LMFDB - Embedded newform 2175.2.c.o.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,2,Mod(349,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2175.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.3674624396$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 224x^{10} + 1023x^{8} + 2364x^{6} + 2612x^{4} + 1241x^{2} + 196 $ x^14 + 24x^12 + 224x^10 + 1023x^8 + 2364x^6 + 2612x^4 + 1241x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$-2.26695i$ of defining polynomial
Character	$\chi$	$=$	2175.349
Dual form			2175.2.c.o.349.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26695i q^{2} +1.00000i q^{3} -3.13907 q^{4} +2.26695 q^{6} -0.159887i q^{7} +2.58223i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.26695i q^{2} +1.00000i q^{3} -3.13907 q^{4} +2.26695 q^{6} -0.159887i q^{7} +2.58223i q^{8} -1.00000 q^{9} -3.24930 q^{11} -3.13907i q^{12} +7.05679i q^{13} -0.362456 q^{14} -0.424361 q^{16} -7.63808i q^{17} +2.26695i q^{18} +3.99028 q^{19} +0.159887 q^{21} +7.36601i q^{22} +2.06402i q^{23} -2.58223 q^{24} +15.9974 q^{26} -1.00000i q^{27} +0.501897i q^{28} +1.00000 q^{29} +10.2044 q^{31} +6.12646i q^{32} -3.24930i q^{33} -17.3152 q^{34} +3.13907 q^{36} +4.27815i q^{37} -9.04576i q^{38} -7.05679 q^{39} -5.12330 q^{41} -0.362456i q^{42} -3.94180i q^{43} +10.1998 q^{44} +4.67903 q^{46} -5.61626i q^{47} -0.424361i q^{48} +6.97444 q^{49} +7.63808 q^{51} -22.1518i q^{52} +12.0822i q^{53} -2.26695 q^{54} +0.412864 q^{56} +3.99028i q^{57} -2.26695i q^{58} +7.06781 q^{59} +11.4310 q^{61} -23.1329i q^{62} +0.159887i q^{63} +13.0397 q^{64} -7.36601 q^{66} +14.9512i q^{67} +23.9765i q^{68} -2.06402 q^{69} +3.43347 q^{71} -2.58223i q^{72} -12.0772i q^{73} +9.69836 q^{74} -12.5258 q^{76} +0.519521i q^{77} +15.9974i q^{78} +12.7441 q^{79} +1.00000 q^{81} +11.6143i q^{82} -2.59792i q^{83} -0.501897 q^{84} -8.93586 q^{86} +1.00000i q^{87} -8.39044i q^{88} -4.33165 q^{89} +1.12829 q^{91} -6.47910i q^{92} +10.2044i q^{93} -12.7318 q^{94} -6.12646 q^{96} +3.88355i q^{97} -15.8107i q^{98} +3.24930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 20 q^{4} + 4 q^{6} - 14 q^{9}+O(q^{10}) $ 14 * q - 20 * q^4 + 4 * q^6 - 14 * q^9	$ 14 q - 20 q^{4} + 4 q^{6} - 14 q^{9} + 8 q^{11} - 30 q^{14} + 24 q^{16} - 30 q^{19} - 2 q^{21} - 6 q^{24} + 12 q^{26} + 14 q^{29} + 10 q^{31} - 14 q^{34} + 20 q^{36} + 2 q^{39} + 44 q^{41} - 30 q^{44} - 8 q^{46} - 24 q^{49} + 16 q^{51} - 4 q^{54} + 28 q^{56} - 12 q^{59} + 46 q^{61} - 10 q^{64} + 6 q^{66} - 28 q^{69} + 52 q^{71} + 20 q^{74} + 92 q^{76} - 28 q^{79} + 14 q^{81} + 48 q^{84} + 88 q^{86} - 28 q^{89} + 26 q^{91} + 6 q^{94} + 36 q^{96} - 8 q^{99}+O(q^{100}) $ 14 * q - 20 * q^4 + 4 * q^6 - 14 * q^9 + 8 * q^11 - 30 * q^14 + 24 * q^16 - 30 * q^19 - 2 * q^21 - 6 * q^24 + 12 * q^26 + 14 * q^29 + 10 * q^31 - 14 * q^34 + 20 * q^36 + 2 * q^39 + 44 * q^41 - 30 * q^44 - 8 * q^46 - 24 * q^49 + 16 * q^51 - 4 * q^54 + 28 * q^56 - 12 * q^59 + 46 * q^61 - 10 * q^64 + 6 * q^66 - 28 * q^69 + 52 * q^71 + 20 * q^74 + 92 * q^76 - 28 * q^79 + 14 * q^81 + 48 * q^84 + 88 * q^86 - 28 * q^89 + 26 * q^91 + 6 * q^94 + 36 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$2002$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 2.26695i	− 1.60298i	−0.598010	−	0.801489i	$-0.704042\pi$
$2$	− 2.26695i	− 1.60298i	0.598010	−	0.801489i	$-0.295958\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−3.13907	−1.56954
$5$	0	0
$5$	0	0
$6$	2.26695	0.925480
$7$	− 0.159887i	− 0.0604316i	−0.999543	−	0.0302158i	$-0.990381\pi$
$7$	− 0.159887i	− 0.0604316i	0.999543	−	0.0302158i	$-0.00961945\pi$
$8$	2.58223i	0.912955i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.24930	−0.979701	−0.489851	−	0.871806i	$-0.662949\pi$
$11$	−3.24930	−0.979701	−0.489851	+	0.871806i	$0.662949\pi$
$12$	− 3.13907i	− 0.906173i
$13$	7.05679i	1.95720i	0.205770	+	0.978600i	$0.434030\pi$
$13$	7.05679i	1.95720i	−0.205770	+	0.978600i	$0.565970\pi$
$14$	−0.362456	−0.0968704
$15$	0	0
$16$	−0.424361	−0.106090
$17$	− 7.63808i	− 1.85251i	−0.376901	−	0.926254i	$-0.623010\pi$
$17$	− 7.63808i	− 1.85251i	0.376901	−	0.926254i	$-0.376990\pi$
$18$	2.26695i	0.534326i
$19$	3.99028	0.915432	0.457716	−	0.889098i	$-0.348668\pi$
$19$	3.99028	0.915432	0.457716	+	0.889098i	$0.348668\pi$
$20$	0	0
$21$	0.159887	0.0348902
$22$	7.36601i	1.57044i
$23$	2.06402i	0.430377i	0.976572	+	0.215189i	$0.0690366\pi$
$23$	2.06402i	0.430377i	−0.976572	+	0.215189i	$0.930963\pi$
$24$	−2.58223	−0.527095
$25$	0	0
$26$	15.9974	3.13735
$27$	− 1.00000i	− 0.192450i
$28$	0.501897i	0.0948496i
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	10.2044	1.83277	0.916383	−	0.400303i	$-0.131095\pi$
$31$	10.2044	1.83277	0.916383	+	0.400303i	$0.131095\pi$
$32$	6.12646i	1.08302i
$33$	− 3.24930i	− 0.565631i
$34$	−17.3152	−2.96953
$35$	0	0
$36$	3.13907	0.523179
$37$	4.27815i	0.703323i	0.936127	+	0.351662i	$0.114383\pi$
$37$	4.27815i	0.703323i	−0.936127	+	0.351662i	$0.885617\pi$
$38$	− 9.04576i	− 1.46742i
$39$	−7.05679	−1.12999
$40$	0	0
$41$	−5.12330	−0.800125	−0.400063	−	0.916488i	$-0.631012\pi$
$41$	−5.12330	−0.800125	−0.400063	+	0.916488i	$0.631012\pi$
$42$	− 0.362456i	− 0.0559282i
$43$	− 3.94180i	− 0.601118i	−0.953763	−	0.300559i	$-0.902827\pi$
$43$	− 3.94180i	− 0.601118i	0.953763	−	0.300559i	$-0.0971733\pi$
$44$	10.1998	1.53768
$45$	0	0
$46$	4.67903	0.689885
$47$	− 5.61626i	− 0.819215i	−0.912262	−	0.409608i	$-0.865666\pi$
$47$	− 5.61626i	− 0.819215i	0.912262	−	0.409608i	$-0.134334\pi$
$48$	− 0.424361i	− 0.0612513i
$49$	6.97444	0.996348
$50$	0	0
$51$	7.63808	1.06955
$52$	− 22.1518i	− 3.07190i
$53$	12.0822i	1.65962i	0.558049	+	0.829808i	$0.311550\pi$
