LMFDB - Embedded newform 1805.2.a.r.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.08935$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70739 q^{2} +0.0506943 q^{3} +5.32995 q^{4} -1.00000 q^{5} +0.137249 q^{6} +4.62536 q^{7} +9.01547 q^{8} -2.99743 q^{9} +O(q^{10})$	\(q+2.70739 q^{2} +0.0506943 q^{3} +5.32995 q^{4} -1.00000 q^{5} +0.137249 q^{6} +4.62536 q^{7} +9.01547 q^{8} -2.99743 q^{9} -2.70739 q^{10} +2.69792 q^{11} +0.270198 q^{12} -0.983436 q^{13} +12.5227 q^{14} -0.0506943 q^{15} +13.7485 q^{16} -4.02257 q^{17} -8.11521 q^{18} -5.32995 q^{20} +0.234480 q^{21} +7.30433 q^{22} +0.820744 q^{23} +0.457033 q^{24} +1.00000 q^{25} -2.66254 q^{26} -0.304036 q^{27} +24.6530 q^{28} -6.26663 q^{29} -0.137249 q^{30} -2.21950 q^{31} +19.1915 q^{32} +0.136769 q^{33} -10.8907 q^{34} -4.62536 q^{35} -15.9762 q^{36} +2.80473 q^{37} -0.0498546 q^{39} -9.01547 q^{40} -4.38798 q^{41} +0.634828 q^{42} +2.06601 q^{43} +14.3798 q^{44} +2.99743 q^{45} +2.22207 q^{46} -3.21129 q^{47} +0.696970 q^{48} +14.3940 q^{49} +2.70739 q^{50} -0.203922 q^{51} -5.24167 q^{52} +2.30738 q^{53} -0.823143 q^{54} -2.69792 q^{55} +41.6998 q^{56} -16.9662 q^{58} -8.99135 q^{59} -0.270198 q^{60} +9.11348 q^{61} -6.00906 q^{62} -13.8642 q^{63} +24.4620 q^{64} +0.983436 q^{65} +0.370288 q^{66} +4.54135 q^{67} -21.4401 q^{68} +0.0416071 q^{69} -12.5227 q^{70} -12.4378 q^{71} -27.0233 q^{72} +0.461968 q^{73} +7.59349 q^{74} +0.0506943 q^{75} +12.4789 q^{77} -0.134976 q^{78} +8.22856 q^{79} -13.7485 q^{80} +8.97688 q^{81} -11.8800 q^{82} -13.5897 q^{83} +1.24977 q^{84} +4.02257 q^{85} +5.59349 q^{86} -0.317682 q^{87} +24.3231 q^{88} +9.48072 q^{89} +8.11521 q^{90} -4.54875 q^{91} +4.37453 q^{92} -0.112516 q^{93} -8.69421 q^{94} +0.972902 q^{96} +13.3177 q^{97} +38.9701 q^{98} -8.08684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * 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 $

$2$	2.70739	1.91441	0.957206	−	0.289406i	$-0.0934578\pi$
$2$	2.70739	1.91441	0.957206	+	0.289406i	$0.0934578\pi$
$3$	0.0506943	0.0292684	0.0146342	−	0.999893i	$-0.495342\pi$
$3$	0.0506943	0.0292684	0.0146342	+	0.999893i	$0.495342\pi$
$4$	5.32995	2.66498
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.137249	0.0560318
$7$	4.62536	1.74822	0.874112	−	0.485725i	$-0.161444\pi$
$7$	4.62536	1.74822	0.874112	+	0.485725i	$0.161444\pi$
$8$	9.01547	3.18745
$9$	−2.99743	−0.999143
$10$	−2.70739	−0.856151
$11$	2.69792	0.813455	0.406727	−	0.913550i	$-0.366670\pi$
$11$	2.69792	0.813455	0.406727	+	0.913550i	$0.366670\pi$
$12$	0.270198	0.0779995
$13$	−0.983436	−0.272756	−0.136378	−	0.990657i	$-0.543546\pi$
$13$	−0.983436	−0.272756	−0.136378	+	0.990657i	$0.543546\pi$
$14$	12.5227	3.34682
$15$	−0.0506943	−0.0130892
$16$	13.7485	3.43712
$17$	−4.02257	−0.975617	−0.487809	−	0.872951i	$-0.662204\pi$
$17$	−4.02257	−0.975617	−0.487809	+	0.872951i	$0.662204\pi$
$18$	−8.11521	−1.91277
$19$	0	0
$19$	0	0
$20$	−5.32995	−1.19181
$21$	0.234480	0.0511677
$22$	7.30433	1.55729
$23$	0.820744	0.171137	0.0855685	−	0.996332i	$-0.472729\pi$
$23$	0.820744	0.171137	0.0855685	+	0.996332i	$0.472729\pi$
$24$	0.457033	0.0932916
$25$	1.00000	0.200000
$26$	−2.66254	−0.522168
$27$	−0.304036	−0.0585117
$28$	24.6530	4.65897
$29$	−6.26663	−1.16368	−0.581842	−	0.813302i	$-0.697668\pi$
$29$	−6.26663	−1.16368	−0.581842	+	0.813302i	$0.697668\pi$
$30$	−0.137249	−0.0250582
$31$	−2.21950	−0.398635	−0.199317	−	0.979935i	$-0.563872\pi$
$31$	−2.21950	−0.398635	−0.199317	+	0.979935i	$0.563872\pi$
$32$	19.1915	3.39262
$33$	0.136769	0.0238085
$34$	−10.8907	−1.86773
$35$	−4.62536	−0.781829
$36$	−15.9762	−2.66269
$37$	2.80473	0.461094	0.230547	−	0.973061i	$-0.425948\pi$
$37$	2.80473	0.461094	0.230547	+	0.973061i	$0.425948\pi$
$38$	0	0
$39$	−0.0498546	−0.00798313
$40$	−9.01547	−1.42547
$41$	−4.38798	−0.685287	−0.342643	−	0.939466i	$-0.611322\pi$
$41$	−4.38798	−0.685287	−0.342643	+	0.939466i	$0.611322\pi$
$42$	0.634828	0.0979560
$43$	2.06601	0.315063	0.157532	−	0.987514i	$-0.449646\pi$
$43$	2.06601	0.315063	0.157532	+	0.987514i	$0.449646\pi$
$44$	14.3798	2.16784
$45$	2.99743	0.446830
$46$	2.22207	0.327627
$47$	−3.21129	−0.468415	−0.234207	−	0.972187i	$-0.575249\pi$
$47$	−3.21129	−0.468415	−0.234207	+	0.972187i	$0.575249\pi$
$48$	0.696970	0.100599
$49$	14.3940	2.05628
$50$	2.70739	0.382883
$51$	−0.203922	−0.0285547
$52$	−5.24167	−0.726888
$53$	2.30738	0.316943	0.158471	−	0.987364i	$-0.449343\pi$
$53$	2.30738	0.316943	0.158471	+	0.987364i	$0.449343\pi$
$54$	−0.823143	−0.112016
$55$	−2.69792	−0.363788
$56$	41.6998	5.57238
$57$	0	0
$58$	−16.9662	−2.22777
$59$	−8.99135	−1.17057	−0.585287	−	0.810826i	$-0.699018\pi$
$59$	−8.99135	−1.17057	−0.585287	+	0.810826i	$0.699018\pi$
$60$	−0.270198	−0.0348825
$61$	9.11348	1.16686	0.583431	−	0.812163i	$-0.301710\pi$
$61$	9.11348	1.16686	0.583431	+	0.812163i	$0.301710\pi$
$62$	−6.00906	−0.763151
$63$	−13.8642	−1.74673
$64$	24.4620	3.05775
$65$	0.983436	0.121980
$66$	0.370288	0.0455793
$67$	4.54135	0.554815	0.277407	−	0.960752i	$-0.410525\pi$
$67$	4.54135	0.554815	0.277407	+	0.960752i	$0.410525\pi$
$68$	−21.4401	−2.60000
$69$	0.0416071	0.00500890
$70$	−12.5227	−1.49674
$71$	−12.4378	−1.47609	−0.738045	−	0.674751i	$-0.764251\pi$
$71$	−12.4378	−1.47609	−0.738045	+	0.674751i	$0.764251\pi$
$72$	−27.0233	−3.18472
$73$	0.461968	0.0540693	0.0270346	−	0.999634i	$-0.491394\pi$
$73$	0.461968	0.0540693	0.0270346	+	0.999634i	$0.491394\pi$
$74$	7.59349	0.882725
$75$	0.0506943	0.00585368
