LMFDB - Embedded newform 4334.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} + \cdots - 400 $ x^17 - 7x^16 - 7x^15 + 137x^14 - 98x^13 - 1048x^12 + 1313x^11 + 4085x^10 - 6021x^9 - 8879x^8 + 13530x^7 + 11150x^6 - 15676x^5 - 8037x^4 + 8646x^3 + 3040x^2 - 1640x - 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.577346$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -0.577346 q^{3} +1.00000 q^{4} +0.543375 q^{5} -0.577346 q^{6} +4.26235 q^{7} +1.00000 q^{8} -2.66667 q^{9} +0.543375 q^{10} -1.00000 q^{11} -0.577346 q^{12} -3.04123 q^{13} +4.26235 q^{14} -0.313715 q^{15} +1.00000 q^{16} -2.22115 q^{17} -2.66667 q^{18} -5.66435 q^{19} +0.543375 q^{20} -2.46085 q^{21} -1.00000 q^{22} -0.371480 q^{23} -0.577346 q^{24} -4.70474 q^{25} -3.04123 q^{26} +3.27163 q^{27} +4.26235 q^{28} -6.58172 q^{29} -0.313715 q^{30} -0.214944 q^{31} +1.00000 q^{32} +0.577346 q^{33} -2.22115 q^{34} +2.31605 q^{35} -2.66667 q^{36} -11.6601 q^{37} -5.66435 q^{38} +1.75584 q^{39} +0.543375 q^{40} -5.07997 q^{41} -2.46085 q^{42} -8.25748 q^{43} -1.00000 q^{44} -1.44900 q^{45} -0.371480 q^{46} +11.6915 q^{47} -0.577346 q^{48} +11.1676 q^{49} -4.70474 q^{50} +1.28237 q^{51} -3.04123 q^{52} -6.06095 q^{53} +3.27163 q^{54} -0.543375 q^{55} +4.26235 q^{56} +3.27029 q^{57} -6.58172 q^{58} -6.42928 q^{59} -0.313715 q^{60} -3.47258 q^{61} -0.214944 q^{62} -11.3663 q^{63} +1.00000 q^{64} -1.65253 q^{65} +0.577346 q^{66} +3.91271 q^{67} -2.22115 q^{68} +0.214472 q^{69} +2.31605 q^{70} +6.54262 q^{71} -2.66667 q^{72} -3.23188 q^{73} -11.6601 q^{74} +2.71626 q^{75} -5.66435 q^{76} -4.26235 q^{77} +1.75584 q^{78} +16.9399 q^{79} +0.543375 q^{80} +6.11116 q^{81} -5.07997 q^{82} -6.45250 q^{83} -2.46085 q^{84} -1.20692 q^{85} -8.25748 q^{86} +3.79993 q^{87} -1.00000 q^{88} +3.09773 q^{89} -1.44900 q^{90} -12.9628 q^{91} -0.371480 q^{92} +0.124097 q^{93} +11.6915 q^{94} -3.07787 q^{95} -0.577346 q^{96} +15.7586 q^{97} +11.1676 q^{98} +2.66667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.577346	−0.333331	−0.166665	−	0.986014i	$-0.553300\pi$
$3$	−0.577346	−0.333331	−0.166665	+	0.986014i	$0.553300\pi$
$4$	1.00000	0.500000
$5$	0.543375	0.243005	0.121502	−	0.992591i	$-0.461229\pi$
$5$	0.543375	0.243005	0.121502	+	0.992591i	$0.461229\pi$
$6$	−0.577346	−0.235700
$7$	4.26235	1.61102	0.805508	−	0.592585i	$-0.201893\pi$
$7$	4.26235	1.61102	0.805508	+	0.592585i	$0.201893\pi$
$8$	1.00000	0.353553
$9$	−2.66667	−0.888891
$10$	0.543375	0.171830
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.577346	−0.166665
$13$	−3.04123	−0.843487	−0.421743	−	0.906715i	$-0.638582\pi$
$13$	−3.04123	−0.843487	−0.421743	+	0.906715i	$0.638582\pi$
$14$	4.26235	1.13916
$15$	−0.313715	−0.0810009
$16$	1.00000	0.250000
$17$	−2.22115	−0.538708	−0.269354	−	0.963041i	$-0.586810\pi$
$17$	−2.22115	−0.538708	−0.269354	+	0.963041i	$0.586810\pi$
$18$	−2.66667	−0.628541
$19$	−5.66435	−1.29949	−0.649746	−	0.760152i	$-0.725125\pi$
$19$	−5.66435	−1.29949	−0.649746	+	0.760152i	$0.725125\pi$
$20$	0.543375	0.121502
$21$	−2.46085	−0.537001
$22$	−1.00000	−0.213201
$23$	−0.371480	−0.0774589	−0.0387295	−	0.999250i	$-0.512331\pi$
$23$	−0.371480	−0.0774589	−0.0387295	+	0.999250i	$0.512331\pi$
$24$	−0.577346	−0.117850
$25$	−4.70474	−0.940949
$26$	−3.04123	−0.596435
$27$	3.27163	0.629625
$28$	4.26235	0.805508
$29$	−6.58172	−1.22219	−0.611097	−	0.791556i	$-0.709272\pi$
$29$	−6.58172	−1.22219	−0.611097	+	0.791556i	$0.709272\pi$
$30$	−0.313715	−0.0572763
$31$	−0.214944	−0.0386051	−0.0193025	−	0.999814i	$-0.506145\pi$
$31$	−0.214944	−0.0386051	−0.0193025	+	0.999814i	$0.506145\pi$
$32$	1.00000	0.176777
$33$	0.577346	0.100503
$34$	−2.22115	−0.380924
$35$	2.31605	0.391484
$36$	−2.66667	−0.444445
$37$	−11.6601	−1.91691	−0.958457	−	0.285236i	$-0.907928\pi$
$37$	−11.6601	−1.91691	−0.958457	+	0.285236i	$0.907928\pi$
$38$	−5.66435	−0.918879
$39$	1.75584	0.281160
$40$	0.543375	0.0859152
$41$	−5.07997	−0.793359	−0.396679	−	0.917957i	$-0.629838\pi$
$41$	−5.07997	−0.793359	−0.396679	+	0.917957i	$0.629838\pi$
$42$	−2.46085	−0.379717
$43$	−8.25748	−1.25925	−0.629627	−	0.776897i	$-0.716792\pi$
$43$	−8.25748	−1.25925	−0.629627	+	0.776897i	$0.716792\pi$
$44$	−1.00000	−0.150756
$45$	−1.44900	−0.216005
$46$	−0.371480	−0.0547717
$47$	11.6915	1.70538	0.852691	−	0.522416i	$-0.174969\pi$
$47$	11.6915	1.70538	0.852691	+	0.522416i	$0.174969\pi$
$48$	−0.577346	−0.0833326
$49$	11.1676	1.59537
$50$	−4.70474	−0.665351
$51$	1.28237	0.179568
$52$	−3.04123	−0.421743
$53$	−6.06095	−0.832536	−0.416268	−	0.909242i	$-0.636662\pi$
$53$	−6.06095	−0.832536	−0.416268	+	0.909242i	$0.636662\pi$
$54$	3.27163	0.445212
$55$	−0.543375	−0.0732687
$56$	4.26235	0.569580
$57$	3.27029	0.433160
$58$	−6.58172	−0.864222
$59$	−6.42928	−0.837021	−0.418511	−	0.908212i	$-0.637448\pi$
$59$	−6.42928	−0.837021	−0.418511	+	0.908212i	$0.637448\pi$
$60$	−0.313715	−0.0405005
$61$	−3.47258	−0.444618	−0.222309	−	0.974976i	$-0.571359\pi$
$61$	−3.47258	−0.444618	−0.222309	+	0.974976i	$0.571359\pi$
$62$	−0.214944	−0.0272979
$63$	−11.3663	−1.43202
$64$	1.00000	0.125000
$65$	−1.65253	−0.204971
$66$	0.577346	0.0710663
$67$	3.91271	0.478013	0.239007	−	0.971018i	$-0.423178\pi$
$67$	3.91271	0.478013	0.239007	+	0.971018i	$0.423178\pi$
$68$	−2.22115	−0.269354
$69$	0.214472	0.0258194
$70$	2.31605	0.276821
$71$	6.54262	0.776466	0.388233	−	0.921561i	$-0.373086\pi$
$71$	6.54262	0.776466	0.388233	+	0.921561i	$0.373086\pi$
$72$	−2.66667	−0.314270
$73$	−3.23188	−0.378263	−0.189131	−	0.981952i	$-0.560567\pi$