$53$	12.0822i	1.65962i	−0.558049	+	0.829808i	$0.688450\pi$
$54$	−2.26695	−0.308493
$55$	0	0
$56$	0.412864	0.0551713
$57$	3.99028i	0.528525i
$58$	− 2.26695i	− 0.297665i
$59$	7.06781	0.920151	0.460075	−	0.887880i	$-0.347822\pi$
$59$	7.06781	0.920151	0.460075	+	0.887880i	$0.347822\pi$
$60$	0	0
$61$	11.4310	1.46359	0.731796	−	0.681524i	$-0.238682\pi$
$61$	11.4310	1.46359	0.731796	+	0.681524i	$0.238682\pi$
$62$	− 23.1329i	− 2.93788i
$63$	0.159887i	0.0201439i
$64$	13.0397	1.62996
$65$	0	0
$66$	−7.36601	−0.906694
$67$	14.9512i	1.82658i	0.407311	+	0.913289i	$0.366466\pi$
$67$	14.9512i	1.82658i	−0.407311	+	0.913289i	$0.633534\pi$
$68$	23.9765i	2.90758i
$69$	−2.06402	−0.248478
$70$	0	0
$71$	3.43347	0.407478	0.203739	−	0.979025i	$-0.434691\pi$
$71$	3.43347	0.407478	0.203739	+	0.979025i	$0.434691\pi$
$72$	− 2.58223i	− 0.304318i
$73$	− 12.0772i	− 1.41353i	−0.707449	−	0.706764i	$-0.750154\pi$
$73$	− 12.0772i	− 1.41353i	0.707449	−	0.706764i	$-0.249846\pi$
$74$	9.69836	1.12741
$75$	0	0
$76$	−12.5258	−1.43680
$77$	0.519521i	0.0592049i
$78$	15.9974i	1.81135i
$79$	12.7441	1.43383	0.716913	−	0.697163i	$-0.245554\pi$
$79$	12.7441	1.43383	0.716913	+	0.697163i	$0.245554\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.6143i	1.28258i
$83$	− 2.59792i	− 0.285159i	−0.989783	−	0.142580i	$-0.954460\pi$
$83$	− 2.59792i	− 0.285159i	0.989783	−	0.142580i	$-0.0455397\pi$
$84$	−0.501897	−0.0547614
$85$	0	0
$86$	−8.93586	−0.963579
$87$	1.00000i	0.107211i
$88$	− 8.39044i	− 0.894423i
$89$	−4.33165	−0.459154	−0.229577	−	0.973290i	$-0.573734\pi$
$89$	−4.33165	−0.459154	−0.229577	+	0.973290i	$0.573734\pi$
$90$	0	0
$91$	1.12829	0.118277
$92$	− 6.47910i	− 0.675493i
$93$	10.2044i	1.05815i
$94$	−12.7318	−1.31318
$95$	0	0
$96$	−6.12646	−0.625279
$97$	3.88355i	0.394315i	0.980372	+	0.197158i	$0.0631711\pi$
$97$	3.88355i	0.394315i	−0.980372	+	0.197158i	$0.936829\pi$
$98$	− 15.8107i	− 1.59712i
$99$	3.24930	0.326567
$100$	0	0
$101$	15.4045	1.53280	0.766400	−	0.642363i	$-0.222046\pi$
$101$	15.4045	1.53280	0.766400	+	0.642363i	$0.222046\pi$
$102$	− 17.3152i	− 1.71446i
$103$	7.68484i	0.757210i	0.925558	+	0.378605i	$0.123596\pi$
$103$	7.68484i	0.757210i	−0.925558	+	0.378605i	$0.876404\pi$
$104$	−18.2222	−1.78684
$105$	0	0
$106$	27.3897	2.66033
$107$	4.60924i	0.445592i	0.974865	+	0.222796i	$0.0715183\pi$
$107$	4.60924i	0.445592i	−0.974865	+	0.222796i	$0.928482\pi$
$108$	3.13907i	0.302058i
$109$	14.4509	1.38415	0.692073	−	0.721827i	$-0.256698\pi$
$109$	14.4509	1.38415	0.692073	+	0.721827i	$0.256698\pi$
$110$	0	0
$111$	−4.27815	−0.406064
$112$	0.0678498i	0.00641120i
$113$	− 4.08614i	− 0.384392i	−0.981357	−	0.192196i	$-0.938439\pi$
$113$	− 4.08614i	− 0.384392i	0.981357	−	0.192196i	$-0.0615610\pi$
$114$	9.04576	0.847213
$115$	0	0
$116$	−3.13907	−0.291456
$117$	− 7.05679i	− 0.652400i
$118$	− 16.0224i	− 1.47498i
$119$	−1.22123	−0.111950
$120$	0	0
$121$	−0.442038	−0.0401853
$122$	− 25.9136i	− 2.34610i
$123$	− 5.12330i	− 0.461952i
$124$	−32.0324	−2.87659
$125$	0	0
$126$	0.362456	0.0322901
$127$	3.69650i	0.328011i	0.986459	+	0.164006i	$0.0524415\pi$
$127$	3.69650i	0.328011i	−0.986459	+	0.164006i	$0.947559\pi$
$128$	− 17.3074i	− 1.52977i
$129$	3.94180	0.347056
$130$	0	0
$131$	−9.92811	−0.867423	−0.433712	−	0.901052i	$-0.642796\pi$
$131$	−9.92811	−0.867423	−0.433712	+	0.901052i	$0.642796\pi$
$132$	10.1998i	0.887779i
$133$	− 0.637993i	− 0.0553210i
$134$	33.8936	2.92797
$135$	0	0
$136$	19.7233	1.69126
$137$	− 3.82810i	− 0.327057i	−0.986539	−	0.163528i	$-0.947712\pi$
$137$	− 3.82810i	− 0.327057i	0.986539	−	0.163528i	$-0.0522875\pi$
$138$	4.67903i	0.398305i
$139$	2.06987	0.175564	0.0877822	−	0.996140i	$-0.472022\pi$
$139$	2.06987	0.175564	0.0877822	+	0.996140i	$0.472022\pi$
$140$	0	0
$141$	5.61626	0.472974
$142$	− 7.78351i	− 0.653177i
$143$	− 22.9296i	− 1.91747i
$144$	0.424361	0.0353634
$145$	0	0
$146$	−27.3784	−2.26585
$147$	6.97444i	0.575242i
$148$	− 13.4294i	− 1.10389i
$149$	1.46609	0.120107	0.0600536	−	0.998195i	$-0.480873\pi$
$149$	1.46609	0.120107	0.0600536	+	0.998195i	$0.480873\pi$
$150$	0	0
$151$	−20.1279	−1.63799	−0.818995	−	0.573801i	$-0.805468\pi$
$151$	−20.1279	−1.63799	−0.818995	+	0.573801i	$0.805468\pi$
$152$	10.3038i	0.835748i
$153$	7.63808i	0.617502i
$154$	1.17773	0.0949041
$155$	0	0
$156$	22.1518	1.77356
$157$	− 7.09106i	− 0.565928i	−0.959131	−	0.282964i	$-0.908682\pi$
$157$	− 7.09106i	− 0.565928i	0.959131	−	0.282964i	$-0.0913177\pi$
$158$	− 28.8903i	− 2.29839i
$159$	−12.0822	−0.958180
$160$	0	0
$161$	0.330009	0.0260084
$162$	− 2.26695i	− 0.178109i
$163$	− 6.58715i	− 0.515946i	−0.966152	−	0.257973i	$-0.916945\pi$
$163$	− 6.58715i	− 0.515946i	0.966152	−	0.257973i	$-0.0830545\pi$
$164$	16.0824	1.25583
$165$	0	0
$166$	−5.88937	−0.457104
$167$	10.6638i	0.825192i	0.910914	+	0.412596i	$0.135378\pi$
$167$	10.6638i	0.825192i	−0.910914	+	0.412596i	$0.864622\pi$
$168$	0.412864i	0.0318532i
$169$	−36.7983	−2.83063
$170$	0	0
$171$	−3.99028	−0.305144
$172$	12.3736i	0.943477i
$173$	− 13.8799i	− 1.05527i	−0.849472	−	0.527633i	$-0.823080\pi$
$173$	− 13.8799i	− 1.05527i	0.849472	−	0.527633i	$-0.176920\pi$
$174$	2.26695	0.171857
$175$	0	0
$176$	1.37888	0.103937
$177$	7.06781i	0.531249i
$178$	9.81965i	0.736014i
$179$	11.1105	0.830439	0.415219	−	0.909721i	$-0.363705\pi$
$179$	11.1105	0.830439	0.415219	+	0.909721i	$0.363705\pi$
$180$	0	0
$181$	10.9453	0.813557	0.406778	−	0.913527i	$-0.366652\pi$
$181$	10.9453	0.813557	0.406778	+	0.913527i	$0.366652\pi$
$182$	− 2.55777i	− 0.189595i
$183$	11.4310i	0.845005i
$184$	−5.32976	−0.392915
$185$	0	0
$186$	23.1329	1.69619
$187$	24.8184i	1.81490i
$188$	17.6298i	1.28579i
$189$	−0.159887	−0.0116301
$190$	0	0
