LMFDB - Embedded newform 825.4.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.a (trivial)

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:	yes
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56155 q^{2} -3.00000 q^{3} -1.43845 q^{4} -7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.56155 q^{2} -3.00000 q^{3} -1.43845 q^{4} -7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} -11.0000 q^{11} +4.31534 q^{12} +49.1231 q^{13} -16.0000 q^{14} -50.4233 q^{16} -82.7083 q^{17} +23.0540 q^{18} -130.354 q^{19} +18.7386 q^{21} -28.1771 q^{22} +185.693 q^{23} +72.5312 q^{24} +125.831 q^{26} -27.0000 q^{27} +8.98485 q^{28} -8.90720 q^{29} +5.26137 q^{31} +64.2547 q^{32} +33.0000 q^{33} -211.862 q^{34} -12.9460 q^{36} +416.894 q^{37} -333.909 q^{38} -147.369 q^{39} -298.479 q^{41} +48.0000 q^{42} +513.633 q^{43} +15.8229 q^{44} +475.663 q^{46} -557.295 q^{47} +151.270 q^{48} -303.985 q^{49} +248.125 q^{51} -70.6610 q^{52} +168.064 q^{53} -69.1619 q^{54} +151.015 q^{56} +391.062 q^{57} -22.8163 q^{58} +618.773 q^{59} +786.405 q^{61} +13.4773 q^{62} -56.2159 q^{63} +567.978 q^{64} +84.5312 q^{66} +339.015 q^{67} +118.972 q^{68} -557.080 q^{69} +1120.71 q^{71} -217.594 q^{72} +123.430 q^{73} +1067.90 q^{74} +187.508 q^{76} +68.7083 q^{77} -377.494 q^{78} -309.835 q^{79} +81.0000 q^{81} -764.570 q^{82} +1021.22 q^{83} -26.9545 q^{84} +1315.70 q^{86} +26.7216 q^{87} +265.948 q^{88} -141.879 q^{89} -306.833 q^{91} -267.110 q^{92} -15.7841 q^{93} -1427.54 q^{94} -192.764 q^{96} -798.345 q^{97} -778.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	$ 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 22 q^{11} + 21 q^{12} + 90 q^{13} - 32 q^{14} - 39 q^{16} + 16 q^{17} + 9 q^{18} - 170 q^{19} - 12 q^{21} - 11 q^{22} + 124 q^{23} + 9 q^{24} + 62 q^{26} - 54 q^{27} - 48 q^{28} - 158 q^{29} + 60 q^{31} - 123 q^{32} + 66 q^{33} - 366 q^{34} - 63 q^{36} + 372 q^{37} - 272 q^{38} - 270 q^{39} + 38 q^{41} + 96 q^{42} + 516 q^{43} + 77 q^{44} + 572 q^{46} - 224 q^{47} + 117 q^{48} - 542 q^{49} - 48 q^{51} - 298 q^{52} - 472 q^{53} - 27 q^{54} + 368 q^{56} + 510 q^{57} + 210 q^{58} + 248 q^{59} + 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} + 33 q^{66} + 744 q^{67} - 430 q^{68} - 372 q^{69} + 2060 q^{71} - 27 q^{72} + 486 q^{73} + 1138 q^{74} + 408 q^{76} - 44 q^{77} - 186 q^{78} + 642 q^{79} + 162 q^{81} - 1290 q^{82} + 286 q^{83} + 144 q^{84} + 1312 q^{86} + 474 q^{87} + 33 q^{88} + 244 q^{89} + 112 q^{91} + 76 q^{92} - 180 q^{93} - 1948 q^{94} + 369 q^{96} + 168 q^{97} - 407 q^{98} - 198 q^{99}+O(q^{100}) $ 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 22 * q^11 + 21 * q^12 + 90 * q^13 - 32 * q^14 - 39 * q^16 + 16 * q^17 + 9 * q^18 - 170 * q^19 - 12 * q^21 - 11 * q^22 + 124 * q^23 + 9 * q^24 + 62 * q^26 - 54 * q^27 - 48 * q^28 - 158 * q^29 + 60 * q^31 - 123 * q^32 + 66 * q^33 - 366 * q^34 - 63 * q^36 + 372 * q^37 - 272 * q^38 - 270 * q^39 + 38 * q^41 + 96 * q^42 + 516 * q^43 + 77 * q^44 + 572 * q^46 - 224 * q^47 + 117 * q^48 - 542 * q^49 - 48 * q^51 - 298 * q^52 - 472 * q^53 - 27 * q^54 + 368 * q^56 + 510 * q^57 + 210 * q^58 + 248 * q^59 + 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 + 33 * q^66 + 744 * q^67 - 430 * q^68 - 372 * q^69 + 2060 * q^71 - 27 * q^72 + 486 * q^73 + 1138 * q^74 + 408 * q^76 - 44 * q^77 - 186 * q^78 + 642 * q^79 + 162 * q^81 - 1290 * q^82 + 286 * q^83 + 144 * q^84 + 1312 * q^86 + 474 * q^87 + 33 * q^88 + 244 * q^89 + 112 * q^91 + 76 * q^92 - 180 * q^93 - 1948 * q^94 + 369 * q^96 + 168 * q^97 - 407 * q^98 - 198 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.56155	0.905646	0.452823	−	0.891601i	$-0.350417\pi$
$2$	2.56155	0.905646	0.452823	+	0.891601i	$0.350417\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−1.43845	−0.179806
$5$	0	0
$5$	0	0
$6$	−7.68466	−0.522875
$7$	−6.24621	−0.337264	−0.168632	−	0.985679i	$-0.553935\pi$
$7$	−6.24621	−0.337264	−0.168632	+	0.985679i	$0.553935\pi$
$8$	−24.1771	−1.06849
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	4.31534	0.103811
$13$	49.1231	1.04802	0.524011	−	0.851711i	$-0.324435\pi$
$13$	49.1231	1.04802	0.524011	+	0.851711i	$0.324435\pi$
$14$	−16.0000	−0.305441
$15$	0	0
$16$	−50.4233	−0.787864
$17$	−82.7083	−1.17998	−0.589992	−	0.807409i	$-0.700869\pi$
$17$	−82.7083	−1.17998	−0.589992	+	0.807409i	$0.700869\pi$
$18$	23.0540	0.301882
$19$	−130.354	−1.57396	−0.786981	−	0.616977i	$-0.788357\pi$
$19$	−130.354	−1.57396	−0.786981	+	0.616977i	$0.788357\pi$
$20$	0	0
$21$	18.7386	0.194719
$22$	−28.1771	−0.273062
$23$	185.693	1.68347	0.841733	−	0.539895i	$-0.181536\pi$
$23$	185.693	1.68347	0.841733	+	0.539895i	$0.181536\pi$
$24$	72.5312	0.616891
$25$	0	0
$26$	125.831	0.949137
$27$	−27.0000	−0.192450
$28$	8.98485	0.0606420
$29$	−8.90720	−0.0570354	−0.0285177	−	0.999593i	$-0.509079\pi$
$29$	−8.90720	−0.0570354	−0.0285177	+	0.999593i	$0.509079\pi$
$30$	0	0
$31$	5.26137	0.0304829	0.0152414	−	0.999884i	$-0.495148\pi$
$31$	5.26137	0.0304829	0.0152414	+	0.999884i	$0.495148\pi$
$32$	64.2547	0.354961
$33$	33.0000	0.174078
$34$	−211.862	−1.06865
$35$	0	0
$36$	−12.9460	−0.0599353
$37$	416.894	1.85235	0.926175	−	0.377094i	$-0.123077\pi$
$37$	416.894	1.85235	0.926175	+	0.377094i	$0.123077\pi$
$38$	−333.909	−1.42545
$39$	−147.369	−0.605076
$40$	0	0
$41$	−298.479	−1.13694	−0.568471	−	0.822703i	$-0.692465\pi$
$41$	−298.479	−1.13694	−0.568471	+	0.822703i	$0.692465\pi$
$42$	48.0000	0.176347
$43$	513.633	1.82159	0.910793	−	0.412863i	$-0.135471\pi$
$43$	513.633	1.82159	0.910793	+	0.412863i	$0.135471\pi$
$44$	15.8229	0.0542135
$45$	0	0
$46$	475.663	1.52462
