LMFDB - Embedded newform 1408.2.i.b.351.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, degree $2$, not 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:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.8
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15889 + 1.15889i) q^{3} +(2.51141 - 2.51141i) q^{5} +4.37614i q^{7} +0.313934i q^{9} +O(q^{10})$	\(q+(-1.15889 + 1.15889i) q^{3} +(2.51141 - 2.51141i) q^{5} +4.37614i q^{7} +0.313934i q^{9} +(-3.31405 + 0.130539i) q^{11} +(-2.19876 + 2.19876i) q^{13} +5.82090i q^{15} -0.470816i q^{17} +(-0.632217 - 0.632217i) q^{19} +(-5.07148 - 5.07148i) q^{21} -6.62637 q^{23} -7.61433i q^{25} +(-3.84049 - 3.84049i) q^{27} +(-0.0549639 + 0.0549639i) q^{29} +0.184831i q^{31} +(3.68935 - 3.99192i) q^{33} +(10.9903 + 10.9903i) q^{35} +(-3.55208 + 3.55208i) q^{37} -5.09625i q^{39} +3.77969 q^{41} +(4.82127 - 4.82127i) q^{43} +(0.788415 + 0.788415i) q^{45} -0.258542i q^{47} -12.1506 q^{49} +(0.545625 + 0.545625i) q^{51} +(-5.27899 + 5.27899i) q^{53} +(-7.99510 + 8.65078i) q^{55} +1.46534 q^{57} +(1.64990 + 1.64990i) q^{59} +(-9.05654 + 9.05654i) q^{61} -1.37382 q^{63} +11.0440i q^{65} +(-1.83292 + 1.83292i) q^{67} +(7.67925 - 7.67925i) q^{69} +13.1816 q^{71} -10.7788 q^{73} +(8.82419 + 8.82419i) q^{75} +(-0.571258 - 14.5028i) q^{77} +1.80400 q^{79} +7.95965 q^{81} +(-8.61736 - 8.61736i) q^{83} +(-1.18241 - 1.18241i) q^{85} -0.127395i q^{87} -14.8267i q^{89} +(-9.62208 - 9.62208i) q^{91} +(-0.214199 - 0.214199i) q^{93} -3.17551 q^{95} -9.13445 q^{97} +(-0.0409806 - 1.04039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.15889	+	1.15889i	−0.669087	+	0.669087i	−0.957505	−	0.288418i	$-0.906871\pi$
$3$	−1.15889	+	1.15889i	−0.669087	+	0.669087i	0.288418	+	0.957505i	$0.406871\pi$
$4$		0			0
$5$	2.51141	−	2.51141i	1.12314	−	1.12314i	0.131868	−	0.991267i	$-0.457903\pi$
$5$	2.51141	−	2.51141i	1.12314	−	1.12314i	0.991267	−	0.131868i	$-0.0420975\pi$
$6$		0			0
$7$			4.37614i			1.65403i	0.562183	+	0.827013i	$0.309962\pi$
$7$			4.37614i			1.65403i	−0.562183	+	0.827013i	$0.690038\pi$
$8$		0			0
$9$			0.313934i			0.104645i
$10$		0			0
$11$	−3.31405	+	0.130539i	−0.999225	+	0.0393591i
$11$	−3.31405	+	0.130539i	−0.999225	+	0.0393591i
$12$		0			0
$13$	−2.19876	+	2.19876i	−0.609826	+	0.609826i	−0.942901	−	0.333074i	$-0.891914\pi$
$13$	−2.19876	+	2.19876i	−0.609826	+	0.609826i	0.333074	+	0.942901i	$0.391914\pi$
$14$		0			0
$15$			5.82090i			1.50295i
$16$		0			0
$17$		−	0.470816i		−	0.114190i	−0.998369	−	0.0570948i	$-0.981816\pi$
$17$		−	0.470816i		−	0.114190i	0.998369	−	0.0570948i	$-0.0181837\pi$
$18$		0			0
$19$	−0.632217	−	0.632217i	−0.145040	−	0.145040i	0.630858	−	0.775898i	$-0.282703\pi$
$19$	−0.632217	−	0.632217i	−0.145040	−	0.145040i	−0.775898	+	0.630858i	$0.782703\pi$
$20$		0			0
$21$	−5.07148	−	5.07148i	−1.10669	−	1.10669i
$22$		0			0
$23$	−6.62637			−1.38169			−0.690846	−	0.723002i	$-0.742762\pi$
$23$	−6.62637			−1.38169			−0.690846	+	0.723002i	$0.742762\pi$
$24$		0			0
$25$		−	7.61433i		−	1.52287i
$26$		0			0
$27$	−3.84049	−	3.84049i	−0.739104	−	0.739104i
$28$		0			0
$29$	−0.0549639	+	0.0549639i	−0.0102065	+	0.0102065i	−0.712192	−	0.701985i	$-0.752297\pi$
$29$	−0.0549639	+	0.0549639i	−0.0102065	+	0.0102065i	0.701985	+	0.712192i	$0.252297\pi$
$30$		0			0
$31$			0.184831i			0.0331965i	0.999862	+	0.0165983i	$0.00528364\pi$
$31$			0.184831i			0.0331965i	−0.999862	+	0.0165983i	$0.994716\pi$
$32$		0			0
$33$	3.68935	−	3.99192i	0.642234	−	0.694903i
$34$		0			0
$35$	10.9903	+	10.9903i	1.85769	+	1.85769i
$36$		0			0
$37$	−3.55208	+	3.55208i	−0.583959	+	0.583959i	−0.935989	−	0.352030i	$-0.885491\pi$
$37$	−3.55208	+	3.55208i	−0.583959	+	0.583959i	0.352030	+	0.935989i	$0.385491\pi$
$38$		0			0
$39$		−	5.09625i		−	0.816054i
$40$		0			0
$41$	3.77969			0.590288			0.295144	−	0.955453i	$-0.404632\pi$
$41$	3.77969			0.590288			0.295144	+	0.955453i	$0.404632\pi$
$42$		0			0
$43$	4.82127	−	4.82127i	0.735237	−	0.735237i	−0.236415	−	0.971652i	$-0.575972\pi$
$43$	4.82127	−	4.82127i	0.735237	−	0.735237i	0.971652	+	0.236415i	$0.0759724\pi$
$44$		0			0
$45$	0.788415	+	0.788415i	0.117530	+	0.117530i
$46$		0			0
$47$		−	0.258542i		−	0.0377123i	−0.999822	−	0.0188561i	$-0.993998\pi$
$47$		−	0.258542i		−	0.0377123i	0.999822	−	0.0188561i	$-0.00600245\pi$
$48$		0			0
$49$	−12.1506			−1.73580
$50$		0			0
$51$	0.545625	+	0.545625i	0.0764028	+	0.0764028i
$52$		0			0
$53$	−5.27899	+	5.27899i	−0.725126	+	0.725126i	−0.969645	−	0.244519i	$-0.921370\pi$
$53$	−5.27899	+	5.27899i	−0.725126	+	0.725126i	0.244519	+	0.969645i	$0.421370\pi$
$54$		0			0
$55$	−7.99510	+	8.65078i	−1.07806	+	1.16647i
$56$		0			0
$57$	1.46534			0.194089
$58$		0			0
$59$	1.64990	+	1.64990i	0.214799	+	0.214799i	0.806303	−	0.591503i	$-0.201465\pi$
$59$	1.64990	+	1.64990i	0.214799	+	0.214799i	−0.591503	+	0.806303i	$0.701465\pi$
$60$		0			0
$61$	−9.05654	+	9.05654i	−1.15957	+	1.15957i	−0.175004	+	0.984568i	$0.555994\pi$
$61$	−9.05654	+	9.05654i	−1.15957	+	1.15957i	−0.984568	+	0.175004i	$0.944006\pi$
$62$		0			0
$63$	−1.37382			−0.173085
$64$		0			0
$65$			11.0440i			1.36983i
$66$		0			0
$67$	−1.83292	+	1.83292i	−0.223927	+	0.223927i	−0.810150	−	0.586223i	$-0.800614\pi$
$67$	−1.83292	+	1.83292i	−0.223927	+	0.223927i	0.586223	+	0.810150i	$0.300614\pi$
$68$		0			0
$69$	7.67925	−	7.67925i	0.924473	−	0.924473i
$70$		0			0
$71$	13.1816			1.56437			0.782184	−	0.623047i	$-0.214106\pi$
$71$	13.1816			1.56437			0.782184	+	0.623047i	$0.214106\pi$
$72$		0			0
$73$	−10.7788			−1.26156			−0.630782	−	0.775960i	$-0.717266\pi$
$73$	−10.7788			−1.26156			−0.630782	+	0.775960i	$0.717266\pi$
$74$		0			0
$75$	8.82419	+	8.82419i	1.01893	+	1.01893i
$76$		0			0
$77$	−0.571258	−	14.5028i	−0.0651009	−	1.65274i
$78$		0			0
$79$	1.80400			0.202966			0.101483	−	0.994837i	$-0.467641\pi$
$79$	1.80400			0.202966			0.101483	+	0.994837i	$0.467641\pi$
$80$		0			0
$81$	7.95965			0.884405
$82$		0			0
$83$	−8.61736	−	8.61736i	−0.945878	−	0.945878i	0.0527311	−	0.998609i	$-0.483207\pi$
$83$	−8.61736	−	8.61736i	−0.945878	−	0.945878i	−0.998609	+	0.0527311i	$0.983207\pi$
$84$		0			0
$85$	−1.18241	−	1.18241i	−0.128250	−	0.128250i
