LMFDB - Embedded newform 336.7.bh.d.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.2
Root			$2.26350 - 3.92050i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.d.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 + 7.79423i) q^{3} +(-57.9943 + 33.4830i) q^{5} +(240.457 - 244.600i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 + 7.79423i) q^{3} +(-57.9943 + 33.4830i) q^{5} +(240.457 - 244.600i) q^{7} +(121.500 + 210.444i) q^{9} +(862.868 - 1494.53i) q^{11} -2807.43i q^{13} -1043.90 q^{15} +(-5323.58 - 3073.57i) q^{17} +(-7737.30 + 4467.13i) q^{19} +(5152.64 - 1427.92i) q^{21} +(4950.64 + 8574.76i) q^{23} +(-5570.27 + 9648.00i) q^{25} +3788.00i q^{27} -13610.4 q^{29} +(21833.0 + 12605.3i) q^{31} +(23297.4 - 13450.8i) q^{33} +(-5755.21 + 22236.7i) q^{35} +(-11366.4 - 19687.1i) q^{37} +(21881.7 - 37900.2i) q^{39} +37897.2i q^{41} -73646.2 q^{43} +(-14092.6 - 8136.38i) q^{45} +(-120523. + 69583.9i) q^{47} +(-2009.47 - 117632. i) q^{49} +(-47912.2 - 82986.3i) q^{51} +(8258.79 - 14304.7i) q^{53} +115566. i q^{55} -139271. q^{57} +(61989.7 + 35789.8i) q^{59} +(-228557. + 131958. i) q^{61} +(80690.3 + 20883.9i) q^{63} +(94001.1 + 162815. i) q^{65} +(274333. - 475159. i) q^{67} +154346. i q^{69} -465655. q^{71} +(-289020. - 166866. i) q^{73} +(-150397. + 86832.0i) q^{75} +(-158080. - 570429. i) q^{77} +(-205012. - 355091. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +71948.9i q^{83} +411649. q^{85} +(-183740. - 106082. i) q^{87} +(-141505. + 81698.0i) q^{89} +(-686697. - 675066. i) q^{91} +(196497. + 340342. i) q^{93} +(299146. - 518137. i) q^{95} -651914. i q^{97} +419354. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$4$		0			0
$5$	−57.9943	+	33.4830i	−0.463955	+	0.267864i	−0.713706	−	0.700446i	$-0.752985\pi$
$5$	−57.9943	+	33.4830i	−0.463955	+	0.267864i	0.249751	+	0.968310i	$0.419651\pi$
$6$		0			0
$7$	240.457	−	244.600i	0.701042	−	0.713120i
$7$	240.457	−	244.600i	0.701042	−	0.713120i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	862.868	−	1494.53i	0.648285	−	1.12286i	−0.335247	−	0.942130i	$-0.608820\pi$
$11$	862.868	−	1494.53i	0.648285	−	1.12286i	0.983532	−	0.180733i	$-0.0578470\pi$
$12$		0			0
$13$		−	2807.43i		−	1.27785i	−0.769271	−	0.638923i	$-0.779380\pi$
$13$		−	2807.43i		−	1.27785i	0.769271	−	0.638923i	$-0.220620\pi$
$14$		0			0
$15$	−1043.90			−0.309303
$16$		0			0
$17$	−5323.58	−	3073.57i	−1.08357	−	0.625599i	−0.151712	−	0.988425i	$-0.548479\pi$
$17$	−5323.58	−	3073.57i	−1.08357	−	0.625599i	−0.931857	+	0.362826i	$0.881812\pi$
$18$		0			0
$19$	−7737.30	+	4467.13i	−1.12805	+	0.651281i	−0.943444	−	0.331532i	$-0.892435\pi$
$19$	−7737.30	+	4467.13i	−1.12805	+	0.651281i	−0.184607	+	0.982812i	$0.559101\pi$
$20$		0			0
$21$	5152.64	−	1427.92i	0.556381	−	0.154187i
$22$		0			0
$23$	4950.64	+	8574.76i	0.406891	+	0.704755i	0.994540	−	0.104361i	$-0.0332796\pi$
$23$	4950.64	+	8574.76i	0.406891	+	0.704755i	−0.587649	+	0.809116i	$0.699946\pi$
$24$		0			0
$25$	−5570.27	+	9648.00i	−0.356497	+	0.617472i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−13610.4			−0.558054			−0.279027	−	0.960283i	$-0.590012\pi$
$29$	−13610.4			−0.558054			−0.279027	+	0.960283i	$0.590012\pi$
$30$		0			0
$31$	21833.0	+	12605.3i	0.732871	+	0.423123i	0.819472	−	0.573120i	$-0.194267\pi$
$31$	21833.0	+	12605.3i	0.732871	+	0.423123i	−0.0866007	+	0.996243i	$0.527600\pi$
$32$		0			0
$33$	23297.4	−	13450.8i	0.648285	−	0.374288i
$34$		0			0
$35$	−5755.21	+	22236.7i	−0.134232	+	0.518639i
$36$		0			0
$37$	−11366.4	−	19687.1i	−0.224397	−	0.388666i	0.731742	−	0.681582i	$-0.238708\pi$
$37$	−11366.4	−	19687.1i	−0.224397	−	0.388666i	−0.956138	+	0.292916i	$0.905374\pi$
$38$		0			0
$39$	21881.7	−	37900.2i	0.368882	−	0.638923i
$40$		0			0
$41$			37897.2i			0.549865i	0.961464	+	0.274932i	$0.0886554\pi$
$41$			37897.2i			0.549865i	−0.961464	+	0.274932i	$0.911345\pi$
$42$		0			0
$43$	−73646.2			−0.926286			−0.463143	−	0.886284i	$-0.653278\pi$
$43$	−73646.2			−0.926286			−0.463143	+	0.886284i	$0.653278\pi$
$44$		0			0
$45$	−14092.6	−	8136.38i	−0.154652	−	0.0892881i
$46$		0			0
$47$	−120523.	+	69583.9i	−1.16085	+	0.670216i	−0.951507	−	0.307626i	$-0.900465\pi$
$47$	−120523.	+	69583.9i	−1.16085	+	0.670216i	−0.209342	+	0.977843i	$0.567132\pi$
$48$		0			0
$49$	−2009.47	−	117632.i	−0.0170802	−	0.999854i
$50$		0			0
$51$	−47912.2	−	82986.3i	−0.361190	−	0.625599i
$52$		0			0
$53$	8258.79	−	14304.7i	0.0554739	−	0.0960837i	−0.836955	−	0.547272i	$-0.815666\pi$
$53$	8258.79	−	14304.7i	0.0554739	−	0.0960837i	0.892429	+	0.451188i	$0.149000\pi$
$54$		0			0
$55$			115566.i			0.694610i
$56$		0			0
$57$	−139271.			−0.752034
$58$		0			0
$59$	61989.7	+	35789.8i	0.301831	+	0.174262i	0.643265	−	0.765644i	$-0.277579\pi$
$59$	61989.7	+	35789.8i	0.301831	+	0.174262i	−0.341434	+	0.939906i	$0.610913\pi$
$60$		0			0
$61$	−228557.	+	131958.i	−1.00695	+	0.581360i	−0.910296	−	0.413958i	$-0.864146\pi$
$61$	−228557.	+	131958.i	−1.00695	+	0.581360i	−0.0966496	+	0.995318i	$0.530813\pi$
$62$		0			0
$63$	80690.3	+	20883.9i	0.322700	+	0.0835201i
$64$		0			0
$65$	94001.1	+	162815.i	0.342289	+	0.592862i
$66$		0			0
$67$	274333.	−	475159.i	0.912125	−	1.57985i	0.101068	−	0.994880i	$-0.467774\pi$
$67$	274333.	−	475159.i	0.912125	−	1.57985i	0.811057	−	0.584967i	$-0.198893\pi$
$68$		0			0
$69$			154346.i			0.469837i
$70$		0			0
$71$	−465655.			−1.30103			−0.650517	−	0.759491i	$-0.725448\pi$
$71$	−465655.			−1.30103			−0.650517	+	0.759491i	$0.725448\pi$
$72$		0			0
$73$	−289020.	−	166866.i	−0.742950	−	0.428942i	0.0801910	−	0.996780i	$-0.474447\pi$
$73$	−289020.	−	166866.i	−0.742950	−	0.428942i	−0.823141	+	0.567837i	$0.807780\pi$
$74$		0			0
$75$	−150397.	+	86832.0i	−0.356497	+	0.205824i
$76$		0			0
$77$	−158080.	−	570429.i	−0.346261	−	1.24948i
$78$		0			0
$79$	−205012.	−	355091.i	−0.415813	−	0.720209i	0.579700	−	0.814830i	$-0.303170\pi$
$79$	−205012.	−	355091.i	−0.415813	−	0.720209i	−0.995513	+	0.0946203i	$0.969836\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			71948.9i			0.125832i	0.998019	+	0.0629158i	$0.0200400\pi$
$83$			71948.9i			0.125832i	−0.998019	+	0.0629158i	$0.979960\pi$
$84$		0			0
$85$	411649.			0.670302
$86$		0			0
$87$	−183740.	−	106082.i	−0.279027	−	0.161096i
$88$		0			0
$89$	−141505.	+	81698.0i	−0.200725	+	0.115889i	−0.596994	−	0.802246i	$-0.703638\pi$
$89$	−141505.	+	81698.0i	−0.200725	+	0.115889i	0.396269	+	0.918135i	$0.370305\pi$
$90$		0			0
$91$	−686697.	−	675066.i	−0.911257	−	0.895823i
$92$		0			0
$93$	196497.	+	340342.i	0.244290	+	0.423123i
$94$		0			0
$95$	299146.	−	518137.i	0.348910	−	0.604329i
$96$		0			0
$97$		−	651914.i		−	0.714291i	−0.934049	−	0.357146i	$-0.883750\pi$
$97$		−	651914.i		−	0.714291i	0.934049	−	0.357146i	$-0.116250\pi$