$76$	0	0
$77$	12.4789	1.42210
$78$	−0.134976	−0.0152830
$79$	8.22856	0.925786	0.462893	−	0.886414i	$-0.346811\pi$
$79$	8.22856	0.925786	0.462893	+	0.886414i	$0.346811\pi$
$80$	−13.7485	−1.53713
$81$	8.97688	0.997431
$82$	−11.8800	−1.31192
$83$	−13.5897	−1.49167	−0.745834	−	0.666132i	$-0.767949\pi$
$83$	−13.5897	−1.49167	−0.745834	+	0.666132i	$0.767949\pi$
$84$	1.24977	0.136361
$85$	4.02257	0.436309
$86$	5.59349	0.603161
$87$	−0.317682	−0.0340591
$88$	24.3231	2.59285
$89$	9.48072	1.00495	0.502477	−	0.864591i	$-0.332422\pi$
$89$	9.48072	1.00495	0.502477	+	0.864591i	$0.332422\pi$
$90$	8.11521	0.855418
$91$	−4.54875	−0.476838
$92$	4.37453	0.456076
$93$	−0.112516	−0.0116674
$94$	−8.69421	−0.896739
$95$	0	0
$96$	0.972902	0.0992964
$97$	13.3177	1.35221	0.676106	−	0.736805i	$-0.263666\pi$
$97$	13.3177	1.35221	0.676106	+	0.736805i	$0.263666\pi$
$98$	38.9701	3.93658
$99$	−8.08684	−0.812758
$100$	5.32995	0.532995
$101$	−9.41482	−0.936810	−0.468405	−	0.883514i	$-0.655171\pi$
$101$	−9.41482	−0.936810	−0.468405	+	0.883514i	$0.655171\pi$
$102$	−0.552095	−0.0546656
$103$	−9.80154	−0.965775	−0.482887	−	0.875683i	$-0.660412\pi$
$103$	−9.80154	−0.965775	−0.482887	+	0.875683i	$0.660412\pi$
$104$	−8.86614	−0.869397
$105$	−0.234480	−0.0228829
$106$	6.24697	0.606759
$107$	14.1247	1.36548	0.682742	−	0.730660i	$-0.260787\pi$
$107$	14.1247	1.36548	0.682742	+	0.730660i	$0.260787\pi$
$108$	−1.62050	−0.155932
$109$	−9.48443	−0.908444	−0.454222	−	0.890889i	$-0.650083\pi$
$109$	−9.48443	−0.908444	−0.454222	+	0.890889i	$0.650083\pi$
$110$	−7.30433	−0.696440
$111$	0.142184	0.0134955
$112$	63.5917	6.00885
$113$	−17.8778	−1.68180	−0.840899	−	0.541193i	$-0.817973\pi$
$113$	−17.8778	−1.68180	−0.840899	+	0.541193i	$0.817973\pi$
$114$	0	0
$115$	−0.820744	−0.0765348
$116$	−33.4008	−3.10119
$117$	2.94778	0.272522
$118$	−24.3431	−2.24096
$119$	−18.6059	−1.70560
$120$	−0.457033	−0.0417213
$121$	−3.72121	−0.338291
$122$	24.6737	2.23385
$123$	−0.222445	−0.0200572
$124$	−11.8299	−1.06235
$125$	−1.00000	−0.0894427
$126$	−37.5358	−3.34395
$127$	−14.5819	−1.29394	−0.646968	−	0.762517i	$-0.723963\pi$
$127$	−14.5819	−1.29394	−0.646968	+	0.762517i	$0.723963\pi$
$128$	27.8450	2.46118
$129$	0.104735	0.00922139
$130$	2.66254	0.233521
$131$	7.83440	0.684495	0.342248	−	0.939610i	$-0.388812\pi$
$131$	7.83440	0.684495	0.342248	+	0.939610i	$0.388812\pi$
$132$	0.728975	0.0634491
$133$	0	0
$134$	12.2952	1.06214
$135$	0.304036	0.0261672
$136$	−36.2654	−3.10973
$137$	21.4916	1.83615	0.918074	−	0.396409i	$-0.129744\pi$
$137$	21.4916	1.83615	0.918074	+	0.396409i	$0.129744\pi$
$138$	0.112647	0.00958911
$139$	−22.3722	−1.89759	−0.948793	−	0.315898i	$-0.897694\pi$
$139$	−22.3722	−1.89759	−0.948793	+	0.315898i	$0.897694\pi$
$140$	−24.6530	−2.08356
$141$	−0.162794	−0.0137097
$142$	−33.6739	−2.82585
$143$	−2.65324	−0.221875
$144$	−41.2101	−3.43418
$145$	6.26663	0.520415
$146$	1.25073	0.103511
$147$	0.729693	0.0601841
$148$	14.9491	1.22881
$149$	7.62271	0.624477	0.312239	−	0.950004i	$-0.398921\pi$
$149$	7.62271	0.624477	0.312239	+	0.950004i	$0.398921\pi$
$150$	0.137249	0.0112064
$151$	5.03245	0.409535	0.204767	−	0.978811i	$-0.434356\pi$
$151$	5.03245	0.409535	0.204767	+	0.978811i	$0.434356\pi$
$152$	0	0
$153$	12.0574	0.974782
$154$	33.7852	2.72249
$155$	2.21950	0.178275
$156$	−0.265723	−0.0212748
$157$	13.4538	1.07373	0.536864	−	0.843669i	$-0.319609\pi$
$157$	13.4538	1.07373	0.536864	+	0.843669i	$0.319609\pi$
$158$	22.2779	1.77234
$159$	0.116971	0.00927640
$160$	−19.1915	−1.51722
$161$	3.79624	0.299186
$162$	24.3039	1.90949
$163$	0.698984	0.0547486	0.0273743	−	0.999625i	$-0.491285\pi$
$163$	0.698984	0.0547486	0.0273743	+	0.999625i	$0.491285\pi$
$164$	−23.3877	−1.82627
$165$	−0.136769	−0.0106475
$166$	−36.7927	−2.85567
$167$	4.37009	0.338168	0.169084	−	0.985602i	$-0.445919\pi$
$167$	4.37009	0.338168	0.169084	+	0.985602i	$0.445919\pi$
$168$	2.11395	0.163094
$169$	−12.0329	−0.925604
$170$	10.8907	0.835276
$171$	0	0
$172$	11.0117	0.839636
$173$	−10.9092	−0.829410	−0.414705	−	0.909956i	$-0.636115\pi$
$173$	−10.9092	−0.829410	−0.414705	+	0.909956i	$0.636115\pi$
$174$	−0.860090	−0.0652032
$175$	4.62536	0.349645
$176$	37.0924	2.79594
$177$	−0.455811	−0.0342608
$178$	25.6680	1.92390
$179$	−2.48177	−0.185496	−0.0927480	−	0.995690i	$-0.529565\pi$
$179$	−2.48177	−0.185496	−0.0927480	+	0.995690i	$0.529565\pi$
$180$	15.9762	1.19079
$181$	−19.5142	−1.45048	−0.725239	−	0.688497i	$-0.758271\pi$
$181$	−19.5142	−1.45048	−0.725239	+	0.688497i	$0.758271\pi$
$182$	−12.3152	−0.912866
$183$	0.462002	0.0341521
$184$	7.39940	0.545491
$185$	−2.80473	−0.206208
$186$	−0.304625	−0.0223362
$187$	−10.8526	−0.793621
$188$	−17.1160	−1.24831
$189$	−1.40628	−0.102291
$190$	0	0
$191$	13.3130	0.963294	0.481647	−	0.876365i	$-0.340039\pi$
$191$	13.3130	0.963294	0.481647	+	0.876365i	$0.340039\pi$
$192$	1.24008	0.0894954
$193$	−9.78430	−0.704289	−0.352145	−	0.935946i	$-0.614548\pi$
$193$	−9.78430	−0.704289	−0.352145	+	0.935946i	$0.614548\pi$
$194$	36.0563	2.58869
$195$	0.0498546	0.00357016
$196$	76.7193	5.47995
$197$	16.6241	1.18442	0.592210	−	0.805783i	$-0.298255\pi$
$197$	16.6241	1.18442	0.592210	+	0.805783i	$0.298255\pi$
$198$	−21.8942	−1.55595
$199$	15.6086	1.10647	0.553233	−	0.833027i	$-0.313394\pi$
$199$	15.6086	1.10647	0.553233	+	0.833027i	$0.313394\pi$
$200$	9.01547	0.637490
$201$	0.230221	0.0162385
$202$	−25.4896	−1.79344
$203$	−28.9854	−2.03438
$204$	−1.08689	−0.0760977
