LMFDB - Embedded newform 1694.4.a.bh.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1694,4,Mod(1,1694)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1694, 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("1694.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1694 = 2 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1694.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:	$99.9492355497$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 170 x^{8} + 272 x^{7} + 9867 x^{6} - 15814 x^{5} - 224781 x^{4} + 465188 x^{3} + \cdots + 3321791 $ x^10 - 2x^9 - 170x^8 + 272x^7 + 9867x^6 - 15814x^5 - 224781x^4 + 465188x^3 + 1558988x^2 - 4839884*x + 3321791
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 11^{3} $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-7.61218$ of defining polynomial
Character	$\chi$	$=$	1694.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -9.23021 q^{3} +4.00000 q^{4} +21.4359 q^{5} +18.4604 q^{6} +7.00000 q^{7} -8.00000 q^{8} +58.1968 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -9.23021 q^{3} +4.00000 q^{4} +21.4359 q^{5} +18.4604 q^{6} +7.00000 q^{7} -8.00000 q^{8} +58.1968 q^{9} -42.8717 q^{10} -36.9209 q^{12} -21.9077 q^{13} -14.0000 q^{14} -197.858 q^{15} +16.0000 q^{16} +51.8835 q^{17} -116.394 q^{18} -7.23231 q^{19} +85.7435 q^{20} -64.6115 q^{21} -210.459 q^{23} +73.8417 q^{24} +334.497 q^{25} +43.8154 q^{26} -287.954 q^{27} +28.0000 q^{28} +174.591 q^{29} +395.715 q^{30} -182.323 q^{31} -32.0000 q^{32} -103.767 q^{34} +150.051 q^{35} +232.787 q^{36} -53.1781 q^{37} +14.4646 q^{38} +202.213 q^{39} -171.487 q^{40} +339.243 q^{41} +129.223 q^{42} +245.040 q^{43} +1247.50 q^{45} +420.918 q^{46} +170.721 q^{47} -147.683 q^{48} +49.0000 q^{49} -668.993 q^{50} -478.896 q^{51} -87.6308 q^{52} +76.4223 q^{53} +575.907 q^{54} -56.0000 q^{56} +66.7558 q^{57} -349.183 q^{58} +316.293 q^{59} -791.431 q^{60} +395.412 q^{61} +364.646 q^{62} +407.378 q^{63} +64.0000 q^{64} -469.611 q^{65} +5.26778 q^{67} +207.534 q^{68} +1942.58 q^{69} -300.102 q^{70} +160.144 q^{71} -465.575 q^{72} -322.908 q^{73} +106.356 q^{74} -3087.47 q^{75} -28.9292 q^{76} -404.425 q^{78} +783.992 q^{79} +342.974 q^{80} +1086.56 q^{81} -678.487 q^{82} +288.559 q^{83} -258.446 q^{84} +1112.17 q^{85} -490.080 q^{86} -1611.52 q^{87} -666.266 q^{89} -2495.00 q^{90} -153.354 q^{91} -841.836 q^{92} +1682.88 q^{93} -341.442 q^{94} -155.031 q^{95} +295.367 q^{96} -557.955 q^{97} -98.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 20 q^{2} - 3 q^{3} + 40 q^{4} - 27 q^{5} + 6 q^{6} + 70 q^{7} - 80 q^{8} + 97 q^{9}+O(q^{10}) $ 10 * q - 20 * q^2 - 3 * q^3 + 40 * q^4 - 27 * q^5 + 6 * q^6 + 70 * q^7 - 80 * q^8 + 97 * q^9	\( 10 q - 20 q^{2} - 3 q^{3} + 40 q^{4} - 27 q^{5} + 6 q^{6} + 70 q^{7} - 80 q^{8} + 97 q^{9} + 54 q^{10} - 12 q^{12} + 78 q^{13} - 140 q^{14} - 72 q^{15} + 160 q^{16} + 80 q^{17} - 194 q^{18} + 178 q^{19} - 108 q^{20} - 21 q^{21} - 99 q^{23} + 24 q^{24} + 669 q^{25} - 156 q^{26} - 258 q^{27} + 280 q^{28} + 346 q^{29} + 144 q^{30} - 359 q^{31} - 320 q^{32} - 160 q^{34} - 189 q^{35} + 388 q^{36} + 645 q^{37} - 356 q^{38} + 453 q^{39} + 216 q^{40} + 177 q^{41} + 42 q^{42} + 1817 q^{43} - 1009 q^{45} + 198 q^{46} - 873 q^{47} - 48 q^{48} + 490 q^{49} - 1338 q^{50} + 525 q^{51} + 312 q^{52} - 854 q^{53} + 516 q^{54} - 560 q^{56} + 806 q^{57} - 692 q^{58} - 513 q^{59} - 288 q^{60} + 2084 q^{61} + 718 q^{62} + 679 q^{63} + 640 q^{64} - 425 q^{65} - 119 q^{67} + 320 q^{68} + 308 q^{69} + 378 q^{70} - 276 q^{71} - 776 q^{72} + 779 q^{73} - 1290 q^{74} - 6417 q^{75} + 712 q^{76} - 906 q^{78} + 2475 q^{79} - 432 q^{80} + 2946 q^{81} - 354 q^{82} + 463 q^{83} - 84 q^{84} - 580 q^{85} - 3634 q^{86} + 1014 q^{87} - 2065 q^{89} + 2018 q^{90} + 546 q^{91} - 396 q^{92} - 487 q^{93} + 1746 q^{94} + 2612 q^{95} + 96 q^{96} - 3666 q^{97} - 980 q^{98}+O(q^{100}) \) 10 * q - 20 * q^2 - 3 * q^3 + 40 * q^4 - 27 * q^5 + 6 * q^6 + 70 * q^7 - 80 * q^8 + 97 * q^9 + 54 * q^10 - 12 * q^12 + 78 * q^13 - 140 * q^14 - 72 * q^15 + 160 * q^16 + 80 * q^17 - 194 * q^18 + 178 * q^19 - 108 * q^20 - 21 * q^21 - 99 * q^23 + 24 * q^24 + 669 * q^25 - 156 * q^26 - 258 * q^27 + 280 * q^28 + 346 * q^29 + 144 * q^30 - 359 * q^31 - 320 * q^32 - 160 * q^34 - 189 * q^35 + 388 * q^36 + 645 * q^37 - 356 * q^38 + 453 * q^39 + 216 * q^40 + 177 * q^41 + 42 * q^42 + 1817 * q^43 - 1009 * q^45 + 198 * q^46 - 873 * q^47 - 48 * q^48 + 490 * q^49 - 1338 * q^50 + 525 * q^51 + 312 * q^52 - 854 * q^53 + 516 * q^54 - 560 * q^56 + 806 * q^57 - 692 * q^58 - 513 * q^59 - 288 * q^60 + 2084 * q^61 + 718 * q^62 + 679 * q^63 + 640 * q^64 - 425 * q^65 - 119 * q^67 + 320 * q^68 + 308 * q^69 + 378 * q^70 - 276 * q^71 - 776 * q^72 + 779 * q^73 - 1290 * q^74 - 6417 * q^75 + 712 * q^76 - 906 * q^78 + 2475 * q^79 - 432 * q^80 + 2946 * q^81 - 354 * q^82 + 463 * q^83 - 84 * q^84 - 580 * q^85 - 3634 * q^86 + 1014 * q^87 - 2065 * q^89 + 2018 * q^90 + 546 * q^91 - 396 * q^92 - 487 * q^93 + 1746 * q^94 + 2612 * q^95 + 96 * q^96 - 3666 * q^97 - 980 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−9.23021	−1.77636	−0.888178	−	0.459500i	$-0.848029\pi$
$3$	−9.23021	−1.77636	−0.888178	+	0.459500i	$0.848029\pi$
$4$	4.00000	0.500000
$5$	21.4359	1.91728	0.958641	−	0.284617i	$-0.0918664\pi$
$5$	21.4359	1.91728	0.958641	+	0.284617i	$0.0918664\pi$
$6$	18.4604	1.25607
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	58.1968	2.15544
$10$	−42.8717	−1.35572
$11$	0	0
$11$	0	0
$12$	−36.9209	−0.888178
$13$	−21.9077	−0.467392	−0.233696	−	0.972310i	$-0.575082\pi$
$13$	−21.9077	−0.467392	−0.233696	+	0.972310i	$0.575082\pi$
$14$	−14.0000	−0.267261
$15$	−197.858	−3.40578
$16$	16.0000	0.250000
$17$	51.8835	0.740212	0.370106	−	0.928989i	$-0.379321\pi$
$17$	51.8835	0.740212	0.370106	+	0.928989i	$0.379321\pi$
$18$	−116.394	−1.52413
$19$	−7.23231	−0.0873266	−0.0436633	−	0.999046i	$-0.513903\pi$
$19$	−7.23231	−0.0873266	−0.0436633	+	0.999046i	$0.513903\pi$
$20$	85.7435	0.958641
$21$	−64.6115	−0.671399
$22$	0	0
$23$	−210.459	−1.90799	−0.953995	−	0.299823i	$-0.903072\pi$
