LMFDB - Embedded newform 315.3.o.b.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	315.127
Dual form			315.3.o.b.253.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992944 - 0.992944i) q^{2} -2.02813i q^{4} +(2.01954 + 4.57400i) q^{5} +(1.87083 + 1.87083i) q^{7} +(-5.98559 + 5.98559i) q^{8} +O(q^{10})$	\(q+(-0.992944 - 0.992944i) q^{2} -2.02813i q^{4} +(2.01954 + 4.57400i) q^{5} +(1.87083 + 1.87083i) q^{7} +(-5.98559 + 5.98559i) q^{8} +(2.53644 - 6.54701i) q^{10} -6.89922 q^{11} +(-11.8879 + 11.8879i) q^{13} -3.71526i q^{14} +3.77421 q^{16} +(-16.7997 - 16.7997i) q^{17} +8.54896i q^{19} +(9.27664 - 4.09587i) q^{20} +(6.85053 + 6.85053i) q^{22} +(-12.4881 + 12.4881i) q^{23} +(-16.8429 + 18.4747i) q^{25} +23.6079 q^{26} +(3.79427 - 3.79427i) q^{28} +1.33880i q^{29} -18.4055 q^{31} +(20.1948 + 20.1948i) q^{32} +33.3623i q^{34} +(-4.77896 + 12.3354i) q^{35} +(31.4003 + 31.4003i) q^{37} +(8.48863 - 8.48863i) q^{38} +(-39.4662 - 15.2900i) q^{40} +26.7387 q^{41} +(-15.5575 + 15.5575i) q^{43} +13.9925i q^{44} +24.7999 q^{46} +(22.1535 + 22.1535i) q^{47} +7.00000i q^{49} +(35.0685 - 1.62028i) q^{50} +(24.1101 + 24.1101i) q^{52} +(-66.4707 + 66.4707i) q^{53} +(-13.9332 - 31.5570i) q^{55} -22.3960 q^{56} +(1.32935 - 1.32935i) q^{58} -81.8790i q^{59} -92.0711 q^{61} +(18.2756 + 18.2756i) q^{62} -55.2014i q^{64} +(-78.3830 - 30.3671i) q^{65} +(79.2670 + 79.2670i) q^{67} +(-34.0719 + 34.0719i) q^{68} +(16.9936 - 7.50310i) q^{70} +63.1779 q^{71} +(92.9816 - 92.9816i) q^{73} -62.3574i q^{74} +17.3384 q^{76} +(-12.9072 - 12.9072i) q^{77} +8.46427i q^{79} +(7.62216 + 17.2632i) q^{80} +(-26.5501 - 26.5501i) q^{82} +(-36.2768 + 36.2768i) q^{83} +(42.9141 - 110.769i) q^{85} +30.8955 q^{86} +(41.2959 - 41.2959i) q^{88} -32.5098i q^{89} -44.4803 q^{91} +(25.3273 + 25.3273i) q^{92} -43.9943i q^{94} +(-39.1029 + 17.2649i) q^{95} +(-79.2404 - 79.2404i) q^{97} +(6.95061 - 6.95061i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−0.992944	−	0.992944i	−0.496472	−	0.496472i	0.413866	−	0.910338i	$-0.364178\pi$
$2$	−0.992944	−	0.992944i	−0.496472	−	0.496472i	−0.910338	+	0.413866i	$0.864178\pi$
$3$		0			0
$3$		0			0
$4$		−	2.02813i		−	0.507031i
$5$	2.01954	+	4.57400i	0.403908	+	0.914800i
$5$	2.01954	+	4.57400i	0.403908	+	0.914800i
$6$		0			0
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	−5.98559	+	5.98559i	−0.748199	+	0.748199i
$9$		0			0
$10$	2.53644	−	6.54701i	0.253644	−	0.654701i
$11$	−6.89922			−0.627201			−0.313601	−	0.949555i	$-0.601535\pi$
$11$	−6.89922			−0.627201			−0.313601	+	0.949555i	$0.601535\pi$
$12$		0			0
$13$	−11.8879	+	11.8879i	−0.914450	+	0.914450i	−0.996618	−	0.0821681i	$-0.973816\pi$
$13$	−11.8879	+	11.8879i	−0.914450	+	0.914450i	0.0821681	+	0.996618i	$0.473816\pi$
$14$		−	3.71526i		−	0.265375i
$15$		0			0
$16$	3.77421			0.235888
$17$	−16.7997	−	16.7997i	−0.988216	−	0.988216i	0.0117149	−	0.999931i	$-0.496271\pi$
$17$	−16.7997	−	16.7997i	−0.988216	−	0.988216i	−0.999931	+	0.0117149i	$0.996271\pi$
$18$		0			0
$19$			8.54896i			0.449945i	0.974365	+	0.224973i	$0.0722292\pi$
$19$			8.54896i			0.449945i	−0.974365	+	0.224973i	$0.927771\pi$
$20$	9.27664	−	4.09587i	0.463832	−	0.204794i
$21$		0			0
$22$	6.85053	+	6.85053i	0.311388	+	0.311388i
$23$	−12.4881	+	12.4881i	−0.542959	+	0.542959i	−0.924395	−	0.381436i	$-0.875430\pi$
$23$	−12.4881	+	12.4881i	−0.542959	+	0.542959i	0.381436	+	0.924395i	$0.375430\pi$
$24$		0			0
$25$	−16.8429	+	18.4747i	−0.673717	+	0.738989i
$26$	23.6079			0.907998
$27$		0			0
$28$	3.79427	−	3.79427i	0.135510	−	0.135510i
$29$			1.33880i			0.0461655i	0.999734	+	0.0230828i	$0.00734813\pi$
$29$			1.33880i			0.0461655i	−0.999734	+	0.0230828i	$0.992652\pi$
$30$		0			0
$31$	−18.4055			−0.593726			−0.296863	−	0.954920i	$-0.595940\pi$
$31$	−18.4055			−0.593726			−0.296863	+	0.954920i	$0.595940\pi$
$32$	20.1948	+	20.1948i	0.631087	+	0.631087i
$33$		0			0
$34$			33.3623i			0.981243i
$35$	−4.77896	+	12.3354i	−0.136542	+	0.352439i
$36$		0			0
$37$	31.4003	+	31.4003i	0.848656	+	0.848656i	0.989966	−	0.141309i	$-0.0451311\pi$
$37$	31.4003	+	31.4003i	0.848656	+	0.848656i	−0.141309	+	0.989966i	$0.545131\pi$
$38$	8.48863	−	8.48863i	0.223385	−	0.223385i
$39$		0			0
$40$	−39.4662	−	15.2900i	−0.986655	−	0.382249i
$41$	26.7387			0.652164			0.326082	−	0.945341i	$-0.394271\pi$
$41$	26.7387			0.652164			0.326082	+	0.945341i	$0.394271\pi$
$42$		0			0
$43$	−15.5575	+	15.5575i	−0.361803	+	0.361803i	−0.864476	−	0.502673i	$-0.832350\pi$
$43$	−15.5575	+	15.5575i	−0.361803	+	0.361803i	0.502673	+	0.864476i	$0.332350\pi$
$44$			13.9925i			0.318011i
$45$		0			0
$46$	24.7999			0.539128
$47$	22.1535	+	22.1535i	0.471350	+	0.471350i	0.902351	−	0.431001i	$-0.141840\pi$
$47$	22.1535	+	22.1535i	0.471350	+	0.471350i	−0.431001	+	0.902351i	$0.641840\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	35.0685	−	1.62028i	0.701369	−	0.0324055i
$51$		0			0
$52$	24.1101	+	24.1101i	0.463655	+	0.463655i
$53$	−66.4707	+	66.4707i	−1.25416	+	1.25416i	−0.300328	+	0.953836i	$0.597096\pi$
$53$	−66.4707	+	66.4707i	−1.25416	+	1.25416i	−0.953836	+	0.300328i	$0.902904\pi$
$54$		0			0
$55$	−13.9332	−	31.5570i	−0.253331	−	0.573764i
$56$	−22.3960			−0.399929
$57$		0			0
$58$	1.32935	−	1.32935i	0.0229199	−	0.0229199i
$59$		−	81.8790i		−	1.38778i	−0.720081	−	0.693890i	$-0.755895\pi$
$59$		−	81.8790i		−	1.38778i	0.720081	−	0.693890i	$-0.244105\pi$
$60$		0			0
$61$	−92.0711			−1.50936			−0.754681	−	0.656092i	$-0.772208\pi$
$61$	−92.0711			−1.50936			−0.754681	+	0.656092i	$0.772208\pi$
$62$	18.2756	+	18.2756i	0.294768	+	0.294768i
$63$		0			0
$64$		−	55.2014i		−	0.862522i
$65$	−78.3830	−	30.3671i	−1.20589	−	0.467186i
$66$		0			0
$67$	79.2670	+	79.2670i	1.18309	+	1.18309i	0.978940	+	0.204149i	$0.0654428\pi$
$67$	79.2670	+	79.2670i	1.18309	+	1.18309i	0.204149	+	0.978940i	$0.434557\pi$
$68$	−34.0719	+	34.0719i	−0.501057	+	0.501057i
$69$		0			0
$70$	16.9936	−	7.50310i	0.242765	−	0.107187i
$71$	63.1779			0.889829			0.444915	−	0.895573i	$-0.353234\pi$
$71$	63.1779			0.889829			0.444915	+	0.895573i	$0.353234\pi$
$72$		0			0
$73$	92.9816	−	92.9816i	1.27372	−	1.27372i	0.329600	−	0.944121i	$-0.393086\pi$
$73$	92.9816	−	92.9816i	1.27372	−	1.27372i	0.944121	−	0.329600i	$-0.106914\pi$
$74$		−	62.3574i		−	0.842668i
$75$		0			0
$76$	17.3384			0.228136
$77$	−12.9072	−	12.9072i	−0.167627	−	0.167627i
$78$		0			0
$79$			8.46427i			0.107143i	0.998564	+	0.0535713i	$0.0170605\pi$
$79$			8.46427i			0.107143i	−0.998564	+	0.0535713i	$0.982940\pi$
$80$	7.62216	+	17.2632i	0.0952769	+	0.215790i
$81$		0			0
$82$	−26.5501	−	26.5501i	−0.323781	−	0.323781i
$83$	−36.2768	+	36.2768i	−0.437070	+	0.437070i	−0.891025	−	0.453955i	$-0.850013\pi$
$83$	−36.2768	+	36.2768i	−0.437070	+	0.437070i	0.453955	+	0.891025i	$0.350013\pi$