$205$	4.38798	0.306470
$206$	−26.5366	−1.84889
$207$	−2.46012	−0.170990
$208$	−13.5208	−0.937496
$209$	0	0
$210$	−0.634828	−0.0438073
$211$	−13.5272	−0.931249	−0.465625	−	0.884982i	$-0.654170\pi$
$211$	−13.5272	−0.931249	−0.465625	+	0.884982i	$0.654170\pi$
$212$	12.2982	0.844645
$213$	−0.630524	−0.0432028
$214$	38.2410	2.61410
$215$	−2.06601	−0.140901
$216$	−2.74103	−0.186503
$217$	−10.2660	−0.696902
$218$	−25.6780	−1.73914
$219$	0.0234192	0.00158252
$220$	−14.3798	−0.969486
$221$	3.95594	0.266106
$222$	0.384947	0.0258359
$223$	18.5642	1.24315	0.621575	−	0.783354i	$-0.286493\pi$
$223$	18.5642	1.24315	0.621575	+	0.783354i	$0.286493\pi$
$224$	88.7679	5.93105
$225$	−2.99743	−0.199829
$226$	−48.4020	−3.21965
$227$	−15.3887	−1.02138	−0.510692	−	0.859764i	$-0.670611\pi$
$227$	−15.3887	−1.02138	−0.510692	+	0.859764i	$0.670611\pi$
$228$	0	0
$229$	−10.5695	−0.698450	−0.349225	−	0.937039i	$-0.613555\pi$
$229$	−10.5695	−0.698450	−0.349225	+	0.937039i	$0.613555\pi$
$230$	−2.22207	−0.146519
$231$	0.632608	0.0416226
$232$	−56.4966	−3.70918
$233$	4.60393	0.301613	0.150807	−	0.988563i	$-0.451813\pi$
$233$	4.60393	0.301613	0.150807	+	0.988563i	$0.451813\pi$
$234$	7.98079	0.521720
$235$	3.21129	0.209481
$236$	−47.9235	−3.11955
$237$	0.417141	0.0270963
$238$	−50.3733	−3.26522
$239$	9.31641	0.602629	0.301314	−	0.953525i	$-0.402575\pi$
$239$	9.31641	0.602629	0.301314	+	0.953525i	$0.402575\pi$
$240$	−0.696970	−0.0449892
$241$	−26.4050	−1.70089	−0.850447	−	0.526061i	$-0.823668\pi$
$241$	−26.4050	−1.70089	−0.850447	+	0.526061i	$0.823668\pi$
$242$	−10.0747	−0.647629
$243$	1.36718	0.0877049
$244$	48.5744	3.10966
$245$	−14.3940	−0.919598
$246$	−0.602246	−0.0383978
$247$	0	0
$248$	−20.0099	−1.27063
$249$	−0.688923	−0.0436587
$250$	−2.70739	−0.171230
$251$	3.42688	0.216303	0.108151	−	0.994134i	$-0.465507\pi$
$251$	3.42688	0.216303	0.108151	+	0.994134i	$0.465507\pi$
$252$	−73.8955	−4.65498
$253$	2.21431	0.139212
$254$	−39.4789	−2.47713
$255$	0.203922	0.0127701
$256$	26.4633	1.65396
$257$	−23.4581	−1.46328	−0.731639	−	0.681693i	$-0.761244\pi$
$257$	−23.4581	−1.46328	−0.731639	+	0.681693i	$0.761244\pi$
$258$	0.283558	0.0176536
$259$	12.9729	0.806096
$260$	5.24167	0.325074
$261$	18.7838	1.16269
$262$	21.2108	1.31041
$263$	−15.3426	−0.946066	−0.473033	−	0.881045i	$-0.656841\pi$
$263$	−15.3426	−0.946066	−0.473033	+	0.881045i	$0.656841\pi$
$264$	1.23304	0.0758885
$265$	−2.30738	−0.141741
$266$	0	0
$267$	0.480619	0.0294134
$268$	24.2052	1.47857
$269$	5.00587	0.305213	0.152607	−	0.988287i	$-0.451233\pi$
$269$	5.00587	0.305213	0.152607	+	0.988287i	$0.451233\pi$
$270$	0.823143	0.0500949
$271$	3.33930	0.202848	0.101424	−	0.994843i	$-0.467660\pi$
$271$	3.33930	0.202848	0.101424	+	0.994843i	$0.467660\pi$
$272$	−55.3043	−3.35332
$273$	−0.230596	−0.0139563
$274$	58.1860	3.51514
$275$	2.69792	0.162691
$276$	0.221764	0.0133486
$277$	5.77307	0.346870	0.173435	−	0.984845i	$-0.444513\pi$
$277$	5.77307	0.346870	0.173435	+	0.984845i	$0.444513\pi$
$278$	−60.5703	−3.63276
$279$	6.65281	0.398293
$280$	−41.6998	−2.49204
$281$	11.9223	0.711224	0.355612	−	0.934634i	$-0.384272\pi$
$281$	11.9223	0.711224	0.355612	+	0.934634i	$0.384272\pi$
$282$	−0.440747	−0.0262461
$283$	29.8298	1.77320	0.886600	−	0.462537i	$-0.153061\pi$
$283$	29.8298	1.77320	0.886600	+	0.462537i	$0.153061\pi$
$284$	−66.2927	−3.93375
$285$	0	0
$286$	−7.18334	−0.424760
$287$	−20.2960	−1.19803
$288$	−57.5253	−3.38971
$289$	−0.818900	−0.0481706
$290$	16.9662	0.996289
$291$	0.675134	0.0395771
$292$	2.46227	0.144093
$293$	−4.51222	−0.263607	−0.131803	−	0.991276i	$-0.542077\pi$
$293$	−4.51222	−0.263607	−0.131803	+	0.991276i	$0.542077\pi$
$294$	1.97556	0.115217
$295$	8.99135	0.523497
$296$	25.2859	1.46972
$297$	−0.820265	−0.0475966
$298$	20.6376	1.19551
$299$	−0.807150	−0.0466787
$300$	0.270198	0.0155999
$301$	9.55604	0.550801
$302$	13.6248	0.784018
$303$	−0.477278	−0.0274189
$304$	0	0
$305$	−9.11348	−0.521836
$306$	32.6440	1.86613
$307$	26.1852	1.49447	0.747233	−	0.664562i	$-0.231382\pi$
$307$	26.1852	1.49447	0.747233	+	0.664562i	$0.231382\pi$
$308$	66.5118	3.78986
$309$	−0.496883	−0.0282667
$310$	6.00906	0.341292
$311$	8.45362	0.479361	0.239680	−	0.970852i	$-0.422957\pi$
$311$	8.45362	0.479361	0.239680	+	0.970852i	$0.422957\pi$
$312$	−0.449463	−0.0254458
$313$	−19.0223	−1.07520	−0.537602	−	0.843199i	$-0.680670\pi$
$313$	−19.0223	−1.07520	−0.537602	+	0.843199i	$0.680670\pi$
$314$	36.4246	2.05556
$315$	13.8642	0.781159
$316$	43.8579	2.46720
$317$	26.8222	1.50649	0.753243	−	0.657743i	$-0.228489\pi$
$317$	26.8222	1.50649	0.753243	+	0.657743i	$0.228489\pi$
$318$	0.316686	0.0177589
$319$	−16.9069	−0.946604
$320$	−24.4620	−1.36747
$321$	0.716041	0.0399655
$322$	10.2779	0.572765
$323$	0	0
$324$	47.8463	2.65813
$325$	−0.983436	−0.0545512
$326$	1.89242	0.104811
$327$	−0.480807	−0.0265887
$328$	−39.5597	−2.18432
$329$	−14.8534	−0.818894
$330$	−0.370288	−0.0203837
$331$	−26.9566	−1.48167	−0.740834	−	0.671688i	$-0.765570\pi$
$331$	−26.9566	−1.48167	−0.740834	+	0.671688i	$0.765570\pi$
$332$	−72.4327	−3.97526
$333$	−8.40697	−0.460699
$334$	11.8315	0.647392
$335$	−4.54135	−0.248121
$336$	3.22374	0.175869
$337$	−0.104550	−0.00569521	−0.00284760	−	0.999996i	$-0.500906\pi$
$337$	−0.104550	−0.00569521	−0.00284760	+	0.999996i	$0.500906\pi$
$338$	−32.5776	−1.77199
$339$	−0.906301	−0.0492235
$340$	21.4401	1.16275
$341$	−5.98805	−0.324271
$342$	0	0
$343$	34.1999	1.84662
$344$	18.6260	1.00425
$345$	−0.0416071	−0.00224005
