LMFDB - Embedded newform 9702.2.a.cu.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.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:	$77.4708600410$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{8} +O(q^{10})$	$q-1.00000 q^{2} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{8} -3.23607 q^{10} -1.00000 q^{11} -1.23607 q^{13} +1.00000 q^{16} -6.47214 q^{17} +2.76393 q^{19} +3.23607 q^{20} +1.00000 q^{22} -4.00000 q^{23} +5.47214 q^{25} +1.23607 q^{26} +4.47214 q^{29} -2.00000 q^{31} -1.00000 q^{32} +6.47214 q^{34} -10.9443 q^{37} -2.76393 q^{38} -3.23607 q^{40} +6.47214 q^{41} -1.52786 q^{43} -1.00000 q^{44} +4.00000 q^{46} -2.00000 q^{47} -5.47214 q^{50} -1.23607 q^{52} +0.472136 q^{53} -3.23607 q^{55} -4.47214 q^{58} +7.23607 q^{59} +5.23607 q^{61} +2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -15.4164 q^{67} -6.47214 q^{68} +2.47214 q^{71} +4.94427 q^{73} +10.9443 q^{74} +2.76393 q^{76} +3.23607 q^{80} -6.47214 q^{82} +10.1803 q^{83} -20.9443 q^{85} +1.52786 q^{86} +1.00000 q^{88} +10.0000 q^{89} -4.00000 q^{92} +2.00000 q^{94} +8.94427 q^{95} -3.52786 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} + 2 q^{16} - 4 q^{17} + 10 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} + 2 q^{25} - 2 q^{26} - 4 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38} - 2 q^{40} + 4 q^{41} - 12 q^{43} - 2 q^{44} + 8 q^{46} - 4 q^{47} - 2 q^{50} + 2 q^{52} - 8 q^{53} - 2 q^{55} + 10 q^{59} + 6 q^{61} + 4 q^{62} + 2 q^{64} - 8 q^{65} - 4 q^{67} - 4 q^{68} - 4 q^{71} - 8 q^{73} + 4 q^{74} + 10 q^{76} + 2 q^{80} - 4 q^{82} - 2 q^{83} - 24 q^{85} + 12 q^{86} + 2 q^{88} + 20 q^{89} - 8 q^{92} + 4 q^{94} - 16 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8 - 2 * q^10 - 2 * q^11 + 2 * q^13 + 2 * q^16 - 4 * q^17 + 10 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 + 2 * q^25 - 2 * q^26 - 4 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^37 - 10 * q^38 - 2 * q^40 + 4 * q^41 - 12 * q^43 - 2 * q^44 + 8 * q^46 - 4 * q^47 - 2 * q^50 + 2 * q^52 - 8 * q^53 - 2 * q^55 + 10 * q^59 + 6 * q^61 + 4 * q^62 + 2 * q^64 - 8 * q^65 - 4 * q^67 - 4 * q^68 - 4 * q^71 - 8 * q^73 + 4 * q^74 + 10 * q^76 + 2 * q^80 - 4 * q^82 - 2 * q^83 - 24 * q^85 + 12 * q^86 + 2 * q^88 + 20 * q^89 - 8 * q^92 + 4 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−3.23607	−1.02333
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.47214	−1.56972	−0.784862	−	0.619671i	$-0.787266\pi$
$17$	−6.47214	−1.56972	−0.784862	+	0.619671i	$0.787266\pi$
$18$	0	0
$19$	2.76393	0.634089	0.317045	−	0.948411i	$-0.397309\pi$
$19$	2.76393	0.634089	0.317045	+	0.948411i	$0.397309\pi$
$20$	3.23607	0.723607
$21$	0	0
$22$	1.00000	0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	5.47214	1.09443
$26$	1.23607	0.242413
$27$	0	0
$28$	0	0
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.47214	1.10996
$35$	0	0
$36$	0	0
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	−2.76393	−0.448369
$39$	0	0
$40$	−3.23607	−0.511667
$41$	6.47214	1.01078	0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214	1.01078	0.505389	+	0.862892i	$0.331349\pi$
$42$	0	0
$43$	−1.52786	−0.232997	−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786	−0.232997	−0.116499	+	0.993191i	$0.537167\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	4.00000	0.589768
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	0	0
$50$	−5.47214	−0.773877
$51$	0	0
$52$	−1.23607	−0.171412
$53$	0.472136	0.0648529	0.0324264	−	0.999474i	$-0.489677\pi$
$53$	0.472136	0.0648529	0.0324264	+	0.999474i	$0.489677\pi$
$54$	0	0
$55$	−3.23607	−0.436351
$56$	0	0
$57$	0	0
$58$	−4.47214	−0.587220
$59$	7.23607	0.942056	0.471028	−	0.882118i	$-0.343883\pi$
$59$	7.23607	0.942056	0.471028	+	0.882118i	$0.343883\pi$
$60$	0	0
$61$	5.23607	0.670410	0.335205	−	0.942145i	$-0.391194\pi$
$61$	5.23607	0.670410	0.335205	+	0.942145i	$0.391194\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	−15.4164	−1.88341	−0.941707	−	0.336434i	$-0.890779\pi$
$67$	−15.4164	−1.88341	−0.941707	+	0.336434i	$0.890779\pi$
$68$	−6.47214	−0.784862
$69$	0	0
$70$	0	0
$71$	2.47214	0.293389	0.146694	−	0.989182i	$-0.453137\pi$
$71$	2.47214	0.293389	0.146694	+	0.989182i	$0.453137\pi$
$72$	0	0
$73$	4.94427	0.578683	0.289342	−	0.957226i	$-0.406564\pi$
$73$	4.94427	0.578683	0.289342	+	0.957226i	$0.406564\pi$
$74$	10.9443	1.27225
$75$	0	0
$76$	2.76393	0.317045
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	3.23607	0.361803
$81$	0	0
$82$	−6.47214	−0.714728
$83$	10.1803	1.11744	0.558719	−	0.829357i	$-0.311293\pi$
$83$	10.1803	1.11744	0.558719	+	0.829357i	$0.311293\pi$
$84$	0	0
$85$	−20.9443	−2.27173
$86$	1.52786	0.164754
$87$	0	0
