LMFDB - Embedded newform 3467.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3467,2,Mod(1,3467)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3467, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3467.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3467.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:	$27.6841343808$
Analytic rank:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	3467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.74906 q^{2} -0.534947 q^{3} +5.55732 q^{4} +1.27817 q^{5} +1.47060 q^{6} +0.611481 q^{7} -9.77929 q^{8} -2.71383 q^{9} -3.51376 q^{10} -3.27630 q^{11} -2.97287 q^{12} +2.00815 q^{13} -1.68100 q^{14} -0.683753 q^{15} +15.7692 q^{16} +4.18042 q^{17} +7.46048 q^{18} +6.77567 q^{19} +7.10320 q^{20} -0.327110 q^{21} +9.00674 q^{22} -8.49423 q^{23} +5.23140 q^{24} -3.36628 q^{25} -5.52051 q^{26} +3.05660 q^{27} +3.39820 q^{28} -4.01552 q^{29} +1.87968 q^{30} +6.29765 q^{31} -23.7919 q^{32} +1.75265 q^{33} -11.4922 q^{34} +0.781576 q^{35} -15.0816 q^{36} +8.31408 q^{37} -18.6267 q^{38} -1.07425 q^{39} -12.4996 q^{40} -5.08677 q^{41} +0.899244 q^{42} -5.26383 q^{43} -18.2075 q^{44} -3.46874 q^{45} +23.3511 q^{46} +8.83759 q^{47} -8.43569 q^{48} -6.62609 q^{49} +9.25411 q^{50} -2.23630 q^{51} +11.1599 q^{52} +0.906076 q^{53} -8.40276 q^{54} -4.18767 q^{55} -5.97985 q^{56} -3.62463 q^{57} +11.0389 q^{58} -4.95028 q^{59} -3.79984 q^{60} -0.282836 q^{61} -17.3126 q^{62} -1.65946 q^{63} +33.8669 q^{64} +2.56675 q^{65} -4.81813 q^{66} -8.95059 q^{67} +23.2319 q^{68} +4.54396 q^{69} -2.14860 q^{70} +6.48975 q^{71} +26.5394 q^{72} +11.2387 q^{73} -22.8559 q^{74} +1.80078 q^{75} +37.6546 q^{76} -2.00340 q^{77} +2.95318 q^{78} -5.50432 q^{79} +20.1557 q^{80} +6.50638 q^{81} +13.9838 q^{82} +13.2287 q^{83} -1.81786 q^{84} +5.34328 q^{85} +14.4706 q^{86} +2.14809 q^{87} +32.0399 q^{88} +3.76833 q^{89} +9.53576 q^{90} +1.22794 q^{91} -47.2052 q^{92} -3.36891 q^{93} -24.2950 q^{94} +8.66046 q^{95} +12.7274 q^{96} +7.72574 q^{97} +18.2155 q^{98} +8.89133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 9 q^{2} + 24 q^{3} + 189 q^{4} + 32 q^{5} + 9 q^{6} + 23 q^{7} + 27 q^{8} + 196 q^{9} + 50 q^{10} + 12 q^{11} + 69 q^{12} + 144 q^{13} + 11 q^{14} + 17 q^{15} + 223 q^{16} + 33 q^{17} + 39 q^{18}+ \cdots - 25 q^{99}+O(q^{100}) $ 162 * q + 9 * q^2 + 24 * q^3 + 189 * q^4 + 32 * q^5 + 9 * q^6 + 23 * q^7 + 27 * q^8 + 196 * q^9 + 50 * q^10 + 12 * q^11 + 69 * q^12 + 144 * q^13 + 11 * q^14 + 17 * q^15 + 223 * q^16 + 33 * q^17 + 39 * q^18 + 35 * q^19 + 52 * q^20 + 44 * q^21 + 53 * q^22 + 31 * q^23 + 21 * q^24 + 266 * q^25 + 22 * q^26 + 93 * q^27 + 65 * q^28 + 25 * q^29 + 11 * q^30 + 81 * q^31 + 38 * q^32 + 96 * q^33 + 47 * q^34 + 14 * q^35 + 234 * q^36 + 153 * q^37 + 57 * q^38 + 18 * q^39 + 124 * q^40 + 19 * q^41 + 22 * q^42 + 87 * q^43 - 22 * q^44 + 135 * q^45 - 5 * q^46 + 53 * q^47 + 133 * q^48 + 291 * q^49 + 14 * q^50 - q^51 + 280 * q^52 + 122 * q^53 - 6 * q^54 + 88 * q^55 + 8 * q^56 + 37 * q^57 + 62 * q^58 + 26 * q^59 - 22 * q^60 + 128 * q^61 + 9 * q^62 + 11 * q^63 + 281 * q^64 + 23 * q^65 - 34 * q^66 + 124 * q^67 + 32 * q^68 + 138 * q^69 + 39 * q^70 + 16 * q^71 + 53 * q^72 + 161 * q^73 - 32 * q^74 + 71 * q^75 + 96 * q^76 + 126 * q^77 + 31 * q^78 + 34 * q^79 + 73 * q^80 + 242 * q^81 + 173 * q^82 + 27 * q^83 - 11 * q^84 + 130 * q^85 - 51 * q^86 + 87 * q^87 + 121 * q^88 + 33 * q^89 + 62 * q^90 + 66 * q^91 + 50 * q^92 + 173 * q^93 + 85 * q^94 - 11 * q^95 - 15 * q^96 + 205 * q^97 + 40 * q^98 - 25 * 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 $

$2$	−2.74906	−1.94388	−0.971939	−	0.235233i	$-0.924415\pi$
$2$	−2.74906	−1.94388	−0.971939	+	0.235233i	$0.924415\pi$
$3$	−0.534947	−0.308852	−0.154426	−	0.988004i	$-0.549353\pi$
$3$	−0.534947	−0.308852	−0.154426	+	0.988004i	$0.549353\pi$
$4$	5.55732	2.77866
$5$	1.27817	0.571615	0.285807	−	0.958287i	$-0.407738\pi$
$5$	1.27817	0.571615	0.285807	+	0.958287i	$0.407738\pi$
$6$	1.47060	0.600370
$7$	0.611481	0.231118	0.115559	−	0.993301i	$-0.463134\pi$
$7$	0.611481	0.231118	0.115559	+	0.993301i	$0.463134\pi$
$8$	−9.77929	−3.45750
$9$	−2.71383	−0.904611
$10$	−3.51376	−1.11115
$11$	−3.27630	−0.987842	−0.493921	−	0.869507i	$-0.664437\pi$
$11$	−3.27630	−0.987842	−0.493921	+	0.869507i	$0.664437\pi$
$12$	−2.97287	−0.858195
$13$	2.00815	0.556960	0.278480	−	0.960442i	$-0.410169\pi$
$13$	2.00815	0.556960	0.278480	+	0.960442i	$0.410169\pi$
$14$	−1.68100	−0.449265
$15$	−0.683753	−0.176544
$16$	15.7692	3.94230
$17$	4.18042	1.01390	0.506950	−	0.861975i	$-0.330773\pi$
$17$	4.18042	1.01390	0.506950	+	0.861975i	$0.330773\pi$
$18$	7.46048	1.75845
$19$	6.77567	1.55445	0.777223	−	0.629225i	$-0.216628\pi$
$19$	6.77567	1.55445	0.777223	+	0.629225i	$0.216628\pi$
$20$	7.10320	1.58832
$21$	−0.327110	−0.0713812
$22$	9.00674	1.92024
$23$	−8.49423	−1.77117	−0.885584	−	0.464479i	$-0.846242\pi$
$23$	−8.49423	−1.77117	−0.885584	+	0.464479i	$0.846242\pi$
$24$	5.23140	1.06786
$25$	−3.36628	−0.673257
$26$	−5.52051	−1.08266
$27$	3.05660	0.588242
$28$	3.39820	0.642199
$29$	−4.01552	−0.745663	−0.372831	−	0.927899i	$-0.621613\pi$
$29$	−4.01552	−0.745663	−0.372831	+	0.927899i	$0.621613\pi$
$30$	1.87968	0.343180
$31$	6.29765	1.13109	0.565546	−	0.824717i	$-0.308665\pi$
$31$	6.29765	1.13109	0.565546	+	0.824717i	$0.308665\pi$
$32$	−23.7919	−4.20585
$33$	1.75265	0.305097
$34$	−11.4922	−1.97090
$35$	0.781576	0.132111
$36$	−15.0816	−2.51361
$37$	8.31408	1.36683	0.683413	−	0.730032i	$-0.260495\pi$
$37$	8.31408	1.36683	0.683413	+	0.730032i	$0.260495\pi$
$38$	−18.6267	−3.02165
$39$	−1.07425	−0.172018
$40$	−12.4996	−1.97636
$41$	−5.08677	−0.794421	−0.397210	−	0.917728i	$-0.630022\pi$
$41$	−5.08677	−0.794421	−0.397210	+	0.917728i	$0.630022\pi$
$42$	0.899244	0.138756
$43$	−5.26383	−0.802727	−0.401364	−	0.915919i	$-0.631464\pi$
$43$	−5.26383	−0.802727	−0.401364	+	0.915919i	$0.631464\pi$
