LMFDB - Embedded newform 9196.2.a.u.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9196,2,Mod(1,9196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9196, 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("9196.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9196 = 2^{2} \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9196.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:	$73.4304296988$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 25 x^{12} + 52 x^{11} + 222 x^{10} - 492 x^{9} - 800 x^{8} + 1984 x^{7} + 854 x^{6} + \cdots + 13 $ x^14 - 2x^13 - 25x^12 + 52x^11 + 222x^10 - 492x^9 - 800x^8 + 1984x^7 + 854x^6 - 2946x^5 + 300x^4 + 878x^3 - 194x^2 - 52*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.54751$ of defining polynomial
Character	$\chi$	$=$	9196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54751 q^{3} -2.33168 q^{5} +1.70655 q^{7} -0.605224 q^{9} +1.98486 q^{13} -3.60829 q^{15} -0.974883 q^{17} +1.00000 q^{19} +2.64089 q^{21} +1.88770 q^{23} +0.436736 q^{25} -5.57911 q^{27} -3.33750 q^{29} -5.66011 q^{31} -3.97912 q^{35} +9.03337 q^{37} +3.07158 q^{39} +6.69729 q^{41} -5.24503 q^{43} +1.41119 q^{45} -3.38697 q^{47} -4.08770 q^{49} -1.50864 q^{51} -7.39938 q^{53} +1.54751 q^{57} +4.82288 q^{59} -0.594539 q^{61} -1.03284 q^{63} -4.62806 q^{65} +11.8560 q^{67} +2.92123 q^{69} -9.09114 q^{71} +0.717226 q^{73} +0.675852 q^{75} +2.46354 q^{79} -6.81803 q^{81} -5.36866 q^{83} +2.27312 q^{85} -5.16479 q^{87} -8.20577 q^{89} +3.38726 q^{91} -8.75906 q^{93} -2.33168 q^{95} +6.15317 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} - 6 q^{5} - 4 q^{7} + 12 q^{9} - 4 q^{13} + 2 q^{15} - 8 q^{17} + 14 q^{19} - 18 q^{21} - 2 q^{23} + 8 q^{25} + 10 q^{27} + 4 q^{29} - 2 q^{31} - 24 q^{35} - 10 q^{37} - 24 q^{39} - 4 q^{41}+ \cdots - 20 q^{97}+O(q^{100}) $ 14 * q - 2 * q^3 - 6 * q^5 - 4 * q^7 + 12 * q^9 - 4 * q^13 + 2 * q^15 - 8 * q^17 + 14 * q^19 - 18 * q^21 - 2 * q^23 + 8 * q^25 + 10 * q^27 + 4 * q^29 - 2 * q^31 - 24 * q^35 - 10 * q^37 - 24 * q^39 - 4 * q^41 - 32 * q^43 - 20 * q^45 - 4 * q^47 - 14 * q^49 - 22 * q^51 + 6 * q^53 - 2 * q^57 - 6 * q^59 + 4 * q^61 + 16 * q^63 - 54 * q^65 + 6 * q^67 + 4 * q^69 - 6 * q^71 + 24 * q^73 - 10 * q^75 - 48 * q^79 + 2 * q^81 + 40 * q^85 - 28 * q^87 + 2 * q^89 + 28 * q^91 + 34 * q^93 - 6 * q^95 - 20 * q^97

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	1.54751	0.893453	0.446727	−	0.894671i	$-0.352590\pi$
$3$	1.54751	0.893453	0.446727	+	0.894671i	$0.352590\pi$
$4$	0	0
$5$	−2.33168	−1.04276	−0.521380	−	0.853325i	$-0.674582\pi$
$5$	−2.33168	−1.04276	−0.521380	+	0.853325i	$0.674582\pi$
$6$	0	0
$7$	1.70655	0.645014	0.322507	−	0.946567i	$-0.395474\pi$
$7$	1.70655	0.645014	0.322507	+	0.946567i	$0.395474\pi$
$8$	0	0
$9$	−0.605224	−0.201741
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	1.98486	0.550501	0.275251	−	0.961372i	$-0.411239\pi$
$13$	1.98486	0.550501	0.275251	+	0.961372i	$0.411239\pi$
$14$	0	0
$15$	−3.60829	−0.931657
$16$	0	0
$17$	−0.974883	−0.236444	−0.118222	−	0.992987i	$-0.537719\pi$
$17$	−0.974883	−0.236444	−0.118222	+	0.992987i	$0.537719\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	2.64089	0.576290
$22$	0	0
$23$	1.88770	0.393613	0.196806	−	0.980442i	$-0.436943\pi$
$23$	1.88770	0.393613	0.196806	+	0.980442i	$0.436943\pi$
$24$	0	0
$25$	0.436736	0.0873472
$26$	0	0
$27$	−5.57911	−1.07370
$28$	0	0
$29$	−3.33750	−0.619757	−0.309879	−	0.950776i	$-0.600288\pi$
$29$	−3.33750	−0.619757	−0.309879	+	0.950776i	$0.600288\pi$
$30$	0	0
$31$	−5.66011	−1.01659	−0.508293	−	0.861184i	$-0.669723\pi$
$31$	−5.66011	−1.01659	−0.508293	+	0.861184i	$0.669723\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−3.97912	−0.672594
$36$	0	0
$37$	9.03337	1.48508	0.742538	−	0.669804i	$-0.233622\pi$
$37$	9.03337	1.48508	0.742538	+	0.669804i	$0.233622\pi$
$38$	0	0
$39$	3.07158	0.491847
$40$	0	0
$41$	6.69729	1.04594	0.522971	−	0.852351i	$-0.324824\pi$
$41$	6.69729	1.04594	0.522971	+	0.852351i	$0.324824\pi$
$42$	0	0
$43$	−5.24503	−0.799860	−0.399930	−	0.916546i	$-0.630966\pi$
$43$	−5.24503	−0.799860	−0.399930	+	0.916546i	$0.630966\pi$
$44$	0	0
$45$	1.41119	0.210368
$46$	0	0
$47$	−3.38697	−0.494041	−0.247020	−	0.969010i	$-0.579451\pi$
$47$	−3.38697	−0.494041	−0.247020	+	0.969010i	$0.579451\pi$
$48$	0	0
$49$	−4.08770	−0.583957
$50$	0	0
$51$	−1.50864	−0.211251
$52$	0	0
$53$	−7.39938	−1.01638	−0.508191	−	0.861244i	$-0.669686\pi$
$53$	−7.39938	−1.01638	−0.508191	+	0.861244i	$0.669686\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.54751	0.204972
$58$	0	0
$59$	4.82288	0.627886	0.313943	−	0.949442i	$-0.398350\pi$
