LMFDB - Embedded newform 1148.2.k.b.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, degree $2$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.1
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +O(q^{10})$	\(q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +(0.604261 - 0.604261i) q^{11} +(0.252118 - 0.252118i) q^{13} +(9.11934 + 9.11934i) q^{15} +(2.82692 + 2.82692i) q^{17} +(-1.41581 - 1.41581i) q^{19} -3.30203i q^{21} -8.08621 q^{23} -10.2544 q^{25} +(11.4489 + 11.4489i) q^{27} +(-5.73525 + 5.73525i) q^{29} +10.8735 q^{31} +2.82177i q^{33} +(2.76174 + 2.76174i) q^{35} +0.470242 q^{37} +1.17734i q^{39} +(-5.11381 - 3.85343i) q^{41} +11.3006i q^{43} -30.8682 q^{45} +(1.33189 + 1.33189i) q^{47} -1.00000i q^{49} -13.2011 q^{51} +(-4.21493 + 4.21493i) q^{53} +(-2.36005 - 2.36005i) q^{55} +6.61154 q^{57} -10.4168 q^{59} -8.63089i q^{61} +(5.58856 + 5.58856i) q^{63} +(-0.984695 - 0.984695i) q^{65} +(-5.76041 - 5.76041i) q^{67} +(18.8804 - 18.8804i) q^{69} +(1.36090 - 1.36090i) q^{71} +1.88354i q^{73} +(23.9428 - 23.9428i) q^{75} +0.854555i q^{77} +(-5.15390 + 5.15390i) q^{79} -29.7537 q^{81} -8.02941 q^{83} +(11.0411 - 11.0411i) q^{85} -26.7823i q^{87} +(1.89785 - 1.89785i) q^{89} +0.356549i q^{91} +(-25.3885 + 25.3885i) q^{93} +(-5.52972 + 5.52972i) q^{95} +(3.77435 + 3.77435i) q^{97} +(-4.77573 - 4.77573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.33489	+	2.33489i	−1.34805	+	1.34805i	−0.460270	+	0.887779i	$0.652247\pi$
$3$	−2.33489	+	2.33489i	−1.34805	+	1.34805i	−0.887779	+	0.460270i	$0.847753\pi$
$4$		0			0
$5$		−	3.90568i		−	1.74668i	−0.487116	−	0.873338i	$-0.661951\pi$
$5$		−	3.90568i		−	1.74668i	0.487116	−	0.873338i	$-0.338049\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$		−	7.90342i		−	2.63447i
$10$		0			0
$11$	0.604261	−	0.604261i	0.182192	−	0.182192i	−0.610119	−	0.792310i	$-0.708878\pi$
$11$	0.604261	−	0.604261i	0.182192	−	0.182192i	0.792310	+	0.610119i	$0.208878\pi$
$12$		0			0
$13$	0.252118	−	0.252118i	0.0699251	−	0.0699251i	−0.671279	−	0.741204i	$-0.734255\pi$
$13$	0.252118	−	0.252118i	0.0699251	−	0.0699251i	0.741204	+	0.671279i	$0.234255\pi$
$14$		0			0
$15$	9.11934	+	9.11934i	2.35460	+	2.35460i
$16$		0			0
$17$	2.82692	+	2.82692i	0.685629	+	0.685629i	0.961263	−	0.275633i	$-0.0888876\pi$
$17$	2.82692	+	2.82692i	0.685629	+	0.685629i	−0.275633	+	0.961263i	$0.588888\pi$
$18$		0			0
$19$	−1.41581	−	1.41581i	−0.324810	−	0.324810i	0.525799	−	0.850609i	$-0.323766\pi$
$19$	−1.41581	−	1.41581i	−0.324810	−	0.324810i	−0.850609	+	0.525799i	$0.823766\pi$
$20$		0			0
$21$		−	3.30203i		−	0.720562i
$22$		0			0
$23$	−8.08621			−1.68609			−0.843045	−	0.537843i	$-0.819239\pi$
$23$	−8.08621			−1.68609			−0.843045	+	0.537843i	$0.819239\pi$
$24$		0			0
$25$	−10.2544			−2.05087
$26$		0			0
$27$	11.4489	+	11.4489i	2.20335	+	2.20335i
$28$		0			0
$29$	−5.73525	+	5.73525i	−1.06501	+	1.06501i	−0.0672747	+	0.997734i	$0.521430\pi$
$29$	−5.73525	+	5.73525i	−1.06501	+	1.06501i	−0.997734	+	0.0672747i	$0.978570\pi$
$30$		0			0
$31$	10.8735			1.95294			0.976471	−	0.215647i	$-0.0691862\pi$
$31$	10.8735			1.95294			0.976471	+	0.215647i	$0.0691862\pi$
$32$		0			0
$33$			2.82177i			0.491206i
$34$		0			0
$35$	2.76174	+	2.76174i	0.466819	+	0.466819i
$36$		0			0
$37$	0.470242			0.0773073			0.0386537	−	0.999253i	$-0.487693\pi$
$37$	0.470242			0.0773073			0.0386537	+	0.999253i	$0.487693\pi$
$38$		0			0
$39$			1.17734i			0.188525i
$40$		0			0
$41$	−5.11381	−	3.85343i	−0.798643	−	0.601805i
$41$	−5.11381	−	3.85343i	−0.798643	−	0.601805i
$42$		0			0
$43$			11.3006i			1.72332i	0.507482	+	0.861662i	$0.330576\pi$
$43$			11.3006i			1.72332i	−0.507482	+	0.861662i	$0.669424\pi$
$44$		0			0
$45$	−30.8682			−4.60157
$46$		0			0
$47$	1.33189	+	1.33189i	0.194276	+	0.194276i	0.797541	−	0.603265i	$-0.206134\pi$
$47$	1.33189	+	1.33189i	0.194276	+	0.194276i	−0.603265	+	0.797541i	$0.706134\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−13.2011			−1.84852
$52$		0			0
$53$	−4.21493	+	4.21493i	−0.578964	+	0.578964i	−0.934618	−	0.355653i	$-0.884258\pi$
$53$	−4.21493	+	4.21493i	−0.578964	+	0.578964i	0.355653	+	0.934618i	$0.384258\pi$
$54$		0			0
$55$	−2.36005	−	2.36005i	−0.318230	−	0.318230i
$56$		0			0
$57$	6.61154			0.875719
$58$		0			0
$59$	−10.4168			−1.35615			−0.678076	−	0.734992i	$-0.737186\pi$
$59$	−10.4168			−1.35615			−0.678076	+	0.734992i	$0.737186\pi$
$60$		0			0
$61$		−	8.63089i		−	1.10507i	−0.833489	−	0.552536i	$-0.813660\pi$
$61$		−	8.63089i		−	1.10507i	0.833489	−	0.552536i	$-0.186340\pi$
$62$		0			0
$63$	5.58856	+	5.58856i	0.704092	+	0.704092i
$64$		0			0
$65$	−0.984695	−	0.984695i	−0.122136	−	0.122136i
$66$		0			0
$67$	−5.76041	−	5.76041i	−0.703746	−	0.703746i	0.261467	−	0.965212i	$-0.415794\pi$
$67$	−5.76041	−	5.76041i	−0.703746	−	0.703746i	−0.965212	+	0.261467i	$0.915794\pi$
$68$		0			0
$69$	18.8804	−	18.8804i	2.27293	−	2.27293i
$70$		0			0
$71$	1.36090	−	1.36090i	0.161509	−	0.161509i	−0.621726	−	0.783235i	$-0.713568\pi$
$71$	1.36090	−	1.36090i	0.161509	−	0.161509i	0.783235	+	0.621726i	$0.213568\pi$
$72$		0			0
$73$			1.88354i			0.220452i	0.993907	+	0.110226i	$0.0351574\pi$
$73$			1.88354i			0.220452i	−0.993907	+	0.110226i	$0.964843\pi$
$74$		0			0
$75$	23.9428	−	23.9428i	2.76468	−	2.76468i
$76$		0			0
$77$			0.854555i			0.0973855i
$78$		0			0
$79$	−5.15390	+	5.15390i	−0.579859	+	0.579859i	−0.934864	−	0.355005i	$-0.884479\pi$
$79$	−5.15390	+	5.15390i	−0.579859	+	0.579859i	0.355005	+	0.934864i	$0.384479\pi$
$80$		0			0
$81$	−29.7537			−3.30597
$82$		0			0
$83$	−8.02941			−0.881343			−0.440671	−	0.897669i	$-0.645260\pi$
$83$	−8.02941			−0.881343			−0.440671	+	0.897669i	$0.645260\pi$
$84$		0			0
$85$	11.0411	−	11.0411i	1.19757	−	1.19757i
$86$		0			0
$87$		−	26.7823i		−	2.87137i
$88$		0			0
$89$	1.89785	−	1.89785i	0.201171	−	0.201171i	−0.599330	−	0.800502i	$-0.704566\pi$
