LMFDB - Embedded newform 1148.2.k.a.337.1

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.1
Root			$2.77462i$ of defining polynomial
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.a.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96195 - 1.96195i) q^{3} +0.264927i q^{5} +(0.707107 + 0.707107i) q^{7} +4.69853i q^{9} +O(q^{10})$	\(q+(-1.96195 - 1.96195i) q^{3} +0.264927i q^{5} +(0.707107 + 0.707107i) q^{7} +4.69853i q^{9} +(1.34670 + 1.34670i) q^{11} +(-2.27061 - 2.27061i) q^{13} +(0.519775 - 0.519775i) q^{15} +(0.388375 - 0.388375i) q^{17} +(1.69703 - 1.69703i) q^{19} -2.77462i q^{21} +8.48741 q^{23} +4.92981 q^{25} +(3.33244 - 3.33244i) q^{27} +(-4.81835 - 4.81835i) q^{29} +2.85071 q^{31} -5.28432i q^{33} +(-0.187332 + 0.187332i) q^{35} -5.41421 q^{37} +8.90966i q^{39} +(-1.29857 - 6.27006i) q^{41} +4.60518i q^{43} -1.24477 q^{45} +(4.98575 - 4.98575i) q^{47} +1.00000i q^{49} -1.52395 q^{51} +(-1.45740 - 1.45740i) q^{53} +(-0.356777 + 0.356777i) q^{55} -6.65898 q^{57} -7.20096 q^{59} -7.94631i q^{61} +(-3.32236 + 3.32236i) q^{63} +(0.601545 - 0.601545i) q^{65} +(2.37617 - 2.37617i) q^{67} +(-16.6519 - 16.6519i) q^{69} +(-10.1997 - 10.1997i) q^{71} -4.71279i q^{73} +(-9.67207 - 9.67207i) q^{75} +1.90452i q^{77} +(2.09335 + 2.09335i) q^{79} +1.01939 q^{81} +5.22549 q^{83} +(0.102891 + 0.102891i) q^{85} +18.9068i q^{87} +(-8.76187 - 8.76187i) q^{89} -3.21112i q^{91} +(-5.59297 - 5.59297i) q^{93} +(0.449589 + 0.449589i) q^{95} +(1.75373 - 1.75373i) q^{97} +(-6.32750 + 6.32750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3}+O(q^{10}) $ 8 * q - 4 * q^3	$ 8 q - 4 q^{3} + 12 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 8 q^{19} + 28 q^{23} - 4 q^{25} + 8 q^{27} - 16 q^{29} + 28 q^{31} - 8 q^{35} - 32 q^{37} - 4 q^{45} + 20 q^{47} - 20 q^{51} + 32 q^{53} - 4 q^{55} - 36 q^{57} - 20 q^{59} - 8 q^{63} - 4 q^{67} - 44 q^{69} + 8 q^{71} + 12 q^{75} - 12 q^{79} - 16 q^{81} - 64 q^{83} - 56 q^{85} + 4 q^{89} - 4 q^{93} - 52 q^{95} + 56 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 8 * q^19 + 28 * q^23 - 4 * q^25 + 8 * q^27 - 16 * q^29 + 28 * q^31 - 8 * q^35 - 32 * q^37 - 4 * q^45 + 20 * q^47 - 20 * q^51 + 32 * q^53 - 4 * q^55 - 36 * q^57 - 20 * q^59 - 8 * q^63 - 4 * q^67 - 44 * q^69 + 8 * q^71 + 12 * q^75 - 12 * q^79 - 16 * q^81 - 64 * q^83 - 56 * q^85 + 4 * q^89 - 4 * q^93 - 52 * q^95 + 56 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.96195	−	1.96195i	−1.13274	−	1.13274i	−0.989721	−	0.143014i	$-0.954320\pi$
$3$	−1.96195	−	1.96195i	−1.13274	−	1.13274i	−0.143014	−	0.989721i	$-0.545680\pi$
$4$		0			0
$5$			0.264927i			0.118479i	0.998244	+	0.0592395i	$0.0188676\pi$
$5$			0.264927i			0.118479i	−0.998244	+	0.0592395i	$0.981132\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$			4.69853i			1.56618i
$10$		0			0
$11$	1.34670	+	1.34670i	0.406045	+	0.406045i	0.880357	−	0.474312i	$-0.157303\pi$
$11$	1.34670	+	1.34670i	0.406045	+	0.406045i	−0.474312	+	0.880357i	$0.657303\pi$
$12$		0			0
$13$	−2.27061	−	2.27061i	−0.629753	−	0.629753i	0.318253	−	0.948006i	$-0.396904\pi$
$13$	−2.27061	−	2.27061i	−0.629753	−	0.629753i	−0.948006	+	0.318253i	$0.896904\pi$
$14$		0			0
$15$	0.519775	−	0.519775i	0.134205	−	0.134205i
$16$		0			0
$17$	0.388375	−	0.388375i	0.0941949	−	0.0941949i	−0.658439	−	0.752634i	$-0.728783\pi$
$17$	0.388375	−	0.388375i	0.0941949	−	0.0941949i	0.752634	+	0.658439i	$0.228783\pi$
$18$		0			0
$19$	1.69703	−	1.69703i	0.389325	−	0.389325i	−0.485122	−	0.874447i	$-0.661225\pi$
$19$	1.69703	−	1.69703i	0.389325	−	0.389325i	0.874447	+	0.485122i	$0.161225\pi$
$20$		0			0
$21$		−	2.77462i		−	0.605472i
$22$		0			0
$23$	8.48741			1.76975			0.884874	−	0.465831i	$-0.154245\pi$
$23$	8.48741			1.76975			0.884874	+	0.465831i	$0.154245\pi$
$24$		0			0
$25$	4.92981			0.985963
$26$		0			0
$27$	3.33244	−	3.33244i	0.641329	−	0.641329i
$28$		0			0
$29$	−4.81835	−	4.81835i	−0.894745	−	0.894745i	0.100221	−	0.994965i	$-0.468045\pi$
$29$	−4.81835	−	4.81835i	−0.894745	−	0.894745i	−0.994965	+	0.100221i	$0.968045\pi$
$30$		0			0
$31$	2.85071			0.512003			0.256002	−	0.966676i	$-0.417595\pi$
$31$	2.85071			0.512003			0.256002	+	0.966676i	$0.417595\pi$
$32$		0			0
$33$		−	5.28432i		−	0.919882i
$34$		0			0
$35$	−0.187332	+	0.187332i	−0.0316648	+	0.0316648i
$36$		0			0
$37$	−5.41421			−0.890091			−0.445046	−	0.895508i	$-0.646813\pi$
$37$	−5.41421			−0.890091			−0.445046	+	0.895508i	$0.646813\pi$
$38$		0			0
$39$			8.90966i			1.42669i
$40$		0			0
$41$	−1.29857	−	6.27006i	−0.202803	−	0.979220i
$41$	−1.29857	−	6.27006i	−0.202803	−	0.979220i
$42$		0			0
$43$			4.60518i			0.702283i	0.936322	+	0.351142i	$0.114206\pi$
$43$			4.60518i			0.702283i	−0.936322	+	0.351142i	$0.885794\pi$
$44$		0			0
$45$	−1.24477			−0.185559
$46$		0			0
$47$	4.98575	−	4.98575i	0.727246	−	0.727246i	−0.242824	−	0.970070i	$-0.578074\pi$
$47$	4.98575	−	4.98575i	0.727246	−	0.727246i	0.970070	+	0.242824i	$0.0780739\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−1.52395			−0.213396
$52$		0			0
$53$	−1.45740	−	1.45740i	−0.200189	−	0.200189i	0.599892	−	0.800081i	$-0.295210\pi$
$53$	−1.45740	−	1.45740i	−0.200189	−	0.200189i	−0.800081	+	0.599892i	$0.795210\pi$
$54$		0			0
$55$	−0.356777	+	0.356777i	−0.0481078	+	0.0481078i
$56$		0			0
$57$	−6.65898			−0.882004
$58$		0			0
$59$	−7.20096			−0.937485			−0.468743	−	0.883335i	$-0.655293\pi$
$59$	−7.20096			−0.937485			−0.468743	+	0.883335i	$0.655293\pi$
$60$		0			0
$61$		−	7.94631i		−	1.01742i	−0.860938	−	0.508710i	$-0.830122\pi$
$61$		−	7.94631i		−	1.01742i	0.860938	−	0.508710i	$-0.169878\pi$
$62$		0			0
$63$	−3.32236	+	3.32236i	−0.418579	+	0.418579i
$64$		0			0
$65$	0.601545	−	0.601545i	0.0746125	−	0.0746125i
$66$		0			0
$67$	2.37617	−	2.37617i	0.290295	−	0.290295i	−0.546902	−	0.837197i	$-0.684193\pi$
$67$	2.37617	−	2.37617i	0.290295	−	0.290295i	0.837197	+	0.546902i	$0.184193\pi$
$68$		0			0
$69$	−16.6519	−	16.6519i	−2.00465	−	2.00465i
$70$		0			0
$71$	−10.1997	−	10.1997i	−1.21048	−	1.21048i	−0.970870	−	0.239606i	$-0.922982\pi$
$71$	−10.1997	−	10.1997i	−1.21048	−	1.21048i	−0.239606	−	0.970870i	$-0.577018\pi$
$72$		0			0