$98$		0			0
$99$	419354.			0.432190
$100$		0			0
$101$	883850.	+	510291.i	0.857856	+	0.495283i	0.863294	−	0.504702i	$-0.168398\pi$
$101$	883850.	+	510291.i	0.857856	+	0.495283i	−0.00543765	+	0.999985i	$0.501731\pi$
$102$		0			0
$103$	−363147.	+	209663.i	−0.332331	+	0.191871i	−0.656875	−	0.753999i	$-0.728122\pi$
$103$	−363147.	+	209663.i	−0.332331	+	0.191871i	0.324545	+	0.945870i	$0.394789\pi$
$104$		0			0
$105$	−251013.	+	255338.i	−0.216834	+	0.220570i
$106$		0			0
$107$	1.10621e6	+	1.91600e6i	0.902993	+	1.56403i	0.823589	+	0.567187i	$0.191968\pi$
$107$	1.10621e6	+	1.91600e6i	0.902993	+	1.56403i	0.0794039	+	0.996843i	$0.474698\pi$
$108$		0			0
$109$	−382955.	+	663297.i	−0.295711	+	0.512187i	−0.975150	−	0.221545i	$-0.928890\pi$
$109$	−382955.	+	663297.i	−0.295711	+	0.512187i	0.679439	+	0.733732i	$0.262223\pi$
$110$		0			0
$111$		−	354368.i		−	0.259111i
$112$		0			0
$113$	−2.66096e6			−1.84418			−0.922090	−	0.386976i	$-0.873520\pi$
$113$	−2.66096e6			−1.84418			−0.922090	+	0.386976i	$0.873520\pi$
$114$		0			0
$115$	−574218.	−	331525.i	−0.377558	−	0.217983i
$116$		0			0
$117$	590806.	−	341102.i	0.368882	−	0.212974i
$118$		0			0
$119$	−2.03189e6	+	563085.i	−1.20575	+	0.334144i
$120$		0			0
$121$	−603302.	−	1.04495e6i	−0.340548	−	0.589847i
$122$		0			0
$123$	−295380.	+	511612.i	−0.158732	+	0.274932i
$124$		0			0
$125$		−	1.79238e6i		−	0.917700i
$126$		0			0
$127$	1.11648e6			0.545055			0.272527	−	0.962148i	$-0.412141\pi$
$127$	1.11648e6			0.545055			0.272527	+	0.962148i	$0.412141\pi$
$128$		0			0
$129$	−994224.	−	574015.i	−0.463143	−	0.267396i
$130$		0			0
$131$	−247826.	+	143083.i	−0.110239	+	0.0636463i	−0.554106	−	0.832446i	$-0.686940\pi$
$131$	−247826.	+	143083.i	−0.110239	+	0.0636463i	0.443867	+	0.896093i	$0.353606\pi$
$132$		0			0
$133$	−767830.	+	2.96670e6i	−0.326370	+	1.26101i
$134$		0			0
$135$	−126834.	−	219682.i	−0.0515505	−	0.0892881i
$136$		0			0
$137$	1.86697e6	−	3.23368e6i	0.726063	−	1.25758i	−0.232472	−	0.972603i	$-0.574681\pi$
$137$	1.86697e6	−	3.23368e6i	0.726063	−	1.25758i	0.958535	−	0.284975i	$-0.0919854\pi$
$138$		0			0
$139$			618216.i			0.230195i	0.993354	+	0.115097i	$0.0367180\pi$
$139$			618216.i			0.230195i	−0.993354	+	0.115097i	$0.963282\pi$
$140$		0			0
$141$	−2.16941e6			−0.773899
$142$		0			0
$143$	−4.19579e6	−	2.42244e6i	−1.43485	−	0.828408i
$144$		0			0
$145$	789324.	−	455716.i	0.258911	−	0.149483i
$146$		0			0
$147$	889722.	−	1.60369e6i	0.280093	−	0.504858i
$148$		0			0
$149$	−1.86160e6	−	3.22438e6i	−0.562765	−	0.974737i	−0.997254	−	0.0740601i	$-0.976404\pi$
$149$	−1.86160e6	−	3.22438e6i	−0.562765	−	0.974737i	0.434489	−	0.900677i	$-0.356929\pi$
$150$		0			0
$151$	−1.27599e6	+	2.21009e6i	−0.370611	+	0.641917i	−0.989660	−	0.143436i	$-0.954185\pi$
$151$	−1.27599e6	+	2.21009e6i	−0.370611	+	0.641917i	0.619049	+	0.785352i	$0.287518\pi$
$152$		0			0
$153$		−	1.49375e6i		−	0.417066i
$154$		0			0
$155$	−1.68825e6			−0.453358
$156$		0			0
$157$	−5.87057e6	−	3.38938e6i	−1.51699	−	0.875832i	−0.999801	−	0.0199592i	$-0.993646\pi$
$157$	−5.87057e6	−	3.38938e6i	−1.51699	−	0.875832i	−0.517186	−	0.855873i	$-0.673020\pi$
$158$		0			0
$159$	222987.	−	128742.i	0.0554739	−	0.0320279i
$160$		0			0
$161$	3.28781e6	+	850937.i	0.787823	+	0.203901i
$162$		0			0
$163$	−4.13571e6	−	7.16325e6i	−0.954964	−	1.65405i	−0.734451	−	0.678662i	$-0.762560\pi$
$163$	−4.13571e6	−	7.16325e6i	−0.954964	−	1.65405i	−0.220513	−	0.975384i	$-0.570773\pi$
$164$		0			0
$165$	−900746.	+	1.56014e6i	−0.200517	+	0.347305i
$166$		0			0
$167$		−	2.59960e6i		−	0.558158i	−0.960268	−	0.279079i	$-0.909971\pi$
$167$		−	2.59960e6i		−	0.558158i	0.960268	−	0.279079i	$-0.0900291\pi$
$168$		0			0
$169$	−3.05483e6			−0.632888
$170$		0			0
$171$	−1.88016e6	−	1.08551e6i	−0.376017	−	0.217094i
$172$		0			0
$173$	−7.10612e6	+	4.10272e6i	−1.37244	+	0.792380i	−0.991235	−	0.132109i	$-0.957825\pi$
$173$	−7.10612e6	+	4.10272e6i	−1.37244	+	0.792380i	−0.381208	+	0.924489i	$0.624492\pi$
$174$		0			0
$175$	1.02049e6	+	3.68242e6i	0.190412	+	0.687099i
$176$		0			0
$177$	557907.	+	966324.i	0.100610	+	0.174262i
$178$		0			0
$179$	4.09401e6	−	7.09104e6i	0.713822	−	1.23638i	−0.249590	−	0.968352i	$-0.580296\pi$
$179$	4.09401e6	−	7.09104e6i	0.713822	−	1.23638i	0.963412	−	0.268025i	$-0.0863709\pi$
$180$		0			0
$181$			3.25606e6i			0.549106i	0.961572	+	0.274553i	$0.0885298\pi$
$181$			3.25606e6i			0.549106i	−0.961572	+	0.274553i	$0.911470\pi$
$182$		0			0
$183$	−4.11403e6			−0.671297
$184$		0			0
$185$	1.31837e6	+	761161.i	0.208220	+	0.120216i
$186$		0			0
$187$	−9.18709e6	+	5.30417e6i	−1.40492	+	0.811133i
$188$		0			0
$189$	926544.	+	910851.i	0.137240	+	0.134916i
$190$		0			0
$191$	4.30425e6	+	7.45518e6i	0.617728	+	1.06994i	0.989899	+	0.141773i	$0.0452802\pi$
$191$	4.30425e6	+	7.45518e6i	0.617728	+	1.06994i	−0.372171	+	0.928164i	$0.621386\pi$
$192$		0			0
$193$	89943.0	−	155786.i	0.0125111	−	0.0216699i	−0.859702	−	0.510796i	$-0.829351\pi$
$193$	89943.0	−	155786.i	0.0125111	−	0.0216699i	0.872213	+	0.489126i	$0.162684\pi$
$194$		0			0
$195$			2.93067e6i			0.395241i
$196$		0			0
$197$	2.69333e6			0.352283			0.176141	−	0.984365i	$-0.443638\pi$
$197$	2.69333e6			0.352283			0.176141	+	0.984365i	$0.443638\pi$
$198$		0			0
$199$	−5.23271e6	−	3.02111e6i	−0.663999	−	0.383360i	0.129800	−	0.991540i	$-0.458566\pi$
$199$	−5.23271e6	−	3.02111e6i	−0.663999	−	0.383360i	−0.793799	+	0.608180i	$0.791900\pi$
$200$		0			0
$201$	7.40700e6	−	4.27643e6i	0.912125	−	0.526616i
$202$		0			0
$203$	−3.27271e6	+	3.32910e6i	−0.391219	+	0.397959i
$204$		0			0
$205$	−1.26891e6	−	2.19782e6i	−0.147289	−	0.255112i
$206$		0			0
$207$	−1.20301e6	+	2.08367e6i	−0.135630	+	0.234918i
$208$		0			0
$209$			1.54182e7i			1.68886i
$210$		0			0
$211$	1.38113e7			1.47024			0.735118	−	0.677939i	$-0.237127\pi$
$211$	1.38113e7			1.47024			0.735118	+	0.677939i	$0.237127\pi$
$212$		0			0
$213$	−6.28634e6	−	3.62942e6i	−0.650517	−	0.375576i
$214$		0			0
$215$	4.27106e6	−	2.46590e6i	0.429755	−	0.248119i
$216$		0			0
$217$	8.33314e6	−	2.30932e6i	0.815511	−	0.225998i
$218$		0			0
$219$	−2.60118e6	−	4.50538e6i	−0.247650	−	0.428942i
$220$		0			0
$221$	−8.62881e6	+	1.49455e7i	−0.799419	+	1.38463i
$222$		0			0
$223$		−	9.81400e6i		−	0.884976i	−0.896774	−	0.442488i	$-0.854096\pi$
$223$		−	9.81400e6i		−	0.884976i	0.896774	−	0.442488i	$-0.145904\pi$
$224$		0			0
$225$	−2.70715e6			−0.237665
$226$		0			0
$227$	1.26217e7	+	7.28715e6i	1.07905	+	0.622989i	0.930639	−	0.365938i	$-0.119252\pi$
$227$	1.26217e7	+	7.28715e6i	1.07905	+	0.622989i	0.148408	+	0.988926i	$0.452585\pi$
$228$		0			0
$229$	1.27292e7	−	7.34923e6i	1.05998	−	0.611978i	0.134551	−	0.990907i	$-0.457041\pi$
$229$	1.27292e7	−	7.34923e6i	1.05998	−	0.611978i	0.925426	+	0.378929i	$0.123708\pi$