$44$	−18.2075	−2.74488
$45$	−3.46874	−0.517089
$46$	23.3511	3.44294
$47$	8.83759	1.28909	0.644547	−	0.764564i	$-0.277046\pi$
$47$	8.83759	1.28909	0.644547	+	0.764564i	$0.277046\pi$
$48$	−8.43569	−1.21759
$49$	−6.62609	−0.946584
$50$	9.25411	1.30873
$51$	−2.23630	−0.313145
$52$	11.1599	1.54760
$53$	0.906076	0.124459	0.0622296	−	0.998062i	$-0.480179\pi$
$53$	0.906076	0.124459	0.0622296	+	0.998062i	$0.480179\pi$
$54$	−8.40276	−1.14347
$55$	−4.18767	−0.564665
$56$	−5.97985	−0.799091
$57$	−3.62463	−0.480093
$58$	11.0389	1.44948
$59$	−4.95028	−0.644472	−0.322236	−	0.946659i	$-0.604434\pi$
$59$	−4.95028	−0.644472	−0.322236	+	0.946659i	$0.604434\pi$
$60$	−3.79984	−0.490557
$61$	−0.282836	−0.0362134	−0.0181067	−	0.999836i	$-0.505764\pi$
$61$	−0.282836	−0.0362134	−0.0181067	+	0.999836i	$0.505764\pi$
$62$	−17.3126	−2.19871
$63$	−1.65946	−0.209072
$64$	33.8669	4.23336
$65$	2.56675	0.318366
$66$	−4.81813	−0.593071
$67$	−8.95059	−1.09349	−0.546744	−	0.837300i	$-0.684133\pi$
$67$	−8.95059	−1.09349	−0.546744	+	0.837300i	$0.684133\pi$
$68$	23.2319	2.81729
$69$	4.54396	0.547029
$70$	−2.14860	−0.256807
$71$	6.48975	0.770191	0.385096	−	0.922877i	$-0.374168\pi$
$71$	6.48975	0.770191	0.385096	+	0.922877i	$0.374168\pi$
$72$	26.5394	3.12769
$73$	11.2387	1.31539	0.657694	−	0.753286i	$-0.271532\pi$
$73$	11.2387	1.31539	0.657694	+	0.753286i	$0.271532\pi$
$74$	−22.8559	−2.65694
$75$	1.80078	0.207936
$76$	37.6546	4.31928
$77$	−2.00340	−0.228308
$78$	2.95318	0.334382
$79$	−5.50432	−0.619284	−0.309642	−	0.950853i	$-0.600209\pi$
$79$	−5.50432	−0.619284	−0.309642	+	0.950853i	$0.600209\pi$
$80$	20.1557	2.25348
$81$	6.50638	0.722931
$82$	13.9838	1.54426
$83$	13.2287	1.45204	0.726020	−	0.687674i	$-0.241368\pi$
$83$	13.2287	1.45204	0.726020	+	0.687674i	$0.241368\pi$
$84$	−1.81786	−0.198344
$85$	5.34328	0.579560
$86$	14.4706	1.56040
$87$	2.14809	0.230299
$88$	32.0399	3.41547
$89$	3.76833	0.399443	0.199721	−	0.979853i	$-0.435996\pi$
$89$	3.76833	0.399443	0.199721	+	0.979853i	$0.435996\pi$
$90$	9.53576	1.00516
$91$	1.22794	0.128724
$92$	−47.2052	−4.92148
$93$	−3.36891	−0.349340
$94$	−24.2950	−2.50584
$95$	8.66046	0.888544
$96$	12.7274	1.29898
$97$	7.72574	0.784430	0.392215	−	0.919874i	$-0.371709\pi$
$97$	7.72574	0.784430	0.392215	+	0.919874i	$0.371709\pi$
$98$	18.2155	1.84004
$99$	8.89133	0.893612
$100$	−18.7075	−1.87075
$101$	9.49961	0.945246	0.472623	−	0.881265i	$-0.343307\pi$
$101$	9.49961	0.945246	0.472623	+	0.881265i	$0.343307\pi$
$102$	6.14772	0.608715
$103$	−4.39266	−0.432821	−0.216411	−	0.976302i	$-0.569435\pi$
$103$	−4.39266	−0.432821	−0.216411	+	0.976302i	$0.569435\pi$
$104$	−19.6383	−1.92569
$105$	−0.418102	−0.0408026
$106$	−2.49086	−0.241933
$107$	7.85495	0.759367	0.379683	−	0.925117i	$-0.376033\pi$
$107$	7.85495	0.759367	0.379683	+	0.925117i	$0.376033\pi$
$108$	16.9865	1.63453
$109$	−17.1501	−1.64268	−0.821339	−	0.570441i	$-0.806773\pi$
$109$	−17.1501	−1.64268	−0.821339	+	0.570441i	$0.806773\pi$
$110$	11.5121	1.09764
$111$	−4.44759	−0.422146
$112$	9.64257	0.911137
$113$	0.863879	0.0812669	0.0406335	−	0.999174i	$-0.487062\pi$
$113$	0.863879	0.0812669	0.0406335	+	0.999174i	$0.487062\pi$
$114$	9.96431	0.933243
$115$	−10.8571	−1.01243
$116$	−22.3155	−2.07194
$117$	−5.44977	−0.503832
$118$	13.6086	1.25277
$119$	2.55625	0.234331
$120$	6.68662	0.610402
$121$	−0.265854	−0.0241685
$122$	0.777532	0.0703944
$123$	2.72115	0.245358
$124$	34.9981	3.14292
$125$	−10.6935	−0.956458
$126$	4.56194	0.406410
$127$	−6.61958	−0.587393	−0.293696	−	0.955899i	$-0.594885\pi$
$127$	−6.61958	−0.587393	−0.293696	+	0.955899i	$0.594885\pi$
$128$	−45.5183	−4.02329
$129$	2.81587	0.247924
$130$	−7.05615	−0.618866
$131$	4.92568	0.430359	0.215180	−	0.976575i	$-0.430966\pi$
$131$	4.92568	0.430359	0.215180	+	0.976575i	$0.430966\pi$
$132$	9.74003	0.847761
$133$	4.14320	0.359261
$134$	24.6057	2.12561
$135$	3.90685	0.336248
$136$	−40.8815	−3.50556
$137$	18.3221	1.56536	0.782681	−	0.622423i	$-0.213852\pi$
$137$	18.3221	1.56536	0.782681	+	0.622423i	$0.213852\pi$
$138$	−12.4916	−1.06336
$139$	7.90228	0.670263	0.335131	−	0.942171i	$-0.391219\pi$
$139$	7.90228	0.670263	0.335131	+	0.942171i	$0.391219\pi$
$140$	4.34347	0.367091
$141$	−4.72764	−0.398139
$142$	−17.8407	−1.49716
$143$	−6.57929	−0.550188
$144$	−42.7950	−3.56625
$145$	−5.13251	−0.426232
$146$	−30.8958	−2.55695
$147$	3.54461	0.292354
$148$	46.2040	3.79795
$149$	6.33697	0.519145	0.259572	−	0.965724i	$-0.416418\pi$
$149$	6.33697	0.519145	0.259572	+	0.965724i	$0.416418\pi$
$150$	−4.95046	−0.404203
$151$	4.01667	0.326872	0.163436	−	0.986554i	$-0.447742\pi$
$151$	4.01667	0.326872	0.163436	+	0.986554i	$0.447742\pi$
$152$	−66.2613	−5.37450
$153$	−11.3449	−0.917185
$154$	5.50745	0.443803
$155$	8.04947	0.646549
$156$	−5.96997	−0.477980
$157$	4.00217	0.319408	0.159704	−	0.987165i	$-0.448946\pi$
$157$	4.00217	0.319408	0.159704	+	0.987165i	$0.448946\pi$
$158$	15.1317	1.20381
$159$	−0.484703	−0.0384394
$160$	−30.4101	−2.40413
$161$	−5.19406	−0.409349
$162$	−17.8864	−1.40529
$163$	−9.44401	−0.739712	−0.369856	−	0.929089i	$-0.620593\pi$
$163$	−9.44401	−0.739712	−0.369856	+	0.929089i	$0.620593\pi$
$164$	−28.2688	−2.20743
$165$	2.24018	0.174398
$166$	−36.3665	−2.82259
$167$	−15.0973	−1.16827	−0.584134	−	0.811657i	$-0.698566\pi$
$167$	−15.0973	−1.16827	−0.584134	+	0.811657i	$0.698566\pi$
$168$	3.19890	0.246801
$169$	−8.96734	−0.689796
$170$	−14.6890	−1.12659
$171$	−18.3880	−1.40617
$172$	−29.2528	−2.23051
$173$	2.13264	0.162142	0.0810708	−	0.996708i	$-0.474166\pi$
$173$	2.13264	0.162142	0.0810708	+	0.996708i	$0.474166\pi$
$174$	−5.90522	−0.447674
$175$	−2.05842	−0.155602
$176$	−51.6647	−3.89437
$177$	2.64814	0.199046
$178$	−10.3594	−0.776468
$179$	−19.1743	−1.43316	−0.716579	−	0.697506i	$-0.754293\pi$
$179$	−19.1743	−1.43316	−0.716579	+	0.697506i	$0.754293\pi$
$180$	−19.2769	−1.43682
$181$	23.1023	1.71718	0.858589	−	0.512664i	$-0.171341\pi$
