LMFDB - Embedded newform 833.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,4,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("833.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	833.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:	$49.1485910348$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 53x^{7} + 90x^{6} + 880x^{5} - 1087x^{4} - 4674x^{3} + 2515x^{2} + 1814x + 36 $ x^9 - 2x^8 - 53x^7 + 90x^6 + 880x^5 - 1087x^4 - 4674x^3 + 2515x^2 + 1814x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.05606$ of defining polynomial
Character	$\chi$	$=$	833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.05606 q^{2} -2.41760 q^{3} +8.45161 q^{4} -20.0958 q^{5} +9.80593 q^{6} -1.83177 q^{8} -21.1552 q^{9} +O(q^{10})$	\(q-4.05606 q^{2} -2.41760 q^{3} +8.45161 q^{4} -20.0958 q^{5} +9.80593 q^{6} -1.83177 q^{8} -21.1552 q^{9} +81.5097 q^{10} +1.19427 q^{11} -20.4326 q^{12} -13.3922 q^{13} +48.5836 q^{15} -60.1831 q^{16} -17.0000 q^{17} +85.8067 q^{18} -71.4124 q^{19} -169.842 q^{20} -4.84404 q^{22} +50.4349 q^{23} +4.42849 q^{24} +278.841 q^{25} +54.3197 q^{26} +116.420 q^{27} -20.7359 q^{29} -197.058 q^{30} -189.609 q^{31} +258.761 q^{32} -2.88727 q^{33} +68.9530 q^{34} -178.796 q^{36} +231.131 q^{37} +289.653 q^{38} +32.3771 q^{39} +36.8108 q^{40} +324.216 q^{41} -11.4655 q^{43} +10.0935 q^{44} +425.131 q^{45} -204.567 q^{46} +362.345 q^{47} +145.499 q^{48} -1131.00 q^{50} +41.0992 q^{51} -113.186 q^{52} +517.022 q^{53} -472.207 q^{54} -23.9998 q^{55} +172.647 q^{57} +84.1061 q^{58} +395.365 q^{59} +410.610 q^{60} -479.266 q^{61} +769.065 q^{62} -568.083 q^{64} +269.128 q^{65} +11.7109 q^{66} -717.669 q^{67} -143.677 q^{68} -121.932 q^{69} -286.995 q^{71} +38.7514 q^{72} -498.708 q^{73} -937.480 q^{74} -674.127 q^{75} -603.550 q^{76} -131.323 q^{78} +1015.60 q^{79} +1209.43 q^{80} +289.733 q^{81} -1315.04 q^{82} +719.413 q^{83} +341.629 q^{85} +46.5045 q^{86} +50.1312 q^{87} -2.18763 q^{88} -734.471 q^{89} -1724.36 q^{90} +426.256 q^{92} +458.399 q^{93} -1469.69 q^{94} +1435.09 q^{95} -625.580 q^{96} +1221.31 q^{97} -25.2651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9} - 134 q^{10} - 8 q^{11} - 56 q^{12} - 164 q^{13} + 34 q^{15} + 178 q^{16} - 153 q^{17} + 98 q^{18} - 244 q^{19} + 41 q^{20} - 80 q^{22} - 14 q^{23} - 298 q^{24} + 684 q^{25} - 326 q^{26} - 218 q^{27} - 234 q^{29} - 335 q^{30} - 555 q^{31} - 181 q^{32} - 458 q^{33} - 34 q^{34} - 1221 q^{36} - 364 q^{37} + 714 q^{38} - 52 q^{39} - 123 q^{40} + 45 q^{41} - 135 q^{43} - 748 q^{44} + 844 q^{45} - 1576 q^{46} + 172 q^{47} + 949 q^{48} - 2901 q^{50} + 187 q^{51} + 1596 q^{52} + 101 q^{53} + 1163 q^{54} - 1260 q^{55} - 602 q^{57} + 1062 q^{58} - 280 q^{59} - 1727 q^{60} - 639 q^{61} + 1708 q^{62} - 2390 q^{64} + 638 q^{65} + 2476 q^{66} + 35 q^{67} - 646 q^{68} - 1288 q^{69} - 1616 q^{71} + 1335 q^{72} - 1049 q^{73} - 370 q^{74} - 1260 q^{75} - 4964 q^{76} - 4714 q^{78} + 2304 q^{79} + 3996 q^{80} - 791 q^{81} + 215 q^{82} - 2508 q^{83} - 51 q^{85} + 623 q^{86} - 166 q^{87} - 416 q^{88} - 2762 q^{89} - 2935 q^{90} - 2392 q^{92} + 2784 q^{93} + 862 q^{94} - 3462 q^{95} - 2928 q^{96} - 3107 q^{97} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9 - 134 * q^10 - 8 * q^11 - 56 * q^12 - 164 * q^13 + 34 * q^15 + 178 * q^16 - 153 * q^17 + 98 * q^18 - 244 * q^19 + 41 * q^20 - 80 * q^22 - 14 * q^23 - 298 * q^24 + 684 * q^25 - 326 * q^26 - 218 * q^27 - 234 * q^29 - 335 * q^30 - 555 * q^31 - 181 * q^32 - 458 * q^33 - 34 * q^34 - 1221 * q^36 - 364 * q^37 + 714 * q^38 - 52 * q^39 - 123 * q^40 + 45 * q^41 - 135 * q^43 - 748 * q^44 + 844 * q^45 - 1576 * q^46 + 172 * q^47 + 949 * q^48 - 2901 * q^50 + 187 * q^51 + 1596 * q^52 + 101 * q^53 + 1163 * q^54 - 1260 * q^55 - 602 * q^57 + 1062 * q^58 - 280 * q^59 - 1727 * q^60 - 639 * q^61 + 1708 * q^62 - 2390 * q^64 + 638 * q^65 + 2476 * q^66 + 35 * q^67 - 646 * q^68 - 1288 * q^69 - 1616 * q^71 + 1335 * q^72 - 1049 * q^73 - 370 * q^74 - 1260 * q^75 - 4964 * q^76 - 4714 * q^78 + 2304 * q^79 + 3996 * q^80 - 791 * q^81 + 215 * q^82 - 2508 * q^83 - 51 * q^85 + 623 * q^86 - 166 * q^87 - 416 * q^88 - 2762 * q^89 - 2935 * q^90 - 2392 * q^92 + 2784 * q^93 + 862 * q^94 - 3462 * q^95 - 2928 * q^96 - 3107 * q^97 - 2396 * 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 $

$2$	−4.05606	−1.43403	−0.717017	−	0.697056i	$-0.754493\pi$
$2$	−4.05606	−1.43403	−0.717017	+	0.697056i	$0.754493\pi$
$3$	−2.41760	−0.465268	−0.232634	−	0.972564i	$-0.574734\pi$
$3$	−2.41760	−0.465268	−0.232634	+	0.972564i	$0.574734\pi$
$4$	8.45161	1.05645
$5$	−20.0958	−1.79742	−0.898711	−	0.438540i	$-0.855496\pi$
$5$	−20.0958	−1.79742	−0.898711	+	0.438540i	$0.855496\pi$
$6$	9.80593	0.667209
$7$	0	0
$7$	0	0
$8$	−1.83177	−0.0809535
$9$	−21.1552	−0.783526
$10$	81.5097	2.57756
$11$	1.19427	0.0327351	0.0163676	−	0.999866i	$-0.494790\pi$
$11$	1.19427	0.0327351	0.0163676	+	0.999866i	$0.494790\pi$
$12$	−20.4326	−0.491533
$13$	−13.3922	−0.285718	−0.142859	−	0.989743i	$-0.545630\pi$
$13$	−13.3922	−0.285718	−0.142859	+	0.989743i	$0.545630\pi$
$14$	0	0
$15$	48.5836	0.836283
$16$	−60.1831	−0.940362
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	85.8067	1.12360
$19$	−71.4124	−0.862270	−0.431135	−	0.902288i	$-0.641887\pi$
$19$	−71.4124	−0.862270	−0.431135	+	0.902288i	$0.641887\pi$
$20$	−169.842	−1.89889
$21$	0	0
$22$	−4.84404	−0.0469433
$23$	50.4349	0.457235	0.228618	−	0.973516i	$-0.426579\pi$
$23$	50.4349	0.457235	0.228618	+	0.973516i	$0.426579\pi$
$24$	4.42849	0.0376650
$25$	278.841	2.23073
$26$	54.3197	0.409729
$27$	116.420	0.829817
$28$	0	0
$29$	−20.7359	−0.132778	−0.0663890	−	0.997794i	$-0.521148\pi$
$29$	−20.7359	−0.132778	−0.0663890	+	0.997794i	$0.521148\pi$
$30$	−197.058	−1.19926
$31$	−189.609	−1.09854	−0.549270	−	0.835645i	$-0.685094\pi$
$31$	−189.609	−1.09854	−0.549270	+	0.835645i	$0.685094\pi$
