LMFDB - Embedded newform 6018.2.a.x.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 $ x^10 - x^9 - 34x^8 + 30x^7 + 341x^6 - 276x^5 - 1032x^4 + 1176x^3 + 416x^2 - 896x + 272
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.58712$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.58712 q^{5} +1.00000 q^{6} -2.07087 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.58712 q^{5} +1.00000 q^{6} -2.07087 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.58712 q^{10} -4.55602 q^{11} -1.00000 q^{12} -5.49833 q^{13} +2.07087 q^{14} -3.58712 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.37421 q^{19} +3.58712 q^{20} +2.07087 q^{21} +4.55602 q^{22} +7.83990 q^{23} +1.00000 q^{24} +7.86746 q^{25} +5.49833 q^{26} -1.00000 q^{27} -2.07087 q^{28} -2.79396 q^{29} +3.58712 q^{30} -2.56638 q^{31} -1.00000 q^{32} +4.55602 q^{33} -1.00000 q^{34} -7.42847 q^{35} +1.00000 q^{36} -11.2416 q^{37} -4.37421 q^{38} +5.49833 q^{39} -3.58712 q^{40} -0.724227 q^{41} -2.07087 q^{42} +10.3374 q^{43} -4.55602 q^{44} +3.58712 q^{45} -7.83990 q^{46} -0.730276 q^{47} -1.00000 q^{48} -2.71149 q^{49} -7.86746 q^{50} -1.00000 q^{51} -5.49833 q^{52} +1.71812 q^{53} +1.00000 q^{54} -16.3430 q^{55} +2.07087 q^{56} -4.37421 q^{57} +2.79396 q^{58} -1.00000 q^{59} -3.58712 q^{60} -1.71984 q^{61} +2.56638 q^{62} -2.07087 q^{63} +1.00000 q^{64} -19.7232 q^{65} -4.55602 q^{66} -7.85633 q^{67} +1.00000 q^{68} -7.83990 q^{69} +7.42847 q^{70} +14.5658 q^{71} -1.00000 q^{72} +12.3787 q^{73} +11.2416 q^{74} -7.86746 q^{75} +4.37421 q^{76} +9.43493 q^{77} -5.49833 q^{78} +5.20069 q^{79} +3.58712 q^{80} +1.00000 q^{81} +0.724227 q^{82} +8.94601 q^{83} +2.07087 q^{84} +3.58712 q^{85} -10.3374 q^{86} +2.79396 q^{87} +4.55602 q^{88} -6.72491 q^{89} -3.58712 q^{90} +11.3863 q^{91} +7.83990 q^{92} +2.56638 q^{93} +0.730276 q^{94} +15.6908 q^{95} +1.00000 q^{96} -15.7797 q^{97} +2.71149 q^{98} -4.55602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.58712	1.60421	0.802105	−	0.597183i	$-0.203713\pi$
$5$	3.58712	1.60421	0.802105	+	0.597183i	$0.203713\pi$
$6$	1.00000	0.408248
$7$	−2.07087	−0.782716	−0.391358	−	0.920239i	$-0.627995\pi$
$7$	−2.07087	−0.782716	−0.391358	+	0.920239i	$0.627995\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.58712	−1.13435
$11$	−4.55602	−1.37369	−0.686846	−	0.726803i	$-0.741005\pi$
$11$	−4.55602	−1.37369	−0.686846	+	0.726803i	$0.741005\pi$
$12$	−1.00000	−0.288675
$13$	−5.49833	−1.52496	−0.762481	−	0.647011i	$-0.776019\pi$
$13$	−5.49833	−1.52496	−0.762481	+	0.647011i	$0.776019\pi$
$14$	2.07087	0.553464
$15$	−3.58712	−0.926192
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	4.37421	1.00351	0.501756	−	0.865009i	$-0.332687\pi$
$19$	4.37421	1.00351	0.501756	+	0.865009i	$0.332687\pi$
$20$	3.58712	0.802105
$21$	2.07087	0.451901
$22$	4.55602	0.971347
$23$	7.83990	1.63473	0.817366	−	0.576119i	$-0.195434\pi$
$23$	7.83990	1.63473	0.817366	+	0.576119i	$0.195434\pi$
$24$	1.00000	0.204124
$25$	7.86746	1.57349
$26$	5.49833	1.07831
$27$	−1.00000	−0.192450
$28$	−2.07087	−0.391358
$29$	−2.79396	−0.518826	−0.259413	−	0.965766i	$-0.583529\pi$
$29$	−2.79396	−0.518826	−0.259413	+	0.965766i	$0.583529\pi$
$30$	3.58712	0.654916
$31$	−2.56638	−0.460935	−0.230467	−	0.973080i	$-0.574026\pi$
$31$	−2.56638	−0.460935	−0.230467	+	0.973080i	$0.574026\pi$
$32$	−1.00000	−0.176777
$33$	4.55602	0.793101
$34$	−1.00000	−0.171499
$35$	−7.42847	−1.25564
$36$	1.00000	0.166667
$37$	−11.2416	−1.84810	−0.924052	−	0.382266i	$-0.875144\pi$
$37$	−11.2416	−1.84810	−0.924052	+	0.382266i	$0.875144\pi$
$38$	−4.37421	−0.709591
$39$	5.49833	0.880437
$40$	−3.58712	−0.567174
$41$	−0.724227	−0.113105	−0.0565526	−	0.998400i	$-0.518011\pi$
$41$	−0.724227	−0.113105	−0.0565526	+	0.998400i	$0.518011\pi$
$42$	−2.07087	−0.319542
$43$	10.3374	1.57643	0.788217	−	0.615397i	$-0.211004\pi$
$43$	10.3374	1.57643	0.788217	+	0.615397i	$0.211004\pi$
$44$	−4.55602	−0.686846
$45$	3.58712	0.534737
$46$	−7.83990	−1.15593
$47$	−0.730276	−0.106522	−0.0532608	−	0.998581i	$-0.516961\pi$
$47$	−0.730276	−0.106522	−0.0532608	+	0.998581i	$0.516961\pi$
$48$	−1.00000	−0.144338
$49$	−2.71149	−0.387356
$50$	−7.86746	−1.11263
$51$	−1.00000	−0.140028
$52$	−5.49833	−0.762481
$53$	1.71812	0.236002	0.118001	−	0.993013i	$-0.462351\pi$
$53$	1.71812	0.236002	0.118001	+	0.993013i	$0.462351\pi$
$54$	1.00000	0.136083
$55$	−16.3430	−2.20369
$56$	2.07087	0.276732
$57$	−4.37421	−0.579378
$58$	2.79396	0.366865
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.58712	−0.463096
$61$	−1.71984	−0.220202	−0.110101	−	0.993920i	$-0.535117\pi$
$61$	−1.71984	−0.220202	−0.110101	+	0.993920i	$0.535117\pi$
$62$	2.56638	0.325930
$63$	−2.07087	−0.260905
$64$	1.00000	0.125000
$65$	−19.7232	−2.44636
$66$	−4.55602	−0.560807
$67$	−7.85633	−0.959803	−0.479902	−	0.877322i	$-0.659328\pi$
$67$	−7.85633	−0.959803	−0.479902	+	0.877322i	$0.659328\pi$
$68$	1.00000	0.121268
$69$	−7.83990	−0.943812
$70$	7.42847	0.887873
$71$	14.5658	1.72864	0.864320	−	0.502943i	$-0.167749\pi$
$71$	14.5658	1.72864	0.864320	+	0.502943i	$0.167749\pi$
$72$	−1.00000	−0.117851
$73$	12.3787	1.44882	0.724408	−	0.689372i	$-0.242113\pi$
$73$	12.3787	1.44882	0.724408	+	0.689372i	$0.242113\pi$
$74$	11.2416	1.30681
$75$	−7.86746	−0.908456
$76$	4.37421	0.501756
$77$	9.43493	1.07521
$78$	−5.49833	−0.622563
$79$	5.20069	0.585124	0.292562	−	0.956247i	$-0.405492\pi$
$79$	5.20069	0.585124	0.292562	+	0.956247i	$0.405492\pi$
$80$	3.58712	0.401053
