	−13092.0	−1.52646	−0.763229	+	0.646128i	$0.776387\pi$
$420$	0	0
$421$	−322.000	−0.0372763	−0.0186381	−	0.999826i	$-0.505933\pi$
$421$	−322.000	−0.0372763	−0.0186381	+	0.999826i	$0.505933\pi$
$422$	− 9228.00i	− 1.06448i
$423$	2160.00i	0.248281i
$424$	10458.0	1.19784
$425$	0	0
$426$	−6480.00	−0.736988
$427$	− 2786.00i	− 0.315747i
$428$	12.0000i	0.00135524i
$429$	3672.00	0.413254
$430$	0	0
$431$	2616.00	0.292363	0.146181	−	0.989258i	$-0.453302\pi$
$431$	2616.00	0.292363	0.146181	+	0.989258i	$0.453302\pi$
$432$	− 1917.00i	− 0.213499i
$433$	4322.00i	0.479681i	0.970812	+	0.239841i	$0.0770952\pi$
$433$	4322.00i	0.479681i	−0.970812	+	0.239841i	$0.922905\pi$
$434$	−3360.00	−0.371625
$435$	0	0
$436$	1478.00	0.162347
$437$	0	0
$438$	− 4518.00i	− 0.492873i
$439$	9016.00	0.980205	0.490103	−	0.871665i	$-0.336959\pi$
$439$	9016.00	0.980205	0.490103	+	0.871665i	$0.336959\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 4284.00i	− 0.461016i
$443$	− 5268.00i	− 0.564989i	−0.959269	−	0.282495i	$-0.908838\pi$
$443$	− 5268.00i	− 0.564989i	0.959269	−	0.282495i	$-0.0911619\pi$
$444$	1194.00	0.127623
$445$	0	0
$446$	5664.00	0.601341
$447$	− 5238.00i	− 0.554248i
$448$	3031.00i	0.319646i
$449$	5310.00	0.558117	0.279058	−	0.960274i	$-0.409978\pi$
$449$	5310.00	0.558117	0.279058	+	0.960274i	$0.409978\pi$
$450$	0	0
$451$	11448.0	1.19527
$452$	− 402.000i	− 0.0418329i
$453$	696.000i	0.0721875i
$454$	−14148.0	−1.46255
$455$	0	0
$456$	7812.00	0.802260
$457$	− 15770.0i	− 1.61420i	−0.590415	−	0.807100i	$-0.701036\pi$
$457$	− 15770.0i	− 1.61420i	0.590415	−	0.807100i	$-0.298964\pi$
$458$	5070.00i	0.517261i
$459$	1134.00	0.115317
$460$	0	0
$461$	−5370.00	−0.542529	−0.271264	−	0.962505i	$-0.587442\pi$
$461$	−5370.00	−0.542529	−0.271264	+	0.962505i	$0.587442\pi$
$462$	2268.00i	0.228392i
$463$	− 3328.00i	− 0.334050i	−0.985953	−	0.167025i	$-0.946584\pi$
$463$	− 3328.00i	− 0.334050i	0.985953	−	0.167025i	$-0.0534161\pi$
$464$	7242.00	0.724572
$465$	0	0
$466$	−414.000	−0.0411549
$467$	− 4548.00i	− 0.450656i	−0.974283	−	0.225328i	$-0.927655\pi$
$467$	− 4548.00i	− 0.450656i	0.974283	−	0.225328i	$-0.0723454\pi$
$468$	− 306.000i	− 0.0302240i
$469$	−644.000	−0.0634055
$470$	0	0
$471$	−5082.00	−0.497168
$472$	2772.00i	0.270321i
$473$	9648.00i	0.937876i
$474$	9216.00	0.893048
$475$	0	0
$476$	294.000	0.0283098
$477$	4482.00i	0.430224i
$478$	− 5688.00i	− 0.544274i
$479$	8064.00	0.769214	0.384607	−	0.923080i	$-0.374337\pi$
$479$	8064.00	0.769214	0.384607	+	0.923080i	$0.374337\pi$
$480$	0	0
$481$	−13532.0	−1.28276
$482$	− 10794.0i	− 1.02003i
$483$	0	0
$484$	35.0000	0.00328700
$485$	0	0
$486$	729.000	0.0680414
$487$	− 16616.0i	− 1.54608i	−0.634355	−	0.773042i	$-0.718734\pi$
$487$	− 16616.0i	− 1.54608i	0.634355	−	0.773042i	$-0.281266\pi$
$488$	8358.00i	0.775305i
$489$	−8796.00	−0.813433
$490$	0	0
$491$	−7140.00	−0.656260	−0.328130	−	0.944633i	$-0.606418\pi$
$491$	−7140.00	−0.656260	−0.328130	+	0.944633i	$0.606418\pi$
$492$	− 954.000i	− 0.0874180i
$493$	4284.00i	0.391362i
$494$	12648.0	1.15194
$495$	0	0
$496$	11360.0	1.02839
$497$	5040.00i	0.454879i
$498$	− 1836.00i	− 0.165207i
$499$	9124.00	0.818530	0.409265	−	0.912416i	$-0.365785\pi$