$84$		0			0
$85$	42.9141	−	110.769i	0.504872	−	1.30317i
$86$	30.8955			0.359250
$87$		0			0
$88$	41.2959	−	41.2959i	0.469271	−	0.469271i
$89$		−	32.5098i		−	0.365279i	−0.983180	−	0.182639i	$-0.941536\pi$
$89$		−	32.5098i		−	0.365279i	0.983180	−	0.182639i	$-0.0584641\pi$
$90$		0			0
$91$	−44.4803			−0.488794
$92$	25.3273	+	25.3273i	0.275297	+	0.275297i
$93$		0			0
$94$		−	43.9943i		−	0.468024i
$95$	−39.1029	+	17.2649i	−0.411610	+	0.181736i
$96$		0			0
$97$	−79.2404	−	79.2404i	−0.816911	−	0.816911i	0.168748	−	0.985659i	$-0.446028\pi$
$97$	−79.2404	−	79.2404i	−0.816911	−	0.816911i	−0.985659	+	0.168748i	$0.946028\pi$
$98$	6.95061	−	6.95061i	0.0709246	−	0.0709246i
$99$		0			0
$100$	37.4691	+	34.1596i	0.374691	+	0.341596i
$101$	−58.6380			−0.580575			−0.290287	−	0.956940i	$-0.593751\pi$
$101$	−58.6380			−0.580575			−0.290287	+	0.956940i	$0.593751\pi$
$102$		0			0
$103$	−99.0052	+	99.0052i	−0.961215	+	0.961215i	−0.999275	−	0.0380601i	$-0.987882\pi$
$103$	−99.0052	+	99.0052i	−0.961215	+	0.961215i	0.0380601	+	0.999275i	$0.487882\pi$
$104$		−	142.312i		−	1.36838i
$105$		0			0
$106$	132.003			1.24531
$107$	−1.04612	−	1.04612i	−0.00977686	−	0.00977686i	0.702201	−	0.711978i	$-0.252201\pi$
$107$	−1.04612	−	1.04612i	−0.00977686	−	0.00977686i	−0.711978	+	0.702201i	$0.752201\pi$
$108$		0			0
$109$		−	157.350i		−	1.44358i	−0.692111	−	0.721791i	$-0.743319\pi$
$109$		−	157.350i		−	1.44358i	0.692111	−	0.721791i	$-0.256681\pi$
$110$	−17.4994	+	45.1692i	−0.159086	+	0.410629i
$111$		0			0
$112$	7.06090	+	7.06090i	0.0630437	+	0.0630437i
$113$	127.762	−	127.762i	1.13063	−	1.13063i	0.140562	−	0.990072i	$-0.455109\pi$
$113$	127.762	−	127.762i	1.13063	−	1.13063i	0.990072	−	0.140562i	$-0.0448908\pi$
$114$		0			0
$115$	−82.3405	−	31.9003i	−0.716004	−	0.277394i
$116$	2.71525			0.0234074
$117$		0			0
$118$	−81.3013	+	81.3013i	−0.688994	+	0.688994i
$119$		−	62.8586i		−	0.528224i
$120$		0			0
$121$	−73.4008			−0.606618
$122$	91.4214	+	91.4214i	0.749356	+	0.749356i
$123$		0			0
$124$			37.3286i			0.301037i
$125$	−118.518	−	39.7292i	−0.948147	−	0.317833i
$126$		0			0
$127$	−15.3568	−	15.3568i	−0.120920	−	0.120920i	0.644057	−	0.764977i	$-0.277250\pi$
$127$	−15.3568	−	15.3568i	−0.120920	−	0.120920i	−0.764977	+	0.644057i	$0.777250\pi$
$128$	25.9672	−	25.9672i	0.202869	−	0.202869i
$129$		0			0
$130$	47.6771	+	107.983i	0.366747	+	0.830636i
$131$	176.678			1.34869			0.674344	−	0.738417i	$-0.264426\pi$
$131$	176.678			1.34869			0.674344	+	0.738417i	$0.264426\pi$
$132$		0			0
$133$	−15.9936	+	15.9936i	−0.120253	+	0.120253i
$134$		−	157.415i		−	1.17474i
$135$		0			0
$136$	201.112			1.47876
$137$	18.0301	+	18.0301i	0.131607	+	0.131607i	0.769842	−	0.638235i	$-0.220335\pi$
$137$	18.0301	+	18.0301i	0.131607	+	0.131607i	−0.638235	+	0.769842i	$0.720335\pi$
$138$		0			0
$139$		−	158.415i		−	1.13968i	−0.821756	−	0.569839i	$-0.807006\pi$
$139$		−	158.415i		−	1.13968i	0.821756	−	0.569839i	$-0.192994\pi$
$140$	25.0177	+	9.69233i	0.178698	+	0.0692309i
$141$		0			0
$142$	−62.7321	−	62.7321i	−0.441775	−	0.441775i
$143$	82.0169	−	82.0169i	0.573545	−	0.573545i
$144$		0			0
$145$	−6.12367	+	2.70376i	−0.0422322	+	0.0186466i
$146$	−184.651			−1.26473
$147$		0			0
$148$	63.6837	−	63.6837i	0.430295	−	0.430295i
$149$			140.085i			0.940169i	0.882621	+	0.470085i	$0.155777\pi$
$149$			140.085i			0.940169i	−0.882621	+	0.470085i	$0.844223\pi$
$150$		0			0
$151$	−215.189			−1.42509			−0.712546	−	0.701625i	$-0.752458\pi$
$151$	−215.189			−1.42509			−0.712546	+	0.701625i	$0.752458\pi$
$152$	−51.1705	−	51.1705i	−0.336648	−	0.336648i
$153$		0			0
$154$			25.6323i			0.166444i
$155$	−37.1706	−	84.1867i	−0.239810	−	0.543140i
$156$		0			0
$157$	49.6844	+	49.6844i	0.316461	+	0.316461i	0.847406	−	0.530945i	$-0.178163\pi$
$157$	49.6844	+	49.6844i	0.316461	+	0.316461i	−0.530945	+	0.847406i	$0.678163\pi$
$158$	8.40455	−	8.40455i	0.0531933	−	0.0531933i
$159$		0			0
$160$	−51.5868	+	133.155i	−0.322417	+	0.832219i
$161$	−46.7260			−0.290224
$162$		0			0
$163$	−173.503	+	173.503i	−1.06443	+	1.06443i	−0.0666571	+	0.997776i	$0.521233\pi$
$163$	−173.503	+	173.503i	−1.06443	+	1.06443i	−0.997776	+	0.0666571i	$0.978767\pi$
$164$		−	54.2295i		−	0.330668i
$165$		0			0
$166$	72.0417			0.433986
$167$	177.701	+	177.701i	1.06408	+	1.06408i	0.997801	+	0.0662778i	$0.0211124\pi$
$167$	177.701	+	177.701i	1.06408	+	1.06408i	0.0662778	+	0.997801i	$0.478888\pi$
$168$		0			0
$169$		−	113.642i		−	0.672439i
$170$	−152.599	+	67.3764i	−0.897641	+	0.396332i
$171$		0			0
$172$	31.5526	+	31.5526i	0.183445	+	0.183445i
$173$	−216.483	+	216.483i	−1.25135	+	1.25135i	−0.296233	+	0.955116i	$0.595730\pi$
$173$	−216.483	+	216.483i	−1.25135	+	1.25135i	−0.955116	+	0.296233i	$0.904270\pi$
$174$		0			0
$175$	−66.0733	+	3.05280i	−0.377562	+	0.0174446i
$176$	−26.0391			−0.147949
$177$		0			0
$178$	−32.2804	+	32.2804i	−0.181351	+	0.181351i
$179$			243.651i			1.36118i	0.732665	+	0.680590i	$0.238276\pi$
$179$			243.651i			1.36118i	−0.732665	+	0.680590i	$0.761724\pi$
$180$		0			0
$181$	255.169			1.40977			0.704887	−	0.709320i	$-0.250998\pi$
$181$	255.169			1.40977			0.704887	+	0.709320i	$0.250998\pi$
$182$	44.1664	+	44.1664i	0.242673	+	0.242673i
$183$		0			0
$184$		−	149.497i		−	0.812483i
$185$	−80.2108	+	207.039i	−0.433572	+	1.11913i
$186$		0			0
$187$	115.905	+	115.905i	0.619811	+	0.619811i
$188$	44.9300	−	44.9300i	0.238989	−	0.238989i
$189$		0			0
$190$	55.9701	+	21.6839i	0.294580	+	0.114126i
$191$	−7.77927			−0.0407292			−0.0203646	−	0.999793i	$-0.506483\pi$
$191$	−7.77927			−0.0407292			−0.0203646	+	0.999793i	$0.506483\pi$
$192$		0			0
$193$	142.113	−	142.113i	0.736339	−	0.736339i	−0.235528	−	0.971867i	$-0.575682\pi$
$193$	142.113	−	142.113i	0.736339	−	0.736339i	0.971867	+	0.235528i	$0.0756821\pi$
$194$			157.363i			0.811147i
$195$		0			0
$196$	14.1969			0.0724330
$197$	−25.0644	−	25.0644i	−0.127230	−	0.127230i	0.640624	−	0.767855i	$-0.278676\pi$
$197$	−25.0644	−	25.0644i	−0.127230	−	0.127230i	−0.767855	+	0.640624i	$0.778676\pi$
$198$		0			0
$199$			84.2722i			0.423479i	0.977326	+	0.211739i	$0.0679128\pi$
$199$			84.2722i			0.423479i	−0.977326	+	0.211739i	$0.932087\pi$
$200$	−9.76722	−	211.397i	−0.0488361	−	1.05699i
$201$		0			0
$202$	58.2243	+	58.2243i	0.288239	+	0.288239i
$203$	−2.50467	+	2.50467i	−0.0123383	+	0.0123383i
$204$		0			0
$205$	53.9999	+	122.303i	0.263414	+	0.596600i
$206$	196.613			0.954433
$207$		0			0
$208$	−44.8672	+	44.8672i	−0.215708	+	0.215708i
$209$		−	58.9811i		−	0.282206i
$210$		0			0
$211$	365.560			1.73251			0.866255	−	0.499601i	$-0.166520\pi$
$211$	365.560			1.73251			0.866255	+	0.499601i	$0.166520\pi$
$212$	134.811	+	134.811i	0.635900	+	0.635900i
$213$		0			0
$214$			2.07749i			0.00970788i