$59$	4.82288	0.627886	0.313943	+	0.949442i	$0.398350\pi$
$60$	0	0
$61$	−0.594539	−0.0761229	−0.0380614	−	0.999275i	$-0.512118\pi$
$61$	−0.594539	−0.0761229	−0.0380614	+	0.999275i	$0.512118\pi$
$62$	0	0
$63$	−1.03284	−0.130126
$64$	0	0
$65$	−4.62806	−0.574041
$66$	0	0
$67$	11.8560	1.44844	0.724219	−	0.689570i	$-0.242200\pi$
$67$	11.8560	1.44844	0.724219	+	0.689570i	$0.242200\pi$
$68$	0	0
$69$	2.92123	0.351674
$70$	0	0
$71$	−9.09114	−1.07892	−0.539460	−	0.842011i	$-0.681372\pi$
$71$	−9.09114	−1.07892	−0.539460	+	0.842011i	$0.681372\pi$
$72$	0	0
$73$	0.717226	0.0839449	0.0419725	−	0.999119i	$-0.486636\pi$
$73$	0.717226	0.0839449	0.0419725	+	0.999119i	$0.486636\pi$
$74$	0	0
$75$	0.675852	0.0780407
$76$	0	0
$77$	0	0
$78$	0	0
$79$	2.46354	0.277170	0.138585	−	0.990351i	$-0.455745\pi$
$79$	2.46354	0.277170	0.138585	+	0.990351i	$0.455745\pi$
$80$	0	0
$81$	−6.81803	−0.757559
$82$	0	0
$83$	−5.36866	−0.589287	−0.294643	−	0.955607i	$-0.595201\pi$
$83$	−5.36866	−0.589287	−0.294643	+	0.955607i	$0.595201\pi$
$84$	0	0
$85$	2.27312	0.246554
$86$	0	0
$87$	−5.16479	−0.553724
$88$	0	0
$89$	−8.20577	−0.869810	−0.434905	−	0.900476i	$-0.643218\pi$
$89$	−8.20577	−0.869810	−0.434905	+	0.900476i	$0.643218\pi$
$90$	0	0
$91$	3.38726	0.355081
$92$	0	0
$93$	−8.75906	−0.908273
$94$	0	0
$95$	−2.33168	−0.239225
$96$	0	0
$97$	6.15317	0.624760	0.312380	−	0.949957i	$-0.398874\pi$
$97$	6.15317	0.624760	0.312380	+	0.949957i	$0.398874\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−3.10981	−0.309438	−0.154719	−	0.987959i	$-0.549447\pi$
$101$	−3.10981	−0.309438	−0.154719	+	0.987959i	$0.549447\pi$
$102$	0	0
$103$	−11.1358	−1.09724	−0.548619	−	0.836072i	$-0.684846\pi$
$103$	−11.1358	−1.09724	−0.548619	+	0.836072i	$0.684846\pi$
$104$	0	0
$105$	−6.15772	−0.600932
$106$	0	0
$107$	−18.4860	−1.78711	−0.893554	−	0.448957i	$-0.851796\pi$
$107$	−18.4860	−1.78711	−0.893554	+	0.448957i	$0.851796\pi$
$108$	0	0
$109$	−7.10848	−0.680869	−0.340435	−	0.940268i	$-0.610574\pi$
$109$	−7.10848	−0.680869	−0.340435	+	0.940268i	$0.610574\pi$
$110$	0	0
$111$	13.9792	1.32685
$112$	0	0
$113$	8.16158	0.767777	0.383889	−	0.923379i	$-0.374585\pi$
$113$	8.16158	0.767777	0.383889	+	0.923379i	$0.374585\pi$
$114$	0	0
$115$	−4.40151	−0.410443
$116$	0	0
$117$	−1.20129	−0.111059
$118$	0	0
$119$	−1.66368	−0.152510
$120$	0	0
$121$	0	0
$122$	0	0
$123$	10.3641	0.934499
$124$	0	0
$125$	10.6401	0.951677
$126$	0	0
$127$	−1.76440	−0.156565	−0.0782827	−	0.996931i	$-0.524944\pi$
$127$	−1.76440	−0.156565	−0.0782827	+	0.996931i	$0.524944\pi$
$128$	0	0
$129$	−8.11672	−0.714637
$130$	0	0
$131$	−0.191800	−0.0167576	−0.00837882	−	0.999965i	$-0.502667\pi$
$131$	−0.191800	−0.0167576	−0.00837882	+	0.999965i	$0.502667\pi$
$132$	0	0
$133$	1.70655	0.147976
$134$	0	0
$135$	13.0087	1.11961
$136$	0	0
$137$	6.42852	0.549225	0.274613	−	0.961555i	$-0.411450\pi$
$137$	6.42852	0.549225	0.274613	+	0.961555i	$0.411450\pi$
$138$	0	0
$139$	−10.7179	−0.909078	−0.454539	−	0.890727i	$-0.650196\pi$
$139$	−10.7179	−0.909078	−0.454539	+	0.890727i	$0.650196\pi$
$140$	0	0
$141$	−5.24136	−0.441402
$142$	0	0
$143$	0	0
$144$	0	0
$145$	7.78197	0.646258
$146$	0	0
$147$	−6.32574	−0.521738
$148$	0	0
$149$	−14.2858	−1.17034	−0.585168	−	0.810912i	$-0.698972\pi$
$149$	−14.2858	−1.17034	−0.585168	+	0.810912i	$0.698972\pi$
$150$	0	0
$151$	14.1237	1.14937	0.574687	−	0.818374i	$-0.305124\pi$
$151$	14.1237	1.14937	0.574687	+	0.818374i	$0.305124\pi$
$152$	0	0
$153$	0.590023	0.0477005
$154$	0	0
$155$	13.1976	1.06006
$156$	0	0
$157$	0.969590	0.0773817	0.0386909	−	0.999251i	$-0.487681\pi$
$157$	0.969590	0.0773817	0.0386909	+	0.999251i	$0.487681\pi$
$158$	0	0
$159$	−11.4506	−0.908090
$160$	0	0
$161$	3.22145	0.253886
$162$	0	0
$163$	2.18257	0.170952	0.0854760	−	0.996340i	$-0.472759\pi$
$163$	2.18257	0.170952	0.0854760	+	0.996340i	$0.472759\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−12.1140	−0.937412	−0.468706	−	0.883354i	$-0.655280\pi$
$167$	−12.1140	−0.937412	−0.468706	+	0.883354i	$0.655280\pi$
$168$	0	0
$169$	−9.06033	−0.696948
$170$	0	0
$171$	−0.605224	−0.0462827
$172$	0	0
$173$	−3.05460	−0.232237	−0.116118	−	0.993235i	$-0.537045\pi$
$173$	−3.05460	−0.232237	−0.116118	+	0.993235i	$0.537045\pi$
$174$	0	0
$175$	0.745311	0.0563402
$176$	0	0
$177$	7.46344	0.560986
$178$	0	0
$179$	0.502462	0.0375558	0.0187779	−	0.999824i	$-0.494022\pi$
$179$	0.502462	0.0375558	0.0187779	+	0.999824i	$0.494022\pi$
$180$	0	0
$181$	−4.32279	−0.321311	−0.160655	−	0.987011i	$-0.551361\pi$
$181$	−4.32279	−0.321311	−0.160655	+	0.987011i	$0.551361\pi$
$182$	0	0
$183$	−0.920052	−0.0680122
$184$	0	0
$185$	−21.0629	−1.54858
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−9.52101	−0.692551
