LMFDB - Embedded newform 351.3.u.a.341.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,3,Mod(35,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

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

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

chi := DirichletCharacter("351.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	351.u (of order $6$, 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:	$9.56405727905$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.13
Character	$\chi$	$=$	351.341
Dual form			351.3.u.a.35.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.325651 + 0.188014i) q^{2} +(-1.92930 - 3.34165i) q^{4} +(-0.994641 - 0.574256i) q^{5} +5.14423 q^{7} -2.95506i q^{8} +(-0.215937 - 0.374014i) q^{10} +(13.0534 + 7.53640i) q^{11} +(-7.81749 - 10.3869i) q^{13} +(1.67522 + 0.967190i) q^{14} +(-7.16161 + 12.4043i) q^{16} +(-24.4307 - 14.1051i) q^{17} +(10.6901 - 18.5158i) q^{19} +4.43165i q^{20} +(2.83390 + 4.90847i) q^{22} -14.5409i q^{23} +(-11.8405 - 20.5083i) q^{25} +(-0.592890 - 4.85229i) q^{26} +(-9.92477 - 17.1902i) q^{28} +(-46.7423 - 26.9867i) q^{29} +(20.6940 - 35.8431i) q^{31} +(-14.9010 + 8.60310i) q^{32} +(-5.30391 - 9.18664i) q^{34} +(-5.11666 - 2.95411i) q^{35} +(26.5470 + 45.9807i) q^{37} +(6.96249 - 4.01980i) q^{38} +(-1.69696 + 2.93923i) q^{40} +28.8607i q^{41} +42.0583 q^{43} -58.1599i q^{44} +(2.73390 - 4.73525i) q^{46} +(-3.48340 + 2.01114i) q^{47} -22.5369 q^{49} -8.90471i q^{50} +(-19.6269 + 46.1627i) q^{52} -12.6540i q^{53} +(-8.65564 - 14.9920i) q^{55} -15.2015i q^{56} +(-10.1478 - 17.5765i) q^{58} +(19.0560 - 11.0020i) q^{59} +10.3485 q^{61} +(13.4780 - 7.78155i) q^{62} +50.8229 q^{64} +(1.81087 + 14.8204i) q^{65} +74.0229 q^{67} +108.852i q^{68} +(-1.11083 - 1.92401i) q^{70} +(34.1908 + 19.7401i) q^{71} -65.2913 q^{73} +19.9649i q^{74} -82.4979 q^{76} +(67.1498 + 38.7690i) q^{77} +(-9.78025 - 16.9399i) q^{79} +(14.2465 - 8.22520i) q^{80} +(-5.42622 + 9.39850i) q^{82} +(-71.7112 + 41.4025i) q^{83} +(16.1998 + 28.0589i) q^{85} +(13.6963 + 7.90758i) q^{86} +(22.2705 - 38.5737i) q^{88} +(134.830 - 77.8441i) q^{89} +(-40.2150 - 53.4324i) q^{91} +(-48.5905 + 28.0538i) q^{92} -1.51249 q^{94} +(-21.2657 + 12.2777i) q^{95} +19.4397 q^{97} +(-7.33915 - 4.23726i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} + 49 q^{4} + 6 q^{5} + 2 q^{7} - 6 q^{10} - 33 q^{11} + 4 q^{13} + 6 q^{14} - 83 q^{16} + 5 q^{19} - 15 q^{22} + 88 q^{25} - 132 q^{26} - 22 q^{28} + 30 q^{29} + 14 q^{31} + 63 q^{32} - 6 q^{34}+ \cdots - 405 q^{98}+O(q^{100}) $ 52 * q + 3 * q^2 + 49 * q^4 + 6 * q^5 + 2 * q^7 - 6 * q^10 - 33 * q^11 + 4 * q^13 + 6 * q^14 - 83 * q^16 + 5 * q^19 - 15 * q^22 + 88 * q^25 - 132 * q^26 - 22 * q^28 + 30 * q^29 + 14 * q^31 + 63 * q^32 - 6 * q^34 + 228 * q^35 - 13 * q^37 + 192 * q^38 + 72 * q^40 + 62 * q^43 + 6 * q^46 + 69 * q^47 + 246 * q^49 + 112 * q^52 - 27 * q^55 - 105 * q^58 + 435 * q^59 - 16 * q^61 + 471 * q^62 - 98 * q^64 + 435 * q^65 + 68 * q^67 - 57 * q^70 + 144 * q^71 - 106 * q^73 + 158 * q^76 - 282 * q^77 - 25 * q^79 - 1050 * q^80 + 81 * q^82 - 219 * q^83 + 54 * q^85 + 24 * q^86 - 15 * q^88 + 99 * q^89 + 2 * q^91 - 888 * q^92 - 606 * q^94 + 258 * q^95 - 424 * q^97 - 405 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.325651	+	0.188014i	0.162825	+	0.0940072i	0.579198	−	0.815187i	$-0.303366\pi$
$2$	0.325651	+	0.188014i	0.162825	+	0.0940072i	−0.416373	+	0.909194i	$0.636699\pi$
$3$		0			0
$3$		0			0
$4$	−1.92930	−	3.34165i	−0.482325	−	0.835412i
$5$	−0.994641	−	0.574256i	−0.198928	−	0.114851i	0.397227	−	0.917720i	$-0.369972\pi$
$5$	−0.994641	−	0.574256i	−0.198928	−	0.114851i	−0.596155	+	0.802869i	$0.703306\pi$
$6$		0			0
$7$	5.14423			0.734890			0.367445	−	0.930045i	$-0.380233\pi$
$7$	5.14423			0.734890			0.367445	+	0.930045i	$0.380233\pi$
$8$		−	2.95506i		−	0.369383i
$9$		0			0
$10$	−0.215937	−	0.374014i	−0.0215937	−	0.0374014i
$11$	13.0534	+	7.53640i	1.18667	+	0.685127i	0.957549	−	0.288270i	$-0.0930800\pi$
$11$	13.0534	+	7.53640i	1.18667	+	0.685127i	0.229126	+	0.973397i	$0.426413\pi$
$12$		0			0
$13$	−7.81749	−	10.3869i	−0.601345	−	0.798989i
$13$	−7.81749	−	10.3869i	−0.601345	−	0.798989i
$14$	1.67522	+	0.967190i	0.119659	+	0.0690850i
$15$		0			0
$16$	−7.16161	+	12.4043i	−0.447601	+	0.775267i
$17$	−24.4307	−	14.1051i	−1.43710	−	0.829709i	−0.439451	−	0.898266i	$-0.644827\pi$
$17$	−24.4307	−	14.1051i	−1.43710	−	0.829709i	−0.997647	+	0.0685572i	$0.978160\pi$
$18$		0			0
$19$	10.6901	−	18.5158i	0.562638	−	0.974518i	−0.434627	−	0.900611i	$-0.643120\pi$
$19$	10.6901	−	18.5158i	0.562638	−	0.974518i	0.997265	−	0.0739073i	$-0.0235469\pi$
$20$			4.43165i			0.221583i
$21$		0			0
$22$	2.83390	+	4.90847i	0.128814	+	0.223112i
$23$		−	14.5409i		−	0.632213i	−0.948724	−	0.316106i	$-0.897624\pi$
$23$		−	14.5409i		−	0.632213i	0.948724	−	0.316106i	$-0.102376\pi$
$24$		0			0
$25$	−11.8405	−	20.5083i	−0.473618	−	0.820331i
$26$	−0.592890	−	4.85229i	−0.0228035	−	0.186627i
$27$		0			0
$28$	−9.92477	−	17.1902i	−0.354456	−	0.613936i
$29$	−46.7423	−	26.9867i	−1.61180	−	0.930576i	−0.988952	−	0.148236i	$-0.952640\pi$
$29$	−46.7423	−	26.9867i	−1.61180	−	0.930576i	−0.622852	−	0.782339i	$-0.714026\pi$
$30$		0			0
$31$	20.6940	−	35.8431i	0.667549	−	1.15623i	−0.311039	−	0.950397i	$-0.600677\pi$
$31$	20.6940	−	35.8431i	0.667549	−	1.15623i	0.978588	−	0.205831i	$-0.0659897\pi$
$32$	−14.9010	+	8.60310i	−0.465656	+	0.268847i
$33$		0			0
$34$	−5.30391	−	9.18664i	−0.155997	−	0.270195i
$35$	−5.11666	−	2.95411i	−0.146190	−	0.0844030i
$36$		0			0
$37$	26.5470	+	45.9807i	0.717486	+	1.24272i	0.961993	+	0.273074i	$0.0880405\pi$
$37$	26.5470	+	45.9807i	0.717486	+	1.24272i	−0.244507	+	0.969647i	$0.578626\pi$
$38$	6.96249	−	4.01980i	0.183223	−	0.105784i
$39$		0			0
$40$	−1.69696	+	2.93923i	−0.0424241	+	0.0734806i
$41$			28.8607i			0.703919i	0.936015	+	0.351959i	$0.114484\pi$
$41$			28.8607i			0.703919i	−0.936015	+	0.351959i	$0.885516\pi$
$42$		0			0
$43$	42.0583			0.978101			0.489050	−	0.872256i	$-0.337343\pi$
$43$	42.0583			0.978101			0.489050	+	0.872256i	$0.337343\pi$
$44$		−	58.1599i		−	1.32182i
$45$		0			0
$46$	2.73390	−	4.73525i	0.0594326	−	0.102940i
$47$	−3.48340	+	2.01114i	−0.0741148	+	0.0427902i	−0.536599	−	0.843837i	$-0.680291\pi$
$47$	−3.48340	+	2.01114i	−0.0741148	+	0.0427902i	0.462485	+	0.886627i	$0.346958\pi$
$48$		0			0
$49$	−22.5369			−0.459937
$50$		−	8.90471i		−	0.178094i
$51$		0			0
$52$	−19.6269	+	46.1627i	−0.377441	+	0.887744i
$53$		−	12.6540i		−	0.238755i	−0.992849	−	0.119378i	$-0.961910\pi$
$53$		−	12.6540i		−	0.238755i	0.992849	−	0.119378i	$-0.0380899\pi$
$54$		0			0
$55$	−8.65564	−	14.9920i	−0.157375	−	0.272582i
$56$		−	15.2015i		−	0.271456i
$57$		0			0
$58$	−10.1478	−	17.5765i	−0.174962	−	0.303043i
$59$	19.0560	−	11.0020i	0.322983	−	0.186474i	−0.329739	−	0.944072i	$-0.606961\pi$
$59$	19.0560	−	11.0020i	0.322983	−	0.186474i	0.652721	+	0.757598i	$0.273627\pi$
$60$		0			0
$61$	10.3485			0.169648			0.0848239	−	0.996396i	$-0.472967\pi$
$61$	10.3485			0.169648			0.0848239	+	0.996396i	$0.472967\pi$
$62$	13.4780	−	7.78155i	0.217388	−	0.125509i
$63$		0			0
$64$	50.8229			0.794107
$65$	1.81087	+	14.8204i	0.0278596	+	0.228007i
$66$		0			0
$67$	74.0229			1.10482			0.552410	−	0.833573i	$-0.313708\pi$
