LMFDB - Embedded newform 315.4.bj.b.206.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(26,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("315.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			206.6
Character	$\chi$	$=$	315.206
Dual form			315.4.bj.b.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57393 + 0.908710i) q^{2} +(-2.34849 + 4.06771i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.6185 + 8.17469i) q^{7} -23.0758i q^{8} +O(q^{10})$	\(q+(-1.57393 + 0.908710i) q^{2} +(-2.34849 + 4.06771i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.6185 + 8.17469i) q^{7} -23.0758i q^{8} +(-7.86966 - 4.54355i) q^{10} +(-9.99156 - 5.76863i) q^{11} -89.2576i q^{13} +(18.7280 - 27.9678i) q^{14} +(2.18125 + 3.77803i) q^{16} +(-59.0397 + 102.260i) q^{17} +(98.7342 - 57.0042i) q^{19} -23.4849 q^{20} +20.9681 q^{22} +(19.6708 - 11.3569i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(81.1093 + 140.486i) q^{26} +(5.77618 - 86.7973i) q^{28} +38.6235i q^{29} +(-12.6051 - 7.27757i) q^{31} +(153.007 + 88.3388i) q^{32} -214.600i q^{34} +(-76.9437 - 51.5235i) q^{35} +(-43.4623 - 75.2789i) q^{37} +(-103.601 + 179.442i) q^{38} +(99.9210 - 57.6894i) q^{40} +297.321 q^{41} +116.032 q^{43} +(46.9302 - 27.0952i) q^{44} +(-20.6403 + 35.7500i) q^{46} +(-162.997 - 282.319i) q^{47} +(209.349 - 271.702i) q^{49} -45.4355i q^{50} +(363.074 + 209.621i) q^{52} +(322.829 + 186.386i) q^{53} -57.6863i q^{55} +(188.637 + 383.484i) q^{56} +(-35.0976 - 60.7908i) q^{58} +(2.56221 - 4.43788i) q^{59} +(490.677 - 283.293i) q^{61} +26.4528 q^{62} -355.997 q^{64} +(386.497 - 223.144i) q^{65} +(418.238 - 724.409i) q^{67} +(-277.309 - 480.313i) q^{68} +(167.924 + 11.1750i) q^{70} +8.15914i q^{71} +(-887.678 - 512.501i) q^{73} +(136.813 + 78.9892i) q^{74} +535.495i q^{76} +(213.202 + 14.1881i) q^{77} +(359.673 + 622.971i) q^{79} +(-10.9062 + 18.8902i) q^{80} +(-467.964 + 270.179i) q^{82} +1330.07 q^{83} -590.397 q^{85} +(-182.627 + 105.440i) q^{86} +(-133.116 + 230.563i) q^{88} +(-135.540 - 234.762i) q^{89} +(729.653 + 1483.33i) q^{91} +106.686i q^{92} +(513.092 + 296.234i) q^{94} +(493.671 + 285.021i) q^{95} -947.958i q^{97} +(-82.6028 + 617.878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 80 q^{5} - 44 q^{7}+O(q^{10}) $ 32 * q + 64 * q^4 + 80 * q^5 - 44 * q^7	$ 32 q + 64 q^{4} + 80 q^{5} - 44 q^{7} + 72 q^{11} - 108 q^{14} - 196 q^{16} + 396 q^{19} + 640 q^{20} - 480 q^{22} + 36 q^{23} - 400 q^{25} - 120 q^{26} - 316 q^{28} - 300 q^{31} + 1620 q^{32} - 20 q^{35} + 980 q^{37} - 888 q^{38} - 1296 q^{41} + 8 q^{43} + 4068 q^{44} + 540 q^{46} - 120 q^{47} - 1396 q^{49} - 4452 q^{52} + 576 q^{53} - 4260 q^{56} + 828 q^{58} - 96 q^{59} + 336 q^{61} - 4152 q^{62} - 5120 q^{64} + 1020 q^{65} + 700 q^{67} + 60 q^{68} + 540 q^{70} - 756 q^{73} + 5796 q^{74} - 2952 q^{77} + 916 q^{79} + 980 q^{80} + 5832 q^{82} - 2352 q^{83} + 3276 q^{86} - 1212 q^{88} + 1608 q^{89} - 960 q^{91} + 5112 q^{94} + 1980 q^{95} - 5184 q^{98}+O(q^{100}) $ 32 * q + 64 * q^4 + 80 * q^5 - 44 * q^7 + 72 * q^11 - 108 * q^14 - 196 * q^16 + 396 * q^19 + 640 * q^20 - 480 * q^22 + 36 * q^23 - 400 * q^25 - 120 * q^26 - 316 * q^28 - 300 * q^31 + 1620 * q^32 - 20 * q^35 + 980 * q^37 - 888 * q^38 - 1296 * q^41 + 8 * q^43 + 4068 * q^44 + 540 * q^46 - 120 * q^47 - 1396 * q^49 - 4452 * q^52 + 576 * q^53 - 4260 * q^56 + 828 * q^58 - 96 * q^59 + 336 * q^61 - 4152 * q^62 - 5120 * q^64 + 1020 * q^65 + 700 * q^67 + 60 * q^68 + 540 * q^70 - 756 * q^73 + 5796 * q^74 - 2952 * q^77 + 916 * q^79 + 980 * q^80 + 5832 * q^82 - 2352 * q^83 + 3276 * q^86 - 1212 * q^88 + 1608 * q^89 - 960 * q^91 + 5112 * q^94 + 1980 * q^95 - 5184 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.57393	+	0.908710i	−0.556469	+	0.321278i	−0.751727	−	0.659474i	$-0.770779\pi$
$2$	−1.57393	+	0.908710i	−0.556469	+	0.321278i	0.195258	+	0.980752i	$0.437446\pi$
$3$		0			0
$3$		0			0
$4$	−2.34849	+	4.06771i	−0.293561	+	0.508463i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−16.6185	+	8.17469i	−0.897315	+	0.441392i
$7$	−16.6185	+	8.17469i	−0.897315	+	0.441392i
$8$		−	23.0758i		−	1.01981i
$9$		0			0
$10$	−7.86966	−	4.54355i	−0.248861	−	0.143680i
$11$	−9.99156	−	5.76863i	−0.273870	−	0.158119i	0.356775	−	0.934190i	$-0.383876\pi$
$11$	−9.99156	−	5.76863i	−0.273870	−	0.158119i	−0.630645	+	0.776071i	$0.717210\pi$
$12$		0			0
$13$		−	89.2576i		−	1.90428i	−0.305665	−	0.952139i	$-0.598879\pi$
$13$		−	89.2576i		−	1.90428i	0.305665	−	0.952139i	$-0.401121\pi$
$14$	18.7280	−	27.9678i	0.357519	−	0.533908i
$15$		0			0
$16$	2.18125	+	3.77803i	0.0340820	+	0.0590317i
$17$	−59.0397	+	102.260i	−0.842308	+	1.45892i	0.0456302	+	0.998958i	$0.485470\pi$
$17$	−59.0397	+	102.260i	−0.842308	+	1.45892i	−0.887938	+	0.459962i	$0.847863\pi$
$18$		0			0
$19$	98.7342	−	57.0042i	1.19217	−	0.688298i	0.233369	−	0.972388i	$-0.425025\pi$
$19$	98.7342	−	57.0042i	1.19217	−	0.688298i	0.958798	+	0.284090i	$0.0916915\pi$
$20$	−23.4849			−0.262569
$21$		0			0
$22$	20.9681			0.203200
$23$	19.6708	−	11.3569i	0.178332	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$23$	19.6708	−	11.3569i	0.178332	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	81.1093	+	140.486i	0.611802	+	1.05967i
$27$		0			0
$28$	5.77618	−	86.7973i	0.0389856	−	0.585827i
$29$			38.6235i			0.247318i	0.992325	+	0.123659i	$0.0394628\pi$
$29$			38.6235i			0.247318i	−0.992325	+	0.123659i	$0.960537\pi$
$30$		0			0
$31$	−12.6051	−	7.27757i	−0.0730306	−	0.0421642i	0.463040	−	0.886337i	$-0.346759\pi$
$31$	−12.6051	−	7.27757i	−0.0730306	−	0.0421642i	−0.536071	+	0.844173i	$0.680092\pi$
$32$	153.007	+	88.3388i	0.845254	+	0.488007i
$33$		0			0
$34$		−	214.600i		−	1.08246i
$35$	−76.9437	−	51.5235i	−0.371596	−	0.248830i
$36$		0			0
$37$	−43.4623	−	75.2789i	−0.193112	−	0.334480i	0.753168	−	0.657828i	$-0.228525\pi$
$37$	−43.4623	−	75.2789i	−0.193112	−	0.334480i	−0.946280	+	0.323348i	$0.895192\pi$
$38$	−103.601	+	179.442i	−0.442269	+	0.766033i
$39$		0			0
$40$	99.9210	−	57.6894i	0.394972	−	0.228037i
$41$	297.321			1.13253			0.566266	−	0.824223i	$-0.308388\pi$
$41$	297.321			1.13253			0.566266	+	0.824223i	$0.308388\pi$
$42$		0			0
$43$	116.032			0.411506			0.205753	−	0.978604i	$-0.434036\pi$