$81$	1.00000	0.111111
$82$	0.724227	0.0799775
$83$	8.94601	0.981952	0.490976	−	0.871173i	$-0.336640\pi$
$83$	8.94601	0.981952	0.490976	+	0.871173i	$0.336640\pi$
$84$	2.07087	0.225951
$85$	3.58712	0.389078
$86$	−10.3374	−1.11471
$87$	2.79396	0.299544
$88$	4.55602	0.485673
$89$	−6.72491	−0.712839	−0.356420	−	0.934326i	$-0.616003\pi$
$89$	−6.72491	−0.712839	−0.356420	+	0.934326i	$0.616003\pi$
$90$	−3.58712	−0.378116
$91$	11.3863	1.19361
$92$	7.83990	0.817366
$93$	2.56638	0.266121
$94$	0.730276	0.0753222
$95$	15.6908	1.60985
$96$	1.00000	0.102062
$97$	−15.7797	−1.60219	−0.801093	−	0.598539i	$-0.795748\pi$
$97$	−15.7797	−1.60219	−0.801093	+	0.598539i	$0.795748\pi$
$98$	2.71149	0.273902
$99$	−4.55602	−0.457897
$100$	7.86746	0.786746
$101$	−14.4583	−1.43865	−0.719325	−	0.694674i	$-0.755549\pi$
$101$	−14.4583	−1.43865	−0.719325	+	0.694674i	$0.755549\pi$
$102$	1.00000	0.0990148
$103$	2.07792	0.204743	0.102372	−	0.994746i	$-0.467357\pi$
$103$	2.07792	0.204743	0.102372	+	0.994746i	$0.467357\pi$
$104$	5.49833	0.539155
$105$	7.42847	0.724945
$106$	−1.71812	−0.166879
$107$	5.50080	0.531782	0.265891	−	0.964003i	$-0.414334\pi$
$107$	5.50080	0.531782	0.265891	+	0.964003i	$0.414334\pi$
$108$	−1.00000	−0.0962250
$109$	−8.99423	−0.861491	−0.430745	−	0.902473i	$-0.641749\pi$
$109$	−8.99423	−0.861491	−0.430745	+	0.902473i	$0.641749\pi$
$110$	16.3430	1.55825
$111$	11.2416	1.06700
$112$	−2.07087	−0.195679
$113$	19.2369	1.80966	0.904829	−	0.425776i	$-0.139999\pi$
$113$	19.2369	1.80966	0.904829	+	0.425776i	$0.139999\pi$
$114$	4.37421	0.409682
$115$	28.1227	2.62245
$116$	−2.79396	−0.259413
$117$	−5.49833	−0.508320
$118$	1.00000	0.0920575
$119$	−2.07087	−0.189837
$120$	3.58712	0.327458
$121$	9.75732	0.887029
$122$	1.71984	0.155707
$123$	0.724227	0.0653014
$124$	−2.56638	−0.230467
$125$	10.2859	0.920002
$126$	2.07087	0.184488
$127$	13.5868	1.20563	0.602817	−	0.797879i	$-0.294045\pi$
$127$	13.5868	1.20563	0.602817	+	0.797879i	$0.294045\pi$
$128$	−1.00000	−0.0883883
$129$	−10.3374	−0.910155
$130$	19.7232	1.72984
$131$	−3.82871	−0.334516	−0.167258	−	0.985913i	$-0.553491\pi$
$131$	−3.82871	−0.334516	−0.167258	+	0.985913i	$0.553491\pi$
$132$	4.55602	0.396551
$133$	−9.05843	−0.785465
$134$	7.85633	0.678683
$135$	−3.58712	−0.308731
$136$	−1.00000	−0.0857493
$137$	12.0238	1.02726	0.513631	−	0.858011i	$-0.328300\pi$
$137$	12.0238	1.02726	0.513631	+	0.858011i	$0.328300\pi$
$138$	7.83990	0.667376
$139$	19.1771	1.62658	0.813291	−	0.581857i	$-0.197674\pi$
$139$	19.1771	1.62658	0.813291	+	0.581857i	$0.197674\pi$
$140$	−7.42847	−0.627821
$141$	0.730276	0.0615003
$142$	−14.5658	−1.22233
$143$	25.0505	2.09483
$144$	1.00000	0.0833333
$145$	−10.0223	−0.832306
$146$	−12.3787	−1.02447
$147$	2.71149	0.223640
$148$	−11.2416	−0.924052
$149$	24.2284	1.98487	0.992436	−	0.122765i	$-0.0391760\pi$
$149$	24.2284	1.98487	0.992436	+	0.122765i	$0.0391760\pi$
$150$	7.86746	0.642376
$151$	4.85210	0.394859	0.197429	−	0.980317i	$-0.436741\pi$
$151$	4.85210	0.394859	0.197429	+	0.980317i	$0.436741\pi$
$152$	−4.37421	−0.354795
$153$	1.00000	0.0808452
$154$	−9.43493	−0.760289
$155$	−9.20591	−0.739437
$156$	5.49833	0.440218
$157$	14.7078	1.17381	0.586907	−	0.809655i	$-0.300346\pi$
$157$	14.7078	1.17381	0.586907	+	0.809655i	$0.300346\pi$
$158$	−5.20069	−0.413745
$159$	−1.71812	−0.136256
$160$	−3.58712	−0.283587
$161$	−16.2354	−1.27953
$162$	−1.00000	−0.0785674
$163$	11.4575	0.897420	0.448710	−	0.893677i	$-0.351884\pi$
$163$	11.4575	0.897420	0.448710	+	0.893677i	$0.351884\pi$
$164$	−0.724227	−0.0565526
$165$	16.3430	1.27230
$166$	−8.94601	−0.694345
$167$	−0.349784	−0.0270671	−0.0135335	−	0.999908i	$-0.504308\pi$
$167$	−0.349784	−0.0270671	−0.0135335	+	0.999908i	$0.504308\pi$
$168$	−2.07087	−0.159771
$169$	17.2316	1.32551
$170$	−3.58712	−0.275120
$171$	4.37421	0.334504
$172$	10.3374	0.788217
$173$	−12.4036	−0.943030	−0.471515	−	0.881858i	$-0.656293\pi$
$173$	−12.4036	−0.943030	−0.471515	+	0.881858i	$0.656293\pi$
$174$	−2.79396	−0.211810
$175$	−16.2925	−1.23160
$176$	−4.55602	−0.343423
$177$	1.00000	0.0751646
$178$	6.72491	0.504053
$179$	−18.5426	−1.38594	−0.692970	−	0.720966i	$-0.743698\pi$
$179$	−18.5426	−1.38594	−0.692970	+	0.720966i	$0.743698\pi$
$180$	3.58712	0.267368
$181$	−5.78630	−0.430092	−0.215046	−	0.976604i	$-0.568990\pi$
$181$	−5.78630	−0.430092	−0.215046	+	0.976604i	$0.568990\pi$
$182$	−11.3863	−0.844011
$183$	1.71984	0.127134
$184$	−7.83990	−0.577965
$185$	−40.3250	−2.96475
$186$	−2.56638	−0.188176
$187$	−4.55602	−0.333169
$188$	−0.730276	−0.0532608
$189$	2.07087	0.150634
$190$	−15.6908	−1.13833
$191$	11.4802	0.830679	0.415339	−	0.909667i	$-0.363663\pi$
$191$	11.4802	0.830679	0.415339	+	0.909667i	$0.363663\pi$
$192$	−1.00000	−0.0721688
$193$	7.19848	0.518158	0.259079	−	0.965856i	$-0.416581\pi$
$193$	7.19848	0.518158	0.259079	+	0.965856i	$0.416581\pi$
$194$	15.7797	1.13292
$195$	19.7232	1.41241
$196$	−2.71149	−0.193678
$197$	−0.526011	−0.0374767	−0.0187384	−	0.999824i	$-0.505965\pi$
$197$	−0.526011	−0.0374767	−0.0187384	+	0.999824i	$0.505965\pi$
$198$	4.55602	0.323782
$199$	−24.8565	−1.76203	−0.881014	−	0.473090i	$-0.843138\pi$
$199$	−24.8565	−1.76203	−0.881014	+	0.473090i	$0.843138\pi$
$200$	−7.86746	−0.556314
$201$	7.85633	0.554143
$202$	14.4583	1.01728
$203$	5.78594	0.406093
$204$	−1.00000	−0.0700140
$205$	−2.59789	−0.181445
$206$	−2.07792	−0.144775
$207$	7.83990	0.544910
$208$	−5.49833	−0.381240
$209$	−19.9290	−1.37852
$210$	−7.42847	−0.512613