$88$	1.00000	0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	0	0
$92$	−4.00000	−0.417029
$93$	0	0
$94$	2.00000	0.206284
$95$	8.94427	0.917663
$96$	0	0
$97$	−3.52786	−0.358200	−0.179100	−	0.983831i	$-0.557319\pi$
$97$	−3.52786	−0.358200	−0.179100	+	0.983831i	$0.557319\pi$
$98$	0	0
$99$	0	0
$100$	5.47214	0.547214
$101$	−14.1803	−1.41100	−0.705498	−	0.708712i	$-0.749277\pi$
$101$	−14.1803	−1.41100	−0.705498	+	0.708712i	$0.749277\pi$
$102$	0	0
$103$	−2.94427	−0.290108	−0.145054	−	0.989424i	$-0.546336\pi$
$103$	−2.94427	−0.290108	−0.145054	+	0.989424i	$0.546336\pi$
$104$	1.23607	0.121206
$105$	0	0
$106$	−0.472136	−0.0458579
$107$	6.47214	0.625685	0.312842	−	0.949805i	$-0.398719\pi$
$107$	6.47214	0.625685	0.312842	+	0.949805i	$0.398719\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	3.23607	0.308547
$111$	0	0
$112$	0	0
$113$	−8.47214	−0.796992	−0.398496	−	0.917170i	$-0.630468\pi$
$113$	−8.47214	−0.796992	−0.398496	+	0.917170i	$0.630468\pi$
$114$	0	0
$115$	−12.9443	−1.20706
$116$	4.47214	0.415227
$117$	0	0
$118$	−7.23607	−0.666134
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−5.23607	−0.474051
$123$	0	0
$124$	−2.00000	−0.179605
$125$	1.52786	0.136656
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	9.23607	0.806959	0.403480	−	0.914989i	$-0.367801\pi$
$131$	9.23607	0.806959	0.403480	+	0.914989i	$0.367801\pi$
$132$	0	0
$133$	0	0
$134$	15.4164	1.33177
$135$	0	0
$136$	6.47214	0.554981
$137$	−15.8885	−1.35745	−0.678725	−	0.734393i	$-0.737467\pi$
$137$	−15.8885	−1.35745	−0.678725	+	0.734393i	$0.737467\pi$
$138$	0	0
$139$	8.29180	0.703301	0.351650	−	0.936131i	$-0.385621\pi$
$139$	8.29180	0.703301	0.351650	+	0.936131i	$0.385621\pi$
$140$	0	0
$141$	0	0
$142$	−2.47214	−0.207457
$143$	1.23607	0.103365
$144$	0	0
$145$	14.4721	1.20185
$146$	−4.94427	−0.409191
$147$	0	0
$148$	−10.9443	−0.899614
$149$	−22.3607	−1.83186	−0.915929	−	0.401340i	$-0.868545\pi$
$149$	−22.3607	−1.83186	−0.915929	+	0.401340i	$0.868545\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	−2.76393	−0.224184
$153$	0	0
$154$	0	0
$155$	−6.47214	−0.519854
$156$	0	0
$157$	−18.6525	−1.48863	−0.744315	−	0.667829i	$-0.767224\pi$
$157$	−18.6525	−1.48863	−0.744315	+	0.667829i	$0.767224\pi$
$158$	0	0
$159$	0	0
$160$	−3.23607	−0.255834
$161$	0	0
$162$	0	0
$163$	7.41641	0.580898	0.290449	−	0.956890i	$-0.406195\pi$
$163$	7.41641	0.580898	0.290449	+	0.956890i	$0.406195\pi$
$164$	6.47214	0.505389
$165$	0	0
$166$	−10.1803	−0.790148
$167$	−15.4164	−1.19296	−0.596479	−	0.802629i	$-0.703434\pi$
$167$	−15.4164	−1.19296	−0.596479	+	0.802629i	$0.703434\pi$
$168$	0	0
$169$	−11.4721	−0.882472
$170$	20.9443	1.60635
$171$	0	0
$172$	−1.52786	−0.116499
$173$	1.23607	0.0939765	0.0469883	−	0.998895i	$-0.485038\pi$
$173$	1.23607	0.0939765	0.0469883	+	0.998895i	$0.485038\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−10.0000	−0.749532
$179$	−8.94427	−0.668526	−0.334263	−	0.942480i	$-0.608487\pi$
$179$	−8.94427	−0.668526	−0.334263	+	0.942480i	$0.608487\pi$
$180$	0	0
$181$	−4.76393	−0.354100	−0.177050	−	0.984202i	$-0.556655\pi$
$181$	−4.76393	−0.354100	−0.177050	+	0.984202i	$0.556655\pi$
$182$	0	0
$183$	0	0
$184$	4.00000	0.294884
$185$	−35.4164	−2.60387
$186$	0	0
$187$	6.47214	0.473289
$188$	−2.00000	−0.145865
$189$	0	0
$190$	−8.94427	−0.648886
$191$	−6.47214	−0.468307	−0.234154	−	0.972200i	$-0.575232\pi$
$191$	−6.47214	−0.468307	−0.234154	+	0.972200i	$0.575232\pi$
$192$	0	0
$193$	2.94427	0.211933	0.105967	−	0.994370i	$-0.466206\pi$
$193$	2.94427	0.211933	0.105967	+	0.994370i	$0.466206\pi$
$194$	3.52786	0.253286
$195$	0	0
$196$	0	0
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−1.05573	−0.0748386	−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573	−0.0748386	−0.0374193	+	0.999300i	$0.511914\pi$
$200$	−5.47214	−0.386938
$201$	0	0
$202$	14.1803	0.997725
$203$	0	0
$204$	0	0
$205$	20.9443	1.46281
$206$	2.94427	0.205137
$207$	0	0
$208$	−1.23607	−0.0857059
$209$	−2.76393	−0.191185
$210$	0	0
$211$	−22.4721	−1.54705	−0.773523	−	0.633768i	$-0.781507\pi$
$211$	−22.4721	−1.54705	−0.773523	+	0.633768i	$0.781507\pi$
$212$	0.472136	0.0324264
$213$	0	0
$214$	−6.47214	−0.442426
$215$	−4.94427	−0.337197
$216$	0	0
$217$	0	0
$218$	10.0000	0.677285
$219$	0	0
$220$	−3.23607	−0.218176
$221$	8.00000	0.538138
$222$	0	0
$223$	−8.47214	−0.567336	−0.283668	−	0.958923i	$-0.591551\pi$
$223$	−8.47214	−0.567336	−0.283668	+	0.958923i	$0.591551\pi$
$224$	0	0
$225$	0	0
$226$	8.47214	0.563558
$227$	−14.7639	−0.979917	−0.489958	−	0.871746i	$-0.662988\pi$
$227$	−14.7639	−0.979917	−0.489958	+	0.871746i	$0.662988\pi$
$228$	0	0
$229$	−12.7639	−0.843464	−0.421732	−	0.906720i	$-0.638578\pi$
$229$	−12.7639	−0.843464	−0.421732	+	0.906720i	$0.638578\pi$
$230$	12.9443	0.853520
