LMFDB - Embedded newform 6025.2.a.n.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.11018 q^{2} -0.936293 q^{3} -0.767491 q^{4} +1.03946 q^{6} -2.02452 q^{7} +3.07242 q^{8} -2.12335 q^{9} +O(q^{10})$	\(q-1.11018 q^{2} -0.936293 q^{3} -0.767491 q^{4} +1.03946 q^{6} -2.02452 q^{7} +3.07242 q^{8} -2.12335 q^{9} +0.335721 q^{11} +0.718597 q^{12} -1.60715 q^{13} +2.24759 q^{14} -1.87598 q^{16} -0.0940948 q^{17} +2.35731 q^{18} -8.15102 q^{19} +1.89555 q^{21} -0.372712 q^{22} -8.72209 q^{23} -2.87669 q^{24} +1.78424 q^{26} +4.79696 q^{27} +1.55380 q^{28} -2.89254 q^{29} -0.472640 q^{31} -4.06217 q^{32} -0.314333 q^{33} +0.104463 q^{34} +1.62966 q^{36} +0.470775 q^{37} +9.04913 q^{38} +1.50477 q^{39} -2.89531 q^{41} -2.10441 q^{42} -8.33318 q^{43} -0.257663 q^{44} +9.68312 q^{46} +10.8023 q^{47} +1.75646 q^{48} -2.90131 q^{49} +0.0881004 q^{51} +1.23348 q^{52} -5.02449 q^{53} -5.32551 q^{54} -6.22020 q^{56} +7.63175 q^{57} +3.21125 q^{58} -5.99027 q^{59} -2.64144 q^{61} +0.524718 q^{62} +4.29878 q^{63} +8.26171 q^{64} +0.348968 q^{66} +4.48853 q^{67} +0.0722169 q^{68} +8.16643 q^{69} -9.82049 q^{71} -6.52385 q^{72} +7.64260 q^{73} -0.522647 q^{74} +6.25584 q^{76} -0.679674 q^{77} -1.67057 q^{78} -7.18860 q^{79} +1.87870 q^{81} +3.21433 q^{82} +0.911638 q^{83} -1.45482 q^{84} +9.25136 q^{86} +2.70826 q^{87} +1.03148 q^{88} -16.8596 q^{89} +3.25372 q^{91} +6.69413 q^{92} +0.442530 q^{93} -11.9926 q^{94} +3.80339 q^{96} -16.5498 q^{97} +3.22098 q^{98} -0.712854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * 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 $

$2$	−1.11018	−0.785019	−0.392509	−	0.919748i	$-0.628393\pi$
$2$	−1.11018	−0.785019	−0.392509	+	0.919748i	$0.628393\pi$
$3$	−0.936293	−0.540569	−0.270285	−	0.962780i	$-0.587118\pi$
$3$	−0.936293	−0.540569	−0.270285	+	0.962780i	$0.587118\pi$
$4$	−0.767491	−0.383746
$5$	0	0
$5$	0	0
$6$	1.03946	0.424357
$7$	−2.02452	−0.765198	−0.382599	−	0.923915i	$-0.624971\pi$
$7$	−2.02452	−0.765198	−0.382599	+	0.923915i	$0.624971\pi$
$8$	3.07242	1.08627
$9$	−2.12335	−0.707785
$10$	0	0
$11$	0.335721	0.101224	0.0506118	−	0.998718i	$-0.483883\pi$
$11$	0.335721	0.101224	0.0506118	+	0.998718i	$0.483883\pi$
$12$	0.718597	0.207441
$13$	−1.60715	−0.445744	−0.222872	−	0.974848i	$-0.571543\pi$
$13$	−1.60715	−0.445744	−0.222872	+	0.974848i	$0.571543\pi$
$14$	2.24759	0.600695
$15$	0	0
$16$	−1.87598	−0.468994
$17$	−0.0940948	−0.0228213	−0.0114107	−	0.999935i	$-0.503632\pi$
$17$	−0.0940948	−0.0228213	−0.0114107	+	0.999935i	$0.503632\pi$
$18$	2.35731	0.555624
$19$	−8.15102	−1.86997	−0.934986	−	0.354684i	$-0.884588\pi$
$19$	−8.15102	−1.86997	−0.934986	+	0.354684i	$0.884588\pi$
$20$	0	0
$21$	1.89555	0.413642
$22$	−0.372712	−0.0794624
$23$	−8.72209	−1.81868	−0.909341	−	0.416052i	$-0.863413\pi$
$23$	−8.72209	−1.81868	−0.909341	+	0.416052i	$0.863413\pi$
$24$	−2.87669	−0.587202
$25$	0	0
$26$	1.78424	0.349918
$27$	4.79696	0.923176
$28$	1.55380	0.293641
$29$	−2.89254	−0.537131	−0.268565	−	0.963261i	$-0.586550\pi$
$29$	−2.89254	−0.537131	−0.268565	+	0.963261i	$0.586550\pi$
$30$	0	0
$31$	−0.472640	−0.0848887	−0.0424444	−	0.999099i	$-0.513515\pi$
$31$	−0.472640	−0.0848887	−0.0424444	+	0.999099i	$0.513515\pi$
$32$	−4.06217	−0.718097
$33$	−0.314333	−0.0547184
$34$	0.104463	0.0179152
$35$	0	0
$36$	1.62966	0.271609
$37$	0.470775	0.0773950	0.0386975	−	0.999251i	$-0.487679\pi$
$37$	0.470775	0.0773950	0.0386975	+	0.999251i	$0.487679\pi$
$38$	9.04913	1.46796
$39$	1.50477	0.240956
$40$	0	0
$41$	−2.89531	−0.452172	−0.226086	−	0.974107i	$-0.572593\pi$
$41$	−2.89531	−0.452172	−0.226086	+	0.974107i	$0.572593\pi$
$42$	−2.10441	−0.324717
$43$	−8.33318	−1.27080	−0.635399	−	0.772184i	$-0.719164\pi$
$43$	−8.33318	−1.27080	−0.635399	+	0.772184i	$0.719164\pi$
$44$	−0.257663	−0.0388441
$45$	0	0
$46$	9.68312	1.42770
$47$	10.8023	1.57568	0.787842	−	0.615877i	$-0.211198\pi$
$47$	10.8023	1.57568	0.787842	+	0.615877i	$0.211198\pi$
$48$	1.75646	0.253524
$49$	−2.90131	−0.414472
$50$	0	0
$51$	0.0881004	0.0123365
$52$	1.23348	0.171052
$53$	−5.02449	−0.690167	−0.345083	−	0.938572i	$-0.612149\pi$
$53$	−5.02449	−0.690167	−0.345083	+	0.938572i	$0.612149\pi$
$54$	−5.32551	−0.724710
$55$	0	0
$56$	−6.22020	−0.831209
$57$	7.63175	1.01085
$58$	3.21125	0.421658
$59$	−5.99027	−0.779867	−0.389933	−	0.920843i	$-0.627502\pi$
$59$	−5.99027	−0.779867	−0.389933	+	0.920843i	$0.627502\pi$
$60$	0	0
$61$	−2.64144	−0.338201	−0.169101	−	0.985599i	$-0.554086\pi$
$61$	−2.64144	−0.338201	−0.169101	+	0.985599i	$0.554086\pi$
$62$	0.524718	0.0666392
$63$	4.29878	0.541595
$64$	8.26171	1.03271
$65$	0	0
$66$	0.348968	0.0429549
$67$	4.48853	0.548361	0.274181	−	0.961678i	$-0.411593\pi$
$67$	4.48853	0.548361	0.274181	+	0.961678i	$0.411593\pi$
$68$	0.0722169	0.00875759
$69$	8.16643	0.983123
$70$	0	0
$71$	−9.82049	−1.16548	−0.582739	−	0.812659i	$-0.698019\pi$
$71$	−9.82049	−1.16548	−0.582739	+	0.812659i	$0.698019\pi$
$72$	−6.52385	−0.768843
$73$	7.64260	0.894499	0.447249	−	0.894409i	$-0.352404\pi$
$73$	7.64260	0.894499	0.447249	+	0.894409i	$0.352404\pi$
$74$	−0.522647	−0.0607565
$75$	0	0
$76$	6.25584	0.717594
$77$	−0.679674	−0.0774561