$190$	0	0
$191$	7.75241	0.560945	0.280472	−	0.959862i	$-0.409509\pi$
$191$	7.75241	0.560945	0.280472	+	0.959862i	$0.409509\pi$
$192$	0	0
$193$	−8.95673	−0.644720	−0.322360	−	0.946617i	$-0.604476\pi$
$193$	−8.95673	−0.644720	−0.322360	+	0.946617i	$0.604476\pi$
$194$	0	0
$195$	−7.16196	−0.512878
$196$	0	0
$197$	−2.53623	−0.180699	−0.0903494	−	0.995910i	$-0.528798\pi$
$197$	−2.53623	−0.180699	−0.0903494	+	0.995910i	$0.528798\pi$
$198$	0	0
$199$	13.0876	0.927756	0.463878	−	0.885899i	$-0.346458\pi$
$199$	13.0876	0.927756	0.463878	+	0.885899i	$0.346458\pi$
$200$	0	0
$201$	18.3472	1.29411
$202$	0	0
$203$	−5.69559	−0.399752
$204$	0	0
$205$	−15.6159	−1.09066
$206$	0	0
$207$	−1.14248	−0.0794080
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−15.4413	−1.06303	−0.531513	−	0.847050i	$-0.678376\pi$
$211$	−15.4413	−1.06303	−0.531513	+	0.847050i	$0.678376\pi$
$212$	0	0
$213$	−14.0686	−0.963964
$214$	0	0
$215$	12.2297	0.834061
$216$	0	0
$217$	−9.65925	−0.655713
$218$	0	0
$219$	1.10991	0.0750008
$220$	0	0
$221$	−1.93501	−0.130163
$222$	0	0
$223$	5.25235	0.351723	0.175862	−	0.984415i	$-0.443729\pi$
$223$	5.25235	0.351723	0.175862	+	0.984415i	$0.443729\pi$
$224$	0	0
$225$	−0.264323	−0.0176216
$226$	0	0
$227$	−20.2029	−1.34091	−0.670456	−	0.741949i	$-0.733901\pi$
$227$	−20.2029	−1.34091	−0.670456	+	0.741949i	$0.733901\pi$
$228$	0	0
$229$	4.06286	0.268481	0.134241	−	0.990949i	$-0.457140\pi$
$229$	4.06286	0.268481	0.134241	+	0.990949i	$0.457140\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−21.2259	−1.39055	−0.695276	−	0.718742i	$-0.744718\pi$
$233$	−21.2259	−1.39055	−0.695276	+	0.718742i	$0.744718\pi$
$234$	0	0
$235$	7.89734	0.515166
$236$	0	0
$237$	3.81235	0.247639
$238$	0	0
$239$	21.4992	1.39067	0.695333	−	0.718688i	$-0.255257\pi$
$239$	21.4992	1.39067	0.695333	+	0.718688i	$0.255257\pi$
$240$	0	0
$241$	−20.7994	−1.33981	−0.669903	−	0.742449i	$-0.733664\pi$
$241$	−20.7994	−1.33981	−0.669903	+	0.742449i	$0.733664\pi$
$242$	0	0
$243$	6.18638	0.396856
$244$	0	0
$245$	9.53121	0.608927
$246$	0	0
$247$	1.98486	0.126294
$248$	0	0
$249$	−8.30803	−0.526500
$250$	0	0
$251$	−9.39204	−0.592820	−0.296410	−	0.955061i	$-0.595789\pi$
$251$	−9.39204	−0.592820	−0.296410	+	0.955061i	$0.595789\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	3.51766	0.220284
$256$	0	0
$257$	−14.7053	−0.917293	−0.458647	−	0.888619i	$-0.651666\pi$
$257$	−14.7053	−0.917293	−0.458647	+	0.888619i	$0.651666\pi$
$258$	0	0
$259$	15.4159	0.957895
$260$	0	0
$261$	2.01993	0.125031
$262$	0	0
$263$	1.07683	0.0664003	0.0332002	−	0.999449i	$-0.489430\pi$
$263$	1.07683	0.0664003	0.0332002	+	0.999449i	$0.489430\pi$
$264$	0	0
$265$	17.2530	1.05984
$266$	0	0
$267$	−12.6985	−0.777135
$268$	0	0
$269$	−1.45919	−0.0889682	−0.0444841	−	0.999010i	$-0.514164\pi$
$269$	−1.45919	−0.0889682	−0.0444841	+	0.999010i	$0.514164\pi$
$270$	0	0
$271$	13.1604	0.799439	0.399720	−	0.916637i	$-0.369107\pi$
$271$	13.1604	0.799439	0.399720	+	0.916637i	$0.369107\pi$
$272$	0	0
$273$	5.24180	0.317248
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−30.2766	−1.81914	−0.909572	−	0.415547i	$-0.863590\pi$
$277$	−30.2766	−1.81914	−0.909572	+	0.415547i	$0.863590\pi$
$278$	0	0
$279$	3.42564	0.205088
$280$	0	0
$281$	−8.38489	−0.500200	−0.250100	−	0.968220i	$-0.580464\pi$
$281$	−8.38489	−0.500200	−0.250100	+	0.968220i	$0.580464\pi$
$282$	0	0
$283$	−0.662916	−0.0394063	−0.0197031	−	0.999806i	$-0.506272\pi$
$283$	−0.662916	−0.0394063	−0.0197031	+	0.999806i	$0.506272\pi$
$284$	0	0
$285$	−3.60829	−0.213737
$286$	0	0
$287$	11.4292	0.674647
$288$	0	0
$289$	−16.0496	−0.944094
$290$	0	0
$291$	9.52207	0.558194
$292$	0	0
$293$	0.204708	0.0119592	0.00597958	−	0.999982i	$-0.498097\pi$
$293$	0.204708	0.0119592	0.00597958	+	0.999982i	$0.498097\pi$
$294$	0	0
$295$	−11.2454	−0.654734
$296$	0	0
$297$	0	0
$298$	0	0
$299$	3.74682	0.216684
$300$	0	0
$301$	−8.95089	−0.515921
$302$	0	0
$303$	−4.81245	−0.276468
$304$	0	0
$305$	1.38627	0.0793778
$306$	0	0
$307$	16.8710	0.962881	0.481440	−	0.876479i	$-0.340114\pi$
$307$	16.8710	0.962881	0.481440	+	0.876479i	$0.340114\pi$
$308$	0	0
$309$	−17.2326	−0.980331
$310$	0	0
$311$	−22.5555	−1.27901	−0.639504	−	0.768788i	$-0.720860\pi$
$311$	−22.5555	−1.27901	−0.639504	+	0.768788i	$0.720860\pi$
$312$	0	0
$313$	33.7849	1.90964	0.954819	−	0.297188i	$-0.0960489\pi$
$313$	33.7849	1.90964	0.954819	+	0.297188i	$0.0960489\pi$
$314$	0	0
$315$	2.40826	0.135690
$316$	0	0
$317$	12.1600	0.682972	0.341486	−	0.939887i	$-0.389070\pi$
$317$	12.1600	0.682972	0.341486	+	0.939887i	$0.389070\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−28.6072	−1.59670
$322$	0	0
$323$	−0.974883	−0.0542439
