LMFDB - Embedded newform 2695.2.a.u.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 30*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.777582$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.777582 q^{2} -3.22419 q^{3} -1.39537 q^{4} +1.00000 q^{5} +2.50707 q^{6} +2.64018 q^{8} +7.39539 q^{9} +O(q^{10})$	\(q-0.777582 q^{2} -3.22419 q^{3} -1.39537 q^{4} +1.00000 q^{5} +2.50707 q^{6} +2.64018 q^{8} +7.39539 q^{9} -0.777582 q^{10} +1.00000 q^{11} +4.49892 q^{12} -4.81979 q^{13} -3.22419 q^{15} +0.737779 q^{16} -4.48398 q^{17} -5.75052 q^{18} +0.272567 q^{19} -1.39537 q^{20} -0.777582 q^{22} -2.50938 q^{23} -8.51242 q^{24} +1.00000 q^{25} +3.74778 q^{26} -14.1716 q^{27} -1.76776 q^{29} +2.50707 q^{30} +6.63559 q^{31} -5.85404 q^{32} -3.22419 q^{33} +3.48666 q^{34} -10.3193 q^{36} -2.05480 q^{37} -0.211943 q^{38} +15.5399 q^{39} +2.64018 q^{40} +1.71729 q^{41} +6.71227 q^{43} -1.39537 q^{44} +7.39539 q^{45} +1.95125 q^{46} +9.95579 q^{47} -2.37874 q^{48} -0.777582 q^{50} +14.4572 q^{51} +6.72537 q^{52} +12.7048 q^{53} +11.0195 q^{54} +1.00000 q^{55} -0.878806 q^{57} +1.37458 q^{58} -12.7918 q^{59} +4.49892 q^{60} +11.6235 q^{61} -5.15972 q^{62} +3.07644 q^{64} -4.81979 q^{65} +2.50707 q^{66} -4.44164 q^{67} +6.25679 q^{68} +8.09072 q^{69} +6.58047 q^{71} +19.5251 q^{72} -12.6376 q^{73} +1.59777 q^{74} -3.22419 q^{75} -0.380330 q^{76} -12.0836 q^{78} -9.03106 q^{79} +0.737779 q^{80} +23.5056 q^{81} -1.33533 q^{82} +15.3614 q^{83} -4.48398 q^{85} -5.21934 q^{86} +5.69958 q^{87} +2.64018 q^{88} -8.47190 q^{89} -5.75052 q^{90} +3.50151 q^{92} -21.3944 q^{93} -7.74144 q^{94} +0.272567 q^{95} +18.8745 q^{96} -15.0108 q^{97} +7.39539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * 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 $

$2$	−0.777582	−0.549834	−0.274917	−	0.961468i	$-0.588650\pi$
$2$	−0.777582	−0.549834	−0.274917	+	0.961468i	$0.588650\pi$
$3$	−3.22419	−1.86149	−0.930743	−	0.365674i	$-0.880838\pi$
$3$	−3.22419	−1.86149	−0.930743	+	0.365674i	$0.880838\pi$
$4$	−1.39537	−0.697683
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.50707	1.02351
$7$	0	0
$7$	0	0
$8$	2.64018	0.933443
$9$	7.39539	2.46513
$10$	−0.777582	−0.245893
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.49892	1.29873
$13$	−4.81979	−1.33677	−0.668385	−	0.743816i	$-0.733014\pi$
$13$	−4.81979	−1.33677	−0.668385	+	0.743816i	$0.733014\pi$
$14$	0	0
$15$	−3.22419	−0.832482
$16$	0.737779	0.184445
$17$	−4.48398	−1.08752	−0.543762	−	0.839239i	$-0.683001\pi$
$17$	−4.48398	−1.08752	−0.543762	+	0.839239i	$0.683001\pi$
$18$	−5.75052	−1.35541
$19$	0.272567	0.0625311	0.0312655	−	0.999511i	$-0.490046\pi$
$19$	0.272567	0.0625311	0.0312655	+	0.999511i	$0.490046\pi$
$20$	−1.39537	−0.312013
$21$	0	0
$22$	−0.777582	−0.165781
$23$	−2.50938	−0.523242	−0.261621	−	0.965171i	$-0.584257\pi$
$23$	−2.50938	−0.523242	−0.261621	+	0.965171i	$0.584257\pi$
$24$	−8.51242	−1.73759
$25$	1.00000	0.200000
$26$	3.74778	0.735001
$27$	−14.1716	−2.72732
$28$	0	0
$29$	−1.76776	−0.328264	−0.164132	−	0.986438i	$-0.552482\pi$
$29$	−1.76776	−0.328264	−0.164132	+	0.986438i	$0.552482\pi$
$30$	2.50707	0.457726
$31$	6.63559	1.19179	0.595894	−	0.803063i	$-0.296798\pi$
$31$	6.63559	1.19179	0.595894	+	0.803063i	$0.296798\pi$
$32$	−5.85404	−1.03486
$33$	−3.22419	−0.561259
$34$	3.48666	0.597957
$35$	0	0
$36$	−10.3193	−1.71988
$37$	−2.05480	−0.337807	−0.168903	−	0.985633i	$-0.554023\pi$
$37$	−2.05480	−0.337807	−0.168903	+	0.985633i	$0.554023\pi$
$38$	−0.211943	−0.0343817
$39$	15.5399	2.48838
$40$	2.64018	0.417448
$41$	1.71729	0.268195	0.134097	−	0.990968i	$-0.457186\pi$
$41$	1.71729	0.268195	0.134097	+	0.990968i	$0.457186\pi$
$42$	0	0
$43$	6.71227	1.02361	0.511806	−	0.859101i	$-0.328977\pi$
$43$	6.71227	1.02361	0.511806	+	0.859101i	$0.328977\pi$
$44$	−1.39537	−0.210359
$45$	7.39539	1.10244
$46$	1.95125	0.287696
$47$	9.95579	1.45220	0.726101	−	0.687589i	$-0.241331\pi$
$47$	9.95579	1.45220	0.726101	+	0.687589i	$0.241331\pi$
$48$	−2.37874	−0.343341
$49$	0	0
$50$	−0.777582	−0.109967
$51$	14.4572	2.02441
$52$	6.72537	0.932642
$53$	12.7048	1.74514	0.872568	−	0.488493i	$-0.162453\pi$
$53$	12.7048	1.74514	0.872568	+	0.488493i	$0.162453\pi$
$54$	11.0195	1.49957
$55$	1.00000	0.134840
$56$	0	0
$57$	−0.878806	−0.116401
$58$	1.37458	0.180491
$59$	−12.7918	−1.66535	−0.832675	−	0.553761i	$-0.813192\pi$
$59$	−12.7918	−1.66535	−0.832675	+	0.553761i	$0.813192\pi$
$60$	4.49892	0.580808
$61$	11.6235	1.48824	0.744120	−	0.668046i	$-0.232869\pi$
$61$	11.6235	1.48824	0.744120	+	0.668046i	$0.232869\pi$
$62$	−5.15972	−0.655285
$63$	0	0
$64$	3.07644	0.384554
$65$	−4.81979	−0.597822
$66$	2.50707	0.308599
$67$	−4.44164	−0.542632	−0.271316	−	0.962490i	$-0.587459\pi$
$67$	−4.44164	−0.542632	−0.271316	+	0.962490i	$0.587459\pi$
$68$	6.25679	0.758747
$69$	8.09072	0.974008
$70$	0	0
$71$	6.58047	0.780958	0.390479	−	0.920612i	$-0.372309\pi$
$71$	6.58047	0.780958	0.390479	+	0.920612i	$0.372309\pi$
$72$	19.5251	2.30106
$73$	−12.6376	−1.47912	−0.739562	−	0.673088i	$-0.764967\pi$
$73$	−12.6376	−1.47912	−0.739562	+	0.673088i	$0.764967\pi$
$74$	1.59777	0.185737
$75$	−3.22419	−0.372297
$76$	−0.380330	−0.0436269
$77$	0	0
$78$	−12.0836	−1.36819
$79$	−9.03106	−1.01607	−0.508037	−	0.861335i	$-0.669629\pi$
$79$	−9.03106	−1.01607	−0.508037	+	0.861335i	$0.669629\pi$
$80$	0.737779	0.0824862