$230$		0			0
$231$	2.31198e6	−	8.93290e6i	0.187563	−	0.724697i
$232$		0			0
$233$	−2.87597e6	−	4.98133e6i	−0.227362	−	0.393802i	0.729664	−	0.683806i	$-0.239677\pi$
$233$	−2.87597e6	−	4.98133e6i	−0.227362	−	0.393802i	−0.957025	+	0.290004i	$0.906343\pi$
$234$		0			0
$235$	4.65976e6	−	8.07094e6i	0.359054	−	0.621900i
$236$		0			0
$237$		−	6.39164e6i		−	0.480140i
$238$		0			0
$239$	−1.60167e7			−1.17322			−0.586610	−	0.809869i	$-0.699538\pi$
$239$	−1.60167e7			−1.17322			−0.586610	+	0.809869i	$0.699538\pi$
$240$		0			0
$241$	−2.23613e7	−	1.29103e7i	−1.59752	−	0.922327i	−0.991964	−	0.126522i	$-0.959618\pi$
$241$	−2.23613e7	−	1.29103e7i	−1.59752	−	0.922327i	−0.605553	−	0.795805i	$-0.707048\pi$
$242$		0			0
$243$	−797162.	+	460241.i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	4.05521e6	+	6.75469e6i	0.275750	+	0.459312i
$246$		0			0
$247$	1.25411e7	+	2.17219e7i	0.832236	+	1.44147i
$248$		0			0
$249$	−560786.	+	971311.i	−0.0363245	+	0.0629158i
$250$		0			0
$251$			9.51912e6i			0.601971i	0.953629	+	0.300985i	$0.0973156\pi$
$251$			9.51912e6i			0.601971i	−0.953629	+	0.300985i	$0.902684\pi$
$252$		0			0
$253$	1.70870e7			1.05513
$254$		0			0
$255$	5.55727e6	+	3.20849e6i	0.335151	+	0.193500i
$256$		0			0
$257$	1.93872e7	−	1.11932e7i	1.14213	−	0.659408i	0.195171	−	0.980769i	$-0.437474\pi$
$257$	1.93872e7	−	1.11932e7i	1.14213	−	0.659408i	0.946957	+	0.321361i	$0.104140\pi$
$258$		0			0
$259$	−7.54860e6	−	1.95370e6i	−0.434477	−	0.112450i
$260$		0			0
$261$	−1.65366e6	−	2.86422e6i	−0.0930089	−	0.161096i
$262$		0			0
$263$	5.24659e6	−	9.08736e6i	0.288410	−	0.499540i	−0.685021	−	0.728524i	$-0.740207\pi$
$263$	5.24659e6	−	9.08736e6i	0.288410	−	0.499540i	0.973430	+	0.228983i	$0.0735402\pi$
$264$		0			0
$265$			1.10612e6i			0.0594380i
$266$		0			0
$267$	−2.54709e6			−0.133817
$268$		0			0
$269$	2.33663e7	+	1.34905e7i	1.20042	+	0.693063i	0.960649	−	0.277766i	$-0.0895941\pi$
$269$	2.33663e7	+	1.34905e7i	1.20042	+	0.693063i	0.239772	+	0.970829i	$0.422927\pi$
$270$		0			0
$271$	1.09955e6	−	634826.i	0.0552468	−	0.0318968i	−0.472122	−	0.881533i	$-0.656512\pi$
$271$	1.09955e6	−	634826.i	0.0552468	−	0.0318968i	0.527369	+	0.849636i	$0.323179\pi$
$272$		0			0
$273$	−4.00878e6	−	1.44657e7i	−0.197027	−	0.710969i
$274$		0			0
$275$	9.61282e6	+	1.66499e7i	0.462224	+	0.800596i
$276$		0			0
$277$	3.35016e6	−	5.80265e6i	0.157626	−	0.273016i	−0.776386	−	0.630257i	$-0.782949\pi$
$277$	3.35016e6	−	5.80265e6i	0.157626	−	0.273016i	0.934012	+	0.357242i	$0.116283\pi$
$278$		0			0
$279$			6.12616e6i			0.282082i
$280$		0			0
$281$	−321000.			−0.0144673			−0.00723363	−	0.999974i	$-0.502303\pi$
$281$	−321000.			−0.0144673			−0.00723363	+	0.999974i	$0.502303\pi$
$282$		0			0
$283$	−2.77311e6	−	1.60105e6i	−0.122351	−	0.0706394i	0.437575	−	0.899182i	$-0.355837\pi$
$283$	−2.77311e6	−	1.60105e6i	−0.122351	−	0.0706394i	−0.559926	+	0.828542i	$0.689171\pi$
$284$		0			0
$285$	8.07695e6	−	4.66323e6i	0.348910	−	0.201443i
$286$		0			0
$287$	9.26967e6	+	9.11267e6i	0.392119	+	0.385478i
$288$		0			0
$289$	6.82485e6	+	1.18210e7i	0.282748	+	0.489734i
$290$		0			0
$291$	5.08117e6	−	8.80084e6i	0.206198	−	0.357146i
$292$		0			0
$293$		−	2.67440e6i		−	0.106322i	−0.998586	−	0.0531610i	$-0.983070\pi$
$293$		−	2.67440e6i		−	0.106322i	0.998586	−	0.0531610i	$-0.0169297\pi$
$294$		0			0
$295$	−4.79340e6			−0.186714
$296$		0			0
$297$	5.66128e6	+	3.26854e6i	0.216095	+	0.124763i
$298$		0			0
$299$	2.40730e7	−	1.38986e7i	0.900568	−	0.519943i
$300$		0			0
$301$	−1.77088e7	+	1.80139e7i	−0.649365	+	0.660553i
$302$		0			0
$303$	7.95465e6	+	1.37779e7i	0.285952	+	0.495283i
$304$		0			0
$305$	8.83669e6	−	1.53056e7i	0.311451	−	0.539449i
$306$		0			0
$307$		−	1.98765e7i		−	0.686950i	−0.939162	−	0.343475i	$-0.888396\pi$
$307$		−	1.98765e7i		−	0.686950i	0.939162	−	0.343475i	$-0.111604\pi$
$308$		0			0
$309$	−6.53664e6			−0.221554
$310$		0			0
$311$	1.36580e7	+	7.88548e6i	0.454054	+	0.262148i	0.709541	−	0.704664i	$-0.248902\pi$
$311$	1.36580e7	+	7.88548e6i	0.454054	+	0.262148i	−0.255487	+	0.966813i	$0.582236\pi$
$312$		0			0
$313$	−9.13939e6	+	5.27663e6i	−0.298047	+	0.172077i	−0.641565	−	0.767069i	$-0.721715\pi$
$313$	−9.13939e6	+	5.27663e6i	−0.298047	+	0.172077i	0.343518	+	0.939146i	$0.388381\pi$
$314$		0			0
$315$	−5.37883e6	+	1.49060e6i	−0.172090	+	0.0476904i
$316$		0			0
$317$	1.61613e7	+	2.79923e7i	0.507341	+	0.878740i	0.999964	+	0.00849733i	$0.00270482\pi$
$317$	1.61613e7	+	2.79923e7i	0.507341	+	0.878740i	−0.492623	+	0.870243i	$0.663962\pi$
$318$		0			0
$319$	−1.17440e7	+	2.03411e7i	−0.361778	+	0.626618i
$320$		0			0
$321$			3.44881e7i			1.04269i
$322$		0			0
$323$	5.49201e7			1.62976
$324$		0			0
$325$	2.70860e7	+	1.56381e7i	0.789033	+	0.455549i
$326$		0			0
$327$	−1.03398e7	+	5.96968e6i	−0.295711	+	0.170729i
$328$		0			0
$329$	−1.19604e7	+	4.62119e7i	−0.335859	+	1.29767i
$330$		0			0
$331$	1.00165e7	+	1.73490e7i	0.276205	+	0.478400i	0.970438	−	0.241349i	$-0.0775899\pi$
$331$	1.00165e7	+	1.73490e7i	0.276205	+	0.478400i	−0.694234	+	0.719750i	$0.744257\pi$
$332$		0			0
$333$	2.76203e6	−	4.78397e6i	0.0747989	−	0.129555i
$334$		0			0
$335$			3.67421e7i			0.977303i
$336$		0			0
$337$	−3.66702e6			−0.0958128			−0.0479064	−	0.998852i	$-0.515255\pi$
$337$	−3.66702e6			−0.0958128			−0.0479064	+	0.998852i	$0.515255\pi$
$338$		0			0
$339$	−3.59230e7	−	2.07401e7i	−0.922090	−	0.532369i
$340$		0			0
$341$	3.76779e7	−	2.17534e7i	0.950219	−	0.548609i
$342$		0			0
$343$	−2.92560e7	−	2.77939e7i	−0.724990	−	0.688760i
$344$		0			0
$345$	−5.16796e6	−	8.95117e6i	−0.125853	−	0.217983i
$346$		0			0
$347$	3.22802e6	−	5.59109e6i	0.0772587	−	0.133816i	−0.824808	−	0.565414i	$-0.808717\pi$
$347$	3.22802e6	−	5.59109e6i	0.0772587	−	0.133816i	0.902066	+	0.431598i	$0.142050\pi$
$348$		0			0
$349$		−	4.01536e7i		−	0.944600i	−0.881438	−	0.472300i	$-0.843424\pi$
$349$		−	4.01536e7i		−	0.944600i	0.881438	−	0.472300i	$-0.156576\pi$
$350$		0			0
$351$	1.06345e7			0.245921
$352$		0			0
$353$	7.02915e6	+	4.05828e6i	0.159801	+	0.0922610i	0.577768	−	0.816201i	$-0.303924\pi$
$353$	7.02915e6	+	4.05828e6i	0.159801	+	0.0922610i	−0.417967	+	0.908462i	$0.637257\pi$
$354$		0			0
$355$	2.70053e7	−	1.55915e7i	0.603621	−	0.348501i
$356$		0			0
$357$	−3.18193e7	−	8.23535e6i	−0.699336	−	0.181000i
$358$		0			0
$359$	1.84586e7	+	3.19712e7i	0.398946	+	0.690996i	0.993596	−	0.112989i	$-0.0360426\pi$
$359$	1.84586e7	+	3.19712e7i	0.398946	+	0.690996i	−0.594650	+	0.803985i	$0.702709\pi$
$360$		0			0
$361$	1.63876e7	−	2.83842e7i	0.348333	−	0.603330i
$362$		0			0
$363$		−	1.88091e7i		−	0.393231i
$364$		0			0
$365$	2.23487e7			0.459593
$366$		0			0
$367$	−1.70742e7	−	9.85777e6i	−0.345415	−	0.199425i	0.317249	−	0.948342i	$-0.397241\pi$
