LMFDB - Embedded newform 1205.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.0849802$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0849802 q^{2} -1.30288 q^{3} -1.99278 q^{4} -1.00000 q^{5} +0.110719 q^{6} +0.925444 q^{7} +0.339307 q^{8} -1.30250 q^{9} +O(q^{10})$	\(q-0.0849802 q^{2} -1.30288 q^{3} -1.99278 q^{4} -1.00000 q^{5} +0.110719 q^{6} +0.925444 q^{7} +0.339307 q^{8} -1.30250 q^{9} +0.0849802 q^{10} +3.08405 q^{11} +2.59635 q^{12} +0.928417 q^{13} -0.0786445 q^{14} +1.30288 q^{15} +3.95672 q^{16} +0.233917 q^{17} +0.110687 q^{18} +4.41397 q^{19} +1.99278 q^{20} -1.20574 q^{21} -0.262083 q^{22} -0.167895 q^{23} -0.442077 q^{24} +1.00000 q^{25} -0.0788971 q^{26} +5.60565 q^{27} -1.84421 q^{28} -7.54323 q^{29} -0.110719 q^{30} -8.34292 q^{31} -1.01486 q^{32} -4.01815 q^{33} -0.0198783 q^{34} -0.925444 q^{35} +2.59560 q^{36} -9.22182 q^{37} -0.375100 q^{38} -1.20962 q^{39} -0.339307 q^{40} +2.33892 q^{41} +0.102464 q^{42} -6.63273 q^{43} -6.14583 q^{44} +1.30250 q^{45} +0.0142677 q^{46} +10.0939 q^{47} -5.15514 q^{48} -6.14355 q^{49} -0.0849802 q^{50} -0.304765 q^{51} -1.85013 q^{52} -4.19636 q^{53} -0.476369 q^{54} -3.08405 q^{55} +0.314010 q^{56} -5.75088 q^{57} +0.641026 q^{58} -2.28311 q^{59} -2.59635 q^{60} +11.2190 q^{61} +0.708983 q^{62} -1.20539 q^{63} -7.82720 q^{64} -0.928417 q^{65} +0.341463 q^{66} +6.13650 q^{67} -0.466144 q^{68} +0.218747 q^{69} +0.0786445 q^{70} -8.46831 q^{71} -0.441948 q^{72} -5.93109 q^{73} +0.783673 q^{74} -1.30288 q^{75} -8.79607 q^{76} +2.85412 q^{77} +0.102793 q^{78} -5.88910 q^{79} -3.95672 q^{80} -3.39598 q^{81} -0.198762 q^{82} -3.10723 q^{83} +2.40278 q^{84} -0.233917 q^{85} +0.563651 q^{86} +9.82793 q^{87} +1.04644 q^{88} -10.3808 q^{89} -0.110687 q^{90} +0.859198 q^{91} +0.334577 q^{92} +10.8698 q^{93} -0.857781 q^{94} -4.41397 q^{95} +1.32224 q^{96} -8.84558 q^{97} +0.522081 q^{98} -4.01698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * 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 $

$2$	−0.0849802	−0.0600901	−0.0300451	−	0.999549i	$-0.509565\pi$
$2$	−0.0849802	−0.0600901	−0.0300451	+	0.999549i	$0.509565\pi$
$3$	−1.30288	−0.752218	−0.376109	−	0.926575i	$-0.622738\pi$
$3$	−1.30288	−0.752218	−0.376109	+	0.926575i	$0.622738\pi$
$4$	−1.99278	−0.996389
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.110719	0.0452009
$7$	0.925444	0.349785	0.174893	−	0.984588i	$-0.444042\pi$
$7$	0.925444	0.349785	0.174893	+	0.984588i	$0.444042\pi$
$8$	0.339307	0.119963
$9$	−1.30250	−0.434167
$10$	0.0849802	0.0268731
$11$	3.08405	0.929876	0.464938	−	0.885343i	$-0.346077\pi$
$11$	3.08405	0.929876	0.464938	+	0.885343i	$0.346077\pi$
$12$	2.59635	0.749502
$13$	0.928417	0.257496	0.128748	−	0.991677i	$-0.458904\pi$
$13$	0.928417	0.257496	0.128748	+	0.991677i	$0.458904\pi$
$14$	−0.0786445	−0.0210186
$15$	1.30288	0.336402
$16$	3.95672	0.989181
$17$	0.233917	0.0567331	0.0283666	−	0.999598i	$-0.490969\pi$
$17$	0.233917	0.0567331	0.0283666	+	0.999598i	$0.490969\pi$
$18$	0.110687	0.0260892
$19$	4.41397	1.01263	0.506317	−	0.862347i	$-0.331006\pi$
$19$	4.41397	1.01263	0.506317	+	0.862347i	$0.331006\pi$
$20$	1.99278	0.445599
$21$	−1.20574	−0.263115
$22$	−0.262083	−0.0558763
$23$	−0.167895	−0.0350085	−0.0175042	−	0.999847i	$-0.505572\pi$
$23$	−0.167895	−0.0350085	−0.0175042	+	0.999847i	$0.505572\pi$
$24$	−0.442077	−0.0902386
$25$	1.00000	0.200000
$26$	−0.0788971	−0.0154730
$27$	5.60565	1.07881
$28$	−1.84421	−0.348522
$29$	−7.54323	−1.40074	−0.700372	−	0.713778i	$-0.746982\pi$
$29$	−7.54323	−1.40074	−0.700372	+	0.713778i	$0.746982\pi$
$30$	−0.110719	−0.0202145
$31$	−8.34292	−1.49843	−0.749216	−	0.662326i	$-0.769570\pi$
$31$	−8.34292	−1.49843	−0.749216	+	0.662326i	$0.769570\pi$
$32$	−1.01486	−0.179403
$33$	−4.01815	−0.699470
$34$	−0.0198783	−0.00340910
$35$	−0.925444	−0.156429
$36$	2.59560	0.432600
$37$	−9.22182	−1.51606	−0.758029	−	0.652221i	$-0.773837\pi$
$37$	−9.22182	−1.51606	−0.758029	+	0.652221i	$0.773837\pi$
$38$	−0.375100	−0.0608493
$39$	−1.20962	−0.193694
$40$	−0.339307	−0.0536492
$41$	2.33892	0.365277	0.182639	−	0.983180i	$-0.441536\pi$
$41$	2.33892	0.365277	0.182639	+	0.983180i	$0.441536\pi$
$42$	0.102464	0.0158106
$43$	−6.63273	−1.01148	−0.505741	−	0.862685i	$-0.668781\pi$
$43$	−6.63273	−1.01148	−0.505741	+	0.862685i	$0.668781\pi$
$44$	−6.14583	−0.926518
$45$	1.30250	0.194166
$46$	0.0142677	0.00210366
$47$	10.0939	1.47235	0.736173	−	0.676794i	$-0.236631\pi$
$47$	10.0939	1.47235	0.736173	+	0.676794i	$0.236631\pi$
$48$	−5.15514	−0.744080
$49$	−6.14355	−0.877650
$50$	−0.0849802	−0.0120180
$51$	−0.304765	−0.0426757
$52$	−1.85013	−0.256567
$53$	−4.19636	−0.576415	−0.288207	−	0.957568i	$-0.593059\pi$
$53$	−4.19636	−0.576415	−0.288207	+	0.957568i	$0.593059\pi$
$54$	−0.476369	−0.0648256
$55$	−3.08405	−0.415853
$56$	0.314010	0.0419614
$57$	−5.75088	−0.761722
$58$	0.641026	0.0841708
$59$	−2.28311	−0.297236	−0.148618	−	0.988895i	$-0.547482\pi$
$59$	−2.28311	−0.297236	−0.148618	+	0.988895i	$0.547482\pi$
$60$	−2.59635	−0.335188
$61$	11.2190	1.43645	0.718225	−	0.695811i	$-0.244955\pi$
$61$	11.2190	1.43645	0.718225	+	0.695811i	$0.244955\pi$
$62$	0.708983	0.0900410
$63$	−1.20539	−0.151865
$64$	−7.82720	−0.978400
$65$	−0.928417	−0.115156
$66$	0.341463	0.0420312
$67$	6.13650	0.749693	0.374847	−	0.927087i	$-0.377695\pi$
$67$	6.13650	0.749693	0.374847	+	0.927087i	$0.377695\pi$
$68$	−0.466144	−0.0565283
$69$	0.218747	0.0263340
$70$	0.0786445	0.00939982
$71$	−8.46831	−1.00500	−0.502502	−	0.864576i	$-0.667587\pi$
$71$	−8.46831	−1.00500	−0.502502	+	0.864576i	$0.667587\pi$
$72$	−0.441948	−0.0520841
$73$	−5.93109	−0.694181	−0.347091	−	0.937832i	$-0.612830\pi$