$78$	−1.67057	−0.189155
$79$	−7.18860	−0.808781	−0.404391	−	0.914586i	$-0.632516\pi$
$79$	−7.18860	−0.808781	−0.404391	+	0.914586i	$0.632516\pi$
$80$	0	0
$81$	1.87870	0.208744
$82$	3.21433	0.354963
$83$	0.911638	0.100065	0.0500326	−	0.998748i	$-0.484067\pi$
$83$	0.911638	0.100065	0.0500326	+	0.998748i	$0.484067\pi$
$84$	−1.45482	−0.158733
$85$	0	0
$86$	9.25136	0.997600
$87$	2.70826	0.290356
$88$	1.03148	0.109956
$89$	−16.8596	−1.78711	−0.893555	−	0.448954i	$-0.851797\pi$
$89$	−16.8596	−1.78711	−0.893555	+	0.448954i	$0.851797\pi$
$90$	0	0
$91$	3.25372	0.341083
$92$	6.69413	0.697911
$93$	0.442530	0.0458882
$94$	−11.9926	−1.23694
$95$	0	0
$96$	3.80339	0.388181
$97$	−16.5498	−1.68038	−0.840190	−	0.542291i	$-0.817557\pi$
$97$	−16.5498	−1.68038	−0.840190	+	0.542291i	$0.817557\pi$
$98$	3.22098	0.325368
$99$	−0.712854	−0.0716445
$100$	0	0
$101$	−10.6373	−1.05845	−0.529227	−	0.848480i	$-0.677518\pi$
$101$	−10.6373	−1.05845	−0.529227	+	0.848480i	$0.677518\pi$
$102$	−0.0978076	−0.00968440
$103$	8.22810	0.810739	0.405370	−	0.914153i	$-0.367143\pi$
$103$	8.22810	0.810739	0.405370	+	0.914153i	$0.367143\pi$
$104$	−4.93786	−0.484197
$105$	0	0
$106$	5.57811	0.541794
$107$	6.04596	0.584485	0.292243	−	0.956344i	$-0.405598\pi$
$107$	6.04596	0.584485	0.292243	+	0.956344i	$0.405598\pi$
$108$	−3.68163	−0.354265
$109$	−7.35102	−0.704100	−0.352050	−	0.935981i	$-0.614515\pi$
$109$	−7.35102	−0.704100	−0.352050	+	0.935981i	$0.614515\pi$
$110$	0	0
$111$	−0.440784	−0.0418374
$112$	3.79796	0.358873
$113$	−5.54394	−0.521530	−0.260765	−	0.965402i	$-0.583975\pi$
$113$	−5.54394	−0.521530	−0.260765	+	0.965402i	$0.583975\pi$
$114$	−8.47264	−0.793536
$115$	0	0
$116$	2.22000	0.206122
$117$	3.41256	0.315491
$118$	6.65030	0.612210
$119$	0.190497	0.0174628
$120$	0	0
$121$	−10.8873	−0.989754
$122$	2.93248	0.265494
$123$	2.71086	0.244430
$124$	0.362747	0.0325757
$125$	0	0
$126$	−4.77244	−0.425163
$127$	1.01372	0.0899528	0.0449764	−	0.998988i	$-0.485679\pi$
$127$	1.01372	0.0899528	0.0449764	+	0.998988i	$0.485679\pi$
$128$	−1.04767	−0.0926022
$129$	7.80230	0.686954
$130$	0	0
$131$	−0.147575	−0.0128937	−0.00644683	−	0.999979i	$-0.502052\pi$
$131$	−0.147575	−0.0128937	−0.00644683	+	0.999979i	$0.502052\pi$
$132$	0.241248	0.0209979
$133$	16.5019	1.43090
$134$	−4.98310	−0.430474
$135$	0	0
$136$	−0.289099	−0.0247901
$137$	−8.76089	−0.748493	−0.374247	−	0.927329i	$-0.622099\pi$
$137$	−8.76089	−0.748493	−0.374247	+	0.927329i	$0.622099\pi$
$138$	−9.06625	−0.771770
$139$	1.74617	0.148108	0.0740540	−	0.997254i	$-0.476406\pi$
$139$	1.74617	0.148108	0.0740540	+	0.997254i	$0.476406\pi$
$140$	0	0
$141$	−10.1142	−0.851766
$142$	10.9026	0.914922
$143$	−0.539555	−0.0451198
$144$	3.98336	0.331947
$145$	0	0
$146$	−8.48469	−0.702198
$147$	2.71647	0.224051
$148$	−0.361316	−0.0297000
$149$	5.52371	0.452520	0.226260	−	0.974067i	$-0.427350\pi$
$149$	5.52371	0.452520	0.226260	+	0.974067i	$0.427350\pi$
$150$	0	0
$151$	−3.12804	−0.254556	−0.127278	−	0.991867i	$-0.540624\pi$
$151$	−3.12804	−0.254556	−0.127278	+	0.991867i	$0.540624\pi$
$152$	−25.0434	−2.03129
$153$	0.199797	0.0161526
$154$	0.754564	0.0608045
$155$	0	0
$156$	−1.15490	−0.0924657
$157$	−8.40238	−0.670583	−0.335291	−	0.942114i	$-0.608835\pi$
$157$	−8.40238	−0.670583	−0.335291	+	0.942114i	$0.608835\pi$
$158$	7.98067	0.634908
$159$	4.70440	0.373083
$160$	0	0
$161$	17.6581	1.39165
$162$	−2.08570	−0.163868
$163$	14.7181	1.15281	0.576404	−	0.817165i	$-0.304456\pi$
$163$	14.7181	1.15281	0.576404	+	0.817165i	$0.304456\pi$
$164$	2.22213	0.173519
$165$	0	0
$166$	−1.01209	−0.0785531
$167$	−21.6102	−1.67225	−0.836125	−	0.548538i	$-0.815185\pi$
$167$	−21.6102	−1.67225	−0.836125	+	0.548538i	$0.815185\pi$
$168$	5.82393	0.449326
$169$	−10.4171	−0.801312
$170$	0	0
$171$	17.3075	1.32354
$172$	6.39564	0.487663
$173$	−21.1413	−1.60734	−0.803671	−	0.595073i	$-0.797123\pi$
$173$	−21.1413	−1.60734	−0.803671	+	0.595073i	$0.797123\pi$
$174$	−3.00667	−0.227935
$175$	0	0
$176$	−0.629804	−0.0474732
$177$	5.60865	0.421572
$178$	18.7172	1.40291
$179$	−20.9441	−1.56543	−0.782717	−	0.622378i	$-0.786167\pi$
$179$	−20.9441	−1.56543	−0.782717	+	0.622378i	$0.786167\pi$
$180$	0	0
$181$	−13.9714	−1.03848	−0.519241	−	0.854628i	$-0.673785\pi$
$181$	−13.9714	−1.03848	−0.519241	+	0.854628i	$0.673785\pi$
$182$	−3.61223	−0.267756
$183$	2.47316	0.182821
$184$	−26.7980	−1.97557
$185$	0	0
$186$	−0.491290	−0.0360231
$187$	−0.0315896	−0.00231006
$188$	−8.29070	−0.604662
$189$	−9.71156	−0.706412
$190$	0	0
$191$	0.507269	0.0367047	0.0183524	−	0.999832i	$-0.494158\pi$
$191$	0.507269	0.0367047	0.0183524	+	0.999832i	$0.494158\pi$
$192$	−7.73538	−0.558253
$193$	16.6090	1.19554	0.597771	−	0.801667i	$-0.296053\pi$
$193$	16.6090	1.19554	0.597771	+	0.801667i	$0.296053\pi$
$194$	18.3734	1.31913
$195$	0	0
$196$	2.22673	0.159052
$197$	5.85560	0.417194	0.208597	−	0.978002i	$-0.433110\pi$
$197$	5.85560	0.417194	0.208597	+	0.978002i	$0.433110\pi$
$198$	0.791399	0.0562423
$199$	15.8208	1.12151	0.560754	−	0.827982i	$-0.310511\pi$
$199$	15.8208	1.12151	0.560754	+	0.827982i	$0.310511\pi$
$200$	0	0
$201$	−4.20258	−0.296427
$202$	11.8094	0.830906