$43$	116.032			0.411506			0.205753	+	0.978604i	$0.434036\pi$
$44$	46.9302	−	27.0952i	0.160795	−	0.0928352i
$45$		0			0
$46$	−20.6403	+	35.7500i	−0.0661575	+	0.114588i
$47$	−162.997	−	282.319i	−0.505863	−	0.876180i	−0.999977	−	0.00678301i	$-0.997841\pi$
$47$	−162.997	−	282.319i	−0.505863	−	0.876180i	0.494114	−	0.869397i	$-0.335492\pi$
$48$		0			0
$49$	209.349	−	271.702i	0.610347	−	0.792134i
$50$		−	45.4355i		−	0.128511i
$51$		0			0
$52$	363.074	+	209.621i	0.968256	+	0.559023i
$53$	322.829	+	186.386i	0.836680	+	0.483057i	0.856134	−	0.516753i	$-0.172860\pi$
$53$	322.829	+	186.386i	0.836680	+	0.483057i	−0.0194545	+	0.999811i	$0.506193\pi$
$54$		0			0
$55$		−	57.6863i		−	0.141426i
$56$	188.637	+	383.484i	0.450137	+	0.915094i
$57$		0			0
$58$	−35.0976	−	60.7908i	−0.0794576	−	0.137625i
$59$	2.56221	−	4.43788i	0.00565376	−	0.00979260i	−0.863185	−	0.504888i	$-0.831534\pi$
$59$	2.56221	−	4.43788i	0.00565376	−	0.00979260i	0.868838	+	0.495096i	$0.164867\pi$
$60$		0			0
$61$	490.677	−	283.293i	1.02991	−	0.594621i	0.112954	−	0.993600i	$-0.463969\pi$
$61$	490.677	−	283.293i	1.02991	−	0.594621i	0.916960	+	0.398979i	$0.130635\pi$
$62$	26.4528			0.0541857
$63$		0			0
$64$	−355.997			−0.695307
$65$	386.497	−	223.144i	0.737524	−	0.425810i
$66$		0			0
$67$	418.238	−	724.409i	0.762625	−	1.32091i	−0.178868	−	0.983873i	$-0.557243\pi$
$67$	418.238	−	724.409i	0.762625	−	1.32091i	0.941493	−	0.337033i	$-0.109423\pi$
$68$	−277.309	−	480.313i	−0.494538	−	0.856566i
$69$		0			0
$70$	167.924	+	11.1750i	0.286725	+	0.0190810i
$71$			8.15914i			0.0136382i	0.999977	+	0.00681910i	$0.00217060\pi$
$71$			8.15914i			0.0136382i	−0.999977	+	0.00681910i	$0.997829\pi$
$72$		0			0
$73$	−887.678	−	512.501i	−1.42322	−	0.821695i	−0.426645	−	0.904419i	$-0.640305\pi$
$73$	−887.678	−	512.501i	−1.42322	−	0.821695i	−0.996573	+	0.0827238i	$0.973638\pi$
$74$	136.813	+	78.9892i	0.214922	+	0.124085i
$75$		0			0
$76$			535.495i			0.808231i
$77$	213.202	+	14.1881i	0.315540	+	0.0209985i
$78$		0			0
$79$	359.673	+	622.971i	0.512232	+	0.887212i	0.999899	+	0.0141825i	$0.00451457\pi$
$79$	359.673	+	622.971i	0.512232	+	0.887212i	−0.487667	+	0.873030i	$0.662152\pi$
$80$	−10.9062	+	18.8902i	−0.0152419	+	0.0263998i
$81$		0			0
$82$	−467.964	+	270.179i	−0.630219	+	0.363857i
$83$	1330.07			1.75897			0.879484	−	0.475928i	$-0.157888\pi$
$83$	1330.07			1.75897			0.879484	+	0.475928i	$0.157888\pi$
$84$		0			0
$85$	−590.397			−0.753383
$86$	−182.627	+	105.440i	−0.228990	+	0.132208i
$87$		0			0
$88$	−133.116	+	230.563i	−0.161252	+	0.279296i
$89$	−135.540	−	234.762i	−0.161429	−	0.279604i	0.773952	−	0.633244i	$-0.218277\pi$
$89$	−135.540	−	234.762i	−0.161429	−	0.279604i	−0.935382	+	0.353640i	$0.884944\pi$
$90$		0			0
$91$	729.653	+	1483.33i	0.840532	+	1.70874i
$92$			106.686i			0.120900i
$93$		0			0
$94$	513.092	+	296.234i	0.562994	+	0.325045i
$95$	493.671	+	285.021i	0.533153	+	0.307816i
$96$		0			0
$97$		−	947.958i		−	0.992273i	−0.868244	−	0.496137i	$-0.834752\pi$
$97$		−	947.958i		−	0.992273i	0.868244	−	0.496137i	$-0.165248\pi$
$98$	−82.6028	+	617.878i	−0.0851443	+	0.636889i
$99$		0			0
$100$	−58.7123	−	101.693i	−0.0587123	−	0.101693i
$101$	224.871	−	389.488i	0.221540	−	0.383718i	−0.733736	−	0.679435i	$-0.762225\pi$
$101$	224.871	−	389.488i	0.221540	−	0.383718i	0.955276	+	0.295717i	$0.0955585\pi$
$102$		0			0
$103$	−211.511	+	122.116i	−0.202338	+	0.116820i	−0.597745	−	0.801686i	$-0.703937\pi$
$103$	−211.511	+	122.116i	−0.202338	+	0.116820i	0.395408	+	0.918506i	$0.370603\pi$
$104$	−2059.69			−1.94201
$105$		0			0
$106$	−677.482			−0.620782
$107$	−1616.58	+	933.335i	−1.46057	+	0.843261i	−0.999038	−	0.0438617i	$-0.986034\pi$
$107$	−1616.58	+	933.335i	−1.46057	+	0.843261i	−0.461533	+	0.887123i	$0.652701\pi$
$108$		0			0
$109$	119.585	−	207.128i	0.105084	−	0.182012i	−0.808688	−	0.588237i	$-0.799822\pi$
$109$	119.585	−	207.128i	0.105084	−	0.182012i	0.913773	+	0.406226i	$0.133155\pi$
$110$	52.4201	+	90.7944i	0.0454370	+	0.0786991i
$111$		0			0
$112$	−67.1333	−	44.9542i	−0.0566384	−	0.0379265i
$113$		−	1795.96i		−	1.49513i	−0.664189	−	0.747564i	$-0.731223\pi$
$113$		−	1795.96i		−	1.49513i	0.664189	−	0.747564i	$-0.268777\pi$
$114$		0			0
$115$	98.3538	+	56.7846i	0.0797525	+	0.0460451i
$116$	−157.109	−	90.7070i	−0.125752	−	0.0726029i
$117$		0			0
$118$			9.31324i			0.00726571i
$119$	145.210	−	2182.04i	0.111860	−	1.68090i
$120$		0			0
$121$	−598.946	−	1037.40i	−0.449997	−	0.779417i
$122$	−514.862	+	891.767i	−0.382077	+	0.661777i
$123$		0			0
$124$	59.2060	−	34.1826i	0.0428779	−	0.0247556i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−426.315			−0.297869			−0.148934	−	0.988847i	$-0.547584\pi$
$127$	−426.315			−0.297869			−0.148934	+	0.988847i	$0.547584\pi$
$128$	−663.742	+	383.212i	−0.458337	+	0.264621i
$129$		0			0
$130$	−405.547	+	702.428i	−0.273606	+	0.473900i
$131$	303.267	+	525.273i	0.202264	+	0.350331i	0.949257	−	0.314500i	$-0.101837\pi$
$131$	303.267	+	525.273i	0.202264	+	0.350331i	−0.746994	+	0.664831i	$0.768504\pi$
$132$		0			0
$133$	−1174.82	+	1754.45i	−0.765940	+	1.14383i
$134$			1520.23i			0.980058i
$135$		0			0
$136$	2359.72	+	1362.39i	1.48783	+	0.858998i
$137$	−1339.02	−	773.081i	−0.835035	−	0.482108i	0.0205385	−	0.999789i	$-0.493462\pi$
$137$	−1339.02	−	773.081i	−0.835035	−	0.482108i	−0.855573	+	0.517681i	$0.826795\pi$
$138$		0			0
$139$		−	918.929i		−	0.560738i	−0.959892	−	0.280369i	$-0.909543\pi$
$139$		−	918.929i		−	0.560738i	0.959892	−	0.280369i	$-0.0904568\pi$
$140$	390.284	−	191.982i	0.235607	−	0.115896i
$141$		0			0
$142$	−7.41429	−	12.8419i	−0.00438165	−	0.00758923i
$143$	−514.894	+	891.823i	−0.301102	+	0.521525i
$144$		0			0
$145$	−167.245	+	96.5588i	−0.0957857	+	0.0553019i
$146$	1862.86			1.05597
$147$		0			0
$148$	408.283			0.226761
$149$	−860.987	+	497.091i	−0.473388	+	0.273311i	−0.717657	−	0.696397i	$-0.754785\pi$
$149$	−860.987	+	497.091i	−0.473388	+	0.273311i	0.244269	+	0.969708i	$0.421452\pi$
$150$		0			0
$151$	−975.133	+	1688.98i	−0.525531	+	0.910246i	0.474027	+	0.880510i	$0.342800\pi$
$151$	−975.133	+	1688.98i	−0.525531	+	0.910246i	−0.999558	+	0.0297358i	$0.990533\pi$
$152$	−1315.42	−	2278.37i	−0.701936	−	1.21579i
$153$		0			0