$324$	0	0
$325$	0.866861	0.0480848
$326$	0	0
$327$	−11.0004	−0.608325
$328$	0	0
$329$	−5.78003	−0.318663
$330$	0	0
$331$	3.88967	0.213796	0.106898	−	0.994270i	$-0.465908\pi$
$331$	3.88967	0.213796	0.106898	+	0.994270i	$0.465908\pi$
$332$	0	0
$333$	−5.46722	−0.299602
$334$	0	0
$335$	−27.6444	−1.51037
$336$	0	0
$337$	−1.16645	−0.0635408	−0.0317704	−	0.999495i	$-0.510115\pi$
$337$	−1.16645	−0.0635408	−0.0317704	+	0.999495i	$0.510115\pi$
$338$	0	0
$339$	12.6301	0.685973
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−18.9217	−1.02167
$344$	0	0
$345$	−6.81137	−0.366712
$346$	0	0
$347$	14.7592	0.792318	0.396159	−	0.918182i	$-0.370343\pi$
$347$	14.7592	0.792318	0.396159	+	0.918182i	$0.370343\pi$
$348$	0	0
$349$	−5.83928	−0.312570	−0.156285	−	0.987712i	$-0.549952\pi$
$349$	−5.83928	−0.312570	−0.156285	+	0.987712i	$0.549952\pi$
$350$	0	0
$351$	−11.0738	−0.591073
$352$	0	0
$353$	1.93898	0.103202	0.0516008	−	0.998668i	$-0.483568\pi$
$353$	1.93898	0.103202	0.0516008	+	0.998668i	$0.483568\pi$
$354$	0	0
$355$	21.1976	1.12505
$356$	0	0
$357$	−2.57456	−0.136260
$358$	0	0
$359$	−16.3567	−0.863273	−0.431637	−	0.902048i	$-0.642064\pi$
$359$	−16.3567	−0.863273	−0.431637	+	0.902048i	$0.642064\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−1.67234	−0.0875343
$366$	0	0
$367$	−21.7981	−1.13785	−0.568925	−	0.822390i	$-0.692640\pi$
$367$	−21.7981	−1.13785	−0.568925	+	0.822390i	$0.692640\pi$
$368$	0	0
$369$	−4.05336	−0.211010
$370$	0	0
$371$	−12.6274	−0.655581
$372$	0	0
$373$	−26.9769	−1.39681	−0.698405	−	0.715703i	$-0.746106\pi$
$373$	−26.9769	−1.39681	−0.698405	+	0.715703i	$0.746106\pi$
$374$	0	0
$375$	16.4656	0.850279
$376$	0	0
$377$	−6.62446	−0.341177
$378$	0	0
$379$	4.81784	0.247476	0.123738	−	0.992315i	$-0.460512\pi$
$379$	4.81784	0.247476	0.123738	+	0.992315i	$0.460512\pi$
$380$	0	0
$381$	−2.73042	−0.139884
$382$	0	0
$383$	3.61641	0.184790	0.0923948	−	0.995722i	$-0.470548\pi$
$383$	3.61641	0.184790	0.0923948	+	0.995722i	$0.470548\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	3.17442	0.161365
$388$	0	0
$389$	−24.5504	−1.24475	−0.622377	−	0.782718i	$-0.713833\pi$
$389$	−24.5504	−1.24475	−0.622377	+	0.782718i	$0.713833\pi$
$390$	0	0
$391$	−1.84029	−0.0930672
$392$	0	0
$393$	−0.296812	−0.0149722
$394$	0	0
$395$	−5.74420	−0.289022
$396$	0	0
$397$	−11.4961	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$397$	−11.4961	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$398$	0	0
$399$	2.64089	0.132210
$400$	0	0
$401$	5.07574	0.253470	0.126735	−	0.991937i	$-0.459550\pi$
$401$	5.07574	0.253470	0.126735	+	0.991937i	$0.459550\pi$
$402$	0	0
$403$	−11.2345	−0.559632
$404$	0	0
$405$	15.8975	0.789952
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−7.82454	−0.386899	−0.193449	−	0.981110i	$-0.561968\pi$
$409$	−7.82454	−0.386899	−0.193449	+	0.981110i	$0.561968\pi$
$410$	0	0
$411$	9.94817	0.490707
$412$	0	0
$413$	8.23047	0.404995
$414$	0	0
$415$	12.5180	0.614485
$416$	0	0
$417$	−16.5860	−0.812219
$418$	0	0
$419$	17.5591	0.857820	0.428910	−	0.903347i	$-0.358898\pi$
$419$	17.5591	0.857820	0.428910	+	0.903347i	$0.358898\pi$
$420$	0	0
$421$	26.2628	1.27997	0.639985	−	0.768387i	$-0.278940\pi$
$421$	26.2628	1.27997	0.639985	+	0.768387i	$0.278940\pi$
$422$	0	0
$423$	2.04988	0.0996685
$424$	0	0
$425$	−0.425767	−0.0206527
$426$	0	0
$427$	−1.01461	−0.0491003
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−37.9010	−1.82563	−0.912814	−	0.408375i	$-0.866096\pi$
$431$	−37.9010	−1.82563	−0.912814	+	0.408375i	$0.866096\pi$
$432$	0	0
$433$	−20.4689	−0.983670	−0.491835	−	0.870688i	$-0.663674\pi$
$433$	−20.4689	−0.983670	−0.491835	+	0.870688i	$0.663674\pi$
$434$	0	0
$435$	12.0427	0.577401
$436$	0	0
$437$	1.88770	0.0903009
$438$	0	0
$439$	−0.403662	−0.0192657	−0.00963287	−	0.999954i	$-0.503066\pi$
$439$	−0.403662	−0.0192657	−0.00963287	+	0.999954i	$0.503066\pi$
$440$	0	0
$441$	2.47397	0.117808
$442$	0	0
$443$	−7.64307	−0.363133	−0.181567	−	0.983379i	$-0.558117\pi$
$443$	−7.64307	−0.363133	−0.181567	+	0.983379i	$0.558117\pi$
$444$	0	0
$445$	19.1332	0.907003
$446$	0	0
$447$	−22.1073	−1.04564
$448$	0	0
$449$	−0.648123	−0.0305868	−0.0152934	−	0.999883i	$-0.504868\pi$
$449$	−0.648123	−0.0305868	−0.0152934	+	0.999883i	$0.504868\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	21.8566	1.02691
$454$	0	0
$455$	−7.89801	−0.370264
$456$	0	0
$457$	−1.32011	−0.0617520	−0.0308760	−	0.999523i	$-0.509830\pi$
$457$	−1.32011	−0.0617520	−0.0308760	+	0.999523i	$0.509830\pi$
$458$	0	0
$459$	5.43898	0.253870
$460$	0	0
$461$	−1.04039	−0.0484557	−0.0242279	−	0.999706i	$-0.507713\pi$
$461$	−1.04039	−0.0484557	−0.0242279	+	0.999706i	$0.507713\pi$