$191$	18.1472	1.31309	0.656544	−	0.754287i	$-0.272017\pi$
$191$	18.1472	1.31309	0.656544	+	0.754287i	$0.272017\pi$
$192$	13.0397i	0.941058i
$193$	− 17.3305i	− 1.24747i	−0.781634	−	0.623737i	$-0.785614\pi$
$193$	− 17.3305i	− 1.24747i	0.781634	−	0.623737i	$-0.214386\pi$
$194$	8.80383	0.632078
$195$	0	0
$196$	−21.8933	−1.56381
$197$	10.4273i	0.742915i	0.928450	+	0.371458i	$0.121142\pi$
$197$	10.4273i	0.742915i	−0.928450	+	0.371458i	$0.878858\pi$
$198$	− 7.36601i	− 0.523480i
$199$	−11.5570	−0.819256	−0.409628	−	0.912253i	$-0.634341\pi$
$199$	−11.5570	−0.819256	−0.409628	+	0.912253i	$0.634341\pi$
$200$	0	0
$201$	−14.9512	−1.05458
$202$	− 34.9212i	− 2.45704i
$203$	− 0.159887i	− 0.0112219i
$204$	−23.9765	−1.67869
$205$	0	0
$206$	17.4212	1.21379
$207$	− 2.06402i	− 0.143459i
$208$	− 2.99463i	− 0.207640i
$209$	−12.9656	−0.896850
$210$	0	0
$211$	−21.1616	−1.45682	−0.728412	−	0.685140i	$-0.759741\pi$
$211$	−21.1616	−1.45682	−0.728412	+	0.685140i	$0.759741\pi$
$212$	− 37.9269i	− 2.60483i
$213$	3.43347i	0.235257i
$214$	10.4489	0.714274
$215$	0	0
$216$	2.58223	0.175698
$217$	− 1.63155i	− 0.110757i
$218$	− 32.7595i	− 2.21876i
$219$	12.0772	0.816101
$220$	0	0
$221$	53.9003	3.62573
$222$	9.69836i	0.650911i
$223$	9.46925i	0.634108i	0.948408	+	0.317054i	$0.102694\pi$
$223$	9.46925i	0.634108i	−0.948408	+	0.317054i	$0.897306\pi$
$224$	0.979541	0.0654483
$225$	0	0
$226$	−9.26310	−0.616172
$227$	− 22.4030i	− 1.48694i	−0.668768	−	0.743471i	$-0.733178\pi$
$227$	− 22.4030i	− 1.48694i	0.668768	−	0.743471i	$-0.266822\pi$
$228$	− 12.5258i	− 0.829539i
$229$	−2.03117	−0.134223	−0.0671117	−	0.997745i	$-0.521378\pi$
$229$	−2.03117	−0.134223	−0.0671117	+	0.997745i	$0.521378\pi$
$230$	0	0
$231$	−0.519521	−0.0341820
$232$	2.58223i	0.169532i
$233$	11.0704i	0.725249i	0.931935	+	0.362624i	$0.118119\pi$
$233$	11.0704i	0.725249i	−0.931935	+	0.362624i	$0.881881\pi$
$234$	−15.9974	−1.04578
$235$	0	0
$236$	−22.1864	−1.44421
$237$	12.7441i	0.827820i
$238$	2.76847i	0.179453i
$239$	2.24098	0.144957	0.0724786	−	0.997370i	$-0.476909\pi$
$239$	2.24098	0.144957	0.0724786	+	0.997370i	$0.476909\pi$
$240$	0	0
$241$	14.4838	0.932986	0.466493	−	0.884525i	$-0.345517\pi$
$241$	14.4838	0.932986	0.466493	+	0.884525i	$0.345517\pi$
$242$	1.00208i	0.0644161i
$243$	1.00000i	0.0641500i
$244$	−35.8828	−2.29716
$245$	0	0
$246$	−11.6143	−0.740499
$247$	28.1585i	1.79168i
$248$	26.3501i	1.67323i
$249$	2.59792	0.164637
$250$	0	0
$251$	−16.2044	−1.02281	−0.511407	−	0.859339i	$-0.670875\pi$
$251$	−16.2044	−1.02281	−0.511407	+	0.859339i	$0.670875\pi$
$252$	− 0.501897i	− 0.0316165i
$253$	− 6.70661i	− 0.421641i
$254$	8.37978	0.525794
$255$	0	0
$256$	−13.1557	−0.822232
$257$	3.36942i	0.210178i	0.994463	+	0.105089i	$0.0335128\pi$
$257$	3.36942i	0.210178i	−0.994463	+	0.105089i	$0.966487\pi$
$258$	− 8.93586i	− 0.556323i
$259$	0.684020	0.0425029
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	22.5066i	1.39046i
$263$	1.79671i	0.110790i	0.998465	+	0.0553950i	$0.0176418\pi$
$263$	1.79671i	0.110790i	−0.998465	+	0.0553950i	$0.982358\pi$
$264$	8.39044	0.516396
$265$	0	0
$266$	−1.44630	−0.0886783
$267$	− 4.33165i	− 0.265093i
$268$	− 46.9329i	− 2.86688i
$269$	0.117055	0.00713699	0.00356849	−	0.999994i	$-0.498864\pi$
$269$	0.117055	0.00713699	0.00356849	+	0.999994i	$0.498864\pi$
$270$	0	0
$271$	−4.06294	−0.246806	−0.123403	−	0.992357i	$-0.539381\pi$
$271$	−4.06294	−0.246806	−0.123403	+	0.992357i	$0.539381\pi$
$272$	3.24131i	0.196533i
$273$	1.12829i	0.0682871i
$274$	−8.67813	−0.524265
$275$	0	0
$276$	6.47910	0.389996
$277$	12.5436i	0.753674i	0.926279	+	0.376837i	$0.122988\pi$
$277$	12.5436i	0.753674i	−0.926279	+	0.376837i	$0.877012\pi$
$278$	− 4.69231i	− 0.281426i
$279$	−10.2044	−0.610922
$280$	0	0
$281$	−2.83163	−0.168921	−0.0844605	−	0.996427i	$-0.526917\pi$
$281$	−2.83163	−0.168921	−0.0844605	+	0.996427i	$0.526917\pi$
$282$	− 12.7318i	− 0.758167i
$283$	28.2249i	1.67780i	0.544288	+	0.838898i	$0.316800\pi$
$283$	28.2249i	1.67780i	−0.544288	+	0.838898i	$0.683200\pi$
$284$	−10.7779	−0.639551
$285$	0	0
$286$	−51.9804	−3.07366
$287$	0.819148i	0.0483528i
$288$	− 6.12646i	− 0.361005i
$289$	−41.3403	−2.43178
$290$	0	0
$291$	−3.88355	−0.227658
$292$	37.9112i	2.21859i
$293$	21.9337i	1.28138i	0.767799	+	0.640691i	$0.221352\pi$
$293$	21.9337i	1.28138i	−0.767799	+	0.640691i	$0.778648\pi$
$294$	15.8107	0.922100
$295$	0	0
$296$	−11.0472	−0.642103
$297$	3.24930i	0.188544i
$298$	− 3.32357i	− 0.192529i
$299$	−14.5653	−0.842335
$300$	0	0
$301$	−0.630241	−0.0363265
$302$	45.6291i	2.62566i
$303$	15.4045i	0.884963i
$304$	−1.69332	−0.0971185
$305$	0	0
$306$	17.3152	0.989843
$307$	0.461574i	0.0263434i	0.999913	+	0.0131717i	$0.00419281\pi$
$307$	0.461574i	0.0263434i	−0.999913	+	0.0131717i	$0.995807\pi$
$308$	− 1.63081i	− 0.0929243i
$309$	−7.68484	−0.437175
$310$	0	0
$311$	27.5507	1.56226	0.781128	−	0.624371i	$-0.214645\pi$
$311$	27.5507	1.56226	0.781128	+	0.624371i	$0.214645\pi$
$312$	− 18.2222i	− 1.03163i
$313$	14.9121i	0.842882i	0.906856	+	0.421441i	$0.138476\pi$
$313$	14.9121i	0.842882i	−0.906856	+	0.421441i	$0.861524\pi$
$314$	−16.0751	−0.907170
$315$	0	0
$316$	−40.0048	−2.25044
$317$	22.9266i	1.28769i	0.765157	+	0.643843i	$0.222661\pi$
$317$	22.9266i	1.28769i	−0.765157	+	0.643843i	$0.777339\pi$
$318$	27.3897i	1.53594i
$319$	−3.24930	−0.181926
$320$	0	0
$321$	−4.60924	−0.257263
$322$	− 0.748115i	− 0.0416908i
$323$	− 30.4781i	− 1.69584i
$324$	−3.13907	−0.174393
$325$	0	0
$326$	−14.9328	−0.827049
$327$	14.4509i	0.799137i
$328$	− 13.2295i	− 0.730478i
$329$	−0.897966	−0.0495065
$330$	0	0
$331$	−3.23147	−0.177618	−0.0888088	−	0.996049i	$-0.528306\pi$
$331$	−3.23147	−0.177618	−0.0888088	+	0.996049i	$0.528306\pi$