$32$	258.761	1.42946
$33$	−2.88727	−0.0152306
$34$	68.9530	0.347804
$35$	0	0
$36$	−178.796	−0.827757
$37$	231.131	1.02696	0.513482	−	0.858100i	$-0.328355\pi$
$37$	231.131	1.02696	0.513482	+	0.858100i	$0.328355\pi$
$38$	289.653	1.23652
$39$	32.3771	0.132935
$40$	36.8108	0.145508
$41$	324.216	1.23498	0.617488	−	0.786580i	$-0.288150\pi$
$41$	324.216	1.23498	0.617488	+	0.786580i	$0.288150\pi$
$42$	0	0
$43$	−11.4655	−0.0406620	−0.0203310	−	0.999793i	$-0.506472\pi$
$43$	−11.4655	−0.0406620	−0.0203310	+	0.999793i	$0.506472\pi$
$44$	10.0935	0.0345831
$45$	425.131	1.40833
$46$	−204.567	−0.655690
$47$	362.345	1.12454	0.562271	−	0.826953i	$-0.309928\pi$
$47$	362.345	1.12454	0.562271	+	0.826953i	$0.309928\pi$
$48$	145.499	0.437520
$49$	0	0
$50$	−1131.00	−3.19894
$51$	41.0992	0.112844
$52$	−113.186	−0.301848
$53$	517.022	1.33997	0.669985	−	0.742374i	$-0.266300\pi$
$53$	517.022	1.33997	0.669985	+	0.742374i	$0.266300\pi$
$54$	−472.207	−1.18999
$55$	−23.9998	−0.0588389
$56$	0	0
$57$	172.647	0.401186
$58$	84.1061	0.190408
$59$	395.365	0.872409	0.436205	−	0.899848i	$-0.356322\pi$
$59$	395.365	0.872409	0.436205	+	0.899848i	$0.356322\pi$
$60$	410.610	0.883492
$61$	−479.266	−1.00596	−0.502981	−	0.864297i	$-0.667763\pi$
$61$	−479.266	−1.00596	−0.502981	+	0.864297i	$0.667763\pi$
$62$	769.065	1.57534
$63$	0	0
$64$	−568.083	−1.10954
$65$	269.128	0.513557
$66$	11.7109	0.0218412
$67$	−717.669	−1.30862	−0.654308	−	0.756228i	$-0.727040\pi$
$67$	−717.669	−1.30862	−0.654308	+	0.756228i	$0.727040\pi$
$68$	−143.677	−0.256227
$69$	−121.932	−0.212737
$70$	0	0
$71$	−286.995	−0.479719	−0.239859	−	0.970808i	$-0.577101\pi$
$71$	−286.995	−0.479719	−0.239859	+	0.970808i	$0.577101\pi$
$72$	38.7514	0.0634292
$73$	−498.708	−0.799580	−0.399790	−	0.916607i	$-0.630917\pi$
$73$	−498.708	−0.799580	−0.399790	+	0.916607i	$0.630917\pi$
$74$	−937.480	−1.47270
$75$	−674.127	−1.03789
$76$	−603.550	−0.910946
$77$	0	0
$78$	−131.323	−0.190634
$79$	1015.60	1.44639	0.723193	−	0.690646i	$-0.242674\pi$
$79$	1015.60	1.44639	0.723193	+	0.690646i	$0.242674\pi$
$80$	1209.43	1.69023
$81$	289.733	0.397439
$82$	−1315.04	−1.77100
$83$	719.413	0.951395	0.475698	−	0.879609i	$-0.342196\pi$
$83$	719.413	0.951395	0.475698	+	0.879609i	$0.342196\pi$
$84$	0	0
$85$	341.629	0.435939
$86$	46.5045	0.0583106
$87$	50.1312	0.0617773
$88$	−2.18763	−0.00265002
$89$	−734.471	−0.874761	−0.437380	−	0.899277i	$-0.644094\pi$
$89$	−734.471	−0.874761	−0.437380	+	0.899277i	$0.644094\pi$
$90$	−1724.36	−2.01959
$91$	0	0
$92$	426.256	0.483047
$93$	458.399	0.511115
$94$	−1469.69	−1.61263
$95$	1435.09	1.54986
$96$	−625.580	−0.665083
$97$	1221.31	1.27841	0.639205	−	0.769036i	$-0.279264\pi$
$97$	1221.31	1.27841	0.639205	+	0.769036i	$0.279264\pi$
$98$	0	0
$99$	−25.2651	−0.0256488
$100$	2356.66	2.35666
$101$	1125.27	1.10860	0.554301	−	0.832316i	$-0.312986\pi$
$101$	1125.27	1.10860	0.554301	+	0.832316i	$0.312986\pi$
$102$	−166.701	−0.161822
$103$	1707.02	1.63299	0.816494	−	0.577354i	$-0.195915\pi$
$103$	1707.02	1.63299	0.816494	+	0.577354i	$0.195915\pi$
$104$	24.5315	0.0231299
$105$	0	0
$106$	−2097.07	−1.92156
$107$	626.769	0.566281	0.283141	−	0.959078i	$-0.408624\pi$
$107$	626.769	0.566281	0.283141	+	0.959078i	$0.408624\pi$
$108$	983.938	0.876661
$109$	1396.79	1.22741	0.613706	−	0.789535i	$-0.289678\pi$
$109$	1396.79	1.22741	0.613706	+	0.789535i	$0.289678\pi$
$110$	97.3448	0.0843769
$111$	−558.782	−0.477813
$112$	0	0
$113$	−2319.36	−1.93086	−0.965428	−	0.260671i	$-0.916056\pi$
$113$	−2319.36	−1.93086	−0.965428	+	0.260671i	$0.916056\pi$
$114$	−700.265	−0.575314
$115$	−1013.53	−0.821845
$116$	−175.252	−0.140274
$117$	283.315	0.223868
$118$	−1603.62	−1.25106
$119$	0	0
$120$	−88.9939	−0.0677000
$121$	−1329.57	−0.998928
$122$	1943.93	1.44258
$123$	−783.825	−0.574595
$124$	−1602.50	−1.16055
$125$	−3091.56	−2.21214
$126$	0	0
$127$	−2218.26	−1.54991	−0.774956	−	0.632015i	$-0.782228\pi$
$127$	−2218.26	−1.54991	−0.774956	+	0.632015i	$0.782228\pi$
$128$	234.093	0.161649
$129$	27.7189	0.0189187
$130$	−1091.60	−0.736457
$131$	2130.89	1.42119	0.710597	−	0.703599i	$-0.248425\pi$
$131$	2130.89	1.42119	0.710597	+	0.703599i	$0.248425\pi$
$132$	−24.4021	−0.0160904
$133$	0	0
$134$	2910.91	1.87660
$135$	−2339.55	−1.49153
$136$	31.1401	0.0196341
$137$	−2753.57	−1.71718	−0.858588	−	0.512667i	$-0.828658\pi$
$137$	−2753.57	−1.71718	−0.858588	+	0.512667i	$0.828658\pi$
$138$	494.561	0.305072
$139$	−976.087	−0.595616	−0.297808	−	0.954626i	$-0.596256\pi$
$139$	−976.087	−0.595616	−0.297808	+	0.954626i	$0.596256\pi$
$140$	0	0
$141$	−876.005	−0.523213
$142$	1164.07	0.687932
$143$	−15.9940	−0.00935302
$144$	1273.19	0.736798
$145$	416.705	0.238658
$146$	2022.79	1.14662
$147$	0	0
$148$	1953.43	1.08494
$149$	−546.241	−0.300334	−0.150167	−	0.988661i	$-0.547981\pi$
$149$	−546.241	−0.300334	−0.150167	+	0.988661i	$0.547981\pi$
$150$	2734.30	1.48836
$151$	294.037	0.158466	0.0792332	−	0.996856i	$-0.474753\pi$
$151$	294.037	0.158466	0.0792332	+	0.996856i	$0.474753\pi$
$152$	130.811	0.0698037
$153$	359.638	0.190033
$154$	0	0
$155$	3810.34	1.97454
$156$	273.639	0.140440
$157$	−2724.66	−1.38504	−0.692520	−	0.721399i	$-0.743499\pi$
$157$	−2724.66	−1.38504	−0.692520	+	0.721399i	$0.743499\pi$
$158$	−4119.35	−2.07417
$159$	−1249.95	−0.623445
$160$	−5200.00	−2.56935
$161$	0	0
$162$	−1175.17	−0.569941
$163$	−2550.48	−1.22558	−0.612788	−	0.790247i	$-0.709952\pi$
$163$	−2550.48	−1.22558	−0.612788	+	0.790247i	$0.709952\pi$
$164$	2740.15	1.30469
$165$	58.0221	0.0273758
$166$	−2917.98	−1.36433
$167$	1342.04	0.621858	0.310929	−	0.950433i	$-0.399360\pi$
$167$	1342.04	0.621858	0.310929	+	0.950433i	$0.399360\pi$
$168$	0	0
$169$	−2017.65	−0.918365
$170$	−1385.67	−0.625151
$171$	1510.74	0.675611
$172$	−96.9015	−0.0429574
$173$	−3804.48	−1.67196	−0.835982	−	0.548758i	$-0.815101\pi$
$173$	−3804.48	−1.67196	−0.835982	+	0.548758i	$0.815101\pi$