$86$		0			0
$87$		−	0.127395i		−	0.0136581i
$88$		0			0
$89$		−	14.8267i		−	1.57163i	−0.618462	−	0.785815i	$-0.712244\pi$
$89$		−	14.8267i		−	1.57163i	0.618462	−	0.785815i	$-0.287756\pi$
$90$		0			0
$91$	−9.62208	−	9.62208i	−1.00867	−	1.00867i
$92$		0			0
$93$	−0.214199	−	0.214199i	−0.0222114	−	0.0222114i
$94$		0			0
$95$	−3.17551			−0.325800
$96$		0			0
$97$	−9.13445			−0.927463			−0.463731	−	0.885976i	$-0.653490\pi$
$97$	−9.13445			−0.927463			−0.463731	+	0.885976i	$0.653490\pi$
$98$		0			0
$99$	−0.0409806	−	1.04039i	−0.00411871	−	0.104563i
$100$		0			0
$101$	13.6977	+	13.6977i	1.36297	+	1.36297i	0.870107	+	0.492863i	$0.164049\pi$
$101$	13.6977	+	13.6977i	1.36297	+	1.36297i	0.492863	+	0.870107i	$0.335951\pi$
$102$		0			0
$103$	−1.35412			−0.133425			−0.0667127	−	0.997772i	$-0.521251\pi$
$103$	−1.35412			−0.133425			−0.0667127	+	0.997772i	$0.521251\pi$
$104$		0			0
$105$	−25.4731			−2.48592
$106$		0			0
$107$	−6.92429	+	6.92429i	−0.669397	+	0.669397i	−0.957576	−	0.288180i	$-0.906950\pi$
$107$	−6.92429	+	6.92429i	−0.669397	+	0.669397i	0.288180	+	0.957576i	$0.406950\pi$
$108$		0			0
$109$	−4.33436	+	4.33436i	−0.415156	+	0.415156i	−0.883530	−	0.468374i	$-0.844840\pi$
$109$	−4.33436	+	4.33436i	−0.415156	+	0.415156i	0.468374	+	0.883530i	$0.344840\pi$
$110$		0			0
$111$		−	8.23296i		−	0.781438i
$112$		0			0
$113$	6.26773			0.589619			0.294809	−	0.955556i	$-0.404744\pi$
$113$	6.26773			0.589619			0.294809	+	0.955556i	$0.404744\pi$
$114$		0			0
$115$	−16.6415	+	16.6415i	−1.55183	+	1.55183i
$116$		0			0
$117$	−0.690264	−	0.690264i	−0.0638150	−	0.0638150i
$118$		0			0
$119$	2.06035			0.188872
$120$		0			0
$121$	10.9659	−	0.865228i	0.996902	−	0.0786571i
$122$		0			0
$123$	−4.38025	+	4.38025i	−0.394954	+	0.394954i
$124$		0			0
$125$	−6.56564	−	6.56564i	−0.587249	−	0.587249i
$126$		0			0
$127$	−12.1385			−1.07711			−0.538557	−	0.842589i	$-0.681030\pi$
$127$	−12.1385			−1.07711			−0.538557	+	0.842589i	$0.681030\pi$
$128$		0			0
$129$			11.1747i			0.983876i
$130$		0			0
$131$	1.68744	+	1.68744i	0.147433	+	0.147433i	0.776970	−	0.629537i	$-0.216756\pi$
$131$	1.68744	+	1.68744i	0.147433	+	0.147433i	−0.629537	+	0.776970i	$0.716756\pi$
$132$		0			0
$133$	2.76667	−	2.76667i	0.239901	−	0.239901i
$134$		0			0
$135$	−19.2901			−1.66023
$136$		0			0
$137$			13.2802i			1.13460i	0.823511	+	0.567301i	$0.192012\pi$
$137$			13.2802i			1.13460i	−0.823511	+	0.567301i	$0.807988\pi$
$138$		0			0
$139$	−6.73585	+	6.73585i	−0.571328	+	0.571328i	−0.932499	−	0.361172i	$-0.882377\pi$
$139$	−6.73585	+	6.73585i	−0.571328	+	0.571328i	0.361172	+	0.932499i	$0.382377\pi$
$140$		0			0
$141$	0.299623	+	0.299623i	0.0252328	+	0.0252328i
$142$		0			0
$143$	6.99979	−	7.57383i	0.585351	−	0.633356i
$144$		0			0
$145$			0.276073i			0.0229266i
$146$		0			0
$147$	14.0812	−	14.0812i	1.16140	−	1.16140i
$148$		0			0
$149$	−11.8159	−	11.8159i	−0.967995	−	0.967995i	0.0315085	−	0.999503i	$-0.489969\pi$
$149$	−11.8159	−	11.8159i	−0.967995	−	0.967995i	−0.999503	+	0.0315085i	$0.989969\pi$
$150$		0			0
$151$			12.1931i			0.992257i	0.868249	+	0.496129i	$0.165246\pi$
$151$			12.1931i			0.992257i	−0.868249	+	0.496129i	$0.834754\pi$
$152$		0			0
$153$	0.147805			0.0119493
$154$		0			0
$155$	0.464185	+	0.464185i	0.0372842	+	0.0372842i
$156$		0			0
$157$	−0.597749	−	0.597749i	−0.0477055	−	0.0477055i	0.682852	−	0.730557i	$-0.260740\pi$
$157$	−0.597749	−	0.597749i	−0.0477055	−	0.0477055i	−0.730557	+	0.682852i	$0.760740\pi$
$158$		0			0
$159$		−	12.2356i		−	0.970344i
$160$		0			0
$161$		−	28.9979i		−	2.28535i
$162$		0			0
$163$	0.174199	−	0.174199i	0.0136443	−	0.0136443i	−0.700252	−	0.713896i	$-0.746929\pi$
$163$	0.174199	−	0.174199i	0.0136443	−	0.0136443i	0.713896	+	0.700252i	$0.246929\pi$
$164$		0			0
$165$	−0.759856	−	19.2908i	−0.0591547	−	1.50179i
$166$		0			0
$167$			7.97877i			0.617416i	0.951157	+	0.308708i	$0.0998965\pi$
$167$			7.97877i			0.617416i	−0.951157	+	0.308708i	$0.900103\pi$
$168$		0			0
$169$			3.33091i			0.256224i
$170$		0			0
$171$	0.198474	−	0.198474i	0.0151777	−	0.0151777i
$172$		0			0
$173$	−9.79344	+	9.79344i	−0.744581	+	0.744581i	−0.973456	−	0.228875i	$-0.926495\pi$
$173$	−9.79344	+	9.79344i	−0.744581	+	0.744581i	0.228875	+	0.973456i	$0.426495\pi$
$174$		0			0
$175$	33.3214			2.51886
$176$		0			0
$177$	−3.82413			−0.287439
$178$		0			0
$179$	4.33782	−	4.33782i	0.324224	−	0.324224i	−0.526161	−	0.850385i	$-0.676369\pi$
$179$	4.33782	−	4.33782i	0.324224	−	0.324224i	0.850385	+	0.526161i	$0.176369\pi$
$180$		0			0
$181$	14.6008	−	14.6008i	1.08527	−	1.08527i	0.0892635	−	0.996008i	$-0.471549\pi$
$181$	14.6008	−	14.6008i	1.08527	−	1.08527i	0.996008	−	0.0892635i	$-0.0284513\pi$
$182$		0			0
$183$		−	20.9911i		−	1.55171i
$184$		0			0
$185$			17.8414i			1.31173i
$186$		0			0
$187$	0.0614599	+	1.56031i	0.00449439	+	0.114101i
$188$		0			0
$189$	16.8065	−	16.8065i	1.22250	−	1.22250i
$190$		0			0
$191$			18.0573i			1.30658i	0.757107	+	0.653291i	$0.226612\pi$
$191$			18.0573i			1.30658i	−0.757107	+	0.653291i	$0.773388\pi$
$192$		0			0
$193$			8.63459i			0.621531i	0.950487	+	0.310766i	$0.100585\pi$
$193$			8.63459i			0.621531i	−0.950487	+	0.310766i	$0.899415\pi$
$194$		0			0
$195$	−12.7988	−	12.7988i	−0.916539	−	0.916539i
$196$		0			0
$197$	15.6355	+	15.6355i	1.11398	+	1.11398i	0.992606	+	0.121377i	$0.0387310\pi$
$197$	15.6355	+	15.6355i	1.11398	+	1.11398i	0.121377	+	0.992606i	$0.461269\pi$
$198$		0			0
$199$	8.49230			0.602003			0.301002	−	0.953624i	$-0.402679\pi$
$199$	8.49230			0.602003			0.301002	+	0.953624i	$0.402679\pi$
$200$		0			0
$201$		−	4.24832i		−	0.299653i
$202$		0			0
$203$	−0.240530	−	0.240530i	−0.0168819	−	0.0168819i
$204$		0			0
$205$	9.49233	−	9.49233i	0.662973	−	0.662973i
$206$		0			0
$207$		−	2.08024i		−	0.144587i
$208$		0			0
$209$	2.17773	+	2.01267i	0.150637	+	0.139219i
$210$		0			0
$211$	−0.567110	−	0.567110i	−0.0390415	−	0.0390415i	0.687317	−	0.726358i	$-0.258789\pi$
$211$	−0.567110	−	0.567110i	−0.0390415	−	0.0390415i	−0.726358	+	0.687317i	$0.758789\pi$
$212$		0			0
$213$	−15.2761	+	15.2761i	−1.04670	+	1.04670i
$214$		0			0
$215$		−	24.2164i		−	1.65154i