$231$	0	0
$232$	−4.47214	−0.293610
$233$	−2.94427	−0.192886	−0.0964428	−	0.995339i	$-0.530746\pi$
$233$	−2.94427	−0.192886	−0.0964428	+	0.995339i	$0.530746\pi$
$234$	0	0
$235$	−6.47214	−0.422196
$236$	7.23607	0.471028
$237$	0	0
$238$	0	0
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	0	0
$241$	11.4164	0.735395	0.367698	−	0.929945i	$-0.380146\pi$
$241$	11.4164	0.735395	0.367698	+	0.929945i	$0.380146\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	5.23607	0.335205
$245$	0	0
$246$	0	0
$247$	−3.41641	−0.217381
$248$	2.00000	0.127000
$249$	0	0
$250$	−1.52786	−0.0966306
$251$	24.7639	1.56309	0.781543	−	0.623852i	$-0.214433\pi$
$251$	24.7639	1.56309	0.781543	+	0.623852i	$0.214433\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	12.0000	0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	−10.9443	−0.682685	−0.341342	−	0.939939i	$-0.610882\pi$
$257$	−10.9443	−0.682685	−0.341342	+	0.939939i	$0.610882\pi$
$258$	0	0
$259$	0	0
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−9.23607	−0.570606
$263$	−12.9443	−0.798178	−0.399089	−	0.916912i	$-0.630674\pi$
$263$	−12.9443	−0.798178	−0.399089	+	0.916912i	$0.630674\pi$
$264$	0	0
$265$	1.52786	0.0938559
$266$	0	0
$267$	0	0
$268$	−15.4164	−0.941707
$269$	−27.2361	−1.66061	−0.830306	−	0.557307i	$-0.811834\pi$
$269$	−27.2361	−1.66061	−0.830306	+	0.557307i	$0.811834\pi$
$270$	0	0
$271$	16.9443	1.02929	0.514646	−	0.857403i	$-0.327924\pi$
$271$	16.9443	1.02929	0.514646	+	0.857403i	$0.327924\pi$
$272$	−6.47214	−0.392431
$273$	0	0
$274$	15.8885	0.959862
$275$	−5.47214	−0.329982
$276$	0	0
$277$	12.4721	0.749378	0.374689	−	0.927151i	$-0.377749\pi$
$277$	12.4721	0.749378	0.374689	+	0.927151i	$0.377749\pi$
$278$	−8.29180	−0.497309
$279$	0	0
$280$	0	0
$281$	24.8328	1.48140	0.740701	−	0.671835i	$-0.234494\pi$
$281$	24.8328	1.48140	0.740701	+	0.671835i	$0.234494\pi$
$282$	0	0
$283$	16.6525	0.989887	0.494943	−	0.868925i	$-0.335189\pi$
$283$	16.6525	0.989887	0.494943	+	0.868925i	$0.335189\pi$
$284$	2.47214	0.146694
$285$	0	0
$286$	−1.23607	−0.0730902
$287$	0	0
$288$	0	0
$289$	24.8885	1.46403
$290$	−14.4721	−0.849833
$291$	0	0
$292$	4.94427	0.289342
$293$	4.65248	0.271801	0.135900	−	0.990723i	$-0.456607\pi$
$293$	4.65248	0.271801	0.135900	+	0.990723i	$0.456607\pi$
$294$	0	0
$295$	23.4164	1.36336
$296$	10.9443	0.636123
$297$	0	0
$298$	22.3607	1.29532
$299$	4.94427	0.285935
$300$	0	0
$301$	0	0
$302$	−12.0000	−0.690522
$303$	0	0
$304$	2.76393	0.158522
$305$	16.9443	0.970226
$306$	0	0
$307$	−32.0689	−1.83027	−0.915134	−	0.403150i	$-0.867915\pi$
$307$	−32.0689	−1.83027	−0.915134	+	0.403150i	$0.867915\pi$
$308$	0	0
$309$	0	0
$310$	6.47214	0.367593
$311$	5.41641	0.307136	0.153568	−	0.988138i	$-0.450924\pi$
$311$	5.41641	0.307136	0.153568	+	0.988138i	$0.450924\pi$
$312$	0	0
$313$	−28.4721	−1.60934	−0.804670	−	0.593722i	$-0.797658\pi$
$313$	−28.4721	−1.60934	−0.804670	+	0.593722i	$0.797658\pi$
$314$	18.6525	1.05262
$315$	0	0
$316$	0	0
$317$	13.0557	0.733283	0.366641	−	0.930362i	$-0.380508\pi$
$317$	13.0557	0.733283	0.366641	+	0.930362i	$0.380508\pi$
$318$	0	0
$319$	−4.47214	−0.250392
$320$	3.23607	0.180902
$321$	0	0
$322$	0	0
$323$	−17.8885	−0.995345
$324$	0	0
$325$	−6.76393	−0.375195
$326$	−7.41641	−0.410757
$327$	0	0
$328$	−6.47214	−0.357364
$329$	0	0
$330$	0	0
$331$	0.944272	0.0519019	0.0259509	−	0.999663i	$-0.491739\pi$
$331$	0.944272	0.0519019	0.0259509	+	0.999663i	$0.491739\pi$
$332$	10.1803	0.558719
$333$	0	0
$334$	15.4164	0.843548
$335$	−49.8885	−2.72570
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	11.4721	0.624002
$339$	0	0
$340$	−20.9443	−1.13586
$341$	2.00000	0.108306
$342$	0	0
$343$	0	0
$344$	1.52786	0.0823769
$345$	0	0
$346$	−1.23607	−0.0664514
$347$	6.47214	0.347442	0.173721	−	0.984795i	$-0.444421\pi$
$347$	6.47214	0.347442	0.173721	+	0.984795i	$0.444421\pi$
$348$	0	0
$349$	−8.29180	−0.443850	−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180	−0.443850	−0.221925	+	0.975064i	$0.571234\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−34.9443	−1.85990	−0.929948	−	0.367691i	$-0.880148\pi$
$353$	−34.9443	−1.85990	−0.929948	+	0.367691i	$0.880148\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	10.0000	0.529999
$357$	0	0
$358$	8.94427	0.472719
$359$	26.8328	1.41618	0.708091	−	0.706121i	$-0.249557\pi$
$359$	26.8328	1.41618	0.708091	+	0.706121i	$0.249557\pi$
$360$	0	0
$361$	−11.3607	−0.597931
$362$	4.76393	0.250387
$363$	0	0
$364$	0	0
$365$	16.0000	0.837478
$366$	0	0
$367$	−21.4164	−1.11793	−0.558964	−	0.829192i	$-0.688801\pi$
$367$	−21.4164	−1.11793	−0.558964	+	0.829192i	$0.688801\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	35.4164	1.84121
$371$	0	0
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−6.47214	−0.334666