$67$	74.0229			1.10482			0.552410	+	0.833573i	$0.313708\pi$
$68$			108.852i			1.60076i
$69$		0			0
$70$	−1.11083	−	1.92401i	−0.0158690	−	0.0274859i
$71$	34.1908	+	19.7401i	0.481561	+	0.278029i	0.721067	−	0.692865i	$-0.243652\pi$
$71$	34.1908	+	19.7401i	0.481561	+	0.278029i	−0.239506	+	0.970895i	$0.576985\pi$
$72$		0			0
$73$	−65.2913			−0.894402			−0.447201	−	0.894434i	$-0.647579\pi$
$73$	−65.2913			−0.894402			−0.447201	+	0.894434i	$0.647579\pi$
$74$			19.9649i			0.269795i
$75$		0			0
$76$	−82.4979			−1.08550
$77$	67.1498	+	38.7690i	0.872076	+	0.503493i
$78$		0			0
$79$	−9.78025	−	16.9399i	−0.123801	−	0.214429i	0.797463	−	0.603368i	$-0.206175\pi$
$79$	−9.78025	−	16.9399i	−0.123801	−	0.214429i	−0.921263	+	0.388939i	$0.872842\pi$
$80$	14.2465	−	8.22520i	0.178081	−	0.102815i
$81$		0			0
$82$	−5.42622	+	9.39850i	−0.0661735	+	0.114616i
$83$	−71.7112	+	41.4025i	−0.863991	+	0.498825i	−0.865347	−	0.501174i	$-0.832902\pi$
$83$	−71.7112	+	41.4025i	−0.863991	+	0.498825i	0.00135589	+	0.999999i	$0.499568\pi$
$84$		0			0
$85$	16.1998	+	28.0589i	0.190586	+	0.330105i
$86$	13.6963	+	7.90758i	0.159260	+	0.0919486i
$87$		0			0
$88$	22.2705	−	38.5737i	0.253074	−	0.438337i
$89$	134.830	−	77.8441i	1.51494	−	0.874653i	0.515097	−	0.857132i	$-0.327756\pi$
$89$	134.830	−	77.8441i	1.51494	−	0.874653i	0.999846	−	0.0175212i	$-0.00557746\pi$
$90$		0			0
$91$	−40.2150	−	53.4324i	−0.441923	−	0.587169i
$92$	−48.5905	+	28.0538i	−0.528158	+	0.304932i
$93$		0			0
$94$	−1.51249			−0.0160904
$95$	−21.2657	+	12.2777i	−0.223849	+	0.129239i
$96$		0			0
$97$	19.4397			0.200409			0.100205	−	0.994967i	$-0.468050\pi$
$97$	19.4397			0.200409			0.100205	+	0.994967i	$0.468050\pi$
$98$	−7.33915	−	4.23726i	−0.0748893	−	0.0432374i
$99$		0			0
$100$	−45.6876	+	79.1333i	−0.456876	+	0.791333i
$101$	−71.7887	−	41.4472i	−0.710779	−	0.410369i	0.100570	−	0.994930i	$-0.467933\pi$
$101$	−71.7887	−	41.4472i	−0.710779	−	0.410369i	−0.811349	+	0.584561i	$0.801267\pi$
$102$		0			0
$103$	−38.2718	+	66.2886i	−0.371571	+	0.643579i	−0.989807	−	0.142413i	$-0.954514\pi$
$103$	−38.2718	+	66.2886i	−0.371571	+	0.643579i	0.618237	+	0.785992i	$0.287847\pi$
$104$	−30.6938	+	23.1012i	−0.295133	+	0.222127i
$105$		0			0
$106$	2.37914	−	4.12079i	0.0224447	−	0.0388754i
$107$	20.6786	−	11.9388i	0.193258	−	0.111578i	−0.400249	−	0.916407i	$-0.631076\pi$
$107$	20.6786	−	11.9388i	0.193258	−	0.111578i	0.593507	+	0.804829i	$0.297743\pi$
$108$		0			0
$109$	5.84222			0.0535983			0.0267992	−	0.999641i	$-0.491469\pi$
$109$	5.84222			0.0535983			0.0267992	+	0.999641i	$0.491469\pi$
$110$		−	6.50955i		−	0.0591777i
$111$		0			0
$112$	−36.8410	+	63.8104i	−0.328937	+	0.569736i
$113$	115.545	−	66.7097i	1.02252	−	0.590351i	0.107686	−	0.994185i	$-0.465656\pi$
$113$	115.545	−	66.7097i	1.02252	−	0.590351i	0.914832	+	0.403834i	$0.132322\pi$
$114$		0			0
$115$	−8.35020	+	14.4630i	−0.0726104	+	0.125765i
$116$			208.262i			1.79536i
$117$		0			0
$118$	8.27412			0.0701197
$119$	−125.677	−	72.5597i	−1.05611	−	0.609745i
$120$		0			0
$121$	53.0946	+	91.9625i	0.438798	+	0.760020i
$122$	3.37000	+	1.94567i	0.0276230	+	0.0159481i
$123$		0			0
$124$	−159.700			−1.28790
$125$			55.9106i			0.447285i
$126$		0			0
$127$	5.22700	+	9.05343i	0.0411575	+	0.0712869i	0.885870	−	0.463933i	$-0.153562\pi$
$127$	5.22700	+	9.05343i	0.0411575	+	0.0712869i	−0.844713	+	0.535220i	$0.820229\pi$
$128$	76.1545	+	43.9678i	0.594957	+	0.343499i
$129$		0			0
$130$	−2.19674	+	5.16676i	−0.0168980	+	0.0397443i
$131$	74.2522	+	42.8695i	0.566811	+	0.327248i	0.755875	−	0.654716i	$-0.227212\pi$
$131$	74.2522	+	42.8695i	0.566811	+	0.327248i	−0.189064	+	0.981965i	$0.560545\pi$
$132$		0			0
$133$	54.9925	−	95.2497i	0.413477	−	0.716164i
$134$	24.1056	+	13.9174i	0.179893	+	0.103861i
$135$		0			0
$136$	−41.6813	+	72.1942i	−0.306480	+	0.530839i
$137$			111.047i			0.810558i	0.914193	+	0.405279i	$0.132826\pi$
$137$			111.047i			0.810558i	−0.914193	+	0.405279i	$0.867174\pi$
$138$		0			0
$139$	101.422	+	175.667i	0.729652	+	1.26379i	0.957030	+	0.289988i	$0.0936514\pi$
$139$	101.422	+	175.667i	0.729652	+	1.26379i	−0.227378	+	0.973807i	$0.573015\pi$
$140$			22.7974i			0.162839i
$141$		0			0
$142$	7.42285	+	12.8567i	0.0522736	+	0.0905405i
$143$	−23.7655	−	194.500i	−0.166192	−	1.36014i
$144$		0			0
$145$	30.9945	+	53.6841i	0.213755	+	0.370235i
$146$	−21.2622	−	12.2757i	−0.145631	−	0.0840803i
$147$		0			0
$148$	102.434	−	177.421i	0.692123	−	1.19879i
$149$	203.709	−	117.612i	1.36718	−	0.789340i	0.376610	−	0.926372i	$-0.377090\pi$
$149$	203.709	−	117.612i	1.36718	−	0.789340i	0.990567	+	0.137032i	$0.0437563\pi$
$150$		0			0
$151$	133.267	+	230.825i	0.882561	+	1.52864i	0.848483	+	0.529222i	$0.177516\pi$
$151$	133.267	+	230.825i	0.882561	+	1.52864i	0.0340779	+	0.999419i	$0.489151\pi$
$152$	−54.7155	−	31.5900i	−0.359970	−	0.207829i
$153$		0			0
$154$	14.5783	+	25.2503i	0.0946640	+	0.163963i
$155$	−41.1662	+	23.7673i	−0.265588	+	0.153338i
$156$		0			0
$157$	29.0426	−	50.3033i	0.184985	−	0.320403i	−0.758587	−	0.651572i	$-0.774110\pi$
$157$	29.0426	−	50.3033i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$158$		−	7.35531i		−	0.0465526i
$159$		0			0
$160$	19.7615			0.123510
$161$		−	74.8017i		−	0.464607i
$162$		0			0
$163$	−8.10087	+	14.0311i	−0.0496986	+	0.0860805i	−0.889805	−	0.456342i	$-0.849159\pi$
$163$	−8.10087	+	14.0311i	−0.0496986	+	0.0860805i	0.840106	+	0.542422i	$0.182493\pi$
$164$	96.4422	−	55.6809i	0.588062	−	0.339518i
$165$		0			0
$166$	−31.1371			−0.187573
$167$			31.2855i			0.187338i	0.995603	+	0.0936691i	$0.0298596\pi$
$167$			31.2855i			0.187338i	−0.995603	+	0.0936691i	$0.970140\pi$
$168$		0			0
$169$	−46.7737	+	162.398i	−0.276768	+	0.960937i
$170$			12.1832i			0.0716659i
$171$		0			0
$172$	−81.1432	−	140.544i	−0.471763	−	0.817117i
$173$			4.32233i			0.0249846i	0.999922	+	0.0124923i	$0.00397652\pi$
$173$			4.32233i			0.0249846i	−0.999922	+	0.0124923i	$0.996023\pi$
$174$		0			0
$175$	−60.9101	−	105.499i	−0.348057	−	0.602853i
$176$	−186.967	+	107.945i	−1.06231	+	0.613327i
$177$		0			0
$178$	58.5433			0.328895
$179$	−1.59962	+	0.923541i	−0.00893642	+	0.00515945i	−0.504462	−	0.863434i	$-0.668309\pi$
$179$	−1.59962	+	0.923541i	−0.00893642	+	0.00515945i	0.495525	+	0.868594i	$0.334976\pi$
$180$		0			0
$181$	−10.7339			−0.0593032			−0.0296516	−	0.999560i	$-0.509440\pi$
$181$	−10.7339			−0.0593032			−0.0296516	+	0.999560i	$0.509440\pi$
$182$	−3.04996	−	24.9613i	−0.0167580	−	0.137150i
$183$		0			0
$184$	−42.9692			−0.233529
$185$		−	60.9790i		−	0.329616i
$186$		0			0
$187$	−212.603	−	368.239i	−1.13691	−	1.96919i
$188$	13.4410	+	7.76019i	0.0714949	+	0.0412776i
$189$		0			0
$190$	−9.23357			−0.0485977
$191$			65.9244i			0.345154i	0.984996	+	0.172577i	$0.0552094\pi$
$191$			65.9244i			0.345154i	−0.984996	+	0.172577i	$0.944791\pi$
$192$		0			0
$193$	−111.858			−0.579578			−0.289789	−	0.957091i	$-0.593585\pi$
$193$	−111.858			−0.579578			−0.289789	+	0.957091i	$0.593585\pi$
$194$	6.33055	+	3.65494i	0.0326317	+	0.0188399i
$195$		0			0
$196$	43.4804	+	75.3103i	0.221839	+	0.384236i
$197$	10.1710	−	5.87226i	0.0516297	−	0.0298084i	−0.473963	−	0.880545i	$-0.657177\pi$
$197$	10.1710	−	5.87226i	0.0516297	−	0.0298084i	0.525593	+	0.850736i	$0.323844\pi$
$198$		0			0
$199$	9.23826	−	16.0011i	0.0464234	−	0.0804077i	−0.841880	−	0.539665i	$-0.818551\pi$