$73$		−	4.71279i		−	0.551590i	−0.961216	−	0.275795i	$-0.911059\pi$
$73$		−	4.71279i		−	0.551590i	0.961216	−	0.275795i	$-0.0889411\pi$
$74$		0			0
$75$	−9.67207	−	9.67207i	−1.11683	−	1.11683i
$76$		0			0
$77$			1.90452i			0.217040i
$78$		0			0
$79$	2.09335	+	2.09335i	0.235521	+	0.235521i	0.814992	−	0.579472i	$-0.196741\pi$
$79$	2.09335	+	2.09335i	0.235521	+	0.235521i	−0.579472	+	0.814992i	$0.696741\pi$
$80$		0			0
$81$	1.01939			0.113266
$82$		0			0
$83$	5.22549			0.573572			0.286786	−	0.957995i	$-0.407413\pi$
$83$	5.22549			0.573572			0.286786	+	0.957995i	$0.407413\pi$
$84$		0			0
$85$	0.102891	+	0.102891i	0.0111601	+	0.0111601i
$86$		0			0
$87$			18.9068i			2.02702i
$88$		0			0
$89$	−8.76187	−	8.76187i	−0.928757	−	0.928757i	0.0688690	−	0.997626i	$-0.478061\pi$
$89$	−8.76187	−	8.76187i	−0.928757	−	0.928757i	−0.997626	+	0.0688690i	$0.978061\pi$
$90$		0			0
$91$		−	3.21112i		−	0.336617i
$92$		0			0
$93$	−5.59297	−	5.59297i	−0.579964	−	0.579964i
$94$		0			0
$95$	0.449589	+	0.449589i	0.0461268	+	0.0461268i
$96$		0			0
$97$	1.75373	−	1.75373i	0.178064	−	0.178064i	−0.612447	−	0.790511i	$-0.709815\pi$
$97$	1.75373	−	1.75373i	0.178064	−	0.178064i	0.790511	+	0.612447i	$0.209815\pi$
$98$		0			0
$99$	−6.32750	+	6.32750i	−0.635938	+	0.635938i
$100$		0			0
$101$	−9.64419	+	9.64419i	−0.959632	+	0.959632i	−0.999216	−	0.0395839i	$-0.987397\pi$
$101$	−9.64419	+	9.64419i	−0.959632	+	0.959632i	0.0395839	+	0.999216i	$0.487397\pi$
$102$		0			0
$103$		−	15.8061i		−	1.55743i	−0.627381	−	0.778713i	$-0.715873\pi$
$103$		−	15.8061i		−	1.55743i	0.627381	−	0.778713i	$-0.284127\pi$
$104$		0			0
$105$	0.735073			0.0717358
$106$		0			0
$107$	13.8551			1.33942			0.669711	−	0.742622i	$-0.266418\pi$
$107$	13.8551			1.33942			0.669711	+	0.742622i	$0.266418\pi$
$108$		0			0
$109$	1.32387	−	1.32387i	0.126804	−	0.126804i	−0.640857	−	0.767660i	$-0.721421\pi$
$109$	1.32387	−	1.32387i	0.126804	−	0.126804i	0.767660	+	0.640857i	$0.221421\pi$
$110$		0			0
$111$	10.6224	+	10.6224i	1.00824	+	1.00824i
$112$		0			0
$113$	7.30737			0.687420			0.343710	−	0.939076i	$-0.388316\pi$
$113$	7.30737			0.687420			0.343710	+	0.939076i	$0.388316\pi$
$114$		0			0
$115$			2.24854i			0.209678i
$116$		0			0
$117$	10.6685	−	10.6685i	0.986305	−	0.986305i
$118$		0			0
$119$	0.549246			0.0503493
$120$		0			0
$121$		−	7.37281i		−	0.670256i
$122$		0			0
$123$	−9.75384	+	14.8493i	−0.879474	+	1.33892i
$124$		0			0
$125$			2.63068i			0.235295i
$126$		0			0
$127$	15.6246			1.38646			0.693228	−	0.720718i	$-0.256188\pi$
$127$	15.6246			1.38646			0.693228	+	0.720718i	$0.256188\pi$
$128$		0			0
$129$	9.03515	−	9.03515i	0.795501	−	0.795501i
$130$		0			0
$131$			3.39919i			0.296989i	0.988913	+	0.148494i	$0.0474427\pi$
$131$			3.39919i			0.296989i	−0.988913	+	0.148494i	$0.952557\pi$
$132$		0			0
$133$	2.39996			0.208103
$134$		0			0
$135$	0.882855	+	0.882855i	0.0759840	+	0.0759840i
$136$		0			0
$137$	−4.00664	+	4.00664i	−0.342311	+	0.342311i	−0.857235	−	0.514925i	$-0.827820\pi$
$137$	−4.00664	+	4.00664i	−0.342311	+	0.342311i	0.514925	+	0.857235i	$0.327820\pi$
$138$		0			0
$139$	−6.88404			−0.583897			−0.291948	−	0.956434i	$-0.594304\pi$
$139$	−6.88404			−0.583897			−0.291948	+	0.956434i	$0.594304\pi$
$140$		0			0
$141$	−19.5636			−1.64755
$142$		0			0
$143$		−	6.11564i		−	0.511416i
$144$		0			0
$145$	1.27651	−	1.27651i	0.106008	−	0.106008i
$146$		0			0
$147$	1.96195	−	1.96195i	0.161819	−	0.161819i
$148$		0			0
$149$	−6.76659	+	6.76659i	−0.554341	+	0.554341i	−0.927691	−	0.373350i	$-0.878209\pi$
$149$	−6.76659	+	6.76659i	−0.554341	+	0.554341i	0.373350	+	0.927691i	$0.378209\pi$
$150$		0			0
$151$	2.11843	+	2.11843i	0.172395	+	0.172395i	0.788031	−	0.615636i	$-0.211101\pi$
$151$	2.11843	+	2.11843i	0.172395	+	0.172395i	−0.615636	+	0.788031i	$0.711101\pi$
$152$		0			0
$153$	1.82479	+	1.82479i	0.147526	+	0.147526i
$154$		0			0
$155$			0.755231i			0.0606616i
$156$		0			0
$157$	11.8925	+	11.8925i	0.949125	+	0.949125i	0.998767	−	0.0496418i	$-0.0158080\pi$
$157$	11.8925	+	11.8925i	0.949125	+	0.949125i	−0.0496418	+	0.998767i	$0.515808\pi$
$158$		0			0
$159$			5.71869i			0.453522i
$160$		0			0
$161$	6.00150	+	6.00150i	0.472985	+	0.472985i
$162$		0			0
$163$	−1.33403			−0.104489			−0.0522446	−	0.998634i	$-0.516638\pi$
$163$	−1.33403			−0.104489			−0.0522446	+	0.998634i	$0.516638\pi$
$164$		0			0
$165$	1.39996			0.108987
$166$		0			0
$167$	7.52963	+	7.52963i	0.582660	+	0.582660i	0.935633	−	0.352973i	$-0.114829\pi$
$167$	7.52963	+	7.52963i	0.582660	+	0.582660i	−0.352973	+	0.935633i	$0.614829\pi$
$168$		0			0
$169$		−	2.68869i		−	0.206822i
$170$		0			0
$171$	7.97354	+	7.97354i	0.609752	+	0.609752i
$172$		0			0
$173$		−	8.87223i		−	0.674543i	−0.941407	−	0.337272i	$-0.890496\pi$
$173$		−	8.87223i		−	0.674543i	0.941407	−	0.337272i	$-0.109504\pi$
$174$		0			0
$175$	3.48590	+	3.48590i	0.263510	+	0.263510i
$176$		0			0
$177$	14.1280	+	14.1280i	1.06192	+	1.06192i
$178$		0			0
$179$	−11.5723	+	11.5723i	−0.864952	+	0.864952i	−0.991908	−	0.126956i	$-0.959479\pi$
$179$	−11.5723	+	11.5723i	−0.864952	+	0.864952i	0.126956	+	0.991908i	$0.459479\pi$
$180$		0			0
$181$	17.1911	−	17.1911i	1.27780	−	1.27780i	0.335908	−	0.941895i	$-0.390957\pi$
$181$	17.1911	−	17.1911i	1.27780	−	1.27780i	0.941895	−	0.335908i	$-0.109043\pi$
$182$		0			0
$183$	−15.5903	+	15.5903i	−1.15247	+	1.15247i
$184$		0			0
$185$		−	1.43437i		−	0.105457i
$186$		0			0
$187$	1.04605			0.0764946
$188$		0			0
$189$	4.71279			0.342805
$190$		0			0
$191$	−4.16868	+	4.16868i	−0.301635	+	0.301635i	−0.841653	−	0.540018i	$-0.818417\pi$
$191$	−4.16868	+	4.16868i	−0.301635	+	0.301635i	0.540018	+	0.841653i	$0.318417\pi$
$192$		0			0
$193$	−2.32731	−	2.32731i	−0.167523	−	0.167523i	0.618367	−	0.785890i	$-0.287795\pi$
$193$	−2.32731	−	2.32731i	−0.167523	−	0.167523i	−0.785890	+	0.618367i	$0.787795\pi$
$194$		0			0
$195$	−2.36041			−0.169032
$196$		0			0
$197$			5.23565i			0.373025i	0.982453	+	0.186512i	$0.0597184\pi$
$197$			5.23565i			0.373025i	−0.982453	+	0.186512i	$0.940282\pi$
$198$		0			0
$199$	−0.292893	+	0.292893i	−0.0207626	+	0.0207626i	−0.717412	−	0.696649i	$-0.754673\pi$