$47$	−557.295	−1.72957	−0.864786	−	0.502140i	$-0.832546\pi$
$47$	−557.295	−1.72957	−0.864786	+	0.502140i	$0.832546\pi$
$48$	151.270	0.454873
$49$	−303.985	−0.886253
$50$	0	0
$51$	248.125	0.681264
$52$	−70.6610	−0.188441
$53$	168.064	0.435574	0.217787	−	0.975996i	$-0.430116\pi$
$53$	168.064	0.435574	0.217787	+	0.975996i	$0.430116\pi$
$54$	−69.1619	−0.174292
$55$	0	0
$56$	151.015	0.360362
$57$	391.062	0.908728
$58$	−22.8163	−0.0516539
$59$	618.773	1.36538	0.682689	−	0.730709i	$-0.260810\pi$
$59$	618.773	1.36538	0.682689	+	0.730709i	$0.260810\pi$
$60$	0	0
$61$	786.405	1.65064	0.825319	−	0.564667i	$-0.190996\pi$
$61$	786.405	1.65064	0.825319	+	0.564667i	$0.190996\pi$
$62$	13.4773	0.0276067
$63$	−56.2159	−0.112421
$64$	567.978	1.10933
$65$	0	0
$66$	84.5312	0.157653
$67$	339.015	0.618169	0.309084	−	0.951035i	$-0.399977\pi$
$67$	339.015	0.618169	0.309084	+	0.951035i	$0.399977\pi$
$68$	118.972	0.212168
$69$	−557.080	−0.971949
$70$	0	0
$71$	1120.71	1.87329	0.936645	−	0.350280i	$-0.113913\pi$
$71$	1120.71	1.87329	0.936645	+	0.350280i	$0.113913\pi$
$72$	−217.594	−0.356162
$73$	123.430	0.197896	0.0989478	−	0.995093i	$-0.468452\pi$
$73$	123.430	0.197896	0.0989478	+	0.995093i	$0.468452\pi$
$74$	1067.90	1.67757
$75$	0	0
$76$	187.508	0.283008
$77$	68.7083	0.101689
$78$	−377.494	−0.547985
$79$	−309.835	−0.441255	−0.220628	−	0.975358i	$-0.570811\pi$
$79$	−309.835	−0.441255	−0.220628	+	0.975358i	$0.570811\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−764.570	−1.02967
$83$	1021.22	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$83$	1021.22	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$84$	−26.9545	−0.0350117
$85$	0	0
$86$	1315.70	1.64971
$87$	26.7216	0.0329294
$88$	265.948	0.322161
$89$	−141.879	−0.168979	−0.0844894	−	0.996424i	$-0.526926\pi$
$89$	−141.879	−0.168979	−0.0844894	+	0.996424i	$0.526926\pi$
$90$	0	0
$91$	−306.833	−0.353460
$92$	−267.110	−0.302697
$93$	−15.7841	−0.0175993
$94$	−1427.54	−1.56638
$95$	0	0
$96$	−192.764	−0.204937
$97$	−798.345	−0.835666	−0.417833	−	0.908524i	$-0.637210\pi$
$97$	−798.345	−0.835666	−0.417833	+	0.908524i	$0.637210\pi$
$98$	−778.673	−0.802631
$99$	−99.0000	−0.100504
$100$	0	0
$101$	241.400	0.237823	0.118912	−	0.992905i	$-0.462059\pi$
$101$	241.400	0.237823	0.118912	+	0.992905i	$0.462059\pi$
$102$	635.585	0.616983
$103$	−1168.38	−1.11771	−0.558853	−	0.829267i	$-0.688758\pi$
$103$	−1168.38	−1.11771	−0.558853	+	0.829267i	$0.688758\pi$
$104$	−1187.65	−1.11980
$105$	0	0
$106$	430.506	0.394476
$107$	2106.82	1.90350	0.951748	−	0.306882i	$-0.0992857\pi$
$107$	2106.82	1.90350	0.951748	+	0.306882i	$0.0992857\pi$
$108$	38.8381	0.0346037
$109$	493.792	0.433914	0.216957	−	0.976181i	$-0.430387\pi$
$109$	493.792	0.433914	0.216957	+	0.976181i	$0.430387\pi$
$110$	0	0
$111$	−1250.68	−1.06945
$112$	314.955	0.265718
$113$	−170.000	−0.141524	−0.0707622	−	0.997493i	$-0.522543\pi$
$113$	−170.000	−0.141524	−0.0707622	+	0.997493i	$0.522543\pi$
$114$	1001.73	0.822986
$115$	0	0
$116$	12.8125	0.0102553
$117$	442.108	0.349341
$118$	1585.02	1.23655
$119$	516.614	0.397966
$120$	0	0
$121$	121.000	0.0909091
$122$	2014.42	1.49489
$123$	895.437	0.656414
$124$	−7.56820	−0.00548100
$125$	0	0
$126$	−144.000	−0.101814
$127$	948.182	0.662500	0.331250	−	0.943543i	$-0.392530\pi$
$127$	948.182	0.662500	0.331250	+	0.943543i	$0.392530\pi$
$128$	940.868	0.649702
$129$	−1540.90	−1.05169
$130$	0	0
$131$	−1484.84	−0.990312	−0.495156	−	0.868804i	$-0.664889\pi$
$131$	−1484.84	−0.990312	−0.495156	+	0.868804i	$0.664889\pi$
$132$	−47.4688	−0.0313002
$133$	814.220	0.530841
$134$	868.405	0.559842
$135$	0	0
$136$	1999.65	1.26080
$137$	−684.928	−0.427134	−0.213567	−	0.976928i	$-0.568508\pi$
$137$	−684.928	−0.427134	−0.213567	+	0.976928i	$0.568508\pi$
$138$	−1426.99	−0.880242
$139$	830.483	0.506767	0.253384	−	0.967366i	$-0.418457\pi$
$139$	830.483	0.506767	0.253384	+	0.967366i	$0.418457\pi$
$140$	0	0
$141$	1671.89	0.998569
$142$	2870.75	1.69654
$143$	−540.354	−0.315991
$144$	−453.810	−0.262621
$145$	0	0
$146$	316.172	0.179223
$147$	911.955	0.511679
$148$	−599.680	−0.333063
$149$	−1213.64	−0.667285	−0.333642	−	0.942700i	$-0.608278\pi$
$149$	−1213.64	−0.667285	−0.333642	+	0.942700i	$0.608278\pi$
$150$	0	0
$151$	30.8466	0.0166242	0.00831212	−	0.999965i	$-0.497354\pi$
$151$	30.8466	0.0166242	0.00831212	+	0.999965i	$0.497354\pi$
$152$	3151.58	1.68176
$153$	−744.375	−0.393328
$154$	176.000	0.0920941
$155$	0	0
$156$	211.983	0.108796
$157$	−345.239	−0.175497	−0.0877485	−	0.996143i	$-0.527967\pi$
$157$	−345.239	−0.175497	−0.0877485	+	0.996143i	$0.527967\pi$
$158$	−793.659	−0.399621
$159$	−504.193	−0.251479
$160$	0	0
$161$	−1159.88	−0.567772
$162$	207.486	0.100627
$163$	−1921.49	−0.923331	−0.461665	−	0.887054i	$-0.652748\pi$
$163$	−1921.49	−0.923331	−0.461665	+	0.887054i	$0.652748\pi$
$164$	429.346	0.204429
$165$	0	0
$166$	2615.91	1.22310
$167$	−172.297	−0.0798369	−0.0399185	−	0.999203i	$-0.512710\pi$
$167$	−172.297	−0.0798369	−0.0399185	+	0.999203i	$0.512710\pi$
$168$	−453.045	−0.208055
$169$	216.080	0.0983521
$170$	0	0
$171$	−1173.19	−0.524654
$172$	−738.833	−0.327532
$173$	1025.29	0.450587	0.225293	−	0.974291i	$-0.427666\pi$
$173$	1025.29	0.450587	0.225293	+	0.974291i	$0.427666\pi$
$174$	68.4488	0.0298224
$175$	0	0
$176$	554.656	0.237550
$177$	−1856.32	−0.788302
$178$	−363.430	−0.153035
$179$	1658.29	0.692437	0.346219	−	0.938154i	$-0.387466\pi$
$179$	1658.29	0.692437	0.346219	+	0.938154i	$0.387466\pi$
$180$	0	0
$181$	−2021.81	−0.830275	−0.415137	−	0.909759i	$-0.636266\pi$
$181$	−2021.81	−0.830275	−0.415137	+	0.909759i	$0.636266\pi$
$182$	−785.970	−0.320110
$183$	−2359.22	−0.952996
