LMFDB - Embedded newform 595.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [595,2,Mod(1,595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(595, 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("595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.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:	$4.75109892027$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.273891$ of defining polynomial
Character	$\chi$	$=$	595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27389 q^{2} -2.37720 q^{3} -0.377203 q^{4} -1.00000 q^{5} +3.02830 q^{6} +1.00000 q^{7} +3.02830 q^{8} +2.65109 q^{9} +O(q^{10})$	\(q-1.27389 q^{2} -2.37720 q^{3} -0.377203 q^{4} -1.00000 q^{5} +3.02830 q^{6} +1.00000 q^{7} +3.02830 q^{8} +2.65109 q^{9} +1.27389 q^{10} -3.00000 q^{11} +0.896688 q^{12} +3.02830 q^{13} -1.27389 q^{14} +2.37720 q^{15} -3.10331 q^{16} +1.00000 q^{17} -3.37720 q^{18} +3.75441 q^{19} +0.377203 q^{20} -2.37720 q^{21} +3.82167 q^{22} +7.60437 q^{23} -7.19887 q^{24} +1.00000 q^{25} -3.85772 q^{26} +0.829422 q^{27} -0.377203 q^{28} -8.27389 q^{29} -3.02830 q^{30} -5.40550 q^{31} -2.10331 q^{32} +7.13161 q^{33} -1.27389 q^{34} -1.00000 q^{35} -1.00000 q^{36} -9.88601 q^{37} -4.78270 q^{38} -7.19887 q^{39} -3.02830 q^{40} -10.1239 q^{41} +3.02830 q^{42} +6.27389 q^{43} +1.13161 q^{44} -2.65109 q^{45} -9.68714 q^{46} -6.13161 q^{47} +7.37720 q^{48} +1.00000 q^{49} -1.27389 q^{50} -2.37720 q^{51} -1.14228 q^{52} -14.5011 q^{53} -1.05659 q^{54} +3.00000 q^{55} +3.02830 q^{56} -8.92498 q^{57} +10.5400 q^{58} +9.43380 q^{59} -0.896688 q^{60} +3.22717 q^{61} +6.88601 q^{62} +2.65109 q^{63} +8.88601 q^{64} -3.02830 q^{65} -9.08489 q^{66} -5.02055 q^{67} -0.377203 q^{68} -18.0771 q^{69} +1.27389 q^{70} +5.22717 q^{71} +8.02830 q^{72} +15.9533 q^{73} +12.5937 q^{74} -2.37720 q^{75} -1.41617 q^{76} -3.00000 q^{77} +9.17058 q^{78} -12.0205 q^{79} +3.10331 q^{80} -9.92498 q^{81} +12.8967 q^{82} -3.44447 q^{83} +0.896688 q^{84} -1.00000 q^{85} -7.99225 q^{86} +19.6687 q^{87} -9.08489 q^{88} +5.54778 q^{89} +3.37720 q^{90} +3.02830 q^{91} -2.86839 q^{92} +12.8500 q^{93} +7.81100 q^{94} -3.75441 q^{95} +5.00000 q^{96} +3.65109 q^{97} -1.27389 q^{98} -7.95328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9	\( 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - 9 q^{11} + 6 q^{12} - 3 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} - 4 q^{20} - 2 q^{21} + 6 q^{22} - 5 q^{23} - 11 q^{24} + 3 q^{25} + 2 q^{26} + q^{27} + 4 q^{28} - 23 q^{29} + 3 q^{30} + q^{31} - 3 q^{32} + 6 q^{33} - 2 q^{34} - 3 q^{35} - 3 q^{36} - 4 q^{37} + 8 q^{38} - 11 q^{39} + 3 q^{40} - 11 q^{41} - 3 q^{42} + 17 q^{43} - 12 q^{44} - q^{45} - 14 q^{46} - 3 q^{47} + 17 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 17 q^{52} - 19 q^{53} + 21 q^{54} + 9 q^{55} - 3 q^{56} - 18 q^{57} + 24 q^{58} - q^{59} - 6 q^{60} - 13 q^{61} - 5 q^{62} + q^{63} + q^{64} + 3 q^{65} + 9 q^{66} + q^{67} + 4 q^{68} - 14 q^{69} + 2 q^{70} - 7 q^{71} + 12 q^{72} + 27 q^{73} - 19 q^{74} - 2 q^{75} - 16 q^{76} - 9 q^{77} + 29 q^{78} - 20 q^{79} + 6 q^{80} - 21 q^{81} + 42 q^{82} - 10 q^{83} + 6 q^{84} - 3 q^{85} - 20 q^{86} + 11 q^{87} + 9 q^{88} + 13 q^{89} + 5 q^{90} - 3 q^{91} - 24 q^{92} + 21 q^{93} - 11 q^{94} - q^{95} + 15 q^{96} + 4 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 - 9 * q^11 + 6 * q^12 - 3 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 + 3 * q^17 - 5 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 6 * q^22 - 5 * q^23 - 11 * q^24 + 3 * q^25 + 2 * q^26 + q^27 + 4 * q^28 - 23 * q^29 + 3 * q^30 + q^31 - 3 * q^32 + 6 * q^33 - 2 * q^34 - 3 * q^35 - 3 * q^36 - 4 * q^37 + 8 * q^38 - 11 * q^39 + 3 * q^40 - 11 * q^41 - 3 * q^42 + 17 * q^43 - 12 * q^44 - q^45 - 14 * q^46 - 3 * q^47 + 17 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 17 * q^52 - 19 * q^53 + 21 * q^54 + 9 * q^55 - 3 * q^56 - 18 * q^57 + 24 * q^58 - q^59 - 6 * q^60 - 13 * q^61 - 5 * q^62 + q^63 + q^64 + 3 * q^65 + 9 * q^66 + q^67 + 4 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^71 + 12 * q^72 + 27 * q^73 - 19 * q^74 - 2 * q^75 - 16 * q^76 - 9 * q^77 + 29 * q^78 - 20 * q^79 + 6 * q^80 - 21 * q^81 + 42 * q^82 - 10 * q^83 + 6 * q^84 - 3 * q^85 - 20 * q^86 + 11 * q^87 + 9 * q^88 + 13 * q^89 + 5 * q^90 - 3 * q^91 - 24 * q^92 + 21 * q^93 - 11 * q^94 - q^95 + 15 * q^96 + 4 * q^97 - 2 * q^98 - 3 * 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 $

$2$	−1.27389	−0.900777	−0.450388	−	0.892833i	$-0.648714\pi$
$2$	−1.27389	−0.900777	−0.450388	+	0.892833i	$0.648714\pi$
$3$	−2.37720	−1.37248	−0.686239	−	0.727376i	$-0.740740\pi$
$3$	−2.37720	−1.37248	−0.686239	+	0.727376i	$0.740740\pi$
$4$	−0.377203	−0.188601
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.02830	1.23630
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.02830	1.07066
$9$	2.65109	0.883698
$10$	1.27389	0.402840
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0.896688	0.258851
$13$	3.02830	0.839898	0.419949	−	0.907548i	$-0.362048\pi$
$13$	3.02830	0.839898	0.419949	+	0.907548i	$0.362048\pi$
$14$	−1.27389	−0.340462
$15$	2.37720	0.613791
$16$	−3.10331	−0.775828
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.37720	−0.796014
$19$	3.75441	0.861320	0.430660	−	0.902514i	$-0.358281\pi$
$19$	3.75441	0.861320	0.430660	+	0.902514i	$0.358281\pi$
$20$	0.377203	0.0843451
$21$	−2.37720	−0.518748
$22$	3.82167	0.814783
$23$	7.60437	1.58562	0.792811	−	0.609468i	$-0.208617\pi$
$23$	7.60437	1.58562	0.792811	+	0.609468i	$0.208617\pi$
$24$	−7.19887	−1.46946
$25$	1.00000	0.200000
$26$	−3.85772	−0.756561
$27$	0.829422	0.159622
$28$	−0.377203	−0.0712846
$29$	−8.27389	−1.53642	−0.768211	−	0.640196i	$-0.778853\pi$
$29$	−8.27389	−1.53642	−0.768211	+	0.640196i	$0.778853\pi$
$30$	−3.02830	−0.552889
$31$	−5.40550	−0.970856	−0.485428	−	0.874277i	$-0.661336\pi$
$31$	−5.40550	−0.970856	−0.485428	+	0.874277i	$0.661336\pi$
$32$	−2.10331	−0.371817
$33$	7.13161	1.24145
$34$	−1.27389	−0.218470
$35$	−1.00000	−0.169031
$36$	−1.00000	−0.166667
$37$	−9.88601	−1.62525	−0.812625	−	0.582786i	$-0.801962\pi$