$199$	−0.292893	+	0.292893i	−0.0207626	+	0.0207626i	0.696649	+	0.717412i	$0.254673\pi$
$200$		0			0
$201$	−9.32387			−0.657655
$202$		0			0
$203$		−	6.81417i		−	0.478261i
$204$		0			0
$205$	1.66111	−	0.344027i	0.116017	−	0.0240279i
$206$		0			0
$207$			39.8784i			2.77174i
$208$		0			0
$209$	4.57077			0.316166
$210$		0			0
$211$	18.2894	−	18.2894i	1.25909	−	1.25909i	0.307566	−	0.951527i	$-0.400486\pi$
$211$	18.2894	−	18.2894i	1.25909	−	1.25909i	0.951527	−	0.307566i	$-0.0995144\pi$
$212$		0			0
$213$			40.0225i			2.74230i
$214$		0			0
$215$	−1.22004			−0.0832058
$216$		0			0
$217$	2.01576	+	2.01576i	0.136839	+	0.136839i
$218$		0			0
$219$	−9.24627	+	9.24627i	−0.624805	+	0.624805i
$220$		0			0
$221$	−1.76370			−0.118639
$222$		0			0
$223$	19.9404			1.33531			0.667654	−	0.744472i	$-0.267298\pi$
$223$	19.9404			1.33531			0.667654	+	0.744472i	$0.267298\pi$
$224$		0			0
$225$			23.1629i			1.54419i
$226$		0			0
$227$	6.48795	−	6.48795i	0.430620	−	0.430620i	−0.458219	−	0.888839i	$-0.651512\pi$
$227$	6.48795	−	6.48795i	0.430620	−	0.430620i	0.888839	+	0.458219i	$0.151512\pi$
$228$		0			0
$229$	14.5372	−	14.5372i	0.960647	−	0.960647i	−0.0386070	−	0.999254i	$-0.512292\pi$
$229$	14.5372	−	14.5372i	0.960647	−	0.960647i	0.999254	+	0.0386070i	$0.0122920\pi$
$230$		0			0
$231$	3.73658	−	3.73658i	0.245849	−	0.245849i
$232$		0			0
$233$	−13.5652	−	13.5652i	−0.888688	−	0.888688i	0.105709	−	0.994397i	$-0.466289\pi$
$233$	−13.5652	−	13.5652i	−0.888688	−	0.888688i	−0.994397	+	0.105709i	$0.966289\pi$
$234$		0			0
$235$	1.32086	+	1.32086i	0.0861634	+	0.0861634i
$236$		0			0
$237$		−	8.21413i		−	0.533565i
$238$		0			0
$239$	1.25999	+	1.25999i	0.0815017	+	0.0815017i	0.746682	−	0.665181i	$-0.231646\pi$
$239$	1.25999	+	1.25999i	0.0815017	+	0.0815017i	−0.665181	+	0.746682i	$0.731646\pi$
$240$		0			0
$241$			22.0935i			1.42317i	0.702602	+	0.711583i	$0.252021\pi$
$241$			22.0935i			1.42317i	−0.702602	+	0.711583i	$0.747979\pi$
$242$		0			0
$243$	−11.9973	−	11.9973i	−0.769629	−	0.769629i
$244$		0			0
$245$	−0.264927			−0.0169256
$246$		0			0
$247$	−7.70656			−0.490357
$248$		0			0
$249$	−10.2522	−	10.2522i	−0.649705	−	0.649705i
$250$		0			0
$251$			1.40510i			0.0886889i	0.999016	+	0.0443445i	$0.0141199\pi$
$251$			1.40510i			0.0886889i	−0.999016	+	0.0443445i	$0.985880\pi$
$252$		0			0
$253$	11.4300	+	11.4300i	0.718596	+	0.718596i
$254$		0			0
$255$		−	0.403736i		−	0.0252829i
$256$		0			0
$257$	10.0087	+	10.0087i	0.624325	+	0.624325i	0.946634	−	0.322309i	$-0.104459\pi$
$257$	10.0087	+	10.0087i	0.624325	+	0.624325i	−0.322309	+	0.946634i	$0.604459\pi$
$258$		0			0
$259$	−3.82843	−	3.82843i	−0.237887	−	0.237887i
$260$		0			0
$261$	22.6392	−	22.6392i	1.40133	−	1.40133i
$262$		0			0
$263$	12.6340	−	12.6340i	0.779047	−	0.779047i	−0.200621	−	0.979669i	$-0.564296\pi$
$263$	12.6340	−	12.6340i	0.779047	−	0.779047i	0.979669	+	0.200621i	$0.0642961\pi$
$264$		0			0
$265$	0.386104	−	0.386104i	0.0237182	−	0.0237182i
$266$		0			0
$267$			34.3808i			2.10407i
$268$		0			0
$269$	−2.93740			−0.179096			−0.0895481	−	0.995982i	$-0.528542\pi$
$269$	−2.93740			−0.179096			−0.0895481	+	0.995982i	$0.528542\pi$
$270$		0			0
$271$	28.2650			1.71698			0.858490	−	0.512831i	$-0.171403\pi$
$271$	28.2650			1.71698			0.858490	+	0.512831i	$0.171403\pi$
$272$		0			0
$273$	−6.30008	+	6.30008i	−0.381298	+	0.381298i
$274$		0			0
$275$	6.63897	+	6.63897i	0.400345	+	0.400345i
$276$		0			0
$277$	6.51773			0.391612			0.195806	−	0.980643i	$-0.437268\pi$
$277$	6.51773			0.391612			0.195806	+	0.980643i	$0.437268\pi$
$278$		0			0
$279$			13.3942i			0.801888i
$280$		0			0
$281$	−9.24423	+	9.24423i	−0.551464	+	0.551464i	−0.926863	−	0.375399i	$-0.877506\pi$
$281$	−9.24423	+	9.24423i	−0.551464	+	0.551464i	0.375399	+	0.926863i	$0.377506\pi$
$282$		0			0
$283$	−10.8916			−0.647440			−0.323720	−	0.946153i	$-0.604934\pi$
$283$	−10.8916			−0.647440			−0.323720	+	0.946153i	$0.604934\pi$
$284$		0			0
$285$		−	1.76415i		−	0.104499i
$286$		0			0
$287$	3.51538	−	5.35183i	0.207506	−	0.315909i
$288$		0			0
$289$			16.6983i			0.982255i
$290$		0			0
$291$	−6.88146			−0.403399
$292$		0			0
$293$	17.6563	−	17.6563i	1.03149	−	1.03149i	0.0320051	−	0.999488i	$-0.489811\pi$
$293$	17.6563	−	17.6563i	1.03149	−	1.03149i	0.999488	−	0.0320051i	$-0.0101893\pi$
$294$		0			0
$295$		−	1.90773i		−	0.111072i
$296$		0			0
$297$	8.97559			0.520816
$298$		0			0
$299$	−19.2716	−	19.2716i	−1.11450	−	1.11450i
$300$		0			0
$301$	−3.25635	+	3.25635i	−0.187693	+	0.187693i
$302$		0			0
$303$	37.8429			2.17402
$304$		0			0
$305$	2.10519			0.120543
$306$		0			0
$307$			4.96454i			0.283341i	0.989914	+	0.141671i	$0.0452474\pi$
$307$			4.96454i			0.283341i	−0.989914	+	0.141671i	$0.954753\pi$
$308$		0			0
$309$	−31.0109	+	31.0109i	−1.76415	+	1.76415i
$310$		0			0
$311$	−18.5981	+	18.5981i	−1.05460	+	1.05460i	−0.0561814	+	0.998421i	$0.517893\pi$
$311$	−18.5981	+	18.5981i	−1.05460	+	1.05460i	−0.998421	+	0.0561814i	$0.982107\pi$
$312$		0			0
$313$	−14.1404	+	14.1404i	−0.799262	+	0.799262i	−0.982979	−	0.183717i	$-0.941187\pi$
$313$	−14.1404	+	14.1404i	−0.799262	+	0.799262i	0.183717	+	0.982979i	$0.441187\pi$
$314$		0			0
$315$	−0.880184	−	0.880184i	−0.0495928	−	0.0495928i
$316$		0			0
$317$	3.46643	+	3.46643i	0.194694	+	0.194694i	0.797721	−	0.603027i	$-0.206039\pi$
$317$	3.46643	+	3.46643i	0.194694	+	0.194694i	−0.603027	+	0.797721i	$0.706039\pi$
$318$		0			0
$319$		−	12.9777i		−	0.726612i
$320$		0			0
$321$	−27.1830	−	27.1830i	−1.51721	−	1.51721i
$322$		0			0
$323$		−	1.31817i		−	0.0733448i
$324$		0			0
$325$	−11.1937	−	11.1937i	−0.620913	−	0.620913i
$326$		0			0
$327$	−5.19474			−0.287270
$328$		0			0
$329$	7.05091			0.388729
$330$		0			0
$331$	−15.2485	−	15.2485i	−0.838136	−	0.838136i	0.150478	−	0.988613i	$-0.451919\pi$
$331$	−15.2485	−	15.2485i	−0.838136	−	0.838136i	−0.988613	+	0.150478i	$0.951919\pi$
$332$		0			0
$333$		−	25.4389i		−	1.39404i
$334$		0			0
$335$	0.629511	+	0.629511i	0.0343939	+	0.0343939i
$336$		0			0
$337$			18.3839i			1.00143i	0.865612	+	0.500716i	$0.166930\pi$
$337$			18.3839i			1.00143i	−0.865612	+	0.500716i	$0.833070\pi$
$338$		0			0
$339$	−14.3367	−	14.3367i	−0.778664	−	0.778664i
$340$		0			0