$346$	−29.5354	−1.58783
$347$	−3.92015	−0.210444	−0.105222	−	0.994449i	$-0.533555\pi$
$347$	−3.92015	−0.210444	−0.105222	+	0.994449i	$0.533555\pi$
$348$	−1.69323	−0.0907668
$349$	26.9004	1.43995	0.719973	−	0.694003i	$-0.244154\pi$
$349$	26.9004	1.43995	0.719973	+	0.694003i	$0.244154\pi$
$350$	12.5227	0.669364
$351$	0.299000	0.0159594
$352$	51.7773	2.75974
$353$	2.70152	0.143787	0.0718937	−	0.997412i	$-0.477096\pi$
$353$	2.70152	0.143787	0.0718937	+	0.997412i	$0.477096\pi$
$354$	−1.23406	−0.0655893
$355$	12.4378	0.660128
$356$	50.5318	2.67818
$357$	−0.943212	−0.0499201
$358$	−6.71911	−0.355116
$359$	−2.02574	−0.106914	−0.0534571	−	0.998570i	$-0.517024\pi$
$359$	−2.02574	−0.106914	−0.0534571	+	0.998570i	$0.517024\pi$
$360$	27.0233	1.42425
$361$	0	0
$362$	−52.8325	−2.77681
$363$	−0.188644	−0.00990124
$364$	−24.2446	−1.27076
$365$	−0.461968	−0.0241805
$366$	1.25082	0.0653813
$367$	−9.11202	−0.475644	−0.237822	−	0.971309i	$-0.576433\pi$
$367$	−9.11202	−0.475644	−0.237822	+	0.971309i	$0.576433\pi$
$368$	11.2840	0.588219
$369$	13.1527	0.684700
$370$	−7.59349	−0.394767
$371$	10.6725	0.554087
$372$	−0.599706	−0.0310933
$373$	4.43869	0.229826	0.114913	−	0.993376i	$-0.463341\pi$
$373$	4.43869	0.229826	0.114913	+	0.993376i	$0.463341\pi$
$374$	−29.3822	−1.51932
$375$	−0.0506943	−0.00261784
$376$	−28.9513	−1.49305
$377$	6.16283	0.317402
$378$	−3.80733	−0.195828
$379$	25.0589	1.28719	0.643594	−	0.765367i	$-0.277443\pi$
$379$	25.0589	1.28719	0.643594	+	0.765367i	$0.277443\pi$
$380$	0	0
$381$	−0.739221	−0.0378714
$382$	36.0434	1.84414
$383$	−22.7732	−1.16366	−0.581829	−	0.813311i	$-0.697663\pi$
$383$	−22.7732	−1.16366	−0.581829	+	0.813311i	$0.697663\pi$
$384$	1.41158	0.0720346
$385$	−12.4789	−0.635983
$386$	−26.4899	−1.34830
$387$	−6.19271	−0.314793
$388$	70.9829	3.60361
$389$	14.3598	0.728072	0.364036	−	0.931385i	$-0.381398\pi$
$389$	14.3598	0.728072	0.364036	+	0.931385i	$0.381398\pi$
$390$	0.134976	0.00683477
$391$	−3.30150	−0.166964
$392$	129.769	6.55430
$393$	0.397160	0.0200341
$394$	45.0080	2.26747
$395$	−8.22856	−0.414024
$396$	−43.1025	−2.16598
$397$	17.2920	0.867863	0.433931	−	0.900946i	$-0.357126\pi$
$397$	17.2920	0.867863	0.433931	+	0.900946i	$0.357126\pi$
$398$	42.2586	2.11823
$399$	0	0
$400$	13.7485	0.687424
$401$	−7.80055	−0.389541	−0.194770	−	0.980849i	$-0.562396\pi$
$401$	−7.80055	−0.389541	−0.194770	+	0.980849i	$0.562396\pi$
$402$	0.623297	0.0310872
$403$	2.18274	0.108730
$404$	−50.1805	−2.49658
$405$	−8.97688	−0.446065
$406$	−78.4748	−3.89464
$407$	7.56694	0.375079
$408$	−1.83845	−0.0910169
$409$	16.0855	0.795379	0.397689	−	0.917520i	$-0.369812\pi$
$409$	16.0855	0.795379	0.397689	+	0.917520i	$0.369812\pi$
$410$	11.8800	0.586709
$411$	1.08950	0.0537411
$412$	−52.2417	−2.57377
$413$	−41.5883	−2.04642
$414$	−6.66051	−0.327346
$415$	13.5897	0.667094
$416$	−18.8737	−0.925357
$417$	−1.13414	−0.0555393
$418$	0	0
$419$	−36.1482	−1.76596	−0.882979	−	0.469413i	$-0.844466\pi$
$419$	−36.1482	−1.76596	−0.882979	+	0.469413i	$0.844466\pi$
$420$	−1.24977	−0.0609823
$421$	23.3780	1.13937	0.569687	−	0.821862i	$-0.307064\pi$
$421$	23.3780	1.13937	0.569687	+	0.821862i	$0.307064\pi$
$422$	−36.6233	−1.78280
$423$	9.62562	0.468014
$424$	20.8021	1.01024
$425$	−4.02257	−0.195123
$426$	−1.70707	−0.0827080
$427$	42.1531	2.03993
$428$	75.2838	3.63898
$429$	−0.134504	−0.00649391
$430$	−5.59349	−0.269742
$431$	15.9481	0.768194	0.384097	−	0.923293i	$-0.374513\pi$
$431$	15.9481	0.768194	0.384097	+	0.923293i	$0.374513\pi$
$432$	−4.18003	−0.201112
$433$	35.7622	1.71862	0.859312	−	0.511452i	$-0.170892\pi$
$433$	35.7622	1.71862	0.859312	+	0.511452i	$0.170892\pi$
$434$	−27.7941	−1.33416
$435$	0.317682	0.0152317
$436$	−50.5516	−2.42098
$437$	0	0
$438$	0.0634047	0.00302960
$439$	7.09780	0.338759	0.169380	−	0.985551i	$-0.445824\pi$
$439$	7.09780	0.338759	0.169380	+	0.985551i	$0.445824\pi$
$440$	−24.3231	−1.15956
$441$	−43.1450	−2.05452
$442$	10.7103	0.509436
$443$	6.43765	0.305862	0.152931	−	0.988237i	$-0.451129\pi$
$443$	6.43765	0.305862	0.152931	+	0.988237i	$0.451129\pi$
$444$	0.757833	0.0359651
$445$	−9.48072	−0.449429
$446$	50.2605	2.37990
$447$	0.386428	0.0182774
$448$	113.146	5.34563
$449$	23.4226	1.10538	0.552690	−	0.833387i	$-0.313601\pi$
$449$	23.4226	1.10538	0.552690	+	0.833387i	$0.313601\pi$
$450$	−8.11521	−0.382555
$451$	−11.8384	−0.557450
$452$	−95.2876	−4.48195
$453$	0.255116	0.0119864
$454$	−41.6632	−1.95535
$455$	4.54875	0.213249
$456$	0	0
$457$	16.2761	0.761365	0.380683	−	0.924706i	$-0.375689\pi$
$457$	16.2761	0.761365	0.380683	+	0.924706i	$0.375689\pi$
$458$	−28.6156	−1.33712
$459$	1.22301	0.0570850
$460$	−4.37453	−0.203963
$461$	23.1172	1.07667	0.538337	−	0.842730i	$-0.319053\pi$
$461$	23.1172	1.07667	0.538337	+	0.842730i	$0.319053\pi$
$462$	1.71272	0.0796828
$463$	−5.95682	−0.276837	−0.138418	−	0.990374i	$-0.544202\pi$
$463$	−5.95682	−0.276837	−0.138418	+	0.990374i	$0.544202\pi$
$464$	−86.1566	−3.99972
$465$	0.112516	0.00521782
$466$	12.4646	0.577412
$467$	−9.02736	−0.417736	−0.208868	−	0.977944i	$-0.566978\pi$
$467$	−9.02736	−0.417736	−0.208868	+	0.977944i	$0.566978\pi$
$468$	15.7115	0.726266
$469$	21.0054	0.969940
$470$	8.69421	0.401034
$471$	0.682030	0.0314263
$472$	−81.0613	−3.73115
$473$	5.57393	0.256290
$474$	1.12936	0.0518734
$475$	0	0
$476$	−99.1684	−4.54537
$477$	−6.91621	−0.316671
$478$	25.2231	1.15368
$479$	34.6097	1.58136	0.790678	−	0.612232i	$-0.209728\pi$
$479$	34.6097	1.58136	0.790678	+	0.612232i	$0.209728\pi$