$199$	9.23826	−	16.0011i	0.0464234	−	0.0804077i	0.888303	+	0.459257i	$0.151884\pi$
$200$	−60.6032	+	34.9893i	−0.303016	+	0.174946i
$201$		0			0
$202$	−15.5854	−	26.9946i	−0.0771552	−	0.133637i
$203$	−240.453	−	138.826i	−1.18450	−	0.683871i
$204$		0			0
$205$	16.5734	−	28.7060i	0.0808459	−	0.140029i
$206$	−24.9265	+	14.3913i	−0.121002	+	0.0698607i
$207$		0			0
$208$	184.827	−	22.5836i	0.888593	−	0.108575i
$209$	279.085	−	161.130i	1.33534	−	0.770957i
$210$		0			0
$211$	26.1820			0.124085			0.0620426	−	0.998074i	$-0.480239\pi$
$211$	26.1820			0.124085			0.0620426	+	0.998074i	$0.480239\pi$
$212$	−42.2853	+	24.4134i	−0.199459	+	0.115158i
$213$		0			0
$214$	8.97868			0.0419565
$215$	−41.8329	−	24.1523i	−0.194572	−	0.112336i
$216$		0			0
$217$	106.455	−	184.385i	0.490575	−	0.849701i
$218$	1.90252	+	1.09842i	0.00872717	+	0.00503863i
$219$		0			0
$220$	−33.3987	+	57.8482i	−0.151812	+	0.262946i
$221$	44.4793	+	364.024i	0.201264	+	1.64717i
$222$		0			0
$223$	161.459	−	279.656i	0.724033	−	1.25406i	−0.235338	−	0.971914i	$-0.575620\pi$
$223$	161.459	−	279.656i	0.724033	−	1.25406i	0.959371	−	0.282149i	$-0.0910471\pi$
$224$	−76.6542	+	44.2563i	−0.342206	+	0.197573i
$225$		0			0
$226$	50.1696			0.221989
$227$			253.520i			1.11683i	0.829563	+	0.558413i	$0.188590\pi$
$227$			253.520i			1.11683i	−0.829563	+	0.558413i	$0.811410\pi$
$228$		0			0
$229$	119.446	−	206.887i	0.521600	−	0.903437i	−0.478085	−	0.878314i	$-0.658669\pi$
$229$	119.446	−	206.887i	0.521600	−	0.903437i	0.999684	−	0.0251232i	$-0.00799781\pi$
$230$	−5.43849	+	3.13992i	−0.0236456	+	0.0136518i
$231$		0			0
$232$	−79.7474	+	138.126i	−0.343739	+	0.595373i
$233$			42.9145i			0.184182i	0.995751	+	0.0920912i	$0.0293551\pi$
$233$			42.9145i			0.184182i	−0.995751	+	0.0920912i	$0.970645\pi$
$234$		0			0
$235$	4.61964			0.0196580
$236$	−73.5294	−	42.4522i	−0.311565	−	0.179882i
$237$		0			0
$238$	−27.2845	−	47.2582i	−0.114641	−	0.198564i
$239$	−67.0524	−	38.7127i	−0.280554	−	0.161978i	0.353120	−	0.935578i	$-0.385121\pi$
$239$	−67.0524	−	38.7127i	−0.280554	−	0.161978i	−0.633674	+	0.773600i	$0.718454\pi$
$240$		0			0
$241$	−95.7696			−0.397384			−0.198692	−	0.980062i	$-0.563669\pi$
$241$	−95.7696			−0.397384			−0.198692	+	0.980062i	$0.563669\pi$
$242$			39.9302i			0.165001i
$243$		0			0
$244$	−19.9654	−	34.5811i	−0.0818254	−	0.141726i
$245$	22.4161	+	12.9419i	0.0914943	+	0.0528243i
$246$		0			0
$247$	−275.891	+	33.7105i	−1.11697	+	0.136480i
$248$	−105.919	−	61.1521i	−0.427091	−	0.246581i
$249$		0			0
$250$	−10.5120	+	18.2073i	−0.0420480	+	0.0728293i
$251$	−365.360	−	210.940i	−1.45562	−	0.840400i	−0.456825	−	0.889557i	$-0.651013\pi$
$251$	−365.360	−	210.940i	−1.45562	−	0.840400i	−0.998791	+	0.0491566i	$0.984347\pi$
$252$		0			0
$253$	109.586	−	189.808i	0.433146	−	0.750231i
$254$			3.93101i			0.0154764i
$255$		0			0
$256$	−85.1125	−	147.419i	−0.332471	−	0.575856i
$257$		−	388.354i		−	1.51110i	−0.655089	−	0.755552i	$-0.727369\pi$
$257$		−	388.354i		−	1.51110i	0.655089	−	0.755552i	$-0.272631\pi$
$258$		0			0
$259$	136.564	+	236.535i	0.527273	+	0.913264i
$260$	46.0309	−	34.6444i	0.177042	−	0.133248i
$261$		0			0
$262$	16.1202	+	27.9210i	0.0615275	+	0.106569i
$263$	−138.032	−	79.6926i	−0.524835	−	0.303014i	0.214076	−	0.976817i	$-0.431326\pi$
$263$	−138.032	−	79.6926i	−0.524835	−	0.303014i	−0.738911	+	0.673803i	$0.764659\pi$
$264$		0			0
$265$	−7.26665	+	12.5862i	−0.0274213	+	0.0474951i
$266$	35.8167	−	20.6788i	0.134649	−	0.0777397i
$267$		0			0
$268$	−142.813	−	247.359i	−0.532883	−	0.922980i
$269$	−138.125	−	79.7468i	−0.513478	−	0.296456i	0.220784	−	0.975323i	$-0.429138\pi$
$269$	−138.125	−	79.7468i	−0.513478	−	0.296456i	−0.734262	+	0.678866i	$0.762472\pi$
$270$		0			0
$271$	−96.7532	−	167.581i	−0.357023	−	0.618382i	0.630439	−	0.776239i	$-0.282875\pi$
$271$	−96.7532	−	167.581i	−0.357023	−	0.618382i	−0.987462	+	0.157857i	$0.949542\pi$
$272$	349.926	−	202.030i	1.28649	−	0.742757i
$273$		0			0
$274$	−20.8784	+	36.1624i	−0.0761984	+	0.131979i
$275$		−	356.938i		−	1.29795i
$276$		0			0
$277$	−321.962			−1.16232			−0.581159	−	0.813790i	$-0.697401\pi$
$277$	−321.962			−1.16232			−0.581159	+	0.813790i	$0.697401\pi$
$278$			76.2750i			0.274370i
$279$		0			0
$280$	−8.72957	+	15.1201i	−0.0311770	+	0.0540002i
$281$	357.552	−	206.433i	1.27243	−	0.734637i	0.296984	−	0.954883i	$-0.404019\pi$
$281$	357.552	−	206.433i	1.27243	−	0.734637i	0.975444	+	0.220246i	$0.0706860\pi$
$282$		0			0
$283$	487.758			1.72353			0.861764	−	0.507310i	$-0.169360\pi$
$283$	487.758			1.72353			0.861764	+	0.507310i	$0.169360\pi$
$284$		−	152.338i		−	0.536403i
$285$		0			0
$286$	28.8295	−	67.8072i	0.100803	−	0.237088i
$287$			148.466i			0.517303i
$288$		0			0
$289$	253.405	+	438.911i	0.876835	+	1.51872i
$290$			23.3097i			0.0803783i
$291$		0			0
$292$	125.967	+	218.181i	0.431393	+	0.747194i
$293$	−475.133	+	274.318i	−1.62162	+	0.936240i	−0.635128	+	0.772407i	$0.719053\pi$
$293$	−475.133	+	274.318i	−1.62162	+	0.936240i	−0.986488	+	0.163833i	$0.947614\pi$
$294$		0			0
$295$	−25.2718			−0.0856671
$296$	135.876	−	78.4479i	0.459040	−	0.265027i
$297$		0			0
$298$	88.4508			0.296815
$299$	−151.034	+	113.673i	−0.505131	+	0.380178i
$300$		0			0
$301$	216.358			0.718797
$302$			100.224i			0.331869i
$303$		0			0
$304$	153.117	+	265.206i	0.503674	+	0.872390i
$305$	−10.2931	−	5.94270i	−0.0337477	−	0.0194843i
$306$		0			0
$307$	78.3446			0.255194			0.127597	−	0.991826i	$-0.459274\pi$
$307$	78.3446			0.255194			0.127597	+	0.991826i	$0.459274\pi$
$308$		−	299.188i		−	0.971390i
$309$		0			0
$310$	−17.8744			−0.0576594
$311$	390.829	+	225.645i	1.25668	+	0.725547i	0.972428	−	0.233202i	$-0.0749204\pi$
$311$	390.829	+	225.645i	1.25668	+	0.725547i	0.284255	+	0.958749i	$0.408254\pi$
$312$		0			0
$313$	117.824	+	204.077i	0.376435	+	0.652004i	0.990541	−	0.137220i	$-0.0438166\pi$
$313$	117.824	+	204.077i	0.376435	+	0.652004i	−0.614106	+	0.789224i	$0.710483\pi$
$314$	18.9155	−	10.9209i	0.0602404	−	0.0347798i
$315$		0			0
$316$	−37.7381	+	65.3643i	−0.119424	+	0.206849i
$317$	−107.908	+	62.3008i	−0.340404	+	0.196532i	−0.660451	−	0.750869i	$-0.729635\pi$
$317$	−107.908	+	62.3008i	−0.340404	+	0.196532i	0.320047	+	0.947402i	$0.396301\pi$
$318$		0			0
$319$	−406.765	−	704.537i	−1.27512	−	2.20858i
$320$	−50.5505	−	29.1853i	−0.157970	−	0.0912042i
$321$		0			0
$322$	14.0638	−	24.3592i	0.0436764	−	0.0756498i
$323$	−522.334	+	301.570i	−1.61713	+	0.933652i
$324$		0			0
$325$	−120.454	+	283.308i	−0.370628	+	0.871718i
$326$	−5.27611	+	3.04616i	−0.0161844	+	0.00934406i
$327$		0			0
$328$	85.2851			0.260015
$329$	−17.9194	+	10.3458i	−0.0544662	+	0.0314461i
$330$		0			0
$331$	334.583			1.01083			0.505413	−	0.862878i	$-0.331340\pi$
$331$	334.583			1.01083			0.505413	+	0.862878i	$0.331340\pi$
$332$	276.705	+	159.756i	0.833449	+	0.481192i
$333$		0			0
$334$	−5.88212	+	10.1881i	−0.0176111	+	0.0305034i
$335$	−73.6262	−	42.5081i	−0.219780	−	0.126890i
$336$		0			0
$337$	−185.957	+	322.088i	−0.551802	+	0.955750i	0.446342	+	0.894862i	$0.352726\pi$
$337$	−185.957	+	322.088i	−0.551802	+	0.955750i	−0.998145	+	0.0608873i	$0.980607\pi$
$338$	−45.7651	+	44.0910i	−0.135400	+	0.130447i
$339$		0			0
$340$	62.5087	−	108.268i	0.183849	−	0.318436i
$341$	540.255	−	311.916i	1.58433	−	0.914711i