$499$	9124.00	0.818530	0.409265	+	0.912416i	$0.365785\pi$
$500$	0	0
$501$	−3528.00	−0.314610
$502$	− 9180.00i	− 0.816182i
$503$	− 6552.00i	− 0.580794i	−0.956906	−	0.290397i	$-0.906213\pi$
$503$	− 6552.00i	− 0.580794i	0.956906	−	0.290397i	$-0.0937873\pi$
$504$	−1323.00	−0.116927
$505$	0	0
$506$	0	0
$507$	− 3123.00i	− 0.273565i
$508$	1280.00i	0.111793i
$509$	−2790.00	−0.242956	−0.121478	−	0.992594i	$-0.538763\pi$
$509$	−2790.00	−0.242956	−0.121478	+	0.992594i	$0.538763\pi$
$510$	0	0
$511$	−3514.00	−0.304208
$512$	− 8733.00i	− 0.753804i
$513$	3348.00i	0.288144i
$514$	−20466.0	−1.75626
$515$	0	0
$516$	804.000	0.0685933
$517$	8640.00i	0.734984i
$518$	− 8358.00i	− 0.708937i
$519$	2610.00	0.220744
$520$	0	0
$521$	−14862.0	−1.24974	−0.624871	−	0.780728i	$-0.714849\pi$
$521$	−14862.0	−1.24974	−0.624871	+	0.780728i	$0.714849\pi$
$522$	2754.00i	0.230918i
$523$	17660.0i	1.47652i	0.674518	+	0.738258i	$0.264351\pi$
$523$	17660.0i	1.47652i	−0.674518	+	0.738258i	$0.735649\pi$
$524$	−1764.00	−0.147062
$525$	0	0
$526$	−7776.00	−0.644581
$527$	6720.00i	0.555461i
$528$	− 7668.00i	− 0.632021i
$529$	12167.0	1.00000
$530$	0	0
$531$	−1188.00	−0.0970900
$532$	868.000i	0.0707379i
$533$	10812.0i	0.878649i
$534$	−3186.00	−0.258187
$535$	0	0
$536$	1932.00	0.155690
$537$	− 6948.00i	− 0.558340i
$538$	− 24642.0i	− 1.97471i
$539$	1764.00	0.140966
$540$	0	0
$541$	−19834.0	−1.57621	−0.788106	−	0.615540i	$-0.788938\pi$
$541$	−19834.0	−1.57621	−0.788106	+	0.615540i	$0.788938\pi$
$542$	− 16032.0i	− 1.27054i
$543$	318.000i	0.0251320i
$544$	−1890.00	−0.148958
$545$	0	0
$546$	−2142.00	−0.167892
$547$	− 20972.0i	− 1.63930i	−0.572863	−	0.819651i	$-0.694167\pi$
$547$	− 20972.0i	− 1.63930i	0.572863	−	0.819651i	$-0.305833\pi$
$548$	− 2358.00i	− 0.183812i
$549$	−3582.00	−0.278463
$550$	0	0
$551$	−12648.0	−0.977900
$552$	0	0
$553$	− 7168.00i	− 0.551201i
$554$	−19542.0	−1.49866
$555$	0	0
$556$	−52.0000	−0.00396635
$557$	− 21174.0i	− 1.61072i	−0.592786	−	0.805360i	$-0.701972\pi$
$557$	− 21174.0i	− 1.61072i	0.592786	−	0.805360i	$-0.298028\pi$
$558$	4320.00i	0.327742i
$559$	−9112.00	−0.689439
$560$	0	0
$561$	4536.00	0.341373
$562$	19854.0i	1.49020i
$563$	− 17772.0i	− 1.33037i	−0.746677	−	0.665187i	$-0.768352\pi$
$563$	− 17772.0i	− 1.33037i	0.746677	−	0.665187i	$-0.231648\pi$
$564$	720.000	0.0537544
$565$	0	0
$566$	−9780.00	−0.726297
$567$	− 567.000i	− 0.0419961i
$568$	− 15120.0i	− 1.11694i
$569$	−8250.00	−0.607835	−0.303917	−	0.952698i	$-0.598295\pi$
$569$	−8250.00	−0.607835	−0.303917	+	0.952698i	$0.598295\pi$
$570$	0	0
$571$	20756.0	1.52121	0.760606	−	0.649214i	$-0.224902\pi$
$571$	20756.0	1.52121	0.760606	+	0.649214i	$0.224902\pi$
$572$	− 1224.00i	− 0.0894720i
$573$	3384.00i	0.246717i
$574$	−6678.00	−0.485600
$575$	0	0
$576$	3897.00	0.281901
$577$	− 2.00000i	0 0.000144300i	−1.00000		7.21500e-5i	$-0.999977\pi$
$577$	− 2.00000i	0 0.000144300i	1.00000		7.21500e-5i	$-2.29661e-5\pi$
$578$	9447.00i	0.679833i
$579$	12102.0	0.868639
$580$	0	0
$581$	−1428.00	−0.101968
$582$	2574.00i	0.183326i
$583$	17928.0i	1.27359i
$584$	10542.0	0.746971
$585$	0	0
$586$	−15354.0	−1.08237
$587$	− 26364.0i	− 1.85376i	−0.375354	−	0.926881i	$-0.622479\pi$