$216$		0			0
$217$	−0.808844			−0.0549079
$218$		0			0
$219$	12.4915	−	12.4915i	0.844096	−	0.844096i
$220$		0			0
$221$	1.03521	+	1.03521i	0.0696358	+	0.0696358i
$222$		0			0
$223$			6.20080i			0.415236i	0.978210	+	0.207618i	$0.0665712\pi$
$223$			6.20080i			0.415236i	−0.978210	+	0.207618i	$0.933429\pi$
$224$		0			0
$225$	2.39039			0.159360
$226$		0			0
$227$	9.04652	+	9.04652i	0.600439	+	0.600439i	0.940429	−	0.339990i	$-0.110424\pi$
$227$	9.04652	+	9.04652i	0.600439	+	0.600439i	−0.339990	+	0.940429i	$0.610424\pi$
$228$		0			0
$229$	2.24078	−	2.24078i	0.148075	−	0.148075i	−0.629183	−	0.777258i	$-0.716610\pi$
$229$	2.24078	−	2.24078i	0.148075	−	0.148075i	0.777258	+	0.629183i	$0.216610\pi$
$230$		0			0
$231$	17.4692	+	16.1451i	1.14939	+	1.06227i
$232$		0			0
$233$	11.7198			0.767791			0.383896	−	0.923376i	$-0.374582\pi$
$233$	11.7198			0.767791			0.383896	+	0.923376i	$0.374582\pi$
$234$		0			0
$235$	−0.649305	−	0.649305i	−0.0423560	−	0.0423560i
$236$		0			0
$237$	−2.09065	+	2.09065i	−0.135802	+	0.135802i
$238$		0			0
$239$	8.99979			0.582148			0.291074	−	0.956701i	$-0.405987\pi$
$239$	8.99979			0.582148			0.291074	+	0.956701i	$0.405987\pi$
$240$		0			0
$241$		−	13.4918i		−	0.869086i	−0.900651	−	0.434543i	$-0.856910\pi$
$241$		−	13.4918i		−	0.869086i	0.900651	−	0.434543i	$-0.143090\pi$
$242$		0			0
$243$	2.29711	−	2.29711i	0.147359	−	0.147359i
$244$		0			0
$245$	−30.5151	+	30.5151i	−1.94954	+	1.94954i
$246$		0			0
$247$	2.78019			0.176899
$248$		0			0
$249$	19.9732			1.26575
$250$		0			0
$251$	5.34191	+	5.34191i	0.337178	+	0.337178i	0.855304	−	0.518126i	$-0.173370\pi$
$251$	5.34191	+	5.34191i	0.337178	+	0.337178i	−0.518126	+	0.855304i	$0.673370\pi$
$252$		0			0
$253$	21.9601	−	0.865001i	1.38062	−	0.0543821i
$254$		0			0
$255$	2.74057			0.171621
$256$		0			0
$257$	−10.1778			−0.634871			−0.317436	−	0.948280i	$-0.602822\pi$
$257$	−10.1778			−0.634871			−0.317436	+	0.948280i	$0.602822\pi$
$258$		0			0
$259$	−15.5444	−	15.5444i	−0.965882	−	0.965882i
$260$		0			0
$261$	−0.0172550	−	0.0172550i	−0.00106806	−	0.00106806i
$262$		0			0
$263$		−	9.13586i		−	0.563341i	−0.959511	−	0.281670i	$-0.909112\pi$
$263$		−	9.13586i		−	0.563341i	0.959511	−	0.281670i	$-0.0908885\pi$
$264$		0			0
$265$			26.5154i			1.62883i
$266$		0			0
$267$	17.1826	+	17.1826i	1.05156	+	1.05156i
$268$		0			0
$269$	13.4420	+	13.4420i	0.819573	+	0.819573i	0.986046	−	0.166473i	$-0.0532379\pi$
$269$	13.4420	+	13.4420i	0.819573	+	0.819573i	−0.166473	+	0.986046i	$0.553238\pi$
$270$		0			0
$271$	−30.6504			−1.86188			−0.930939	−	0.365175i	$-0.881009\pi$
$271$	−30.6504			−1.86188			−0.930939	+	0.365175i	$0.881009\pi$
$272$		0			0
$273$	22.3019			1.34977
$274$		0			0
$275$	0.993969	+	25.2343i	0.0599386	+	1.52169i
$276$		0			0
$277$	13.0577	+	13.0577i	0.784564	+	0.784564i	0.980597	−	0.196033i	$-0.0628061\pi$
$277$	13.0577	+	13.0577i	0.784564	+	0.784564i	−0.196033	+	0.980597i	$0.562806\pi$
$278$		0			0
$279$	−0.0580245			−0.00347384
$280$		0			0
$281$	14.7120			0.877642			0.438821	−	0.898575i	$-0.355396\pi$
$281$	14.7120			0.877642			0.438821	+	0.898575i	$0.355396\pi$
$282$		0			0
$283$	13.1033	−	13.1033i	0.778912	−	0.778912i	−0.200734	−	0.979646i	$-0.564333\pi$
$283$	13.1033	−	13.1033i	0.778912	−	0.778912i	0.979646	+	0.200734i	$0.0643327\pi$
$284$		0			0
$285$	3.68007	−	3.68007i	0.217989	−	0.217989i
$286$		0			0
$287$			16.5404i			0.976351i
$288$		0			0
$289$	16.7783			0.986961
$290$		0			0
$291$	10.5858	−	10.5858i	0.620553	−	0.620553i
$292$		0			0
$293$	−8.53843	−	8.53843i	−0.498821	−	0.498821i	0.412250	−	0.911071i	$-0.364743\pi$
$293$	−8.53843	−	8.53843i	−0.498821	−	0.498821i	−0.911071	+	0.412250i	$0.864743\pi$
$294$		0			0
$295$	8.28716			0.482497
$296$		0			0
$297$	13.2289	+	12.2263i	0.767621	+	0.709440i
$298$		0			0
$299$	14.5698	−	14.5698i	0.842592	−	0.842592i
$300$		0			0
$301$	21.0986	+	21.0986i	1.21610	+	1.21610i
$302$		0			0
$303$	−31.7483			−1.82389
$304$		0			0
$305$			45.4893i			2.60471i
$306$		0			0
$307$	6.52223	+	6.52223i	0.372243	+	0.372243i	0.868294	−	0.496050i	$-0.165217\pi$
$307$	6.52223	+	6.52223i	0.372243	+	0.372243i	−0.496050	+	0.868294i	$0.665217\pi$
$308$		0			0
$309$	1.56928	−	1.56928i	0.0892733	−	0.0892733i
$310$		0			0
$311$	7.11790			0.403619			0.201809	−	0.979425i	$-0.435318\pi$
$311$	7.11790			0.403619			0.201809	+	0.979425i	$0.435318\pi$
$312$		0			0
$313$			5.93174i			0.335282i	0.985848	+	0.167641i	$0.0536149\pi$
$313$			5.93174i			0.335282i	−0.985848	+	0.167641i	$0.946385\pi$
$314$		0			0
$315$	−3.45021	+	3.45021i	−0.194397	+	0.194397i
$316$		0			0
$317$	−2.20073	−	2.20073i	−0.123605	−	0.123605i	0.642598	−	0.766203i	$-0.277857\pi$
$317$	−2.20073	−	2.20073i	−0.123605	−	0.123605i	−0.766203	+	0.642598i	$0.777857\pi$
$318$		0			0
$319$	0.174978	−	0.189328i	0.00979691	−	0.0106003i
$320$		0			0
$321$		−	16.0490i		−	0.895769i
$322$		0			0
$323$	−0.297657	+	0.297657i	−0.0165621	+	0.0165621i
$324$		0			0
$325$	16.7421	+	16.7421i	0.928683	+	0.928683i
$326$		0			0
$327$		−	10.0461i		−	0.555551i
$328$		0			0
$329$	1.13142			0.0623771
$330$		0			0
$331$	−8.40197	−	8.40197i	−0.461814	−	0.461814i	0.437436	−	0.899250i	$-0.355887\pi$
$331$	−8.40197	−	8.40197i	−0.461814	−	0.461814i	−0.899250	+	0.437436i	$0.855887\pi$
$332$		0			0
$333$	−1.11512	−	1.11512i	−0.0611081	−	0.0611081i
$334$		0			0
$335$			9.20642i			0.503001i
$336$		0			0
$337$		−	4.46584i		−	0.243270i	−0.992575	−	0.121635i	$-0.961186\pi$
$337$		−	4.46584i		−	0.243270i	0.992575	−	0.121635i	$-0.0388137\pi$
$338$		0			0
$339$	−7.26363	+	7.26363i	−0.394506	+	0.394506i
$340$		0			0
$341$	−0.0241276	−	0.612539i	−0.00130658	−	0.0331708i
$342$		0			0
$343$		−	22.5398i		−	1.21703i
$344$		0			0
$345$		−	38.5714i		−	2.07662i
$346$		0			0
$347$	3.23492	−	3.23492i	0.173660	−	0.173660i	−0.614926	−	0.788585i	$-0.710814\pi$
$347$	3.23492	−	3.23492i	0.173660	−	0.173660i	0.788585	+	0.614926i	$0.210814\pi$
$348$		0			0
$349$	2.27936	−	2.27936i	0.122011	−	0.122011i	−0.643464	−	0.765476i	$-0.722504\pi$
$349$	2.27936	−	2.27936i	0.122011	−	0.122011i	0.765476	+	0.643464i	$0.222504\pi$
$350$		0			0
$351$	16.8887			0.901449