$154$	−348.458	+	171.407i	−0.182335	+	0.0896909i
$155$		−	72.7757i		−	0.0377128i
$156$		0			0
$157$	907.757	+	524.094i	0.461445	+	0.266415i	0.712652	−	0.701518i	$-0.247494\pi$
$157$	907.757	+	524.094i	0.461445	+	0.266415i	−0.251207	+	0.967933i	$0.580827\pi$
$158$	−1132.20	−	653.676i	−0.570083	−	0.329137i
$159$		0			0
$160$			883.388i			0.436487i
$161$	−234.059	+	349.537i	−0.114574	+	0.171102i
$162$		0			0
$163$	−1853.52	−	3210.39i	−0.890666	−	1.54268i	−0.839078	−	0.544011i	$-0.816905\pi$
$163$	−1853.52	−	3210.39i	−0.890666	−	1.54268i	−0.0515885	−	0.998668i	$-0.516428\pi$
$164$	−698.257	+	1209.42i	−0.332468	+	0.575851i
$165$		0			0
$166$	−2093.44	+	1208.65i	−0.978812	+	0.565117i
$167$	−1262.09			−0.584809			−0.292405	−	0.956295i	$-0.594455\pi$
$167$	−1262.09			−0.584809			−0.292405	+	0.956295i	$0.594455\pi$
$168$		0			0
$169$	−5769.93			−2.62628
$170$	929.246	−	536.500i	0.419235	−	0.242045i
$171$		0			0
$172$	−272.501	+	471.985i	−0.120802	+	0.209236i
$173$	−1979.08	−	3427.87i	−0.869750	−	1.50645i	−0.862252	−	0.506480i	$-0.830946\pi$
$173$	−1979.08	−	3427.87i	−0.869750	−	1.50645i	−0.00749851	−	0.999972i	$-0.502387\pi$
$174$		0			0
$175$	30.7441	−	461.985i	0.0132802	−	0.199559i
$176$		−	50.3313i		−	0.0215560i
$177$		0			0
$178$	426.662	+	246.333i	0.179661	+	0.103727i
$179$	2769.40	+	1598.91i	1.15640	+	0.667645i	0.950437	−	0.310916i	$-0.100636\pi$
$179$	2769.40	+	1598.91i	1.15640	+	0.667645i	0.205958	+	0.978561i	$0.433969\pi$
$180$		0			0
$181$			3272.44i			1.34386i	0.740614	+	0.671931i	$0.234535\pi$
$181$			3272.44i			1.34386i	−0.740614	+	0.671931i	$0.765465\pi$
$182$	−2496.34	−	1671.61i	−1.01671	−	0.680815i
$183$		0			0
$184$	−262.069	−	453.918i	−0.105000	−	0.181865i
$185$	217.311	−	376.394i	0.0863624	−	0.149584i
$186$		0			0
$187$	1179.80	−	681.157i	0.461366	−	0.266370i
$188$	1531.19			0.594007
$189$		0			0
$190$	−1036.01			−0.395578
$191$	1847.07	−	1066.41i	0.699736	−	0.403993i	−0.107513	−	0.994204i	$-0.534289\pi$
$191$	1847.07	−	1066.41i	0.699736	−	0.403993i	0.807249	+	0.590211i	$0.200955\pi$
$192$		0			0
$193$	1534.66	−	2658.11i	0.572369	−	0.991372i	−0.423953	−	0.905684i	$-0.639358\pi$
$193$	1534.66	−	2658.11i	0.572369	−	0.991372i	0.996322	−	0.0856876i	$-0.0273087\pi$
$194$	861.419	+	1492.02i	0.318795	+	0.552169i
$195$		0			0
$196$	613.550	+	1489.66i	0.223597	+	0.542879i
$197$			601.003i			0.217359i	0.994077	+	0.108679i	$0.0346622\pi$
$197$			601.003i			0.217359i	−0.994077	+	0.108679i	$0.965338\pi$
$198$		0			0
$199$	2405.49	+	1388.81i	0.856887	+	0.494724i	0.862969	−	0.505258i	$-0.168603\pi$
$199$	2405.49	+	1388.81i	0.856887	+	0.494724i	−0.00608174	+	0.999982i	$0.501936\pi$
$200$	499.605	+	288.447i	0.176637	+	0.101981i
$201$		0			0
$202$			817.370i			0.284703i
$203$	−315.735	−	641.865i	−0.109164	−	0.221922i
$204$		0			0
$205$	743.304	+	1287.44i	0.253242	+	0.438628i
$206$	221.936	−	384.404i	0.0750632	−	0.130013i
$207$		0			0
$208$	337.218	−	194.693i	0.112413	−	0.0649016i
$209$	−1315.34			−0.435332
$210$		0			0
$211$	2866.13			0.935129			0.467565	−	0.883959i	$-0.345131\pi$
$211$	2866.13			0.935129			0.467565	+	0.883959i	$0.345131\pi$
$212$	−1516.32	+	875.450i	−0.491234	+	0.283614i
$213$		0			0
$214$	1696.26	−	2938.01i	0.541842	−	0.938498i
$215$	290.080	+	502.434i	0.0920155	+	0.159375i
$216$		0			0
$217$	268.970	+	17.8994i	0.0841423	+	0.00559949i
$218$			434.674i			0.135045i
$219$		0			0
$220$	234.651	+	135.476i	0.0719098	+	0.0415172i
$221$	9127.47	+	5269.75i	2.77819	+	1.60399i
$222$		0			0
$223$		−	3080.88i		−	0.925161i	−0.886577	−	0.462581i	$-0.846924\pi$
$223$		−	3080.88i		−	0.925161i	0.886577	−	0.462581i	$-0.153076\pi$
$224$	−3264.89	−	217.272i	−0.973861	−	0.0648084i
$225$		0			0
$226$	1632.01	+	2826.72i	0.480351	+	0.831993i
$227$	−725.695	+	1256.94i	−0.212185	+	0.367516i	−0.952398	−	0.304857i	$-0.901391\pi$
$227$	−725.695	+	1256.94i	−0.212185	+	0.367516i	0.740213	+	0.672373i	$0.234725\pi$
$228$		0			0
$229$	2880.54	−	1663.08i	0.831230	−	0.479911i	−0.0230433	−	0.999734i	$-0.507336\pi$
$229$	2880.54	−	1663.08i	0.831230	−	0.479911i	0.854274	+	0.519823i	$0.174002\pi$
$230$	−206.403			−0.0591731
$231$		0			0
$232$	891.267			0.252218
$233$	187.415	−	108.204i	0.0526951	−	0.0304235i	−0.473421	−	0.880836i	$-0.656981\pi$
$233$	187.415	−	108.204i	0.0526951	−	0.0304235i	0.526116	+	0.850413i	$0.323648\pi$
$234$		0			0
$235$	814.985	−	1411.60i	0.226229	−	0.391840i
$236$	12.0347	+	20.8447i	0.00331945	+	0.00574946i
$237$		0			0
$238$	1754.29	+	3566.33i	0.477788	+	0.971306i
$239$		−	7354.42i		−	1.99045i	−0.0975992	−	0.995226i	$-0.531116\pi$
$239$		−	7354.42i		−	1.99045i	0.0975992	−	0.995226i	$-0.468884\pi$
$240$		0			0
$241$	−2307.09	−	1332.00i	−0.616650	−	0.356023i	0.158914	−	0.987293i	$-0.449201\pi$
$241$	−2307.09	−	1332.00i	−0.616650	−	0.356023i	−0.775564	+	0.631269i	$0.782534\pi$
$242$	1885.40	+	1088.54i	0.500819	+	0.289148i
$243$		0			0
$244$			2661.24i			0.698231i
$245$	1699.88	+	227.253i	0.443270	+	0.0592598i
$246$		0			0
$247$	−5088.06	−	8812.78i	−1.31071	−	2.27022i
$248$	−167.935	+	290.873i	−0.0429997	+	0.0744776i
$249$		0			0
$250$	196.742	−	113.589i	0.0497721	−	0.0287359i
$251$	6971.13			1.75304			0.876521	−	0.481363i	$-0.159858\pi$
$251$	6971.13			1.75304			0.876521	+	0.481363i	$0.159858\pi$
$252$		0			0
$253$	−262.055			−0.0651197
$254$	670.991	−	387.397i	0.165755	−	0.0956986i
$255$		0			0
$256$	2120.45	−	3672.72i	0.517687	−	0.896660i
$257$	936.319	+	1621.75i	0.227260	+	0.393627i	0.956995	−	0.290104i	$-0.0936898\pi$
$257$	936.319	+	1621.75i	0.227260	+	0.393627i	−0.729735	+	0.683730i	$0.760356\pi$
$258$		0			0
$259$	1337.66	+	895.731i	0.320919	+	0.214896i
$260$			2096.21i			0.500005i
$261$		0			0
$262$	−954.642	−	551.163i	−0.225107	−	0.129965i
$263$	2734.02	+	1578.49i	0.641016	+	0.370091i	0.785006	−	0.619489i	$-0.212660\pi$
$263$	2734.02	+	1578.49i	0.641016	+	0.370091i	−0.143990	+	0.989579i	$0.545993\pi$
$264$		0			0
$265$			1863.86i			0.432060i
$266$	254.809	−	3828.95i	0.0587343	−	0.882587i
$267$		0			0
$268$	1964.46	+	3402.54i	0.447755	+	0.775534i
$269$	−2494.49	+	4320.58i	−0.565397	+	0.979296i	0.431616	+	0.902058i	$0.357944\pi$
$269$	−2494.49	+	4320.58i	−0.565397	+	0.979296i	−0.997013	+	0.0772387i	$0.975390\pi$