$341$	3.83905	+	3.83905i	0.207896	+	0.207896i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	4.41154	−	4.41154i	0.237510	−	0.237510i
$346$		0			0
$347$	−7.61244	+	7.61244i	−0.408657	+	0.408657i	−0.881270	−	0.472613i	$-0.843311\pi$
$347$	−7.61244	+	7.61244i	−0.408657	+	0.408657i	0.472613	+	0.881270i	$0.343311\pi$
$348$		0			0
$349$		−	21.3533i		−	1.14301i	−0.820597	−	0.571507i	$-0.806359\pi$
$349$		−	21.3533i		−	1.14301i	0.820597	−	0.571507i	$-0.193641\pi$
$350$		0			0
$351$	−15.1333			−0.807758
$352$		0			0
$353$	−5.97149			−0.317830			−0.158915	−	0.987292i	$-0.550800\pi$
$353$	−5.97149			−0.317830			−0.158915	+	0.987292i	$0.550800\pi$
$354$		0			0
$355$	2.70216	−	2.70216i	0.143416	−	0.143416i
$356$		0			0
$357$	−1.07760	−	1.07760i	−0.0570324	−	0.0570324i
$358$		0			0
$359$	−16.2872			−0.859606			−0.429803	−	0.902923i	$-0.641417\pi$
$359$	−16.2872			−0.859606			−0.429803	+	0.902923i	$0.641417\pi$
$360$		0			0
$361$			13.2402i			0.696852i
$362$		0			0
$363$	−14.4651	+	14.4651i	−0.759222	+	0.759222i
$364$		0			0
$365$	1.24854			0.0653518
$366$		0			0
$367$		−	4.58443i		−	0.239305i	−0.992816	−	0.119653i	$-0.961822\pi$
$367$		−	4.58443i		−	0.239305i	0.992816	−	0.119653i	$-0.0381781\pi$
$368$		0			0
$369$	29.4601	−	6.10139i	1.53363	−	0.317625i
$370$		0			0
$371$		−	2.06107i		−	0.107005i
$372$		0			0
$373$	12.1200			0.627550			0.313775	−	0.949497i	$-0.398406\pi$
$373$	12.1200			0.627550			0.313775	+	0.949497i	$0.398406\pi$
$374$		0			0
$375$	5.16127	−	5.16127i	0.266527	−	0.266527i
$376$		0			0
$377$			21.8811i			1.12694i
$378$		0			0
$379$	−30.2921			−1.55600			−0.778002	−	0.628262i	$-0.783766\pi$
$379$	−30.2921			−1.55600			−0.778002	+	0.628262i	$0.783766\pi$
$380$		0			0
$381$	−30.6547	−	30.6547i	−1.57049	−	1.57049i
$382$		0			0
$383$	−15.7844	+	15.7844i	−0.806545	+	0.806545i	−0.984109	−	0.177564i	$-0.943178\pi$
$383$	−15.7844	+	15.7844i	−0.806545	+	0.806545i	0.177564	+	0.984109i	$0.443178\pi$
$384$		0			0
$385$	−0.504558			−0.0257147
$386$		0			0
$387$	−21.6376			−1.09990
$388$		0			0
$389$		−	16.8519i		−	0.854424i	−0.904152	−	0.427212i	$-0.859496\pi$
$389$		−	16.8519i		−	0.854424i	0.904152	−	0.427212i	$-0.140504\pi$
$390$		0			0
$391$	3.29630	−	3.29630i	0.166701	−	0.166701i
$392$		0			0
$393$	6.66906	−	6.66906i	0.336410	−	0.336410i
$394$		0			0
$395$	−0.554586	+	0.554586i	−0.0279043	+	0.0279043i
$396$		0			0
$397$	8.74658	+	8.74658i	0.438978	+	0.438978i	0.891668	−	0.452690i	$-0.149536\pi$
$397$	8.74658	+	8.74658i	0.438978	+	0.438978i	−0.452690	+	0.891668i	$0.649536\pi$
$398$		0			0
$399$	−4.70861	−	4.70861i	−0.235725	−	0.235725i
$400$		0			0
$401$		−	5.45453i		−	0.272386i	−0.990682	−	0.136193i	$-0.956513\pi$
$401$		−	5.45453i		−	0.272386i	0.990682	−	0.136193i	$-0.0434868\pi$
$402$		0			0
$403$	−6.47285	−	6.47285i	−0.322436	−	0.322436i
$404$		0			0
$405$			0.270064i			0.0134196i
$406$		0			0
$407$	−7.29131	−	7.29131i	−0.361417	−	0.361417i
$408$		0			0
$409$	−7.93025			−0.392125			−0.196063	−	0.980591i	$-0.562816\pi$
$409$	−7.93025			−0.392125			−0.196063	+	0.980591i	$0.562816\pi$
$410$		0			0
$411$	15.7217			0.775494
$412$		0			0
$413$	−5.09185	−	5.09185i	−0.250554	−	0.250554i
$414$		0			0
$415$			1.38437i			0.0679563i
$416$		0			0
$417$	13.5062	+	13.5062i	0.661400	+	0.661400i
$418$		0			0
$419$		−	0.174150i		−	0.00850779i	−0.999991	−	0.00425389i	$-0.998646\pi$
$419$		−	0.174150i		−	0.00850779i	0.999991	−	0.00425389i	$-0.00135406\pi$
$420$		0			0
$421$	18.4110	+	18.4110i	0.897297	+	0.897297i	0.995196	−	0.0978991i	$-0.0312122\pi$
$421$	18.4110	+	18.4110i	0.897297	+	0.897297i	−0.0978991	+	0.995196i	$0.531212\pi$
$422$		0			0
$423$	23.4257	+	23.4257i	1.13900	+	1.13900i
$424$		0			0
$425$	1.91462	−	1.91462i	0.0928726	−	0.0928726i
$426$		0			0
$427$	5.61889	−	5.61889i	0.271917	−	0.271917i
$428$		0			0
$429$	−11.9986	+	11.9986i	−0.579298	+	0.579298i
$430$		0			0
$431$			9.31765i			0.448815i	0.974495	+	0.224408i	$0.0720447\pi$
$431$			9.31765i			0.448815i	−0.974495	+	0.224408i	$0.927955\pi$
$432$		0			0
$433$	−25.1797			−1.21006			−0.605030	−	0.796203i	$-0.706839\pi$
$433$	−25.1797			−1.21006			−0.605030	+	0.796203i	$0.706839\pi$
$434$		0			0
$435$	−5.00891			−0.240159
$436$		0			0
$437$	14.4034	−	14.4034i	0.689007	−	0.689007i
$438$		0			0
$439$	23.8045	+	23.8045i	1.13613	+	1.13613i	0.989138	+	0.146989i	$0.0469583\pi$
$439$	23.8045	+	23.8045i	1.13613	+	1.13613i	0.146989	+	0.989138i	$0.453042\pi$
$440$		0			0
$441$	−4.69853			−0.223740
$442$		0			0
$443$		−	9.08865i		−	0.431815i	−0.976414	−	0.215907i	$-0.930729\pi$
$443$		−	9.08865i		−	0.431815i	0.976414	−	0.215907i	$-0.0692709\pi$
$444$		0			0
$445$	2.32126	−	2.32126i	0.110038	−	0.110038i
$446$		0			0
$447$	26.5515			1.25584
$448$		0			0
$449$			16.1623i			0.762746i	0.924421	+	0.381373i	$0.124549\pi$
$449$			16.1623i			0.762746i	−0.924421	+	0.381373i	$0.875451\pi$
$450$		0			0
$451$	6.69510	−	10.1927i	0.315260	−	0.479954i
$452$		0			0
$453$		−	8.31251i		−	0.390556i
$454$		0			0
$455$	0.850714			0.0398821
$456$		0			0
$457$	19.5663	−	19.5663i	0.915272	−	0.915272i	−0.0814086	−	0.996681i	$-0.525942\pi$
$457$	19.5663	−	19.5663i	0.915272	−	0.915272i	0.996681	+	0.0814086i	$0.0259419\pi$
$458$		0			0
$459$		−	2.58848i		−	0.120820i
$460$		0			0
$461$	−21.0298			−0.979456			−0.489728	−	0.871875i	$-0.662904\pi$
$461$	−21.0298			−0.979456			−0.489728	+	0.871875i	$0.662904\pi$
$462$		0			0
$463$	−18.6948	−	18.6948i	−0.868821	−	0.868821i	0.123521	−	0.992342i	$-0.460581\pi$
$463$	−18.6948	−	18.6948i	−0.868821	−	0.868821i	−0.992342	+	0.123521i	$0.960581\pi$
$464$		0			0
$465$	1.48173	−	1.48173i	0.0687136	−	0.0687136i
$466$		0			0
$467$	−0.476776			−0.0220625			−0.0110313	−	0.999939i	$-0.503511\pi$
$467$	−0.476776			−0.0220625			−0.0110313	+	0.999939i	$0.503511\pi$
$468$		0			0
$469$	3.36041			0.155169
$470$		0			0
$471$		−	46.6651i		−	2.15022i
$472$		0			0
$473$	−6.20178	+	6.20178i	−0.285158	+	0.285158i
$474$		0			0
$475$	8.36603	−	8.36603i	0.383860	−	0.383860i
$476$		0			0
$477$	6.84762	−	6.84762i	0.313531	−	0.313531i
$478$		0			0
$479$	−21.1157	−	21.1157i	−0.964802	−	0.964802i	0.0345991	−	0.999401i	$-0.488985\pi$