$352$		0			0
$353$	−5.59861			−0.297984			−0.148992	−	0.988838i	$-0.547603\pi$
$353$	−5.59861			−0.297984			−0.148992	+	0.988838i	$0.547603\pi$
$354$		0			0
$355$	33.1044	−	33.1044i	1.75700	−	1.75700i
$356$		0			0
$357$	−2.38773	+	2.38773i	−0.126372	+	0.126372i
$358$		0			0
$359$			16.8190i			0.887673i	0.896108	+	0.443837i	$0.146383\pi$
$359$			16.8190i			0.887673i	−0.896108	+	0.443837i	$0.853617\pi$
$360$		0			0
$361$		−	18.2006i		−	0.957927i
$362$		0			0
$363$	−11.7056	+	13.7110i	−0.614386	+	0.719643i
$364$		0			0
$365$	−27.0700	+	27.0700i	−1.41691	+	1.41691i
$366$		0			0
$367$		−	30.3527i		−	1.58440i	−0.610262	−	0.792199i	$-0.708936\pi$
$367$		−	30.3527i		−	1.58440i	0.610262	−	0.792199i	$-0.291064\pi$
$368$		0			0
$369$			1.18657i			0.0617704i
$370$		0			0
$371$	−23.1016	−	23.1016i	−1.19938	−	1.19938i
$372$		0			0
$373$	−11.0235	−	11.0235i	−0.570776	−	0.570776i	0.361569	−	0.932345i	$-0.382241\pi$
$373$	−11.0235	−	11.0235i	−0.570776	−	0.570776i	−0.932345	+	0.361569i	$0.882241\pi$
$374$		0			0
$375$	15.2177			0.785841
$376$		0			0
$377$		−	0.241705i		−	0.0124484i
$378$		0			0
$379$	26.0976	+	26.0976i	1.34054	+	1.34054i	0.895517	+	0.445028i	$0.146806\pi$
$379$	26.0976	+	26.0976i	1.34054	+	1.34054i	0.445028	+	0.895517i	$0.353194\pi$
$380$		0			0
$381$	14.0672	−	14.0672i	0.720683	−	0.720683i
$382$		0			0
$383$		−	15.2346i		−	0.778452i	−0.921142	−	0.389226i	$-0.872742\pi$
$383$		−	15.2346i		−	0.778452i	0.921142	−	0.389226i	$-0.127258\pi$
$384$		0			0
$385$	−37.8570	−	34.9877i	−1.92937	−	1.78314i
$386$		0			0
$387$	1.51356	+	1.51356i	0.0769386	+	0.0769386i
$388$		0			0
$389$	−6.66327	+	6.66327i	−0.337841	+	0.337841i	−0.855554	−	0.517713i	$-0.826784\pi$
$389$	−6.66327	+	6.66327i	−0.337841	+	0.337841i	0.517713	+	0.855554i	$0.326784\pi$
$390$		0			0
$391$			3.11980i			0.157775i
$392$		0			0
$393$	−3.91114			−0.197291
$394$		0			0
$395$	4.53059	−	4.53059i	0.227959	−	0.227959i
$396$		0			0
$397$	10.4934	+	10.4934i	0.526647	+	0.526647i	0.919571	−	0.392924i	$-0.128536\pi$
$397$	10.4934	+	10.4934i	0.526647	+	0.526647i	−0.392924	+	0.919571i	$0.628536\pi$
$398$		0			0
$399$			6.41255i			0.321029i
$400$		0			0
$401$	−2.87979			−0.143810			−0.0719049	−	0.997411i	$-0.522908\pi$
$401$	−2.87979			−0.143810			−0.0719049	+	0.997411i	$0.522908\pi$
$402$		0			0
$403$	−0.406398	−	0.406398i	−0.0202441	−	0.0202441i
$404$		0			0
$405$	19.9899	−	19.9899i	0.993306	−	0.993306i
$406$		0			0
$407$	11.3081	−	12.2355i	0.560522	−	0.606490i
$408$		0			0
$409$	−20.1494			−0.996322			−0.498161	−	0.867085i	$-0.665991\pi$
$409$	−20.1494			−0.996322			−0.498161	+	0.867085i	$0.665991\pi$
$410$		0			0
$411$	−15.3903	−	15.3903i	−0.759148	−	0.759148i
$412$		0			0
$413$	−7.22021	+	7.22021i	−0.355283	+	0.355283i
$414$		0			0
$415$	−43.2834			−2.12470
$416$		0			0
$417$		−	15.6123i		−	0.764536i
$418$		0			0
$419$	2.93260	−	2.93260i	0.143267	−	0.143267i	−0.631836	−	0.775102i	$-0.717698\pi$
$419$	2.93260	−	2.93260i	0.143267	−	0.143267i	0.775102	+	0.631836i	$0.217698\pi$
$420$		0			0
$421$	−3.24384	+	3.24384i	−0.158095	+	0.158095i	−0.781722	−	0.623627i	$-0.785658\pi$
$421$	−3.24384	+	3.24384i	−0.158095	+	0.158095i	0.623627	+	0.781722i	$0.285658\pi$
$422$		0			0
$423$	0.0811651			0.00394638
$424$		0			0
$425$	−3.58494			−0.173895
$426$		0			0
$427$	−39.6327	−	39.6327i	−1.91796	−	1.91796i
$428$		0			0
$429$	0.665261	+	16.8893i	0.0321191	+	0.815422i
$430$		0			0
$431$	−11.5019			−0.554029			−0.277015	−	0.960866i	$-0.589345\pi$
$431$	−11.5019			−0.554029			−0.277015	+	0.960866i	$0.589345\pi$
$432$		0			0
$433$	35.2111			1.69214			0.846070	−	0.533072i	$-0.178963\pi$
$433$	35.2111			1.69214			0.846070	+	0.533072i	$0.178963\pi$
$434$		0			0
$435$	−0.319939	−	0.319939i	−0.0153399	−	0.0153399i
$436$		0			0
$437$	4.18930	+	4.18930i	0.200401	+	0.200401i
$438$		0			0
$439$			29.3770i			1.40209i	0.713118	+	0.701044i	$0.247282\pi$
$439$			29.3770i			1.40209i	−0.713118	+	0.701044i	$0.752718\pi$
$440$		0			0
$441$		−	3.81448i		−	0.181642i
$442$		0			0
$443$	−1.52871	−	1.52871i	−0.0726311	−	0.0726311i	0.669858	−	0.742489i	$-0.266355\pi$
$443$	−1.52871	−	1.52871i	−0.0726311	−	0.0726311i	−0.742489	+	0.669858i	$0.766355\pi$
$444$		0			0
$445$	−37.2359	−	37.2359i	−1.76515	−	1.76515i
$446$		0			0
$447$	27.3867			1.29535
$448$		0			0
$449$	−29.2277			−1.37934			−0.689671	−	0.724123i	$-0.742245\pi$
$449$	−29.2277			−1.37934			−0.689671	+	0.724123i	$0.742245\pi$
$450$		0			0
$451$	−12.5261	+	0.493397i	−0.589830	+	0.0232332i
$452$		0			0
$453$	−14.1305	−	14.1305i	−0.663907	−	0.663907i
$454$		0			0
$455$	−48.3299			−2.26574
$456$		0			0
$457$	−2.44312			−0.114284			−0.0571422	−	0.998366i	$-0.518199\pi$
$457$	−2.44312			−0.114284			−0.0571422	+	0.998366i	$0.518199\pi$
$458$		0			0
$459$	−1.80816	+	1.80816i	−0.0843979	+	0.0843979i
$460$		0			0
$461$	26.1834	−	26.1834i	1.21948	−	1.21948i	0.251670	−	0.967813i	$-0.419020\pi$
$461$	26.1834	−	26.1834i	1.21948	−	1.21948i	0.967813	−	0.251670i	$-0.0809798\pi$
$462$		0			0
$463$			6.41470i			0.298116i	0.988828	+	0.149058i	$0.0476241\pi$
$463$			6.41470i			0.298116i	−0.988828	+	0.149058i	$0.952376\pi$
$464$		0			0
$465$	−1.07588			−0.0498928
$466$		0			0
$467$	−5.14076	+	5.14076i	−0.237886	+	0.237886i	−0.815974	−	0.578088i	$-0.803799\pi$
$467$	−5.14076	+	5.14076i	−0.237886	+	0.237886i	0.578088	+	0.815974i	$0.303799\pi$
$468$		0			0
$469$	−8.02112	−	8.02112i	−0.370381	−	0.370381i
$470$		0			0
$471$	1.38545			0.0638383
$472$		0			0
$473$	−15.3486	+	16.6073i	−0.705729	+	0.763606i
$474$		0			0
$475$	−4.81391	+	4.81391i	−0.220877	+	0.220877i
$476$		0			0
$477$	−1.65725	−	1.65725i	−0.0758804	−	0.0758804i
$478$		0			0
$479$	15.7269			0.718579			0.359289	−	0.933226i	$-0.383019\pi$
$479$	15.7269			0.718579			0.359289	+	0.933226i	$0.383019\pi$
$480$		0			0
$481$		−	15.6203i		−	0.712226i
$482$		0			0
$483$	33.6055	+	33.6055i	1.52910	+	1.52910i
$484$		0			0
$485$	−22.9403	+	22.9403i	−1.04167	+	1.04167i
$486$		0			0
$487$	12.3454			0.559425			0.279712	−	0.960084i	$-0.409761\pi$
$487$	12.3454			0.559425			0.279712	+	0.960084i	$0.409761\pi$
$488$		0			0
$489$			0.403755i			0.0182584i