$89$	1.89785	−	1.89785i	0.201171	−	0.201171i	0.800502	+	0.599330i	$0.204566\pi$
$90$		0			0
$91$			0.356549i			0.0373765i
$92$		0			0
$93$	−25.3885	+	25.3885i	−2.63266	+	2.63266i
$94$		0			0
$95$	−5.52972	+	5.52972i	−0.567337	+	0.567337i
$96$		0			0
$97$	3.77435	+	3.77435i	0.383227	+	0.383227i	0.872263	−	0.489036i	$-0.162651\pi$
$97$	3.77435	+	3.77435i	0.383227	+	0.383227i	−0.489036	+	0.872263i	$0.662651\pi$
$98$		0			0
$99$	−4.77573	−	4.77573i	−0.479979	−	0.479979i
$100$		0			0
$101$	−1.27902	−	1.27902i	−0.127267	−	0.127267i	0.640604	−	0.767871i	$-0.278684\pi$
$101$	−1.27902	−	1.27902i	−0.127267	−	0.127267i	−0.767871	+	0.640604i	$0.778684\pi$
$102$		0			0
$103$			3.35602i			0.330678i	0.986237	+	0.165339i	$0.0528719\pi$
$103$			3.35602i			0.330678i	−0.986237	+	0.165339i	$0.947128\pi$
$104$		0			0
$105$	−12.8967			−1.25859
$106$		0			0
$107$	−7.99339			−0.772750			−0.386375	−	0.922342i	$-0.626273\pi$
$107$	−7.99339			−0.772750			−0.386375	+	0.922342i	$0.626273\pi$
$108$		0			0
$109$	4.40084	+	4.40084i	0.421524	+	0.421524i	0.885728	−	0.464204i	$-0.153660\pi$
$109$	4.40084	+	4.40084i	0.421524	+	0.421524i	−0.464204	+	0.885728i	$0.653660\pi$
$110$		0			0
$111$	−1.09796	+	1.09796i	−0.104214	+	0.104214i
$112$		0			0
$113$	−16.8928			−1.58914			−0.794569	−	0.607174i	$-0.792303\pi$
$113$	−16.8928			−1.58914			−0.794569	+	0.607174i	$0.792303\pi$
$114$		0			0
$115$			31.5822i			2.94505i
$116$		0			0
$117$	−1.99260	−	1.99260i	−0.184216	−	0.184216i
$118$		0			0
$119$	−3.99787			−0.366484
$120$		0			0
$121$			10.2697i			0.933612i
$122$		0			0
$123$	20.9375	−	2.94286i	1.88787	−	0.265348i
$124$		0			0
$125$			20.5219i			1.83554i
$126$		0			0
$127$	8.28929			0.735555			0.367778	−	0.929914i	$-0.380119\pi$
$127$	8.28929			0.735555			0.367778	+	0.929914i	$0.380119\pi$
$128$		0			0
$129$	−26.3856	−	26.3856i	−2.32313	−	2.32313i
$130$		0			0
$131$			19.8121i			1.73099i	0.500915	+	0.865496i	$0.332997\pi$
$131$			19.8121i			1.73099i	−0.500915	+	0.865496i	$0.667003\pi$
$132$		0			0
$133$	2.00226			0.173618
$134$		0			0
$135$	44.7159	−	44.7159i	3.84853	−	3.84853i
$136$		0			0
$137$	15.6890	+	15.6890i	1.34040	+	1.34040i	0.895658	+	0.444743i	$0.146705\pi$
$137$	15.6890	+	15.6890i	1.34040	+	1.34040i	0.444743	+	0.895658i	$0.353295\pi$
$138$		0			0
$139$	−5.57897			−0.473202			−0.236601	−	0.971607i	$-0.576033\pi$
$139$	−5.57897			−0.473202			−0.236601	+	0.971607i	$0.576033\pi$
$140$		0			0
$141$	−6.21962			−0.523786
$142$		0			0
$143$		−	0.304691i		−	0.0254795i
$144$		0			0
$145$	22.4001	+	22.4001i	1.86023	+	1.86023i
$146$		0			0
$147$	2.33489	+	2.33489i	0.192578	+	0.192578i
$148$		0			0
$149$	−9.93354	−	9.93354i	−0.813787	−	0.813787i	0.171412	−	0.985199i	$-0.445167\pi$
$149$	−9.93354	−	9.93354i	−0.813787	−	0.813787i	−0.985199	+	0.171412i	$0.945167\pi$
$150$		0			0
$151$	−2.22594	+	2.22594i	−0.181144	+	0.181144i	−0.791854	−	0.610710i	$-0.790884\pi$
$151$	−2.22594	+	2.22594i	−0.181144	+	0.181144i	0.610710	+	0.791854i	$0.290884\pi$
$152$		0			0
$153$	22.3423	−	22.3423i	1.80627	−	1.80627i
$154$		0			0
$155$		−	42.4686i		−	3.41116i
$156$		0			0
$157$	−1.46203	+	1.46203i	−0.116683	+	0.116683i	−0.763037	−	0.646354i	$-0.776293\pi$
$157$	−1.46203	+	1.46203i	−0.116683	+	0.116683i	0.646354	+	0.763037i	$0.276293\pi$
$158$		0			0
$159$		−	19.6828i		−	1.56094i
$160$		0			0
$161$	5.71781	−	5.71781i	0.450627	−	0.450627i
$162$		0			0
$163$	−6.76472			−0.529854			−0.264927	−	0.964269i	$-0.585348\pi$
$163$	−6.76472			−0.529854			−0.264927	+	0.964269i	$0.585348\pi$
$164$		0			0
$165$	11.0209			0.857978
$166$		0			0
$167$	−10.1354	+	10.1354i	−0.784297	+	0.784297i	−0.980553	−	0.196256i	$-0.937122\pi$
$167$	−10.1354	+	10.1354i	−0.784297	+	0.784297i	0.196256	+	0.980553i	$0.437122\pi$
$168$		0			0
$169$			12.8729i			0.990221i
$170$		0			0
$171$	−11.1898	+	11.1898i	−0.855703	+	0.855703i
$172$		0			0
$173$			1.61515i			0.122797i	0.998113	+	0.0613987i	$0.0195561\pi$
$173$			1.61515i			0.122797i	−0.998113	+	0.0613987i	$0.980444\pi$
$174$		0			0
$175$	7.25093	−	7.25093i	0.548119	−	0.548119i
$176$		0			0
$177$	24.3221	−	24.3221i	1.82816	−	1.82816i
$178$		0			0
$179$	−11.4527	−	11.4527i	−0.856015	−	0.856015i	0.134851	−	0.990866i	$-0.456944\pi$
$179$	−11.4527	−	11.4527i	−0.856015	−	0.856015i	−0.990866	+	0.134851i	$0.956944\pi$
$180$		0			0
$181$	8.29754	+	8.29754i	0.616751	+	0.616751i	0.944697	−	0.327945i	$-0.106356\pi$
$181$	8.29754	+	8.29754i	0.616751	+	0.616751i	−0.327945	+	0.944697i	$0.606356\pi$
$182$		0			0
$183$	20.1522	+	20.1522i	1.48969	+	1.48969i
$184$		0			0
$185$		−	1.83662i		−	0.135031i
$186$		0			0
$187$	3.41640			0.249832
$188$		0			0
$189$	−16.1912			−1.17774
$190$		0			0
$191$	8.41481	+	8.41481i	0.608874	+	0.608874i	0.942652	−	0.333778i	$-0.108324\pi$
$191$	8.41481	+	8.41481i	0.608874	+	0.608874i	−0.333778	+	0.942652i	$0.608324\pi$
$192$		0			0
$193$	11.1471	−	11.1471i	0.802384	−	0.802384i	−0.181083	−	0.983468i	$-0.557960\pi$
$193$	11.1471	−	11.1471i	0.802384	−	0.802384i	0.983468	+	0.181083i	$0.0579604\pi$
$194$		0			0
$195$	4.59831			0.329292
$196$		0			0
$197$			9.13567i			0.650889i	0.945561	+	0.325445i	$0.105514\pi$
$197$			9.13567i			0.650889i	−0.945561	+	0.325445i	$0.894486\pi$
$198$		0			0
$199$	7.25035	+	7.25035i	0.513964	+	0.513964i	0.915739	−	0.401775i	$-0.131606\pi$
$199$	7.25035	+	7.25035i	0.513964	+	0.513964i	−0.401775	+	0.915739i	$0.631606\pi$
$200$		0			0
$201$	26.8998			1.89737
$202$		0			0
$203$		−	8.11087i		−	0.569271i
$204$		0			0
$205$	−15.0503	+	19.9729i	−1.05116	+	1.39497i
$206$		0			0
$207$			63.9086i			4.44196i
$208$		0			0
$209$	−1.71104			−0.118355
$210$		0			0
$211$	−17.1559	−	17.1559i	−1.18106	−	1.18106i	−0.979470	−	0.201590i	$-0.935389\pi$
$211$	−17.1559	−	17.1559i	−1.18106	−	1.18106i	−0.201590	−	0.979470i	$-0.564611\pi$
$212$		0			0
$213$			6.35509i			0.435444i
$214$		0			0
$215$	44.1366			3.01009
$216$		0			0