$73$	−3.23188	−0.378263	−0.189131	+	0.981952i	$0.560567\pi$
$74$	−11.6601	−1.35546
$75$	2.71626	0.313647
$76$	−5.66435	−0.649746
$77$	−4.26235	−0.485739
$78$	1.75584	0.198810
$79$	16.9399	1.90589	0.952945	−	0.303144i	$-0.0980362\pi$
$79$	16.9399	1.90589	0.952945	+	0.303144i	$0.0980362\pi$
$80$	0.543375	0.0607512
$81$	6.11116	0.679017
$82$	−5.07997	−0.560989
$83$	−6.45250	−0.708254	−0.354127	−	0.935197i	$-0.615222\pi$
$83$	−6.45250	−0.708254	−0.354127	+	0.935197i	$0.615222\pi$
$84$	−2.46085	−0.268500
$85$	−1.20692	−0.130909
$86$	−8.25748	−0.890427
$87$	3.79993	0.407395
$88$	−1.00000	−0.106600
$89$	3.09773	0.328358	0.164179	−	0.986431i	$-0.447502\pi$
$89$	3.09773	0.328358	0.164179	+	0.986431i	$0.447502\pi$
$90$	−1.44900	−0.152738
$91$	−12.9628	−1.35887
$92$	−0.371480	−0.0387295
$93$	0.124097	0.0128683
$94$	11.6915	1.20589
$95$	−3.07787	−0.315783
$96$	−0.577346	−0.0589251
$97$	15.7586	1.60004	0.800020	−	0.599974i	$-0.204822\pi$
$97$	15.7586	1.60004	0.800020	+	0.599974i	$0.204822\pi$
$98$	11.1676	1.12810
$99$	2.66667	0.268011
$100$	−4.70474	−0.470474
$101$	−11.4310	−1.13743	−0.568713	−	0.822536i	$-0.692558\pi$
$101$	−11.4310	−1.13743	−0.568713	+	0.822536i	$0.692558\pi$
$102$	1.28237	0.126974
$103$	11.8800	1.17057	0.585286	−	0.810827i	$-0.300982\pi$
$103$	11.8800	1.17057	0.585286	+	0.810827i	$0.300982\pi$
$104$	−3.04123	−0.298218
$105$	−1.33716	−0.130494
$106$	−6.06095	−0.588692
$107$	1.40966	0.136277	0.0681383	−	0.997676i	$-0.478294\pi$
$107$	1.40966	0.136277	0.0681383	+	0.997676i	$0.478294\pi$
$108$	3.27163	0.314813
$109$	−8.26500	−0.791644	−0.395822	−	0.918327i	$-0.629540\pi$
$109$	−8.26500	−0.791644	−0.395822	+	0.918327i	$0.629540\pi$
$110$	−0.543375	−0.0518088
$111$	6.73193	0.638966
$112$	4.26235	0.402754
$113$	7.06090	0.664234	0.332117	−	0.943238i	$-0.392237\pi$
$113$	7.06090	0.664234	0.332117	+	0.943238i	$0.392237\pi$
$114$	3.27029	0.306290
$115$	−0.201853	−0.0188229
$116$	−6.58172	−0.611097
$117$	8.10997	0.749767
$118$	−6.42928	−0.591863
$119$	−9.46732	−0.867867
$120$	−0.313715	−0.0286382
$121$	1.00000	0.0909091
$122$	−3.47258	−0.314393
$123$	2.93290	0.264451
$124$	−0.214944	−0.0193025
$125$	−5.27332	−0.471660
$126$	−11.3663	−1.01259
$127$	−12.6007	−1.11813	−0.559065	−	0.829124i	$-0.688840\pi$
$127$	−12.6007	−1.11813	−0.559065	+	0.829124i	$0.688840\pi$
$128$	1.00000	0.0883883
$129$	4.76742	0.419748
$130$	−1.65253	−0.144937
$131$	3.03640	0.265292	0.132646	−	0.991163i	$-0.457653\pi$
$131$	3.03640	0.265292	0.132646	+	0.991163i	$0.457653\pi$
$132$	0.577346	0.0502515
$133$	−24.1434	−2.09350
$134$	3.91271	0.338006
$135$	1.77772	0.153002
$136$	−2.22115	−0.190462
$137$	−10.2838	−0.878603	−0.439301	−	0.898340i	$-0.644774\pi$
$137$	−10.2838	−0.878603	−0.439301	+	0.898340i	$0.644774\pi$
$138$	0.214472	0.0182571
$139$	8.09845	0.686902	0.343451	−	0.939171i	$-0.388404\pi$
$139$	8.09845	0.686902	0.343451	+	0.939171i	$0.388404\pi$
$140$	2.31605	0.195742
$141$	−6.75004	−0.568456
$142$	6.54262	0.549044
$143$	3.04123	0.254321
$144$	−2.66667	−0.222223
$145$	−3.57634	−0.296999
$146$	−3.23188	−0.267472
$147$	−6.44756	−0.531786
$148$	−11.6601	−0.958457
$149$	7.94122	0.650570	0.325285	−	0.945616i	$-0.394540\pi$
$149$	7.94122	0.650570	0.325285	+	0.945616i	$0.394540\pi$
$150$	2.71626	0.221782
$151$	16.0787	1.30847	0.654234	−	0.756292i	$-0.272991\pi$
$151$	16.0787	1.30847	0.654234	+	0.756292i	$0.272991\pi$
$152$	−5.66435	−0.459439
$153$	5.92308	0.478853
$154$	−4.26235	−0.343470
$155$	−0.116795	−0.00938122
$156$	1.75584	0.140580
$157$	15.3756	1.22710	0.613552	−	0.789654i	$-0.289740\pi$
$157$	15.3756	1.22710	0.613552	+	0.789654i	$0.289740\pi$
$158$	16.9399	1.34767
$159$	3.49926	0.277510
$160$	0.543375	0.0429576
$161$	−1.58338	−0.124787
$162$	6.11116	0.480138
$163$	9.50432	0.744436	0.372218	−	0.928145i	$-0.378597\pi$
$163$	9.50432	0.744436	0.372218	+	0.928145i	$0.378597\pi$
$164$	−5.07997	−0.396679
$165$	0.313715	0.0244227
$166$	−6.45250	−0.500811
$167$	12.1221	0.938033	0.469017	−	0.883189i	$-0.344608\pi$
$167$	12.1221	0.938033	0.469017	+	0.883189i	$0.344608\pi$
$168$	−2.46085	−0.189858
$169$	−3.75090	−0.288530
$170$	−1.20692	−0.0925664
$171$	15.1050	1.15511
$172$	−8.25748	−0.629627
$173$	3.24690	0.246857	0.123428	−	0.992353i	$-0.460611\pi$
$173$	3.24690	0.246857	0.123428	+	0.992353i	$0.460611\pi$
$174$	3.79993	0.288072
$175$	−20.0532	−1.51588
$176$	−1.00000	−0.0753778
$177$	3.71192	0.279005
$178$	3.09773	0.232184
$179$	−2.55255	−0.190787	−0.0953934	−	0.995440i	$-0.530411\pi$
$179$	−2.55255	−0.190787	−0.0953934	+	0.995440i	$0.530411\pi$
$180$	−1.44900	−0.108002
$181$	−2.74731	−0.204206	−0.102103	−	0.994774i	$-0.532557\pi$
$181$	−2.74731	−0.204206	−0.102103	+	0.994774i	$0.532557\pi$
$182$	−12.9628	−0.960866
$183$	2.00488	0.148205
$184$	−0.371480	−0.0273859
$185$	−6.33583	−0.465819
$186$	0.124097	0.00909923
$187$	2.22115	0.162427
$188$	11.6915	0.852691
$189$	13.9448	1.01434
$190$	−3.07787	−0.223292
$191$	−19.9264	−1.44182	−0.720912	−	0.693027i	$-0.756277\pi$
$191$	−19.9264	−1.44182	−0.720912	+	0.693027i	$0.756277\pi$
$192$	−0.577346	−0.0416663
$193$	−4.92907	−0.354803	−0.177401	−	0.984139i	$-0.556769\pi$
$193$	−4.92907	−0.354803	−0.177401	+	0.984139i	$0.556769\pi$
$194$	15.7586	1.13140
$195$	0.954081	0.0683232
$196$	11.1676	0.797685
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.66667	0.189512
$199$	−9.26803	−0.656993	−0.328496	−	0.944505i	$-0.606542\pi$
$199$	−9.26803	−0.656993	−0.328496	+	0.944505i	$0.606542\pi$
$200$	−4.70474	−0.332676
$201$	−2.25898	−0.159336
$202$	−11.4310	−0.804281
$203$	−28.0536	−1.96897
