LMFDB - Embedded newform 35.3.d.a.6.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(6,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("35.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-5}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 5 $ x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.2
Root			$2.23607i$ of defining polynomial
Character	$\chi$	$=$	35.6
Dual form			35.3.d.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +4.47214i q^{3} -3.00000 q^{4} +2.23607i q^{5} -4.47214i q^{6} +7.00000 q^{7} +7.00000 q^{8} -11.0000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +4.47214i q^{3} -3.00000 q^{4} +2.23607i q^{5} -4.47214i q^{6} +7.00000 q^{7} +7.00000 q^{8} -11.0000 q^{9} -2.23607i q^{10} +2.00000 q^{11} -13.4164i q^{12} -13.4164i q^{13} -7.00000 q^{14} -10.0000 q^{15} +5.00000 q^{16} +26.8328i q^{17} +11.0000 q^{18} -13.4164i q^{19} -6.70820i q^{20} +31.3050i q^{21} -2.00000 q^{22} +26.0000 q^{23} +31.3050i q^{24} -5.00000 q^{25} +13.4164i q^{26} -8.94427i q^{27} -21.0000 q^{28} -22.0000 q^{29} +10.0000 q^{30} -53.6656i q^{31} -33.0000 q^{32} +8.94427i q^{33} -26.8328i q^{34} +15.6525i q^{35} +33.0000 q^{36} +14.0000 q^{37} +13.4164i q^{38} +60.0000 q^{39} +15.6525i q^{40} -26.8328i q^{41} -31.3050i q^{42} -34.0000 q^{43} -6.00000 q^{44} -24.5967i q^{45} -26.0000 q^{46} -26.8328i q^{47} +22.3607i q^{48} +49.0000 q^{49} +5.00000 q^{50} -120.000 q^{51} +40.2492i q^{52} -34.0000 q^{53} +8.94427i q^{54} +4.47214i q^{55} +49.0000 q^{56} +60.0000 q^{57} +22.0000 q^{58} -40.2492i q^{59} +30.0000 q^{60} +93.9149i q^{61} +53.6656i q^{62} -77.0000 q^{63} +13.0000 q^{64} +30.0000 q^{65} -8.94427i q^{66} +14.0000 q^{67} -80.4984i q^{68} +116.276i q^{69} -15.6525i q^{70} +62.0000 q^{71} -77.0000 q^{72} -53.6656i q^{73} -14.0000 q^{74} -22.3607i q^{75} +40.2492i q^{76} +14.0000 q^{77} -60.0000 q^{78} +38.0000 q^{79} +11.1803i q^{80} -59.0000 q^{81} +26.8328i q^{82} +40.2492i q^{83} -93.9149i q^{84} -60.0000 q^{85} +34.0000 q^{86} -98.3870i q^{87} +14.0000 q^{88} -26.8328i q^{89} +24.5967i q^{90} -93.9149i q^{91} -78.0000 q^{92} +240.000 q^{93} +26.8328i q^{94} +30.0000 q^{95} -147.580i q^{96} -26.8328i q^{97} -49.0000 q^{98} -22.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 6 q^{4} + 14 q^{7} + 14 q^{8} - 22 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 6 * q^4 + 14 * q^7 + 14 * q^8 - 22 * q^9	$ 2 q - 2 q^{2} - 6 q^{4} + 14 q^{7} + 14 q^{8} - 22 q^{9} + 4 q^{11} - 14 q^{14} - 20 q^{15} + 10 q^{16} + 22 q^{18} - 4 q^{22} + 52 q^{23} - 10 q^{25} - 42 q^{28} - 44 q^{29} + 20 q^{30} - 66 q^{32} + 66 q^{36} + 28 q^{37} + 120 q^{39} - 68 q^{43} - 12 q^{44} - 52 q^{46} + 98 q^{49} + 10 q^{50} - 240 q^{51} - 68 q^{53} + 98 q^{56} + 120 q^{57} + 44 q^{58} + 60 q^{60} - 154 q^{63} + 26 q^{64} + 60 q^{65} + 28 q^{67} + 124 q^{71} - 154 q^{72} - 28 q^{74} + 28 q^{77} - 120 q^{78} + 76 q^{79} - 118 q^{81} - 120 q^{85} + 68 q^{86} + 28 q^{88} - 156 q^{92} + 480 q^{93} + 60 q^{95} - 98 q^{98} - 44 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 6 * q^4 + 14 * q^7 + 14 * q^8 - 22 * q^9 + 4 * q^11 - 14 * q^14 - 20 * q^15 + 10 * q^16 + 22 * q^18 - 4 * q^22 + 52 * q^23 - 10 * q^25 - 42 * q^28 - 44 * q^29 + 20 * q^30 - 66 * q^32 + 66 * q^36 + 28 * q^37 + 120 * q^39 - 68 * q^43 - 12 * q^44 - 52 * q^46 + 98 * q^49 + 10 * q^50 - 240 * q^51 - 68 * q^53 + 98 * q^56 + 120 * q^57 + 44 * q^58 + 60 * q^60 - 154 * q^63 + 26 * q^64 + 60 * q^65 + 28 * q^67 + 124 * q^71 - 154 * q^72 - 28 * q^74 + 28 * q^77 - 120 * q^78 + 76 * q^79 - 118 * q^81 - 120 * q^85 + 68 * q^86 + 28 * q^88 - 156 * q^92 + 480 * q^93 + 60 * q^95 - 98 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000	−0.500000	−0.250000	−	0.968246i	$-0.580431\pi$
$2$	−1.00000	−0.500000	−0.250000	+	0.968246i	$0.580431\pi$
$3$	4.47214i	1.49071i	0.666667	+	0.745356i	$0.267720\pi$
$3$	4.47214i	1.49071i	−0.666667	+	0.745356i	$0.732280\pi$
$4$	−3.00000	−0.750000
$5$	2.23607i	0.447214i
$5$	2.23607i	0.447214i
$6$	− 4.47214i	− 0.745356i
$7$	7.00000	1.00000
$7$	7.00000	1.00000
$8$	7.00000	0.875000
$9$	−11.0000	−1.22222
$10$	− 2.23607i	− 0.223607i
$11$	2.00000	0.181818	0.0909091	−	0.995859i	$-0.471023\pi$
$11$	2.00000	0.181818	0.0909091	+	0.995859i	$0.471023\pi$
$12$	− 13.4164i	− 1.11803i
$13$	− 13.4164i	− 1.03203i	−0.856579	−	0.516016i	$-0.827415\pi$
$13$	− 13.4164i	− 1.03203i	0.856579	−	0.516016i	$-0.172585\pi$
$14$	−7.00000	−0.500000
$15$	−10.0000	−0.666667
$16$	5.00000	0.312500
$17$	26.8328i	1.57840i	0.614136	+	0.789200i	$0.289505\pi$
$17$	26.8328i	1.57840i	−0.614136	+	0.789200i	$0.710495\pi$
$18$	11.0000	0.611111
$19$	− 13.4164i	− 0.706127i	−0.935599	−	0.353063i	$-0.885140\pi$
$19$	− 13.4164i	− 0.706127i	0.935599	−	0.353063i	$-0.114860\pi$
$20$	− 6.70820i	− 0.335410i
$21$	31.3050i	1.49071i
$22$	−2.00000	−0.0909091
$23$	26.0000	1.13043	0.565217	−	0.824942i	$-0.308792\pi$
$23$	26.0000	1.13043	0.565217	+	0.824942i	$0.308792\pi$
$24$	31.3050i	1.30437i
$25$	−5.00000	−0.200000
$26$	13.4164i	0.516016i
$27$	− 8.94427i	− 0.331269i
$28$	−21.0000	−0.750000
$29$	−22.0000	−0.758621	−0.379310	−	0.925270i	$-0.623839\pi$
$29$	−22.0000	−0.758621	−0.379310	+	0.925270i	$0.623839\pi$
$30$	10.0000	0.333333
$31$	− 53.6656i	− 1.73115i	−0.500780	−	0.865575i	$-0.666953\pi$
$31$	− 53.6656i	− 1.73115i	0.500780	−	0.865575i	$-0.333047\pi$
$32$	−33.0000	−1.03125
$33$	8.94427i	0.271039i
$34$	− 26.8328i	− 0.789200i
$35$	15.6525i	0.447214i
$36$	33.0000	0.916667
$37$	14.0000	0.378378	0.189189	−	0.981941i	$-0.439414\pi$
$37$	14.0000	0.378378	0.189189	+	0.981941i	$0.439414\pi$
$38$	13.4164i	0.353063i
$39$	60.0000	1.53846
$40$	15.6525i	0.391312i
$41$	− 26.8328i	− 0.654459i	−0.944945	−	0.327229i	$-0.893885\pi$
$41$	− 26.8328i	− 0.654459i	0.944945	−	0.327229i	$-0.106115\pi$
$42$	− 31.3050i	− 0.745356i
$43$	−34.0000	−0.790698	−0.395349	−	0.918531i	$-0.629376\pi$
$43$	−34.0000	−0.790698	−0.395349	+	0.918531i	$0.629376\pi$
$44$	−6.00000	−0.136364
$45$	− 24.5967i	− 0.546594i
$46$	−26.0000	−0.565217
$47$	− 26.8328i	− 0.570911i	−0.958392	−	0.285455i	$-0.907855\pi$
$47$	− 26.8328i	− 0.570911i	0.958392	−	0.285455i	$-0.0921449\pi$
$48$	22.3607i	0.465847i
$49$	49.0000	1.00000
$50$	5.00000	0.100000
$51$	−120.000	−2.35294
$52$	40.2492i	0.774024i