$480$	−0.972902	−0.0444067
$481$	−2.75827	−0.125766
$482$	−71.4885	−3.25621
$483$	0.192448	0.00875668
$484$	−19.8338	−0.901538
$485$	−13.3177	−0.604727
$486$	3.70150	0.167903
$487$	−40.3707	−1.82937	−0.914685	−	0.404168i	$-0.867561\pi$
$487$	−40.3707	−1.82937	−0.914685	+	0.404168i	$0.867561\pi$
$488$	82.1623	3.71931
$489$	0.0354345	0.00160240
$490$	−38.9701	−1.76049
$491$	11.6820	0.527202	0.263601	−	0.964632i	$-0.415090\pi$
$491$	11.6820	0.527202	0.263601	+	0.964632i	$0.415090\pi$
$492$	−1.18562	−0.0534520
$493$	25.2080	1.13531
$494$	0	0
$495$	8.08684	0.363476
$496$	−30.5148	−1.37016
$497$	−57.5292	−2.58054
$498$	−1.86518	−0.0835808
$499$	−24.4115	−1.09281	−0.546405	−	0.837521i	$-0.684004\pi$
$499$	−24.4115	−1.09281	−0.546405	+	0.837521i	$0.684004\pi$
$500$	−5.32995	−0.238363
$501$	0.221539	0.00989762
$502$	9.27789	0.414092
$503$	−4.31551	−0.192419	−0.0962096	−	0.995361i	$-0.530672\pi$
$503$	−4.31551	−0.192419	−0.0962096	+	0.995361i	$0.530672\pi$
$504$	−124.992	−5.56760
$505$	9.41482	0.418954
$506$	5.99499	0.266510
$507$	−0.609997	−0.0270909
$508$	−77.7210	−3.44831
$509$	−29.0220	−1.28638	−0.643189	−	0.765707i	$-0.722389\pi$
$509$	−29.0220	−1.28638	−0.643189	+	0.765707i	$0.722389\pi$
$510$	0.552095	0.0244472
$511$	2.13677	0.0945251
$512$	15.9564	0.705181
$513$	0	0
$514$	−63.5103	−2.80132
$515$	9.80154	0.431908
$516$	0.558232	0.0245748
$517$	−8.66382	−0.381034
$518$	35.1226	1.54320
$519$	−0.553034	−0.0242755
$520$	8.86614	0.388806
$521$	21.8159	0.955772	0.477886	−	0.878422i	$-0.341403\pi$
$521$	21.8159	0.955772	0.477886	+	0.878422i	$0.341403\pi$
$522$	50.8550	2.22586
$523$	42.2516	1.84753	0.923767	−	0.382956i	$-0.125094\pi$
$523$	42.2516	1.84753	0.923767	+	0.382956i	$0.125094\pi$
$524$	41.7570	1.82416
$525$	0.234480	0.0102335
$526$	−41.5384	−1.81116
$527$	8.92812	0.388915
$528$	1.88037	0.0818327
$529$	−22.3264	−0.970712
$530$	−6.24697	−0.271351
$531$	26.9509	1.16957
$532$	0	0
$533$	4.31529	0.186916
$534$	1.30122	0.0563093
$535$	−14.1247	−0.610663
$536$	40.9425	1.76844
$537$	−0.125811	−0.00542917
$538$	13.5528	0.584304
$539$	38.8339	1.67269
$540$	1.62050	0.0697350
$541$	11.1056	0.477467	0.238734	−	0.971085i	$-0.423268\pi$
$541$	11.1056	0.477467	0.238734	+	0.971085i	$0.423268\pi$
$542$	9.04079	0.388335
$543$	−0.989259	−0.0424532
$544$	−77.1994	−3.30990
$545$	9.48443	0.406268
$546$	−0.624312	−0.0267181
$547$	8.25356	0.352897	0.176448	−	0.984310i	$-0.443539\pi$
$547$	8.25356	0.352897	0.176448	+	0.984310i	$0.443539\pi$
$548$	114.549	4.89329
$549$	−27.3170	−1.16586
$550$	7.30433	0.311458
$551$	0	0
$552$	0.375108	0.0159656
$553$	38.0601	1.61848
$554$	15.6299	0.664052
$555$	−0.142184	−0.00603536
$556$	−119.243	−5.05702
$557$	−9.67516	−0.409950	−0.204975	−	0.978767i	$-0.565711\pi$
$557$	−9.67516	−0.409950	−0.204975	+	0.978767i	$0.565711\pi$
$558$	18.0117	0.762498
$559$	−2.03179	−0.0859354
$560$	−63.5917	−2.68724
$561$	−0.550165	−0.0232280
$562$	32.2783	1.36158
$563$	−13.0535	−0.550139	−0.275070	−	0.961424i	$-0.588701\pi$
$563$	−13.0535	−0.550139	−0.275070	+	0.961424i	$0.588701\pi$
$564$	−0.867685	−0.0365361
$565$	17.8778	0.752123
$566$	80.7609	3.39464
$567$	41.5213	1.74373
$568$	−112.132	−4.70497
$569$	35.4050	1.48425	0.742127	−	0.670259i	$-0.233817\pi$
$569$	35.4050	1.48425	0.742127	+	0.670259i	$0.233817\pi$
$570$	0	0
$571$	36.1565	1.51310	0.756551	−	0.653934i	$-0.226883\pi$
$571$	36.1565	1.51310	0.756551	+	0.653934i	$0.226883\pi$
$572$	−14.1416	−0.591291
$573$	0.674893	0.0281941
$574$	−54.9491	−2.29353
$575$	0.820744	0.0342274
$576$	−73.3231	−3.05513
$577$	−19.6308	−0.817242	−0.408621	−	0.912704i	$-0.633990\pi$
$577$	−19.6308	−0.817242	−0.408621	+	0.912704i	$0.633990\pi$
$578$	−2.21708	−0.0922184
$579$	−0.496009	−0.0206134
$580$	33.4008	1.38689
$581$	−62.8575	−2.60777
$582$	1.82785	0.0757668
$583$	6.22513	0.257819
$584$	4.16486	0.172343
$585$	−2.94778	−0.121876
$586$	−12.2163	−0.504652
$587$	21.7991	0.899745	0.449873	−	0.893093i	$-0.351469\pi$
$587$	21.7991	0.899745	0.449873	+	0.893093i	$0.351469\pi$
$588$	3.88923	0.160389
$589$	0	0
$590$	24.3431	1.00219
$591$	0.842749	0.0346661
$592$	38.5608	1.58484
$593$	−1.74447	−0.0716366	−0.0358183	−	0.999358i	$-0.511404\pi$
$593$	−1.74447	−0.0716366	−0.0358183	+	0.999358i	$0.511404\pi$
$594$	−2.22078	−0.0911196
$595$	18.6059	0.762766
$596$	40.6287	1.66422
$597$	0.791268	0.0323845
$598$	−2.18527	−0.0893622
$599$	11.2977	0.461613	0.230807	−	0.973000i	$-0.425864\pi$
$599$	11.2977	0.461613	0.230807	+	0.973000i	$0.425864\pi$
$600$	0.457033	0.0186583
$601$	37.3245	1.52250	0.761250	−	0.648459i	$-0.224586\pi$
$601$	37.3245	1.52250	0.761250	+	0.648459i	$0.224586\pi$
$602$	25.8719	1.05446
$603$	−13.6124	−0.554339
$604$	26.8227	1.09140
$605$	3.72121	0.151289
$606$	−1.29218	−0.0524911
$607$	−18.4399	−0.748453	−0.374226	−	0.927337i	$-0.622092\pi$
$607$	−18.4399	−0.748453	−0.374226	+	0.927337i	$0.622092\pi$
$608$	0	0
$609$	−1.46940	−0.0595429
$610$	−24.6737	−0.999010
$611$	3.15810	0.127763
$612$	64.2653	2.59777
$613$	4.50009	0.181757	0.0908784	−	0.995862i	$-0.471033\pi$
$613$	4.50009	0.181757	0.0908784	+	0.995862i	$0.471033\pi$
$614$	70.8934	2.86102
$615$	0.222445	0.00896987
$616$	112.503	4.53288
$617$	−17.6582	−0.710893	−0.355446	−	0.934697i	$-0.615671\pi$
$617$	−17.6582	−0.710893	−0.355446	+	0.934697i	$0.615671\pi$
$618$	−1.34525	−0.0541141
$619$	14.1707	0.569569	0.284784	−	0.958592i	$-0.408078\pi$
$619$	14.1707	0.569569	0.284784	+	0.958592i	$0.408078\pi$