$181$	23.1023	1.71718	0.858589	+	0.512664i	$0.171341\pi$
$182$	−3.37569	−0.250223
$183$	0.151302	0.0111846
$184$	83.0675	6.12382
$185$	10.6268	0.781298
$186$	9.26133	0.679074
$187$	−13.6963	−1.00157
$188$	49.1133	3.58196
$189$	1.86905	0.135953
$190$	−23.8081	−1.72722
$191$	−2.95039	−0.213483	−0.106742	−	0.994287i	$-0.534042\pi$
$191$	−2.95039	−0.213483	−0.106742	+	0.994287i	$0.534042\pi$
$192$	−18.1170	−1.30748
$193$	2.35167	0.169277	0.0846384	−	0.996412i	$-0.473027\pi$
$193$	2.35167	0.169277	0.0846384	+	0.996412i	$0.473027\pi$
$194$	−21.2385	−1.52484
$195$	−1.37308	−0.0983280
$196$	−36.8233	−2.63024
$197$	3.13703	0.223504	0.111752	−	0.993736i	$-0.464354\pi$
$197$	3.13703	0.223504	0.111752	+	0.993736i	$0.464354\pi$
$198$	−24.4428	−1.73707
$199$	3.92409	0.278172	0.139086	−	0.990280i	$-0.455584\pi$
$199$	3.92409	0.278172	0.139086	+	0.990280i	$0.455584\pi$
$200$	32.9199	2.32779
$201$	4.78809	0.337726
$202$	−26.1150	−1.83744
$203$	−2.45541	−0.172336
$204$	−12.4279	−0.870124
$205$	−6.50176	−0.454103
$206$	12.0757	0.841352
$207$	23.0519	1.60222
$208$	31.6669	2.19570
$209$	−22.1991	−1.53555
$210$	1.14939	0.0793152
$211$	18.4769	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$211$	18.4769	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$212$	5.03536	0.345830
$213$	−3.47167	−0.237875
$214$	−21.5937	−1.47612
$215$	−6.72807	−0.458851
$216$	−29.8914	−2.03385
$217$	3.85090	0.261416
$218$	47.1465	3.19317
$219$	−6.01209	−0.406260
$220$	−23.2722	−1.56901
$221$	8.39489	0.564702
$222$	12.2267	0.820601
$223$	12.8486	0.860405	0.430202	−	0.902732i	$-0.358442\pi$
$223$	12.8486	0.860405	0.430202	+	0.902732i	$0.358442\pi$
$224$	−14.5483	−0.972048
$225$	9.13552	0.609035
$226$	−2.37485	−0.157973
$227$	8.00705	0.531447	0.265723	−	0.964049i	$-0.414389\pi$
$227$	8.00705	0.531447	0.265723	+	0.964049i	$0.414389\pi$
$228$	−20.1432	−1.33402
$229$	3.75266	0.247983	0.123992	−	0.992283i	$-0.460430\pi$
$229$	3.75266	0.247983	0.123992	+	0.992283i	$0.460430\pi$
$230$	29.8467	1.96803
$231$	1.07171	0.0705134
$232$	39.2689	2.57813
$233$	9.34020	0.611897	0.305948	−	0.952048i	$-0.401027\pi$
$233$	9.34020	0.611897	0.305948	+	0.952048i	$0.401027\pi$
$234$	14.9817	0.979388
$235$	11.2959	0.736866
$236$	−27.5103	−1.79077
$237$	2.94452	0.191267
$238$	−7.02727	−0.455510
$239$	19.4564	1.25853	0.629266	−	0.777190i	$-0.283356\pi$
$239$	19.4564	1.25853	0.629266	+	0.777190i	$0.283356\pi$
$240$	−10.7822	−0.695991
$241$	8.59519	0.553665	0.276832	−	0.960918i	$-0.410715\pi$
$241$	8.59519	0.553665	0.276832	+	0.960918i	$0.410715\pi$
$242$	0.730848	0.0469807
$243$	−12.6504	−0.811521
$244$	−1.57181	−0.100625
$245$	−8.46927	−0.541082
$246$	−7.48061	−0.476946
$247$	13.6066	0.865764
$248$	−61.5866	−3.91075
$249$	−7.07666	−0.448465
$250$	29.3971	1.85924
$251$	−12.4945	−0.788648	−0.394324	−	0.918972i	$-0.629021\pi$
$251$	−12.4945	−0.788648	−0.394324	+	0.918972i	$0.629021\pi$
$252$	−9.22214	−0.580940
$253$	27.8296	1.74963
$254$	18.1976	1.14182
$255$	−2.85837	−0.178998
$256$	57.3987	3.58742
$257$	6.80937	0.424757	0.212379	−	0.977187i	$-0.431879\pi$
$257$	6.80937	0.424757	0.212379	+	0.977187i	$0.431879\pi$
$258$	−7.74100	−0.481933
$259$	5.08390	0.315898
$260$	14.2643	0.884633
$261$	10.8974	0.674534
$262$	−13.5410	−0.836566
$263$	19.2459	1.18675	0.593376	−	0.804925i	$-0.297795\pi$
$263$	19.2459	1.18675	0.593376	+	0.804925i	$0.297795\pi$
$264$	−17.1396	−1.05487
$265$	1.15812	0.0711427
$266$	−11.3899	−0.698359
$267$	−2.01586	−0.123369
$268$	−49.7413	−3.03844
$269$	−18.2925	−1.11531	−0.557656	−	0.830072i	$-0.688299\pi$
$269$	−18.2925	−1.11531	−0.557656	+	0.830072i	$0.688299\pi$
$270$	−10.7402	−0.653625
$271$	6.70707	0.407425	0.203713	−	0.979031i	$-0.434699\pi$
$271$	6.70707	0.407425	0.203713	+	0.979031i	$0.434699\pi$
$272$	65.9219	3.99710
$273$	−0.656885	−0.0397565
$274$	−50.3685	−3.04287
$275$	11.0290	0.665071
$276$	25.2523	1.52001
$277$	28.9801	1.74125	0.870624	−	0.491950i	$-0.163716\pi$
$277$	28.9801	1.74125	0.870624	+	0.491950i	$0.163716\pi$
$278$	−21.7238	−1.30291
$279$	−17.0908	−1.02320
$280$	−7.64327	−0.456772
$281$	−5.25573	−0.313531	−0.156765	−	0.987636i	$-0.550107\pi$
$281$	−5.25573	−0.313531	−0.156765	+	0.987636i	$0.550107\pi$
$282$	12.9966	0.773934
$283$	2.88046	0.171226	0.0856128	−	0.996328i	$-0.472715\pi$
$283$	2.88046	0.171226	0.0856128	+	0.996328i	$0.472715\pi$
$284$	36.0656	2.14010
$285$	−4.63289	−0.274429
$286$	18.0869	1.06950
$287$	−3.11047	−0.183605
$288$	64.5672	3.80466
$289$	0.475886	0.0279933
$290$	14.1096	0.828543
$291$	−4.13286	−0.242273
$292$	62.4569	3.65502
$293$	−3.54115	−0.206876	−0.103438	−	0.994636i	$-0.532984\pi$
$293$	−3.54115	−0.206876	−0.103438	+	0.994636i	$0.532984\pi$
$294$	−9.74433	−0.568301
$295$	−6.32730	−0.368390
$296$	−81.3058	−4.72580
$297$	−10.0143	−0.581090
$298$	−17.4207	−1.00915
$299$	−17.0577	−0.986470
$300$	10.0075	0.577785
$301$	−3.21873	−0.185525
$302$	−11.0421	−0.635400
$303$	−5.08179	−0.291941
$304$	106.847	6.12810
$305$	−0.361512	−0.0207001
$306$	31.1879	1.78290
$307$	24.8310	1.41718	0.708589	−	0.705622i	$-0.249332\pi$
$307$	24.8310	1.41718	0.708589	+	0.705622i	$0.249332\pi$
$308$	−11.1335	−0.634391
$309$	2.34984	0.133678
$310$	−22.1285	−1.25681
$311$	−24.1200	−1.36772	−0.683859	−	0.729614i	$-0.739700\pi$
$311$	−24.1200	−1.36772	−0.683859	+	0.729614i	$0.739700\pi$
$312$	10.5054	0.594753
$313$	27.2418	1.53980	0.769900	−	0.638164i	$-0.220306\pi$
$313$	27.2418	1.53980	0.769900	+	0.638164i	$0.220306\pi$
$314$	−11.0022	−0.620889
$315$	−2.12107	−0.119509
$316$	−30.5893	−1.72078
$317$	8.70754	0.489064	0.244532	−	0.969641i	$-0.421366\pi$
$317$	8.70754	0.489064	0.244532	+	0.969641i	$0.421366\pi$
$318$	1.33248	0.0747215
$319$	13.1560	0.736597
$320$	43.2876	2.41985
$321$	−4.20198	−0.234532
$322$	14.2788	0.795725
$323$	28.3251	1.57605
$324$	36.1581	2.00878
$325$	−6.75999	−0.374977
$326$	25.9621	1.43791
$327$	9.17437	0.507344