$53$	−34.0000	−0.641509	−0.320755	−	0.947162i	$-0.603937\pi$
$53$	−34.0000	−0.641509	−0.320755	+	0.947162i	$0.603937\pi$
$54$	8.94427i	0.165635i
$55$	4.47214i	0.0813116i
$56$	49.0000	0.875000
$57$	60.0000	1.05263
$58$	22.0000	0.379310
$59$	− 40.2492i	− 0.682190i	−0.940029	−	0.341095i	$-0.889202\pi$
$59$	− 40.2492i	− 0.682190i	0.940029	−	0.341095i	$-0.110798\pi$
$60$	30.0000	0.500000
$61$	93.9149i	1.53959i	0.638293	+	0.769794i	$0.279641\pi$
$61$	93.9149i	1.53959i	−0.638293	+	0.769794i	$0.720359\pi$
$62$	53.6656i	0.865575i
$63$	−77.0000	−1.22222
$64$	13.0000	0.203125
$65$	30.0000	0.461538
$66$	− 8.94427i	− 0.135519i
$67$	14.0000	0.208955	0.104478	−	0.994527i	$-0.466683\pi$
$67$	14.0000	0.208955	0.104478	+	0.994527i	$0.466683\pi$
$68$	− 80.4984i	− 1.18380i
$69$	116.276i	1.68515i
$70$	− 15.6525i	− 0.223607i
$71$	62.0000	0.873239	0.436620	−	0.899646i	$-0.356176\pi$
$71$	62.0000	0.873239	0.436620	+	0.899646i	$0.356176\pi$
$72$	−77.0000	−1.06944
$73$	− 53.6656i	− 0.735146i	−0.929995	−	0.367573i	$-0.880189\pi$
$73$	− 53.6656i	− 0.735146i	0.929995	−	0.367573i	$-0.119811\pi$
$74$	−14.0000	−0.189189
$75$	− 22.3607i	− 0.298142i
$76$	40.2492i	0.529595i
$77$	14.0000	0.181818
$78$	−60.0000	−0.769231
$79$	38.0000	0.481013	0.240506	−	0.970648i	$-0.422687\pi$
$79$	38.0000	0.481013	0.240506	+	0.970648i	$0.422687\pi$
$80$	11.1803i	0.139754i
$81$	−59.0000	−0.728395
$82$	26.8328i	0.327229i
$83$	40.2492i	0.484930i	0.970160	+	0.242465i	$0.0779560\pi$
$83$	40.2492i	0.484930i	−0.970160	+	0.242465i	$0.922044\pi$
$84$	− 93.9149i	− 1.11803i
$85$	−60.0000	−0.705882
$86$	34.0000	0.395349
$87$	− 98.3870i	− 1.13088i
$88$	14.0000	0.159091
$89$	− 26.8328i	− 0.301492i	−0.988573	−	0.150746i	$-0.951832\pi$
$89$	− 26.8328i	− 0.301492i	0.988573	−	0.150746i	$-0.0481676\pi$
$90$	24.5967i	0.273297i
$91$	− 93.9149i	− 1.03203i
$92$	−78.0000	−0.847826
$93$	240.000	2.58065
$94$	26.8328i	0.285455i
$95$	30.0000	0.315789
$96$	− 147.580i	− 1.53730i
$97$	− 26.8328i	− 0.276627i	−0.990388	−	0.138313i	$-0.955832\pi$
$97$	− 26.8328i	− 0.276627i	0.990388	−	0.138313i	$-0.0441681\pi$
$98$	−49.0000	−0.500000
$99$	−22.0000	−0.222222
$100$	15.0000	0.150000
$101$	67.0820i	0.664179i	0.943248	+	0.332089i	$0.107754\pi$
$101$	67.0820i	0.664179i	−0.943248	+	0.332089i	$0.892246\pi$
$102$	120.000	1.17647
$103$	160.997i	1.56308i	0.623857	+	0.781538i	$0.285565\pi$
$103$	160.997i	1.56308i	−0.623857	+	0.781538i	$0.714435\pi$
$104$	− 93.9149i	− 0.903027i
$105$	−70.0000	−0.666667
$106$	34.0000	0.320755
$107$	−106.000	−0.990654	−0.495327	−	0.868707i	$-0.664952\pi$
$107$	−106.000	−0.990654	−0.495327	+	0.868707i	$0.664952\pi$
$108$	26.8328i	0.248452i
$109$	−142.000	−1.30275	−0.651376	−	0.758755i	$-0.725808\pi$
$109$	−142.000	−1.30275	−0.651376	+	0.758755i	$0.725808\pi$
$110$	− 4.47214i	− 0.0406558i
$111$	62.6099i	0.564053i
$112$	35.0000	0.312500
$113$	−34.0000	−0.300885	−0.150442	−	0.988619i	$-0.548070\pi$
$113$	−34.0000	−0.300885	−0.150442	+	0.988619i	$0.548070\pi$
$114$	−60.0000	−0.526316
$115$	58.1378i	0.505546i
$116$	66.0000	0.568966
$117$	147.580i	1.26137i
$118$	40.2492i	0.341095i
$119$	187.830i	1.57840i
$120$	−70.0000	−0.583333
$121$	−117.000	−0.966942
$122$	− 93.9149i	− 0.769794i
$123$	120.000	0.975610
$124$	160.997i	1.29836i
$125$	− 11.1803i	− 0.0894427i
$126$	77.0000	0.611111
$127$	194.000	1.52756	0.763780	−	0.645477i	$-0.223341\pi$
$127$	194.000	1.52756	0.763780	+	0.645477i	$0.223341\pi$
$128$	119.000	0.929688
$129$	− 152.053i	− 1.17870i
$130$	−30.0000	−0.230769
$131$	− 120.748i	− 0.921738i	−0.887468	−	0.460869i	$-0.847538\pi$
$131$	− 120.748i	− 0.921738i	0.887468	−	0.460869i	$-0.152462\pi$
$132$	− 26.8328i	− 0.203279i
$133$	− 93.9149i	− 0.706127i
$134$	−14.0000	−0.104478
$135$	20.0000	0.148148
$136$	187.830i	1.38110i
$137$	−166.000	−1.21168	−0.605839	−	0.795587i	$-0.707163\pi$
$137$	−166.000	−1.21168	−0.605839	+	0.795587i	$0.707163\pi$
$138$	− 116.276i	− 0.842576i
$139$	− 93.9149i	− 0.675646i	−0.941210	−	0.337823i	$-0.890309\pi$
$139$	− 93.9149i	− 0.675646i	0.941210	−	0.337823i	$-0.109691\pi$
$140$	− 46.9574i	− 0.335410i
$141$	120.000	0.851064
$142$	−62.0000	−0.436620
$143$	− 26.8328i	− 0.187642i
$144$	−55.0000	−0.381944
$145$	− 49.1935i	− 0.339265i
$146$	53.6656i	0.367573i
$147$	219.135i	1.49071i
$148$	−42.0000	−0.283784
$149$	−142.000	−0.953020	−0.476510	−	0.879169i	$-0.658098\pi$
$149$	−142.000	−0.953020	−0.476510	+	0.879169i	$0.658098\pi$
$150$	22.3607i	0.149071i
$151$	2.00000	0.0132450	0.00662252	−	0.999978i	$-0.497892\pi$
$151$	2.00000	0.0132450	0.00662252	+	0.999978i	$0.497892\pi$
$152$	− 93.9149i	− 0.617861i
$153$	− 295.161i	− 1.92916i
$154$	−14.0000	−0.0909091
$155$	120.000	0.774194
$156$	−180.000	−1.15385
$157$	− 67.0820i	− 0.427274i	−0.976913	−	0.213637i	$-0.931469\pi$
$157$	− 67.0820i	− 0.427274i	0.976913	−	0.213637i	$-0.0685310\pi$
$158$	−38.0000	−0.240506
$159$	− 152.053i	− 0.956306i
$160$	− 73.7902i	− 0.461189i
$161$	182.000	1.13043
$162$	59.0000	0.364198
$163$	−34.0000	−0.208589	−0.104294	−	0.994546i	$-0.533258\pi$
$163$	−34.0000	−0.208589	−0.104294	+	0.994546i	$0.533258\pi$
$164$	80.4984i	0.490844i
$165$	−20.0000	−0.121212
$166$	− 40.2492i	− 0.242465i
$167$	− 107.331i	− 0.642702i	−0.946960	−	0.321351i	$-0.895863\pi$
$167$	− 107.331i	− 0.642702i	0.946960	−	0.321351i	$-0.104137\pi$
$168$	219.135i	1.30437i
$169$	−11.0000	−0.0650888
$170$	60.0000	0.352941
$171$	147.580i	0.863044i
$172$	102.000	0.593023
$173$	147.580i	0.853066i	0.904472	+	0.426533i	$0.140265\pi$
$173$	147.580i	0.853066i	−0.904472	+	0.426533i	$0.859735\pi$
$174$	98.3870i	0.565442i
$175$	−35.0000	−0.200000
$176$	10.0000	0.0568182
$177$	180.000	1.01695
$178$	26.8328i	0.150746i
$179$	218.000	1.21788	0.608939	−	0.793217i	$-0.291596\pi$
$179$	218.000	1.21788	0.608939	+	0.793217i	$0.291596\pi$
$180$	73.7902i	0.409946i
$181$	− 254.912i	− 1.40835i	−0.710025	−	0.704176i	$-0.751317\pi$
$181$	− 254.912i	− 1.40835i	0.710025	−	0.704176i	$-0.248683\pi$
$182$	93.9149i	0.516016i
$183$	−420.000	−2.29508
$184$	182.000	0.989130
$185$	31.3050i	0.169216i
$186$	−240.000	−1.29032
$187$	53.6656i	0.286982i
$188$	80.4984i	0.428183i
$189$	− 62.6099i	− 0.331269i
$190$	−30.0000	−0.157895
$191$	−58.0000	−0.303665	−0.151832	−	0.988406i	$-0.548517\pi$
$191$	−58.0000	−0.303665	−0.151832	+	0.988406i	$0.548517\pi$