$184$	−4489.52	−1.79876
$185$	0	0
$186$	−40.4318	−0.0159387
$187$	909.792	0.355778
$188$	801.640	0.310987
$189$	168.648	0.0649064
$190$	0	0
$191$	1440.22	0.545607	0.272803	−	0.962070i	$-0.412049\pi$
$191$	1440.22	0.545607	0.272803	+	0.962070i	$0.412049\pi$
$192$	−1703.93	−0.640473
$193$	2798.05	1.04356	0.521782	−	0.853079i	$-0.325267\pi$
$193$	2798.05	1.04356	0.521782	+	0.853079i	$0.325267\pi$
$194$	−2045.00	−0.756817
$195$	0	0
$196$	437.266	0.159354
$197$	−458.943	−0.165982	−0.0829908	−	0.996550i	$-0.526447\pi$
$197$	−458.943	−0.165982	−0.0829908	+	0.996550i	$0.526447\pi$
$198$	−253.594	−0.0910208
$199$	−2371.04	−0.844615	−0.422308	−	0.906453i	$-0.638780\pi$
$199$	−2371.04	−0.844615	−0.422308	+	0.906453i	$0.638780\pi$
$200$	0	0
$201$	−1017.05	−0.356900
$202$	618.358	0.215384
$203$	55.6363	0.0192360
$204$	−356.915	−0.122495
$205$	0	0
$206$	−2992.86	−1.01225
$207$	1671.24	0.561155
$208$	−2476.95	−0.825699
$209$	1433.90	0.474568
$210$	0	0
$211$	4319.87	1.40944	0.704721	−	0.709484i	$-0.251072\pi$
$211$	4319.87	1.40944	0.704721	+	0.709484i	$0.251072\pi$
$212$	−241.752	−0.0783187
$213$	−3362.12	−1.08154
$214$	5396.73	1.72389
$215$	0	0
$216$	652.781	0.205630
$217$	−32.8636	−0.0102808
$218$	1264.87	0.392973
$219$	−370.290	−0.114255
$220$	0	0
$221$	−4062.89	−1.23665
$222$	−3203.69	−0.968547
$223$	3837.73	1.15244	0.576219	−	0.817295i	$-0.304527\pi$
$223$	3837.73	1.15244	0.576219	+	0.817295i	$0.304527\pi$
$224$	−401.349	−0.119715
$225$	0	0
$226$	−435.464	−0.128171
$227$	5003.71	1.46303	0.731515	−	0.681825i	$-0.238813\pi$
$227$	5003.71	1.46303	0.731515	+	0.681825i	$0.238813\pi$
$228$	−562.523	−0.163395
$229$	−277.375	−0.0800412	−0.0400206	−	0.999199i	$-0.512742\pi$
$229$	−277.375	−0.0800412	−0.0400206	+	0.999199i	$0.512742\pi$
$230$	0	0
$231$	−206.125	−0.0587101
$232$	215.350	0.0609415
$233$	−2269.91	−0.638225	−0.319113	−	0.947717i	$-0.603385\pi$
$233$	−2269.91	−0.638225	−0.319113	+	0.947717i	$0.603385\pi$
$234$	1132.48	0.316379
$235$	0	0
$236$	−890.072	−0.245503
$237$	929.505	0.254759
$238$	1323.33	0.360416
$239$	−1617.11	−0.437665	−0.218832	−	0.975762i	$-0.570225\pi$
$239$	−1617.11	−0.437665	−0.218832	+	0.975762i	$0.570225\pi$
$240$	0	0
$241$	5646.63	1.50926	0.754629	−	0.656151i	$-0.227817\pi$
$241$	5646.63	1.50926	0.754629	+	0.656151i	$0.227817\pi$
$242$	309.948	0.0823314
$243$	−243.000	−0.0641500
$244$	−1131.20	−0.296794
$245$	0	0
$246$	2293.71	0.594478
$247$	−6403.40	−1.64955
$248$	−127.204	−0.0325705
$249$	−3063.66	−0.779726
$250$	0	0
$251$	−6217.61	−1.56355	−0.781777	−	0.623558i	$-0.785687\pi$
$251$	−6217.61	−1.56355	−0.781777	+	0.623558i	$0.785687\pi$
$252$	80.8636	0.0202140
$253$	−2042.62	−0.507584
$254$	2428.82	0.599991
$255$	0	0
$256$	−2133.74	−0.520933
$257$	−7712.75	−1.87202	−0.936008	−	0.351980i	$-0.885509\pi$
$257$	−7712.75	−1.87202	−0.936008	+	0.351980i	$0.885509\pi$
$258$	−3947.09	−0.952462
$259$	−2604.01	−0.624730
$260$	0	0
$261$	−80.1648	−0.0190118
$262$	−3803.49	−0.896871
$263$	−206.347	−0.0483798	−0.0241899	−	0.999707i	$-0.507701\pi$
$263$	−206.347	−0.0483798	−0.0241899	+	0.999707i	$0.507701\pi$
$264$	−797.844	−0.186000
$265$	0	0
$266$	2085.67	0.480753
$267$	425.636	0.0975600
$268$	−487.655	−0.111150
$269$	1712.47	0.388146	0.194073	−	0.980987i	$-0.437830\pi$
$269$	1712.47	0.388146	0.194073	+	0.980987i	$0.437830\pi$
$270$	0	0
$271$	−477.081	−0.106940	−0.0534698	−	0.998569i	$-0.517028\pi$
$271$	−477.081	−0.106940	−0.0534698	+	0.998569i	$0.517028\pi$
$272$	4170.43	0.929666
$273$	920.500	0.204070
$274$	−1754.48	−0.386832
$275$	0	0
$276$	801.329	0.174762
$277$	−4283.48	−0.929130	−0.464565	−	0.885539i	$-0.653789\pi$
$277$	−4283.48	−0.929130	−0.464565	+	0.885539i	$0.653789\pi$
$278$	2127.33	0.458952
$279$	47.3523	0.0101610
$280$	0	0
$281$	3477.79	0.738319	0.369160	−	0.929366i	$-0.379646\pi$
$281$	3477.79	0.738319	0.369160	+	0.929366i	$0.379646\pi$
$282$	4282.62	0.904350
$283$	6568.27	1.37966	0.689829	−	0.723973i	$-0.257686\pi$
$283$	6568.27	1.37966	0.689829	+	0.723973i	$0.257686\pi$
$284$	−1612.08	−0.336829
$285$	0	0
$286$	−1384.15	−0.286176
$287$	1864.36	0.383449
$288$	578.292	0.118320
$289$	1927.67	0.392360
$290$	0	0
$291$	2395.03	0.482472
$292$	−177.547	−0.0355828
$293$	−8352.29	−1.66534	−0.832672	−	0.553766i	$-0.813190\pi$
$293$	−8352.29	−1.66534	−0.832672	+	0.553766i	$0.813190\pi$
$294$	2336.02	0.463399
$295$	0	0
$296$	−10079.3	−1.97921
$297$	297.000	0.0580259
$298$	−3108.81	−0.604324
$299$	9121.83	1.76431
$300$	0	0
$301$	−3208.26	−0.614355
$302$	79.0152	0.0150557
$303$	−724.199	−0.137307
$304$	6572.89	1.24007
$305$	0	0
$306$	−1906.76	−0.356216
$307$	−5383.89	−1.00090	−0.500448	−	0.865767i	$-0.666831\pi$
$307$	−5383.89	−1.00090	−0.500448	+	0.865767i	$0.666831\pi$
$308$	−98.8333	−0.0182843
$309$	3505.14	0.645308
$310$	0	0
$311$	−1790.41	−0.326447	−0.163223	−	0.986589i	$-0.552189\pi$
$311$	−1790.41	−0.326447	−0.163223	+	0.986589i	$0.552189\pi$
$312$	3562.96	0.646516
$313$	809.076	0.146108	0.0730538	−	0.997328i	$-0.476726\pi$
$313$	809.076	0.146108	0.0730538	+	0.997328i	$0.476726\pi$
$314$	−884.347	−0.158938
$315$	0	0
$316$	445.682	0.0793403
$317$	−10744.5	−1.90370	−0.951849	−	0.306567i	$-0.900820\pi$
$317$	−10744.5	−1.90370	−0.951849	+	0.306567i	$0.900820\pi$
$318$	−1291.52	−0.227751
$319$	97.9792	0.0171968
$320$	0	0
$321$	−6320.46	−1.09898
$322$	−2971.09	−0.514200
$323$	10781.4	1.85725
$324$	−116.514	−0.0199784
$325$	0	0
$326$	−4922.00	−0.836210
$327$	−1481.37	−0.250521
$328$	7216.35	1.21481
$329$	3480.98	0.583322
$330$	0	0
$331$	3399.12	0.564449	0.282224	−	0.959348i	$-0.408928\pi$
$331$	3399.12	0.564449	0.282224	+	0.959348i	$0.408928\pi$