$490$		0			0
$491$	12.1242	−	12.1242i	0.547156	−	0.547156i	−0.378461	−	0.925617i	$-0.623547\pi$
$491$	12.1242	−	12.1242i	0.547156	−	0.547156i	0.925617	+	0.378461i	$0.123547\pi$
$492$		0			0
$493$	0.0258778	+	0.0258778i	0.00116548	+	0.00116548i
$494$		0			0
$495$	−2.71577	−	2.50993i	−0.122065	−	0.112813i
$496$		0			0
$497$			57.6845i			2.58750i
$498$		0			0
$499$	22.0301	−	22.0301i	0.986204	−	0.986204i	−0.0137022	−	0.999906i	$-0.504362\pi$
$499$	22.0301	−	22.0301i	0.986204	−	0.986204i	0.999906	+	0.0137022i	$0.00436170\pi$
$500$		0			0
$501$	−9.24654	−	9.24654i	−0.413105	−	0.413105i
$502$		0			0
$503$		−	39.0780i		−	1.74240i	−0.490926	−	0.871201i	$-0.663342\pi$
$503$		−	39.0780i		−	1.74240i	0.490926	−	0.871201i	$-0.336658\pi$
$504$		0			0
$505$	68.8009			3.06160
$506$		0			0
$507$	−3.86017	−	3.86017i	−0.171436	−	0.171436i
$508$		0			0
$509$	−5.76291	−	5.76291i	−0.255437	−	0.255437i	0.567759	−	0.823195i	$-0.307811\pi$
$509$	−5.76291	−	5.76291i	−0.255437	−	0.255437i	−0.823195	+	0.567759i	$0.807811\pi$
$510$		0			0
$511$		−	47.1695i		−	2.08666i
$512$		0			0
$513$			4.85605i			0.214400i
$514$		0			0
$515$	−3.40075	+	3.40075i	−0.149855	+	0.149855i
$516$		0			0
$517$	0.0337499	+	0.856824i	0.00148432	+	0.0376831i
$518$		0			0
$519$		−	22.6991i		−	0.996380i
$520$		0			0
$521$		−	12.0931i		−	0.529810i	−0.964275	−	0.264905i	$-0.914659\pi$
$521$		−	12.0931i		−	0.529810i	0.964275	−	0.264905i	$-0.0853406\pi$
$522$		0			0
$523$	−25.2888	+	25.2888i	−1.10580	+	1.10580i	−0.112106	+	0.993696i	$0.535760\pi$
$523$	−25.2888	+	25.2888i	−1.10580	+	1.10580i	−0.993696	+	0.112106i	$0.964240\pi$
$524$		0			0
$525$	−38.6159	+	38.6159i	−1.68534	+	1.68534i
$526$		0			0
$527$	0.0870211			0.00379070
$528$		0			0
$529$	20.9087			0.909075
$530$		0			0
$531$	−0.517960	+	0.517960i	−0.0224776	+	0.0224776i
$532$		0			0
$533$	−8.31062	+	8.31062i	−0.359973	+	0.359973i
$534$		0			0
$535$			34.7794i			1.50365i
$536$		0			0
$537$			10.0541i			0.433868i
$538$		0			0
$539$	40.2678	−	1.58613i	1.73446	−	0.0683195i
$540$		0			0
$541$	−8.40728	+	8.40728i	−0.361457	+	0.361457i	−0.864349	−	0.502892i	$-0.832269\pi$
$541$	−8.40728	+	8.40728i	−0.361457	+	0.361457i	0.502892	+	0.864349i	$0.332269\pi$
$542$		0			0
$543$			33.8416i			1.45228i
$544$		0			0
$545$			21.7707i			0.932553i
$546$		0			0
$547$	−17.3256	−	17.3256i	−0.740787	−	0.740787i	0.231942	−	0.972730i	$-0.425492\pi$
$547$	−17.3256	−	17.3256i	−0.740787	−	0.740787i	−0.972730	+	0.231942i	$0.925492\pi$
$548$		0			0
$549$	−2.84315	−	2.84315i	−0.121343	−	0.121343i
$550$		0			0
$551$	0.0694982			0.00296072
$552$		0			0
$553$			7.89458i			0.335712i
$554$		0			0
$555$	−20.6763	−	20.6763i	−0.877661	−	0.877661i
$556$		0			0
$557$	−6.89429	+	6.89429i	−0.292120	+	0.292120i	−0.837917	−	0.545797i	$-0.816227\pi$
$557$	−6.89429	+	6.89429i	−0.292120	+	0.292120i	0.545797	+	0.837917i	$0.316227\pi$
$558$		0			0
$559$			21.2016i			0.896734i
$560$		0			0
$561$	−1.87946	−	1.73701i	−0.0793507	−	0.0733364i
$562$		0			0
$563$	−7.66844	−	7.66844i	−0.323186	−	0.323186i	0.526802	−	0.849988i	$-0.323391\pi$
$563$	−7.66844	−	7.66844i	−0.323186	−	0.323186i	−0.849988	+	0.526802i	$0.823391\pi$
$564$		0			0
$565$	15.7408	−	15.7408i	0.662221	−	0.662221i
$566$		0			0
$567$			34.8325i			1.46283i
$568$		0			0
$569$	−29.7373			−1.24665			−0.623327	−	0.781961i	$-0.714219\pi$
$569$	−29.7373			−1.24665			−0.623327	+	0.781961i	$0.714219\pi$
$570$		0			0
$571$	−10.8230	+	10.8230i	−0.452926	+	0.452926i	−0.896325	−	0.443398i	$-0.853773\pi$
$571$	−10.8230	+	10.8230i	−0.452926	+	0.452926i	0.443398	+	0.896325i	$0.353773\pi$
$572$		0			0
$573$	−20.9265	−	20.9265i	−0.874217	−	0.874217i
$574$		0			0
$575$			50.4553i			2.10413i
$576$		0			0
$577$	11.5084			0.479102			0.239551	−	0.970884i	$-0.423000\pi$
$577$	11.5084			0.479102			0.239551	+	0.970884i	$0.423000\pi$
$578$		0			0
$579$	−10.0066	−	10.0066i	−0.415859	−	0.415859i
$580$		0			0
$581$	37.7108	−	37.7108i	1.56451	−	1.56451i
$582$		0			0
$583$	16.8058	−	18.1840i	0.696023	−	0.753104i
$584$		0			0
$585$	−3.46707			−0.143346
$586$		0			0
$587$	25.7068	+	25.7068i	1.06103	+	1.06103i	0.998012	+	0.0630204i	$0.0200733\pi$
$587$	25.7068	+	25.7068i	1.06103	+	1.06103i	0.0630204	+	0.998012i	$0.479927\pi$
$588$		0			0
$589$	0.116853	−	0.116853i	0.00481484	−	0.00481484i
$590$		0			0
$591$	−36.2398			−1.49070
$592$		0			0
$593$			13.3863i			0.549711i	0.961485	+	0.274856i	$0.0886301\pi$
$593$			13.3863i			0.549711i	−0.961485	+	0.274856i	$0.911370\pi$
$594$		0			0
$595$	5.17439	−	5.17439i	0.212129	−	0.212129i
$596$		0			0
$597$	−9.84167	+	9.84167i	−0.402793	+	0.402793i
$598$		0			0
$599$	−23.3612			−0.954513			−0.477256	−	0.878764i	$-0.658369\pi$
$599$	−23.3612			−0.954513			−0.477256	+	0.878764i	$0.658369\pi$
$600$		0			0
$601$	−21.4418			−0.874630			−0.437315	−	0.899308i	$-0.644070\pi$
$601$	−21.4418			−0.874630			−0.437315	+	0.899308i	$0.644070\pi$
$602$		0			0
$603$	−0.575416	−	0.575416i	−0.0234327	−	0.0234327i
$604$		0			0
$605$	25.3669	−	29.7128i	1.03131	−	1.20800i
$606$		0			0
$607$	15.9325			0.646680			0.323340	−	0.946283i	$-0.395194\pi$
$607$	15.9325			0.646680			0.323340	+	0.946283i	$0.395194\pi$
$608$		0			0
$609$	0.557496			0.0225909
$610$		0			0
$611$	0.568472	+	0.568472i	0.0229979	+	0.0229979i
$612$		0			0
$613$	5.61164	+	5.61164i	0.226652	+	0.226652i	0.811292	−	0.584641i	$-0.198764\pi$
$613$	5.61164	+	5.61164i	0.226652	+	0.226652i	−0.584641	+	0.811292i	$0.698764\pi$
$614$		0			0
$615$			22.0012i			0.887173i
$616$		0			0
$617$			11.4458i			0.460790i	0.973097	+	0.230395i	$0.0740019\pi$
$617$			11.4458i			0.460790i	−0.973097	+	0.230395i	$0.925998\pi$
$618$		0			0
$619$	17.0939	+	17.0939i	0.687063	+	0.687063i	0.961582	−	0.274519i	$-0.0885186\pi$
$619$	17.0939	+	17.0939i	0.687063	+	0.687063i	−0.274519	+	0.961582i	$0.588519\pi$
$620$		0			0
$621$	25.4485	+	25.4485i	1.02121	+	1.02121i
$622$		0			0
$623$	64.8838			2.59952
$624$		0			0
$625$	5.09365			0.203746
$626$		0			0
$627$	−4.85623	+	0.191285i	−0.193939	+	0.00763918i
$628$		0			0
$629$	1.67237	+	1.67237i	0.0666820	+	0.0666820i
$630$		0			0
$631$	16.2095			0.645289			0.322644	−	0.946520i	$-0.395428\pi$