$192$	58.1378i	0.302801i
$193$	206.000	1.06736	0.533679	−	0.845687i	$-0.320809\pi$
$193$	206.000	1.06736	0.533679	+	0.845687i	$0.320809\pi$
$194$	26.8328i	0.138313i
$195$	134.164i	0.688021i
$196$	−147.000	−0.750000
$197$	−226.000	−1.14721	−0.573604	−	0.819133i	$-0.694455\pi$
$197$	−226.000	−1.14721	−0.573604	+	0.819133i	$0.694455\pi$
$198$	22.0000	0.111111
$199$	134.164i	0.674191i	0.941470	+	0.337096i	$0.109445\pi$
$199$	134.164i	0.674191i	−0.941470	+	0.337096i	$0.890555\pi$
$200$	−35.0000	−0.175000
$201$	62.6099i	0.311492i
$202$	− 67.0820i	− 0.332089i
$203$	−154.000	−0.758621
$204$	360.000	1.76471
$205$	60.0000	0.292683
$206$	− 160.997i	− 0.781538i
$207$	−286.000	−1.38164
$208$	− 67.0820i	− 0.322510i
$209$	− 26.8328i	− 0.128387i
$210$	70.0000	0.333333
$211$	−118.000	−0.559242	−0.279621	−	0.960111i	$-0.590209\pi$
$211$	−118.000	−0.559242	−0.279621	+	0.960111i	$0.590209\pi$
$212$	102.000	0.481132
$213$	277.272i	1.30175i
$214$	106.000	0.495327
$215$	− 76.0263i	− 0.353611i
$216$	− 62.6099i	− 0.289861i
$217$	− 375.659i	− 1.73115i
$218$	142.000	0.651376
$219$	240.000	1.09589
$220$	− 13.4164i	− 0.0609837i
$221$	360.000	1.62896
$222$	− 62.6099i	− 0.282027i
$223$	80.4984i	0.360980i	0.983577	+	0.180490i	$0.0577683\pi$
$223$	80.4984i	0.360980i	−0.983577	+	0.180490i	$0.942232\pi$
$224$	−231.000	−1.03125
$225$	55.0000	0.244444
$226$	34.0000	0.150442
$227$	254.912i	1.12296i	0.827491	+	0.561480i	$0.189768\pi$
$227$	254.912i	1.12296i	−0.827491	+	0.561480i	$0.810232\pi$
$228$	−180.000	−0.789474
$229$	13.4164i	0.0585869i	0.999571	+	0.0292935i	$0.00932573\pi$
$229$	13.4164i	0.0585869i	−0.999571	+	0.0292935i	$0.990674\pi$
$230$	− 58.1378i	− 0.252773i
$231$	62.6099i	0.271039i
$232$	−154.000	−0.663793
$233$	−214.000	−0.918455	−0.459227	−	0.888319i	$-0.651874\pi$
$233$	−214.000	−0.918455	−0.459227	+	0.888319i	$0.651874\pi$
$234$	− 147.580i	− 0.630686i
$235$	60.0000	0.255319
$236$	120.748i	0.511643i
$237$	169.941i	0.717051i
$238$	− 187.830i	− 0.789200i
$239$	98.0000	0.410042	0.205021	−	0.978758i	$-0.434274\pi$
$239$	98.0000	0.410042	0.205021	+	0.978758i	$0.434274\pi$
$240$	−50.0000	−0.208333
$241$	− 160.997i	− 0.668037i	−0.942567	−	0.334018i	$-0.891595\pi$
$241$	− 160.997i	− 0.668037i	0.942567	−	0.334018i	$-0.108405\pi$
$242$	117.000	0.483471
$243$	− 344.354i	− 1.41710i
$244$	− 281.745i	− 1.15469i
$245$	109.567i	0.447214i
$246$	−120.000	−0.487805
$247$	−180.000	−0.728745
$248$	− 375.659i	− 1.51476i
$249$	−180.000	−0.722892
$250$	11.1803i	0.0447214i
$251$	335.410i	1.33630i	0.744029	+	0.668148i	$0.232913\pi$
$251$	335.410i	1.33630i	−0.744029	+	0.668148i	$0.767087\pi$
$252$	231.000	0.916667
$253$	52.0000	0.205534
$254$	−194.000	−0.763780
$255$	− 268.328i	− 1.05227i
$256$	−171.000	−0.667969
$257$	− 134.164i	− 0.522039i	−0.965333	−	0.261020i	$-0.915941\pi$
$257$	− 134.164i	− 0.522039i	0.965333	−	0.261020i	$-0.0840587\pi$
$258$	152.053i	0.589351i
$259$	98.0000	0.378378
$260$	−90.0000	−0.346154
$261$	242.000	0.927203
$262$	120.748i	0.460869i
$263$	−34.0000	−0.129278	−0.0646388	−	0.997909i	$-0.520590\pi$
$263$	−34.0000	−0.129278	−0.0646388	+	0.997909i	$0.520590\pi$
$264$	62.6099i	0.237159i
$265$	− 76.0263i	− 0.286892i
$266$	93.9149i	0.353063i
$267$	120.000	0.449438
$268$	−42.0000	−0.156716
$269$	254.912i	0.947627i	0.880625	+	0.473814i	$0.157123\pi$
$269$	254.912i	0.947627i	−0.880625	+	0.473814i	$0.842877\pi$
$270$	−20.0000	−0.0740741
$271$	321.994i	1.18817i	0.804403	+	0.594084i	$0.202486\pi$
$271$	321.994i	1.18817i	−0.804403	+	0.594084i	$0.797514\pi$
$272$	134.164i	0.493250i
$273$	420.000	1.53846
$274$	166.000	0.605839
$275$	−10.0000	−0.0363636
$276$	− 348.827i	− 1.26386i
$277$	14.0000	0.0505415	0.0252708	−	0.999681i	$-0.491955\pi$
$277$	14.0000	0.0505415	0.0252708	+	0.999681i	$0.491955\pi$
$278$	93.9149i	0.337823i
$279$	590.322i	2.11585i
$280$	109.567i	0.391312i
$281$	2.00000	0.00711744	0.00355872	−	0.999994i	$-0.498867\pi$
$281$	2.00000	0.00711744	0.00355872	+	0.999994i	$0.498867\pi$
$282$	−120.000	−0.425532
$283$	− 93.9149i	− 0.331855i	−0.986138	−	0.165927i	$-0.946938\pi$
$283$	− 93.9149i	− 0.331855i	0.986138	−	0.165927i	$-0.0530617\pi$
$284$	−186.000	−0.654930
$285$	134.164i	0.470751i
$286$	26.8328i	0.0938210i
$287$	− 187.830i	− 0.654459i
$288$	363.000	1.26042
$289$	−431.000	−1.49135
$290$	49.1935i	0.169633i
$291$	120.000	0.412371
$292$	160.997i	0.551359i
$293$	335.410i	1.14474i	0.819994	+	0.572372i	$0.193977\pi$
$293$	335.410i	1.14474i	−0.819994	+	0.572372i	$0.806023\pi$
$294$	− 219.135i	− 0.745356i
$295$	90.0000	0.305085
$296$	98.0000	0.331081
$297$	− 17.8885i	− 0.0602308i
$298$	142.000	0.476510
$299$	− 348.827i	− 1.16664i
$300$	67.0820i	0.223607i
$301$	−238.000	−0.790698
$302$	−2.00000	−0.00662252
$303$	−300.000	−0.990099
$304$	− 67.0820i	− 0.220665i
$305$	−210.000	−0.688525
$306$	295.161i	0.964578i
$307$	201.246i	0.655525i	0.944760	+	0.327762i	$0.106295\pi$
$307$	201.246i	0.655525i	−0.944760	+	0.327762i	$0.893705\pi$
$308$	−42.0000	−0.136364
$309$	−720.000	−2.33010
$310$	−120.000	−0.387097
$311$	− 509.823i	− 1.63930i	−0.572862	−	0.819652i	$-0.694167\pi$
$311$	− 509.823i	− 1.63930i	0.572862	−	0.819652i	$-0.305833\pi$
$312$	420.000	1.34615
$313$	321.994i	1.02873i	0.857570	+	0.514367i	$0.171973\pi$
$313$	321.994i	1.02873i	−0.857570	+	0.514367i	$0.828027\pi$
$314$	67.0820i	0.213637i
$315$	− 172.177i	− 0.546594i
$316$	−114.000	−0.360759
$317$	374.000	1.17981	0.589905	−	0.807472i	$-0.299165\pi$
$317$	374.000	1.17981	0.589905	+	0.807472i	$0.299165\pi$
$318$	152.053i	0.478153i
$319$	−44.0000	−0.137931
$320$	29.0689i	0.0908403i
$321$	− 474.046i	− 1.47678i
$322$	−182.000	−0.565217
$323$	360.000	1.11455
$324$	177.000	0.546296
$325$	67.0820i	0.206406i
$326$	34.0000	0.104294
$327$	− 635.043i	− 1.94203i
$328$	− 187.830i	− 0.572652i
$329$	− 187.830i	− 0.570911i
$330$	20.0000	0.0606061
$331$	482.000	1.45619	0.728097	−	0.685474i	$-0.240405\pi$
$331$	482.000	1.45619	0.728097	+	0.685474i	$0.240405\pi$
$332$	− 120.748i	− 0.363698i
$333$	−154.000	−0.462462
$334$	107.331i	0.321351i
$335$	31.3050i	0.0934476i
$336$	156.525i	0.465847i
$337$	494.000	1.46588	0.732938	−	0.680296i	$-0.238149\pi$
$337$	494.000	1.46588	0.732938	+	0.680296i	$0.238149\pi$
$338$	11.0000	0.0325444