$479$	−21.1157	−	21.1157i	−0.964802	−	0.964802i	−0.999401	+	0.0345991i	$0.988985\pi$
$480$		0			0
$481$	12.2936	+	12.2936i	0.560538	+	0.560538i
$482$		0			0
$483$		−	23.5494i		−	1.07153i
$484$		0			0
$485$	0.464610	+	0.464610i	0.0210968	+	0.0210968i
$486$		0			0
$487$			32.6793i			1.48084i	0.672145	+	0.740419i	$0.265373\pi$
$487$			32.6793i			1.48084i	−0.672145	+	0.740419i	$0.734627\pi$
$488$		0			0
$489$	2.61730	+	2.61730i	0.118359	+	0.118359i
$490$		0			0
$491$	15.9847			0.721378			0.360689	−	0.932686i	$-0.382542\pi$
$491$	15.9847			0.721378			0.360689	+	0.932686i	$0.382542\pi$
$492$		0			0
$493$	−3.74266			−0.168561
$494$		0			0
$495$	−1.67633	−	1.67633i	−0.0753453	−	0.0753453i
$496$		0			0
$497$		−	14.4245i		−	0.647027i
$498$		0			0
$499$	0.957123	+	0.957123i	0.0428467	+	0.0428467i	0.728206	−	0.685359i	$-0.240355\pi$
$499$	0.957123	+	0.957123i	0.0428467	+	0.0428467i	−0.685359	+	0.728206i	$0.740355\pi$
$500$		0			0
$501$		−	29.5456i		−	1.32000i
$502$		0			0
$503$	2.82457	+	2.82457i	0.125941	+	0.125941i	0.767268	−	0.641327i	$-0.221616\pi$
$503$	2.82457	+	2.82457i	0.125941	+	0.125941i	−0.641327	+	0.767268i	$0.721616\pi$
$504$		0			0
$505$	−2.55501	−	2.55501i	−0.113696	−	0.113696i
$506$		0			0
$507$	−5.27509	+	5.27509i	−0.234275	+	0.234275i
$508$		0			0
$509$	−10.1342	+	10.1342i	−0.449190	+	0.449190i	−0.895085	−	0.445895i	$-0.852885\pi$
$509$	−10.1342	+	10.1342i	−0.449190	+	0.449190i	0.445895	+	0.895085i	$0.352885\pi$
$510$		0			0
$511$	3.33244	−	3.33244i	0.147419	−	0.147419i
$512$		0			0
$513$		−	11.3105i		−	0.499371i
$514$		0			0
$515$	4.18748			0.184522
$516$		0			0
$517$	13.4286			0.590588
$518$		0			0
$519$	−17.4069	+	17.4069i	−0.764079	+	0.764079i
$520$		0			0
$521$	−14.8728	−	14.8728i	−0.651590	−	0.651590i	0.301786	−	0.953376i	$-0.402417\pi$
$521$	−14.8728	−	14.8728i	−0.651590	−	0.651590i	−0.953376	+	0.301786i	$0.902417\pi$
$522$		0			0
$523$	9.18217			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$523$	9.18217			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$524$		0			0
$525$		−	13.6784i		−	0.596973i
$526$		0			0
$527$	1.10715	−	1.10715i	0.0482281	−	0.0482281i
$528$		0			0
$529$	49.0361			2.13201
$530$		0			0
$531$		−	33.8340i		−	1.46827i
$532$		0			0
$533$	−11.2883	+	17.1854i	−0.488951	+	0.744382i
$534$		0			0
$535$			3.67059i			0.158693i
$536$		0			0
$537$	45.4085			1.95952
$538$		0			0
$539$	−1.34670	+	1.34670i	−0.0580064	+	0.0580064i
$540$		0			0
$541$			13.7837i			0.592609i	0.955093	+	0.296305i	$0.0957544\pi$
$541$			13.7837i			0.592609i	−0.955093	+	0.296305i	$0.904246\pi$
$542$		0			0
$543$	−67.4562			−2.89482
$544$		0			0
$545$	0.350729	+	0.350729i	0.0150236	+	0.0150236i
$546$		0			0
$547$	−4.43809	+	4.43809i	−0.189759	+	0.189759i	−0.795592	−	0.605833i	$-0.792840\pi$
$547$	−4.43809	+	4.43809i	−0.189759	+	0.189759i	0.605833	+	0.795592i	$0.292840\pi$
$548$		0			0
$549$	37.3360			1.59346
$550$		0			0
$551$	−16.3537			−0.696693
$552$		0			0
$553$			2.96045i			0.125891i
$554$		0			0
$555$	−2.81417	+	2.81417i	−0.119455	+	0.119455i
$556$		0			0
$557$	1.25894	−	1.25894i	0.0533431	−	0.0533431i	−0.679932	−	0.733275i	$-0.737991\pi$
$557$	1.25894	−	1.25894i	0.0533431	−	0.0533431i	0.733275	+	0.679932i	$0.237991\pi$
$558$		0			0
$559$	10.4565	−	10.4565i	0.442265	−	0.442265i
$560$		0			0
$561$	−2.05230	−	2.05230i	−0.0866482	−	0.0866482i
$562$		0			0
$563$	14.0050	+	14.0050i	0.590242	+	0.590242i	0.937697	−	0.347455i	$-0.112954\pi$
$563$	14.0050	+	14.0050i	0.590242	+	0.590242i	−0.347455	+	0.937697i	$0.612954\pi$
$564$		0			0
$565$			1.93592i			0.0814448i
$566$		0			0
$567$	0.720819	+	0.720819i	0.0302715	+	0.0302715i
$568$		0			0
$569$			5.90873i			0.247707i	0.992301	+	0.123853i	$0.0395252\pi$
$569$			5.90873i			0.247707i	−0.992301	+	0.123853i	$0.960475\pi$
$570$		0			0
$571$	13.1937	+	13.1937i	0.552137	+	0.552137i	0.927057	−	0.374920i	$-0.122330\pi$
$571$	13.1937	+	13.1937i	0.552137	+	0.552137i	−0.374920	+	0.927057i	$0.622330\pi$
$572$		0			0
$573$	16.3575			0.683345
$574$		0			0
$575$	41.8413			1.74490
$576$		0			0
$577$	−26.6879	−	26.6879i	−1.11103	−	1.11103i	−0.993011	−	0.118023i	$-0.962344\pi$
$577$	−26.6879	−	26.6879i	−1.11103	−	1.11103i	−0.118023	−	0.993011i	$-0.537656\pi$
$578$		0			0
$579$			9.13214i			0.379519i
$580$		0			0
$581$	3.69498	+	3.69498i	0.153294	+	0.153294i
$582$		0			0
$583$		−	3.92534i		−	0.162571i
$584$		0			0
$585$	2.82638	+	2.82638i	0.116856	+	0.116856i
$586$		0			0
$587$	−26.6502	−	26.6502i	−1.09997	−	1.09997i	−0.994413	−	0.105559i	$-0.966337\pi$
$587$	−26.6502	−	26.6502i	−1.09997	−	1.09997i	−0.105559	−	0.994413i	$-0.533663\pi$
$588$		0			0
$589$	4.83774	−	4.83774i	0.199336	−	0.199336i
$590$		0			0
$591$	10.2721	−	10.2721i	0.422538	−	0.422538i
$592$		0			0
$593$	−32.1291	+	32.1291i	−1.31938	+	1.31938i	−0.405119	+	0.914264i	$0.632770\pi$
$593$	−32.1291	+	32.1291i	−1.31938	+	1.31938i	−0.914264	+	0.405119i	$0.867230\pi$
$594$		0			0
$595$			0.145510i			0.00596533i
$596$		0			0
$597$	1.14929			0.0470372
$598$		0			0
$599$	30.7755			1.25745			0.628727	−	0.777627i	$-0.283577\pi$
$599$	30.7755			1.25745			0.628727	+	0.777627i	$0.283577\pi$
$600$		0			0
$601$	−7.73391	+	7.73391i	−0.315473	+	0.315473i	−0.847025	−	0.531553i	$-0.821609\pi$
$601$	−7.73391	+	7.73391i	−0.315473	+	0.315473i	0.531553	+	0.847025i	$0.321609\pi$
$602$		0			0
$603$	11.1645	+	11.1645i	0.454654	+	0.454654i
$604$		0			0
$605$	1.95326			0.0794112
$606$		0			0
$607$			7.88845i			0.320182i	0.987102	+	0.160091i	$0.0511788\pi$
$607$			7.88845i			0.320182i	−0.987102	+	0.160091i	$0.948821\pi$
$608$		0			0
$609$	−13.3691	+	13.3691i	−0.541743	+	0.541743i
$610$		0			0
$611$	−22.6413			−0.915970
$612$		0			0
$613$		−	35.3094i		−	1.42613i	−0.701096	−	0.713067i	$-0.747306\pi$
$613$		−	35.3094i		−	1.42613i	0.701096	−	0.713067i	$-0.252694\pi$
$614$		0			0
$615$	−3.93399	−	2.58406i	−0.158634	−	0.104199i
$616$		0			0
$617$			29.2802i			1.17878i	0.807850	+	0.589388i	$0.200631\pi$
$617$			29.2802i			1.17878i	−0.807850	+	0.589388i	$0.799369\pi$
$618$		0			0
$619$	24.0348			0.966040			0.483020	−	0.875609i	$-0.339540\pi$
$619$	24.0348			0.966040			0.483020	+	0.875609i	$0.339540\pi$