$217$	−7.68874	+	7.68874i	−0.521946	+	0.521946i
$218$		0			0
$219$	−4.39786	−	4.39786i	−0.297180	−	0.297180i
$220$		0			0
$221$	1.42544			0.0958854
$222$		0			0
$223$	−5.80697			−0.388864			−0.194432	−	0.980916i	$-0.562286\pi$
$223$	−5.80697			−0.388864			−0.194432	+	0.980916i	$0.562286\pi$
$224$		0			0
$225$			81.0445i			5.40297i
$226$		0			0
$227$	2.50663	+	2.50663i	0.166371	+	0.166371i	0.785382	−	0.619011i	$-0.212466\pi$
$227$	2.50663	+	2.50663i	0.166371	+	0.166371i	−0.619011	+	0.785382i	$0.712466\pi$
$228$		0			0
$229$	1.37349	+	1.37349i	0.0907628	+	0.0907628i	0.751030	−	0.660268i	$-0.229557\pi$
$229$	1.37349	+	1.37349i	0.0907628	+	0.0907628i	−0.660268	+	0.751030i	$0.729557\pi$
$230$		0			0
$231$	−1.99529	−	1.99529i	−0.131280	−	0.131280i
$232$		0			0
$233$	8.00299	−	8.00299i	0.524293	−	0.524293i	−0.394572	−	0.918865i	$-0.629107\pi$
$233$	8.00299	−	8.00299i	0.524293	−	0.524293i	0.918865	+	0.394572i	$0.129107\pi$
$234$		0			0
$235$	5.20193	−	5.20193i	0.339337	−	0.339337i
$236$		0			0
$237$		−	24.0676i		−	1.56336i
$238$		0			0
$239$	−4.43313	+	4.43313i	−0.286755	+	0.286755i	−0.835796	−	0.549041i	$-0.814993\pi$
$239$	−4.43313	+	4.43313i	−0.286755	+	0.286755i	0.549041	+	0.835796i	$0.314993\pi$
$240$		0			0
$241$		−	6.25570i		−	0.402965i	−0.979492	−	0.201482i	$-0.935424\pi$
$241$		−	6.25570i		−	0.402965i	0.979492	−	0.201482i	$-0.0645759\pi$
$242$		0			0
$243$	35.1249	−	35.1249i	2.25326	−	2.25326i
$244$		0			0
$245$	−3.90568			−0.249525
$246$		0			0
$247$	−0.713905			−0.0454247
$248$		0			0
$249$	18.7478	−	18.7478i	1.18809	−	1.18809i
$250$		0			0
$251$		−	12.9520i		−	0.817524i	−0.912641	−	0.408762i	$-0.865961\pi$
$251$		−	12.9520i		−	0.817524i	0.912641	−	0.408762i	$-0.134039\pi$
$252$		0			0
$253$	−4.88618	+	4.88618i	−0.307192	+	0.307192i
$254$		0			0
$255$			51.5593i			3.22877i
$256$		0			0
$257$	13.4896	−	13.4896i	0.841457	−	0.841457i	−0.147591	−	0.989048i	$-0.547152\pi$
$257$	13.4896	−	13.4896i	0.841457	−	0.841457i	0.989048	+	0.147591i	$0.0471520\pi$
$258$		0			0
$259$	−0.332511	+	0.332511i	−0.0206613	+	0.0206613i
$260$		0			0
$261$	45.3281	+	45.3281i	2.80574	+	2.80574i
$262$		0			0
$263$	11.2174	+	11.2174i	0.691694	+	0.691694i	0.962605	−	0.270910i	$-0.0873246\pi$
$263$	11.2174	+	11.2174i	0.691694	+	0.691694i	−0.270910	+	0.962605i	$0.587325\pi$
$264$		0			0
$265$	16.4622	+	16.4622i	1.01126	+	1.01126i
$266$		0			0
$267$			8.86253i			0.542378i
$268$		0			0
$269$	9.92609			0.605204			0.302602	−	0.953117i	$-0.402145\pi$
$269$	9.92609			0.605204			0.302602	+	0.953117i	$0.402145\pi$
$270$		0			0
$271$	−31.0940			−1.88883			−0.944413	−	0.328761i	$-0.893369\pi$
$271$	−31.0940			−1.88883			−0.944413	+	0.328761i	$0.893369\pi$
$272$		0			0
$273$	−0.832503	−	0.832503i	−0.0503854	−	0.0503854i
$274$		0			0
$275$	−6.19632	+	6.19632i	−0.373652	+	0.373652i
$276$		0			0
$277$	−8.93861			−0.537069			−0.268534	−	0.963270i	$-0.586539\pi$
$277$	−8.93861			−0.537069			−0.268534	+	0.963270i	$0.586539\pi$
$278$		0			0
$279$		−	85.9380i		−	5.14497i
$280$		0			0
$281$	−14.5726	−	14.5726i	−0.869330	−	0.869330i	0.123068	−	0.992398i	$-0.460727\pi$
$281$	−14.5726	−	14.5726i	−0.869330	−	0.869330i	−0.992398	+	0.123068i	$0.960727\pi$
$282$		0			0
$283$	−0.0724424			−0.00430625			−0.00215313	−	0.999998i	$-0.500685\pi$
$283$	−0.0724424			−0.00430625			−0.00215313	+	0.999998i	$0.500685\pi$
$284$		0			0
$285$		−	25.8226i		−	1.52960i
$286$		0			0
$287$	6.34080	−	0.891226i	0.374285	−	0.0526074i
$288$		0			0
$289$		−	1.01702i		−	0.0598246i
$290$		0			0
$291$	−17.6254			−1.03322
$292$		0			0
$293$	−12.4244	−	12.4244i	−0.725839	−	0.725839i	0.243949	−	0.969788i	$-0.421557\pi$
$293$	−12.4244	−	12.4244i	−0.725839	−	0.725839i	−0.969788	+	0.243949i	$0.921557\pi$
$294$		0			0
$295$			40.6848i			2.36876i
$296$		0			0
$297$	13.8363			0.802863
$298$		0			0
$299$	−2.03868	+	2.03868i	−0.117900	+	0.117900i
$300$		0			0
$301$	−7.99073	−	7.99073i	−0.460578	−	0.460578i
$302$		0			0
$303$	5.97274			0.343125
$304$		0			0
$305$	−33.7095			−1.93020
$306$		0			0
$307$		−	22.8144i		−	1.30208i	−0.759042	−	0.651042i	$-0.774332\pi$
$307$		−	22.8144i		−	1.30208i	0.759042	−	0.651042i	$-0.225668\pi$
$308$		0			0
$309$	−7.83593	−	7.83593i	−0.445771	−	0.445771i
$310$		0			0
$311$	13.4277	+	13.4277i	0.761414	+	0.761414i	0.976578	−	0.215164i	$-0.0690286\pi$
$311$	13.4277	+	13.4277i	0.761414	+	0.761414i	−0.215164	+	0.976578i	$0.569029\pi$
$312$		0			0
$313$	1.64313	+	1.64313i	0.0928753	+	0.0928753i	0.752018	−	0.659143i	$-0.229081\pi$
$313$	1.64313	+	1.64313i	0.0928753	+	0.0928753i	−0.659143	+	0.752018i	$0.729081\pi$
$314$		0			0
$315$	21.8271	−	21.8271i	1.22982	−	1.22982i
$316$		0			0
$317$	−8.33677	+	8.33677i	−0.468240	+	0.468240i	−0.901344	−	0.433104i	$-0.857418\pi$
$317$	−8.33677	+	8.33677i	−0.468240	+	0.468240i	0.433104	+	0.901344i	$0.357418\pi$
$318$		0			0
$319$			6.93118i			0.388072i
$320$		0			0
$321$	18.6637	−	18.6637i	1.04170	−	1.04170i
$322$		0			0
$323$		−	8.00479i		−	0.445399i
$324$		0			0
$325$	−2.58532	+	2.58532i	−0.143408	+	0.143408i
$326$		0			0
$327$	−20.5510			−1.13647
$328$		0			0
$329$	−1.88357			−0.103845
$330$		0			0
$331$	−4.74328	+	4.74328i	−0.260714	+	0.260714i	−0.825344	−	0.564630i	$-0.809019\pi$
$331$	−4.74328	+	4.74328i	−0.260714	+	0.260714i	0.564630	+	0.825344i	$0.309019\pi$
$332$		0			0
$333$		−	3.71652i		−	0.203664i
$334$		0			0
$335$	−22.4983	+	22.4983i	−1.22922	+	1.22922i
$336$		0			0
$337$			22.7509i			1.23932i	0.784871	+	0.619659i	$0.212729\pi$
$337$			22.7509i			1.23932i	−0.784871	+	0.619659i	$0.787271\pi$
$338$		0			0
$339$	39.4427	−	39.4427i	2.14224	−	2.14224i
$340$		0			0
$341$	6.57045	−	6.57045i	0.355810	−	0.355810i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−73.7409	−	73.7409i	−3.97007	−	3.97007i
$346$		0			0
$347$	−2.64443	−	2.64443i	−0.141961	−	0.141961i	0.632555	−	0.774515i	$-0.282006\pi$