$270$		0			0
$271$	−4563.57	+	2634.78i	−1.02294	+	0.590595i	−0.914954	−	0.403557i	$-0.867774\pi$
$271$	−4563.57	+	2634.78i	−1.02294	+	0.590595i	−0.107987	+	0.994152i	$0.534440\pi$
$272$	−515.121			−0.114830
$273$		0			0
$274$	2810.03			0.619562
$275$	249.789	−	144.216i	0.0547740	−	0.0316238i
$276$		0			0
$277$	3063.26	−	5305.71i	0.664452	−	1.15086i	−0.314982	−	0.949098i	$-0.601998\pi$
$277$	3063.26	−	5305.71i	0.664452	−	1.15086i	0.979434	−	0.201767i	$-0.0646683\pi$
$278$	835.040	+	1446.33i	0.180153	+	0.312033i
$279$		0			0
$280$	−1188.94	+	1775.53i	−0.253761	+	0.378959i
$281$		−	4795.11i		−	1.01798i	−0.860773	−	0.508990i	$-0.830019\pi$
$281$		−	4795.11i		−	1.01798i	0.860773	−	0.508990i	$-0.169981\pi$
$282$		0			0
$283$	3758.87	+	2170.19i	0.789547	+	0.455845i	0.839803	−	0.542891i	$-0.182670\pi$
$283$	3758.87	+	2170.19i	0.789547	+	0.455845i	−0.0502560	+	0.998736i	$0.516004\pi$
$284$	−33.1890	−	19.1617i	−0.00693452	−	0.00400365i
$285$		0			0
$286$		−	1871.56i		−	0.386950i
$287$	−4941.04	+	2430.51i	−1.01624	+	0.499890i
$288$		0			0
$289$	−4514.88	−	7820.00i	−0.918966	−	1.59170i
$290$	175.488	−	303.954i	0.0355345	−	0.0615476i
$291$		0			0
$292$	4169.41	−	2407.21i	0.835604	−	0.482436i
$293$	−5945.85			−1.18553			−0.592765	−	0.805376i	$-0.701964\pi$
$293$	−5945.85			−1.18553			−0.592765	+	0.805376i	$0.701964\pi$
$294$		0			0
$295$	25.6221			0.00505688
$296$	−1737.12	+	1002.93i	−0.341108	+	0.196939i
$297$		0			0
$298$	903.423	−	1564.77i	0.175617	−	0.304178i
$299$	−1013.69	−	1755.77i	−0.196065	−	0.339594i
$300$		0			0
$301$	−1928.28	+	948.527i	−0.369250	+	0.181635i
$302$		−	3544.45i		−	0.675365i
$303$		0			0
$304$	430.727	+	248.681i	0.0812629	+	0.0469171i
$305$	2453.39	+	1416.46i	0.460592	+	0.265923i
$306$		0			0
$307$		−	6012.75i		−	1.11780i	−0.829234	−	0.558902i	$-0.811223\pi$
$307$		−	6012.75i		−	1.11780i	0.829234	−	0.558902i	$-0.188777\pi$
$308$	−558.415	+	833.920i	−0.103307	+	0.154276i
$309$		0			0
$310$	66.1320	+	114.544i	0.0121163	+	0.0209860i
$311$	−677.179	+	1172.91i	−0.123470	+	0.213857i	−0.921134	−	0.389246i	$-0.872736\pi$
$311$	−677.179	+	1172.91i	−0.123470	+	0.213857i	0.797664	+	0.603103i	$0.206069\pi$
$312$		0			0
$313$	−1422.85	+	821.485i	−0.256947	+	0.148348i	−0.622941	−	0.782269i	$-0.714062\pi$
$313$	−1422.85	+	821.485i	−0.256947	+	0.148348i	0.365994	+	0.930617i	$0.380729\pi$
$314$	−1905.00			−0.342373
$315$		0			0
$316$	−3378.75			−0.601486
$317$	5624.76	−	3247.46i	0.996586	−	0.575379i	0.0893498	−	0.996000i	$-0.471521\pi$
$317$	5624.76	−	3247.46i	0.996586	−	0.575379i	0.907236	+	0.420621i	$0.138188\pi$
$318$		0			0
$319$	222.805	−	385.909i	0.0391056	−	0.0677328i
$320$	−889.994	−	1541.51i	−0.155475	−	0.269291i
$321$		0			0
$322$	50.7654	−	762.840i	0.00878585	−	0.132023i
$323$			13462.1i			2.31904i
$324$		0			0
$325$	1932.48	+	1115.72i	0.329831	+	0.190428i
$326$	5834.62	+	3368.62i	0.991257	+	0.572302i
$327$		0			0
$328$		−	6860.92i		−	1.15497i
$329$	5016.63	+	3359.27i	0.840656	+	0.562926i
$330$		0			0
$331$	−496.756	−	860.406i	−0.0824899	−	0.142877i	0.821829	−	0.569734i	$-0.192954\pi$
$331$	−496.756	−	860.406i	−0.0824899	−	0.142877i	−0.904319	+	0.426858i	$0.859621\pi$
$332$	−3123.66	+	5410.34i	−0.516365	+	0.894371i
$333$		0			0
$334$	1986.44	−	1146.87i	0.325428	−	0.187886i
$335$	4182.38			0.682113
$336$		0			0
$337$	−5846.79			−0.945089			−0.472545	−	0.881307i	$-0.656664\pi$
$337$	−5846.79			−0.945089			−0.472545	+	0.881307i	$0.656664\pi$
$338$	9081.48	−	5243.19i	1.46144	−	0.843764i
$339$		0			0
$340$	1386.54	−	2401.56i	0.221164	−	0.383068i
$341$	83.9633	+	145.429i	0.0133339	+	0.0230950i
$342$		0			0
$343$	−1257.99	+	6226.64i	−0.198032	+	0.980196i
$344$		−	2677.53i		−	0.419659i
$345$		0			0
$346$	6229.88	+	3596.82i	0.967978	+	0.558863i
$347$	−8301.55	−	4792.90i	−1.28430	−	0.741489i	−0.306665	−	0.951817i	$-0.599213\pi$
$347$	−8301.55	−	4792.90i	−1.28430	−	0.741489i	−0.977631	+	0.210329i	$0.932547\pi$
$348$		0			0
$349$		−	1384.95i		−	0.212421i	−0.994344	−	0.106210i	$-0.966128\pi$
$349$		−	1384.95i		−	0.212421i	0.994344	−	0.106210i	$-0.0338717\pi$
$350$	371.421	+	755.070i	0.0567237	+	0.115315i
$351$		0			0
$352$	−1019.19	−	1765.28i	−0.154326	−	0.267301i
$353$	−3385.35	+	5863.60i	−0.510437	+	0.884102i	0.489490	+	0.872009i	$0.337183\pi$
$353$	−3385.35	+	5863.60i	−0.510437	+	0.884102i	−0.999927	+	0.0120933i	$0.996150\pi$
$354$		0			0
$355$	−35.3301	+	20.3979i	−0.00528205	+	0.00304959i
$356$	1273.26			0.189558
$357$		0			0
$358$	−5811.80			−0.857998
$359$	−4070.18	+	2349.92i	−0.598373	+	0.345471i	−0.768401	−	0.639969i	$-0.778947\pi$
$359$	−4070.18	+	2349.92i	−0.598373	+	0.345471i	0.170028	+	0.985439i	$0.445614\pi$
$360$		0			0
$361$	3069.46	−	5316.46i	0.447508	−	0.775107i
$362$	−2973.70	−	5150.61i	−0.431752	−	0.747817i
$363$		0			0
$364$	−7747.33	−	515.568i	−1.11558	−	0.0742393i
$365$		−	5125.01i		−	0.734947i
$366$		0			0
$367$	11897.4	+	6868.99i	1.69221	+	0.976999i	0.952728	+	0.303825i	$0.0982637\pi$
$367$	11897.4	+	6868.99i	1.69221	+	0.976999i	0.739484	+	0.673174i	$0.235070\pi$
$368$	85.8136	+	49.5445i	0.0121558	+	0.00701816i
$369$		0			0
$370$			789.892i			0.110985i
$371$	−6888.58	−	458.421i	−0.963982	−	0.0641510i
$372$		0			0
$373$	654.571	+	1133.75i	0.0908643	+	0.157382i	0.907875	−	0.419241i	$-0.137704\pi$
$373$	654.571	+	1133.75i	0.0908643	+	0.157382i	−0.817011	+	0.576622i	$0.804370\pi$
$374$	−1237.95	+	2144.19i	−0.171157	+	0.296453i
$375$		0			0
$376$	−6514.72	+	3761.28i	−0.893541	+	0.515886i
$377$	3447.44			0.470961
$378$		0			0
$379$	3784.67			0.512942			0.256471	−	0.966552i	$-0.417440\pi$
$379$	3784.67			0.512942			0.256471	+	0.966552i	$0.417440\pi$
$380$	−2318.76	+	1338.74i	−0.313026	+	0.180726i
$381$		0			0
$382$	−1938.11	+	3356.91i	−0.259588	+	0.449619i
$383$	760.075	+	1316.49i	0.101405	+	0.175638i	0.912264	−	0.409604i	$-0.134333\pi$
$383$	760.075	+	1316.49i	0.101405	+	0.175638i	−0.810859	+	0.585242i	$0.801000\pi$
$384$		0			0
$385$	471.567	+	958.660i	0.0624242	+	0.126903i
$386$			5578.24i			0.735557i
$387$		0			0
$388$	3856.01	+	2226.27i	0.504535	+	0.291293i
$389$	−12928.0	−	7463.96i	−1.68502	−	0.972848i	−0.958234	−	0.285986i	$-0.907679\pi$
$389$	−12928.0	−	7463.96i	−1.68502	−	0.972848i	−0.726788	−	0.686862i	$-0.758988\pi$