$332$	−1468.97	−0.242832
$333$	3752.05	0.617450
$334$	−441.349	−0.0723039
$335$	0	0
$336$	−944.864	−0.153412
$337$	11840.0	1.91384	0.956919	−	0.290356i	$-0.0937736\pi$
$337$	11840.0	1.91384	0.956919	+	0.290356i	$0.0937736\pi$
$338$	553.499	0.0890721
$339$	510.000	0.0817091
$340$	0	0
$341$	−57.8750	−0.00919093
$342$	−3005.18	−0.475151
$343$	4041.20	0.636165
$344$	−12418.1	−1.94634
$345$	0	0
$346$	2626.34	0.408072
$347$	2076.67	0.321272	0.160636	−	0.987014i	$-0.448645\pi$
$347$	2076.67	0.321272	0.160636	+	0.987014i	$0.448645\pi$
$348$	−38.4376	−0.00592090
$349$	5837.37	0.895322	0.447661	−	0.894203i	$-0.352257\pi$
$349$	5837.37	0.895322	0.447661	+	0.894203i	$0.352257\pi$
$350$	0	0
$351$	−1326.32	−0.201692
$352$	−706.802	−0.107025
$353$	2423.64	0.365431	0.182715	−	0.983166i	$-0.441511\pi$
$353$	2423.64	0.365431	0.182715	+	0.983166i	$0.441511\pi$
$354$	−4755.06	−0.713922
$355$	0	0
$356$	204.085	0.0303834
$357$	−1549.84	−0.229765
$358$	4247.79	0.627103
$359$	−3882.22	−0.570740	−0.285370	−	0.958417i	$-0.592116\pi$
$359$	−3882.22	−0.570740	−0.285370	+	0.958417i	$0.592116\pi$
$360$	0	0
$361$	10133.2	1.47736
$362$	−5178.96	−0.751935
$363$	−363.000	−0.0524864
$364$	441.363	0.0635542
$365$	0	0
$366$	−6043.26	−0.863077
$367$	−5666.65	−0.805986	−0.402993	−	0.915203i	$-0.632030\pi$
$367$	−5666.65	−0.805986	−0.402993	+	0.915203i	$0.632030\pi$
$368$	−9363.26	−1.32634
$369$	−2686.31	−0.378981
$370$	0	0
$371$	−1049.77	−0.146903
$372$	22.7046	0.00316446
$373$	−174.771	−0.0242608	−0.0121304	−	0.999926i	$-0.503861\pi$
$373$	−174.771	−0.0242608	−0.0121304	+	0.999926i	$0.503861\pi$
$374$	2330.48	0.322209
$375$	0	0
$376$	13473.8	1.84802
$377$	−437.550	−0.0597744
$378$	432.000	0.0587822
$379$	252.686	0.0342470	0.0171235	−	0.999853i	$-0.494549\pi$
$379$	252.686	0.0342470	0.0171235	+	0.999853i	$0.494549\pi$
$380$	0	0
$381$	−2844.55	−0.382495
$382$	3689.21	0.494126
$383$	11014.5	1.46950	0.734748	−	0.678340i	$-0.237300\pi$
$383$	11014.5	1.46950	0.734748	+	0.678340i	$0.237300\pi$
$384$	−2822.61	−0.375105
$385$	0	0
$386$	7167.35	0.945099
$387$	4622.69	0.607196
$388$	1148.38	0.150258
$389$	8099.40	1.05567	0.527835	−	0.849347i	$-0.323004\pi$
$389$	8099.40	1.05567	0.527835	+	0.849347i	$0.323004\pi$
$390$	0	0
$391$	−15358.4	−1.98646
$392$	7349.47	0.946949
$393$	4454.51	0.571757
$394$	−1175.61	−0.150320
$395$	0	0
$396$	142.406	0.0180712
$397$	424.353	0.0536465	0.0268232	−	0.999640i	$-0.491461\pi$
$397$	424.353	0.0536465	0.0268232	+	0.999640i	$0.491461\pi$
$398$	−6073.54	−0.764922
$399$	−2442.66	−0.306481
$400$	0	0
$401$	−5904.18	−0.735263	−0.367632	−	0.929972i	$-0.619831\pi$
$401$	−5904.18	−0.735263	−0.367632	+	0.929972i	$0.619831\pi$
$402$	−2605.22	−0.323225
$403$	258.455	0.0319468
$404$	−347.241	−0.0427620
$405$	0	0
$406$	142.515	0.0174210
$407$	−4585.83	−0.558504
$408$	−5998.94	−0.727921
$409$	1370.47	0.165686	0.0828430	−	0.996563i	$-0.473600\pi$
$409$	1370.47	0.165686	0.0828430	+	0.996563i	$0.473600\pi$
$410$	0	0
$411$	2054.78	0.246606
$412$	1680.65	0.200970
$413$	−3864.98	−0.460493
$414$	4280.97	0.508208
$415$	0	0
$416$	3156.39	0.372007
$417$	−2491.45	−0.292582
$418$	3673.00	0.429790
$419$	1268.73	0.147927	0.0739635	−	0.997261i	$-0.476435\pi$
$419$	1268.73	0.147927	0.0739635	+	0.997261i	$0.476435\pi$
$420$	0	0
$421$	−12241.9	−1.41719	−0.708594	−	0.705617i	$-0.750670\pi$
$421$	−12241.9	−1.41719	−0.708594	+	0.705617i	$0.750670\pi$
$422$	11065.6	1.27646
$423$	−5015.66	−0.576524
$424$	−4063.31	−0.465405
$425$	0	0
$426$	−8612.26	−0.979496
$427$	−4912.05	−0.556700
$428$	−3030.55	−0.342260
$429$	1621.06	0.182437
$430$	0	0
$431$	8050.11	0.899675	0.449838	−	0.893110i	$-0.351482\pi$
$431$	8050.11	0.899675	0.449838	+	0.893110i	$0.351482\pi$
$432$	1361.43	0.151624
$433$	16565.7	1.83856	0.919282	−	0.393600i	$-0.128770\pi$
$433$	16565.7	1.83856	0.919282	+	0.393600i	$0.128770\pi$
$434$	−84.1819	−0.00931073
$435$	0	0
$436$	−710.293	−0.0780203
$437$	−24205.9	−2.64971
$438$	−948.517	−0.103475
$439$	4705.80	0.511607	0.255804	−	0.966729i	$-0.417660\pi$
$439$	4705.80	0.511607	0.255804	+	0.966729i	$0.417660\pi$
$440$	0	0
$441$	−2735.86	−0.295418
$442$	−10407.3	−1.11997
$443$	−15094.0	−1.61882	−0.809408	−	0.587246i	$-0.800212\pi$
$443$	−15094.0	−1.61882	−0.809408	+	0.587246i	$0.800212\pi$
$444$	1799.04	0.192294
$445$	0	0
$446$	9830.56	1.04370
$447$	3640.93	0.385257
$448$	−3547.71	−0.374138
$449$	973.478	0.102319	0.0511595	−	0.998690i	$-0.483708\pi$
$449$	973.478	0.102319	0.0511595	+	0.998690i	$0.483708\pi$
$450$	0	0
$451$	3283.27	0.342801
$452$	244.536	0.0254469
$453$	−92.5398	−0.00959801
$454$	12817.3	1.32499
$455$	0	0
$456$	−9454.75	−0.970963
$457$	−62.6577	−0.00641358	−0.00320679	−	0.999995i	$-0.501021\pi$
$457$	−62.6577	−0.00641358	−0.00320679	+	0.999995i	$0.501021\pi$
$458$	−710.510	−0.0724890
$459$	2233.12	0.227088
$460$	0	0
$461$	−11866.2	−1.19884	−0.599419	−	0.800436i	$-0.704602\pi$
$461$	−11866.2	−1.19884	−0.599419	+	0.800436i	$0.704602\pi$
$462$	−528.000	−0.0531705
$463$	13144.8	1.31942	0.659711	−	0.751519i	$-0.270679\pi$
$463$	13144.8	1.31942	0.659711	+	0.751519i	$0.270679\pi$
$464$	449.131	0.0449361
$465$	0	0
$466$	−5814.48	−0.578006
$467$	10176.8	1.00840	0.504201	−	0.863586i	$-0.331787\pi$
$467$	10176.8	1.00840	0.504201	+	0.863586i	$0.331787\pi$
$468$	−635.949	−0.0628136
$469$	−2117.56	−0.208486
$470$	0	0
$471$	1035.72	0.101323
$472$	−14960.1	−1.45889
$473$	−5649.96	−0.549229
$474$	2380.98	0.230721
$475$	0	0
$476$	−743.121	−0.0715565
$477$	1512.58	0.145191
$478$	−4142.30	−0.396369
$479$	3431.25	0.327302	0.163651	−	0.986518i	$-0.447673\pi$
$479$	3431.25	0.327302	0.163651	+	0.986518i	$0.447673\pi$
$480$	0	0