$211$	−5.81345	−0.400215	−0.200107	−	0.979774i	$-0.564129\pi$
$211$	−5.81345	−0.400215	−0.200107	+	0.979774i	$0.564129\pi$
$212$	1.71812	0.118001
$213$	−14.5658	−0.998031
$214$	−5.50080	−0.376027
$215$	37.0814	2.52893
$216$	1.00000	0.0680414
$217$	5.31464	0.360781
$218$	8.99423	0.609166
$219$	−12.3787	−0.836474
$220$	−16.3430	−1.10185
$221$	−5.49833	−0.369857
$222$	−11.2416	−0.754486
$223$	10.7245	0.718165	0.359082	−	0.933306i	$-0.383090\pi$
$223$	10.7245	0.718165	0.359082	+	0.933306i	$0.383090\pi$
$224$	2.07087	0.138366
$225$	7.86746	0.524497
$226$	−19.2369	−1.27962
$227$	−7.37192	−0.489291	−0.244646	−	0.969613i	$-0.578672\pi$
$227$	−7.37192	−0.489291	−0.244646	+	0.969613i	$0.578672\pi$
$228$	−4.37421	−0.289689
$229$	29.2261	1.93132	0.965658	−	0.259817i	$-0.0836624\pi$
$229$	29.2261	1.93132	0.965658	+	0.259817i	$0.0836624\pi$
$230$	−28.1227	−1.85435
$231$	−9.43493	−0.620773
$232$	2.79396	0.183433
$233$	20.9187	1.37043	0.685216	−	0.728340i	$-0.259708\pi$
$233$	20.9187	1.37043	0.685216	+	0.728340i	$0.259708\pi$
$234$	5.49833	0.359437
$235$	−2.61959	−0.170883
$236$	−1.00000	−0.0650945
$237$	−5.20069	−0.337821
$238$	2.07087	0.134235
$239$	7.75630	0.501713	0.250857	−	0.968024i	$-0.419288\pi$
$239$	7.75630	0.501713	0.250857	+	0.968024i	$0.419288\pi$
$240$	−3.58712	−0.231548
$241$	2.52091	0.162386	0.0811930	−	0.996698i	$-0.474127\pi$
$241$	2.52091	0.162386	0.0811930	+	0.996698i	$0.474127\pi$
$242$	−9.75732	−0.627224
$243$	−1.00000	−0.0641500
$244$	−1.71984	−0.110101
$245$	−9.72645	−0.621400
$246$	−0.724227	−0.0461750
$247$	−24.0508	−1.53032
$248$	2.56638	0.162965
$249$	−8.94601	−0.566930
$250$	−10.2859	−0.650540
$251$	−4.01694	−0.253547	−0.126774	−	0.991932i	$-0.540462\pi$
$251$	−4.01694	−0.253547	−0.126774	+	0.991932i	$0.540462\pi$
$252$	−2.07087	−0.130453
$253$	−35.7187	−2.24562
$254$	−13.5868	−0.852512
$255$	−3.58712	−0.224634
$256$	1.00000	0.0625000
$257$	−28.2401	−1.76157	−0.880784	−	0.473517i	$-0.842984\pi$
$257$	−28.2401	−1.76157	−0.880784	+	0.473517i	$0.842984\pi$
$258$	10.3374	0.643577
$259$	23.2799	1.44654
$260$	−19.7232	−1.22318
$261$	−2.79396	−0.172942
$262$	3.82871	0.236539
$263$	−4.41162	−0.272032	−0.136016	−	0.990707i	$-0.543430\pi$
$263$	−4.41162	−0.272032	−0.136016	+	0.990707i	$0.543430\pi$
$264$	−4.55602	−0.280404
$265$	6.16311	0.378597
$266$	9.05843	0.555408
$267$	6.72491	0.411558
$268$	−7.85633	−0.479902
$269$	−23.2959	−1.42037	−0.710187	−	0.704013i	$-0.751390\pi$
$269$	−23.2959	−1.42037	−0.710187	+	0.704013i	$0.751390\pi$
$270$	3.58712	0.218305
$271$	28.3262	1.72069	0.860347	−	0.509708i	$-0.170247\pi$
$271$	28.3262	1.72069	0.860347	+	0.509708i	$0.170247\pi$
$272$	1.00000	0.0606339
$273$	−11.3863	−0.689132
$274$	−12.0238	−0.726384
$275$	−35.8443	−2.16149
$276$	−7.83990	−0.471906
$277$	25.5118	1.53286	0.766429	−	0.642329i	$-0.222032\pi$
$277$	25.5118	1.53286	0.766429	+	0.642329i	$0.222032\pi$
$278$	−19.1771	−1.15017
$279$	−2.56638	−0.153645
$280$	7.42847	0.443936
$281$	0.00124065	7.40112e−5 0	3.70056e−5	−	1.00000i	$-0.499988\pi$
$281$	0.00124065	7.40112e−5 0	3.70056e−5		1.00000i	$0.499988\pi$
$282$	−0.730276	−0.0434873
$283$	−14.2851	−0.849162	−0.424581	−	0.905390i	$-0.639579\pi$
$283$	−14.2851	−0.849162	−0.424581	+	0.905390i	$0.639579\pi$
$284$	14.5658	0.864320
$285$	−15.6908	−0.929445
$286$	−25.0505	−1.48127
$287$	1.49978	0.0885293
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	10.0223	0.588529
$291$	15.7797	0.925023
$292$	12.3787	0.724408
$293$	25.8301	1.50901	0.754505	−	0.656294i	$-0.227877\pi$
$293$	25.8301	1.50901	0.754505	+	0.656294i	$0.227877\pi$
$294$	−2.71149	−0.158137
$295$	−3.58712	−0.208850
$296$	11.2416	0.653404
$297$	4.55602	0.264367
$298$	−24.2284	−1.40352
$299$	−43.1063	−2.49290
$300$	−7.86746	−0.454228
$301$	−21.4074	−1.23390
$302$	−4.85210	−0.279207
$303$	14.4583	0.830605
$304$	4.37421	0.250878
$305$	−6.16926	−0.353251
$306$	−1.00000	−0.0571662
$307$	−3.76155	−0.214683	−0.107341	−	0.994222i	$-0.534234\pi$
$307$	−3.76155	−0.214683	−0.107341	+	0.994222i	$0.534234\pi$
$308$	9.43493	0.537605
$309$	−2.07792	−0.118208
$310$	9.20591	0.522861
$311$	13.0825	0.741841	0.370921	−	0.928665i	$-0.379042\pi$
$311$	13.0825	0.741841	0.370921	+	0.928665i	$0.379042\pi$
$312$	−5.49833	−0.311281
$313$	13.7209	0.775553	0.387776	−	0.921753i	$-0.373243\pi$
$313$	13.7209	0.775553	0.387776	+	0.921753i	$0.373243\pi$
$314$	−14.7078	−0.830011
$315$	−7.42847	−0.418547
$316$	5.20069	0.292562
$317$	−28.1336	−1.58014	−0.790070	−	0.613017i	$-0.789956\pi$
$317$	−28.1336	−1.58014	−0.790070	+	0.613017i	$0.789956\pi$
$318$	1.71812	0.0963475
$319$	12.7294	0.712707
$320$	3.58712	0.200526
$321$	−5.50080	−0.307025
$322$	16.2354	0.904764
$323$	4.37421	0.243388
$324$	1.00000	0.0555556
$325$	−43.2579	−2.39951
$326$	−11.4575	−0.634572
$327$	8.99423	0.497382
$328$	0.724227	0.0399888
$329$	1.51231	0.0833762
$330$	−16.3430	−0.899653
$331$	−7.34579	−0.403761	−0.201881	−	0.979410i	$-0.564705\pi$
$331$	−7.34579	−0.403761	−0.201881	+	0.979410i	$0.564705\pi$
$332$	8.94601	0.490976
$333$	−11.2416	−0.616035
$334$	0.349784	0.0191393
$335$	−28.1816	−1.53973
$336$	2.07087	0.112975
$337$	31.1016	1.69421	0.847106	−	0.531424i	$-0.178343\pi$
$337$	31.1016	1.69421	0.847106	+	0.531424i	$0.178343\pi$
$338$	−17.2316	−0.937275
$339$	−19.2369	−1.04481
$340$	3.58712	0.194539
$341$	11.6925	0.633183
$342$	−4.37421	−0.236530
$343$	20.1113	1.08591
$344$	−10.3374	−0.557354
$345$	−28.1227	−1.51407
$346$	12.4036	0.666823
$347$	−4.23975	−0.227602	−0.113801	−	0.993504i	$-0.536303\pi$