$204$	1.28237	0.0897840
$205$	−2.76033	−0.192790
$206$	11.8800	0.827720
$207$	0.990615	0.0688525
$208$	−3.04123	−0.210872
$209$	5.66435	0.391811
$210$	−1.33716	−0.0922730
$211$	−25.3840	−1.74750	−0.873752	−	0.486372i	$-0.838320\pi$
$211$	−25.3840	−1.74750	−0.873752	+	0.486372i	$0.838320\pi$
$212$	−6.06095	−0.416268
$213$	−3.77735	−0.258820
$214$	1.40966	0.0963621
$215$	−4.48691	−0.306005
$216$	3.27163	0.222606
$217$	−0.916165	−0.0621934
$218$	−8.26500	−0.559777
$219$	1.86591	0.126087
$220$	−0.543375	−0.0366343
$221$	6.75504	0.454393
$222$	6.73193	0.451817
$223$	6.11272	0.409338	0.204669	−	0.978831i	$-0.434388\pi$
$223$	6.11272	0.409338	0.204669	+	0.978831i	$0.434388\pi$
$224$	4.26235	0.284790
$225$	12.5460	0.836401
$226$	7.06090	0.469684
$227$	−22.6472	−1.50315	−0.751575	−	0.659647i	$-0.770706\pi$
$227$	−22.6472	−1.50315	−0.751575	+	0.659647i	$0.770706\pi$
$228$	3.27029	0.216580
$229$	−8.94455	−0.591072	−0.295536	−	0.955332i	$-0.595498\pi$
$229$	−8.94455	−0.591072	−0.295536	+	0.955332i	$0.595498\pi$
$230$	−0.201853	−0.0133098
$231$	2.46085	0.161912
$232$	−6.58172	−0.432111
$233$	2.06997	0.135608	0.0678040	−	0.997699i	$-0.478401\pi$
$233$	2.06997	0.135608	0.0678040	+	0.997699i	$0.478401\pi$
$234$	8.10997	0.530166
$235$	6.35287	0.414416
$236$	−6.42928	−0.418511
$237$	−9.78019	−0.635291
$238$	−9.46732	−0.613675
$239$	6.45225	0.417361	0.208681	−	0.977984i	$-0.433083\pi$
$239$	6.45225	0.417361	0.208681	+	0.977984i	$0.433083\pi$
$240$	−0.313715	−0.0202502
$241$	−19.8363	−1.27777	−0.638884	−	0.769303i	$-0.720604\pi$
$241$	−19.8363	−1.27777	−0.638884	+	0.769303i	$0.720604\pi$
$242$	1.00000	0.0642824
$243$	−13.3431	−0.855962
$244$	−3.47258	−0.222309
$245$	6.06819	0.387683
$246$	2.93290	0.186995
$247$	17.2266	1.09610
$248$	−0.214944	−0.0136490
$249$	3.72532	0.236083
$250$	−5.27332	−0.333514
$251$	12.1367	0.766059	0.383029	−	0.923736i	$-0.374881\pi$
$251$	12.1367	0.766059	0.383029	+	0.923736i	$0.374881\pi$
$252$	−11.3663	−0.716008
$253$	0.371480	0.0233547
$254$	−12.6007	−0.790637
$255$	0.696809	0.0436359
$256$	1.00000	0.0625000
$257$	7.28629	0.454506	0.227253	−	0.973836i	$-0.427026\pi$
$257$	7.28629	0.454506	0.227253	+	0.973836i	$0.427026\pi$
$258$	4.76742	0.296807
$259$	−49.6995	−3.08818
$260$	−1.65253	−0.102486
$261$	17.5513	1.08640
$262$	3.03640	0.187590
$263$	12.1105	0.746763	0.373382	−	0.927678i	$-0.378198\pi$
$263$	12.1105	0.746763	0.373382	+	0.927678i	$0.378198\pi$
$264$	0.577346	0.0355332
$265$	−3.29337	−0.202310
$266$	−24.1434	−1.48033
$267$	−1.78846	−0.109452
$268$	3.91271	0.239007
$269$	17.5560	1.07041	0.535205	−	0.844722i	$-0.320234\pi$
$269$	17.5560	1.07041	0.535205	+	0.844722i	$0.320234\pi$
$270$	1.77772	0.108189
$271$	−1.29395	−0.0786020	−0.0393010	−	0.999227i	$-0.512513\pi$
$271$	−1.29395	−0.0786020	−0.0393010	+	0.999227i	$0.512513\pi$
$272$	−2.22115	−0.134677
$273$	7.48401	0.452953
$274$	−10.2838	−0.621266
$275$	4.70474	0.283707
$276$	0.214472	0.0129097
$277$	14.3459	0.861964	0.430982	−	0.902361i	$-0.358167\pi$
$277$	14.3459	0.861964	0.430982	+	0.902361i	$0.358167\pi$
$278$	8.09845	0.485713
$279$	0.573185	0.0343157
$280$	2.31605	0.138411
$281$	0.881377	0.0525786	0.0262893	−	0.999654i	$-0.491631\pi$
$281$	0.881377	0.0525786	0.0262893	+	0.999654i	$0.491631\pi$
$282$	−6.75004	−0.401959
$283$	8.73102	0.519005	0.259503	−	0.965742i	$-0.416441\pi$
$283$	8.73102	0.519005	0.259503	+	0.965742i	$0.416441\pi$
$284$	6.54262	0.388233
$285$	1.77699	0.105260
$286$	3.04123	0.179832
$287$	−21.6526	−1.27811
$288$	−2.66667	−0.157135
$289$	−12.0665	−0.709793
$290$	−3.57634	−0.210010
$291$	−9.09813	−0.533342
$292$	−3.23188	−0.189131
$293$	−25.6867	−1.50063	−0.750316	−	0.661080i	$-0.770099\pi$
$293$	−25.6867	−1.50063	−0.750316	+	0.661080i	$0.770099\pi$
$294$	−6.44756	−0.376029
$295$	−3.49351	−0.203400
$296$	−11.6601	−0.677732
$297$	−3.27163	−0.189839
$298$	7.94122	0.460023
$299$	1.12976	0.0653355
$300$	2.71626	0.156823
$301$	−35.1962	−2.02868
$302$	16.0787	0.925227
$303$	6.59963	0.379139
$304$	−5.66435	−0.324873
$305$	−1.88691	−0.108044
$306$	5.92308	0.338600
$307$	−16.5178	−0.942720	−0.471360	−	0.881941i	$-0.656237\pi$
$307$	−16.5178	−0.942720	−0.471360	+	0.881941i	$0.656237\pi$
$308$	−4.26235	−0.242870
$309$	−6.85887	−0.390188
$310$	−0.116795	−0.00663352
$311$	29.5386	1.67498	0.837491	−	0.546451i	$-0.184022\pi$
$311$	29.5386	1.67498	0.837491	+	0.546451i	$0.184022\pi$
$312$	1.75584	0.0994050
$313$	−19.9854	−1.12964	−0.564821	−	0.825213i	$-0.691055\pi$
$313$	−19.9854	−1.12964	−0.564821	+	0.825213i	$0.691055\pi$
$314$	15.3756	0.867693
$315$	−6.17615	−0.347987
$316$	16.9399	0.952945
$317$	10.2716	0.576912	0.288456	−	0.957493i	$-0.406858\pi$
$317$	10.2716	0.576912	0.288456	+	0.957493i	$0.406858\pi$
$318$	3.49926	0.196229
$319$	6.58172	0.368505
$320$	0.543375	0.0303756
$321$	−0.813858	−0.0454251
$322$	−1.58338	−0.0882381
$323$	12.5814	0.700047
$324$	6.11116	0.339509
$325$	14.3082	0.793678
$326$	9.50432	0.526396
$327$	4.77176	0.263879
$328$	−5.07997	−0.280495
$329$	49.8332	2.74740
$330$	0.313715	0.0172695
$331$	−0.0160706	−0.000883318 0	−0.000441659	−	1.00000i	$-0.500141\pi$
$331$	−0.0160706	−0.000883318 0	−0.000441659		1.00000i	$0.500141\pi$
$332$	−6.45250	−0.354127
$333$	31.0938	1.70393
$334$	12.1221	0.663290
$335$	2.12607	0.116159
$336$	−2.46085	−0.134250
$337$	−19.5074	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$337$	−19.5074	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$338$	−3.75090	−0.204022
$339$	−4.07658	−0.221409
$340$	−1.20692	−0.0654544