$347$	−2.64443	−	2.64443i	−0.141961	−	0.141961i	−0.774515	+	0.632555i	$0.782006\pi$
$348$		0			0
$349$			19.3625i			1.03645i	0.855244	+	0.518226i	$0.173407\pi$
$349$			19.3625i			1.03645i	−0.855244	+	0.518226i	$0.826593\pi$
$350$		0			0
$351$	5.77297			0.308139
$352$		0			0
$353$	4.90514			0.261074			0.130537	−	0.991443i	$-0.458330\pi$
$353$	4.90514			0.261074			0.130537	+	0.991443i	$0.458330\pi$
$354$		0			0
$355$	−5.31524	−	5.31524i	−0.282103	−	0.282103i
$356$		0			0
$357$	9.33459	−	9.33459i	0.494039	−	0.494039i
$358$		0			0
$359$	17.2354			0.909648			0.454824	−	0.890581i	$-0.349702\pi$
$359$	17.2354			0.909648			0.454824	+	0.890581i	$0.349702\pi$
$360$		0			0
$361$		−	14.9909i		−	0.788997i
$362$		0			0
$363$	−23.9787	−	23.9787i	−1.25856	−	1.25856i
$364$		0			0
$365$	7.35651			0.385057
$366$		0			0
$367$		−	22.8287i		−	1.19165i	−0.803116	−	0.595823i	$-0.796826\pi$
$367$		−	22.8287i		−	1.19165i	0.803116	−	0.595823i	$-0.203174\pi$
$368$		0			0
$369$	−30.4552	+	40.4166i	−1.58544	+	2.10400i
$370$		0			0
$371$		−	5.96080i		−	0.309470i
$372$		0			0
$373$	−0.870831			−0.0450899			−0.0225450	−	0.999746i	$-0.507177\pi$
$373$	−0.870831			−0.0450899			−0.0225450	+	0.999746i	$0.507177\pi$
$374$		0			0
$375$	−47.9164	−	47.9164i	−2.47439	−	2.47439i
$376$		0			0
$377$			2.89192i			0.148942i
$378$		0			0
$379$	−19.3295			−0.992891			−0.496445	−	0.868068i	$-0.665362\pi$
$379$	−19.3295			−0.992891			−0.496445	+	0.868068i	$0.665362\pi$
$380$		0			0
$381$	−19.3546	+	19.3546i	−0.991564	+	0.991564i
$382$		0			0
$383$	9.33099	+	9.33099i	0.476791	+	0.476791i	0.904104	−	0.427313i	$-0.140540\pi$
$383$	9.33099	+	9.33099i	0.476791	+	0.476791i	−0.427313	+	0.904104i	$0.640540\pi$
$384$		0			0
$385$	3.33762			0.170101
$386$		0			0
$387$	89.3133			4.54005
$388$		0			0
$389$		−	24.2825i		−	1.23117i	−0.788069	−	0.615587i	$-0.788919\pi$
$389$		−	24.2825i		−	1.23117i	0.788069	−	0.615587i	$-0.211081\pi$
$390$		0			0
$391$	−22.8591	−	22.8591i	−1.15603	−	1.15603i
$392$		0			0
$393$	−46.2591	−	46.2591i	−2.33346	−	2.33346i
$394$		0			0
$395$	20.1295	+	20.1295i	1.01283	+	1.01283i
$396$		0			0
$397$	6.71206	−	6.71206i	0.336869	−	0.336869i	−0.518319	−	0.855187i	$-0.673442\pi$
$397$	6.71206	−	6.71206i	0.336869	−	0.336869i	0.855187	+	0.518319i	$0.173442\pi$
$398$		0			0
$399$	−4.67506	+	4.67506i	−0.234046	+	0.234046i
$400$		0			0
$401$		−	32.7023i		−	1.63307i	−0.577293	−	0.816537i	$-0.695891\pi$
$401$		−	32.7023i		−	1.63307i	0.577293	−	0.816537i	$-0.304109\pi$
$402$		0			0
$403$	2.74142	−	2.74142i	0.136560	−	0.136560i
$404$		0			0
$405$			116.209i			5.77445i
$406$		0			0
$407$	0.284149	−	0.284149i	0.0140847	−	0.0140847i
$408$		0			0
$409$	6.26430			0.309750			0.154875	−	0.987934i	$-0.450503\pi$
$409$	6.26430			0.309750			0.154875	+	0.987934i	$0.450503\pi$
$410$		0			0
$411$	−73.2641			−3.61385
$412$		0			0
$413$	7.36579	−	7.36579i	0.362447	−	0.362447i
$414$		0			0
$415$			31.3604i			1.53942i
$416$		0			0
$417$	13.0263	−	13.0263i	0.637900	−	0.637900i
$418$		0			0
$419$		−	14.1392i		−	0.690745i	−0.938466	−	0.345373i	$-0.887752\pi$
$419$		−	14.1392i		−	0.690745i	0.938466	−	0.345373i	$-0.112248\pi$
$420$		0			0
$421$	−2.79838	+	2.79838i	−0.136385	+	0.136385i	−0.772003	−	0.635619i	$-0.780745\pi$
$421$	−2.79838	+	2.79838i	−0.136385	+	0.136385i	0.635619	+	0.772003i	$0.280745\pi$
$422$		0			0
$423$	10.5265	−	10.5265i	0.511814	−	0.511814i
$424$		0			0
$425$	−28.9883	−	28.9883i	−1.40614	−	1.40614i
$426$		0			0
$427$	6.10296	+	6.10296i	0.295343	+	0.295343i
$428$		0			0
$429$	0.711419	+	0.711419i	0.0343476	+	0.0343476i
$430$		0			0
$431$			3.13515i			0.151015i	0.997145	+	0.0755074i	$0.0240576\pi$
$431$			3.13515i			0.151015i	−0.997145	+	0.0755074i	$0.975942\pi$
$432$		0			0
$433$	4.38905			0.210924			0.105462	−	0.994423i	$-0.466368\pi$
$433$	4.38905			0.210924			0.105462	+	0.994423i	$0.466368\pi$
$434$		0			0
$435$	−104.603			−5.01535
$436$		0			0
$437$	11.4486	+	11.4486i	0.547659	+	0.547659i
$438$		0			0
$439$	0.742883	−	0.742883i	0.0354559	−	0.0354559i	−0.689157	−	0.724612i	$-0.742019\pi$
$439$	0.742883	−	0.742883i	0.0354559	−	0.0354559i	0.724612	+	0.689157i	$0.242019\pi$
$440$		0			0
$441$	−7.90342			−0.376353
$442$		0			0
$443$		−	34.6887i		−	1.64811i	−0.566511	−	0.824054i	$-0.691707\pi$
$443$		−	34.6887i		−	1.64811i	0.566511	−	0.824054i	$-0.308293\pi$
$444$		0			0
$445$	−7.41239	−	7.41239i	−0.351381	−	0.351381i
$446$		0			0
$447$	46.3874			2.19405
$448$		0			0
$449$		−	22.7931i		−	1.07567i	−0.843050	−	0.537835i	$-0.819242\pi$
$449$		−	22.7931i		−	1.07567i	0.843050	−	0.537835i	$-0.180758\pi$
$450$		0			0
$451$	−5.41856	+	0.761601i	−0.255150	+	0.0358624i
$452$		0			0
$453$		−	10.3946i		−	0.488383i
$454$		0			0
$455$	1.39257			0.0652846
$456$		0			0
$457$	20.1099	+	20.1099i	0.940702	+	0.940702i	0.998338	−	0.0576354i	$-0.0183561\pi$
$457$	20.1099	+	20.1099i	0.940702	+	0.940702i	−0.0576354	+	0.998338i	$0.518356\pi$
$458$		0			0
$459$			64.7305i			3.02136i
$460$		0			0
$461$	28.9855			1.34999			0.674995	−	0.737823i	$-0.264146\pi$
$461$	28.9855			1.34999			0.674995	+	0.737823i	$0.264146\pi$
$462$		0			0
$463$	15.5420	−	15.5420i	0.722299	−	0.722299i	−0.246774	−	0.969073i	$-0.579370\pi$
$463$	15.5420	−	15.5420i	0.722299	−	0.722299i	0.969073	+	0.246774i	$0.0793705\pi$
$464$		0			0
$465$	99.1594	+	99.1594i	4.59841	+	4.59841i
$466$		0			0
$467$	−7.72154			−0.357310			−0.178655	−	0.983912i	$-0.557175\pi$
$467$	−7.72154			−0.357310			−0.178655	+	0.983912i	$0.557175\pi$
$468$		0			0
$469$	8.14645			0.376168
$470$		0			0
$471$		−	6.82736i		−	0.314588i
$472$		0			0
$473$	6.82851	+	6.82851i	0.313975	+	0.313975i
$474$		0			0
$475$	14.5183	+	14.5183i	0.666144	+	0.666144i
$476$		0			0
$477$	33.3123	+	33.3123i	1.52527	+	1.52527i
$478$		0			0
$479$	−18.0696	+	18.0696i	−0.825620	+	0.825620i	−0.986907	−	0.161288i	$-0.948435\pi$