$587$	− 26364.0i	− 1.85376i	0.375354	−	0.926881i	$-0.377521\pi$
$588$	− 147.000i	− 0.0103098i
$589$	−19840.0	−1.38793
$590$	0	0
$591$	3942.00	0.274369
$592$	28258.0i	1.96182i
$593$	2298.00i	0.159136i	0.996829	+	0.0795679i	$0.0253541\pi$
$593$	2298.00i	0.159136i	−0.996829	+	0.0795679i	$0.974646\pi$
$594$	2916.00	0.201422
$595$	0	0
$596$	−1746.00	−0.119998
$597$	15288.0i	1.04807i
$598$	0	0
$599$	−3072.00	−0.209547	−0.104773	−	0.994496i	$-0.533412\pi$
$599$	−3072.00	−0.209547	−0.104773	+	0.994496i	$0.533412\pi$
$600$	0	0
$601$	24554.0	1.66652	0.833260	−	0.552881i	$-0.186472\pi$
$601$	24554.0	1.66652	0.833260	+	0.552881i	$0.186472\pi$
$602$	− 5628.00i	− 0.381030i
$603$	828.000i	0.0559184i
$604$	232.000	0.0156290
$605$	0	0
$606$	3726.00	0.249766
$607$	− 16832.0i	− 1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$607$	− 16832.0i	− 1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$608$	− 5580.00i	− 0.372202i
$609$	2142.00	0.142526
$610$	0	0
$611$	−8160.00	−0.540292
$612$	− 378.000i	− 0.0249669i
$613$	− 2482.00i	− 0.163535i	−0.996651	−	0.0817676i	$-0.973943\pi$
$613$	− 2482.00i	− 0.163535i	0.996651	−	0.0817676i	$-0.0260565\pi$
$614$	1356.00	0.0891266
$615$	0	0
$616$	−5292.00	−0.346138
$617$	15798.0i	1.03080i	0.856950	+	0.515400i	$0.172357\pi$
$617$	15798.0i	1.03080i	−0.856950	+	0.515400i	$0.827643\pi$
$618$	504.000i	0.0328056i
$619$	15460.0	1.00386	0.501930	−	0.864908i	$-0.332623\pi$
$619$	15460.0	1.00386	0.501930	+	0.864908i	$0.332623\pi$
$620$	0	0
$621$	0	0
$622$	15048.0i	0.970048i
$623$	2478.00i	0.159356i
$624$	7242.00	0.464603
$625$	0	0
$626$	−16206.0	−1.03470
$627$	13392.0i	0.852990i
$628$	1694.00i	0.107640i
$629$	−16716.0	−1.05964
$630$	0	0
$631$	−7720.00	−0.487050	−0.243525	−	0.969895i	$-0.578304\pi$
$631$	−7720.00	−0.487050	−0.243525	+	0.969895i	$0.578304\pi$
$632$	21504.0i	1.35345i
$633$	9228.00i	0.579431i
$634$	30258.0	1.89542
$635$	0	0
$636$	1494.00	0.0931462
$637$	1666.00i	0.103625i
$638$	11016.0i	0.683586i
$639$	6480.00	0.401166
$640$	0	0
$641$	−17262.0	−1.06366	−0.531832	−	0.846850i	$-0.678496\pi$
$641$	−17262.0	−1.06366	−0.531832	+	0.846850i	$0.678496\pi$
$642$	− 108.000i	− 0.00663928i
$643$	− 12220.0i	− 0.749471i	−0.927132	−	0.374735i	$-0.877734\pi$
$643$	− 12220.0i	− 0.749471i	0.927132	−	0.374735i	$-0.122266\pi$
$644$	0	0
$645$	0	0
$646$	15624.0	0.951576
$647$	− 13560.0i	− 0.823955i	−0.911194	−	0.411977i	$-0.864838\pi$
$647$	− 13560.0i	− 0.823955i	0.911194	−	0.411977i	$-0.135162\pi$
$648$	1701.00i	0.103120i
$649$	−4752.00	−0.287415
$650$	0	0
$651$	3360.00	0.202287
$652$	2932.00i	0.176113i
$653$	23094.0i	1.38398i	0.721908	+	0.691989i	$0.243265\pi$
$653$	23094.0i	1.38398i	−0.721908	+	0.691989i	$0.756735\pi$
$654$	−13302.0	−0.795335
$655$	0	0
$656$	22578.0	1.34378
$657$	4518.00i	0.268286i
$658$	− 5040.00i	− 0.298601i
$659$	−22548.0	−1.33285	−0.666423	−	0.745574i	$-0.732175\pi$
$659$	−22548.0	−1.33285	−0.666423	+	0.745574i	$0.732175\pi$
$660$	0	0
$661$	17462.0	1.02752	0.513762	−	0.857933i	$-0.328252\pi$
$661$	17462.0	1.02752	0.513762	+	0.857933i	$0.328252\pi$
$662$	− 24132.0i	− 1.41679i
$663$	4284.00i	0.250945i
$664$	4284.00	0.250379
$665$	0	0
$666$	−10746.0	−0.625224
$667$	0	0
$668$	1176.00i	0.0681150i