$174$	−203.335	−0.0885908
$175$	0	0
$176$	−71.8750	−0.0307829
$177$	−955.835	−0.405904
$178$	2979.06	1.25444
$179$	1215.57	0.507575	0.253788	−	0.967260i	$-0.418324\pi$
$179$	1215.57	0.507575	0.253788	+	0.967260i	$0.418324\pi$
$180$	3593.04	1.48783
$181$	60.0011	0.0246400	0.0123200	−	0.999924i	$-0.496078\pi$
$181$	60.0011	0.0246400	0.0123200	+	0.999924i	$0.496078\pi$
$182$	0	0
$183$	1158.67	0.468042
$184$	−92.3851	−0.0370148
$185$	−4644.76	−1.84589
$186$	−1859.29	−0.732956
$187$	−20.3026	−0.00793944
$188$	3062.40	1.18802
$189$	0	0
$190$	−5820.80	−2.22256
$191$	−1257.17	−0.476261	−0.238130	−	0.971233i	$-0.576535\pi$
$191$	−1257.17	−0.476261	−0.238130	+	0.971233i	$0.576535\pi$
$192$	1373.40	0.516231
$193$	−1729.48	−0.645029	−0.322514	−	0.946565i	$-0.604528\pi$
$193$	−1729.48	−0.645029	−0.322514	+	0.946565i	$0.604528\pi$
$194$	−4953.73	−1.83328
$195$	−650.643	−0.238941
$196$	0	0
$197$	4640.08	1.67813	0.839065	−	0.544031i	$-0.183103\pi$
$197$	4640.08	1.67813	0.839065	+	0.544031i	$0.183103\pi$
$198$	102.477	0.0367813
$199$	−5035.05	−1.79359	−0.896797	−	0.442443i	$-0.854112\pi$
$199$	−5035.05	−1.79359	−0.896797	+	0.442443i	$0.854112\pi$
$200$	−510.772	−0.180585
$201$	1735.04	0.608856
$202$	−4564.17	−1.58977
$203$	0	0
$204$	347.355	0.119214
$205$	−6515.38	−2.21978
$206$	−6923.78	−2.34176
$207$	−1066.96	−0.358256
$208$	805.987	0.268678
$209$	−85.2858	−0.0282265
$210$	0	0
$211$	55.2977	0.0180420	0.00902098	−	0.999959i	$-0.497128\pi$
$211$	55.2977	0.0180420	0.00902098	+	0.999959i	$0.497128\pi$
$212$	4369.67	1.41561
$213$	693.839	0.223198
$214$	−2542.21	−0.812066
$215$	230.407	0.0730868
$216$	−213.255	−0.0671766
$217$	0	0
$218$	−5665.45	−1.76015
$219$	1205.68	0.372019
$220$	−202.837	−0.0621604
$221$	227.668	0.0692969
$222$	2266.45	0.685200
$223$	5599.34	1.68143	0.840716	−	0.541476i	$-0.182134\pi$
$223$	5599.34	1.68143	0.840716	+	0.541476i	$0.182134\pi$
$224$	0	0
$225$	−5898.94	−1.74783
$226$	9407.44	2.76891
$227$	90.6567	0.0265070	0.0132535	−	0.999912i	$-0.495781\pi$
$227$	90.6567	0.0265070	0.0132535	+	0.999912i	$0.495781\pi$
$228$	1459.14	0.423834
$229$	2091.94	0.603666	0.301833	−	0.953361i	$-0.402402\pi$
$229$	2091.94	0.603666	0.301833	+	0.953361i	$0.402402\pi$
$230$	4110.94	1.17855
$231$	0	0
$232$	37.9834	0.0107488
$233$	1626.67	0.457369	0.228684	−	0.973501i	$-0.426558\pi$
$233$	1626.67	0.457369	0.228684	+	0.973501i	$0.426558\pi$
$234$	−1149.14	−0.321034
$235$	−7281.61	−2.02128
$236$	3341.47	0.921658
$237$	−2455.33	−0.672956
$238$	0	0
$239$	1085.20	0.293705	0.146853	−	0.989158i	$-0.453086\pi$
$239$	1085.20	0.293705	0.146853	+	0.989158i	$0.453086\pi$
$240$	−2923.92	−0.786408
$241$	291.973	0.0780400	0.0390200	−	0.999238i	$-0.487576\pi$
$241$	291.973	0.0780400	0.0390200	+	0.999238i	$0.487576\pi$
$242$	5392.83	1.43250
$243$	−3843.80	−1.01473
$244$	−4050.57	−1.06275
$245$	0	0
$246$	3179.24	0.823988
$247$	956.371	0.246366
$248$	347.319	0.0889307
$249$	−1739.25	−0.442653
$250$	12539.6	3.17228
$251$	7406.89	1.86263	0.931313	−	0.364220i	$-0.118664\pi$
$251$	7406.89	1.86263	0.931313	+	0.364220i	$0.118664\pi$
$252$	0	0
$253$	60.2330	0.0149677
$254$	8997.40	2.22263
$255$	−825.922	−0.202828
$256$	3595.17	0.877727
$257$	2415.63	0.586315	0.293157	−	0.956064i	$-0.405294\pi$
$257$	2415.63	0.586315	0.293157	+	0.956064i	$0.405294\pi$
$258$	−112.429	−0.0271300
$259$	0	0
$260$	2274.56	0.542548
$261$	438.673	0.104035
$262$	−8643.00	−2.03804
$263$	−5746.51	−1.34732	−0.673659	−	0.739042i	$-0.735279\pi$
$263$	−5746.51	−1.34732	−0.673659	+	0.739042i	$0.735279\pi$
$264$	5.28881	0.00123297
$265$	−10390.0	−2.40849
$266$	0	0
$267$	1775.66	0.406998
$268$	−6065.46	−1.38249
$269$	−4371.32	−0.990797	−0.495398	−	0.868666i	$-0.664978\pi$
$269$	−4371.32	−0.990797	−0.495398	+	0.868666i	$0.664978\pi$
$270$	9489.37	2.13891
$271$	−6582.36	−1.47546	−0.737731	−	0.675095i	$-0.764103\pi$
$271$	−6582.36	−1.47546	−0.737731	+	0.675095i	$0.764103\pi$
$272$	1023.11	0.228071
$273$	0	0
$274$	11168.6	2.46249
$275$	333.012	0.0730232
$276$	−1030.52	−0.224746
$277$	504.861	0.109510	0.0547548	−	0.998500i	$-0.482562\pi$
$277$	504.861	0.109510	0.0547548	+	0.998500i	$0.482562\pi$
$278$	3959.07	0.854133
$279$	4011.21	0.860735
$280$	0	0
$281$	6301.20	1.33772	0.668858	−	0.743390i	$-0.266783\pi$
$281$	6301.20	1.33772	0.668858	+	0.743390i	$0.266783\pi$
$282$	3553.13	0.750304
$283$	4188.99	0.879892	0.439946	−	0.898024i	$-0.354998\pi$
$283$	4188.99	0.879892	0.439946	+	0.898024i	$0.354998\pi$
$284$	−2425.57	−0.506799
$285$	−3469.47	−0.721101
$286$	64.8725	0.0134125
$287$	0	0
$288$	−5474.13	−1.12002
$289$	289.000	0.0588235
$290$	−1690.18	−0.342244
$291$	−2952.65	−0.594803
$292$	−4214.88	−0.844717
$293$	−6406.22	−1.27732	−0.638661	−	0.769488i	$-0.720512\pi$
$293$	−6406.22	−1.27732	−0.638661	+	0.769488i	$0.720512\pi$
$294$	0	0
$295$	−7945.18	−1.56809
$296$	−423.378	−0.0831363
$297$	139.037	0.0271642
$298$	2215.59	0.430689
$299$	−675.436	−0.130640
$300$	−5697.46	−1.09648
$301$	0	0
$302$	−1192.63	−0.227246
$303$	−2720.46	−0.515796
$304$	4297.82	0.810845
$305$	9631.23	1.80814
$306$	−1458.71	−0.272514
$307$	1192.42	0.221678	0.110839	−	0.993838i	$-0.464646\pi$
$307$	1192.42	0.221678	0.110839	+	0.993838i	$0.464646\pi$
$308$	0	0
$309$	−4126.90	−0.759777
$310$	−15455.0	−2.83156
$311$	6937.33	1.26489	0.632444	−	0.774606i	$-0.282052\pi$
$311$	6937.33	1.26489	0.632444	+	0.774606i	$0.282052\pi$
$312$	−59.3073	−0.0107616
$313$	780.311	0.140913	0.0704565	−	0.997515i	$-0.477554\pi$
$313$	780.311	0.140913	0.0704565	+	0.997515i	$0.477554\pi$
$314$	11051.4	1.98619
$315$	0	0
$316$	8583.50	1.52804
$317$	−3645.67	−0.645934	−0.322967	−	0.946410i	$-0.604680\pi$
$317$	−3645.67	−0.645934	−0.322967	+	0.946410i	$0.604680\pi$
$318$	5069.88	0.894041
$319$	−24.7643	−0.00434651
$320$	11416.1	1.99431
$321$	−1515.28	−0.263472
$322$	0	0
$323$	1214.01	0.209131