$81$	23.5056	2.61173
$82$	−1.33533	−0.147463
$83$	15.3614	1.68613	0.843065	−	0.537811i	$-0.180749\pi$
$83$	15.3614	1.68613	0.843065	+	0.537811i	$0.180749\pi$
$84$	0	0
$85$	−4.48398	−0.486355
$86$	−5.21934	−0.562816
$87$	5.69958	0.611059
$88$	2.64018	0.281444
$89$	−8.47190	−0.898020	−0.449010	−	0.893527i	$-0.648223\pi$
$89$	−8.47190	−0.898020	−0.449010	+	0.893527i	$0.648223\pi$
$90$	−5.75052	−0.606158
$91$	0	0
$92$	3.50151	0.365057
$93$	−21.3944	−2.21850
$94$	−7.74144	−0.798469
$95$	0.272567	0.0279647
$96$	18.8745	1.92637
$97$	−15.0108	−1.52412	−0.762060	−	0.647506i	$-0.775812\pi$
$97$	−15.0108	−1.52412	−0.762060	+	0.647506i	$0.775812\pi$
$98$	0	0
$99$	7.39539	0.743264
$100$	−1.39537	−0.139537
$101$	−0.501509	−0.0499020	−0.0249510	−	0.999689i	$-0.507943\pi$
$101$	−0.501509	−0.0499020	−0.0249510	+	0.999689i	$0.507943\pi$
$102$	−11.2416	−1.11309
$103$	−13.0053	−1.28145	−0.640727	−	0.767769i	$-0.721367\pi$
$103$	−13.0053	−1.28145	−0.640727	+	0.767769i	$0.721367\pi$
$104$	−12.7251	−1.24780
$105$	0	0
$106$	−9.87901	−0.959534
$107$	15.0309	1.45309	0.726547	−	0.687117i	$-0.241124\pi$
$107$	15.0309	1.45309	0.726547	+	0.687117i	$0.241124\pi$
$108$	19.7745	1.90280
$109$	4.16571	0.399003	0.199502	−	0.979898i	$-0.436068\pi$
$109$	4.16571	0.399003	0.199502	+	0.979898i	$0.436068\pi$
$110$	−0.777582	−0.0741395
$111$	6.62506	0.628822
$112$	0	0
$113$	−3.83393	−0.360666	−0.180333	−	0.983606i	$-0.557718\pi$
$113$	−3.83393	−0.360666	−0.180333	+	0.983606i	$0.557718\pi$
$114$	0.683344	0.0640010
$115$	−2.50938	−0.234001
$116$	2.46667	0.229024
$117$	−35.6442	−3.29531
$118$	9.94668	0.915666
$119$	0	0
$120$	−8.51242	−0.777074
$121$	1.00000	0.0909091
$122$	−9.03824	−0.818284
$123$	−5.53685	−0.499241
$124$	−9.25908	−0.831490
$125$	1.00000	0.0894427
$126$	0	0
$127$	14.9208	1.32400	0.662002	−	0.749502i	$-0.269707\pi$
$127$	14.9208	1.32400	0.662002	+	0.749502i	$0.269707\pi$
$128$	9.31589	0.823416
$129$	−21.6416	−1.90544
$130$	3.74778	0.328702
$131$	3.71333	0.324435	0.162218	−	0.986755i	$-0.448135\pi$
$131$	3.71333	0.324435	0.162218	+	0.986755i	$0.448135\pi$
$132$	4.49892	0.391581
$133$	0	0
$134$	3.45374	0.298358
$135$	−14.1716	−1.21969
$136$	−11.8385	−1.01514
$137$	6.77178	0.578552	0.289276	−	0.957246i	$-0.406585\pi$
$137$	6.77178	0.578552	0.289276	+	0.957246i	$0.406585\pi$
$138$	−6.29120	−0.535542
$139$	15.5779	1.32130	0.660648	−	0.750696i	$-0.270282\pi$
$139$	15.5779	1.32130	0.660648	+	0.750696i	$0.270282\pi$
$140$	0	0
$141$	−32.0993	−2.70325
$142$	−5.11686	−0.429397
$143$	−4.81979	−0.403051
$144$	5.45616	0.454680
$145$	−1.76776	−0.146804
$146$	9.82681	0.813272
$147$	0	0
$148$	2.86720	0.235682
$149$	9.75490	0.799153	0.399576	−	0.916700i	$-0.369157\pi$
$149$	9.75490	0.799153	0.399576	+	0.916700i	$0.369157\pi$
$150$	2.50707	0.204701
$151$	−12.1342	−0.987467	−0.493733	−	0.869613i	$-0.664368\pi$
$151$	−12.1342	−0.987467	−0.493733	+	0.869613i	$0.664368\pi$
$152$	0.719624	0.0583692
$153$	−33.1607	−2.68089
$154$	0	0
$155$	6.63559	0.532984
$156$	−21.6839	−1.73610
$157$	−21.0132	−1.67704	−0.838518	−	0.544874i	$-0.816577\pi$
$157$	−21.0132	−1.67704	−0.838518	+	0.544874i	$0.816577\pi$
$158$	7.02239	0.558672
$159$	−40.9626	−3.24855
$160$	−5.85404	−0.462802
$161$	0	0
$162$	−18.2775	−1.43602
$163$	−1.54236	−0.120807	−0.0604036	−	0.998174i	$-0.519239\pi$
$163$	−1.54236	−0.120807	−0.0604036	+	0.998174i	$0.519239\pi$
$164$	−2.39624	−0.187115
$165$	−3.22419	−0.251003
$166$	−11.9447	−0.927091
$167$	−11.9367	−0.923689	−0.461845	−	0.886961i	$-0.652812\pi$
$167$	−11.9367	−0.923689	−0.461845	+	0.886961i	$0.652812\pi$
$168$	0	0
$169$	10.2304	0.786954
$170$	3.48666	0.267415
$171$	2.01574	0.154147
$172$	−9.36608	−0.714157
$173$	−4.31104	−0.327762	−0.163881	−	0.986480i	$-0.552401\pi$
$173$	−4.31104	−0.327762	−0.163881	+	0.986480i	$0.552401\pi$
$174$	−4.43189	−0.335981
$175$	0	0
$176$	0.737779	0.0556122
$177$	41.2432	3.10003
$178$	6.58760	0.493761
$179$	−6.29887	−0.470799	−0.235400	−	0.971899i	$-0.575640\pi$
$179$	−6.29887	−0.470799	−0.235400	+	0.971899i	$0.575640\pi$
$180$	−10.3193	−0.769153
$181$	−7.11144	−0.528589	−0.264295	−	0.964442i	$-0.585139\pi$
$181$	−7.11144	−0.528589	−0.264295	+	0.964442i	$0.585139\pi$
$182$	0	0
$183$	−37.4764	−2.77034
$184$	−6.62521	−0.488417
$185$	−2.05480	−0.151072
$186$	16.6359	1.21980
$187$	−4.48398	−0.327901
$188$	−13.8920	−1.01318
$189$	0	0
$190$	−0.211943	−0.0153760
$191$	−16.8125	−1.21651	−0.608256	−	0.793741i	$-0.708131\pi$
$191$	−16.8125	−1.21651	−0.608256	+	0.793741i	$0.708131\pi$
$192$	−9.91901	−0.715843
$193$	−15.2019	−1.09426	−0.547129	−	0.837048i	$-0.684279\pi$
$193$	−15.2019	−1.09426	−0.547129	+	0.837048i	$0.684279\pi$
$194$	11.6722	0.838013
$195$	15.5399	1.11284
$196$	0	0
$197$	−8.67683	−0.618199	−0.309099	−	0.951030i	$-0.600028\pi$
$197$	−8.67683	−0.618199	−0.309099	+	0.951030i	$0.600028\pi$
$198$	−5.75052	−0.408672
$199$	20.2844	1.43792	0.718962	−	0.695049i	$-0.244618\pi$
$199$	20.2844	1.43792	0.718962	+	0.695049i	$0.244618\pi$
$200$	2.64018	0.186689
$201$	14.3207	1.01010
$202$	0.389964	0.0274378
$203$	0	0
$204$	−20.1731	−1.41240
$205$	1.71729	0.119940
$206$	10.1127	0.704587
$207$	−18.5578	−1.28986
$208$	−3.55594	−0.246560
$209$	0.272567	0.0188538
$210$	0	0
$211$	−1.33294	−0.0917633	−0.0458817	−	0.998947i	$-0.514610\pi$
$211$	−1.33294	−0.0917633	−0.0458817	+	0.998947i	$0.514610\pi$