$342$		0			0
$343$	−368.002			−1.07289
$344$		−	124.285i		−	0.361294i
$345$		0			0
$346$	−0.812660	+	1.40757i	−0.00234873	+	0.00406812i
$347$	147.917	−	85.4000i	0.426274	−	0.246110i	−0.271484	−	0.962443i	$-0.587514\pi$
$347$	147.917	−	85.4000i	0.426274	−	0.246110i	0.697758	+	0.716333i	$0.254181\pi$
$348$		0			0
$349$	−67.3588	+	116.669i	−0.193005	+	0.334295i	−0.946245	−	0.323452i	$-0.895157\pi$
$349$	−67.3588	+	116.669i	−0.193005	+	0.334295i	0.753240	+	0.657746i	$0.228490\pi$
$350$		−	45.8079i		−	0.130880i
$351$		0			0
$352$	−259.345			−0.736777
$353$	109.964	+	63.4880i	0.311514	+	0.179853i	0.647604	−	0.761977i	$-0.275771\pi$
$353$	109.964	+	63.4880i	0.311514	+	0.179853i	−0.336090	+	0.941830i	$0.609105\pi$
$354$		0			0
$355$	−22.6717	−	39.2686i	−0.0638640	−	0.110616i
$356$	−520.255	−	300.370i	−1.46139	−	0.843735i
$357$		0			0
$358$	−0.694556			−0.00194010
$359$			443.856i			1.23637i	0.786034	+	0.618184i	$0.212131\pi$
$359$			443.856i			1.23637i	−0.786034	+	0.618184i	$0.787869\pi$
$360$		0			0
$361$	−48.0575	−	83.2381i	−0.133123	−	0.230576i
$362$	−3.49550	−	2.01813i	−0.00965606	−	0.00557493i
$363$		0			0
$364$	−100.965	+	237.471i	−0.277378	+	0.652394i
$365$	64.9414	+	37.4939i	0.177922	+	0.102723i
$366$		0			0
$367$	58.0864	−	100.609i	0.158274	−	0.274138i	−0.775973	−	0.630767i	$-0.782741\pi$
$367$	58.0864	−	100.609i	0.158274	−	0.274138i	0.934246	+	0.356629i	$0.116074\pi$
$368$	180.369	+	104.136i	0.490134	+	0.282979i
$369$		0			0
$370$	11.4649	−	19.8579i	0.0309863	−	0.0536699i
$371$		−	65.0952i		−	0.175459i
$372$		0			0
$373$	−105.494	−	182.720i	−0.282825	−	0.489866i	0.689255	−	0.724519i	$-0.257938\pi$
$373$	−105.494	−	182.720i	−0.282825	−	0.489866i	−0.972079	+	0.234653i	$0.924605\pi$
$374$		−	159.889i		−	0.427512i
$375$		0			0
$376$	5.94304	+	10.2936i	0.0158060	+	0.0273767i
$377$	85.1006	+	696.474i	0.225731	+	1.84741i
$378$		0			0
$379$	−190.883	−	330.619i	−0.503650	−	0.872347i	−0.999991	−	0.00421947i	$-0.998657\pi$
$379$	−190.883	−	330.619i	−0.503650	−	0.872347i	0.496341	−	0.868127i	$-0.334676\pi$
$380$	82.0557	+	47.3749i	0.215936	+	0.124671i
$381$		0			0
$382$	−12.3947	+	21.4683i	−0.0324470	+	0.0561998i
$383$	219.929	−	126.976i	0.574227	−	0.331530i	−0.184609	−	0.982812i	$-0.559102\pi$
$383$	219.929	−	126.976i	0.574227	−	0.331530i	0.758836	+	0.651282i	$0.225768\pi$
$384$		0			0
$385$	−44.5266	−	77.1224i	−0.115654	−	0.200318i
$386$	−36.4268	−	21.0310i	−0.0943699	−	0.0544845i
$387$		0			0
$388$	−37.5050	−	64.9606i	−0.0966624	−	0.167424i
$389$	291.388	−	168.233i	0.749070	−	0.432476i	−0.0762879	−	0.997086i	$-0.524307\pi$
$389$	291.388	−	168.233i	0.749070	−	0.432476i	0.825358	+	0.564610i	$0.190973\pi$
$390$		0			0
$391$	−205.100	+	355.244i	−0.524553	+	0.908552i
$392$			66.5979i			0.169893i
$393$		0			0
$394$	4.41628			0.0112088
$395$			22.4655i			0.0568746i
$396$		0			0
$397$	−124.854	+	216.254i	−0.314494	+	0.544720i	−0.979330	−	0.202269i	$-0.935168\pi$
$397$	−124.854	+	216.254i	−0.314494	+	0.544720i	0.664835	+	0.746990i	$0.268502\pi$
$398$	6.01689	−	3.47385i	0.0151178	−	0.00872828i
$399$		0			0
$400$	339.187			0.847968
$401$			562.927i			1.40381i	0.712271	+	0.701904i	$0.247667\pi$
$401$			562.927i			1.40381i	−0.712271	+	0.701904i	$0.752333\pi$
$402$		0			0
$403$	−534.072	+	65.2570i	−1.32524	+	0.161928i
$404$			319.857i			0.791724i
$405$		0			0
$406$	−52.2025	−	90.4174i	−0.128578	−	0.222703i
$407$			800.274i			1.96628i
$408$		0			0
$409$	370.218	+	641.237i	0.905179	+	1.56782i	0.820676	+	0.571393i	$0.193597\pi$
$409$	370.218	+	641.237i	0.905179	+	1.56782i	0.0845027	+	0.996423i	$0.473070\pi$
$410$	10.7943	−	6.23208i	0.0263275	−	0.0152002i
$411$		0			0
$412$	295.351			0.716872
$413$	98.0284	−	56.5967i	0.237357	−	0.137038i
$414$		0			0
$415$	95.1026			0.229163
$416$	205.848	+	87.5200i	0.494826	+	0.210385i
$417$		0			0
$418$	121.179			0.289902
$419$		−	447.245i		−	1.06741i	−0.845670	−	0.533705i	$-0.820799\pi$
$419$		−	447.245i		−	1.06741i	0.845670	−	0.533705i	$-0.179201\pi$
$420$		0			0
$421$	−159.450	−	276.175i	−0.378741	−	0.655999i	0.612138	−	0.790751i	$-0.290310\pi$
$421$	−159.450	−	276.175i	−0.378741	−	0.655999i	−0.990879	+	0.134752i	$0.956976\pi$
$422$	8.52618	+	4.92259i	0.0202042	+	0.0116649i
$423$		0			0
$424$	−37.3934			−0.0881920
$425$			668.041i			1.57186i
$426$		0			0
$427$	53.2351			0.124672
$428$	−79.7906	−	46.0671i	−0.186427	−	0.107634i
$429$		0			0
$430$	−9.08195	−	15.7304i	−0.0211208	−	0.0365823i
$431$	101.578	−	58.6459i	0.235679	−	0.136069i	−0.377510	−	0.926005i	$-0.623220\pi$
$431$	101.578	−	58.6459i	0.235679	−	0.136069i	0.613189	+	0.789936i	$0.289886\pi$
$432$		0			0
$433$	211.520	−	366.363i	0.488498	−	0.846104i	−0.511414	−	0.859334i	$-0.670878\pi$
$433$	211.520	−	366.363i	0.488498	−	0.846104i	0.999912	+	0.0132303i	$0.00421145\pi$
$434$	69.3341	−	40.0301i	0.159756	−	0.0922352i
$435$		0			0
$436$	−11.2714	−	19.5226i	−0.0258518	−	0.0447767i
$437$	−269.237	−	155.444i	−0.616103	−	0.355707i
$438$		0			0
$439$	134.308	−	232.629i	0.305941	−	0.529906i	−0.671529	−	0.740978i	$-0.734362\pi$
$439$	134.308	−	232.629i	0.305941	−	0.529906i	0.977470	+	0.211072i	$0.0676956\pi$
$440$	−44.3023	+	25.5780i	−0.100687	+	0.0581317i
$441$		0			0
$442$	−53.9571	+	126.907i	−0.122075	+	0.287121i
$443$	−33.2832	+	19.2161i	−0.0751314	+	0.0433771i	−0.537095	−	0.843522i	$-0.680478\pi$
$443$	−33.2832	+	19.2161i	−0.0751314	+	0.0433771i	0.461964	+	0.886899i	$0.347145\pi$
$444$		0			0
$445$	−178.810			−0.401820
$446$	105.159	−	60.7134i	0.235782	−	0.136129i
$447$		0			0
$448$	261.444			0.583581
$449$	−521.983	−	301.367i	−1.16254	−	0.671196i	−0.210632	−	0.977565i	$-0.567552\pi$
$449$	−521.983	−	301.367i	−1.16254	−	0.671196i	−0.951913	+	0.306370i	$0.900886\pi$
$450$		0			0
$451$	−217.505	+	376.730i	−0.482274	+	0.835323i
$452$	−445.841	−	257.406i	−0.986373	−	0.569483i
$453$		0			0
$454$	−47.6654	+	82.5589i	−0.104990	+	0.181848i
$455$	9.31556	+	76.2397i	0.0204738	+	0.167560i
$456$		0			0
$457$	−129.801	+	224.822i	−0.284029	+	0.491952i	−0.972373	−	0.233432i	$-0.925004\pi$
$457$	−129.801	+	224.822i	−0.284029	+	0.491952i	0.688344	+	0.725384i	$0.258338\pi$
$458$	77.7955	−	44.9153i	0.169859	−	0.0980683i
$459$		0			0
$460$	64.4402			0.140087
$461$		−	534.455i		−	1.15934i	−0.814852	−	0.579669i	$-0.803182\pi$
$461$		−	534.455i		−	1.15934i	0.814852	−	0.579669i	$-0.196818\pi$
$462$		0			0
$463$	−307.484	+	532.579i	−0.664113	+	1.15028i	0.315412	+	0.948955i	$0.397857\pi$
$463$	−307.484	+	532.579i	−0.664113	+	1.15028i	−0.979525	+	0.201323i	$0.935476\pi$
$464$	669.501	−	386.536i	1.44289	−	0.833052i
$465$		0			0
$466$	−8.06855	+	13.9751i	−0.0173145	+	0.0299896i
$467$			247.090i			0.529100i	0.964372	+	0.264550i	$0.0852234\pi$
$467$			247.090i			0.529100i	−0.964372	+	0.264550i	$0.914777\pi$
$468$		0			0
$469$	380.791			0.811921
$470$	1.50439	+	0.868558i	0.00320082	+	0.00184800i
$471$		0			0
$472$	−32.5115	−	56.3116i	−0.0688803	−	0.119304i
$473$	549.005	+	316.968i	1.16069	+	0.670123i
$474$		0			0
$475$	−506.304			−1.06590
$476$			559.958i			1.17638i
$477$		0			0
$478$	−14.5571	−	25.2136i	−0.0304542	−	0.0527482i
$479$	710.396	+	410.147i	1.48308	+	0.856257i	0.999815	−	0.0192166i	$-0.00611721\pi$
$479$	710.396	+	410.147i	1.48308	+	0.856257i	0.483266	+	0.875474i	$0.339451\pi$
$480$		0			0