$339$	− 152.053i	− 0.448533i
$340$	180.000	0.529412
$341$	− 107.331i	− 0.314754i
$342$	− 147.580i	− 0.431522i
$343$	343.000	1.00000
$344$	−238.000	−0.691860
$345$	−260.000	−0.753623
$346$	− 147.580i	− 0.426533i
$347$	−346.000	−0.997118	−0.498559	−	0.866856i	$-0.666137\pi$
$347$	−346.000	−0.997118	−0.498559	+	0.866856i	$0.666137\pi$
$348$	295.161i	0.848164i
$349$	− 335.410i	− 0.961061i	−0.876978	−	0.480530i	$-0.840444\pi$
$349$	− 335.410i	− 0.961061i	0.876978	−	0.480530i	$-0.159556\pi$
$350$	35.0000	0.100000
$351$	−120.000	−0.341880
$352$	−66.0000	−0.187500
$353$	26.8328i	0.0760136i	0.999277	+	0.0380068i	$0.0121009\pi$
$353$	26.8328i	0.0760136i	−0.999277	+	0.0380068i	$0.987899\pi$
$354$	−180.000	−0.508475
$355$	138.636i	0.390525i
$356$	80.4984i	0.226119i
$357$	−840.000	−2.35294
$358$	−218.000	−0.608939
$359$	338.000	0.941504	0.470752	−	0.882266i	$-0.343983\pi$
$359$	338.000	0.941504	0.470752	+	0.882266i	$0.343983\pi$
$360$	− 172.177i	− 0.478270i
$361$	181.000	0.501385
$362$	254.912i	0.704176i
$363$	− 523.240i	− 1.44143i
$364$	281.745i	0.774024i
$365$	120.000	0.328767
$366$	420.000	1.14754
$367$	295.161i	0.804253i	0.915584	+	0.402127i	$0.131729\pi$
$367$	295.161i	0.804253i	−0.915584	+	0.402127i	$0.868271\pi$
$368$	130.000	0.353261
$369$	295.161i	0.799894i
$370$	− 31.3050i	− 0.0846080i
$371$	−238.000	−0.641509
$372$	−720.000	−1.93548
$373$	86.0000	0.230563	0.115282	−	0.993333i	$-0.463223\pi$
$373$	86.0000	0.230563	0.115282	+	0.993333i	$0.463223\pi$
$374$	− 53.6656i	− 0.143491i
$375$	50.0000	0.133333
$376$	− 187.830i	− 0.499547i
$377$	295.161i	0.782920i
$378$	62.6099i	0.165635i
$379$	−262.000	−0.691293	−0.345646	−	0.938365i	$-0.612340\pi$
$379$	−262.000	−0.691293	−0.345646	+	0.938365i	$0.612340\pi$
$380$	−90.0000	−0.236842
$381$	867.594i	2.27715i
$382$	58.0000	0.151832
$383$	− 563.489i	− 1.47125i	−0.677388	−	0.735625i	$-0.736888\pi$
$383$	− 563.489i	− 1.47125i	0.677388	−	0.735625i	$-0.263112\pi$
$384$	532.184i	1.38590i
$385$	31.3050i	0.0813116i
$386$	−206.000	−0.533679
$387$	374.000	0.966408
$388$	80.4984i	0.207470i
$389$	698.000	1.79434	0.897172	−	0.441681i	$-0.145618\pi$
$389$	698.000	1.79434	0.897172	+	0.441681i	$0.145618\pi$
$390$	− 134.164i	− 0.344010i
$391$	697.653i	1.78428i
$392$	343.000	0.875000
$393$	540.000	1.37405
$394$	226.000	0.573604
$395$	84.9706i	0.215115i
$396$	66.0000	0.166667
$397$	308.577i	0.777273i	0.921391	+	0.388636i	$0.127054\pi$
$397$	308.577i	0.777273i	−0.921391	+	0.388636i	$0.872946\pi$
$398$	− 134.164i	− 0.337096i
$399$	420.000	1.05263
$400$	−25.0000	−0.0625000
$401$	−538.000	−1.34165	−0.670823	−	0.741618i	$-0.734059\pi$
$401$	−538.000	−1.34165	−0.670823	+	0.741618i	$0.734059\pi$
$402$	− 62.6099i	− 0.155746i
$403$	−720.000	−1.78660
$404$	− 201.246i	− 0.498134i
$405$	− 131.928i	− 0.325748i
$406$	154.000	0.379310
$407$	28.0000	0.0687961
$408$	−840.000	−2.05882
$409$	295.161i	0.721665i	0.932631	+	0.360832i	$0.117507\pi$
$409$	295.161i	0.721665i	−0.932631	+	0.360832i	$0.882493\pi$
$410$	−60.0000	−0.146341
$411$	− 742.375i	− 1.80626i
$412$	− 482.991i	− 1.17231i
$413$	− 281.745i	− 0.682190i
$414$	286.000	0.690821
$415$	−90.0000	−0.216867
$416$	442.741i	1.06428i
$417$	420.000	1.00719
$418$	26.8328i	0.0641933i
$419$	− 818.401i	− 1.95322i	−0.215009	−	0.976612i	$-0.568978\pi$
$419$	− 818.401i	− 1.95322i	0.215009	−	0.976612i	$-0.431022\pi$
$420$	210.000	0.500000
$421$	−118.000	−0.280285	−0.140143	−	0.990131i	$-0.544756\pi$
$421$	−118.000	−0.280285	−0.140143	+	0.990131i	$0.544756\pi$
$422$	118.000	0.279621
$423$	295.161i	0.697780i
$424$	−238.000	−0.561321
$425$	− 134.164i	− 0.315680i
$426$	− 277.272i	− 0.650874i
$427$	657.404i	1.53959i
$428$	318.000	0.742991
$429$	120.000	0.279720
$430$	76.0263i	0.176805i
$431$	−718.000	−1.66589	−0.832947	−	0.553353i	$-0.813348\pi$
$431$	−718.000	−1.66589	−0.832947	+	0.553353i	$0.813348\pi$
$432$	− 44.7214i	− 0.103522i
$433$	509.823i	1.17742i	0.808344	+	0.588711i	$0.200364\pi$
$433$	509.823i	1.17742i	−0.808344	+	0.588711i	$0.799636\pi$
$434$	375.659i	0.865575i
$435$	220.000	0.505747
$436$	426.000	0.977064
$437$	− 348.827i	− 0.798230i
$438$	−240.000	−0.547945
$439$	− 26.8328i	− 0.0611226i	−0.999533	−	0.0305613i	$-0.990271\pi$
$439$	− 26.8328i	− 0.0611226i	0.999533	−	0.0305613i	$-0.00972948\pi$
$440$	31.3050i	0.0711476i
$441$	−539.000	−1.22222
$442$	−360.000	−0.814480
$443$	−634.000	−1.43115	−0.715576	−	0.698535i	$-0.753836\pi$
$443$	−634.000	−1.43115	−0.715576	+	0.698535i	$0.753836\pi$
$444$	− 187.830i	− 0.423040i
$445$	60.0000	0.134831
$446$	− 80.4984i	− 0.180490i
$447$	− 635.043i	− 1.42068i
$448$	91.0000	0.203125
$449$	338.000	0.752784	0.376392	−	0.926461i	$-0.377165\pi$
$449$	338.000	0.752784	0.376392	+	0.926461i	$0.377165\pi$
$450$	−55.0000	−0.122222
$451$	− 53.6656i	− 0.118993i
$452$	102.000	0.225664
$453$	8.94427i	0.0197445i
$454$	− 254.912i	− 0.561480i
$455$	210.000	0.461538
$456$	420.000	0.921053
$457$	−466.000	−1.01969	−0.509847	−	0.860265i	$-0.670298\pi$
$457$	−466.000	−1.01969	−0.509847	+	0.860265i	$0.670298\pi$
$458$	− 13.4164i	− 0.0292935i
$459$	240.000	0.522876
$460$	− 174.413i	− 0.379159i
$461$	− 442.741i	− 0.960394i	−0.877161	−	0.480197i	$-0.840565\pi$
$461$	− 442.741i	− 0.960394i	0.877161	−	0.480197i	$-0.159435\pi$
$462$	− 62.6099i	− 0.135519i
$463$	206.000	0.444924	0.222462	−	0.974941i	$-0.428591\pi$
$463$	206.000	0.444924	0.222462	+	0.974941i	$0.428591\pi$
$464$	−110.000	−0.237069
$465$	536.656i	1.15410i
$466$	214.000	0.459227
$467$	362.243i	0.775681i	0.921727	+	0.387840i	$0.126779\pi$
$467$	362.243i	0.775681i	−0.921727	+	0.387840i	$0.873221\pi$
$468$	− 442.741i	− 0.946029i
$469$	98.0000	0.208955
$470$	−60.0000	−0.127660
$471$	300.000	0.636943
$472$	− 281.745i	− 0.596916i
$473$	−68.0000	−0.143763
$474$	− 169.941i	− 0.358526i
$475$	67.0820i	0.141225i
$476$	− 563.489i	− 1.18380i
$477$	374.000	0.784067
$478$	−98.0000	−0.205021
$479$	214.663i	0.448147i	0.974572	+	0.224074i	$0.0719356\pi$
$479$	214.663i	0.448147i	−0.974572	+	0.224074i	$0.928064\pi$
$480$	330.000	0.687500
$481$	− 187.830i	− 0.390498i
$482$	160.997i	0.334018i
$483$	813.929i	1.68515i
$484$	351.000	0.725207
$485$	60.0000	0.123711
$486$	344.354i	0.708548i
$487$	−166.000	−0.340862	−0.170431	−	0.985370i	$-0.554516\pi$
$487$	−166.000	−0.340862	−0.170431	+	0.985370i	$0.554516\pi$