$73$	−5.93109	−0.694181	−0.347091	+	0.937832i	$0.612830\pi$
$74$	0.783673	0.0911001
$75$	−1.30288	−0.150444
$76$	−8.79607	−1.00898
$77$	2.85412	0.325257
$78$	0.102793	0.0116391
$79$	−5.88910	−0.662576	−0.331288	−	0.943530i	$-0.607483\pi$
$79$	−5.88910	−0.662576	−0.331288	+	0.943530i	$0.607483\pi$
$80$	−3.95672	−0.442375
$81$	−3.39598	−0.377331
$82$	−0.198762	−0.0219495
$83$	−3.10723	−0.341063	−0.170532	−	0.985352i	$-0.554549\pi$
$83$	−3.10723	−0.341063	−0.170532	+	0.985352i	$0.554549\pi$
$84$	2.40278	0.262165
$85$	−0.233917	−0.0253718
$86$	0.563651	0.0607801
$87$	9.82793	1.05367
$88$	1.04644	0.111551
$89$	−10.3808	−1.10037	−0.550184	−	0.835044i	$-0.685442\pi$
$89$	−10.3808	−1.10037	−0.550184	+	0.835044i	$0.685442\pi$
$90$	−0.110687	−0.0116674
$91$	0.859198	0.0900684
$92$	0.334577	0.0348821
$93$	10.8698	1.12715
$94$	−0.857781	−0.0884734
$95$	−4.41397	−0.452864
$96$	1.32224	0.134950
$97$	−8.84558	−0.898132	−0.449066	−	0.893498i	$-0.648243\pi$
$97$	−8.84558	−0.898132	−0.449066	+	0.893498i	$0.648243\pi$
$98$	0.522081	0.0527381
$99$	−4.01698	−0.403722
$100$	−1.99278	−0.199278
$101$	−1.25997	−0.125372	−0.0626860	−	0.998033i	$-0.519967\pi$
$101$	−1.25997	−0.125372	−0.0626860	+	0.998033i	$0.519967\pi$
$102$	0.0258990	0.00256439
$103$	−3.28222	−0.323407	−0.161703	−	0.986839i	$-0.551699\pi$
$103$	−3.28222	−0.323407	−0.161703	+	0.986839i	$0.551699\pi$
$104$	0.315019	0.0308901
$105$	1.20574	0.117669
$106$	0.356608	0.0346368
$107$	−9.90586	−0.957635	−0.478818	−	0.877914i	$-0.658935\pi$
$107$	−9.90586	−0.957635	−0.478818	+	0.877914i	$0.658935\pi$
$108$	−11.1708	−1.07491
$109$	10.1138	0.968730	0.484365	−	0.874866i	$-0.339051\pi$
$109$	10.1138	0.968730	0.484365	+	0.874866i	$0.339051\pi$
$110$	0.262083	0.0249887
$111$	12.0149	1.14041
$112$	3.66173	0.346001
$113$	5.69830	0.536051	0.268026	−	0.963412i	$-0.413629\pi$
$113$	5.69830	0.536051	0.268026	+	0.963412i	$0.413629\pi$
$114$	0.488711	0.0457720
$115$	0.167895	0.0156563
$116$	15.0320	1.39569
$117$	−1.20926	−0.111797
$118$	0.194020	0.0178609
$119$	0.216477	0.0198444
$120$	0.442077	0.0403559
$121$	−1.48864	−0.135331
$122$	−0.953397	−0.0863165
$123$	−3.04733	−0.274768
$124$	16.6256	1.49302
$125$	−1.00000	−0.0894427
$126$	0.102435	0.00912560
$127$	−2.12101	−0.188209	−0.0941045	−	0.995562i	$-0.529999\pi$
$127$	−2.12101	−0.188209	−0.0941045	+	0.995562i	$0.529999\pi$
$128$	2.69487	0.238195
$129$	8.64166	0.760855
$130$	0.0788971	0.00691973
$131$	−14.0117	−1.22421	−0.612103	−	0.790778i	$-0.709676\pi$
$131$	−14.0117	−1.22421	−0.612103	+	0.790778i	$0.709676\pi$
$132$	8.00728	0.696944
$133$	4.08489	0.354204
$134$	−0.521482	−0.0450491
$135$	−5.60565	−0.482457
$136$	0.0793696	0.00680589
$137$	−5.80450	−0.495912	−0.247956	−	0.968771i	$-0.579759\pi$
$137$	−5.80450	−0.495912	−0.247956	+	0.968771i	$0.579759\pi$
$138$	−0.0185892	−0.00158241
$139$	−21.7007	−1.84063	−0.920316	−	0.391175i	$-0.872069\pi$
$139$	−21.7007	−1.84063	−0.920316	+	0.391175i	$0.872069\pi$
$140$	1.84421	0.155864
$141$	−13.1511	−1.10753
$142$	0.719639	0.0603908
$143$	2.86328	0.239440
$144$	−5.15364	−0.429470
$145$	7.54323	0.626432
$146$	0.504025	0.0417134
$147$	8.00432	0.660185
$148$	18.3770	1.51058
$149$	−10.3263	−0.845964	−0.422982	−	0.906138i	$-0.639017\pi$
$149$	−10.3263	−0.845964	−0.422982	+	0.906138i	$0.639017\pi$
$150$	0.110719	0.00904018
$151$	−1.87469	−0.152560	−0.0762799	−	0.997086i	$-0.524304\pi$
$151$	−1.87469	−0.152560	−0.0762799	+	0.997086i	$0.524304\pi$
$152$	1.49769	0.121479
$153$	−0.304677	−0.0246317
$154$	−0.242544	−0.0195447
$155$	8.34292	0.670119
$156$	2.41050	0.192994
$157$	13.9052	1.10976	0.554879	−	0.831931i	$-0.312765\pi$
$157$	13.9052	1.10976	0.554879	+	0.831931i	$0.312765\pi$
$158$	0.500457	0.0398142
$159$	5.46736	0.433590
$160$	1.01486	0.0802316
$161$	−0.155377	−0.0122454
$162$	0.288591	0.0226739
$163$	6.38330	0.499978	0.249989	−	0.968249i	$-0.419573\pi$
$163$	6.38330	0.499978	0.249989	+	0.968249i	$0.419573\pi$
$164$	−4.66094	−0.363958
$165$	4.01815	0.312812
$166$	0.264054	0.0204945
$167$	20.4408	1.58176	0.790878	−	0.611974i	$-0.209624\pi$
$167$	20.4408	1.58176	0.790878	+	0.611974i	$0.209624\pi$
$168$	−0.409118	−0.0315641
$169$	−12.1380	−0.933696
$170$	0.0198783	0.00152460
$171$	−5.74921	−0.439653
$172$	13.2176	1.00783
$173$	14.7083	1.11825	0.559127	−	0.829082i	$-0.311136\pi$
$173$	14.7083	1.11825	0.559127	+	0.829082i	$0.311136\pi$
$174$	−0.835180	−0.0633149
$175$	0.925444	0.0699570
$176$	12.2027	0.919815
$177$	2.97462	0.223586
$178$	0.882167	0.0661212
$179$	−1.83856	−0.137420	−0.0687102	−	0.997637i	$-0.521888\pi$
$179$	−1.83856	−0.137420	−0.0687102	+	0.997637i	$0.521888\pi$
$180$	−2.59560	−0.193464
$181$	−3.58723	−0.266636	−0.133318	−	0.991073i	$-0.542563\pi$
$181$	−3.58723	−0.266636	−0.133318	+	0.991073i	$0.542563\pi$
$182$	−0.0730149	−0.00541222
$183$	−14.6171	−1.08052
$184$	−0.0569679	−0.00419973
$185$	9.22182	0.678002
$186$	−0.923720	−0.0677305
$187$	0.721410	0.0527548
$188$	−20.1149	−1.46703
$189$	5.18771	0.377351
$190$	0.375100	0.0272126
$191$	9.32398	0.674659	0.337330	−	0.941387i	$-0.390476\pi$
$191$	9.32398	0.674659	0.337330	+	0.941387i	$0.390476\pi$
$192$	10.1979	0.735971
$193$	11.3149	0.814467	0.407233	−	0.913324i	$-0.366494\pi$
$193$	11.3149	0.814467	0.407233	+	0.913324i	$0.366494\pi$
$194$	0.751699	0.0539689
$195$	1.20962	0.0866224
$196$	12.2427	0.874481
$197$	7.52938	0.536446	0.268223	−	0.963357i	$-0.413564\pi$
$197$	7.52938	0.536446	0.268223	+	0.963357i	$0.413564\pi$
$198$	0.341364	0.0242597
$199$	−0.902676	−0.0639890	−0.0319945	−	0.999488i	$-0.510186\pi$
$199$	−0.902676	−0.0639890	−0.0319945	+	0.999488i	$0.510186\pi$
$200$	0.339307	0.0239926