$23$	−210.459	−1.90799	−0.953995	+	0.299823i	$0.903072\pi$
$24$	73.8417	0.628037
$25$	334.497	2.67597
$26$	43.8154	0.330496
$27$	−287.954	−2.05247
$28$	28.0000	0.188982
$29$	174.591	1.11796	0.558979	−	0.829182i	$-0.311193\pi$
$29$	174.591	1.11796	0.558979	+	0.829182i	$0.311193\pi$
$30$	395.715	2.40825
$31$	−182.323	−1.05633	−0.528165	−	0.849142i	$-0.677120\pi$
$31$	−182.323	−1.05633	−0.528165	+	0.849142i	$0.677120\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−103.767	−0.523409
$35$	150.051	0.724665
$36$	232.787	1.07772
$37$	−53.1781	−0.236282	−0.118141	−	0.992997i	$-0.537693\pi$
$37$	−53.1781	−0.236282	−0.118141	+	0.992997i	$0.537693\pi$
$38$	14.4646	0.0617493
$39$	202.213	0.830255
$40$	−171.487	−0.677862
$41$	339.243	1.29222	0.646109	−	0.763245i	$-0.276395\pi$
$41$	339.243	1.29222	0.646109	+	0.763245i	$0.276395\pi$
$42$	129.223	0.474751
$43$	245.040	0.869029	0.434515	−	0.900665i	$-0.356920\pi$
$43$	245.040	0.869029	0.434515	+	0.900665i	$0.356920\pi$
$44$	0	0
$45$	1247.50	4.13259
$46$	420.918	1.34915
$47$	170.721	0.529834	0.264917	−	0.964271i	$-0.414655\pi$
$47$	170.721	0.529834	0.264917	+	0.964271i	$0.414655\pi$
$48$	−147.683	−0.444089
$49$	49.0000	0.142857
$50$	−668.993	−1.89220
$51$	−478.896	−1.31488
$52$	−87.6308	−0.233696
$53$	76.4223	0.198064	0.0990322	−	0.995084i	$-0.468425\pi$
$53$	76.4223	0.198064	0.0990322	+	0.995084i	$0.468425\pi$
$54$	575.907	1.45132
$55$	0	0
$56$	−56.0000	−0.133631
$57$	66.7558	0.155123
$58$	−349.183	−0.790516
$59$	316.293	0.697929	0.348965	−	0.937136i	$-0.386533\pi$
$59$	316.293	0.697929	0.348965	+	0.937136i	$0.386533\pi$
$60$	−791.431	−1.70289
$61$	395.412	0.829955	0.414978	−	0.909832i	$-0.363789\pi$
$61$	395.412	0.829955	0.414978	+	0.909832i	$0.363789\pi$
$62$	364.646	0.746938
$63$	407.378	0.814679
$64$	64.0000	0.125000
$65$	−469.611	−0.896123
$66$	0	0
$67$	5.26778	0.00960541	0.00480270	−	0.999988i	$-0.498471\pi$
$67$	5.26778	0.00960541	0.00480270	+	0.999988i	$0.498471\pi$
$68$	207.534	0.370106
$69$	1942.58	3.38927
$70$	−300.102	−0.512415
$71$	160.144	0.267684	0.133842	−	0.991003i	$-0.457268\pi$
$71$	160.144	0.267684	0.133842	+	0.991003i	$0.457268\pi$
$72$	−465.575	−0.762063
$73$	−322.908	−0.517720	−0.258860	−	0.965915i	$-0.583347\pi$
$73$	−322.908	−0.517720	−0.258860	+	0.965915i	$0.583347\pi$
$74$	106.356	0.167076
$75$	−3087.47	−4.75348
$76$	−28.9292	−0.0436633
$77$	0	0
$78$	−404.425	−0.587079
$79$	783.992	1.11653	0.558266	−	0.829662i	$-0.311467\pi$
$79$	783.992	1.11653	0.558266	+	0.829662i	$0.311467\pi$
$80$	342.974	0.479321
$81$	1086.56	1.49048
$82$	−678.487	−0.913736
$83$	288.559	0.381609	0.190804	−	0.981628i	$-0.438890\pi$
$83$	288.559	0.381609	0.190804	+	0.981628i	$0.438890\pi$
$84$	−258.446	−0.335700
$85$	1112.17	1.41920
$86$	−490.080	−0.614496
$87$	−1611.52	−1.98589
$88$	0	0
$89$	−666.266	−0.793529	−0.396764	−	0.917921i	$-0.629867\pi$
$89$	−666.266	−0.793529	−0.396764	+	0.917921i	$0.629867\pi$
$90$	−2495.00	−2.92218
$91$	−153.354	−0.176658
$92$	−841.836	−0.953995
$93$	1682.88	1.87642
$94$	−341.442	−0.374649
$95$	−155.031	−0.167430
$96$	295.367	0.314018
$97$	−557.955	−0.584039	−0.292019	−	0.956412i	$-0.594327\pi$
$97$	−557.955	−0.584039	−0.292019	+	0.956412i	$0.594327\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	1337.99	1.33799
$101$	−771.512	−0.760083	−0.380041	−	0.924969i	$-0.624090\pi$
$101$	−771.512	−0.760083	−0.380041	+	0.924969i	$0.624090\pi$
$102$	957.792	0.929761
$103$	−663.584	−0.634804	−0.317402	−	0.948291i	$-0.602811\pi$
$103$	−663.584	−0.634804	−0.317402	+	0.948291i	$0.602811\pi$
$104$	175.262	0.165248
$105$	−1385.00	−1.28726
$106$	−152.845	−0.140053
$107$	−1950.57	−1.76233	−0.881164	−	0.472811i	$-0.843239\pi$
$107$	−1950.57	−1.76233	−0.881164	+	0.472811i	$0.843239\pi$
$108$	−1151.81	−1.02623
$109$	−1908.33	−1.67693	−0.838465	−	0.544956i	$-0.816546\pi$
$109$	−1908.33	−1.67693	−0.838465	+	0.544956i	$0.816546\pi$
$110$	0	0
$111$	490.845	0.419720
$112$	112.000	0.0944911
$113$	38.6733	0.0321954	0.0160977	−	0.999870i	$-0.494876\pi$
$113$	38.6733	0.0321954	0.0160977	+	0.999870i	$0.494876\pi$
$114$	−133.512	−0.109689
$115$	−4511.37	−3.65815
$116$	698.366	0.558979
$117$	−1274.96	−1.00744
$118$	−632.586	−0.493511
$119$	363.185	0.279774
$120$	1582.86	1.20412
$121$	0	0
$122$	−790.823	−0.586867
$123$	−3131.29	−2.29544
$124$	−729.293	−0.528165
$125$	4490.74	3.21331
$126$	−814.756	−0.576065
$127$	−472.947	−0.330451	−0.165225	−	0.986256i	$-0.552835\pi$
$127$	−472.947	−0.330451	−0.165225	+	0.986256i	$0.552835\pi$
$128$	−128.000	−0.0883883
$129$	−2261.77	−1.54370
$130$	939.221	0.633655
$131$	1631.08	1.08785	0.543926	−	0.839133i	$-0.316937\pi$
$131$	1631.08	1.08785	0.543926	+	0.839133i	$0.316937\pi$
$132$	0	0
$133$	−50.6262	−0.0330064
$134$	−10.5356	−0.00679205
$135$	−6172.54	−3.93517
$136$	−415.068	−0.261705
$137$	1908.40	1.19011	0.595056	−	0.803684i	$-0.297130\pi$
$137$	1908.40	1.19011	0.595056	+	0.803684i	$0.297130\pi$
$138$	−3885.17	−2.39657
$139$	2940.04	1.79404	0.897018	−	0.441993i	$-0.145729\pi$
$139$	2940.04	1.79404	0.897018	+	0.441993i	$0.145729\pi$
$140$	600.204	0.362332
$141$	−1575.79	−0.941174
$142$	−320.288	−0.189282
$143$	0	0
$144$	931.150	0.538860
$145$	3742.52	2.14344
$146$	645.816	0.366083
$147$	−452.280	−0.253765
$148$	−212.712	−0.118141
$149$	2556.67	1.40571	0.702855	−	0.711333i	$-0.251908\pi$
$149$	2556.67	1.40571	0.702855	+	0.711333i	$0.251908\pi$
$150$	6174.95	3.36122
$151$	2453.41	1.32222	0.661110	−	0.750289i	$-0.270086\pi$
$151$	2453.41	1.32222	0.661110	+	0.750289i	$0.270086\pi$
$152$	57.8585	0.0308746
$153$	3019.46	1.59548
$154$	0	0
$155$	−3908.26	−2.02528
$156$	808.851	0.415128
$157$	−681.888	−0.346628	−0.173314	−	0.984867i	$-0.555448\pi$
$157$	−681.888	−0.346628	−0.173314	+	0.984867i	$0.555448\pi$
$158$	−1567.98	−0.789507
$159$	−705.394	−0.351833
$160$	−685.948	−0.338931
$161$	−1473.21	−0.721152
$162$	−2173.12	−1.05393
$163$	2024.99	0.973066	0.486533	−	0.873662i	$-0.338261\pi$
$163$	2024.99	0.973066	0.486533	+	0.873662i	$0.338261\pi$
$164$	1356.97	0.646109
$165$	0	0
$166$	−577.119	−0.269838