$620$	11.8299	0.475098
$621$	−0.249536	−0.0100135
$622$	22.8872	0.917694
$623$	43.8518	1.75688
$624$	−0.685426	−0.0274390
$625$	1.00000	0.0400000
$626$	−51.5008	−2.05838
$627$	0	0
$628$	71.7080	2.86146
$629$	−11.2822	−0.449852
$630$	37.5358	1.49546
$631$	44.4336	1.76887	0.884437	−	0.466660i	$-0.154543\pi$
$631$	44.4336	1.76887	0.884437	+	0.466660i	$0.154543\pi$
$632$	74.1844	2.95090
$633$	−0.685751	−0.0272562
$634$	72.6181	2.88403
$635$	14.5819	0.578666
$636$	0.623450	0.0247214
$637$	−14.1556	−0.560864
$638$	−45.7735	−1.81219
$639$	37.2813	1.47483
$640$	−27.8450	−1.10067
$641$	24.6294	0.972804	0.486402	−	0.873735i	$-0.338309\pi$
$641$	24.6294	0.972804	0.486402	+	0.873735i	$0.338309\pi$
$642$	1.93860	0.0765105
$643$	5.84864	0.230648	0.115324	−	0.993328i	$-0.463209\pi$
$643$	5.84864	0.230648	0.115324	+	0.993328i	$0.463209\pi$
$644$	20.2338	0.797323
$645$	−0.104735	−0.00412393
$646$	0	0
$647$	−35.2320	−1.38511	−0.692557	−	0.721363i	$-0.743516\pi$
$647$	−35.2320	−1.38511	−0.692557	+	0.721363i	$0.743516\pi$
$648$	80.9308	3.17926
$649$	−24.2580	−0.952209
$650$	−2.66254	−0.104434
$651$	−0.520429	−0.0203972
$652$	3.72555	0.145904
$653$	9.97371	0.390302	0.195151	−	0.980773i	$-0.437480\pi$
$653$	9.97371	0.390302	0.195151	+	0.980773i	$0.437480\pi$
$654$	−1.30173	−0.0509017
$655$	−7.83440	−0.306115
$656$	−60.3280	−2.35541
$657$	−1.38472	−0.0540229
$658$	−40.2139	−1.56770
$659$	0.231824	0.00903060	0.00451530	−	0.999990i	$-0.498563\pi$
$659$	0.231824	0.00903060	0.00451530	+	0.999990i	$0.498563\pi$
$660$	−0.728975	−0.0283753
$661$	−6.50609	−0.253058	−0.126529	−	0.991963i	$-0.540384\pi$
$661$	−6.50609	−0.253058	−0.126529	+	0.991963i	$0.540384\pi$
$662$	−72.9820	−2.83653
$663$	0.200544	0.00778848
$664$	−122.518	−4.75462
$665$	0	0
$666$	−22.7609	−0.881969
$667$	−5.14330	−0.199149
$668$	23.2924	0.901209
$669$	0.941100	0.0363850
$670$	−12.2952	−0.475005
$671$	24.5875	0.949189
$672$	4.50003	0.173592
$673$	−33.4539	−1.28955	−0.644776	−	0.764372i	$-0.723049\pi$
$673$	−33.4539	−1.28955	−0.644776	+	0.764372i	$0.723049\pi$
$674$	−0.283058	−0.0109030
$675$	−0.304036	−0.0117023
$676$	−64.1345	−2.46671
$677$	2.01330	0.0773776	0.0386888	−	0.999251i	$-0.487682\pi$
$677$	2.01330	0.0773776	0.0386888	+	0.999251i	$0.487682\pi$
$678$	−2.45371	−0.0942341
$679$	61.5994	2.36397
$680$	36.2654	1.39071
$681$	−0.780119	−0.0298942
$682$	−16.2120	−0.620789
$683$	−12.4838	−0.477680	−0.238840	−	0.971059i	$-0.576767\pi$
$683$	−12.4838	−0.477680	−0.238840	+	0.971059i	$0.576767\pi$
$684$	0	0
$685$	−21.4916	−0.821150
$686$	92.5923	3.53519
$687$	−0.535812	−0.0204425
$688$	28.4045	1.08291
$689$	−2.26916	−0.0864481
$690$	−0.112647	−0.00428838
$691$	29.3888	1.11800	0.559001	−	0.829167i	$-0.311185\pi$
$691$	29.3888	1.11800	0.559001	+	0.829167i	$0.311185\pi$
$692$	−58.1455	−2.21036
$693$	−37.4046	−1.42088
$694$	−10.6134	−0.402877
$695$	22.3722	0.848626
$696$	−2.86406	−0.108562
$697$	17.6510	0.668578
$698$	72.8298	2.75665
$699$	0.233393	0.00882774
$700$	24.6530	0.931795
$701$	33.1570	1.25232	0.626161	−	0.779694i	$-0.284625\pi$
$701$	33.1570	1.25232	0.626161	+	0.779694i	$0.284625\pi$
$702$	0.809508	0.0305529
$703$	0	0
$704$	65.9966	2.48734
$705$	0.162794	0.00613118
$706$	7.31406	0.275268
$707$	−43.5470	−1.63775
$708$	−2.42945	−0.0913043
$709$	31.6217	1.18758	0.593789	−	0.804621i	$-0.297631\pi$
$709$	31.6217	1.18758	0.593789	+	0.804621i	$0.297631\pi$
$710$	33.6739	1.26376
$711$	−24.6645	−0.924993
$712$	85.4731	3.20324
$713$	−1.82165	−0.0682212
$714$	−2.55364	−0.0955676
$715$	2.65324	0.0992254
$716$	−13.2277	−0.494342
$717$	0.472289	0.0176380
$718$	−5.48445	−0.204678
$719$	−14.5917	−0.544179	−0.272090	−	0.962272i	$-0.587715\pi$
$719$	−14.5917	−0.544179	−0.272090	+	0.962272i	$0.587715\pi$
$720$	41.2101	1.53581
$721$	−45.3357	−1.68839
$722$	0	0
$723$	−1.33858	−0.0497824
$724$	−104.010	−3.86549
$725$	−6.26663	−0.232737
$726$	−0.510733	−0.0189551
$727$	−22.5744	−0.837238	−0.418619	−	0.908162i	$-0.637486\pi$
$727$	−22.5744	−0.837238	−0.418619	+	0.908162i	$0.637486\pi$
$728$	−41.0091	−1.51990
$729$	−26.8613	−0.994864
$730$	−1.25073	−0.0462915
$731$	−8.31067	−0.307381
$732$	2.46245	0.0910146
$733$	−47.6045	−1.75831	−0.879156	−	0.476535i	$-0.841893\pi$
$733$	−47.6045	−1.75831	−0.879156	+	0.476535i	$0.841893\pi$
$734$	−24.6698	−0.910578
$735$	−0.729693	−0.0269151
$736$	15.7514	0.580603
$737$	12.2522	0.451317
$738$	35.6093	1.31080
$739$	−8.32304	−0.306168	−0.153084	−	0.988213i	$-0.548920\pi$
$739$	−8.32304	−0.306168	−0.153084	+	0.988213i	$0.548920\pi$
$740$	−14.9491	−0.549538
$741$	0	0
$742$	28.8945	1.06075
$743$	2.64935	0.0971952	0.0485976	−	0.998818i	$-0.484525\pi$
$743$	2.64935	0.0971952	0.0485976	+	0.998818i	$0.484525\pi$
$744$	−1.01439	−0.0371892
$745$	−7.62271	−0.279275
$746$	12.0172	0.439983
$747$	40.7343	1.49039
$748$	−57.8438	−2.11498
$749$	65.3317	2.38717
$750$	−0.137249	−0.00501163
$751$	2.19432	0.0800718	0.0400359	−	0.999198i	$-0.487253\pi$
$751$	2.19432	0.0800718	0.0400359	+	0.999198i	$0.487253\pi$
$752$	−44.1504	−1.61000
$753$	0.173723	0.00633083
$754$	16.6852	0.607638
$755$	−5.03245	−0.183149
$756$	−7.49538	−0.272604
$757$	28.5999	1.03948	0.519741	−	0.854324i	$-0.326029\pi$
$757$	28.5999	1.03948	0.519741	+	0.854324i	$0.326029\pi$
$758$	67.8441	2.46421
$759$	0.112253	0.00407452
$760$	0	0
$761$	−27.1217	−0.983160	−0.491580	−	0.870832i	$-0.663581\pi$
$761$	−27.1217	−0.983160	−0.491580	+	0.870832i	$0.663581\pi$
$762$	−2.00136	−0.0725016
$763$	−43.8689	−1.58816