$324$	2448.71	0.419875
$325$	−3734.31	−0.637360
$326$	10344.9	1.75752
$327$	−3376.87	−0.571075
$328$	−593.889	−0.0999757
$329$	0	0
$330$	−235.341	−0.0392578
$331$	5299.61	0.880039	0.440019	−	0.897988i	$-0.354972\pi$
$331$	5299.61	0.880039	0.440019	+	0.897988i	$0.354972\pi$
$332$	6080.20	1.00510
$333$	−4889.62	−0.804653
$334$	−5443.40	−0.891765
$335$	14422.1	2.35214
$336$	0	0
$337$	9320.41	1.50657	0.753287	−	0.657693i	$-0.228467\pi$
$337$	9320.41	1.50657	0.753287	+	0.657693i	$0.228467\pi$
$338$	8183.70	1.31697
$339$	5607.28	0.898365
$340$	2887.31	0.460549
$341$	−226.444	−0.0359609
$342$	−6127.66	−0.968848
$343$	0	0
$344$	21.0020	0.00329173
$345$	2450.31	0.382378
$346$	15431.2	2.39765
$347$	−5709.04	−0.883220	−0.441610	−	0.897207i	$-0.645593\pi$
$347$	−5709.04	−0.883220	−0.441610	+	0.897207i	$0.645593\pi$
$348$	423.689	0.0652648
$349$	2095.14	0.321347	0.160674	−	0.987008i	$-0.448633\pi$
$349$	2095.14	0.321347	0.160674	+	0.987008i	$0.448633\pi$
$350$	0	0
$351$	−1559.13	−0.237094
$352$	309.030	0.0467937
$353$	5354.74	0.807377	0.403688	−	0.914897i	$-0.367728\pi$
$353$	5354.74	0.807377	0.403688	+	0.914897i	$0.367728\pi$
$354$	3876.92	0.582080
$355$	5767.39	0.862257
$356$	−6207.46	−0.924143
$357$	0	0
$358$	−4930.42	−0.727880
$359$	−9199.74	−1.35249	−0.676245	−	0.736677i	$-0.736394\pi$
$359$	−9199.74	−1.35249	−0.676245	+	0.736677i	$0.736394\pi$
$360$	−778.741	−0.114009
$361$	−1759.27	−0.256491
$362$	−243.368	−0.0353346
$363$	3214.38	0.464769
$364$	0	0
$365$	10021.9	1.43718
$366$	−4699.65	−0.671187
$367$	−1106.05	−0.157317	−0.0786583	−	0.996902i	$-0.525064\pi$
$367$	−1106.05	−0.157317	−0.0786583	+	0.996902i	$0.525064\pi$
$368$	−3035.33	−0.429966
$369$	−6858.86	−0.967636
$370$	18839.4	2.64707
$371$	0	0
$372$	3874.21	0.539969
$373$	1788.02	0.248204	0.124102	−	0.992269i	$-0.460395\pi$
$373$	1788.02	0.248204	0.124102	+	0.992269i	$0.460395\pi$
$374$	82.3486	0.0113854
$375$	7474.16	1.02924
$376$	−663.732	−0.0910355
$377$	277.700	0.0379371
$378$	0	0
$379$	11618.2	1.57464	0.787319	−	0.616545i	$-0.211468\pi$
$379$	11618.2	1.57464	0.787319	+	0.616545i	$0.211468\pi$
$380$	12128.8	1.63736
$381$	5362.87	0.721124
$382$	5099.17	0.682974
$383$	−2903.09	−0.387313	−0.193656	−	0.981069i	$-0.562035\pi$
$383$	−2903.09	−0.387313	−0.193656	+	0.981069i	$0.562035\pi$
$384$	−565.943	−0.0752100
$385$	0	0
$386$	7014.87	0.924993
$387$	242.554	0.0318597
$388$	10322.1	1.35058
$389$	10117.3	1.31869	0.659344	−	0.751841i	$-0.270834\pi$
$389$	10117.3	1.31869	0.659344	+	0.751841i	$0.270834\pi$
$390$	2639.05	0.342650
$391$	−857.394	−0.110896
$392$	0	0
$393$	−5151.63	−0.661235
$394$	−18820.4	−2.40650
$395$	−20409.4	−2.59977
$396$	−213.531	−0.0270967
$397$	9070.47	1.14669	0.573343	−	0.819316i	$-0.305646\pi$
$397$	9070.47	1.14669	0.573343	+	0.819316i	$0.305646\pi$
$398$	20422.4	2.57207
$399$	0	0
$400$	−16781.5	−2.09769
$401$	−8942.35	−1.11362	−0.556808	−	0.830641i	$-0.687974\pi$
$401$	−8942.35	−1.11362	−0.556808	+	0.830641i	$0.687974\pi$
$402$	−7037.42	−0.873120
$403$	2539.29	0.313873
$404$	9510.36	1.17118
$405$	−5822.42	−0.714366
$406$	0	0
$407$	276.033	0.0336178
$408$	−75.2842	−0.00913511
$409$	−3451.20	−0.417239	−0.208620	−	0.977997i	$-0.566897\pi$
$409$	−3451.20	−0.417239	−0.208620	+	0.977997i	$0.566897\pi$
$410$	26426.8	3.18323
$411$	6657.03	0.798946
$412$	14427.1	1.72517
$413$	0	0
$414$	4327.66	0.513751
$415$	−14457.2	−1.71006
$416$	−3465.38	−0.408424
$417$	2359.79	0.277121
$418$	345.924	0.0404778
$419$	6173.72	0.719823	0.359912	−	0.932986i	$-0.382807\pi$
$419$	6173.72	0.719823	0.359912	+	0.932986i	$0.382807\pi$
$420$	0	0
$421$	711.474	0.0823638	0.0411819	−	0.999152i	$-0.486888\pi$
$421$	711.474	0.0823638	0.0411819	+	0.999152i	$0.486888\pi$
$422$	−224.291	−0.0258728
$423$	−7665.48	−0.881107
$424$	−947.064	−0.108475
$425$	−4740.30	−0.541031
$426$	−2814.25	−0.320073
$427$	0	0
$428$	5297.21	0.598249
$429$	38.6670	0.00435166
$430$	−934.546	−0.104809
$431$	−7115.39	−0.795212	−0.397606	−	0.917556i	$-0.630159\pi$
$431$	−7115.39	−0.795212	−0.397606	+	0.917556i	$0.630159\pi$
$432$	−7006.53	−0.780328
$433$	−8784.62	−0.974970	−0.487485	−	0.873131i	$-0.662086\pi$
$433$	−8784.62	−0.974970	−0.487485	+	0.873131i	$0.662086\pi$
$434$	0	0
$435$	−1007.43	−0.111040
$436$	11805.1	1.29670
$437$	−3601.68	−0.394260
$438$	−4890.29	−0.533487
$439$	5447.31	0.592223	0.296111	−	0.955153i	$-0.404310\pi$
$439$	5447.31	0.592223	0.296111	+	0.955153i	$0.404310\pi$
$440$	43.9621	0.00476321
$441$	0	0
$442$	−923.435	−0.0993740
$443$	465.413	0.0499152	0.0249576	−	0.999689i	$-0.492055\pi$
$443$	465.413	0.0499152	0.0249576	+	0.999689i	$0.492055\pi$
$444$	−4722.61	−0.504787
$445$	14759.8	1.57232
$446$	−22711.2	−2.41123
$447$	1320.59	0.139736
$448$	0	0
$449$	3901.83	0.410109	0.205054	−	0.978751i	$-0.434263\pi$
$449$	3901.83	0.410109	0.205054	+	0.978751i	$0.434263\pi$
$450$	23926.5	2.50645
$451$	387.202	0.0404271
$452$	−19602.3	−2.03986
$453$	−710.865	−0.0737293
$454$	−367.709	−0.0380120
$455$	0	0
$456$	−316.249	−0.0324774
$457$	10160.5	1.04002	0.520008	−	0.854162i	$-0.325929\pi$
$457$	10160.5	1.04002	0.520008	+	0.854162i	$0.325929\pi$
$458$	−8485.04	−0.865677
$459$	−1979.14	−0.201260
$460$	−8565.96	−0.868239
$461$	−11899.0	−1.20215	−0.601076	−	0.799192i	$-0.705261\pi$
$461$	−11899.0	−1.20215	−0.601076	+	0.799192i	$0.705261\pi$
$462$	0	0
$463$	3915.58	0.393029	0.196514	−	0.980501i	$-0.437038\pi$
$463$	3915.58	0.393029	0.196514	+	0.980501i	$0.437038\pi$
$464$	1247.95	0.124859
$465$	−9211.89	−0.918690
$466$	−6597.88	−0.655882
$467$	1343.16	0.133093	0.0665463	−	0.997783i	$-0.478802\pi$
$467$	1343.16	0.133093	0.0665463	+	0.997783i	$0.478802\pi$
$468$	2394.47	0.236505
$469$	0	0
$470$	29534.6	2.89858
$471$	6587.13	0.644414
$472$	−724.217	−0.0706246
$473$	−13.6929	−0.00133108
$474$	9958.95	0.965042
$475$	−19912.7	−1.92349
$476$	0	0
$477$	−10937.7	−1.04990