$203$	5.85601	0.411011
$204$	−0.0676163	−0.00473408
$205$	0	0
$206$	−9.13471	−0.636445
$207$	18.5201	1.28724
$208$	3.01498	0.209051
$209$	−2.73647	−0.189285
$210$	0	0
$211$	−4.12987	−0.284312	−0.142156	−	0.989844i	$-0.545403\pi$
$211$	−4.12987	−0.284312	−0.142156	+	0.989844i	$0.545403\pi$
$212$	3.85625	0.264849
$213$	9.19486	0.630022
$214$	−6.71213	−0.458832
$215$	0	0
$216$	14.7383	1.00281
$217$	0.956871	0.0649567
$218$	8.16099	0.552732
$219$	−7.15572	−0.483539
$220$	0	0
$221$	0.151225	0.0101725
$222$	0.489351	0.0328431
$223$	−15.9361	−1.06716	−0.533580	−	0.845750i	$-0.679154\pi$
$223$	−15.9361	−1.06716	−0.533580	+	0.845750i	$0.679154\pi$
$224$	8.22396	0.549487
$225$	0	0
$226$	6.15479	0.409410
$227$	7.21081	0.478598	0.239299	−	0.970946i	$-0.423082\pi$
$227$	7.21081	0.478598	0.239299	+	0.970946i	$0.423082\pi$
$228$	−5.85730	−0.387909
$229$	17.0417	1.12615	0.563075	−	0.826406i	$-0.309618\pi$
$229$	17.0417	1.12615	0.563075	+	0.826406i	$0.309618\pi$
$230$	0	0
$231$	0.636375	0.0418704
$232$	−8.88711	−0.583467
$233$	18.5242	1.21356	0.606781	−	0.794869i	$-0.292460\pi$
$233$	18.5242	1.21356	0.606781	+	0.794869i	$0.292460\pi$
$234$	−3.78857	−0.247666
$235$	0	0
$236$	4.59748	0.299270
$237$	6.73064	0.437202
$238$	−0.211487	−0.0137087
$239$	14.7483	0.953991	0.476996	−	0.878906i	$-0.341726\pi$
$239$	14.7483	0.953991	0.476996	+	0.878906i	$0.341726\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	12.0869	0.776975
$243$	−16.1499	−1.03602
$244$	2.02728	0.129783
$245$	0	0
$246$	−3.00955	−0.191882
$247$	13.0999	0.833529
$248$	−1.45215	−0.0922117
$249$	−0.853560	−0.0540922
$250$	0	0
$251$	2.16602	0.136718	0.0683589	−	0.997661i	$-0.478224\pi$
$251$	2.16602	0.136718	0.0683589	+	0.997661i	$0.478224\pi$
$252$	−3.29928	−0.207835
$253$	−2.92819	−0.184093
$254$	−1.12541	−0.0706147
$255$	0	0
$256$	−15.3603	−0.960019
$257$	17.6587	1.10152	0.550761	−	0.834663i	$-0.314338\pi$
$257$	17.6587	1.10152	0.550761	+	0.834663i	$0.314338\pi$
$258$	−8.66199	−0.539272
$259$	−0.953096	−0.0592225
$260$	0	0
$261$	6.14188	0.380173
$262$	0.163835	0.0101218
$263$	7.66616	0.472715	0.236358	−	0.971666i	$-0.424046\pi$
$263$	7.66616	0.472715	0.236358	+	0.971666i	$0.424046\pi$
$264$	−0.965765	−0.0594387
$265$	0	0
$266$	−18.3202	−1.12328
$267$	15.7855	0.966056
$268$	−3.44491	−0.210431
$269$	−11.8894	−0.724907	−0.362454	−	0.932002i	$-0.618061\pi$
$269$	−11.8894	−0.724907	−0.362454	+	0.932002i	$0.618061\pi$
$270$	0	0
$271$	23.3227	1.41675	0.708377	−	0.705834i	$-0.249428\pi$
$271$	23.3227	1.41675	0.708377	+	0.705834i	$0.249428\pi$
$272$	0.176520	0.0107031
$273$	−3.04644	−0.184379
$274$	9.72620	0.587581
$275$	0	0
$276$	−6.26767	−0.377269
$277$	18.7106	1.12421	0.562105	−	0.827066i	$-0.309992\pi$
$277$	18.7106	1.12421	0.562105	+	0.827066i	$0.309992\pi$
$278$	−1.93857	−0.116268
$279$	1.00358	0.0600829
$280$	0	0
$281$	−11.1893	−0.667498	−0.333749	−	0.942662i	$-0.608314\pi$
$281$	−11.1893	−0.667498	−0.333749	+	0.942662i	$0.608314\pi$
$282$	11.2286	0.668653
$283$	23.4381	1.39325	0.696624	−	0.717436i	$-0.254685\pi$
$283$	23.4381	1.39325	0.696624	+	0.717436i	$0.254685\pi$
$284$	7.53714	0.447247
$285$	0	0
$286$	0.599005	0.0354199
$287$	5.86162	0.346001
$288$	8.62543	0.508258
$289$	−16.9911	−0.999479
$290$	0	0
$291$	15.4955	0.908362
$292$	−5.86563	−0.343260
$293$	−17.3036	−1.01089	−0.505443	−	0.862860i	$-0.668671\pi$
$293$	−17.3036	−1.01089	−0.505443	+	0.862860i	$0.668671\pi$
$294$	−3.01579	−0.175884
$295$	0	0
$296$	1.44642	0.0840716
$297$	1.61044	0.0934472
$298$	−6.13234	−0.355237
$299$	14.0177	0.810667
$300$	0	0
$301$	16.8707	0.972412
$302$	3.47270	0.199832
$303$	9.95966	0.572168
$304$	15.2911	0.877005
$305$	0	0
$306$	−0.221811	−0.0126801
$307$	−1.44826	−0.0826564	−0.0413282	−	0.999146i	$-0.513159\pi$
$307$	−1.44826	−0.0826564	−0.0413282	+	0.999146i	$0.513159\pi$
$308$	0.521644	0.0297234
$309$	−7.70392	−0.438261
$310$	0	0
$311$	25.8517	1.46592	0.732958	−	0.680273i	$-0.238139\pi$
$311$	25.8517	1.46592	0.732958	+	0.680273i	$0.238139\pi$
$312$	4.62329	0.261742
$313$	−8.04132	−0.454522	−0.227261	−	0.973834i	$-0.572977\pi$
$313$	−8.04132	−0.454522	−0.227261	+	0.973834i	$0.572977\pi$
$314$	9.32819	0.526420
$315$	0	0
$316$	5.51719	0.310366
$317$	−15.4574	−0.868174	−0.434087	−	0.900871i	$-0.642929\pi$
$317$	−15.4574	−0.868174	−0.434087	+	0.900871i	$0.642929\pi$
$318$	−5.22275	−0.292877
$319$	−0.971085	−0.0543703
$320$	0	0
$321$	−5.66080	−0.315955
$322$	−19.6037	−1.09247
$323$	0.766969	0.0426753
$324$	−1.44188	−0.0801047
$325$	0	0
$326$	−16.3398	−0.904976
$327$	6.88271	0.380615
$328$	−8.89562	−0.491179
$329$	−21.8696	−1.20571
$330$	0	0
$331$	−11.8025	−0.648724	−0.324362	−	0.945933i	$-0.605150\pi$
$331$	−11.8025	−0.648724	−0.324362	+	0.945933i	$0.605150\pi$
$332$	−0.699674	−0.0383996
$333$	−0.999623	−0.0547790
$334$	23.9914	1.31275
$335$	0	0
$336$	−3.55600	−0.193996
$337$	−7.50592	−0.408873	−0.204437	−	0.978880i	$-0.565536\pi$
$337$	−7.50592	−0.408873	−0.204437	+	0.978880i	$0.565536\pi$
$338$	11.5649	0.629045
$339$	5.19075	0.281923
$340$	0	0
$341$	−0.158675	−0.00859274
$342$	−19.2145	−1.03900
$343$	20.0454	1.08235
$344$	−25.6031	−1.38042
$345$	0	0
$346$	23.4707	1.26179