$669$	−5664.00	−0.327329
$670$	0	0
$671$	−14328.0	−0.824331
$672$	945.000i	0.0542473i
$673$	− 22462.0i	− 1.28655i	−0.765636	−	0.643274i	$-0.777576\pi$
$673$	− 22462.0i	− 1.28655i	0.765636	−	0.643274i	$-0.222424\pi$
$674$	12534.0	0.716308
$675$	0	0
$676$	−1041.00	−0.0592285
$677$	25554.0i	1.45069i	0.688383	+	0.725347i	$0.258321\pi$
$677$	25554.0i	1.45069i	−0.688383	+	0.725347i	$0.741679\pi$
$678$	3618.00i	0.204939i
$679$	2002.00	0.113151
$680$	0	0
$681$	14148.0	0.796112
$682$	17280.0i	0.970213i
$683$	9276.00i	0.519672i	0.965653	+	0.259836i	$0.0836686\pi$
$683$	9276.00i	0.519672i	−0.965653	+	0.259836i	$0.916331\pi$
$684$	1116.00	0.0623850
$685$	0	0
$686$	−1029.00	−0.0572703
$687$	− 5070.00i	− 0.281561i
$688$	19028.0i	1.05441i
$689$	−16932.0	−0.936223
$690$	0	0
$691$	27380.0	1.50736	0.753679	−	0.657243i	$-0.228277\pi$
$691$	27380.0	1.50736	0.753679	+	0.657243i	$0.228277\pi$
$692$	− 870.000i	− 0.0477925i
$693$	− 2268.00i	− 0.124321i
$694$	468.000	0.0255980
$695$	0	0
$696$	−6426.00	−0.349967
$697$	13356.0i	0.725817i
$698$	37254.0i	2.02018i
$699$	414.000	0.0224019
$700$	0	0
$701$	25830.0	1.39171	0.695853	−	0.718184i	$-0.255027\pi$
$701$	25830.0	1.39171	0.695853	+	0.718184i	$0.255027\pi$
$702$	2754.00i	0.148067i
$703$	− 49352.0i	− 2.64772i
$704$	15588.0	0.834510
$705$	0	0
$706$	23490.0	1.25221
$707$	− 2898.00i	− 0.154159i
$708$	396.000i	0.0210206i
$709$	6226.00	0.329792	0.164896	−	0.986311i	$-0.447271\pi$
$709$	6226.00	0.329792	0.164896	+	0.986311i	$0.447271\pi$
$710$	0	0
$711$	−9216.00	−0.486114
$712$	− 7434.00i	− 0.391293i
$713$	0	0
$714$	−2646.00	−0.138689
$715$	0	0
$716$	−2316.00	−0.120884
$717$	5688.00i	0.296265i
$718$	27936.0i	1.45204i
$719$	15072.0	0.781767	0.390884	−	0.920440i	$-0.372169\pi$
$719$	15072.0	0.781767	0.390884	+	0.920440i	$0.372169\pi$
$720$	0	0
$721$	392.000	0.0202480
$722$	25551.0i	1.31705i
$723$	10794.0i	0.555233i
$724$	106.000	0.00544124
$725$	0	0
$726$	−315.000	−0.0161030
$727$	32920.0i	1.67942i	0.543038	+	0.839708i	$0.317274\pi$
$727$	32920.0i	1.67942i	−0.543038	+	0.839708i	$0.682726\pi$
$728$	− 4998.00i	− 0.254448i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−11256.0	−0.569519
$732$	1194.00i	0.0602889i
$733$	− 6946.00i	− 0.350009i	−0.984568	−	0.175004i	$-0.944006\pi$
$733$	− 6946.00i	− 0.350009i	0.984568	−	0.175004i	$-0.0559939\pi$
$734$	−11280.0	−0.567238
$735$	0	0
$736$	0	0
$737$	3312.00i	0.165535i
$738$	8586.00i	0.428259i
$739$	2356.00	0.117276	0.0586379	−	0.998279i	$-0.481324\pi$
$739$	2356.00	0.117276	0.0586379	+	0.998279i	$0.481324\pi$
$740$	0	0
$741$	−12648.0	−0.627039
$742$	− 10458.0i	− 0.517419i
$743$	− 23520.0i	− 1.16133i	−0.814144	−	0.580663i	$-0.802793\pi$
$743$	− 23520.0i	− 1.16133i	0.814144	−	0.580663i	$-0.197207\pi$
$744$	−10080.0	−0.496708
$745$	0	0
$746$	−17610.0	−0.864273
$747$	1836.00i	0.0899273i
$748$	− 1512.00i	− 0.0739094i
$749$	−84.0000	−0.00409785
$750$	0	0
$751$	3008.00	0.146156	0.0730782	−	0.997326i	$-0.476718\pi$
$751$	3008.00	0.146156	0.0730782	+	0.997326i	$0.476718\pi$
$752$	17040.0i	0.826310i
$753$	9180.00i	0.444273i
$754$	−10404.0	−0.502508
$755$	0	0
$756$	−189.000	−0.00909241
$757$	20770.0i	0.997224i	0.866825	+	0.498612i	$0.166157\pi$