$347$	−4.23975	−0.227602	−0.113801	+	0.993504i	$0.536303\pi$
$348$	2.79396	0.149772
$349$	−7.77181	−0.416015	−0.208008	−	0.978127i	$-0.566698\pi$
$349$	−7.77181	−0.416015	−0.208008	+	0.978127i	$0.566698\pi$
$350$	16.2925	0.870871
$351$	5.49833	0.293479
$352$	4.55602	0.242837
$353$	8.91885	0.474702	0.237351	−	0.971424i	$-0.423721\pi$
$353$	8.91885	0.474702	0.237351	+	0.971424i	$0.423721\pi$
$354$	−1.00000	−0.0531494
$355$	52.2493	2.77310
$356$	−6.72491	−0.356420
$357$	2.07087	0.109602
$358$	18.5426	0.980008
$359$	17.3096	0.913566	0.456783	−	0.889578i	$-0.349002\pi$
$359$	17.3096	0.913566	0.456783	+	0.889578i	$0.349002\pi$
$360$	−3.58712	−0.189058
$361$	0.133717	0.00703774
$362$	5.78630	0.304121
$363$	−9.75732	−0.512127
$364$	11.3863	0.596806
$365$	44.4039	2.32421
$366$	−1.71984	−0.0898972
$367$	22.2404	1.16094	0.580471	−	0.814281i	$-0.302869\pi$
$367$	22.2404	1.16094	0.580471	+	0.814281i	$0.302869\pi$
$368$	7.83990	0.408683
$369$	−0.724227	−0.0377018
$370$	40.3250	2.09639
$371$	−3.55801	−0.184723
$372$	2.56638	0.133060
$373$	31.5462	1.63340	0.816701	−	0.577061i	$-0.195801\pi$
$373$	31.5462	1.63340	0.816701	+	0.577061i	$0.195801\pi$
$374$	4.55602	0.235586
$375$	−10.2859	−0.531164
$376$	0.730276	0.0376611
$377$	15.3621	0.791189
$378$	−2.07087	−0.106514
$379$	20.0362	1.02919	0.514594	−	0.857434i	$-0.327943\pi$
$379$	20.0362	1.02919	0.514594	+	0.857434i	$0.327943\pi$
$380$	15.6908	0.804923
$381$	−13.5868	−0.696073
$382$	−11.4802	−0.587379
$383$	36.2909	1.85438	0.927189	−	0.374595i	$-0.122218\pi$
$383$	36.2909	1.85438	0.927189	+	0.374595i	$0.122218\pi$
$384$	1.00000	0.0510310
$385$	33.8443	1.72486
$386$	−7.19848	−0.366393
$387$	10.3374	0.525478
$388$	−15.7797	−0.801093
$389$	−30.0011	−1.52112	−0.760559	−	0.649269i	$-0.775075\pi$
$389$	−30.0011	−1.52112	−0.760559	+	0.649269i	$0.775075\pi$
$390$	−19.7232	−0.998722
$391$	7.83990	0.396481
$392$	2.71149	0.136951
$393$	3.82871	0.193133
$394$	0.526011	0.0265001
$395$	18.6555	0.938662
$396$	−4.55602	−0.228949
$397$	0.828924	0.0416025	0.0208013	−	0.999784i	$-0.493378\pi$
$397$	0.828924	0.0416025	0.0208013	+	0.999784i	$0.493378\pi$
$398$	24.8565	1.24594
$399$	9.05843	0.453489
$400$	7.86746	0.393373
$401$	−1.67975	−0.0838829	−0.0419414	−	0.999120i	$-0.513354\pi$
$401$	−1.67975	−0.0838829	−0.0419414	+	0.999120i	$0.513354\pi$
$402$	−7.85633	−0.391838
$403$	14.1108	0.702908
$404$	−14.4583	−0.719325
$405$	3.58712	0.178246
$406$	−5.78594	−0.287151
$407$	51.2169	2.53873
$408$	1.00000	0.0495074
$409$	−7.82390	−0.386867	−0.193433	−	0.981113i	$-0.561962\pi$
$409$	−7.82390	−0.386867	−0.193433	+	0.981113i	$0.561962\pi$
$410$	2.59789	0.128301
$411$	−12.0238	−0.593090
$412$	2.07792	0.102372
$413$	2.07087	0.101901
$414$	−7.83990	−0.385310
$415$	32.0904	1.57526
$416$	5.49833	0.269578
$417$	−19.1771	−0.939107
$418$	19.9290	0.974759
$419$	1.90373	0.0930031	0.0465016	−	0.998918i	$-0.485193\pi$
$419$	1.90373	0.0930031	0.0465016	+	0.998918i	$0.485193\pi$
$420$	7.42847	0.362472
$421$	29.6057	1.44289	0.721446	−	0.692471i	$-0.243478\pi$
$421$	29.6057	1.44289	0.721446	+	0.692471i	$0.243478\pi$
$422$	5.81345	0.282995
$423$	−0.730276	−0.0355072
$424$	−1.71812	−0.0834393
$425$	7.86746	0.381628
$426$	14.5658	0.705714
$427$	3.56156	0.172356
$428$	5.50080	0.265891
$429$	−25.0505	−1.20945
$430$	−37.0814	−1.78823
$431$	10.0968	0.486347	0.243174	−	0.969983i	$-0.421811\pi$
$431$	10.0968	0.486347	0.243174	+	0.969983i	$0.421811\pi$
$432$	−1.00000	−0.0481125
$433$	−3.39173	−0.162996	−0.0814982	−	0.996673i	$-0.525970\pi$
$433$	−3.39173	−0.162996	−0.0814982	+	0.996673i	$0.525970\pi$
$434$	−5.31464	−0.255111
$435$	10.0223	0.480532
$436$	−8.99423	−0.430745
$437$	34.2934	1.64047
$438$	12.3787	0.591476
$439$	20.4111	0.974166	0.487083	−	0.873356i	$-0.338061\pi$
$439$	20.4111	0.974166	0.487083	+	0.873356i	$0.338061\pi$
$440$	16.3430	0.779123
$441$	−2.71149	−0.129119
$442$	5.49833	0.261529
$443$	12.4200	0.590091	0.295046	−	0.955483i	$-0.404665\pi$
$443$	12.4200	0.590091	0.295046	+	0.955483i	$0.404665\pi$
$444$	11.2416	0.533502
$445$	−24.1231	−1.14354
$446$	−10.7245	−0.507819
$447$	−24.2284	−1.14597
$448$	−2.07087	−0.0978395
$449$	−32.8680	−1.55113	−0.775567	−	0.631265i	$-0.782536\pi$
$449$	−32.8680	−1.55113	−0.775567	+	0.631265i	$0.782536\pi$
$450$	−7.86746	−0.370876
$451$	3.29959	0.155372
$452$	19.2369	0.904829
$453$	−4.85210	−0.227972
$454$	7.37192	0.345981
$455$	40.8442	1.91480
$456$	4.37421	0.204841
$457$	−8.26897	−0.386806	−0.193403	−	0.981119i	$-0.561952\pi$
$457$	−8.26897	−0.386806	−0.193403	+	0.981119i	$0.561952\pi$
$458$	−29.2261	−1.36565
$459$	−1.00000	−0.0466760
$460$	28.1227	1.31123
$461$	8.13695	0.378976	0.189488	−	0.981883i	$-0.439317\pi$
$461$	8.13695	0.378976	0.189488	+	0.981883i	$0.439317\pi$
$462$	9.43493	0.438953
$463$	−23.5279	−1.09343	−0.546717	−	0.837317i	$-0.684123\pi$
$463$	−23.5279	−1.09343	−0.546717	+	0.837317i	$0.684123\pi$
$464$	−2.79396	−0.129706
$465$	9.20591	0.426914
$466$	−20.9187	−0.969041
$467$	32.0031	1.48093	0.740464	−	0.672096i	$-0.234606\pi$
$467$	32.0031	1.48093	0.740464	+	0.672096i	$0.234606\pi$
$468$	−5.49833	−0.254160
$469$	16.2694	0.751253
$470$	2.61959	0.120833
$471$	−14.7078	−0.677701
$472$	1.00000	0.0460287
$473$	−47.0973	−2.16553
$474$	5.20069	0.238876
$475$	34.4139	1.57902
$476$	−2.07087	−0.0949183
$477$	1.71812	0.0786674
$478$	−7.75630	−0.354765
$479$	−34.0009	−1.55354	−0.776771	−	0.629783i	$-0.783144\pi$
$479$	−34.0009	−1.55354	−0.776771	+	0.629783i	$0.783144\pi$