$367$	−1.70742e7	−	9.85777e6i	−0.345415	−	0.199425i	−0.662664	+	0.748917i	$0.730574\pi$
$368$		0			0
$369$	−7.97525e6	+	4.60451e6i	−0.158732	+	0.0916441i
$370$		0			0
$371$	−1.51303e6	−	5.45976e6i	−0.0296296	−	0.106918i
$372$		0			0
$373$	−5.21653e6	−	9.03530e6i	−0.100521	−	0.174107i	0.811379	−	0.584521i	$-0.198718\pi$
$373$	−5.21653e6	−	9.03530e6i	−0.100521	−	0.174107i	−0.911899	+	0.410414i	$0.865384\pi$
$374$		0			0
$375$	1.39702e7	−	2.41972e7i	0.264917	−	0.458850i
$376$		0			0
$377$			3.82101e7i			0.713106i
$378$		0			0
$379$	5.26018e7			0.966235			0.483118	−	0.875556i	$-0.339504\pi$
$379$	5.26018e7			0.966235			0.483118	+	0.875556i	$0.339504\pi$
$380$		0			0
$381$	1.50725e7	+	8.70210e6i	0.272527	+	0.157344i
$382$		0			0
$383$	−6.36846e7	+	3.67683e7i	−1.13354	+	0.654451i	−0.944823	−	0.327580i	$-0.893767\pi$
$383$	−6.36846e7	+	3.67683e7i	−1.13354	+	0.654451i	−0.188719	+	0.982031i	$0.560434\pi$
$384$		0			0
$385$	2.82674e7	+	2.77886e7i	0.495340	+	0.486951i
$386$		0			0
$387$	−8.94802e6	−	1.54984e7i	−0.154381	−	0.267396i
$388$		0			0
$389$	−8.60695e6	+	1.49077e7i	−0.146218	+	0.253257i	−0.929827	−	0.367998i	$-0.880043\pi$
$389$	−8.60695e6	+	1.49077e7i	−0.146218	+	0.253257i	0.783609	+	0.621255i	$0.213377\pi$
$390$		0			0
$391$		−	6.08645e7i		−	1.01820i
$392$		0			0
$393$	−4.46088e6			−0.0734924
$394$		0			0
$395$	2.37791e7	+	1.37289e7i	0.385837	+	0.222763i
$396$		0			0
$397$	−5.31024e7	+	3.06587e7i	−0.848678	+	0.489984i	−0.860205	−	0.509949i	$-0.829664\pi$
$397$	−5.31024e7	+	3.06587e7i	−0.848678	+	0.489984i	0.0115267	+	0.999934i	$0.496331\pi$
$398$		0			0
$399$	−3.34888e7	+	3.40658e7i	−0.527207	+	0.536290i
$400$		0			0
$401$	2.30735e7	+	3.99645e7i	0.357833	+	0.619785i	0.987599	−	0.157000i	$-0.0501823\pi$
$401$	2.30735e7	+	3.99645e7i	0.357833	+	0.619785i	−0.629765	+	0.776785i	$0.716849\pi$
$402$		0			0
$403$	3.53883e7	−	6.12944e7i	0.540686	−	0.936495i
$404$		0			0
$405$		−	3.95428e6i		−	0.0595254i
$406$		0			0
$407$	−3.92307e7			−0.581892
$408$		0			0
$409$	−5.25613e7	−	3.03463e7i	−0.768239	−	0.443543i	0.0640071	−	0.997949i	$-0.479612\pi$
$409$	−5.25613e7	−	3.03463e7i	−0.768239	−	0.443543i	−0.832246	+	0.554406i	$0.812945\pi$
$410$		0			0
$411$	5.04081e7	−	2.91031e7i	0.726063	−	0.419193i
$412$		0			0
$413$	2.36601e7	−	6.55677e6i	0.335866	−	0.0930765i
$414$		0			0
$415$	−2.40907e6	−	4.17263e6i	−0.0337058	−	0.0583802i
$416$		0			0
$417$	−4.81852e6	+	8.34592e6i	−0.0664516	+	0.115097i
$418$		0			0
$419$			1.17371e8i			1.59558i	0.602939	+	0.797788i	$0.293996\pi$
$419$			1.17371e8i			1.59558i	−0.602939	+	0.797788i	$0.706004\pi$
$420$		0			0
$421$	−1.28510e7			−0.172222			−0.0861111	−	0.996286i	$-0.527444\pi$
$421$	−1.28510e7			−0.172222			−0.0861111	+	0.996286i	$0.527444\pi$
$422$		0			0
$423$	−2.92870e7	−	1.69089e7i	−0.386950	−	0.223405i
$424$		0			0
$425$	5.93075e7	−	3.42412e7i	0.772579	−	0.446049i
$426$		0			0
$427$	−2.26815e7	+	8.76354e7i	−0.291331	+	1.12563i
$428$		0			0
$429$	−3.77621e7	−	6.54058e7i	−0.478282	−	0.828408i
$430$		0			0
$431$	−5.69282e7	+	9.86026e7i	−0.711043	+	1.23156i	0.253423	+	0.967356i	$0.418444\pi$
$431$	−5.69282e7	+	9.86026e7i	−0.711043	+	1.23156i	−0.964466	+	0.264207i	$0.914890\pi$
$432$		0			0
$433$		−	2.76112e7i		−	0.340111i	−0.985434	−	0.170056i	$-0.945605\pi$
$433$		−	2.76112e7i		−	0.340111i	0.985434	−	0.170056i	$-0.0543947\pi$
$434$		0			0
$435$	1.42078e7			0.172608
$436$		0			0
$437$	−7.66092e7	−	4.42303e7i	−0.917987	−	0.530000i
$438$		0			0
$439$	−6.22452e7	+	3.59373e7i	−0.735720	+	0.424768i	−0.820511	−	0.571631i	$-0.806311\pi$
$439$	−6.22452e7	+	3.59373e7i	−0.735720	+	0.424768i	0.0847914	+	0.996399i	$0.472978\pi$
$440$		0			0
$441$	2.45108e7	−	1.47151e7i	0.285786	−	0.171573i
$442$		0			0
$443$	−4.75145e7	−	8.22975e7i	−0.546531	−	0.946620i	−0.998509	−	0.0545904i	$-0.982615\pi$
$443$	−4.75145e7	−	8.22975e7i	−0.546531	−	0.946620i	0.451978	−	0.892029i	$-0.350719\pi$
$444$		0			0
$445$	5.47099e6	−	9.47603e6i	0.0620849	−	0.107534i
$446$		0			0
$447$		−	5.80389e7i		−	0.649825i
$448$		0			0
$449$	1.15401e8			1.27488			0.637440	−	0.770500i	$-0.279993\pi$
$449$	1.15401e8			1.27488			0.637440	+	0.770500i	$0.279993\pi$
$450$		0			0
$451$	5.66386e7	+	3.27003e7i	0.617423	+	0.356469i
$452$		0			0
$453$	−3.44518e7	+	1.98908e7i	−0.370611	+	0.213972i
$454$		0			0
$455$	6.24278e7	+	1.61573e7i	0.662741	+	0.171528i
$456$		0			0
$457$	−4.58763e6	−	7.94601e6i	−0.0480662	−	0.0832531i	0.840991	−	0.541049i	$-0.181973\pi$
$457$	−4.58763e6	−	7.94601e6i	−0.0480662	−	0.0832531i	−0.889058	+	0.457796i	$0.848639\pi$
$458$		0			0
$459$	1.16427e7	−	2.01657e7i	0.120397	−	0.208533i
$460$		0			0
$461$		−	5.79354e7i		−	0.591346i	−0.955289	−	0.295673i	$-0.904456\pi$
$461$		−	5.79354e7i		−	0.591346i	0.955289	−	0.295673i	$-0.0955438\pi$
$462$		0			0
$463$	−6.51781e7			−0.656687			−0.328344	−	0.944558i	$-0.606490\pi$
$463$	−6.51781e7			−0.656687			−0.328344	+	0.944558i	$0.606490\pi$
$464$		0			0
$465$	−2.27914e7	−	1.31586e7i	−0.226679	−	0.130873i
$466$		0			0
$467$	1.46749e8	−	8.47258e7i	1.44087	−	0.831888i	0.442965	−	0.896539i	$-0.353927\pi$
$467$	1.46749e8	−	8.47258e7i	1.44087	−	0.831888i	0.997908	+	0.0646508i	$0.0205933\pi$
$468$		0			0
$469$	−5.02586e7	−	1.81358e8i	−0.487182	−	1.75799i
$470$		0			0
$471$	−5.28352e7	−	9.15132e7i	−0.505662	−	0.875832i
$472$		0			0
$473$	−6.35470e7	+	1.10067e8i	−0.600498	+	1.04009i
$474$		0			0
$475$		−	9.95326e7i		−	0.928719i
$476$		0			0
$477$	4.01377e6			0.0369826
$478$		0			0
$479$	7.92689e7	+	4.57659e7i	0.721268	+	0.416424i	0.815219	−	0.579153i	$-0.196617\pi$
$479$	7.92689e7	+	4.57659e7i	0.721268	+	0.416424i	−0.0939514	+	0.995577i	$0.529950\pi$
$480$		0			0
$481$	−5.52701e7	+	3.19102e7i	−0.496656	+	0.286744i
$482$		0			0
$483$	3.77530e7	+	3.71136e7i	0.335050	+	0.329375i
$484$		0			0
$485$	2.18281e7	+	3.78073e7i	0.191333	+	0.331399i
$486$		0			0
$487$	−6.56199e7	+	1.13657e8i	−0.568131	+	0.984032i	0.428620	+	0.903485i	$0.359000\pi$
$487$	−6.56199e7	+	1.13657e8i	−0.568131	+	0.984032i	−0.996751	+	0.0805467i	$0.974333\pi$
$488$		0			0
$489$		−	1.28939e8i		−	1.10270i
$490$		0			0
$491$	8.81776e7			0.744927			0.372463	−	0.928047i	$-0.378513\pi$
$491$	8.81776e7			0.744927			0.372463	+	0.928047i	$0.378513\pi$
$492$		0			0
$493$	7.24558e7	+	4.18324e7i	0.604690	+	0.349118i
$494$		0			0
$495$	−2.43201e7	+	1.40412e7i	−0.200517	+	0.115768i
$496$		0			0
$497$	−1.11970e8	+	1.13899e8i	−0.912080	+	0.927794i
$498$		0			0
$499$	−1.14235e8	−	1.97862e8i	−0.919389	−	1.59243i	−0.800346	−	0.599539i	$-0.795351\pi$
$499$	−1.14235e8	−	1.97862e8i	−0.919389	−	1.59243i	−0.119043	−	0.992889i	$-0.537983\pi$
$500$		0			0
$501$	2.02619e7	−	3.50946e7i	0.161126	−	0.279079i
$502$		0			0
$503$			2.07735e8i			1.63232i	0.577824	+	0.816161i	$0.303902\pi$