$479$	−18.0696	+	18.0696i	−0.825620	+	0.825620i	0.161288	+	0.986907i	$0.448435\pi$
$480$		0			0
$481$	0.118557	−	0.118557i	0.00540572	−	0.00540572i
$482$		0			0
$483$			26.7009i			1.21493i
$484$		0			0
$485$	14.7414	−	14.7414i	0.669373	−	0.669373i
$486$		0			0
$487$			10.9869i			0.497865i	0.968521	+	0.248932i	$0.0800797\pi$
$487$			10.9869i			0.497865i	−0.968521	+	0.248932i	$0.919920\pi$
$488$		0			0
$489$	15.7949	−	15.7949i	0.714269	−	0.714269i
$490$		0			0
$491$	12.8301			0.579015			0.289507	−	0.957176i	$-0.406508\pi$
$491$	12.8301			0.579015			0.289507	+	0.957176i	$0.406508\pi$
$492$		0			0
$493$	−32.4262			−1.46040
$494$		0			0
$495$	−18.6525	+	18.6525i	−0.838367	+	0.838367i
$496$		0			0
$497$			1.92460i			0.0863301i
$498$		0			0
$499$	−28.2708	+	28.2708i	−1.26557	+	1.26557i	−0.317224	+	0.948351i	$0.602751\pi$
$499$	−28.2708	+	28.2708i	−1.26557	+	1.26557i	−0.948351	+	0.317224i	$0.897249\pi$
$500$		0			0
$501$		−	47.3298i		−	2.11454i
$502$		0			0
$503$	−27.4481	+	27.4481i	−1.22385	+	1.22385i	−0.257598	+	0.966252i	$0.582931\pi$
$503$	−27.4481	+	27.4481i	−1.22385	+	1.22385i	−0.966252	+	0.257598i	$0.917069\pi$
$504$		0			0
$505$	−4.99545	+	4.99545i	−0.222295	+	0.222295i
$506$		0			0
$507$	−30.0567	−	30.0567i	−1.33487	−	1.33487i
$508$		0			0
$509$	−15.3085	−	15.3085i	−0.678538	−	0.678538i	0.281132	−	0.959669i	$-0.409290\pi$
$509$	−15.3085	−	15.3085i	−0.678538	−	0.678538i	−0.959669	+	0.281132i	$0.909290\pi$
$510$		0			0
$511$	−1.33186	−	1.33186i	−0.0589182	−	0.0589182i
$512$		0			0
$513$		−	32.4191i		−	1.43134i
$514$		0			0
$515$	13.1076			0.577588
$516$		0			0
$517$	1.60962			0.0707908
$518$		0			0
$519$	−3.77119	−	3.77119i	−0.165537	−	0.165537i
$520$		0			0
$521$	−9.52829	+	9.52829i	−0.417442	+	0.417442i	−0.884321	−	0.466879i	$-0.845378\pi$
$521$	−9.52829	+	9.52829i	−0.417442	+	0.417442i	0.466879	+	0.884321i	$0.345378\pi$
$522$		0			0
$523$	−7.33546			−0.320757			−0.160379	−	0.987056i	$-0.551272\pi$
$523$	−7.33546			−0.320757			−0.160379	+	0.987056i	$0.551272\pi$
$524$		0			0
$525$			33.8603i			1.47778i
$526$		0			0
$527$	30.7386	+	30.7386i	1.33899	+	1.33899i
$528$		0			0
$529$	42.3867			1.84290
$530$		0			0
$531$			82.3283i			3.57275i
$532$		0			0
$533$	−2.26081	+	0.317766i	−0.0979264	+	0.0137640i
$534$		0			0
$535$			31.2197i			1.34974i
$536$		0			0
$537$	53.4816			2.30790
$538$		0			0
$539$	−0.604261	−	0.604261i	−0.0260274	−	0.0260274i
$540$		0			0
$541$			30.9228i			1.32948i	0.747077	+	0.664738i	$0.231457\pi$
$541$			30.9228i			1.32948i	−0.747077	+	0.664738i	$0.768543\pi$
$542$		0			0
$543$	−38.7477			−1.66282
$544$		0			0
$545$	17.1883	−	17.1883i	0.736266	−	0.736266i
$546$		0			0
$547$	−12.5722	−	12.5722i	−0.537547	−	0.537547i	0.385261	−	0.922808i	$-0.374112\pi$
$547$	−12.5722	−	12.5722i	−0.537547	−	0.537547i	−0.922808	+	0.385261i	$0.874112\pi$
$548$		0			0
$549$	−68.2135			−2.91128
$550$		0			0
$551$	16.2401			0.691851
$552$		0			0
$553$		−	7.28872i		−	0.309948i
$554$		0			0
$555$	4.28830	+	4.28830i	0.182028	+	0.182028i
$556$		0			0
$557$	−17.9650	−	17.9650i	−0.761202	−	0.761202i	0.215337	−	0.976540i	$-0.430915\pi$
$557$	−17.9650	−	17.9650i	−0.761202	−	0.761202i	−0.976540	+	0.215337i	$0.930915\pi$
$558$		0			0
$559$	2.84909	+	2.84909i	0.120504	+	0.120504i
$560$		0			0
$561$	−7.97691	+	7.97691i	−0.336786	+	0.336786i
$562$		0			0
$563$	18.2877	−	18.2877i	0.770733	−	0.770733i	−0.207502	−	0.978235i	$-0.566533\pi$
$563$	18.2877	−	18.2877i	0.770733	−	0.770733i	0.978235	+	0.207502i	$0.0665333\pi$
$564$		0			0
$565$			65.9778i			2.77571i
$566$		0			0
$567$	21.0391	−	21.0391i	0.883557	−	0.883557i
$568$		0			0
$569$			11.9030i			0.498998i	0.968375	+	0.249499i	$0.0802659\pi$
$569$			11.9030i			0.498998i	−0.968375	+	0.249499i	$0.919734\pi$
$570$		0			0
$571$	−17.9514	+	17.9514i	−0.751242	+	0.751242i	−0.974711	−	0.223469i	$-0.928262\pi$
$571$	−17.9514	+	17.9514i	−0.751242	+	0.751242i	0.223469	+	0.974711i	$0.428262\pi$
$572$		0			0
$573$	−39.2953			−1.64158
$574$		0			0
$575$	82.9189			3.45796
$576$		0			0
$577$	−7.97498	+	7.97498i	−0.332003	+	0.332003i	−0.853347	−	0.521344i	$-0.825431\pi$
$577$	−7.97498	+	7.97498i	−0.332003	+	0.332003i	0.521344	+	0.853347i	$0.325431\pi$
$578$		0			0
$579$			52.0544i			2.16331i
$580$		0			0
$581$	5.67765	−	5.67765i	0.235549	−	0.235549i
$582$		0			0
$583$			5.09383i			0.210965i
$584$		0			0
$585$	−7.78245	+	7.78245i	−0.321765	+	0.321765i
$586$		0			0
$587$	−2.68198	+	2.68198i	−0.110697	+	0.110697i	−0.760286	−	0.649589i	$-0.774941\pi$
$587$	−2.68198	+	2.68198i	−0.110697	+	0.110697i	0.649589	+	0.760286i	$0.274941\pi$
$588$		0			0
$589$	−15.3949	−	15.3949i	−0.634335	−	0.634335i
$590$		0			0
$591$	−21.3308	−	21.3308i	−0.877431	−	0.877431i
$592$		0			0
$593$	−19.4170	−	19.4170i	−0.797362	−	0.797362i	0.185317	−	0.982679i	$-0.440669\pi$
$593$	−19.4170	−	19.4170i	−0.797362	−	0.797362i	−0.982679	+	0.185317i	$0.940669\pi$
$594$		0			0
$595$			15.6144i			0.640129i
$596$		0			0
$597$	−33.8575			−1.38570
$598$		0			0
$599$	−5.81743			−0.237694			−0.118847	−	0.992913i	$-0.537920\pi$
$599$	−5.81743			−0.237694			−0.118847	+	0.992913i	$0.537920\pi$
$600$		0			0
$601$	−25.5731	−	25.5731i	−1.04315	−	1.04315i	−0.999026	−	0.0441241i	$-0.985950\pi$
$601$	−25.5731	−	25.5731i	−1.04315	−	1.04315i	−0.0441241	−	0.999026i	$-0.514050\pi$
$602$		0			0
$603$	−45.5269	+	45.5269i	−1.85400	+	1.85400i
$604$		0			0
$605$	40.1103			1.63072
$606$		0			0
$607$		−	28.3183i		−	1.14941i	−0.818362	−	0.574703i	$-0.805118\pi$
$607$		−	28.3183i		−	1.14941i	0.818362	−	0.574703i	$-0.194882\pi$
$608$		0			0
$609$	18.9380	+	18.9380i	0.767406	+	0.767406i
$610$		0			0
$611$	0.671587			0.0271695
$612$		0			0
$613$			6.73353i			0.271965i	0.990711	+	0.135982i	$0.0434190\pi$
$613$			6.73353i			0.271965i	−0.990711	+	0.135982i	$0.956581\pi$
$614$		0			0
$615$	−11.4939	−	81.7753i	−0.463478	−	3.29750i
$616$		0			0
$617$			4.05005i			0.163049i	0.996671	+	0.0815245i	$0.0259789\pi$