$215$	−102.579	−	39.7411i	−0.477112	−	0.184842i
$216$		0			0
$217$	−34.4335	−	34.4335i	−0.158680	−	0.158680i
$218$	−156.240	+	156.240i	−0.716698	+	0.716698i
$219$		0			0
$220$	−64.0016	+	28.2583i	−0.290916	+	0.128447i
$221$	399.424			1.80735
$222$		0			0
$223$	−258.830	+	258.830i	−1.16067	+	1.16067i	−0.176343	+	0.984329i	$0.556427\pi$
$223$	−258.830	+	258.830i	−1.16067	+	1.16067i	−0.984329	+	0.176343i	$0.943573\pi$
$224$			75.5620i			0.337330i
$225$		0			0
$226$	−253.720			−1.12266
$227$	−107.905	−	107.905i	−0.475354	−	0.475354i	0.428288	−	0.903642i	$-0.359117\pi$
$227$	−107.905	−	107.905i	−0.475354	−	0.475354i	−0.903642	+	0.428288i	$0.859117\pi$
$228$		0			0
$229$			253.800i			1.10829i	0.832419	+	0.554147i	$0.186956\pi$
$229$			253.800i			1.10829i	−0.832419	+	0.554147i	$0.813044\pi$
$230$	50.0843	+	113.435i	0.217758	+	0.493194i
$231$		0			0
$232$	−8.01351	−	8.01351i	−0.0345410	−	0.0345410i
$233$	242.257	−	242.257i	1.03973	−	1.03973i	0.0405526	−	0.999177i	$-0.487088\pi$
$233$	242.257	−	242.257i	1.03973	−	1.03973i	0.999177	−	0.0405526i	$-0.0129118\pi$
$234$		0			0
$235$	−56.5901	+	146.070i	−0.240809	+	0.621573i
$236$	−166.061			−0.703648
$237$		0			0
$238$	−62.4151	+	62.4151i	−0.262248	+	0.262248i
$239$		−	65.4432i		−	0.273821i	−0.990583	−	0.136910i	$-0.956283\pi$
$239$		−	65.4432i		−	0.273821i	0.990583	−	0.136910i	$-0.0437172\pi$
$240$		0			0
$241$	72.8224			0.302168			0.151084	−	0.988521i	$-0.451724\pi$
$241$	72.8224			0.302168			0.151084	+	0.988521i	$0.451724\pi$
$242$	72.8829	+	72.8829i	0.301169	+	0.301169i
$243$		0			0
$244$			186.732i			0.765294i
$245$	−32.0180	+	14.1368i	−0.130686	+	0.0577011i
$246$		0			0
$247$	−101.629	−	101.629i	−0.411452	−	0.411452i
$248$	110.168	−	110.168i	0.444225	−	0.444225i
$249$		0			0
$250$	78.2332	+	157.131i	0.312933	+	0.628524i
$251$	−77.1502			−0.307371			−0.153686	−	0.988120i	$-0.549114\pi$
$251$	−77.1502			−0.307371			−0.153686	+	0.988120i	$0.549114\pi$
$252$		0			0
$253$	86.1578	−	86.1578i	0.340545	−	0.340545i
$254$			30.4969i			0.120066i
$255$		0			0
$256$	−272.374			−1.06396
$257$	−321.516	−	321.516i	−1.25104	−	1.25104i	−0.955256	−	0.295779i	$-0.904421\pi$
$257$	−321.516	−	321.516i	−1.25104	−	1.25104i	−0.295779	−	0.955256i	$-0.595579\pi$
$258$		0			0
$259$			117.489i			0.453626i
$260$	−61.5882	+	158.971i	−0.236878	+	0.611425i
$261$		0			0
$262$	−175.432	−	175.432i	−0.669586	−	0.669586i
$263$	−52.5498	+	52.5498i	−0.199809	+	0.199809i	−0.799918	−	0.600109i	$-0.795124\pi$
$263$	−52.5498	+	52.5498i	−0.199809	+	0.199809i	0.600109	+	0.799918i	$0.295124\pi$
$264$		0			0
$265$	−438.277	−	169.797i	−1.65387	−	0.640743i
$266$	31.7616			0.119404
$267$		0			0
$268$	160.763	−	160.763i	0.599863	−	0.599863i
$269$		−	25.6548i		−	0.0953709i	−0.998862	−	0.0476855i	$-0.984815\pi$
$269$		−	25.6548i		−	0.0953709i	0.998862	−	0.0476855i	$-0.0151845\pi$
$270$		0			0
$271$	−62.2867			−0.229840			−0.114920	−	0.993375i	$-0.536661\pi$
$271$	−62.2867			−0.229840			−0.114920	+	0.993375i	$0.536661\pi$
$272$	−63.4055	−	63.4055i	−0.233108	−	0.233108i
$273$		0			0
$274$		−	35.8058i		−	0.130678i
$275$	116.203	−	127.461i	0.422557	−	0.463495i
$276$		0			0
$277$	50.5633	+	50.5633i	0.182539	+	0.182539i	0.792461	−	0.609922i	$-0.208799\pi$
$277$	50.5633	+	50.5633i	0.182539	+	0.182539i	−0.609922	+	0.792461i	$0.708799\pi$
$278$	−157.297	+	157.297i	−0.565818	+	0.565818i
$279$		0			0
$280$	−45.2296	−	102.439i	−0.161534	−	0.365855i
$281$	30.1715			0.107372			0.0536859	−	0.998558i	$-0.482903\pi$
$281$	30.1715			0.107372			0.0536859	+	0.998558i	$0.482903\pi$
$282$		0			0
$283$	17.6667	−	17.6667i	0.0624264	−	0.0624264i	−0.675204	−	0.737631i	$-0.735945\pi$
$283$	17.6667	−	17.6667i	0.0624264	−	0.0624264i	0.737631	+	0.675204i	$0.235945\pi$
$284$		−	128.133i		−	0.451171i
$285$		0			0
$286$	−162.876			−0.569497
$287$	50.0236	+	50.0236i	0.174298	+	0.174298i
$288$		0			0
$289$			275.459i			0.953144i
$290$	8.76514	+	3.39578i	0.0302246	+	0.0117096i
$291$		0			0
$292$	−188.578	−	188.578i	−0.645816	−	0.645816i
$293$	−58.3820	+	58.3820i	−0.199256	+	0.199256i	−0.799681	−	0.600425i	$-0.794998\pi$
$293$	−58.3820	+	58.3820i	−0.199256	+	0.199256i	0.600425	+	0.799681i	$0.294998\pi$
$294$		0			0
$295$	374.515	−	165.358i	1.26954	−	0.560535i
$296$	−375.898			−1.26993
$297$		0			0
$298$	139.097	−	139.097i	0.466768	−	0.466768i
$299$		−	296.912i		−	0.993018i
$300$		0			0
$301$	−58.2109			−0.193392
$302$	213.671	+	213.671i	0.707519	+	0.707519i
$303$		0			0
$304$			32.2655i			0.106137i
$305$	−185.941	−	421.133i	−0.609643	−	1.38076i
$306$		0			0
$307$	148.513	+	148.513i	0.483756	+	0.483756i	0.906329	−	0.422573i	$-0.138873\pi$
$307$	148.513	+	148.513i	0.483756	+	0.483756i	−0.422573	+	0.906329i	$0.638873\pi$
$308$	−26.1775	+	26.1775i	−0.0849919	+	0.0849919i
$309$		0			0
$310$	−46.6844	+	120.501i	−0.150595	+	0.388713i
$311$	200.767			0.645555			0.322777	−	0.946475i	$-0.395384\pi$
$311$	200.767			0.645555			0.322777	+	0.946475i	$0.395384\pi$
$312$		0			0
$313$	288.120	−	288.120i	0.920511	−	0.920511i	−0.0765549	−	0.997065i	$-0.524392\pi$
$313$	288.120	−	288.120i	0.920511	−	0.920511i	0.997065	+	0.0765549i	$0.0243920\pi$
$314$		−	98.6676i		−	0.314228i
$315$		0			0
$316$	17.1666			0.0543247
$317$	−85.7613	−	85.7613i	−0.270540	−	0.270540i	0.558777	−	0.829318i	$-0.311271\pi$
$317$	−85.7613	−	85.7613i	−0.270540	−	0.270540i	−0.829318	+	0.558777i	$0.811271\pi$
$318$		0			0
$319$		−	9.23667i		−	0.0289551i
$320$	252.491	−	111.481i	0.789035	−	0.348379i
$321$		0			0
$322$	46.3963	+	46.3963i	0.144088	+	0.144088i
$323$	143.620	−	143.620i	0.444643	−	0.444643i
$324$		0			0
$325$	−19.3985	−	419.851i	−0.0596876	−	1.29185i
$326$	344.557			1.05692
$327$		0			0
$328$	−160.047	+	160.047i	−0.487949	+	0.487949i
$329$			82.8906i			0.251947i
$330$		0			0
$331$	118.330			0.357494			0.178747	−	0.983895i	$-0.442796\pi$
$331$	118.330			0.357494			0.178747	+	0.983895i	$0.442796\pi$
$332$	73.5739	+	73.5739i	0.221608	+	0.221608i
$333$		0			0
$334$		−	352.895i		−	1.05657i
$335$	−202.484	+	522.650i	−0.604431	+	1.56015i
$336$		0			0
$337$	64.4724	+	64.4724i	0.191313	+	0.191313i	0.796263	−	0.604950i	$-0.206807\pi$
$337$	64.4724	+	64.4724i	0.191313	+	0.191313i	−0.604950	+	0.796263i	$0.706807\pi$
$338$	−112.840	+	112.840i	−0.333847	+	0.333847i
$339$		0			0
$340$	−224.654	−	87.0352i	−0.660747	−	0.255986i
$341$	126.983			0.372385
$342$		0			0
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	186.242i		−	0.541401i
$345$		0			0
$346$	429.911			1.24252
$347$	−88.5274	−	88.5274i	−0.255122	−	0.255122i	0.567945	−	0.823067i	$-0.307739\pi$
$347$	−88.5274	−	88.5274i	−0.255122	−	0.255122i	−0.823067	+	0.567945i	$0.807739\pi$
$348$		0			0
$349$		−	286.340i		−	0.820458i	−0.911982	−	0.410229i	$-0.865449\pi$