$212$	−17.7278	−1.21755
$213$	−21.2167	−1.45374
$214$	−11.6878	−0.798960
$215$	6.71227	0.457773
$216$	−37.4154	−2.54580
$217$	0	0
$218$	−3.23918	−0.219385
$219$	40.7461	2.75337
$220$	−1.39537	−0.0940756
$221$	21.6118	1.45377
$222$	−5.15152	−0.345748
$223$	−0.593022	−0.0397117	−0.0198558	−	0.999803i	$-0.506321\pi$
$223$	−0.593022	−0.0397117	−0.0198558	+	0.999803i	$0.506321\pi$
$224$	0	0
$225$	7.39539	0.493026
$226$	2.98120	0.198306
$227$	27.7272	1.84032	0.920158	−	0.391547i	$-0.128060\pi$
$227$	27.7272	1.84032	0.920158	+	0.391547i	$0.128060\pi$
$228$	1.22626	0.0812108
$229$	13.5291	0.894027	0.447014	−	0.894527i	$-0.352488\pi$
$229$	13.5291	0.894027	0.447014	+	0.894527i	$0.352488\pi$
$230$	1.95125	0.128662
$231$	0	0
$232$	−4.66719	−0.306416
$233$	−18.2930	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$233$	−18.2930	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$234$	27.7163	1.81187
$235$	9.95579	0.649444
$236$	17.8492	1.16189
$237$	29.1178	1.89141
$238$	0	0
$239$	−26.0228	−1.68328	−0.841639	−	0.540041i	$-0.818409\pi$
$239$	−26.0228	−1.68328	−0.841639	+	0.540041i	$0.818409\pi$
$240$	−2.37874	−0.153547
$241$	20.1825	1.30007	0.650034	−	0.759905i	$-0.274754\pi$
$241$	20.1825	1.30007	0.650034	+	0.759905i	$0.274754\pi$
$242$	−0.777582	−0.0499849
$243$	−33.2718	−2.13439
$244$	−16.2191	−1.03832
$245$	0	0
$246$	4.30536	0.274499
$247$	−1.31371	−0.0835896
$248$	17.5191	1.11247
$249$	−49.5280	−3.13871
$250$	−0.777582	−0.0491786
$251$	3.90243	0.246319	0.123160	−	0.992387i	$-0.460697\pi$
$251$	3.90243	0.246319	0.123160	+	0.992387i	$0.460697\pi$
$252$	0	0
$253$	−2.50938	−0.157763
$254$	−11.6021	−0.727982
$255$	14.4572	0.905344
$256$	−13.3967	−0.837296
$257$	−27.0860	−1.68958	−0.844790	−	0.535098i	$-0.820275\pi$
$257$	−27.0860	−1.68958	−0.844790	+	0.535098i	$0.820275\pi$
$258$	16.8281	1.04767
$259$	0	0
$260$	6.72537	0.417090
$261$	−13.0732	−0.809214
$262$	−2.88742	−0.178385
$263$	−12.2491	−0.755313	−0.377657	−	0.925946i	$-0.623270\pi$
$263$	−12.2491	−0.755313	−0.377657	+	0.925946i	$0.623270\pi$
$264$	−8.51242	−0.523903
$265$	12.7048	0.780449
$266$	0	0
$267$	27.3150	1.67165
$268$	6.19771	0.378585
$269$	−27.2503	−1.66148	−0.830741	−	0.556659i	$-0.812083\pi$
$269$	−27.2503	−1.66148	−0.830741	+	0.556659i	$0.812083\pi$
$270$	11.0195	0.670628
$271$	21.1302	1.28357	0.641783	−	0.766886i	$-0.278195\pi$
$271$	21.1302	1.28357	0.641783	+	0.766886i	$0.278195\pi$
$272$	−3.30818	−0.200588
$273$	0	0
$274$	−5.26562	−0.318107
$275$	1.00000	0.0603023
$276$	−11.2895	−0.679549
$277$	−3.18544	−0.191395	−0.0956973	−	0.995410i	$-0.530508\pi$
$277$	−3.18544	−0.191395	−0.0956973	+	0.995410i	$0.530508\pi$
$278$	−12.1131	−0.726493
$279$	49.0728	2.93791
$280$	0	0
$281$	−2.73681	−0.163264	−0.0816321	−	0.996663i	$-0.526013\pi$
$281$	−2.73681	−0.163264	−0.0816321	+	0.996663i	$0.526013\pi$
$282$	24.9599	1.48634
$283$	−27.6511	−1.64369	−0.821843	−	0.569714i	$-0.807054\pi$
$283$	−27.6511	−1.64369	−0.821843	+	0.569714i	$0.807054\pi$
$284$	−9.18216	−0.544861
$285$	−0.878806	−0.0520560
$286$	3.74778	0.221611
$287$	0	0
$288$	−43.2929	−2.55106
$289$	3.10604	0.182708
$290$	1.37458	0.0807179
$291$	48.3978	2.83713
$292$	17.6341	1.03196
$293$	−0.846601	−0.0494590	−0.0247295	−	0.999694i	$-0.507872\pi$
$293$	−0.846601	−0.0494590	−0.0247295	+	0.999694i	$0.507872\pi$
$294$	0	0
$295$	−12.7918	−0.744767
$296$	−5.42503	−0.315323
$297$	−14.1716	−0.822317
$298$	−7.58524	−0.439401
$299$	12.0947	0.699454
$300$	4.49892	0.259745
$301$	0	0
$302$	9.43533	0.542942
$303$	1.61696	0.0928918
$304$	0.201094	0.0115335
$305$	11.6235	0.665561
$306$	25.7852	1.47404
$307$	28.5371	1.62870	0.814348	−	0.580376i	$-0.197095\pi$
$307$	28.5371	1.62870	0.814348	+	0.580376i	$0.197095\pi$
$308$	0	0
$309$	41.9317	2.38541
$310$	−5.15972	−0.293052
$311$	−10.3436	−0.586531	−0.293266	−	0.956031i	$-0.594742\pi$
$311$	−10.3436	−0.586531	−0.293266	+	0.956031i	$0.594742\pi$
$312$	41.0281	2.32276
$313$	9.82089	0.555110	0.277555	−	0.960710i	$-0.410476\pi$
$313$	9.82089	0.555110	0.277555	+	0.960710i	$0.410476\pi$
$314$	16.3395	0.922090
$315$	0	0
$316$	12.6016	0.708898
$317$	−32.3962	−1.81955	−0.909776	−	0.415099i	$-0.863747\pi$
$317$	−32.3962	−1.81955	−0.909776	+	0.415099i	$0.863747\pi$
$318$	31.8518	1.78616
$319$	−1.76776	−0.0989754
$320$	3.07644	0.171978
$321$	−48.4625	−2.70491
$322$	0	0
$323$	−1.22218	−0.0680040
$324$	−32.7989	−1.82216
$325$	−4.81979	−0.267354
$326$	1.19931	0.0664238
$327$	−13.4310	−0.742738
$328$	4.53394	0.250345
$329$	0	0
$330$	2.50707	0.138010
$331$	−2.38628	−0.131162	−0.0655809	−	0.997847i	$-0.520890\pi$
$331$	−2.38628	−0.131162	−0.0655809	+	0.997847i	$0.520890\pi$
$332$	−21.4348	−1.17638
$333$	−15.1960	−0.832737
$334$	9.28176	0.507875
$335$	−4.44164	−0.242673
$336$	0	0
$337$	−2.32683	−0.126750	−0.0633751	−	0.997990i	$-0.520186\pi$
$337$	−2.32683	−0.126750	−0.0633751	+	0.997990i	$0.520186\pi$
$338$	−7.95497	−0.432694
$339$	12.3613	0.671375
$340$	6.25679	0.339322
$341$	6.63559	0.359337
$342$	−1.56740	−0.0847553
$343$	0	0
$344$	17.7216	0.955484
$345$	8.09072	0.435590
$346$	3.35219	0.180215
$347$	12.4703	0.669442	0.334721	−	0.942317i	$-0.391358\pi$
$347$	12.4703	0.669442	0.334721	+	0.942317i	$0.391358\pi$
$348$	−7.95300	−0.426326
$349$	−20.6659	−1.10622	−0.553110	−	0.833108i	$-0.686559\pi$
$349$	−20.6659	−1.10622	−0.553110	+	0.833108i	$0.686559\pi$
$350$	0	0