$503$			2.07735e8i			1.63232i	−0.577824	+	0.816161i	$0.696098\pi$
$504$		0			0
$505$	−6.83444e7			−0.530675
$506$		0			0
$507$	−4.12402e7	−	2.38100e7i	−0.316444	−	0.182699i
$508$		0			0
$509$	−4.74960e7	+	2.74218e7i	−0.360167	+	0.207942i	−0.669154	−	0.743124i	$-0.733343\pi$
$509$	−4.74960e7	+	2.74218e7i	−0.360167	+	0.207942i	0.308987	+	0.951066i	$0.400010\pi$
$510$		0			0
$511$	−1.10312e8	+	3.05702e7i	−0.826726	+	0.229106i
$512$		0			0
$513$	−1.69215e7	−	2.93089e7i	−0.125339	−	0.217094i
$514$		0			0
$515$	1.40403e7	−	2.43185e7i	0.102791	−	0.178039i
$516$		0			0
$517$			2.40167e8i			1.73797i
$518$		0			0
$519$	−1.27910e8			−0.914962
$520$		0			0
$521$	−2.47035e7	−	1.42626e7i	−0.174681	−	0.100852i	0.410110	−	0.912036i	$-0.365490\pi$
$521$	−2.47035e7	−	1.42626e7i	−0.174681	−	0.100852i	−0.584791	+	0.811184i	$0.698824\pi$
$522$		0			0
$523$	9.32394e7	−	5.38318e7i	0.651770	−	0.376300i	−0.137364	−	0.990521i	$-0.543863\pi$
$523$	9.32394e7	−	5.38318e7i	0.651770	−	0.376300i	0.789134	+	0.614221i	$0.210530\pi$
$524$		0			0
$525$	−1.49251e7	+	5.76666e7i	−0.103143	+	0.398517i
$526$		0			0
$527$	−7.74863e7	−	1.34210e8i	−0.529411	−	0.916966i
$528$		0			0
$529$	2.50003e7	−	4.33018e7i	0.168880	−	0.292509i
$530$		0			0
$531$			1.73938e7i			0.116175i
$532$		0			0
$533$	1.06394e8			0.702642
$534$		0			0
$535$	−1.28307e8	−	7.40782e7i	−0.837895	−	0.483759i
$536$		0			0
$537$	1.10538e8	−	6.38193e7i	0.713822	−	0.412125i
$538$		0			0
$539$	−1.77538e8	−	9.84975e7i	−1.13377	−	0.629012i
$540$		0			0
$541$	−2.77877e7	−	4.81297e7i	−0.175493	−	0.303963i	0.764839	−	0.644222i	$-0.222819\pi$
$541$	−2.77877e7	−	4.81297e7i	−0.175493	−	0.303963i	−0.940332	+	0.340259i	$0.889485\pi$
$542$		0			0
$543$	−2.53784e7	+	4.39567e7i	−0.158513	+	0.274553i
$544$		0			0
$545$		−	5.12900e7i		−	0.316842i
$546$		0			0
$547$	−5.44170e7			−0.332485			−0.166243	−	0.986085i	$-0.553163\pi$
$547$	−5.44170e7			−0.332485			−0.166243	+	0.986085i	$0.553163\pi$
$548$		0			0
$549$	−5.55395e7	−	3.20657e7i	−0.335648	−	0.193787i
$550$		0			0
$551$	1.05308e8	−	6.07993e7i	0.629513	−	0.363449i
$552$		0			0
$553$	−1.36152e8	−	3.52384e7i	−0.805098	−	0.208372i
$554$		0			0
$555$	1.18653e7	+	2.05513e7i	0.0694066	+	0.120216i
$556$		0			0
$557$	−6.26135e6	+	1.08450e7i	−0.0362329	+	0.0627571i	−0.883573	−	0.468293i	$-0.844869\pi$
$557$	−6.26135e6	+	1.08450e7i	−0.0362329	+	0.0627571i	0.847340	+	0.531050i	$0.178202\pi$
$558$		0			0
$559$			2.06756e8i			1.18365i
$560$		0			0
$561$	−1.65368e8			−0.936616
$562$		0			0
$563$	−1.50742e8	−	8.70310e7i	−0.844713	−	0.487695i	0.0141502	−	0.999900i	$-0.495496\pi$
$563$	−1.50742e8	−	8.70310e7i	−0.844713	−	0.487695i	−0.858864	+	0.512204i	$0.828829\pi$
$564$		0			0
$565$	1.54321e8	−	8.90971e7i	0.855616	−	0.493990i
$566$		0			0
$567$	5.40896e6	+	1.95182e7i	0.0296732	+	0.107076i
$568$		0			0
$569$	−2.37803e7	−	4.11886e7i	−0.129086	−	0.223584i	0.794237	−	0.607609i	$-0.207871\pi$
$569$	−2.37803e7	−	4.11886e7i	−0.129086	−	0.223584i	−0.923323	+	0.384025i	$0.874538\pi$
$570$		0			0
$571$	8.27707e7	−	1.43363e8i	0.444599	−	0.770068i	−0.553425	−	0.832899i	$-0.686680\pi$
$571$	8.27707e7	−	1.43363e8i	0.444599	−	0.770068i	0.998024	+	0.0628311i	$0.0200129\pi$
$572$		0			0
$573$			1.34193e8i			0.713291i
$574$		0			0
$575$	−1.10306e8			−0.580222
$576$		0			0
$577$	−4.44692e7	−	2.56743e7i	−0.231490	−	0.133651i	0.379769	−	0.925081i	$-0.376003\pi$
$577$	−4.44692e7	−	2.56743e7i	−0.231490	−	0.133651i	−0.611259	+	0.791431i	$0.709337\pi$
$578$		0			0
$579$	2.42846e6	−	1.40207e6i	0.0125111	−	0.00722328i
$580$		0			0
$581$	1.75987e7	+	1.73007e7i	0.0897331	+	0.0882133i
$582$		0			0
$583$	−1.42525e7	−	2.46861e7i	−0.0719259	−	0.124579i
$584$		0			0
$585$	−2.28423e7	+	3.95640e7i	−0.114096	+	0.197621i
$586$		0			0
$587$		−	2.37624e8i		−	1.17483i	−0.809285	−	0.587416i	$-0.800145\pi$
$587$		−	2.37624e8i		−	1.17483i	0.809285	−	0.587416i	$-0.199855\pi$
$588$		0			0
$589$	−2.25238e8			−1.10229
$590$		0			0
$591$	3.63600e7	+	2.09925e7i	0.176141	+	0.101695i
$592$		0			0
$593$	−3.20624e8	+	1.85112e8i	−1.53756	+	0.887711i	−0.538579	+	0.842575i	$0.681039\pi$
$593$	−3.20624e8	+	1.85112e8i	−1.53756	+	0.887711i	−0.998981	+	0.0451361i	$0.985628\pi$
$594$		0			0
$595$	9.89842e7	−	1.00690e8i	0.469910	−	0.478006i
$596$		0			0
$597$	−4.70944e7	−	8.15699e7i	−0.221333	−	0.383360i
$598$		0			0
$599$	−1.87938e7	+	3.25519e7i	−0.0874451	+	0.151459i	−0.906430	−	0.422355i	$-0.861204\pi$
$599$	−1.87938e7	+	3.25519e7i	−0.0874451	+	0.151459i	0.818985	+	0.573814i	$0.194537\pi$
$600$		0			0
$601$			2.67605e7i			0.123274i	0.998099	+	0.0616369i	$0.0196321\pi$
$601$			2.67605e7i			0.123274i	−0.998099	+	0.0616369i	$0.980368\pi$
$602$		0			0
$603$	1.33326e8			0.608083
$604$		0			0
$605$	6.99761e7	+	4.04007e7i	0.315998	+	0.182441i
$606$		0			0
$607$	−6.69071e7	+	3.86288e7i	−0.299162	+	0.172721i	−0.642066	−	0.766649i	$-0.721923\pi$
$607$	−6.69071e7	+	3.86288e7i	−0.299162	+	0.172721i	0.342905	+	0.939370i	$0.388589\pi$
$608$		0			0
$609$	−7.01294e7	+	1.94345e7i	−0.310490	+	0.0860444i
$610$		0			0
$611$	1.95352e8	+	3.38359e8i	0.856433	+	1.48338i
$612$		0			0
$613$	1.76486e8	−	3.05682e8i	0.766174	−	1.32705i	−0.173449	−	0.984843i	$-0.555491\pi$
$613$	1.76486e8	−	3.05682e8i	0.766174	−	1.32705i	0.939623	−	0.342210i	$-0.111175\pi$
$614$		0			0
$615$		−	3.95608e7i		−	0.170075i
$616$		0			0
$617$	1.82109e8			0.775310			0.387655	−	0.921805i	$-0.373285\pi$
$617$	1.82109e8			0.775310			0.387655	+	0.921805i	$0.373285\pi$
$618$		0			0
$619$	−8.43335e7	−	4.86900e7i	−0.355573	−	0.205290i	0.311564	−	0.950225i	$-0.399147\pi$
$619$	−8.43335e7	−	4.86900e7i	−0.355573	−	0.205290i	−0.667137	+	0.744935i	$0.732480\pi$
$620$		0			0
$621$	−3.24811e7	+	1.87530e7i	−0.135630	+	0.0783062i
$622$		0			0
$623$	−1.40426e7	+	5.42570e7i	−0.0580742	+	0.224384i
$624$		0			0
$625$	−2.70211e7	−	4.68019e7i	−0.110678	−	0.191701i
$626$		0			0
$627$	−1.20173e8	+	2.08145e8i	−0.487533	+	0.844431i
$628$		0			0
$629$			1.39741e8i			0.561529i
$630$		0			0
$631$	1.37285e8			0.546430			0.273215	−	0.961953i	$-0.411913\pi$
$631$	1.37285e8			0.546430			0.273215	+	0.961953i	$0.411913\pi$
$632$		0			0
$633$	1.86453e8	+	1.07648e8i	0.735118	+	0.424421i
$634$		0			0
$635$	−6.47495e7	+	3.73832e7i	−0.252881	+	0.146001i
$636$		0			0
$637$	−3.30243e8	+	5.64143e6i	−1.27766	+	0.0218258i
$638$		0			0
$639$	−5.65770e7	−	9.79943e7i	−0.216839	−	0.375576i
$640$		0			0
$641$	1.04673e8	−	1.81298e8i	0.397428	−	0.688366i	−0.595979	−	0.803000i	$-0.703236\pi$
$641$	1.04673e8	−	1.81298e8i	0.397428	−	0.688366i	0.993408	+	0.114633i	$0.0365693\pi$
$642$		0			0
$643$			3.49818e8i			1.31586i	0.753079	+	0.657930i	$0.228568\pi$
$643$			3.49818e8i			1.31586i	−0.753079	+	0.657930i	$0.771432\pi$
$644$		0			0