$375$	0	0
$376$	2.00000	0.103142
$377$	−5.52786	−0.284699
$378$	0	0
$379$	5.52786	0.283947	0.141974	−	0.989870i	$-0.454655\pi$
$379$	5.52786	0.283947	0.141974	+	0.989870i	$0.454655\pi$
$380$	8.94427	0.458831
$381$	0	0
$382$	6.47214	0.331143
$383$	11.8885	0.607476	0.303738	−	0.952756i	$-0.401765\pi$
$383$	11.8885	0.607476	0.303738	+	0.952756i	$0.401765\pi$
$384$	0	0
$385$	0	0
$386$	−2.94427	−0.149859
$387$	0	0
$388$	−3.52786	−0.179100
$389$	−6.58359	−0.333801	−0.166901	−	0.985974i	$-0.553376\pi$
$389$	−6.58359	−0.333801	−0.166901	+	0.985974i	$0.553376\pi$
$390$	0	0
$391$	25.8885	1.30924
$392$	0	0
$393$	0	0
$394$	18.0000	0.906827
$395$	0	0
$396$	0	0
$397$	10.2918	0.516530	0.258265	−	0.966074i	$-0.416849\pi$
$397$	10.2918	0.516530	0.258265	+	0.966074i	$0.416849\pi$
$398$	1.05573	0.0529189
$399$	0	0
$400$	5.47214	0.273607
$401$	30.3607	1.51614	0.758070	−	0.652173i	$-0.226143\pi$
$401$	30.3607	1.51614	0.758070	+	0.652173i	$0.226143\pi$
$402$	0	0
$403$	2.47214	0.123146
$404$	−14.1803	−0.705498
$405$	0	0
$406$	0	0
$407$	10.9443	0.542487
$408$	0	0
$409$	23.4164	1.15787	0.578933	−	0.815375i	$-0.303469\pi$
$409$	23.4164	1.15787	0.578933	+	0.815375i	$0.303469\pi$
$410$	−20.9443	−1.03436
$411$	0	0
$412$	−2.94427	−0.145054
$413$	0	0
$414$	0	0
$415$	32.9443	1.61717
$416$	1.23607	0.0606032
$417$	0	0
$418$	2.76393	0.135188
$419$	12.7639	0.623559	0.311779	−	0.950155i	$-0.399075\pi$
$419$	12.7639	0.623559	0.311779	+	0.950155i	$0.399075\pi$
$420$	0	0
$421$	7.52786	0.366886	0.183443	−	0.983030i	$-0.441276\pi$
$421$	7.52786	0.366886	0.183443	+	0.983030i	$0.441276\pi$
$422$	22.4721	1.09393
$423$	0	0
$424$	−0.472136	−0.0229289
$425$	−35.4164	−1.71795
$426$	0	0
$427$	0	0
$428$	6.47214	0.312842
$429$	0	0
$430$	4.94427	0.238434
$431$	−40.9443	−1.97222	−0.986108	−	0.166105i	$-0.946881\pi$
$431$	−40.9443	−1.97222	−0.986108	+	0.166105i	$0.946881\pi$
$432$	0	0
$433$	−19.5279	−0.938449	−0.469225	−	0.883079i	$-0.655467\pi$
$433$	−19.5279	−0.938449	−0.469225	+	0.883079i	$0.655467\pi$
$434$	0	0
$435$	0	0
$436$	−10.0000	−0.478913
$437$	−11.0557	−0.528867
$438$	0	0
$439$	8.94427	0.426887	0.213443	−	0.976955i	$-0.431532\pi$
$439$	8.94427	0.426887	0.213443	+	0.976955i	$0.431532\pi$
$440$	3.23607	0.154273
$441$	0	0
$442$	−8.00000	−0.380521
$443$	7.05573	0.335228	0.167614	−	0.985853i	$-0.446394\pi$
$443$	7.05573	0.335228	0.167614	+	0.985853i	$0.446394\pi$
$444$	0	0
$445$	32.3607	1.53404
$446$	8.47214	0.401167
$447$	0	0
$448$	0	0
$449$	−1.05573	−0.0498229	−0.0249114	−	0.999690i	$-0.507930\pi$
$449$	−1.05573	−0.0498229	−0.0249114	+	0.999690i	$0.507930\pi$
$450$	0	0
$451$	−6.47214	−0.304761
$452$	−8.47214	−0.398496
$453$	0	0
$454$	14.7639	0.692906
$455$	0	0
$456$	0	0
$457$	9.05573	0.423609	0.211805	−	0.977312i	$-0.432066\pi$
$457$	9.05573	0.423609	0.211805	+	0.977312i	$0.432066\pi$
$458$	12.7639	0.596419
$459$	0	0
$460$	−12.9443	−0.603530
$461$	29.2361	1.36166	0.680830	−	0.732442i	$-0.261619\pi$
$461$	29.2361	1.36166	0.680830	+	0.732442i	$0.261619\pi$
$462$	0	0
$463$	−21.5279	−1.00048	−0.500242	−	0.865885i	$-0.666756\pi$
$463$	−21.5279	−1.00048	−0.500242	+	0.865885i	$0.666756\pi$
$464$	4.47214	0.207614
$465$	0	0
$466$	2.94427	0.136391
$467$	13.1246	0.607335	0.303667	−	0.952778i	$-0.401789\pi$
$467$	13.1246	0.607335	0.303667	+	0.952778i	$0.401789\pi$
$468$	0	0
$469$	0	0
$470$	6.47214	0.298537
$471$	0	0
$472$	−7.23607	−0.333067
$473$	1.52786	0.0702513
$474$	0	0
$475$	15.1246	0.693965
$476$	0	0
$477$	0	0
$478$	20.0000	0.914779
$479$	−32.3607	−1.47860	−0.739299	−	0.673378i	$-0.764843\pi$
$479$	−32.3607	−1.47860	−0.739299	+	0.673378i	$0.764843\pi$
$480$	0	0
$481$	13.5279	0.616818
$482$	−11.4164	−0.520003
$483$	0	0
$484$	1.00000	0.0454545
$485$	−11.4164	−0.518392
$486$	0	0
$487$	−0.944272	−0.0427890	−0.0213945	−	0.999771i	$-0.506811\pi$
$487$	−0.944272	−0.0427890	−0.0213945	+	0.999771i	$0.506811\pi$
$488$	−5.23607	−0.237026
$489$	0	0
$490$	0	0
$491$	−0.944272	−0.0426144	−0.0213072	−	0.999773i	$-0.506783\pi$
$491$	−0.944272	−0.0426144	−0.0213072	+	0.999773i	$0.506783\pi$
$492$	0	0
$493$	−28.9443	−1.30358
$494$	3.41641	0.153711
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0	0
$499$	12.3607	0.553340	0.276670	−	0.960965i	$-0.410769\pi$
$499$	12.3607	0.553340	0.276670	+	0.960965i	$0.410769\pi$
$500$	1.52786	0.0683282
$501$	0	0
$502$	−24.7639	−1.10527
$503$	4.00000	0.178351	0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000	0.178351	0.0891756	+	0.996016i	$0.471577\pi$
$504$	0	0
$505$	−45.8885	−2.04201
$506$	−4.00000	−0.177822
$507$	0	0
$508$	−12.0000	−0.532414
$509$	−34.0689	−1.51008	−0.755038	−	0.655681i	$-0.772382\pi$