$332$	8.15507i	0.447568i
$333$	− 4.27815i	− 0.234441i
$334$	24.1744	1.32277
$335$	0	0
$336$	−0.0678498	−0.00370151
$337$	− 28.8026i	− 1.56898i	−0.620143	−	0.784489i	$-0.712925\pi$
$337$	− 28.8026i	− 1.56898i	0.620143	−	0.784489i	$-0.287075\pi$
$338$	83.4199i	4.53744i
$339$	4.08614	0.221929
$340$	0	0
$341$	−33.1572	−1.79556
$342$	9.04576i	0.489139i
$343$	− 2.23433i	− 0.120642i
$344$	10.1786	0.548794
$345$	0	0
$346$	−31.4650	−1.69157
$347$	16.4175i	0.881337i	0.897670	+	0.440669i	$0.145259\pi$
$347$	16.4175i	0.881337i	−0.897670	+	0.440669i	$0.854741\pi$
$348$	− 3.13907i	− 0.168272i
$349$	18.2107	0.974796	0.487398	−	0.873180i	$-0.337946\pi$
$349$	18.2107	0.974796	0.487398	+	0.873180i	$0.337946\pi$
$350$	0	0
$351$	7.05679	0.376663
$352$	− 19.9067i	− 1.06103i
$353$	− 18.8790i	− 1.00483i	−0.864627	−	0.502414i	$-0.832445\pi$
$353$	− 18.8790i	− 1.00483i	0.864627	−	0.502414i	$-0.167555\pi$
$354$	16.0224	0.851581
$355$	0	0
$356$	13.5974	0.720660
$357$	− 1.22123i	− 0.0646343i
$358$	− 25.1870i	− 1.33117i
$359$	−14.4500	−0.762640	−0.381320	−	0.924443i	$-0.624530\pi$
$359$	−14.4500	−0.762640	−0.381320	+	0.924443i	$0.624530\pi$
$360$	0	0
$361$	−3.07770	−0.161984
$362$	− 24.8125i	− 1.30411i
$363$	− 0.442038i	− 0.0232010i
$364$	−3.54178	−0.185640
$365$	0	0
$366$	25.9136	1.35452
$367$	21.1171i	1.10231i	0.834404	+	0.551153i	$0.185812\pi$
$367$	21.1171i	1.10231i	−0.834404	+	0.551153i	$0.814188\pi$
$368$	− 0.875889i	− 0.0456589i
$369$	5.12330	0.266708
$370$	0	0
$371$	1.93178	0.100293
$372$	− 32.0324i	− 1.66080i
$373$	− 17.1185i	− 0.886361i	−0.896432	−	0.443181i	$-0.853850\pi$
$373$	− 17.1185i	− 0.886361i	0.896432	−	0.443181i	$-0.146150\pi$
$374$	56.2622	2.90925
$375$	0	0
$376$	14.5025	0.747907
$377$	7.05679i	0.363443i
$378$	0.362456i	0.0186427i
$379$	0.206688	0.0106169	0.00530844	−	0.999986i	$-0.498310\pi$
$379$	0.206688	0.0106169	0.00530844	+	0.999986i	$0.498310\pi$
$380$	0	0
$381$	−3.69650	−0.189377
$382$	− 41.1389i	− 2.10485i
$383$	16.3701i	0.836474i	0.908338	+	0.418237i	$0.137352\pi$
$383$	16.3701i	0.836474i	−0.908338	+	0.418237i	$0.862648\pi$
$384$	17.3074	0.883215
$385$	0	0
$386$	−39.2873	−1.99967
$387$	3.94180i	0.200373i
$388$	− 12.1908i	− 0.618892i
$389$	−11.7627	−0.596393	−0.298197	−	0.954504i	$-0.596385\pi$
$389$	−11.7627	−0.596393	−0.298197	+	0.954504i	$0.596385\pi$
$390$	0	0
$391$	15.7651	0.797277
$392$	18.0096i	0.909621i
$393$	− 9.92811i	− 0.500807i
$394$	23.6382	1.19088
$395$	0	0
$396$	−10.1998	−0.512559
$397$	4.96134i	0.249002i	0.992219	+	0.124501i	$0.0397331\pi$
$397$	4.96134i	0.249002i	−0.992219	+	0.124501i	$0.960267\pi$
$398$	26.1992i	1.31325i
$399$	0.637993	0.0319396
$400$	0	0
$401$	36.1967	1.80758	0.903789	−	0.427979i	$-0.140774\pi$
$401$	36.1967	1.80758	0.903789	+	0.427979i	$0.140774\pi$
$402$	33.8936i	1.69046i
$403$	72.0103i	3.58709i
$404$	−48.3557	−2.40579
$405$	0	0
$406$	−0.362456	−0.0179884
$407$	− 13.9010i	− 0.689047i
$408$	19.7233i	0.976447i
$409$	16.1607	0.799094	0.399547	−	0.916713i	$-0.369168\pi$
$409$	16.1607	0.799094	0.399547	+	0.916713i	$0.369168\pi$
$410$	0	0
$411$	3.82810	0.188826
$412$	− 24.1233i	− 1.18847i
$413$	− 1.13005i	− 0.0556061i
$414$	−4.67903	−0.229962
$415$	0	0
$416$	−43.2331	−2.11968
$417$	2.06987i	0.101362i
$418$	29.3924i	1.43763i
$419$	33.5544	1.63924	0.819621	−	0.572906i	$-0.194184\pi$
$419$	33.5544	1.63924	0.819621	+	0.572906i	$0.194184\pi$
$420$	0	0
$421$	26.9847	1.31515	0.657577	−	0.753388i	$-0.271582\pi$
$421$	26.9847	1.31515	0.657577	+	0.753388i	$0.271582\pi$
$422$	47.9723i	2.33526i
$423$	5.61626i	0.273072i
$424$	−31.1990	−1.51515
$425$	0	0
$426$	7.78351	0.377112
$427$	− 1.82767i	− 0.0884471i
$428$	− 14.4687i	− 0.699373i
$429$	22.9296	1.10705
$430$	0	0
$431$	0.832366	0.0400937	0.0200468	−	0.999799i	$-0.493618\pi$
$431$	0.832366	0.0400937	0.0200468	+	0.999799i	$0.493618\pi$
$432$	0.424361i	0.0204171i
$433$	− 22.5647i	− 1.08439i	−0.840253	−	0.542195i	$-0.817593\pi$
$433$	− 22.5647i	− 1.08439i	0.840253	−	0.542195i	$-0.182407\pi$
$434$	−3.69865	−0.177541
$435$	0	0
$436$	−45.3625	−2.17247
$437$	8.23600i	0.393981i
$438$	− 27.3784i	− 1.30819i
$439$	−23.9583	−1.14347	−0.571734	−	0.820439i	$-0.693729\pi$
$439$	−23.9583	−1.14347	−0.571734	+	0.820439i	$0.693729\pi$
$440$	0	0
$441$	−6.97444	−0.332116
$442$	− 122.190i	− 5.81196i
$443$	17.4925i	0.831092i	0.909572	+	0.415546i	$0.136409\pi$
$443$	17.4925i	0.831092i	−0.909572	+	0.415546i	$0.863591\pi$
$444$	13.4294	0.637332
$445$	0	0
$446$	21.4663	1.01646
$447$	1.46609i	0.0693439i
$448$	− 2.08487i	− 0.0985010i
$449$	−4.22200	−0.199249	−0.0996243	−	0.995025i	$-0.531764\pi$
$449$	−4.22200	−0.199249	−0.0996243	+	0.995025i	$0.531764\pi$
$450$	0	0
$451$	16.6471	0.783884
$452$	12.8267i	0.603318i
$453$	− 20.1279i	− 0.945694i
$454$	−50.7866	−2.38353
$455$	0	0
$456$	−10.3038	−0.482520
$457$	1.28562i	0.0601389i	0.999548	+	0.0300694i	$0.00957284\pi$
$457$	1.28562i	0.0601389i	−0.999548	+	0.0300694i	$0.990427\pi$
$458$	4.60456i	0.215157i
$459$	−7.63808	−0.356515
$460$	0	0
$461$	−23.8534	−1.11097	−0.555483	−	0.831528i	$-0.687466\pi$
$461$	−23.8534	−1.11097	−0.555483	+	0.831528i	$0.687466\pi$
$462$	1.17773i	0.0547929i
$463$	14.1402i	0.657152i	0.944478	+	0.328576i	$0.106569\pi$
$463$	14.1402i	0.657152i	−0.944478	+	0.328576i	$0.893431\pi$
$464$	−0.424361	−0.0197005
$465$	0	0
$466$	25.0962	1.16256
$467$	− 7.06487i	− 0.326923i	−0.986550	−	0.163462i	$-0.947734\pi$
$467$	− 7.06487i	− 0.326923i	0.986550	−	0.163462i	$-0.0522660\pi$
$468$	22.1518i	1.02397i
$469$	2.39050	0.110383
$470$	0	0
$471$	7.09106	0.326739
$472$	18.2507i	0.840056i
$473$	12.8081i	0.588916i
$474$	28.8903	1.32698
$475$	0	0
$476$	3.83353	0.175710
$477$	− 12.0822i	− 0.553205i