$481$	20479.1	1.94130
$482$	14464.1	1.36685
$483$	3479.64	0.327803
$484$	−174.052	−0.0163460
$485$	0	0
$486$	−622.457	−0.0580972
$487$	2833.20	0.263624	0.131812	−	0.991275i	$-0.457921\pi$
$487$	2833.20	0.263624	0.131812	+	0.991275i	$0.457921\pi$
$488$	−19013.0	−1.76368
$489$	5764.48	0.533085
$490$	0	0
$491$	−2667.29	−0.245159	−0.122580	−	0.992459i	$-0.539117\pi$
$491$	−2667.29	−0.245159	−0.122580	+	0.992459i	$0.539117\pi$
$492$	−1288.04	−0.118027
$493$	736.700	0.0673008
$494$	−16402.7	−1.49391
$495$	0	0
$496$	−265.295	−0.0240164
$497$	−7000.18	−0.631793
$498$	−7847.74	−0.706156
$499$	−11137.0	−0.999120	−0.499560	−	0.866279i	$-0.666505\pi$
$499$	−11137.0	−0.999120	−0.499560	+	0.866279i	$0.666505\pi$
$500$	0	0
$501$	516.892	0.0460939
$502$	−15926.7	−1.41603
$503$	−8780.30	−0.778319	−0.389159	−	0.921170i	$-0.627234\pi$
$503$	−8780.30	−0.778319	−0.389159	+	0.921170i	$0.627234\pi$
$504$	1359.14	0.120121
$505$	0	0
$506$	−5232.29	−0.459691
$507$	−648.239	−0.0567836
$508$	−1363.91	−0.119121
$509$	13597.4	1.18408	0.592039	−	0.805910i	$-0.298323\pi$
$509$	13597.4	1.18408	0.592039	+	0.805910i	$0.298323\pi$
$510$	0	0
$511$	−770.969	−0.0667430
$512$	−12992.6	−1.12148
$513$	3519.56	0.302909
$514$	−19756.6	−1.69538
$515$	0	0
$516$	2216.50	0.189101
$517$	6130.25	0.521486
$518$	−6670.30	−0.565784
$519$	−3075.88	−0.260146
$520$	0	0
$521$	14001.3	1.17736	0.588682	−	0.808364i	$-0.299647\pi$
$521$	14001.3	1.17736	0.588682	+	0.808364i	$0.299647\pi$
$522$	−205.346	−0.0172180
$523$	14749.8	1.23320	0.616602	−	0.787275i	$-0.288509\pi$
$523$	14749.8	1.23320	0.616602	+	0.787275i	$0.288509\pi$
$524$	2135.86	0.178064
$525$	0	0
$526$	−528.568	−0.0438149
$527$	−435.159	−0.0359693
$528$	−1663.97	−0.137150
$529$	22315.0	1.83406
$530$	0	0
$531$	5568.95	0.455126
$532$	−1171.21	−0.0954483
$533$	−14662.2	−1.19154
$534$	1090.29	0.0883548
$535$	0	0
$536$	−8196.40	−0.660505
$537$	−4974.86	−0.399779
$538$	4386.59	0.351523
$539$	3343.83	0.267215
$540$	0	0
$541$	1484.06	0.117939	0.0589694	−	0.998260i	$-0.481219\pi$
$541$	1484.06	0.117939	0.0589694	+	0.998260i	$0.481219\pi$
$542$	−1222.07	−0.0968493
$543$	6065.42	0.479359
$544$	−5314.40	−0.418847
$545$	0	0
$546$	2357.91	0.184815
$547$	16562.2	1.29460	0.647302	−	0.762234i	$-0.275897\pi$
$547$	16562.2	1.29460	0.647302	+	0.762234i	$0.275897\pi$
$548$	985.233	0.0768012
$549$	7077.65	0.550212
$550$	0	0
$551$	1161.09	0.0897716
$552$	13468.6	1.03851
$553$	1935.30	0.148819
$554$	−10972.3	−0.841463
$555$	0	0
$556$	−1194.61	−0.0911197
$557$	8821.52	0.671059	0.335529	−	0.942030i	$-0.391085\pi$
$557$	8821.52	0.671059	0.335529	+	0.942030i	$0.391085\pi$
$558$	121.295	0.00920223
$559$	25231.2	1.90906
$560$	0	0
$561$	−2729.37	−0.205409
$562$	8908.55	0.668656
$563$	5985.53	0.448064	0.224032	−	0.974582i	$-0.428078\pi$
$563$	5985.53	0.448064	0.224032	+	0.974582i	$0.428078\pi$
$564$	−2404.92	−0.179549
$565$	0	0
$566$	16825.0	1.24948
$567$	−505.943	−0.0374737
$568$	−27095.5	−2.00158
$569$	−3453.08	−0.254413	−0.127206	−	0.991876i	$-0.540601\pi$
$569$	−3453.08	−0.254413	−0.127206	+	0.991876i	$0.540601\pi$
$570$	0	0
$571$	−21484.5	−1.57460	−0.787302	−	0.616568i	$-0.788523\pi$
$571$	−21484.5	−1.57460	−0.787302	+	0.616568i	$0.788523\pi$
$572$	777.271	0.0568170
$573$	−4320.67	−0.315006
$574$	4775.67	0.347269
$575$	0	0
$576$	5111.80	0.369777
$577$	13294.4	0.959189	0.479594	−	0.877490i	$-0.340784\pi$
$577$	13294.4	0.959189	0.479594	+	0.877490i	$0.340784\pi$
$578$	4937.82	0.355340
$579$	−8394.14	−0.602502
$580$	0	0
$581$	−6378.77	−0.455483
$582$	6135.01	0.436949
$583$	−1848.71	−0.131330
$584$	−2984.18	−0.211449
$585$	0	0
$586$	−21394.8	−1.50821
$587$	−6695.73	−0.470805	−0.235402	−	0.971898i	$-0.575641\pi$
$587$	−6695.73	−0.470805	−0.235402	+	0.971898i	$0.575641\pi$
$588$	−1311.80	−0.0920028
$589$	−685.841	−0.0479789
$590$	0	0
$591$	1376.83	0.0958295
$592$	−21021.2	−1.45940
$593$	10239.6	0.709088	0.354544	−	0.935039i	$-0.384636\pi$
$593$	10239.6	0.709088	0.354544	+	0.935039i	$0.384636\pi$
$594$	760.781	0.0525509
$595$	0	0
$596$	1745.76	0.119982
$597$	7113.11	0.487639
$598$	23366.0	1.59784
$599$	−23890.8	−1.62963	−0.814817	−	0.579719i	$-0.803162\pi$
$599$	−23890.8	−1.62963	−0.814817	+	0.579719i	$0.803162\pi$
$600$	0	0
$601$	−11343.8	−0.769920	−0.384960	−	0.922933i	$-0.625785\pi$
$601$	−11343.8	−0.769920	−0.384960	+	0.922933i	$0.625785\pi$
$602$	−8218.12	−0.556388
$603$	3051.14	0.206056
$604$	−44.3712	−0.00298914
$605$	0	0
$606$	−1855.07	−0.124352
$607$	26032.5	1.74074	0.870369	−	0.492399i	$-0.163880\pi$
$607$	26032.5	1.74074	0.870369	+	0.492399i	$0.163880\pi$
$608$	−8375.87	−0.558695
$609$	−166.909	−0.0111059
$610$	0	0
$611$	−27376.1	−1.81263
$612$	1070.74	0.0707226
$613$	4568.13	0.300987	0.150493	−	0.988611i	$-0.451914\pi$
$613$	4568.13	0.300987	0.150493	+	0.988611i	$0.451914\pi$
$614$	−13791.1	−0.906457
$615$	0	0
$616$	−1661.17	−0.108653
$617$	12755.9	0.832308	0.416154	−	0.909294i	$-0.363378\pi$
$617$	12755.9	0.832308	0.416154	+	0.909294i	$0.363378\pi$
$618$	8978.59	0.584421
$619$	−1138.94	−0.0739545	−0.0369772	−	0.999316i	$-0.511773\pi$
$619$	−1138.94	−0.0739545	−0.0369772	+	0.999316i	$0.511773\pi$
$620$	0	0
$621$	−5013.72	−0.323983
$622$	−4586.24	−0.295645
$623$	886.205	0.0569904
$624$	7430.85	0.476718
$625$	0	0
$626$	2072.49	0.132322
$627$	−4301.69	−0.273992
$628$	496.607	0.0315554
$629$	−34480.6	−2.18574
$630$	0	0
$631$	7997.36	0.504548	0.252274	−	0.967656i	$-0.418822\pi$
$631$	7997.36	0.504548	0.252274	+	0.967656i	$0.418822\pi$
$632$	7490.91	0.471475
$633$	−12959.6	−0.813742
$634$	−27522.7	−1.72408
$635$	0	0
$636$	725.255	0.0452173
$637$	−14932.7	−0.928814