$509$	−34.0689	−1.51008	−0.755038	+	0.655681i	$0.772382\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	10.9443	0.482731
$515$	−9.52786	−0.419848
$516$	0	0
$517$	2.00000	0.0879599
$518$	0	0
$519$	0	0
$520$	4.00000	0.175412
$521$	34.3607	1.50537	0.752684	−	0.658382i	$-0.228759\pi$
$521$	34.3607	1.50537	0.752684	+	0.658382i	$0.228759\pi$
$522$	0	0
$523$	27.7082	1.21160	0.605798	−	0.795619i	$-0.292854\pi$
$523$	27.7082	1.21160	0.605798	+	0.795619i	$0.292854\pi$
$524$	9.23607	0.403480
$525$	0	0
$526$	12.9443	0.564397
$527$	12.9443	0.563861
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−1.52786	−0.0663662
$531$	0	0
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	20.9443	0.905500
$536$	15.4164	0.665887
$537$	0	0
$538$	27.2361	1.17423
$539$	0	0
$540$	0	0
$541$	−9.05573	−0.389336	−0.194668	−	0.980869i	$-0.562363\pi$
$541$	−9.05573	−0.389336	−0.194668	+	0.980869i	$0.562363\pi$
$542$	−16.9443	−0.727819
$543$	0	0
$544$	6.47214	0.277491
$545$	−32.3607	−1.38618
$546$	0	0
$547$	16.9443	0.724485	0.362242	−	0.932084i	$-0.382011\pi$
$547$	16.9443	0.724485	0.362242	+	0.932084i	$0.382011\pi$
$548$	−15.8885	−0.678725
$549$	0	0
$550$	5.47214	0.233333
$551$	12.3607	0.526583
$552$	0	0
$553$	0	0
$554$	−12.4721	−0.529890
$555$	0	0
$556$	8.29180	0.351650
$557$	28.8328	1.22169	0.610843	−	0.791752i	$-0.290831\pi$
$557$	28.8328	1.22169	0.610843	+	0.791752i	$0.290831\pi$
$558$	0	0
$559$	1.88854	0.0798769
$560$	0	0
$561$	0	0
$562$	−24.8328	−1.04751
$563$	26.7639	1.12797	0.563983	−	0.825787i	$-0.309268\pi$
$563$	26.7639	1.12797	0.563983	+	0.825787i	$0.309268\pi$
$564$	0	0
$565$	−27.4164	−1.15342
$566$	−16.6525	−0.699956
$567$	0	0
$568$	−2.47214	−0.103729
$569$	−16.8328	−0.705668	−0.352834	−	0.935686i	$-0.614782\pi$
$569$	−16.8328	−0.705668	−0.352834	+	0.935686i	$0.614782\pi$
$570$	0	0
$571$	−45.8885	−1.92038	−0.960188	−	0.279355i	$-0.909879\pi$
$571$	−45.8885	−1.92038	−0.960188	+	0.279355i	$0.909879\pi$
$572$	1.23607	0.0516826
$573$	0	0
$574$	0	0
$575$	−21.8885	−0.912815
$576$	0	0
$577$	−9.05573	−0.376995	−0.188497	−	0.982074i	$-0.560362\pi$
$577$	−9.05573	−0.376995	−0.188497	+	0.982074i	$0.560362\pi$
$578$	−24.8885	−1.03523
$579$	0	0
$580$	14.4721	0.600923
$581$	0	0
$582$	0	0
$583$	−0.472136	−0.0195539
$584$	−4.94427	−0.204595
$585$	0	0
$586$	−4.65248	−0.192192
$587$	−28.1803	−1.16313	−0.581564	−	0.813501i	$-0.697559\pi$
$587$	−28.1803	−1.16313	−0.581564	+	0.813501i	$0.697559\pi$
$588$	0	0
$589$	−5.52786	−0.227772
$590$	−23.4164	−0.964038
$591$	0	0
$592$	−10.9443	−0.449807
$593$	24.0000	0.985562	0.492781	−	0.870153i	$-0.335980\pi$
$593$	24.0000	0.985562	0.492781	+	0.870153i	$0.335980\pi$
$594$	0	0
$595$	0	0
$596$	−22.3607	−0.915929
$597$	0	0
$598$	−4.94427	−0.202186
$599$	−12.3607	−0.505044	−0.252522	−	0.967591i	$-0.581260\pi$
$599$	−12.3607	−0.505044	−0.252522	+	0.967591i	$0.581260\pi$
$600$	0	0
$601$	−18.8328	−0.768207	−0.384103	−	0.923290i	$-0.625489\pi$
$601$	−18.8328	−0.768207	−0.384103	+	0.923290i	$0.625489\pi$
$602$	0	0
$603$	0	0
$604$	12.0000	0.488273
$605$	3.23607	0.131565
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−2.76393	−0.112092
$609$	0	0
$610$	−16.9443	−0.686054
$611$	2.47214	0.100012
$612$	0	0
$613$	19.5279	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$613$	19.5279	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$614$	32.0689	1.29419
$615$	0	0
$616$	0	0
$617$	5.41641	0.218056	0.109028	−	0.994039i	$-0.465226\pi$
$617$	5.41641	0.218056	0.109028	+	0.994039i	$0.465226\pi$
$618$	0	0
$619$	48.5410	1.95103	0.975514	−	0.219937i	$-0.0705851\pi$
$619$	48.5410	1.95103	0.975514	+	0.219937i	$0.0705851\pi$
$620$	−6.47214	−0.259927
$621$	0	0
$622$	−5.41641	−0.217178
$623$	0	0
$624$	0	0
$625$	−22.4164	−0.896656
$626$	28.4721	1.13798
$627$	0	0
$628$	−18.6525	−0.744315
$629$	70.8328	2.82429
$630$	0	0
$631$	−4.58359	−0.182470	−0.0912350	−	0.995829i	$-0.529081\pi$
$631$	−4.58359	−0.182470	−0.0912350	+	0.995829i	$0.529081\pi$
$632$	0	0
$633$	0	0
$634$	−13.0557	−0.518509
$635$	−38.8328	−1.54103
$636$	0	0
$637$	0	0
$638$	4.47214	0.177054
$639$	0	0
$640$	−3.23607	−0.127917
$641$	−36.4721	−1.44056	−0.720281	−	0.693682i	$-0.755987\pi$
$641$	−36.4721	−1.44056	−0.720281	+	0.693682i	$0.755987\pi$
$642$	0	0
$643$	23.2361	0.916341	0.458171	−	0.888864i	$-0.348505\pi$
$643$	23.2361	0.916341	0.458171	+	0.888864i	$0.348505\pi$
$644$	0	0
$645$	0	0
$646$	17.8885	0.703815
$647$	24.8328	0.976279	0.488139	−	0.872766i	$-0.337676\pi$
$647$	24.8328	0.976279	0.488139	+	0.872766i	$0.337676\pi$
$648$	0	0
$649$	−7.23607	−0.284041
$650$	6.76393	0.265303
$651$	0	0
$652$	7.41641	0.290449
$653$	−1.63932	−0.0641516	−0.0320758	−	0.999485i	$-0.510212\pi$
$653$	−1.63932	−0.0641516	−0.0320758	+	0.999485i	$0.510212\pi$
$654$	0	0
$655$	29.8885	1.16784