$645$	7.68791e7			0.286503
$646$		0			0
$647$	−3.20197e8	−	1.84866e8i	−1.18224	−	0.682566i	−0.225707	−	0.974195i	$-0.572469\pi$
$647$	−3.20197e8	−	1.84866e8i	−1.18224	−	0.682566i	−0.956531	+	0.291630i	$0.905803\pi$
$648$		0			0
$649$	1.06978e8	−	6.17637e7i	0.391345	−	0.225943i
$650$		0			0
$651$	1.30497e8	+	3.37747e7i	0.472995	+	0.122419i
$652$		0			0
$653$	1.97623e7	+	3.42293e7i	0.0709737	+	0.122930i	0.899328	−	0.437274i	$-0.144056\pi$
$653$	1.97623e7	+	3.42293e7i	0.0709737	+	0.122930i	−0.828355	+	0.560204i	$0.810723\pi$
$654$		0			0
$655$	9.58169e6	−	1.65960e7i	0.0340971	−	0.0590580i
$656$		0			0
$657$		−	8.10968e7i		−	0.285962i
$658$		0			0
$659$	3.29124e8			1.15002			0.575008	−	0.818148i	$-0.304999\pi$
$659$	3.29124e8			1.15002			0.575008	+	0.818148i	$0.304999\pi$
$660$		0			0
$661$	−1.39292e8	−	8.04205e7i	−0.482306	−	0.278460i	0.239071	−	0.971002i	$-0.423157\pi$
$661$	−1.39292e8	−	8.04205e7i	−0.482306	−	0.278460i	−0.721377	+	0.692543i	$0.756491\pi$
$662$		0			0
$663$	−2.32978e8	+	1.34510e8i	−0.799419	+	0.461545i
$664$		0			0
$665$	−5.48044e7	−	1.97761e8i	−0.186359	−	0.672474i
$666$		0			0
$667$	−6.73800e7	−	1.16706e8i	−0.227067	−	0.393291i
$668$		0			0
$669$	7.64926e7	−	1.32489e8i	0.255471	−	0.442488i
$670$		0			0
$671$			4.55448e8i			1.50755i
$672$		0			0
$673$	5.32162e8			1.74582			0.872908	−	0.487886i	$-0.162232\pi$
$673$	5.32162e8			1.74582			0.872908	+	0.487886i	$0.162232\pi$
$674$		0			0
$675$	−3.65466e7	−	2.11002e7i	−0.118832	−	0.0686080i
$676$		0			0
$677$	−4.68878e8	+	2.70707e8i	−1.51110	+	0.872435i	−0.511186	+	0.859470i	$0.670794\pi$
$677$	−4.68878e8	+	2.70707e8i	−1.51110	+	0.872435i	−0.999916	+	0.0129645i	$0.995873\pi$
$678$		0			0
$679$	−1.59458e8	−	1.56758e8i	−0.509375	−	0.500748i
$680$		0			0
$681$	1.13595e8	+	1.96753e8i	0.359683	+	0.622989i
$682$		0			0
$683$	1.24469e8	−	2.15587e8i	0.390662	−	0.676646i	−0.601875	−	0.798590i	$-0.705580\pi$
$683$	1.24469e8	−	2.15587e8i	0.390662	−	0.676646i	0.992537	+	0.121944i	$0.0389129\pi$
$684$		0			0
$685$			2.50047e8i			0.777946i
$686$		0			0
$687$	2.29126e8			0.706651
$688$		0			0
$689$	−4.01592e7	−	2.31860e7i	−0.122780	−	0.0708871i
$690$		0			0
$691$	−8.00565e7	+	4.62206e7i	−0.242640	+	0.140088i	−0.616390	−	0.787441i	$-0.711405\pi$
$691$	−8.00565e7	+	4.62206e7i	−0.242640	+	0.140088i	0.373749	+	0.927530i	$0.378072\pi$
$692$		0			0
$693$	1.00837e8	−	1.02574e8i	0.302984	−	0.308204i
$694$		0			0
$695$	−2.06997e7	−	3.58530e7i	−0.0616610	−	0.106800i
$696$		0			0
$697$	1.16480e8	−	2.01749e8i	0.343995	−	0.595816i
$698$		0			0
$699$		−	8.96640e7i		−	0.262535i
$700$		0			0
$701$	5.38435e8			1.56307			0.781537	−	0.623859i	$-0.214436\pi$
$701$	5.38435e8			1.56307			0.781537	+	0.623859i	$0.214436\pi$
$702$		0			0
$703$	1.75890e8	+	1.01550e8i	0.506262	+	0.292290i
$704$		0			0
$705$	1.25813e8	−	7.26384e7i	0.359054	−	0.207300i
$706$		0			0
$707$	3.37346e8	−	9.34866e7i	0.954590	−	0.264540i
$708$		0			0
$709$	−3.53455e7	−	6.12202e7i	−0.0991735	−	0.171773i	0.812169	−	0.583422i	$-0.198287\pi$
$709$	−3.53455e7	−	6.12202e7i	−0.0991735	−	0.171773i	−0.911343	+	0.411648i	$0.864953\pi$
$710$		0			0
$711$	4.98179e7	−	8.62872e7i	0.138604	−	0.240070i
$712$		0			0
$713$			2.49616e8i			0.688660i
$714$		0			0
$715$	3.24442e8			0.887604
$716$		0			0
$717$	−2.16226e8	−	1.24838e8i	−0.586610	−	0.338680i
$718$		0			0
$719$	3.38940e8	−	1.95687e8i	0.911876	−	0.526472i	0.0308415	−	0.999524i	$-0.490181\pi$
$719$	3.38940e8	−	1.95687e8i	0.911876	−	0.526472i	0.881034	+	0.473053i	$0.156848\pi$
$720$		0			0
$721$	−3.60378e7	+	1.39241e8i	−0.0961506	+	0.371501i
$722$		0			0
$723$	−2.01252e8	−	3.48578e8i	−0.532506	−	0.922327i
$724$		0			0
$725$	7.58135e7	−	1.31313e8i	0.198945	−	0.344582i
$726$		0			0
$727$			4.83550e8i			1.25846i	0.777221	+	0.629228i	$0.216629\pi$
$727$			4.83550e8i			1.25846i	−0.777221	+	0.629228i	$0.783371\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	3.92061e8	+	2.26357e8i	1.00369	+	0.579484i
$732$		0			0
$733$	−2.76711e8	+	1.59759e8i	−0.702611	+	0.405653i	−0.808319	−	0.588745i	$-0.799622\pi$
$733$	−2.76711e8	+	1.59759e8i	−0.702611	+	0.405653i	0.105708	+	0.994397i	$0.466289\pi$
$734$		0			0
$735$	2.09768e6	+	1.22796e8i	0.00528295	+	0.309258i
$736$		0			0
$737$	−4.73427e8	−	8.20000e8i	−1.18263	−	2.04838i
$738$		0			0
$739$	1.76757e8	−	3.06151e8i	0.437968	−	0.758582i	−0.559565	−	0.828787i	$-0.689032\pi$
$739$	1.76757e8	−	3.06151e8i	0.437968	−	0.758582i	0.997533	+	0.0702042i	$0.0223651\pi$
$740$		0			0
$741$			3.90994e8i			0.960983i
$742$		0			0
$743$	−4.63396e8			−1.12976			−0.564880	−	0.825173i	$-0.691077\pi$
$743$	−4.63396e8			−1.12976			−0.564880	+	0.825173i	$0.691077\pi$
$744$		0			0
$745$	2.15924e8	+	1.24664e8i	0.522195	+	0.301489i
$746$		0			0
$747$	−1.51412e7	+	8.74179e6i	−0.0363245	+	0.0209719i
$748$		0			0
$749$	7.34650e8	+	1.90139e8i	1.74838	+	0.452508i
$750$		0			0
$751$	−1.48510e7	−	2.57226e7i	−0.0350618	−	0.0607289i	0.847962	−	0.530057i	$-0.177829\pi$
$751$	−1.48510e7	−	2.57226e7i	−0.0350618	−	0.0607289i	−0.883024	+	0.469328i	$0.844496\pi$
$752$		0			0
$753$	−7.41942e7	+	1.28508e8i	−0.173774	+	0.300985i
$754$		0			0
$755$		−	1.70897e8i		−	0.397093i
$756$		0			0
$757$	7.11235e8			1.63955			0.819776	−	0.572684i	$-0.194098\pi$
$757$	7.11235e8			1.63955			0.819776	+	0.572684i	$0.194098\pi$
$758$		0			0
$759$	2.30674e8	+	1.33180e8i	0.527563	+	0.304588i
$760$		0			0
$761$	3.18255e8	−	1.83745e8i	0.722140	−	0.416928i	−0.0933998	−	0.995629i	$-0.529773\pi$
$761$	3.18255e8	−	1.83745e8i	0.722140	−	0.416928i	0.815540	+	0.578701i	$0.196440\pi$
$762$		0			0
$763$	7.01583e7	+	2.53166e8i	0.157945	+	0.569942i
$764$		0			0
$765$	5.00154e7	+	8.66292e7i	0.111717	+	0.193500i
$766$		0			0
$767$	1.00477e8	−	1.74031e8i	0.222680	−	0.385693i
$768$		0			0
$769$			3.18891e8i			0.701235i	0.936519	+	0.350617i	$0.114028\pi$
$769$			3.18891e8i			0.701235i	−0.936519	+	0.350617i	$0.885972\pi$
$770$		0			0
$771$	3.48969e8			0.761419
$772$		0			0
$773$	1.35153e8	+	7.80307e7i	0.292609	+	0.168938i	0.639118	−	0.769109i	$-0.279300\pi$
$773$	1.35153e8	+	7.80307e7i	0.292609	+	0.168938i	−0.346509	+	0.938047i	$0.612633\pi$
$774$		0			0
$775$	−2.43231e8	+	1.40430e8i	−0.522533	+	0.301685i
$776$		0			0
$777$	−8.66785e7	−	8.52105e7i	−0.184777	−	0.181648i
$778$		0			0
$779$	−1.69292e8	−	2.93222e8i	−0.358116	−	0.620275i
$780$		0			0
$781$	−4.01798e8	+	6.95935e8i	−0.843442	+	1.46088i
$782$		0			0
$783$		−	5.15560e7i		−	0.107397i
$784$		0			0
$785$	4.53947e8			0.938417
$786$		0			0
$787$	6.50044e8	+	3.75303e8i	1.33358	+	0.769942i	0.985846	−	0.167651i	$-0.0536183\pi$
$787$	6.50044e8	+	3.75303e8i	1.33358	+	0.769942i	0.347733	+	0.937594i	$0.386952\pi$
$788$		0			0
$789$	1.41658e8	−	8.17862e7i	0.288410	−	0.166513i
$790$		0			0