$481$	270.065	−	635.193i	0.561465	−	1.32057i
$482$	−31.1874	−	18.0061i	−0.0647042	−	0.0373570i
$483$		0			0
$484$	204.871	−	354.847i	0.423287	−	0.733154i
$485$	−19.3355	−	11.1634i	−0.0398670	−	0.0230172i
$486$		0			0
$487$	−367.489	+	636.510i	−0.754598	+	1.30700i	0.190976	+	0.981595i	$0.438835\pi$
$487$	−367.489	+	636.510i	−0.754598	+	1.30700i	−0.945574	+	0.325407i	$0.894499\pi$
$488$		−	30.5805i		−	0.0626650i
$489$		0			0
$490$	4.86655	+	8.42911i	0.00993173	+	0.0172023i
$491$		−	130.593i		−	0.265974i	−0.991118	−	0.132987i	$-0.957543\pi$
$491$		−	130.593i		−	0.265974i	0.991118	−	0.132987i	$-0.0424569\pi$
$492$		0			0
$493$	761.298	+	1318.61i	1.54421	+	2.67466i
$494$	−96.1823	−	40.8937i	−0.194701	−	0.0827808i
$495$		0			0
$496$	296.405	+	513.388i	0.597590	+	1.03506i
$497$	175.886	+	101.548i	0.353895	+	0.204321i
$498$		0			0
$499$	−14.4740	+	25.0696i	−0.0290059	+	0.0502397i	−0.880164	−	0.474670i	$-0.842568\pi$
$499$	−14.4740	+	25.0696i	−0.0290059	+	0.0502397i	0.851158	+	0.524909i	$0.175901\pi$
$500$	186.834	−	107.868i	0.373667	−	0.215737i
$501$		0			0
$502$	−79.3197	−	137.386i	−0.158007	−	0.273677i
$503$	−255.144	−	147.308i	−0.507245	−	0.292858i	0.224455	−	0.974484i	$-0.427940\pi$
$503$	−255.144	−	147.308i	−0.507245	−	0.292858i	−0.731701	+	0.681626i	$0.761273\pi$
$504$		0			0
$505$	47.6026	+	82.4502i	0.0942627	+	0.163268i
$506$	71.3735	−	41.2075i	0.141054	−	0.0814377i
$507$		0			0
$508$	20.1689	−	34.9336i	0.0397026	−	0.0687669i
$509$		−	621.265i		−	1.22056i	−0.792186	−	0.610280i	$-0.791057\pi$
$509$		−	621.265i		−	1.22056i	0.792186	−	0.610280i	$-0.208943\pi$
$510$		0			0
$511$	−335.874			−0.657287
$512$		−	415.752i		−	0.812016i
$513$		0			0
$514$	73.0161	−	126.468i	0.142055	−	0.246046i
$515$	76.1333	−	43.9556i	0.147832	−	0.0853507i
$516$		0			0
$517$	−60.6270			−0.117267
$518$			102.704i			0.198270i
$519$		0			0
$520$	43.7953	−	5.35125i	0.0842217	−	0.0102909i
$521$		−	166.583i		−	0.319738i	−0.987138	−	0.159869i	$-0.948893\pi$
$521$		−	166.583i		−	0.319738i	0.987138	−	0.159869i	$-0.0511071\pi$
$522$		0			0
$523$	−51.1561	−	88.6049i	−0.0978127	−	0.169417i	0.812966	−	0.582311i	$-0.197851\pi$
$523$	−51.1561	−	88.6049i	−0.0978127	−	0.169417i	−0.910779	+	0.412894i	$0.864518\pi$
$524$		−	330.833i		−	0.631361i
$525$		0			0
$526$	−29.9667	−	51.9039i	−0.0569709	−	0.0986766i
$527$	−1011.14	+	583.780i	−1.91867	+	1.10774i
$528$		0			0
$529$	317.562			0.600307
$530$	−4.73278	+	2.73247i	−0.00892977	+	0.00515560i
$531$		0			0
$532$	−424.388			−0.797722
$533$	299.772	−	225.618i	0.562424	−	0.423298i
$534$		0			0
$535$	−27.4238			−0.0512594
$536$		−	218.742i		−	0.408102i
$537$		0			0
$538$	−29.9871	−	51.9392i	−0.0557381	−	0.0965412i
$539$	−294.184	−	169.847i	−0.545795	−	0.315115i
$540$		0			0
$541$	638.732			1.18065			0.590325	−	0.807166i	$-0.299000\pi$
$541$	638.732			1.18065			0.590325	+	0.807166i	$0.299000\pi$
$542$		−	72.7640i		−	0.134251i
$543$		0			0
$544$	485.389			0.892259
$545$	−5.81091	−	3.35493i	−0.0106622	−	0.00615583i
$546$		0			0
$547$	−250.228	−	433.408i	−0.457456	−	0.792337i	0.541370	−	0.840785i	$-0.317906\pi$
$547$	−250.228	−	433.408i	−0.457456	−	0.792337i	−0.998826	+	0.0484477i	$0.984573\pi$
$548$	371.078	−	214.242i	0.677150	−	0.390953i
$549$		0			0
$550$	67.1094	−	116.237i	0.122017	−	0.211340i
$551$	−999.363	+	576.982i	−1.81373	+	1.04715i
$552$		0			0
$553$	−50.3119	−	87.1427i	−0.0909798	−	0.157582i
$554$	−104.847	−	60.5336i	−0.189255	−	0.109266i
$555$		0			0
$556$	391.346	−	677.831i	0.703859	−	1.21912i
$557$	−217.719	+	125.700i	−0.390877	+	0.225673i	−0.682540	−	0.730848i	$-0.739125\pi$
$557$	−217.719	+	125.700i	−0.390877	+	0.225673i	0.291663	+	0.956521i	$0.405791\pi$
$558$		0			0
$559$	−328.791	−	436.854i	−0.588176	−	0.781492i
$560$	73.2871	−	42.3123i	0.130870	−	0.0755577i
$561$		0			0
$562$	155.249			0.276245
$563$	651.090	−	375.907i	1.15647	−	0.667685i	0.206011	−	0.978550i	$-0.433952\pi$
$563$	651.090	−	375.907i	1.15647	−	0.667685i	0.950454	+	0.310864i	$0.100618\pi$
$564$		0			0
$565$	−153.234			−0.271210
$566$	158.839	+	91.7056i	0.280634	+	0.162024i
$567$		0			0
$568$	58.3332	−	101.036i	0.102699	−	0.177880i
$569$	−464.413	−	268.129i	−0.816191	−	0.471228i	0.0329102	−	0.999458i	$-0.489522\pi$
$569$	−464.413	−	268.129i	−0.816191	−	0.471228i	−0.849101	+	0.528230i	$0.822856\pi$
$570$		0			0
$571$	−50.9656	+	88.2750i	−0.0892567	+	0.154597i	−0.907197	−	0.420706i	$-0.861782\pi$
$571$	−50.9656	+	88.2750i	−0.0892567	+	0.154597i	0.817940	+	0.575303i	$0.195116\pi$
$572$	−604.099	+	454.664i	−1.05612	+	0.794868i
$573$		0			0
$574$	−27.9137	+	48.3480i	−0.0486302	+	0.0842300i
$575$	−298.209	+	172.171i	−0.518624	+	0.299428i
$576$		0			0
$577$	−6.86778			−0.0119026			−0.00595128	−	0.999982i	$-0.501894\pi$
$577$	−6.86778			−0.0119026			−0.00595128	+	0.999982i	$0.501894\pi$
$578$			190.575i			0.329715i
$579$		0			0
$580$	119.596	−	207.146i	0.206199	−	0.357148i
$581$	−368.899	+	212.984i	−0.634938	+	0.366582i
$582$		0			0
$583$	95.3657	−	165.178i	0.163578	−	0.283325i
$584$			192.940i			0.330377i
$585$		0			0
$586$	−206.303			−0.352054
$587$	−452.291	−	261.130i	−0.770512	−	0.444855i	0.0625452	−	0.998042i	$-0.480078\pi$
$587$	−452.291	−	261.130i	−0.770512	−	0.444855i	−0.833057	+	0.553187i	$0.813412\pi$
$588$		0			0
$589$	−442.443	−	766.334i	−0.751177	−	1.30108i
$590$	−8.22978	−	4.75147i	−0.0139488	−	0.00805333i
$591$		0			0
$592$	−760.476			−1.28459
$593$		−	624.635i		−	1.05335i	−0.850068	−	0.526674i	$-0.823439\pi$
$593$		−	624.635i		−	1.05335i	0.850068	−	0.526674i	$-0.176561\pi$
$594$		0			0
$595$	83.3357	+	144.342i	0.140060	+	0.242591i
$596$	−786.033	−	453.817i	−1.31885	−	0.761437i
$597$		0			0
$598$	−70.5566	+	8.62115i	−0.117988	+	0.0144166i
$599$	472.937	+	273.050i	0.789544	+	0.455843i	0.839802	−	0.542893i	$-0.182671\pi$
$599$	472.937	+	273.050i	0.789544	+	0.455843i	−0.0502581	+	0.998736i	$0.516004\pi$
$600$		0			0
$601$	−281.855	+	488.187i	−0.468977	+	0.812291i	−0.999371	−	0.0354598i	$-0.988710\pi$
$601$	−281.855	+	488.187i	−0.468977	+	0.812291i	0.530395	+	0.847751i	$0.322044\pi$
$602$	70.4571	+	40.6784i	0.117038	+	0.0675721i
$603$		0			0
$604$	514.223	−	890.661i	0.851363	−	1.47460i
$605$		−	121.959i		−	0.201586i
$606$		0			0
$607$	−100.683	−	174.388i	−0.165869	−	0.287294i	0.771094	−	0.636721i	$-0.219710\pi$
$607$	−100.683	−	174.388i	−0.165869	−	0.287294i	−0.936964	+	0.349427i	$0.886376\pi$
$608$			367.873i			0.605054i
$609$		0			0
$610$	−2.23463	−	3.87049i	−0.00366332	−	0.00634506i
$611$	48.1208	+	20.4595i	0.0787575	+	0.0334852i
$612$		0			0
$613$	−317.568	−	550.044i	−0.518055	−	0.897298i	−0.999780	−	0.0209752i	$-0.993323\pi$
$613$	−317.568	−	550.044i	−0.518055	−	0.897298i	0.481725	−	0.876322i	$-0.340010\pi$
$614$	25.5130	+	14.7299i	0.0415521	+	0.0239901i
$615$		0			0
$616$	114.565	−	198.432i	0.185982	−	0.322130i
$617$	−55.5849	+	32.0919i	−0.0900889	+	0.0520129i	−0.544368	−	0.838847i	$-0.683230\pi$
$617$	−55.5849	+	32.0919i	−0.0900889	+	0.0520129i	0.454279	+	0.890860i	$0.349897\pi$
$618$		0			0
$619$	3.79581	+	6.57454i	0.00613217	+	0.0106212i	0.869075	−	0.494680i	$-0.164715\pi$
$619$	3.79581	+	6.57454i	0.00613217	+	0.0106212i	−0.862943	+	0.505301i	$0.831381\pi$
$620$	158.844	+	91.7086i	0.256200	+	0.147917i
$621$		0			0
$622$	84.8491	+	146.963i	0.136413	+	0.236275i