$480$	3.58712	0.163729
$481$	61.8099	2.81829
$482$	−2.52091	−0.114824
$483$	16.2354	0.738737
$484$	9.75732	0.443515
$485$	−56.6038	−2.57024
$486$	1.00000	0.0453609
$487$	24.5864	1.11412	0.557058	−	0.830474i	$-0.311930\pi$
$487$	24.5864	1.11412	0.557058	+	0.830474i	$0.311930\pi$
$488$	1.71984	0.0778533
$489$	−11.4575	−0.518126
$490$	9.72645	0.439396
$491$	−6.40386	−0.289002	−0.144501	−	0.989505i	$-0.546158\pi$
$491$	−6.40386	−0.289002	−0.144501	+	0.989505i	$0.546158\pi$
$492$	0.724227	0.0326507
$493$	−2.79396	−0.125834
$494$	24.0508	1.08210
$495$	−16.3430	−0.734564
$496$	−2.56638	−0.115234
$497$	−30.1639	−1.35303
$498$	8.94601	0.400880
$499$	−23.3733	−1.04633	−0.523166	−	0.852231i	$-0.675249\pi$
$499$	−23.3733	−1.04633	−0.523166	+	0.852231i	$0.675249\pi$
$500$	10.2859	0.460001
$501$	0.349784	0.0156272
$502$	4.01694	0.179285
$503$	1.35293	0.0603240	0.0301620	−	0.999545i	$-0.490398\pi$
$503$	1.35293	0.0603240	0.0301620	+	0.999545i	$0.490398\pi$
$504$	2.07087	0.0922440
$505$	−51.8636	−2.30790
$506$	35.7187	1.58789
$507$	−17.2316	−0.765282
$508$	13.5868	0.602817
$509$	−25.3247	−1.12250	−0.561248	−	0.827648i	$-0.689679\pi$
$509$	−25.3247	−1.12250	−0.561248	+	0.827648i	$0.689679\pi$
$510$	3.58712	0.158841
$511$	−25.6347	−1.13401
$512$	−1.00000	−0.0441942
$513$	−4.37421	−0.193126
$514$	28.2401	1.24562
$515$	7.45374	0.328451
$516$	−10.3374	−0.455077
$517$	3.32715	0.146328
$518$	−23.2799	−1.02286
$519$	12.4036	0.544459
$520$	19.7232	0.864919
$521$	34.8942	1.52874	0.764370	−	0.644777i	$-0.223050\pi$
$521$	34.8942	1.52874	0.764370	+	0.644777i	$0.223050\pi$
$522$	2.79396	0.122288
$523$	11.6295	0.508521	0.254261	−	0.967136i	$-0.418168\pi$
$523$	11.6295	0.508521	0.254261	+	0.967136i	$0.418168\pi$
$524$	−3.82871	−0.167258
$525$	16.2925	0.711063
$526$	4.41162	0.192356
$527$	−2.56638	−0.111793
$528$	4.55602	0.198275
$529$	38.4640	1.67235
$530$	−6.16311	−0.267709
$531$	−1.00000	−0.0433963
$532$	−9.05843	−0.392733
$533$	3.98204	0.172481
$534$	−6.72491	−0.291015
$535$	19.7321	0.853091
$536$	7.85633	0.339342
$537$	18.5426	0.800173
$538$	23.2959	1.00436
$539$	12.3536	0.532107
$540$	−3.58712	−0.154365
$541$	5.75002	0.247213	0.123606	−	0.992331i	$-0.460554\pi$
$541$	5.75002	0.247213	0.123606	+	0.992331i	$0.460554\pi$
$542$	−28.3262	−1.21671
$543$	5.78630	0.248314
$544$	−1.00000	−0.0428746
$545$	−32.2634	−1.38201
$546$	11.3863	0.487290
$547$	−17.4610	−0.746578	−0.373289	−	0.927715i	$-0.621770\pi$
$547$	−17.4610	−0.746578	−0.373289	+	0.927715i	$0.621770\pi$
$548$	12.0238	0.513631
$549$	−1.71984	−0.0734008
$550$	35.8443	1.52841
$551$	−12.2214	−0.520648
$552$	7.83990	0.333688
$553$	−10.7700	−0.457986
$554$	−25.5118	−1.08389
$555$	40.3250	1.71170
$556$	19.1771	0.813291
$557$	−13.0661	−0.553629	−0.276814	−	0.960923i	$-0.589279\pi$
$557$	−13.0661	−0.553629	−0.276814	+	0.960923i	$0.589279\pi$
$558$	2.56638	0.108643
$559$	−56.8382	−2.40400
$560$	−7.42847	−0.313910
$561$	4.55602	0.192355
$562$	−0.00124065	−5.23338e−5 0
$563$	−31.1773	−1.31396	−0.656982	−	0.753906i	$-0.728167\pi$
$563$	−31.1773	−1.31396	−0.656982	+	0.753906i	$0.728167\pi$
$564$	0.730276	0.0307502
$565$	69.0052	2.90307
$566$	14.2851	0.600448
$567$	−2.07087	−0.0869684
$568$	−14.5658	−0.611166
$569$	22.5507	0.945373	0.472687	−	0.881231i	$-0.343284\pi$
$569$	22.5507	0.945373	0.472687	+	0.881231i	$0.343284\pi$
$570$	15.6908	0.657217
$571$	5.36676	0.224592	0.112296	−	0.993675i	$-0.464180\pi$
$571$	5.36676	0.224592	0.112296	+	0.993675i	$0.464180\pi$
$572$	25.0505	1.04741
$573$	−11.4802	−0.479593
$574$	−1.49978	−0.0625997
$575$	61.6801	2.57224
$576$	1.00000	0.0416667
$577$	−25.3315	−1.05457	−0.527283	−	0.849690i	$-0.676789\pi$
$577$	−25.3315	−1.05457	−0.527283	+	0.849690i	$0.676789\pi$
$578$	−1.00000	−0.0415945
$579$	−7.19848	−0.299158
$580$	−10.0223	−0.416153
$581$	−18.5260	−0.768589
$582$	−15.7797	−0.654090
$583$	−7.82779	−0.324194
$584$	−12.3787	−0.512234
$585$	−19.7232	−0.815453
$586$	−25.8301	−1.06703
$587$	7.53949	0.311188	0.155594	−	0.987821i	$-0.450271\pi$
$587$	7.53949	0.311188	0.155594	+	0.987821i	$0.450271\pi$
$588$	2.71149	0.111820
$589$	−11.2259	−0.462554
$590$	3.58712	0.147680
$591$	0.526011	0.0216372
$592$	−11.2416	−0.462026
$593$	−30.2964	−1.24412	−0.622062	−	0.782968i	$-0.713705\pi$
$593$	−30.2964	−1.24412	−0.622062	+	0.782968i	$0.713705\pi$
$594$	−4.55602	−0.186936
$595$	−7.42847	−0.304538
$596$	24.2284	0.992436
$597$	24.8565	1.01731
$598$	43.1063	1.76275
$599$	−18.3140	−0.748290	−0.374145	−	0.927370i	$-0.622064\pi$
$599$	−18.3140	−0.748290	−0.374145	+	0.927370i	$0.622064\pi$
$600$	7.86746	0.321188
$601$	18.7319	0.764088	0.382044	−	0.924144i	$-0.375220\pi$
$601$	18.7319	0.764088	0.382044	+	0.924144i	$0.375220\pi$
$602$	21.4074	0.872499
$603$	−7.85633	−0.319934
$604$	4.85210	0.197429
$605$	35.0007	1.42298
$606$	−14.4583	−0.587326
$607$	17.3895	0.705818	0.352909	−	0.935658i	$-0.385192\pi$
$607$	17.3895	0.705818	0.352909	+	0.935658i	$0.385192\pi$
$608$	−4.37421	−0.177398
$609$	−5.78594	−0.234458
$610$	6.16926	0.249786
$611$	4.01529	0.162441
$612$	1.00000	0.0404226
$613$	−29.5705	−1.19434	−0.597170	−	0.802115i	$-0.703708\pi$
$613$	−29.5705	−1.19434	−0.597170	+	0.802115i	$0.703708\pi$
$614$	3.76155	0.151804
$615$	2.59789	0.104757
$616$	−9.43493	−0.380144
$617$	−4.22055	−0.169913	−0.0849564	−	0.996385i	$-0.527075\pi$
$617$	−4.22055	−0.169913	−0.0849564	+	0.996385i	$0.527075\pi$
$618$	2.07792	0.0835860
$619$	−38.2421	−1.53708	−0.768540	−	0.639802i	$-0.779016\pi$