$201$	−7.99513	−0.563933
$202$	0.107073	0.00753362
$203$	−6.98084	−0.489959
$204$	0.607330	0.0425216
$205$	−2.33892	−0.163357
$206$	0.278924	0.0194335
$207$	0.218683	0.0151995
$208$	3.67349	0.254711
$209$	13.6129	0.941624
$210$	−0.102464	−0.00707072
$211$	−13.7333	−0.945441	−0.472721	−	0.881212i	$-0.656728\pi$
$211$	−13.7333	−0.945441	−0.472721	+	0.881212i	$0.656728\pi$
$212$	8.36242	0.574333
$213$	11.0332	0.755982
$214$	0.841802	0.0575444
$215$	6.63273	0.452349
$216$	1.90204	0.129417
$217$	−7.72091	−0.524129
$218$	−0.859477	−0.0582111
$219$	7.72750	0.522176
$220$	6.14583	0.414352
$221$	0.217172	0.0146086
$222$	−1.02103	−0.0685272
$223$	2.69771	0.180652	0.0903261	−	0.995912i	$-0.471209\pi$
$223$	2.69771	0.180652	0.0903261	+	0.995912i	$0.471209\pi$
$224$	−0.939195	−0.0627526
$225$	−1.30250	−0.0868335
$226$	−0.484243	−0.0322114
$227$	6.10095	0.404934	0.202467	−	0.979289i	$-0.435104\pi$
$227$	6.10095	0.404934	0.202467	+	0.979289i	$0.435104\pi$
$228$	11.4602	0.758972
$229$	−19.2215	−1.27019	−0.635095	−	0.772434i	$-0.719039\pi$
$229$	−19.2215	−1.27019	−0.635095	+	0.772434i	$0.719039\pi$
$230$	−0.0142677	−0.000940787 0
$231$	−3.71857	−0.244664
$232$	−2.55947	−0.168038
$233$	18.1252	1.18742	0.593710	−	0.804679i	$-0.297663\pi$
$233$	18.1252	1.18742	0.593710	+	0.804679i	$0.297663\pi$
$234$	0.102764	0.00671787
$235$	−10.0939	−0.658453
$236$	4.54974	0.296163
$237$	7.67279	0.498402
$238$	−0.0183963	−0.00119245
$239$	0.537170	0.0347466	0.0173733	−	0.999849i	$-0.494470\pi$
$239$	0.537170	0.0347466	0.0173733	+	0.999849i	$0.494470\pi$
$240$	5.15514	0.332763
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	0.126505	0.00813205
$243$	−12.3924	−0.794972
$244$	−22.3571	−1.43126
$245$	6.14355	0.392497
$246$	0.258963	0.0165109
$247$	4.09801	0.260750
$248$	−2.83081	−0.179757
$249$	4.04836	0.256554
$250$	0.0849802	0.00537462
$251$	−21.3085	−1.34498	−0.672492	−	0.740105i	$-0.734776\pi$
$251$	−21.3085	−1.34498	−0.672492	+	0.740105i	$0.734776\pi$
$252$	2.40208	0.151317
$253$	−0.517796	−0.0325535
$254$	0.180244	0.0113095
$255$	0.304765	0.0190852
$256$	15.4254	0.964087
$257$	4.93472	0.307820	0.153910	−	0.988085i	$-0.450813\pi$
$257$	4.93472	0.307820	0.153910	+	0.988085i	$0.450813\pi$
$258$	−0.734370	−0.0457199
$259$	−8.53428	−0.530295
$260$	1.85013	0.114740
$261$	9.82508	0.608157
$262$	1.19072	0.0735626
$263$	10.3217	0.636464	0.318232	−	0.948013i	$-0.396911\pi$
$263$	10.3217	0.636464	0.318232	+	0.948013i	$0.396911\pi$
$264$	−1.36339	−0.0839107
$265$	4.19636	0.257780
$266$	−0.347135	−0.0212842
$267$	13.5250	0.827717
$268$	−12.2287	−0.746986
$269$	−2.26515	−0.138109	−0.0690544	−	0.997613i	$-0.521998\pi$
$269$	−2.26515	−0.138109	−0.0690544	+	0.997613i	$0.521998\pi$
$270$	0.476369	0.0289909
$271$	−21.0203	−1.27689	−0.638447	−	0.769666i	$-0.720423\pi$
$271$	−21.0203	−1.27689	−0.638447	+	0.769666i	$0.720423\pi$
$272$	0.925543	0.0561193
$273$	−1.11943	−0.0677512
$274$	0.493268	0.0297994
$275$	3.08405	0.185975
$276$	−0.435914	−0.0262389
$277$	10.8133	0.649710	0.324855	−	0.945764i	$-0.394685\pi$
$277$	10.8133	0.649710	0.324855	+	0.945764i	$0.394685\pi$
$278$	1.84413	0.110604
$279$	10.8667	0.650570
$280$	−0.314010	−0.0187657
$281$	−13.3331	−0.795387	−0.397694	−	0.917518i	$-0.630189\pi$
$281$	−13.3331	−0.795387	−0.397694	+	0.917518i	$0.630189\pi$
$282$	1.11759	0.0665513
$283$	−24.8210	−1.47545	−0.737727	−	0.675099i	$-0.764101\pi$
$283$	−24.8210	−1.47545	−0.737727	+	0.675099i	$0.764101\pi$
$284$	16.8755	1.00137
$285$	5.75088	0.340653
$286$	−0.243323	−0.0143880
$287$	2.16454	0.127769
$288$	1.32185	0.0778910
$289$	−16.9453	−0.996781
$290$	−0.641026	−0.0376423
$291$	11.5247	0.675592
$292$	11.8193	0.691675
$293$	3.64458	0.212918	0.106459	−	0.994317i	$-0.466049\pi$
$293$	3.64458	0.212918	0.106459	+	0.994317i	$0.466049\pi$
$294$	−0.680209	−0.0396706
$295$	2.28311	0.132928
$296$	−3.12903	−0.181871
$297$	17.2881	1.00316
$298$	0.877532	0.0508341
$299$	−0.155876	−0.00901456
$300$	2.59635	0.149900
$301$	−6.13822	−0.353801
$302$	0.159311	0.00916733
$303$	1.64159	0.0943071
$304$	17.4649	1.00168
$305$	−11.2190	−0.642400
$306$	0.0258915	0.00148012
$307$	−28.7469	−1.64067	−0.820335	−	0.571883i	$-0.806213\pi$
$307$	−28.7469	−1.64067	−0.820335	+	0.571883i	$0.806213\pi$
$308$	−5.68762	−0.324082
$309$	4.27634	0.243272
$310$	−0.708983	−0.0402675
$311$	10.1919	0.577929	0.288965	−	0.957340i	$-0.406689\pi$
$311$	10.1919	0.577929	0.288965	+	0.957340i	$0.406689\pi$
$312$	−0.410432	−0.0232361
$313$	−31.7255	−1.79323	−0.896617	−	0.442808i	$-0.853982\pi$
$313$	−31.7255	−1.79323	−0.896617	+	0.442808i	$0.853982\pi$
$314$	−1.18167	−0.0666855
$315$	1.20539	0.0679162
$316$	11.7357	0.660183
$317$	−20.2760	−1.13881	−0.569406	−	0.822057i	$-0.692827\pi$
$317$	−20.2760	−1.13881	−0.569406	+	0.822057i	$0.692827\pi$
$318$	−0.464618	−0.0260545
$319$	−23.2637	−1.30252
$320$	7.82720	0.437554
$321$	12.9062	0.720351
$322$	0.0132040	0.000735830 0
$323$	1.03250	0.0574499
$324$	6.76744	0.375969
$325$	0.928417	0.0514993
$326$	−0.542454	−0.0300438
$327$	−13.1771	−0.728697
$328$	0.793611	0.0438198
$329$	9.34134	0.515005
$330$	−0.341463	−0.0187969
$331$	9.14826	0.502834	0.251417	−	0.967879i	$-0.419103\pi$
$331$	9.14826	0.502834	0.251417	+	0.967879i	$0.419103\pi$
$332$	6.19203	0.339832
$333$	12.0114	0.658223
$334$	−1.73706	−0.0950479
$335$	−6.13650	−0.335273
$336$	−4.77079	−0.260268
$337$	33.8436	1.84358	0.921788	−	0.387694i	$-0.126728\pi$
$337$	33.8436	1.84358	0.921788	+	0.387694i	$0.126728\pi$
$338$	1.03149	0.0561059
$339$	−7.42421	−0.403228
$340$	0.466144	0.0252802
$341$	−25.7300	−1.39336
$342$	0.488569	0.0264188
$343$	−12.1636	−0.656774
$344$	−2.25053	−0.121341