$623$	693.597	−	400.448i	1.11332	−	0.642774i
$624$		0			0
$625$	−263.904	+	457.096i	−0.422247	+	0.731354i
$626$			88.6105i			0.141550i
$627$		0			0
$628$	−224.128			−0.356891
$629$		−	1497.79i		−	2.38122i
$630$		0			0
$631$	423.578	−	733.658i	0.671280	−	1.16269i	−0.306262	−	0.951947i	$-0.599078\pi$
$631$	423.578	−	733.658i	0.671280	−	1.16269i	0.977541	−	0.210743i	$-0.0675884\pi$
$632$	−50.0584	+	28.9012i	−0.0792064	+	0.0457298i
$633$		0			0
$634$	−46.8538			−0.0739019
$635$		−	12.0065i		−	0.0189080i
$636$		0			0
$637$	176.182	+	234.088i	0.276581	+	0.367484i
$638$		−	305.911i		−	0.479484i
$639$		0			0
$640$	−50.4976	−	87.4644i	−0.0789025	−	0.136663i
$641$			1071.90i			1.67222i	0.548559	+	0.836112i	$0.315177\pi$
$641$			1071.90i			1.67222i	−0.548559	+	0.836112i	$0.684823\pi$
$642$		0			0
$643$	−205.775	−	356.413i	−0.320023	−	0.554297i	0.660469	−	0.750853i	$-0.270357\pi$
$643$	−205.775	−	356.413i	−0.320023	−	0.554297i	−0.980492	+	0.196557i	$0.937024\pi$
$644$	−249.961	+	144.315i	−0.388138	+	0.224092i
$645$		0			0
$646$	−226.798			−0.351080
$647$	872.018	−	503.460i	1.34779	−	0.778145i	0.359851	−	0.933010i	$-0.382828\pi$
$647$	872.018	−	503.460i	1.34779	−	0.778145i	0.987936	+	0.154865i	$0.0494943\pi$
$648$		0			0
$649$	331.661			0.511034
$650$	−92.4920	+	69.6125i	−0.142295	+	0.107096i
$651$		0			0
$652$	62.5161			0.0958836
$653$			1153.60i			1.76662i	0.468791	+	0.883309i	$0.344690\pi$
$653$			1153.60i			1.76662i	−0.468791	+	0.883309i	$0.655310\pi$
$654$		0			0
$655$	−49.2362	−	85.2796i	−0.0751698	−	0.130198i
$656$	−357.996	−	206.689i	−0.545725	−	0.315074i
$657$		0			0
$658$	−7.78061			−0.0118246
$659$		−	310.724i		−	0.471509i	−0.971813	−	0.235754i	$-0.924244\pi$
$659$		−	310.724i		−	0.471509i	0.971813	−	0.235754i	$-0.0757561\pi$
$660$		0			0
$661$	−515.710			−0.780197			−0.390099	−	0.920773i	$-0.627559\pi$
$661$	−515.710			−0.780197			−0.390099	+	0.920773i	$0.627559\pi$
$662$	108.957	+	62.9065i	0.164588	+	0.0950250i
$663$		0			0
$664$	122.347	+	211.911i	0.184257	+	0.319143i
$665$	−109.395	+	63.1595i	−0.164505	+	0.0949767i
$666$		0			0
$667$	−392.411	+	679.675i	−0.588322	+	1.01900i
$668$	104.545	−	60.3591i	0.156505	−	0.0903580i
$669$		0			0
$670$	−15.9843	−	27.6856i	−0.0238571	−	0.0413218i
$671$	135.084	+	77.9905i	0.201317	+	0.116230i
$672$		0			0
$673$	104.909	−	181.708i	0.155883	−	0.269997i	−0.777497	−	0.628886i	$-0.783511\pi$
$673$	104.909	−	181.708i	0.155883	−	0.269997i	0.933380	+	0.358889i	$0.116844\pi$
$674$	−121.114	+	69.9254i	−0.179695	+	0.103747i
$675$		0			0
$676$	632.919	−	157.014i	0.936270	−	0.232269i
$677$	−11.9220	+	6.88315i	−0.0176100	+	0.0101671i	−0.508779	−	0.860897i	$-0.669903\pi$
$677$	−11.9220	+	6.88315i	−0.0176100	+	0.0101671i	0.491169	+	0.871064i	$0.336570\pi$
$678$		0			0
$679$	100.002			0.147279
$680$	82.9159	−	47.8715i	0.121935	−	0.0703993i
$681$		0			0
$682$	234.579			0.343958
$683$	402.924	+	232.628i	0.589933	+	0.340598i	0.765071	−	0.643946i	$-0.222704\pi$
$683$	402.924	+	232.628i	0.589933	+	0.340598i	−0.175138	+	0.984544i	$0.556037\pi$
$684$		0			0
$685$	63.7691	−	110.451i	0.0930936	−	0.161243i
$686$	−119.840	−	69.1898i	−0.174694	−	0.100860i
$687$		0			0
$688$	−301.205	+	521.703i	−0.437799	+	0.758289i
$689$	−131.436	+	98.9226i	−0.190763	+	0.143574i
$690$		0			0
$691$	259.190	−	448.930i	0.375094	−	0.649681i	−0.615247	−	0.788334i	$-0.710944\pi$
$691$	259.190	−	448.930i	0.375094	−	0.649681i	0.990341	+	0.138653i	$0.0442772\pi$
$692$	14.4437	−	8.33907i	0.0208724	−	0.0120507i
$693$		0			0
$694$	64.2258			0.0925443
$695$		−	232.968i		−	0.335206i
$696$		0			0
$697$	407.081	−	705.086i	0.584048	−	1.01160i
$698$	−43.8709	+	25.3289i	−0.0628522	+	0.0362878i
$699$		0			0
$700$	−235.028	+	407.080i	−0.335754	+	0.581543i
$701$		−	775.035i		−	1.10561i	−0.833310	−	0.552806i	$-0.813557\pi$
$701$		−	775.035i		−	1.10561i	0.833310	−	0.552806i	$-0.186443\pi$
$702$		0			0
$703$	1135.16			1.61474
$704$	663.412	+	383.021i	0.942347	+	0.544064i
$705$		0			0
$706$	23.8733	+	41.3498i	0.0338149	+	0.0585691i
$707$	−369.298	−	213.214i	−0.522345	−	0.301576i
$708$		0			0
$709$	617.138			0.870435			0.435217	−	0.900325i	$-0.356671\pi$
$709$	617.138			0.870435			0.435217	+	0.900325i	$0.356671\pi$
$710$		−	17.0505i		−	0.0240147i
$711$		0			0
$712$	−230.034	−	398.431i	−0.323082	−	0.559594i
$713$	−521.190	−	300.909i	−0.730982	−	0.422033i
$714$		0			0
$715$	−88.0546	+	207.105i	−0.123153	+	0.289657i
$716$	6.17230	+	3.56358i	0.00862052	+	0.00497706i
$717$		0			0
$718$	−83.4513	+	144.542i	−0.116227	+	0.201312i
$719$	−534.714	−	308.717i	−0.743692	−	0.429371i	0.0797184	−	0.996817i	$-0.474598\pi$
$719$	−534.714	−	308.717i	−0.743692	−	0.429371i	−0.823410	+	0.567447i	$0.807931\pi$
$720$		0			0
$721$	−196.879	+	341.004i	−0.273064	+	0.472960i
$722$		−	36.1420i		−	0.0500582i
$723$		0			0
$724$	20.7089	+	35.8688i	0.0286034	+	0.0495426i
$725$			1278.14i			1.76295i
$726$		0			0
$727$	−527.853	−	914.268i	−0.726070	−	1.25759i	−0.958532	−	0.284984i	$-0.908012\pi$
$727$	−527.853	−	914.268i	−0.726070	−	1.25759i	0.232462	−	0.972605i	$-0.425322\pi$
$728$	−157.896	+	118.838i	−0.216890	+	0.163239i
$729$		0			0
$730$	14.0988	+	24.4199i	0.0193134	+	0.0334519i
$731$	−1027.51	−	593.235i	−1.40563	−	0.811539i
$732$		0			0
$733$	435.712	−	754.675i	0.594422	−	1.02957i	−0.399206	−	0.916861i	$-0.630714\pi$
$733$	435.712	−	754.675i	0.594422	−	1.02957i	0.993628	−	0.112708i	$-0.0359526\pi$
$734$	37.8318	−	21.8422i	0.0515419	−	0.0297577i
$735$		0			0
$736$	125.097	+	216.674i	0.169968	+	0.294394i
$737$	966.253	+	557.866i	1.31106	+	0.756942i
$738$		0			0
$739$	38.1201	+	66.0259i	0.0515833	+	0.0893449i	0.890664	−	0.454662i	$-0.150240\pi$
$739$	38.1201	+	66.0259i	0.0515833	+	0.0893449i	−0.839081	+	0.544007i	$0.816907\pi$
$740$	−203.770	+	117.647i	−0.275365	+	0.158982i
$741$		0			0
$742$	12.2388	−	21.1983i	0.0164944	−	0.0285691i
$743$		−	492.520i		−	0.662880i	−0.943476	−	0.331440i	$-0.892466\pi$
$743$		−	492.520i		−	0.662880i	0.943476	−	0.331440i	$-0.107534\pi$
$744$		0			0
$745$	−270.157			−0.362627
$746$		−	79.3373i		−	0.106350i
$747$		0			0
$748$	−820.349	+	1420.89i	−1.09672	+	1.89958i
$749$	106.376	−	61.4160i	0.142024	−	0.0819974i
$750$		0			0
$751$	394.887			0.525815			0.262907	−	0.964821i	$-0.415319\pi$
$751$	394.887			0.525815			0.262907	+	0.964821i	$0.415319\pi$
$752$		−	57.6120i		−	0.0766117i
$753$		0			0
$754$	−103.234	+	242.807i	−0.136915	+	0.322026i
$755$		−	306.117i		−	0.405453i
$756$		0			0
$757$	45.1326	+	78.1720i	0.0596204	+	0.103266i	0.894295	−	0.447478i	$-0.147678\pi$
$757$	45.1326	+	78.1720i	0.0596204	+	0.103266i	−0.834675	+	0.550743i	$0.814344\pi$
$758$		−	143.555i		−	0.189387i
$759$		0			0
$760$	36.2815	+	62.8414i	0.0477388	+	0.0826860i
$761$	649.252	−	374.846i	0.853156	−	0.492570i	−0.00855819	−	0.999963i	$-0.502724\pi$
$761$	649.252	−	374.846i	0.853156	−	0.492570i	0.861715	+	0.507393i	$0.169391\pi$
$762$		0			0
$763$	30.0537			0.0393889
$764$	220.296	−	127.188i	0.288346	−	0.166477i
$765$		0			0
$766$	95.4934			0.124665
$767$	−263.246	−	111.924i	−0.343215	−	0.145924i
$768$		0			0
$769$	−13.5920			−0.0176749			−0.00883743	−	0.999961i	$-0.502813\pi$
$769$	−13.5920			−0.0176749			−0.00883743	+	0.999961i	$0.502813\pi$
$770$		−	33.4866i		−	0.0434891i
$771$		0			0