$390$		0			0
$391$			2682.04i			0.346896i
$392$	−6269.73	−	4830.89i	−0.807830	−	0.622440i
$393$		0			0
$394$	−546.138	−	945.939i	−0.0698326	−	0.120954i
$395$	−1798.36	+	3114.86i	−0.229077	+	0.396773i
$396$		0			0
$397$	−1853.82	+	1070.30i	−0.234359	+	0.135307i	−0.612582	−	0.790407i	$-0.709869\pi$
$397$	−1853.82	+	1070.30i	−0.234359	+	0.135307i	0.378222	+	0.925715i	$0.376536\pi$
$398$	−5048.10			−0.635775
$399$		0			0
$400$	−109.062			−0.0136328
$401$	6850.99	−	3955.42i	0.853172	−	0.492579i	−0.00854757	−	0.999963i	$-0.502721\pi$
$401$	6850.99	−	3955.42i	0.853172	−	0.492579i	0.861720	+	0.507384i	$0.169387\pi$
$402$		0			0
$403$	−649.579	+	1125.10i	−0.0802924	+	0.139070i
$404$	1056.21	+	1829.42i	0.130071	+	0.225289i
$405$		0			0
$406$	1080.22	+	723.340i	0.132045	+	0.0884206i
$407$			1002.87i			0.122139i
$408$		0			0
$409$	4309.13	+	2487.88i	0.520960	+	0.300777i	0.737327	−	0.675535i	$-0.236087\pi$
$409$	4309.13	+	2487.88i	0.520960	+	0.300777i	−0.216367	+	0.976312i	$0.569421\pi$
$410$	−2339.82	−	1350.90i	−0.281843	−	0.162722i
$411$		0			0
$412$		−	1147.15i		−	0.137175i
$413$	−6.30184	+	94.6963i	−0.000750831	+	0.0112826i
$414$		0			0
$415$	3325.18	+	5759.38i	0.393317	+	0.681246i
$416$	7884.91	−	13657.1i	0.929302	−	1.60960i
$417$		0			0
$418$	2070.26	−	1195.27i	0.242249	−	0.139862i
$419$	10273.1			1.19779			0.598897	−	0.800826i	$-0.295606\pi$
$419$	10273.1			1.19779			0.598897	+	0.800826i	$0.295606\pi$
$420$		0			0
$421$	−12789.8			−1.48061			−0.740307	−	0.672269i	$-0.765320\pi$
$421$	−12789.8			−1.48061			−0.740307	+	0.672269i	$0.765320\pi$
$422$	−4511.09	+	2604.48i	−0.520371	+	0.300436i
$423$		0			0
$424$	4300.99	−	7449.53i	0.492629	−	0.853258i
$425$	−1475.99	−	2556.50i	−0.168462	−	0.291784i
$426$		0			0
$427$	−5838.49	+	8719.03i	−0.661696	+	0.988158i
$428$		−	8767.72i		−	0.990196i
$429$		0			0
$430$	−913.134	−	527.198i	−0.102408	−	0.0591250i
$431$	1261.15	+	728.128i	0.140946	+	0.0813751i	0.568815	−	0.822466i	$-0.307402\pi$
$431$	1261.15	+	728.128i	0.140946	+	0.0813751i	−0.427869	+	0.903841i	$0.640735\pi$
$432$		0			0
$433$			6714.16i			0.745178i	0.927997	+	0.372589i	$0.121530\pi$
$433$			6714.16i			0.745178i	−0.927997	+	0.372589i	$0.878470\pi$
$434$	−439.606	+	216.243i	−0.0486216	+	0.0239171i
$435$		0			0
$436$	561.690	+	972.876i	0.0616975	+	0.106863i
$437$	1294.78	−	2242.63i	0.141734	−	0.245491i
$438$		0			0
$439$	−8808.35	+	5085.50i	−0.957630	+	0.552888i	−0.895443	−	0.445177i	$-0.853141\pi$
$439$	−8808.35	+	5085.50i	−0.957630	+	0.552888i	−0.0621870	+	0.998065i	$0.519808\pi$
$440$	−1331.16			−0.144228
$441$		0			0
$442$	−19154.7			−2.06130
$443$	1870.42	−	1079.89i	0.200601	−	0.115817i	−0.396335	−	0.918106i	$-0.629718\pi$
$443$	1870.42	−	1079.89i	0.200601	−	0.115817i	0.596936	+	0.802289i	$0.296385\pi$
$444$		0			0
$445$	677.700	−	1173.81i	0.0721934	−	0.125043i
$446$	2799.63	+	4849.10i	0.297234	+	0.514824i
$447$		0			0
$448$	5916.14	−	2910.17i	0.623910	−	0.306903i
$449$		−	16937.0i		−	1.78019i	−0.455772	−	0.890097i	$-0.650637\pi$
$449$		−	16937.0i		−	1.78019i	0.455772	−	0.890097i	$-0.349363\pi$
$450$		0			0
$451$	−2970.71	−	1715.14i	−0.310166	−	0.179075i
$452$	7305.43	+	4217.79i	0.760218	+	0.438912i
$453$		0			0
$454$		−	2637.79i		−	0.272681i
$455$	−4598.87	+	6867.81i	−0.473842	+	0.707622i
$456$		0			0
$457$	5249.95	+	9093.18i	0.537379	+	0.930768i	0.999044	+	0.0437140i	$0.0139190\pi$
$457$	5249.95	+	9093.18i	0.537379	+	0.930768i	−0.461665	+	0.887055i	$0.652748\pi$
$458$	−3022.52	+	5235.16i	−0.308369	+	0.534111i
$459$		0			0
$460$	−461.966	+	266.716i	−0.0468245	+	0.0270341i
$461$	−17245.4			−1.74229			−0.871147	−	0.491022i	$-0.836624\pi$
$461$	−17245.4			−1.74229			−0.871147	+	0.491022i	$0.836624\pi$
$462$		0			0
$463$	−1740.01			−0.174654			−0.0873272	−	0.996180i	$-0.527833\pi$
$463$	−1740.01			−0.174654			−0.0873272	+	0.996180i	$0.527833\pi$
$464$	−145.921	+	84.2475i	−0.0145996	+	0.00842907i
$465$		0			0
$466$	−196.652	+	340.612i	−0.0195488	+	0.0338595i
$467$	5193.62	+	8995.62i	0.514630	+	0.891365i	0.999856	+	0.0169765i	$0.00540404\pi$
$467$	5193.62	+	8995.62i	0.514630	+	0.891365i	−0.485226	+	0.874389i	$0.661263\pi$
$468$		0			0
$469$	−1028.67	+	15457.6i	−0.101278	+	1.52188i
$470$			2962.34i			0.290729i
$471$		0			0
$472$	−102.408	−	59.1250i	−0.00998663	−	0.00576578i
$473$	−1159.34	−	669.347i	−0.112699	−	0.0650668i
$474$		0			0
$475$			2850.21i			0.275319i
$476$	8534.86	+	5715.16i	0.821837	+	0.550324i
$477$		0			0
$478$	6683.04	+	11575.4i	0.639488	+	1.10762i
$479$	665.363	−	1152.44i	0.0634681	−	0.109930i	−0.832545	−	0.553957i	$-0.813117\pi$
$479$	665.363	−	1152.44i	0.0634681	−	0.109930i	0.896013	+	0.444027i	$0.146451\pi$
$480$		0			0
$481$	−6719.22	+	3879.34i	−0.636944	+	0.367740i
$482$	4841.60			0.457529
$483$		0			0
$484$	5626.48			0.528407
$485$	4104.78	−	2369.89i	0.384306	−	0.221879i
$486$		0			0
$487$	3447.94	−	5972.01i	0.320824	−	0.555683i	−0.659834	−	0.751411i	$-0.729374\pi$
$487$	3447.94	−	5972.01i	0.320824	−	0.555683i	0.980658	+	0.195728i	$0.0627069\pi$
$488$	−6537.19	−	11322.7i	−0.606403	−	1.05032i
$489$		0			0
$490$	−2882.00	+	1187.01i	−0.265705	+	0.109436i
$491$		−	10644.6i		−	0.978374i	−0.872179	−	0.489187i	$-0.837293\pi$
$491$		−	10644.6i		−	0.978374i	0.872179	−	0.489187i	$-0.162707\pi$
$492$		0			0
$493$	−3949.63	−	2280.32i	−0.360817	−	0.208318i
$494$	16016.5	+	9247.15i	1.45874	+	0.842204i
$495$		0			0
$496$		−	63.4967i		−	0.00574816i
$497$	−66.6984	−	135.593i	−0.00601978	−	0.0122378i
$498$		0			0
$499$	3575.62	+	6193.15i	0.320775	+	0.555598i	0.980648	−	0.195778i	$-0.0627234\pi$
$499$	3575.62	+	6193.15i	0.320775	+	0.555598i	−0.659873	+	0.751377i	$0.729390\pi$
$500$	293.561	−	508.463i	0.0262569	−	0.0454783i
$501$		0			0
$502$	−10972.1	+	6334.74i	−0.975514	+	0.563213i
$503$	−14065.9			−1.24685			−0.623425	−	0.781883i	$-0.714259\pi$
$503$	−14065.9			−1.24685			−0.623425	+	0.781883i	$0.714259\pi$
$504$		0			0
$505$	2248.71			0.198151
$506$	412.457	−	238.132i	0.0362371	−	0.0209215i
$507$		0			0
$508$	1001.20	−	1734.12i	0.0874428	−	0.151455i
$509$	62.4152	+	108.106i	0.00543517	+	0.00941400i	0.868730	−	0.495286i	$-0.164937\pi$
$509$	62.4152	+	108.106i	0.00543517	+	0.00941400i	−0.863295	+	0.504700i	$0.831603\pi$