$347$	−29.4633	−1.58167	−0.790837	−	0.612027i	$-0.790354\pi$
$347$	−29.4633	−1.58167	−0.790837	+	0.612027i	$0.790354\pi$
$348$	−2.07857	−0.111423
$349$	−6.56325	−0.351323	−0.175661	−	0.984451i	$-0.556206\pi$
$349$	−6.56325	−0.351323	−0.175661	+	0.984451i	$0.556206\pi$
$350$	0	0
$351$	−7.70946	−0.411500
$352$	−1.36375	−0.0726884
$353$	25.0982	1.33584	0.667922	−	0.744231i	$-0.267184\pi$
$353$	25.0982	1.33584	0.667922	+	0.744231i	$0.267184\pi$
$354$	−6.22663	−0.330942
$355$	0	0
$356$	12.9396	0.685795
$357$	−0.178361	−0.00943988
$358$	23.2518	1.22890
$359$	−36.0008	−1.90005	−0.950024	−	0.312177i	$-0.898942\pi$
$359$	−36.0008	−1.90005	−0.950024	+	0.312177i	$0.898942\pi$
$360$	0	0
$361$	47.4391	2.49680
$362$	15.5108	0.815228
$363$	10.1937	0.535030
$364$	−2.49720	−0.130889
$365$	0	0
$366$	−2.74566	−0.143518
$367$	5.12988	0.267778	0.133889	−	0.990996i	$-0.457253\pi$
$367$	5.12988	0.267778	0.133889	+	0.990996i	$0.457253\pi$
$368$	16.3624	0.852950
$369$	6.14777	0.320040
$370$	0	0
$371$	10.1722	0.528114
$372$	−0.339638	−0.0176094
$373$	−12.3058	−0.637172	−0.318586	−	0.947894i	$-0.603208\pi$
$373$	−12.3058	−0.637172	−0.318586	+	0.947894i	$0.603208\pi$
$374$	0.0350702	0.00181344
$375$	0	0
$376$	33.1894	1.71161
$377$	4.64875	0.239423
$378$	10.7816	0.554547
$379$	−2.16989	−0.111460	−0.0557298	−	0.998446i	$-0.517749\pi$
$379$	−2.16989	−0.111460	−0.0557298	+	0.998446i	$0.517749\pi$
$380$	0	0
$381$	−0.949137	−0.0486257
$382$	−0.563162	−0.0288139
$383$	−7.51755	−0.384129	−0.192064	−	0.981382i	$-0.561518\pi$
$383$	−7.51755	−0.384129	−0.192064	+	0.981382i	$0.561518\pi$
$384$	0.980931	0.0500579
$385$	0	0
$386$	−18.4390	−0.938523
$387$	17.6943	0.899451
$388$	12.7019	0.644839
$389$	13.0391	0.661111	0.330556	−	0.943787i	$-0.392764\pi$
$389$	13.0391	0.661111	0.330556	+	0.943787i	$0.392764\pi$
$390$	0	0
$391$	0.820703	0.0415048
$392$	−8.91404	−0.450227
$393$	0.138173	0.00696992
$394$	−6.50079	−0.327505
$395$	0	0
$396$	0.547109	0.0274933
$397$	−2.50774	−0.125860	−0.0629299	−	0.998018i	$-0.520044\pi$
$397$	−2.50774	−0.125860	−0.0629299	+	0.998018i	$0.520044\pi$
$398$	−17.5640	−0.880405
$399$	−15.4506	−0.773500
$400$	0	0
$401$	−3.52097	−0.175829	−0.0879145	−	0.996128i	$-0.528020\pi$
$401$	−3.52097	−0.175829	−0.0879145	+	0.996128i	$0.528020\pi$
$402$	4.66564	0.232701
$403$	0.759606	0.0378387
$404$	8.16406	0.406177
$405$	0	0
$406$	−6.50125	−0.322652
$407$	0.158049	0.00783420
$408$	0.270682	0.0134007
$409$	2.08632	0.103162	0.0515809	−	0.998669i	$-0.483574\pi$
$409$	2.08632	0.103162	0.0515809	+	0.998669i	$0.483574\pi$
$410$	0	0
$411$	8.20276	0.404612
$412$	−6.31500	−0.311118
$413$	12.1274	0.596752
$414$	−20.5607	−1.01050
$415$	0	0
$416$	6.52854	0.320088
$417$	−1.63493	−0.0800627
$418$	3.03798	0.148592
$419$	24.7167	1.20749	0.603746	−	0.797177i	$-0.293674\pi$
$419$	24.7167	1.20749	0.603746	+	0.797177i	$0.293674\pi$
$420$	0	0
$421$	−20.6378	−1.00583	−0.502913	−	0.864337i	$-0.667738\pi$
$421$	−20.6378	−1.00583	−0.502913	+	0.864337i	$0.667738\pi$
$422$	4.58491	0.223190
$423$	−22.9372	−1.11525
$424$	−15.4374	−0.749705
$425$	0	0
$426$	−10.2080	−0.494579
$427$	5.34765	0.258791
$428$	−4.64022	−0.224294
$429$	0.505182	0.0243904
$430$	0	0
$431$	−8.40763	−0.404981	−0.202491	−	0.979284i	$-0.564904\pi$
$431$	−8.40763	−0.404981	−0.202491	+	0.979284i	$0.564904\pi$
$432$	−8.99898	−0.432964
$433$	−1.69304	−0.0813623	−0.0406812	−	0.999172i	$-0.512953\pi$
$433$	−1.69304	−0.0813623	−0.0406812	+	0.999172i	$0.512953\pi$
$434$	−1.06230	−0.0509922
$435$	0	0
$436$	5.64184	0.270195
$437$	71.0939	3.40088
$438$	7.94416	0.379587
$439$	5.62599	0.268514	0.134257	−	0.990947i	$-0.457135\pi$
$439$	5.62599	0.268514	0.134257	+	0.990947i	$0.457135\pi$
$440$	0	0
$441$	6.16050	0.293357
$442$	−0.167887	−0.00798559
$443$	18.1644	0.863016	0.431508	−	0.902109i	$-0.357982\pi$
$443$	18.1644	0.863016	0.431508	+	0.902109i	$0.357982\pi$
$444$	0.338298	0.0160549
$445$	0	0
$446$	17.6920	0.837741
$447$	−5.17181	−0.244618
$448$	−16.7260	−0.790230
$449$	19.3699	0.914122	0.457061	−	0.889435i	$-0.348902\pi$
$449$	19.3699	0.914122	0.457061	+	0.889435i	$0.348902\pi$
$450$	0	0
$451$	−0.972016	−0.0457704
$452$	4.25492	0.200135
$453$	2.92877	0.137605
$454$	−8.00532	−0.375709
$455$	0	0
$456$	23.4480	1.09805
$457$	−16.7129	−0.781798	−0.390899	−	0.920434i	$-0.627836\pi$
$457$	−16.7129	−0.781798	−0.390899	+	0.920434i	$0.627836\pi$
$458$	−18.9195	−0.884049
$459$	−0.451369	−0.0210681
$460$	0	0
$461$	22.9200	1.06749	0.533746	−	0.845645i	$-0.320784\pi$
$461$	22.9200	1.06749	0.533746	+	0.845645i	$0.320784\pi$
$462$	−0.706493	−0.0328690
$463$	−10.7378	−0.499028	−0.249514	−	0.968371i	$-0.580271\pi$
$463$	−10.7378	−0.499028	−0.249514	+	0.968371i	$0.580271\pi$
$464$	5.42633	0.251911
$465$	0	0
$466$	−20.5653	−0.952669
$467$	16.6596	0.770914	0.385457	−	0.922726i	$-0.374044\pi$
$467$	16.6596	0.770914	0.385457	+	0.922726i	$0.374044\pi$
$468$	−2.61911	−0.121068
$469$	−9.08713	−0.419605
$470$	0	0
$471$	7.86709	0.362496
$472$	−18.4047	−0.847143
$473$	−2.79762	−0.128635
$474$	−7.47225	−0.343212
$475$	0	0
$476$	−0.146205	−0.00670129
$477$	10.6688	0.488490
$478$	−16.3734	−0.748901