$341$	0.214944	0.0116399
$342$	15.1050	0.816783
$343$	17.7637	0.959151
$344$	−8.25748	−0.445214
$345$	0.116539	0.00627424
$346$	3.24690	0.174554
$347$	−12.9180	−0.693472	−0.346736	−	0.937963i	$-0.612710\pi$
$347$	−12.9180	−0.693472	−0.346736	+	0.937963i	$0.612710\pi$
$348$	3.79993	0.203697
$349$	−0.975358	−0.0522097	−0.0261049	−	0.999659i	$-0.508310\pi$
$349$	−0.975358	−0.0522097	−0.0261049	+	0.999659i	$0.508310\pi$
$350$	−20.0532	−1.07189
$351$	−9.94979	−0.531080
$352$	−1.00000	−0.0533002
$353$	−31.6053	−1.68218	−0.841091	−	0.540893i	$-0.818086\pi$
$353$	−31.6053	−1.68218	−0.841091	+	0.540893i	$0.818086\pi$
$354$	3.71192	0.197286
$355$	3.55510	0.188685
$356$	3.09773	0.164179
$357$	5.46591	0.289287
$358$	−2.55255	−0.134907
$359$	9.98162	0.526810	0.263405	−	0.964685i	$-0.415154\pi$
$359$	9.98162	0.526810	0.263405	+	0.964685i	$0.415154\pi$
$360$	−1.44900	−0.0763692
$361$	13.0849	0.688677
$362$	−2.74731	−0.144395
$363$	−0.577346	−0.0303028
$364$	−12.9628	−0.679435
$365$	−1.75612	−0.0919197
$366$	2.00488	0.104797
$367$	−33.6940	−1.75881	−0.879406	−	0.476073i	$-0.842060\pi$
$367$	−33.6940	−1.75881	−0.879406	+	0.476073i	$0.842060\pi$
$368$	−0.371480	−0.0193647
$369$	13.5466	0.705209
$370$	−6.33583	−0.329384
$371$	−25.8339	−1.34123
$372$	0.124097	0.00643413
$373$	14.9247	0.772773	0.386387	−	0.922337i	$-0.373723\pi$
$373$	14.9247	0.772773	0.386387	+	0.922337i	$0.373723\pi$
$374$	2.22115	0.114853
$375$	3.04453	0.157219
$376$	11.6915	0.602943
$377$	20.0165	1.03090
$378$	13.9448	0.717244
$379$	32.9765	1.69389	0.846945	−	0.531681i	$-0.178439\pi$
$379$	32.9765	1.69389	0.846945	+	0.531681i	$0.178439\pi$
$380$	−3.07787	−0.157891
$381$	7.27495	0.372707
$382$	−19.9264	−1.01952
$383$	−28.6521	−1.46406	−0.732028	−	0.681275i	$-0.761426\pi$
$383$	−28.6521	−1.46406	−0.732028	+	0.681275i	$0.761426\pi$
$384$	−0.577346	−0.0294625
$385$	−2.31605	−0.118037
$386$	−4.92907	−0.250883
$387$	22.0200	1.11934
$388$	15.7586	0.800020
$389$	−29.9562	−1.51884	−0.759419	−	0.650601i	$-0.774517\pi$
$389$	−29.9562	−1.51884	−0.759419	+	0.650601i	$0.774517\pi$
$390$	0.954081	0.0483118
$391$	0.825113	0.0417278
$392$	11.1676	0.564049
$393$	−1.75305	−0.0884299
$394$	1.00000	0.0503793
$395$	9.20473	0.463140
$396$	2.66667	0.134005
$397$	−12.5466	−0.629697	−0.314849	−	0.949142i	$-0.601954\pi$
$397$	−12.5466	−0.629697	−0.314849	+	0.949142i	$0.601954\pi$
$398$	−9.26803	−0.464564
$399$	13.9391	0.697828
$400$	−4.70474	−0.235237
$401$	−27.4744	−1.37201	−0.686003	−	0.727599i	$-0.740636\pi$
$401$	−27.4744	−1.37201	−0.686003	+	0.727599i	$0.740636\pi$
$402$	−2.25898	−0.112668
$403$	0.653695	0.0325629
$404$	−11.4310	−0.568713
$405$	3.32065	0.165004
$406$	−28.0536	−1.39227
$407$	11.6601	0.577971
$408$	1.28237	0.0634869
$409$	−28.5484	−1.41163	−0.705814	−	0.708397i	$-0.749418\pi$
$409$	−28.5484	−1.41163	−0.705814	+	0.708397i	$0.749418\pi$
$410$	−2.76033	−0.136323
$411$	5.93729	0.292865
$412$	11.8800	0.585286
$413$	−27.4038	−1.34845
$414$	0.990615	0.0486861
$415$	−3.50613	−0.172109
$416$	−3.04123	−0.149109
$417$	−4.67561	−0.228965
$418$	5.66435	0.277052
$419$	12.2932	0.600561	0.300280	−	0.953851i	$-0.402920\pi$
$419$	12.2932	0.600561	0.300280	+	0.953851i	$0.402920\pi$
$420$	−1.33716	−0.0652469
$421$	29.5043	1.43795	0.718976	−	0.695034i	$-0.244611\pi$
$421$	29.5043	1.43795	0.718976	+	0.695034i	$0.244611\pi$
$422$	−25.3840	−1.23567
$423$	−31.1774	−1.51590
$424$	−6.06095	−0.294346
$425$	10.4499	0.506897
$426$	−3.77735	−0.183013
$427$	−14.8013	−0.716287
$428$	1.40966	0.0681383
$429$	−1.75584	−0.0847729
$430$	−4.48691	−0.216378
$431$	16.2220	0.781386	0.390693	−	0.920521i	$-0.372235\pi$
$431$	16.2220	0.781386	0.390693	+	0.920521i	$0.372235\pi$
$432$	3.27163	0.157406
$433$	−26.0231	−1.25059	−0.625295	−	0.780388i	$-0.715021\pi$
$433$	−26.0231	−1.25059	−0.625295	+	0.780388i	$0.715021\pi$
$434$	−0.916165	−0.0439773
$435$	2.06479	0.0989989
$436$	−8.26500	−0.395822
$437$	2.10419	0.100657
$438$	1.86591	0.0891567
$439$	−19.3226	−0.922218	−0.461109	−	0.887343i	$-0.652548\pi$
$439$	−19.3226	−0.922218	−0.461109	+	0.887343i	$0.652548\pi$
$440$	−0.543375	−0.0259044
$441$	−29.7803	−1.41811
$442$	6.75504	0.321305
$443$	−15.4052	−0.731922	−0.365961	−	0.930630i	$-0.619260\pi$
$443$	−15.4052	−0.731922	−0.365961	+	0.930630i	$0.619260\pi$
$444$	6.73193	0.319483
$445$	1.68323	0.0797927
$446$	6.11272	0.289445
$447$	−4.58483	−0.216855
$448$	4.26235	0.201377
$449$	−0.282425	−0.0133284	−0.00666422	−	0.999978i	$-0.502121\pi$
$449$	−0.282425	−0.0133284	−0.00666422	+	0.999978i	$0.502121\pi$
$450$	12.5460	0.591424
$451$	5.07997	0.239207
$452$	7.06090	0.332117
$453$	−9.28298	−0.436152
$454$	−22.6472	−1.06289
$455$	−7.04366	−0.330212
$456$	3.27029	0.153145
$457$	−15.3844	−0.719653	−0.359826	−	0.933019i	$-0.617164\pi$
$457$	−15.3844	−0.719653	−0.359826	+	0.933019i	$0.617164\pi$
$458$	−8.94455	−0.417951
$459$	−7.26678	−0.339184
$460$	−0.201853	−0.00941144
$461$	33.8126	1.57481	0.787404	−	0.616437i	$-0.211424\pi$
$461$	33.8126	1.57481	0.787404	+	0.616437i	$0.211424\pi$
$462$	2.46085	0.114489
$463$	−7.83856	−0.364289	−0.182144	−	0.983272i	$-0.558304\pi$
$463$	−7.83856	−0.364289	−0.182144	+	0.983272i	$0.558304\pi$
$464$	−6.58172	−0.305549
$465$	0.0674312	0.00312705
$466$	2.06997	0.0958894
$467$	−15.1724	−0.702093	−0.351046	−	0.936358i	$-0.614174\pi$
$467$	−15.1724	−0.702093	−0.351046	+	0.936358i	$0.614174\pi$
$468$	8.10997	0.374884
$469$	16.6773	0.770087
$470$	6.35287	0.293036
$471$	−8.87701	−0.409031
$472$	−6.42928	−0.295932
$473$	8.25748	0.379679
$474$	−9.78019	−0.449219