$488$	657.404i	1.34714i
$489$	− 152.053i	− 0.310946i
$490$	− 109.567i	− 0.223607i
$491$	−838.000	−1.70672	−0.853360	−	0.521321i	$-0.825439\pi$
$491$	−838.000	−1.70672	−0.853360	+	0.521321i	$0.825439\pi$
$492$	−360.000	−0.731707
$493$	− 590.322i	− 1.19741i
$494$	180.000	0.364372
$495$	− 49.1935i	− 0.0993808i
$496$	− 268.328i	− 0.540984i
$497$	434.000	0.873239
$498$	180.000	0.361446
$499$	−262.000	−0.525050	−0.262525	−	0.964925i	$-0.584555\pi$
$499$	−262.000	−0.525050	−0.262525	+	0.964925i	$0.584555\pi$
$500$	33.5410i	0.0670820i
$501$	480.000	0.958084
$502$	− 335.410i	− 0.668148i
$503$	429.325i	0.853529i	0.904363	+	0.426764i	$0.140347\pi$
$503$	429.325i	0.853529i	−0.904363	+	0.426764i	$0.859653\pi$
$504$	−539.000	−1.06944
$505$	−150.000	−0.297030
$506$	−52.0000	−0.102767
$507$	− 49.1935i	− 0.0970286i
$508$	−582.000	−1.14567
$509$	898.899i	1.76601i	0.469363	+	0.883005i	$0.344484\pi$
$509$	898.899i	1.76601i	−0.469363	+	0.883005i	$0.655516\pi$
$510$	268.328i	0.526134i
$511$	− 375.659i	− 0.735146i
$512$	−305.000	−0.595703
$513$	−120.000	−0.233918
$514$	134.164i	0.261020i
$515$	−360.000	−0.699029
$516$	456.158i	0.884027i
$517$	− 53.6656i	− 0.103802i
$518$	−98.0000	−0.189189
$519$	−660.000	−1.27168
$520$	210.000	0.403846
$521$	724.486i	1.39057i	0.718735	+	0.695284i	$0.244721\pi$
$521$	724.486i	1.39057i	−0.718735	+	0.695284i	$0.755279\pi$
$522$	−242.000	−0.463602
$523$	− 523.240i	− 1.00046i	−0.865893	−	0.500229i	$-0.833249\pi$
$523$	− 523.240i	− 1.00046i	0.865893	−	0.500229i	$-0.166751\pi$
$524$	362.243i	0.691303i
$525$	− 156.525i	− 0.298142i
$526$	34.0000	0.0646388
$527$	1440.00	2.73245
$528$	44.7214i	0.0846995i
$529$	147.000	0.277883
$530$	76.0263i	0.143446i
$531$	442.741i	0.833788i
$532$	281.745i	0.529595i
$533$	−360.000	−0.675422
$534$	−120.000	−0.224719
$535$	− 237.023i	− 0.443034i
$536$	98.0000	0.182836
$537$	974.926i	1.81550i
$538$	− 254.912i	− 0.473814i
$539$	98.0000	0.181818
$540$	−60.0000	−0.111111
$541$	842.000	1.55638	0.778189	−	0.628031i	$-0.216139\pi$
$541$	842.000	1.55638	0.778189	+	0.628031i	$0.216139\pi$
$542$	− 321.994i	− 0.594084i
$543$	1140.00	2.09945
$544$	− 885.483i	− 1.62773i
$545$	− 317.522i	− 0.582609i
$546$	−420.000	−0.769231
$547$	134.000	0.244973	0.122486	−	0.992470i	$-0.460913\pi$
$547$	134.000	0.244973	0.122486	+	0.992470i	$0.460913\pi$
$548$	498.000	0.908759
$549$	− 1033.06i	− 1.88172i
$550$	10.0000	0.0181818
$551$	295.161i	0.535682i
$552$	813.929i	1.47451i
$553$	266.000	0.481013
$554$	−14.0000	−0.0252708
$555$	−140.000	−0.252252
$556$	281.745i	0.506735i
$557$	−706.000	−1.26750	−0.633752	−	0.773536i	$-0.718486\pi$
$557$	−706.000	−1.26750	−0.633752	+	0.773536i	$0.718486\pi$
$558$	− 590.322i	− 1.05792i
$559$	456.158i	0.816025i
$560$	78.2624i	0.139754i
$561$	−240.000	−0.427807
$562$	−2.00000	−0.00355872
$563$	− 13.4164i	− 0.0238302i	−0.999929	−	0.0119151i	$-0.996207\pi$
$563$	− 13.4164i	− 0.0238302i	0.999929	−	0.0119151i	$-0.00379279\pi$
$564$	−360.000	−0.638298
$565$	− 76.0263i	− 0.134560i
$566$	93.9149i	0.165927i
$567$	−413.000	−0.728395
$568$	434.000	0.764085
$569$	−82.0000	−0.144112	−0.0720562	−	0.997401i	$-0.522956\pi$
$569$	−82.0000	−0.144112	−0.0720562	+	0.997401i	$0.522956\pi$
$570$	− 134.164i	− 0.235376i
$571$	−118.000	−0.206655	−0.103327	−	0.994647i	$-0.532949\pi$
$571$	−118.000	−0.206655	−0.103327	+	0.994647i	$0.532949\pi$
$572$	80.4984i	0.140732i
$573$	− 259.384i	− 0.452677i
$574$	187.830i	0.327229i
$575$	−130.000	−0.226087
$576$	−143.000	−0.248264
$577$	− 885.483i	− 1.53463i	−0.641269	−	0.767316i	$-0.721592\pi$
$577$	− 885.483i	− 1.53463i	0.641269	−	0.767316i	$-0.278408\pi$
$578$	431.000	0.745675
$579$	921.260i	1.59112i
$580$	147.580i	0.254449i
$581$	281.745i	0.484930i
$582$	−120.000	−0.206186
$583$	−68.0000	−0.116638
$584$	− 375.659i	− 0.643252i
$585$	−330.000	−0.564103
$586$	− 335.410i	− 0.572372i
$587$	− 791.568i	− 1.34850i	−0.738504	−	0.674249i	$-0.764468\pi$
$587$	− 791.568i	− 1.34850i	0.738504	−	0.674249i	$-0.235532\pi$
$588$	− 657.404i	− 1.11803i
$589$	−720.000	−1.22241
$590$	−90.0000	−0.152542
$591$	− 1010.70i	− 1.71016i
$592$	70.0000	0.118243
$593$	− 134.164i	− 0.226246i	−0.993581	−	0.113123i	$-0.963915\pi$
$593$	− 134.164i	− 0.226246i	0.993581	−	0.113123i	$-0.0360855\pi$
$594$	17.8885i	0.0301154i
$595$	−420.000	−0.705882
$596$	426.000	0.714765
$597$	−600.000	−1.00503
$598$	348.827i	0.583322i
$599$	398.000	0.664441	0.332220	−	0.943202i	$-0.392202\pi$
$599$	398.000	0.664441	0.332220	+	0.943202i	$0.392202\pi$
$600$	− 156.525i	− 0.260875i
$601$	134.164i	0.223235i	0.993751	+	0.111617i	$0.0356031\pi$
$601$	134.164i	0.223235i	−0.993751	+	0.111617i	$0.964397\pi$
$602$	238.000	0.395349
$603$	−154.000	−0.255390
$604$	−6.00000	−0.00993377
$605$	− 261.620i	− 0.432430i
$606$	300.000	0.495050
$607$	− 939.149i	− 1.54720i	−0.633676	−	0.773598i	$-0.718455\pi$
$607$	− 939.149i	− 1.54720i	0.633676	−	0.773598i	$-0.281545\pi$
$608$	442.741i	0.728193i
$609$	− 688.709i	− 1.13088i
$610$	210.000	0.344262
$611$	−360.000	−0.589198
$612$	885.483i	1.44687i
$613$	206.000	0.336052	0.168026	−	0.985783i	$-0.446261\pi$
$613$	206.000	0.336052	0.168026	+	0.985783i	$0.446261\pi$
$614$	− 201.246i	− 0.327762i
$615$	268.328i	0.436306i
$616$	98.0000	0.159091
$617$	494.000	0.800648	0.400324	−	0.916374i	$-0.368898\pi$
$617$	494.000	0.800648	0.400324	+	0.916374i	$0.368898\pi$
$618$	720.000	1.16505
$619$	120.748i	0.195069i	0.995232	+	0.0975345i	$0.0310956\pi$
$619$	120.748i	0.195069i	−0.995232	+	0.0975345i	$0.968904\pi$
$620$	−360.000	−0.580645
$621$	− 232.551i	− 0.374478i
$622$	509.823i	0.819652i
$623$	− 187.830i	− 0.301492i
$624$	300.000	0.480769
$625$	25.0000	0.0400000
$626$	− 321.994i	− 0.514367i
$627$	120.000	0.191388
$628$	201.246i	0.320456i
$629$	375.659i	0.597233i
$630$	172.177i	0.273297i
$631$	542.000	0.858954	0.429477	−	0.903078i	$-0.358698\pi$
$631$	542.000	0.858954	0.429477	+	0.903078i	$0.358698\pi$
$632$	266.000	0.420886
$633$	− 527.712i	− 0.833668i
$634$	−374.000	−0.589905
$635$	433.797i	0.683145i
$636$	456.158i	0.717229i
$637$	− 657.404i	− 1.03203i
$638$	44.0000	0.0689655
$639$	−682.000	−1.06729
$640$	266.092i	0.415769i
$641$	−298.000	−0.464899	−0.232449	−	0.972609i	$-0.574674\pi$
$641$	−298.000	−0.464899	−0.232449	+	0.972609i	$0.574674\pi$