$478$	−4401.62	−0.421183
$479$	−11153.4	−1.06391	−0.531953	−	0.846774i	$-0.678542\pi$
$479$	−11153.4	−1.06391	−0.531953	+	0.846774i	$0.678542\pi$
$480$	12571.5	1.19544
$481$	−3095.36	−0.293422
$482$	−1184.26	−0.111912
$483$	0	0
$484$	−11237.0	−1.05532
$485$	−24543.3	−2.29784
$486$	15590.7	1.45516
$487$	1765.27	0.164255	0.0821273	−	0.996622i	$-0.473829\pi$
$487$	1765.27	0.164255	0.0821273	+	0.996622i	$0.473829\pi$
$488$	877.904	0.0814361
$489$	6166.04	0.570221
$490$	0	0
$491$	−129.551	−0.0119075	−0.00595374	−	0.999982i	$-0.501895\pi$
$491$	−129.551	−0.0119075	−0.00595374	+	0.999982i	$0.501895\pi$
$492$	−6624.59	−0.607031
$493$	352.511	0.0322034
$494$	−3879.10	−0.353297
$495$	507.722	0.0461018
$496$	11411.3	1.03303
$497$	0	0
$498$	7054.51	0.634780
$499$	3464.69	0.310823	0.155412	−	0.987850i	$-0.450330\pi$
$499$	3464.69	0.310823	0.155412	+	0.987850i	$0.450330\pi$
$500$	−26128.7	−2.33702
$501$	−3244.52	−0.289330
$502$	−30042.8	−2.67107
$503$	−5741.59	−0.508956	−0.254478	−	0.967079i	$-0.581904\pi$
$503$	−5741.59	−0.508956	−0.254478	+	0.967079i	$0.581904\pi$
$504$	0	0
$505$	−22613.2	−1.99263
$506$	−244.309	−0.0214641
$507$	4877.87	0.427286
$508$	−18747.9	−1.63741
$509$	9224.79	0.803304	0.401652	−	0.915792i	$-0.368436\pi$
$509$	9224.79	0.803304	0.401652	+	0.915792i	$0.368436\pi$
$510$	3349.99	0.290863
$511$	0	0
$512$	−16455.0	−1.42034
$513$	−8313.83	−0.715526
$514$	−9797.94	−0.840795
$515$	−34304.0	−2.93517
$516$	234.269	0.0199867
$517$	432.738	0.0368120
$518$	0	0
$519$	9197.73	0.777910
$520$	−492.979	−0.0415742
$521$	10452.0	0.878908	0.439454	−	0.898265i	$-0.355172\pi$
$521$	10452.0	0.878908	0.439454	+	0.898265i	$0.355172\pi$
$522$	−1779.28	−0.149190
$523$	−19285.9	−1.61246	−0.806229	−	0.591604i	$-0.798495\pi$
$523$	−19285.9	−1.61246	−0.806229	+	0.591604i	$0.798495\pi$
$524$	18009.4	1.50142
$525$	0	0
$526$	23308.2	1.93210
$527$	3223.35	0.266435
$528$	173.765	0.0143223
$529$	−9623.32	−0.790936
$530$	42142.3	3.45386
$531$	−8364.03	−0.683555
$532$	0	0
$533$	−4341.98	−0.352855
$534$	−7202.17	−0.583649
$535$	−12595.4	−1.01785
$536$	1314.60	0.105937
$537$	−2938.76	−0.236158
$538$	17730.3	1.42084
$539$	0	0
$540$	−19773.0	−1.57573
$541$	5729.73	0.455342	0.227671	−	0.973738i	$-0.426889\pi$
$541$	5729.73	0.455342	0.227671	+	0.973738i	$0.426889\pi$
$542$	26698.5	2.11586
$543$	−145.059	−0.0114642
$544$	−4398.93	−0.346696
$545$	−28069.5	−2.20618
$546$	0	0
$547$	−13708.5	−1.07154	−0.535769	−	0.844365i	$-0.679978\pi$
$547$	−13708.5	−1.07154	−0.535769	+	0.844365i	$0.679978\pi$
$548$	−23272.1	−1.81411
$549$	10139.0	0.788197
$550$	−1350.72	−0.104718
$551$	1480.80	0.114490
$552$	223.350	0.0172218
$553$	0	0
$554$	−2047.74	−0.157040
$555$	11229.2	0.858833
$556$	−8249.51	−0.629240
$557$	2846.21	0.216513	0.108257	−	0.994123i	$-0.465473\pi$
$557$	2846.21	0.216513	0.108257	+	0.994123i	$0.465473\pi$
$558$	−16269.7	−1.23432
$559$	153.548	0.0116179
$560$	0	0
$561$	49.0836	0.00369396
$562$	−25558.0	−1.91833
$563$	17.1318	0.00128245	0.000641226	−	1.00000i	$-0.499796\pi$
$563$	17.1318	0.00128245	0.000641226		1.00000i	$0.499796\pi$
$564$	−7403.66	−0.552749
$565$	46609.3	3.47056
$566$	−16990.8	−1.26179
$567$	0	0
$568$	525.708	0.0388349
$569$	4499.52	0.331511	0.165756	−	0.986167i	$-0.446994\pi$
$569$	4499.52	0.331511	0.165756	+	0.986167i	$0.446994\pi$
$570$	14072.4	1.03408
$571$	24343.9	1.78417	0.892083	−	0.451871i	$-0.149243\pi$
$571$	24343.9	1.78417	0.892083	+	0.451871i	$0.149243\pi$
$572$	−135.175	−0.00988102
$573$	3039.34	0.221589
$574$	0	0
$575$	14063.3	1.01997
$576$	12017.9	0.869351
$577$	−20603.1	−1.48651	−0.743256	−	0.669007i	$-0.766720\pi$
$577$	−20603.1	−1.48651	−0.743256	+	0.669007i	$0.766720\pi$
$578$	−1172.20	−0.0843549
$579$	4181.19	0.300111
$580$	3521.83	0.252131
$581$	0	0
$582$	11976.1	0.852967
$583$	617.465	0.0438641
$584$	913.517	0.0647288
$585$	−5693.45	−0.402385
$586$	25984.0	1.83172
$587$	−12336.4	−0.867426	−0.433713	−	0.901051i	$-0.642797\pi$
$587$	−12336.4	−0.867426	−0.433713	+	0.901051i	$0.642797\pi$
$588$	0	0
$589$	13540.4	0.947238
$590$	32226.1	2.24869
$591$	−11217.9	−0.780780
$592$	−13910.2	−0.965718
$593$	20768.6	1.43822	0.719109	−	0.694897i	$-0.244550\pi$
$593$	20768.6	1.43822	0.719109	+	0.694897i	$0.244550\pi$
$594$	−563.943	−0.0389543
$595$	0	0
$596$	−4616.62	−0.317289
$597$	12172.7	0.834501
$598$	2739.61	0.187343
$599$	6087.20	0.415219	0.207609	−	0.978212i	$-0.433432\pi$
$599$	6087.20	0.415219	0.207609	+	0.978212i	$0.433432\pi$
$600$	1234.84	0.0840205
$601$	−24077.3	−1.63417	−0.817083	−	0.576520i	$-0.804410\pi$
$601$	−24077.3	−1.63417	−0.817083	+	0.576520i	$0.804410\pi$
$602$	0	0
$603$	15182.4	1.02533
$604$	2485.09	0.167412
$605$	26718.8	1.79550
$606$	11034.3	0.739669
$607$	−748.270	−0.0500351	−0.0250176	−	0.999687i	$-0.507964\pi$
$607$	−748.270	−0.0500351	−0.0250176	+	0.999687i	$0.507964\pi$
$608$	−18478.7	−1.23258
$609$	0	0
$610$	−39064.8	−2.59293
$611$	−4852.61	−0.321302
$612$	3039.52	0.200761
$613$	−25216.1	−1.66145	−0.830725	−	0.556682i	$-0.812074\pi$
$613$	−25216.1	−1.66145	−0.830725	+	0.556682i	$0.812074\pi$
$614$	−4836.54	−0.317894
$615$	15751.6	1.03279
$616$	0	0
$617$	23260.6	1.51773	0.758863	−	0.651250i	$-0.225755\pi$
$617$	23260.6	1.51773	0.758863	+	0.651250i	$0.225755\pi$
$618$	16738.9	1.08955
$619$	−2032.22	−0.131958	−0.0659789	−	0.997821i	$-0.521017\pi$
$619$	−2032.22	−0.131958	−0.0659789	+	0.997821i	$0.521017\pi$
$620$	32203.5	2.08601
$621$	5871.64	0.379421
$622$	−28138.2	−1.81389
$623$	0	0
$624$	−1948.55	−0.125007
$625$	27272.2	1.74542
$626$	−3164.99	−0.202074
$627$	206.187	0.0131329
$628$	−23027.7	−1.46323
$629$	−3929.23	−0.249075
$630$	0	0
$631$	−30595.2	−1.93023	−0.965115	−	0.261828i	$-0.915675\pi$
$631$	−30595.2	−1.93023	−0.965115	+	0.261828i	$0.915675\pi$
$632$	−1860.35	−0.117090
$633$	−133.688	−0.00839434
$634$	14787.0	0.926291
$635$	44577.7	2.78585
$636$	−10564.1	−0.658639