$475$	26.6493	1.22275
$476$	−9.46732	−0.433934
$477$	16.1626	0.740033
$478$	6.45225	0.295119
$479$	19.4182	0.887241	0.443621	−	0.896215i	$-0.353694\pi$
$479$	19.4182	0.887241	0.443621	+	0.896215i	$0.353694\pi$
$480$	−0.313715	−0.0143191
$481$	35.4612	1.61689
$482$	−19.8363	−0.903518
$483$	0.914155	0.0415955
$484$	1.00000	0.0454545
$485$	8.56281	0.388817
$486$	−13.3431	−0.605257
$487$	−32.6899	−1.48132	−0.740662	−	0.671878i	$-0.765488\pi$
$487$	−32.6899	−1.48132	−0.740662	+	0.671878i	$0.765488\pi$
$488$	−3.47258	−0.157196
$489$	−5.48728	−0.248143
$490$	6.06819	0.274133
$491$	12.9260	0.583341	0.291670	−	0.956519i	$-0.405789\pi$
$491$	12.9260	0.583341	0.291670	+	0.956519i	$0.405789\pi$
$492$	2.93290	0.132225
$493$	14.6190	0.658406
$494$	17.2266	0.775062
$495$	1.44900	0.0651279
$496$	−0.214944	−0.00965127
$497$	27.8869	1.25090
$498$	3.72532	0.166936
$499$	25.7188	1.15133	0.575666	−	0.817685i	$-0.304743\pi$
$499$	25.7188	1.15133	0.575666	+	0.817685i	$0.304743\pi$
$500$	−5.27332	−0.235830
$501$	−6.99862	−0.312675
$502$	12.1367	0.541685
$503$	−15.3846	−0.685963	−0.342982	−	0.939342i	$-0.611437\pi$
$503$	−15.3846	−0.685963	−0.342982	+	0.939342i	$0.611437\pi$
$504$	−11.3663	−0.506294
$505$	−6.21131	−0.276400
$506$	0.371480	0.0165143
$507$	2.16556	0.0961760
$508$	−12.6007	−0.559065
$509$	30.9021	1.36971	0.684857	−	0.728678i	$-0.259865\pi$
$509$	30.9021	1.36971	0.684857	+	0.728678i	$0.259865\pi$
$510$	0.696809	0.0308552
$511$	−13.7754	−0.609387
$512$	1.00000	0.0441942
$513$	−18.5316	−0.818192
$514$	7.28629	0.321384
$515$	6.45530	0.284455
$516$	4.76742	0.209874
$517$	−11.6915	−0.514192
$518$	−49.6995	−2.18367
$519$	−1.87458	−0.0822850
$520$	−1.65253	−0.0724683
$521$	35.0575	1.53590	0.767948	−	0.640513i	$-0.221278\pi$
$521$	35.0575	1.53590	0.767948	+	0.640513i	$0.221278\pi$
$522$	17.5513	0.768199
$523$	−24.8244	−1.08550	−0.542748	−	0.839896i	$-0.682616\pi$
$523$	−24.8244	−1.08550	−0.542748	+	0.839896i	$0.682616\pi$
$524$	3.03640	0.132646
$525$	11.5777	0.505290
$526$	12.1105	0.528042
$527$	0.477423	0.0207969
$528$	0.577346	0.0251257
$529$	−22.8620	−0.994000
$530$	−3.29337	−0.143055
$531$	17.1448	0.744021
$532$	−24.1434	−1.04675
$533$	15.4494	0.669187
$534$	−1.78846	−0.0773942
$535$	0.765972	0.0331158
$536$	3.91271	0.169003
$537$	1.47370	0.0635951
$538$	17.5560	0.756894
$539$	−11.1676	−0.481022
$540$	1.77772	0.0765009
$541$	17.5317	0.753745	0.376872	−	0.926265i	$-0.377000\pi$
$541$	17.5317	0.753745	0.376872	+	0.926265i	$0.377000\pi$
$542$	−1.29395	−0.0555800
$543$	1.58615	0.0680681
$544$	−2.22115	−0.0952311
$545$	−4.49100	−0.192373
$546$	7.48401	0.320286
$547$	10.9370	0.467634	0.233817	−	0.972281i	$-0.424878\pi$
$547$	10.9370	0.467634	0.233817	+	0.972281i	$0.424878\pi$
$548$	−10.2838	−0.439301
$549$	9.26023	0.395217
$550$	4.70474	0.200611
$551$	37.2812	1.58823
$552$	0.214472	0.00912854
$553$	72.2038	3.07042
$554$	14.3459	0.609501
$555$	3.65796	0.155272
$556$	8.09845	0.343451
$557$	44.1500	1.87070	0.935349	−	0.353728i	$-0.115086\pi$
$557$	44.1500	1.87070	0.935349	+	0.353728i	$0.115086\pi$
$558$	0.573185	0.0242649
$559$	25.1129	1.06216
$560$	2.31605	0.0978711
$561$	−1.28237	−0.0541418
$562$	0.881377	0.0371787
$563$	45.3609	1.91173	0.955866	−	0.293802i	$-0.0949207\pi$
$563$	45.3609	1.91173	0.955866	+	0.293802i	$0.0949207\pi$
$564$	−6.75004	−0.284228
$565$	3.83672	0.161412
$566$	8.73102	0.366992
$567$	26.0479	1.09391
$568$	6.54262	0.274522
$569$	20.9765	0.879381	0.439691	−	0.898149i	$-0.355088\pi$
$569$	20.9765	0.879381	0.439691	+	0.898149i	$0.355088\pi$
$570$	1.77699	0.0744300
$571$	29.2335	1.22338	0.611691	−	0.791097i	$-0.290489\pi$
$571$	29.2335	1.22338	0.611691	+	0.791097i	$0.290489\pi$
$572$	3.04123	0.127160
$573$	11.5044	0.480604
$574$	−21.6526	−0.903762
$575$	1.74772	0.0728849
$576$	−2.66667	−0.111111
$577$	−22.9837	−0.956822	−0.478411	−	0.878136i	$-0.658787\pi$
$577$	−22.9837	−0.956822	−0.478411	+	0.878136i	$0.658787\pi$
$578$	−12.0665	−0.501900
$579$	2.84578	0.118267
$580$	−3.57634	−0.148500
$581$	−27.5028	−1.14101
$582$	−9.09813	−0.377130
$583$	6.06095	0.251019
$584$	−3.23188	−0.133736
$585$	4.40676	0.182197
$586$	−25.6867	−1.06111
$587$	7.70832	0.318156	0.159078	−	0.987266i	$-0.449148\pi$
$587$	7.70832	0.318156	0.159078	+	0.987266i	$0.449148\pi$
$588$	−6.44756	−0.265893
$589$	1.21752	0.0501669
$590$	−3.49351	−0.143826
$591$	−0.577346	−0.0237488
$592$	−11.6601	−0.479229
$593$	−4.89540	−0.201030	−0.100515	−	0.994936i	$-0.532049\pi$
$593$	−4.89540	−0.201030	−0.100515	+	0.994936i	$0.532049\pi$
$594$	−3.27163	−0.134237
$595$	−5.14430	−0.210896
$596$	7.94122	0.325285
$597$	5.35085	0.218996
$598$	1.12976	0.0461992
$599$	42.3017	1.72840	0.864199	−	0.503150i	$-0.167826\pi$
$599$	42.3017	1.72840	0.864199	+	0.503150i	$0.167826\pi$
$600$	2.71626	0.110891
$601$	−32.4040	−1.32179	−0.660894	−	0.750479i	$-0.729823\pi$
$601$	−32.4040	−1.32179	−0.660894	+	0.750479i	$0.729823\pi$
$602$	−35.1962	−1.43449
$603$	−10.4339	−0.424901
$604$	16.0787	0.654234
$605$	0.543375	0.0220913
$606$	6.59963	0.268092
$607$	0.663158	0.0269167	0.0134584	−	0.999909i	$-0.495716\pi$
$607$	0.663158	0.0269167	0.0134584	+	0.999909i	$0.495716\pi$
$608$	−5.66435	−0.229720
$609$	16.1966	0.656319
$610$	−1.88691	−0.0763989
$611$	−35.5566	−1.43847
$612$	5.92308	0.239426
$613$	−35.6846	−1.44129	−0.720644	−	0.693305i	$-0.756154\pi$
$613$	−35.6846	−1.44129	−0.720644	+	0.693305i	$0.756154\pi$
$614$	−16.5178	−0.666604
$615$	1.59367	0.0642628
$616$	−4.26235	−0.171735
$617$	18.2875	0.736227	0.368114	−	0.929781i	$-0.380004\pi$