$642$	474.046i	0.738390i
$643$	1006.23i	1.56490i	0.622714	+	0.782450i	$0.286030\pi$
$643$	1006.23i	1.56490i	−0.622714	+	0.782450i	$0.713970\pi$
$644$	−546.000	−0.847826
$645$	340.000	0.527132
$646$	−360.000	−0.557276
$647$	643.988i	0.995344i	0.867365	+	0.497672i	$0.165812\pi$
$647$	643.988i	0.995344i	−0.867365	+	0.497672i	$0.834188\pi$
$648$	−413.000	−0.637346
$649$	− 80.4984i	− 0.124035i
$650$	− 67.0820i	− 0.103203i
$651$	1680.00	2.58065
$652$	102.000	0.156442
$653$	−154.000	−0.235835	−0.117917	−	0.993023i	$-0.537622\pi$
$653$	−154.000	−0.235835	−0.117917	+	0.993023i	$0.537622\pi$
$654$	635.043i	0.971014i
$655$	270.000	0.412214
$656$	− 134.164i	− 0.204518i
$657$	590.322i	0.898511i
$658$	187.830i	0.285455i
$659$	338.000	0.512898	0.256449	−	0.966558i	$-0.417447\pi$
$659$	338.000	0.512898	0.256449	+	0.966558i	$0.417447\pi$
$660$	60.0000	0.0909091
$661$	− 576.906i	− 0.872777i	−0.899758	−	0.436388i	$-0.856257\pi$
$661$	− 576.906i	− 0.872777i	0.899758	−	0.436388i	$-0.143743\pi$
$662$	−482.000	−0.728097
$663$	1609.97i	2.42831i
$664$	281.745i	0.424314i
$665$	210.000	0.315789
$666$	154.000	0.231231
$667$	−572.000	−0.857571
$668$	321.994i	0.482027i
$669$	−360.000	−0.538117
$670$	− 31.3050i	− 0.0467238i
$671$	187.830i	0.279925i
$672$	− 1033.06i	− 1.53730i
$673$	−814.000	−1.20951	−0.604755	−	0.796412i	$-0.706729\pi$
$673$	−814.000	−1.20951	−0.604755	+	0.796412i	$0.706729\pi$
$674$	−494.000	−0.732938
$675$	44.7214i	0.0662539i
$676$	33.0000	0.0488166
$677$	− 684.237i	− 1.01069i	−0.862918	−	0.505345i	$-0.831365\pi$
$677$	− 684.237i	− 1.01069i	0.862918	−	0.505345i	$-0.168635\pi$
$678$	152.053i	0.224266i
$679$	− 187.830i	− 0.276627i
$680$	−420.000	−0.617647
$681$	−1140.00	−1.67401
$682$	107.331i	0.157377i
$683$	926.000	1.35578	0.677892	−	0.735162i	$-0.262894\pi$
$683$	926.000	1.35578	0.677892	+	0.735162i	$0.262894\pi$
$684$	− 442.741i	− 0.647283i
$685$	− 371.187i	− 0.541879i
$686$	−343.000	−0.500000
$687$	−60.0000	−0.0873362
$688$	−170.000	−0.247093
$689$	456.158i	0.662058i
$690$	260.000	0.376812
$691$	576.906i	0.834885i	0.908703	+	0.417443i	$0.137073\pi$
$691$	576.906i	0.834885i	−0.908703	+	0.417443i	$0.862927\pi$
$692$	− 442.741i	− 0.639800i
$693$	−154.000	−0.222222
$694$	346.000	0.498559
$695$	210.000	0.302158
$696$	− 688.709i	− 0.989524i
$697$	720.000	1.03300
$698$	335.410i	0.480530i
$699$	− 957.037i	− 1.36915i
$700$	105.000	0.150000
$701$	362.000	0.516405	0.258203	−	0.966091i	$-0.416870\pi$
$701$	362.000	0.516405	0.258203	+	0.966091i	$0.416870\pi$
$702$	120.000	0.170940
$703$	− 187.830i	− 0.267183i
$704$	26.0000	0.0369318
$705$	268.328i	0.380607i
$706$	− 26.8328i	− 0.0380068i
$707$	469.574i	0.664179i
$708$	−540.000	−0.762712
$709$	1058.00	1.49224	0.746121	−	0.665810i	$-0.231914\pi$
$709$	1058.00	1.49224	0.746121	+	0.665810i	$0.231914\pi$
$710$	− 138.636i	− 0.195262i
$711$	−418.000	−0.587904
$712$	− 187.830i	− 0.263806i
$713$	− 1395.31i	− 1.95695i
$714$	840.000	1.17647
$715$	60.0000	0.0839161
$716$	−654.000	−0.913408
$717$	438.269i	0.611254i
$718$	−338.000	−0.470752
$719$	− 482.991i	− 0.671753i	−0.941906	−	0.335877i	$-0.890967\pi$
$719$	− 482.991i	− 0.671753i	0.941906	−	0.335877i	$-0.109033\pi$
$720$	− 122.984i	− 0.170811i
$721$	1126.98i	1.56308i
$722$	−181.000	−0.250693
$723$	720.000	0.995851
$724$	764.735i	1.05626i
$725$	110.000	0.151724
$726$	523.240i	0.720716i
$727$	1126.98i	1.55018i	0.631853	+	0.775088i	$0.282295\pi$
$727$	1126.98i	1.55018i	−0.631853	+	0.775088i	$0.717705\pi$
$728$	− 657.404i	− 0.903027i
$729$	1009.00	1.38409
$730$	−120.000	−0.164384
$731$	− 912.316i	− 1.24804i
$732$	1260.00	1.72131
$733$	− 1301.39i	− 1.77543i	−0.460392	−	0.887716i	$-0.652291\pi$
$733$	− 1301.39i	− 1.77543i	0.460392	−	0.887716i	$-0.347709\pi$
$734$	− 295.161i	− 0.402127i
$735$	−490.000	−0.666667
$736$	−858.000	−1.16576
$737$	28.0000	0.0379919
$738$	− 295.161i	− 0.399947i
$739$	−982.000	−1.32882	−0.664411	−	0.747367i	$-0.731318\pi$
$739$	−982.000	−1.32882	−0.664411	+	0.747367i	$0.731318\pi$
$740$	− 93.9149i	− 0.126912i
$741$	− 804.984i	− 1.08635i
$742$	238.000	0.320755
$743$	−694.000	−0.934051	−0.467026	−	0.884244i	$-0.654674\pi$
$743$	−694.000	−0.934051	−0.467026	+	0.884244i	$0.654674\pi$
$744$	1680.00	2.25806
$745$	− 317.522i	− 0.426204i
$746$	−86.0000	−0.115282
$747$	− 442.741i	− 0.592693i
$748$	− 160.997i	− 0.215236i
$749$	−742.000	−0.990654
$750$	−50.0000	−0.0666667
$751$	242.000	0.322237	0.161119	−	0.986935i	$-0.448490\pi$
$751$	242.000	0.322237	0.161119	+	0.986935i	$0.448490\pi$
$752$	− 134.164i	− 0.178410i
$753$	−1500.00	−1.99203
$754$	− 295.161i	− 0.391460i
$755$	4.47214i	0.00592336i
$756$	187.830i	0.248452i
$757$	−106.000	−0.140026	−0.0700132	−	0.997546i	$-0.522304\pi$
$757$	−106.000	−0.140026	−0.0700132	+	0.997546i	$0.522304\pi$
$758$	262.000	0.345646
$759$	232.551i	0.306391i
$760$	210.000	0.276316
$761$	1100.15i	1.44566i	0.691027	+	0.722829i	$0.257158\pi$
$761$	1100.15i	1.44566i	−0.691027	+	0.722829i	$0.742842\pi$
$762$	− 867.594i	− 1.13858i
$763$	−994.000	−1.30275
$764$	174.000	0.227749
$765$	660.000	0.862745
$766$	563.489i	0.735625i
$767$	−540.000	−0.704042
$768$	− 764.735i	− 0.995749i
$769$	1126.98i	1.46551i	0.680492	+	0.732756i	$0.261766\pi$
$769$	1126.98i	1.46551i	−0.680492	+	0.732756i	$0.738234\pi$
$770$	− 31.3050i	− 0.0406558i
$771$	600.000	0.778210
$772$	−618.000	−0.800518
$773$	818.401i	1.05873i	0.848393	+	0.529367i	$0.177570\pi$
$773$	818.401i	1.05873i	−0.848393	+	0.529367i	$0.822430\pi$
$774$	−374.000	−0.483204
$775$	268.328i	0.346230i
$776$	− 187.830i	− 0.242049i
$777$	438.269i	0.564053i
$778$	−698.000	−0.897172
$779$	−360.000	−0.462131
$780$	− 402.492i	− 0.516016i
$781$	124.000	0.158771
$782$	− 697.653i	− 0.892140i
$783$	196.774i	0.251308i
$784$	245.000	0.312500
$785$	150.000	0.191083
$786$	−540.000	−0.687023
$787$	684.237i	0.869424i	0.900569	+	0.434712i	$0.143150\pi$
$787$	684.237i	0.869424i	−0.900569	+	0.434712i	$0.856850\pi$
$788$	678.000	0.860406
$789$	− 152.053i	− 0.192716i
$790$	− 84.9706i	− 0.107558i
$791$	−238.000	−0.300885
$792$	−154.000	−0.194444
$793$	1260.00	1.58890
$794$	− 308.577i	− 0.388636i
$795$	340.000	0.427673
$796$	− 402.492i	− 0.505644i
$797$	308.577i	0.387174i	0.981083	+	0.193587i	$0.0620121\pi$
$797$	308.577i	0.387174i	−0.981083	+	0.193587i	$0.937988\pi$