$479$	−18.3168	−0.836915	−0.418457	−	0.908236i	$-0.637429\pi$
$479$	−18.3168	−0.836915	−0.418457	+	0.908236i	$0.637429\pi$
$480$	0	0
$481$	−0.756608	−0.0344984
$482$	−1.11018	−0.0505675
$483$	−16.5331	−0.752284
$484$	8.35590	0.379814
$485$	0	0
$486$	17.9294	0.813293
$487$	−22.8664	−1.03617	−0.518087	−	0.855328i	$-0.673356\pi$
$487$	−22.8664	−1.03617	−0.518087	+	0.855328i	$0.673356\pi$
$488$	−8.11562	−0.367377
$489$	−13.7804	−0.623172
$490$	0	0
$491$	31.5002	1.42158	0.710792	−	0.703402i	$-0.248337\pi$
$491$	31.5002	1.42158	0.710792	+	0.703402i	$0.248337\pi$
$492$	−2.08056	−0.0937990
$493$	0.272173	0.0122580
$494$	−14.5434	−0.654336
$495$	0	0
$496$	0.886661	0.0398123
$497$	19.8818	0.891821
$498$	0.947609	0.0424634
$499$	−1.56402	−0.0700150	−0.0350075	−	0.999387i	$-0.511146\pi$
$499$	−1.56402	−0.0700150	−0.0350075	+	0.999387i	$0.511146\pi$
$500$	0	0
$501$	20.2335	0.903967
$502$	−2.40468	−0.107326
$503$	11.1990	0.499338	0.249669	−	0.968331i	$-0.419678\pi$
$503$	11.1990	0.499338	0.249669	+	0.968331i	$0.419678\pi$
$504$	13.2077	0.588317
$505$	0	0
$506$	3.25082	0.144517
$507$	9.75342	0.433165
$508$	−0.778019	−0.0345190
$509$	20.0688	0.889535	0.444768	−	0.895646i	$-0.353286\pi$
$509$	20.0688	0.889535	0.444768	+	0.895646i	$0.353286\pi$
$510$	0	0
$511$	−15.4726	−0.684469
$512$	19.1481	0.846235
$513$	−39.1001	−1.72631
$514$	−19.6044	−0.864715
$515$	0	0
$516$	−5.98820	−0.263616
$517$	3.62657	0.159496
$518$	1.05811	0.0464908
$519$	19.7945	0.868880
$520$	0	0
$521$	−10.7524	−0.471070	−0.235535	−	0.971866i	$-0.575684\pi$
$521$	−10.7524	−0.471070	−0.235535	+	0.971866i	$0.575684\pi$
$522$	−6.81862	−0.298443
$523$	23.5585	1.03014	0.515071	−	0.857148i	$-0.327766\pi$
$523$	23.5585	1.03014	0.515071	+	0.857148i	$0.327766\pi$
$524$	0.113262	0.00494788
$525$	0	0
$526$	−8.51085	−0.371091
$527$	0.0444730	0.00193727
$528$	0.589681	0.0256626
$529$	53.0748	2.30760
$530$	0	0
$531$	12.7195	0.551978
$532$	−12.6651	−0.549101
$533$	4.65321	0.201553
$534$	−17.5248	−0.758372
$535$	0	0
$536$	13.7907	0.595666
$537$	19.6098	0.846226
$538$	13.1994	0.569066
$539$	−0.974028	−0.0419544
$540$	0	0
$541$	25.1100	1.07956	0.539782	−	0.841805i	$-0.318507\pi$
$541$	25.1100	1.07956	0.539782	+	0.841805i	$0.318507\pi$
$542$	−25.8925	−1.11218
$543$	13.0813	0.561372
$544$	0.382229	0.0163879
$545$	0	0
$546$	3.38211	0.144741
$547$	−7.45781	−0.318873	−0.159437	−	0.987208i	$-0.550968\pi$
$547$	−7.45781	−0.318873	−0.159437	+	0.987208i	$0.550968\pi$
$548$	6.72390	0.287231
$549$	5.60871	0.239374
$550$	0	0
$551$	23.5771	1.00442
$552$	25.0908	1.06793
$553$	14.5535	0.618878
$554$	−20.7722	−0.882527
$555$	0	0
$556$	−1.34017	−0.0568358
$557$	−32.9587	−1.39650	−0.698252	−	0.715852i	$-0.746039\pi$
$557$	−32.9587	−1.39650	−0.698252	+	0.715852i	$0.746039\pi$
$558$	−1.11416	−0.0471662
$559$	13.3927	0.566451
$560$	0	0
$561$	0.0295771	0.00124875
$562$	12.4222	0.523999
$563$	−17.0288	−0.717677	−0.358838	−	0.933400i	$-0.616827\pi$
$563$	−17.0288	−0.717677	−0.358838	+	0.933400i	$0.616827\pi$
$564$	7.76253	0.326862
$565$	0	0
$566$	−26.0206	−1.09373
$567$	−3.80347	−0.159731
$568$	−30.1727	−1.26602
$569$	−17.1901	−0.720646	−0.360323	−	0.932828i	$-0.617333\pi$
$569$	−17.1901	−0.720646	−0.360323	+	0.932828i	$0.617333\pi$
$570$	0	0
$571$	−16.3015	−0.682196	−0.341098	−	0.940028i	$-0.610799\pi$
$571$	−16.3015	−0.682196	−0.341098	+	0.940028i	$0.610799\pi$
$572$	0.414103	0.0173145
$573$	−0.474953	−0.0198414
$574$	−6.50748	−0.271617
$575$	0	0
$576$	−17.5425	−0.730939
$577$	7.76027	0.323064	0.161532	−	0.986867i	$-0.448356\pi$
$577$	7.76027	0.323064	0.161532	+	0.986867i	$0.448356\pi$
$578$	18.8633	0.784610
$579$	−15.5509	−0.646273
$580$	0	0
$581$	−1.84563	−0.0765697
$582$	−17.2029	−0.713081
$583$	−1.68683	−0.0698612
$584$	23.4813	0.971664
$585$	0	0
$586$	19.2102	0.793565
$587$	28.7702	1.18747	0.593737	−	0.804660i	$-0.297652\pi$
$587$	28.7702	1.18747	0.593737	+	0.804660i	$0.297652\pi$
$588$	−2.08487	−0.0859786
$589$	3.85250	0.158740
$590$	0	0
$591$	−5.48256	−0.225522
$592$	−0.883163	−0.0362978
$593$	−24.9323	−1.02385	−0.511924	−	0.859031i	$-0.671067\pi$
$593$	−24.9323	−1.02385	−0.511924	+	0.859031i	$0.671067\pi$
$594$	−1.78788	−0.0733578
$595$	0	0
$596$	−4.23940	−0.173653
$597$	−14.8129	−0.606253
$598$	−15.5623	−0.636389
$599$	45.8293	1.87253	0.936267	−	0.351288i	$-0.114256\pi$
$599$	45.8293	1.87253	0.936267	+	0.351288i	$0.114256\pi$
$600$	0	0
$601$	13.9618	0.569512	0.284756	−	0.958600i	$-0.408087\pi$
$601$	13.9618	0.569512	0.284756	+	0.958600i	$0.408087\pi$
$602$	−18.7296	−0.763361
$603$	−9.53074	−0.388122
$604$	2.40074	0.0976849
$605$	0	0
$606$	−11.0571	−0.449162
$607$	−23.3670	−0.948438	−0.474219	−	0.880407i	$-0.657269\pi$
$607$	−23.3670	−0.948438	−0.474219	+	0.880407i	$0.657269\pi$
$608$	33.1108	1.34282
$609$	−5.48294	−0.222180
$610$	0	0
$611$	−17.3610	−0.702352
$612$	−0.153342	−0.00619849
$613$	39.4297	1.59255	0.796276	−	0.604934i	$-0.206800\pi$
$613$	39.4297	1.59255	0.796276	+	0.604934i	$0.206800\pi$
$614$	1.60783	0.0648868
$615$	0	0
$616$	−2.08825	−0.0841379
$617$	43.3347	1.74459	0.872295	−	0.488979i	$-0.162631\pi$
$617$	43.3347	1.74459	0.872295	+	0.488979i	$0.162631\pi$