$351$	68.3040	3.64580
$352$	−5.85404	−0.312021
$353$	−17.8200	−0.948460	−0.474230	−	0.880401i	$-0.657274\pi$
$353$	−17.8200	−0.948460	−0.474230	+	0.880401i	$0.657274\pi$
$354$	−32.0700	−1.70450
$355$	6.58047	0.349255
$356$	11.8214	0.626533
$357$	0	0
$358$	4.89789	0.258861
$359$	−11.8545	−0.625656	−0.312828	−	0.949810i	$-0.601276\pi$
$359$	−11.8545	−0.625656	−0.312828	+	0.949810i	$0.601276\pi$
$360$	19.5251	1.02906
$361$	−18.9257	−0.996090
$362$	5.52973	0.290636
$363$	−3.22419	−0.169226
$364$	0	0
$365$	−12.6376	−0.661485
$366$	29.1410	1.52322
$367$	11.0180	0.575133	0.287566	−	0.957761i	$-0.407154\pi$
$367$	11.0180	0.575133	0.287566	+	0.957761i	$0.407154\pi$
$368$	−1.85137	−0.0965092
$369$	12.7000	0.661135
$370$	1.59777	0.0830643
$371$	0	0
$372$	29.8530	1.54781
$373$	−21.6824	−1.12267	−0.561337	−	0.827587i	$-0.689713\pi$
$373$	−21.6824	−1.12267	−0.561337	+	0.827587i	$0.689713\pi$
$374$	3.48666	0.180291
$375$	−3.22419	−0.166496
$376$	26.2850	1.35555
$377$	8.52022	0.438814
$378$	0	0
$379$	−11.5618	−0.593888	−0.296944	−	0.954895i	$-0.595967\pi$
$379$	−11.5618	−0.593888	−0.296944	+	0.954895i	$0.595967\pi$
$380$	−0.380330	−0.0195105
$381$	−48.1073	−2.46461
$382$	13.0731	0.668879
$383$	−17.9459	−0.916992	−0.458496	−	0.888696i	$-0.651612\pi$
$383$	−17.9459	−0.916992	−0.458496	+	0.888696i	$0.651612\pi$
$384$	−30.0362	−1.53278
$385$	0	0
$386$	11.8207	0.601660
$387$	49.6399	2.52334
$388$	20.9456	1.06335
$389$	−5.95721	−0.302043	−0.151021	−	0.988530i	$-0.548256\pi$
$389$	−5.95721	−0.302043	−0.151021	+	0.988530i	$0.548256\pi$
$390$	−12.0836	−0.611875
$391$	11.2520	0.569038
$392$	0	0
$393$	−11.9725	−0.603932
$394$	6.74695	0.339906
$395$	−9.03106	−0.454402
$396$	−10.3193	−0.518563
$397$	15.8607	0.796026	0.398013	−	0.917380i	$-0.369700\pi$
$397$	15.8607	0.796026	0.398013	+	0.917380i	$0.369700\pi$
$398$	−15.7728	−0.790619
$399$	0	0
$400$	0.737779	0.0368889
$401$	24.4775	1.22235	0.611173	−	0.791497i	$-0.290698\pi$
$401$	24.4775	1.22235	0.611173	+	0.791497i	$0.290698\pi$
$402$	−11.1355	−0.555388
$403$	−31.9822	−1.59315
$404$	0.699788	0.0348158
$405$	23.5056	1.16800
$406$	0	0
$407$	−2.05480	−0.101853
$408$	38.1695	1.88967
$409$	−31.0421	−1.53493	−0.767466	−	0.641089i	$-0.778483\pi$
$409$	−31.0421	−1.53493	−0.767466	+	0.641089i	$0.778483\pi$
$410$	−1.33533	−0.0659473
$411$	−21.8335	−1.07697
$412$	18.1472	0.894049
$413$	0	0
$414$	14.4303	0.709208
$415$	15.3614	0.754061
$416$	28.2152	1.38337
$417$	−50.2259	−2.45957
$418$	−0.211943	−0.0103665
$419$	−8.48826	−0.414678	−0.207339	−	0.978269i	$-0.566480\pi$
$419$	−8.48826	−0.414678	−0.207339	+	0.978269i	$0.566480\pi$
$420$	0	0
$421$	−5.03548	−0.245414	−0.122707	−	0.992443i	$-0.539158\pi$
$421$	−5.03548	−0.245414	−0.122707	+	0.992443i	$0.539158\pi$
$422$	1.03647	0.0504546
$423$	73.6269	3.57986
$424$	33.5429	1.62899
$425$	−4.48398	−0.217505
$426$	16.4977	0.799316
$427$	0	0
$428$	−20.9736	−1.01380
$429$	15.5399	0.750274
$430$	−5.21934	−0.251699
$431$	−27.8619	−1.34206	−0.671031	−	0.741429i	$-0.734148\pi$
$431$	−27.8619	−1.34206	−0.671031	+	0.741429i	$0.734148\pi$
$432$	−10.4555	−0.503039
$433$	17.4546	0.838813	0.419407	−	0.907799i	$-0.362238\pi$
$433$	17.4546	0.838813	0.419407	+	0.907799i	$0.362238\pi$
$434$	0	0
$435$	5.69958	0.273274
$436$	−5.81270	−0.278378
$437$	−0.683974	−0.0327189
$438$	−31.6835	−1.51389
$439$	−4.70074	−0.224354	−0.112177	−	0.993688i	$-0.535782\pi$
$439$	−4.70074	−0.224354	−0.112177	+	0.993688i	$0.535782\pi$
$440$	2.64018	0.125865
$441$	0	0
$442$	−16.8050	−0.799331
$443$	8.68040	0.412418	0.206209	−	0.978508i	$-0.433887\pi$
$443$	8.68040	0.412418	0.206209	+	0.978508i	$0.433887\pi$
$444$	−9.24438	−0.438719
$445$	−8.47190	−0.401607
$446$	0.461123	0.0218348
$447$	−31.4516	−1.48761
$448$	0	0
$449$	3.49650	0.165010	0.0825049	−	0.996591i	$-0.473708\pi$
$449$	3.49650	0.165010	0.0825049	+	0.996591i	$0.473708\pi$
$450$	−5.75052	−0.271082
$451$	1.71729	0.0808638
$452$	5.34974	0.251631
$453$	39.1229	1.83816
$454$	−21.5601	−1.01187
$455$	0	0
$456$	−2.32020	−0.108653
$457$	−17.4262	−0.815162	−0.407581	−	0.913169i	$-0.633628\pi$
$457$	−17.4262	−0.815162	−0.407581	+	0.913169i	$0.633628\pi$
$458$	−10.5200	−0.491566
$459$	63.5449	2.96602
$460$	3.50151	0.163259
$461$	−20.0815	−0.935290	−0.467645	−	0.883916i	$-0.654897\pi$
$461$	−20.0815	−0.935290	−0.467645	+	0.883916i	$0.654897\pi$
$462$	0	0
$463$	18.1169	0.841964	0.420982	−	0.907069i	$-0.361686\pi$
$463$	18.1169	0.841964	0.420982	+	0.907069i	$0.361686\pi$
$464$	−1.30421	−0.0605466
$465$	−21.3944	−0.992141
$466$	14.2243	0.658929
$467$	−18.5917	−0.860323	−0.430162	−	0.902752i	$-0.641543\pi$
$467$	−18.5917	−0.860323	−0.430162	+	0.902752i	$0.641543\pi$
$468$	49.7368	2.29908
$469$	0	0
$470$	−7.74144	−0.357086
$471$	67.7505	3.12178
$472$	−33.7726	−1.55451
$473$	6.71227	0.308631
$474$	−22.6415	−1.03996
$475$	0.272567	0.0125062
$476$	0	0
$477$	93.9568	4.30199
$478$	20.2349	0.925522
$479$	−24.8017	−1.13322	−0.566610	−	0.823986i	$-0.691745\pi$
$479$	−24.8017	−1.13322	−0.566610	+	0.823986i	$0.691745\pi$
$480$	18.8745	0.861500
$481$	9.90370	0.451570
$482$	−15.6935	−0.714822
$483$	0	0
$484$	−1.39537	−0.0634257
$485$	−15.0108	−0.681607
$486$	25.8715	1.17356
$487$	−35.0144	−1.58665	−0.793327	−	0.608795i	$-0.791653\pi$
$487$	−35.0144	−1.58665	−0.793327	+	0.608795i	$0.791653\pi$
$488$	30.6881	1.38919
$489$	4.97286	0.224881
$490$	0	0