$620$		0			0
$621$	28.2838	−	28.2838i	1.13499	−	1.13499i
$622$		0			0
$623$		−	12.3912i		−	0.496441i
$624$		0			0
$625$	23.9521			0.958085
$626$		0			0
$627$	−8.96763	−	8.96763i	−0.358133	−	0.358133i
$628$		0			0
$629$	−2.10275	+	2.10275i	−0.0838420	+	0.0838420i
$630$		0			0
$631$	−12.5780			−0.500722			−0.250361	−	0.968153i	$-0.580549\pi$
$631$	−12.5780			−0.500722			−0.250361	+	0.968153i	$0.580549\pi$
$632$		0			0
$633$	−71.7658			−2.85244
$634$		0			0
$635$			4.13937i			0.164266i
$636$		0			0
$637$	2.27061	−	2.27061i	0.0899647	−	0.0899647i
$638$		0			0
$639$	47.9234	−	47.9234i	1.89582	−	1.89582i
$640$		0			0
$641$	−7.81684	+	7.81684i	−0.308747	+	0.308747i	−0.844423	−	0.535677i	$-0.820057\pi$
$641$	−7.81684	+	7.81684i	−0.308747	+	0.308747i	0.535677	+	0.844423i	$0.320057\pi$
$642$		0			0
$643$	21.6495	+	21.6495i	0.853772	+	0.853772i	0.990595	−	0.136824i	$-0.0436894\pi$
$643$	21.6495	+	21.6495i	0.853772	+	0.853772i	−0.136824	+	0.990595i	$0.543689\pi$
$644$		0			0
$645$	2.39366	+	2.39366i	0.0942501	+	0.0942501i
$646$		0			0
$647$			34.4562i			1.35461i	0.735700	+	0.677307i	$0.236853\pi$
$647$			34.4562i			1.35461i	−0.735700	+	0.677307i	$0.763147\pi$
$648$		0			0
$649$	−9.69752	−	9.69752i	−0.380661	−	0.380661i
$650$		0			0
$651$		−	7.90966i		−	0.310004i
$652$		0			0
$653$	−2.18143	−	2.18143i	−0.0853659	−	0.0853659i	0.663134	−	0.748500i	$-0.269226\pi$
$653$	−2.18143	−	2.18143i	−0.0853659	−	0.0853659i	−0.748500	+	0.663134i	$0.769226\pi$
$654$		0			0
$655$	−0.900538			−0.0351869
$656$		0			0
$657$	22.1432			0.863888
$658$		0			0
$659$	24.4481	+	24.4481i	0.952362	+	0.952362i	0.998916	−	0.0465537i	$-0.0148238\pi$
$659$	24.4481	+	24.4481i	0.952362	+	0.952362i	−0.0465537	+	0.998916i	$0.514824\pi$
$660$		0			0
$661$			28.1554i			1.09512i	0.836767	+	0.547559i	$0.184443\pi$
$661$			28.1554i			1.09512i	−0.836767	+	0.547559i	$0.815557\pi$
$662$		0			0
$663$	3.46029	+	3.46029i	0.134387	+	0.134387i
$664$		0			0
$665$			0.635814i			0.0246558i
$666$		0			0
$667$	−40.8953	−	40.8953i	−1.58347	−	1.58347i
$668$		0			0
$669$	−39.1222	−	39.1222i	−1.51255	−	1.51255i
$670$		0			0
$671$	10.7013	−	10.7013i	0.413118	−	0.413118i
$672$		0			0
$673$	2.20479	−	2.20479i	0.0849884	−	0.0849884i	−0.663335	−	0.748323i	$-0.730859\pi$
$673$	2.20479	−	2.20479i	0.0849884	−	0.0849884i	0.748323	+	0.663335i	$0.230859\pi$
$674$		0			0
$675$	16.4283	−	16.4283i	0.632326	−	0.632326i
$676$		0			0
$677$			11.7758i			0.452582i	0.974060	+	0.226291i	$0.0726601\pi$
$677$			11.7758i			0.452582i	−0.974060	+	0.226291i	$0.927340\pi$
$678$		0			0
$679$	2.48014			0.0951792
$680$		0			0
$681$	−25.4581			−0.975558
$682$		0			0
$683$	13.7547	−	13.7547i	0.526309	−	0.526309i	−0.393161	−	0.919470i	$-0.628619\pi$
$683$	13.7547	−	13.7547i	0.526309	−	0.526309i	0.919470	+	0.393161i	$0.128619\pi$
$684$		0			0
$685$	−1.06147	−	1.06147i	−0.0405566	−	0.0405566i
$686$		0			0
$687$	−57.0428			−2.17632
$688$		0			0
$689$			6.61835i			0.252139i
$690$		0			0
$691$	−10.3182	+	10.3182i	−0.392523	+	0.392523i	−0.875586	−	0.483063i	$-0.839524\pi$
$691$	−10.3182	+	10.3182i	−0.392523	+	0.392523i	0.483063	+	0.875586i	$0.339524\pi$
$692$		0			0
$693$	−8.94844			−0.339923
$694$		0			0
$695$		−	1.82377i		−	0.0691795i
$696$		0			0
$697$	−2.93947	−	1.93081i	−0.111340	−	0.0731345i
$698$		0			0
$699$			53.2287i			2.01330i
$700$		0			0
$701$	−17.0764			−0.644965			−0.322483	−	0.946575i	$-0.604517\pi$
$701$	−17.0764			−0.644965			−0.322483	+	0.946575i	$0.604517\pi$
$702$		0			0
$703$	−9.18807	+	9.18807i	−0.346535	+	0.346535i
$704$		0			0
$705$		−	5.18293i		−	0.195201i
$706$		0			0
$707$	−13.6389			−0.512945
$708$		0			0
$709$	−18.9068	−	18.9068i	−0.710058	−	0.710058i	0.256489	−	0.966547i	$-0.417434\pi$
$709$	−18.9068	−	18.9068i	−0.710058	−	0.710058i	−0.966547	+	0.256489i	$0.917434\pi$
$710$		0			0
$711$	−9.83569	+	9.83569i	−0.368867	+	0.368867i
$712$		0			0
$713$	24.1952			0.906116
$714$		0			0
$715$	1.62020			0.0605920
$716$		0			0
$717$		−	4.94407i		−	0.184640i
$718$		0			0
$719$	29.2577	−	29.2577i	1.09113	−	1.09113i	0.0957184	−	0.995408i	$-0.469485\pi$
$719$	29.2577	−	29.2577i	1.09113	−	1.09113i	0.995408	−	0.0957184i	$-0.0305148\pi$
$720$		0			0
$721$	11.1766	−	11.1766i	0.416239	−	0.416239i
$722$		0			0
$723$	43.3464	−	43.3464i	1.61207	−	1.61207i
$724$		0			0
$725$	−23.7536	−	23.7536i	−0.882185	−	0.882185i
$726$		0			0
$727$	4.35820	+	4.35820i	0.161637	+	0.161637i	0.783291	−	0.621655i	$-0.213539\pi$
$727$	4.35820	+	4.35820i	0.161637	+	0.161637i	−0.621655	+	0.783291i	$0.713539\pi$
$728$		0			0
$729$			44.0183i			1.63031i
$730$		0			0
$731$	1.78854	+	1.78854i	0.0661515	+	0.0661515i
$732$		0			0
$733$			18.3057i			0.676138i	0.941121	+	0.338069i	$0.109774\pi$
$733$			18.3057i			0.676138i	−0.941121	+	0.338069i	$0.890226\pi$
$734$		0			0
$735$	0.519775	+	0.519775i	0.0191722	+	0.0191722i
$736$		0			0
$737$	6.39996			0.235746
$738$		0			0
$739$	34.9475			1.28556			0.642782	−	0.766049i	$-0.277780\pi$
$739$	34.9475			1.28556			0.642782	+	0.766049i	$0.277780\pi$
$740$		0			0
$741$	15.1199	+	15.1199i	0.555445	+	0.555445i
$742$		0			0
$743$		−	25.6926i		−	0.942569i	−0.881981	−	0.471285i	$-0.843790\pi$
$743$		−	25.6926i		−	0.942569i	0.881981	−	0.471285i	$-0.156210\pi$
$744$		0			0
$745$	−1.79265	−	1.79265i	−0.0656777	−	0.0656777i
$746$		0			0
$747$			24.5521i			0.898316i
$748$		0			0
$749$	9.79702	+	9.79702i	0.357975	+	0.357975i
$750$		0			0
$751$	−28.8718	−	28.8718i	−1.05355	−	1.05355i	−0.998483	−	0.0550643i	$-0.982464\pi$
$751$	−28.8718	−	28.8718i	−1.05355	−	1.05355i	−0.0550643	−	0.998483i	$-0.517536\pi$
$752$		0			0
$753$	2.75674	−	2.75674i	0.100461	−	0.100461i
$754$		0			0
$755$	−0.561228	+	0.561228i	−0.0204252	+	0.0204252i
$756$		0			0
$757$	29.8572	−	29.8572i	1.08518	−	1.08518i	0.0891598	−	0.996017i	$-0.471582\pi$
$757$	29.8572	−	29.8572i	1.08518	−	1.08518i	0.996017	−	0.0891598i	$-0.0284182\pi$
$758$		0			0
$759$		−	44.8502i		−	1.62796i
$760$		0			0
$761$	−24.8981			−0.902555			−0.451278	−	0.892384i	$-0.649032\pi$
$761$	−24.8981			−0.902555			−0.451278	+	0.892384i	$0.649032\pi$
$762$		0			0
$763$	1.87223			0.0677794
$764$		0			0