$617$	18.2875	0.736227	0.368114	+	0.929781i	$0.380004\pi$
$618$	−6.85887	−0.275904
$619$	17.7899	0.715037	0.357519	−	0.933906i	$-0.383623\pi$
$619$	17.7899	0.715037	0.357519	+	0.933906i	$0.383623\pi$
$620$	−0.116795	−0.00469061
$621$	−1.21534	−0.0487701
$622$	29.5386	1.18439
$623$	13.2036	0.528990
$624$	1.75584	0.0702900
$625$	20.6583	0.826333
$626$	−19.9854	−0.798778
$627$	−3.27029	−0.130603
$628$	15.3756	0.613552
$629$	25.8989	1.03266
$630$	−6.17615	−0.246064
$631$	−20.2350	−0.805542	−0.402771	−	0.915301i	$-0.631953\pi$
$631$	−20.2350	−0.805542	−0.402771	+	0.915301i	$0.631953\pi$
$632$	16.9399	0.673834
$633$	14.6553	0.582496
$634$	10.2716	0.407938
$635$	−6.84690	−0.271711
$636$	3.49926	0.138755
$637$	−33.9633	−1.34567
$638$	6.58172	0.260573
$639$	−17.4470	−0.690193
$640$	0.543375	0.0214788
$641$	35.3802	1.39743	0.698716	−	0.715399i	$-0.253755\pi$
$641$	35.3802	1.39743	0.698716	+	0.715399i	$0.253755\pi$
$642$	−0.813858	−0.0321204
$643$	−37.1995	−1.46701	−0.733503	−	0.679686i	$-0.762116\pi$
$643$	−37.1995	−1.46701	−0.733503	+	0.679686i	$0.762116\pi$
$644$	−1.58338	−0.0623937
$645$	2.59050	0.102001
$646$	12.5814	0.495008
$647$	17.3381	0.681629	0.340815	−	0.940131i	$-0.389297\pi$
$647$	17.3381	0.681629	0.340815	+	0.940131i	$0.389297\pi$
$648$	6.11116	0.240069
$649$	6.42928	0.252371
$650$	14.3082	0.561215
$651$	0.528944	0.0207310
$652$	9.50432	0.372218
$653$	−40.7979	−1.59655	−0.798273	−	0.602296i	$-0.794253\pi$
$653$	−40.7979	−1.59655	−0.798273	+	0.602296i	$0.794253\pi$
$654$	4.77176	0.186591
$655$	1.64991	0.0644672
$656$	−5.07997	−0.198340
$657$	8.61837	0.336234
$658$	49.8332	1.94270
$659$	12.5360	0.488333	0.244166	−	0.969733i	$-0.421486\pi$
$659$	12.5360	0.488333	0.244166	+	0.969733i	$0.421486\pi$
$660$	0.313715	0.0122113
$661$	−30.3291	−1.17966	−0.589832	−	0.807526i	$-0.700806\pi$
$661$	−30.3291	−1.17966	−0.589832	+	0.807526i	$0.700806\pi$
$662$	−0.0160706	−0.000624600 0
$663$	−3.89999	−0.151463
$664$	−6.45250	−0.250405
$665$	−13.1189	−0.508730
$666$	31.0938	1.20486
$667$	2.44498	0.0946698
$668$	12.1221	0.469017
$669$	−3.52915	−0.136445
$670$	2.12607	0.0821372
$671$	3.47258	0.134057
$672$	−2.46085	−0.0949292
$673$	−31.4378	−1.21184	−0.605919	−	0.795527i	$-0.707194\pi$
$673$	−31.4378	−1.21184	−0.605919	+	0.795527i	$0.707194\pi$
$674$	−19.5074	−0.751396
$675$	−15.3922	−0.592445
$676$	−3.75090	−0.144265
$677$	11.5272	0.443028	0.221514	−	0.975157i	$-0.428900\pi$
$677$	11.5272	0.443028	0.221514	+	0.975157i	$0.428900\pi$
$678$	−4.07658	−0.156560
$679$	67.1684	2.57769
$680$	−1.20692	−0.0462832
$681$	13.0753	0.501046
$682$	0.214944	0.00823063
$683$	−6.91408	−0.264560	−0.132280	−	0.991212i	$-0.542230\pi$
$683$	−6.91408	−0.264560	−0.132280	+	0.991212i	$0.542230\pi$
$684$	15.1050	0.577553
$685$	−5.58795	−0.213505
$686$	17.7637	0.678222
$687$	5.16409	0.197022
$688$	−8.25748	−0.314814
$689$	18.4328	0.702233
$690$	0.116539	0.00443656
$691$	−36.0166	−1.37014	−0.685069	−	0.728478i	$-0.740228\pi$
$691$	−36.0166	−1.37014	−0.685069	+	0.728478i	$0.740228\pi$
$692$	3.24690	0.123428
$693$	11.3663	0.431769
$694$	−12.9180	−0.490359
$695$	4.40050	0.166920
$696$	3.79993	0.144036
$697$	11.2834	0.427389
$698$	−0.975358	−0.0369178
$699$	−1.19509	−0.0452023
$700$	−20.0532	−0.757941
$701$	−4.92174	−0.185892	−0.0929458	−	0.995671i	$-0.529628\pi$
$701$	−4.92174	−0.185892	−0.0929458	+	0.995671i	$0.529628\pi$
$702$	−9.94979	−0.375530
$703$	66.0471	2.49101
$704$	−1.00000	−0.0376889
$705$	−3.66780	−0.138137
$706$	−31.6053	−1.18948
$707$	−48.7228	−1.83241
$708$	3.71192	0.139502
$709$	37.1273	1.39435	0.697173	−	0.716903i	$-0.254441\pi$
$709$	37.1273	1.39435	0.697173	+	0.716903i	$0.254441\pi$
$710$	3.55510	0.133420
$711$	−45.1732	−1.69413
$712$	3.09773	0.116092
$713$	0.0798473	0.00299031
$714$	5.46591	0.204557
$715$	1.65253	0.0618012
$716$	−2.55255	−0.0953934
$717$	−3.72518	−0.139119
$718$	9.98162	0.372511
$719$	10.7461	0.400762	0.200381	−	0.979718i	$-0.435782\pi$
$719$	10.7461	0.400762	0.200381	+	0.979718i	$0.435782\pi$
$720$	−1.44900	−0.0540012
$721$	50.6367	1.88581
$722$	13.0849	0.486968
$723$	11.4524	0.425919
$724$	−2.74731	−0.102103
$725$	30.9653	1.15002
$726$	−0.577346	−0.0214273
$727$	−3.05686	−0.113373	−0.0566863	−	0.998392i	$-0.518053\pi$
$727$	−3.05686	−0.113373	−0.0566863	+	0.998392i	$0.518053\pi$
$728$	−12.9628	−0.480433
$729$	−10.6299	−0.393699
$730$	−1.75612	−0.0649970
$731$	18.3411	0.678371
$732$	2.00488	0.0741024
$733$	11.5295	0.425852	0.212926	−	0.977068i	$-0.431701\pi$
$733$	11.5295	0.425852	0.212926	+	0.977068i	$0.431701\pi$
$734$	−33.6940	−1.24367
$735$	−3.50344	−0.129226
$736$	−0.371480	−0.0136929
$737$	−3.91271	−0.144126
$738$	13.5466	0.498658
$739$	−50.2385	−1.84805	−0.924027	−	0.382327i	$-0.875123\pi$
$739$	−50.2385	−1.84805	−0.924027	+	0.382327i	$0.875123\pi$
$740$	−6.33583	−0.232910
$741$	−9.94571	−0.365365
$742$	−25.8339	−0.948391
$743$	24.5377	0.900200	0.450100	−	0.892978i	$-0.351388\pi$
$743$	24.5377	0.900200	0.450100	+	0.892978i	$0.351388\pi$
$744$	0.124097	0.00454961
$745$	4.31506	0.158092
$746$	14.9247	0.546433
$747$	17.2067	0.629560
$748$	2.22115	0.0812133
$749$	6.00844	0.219544
$750$	3.04453	0.111170
$751$	−36.7785	−1.34207	−0.671033	−	0.741428i	$-0.734149\pi$
$751$	−36.7785	−1.34207	−0.671033	+	0.741428i	$0.734149\pi$
$752$	11.6915	0.426345
$753$	−7.00704	−0.255351
$754$	20.0165	0.728960
$755$	8.73678	0.317964
$756$	13.9448	0.507168
$757$	45.7385	1.66240	0.831198	−	0.555977i	$-0.187656\pi$
$757$	45.7385	1.66240	0.831198	+	0.555977i	$0.187656\pi$
$758$	32.9765	1.19776