$757$	20770.0i	0.997224i	−0.866825	+	0.498612i	$0.833843\pi$
$758$	5556.00i	0.266231i
$759$	0	0
$760$	0	0
$761$	11538.0	0.549609	0.274804	−	0.961500i	$-0.411387\pi$
$761$	11538.0	0.549609	0.274804	+	0.961500i	$0.411387\pi$
$762$	− 11520.0i	− 0.547671i
$763$	10346.0i	0.490892i
$764$	1128.00	0.0534157
$765$	0	0
$766$	−6480.00	−0.305655
$767$	− 4488.00i	− 0.211281i
$768$	− 4539.00i	− 0.213264i
$769$	−8498.00	−0.398499	−0.199249	−	0.979949i	$-0.563850\pi$
$769$	−8498.00	−0.398499	−0.199249	+	0.979949i	$0.563850\pi$
$770$	0	0
$771$	20466.0	0.955986
$772$	− 4034.00i	− 0.188066i
$773$	− 32322.0i	− 1.50393i	−0.659200	−	0.751967i	$-0.729105\pi$
$773$	− 32322.0i	− 1.50393i	0.659200	−	0.751967i	$-0.270895\pi$
$774$	−7236.00	−0.336037
$775$	0	0
$776$	−6006.00	−0.277839
$777$	8358.00i	0.385896i
$778$	20358.0i	0.938136i
$779$	−39432.0	−1.81360
$780$	0	0
$781$	25920.0	1.18757
$782$	0	0
$783$	− 2754.00i	− 0.125696i
$784$	3479.00	0.158482
$785$	0	0
$786$	15876.0	0.720456
$787$	− 26228.0i	− 1.18796i	−0.804479	−	0.593982i	$-0.797555\pi$
$787$	− 26228.0i	− 1.18796i	0.804479	−	0.593982i	$-0.202445\pi$
$788$	− 1314.00i	− 0.0594027i
$789$	7776.00	0.350866
$790$	0	0
$791$	2814.00	0.126491
$792$	6804.00i	0.305265i
$793$	− 13532.0i	− 0.605972i
$794$	−19542.0	−0.873450
$795$	0	0
$796$	5096.00	0.226913
$797$	43338.0i	1.92611i	0.269302	+	0.963056i	$0.413207\pi$
$797$	43338.0i	1.92611i	−0.269302	+	0.963056i	$0.586793\pi$
$798$	− 7812.00i	− 0.346544i
$799$	−10080.0	−0.446314
$800$	0	0
$801$	3186.00	0.140539
$802$	9990.00i	0.439849i
$803$	18072.0i	0.794206i
$804$	276.000	0.0121067
$805$	0	0
$806$	−16320.0	−0.713210
$807$	24642.0i	1.07489i
$808$	8694.00i	0.378532i
$809$	28902.0	1.25604	0.628022	−	0.778195i	$-0.283865\pi$
$809$	28902.0	1.25604	0.628022	+	0.778195i	$0.283865\pi$
$810$	0	0
$811$	27164.0	1.17615	0.588075	−	0.808807i	$-0.299886\pi$
$811$	27164.0	1.17615	0.588075	+	0.808807i	$0.299886\pi$
$812$	− 714.000i	− 0.0308577i
$813$	16032.0i	0.691595i
$814$	−42984.0	−1.85085
$815$	0	0
$816$	8946.00	0.383790
$817$	− 33232.0i	− 1.42306i
$818$	16194.0i	0.692188i
$819$	2142.00	0.0913889
$820$	0	0
$821$	−17202.0	−0.731247	−0.365624	−	0.930763i	$-0.619144\pi$
$821$	−17202.0	−0.731247	−0.365624	+	0.930763i	$0.619144\pi$
$822$	21222.0i	0.900489i
$823$	− 5992.00i	− 0.253789i	−0.991916	−	0.126894i	$-0.959499\pi$
$823$	− 5992.00i	− 0.253789i	0.991916	−	0.126894i	$-0.0405009\pi$
$824$	−1176.00	−0.0497183
$825$	0	0
$826$	2772.00	0.116768
$827$	− 25884.0i	− 1.08836i	−0.838968	−	0.544181i	$-0.816841\pi$
$827$	− 25884.0i	− 1.08836i	0.838968	−	0.544181i	$-0.183159\pi$
$828$	0	0
$829$	1474.00	0.0617541	0.0308770	−	0.999523i	$-0.490170\pi$
$829$	1474.00	0.0617541	0.0308770	+	0.999523i	$0.490170\pi$
$830$	0	0
$831$	19542.0	0.815770
$832$	14722.0i	0.613454i
$833$	2058.00i	0.0856008i
$834$	468.000	0.0194311
$835$	0	0
$836$	4464.00	0.184678
$837$	− 4320.00i	− 0.178400i
$838$	− 39276.0i	− 1.61905i
$839$	−33528.0	−1.37964	−0.689818	−	0.723983i	$-0.742310\pi$
$839$	−33528.0	−1.37964	−0.689818	+	0.723983i	$0.742310\pi$
$840$	0	0
$841$	−13985.0	−0.573414
$842$	− 966.000i	− 0.0395375i
$843$	− 19854.0i	− 0.811160i
$844$	3076.00	0.125451
$845$	0	0