$617$			4.05005i			0.163049i	−0.996671	+	0.0815245i	$0.974021\pi$
$618$		0			0
$619$	30.0767			1.20889			0.604443	−	0.796649i	$-0.293396\pi$
$619$	30.0767			1.20889			0.604443	+	0.796649i	$0.293396\pi$
$620$		0			0
$621$	−92.5784	−	92.5784i	−3.71504	−	3.71504i
$622$		0			0
$623$			2.68396i			0.107531i
$624$		0			0
$625$	28.8802			1.15521
$626$		0			0
$627$	3.99510	−	3.99510i	0.159549	−	0.159549i
$628$		0			0
$629$	1.32934	+	1.32934i	0.0530042	+	0.0530042i
$630$		0			0
$631$	33.0127			1.31421			0.657107	−	0.753797i	$-0.271780\pi$
$631$	33.0127			1.31421			0.657107	+	0.753797i	$0.271780\pi$
$632$		0			0
$633$	80.1142			3.18425
$634$		0			0
$635$		−	32.3753i		−	1.28478i
$636$		0			0
$637$	−0.252118	−	0.252118i	−0.00998930	−	0.00998930i
$638$		0			0
$639$	−10.7557	−	10.7557i	−0.425490	−	0.425490i
$640$		0			0
$641$	−15.0452	−	15.0452i	−0.594249	−	0.594249i	0.344528	−	0.938776i	$-0.388039\pi$
$641$	−15.0452	−	15.0452i	−0.594249	−	0.594249i	−0.938776	+	0.344528i	$0.888039\pi$
$642$		0			0
$643$	8.27521	−	8.27521i	0.326343	−	0.326343i	−0.524851	−	0.851194i	$-0.675879\pi$
$643$	8.27521	−	8.27521i	0.326343	−	0.326343i	0.851194	+	0.524851i	$0.175879\pi$
$644$		0			0
$645$	−103.054	+	103.054i	−4.05775	+	4.05775i
$646$		0			0
$647$		−	32.4186i		−	1.27451i	−0.770654	−	0.637254i	$-0.780070\pi$
$647$		−	32.4186i		−	1.27451i	0.770654	−	0.637254i	$-0.219930\pi$
$648$		0			0
$649$	−6.29447	+	6.29447i	−0.247080	+	0.247080i
$650$		0			0
$651$		−	35.9047i		−	1.40722i
$652$		0			0
$653$	−7.86295	+	7.86295i	−0.307701	+	0.307701i	−0.844017	−	0.536316i	$-0.819816\pi$
$653$	−7.86295	+	7.86295i	−0.307701	+	0.307701i	0.536316	+	0.844017i	$0.319816\pi$
$654$		0			0
$655$	77.3799			3.02348
$656$		0			0
$657$	14.8864			0.580773
$658$		0			0
$659$	23.4608	−	23.4608i	0.913904	−	0.913904i	−0.0826724	−	0.996577i	$-0.526346\pi$
$659$	23.4608	−	23.4608i	0.913904	−	0.913904i	0.996577	+	0.0826724i	$0.0263455\pi$
$660$		0			0
$661$		−	32.8166i		−	1.27642i	−0.769863	−	0.638209i	$-0.779676\pi$
$661$		−	32.8166i		−	1.27642i	0.769863	−	0.638209i	$-0.220324\pi$
$662$		0			0
$663$	−3.32824	+	3.32824i	−0.129258	+	0.129258i
$664$		0			0
$665$		−	7.82021i		−	0.303255i
$666$		0			0
$667$	46.3764	−	46.3764i	1.79570	−	1.79570i
$668$		0			0
$669$	13.5586	−	13.5586i	0.524207	−	0.524207i
$670$		0			0
$671$	−5.21531	−	5.21531i	−0.201335	−	0.201335i
$672$		0			0
$673$	−32.8830	−	32.8830i	−1.26755	−	1.26755i	−0.947352	−	0.320195i	$-0.896252\pi$
$673$	−32.8830	−	32.8830i	−1.26755	−	1.26755i	−0.320195	−	0.947352i	$-0.603748\pi$
$674$		0			0
$675$	−117.402	−	117.402i	−4.51879	−	4.51879i
$676$		0			0
$677$			39.9439i			1.53517i	0.640948	+	0.767584i	$0.278541\pi$
$677$			39.9439i			1.53517i	−0.640948	+	0.767584i	$0.721459\pi$
$678$		0			0
$679$	−5.33774			−0.204844
$680$		0			0
$681$	−11.7054			−0.448552
$682$		0			0
$683$	22.2556	+	22.2556i	0.851586	+	0.851586i	0.990329	−	0.138742i	$-0.0443060\pi$
$683$	22.2556	+	22.2556i	0.851586	+	0.851586i	−0.138742	+	0.990329i	$0.544306\pi$
$684$		0			0
$685$	61.2763	−	61.2763i	2.34125	−	2.34125i
$686$		0			0
$687$	−6.41390			−0.244705
$688$		0			0
$689$			2.12532i			0.0809683i
$690$		0			0
$691$	28.8143	+	28.8143i	1.09615	+	1.09615i	0.994857	+	0.101292i	$0.0322977\pi$
$691$	28.8143	+	28.8143i	1.09615	+	1.09615i	0.101292	+	0.994857i	$0.467702\pi$
$692$		0			0
$693$	6.75390			0.256559
$694$		0			0
$695$			21.7897i			0.826531i
$696$		0			0
$697$	−3.56301	−	25.3497i	−0.134959	−	0.960188i
$698$		0			0
$699$			37.3722i			1.41355i
$700$		0			0
$701$	−47.1718			−1.78166			−0.890828	−	0.454341i	$-0.849875\pi$
$701$	−47.1718			−1.78166			−0.890828	+	0.454341i	$0.849875\pi$
$702$		0			0
$703$	−0.665775	−	0.665775i	−0.0251102	−	0.0251102i
$704$		0			0
$705$			24.2919i			0.914885i
$706$		0			0
$707$	1.80881			0.0680273
$708$		0			0
$709$	21.5351	−	21.5351i	0.808766	−	0.808766i	−0.175681	−	0.984447i	$-0.556213\pi$
$709$	21.5351	−	21.5351i	0.808766	−	0.808766i	0.984447	+	0.175681i	$0.0562127\pi$
$710$		0			0
$711$	40.7334	+	40.7334i	1.52762	+	1.52762i
$712$		0			0
$713$	−87.9256			−3.29284
$714$		0			0
$715$	−1.19003			−0.0445045
$716$		0			0
$717$		−	20.7017i		−	0.773120i
$718$		0			0
$719$	−24.1944	−	24.1944i	−0.902299	−	0.902299i	0.0933355	−	0.995635i	$-0.470247\pi$
$719$	−24.1944	−	24.1944i	−0.902299	−	0.902299i	−0.995635	+	0.0933355i	$0.970247\pi$
$720$		0			0
$721$	−2.37306	−	2.37306i	−0.0883775	−	0.0883775i
$722$		0			0
$723$	14.6064	+	14.6064i	0.543216	+	0.543216i
$724$		0			0
$725$	58.8114	−	58.8114i	2.18420	−	2.18420i
$726$		0			0
$727$	6.53856	−	6.53856i	0.242502	−	0.242502i	−0.575383	−	0.817884i	$-0.695147\pi$
$727$	6.53856	−	6.53856i	0.242502	−	0.242502i	0.817884	+	0.575383i	$0.195147\pi$
$728$		0			0
$729$			74.7641i			2.76904i
$730$		0			0
$731$	−31.9459	+	31.9459i	−1.18156	+	1.18156i
$732$		0			0
$733$			28.9164i			1.06805i	0.845469	+	0.534025i	$0.179321\pi$
$733$			28.9164i			1.06805i	−0.845469	+	0.534025i	$0.820679\pi$
$734$		0			0
$735$	9.11934	−	9.11934i	0.336372	−	0.336372i
$736$		0			0
$737$	−6.96158			−0.256433
$738$		0			0
$739$	−19.2957			−0.709804			−0.354902	−	0.934904i	$-0.615486\pi$
$739$	−19.2957			−0.709804			−0.354902	+	0.934904i	$0.615486\pi$
$740$		0			0
$741$	1.66689	−	1.66689i	0.0612347	−	0.0612347i
$742$		0			0
$743$			9.23639i			0.338850i	0.985543	+	0.169425i	$0.0541911\pi$
$743$			9.23639i			0.338850i	−0.985543	+	0.169425i	$0.945809\pi$
$744$		0			0
$745$	−38.7973	+	38.7973i	−1.42142	+	1.42142i
$746$		0			0
$747$			63.4598i			2.32187i
$748$		0			0
$749$	5.65218	−	5.65218i	0.206526	−	0.206526i
$750$		0			0
$751$	18.9416	−	18.9416i	0.691187	−	0.691187i	−0.271306	−	0.962493i	$-0.587456\pi$
$751$	18.9416	−	18.9416i	0.691187	−	0.691187i	0.962493	+	0.271306i	$0.0874556\pi$
$752$		0			0
$753$	30.2415	+	30.2415i	1.10206	+	1.10206i
$754$		0			0