$328$	49.7451	2.74671
$329$	5.40402	0.297933
$330$	−6.15839	−0.339008
$331$	−4.81864	−0.264856	−0.132428	−	0.991193i	$-0.542277\pi$
$331$	−4.81864	−0.264856	−0.132428	+	0.991193i	$0.542277\pi$
$332$	73.5162	4.03473
$333$	−22.5630	−1.23644
$334$	41.5035	2.27097
$335$	−11.4404	−0.625054
$336$	−5.15826	−0.281406
$337$	−3.98157	−0.216890	−0.108445	−	0.994102i	$-0.534587\pi$
$337$	−3.98157	−0.216890	−0.108445	+	0.994102i	$0.534587\pi$
$338$	24.6518	1.34088
$339$	−0.462130	−0.0250994
$340$	29.6943	1.61040
$341$	−20.6330	−1.11734
$342$	50.5498	2.73342
$343$	−8.33210	−0.449891
$344$	51.4766	2.77543
$345$	5.80795	0.312690
$346$	−5.86275	−0.315183
$347$	−28.6313	−1.53701	−0.768504	−	0.639846i	$-0.778998\pi$
$347$	−28.6313	−1.53701	−0.768504	+	0.639846i	$0.778998\pi$
$348$	11.9376	0.639924
$349$	−25.5238	−1.36626	−0.683128	−	0.730299i	$-0.739381\pi$
$349$	−25.5238	−1.36626	−0.683128	+	0.730299i	$0.739381\pi$
$350$	5.65871	0.302471
$351$	6.13810	0.327627
$352$	77.9494	4.15472
$353$	8.90855	0.474154	0.237077	−	0.971491i	$-0.423811\pi$
$353$	8.90855	0.474154	0.237077	+	0.971491i	$0.423811\pi$
$354$	−7.27989	−0.386922
$355$	8.29499	0.440253
$356$	20.9419	1.10992
$357$	−1.36746	−0.0723734
$358$	52.7114	2.78588
$359$	−24.6966	−1.30344	−0.651718	−	0.758461i	$-0.725951\pi$
$359$	−24.6966	−1.30344	−0.651718	+	0.758461i	$0.725951\pi$
$360$	33.9218	1.78784
$361$	26.9098	1.41630
$362$	−63.5095	−3.33799
$363$	0.142218	0.00746449
$364$	6.82408	0.357679
$365$	14.3649	0.751895
$366$	−0.415938	−0.0217414
$367$	−7.12977	−0.372171	−0.186085	−	0.982534i	$-0.559580\pi$
$367$	−7.12977	−0.372171	−0.186085	+	0.982534i	$0.559580\pi$
$368$	−133.947	−6.98248
$369$	13.8046	0.718641
$370$	−29.2137	−1.51875
$371$	0.554048	0.0287648
$372$	−18.7221	−0.970697
$373$	−0.188695	−0.00977027	−0.00488513	−	0.999988i	$-0.501555\pi$
$373$	−0.188695	−0.00977027	−0.00488513	+	0.999988i	$0.501555\pi$
$374$	37.6519	1.94694
$375$	5.72047	0.295404
$376$	−86.4254	−4.45705
$377$	−8.06375	−0.415304
$378$	−5.13813	−0.264277
$379$	−12.6440	−0.649480	−0.324740	−	0.945803i	$-0.605277\pi$
$379$	−12.6440	−0.649480	−0.324740	+	0.945803i	$0.605277\pi$
$380$	48.1290	2.46896
$381$	3.54112	0.181417
$382$	8.11081	0.414985
$383$	37.3971	1.91090	0.955450	−	0.295153i	$-0.0953705\pi$
$383$	37.3971	1.91090	0.955450	+	0.295153i	$0.0953705\pi$
$384$	24.3499	1.24260
$385$	−2.56068	−0.130504
$386$	−6.46487	−0.329053
$387$	14.2852	0.726156
$388$	42.9344	2.17967
$389$	36.3405	1.84253	0.921267	−	0.388930i	$-0.127155\pi$
$389$	36.3405	1.84253	0.921267	+	0.388930i	$0.127155\pi$
$390$	3.77467	0.191138
$391$	−35.5094	−1.79579
$392$	64.7985	3.27282
$393$	−2.63498	−0.132917
$394$	−8.62389	−0.434465
$395$	−7.03545	−0.353992
$396$	49.4120	2.48305
$397$	22.3383	1.12113	0.560563	−	0.828112i	$-0.310585\pi$
$397$	22.3383	1.12113	0.560563	+	0.828112i	$0.310585\pi$
$398$	−10.7876	−0.540732
$399$	−2.21639	−0.110958
$400$	−53.0836	−2.65418
$401$	19.7816	0.987847	0.493923	−	0.869505i	$-0.335562\pi$
$401$	19.7816	0.987847	0.493923	+	0.869505i	$0.335562\pi$
$402$	−13.1627	−0.656498
$403$	12.6466	0.629973
$404$	52.7924	2.62652
$405$	8.31625	0.413238
$406$	6.75007	0.335000
$407$	−27.2394	−1.35021
$408$	21.8694	1.08270
$409$	−10.0692	−0.497890	−0.248945	−	0.968518i	$-0.580084\pi$
$409$	−10.0692	−0.497890	−0.248945	+	0.968518i	$0.580084\pi$
$410$	17.8737	0.882720
$411$	−9.80134	−0.483465
$412$	−24.4114	−1.20266
$413$	−3.02700	−0.148949
$414$	−63.3710	−3.11452
$415$	16.9085	0.830007
$416$	−47.7776	−2.34249
$417$	−4.22730	−0.207012
$418$	61.0268	2.98492
$419$	−6.84703	−0.334499	−0.167250	−	0.985915i	$-0.553489\pi$
$419$	−6.84703	−0.334499	−0.167250	+	0.985915i	$0.553489\pi$
$420$	−2.32353	−0.113377
$421$	−2.61183	−0.127293	−0.0636463	−	0.997973i	$-0.520273\pi$
$421$	−2.61183	−0.127293	−0.0636463	+	0.997973i	$0.520273\pi$
$422$	−50.7939	−2.47261
$423$	−23.9837	−1.16613
$424$	−8.86078	−0.430318
$425$	−14.0725	−0.682615
$426$	9.54382	0.462400
$427$	−0.172949	−0.00836957
$428$	43.6525	2.11002
$429$	3.51957	0.169927
$430$	18.4959	0.891950
$431$	25.9093	1.24801	0.624004	−	0.781421i	$-0.285505\pi$
$431$	25.9093	1.24801	0.624004	+	0.781421i	$0.285505\pi$
$432$	48.2001	2.31903
$433$	39.1389	1.88090	0.940448	−	0.339937i	$-0.110406\pi$
$433$	39.1389	1.88090	0.940448	+	0.339937i	$0.110406\pi$
$434$	−10.5863	−0.508161
$435$	2.74562	0.131642
$436$	−95.3084	−4.56445
$437$	−57.5541	−2.75319
$438$	16.5276	0.789719
$439$	−27.3560	−1.30563	−0.652815	−	0.757517i	$-0.726412\pi$
$439$	−27.3560	−1.30563	−0.652815	+	0.757517i	$0.726412\pi$
$440$	40.9524	1.95233
$441$	17.9821	0.856290
$442$	−23.0781	−1.09771
$443$	−22.8535	−1.08580	−0.542902	−	0.839796i	$-0.682674\pi$
$443$	−22.8535	−1.08580	−0.542902	+	0.839796i	$0.682674\pi$
$444$	−24.7167	−1.17300
$445$	4.81657	0.228327
$446$	−35.3215	−1.67252
$447$	−3.38994	−0.160339
$448$	20.7090	0.978406
$449$	6.81630	0.321681	0.160841	−	0.986980i	$-0.448579\pi$
$449$	6.81630	0.321681	0.160841	+	0.986980i	$0.448579\pi$
$450$	−25.1141	−1.18389
$451$	16.6658	0.784762
$452$	4.80086	0.225813
$453$	−2.14871	−0.100955
$454$	−22.0119	−1.03307
$455$	1.56952	0.0735803
$456$	35.4463	1.65992
$457$	13.4206	0.627790	0.313895	−	0.949458i	$-0.398366\pi$
$457$	13.4206	0.627790	0.313895	+	0.949458i	$0.398366\pi$
$458$	−10.3163	−0.482049
$459$	12.7778	0.596419
$460$	−60.3362	−2.81319
$461$	34.9762	1.62900	0.814501	−	0.580162i	$-0.197011\pi$
$461$	34.9762	1.62900	0.814501	+	0.580162i	$0.197011\pi$
$462$	−2.94619	−0.137069
$463$	7.45912	0.346655	0.173327	−	0.984864i	$-0.444548\pi$
$463$	7.45912	0.346655	0.173327	+	0.984864i	$0.444548\pi$
$464$	−63.3215	−2.93963
$465$	−4.30604	−0.199688
$466$	−25.6768	−1.18945
$467$	10.6323	0.492005	0.246003	−	0.969269i	$-0.420883\pi$
$467$	10.6323	0.492005	0.246003	+	0.969269i	$0.420883\pi$
$468$	−30.2862	−1.39998
$469$	−5.47312	−0.252725
$470$	−31.0532	−1.43238
$471$	−2.14095	−0.0986496