$846$	−6480.00	−0.263342
$847$	245.000i	0.00993896i
$848$	35358.0i	1.43184i
$849$	9780.00	0.395346
$850$	0	0
$851$	0	0
$852$	− 2160.00i	− 0.0868549i
$853$	1190.00i	0.0477665i	0.999715	+	0.0238832i	$0.00760300\pi$
$853$	1190.00i	0.0477665i	−0.999715	+	0.0238832i	$0.992397\pi$
$854$	8358.00	0.334900
$855$	0	0
$856$	252.000	0.0100621
$857$	− 34578.0i	− 1.37825i	−0.724642	−	0.689126i	$-0.757995\pi$
$857$	− 34578.0i	− 1.37825i	0.724642	−	0.689126i	$-0.242005\pi$
$858$	11016.0i	0.438322i
$859$	44404.0	1.76373	0.881865	−	0.471501i	$-0.156288\pi$
$859$	44404.0	1.76373	0.881865	+	0.471501i	$0.156288\pi$
$860$	0	0
$861$	6678.00	0.264327
$862$	7848.00i	0.310097i
$863$	− 38328.0i	− 1.51182i	−0.654676	−	0.755910i	$-0.727195\pi$
$863$	− 38328.0i	− 1.51182i	0.654676	−	0.755910i	$-0.272805\pi$
$864$	1215.00	0.0478416
$865$	0	0
$866$	−12966.0	−0.508779
$867$	− 9447.00i	− 0.370054i
$868$	− 1120.00i	− 0.0437964i
$869$	−36864.0	−1.43904
$870$	0	0
$871$	−3128.00	−0.121686
$872$	− 31038.0i	− 1.20537i
$873$	− 2574.00i	− 0.0997900i
$874$	0	0
$875$	0	0
$876$	1506.00	0.0580856
$877$	38842.0i	1.49555i	0.663950	+	0.747777i	$0.268879\pi$
$877$	38842.0i	1.49555i	−0.663950	+	0.747777i	$0.731121\pi$
$878$	27048.0i	1.03966i
$879$	15354.0	0.589167
$880$	0	0
$881$	−35046.0	−1.34022	−0.670108	−	0.742264i	$-0.733752\pi$
$881$	−35046.0	−1.34022	−0.670108	+	0.742264i	$0.733752\pi$
$882$	1323.00i	0.0505076i
$883$	14204.0i	0.541339i	0.962672	+	0.270670i	$0.0872451\pi$
$883$	14204.0i	0.541339i	−0.962672	+	0.270670i	$0.912755\pi$
$884$	1428.00	0.0543313
$885$	0	0
$886$	15804.0	0.599262
$887$	26136.0i	0.989359i	0.869076	+	0.494679i	$0.164714\pi$
$887$	26136.0i	0.989359i	−0.869076	+	0.494679i	$0.835286\pi$
$888$	− 25074.0i	− 0.947554i
$889$	−8960.00	−0.338030
$890$	0	0
$891$	−2916.00	−0.109640
$892$	1888.00i	0.0708687i
$893$	− 29760.0i	− 1.11521i
$894$	15714.0	0.587869
$895$	0	0
$896$	−11613.0	−0.432995
$897$	0	0
$898$	15930.0i	0.591972i
$899$	16320.0	0.605453
$900$	0	0
$901$	−20916.0	−0.773377
$902$	34344.0i	1.26777i
$903$	5628.00i	0.207407i
$904$	−8442.00	−0.310594
$905$	0	0
$906$	−2088.00	−0.0765664
$907$	9052.00i	0.331386i	0.986177	+	0.165693i	$0.0529860\pi$
$907$	9052.00i	0.331386i	−0.986177	+	0.165693i	$0.947014\pi$
$908$	− 4716.00i	− 0.172363i
$909$	−3726.00	−0.135956
$910$	0	0
$911$	5016.00	0.182423	0.0912116	−	0.995832i	$-0.470926\pi$
$911$	5016.00	0.182423	0.0912116	+	0.995832i	$0.470926\pi$
$912$	26412.0i	0.958979i
$913$	7344.00i	0.266211i
$914$	47310.0	1.71212
$915$	0	0
$916$	−1690.00	−0.0609598
$917$	− 12348.0i	− 0.444675i
$918$	3402.00i	0.122312i
$919$	−44552.0	−1.59917	−0.799584	−	0.600555i	$-0.794946\pi$
$919$	−44552.0	−1.59917	−0.799584	+	0.600555i	$0.794946\pi$
$920$	0	0
$921$	−1356.00	−0.0485144
$922$	− 16110.0i	− 0.575439i
$923$	24480.0i	0.872989i
$924$	−756.000	−0.0269162
$925$	0	0
$926$	9984.00	0.354314
$927$	− 504.000i	− 0.0178571i
$928$	4590.00i	0.162364i
$929$	−24234.0	−0.855858	−0.427929	−	0.903812i	$-0.640757\pi$
$929$	−24234.0	−0.855858	−0.427929	+	0.903812i	$0.640757\pi$
$930$	0	0
$931$	−6076.00	−0.213891
$932$	− 138.000i	− 0.00485015i
$933$	− 15048.0i	− 0.528027i
$934$	13644.0	0.477993
$935$	0	0