$618$	8.55277	0.344043
$619$	6.21814	0.249928	0.124964	−	0.992161i	$-0.460118\pi$
$619$	6.21814	0.249928	0.124964	+	0.992161i	$0.460118\pi$
$620$	0	0
$621$	−41.8395	−1.67896
$622$	−28.7002	−1.15077
$623$	34.1326	1.36749
$624$	−2.82291	−0.113007
$625$	0	0
$626$	8.92734	0.356808
$627$	2.56213	0.102322
$628$	6.44875	0.257333
$629$	−0.0442975	−0.00176626
$630$	0	0
$631$	44.6793	1.77866	0.889328	−	0.457269i	$-0.151172\pi$
$631$	44.6793	1.77866	0.889328	+	0.457269i	$0.151172\pi$
$632$	−22.0864	−0.878551
$633$	3.86677	0.153690
$634$	17.1606	0.681533
$635$	0	0
$636$	−3.61058	−0.143169
$637$	4.66284	0.184749
$638$	1.07808	0.0426817
$639$	20.8524	0.824908
$640$	0	0
$641$	−40.1148	−1.58444	−0.792220	−	0.610235i	$-0.791075\pi$
$641$	−40.1148	−1.58444	−0.792220	+	0.610235i	$0.791075\pi$
$642$	6.28453	0.248031
$643$	−0.266670	−0.0105165	−0.00525823	−	0.999986i	$-0.501674\pi$
$643$	−0.266670	−0.0105165	−0.00525823	+	0.999986i	$0.501674\pi$
$644$	−13.5524	−0.534040
$645$	0	0
$646$	−0.851477	−0.0335009
$647$	46.2497	1.81826	0.909131	−	0.416511i	$-0.136747\pi$
$647$	46.2497	1.81826	0.909131	+	0.416511i	$0.136747\pi$
$648$	5.77216	0.226752
$649$	−2.01106	−0.0789409
$650$	0	0
$651$	−0.895912	−0.0351136
$652$	−11.2960	−0.442385
$653$	−31.3117	−1.22532	−0.612661	−	0.790346i	$-0.709901\pi$
$653$	−31.3117	−1.22532	−0.612661	+	0.790346i	$0.709901\pi$
$654$	−7.64108	−0.298790
$655$	0	0
$656$	5.43153	0.212066
$657$	−16.2280	−0.633113
$658$	24.2793	0.946505
$659$	−0.639395	−0.0249073	−0.0124536	−	0.999922i	$-0.503964\pi$
$659$	−0.639395	−0.0249073	−0.0124536	+	0.999922i	$0.503964\pi$
$660$	0	0
$661$	12.9345	0.503093	0.251547	−	0.967845i	$-0.419061\pi$
$661$	12.9345	0.503093	0.251547	+	0.967845i	$0.419061\pi$
$662$	13.1029	0.509260
$663$	−0.141591	−0.00549893
$664$	2.80094	0.108697
$665$	0	0
$666$	1.10977	0.0430025
$667$	25.2290	0.976870
$668$	16.5857	0.641719
$669$	14.9209	0.576874
$670$	0	0
$671$	−0.886785	−0.0342339
$672$	−7.70004	−0.297036
$673$	7.26643	0.280100	0.140050	−	0.990144i	$-0.455274\pi$
$673$	7.26643	0.280100	0.140050	+	0.990144i	$0.455274\pi$
$674$	8.33295	0.320973
$675$	0	0
$676$	7.99500	0.307500
$677$	25.0186	0.961544	0.480772	−	0.876846i	$-0.340357\pi$
$677$	25.0186	0.961544	0.480772	+	0.876846i	$0.340357\pi$
$678$	−5.76269	−0.221315
$679$	33.5055	1.28582
$680$	0	0
$681$	−6.75143	−0.258715
$682$	0.176159	0.00674546
$683$	26.4789	1.01319	0.506593	−	0.862186i	$-0.330905\pi$
$683$	26.4789	1.01319	0.506593	+	0.862186i	$0.330905\pi$
$684$	−13.2834	−0.507902
$685$	0	0
$686$	−22.2541	−0.849666
$687$	−15.9561	−0.608762
$688$	15.6328	0.595996
$689$	8.07513	0.307638
$690$	0	0
$691$	−50.6926	−1.92844	−0.964219	−	0.265107i	$-0.914593\pi$
$691$	−50.6926	−1.92844	−0.964219	+	0.265107i	$0.914593\pi$
$692$	16.2258	0.616811
$693$	1.44319	0.0548222
$694$	32.7097	1.24164
$695$	0	0
$696$	8.32094	0.315404
$697$	0.272434	0.0103192
$698$	7.28641	0.275795
$699$	−17.3441	−0.656015
$700$	0	0
$701$	−45.9925	−1.73711	−0.868556	−	0.495591i	$-0.834952\pi$
$701$	−45.9925	−1.73711	−0.868556	+	0.495591i	$0.834952\pi$
$702$	8.55892	0.323036
$703$	−3.83730	−0.144726
$704$	2.77363	0.104535
$705$	0	0
$706$	−27.8637	−1.04866
$707$	21.5355	0.809927
$708$	−4.30459	−0.161776
$709$	20.0780	0.754045	0.377023	−	0.926204i	$-0.376948\pi$
$709$	20.0780	0.754045	0.377023	+	0.926204i	$0.376948\pi$
$710$	0	0
$711$	15.2640	0.572443
$712$	−51.7997	−1.94128
$713$	4.12241	0.154386
$714$	0.198014	0.00741048
$715$	0	0
$716$	16.0744	0.600728
$717$	−13.8088	−0.515698
$718$	39.9675	1.49157
$719$	9.14159	0.340924	0.170462	−	0.985364i	$-0.445474\pi$
$719$	9.14159	0.340924	0.170462	+	0.985364i	$0.445474\pi$
$720$	0	0
$721$	−16.6580	−0.620376
$722$	−52.6662	−1.96003
$723$	−0.936293	−0.0348211
$724$	10.7229	0.398513
$725$	0	0
$726$	−11.3169	−0.420009
$727$	−31.1857	−1.15661	−0.578306	−	0.815820i	$-0.696286\pi$
$727$	−31.1857	−1.15661	−0.578306	+	0.815820i	$0.696286\pi$
$728$	9.99681	0.370507
$729$	9.48495	0.351295
$730$	0	0
$731$	0.784109	0.0290013
$732$	−1.89813	−0.0701568
$733$	−19.3947	−0.716360	−0.358180	−	0.933653i	$-0.616603\pi$
$733$	−19.3947	−0.716360	−0.358180	+	0.933653i	$0.616603\pi$
$734$	−5.69512	−0.210211
$735$	0	0
$736$	35.4306	1.30599
$737$	1.50689	0.0555071
$738$	−6.82516	−0.251238
$739$	−7.19469	−0.264661	−0.132330	−	0.991206i	$-0.542246\pi$
$739$	−7.19469	−0.264661	−0.132330	+	0.991206i	$0.542246\pi$
$740$	0	0
$741$	−12.2654	−0.450580
$742$	−11.2930	−0.414580
$743$	32.7079	1.19994	0.599968	−	0.800024i	$-0.295180\pi$
$743$	32.7079	1.19994	0.599968	+	0.800024i	$0.295180\pi$
$744$	1.35964	0.0498468
$745$	0	0
$746$	13.6617	0.500192
$747$	−1.93573	−0.0708247
$748$	0.0242447	0.000886475 0
$749$	−12.2402	−0.447247
$750$	0	0
$751$	−4.64756	−0.169592	−0.0847960	−	0.996398i	$-0.527024\pi$
$751$	−4.64756	−0.169592	−0.0847960	+	0.996398i	$0.527024\pi$
$752$	−20.2649	−0.738986
$753$	−2.02803	−0.0739054
$754$	−5.16097	−0.187952
$755$	0	0
$756$	7.45354	0.271083
$757$	−40.1868	−1.46062	−0.730308	−	0.683119i	$-0.760623\pi$
$757$	−40.1868	−1.46062	−0.730308	+	0.683119i	$0.760623\pi$
$758$	2.40897	0.0874978
$759$	2.74164	0.0995153
$760$	0	0