$798$	−420.000	−0.526316
$799$	720.000	0.901126
$800$	165.000	0.206250
$801$	295.161i	0.368491i
$802$	538.000	0.670823
$803$	− 107.331i	− 0.133663i
$804$	− 187.830i	− 0.233619i
$805$	406.964i	0.505546i
$806$	720.000	0.893300
$807$	−1140.00	−1.41264
$808$	469.574i	0.581156i
$809$	1358.00	1.67862	0.839308	−	0.543657i	$-0.182961\pi$
$809$	1358.00	1.67862	0.839308	+	0.543657i	$0.182961\pi$
$810$	131.928i	0.162874i
$811$	− 308.577i	− 0.380490i	−0.981737	−	0.190245i	$-0.939072\pi$
$811$	− 308.577i	− 0.380490i	0.981737	−	0.190245i	$-0.0609282\pi$
$812$	462.000	0.568966
$813$	−1440.00	−1.77122
$814$	−28.0000	−0.0343980
$815$	− 76.0263i	− 0.0932838i
$816$	−600.000	−0.735294
$817$	456.158i	0.558333i
$818$	− 295.161i	− 0.360832i
$819$	1033.06i	1.26137i
$820$	−180.000	−0.219512
$821$	482.000	0.587089	0.293544	−	0.955945i	$-0.405165\pi$
$821$	482.000	0.587089	0.293544	+	0.955945i	$0.405165\pi$
$822$	742.375i	0.903132i
$823$	926.000	1.12515	0.562576	−	0.826746i	$-0.309810\pi$
$823$	926.000	1.12515	0.562576	+	0.826746i	$0.309810\pi$
$824$	1126.98i	1.36769i
$825$	− 44.7214i	− 0.0542077i
$826$	281.745i	0.341095i
$827$	−226.000	−0.273277	−0.136638	−	0.990621i	$-0.543630\pi$
$827$	−226.000	−0.273277	−0.136638	+	0.990621i	$0.543630\pi$
$828$	858.000	1.03623
$829$	− 1462.39i	− 1.76404i	−0.471213	−	0.882020i	$-0.656184\pi$
$829$	− 1462.39i	− 1.76404i	0.471213	−	0.882020i	$-0.343816\pi$
$830$	90.0000	0.108434
$831$	62.6099i	0.0753428i
$832$	− 174.413i	− 0.209631i
$833$	1314.81i	1.57840i
$834$	−420.000	−0.503597
$835$	240.000	0.287425
$836$	80.4984i	0.0962900i
$837$	−480.000	−0.573477
$838$	818.401i	0.976612i
$839$	− 831.817i	− 0.991439i	−0.868483	−	0.495719i	$-0.834904\pi$
$839$	− 831.817i	− 0.991439i	0.868483	−	0.495719i	$-0.165096\pi$
$840$	−490.000	−0.583333
$841$	−357.000	−0.424495
$842$	118.000	0.140143
$843$	8.94427i	0.0106100i
$844$	354.000	0.419431
$845$	− 24.5967i	− 0.0291086i
$846$	− 295.161i	− 0.348890i
$847$	−819.000	−0.966942
$848$	−170.000	−0.200472
$849$	420.000	0.494700
$850$	134.164i	0.157840i
$851$	364.000	0.427732
$852$	− 831.817i	− 0.976311i
$853$	− 40.2492i	− 0.0471855i	−0.999722	−	0.0235927i	$-0.992489\pi$
$853$	− 40.2492i	− 0.0471855i	0.999722	−	0.0235927i	$-0.00751050\pi$
$854$	− 657.404i	− 0.769794i
$855$	−330.000	−0.385965
$856$	−742.000	−0.866822
$857$	268.328i	0.313102i	0.987670	+	0.156551i	$0.0500375\pi$
$857$	268.328i	0.313102i	−0.987670	+	0.156551i	$0.949962\pi$
$858$	−120.000	−0.139860
$859$	− 308.577i	− 0.359229i	−0.983737	−	0.179614i	$-0.942515\pi$
$859$	− 308.577i	− 0.359229i	0.983737	−	0.179614i	$-0.0574850\pi$
$860$	228.079i	0.265208i
$861$	840.000	0.975610
$862$	718.000	0.832947
$863$	−514.000	−0.595597	−0.297798	−	0.954629i	$-0.596252\pi$
$863$	−514.000	−0.595597	−0.297798	+	0.954629i	$0.596252\pi$
$864$	295.161i	0.341621i
$865$	−330.000	−0.381503
$866$	− 509.823i	− 0.588711i
$867$	− 1927.49i	− 2.22317i
$868$	1126.98i	1.29836i
$869$	76.0000	0.0874568
$870$	−220.000	−0.252874
$871$	− 187.830i	− 0.215648i
$872$	−994.000	−1.13991
$873$	295.161i	0.338100i
$874$	348.827i	0.399115i
$875$	− 78.2624i	− 0.0894427i
$876$	−720.000	−0.821918
$877$	−1306.00	−1.48917	−0.744584	−	0.667529i	$-0.767352\pi$
$877$	−1306.00	−1.48917	−0.744584	+	0.667529i	$0.767352\pi$
$878$	26.8328i	0.0305613i
$879$	−1500.00	−1.70648
$880$	22.3607i	0.0254099i
$881$	− 1126.98i	− 1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$881$	− 1126.98i	− 1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$882$	539.000	0.611111
$883$	1526.00	1.72820	0.864100	−	0.503321i	$-0.167889\pi$
$883$	1526.00	1.72820	0.864100	+	0.503321i	$0.167889\pi$
$884$	−1080.00	−1.22172
$885$	402.492i	0.454793i
$886$	634.000	0.715576
$887$	1556.30i	1.75457i	0.479970	+	0.877285i	$0.340648\pi$
$887$	1556.30i	1.75457i	−0.479970	+	0.877285i	$0.659352\pi$
$888$	438.269i	0.493547i
$889$	1358.00	1.52756
$890$	−60.0000	−0.0674157
$891$	−118.000	−0.132435
$892$	− 241.495i	− 0.270735i
$893$	−360.000	−0.403135
$894$	635.043i	0.710339i
$895$	487.463i	0.544651i
$896$	833.000	0.929688
$897$	1560.00	1.73913
$898$	−338.000	−0.376392
$899$	1180.64i	1.31329i
$900$	−165.000	−0.183333
$901$	− 912.316i	− 1.01256i
$902$	53.6656i	0.0594963i
$903$	− 1064.37i	− 1.17870i
$904$	−238.000	−0.263274
$905$	570.000	0.629834
$906$	− 8.94427i	− 0.00987226i
$907$	734.000	0.809261	0.404631	−	0.914480i	$-0.367400\pi$
$907$	734.000	0.809261	0.404631	+	0.914480i	$0.367400\pi$
$908$	− 764.735i	− 0.842219i
$909$	− 737.902i	− 0.811774i
$910$	−210.000	−0.230769
$911$	1202.00	1.31943	0.659715	−	0.751516i	$-0.270677\pi$
$911$	1202.00	1.31943	0.659715	+	0.751516i	$0.270677\pi$
$912$	300.000	0.328947
$913$	80.4984i	0.0881692i
$914$	466.000	0.509847
$915$	− 939.149i	− 1.02639i
$916$	− 40.2492i	− 0.0439402i
$917$	− 845.234i	− 0.921738i
$918$	−240.000	−0.261438
$919$	−1282.00	−1.39499	−0.697497	−	0.716587i	$-0.745703\pi$
$919$	−1282.00	−1.39499	−0.697497	+	0.716587i	$0.745703\pi$
$920$	406.964i	0.442353i
$921$	−900.000	−0.977199
$922$	442.741i	0.480197i
$923$	− 831.817i	− 0.901210i
$924$	− 187.830i	− 0.203279i
$925$	−70.0000	−0.0756757
$926$	−206.000	−0.222462
$927$	− 1770.97i	− 1.91043i
$928$	726.000	0.782328
$929$	− 1126.98i	− 1.21311i	−0.795042	−	0.606554i	$-0.792551\pi$
$929$	− 1126.98i	− 1.21311i	0.795042	−	0.606554i	$-0.207449\pi$
$930$	− 536.656i	− 0.577050i
$931$	− 657.404i	− 0.706127i
$932$	642.000	0.688841
$933$	2280.00	2.44373
$934$	− 362.243i	− 0.387840i
$935$	−120.000	−0.128342
$936$	1033.06i	1.10370i
$937$	214.663i	0.229096i	0.993418	+	0.114548i	$0.0365419\pi$
$937$	214.663i	0.229096i	−0.993418	+	0.114548i	$0.963458\pi$
$938$	−98.0000	−0.104478
$939$	−1440.00	−1.53355
$940$	−180.000	−0.191489
$941$	845.234i	0.898229i	0.893474	+	0.449115i	$0.148261\pi$
$941$	845.234i	0.898229i	−0.893474	+	0.449115i	$0.851739\pi$
$942$	−300.000	−0.318471
$943$	− 697.653i	− 0.739823i
$944$	− 201.246i	− 0.213184i
$945$	140.000	0.148148
$946$	68.0000	0.0718816
$947$	734.000	0.775079	0.387540	−	0.921853i	$-0.373325\pi$
$947$	734.000	0.775079	0.387540	+	0.921853i	$0.373325\pi$
$948$	− 509.823i	− 0.537789i
$949$	−720.000	−0.758693
$950$	− 67.0820i	− 0.0706127i
$951$	1672.58i	1.75876i
$952$	1314.81i	1.38110i
$953$	−934.000	−0.980063	−0.490031	−	0.871705i	$-0.663015\pi$