$167$	1499.11	0.694639	0.347320	−	0.937747i	$-0.387092\pi$
$167$	1499.11	0.694639	0.347320	+	0.937747i	$0.387092\pi$
$168$	516.892	0.237375
$169$	−1717.05	−0.781544
$170$	−2224.34	−1.00352
$171$	−420.898	−0.188227
$172$	980.160	0.434515
$173$	303.886	0.133549	0.0667747	−	0.997768i	$-0.478729\pi$
$173$	303.886	0.133549	0.0667747	+	0.997768i	$0.478729\pi$
$174$	3223.03	1.40424
$175$	2341.48	1.01142
$176$	0	0
$177$	−2919.45	−1.23977
$178$	1332.53	0.561109
$179$	−1664.35	−0.694968	−0.347484	−	0.937686i	$-0.612964\pi$
$179$	−1664.35	−0.694968	−0.347484	+	0.937686i	$0.612964\pi$
$180$	4990.00	2.06629
$181$	615.476	0.252751	0.126376	−	0.991982i	$-0.459666\pi$
$181$	615.476	0.252751	0.126376	+	0.991982i	$0.459666\pi$
$182$	306.708	0.124916
$183$	−3649.73	−1.47430
$184$	1683.67	0.674576
$185$	−1139.92	−0.453019
$186$	−3365.76	−1.32683
$187$	0	0
$188$	682.884	0.264917
$189$	−2015.67	−0.775761
$190$	310.062	0.118391
$191$	−460.153	−0.174322	−0.0871610	−	0.996194i	$-0.527779\pi$
$191$	−460.153	−0.174322	−0.0871610	+	0.996194i	$0.527779\pi$
$192$	−590.734	−0.222044
$193$	1682.88	0.627651	0.313825	−	0.949481i	$-0.398389\pi$
$193$	1682.88	0.627651	0.313825	+	0.949481i	$0.398389\pi$
$194$	1115.91	0.412978
$195$	4334.61	1.59183
$196$	196.000	0.0714286
$197$	676.383	0.244621	0.122310	−	0.992492i	$-0.460970\pi$
$197$	676.383	0.244621	0.122310	+	0.992492i	$0.460970\pi$
$198$	0	0
$199$	−3817.68	−1.35994	−0.679971	−	0.733239i	$-0.738008\pi$
$199$	−3817.68	−1.35994	−0.679971	+	0.733239i	$0.738008\pi$
$200$	−2675.97	−0.946099
$201$	−48.6228	−0.0170626
$202$	1543.02	0.537460
$203$	1222.14	0.422549
$204$	−1915.58	−0.657440
$205$	7271.98	2.47755
$206$	1327.17	0.448874
$207$	−12248.1	−4.11255
$208$	−350.523	−0.116848
$209$	0	0
$210$	2770.01	0.910232
$211$	−3941.63	−1.28603	−0.643017	−	0.765852i	$-0.722318\pi$
$211$	−3941.63	−1.28603	−0.643017	+	0.765852i	$0.722318\pi$
$212$	305.689	0.0990322
$213$	−1478.16	−0.475503
$214$	3901.15	1.24615
$215$	5252.65	1.66617
$216$	2303.63	0.725658
$217$	−1276.26	−0.399255
$218$	3816.67	1.18577
$219$	2980.51	0.919654
$220$	0	0
$221$	−1136.65	−0.345970
$222$	−981.690	−0.296787
$223$	3371.72	1.01250	0.506249	−	0.862387i	$-0.331032\pi$
$223$	3371.72	1.01250	0.506249	+	0.862387i	$0.331032\pi$
$224$	−224.000	−0.0668153
$225$	19466.6	5.76790
$226$	−77.3467	−0.0227656
$227$	4503.37	1.31674	0.658369	−	0.752696i	$-0.271247\pi$
$227$	4503.37	1.31674	0.658369	+	0.752696i	$0.271247\pi$
$228$	267.023	0.0775616
$229$	−2452.21	−0.707626	−0.353813	−	0.935316i	$-0.615115\pi$
$229$	−2452.21	−0.707626	−0.353813	+	0.935316i	$0.615115\pi$
$230$	9022.75	2.58671
$231$	0	0
$232$	−1396.73	−0.395258
$233$	−1821.61	−0.512179	−0.256089	−	0.966653i	$-0.582434\pi$
$233$	−1821.61	−0.512179	−0.256089	+	0.966653i	$0.582434\pi$
$234$	2549.92	0.712365
$235$	3659.55	1.01584
$236$	1265.17	0.348965
$237$	−7236.41	−1.98336
$238$	−726.370	−0.197830
$239$	3313.84	0.896881	0.448441	−	0.893813i	$-0.351980\pi$
$239$	3313.84	0.896881	0.448441	+	0.893813i	$0.351980\pi$
$240$	−3165.72	−0.851444
$241$	659.528	0.176282	0.0881409	−	0.996108i	$-0.471907\pi$
$241$	659.528	0.176282	0.0881409	+	0.996108i	$0.471907\pi$
$242$	0	0
$243$	−2254.42	−0.595148
$244$	1581.65	0.414978
$245$	1050.36	0.273898
$246$	6262.58	1.62312
$247$	158.443	0.0408158
$248$	1458.59	0.373469
$249$	−2663.47	−0.677873
$250$	−8981.48	−2.27216
$251$	6598.20	1.65926	0.829631	−	0.558312i	$-0.188551\pi$
$251$	6598.20	1.65926	0.829631	+	0.558312i	$0.188551\pi$
$252$	1629.51	0.407340
$253$	0	0
$254$	945.893	0.233664
$255$	−10265.6	−2.52100
$256$	256.000	0.0625000
$257$	−1910.73	−0.463768	−0.231884	−	0.972743i	$-0.574489\pi$
$257$	−1910.73	−0.463768	−0.231884	+	0.972743i	$0.574489\pi$
$258$	4523.54	1.09156
$259$	−372.246	−0.0893061
$260$	−1878.44	−0.448062
$261$	10160.7	2.40969
$262$	−3262.17	−0.769227
$263$	5604.02	1.31391	0.656955	−	0.753930i	$-0.271844\pi$
$263$	5604.02	1.31391	0.656955	+	0.753930i	$0.271844\pi$
$264$	0	0
$265$	1638.18	0.379745
$266$	101.252	0.0233390
$267$	6149.78	1.40959
$268$	21.0711	0.00480270
$269$	−3263.71	−0.739746	−0.369873	−	0.929082i	$-0.620599\pi$
$269$	−3263.71	−0.739746	−0.369873	+	0.929082i	$0.620599\pi$
$270$	12345.1	2.78258
$271$	−2492.25	−0.558647	−0.279323	−	0.960197i	$-0.590110\pi$
$271$	−2492.25	−0.558647	−0.279323	+	0.960197i	$0.590110\pi$
$272$	830.137	0.185053
$273$	1415.49	0.313807
$274$	−3816.79	−0.841536
$275$	0	0
$276$	7770.33	1.69463
$277$	−1550.47	−0.336314	−0.168157	−	0.985760i	$-0.553782\pi$
$277$	−1550.47	−0.336314	−0.168157	+	0.985760i	$0.553782\pi$
$278$	−5880.08	−1.26858
$279$	−10610.6	−2.27685
$280$	−1200.41	−0.256208
$281$	5044.50	1.07092	0.535462	−	0.844559i	$-0.320138\pi$
$281$	5044.50	1.07092	0.535462	+	0.844559i	$0.320138\pi$
$282$	3151.58	0.665510
$283$	2264.48	0.475651	0.237826	−	0.971308i	$-0.423565\pi$
$283$	2264.48	0.475651	0.237826	+	0.971308i	$0.423565\pi$
$284$	640.576	0.133842
$285$	1430.97	0.297415
$286$	0	0
$287$	2374.70	0.488412
$288$	−1862.30	−0.381031
$289$	−2221.10	−0.452086
$290$	−7485.04	−1.51564
$291$	5150.04	1.03746
$292$	−1291.63	−0.258860
$293$	−2586.83	−0.515782	−0.257891	−	0.966174i	$-0.583027\pi$
$293$	−2586.83	−0.515782	−0.257891	+	0.966174i	$0.583027\pi$
$294$	904.561	0.179439
$295$	6780.02	1.33813
$296$	425.425	0.0835382
$297$	0	0
$298$	−5113.34	−0.993987
$299$	4610.67	0.891780
$300$	−12349.9	−2.37674
$301$	1715.28	0.328462
$302$	−4906.81	−0.934951
$303$	7121.22	1.35018
$304$	−115.717	−0.0218317
$305$	8475.99	1.59126
$306$	−6038.92	−1.12818
$307$	−5611.02	−1.04312	−0.521560	−	0.853215i	$-0.674650\pi$
$307$	−5611.02	−1.04312	−0.521560	+	0.853215i	$0.674650\pi$
$308$	0	0
$309$	6125.02	1.12764
$310$	7816.51	1.43209
$311$	−2285.74	−0.416760	−0.208380	−	0.978048i	$-0.566819\pi$
$311$	−2285.74	−0.416760	−0.208380	+	0.978048i	$0.566819\pi$
$312$	−1617.70	−0.293540
$313$	−6003.81	−1.08420	−0.542101	−	0.840313i	$-0.682371\pi$
$313$	−6003.81	−1.08420	−0.542101	+	0.840313i	$0.682371\pi$
$314$	1363.78	0.245103
$315$	8732.50	1.56197
$316$	3135.97	0.558266