$345$	−0.218747	−0.0117769
$346$	−1.24992	−0.0671960
$347$	−13.0196	−0.698928	−0.349464	−	0.936950i	$-0.613636\pi$
$347$	−13.0196	−0.698928	−0.349464	+	0.936950i	$0.613636\pi$
$348$	−19.5849	−1.04986
$349$	−20.3621	−1.08996	−0.544979	−	0.838450i	$-0.683462\pi$
$349$	−20.3621	−1.08996	−0.544979	+	0.838450i	$0.683462\pi$
$350$	−0.0786445	−0.00420373
$351$	5.20438	0.277789
$352$	−3.12987	−0.166823
$353$	−11.9974	−0.638556	−0.319278	−	0.947661i	$-0.603440\pi$
$353$	−11.9974	−0.638556	−0.319278	+	0.947661i	$0.603440\pi$
$354$	−0.252784	−0.0134353
$355$	8.46831	0.449451
$356$	20.6867	1.09639
$357$	−0.282044	−0.0149273
$358$	0.156241	0.00825760
$359$	19.8171	1.04590	0.522952	−	0.852362i	$-0.324831\pi$
$359$	19.8171	1.04590	0.522952	+	0.852362i	$0.324831\pi$
$360$	0.441948	0.0232927
$361$	0.483144	0.0254286
$362$	0.304843	0.0160222
$363$	1.93952	0.101798
$364$	−1.71219	−0.0897432
$365$	5.93109	0.310447
$366$	1.24216	0.0649289
$367$	−19.4643	−1.01603	−0.508015	−	0.861348i	$-0.669621\pi$
$367$	−19.4643	−1.01603	−0.508015	+	0.861348i	$0.669621\pi$
$368$	−0.664313	−0.0346297
$369$	−3.04644	−0.158591
$370$	−0.783673	−0.0407412
$371$	−3.88350	−0.201621
$372$	−21.6612	−1.12308
$373$	24.0788	1.24676	0.623378	−	0.781921i	$-0.285760\pi$
$373$	24.0788	1.24676	0.623378	+	0.781921i	$0.285760\pi$
$374$	−0.0613056	−0.00317004
$375$	1.30288	0.0672805
$376$	3.42493	0.176627
$377$	−7.00327	−0.360687
$378$	−0.440853	−0.0226750
$379$	11.6671	0.599298	0.299649	−	0.954050i	$-0.403130\pi$
$379$	11.6671	0.599298	0.299649	+	0.954050i	$0.403130\pi$
$380$	8.79607	0.451229
$381$	2.76342	0.141574
$382$	−0.792354	−0.0405404
$383$	19.9789	1.02087	0.510436	−	0.859916i	$-0.329484\pi$
$383$	19.9789	1.02087	0.510436	+	0.859916i	$0.329484\pi$
$384$	−3.51110	−0.179175
$385$	−2.85412	−0.145459
$386$	−0.961546	−0.0489414
$387$	8.63915	0.439152
$388$	17.6273	0.894889
$389$	4.56137	0.231271	0.115635	−	0.993292i	$-0.463110\pi$
$389$	4.56137	0.231271	0.115635	+	0.993292i	$0.463110\pi$
$390$	−0.102793	−0.00520515
$391$	−0.0392734	−0.00198614
$392$	−2.08455	−0.105286
$393$	18.2555	0.920870
$394$	−0.639848	−0.0322351
$395$	5.88910	0.296313
$396$	8.00495	0.402264
$397$	24.4174	1.22548	0.612738	−	0.790286i	$-0.290068\pi$
$397$	24.4174	1.22548	0.612738	+	0.790286i	$0.290068\pi$
$398$	0.0767096	0.00384510
$399$	−5.32212	−0.266439
$400$	3.95672	0.197836
$401$	33.7297	1.68438	0.842191	−	0.539180i	$-0.181266\pi$
$401$	33.7297	1.68438	0.842191	+	0.539180i	$0.181266\pi$
$402$	0.679428	0.0338868
$403$	−7.74570	−0.385841
$404$	2.51085	0.124919
$405$	3.39598	0.168748
$406$	0.593234	0.0294417
$407$	−28.4405	−1.40975
$408$	−0.103409	−0.00511952
$409$	1.87731	0.0928268	0.0464134	−	0.998922i	$-0.485221\pi$
$409$	1.87731	0.0928268	0.0464134	+	0.998922i	$0.485221\pi$
$410$	0.198762	0.00981614
$411$	7.56257	0.373034
$412$	6.54073	0.322239
$413$	−2.11289	−0.103969
$414$	−0.0185838	−0.000913342 0
$415$	3.10723	0.152528
$416$	−0.942211	−0.0461957
$417$	28.2735	1.38456
$418$	−1.15683	−0.0565823
$419$	4.05025	0.197868	0.0989339	−	0.995094i	$-0.468457\pi$
$419$	4.05025	0.197868	0.0989339	+	0.995094i	$0.468457\pi$
$420$	−2.40278	−0.117244
$421$	−30.6335	−1.49299	−0.746493	−	0.665393i	$-0.768264\pi$
$421$	−30.6335	−1.49299	−0.746493	+	0.665393i	$0.768264\pi$
$422$	1.16706	0.0568117
$423$	−13.1473	−0.639244
$424$	−1.42386	−0.0691486
$425$	0.233917	0.0113466
$426$	−0.937604	−0.0454271
$427$	10.3826	0.502449
$428$	19.7402	0.954178
$429$	−3.73052	−0.180111
$430$	−0.563651	−0.0271817
$431$	−33.0997	−1.59436	−0.797178	−	0.603745i	$-0.793675\pi$
$431$	−33.0997	−1.59436	−0.797178	+	0.603745i	$0.793675\pi$
$432$	22.1800	1.06714
$433$	−15.5072	−0.745226	−0.372613	−	0.927987i	$-0.621538\pi$
$433$	−15.5072	−0.745226	−0.372613	+	0.927987i	$0.621538\pi$
$434$	0.656125	0.0314950
$435$	−9.82793	−0.471213
$436$	−20.1546	−0.965232
$437$	−0.741083	−0.0354508
$438$	−0.656685	−0.0313776
$439$	10.5751	0.504720	0.252360	−	0.967633i	$-0.418793\pi$
$439$	10.5751	0.504720	0.252360	+	0.967633i	$0.418793\pi$
$440$	−1.04644	−0.0498871
$441$	8.00199	0.381047
$442$	−0.0184553	−0.000877831 0
$443$	30.7308	1.46006	0.730032	−	0.683413i	$-0.239505\pi$
$443$	30.7308	1.46006	0.730032	+	0.683413i	$0.239505\pi$
$444$	−23.9431	−1.13629
$445$	10.3808	0.492099
$446$	−0.229252	−0.0108554
$447$	13.4539	0.636350
$448$	−7.24364	−0.342230
$449$	40.8816	1.92932	0.964660	−	0.263497i	$-0.0848760\pi$
$449$	40.8816	1.92932	0.964660	+	0.263497i	$0.0848760\pi$
$450$	0.110687	0.00521783
$451$	7.21333	0.339662
$452$	−11.3555	−0.534116
$453$	2.44249	0.114758
$454$	−0.518460	−0.0243325
$455$	−0.859198	−0.0402798
$456$	−1.95131	−0.0913787
$457$	18.5130	0.866000	0.433000	−	0.901394i	$-0.357455\pi$
$457$	18.5130	0.866000	0.433000	+	0.901394i	$0.357455\pi$
$458$	1.63344	0.0763259
$459$	1.31125	0.0612041
$460$	−0.334577	−0.0155997
$461$	−14.2832	−0.665234	−0.332617	−	0.943062i	$-0.607932\pi$
$461$	−14.2832	−0.665234	−0.332617	+	0.943062i	$0.607932\pi$
$462$	0.316005	0.0147019
$463$	−38.0719	−1.76935	−0.884676	−	0.466207i	$-0.845620\pi$
$463$	−38.0719	−1.76935	−0.884676	+	0.466207i	$0.845620\pi$
$464$	−29.8465	−1.38559
$465$	−10.8698	−0.504076
$466$	−1.54028	−0.0713522
$467$	−40.2325	−1.86174	−0.930870	−	0.365352i	$-0.880949\pi$
$467$	−40.2325	−1.86174	−0.930870	+	0.365352i	$0.880949\pi$
$468$	2.40980	0.111393
$469$	5.67899	0.262232
$470$	0.857781	0.0395665
$471$	−18.1169	−0.834780
$472$	−0.774677	−0.0356574
$473$	−20.4557	−0.940553
$474$	−0.652036	−0.0299490
$475$	4.41397	0.202527
$476$	−0.431390	−0.0197727
$477$	5.46577	0.250260
$478$	−0.0456488	−0.00208793
$479$	11.6920	0.534222	0.267111	−	0.963666i	$-0.413931\pi$