$791$	−6.39848e8	+	6.50872e8i	−1.29285	+	1.31512i
$792$		0			0
$793$	3.70462e8	+	6.41658e8i	0.742888	+	1.28672i
$794$		0			0
$795$	−8.62134e6	+	1.49326e7i	−0.0171583	+	0.0297190i
$796$		0			0
$797$		−	1.08408e6i		−	0.00214134i	−0.999999	−	0.00107067i	$-0.999659\pi$
$797$		−	1.08408e6i		−	0.00214134i	0.999999	−	0.00107067i	$-0.000340806\pi$
$798$		0			0
$799$	8.55483e8			1.67715
$800$		0			0
$801$	−3.43857e7	−	1.98526e7i	−0.0669084	−	0.0386296i
$802$		0			0
$803$	−4.98772e8	+	2.87966e8i	−0.963287	+	0.556154i
$804$		0			0
$805$	−2.19166e8	+	6.07362e7i	−0.420132	+	0.116429i
$806$		0			0
$807$	2.10297e8	+	3.64245e8i	0.400140	+	0.693063i
$808$		0			0
$809$	−2.23887e8	+	3.87784e8i	−0.422847	+	0.732392i	−0.996217	−	0.0869044i	$-0.972303\pi$
$809$	−2.23887e8	+	3.87784e8i	−0.422847	+	0.732392i	0.573370	+	0.819297i	$0.305636\pi$
$810$		0			0
$811$		−	7.02416e8i		−	1.31684i	−0.752652	−	0.658418i	$-0.771226\pi$
$811$		−	7.02416e8i		−	1.31684i	0.752652	−	0.658418i	$-0.228774\pi$
$812$		0			0
$813$	1.97919e7			0.0368312
$814$		0			0
$815$	4.79695e8	+	2.76952e8i	0.886120	+	0.511601i
$816$		0			0
$817$	5.69823e8	−	3.28987e8i	1.04490	−	0.603272i
$818$		0			0
$819$	5.86301e7	−	2.26532e8i	0.106726	−	0.412361i
$820$		0			0
$821$	−3.31937e8	−	5.74932e8i	−0.599828	−	1.03893i	−0.992846	−	0.119402i	$-0.961902\pi$
$821$	−3.31937e8	−	5.74932e8i	−0.599828	−	1.03893i	0.393018	−	0.919531i	$-0.371431\pi$
$822$		0			0
$823$	2.08427e8	−	3.61007e8i	0.373900	−	0.647614i	−0.616262	−	0.787541i	$-0.711354\pi$
$823$	2.08427e8	−	3.61007e8i	0.373900	−	0.647614i	0.990162	+	0.139928i	$0.0446870\pi$
$824$		0			0
$825$			2.99698e8i			0.533731i
$826$		0			0
$827$	−1.14598e8			−0.202609			−0.101305	−	0.994855i	$-0.532302\pi$
$827$	−1.14598e8			−0.202609			−0.101305	+	0.994855i	$0.532302\pi$
$828$		0			0
$829$	4.05381e8	+	2.34047e8i	0.711541	+	0.410808i	0.811631	−	0.584170i	$-0.198580\pi$
$829$	4.05381e8	+	2.34047e8i	0.711541	+	0.410808i	−0.100090	+	0.994978i	$0.531913\pi$
$830$		0			0
$831$	9.04544e7	−	5.22239e7i	0.157626	−	0.0910052i
$832$		0			0
$833$	−3.50852e8	+	6.32398e8i	−0.607000	+	1.09410i
$834$		0			0
$835$	8.70425e7	+	1.50762e8i	0.149511	+	0.258960i
$836$		0			0
$837$	−4.77487e7	+	8.27031e7i	−0.0814301	+	0.141041i
$838$		0			0
$839$			6.49855e8i			1.10035i	0.835050	+	0.550174i	$0.185439\pi$
$839$			6.49855e8i			1.10035i	−0.835050	+	0.550174i	$0.814561\pi$
$840$		0			0
$841$	−4.09581e8			−0.688576
$842$		0			0
$843$	−4.33350e6	−	2.50195e6i	−0.00723363	−	0.00417634i
$844$		0			0
$845$	1.77163e8	−	1.02285e8i	0.293631	−	0.169528i
$846$		0			0
$847$	−4.00663e8	−	1.03698e8i	−0.659370	−	0.170656i
$848$		0			0
$849$	−2.49580e7	−	4.32285e7i	−0.0407837	−	0.0706394i
$850$		0			0
$851$	1.12542e8	−	1.94928e8i	0.182610	−	0.316290i
$852$		0			0
$853$			7.47082e7i			0.120371i	0.998187	+	0.0601854i	$0.0191692\pi$
$853$			7.47082e7i			0.120371i	−0.998187	+	0.0601854i	$0.980831\pi$
$854$		0			0
$855$	1.45385e8			0.232606
$856$		0			0
$857$	−7.50588e8	−	4.33352e8i	−1.19250	−	0.688491i	−0.233629	−	0.972326i	$-0.575060\pi$
$857$	−7.50588e8	−	4.33352e8i	−1.19250	−	0.688491i	−0.958873	+	0.283835i	$0.908393\pi$
$858$		0			0
$859$	1.51273e7	−	8.73376e6i	0.0238662	−	0.0137791i	−0.488019	−	0.872833i	$-0.662280\pi$
$859$	1.51273e7	−	8.73376e6i	0.0238662	−	0.0137791i	0.511886	+	0.859054i	$0.328947\pi$
$860$		0			0
$861$	5.41143e7	+	1.95271e8i	0.0847817	+	0.305934i
$862$		0			0
$863$	−5.59542e8	−	9.69155e8i	−0.870563	−	1.50786i	−0.861415	−	0.507902i	$-0.830421\pi$
$863$	−5.59542e8	−	9.69155e8i	−0.870563	−	1.50786i	−0.00914866	−	0.999958i	$-0.502912\pi$
$864$		0			0
$865$	2.74743e8	−	4.75869e8i	0.424501	−	0.735257i
$866$		0			0
$867$			2.12778e8i			0.326489i
$868$		0			0
$869$	−7.07593e8			−1.07826
$870$		0			0
$871$	−1.33397e9	−	7.70171e8i	−2.01880	−	1.16555i
$872$		0			0
$873$	1.37192e8	−	7.92076e7i	0.206198	−	0.119049i
$874$		0			0
$875$	−4.38417e8	−	4.30992e8i	−0.654430	−	0.643346i
$876$		0			0
$877$	−5.82730e8	−	1.00932e9i	−0.863910	−	1.49634i	−0.868125	−	0.496345i	$-0.834675\pi$
$877$	−5.82730e8	−	1.00932e9i	−0.863910	−	1.49634i	0.00421521	−	0.999991i	$-0.498658\pi$
$878$		0			0
$879$	2.08449e7	−	3.61044e7i	0.0306925	−	0.0531610i
$880$		0			0
$881$		−	2.07806e8i		−	0.303900i	−0.988388	−	0.151950i	$-0.951445\pi$
$881$		−	2.07806e8i		−	0.303900i	0.988388	−	0.151950i	$-0.0485553\pi$
$882$		0			0
$883$	3.48816e8			0.506657			0.253329	−	0.967380i	$-0.418475\pi$
$883$	3.48816e8			0.506657			0.253329	+	0.967380i	$0.418475\pi$
$884$		0			0
$885$	−6.47109e7	−	3.73609e7i	−0.0933572	−	0.0538998i
$886$		0			0
$887$	7.31382e8	−	4.22263e8i	1.04803	−	0.605080i	0.125932	−	0.992039i	$-0.459808\pi$
$887$	7.31382e8	−	4.22263e8i	1.04803	−	0.605080i	0.922097	+	0.386959i	$0.126475\pi$
$888$		0			0
$889$	2.68466e8	−	2.73091e8i	0.382106	−	0.388689i
$890$		0			0
$891$	5.09515e7	+	8.82506e7i	0.0720317	+	0.124763i
$892$		0			0
$893$	6.21681e8	−	1.07678e9i	0.872998	−	1.51208i
$894$		0			0
$895$			5.48320e8i			0.764830i
$896$		0			0
$897$	4.33314e8			0.600379
$898$		0			0
$899$	−2.97155e8	−	1.71562e8i	−0.408981	−	0.236125i
$900$		0			0
$901$	−8.79326e7	+	5.07679e7i	−0.120220	+	0.0694089i
$902$		0			0
$903$	−3.79473e8	+	1.05161e8i	−0.515368	+	0.142821i
$904$		0			0
$905$	−1.09023e8	−	1.88833e8i	−0.147086	−	0.254760i
$906$		0			0
$907$	−3.99924e8	+	6.92689e8i	−0.535989	+	0.928360i	0.463126	+	0.886293i	$0.346728\pi$
$907$	−3.99924e8	+	6.92689e8i	−0.535989	+	0.928360i	−0.999115	+	0.0420677i	$0.986605\pi$
$908$		0			0
$909$			2.48001e8i			0.330189i
$910$		0			0
$911$	−1.54047e8			−0.203750			−0.101875	−	0.994797i	$-0.532484\pi$
$911$	−1.54047e8			−0.203750			−0.101875	+	0.994797i	$0.532484\pi$
$912$		0			0
$913$	1.07530e8	+	6.20824e7i	0.141292	+	0.0815749i
$914$		0			0
$915$	2.38591e8	−	1.37750e8i	0.311451	−	0.179816i
$916$		0			0
$917$	−2.45937e7	+	9.50237e7i	−0.0318945	+	0.123232i
$918$		0			0
$919$	3.43544e8	+	5.95036e8i	0.442625	+	0.766649i	0.997883	−	0.0650288i	$-0.0207139\pi$
$919$	3.43544e8	+	5.95036e8i	0.442625	+	0.766649i	−0.555258	+	0.831678i	$0.687381\pi$
$920$		0			0
$921$	1.54922e8	−	2.68333e8i	0.198305	−	0.343475i
$922$		0			0
$923$			1.30729e9i			1.66252i
$924$		0			0
$925$	2.53255e8			0.319987
$926$		0			0
$927$	−8.82447e7	−	5.09481e7i	−0.110777	−	0.0639571i
$928$		0			0
$929$	3.27395e8	−	1.89021e8i	0.408342	−	0.235757i	−0.281735	−	0.959492i	$-0.590910\pi$
$929$	3.27395e8	−	1.89021e8i	0.408342	−	0.235757i	0.690077	+	0.723736i	$0.257577\pi$
$930$		0			0
$931$	5.41025e8	+	9.01176e8i	0.670453	+	1.11676i
$932$		0			0
$933$	1.22922e8	+	2.12908e8i	0.151351	+	0.262148i
$934$		0			0
$935$	3.55199e8	−	6.15223e8i	0.434547	−	0.752658i
$936$		0			0
$937$			1.27190e9i			1.54609i	0.634351	+	0.773045i	$0.281268\pi$