$317$	1290.97	0.228732	0.114366	−	0.993439i	$-0.463516\pi$
$317$	1290.97	0.228732	0.114366	+	0.993439i	$0.463516\pi$
$318$	1410.79	0.248783
$319$	0	0
$320$	1371.90	0.239660
$321$	18004.2	3.13052
$322$	2946.43	0.509932
$323$	−375.238	−0.0646402
$324$	4346.23	0.745239
$325$	−7328.05	−1.25073
$326$	−4049.99	−0.688062
$327$	17614.3	2.97882
$328$	−2713.95	−0.456868
$329$	1195.05	0.200258
$330$	0	0
$331$	9822.76	1.63114	0.815571	−	0.578657i	$-0.196423\pi$
$331$	9822.76	1.63114	0.815571	+	0.578657i	$0.196423\pi$
$332$	1154.24	0.190804
$333$	−3094.80	−0.509291
$334$	−2998.22	−0.491184
$335$	112.920	0.0184163
$336$	−1033.78	−0.167850
$337$	6458.34	1.04394	0.521970	−	0.852964i	$-0.325197\pi$
$337$	6458.34	1.04394	0.521970	+	0.852964i	$0.325197\pi$
$338$	3434.11	0.552635
$339$	−356.963	−0.0571905
$340$	4448.68	0.709598
$341$	0	0
$342$	841.795	0.133097
$343$	343.000	0.0539949
$344$	−1960.32	−0.307248
$345$	41640.9	6.49818
$346$	−607.773	−0.0944337
$347$	−5353.18	−0.828167	−0.414083	−	0.910239i	$-0.635898\pi$
$347$	−5353.18	−0.828167	−0.414083	+	0.910239i	$0.635898\pi$
$348$	−6446.06	−0.992946
$349$	4915.58	0.753939	0.376970	−	0.926226i	$-0.376966\pi$
$349$	4915.58	0.753939	0.376970	+	0.926226i	$0.376966\pi$
$350$	−4682.95	−0.715184
$351$	6308.40	0.959309
$352$	0	0
$353$	7736.98	1.16657	0.583283	−	0.812269i	$-0.301768\pi$
$353$	7736.98	1.16657	0.583283	+	0.812269i	$0.301768\pi$
$354$	5838.90	0.876650
$355$	3432.83	0.513227
$356$	−2665.06	−0.396764
$357$	−3352.27	−0.496978
$358$	3328.70	0.491417
$359$	−5463.05	−0.803144	−0.401572	−	0.915827i	$-0.631536\pi$
$359$	−5463.05	−0.803144	−0.401572	+	0.915827i	$0.631536\pi$
$360$	−9980.00	−1.46109
$361$	−6806.69	−0.992374
$362$	−1230.95	−0.178722
$363$	0	0
$364$	−613.416	−0.0883289
$365$	−6921.82	−0.992615
$366$	7299.47	1.04248
$367$	−7352.51	−1.04577	−0.522886	−	0.852403i	$-0.675145\pi$
$367$	−7352.51	−1.04577	−0.522886	+	0.852403i	$0.675145\pi$
$368$	−3367.35	−0.476997
$369$	19742.9	2.78530
$370$	2279.84	0.320333
$371$	534.956	0.0748613
$372$	6731.53	0.938208
$373$	−8972.08	−1.24546	−0.622730	−	0.782437i	$-0.713977\pi$
$373$	−8972.08	−1.24546	−0.622730	+	0.782437i	$0.713977\pi$
$374$	0	0
$375$	−41450.5	−5.70799
$376$	−1365.77	−0.187325
$377$	−3824.90	−0.522526
$378$	4031.35	0.548546
$379$	−1513.96	−0.205189	−0.102595	−	0.994723i	$-0.532714\pi$
$379$	−1513.96	−0.205189	−0.102595	+	0.994723i	$0.532714\pi$
$380$	−620.124	−0.0837149
$381$	4365.40	0.586998
$382$	920.306	0.123264
$383$	−10222.6	−1.36384	−0.681918	−	0.731429i	$-0.738854\pi$
$383$	−10222.6	−1.36384	−0.681918	+	0.731429i	$0.738854\pi$
$384$	1181.47	0.157009
$385$	0	0
$386$	−3365.77	−0.443816
$387$	14260.6	1.87314
$388$	−2231.82	−0.292019
$389$	−697.774	−0.0909474	−0.0454737	−	0.998966i	$-0.514480\pi$
$389$	−697.774	−0.0909474	−0.0454737	+	0.998966i	$0.514480\pi$
$390$	−8669.21	−1.12560
$391$	−10919.4	−1.41232
$392$	−392.000	−0.0505076
$393$	−15055.3	−1.93241
$394$	−1352.77	−0.172973
$395$	16805.5	2.14071
$396$	0	0
$397$	−1699.35	−0.214831	−0.107416	−	0.994214i	$-0.534258\pi$
$397$	−1699.35	−0.214831	−0.107416	+	0.994214i	$0.534258\pi$
$398$	7635.37	0.961624
$399$	467.290	0.0586310
$400$	5351.95	0.668993
$401$	15879.6	1.97753	0.988763	−	0.149489i	$-0.0477630\pi$
$401$	15879.6	1.97753	0.988763	+	0.149489i	$0.0477630\pi$
$402$	97.2455	0.0120651
$403$	3994.28	0.493720
$404$	−3086.05	−0.380041
$405$	23291.3	2.85767
$406$	−2444.28	−0.298787
$407$	0	0
$408$	3831.17	0.464880
$409$	494.428	0.0597748	0.0298874	−	0.999553i	$-0.490485\pi$
$409$	494.428	0.0597748	0.0298874	+	0.999553i	$0.490485\pi$
$410$	−14544.0	−1.75189
$411$	−17614.9	−2.11406
$412$	−2654.34	−0.317402
$413$	2214.05	0.263793
$414$	24496.1	2.90802
$415$	6185.52	0.731652
$416$	701.046	0.0826241
$417$	−27137.2	−3.18685
$418$	0	0
$419$	−5462.62	−0.636912	−0.318456	−	0.947938i	$-0.603164\pi$
$419$	−5462.62	−0.636912	−0.318456	+	0.947938i	$0.603164\pi$
$420$	−5540.01	−0.643631
$421$	7475.31	0.865378	0.432689	−	0.901543i	$-0.357565\pi$
$421$	7475.31	0.865378	0.432689	+	0.901543i	$0.357565\pi$
$422$	7883.27	0.909364
$423$	9935.42	1.14202
$424$	−611.379	−0.0700263
$425$	17354.9	1.98079
$426$	2956.33	0.336231
$427$	2767.88	0.313694
$428$	−7802.30	−0.881164
$429$	0	0
$430$	−10505.3	−1.17816
$431$	−2039.38	−0.227920	−0.113960	−	0.993485i	$-0.536354\pi$
$431$	−2039.38	−0.227920	−0.113960	+	0.993485i	$0.536354\pi$
$432$	−4607.26	−0.513117
$433$	13704.8	1.52104	0.760521	−	0.649313i	$-0.224944\pi$
$433$	13704.8	1.52104	0.760521	+	0.649313i	$0.224944\pi$
$434$	2552.52	0.282316
$435$	−34544.2	−3.80752
$436$	−7633.34	−0.838465
$437$	1522.11	0.166618
$438$	−5961.02	−0.650294
$439$	9465.76	1.02910	0.514551	−	0.857460i	$-0.327959\pi$
$439$	9465.76	1.02910	0.514551	+	0.857460i	$0.327959\pi$
$440$	0	0
$441$	2851.65	0.307920
$442$	2273.30	0.244637
$443$	7672.01	0.822817	0.411409	−	0.911451i	$-0.365037\pi$
$443$	7672.01	0.822817	0.411409	+	0.911451i	$0.365037\pi$
$444$	1963.38	0.209860
$445$	−14282.0	−1.52142
$446$	−6743.44	−0.715944
$447$	−23598.6	−2.49704
$448$	448.000	0.0472456
$449$	2952.37	0.310314	0.155157	−	0.987890i	$-0.450412\pi$
$449$	2952.37	0.310314	0.155157	+	0.987890i	$0.450412\pi$
$450$	−38933.3	−4.07852
$451$	0	0
$452$	154.693	0.0160977
$453$	−22645.5	−2.34873
$454$	−9006.75	−0.931074
$455$	−3287.27	−0.338703
$456$	−534.046	−0.0548443
$457$	−11039.1	−1.12995	−0.564976	−	0.825107i	$-0.691115\pi$
$457$	−11039.1	−1.12995	−0.564976	+	0.825107i	$0.691115\pi$
$458$	4904.42	0.500367
$459$	−14940.1	−1.51926
$460$	−18045.5	−1.82908
$461$	8267.10	0.835222	0.417611	−	0.908626i	$-0.362868\pi$
$461$	8267.10	0.835222	0.417611	+	0.908626i	$0.362868\pi$
$462$	0	0
$463$	16750.1	1.68130	0.840651	−	0.541577i	$-0.182173\pi$
$463$	16750.1	1.68130	0.840651	+	0.541577i	$0.182173\pi$
$464$	2793.46	0.279490
$465$	36074.0	3.59762
$466$	3643.22	0.362165
$467$	−2873.28	−0.284710	−0.142355	−	0.989816i	$-0.545467\pi$
$467$	−2873.28	−0.284710	−0.142355	+	0.989816i	$0.545467\pi$
$468$	−5099.84	−0.503718
$469$	36.8745	0.00363050
$470$	−7319.10	−0.718309
$471$	6293.97	0.615734
$472$	−2530.34	−0.246755