$491$	37.8979	1.71031	0.855155	−	0.518373i	$-0.173462\pi$
$491$	37.8979	1.71031	0.855155	+	0.518373i	$0.173462\pi$
$492$	7.72593	0.348312
$493$	7.92658	0.356995
$494$	1.02152	0.0459604
$495$	7.39539	0.332398
$496$	4.89560	0.219819
$497$	0	0
$498$	38.5121	1.72577
$499$	11.2070	0.501694	0.250847	−	0.968027i	$-0.419291\pi$
$499$	11.2070	0.501694	0.250847	+	0.968027i	$0.419291\pi$
$500$	−1.39537	−0.0624027
$501$	38.4861	1.71943
$502$	−3.03446	−0.135434
$503$	−19.3168	−0.861295	−0.430648	−	0.902520i	$-0.641715\pi$
$503$	−19.3168	−0.861295	−0.430648	+	0.902520i	$0.641715\pi$
$504$	0	0
$505$	−0.501509	−0.0223168
$506$	1.95125	0.0867436
$507$	−32.9847	−1.46490
$508$	−20.8199	−0.923735
$509$	−15.9634	−0.707563	−0.353782	−	0.935328i	$-0.615104\pi$
$509$	−15.9634	−0.707563	−0.353782	+	0.935328i	$0.615104\pi$
$510$	−11.2416	−0.497788
$511$	0	0
$512$	−8.21471	−0.363042
$513$	−3.86269	−0.170542
$514$	21.0616	0.928988
$515$	−13.0053	−0.573084
$516$	30.1980	1.32939
$517$	9.95579	0.437855
$518$	0	0
$519$	13.8996	0.610125
$520$	−12.7251	−0.558033
$521$	5.12020	0.224320	0.112160	−	0.993690i	$-0.464223\pi$
$521$	5.12020	0.224320	0.112160	+	0.993690i	$0.464223\pi$
$522$	10.1655	0.444933
$523$	−6.06687	−0.265286	−0.132643	−	0.991164i	$-0.542346\pi$
$523$	−6.06687	−0.265286	−0.132643	+	0.991164i	$0.542346\pi$
$524$	−5.18146	−0.226353
$525$	0	0
$526$	9.52470	0.415297
$527$	−29.7538	−1.29610
$528$	−2.37874	−0.103521
$529$	−16.7030	−0.726218
$530$	−9.87901	−0.429117
$531$	−94.6003	−4.10530
$532$	0	0
$533$	−8.27696	−0.358515
$534$	−21.2397	−0.919130
$535$	15.0309	0.649843
$536$	−11.7267	−0.506517
$537$	20.3087	0.876386
$538$	21.1894	0.913538
$539$	0	0
$540$	19.7745	0.850959
$541$	−4.25826	−0.183077	−0.0915385	−	0.995802i	$-0.529178\pi$
$541$	−4.25826	−0.183077	−0.0915385	+	0.995802i	$0.529178\pi$
$542$	−16.4304	−0.705748
$543$	22.9286	0.983962
$544$	26.2494	1.12543
$545$	4.16571	0.178440
$546$	0	0
$547$	33.3362	1.42535	0.712675	−	0.701494i	$-0.247483\pi$
$547$	33.3362	1.42535	0.712675	+	0.701494i	$0.247483\pi$
$548$	−9.44911	−0.403646
$549$	85.9604	3.66870
$550$	−0.777582	−0.0331562
$551$	−0.481831	−0.0205267
$552$	21.3609	0.909181
$553$	0	0
$554$	2.47694	0.105235
$555$	6.62506	0.281218
$556$	−21.7368	−0.921846
$557$	14.5935	0.618345	0.309172	−	0.951006i	$-0.399948\pi$
$557$	14.5935	0.618345	0.309172	+	0.951006i	$0.399948\pi$
$558$	−38.1581	−1.61536
$559$	−32.3518	−1.36833
$560$	0	0
$561$	14.4572	0.610383
$562$	2.12809	0.0897682
$563$	19.9769	0.841927	0.420963	−	0.907078i	$-0.361692\pi$
$563$	19.9769	0.841927	0.420963	+	0.907078i	$0.361692\pi$
$564$	44.7903	1.88601
$565$	−3.83393	−0.161295
$566$	21.5010	0.903754
$567$	0	0
$568$	17.3736	0.728980
$569$	−39.3281	−1.64872	−0.824360	−	0.566065i	$-0.808465\pi$
$569$	−39.3281	−1.64872	−0.824360	+	0.566065i	$0.808465\pi$
$570$	0.683344	0.0286221
$571$	−24.4552	−1.02342	−0.511709	−	0.859159i	$-0.670988\pi$
$571$	−24.4552	−1.02342	−0.511709	+	0.859159i	$0.670988\pi$
$572$	6.72537	0.281202
$573$	54.2068	2.26452
$574$	0	0
$575$	−2.50938	−0.104648
$576$	22.7514	0.947976
$577$	28.7835	1.19827	0.599136	−	0.800647i	$-0.295511\pi$
$577$	28.7835	1.19827	0.599136	+	0.800647i	$0.295511\pi$
$578$	−2.41520	−0.100459
$579$	49.0138	2.03695
$580$	2.46667	0.102423
$581$	0	0
$582$	−37.6332	−1.55995
$583$	12.7048	0.526178
$584$	−33.3656	−1.38068
$585$	−35.6442	−1.47371
$586$	0.658302	0.0271942
$587$	−27.2992	−1.12676	−0.563378	−	0.826199i	$-0.690499\pi$
$587$	−27.2992	−1.12676	−0.563378	+	0.826199i	$0.690499\pi$
$588$	0	0
$589$	1.80864	0.0745237
$590$	9.94668	0.409498
$591$	27.9757	1.15077
$592$	−1.51599	−0.0623067
$593$	−2.85364	−0.117185	−0.0585924	−	0.998282i	$-0.518661\pi$
$593$	−2.85364	−0.117185	−0.0585924	+	0.998282i	$0.518661\pi$
$594$	11.0195	0.452138
$595$	0	0
$596$	−13.6117	−0.557555
$597$	−65.4008	−2.67667
$598$	−9.40462	−0.384584
$599$	34.4077	1.40586	0.702930	−	0.711259i	$-0.251875\pi$
$599$	34.4077	1.40586	0.702930	+	0.711259i	$0.251875\pi$
$600$	−8.51242	−0.347518
$601$	0.248552	0.0101387	0.00506933	−	0.999987i	$-0.498386\pi$
$601$	0.248552	0.0101387	0.00506933	+	0.999987i	$0.498386\pi$
$602$	0	0
$603$	−32.8476	−1.33766
$604$	16.9316	0.688939
$605$	1.00000	0.0406558
$606$	−1.25732	−0.0510750
$607$	31.5060	1.27879	0.639396	−	0.768878i	$-0.279185\pi$
$607$	31.5060	1.27879	0.639396	+	0.768878i	$0.279185\pi$
$608$	−1.59561	−0.0647107
$609$	0	0
$610$	−9.03824	−0.365948
$611$	−47.9848	−1.94126
$612$	46.2714	1.87041
$613$	3.43088	0.138572	0.0692860	−	0.997597i	$-0.477928\pi$
$613$	3.43088	0.138572	0.0692860	+	0.997597i	$0.477928\pi$
$614$	−22.1899	−0.895512
$615$	−5.53685	−0.223267
$616$	0	0
$617$	−5.27485	−0.212357	−0.106179	−	0.994347i	$-0.533862\pi$
$617$	−5.27485	−0.212357	−0.106179	+	0.994347i	$0.533862\pi$
$618$	−32.6053	−1.31158
$619$	40.1221	1.61264	0.806322	−	0.591477i	$-0.201455\pi$
$619$	40.1221	1.61264	0.806322	+	0.591477i	$0.201455\pi$
$620$	−9.25908	−0.371854
$621$	35.5618	1.42705
$622$	8.04299	0.322495
$623$	0	0
$624$	11.4650	0.458968
$625$	1.00000	0.0400000
$626$	−7.63655	−0.305218
$627$	−0.878806	−0.0350961
$628$	29.3211	1.17004
$629$	9.21367	0.367373
$630$	0	0
$631$	−2.68482	−0.106881	−0.0534405	−	0.998571i	$-0.517019\pi$
$631$	−2.68482	−0.106881	−0.0534405	+	0.998571i	$0.517019\pi$
$632$	−23.8436	−0.948447
$633$	4.29765	0.170816
$634$	25.1907	1.00045