$638$	250.979	0.0155742
$639$	10086.4	0.624430
$640$	0	0
$641$	−573.115	−0.0353146	−0.0176573	−	0.999844i	$-0.505621\pi$
$641$	−573.115	−0.0353146	−0.0176573	+	0.999844i	$0.505621\pi$
$642$	−16190.2	−0.995290
$643$	16027.8	0.983009	0.491504	−	0.870875i	$-0.336447\pi$
$643$	16027.8	0.983009	0.491504	+	0.870875i	$0.336447\pi$
$644$	1668.42	0.102089
$645$	0	0
$646$	27617.1	1.68201
$647$	2622.74	0.159367	0.0796837	−	0.996820i	$-0.474609\pi$
$647$	2622.74	0.159367	0.0796837	+	0.996820i	$0.474609\pi$
$648$	−1958.34	−0.118721
$649$	−6806.50	−0.411677
$650$	0	0
$651$	98.5908	0.00593560
$652$	2763.97	0.166020
$653$	−3102.00	−0.185897	−0.0929484	−	0.995671i	$-0.529629\pi$
$653$	−3102.00	−0.185897	−0.0929484	+	0.995671i	$0.529629\pi$
$654$	−3794.62	−0.226883
$655$	0	0
$656$	15050.3	0.895755
$657$	1110.87	0.0659652
$658$	8916.73	0.528283
$659$	−20840.2	−1.23190	−0.615948	−	0.787787i	$-0.711227\pi$
$659$	−20840.2	−1.23190	−0.615948	+	0.787787i	$0.711227\pi$
$660$	0	0
$661$	18242.9	1.07348	0.536738	−	0.843749i	$-0.319657\pi$
$661$	18242.9	1.07348	0.536738	+	0.843749i	$0.319657\pi$
$662$	8707.03	0.511191
$663$	12188.7	0.713980
$664$	−24690.2	−1.44302
$665$	0	0
$666$	9611.06	0.559191
$667$	−1654.01	−0.0960171
$668$	247.841	0.0143551
$669$	−11513.2	−0.665361
$670$	0	0
$671$	−8650.46	−0.497686
$672$	1204.05	0.0691177
$673$	12746.6	0.730084	0.365042	−	0.930991i	$-0.381055\pi$
$673$	12746.6	0.730084	0.365042	+	0.930991i	$0.381055\pi$
$674$	30328.7	1.73326
$675$	0	0
$676$	−310.819	−0.0176843
$677$	7683.11	0.436168	0.218084	−	0.975930i	$-0.430019\pi$
$677$	7683.11	0.436168	0.218084	+	0.975930i	$0.430019\pi$
$678$	1306.39	0.0739995
$679$	4986.63	0.281840
$680$	0	0
$681$	−15011.1	−0.844681
$682$	−148.250	−0.00832373
$683$	21397.1	1.19874	0.599368	−	0.800473i	$-0.295418\pi$
$683$	21397.1	1.19874	0.599368	+	0.800473i	$0.295418\pi$
$684$	1687.57	0.0943359
$685$	0	0
$686$	10351.8	0.576140
$687$	832.124	0.0462118
$688$	−25899.0	−1.43516
$689$	8255.84	0.456491
$690$	0	0
$691$	26137.5	1.43895	0.719477	−	0.694516i	$-0.244381\pi$
$691$	26137.5	1.43895	0.719477	+	0.694516i	$0.244381\pi$
$692$	−1474.83	−0.0810181
$693$	618.375	0.0338963
$694$	5319.50	0.290959
$695$	0	0
$696$	−646.051	−0.0351846
$697$	24686.7	1.34157
$698$	14952.7	0.810845
$699$	6809.72	0.368479
$700$	0	0
$701$	13382.4	0.721036	0.360518	−	0.932752i	$-0.382600\pi$
$701$	13382.4	0.721036	0.360518	+	0.932752i	$0.382600\pi$
$702$	−3397.45	−0.182662
$703$	−54343.9	−2.91553
$704$	−6247.76	−0.334476
$705$	0	0
$706$	6208.27	0.330951
$707$	−1507.83	−0.0802092
$708$	2670.22	0.141741
$709$	18164.6	0.962179	0.481090	−	0.876671i	$-0.340241\pi$
$709$	18164.6	0.962179	0.481090	+	0.876671i	$0.340241\pi$
$710$	0	0
$711$	−2788.52	−0.147085
$712$	3430.21	0.180552
$713$	977.000	0.0513169
$714$	−3970.00	−0.208086
$715$	0	0
$716$	−2385.36	−0.124504
$717$	4851.32	0.252686
$718$	−9944.50	−0.516888
$719$	9665.62	0.501344	0.250672	−	0.968072i	$-0.419348\pi$
$719$	9665.62	0.501344	0.250672	+	0.968072i	$0.419348\pi$
$720$	0	0
$721$	7297.94	0.376962
$722$	25956.7	1.33796
$723$	−16939.9	−0.871371
$724$	2908.26	0.149288
$725$	0	0
$726$	−929.844	−0.0475341
$727$	29779.6	1.51921	0.759605	−	0.650385i	$-0.225392\pi$
$727$	29779.6	1.51921	0.759605	+	0.650385i	$0.225392\pi$
$728$	7418.33	0.377667
$729$	729.000	0.0370370
$730$	0	0
$731$	−42481.7	−2.14944
$732$	3393.61	0.171354
$733$	−35029.5	−1.76513	−0.882567	−	0.470187i	$-0.844186\pi$
$733$	−35029.5	−1.76513	−0.882567	+	0.470187i	$0.844186\pi$
$734$	−14515.4	−0.729937
$735$	0	0
$736$	11931.7	0.597564
$737$	−3729.17	−0.186385
$738$	−6881.13	−0.343222
$739$	23297.3	1.15968	0.579842	−	0.814729i	$-0.303114\pi$
$739$	23297.3	1.15968	0.579842	+	0.814729i	$0.303114\pi$
$740$	0	0
$741$	19210.2	0.952368
$742$	−2689.03	−0.133042
$743$	−21570.4	−1.06506	−0.532530	−	0.846411i	$-0.678759\pi$
$743$	−21570.4	−1.06506	−0.532530	+	0.846411i	$0.678759\pi$
$744$	381.613	0.0188046
$745$	0	0
$746$	−447.684	−0.0219717
$747$	9190.99	0.450175
$748$	−1308.69	−0.0639710
$749$	−13159.6	−0.641980
$750$	0	0
$751$	28554.8	1.38746	0.693729	−	0.720236i	$-0.255966\pi$
$751$	28554.8	1.38746	0.693729	+	0.720236i	$0.255966\pi$
$752$	28100.7	1.36267
$753$	18652.8	0.902719
$754$	−1120.81	−0.0541344
$755$	0	0
$756$	−242.591	−0.0116706
$757$	−7812.81	−0.375114	−0.187557	−	0.982254i	$-0.560057\pi$
$757$	−7812.81	−0.375114	−0.187557	+	0.982254i	$0.560057\pi$
$758$	647.268	0.0310156
$759$	6127.87	0.293054
$760$	0	0
$761$	2875.13	0.136956	0.0684778	−	0.997653i	$-0.478186\pi$
$761$	2875.13	0.136956	0.0684778	+	0.997653i	$0.478186\pi$
$762$	−7286.45	−0.346405
$763$	−3084.33	−0.146344
$764$	−2071.69	−0.0981033
$765$	0	0
$766$	28214.3	1.33084
$767$	30396.0	1.43095
$768$	6401.22	0.300761
$769$	−27657.7	−1.29696	−0.648479	−	0.761233i	$-0.724594\pi$
$769$	−27657.7	−1.29696	−0.648479	+	0.761233i	$0.724594\pi$
$770$	0	0
$771$	23138.2	1.08081
$772$	−4024.84	−0.187639
$773$	3929.35	0.182832	0.0914160	−	0.995813i	$-0.470861\pi$
$773$	3929.35	0.182832	0.0914160	+	0.995813i	$0.470861\pi$
$774$	11841.3	0.549904
$775$	0	0
$776$	19301.6	0.892898
$777$	7812.02	0.360688
$778$	20747.0	0.956064
$779$	38908.0	1.78950
$780$	0	0
$781$	−12327.8	−0.564818
$782$	−39341.3	−1.79903
$783$	240.495	0.0109765
$784$	15327.9	0.698247
$785$	0	0
$786$	11410.5	0.517809
$787$	21125.7	0.956860	0.478430	−	0.878126i	$-0.341206\pi$
$787$	21125.7	0.956860	0.478430	+	0.878126i	$0.341206\pi$
$788$	660.166	0.0298445
$789$	619.040	0.0279321
$790$	0	0
$791$	1061.86	0.0477310
$792$	2393.53	0.107387
$793$	38630.7	1.72991
$794$	1087.00	0.0485847
$795$	0	0
$796$	3410.61	0.151867