$473$	0	0
$474$	14472.8	1.40244
$475$	−2419.18	−0.233684
$476$	1452.74	0.139887
$477$	4447.54	0.426916
$478$	−6627.68	−0.634191
$479$	10540.2	1.00542	0.502709	−	0.864456i	$-0.332337\pi$
$479$	10540.2	1.00542	0.502709	+	0.864456i	$0.332337\pi$
$480$	6331.45	0.602062
$481$	1165.01	0.110436
$482$	−1319.06	−0.124650
$483$	13598.1	1.28102
$484$	0	0
$485$	−11960.3	−1.11977
$486$	4508.83	0.420833
$487$	2676.96	0.249085	0.124543	−	0.992214i	$-0.460254\pi$
$487$	2676.96	0.249085	0.124543	+	0.992214i	$0.460254\pi$
$488$	−3163.29	−0.293434
$489$	−18691.1	−1.72851
$490$	−2100.72	−0.193675
$491$	−7382.31	−0.678532	−0.339266	−	0.940690i	$-0.610179\pi$
$491$	−7382.31	−0.678532	−0.339266	+	0.940690i	$0.610179\pi$
$492$	−12525.2	−1.14772
$493$	9058.42	0.827527
$494$	−316.887	−0.0288611
$495$	0	0
$496$	−2917.17	−0.264082
$497$	1121.01	0.101175
$498$	5326.93	0.479328
$499$	1184.74	0.106285	0.0531425	−	0.998587i	$-0.483076\pi$
$499$	1184.74	0.106285	0.0531425	+	0.998587i	$0.483076\pi$
$500$	17963.0	1.60666
$501$	−13837.1	−1.23393
$502$	−13196.4	−1.17328
$503$	−5926.75	−0.525369	−0.262685	−	0.964882i	$-0.584608\pi$
$503$	−5926.75	−0.525369	−0.262685	+	0.964882i	$0.584608\pi$
$504$	−3259.02	−0.288033
$505$	−16538.0	−1.45729
$506$	0	0
$507$	15848.8	1.38830
$508$	−1891.79	−0.165225
$509$	−18821.9	−1.63903	−0.819517	−	0.573055i	$-0.805758\pi$
$509$	−18821.9	−1.63903	−0.819517	+	0.573055i	$0.805758\pi$
$510$	20531.1	1.78261
$511$	−2260.36	−0.195680
$512$	−512.000	−0.0441942
$513$	2082.57	0.179235
$514$	3821.47	0.327933
$515$	−14224.5	−1.21710
$516$	−9047.09	−0.771852
$517$	0	0
$518$	744.493	0.0631489
$519$	−2804.94	−0.237231
$520$	3756.88	0.316827
$521$	6925.66	0.582377	0.291189	−	0.956666i	$-0.405949\pi$
$521$	6925.66	0.582377	0.291189	+	0.956666i	$0.405949\pi$
$522$	−20321.3	−1.70391
$523$	−2658.14	−0.222241	−0.111121	−	0.993807i	$-0.535444\pi$
$523$	−2658.14	−0.222241	−0.111121	+	0.993807i	$0.535444\pi$
$524$	6524.34	0.543926
$525$	−21612.3	−1.79665
$526$	−11208.0	−0.929075
$527$	−9459.57	−0.781908
$528$	0	0
$529$	32126.0	2.64042
$530$	−3276.36	−0.268521
$531$	18407.3	1.50434
$532$	−202.505	−0.0165032
$533$	−7432.04	−0.603973
$534$	−12299.6	−0.996730
$535$	−41812.3	−3.37888
$536$	−42.1423	−0.00339602
$537$	15362.3	1.23451
$538$	6527.42	0.523080
$539$	0	0
$540$	−24690.1	−1.96758
$541$	19898.0	1.58129	0.790647	−	0.612272i	$-0.209744\pi$
$541$	19898.0	1.58129	0.790647	+	0.612272i	$0.209744\pi$
$542$	4984.50	0.395023
$543$	−5680.98	−0.448976
$544$	−1660.27	−0.130852
$545$	−40906.8	−3.21515
$546$	−2830.98	−0.221895
$547$	−6254.90	−0.488922	−0.244461	−	0.969659i	$-0.578611\pi$
$547$	−6254.90	−0.488922	−0.244461	+	0.969659i	$0.578611\pi$
$548$	7633.59	0.595056
$549$	23011.7	1.78892
$550$	0	0
$551$	−1262.70	−0.0976276
$552$	−15540.7	−1.19829
$553$	5487.94	0.422009
$554$	3100.95	0.237810
$555$	10521.7	0.804722
$556$	11760.2	0.897018
$557$	−13155.2	−1.00072	−0.500361	−	0.865817i	$-0.666799\pi$
$557$	−13155.2	−1.00072	−0.500361	+	0.865817i	$0.666799\pi$
$558$	21221.3	1.60998
$559$	−5368.26	−0.406178
$560$	2400.82	0.181166
$561$	0	0
$562$	−10089.0	−0.757257
$563$	−15251.9	−1.14172	−0.570861	−	0.821046i	$-0.693391\pi$
$563$	−15251.9	−1.14172	−0.570861	+	0.821046i	$0.693391\pi$
$564$	−6303.16	−0.470587
$565$	828.997	0.0617277
$566$	−4528.96	−0.336336
$567$	7605.91	0.563348
$568$	−1281.15	−0.0946408
$569$	20141.1	1.48393	0.741967	−	0.670437i	$-0.233893\pi$
$569$	20141.1	1.48393	0.741967	+	0.670437i	$0.233893\pi$
$570$	−2861.94	−0.210304
$571$	17129.6	1.25543	0.627716	−	0.778442i	$-0.283990\pi$
$571$	17129.6	1.25543	0.627716	+	0.778442i	$0.283990\pi$
$572$	0	0
$573$	4247.31	0.309658
$574$	−4749.41	−0.345360
$575$	−70397.9	−5.10573
$576$	3724.60	0.269430
$577$	−10237.3	−0.738620	−0.369310	−	0.929306i	$-0.620406\pi$
$577$	−10237.3	−0.738620	−0.369310	+	0.929306i	$0.620406\pi$
$578$	4442.20	0.319673
$579$	−15533.4	−1.11493
$580$	14970.1	1.07172
$581$	2019.92	0.144235
$582$	−10300.1	−0.733595
$583$	0	0
$584$	2583.27	0.183042
$585$	−27329.9	−1.93154
$586$	5173.65	0.364713
$587$	5107.13	0.359104	0.179552	−	0.983749i	$-0.442535\pi$
$587$	5107.13	0.359104	0.179552	+	0.983749i	$0.442535\pi$
$588$	−1809.12	−0.126883
$589$	1318.62	0.0922457
$590$	−13560.0	−0.946199
$591$	−6243.16	−0.434534
$592$	−850.849	−0.0590704
$593$	17048.5	1.18061	0.590303	−	0.807181i	$-0.299008\pi$
$593$	17048.5	1.18061	0.590303	+	0.807181i	$0.299008\pi$
$594$	0	0
$595$	7785.18	0.536406
$596$	10226.7	0.702855
$597$	35238.0	2.41574
$598$	−9221.35	−0.630584
$599$	18202.8	1.24165	0.620823	−	0.783951i	$-0.286799\pi$
$599$	18202.8	1.24165	0.620823	+	0.783951i	$0.286799\pi$
$600$	24699.8	1.68061
$601$	24342.5	1.65216	0.826082	−	0.563550i	$-0.190565\pi$
$601$	24342.5	1.65216	0.826082	+	0.563550i	$0.190565\pi$
$602$	−3430.56	−0.232258
$603$	306.568	0.0207039
$604$	9813.62	0.661110
$605$	0	0
$606$	−14242.4	−0.954719
$607$	24406.1	1.63198	0.815991	−	0.578065i	$-0.196192\pi$
$607$	24406.1	1.63198	0.815991	+	0.578065i	$0.196192\pi$
$608$	231.434	0.0154373
$609$	−11280.6	−0.750597
$610$	−16952.0	−1.12519
$611$	−3740.10	−0.247640
$612$	12077.8	0.797741
$613$	22591.3	1.48851	0.744254	−	0.667896i	$-0.232805\pi$
$613$	22591.3	1.48851	0.744254	+	0.667896i	$0.232805\pi$
$614$	11222.0	0.737597
$615$	−67121.9	−4.40100
$616$	0	0
$617$	10083.9	0.657962	0.328981	−	0.944336i	$-0.393295\pi$
$617$	10083.9	0.657962	0.328981	+	0.944336i	$0.393295\pi$
$618$	−12250.0	−0.797361
$619$	13463.2	0.874204	0.437102	−	0.899412i	$-0.356005\pi$
$619$	13463.2	0.874204	0.437102	+	0.899412i	$0.356005\pi$
$620$	−15633.0	−1.01264
$621$	60602.4	3.91609
$622$	4571.48	0.294694
$623$	−4663.86	−0.299926
$624$	3235.40	0.207564
$625$	54450.9	3.48486
$626$	12007.6	0.766647
$627$	0	0
$628$	−2727.55	−0.173314
$629$	−2759.07	−0.174899
$630$	−17465.0	−1.10448
$631$	19246.7	1.21426	0.607130	−	0.794603i	$-0.292321\pi$
$631$	19246.7	1.21426	0.607130	+	0.794603i	$0.292321\pi$
$632$	−6271.94	−0.394753
$633$	36382.1	2.28445
$634$	−2581.94	−0.161738
$635$	−10138.0	−0.633567
$636$	−2821.58	−0.175916
$637$	−1073.48	−0.0667703