$478$	− 5.08020i	− 0.232363i
$479$	−22.9561	−1.04889	−0.524444	−	0.851445i	$-0.675727\pi$
$479$	−22.9561	−1.04889	−0.524444	+	0.851445i	$0.675727\pi$
$480$	0	0
$481$	−30.1900	−1.37654
$482$	− 32.8342i	− 1.49556i
$483$	0.330009i	0.0150159i
$484$	1.38759	0.0630723
$485$	0	0
$486$	2.26695	0.102831
$487$	27.0319i	1.22493i	0.790496	+	0.612467i	$0.209823\pi$
$487$	27.0319i	1.22493i	−0.790496	+	0.612467i	$0.790177\pi$
$488$	29.5175i	1.33619i
$489$	6.58715	0.297881
$490$	0	0
$491$	−11.5498	−0.521235	−0.260617	−	0.965442i	$-0.583926\pi$
$491$	−11.5498	−0.521235	−0.260617	+	0.965442i	$0.583926\pi$
$492$	16.0824i	0.725051i
$493$	− 7.63808i	− 0.344002i
$494$	63.8340	2.87203
$495$	0	0
$496$	−4.33036	−0.194439
$497$	− 0.548966i	− 0.0246245i
$498$	− 5.88937i	− 0.263909i
$499$	−3.77942	−0.169190	−0.0845950	−	0.996415i	$-0.526960\pi$
$499$	−3.77942	−0.169190	−0.0845950	+	0.996415i	$0.526960\pi$
$500$	0	0
$501$	−10.6638	−0.476425
$502$	36.7346i	1.63955i
$503$	− 14.7684i	− 0.658489i	−0.944245	−	0.329244i	$-0.893206\pi$
$503$	− 14.7684i	− 0.658489i	0.944245	−	0.329244i	$-0.106794\pi$
$504$	−0.412864	−0.0183904
$505$	0	0
$506$	−15.2036	−0.675881
$507$	− 36.7983i	− 1.63427i
$508$	− 11.6036i	− 0.514826i
$509$	42.4182	1.88015	0.940077	−	0.340962i	$-0.110753\pi$
$509$	42.4182	1.88015	0.940077	+	0.340962i	$0.110753\pi$
$510$	0	0
$511$	−1.93098	−0.0854217
$512$	− 4.79143i	− 0.211753i
$513$	− 3.99028i	− 0.176175i
$514$	7.63831	0.336911
$515$	0	0
$516$	−12.3736	−0.544717
$517$	18.2489i	0.802586i
$518$	− 1.55064i	− 0.0681312i
$519$	13.8799	0.609258
$520$	0	0
$521$	20.3409	0.891152	0.445576	−	0.895244i	$-0.352999\pi$
$521$	20.3409	0.891152	0.445576	+	0.895244i	$0.352999\pi$
$522$	2.26695i	0.0992218i
$523$	1.52190i	0.0665481i	0.999446	+	0.0332740i	$0.0105934\pi$
$523$	1.52190i	0.0665481i	−0.999446	+	0.0332740i	$0.989407\pi$
$524$	31.1651	1.36145
$525$	0	0
$526$	4.07306	0.177594
$527$	− 77.9421i	− 3.39521i
$528$	1.37888i	0.0600080i
$529$	18.7398	0.814775
$530$	0	0
$531$	−7.06781	−0.306717
$532$	2.00271i	0.0868283i
$533$	− 36.1540i	− 1.56601i
$534$	−9.81965	−0.424938
$535$	0	0
$536$	−38.6074	−1.66758
$537$	11.1105i	0.479454i
$538$	− 0.265359i	− 0.0114404i
$539$	−22.6620	−0.976123
$540$	0	0
$541$	−9.40679	−0.404430	−0.202215	−	0.979341i	$-0.564814\pi$
$541$	−9.40679	−0.404430	−0.202215	+	0.979341i	$0.564814\pi$
$542$	9.21049i	0.395624i
$543$	10.9453i	0.469707i
$544$	46.7944	2.00629
$545$	0	0
$546$	2.55777	0.109463
$547$	− 19.7232i	− 0.843304i	−0.906758	−	0.421652i	$-0.861450\pi$
$547$	− 19.7232i	− 0.843304i	0.906758	−	0.421652i	$-0.138550\pi$
$548$	12.0167i	0.513328i
$549$	−11.4310	−0.487864
$550$	0	0
$551$	3.99028	0.169991
$552$	− 5.32976i	− 0.226850i
$553$	− 2.03762i	− 0.0866483i
$554$	28.4358	1.20812
$555$	0	0
$556$	−6.49749	−0.275555
$557$	− 9.01986i	− 0.382184i	−0.981572	−	0.191092i	$-0.938797\pi$
$557$	− 9.01986i	− 0.382184i	0.981572	−	0.191092i	$-0.0612029\pi$
$558$	23.1329i	0.979294i
$559$	27.8164	1.17651
$560$	0	0
$561$	−24.8184	−1.04784
$562$	6.41918i	0.270777i
$563$	17.5283i	0.738728i	0.929285	+	0.369364i	$0.120424\pi$
$563$	17.5283i	0.738728i	−0.929285	+	0.369364i	$0.879576\pi$
$564$	−17.6298	−0.742350
$565$	0	0
$566$	63.9845	2.68947
$567$	− 0.159887i	− 0.00671462i
$568$	8.86599i	0.372009i
$569$	−32.3981	−1.35820	−0.679099	−	0.734046i	$-0.737629\pi$
$569$	−32.3981	−1.35820	−0.679099	+	0.734046i	$0.737629\pi$
$570$	0	0
$571$	−11.8393	−0.495458	−0.247729	−	0.968829i	$-0.579684\pi$
$571$	−11.8393	−0.495458	−0.247729	+	0.968829i	$0.579684\pi$
$572$	71.9778i	3.00954i
$573$	18.1472i	0.758112i
$574$	1.85697	0.0775085
$575$	0	0
$576$	−13.0397	−0.543320
$577$	0.192778i	0.00802545i	0.999992	+	0.00401273i	$0.00127729\pi$
$577$	0.192778i	0.00802545i	−0.999992	+	0.00401273i	$0.998723\pi$
$578$	93.7165i	3.89809i
$579$	17.3305	0.720229
$580$	0	0
$581$	−0.415374	−0.0172326
$582$	8.80383i	0.364931i
$583$	− 39.2587i	− 1.62593i
$584$	31.1861	1.29049
$585$	0	0
$586$	49.7227	2.05403
$587$	− 34.5089i	− 1.42433i	−0.702010	−	0.712167i	$-0.747714\pi$
$587$	− 34.5089i	− 1.42433i	0.702010	−	0.712167i	$-0.252286\pi$
$588$	− 21.8933i	− 0.902863i
$589$	40.7184	1.67777
$590$	0	0
$591$	−10.4273	−0.428922
$592$	− 1.81548i	− 0.0746158i
$593$	2.42748i	0.0996846i	0.998757	+	0.0498423i	$0.0158719\pi$
$593$	2.42748i	0.0996846i	−0.998757	+	0.0498423i	$0.984128\pi$
$594$	7.36601	0.302231
$595$	0	0
$596$	−4.60218	−0.188513
$597$	− 11.5570i	− 0.472997i
$598$	33.0189i	1.35024i
$599$	−29.3312	−1.19844	−0.599220	−	0.800585i	$-0.704522\pi$
$599$	−29.3312	−1.19844	−0.599220	+	0.800585i	$0.704522\pi$
$600$	0	0
$601$	29.5631	1.20590	0.602952	−	0.797778i	$-0.293991\pi$
$601$	29.5631	1.20590	0.602952	+	0.797778i	$0.293991\pi$
$602$	1.42873i	0.0582306i
$603$	− 14.9512i	− 0.608860i
$604$	63.1831	2.57089
$605$	0	0
$606$	34.9212	1.41858
$607$	− 33.1756i	− 1.34656i	−0.739390	−	0.673278i	$-0.764886\pi$
$607$	− 33.1756i	− 1.34656i	0.739390	−	0.673278i	$-0.235114\pi$
$608$	24.4463i	0.991427i
$609$	0.159887	0.00647894
$610$	0	0
$611$	39.6327	1.60337
$612$	− 23.9765i	− 0.969193i
$613$	− 13.9979i	− 0.565371i	−0.959213	−	0.282686i	$-0.908775\pi$
$613$	− 13.9979i	− 0.565371i	0.959213	−	0.282686i	$-0.0912253\pi$
$614$	1.04637	0.0422279
$615$	0	0
$616$	−1.34152	−0.0540514
$617$	29.9344i	1.20511i	0.798077	+	0.602556i	$0.205851\pi$
$617$	29.9344i	1.20511i	−0.798077	+	0.602556i	$0.794149\pi$
$618$	17.4212i	0.700782i
$619$	14.9032	0.599009	0.299505	−	0.954095i	$-0.403179\pi$
$619$	14.9032	0.599009	0.299505	+	0.954095i	$0.403179\pi$
$620$	0	0
$621$	2.06402	0.0828261
$622$	− 62.4561i	− 2.50426i
$623$	0.692574i	0.0277474i
$624$	2.99463	0.119881
$625$	0	0
$626$	33.8050	1.35112