$761$	7.11165	0.257797	0.128899	−	0.991658i	$-0.458856\pi$
$761$	7.11165	0.257797	0.128899	+	0.991658i	$0.458856\pi$
$762$	1.05372	0.0381721
$763$	14.8823	0.538776
$764$	−0.389325	−0.0140853
$765$	0	0
$766$	8.34587	0.301548
$767$	9.62729	0.347621
$768$	14.3818	0.518957
$769$	−15.2224	−0.548934	−0.274467	−	0.961596i	$-0.588501\pi$
$769$	−15.2224	−0.548934	−0.274467	+	0.961596i	$0.588501\pi$
$770$	0	0
$771$	−16.5338	−0.595449
$772$	−12.7473	−0.458784
$773$	13.2747	0.477459	0.238730	−	0.971086i	$-0.423269\pi$
$773$	13.2747	0.477459	0.238730	+	0.971086i	$0.423269\pi$
$774$	−19.6439	−0.706086
$775$	0	0
$776$	−50.8481	−1.82534
$777$	0.892377	0.0320139
$778$	−14.4759	−0.518985
$779$	23.5997	0.845548
$780$	0	0
$781$	−3.29694	−0.117974
$782$	−0.911132	−0.0325820
$783$	−13.8754	−0.495866
$784$	5.44278	0.194385
$785$	0	0
$786$	−0.153398	−0.00547152
$787$	−46.1695	−1.64576	−0.822882	−	0.568212i	$-0.807635\pi$
$787$	−46.1695	−1.64576	−0.822882	+	0.568212i	$0.807635\pi$
$788$	−4.49412	−0.160096
$789$	−7.17777	−0.255535
$790$	0	0
$791$	11.2238	0.399073
$792$	−2.19019	−0.0778250
$793$	4.24520	0.150751
$794$	2.78405	0.0988023
$795$	0	0
$796$	−12.1423	−0.430374
$797$	−28.1907	−0.998567	−0.499283	−	0.866439i	$-0.666403\pi$
$797$	−28.1907	−0.998567	−0.499283	+	0.866439i	$0.666403\pi$
$798$	17.1531	0.607212
$799$	−1.01644	−0.0359592
$800$	0	0
$801$	35.7988	1.26489
$802$	3.90893	0.138029
$803$	2.56578	0.0905444
$804$	3.22544	0.113753
$805$	0	0
$806$	−0.843302	−0.0297041
$807$	11.1319	0.391863
$808$	−32.6824	−1.14976
$809$	12.9044	0.453693	0.226847	−	0.973930i	$-0.427158\pi$
$809$	12.9044	0.453693	0.226847	+	0.973930i	$0.427158\pi$
$810$	0	0
$811$	5.18752	0.182159	0.0910793	−	0.995844i	$-0.470968\pi$
$811$	5.18752	0.182159	0.0910793	+	0.995844i	$0.470968\pi$
$812$	−4.49444	−0.157724
$813$	−21.8369	−0.765854
$814$	−0.175463	−0.00614999
$815$	0	0
$816$	−0.165274	−0.00578575
$817$	67.9239	2.37636
$818$	−2.31620	−0.0809839
$819$	−6.90880	−0.241413
$820$	0	0
$821$	−18.6769	−0.651829	−0.325915	−	0.945399i	$-0.605672\pi$
$821$	−18.6769	−0.651829	−0.325915	+	0.945399i	$0.605672\pi$
$822$	−9.10657	−0.317628
$823$	8.01059	0.279232	0.139616	−	0.990206i	$-0.455413\pi$
$823$	8.01059	0.279232	0.139616	+	0.990206i	$0.455413\pi$
$824$	25.2802	0.880679
$825$	0	0
$826$	−13.4637	−0.468462
$827$	−19.8058	−0.688716	−0.344358	−	0.938838i	$-0.611903\pi$
$827$	−19.8058	−0.688716	−0.344358	+	0.938838i	$0.611903\pi$
$828$	−14.2140	−0.493971
$829$	41.2957	1.43426	0.717129	−	0.696941i	$-0.245456\pi$
$829$	41.2957	1.43426	0.717129	+	0.696941i	$0.245456\pi$
$830$	0	0
$831$	−17.5186	−0.607714
$832$	−13.2778	−0.460326
$833$	0.272998	0.00945881
$834$	1.81507	0.0628507
$835$	0	0
$836$	2.10021	0.0726374
$837$	−2.26724	−0.0783672
$838$	−27.4401	−0.947904
$839$	−33.2878	−1.14922	−0.574611	−	0.818427i	$-0.694847\pi$
$839$	−33.2878	−1.14922	−0.574611	+	0.818427i	$0.694847\pi$
$840$	0	0
$841$	−20.6332	−0.711490
$842$	22.9118	0.789592
$843$	10.4765	0.360829
$844$	3.16964	0.109103
$845$	0	0
$846$	25.4645	0.875488
$847$	22.0416	0.757357
$848$	9.42582	0.323684
$849$	−21.9449	−0.753147
$850$	0	0
$851$	−4.10614	−0.140757
$852$	−7.05698	−0.241768
$853$	−56.1120	−1.92124	−0.960619	−	0.277870i	$-0.910372\pi$
$853$	−56.1120	−1.92124	−0.960619	+	0.277870i	$0.910372\pi$
$854$	−5.93688	−0.203156
$855$	0	0
$856$	18.5758	0.634907
$857$	0.194552	0.00664578	0.00332289	−	0.999994i	$-0.498942\pi$
$857$	0.194552	0.00664578	0.00332289	+	0.999994i	$0.498942\pi$
$858$	−0.560845	−0.0191469
$859$	21.1262	0.720818	0.360409	−	0.932794i	$-0.382637\pi$
$859$	21.1262	0.720818	0.360409	+	0.932794i	$0.382637\pi$
$860$	0	0
$861$	−5.48820	−0.187037
$862$	9.33402	0.317918
$863$	−9.83307	−0.334722	−0.167361	−	0.985896i	$-0.553524\pi$
$863$	−9.83307	−0.334722	−0.167361	+	0.985896i	$0.553524\pi$
$864$	−19.4861	−0.662930
$865$	0	0
$866$	1.87959	0.0638709
$867$	15.9087	0.540288
$868$	−0.734390	−0.0249268
$869$	−2.41336	−0.0818677
$870$	0	0
$871$	−7.21376	−0.244429
$872$	−22.5855	−0.764840
$873$	35.1412	1.18935
$874$	−78.9273	−2.66976
$875$	0	0
$876$	5.49195	0.185556
$877$	−1.45452	−0.0491157	−0.0245579	−	0.999698i	$-0.507818\pi$
$877$	−1.45452	−0.0491157	−0.0245579	+	0.999698i	$0.507818\pi$
$878$	−6.24588	−0.210788
$879$	16.2012	0.546454
$880$	0	0
$881$	22.3492	0.752964	0.376482	−	0.926424i	$-0.377134\pi$
$881$	22.3492	0.752964	0.376482	+	0.926424i	$0.377134\pi$
$882$	−6.83929	−0.230291
$883$	28.2449	0.950518	0.475259	−	0.879846i	$-0.342354\pi$
$883$	28.2449	0.950518	0.475259	+	0.879846i	$0.342354\pi$
$884$	−0.116064	−0.00390365
$885$	0	0
$886$	−20.1658	−0.677484
$887$	−30.5099	−1.02442	−0.512212	−	0.858859i	$-0.671174\pi$
$887$	−30.5099	−1.02442	−0.512212	+	0.858859i	$0.671174\pi$
$888$	−1.35428	−0.0454465
$889$	−2.05229	−0.0688317
$890$	0	0
$891$	0.630718	0.0211298
$892$	12.2308	0.409518
$893$	−88.0501	−2.94649
$894$	5.74167	0.192030
$895$	0	0
$896$	2.12104	0.0708590
$897$	−13.1247	−0.438222
$898$	−21.5041	−0.717603
$899$	1.36713	0.0455963
$900$	0	0
$901$	0.472779	0.0157505
$902$	1.07912	0.0359306
$903$	−15.7959	−0.525656
$904$	−17.0333	−0.566520
$905$	0	0
$906$	−3.25147	−0.108023