$764$	70.9576	2.56716
$765$	−12.0574	−0.435936
$766$	−61.6560	−2.22772
$767$	8.84242	0.319281
$768$	1.34154	0.0484087
$769$	−12.5266	−0.451720	−0.225860	−	0.974160i	$-0.572519\pi$
$769$	−12.5266	−0.451720	−0.225860	+	0.974160i	$0.572519\pi$
$770$	−33.7852	−1.21753
$771$	−1.18919	−0.0428278
$772$	−52.1499	−1.87691
$773$	−10.6355	−0.382534	−0.191267	−	0.981538i	$-0.561260\pi$
$773$	−10.6355	−0.382534	−0.191267	+	0.981538i	$0.561260\pi$
$774$	−16.7661	−0.602644
$775$	−2.21950	−0.0797269
$776$	120.066	4.31011
$777$	0.657652	0.0235931
$778$	38.8776	1.39383
$779$	0	0
$780$	0.265723	0.00951440
$781$	−33.5561	−1.20073
$782$	−8.93846	−0.319639
$783$	1.90528	0.0680891
$784$	197.896	7.06770
$785$	−13.4538	−0.480186
$786$	1.07527	0.0383535
$787$	−6.31654	−0.225160	−0.112580	−	0.993643i	$-0.535912\pi$
$787$	−6.31654	−0.225160	−0.112580	+	0.993643i	$0.535912\pi$
$788$	88.6059	3.15645
$789$	−0.777784	−0.0276898
$790$	−22.2779	−0.792613
$791$	−82.6911	−2.94016
$792$	−72.9067	−2.59063
$793$	−8.96252	−0.318268
$794$	46.8163	1.66145
$795$	−0.116971	−0.00414853
$796$	83.1932	2.94870
$797$	41.1908	1.45905	0.729527	−	0.683952i	$-0.239740\pi$
$797$	41.1908	1.45905	0.729527	+	0.683952i	$0.239740\pi$
$798$	0	0
$799$	12.9177	0.456994
$800$	19.1915	0.678524
$801$	−28.4178	−1.00409
$802$	−21.1191	−0.745742
$803$	1.24635	0.0439829
$804$	1.22707	0.0432753
$805$	−3.79624	−0.133800
$806$	5.90953	0.208154
$807$	0.253769	0.00893310
$808$	−84.8791	−2.98603
$809$	25.2813	0.888843	0.444422	−	0.895818i	$-0.353409\pi$
$809$	25.2813	0.888843	0.444422	+	0.895818i	$0.353409\pi$
$810$	−24.3039	−0.853952
$811$	29.1730	1.02440	0.512201	−	0.858866i	$-0.328830\pi$
$811$	29.1730	1.02440	0.512201	+	0.858866i	$0.328830\pi$
$812$	−154.491	−5.42157
$813$	0.169284	0.00593704
$814$	20.4866	0.718057
$815$	−0.698984	−0.0244843
$816$	−2.80361	−0.0981461
$817$	0	0
$818$	43.5498	1.52268
$819$	13.6346	0.476430
$820$	23.3877	0.816734
$821$	−43.2753	−1.51032	−0.755159	−	0.655542i	$-0.772440\pi$
$821$	−43.2753	−1.51032	−0.755159	+	0.655542i	$0.772440\pi$
$822$	2.94970	0.102883
$823$	50.7319	1.76840	0.884202	−	0.467105i	$-0.154703\pi$
$823$	50.7319	1.76840	0.884202	+	0.467105i	$0.154703\pi$
$824$	−88.3655	−3.07836
$825$	0.136769	0.00476170
$826$	−112.596	−3.91770
$827$	−24.7164	−0.859474	−0.429737	−	0.902954i	$-0.641394\pi$
$827$	−24.7164	−0.859474	−0.429737	+	0.902954i	$0.641394\pi$
$828$	−13.1123	−0.455685
$829$	19.0346	0.661101	0.330550	−	0.943788i	$-0.392766\pi$
$829$	19.0346	0.661101	0.330550	+	0.943788i	$0.392766\pi$
$830$	36.7927	1.27709
$831$	0.292662	0.0101523
$832$	−24.0568	−0.834020
$833$	−57.9009	−2.00615
$834$	−3.07057	−0.106325
$835$	−4.37009	−0.151233
$836$	0	0
$837$	0.674808	0.0233248
$838$	−97.8674	−3.38077
$839$	−2.49865	−0.0862631	−0.0431316	−	0.999069i	$-0.513733\pi$
$839$	−2.49865	−0.0862631	−0.0431316	+	0.999069i	$0.513733\pi$
$840$	−2.11395	−0.0729380
$841$	10.2706	0.354159
$842$	63.2933	2.18123
$843$	0.604393	0.0208164
$844$	−72.0992	−2.48176
$845$	12.0329	0.413943
$846$	26.0603	0.895971
$847$	−17.2119	−0.591409
$848$	31.7230	1.08937
$849$	1.51220	0.0518987
$850$	−10.8907	−0.373547
$851$	2.30196	0.0789103
$852$	−3.36066	−0.115134
$853$	14.1634	0.484945	0.242472	−	0.970158i	$-0.422042\pi$
$853$	14.1634	0.484945	0.242472	+	0.970158i	$0.422042\pi$
$854$	114.125	3.90527
$855$	0	0
$856$	127.341	4.35241
$857$	−22.5038	−0.768714	−0.384357	−	0.923185i	$-0.625577\pi$
$857$	−22.5038	−0.768714	−0.384357	+	0.923185i	$0.625577\pi$
$858$	−0.364155	−0.0124320
$859$	4.04947	0.138166	0.0690830	−	0.997611i	$-0.477993\pi$
$859$	4.04947	0.138166	0.0690830	+	0.997611i	$0.477993\pi$
$860$	−11.0117	−0.375497
$861$	−1.02889	−0.0350645
$862$	43.1777	1.47064
$863$	−48.4795	−1.65026	−0.825131	−	0.564941i	$-0.808899\pi$
$863$	−48.4795	−1.65026	−0.825131	+	0.564941i	$0.808899\pi$
$864$	−5.83491	−0.198508
$865$	10.9092	0.370924
$866$	96.8223	3.29016
$867$	−0.0415136	−0.00140988
$868$	−54.7174	−1.85723
$869$	22.2000	0.753085
$870$	0.860090	0.0291598
$871$	−4.46613	−0.151329
$872$	−85.5066	−2.89562
$873$	−39.9190	−1.35105
$874$	0	0
$875$	−4.62536	−0.156366
$876$	0.124823	0.00421738
$877$	11.3354	0.382769	0.191384	−	0.981515i	$-0.438702\pi$
$877$	11.3354	0.382769	0.191384	+	0.981515i	$0.438702\pi$
$878$	19.2165	0.648525
$879$	−0.228744	−0.00771535
$880$	−37.0924	−1.25038
$881$	−21.3745	−0.720126	−0.360063	−	0.932928i	$-0.617245\pi$
$881$	−21.3745	−0.720126	−0.360063	+	0.932928i	$0.617245\pi$
$882$	−116.810	−3.93320
$883$	2.10718	0.0709124	0.0354562	−	0.999371i	$-0.488712\pi$
$883$	2.10718	0.0709124	0.0354562	+	0.999371i	$0.488712\pi$
$884$	21.0850	0.709165
$885$	0.455811	0.0153219
$886$	17.4292	0.585546
$887$	−0.211839	−0.00711286	−0.00355643	−	0.999994i	$-0.501132\pi$
$887$	−0.211839	−0.00711286	−0.00355643	+	0.999994i	$0.501132\pi$
$888$	1.28185	0.0430162
$889$	−67.4467	−2.26209
$890$	−25.6680	−0.860393
$891$	24.2189	0.811365
$892$	98.9463	3.31297
$893$	0	0
$894$	1.04621	0.0349906
$895$	2.48177	0.0829563
$896$	128.793	4.30268
$897$	−0.0409179	−0.00136621
$898$	63.4141	2.11615
$899$	13.9088	0.463885
$900$	−15.9762	−0.532539
$901$	−9.28160	−0.309215
$902$	−32.0512	−1.06719
$903$	0.484437	0.0161210
$904$	−161.176	−5.36065
$905$	19.5142	0.648674
$906$	0.690699	0.0229469
$907$	23.3886	0.776607	0.388303	−	0.921532i	$-0.373061\pi$
$907$	23.3886	0.776607	0.388303	+	0.921532i	$0.373061\pi$
$908$	−82.0210	−2.72196
$909$	28.2203	0.936007
$910$	12.3152	0.408246