$627$	− 12.9656i	− 0.517796i
$628$	22.2594i	0.888245i
$629$	32.6769	1.30291
$630$	0	0
$631$	−28.8643	−1.14907	−0.574534	−	0.818480i	$-0.694817\pi$
$631$	−28.8643	−1.14907	−0.574534	+	0.818480i	$0.694817\pi$
$632$	32.9082i	1.30902i
$633$	− 21.1616i	− 0.841097i
$634$	51.9735	2.06413
$635$	0	0
$636$	37.9269	1.50390
$637$	49.2171i	1.95005i
$638$	7.36601i	0.291623i
$639$	−3.43347	−0.135826
$640$	0	0
$641$	44.0167	1.73856	0.869278	−	0.494324i	$-0.164585\pi$
$641$	44.0167	1.73856	0.869278	+	0.494324i	$0.164585\pi$
$642$	10.4489i	0.412386i
$643$	− 29.6239i	− 1.16825i	−0.811663	−	0.584125i	$-0.801438\pi$
$643$	− 29.6239i	− 1.16825i	0.811663	−	0.584125i	$-0.198562\pi$
$644$	−1.03592	−0.0408211
$645$	0	0
$646$	−69.0923	−2.71840
$647$	39.3943i	1.54875i	0.632727	+	0.774375i	$0.281936\pi$
$647$	39.3943i	1.54875i	−0.632727	+	0.774375i	$0.718064\pi$
$648$	2.58223i	0.101439i
$649$	−22.9654	−0.901473
$650$	0	0
$651$	1.63155	0.0639455
$652$	20.6776i	0.809796i
$653$	22.3518i	0.874692i	0.899293	+	0.437346i	$0.144082\pi$
$653$	22.3518i	0.874692i	−0.899293	+	0.437346i	$0.855918\pi$
$654$	32.7595	1.28100
$655$	0	0
$656$	2.17413	0.0848855
$657$	12.0772i	0.471176i
$658$	2.03565i	0.0793577i
$659$	−42.1979	−1.64380	−0.821898	−	0.569634i	$-0.807085\pi$
$659$	−42.1979	−1.64380	−0.821898	+	0.569634i	$0.807085\pi$
$660$	0	0
$661$	8.38035	0.325958	0.162979	−	0.986630i	$-0.447890\pi$
$661$	8.38035	0.325958	0.162979	+	0.986630i	$0.447890\pi$
$662$	7.32559i	0.284717i
$663$	53.9003i	2.09332i
$664$	6.70843	0.260337
$665$	0	0
$666$	−9.69836	−0.375804
$667$	2.06402i	0.0799191i
$668$	− 33.4746i	− 1.29517i
$669$	−9.46925	−0.366102
$670$	0	0
$671$	−37.1428	−1.43388
$672$	0.979541i	0.0377866i
$673$	− 3.13725i	− 0.120932i	−0.998170	−	0.0604660i	$-0.980741\pi$
$673$	− 3.13725i	− 0.120932i	0.998170	−	0.0604660i	$-0.0192587\pi$
$674$	−65.2941	−2.51504
$675$	0	0
$676$	115.512	4.44279
$677$	− 16.2776i	− 0.625600i	−0.949819	−	0.312800i	$-0.898733\pi$
$677$	− 16.2776i	− 0.625600i	0.949819	−	0.312800i	$-0.101267\pi$
$678$	− 9.26310i	− 0.355747i
$679$	0.620929	0.0238291
$680$	0	0
$681$	22.4030	0.858486
$682$	75.1658i	2.87825i
$683$	− 1.78249i	− 0.0682050i	−0.999418	−	0.0341025i	$-0.989143\pi$
$683$	− 1.78249i	− 0.0682050i	0.999418	−	0.0341025i	$-0.0108573\pi$
$684$	12.5258	0.478935
$685$	0	0
$686$	−5.06512	−0.193387
$687$	− 2.03117i	− 0.0774939i
$688$	1.67275i	0.0637728i
$689$	−85.2614	−3.24820
$690$	0	0
$691$	−20.8504	−0.793187	−0.396594	−	0.917994i	$-0.629808\pi$
$691$	−20.8504	−0.793187	−0.396594	+	0.917994i	$0.629808\pi$
$692$	43.5699i	1.65628i
$693$	− 0.519521i	− 0.0197350i
$694$	37.2177	1.41276
$695$	0	0
$696$	−2.58223	−0.0978791
$697$	39.1322i	1.48224i
$698$	− 41.2828i	− 1.56258i
$699$	−11.0704	−0.418722
$700$	0	0
$701$	32.5504	1.22941	0.614707	−	0.788756i	$-0.289274\pi$
$701$	32.5504	1.22941	0.614707	+	0.788756i	$0.289274\pi$
$702$	− 15.9974i	− 0.603783i
$703$	17.0710i	0.643845i
$704$	−42.3698	−1.59687
$705$	0	0
$706$	−42.7978	−1.61072
$707$	− 2.46297i	− 0.0926295i
$708$	− 22.1864i	− 0.833815i
$709$	−5.93195	−0.222779	−0.111390	−	0.993777i	$-0.535530\pi$
$709$	−5.93195	−0.222779	−0.111390	+	0.993777i	$0.535530\pi$
$710$	0	0
$711$	−12.7441	−0.477942
$712$	− 11.1853i	− 0.419187i
$713$	21.0621i	0.788781i
$714$	−2.76847	−0.103607
$715$	0	0
$716$	−34.8767	−1.30340
$717$	2.24098i	0.0836911i
$718$	32.7574i	1.22250i
$719$	13.5279	0.504505	0.252252	−	0.967661i	$-0.418829\pi$
$719$	13.5279	0.504505	0.252252	+	0.967661i	$0.418829\pi$
$720$	0	0
$721$	1.22871	0.0457594
$722$	6.97701i	0.259657i
$723$	14.4838i	0.538660i
$724$	−34.3581	−1.27691
$725$	0	0
$726$	−1.00208	−0.0371907
$727$	12.7407i	0.472525i	0.971689	+	0.236263i	$0.0759226\pi$
$727$	12.7407i	0.472525i	−0.971689	+	0.236263i	$0.924077\pi$
$728$	2.91350i	0.107981i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−30.1078	−1.11358
$732$	− 35.8828i	− 1.32627i
$733$	30.9422i	1.14288i	0.820645	+	0.571438i	$0.193614\pi$
$733$	30.9422i	1.14288i	−0.820645	+	0.571438i	$0.806386\pi$
$734$	47.8716	1.76697
$735$	0	0
$736$	−12.6451	−0.466105
$737$	− 48.5809i	− 1.78950i
$738$	− 11.6143i	− 0.427528i
$739$	−35.0047	−1.28767	−0.643834	−	0.765166i	$-0.722657\pi$
$739$	−35.0047	−1.28767	−0.643834	+	0.765166i	$0.722657\pi$
$740$	0	0
$741$	−28.1585	−1.03443
$742$	− 4.37926i	− 0.160768i
$743$	− 12.5515i	− 0.460468i	−0.973135	−	0.230234i	$-0.926051\pi$
$743$	− 12.5515i	− 0.460468i	0.973135	−	0.230234i	$-0.0739492\pi$
$744$	−26.3501	−0.966041
$745$	0	0
$746$	−38.8068	−1.42082
$747$	2.59792i	0.0950530i
$748$	− 77.9069i	− 2.84856i
$749$	0.736956	0.0269278
$750$	0	0
$751$	−33.8278	−1.23439	−0.617197	−	0.786809i	$-0.711732\pi$
$751$	−33.8278	−1.23439	−0.617197	+	0.786809i	$0.711732\pi$
$752$	2.38332i	0.0869108i
$753$	− 16.2044i	− 0.590522i
$754$	15.9974	0.582591
$755$	0	0
$756$	0.501897	0.0182538
$757$	6.60568i	0.240088i	0.992769	+	0.120044i	$0.0383035\pi$
$757$	6.60568i	0.240088i	−0.992769	+	0.120044i	$0.961697\pi$
$758$	− 0.468553i	− 0.0170186i
$759$	6.70661	0.243435
$760$	0	0
$761$	−22.8638	−0.828814	−0.414407	−	0.910092i	$-0.636011\pi$
$761$	−22.8638	−0.828814	−0.414407	+	0.910092i	$0.636011\pi$
$762$	8.37978i	0.303568i
$763$	− 2.31051i	− 0.0836461i
$764$	−56.9656	−2.06094
$765$	0	0
$766$	37.1103	1.34085
$767$	49.8760i	1.80092i
$768$	− 13.1557i	− 0.474716i
$769$	35.0078	1.26241	0.631206	−	0.775615i	$-0.282560\pi$
$769$	35.0078	1.26241	0.631206	+	0.775615i	$0.282560\pi$
$770$	0	0
$771$	−3.36942	−0.121347
$772$	54.4016i	1.95796i
$773$	17.7019i	0.636691i	0.947975	+	0.318346i	$0.103127\pi$
$773$	17.7019i	0.636691i	−0.947975	+	0.318346i	$0.896873\pi$
$774$	8.93586	0.321193
$775$	0	0
$776$	−10.0282	−0.359992