$635$	14.9208	0.592112
$636$	57.1578	2.26646
$637$	0	0
$638$	1.37458	0.0544200
$639$	48.6651	1.92516
$640$	9.31589	0.368243
$641$	−9.28342	−0.366673	−0.183336	−	0.983050i	$-0.558690\pi$
$641$	−9.28342	−0.366673	−0.183336	+	0.983050i	$0.558690\pi$
$642$	37.6836	1.48725
$643$	−4.25520	−0.167809	−0.0839043	−	0.996474i	$-0.526739\pi$
$643$	−4.25520	−0.167809	−0.0839043	+	0.996474i	$0.526739\pi$
$644$	0	0
$645$	−21.6416	−0.852138
$646$	0.950347	0.0373909
$647$	19.8760	0.781406	0.390703	−	0.920517i	$-0.372232\pi$
$647$	19.8760	0.781406	0.390703	+	0.920517i	$0.372232\pi$
$648$	62.0589	2.43790
$649$	−12.7918	−0.502122
$650$	3.74778	0.147000
$651$	0	0
$652$	2.15216	0.0842851
$653$	−34.8967	−1.36561	−0.682806	−	0.730600i	$-0.739240\pi$
$653$	−34.8967	−1.36561	−0.682806	+	0.730600i	$0.739240\pi$
$654$	10.4437	0.408383
$655$	3.71333	0.145092
$656$	1.26698	0.0494671
$657$	−93.4603	−3.64623
$658$	0	0
$659$	−22.1798	−0.864003	−0.432002	−	0.901873i	$-0.642193\pi$
$659$	−22.1798	−0.864003	−0.432002	+	0.901873i	$0.642193\pi$
$660$	4.49892	0.175120
$661$	−13.9387	−0.542152	−0.271076	−	0.962558i	$-0.587379\pi$
$661$	−13.9387	−0.542152	−0.271076	+	0.962558i	$0.587379\pi$
$662$	1.85553	0.0721172
$663$	−69.6806	−2.70617
$664$	40.5568	1.57391
$665$	0	0
$666$	11.8162	0.457867
$667$	4.43598	0.171762
$668$	16.6561	0.644442
$669$	1.91201	0.0739228
$670$	3.45374	0.133430
$671$	11.6235	0.448721
$672$	0	0
$673$	13.7757	0.531015	0.265508	−	0.964109i	$-0.414460\pi$
$673$	13.7757	0.531015	0.265508	+	0.964109i	$0.414460\pi$
$674$	1.80930	0.0696916
$675$	−14.1716	−0.545463
$676$	−14.2752	−0.549044
$677$	13.1497	0.505384	0.252692	−	0.967547i	$-0.418684\pi$
$677$	13.1497	0.505384	0.252692	+	0.967547i	$0.418684\pi$
$678$	−9.61194	−0.369144
$679$	0	0
$680$	−11.8385	−0.453985
$681$	−89.3976	−3.42572
$682$	−5.15972	−0.197576
$683$	−29.5099	−1.12916	−0.564582	−	0.825377i	$-0.690962\pi$
$683$	−29.5099	−1.12916	−0.564582	+	0.825377i	$0.690962\pi$
$684$	−2.81269	−0.107546
$685$	6.77178	0.258736
$686$	0	0
$687$	−43.6203	−1.66422
$688$	4.95217	0.188800
$689$	−61.2344	−2.33285
$690$	−6.29120	−0.239502
$691$	−28.1631	−1.07138	−0.535688	−	0.844416i	$-0.679948\pi$
$691$	−28.1631	−1.07138	−0.535688	+	0.844416i	$0.679948\pi$
$692$	6.01548	0.228674
$693$	0	0
$694$	−9.69670	−0.368082
$695$	15.5779	0.590902
$696$	15.0479	0.570389
$697$	−7.70027	−0.291668
$698$	16.0694	0.608237
$699$	58.9802	2.23083
$700$	0	0
$701$	11.2988	0.426749	0.213375	−	0.976970i	$-0.431555\pi$
$701$	11.2988	0.426749	0.213375	+	0.976970i	$0.431555\pi$
$702$	−53.1119	−2.00458
$703$	−0.560069	−0.0211234
$704$	3.07644	0.115948
$705$	−32.0993	−1.20893
$706$	13.8565	0.521495
$707$	0	0
$708$	−57.5493	−2.16284
$709$	38.4042	1.44230	0.721150	−	0.692779i	$-0.243614\pi$
$709$	38.4042	1.44230	0.721150	+	0.692779i	$0.243614\pi$
$710$	−5.11686	−0.192032
$711$	−66.7882	−2.50475
$712$	−22.3673	−0.838250
$713$	−16.6512	−0.623593
$714$	0	0
$715$	−4.81979	−0.180250
$716$	8.78923	0.328469
$717$	83.9025	3.13340
$718$	9.21784	0.344007
$719$	−31.1106	−1.16023	−0.580115	−	0.814534i	$-0.696993\pi$
$719$	−31.1106	−1.16023	−0.580115	+	0.814534i	$0.696993\pi$
$720$	5.45616	0.203339
$721$	0	0
$722$	14.7163	0.547684
$723$	−65.0722	−2.42006
$724$	9.92307	0.368788
$725$	−1.76776	−0.0656529
$726$	2.50707	0.0930461
$727$	−21.3328	−0.791189	−0.395595	−	0.918425i	$-0.629461\pi$
$727$	−21.3328	−0.791189	−0.395595	+	0.918425i	$0.629461\pi$
$728$	0	0
$729$	36.7577	1.36140
$730$	9.82681	0.363706
$731$	−30.0977	−1.11320
$732$	52.2933	1.93282
$733$	−36.4871	−1.34768	−0.673841	−	0.738876i	$-0.735357\pi$
$733$	−36.4871	−1.34768	−0.673841	+	0.738876i	$0.735357\pi$
$734$	−8.56737	−0.316227
$735$	0	0
$736$	14.6900	0.541481
$737$	−4.44164	−0.163610
$738$	−9.87529	−0.363514
$739$	−20.7370	−0.762823	−0.381412	−	0.924405i	$-0.624562\pi$
$739$	−20.7370	−0.762823	−0.381412	+	0.924405i	$0.624562\pi$
$740$	2.86720	0.105400
$741$	4.23566	0.155601
$742$	0	0
$743$	37.5869	1.37893	0.689464	−	0.724320i	$-0.257846\pi$
$743$	37.5869	1.37893	0.689464	+	0.724320i	$0.257846\pi$
$744$	−56.4850	−2.07084
$745$	9.75490	0.357392
$746$	16.8599	0.617284
$747$	113.603	4.15653
$748$	6.25679	0.228771
$749$	0	0
$750$	2.50707	0.0915453
$751$	−9.59880	−0.350265	−0.175133	−	0.984545i	$-0.556035\pi$
$751$	−9.59880	−0.350265	−0.175133	+	0.984545i	$0.556035\pi$
$752$	7.34517	0.267851
$753$	−12.5822	−0.458519
$754$	−6.62517	−0.241275
$755$	−12.1342	−0.441609
$756$	0	0
$757$	−38.5985	−1.40289	−0.701444	−	0.712725i	$-0.747461\pi$
$757$	−38.5985	−1.40289	−0.701444	+	0.712725i	$0.747461\pi$
$758$	8.99022	0.326539
$759$	8.09072	0.293674
$760$	0.719624	0.0261035
$761$	−14.7846	−0.535942	−0.267971	−	0.963427i	$-0.586353\pi$
$761$	−14.7846	−0.535942	−0.267971	+	0.963427i	$0.586353\pi$
$762$	37.4074	1.35513
$763$	0	0
$764$	23.4596	0.848740
$765$	−33.1607	−1.19893
$766$	13.9544	0.504193
$767$	61.6538	2.22619
$768$	43.1936	1.55862
$769$	50.5854	1.82416	0.912079	−	0.410015i	$-0.134476\pi$
$769$	50.5854	1.82416	0.912079	+	0.410015i	$0.134476\pi$
$770$	0	0
$771$	87.3304	3.14513
$772$	21.2122	0.763445
$773$	54.5775	1.96302	0.981508	−	0.191423i	$-0.0613102\pi$
$773$	54.5775	1.96302	0.981508	+	0.191423i	$0.0613102\pi$
$774$	−38.5991	−1.38741
$775$	6.63559	0.238357
$776$	−39.6313	−1.42268
$777$	0	0
$778$	4.63222	0.166073
$779$	0.468075	0.0167705
$780$	−21.6839	−0.776407