$638$	0	0
$639$	9319.88	0.576977
$640$	−2743.79	−0.169465
$641$	10846.9	0.668372	0.334186	−	0.942507i	$-0.391539\pi$
$641$	10846.9	0.668372	0.334186	+	0.942507i	$0.391539\pi$
$642$	−36008.4	−2.21361
$643$	4776.60	0.292956	0.146478	−	0.989214i	$-0.453206\pi$
$643$	4776.60	0.292956	0.146478	+	0.989214i	$0.453206\pi$
$644$	−5892.85	−0.360576
$645$	−48483.0	−2.95972
$646$	750.476	0.0457076
$647$	−7710.67	−0.468528	−0.234264	−	0.972173i	$-0.575268\pi$
$647$	−7710.67	−0.468528	−0.234264	+	0.972173i	$0.575268\pi$
$648$	−8692.46	−0.526963
$649$	0	0
$650$	14656.1	0.884399
$651$	11780.2	0.709219
$652$	8099.98	0.486533
$653$	−32630.0	−1.95545	−0.977725	−	0.209889i	$-0.932690\pi$
$653$	−32630.0	−1.95545	−0.977725	+	0.209889i	$0.932690\pi$
$654$	−35228.7	−2.10635
$655$	34963.7	2.08572
$656$	5427.89	0.323054
$657$	−18792.2	−1.11591
$658$	−2390.09	−0.141604
$659$	−3758.08	−0.222146	−0.111073	−	0.993812i	$-0.535429\pi$
$659$	−3758.08	−0.222146	−0.111073	+	0.993812i	$0.535429\pi$
$660$	0	0
$661$	1771.87	0.104263	0.0521314	−	0.998640i	$-0.483399\pi$
$661$	1771.87	0.104263	0.0521314	+	0.998640i	$0.483399\pi$
$662$	−19645.5	−1.15339
$663$	10491.5	0.614565
$664$	−2308.48	−0.134919
$665$	−1085.22	−0.0632825
$666$	6189.59	0.360123
$667$	−36744.3	−2.13305
$668$	5996.45	0.347320
$669$	−31121.7	−1.79856
$670$	−225.839	−0.0130223
$671$	0	0
$672$	2067.57	0.118688
$673$	−2541.76	−0.145583	−0.0727917	−	0.997347i	$-0.523191\pi$
$673$	−2541.76	−0.145583	−0.0727917	+	0.997347i	$0.523191\pi$
$674$	−12916.7	−0.738177
$675$	−96319.5	−5.49235
$676$	−6868.21	−0.390772
$677$	−19815.4	−1.12491	−0.562457	−	0.826827i	$-0.690144\pi$
$677$	−19815.4	−1.12491	−0.562457	+	0.826827i	$0.690144\pi$
$678$	713.927	0.0404398
$679$	−3905.69	−0.220746
$680$	−8897.35	−0.501762
$681$	−41567.1	−2.33899
$682$	0	0
$683$	260.965	0.0146201	0.00731006	−	0.999973i	$-0.497673\pi$
$683$	260.965	0.0146201	0.00731006	+	0.999973i	$0.497673\pi$
$684$	−1683.59	−0.0941136
$685$	40908.1	2.28178
$686$	−686.000	−0.0381802
$687$	22634.4	1.25700
$688$	3920.64	0.217257
$689$	−1674.24	−0.0925738
$690$	−83281.9	−4.59491
$691$	14670.6	0.807662	0.403831	−	0.914834i	$-0.367678\pi$
$691$	14670.6	0.807662	0.403831	+	0.914834i	$0.367678\pi$
$692$	1215.55	0.0667747
$693$	0	0
$694$	10706.4	0.585602
$695$	63022.4	3.43968
$696$	12892.1	0.702119
$697$	17601.1	0.956515
$698$	−9831.16	−0.533116
$699$	16813.8	0.909811
$700$	9365.90	0.505711
$701$	−12986.8	−0.699720	−0.349860	−	0.936802i	$-0.613771\pi$
$701$	−12986.8	−0.699720	−0.349860	+	0.936802i	$0.613771\pi$
$702$	−12616.8	−0.678334
$703$	384.600	0.0206337
$704$	0	0
$705$	−33778.4	−1.80450
$706$	−15474.0	−0.824887
$707$	−5400.59	−0.287284
$708$	−11677.8	−0.619885
$709$	30475.6	1.61430	0.807149	−	0.590348i	$-0.201010\pi$
$709$	30475.6	1.61430	0.807149	+	0.590348i	$0.201010\pi$
$710$	−6865.65	−0.362906
$711$	45625.9	2.40662
$712$	5330.13	0.280555
$713$	38371.6	2.01547
$714$	6704.55	0.351416
$715$	0	0
$716$	−6657.40	−0.347484
$717$	−30587.5	−1.59318
$718$	10926.1	0.567908
$719$	12062.6	0.625673	0.312836	−	0.949807i	$-0.398721\pi$
$719$	12062.6	0.625673	0.312836	+	0.949807i	$0.398721\pi$
$720$	19960.0	1.03315
$721$	−4645.09	−0.239934
$722$	13613.4	0.701714
$723$	−6087.58	−0.313139
$724$	2461.90	0.126376
$725$	58400.2	2.99163
$726$	0	0
$727$	−21410.2	−1.09224	−0.546121	−	0.837706i	$-0.683896\pi$
$727$	−21410.2	−1.09224	−0.546121	+	0.837706i	$0.683896\pi$
$728$	1226.83	0.0624579
$729$	−8528.31	−0.433283
$730$	13843.6	0.701885
$731$	12713.5	0.643266
$732$	−14598.9	−0.737148
$733$	34506.9	1.73880	0.869401	−	0.494108i	$-0.164505\pi$
$733$	34506.9	1.73880	0.869401	+	0.494108i	$0.164505\pi$
$734$	14705.0	0.739472
$735$	−9695.03	−0.486539
$736$	6734.69	0.337288
$737$	0	0
$738$	−39485.8	−1.96950
$739$	4280.28	0.213062	0.106531	−	0.994309i	$-0.466026\pi$
$739$	4280.28	0.213062	0.106531	+	0.994309i	$0.466026\pi$
$740$	−4559.67	−0.226509
$741$	−1462.47	−0.0725034
$742$	−1069.91	−0.0529349
$743$	26622.7	1.31453	0.657263	−	0.753662i	$-0.271714\pi$
$743$	26622.7	1.31453	0.657263	+	0.753662i	$0.271714\pi$
$744$	−13463.1	−0.663413
$745$	54804.5	2.69514
$746$	17944.2	0.880673
$747$	16793.3	0.822534
$748$	0	0
$749$	−13654.0	−0.666097
$750$	82901.0	4.03616
$751$	−8941.67	−0.434469	−0.217235	−	0.976119i	$-0.569704\pi$
$751$	−8941.67	−0.434469	−0.217235	+	0.976119i	$0.569704\pi$
$752$	2731.53	0.132459
$753$	−60902.8	−2.94744
$754$	7649.79	0.369481
$755$	52590.9	2.53507
$756$	−8062.70	−0.387880
$757$	14037.9	0.674000	0.337000	−	0.941505i	$-0.390588\pi$
$757$	14037.9	0.674000	0.337000	+	0.941505i	$0.390588\pi$
$758$	3027.91	0.145091
$759$	0	0
$760$	1240.25	0.0591954
$761$	−3611.19	−0.172018	−0.0860088	−	0.996294i	$-0.527411\pi$
$761$	−3611.19	−0.172018	−0.0860088	+	0.996294i	$0.527411\pi$
$762$	−8730.79	−0.415070
$763$	−13358.3	−0.633820
$764$	−1840.61	−0.0871610
$765$	64724.7	3.05899
$766$	20445.1	0.964377
$767$	−6929.25	−0.326207
$768$	−2362.93	−0.111022
$769$	10736.3	0.503461	0.251730	−	0.967797i	$-0.419000\pi$
$769$	10736.3	0.503461	0.251730	+	0.967797i	$0.419000\pi$
$770$	0	0
$771$	17636.5	0.823816
$772$	6731.53	0.313825
$773$	29466.6	1.37107	0.685536	−	0.728039i	$-0.259568\pi$
$773$	29466.6	1.37107	0.685536	+	0.728039i	$0.259568\pi$
$774$	−28521.1	−1.32451
$775$	−60986.5	−2.82671
$776$	4463.64	0.206489
$777$	3435.91	0.158639
$778$	1395.55	0.0643095
$779$	−2453.51	−0.112845
$780$	17338.4	0.795917
$781$	0	0
$782$	21838.7	0.998659
$783$	−50274.2	−2.29458
$784$	784.000	0.0357143
$785$	−14616.9	−0.664584
$786$	30110.5	1.36642
$787$	−11368.7	−0.514929	−0.257465	−	0.966288i	$-0.582887\pi$
$787$	−11368.7	−0.514929	−0.257465	+	0.966288i	$0.582887\pi$
$788$	2705.53	0.122310
$789$	−51726.3	−2.33397
$790$	−33611.1	−1.51371
$791$	270.713	0.0121687
$792$	0	0
$793$	−8662.56	−0.387915
$794$	3398.70	0.151909
$795$	−15120.7	−0.674563
$796$	−15270.7	−0.679971
$797$	−20624.0	−0.916610	−0.458305	−	0.888795i	$-0.651543\pi$
$797$	−20624.0	−0.916610	−0.458305	+	0.888795i	$0.651543\pi$
$798$	−934.581	−0.0414584
$799$	8857.61	0.392190
$800$	−10703.9	−0.473050