$637$	0	0
$638$	100.446	0.00623304
$639$	6071.43	0.375872
$640$	−4704.28	−0.290552
$641$	4133.21	0.254683	0.127342	−	0.991859i	$-0.459356\pi$
$641$	4133.21	0.254683	0.127342	+	0.991859i	$0.459356\pi$
$642$	6146.06	0.377828
$643$	9438.10	0.578853	0.289426	−	0.957200i	$-0.406535\pi$
$643$	9438.10	0.578853	0.289426	+	0.957200i	$0.406535\pi$
$644$	0	0
$645$	−557.033	−0.0340049
$646$	−4924.10	−0.299901
$647$	10122.1	0.615053	0.307527	−	0.951539i	$-0.400499\pi$
$647$	10122.1	0.615053	0.307527	+	0.951539i	$0.400499\pi$
$648$	−530.724	−0.0321741
$649$	472.173	0.0285584
$650$	15146.6	0.913996
$651$	0	0
$652$	−21555.7	−1.29476
$653$	−20456.5	−1.22592	−0.612960	−	0.790114i	$-0.710021\pi$
$653$	−20456.5	−1.22592	−0.612960	+	0.790114i	$0.710021\pi$
$654$	13696.8	0.818941
$655$	−42821.9	−2.55449
$656$	−19512.3	−1.16132
$657$	10550.3	0.626492
$658$	0	0
$659$	17912.9	1.05886	0.529430	−	0.848353i	$-0.322406\pi$
$659$	17912.9	1.05886	0.529430	+	0.848353i	$0.322406\pi$
$660$	490.380	0.0289212
$661$	11480.1	0.675529	0.337764	−	0.941231i	$-0.390329\pi$
$661$	11480.1	0.675529	0.337764	+	0.941231i	$0.390329\pi$
$662$	−21495.5	−1.26201
$663$	−550.410	−0.0322416
$664$	−1317.80	−0.0770188
$665$	0	0
$666$	19832.6	1.15390
$667$	−1045.81	−0.0607108
$668$	11342.4	0.656963
$669$	−13537.0	−0.782316
$670$	−58497.0	−3.37304
$671$	−572.373	−0.0329303
$672$	0	0
$673$	2032.05	0.116389	0.0581945	−	0.998305i	$-0.481466\pi$
$673$	2032.05	0.116389	0.0581945	+	0.998305i	$0.481466\pi$
$674$	−37804.1	−2.16048
$675$	32462.7	1.85110
$676$	−17052.4	−0.970208
$677$	2783.55	0.158021	0.0790107	−	0.996874i	$-0.474824\pi$
$677$	2783.55	0.158021	0.0790107	+	0.996874i	$0.474824\pi$
$678$	−22743.5	−1.28828
$679$	0	0
$680$	−625.784	−0.0352908
$681$	−219.172	−0.0123329
$682$	918.472	0.0515691
$683$	31590.3	1.76979	0.884896	−	0.465788i	$-0.154229\pi$
$683$	31590.3	1.76979	0.884896	+	0.465788i	$0.154229\pi$
$684$	12768.2	0.713750
$685$	55335.1	3.08649
$686$	0	0
$687$	−5057.48	−0.280866
$688$	690.027	0.0382370
$689$	−6924.08	−0.382854
$690$	−9938.61	−0.548343
$691$	−6256.19	−0.344423	−0.172212	−	0.985060i	$-0.555091\pi$
$691$	−6256.19	−0.344423	−0.172212	+	0.985060i	$0.555091\pi$
$692$	−32154.0	−1.76635
$693$	0	0
$694$	23156.2	1.26657
$695$	19615.3	1.07057
$696$	−91.8287	−0.00500109
$697$	−5511.67	−0.299526
$698$	−8498.01	−0.460823
$699$	−3932.65	−0.212799
$700$	0	0
$701$	−9961.74	−0.536733	−0.268366	−	0.963317i	$-0.586484\pi$
$701$	−9961.74	−0.536733	−0.268366	+	0.963317i	$0.586484\pi$
$702$	6323.90	0.340000
$703$	−16505.6	−0.885520
$704$	−678.445	−0.0363208
$705$	17604.0	0.940434
$706$	−21719.1	−1.15781
$707$	0	0
$708$	−8078.35	−0.428818
$709$	18410.2	0.975192	0.487596	−	0.873069i	$-0.337874\pi$
$709$	18410.2	0.975192	0.487596	+	0.873069i	$0.337874\pi$
$710$	−23392.9	−1.23651
$711$	−21485.3	−1.13328
$712$	1345.38	0.0708149
$713$	−9562.91	−0.502291
$714$	0	0
$715$	321.412	0.0168113
$716$	10273.5	0.536229
$717$	−2623.58	−0.136652
$718$	37314.7	1.93952
$719$	−6612.49	−0.342982	−0.171491	−	0.985186i	$-0.554859\pi$
$719$	−6612.49	−0.342982	−0.171491	+	0.985186i	$0.554859\pi$
$720$	−25585.7	−1.32434
$721$	0	0
$722$	7135.72	0.367817
$723$	−705.875	−0.0363095
$724$	507.106	0.0260310
$725$	−5782.03	−0.296192
$726$	−13037.7	−0.666494
$727$	−7352.45	−0.375085	−0.187543	−	0.982256i	$-0.560052\pi$
$727$	−7352.45	−0.375085	−0.187543	+	0.982256i	$0.560052\pi$
$728$	0	0
$729$	1469.99	0.0746830
$730$	−40649.5	−2.06097
$731$	194.913	0.00986198
$732$	9792.66	0.494463
$733$	−10649.5	−0.536630	−0.268315	−	0.963331i	$-0.586467\pi$
$733$	−10649.5	−0.536630	−0.268315	+	0.963331i	$0.586467\pi$
$734$	4486.19	0.225597
$735$	0	0
$736$	13050.6	0.653601
$737$	−857.092	−0.0428377
$738$	27819.9	1.38762
$739$	−31712.5	−1.57857	−0.789284	−	0.614029i	$-0.789548\pi$
$739$	−31712.5	−1.57857	−0.789284	+	0.614029i	$0.789548\pi$
$740$	−39255.7	−1.95009
$741$	−2312.12	−0.114626
$742$	0	0
$743$	−29153.4	−1.43948	−0.719741	−	0.694243i	$-0.755739\pi$
$743$	−29153.4	−1.43948	−0.719741	+	0.694243i	$0.755739\pi$
$744$	−839.680	−0.0413766
$745$	10977.1	0.539828
$746$	−7252.30	−0.355932
$747$	−15219.3	−0.745443
$748$	−171.590	−0.00838763
$749$	0	0
$750$	−30315.6	−1.47596
$751$	29781.7	1.44707	0.723535	−	0.690287i	$-0.242516\pi$
$751$	29781.7	1.44707	0.723535	+	0.690287i	$0.242516\pi$
$752$	−21807.1	−1.05748
$753$	−17906.9	−0.866619
$754$	−1126.37	−0.0544031
$755$	−5908.92	−0.284831
$756$	0	0
$757$	−28726.2	−1.37922	−0.689612	−	0.724179i	$-0.742219\pi$
$757$	−28726.2	−1.37922	−0.689612	+	0.724179i	$0.742219\pi$
$758$	−47124.2	−2.25808
$759$	−145.619	−0.00696396
$760$	−2628.75	−0.125467
$761$	−13567.1	−0.646264	−0.323132	−	0.946354i	$-0.604736\pi$
$761$	−13567.1	−0.646264	−0.323132	+	0.946354i	$0.604736\pi$
$762$	−21752.1	−1.03412
$763$	0	0
$764$	−10625.1	−0.503147
$765$	−7227.22	−0.341570
$766$	11775.1	0.555420
$767$	−5294.82	−0.249263
$768$	−8691.68	−0.408378
$769$	13294.8	0.623436	0.311718	−	0.950175i	$-0.399096\pi$
$769$	13294.8	0.623436	0.311718	+	0.950175i	$0.399096\pi$
$770$	0	0
$771$	−5840.03	−0.272793
$772$	−14616.9	−0.681442
$773$	−24825.8	−1.15514	−0.577569	−	0.816342i	$-0.695999\pi$
$773$	−24825.8	−1.15514	−0.577569	+	0.816342i	$0.695999\pi$
$774$	−983.813	−0.0456879
$775$	−52870.8	−2.45055
$776$	−2237.17	−0.103492
$777$	0	0
$778$	−41036.5	−1.89104
$779$	−23153.0	−1.06488
$780$	−5498.99	−0.252430
$781$	−342.750	−0.0157037
$782$	3477.64	0.159028
$783$	−2414.08	−0.110181
$784$	0	0
$785$	54754.1	2.48950
$786$	20895.3	0.948233
$787$	−11217.2	−0.508068	−0.254034	−	0.967195i	$-0.581757\pi$
$787$	−11217.2	−0.508068	−0.254034	+	0.967195i	$0.581757\pi$
$788$	39216.1	1.77286
$789$	13892.8	0.626864
$790$	82781.7	3.72815
$791$	0	0
$792$	46.2797	0.00207636
$793$	6418.44	0.287422
$794$	−36790.4	−1.64438
$795$	25118.8	1.12059
$796$	−42554.3	−1.89484