$759$	−0.214472	−0.00778485
$760$	−3.07787	−0.111646
$761$	−15.8046	−0.572918	−0.286459	−	0.958093i	$-0.592478\pi$
$761$	−15.8046	−0.572918	−0.286459	+	0.958093i	$0.592478\pi$
$762$	7.27495	0.263543
$763$	−35.2283	−1.27535
$764$	−19.9264	−0.720912
$765$	3.21846	0.116364
$766$	−28.6521	−1.03524
$767$	19.5530	0.706016
$768$	−0.577346	−0.0208332
$769$	−5.53133	−0.199465	−0.0997324	−	0.995014i	$-0.531799\pi$
$769$	−5.53133	−0.199465	−0.0997324	+	0.995014i	$0.531799\pi$
$770$	−2.31605	−0.0834648
$771$	−4.20670	−0.151501
$772$	−4.92907	−0.177401
$773$	−16.3353	−0.587540	−0.293770	−	0.955876i	$-0.594910\pi$
$773$	−16.3353	−0.587540	−0.293770	+	0.955876i	$0.594910\pi$
$774$	22.0200	0.791493
$775$	1.01126	0.0363254
$776$	15.7586	0.565699
$777$	28.6938	1.02938
$778$	−29.9562	−1.07398
$779$	28.7748	1.03096
$780$	0.954081	0.0341616
$781$	−6.54262	−0.234113
$782$	0.825113	0.0295060
$783$	−21.5329	−0.769524
$784$	11.1676	0.398843
$785$	8.35470	0.298192
$786$	−1.75305	−0.0625293
$787$	25.2923	0.901575	0.450787	−	0.892631i	$-0.351143\pi$
$787$	25.2923	0.901575	0.450787	+	0.892631i	$0.351143\pi$
$788$	1.00000	0.0356235
$789$	−6.99193	−0.248919
$790$	9.20473	0.327490
$791$	30.0960	1.07009
$792$	2.66667	0.0947561
$793$	10.5609	0.375030
$794$	−12.5466	−0.445263
$795$	1.90141	0.0674361
$796$	−9.26803	−0.328496
$797$	41.1775	1.45858	0.729291	−	0.684203i	$-0.239850\pi$
$797$	41.1775	1.45858	0.729291	+	0.684203i	$0.239850\pi$
$798$	13.9391	0.493439
$799$	−25.9686	−0.918703
$800$	−4.70474	−0.166338
$801$	−8.26062	−0.291875
$802$	−27.4744	−0.970154
$803$	3.23188	0.114051
$804$	−2.25898	−0.0796682
$805$	−0.860367	−0.0303240
$806$	0.653695	0.0230254
$807$	−10.1359	−0.356800
$808$	−11.4310	−0.402141
$809$	21.5702	0.758369	0.379185	−	0.925321i	$-0.376205\pi$
$809$	21.5702	0.758369	0.379185	+	0.925321i	$0.376205\pi$
$810$	3.32065	0.116676
$811$	−40.4062	−1.41885	−0.709427	−	0.704779i	$-0.751046\pi$
$811$	−40.4062	−1.41885	−0.709427	+	0.704779i	$0.751046\pi$
$812$	−28.0536	−0.984487
$813$	0.747058	0.0262005
$814$	11.6601	0.408688
$815$	5.16441	0.180901
$816$	1.28237	0.0448920
$817$	46.7733	1.63639
$818$	−28.5484	−0.998171
$819$	34.5675	1.20789
$820$	−2.76033	−0.0963950
$821$	16.5128	0.576302	0.288151	−	0.957585i	$-0.406959\pi$
$821$	16.5128	0.576302	0.288151	+	0.957585i	$0.406959\pi$
$822$	5.93729	0.207087
$823$	9.15963	0.319285	0.159642	−	0.987175i	$-0.448966\pi$
$823$	9.15963	0.319285	0.159642	+	0.987175i	$0.448966\pi$
$824$	11.8800	0.413860
$825$	−2.71626	−0.0945681
$826$	−27.4038	−0.953501
$827$	−41.4541	−1.44150	−0.720751	−	0.693194i	$-0.756203\pi$
$827$	−41.4541	−1.44150	−0.720751	+	0.693194i	$0.756203\pi$
$828$	0.990615	0.0344263
$829$	19.8914	0.690855	0.345428	−	0.938445i	$-0.387734\pi$
$829$	19.8914	0.690855	0.345428	+	0.938445i	$0.387734\pi$
$830$	−3.50613	−0.121699
$831$	−8.28256	−0.287319
$832$	−3.04123	−0.105436
$833$	−24.8049	−0.859439
$834$	−4.67561	−0.161903
$835$	6.58683	0.227946
$836$	5.66435	0.195906
$837$	−0.703217	−0.0243067
$838$	12.2932	0.424661
$839$	−15.7693	−0.544417	−0.272208	−	0.962238i	$-0.587754\pi$
$839$	−15.7693	−0.544417	−0.272208	+	0.962238i	$0.587754\pi$
$840$	−1.33716	−0.0461365
$841$	14.3190	0.493759
$842$	29.5043	1.01679
$843$	−0.508859	−0.0175260
$844$	−25.3840	−0.873752
$845$	−2.03814	−0.0701143
$846$	−31.1774	−1.07190
$847$	4.26235	0.146456
$848$	−6.06095	−0.208134
$849$	−5.04082	−0.173000
$850$	10.4499	0.358430
$851$	4.33151	0.148482
$852$	−3.77735	−0.129410
$853$	56.9782	1.95090	0.975448	−	0.220231i	$-0.0706812\pi$
$853$	56.9782	1.95090	0.975448	+	0.220231i	$0.0706812\pi$
$854$	−14.8013	−0.506491
$855$	8.20766	0.280696
$856$	1.40966	0.0481810
$857$	33.5837	1.14720	0.573598	−	0.819137i	$-0.305547\pi$
$857$	33.5837	1.14720	0.573598	+	0.819137i	$0.305547\pi$
$858$	−1.75584	−0.0599435
$859$	−7.61821	−0.259930	−0.129965	−	0.991519i	$-0.541486\pi$
$859$	−7.61821	−0.259930	−0.129965	+	0.991519i	$0.541486\pi$
$860$	−4.48691	−0.153002
$861$	12.5010	0.426034
$862$	16.2220	0.552524
$863$	46.7048	1.58985	0.794926	−	0.606707i	$-0.207510\pi$
$863$	46.7048	1.58985	0.794926	+	0.606707i	$0.207510\pi$
$864$	3.27163	0.111303
$865$	1.76428	0.0599874
$866$	−26.0231	−0.884301
$867$	6.96653	0.236596
$868$	−0.916165	−0.0310967
$869$	−16.9399	−0.574647
$870$	2.06479	0.0700028
$871$	−11.8995	−0.403198
$872$	−8.26500	−0.279888
$873$	−42.0229	−1.42226
$874$	2.10419	0.0711754
$875$	−22.4767	−0.759851
$876$	1.86591	0.0630433
$877$	40.6627	1.37308	0.686541	−	0.727091i	$-0.259128\pi$
$877$	40.6627	1.37308	0.686541	+	0.727091i	$0.259128\pi$
$878$	−19.3226	−0.652107
$879$	14.8301	0.500206
$880$	−0.543375	−0.0183172
$881$	−44.2654	−1.49134	−0.745669	−	0.666317i	$-0.767870\pi$
$881$	−44.2654	−1.49134	−0.745669	+	0.666317i	$0.767870\pi$
$882$	−29.7803	−1.00276
$883$	−39.8339	−1.34052	−0.670259	−	0.742127i	$-0.733817\pi$
$883$	−39.8339	−1.34052	−0.670259	+	0.742127i	$0.733817\pi$
$884$	6.75504	0.227197
$885$	2.01696	0.0677995
$886$	−15.4052	−0.517547
$887$	−28.9752	−0.972892	−0.486446	−	0.873711i	$-0.661707\pi$
$887$	−28.9752	−0.972892	−0.486446	+	0.873711i	$0.661707\pi$
$888$	6.73193	0.225909
$889$	−53.7084	−1.80132
$890$	1.68323	0.0564219
$891$	−6.11116	−0.204731
$892$	6.11272	0.204669
$893$	−66.2248	−2.21613
$894$	−4.58483	−0.153340
$895$	−1.38699	−0.0463621
$896$	4.26235	0.142395
$897$	−0.652260	−0.0217783
$898$	−0.282425	−0.00942464
$899$	1.41470	0.0471829
$900$	12.5460	0.418200
$901$	13.4623	0.448494
$902$	5.07997	0.169145
$903$	20.3204	0.676220
$904$	7.06090	0.234842