$801$	−38774.6	−1.71040
$802$	−31759.2	−1.39832
$803$	0	0
$804$	−194.491	−0.00853131
$805$	−31579.6	−1.38265
$806$	−7988.56	−0.349113
$807$	30124.7	1.31405
$808$	6172.10	0.268730
$809$	10927.8	0.474907	0.237454	−	0.971399i	$-0.423687\pi$
$809$	10927.8	0.474907	0.237454	+	0.971399i	$0.423687\pi$
$810$	−46582.6	−2.02068
$811$	−19842.6	−0.859145	−0.429573	−	0.903032i	$-0.641336\pi$
$811$	−19842.6	−0.859145	−0.429573	+	0.903032i	$0.641336\pi$
$812$	4888.56	0.211274
$813$	23004.0	0.992355
$814$	0	0
$815$	43407.5	1.86564
$816$	−7662.34	−0.328720
$817$	−1772.21	−0.0758894
$818$	−988.857	−0.0422672
$819$	−8924.71	−0.380775
$820$	29087.9	1.23877
$821$	5826.73	0.247691	0.123846	−	0.992302i	$-0.460477\pi$
$821$	5826.73	0.247691	0.123846	+	0.992302i	$0.460477\pi$
$822$	35229.8	1.49487
$823$	6902.80	0.292365	0.146182	−	0.989258i	$-0.453301\pi$
$823$	6902.80	0.292365	0.146182	+	0.989258i	$0.453301\pi$
$824$	5308.67	0.224437
$825$	0	0
$826$	−4428.10	−0.186529
$827$	43119.7	1.81308	0.906540	−	0.422120i	$-0.138714\pi$
$827$	43119.7	1.81308	0.906540	+	0.422120i	$0.138714\pi$
$828$	−48992.2	−2.05628
$829$	−37437.0	−1.56844	−0.784222	−	0.620480i	$-0.786938\pi$
$829$	−37437.0	−1.56844	−0.784222	+	0.620480i	$0.786938\pi$
$830$	−12371.0	−0.517356
$831$	14311.2	0.597413
$832$	−1402.09	−0.0584241
$833$	2542.29	0.105745
$834$	54274.4	2.25344
$835$	32134.8	1.33182
$836$	0	0
$837$	52500.6	2.16808
$838$	10925.2	0.450365
$839$	−45679.5	−1.87966	−0.939828	−	0.341648i	$-0.889015\pi$
$839$	−45679.5	−1.87966	−0.939828	+	0.341648i	$0.889015\pi$
$840$	11080.0	0.455116
$841$	6093.16	0.249832
$842$	−14950.6	−0.611915
$843$	−46561.8	−1.90234
$844$	−15766.5	−0.643017
$845$	−36806.5	−1.49844
$846$	−19870.8	−0.807534
$847$	0	0
$848$	1222.76	0.0495161
$849$	−20901.6	−0.844925
$850$	−34709.7	−1.40063
$851$	11191.8	0.450823
$852$	−5912.65	−0.237751
$853$	31555.6	1.26664	0.633320	−	0.773890i	$-0.281692\pi$
$853$	31555.6	1.26664	0.633320	+	0.773890i	$0.281692\pi$
$854$	−5535.76	−0.221815
$855$	−9022.31	−0.360885
$856$	15604.6	0.623077
$857$	−17169.3	−0.684353	−0.342177	−	0.939636i	$-0.611164\pi$
$857$	−17169.3	−0.684353	−0.342177	+	0.939636i	$0.611164\pi$
$858$	0	0
$859$	6284.80	0.249633	0.124816	−	0.992180i	$-0.460166\pi$
$859$	6284.80	0.249633	0.124816	+	0.992180i	$0.460166\pi$
$860$	21010.6	0.833087
$861$	−21919.0	−0.867594
$862$	4078.76	0.161164
$863$	14217.7	0.560806	0.280403	−	0.959882i	$-0.409532\pi$
$863$	14217.7	0.560806	0.280403	+	0.959882i	$0.409532\pi$
$864$	9214.51	0.362829
$865$	6514.07	0.256052
$866$	−27409.6	−1.07554
$867$	20501.2	0.803065
$868$	−5105.05	−0.199628
$869$	0	0
$870$	69088.5	2.69232
$871$	−115.405	−0.00448949
$872$	15266.7	0.592884
$873$	−32471.2	−1.25886
$874$	−3044.21	−0.117817
$875$	31435.2	1.21452
$876$	11922.0	0.459827
$877$	2539.91	0.0977954	0.0488977	−	0.998804i	$-0.484429\pi$
$877$	2539.91	0.0977954	0.0488977	+	0.998804i	$0.484429\pi$
$878$	−18931.5	−0.727685
$879$	23877.0	0.916212
$880$	0	0
$881$	−5759.28	−0.220244	−0.110122	−	0.993918i	$-0.535124\pi$
$881$	−5759.28	−0.220244	−0.110122	+	0.993918i	$0.535124\pi$
$882$	−5703.29	−0.217732
$883$	19507.5	0.743466	0.371733	−	0.928340i	$-0.378764\pi$
$883$	19507.5	0.743466	0.371733	+	0.928340i	$0.378764\pi$
$884$	−4546.60	−0.172985
$885$	−62581.0	−2.37699
$886$	−15344.0	−0.581820
$887$	−46241.7	−1.75045	−0.875223	−	0.483719i	$-0.839286\pi$
$887$	−46241.7	−1.75045	−0.875223	+	0.483719i	$0.839286\pi$
$888$	−3926.76	−0.148393
$889$	−3310.63	−0.124899
$890$	28564.0	1.07581
$891$	0	0
$892$	13486.9	0.506249
$893$	−1234.71	−0.0462686
$894$	47197.3	1.76567
$895$	−35676.8	−1.33245
$896$	−896.000	−0.0334077
$897$	−42557.5	−1.58412
$898$	−5904.74	−0.219425
$899$	−31832.1	−1.18093
$900$	77866.6	2.88395
$901$	3965.06	0.146610
$902$	0	0
$903$	−15832.4	−0.583465
$904$	−309.387	−0.0113828
$905$	13193.3	0.484596
$906$	45290.9	1.66081
$907$	43918.1	1.60780	0.803901	−	0.594763i	$-0.202754\pi$
$907$	43918.1	1.60780	0.803901	+	0.594763i	$0.202754\pi$
$908$	18013.5	0.658369
$909$	−44899.6	−1.63831
$910$	6574.55	0.239499
$911$	−20073.8	−0.730050	−0.365025	−	0.930998i	$-0.618940\pi$
$911$	−20073.8	−0.730050	−0.365025	+	0.930998i	$0.618940\pi$
$912$	1068.09	0.0387808
$913$	0	0
$914$	22078.2	0.798996
$915$	−78235.2	−2.82664
$916$	−9808.83	−0.353813
$917$	11417.6	0.411169
$918$	29880.1	1.07428
$919$	−8314.89	−0.298458	−0.149229	−	0.988803i	$-0.547679\pi$
$919$	−8314.89	−0.298458	−0.149229	+	0.988803i	$0.547679\pi$
$920$	36091.0	1.29335
$921$	51790.9	1.85295
$922$	−16534.2	−0.590591
$923$	−3508.39	−0.125114
$924$	0	0
$925$	−17787.9	−0.632283
$926$	−33500.2	−1.18886
$927$	−38618.5	−1.36828
$928$	−5586.92	−0.197629
$929$	22775.4	0.804345	0.402173	−	0.915564i	$-0.368255\pi$
$929$	22775.4	0.804345	0.402173	+	0.915564i	$0.368255\pi$
$930$	−72148.1	−2.54390
$931$	−354.383	−0.0124752
$932$	−7286.44	−0.256089
$933$	21097.9	0.740314
$934$	5746.57	0.201321
$935$	0	0
$936$	10199.7	0.356182
$937$	27528.3	0.959777	0.479888	−	0.877330i	$-0.340677\pi$
$937$	27528.3	0.959777	0.479888	+	0.877330i	$0.340677\pi$
$938$	−73.7490	−0.00256715
$939$	55416.5	1.92593
$940$	14638.2	0.507921
$941$	−6605.92	−0.228849	−0.114424	−	0.993432i	$-0.536502\pi$
$941$	−6605.92	−0.228849	−0.114424	+	0.993432i	$0.536502\pi$
$942$	−12587.9	−0.435390
$943$	−71396.9	−2.46554
$944$	5060.69	0.174482
$945$	−43207.7	−1.48735
$946$	0	0
$947$	−15451.6	−0.530211	−0.265105	−	0.964219i	$-0.585407\pi$
$947$	−15451.6	−0.530211	−0.265105	+	0.964219i	$0.585407\pi$
$948$	−28945.7	−0.991678
$949$	7074.17	0.241978
$950$	4838.37	0.165239
$951$	−11915.9	−0.406309
$952$	−2905.48	−0.0989150
$953$	−40532.0	−1.37771	−0.688857	−	0.724898i	$-0.741887\pi$
$953$	−40532.0	−1.37771	−0.688857	+	0.724898i	$0.741887\pi$
$954$	−8895.08	−0.301875
$955$	−9863.78	−0.334225
$956$	13255.4	0.448441
$957$	0	0
$958$	−21080.4	−0.710937
$959$	13358.8	0.449820
$960$	−12662.9	−0.425722
$961$	3450.75	0.115832
$962$	−2330.02	−0.0780902
$963$	−113517.	−3.79859
$964$	2638.11	0.0881409
$965$	36074.1	1.20338
$966$	−27196.2	−0.905820
$967$	11228.1	0.373392	0.186696	−	0.982418i	$-0.440222\pi$