$797$	−11696.3	−0.519828	−0.259914	−	0.965632i	$-0.583694\pi$
$797$	−11696.3	−0.519828	−0.259914	+	0.965632i	$0.583694\pi$
$798$	−6257.00	−0.277563
$799$	46093.0	2.04087
$800$	0	0
$801$	−1276.91	−0.0563263
$802$	−15123.9	−0.665888
$803$	−1357.73	−0.0596678
$804$	1462.97	0.0641727
$805$	0	0
$806$	662.045	0.0289324
$807$	−5137.42	−0.224096
$808$	−5836.34	−0.254111
$809$	14310.2	0.621902	0.310951	−	0.950426i	$-0.399352\pi$
$809$	14310.2	0.621902	0.310951	+	0.950426i	$0.399352\pi$
$810$	0	0
$811$	21697.9	0.939477	0.469739	−	0.882806i	$-0.344348\pi$
$811$	21697.9	0.939477	0.469739	+	0.882806i	$0.344348\pi$
$812$	−80.0299	−0.00345874
$813$	1431.24	0.0617416
$814$	−11746.9	−0.505807
$815$	0	0
$816$	−12511.3	−0.536743
$817$	−66954.1	−2.86711
$818$	3510.54	0.150053
$819$	−2761.50	−0.117820
$820$	0	0
$821$	3613.00	0.153587	0.0767934	−	0.997047i	$-0.475532\pi$
$821$	3613.00	0.153587	0.0767934	+	0.997047i	$0.475532\pi$
$822$	5263.44	0.223338
$823$	4763.98	0.201776	0.100888	−	0.994898i	$-0.467832\pi$
$823$	4763.98	0.201776	0.100888	+	0.994898i	$0.467832\pi$
$824$	28248.0	1.19425
$825$	0	0
$826$	−9900.36	−0.417043
$827$	33571.7	1.41161	0.705806	−	0.708405i	$-0.250585\pi$
$827$	33571.7	1.41161	0.705806	+	0.708405i	$0.250585\pi$
$828$	−2403.99	−0.100899
$829$	17980.5	0.753303	0.376652	−	0.926355i	$-0.377075\pi$
$829$	17980.5	0.753303	0.376652	+	0.926355i	$0.377075\pi$
$830$	0	0
$831$	12850.4	0.536434
$832$	27900.9	1.16261
$833$	25142.1	1.04576
$834$	−6381.98	−0.264976
$835$	0	0
$836$	−2062.58	−0.0853301
$837$	−142.057	−0.00586643
$838$	3249.91	0.133969
$839$	−40139.5	−1.65169	−0.825847	−	0.563895i	$-0.809302\pi$
$839$	−40139.5	−1.65169	−0.825847	+	0.563895i	$0.809302\pi$
$840$	0	0
$841$	−24309.7	−0.996747
$842$	−31358.4	−1.28347
$843$	−10433.4	−0.426269
$844$	−6213.91	−0.253426
$845$	0	0
$846$	−12847.9	−0.522127
$847$	−755.792	−0.0306603
$848$	−8474.36	−0.343173
$849$	−19704.8	−0.796546
$850$	0	0
$851$	77414.4	3.11837
$852$	4836.24	0.194468
$853$	15369.2	0.616919	0.308459	−	0.951237i	$-0.400187\pi$
$853$	15369.2	0.616919	0.308459	+	0.951237i	$0.400187\pi$
$854$	−12582.5	−0.504173
$855$	0	0
$856$	−50936.8	−2.03386
$857$	−10324.9	−0.411541	−0.205770	−	0.978600i	$-0.565970\pi$
$857$	−10324.9	−0.411541	−0.205770	+	0.978600i	$0.565970\pi$
$858$	4152.44	0.165224
$859$	−27112.5	−1.07691	−0.538455	−	0.842655i	$-0.680992\pi$
$859$	−27112.5	−1.07691	−0.538455	+	0.842655i	$0.680992\pi$
$860$	0	0
$861$	−5593.09	−0.221384
$862$	20620.8	0.814787
$863$	−30463.6	−1.20161	−0.600807	−	0.799394i	$-0.705154\pi$
$863$	−30463.6	−1.20161	−0.600807	+	0.799394i	$0.705154\pi$
$864$	−1734.88	−0.0683122
$865$	0	0
$866$	42434.0	1.66509
$867$	−5783.00	−0.226529
$868$	47.2726	0.00184854
$869$	3408.19	0.133044
$870$	0	0
$871$	16653.5	0.647855
$872$	−11938.4	−0.463631
$873$	−7185.10	−0.278555
$874$	−62004.6	−2.39970
$875$	0	0
$876$	532.642	0.0205437
$877$	5086.12	0.195833	0.0979167	−	0.995195i	$-0.468782\pi$
$877$	5086.12	0.195833	0.0979167	+	0.995195i	$0.468782\pi$
$878$	12054.2	0.463335
$879$	25056.9	0.961487
$880$	0	0
$881$	−10625.5	−0.406338	−0.203169	−	0.979144i	$-0.565124\pi$
$881$	−10625.5	−0.406338	−0.203169	+	0.979144i	$0.565124\pi$
$882$	−7008.06	−0.267544
$883$	−13112.2	−0.499728	−0.249864	−	0.968281i	$-0.580386\pi$
$883$	−13112.2	−0.499728	−0.249864	+	0.968281i	$0.580386\pi$
$884$	5844.25	0.222357
$885$	0	0
$886$	−38664.0	−1.46607
$887$	14442.8	0.546719	0.273360	−	0.961912i	$-0.411865\pi$
$887$	14442.8	0.546719	0.273360	+	0.961912i	$0.411865\pi$
$888$	30237.8	1.14270
$889$	−5922.54	−0.223437
$890$	0	0
$891$	−891.000	−0.0335013
$892$	−5520.38	−0.207215
$893$	72645.8	2.72228
$894$	9326.43	0.348906
$895$	0	0
$896$	−5876.86	−0.219121
$897$	−27365.5	−1.01863
$898$	2493.61	0.0926648
$899$	−46.8641	−0.00173860
$900$	0	0
$901$	−13900.3	−0.513970
$902$	8410.27	0.310456
$903$	9624.77	0.354698
$904$	4110.10	0.151217
$905$	0	0
$906$	−237.045	−0.00869239
$907$	44981.9	1.64675	0.823374	−	0.567499i	$-0.192089\pi$
$907$	44981.9	1.64675	0.823374	+	0.567499i	$0.192089\pi$
$908$	−7197.57	−0.263062
$909$	2172.60	0.0792745
$910$	0	0
$911$	6841.96	0.248830	0.124415	−	0.992230i	$-0.460295\pi$
$911$	6841.96	0.248830	0.124415	+	0.992230i	$0.460295\pi$
$912$	−19718.7	−0.715954
$913$	−11233.4	−0.407199
$914$	−160.501	−0.00580843
$915$	0	0
$916$	398.989	0.0143919
$917$	9274.61	0.333996
$918$	5720.27	0.205661
$919$	−4753.54	−0.170625	−0.0853127	−	0.996354i	$-0.527189\pi$
$919$	−4753.54	−0.170625	−0.0853127	+	0.996354i	$0.527189\pi$
$920$	0	0
$921$	16151.7	0.577868
$922$	−30395.9	−1.08572
$923$	55052.7	1.96325
$924$	296.500	0.0105564
$925$	0	0
$926$	33671.2	1.19493
$927$	−10515.4	−0.372569
$928$	−572.330	−0.0202453
$929$	−7507.93	−0.265153	−0.132576	−	0.991173i	$-0.542325\pi$
$929$	−7507.93	−0.265153	−0.132576	+	0.991173i	$0.542325\pi$
$930$	0	0
$931$	39625.7	1.39493
$932$	3265.14	0.114757
$933$	5371.24	0.188474
$934$	26068.3	0.913256
$935$	0	0
$936$	−10688.9	−0.373266
$937$	−8540.47	−0.297764	−0.148882	−	0.988855i	$-0.547567\pi$
$937$	−8540.47	−0.297764	−0.148882	+	0.988855i	$0.547567\pi$
$938$	−5424.24	−0.188814
$939$	−2427.23	−0.0843552
$940$	0	0
$941$	9101.13	0.315290	0.157645	−	0.987496i	$-0.449610\pi$
$941$	9101.13	0.315290	0.157645	+	0.987496i	$0.449610\pi$
$942$	2653.04	0.0917630
$943$	−55425.5	−1.91400
$944$	−31200.6	−1.07573
$945$	0	0
$946$	−14472.7	−0.497407
$947$	−47540.0	−1.63130	−0.815650	−	0.578546i	$-0.803620\pi$
$947$	−47540.0	−1.63130	−0.815650	+	0.578546i	$0.803620\pi$
$948$	−1337.04	−0.0458072
$949$	6063.26	0.207399
$950$	0	0
$951$	32233.6	1.09910
$952$	−12490.2	−0.425221
$953$	−47370.7	−1.61016	−0.805082	−	0.593164i	$-0.797879\pi$