$472$	48.4103	2.22826
$473$	17.2459	0.792967
$474$	−8.09465	−0.371800
$475$	−22.8088	−1.04654
$476$	14.2059	0.651126
$477$	−2.45894	−0.112587
$478$	−53.4869	−2.44643
$479$	−18.4779	−0.844275	−0.422137	−	0.906532i	$-0.638720\pi$
$479$	−18.4779	−0.844275	−0.422137	+	0.906532i	$0.638720\pi$
$480$	16.2678	0.742519
$481$	16.6959	0.761267
$482$	−23.6287	−1.07626
$483$	2.77855	0.126428
$484$	−1.47744	−0.0671562
$485$	9.87481	0.448392
$486$	34.7766	1.57750
$487$	39.7717	1.80223	0.901114	−	0.433582i	$-0.142751\pi$
$487$	39.7717	1.80223	0.901114	+	0.433582i	$0.142751\pi$
$488$	2.76593	0.125208
$489$	5.05205	0.228461
$490$	23.2825	1.05180
$491$	−8.88859	−0.401137	−0.200568	−	0.979680i	$-0.564279\pi$
$491$	−8.88859	−0.401137	−0.200568	+	0.979680i	$0.564279\pi$
$492$	15.1223	0.681767
$493$	−16.7865	−0.756027
$494$	−37.4052	−1.68294
$495$	11.3646	0.510802
$496$	99.3090	4.45911
$497$	3.96836	0.178005
$498$	19.4542	0.871761
$499$	−36.8625	−1.65019	−0.825096	−	0.564993i	$-0.808879\pi$
$499$	−36.8625	−1.65019	−0.825096	+	0.564993i	$0.808879\pi$
$500$	−59.4274	−2.65767
$501$	8.07628	0.360822
$502$	34.3482	1.53304
$503$	14.4473	0.644171	0.322086	−	0.946711i	$-0.395616\pi$
$503$	14.4473	0.644171	0.322086	+	0.946711i	$0.395616\pi$
$504$	16.2283	0.722867
$505$	12.1421	0.540317
$506$	−76.5053	−3.40108
$507$	4.79705	0.213045
$508$	−36.7871	−1.63217
$509$	40.0077	1.77331	0.886654	−	0.462433i	$-0.153023\pi$
$509$	40.0077	1.77331	0.886654	+	0.462433i	$0.153023\pi$
$510$	7.85783	0.347951
$511$	6.87223	0.304010
$512$	−66.7557	−2.95021
$513$	20.7105	0.914391
$514$	−18.7194	−0.825676
$515$	−5.61456	−0.247407
$516$	15.6487	0.688896
$517$	−28.9546	−1.27342
$518$	−13.9759	−0.614067
$519$	−1.14085	−0.0500777
$520$	−25.1010	−1.10075
$521$	27.6917	1.21319	0.606597	−	0.795009i	$-0.292534\pi$
$521$	27.6917	1.21319	0.606597	+	0.795009i	$0.292534\pi$
$522$	−29.9577	−1.31121
$523$	42.3477	1.85174	0.925868	−	0.377848i	$-0.123336\pi$
$523$	42.3477	1.85174	0.925868	+	0.377848i	$0.123336\pi$
$524$	27.3736	1.19582
$525$	1.10114	0.0480579
$526$	−52.9081	−2.30690
$527$	26.3268	1.14681
$528$	27.6378	1.20278
$529$	49.1519	2.13704
$530$	−3.18374	−0.138293
$531$	13.4342	0.582996
$532$	23.0251	0.998264
$533$	−10.2150	−0.442460
$534$	5.54171	0.239813
$535$	10.0400	0.434065
$536$	87.5305	3.78074
$537$	10.2573	0.442633
$538$	50.2871	2.16803
$539$	21.7091	0.935076
$540$	21.7116	0.934320
$541$	10.3399	0.444549	0.222275	−	0.974984i	$-0.428652\pi$
$541$	10.3399	0.444549	0.222275	+	0.974984i	$0.428652\pi$
$542$	−18.4381	−0.791985
$543$	−12.3585	−0.530354
$544$	−99.4600	−4.26431
$545$	−21.9207	−0.938979
$546$	1.80582	0.0772818
$547$	−28.7591	−1.22965	−0.614824	−	0.788664i	$-0.710773\pi$
$547$	−28.7591	−1.22965	−0.614824	+	0.788664i	$0.710773\pi$
$548$	101.822	4.34961
$549$	0.767569	0.0327590
$550$	−30.3192	−1.29282
$551$	−27.2078	−1.15909
$552$	−44.4367	−1.89135
$553$	−3.36578	−0.143128
$554$	−79.6681	−3.38477
$555$	−5.68477	−0.241305
$556$	43.9155	1.86243
$557$	−17.8903	−0.758036	−0.379018	−	0.925389i	$-0.623738\pi$
$557$	−17.8903	−0.758036	−0.379018	+	0.925389i	$0.623738\pi$
$558$	46.9835	1.98897
$559$	−10.5706	−0.447087
$560$	12.3248	0.520820
$561$	7.32680	0.309338
$562$	14.4483	0.609465
$563$	−12.0247	−0.506782	−0.253391	−	0.967364i	$-0.581546\pi$
$563$	−12.0247	−0.506782	−0.253391	+	0.967364i	$0.581546\pi$
$564$	−26.2730	−1.10629
$565$	1.10418	0.0464534
$566$	−7.91856	−0.332842
$567$	3.97853	0.167082
$568$	−63.4651	−2.66294
$569$	−17.4460	−0.731375	−0.365688	−	0.930738i	$-0.619166\pi$
$569$	−17.4460	−0.731375	−0.365688	+	0.930738i	$0.619166\pi$
$570$	12.7361	0.533456
$571$	8.52546	0.356780	0.178390	−	0.983960i	$-0.442911\pi$
$571$	8.52546	0.356780	0.178390	+	0.983960i	$0.442911\pi$
$572$	−36.5633	−1.52879
$573$	1.57830	0.0659346
$574$	8.55085	0.356906
$575$	28.5940	1.19245
$576$	−91.9090	−3.82954
$577$	−8.61347	−0.358584	−0.179292	−	0.983796i	$-0.557381\pi$
$577$	−8.61347	−0.358584	−0.179292	+	0.983796i	$0.557381\pi$
$578$	−1.30824	−0.0544155
$579$	−1.25802	−0.0522814
$580$	−28.5230	−1.18435
$581$	8.08911	0.335593
$582$	11.3615	0.470948
$583$	−2.96858	−0.122946
$584$	−109.906	−4.54795
$585$	−6.96573	−0.287998
$586$	9.73482	0.402142
$587$	38.7122	1.59783	0.798913	−	0.601447i	$-0.205409\pi$
$587$	38.7122	1.59783	0.798913	+	0.601447i	$0.205409\pi$
$588$	19.6985	0.812354
$589$	42.6709	1.75822
$590$	17.3941	0.716104
$591$	−1.67815	−0.0690297
$592$	131.106	5.38844
$593$	−11.9239	−0.489657	−0.244828	−	0.969566i	$-0.578732\pi$
$593$	−11.9239	−0.489657	−0.244828	+	0.969566i	$0.578732\pi$
$594$	27.5300	1.12957
$595$	3.26732	0.133947
$596$	35.2166	1.44253
$597$	−2.09918	−0.0859138
$598$	46.8925	1.91758
$599$	25.2029	1.02976	0.514882	−	0.857261i	$-0.327836\pi$
$599$	25.2029	1.02976	0.514882	+	0.857261i	$0.327836\pi$
$600$	−17.6104	−0.718941
$601$	36.7431	1.49878	0.749392	−	0.662126i	$-0.230346\pi$
$601$	36.7431	1.49878	0.749392	+	0.662126i	$0.230346\pi$
$602$	8.84849	0.360638
$603$	24.2904	0.989181
$604$	22.3220	0.908268
$605$	−0.339806	−0.0138151
$606$	13.9701	0.567498
$607$	2.56573	0.104140	0.0520698	−	0.998643i	$-0.483418\pi$
$607$	2.56573	0.104140	0.0520698	+	0.998643i	$0.483418\pi$
$608$	−161.206	−6.53777
$609$	1.31352	0.0532263
$610$	0.993818	0.0402385
$611$	17.7472	0.717974
$612$	−63.0476	−2.54855
$613$	−43.1288	−1.74196	−0.870978	−	0.491322i	$-0.836514\pi$
$613$	−43.1288	−1.74196	−0.870978	+	0.491322i	$0.836514\pi$
$614$	−68.2618	−2.75482
$615$	3.47810	0.140250
$616$	19.5918	0.789376
$617$	20.1124	0.809693	0.404847	−	0.914385i	$-0.367325\pi$
$617$	20.1124	0.809693	0.404847	+	0.914385i	$0.367325\pi$
$618$	−6.45984	−0.259853
$619$	1.03538	0.0416154	0.0208077	−	0.999783i	$-0.493376\pi$
$619$	1.03538	0.0416154	0.0208077	+	0.999783i	$0.493376\pi$
$620$	44.7335	1.79654
$621$	−25.9634	−1.04188
$622$	66.3072	2.65868
$623$	2.30426	0.0923184
$624$	−16.9401	−0.678147
$625$	3.16327	0.126531