$797$	−4812.12	−0.213869	−0.106935	−	0.994266i	$-0.534104\pi$
$797$	−4812.12	−0.213869	−0.106935	+	0.994266i	$0.534104\pi$
$798$	0	0
$799$	−6159.86	−0.272741
$800$	72153.1	3.18875
$801$	15537.9	0.685398
$802$	36270.7	1.59696
$803$	−595.592	−0.0261743
$804$	14663.9	0.643227
$805$	0	0
$806$	−10299.5	−0.450104
$807$	10568.1	0.460986
$808$	−2061.24	−0.0897452
$809$	−22315.7	−0.969814	−0.484907	−	0.874566i	$-0.661146\pi$
$809$	−22315.7	−0.969814	−0.484907	+	0.874566i	$0.661146\pi$
$810$	23616.1	1.02442
$811$	8366.39	0.362249	0.181124	−	0.983460i	$-0.442026\pi$
$811$	8366.39	0.362249	0.181124	+	0.983460i	$0.442026\pi$
$812$	0	0
$813$	15913.5	0.686485
$814$	−1119.61	−0.0482091
$815$	51253.9	2.20288
$816$	−2473.48	−0.106114
$817$	818.775	0.0350616
$818$	13998.3	0.598335
$819$	0	0
$820$	−55065.5	−2.34509
$821$	23282.4	0.989722	0.494861	−	0.868972i	$-0.335219\pi$
$821$	23282.4	0.989722	0.494861	+	0.868972i	$0.335219\pi$
$822$	−27001.3	−1.14572
$823$	6354.44	0.269140	0.134570	−	0.990904i	$-0.457035\pi$
$823$	6354.44	0.269140	0.134570	+	0.990904i	$0.457035\pi$
$824$	−3126.87	−0.132196
$825$	−805.091	−0.0339753
$826$	0	0
$827$	3951.87	0.166167	0.0830834	−	0.996543i	$-0.473523\pi$
$827$	3951.87	0.166167	0.0830834	+	0.996543i	$0.473523\pi$
$828$	−9017.54	−0.378480
$829$	−9169.30	−0.384153	−0.192077	−	0.981380i	$-0.561522\pi$
$829$	−9169.30	−0.384153	−0.192077	+	0.981380i	$0.561522\pi$
$830$	58639.1	2.45228
$831$	−1220.55	−0.0509512
$832$	7607.90	0.317015
$833$	0	0
$834$	−9571.45	−0.397401
$835$	−26969.4	−1.11774
$836$	−720.802	−0.0298199
$837$	−22074.3	−0.911588
$838$	−25041.0	−1.03225
$839$	2782.58	0.114500	0.0572498	−	0.998360i	$-0.481767\pi$
$839$	2782.58	0.114500	0.0572498	+	0.998360i	$0.481767\pi$
$840$	0	0
$841$	−23959.0	−0.982370
$842$	−2885.78	−0.118112
$843$	−15233.8	−0.622396
$844$	467.355	0.0190605
$845$	40546.3	1.65069
$846$	31091.6	1.26354
$847$	0	0
$848$	−31116.0	−1.26006
$849$	−10127.3	−0.409385
$850$	19226.9	0.775857
$851$	11657.1	0.469564
$852$	5864.06	0.235797
$853$	−15308.3	−0.614475	−0.307237	−	0.951633i	$-0.599405\pi$
$853$	−15308.3	−0.614475	−0.307237	+	0.951633i	$0.599405\pi$
$854$	0	0
$855$	−30359.6	−1.21436
$856$	−1148.10	−0.0458424
$857$	−5104.84	−0.203475	−0.101737	−	0.994811i	$-0.532440\pi$
$857$	−5104.84	−0.203475	−0.101737	+	0.994811i	$0.532440\pi$
$858$	−156.836	−0.00624042
$859$	−48619.9	−1.93119	−0.965594	−	0.260054i	$-0.916259\pi$
$859$	−48619.9	−1.93119	−0.965594	+	0.260054i	$0.916259\pi$
$860$	1947.31	0.0772126
$861$	0	0
$862$	28860.5	1.14036
$863$	41705.6	1.64504	0.822522	−	0.568733i	$-0.192566\pi$
$863$	41705.6	1.64504	0.822522	+	0.568733i	$0.192566\pi$
$864$	30124.9	1.18619
$865$	76454.2	3.00522
$866$	35630.9	1.39814
$867$	−698.687	−0.0273687
$868$	0	0
$869$	1212.91	0.0473476
$870$	4086.18	0.159235
$871$	9611.19	0.373895
$872$	−2558.59	−0.0993632
$873$	−25837.2	−1.00167
$874$	14608.6	0.565382
$875$	0	0
$876$	10189.9	0.393020
$877$	13830.8	0.532533	0.266267	−	0.963899i	$-0.414210\pi$
$877$	13830.8	0.532533	0.266267	+	0.963899i	$0.414210\pi$
$878$	−22094.6	−0.849267
$879$	15487.7	0.594297
$880$	1444.39	0.0553298
$881$	−33276.8	−1.27256	−0.636280	−	0.771458i	$-0.719528\pi$
$881$	−33276.8	−1.27256	−0.636280	+	0.771458i	$0.719528\pi$
$882$	0	0
$883$	−47621.9	−1.81496	−0.907478	−	0.420100i	$-0.861995\pi$
$883$	−47621.9	−1.81496	−0.907478	+	0.420100i	$0.861995\pi$
$884$	1924.16	0.0732088
$885$	19208.3	0.729581
$886$	−1887.74	−0.0715801
$887$	31743.2	1.20162	0.600808	−	0.799394i	$-0.294846\pi$
$887$	31743.2	1.20162	0.600808	+	0.799394i	$0.294846\pi$
$888$	1023.56	0.0386806
$889$	0	0
$890$	−59866.5	−2.25475
$891$	346.020	0.0130102
$892$	47323.4	1.77635
$893$	−25875.9	−0.969657
$894$	−5356.40	−0.200386
$895$	−24427.9	−0.912327
$896$	0	0
$897$	1632.94	0.0607828
$898$	−15826.1	−0.588110
$899$	3931.71	0.145862
$900$	−49855.6	−1.84650
$901$	−8789.37	−0.324991
$902$	−1570.51	−0.0579738
$903$	0	0
$904$	4248.52	0.156309
$905$	−1205.77	−0.0442886
$906$	2883.31	0.105730
$907$	33521.0	1.22717	0.613587	−	0.789627i	$-0.289726\pi$
$907$	33521.0	1.22717	0.613587	+	0.789627i	$0.289726\pi$
$908$	766.195	0.0280034
$909$	−23805.4	−0.868618
$910$	0	0
$911$	22942.4	0.834376	0.417188	−	0.908820i	$-0.363016\pi$
$911$	22942.4	0.834376	0.417188	+	0.908820i	$0.363016\pi$
$912$	−10390.4	−0.377260
$913$	859.174	0.0311440
$914$	−41211.5	−1.49142
$915$	−23284.5	−0.841269
$916$	17680.3	0.637744
$917$	0	0
$918$	8027.51	0.288614
$919$	−6680.27	−0.239784	−0.119892	−	0.992787i	$-0.538255\pi$
$919$	−6680.27	−0.239784	−0.119892	+	0.992787i	$0.538255\pi$
$920$	1856.55	0.0665312
$921$	−2882.81	−0.103140
$922$	48263.1	1.72393
$923$	3843.50	0.137064
$924$	0	0
$925$	64448.8	2.29088
$926$	−15881.8	−0.563616
$927$	−36112.4	−1.27949
$928$	−5365.64	−0.189801
$929$	−2304.25	−0.0813777	−0.0406888	−	0.999172i	$-0.512955\pi$
$929$	−2304.25	−0.0813777	−0.0406888	+	0.999172i	$0.512955\pi$
$930$	37364.0	1.31743
$931$	0	0
$932$	13748.0	0.483188
$933$	−16771.7	−0.588511
$934$	−5447.95	−0.190859
$935$	407.997	0.0142705
$936$	−518.968	−0.0181229
$937$	−7382.23	−0.257382	−0.128691	−	0.991685i	$-0.541078\pi$
$937$	−7382.23	−0.257382	−0.128691	+	0.991685i	$0.541078\pi$
$938$	0	0
$939$	−1886.48	−0.0655623
$940$	−61541.3	−2.13538
$941$	28855.3	0.999635	0.499818	−	0.866131i	$-0.333400\pi$
$941$	28855.3	0.999635	0.499818	+	0.866131i	$0.333400\pi$
$942$	−26717.8	−0.924111
$943$	16351.8	0.564675
$944$	−23794.3	−0.820380
$945$	0	0
$946$	55.5391	0.00190881
$947$	−28200.6	−0.967683	−0.483841	−	0.875156i	$-0.660759\pi$
$947$	−28200.6	−0.967683	−0.483841	+	0.875156i	$0.660759\pi$
$948$	−20751.5	−0.710946
$949$	6678.81	0.228455
$950$	80767.1	2.75835
$951$	8813.77	0.300532
$952$	0	0
$953$	−25766.1	−0.875809	−0.437904	−	0.899022i	$-0.644279\pi$
$953$	−25766.1	−0.875809	−0.437904	+	0.899022i	$0.644279\pi$
$954$	44364.0	1.50559
$955$	25263.9	0.856042