$765$	−0.483438	+	0.483438i	−0.0174787	+	0.0174787i
$766$		0			0
$767$	16.3506	+	16.3506i	0.590384	+	0.590384i
$768$		0			0
$769$	−3.33102			−0.120120			−0.0600598	−	0.998195i	$-0.519129\pi$
$769$	−3.33102			−0.120120			−0.0600598	+	0.998195i	$0.519129\pi$
$770$		0			0
$771$		−	39.2732i		−	1.41439i
$772$		0			0
$773$	−22.9740	+	22.9740i	−0.826316	+	0.826316i	−0.987005	−	0.160689i	$-0.948628\pi$
$773$	−22.9740	+	22.9740i	−0.826316	+	0.826316i	0.160689	+	0.987005i	$0.448628\pi$
$774$		0			0
$775$	14.0535			0.504816
$776$		0			0
$777$			15.0224i			0.538926i
$778$		0			0
$779$	−12.8442	−	8.43676i	−0.460191	−	0.302278i
$780$		0			0
$781$		−	27.4717i		−	0.983015i
$782$		0			0
$783$	−32.1137			−1.14765
$784$		0			0
$785$	−3.15065	+	3.15065i	−0.112451	+	0.112451i
$786$		0			0
$787$			46.1994i			1.64683i	0.567440	+	0.823415i	$0.307934\pi$
$787$			46.1994i			1.64683i	−0.567440	+	0.823415i	$0.692066\pi$
$788$		0			0
$789$	−49.5748			−1.76491
$790$		0			0
$791$	5.16709	+	5.16709i	0.183721	+	0.183721i
$792$		0			0
$793$	−18.0429	+	18.0429i	−0.640724	+	0.640724i
$794$		0			0
$795$	−1.51504			−0.0537328
$796$		0			0
$797$	−50.8500			−1.80120			−0.900599	−	0.434650i	$-0.856872\pi$
$797$	−50.8500			−1.80120			−0.900599	+	0.434650i	$0.856872\pi$
$798$		0			0
$799$		−	3.87268i		−	0.137006i
$800$		0			0
$801$	41.1679	−	41.1679i	1.45460	−	1.45460i
$802$		0			0
$803$	6.34670	−	6.34670i	0.223970	−	0.223970i
$804$		0			0
$805$	−1.58996	+	1.58996i	−0.0560388	+	0.0560388i
$806$		0			0
$807$	5.76304	+	5.76304i	0.202869	+	0.202869i
$808$		0			0
$809$	−27.8275	−	27.8275i	−0.978362	−	0.978362i	0.0214085	−	0.999771i	$-0.493185\pi$
$809$	−27.8275	−	27.8275i	−0.978362	−	0.978362i	−0.999771	+	0.0214085i	$0.993185\pi$
$810$		0			0
$811$		−	15.0900i		−	0.529882i	−0.964265	−	0.264941i	$-0.914648\pi$
$811$		−	15.0900i		−	0.529882i	0.964265	−	0.264941i	$-0.0853525\pi$
$812$		0			0
$813$	−55.4547	−	55.4547i	−1.94488	−	1.94488i
$814$		0			0
$815$		−	0.353420i		−	0.0123798i
$816$		0			0
$817$	7.81511	+	7.81511i	0.273416	+	0.273416i
$818$		0			0
$819$	15.0876			0.527202
$820$		0			0
$821$	−28.0957			−0.980547			−0.490274	−	0.871569i	$-0.663103\pi$
$821$	−28.0957			−0.980547			−0.490274	+	0.871569i	$0.663103\pi$
$822$		0			0
$823$	−3.07633	−	3.07633i	−0.107234	−	0.107234i	0.651454	−	0.758688i	$-0.274159\pi$
$823$	−3.07633	−	3.07633i	−0.107234	−	0.107234i	−0.758688	+	0.651454i	$0.774159\pi$
$824$		0			0
$825$		−	26.0507i		−	0.906969i
$826$		0			0
$827$	35.4926	+	35.4926i	1.23420	+	1.23420i	0.962337	+	0.271860i	$0.0876388\pi$
$827$	35.4926	+	35.4926i	1.23420	+	1.23420i	0.271860	+	0.962337i	$0.412361\pi$
$828$		0			0
$829$		−	25.4034i		−	0.882297i	−0.897434	−	0.441148i	$-0.854571\pi$
$829$		−	25.4034i		−	0.882297i	0.897434	−	0.441148i	$-0.145429\pi$
$830$		0			0
$831$	−12.7875	−	12.7875i	−0.443593	−	0.443593i
$832$		0			0
$833$	0.388375	+	0.388375i	0.0134564	+	0.0134564i
$834$		0			0
$835$	−1.99480	+	1.99480i	−0.0690330	+	0.0690330i
$836$		0			0
$837$	9.49984	−	9.49984i	0.328363	−	0.328363i
$838$		0			0
$839$	17.7919	−	17.7919i	0.614244	−	0.614244i	−0.329805	−	0.944049i	$-0.606983\pi$
$839$	17.7919	−	17.7919i	0.614244	−	0.614244i	0.944049	+	0.329805i	$0.106983\pi$
$840$		0			0
$841$			17.4330i			0.601136i
$842$		0			0
$843$	36.2735			1.24933
$844$		0			0
$845$	0.712307			0.0245041
$846$		0			0
$847$	5.21337	−	5.21337i	0.179133	−	0.179133i
$848$		0			0
$849$	21.3689	+	21.3689i	0.733378	+	0.733378i
$850$		0			0
$851$	−45.9526			−1.57524
$852$		0			0
$853$			23.7561i			0.813394i	0.913563	+	0.406697i	$0.133319\pi$
$853$			23.7561i			0.813394i	−0.913563	+	0.406697i	$0.866681\pi$
$854$		0			0
$855$	−2.11241	+	2.11241i	−0.0722428	+	0.0722428i
$856$		0			0
$857$	−28.7151			−0.980891			−0.490445	−	0.871472i	$-0.663166\pi$
$857$	−28.7151			−0.980891			−0.490445	+	0.871472i	$0.663166\pi$
$858$		0			0
$859$			51.2425i			1.74837i	0.485591	+	0.874186i	$0.338605\pi$
$859$			51.2425i			1.74837i	−0.485591	+	0.874186i	$0.661395\pi$
$860$		0			0
$861$	−17.3971	+	3.60305i	−0.592890	+	0.122792i
$862$		0			0
$863$			26.3448i			0.896787i	0.893836	+	0.448393i	$0.148004\pi$
$863$			26.3448i			0.896787i	−0.893836	+	0.448393i	$0.851996\pi$
$864$		0			0
$865$	2.35050			0.0799192
$866$		0			0
$867$	32.7614	−	32.7614i	1.11263	−	1.11263i
$868$		0			0
$869$			5.63823i			0.191264i
$870$		0			0
$871$	−10.7907			−0.365628
$872$		0			0
$873$	8.23994	+	8.23994i	0.278880	+	0.278880i
$874$		0			0
$875$	−1.86017	+	1.86017i	−0.0628852	+	0.0628852i
$876$		0			0
$877$	28.7938			0.972297			0.486149	−	0.873876i	$-0.338401\pi$
$877$	28.7938			0.972297			0.486149	+	0.873876i	$0.338401\pi$
$878$		0			0
$879$	−69.2818			−2.33682
$880$		0			0
$881$			38.8776i			1.30982i	0.755706	+	0.654911i	$0.227294\pi$
$881$			38.8776i			1.30982i	−0.755706	+	0.654911i	$0.772706\pi$
$882$		0			0
$883$	−13.5326	+	13.5326i	−0.455407	+	0.455407i	−0.897144	−	0.441738i	$-0.854362\pi$
$883$	−13.5326	+	13.5326i	−0.455407	+	0.455407i	0.441738	+	0.897144i	$0.354362\pi$
$884$		0			0
$885$	−3.74288	+	3.74288i	−0.125816	+	0.125816i
$886$		0			0
$887$	−0.136076	+	0.136076i	−0.00456897	+	0.00456897i	−0.709388	−	0.704819i	$-0.751028\pi$
$887$	−0.136076	+	0.136076i	−0.00456897	+	0.00456897i	0.704819	+	0.709388i	$0.251028\pi$
$888$		0			0
$889$	11.0482	+	11.0482i	0.370546	+	0.370546i
$890$		0			0
$891$	1.37281	+	1.37281i	0.0459909	+	0.0459909i
$892$		0			0
$893$		−	16.9219i		−	0.566270i
$894$		0			0
$895$	−3.06581	−	3.06581i	−0.102479	−	0.102479i
$896$		0			0
$897$			75.6199i			2.52487i
$898$		0			0
$899$	−13.7357	−	13.7357i	−0.458112	−	0.458112i
$900$		0			0
$901$	−1.13203			−0.0377135
$902$		0			0
$903$	12.7776			0.425213
$904$		0			0
$905$	4.55438	+	4.55438i	0.151393	+	0.151393i
$906$		0			0
$907$		−	44.1392i		−	1.46562i	−0.680434	−	0.732810i	$-0.738209\pi$
$907$		−	44.1392i		−	1.46562i	0.680434	−	0.732810i	$-0.261791\pi$
$908$		0			0
$909$	−45.3135	−	45.3135i	−1.50295	−	1.50295i
$910$		0			0
$911$		−	32.9596i		−	1.09200i	−0.837785	−	0.546000i	$-0.816150\pi$
$911$		−	32.9596i		−	1.09200i	0.837785	−	0.546000i	$-0.183850\pi$
$912$		0			0
$913$	7.03716	+	7.03716i	0.232896	+	0.232896i