$479$	11.6920	0.534222	0.267111	+	0.963666i	$0.413931\pi$
$480$	−1.32224	−0.0603517
$481$	−8.56169	−0.390380
$482$	0.0849802	0.00387074
$483$	0.202438	0.00921125
$484$	2.96653	0.134842
$485$	8.84558	0.401657
$486$	1.05311	0.0477699
$487$	−8.58859	−0.389186	−0.194593	−	0.980884i	$-0.562339\pi$
$487$	−8.58859	−0.389186	−0.194593	+	0.980884i	$0.562339\pi$
$488$	3.80670	0.172321
$489$	−8.31667	−0.376093
$490$	−0.522081	−0.0235852
$491$	−14.8576	−0.670514	−0.335257	−	0.942127i	$-0.608823\pi$
$491$	−14.8576	−0.670514	−0.335257	+	0.942127i	$0.608823\pi$
$492$	6.07265	0.273776
$493$	−1.76449	−0.0794686
$494$	−0.348250	−0.0156685
$495$	4.01698	0.180550
$496$	−33.0106	−1.48222
$497$	−7.83695	−0.351535
$498$	−0.344030	−0.0154164
$499$	−2.23865	−0.100216	−0.0501079	−	0.998744i	$-0.515957\pi$
$499$	−2.23865	−0.100216	−0.0501079	+	0.998744i	$0.515957\pi$
$500$	1.99278	0.0891198
$501$	−26.6319	−1.18983
$502$	1.81081	0.0808202
$503$	−7.75146	−0.345621	−0.172810	−	0.984955i	$-0.555285\pi$
$503$	−7.75146	−0.345621	−0.172810	+	0.984955i	$0.555285\pi$
$504$	−0.408999	−0.0182183
$505$	1.25997	0.0560681
$506$	0.0440024	0.00195615
$507$	15.8144	0.702343
$508$	4.22670	0.187529
$509$	23.8047	1.05512	0.527561	−	0.849517i	$-0.323106\pi$
$509$	23.8047	1.05512	0.527561	+	0.849517i	$0.323106\pi$
$510$	−0.0258990	−0.00114683
$511$	−5.48889	−0.242814
$512$	−6.70060	−0.296127
$513$	24.7432	1.09244
$514$	−0.419354	−0.0184969
$515$	3.28222	0.144632
$516$	−17.2209	−0.758108
$517$	31.1301	1.36910
$518$	0.725246	0.0318655
$519$	−19.1632	−0.841172
$520$	−0.315019	−0.0138145
$521$	9.12147	0.399619	0.199809	−	0.979835i	$-0.435968\pi$
$521$	9.12147	0.399619	0.199809	+	0.979835i	$0.435968\pi$
$522$	−0.834938	−0.0365442
$523$	−28.4222	−1.24281	−0.621407	−	0.783488i	$-0.713439\pi$
$523$	−28.4222	−1.24281	−0.621407	+	0.783488i	$0.713439\pi$
$524$	27.9222	1.21978
$525$	−1.20574	−0.0526230
$526$	−0.877142	−0.0382452
$527$	−1.95155	−0.0850107
$528$	−15.8987	−0.691902
$529$	−22.9718	−0.998774
$530$	−0.356608	−0.0154901
$531$	2.97376	0.129050
$532$	−8.14027	−0.352926
$533$	2.17149	0.0940576
$534$	−1.14936	−0.0497376
$535$	9.90586	0.428268
$536$	2.08216	0.0899356
$537$	2.39542	0.103370
$538$	0.192493	0.00829897
$539$	−18.9470	−0.816106
$540$	11.1708	0.480715
$541$	−17.8195	−0.766119	−0.383060	−	0.923724i	$-0.625130\pi$
$541$	−17.8195	−0.766119	−0.383060	+	0.923724i	$0.625130\pi$
$542$	1.78631	0.0767287
$543$	4.67373	0.200569
$544$	−0.237392	−0.0101781
$545$	−10.1138	−0.433229
$546$	0.0951297	0.00407117
$547$	−25.4787	−1.08939	−0.544696	−	0.838633i	$-0.683355\pi$
$547$	−25.4787	−1.08939	−0.544696	+	0.838633i	$0.683355\pi$
$548$	11.5671	0.494121
$549$	−14.6128	−0.623660
$550$	−0.262083	−0.0111753
$551$	−33.2956	−1.41844
$552$	0.0742224	0.00315912
$553$	−5.45004	−0.231759
$554$	−0.918919	−0.0390411
$555$	−12.0149	−0.510005
$556$	43.2448	1.83399
$557$	11.4618	0.485651	0.242825	−	0.970070i	$-0.421926\pi$
$557$	11.4618	0.485651	0.242825	+	0.970070i	$0.421926\pi$
$558$	−0.923452	−0.0390928
$559$	−6.15794	−0.260453
$560$	−3.66173	−0.154736
$561$	−0.939912	−0.0396831
$562$	1.13305	0.0477949
$563$	31.1578	1.31315	0.656573	−	0.754262i	$-0.272005\pi$
$563$	31.1578	1.31315	0.656573	+	0.754262i	$0.272005\pi$
$564$	26.2073	1.10353
$565$	−5.69830	−0.239729
$566$	2.10929	0.0886602
$567$	−3.14279	−0.131985
$568$	−2.87336	−0.120563
$569$	10.5255	0.441252	0.220626	−	0.975358i	$-0.429190\pi$
$569$	10.5255	0.441252	0.220626	+	0.975358i	$0.429190\pi$
$570$	−0.488711	−0.0204699
$571$	15.7014	0.657081	0.328541	−	0.944490i	$-0.393443\pi$
$571$	15.7014	0.657081	0.328541	+	0.944490i	$0.393443\pi$
$572$	−5.70589	−0.238575
$573$	−12.1480	−0.507491
$574$	−0.183943	−0.00767763
$575$	−0.167895	−0.00700170
$576$	10.1949	0.424789
$577$	−20.7286	−0.862941	−0.431471	−	0.902127i	$-0.642005\pi$
$577$	−20.7286	−0.862941	−0.431471	+	0.902127i	$0.642005\pi$
$578$	1.44001	0.0598967
$579$	−14.7420	−0.612657
$580$	−15.0320	−0.624170
$581$	−2.87557	−0.119299
$582$	−0.979375	−0.0405964
$583$	−12.9418	−0.535994
$584$	−2.01246	−0.0832762
$585$	1.20926	0.0499969
$586$	−0.309717	−0.0127943
$587$	29.7610	1.22837	0.614185	−	0.789162i	$-0.289485\pi$
$587$	29.7610	1.22837	0.614185	+	0.789162i	$0.289485\pi$
$588$	−15.9508	−0.657801
$589$	−36.8254	−1.51736
$590$	−0.194020	−0.00798766
$591$	−9.80988	−0.403525
$592$	−36.4882	−1.49966
$593$	−8.24320	−0.338508	−0.169254	−	0.985572i	$-0.554136\pi$
$593$	−8.24320	−0.338508	−0.169254	+	0.985572i	$0.554136\pi$
$594$	−1.46915	−0.0602798
$595$	−0.216477	−0.00887469
$596$	20.5780	0.842910
$597$	1.17608	0.0481337
$598$	0.0132464	0.000541686 0
$599$	28.7930	1.17645	0.588225	−	0.808697i	$-0.299827\pi$
$599$	28.7930	1.17645	0.588225	+	0.808697i	$0.299827\pi$
$600$	−0.442077	−0.0180477
$601$	45.8741	1.87124	0.935622	−	0.353004i	$-0.114840\pi$
$601$	45.8741	1.87124	0.935622	+	0.353004i	$0.114840\pi$
$602$	0.521628	0.0212600
$603$	−7.99281	−0.325492
$604$	3.73583	0.152009
$605$	1.48864	0.0605219
$606$	−0.139503	−0.00566692
$607$	4.77785	0.193927	0.0969635	−	0.995288i	$-0.469087\pi$
$607$	4.77785	0.193927	0.0969635	+	0.995288i	$0.469087\pi$
$608$	−4.47955	−0.181670
$609$	9.09521	0.368556
$610$	0.953397	0.0386019
$611$	9.37134	0.379124
$612$	0.607154	0.0245427
$613$	18.7882	0.758849	0.379424	−	0.925223i	$-0.376122\pi$
$613$	18.7882	0.758849	0.379424	+	0.925223i	$0.376122\pi$
$614$	2.44292	0.0985880
$615$	3.04733	0.122880
$616$	0.968422	0.0390189
$617$	−45.3953	−1.82755	−0.913773	−	0.406224i	$-0.866845\pi$
$617$	−45.3953	−1.82755	−0.913773	+	0.406224i	$0.866845\pi$
$618$	−0.363404	−0.0146183
$619$	20.8119	0.836500	0.418250	−	0.908332i	$-0.362644\pi$