$619$	−38.2421	−1.53708	−0.768540	+	0.639802i	$0.779016\pi$
$620$	−9.20591	−0.369718
$621$	−7.83990	−0.314604
$622$	−13.0825	−0.524561
$623$	13.9264	0.557951
$624$	5.49833	0.220109
$625$	−2.44036	−0.0976145
$626$	−13.7209	−0.548399
$627$	19.9290	0.795887
$628$	14.7078	0.586907
$629$	−11.2416	−0.448231
$630$	7.42847	0.295958
$631$	23.3687	0.930295	0.465147	−	0.885233i	$-0.346001\pi$
$631$	23.3687	0.930295	0.465147	+	0.885233i	$0.346001\pi$
$632$	−5.20069	−0.206873
$633$	5.81345	0.231064
$634$	28.1336	1.11733
$635$	48.7376	1.93409
$636$	−1.71812	−0.0681279
$637$	14.9087	0.590702
$638$	−12.7294	−0.503960
$639$	14.5658	0.576213
$640$	−3.58712	−0.141794
$641$	−21.1492	−0.835342	−0.417671	−	0.908598i	$-0.637154\pi$
$641$	−21.1492	−0.835342	−0.417671	+	0.908598i	$0.637154\pi$
$642$	5.50080	0.217099
$643$	−26.5558	−1.04726	−0.523629	−	0.851946i	$-0.675422\pi$
$643$	−26.5558	−1.04726	−0.523629	+	0.851946i	$0.675422\pi$
$644$	−16.2354	−0.639765
$645$	−37.0814	−1.46008
$646$	−4.37421	−0.172101
$647$	−46.4106	−1.82459	−0.912295	−	0.409533i	$-0.865692\pi$
$647$	−46.4106	−1.82459	−0.912295	+	0.409533i	$0.865692\pi$
$648$	−1.00000	−0.0392837
$649$	4.55602	0.178839
$650$	43.2579	1.69671
$651$	−5.31464	−0.208297
$652$	11.4575	0.448710
$653$	20.7094	0.810420	0.405210	−	0.914224i	$-0.367198\pi$
$653$	20.7094	0.810420	0.405210	+	0.914224i	$0.367198\pi$
$654$	−8.99423	−0.351702
$655$	−13.7341	−0.536635
$656$	−0.724227	−0.0282763
$657$	12.3787	0.482939
$658$	−1.51231	−0.0589559
$659$	39.2125	1.52750	0.763751	−	0.645511i	$-0.223355\pi$
$659$	39.2125	1.52750	0.763751	+	0.645511i	$0.223355\pi$
$660$	16.3430	0.636151
$661$	25.5817	0.995011	0.497506	−	0.867461i	$-0.334249\pi$
$661$	25.5817	0.995011	0.497506	+	0.867461i	$0.334249\pi$
$662$	7.34579	0.285502
$663$	5.49833	0.213537
$664$	−8.94601	−0.347172
$665$	−32.4937	−1.26005
$666$	11.2416	0.435602
$667$	−21.9044	−0.848141
$668$	−0.349784	−0.0135335
$669$	−10.7245	−0.414633
$670$	28.1816	1.08875
$671$	7.83560	0.302490
$672$	−2.07087	−0.0798856
$673$	20.3684	0.785144	0.392572	−	0.919721i	$-0.371585\pi$
$673$	20.3684	0.785144	0.392572	+	0.919721i	$0.371585\pi$
$674$	−31.1016	−1.19799
$675$	−7.86746	−0.302819
$676$	17.2316	0.662754
$677$	14.1331	0.543178	0.271589	−	0.962413i	$-0.412451\pi$
$677$	14.1331	0.543178	0.271589	+	0.962413i	$0.412451\pi$
$678$	19.2369	0.738789
$679$	32.6778	1.25406
$680$	−3.58712	−0.137560
$681$	7.37192	0.282493
$682$	−11.6925	−0.447728
$683$	−47.9721	−1.83560	−0.917800	−	0.397042i	$-0.870037\pi$
$683$	−47.9721	−1.83560	−0.917800	+	0.397042i	$0.870037\pi$
$684$	4.37421	0.167252
$685$	43.1308	1.64794
$686$	−20.1113	−0.767851
$687$	−29.2261	−1.11505
$688$	10.3374	0.394109
$689$	−9.44679	−0.359894
$690$	28.1227	1.07061
$691$	−5.13239	−0.195245	−0.0976226	−	0.995224i	$-0.531124\pi$
$691$	−5.13239	−0.195245	−0.0976226	+	0.995224i	$0.531124\pi$
$692$	−12.4036	−0.471515
$693$	9.43493	0.358404
$694$	4.23975	0.160939
$695$	68.7907	2.60938
$696$	−2.79396	−0.105905
$697$	−0.724227	−0.0274321
$698$	7.77181	0.294167
$699$	−20.9187	−0.791219
$700$	−16.2925	−0.615799
$701$	−4.91086	−0.185481	−0.0927404	−	0.995690i	$-0.529563\pi$
$701$	−4.91086	−0.185481	−0.0927404	+	0.995690i	$0.529563\pi$
$702$	−5.49833	−0.207521
$703$	−49.1730	−1.85460
$704$	−4.55602	−0.171711
$705$	2.61959	0.0986595
$706$	−8.91885	−0.335665
$707$	29.9412	1.12605
$708$	1.00000	0.0375823
$709$	9.38535	0.352474	0.176237	−	0.984348i	$-0.443607\pi$
$709$	9.38535	0.352474	0.176237	+	0.984348i	$0.443607\pi$
$710$	−52.2493	−1.96088
$711$	5.20069	0.195041
$712$	6.72491	0.252027
$713$	−20.1201	−0.753505
$714$	−2.07087	−0.0775004
$715$	89.8592	3.36054
$716$	−18.5426	−0.692970
$717$	−7.75630	−0.289664
$718$	−17.3096	−0.645988
$719$	−25.6432	−0.956329	−0.478165	−	0.878270i	$-0.658698\pi$
$719$	−25.6432	−0.956329	−0.478165	+	0.878270i	$0.658698\pi$
$720$	3.58712	0.133684
$721$	−4.30310	−0.160256
$722$	−0.133717	−0.00497644
$723$	−2.52091	−0.0937536
$724$	−5.78630	−0.215046
$725$	−21.9814	−0.816368
$726$	9.75732	0.362128
$727$	8.94719	0.331833	0.165917	−	0.986140i	$-0.446942\pi$
$727$	8.94719	0.331833	0.165917	+	0.986140i	$0.446942\pi$
$728$	−11.3863	−0.422005
$729$	1.00000	0.0370370
$730$	−44.4039	−1.64346
$731$	10.3374	0.382341
$732$	1.71984	0.0635669
$733$	33.9214	1.25291	0.626457	−	0.779456i	$-0.284504\pi$
$733$	33.9214	1.25291	0.626457	+	0.779456i	$0.284504\pi$
$734$	−22.2404	−0.820910
$735$	9.72645	0.358766
$736$	−7.83990	−0.288982
$737$	35.7936	1.31847
$738$	0.724227	0.0266592
$739$	−31.5077	−1.15903	−0.579515	−	0.814962i	$-0.696758\pi$
$739$	−31.5077	−1.15903	−0.579515	+	0.814962i	$0.696758\pi$
$740$	−40.3250	−1.48237
$741$	24.0508	0.883530
$742$	3.55801	0.130619
$743$	45.3892	1.66517	0.832584	−	0.553899i	$-0.186861\pi$
$743$	45.3892	1.66517	0.832584	+	0.553899i	$0.186861\pi$
$744$	−2.56638	−0.0940880
$745$	86.9104	3.18415
$746$	−31.5462	−1.15499
$747$	8.94601	0.327317
$748$	−4.55602	−0.166585
$749$	−11.3915	−0.416235
$750$	10.2859	0.375589
$751$	37.8500	1.38117	0.690584	−	0.723252i	$-0.257354\pi$
$751$	37.8500	1.38117	0.690584	+	0.723252i	$0.257354\pi$
$752$	−0.730276	−0.0266304
$753$	4.01694	0.146386
$754$	−15.3621	−0.559455
$755$	17.4051	0.633437
$756$	2.07087	0.0753169
$757$	36.7690	1.33639	0.668195	−	0.743986i	$-0.267067\pi$
$757$	36.7690	1.33639	0.668195	+	0.743986i	$0.267067\pi$
$758$	−20.0362	−0.727746
$759$	35.7187	1.29651
$760$	−15.6908	−0.569166