$37$	−9.88601	−1.62525	−0.812625	+	0.582786i	$0.801962\pi$
$38$	−4.78270	−0.775857
$39$	−7.19887	−1.15274
$40$	−3.02830	−0.478816
$41$	−10.1239	−1.58108	−0.790541	−	0.612410i	$-0.790200\pi$
$41$	−10.1239	−1.58108	−0.790541	+	0.612410i	$0.790200\pi$
$42$	3.02830	0.467276
$43$	6.27389	0.956759	0.478380	−	0.878153i	$-0.341224\pi$
$43$	6.27389	0.956759	0.478380	+	0.878153i	$0.341224\pi$
$44$	1.13161	0.170596
$45$	−2.65109	−0.395202
$46$	−9.68714	−1.42829
$47$	−6.13161	−0.894387	−0.447194	−	0.894437i	$-0.647576\pi$
$47$	−6.13161	−0.894387	−0.447194	+	0.894437i	$0.647576\pi$
$48$	7.37720	1.06481
$49$	1.00000	0.142857
$50$	−1.27389	−0.180155
$51$	−2.37720	−0.332875
$52$	−1.14228	−0.158406
$53$	−14.5011	−1.99187	−0.995937	−	0.0900529i	$-0.971296\pi$
$53$	−14.5011	−1.99187	−0.995937	+	0.0900529i	$0.971296\pi$
$54$	−1.05659	−0.143784
$55$	3.00000	0.404520
$56$	3.02830	0.404673
$57$	−8.92498	−1.18214
$58$	10.5400	1.38397
$59$	9.43380	1.22818	0.614088	−	0.789238i	$-0.289524\pi$
$59$	9.43380	1.22818	0.614088	+	0.789238i	$0.289524\pi$
$60$	−0.896688	−0.115762
$61$	3.22717	0.413197	0.206598	−	0.978426i	$-0.433761\pi$
$61$	3.22717	0.413197	0.206598	+	0.978426i	$0.433761\pi$
$62$	6.88601	0.874525
$63$	2.65109	0.334006
$64$	8.88601	1.11075
$65$	−3.02830	−0.375614
$66$	−9.08489	−1.11827
$67$	−5.02055	−0.613357	−0.306679	−	0.951813i	$-0.599218\pi$
$67$	−5.02055	−0.613357	−0.306679	+	0.951813i	$0.599218\pi$
$68$	−0.377203	−0.0457426
$69$	−18.0771	−2.17623
$70$	1.27389	0.152259
$71$	5.22717	0.620351	0.310176	−	0.950679i	$-0.399612\pi$
$71$	5.22717	0.620351	0.310176	+	0.950679i	$0.399612\pi$
$72$	8.02830	0.946144
$73$	15.9533	1.86719	0.933595	−	0.358330i	$-0.116654\pi$
$73$	15.9533	1.86719	0.933595	+	0.358330i	$0.116654\pi$
$74$	12.5937	1.46399
$75$	−2.37720	−0.274496
$76$	−1.41617	−0.162446
$77$	−3.00000	−0.341882
$78$	9.17058	1.03836
$79$	−12.0205	−1.35242	−0.676209	−	0.736710i	$-0.736378\pi$
$79$	−12.0205	−1.35242	−0.676209	+	0.736710i	$0.736378\pi$
$80$	3.10331	0.346961
$81$	−9.92498	−1.10278
$82$	12.8967	1.42420
$83$	−3.44447	−0.378080	−0.189040	−	0.981969i	$-0.560538\pi$
$83$	−3.44447	−0.378080	−0.189040	+	0.981969i	$0.560538\pi$
$84$	0.896688	0.0978366
$85$	−1.00000	−0.108465
$86$	−7.99225	−0.861826
$87$	19.6687	2.10871
$88$	−9.08489	−0.968452
$89$	5.54778	0.588064	0.294032	−	0.955796i	$-0.405003\pi$
$89$	5.54778	0.588064	0.294032	+	0.955796i	$0.405003\pi$
$90$	3.37720	0.355988
$91$	3.02830	0.317452
$92$	−2.86839	−0.299050
$93$	12.8500	1.33248
$94$	7.81100	0.805643
$95$	−3.75441	−0.385194
$96$	5.00000	0.510310
$97$	3.65109	0.370712	0.185356	−	0.982671i	$-0.440656\pi$
$97$	3.65109	0.370712	0.185356	+	0.982671i	$0.440656\pi$
$98$	−1.27389	−0.128682
$99$	−7.95328	−0.799335
$100$	−0.377203	−0.0377203
$101$	−6.23492	−0.620398	−0.310199	−	0.950672i	$-0.600396\pi$
$101$	−6.23492	−0.620398	−0.310199	+	0.950672i	$0.600396\pi$
$102$	3.02830	0.299846
$103$	−0.444469	−0.0437948	−0.0218974	−	0.999760i	$-0.506971\pi$
$103$	−0.444469	−0.0437948	−0.0218974	+	0.999760i	$0.506971\pi$
$104$	9.17058	0.899249
$105$	2.37720	0.231991
$106$	18.4728	1.79423
$107$	−1.80113	−0.174121	−0.0870607	−	0.996203i	$-0.527747\pi$
$107$	−1.80113	−0.174121	−0.0870607	+	0.996203i	$0.527747\pi$
$108$	−0.312860	−0.0301050
$109$	−13.4055	−1.28401	−0.642007	−	0.766699i	$-0.721898\pi$
$109$	−13.4055	−1.28401	−0.642007	+	0.766699i	$0.721898\pi$
$110$	−3.82167	−0.364382
$111$	23.5011	2.23062
$112$	−3.10331	−0.293235
$113$	−1.23492	−0.116172	−0.0580858	−	0.998312i	$-0.518500\pi$
$113$	−1.23492	−0.116172	−0.0580858	+	0.998312i	$0.518500\pi$
$114$	11.3695	1.06485
$115$	−7.60437	−0.709111
$116$	3.12094	0.289772
$117$	8.02830	0.742216
$118$	−12.0176	−1.10631
$119$	1.00000	0.0916698
$120$	7.19887	0.657164
$121$	−2.00000	−0.181818
$122$	−4.11106	−0.372198
$123$	24.0665	2.17000
$124$	2.03897	0.183105
$125$	−1.00000	−0.0894427
$126$	−3.37720	−0.300865
$127$	3.90444	0.346463	0.173231	−	0.984881i	$-0.444579\pi$
$127$	3.90444	0.346463	0.173231	+	0.984881i	$0.444579\pi$
$128$	−7.11319	−0.628723
$129$	−14.9143	−1.31313
$130$	3.85772	0.338344
$131$	−14.6404	−1.27914	−0.639570	−	0.768733i	$-0.720887\pi$
$131$	−14.6404	−1.27914	−0.639570	+	0.768733i	$0.720887\pi$
$132$	−2.69006	−0.234140
$133$	3.75441	0.325548
$134$	6.39563	0.552498
$135$	−0.829422	−0.0713853
$136$	3.02830	0.259674
$137$	−22.1415	−1.89167	−0.945837	−	0.324641i	$-0.894756\pi$
$137$	−22.1415	−1.89167	−0.945837	+	0.324641i	$0.894756\pi$
$138$	23.0283	1.96030
$139$	−16.3588	−1.38753	−0.693767	−	0.720200i	$-0.744050\pi$
$139$	−16.3588	−1.38753	−0.693767	+	0.720200i	$0.744050\pi$
$140$	0.377203	0.0318795
$141$	14.5761	1.22753
$142$	−6.65884	−0.558798
$143$	−9.08489	−0.759717
$144$	−8.22717	−0.685598
$145$	8.27389	0.687109
$146$	−20.3227	−1.68192
$147$	−2.37720	−0.196068
$148$	3.72903	0.306525
$149$	−2.17833	−0.178456	−0.0892278	−	0.996011i	$-0.528440\pi$
$149$	−2.17833	−0.178456	−0.0892278	+	0.996011i	$0.528440\pi$
$150$	3.02830	0.247259
$151$	22.0021	1.79051	0.895254	−	0.445557i	$-0.146994\pi$
$151$	22.0021	1.79051	0.895254	+	0.445557i	$0.146994\pi$
$152$	11.3695	0.922184
$153$	2.65109	0.214328
$154$	3.82167	0.307959
$155$	5.40550	0.434180
$156$	2.71544	0.217409
$157$	5.28376	0.421690	0.210845	−	0.977519i	$-0.432378\pi$
$157$	5.28376	0.421690	0.210845	+	0.977519i	$0.432378\pi$
$158$	15.3129	1.21823
$159$	34.4720	2.73380
$160$	2.10331	0.166281
$161$	7.60437	0.599309
$162$	12.6433	0.993355
$163$	−2.32836	−0.182371	−0.0911856	−	0.995834i	$-0.529066\pi$
$163$	−2.32836	−0.182371	−0.0911856	+	0.995834i	$0.529066\pi$
$164$	3.81875	0.298194
$165$	−7.13161	−0.555195
$166$	4.38788	0.340565
$167$	−2.04884	−0.158544	−0.0792721	−	0.996853i	$-0.525260\pi$
$167$	−2.04884	−0.158544	−0.0792721	+	0.996853i	$0.525260\pi$
$168$	−7.19887	−0.555405
$169$	−3.82942	−0.294571
$170$	1.27389	0.0977029
$171$	9.95328	0.761146
$172$	−2.36653	−0.180446
$173$	−6.51173	−0.495078	−0.247539	−	0.968878i	$-0.579622\pi$
$173$	−6.51173	−0.495078	−0.247539	+	0.968878i	$0.579622\pi$
$174$	−25.0558	−1.89947
$175$	1.00000	0.0755929
$176$	9.30994	0.701763
$177$	−22.4260	−1.68564
$178$	−7.06727	−0.529714