$349$		−	286.340i		−	0.820458i	0.911982	−	0.410229i	$-0.134551\pi$
$350$	68.6383	+	62.5758i	0.196110	+	0.178788i
$351$		0			0
$352$	−139.328	−	139.328i	−0.395819	−	0.395819i
$353$	−99.9512	+	99.9512i	−0.283148	+	0.283148i	−0.834363	−	0.551215i	$-0.814164\pi$
$353$	−99.9512	+	99.9512i	−0.283148	+	0.283148i	0.551215	+	0.834363i	$0.314164\pi$
$354$		0			0
$355$	127.590	+	288.976i	0.359409	+	0.814016i
$356$	−65.9340			−0.185208
$357$		0			0
$358$	241.932	−	241.932i	0.675788	−	0.675788i
$359$			166.393i			0.463491i	0.972776	+	0.231745i	$0.0744437\pi$
$359$			166.393i			0.463491i	−0.972776	+	0.231745i	$0.925556\pi$
$360$		0			0
$361$	287.915			0.797549
$362$	−253.369	−	253.369i	−0.699913	−	0.699913i
$363$		0			0
$364$			90.2116i			0.247834i
$365$	613.078	+	237.518i	1.67967	+	0.650734i
$366$		0			0
$367$	−185.150	−	185.150i	−0.504495	−	0.504495i	0.408336	−	0.912832i	$-0.366109\pi$
$367$	−185.150	−	185.150i	−0.504495	−	0.504495i	−0.912832	+	0.408336i	$0.866109\pi$
$368$	−47.1325	+	47.1325i	−0.128078	+	0.128078i
$369$		0			0
$370$	285.223	−	125.933i	0.770873	−	0.340360i
$371$	−248.710			−0.670379
$372$		0			0
$373$	302.569	−	302.569i	0.811176	−	0.811176i	−0.173634	−	0.984810i	$-0.555551\pi$
$373$	302.569	−	302.569i	0.811176	−	0.811176i	0.984810	+	0.173634i	$0.0555511\pi$
$374$		−	230.174i		−	0.615437i
$375$		0			0
$376$	−265.203			−0.705327
$377$	−15.9155	−	15.9155i	−0.0422161	−	0.0422161i
$378$		0			0
$379$			651.952i			1.72019i	0.510134	+	0.860095i	$0.329596\pi$
$379$			651.952i			1.72019i	−0.510134	+	0.860095i	$0.670404\pi$
$380$	35.0155	+	79.3056i	0.0921459	+	0.208699i
$381$		0			0
$382$	7.72438	+	7.72438i	0.0202209	+	0.0202209i
$383$	−262.099	+	262.099i	−0.684333	+	0.684333i	−0.960973	−	0.276641i	$-0.910779\pi$
$383$	−262.099	+	262.099i	−0.684333	+	0.684333i	0.276641	+	0.960973i	$0.410779\pi$
$384$		0			0
$385$	32.9711	−	85.1044i	0.0856392	−	0.221050i
$386$	−282.221			−0.731143
$387$		0			0
$388$	−160.709	+	160.709i	−0.414200	+	0.414200i
$389$			143.489i			0.368866i	0.982845	+	0.184433i	$0.0590449\pi$
$389$			143.489i			0.368866i	−0.982845	+	0.184433i	$0.940955\pi$
$390$		0			0
$391$	419.591			1.07312
$392$	−41.8991	−	41.8991i	−0.106886	−	0.106886i
$393$		0			0
$394$			49.7751i			0.126333i
$395$	−38.7156	+	17.0939i	−0.0980141	+	0.0432757i
$396$		0			0
$397$	−96.1908	−	96.1908i	−0.242294	−	0.242294i	0.575504	−	0.817799i	$-0.304806\pi$
$397$	−96.1908	−	96.1908i	−0.242294	−	0.242294i	−0.817799	+	0.575504i	$0.804806\pi$
$398$	83.6776	−	83.6776i	0.210245	−	0.210245i
$399$		0			0
$400$	−63.5687	+	69.7275i	−0.158922	+	0.174319i
$401$	537.127			1.33947			0.669735	−	0.742600i	$-0.266408\pi$
$401$	537.127			1.33947			0.669735	+	0.742600i	$0.266408\pi$
$402$		0			0
$403$	218.802	−	218.802i	0.542933	−	0.542933i
$404$			118.925i			0.294369i
$405$		0			0
$406$	4.97399			0.0122512
$407$	−216.637	−	216.637i	−0.532279	−	0.532279i
$408$		0			0
$409$		−	63.6521i		−	0.155629i	−0.996968	−	0.0778144i	$-0.975206\pi$
$409$		−	63.6521i		−	0.155629i	0.996968	−	0.0778144i	$-0.0247941\pi$
$410$	67.8211	−	175.059i	0.165417	−	0.426973i
$411$		0			0
$412$	200.795	+	200.795i	0.487366	+	0.487366i
$413$	153.182	−	153.182i	0.370900	−	0.370900i
$414$		0			0
$415$	−239.193	−	92.6677i	−0.576368	−	0.223296i
$416$	−480.145			−1.15420
$417$		0			0
$418$	−58.5649	+	58.5649i	−0.140107	+	0.140107i
$419$			259.412i			0.619123i	0.950879	+	0.309561i	$0.100182\pi$
$419$			259.412i			0.619123i	−0.950879	+	0.309561i	$0.899818\pi$
$420$		0			0
$421$	−691.062			−1.64148			−0.820739	−	0.571303i	$-0.806438\pi$
$421$	−691.062			−1.64148			−0.820739	+	0.571303i	$0.806438\pi$
$422$	−362.980	−	362.980i	−0.860143	−	0.860143i
$423$		0			0
$424$		−	795.732i		−	1.87673i
$425$	593.325	−	27.4135i	1.39606	−	0.0645024i
$426$		0			0
$427$	−172.249	−	172.249i	−0.403394	−	0.403394i
$428$	−2.12167	+	2.12167i	−0.00495717	+	0.00495717i
$429$		0			0
$430$	62.3946	+	141.316i	0.145104	+	0.328642i
$431$	−22.7256			−0.0527277			−0.0263639	−	0.999652i	$-0.508393\pi$
$431$	−22.7256			−0.0527277			−0.0263639	+	0.999652i	$0.508393\pi$
$432$		0			0
$433$	120.702	−	120.702i	0.278757	−	0.278757i	−0.553856	−	0.832612i	$-0.686844\pi$
$433$	120.702	−	120.702i	0.278757	−	0.278757i	0.832612	+	0.553856i	$0.186844\pi$
$434$			68.3811i			0.157560i
$435$		0			0
$436$	−319.126			−0.731941
$437$	−106.760	−	106.760i	−0.244302	−	0.244302i
$438$		0			0
$439$		−	330.633i		−	0.753151i	−0.926386	−	0.376576i	$-0.877101\pi$
$439$		−	330.633i		−	0.753151i	0.926386	−	0.376576i	$-0.122899\pi$
$440$	272.286	+	105.489i	0.618831	+	0.239747i
$441$		0			0
$442$	−396.606	−	396.606i	−0.897298	−	0.897298i
$443$	13.7007	−	13.7007i	0.0309271	−	0.0309271i	−0.691474	−	0.722401i	$-0.743038\pi$
$443$	13.7007	−	13.7007i	0.0309271	−	0.0309271i	0.722401	+	0.691474i	$0.243038\pi$
$444$		0			0
$445$	148.700	−	65.6548i	0.334157	−	0.147539i
$446$	514.007			1.15248
$447$		0			0
$448$	103.272	−	103.272i	0.230519	−	0.230519i
$449$			205.185i			0.456982i	0.973546	+	0.228491i	$0.0733792\pi$
$449$			205.185i			0.456982i	−0.973546	+	0.228491i	$0.926621\pi$
$450$		0			0
$451$	−184.476			−0.409038
$452$	−259.117	−	259.117i	−0.573267	−	0.573267i
$453$		0			0
$454$			214.288i			0.472000i
$455$	−89.8296	−	203.453i	−0.197428	−	0.447149i
$456$		0			0
$457$	354.569	+	354.569i	0.775863	+	0.775863i	0.979124	−	0.203262i	$-0.0651542\pi$
$457$	354.569	+	354.569i	0.775863	+	0.775863i	−0.203262	+	0.979124i	$0.565154\pi$
$458$	252.009	−	252.009i	0.550237	−	0.550237i
$459$		0			0
$460$	−64.6977	+	166.997i	−0.140647	+	0.363037i
$461$	−15.0039			−0.0325465			−0.0162733	−	0.999868i	$-0.505180\pi$
$461$	−15.0039			−0.0325465			−0.0162733	+	0.999868i	$0.505180\pi$
$462$		0			0
$463$	−281.077	+	281.077i	−0.607078	+	0.607078i	−0.942181	−	0.335103i	$-0.891229\pi$
$463$	−281.077	+	281.077i	−0.607078	+	0.607078i	0.335103	+	0.942181i	$0.391229\pi$
$464$			5.05291i			0.0108899i
$465$		0			0
$466$	−481.095			−1.03239
$467$	336.527	+	336.527i	0.720616	+	0.720616i	0.968731	−	0.248115i	$-0.0798111\pi$
$467$	336.527	+	336.527i	0.720616	+	0.720616i	−0.248115	+	0.968731i	$0.579811\pi$
$468$		0			0
$469$			296.590i			0.632388i
$470$	201.230	−	88.8481i	0.428148	−	0.189038i
$471$		0			0
$472$	490.094	+	490.094i	1.03834	+	1.03834i
$473$	107.335	−	107.335i	0.226923	−	0.226923i
$474$		0			0
$475$	−157.940	−	143.990i	−0.332504	−	0.303136i
$476$	−127.485			−0.267826
$477$		0			0
$478$	−64.9814	+	64.9814i	−0.135944	+	0.135944i
$479$			778.915i			1.62613i	0.582175	+	0.813063i	$0.302202\pi$
$479$			778.915i			1.62613i	−0.582175	+	0.813063i	$0.697798\pi$
$480$		0			0
$481$	−746.564			−1.55211
$482$	−72.3086	−	72.3086i	−0.150018	−	0.150018i
$483$		0			0
$484$			148.866i			0.307575i
$485$	202.417	−	522.475i	0.417354	−	1.07727i