$656$	6.47214	0.252694
$657$	0	0
$658$	0	0
$659$	−43.4164	−1.69126	−0.845632	−	0.533767i	$-0.820776\pi$
$659$	−43.4164	−1.69126	−0.845632	+	0.533767i	$0.820776\pi$
$660$	0	0
$661$	−37.1246	−1.44398	−0.721990	−	0.691903i	$-0.756772\pi$
$661$	−37.1246	−1.44398	−0.721990	+	0.691903i	$0.756772\pi$
$662$	−0.944272	−0.0367002
$663$	0	0
$664$	−10.1803	−0.395074
$665$	0	0
$666$	0	0
$667$	−17.8885	−0.692647
$668$	−15.4164	−0.596479
$669$	0	0
$670$	49.8885	1.92736
$671$	−5.23607	−0.202136
$672$	0	0
$673$	31.8885	1.22921	0.614607	−	0.788834i	$-0.289315\pi$
$673$	31.8885	1.22921	0.614607	+	0.788834i	$0.289315\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	−11.4721	−0.441236
$677$	32.0689	1.23251	0.616254	−	0.787548i	$-0.288650\pi$
$677$	32.0689	1.23251	0.616254	+	0.787548i	$0.288650\pi$
$678$	0	0
$679$	0	0
$680$	20.9443	0.803176
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	−15.0557	−0.576091	−0.288046	−	0.957617i	$-0.593006\pi$
$683$	−15.0557	−0.576091	−0.288046	+	0.957617i	$0.593006\pi$
$684$	0	0
$685$	−51.4164	−1.96452
$686$	0	0
$687$	0	0
$688$	−1.52786	−0.0582493
$689$	−0.583592	−0.0222331
$690$	0	0
$691$	18.6525	0.709574	0.354787	−	0.934947i	$-0.384553\pi$
$691$	18.6525	0.709574	0.354787	+	0.934947i	$0.384553\pi$
$692$	1.23607	0.0469883
$693$	0	0
$694$	−6.47214	−0.245679
$695$	26.8328	1.01783
$696$	0	0
$697$	−41.8885	−1.58664
$698$	8.29180	0.313849
$699$	0	0
$700$	0	0
$701$	−46.7214	−1.76464	−0.882321	−	0.470649i	$-0.844020\pi$
$701$	−46.7214	−1.76464	−0.882321	+	0.470649i	$0.844020\pi$
$702$	0	0
$703$	−30.2492	−1.14087
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	34.9443	1.31515
$707$	0	0
$708$	0	0
$709$	−4.47214	−0.167955	−0.0839773	−	0.996468i	$-0.526762\pi$
$709$	−4.47214	−0.167955	−0.0839773	+	0.996468i	$0.526762\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	−10.0000	−0.374766
$713$	8.00000	0.299602
$714$	0	0
$715$	4.00000	0.149592
$716$	−8.94427	−0.334263
$717$	0	0
$718$	−26.8328	−1.00139
$719$	−36.8328	−1.37363	−0.686816	−	0.726831i	$-0.740992\pi$
$719$	−36.8328	−1.37363	−0.686816	+	0.726831i	$0.740992\pi$
$720$	0	0
$721$	0	0
$722$	11.3607	0.422801
$723$	0	0
$724$	−4.76393	−0.177050
$725$	24.4721	0.908872
$726$	0	0
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	0	0
$729$	0	0
$730$	−16.0000	−0.592187
$731$	9.88854	0.365741
$732$	0	0
$733$	−8.87539	−0.327820	−0.163910	−	0.986475i	$-0.552411\pi$
$733$	−8.87539	−0.327820	−0.163910	+	0.986475i	$0.552411\pi$
$734$	21.4164	0.790494
$735$	0	0
$736$	4.00000	0.147442
$737$	15.4164	0.567871
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	−35.4164	−1.30193
$741$	0	0
$742$	0	0
$743$	13.8885	0.509521	0.254761	−	0.967004i	$-0.418003\pi$
$743$	13.8885	0.509521	0.254761	+	0.967004i	$0.418003\pi$
$744$	0	0
$745$	−72.3607	−2.65109
$746$	6.00000	0.219676
$747$	0	0
$748$	6.47214	0.236645
$749$	0	0
$750$	0	0
$751$	0.944272	0.0344570	0.0172285	−	0.999852i	$-0.494516\pi$
$751$	0.944272	0.0344570	0.0172285	+	0.999852i	$0.494516\pi$
$752$	−2.00000	−0.0729325
$753$	0	0
$754$	5.52786	0.201313
$755$	38.8328	1.41327
$756$	0	0
$757$	39.3050	1.42856	0.714281	−	0.699859i	$-0.246754\pi$
$757$	39.3050	1.42856	0.714281	+	0.699859i	$0.246754\pi$
$758$	−5.52786	−0.200781
$759$	0	0
$760$	−8.94427	−0.324443
$761$	15.4164	0.558844	0.279422	−	0.960168i	$-0.409857\pi$
$761$	15.4164	0.558844	0.279422	+	0.960168i	$0.409857\pi$
$762$	0	0
$763$	0	0
$764$	−6.47214	−0.234154
$765$	0	0
$766$	−11.8885	−0.429551
$767$	−8.94427	−0.322959
$768$	0	0
$769$	16.5836	0.598020	0.299010	−	0.954250i	$-0.403344\pi$
$769$	16.5836	0.598020	0.299010	+	0.954250i	$0.403344\pi$
$770$	0	0
$771$	0	0
$772$	2.94427	0.105967
$773$	2.29180	0.0824302	0.0412151	−	0.999150i	$-0.486877\pi$
$773$	2.29180	0.0824302	0.0412151	+	0.999150i	$0.486877\pi$
$774$	0	0
$775$	−10.9443	−0.393130
$776$	3.52786	0.126643
$777$	0	0
$778$	6.58359	0.236033
$779$	17.8885	0.640924
$780$	0	0
$781$	−2.47214	−0.0884600
$782$	−25.8885	−0.925772
$783$	0	0
$784$	0	0
$785$	−60.3607	−2.15437
$786$	0	0
$787$	5.81966	0.207448	0.103724	−	0.994606i	$-0.466924\pi$
$787$	5.81966	0.207448	0.103724	+	0.994606i	$0.466924\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−6.47214	−0.229832
$794$	−10.2918	−0.365242
$795$	0	0
$796$	−1.05573	−0.0374193
$797$	7.59675	0.269091	0.134545	−	0.990907i	$-0.457043\pi$
$797$	7.59675	0.269091	0.134545	+	0.990907i	$0.457043\pi$
$798$	0	0
$799$	12.9443	0.457935
$800$	−5.47214	−0.193469
$801$	0	0
$802$	−30.3607	−1.07207
$803$	−4.94427	−0.174480
$804$	0	0
$805$	0	0
$806$	−2.47214	−0.0870773
$807$	0	0
$808$	14.1803	0.498863
$809$	38.9443	1.36921	0.684604	−	0.728915i	$-0.259975\pi$
$809$	38.9443	1.36921	0.684604	+	0.728915i	$0.259975\pi$
$810$	0	0