$179$	−11.2915	−0.843967	−0.421984	−	0.906603i	$-0.638666\pi$
$179$	−11.2915	−0.843967	−0.421984	+	0.906603i	$0.638666\pi$
$180$	1.00000	0.0745356
$181$	4.08489	0.303627	0.151814	−	0.988409i	$-0.451489\pi$
$181$	4.08489	0.303627	0.151814	+	0.988409i	$0.451489\pi$
$182$	−3.85772	−0.285953
$183$	−7.67164	−0.567104
$184$	23.0283	1.69767
$185$	9.88601	0.726834
$186$	−16.3695	−1.20027
$187$	−3.00000	−0.219382
$188$	2.31286	0.168683
$189$	0.829422	0.0603316
$190$	4.78270	0.346974
$191$	−17.1882	−1.24369	−0.621847	−	0.783139i	$-0.713618\pi$
$191$	−17.1882	−1.24369	−0.621847	+	0.783139i	$0.713618\pi$
$192$	−21.1239	−1.52448
$193$	5.61505	0.404180	0.202090	−	0.979367i	$-0.435227\pi$
$193$	5.61505	0.404180	0.202090	+	0.979367i	$0.435227\pi$
$194$	−4.65109	−0.333929
$195$	7.19887	0.515522
$196$	−0.377203	−0.0269431
$197$	−17.2710	−1.23051	−0.615253	−	0.788330i	$-0.710946\pi$
$197$	−17.2710	−1.23051	−0.615253	+	0.788330i	$0.710946\pi$
$198$	10.1316	0.720022
$199$	17.4466	1.23676	0.618378	−	0.785881i	$-0.287790\pi$
$199$	17.4466	1.23676	0.618378	+	0.785881i	$0.287790\pi$
$200$	3.02830	0.214133
$201$	11.9349	0.841820
$202$	7.94261	0.558840
$203$	−8.27389	−0.580713
$204$	0.896688	0.0627807
$205$	10.1239	0.707081
$206$	0.566205	0.0394493
$207$	20.1599	1.40121
$208$	−9.39775	−0.651617
$209$	−11.2632	−0.779093
$210$	−3.02830	−0.208972
$211$	−12.8422	−0.884095	−0.442047	−	0.896992i	$-0.645748\pi$
$211$	−12.8422	−0.884095	−0.442047	+	0.896992i	$0.645748\pi$
$212$	5.46984	0.375670
$213$	−12.4260	−0.851419
$214$	2.29444	0.156844
$215$	−6.27389	−0.427876
$216$	2.51173	0.170902
$217$	−5.40550	−0.366949
$218$	17.0771	1.15661
$219$	−37.9242	−2.56268
$220$	−1.13161	−0.0762930
$221$	3.02830	0.203705
$222$	−29.9378	−2.00929
$223$	−5.15215	−0.345014	−0.172507	−	0.985008i	$-0.555187\pi$
$223$	−5.15215	−0.345014	−0.172507	+	0.985008i	$0.555187\pi$
$224$	−2.10331	−0.140533
$225$	2.65109	0.176740
$226$	1.57315	0.104645
$227$	−10.3665	−0.688051	−0.344025	−	0.938960i	$-0.611791\pi$
$227$	−10.3665	−0.688051	−0.344025	+	0.938960i	$0.611791\pi$
$228$	3.36653	0.222954
$229$	−1.41617	−0.0935833	−0.0467917	−	0.998905i	$-0.514900\pi$
$229$	−1.41617	−0.0935833	−0.0467917	+	0.998905i	$0.514900\pi$
$230$	9.68714	0.638751
$231$	7.13161	0.469225
$232$	−25.0558	−1.64499
$233$	12.9632	0.849244	0.424622	−	0.905371i	$-0.360407\pi$
$233$	12.9632	0.849244	0.424622	+	0.905371i	$0.360407\pi$
$234$	−10.2272	−0.668571
$235$	6.13161	0.399982
$236$	−3.55845	−0.231636
$237$	28.5753	1.85616
$238$	−1.27389	−0.0825741
$239$	18.7926	1.21559	0.607795	−	0.794094i	$-0.292054\pi$
$239$	18.7926	1.21559	0.607795	+	0.794094i	$0.292054\pi$
$240$	−7.37720	−0.476196
$241$	−4.45997	−0.287292	−0.143646	−	0.989629i	$-0.545883\pi$
$241$	−4.45997	−0.287292	−0.143646	+	0.989629i	$0.545883\pi$
$242$	2.54778	0.163778
$243$	21.1054	1.35391
$244$	−1.21730	−0.0779295
$245$	−1.00000	−0.0638877
$246$	−30.6580	−1.95469
$247$	11.3695	0.723421
$248$	−16.3695	−1.03946
$249$	8.18820	0.518906
$250$	1.27389	0.0805679
$251$	−17.1415	−1.08196	−0.540980	−	0.841035i	$-0.681947\pi$
$251$	−17.1415	−1.08196	−0.540980	+	0.841035i	$0.681947\pi$
$252$	−1.00000	−0.0629941
$253$	−22.8131	−1.43425
$254$	−4.97383	−0.312086
$255$	2.37720	0.148866
$256$	−8.71061	−0.544413
$257$	7.54778	0.470818	0.235409	−	0.971896i	$-0.424357\pi$
$257$	7.54778	0.470818	0.235409	+	0.971896i	$0.424357\pi$
$258$	18.9992	1.18284
$259$	−9.88601	−0.614287
$260$	1.14228	0.0708413
$261$	−21.9349	−1.35773
$262$	18.6503	1.15222
$263$	−25.6922	−1.58425	−0.792124	−	0.610360i	$-0.791025\pi$
$263$	−25.6922	−1.58425	−0.792124	+	0.610360i	$0.791025\pi$
$264$	21.5966	1.32918
$265$	14.5011	0.890793
$266$	−4.78270	−0.293246
$267$	−13.1882	−0.807105
$268$	1.89376	0.115680
$269$	−26.2632	−1.60130	−0.800648	−	0.599135i	$-0.795511\pi$
$269$	−26.2632	−1.60130	−0.800648	+	0.599135i	$0.795511\pi$
$270$	1.05659	0.0643022
$271$	7.63055	0.463523	0.231761	−	0.972773i	$-0.425551\pi$
$271$	7.63055	0.463523	0.231761	+	0.972773i	$0.425551\pi$
$272$	−3.10331	−0.188166
$273$	−7.19887	−0.435696
$274$	28.2058	1.70398
$275$	−3.00000	−0.180907
$276$	6.81875	0.410440
$277$	9.94048	0.597266	0.298633	−	0.954368i	$-0.403469\pi$
$277$	9.94048	0.597266	0.298633	+	0.954368i	$0.403469\pi$
$278$	20.8393	1.24986
$279$	−14.3305	−0.857944
$280$	−3.02830	−0.180975
$281$	8.82942	0.526719	0.263360	−	0.964698i	$-0.415169\pi$
$281$	8.82942	0.526719	0.263360	+	0.964698i	$0.415169\pi$
$282$	−18.5683	−1.10573
$283$	24.1492	1.43552	0.717761	−	0.696289i	$-0.245167\pi$
$283$	24.1492	1.43552	0.717761	+	0.696289i	$0.245167\pi$
$284$	−1.97170	−0.116999
$285$	8.92498	0.528670
$286$	11.5732	0.684335
$287$	−10.1239	−0.597592
$288$	−5.57608	−0.328574
$289$	1.00000	0.0588235
$290$	−10.5400	−0.618932
$291$	−8.67939	−0.508795
$292$	−6.01762	−0.352155
$293$	24.2966	1.41942	0.709710	−	0.704494i	$-0.248826\pi$
$293$	24.2966	1.41942	0.709710	+	0.704494i	$0.248826\pi$
$294$	3.02830	0.176614
$295$	−9.43380	−0.549257
$296$	−29.9378	−1.74010
$297$	−2.48827	−0.144384
$298$	2.77495	0.160749
$299$	23.0283	1.33176
$300$	0.896688	0.0517703
$301$	6.27389	0.361621
$302$	−28.0283	−1.61285
$303$	14.8217	0.851483
$304$	−11.6511	−0.668236
$305$	−3.22717	−0.184787
$306$	−3.37720	−0.193062
$307$	1.66177	0.0948420	0.0474210	−	0.998875i	$-0.484900\pi$
$307$	1.66177	0.0948420	0.0474210	+	0.998875i	$0.484900\pi$
$308$	1.13161	0.0644794
$309$	1.05659	0.0601074
$310$	−6.88601	−0.391099
$311$	7.29231	0.413509	0.206755	−	0.978393i	$-0.433710\pi$
$311$	7.29231	0.413509	0.206755	+	0.978393i	$0.433710\pi$
$312$	−21.8003	−1.23420
$313$	−29.4047	−1.66205	−0.831026	−	0.556234i	$-0.812246\pi$
$313$	−29.4047	−1.66205	−0.831026	+	0.556234i	$0.812246\pi$
$314$	−6.73094	−0.379849
$315$	−2.65109	−0.149372
$316$	4.53418	0.255068
$317$	−29.8598	−1.67710	−0.838548	−	0.544828i	$-0.816595\pi$
$317$	−29.8598	−1.67710	−0.838548	+	0.544828i	$0.816595\pi$
$318$	−43.9135	−2.46255
$319$	24.8217	1.38975
$320$	−8.88601	−0.496743
$321$	4.28164	0.238978
$322$	−9.68714	−0.539843
$323$	3.75441	0.208901
$324$	3.74373	0.207985
$325$	3.02830	0.167980
$326$	2.96608	0.164276