$626$	−74.8894	−2.99318
$627$	11.8754	0.474256
$628$	22.2413	0.887526
$629$	34.7563	1.38582
$630$	5.83094	0.232310
$631$	−18.7016	−0.744501	−0.372250	−	0.928132i	$-0.621414\pi$
$631$	−18.7016	−0.744501	−0.372250	+	0.928132i	$0.621414\pi$
$632$	53.8283	2.14118
$633$	−9.88413	−0.392859
$634$	−23.9375	−0.950681
$635$	−8.46094	−0.335762
$636$	−2.69365	−0.106810
$637$	−13.3062	−0.527210
$638$	−36.1667	−1.43185
$639$	−17.6121	−0.696723
$640$	−58.1801	−2.29977
$641$	21.4635	0.847759	0.423880	−	0.905719i	$-0.360668\pi$
$641$	21.4635	0.847759	0.423880	+	0.905719i	$0.360668\pi$
$642$	11.5515	0.455901
$643$	−23.8594	−0.940923	−0.470461	−	0.882421i	$-0.655913\pi$
$643$	−23.8594	−0.940923	−0.470461	+	0.882421i	$0.655913\pi$
$644$	−28.8651	−1.13744
$645$	3.59916	0.141717
$646$	−77.8675	−3.06366
$647$	−34.8561	−1.37034	−0.685168	−	0.728385i	$-0.740271\pi$
$647$	−34.8561	−1.37034	−0.685168	+	0.728385i	$0.740271\pi$
$648$	−63.6278	−2.49954
$649$	16.2186	0.636636
$650$	18.5836	0.728909
$651$	−2.06003	−0.0807388
$652$	−52.4834	−2.05541
$653$	33.1057	1.29553	0.647763	−	0.761842i	$-0.275705\pi$
$653$	33.1057	1.29553	0.647763	+	0.761842i	$0.275705\pi$
$654$	−25.2209	−0.986215
$655$	6.29586	0.246000
$656$	−80.2144	−3.13185
$657$	−30.4999	−1.18991
$658$	−14.8560	−0.579146
$659$	29.5738	1.15203	0.576016	−	0.817439i	$-0.304607\pi$
$659$	29.5738	1.15203	0.576016	+	0.817439i	$0.304607\pi$
$660$	12.4494	0.484592
$661$	12.4349	0.483660	0.241830	−	0.970319i	$-0.422252\pi$
$661$	12.4349	0.483660	0.241830	+	0.970319i	$0.422252\pi$
$662$	13.2467	0.514848
$663$	−4.49082	−0.174409
$664$	−129.367	−5.02043
$665$	5.29571	0.205359
$666$	62.0270	2.40350
$667$	34.1087	1.32069
$668$	−83.9009	−3.24622
$669$	−6.87331	−0.265737
$670$	31.4503	1.21503
$671$	0.926655	0.0357731
$672$	7.78256	0.300219
$673$	27.5623	1.06245	0.531224	−	0.847231i	$-0.321732\pi$
$673$	27.5623	1.06245	0.531224	+	0.847231i	$0.321732\pi$
$674$	10.9456	0.421607
$675$	−10.2894	−0.396038
$676$	−49.8344	−1.91671
$677$	−26.5274	−1.01953	−0.509765	−	0.860313i	$-0.670268\pi$
$677$	−26.5274	−1.01953	−0.509765	+	0.860313i	$0.670268\pi$
$678$	1.27042	0.0487902
$679$	4.72414	0.181296
$680$	−52.2535	−2.00383
$681$	−4.28335	−0.164138
$682$	56.7214	2.17197
$683$	38.7238	1.48173	0.740863	−	0.671657i	$-0.234417\pi$
$683$	38.7238	1.48173	0.740863	+	0.671657i	$0.234417\pi$
$684$	−102.188	−3.90727
$685$	23.4187	0.894784
$686$	22.9054	0.874533
$687$	−2.00748	−0.0765900
$688$	−83.0065	−3.16459
$689$	1.81953	0.0693187
$690$	−15.9664	−0.607830
$691$	4.67604	0.177885	0.0889424	−	0.996037i	$-0.471651\pi$
$691$	4.67604	0.177885	0.0889424	+	0.996037i	$0.471651\pi$
$692$	11.8518	0.450537
$693$	5.43688	0.206530
$694$	78.7090	2.98775
$695$	10.1005	0.383132
$696$	−21.0068	−0.796260
$697$	−21.2648	−0.805463
$698$	70.1663	2.65583
$699$	−4.99651	−0.188985
$700$	−11.4393	−0.432365
$701$	−4.24831	−0.160456	−0.0802282	−	0.996777i	$-0.525565\pi$
$701$	−4.24831	−0.160456	−0.0802282	+	0.996777i	$0.525565\pi$
$702$	−16.8740	−0.636868
$703$	56.3335	2.12466
$704$	−110.958	−4.18189
$705$	−6.04273	−0.227582
$706$	−24.4901	−0.921698
$707$	5.80883	0.218464
$708$	14.7166	0.553082
$709$	0.687284	0.0258115	0.0129057	−	0.999917i	$-0.495892\pi$
$709$	0.687284	0.0258115	0.0129057	+	0.999917i	$0.495892\pi$
$710$	−22.8034	−0.855797
$711$	14.9378	0.560211
$712$	−36.8516	−1.38107
$713$	−53.4937	−2.00335
$714$	3.75922	0.140685
$715$	−8.40945	−0.314496
$716$	−106.558	−3.98226
$717$	−10.4082	−0.388700
$718$	67.8924	2.53372
$719$	16.6589	0.621271	0.310636	−	0.950529i	$-0.399458\pi$
$719$	16.6589	0.621271	0.310636	+	0.950529i	$0.399458\pi$
$720$	−54.6992	−2.03852
$721$	−2.68603	−0.100033
$722$	−73.9765	−2.75312
$723$	−4.59797	−0.171000
$724$	128.387	4.77146
$725$	13.5174	0.502022
$726$	−0.390965	−0.0145101
$727$	35.4018	1.31298	0.656490	−	0.754335i	$-0.272041\pi$
$727$	35.4018	1.31298	0.656490	+	0.754335i	$0.272041\pi$
$728$	−12.0084	−0.445062
$729$	−12.7519	−0.472291
$730$	−39.4900	−1.46159
$731$	−22.0050	−0.813885
$732$	0.840835	0.0310781
$733$	−40.1142	−1.48165	−0.740826	−	0.671697i	$-0.765566\pi$
$733$	−40.1142	−1.48165	−0.740826	+	0.671697i	$0.765566\pi$
$734$	19.6002	0.723455
$735$	4.53061	0.167114
$736$	202.094	7.44927
$737$	29.3248	1.08019
$738$	−37.9498	−1.39695
$739$	45.1916	1.66240	0.831199	−	0.555975i	$-0.187655\pi$
$739$	45.1916	1.66240	0.831199	+	0.555975i	$0.187655\pi$
$740$	59.0566	2.17096
$741$	−7.27878	−0.267393
$742$	−1.52311	−0.0559152
$743$	−7.41336	−0.271970	−0.135985	−	0.990711i	$-0.543420\pi$
$743$	−7.41336	−0.271970	−0.135985	+	0.990711i	$0.543420\pi$
$744$	32.9456	1.20784
$745$	8.09972	0.296751
$746$	0.518734	0.0189922
$747$	−35.9005	−1.31353
$748$	−76.1148	−2.78303
$749$	4.80315	0.175503
$750$	−15.7259	−0.574229
$751$	−40.1888	−1.46651	−0.733256	−	0.679953i	$-0.762000\pi$
$751$	−40.1888	−1.46651	−0.733256	+	0.679953i	$0.762000\pi$
$752$	139.362	5.08200
$753$	6.68391	0.243575
$754$	22.1677	0.807301
$755$	5.13399	0.186845
$756$	10.3869	0.377769
$757$	24.5439	0.892062	0.446031	−	0.895018i	$-0.352837\pi$
$757$	24.5439	0.892062	0.446031	+	0.895018i	$0.352837\pi$
$758$	34.7592	1.26251
$759$	−14.8874	−0.540378
$760$	−84.6932	−3.07214
$761$	−13.5929	−0.492741	−0.246371	−	0.969176i	$-0.579238\pi$
$761$	−13.5929	−0.492741	−0.246371	+	0.969176i	$0.579238\pi$
$762$	−9.73475	−0.352653
$763$	−10.4869	−0.379653
$764$	−16.3963	−0.593197
$765$	−14.5008	−0.524276
$766$	−102.807	−3.71456
$767$	−9.94089	−0.358945
$768$	−30.7052	−1.10798
$769$	−21.4012	−0.771745	−0.385873	−	0.922552i	$-0.626100\pi$
$769$	−21.4012	−0.771745	−0.385873	+	0.922552i	$0.626100\pi$
$770$	7.03946	0.253684
$771$	−3.64265	−0.131187
$772$	13.0690	0.470363
$773$	14.4541	0.519877	0.259938	−	0.965625i	$-0.416298\pi$
$773$	14.4541	0.519877	0.259938	+	0.965625i	$0.416298\pi$
$774$	−39.2707	−1.41156
$775$	−21.1997	−0.761515
$776$	−75.5523	−2.71217
$777$	−2.71962	−0.0975657