$914$		0			0
$915$	−4.13029	−	4.13029i	−0.136543	−	0.136543i
$916$		0			0
$917$	−2.40359	+	2.40359i	−0.0793736	+	0.0793736i
$918$		0			0
$919$	−39.5210	+	39.5210i	−1.30368	+	1.30368i	−0.377786	+	0.925893i	$0.623315\pi$
$919$	−39.5210	+	39.5210i	−1.30368	+	1.30368i	−0.925893	+	0.377786i	$0.876685\pi$
$920$		0			0
$921$	9.74021	−	9.74021i	0.320951	−	0.320951i
$922$		0			0
$923$			46.3188i			1.52460i
$924$		0			0
$925$	−26.6911			−0.877597
$926$		0			0
$927$	74.2657			2.43920
$928$		0			0
$929$	30.7928	−	30.7928i	1.01028	−	1.01028i	0.0103340	−	0.999947i	$-0.496711\pi$
$929$	30.7928	−	30.7928i	1.01028	−	1.01028i	0.999947	−	0.0103340i	$-0.00328947\pi$
$930$		0			0
$931$	1.69703	+	1.69703i	0.0556178	+	0.0556178i
$932$		0			0
$933$	72.9773			2.38917
$934$		0			0
$935$			0.277127i			0.00906301i
$936$		0			0
$937$	−4.93882	+	4.93882i	−0.161344	+	0.161344i	−0.783162	−	0.621818i	$-0.786394\pi$
$937$	−4.93882	+	4.93882i	−0.161344	+	0.161344i	0.621818	+	0.783162i	$0.286394\pi$
$938$		0			0
$939$	55.4856			1.81070
$940$		0			0
$941$			49.9147i			1.62717i	0.581443	+	0.813587i	$0.302488\pi$
$941$			49.9147i			1.62717i	−0.581443	+	0.813587i	$0.697512\pi$
$942$		0			0
$943$	−11.0215	−	53.2166i	−0.358910	−	1.73297i
$944$		0			0
$945$			1.24854i			0.0406152i
$946$		0			0
$947$	−40.4419			−1.31419			−0.657093	−	0.753810i	$-0.728214\pi$
$947$	−40.4419			−1.31419			−0.657093	+	0.753810i	$0.728214\pi$
$948$		0			0
$949$	−10.7009	+	10.7009i	−0.347365	+	0.347365i
$950$		0			0
$951$		−	13.6020i		−	0.441074i
$952$		0			0
$953$	19.2628			0.623983			0.311991	−	0.950085i	$-0.399004\pi$
$953$	19.2628			0.623983			0.311991	+	0.950085i	$0.399004\pi$
$954$		0			0
$955$	−1.10440	−	1.10440i	−0.0357374	−	0.0357374i
$956$		0			0
$957$	−25.4617	+	25.4617i	−0.823059	+	0.823059i
$958$		0			0
$959$	−5.66625			−0.182973
$960$		0			0
$961$	−22.8734			−0.737853
$962$		0			0
$963$			65.0986i			2.09777i
$964$		0			0
$965$	0.616566	−	0.616566i	0.0198480	−	0.0198480i
$966$		0			0
$967$	16.9442	−	16.9442i	0.544888	−	0.544888i	−0.380070	−	0.924958i	$-0.624100\pi$
$967$	16.9442	−	16.9442i	0.544888	−	0.544888i	0.924958	+	0.380070i	$0.124100\pi$
$968$		0			0
$969$	−2.58619	+	2.58619i	−0.0830802	+	0.0830802i
$970$		0			0
$971$	18.9234	+	18.9234i	0.607280	+	0.607280i	0.942234	−	0.334955i	$-0.108721\pi$
$971$	18.9234	+	18.9234i	0.607280	+	0.607280i	−0.334955	+	0.942234i	$0.608721\pi$
$972$		0			0
$973$	−4.86775	−	4.86775i	−0.156053	−	0.156053i
$974$		0			0
$975$			43.9229i			1.40666i
$976$		0			0
$977$	−7.18434	−	7.18434i	−0.229848	−	0.229848i	0.582781	−	0.812629i	$-0.301964\pi$
$977$	−7.18434	−	7.18434i	−0.229848	−	0.229848i	−0.812629	+	0.582781i	$0.801964\pi$
$978$		0			0
$979$		−	23.5992i		−	0.754233i
$980$		0			0
$981$	6.22024	+	6.22024i	0.198597	+	0.198597i
$982$		0			0
$983$	−47.2815			−1.50805			−0.754023	−	0.656848i	$-0.771889\pi$
$983$	−47.2815			−1.50805			−0.754023	+	0.656848i	$0.771889\pi$
$984$		0			0
$985$	−1.38707			−0.0441956
$986$		0			0
$987$	−13.8336	−	13.8336i	−0.440327	−	0.440327i
$988$		0			0
$989$			39.0860i			1.24286i
$990$		0			0
$991$	14.2015	+	14.2015i	0.451124	+	0.451124i	0.895728	−	0.444603i	$-0.146655\pi$
$991$	14.2015	+	14.2015i	0.451124	+	0.451124i	−0.444603	+	0.895728i	$0.646655\pi$
$992$		0			0
$993$			59.8339i			1.89877i
$994$		0			0
$995$	−0.0775954	−	0.0775954i	−0.00245994	−	0.00245994i
$996$		0			0
$997$	32.3695	+	32.3695i	1.02515	+	1.02515i	0.999675	+	0.0254770i	$0.00811045\pi$
$997$	32.3695	+	32.3695i	1.02515	+	1.02515i	0.0254770	+	0.999675i	$0.491890\pi$
$998$		0			0
$999$	−18.0426	+	18.0426i	−0.570841	+	0.570841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.a.337.1	✓	8
41.32	even	4	inner	1148.2.k.a.729.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.a.337.1	✓	8	1.1	even	1	trivial
1148.2.k.a.729.1	yes	8	41.32	even	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.96195 - 1.96195i) q^{3} +0.264927i q^{5} +(0.707107 + 0.707107i) q^{7} +4.69853i q^{9} +O(q^{10})\)	\(q+(-1.96195 - 1.96195i) q^{3} +0.264927i q^{5} +(0.707107 + 0.707107i) q^{7} +4.69853i q^{9} +(1.34670 + 1.34670i) q^{11} +(-2.27061 - 2.27061i) q^{13} +(0.519775 - 0.519775i) q^{15} +(0.388375 - 0.388375i) q^{17} +(1.69703 - 1.69703i) q^{19} -2.77462i q^{21} +8.48741 q^{23} +4.92981 q^{25} +(3.33244 - 3.33244i) q^{27} +(-4.81835 - 4.81835i) q^{29} +2.85071 q^{31} -5.28432i q^{33} +(-0.187332 + 0.187332i) q^{35} -5.41421 q^{37} +8.90966i q^{39} +(-1.29857 - 6.27006i) q^{41} +4.60518i q^{43} -1.24477 q^{45} +(4.98575 - 4.98575i) q^{47} +1.00000i q^{49} -1.52395 q^{51} +(-1.45740 - 1.45740i) q^{53} +(-0.356777 + 0.356777i) q^{55} -6.65898 q^{57} -7.20096 q^{59} -7.94631i q^{61} +(-3.32236 + 3.32236i) q^{63} +(0.601545 - 0.601545i) q^{65} +(2.37617 - 2.37617i) q^{67} +(-16.6519 - 16.6519i) q^{69} +(-10.1997 - 10.1997i) q^{71} -4.71279i q^{73} +(-9.67207 - 9.67207i) q^{75} +1.90452i q^{77} +(2.09335 + 2.09335i) q^{79} +1.01939 q^{81} +5.22549 q^{83} +(0.102891 + 0.102891i) q^{85} +18.9068i q^{87} +(-8.76187 - 8.76187i) q^{89} -3.21112i q^{91} +(-5.59297 - 5.59297i) q^{93} +(0.449589 + 0.449589i) q^{95} +(1.75373 - 1.75373i) q^{97} +(-6.32750 + 6.32750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3}+O(q^{10}) \) 8 * q - 4 * q^3	\( 8 q - 4 q^{3} + 12 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 8 q^{19} + 28 q^{23} - 4 q^{25} + 8 q^{27} - 16 q^{29} + 28 q^{31} - 8 q^{35} - 32 q^{37} - 4 q^{45} + 20 q^{47} - 20 q^{51} + 32 q^{53} - 4 q^{55} - 36 q^{57} - 20 q^{59} - 8 q^{63} - 4 q^{67} - 44 q^{69} + 8 q^{71} + 12 q^{75} - 12 q^{79} - 16 q^{81} - 64 q^{83} - 56 q^{85} + 4 q^{89} - 4 q^{93} - 52 q^{95} + 56 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 8 * q^19 + 28 * q^23 - 4 * q^25 + 8 * q^27 - 16 * q^29 + 28 * q^31 - 8 * q^35 - 32 * q^37 - 4 * q^45 + 20 * q^47 - 20 * q^51 + 32 * q^53 - 4 * q^55 - 36 * q^57 - 20 * q^59 - 8 * q^63 - 4 * q^67 - 44 * q^69 + 8 * q^71 + 12 * q^75 - 12 * q^79 - 16 * q^81 - 64 * q^83 - 56 * q^85 + 4 * q^89 - 4 * q^93 - 52 * q^95 + 56 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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