$781$	6.58047	0.235468
$782$	−8.74936	−0.312876
$783$	25.0519	0.895281
$784$	0	0
$785$	−21.0132	−0.749993
$786$	9.30959	0.332062
$787$	23.4875	0.837239	0.418619	−	0.908162i	$-0.362514\pi$
$787$	23.4875	0.837239	0.418619	+	0.908162i	$0.362514\pi$
$788$	12.1074	0.431307
$789$	39.4935	1.40600
$790$	7.02239	0.249846
$791$	0	0
$792$	19.5251	0.693795
$793$	−56.0230	−1.98943
$794$	−12.3330	−0.437682
$795$	−40.9626	−1.45279
$796$	−28.3042	−1.00322
$797$	−12.7236	−0.450694	−0.225347	−	0.974279i	$-0.572352\pi$
$797$	−12.7236	−0.450694	−0.225347	+	0.974279i	$0.572352\pi$
$798$	0	0
$799$	−44.6415	−1.57930
$800$	−5.85404	−0.206971
$801$	−62.6530	−2.21373
$802$	−19.0332	−0.672087
$803$	−12.6376	−0.445973
$804$	−19.9826	−0.704731
$805$	0	0
$806$	24.8688	0.875965
$807$	87.8602	3.09282
$808$	−1.32407	−0.0465806
$809$	−17.5134	−0.615737	−0.307868	−	0.951429i	$-0.599616\pi$
$809$	−17.5134	−0.615737	−0.307868	+	0.951429i	$0.599616\pi$
$810$	−18.2775	−0.642207
$811$	30.0726	1.05599	0.527996	−	0.849247i	$-0.322944\pi$
$811$	30.0726	1.05599	0.527996	+	0.849247i	$0.322944\pi$
$812$	0	0
$813$	−68.1276	−2.38934
$814$	1.59777	0.0560020
$815$	−1.54236	−0.0540266
$816$	10.6662	0.373392
$817$	1.82954	0.0640075
$818$	24.1378	0.843957
$819$	0	0
$820$	−2.39624	−0.0836804
$821$	33.3755	1.16481	0.582406	−	0.812898i	$-0.302111\pi$
$821$	33.3755	1.16481	0.582406	+	0.812898i	$0.302111\pi$
$822$	16.9773	0.592153
$823$	−12.8961	−0.449528	−0.224764	−	0.974413i	$-0.572161\pi$
$823$	−12.8961	−0.449528	−0.224764	+	0.974413i	$0.572161\pi$
$824$	−34.3364	−1.19616
$825$	−3.22419	−0.112252
$826$	0	0
$827$	−26.7051	−0.928627	−0.464314	−	0.885671i	$-0.653699\pi$
$827$	−26.7051	−0.928627	−0.464314	+	0.885671i	$0.653699\pi$
$828$	25.8950	0.899913
$829$	−43.8387	−1.52258	−0.761291	−	0.648411i	$-0.775434\pi$
$829$	−43.8387	−1.52258	−0.761291	+	0.648411i	$0.775434\pi$
$830$	−11.9447	−0.414608
$831$	10.2705	0.356278
$832$	−14.8278	−0.514061
$833$	0	0
$834$	39.0548	1.35236
$835$	−11.9367	−0.413086
$836$	−0.380330	−0.0131540
$837$	−94.0366	−3.25038
$838$	6.60032	0.228004
$839$	−8.55155	−0.295232	−0.147616	−	0.989045i	$-0.547160\pi$
$839$	−8.55155	−0.295232	−0.147616	+	0.989045i	$0.547160\pi$
$840$	0	0
$841$	−25.8750	−0.892243
$842$	3.91550	0.134937
$843$	8.82398	0.303914
$844$	1.85994	0.0640217
$845$	10.2304	0.351936
$846$	−57.2510	−1.96833
$847$	0	0
$848$	9.37332	0.321881
$849$	89.1523	3.05970
$850$	3.48666	0.119591
$851$	5.15627	0.176755
$852$	29.6050	1.01425
$853$	30.1106	1.03097	0.515484	−	0.856899i	$-0.327612\pi$
$853$	30.1106	1.03097	0.515484	+	0.856899i	$0.327612\pi$
$854$	0	0
$855$	2.01574	0.0689367
$856$	39.6843	1.35638
$857$	41.2521	1.40915	0.704573	−	0.709631i	$-0.251139\pi$
$857$	41.2521	1.40915	0.704573	+	0.709631i	$0.251139\pi$
$858$	−12.0836	−0.412526
$859$	−10.9327	−0.373018	−0.186509	−	0.982453i	$-0.559717\pi$
$859$	−10.9327	−0.373018	−0.186509	+	0.982453i	$0.559717\pi$
$860$	−9.36608	−0.319381
$861$	0	0
$862$	21.6650	0.737911
$863$	−36.9008	−1.25612	−0.628059	−	0.778166i	$-0.716150\pi$
$863$	−36.9008	−1.25612	−0.628059	+	0.778166i	$0.716150\pi$
$864$	82.9608	2.82238
$865$	−4.31104	−0.146580
$866$	−13.5724	−0.461208
$867$	−10.0145	−0.340109
$868$	0	0
$869$	−9.03106	−0.306358
$870$	−4.43189	−0.150255
$871$	21.4078	0.725375
$872$	10.9982	0.372447
$873$	−111.011	−3.75715
$874$	0.531846	0.0179899
$875$	0	0
$876$	−56.8558	−1.92098
$877$	−52.5222	−1.77355	−0.886774	−	0.462203i	$-0.847059\pi$
$877$	−52.5222	−1.77355	−0.886774	+	0.462203i	$0.847059\pi$
$878$	3.65521	0.123357
$879$	2.72960	0.0920671
$880$	0.737779	0.0248705
$881$	−28.2466	−0.951652	−0.475826	−	0.879540i	$-0.657851\pi$
$881$	−28.2466	−0.951652	−0.475826	+	0.879540i	$0.657851\pi$
$882$	0	0
$883$	1.22971	0.0413830	0.0206915	−	0.999786i	$-0.493413\pi$
$883$	1.22971	0.0413830	0.0206915	+	0.999786i	$0.493413\pi$
$884$	−30.1564	−1.01427
$885$	41.2432	1.38637
$886$	−6.74972	−0.226761
$887$	23.4303	0.786713	0.393356	−	0.919386i	$-0.371314\pi$
$887$	23.4303	0.786713	0.393356	+	0.919386i	$0.371314\pi$
$888$	17.4913	0.586970
$889$	0	0
$890$	6.58760	0.220817
$891$	23.5056	0.787467
$892$	0.827483	0.0277062
$893$	2.71362	0.0908077
$894$	24.4562	0.817939
$895$	−6.29887	−0.210548
$896$	0	0
$897$	−38.9956	−1.30202
$898$	−2.71881	−0.0907279
$899$	−11.7301	−0.391221
$900$	−10.3193	−0.343976
$901$	−56.9679	−1.89788
$902$	−1.33533	−0.0444616
$903$	0	0
$904$	−10.1223	−0.336661
$905$	−7.11144	−0.236392
$906$	−30.4213	−1.01068
$907$	45.6816	1.51683	0.758416	−	0.651771i	$-0.225974\pi$
$907$	45.6816	1.51683	0.758416	+	0.651771i	$0.225974\pi$
$908$	−38.6895	−1.28396
$909$	−3.70885	−0.123015
$910$	0	0
$911$	−20.1886	−0.668880	−0.334440	−	0.942417i	$-0.608547\pi$
$911$	−20.1886	−0.668880	−0.334440	+	0.942417i	$0.608547\pi$
$912$	−0.648364	−0.0214695
$913$	15.3614	0.508388
$914$	13.5503	0.448203
$915$	−37.4764	−1.23893
$916$	−18.8780	−0.623748
$917$	0	0
$918$	−49.4114	−1.63082
$919$	0.176719	0.00582944	0.00291472	−	0.999996i	$-0.499072\pi$
$919$	0.176719	0.00582944	0.00291472	+	0.999996i	$0.499072\pi$
$920$	−6.62521	−0.218427
$921$	−92.0089	−3.03180
$922$	15.6150	0.514254
$923$	−31.7165	−1.04396
$924$	0	0
$925$	−2.05480	−0.0675613
$926$	−14.0874	−0.462940
$927$	−96.1795	−3.15895
$928$	10.3485	0.339707
$929$	3.94773	0.129521	0.0647604	−	0.997901i	$-0.479372\pi$
$929$	3.94773	0.129521	0.0647604	+	0.997901i	$0.479372\pi$