$777$	0.684020i	0.0245391i
$778$	26.6655i	0.956005i
$779$	−20.4434	−0.732460
$780$	0	0
$781$	−11.1564	−0.399206
$782$	− 35.7388i	− 1.27802i
$783$	− 1.00000i	− 0.0357371i
$784$	−2.95968	−0.105703
$785$	0	0
$786$	−22.5066	−0.802782
$787$	− 5.13176i	− 0.182928i	−0.995808	−	0.0914638i	$-0.970845\pi$
$787$	− 5.13176i	− 0.182928i	0.995808	−	0.0914638i	$-0.0291546\pi$
$788$	− 32.7321i	− 1.16603i
$789$	−1.79671	−0.0639647
$790$	0	0
$791$	−0.653321	−0.0232294
$792$	8.39044i	0.298141i
$793$	80.6662i	2.86454i
$794$	11.2471	0.399145
$795$	0	0
$796$	36.2783	1.28585
$797$	− 27.5492i	− 0.975842i	−0.872888	−	0.487921i	$-0.837755\pi$
$797$	− 27.5492i	− 0.975842i	0.872888	−	0.487921i	$-0.162245\pi$
$798$	− 1.44630i	− 0.0511984i
$799$	−42.8974	−1.51760
$800$	0	0
$801$	4.33165	0.153051
$802$	− 82.0562i	− 2.89751i
$803$	39.2424i	1.38484i
$804$	46.9329	1.65520
$805$	0	0
$806$	163.244	5.75002
$807$	0.117055i	0.00412054i
$808$	39.7778i	1.39938i
$809$	5.51555	0.193917	0.0969583	−	0.995288i	$-0.469089\pi$
$809$	5.51555	0.193917	0.0969583	+	0.995288i	$0.469089\pi$
$810$	0	0
$811$	−17.1711	−0.602959	−0.301479	−	0.953473i	$-0.597480\pi$
$811$	−17.1711	−0.602959	−0.301479	+	0.953473i	$0.597480\pi$
$812$	0.501897i	0.0176131i
$813$	− 4.06294i	− 0.142493i
$814$	−31.5129	−1.10453
$815$	0	0
$816$	−3.24131	−0.113468
$817$	− 15.7288i	− 0.550283i
$818$	− 36.6355i	− 1.28093i
$819$	−1.12829	−0.0394256
$820$	0	0
$821$	6.53740	0.228157	0.114078	−	0.993472i	$-0.463609\pi$
$821$	6.53740	0.228157	0.114078	+	0.993472i	$0.463609\pi$
$822$	− 8.67813i	− 0.302684i
$823$	− 35.8588i	− 1.24996i	−0.780641	−	0.624979i	$-0.785107\pi$
$823$	− 35.8588i	− 1.24996i	0.780641	−	0.624979i	$-0.214893\pi$
$824$	−19.8440	−0.691299
$825$	0	0
$826$	−2.56177	−0.0891354
$827$	2.36177i	0.0821269i	0.999157	+	0.0410635i	$0.0130746\pi$
$827$	2.36177i	0.0821269i	−0.999157	+	0.0410635i	$0.986925\pi$
$828$	6.47910i	0.225164i
$829$	−54.0332	−1.87665	−0.938325	−	0.345754i	$-0.887623\pi$
$829$	−54.0332	−1.87665	−0.938325	+	0.345754i	$0.887623\pi$
$830$	0	0
$831$	−12.5436	−0.435134
$832$	92.0182i	3.19016i
$833$	− 53.2713i	− 1.84574i
$834$	4.69231	0.162481
$835$	0	0
$836$	40.7000	1.40764
$837$	− 10.2044i	− 0.352716i
$838$	− 76.0663i	− 2.62767i
$839$	−27.6639	−0.955063	−0.477532	−	0.878615i	$-0.658468\pi$
$839$	−27.6639	−0.955063	−0.477532	+	0.878615i	$0.658468\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 61.1730i	− 2.10816i
$843$	− 2.83163i	− 0.0975266i
$844$	66.4278	2.28654
$845$	0	0
$846$	12.7318	0.437728
$847$	0.0706761i	0.00242846i
$848$	− 5.12721i	− 0.176069i
$849$	−28.2249	−0.968676
$850$	0	0
$851$	−8.83017	−0.302694
$852$	− 10.7779i	− 0.369245i
$853$	16.7180i	0.572413i	0.958168	+	0.286207i	$0.0923944\pi$
$853$	16.7180i	0.572413i	−0.958168	+	0.286207i	$0.907606\pi$
$854$	−4.14324	−0.141779
$855$	0	0
$856$	−11.9021	−0.406805
$857$	50.6304i	1.72950i	0.502202	+	0.864750i	$0.332523\pi$
$857$	50.6304i	1.72950i	−0.502202	+	0.864750i	$0.667477\pi$
$858$	− 51.9804i	− 1.77458i
$859$	23.0473	0.786363	0.393182	−	0.919461i	$-0.371374\pi$
$859$	23.0473	0.786363	0.393182	+	0.919461i	$0.371374\pi$
$860$	0	0
$861$	−0.819148	−0.0279165
$862$	− 1.88693i	− 0.0642692i
$863$	45.4971i	1.54874i	0.632733	+	0.774370i	$0.281933\pi$
$863$	45.4971i	1.54874i	−0.632733	+	0.774370i	$0.718067\pi$
$864$	6.12646	0.208426
$865$	0	0
$866$	−51.1531	−1.73825
$867$	− 41.3403i	− 1.40399i
$868$	5.12156i	0.173837i
$869$	−41.4095	−1.40472
$870$	0	0
$871$	−105.507	−3.57498
$872$	37.3155i	1.26366i
$873$	− 3.88355i	− 0.131438i
$874$	18.6706	0.631543
$875$	0	0
$876$	−37.9112	−1.28090
$877$	− 6.44199i	− 0.217531i	−0.994067	−	0.108765i	$-0.965310\pi$
$877$	− 6.44199i	− 0.217531i	0.994067	−	0.108765i	$-0.0346897\pi$
$878$	54.3124i	1.83295i
$879$	−21.9337	−0.739806
$880$	0	0
$881$	−43.3346	−1.45998	−0.729990	−	0.683458i	$-0.760475\pi$
$881$	−43.3346	−1.45998	−0.729990	+	0.683458i	$0.760475\pi$
$882$	15.8107i	0.532375i
$883$	− 24.6736i	− 0.830333i	−0.909745	−	0.415166i	$-0.863723\pi$
$883$	− 24.6736i	− 0.830333i	0.909745	−	0.415166i	$-0.136277\pi$
$884$	−169.197	−5.69072
$885$	0	0
$886$	39.6546	1.33222
$887$	− 37.1527i	− 1.24747i	−0.781637	−	0.623733i	$-0.785615\pi$
$887$	− 37.1527i	− 1.24747i	0.781637	−	0.623733i	$-0.214385\pi$
$888$	− 11.0472i	− 0.370718i
$889$	0.591021	0.0198222
$890$	0	0
$891$	−3.24930	−0.108856
$892$	− 29.7247i	− 0.995255i
$893$	− 22.4104i	− 0.749936i
$894$	3.32357	0.111157
$895$	0	0
$896$	−2.76723	−0.0924466
$897$	− 14.5653i	− 0.486322i
$898$	9.57108i	0.319391i
$899$	10.2044	0.340336
$900$	0	0
$901$	92.2847	3.07445
$902$	− 37.7383i	− 1.25655i
$903$	− 0.630241i	− 0.0209731i
$904$	10.5514	0.350933
$905$	0	0
$906$	−45.6291	−1.51593
$907$	− 7.49457i	− 0.248853i	−0.992229	−	0.124427i	$-0.960291\pi$
$907$	− 7.49457i	− 0.248853i	0.992229	−	0.124427i	$-0.0397091\pi$
$908$	70.3248i	2.33381i
$909$	−15.4045	−0.510934
$910$	0	0
$911$	48.6818	1.61290	0.806449	−	0.591303i	$-0.201386\pi$
$911$	48.6818	1.61290	0.806449	+	0.591303i	$0.201386\pi$
$912$	− 1.69332i	− 0.0560714i
$913$	8.44143i	0.279371i
$914$	2.91444	0.0964012
$915$	0	0
$916$	6.37598	0.210668
$917$	1.58737i	0.0524197i
$918$	17.3152i	0.571486i
$919$	26.1563	0.862816	0.431408	−	0.902157i	$-0.358017\pi$
$919$	26.1563	0.862816	0.431408	+	0.902157i	$0.358017\pi$
$920$	0	0
$921$	−0.461574	−0.0152094
$922$	54.0746i	1.78085i
$923$	24.2293i	0.797515i
$924$	1.63081	0.0536498
$925$	0	0
$926$	32.0552	1.05340
$927$	− 7.68484i	− 0.252403i
$928$	6.12646i	0.201111i
$929$	8.15366	0.267513	0.133756	−	0.991014i	$-0.457296\pi$
$929$	8.15366	0.267513	0.133756	+	0.991014i	$0.457296\pi$
$930$	0	0
$931$	27.8299	0.912089
$932$	− 34.7509i	− 1.13830i
$933$	27.5507i	0.901968i