$486$		0			0
$487$	644.143	+	644.143i	1.32268	+	1.32268i	0.911602	+	0.411074i	$0.134846\pi$
$487$	644.143	+	644.143i	1.32268	+	1.32268i	0.411074	+	0.911602i	$0.365154\pi$
$488$	551.100	−	551.100i	1.12930	−	1.12930i
$489$		0			0
$490$	45.8291	+	17.7551i	0.0935287	+	0.0362348i
$491$	−582.633			−1.18662			−0.593312	−	0.804972i	$-0.702180\pi$
$491$	−582.633			−1.18662			−0.593312	+	0.804972i	$0.702180\pi$
$492$		0			0
$493$	22.4914	−	22.4914i	0.0456215	−	0.0456215i
$494$			201.823i			0.408549i
$495$		0			0
$496$	−69.4662			−0.140053
$497$	118.195	+	118.195i	0.237817	+	0.237817i
$498$		0			0
$499$			656.490i			1.31561i	0.753188	+	0.657806i	$0.228515\pi$
$499$			656.490i			1.31561i	−0.753188	+	0.657806i	$0.771485\pi$
$500$	−80.5757	+	240.370i	−0.161151	+	0.480740i
$501$		0			0
$502$	76.6058	+	76.6058i	0.152601	+	0.152601i
$503$	−72.1236	+	72.1236i	−0.143387	+	0.143387i	−0.775156	−	0.631769i	$-0.782329\pi$
$503$	−72.1236	+	72.1236i	−0.143387	+	0.143387i	0.631769	+	0.775156i	$0.282329\pi$
$504$		0			0
$505$	−118.422	−	268.210i	−0.234498	−	0.531109i
$506$	−171.100			−0.338142
$507$		0			0
$508$	−31.1455	+	31.1455i	−0.0613100	+	0.0613100i
$509$		−	143.879i		−	0.282670i	−0.989962	−	0.141335i	$-0.954860\pi$
$509$		−	143.879i		−	0.282670i	0.989962	−	0.141335i	$-0.0451395\pi$
$510$		0			0
$511$	347.905			0.680832
$512$	166.583	+	166.583i	0.325357	+	0.325357i
$513$		0			0
$514$			638.495i			1.24221i
$515$	−652.794	−	252.905i	−1.26756	−	0.491078i
$516$		0			0
$517$	−152.841	−	152.841i	−0.295631	−	0.295631i
$518$	116.660	−	116.660i	0.225213	−	0.225213i
$519$		0			0
$520$	650.933	−	287.404i	1.25179	−	0.552699i
$521$	−731.203			−1.40346			−0.701730	−	0.712443i	$-0.747589\pi$
$521$	−731.203			−1.40346			−0.701730	+	0.712443i	$0.747589\pi$
$522$		0			0
$523$	−351.808	+	351.808i	−0.672674	+	0.672674i	−0.958332	−	0.285658i	$-0.907788\pi$
$523$	−351.808	+	351.808i	−0.672674	+	0.672674i	0.285658	+	0.958332i	$0.407788\pi$
$524$		−	358.326i		−	0.683827i
$525$		0			0
$526$	104.358			0.198399
$527$	309.206	+	309.206i	0.586729	+	0.586729i
$528$		0			0
$529$			217.097i			0.410391i
$530$	266.586	+	603.783i	0.502992	+	1.13921i
$531$		0			0
$532$	32.4371	+	32.4371i	0.0609720	+	0.0609720i
$533$	−317.866	+	317.866i	−0.596372	+	0.596372i
$534$		0			0
$535$	2.67228	−	6.89766i	0.00499492	−	0.0128928i
$536$	−948.919			−1.77037
$537$		0			0
$538$	−25.4737	+	25.4737i	−0.0473490	+	0.0473490i
$539$		−	48.2945i		−	0.0896002i
$540$		0			0
$541$	562.933			1.04054			0.520271	−	0.854001i	$-0.325831\pi$
$541$	562.933			1.04054			0.520271	+	0.854001i	$0.325831\pi$
$542$	61.8472	+	61.8472i	0.114109	+	0.114109i
$543$		0			0
$544$		−	678.532i		−	1.24730i
$545$	719.721	−	317.775i	1.32059	−	0.583074i
$546$		0			0
$547$	−300.932	−	300.932i	−0.550149	−	0.550149i	0.376334	−	0.926484i	$-0.377184\pi$
$547$	−300.932	−	300.932i	−0.550149	−	0.550149i	−0.926484	+	0.376334i	$0.877184\pi$
$548$	36.5673	−	36.5673i	0.0667287	−	0.0667287i
$549$		0			0
$550$	−241.945	+	11.1786i	−0.439900	+	0.0203248i
$551$	−11.4453			−0.0207720
$552$		0			0
$553$	−15.8352	+	15.8352i	−0.0286351	+	0.0286351i
$554$		−	100.413i		−	0.181251i
$555$		0			0
$556$	−321.286			−0.577852
$557$	134.801	+	134.801i	0.242013	+	0.242013i	0.817682	−	0.575670i	$-0.195259\pi$
$557$	134.801	+	134.801i	0.242013	+	0.242013i	−0.575670	+	0.817682i	$0.695259\pi$
$558$		0			0
$559$		−	369.891i		−	0.661702i
$560$	−18.0368	+	46.5563i	−0.0322086	+	0.0831362i
$561$		0			0
$562$	−29.9586	−	29.9586i	−0.0533070	−	0.0533070i
$563$	202.903	−	202.903i	0.360395	−	0.360395i	−0.503563	−	0.863958i	$-0.667978\pi$
$563$	202.903	−	202.903i	0.360395	−	0.360395i	0.863958	+	0.503563i	$0.167978\pi$
$564$		0			0
$565$	842.401	+	326.362i	1.49097	+	0.577632i
$566$	−35.0840			−0.0619859
$567$		0			0
$568$	−378.157	+	378.157i	−0.665769	+	0.665769i
$569$			924.085i			1.62405i	0.583622	+	0.812025i	$0.301635\pi$
$569$			924.085i			1.62405i	−0.583622	+	0.812025i	$0.698365\pi$
$570$		0			0
$571$	303.388			0.531328			0.265664	−	0.964066i	$-0.414409\pi$
$571$	303.388			0.531328			0.265664	+	0.964066i	$0.414409\pi$
$572$	−166.340	−	166.340i	−0.290805	−	0.290805i
$573$		0			0
$574$		−	99.3413i		−	0.173068i
$575$	−20.3779	−	441.049i	−0.0354398	−	0.767042i
$576$		0			0
$577$	−143.967	−	143.967i	−0.249510	−	0.249510i	0.571259	−	0.820770i	$-0.306455\pi$
$577$	−143.967	−	143.967i	−0.249510	−	0.249510i	−0.820770	+	0.571259i	$0.806455\pi$
$578$	273.515	−	273.515i	0.473209	−	0.473209i
$579$		0			0
$580$	5.48356	+	12.4196i	0.00945441	+	0.0214131i
$581$	−135.735			−0.233624
$582$		0			0
$583$	458.596	−	458.596i	0.786613	−	0.786613i
$584$			1113.10i			1.90599i
$585$		0			0
$586$	115.940			0.197850
$587$	−19.0650	−	19.0650i	−0.0324788	−	0.0324788i	0.690681	−	0.723160i	$-0.257311\pi$
$587$	−19.0650	−	19.0650i	−0.0324788	−	0.0324788i	−0.723160	+	0.690681i	$0.757311\pi$
$588$		0			0
$589$		−	157.348i		−	0.267144i
$590$	−536.063	−	207.681i	−0.908581	−	0.352002i
$591$		0			0
$592$	118.511	+	118.511i	0.200188	+	0.200188i
$593$	−355.233	+	355.233i	−0.599044	+	0.599044i	−0.940058	−	0.341014i	$-0.889230\pi$
$593$	−355.233	+	355.233i	−0.599044	+	0.599044i	0.341014	+	0.940058i	$0.389230\pi$
$594$		0			0
$595$	287.515	−	126.945i	0.483219	−	0.213354i
$596$	284.110			0.476695
$597$		0			0
$598$	−294.817	+	294.817i	−0.493006	+	0.493006i
$599$			869.938i			1.45232i	0.687527	+	0.726159i	$0.258696\pi$
$599$			869.938i			1.45232i	−0.687527	+	0.726159i	$0.741304\pi$
$600$		0			0
$601$	136.014			0.226312			0.113156	−	0.993577i	$-0.463904\pi$
$601$	136.014			0.226312			0.113156	+	0.993577i	$0.463904\pi$
$602$	57.8002	+	57.8002i	0.0960136	+	0.0960136i
$603$		0			0
$604$			436.430i			0.722567i
$605$	−148.236	−	335.735i	−0.245018	−	0.554934i
$606$		0			0
$607$	−530.632	−	530.632i	−0.874189	−	0.874189i	0.118737	−	0.992926i	$-0.462115\pi$
$607$	−530.632	−	530.632i	−0.874189	−	0.874189i	−0.992926	+	0.118737i	$0.962115\pi$
$608$	−172.644	+	172.644i	−0.283954	+	0.283954i
$609$		0			0
$610$	−233.532	+	602.790i	−0.382840	+	0.988181i
$611$	−526.714			−0.862052
$612$		0			0
$613$	−600.328	+	600.328i	−0.979328	+	0.979328i	−0.999791	−	0.0204626i	$-0.993486\pi$
$613$	−600.328	+	600.328i	−0.979328	+	0.979328i	0.0204626	+	0.999791i	$0.493486\pi$
$614$		−	294.931i		−	0.480343i
$615$		0			0
$616$	154.515			0.250836
$617$	−549.965	−	549.965i	−0.891354	−	0.891354i	0.103297	−	0.994651i	$-0.467061\pi$
$617$	−549.965	−	549.965i	−0.891354	−	0.891354i	−0.994651	+	0.103297i	$0.967061\pi$
$618$		0			0
$619$		−	63.1436i		−	0.102009i	−0.998698	−	0.0510046i	$-0.983758\pi$
$619$		−	63.1436i		−	0.102009i	0.998698	−	0.0510046i	$-0.0162423\pi$
$620$	−170.741	+	75.3866i	−0.275389	+	0.121591i
$621$		0			0