$462$	0	0
$463$	18.9585	0.881077	0.440539	−	0.897734i	$-0.354787\pi$
$463$	18.9585	0.881077	0.440539	+	0.897734i	$0.354787\pi$
$464$	0	0
$465$	20.4233	0.947110
$466$	0	0
$467$	−21.0562	−0.974363	−0.487181	−	0.873301i	$-0.661975\pi$
$467$	−21.0562	−0.974363	−0.487181	+	0.873301i	$0.661975\pi$
$468$	0	0
$469$	20.2328	0.934263
$470$	0	0
$471$	1.50045	0.0691370
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0.436736	0.0200388
$476$	0	0
$477$	4.47828	0.205046
$478$	0	0
$479$	24.4224	1.11589	0.557944	−	0.829878i	$-0.311590\pi$
$479$	24.4224	1.11589	0.557944	+	0.829878i	$0.311590\pi$
$480$	0	0
$481$	17.9300	0.817537
$482$	0	0
$483$	4.98521	0.226835
$484$	0	0
$485$	−14.3472	−0.651474
$486$	0	0
$487$	14.3373	0.649686	0.324843	−	0.945768i	$-0.394688\pi$
$487$	14.3373	0.649686	0.324843	+	0.945768i	$0.394688\pi$
$488$	0	0
$489$	3.37754	0.152738
$490$	0	0
$491$	−18.2947	−0.825628	−0.412814	−	0.910815i	$-0.635454\pi$
$491$	−18.2947	−0.825628	−0.412814	+	0.910815i	$0.635454\pi$
$492$	0	0
$493$	3.25367	0.146538
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−15.5145	−0.695919
$498$	0	0
$499$	−8.22939	−0.368398	−0.184199	−	0.982889i	$-0.558969\pi$
$499$	−8.22939	−0.368398	−0.184199	+	0.982889i	$0.558969\pi$
$500$	0	0
$501$	−18.7465	−0.837534
$502$	0	0
$503$	−23.4861	−1.04719	−0.523596	−	0.851966i	$-0.675410\pi$
$503$	−23.4861	−1.04719	−0.523596	+	0.851966i	$0.675410\pi$
$504$	0	0
$505$	7.25109	0.322669
$506$	0	0
$507$	−14.0209	−0.622691
$508$	0	0
$509$	−6.87306	−0.304643	−0.152322	−	0.988331i	$-0.548675\pi$
$509$	−6.87306	−0.304643	−0.152322	+	0.988331i	$0.548675\pi$
$510$	0	0
$511$	1.22398	0.0541456
$512$	0	0
$513$	−5.57911	−0.246324
$514$	0	0
$515$	25.9650	1.14416
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−4.72701	−0.207493
$520$	0	0
$521$	−15.1088	−0.661930	−0.330965	−	0.943643i	$-0.607374\pi$
$521$	−15.1088	−0.661930	−0.330965	+	0.943643i	$0.607374\pi$
$522$	0	0
$523$	18.5541	0.811315	0.405657	−	0.914025i	$-0.367043\pi$
$523$	18.5541	0.811315	0.405657	+	0.914025i	$0.367043\pi$
$524$	0	0
$525$	1.15337	0.0503373
$526$	0	0
$527$	5.51795	0.240366
$528$	0	0
$529$	−19.4366	−0.845069
$530$	0	0
$531$	−2.91893	−0.126671
$532$	0	0
$533$	13.2932	0.575792
$534$	0	0
$535$	43.1034	1.86352
$536$	0	0
$537$	0.777563	0.0335543
$538$	0	0
$539$	0	0
$540$	0	0
$541$	31.7786	1.36627	0.683134	−	0.730293i	$-0.260617\pi$
$541$	31.7786	1.36627	0.683134	+	0.730293i	$0.260617\pi$
$542$	0	0
$543$	−6.68955	−0.287076
$544$	0	0
$545$	16.5747	0.709983
$546$	0	0
$547$	25.3977	1.08593	0.542965	−	0.839756i	$-0.317302\pi$
$547$	25.3977	1.08593	0.542965	+	0.839756i	$0.317302\pi$
$548$	0	0
$549$	0.359829	0.0153571
$550$	0	0
$551$	−3.33750	−0.142182
$552$	0	0
$553$	4.20415	0.178779
$554$	0	0
$555$	−32.5950	−1.38358
$556$	0	0
$557$	−9.64055	−0.408483	−0.204242	−	0.978920i	$-0.565473\pi$
$557$	−9.64055	−0.408483	−0.204242	+	0.978920i	$0.565473\pi$
$558$	0	0
$559$	−10.4107	−0.440324
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−33.8442	−1.42636	−0.713182	−	0.700979i	$-0.752746\pi$
$563$	−33.8442	−1.42636	−0.713182	+	0.700979i	$0.752746\pi$
$564$	0	0
$565$	−19.0302	−0.800607
$566$	0	0
$567$	−11.6353	−0.488636
$568$	0	0
$569$	21.3576	0.895356	0.447678	−	0.894195i	$-0.352251\pi$
$569$	21.3576	0.895356	0.447678	+	0.894195i	$0.352251\pi$
$570$	0	0
$571$	−15.9134	−0.665955	−0.332977	−	0.942935i	$-0.608053\pi$
$571$	−15.9134	−0.665955	−0.332977	+	0.942935i	$0.608053\pi$
$572$	0	0
$573$	11.9969	0.501178
$574$	0	0
$575$	0.824427	0.0343810
$576$	0	0
$577$	18.3662	0.764594	0.382297	−	0.924040i	$-0.375133\pi$
$577$	18.3662	0.764594	0.382297	+	0.924040i	$0.375133\pi$
$578$	0	0
$579$	−13.8606	−0.576027
$580$	0	0
$581$	−9.16187	−0.380098
$582$	0	0
$583$	0	0
$584$	0	0
$585$	2.80102	0.115808
$586$	0	0
$587$	−14.1957	−0.585918	−0.292959	−	0.956125i	$-0.594640\pi$
$587$	−14.1957	−0.585918	−0.292959	+	0.956125i	$0.594640\pi$
$588$	0	0
$589$	−5.66011	−0.233221
$590$	0	0
$591$	−3.92483	−0.161446
$592$	0	0
$593$	−41.7669	−1.71516	−0.857581	−	0.514348i	$-0.828034\pi$
$593$	−41.7669	−1.71516	−0.857581	+	0.514348i	$0.828034\pi$
$594$	0	0
$595$	3.87918	0.159031
$596$	0	0
$597$	20.2532	0.828906
$598$	0	0
$599$	17.7582	0.725582	0.362791	−	0.931870i	$-0.381824\pi$
$599$	17.7582	0.725582	0.362791	+	0.931870i	$0.381824\pi$
$600$	0	0
$601$	18.8268	0.767960	0.383980	−	0.923341i	$-0.374553\pi$
$601$	18.8268	0.767960	0.383980	+	0.923341i	$0.374553\pi$
$602$	0	0
$603$	−7.17553	−0.292210
$604$	0	0
$605$	0	0
$606$	0	0
$607$	14.3913	0.584124	0.292062	−	0.956399i	$-0.405659\pi$
$607$	14.3913	0.584124	0.292062	+	0.956399i	$0.405659\pi$
$608$	0	0
$609$	−8.81396	−0.357160
$610$	0	0