$619$	20.8119	0.836500	0.418250	+	0.908332i	$0.362644\pi$
$620$	−16.6256	−0.667700
$621$	−0.941159	−0.0377674
$622$	−0.866110	−0.0347278
$623$	−9.60690	−0.384892
$624$	−4.78612	−0.191598
$625$	1.00000	0.0400000
$626$	2.69604	0.107756
$627$	−17.7360	−0.708307
$628$	−27.7100	−1.10575
$629$	−2.15714	−0.0860107
$630$	−0.102435	−0.00408109
$631$	−26.9460	−1.07270	−0.536351	−	0.843995i	$-0.680198\pi$
$631$	−26.9460	−1.07270	−0.536351	+	0.843995i	$0.680198\pi$
$632$	−1.99821	−0.0794847
$633$	17.8929	0.711178
$634$	1.72306	0.0684313
$635$	2.12101	0.0841696
$636$	−10.8952	−0.432024
$637$	−5.70378	−0.225992
$638$	1.97696	0.0782684
$639$	11.0300	0.436340
$640$	−2.69487	−0.106524
$641$	21.4228	0.846148	0.423074	−	0.906095i	$-0.360951\pi$
$641$	21.4228	0.846148	0.423074	+	0.906095i	$0.360951\pi$
$642$	−1.09677	−0.0432860
$643$	−6.93373	−0.273439	−0.136720	−	0.990610i	$-0.543656\pi$
$643$	−6.93373	−0.273439	−0.136720	+	0.990610i	$0.543656\pi$
$644$	0.309633	0.0122012
$645$	−8.64166	−0.340265
$646$	−0.0877422	−0.00345217
$647$	−26.6861	−1.04914	−0.524569	−	0.851368i	$-0.675774\pi$
$647$	−26.6861	−1.04914	−0.524569	+	0.851368i	$0.675774\pi$
$648$	−1.15228	−0.0452659
$649$	−7.04123	−0.276393
$650$	−0.0788971	−0.00309460
$651$	10.0594	0.394260
$652$	−12.7205	−0.498173
$653$	−11.8154	−0.462374	−0.231187	−	0.972909i	$-0.574261\pi$
$653$	−11.8154	−0.462374	−0.231187	+	0.972909i	$0.574261\pi$
$654$	1.11980	0.0437875
$655$	14.0117	0.547481
$656$	9.25444	0.361325
$657$	7.72525	0.301391
$658$	−0.793829	−0.0309467
$659$	−38.7912	−1.51109	−0.755546	−	0.655096i	$-0.772628\pi$
$659$	−38.7912	−1.51109	−0.755546	+	0.655096i	$0.772628\pi$
$660$	−8.00728	−0.311683
$661$	32.4919	1.26379	0.631893	−	0.775055i	$-0.282278\pi$
$661$	32.4919	1.26379	0.631893	+	0.775055i	$0.282278\pi$
$662$	−0.777421	−0.0302153
$663$	−0.282949	−0.0109888
$664$	−1.05431	−0.0409151
$665$	−4.08489	−0.158405
$666$	−1.02074	−0.0395527
$667$	1.26647	0.0490379
$668$	−40.7340	−1.57604
$669$	−3.51480	−0.135890
$670$	0.521482	0.0201466
$671$	34.6001	1.33572
$672$	1.22366	0.0472036
$673$	20.2929	0.782232	0.391116	−	0.920341i	$-0.372089\pi$
$673$	20.2929	0.782232	0.391116	+	0.920341i	$0.372089\pi$
$674$	−2.87603	−0.110781
$675$	5.60565	0.215761
$676$	24.1884	0.930324
$677$	27.8818	1.07158	0.535792	−	0.844350i	$-0.320013\pi$
$677$	27.8818	1.07158	0.535792	+	0.844350i	$0.320013\pi$
$678$	0.630911	0.0242300
$679$	−8.18609	−0.314153
$680$	−0.0793696	−0.00304369
$681$	−7.94881	−0.304599
$682$	2.18654	0.0837269
$683$	12.5172	0.478955	0.239478	−	0.970902i	$-0.423024\pi$
$683$	12.5172	0.478955	0.239478	+	0.970902i	$0.423024\pi$
$684$	11.4569	0.438065
$685$	5.80450	0.221779
$686$	1.03367	0.0394656
$687$	25.0433	0.955460
$688$	−26.2439	−1.00054
$689$	−3.89597	−0.148425
$690$	0.0185892	0.000707677 0
$691$	13.4228	0.510626	0.255313	−	0.966858i	$-0.417821\pi$
$691$	13.4228	0.510626	0.255313	+	0.966858i	$0.417821\pi$
$692$	−29.3105	−1.11422
$693$	−3.71749	−0.141216
$694$	1.10641	0.0419987
$695$	21.7007	0.823156
$696$	3.33469	0.126401
$697$	0.547111	0.0207233
$698$	1.73037	0.0654957
$699$	−23.6150	−0.893200
$700$	−1.84421	−0.0697044
$701$	−8.82337	−0.333254	−0.166627	−	0.986020i	$-0.553288\pi$
$701$	−8.82337	−0.333254	−0.166627	+	0.986020i	$0.553288\pi$
$702$	−0.442269	−0.0166924
$703$	−40.7049	−1.53521
$704$	−24.1395	−0.909791
$705$	13.1511	0.495300
$706$	1.01954	0.0383709
$707$	−1.16603	−0.0438533
$708$	−5.92777	−0.222779
$709$	10.6041	0.398246	0.199123	−	0.979974i	$-0.436191\pi$
$709$	10.6041	0.398246	0.199123	+	0.979974i	$0.436191\pi$
$710$	−0.719639	−0.0270076
$711$	7.67057	0.287669
$712$	−3.52230	−0.132004
$713$	1.40073	0.0524578
$714$	0.0239681	0.000896985 0
$715$	−2.86328	−0.107081
$716$	3.66384	0.136924
$717$	−0.699868	−0.0261370
$718$	−1.68406	−0.0628485
$719$	−0.872129	−0.0325249	−0.0162625	−	0.999868i	$-0.505177\pi$
$719$	−0.872129	−0.0325249	−0.0162625	+	0.999868i	$0.505177\pi$
$720$	5.15364	0.192065
$721$	−3.03751	−0.113123
$722$	−0.0410577	−0.00152801
$723$	1.30288	0.0484547
$724$	7.14855	0.265674
$725$	−7.54323	−0.280149
$726$	−0.164821	−0.00611708
$727$	17.9554	0.665928	0.332964	−	0.942940i	$-0.391951\pi$
$727$	17.9554	0.665928	0.332964	+	0.942940i	$0.391951\pi$
$728$	0.291532	0.0108049
$729$	26.3337	0.975324
$730$	−0.504025	−0.0186548
$731$	−1.55151	−0.0573845
$732$	29.1286	1.07662
$733$	−37.3166	−1.37832	−0.689159	−	0.724610i	$-0.742020\pi$
$733$	−37.3166	−1.37832	−0.689159	+	0.724610i	$0.742020\pi$
$734$	1.65408	0.0610534
$735$	−8.00432	−0.295244
$736$	0.170389	0.00628063
$737$	18.9253	0.697121
$738$	0.258887	0.00952978
$739$	2.96677	0.109135	0.0545673	−	0.998510i	$-0.482622\pi$
$739$	2.96677	0.109135	0.0545673	+	0.998510i	$0.482622\pi$
$740$	−18.3770	−0.675554
$741$	−5.33921	−0.196141
$742$	0.330021	0.0121154
$743$	2.57097	0.0943197	0.0471598	−	0.998887i	$-0.484983\pi$
$743$	2.57097	0.0943197	0.0471598	+	0.998887i	$0.484983\pi$
$744$	3.68821	0.135216
$745$	10.3263	0.378327
$746$	−2.04623	−0.0749177
$747$	4.04718	0.148079
$748$	−1.43761	−0.0525643
$749$	−9.16732	−0.334967
$750$	−0.110719	−0.00404289
$751$	−42.2775	−1.54273	−0.771363	−	0.636395i	$-0.780425\pi$
$751$	−42.2775	−1.54273	−0.771363	+	0.636395i	$0.780425\pi$
$752$	39.9387	1.45642
$753$	27.7625	1.01172
$754$	0.595139	0.0216737
$755$	1.87469	0.0682268
$756$	−10.3380	−0.375988
$757$	22.2147	0.807408	0.403704	−	0.914890i	$-0.367722\pi$
$757$	22.2147	0.807408	0.403704	+	0.914890i	$0.367722\pi$
$758$	−0.991472	−0.0360119
$759$	0.674626	0.0244874
$760$	−1.49769	−0.0543270
$761$	28.0264	1.01596	0.507979	−	0.861370i	$-0.330393\pi$
$761$	28.0264	1.01596	0.507979	+	0.861370i	$0.330393\pi$