$811$	−9.23607	−0.324322	−0.162161	−	0.986764i	$-0.551846\pi$
$811$	−9.23607	−0.324322	−0.162161	+	0.986764i	$0.551846\pi$
$812$	0	0
$813$	0	0
$814$	−10.9443	−0.383597
$815$	24.0000	0.840683
$816$	0	0
$817$	−4.22291	−0.147741
$818$	−23.4164	−0.818736
$819$	0	0
$820$	20.9443	0.731406
$821$	−25.4164	−0.887039	−0.443519	−	0.896265i	$-0.646270\pi$
$821$	−25.4164	−0.887039	−0.443519	+	0.896265i	$0.646270\pi$
$822$	0	0
$823$	34.2492	1.19385	0.596926	−	0.802296i	$-0.296388\pi$
$823$	34.2492	1.19385	0.596926	+	0.802296i	$0.296388\pi$
$824$	2.94427	0.102569
$825$	0	0
$826$	0	0
$827$	0.944272	0.0328356	0.0164178	−	0.999865i	$-0.494774\pi$
$827$	0.944272	0.0328356	0.0164178	+	0.999865i	$0.494774\pi$
$828$	0	0
$829$	1.70820	0.0593284	0.0296642	−	0.999560i	$-0.490556\pi$
$829$	1.70820	0.0593284	0.0296642	+	0.999560i	$0.490556\pi$
$830$	−32.9443	−1.14351
$831$	0	0
$832$	−1.23607	−0.0428529
$833$	0	0
$834$	0	0
$835$	−49.8885	−1.72646
$836$	−2.76393	−0.0955926
$837$	0	0
$838$	−12.7639	−0.440923
$839$	−36.8328	−1.27161	−0.635805	−	0.771850i	$-0.719332\pi$
$839$	−36.8328	−1.27161	−0.635805	+	0.771850i	$0.719332\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	−7.52786	−0.259427
$843$	0	0
$844$	−22.4721	−0.773523
$845$	−37.1246	−1.27713
$846$	0	0
$847$	0	0
$848$	0.472136	0.0162132
$849$	0	0
$850$	35.4164	1.21477
$851$	43.7771	1.50066
$852$	0	0
$853$	34.5410	1.18266	0.591331	−	0.806429i	$-0.298603\pi$
$853$	34.5410	1.18266	0.591331	+	0.806429i	$0.298603\pi$
$854$	0	0
$855$	0	0
$856$	−6.47214	−0.221213
$857$	−37.5279	−1.28193	−0.640964	−	0.767571i	$-0.721465\pi$
$857$	−37.5279	−1.28193	−0.640964	+	0.767571i	$0.721465\pi$
$858$	0	0
$859$	25.1246	0.857241	0.428620	−	0.903485i	$-0.359000\pi$
$859$	25.1246	0.857241	0.428620	+	0.903485i	$0.359000\pi$
$860$	−4.94427	−0.168598
$861$	0	0
$862$	40.9443	1.39457
$863$	−27.4164	−0.933265	−0.466633	−	0.884451i	$-0.654533\pi$
$863$	−27.4164	−0.933265	−0.466633	+	0.884451i	$0.654533\pi$
$864$	0	0
$865$	4.00000	0.136004
$866$	19.5279	0.663584
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	19.0557	0.645679
$872$	10.0000	0.338643
$873$	0	0
$874$	11.0557	0.373966
$875$	0	0
$876$	0	0
$877$	26.9443	0.909843	0.454922	−	0.890531i	$-0.349667\pi$
$877$	26.9443	0.909843	0.454922	+	0.890531i	$0.349667\pi$
$878$	−8.94427	−0.301855
$879$	0	0
$880$	−3.23607	−0.109088
$881$	−24.8328	−0.836639	−0.418319	−	0.908300i	$-0.637381\pi$
$881$	−24.8328	−0.836639	−0.418319	+	0.908300i	$0.637381\pi$
$882$	0	0
$883$	50.8328	1.71066	0.855330	−	0.518083i	$-0.173354\pi$
$883$	50.8328	1.71066	0.855330	+	0.518083i	$0.173354\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	−7.05573	−0.237042
$887$	0.360680	0.0121104	0.00605522	−	0.999982i	$-0.498073\pi$
$887$	0.360680	0.0121104	0.00605522	+	0.999982i	$0.498073\pi$
$888$	0	0
$889$	0	0
$890$	−32.3607	−1.08473
$891$	0	0
$892$	−8.47214	−0.283668
$893$	−5.52786	−0.184983
$894$	0	0
$895$	−28.9443	−0.967500
$896$	0	0
$897$	0	0
$898$	1.05573	0.0352301
$899$	−8.94427	−0.298308
$900$	0	0
$901$	−3.05573	−0.101801
$902$	6.47214	0.215499
$903$	0	0
$904$	8.47214	0.281779
$905$	−15.4164	−0.512459
$906$	0	0
$907$	20.3607	0.676065	0.338033	−	0.941134i	$-0.390239\pi$
$907$	20.3607	0.676065	0.338033	+	0.941134i	$0.390239\pi$
$908$	−14.7639	−0.489958
$909$	0	0
$910$	0	0
$911$	28.0000	0.927681	0.463841	−	0.885919i	$-0.346471\pi$
$911$	28.0000	0.927681	0.463841	+	0.885919i	$0.346471\pi$
$912$	0	0
$913$	−10.1803	−0.336920
$914$	−9.05573	−0.299537
$915$	0	0
$916$	−12.7639	−0.421732
$917$	0	0
$918$	0	0
$919$	−57.8885	−1.90957	−0.954783	−	0.297302i	$-0.903913\pi$
$919$	−57.8885	−1.90957	−0.954783	+	0.297302i	$0.903913\pi$
$920$	12.9443	0.426760
$921$	0	0
$922$	−29.2361	−0.962839
$923$	−3.05573	−0.100581
$924$	0	0
$925$	−59.8885	−1.96912
$926$	21.5279	0.707450
$927$	0	0
$928$	−4.47214	−0.146805
$929$	−40.2492	−1.32053	−0.660267	−	0.751031i	$-0.729557\pi$
$929$	−40.2492	−1.32053	−0.660267	+	0.751031i	$0.729557\pi$
$930$	0	0
$931$	0	0
$932$	−2.94427	−0.0964428
$933$	0	0
$934$	−13.1246	−0.429450
$935$	20.9443	0.684951
$936$	0	0
$937$	20.9443	0.684220	0.342110	−	0.939660i	$-0.388859\pi$
$937$	20.9443	0.684220	0.342110	+	0.939660i	$0.388859\pi$
$938$	0	0
$939$	0	0
$940$	−6.47214	−0.211098
$941$	−34.1803	−1.11425	−0.557124	−	0.830430i	$-0.688095\pi$
$941$	−34.1803	−1.11425	−0.557124	+	0.830430i	$0.688095\pi$
$942$	0	0
$943$	−25.8885	−0.843047
$944$	7.23607	0.235514
$945$	0	0
$946$	−1.52786	−0.0496751
$947$	0.944272	0.0306847	0.0153424	−	0.999882i	$-0.495116\pi$
$947$	0.944272	0.0306847	0.0153424	+	0.999882i	$0.495116\pi$
$948$	0	0
$949$	−6.11146	−0.198386
$950$	−15.1246	−0.490707
$951$	0	0
$952$	0	0
$953$	−5.05573	−0.163771	−0.0818855	−	0.996642i	$-0.526094\pi$