$967$	11228.1	0.373392	0.186696	+	0.982418i	$0.440222\pi$
$968$	0	0
$969$	3463.53	0.114824
$970$	23920.5	0.791795
$971$	−37249.5	−1.23109	−0.615547	−	0.788100i	$-0.711065\pi$
$971$	−37249.5	−1.23109	−0.615547	+	0.788100i	$0.711065\pi$
$972$	−9017.67	−0.297574
$973$	20580.3	0.678082
$974$	−5353.91	−0.176130
$975$	67639.5	2.22174
$976$	6326.59	0.207489
$977$	50774.3	1.66265	0.831327	−	0.555784i	$-0.187582\pi$
$977$	50774.3	1.66265	0.831327	+	0.555784i	$0.187582\pi$
$978$	37382.3	1.22224
$979$	0	0
$980$	4201.43	0.136949
$981$	−111059.	−3.61452
$982$	14764.6	0.479795
$983$	−6003.09	−0.194780	−0.0973900	−	0.995246i	$-0.531049\pi$
$983$	−6003.09	−0.194780	−0.0973900	+	0.995246i	$0.531049\pi$
$984$	25050.3	0.811560
$985$	14498.9	0.469007
$986$	−18116.8	−0.585150
$987$	−11030.5	−0.355730
$988$	633.773	0.0204079
$989$	−51570.9	−1.65810
$990$	0	0
$991$	−7215.04	−0.231275	−0.115637	−	0.993291i	$-0.536891\pi$
$991$	−7215.04	−0.231275	−0.115637	+	0.993291i	$0.536891\pi$
$992$	5834.34	0.186734
$993$	−90666.2	−2.89749
$994$	−2242.02	−0.0715417
$995$	−81835.4	−2.60739
$996$	−10653.9	−0.338936
$997$	4098.56	0.130193	0.0650966	−	0.997879i	$-0.479264\pi$
$997$	4098.56	0.130193	0.0650966	+	0.997879i	$0.479264\pi$
$998$	−2369.48	−0.0751549
$999$	15312.8	0.484961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1694.4.a.bh.1.1		10
11.7	odd	10		154.4.f.f.71.5	✓	20
11.8	odd	10		154.4.f.f.141.5	yes	20
11.10	odd	2		1694.4.a.bk.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.f.f.71.5	✓	20	11.7	odd	10
154.4.f.f.141.5	yes	20	11.8	odd	10
1694.4.a.bh.1.1		10	1.1	even	1	trivial
1694.4.a.bk.1.1		10	11.10	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:	\( N \)	\(=\)	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1694.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -9.23021 q^{3} +4.00000 q^{4} +21.4359 q^{5} +18.4604 q^{6} +7.00000 q^{7} -8.00000 q^{8} +58.1968 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -9.23021 q^{3} +4.00000 q^{4} +21.4359 q^{5} +18.4604 q^{6} +7.00000 q^{7} -8.00000 q^{8} +58.1968 q^{9} -42.8717 q^{10} -36.9209 q^{12} -21.9077 q^{13} -14.0000 q^{14} -197.858 q^{15} +16.0000 q^{16} +51.8835 q^{17} -116.394 q^{18} -7.23231 q^{19} +85.7435 q^{20} -64.6115 q^{21} -210.459 q^{23} +73.8417 q^{24} +334.497 q^{25} +43.8154 q^{26} -287.954 q^{27} +28.0000 q^{28} +174.591 q^{29} +395.715 q^{30} -182.323 q^{31} -32.0000 q^{32} -103.767 q^{34} +150.051 q^{35} +232.787 q^{36} -53.1781 q^{37} +14.4646 q^{38} +202.213 q^{39} -171.487 q^{40} +339.243 q^{41} +129.223 q^{42} +245.040 q^{43} +1247.50 q^{45} +420.918 q^{46} +170.721 q^{47} -147.683 q^{48} +49.0000 q^{49} -668.993 q^{50} -478.896 q^{51} -87.6308 q^{52} +76.4223 q^{53} +575.907 q^{54} -56.0000 q^{56} +66.7558 q^{57} -349.183 q^{58} +316.293 q^{59} -791.431 q^{60} +395.412 q^{61} +364.646 q^{62} +407.378 q^{63} +64.0000 q^{64} -469.611 q^{65} +5.26778 q^{67} +207.534 q^{68} +1942.58 q^{69} -300.102 q^{70} +160.144 q^{71} -465.575 q^{72} -322.908 q^{73} +106.356 q^{74} -3087.47 q^{75} -28.9292 q^{76} -404.425 q^{78} +783.992 q^{79} +342.974 q^{80} +1086.56 q^{81} -678.487 q^{82} +288.559 q^{83} -258.446 q^{84} +1112.17 q^{85} -490.080 q^{86} -1611.52 q^{87} -666.266 q^{89} -2495.00 q^{90} -153.354 q^{91} -841.836 q^{92} +1682.88 q^{93} -341.442 q^{94} -155.031 q^{95} +295.367 q^{96} -557.955 q^{97} -98.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{2} - 3 q^{3} + 40 q^{4} - 27 q^{5} + 6 q^{6} + 70 q^{7} - 80 q^{8} + 97 q^{9}+O(q^{10}) \) 10 * q - 20 * q^2 - 3 * q^3 + 40 * q^4 - 27 * q^5 + 6 * q^6 + 70 * q^7 - 80 * q^8 + 97 * q^9	\( 10 q - 20 q^{2} - 3 q^{3} + 40 q^{4} - 27 q^{5} + 6 q^{6} + 70 q^{7} - 80 q^{8} + 97 q^{9} + 54 q^{10} - 12 q^{12} + 78 q^{13} - 140 q^{14} - 72 q^{15} + 160 q^{16} + 80 q^{17} - 194 q^{18} + 178 q^{19} - 108 q^{20} - 21 q^{21} - 99 q^{23} + 24 q^{24} + 669 q^{25} - 156 q^{26} - 258 q^{27} + 280 q^{28} + 346 q^{29} + 144 q^{30} - 359 q^{31} - 320 q^{32} - 160 q^{34} - 189 q^{35} + 388 q^{36} + 645 q^{37} - 356 q^{38} + 453 q^{39} + 216 q^{40} + 177 q^{41} + 42 q^{42} + 1817 q^{43} - 1009 q^{45} + 198 q^{46} - 873 q^{47} - 48 q^{48} + 490 q^{49} - 1338 q^{50} + 525 q^{51} + 312 q^{52} - 854 q^{53} + 516 q^{54} - 560 q^{56} + 806 q^{57} - 692 q^{58} - 513 q^{59} - 288 q^{60} + 2084 q^{61} + 718 q^{62} + 679 q^{63} + 640 q^{64} - 425 q^{65} - 119 q^{67} + 320 q^{68} + 308 q^{69} + 378 q^{70} - 276 q^{71} - 776 q^{72} + 779 q^{73} - 1290 q^{74} - 6417 q^{75} + 712 q^{76} - 906 q^{78} + 2475 q^{79} - 432 q^{80} + 2946 q^{81} - 354 q^{82} + 463 q^{83} - 84 q^{84} - 580 q^{85} - 3634 q^{86} + 1014 q^{87} - 2065 q^{89} + 2018 q^{90} + 546 q^{91} - 396 q^{92} - 487 q^{93} + 1746 q^{94} + 2612 q^{95} + 96 q^{96} - 3666 q^{97} - 980 q^{98}+O(q^{100}) \) 10 * q - 20 * q^2 - 3 * q^3 + 40 * q^4 - 27 * q^5 + 6 * q^6 + 70 * q^7 - 80 * q^8 + 97 * q^9 + 54 * q^10 - 12 * q^12 + 78 * q^13 - 140 * q^14 - 72 * q^15 + 160 * q^16 + 80 * q^17 - 194 * q^18 + 178 * q^19 - 108 * q^20 - 21 * q^21 - 99 * q^23 + 24 * q^24 + 669 * q^25 - 156 * q^26 - 258 * q^27 + 280 * q^28 + 346 * q^29 + 144 * q^30 - 359 * q^31 - 320 * q^32 - 160 * q^34 - 189 * q^35 + 388 * q^36 + 645 * q^37 - 356 * q^38 + 453 * q^39 + 216 * q^40 + 177 * q^41 + 42 * q^42 + 1817 * q^43 - 1009 * q^45 + 198 * q^46 - 873 * q^47 - 48 * q^48 + 490 * q^49 - 1338 * q^50 + 525 * q^51 + 312 * q^52 - 854 * q^53 + 516 * q^54 - 560 * q^56 + 806 * q^57 - 692 * q^58 - 513 * q^59 - 288 * q^60 + 2084 * q^61 + 718 * q^62 + 679 * q^63 + 640 * q^64 - 425 * q^65 - 119 * q^67 + 320 * q^68 + 308 * q^69 + 378 * q^70 - 276 * q^71 - 776 * q^72 + 779 * q^73 - 1290 * q^74 - 6417 * q^75 + 712 * q^76 - 906 * q^78 + 2475 * q^79 - 432 * q^80 + 2946 * q^81 - 354 * q^82 + 463 * q^83 - 84 * q^84 - 580 * q^85 - 3634 * q^86 + 1014 * q^87 - 2065 * q^89 + 2018 * q^90 + 546 * q^91 - 396 * q^92 - 487 * q^93 + 1746 * q^94 + 2612 * q^95 + 96 * q^96 - 3666 * q^97 - 980 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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