$905$	−1.49282	−0.0496230
$906$	−9.28298	−0.308406
$907$	13.4780	0.447530	0.223765	−	0.974643i	$-0.428165\pi$
$907$	13.4780	0.447530	0.223765	+	0.974643i	$0.428165\pi$
$908$	−22.6472	−0.751575
$909$	30.4827	1.01105
$910$	−7.04366	−0.233495
$911$	38.5358	1.27675	0.638374	−	0.769726i	$-0.279607\pi$
$911$	38.5358	1.27675	0.638374	+	0.769726i	$0.279607\pi$
$912$	3.27029	0.108290
$913$	6.45250	0.213547
$914$	−15.3844	−0.508871
$915$	1.08940	0.0360145
$916$	−8.94455	−0.295536
$917$	12.9422	0.427389
$918$	−7.26678	−0.239840
$919$	−11.3858	−0.375583	−0.187792	−	0.982209i	$-0.560133\pi$
$919$	−11.3858	−0.375583	−0.187792	+	0.982209i	$0.560133\pi$
$920$	−0.201853	−0.00665489
$921$	9.53648	0.314238
$922$	33.8126	1.11356
$923$	−19.8976	−0.654938
$924$	2.46085	0.0809559
$925$	54.8579	1.80372
$926$	−7.83856	−0.257591
$927$	−31.6801	−1.04051
$928$	−6.58172	−0.216055
$929$	31.0358	1.01825	0.509126	−	0.860692i	$-0.329969\pi$
$929$	31.0358	1.01825	0.509126	+	0.860692i	$0.329969\pi$
$930$	0.0674312	0.00221116
$931$	−63.2572	−2.07317
$932$	2.06997	0.0678040
$933$	−17.0540	−0.558323
$934$	−15.1724	−0.496455
$935$	1.20692	0.0394705
$936$	8.10997	0.265083
$937$	27.5758	0.900862	0.450431	−	0.892811i	$-0.351270\pi$
$937$	27.5758	0.900862	0.450431	+	0.892811i	$0.351270\pi$
$938$	16.6773	0.544533
$939$	11.5385	0.376544
$940$	6.35287	0.207208
$941$	−16.2567	−0.529955	−0.264977	−	0.964255i	$-0.585364\pi$
$941$	−16.2567	−0.529955	−0.264977	+	0.964255i	$0.585364\pi$
$942$	−8.87701	−0.289229
$943$	1.88711	0.0614527
$944$	−6.42928	−0.209255
$945$	7.57726	0.246488
$946$	8.25748	0.268474
$947$	−55.2041	−1.79389	−0.896946	−	0.442140i	$-0.854219\pi$
$947$	−55.2041	−1.79389	−0.896946	+	0.442140i	$0.854219\pi$
$948$	−9.78019	−0.317646
$949$	9.82890	0.319060
$950$	26.6493	0.864618
$951$	−5.93028	−0.192302
$952$	−9.46732	−0.306837
$953$	57.9092	1.87586	0.937931	−	0.346822i	$-0.112739\pi$
$953$	57.9092	1.87586	0.937931	+	0.346822i	$0.112739\pi$
$954$	16.1626	0.523282
$955$	−10.8275	−0.350370
$956$	6.45225	0.208681
$957$	−3.79993	−0.122834
$958$	19.4182	0.627374
$959$	−43.8330	−1.41544
$960$	−0.313715	−0.0101251
$961$	−30.9538	−0.998510
$962$	35.4612	1.14331
$963$	−3.75909	−0.121135
$964$	−19.8363	−0.638884
$965$	−2.67834	−0.0862187
$966$	0.914155	0.0294124
$967$	−2.26108	−0.0727114	−0.0363557	−	0.999339i	$-0.511575\pi$
$967$	−2.26108	−0.0727114	−0.0363557	+	0.999339i	$0.511575\pi$
$968$	1.00000	0.0321412
$969$	−7.26380	−0.233347
$970$	8.56281	0.274935
$971$	−45.2687	−1.45274	−0.726371	−	0.687303i	$-0.758794\pi$
$971$	−45.2687	−1.45274	−0.726371	+	0.687303i	$0.758794\pi$
$972$	−13.3431	−0.427981
$973$	34.5184	1.10661
$974$	−32.6899	−1.04745
$975$	−8.26079	−0.264557
$976$	−3.47258	−0.111155
$977$	25.3979	0.812552	0.406276	−	0.913750i	$-0.366827\pi$
$977$	25.3979	0.812552	0.406276	+	0.913750i	$0.366827\pi$
$978$	−5.48728	−0.175464
$979$	−3.09773	−0.0990038
$980$	6.06819	0.193841
$981$	22.0401	0.703685
$982$	12.9260	0.412484
$983$	−33.3803	−1.06467	−0.532334	−	0.846535i	$-0.678685\pi$
$983$	−33.3803	−1.06467	−0.532334	+	0.846535i	$0.678685\pi$
$984$	2.93290	0.0934975
$985$	0.543375	0.0173134
$986$	14.6190	0.465564
$987$	−28.7710	−0.915791
$988$	17.2266	0.548052
$989$	3.06749	0.0975405
$990$	1.44900	0.0460524
$991$	−41.0135	−1.30284	−0.651418	−	0.758719i	$-0.725826\pi$
$991$	−41.0135	−1.30284	−0.651418	+	0.758719i	$0.725826\pi$
$992$	−0.214944	−0.00682448
$993$	0.00927827	0.000294437 0
$994$	27.8869	0.884519
$995$	−5.03602	−0.159652
$996$	3.72532	0.118041
$997$	−9.56023	−0.302776	−0.151388	−	0.988474i	$-0.548374\pi$
$997$	−9.56023	−0.302776	−0.151388	+	0.988474i	$0.548374\pi$
$998$	25.7188	0.814115
$999$	−38.1476	−1.20694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.9	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.9	✓	17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.577346 q^{3} +1.00000 q^{4} +0.543375 q^{5} -0.577346 q^{6} +4.26235 q^{7} +1.00000 q^{8} -2.66667 q^{9} +0.543375 q^{10} -1.00000 q^{11} -0.577346 q^{12} -3.04123 q^{13} +4.26235 q^{14} -0.313715 q^{15} +1.00000 q^{16} -2.22115 q^{17} -2.66667 q^{18} -5.66435 q^{19} +0.543375 q^{20} -2.46085 q^{21} -1.00000 q^{22} -0.371480 q^{23} -0.577346 q^{24} -4.70474 q^{25} -3.04123 q^{26} +3.27163 q^{27} +4.26235 q^{28} -6.58172 q^{29} -0.313715 q^{30} -0.214944 q^{31} +1.00000 q^{32} +0.577346 q^{33} -2.22115 q^{34} +2.31605 q^{35} -2.66667 q^{36} -11.6601 q^{37} -5.66435 q^{38} +1.75584 q^{39} +0.543375 q^{40} -5.07997 q^{41} -2.46085 q^{42} -8.25748 q^{43} -1.00000 q^{44} -1.44900 q^{45} -0.371480 q^{46} +11.6915 q^{47} -0.577346 q^{48} +11.1676 q^{49} -4.70474 q^{50} +1.28237 q^{51} -3.04123 q^{52} -6.06095 q^{53} +3.27163 q^{54} -0.543375 q^{55} +4.26235 q^{56} +3.27029 q^{57} -6.58172 q^{58} -6.42928 q^{59} -0.313715 q^{60} -3.47258 q^{61} -0.214944 q^{62} -11.3663 q^{63} +1.00000 q^{64} -1.65253 q^{65} +0.577346 q^{66} +3.91271 q^{67} -2.22115 q^{68} +0.214472 q^{69} +2.31605 q^{70} +6.54262 q^{71} -2.66667 q^{72} -3.23188 q^{73} -11.6601 q^{74} +2.71626 q^{75} -5.66435 q^{76} -4.26235 q^{77} +1.75584 q^{78} +16.9399 q^{79} +0.543375 q^{80} +6.11116 q^{81} -5.07997 q^{82} -6.45250 q^{83} -2.46085 q^{84} -1.20692 q^{85} -8.25748 q^{86} +3.79993 q^{87} -1.00000 q^{88} +3.09773 q^{89} -1.44900 q^{90} -12.9628 q^{91} -0.371480 q^{92} +0.124097 q^{93} +11.6915 q^{94} -3.07787 q^{95} -0.577346 q^{96} +15.7586 q^{97} +11.1676 q^{98} +2.66667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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