$953$	−5.05573	−0.163771	−0.0818855	+	0.996642i	$0.526094\pi$
$954$	0	0
$955$	−20.9443	−0.677741
$956$	−20.0000	−0.646846
$957$	0	0
$958$	32.3607	1.04553
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−13.5279	−0.436156
$963$	0	0
$964$	11.4164	0.367698
$965$	9.52786	0.306713
$966$	0	0
$967$	10.1115	0.325163	0.162581	−	0.986695i	$-0.448018\pi$
$967$	10.1115	0.325163	0.162581	+	0.986695i	$0.448018\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	11.4164	0.366559
$971$	−16.5410	−0.530827	−0.265413	−	0.964135i	$-0.585508\pi$
$971$	−16.5410	−0.530827	−0.265413	+	0.964135i	$0.585508\pi$
$972$	0	0
$973$	0	0
$974$	0.944272	0.0302564
$975$	0	0
$976$	5.23607	0.167602
$977$	−24.8328	−0.794472	−0.397236	−	0.917716i	$-0.630031\pi$
$977$	−24.8328	−0.794472	−0.397236	+	0.917716i	$0.630031\pi$
$978$	0	0
$979$	−10.0000	−0.319601
$980$	0	0
$981$	0	0
$982$	0.944272	0.0301329
$983$	14.0000	0.446531	0.223265	−	0.974758i	$-0.428328\pi$
$983$	14.0000	0.446531	0.223265	+	0.974758i	$0.428328\pi$
$984$	0	0
$985$	−58.2492	−1.85597
$986$	28.9443	0.921773
$987$	0	0
$988$	−3.41641	−0.108690
$989$	6.11146	0.194333
$990$	0	0
$991$	44.3607	1.40916	0.704582	−	0.709623i	$-0.251135\pi$
$991$	44.3607	1.40916	0.704582	+	0.709623i	$0.251135\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	0	0
$995$	−3.41641	−0.108307
$996$	0	0
$997$	−1.81966	−0.0576292	−0.0288146	−	0.999585i	$-0.509173\pi$
$997$	−1.81966	−0.0576292	−0.0288146	+	0.999585i	$0.509173\pi$
$998$	−12.3607	−0.391270
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.cu.1.2		2
3.2	odd	2		1078.2.a.w.1.2		2
7.6	odd	2		1386.2.a.m.1.1		2
12.11	even	2		8624.2.a.bf.1.1		2
21.2	odd	6		1078.2.e.n.67.1		4
21.5	even	6		1078.2.e.q.67.2		4
21.11	odd	6		1078.2.e.n.177.1		4
21.17	even	6		1078.2.e.q.177.2		4
21.20	even	2		154.2.a.d.1.1	✓	2
84.83	odd	2		1232.2.a.p.1.2		2
105.62	odd	4		3850.2.c.q.1849.4		4
105.83	odd	4		3850.2.c.q.1849.1		4
105.104	even	2		3850.2.a.bj.1.2		2
168.83	odd	2		4928.2.a.bk.1.1		2
168.125	even	2		4928.2.a.bt.1.2		2
231.230	odd	2		1694.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.d.1.1	✓	2	21.20	even	2
1078.2.a.w.1.2		2	3.2	odd	2
1078.2.e.n.67.1		4	21.2	odd	6
1078.2.e.n.177.1		4	21.11	odd	6
1078.2.e.q.67.2		4	21.5	even	6
1078.2.e.q.177.2		4	21.17	even	6
1232.2.a.p.1.2		2	84.83	odd	2
1386.2.a.m.1.1		2	7.6	odd	2
1694.2.a.l.1.1		2	231.230	odd	2
3850.2.a.bj.1.2		2	105.104	even	2
3850.2.c.q.1849.1		4	105.83	odd	4
3850.2.c.q.1849.4		4	105.62	odd	4
4928.2.a.bk.1.1		2	168.83	odd	2
4928.2.a.bt.1.2		2	168.125	even	2
8624.2.a.bf.1.1		2	12.11	even	2
9702.2.a.cu.1.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{8} -3.23607 q^{10} -1.00000 q^{11} -1.23607 q^{13} +1.00000 q^{16} -6.47214 q^{17} +2.76393 q^{19} +3.23607 q^{20} +1.00000 q^{22} -4.00000 q^{23} +5.47214 q^{25} +1.23607 q^{26} +4.47214 q^{29} -2.00000 q^{31} -1.00000 q^{32} +6.47214 q^{34} -10.9443 q^{37} -2.76393 q^{38} -3.23607 q^{40} +6.47214 q^{41} -1.52786 q^{43} -1.00000 q^{44} +4.00000 q^{46} -2.00000 q^{47} -5.47214 q^{50} -1.23607 q^{52} +0.472136 q^{53} -3.23607 q^{55} -4.47214 q^{58} +7.23607 q^{59} +5.23607 q^{61} +2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -15.4164 q^{67} -6.47214 q^{68} +2.47214 q^{71} +4.94427 q^{73} +10.9443 q^{74} +2.76393 q^{76} +3.23607 q^{80} -6.47214 q^{82} +10.1803 q^{83} -20.9443 q^{85} +1.52786 q^{86} +1.00000 q^{88} +10.0000 q^{89} -4.00000 q^{92} +2.00000 q^{94} +8.94427 q^{95} -3.52786 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} + 2 q^{16} - 4 q^{17} + 10 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} + 2 q^{25} - 2 q^{26} - 4 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38} - 2 q^{40} + 4 q^{41} - 12 q^{43} - 2 q^{44} + 8 q^{46} - 4 q^{47} - 2 q^{50} + 2 q^{52} - 8 q^{53} - 2 q^{55} + 10 q^{59} + 6 q^{61} + 4 q^{62} + 2 q^{64} - 8 q^{65} - 4 q^{67} - 4 q^{68} - 4 q^{71} - 8 q^{73} + 4 q^{74} + 10 q^{76} + 2 q^{80} - 4 q^{82} - 2 q^{83} - 24 q^{85} + 12 q^{86} + 2 q^{88} + 20 q^{89} - 8 q^{92} + 4 q^{94} - 16 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 2 * q^8 - 2 * q^10 - 2 * q^11 + 2 * q^13 + 2 * q^16 - 4 * q^17 + 10 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 + 2 * q^25 - 2 * q^26 - 4 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^37 - 10 * q^38 - 2 * q^40 + 4 * q^41 - 12 * q^43 - 2 * q^44 + 8 * q^46 - 4 * q^47 - 2 * q^50 + 2 * q^52 - 8 * q^53 - 2 * q^55 + 10 * q^59 + 6 * q^61 + 4 * q^62 + 2 * q^64 - 8 * q^65 - 4 * q^67 - 4 * q^68 - 4 * q^71 - 8 * q^73 + 4 * q^74 + 10 * q^76 + 2 * q^80 - 4 * q^82 - 2 * q^83 - 24 * q^85 + 12 * q^86 + 2 * q^88 + 20 * q^89 - 8 * q^92 + 4 * q^94 - 16 * q^97

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