$907$	−55.4062	−1.83973	−0.919866	−	0.392233i	$-0.871703\pi$
$907$	−55.4062	−1.83973	−0.919866	+	0.392233i	$0.871703\pi$
$908$	−5.53423	−0.183660
$909$	22.5868	0.749158
$910$	0	0
$911$	−4.49813	−0.149030	−0.0745149	−	0.997220i	$-0.523741\pi$
$911$	−4.49813	−0.149030	−0.0745149	+	0.997220i	$0.523741\pi$
$912$	−14.3170	−0.474082
$913$	0.306056	0.0101290
$914$	18.5544	0.613726
$915$	0	0
$916$	−13.0794	−0.432155
$917$	0.298768	0.00986620
$918$	0.501103	0.0165389
$919$	0.452844	0.0149380	0.00746898	−	0.999972i	$-0.497623\pi$
$919$	0.452844	0.0149380	0.00746898	+	0.999972i	$0.497623\pi$
$920$	0	0
$921$	1.35599	0.0446815
$922$	−25.4455	−0.838002
$923$	15.7830	0.519505
$924$	−0.488412	−0.0160676
$925$	0	0
$926$	11.9209	0.391746
$927$	−17.4712	−0.573829
$928$	11.7500	0.385712
$929$	18.1736	0.596257	0.298128	−	0.954526i	$-0.403638\pi$
$929$	18.1736	0.596257	0.298128	+	0.954526i	$0.403638\pi$
$930$	0	0
$931$	23.6486	0.775052
$932$	−14.2172	−0.465699
$933$	−24.2048	−0.792430
$934$	−18.4952	−0.605182
$935$	0	0
$936$	10.4848	0.342707
$937$	11.7341	0.383337	0.191668	−	0.981460i	$-0.438610\pi$
$937$	11.7341	0.383337	0.191668	+	0.981460i	$0.438610\pi$
$938$	10.0884	0.329398
$939$	7.52903	0.245701
$940$	0	0
$941$	34.3816	1.12081	0.560404	−	0.828220i	$-0.310646\pi$
$941$	34.3816	1.12081	0.560404	+	0.828220i	$0.310646\pi$
$942$	−8.73392	−0.284566
$943$	25.2532	0.822356
$944$	11.2376	0.365753
$945$	0	0
$946$	3.10587	0.100981
$947$	−28.6199	−0.930023	−0.465011	−	0.885305i	$-0.653950\pi$
$947$	−28.6199	−0.930023	−0.465011	+	0.885305i	$0.653950\pi$
$948$	−5.16571	−0.167774
$949$	−12.2828	−0.398718
$950$	0	0
$951$	14.4727	0.469308
$952$	0.585288	0.0189693
$953$	26.3003	0.851949	0.425974	−	0.904735i	$-0.359931\pi$
$953$	26.3003	0.851949	0.425974	+	0.904735i	$0.359931\pi$
$954$	−11.8443	−0.383474
$955$	0	0
$956$	−11.3192	−0.366090
$957$	0.909220	0.0293909
$958$	20.3350	0.656994
$959$	17.7366	0.572745
$960$	0	0
$961$	−30.7766	−0.992794
$962$	0.839975	0.0270819
$963$	−12.8377	−0.413690
$964$	−0.767491	−0.0247192
$965$	0	0
$966$	18.3548	0.590557
$967$	−24.1905	−0.777913	−0.388957	−	0.921256i	$-0.627164\pi$
$967$	−24.1905	−0.777913	−0.388957	+	0.921256i	$0.627164\pi$
$968$	−33.4504	−1.07514
$969$	−0.718108	−0.0230689
$970$	0	0
$971$	−8.43403	−0.270661	−0.135330	−	0.990801i	$-0.543210\pi$
$971$	−8.43403	−0.270661	−0.135330	+	0.990801i	$0.543210\pi$
$972$	12.3949	0.397567
$973$	−3.53516	−0.113332
$974$	25.3859	0.813417
$975$	0	0
$976$	4.95527	0.158614
$977$	2.24255	0.0717455	0.0358727	−	0.999356i	$-0.488579\pi$
$977$	2.24255	0.0717455	0.0358727	+	0.999356i	$0.488579\pi$
$978$	15.2988	0.489202
$979$	−5.66010	−0.180898
$980$	0	0
$981$	15.6088	0.498351
$982$	−34.9710	−1.11597
$983$	−14.9766	−0.477678	−0.238839	−	0.971059i	$-0.576767\pi$
$983$	−14.9766	−0.477678	−0.238839	+	0.971059i	$0.576767\pi$
$984$	8.32892	0.265516
$985$	0	0
$986$	−0.302162	−0.00962280
$987$	20.4764	0.651770
$988$	−10.0541	−0.319863
$989$	72.6827	2.31118
$990$	0	0
$991$	−10.2047	−0.324163	−0.162082	−	0.986777i	$-0.551821\pi$
$991$	−10.2047	−0.324163	−0.162082	+	0.986777i	$0.551821\pi$
$992$	1.91995	0.0609584
$993$	11.0506	0.350680
$994$	−22.0725	−0.700096
$995$	0	0
$996$	0.655100	0.0207576
$997$	9.04220	0.286369	0.143185	−	0.989696i	$-0.454266\pi$
$997$	9.04220	0.286369	0.143185	+	0.989696i	$0.454266\pi$
$998$	1.73635	0.0549631
$999$	2.25829	0.0714492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.12	yes	40
5.4	even	2		6025.2.a.m.1.29	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.29	✓	40	5.4	even	2
6025.2.a.n.1.12	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.11018 q^{2} -0.936293 q^{3} -0.767491 q^{4} +1.03946 q^{6} -2.02452 q^{7} +3.07242 q^{8} -2.12335 q^{9} +O(q^{10})\)	\(q-1.11018 q^{2} -0.936293 q^{3} -0.767491 q^{4} +1.03946 q^{6} -2.02452 q^{7} +3.07242 q^{8} -2.12335 q^{9} +0.335721 q^{11} +0.718597 q^{12} -1.60715 q^{13} +2.24759 q^{14} -1.87598 q^{16} -0.0940948 q^{17} +2.35731 q^{18} -8.15102 q^{19} +1.89555 q^{21} -0.372712 q^{22} -8.72209 q^{23} -2.87669 q^{24} +1.78424 q^{26} +4.79696 q^{27} +1.55380 q^{28} -2.89254 q^{29} -0.472640 q^{31} -4.06217 q^{32} -0.314333 q^{33} +0.104463 q^{34} +1.62966 q^{36} +0.470775 q^{37} +9.04913 q^{38} +1.50477 q^{39} -2.89531 q^{41} -2.10441 q^{42} -8.33318 q^{43} -0.257663 q^{44} +9.68312 q^{46} +10.8023 q^{47} +1.75646 q^{48} -2.90131 q^{49} +0.0881004 q^{51} +1.23348 q^{52} -5.02449 q^{53} -5.32551 q^{54} -6.22020 q^{56} +7.63175 q^{57} +3.21125 q^{58} -5.99027 q^{59} -2.64144 q^{61} +0.524718 q^{62} +4.29878 q^{63} +8.26171 q^{64} +0.348968 q^{66} +4.48853 q^{67} +0.0722169 q^{68} +8.16643 q^{69} -9.82049 q^{71} -6.52385 q^{72} +7.64260 q^{73} -0.522647 q^{74} +6.25584 q^{76} -0.679674 q^{77} -1.67057 q^{78} -7.18860 q^{79} +1.87870 q^{81} +3.21433 q^{82} +0.911638 q^{83} -1.45482 q^{84} +9.25136 q^{86} +2.70826 q^{87} +1.03148 q^{88} -16.8596 q^{89} +3.25372 q^{91} +6.69413 q^{92} +0.442530 q^{93} -11.9926 q^{94} +3.80339 q^{96} -16.5498 q^{97} +3.22098 q^{98} -0.712854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

L-functions

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