$631$	16.2095			0.645289			0.322644	+	0.946520i	$0.395428\pi$
$632$		0			0
$633$	1.31444			0.0522443
$634$		0			0
$635$	−30.4846	+	30.4846i	−1.20974	+	1.20974i
$636$		0			0
$637$	26.7163	−	26.7163i	1.05854	−	1.05854i
$638$		0			0
$639$			4.13815i			0.163703i
$640$		0			0
$641$	−29.8661			−1.17964			−0.589821	−	0.807534i	$-0.700802\pi$
$641$	−29.8661			−1.17964			−0.589821	+	0.807534i	$0.700802\pi$
$642$		0			0
$643$	−19.9367	+	19.9367i	−0.786229	+	0.786229i	−0.980874	−	0.194645i	$-0.937644\pi$
$643$	−19.9367	+	19.9367i	−0.786229	+	0.786229i	0.194645	+	0.980874i	$0.437644\pi$
$644$		0			0
$645$	28.0642	+	28.0642i	1.10503	+	1.10503i
$646$		0			0
$647$	−17.1425			−0.673942			−0.336971	−	0.941515i	$-0.609402\pi$
$647$	−17.1425			−0.673942			−0.336971	+	0.941515i	$0.609402\pi$
$648$		0			0
$649$	−5.68325	−	5.25250i	−0.223087	−	0.206179i
$650$		0			0
$651$	0.937364	−	0.937364i	0.0367382	−	0.0367382i
$652$		0			0
$653$	−24.6531	−	24.6531i	−0.964752	−	0.964752i	0.0346480	−	0.999400i	$-0.488969\pi$
$653$	−24.6531	−	24.6531i	−0.964752	−	0.964752i	−0.999400	+	0.0346480i	$0.988969\pi$
$654$		0			0
$655$	8.47572			0.331174
$656$		0			0
$657$		−	3.38383i		−	0.132016i
$658$		0			0
$659$	22.8906	+	22.8906i	0.891692	+	0.891692i	0.994682	−	0.102990i	$-0.0328409\pi$
$659$	22.8906	+	22.8906i	0.891692	+	0.891692i	−0.102990	+	0.994682i	$0.532841\pi$
$660$		0			0
$661$	9.77116	−	9.77116i	0.380054	−	0.380054i	−0.491068	−	0.871121i	$-0.663393\pi$
$661$	9.77116	−	9.77116i	0.380054	−	0.380054i	0.871121	+	0.491068i	$0.163393\pi$
$662$		0			0
$663$	−2.39940			−0.0931848
$664$		0			0
$665$		−	13.8965i		−	0.538882i
$666$		0			0
$667$	0.364211	−	0.364211i	0.0141023	−	0.0141023i
$668$		0			0
$669$	−7.18607	−	7.18607i	−0.277829	−	0.277829i
$670$		0			0
$671$	28.8316	−	31.1961i	1.11303	−	1.20431i
$672$		0			0
$673$		−	17.9646i		−	0.692486i	−0.938145	−	0.346243i	$-0.887457\pi$
$673$		−	17.9646i		−	0.692486i	0.938145	−	0.346243i	$-0.112543\pi$
$674$		0			0
$675$	−29.2428	+	29.2428i	−1.12556	+	1.12556i
$676$		0			0
$677$	25.1248	+	25.1248i	0.965623	+	0.965623i	0.999428	−	0.0338053i	$-0.0107626\pi$
$677$	25.1248	+	25.1248i	0.965623	+	0.965623i	−0.0338053	+	0.999428i	$0.510763\pi$
$678$		0			0
$679$		−	39.9736i		−	1.53405i
$680$		0			0
$681$	−20.9679			−0.803492
$682$		0			0
$683$	34.8197	+	34.8197i	1.33234	+	1.33234i	0.903274	+	0.429064i	$0.141157\pi$
$683$	34.8197	+	34.8197i	1.33234	+	1.33234i	0.429064	+	0.903274i	$0.358843\pi$
$684$		0			0
$685$	33.3519	+	33.3519i	1.27431	+	1.27431i
$686$		0			0
$687$			5.19365i			0.198150i
$688$		0			0
$689$		−	23.2145i		−	0.884401i
$690$		0			0
$691$	−19.6641	+	19.6641i	−0.748056	+	0.748056i	−0.974114	−	0.226058i	$-0.927416\pi$
$691$	−19.6641	+	19.6641i	−0.748056	+	0.748056i	0.226058	+	0.974114i	$0.427416\pi$
$692$		0			0
$693$	4.55290	−	0.179337i	0.172951	−	0.00681245i
$694$		0			0
$695$			33.8329i			1.28336i
$696$		0			0
$697$		−	1.77953i		−	0.0674047i
$698$		0			0
$699$	−13.5820	+	13.5820i	−0.513719	+	0.513719i
$700$		0			0
$701$	−17.1576	+	17.1576i	−0.648033	+	0.648033i	−0.952517	−	0.304484i	$-0.901516\pi$
$701$	−17.1576	+	17.1576i	−0.648033	+	0.648033i	0.304484	+	0.952517i	$0.401516\pi$
$702$		0			0
$703$	4.49137			0.169395
$704$		0			0
$705$	1.50495			0.0566797
$706$		0			0
$707$	−59.9429	+	59.9429i	−2.25439	+	2.25439i
$708$		0			0
$709$	21.3086	−	21.3086i	0.800262	−	0.800262i	−0.182874	−	0.983136i	$-0.558540\pi$
$709$	21.3086	−	21.3086i	0.800262	−	0.800262i	0.983136	+	0.182874i	$0.0585400\pi$
$710$		0			0
$711$			0.566337i			0.0212393i
$712$		0			0
$713$		−	1.22475i		−	0.0458674i
$714$		0			0
$715$	−1.44167	−	36.6003i	−0.0539154	−	1.36877i
$716$		0			0
$717$	−10.4298	+	10.4298i	−0.389508	+	0.389508i
$718$		0			0
$719$			13.6719i			0.509877i	0.966957	+	0.254938i	$0.0820552\pi$
$719$			13.6719i			0.509877i	−0.966957	+	0.254938i	$0.917945\pi$
$720$		0			0
$721$		−	5.92582i		−	0.220689i
$722$		0			0
$723$	15.6356	+	15.6356i	0.581495	+	0.581495i
$724$		0			0
$725$	0.418513	+	0.418513i	0.0155432	+	0.0155432i
$726$		0			0
$727$	−37.6482			−1.39630			−0.698148	−	0.715953i	$-0.745992\pi$
$727$	−37.6482			−1.39630			−0.698148	+	0.715953i	$0.745992\pi$
$728$		0			0
$729$			29.2031i			1.08160i
$730$		0			0
$731$	−2.26993	−	2.26993i	−0.0839564	−	0.0839564i
$732$		0			0
$733$	12.8029	−	12.8029i	0.472886	−	0.472886i	−0.429961	−	0.902847i	$-0.641473\pi$
$733$	12.8029	−	12.8029i	0.472886	−	0.472886i	0.902847	+	0.429961i	$0.141473\pi$
$734$		0			0
$735$		−	70.7275i		−	2.60882i
$736$		0			0
$737$	5.83513	−	6.31367i	0.214940	−	0.232567i
$738$		0			0
$739$	−21.1363	−	21.1363i	−0.777510	−	0.777510i	0.201897	−	0.979407i	$-0.435289\pi$
$739$	−21.1363	−	21.1363i	−0.777510	−	0.777510i	−0.979407	+	0.201897i	$0.935289\pi$
$740$		0			0
$741$	−3.22194	+	3.22194i	−0.118361	+	0.118361i
$742$		0			0
$743$			22.9668i			0.842570i	0.906928	+	0.421285i	$0.138421\pi$
$743$			22.9668i			0.842570i	−0.906928	+	0.421285i	$0.861579\pi$
$744$		0			0
$745$	−59.3490			−2.17438
$746$		0			0
$747$	2.70528	−	2.70528i	0.0989809	−	0.0989809i
$748$		0			0
$749$	−30.3017	−	30.3017i	−1.10720	−	1.10720i
$750$		0			0
$751$		−	45.1129i		−	1.64619i	−0.567901	−	0.823097i	$-0.692245\pi$
$751$		−	45.1129i		−	1.64619i	0.567901	−	0.823097i	$-0.307755\pi$
$752$		0			0
$753$	−12.3814			−0.451204
$754$		0			0
$755$	30.6217	+	30.6217i	1.11444	+	1.11444i
$756$		0			0
$757$	−32.2181	+	32.2181i	−1.17099	+	1.17099i	−0.189013	+	0.981975i	$0.560529\pi$
$757$	−32.2181	+	32.2181i	−1.17099	+	1.17099i	−0.981975	+	0.189013i	$0.939471\pi$
$758$		0			0
$759$	−24.4470	+	26.4519i	−0.887370	+	0.960143i
$760$		0			0
$761$	−29.9084			−1.08418			−0.542089	−	0.840321i	$-0.682366\pi$
$761$	−29.9084			−1.08418			−0.542089	+	0.840321i	$0.682366\pi$
$762$		0			0
$763$	−18.9677	−	18.9677i	−0.686679	−	0.686679i
$764$		0			0
$765$	0.371198	−	0.371198i	0.0134207	−	0.0134207i
$766$		0			0
$767$	−7.25549			−0.261980
$768$		0			0
$769$		−	52.0503i		−	1.87698i	−0.345303	−	0.938491i	$-0.612224\pi$
$769$		−	52.0503i		−	1.87698i	0.345303	−	0.938491i	$-0.387776\pi$
$770$		0			0
$771$	11.7949	−	11.7949i	0.424784	−	0.424784i