$778$	−99.9021	−3.58166
$779$	−34.4663	−1.23488
$780$	−7.63063	−0.273220
$781$	−21.2624	−0.760827
$782$	97.6174	3.49079
$783$	−12.2738	−0.438630
$784$	−104.488	−3.73172
$785$	5.11545	0.182578
$786$	7.24371	0.258375
$787$	20.6139	0.734805	0.367403	−	0.930062i	$-0.380247\pi$
$787$	20.6139	0.734805	0.367403	+	0.930062i	$0.380247\pi$
$788$	17.4335	0.621043
$789$	−10.2955	−0.366531
$790$	19.3409	0.688117
$791$	0.528246	0.0187823
$792$	−86.9509	−3.08967
$793$	−0.567976	−0.0201694
$794$	−61.4093	−2.17933
$795$	−0.619532	−0.0219725
$796$	21.8075	0.772945
$797$	23.7941	0.842830	0.421415	−	0.906868i	$-0.361534\pi$
$797$	23.7941	0.842830	0.421415	+	0.906868i	$0.361534\pi$
$798$	6.09299	0.215689
$799$	36.9448	1.30701
$800$	80.0902	2.83162
$801$	−10.2266	−0.361340
$802$	−54.3808	−1.92025
$803$	−36.8213	−1.29939
$804$	26.6090	0.938426
$805$	−6.63889	−0.233990
$806$	−34.7663	−1.22459
$807$	9.78550	0.344466
$808$	−92.8995	−3.26819
$809$	−36.9397	−1.29873	−0.649365	−	0.760477i	$-0.724965\pi$
$809$	−36.9397	−1.29873	−0.649365	+	0.760477i	$0.724965\pi$
$810$	−22.8619	−0.803284
$811$	−3.97391	−0.139543	−0.0697715	−	0.997563i	$-0.522227\pi$
$811$	−3.97391	−0.139543	−0.0697715	+	0.997563i	$0.522227\pi$
$812$	−13.6455	−0.478864
$813$	−3.58793	−0.125834
$814$	74.8827	2.62464
$815$	−12.0710	−0.422830
$816$	−35.2647	−1.23451
$817$	−35.6660	−1.24780
$818$	27.6809	0.967838
$819$	−3.33243	−0.116445
$820$	−36.1324	−1.26180
$821$	11.3688	0.396773	0.198387	−	0.980124i	$-0.436430\pi$
$821$	11.3688	0.396773	0.198387	+	0.980124i	$0.436430\pi$
$822$	26.9445	0.939796
$823$	31.5527	1.09986	0.549929	−	0.835211i	$-0.314655\pi$
$823$	31.5527	1.09986	0.549929	+	0.835211i	$0.314655\pi$
$824$	42.9571	1.49648
$825$	−5.89991	−0.205408
$826$	8.32141	0.289539
$827$	−5.38102	−0.187116	−0.0935582	−	0.995614i	$-0.529824\pi$
$827$	−5.38102	−0.187116	−0.0935582	+	0.995614i	$0.529824\pi$
$828$	128.107	4.45202
$829$	−39.4577	−1.37042	−0.685211	−	0.728344i	$-0.740290\pi$
$829$	−39.4577	−1.37042	−0.685211	+	0.728344i	$0.740290\pi$
$830$	−46.4826	−1.61343
$831$	−15.5028	−0.537787
$832$	68.0097	2.35781
$833$	−27.6998	−0.959742
$834$	11.6211	0.402406
$835$	−19.2970	−0.667799
$836$	−123.368	−4.26677
$837$	19.2494	0.665356
$838$	18.8229	0.650226
$839$	35.4136	1.22261	0.611307	−	0.791394i	$-0.290644\pi$
$839$	35.4136	1.22261	0.611307	+	0.791394i	$0.290644\pi$
$840$	4.08874	0.141075
$841$	−12.8756	−0.443987
$842$	7.18006	0.247441
$843$	2.81154	0.0968345
$844$	102.682	3.53446
$845$	−11.4618	−0.394297
$846$	65.9327	2.26681
$847$	−0.162565	−0.00558579
$848$	14.2881	0.490655
$849$	−1.54089	−0.0528834
$850$	38.6860	1.32692
$851$	−70.6216	−2.42088
$852$	−19.2932	−0.660974
$853$	−56.0832	−1.92025	−0.960126	−	0.279566i	$-0.909809\pi$
$853$	−56.0832	−1.92025	−0.960126	+	0.279566i	$0.909809\pi$
$854$	0.475446	0.0162694
$855$	−23.5030	−0.803787
$856$	−76.8158	−2.62551
$857$	−10.2678	−0.350742	−0.175371	−	0.984502i	$-0.556112\pi$
$857$	−10.2678	−0.350742	−0.175371	+	0.984502i	$0.556112\pi$
$858$	−9.67551	−0.330317
$859$	−2.09877	−0.0716091	−0.0358045	−	0.999359i	$-0.511399\pi$
$859$	−2.09877	−0.0716091	−0.0358045	+	0.999359i	$0.511399\pi$
$860$	−37.3901	−1.27499
$861$	1.66393	0.0567067
$862$	−71.2263	−2.42598
$863$	−7.62428	−0.259534	−0.129767	−	0.991545i	$-0.541423\pi$
$863$	−7.62428	−0.259534	−0.129767	+	0.991545i	$0.541423\pi$
$864$	−72.7222	−2.47406
$865$	2.72587	0.0926825
$866$	−107.595	−3.65623
$867$	−0.254574	−0.00864577
$868$	21.4007	0.726386
$869$	18.0338	0.611754
$870$	−7.54787	−0.255897
$871$	−17.9741	−0.609029
$872$	167.715	5.67956
$873$	−20.9664	−0.709604
$874$	158.220	5.35186
$875$	−6.53889	−0.221055
$876$	−33.4112	−1.12886
$877$	−45.5091	−1.53673	−0.768366	−	0.640010i	$-0.778930\pi$
$877$	−45.5091	−1.53673	−0.768366	+	0.640010i	$0.778930\pi$
$878$	75.2032	2.53799
$879$	1.89432	0.0638940
$880$	−66.0362	−2.22608
$881$	35.2441	1.18740	0.593701	−	0.804685i	$-0.297666\pi$
$881$	35.2441	1.18740	0.593701	+	0.804685i	$0.297666\pi$
$882$	−49.4338	−1.66452
$883$	−11.5552	−0.388863	−0.194432	−	0.980916i	$-0.562286\pi$
$883$	−11.5552	−0.388863	−0.194432	+	0.980916i	$0.562286\pi$
$884$	46.6531	1.56911
$885$	3.38477	0.113778
$886$	62.8257	2.11067
$887$	−46.7050	−1.56820	−0.784101	−	0.620633i	$-0.786876\pi$
$887$	−46.7050	−1.56820	−0.784101	+	0.620633i	$0.786876\pi$
$888$	43.4943	1.45957
$889$	−4.04775	−0.135757
$890$	−13.2410	−0.443840
$891$	−21.3169	−0.714141
$892$	71.4037	2.39077
$893$	59.8806	2.00383
$894$	9.31915	0.311679
$895$	−24.5081	−0.819214
$896$	−27.8336	−0.929854
$897$	9.12494	0.304673
$898$	−18.7384	−0.625309
$899$	−25.2883	−0.843413
$900$	50.7691	1.69230
$901$	3.78778	0.126189
$902$	−45.8153	−1.52548
$903$	1.72185	0.0572997
$904$	−8.44813	−0.280981
$905$	29.5286	0.981565
$906$	5.90692	0.196244
$907$	42.6112	1.41488	0.707441	−	0.706773i	$-0.249850\pi$
$907$	42.6112	1.41488	0.707441	+	0.706773i	$0.249850\pi$
$908$	44.4978	1.47671
$909$	−25.7803	−0.855080
$910$	−4.31470	−0.143031
$911$	10.4250	0.345397	0.172698	−	0.984975i	$-0.444751\pi$
$911$	10.4250	0.345397	0.172698	+	0.984975i	$0.444751\pi$
$912$	−57.1575	−1.89267
$913$	−43.3412	−1.43439
$914$	−36.8940	−1.22035
$915$	0.193390	0.00639327
$916$	20.8548	0.689061
$917$	3.01196	0.0994638
$918$	−35.1271	−1.15937
$919$	−21.2678	−0.701561	−0.350781	−	0.936458i	$-0.614084\pi$
$919$	−21.2678	−0.701561	−0.350781	+	0.936458i	$0.614084\pi$
$920$	106.174	3.50047
$921$	−13.2832	−0.437698
$922$	−96.1515	−3.16658
$923$	13.0324	0.428965
$924$	5.95584	0.195933
$925$	−27.9875	−0.920224
$926$	−20.5056	−0.673854
$927$	11.9209	0.391535
$928$	95.5367	3.13615
$929$	−51.5682	−1.69190	−0.845949	−	0.533264i	$-0.820965\pi$
$929$	−51.5682	−1.69190	−0.845949	+	0.533264i	$0.820965\pi$
$930$	11.8376	0.388169
$931$	−44.8962	−1.47141
$932$	51.9065	1.70025
$933$	12.9029	0.422422
$934$	−29.2289	−0.956398
$935$	−17.5062	−0.572514
$936$	53.2949	1.74200