$934$	−16.0157	−0.524051
$935$	0	0
$936$	18.2222	0.595612
$937$	− 41.9169i	− 1.36936i	−0.728842	−	0.684682i	$-0.759941\pi$
$937$	− 41.9169i	− 1.36936i	0.728842	−	0.684682i	$-0.240059\pi$
$938$	− 5.41915i	− 0.176941i
$939$	−14.9121	−0.486638
$940$	0	0
$941$	14.4789	0.471998	0.235999	−	0.971753i	$-0.424164\pi$
$941$	14.4789	0.471998	0.235999	+	0.971753i	$0.424164\pi$
$942$	− 16.0751i	− 0.523755i
$943$	− 10.5746i	− 0.344356i
$944$	−2.99931	−0.0976191
$945$	0	0
$946$	29.0353	0.944020
$947$	− 1.83838i	− 0.0597392i	−0.999554	−	0.0298696i	$-0.990491\pi$
$947$	− 1.83838i	− 0.0597392i	0.999554	−	0.0298696i	$-0.00950921\pi$
$948$	− 40.0048i	− 1.29929i
$949$	85.2262	2.76656
$950$	0	0
$951$	−22.9266	−0.743446
$952$	− 3.15349i	− 0.102205i
$953$	− 49.5140i	− 1.60391i	−0.597382	−	0.801957i	$-0.703792\pi$
$953$	− 49.5140i	− 1.60391i	0.597382	−	0.801957i	$-0.296208\pi$
$954$	−27.3897	−0.886776
$955$	0	0
$956$	−7.03461	−0.227516
$957$	− 3.24930i	− 0.105035i
$958$	52.0403i	1.68135i
$959$	−0.612063	−0.0197646
$960$	0	0
$961$	73.1299	2.35903
$962$	68.4393i	2.20657i
$963$	− 4.60924i	− 0.148531i
$964$	−45.4658	−1.46436
$965$	0	0
$966$	0.748115	0.0240702
$967$	− 5.90299i	− 0.189827i	−0.995486	−	0.0949137i	$-0.969742\pi$
$967$	− 5.90299i	− 0.189827i	0.995486	−	0.0949137i	$-0.0302575\pi$
$968$	− 1.14144i	− 0.0366874i
$969$	30.4781	0.979096
$970$	0	0
$971$	−35.7964	−1.14876	−0.574380	−	0.818588i	$-0.694757\pi$
$971$	−35.7964	−1.14876	−0.574380	+	0.818588i	$0.694757\pi$
$972$	− 3.13907i	− 0.100686i
$973$	− 0.330946i	− 0.0106096i
$974$	61.2801	1.96354
$975$	0	0
$976$	−4.85088	−0.155273
$977$	1.79673i	0.0574825i	0.999587	+	0.0287412i	$0.00914988\pi$
$977$	1.79673i	0.0574825i	−0.999587	+	0.0287412i	$0.990850\pi$
$978$	− 14.9328i	− 0.477497i
$979$	14.0748	0.449834
$980$	0	0
$981$	−14.4509	−0.461382
$982$	26.1828i	0.835528i
$983$	6.24151i	0.199073i	0.995034	+	0.0995365i	$0.0317360\pi$
$983$	6.24151i	0.199073i	−0.995034	+	0.0995365i	$0.968264\pi$
$984$	13.2295	0.421742
$985$	0	0
$986$	−17.3152	−0.551427
$987$	− 0.897966i	− 0.0285826i
$988$	− 88.3917i	− 2.81211i
$989$	8.13593	0.258708
$990$	0	0
$991$	41.0410	1.30371	0.651855	−	0.758344i	$-0.273991\pi$
$991$	41.0410	1.30371	0.651855	+	0.758344i	$0.273991\pi$
$992$	62.5169i	1.98491i
$993$	− 3.23147i	− 0.102548i
$994$	−1.24448	−0.0394725
$995$	0	0
$996$	−8.15507	−0.258403
$997$	− 29.8910i	− 0.946657i	−0.880886	−	0.473329i	$-0.843052\pi$
$997$	− 29.8910i	− 0.946657i	0.880886	−	0.473329i	$-0.156948\pi$
$998$	8.56776i	0.271208i
$999$	4.27815	0.135355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.c.o.349.3		14
5.2	odd	4		2175.2.a.bb.1.6	yes	7
5.3	odd	4		2175.2.a.ba.1.2	✓	7
5.4	even	2	inner	2175.2.c.o.349.12		14
15.2	even	4		6525.2.a.bu.1.2		7
15.8	even	4		6525.2.a.bx.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2175.2.a.ba.1.2	✓	7	5.3	odd	4
2175.2.a.bb.1.6	yes	7	5.2	odd	4
2175.2.c.o.349.3		14	1.1	even	1	trivial
2175.2.c.o.349.12		14	5.4	even	2	inner
6525.2.a.bu.1.2		7	15.2	even	4
6525.2.a.bx.1.6		7	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.26695i q^{2} +1.00000i q^{3} -3.13907 q^{4} +2.26695 q^{6} -0.159887i q^{7} +2.58223i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.26695i q^{2} +1.00000i q^{3} -3.13907 q^{4} +2.26695 q^{6} -0.159887i q^{7} +2.58223i q^{8} -1.00000 q^{9} -3.24930 q^{11} -3.13907i q^{12} +7.05679i q^{13} -0.362456 q^{14} -0.424361 q^{16} -7.63808i q^{17} +2.26695i q^{18} +3.99028 q^{19} +0.159887 q^{21} +7.36601i q^{22} +2.06402i q^{23} -2.58223 q^{24} +15.9974 q^{26} -1.00000i q^{27} +0.501897i q^{28} +1.00000 q^{29} +10.2044 q^{31} +6.12646i q^{32} -3.24930i q^{33} -17.3152 q^{34} +3.13907 q^{36} +4.27815i q^{37} -9.04576i q^{38} -7.05679 q^{39} -5.12330 q^{41} -0.362456i q^{42} -3.94180i q^{43} +10.1998 q^{44} +4.67903 q^{46} -5.61626i q^{47} -0.424361i q^{48} +6.97444 q^{49} +7.63808 q^{51} -22.1518i q^{52} +12.0822i q^{53} -2.26695 q^{54} +0.412864 q^{56} +3.99028i q^{57} -2.26695i q^{58} +7.06781 q^{59} +11.4310 q^{61} -23.1329i q^{62} +0.159887i q^{63} +13.0397 q^{64} -7.36601 q^{66} +14.9512i q^{67} +23.9765i q^{68} -2.06402 q^{69} +3.43347 q^{71} -2.58223i q^{72} -12.0772i q^{73} +9.69836 q^{74} -12.5258 q^{76} +0.519521i q^{77} +15.9974i q^{78} +12.7441 q^{79} +1.00000 q^{81} +11.6143i q^{82} -2.59792i q^{83} -0.501897 q^{84} -8.93586 q^{86} +1.00000i q^{87} -8.39044i q^{88} -4.33165 q^{89} +1.12829 q^{91} -6.47910i q^{92} +10.2044i q^{93} -12.7318 q^{94} -6.12646 q^{96} +3.88355i q^{97} -15.8107i q^{98} +3.24930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 20 q^{4} + 4 q^{6} - 14 q^{9}+O(q^{10}) \) 14 * q - 20 * q^4 + 4 * q^6 - 14 * q^9	\( 14 q - 20 q^{4} + 4 q^{6} - 14 q^{9} + 8 q^{11} - 30 q^{14} + 24 q^{16} - 30 q^{19} - 2 q^{21} - 6 q^{24} + 12 q^{26} + 14 q^{29} + 10 q^{31} - 14 q^{34} + 20 q^{36} + 2 q^{39} + 44 q^{41} - 30 q^{44} - 8 q^{46} - 24 q^{49} + 16 q^{51} - 4 q^{54} + 28 q^{56} - 12 q^{59} + 46 q^{61} - 10 q^{64} + 6 q^{66} - 28 q^{69} + 52 q^{71} + 20 q^{74} + 92 q^{76} - 28 q^{79} + 14 q^{81} + 48 q^{84} + 88 q^{86} - 28 q^{89} + 26 q^{91} + 6 q^{94} + 36 q^{96} - 8 q^{99}+O(q^{100}) \) 14 * q - 20 * q^4 + 4 * q^6 - 14 * q^9 + 8 * q^11 - 30 * q^14 + 24 * q^16 - 30 * q^19 - 2 * q^21 - 6 * q^24 + 12 * q^26 + 14 * q^29 + 10 * q^31 - 14 * q^34 + 20 * q^36 + 2 * q^39 + 44 * q^41 - 30 * q^44 - 8 * q^46 - 24 * q^49 + 16 * q^51 - 4 * q^54 + 28 * q^56 - 12 * q^59 + 46 * q^61 - 10 * q^64 + 6 * q^66 - 28 * q^69 + 52 * q^71 + 20 * q^74 + 92 * q^76 - 28 * q^79 + 14 * q^81 + 48 * q^84 + 88 * q^86 - 28 * q^89 + 26 * q^91 + 6 * q^94 + 36 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more