$761$	−29.0255	−1.05218	−0.526088	−	0.850430i	$-0.676342\pi$
$761$	−29.0255	−1.05218	−0.526088	+	0.850430i	$0.676342\pi$
$762$	13.5868	0.492198
$763$	18.6259	0.674303
$764$	11.4802	0.415339
$765$	3.58712	0.129693
$766$	−36.2909	−1.31124
$767$	5.49833	0.198533
$768$	−1.00000	−0.0360844
$769$	44.7653	1.61428	0.807140	−	0.590360i	$-0.201014\pi$
$769$	44.7653	1.61428	0.807140	+	0.590360i	$0.201014\pi$
$770$	−33.8443	−1.21966
$771$	28.2401	1.01704
$772$	7.19848	0.259079
$773$	−19.2931	−0.693924	−0.346962	−	0.937879i	$-0.612787\pi$
$773$	−19.2931	−0.693924	−0.346962	+	0.937879i	$0.612787\pi$
$774$	−10.3374	−0.371569
$775$	−20.1909	−0.725278
$776$	15.7797	0.566459
$777$	−23.2799	−0.835161
$778$	30.0011	1.07559
$779$	−3.16792	−0.113503
$780$	19.7232	0.706203
$781$	−66.3620	−2.37462
$782$	−7.83990	−0.280354
$783$	2.79396	0.0998481
$784$	−2.71149	−0.0968389
$785$	52.7588	1.88304
$786$	−3.82871	−0.136566
$787$	5.63942	0.201023	0.100512	−	0.994936i	$-0.467952\pi$
$787$	5.63942	0.201023	0.100512	+	0.994936i	$0.467952\pi$
$788$	−0.526011	−0.0187384
$789$	4.41162	0.157058
$790$	−18.6555	−0.663734
$791$	−39.8372	−1.41645
$792$	4.55602	0.161891
$793$	9.45621	0.335800
$794$	−0.828924	−0.0294174
$795$	−6.16311	−0.218583
$796$	−24.8565	−0.881014
$797$	−4.14399	−0.146788	−0.0733938	−	0.997303i	$-0.523383\pi$
$797$	−4.14399	−0.146788	−0.0733938	+	0.997303i	$0.523383\pi$
$798$	−9.05843	−0.320665
$799$	−0.730276	−0.0258353
$800$	−7.86746	−0.278157
$801$	−6.72491	−0.237613
$802$	1.67975	0.0593142
$803$	−56.3975	−1.99023
$804$	7.85633	0.277071
$805$	−58.2385	−2.05264
$806$	−14.1108	−0.497031
$807$	23.2959	0.820054
$808$	14.4583	0.508640
$809$	−8.80361	−0.309518	−0.154759	−	0.987952i	$-0.549460\pi$
$809$	−8.80361	−0.309518	−0.154759	+	0.987952i	$0.549460\pi$
$810$	−3.58712	−0.126039
$811$	−5.23877	−0.183958	−0.0919791	−	0.995761i	$-0.529319\pi$
$811$	−5.23877	−0.183958	−0.0919791	+	0.995761i	$0.529319\pi$
$812$	5.78594	0.203047
$813$	−28.3262	−0.993444
$814$	−51.2169	−1.79515
$815$	41.0995	1.43965
$816$	−1.00000	−0.0350070
$817$	45.2178	1.58197
$818$	7.82390	0.273556
$819$	11.3863	0.397871
$820$	−2.59789	−0.0907224
$821$	30.5111	1.06484	0.532422	−	0.846479i	$-0.321282\pi$
$821$	30.5111	1.06484	0.532422	+	0.846479i	$0.321282\pi$
$822$	12.0238	0.419378
$823$	24.9661	0.870262	0.435131	−	0.900367i	$-0.356702\pi$
$823$	24.9661	0.870262	0.435131	+	0.900367i	$0.356702\pi$
$824$	−2.07792	−0.0723876
$825$	35.8443	1.24794
$826$	−2.07087	−0.0720548
$827$	54.2217	1.88547	0.942736	−	0.333539i	$-0.108243\pi$
$827$	54.2217	1.88547	0.942736	+	0.333539i	$0.108243\pi$
$828$	7.83990	0.272455
$829$	10.7849	0.374575	0.187287	−	0.982305i	$-0.440030\pi$
$829$	10.7849	0.374575	0.187287	+	0.982305i	$0.440030\pi$
$830$	−32.0904	−1.11388
$831$	−25.5118	−0.884996
$832$	−5.49833	−0.190620
$833$	−2.71149	−0.0939476
$834$	19.1771	0.664049
$835$	−1.25472	−0.0434213
$836$	−19.9290	−0.689259
$837$	2.56638	0.0887070
$838$	−1.90373	−0.0657631
$839$	7.63899	0.263727	0.131864	−	0.991268i	$-0.457904\pi$
$839$	7.63899	0.263727	0.131864	+	0.991268i	$0.457904\pi$
$840$	−7.42847	−0.256307
$841$	−21.1938	−0.730820
$842$	−29.6057	−1.02028
$843$	−0.00124065	−4.27304e−5 0
$844$	−5.81345	−0.200107
$845$	61.8119	2.12639
$846$	0.730276	0.0251074
$847$	−20.2062	−0.694292
$848$	1.71812	0.0590005
$849$	14.2851	0.490264
$850$	−7.86746	−0.269852
$851$	−88.1328	−3.02115
$852$	−14.5658	−0.499015
$853$	51.3621	1.75860	0.879302	−	0.476265i	$-0.158010\pi$
$853$	51.3621	1.75860	0.879302	+	0.476265i	$0.158010\pi$
$854$	−3.56156	−0.121874
$855$	15.6908	0.536615
$856$	−5.50080	−0.188013
$857$	33.2686	1.13643	0.568217	−	0.822879i	$-0.307633\pi$
$857$	33.2686	1.13643	0.568217	+	0.822879i	$0.307633\pi$
$858$	25.0505	0.855210
$859$	42.1122	1.43685	0.718424	−	0.695605i	$-0.244864\pi$
$859$	42.1122	1.43685	0.718424	+	0.695605i	$0.244864\pi$
$860$	37.0814	1.26447
$861$	−1.49978	−0.0511124
$862$	−10.0968	−0.343900
$863$	34.0570	1.15931	0.579657	−	0.814861i	$-0.303187\pi$
$863$	34.0570	1.15931	0.579657	+	0.814861i	$0.303187\pi$
$864$	1.00000	0.0340207
$865$	−44.4934	−1.51282
$866$	3.39173	0.115256
$867$	−1.00000	−0.0339618
$868$	5.31464	0.180391
$869$	−23.6945	−0.803780
$870$	−10.0223	−0.339788
$871$	43.1966	1.46366
$872$	8.99423	0.304583
$873$	−15.7797	−0.534062
$874$	−34.2934	−1.15999
$875$	−21.3009	−0.720101
$876$	−12.3787	−0.418237
$877$	−50.2619	−1.69722	−0.848612	−	0.529016i	$-0.822561\pi$
$877$	−50.2619	−1.69722	−0.848612	+	0.529016i	$0.822561\pi$
$878$	−20.4111	−0.688840
$879$	−25.8301	−0.871228
$880$	−16.3430	−0.550923
$881$	−49.1525	−1.65599	−0.827994	−	0.560737i	$-0.810518\pi$
$881$	−49.1525	−1.65599	−0.827994	+	0.560737i	$0.810518\pi$
$882$	2.71149	0.0913006
$883$	49.0225	1.64974	0.824870	−	0.565322i	$-0.191248\pi$
$883$	49.0225	1.64974	0.824870	+	0.565322i	$0.191248\pi$
$884$	−5.49833	−0.184929
$885$	3.58712	0.120580
$886$	−12.4200	−0.417258
$887$	−25.3497	−0.851161	−0.425581	−	0.904921i	$-0.639930\pi$
$887$	−25.3497	−0.851161	−0.425581	+	0.904921i	$0.639930\pi$
$888$	−11.2416	−0.377243
$889$	−28.1365	−0.943669
$890$	24.1231	0.808608
$891$	−4.55602	−0.152632
$892$	10.7245	0.359082
$893$	−3.19438	−0.106896
$894$	24.2284	0.810320
$895$	−66.5147	−2.22334
$896$	2.07087	0.0691830
$897$	43.1063	1.43928
$898$	32.8680	1.09682
$899$	7.17036	0.239145
$900$	7.86746	0.262249
$901$	1.71812	0.0572389
$902$	−3.29959	−0.109864
$903$	21.4074	0.712393
$904$	−19.2369	−0.639810
$905$	−20.7562	−0.689958
$906$	4.85210	0.161200