$937$			1.27190e9i			1.54609i	−0.634351	+	0.773045i	$0.718732\pi$
$938$		0			0
$939$	−1.64509e8			−0.198698
$940$		0			0
$941$	−6.05181e8	−	3.49402e8i	−0.726301	−	0.419330i	0.0907665	−	0.995872i	$-0.471068\pi$
$941$	−6.05181e8	−	3.49402e8i	−0.726301	−	0.419330i	−0.817067	+	0.576542i	$0.804402\pi$
$942$		0			0
$943$	−3.24960e8	+	1.87615e8i	−0.387520	+	0.223735i
$944$		0			0
$945$	−8.42324e7	−	2.18007e7i	−0.0998122	−	0.0258330i
$946$		0			0
$947$	−1.95719e8	−	3.38995e8i	−0.230453	−	0.399157i	0.727488	−	0.686120i	$-0.240688\pi$
$947$	−1.95719e8	−	3.38995e8i	−0.230453	−	0.399157i	−0.957942	+	0.286963i	$0.907354\pi$
$948$		0			0
$949$	−4.68464e8	+	8.11403e8i	−0.548122	+	0.949375i
$950$		0			0
$951$			5.03861e8i			0.585827i
$952$		0			0
$953$	−9.05418e8			−1.04609			−0.523047	−	0.852304i	$-0.675205\pi$
$953$	−9.05418e8			−1.04609			−0.523047	+	0.852304i	$0.675205\pi$
$954$		0			0
$955$	−4.99244e8	−	2.88239e8i	−0.573196	−	0.330935i
$956$		0			0
$957$	−3.17087e8	+	1.83070e8i	−0.361778	+	0.208873i
$958$		0			0
$959$	−3.42033e8	−	1.23422e9i	−0.387803	−	1.39939i
$960$		0			0
$961$	−1.25967e8	−	2.18180e8i	−0.141934	−	0.245836i
$962$		0			0
$963$	−2.68808e8	+	4.65589e8i	−0.300998	+	0.521343i
$964$		0			0
$965$			1.20463e7i			0.0134051i
$966$		0			0
$967$	1.33523e9			1.47665			0.738323	−	0.674448i	$-0.235618\pi$
$967$	1.33523e9			1.47665			0.738323	+	0.674448i	$0.235618\pi$
$968$		0			0
$969$	7.41422e8	+	4.28060e8i	0.814881	+	0.470472i
$970$		0			0
$971$	5.45806e8	−	3.15121e8i	0.596184	−	0.344207i	−0.171355	−	0.985209i	$-0.554814\pi$
$971$	5.45806e8	−	3.15121e8i	0.596184	−	0.344207i	0.767539	+	0.641002i	$0.221481\pi$
$972$		0			0
$973$	1.51216e8	+	1.48655e8i	0.164157	+	0.161376i
$974$		0			0
$975$	2.43774e8	+	4.22229e8i	0.263011	+	0.455549i
$976$		0			0
$977$	2.04552e8	−	3.54294e8i	0.219341	−	0.379910i	−0.735266	−	0.677779i	$-0.762943\pi$
$977$	2.04552e8	−	3.54294e8i	0.219341	−	0.379910i	0.954607	+	0.297869i	$0.0962760\pi$
$978$		0			0
$979$			2.81978e8i			0.300516i
$980$		0			0
$981$	−1.86116e8			−0.197141
$982$		0			0
$983$	−7.95291e8	−	4.59161e8i	−0.837270	−	0.483398i	0.0190654	−	0.999818i	$-0.493931\pi$
$983$	−7.95291e8	−	4.59161e8i	−0.837270	−	0.483398i	−0.856335	+	0.516420i	$0.827264\pi$
$984$		0			0
$985$	−1.56198e8	+	9.01810e7i	−0.163443	+	0.0943640i
$986$		0			0
$987$	−5.21651e8	+	5.30638e8i	−0.542536	+	0.551883i
$988$		0			0
$989$	−3.64596e8	−	6.31499e8i	−0.376897	−	0.652805i
$990$		0			0
$991$	−2.59369e8	+	4.49241e8i	−0.266500	+	0.461592i	−0.967956	−	0.251122i	$-0.919201\pi$
$991$	−2.59369e8	+	4.49241e8i	−0.266500	+	0.461592i	0.701455	+	0.712713i	$0.252534\pi$
$992$		0			0
$993$			3.12283e8i			0.318934i
$994$		0			0
$995$	4.04623e8			0.410754
$996$		0			0
$997$	3.12596e8	+	1.80477e8i	0.315426	+	0.182111i	0.649352	−	0.760488i	$-0.275040\pi$
$997$	3.12596e8	+	1.80477e8i	0.315426	+	0.182111i	−0.333926	+	0.942599i	$0.608374\pi$
$998$		0			0
$999$	7.45747e7	−	4.30557e7i	0.0747989	−	0.0431852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.d.241.2		8
4.3	odd	2		21.7.f.a.10.2	✓	8
7.5	odd	6	inner	336.7.bh.d.145.2		8
12.11	even	2		63.7.m.d.10.3		8
28.3	even	6		147.7.d.b.97.5		8
28.11	odd	6		147.7.d.b.97.6		8
28.19	even	6		21.7.f.a.19.2	yes	8
28.23	odd	6		147.7.f.d.19.2		8
28.27	even	2		147.7.f.d.31.2		8
84.11	even	6		441.7.d.c.244.4		8
84.47	odd	6		63.7.m.d.19.3		8
84.59	odd	6		441.7.d.c.244.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.2	✓	8	4.3	odd	2
21.7.f.a.19.2	yes	8	28.19	even	6
63.7.m.d.10.3		8	12.11	even	2
63.7.m.d.19.3		8	84.47	odd	6
147.7.d.b.97.5		8	28.3	even	6
147.7.d.b.97.6		8	28.11	odd	6
147.7.f.d.19.2		8	28.23	odd	6
147.7.f.d.31.2		8	28.27	even	2
336.7.bh.d.145.2		8	7.5	odd	6	inner
336.7.bh.d.241.2		8	1.1	even	1	trivial
441.7.d.c.244.3		8	84.59	odd	6
441.7.d.c.244.4		8	84.11	even	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.5000 + 7.79423i) q^{3} +(-57.9943 + 33.4830i) q^{5} +(240.457 - 244.600i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 + 7.79423i) q^{3} +(-57.9943 + 33.4830i) q^{5} +(240.457 - 244.600i) q^{7} +(121.500 + 210.444i) q^{9} +(862.868 - 1494.53i) q^{11} -2807.43i q^{13} -1043.90 q^{15} +(-5323.58 - 3073.57i) q^{17} +(-7737.30 + 4467.13i) q^{19} +(5152.64 - 1427.92i) q^{21} +(4950.64 + 8574.76i) q^{23} +(-5570.27 + 9648.00i) q^{25} +3788.00i q^{27} -13610.4 q^{29} +(21833.0 + 12605.3i) q^{31} +(23297.4 - 13450.8i) q^{33} +(-5755.21 + 22236.7i) q^{35} +(-11366.4 - 19687.1i) q^{37} +(21881.7 - 37900.2i) q^{39} +37897.2i q^{41} -73646.2 q^{43} +(-14092.6 - 8136.38i) q^{45} +(-120523. + 69583.9i) q^{47} +(-2009.47 - 117632. i) q^{49} +(-47912.2 - 82986.3i) q^{51} +(8258.79 - 14304.7i) q^{53} +115566. i q^{55} -139271. q^{57} +(61989.7 + 35789.8i) q^{59} +(-228557. + 131958. i) q^{61} +(80690.3 + 20883.9i) q^{63} +(94001.1 + 162815. i) q^{65} +(274333. - 475159. i) q^{67} +154346. i q^{69} -465655. q^{71} +(-289020. - 166866. i) q^{73} +(-150397. + 86832.0i) q^{75} +(-158080. - 570429. i) q^{77} +(-205012. - 355091. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +71948.9i q^{83} +411649. q^{85} +(-183740. - 106082. i) q^{87} +(-141505. + 81698.0i) q^{89} +(-686697. - 675066. i) q^{91} +(196497. + 340342. i) q^{93} +(299146. - 518137. i) q^{95} -651914. i q^{97} +419354. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} - 294 q^{5} + 656 q^{7} + 972 q^{9} + 314 q^{11} - 5292 q^{15} - 5532 q^{17} + 18234 q^{19} + 9342 q^{21} - 3928 q^{23} - 17038 q^{25} - 8300 q^{29} + 89508 q^{31} + 8478 q^{33} + 25860 q^{35} + 64706 q^{37} - 29106 q^{39} - 45740 q^{43} - 71442 q^{45} - 483276 q^{47} - 310684 q^{49} - 49788 q^{51} - 540974 q^{53} + 328212 q^{57} + 181770 q^{59} + 418224 q^{61} + 92826 q^{63} - 414204 q^{65} + 1158902 q^{67} - 1442344 q^{71} - 378666 q^{73} - 460026 q^{75} + 1065994 q^{77} - 611452 q^{79} - 236196 q^{81} - 275112 q^{85} - 112050 q^{87} - 989196 q^{89} - 304446 q^{91} + 805572 q^{93} + 591792 q^{95} + 152604 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 - 294 * q^5 + 656 * q^7 + 972 * q^9 + 314 * q^11 - 5292 * q^15 - 5532 * q^17 + 18234 * q^19 + 9342 * q^21 - 3928 * q^23 - 17038 * q^25 - 8300 * q^29 + 89508 * q^31 + 8478 * q^33 + 25860 * q^35 + 64706 * q^37 - 29106 * q^39 - 45740 * q^43 - 71442 * q^45 - 483276 * q^47 - 310684 * q^49 - 49788 * q^51 - 540974 * q^53 + 328212 * q^57 + 181770 * q^59 + 418224 * q^61 + 92826 * q^63 - 414204 * q^65 + 1158902 * q^67 - 1442344 * q^71 - 378666 * q^73 - 460026 * q^75 + 1065994 * q^77 - 611452 * q^79 - 236196 * q^81 - 275112 * q^85 - 112050 * q^87 - 989196 * q^89 - 304446 * q^91 + 805572 * q^93 + 591792 * q^95 + 152604 * q^99

Introduction

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