$327$	31.8676	1.76228
$328$	−30.6580	−1.69281
$329$	−6.13161	−0.338047
$330$	9.08489	0.500107
$331$	−13.3948	−0.736246	−0.368123	−	0.929777i	$-0.620000\pi$
$331$	−13.3948	−0.736246	−0.368123	+	0.929777i	$0.620000\pi$
$332$	1.29926	0.0713063
$333$	−26.2087	−1.43623
$334$	2.61000	0.142813
$335$	5.02055	0.274302
$336$	7.37720	0.402459
$337$	−10.1084	−0.550637	−0.275319	−	0.961353i	$-0.588783\pi$
$337$	−10.1084	−0.550637	−0.275319	+	0.961353i	$0.588783\pi$
$338$	4.87826	0.265343
$339$	2.93566	0.159443
$340$	0.377203	0.0204567
$341$	16.2165	0.878173
$342$	−12.6794	−0.685623
$343$	1.00000	0.0539949
$344$	18.9992	1.02437
$345$	18.0771	0.973240
$346$	8.29524	0.445955
$347$	34.9525	1.87635	0.938174	−	0.346165i	$-0.112516\pi$
$347$	34.9525	1.87635	0.938174	+	0.346165i	$0.112516\pi$
$348$	−7.41910	−0.397705
$349$	−19.4805	−1.04277	−0.521384	−	0.853322i	$-0.674584\pi$
$349$	−19.4805	−1.04277	−0.521384	+	0.853322i	$0.674584\pi$
$350$	−1.27389	−0.0680923
$351$	2.51173	0.134066
$352$	6.30994	0.336321
$353$	6.92206	0.368424	0.184212	−	0.982887i	$-0.441027\pi$
$353$	6.92206	0.368424	0.184212	+	0.982887i	$0.441027\pi$
$354$	28.5683	1.51839
$355$	−5.22717	−0.277429
$356$	−2.09264	−0.110910
$357$	−2.37720	−0.125815
$358$	14.3842	0.760226
$359$	25.5470	1.34832	0.674159	−	0.738586i	$-0.264506\pi$
$359$	25.5470	1.34832	0.674159	+	0.738586i	$0.264506\pi$
$360$	−8.02830	−0.423128
$361$	−4.90444	−0.258128
$362$	−5.20370	−0.273500
$363$	4.75441	0.249542
$364$	−1.14228	−0.0598718
$365$	−15.9533	−0.835033
$366$	9.77283	0.510834
$367$	−9.03042	−0.471384	−0.235692	−	0.971828i	$-0.575736\pi$
$367$	−9.03042	−0.471384	−0.235692	+	0.971828i	$0.575736\pi$
$368$	−23.5987	−1.23017
$369$	−26.8393	−1.39720
$370$	−12.5937	−0.654715
$371$	−14.5011	−0.752858
$372$	−4.84704	−0.251308
$373$	16.6220	0.860654	0.430327	−	0.902673i	$-0.358398\pi$
$373$	16.6220	0.860654	0.430327	+	0.902673i	$0.358398\pi$
$374$	3.82167	0.197614
$375$	2.37720	0.122758
$376$	−18.5683	−0.957588
$377$	−25.0558	−1.29044
$378$	−1.05659	−0.0543453
$379$	1.97170	0.101280	0.0506398	−	0.998717i	$-0.483874\pi$
$379$	1.97170	0.101280	0.0506398	+	0.998717i	$0.483874\pi$
$380$	1.41617	0.0726481
$381$	−9.28164	−0.475513
$382$	21.8959	1.12029
$383$	−11.6044	−0.592956	−0.296478	−	0.955040i	$-0.595812\pi$
$383$	−11.6044	−0.592956	−0.296478	+	0.955040i	$0.595812\pi$
$384$	16.9095	0.862908
$385$	3.00000	0.152894
$386$	−7.15296	−0.364076
$387$	16.6327	0.845486
$388$	−1.37720	−0.0699169
$389$	9.64334	0.488937	0.244468	−	0.969657i	$-0.421387\pi$
$389$	9.64334	0.488937	0.244468	+	0.969657i	$0.421387\pi$
$390$	−9.17058	−0.464370
$391$	7.60437	0.384570
$392$	3.02830	0.152952
$393$	34.8032	1.75559
$394$	22.0013	1.10841
$395$	12.0205	0.604819
$396$	3.00000	0.150756
$397$	−15.1054	−0.758120	−0.379060	−	0.925372i	$-0.623753\pi$
$397$	−15.1054	−0.758120	−0.379060	+	0.925372i	$0.623753\pi$
$398$	−22.2250	−1.11404
$399$	−8.92498	−0.446808
$400$	−3.10331	−0.155166
$401$	−2.66952	−0.133309	−0.0666547	−	0.997776i	$-0.521233\pi$
$401$	−2.66952	−0.133309	−0.0666547	+	0.997776i	$0.521233\pi$
$402$	−15.2037	−0.758292
$403$	−16.3695	−0.815421
$404$	2.35183	0.117008
$405$	9.92498	0.493176
$406$	10.5400	0.523093
$407$	29.6580	1.47009
$408$	−7.19887	−0.356397
$409$	−26.3489	−1.30287	−0.651435	−	0.758705i	$-0.725833\pi$
$409$	−26.3489	−1.30287	−0.651435	+	0.758705i	$0.725833\pi$
$410$	−12.8967	−0.636922
$411$	52.6348	2.59628
$412$	0.167655	0.00825976
$413$	9.43380	0.464207
$414$	−25.6815	−1.26218
$415$	3.44447	0.169082
$416$	−6.36945	−0.312288
$417$	38.8881	1.90436
$418$	14.3481	0.701789
$419$	37.0325	1.80916	0.904579	−	0.426306i	$-0.140185\pi$
$419$	37.0325	1.80916	0.904579	+	0.426306i	$0.140185\pi$
$420$	−0.896688	−0.0437539
$421$	−16.5088	−0.804590	−0.402295	−	0.915510i	$-0.631787\pi$
$421$	−16.5088	−0.804590	−0.402295	+	0.915510i	$0.631787\pi$
$422$	16.3596	0.796372
$423$	−16.2555	−0.790368
$424$	−43.9135	−2.13263
$425$	1.00000	0.0485071
$426$	15.8294	0.766938
$427$	3.22717	0.156174
$428$	0.679390	0.0328395
$429$	21.5966	1.04269
$430$	7.99225	0.385421
$431$	−24.0459	−1.15825	−0.579126	−	0.815238i	$-0.696606\pi$
$431$	−24.0459	−1.15825	−0.579126	+	0.815238i	$0.696606\pi$
$432$	−2.57395	−0.123839
$433$	−20.6991	−0.994737	−0.497368	−	0.867539i	$-0.665700\pi$
$433$	−20.6991	−0.994737	−0.497368	+	0.867539i	$0.665700\pi$
$434$	6.88601	0.330539
$435$	−19.6687	−0.943043
$436$	5.05659	0.242167
$437$	28.5499	1.36573
$438$	48.3113	2.30840
$439$	−4.05952	−0.193750	−0.0968751	−	0.995297i	$-0.530885\pi$
$439$	−4.05952	−0.193750	−0.0968751	+	0.995297i	$0.530885\pi$
$440$	9.08489	0.433105
$441$	2.65109	0.126243
$442$	−3.85772	−0.183493
$443$	−29.3198	−1.39303	−0.696513	−	0.717544i	$-0.745266\pi$
$443$	−29.3198	−1.39303	−0.696513	+	0.717544i	$0.745266\pi$
$444$	−8.86467	−0.420698
$445$	−5.54778	−0.262990
$446$	6.56328	0.310780
$447$	5.17833	0.244927
$448$	8.88601	0.419825
$449$	−7.71624	−0.364152	−0.182076	−	0.983284i	$-0.558282\pi$
$449$	−7.71624	−0.364152	−0.182076	+	0.983284i	$0.558282\pi$
$450$	−3.37720	−0.159203
$451$	30.3716	1.43014
$452$	0.465816	0.0219101
$453$	−52.3035	−2.45743
$454$	13.2058	0.619780
$455$	−3.02830	−0.141969
$456$	−27.0275	−1.26568
$457$	23.5264	1.10052	0.550260	−	0.834993i	$-0.314529\pi$
$457$	23.5264	1.10052	0.550260	+	0.834993i	$0.314529\pi$
$458$	1.80405	0.0842977
$459$	0.829422	0.0387141
$460$	2.86839	0.133739
$461$	4.28164	0.199416	0.0997079	−	0.995017i	$-0.468209\pi$
$461$	4.28164	0.199416	0.0997079	+	0.995017i	$0.468209\pi$
$462$	−9.08489	−0.422667
$463$	−4.33611	−0.201516	−0.100758	−	0.994911i	$-0.532127\pi$
$463$	−4.33611	−0.201516	−0.100758	+	0.994911i	$0.532127\pi$
$464$	25.6765	1.19200
$465$	−12.8500	−0.595903
$466$	−16.5136	−0.764980
$467$	26.7381	1.23729	0.618646	−	0.785670i	$-0.287682\pi$
$467$	26.7381	1.23729	0.618646	+	0.785670i	$0.287682\pi$
$468$	−3.02830	−0.139983
$469$	−5.02055	−0.231827
$470$	−7.81100	−0.360294
$471$	−12.5606	−0.578761
$472$	28.5683	1.31496
$473$	−18.8217	−0.865421
$474$	−36.4018	−1.67199
$475$	3.75441	0.172264
$476$	−0.377203	−0.0172891
$477$	−38.4437	−1.76021
$478$	−23.9397	−1.09498