$611$	−6.72267	−0.271970
$612$	0	0
$613$	44.5077	1.79765	0.898824	−	0.438309i	$-0.144422\pi$
$613$	44.5077	1.79765	0.898824	+	0.438309i	$0.144422\pi$
$614$	0	0
$615$	−24.1658	−0.974458
$616$	0	0
$617$	33.9511	1.36682	0.683410	−	0.730035i	$-0.260496\pi$
$617$	33.9511	1.36682	0.683410	+	0.730035i	$0.260496\pi$
$618$	0	0
$619$	−17.0993	−0.687278	−0.343639	−	0.939102i	$-0.611660\pi$
$619$	−17.0993	−0.687278	−0.343639	+	0.939102i	$0.611660\pi$
$620$	0	0
$621$	−10.5317	−0.422622
$622$	0	0
$623$	−14.0035	−0.561040
$624$	0	0
$625$	−26.9929	−1.07972
$626$	0	0
$627$	0	0
$628$	0	0
$629$	−8.80647	−0.351137
$630$	0	0
$631$	−12.4644	−0.496200	−0.248100	−	0.968734i	$-0.579806\pi$
$631$	−12.4644	−0.496200	−0.248100	+	0.968734i	$0.579806\pi$
$632$	0	0
$633$	−23.8956	−0.949764
$634$	0	0
$635$	4.11402	0.163260
$636$	0	0
$637$	−8.11351	−0.321469
$638$	0	0
$639$	5.50218	0.217663
$640$	0	0
$641$	12.6736	0.500577	0.250288	−	0.968171i	$-0.419475\pi$
$641$	12.6736	0.500577	0.250288	+	0.968171i	$0.419475\pi$
$642$	0	0
$643$	−14.6862	−0.579166	−0.289583	−	0.957153i	$-0.593517\pi$
$643$	−14.6862	−0.579166	−0.289583	+	0.957153i	$0.593517\pi$
$644$	0	0
$645$	18.9256	0.745195
$646$	0	0
$647$	12.6505	0.497342	0.248671	−	0.968588i	$-0.420006\pi$
$647$	12.6505	0.497342	0.248671	+	0.968588i	$0.420006\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−14.9478	−0.585849
$652$	0	0
$653$	−27.2000	−1.06442	−0.532210	−	0.846613i	$-0.678638\pi$
$653$	−27.2000	−1.06442	−0.532210	+	0.846613i	$0.678638\pi$
$654$	0	0
$655$	0.447216	0.0174742
$656$	0	0
$657$	−0.434082	−0.0169352
$658$	0	0
$659$	−7.36076	−0.286734	−0.143367	−	0.989670i	$-0.545793\pi$
$659$	−7.36076	−0.286734	−0.143367	+	0.989670i	$0.545793\pi$
$660$	0	0
$661$	−26.7185	−1.03923	−0.519614	−	0.854401i	$-0.673924\pi$
$661$	−26.7185	−1.03923	−0.519614	+	0.854401i	$0.673924\pi$
$662$	0	0
$663$	−2.99444	−0.116294
$664$	0	0
$665$	−3.97912	−0.154304
$666$	0	0
$667$	−6.30019	−0.243944
$668$	0	0
$669$	8.12804	0.314248
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−46.9256	−1.80885	−0.904424	−	0.426636i	$-0.859699\pi$
$673$	−46.9256	−1.80885	−0.904424	+	0.426636i	$0.859699\pi$
$674$	0	0
$675$	−2.43660	−0.0937847
$676$	0	0
$677$	15.4570	0.594059	0.297029	−	0.954868i	$-0.404004\pi$
$677$	15.4570	0.594059	0.297029	+	0.954868i	$0.404004\pi$
$678$	0	0
$679$	10.5007	0.402979
$680$	0	0
$681$	−31.2641	−1.19804
$682$	0	0
$683$	−2.03010	−0.0776794	−0.0388397	−	0.999245i	$-0.512366\pi$
$683$	−2.03010	−0.0776794	−0.0388397	+	0.999245i	$0.512366\pi$
$684$	0	0
$685$	−14.9893	−0.572710
$686$	0	0
$687$	6.28730	0.239876
$688$	0	0
$689$	−14.6867	−0.559520
$690$	0	0
$691$	34.2177	1.30170	0.650852	−	0.759205i	$-0.274412\pi$
$691$	34.2177	1.30170	0.650852	+	0.759205i	$0.274412\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	24.9907	0.947950
$696$	0	0
$697$	−6.52907	−0.247306
$698$	0	0
$699$	−32.8472	−1.24239
$700$	0	0
$701$	−14.9584	−0.564969	−0.282485	−	0.959272i	$-0.591159\pi$
$701$	−14.9584	−0.564969	−0.282485	+	0.959272i	$0.591159\pi$
$702$	0	0
$703$	9.03337	0.340700
$704$	0	0
$705$	12.2212	0.460276
$706$	0	0
$707$	−5.30704	−0.199592
$708$	0	0
$709$	35.3086	1.32604	0.663022	−	0.748600i	$-0.269274\pi$
$709$	35.3086	1.32604	0.663022	+	0.748600i	$0.269274\pi$
$710$	0	0
$711$	−1.49100	−0.0559167
$712$	0	0
$713$	−10.6846	−0.400141
$714$	0	0
$715$	0	0
$716$	0	0
$717$	33.2701	1.24249
$718$	0	0
$719$	−13.5406	−0.504981	−0.252490	−	0.967599i	$-0.581250\pi$
$719$	−13.5406	−0.504981	−0.252490	+	0.967599i	$0.581250\pi$
$720$	0	0
$721$	−19.0037	−0.707734
$722$	0	0
$723$	−32.1872	−1.19705
$724$	0	0
$725$	−1.45760	−0.0541341
$726$	0	0
$727$	−3.90918	−0.144983	−0.0724917	−	0.997369i	$-0.523095\pi$
$727$	−3.90918	−0.144983	−0.0724917	+	0.997369i	$0.523095\pi$
$728$	0	0
$729$	30.0275	1.11213
$730$	0	0
$731$	5.11329	0.189122
$732$	0	0
$733$	22.0297	0.813685	0.406842	−	0.913498i	$-0.366630\pi$
$733$	22.0297	0.813685	0.406842	+	0.913498i	$0.366630\pi$
$734$	0	0
$735$	14.7496	0.544047
$736$	0	0
$737$	0	0
$738$	0	0
$739$	36.1464	1.32967	0.664834	−	0.746991i	$-0.268502\pi$
$739$	36.1464	1.32967	0.664834	+	0.746991i	$0.268502\pi$
$740$	0	0
$741$	3.07158	0.112837
$742$	0	0
$743$	−32.4389	−1.19007	−0.595034	−	0.803700i	$-0.702862\pi$
$743$	−32.4389	−1.19007	−0.595034	+	0.803700i	$0.702862\pi$
$744$	0	0
$745$	33.3099	1.22038
$746$	0	0
$747$	3.24924	0.118884
$748$	0	0
$749$	−31.5472	−1.15271
$750$	0	0
$751$	7.97727	0.291095	0.145547	−	0.989351i	$-0.453506\pi$
$751$	7.97727	0.291095	0.145547	+	0.989351i	$0.453506\pi$
$752$	0	0
$753$	−14.5342	−0.529657
$754$	0	0
$755$	−32.9320	−1.19852
$756$	0	0
$757$	−32.0088	−1.16338	−0.581690	−	0.813411i	$-0.697608\pi$