$510$		0			0
$511$	18941.4	+	1260.51i	1.63976	+	0.109123i
$512$			1576.10i			0.136044i
$513$		0			0
$514$	−2947.40	−	1701.68i	−0.252927	−	0.146027i
$515$	−1057.56	−	610.580i	−0.0904882	−	0.0522434i
$516$		0			0
$517$			3761.08i			0.319946i
$518$	−2919.35	−	194.276i	−0.247623	−	0.0164788i
$519$		0			0
$520$	−5149.22	−	8918.71i	−0.434247	−	0.752137i
$521$	−2807.22	+	4862.25i	−0.236059	+	0.408866i	−0.959580	−	0.281436i	$-0.909189\pi$
$521$	−2807.22	+	4862.25i	−0.236059	+	0.408866i	0.723521	+	0.690302i	$0.242522\pi$
$522$		0			0
$523$	2117.53	−	1222.56i	0.177042	−	0.102215i	−0.408860	−	0.912597i	$-0.634074\pi$
$523$	2117.53	−	1222.56i	0.177042	−	0.102215i	0.585902	+	0.810382i	$0.300740\pi$
$524$	−2848.88			−0.237507
$525$		0			0
$526$	−5737.56			−0.475607
$527$	1488.41	−	859.332i	0.123028	−	0.0710305i
$528$		0			0
$529$	−5825.54	+	10090.1i	−0.478798	+	0.829303i
$530$	−1693.71	−	2933.58i	−0.138811	−	0.240428i
$531$		0			0
$532$	−4377.51	−	8899.13i	−0.356746	−	0.725237i
$533$		−	26538.2i		−	2.15666i
$534$		0			0
$535$	−8082.92	−	4666.68i	−0.653187	−	0.377118i
$536$	−16716.3	−	9651.16i	−1.34708	−	0.777736i
$537$		0			0
$538$		−	9067.08i		−	0.726598i
$539$	−3659.07	+	1507.07i	−0.292407	+	0.120434i
$540$		0			0
$541$	−4202.56	−	7279.05i	−0.333978	−	0.578467i	0.649310	−	0.760524i	$-0.275058\pi$
$541$	−4202.56	−	7279.05i	−0.333978	−	0.578467i	−0.983288	+	0.182057i	$0.941724\pi$
$542$	4788.50	−	8293.92i	0.379490	−	0.657296i
$543$		0			0
$544$	−18067.0	+	10431.0i	−1.42393	+	0.822105i
$545$	1195.85			0.0939904
$546$		0			0
$547$	16275.1			1.27216			0.636081	−	0.771623i	$-0.280555\pi$
$547$	16275.1			1.27216			0.636081	+	0.771623i	$0.280555\pi$
$548$	6289.33	−	3631.15i	0.490268	−	0.283056i
$549$		0			0
$550$	−262.101	+	453.972i	−0.0203200	+	0.0351953i
$551$	2201.70	+	3813.46i	0.170228	+	0.294844i
$552$		0			0
$553$	−11069.8	−	7412.64i	−0.851241	−	0.570013i
$554$			11134.4i			0.853894i
$555$		0			0
$556$	3737.93	+	2158.10i	0.285115	+	0.164611i
$557$	−5817.05	−	3358.48i	−0.442507	−	0.255482i	0.262153	−	0.965026i	$-0.415567\pi$
$557$	−5817.05	−	3358.48i	−0.442507	−	0.255482i	−0.704661	+	0.709545i	$0.748901\pi$
$558$		0			0
$559$		−	10356.8i		−	0.783621i
$560$	26.8242	−	403.081i	0.00202416	−	0.0304166i
$561$		0			0
$562$	4357.36	+	7547.18i	0.327054	+	0.566474i
$563$	−8351.30	+	14464.9i	−0.625161	+	1.08281i	0.363349	+	0.931653i	$0.381633\pi$
$563$	−8351.30	+	14464.9i	−0.625161	+	1.08281i	−0.988510	+	0.151157i	$0.951700\pi$
$564$		0			0
$565$	7776.73	−	4489.90i	0.579061	−	0.334321i
$566$	−7888.28			−0.585811
$567$		0			0
$568$	188.278			0.0139084
$569$	5150.28	−	2973.52i	0.379457	−	0.219080i	−0.298125	−	0.954527i	$-0.596361\pi$
$569$	5150.28	−	2973.52i	0.379457	−	0.219080i	0.677582	+	0.735447i	$0.263028\pi$
$570$		0			0
$571$	6863.17	−	11887.4i	0.503003	−	0.871226i	−0.496991	−	0.867756i	$-0.665562\pi$
$571$	6863.17	−	11887.4i	0.503003	−	0.871226i	0.999994	−	0.00347082i	$-0.00110480\pi$
$572$	−2418.45	−	4188.88i	−0.176784	−	0.306199i
$573$		0			0
$574$	5568.23	−	8315.43i	0.404901	−	0.604668i
$575$			567.846i			0.0411840i
$576$		0			0
$577$	15803.2	+	9124.00i	1.14020	+	0.658296i	0.946481	−	0.322760i	$-0.104611\pi$
$577$	15803.2	+	9124.00i	1.14020	+	0.658296i	0.193722	+	0.981057i	$0.437944\pi$
$578$	14212.2	+	8205.44i	1.02275	+	0.590487i
$579$		0			0
$580$		−	907.070i		−	0.0649380i
$581$	−22103.8	+	10872.9i	−1.57835	+	0.776394i
$582$		0			0
$583$	−2150.38	−	3724.57i	−0.152761	−	0.264590i
$584$	−11826.4	+	20483.9i	−0.837976	+	1.45142i
$585$		0			0
$586$	9358.37	−	5403.05i	0.659711	−	0.380884i
$587$	26428.8			1.85832			0.929158	−	0.369682i	$-0.120533\pi$
$587$	26428.8			1.85832			0.929158	+	0.369682i	$0.120533\pi$
$588$		0			0
$589$	−1659.41			−0.116086
$590$	−40.3275	+	23.2831i	−0.00281400	+	0.00162466i
$591$		0			0
$592$	189.604	−	328.404i	0.0131633	−	0.0227995i
$593$	8752.89	+	15160.4i	0.606135	+	1.04986i	0.991871	+	0.127247i	$0.0406142\pi$
$593$	8752.89	+	15160.4i	0.606135	+	1.04986i	−0.385736	+	0.922609i	$0.626052\pi$
$594$		0			0
$595$	9811.52	−	4826.31i	0.676022	−	0.332537i
$596$		−	4669.65i		−	0.320934i
$597$		0			0
$598$	3190.96	+	1842.30i	0.218208	+	0.125982i
$599$	−2808.49	−	1621.48i	−0.191572	−	0.110604i	0.401146	−	0.916014i	$-0.368612\pi$
$599$	−2808.49	−	1621.48i	−0.191572	−	0.110604i	−0.592718	+	0.805410i	$0.701945\pi$
$600$		0			0
$601$			11847.8i			0.804128i	0.915612	+	0.402064i	$0.131707\pi$
$601$			11847.8i			0.804128i	−0.915612	+	0.402064i	$0.868293\pi$
$602$	2173.05	−	3245.17i	0.147121	−	0.219706i
$603$		0			0
$604$	−4580.18	−	7933.11i	−0.308551	−	0.534426i
$605$	2994.73	−	5187.02i	0.201245	−	0.348566i
$606$		0			0
$607$	18267.4	−	10546.7i	1.22150	−	0.705233i	0.256262	−	0.966607i	$-0.417509\pi$
$607$	18267.4	−	10546.7i	1.22150	−	0.705233i	0.965238	+	0.261374i	$0.0841756\pi$
$608$	20142.7			1.34358
$609$		0			0
$610$	−5148.62			−0.341740
$611$	−25199.1	+	14548.7i	−1.66849	+	0.963303i
$612$		0			0
$613$	1571.72	−	2722.29i	0.103558	−	0.179368i	−0.809590	−	0.586996i	$-0.800311\pi$
$613$	1571.72	−	2722.29i	0.103558	−	0.179368i	0.913148	+	0.407628i	$0.133644\pi$
$614$	5463.85	+	9463.66i	0.359125	+	0.622023i
$615$		0			0
$616$	327.401	−	4919.79i	0.0214146	−	0.321792i
$617$			20883.5i			1.36262i	0.731995	+	0.681310i	$0.238589\pi$
$617$			20883.5i			1.36262i	−0.731995	+	0.681310i	$0.761411\pi$
$618$		0			0
$619$	14891.6	+	8597.66i	0.966952	+	0.558270i	0.898306	−	0.439371i	$-0.144799\pi$
$619$	14891.6	+	8597.66i	0.966952	+	0.558270i	0.0686460	+	0.997641i	$0.478132\pi$
$620$	296.030	+	170.913i	0.0191756	+	0.0110710i
$621$		0			0
$622$		−	2461.44i		−	0.158673i
$623$	4171.58	+	2793.40i	0.268268	+	0.179639i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	1492.98	−	2585.92i	0.0953221	−	0.165103i
$627$		0			0
$628$	−4263.72	+	2461.66i	−0.270925	+	0.156419i
$629$	10264.0			0.650640
$630$		0			0
$631$	17004.0			1.07277			0.536385	−	0.843973i	$-0.319789\pi$
$631$	17004.0			1.07277			0.536385	+	0.843973i	$0.319789\pi$
$632$	14375.5	−	8299.72i	0.904791	−	0.522381i
$633$		0			0
$634$	−5901.99	+	10222.5i	−0.369713	+	0.640362i
$635$	−1065.79	−	1846.00i	−0.0666055	−	0.115364i
$636$		0			0