$479$	26.6588	1.21807	0.609037	−	0.793142i	$-0.291556\pi$
$479$	26.6588	1.21807	0.609037	+	0.793142i	$0.291556\pi$
$480$	−5.00000	−0.228218
$481$	−29.9378	−1.36505
$482$	5.68151	0.258786
$483$	−18.0771	−0.822538
$484$	0.754406	0.0342912
$485$	−3.65109	−0.165788
$486$	−26.8860	−1.21957
$487$	24.7905	1.12336	0.561681	−	0.827354i	$-0.310155\pi$
$487$	24.7905	1.12336	0.561681	+	0.827354i	$0.310155\pi$
$488$	9.77283	0.442395
$489$	5.53499	0.250301
$490$	1.27389	0.0575485
$491$	8.31769	0.375372	0.187686	−	0.982229i	$-0.439901\pi$
$491$	8.31769	0.375372	0.187686	+	0.982229i	$0.439901\pi$
$492$	−9.07794	−0.409265
$493$	−8.27389	−0.372637
$494$	−14.4834	−0.651641
$495$	7.95328	0.357473
$496$	16.7750	0.753218
$497$	5.22717	0.234471
$498$	−10.4309	−0.467419
$499$	−31.7274	−1.42031	−0.710157	−	0.704043i	$-0.751376\pi$
$499$	−31.7274	−1.42031	−0.710157	+	0.704043i	$0.751376\pi$
$500$	0.377203	0.0168690
$501$	4.87051	0.217599
$502$	21.8364	0.974605
$503$	8.11611	0.361879	0.180940	−	0.983494i	$-0.442086\pi$
$503$	8.11611	0.361879	0.180940	+	0.983494i	$0.442086\pi$
$504$	8.02830	0.357609
$505$	6.23492	0.277450
$506$	29.0614	1.29194
$507$	9.10331	0.404292
$508$	−1.47277	−0.0653434
$509$	6.96878	0.308886	0.154443	−	0.988002i	$-0.450642\pi$
$509$	6.96878	0.308886	0.154443	+	0.988002i	$0.450642\pi$
$510$	−3.02830	−0.134095
$511$	15.9533	0.705732
$512$	25.3227	1.11912
$513$	3.11399	0.137486
$514$	−9.61505	−0.424102
$515$	0.444469	0.0195856
$516$	5.62572	0.247659
$517$	18.3948	0.809004
$518$	12.5937	0.553335
$519$	15.4797	0.679484
$520$	−9.17058	−0.402156
$521$	15.5117	0.679581	0.339791	−	0.940501i	$-0.389644\pi$
$521$	15.5117	0.679581	0.339791	+	0.940501i	$0.389644\pi$
$522$	27.9426	1.22301
$523$	−24.6348	−1.07720	−0.538602	−	0.842560i	$-0.681047\pi$
$523$	−24.6348	−1.07720	−0.538602	+	0.842560i	$0.681047\pi$
$524$	5.52241	0.241248
$525$	−2.37720	−0.103750
$526$	32.7290	1.42705
$527$	−5.40550	−0.235467
$528$	−22.1316	−0.963155
$529$	34.8265	1.51420
$530$	−18.4728	−0.802406
$531$	25.0099	1.08534
$532$	−1.41617	−0.0613989
$533$	−30.6580	−1.32795
$534$	16.8003	0.727021
$535$	1.80113	0.0778694
$536$	−15.2037	−0.656700
$537$	26.8422	1.15833
$538$	33.4565	1.44241
$539$	−3.00000	−0.129219
$540$	0.312860	0.0134634
$541$	−20.9455	−0.900519	−0.450259	−	0.892898i	$-0.648668\pi$
$541$	−20.9455	−0.900519	−0.450259	+	0.892898i	$0.648668\pi$
$542$	−9.72048	−0.417530
$543$	−9.71061	−0.416722
$544$	−2.10331	−0.0901788
$545$	13.4055	0.574228
$546$	9.17058	0.392465
$547$	3.45705	0.147813	0.0739063	−	0.997265i	$-0.476453\pi$
$547$	3.45705	0.147813	0.0739063	+	0.997265i	$0.476453\pi$
$548$	8.35183	0.356772
$549$	8.55553	0.365141
$550$	3.82167	0.162957
$551$	−31.0635	−1.32335
$552$	−54.7429	−2.33001
$553$	−12.0205	−0.511166
$554$	−12.6631	−0.538003
$555$	−23.5011	−0.997564
$556$	6.17058	0.261691
$557$	40.8620	1.73138	0.865688	−	0.500583i	$-0.166881\pi$
$557$	40.8620	1.73138	0.865688	+	0.500583i	$0.166881\pi$
$558$	18.2555	0.772816
$559$	18.9992	0.803581
$560$	3.10331	0.131139
$561$	7.13161	0.301097
$562$	−11.2477	−0.474456
$563$	42.9554	1.81035	0.905177	−	0.425034i	$-0.139738\pi$
$563$	42.9554	1.81035	0.905177	+	0.425034i	$0.139738\pi$
$564$	−5.49814	−0.231513
$565$	1.23492	0.0519535
$566$	−30.7635	−1.29309
$567$	−9.92498	−0.416810
$568$	15.8294	0.664188
$569$	−3.98158	−0.166916	−0.0834582	−	0.996511i	$-0.526597\pi$
$569$	−3.98158	−0.166916	−0.0834582	+	0.996511i	$0.526597\pi$
$570$	−11.3695	−0.476214
$571$	11.7672	0.492442	0.246221	−	0.969214i	$-0.420811\pi$
$571$	11.7672	0.492442	0.246221	+	0.969214i	$0.420811\pi$
$572$	3.42685	0.143284
$573$	40.8598	1.70694
$574$	12.8967	0.538297
$575$	7.60437	0.317124
$576$	23.5577	0.981569
$577$	10.3305	0.430064	0.215032	−	0.976607i	$-0.431014\pi$
$577$	10.3305	0.430064	0.215032	+	0.976607i	$0.431014\pi$
$578$	−1.27389	−0.0529869
$579$	−13.3481	−0.554728
$580$	−3.12094	−0.129590
$581$	−3.44447	−0.142901
$582$	11.0566	0.458311
$583$	43.5032	1.80172
$584$	48.3113	1.99913
$585$	−8.02830	−0.331929
$586$	−30.9512	−1.27858
$587$	17.8761	0.737827	0.368914	−	0.929464i	$-0.379730\pi$
$587$	17.8761	0.737827	0.368914	+	0.929464i	$0.379730\pi$
$588$	0.896688	0.0369788
$589$	−20.2944	−0.836218
$590$	12.0176	0.494758
$591$	41.0566	1.68884
$592$	30.6794	1.26092
$593$	14.5187	0.596211	0.298105	−	0.954533i	$-0.403645\pi$
$593$	14.5187	0.596211	0.298105	+	0.954533i	$0.403645\pi$
$594$	3.16978	0.130058
$595$	−1.00000	−0.0409960
$596$	0.821672	0.0336570
$597$	−41.4741	−1.69742
$598$	−29.3355	−1.19962
$599$	−26.2576	−1.07286	−0.536428	−	0.843946i	$-0.680227\pi$
$599$	−26.2576	−1.07286	−0.536428	+	0.843946i	$0.680227\pi$
$600$	−7.19887	−0.293893
$601$	47.1853	1.92473	0.962364	−	0.271764i	$-0.0876071\pi$
$601$	47.1853	1.92473	0.962364	+	0.271764i	$0.0876071\pi$
$602$	−7.99225	−0.325740
$603$	−13.3099	−0.542023
$604$	−8.29926	−0.337692
$605$	2.00000	0.0813116
$606$	−18.8812	−0.766996
$607$	−17.7467	−0.720315	−0.360157	−	0.932892i	$-0.617277\pi$
$607$	−17.7467	−0.720315	−0.360157	+	0.932892i	$0.617277\pi$
$608$	−7.89669	−0.320253
$609$	19.6687	0.797017
$610$	4.11106	0.166452
$611$	−18.5683	−0.751194
$612$	−1.00000	−0.0404226
$613$	14.7029	0.593843	0.296921	−	0.954902i	$-0.404040\pi$
$613$	14.7029	0.593843	0.296921	+	0.954902i	$0.404040\pi$
$614$	−2.11691	−0.0854315
$615$	−24.0665	−0.970454
$616$	−9.08489	−0.366041
$617$	14.9787	0.603018	0.301509	−	0.953463i	$-0.402510\pi$
$617$	14.9787	0.603018	0.301509	+	0.953463i	$0.402510\pi$
$618$	−1.34598	−0.0541434
$619$	−2.31498	−0.0930470	−0.0465235	−	0.998917i	$-0.514814\pi$
$619$	−2.31498	−0.0930470	−0.0465235	+	0.998917i	$0.514814\pi$
$620$	−2.03897	−0.0818870
$621$	6.30723	0.253101
$622$	−9.28961	−0.372479
$623$	5.54778	0.222267
$624$	22.3404	0.894330
$625$	1.00000	0.0400000
$626$	37.4584	1.49714
$627$	26.7750	1.06929
$628$	−1.99305	−0.0795314
$629$	−9.88601	−0.394181
$630$	3.37720	0.134551
$631$	−15.5528	−0.619148	−0.309574	−	0.950875i	$-0.600186\pi$
$631$	−15.5528	−0.619148	−0.309574	+	0.950875i	$0.600186\pi$
$632$	−36.4018	−1.44798
$633$	30.5286	1.21340
$634$	38.0382	1.51069
$635$	−3.90444	−0.154943
$636$	−13.0029	−0.515599