$762$	−0.234836	−0.00850721
$763$	9.35980	0.338847
$764$	−18.5806	−0.672223
$765$	0.304677	0.0110156
$766$	−1.69781	−0.0613443
$767$	−2.11968	−0.0765372
$768$	−20.0974	−0.725204
$769$	−25.6953	−0.926597	−0.463298	−	0.886202i	$-0.653334\pi$
$769$	−25.6953	−0.926597	−0.463298	+	0.886202i	$0.653334\pi$
$770$	0.242544	0.00874066
$771$	−6.42936	−0.231548
$772$	−22.5482	−0.811526
$773$	35.9222	1.29203	0.646016	−	0.763324i	$-0.276434\pi$
$773$	35.9222	1.29203	0.646016	+	0.763324i	$0.276434\pi$
$774$	−0.734157	−0.0263887
$775$	−8.34292	−0.299686
$776$	−3.00137	−0.107743
$777$	11.1192	0.398897
$778$	−0.387627	−0.0138971
$779$	10.3239	0.369892
$780$	−2.41050	−0.0863096
$781$	−26.1167	−0.934529
$782$	0.00333746	0.000119347 0
$783$	−42.2847	−1.51113
$784$	−24.3083	−0.868155
$785$	−13.9052	−0.496299
$786$	−1.55136	−0.0553352
$787$	−30.2090	−1.07684	−0.538418	−	0.842678i	$-0.680978\pi$
$787$	−30.2090	−1.07684	−0.538418	+	0.842678i	$0.680978\pi$
$788$	−15.0044	−0.534509
$789$	−13.4480	−0.478760
$790$	−0.500457	−0.0178055
$791$	5.27346	0.187503
$792$	−1.36299	−0.0484318
$793$	10.4159	0.369881
$794$	−2.07500	−0.0736390
$795$	−5.46736	−0.193907
$796$	1.79883	0.0637579
$797$	−31.6858	−1.12237	−0.561184	−	0.827691i	$-0.689654\pi$
$797$	−31.6858	−1.12237	−0.561184	+	0.827691i	$0.689654\pi$
$798$	0.452275	0.0160104
$799$	2.36113	0.0835307
$800$	−1.01486	−0.0358806
$801$	13.5211	0.477744
$802$	−2.86636	−0.101215
$803$	−18.2918	−0.645502
$804$	15.9325	0.561897
$805$	0.155377	0.00547633
$806$	0.658232	0.0231852
$807$	2.95122	0.103888
$808$	−0.427518	−0.0150400
$809$	28.0941	0.987736	0.493868	−	0.869537i	$-0.335583\pi$
$809$	28.0941	0.987736	0.493868	+	0.869537i	$0.335583\pi$
$810$	−0.288591	−0.0101401
$811$	−53.7365	−1.88694	−0.943472	−	0.331451i	$-0.892462\pi$
$811$	−53.7365	−1.88694	−0.943472	+	0.331451i	$0.892462\pi$
$812$	13.9113	0.488190
$813$	27.3870	0.960503
$814$	2.41688	0.0847118
$815$	−6.38330	−0.223597
$816$	−1.20587	−0.0422140
$817$	−29.2767	−1.02426
$818$	−0.159534	−0.00557797
$819$	−1.11911	−0.0391048
$820$	4.66094	0.162767
$821$	−37.7308	−1.31681	−0.658407	−	0.752662i	$-0.728769\pi$
$821$	−37.7308	−1.31681	−0.658407	+	0.752662i	$0.728769\pi$
$822$	−0.642669	−0.0224157
$823$	47.8566	1.66818	0.834088	−	0.551631i	$-0.185994\pi$
$823$	47.8566	1.66818	0.834088	+	0.551631i	$0.185994\pi$
$824$	−1.11368	−0.0387969
$825$	−4.01815	−0.139894
$826$	0.179554	0.00624749
$827$	−20.2430	−0.703918	−0.351959	−	0.936015i	$-0.614484\pi$
$827$	−20.2430	−0.703918	−0.351959	+	0.936015i	$0.614484\pi$
$828$	−0.435787	−0.0151447
$829$	37.2432	1.29351	0.646756	−	0.762697i	$-0.276125\pi$
$829$	37.2432	1.29351	0.646756	+	0.762697i	$0.276125\pi$
$830$	−0.264054	−0.00916543
$831$	−14.0885	−0.488724
$832$	−7.26691	−0.251935
$833$	−1.43708	−0.0497918
$834$	−2.40269	−0.0831982
$835$	−20.4408	−0.707383
$836$	−27.1275	−0.938224
$837$	−46.7674	−1.61652
$838$	−0.344192	−0.0118899
$839$	−7.22597	−0.249468	−0.124734	−	0.992190i	$-0.539808\pi$
$839$	−7.22597	−0.249468	−0.124734	+	0.992190i	$0.539808\pi$
$840$	0.409118	0.0141159
$841$	27.9004	0.962082
$842$	2.60325	0.0897137
$843$	17.3715	0.598305
$844$	27.3675	0.942027
$845$	12.1380	0.417561
$846$	1.11726	0.0384123
$847$	−1.37765	−0.0473368
$848$	−16.6038	−0.570178
$849$	32.3388	1.10986
$850$	−0.0198783	−0.000681820 0
$851$	1.54830	0.0530749
$852$	−21.9867	−0.753253
$853$	−2.75703	−0.0943991	−0.0471995	−	0.998885i	$-0.515030\pi$
$853$	−2.75703	−0.0943991	−0.0471995	+	0.998885i	$0.515030\pi$
$854$	−0.882316	−0.0301922
$855$	5.74921	0.196619
$856$	−3.36113	−0.114881
$857$	53.8843	1.84065	0.920326	−	0.391152i	$-0.127923\pi$
$857$	53.8843	1.84065	0.920326	+	0.391152i	$0.127923\pi$
$858$	0.317020	0.0108229
$859$	−47.2920	−1.61358	−0.806792	−	0.590836i	$-0.798798\pi$
$859$	−47.2920	−1.61358	−0.806792	+	0.590836i	$0.798798\pi$
$860$	−13.2176	−0.450715
$861$	−2.82013	−0.0961099
$862$	2.81282	0.0958050
$863$	38.8347	1.32195	0.660974	−	0.750409i	$-0.270143\pi$
$863$	38.8347	1.32195	0.660974	+	0.750409i	$0.270143\pi$
$864$	−5.68893	−0.193541
$865$	−14.7083	−0.500099
$866$	1.31780	0.0447807
$867$	22.0777	0.749797
$868$	15.3861	0.522237
$869$	−18.1623	−0.616113
$870$	0.835180	0.0283153
$871$	5.69723	0.193043
$872$	3.43170	0.116212
$873$	11.5214	0.389940
$874$	0.0629774	0.00213024
$875$	−0.925444	−0.0312857
$876$	−15.3992	−0.520291
$877$	−13.1563	−0.444258	−0.222129	−	0.975017i	$-0.571301\pi$
$877$	−13.1563	−0.444258	−0.222129	+	0.975017i	$0.571301\pi$
$878$	−0.898671	−0.0303287
$879$	−4.74845	−0.160161
$880$	−12.2027	−0.411354
$881$	2.96390	0.0998562	0.0499281	−	0.998753i	$-0.484101\pi$
$881$	2.96390	0.0998562	0.0499281	+	0.998753i	$0.484101\pi$
$882$	−0.680011	−0.0228972
$883$	−1.29549	−0.0435967	−0.0217984	−	0.999762i	$-0.506939\pi$
$883$	−1.29549	−0.0435967	−0.0217984	+	0.999762i	$0.506939\pi$
$884$	−0.432776	−0.0145558
$885$	−2.97462	−0.0999909
$886$	−2.61151	−0.0877354
$887$	37.6642	1.26464	0.632320	−	0.774707i	$-0.282103\pi$
$887$	37.6642	1.26464	0.632320	+	0.774707i	$0.282103\pi$
$888$	4.07675	0.136807
$889$	−1.96287	−0.0658327
$890$	−0.882167	−0.0295703
$891$	−10.4734	−0.350871
$892$	−5.37594	−0.180000
$893$	44.5541	1.49095
$894$	−1.14332	−0.0382383
$895$	1.83856	0.0614563
$896$	2.49396	0.0833172
$897$	0.203088	0.00678092
$898$	−3.47413	−0.115933
$899$	62.9326	2.09892
$900$	2.59560	0.0865199
$901$	−0.981599	−0.0327018
$902$	−0.612991	−0.0204104
$903$	7.99737	0.266136
$904$	1.93348	0.0643065
$905$	3.58723	0.119243
$906$	−0.207564	−0.00689584
$907$	17.1375	0.569042	0.284521	−	0.958670i	$-0.408165\pi$
$907$	17.1375	0.569042	0.284521	+	0.958670i	$0.408165\pi$
$908$	−12.1578	−0.403472
$909$	1.64112	0.0544324