$637$	−24251.5	−	18686.0i	−1.50844	−	1.16227i
$638$			809.860i			0.0502550i
$639$		0			0
$640$	−3318.71	−	1916.06i	−0.204974	−	0.118342i
$641$	2395.73	+	1383.17i	0.147622	+	0.0852295i	0.571992	−	0.820260i	$-0.306171\pi$
$641$	2395.73	+	1383.17i	0.147622	+	0.0852295i	−0.424370	+	0.905489i	$0.639504\pi$
$642$		0			0
$643$			4893.65i			0.300135i	0.988676	+	0.150068i	$0.0479491\pi$
$643$			4893.65i			0.300135i	−0.988676	+	0.150068i	$0.952051\pi$
$644$	−872.128	−	1772.97i	−0.0533644	−	0.108486i
$645$		0			0
$646$	−12233.1	−	21188.4i	−0.745054	−	1.29047i
$647$	579.517	−	1003.75i	0.0352136	−	0.0609917i	−0.847882	−	0.530186i	$-0.822122\pi$
$647$	579.517	−	1003.75i	0.0352136	−	0.0609917i	0.883095	+	0.469194i	$0.155456\pi$
$648$		0			0
$649$	−51.2010	+	29.5609i	−0.00309679	+	0.00178793i
$650$	−4055.47			−0.244721
$651$		0			0
$652$	17411.9			1.04586
$653$	1102.57	−	636.566i	0.0660746	−	0.0381482i	−0.466599	−	0.884469i	$-0.654521\pi$
$653$	1102.57	−	636.566i	0.0660746	−	0.0381482i	0.532673	+	0.846321i	$0.321187\pi$
$654$		0			0
$655$	−1516.33	+	2626.37i	−0.0904550	+	0.156673i
$656$	648.532	+	1123.29i	0.0385989	+	0.0668553i
$657$		0			0
$658$	−10948.4	−	728.596i	−0.648655	−	0.0431666i
$659$			10731.2i			0.634338i	0.948369	+	0.317169i	$0.102732\pi$
$659$			10731.2i			0.634338i	−0.948369	+	0.317169i	$0.897268\pi$
$660$		0			0
$661$	−17359.2	−	10022.4i	−1.02148	−	0.589750i	−0.106945	−	0.994265i	$-0.534107\pi$
$661$	−17359.2	−	10022.4i	−1.02148	−	0.589750i	−0.914531	+	0.404515i	$0.867440\pi$
$662$	1563.72	+	902.814i	0.0918062	+	0.0530043i
$663$		0			0
$664$		−	30692.4i		−	1.79382i
$665$	−10534.0	−	701.017i	−0.614274	−	0.0408786i
$666$		0			0
$667$	438.644	+	759.754i	0.0254638	+	0.0441046i
$668$	2964.00	−	5133.80i	0.171677	−	0.297354i
$669$		0			0
$670$	−6582.78	+	3800.57i	−0.379575	+	0.219148i
$671$	−6536.84			−0.376083
$672$		0			0
$673$	−8250.77			−0.472576			−0.236288	−	0.971683i	$-0.575931\pi$
$673$	−8250.77			−0.472576			−0.236288	+	0.971683i	$0.575931\pi$
$674$	9202.46	−	5313.04i	0.525913	−	0.303636i
$675$		0			0
$676$	13550.6	−	23470.4i	0.770973	−	1.33536i
$677$	2379.84	+	4122.00i	0.135103	+	0.234005i	0.925637	−	0.378413i	$-0.123530\pi$
$677$	2379.84	+	4122.00i	0.135103	+	0.234005i	−0.790534	+	0.612418i	$0.790197\pi$
$678$		0			0
$679$	7749.26	+	15753.6i	0.437981	+	0.890381i
$680$			13623.9i			0.768311i
$681$		0			0
$682$	−264.305	−	152.597i	−0.0148398	−	0.00856778i
$683$	−11346.4	−	6550.83i	−0.635661	−	0.366999i	0.147280	−	0.989095i	$-0.452948\pi$
$683$	−11346.4	−	6550.83i	−0.635661	−	0.366999i	−0.782941	+	0.622096i	$0.786282\pi$
$684$		0			0
$685$		−	7730.81i		−	0.431210i
$686$	−3678.23	−	10943.5i	−0.204716	−	0.609072i
$687$		0			0
$688$	253.095	+	438.373i	0.0140249	+	0.0242919i
$689$	16636.3	−	28815.0i	0.919875	−	1.59327i
$690$		0			0
$691$	28094.4	−	16220.3i	1.54669	−	0.892979i	0.548294	−	0.836286i	$-0.315278\pi$
$691$	28094.4	−	16220.3i	1.54669	−	0.892979i	0.998392	−	0.0566934i	$-0.0180558\pi$
$692$	18591.4			1.02130
$693$		0			0
$694$	17421.4			0.952895
$695$	3979.08	−	2297.32i	0.217173	−	0.125385i
$696$		0			0
$697$	−17553.8	+	30404.0i	−0.953941	+	1.65227i
$698$	1258.52	+	2179.82i	0.0682461	+	0.118206i
$699$		0			0
$700$	1807.02	+	1210.02i	0.0975697	+	0.0653352i
$701$		−	12142.5i		−	0.654230i	−0.944985	−	0.327115i	$-0.893924\pi$
$701$		−	12142.5i		−	0.654230i	0.944985	−	0.327115i	$-0.106076\pi$
$702$		0			0
$703$	−8582.42	−	4955.07i	−0.460444	−	0.265838i
$704$	3556.97	+	2053.62i	0.190424	+	0.109941i
$705$		0			0
$706$		−	12305.2i		−	0.655967i
$707$	−553.076	+	8310.95i	−0.0294209	+	0.442101i
$708$		0			0
$709$	8695.16	+	15060.5i	0.460583	+	0.797754i	0.998990	−	0.0449314i	$-0.0143069\pi$
$709$	8695.16	+	15060.5i	0.460583	+	0.797754i	−0.538407	+	0.842685i	$0.680974\pi$
$710$	37.0715	−	64.2097i	0.00195953	−	0.00339401i
$711$		0			0
$712$	−5417.32	+	3127.69i	−0.285144	+	0.164628i
$713$	−330.603			−0.0173649
$714$		0			0
$715$	−5148.94			−0.269314
$716$	−13007.8	+	7510.07i	−0.678946	+	0.391990i
$717$		0			0
$718$	4270.79	−	7397.23i	0.221984	−	0.384488i
$719$	9000.15	+	15588.7i	0.466827	+	0.808569i	0.999282	−	0.0378899i	$-0.0120636\pi$
$719$	9000.15	+	15588.7i	0.466827	+	0.808569i	−0.532455	+	0.846459i	$0.678730\pi$
$720$		0			0
$721$	2516.74	−	3758.42i	0.129997	−	0.194134i
$722$			11157.0i			0.575097i
$723$		0			0
$724$	−13311.3	−	7685.31i	−0.683304	−	0.394506i
$725$	−836.224	−	482.794i	−0.0428366	−	0.0247318i
$726$		0			0
$727$			28129.2i			1.43501i	0.696552	+	0.717506i	$0.254717\pi$
$727$			28129.2i			1.43501i	−0.696552	+	0.717506i	$0.745283\pi$
$728$	34228.9	−	16837.3i	1.74259	−	0.857187i
$729$		0			0
$730$	4657.15	+	8066.43i	0.236122	+	0.408975i
$731$	−6850.51	+	11865.4i	−0.346615	+	0.600354i
$732$		0			0
$733$	14859.4	−	8579.10i	0.748767	−	0.432301i	−0.0764815	−	0.997071i	$-0.524369\pi$
$733$	14859.4	−	8579.10i	0.748767	−	0.432301i	0.825248	+	0.564770i	$0.191035\pi$
$734$	−24967.7			−1.25555
$735$		0			0
$736$	4013.02			0.200981
$737$	−8357.70	+	4825.32i	−0.417720	+	0.241171i
$738$		0			0
$739$	−670.142	+	1160.72i	−0.0333580	+	0.0577777i	−0.882222	−	0.470833i	$-0.843953\pi$
$739$	−670.142	+	1160.72i	−0.0333580	+	0.0577777i	0.848864	+	0.528611i	$0.177287\pi$
$740$	1020.71	+	1767.92i	0.0507054	+	0.0878243i
$741$		0			0
$742$	11258.7	−	5538.20i	0.557037	−	0.274008i
$743$		−	2353.83i		−	0.116223i	−0.998310	−	0.0581114i	$-0.981492\pi$
$743$		−	2353.83i		−	0.116223i	0.998310	−	0.0581114i	$-0.0185079\pi$
$744$		0			0
$745$	−4304.93	−	2485.45i	−0.211705	−	0.122228i
$746$	−2060.50	−	1189.63i	−0.101126	−	0.0583853i
$747$		0			0
$748$			6398.76i			0.312783i
$749$	19235.5	−	28725.7i	0.938383	−	1.40135i
$750$		0			0
$751$	7860.92	+	13615.5i	0.381956	+	0.661568i	0.991342	−	0.131306i	$-0.0419172\pi$
$751$	7860.92	+	13615.5i	0.381956	+	0.661568i	−0.609386	+	0.792874i	$0.708584\pi$
$752$	711.073	−	1231.62i	0.0344816	−	0.0597239i
$753$		0			0
$754$	−5426.04	+	3132.73i	−0.262075	+	0.151309i
$755$	−9751.33			−0.470049
$756$		0			0
$757$	−28022.3			−1.34543			−0.672714	−	0.739902i	$-0.734872\pi$
$757$	−28022.3			−1.34543			−0.672714	+	0.739902i	$0.734872\pi$
$758$	−5956.81	+	3439.16i	−0.285437	+	0.164797i
$759$		0			0