$755$	8.69381	+	8.69381i	0.316400	+	0.316400i
$756$		0			0
$757$	25.0860	+	25.0860i	0.911768	+	0.911768i	0.996411	−	0.0846433i	$-0.0269751\pi$
$757$	25.0860	+	25.0860i	0.911768	+	0.911768i	−0.0846433	+	0.996411i	$0.526975\pi$
$758$		0			0
$759$		−	22.8174i		−	0.828219i
$760$		0			0
$761$	5.10912			0.185205			0.0926027	−	0.995703i	$-0.470481\pi$
$761$	5.10912			0.185205			0.0926027	+	0.995703i	$0.470481\pi$
$762$		0			0
$763$	−6.22373			−0.225314
$764$		0			0
$765$	−87.2621	−	87.2621i	−3.15497	−	3.15497i
$766$		0			0
$767$	−2.62627	+	2.62627i	−0.0948291	+	0.0948291i
$768$		0			0
$769$	50.1889			1.80986			0.904928	−	0.425564i	$-0.139924\pi$
$769$	50.1889			1.80986			0.904928	+	0.425564i	$0.139924\pi$
$770$		0			0
$771$			62.9934i			2.26865i
$772$		0			0
$773$	−2.49807	−	2.49807i	−0.0898492	−	0.0898492i	0.660754	−	0.750603i	$-0.270237\pi$
$773$	−2.49807	−	2.49807i	−0.0898492	−	0.0898492i	−0.750603	+	0.660754i	$0.770237\pi$
$774$		0			0
$775$	−111.501			−4.00524
$776$		0			0
$777$		−	1.55275i		−	0.0557048i
$778$		0			0
$779$	1.78447	+	12.6959i	0.0639352	+	0.454879i
$780$		0			0
$781$		−	1.64468i		−	0.0588511i
$782$		0			0
$783$	−131.325			−4.69317
$784$		0			0
$785$	5.71023	+	5.71023i	0.203807	+	0.203807i
$786$		0			0
$787$			16.8884i			0.602008i	0.953623	+	0.301004i	$0.0973217\pi$
$787$			16.8884i			0.602008i	−0.953623	+	0.301004i	$0.902678\pi$
$788$		0			0
$789$	−52.3828			−1.86488
$790$		0			0
$791$	11.9450	−	11.9450i	0.424715	−	0.424715i
$792$		0			0
$793$	−2.17601	−	2.17601i	−0.0772723	−	0.0772723i
$794$		0			0
$795$	−76.8747			−2.72646
$796$		0			0
$797$	23.7983			0.842979			0.421490	−	0.906833i	$-0.361507\pi$
$797$	23.7983			0.842979			0.421490	+	0.906833i	$0.361507\pi$
$798$		0			0
$799$			7.53029i			0.266402i
$800$		0			0
$801$	−14.9995	−	14.9995i	−0.529981	−	0.529981i
$802$		0			0
$803$	1.13815	+	1.13815i	0.0401644	+	0.0401644i
$804$		0			0
$805$	−22.3320	−	22.3320i	−0.787098	−	0.787098i
$806$		0			0
$807$	−23.1763	+	23.1763i	−0.815845	+	0.815845i
$808$		0			0
$809$	−25.2868	+	25.2868i	−0.889038	+	0.889038i	−0.994431	−	0.105393i	$-0.966390\pi$
$809$	−25.2868	+	25.2868i	−0.889038	+	0.889038i	0.105393	+	0.994431i	$0.466390\pi$
$810$		0			0
$811$			32.5015i			1.14128i	0.821199	+	0.570642i	$0.193305\pi$
$811$			32.5015i			1.14128i	−0.821199	+	0.570642i	$0.806695\pi$
$812$		0			0
$813$	72.6010	−	72.6010i	2.54623	−	2.54623i
$814$		0			0
$815$			26.4209i			0.925482i
$816$		0			0
$817$	15.9995	−	15.9995i	0.559753	−	0.559753i
$818$		0			0
$819$	2.81796			0.0984674
$820$		0			0
$821$	−6.86069			−0.239440			−0.119720	−	0.992808i	$-0.538200\pi$
$821$	−6.86069			−0.239440			−0.119720	+	0.992808i	$0.538200\pi$
$822$		0			0
$823$	−13.2330	+	13.2330i	−0.461272	+	0.461272i	−0.899072	−	0.437800i	$-0.855758\pi$
$823$	−13.2330	+	13.2330i	−0.461272	+	0.461272i	0.437800	+	0.899072i	$0.355758\pi$
$824$		0			0
$825$		−	28.9354i		−	1.00740i
$826$		0			0
$827$	17.0363	−	17.0363i	0.592409	−	0.592409i	−0.345873	−	0.938282i	$-0.612417\pi$
$827$	17.0363	−	17.0363i	0.592409	−	0.592409i	0.938282	+	0.345873i	$0.112417\pi$
$828$		0			0
$829$			29.2692i			1.01656i	0.861191	+	0.508281i	$0.169719\pi$
$829$			29.2692i			1.01656i	−0.861191	+	0.508281i	$0.830281\pi$
$830$		0			0
$831$	20.8707	−	20.8707i	0.723995	−	0.723995i
$832$		0			0
$833$	2.82692	−	2.82692i	0.0979471	−	0.0979471i
$834$		0			0
$835$	39.5855	+	39.5855i	1.36991	+	1.36991i
$836$		0			0
$837$	124.490	+	124.490i	4.30301	+	4.30301i
$838$		0			0
$839$	16.1307	+	16.1307i	0.556894	+	0.556894i	0.928422	−	0.371528i	$-0.121166\pi$
$839$	16.1307	+	16.1307i	0.556894	+	0.556894i	−0.371528	+	0.928422i	$0.621166\pi$
$840$		0			0
$841$		−	36.7862i		−	1.26849i
$842$		0			0
$843$	68.0509			2.34380
$844$		0			0
$845$	50.2774			1.72959
$846$		0			0
$847$	−7.26180	−	7.26180i	−0.249518	−	0.249518i
$848$		0			0
$849$	0.169145	−	0.169145i	0.00580504	−	0.00580504i
$850$		0			0
$851$	−3.80247			−0.130347
$852$		0			0
$853$		−	36.2539i		−	1.24131i	−0.784084	−	0.620655i	$-0.786867\pi$
$853$		−	36.2539i		−	1.24131i	0.784084	−	0.620655i	$-0.213133\pi$
$854$		0			0
$855$	43.7037	+	43.7037i	1.49463	+	1.49463i
$856$		0			0
$857$	−10.5902			−0.361755			−0.180877	−	0.983506i	$-0.557894\pi$
$857$	−10.5902			−0.361755			−0.180877	+	0.983506i	$0.557894\pi$
$858$		0			0
$859$		−	51.6633i		−	1.76273i	−0.472436	−	0.881365i	$-0.656625\pi$
$859$		−	51.6633i		−	1.76273i	0.472436	−	0.881365i	$-0.343375\pi$
$860$		0			0
$861$	−12.7241	+	16.8860i	−0.433638	+	0.575472i
$862$		0			0
$863$		−	58.5729i		−	1.99384i	−0.0783999	−	0.996922i	$-0.524981\pi$
$863$		−	58.5729i		−	1.99384i	0.0783999	−	0.996922i	$-0.475019\pi$
$864$		0			0
$865$	6.30826			0.214487
$866$		0			0
$867$	2.37463	+	2.37463i	0.0806465	+	0.0806465i
$868$		0			0
$869$			6.22861i			0.211291i
$870$		0			0
$871$	−2.90461			−0.0984190
$872$		0			0
$873$	29.8302	−	29.8302i	1.00960	−	1.00960i
$874$		0			0
$875$	−14.5112	−	14.5112i	−0.490567	−	0.490567i
$876$		0			0
$877$	−22.5866			−0.762695			−0.381348	−	0.924432i	$-0.624540\pi$
$877$	−22.5866			−0.762695			−0.381348	+	0.924432i	$0.624540\pi$
$878$		0			0
$879$	58.0190			1.95693
$880$		0			0
$881$			28.0914i			0.946424i	0.880949	+	0.473212i	$0.156906\pi$
$881$			28.0914i			0.946424i	−0.880949	+	0.473212i	$0.843094\pi$
$882$		0			0
$883$	−17.1047	−	17.1047i	−0.575619	−	0.575619i	0.358074	−	0.933693i	$-0.383433\pi$
$883$	−17.1047	−	17.1047i	−0.575619	−	0.575619i	−0.933693	+	0.358074i	$0.883433\pi$
$884$		0			0
$885$	−94.9944	−	94.9944i	−3.19320	−	3.19320i
$886$		0			0
$887$	−25.3742	−	25.3742i	−0.851981	−	0.851981i	0.138396	−	0.990377i	$-0.455805\pi$
$887$	−25.3742	−	25.3742i	−0.851981	−	0.851981i	−0.990377	+	0.138396i	$0.955805\pi$
$888$		0			0
$889$	−5.86141	+	5.86141i	−0.196585	+	0.196585i
$890$		0			0
$891$	−17.9790	+	17.9790i	−0.602320	+	0.602320i
$892$		0			0
$893$		−	3.77141i		−	0.126205i
$894$		0			0