$936$	−6426.00	−0.224402
$937$	13894.0i	0.484415i	0.970224	+	0.242208i	$0.0778715\pi$
$937$	13894.0i	0.484415i	−0.970224	+	0.242208i	$0.922128\pi$
$938$	− 1932.00i	− 0.0672516i
$939$	16206.0	0.563219
$940$	0	0
$941$	46758.0	1.61984	0.809919	−	0.586542i	$-0.199511\pi$
$941$	46758.0	1.61984	0.809919	+	0.586542i	$0.199511\pi$
$942$	− 15246.0i	− 0.527326i
$943$	0	0
$944$	−9372.00	−0.323128
$945$	0	0
$946$	−28944.0	−0.994768
$947$	− 13812.0i	− 0.473949i	−0.971516	−	0.236974i	$-0.923844\pi$
$947$	− 13812.0i	− 0.473949i	0.971516	−	0.236974i	$-0.0761558\pi$
$948$	3072.00i	0.105247i
$949$	−17068.0	−0.583826
$950$	0	0
$951$	−30258.0	−1.03174
$952$	− 6174.00i	− 0.210190i
$953$	− 58518.0i	− 1.98907i	−0.104402	−	0.994535i	$-0.533293\pi$
$953$	− 58518.0i	− 1.98907i	0.104402	−	0.994535i	$-0.466707\pi$
$954$	−13446.0	−0.456321
$955$	0	0
$956$	1896.00	0.0641433
$957$	− 11016.0i	− 0.372097i
$958$	24192.0i	0.815875i
$959$	16506.0	0.555794
$960$	0	0
$961$	−4191.00	−0.140680
$962$	− 40596.0i	− 1.36057i
$963$	108.000i	0.00361397i
$964$	3598.00	0.120211
$965$	0	0
$966$	0	0
$967$	− 19640.0i	− 0.653133i	−0.945174	−	0.326567i	$-0.894108\pi$
$967$	− 19640.0i	− 0.653133i	0.945174	−	0.326567i	$-0.105892\pi$
$968$	− 735.000i	− 0.0244047i
$969$	−15624.0	−0.517972
$970$	0	0
$971$	−58308.0	−1.92708	−0.963539	−	0.267568i	$-0.913780\pi$
$971$	−58308.0	−1.92708	−0.963539	+	0.267568i	$0.913780\pi$
$972$	243.000i	0.00801875i
$973$	− 364.000i	− 0.0119931i
$974$	49848.0	1.63987
$975$	0	0
$976$	−28258.0	−0.926759
$977$	23550.0i	0.771168i	0.922673	+	0.385584i	$0.126000\pi$
$977$	23550.0i	0.771168i	−0.922673	+	0.385584i	$0.874000\pi$
$978$	− 26388.0i	− 0.862776i
$979$	12744.0	0.416037
$980$	0	0
$981$	13302.0	0.432926
$982$	− 21420.0i	− 0.696069i
$983$	15768.0i	0.511619i	0.966727	+	0.255809i	$0.0823419\pi$
$983$	15768.0i	0.511619i	−0.966727	+	0.255809i	$0.917658\pi$
$984$	−20034.0	−0.649045
$985$	0	0
$986$	−12852.0	−0.415102
$987$	5040.00i	0.162538i
$988$	4216.00i	0.135758i
$989$	0	0
$990$	0	0
$991$	35264.0	1.13037	0.565186	−	0.824964i	$-0.308805\pi$
$991$	35264.0	1.13037	0.565186	+	0.824964i	$0.308805\pi$
$992$	7200.00i	0.230444i
$993$	24132.0i	0.771204i
$994$	−15120.0	−0.482472
$995$	0	0
$996$	612.000	0.0194698
$997$	29338.0i	0.931940i	0.884801	+	0.465970i	$0.154294\pi$
$997$	29338.0i	0.931940i	−0.884801	+	0.465970i	$0.845706\pi$
$998$	27372.0i	0.868182i
$999$	10746.0	0.340329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.c.274.2		2
5.2	odd	4		21.4.a.a.1.1	✓	1
5.3	odd	4		525.4.a.g.1.1		1
5.4	even	2	inner	525.4.d.c.274.1		2
15.2	even	4		63.4.a.c.1.1		1
15.8	even	4		1575.4.a.b.1.1		1
20.7	even	4		336.4.a.f.1.1		1
35.2	odd	12		147.4.e.i.67.1		2
35.12	even	12		147.4.e.g.67.1		2
35.17	even	12		147.4.e.g.79.1		2
35.27	even	4		147.4.a.c.1.1		1
35.32	odd	12		147.4.e.i.79.1		2
40.27	even	4		1344.4.a.n.1.1		1
40.37	odd	4		1344.4.a.ba.1.1		1
60.47	odd	4		1008.4.a.v.1.1		1
105.2	even	12		441.4.e.b.361.1		2
105.17	odd	12		441.4.e.d.226.1		2
105.32	even	12		441.4.e.b.226.1		2
105.47	odd	12		441.4.e.d.361.1		2
105.62	odd	4		441.4.a.j.1.1		1
140.27	odd	4		2352.4.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.a.1.1	✓	1	5.2	odd	4