$637$	3.02830	0.119985
$638$	−31.6201	−1.25185
$639$	13.8577	0.548203
$640$	7.11319	0.281173
$641$	14.6637	0.579180	0.289590	−	0.957151i	$-0.406481\pi$
$641$	14.6637	0.579180	0.289590	+	0.957151i	$0.406481\pi$
$642$	−5.45434	−0.215266
$643$	−13.7232	−0.541190	−0.270595	−	0.962693i	$-0.587220\pi$
$643$	−13.7232	−0.541190	−0.270595	+	0.962693i	$0.587220\pi$
$644$	−2.86839	−0.113030
$645$	14.9143	0.587250
$646$	−4.78270	−0.188173
$647$	−22.3636	−0.879204	−0.439602	−	0.898193i	$-0.644881\pi$
$647$	−22.3636	−0.879204	−0.439602	+	0.898193i	$0.644881\pi$
$648$	−30.0558	−1.18070
$649$	−28.3014	−1.11093
$650$	−3.85772	−0.151312
$651$	12.8500	0.503630
$652$	0.878264	0.0343955
$653$	−12.9717	−0.507622	−0.253811	−	0.967254i	$-0.581684\pi$
$653$	−12.9717	−0.507622	−0.253811	+	0.967254i	$0.581684\pi$
$654$	−40.5958	−1.58742
$655$	14.6404	0.572049
$656$	31.4175	1.22665
$657$	42.2936	1.65003
$658$	7.81100	0.304504
$659$	31.3892	1.22275	0.611375	−	0.791341i	$-0.290617\pi$
$659$	31.3892	1.22275	0.611375	+	0.791341i	$0.290617\pi$
$660$	2.69006	0.104711
$661$	26.6708	1.03738	0.518688	−	0.854964i	$-0.326421\pi$
$661$	26.6708	1.03738	0.518688	+	0.854964i	$0.326421\pi$
$662$	17.0635	0.663193
$663$	−7.19887	−0.279581
$664$	−10.4309	−0.404796
$665$	−3.75441	−0.145590
$666$	33.3871	1.29372
$667$	−62.9178	−2.43619
$668$	0.772829	0.0299017
$669$	12.2477	0.473524
$670$	−6.39563	−0.247085
$671$	−9.68151	−0.373751
$672$	5.00000	0.192879
$673$	40.5646	1.56365	0.781825	−	0.623498i	$-0.214289\pi$
$673$	40.5646	1.56365	0.781825	+	0.623498i	$0.214289\pi$
$674$	12.8769	0.496001
$675$	0.829422	0.0319245
$676$	1.44447	0.0555565
$677$	−43.4565	−1.67017	−0.835084	−	0.550123i	$-0.814581\pi$
$677$	−43.4565	−1.67017	−0.835084	+	0.550123i	$0.814581\pi$
$678$	−3.73971	−0.143623
$679$	3.65109	0.140116
$680$	−3.02830	−0.116130
$681$	24.6433	0.944335
$682$	−20.6580	−0.791037
$683$	6.56620	0.251249	0.125624	−	0.992078i	$-0.459907\pi$
$683$	6.56620	0.251249	0.125624	+	0.992078i	$0.459907\pi$
$684$	−3.75441	−0.143553
$685$	22.1415	0.845983
$686$	−1.27389	−0.0486374
$687$	3.36653	0.128441
$688$	−19.4698	−0.742281
$689$	−43.9135	−1.67297
$690$	−23.0283	−0.876672
$691$	−18.0820	−0.687870	−0.343935	−	0.938993i	$-0.611760\pi$
$691$	−18.0820	−0.687870	−0.343935	+	0.938993i	$0.611760\pi$
$692$	2.45624	0.0933724
$693$	−7.95328	−0.302120
$694$	−44.5256	−1.69017
$695$	16.3588	0.620524
$696$	59.5627	2.25772
$697$	−10.1239	−0.383468
$698$	24.8160	0.939301
$699$	−30.8160	−1.16557
$700$	−0.377203	−0.0142569
$701$	−25.3072	−0.955841	−0.477920	−	0.878403i	$-0.658609\pi$
$701$	−25.3072	−0.955841	−0.477920	+	0.878403i	$0.658609\pi$
$702$	−3.19968	−0.120764
$703$	−37.1161	−1.39986
$704$	−26.6580	−1.00471
$705$	−14.5761	−0.548967
$706$	−8.81795	−0.331868
$707$	−6.23492	−0.234488
$708$	8.45917	0.317915
$709$	−41.2477	−1.54909	−0.774545	−	0.632518i	$-0.782021\pi$
$709$	−41.2477	−1.54909	−0.774545	+	0.632518i	$0.782021\pi$
$710$	6.65884	0.249902
$711$	−31.8676	−1.19513
$712$	16.8003	0.629619
$713$	−41.1054	−1.53941
$714$	3.02830	0.113331
$715$	9.08489	0.339756
$716$	4.25919	0.159173
$717$	−44.6738	−1.66837
$718$	−32.5441	−1.21453
$719$	−34.8187	−1.29852	−0.649260	−	0.760566i	$-0.724921\pi$
$719$	−34.8187	−1.29852	−0.649260	+	0.760566i	$0.724921\pi$
$720$	8.22717	0.306609
$721$	−0.444469	−0.0165529
$722$	6.24772	0.232516
$723$	10.6023	0.394302
$724$	−1.54083	−0.0572646
$725$	−8.27389	−0.307285
$726$	−6.05659	−0.224781
$727$	−20.1960	−0.749026	−0.374513	−	0.927222i	$-0.622190\pi$
$727$	−20.1960	−0.749026	−0.374513	+	0.927222i	$0.622190\pi$
$728$	9.17058	0.339884
$729$	−20.3969	−0.755443
$730$	20.3227	0.752178
$731$	6.27389	0.232048
$732$	2.89376	0.106957
$733$	−9.56833	−0.353414	−0.176707	−	0.984263i	$-0.556545\pi$
$733$	−9.56833	−0.353414	−0.176707	+	0.984263i	$0.556545\pi$
$734$	11.5038	0.424612
$735$	2.37720	0.0876844
$736$	−15.9944	−0.589560
$737$	15.0616	0.554803
$738$	34.1903	1.25856
$739$	9.67939	0.356062	0.178031	−	0.984025i	$-0.443027\pi$
$739$	9.67939	0.356062	0.178031	+	0.984025i	$0.443027\pi$
$740$	−3.72903	−0.137082
$741$	−27.0275	−0.992880
$742$	18.4728	0.678157
$743$	−47.7798	−1.75287	−0.876435	−	0.481520i	$-0.840085\pi$
$743$	−47.7798	−1.75287	−0.876435	+	0.481520i	$0.840085\pi$
$744$	38.9135	1.42664
$745$	2.17833	0.0798078
$746$	−21.1746	−0.775257
$747$	−9.13161	−0.334108
$748$	1.13161	0.0413757
$749$	−1.80113	−0.0658117
$750$	−3.02830	−0.110578
$751$	−21.4834	−0.783942	−0.391971	−	0.919978i	$-0.628207\pi$
$751$	−21.4834	−0.783942	−0.391971	+	0.919978i	$0.628207\pi$
$752$	19.0283	0.693891
$753$	40.7488	1.48497
$754$	31.9183	1.16240
$755$	−22.0021	−0.800739
$756$	−0.312860	−0.0113786
$757$	−11.0360	−0.401112	−0.200556	−	0.979682i	$-0.564275\pi$
$757$	−11.0360	−0.401112	−0.200556	+	0.979682i	$0.564275\pi$
$758$	−2.51173	−0.0912303
$759$	54.2314	1.96848
$760$	−11.3695	−0.412413
$761$	−6.94823	−0.251873	−0.125937	−	0.992038i	$-0.540194\pi$
$761$	−6.94823	−0.251873	−0.125937	+	0.992038i	$0.540194\pi$
$762$	11.8238	0.428331
$763$	−13.4055	−0.485312
$764$	6.48344	0.234563
$765$	−2.65109	−0.0958505
$766$	14.7827	0.534121
$767$	28.5683	1.03154
$768$	20.7069	0.747195
$769$	1.70556	0.0615042	0.0307521	−	0.999527i	$-0.490210\pi$
$769$	1.70556	0.0615042	0.0307521	+	0.999527i	$0.490210\pi$
$770$	−3.82167	−0.137723
$771$	−17.9426	−0.646187
$772$	−2.11801	−0.0762289
$773$	33.4720	1.20390	0.601951	−	0.798533i	$-0.294390\pi$
$773$	33.4720	1.20390	0.601951	+	0.798533i	$0.294390\pi$
$774$	−21.1882	−0.761594
$775$	−5.40550	−0.194171
$776$	11.0566	0.396909
$777$	23.5011	0.843096
$778$	−12.2846	−0.440423
$779$	−38.0091	−1.36182
$780$	−2.71544	−0.0972282
$781$	−15.6815	−0.561129
$782$	−9.68714	−0.346411
$783$	−6.86254	−0.245247
$784$	−3.10331	−0.110833
$785$	−5.28376	−0.188586
$786$	−44.3355	−1.58140
$787$	−2.34036	−0.0834247	−0.0417123	−	0.999130i	$-0.513281\pi$
$787$	−2.34036	−0.0834247	−0.0417123	+	0.999130i	$0.513281\pi$
$788$	6.51466	0.232075
$789$	61.0755	2.17435
$790$	−15.3129	−0.544807
$791$	−1.23492	−0.0439087
$792$	−24.0849	−0.855819
$793$	9.77283	0.347043
$794$	19.2427	0.682897
$795$	−34.4720	−1.22259