$953$	−934.000	−0.980063	−0.490031	+	0.871705i	$0.663015\pi$
$954$	−374.000	−0.392034
$955$	− 129.692i	− 0.135803i
$956$	−294.000	−0.307531
$957$	− 196.774i	− 0.205615i
$958$	− 214.663i	− 0.224074i
$959$	−1162.00	−1.21168
$960$	−130.000	−0.135417
$961$	−1919.00	−1.99688
$962$	187.830i	0.195249i
$963$	1166.00	1.21080
$964$	482.991i	0.501028i
$965$	460.630i	0.477337i
$966$	− 813.929i	− 0.842576i
$967$	314.000	0.324716	0.162358	−	0.986732i	$-0.448090\pi$
$967$	314.000	0.324716	0.162358	+	0.986732i	$0.448090\pi$
$968$	−819.000	−0.846074
$969$	1609.97i	1.66147i
$970$	−60.0000	−0.0618557
$971$	− 147.580i	− 0.151988i	−0.997108	−	0.0759941i	$-0.975787\pi$
$971$	− 147.580i	− 0.151988i	0.997108	−	0.0759941i	$-0.0242130\pi$
$972$	1033.06i	1.06282i
$973$	− 657.404i	− 0.675646i
$974$	166.000	0.170431
$975$	−300.000	−0.307692
$976$	469.574i	0.481121i
$977$	−1486.00	−1.52098	−0.760491	−	0.649348i	$-0.775042\pi$
$977$	−1486.00	−1.52098	−0.760491	+	0.649348i	$0.775042\pi$
$978$	152.053i	0.155473i
$979$	− 53.6656i	− 0.0548168i
$980$	− 328.702i	− 0.335410i
$981$	1562.00	1.59225
$982$	838.000	0.853360
$983$	− 965.981i	− 0.982687i	−0.870966	−	0.491344i	$-0.836506\pi$
$983$	− 965.981i	− 0.982687i	0.870966	−	0.491344i	$-0.163494\pi$
$984$	840.000	0.853659
$985$	− 505.351i	− 0.513047i
$986$	590.322i	0.598704i
$987$	840.000	0.851064
$988$	540.000	0.546559
$989$	−884.000	−0.893832
$990$	49.1935i	0.0496904i
$991$	−58.0000	−0.0585267	−0.0292634	−	0.999572i	$-0.509316\pi$
$991$	−58.0000	−0.0585267	−0.0292634	+	0.999572i	$0.509316\pi$
$992$	1770.97i	1.78525i
$993$	2155.57i	2.17076i
$994$	−434.000	−0.436620
$995$	−300.000	−0.301508
$996$	540.000	0.542169
$997$	− 630.571i	− 0.632469i	−0.948681	−	0.316234i	$-0.897581\pi$
$997$	− 630.571i	− 0.632469i	0.948681	−	0.316234i	$-0.102419\pi$
$998$	262.000	0.262525
$999$	− 125.220i	− 0.125345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.d.a.6.2	yes	2
3.2	odd	2		315.3.h.b.181.1		2
4.3	odd	2		560.3.f.a.321.1		2
5.2	odd	4		175.3.c.d.174.2		4
5.3	odd	4		175.3.c.d.174.3		4
5.4	even	2		175.3.d.f.76.1		2
7.2	even	3		245.3.h.b.31.1		4
7.3	odd	6		245.3.h.b.166.1		4
7.4	even	3		245.3.h.b.166.2		4
7.5	odd	6		245.3.h.b.31.2		4
7.6	odd	2	inner	35.3.d.a.6.1	✓	2
21.20	even	2		315.3.h.b.181.2		2
28.27	even	2		560.3.f.a.321.2		2
35.13	even	4		175.3.c.d.174.4		4
35.27	even	4		175.3.c.d.174.1		4
35.34	odd	2		175.3.d.f.76.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.d.a.6.1	✓	2	7.6	odd	2	inner
35.3.d.a.6.2	yes	2	1.1	even	1	trivial
175.3.c.d.174.1		4	35.27	even	4
175.3.c.d.174.2		4	5.2	odd	4
175.3.c.d.174.3		4	5.3	odd	4
175.3.c.d.174.4		4	35.13	even	4
175.3.d.f.76.1		2	5.4	even	2
175.3.d.f.76.2		2	35.34	odd	2
245.3.h.b.31.1		4	7.2	even	3
245.3.h.b.31.2		4	7.5	odd	6
245.3.h.b.166.1		4	7.3	odd	6
245.3.h.b.166.2		4	7.4	even	3
315.3.h.b.181.1		2	3.2	odd	2
315.3.h.b.181.2		2	21.20	even	2
560.3.f.a.321.1		2	4.3	odd	2
560.3.f.a.321.2		2	28.27	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +4.47214i q^{3} -3.00000 q^{4} +2.23607i q^{5} -4.47214i q^{6} +7.00000 q^{7} +7.00000 q^{8} -11.0000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +4.47214i q^{3} -3.00000 q^{4} +2.23607i q^{5} -4.47214i q^{6} +7.00000 q^{7} +7.00000 q^{8} -11.0000 q^{9} -2.23607i q^{10} +2.00000 q^{11} -13.4164i q^{12} -13.4164i q^{13} -7.00000 q^{14} -10.0000 q^{15} +5.00000 q^{16} +26.8328i q^{17} +11.0000 q^{18} -13.4164i q^{19} -6.70820i q^{20} +31.3050i q^{21} -2.00000 q^{22} +26.0000 q^{23} +31.3050i q^{24} -5.00000 q^{25} +13.4164i q^{26} -8.94427i q^{27} -21.0000 q^{28} -22.0000 q^{29} +10.0000 q^{30} -53.6656i q^{31} -33.0000 q^{32} +8.94427i q^{33} -26.8328i q^{34} +15.6525i q^{35} +33.0000 q^{36} +14.0000 q^{37} +13.4164i q^{38} +60.0000 q^{39} +15.6525i q^{40} -26.8328i q^{41} -31.3050i q^{42} -34.0000 q^{43} -6.00000 q^{44} -24.5967i q^{45} -26.0000 q^{46} -26.8328i q^{47} +22.3607i q^{48} +49.0000 q^{49} +5.00000 q^{50} -120.000 q^{51} +40.2492i q^{52} -34.0000 q^{53} +8.94427i q^{54} +4.47214i q^{55} +49.0000 q^{56} +60.0000 q^{57} +22.0000 q^{58} -40.2492i q^{59} +30.0000 q^{60} +93.9149i q^{61} +53.6656i q^{62} -77.0000 q^{63} +13.0000 q^{64} +30.0000 q^{65} -8.94427i q^{66} +14.0000 q^{67} -80.4984i q^{68} +116.276i q^{69} -15.6525i q^{70} +62.0000 q^{71} -77.0000 q^{72} -53.6656i q^{73} -14.0000 q^{74} -22.3607i q^{75} +40.2492i q^{76} +14.0000 q^{77} -60.0000 q^{78} +38.0000 q^{79} +11.1803i q^{80} -59.0000 q^{81} +26.8328i q^{82} +40.2492i q^{83} -93.9149i q^{84} -60.0000 q^{85} +34.0000 q^{86} -98.3870i q^{87} +14.0000 q^{88} -26.8328i q^{89} +24.5967i q^{90} -93.9149i q^{91} -78.0000 q^{92} +240.000 q^{93} +26.8328i q^{94} +30.0000 q^{95} -147.580i q^{96} -26.8328i q^{97} -49.0000 q^{98} -22.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 6 q^{4} + 14 q^{7} + 14 q^{8} - 22 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 6 * q^4 + 14 * q^7 + 14 * q^8 - 22 * q^9	\( 2 q - 2 q^{2} - 6 q^{4} + 14 q^{7} + 14 q^{8} - 22 q^{9} + 4 q^{11} - 14 q^{14} - 20 q^{15} + 10 q^{16} + 22 q^{18} - 4 q^{22} + 52 q^{23} - 10 q^{25} - 42 q^{28} - 44 q^{29} + 20 q^{30} - 66 q^{32} + 66 q^{36} + 28 q^{37} + 120 q^{39} - 68 q^{43} - 12 q^{44} - 52 q^{46} + 98 q^{49} + 10 q^{50} - 240 q^{51} - 68 q^{53} + 98 q^{56} + 120 q^{57} + 44 q^{58} + 60 q^{60} - 154 q^{63} + 26 q^{64} + 60 q^{65} + 28 q^{67} + 124 q^{71} - 154 q^{72} - 28 q^{74} + 28 q^{77} - 120 q^{78} + 76 q^{79} - 118 q^{81} - 120 q^{85} + 68 q^{86} + 28 q^{88} - 156 q^{92} + 480 q^{93} + 60 q^{95} - 98 q^{98} - 44 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 6 * q^4 + 14 * q^7 + 14 * q^8 - 22 * q^9 + 4 * q^11 - 14 * q^14 - 20 * q^15 + 10 * q^16 + 22 * q^18 - 4 * q^22 + 52 * q^23 - 10 * q^25 - 42 * q^28 - 44 * q^29 + 20 * q^30 - 66 * q^32 + 66 * q^36 + 28 * q^37 + 120 * q^39 - 68 * q^43 - 12 * q^44 - 52 * q^46 + 98 * q^49 + 10 * q^50 - 240 * q^51 - 68 * q^53 + 98 * q^56 + 120 * q^57 + 44 * q^58 + 60 * q^60 - 154 * q^63 + 26 * q^64 + 60 * q^65 + 28 * q^67 + 124 * q^71 - 154 * q^72 - 28 * q^74 + 28 * q^77 - 120 * q^78 + 76 * q^79 - 118 * q^81 - 120 * q^85 + 68 * q^86 + 28 * q^88 - 156 * q^92 + 480 * q^93 + 60 * q^95 - 98 * q^98 - 44 * q^99

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