$772$	215.809	+	373.792i	0.279545	+	0.484186i
$773$	−20.8183	−	12.0195i	−0.0269318	−	0.0155491i	0.486474	−	0.873695i	$-0.338283\pi$
$773$	−20.8183	−	12.0195i	−0.0269318	−	0.0155491i	−0.513405	+	0.858146i	$0.671616\pi$
$774$		0			0
$775$	−980.106			−1.26465
$776$		−	57.4455i		−	0.0740277i
$777$		0			0
$778$	126.521			0.162623
$779$	534.379	+	308.524i	0.685981	+	0.396052i
$780$		0			0
$781$	297.538	+	515.351i	0.380971	+	0.659861i
$782$	−133.582	+	77.1236i	−0.170821	+	0.0986235i
$783$		0			0
$784$	161.400	−	279.554i	0.205868	−	0.356574i
$785$	−57.7739	+	33.3558i	−0.0735974	+	0.0424915i
$786$		0			0
$787$	282.354	+	489.052i	0.358773	+	0.621413i	0.987756	−	0.156006i	$-0.0498619\pi$
$787$	282.354	+	489.052i	0.358773	+	0.621413i	−0.628983	+	0.777419i	$0.716529\pi$
$788$	−39.2460	−	22.6587i	−0.0498046	−	0.0287547i
$789$		0			0
$790$	−4.22383	+	7.31589i	−0.00534663	+	0.00926063i
$791$	594.388	−	343.170i	0.751439	−	0.433843i
$792$		0			0
$793$	−80.8994	−	107.489i	−0.102017	−	0.135547i
$794$	−81.3178	+	46.9488i	−0.102415	+	0.0591295i
$795$		0			0
$796$	−71.2936			−0.0895648
$797$	355.367	−	205.171i	0.445880	−	0.257429i	−0.260208	−	0.965552i	$-0.583791\pi$
$797$	355.367	−	205.171i	0.445880	−	0.257429i	0.706089	+	0.708123i	$0.250458\pi$
$798$		0			0
$799$	113.469			0.142014
$800$	352.869	+	203.729i	0.441087	+	0.254662i
$801$		0			0
$802$	−105.838	+	183.318i	−0.131968	+	0.228576i
$803$	−852.275	−	492.061i	−1.06136	−	0.612779i
$804$		0			0
$805$	−42.9553	+	74.4008i	−0.0533607	+	0.0924234i
$806$	−186.190	−	79.1623i	−0.231005	−	0.0982163i
$807$		0			0
$808$	−122.479	+	212.140i	−0.151583	+	0.262550i
$809$	−518.289	+	299.234i	−0.640654	+	0.369882i	−0.784867	−	0.619665i	$-0.787269\pi$
$809$	−518.289	+	299.234i	−0.640654	+	0.369882i	0.144212	+	0.989547i	$0.453935\pi$
$810$		0			0
$811$	−427.373			−0.526971			−0.263485	−	0.964663i	$-0.584872\pi$
$811$	−427.373			−0.526971			−0.263485	+	0.964663i	$0.584872\pi$
$812$			1071.35i			1.31939i
$813$		0			0
$814$	−150.463	+	260.610i	−0.184844	+	0.320159i
$815$	16.1149	−	9.30395i	0.0197729	−	0.0114159i
$816$		0			0
$817$	449.609	−	778.745i	0.550317	−	0.953177i
$818$			278.426i			0.340374i
$819$		0			0
$820$	−127.900			−0.155976
$821$	446.131	+	257.574i	0.543399	+	0.313732i	0.746455	−	0.665435i	$-0.231754\pi$
$821$	446.131	+	257.574i	0.543399	+	0.313732i	−0.203056	+	0.979167i	$0.565087\pi$
$822$		0			0
$823$	496.291	+	859.601i	0.603026	+	1.04447i	0.992360	+	0.123376i	$0.0393720\pi$
$823$	496.291	+	859.601i	0.603026	+	1.04447i	−0.389334	+	0.921097i	$0.627295\pi$
$824$	195.887	+	113.095i	0.237727	+	0.137252i
$825$		0			0
$826$	42.5640			0.0515303
$827$			943.762i			1.14119i	0.821233	+	0.570594i	$0.193287\pi$
$827$			943.762i			1.14119i	−0.821233	+	0.570594i	$0.806713\pi$
$828$		0			0
$829$	133.486	+	231.205i	0.161021	+	0.278896i	0.935235	−	0.354027i	$-0.115188\pi$
$829$	133.486	+	231.205i	0.161021	+	0.278896i	−0.774214	+	0.632924i	$0.781855\pi$
$830$	30.9702	+	17.8807i	0.0373135	+	0.0215430i
$831$		0			0
$832$	−397.307	−	527.890i	−0.477533	−	0.634483i
$833$	550.591	+	317.884i	0.660974	+	0.381614i
$834$		0			0
$835$	17.9659	−	31.1178i	0.0215160	−	0.0372668i
$836$	−1076.88	−	621.737i	−1.28813	−	0.743704i
$837$		0			0
$838$	84.0886	−	145.646i	0.100344	−	0.173802i
$839$			811.237i			0.966909i	0.875369	+	0.483455i	$0.160618\pi$
$839$			811.237i			0.966909i	−0.875369	+	0.483455i	$0.839382\pi$
$840$		0			0
$841$	1036.06	+	1794.51i	1.23194	+	2.13379i
$842$		−	119.916i		−	0.142418i
$843$		0			0
$844$	−50.5129	−	87.4909i	−0.0598494	−	0.103662i
$845$	139.781	−	134.668i	0.165422	−	0.159370i
$846$		0			0
$847$	273.131	+	473.076i	0.322468	+	0.558531i
$848$	156.964	+	90.6231i	0.185099	+	0.106867i
$849$		0			0
$850$	−125.601	+	217.548i	−0.147766	+	0.255939i
$851$	668.601	−	386.017i	0.785665	−	0.453604i
$852$		0			0
$853$	294.569	+	510.209i	0.345333	+	0.598135i	0.985414	−	0.170173i	$-0.0544326\pi$
$853$	294.569	+	510.209i	0.345333	+	0.598135i	−0.640081	+	0.768307i	$0.721099\pi$
$854$	17.3361	+	10.0090i	0.0202998	+	0.0117201i
$855$		0			0
$856$	−35.2799	−	61.1067i	−0.0412149	−	0.0713863i
$857$	−1354.80	+	782.195i	−1.58086	+	0.912713i	−0.586131	+	0.810216i	$0.699350\pi$
$857$	−1354.80	+	782.195i	−1.58086	+	0.912713i	−0.994733	+	0.102496i	$0.967317\pi$
$858$		0			0
$859$	219.269	−	379.785i	0.255261	−	0.442124i	−0.709706	−	0.704498i	$-0.751172\pi$
$859$	219.269	−	379.785i	0.255261	−	0.442124i	0.964966	+	0.262374i	$0.0845054\pi$
$860$			186.388i			0.216730i
$861$		0			0
$862$	44.1051			0.0511660
$863$			1057.49i			1.22536i	0.790331	+	0.612680i	$0.209909\pi$
$863$			1057.49i			1.22536i	−0.790331	+	0.612680i	$0.790091\pi$
$864$		0			0
$865$	2.48212	−	4.29916i	0.00286951	−	0.00497013i
$866$	137.763	−	79.5376i	0.159080	−	0.0918448i
$867$		0			0
$868$	−821.533			−0.946467
$869$		−	294.831i		−	0.339277i
$870$		0			0
$871$	−578.674	−	768.866i	−0.664378	−	0.882739i
$872$		−	17.2641i		−	0.0197983i
$873$		0			0
$874$	−58.4514	−	101.241i	−0.0668781	−	0.115836i
$875$			287.617i			0.328705i
$876$		0			0
$877$	−76.3797	−	132.293i	−0.0870920	−	0.150848i	0.819189	−	0.573524i	$-0.194424\pi$
$877$	−76.3797	−	132.293i	−0.0870920	−	0.150848i	−0.906281	+	0.422676i	$0.861091\pi$
$878$	87.4751	−	50.5038i	0.0996299	−	0.0575214i
$879$		0			0
$880$	247.953			0.281765
$881$	1343.46	−	775.645i	1.52492	−	0.880414i	0.525358	−	0.850882i	$-0.323932\pi$
$881$	1343.46	−	775.645i	1.52492	−	0.880414i	0.999564	−	0.0295323i	$-0.00940179\pi$
$882$		0			0
$883$	−613.125			−0.694366			−0.347183	−	0.937797i	$-0.612862\pi$
$883$	−613.125			−0.694366			−0.347183	+	0.937797i	$0.612862\pi$
$884$	1130.63	−	850.946i	1.27899	−	0.962609i
$885$		0			0
$886$	−14.4516			−0.0163110
$887$		−	935.026i		−	1.05414i	−0.849821	−	0.527072i	$-0.823290\pi$
$887$		−	935.026i		−	1.05414i	0.849821	−	0.527072i	$-0.176710\pi$
$888$		0			0
$889$	26.8889	+	46.5729i	0.0302462	+	0.0523880i
$890$	−58.2295	−	33.6188i	−0.0654265	−	0.0377740i
$891$		0			0
$892$	−1246.02			−1.39688
$893$			85.9973i			0.0963016i
$894$		0			0
$895$	2.12140			0.00237027
$896$	391.756	+	226.181i	0.437228	+	0.252434i
$897$		0			0
$898$	−113.323	−	196.281i	−0.126195	−	0.218575i
$899$	−1934.57	+	1116.93i	−2.15192	+	1.24241i
$900$		0			0
$901$	−178.486	+	309.146i	−0.198097	+	0.343115i
$902$	−141.662	+	81.7884i	−0.157053	+	0.0906745i
$903$		0			0
$904$	−197.131	−	341.442i	−0.218066	−	0.377701i
$905$	10.6764	+	6.16400i	0.0117971	+	0.00681105i
$906$		0			0
$907$	−574.524	+	995.104i	−0.633433	+	1.09714i	0.353412	+	0.935468i	$0.385021\pi$
$907$	−574.524	+	995.104i	−0.633433	+	1.09714i	−0.986845	+	0.161670i	$0.948312\pi$
$908$	847.173	−	489.116i	0.933010	−	0.538674i
$909$		0			0
$910$	−11.3006	+	26.5790i	−0.0124182	+	0.0292077i
$911$	−443.854	+	256.259i	−0.487216	+	0.281294i	−0.723419	−	0.690410i	$-0.757430\pi$
$911$	−443.854	+	256.259i	−0.487216	+	0.281294i	0.236203	+	0.971704i	$0.424097\pi$
$912$		0			0
$913$	−1248.10			−1.36703
$914$	−84.5397	+	48.8090i	−0.0924942	+	0.0534015i
$915$		0			0
$916$	−921.791			−1.00632
$917$	381.971	+	220.531i	0.416544	+	0.240492i
$918$		0			0
$919$	314.275	−	544.341i	0.341975	−	0.592318i	−0.642824	−	0.766014i	$-0.722237\pi$
$919$	314.275	−	544.341i	0.341975	−	0.592318i	0.984799	+	0.173695i	$0.0555708\pi$
$920$	42.7390	+	24.6754i	0.0464554	+	0.0268210i