$622$	−199.351	−	199.351i	−0.320500	−	0.320500i
$623$	60.8203	−	60.8203i	0.0976249	−	0.0976249i
$624$		0			0
$625$	−57.6310	−	622.337i	−0.0922096	−	0.995740i
$626$	−572.174			−0.914015
$627$		0			0
$628$	100.766	−	100.766i	0.160456	−	0.160456i
$629$		−	1055.03i		−	1.67731i
$630$		0			0
$631$	−463.289			−0.734213			−0.367107	−	0.930179i	$-0.619652\pi$
$631$	−463.289			−0.734213			−0.367107	+	0.930179i	$0.619652\pi$
$632$	−50.6636	−	50.6636i	−0.0801640	−	0.0801640i
$633$		0			0
$634$			170.312i			0.268631i
$635$	39.2283	−	101.256i	0.0617769	−	0.159458i
$636$		0			0
$637$	−83.2150	−	83.2150i	−0.130636	−	0.130636i
$638$	−9.17150	+	9.17150i	−0.0143754	+	0.0143754i
$639$		0			0
$640$	171.216	+	66.3323i	0.267525	+	0.103644i
$641$	741.985			1.15754			0.578772	−	0.815490i	$-0.303532\pi$
$641$	741.985			1.15754			0.578772	+	0.815490i	$0.303532\pi$
$642$		0			0
$643$	−230.657	+	230.657i	−0.358720	+	0.358720i	−0.863341	−	0.504621i	$-0.831632\pi$
$643$	−230.657	+	230.657i	−0.358720	+	0.358720i	0.504621	+	0.863341i	$0.331632\pi$
$644$			94.7663i			0.147153i
$645$		0			0
$646$	−285.213			−0.441506
$647$	763.503	+	763.503i	1.18007	+	1.18007i	0.979726	+	0.200341i	$0.0642049\pi$
$647$	763.503	+	763.503i	1.18007	+	1.18007i	0.200341	+	0.979726i	$0.435795\pi$
$648$		0			0
$649$			564.901i			0.870418i
$650$	−397.627	+	436.150i	−0.611734	+	0.671000i
$651$		0			0
$652$	351.885	+	351.885i	0.539701	+	0.539701i
$653$	−381.398	+	381.398i	−0.584070	+	0.584070i	−0.936019	−	0.351949i	$-0.885519\pi$
$653$	−381.398	+	381.398i	−0.584070	+	0.584070i	0.351949	+	0.936019i	$0.385519\pi$
$654$		0			0
$655$	356.808	+	808.126i	0.544745	+	1.23378i
$656$	100.918			0.153838
$657$		0			0
$658$	82.3057	−	82.3057i	0.125085	−	0.125085i
$659$			608.628i			0.923563i	0.886994	+	0.461781i	$0.152790\pi$
$659$			608.628i			0.923563i	−0.886994	+	0.461781i	$0.847210\pi$
$660$		0			0
$661$	108.770			0.164554			0.0822770	−	0.996609i	$-0.473781\pi$
$661$	108.770			0.164554			0.0822770	+	0.996609i	$0.473781\pi$
$662$	−117.495	−	117.495i	−0.177486	−	0.177486i
$663$		0			0
$664$		−	434.276i		−	0.654031i
$665$	−105.455	−	40.8551i	−0.158578	−	0.0614363i
$666$		0			0
$667$	−16.7190	−	16.7190i	−0.0250660	−	0.0250660i
$668$	360.400	−	360.400i	0.539521	−	0.539521i
$669$		0			0
$670$	720.017	−	317.906i	1.07465	−	0.474487i
$671$	635.218			0.946674
$672$		0			0
$673$	−717.128	+	717.128i	−1.06557	+	1.06557i	−0.0678751	+	0.997694i	$0.521622\pi$
$673$	−717.128	+	717.128i	−1.06557	+	1.06557i	−0.997694	+	0.0678751i	$0.978378\pi$
$674$		−	128.035i		−	0.189963i
$675$		0			0
$676$	−230.481			−0.340948
$677$	120.083	+	120.083i	0.177376	+	0.177376i	0.790211	−	0.612835i	$-0.209971\pi$
$677$	120.083	+	120.083i	0.177376	+	0.177376i	−0.612835	+	0.790211i	$0.709971\pi$
$678$		0			0
$679$		−	296.490i		−	0.436658i
$680$	406.153	+	919.886i	0.597284	+	1.35277i
$681$		0			0
$682$	−126.087	−	126.087i	−0.184879	−	0.184879i
$683$	382.924	−	382.924i	0.560651	−	0.560651i	−0.368842	−	0.929492i	$-0.620245\pi$
$683$	382.924	−	382.924i	0.560651	−	0.560651i	0.929492	+	0.368842i	$0.120245\pi$
$684$		0			0
$685$	−46.0572	+	118.882i	−0.0672369	+	0.173551i
$686$	26.0068			0.0379108
$687$		0			0
$688$	−58.7173	+	58.7173i	−0.0853450	+	0.0853450i
$689$		−	1580.39i		−	2.29374i
$690$		0			0
$691$	1016.89			1.47162			0.735809	−	0.677190i	$-0.236802\pi$
$691$	1016.89			1.47162			0.735809	+	0.677190i	$0.236802\pi$
$692$	439.055	+	439.055i	0.634473	+	0.634473i
$693$		0			0
$694$			175.806i			0.253322i
$695$	724.591	−	319.925i	1.04258	−	0.460324i
$696$		0			0
$697$	−449.202	−	449.202i	−0.644480	−	0.644480i
$698$	−284.319	+	284.319i	−0.407335	+	0.407335i
$699$		0			0
$700$	6.19146	+	134.005i	0.00884494	+	0.191436i
$701$	603.636			0.861106			0.430553	−	0.902565i	$-0.358318\pi$
$701$	603.636			0.861106			0.430553	+	0.902565i	$0.358318\pi$
$702$		0			0
$703$	−268.440	+	268.440i	−0.381849	+	0.381849i
$704$			380.846i			0.540975i
$705$		0			0
$706$	198.492			0.281150
$707$	−109.702	−	109.702i	−0.155165	−	0.155165i
$708$		0			0
$709$		−	137.621i		−	0.194106i	−0.995279	−	0.0970528i	$-0.969058\pi$
$709$		−	137.621i		−	0.194106i	0.995279	−	0.0970528i	$-0.0309416\pi$
$710$	160.247	−	413.626i	0.225700	−	0.582572i
$711$		0			0
$712$	194.591	+	194.591i	0.273301	+	0.273301i
$713$	229.849	−	229.849i	0.322369	−	0.322369i
$714$		0			0
$715$	540.781	+	209.509i	0.756337	+	0.293019i
$716$	494.155			0.690161
$717$		0			0
$718$	165.219	−	165.219i	0.230110	−	0.230110i
$719$			171.289i			0.238233i	0.992880	+	0.119116i	$0.0380062\pi$
$719$			171.289i			0.238233i	−0.992880	+	0.119116i	$0.961994\pi$
$720$		0			0
$721$	−370.443			−0.513791
$722$	−285.884	−	285.884i	−0.395961	−	0.395961i
$723$		0			0
$724$		−	517.515i		−	0.714799i
$725$	−24.7340	−	22.5493i	−0.0341158	−	0.0311025i
$726$		0			0
$727$	277.598	+	277.598i	0.381840	+	0.381840i	0.871765	−	0.489925i	$-0.162976\pi$
$727$	277.598	+	277.598i	0.381840	+	0.381840i	−0.489925	+	0.871765i	$0.662976\pi$
$728$	266.241	−	266.241i	0.365715	−	0.365715i
$729$		0			0
$730$	−372.910	−	844.594i	−0.510835	−	1.15698i
$731$	522.723			0.715079
$732$		0			0
$733$	41.4717	−	41.4717i	0.0565780	−	0.0565780i	−0.678252	−	0.734830i	$-0.737262\pi$
$733$	41.4717	−	41.4717i	0.0565780	−	0.0565780i	0.734830	+	0.678252i	$0.237262\pi$
$734$			367.687i			0.500936i
$735$		0			0
$736$	−504.387			−0.685309
$737$	−546.880	−	546.880i	−0.742035	−	0.742035i
$738$		0			0
$739$			991.780i			1.34206i	0.741432	+	0.671028i	$0.234147\pi$
$739$			991.780i			1.34206i	−0.741432	+	0.671028i	$0.765853\pi$
$740$	419.901	+	162.678i	0.567434	+	0.219835i
$741$		0			0
$742$	246.956	+	246.956i	0.332824	+	0.332824i
$743$	−569.850	+	569.850i	−0.766958	+	0.766958i	−0.977570	−	0.210611i	$-0.932455\pi$
$743$	−569.850	+	569.850i	−0.766958	+	0.766958i	0.210611	+	0.977570i	$0.432455\pi$
$744$		0			0
$745$	−640.750	+	282.907i	−0.860067	+	0.379741i
$746$	−600.867			−0.805452
$747$		0			0
$748$	235.069	−	235.069i	0.314263	−	0.314263i
$749$		−	3.91424i		−	0.00522595i
$750$		0			0
$751$	−774.252			−1.03096			−0.515480	−	0.856901i	$-0.672387\pi$
$751$	−774.252			−1.03096			−0.515480	+	0.856901i	$0.672387\pi$
$752$	83.6117	+	83.6117i	0.111186	+	0.111186i
$753$		0			0
$754$			31.6063i			0.0419182i
$755$	−434.582	−	984.274i	−0.575606	−	1.30367i
$756$		0			0
$757$	−404.173	−	404.173i	−0.533914	−	0.533914i	0.387821	−	0.921735i	$-0.373228\pi$
$757$	−404.173	−	404.173i	−0.533914	−	0.533914i	−0.921735	+	0.387821i	$0.873228\pi$
$758$	647.352	−	647.352i	0.854026	−	0.854026i
$759$		0			0
$760$	130.713	−	337.395i	0.171991	−	0.443941i
$761$	−287.708			−0.378065			−0.189033	−	0.981971i	$-0.560535\pi$
$761$	−287.708			−0.378065			−0.189033	+	0.981971i	$0.560535\pi$
$762$		0			0
$763$	294.376	−	294.376i	0.385814	−	0.385814i