$796$	−6.58090	−0.233254
$797$	8.32486	0.294882	0.147441	−	0.989071i	$-0.452896\pi$
$797$	8.32486	0.294882	0.147441	+	0.989071i	$0.452896\pi$
$798$	11.3695	0.402474
$799$	−6.13161	−0.216921
$800$	−2.10331	−0.0743633
$801$	14.7077	0.519671
$802$	3.40067	0.120082
$803$	−47.8598	−1.68894
$804$	−4.50186	−0.158768
$805$	−7.60437	−0.268019
$806$	20.8529	0.734512
$807$	62.4330	2.19775
$808$	−18.8812	−0.664238
$809$	1.84010	0.0646943	0.0323472	−	0.999477i	$-0.489702\pi$
$809$	1.84010	0.0646943	0.0323472	+	0.999477i	$0.489702\pi$
$810$	−12.6433	−0.444242
$811$	−32.7691	−1.15068	−0.575339	−	0.817915i	$-0.695130\pi$
$811$	−32.7691	−1.15068	−0.575339	+	0.817915i	$0.695130\pi$
$812$	3.12094	0.109523
$813$	−18.1394	−0.636175
$814$	−37.7811	−1.32423
$815$	2.32836	0.0815589
$816$	7.37720	0.258254
$817$	23.5547	0.824076
$818$	33.5656	1.17359
$819$	8.02830	0.280531
$820$	−3.81875	−0.133356
$821$	23.9376	0.835427	0.417713	−	0.908579i	$-0.362832\pi$
$821$	23.9376	0.835427	0.417713	+	0.908579i	$0.362832\pi$
$822$	−67.0510	−2.33867
$823$	26.8366	0.935465	0.467732	−	0.883870i	$-0.345071\pi$
$823$	26.8366	0.935465	0.467732	+	0.883870i	$0.345071\pi$
$824$	−1.34598	−0.0468895
$825$	7.13161	0.248291
$826$	−12.0176	−0.418147
$827$	3.52936	0.122728	0.0613639	−	0.998115i	$-0.480455\pi$
$827$	3.52936	0.122728	0.0613639	+	0.998115i	$0.480455\pi$
$828$	−7.60437	−0.264270
$829$	−4.97865	−0.172916	−0.0864579	−	0.996256i	$-0.527555\pi$
$829$	−4.97865	−0.172916	−0.0864579	+	0.996256i	$0.527555\pi$
$830$	−4.38788	−0.152305
$831$	−23.6305	−0.819735
$832$	26.9095	0.932918
$833$	1.00000	0.0346479
$834$	−49.5392	−1.71540
$835$	2.04884	0.0709031
$836$	4.24852	0.146938
$837$	−4.48344	−0.154970
$838$	−47.1754	−1.62965
$839$	−1.47357	−0.0508731	−0.0254366	−	0.999676i	$-0.508098\pi$
$839$	−1.47357	−0.0508731	−0.0254366	+	0.999676i	$0.508098\pi$
$840$	7.19887	0.248385
$841$	39.4573	1.36060
$842$	21.0304	0.724756
$843$	−20.9893	−0.722911
$844$	4.84412	0.166742
$845$	3.82942	0.131736
$846$	20.7077	0.711945
$847$	−2.00000	−0.0687208
$848$	45.0013	1.54535
$849$	−57.4076	−1.97022
$850$	−1.27389	−0.0436941
$851$	−75.1769	−2.57703
$852$	4.68714	0.160579
$853$	−54.7042	−1.87304	−0.936518	−	0.350620i	$-0.885971\pi$
$853$	−54.7042	−1.87304	−0.936518	+	0.350620i	$0.885971\pi$
$854$	−4.11106	−0.140678
$855$	−9.95328	−0.340395
$856$	−5.45434	−0.186426
$857$	−24.2039	−0.826790	−0.413395	−	0.910552i	$-0.635657\pi$
$857$	−24.2039	−0.826790	−0.413395	+	0.910552i	$0.635657\pi$
$858$	−27.5117	−0.939235
$859$	−27.8911	−0.951631	−0.475815	−	0.879545i	$-0.657847\pi$
$859$	−27.8911	−0.951631	−0.475815	+	0.879545i	$0.657847\pi$
$860$	2.36653	0.0806980
$861$	24.0665	0.820183
$862$	30.6319	1.04333
$863$	44.4741	1.51392	0.756958	−	0.653464i	$-0.226685\pi$
$863$	44.4741	1.51392	0.756958	+	0.653464i	$0.226685\pi$
$864$	−1.74453	−0.0593502
$865$	6.51173	0.221406
$866$	26.3684	0.896036
$867$	−2.37720	−0.0807340
$868$	2.03897	0.0692071
$869$	36.0616	1.22331
$870$	25.0558	0.849471
$871$	−15.2037	−0.515158
$872$	−40.5958	−1.37475
$873$	9.67939	0.327598
$874$	−36.3695	−1.23022
$875$	−1.00000	−0.0338062
$876$	14.3051	0.483325
$877$	40.8726	1.38017	0.690085	−	0.723728i	$-0.257573\pi$
$877$	40.8726	1.38017	0.690085	+	0.723728i	$0.257573\pi$
$878$	5.17138	0.174526
$879$	−57.7579	−1.94812
$880$	−9.30994	−0.313838
$881$	27.2349	0.917568	0.458784	−	0.888548i	$-0.348285\pi$
$881$	27.2349	0.917568	0.458784	+	0.888548i	$0.348285\pi$
$882$	−3.37720	−0.113716
$883$	39.5851	1.33215	0.666073	−	0.745886i	$-0.267974\pi$
$883$	39.5851	1.33215	0.666073	+	0.745886i	$0.267974\pi$
$884$	−1.14228	−0.0384191
$885$	22.4260	0.753843
$886$	37.3502	1.25481
$887$	52.1855	1.75222	0.876109	−	0.482114i	$-0.160131\pi$
$887$	52.1855	1.75222	0.876109	+	0.482114i	$0.160131\pi$
$888$	71.1682	2.38825
$889$	3.90444	0.130951
$890$	7.06727	0.236895
$891$	29.7750	0.997498
$892$	1.94341	0.0650701
$893$	−23.0205	−0.770353
$894$	−6.59662	−0.220624
$895$	11.2915	0.377434
$896$	−7.11319	−0.237635
$897$	−54.7429	−1.82781
$898$	9.82964	0.328019
$899$	44.7245	1.49165
$900$	−1.00000	−0.0333333
$901$	−14.5011	−0.483100
$902$	−38.6901	−1.28824
$903$	−14.9143	−0.496317
$904$	−3.73971	−0.124381
$905$	−4.08489	−0.135786
$906$	66.6289	2.21360
$907$	−44.0956	−1.46417	−0.732085	−	0.681214i	$-0.761452\pi$
$907$	−44.0956	−1.46417	−0.732085	+	0.681214i	$0.761452\pi$
$908$	3.91028	0.129767
$909$	−16.5294	−0.548244
$910$	3.85772	0.127882
$911$	3.49814	0.115898	0.0579492	−	0.998320i	$-0.481544\pi$
$911$	3.49814	0.115898	0.0579492	+	0.998320i	$0.481544\pi$
$912$	27.6970	0.917140
$913$	10.3334	0.341986
$914$	−29.9701	−0.991323
$915$	7.67164	0.253617
$916$	0.534184	0.0176499
$917$	−14.6404	−0.483469
$918$	−1.05659	−0.0348727
$919$	5.92418	0.195421	0.0977104	−	0.995215i	$-0.468848\pi$
$919$	5.92418	0.195421	0.0977104	+	0.995215i	$0.468848\pi$
$920$	−23.0283	−0.759220
$921$	−3.95036	−0.130169
$922$	−5.45434	−0.179629
$923$	15.8294	0.521032
$924$	−2.69006	−0.0884966
$925$	−9.88601	−0.325050
$926$	5.52373	0.181521
$927$	−1.17833	−0.0387014
$928$	17.4026	0.571268
$929$	1.03334	0.0339029	0.0169514	−	0.999856i	$-0.494604\pi$
$929$	1.03334	0.0339029	0.0169514	+	0.999856i	$0.494604\pi$
$930$	16.3695	0.536776
$931$	3.75441	0.123046
$932$	−4.88974	−0.160169
$933$	−17.3353	−0.567533
$934$	−34.0614	−1.11452
$935$	3.00000	0.0981105
$936$	24.3121	0.794665
$937$	−27.6474	−0.903200	−0.451600	−	0.892220i	$-0.649147\pi$
$937$	−27.6474	−0.903200	−0.451600	+	0.892220i	$0.649147\pi$
$938$	6.39563	0.208825
$939$	69.9009	2.28113
$940$	−2.31286	−0.0754372
$941$	36.4973	1.18978	0.594890	−	0.803807i	$-0.297196\pi$
$941$	36.4973	1.18978	0.594890	+	0.803807i	$0.297196\pi$
$942$	16.0008	0.521334
$943$	−76.9856	−2.50700
$944$	−29.2760	−0.952853
$945$	−0.829422	−0.0269811
$946$	23.9767	0.779551
$947$	47.4223	1.54102	0.770509	−	0.637429i	$-0.220002\pi$
$947$	47.4223	1.54102	0.770509	+	0.637429i	$0.220002\pi$
$948$	−10.7787	−0.350075
$949$	48.3113	1.56825
$950$	−4.78270	−0.155171
$951$	70.9829	2.30178
$952$	3.02830	0.0981476
$953$	−5.10814	−0.165469	−0.0827344	−	0.996572i	$-0.526365\pi$