$921$		0			0
$922$	100.485	−	174.046i	0.108986	−	0.188770i
$923$	−62.2489	−	509.453i	−0.0674420	−	0.551954i
$924$		0			0
$925$	628.657	−	1088.87i	0.679629	−	1.17715i
$926$	−200.265	+	115.623i	−0.216269	+	0.124863i
$927$		0			0
$928$	928.677			1.00073
$929$			234.522i			0.252446i	0.992002	+	0.126223i	$0.0402855\pi$
$929$			234.522i			0.252446i	−0.992002	+	0.126223i	$0.959714\pi$
$930$		0			0
$931$	−240.922	+	417.289i	−0.258778	+	0.448216i
$932$	143.405	−	82.7950i	0.153868	−	0.0888358i
$933$		0			0
$934$	−46.4564	+	80.4649i	−0.0497392	+	0.0861508i
$935$			488.353i			0.522303i
$936$		0			0
$937$	−598.868			−0.639133			−0.319567	−	0.947564i	$-0.603537\pi$
$937$	−598.868			−0.639133			−0.319567	+	0.947564i	$0.603537\pi$
$938$	124.005	+	71.5943i	0.132201	+	0.0763265i
$939$		0			0
$940$	−8.91267	−	15.4372i	−0.00948156	−	0.0164225i
$941$	219.420	+	126.682i	0.233178	+	0.134625i	0.612037	−	0.790829i	$-0.290350\pi$
$941$	219.420	+	126.682i	0.233178	+	0.134625i	−0.378859	+	0.925454i	$0.623684\pi$
$942$		0			0
$943$	419.660			0.445026
$944$			315.167i			0.333864i
$945$		0			0
$946$	119.189	+	206.442i	0.125993	+	0.218226i
$947$	1345.27	+	776.694i	1.42056	+	0.820163i	0.996347	−	0.0853978i	$-0.0272161\pi$
$947$	1345.27	+	776.694i	1.42056	+	0.820163i	0.424217	+	0.905561i	$0.360549\pi$
$948$		0			0
$949$	510.414	+	678.172i	0.537844	+	0.714617i
$950$	−164.878	−	95.1925i	−0.173556	−	0.100203i
$951$		0			0
$952$	−214.418	+	371.383i	−0.225229	+	0.390109i
$953$	373.494	+	215.637i	0.391914	+	0.226272i	0.682989	−	0.730429i	$-0.260680\pi$
$953$	373.494	+	215.637i	0.391914	+	0.226272i	−0.291075	+	0.956700i	$0.594013\pi$
$954$		0			0
$955$	37.8575	−	65.5711i	0.0396414	−	0.0686609i
$956$			298.754i			0.312504i
$957$		0			0
$958$	154.227	+	267.129i	0.160989	+	0.278841i
$959$			571.249i			0.595671i
$960$		0			0
$961$	−375.984	−	651.223i	−0.391242	−	0.677651i
$962$	207.372	−	156.075i	0.215564	−	0.162240i
$963$		0			0
$964$	184.768	+	320.028i	0.191668	+	0.331980i
$965$	111.259	+	64.2354i	0.115294	+	0.0665652i
$966$		0			0
$967$	548.133	−	949.394i	0.566839	−	0.981794i	−0.430037	−	0.902811i	$-0.641500\pi$
$967$	548.133	−	949.394i	0.566839	−	0.981794i	0.996876	−	0.0789825i	$-0.0251671\pi$
$968$	271.755	−	156.898i	0.280738	−	0.162084i
$969$		0			0
$970$	−4.19775	−	7.27071i	−0.00432757	−	0.00749558i
$971$	88.2684	+	50.9618i	0.0909046	+	0.0524838i	0.544763	−	0.838590i	$-0.316620\pi$
$971$	88.2684	+	50.9618i	0.0909046	+	0.0524838i	−0.453859	+	0.891074i	$0.649953\pi$
$972$		0			0
$973$	521.736	+	903.674i	0.536214	+	0.928750i
$974$	−239.346	+	138.187i	−0.245735	+	0.141875i
$975$		0			0
$976$	−74.1120	+	128.366i	−0.0759345	+	0.131522i
$977$		−	1009.99i		−	1.03377i	−0.856054	−	0.516886i	$-0.827091\pi$
$977$		−	1009.99i		−	1.03377i	0.856054	−	0.516886i	$-0.172909\pi$
$978$		0			0
$979$	2346.66			2.39699
$980$		−	99.8756i		−	0.101914i
$981$		0			0
$982$	24.5534	−	42.5278i	0.0250035	−	0.0433073i
$983$	1248.07	−	720.573i	1.26965	−	0.733035i	0.294731	−	0.955580i	$-0.404770\pi$
$983$	1248.07	−	720.573i	1.26965	−	0.733035i	0.974922	+	0.222546i	$0.0714367\pi$
$984$		0			0
$985$	−13.4887			−0.0136941
$986$			572.540i			0.580669i
$987$		0			0
$988$	644.926	+	856.894i	0.652759	+	0.867302i
$989$		−	611.566i		−	0.618368i
$990$		0			0
$991$	−698.522	−	1209.87i	−0.704865	−	1.22086i	−0.966740	−	0.255761i	$-0.917674\pi$
$991$	−698.522	−	1209.87i	−0.704865	−	1.22086i	0.261875	−	0.965102i	$-0.415659\pi$
$992$			712.130i			0.717873i
$993$		0			0
$994$	38.1848	+	66.1381i	0.0384153	+	0.0665373i
$995$	−18.3775	+	10.6103i	−0.0184699	+	0.0106636i
$996$		0			0
$997$	−1364.39			−1.36849			−0.684247	−	0.729250i	$-0.739869\pi$
$997$	−1364.39			−1.36849			−0.684247	+	0.729250i	$0.739869\pi$
$998$	−9.42691	+	5.44263i	−0.00944580	+	0.00545354i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.3.u.a.341.13		52
3.2	odd	2		117.3.u.a.68.14	yes	52
9.2	odd	6		351.3.k.a.224.13		52
9.7	even	3		117.3.k.a.29.14	✓	52
13.9	even	3		351.3.k.a.152.14		52
39.35	odd	6		117.3.k.a.113.13	yes	52
117.61	even	3		117.3.u.a.74.14	yes	52
117.74	odd	6	inner	351.3.u.a.35.13		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.14	✓	52	9.7	even	3
117.3.k.a.113.13	yes	52	39.35	odd	6
117.3.u.a.68.14	yes	52	3.2	odd	2
117.3.u.a.74.14	yes	52	117.61	even	3
351.3.k.a.152.14		52	13.9	even	3
351.3.k.a.224.13		52	9.2	odd	6
351.3.u.a.35.13		52	117.74	odd	6	inner
351.3.u.a.341.13		52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	351.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.325651 + 0.188014i) q^{2} +(-1.92930 - 3.34165i) q^{4} +(-0.994641 - 0.574256i) q^{5} +5.14423 q^{7} -2.95506i q^{8} +(-0.215937 - 0.374014i) q^{10} +(13.0534 + 7.53640i) q^{11} +(-7.81749 - 10.3869i) q^{13} +(1.67522 + 0.967190i) q^{14} +(-7.16161 + 12.4043i) q^{16} +(-24.4307 - 14.1051i) q^{17} +(10.6901 - 18.5158i) q^{19} +4.43165i q^{20} +(2.83390 + 4.90847i) q^{22} -14.5409i q^{23} +(-11.8405 - 20.5083i) q^{25} +(-0.592890 - 4.85229i) q^{26} +(-9.92477 - 17.1902i) q^{28} +(-46.7423 - 26.9867i) q^{29} +(20.6940 - 35.8431i) q^{31} +(-14.9010 + 8.60310i) q^{32} +(-5.30391 - 9.18664i) q^{34} +(-5.11666 - 2.95411i) q^{35} +(26.5470 + 45.9807i) q^{37} +(6.96249 - 4.01980i) q^{38} +(-1.69696 + 2.93923i) q^{40} +28.8607i q^{41} +42.0583 q^{43} -58.1599i q^{44} +(2.73390 - 4.73525i) q^{46} +(-3.48340 + 2.01114i) q^{47} -22.5369 q^{49} -8.90471i q^{50} +(-19.6269 + 46.1627i) q^{52} -12.6540i q^{53} +(-8.65564 - 14.9920i) q^{55} -15.2015i q^{56} +(-10.1478 - 17.5765i) q^{58} +(19.0560 - 11.0020i) q^{59} +10.3485 q^{61} +(13.4780 - 7.78155i) q^{62} +50.8229 q^{64} +(1.81087 + 14.8204i) q^{65} +74.0229 q^{67} +108.852i q^{68} +(-1.11083 - 1.92401i) q^{70} +(34.1908 + 19.7401i) q^{71} -65.2913 q^{73} +19.9649i q^{74} -82.4979 q^{76} +(67.1498 + 38.7690i) q^{77} +(-9.78025 - 16.9399i) q^{79} +(14.2465 - 8.22520i) q^{80} +(-5.42622 + 9.39850i) q^{82} +(-71.7112 + 41.4025i) q^{83} +(16.1998 + 28.0589i) q^{85} +(13.6963 + 7.90758i) q^{86} +(22.2705 - 38.5737i) q^{88} +(134.830 - 77.8441i) q^{89} +(-40.2150 - 53.4324i) q^{91} +(-48.5905 + 28.0538i) q^{92} -1.51249 q^{94} +(-21.2657 + 12.2777i) q^{95} +19.4397 q^{97} +(-7.33915 - 4.23726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} + 49 q^{4} + 6 q^{5} + 2 q^{7} - 6 q^{10} - 33 q^{11} + 4 q^{13} + 6 q^{14} - 83 q^{16} + 5 q^{19} - 15 q^{22} + 88 q^{25} - 132 q^{26} - 22 q^{28} + 30 q^{29} + 14 q^{31} + 63 q^{32} - 6 q^{34}+ \cdots - 405 q^{98}+O(q^{100}) \) 52 * q + 3 * q^2 + 49 * q^4 + 6 * q^5 + 2 * q^7 - 6 * q^10 - 33 * q^11 + 4 * q^13 + 6 * q^14 - 83 * q^16 + 5 * q^19 - 15 * q^22 + 88 * q^25 - 132 * q^26 - 22 * q^28 + 30 * q^29 + 14 * q^31 + 63 * q^32 - 6 * q^34 + 228 * q^35 - 13 * q^37 + 192 * q^38 + 72 * q^40 + 62 * q^43 + 6 * q^46 + 69 * q^47 + 246 * q^49 + 112 * q^52 - 27 * q^55 - 105 * q^58 + 435 * q^59 - 16 * q^61 + 471 * q^62 - 98 * q^64 + 435 * q^65 + 68 * q^67 - 57 * q^70 + 144 * q^71 - 106 * q^73 + 158 * q^76 - 282 * q^77 - 25 * q^79 - 1050 * q^80 + 81 * q^82 - 219 * q^83 + 54 * q^85 + 24 * q^86 - 15 * q^88 + 99 * q^89 + 2 * q^91 - 888 * q^92 - 606 * q^94 + 258 * q^95 - 424 * q^97 - 405 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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