$764$			15.7773i			0.0206510i
$765$		0			0
$766$	520.500			0.679504
$767$	973.366	+	973.366i	1.26906	+	1.26906i
$768$		0			0
$769$		−	1001.09i		−	1.30181i	−0.759160	−	0.650905i	$-0.774390\pi$
$769$		−	1001.09i		−	1.30181i	0.759160	−	0.650905i	$-0.225610\pi$
$770$	−117.242	+	51.7655i	−0.152263	+	0.0672279i
$771$		0			0
$772$	−288.224	−	288.224i	−0.373347	−	0.373347i
$773$	221.889	−	221.889i	0.287049	−	0.287049i	−0.548863	−	0.835912i	$-0.684939\pi$
$773$	221.889	−	221.889i	0.287049	−	0.287049i	0.835912	+	0.548863i	$0.184939\pi$
$774$		0			0
$775$	310.003	−	340.036i	0.400003	−	0.438757i
$776$	948.601			1.22242
$777$		0			0
$778$	142.476	−	142.476i	0.183132	−	0.183132i
$779$			228.588i			0.293438i
$780$		0			0
$781$	−435.878			−0.558102
$782$	−416.630	−	416.630i	−0.532775	−	0.532775i
$783$		0			0
$784$			26.4195i			0.0336983i
$785$	−126.917	+	327.596i	−0.161678	+	0.417320i
$786$		0			0
$787$	−129.494	−	129.494i	−0.164541	−	0.164541i	0.620034	−	0.784575i	$-0.287119\pi$
$787$	−129.494	−	129.494i	−0.164541	−	0.164541i	−0.784575	+	0.620034i	$0.787119\pi$
$788$	−50.8337	+	50.8337i	−0.0645098	+	0.0645098i
$789$		0			0
$790$	55.4157	+	21.4691i	0.0701464	+	0.0271761i
$791$	478.040			0.604349
$792$		0			0
$793$	1094.53	−	1094.53i	1.38024	−	1.38024i
$794$			191.024i			0.240585i
$795$		0			0
$796$	170.915			0.214717
$797$	−824.725	−	824.725i	−1.03479	−	1.03479i	−0.999373	−	0.0354133i	$-0.988725\pi$
$797$	−824.725	−	824.725i	−1.03479	−	1.03479i	−0.0354133	−	0.999373i	$-0.511275\pi$
$798$		0			0
$799$		−	744.342i		−	0.931592i
$800$	−713.232	+	32.9536i	−0.891541	+	0.0411920i
$801$		0			0
$802$	−533.337	−	533.337i	−0.665009	−	0.665009i
$803$	−641.500	+	641.500i	−0.798880	+	0.798880i
$804$		0			0
$805$	−94.3650	−	213.725i	−0.117224	−	0.265497i
$806$	−434.516			−0.539102
$807$		0			0
$808$	350.983	−	350.983i	0.434385	−	0.434385i
$809$			825.281i			1.02013i	0.860137	+	0.510063i	$0.170378\pi$
$809$			825.281i			1.02013i	−0.860137	+	0.510063i	$0.829622\pi$
$810$		0			0
$811$	1313.83			1.62001			0.810007	−	0.586420i	$-0.199463\pi$
$811$	1313.83			1.62001			0.810007	+	0.586420i	$0.199463\pi$
$812$	5.07978	+	5.07978i	0.00625588	+	0.00625588i
$813$		0			0
$814$			430.217i			0.528523i
$815$	−1144.00	−	443.206i	−1.40368	−	0.543811i
$816$		0			0
$817$	−133.001	−	133.001i	−0.162791	−	0.162791i
$818$	−63.2030	+	63.2030i	−0.0772653	+	0.0772653i
$819$		0			0
$820$	248.046	−	109.519i	0.302495	−	0.133559i
$821$	−438.385			−0.533965			−0.266982	−	0.963701i	$-0.586027\pi$
$821$	−438.385			−0.533965			−0.266982	+	0.963701i	$0.586027\pi$
$822$		0			0
$823$	305.479	−	305.479i	0.371178	−	0.371178i	−0.496728	−	0.867906i	$-0.665465\pi$
$823$	305.479	−	305.479i	0.371178	−	0.371178i	0.867906	+	0.496728i	$0.165465\pi$
$824$		−	1185.21i		−	1.43836i
$825$		0			0
$826$	−304.202			−0.368283
$827$	−993.549	−	993.549i	−1.20139	−	1.20139i	−0.973744	−	0.227645i	$-0.926898\pi$
$827$	−993.549	−	993.549i	−1.20139	−	1.20139i	−0.227645	−	0.973744i	$-0.573102\pi$
$828$		0			0
$829$		−	12.6418i		−	0.0152494i	−0.999971	−	0.00762471i	$-0.997573\pi$
$829$		−	12.6418i		−	0.0152494i	0.999971	−	0.00762471i	$-0.00242705\pi$
$830$	145.491	+	329.519i	0.175290	+	0.397010i
$831$		0			0
$832$	656.226	+	656.226i	0.788733	+	0.788733i
$833$	117.598	−	117.598i	0.141174	−	0.141174i
$834$		0			0
$835$	−453.931	+	1171.68i	−0.543630	+	1.40321i
$836$	−119.621			−0.143087
$837$		0			0
$838$	257.582	−	257.582i	0.307377	−	0.307377i
$839$		−	462.179i		−	0.550869i	−0.961320	−	0.275434i	$-0.911178\pi$
$839$		−	462.179i		−	0.550869i	0.961320	−	0.275434i	$-0.0888217\pi$
$840$		0			0
$841$	839.208			0.997869
$842$	686.186	+	686.186i	0.814948	+	0.814948i
$843$		0			0
$844$		−	741.401i		−	0.878437i
$845$	519.799	−	229.505i	0.615147	−	0.271603i
$846$		0			0
$847$	−137.320	−	137.320i	−0.162126	−	0.162126i
$848$	−250.874	+	250.874i	−0.295842	+	0.295842i
$849$		0			0
$850$	−616.359	−	561.919i	−0.725128	−	0.661081i
$851$	−784.257			−0.921572
$852$		0			0
$853$	866.028	−	866.028i	1.01527	−	1.01527i	0.0153912	−	0.999882i	$-0.495101\pi$
$853$	866.028	−	866.028i	1.01527	−	1.01527i	0.999882	−	0.0153912i	$-0.00489936\pi$
$854$			342.068i			0.400548i
$855$		0			0
$856$	12.5233			0.0146301
$857$	−796.378	−	796.378i	−0.929262	−	0.929262i	0.0683962	−	0.997658i	$-0.478212\pi$
$857$	−796.378	−	796.378i	−0.929262	−	0.929262i	−0.997658	+	0.0683962i	$0.978212\pi$
$858$		0			0
$859$		−	262.615i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$859$		−	262.615i		−	0.305721i	0.988248	−	0.152861i	$-0.0488486\pi$
$860$	−80.5999	+	208.043i	−0.0937209	+	0.241911i
$861$		0			0
$862$	22.5653	+	22.5653i	0.0261778	+	0.0261778i
$863$	957.363	−	957.363i	1.10934	−	1.10934i	0.116106	−	0.993237i	$-0.462959\pi$
$863$	957.363	−	957.363i	1.10934	−	1.10934i	0.993237	−	0.116106i	$-0.0370413\pi$
$864$		0			0
$865$	−1427.39	−	552.998i	−1.65016	−	0.639304i
$866$	−239.700			−0.276790
$867$		0			0
$868$	−69.8355	+	69.8355i	−0.0804556	+	0.0804556i
$869$		−	58.3968i		−	0.0672000i
$870$		0			0
$871$	−1884.63			−2.16375
$872$	941.835	+	941.835i	1.08009	+	1.08009i
$873$		0			0
$874$			212.013i			0.242578i
$875$	−147.401	−	296.054i	−0.168458	−	0.338347i
$876$		0			0
$877$	415.953	+	415.953i	0.474290	+	0.474290i	0.903300	−	0.429010i	$-0.141137\pi$
$877$	415.953	+	415.953i	0.474290	+	0.474290i	−0.429010	+	0.903300i	$0.641137\pi$
$878$	−328.300	+	328.300i	−0.373919	+	0.373919i
$879$		0			0
$880$	−52.5869	−	119.103i	−0.0597578	−	0.135344i
$881$	−295.584			−0.335509			−0.167755	−	0.985829i	$-0.553652\pi$
$881$	−295.584			−0.335509			−0.167755	+	0.985829i	$0.553652\pi$
$882$		0			0
$883$	−377.332	+	377.332i	−0.427329	+	0.427329i	−0.887718	−	0.460388i	$-0.847710\pi$
$883$	−377.332	+	377.332i	−0.427329	+	0.427329i	0.460388	+	0.887718i	$0.347710\pi$
$884$		−	810.082i		−	0.916383i
$885$		0			0
$886$	−27.2081			−0.0307089
$887$	−1016.82	−	1016.82i	−1.14635	−	1.14635i	−0.987264	−	0.159089i	$-0.949144\pi$
$887$	−1016.82	−	1016.82i	−1.14635	−	1.14635i	−0.159089	−	0.987264i	$-0.550856\pi$
$888$		0			0
$889$		−	57.4599i		−	0.0646343i
$890$	−212.842	−	82.4591i	−0.239149	−	0.0926507i
$891$		0			0
$892$	524.939	+	524.939i	0.588497	+	0.588497i
$893$	−189.389	+	189.389i	−0.212082	+	0.212082i
$894$		0			0
$895$	−1114.46	+	492.063i	−1.24521	+	0.549791i
$896$	97.1605			0.108438
$897$		0			0
$898$	203.737	−	203.737i	0.226879	−	0.226879i
$899$		−	24.6413i		−	0.0274097i
$900$		0			0
$901$	2233.37			2.47877
$902$	183.175	+	183.175i	0.203076	+	0.203076i
$903$		0			0
$904$			1529.46i			1.69188i
$905$	515.324	+	1167.14i	0.569418	+	1.28966i
$906$		0			0
$907$	−93.8410	−	93.8410i	−0.103463	−	0.103463i	0.653480	−	0.756943i	$-0.273308\pi$