$911$	33.2724	1.10236	0.551181	−	0.834386i	$-0.314177\pi$
$911$	33.2724	1.10236	0.551181	+	0.834386i	$0.314177\pi$
$912$	0	0
$913$	−36.6641	−1.21340
$914$	44.0658	1.45757
$915$	−0.462002	−0.0152733
$916$	−56.3347	−1.86135
$917$	36.2370	1.19665
$918$	3.31115	0.109284
$919$	−41.9433	−1.38358	−0.691792	−	0.722097i	$-0.743178\pi$
$919$	−41.9433	−1.38358	−0.691792	+	0.722097i	$0.743178\pi$
$920$	−7.39940	−0.243951
$921$	1.32744	0.0437406
$922$	62.5872	2.06120
$923$	12.2317	0.402613
$924$	3.37177	0.110923
$925$	2.80473	0.0922189
$926$	−16.1274	−0.529980
$927$	29.3794	0.964947
$928$	−120.266	−3.94793
$929$	18.5140	0.607424	0.303712	−	0.952764i	$-0.401774\pi$
$929$	18.5140	0.607424	0.303712	+	0.952764i	$0.401774\pi$
$930$	0.304625	0.00998905
$931$	0	0
$932$	24.5387	0.803792
$933$	0.428550	0.0140301
$934$	−24.4406	−0.799720
$935$	10.8526	0.354918
$936$	26.5756	0.868652
$937$	−15.7208	−0.513576	−0.256788	−	0.966468i	$-0.582664\pi$
$937$	−15.7208	−0.513576	−0.256788	+	0.966468i	$0.582664\pi$
$938$	56.8698	1.85687
$939$	−0.964323	−0.0314695
$940$	17.1160	0.558263
$941$	−4.62589	−0.150800	−0.0753999	−	0.997153i	$-0.524023\pi$
$941$	−4.62589	−0.150800	−0.0753999	+	0.997153i	$0.524023\pi$
$942$	1.84652	0.0601629
$943$	−3.60141	−0.117278
$944$	−123.617	−4.02341
$945$	1.40628	0.0457461
$946$	15.0908	0.490644
$947$	−22.5068	−0.731372	−0.365686	−	0.930738i	$-0.619166\pi$
$947$	−22.5068	−0.731372	−0.365686	+	0.930738i	$0.619166\pi$
$948$	2.22334	0.0722109
$949$	−0.454316	−0.0147477
$950$	0	0
$951$	1.35973	0.0440924
$952$	−167.741	−5.43651
$953$	−21.0552	−0.682046	−0.341023	−	0.940055i	$-0.610773\pi$
$953$	−21.0552	−0.682046	−0.341023	+	0.940055i	$0.610773\pi$
$954$	−18.7249	−0.606240
$955$	−13.3130	−0.430798
$956$	49.6560	1.60599
$957$	−0.857083	−0.0277056
$958$	93.7018	3.02737
$959$	99.4063	3.21000
$960$	−1.24008	−0.0400235
$961$	−26.0738	−0.841090
$962$	−7.46771	−0.240769
$963$	−42.3377	−1.36431
$964$	−140.737	−4.53284
$965$	9.78430	0.314968
$966$	0.521031	0.0167639
$967$	−40.9471	−1.31677	−0.658384	−	0.752682i	$-0.728760\pi$
$967$	−40.9471	−1.31677	−0.658384	+	0.752682i	$0.728760\pi$
$968$	−33.5484	−1.07829
$969$	0	0
$970$	−36.0563	−1.15770
$971$	33.1052	1.06240	0.531198	−	0.847248i	$-0.321742\pi$
$971$	33.1052	1.06240	0.531198	+	0.847248i	$0.321742\pi$
$972$	7.28702	0.233731
$973$	−103.480	−3.31740
$974$	−109.299	−3.50217
$975$	−0.0498546	−0.00159663
$976$	125.297	4.01064
$977$	5.99974	0.191949	0.0959743	−	0.995384i	$-0.469403\pi$
$977$	5.99974	0.191949	0.0959743	+	0.995384i	$0.469403\pi$
$978$	0.0959350	0.00306766
$979$	25.5783	0.817484
$980$	−76.7193	−2.45071
$981$	28.4289	0.907665
$982$	31.6278	1.00928
$983$	−14.5281	−0.463374	−0.231687	−	0.972790i	$-0.574424\pi$
$983$	−14.5281	−0.463374	−0.231687	+	0.972790i	$0.574424\pi$
$984$	−2.00545	−0.0639315
$985$	−16.6241	−0.529689
$986$	68.2478	2.17345
$987$	−0.752982	−0.0239677
$988$	0	0
$989$	1.69566	0.0539190
$990$	21.8942	0.695844
$991$	20.4379	0.649232	0.324616	−	0.945846i	$-0.394765\pi$
$991$	20.4379	0.649232	0.324616	+	0.945846i	$0.394765\pi$
$992$	−42.5957	−1.35242
$993$	−1.36655	−0.0433660
$994$	−155.754	−4.94021
$995$	−15.6086	−0.494826
$996$	−3.67192	−0.116349
$997$	−24.6373	−0.780270	−0.390135	−	0.920758i	$-0.627572\pi$
$997$	−24.6373	−0.780270	−0.390135	+	0.920758i	$0.627572\pi$
$998$	−66.0914	−2.09209
$999$	−0.852737	−0.0269794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.r.1.6	yes	6
5.4	even	2		9025.2.a.bq.1.1		6
19.18	odd	2		1805.2.a.q.1.1	✓	6
95.94	odd	2		9025.2.a.ca.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.1	✓	6	19.18	odd	2
1805.2.a.r.1.6	yes	6	1.1	even	1	trivial
9025.2.a.bq.1.1		6	5.4	even	2
9025.2.a.ca.1.6		6	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70739 q^{2} +0.0506943 q^{3} +5.32995 q^{4} -1.00000 q^{5} +0.137249 q^{6} +4.62536 q^{7} +9.01547 q^{8} -2.99743 q^{9} +O(q^{10})\)	\(q+2.70739 q^{2} +0.0506943 q^{3} +5.32995 q^{4} -1.00000 q^{5} +0.137249 q^{6} +4.62536 q^{7} +9.01547 q^{8} -2.99743 q^{9} -2.70739 q^{10} +2.69792 q^{11} +0.270198 q^{12} -0.983436 q^{13} +12.5227 q^{14} -0.0506943 q^{15} +13.7485 q^{16} -4.02257 q^{17} -8.11521 q^{18} -5.32995 q^{20} +0.234480 q^{21} +7.30433 q^{22} +0.820744 q^{23} +0.457033 q^{24} +1.00000 q^{25} -2.66254 q^{26} -0.304036 q^{27} +24.6530 q^{28} -6.26663 q^{29} -0.137249 q^{30} -2.21950 q^{31} +19.1915 q^{32} +0.136769 q^{33} -10.8907 q^{34} -4.62536 q^{35} -15.9762 q^{36} +2.80473 q^{37} -0.0498546 q^{39} -9.01547 q^{40} -4.38798 q^{41} +0.634828 q^{42} +2.06601 q^{43} +14.3798 q^{44} +2.99743 q^{45} +2.22207 q^{46} -3.21129 q^{47} +0.696970 q^{48} +14.3940 q^{49} +2.70739 q^{50} -0.203922 q^{51} -5.24167 q^{52} +2.30738 q^{53} -0.823143 q^{54} -2.69792 q^{55} +41.6998 q^{56} -16.9662 q^{58} -8.99135 q^{59} -0.270198 q^{60} +9.11348 q^{61} -6.00906 q^{62} -13.8642 q^{63} +24.4620 q^{64} +0.983436 q^{65} +0.370288 q^{66} +4.54135 q^{67} -21.4401 q^{68} +0.0416071 q^{69} -12.5227 q^{70} -12.4378 q^{71} -27.0233 q^{72} +0.461968 q^{73} +7.59349 q^{74} +0.0506943 q^{75} +12.4789 q^{77} -0.134976 q^{78} +8.22856 q^{79} -13.7485 q^{80} +8.97688 q^{81} -11.8800 q^{82} -13.5897 q^{83} +1.24977 q^{84} +4.02257 q^{85} +5.59349 q^{86} -0.317682 q^{87} +24.3231 q^{88} +9.48072 q^{89} +8.11521 q^{90} -4.54875 q^{91} +4.37453 q^{92} -0.112516 q^{93} -8.69421 q^{94} +0.972902 q^{96} +13.3177 q^{97} +38.9701 q^{98} -8.08684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more