$910$	0.0730149	0.00242042
$911$	58.0194	1.92227	0.961134	−	0.276082i	$-0.0890362\pi$
$911$	58.0194	1.92227	0.961134	+	0.276082i	$0.0890362\pi$
$912$	−22.7546	−0.753481
$913$	−9.58286	−0.317147
$914$	−1.57324	−0.0520381
$915$	14.6171	0.483225
$916$	38.3041	1.26560
$917$	−12.9670	−0.428209
$918$	−0.111431	−0.00367776
$919$	16.8294	0.555152	0.277576	−	0.960704i	$-0.410469\pi$
$919$	16.8294	0.555152	0.277576	+	0.960704i	$0.410469\pi$
$920$	0.0569679	0.00187818
$921$	37.4537	1.23414
$922$	1.21379	0.0399740
$923$	−7.86212	−0.258785
$924$	7.41029	0.243781
$925$	−9.22182	−0.303212
$926$	3.23536	0.106321
$927$	4.27510	0.140413
$928$	7.65531	0.251298
$929$	−2.00211	−0.0656871	−0.0328435	−	0.999461i	$-0.510456\pi$
$929$	−2.00211	−0.0656871	−0.0328435	+	0.999461i	$0.510456\pi$
$930$	0.923720	0.0302900
$931$	−27.1175	−0.888739
$932$	−36.1195	−1.18313
$933$	−13.2788	−0.434729
$934$	3.41897	0.111872
$935$	−0.721410	−0.0235926
$936$	−0.410312	−0.0134115
$937$	−31.8957	−1.04199	−0.520994	−	0.853560i	$-0.674439\pi$
$937$	−31.8957	−1.04199	−0.520994	+	0.853560i	$0.674439\pi$
$938$	−0.482602	−0.0157575
$939$	41.3346	1.34890
$940$	20.1149	0.656075
$941$	29.1726	0.951000	0.475500	−	0.879716i	$-0.342267\pi$
$941$	29.1726	0.951000	0.475500	+	0.879716i	$0.342267\pi$
$942$	1.53957	0.0501620
$943$	−0.392692	−0.0127878
$944$	−9.03364	−0.294020
$945$	−5.18771	−0.168756
$946$	1.73833	0.0565179
$947$	−33.7919	−1.09809	−0.549045	−	0.835793i	$-0.685009\pi$
$947$	−33.7919	−1.09809	−0.549045	+	0.835793i	$0.685009\pi$
$948$	−15.2902	−0.496602
$949$	−5.50652	−0.178749
$950$	−0.375100	−0.0121699
$951$	26.4171	0.856635
$952$	0.0734522	0.00238060
$953$	2.62660	0.0850838	0.0425419	−	0.999095i	$-0.486454\pi$
$953$	2.62660	0.0850838	0.0425419	+	0.999095i	$0.486454\pi$
$954$	−0.464483	−0.0150382
$955$	−9.32398	−0.301717
$956$	−1.07046	−0.0346211
$957$	30.3098	0.979778
$958$	−0.993591	−0.0321015
$959$	−5.37174	−0.173463
$960$	−10.1979	−0.329136
$961$	38.6043	1.24530
$962$	0.727575	0.0234580
$963$	12.9024	0.415774
$964$	1.99278	0.0641831
$965$	−11.3149	−0.364241
$966$	−0.0172032	−0.000553505 0
$967$	−8.79664	−0.282881	−0.141440	−	0.989947i	$-0.545173\pi$
$967$	−8.79664	−0.282881	−0.141440	+	0.989947i	$0.545173\pi$
$968$	−0.505107	−0.0162347
$969$	−1.34523	−0.0432149
$970$	−0.751699	−0.0241356
$971$	19.1455	0.614407	0.307204	−	0.951644i	$-0.400607\pi$
$971$	19.1455	0.614407	0.307204	+	0.951644i	$0.400607\pi$
$972$	24.6953	0.792101
$973$	−20.0828	−0.643826
$974$	0.729861	0.0233862
$975$	−1.20962	−0.0387387
$976$	44.3906	1.42091
$977$	45.7736	1.46443	0.732214	−	0.681075i	$-0.238487\pi$
$977$	45.7736	1.46443	0.732214	+	0.681075i	$0.238487\pi$
$978$	0.706753	0.0225995
$979$	−32.0150	−1.02321
$980$	−12.2427	−0.391080
$981$	−13.1733	−0.420591
$982$	1.26260	0.0402913
$983$	53.9692	1.72135	0.860675	−	0.509155i	$-0.170042\pi$
$983$	53.9692	1.72135	0.860675	+	0.509155i	$0.170042\pi$
$984$	−1.03398	−0.0329621
$985$	−7.52938	−0.239906
$986$	0.149947	0.00477527
$987$	−12.1706	−0.387396
$988$	−8.16642	−0.259808
$989$	1.11360	0.0354105
$990$	−0.341364	−0.0108493
$991$	30.4375	0.966878	0.483439	−	0.875378i	$-0.339387\pi$
$991$	30.4375	0.966878	0.483439	+	0.875378i	$0.339387\pi$
$992$	8.46687	0.268824
$993$	−11.9191	−0.378241
$994$	0.665986	0.0211238
$995$	0.902676	0.0286167
$996$	−8.06748	−0.255628
$997$	−31.7021	−1.00402	−0.502008	−	0.864863i	$-0.667405\pi$
$997$	−31.7021	−1.00402	−0.502008	+	0.864863i	$0.667405\pi$
$998$	0.190241	0.00602198
$999$	−51.6943	−1.63553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.c.1.8	✓	15
5.4	even	2		6025.2.a.i.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.8	✓	15	1.1	even	1	trivial
6025.2.a.i.1.8		15	5.4	even	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0849802 q^{2} -1.30288 q^{3} -1.99278 q^{4} -1.00000 q^{5} +0.110719 q^{6} +0.925444 q^{7} +0.339307 q^{8} -1.30250 q^{9} +O(q^{10})\)	\(q-0.0849802 q^{2} -1.30288 q^{3} -1.99278 q^{4} -1.00000 q^{5} +0.110719 q^{6} +0.925444 q^{7} +0.339307 q^{8} -1.30250 q^{9} +0.0849802 q^{10} +3.08405 q^{11} +2.59635 q^{12} +0.928417 q^{13} -0.0786445 q^{14} +1.30288 q^{15} +3.95672 q^{16} +0.233917 q^{17} +0.110687 q^{18} +4.41397 q^{19} +1.99278 q^{20} -1.20574 q^{21} -0.262083 q^{22} -0.167895 q^{23} -0.442077 q^{24} +1.00000 q^{25} -0.0788971 q^{26} +5.60565 q^{27} -1.84421 q^{28} -7.54323 q^{29} -0.110719 q^{30} -8.34292 q^{31} -1.01486 q^{32} -4.01815 q^{33} -0.0198783 q^{34} -0.925444 q^{35} +2.59560 q^{36} -9.22182 q^{37} -0.375100 q^{38} -1.20962 q^{39} -0.339307 q^{40} +2.33892 q^{41} +0.102464 q^{42} -6.63273 q^{43} -6.14583 q^{44} +1.30250 q^{45} +0.0142677 q^{46} +10.0939 q^{47} -5.15514 q^{48} -6.14355 q^{49} -0.0849802 q^{50} -0.304765 q^{51} -1.85013 q^{52} -4.19636 q^{53} -0.476369 q^{54} -3.08405 q^{55} +0.314010 q^{56} -5.75088 q^{57} +0.641026 q^{58} -2.28311 q^{59} -2.59635 q^{60} +11.2190 q^{61} +0.708983 q^{62} -1.20539 q^{63} -7.82720 q^{64} -0.928417 q^{65} +0.341463 q^{66} +6.13650 q^{67} -0.466144 q^{68} +0.218747 q^{69} +0.0786445 q^{70} -8.46831 q^{71} -0.441948 q^{72} -5.93109 q^{73} +0.783673 q^{74} -1.30288 q^{75} -8.79607 q^{76} +2.85412 q^{77} +0.102793 q^{78} -5.88910 q^{79} -3.95672 q^{80} -3.39598 q^{81} -0.198762 q^{82} -3.10723 q^{83} +2.40278 q^{84} -0.233917 q^{85} +0.563651 q^{86} +9.82793 q^{87} +1.04644 q^{88} -10.3808 q^{89} -0.110687 q^{90} +0.859198 q^{91} +0.334577 q^{92} +10.8698 q^{93} -0.857781 q^{94} -4.41397 q^{95} +1.32224 q^{96} -8.84558 q^{97} +0.522081 q^{98} -4.01698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * q^99

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