$907$	−1.99195	−0.0661416	−0.0330708	−	0.999453i	$-0.510529\pi$
$907$	−1.99195	−0.0661416	−0.0330708	+	0.999453i	$0.510529\pi$
$908$	−7.37192	−0.244646
$909$	−14.4583	−0.479550
$910$	−40.8442	−1.35397
$911$	42.3133	1.40190	0.700952	−	0.713209i	$-0.252759\pi$
$911$	42.3133	1.40190	0.700952	+	0.713209i	$0.252759\pi$
$912$	−4.37421	−0.144845
$913$	−40.7582	−1.34890
$914$	8.26897	0.273513
$915$	6.16926	0.203950
$916$	29.2261	0.965658
$917$	7.92877	0.261831
$918$	1.00000	0.0330049
$919$	−48.9028	−1.61316	−0.806578	−	0.591128i	$-0.798683\pi$
$919$	−48.9028	−1.61316	−0.806578	+	0.591128i	$0.798683\pi$
$920$	−28.1227	−0.927177
$921$	3.76155	0.123947
$922$	−8.13695	−0.267976
$923$	−80.0874	−2.63611
$924$	−9.43493	−0.310387
$925$	−88.4427	−2.90798
$926$	23.5279	0.773175
$927$	2.07792	0.0682477
$928$	2.79396	0.0917163
$929$	5.59811	0.183668	0.0918341	−	0.995774i	$-0.470727\pi$
$929$	5.59811	0.183668	0.0918341	+	0.995774i	$0.470727\pi$
$930$	−9.20591	−0.301874
$931$	−11.8606	−0.388716
$932$	20.9187	0.685216
$933$	−13.0825	−0.428302
$934$	−32.0031	−1.04717
$935$	−16.3430	−0.534474
$936$	5.49833	0.179718
$937$	27.0752	0.884507	0.442253	−	0.896890i	$-0.354179\pi$
$937$	27.0752	0.884507	0.442253	+	0.896890i	$0.354179\pi$
$938$	−16.2694	−0.531216
$939$	−13.7209	−0.447766
$940$	−2.61959	−0.0854416
$941$	38.3714	1.25087	0.625436	−	0.780275i	$-0.284921\pi$
$941$	38.3714	1.25087	0.625436	+	0.780275i	$0.284921\pi$
$942$	14.7078	0.479207
$943$	−5.67787	−0.184897
$944$	−1.00000	−0.0325472
$945$	7.42847	0.241648
$946$	47.0973	1.53126
$947$	20.1674	0.655353	0.327677	−	0.944790i	$-0.393734\pi$
$947$	20.1674	0.655353	0.327677	+	0.944790i	$0.393734\pi$
$948$	−5.20069	−0.168911
$949$	−68.0621	−2.20939
$950$	−34.4139	−1.11654
$951$	28.1336	0.912294
$952$	2.07087	0.0671173
$953$	−24.9545	−0.808355	−0.404178	−	0.914681i	$-0.632442\pi$
$953$	−24.9545	−0.808355	−0.404178	+	0.914681i	$0.632442\pi$
$954$	−1.71812	−0.0556262
$955$	41.1809	1.33258
$956$	7.75630	0.250857
$957$	−12.7294	−0.411481
$958$	34.0009	1.09852
$959$	−24.8997	−0.804054
$960$	−3.58712	−0.115774
$961$	−24.4137	−0.787539
$962$	−61.8099	−1.99283
$963$	5.50080	0.177261
$964$	2.52091	0.0811930
$965$	25.8218	0.831234
$966$	−16.2354	−0.522366
$967$	23.9707	0.770846	0.385423	−	0.922740i	$-0.374056\pi$
$967$	23.9707	0.770846	0.385423	+	0.922740i	$0.374056\pi$
$968$	−9.75732	−0.313612
$969$	−4.37421	−0.140520
$970$	56.6038	1.81744
$971$	36.5067	1.17155	0.585777	−	0.810472i	$-0.300789\pi$
$971$	36.5067	1.17155	0.585777	+	0.810472i	$0.300789\pi$
$972$	−1.00000	−0.0320750
$973$	−39.7134	−1.27315
$974$	−24.5864	−0.787799
$975$	43.2579	1.38536
$976$	−1.71984	−0.0550506
$977$	−27.2581	−0.872063	−0.436032	−	0.899931i	$-0.643616\pi$
$977$	−27.2581	−0.872063	−0.436032	+	0.899931i	$0.643616\pi$
$978$	11.4575	0.366370
$979$	30.6388	0.979221
$980$	−9.72645	−0.310700
$981$	−8.99423	−0.287164
$982$	6.40386	0.204355
$983$	3.67125	0.117095	0.0585474	−	0.998285i	$-0.481353\pi$
$983$	3.67125	0.117095	0.0585474	+	0.998285i	$0.481353\pi$
$984$	−0.724227	−0.0230875
$985$	−1.88687	−0.0601206
$986$	2.79396	0.0889779
$987$	−1.51231	−0.0481373
$988$	−24.0508	−0.765159
$989$	81.0439	2.57705
$990$	16.3430	0.519415
$991$	25.9358	0.823879	0.411939	−	0.911211i	$-0.364852\pi$
$991$	25.9358	0.823879	0.411939	+	0.911211i	$0.364852\pi$
$992$	2.56638	0.0814826
$993$	7.34579	0.233112
$994$	30.1639	0.956739
$995$	−89.1632	−2.82666
$996$	−8.94601	−0.283465
$997$	−45.3563	−1.43645	−0.718225	−	0.695811i	$-0.755045\pi$
$997$	−45.3563	−1.43645	−0.718225	+	0.695811i	$0.755045\pi$
$998$	23.3733	0.739868
$999$	11.2416	0.355668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.x.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.x.1.9	✓	10	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.58712 q^{5} +1.00000 q^{6} -2.07087 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.58712 q^{5} +1.00000 q^{6} -2.07087 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.58712 q^{10} -4.55602 q^{11} -1.00000 q^{12} -5.49833 q^{13} +2.07087 q^{14} -3.58712 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.37421 q^{19} +3.58712 q^{20} +2.07087 q^{21} +4.55602 q^{22} +7.83990 q^{23} +1.00000 q^{24} +7.86746 q^{25} +5.49833 q^{26} -1.00000 q^{27} -2.07087 q^{28} -2.79396 q^{29} +3.58712 q^{30} -2.56638 q^{31} -1.00000 q^{32} +4.55602 q^{33} -1.00000 q^{34} -7.42847 q^{35} +1.00000 q^{36} -11.2416 q^{37} -4.37421 q^{38} +5.49833 q^{39} -3.58712 q^{40} -0.724227 q^{41} -2.07087 q^{42} +10.3374 q^{43} -4.55602 q^{44} +3.58712 q^{45} -7.83990 q^{46} -0.730276 q^{47} -1.00000 q^{48} -2.71149 q^{49} -7.86746 q^{50} -1.00000 q^{51} -5.49833 q^{52} +1.71812 q^{53} +1.00000 q^{54} -16.3430 q^{55} +2.07087 q^{56} -4.37421 q^{57} +2.79396 q^{58} -1.00000 q^{59} -3.58712 q^{60} -1.71984 q^{61} +2.56638 q^{62} -2.07087 q^{63} +1.00000 q^{64} -19.7232 q^{65} -4.55602 q^{66} -7.85633 q^{67} +1.00000 q^{68} -7.83990 q^{69} +7.42847 q^{70} +14.5658 q^{71} -1.00000 q^{72} +12.3787 q^{73} +11.2416 q^{74} -7.86746 q^{75} +4.37421 q^{76} +9.43493 q^{77} -5.49833 q^{78} +5.20069 q^{79} +3.58712 q^{80} +1.00000 q^{81} +0.724227 q^{82} +8.94601 q^{83} +2.07087 q^{84} +3.58712 q^{85} -10.3374 q^{86} +2.79396 q^{87} +4.55602 q^{88} -6.72491 q^{89} -3.58712 q^{90} +11.3863 q^{91} +7.83990 q^{92} +2.56638 q^{93} +0.730276 q^{94} +15.6908 q^{95} +1.00000 q^{96} -15.7797 q^{97} +2.71149 q^{98} -4.55602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more