$757$	−32.0088	−1.16338	−0.581690	+	0.813411i	$0.697608\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−16.6416	−0.603258	−0.301629	−	0.953425i	$-0.597530\pi$
$761$	−16.6416	−0.603258	−0.301629	+	0.953425i	$0.597530\pi$
$762$	0	0
$763$	−12.1310	−0.439170
$764$	0	0
$765$	−1.37575	−0.0497402
$766$	0	0
$767$	9.57275	0.345652
$768$	0	0
$769$	−33.5772	−1.21083	−0.605413	−	0.795911i	$-0.706992\pi$
$769$	−33.5772	−1.21083	−0.605413	+	0.795911i	$0.706992\pi$
$770$	0	0
$771$	−22.7566	−0.819559
$772$	0	0
$773$	−51.9249	−1.86761	−0.933805	−	0.357783i	$-0.883533\pi$
$773$	−51.9249	−1.86761	−0.933805	+	0.357783i	$0.883533\pi$
$774$	0	0
$775$	−2.47198	−0.0887960
$776$	0	0
$777$	23.8561	0.855834
$778$	0	0
$779$	6.69729	0.239955
$780$	0	0
$781$	0	0
$782$	0	0
$783$	18.6202	0.665433
$784$	0	0
$785$	−2.26078	−0.0806905
$786$	0	0
$787$	31.5694	1.12533	0.562664	−	0.826685i	$-0.309776\pi$
$787$	31.5694	1.12533	0.562664	+	0.826685i	$0.309776\pi$
$788$	0	0
$789$	1.66641	0.0593256
$790$	0	0
$791$	13.9281	0.495227
$792$	0	0
$793$	−1.18008	−0.0419057
$794$	0	0
$795$	26.6991	0.946919
$796$	0	0
$797$	10.0915	0.357459	0.178730	−	0.983898i	$-0.442801\pi$
$797$	10.0915	0.357459	0.178730	+	0.983898i	$0.442801\pi$
$798$	0	0
$799$	3.30190	0.116813
$800$	0	0
$801$	4.96633	0.175477
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−7.51139	−0.264742
$806$	0	0
$807$	−2.25810	−0.0794890
$808$	0	0
$809$	40.4288	1.42140	0.710700	−	0.703495i	$-0.248378\pi$
$809$	40.4288	1.42140	0.710700	+	0.703495i	$0.248378\pi$
$810$	0	0
$811$	18.7913	0.659852	0.329926	−	0.944007i	$-0.392976\pi$
$811$	18.7913	0.659852	0.329926	+	0.944007i	$0.392976\pi$
$812$	0	0
$813$	20.3659	0.714262
$814$	0	0
$815$	−5.08905	−0.178262
$816$	0	0
$817$	−5.24503	−0.183500
$818$	0	0
$819$	−2.05005	−0.0716346
$820$	0	0
$821$	19.2131	0.670543	0.335272	−	0.942122i	$-0.391172\pi$
$821$	19.2131	0.670543	0.335272	+	0.942122i	$0.391172\pi$
$822$	0	0
$823$	19.8905	0.693339	0.346669	−	0.937987i	$-0.387313\pi$
$823$	19.8905	0.693339	0.346669	+	0.937987i	$0.387313\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−16.5661	−0.576059	−0.288030	−	0.957622i	$-0.593000\pi$
$827$	−16.5661	−0.576059	−0.288030	+	0.957622i	$0.593000\pi$
$828$	0	0
$829$	8.65197	0.300495	0.150248	−	0.988648i	$-0.451993\pi$
$829$	8.65197	0.300495	0.150248	+	0.988648i	$0.451993\pi$
$830$	0	0
$831$	−46.8532	−1.62532
$832$	0	0
$833$	3.98503	0.138073
$834$	0	0
$835$	28.2461	0.977495
$836$	0	0
$837$	31.5784	1.09151
$838$	0	0
$839$	15.3559	0.530143	0.265072	−	0.964229i	$-0.414604\pi$
$839$	15.3559	0.530143	0.265072	+	0.964229i	$0.414604\pi$
$840$	0	0
$841$	−17.8611	−0.615901
$842$	0	0
$843$	−12.9757	−0.446906
$844$	0	0
$845$	21.1258	0.726749
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−1.02587	−0.0352077
$850$	0	0
$851$	17.0523	0.584545
$852$	0	0
$853$	31.4195	1.07578	0.537892	−	0.843014i	$-0.319221\pi$
$853$	31.4195	1.07578	0.537892	+	0.843014i	$0.319221\pi$
$854$	0	0
$855$	1.41119	0.0482617
$856$	0	0
$857$	16.8414	0.575293	0.287646	−	0.957737i	$-0.407127\pi$
$857$	16.8414	0.575293	0.287646	+	0.957737i	$0.407127\pi$
$858$	0	0
$859$	1.05850	0.0361156	0.0180578	−	0.999837i	$-0.494252\pi$
$859$	1.05850	0.0361156	0.0180578	+	0.999837i	$0.494252\pi$
$860$	0	0
$861$	17.6868	0.602765
$862$	0	0
$863$	−28.6249	−0.974403	−0.487201	−	0.873290i	$-0.661982\pi$
$863$	−28.6249	−0.974403	−0.487201	+	0.873290i	$0.661982\pi$
$864$	0	0
$865$	7.12234	0.242167
$866$	0	0
$867$	−24.8369	−0.843504
$868$	0	0
$869$	0	0
$870$	0	0
$871$	23.5325	0.797367
$872$	0	0
$873$	−3.72405	−0.126040
$874$	0	0
$875$	18.1578	0.613845
$876$	0	0
$877$	29.3894	0.992408	0.496204	−	0.868206i	$-0.334727\pi$
$877$	29.3894	0.992408	0.496204	+	0.868206i	$0.334727\pi$
$878$	0	0
$879$	0.316787	0.0106850
$880$	0	0
$881$	31.8789	1.07403	0.537013	−	0.843574i	$-0.319553\pi$
$881$	31.8789	1.07403	0.537013	+	0.843574i	$0.319553\pi$
$882$	0	0
$883$	12.7766	0.429965	0.214983	−	0.976618i	$-0.431031\pi$
$883$	12.7766	0.429965	0.214983	+	0.976618i	$0.431031\pi$
$884$	0	0
$885$	−17.4024	−0.584974
$886$	0	0
$887$	39.7247	1.33382	0.666912	−	0.745137i	$-0.267616\pi$
$887$	39.7247	1.33382	0.666912	+	0.745137i	$0.267616\pi$
$888$	0	0
$889$	−3.01103	−0.100987
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−3.38697	−0.113341
$894$	0	0
$895$	−1.17158	−0.0391616
$896$	0	0
$897$	5.79823	0.193597
$898$	0	0
$899$	18.8906	0.630037
$900$	0	0
$901$	7.21352	0.240317
$902$	0	0
$903$	−13.8516	−0.460951
$904$	0	0
$905$	10.0794	0.335050
$906$	0	0
$907$	10.5139	0.349109	0.174554	−	0.984648i	$-0.444152\pi$
$907$	10.5139	0.349109	0.174554	+	0.984648i	$0.444152\pi$
$908$	0	0