$930$	16.6359	0.545513
$931$	0	0
$932$	25.5255	0.836115
$933$	33.3497	1.09182
$934$	14.4566	0.473035
$935$	−4.48398	−0.146642
$936$	−94.1070	−3.07598
$937$	37.7681	1.23383	0.616915	−	0.787030i	$-0.288382\pi$
$937$	37.7681	1.23383	0.616915	+	0.787030i	$0.288382\pi$
$938$	0	0
$939$	−31.6644	−1.03333
$940$	−13.8920	−0.453106
$941$	−22.9296	−0.747483	−0.373741	−	0.927533i	$-0.621925\pi$
$941$	−22.9296	−0.747483	−0.373741	+	0.927533i	$0.621925\pi$
$942$	−52.6816	−1.71646
$943$	−4.30932	−0.140331
$944$	−9.43752	−0.307165
$945$	0	0
$946$	−5.21934	−0.169695
$947$	1.61759	0.0525646	0.0262823	−	0.999655i	$-0.491633\pi$
$947$	1.61759	0.0525646	0.0262823	+	0.999655i	$0.491633\pi$
$948$	−40.6301	−1.31960
$949$	60.9108	1.97725
$950$	−0.211943	−0.00687634
$951$	104.451	3.38707
$952$	0	0
$953$	59.2433	1.91908	0.959539	−	0.281575i	$-0.0908567\pi$
$953$	59.2433	1.91908	0.959539	+	0.281575i	$0.0908567\pi$
$954$	−73.0591	−2.36538
$955$	−16.8125	−0.544041
$956$	36.3114	1.17439
$957$	5.69958	0.184241
$958$	19.2854	0.623082
$959$	0	0
$960$	−9.91901	−0.320135
$961$	13.0311	0.420357
$962$	−7.70094	−0.248288
$963$	111.159	3.58206
$964$	−28.1620	−0.907036
$965$	−15.2019	−0.489367
$966$	0	0
$967$	−15.1623	−0.487585	−0.243793	−	0.969827i	$-0.578392\pi$
$967$	−15.1623	−0.487585	−0.243793	+	0.969827i	$0.578392\pi$
$968$	2.64018	0.0848585
$969$	3.94054	0.126589
$970$	11.6722	0.374771
$971$	−35.4575	−1.13789	−0.568943	−	0.822377i	$-0.692648\pi$
$971$	−35.4575	−1.13789	−0.568943	+	0.822377i	$0.692648\pi$
$972$	46.4263	1.48912
$973$	0	0
$974$	27.2266	0.872396
$975$	15.5399	0.497676
$976$	8.57559	0.274498
$977$	−23.3361	−0.746587	−0.373294	−	0.927713i	$-0.621772\pi$
$977$	−23.3361	−0.746587	−0.373294	+	0.927713i	$0.621772\pi$
$978$	−3.86681	−0.123647
$979$	−8.47190	−0.270763
$980$	0	0
$981$	30.8071	0.983594
$982$	−29.4688	−0.940386
$983$	25.8840	0.825571	0.412786	−	0.910828i	$-0.364556\pi$
$983$	25.8840	0.825571	0.412786	+	0.910828i	$0.364556\pi$
$984$	−14.6183	−0.466013
$985$	−8.67683	−0.276467
$986$	−6.16357	−0.196288
$987$	0	0
$988$	1.83311	0.0583191
$989$	−16.8437	−0.535597
$990$	−5.75052	−0.182764
$991$	−51.5987	−1.63909	−0.819543	−	0.573018i	$-0.805773\pi$
$991$	−51.5987	−1.63909	−0.819543	+	0.573018i	$0.805773\pi$
$992$	−38.8450	−1.23333
$993$	7.69382	0.244156
$994$	0	0
$995$	20.2844	0.643059
$996$	69.1097	2.18982
$997$	16.8559	0.533832	0.266916	−	0.963720i	$-0.413995\pi$
$997$	16.8559	0.533832	0.266916	+	0.963720i	$0.413995\pi$
$998$	−8.71436	−0.275848
$999$	29.1197	0.921306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.u.1.5	✓	10
7.6	odd	2		2695.2.a.v.1.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.u.1.5	✓	10	1.1	even	1	trivial
2695.2.a.v.1.5	yes	10	7.6	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-0.777582 q^{2} -3.22419 q^{3} -1.39537 q^{4} +1.00000 q^{5} +2.50707 q^{6} +2.64018 q^{8} +7.39539 q^{9} +O(q^{10})\)	\(q-0.777582 q^{2} -3.22419 q^{3} -1.39537 q^{4} +1.00000 q^{5} +2.50707 q^{6} +2.64018 q^{8} +7.39539 q^{9} -0.777582 q^{10} +1.00000 q^{11} +4.49892 q^{12} -4.81979 q^{13} -3.22419 q^{15} +0.737779 q^{16} -4.48398 q^{17} -5.75052 q^{18} +0.272567 q^{19} -1.39537 q^{20} -0.777582 q^{22} -2.50938 q^{23} -8.51242 q^{24} +1.00000 q^{25} +3.74778 q^{26} -14.1716 q^{27} -1.76776 q^{29} +2.50707 q^{30} +6.63559 q^{31} -5.85404 q^{32} -3.22419 q^{33} +3.48666 q^{34} -10.3193 q^{36} -2.05480 q^{37} -0.211943 q^{38} +15.5399 q^{39} +2.64018 q^{40} +1.71729 q^{41} +6.71227 q^{43} -1.39537 q^{44} +7.39539 q^{45} +1.95125 q^{46} +9.95579 q^{47} -2.37874 q^{48} -0.777582 q^{50} +14.4572 q^{51} +6.72537 q^{52} +12.7048 q^{53} +11.0195 q^{54} +1.00000 q^{55} -0.878806 q^{57} +1.37458 q^{58} -12.7918 q^{59} +4.49892 q^{60} +11.6235 q^{61} -5.15972 q^{62} +3.07644 q^{64} -4.81979 q^{65} +2.50707 q^{66} -4.44164 q^{67} +6.25679 q^{68} +8.09072 q^{69} +6.58047 q^{71} +19.5251 q^{72} -12.6376 q^{73} +1.59777 q^{74} -3.22419 q^{75} -0.380330 q^{76} -12.0836 q^{78} -9.03106 q^{79} +0.737779 q^{80} +23.5056 q^{81} -1.33533 q^{82} +15.3614 q^{83} -4.48398 q^{85} -5.21934 q^{86} +5.69958 q^{87} +2.64018 q^{88} -8.47190 q^{89} -5.75052 q^{90} +3.50151 q^{92} -21.3944 q^{93} -7.74144 q^{94} +0.272567 q^{95} +18.8745 q^{96} -15.0108 q^{97} +7.39539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 6 * q^8 + 10 * q^9 - 2 * q^10 + 10 * q^11 - 20 * q^12 - 8 * q^13 - 8 * q^15 + 6 * q^16 - 28 * q^17 - 14 * q^18 + 10 * q^20 - 2 * q^22 - 16 * q^23 + 8 * q^24 + 10 * q^25 - 20 * q^26 - 32 * q^27 - 4 * q^30 - 20 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 + 42 * q^36 - 36 * q^37 - 24 * q^38 + 24 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^43 + 10 * q^44 + 10 * q^45 - 4 * q^46 - 12 * q^47 - 40 * q^48 - 2 * q^50 + 20 * q^51 - 4 * q^52 - 16 * q^53 + 48 * q^54 + 10 * q^55 + 4 * q^57 + 16 * q^58 - 32 * q^59 - 20 * q^60 + 16 * q^61 + 4 * q^62 - 34 * q^64 - 8 * q^65 - 4 * q^66 - 20 * q^67 - 32 * q^68 - 28 * q^69 + 12 * q^71 - 2 * q^72 - 20 * q^73 + 32 * q^74 - 8 * q^75 - 12 * q^76 + 20 * q^78 + 12 * q^79 + 6 * q^80 + 42 * q^81 + 40 * q^82 - 8 * q^83 - 28 * q^85 - 4 * q^86 - 28 * q^87 - 6 * q^88 - 68 * q^89 - 14 * q^90 + 32 * q^92 - 32 * q^93 - 16 * q^94 + 80 * q^96 - 36 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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