63.4.a.c.1.1		1	15.2	even	4
147.4.a.c.1.1		1	35.27	even	4
147.4.e.g.67.1		2	35.12	even	12
147.4.e.g.79.1		2	35.17	even	12
147.4.e.i.67.1		2	35.2	odd	12
147.4.e.i.79.1		2	35.32	odd	12
336.4.a.f.1.1		1	20.7	even	4
441.4.a.j.1.1		1	105.62	odd	4
441.4.e.b.226.1		2	105.32	even	12
441.4.e.b.361.1		2	105.2	even	12
441.4.e.d.226.1		2	105.17	odd	12
441.4.e.d.361.1		2	105.47	odd	12
525.4.a.g.1.1		1	5.3	odd	4
525.4.d.c.274.1		2	5.4	even	2	inner
525.4.d.c.274.2		2	1.1	even	1	trivial
1008.4.a.v.1.1		1	60.47	odd	4
1344.4.a.n.1.1		1	40.27	even	4
1344.4.a.ba.1.1		1	40.37	odd	4
1575.4.a.b.1.1		1	15.8	even	4
2352.4.a.r.1.1		1	140.27	odd	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +9.00000 q^{6} -7.00000i q^{7} +21.0000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +9.00000 q^{6} -7.00000i q^{7} +21.0000i q^{8} -9.00000 q^{9} -36.0000 q^{11} +3.00000i q^{12} -34.0000i q^{13} +21.0000 q^{14} -71.0000 q^{16} -42.0000i q^{17} -27.0000i q^{18} +124.000 q^{19} -21.0000 q^{21} -108.000i q^{22} +63.0000 q^{24} +102.000 q^{26} +27.0000i q^{27} +7.00000i q^{28} -102.000 q^{29} -160.000 q^{31} -45.0000i q^{32} +108.000i q^{33} +126.000 q^{34} +9.00000 q^{36} -398.000i q^{37} +372.000i q^{38} -102.000 q^{39} -318.000 q^{41} -63.0000i q^{42} -268.000i q^{43} +36.0000 q^{44} -240.000i q^{47} +213.000i q^{48} -49.0000 q^{49} -126.000 q^{51} +34.0000i q^{52} -498.000i q^{53} -81.0000 q^{54} +147.000 q^{56} -372.000i q^{57} -306.000i q^{58} +132.000 q^{59} +398.000 q^{61} -480.000i q^{62} +63.0000i q^{63} -433.000 q^{64} -324.000 q^{66} -92.0000i q^{67} +42.0000i q^{68} -720.000 q^{71} -189.000i q^{72} -502.000i q^{73} +1194.00 q^{74} -124.000 q^{76} +252.000i q^{77} -306.000i q^{78} +1024.00 q^{79} +81.0000 q^{81} -954.000i q^{82} -204.000i q^{83} +21.0000 q^{84} +804.000 q^{86} +306.000i q^{87} -756.000i q^{88} -354.000 q^{89} -238.000 q^{91} +480.000i q^{93} +720.000 q^{94} -135.000 q^{96} +286.000i q^{97} -147.000i q^{98} +324.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 18 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 18 * q^6 - 18 * q^9	\( 2 q - 2 q^{4} + 18 q^{6} - 18 q^{9} - 72 q^{11} + 42 q^{14} - 142 q^{16} + 248 q^{19} - 42 q^{21} + 126 q^{24} + 204 q^{26} - 204 q^{29} - 320 q^{31} + 252 q^{34} + 18 q^{36} - 204 q^{39} - 636 q^{41} + 72 q^{44} - 98 q^{49} - 252 q^{51} - 162 q^{54} + 294 q^{56} + 264 q^{59} + 796 q^{61} - 866 q^{64} - 648 q^{66} - 1440 q^{71} + 2388 q^{74} - 248 q^{76} + 2048 q^{79} + 162 q^{81} + 42 q^{84} + 1608 q^{86} - 708 q^{89} - 476 q^{91} + 1440 q^{94} - 270 q^{96} + 648 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 18 * q^6 - 18 * q^9 - 72 * q^11 + 42 * q^14 - 142 * q^16 + 248 * q^19 - 42 * q^21 + 126 * q^24 + 204 * q^26 - 204 * q^29 - 320 * q^31 + 252 * q^34 + 18 * q^36 - 204 * q^39 - 636 * q^41 + 72 * q^44 - 98 * q^49 - 252 * q^51 - 162 * q^54 + 294 * q^56 + 264 * q^59 + 796 * q^61 - 866 * q^64 - 648 * q^66 - 1440 * q^71 + 2388 * q^74 - 248 * q^76 + 2048 * q^79 + 162 * q^81 + 42 * q^84 + 1608 * q^86 - 708 * q^89 - 476 * q^91 + 1440 * q^94 - 270 * q^96 + 648 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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