$937$	60.2595	1.96859	0.984296	−	0.176529i	$-0.0564868\pi$
$937$	60.2595	1.96859	0.984296	+	0.176529i	$0.0564868\pi$
$938$	15.0459	0.491267
$939$	−14.5729	−0.475570
$940$	62.7752	2.04750
$941$	−0.450150	−0.0146745	−0.00733724	−	0.999973i	$-0.502336\pi$
$941$	−0.450150	−0.0146745	−0.00733724	+	0.999973i	$0.502336\pi$
$942$	5.88559	0.191763
$943$	43.2082	1.40705
$944$	−78.0620	−2.54070
$945$	2.38896	0.0777130
$946$	−47.4100	−1.54143
$947$	−30.5996	−0.994355	−0.497177	−	0.867649i	$-0.665630\pi$
$947$	−30.5996	−0.994355	−0.497177	+	0.867649i	$0.665630\pi$
$948$	16.3636	0.531466
$949$	22.5689	0.732618
$950$	62.7028	2.03435
$951$	−4.65807	−0.151048
$952$	−24.9983	−0.810199
$953$	22.1259	0.716727	0.358363	−	0.933582i	$-0.383335\pi$
$953$	22.1259	0.716727	0.358363	+	0.933582i	$0.383335\pi$
$954$	6.75977	0.218855
$955$	−3.77110	−0.122030
$956$	108.126	3.49703
$957$	−7.03778	−0.227499
$958$	50.7967	1.64117
$959$	11.2036	0.361783
$960$	−23.1566	−0.747375
$961$	8.66045	0.279369
$962$	−45.8980	−1.47981
$963$	−21.3170	−0.686931
$964$	47.7662	1.53845
$965$	3.00583	0.0967611
$966$	−7.63838	−0.245761
$967$	25.0969	0.807062	0.403531	−	0.914966i	$-0.367783\pi$
$967$	25.0969	0.807062	0.403531	+	0.914966i	$0.367783\pi$
$968$	2.59986	0.0835628
$969$	−15.1524	−0.486767
$970$	−27.1464	−0.871619
$971$	−14.4303	−0.463090	−0.231545	−	0.972824i	$-0.574378\pi$
$971$	−14.4303	−0.463090	−0.231545	+	0.972824i	$0.574378\pi$
$972$	−70.3021	−2.25494
$973$	4.83210	0.154910
$974$	−109.335	−3.50331
$975$	3.61624	0.115812
$976$	−4.46009	−0.142764
$977$	37.0337	1.18481	0.592407	−	0.805639i	$-0.298178\pi$
$977$	37.0337	1.18481	0.592407	+	0.805639i	$0.298178\pi$
$978$	−13.8884	−0.444101
$979$	−12.3462	−0.394586
$980$	−47.0665	−1.50348
$981$	46.5424	1.48598
$982$	24.4353	0.779761
$983$	−0.739109	−0.0235739	−0.0117870	−	0.999931i	$-0.503752\pi$
$983$	−0.739109	−0.0235739	−0.0117870	+	0.999931i	$0.503752\pi$
$984$	−26.6110	−0.848326
$985$	4.00966	0.127758
$986$	46.1472	1.46963
$987$	−2.89086	−0.0920172
$988$	75.6160	2.40567
$989$	44.7122	1.42177
$990$	−31.2420	−0.992937
$991$	50.9272	1.61776	0.808878	−	0.587976i	$-0.200075\pi$
$991$	50.9272	1.61776	0.808878	+	0.587976i	$0.200075\pi$
$992$	−149.833	−4.75720
$993$	2.57772	0.0818014
$994$	−10.9092	−0.346020
$995$	5.01566	0.159007
$996$	−39.3273	−1.24613
$997$	17.6099	0.557710	0.278855	−	0.960333i	$-0.410045\pi$
$997$	17.6099	0.557710	0.278855	+	0.960333i	$0.410045\pi$
$998$	101.337	3.20777
$999$	25.4128	0.804025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.2.a.c.1.4	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.2.a.c.1.4	✓	162	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3467.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74906 q^{2} -0.534947 q^{3} +5.55732 q^{4} +1.27817 q^{5} +1.47060 q^{6} +0.611481 q^{7} -9.77929 q^{8} -2.71383 q^{9} -3.51376 q^{10} -3.27630 q^{11} -2.97287 q^{12} +2.00815 q^{13} -1.68100 q^{14} -0.683753 q^{15} +15.7692 q^{16} +4.18042 q^{17} +7.46048 q^{18} +6.77567 q^{19} +7.10320 q^{20} -0.327110 q^{21} +9.00674 q^{22} -8.49423 q^{23} +5.23140 q^{24} -3.36628 q^{25} -5.52051 q^{26} +3.05660 q^{27} +3.39820 q^{28} -4.01552 q^{29} +1.87968 q^{30} +6.29765 q^{31} -23.7919 q^{32} +1.75265 q^{33} -11.4922 q^{34} +0.781576 q^{35} -15.0816 q^{36} +8.31408 q^{37} -18.6267 q^{38} -1.07425 q^{39} -12.4996 q^{40} -5.08677 q^{41} +0.899244 q^{42} -5.26383 q^{43} -18.2075 q^{44} -3.46874 q^{45} +23.3511 q^{46} +8.83759 q^{47} -8.43569 q^{48} -6.62609 q^{49} +9.25411 q^{50} -2.23630 q^{51} +11.1599 q^{52} +0.906076 q^{53} -8.40276 q^{54} -4.18767 q^{55} -5.97985 q^{56} -3.62463 q^{57} +11.0389 q^{58} -4.95028 q^{59} -3.79984 q^{60} -0.282836 q^{61} -17.3126 q^{62} -1.65946 q^{63} +33.8669 q^{64} +2.56675 q^{65} -4.81813 q^{66} -8.95059 q^{67} +23.2319 q^{68} +4.54396 q^{69} -2.14860 q^{70} +6.48975 q^{71} +26.5394 q^{72} +11.2387 q^{73} -22.8559 q^{74} +1.80078 q^{75} +37.6546 q^{76} -2.00340 q^{77} +2.95318 q^{78} -5.50432 q^{79} +20.1557 q^{80} +6.50638 q^{81} +13.9838 q^{82} +13.2287 q^{83} -1.81786 q^{84} +5.34328 q^{85} +14.4706 q^{86} +2.14809 q^{87} +32.0399 q^{88} +3.76833 q^{89} +9.53576 q^{90} +1.22794 q^{91} -47.2052 q^{92} -3.36891 q^{93} -24.2950 q^{94} +8.66046 q^{95} +12.7274 q^{96} +7.72574 q^{97} +18.2155 q^{98} +8.89133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 9 q^{2} + 24 q^{3} + 189 q^{4} + 32 q^{5} + 9 q^{6} + 23 q^{7} + 27 q^{8} + 196 q^{9} + 50 q^{10} + 12 q^{11} + 69 q^{12} + 144 q^{13} + 11 q^{14} + 17 q^{15} + 223 q^{16} + 33 q^{17} + 39 q^{18}+ \cdots - 25 q^{99}+O(q^{100}) \) 162 * q + 9 * q^2 + 24 * q^3 + 189 * q^4 + 32 * q^5 + 9 * q^6 + 23 * q^7 + 27 * q^8 + 196 * q^9 + 50 * q^10 + 12 * q^11 + 69 * q^12 + 144 * q^13 + 11 * q^14 + 17 * q^15 + 223 * q^16 + 33 * q^17 + 39 * q^18 + 35 * q^19 + 52 * q^20 + 44 * q^21 + 53 * q^22 + 31 * q^23 + 21 * q^24 + 266 * q^25 + 22 * q^26 + 93 * q^27 + 65 * q^28 + 25 * q^29 + 11 * q^30 + 81 * q^31 + 38 * q^32 + 96 * q^33 + 47 * q^34 + 14 * q^35 + 234 * q^36 + 153 * q^37 + 57 * q^38 + 18 * q^39 + 124 * q^40 + 19 * q^41 + 22 * q^42 + 87 * q^43 - 22 * q^44 + 135 * q^45 - 5 * q^46 + 53 * q^47 + 133 * q^48 + 291 * q^49 + 14 * q^50 - q^51 + 280 * q^52 + 122 * q^53 - 6 * q^54 + 88 * q^55 + 8 * q^56 + 37 * q^57 + 62 * q^58 + 26 * q^59 - 22 * q^60 + 128 * q^61 + 9 * q^62 + 11 * q^63 + 281 * q^64 + 23 * q^65 - 34 * q^66 + 124 * q^67 + 32 * q^68 + 138 * q^69 + 39 * q^70 + 16 * q^71 + 53 * q^72 + 161 * q^73 - 32 * q^74 + 71 * q^75 + 96 * q^76 + 126 * q^77 + 31 * q^78 + 34 * q^79 + 73 * q^80 + 242 * q^81 + 173 * q^82 + 27 * q^83 - 11 * q^84 + 130 * q^85 - 51 * q^86 + 87 * q^87 + 121 * q^88 + 33 * q^89 + 62 * q^90 + 66 * q^91 + 50 * q^92 + 173 * q^93 + 85 * q^94 - 11 * q^95 - 15 * q^96 + 205 * q^97 + 40 * q^98 - 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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