$953$	−47370.7	−1.61016	−0.805082	+	0.593164i	$0.797879\pi$
$954$	3874.55	0.131492
$955$	0	0
$956$	2326.12	0.0786947
$957$	−293.938	−0.00992859
$958$	8789.33	0.296420
$959$	4278.20	0.144057
$960$	0	0
$961$	−29763.3	−0.999071
$962$	52458.4	1.75813
$963$	18961.4	0.634498
$964$	−8122.38	−0.271374
$965$	0	0
$966$	8913.27	0.296874
$967$	36171.6	1.20290	0.601448	−	0.798912i	$-0.294591\pi$
$967$	36171.6	1.20290	0.601448	+	0.798912i	$0.294591\pi$
$968$	−2925.43	−0.0971351
$969$	−32344.1	−1.07228
$970$	0	0
$971$	−31713.2	−1.04812	−0.524060	−	0.851681i	$-0.675583\pi$
$971$	−31713.2	−1.04812	−0.524060	+	0.851681i	$0.675583\pi$
$972$	349.543	0.0115346
$973$	−5187.37	−0.170914
$974$	7257.40	0.238750
$975$	0	0
$976$	−39653.1	−1.30048
$977$	−22800.5	−0.746626	−0.373313	−	0.927706i	$-0.621778\pi$
$977$	−22800.5	−0.746626	−0.373313	+	0.927706i	$0.621778\pi$
$978$	14766.0	0.482786
$979$	1560.67	0.0509490
$980$	0	0
$981$	4444.12	0.144638
$982$	−6832.41	−0.222027
$983$	44597.4	1.44704	0.723518	−	0.690305i	$-0.242524\pi$
$983$	44597.4	1.44704	0.723518	+	0.690305i	$0.242524\pi$
$984$	−21649.1	−0.701369
$985$	0	0
$986$	1887.10	0.0609507
$987$	−10443.0	−0.336781
$988$	9210.95	0.296599
$989$	95378.1	3.06658
$990$	0	0
$991$	−34788.1	−1.11512	−0.557558	−	0.830138i	$-0.688261\pi$
$991$	−34788.1	−1.11512	−0.557558	+	0.830138i	$0.688261\pi$
$992$	338.068	0.0108202
$993$	−10197.4	−0.325885
$994$	−17931.3	−0.572180
$995$	0	0
$996$	4406.92	0.140199
$997$	20360.5	0.646765	0.323383	−	0.946268i	$-0.395180\pi$
$997$	20360.5	0.646765	0.323383	+	0.946268i	$0.395180\pi$
$998$	−28528.0	−0.904849
$999$	−11256.1	−0.356485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.m.1.2		2
3.2	odd	2		2475.4.a.n.1.1		2
5.2	odd	4		825.4.c.j.199.4		4
5.3	odd	4		825.4.c.j.199.1		4
5.4	even	2		165.4.a.c.1.1	✓	2
15.14	odd	2		495.4.a.d.1.2		2
55.54	odd	2		1815.4.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.c.1.1	✓	2	5.4	even	2
495.4.a.d.1.2		2	15.14	odd	2
825.4.a.m.1.2		2	1.1	even	1	trivial
825.4.c.j.199.1		4	5.3	odd	4
825.4.c.j.199.4		4	5.2	odd	4
1815.4.a.n.1.2		2	55.54	odd	2
2475.4.a.n.1.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56155 q^{2} -3.00000 q^{3} -1.43845 q^{4} -7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.56155 q^{2} -3.00000 q^{3} -1.43845 q^{4} -7.68466 q^{6} -6.24621 q^{7} -24.1771 q^{8} +9.00000 q^{9} -11.0000 q^{11} +4.31534 q^{12} +49.1231 q^{13} -16.0000 q^{14} -50.4233 q^{16} -82.7083 q^{17} +23.0540 q^{18} -130.354 q^{19} +18.7386 q^{21} -28.1771 q^{22} +185.693 q^{23} +72.5312 q^{24} +125.831 q^{26} -27.0000 q^{27} +8.98485 q^{28} -8.90720 q^{29} +5.26137 q^{31} +64.2547 q^{32} +33.0000 q^{33} -211.862 q^{34} -12.9460 q^{36} +416.894 q^{37} -333.909 q^{38} -147.369 q^{39} -298.479 q^{41} +48.0000 q^{42} +513.633 q^{43} +15.8229 q^{44} +475.663 q^{46} -557.295 q^{47} +151.270 q^{48} -303.985 q^{49} +248.125 q^{51} -70.6610 q^{52} +168.064 q^{53} -69.1619 q^{54} +151.015 q^{56} +391.062 q^{57} -22.8163 q^{58} +618.773 q^{59} +786.405 q^{61} +13.4773 q^{62} -56.2159 q^{63} +567.978 q^{64} +84.5312 q^{66} +339.015 q^{67} +118.972 q^{68} -557.080 q^{69} +1120.71 q^{71} -217.594 q^{72} +123.430 q^{73} +1067.90 q^{74} +187.508 q^{76} +68.7083 q^{77} -377.494 q^{78} -309.835 q^{79} +81.0000 q^{81} -764.570 q^{82} +1021.22 q^{83} -26.9545 q^{84} +1315.70 q^{86} +26.7216 q^{87} +265.948 q^{88} -141.879 q^{89} -306.833 q^{91} -267.110 q^{92} -15.7841 q^{93} -1427.54 q^{94} -192.764 q^{96} -798.345 q^{97} -778.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} - 7 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 18 q^{9} - 22 q^{11} + 21 q^{12} + 90 q^{13} - 32 q^{14} - 39 q^{16} + 16 q^{17} + 9 q^{18} - 170 q^{19} - 12 q^{21} - 11 q^{22} + 124 q^{23} + 9 q^{24} + 62 q^{26} - 54 q^{27} - 48 q^{28} - 158 q^{29} + 60 q^{31} - 123 q^{32} + 66 q^{33} - 366 q^{34} - 63 q^{36} + 372 q^{37} - 272 q^{38} - 270 q^{39} + 38 q^{41} + 96 q^{42} + 516 q^{43} + 77 q^{44} + 572 q^{46} - 224 q^{47} + 117 q^{48} - 542 q^{49} - 48 q^{51} - 298 q^{52} - 472 q^{53} - 27 q^{54} + 368 q^{56} + 510 q^{57} + 210 q^{58} + 248 q^{59} + 72 q^{61} - 72 q^{62} + 36 q^{63} + 769 q^{64} + 33 q^{66} + 744 q^{67} - 430 q^{68} - 372 q^{69} + 2060 q^{71} - 27 q^{72} + 486 q^{73} + 1138 q^{74} + 408 q^{76} - 44 q^{77} - 186 q^{78} + 642 q^{79} + 162 q^{81} - 1290 q^{82} + 286 q^{83} + 144 q^{84} + 1312 q^{86} + 474 q^{87} + 33 q^{88} + 244 q^{89} + 112 q^{91} + 76 q^{92} - 180 q^{93} - 1948 q^{94} + 369 q^{96} + 168 q^{97} - 407 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 - 7 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 18 * q^9 - 22 * q^11 + 21 * q^12 + 90 * q^13 - 32 * q^14 - 39 * q^16 + 16 * q^17 + 9 * q^18 - 170 * q^19 - 12 * q^21 - 11 * q^22 + 124 * q^23 + 9 * q^24 + 62 * q^26 - 54 * q^27 - 48 * q^28 - 158 * q^29 + 60 * q^31 - 123 * q^32 + 66 * q^33 - 366 * q^34 - 63 * q^36 + 372 * q^37 - 272 * q^38 - 270 * q^39 + 38 * q^41 + 96 * q^42 + 516 * q^43 + 77 * q^44 + 572 * q^46 - 224 * q^47 + 117 * q^48 - 542 * q^49 - 48 * q^51 - 298 * q^52 - 472 * q^53 - 27 * q^54 + 368 * q^56 + 510 * q^57 + 210 * q^58 + 248 * q^59 + 72 * q^61 - 72 * q^62 + 36 * q^63 + 769 * q^64 + 33 * q^66 + 744 * q^67 - 430 * q^68 - 372 * q^69 + 2060 * q^71 - 27 * q^72 + 486 * q^73 + 1138 * q^74 + 408 * q^76 - 44 * q^77 - 186 * q^78 + 642 * q^79 + 162 * q^81 - 1290 * q^82 + 286 * q^83 + 144 * q^84 + 1312 * q^86 + 474 * q^87 + 33 * q^88 + 244 * q^89 + 112 * q^91 + 76 * q^92 - 180 * q^93 - 1948 * q^94 + 369 * q^96 + 168 * q^97 - 407 * q^98 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more