$953$	−5.10814	−0.165469	−0.0827344	+	0.996572i	$0.526365\pi$
$954$	48.9730	1.58556
$955$	17.1882	0.556197
$956$	−7.08861	−0.229262
$957$	−59.0061	−1.90740
$958$	−33.9604	−1.09721
$959$	−22.1415	−0.714986
$960$	21.1239	0.681770
$961$	−1.78058	−0.0574380
$962$	38.1375	1.22960
$963$	−4.77495	−0.153871
$964$	1.68231	0.0541837
$965$	−5.61505	−0.180755
$966$	23.0283	0.740923
$967$	36.7360	1.18135	0.590675	−	0.806910i	$-0.298862\pi$
$967$	36.7360	1.18135	0.590675	+	0.806910i	$0.298862\pi$
$968$	−6.05659	−0.194666
$969$	−8.92498	−0.286712
$970$	4.65109	0.149338
$971$	−10.4026	−0.333835	−0.166917	−	0.985971i	$-0.553381\pi$
$971$	−10.4026	−0.333835	−0.166917	+	0.985971i	$0.553381\pi$
$972$	−7.96103	−0.255350
$973$	−16.3588	−0.524438
$974$	−31.5803	−1.01190
$975$	−7.19887	−0.230548
$976$	−10.0149	−0.320570
$977$	−13.4458	−0.430169	−0.215084	−	0.976595i	$-0.569003\pi$
$977$	−13.4458	−0.430169	−0.215084	+	0.976595i	$0.569003\pi$
$978$	−7.05097	−0.225465
$979$	−16.6433	−0.531924
$980$	0.377203	0.0120493
$981$	−35.5392	−1.13468
$982$	−10.5958	−0.338126
$983$	−1.85289	−0.0590981	−0.0295490	−	0.999563i	$-0.509407\pi$
$983$	−1.85289	−0.0590981	−0.0295490	+	0.999563i	$0.509407\pi$
$984$	72.8804	2.32334
$985$	17.2710	0.550299
$986$	10.5400	0.335663
$987$	14.5761	0.463962
$988$	−4.28859	−0.136438
$989$	47.7090	1.51706
$990$	−10.1316	−0.322004
$991$	8.77495	0.278746	0.139373	−	0.990240i	$-0.455491\pi$
$991$	8.77495	0.278746	0.139373	+	0.990240i	$0.455491\pi$
$992$	11.3695	0.360980
$993$	31.8422	1.01048
$994$	−6.65884	−0.211206
$995$	−17.4466	−0.553094
$996$	−3.08861	−0.0978664
$997$	−47.0224	−1.48922	−0.744608	−	0.667502i	$-0.767364\pi$
$997$	−47.0224	−1.48922	−0.744608	+	0.667502i	$0.767364\pi$
$998$	40.4173	1.27939
$999$	−8.19968	−0.259426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.a.f.1.2	✓	3
3.2	odd	2		5355.2.a.bf.1.2		3
4.3	odd	2		9520.2.a.ba.1.3		3
5.4	even	2		2975.2.a.f.1.2		3
7.6	odd	2		4165.2.a.z.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.a.f.1.2	✓	3	1.1	even	1	trivial
2975.2.a.f.1.2		3	5.4	even	2
4165.2.a.z.1.2		3	7.6	odd	2
5355.2.a.bf.1.2		3	3.2	odd	2
9520.2.a.ba.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27389 q^{2} -2.37720 q^{3} -0.377203 q^{4} -1.00000 q^{5} +3.02830 q^{6} +1.00000 q^{7} +3.02830 q^{8} +2.65109 q^{9} +O(q^{10})\)	\(q-1.27389 q^{2} -2.37720 q^{3} -0.377203 q^{4} -1.00000 q^{5} +3.02830 q^{6} +1.00000 q^{7} +3.02830 q^{8} +2.65109 q^{9} +1.27389 q^{10} -3.00000 q^{11} +0.896688 q^{12} +3.02830 q^{13} -1.27389 q^{14} +2.37720 q^{15} -3.10331 q^{16} +1.00000 q^{17} -3.37720 q^{18} +3.75441 q^{19} +0.377203 q^{20} -2.37720 q^{21} +3.82167 q^{22} +7.60437 q^{23} -7.19887 q^{24} +1.00000 q^{25} -3.85772 q^{26} +0.829422 q^{27} -0.377203 q^{28} -8.27389 q^{29} -3.02830 q^{30} -5.40550 q^{31} -2.10331 q^{32} +7.13161 q^{33} -1.27389 q^{34} -1.00000 q^{35} -1.00000 q^{36} -9.88601 q^{37} -4.78270 q^{38} -7.19887 q^{39} -3.02830 q^{40} -10.1239 q^{41} +3.02830 q^{42} +6.27389 q^{43} +1.13161 q^{44} -2.65109 q^{45} -9.68714 q^{46} -6.13161 q^{47} +7.37720 q^{48} +1.00000 q^{49} -1.27389 q^{50} -2.37720 q^{51} -1.14228 q^{52} -14.5011 q^{53} -1.05659 q^{54} +3.00000 q^{55} +3.02830 q^{56} -8.92498 q^{57} +10.5400 q^{58} +9.43380 q^{59} -0.896688 q^{60} +3.22717 q^{61} +6.88601 q^{62} +2.65109 q^{63} +8.88601 q^{64} -3.02830 q^{65} -9.08489 q^{66} -5.02055 q^{67} -0.377203 q^{68} -18.0771 q^{69} +1.27389 q^{70} +5.22717 q^{71} +8.02830 q^{72} +15.9533 q^{73} +12.5937 q^{74} -2.37720 q^{75} -1.41617 q^{76} -3.00000 q^{77} +9.17058 q^{78} -12.0205 q^{79} +3.10331 q^{80} -9.92498 q^{81} +12.8967 q^{82} -3.44447 q^{83} +0.896688 q^{84} -1.00000 q^{85} -7.99225 q^{86} +19.6687 q^{87} -9.08489 q^{88} +5.54778 q^{89} +3.37720 q^{90} +3.02830 q^{91} -2.86839 q^{92} +12.8500 q^{93} +7.81100 q^{94} -3.75441 q^{95} +5.00000 q^{96} +3.65109 q^{97} -1.27389 q^{98} -7.95328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9	\( 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - 9 q^{11} + 6 q^{12} - 3 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} - 4 q^{20} - 2 q^{21} + 6 q^{22} - 5 q^{23} - 11 q^{24} + 3 q^{25} + 2 q^{26} + q^{27} + 4 q^{28} - 23 q^{29} + 3 q^{30} + q^{31} - 3 q^{32} + 6 q^{33} - 2 q^{34} - 3 q^{35} - 3 q^{36} - 4 q^{37} + 8 q^{38} - 11 q^{39} + 3 q^{40} - 11 q^{41} - 3 q^{42} + 17 q^{43} - 12 q^{44} - q^{45} - 14 q^{46} - 3 q^{47} + 17 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 17 q^{52} - 19 q^{53} + 21 q^{54} + 9 q^{55} - 3 q^{56} - 18 q^{57} + 24 q^{58} - q^{59} - 6 q^{60} - 13 q^{61} - 5 q^{62} + q^{63} + q^{64} + 3 q^{65} + 9 q^{66} + q^{67} + 4 q^{68} - 14 q^{69} + 2 q^{70} - 7 q^{71} + 12 q^{72} + 27 q^{73} - 19 q^{74} - 2 q^{75} - 16 q^{76} - 9 q^{77} + 29 q^{78} - 20 q^{79} + 6 q^{80} - 21 q^{81} + 42 q^{82} - 10 q^{83} + 6 q^{84} - 3 q^{85} - 20 q^{86} + 11 q^{87} + 9 q^{88} + 13 q^{89} + 5 q^{90} - 3 q^{91} - 24 q^{92} + 21 q^{93} - 11 q^{94} - q^{95} + 15 q^{96} + 4 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 - 9 * q^11 + 6 * q^12 - 3 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 + 3 * q^17 - 5 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 6 * q^22 - 5 * q^23 - 11 * q^24 + 3 * q^25 + 2 * q^26 + q^27 + 4 * q^28 - 23 * q^29 + 3 * q^30 + q^31 - 3 * q^32 + 6 * q^33 - 2 * q^34 - 3 * q^35 - 3 * q^36 - 4 * q^37 + 8 * q^38 - 11 * q^39 + 3 * q^40 - 11 * q^41 - 3 * q^42 + 17 * q^43 - 12 * q^44 - q^45 - 14 * q^46 - 3 * q^47 + 17 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 17 * q^52 - 19 * q^53 + 21 * q^54 + 9 * q^55 - 3 * q^56 - 18 * q^57 + 24 * q^58 - q^59 - 6 * q^60 - 13 * q^61 - 5 * q^62 + q^63 + q^64 + 3 * q^65 + 9 * q^66 + q^67 + 4 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^71 + 12 * q^72 + 27 * q^73 - 19 * q^74 - 2 * q^75 - 16 * q^76 - 9 * q^77 + 29 * q^78 - 20 * q^79 + 6 * q^80 - 21 * q^81 + 42 * q^82 - 10 * q^83 + 6 * q^84 - 3 * q^85 - 20 * q^86 + 11 * q^87 + 9 * q^88 + 13 * q^89 + 5 * q^90 - 3 * q^91 - 24 * q^92 + 21 * q^93 - 11 * q^94 - q^95 + 15 * q^96 + 4 * q^97 - 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more