$772$		0			0
$773$	25.5905	−	25.5905i	0.920427	−	0.920427i	−0.0766324	−	0.997059i	$-0.524417\pi$
$773$	25.5905	−	25.5905i	0.920427	−	0.920427i	0.997059	+	0.0766324i	$0.0244168\pi$
$774$		0			0
$775$	1.40736			0.0505539
$776$		0			0
$777$	36.0286			1.29252
$778$		0			0
$779$	−2.38958	−	2.38958i	−0.0856156	−	0.0856156i
$780$		0			0
$781$	−43.6845	+	1.72072i	−1.56316	+	0.0615721i
$782$		0			0
$783$	0.422177			0.0150874
$784$		0			0
$785$	−3.00238			−0.107160
$786$		0			0
$787$	7.95878	+	7.95878i	0.283700	+	0.283700i	0.834583	−	0.550883i	$-0.185709\pi$
$787$	7.95878	+	7.95878i	0.283700	+	0.283700i	−0.550883	+	0.834583i	$0.685709\pi$
$788$		0			0
$789$	10.5875	+	10.5875i	0.376924	+	0.376924i
$790$		0			0
$791$			27.4285i			0.975244i
$792$		0			0
$793$		−	39.8263i		−	1.41427i
$794$		0			0
$795$	−30.7285	−	30.7285i	−1.08983	−	1.08983i
$796$		0			0
$797$	1.72371	+	1.72371i	0.0610568	+	0.0610568i	0.736976	−	0.675919i	$-0.236253\pi$
$797$	1.72371	+	1.72371i	0.0610568	+	0.0610568i	−0.675919	+	0.736976i	$0.736253\pi$
$798$		0			0
$799$	−0.121726			−0.00430635
$800$		0			0
$801$	4.65461			0.164462
$802$		0			0
$803$	35.7215	−	1.40706i	1.26059	−	0.0496539i
$804$		0			0
$805$	−72.8255	−	72.8255i	−2.56676	−	2.56676i
$806$		0			0
$807$	−31.1557			−1.09673
$808$		0			0
$809$	−18.6487			−0.655652			−0.327826	−	0.944738i	$-0.606316\pi$
$809$	−18.6487			−0.655652			−0.327826	+	0.944738i	$0.606316\pi$
$810$		0			0
$811$	2.99433	−	2.99433i	0.105145	−	0.105145i	−0.652577	−	0.757722i	$-0.726312\pi$
$811$	2.99433	−	2.99433i	0.105145	−	0.105145i	0.757722	+	0.652577i	$0.226312\pi$
$812$		0			0
$813$	35.5205	−	35.5205i	1.24576	−	1.24576i
$814$		0			0
$815$		−	0.874967i		−	0.0306488i
$816$		0			0
$817$	−6.09618			−0.213278
$818$		0			0
$819$	3.02069	−	3.02069i	0.105552	−	0.105552i
$820$		0			0
$821$	−32.2594	−	32.2594i	−1.12586	−	1.12586i	−0.990843	−	0.135019i	$-0.956890\pi$
$821$	−32.2594	−	32.2594i	−1.12586	−	1.12586i	−0.135019	−	0.990843i	$-0.543110\pi$
$822$		0			0
$823$	8.72386			0.304095			0.152047	−	0.988373i	$-0.451413\pi$
$823$	8.72386			0.304095			0.152047	+	0.988373i	$0.451413\pi$
$824$		0			0
$825$	−30.3958	−	28.0920i	−1.05824	−	0.978036i
$826$		0			0
$827$	2.72468	−	2.72468i	0.0947466	−	0.0947466i	−0.658145	−	0.752891i	$-0.728659\pi$
$827$	2.72468	−	2.72468i	0.0947466	−	0.0947466i	0.752891	+	0.658145i	$0.228659\pi$
$828$		0			0
$829$	9.27359	+	9.27359i	0.322085	+	0.322085i	0.849566	−	0.527482i	$-0.176864\pi$
$829$	9.27359	+	9.27359i	0.322085	+	0.322085i	−0.527482	+	0.849566i	$0.676864\pi$
$830$		0			0
$831$	−30.2651			−1.04988
$832$		0			0
$833$			5.72069i			0.198210i
$834$		0			0
$835$	20.0379	+	20.0379i	0.693441	+	0.693441i
$836$		0			0
$837$	0.709841	−	0.709841i	0.0245357	−	0.0245357i
$838$		0			0
$839$	9.96939			0.344182			0.172091	−	0.985081i	$-0.444948\pi$
$839$	9.96939			0.344182			0.172091	+	0.985081i	$0.444948\pi$
$840$		0			0
$841$			28.9940i			0.999792i
$842$		0			0
$843$	−17.0496	+	17.0496i	−0.587219	+	0.587219i
$844$		0			0
$845$	8.36527	+	8.36527i	0.287774	+	0.287774i
$846$		0			0
$847$	3.78636	+	47.9884i	0.130101	+	1.64890i
$848$		0			0
$849$			30.3707i			1.04232i
$850$		0			0
$851$	23.5374	−	23.5374i	0.806851	−	0.806851i
$852$		0			0
$853$	−0.460287	−	0.460287i	−0.0157599	−	0.0157599i	0.699183	−	0.714943i	$-0.253547\pi$
$853$	−0.460287	−	0.460287i	−0.0157599	−	0.0157599i	−0.714943	+	0.699183i	$0.753547\pi$
$854$		0			0
$855$		−	0.996898i		−	0.0340932i
$856$		0			0
$857$	16.4248			0.561061			0.280531	−	0.959845i	$-0.409490\pi$
$857$	16.4248			0.561061			0.280531	+	0.959845i	$0.409490\pi$
$858$		0			0
$859$	−0.996253	−	0.996253i	−0.0339917	−	0.0339917i	0.689907	−	0.723898i	$-0.257652\pi$
$859$	−0.996253	−	0.996253i	−0.0339917	−	0.0339917i	−0.723898	+	0.689907i	$0.757652\pi$
$860$		0			0
$861$	−19.1686	−	19.1686i	−0.653264	−	0.653264i
$862$		0			0
$863$			25.0692i			0.853367i	0.904401	+	0.426683i	$0.140318\pi$
$863$			25.0692i			0.853367i	−0.904401	+	0.426683i	$0.859682\pi$
$864$		0			0
$865$			49.1906i			1.67253i
$866$		0			0
$867$	−19.4443	+	19.4443i	−0.660363	+	0.660363i
$868$		0			0
$869$	−5.97857	+	0.235493i	−0.202809	+	0.00798857i
$870$		0			0
$871$		−	8.06031i		−	0.273113i
$872$		0			0
$873$		−	2.86761i		−	0.0970539i
$874$		0			0
$875$	28.7322	−	28.7322i	0.971324	−	0.971324i
$876$		0			0
$877$	−28.2256	+	28.2256i	−0.953109	+	0.953109i	−0.998949	−	0.0458394i	$-0.985404\pi$
$877$	−28.2256	+	28.2256i	−0.953109	+	0.953109i	0.0458394	+	0.998949i	$0.485404\pi$
$878$		0			0
$879$	19.7903			0.667509
$880$		0			0
$881$	32.2947			1.08804			0.544018	−	0.839074i	$-0.316902\pi$
$881$	32.2947			1.08804			0.544018	+	0.839074i	$0.316902\pi$
$882$		0			0
$883$	23.4327	−	23.4327i	0.788574	−	0.788574i	−0.192687	−	0.981260i	$-0.561720\pi$
$883$	23.4327	−	23.4327i	0.788574	−	0.788574i	0.981260	+	0.192687i	$0.0617201\pi$
$884$		0			0
$885$	−9.60394	+	9.60394i	−0.322833	+	0.322833i
$886$		0			0
$887$			2.24737i			0.0754593i	0.999288	+	0.0377297i	$0.0120126\pi$
$887$			2.24737i			0.0754593i	−0.999288	+	0.0377297i	$0.987987\pi$
$888$		0			0
$889$		−	53.1196i		−	1.78157i
$890$		0			0
$891$	−26.3787	+	1.03905i	−0.883720	+	0.0348094i
$892$		0			0
$893$	−0.163455	+	0.163455i	−0.00546981	+	0.00546981i
$894$		0			0
$895$		−	21.7880i		−	0.728294i
$896$		0			0
$897$			33.7696i			1.12754i
$898$		0			0
$899$	−0.0101590	−	0.0101590i	−0.000338822	−	0.000338822i
$900$		0			0
$901$	2.48543	+	2.48543i	0.0828017	+	0.0828017i
$902$		0			0
$903$	−48.9020			−1.62736
$904$		0			0
$905$		−	73.3373i		−	2.43781i
$906$		0			0
$907$	−10.8367	−	10.8367i	−0.359827	−	0.359827i	0.503922	−	0.863749i	$-0.331890\pi$
$907$	−10.8367	−	10.8367i	−0.359827	−	0.359827i	−0.863749	+	0.503922i	$0.831890\pi$
$908$		0			0
$909$	−4.30016	+	4.30016i	−0.142627	+	0.142627i
$910$		0			0
$911$			55.8319i			1.84979i	0.380217	+	0.924897i	$0.375849\pi$
$911$			55.8319i			1.84979i	−0.380217	+	0.924897i	$0.624151\pi$
$912$		0			0
$913$	29.6833	+	27.4335i	0.982374	+	0.907916i
$914$		0			0
$915$	−52.7173	−	52.7173i	−1.74278	−	1.74278i
$916$		0			0
$917$	−7.38450	+	7.38450i	−0.243858	+	0.243858i