$907$	−93.8410	−	93.8410i	−0.103463	−	0.103463i	−0.756943	+	0.653480i	$0.773308\pi$
$908$	−218.846	+	218.846i	−0.241019	+	0.241019i
$909$		0			0
$910$	−112.821	+	291.213i	−0.123980	+	0.320014i
$911$	481.808			0.528878			0.264439	−	0.964402i	$-0.414813\pi$
$911$	481.808			0.528878			0.264439	+	0.964402i	$0.414813\pi$
$912$		0			0
$913$	250.282	−	250.282i	0.274131	−	0.274131i
$914$		−	704.135i		−	0.770388i
$915$		0			0
$916$	514.737			0.561940
$917$	330.535	+	330.535i	0.360452	+	0.360452i
$918$		0			0
$919$		−	1351.61i		−	1.47074i	−0.677667	−	0.735369i	$-0.737009\pi$
$919$		−	1351.61i		−	1.47074i	0.677667	−	0.735369i	$-0.262991\pi$
$920$	683.798	−	301.914i	0.743259	−	0.328168i
$921$		0			0
$922$	14.8981	+	14.8981i	0.0161584	+	0.0161584i
$923$	−751.049	+	751.049i	−0.813705	+	0.813705i
$924$		0			0
$925$	−1108.98	+	51.2387i	−1.19890	+	0.0553931i
$926$	558.188			0.602795
$927$		0			0
$928$	−27.0368	+	27.0368i	−0.0291345	+	0.0291345i
$929$		−	451.029i		−	0.485500i	−0.970089	−	0.242750i	$-0.921951\pi$
$929$		−	451.029i		−	0.485500i	0.970089	−	0.242750i	$-0.0780494\pi$
$930$		0			0
$931$	−59.8427			−0.0642779
$932$	−491.328	−	491.328i	−0.527176	−	0.527176i
$933$		0			0
$934$		−	668.306i		−	0.715531i
$935$	−296.074	+	764.221i	−0.316657	+	0.817349i
$936$		0			0
$937$	−1022.86	−	1022.86i	−1.09163	−	1.09163i	−0.995355	−	0.0962771i	$-0.969307\pi$
$937$	−1022.86	−	1022.86i	−1.09163	−	1.09163i	−0.0962771	−	0.995355i	$-0.530693\pi$
$938$	294.497	−	294.497i	0.313963	−	0.313963i
$939$		0			0
$940$	296.247	+	114.772i	0.315157	+	0.122098i
$941$	−18.0862			−0.0192202			−0.00961008	−	0.999954i	$-0.503059\pi$
$941$	−18.0862			−0.0192202			−0.00961008	+	0.999954i	$0.503059\pi$
$942$		0			0
$943$	−333.915	+	333.915i	−0.354099	+	0.354099i
$944$		−	309.029i		−	0.327361i
$945$		0			0
$946$	−213.155			−0.225322
$947$	1216.09	+	1216.09i	1.28415	+	1.28415i	0.938283	+	0.345869i	$0.112416\pi$
$947$	1216.09	+	1216.09i	1.28415	+	1.28415i	0.345869	+	0.938283i	$0.387584\pi$
$948$		0			0
$949$			2210.70i			2.32951i
$950$	13.8517	+	299.799i	0.0145807	+	0.315578i
$951$		0			0
$952$	376.246	+	376.246i	0.395216	+	0.395216i
$953$	−465.081	+	465.081i	−0.488017	+	0.488017i	−0.907680	−	0.419663i	$-0.862148\pi$
$953$	−465.081	+	465.081i	−0.488017	+	0.488017i	0.419663	+	0.907680i	$0.362148\pi$
$954$		0			0
$955$	−15.7105	−	35.5824i	−0.0164508	−	0.0372590i
$956$	−132.727			−0.138836
$957$		0			0
$958$	773.419	−	773.419i	0.807326	−	0.807326i
$959$			67.4625i			0.0703467i
$960$		0			0
$961$	−622.238			−0.647490
$962$	741.296	+	741.296i	0.770578	+	0.770578i
$963$		0			0
$964$		−	147.693i		−	0.153208i
$965$	937.030	+	363.023i	0.971016	+	0.376190i
$966$		0			0
$967$	−50.3612	−	50.3612i	−0.0520798	−	0.0520798i	0.680587	−	0.732667i	$-0.261725\pi$
$967$	−50.3612	−	50.3612i	−0.0520798	−	0.0520798i	−0.732667	+	0.680587i	$0.761725\pi$
$968$	439.347	−	439.347i	0.453871	−	0.453871i
$969$		0			0
$970$	−719.776	+	317.800i	−0.742037	+	0.327628i
$971$	1794.36			1.84795			0.923974	−	0.382455i	$-0.124921\pi$
$971$	1794.36			1.84795			0.923974	+	0.382455i	$0.124921\pi$
$972$		0			0
$973$	296.368	−	296.368i	0.304592	−	0.304592i
$974$		−	1279.20i		−	1.31334i
$975$		0			0
$976$	−347.495			−0.356040
$977$	−218.541	−	218.541i	−0.223686	−	0.223686i	0.586363	−	0.810049i	$-0.300559\pi$
$977$	−218.541	−	218.541i	−0.223686	−	0.223686i	−0.810049	+	0.586363i	$0.800559\pi$
$978$		0			0
$979$			224.292i			0.229103i
$980$	28.6711	+	64.9365i	0.0292562	+	0.0662617i
$981$		0			0
$982$	578.522	+	578.522i	0.589126	+	0.589126i
$983$	−157.458	+	157.458i	−0.160181	+	0.160181i	−0.782647	−	0.622466i	$-0.786131\pi$
$983$	−157.458	+	157.458i	−0.160181	+	0.160181i	0.622466	+	0.782647i	$0.286131\pi$
$984$		0			0
$985$	64.0260	−	165.263i	0.0650010	−	0.167780i
$986$	−44.6654			−0.0452996
$987$		0			0
$988$	−206.116	+	206.116i	−0.208619	+	0.208619i
$989$		−	388.567i		−	0.392888i
$990$		0			0
$991$	1611.30			1.62594			0.812968	−	0.582309i	$-0.197850\pi$
$991$	1611.30			1.62594			0.812968	+	0.582309i	$0.197850\pi$
$992$	−371.695	−	371.695i	−0.374692	−	0.374692i
$993$		0			0
$994$		−	234.722i		−	0.236139i
$995$	−385.461	+	170.191i	−0.387398	+	0.171046i
$996$		0			0
$997$	601.501	+	601.501i	0.603311	+	0.603311i	0.941190	−	0.337878i	$-0.109709\pi$
$997$	601.501	+	601.501i	0.603311	+	0.603311i	−0.337878	+	0.941190i	$0.609709\pi$
$998$	651.858	−	651.858i	0.653164	−	0.653164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.127.5		24
3.2	odd	2		105.3.l.a.22.8	✓	24
5.3	odd	4	inner	315.3.o.b.253.5		24
15.2	even	4		525.3.l.e.43.5		24
15.8	even	4		105.3.l.a.43.8	yes	24
15.14	odd	2		525.3.l.e.232.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.8	✓	24	3.2	odd	2
105.3.l.a.43.8	yes	24	15.8	even	4
315.3.o.b.127.5		24	1.1	even	1	trivial
315.3.o.b.253.5		24	5.3	odd	4	inner
525.3.l.e.43.5		24	15.2	even	4
525.3.l.e.232.5		24	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992944 - 0.992944i) q^{2} -2.02813i q^{4} +(2.01954 + 4.57400i) q^{5} +(1.87083 + 1.87083i) q^{7} +(-5.98559 + 5.98559i) q^{8} +O(q^{10})\)	\(q+(-0.992944 - 0.992944i) q^{2} -2.02813i q^{4} +(2.01954 + 4.57400i) q^{5} +(1.87083 + 1.87083i) q^{7} +(-5.98559 + 5.98559i) q^{8} +(2.53644 - 6.54701i) q^{10} -6.89922 q^{11} +(-11.8879 + 11.8879i) q^{13} -3.71526i q^{14} +3.77421 q^{16} +(-16.7997 - 16.7997i) q^{17} +8.54896i q^{19} +(9.27664 - 4.09587i) q^{20} +(6.85053 + 6.85053i) q^{22} +(-12.4881 + 12.4881i) q^{23} +(-16.8429 + 18.4747i) q^{25} +23.6079 q^{26} +(3.79427 - 3.79427i) q^{28} +1.33880i q^{29} -18.4055 q^{31} +(20.1948 + 20.1948i) q^{32} +33.3623i q^{34} +(-4.77896 + 12.3354i) q^{35} +(31.4003 + 31.4003i) q^{37} +(8.48863 - 8.48863i) q^{38} +(-39.4662 - 15.2900i) q^{40} +26.7387 q^{41} +(-15.5575 + 15.5575i) q^{43} +13.9925i q^{44} +24.7999 q^{46} +(22.1535 + 22.1535i) q^{47} +7.00000i q^{49} +(35.0685 - 1.62028i) q^{50} +(24.1101 + 24.1101i) q^{52} +(-66.4707 + 66.4707i) q^{53} +(-13.9332 - 31.5570i) q^{55} -22.3960 q^{56} +(1.32935 - 1.32935i) q^{58} -81.8790i q^{59} -92.0711 q^{61} +(18.2756 + 18.2756i) q^{62} -55.2014i q^{64} +(-78.3830 - 30.3671i) q^{65} +(79.2670 + 79.2670i) q^{67} +(-34.0719 + 34.0719i) q^{68} +(16.9936 - 7.50310i) q^{70} +63.1779 q^{71} +(92.9816 - 92.9816i) q^{73} -62.3574i q^{74} +17.3384 q^{76} +(-12.9072 - 12.9072i) q^{77} +8.46427i q^{79} +(7.62216 + 17.2632i) q^{80} +(-26.5501 - 26.5501i) q^{82} +(-36.2768 + 36.2768i) q^{83} +(42.9141 - 110.769i) q^{85} +30.8955 q^{86} +(41.2959 - 41.2959i) q^{88} -32.5098i q^{89} -44.4803 q^{91} +(25.3273 + 25.3273i) q^{92} -43.9943i q^{94} +(-39.1029 + 17.2649i) q^{95} +(-79.2404 - 79.2404i) q^{97} +(6.95061 - 6.95061i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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