$909$	1.88213	0.0624265
$910$	0	0
$911$	−2.69026	−0.0891322	−0.0445661	−	0.999006i	$-0.514191\pi$
$911$	−2.69026	−0.0891322	−0.0445661	+	0.999006i	$0.514191\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	2.14527	0.0709204
$916$	0	0
$917$	−0.327316	−0.0108089
$918$	0	0
$919$	36.8553	1.21575	0.607873	−	0.794035i	$-0.292023\pi$
$919$	36.8553	1.21575	0.607873	+	0.794035i	$0.292023\pi$
$920$	0	0
$921$	26.1080	0.860289
$922$	0	0
$923$	−18.0447	−0.593947
$924$	0	0
$925$	3.94520	0.129717
$926$	0	0
$927$	6.73963	0.221358
$928$	0	0
$929$	59.6049	1.95557	0.977786	−	0.209606i	$-0.0672182\pi$
$929$	59.6049	1.95557	0.977786	+	0.209606i	$0.0672182\pi$
$930$	0	0
$931$	−4.08770	−0.133969
$932$	0	0
$933$	−34.9048	−1.14273
$934$	0	0
$935$	0	0
$936$	0	0
$937$	16.1224	0.526697	0.263348	−	0.964701i	$-0.415173\pi$
$937$	16.1224	0.526697	0.263348	+	0.964701i	$0.415173\pi$
$938$	0	0
$939$	52.2824	1.70617
$940$	0	0
$941$	32.1194	1.04706	0.523531	−	0.852007i	$-0.324615\pi$
$941$	32.1194	1.04706	0.523531	+	0.852007i	$0.324615\pi$
$942$	0	0
$943$	12.6425	0.411696
$944$	0	0
$945$	22.2000	0.722165
$946$	0	0
$947$	48.0137	1.56024	0.780118	−	0.625632i	$-0.215159\pi$
$947$	48.0137	1.56024	0.780118	+	0.625632i	$0.215159\pi$
$948$	0	0
$949$	1.42359	0.0462118
$950$	0	0
$951$	18.8176	0.610204
$952$	0	0
$953$	−2.47665	−0.0802265	−0.0401132	−	0.999195i	$-0.512772\pi$
$953$	−2.47665	−0.0802265	−0.0401132	+	0.999195i	$0.512772\pi$
$954$	0	0
$955$	−18.0761	−0.584930
$956$	0	0
$957$	0	0
$958$	0	0
$959$	10.9706	0.354258
$960$	0	0
$961$	1.03690	0.0334484
$962$	0	0
$963$	11.1882	0.360534
$964$	0	0
$965$	20.8842	0.672288
$966$	0	0
$967$	13.2766	0.426946	0.213473	−	0.976949i	$-0.431522\pi$
$967$	13.2766	0.426946	0.213473	+	0.976949i	$0.431522\pi$
$968$	0	0
$969$	−1.50864	−0.0484644
$970$	0	0
$971$	−3.07763	−0.0987657	−0.0493828	−	0.998780i	$-0.515725\pi$
$971$	−3.07763	−0.0987657	−0.0493828	+	0.998780i	$0.515725\pi$
$972$	0	0
$973$	−18.2906	−0.586368
$974$	0	0
$975$	1.34147	0.0429615
$976$	0	0
$977$	−34.8148	−1.11382	−0.556911	−	0.830572i	$-0.688014\pi$
$977$	−34.8148	−1.11382	−0.556911	+	0.830572i	$0.688014\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	4.30223	0.137360
$982$	0	0
$983$	25.9516	0.827727	0.413864	−	0.910339i	$-0.364179\pi$
$983$	25.9516	0.827727	0.413864	+	0.910339i	$0.364179\pi$
$984$	0	0
$985$	5.91367	0.188425
$986$	0	0
$987$	−8.94463	−0.284711
$988$	0	0
$989$	−9.90104	−0.314835
$990$	0	0
$991$	24.5129	0.778678	0.389339	−	0.921095i	$-0.372703\pi$
$991$	24.5129	0.778678	0.389339	+	0.921095i	$0.372703\pi$
$992$	0	0
$993$	6.01930	0.191017
$994$	0	0
$995$	−30.5161	−0.967426
$996$	0	0
$997$	35.7909	1.13351	0.566754	−	0.823887i	$-0.308199\pi$
$997$	35.7909	1.13351	0.566754	+	0.823887i	$0.308199\pi$
$998$	0	0
$999$	−50.3981	−1.59453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9196.2.a.u.1.11	✓	14
11.10	odd	2		9196.2.a.v.1.11	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9196.2.a.u.1.11	✓	14	1.1	even	1	trivial
9196.2.a.v.1.11	yes	14	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9196.a (trivial)

\(f(q)\)	\(=\)	\(q+1.54751 q^{3} -2.33168 q^{5} +1.70655 q^{7} -0.605224 q^{9} +1.98486 q^{13} -3.60829 q^{15} -0.974883 q^{17} +1.00000 q^{19} +2.64089 q^{21} +1.88770 q^{23} +0.436736 q^{25} -5.57911 q^{27} -3.33750 q^{29} -5.66011 q^{31} -3.97912 q^{35} +9.03337 q^{37} +3.07158 q^{39} +6.69729 q^{41} -5.24503 q^{43} +1.41119 q^{45} -3.38697 q^{47} -4.08770 q^{49} -1.50864 q^{51} -7.39938 q^{53} +1.54751 q^{57} +4.82288 q^{59} -0.594539 q^{61} -1.03284 q^{63} -4.62806 q^{65} +11.8560 q^{67} +2.92123 q^{69} -9.09114 q^{71} +0.717226 q^{73} +0.675852 q^{75} +2.46354 q^{79} -6.81803 q^{81} -5.36866 q^{83} +2.27312 q^{85} -5.16479 q^{87} -8.20577 q^{89} +3.38726 q^{91} -8.75906 q^{93} -2.33168 q^{95} +6.15317 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 6 q^{5} - 4 q^{7} + 12 q^{9} - 4 q^{13} + 2 q^{15} - 8 q^{17} + 14 q^{19} - 18 q^{21} - 2 q^{23} + 8 q^{25} + 10 q^{27} + 4 q^{29} - 2 q^{31} - 24 q^{35} - 10 q^{37} - 24 q^{39} - 4 q^{41}+ \cdots - 20 q^{97}+O(q^{100}) \) 14 * q - 2 * q^3 - 6 * q^5 - 4 * q^7 + 12 * q^9 - 4 * q^13 + 2 * q^15 - 8 * q^17 + 14 * q^19 - 18 * q^21 - 2 * q^23 + 8 * q^25 + 10 * q^27 + 4 * q^29 - 2 * q^31 - 24 * q^35 - 10 * q^37 - 24 * q^39 - 4 * q^41 - 32 * q^43 - 20 * q^45 - 4 * q^47 - 14 * q^49 - 22 * q^51 + 6 * q^53 - 2 * q^57 - 6 * q^59 + 4 * q^61 + 16 * q^63 - 54 * q^65 + 6 * q^67 + 4 * q^69 - 6 * q^71 + 24 * q^73 - 10 * q^75 - 48 * q^79 + 2 * q^81 + 40 * q^85 - 28 * q^87 + 2 * q^89 + 28 * q^91 + 34 * q^93 - 6 * q^95 - 20 * q^97

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