$918$		0			0
$919$		−	25.4033i		−	0.837977i	−0.907992	−	0.418988i	$-0.862385\pi$
$919$		−	25.4033i		−	0.837977i	0.907992	−	0.418988i	$-0.137615\pi$
$920$		0			0
$921$	−15.1171			−0.498127
$922$		0			0
$923$	−28.9832	+	28.9832i	−0.953993	+	0.953993i
$924$		0			0
$925$	27.0467	+	27.0467i	0.889290	+	0.889290i
$926$		0			0
$927$		−	0.425104i		−	0.0139622i
$928$		0			0
$929$	−29.9291			−0.981941			−0.490971	−	0.871176i	$-0.663358\pi$
$929$	−29.9291			−0.981941			−0.490971	+	0.871176i	$0.663358\pi$
$930$		0			0
$931$	7.68181	+	7.68181i	0.251761	+	0.251761i
$932$		0			0
$933$	−8.24888	+	8.24888i	−0.270056	+	0.270056i
$934$		0			0
$935$	4.07292	+	3.76422i	0.133199	+	0.123103i
$936$		0			0
$937$	−7.90951			−0.258392			−0.129196	−	0.991619i	$-0.541240\pi$
$937$	−7.90951			−0.258392			−0.129196	+	0.991619i	$0.541240\pi$
$938$		0			0
$939$	−6.87425	−	6.87425i	−0.224333	−	0.224333i
$940$		0			0
$941$	−2.16112	+	2.16112i	−0.0704504	+	0.0704504i	−0.741454	−	0.671004i	$-0.765863\pi$
$941$	−2.16112	+	2.16112i	−0.0704504	+	0.0704504i	0.671004	+	0.741454i	$0.265863\pi$
$942$		0			0
$943$	−25.0456			−0.815596
$944$		0			0
$945$		−	84.4161i		−	2.74606i
$946$		0			0
$947$	−4.16232	+	4.16232i	−0.135257	+	0.135257i	−0.771494	−	0.636237i	$-0.780490\pi$
$947$	−4.16232	+	4.16232i	−0.135257	+	0.135257i	0.636237	+	0.771494i	$0.280490\pi$
$948$		0			0
$949$	23.7000	−	23.7000i	0.769334	−	0.769334i
$950$		0			0
$951$	5.10082			0.165405
$952$		0			0
$953$	48.5854			1.57384			0.786918	−	0.617058i	$-0.211676\pi$
$953$	48.5854			1.57384			0.786918	+	0.617058i	$0.211676\pi$
$954$		0			0
$955$	45.3493	+	45.3493i	1.46747	+	1.46747i
$956$		0			0
$957$	0.0166300	+	0.422192i	0.000537571	+	0.0136475i
$958$		0			0
$959$	−58.1159			−1.87666
$960$		0			0
$961$	30.9658			0.998898
$962$		0			0
$963$	−2.17377	−	2.17377i	−0.0700487	−	0.0700487i
$964$		0			0
$965$	21.6850	+	21.6850i	0.698064	+	0.698064i
$966$		0			0
$967$			4.66415i			0.149989i	0.997184	+	0.0749945i	$0.0238939\pi$
$967$			4.66415i			0.149989i	−0.997184	+	0.0749945i	$0.976106\pi$
$968$		0			0
$969$		−	0.689906i		−	0.0221630i
$970$		0			0
$971$	−26.2171	−	26.2171i	−0.841348	−	0.841348i	0.147686	−	0.989034i	$-0.452817\pi$
$971$	−26.2171	−	26.2171i	−0.841348	−	0.841348i	−0.989034	+	0.147686i	$0.952817\pi$
$972$		0			0
$973$	−29.4770	−	29.4770i	−0.944991	−	0.944991i
$974$		0			0
$975$	−38.8046			−1.24274
$976$		0			0
$977$	−40.6512			−1.30055			−0.650273	−	0.759700i	$-0.725346\pi$
$977$	−40.6512			−1.30055			−0.650273	+	0.759700i	$0.725346\pi$
$978$		0			0
$979$	1.93547	+	49.1366i	0.0618579	+	1.57041i
$980$		0			0
$981$	−1.36070	−	1.36070i	−0.0434438	−	0.0434438i
$982$		0			0
$983$	53.1772			1.69609			0.848045	−	0.529924i	$-0.177780\pi$
$983$	53.1772			1.69609			0.848045	+	0.529924i	$0.177780\pi$
$984$		0			0
$985$	78.5342			2.50231
$986$		0			0
$987$	−1.31119	+	1.31119i	−0.0417357	+	0.0417357i
$988$		0			0
$989$	−31.9475	+	31.9475i	−1.01587	+	1.01587i
$990$		0			0
$991$		−	31.9546i		−	1.01507i	−0.861631	−	0.507536i	$-0.830557\pi$
$991$		−	31.9546i		−	1.01507i	0.861631	−	0.507536i	$-0.169443\pi$
$992$		0			0
$993$	19.4740			0.617988
$994$		0			0
$995$	21.3276	−	21.3276i	0.676131	−	0.676131i
$996$		0			0
$997$	5.97842	+	5.97842i	0.189339	+	0.189339i	0.795410	−	0.606072i	$-0.207256\pi$
$997$	5.97842	+	5.97842i	0.189339	+	0.189339i	−0.606072	+	0.795410i	$0.707256\pi$
$998$		0			0
$999$	27.2835			0.863212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.8		44
4.3	odd	2		1408.2.i.a.351.15		44
8.3	odd	2		704.2.i.a.175.7		44
8.5	even	2		176.2.i.a.131.1	yes	44
11.10	odd	2	inner	1408.2.i.b.351.7		44
16.3	odd	4		176.2.i.a.43.22	yes	44
16.5	even	4		1408.2.i.a.1055.16		44
16.11	odd	4	inner	1408.2.i.b.1055.7		44
16.13	even	4		704.2.i.a.527.7		44
44.43	even	2		1408.2.i.a.351.16		44
88.21	odd	2		176.2.i.a.131.22	yes	44
88.43	even	2		704.2.i.a.175.8		44
176.21	odd	4		1408.2.i.a.1055.15		44
176.43	even	4	inner	1408.2.i.b.1055.8		44
176.109	odd	4		704.2.i.a.527.8		44
176.131	even	4		176.2.i.a.43.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.1	✓	44	176.131	even	4
176.2.i.a.43.22	yes	44	16.3	odd	4
176.2.i.a.131.1	yes	44	8.5	even	2
176.2.i.a.131.22	yes	44	88.21	odd	2
704.2.i.a.175.7		44	8.3	odd	2
704.2.i.a.175.8		44	88.43	even	2
704.2.i.a.527.7		44	16.13	even	4
704.2.i.a.527.8		44	176.109	odd	4
1408.2.i.a.351.15		44	4.3	odd	2
1408.2.i.a.351.16		44	44.43	even	2
1408.2.i.a.1055.15		44	176.21	odd	4
1408.2.i.a.1055.16		44	16.5	even	4
1408.2.i.b.351.7		44	11.10	odd	2	inner
1408.2.i.b.351.8		44	1.1	even	1	trivial
1408.2.i.b.1055.7		44	16.11	odd	4	inner
1408.2.i.b.1055.8		44	176.43	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:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15889 + 1.15889i) q^{3} +(2.51141 - 2.51141i) q^{5} +4.37614i q^{7} +0.313934i q^{9} +O(q^{10})\)	\(q+(-1.15889 + 1.15889i) q^{3} +(2.51141 - 2.51141i) q^{5} +4.37614i q^{7} +0.313934i q^{9} +(-3.31405 + 0.130539i) q^{11} +(-2.19876 + 2.19876i) q^{13} +5.82090i q^{15} -0.470816i q^{17} +(-0.632217 - 0.632217i) q^{19} +(-5.07148 - 5.07148i) q^{21} -6.62637 q^{23} -7.61433i q^{25} +(-3.84049 - 3.84049i) q^{27} +(-0.0549639 + 0.0549639i) q^{29} +0.184831i q^{31} +(3.68935 - 3.99192i) q^{33} +(10.9903 + 10.9903i) q^{35} +(-3.55208 + 3.55208i) q^{37} -5.09625i q^{39} +3.77969 q^{41} +(4.82127 - 4.82127i) q^{43} +(0.788415 + 0.788415i) q^{45} -0.258542i q^{47} -12.1506 q^{49} +(0.545625 + 0.545625i) q^{51} +(-5.27899 + 5.27899i) q^{53} +(-7.99510 + 8.65078i) q^{55} +1.46534 q^{57} +(1.64990 + 1.64990i) q^{59} +(-9.05654 + 9.05654i) q^{61} -1.37382 q^{63} +11.0440i q^{65} +(-1.83292 + 1.83292i) q^{67} +(7.67925 - 7.67925i) q^{69} +13.1816 q^{71} -10.7788 q^{73} +(8.82419 + 8.82419i) q^{75} +(-0.571258 - 14.5028i) q^{77} +1.80400 q^{79} +7.95965 q^{81} +(-8.61736 - 8.61736i) q^{83} +(-1.18241 - 1.18241i) q^{85} -0.127395i q^{87} -14.8267i q^{89} +(-9.62208 - 9.62208i) q^{91} +(-0.214199 - 0.214199i) q^{93} -3.17551 q^{95} -9.13445 q^{97} +(-0.0409806 - 1.04039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

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