$895$	−44.7306	+	44.7306i	−1.49518	+	1.49518i
$896$		0			0
$897$		−	9.52019i		−	0.317870i
$898$		0			0
$899$	−62.3624	+	62.3624i	−2.07990	+	2.07990i
$900$		0			0
$901$	−23.8305			−0.793910
$902$		0			0
$903$	37.3149			1.24176
$904$		0			0
$905$	32.4076	−	32.4076i	1.07726	−	1.07726i
$906$		0			0
$907$		−	5.29656i		−	0.175869i	−0.996126	−	0.0879347i	$-0.971973\pi$
$907$		−	5.29656i		−	0.175869i	0.996126	−	0.0879347i	$-0.0280267\pi$
$908$		0			0
$909$	−10.1086	+	10.1086i	−0.335282	+	0.335282i
$910$		0			0
$911$		−	50.1707i		−	1.66223i	−0.556102	−	0.831114i	$-0.687704\pi$
$911$		−	50.1707i		−	1.66223i	0.556102	−	0.831114i	$-0.312296\pi$
$912$		0			0
$913$	−4.85186	+	4.85186i	−0.160573	+	0.160573i
$914$		0			0
$915$	78.7080	−	78.7080i	2.60201	−	2.60201i
$916$		0			0
$917$	−14.0093	−	14.0093i	−0.462627	−	0.462627i
$918$		0			0
$919$	8.90836	+	8.90836i	0.293860	+	0.293860i	0.838603	−	0.544743i	$-0.183373\pi$
$919$	8.90836	+	8.90836i	0.293860	+	0.293860i	−0.544743	+	0.838603i	$0.683373\pi$
$920$		0			0
$921$	53.2690	+	53.2690i	1.75527	+	1.75527i
$922$		0			0
$923$		−	0.686215i		−	0.0225870i
$924$		0			0
$925$	−4.82204			−0.158548
$926$		0			0
$927$	26.5240			0.871163
$928$		0			0
$929$	6.59496	+	6.59496i	0.216373	+	0.216373i	0.806968	−	0.590595i	$-0.201107\pi$
$929$	6.59496	+	6.59496i	0.216373	+	0.216373i	−0.590595	+	0.806968i	$0.701107\pi$
$930$		0			0
$931$	−1.41581	+	1.41581i	−0.0464014	+	0.0464014i
$932$		0			0
$933$	−62.7043			−2.05285
$934$		0			0
$935$		−	13.3434i		−	0.436375i
$936$		0			0
$937$	−14.0004	−	14.0004i	−0.457374	−	0.457374i	0.440419	−	0.897792i	$-0.354830\pi$
$937$	−14.0004	−	14.0004i	−0.457374	−	0.457374i	−0.897792	+	0.440419i	$0.854830\pi$
$938$		0			0
$939$	−7.67306			−0.250401
$940$		0			0
$941$			13.5634i			0.442156i	0.975256	+	0.221078i	$0.0709575\pi$
$941$			13.5634i			0.442156i	−0.975256	+	0.221078i	$0.929043\pi$
$942$		0			0
$943$	41.3513	+	31.1596i	1.34659	+	1.01470i
$944$		0			0
$945$			63.2378i			2.05713i
$946$		0			0
$947$	−22.9043			−0.744289			−0.372144	−	0.928175i	$-0.621377\pi$
$947$	−22.9043			−0.744289			−0.372144	+	0.928175i	$0.621377\pi$
$948$		0			0
$949$	0.474875	+	0.474875i	0.0154151	+	0.0154151i
$950$		0			0
$951$		−	38.9309i		−	1.26242i
$952$		0			0
$953$	−9.71926			−0.314838			−0.157419	−	0.987532i	$-0.550317\pi$
$953$	−9.71926			−0.314838			−0.157419	+	0.987532i	$0.550317\pi$
$954$		0			0
$955$	32.8656	−	32.8656i	1.06350	−	1.06350i
$956$		0			0
$957$	−16.1835	−	16.1835i	−0.523139	−	0.523139i
$958$		0			0
$959$	−22.1876			−0.716475
$960$		0			0
$961$	87.2335			2.81398
$962$		0			0
$963$			63.1751i			2.03579i
$964$		0			0
$965$	−43.5370	−	43.5370i	−1.40150	−	1.40150i
$966$		0			0
$967$	20.8288	+	20.8288i	0.669810	+	0.669810i	0.957672	−	0.287862i	$-0.0929444\pi$
$967$	20.8288	+	20.8288i	0.669810	+	0.669810i	−0.287862	+	0.957672i	$0.592944\pi$
$968$		0			0
$969$	18.6903	+	18.6903i	0.600419	+	0.600419i
$970$		0			0
$971$	−21.0041	+	21.0041i	−0.674055	+	0.674055i	−0.958648	−	0.284593i	$-0.908141\pi$
$971$	−21.0041	+	21.0041i	−0.674055	+	0.674055i	0.284593	+	0.958648i	$0.408141\pi$
$972$		0			0
$973$	3.94493	−	3.94493i	0.126469	−	0.126469i
$974$		0			0
$975$		−	12.0729i		−	0.386641i
$976$		0			0
$977$	−21.0885	+	21.0885i	−0.674682	+	0.674682i	−0.958792	−	0.284110i	$-0.908302\pi$
$977$	−21.0885	+	21.0885i	−0.674682	+	0.674682i	0.284110	+	0.958792i	$0.408302\pi$
$978$		0			0
$979$		−	2.29359i		−	0.0733035i
$980$		0			0
$981$	34.7817	−	34.7817i	1.11049	−	1.11049i
$982$		0			0
$983$	−17.4133			−0.555400			−0.277700	−	0.960668i	$-0.589572\pi$
$983$	−17.4133			−0.555400			−0.277700	+	0.960668i	$0.589572\pi$
$984$		0			0
$985$	35.6810			1.13689
$986$		0			0
$987$	4.39793	−	4.39793i	0.139988	−	0.139988i
$988$		0			0
$989$		−	91.3790i		−	2.90568i
$990$		0			0
$991$	−37.4514	+	37.4514i	−1.18968	+	1.18968i	−0.212529	+	0.977155i	$0.568170\pi$
$991$	−37.4514	+	37.4514i	−1.18968	+	1.18968i	−0.977155	+	0.212529i	$0.931830\pi$
$992$		0			0
$993$		−	22.1501i		−	0.702912i
$994$		0			0
$995$	28.3176	−	28.3176i	0.897728	−	0.897728i
$996$		0			0
$997$	−2.44221	+	2.44221i	−0.0773455	+	0.0773455i	−0.744721	−	0.667376i	$-0.767418\pi$
$997$	−2.44221	+	2.44221i	−0.0773455	+	0.0773455i	0.667376	+	0.744721i	$0.267418\pi$
$998$		0			0
$999$	5.38377	+	5.38377i	0.170335	+	0.170335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.1	yes	36
41.9	even	4	inner	1148.2.k.b.337.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.1	✓	36	41.9	even	4	inner
1148.2.k.b.729.1	yes	36	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +O(q^{10})\)	\(q+(-2.33489 + 2.33489i) q^{3} -3.90568i q^{5} +(-0.707107 + 0.707107i) q^{7} -7.90342i q^{9} +(0.604261 - 0.604261i) q^{11} +(0.252118 - 0.252118i) q^{13} +(9.11934 + 9.11934i) q^{15} +(2.82692 + 2.82692i) q^{17} +(-1.41581 - 1.41581i) q^{19} -3.30203i q^{21} -8.08621 q^{23} -10.2544 q^{25} +(11.4489 + 11.4489i) q^{27} +(-5.73525 + 5.73525i) q^{29} +10.8735 q^{31} +2.82177i q^{33} +(2.76174 + 2.76174i) q^{35} +0.470242 q^{37} +1.17734i q^{39} +(-5.11381 - 3.85343i) q^{41} +11.3006i q^{43} -30.8682 q^{45} +(1.33189 + 1.33189i) q^{47} -1.00000i q^{49} -13.2011 q^{51} +(-4.21493 + 4.21493i) q^{53} +(-2.36005 - 2.36005i) q^{55} +6.61154 q^{57} -10.4168 q^{59} -8.63089i q^{61} +(5.58856 + 5.58856i) q^{63} +(-0.984695 - 0.984695i) q^{65} +(-5.76041 - 5.76041i) q^{67} +(18.8804 - 18.8804i) q^{69} +(1.36090 - 1.36090i) q^{71} +1.88354i q^{73} +(23.9428 - 23.9428i) q^{75} +0.854555i q^{77} +(-5.15390 + 5.15390i) q^{79} -29.7537 q^{81} -8.02941 q^{83} +(11.0411 - 11.0411i) q^{85} -26.7823i q^{87} +(1.89785 - 1.89785i) q^{89} +0.356549i q^{91} +(-25.3885 + 25.3885i) q^{93} +(-5.52972 + 5.52972i) q^{95} +(3.77435 + 3.77435i) q^{97} +(-4.77573 - 4.77573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

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