$956$	9171.67	0.310286
$957$	59.8703	0.00202229
$958$	45238.7	1.52568
$959$	0	0
$960$	−27599.5	−0.927886
$961$	6160.52	0.206791
$962$	12555.0	0.420778
$963$	−13259.4	−0.443696
$964$	2467.65	0.0824455
$965$	34755.2	1.15939
$966$	0	0
$967$	5615.26	0.186737	0.0933684	−	0.995632i	$-0.470237\pi$
$967$	5615.26	0.186737	0.0933684	+	0.995632i	$0.470237\pi$
$968$	2435.47	0.0808667
$969$	−2934.99	−0.0973019
$970$	99549.1	3.29518
$971$	36408.6	1.20330	0.601652	−	0.798758i	$-0.294509\pi$
$971$	36408.6	1.20330	0.601652	+	0.798758i	$0.294509\pi$
$972$	−32486.3	−1.07202
$973$	0	0
$974$	−7160.04	−0.235547
$975$	9028.06	0.296543
$976$	28843.7	0.945968
$977$	−25476.3	−0.834248	−0.417124	−	0.908850i	$-0.636962\pi$
$977$	−25476.3	−0.834248	−0.417124	+	0.908850i	$0.636962\pi$
$978$	−25009.8	−0.817716
$979$	−877.157	−0.0286354
$980$	0	0
$981$	−29549.3	−0.961709
$982$	525.468	0.0170757
$983$	−54918.7	−1.78193	−0.890963	−	0.454075i	$-0.849970\pi$
$983$	−54918.7	−1.78193	−0.890963	+	0.454075i	$0.849970\pi$
$984$	1435.79	0.0465154
$985$	−93246.0	−3.01631
$986$	−1429.80	−0.0461808
$987$	0	0
$988$	8082.88	0.260274
$989$	−578.259	−0.0185921
$990$	−2059.35	−0.0661115
$991$	34947.1	1.12021	0.560106	−	0.828421i	$-0.310760\pi$
$991$	34947.1	1.12021	0.560106	+	0.828421i	$0.310760\pi$
$992$	−49063.3	−1.57032
$993$	−12812.3	−0.409454
$994$	0	0
$995$	101183.	3.22385
$996$	−14699.5	−0.467642
$997$	47930.2	1.52253	0.761267	−	0.648439i	$-0.224578\pi$
$997$	47930.2	1.52253	0.761267	+	0.648439i	$0.224578\pi$
$998$	−14053.0	−0.445731
$999$	26908.3	0.852192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.4.a.g.1.2		9
7.6	odd	2		119.4.a.e.1.2	✓	9
21.20	even	2		1071.4.a.r.1.8		9
28.27	even	2		1904.4.a.s.1.5		9
119.118	odd	2		2023.4.a.h.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.2	✓	9	7.6	odd	2
833.4.a.g.1.2		9	1.1	even	1	trivial
1071.4.a.r.1.8		9	21.20	even	2
1904.4.a.s.1.5		9	28.27	even	2
2023.4.a.h.1.2		9	119.118	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)

\(f(q)\)	\(=\)	\(q-4.05606 q^{2} -2.41760 q^{3} +8.45161 q^{4} -20.0958 q^{5} +9.80593 q^{6} -1.83177 q^{8} -21.1552 q^{9} +O(q^{10})\)	\(q-4.05606 q^{2} -2.41760 q^{3} +8.45161 q^{4} -20.0958 q^{5} +9.80593 q^{6} -1.83177 q^{8} -21.1552 q^{9} +81.5097 q^{10} +1.19427 q^{11} -20.4326 q^{12} -13.3922 q^{13} +48.5836 q^{15} -60.1831 q^{16} -17.0000 q^{17} +85.8067 q^{18} -71.4124 q^{19} -169.842 q^{20} -4.84404 q^{22} +50.4349 q^{23} +4.42849 q^{24} +278.841 q^{25} +54.3197 q^{26} +116.420 q^{27} -20.7359 q^{29} -197.058 q^{30} -189.609 q^{31} +258.761 q^{32} -2.88727 q^{33} +68.9530 q^{34} -178.796 q^{36} +231.131 q^{37} +289.653 q^{38} +32.3771 q^{39} +36.8108 q^{40} +324.216 q^{41} -11.4655 q^{43} +10.0935 q^{44} +425.131 q^{45} -204.567 q^{46} +362.345 q^{47} +145.499 q^{48} -1131.00 q^{50} +41.0992 q^{51} -113.186 q^{52} +517.022 q^{53} -472.207 q^{54} -23.9998 q^{55} +172.647 q^{57} +84.1061 q^{58} +395.365 q^{59} +410.610 q^{60} -479.266 q^{61} +769.065 q^{62} -568.083 q^{64} +269.128 q^{65} +11.7109 q^{66} -717.669 q^{67} -143.677 q^{68} -121.932 q^{69} -286.995 q^{71} +38.7514 q^{72} -498.708 q^{73} -937.480 q^{74} -674.127 q^{75} -603.550 q^{76} -131.323 q^{78} +1015.60 q^{79} +1209.43 q^{80} +289.733 q^{81} -1315.04 q^{82} +719.413 q^{83} +341.629 q^{85} +46.5045 q^{86} +50.1312 q^{87} -2.18763 q^{88} -734.471 q^{89} -1724.36 q^{90} +426.256 q^{92} +458.399 q^{93} -1469.69 q^{94} +1435.09 q^{95} -625.580 q^{96} +1221.31 q^{97} -25.2651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} - 11 q^{3} + 38 q^{4} + 3 q^{5} - 9 q^{6} + 24 q^{8} + 74 q^{9} - 134 q^{10} - 8 q^{11} - 56 q^{12} - 164 q^{13} + 34 q^{15} + 178 q^{16} - 153 q^{17} + 98 q^{18} - 244 q^{19} + 41 q^{20} - 80 q^{22} - 14 q^{23} - 298 q^{24} + 684 q^{25} - 326 q^{26} - 218 q^{27} - 234 q^{29} - 335 q^{30} - 555 q^{31} - 181 q^{32} - 458 q^{33} - 34 q^{34} - 1221 q^{36} - 364 q^{37} + 714 q^{38} - 52 q^{39} - 123 q^{40} + 45 q^{41} - 135 q^{43} - 748 q^{44} + 844 q^{45} - 1576 q^{46} + 172 q^{47} + 949 q^{48} - 2901 q^{50} + 187 q^{51} + 1596 q^{52} + 101 q^{53} + 1163 q^{54} - 1260 q^{55} - 602 q^{57} + 1062 q^{58} - 280 q^{59} - 1727 q^{60} - 639 q^{61} + 1708 q^{62} - 2390 q^{64} + 638 q^{65} + 2476 q^{66} + 35 q^{67} - 646 q^{68} - 1288 q^{69} - 1616 q^{71} + 1335 q^{72} - 1049 q^{73} - 370 q^{74} - 1260 q^{75} - 4964 q^{76} - 4714 q^{78} + 2304 q^{79} + 3996 q^{80} - 791 q^{81} + 215 q^{82} - 2508 q^{83} - 51 q^{85} + 623 q^{86} - 166 q^{87} - 416 q^{88} - 2762 q^{89} - 2935 q^{90} - 2392 q^{92} + 2784 q^{93} + 862 q^{94} - 3462 q^{95} - 2928 q^{96} - 3107 q^{97} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 - 11 * q^3 + 38 * q^4 + 3 * q^5 - 9 * q^6 + 24 * q^8 + 74 * q^9 - 134 * q^10 - 8 * q^11 - 56 * q^12 - 164 * q^13 + 34 * q^15 + 178 * q^16 - 153 * q^17 + 98 * q^18 - 244 * q^19 + 41 * q^20 - 80 * q^22 - 14 * q^23 - 298 * q^24 + 684 * q^25 - 326 * q^26 - 218 * q^27 - 234 * q^29 - 335 * q^30 - 555 * q^31 - 181 * q^32 - 458 * q^33 - 34 * q^34 - 1221 * q^36 - 364 * q^37 + 714 * q^38 - 52 * q^39 - 123 * q^40 + 45 * q^41 - 135 * q^43 - 748 * q^44 + 844 * q^45 - 1576 * q^46 + 172 * q^47 + 949 * q^48 - 2901 * q^50 + 187 * q^51 + 1596 * q^52 + 101 * q^53 + 1163 * q^54 - 1260 * q^55 - 602 * q^57 + 1062 * q^58 - 280 * q^59 - 1727 * q^60 - 639 * q^61 + 1708 * q^62 - 2390 * q^64 + 638 * q^65 + 2476 * q^66 + 35 * q^67 - 646 * q^68 - 1288 * q^69 - 1616 * q^71 + 1335 * q^72 - 1049 * q^73 - 370 * q^74 - 1260 * q^75 - 4964 * q^76 - 4714 * q^78 + 2304 * q^79 + 3996 * q^80 - 791 * q^81 + 215 * q^82 - 2508 * q^83 - 51 * q^85 + 623 * q^86 - 166 * q^87 - 416 * q^88 - 2762 * q^89 - 2935 * q^90 - 2392 * q^92 + 2784 * q^93 + 862 * q^94 - 3462 * q^95 - 2928 * q^96 - 3107 * q^97 - 2396 * q^99

Introduction

L-functions

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