$760$	6577.08	−	11391.8i	0.313915	−	0.543717i
$761$	−4777.46	−	8274.80i	−0.227573	−	0.394167i	0.729516	−	0.683964i	$-0.239746\pi$
$761$	−4777.46	−	8274.80i	−0.227573	−	0.394167i	−0.957088	+	0.289797i	$0.906412\pi$
$762$		0			0
$763$	−294.124	+	4419.73i	−0.0139554	+	0.209705i
$764$			10017.8i			0.474387i
$765$		0			0
$766$	−2392.61	−	1381.38i	−0.112857	−	0.0651582i
$767$	−396.115	−	228.697i	−0.0186478	−	0.0107663i
$768$		0			0
$769$		−	5453.31i		−	0.255723i	−0.991792	−	0.127862i	$-0.959189\pi$
$769$		−	5453.31i		−	0.255723i	0.991792	−	0.127862i	$-0.0408114\pi$
$770$	−1613.36	−	1080.35i	−0.0755084	−	0.0505624i
$771$		0			0
$772$	7208.26	+	12485.1i	0.336051	+	0.582057i
$773$	13598.0	−	23552.4i	0.632710	−	1.09589i	−0.354285	−	0.935137i	$-0.615276\pi$
$773$	13598.0	−	23552.4i	0.632710	−	1.09589i	0.986995	−	0.160748i	$-0.0513908\pi$
$774$		0			0
$775$	315.128	−	181.939i	0.0146061	−	0.00843284i
$776$	−21874.8			−1.01193
$777$		0			0
$778$	27130.3			1.25022
$779$	29355.8	−	16948.6i	1.35017	−	0.779519i
$780$		0			0
$781$	47.0671	−	81.5226i	0.00215646	−	0.00373509i
$782$	−2437.19	−	4221.34i	−0.111450	−	0.193037i
$783$		0			0
$784$	1483.14	+	198.278i	0.0675629	+	0.00903234i
$785$			5240.94i			0.238289i
$786$		0			0
$787$	19382.7	+	11190.6i	0.877915	+	0.506864i	0.869970	−	0.493104i	$-0.164138\pi$
$787$	19382.7	+	11190.6i	0.877915	+	0.506864i	0.00794435	+	0.999968i	$0.497471\pi$
$788$	−2444.71	−	1411.45i	−0.110519	−	0.0638082i
$789$		0			0
$790$		−	6536.76i		−	0.294389i
$791$	14681.4	+	29846.1i	0.659937	+	1.34160i
$792$		0			0
$793$	−25286.0	−	43796.7i	−1.13232	−	1.96124i
$794$	1945.19	−	3369.17i	0.0869425	−	0.150589i
$795$		0			0
$796$	−11298.5	+	6523.21i	−0.503098	+	0.290464i
$797$	29485.5			1.31045			0.655226	−	0.755433i	$-0.272574\pi$
$797$	29485.5			1.31045			0.655226	+	0.755433i	$0.272574\pi$
$798$		0			0
$799$	38493.2			1.70437
$800$	−3825.18	+	2208.47i	−0.169051	+	0.0976015i
$801$		0			0
$802$	−7188.66	+	12451.1i	−0.316509	+	0.548210i
$803$	5912.86	+	10241.4i	0.259851	+	0.450075i
$804$		0			0
$805$	−2098.69	−	139.663i	−0.0918870	−	0.00611489i
$806$		−	2361.12i		−	0.103185i
$807$		0			0
$808$	−8987.73	−	5189.07i	−0.391321	−	0.225929i
$809$	18601.5	+	10739.6i	0.808400	+	0.466730i	0.846400	−	0.532548i	$-0.178765\pi$
$809$	18601.5	+	10739.6i	0.808400	+	0.466730i	−0.0380001	+	0.999278i	$0.512099\pi$
$810$		0			0
$811$			26425.8i			1.14419i	0.820189	+	0.572093i	$0.193868\pi$
$811$			26425.8i			1.14419i	−0.820189	+	0.572093i	$0.806132\pi$
$812$	3352.42	+	223.096i	0.144885	+	0.00964181i
$813$		0			0
$814$	−911.320	−	1578.45i	−0.0392405	−	0.0679665i
$815$	9267.58	−	16051.9i	0.398318	−	0.689907i
$816$		0			0
$817$	11456.3	−	6614.32i	0.490583	−	0.283238i
$818$	−9043.04			−0.386531
$819$		0			0
$820$	−6982.57			−0.297368
$821$	−17864.8	+	10314.2i	−0.759422	+	0.438452i	−0.829088	−	0.559118i	$-0.811140\pi$
$821$	−17864.8	+	10314.2i	−0.759422	+	0.438452i	0.0696663	+	0.997570i	$0.477807\pi$
$822$		0			0
$823$	−11016.3	+	19080.8i	−0.466590	+	0.808157i	−0.999272	−	0.0381582i	$-0.987851\pi$
$823$	−11016.3	+	19080.8i	−0.466590	+	0.808157i	0.532682	+	0.846316i	$0.321184\pi$
$824$	2817.92	+	4880.78i	0.119134	+	0.206347i
$825$		0			0
$826$	−76.1328	−	154.772i	−0.00320702	−	0.00651962i
$827$			21926.0i			0.921937i	0.887417	+	0.460968i	$0.152498\pi$
$827$			21926.0i			0.921937i	−0.887417	+	0.460968i	$0.847502\pi$
$828$		0			0
$829$	−12495.9	−	7214.50i	−0.523522	−	0.302256i	0.214852	−	0.976647i	$-0.431073\pi$
$829$	−12495.9	−	7214.50i	−0.523522	−	0.302256i	−0.738375	+	0.674391i	$0.764406\pi$
$830$	−10467.2	−	6043.25i	−0.437738	−	0.252728i
$831$		0			0
$832$			31775.5i			1.32406i
$833$	15424.3	+	37449.2i	0.641561	+	1.55767i
$834$		0			0
$835$	−3155.22	−	5464.99i	−0.130767	−	0.226496i
$836$	3089.08	−	5350.44i	0.127797	−	0.221350i
$837$		0			0
$838$	−16169.2	+	9335.31i	−0.666536	+	0.384825i
$839$	−38559.9			−1.58669			−0.793346	−	0.608770i	$-0.791663\pi$
$839$	−38559.9			−1.58669			−0.793346	+	0.608770i	$0.791663\pi$
$840$		0			0
$841$	22897.2			0.938834
$842$	20130.3	−	11622.3i	0.823916	−	0.475688i
$843$		0			0
$844$	−6731.07	+	11658.6i	−0.274518	+	0.475479i
$845$	−14424.8	−	24984.5i	−0.587253	−	1.01715i
$846$		0			0
$847$	18434.0	+	12343.9i	0.747817	+	0.500758i
$848$			1626.21i			0.0658542i
$849$		0			0
$850$	4646.23	+	2682.50i	0.187487	+	0.108246i
$851$	−1709.87	−	987.195i	−0.0688762	−	0.0397657i
$852$		0			0
$853$			19895.1i			0.798588i	0.916823	+	0.399294i	$0.130745\pi$
$853$			19895.1i			0.798588i	−0.916823	+	0.399294i	$0.869255\pi$
$854$	1266.32	−	19028.7i	0.0507406	−	0.762467i
$855$		0			0
$856$	21537.4	+	37303.9i	0.859970	+	1.48951i
$857$	−195.788	+	339.115i	−0.00780397	+	0.0135169i	−0.869901	−	0.493226i	$-0.835817\pi$
$857$	−195.788	+	339.115i	−0.00780397	+	0.0135169i	0.862097	+	0.506743i	$0.169151\pi$
$858$		0			0
$859$	6490.99	−	3747.58i	0.257823	−	0.148854i	−0.365518	−	0.930804i	$-0.619108\pi$
$859$	6490.99	−	3747.58i	0.257823	−	0.148854i	0.623341	+	0.781950i	$0.285775\pi$
$860$	−2725.01			−0.108049
$861$		0			0
$862$	−2646.63			−0.104576
$863$	−27747.5	+	16020.0i	−1.09448	+	0.631899i	−0.934766	−	0.355265i	$-0.884391\pi$
$863$	−27747.5	+	16020.0i	−1.09448	+	0.631899i	−0.159715	+	0.987163i	$0.551057\pi$
$864$		0			0
$865$	9895.41	−	17139.4i	0.388964	−	0.673706i
$866$	−6101.23	−	10567.6i	−0.239409	−	0.414668i
$867$		0			0
$868$	−704.483	+	1052.05i	−0.0275481	+	0.0411395i
$869$		−	8299.28i		−	0.323974i
$870$		0			0
$871$	−64659.1	−	37330.9i	−2.51537	−	1.45225i
$872$	−4779.63	−	2759.52i	−0.185618	−	0.107167i
$873$		0			0
$874$			4706.33i			0.182144i
$875$	2077.31	−	1021.84i	0.0802583	−	0.0394793i
$876$		0			0
$877$	−19981.8	−	34609.5i	−0.769371	−	1.33259i	−0.937905	−	0.346893i	$-0.887237\pi$
$877$	−19981.8	−	34609.5i	−0.769371	−	1.33259i	0.168534	−	0.985696i	$-0.446097\pi$
$878$	9242.50	−	16008.5i	0.355261	−	0.615330i
$879$		0			0
$880$	217.941	−	125.828i	0.00834861	−	0.00482007i
$881$	−32349.9			−1.23711			−0.618557	−	0.785740i	$-0.712282\pi$
$881$	−32349.9			−1.23711			−0.618557	+	0.785740i	$0.712282\pi$
$882$		0			0
$883$	−17595.7			−0.670603			−0.335301	−	0.942111i	$-0.608838\pi$
$883$	−17595.7			−0.670603			−0.335301	+	0.942111i	$0.608838\pi$
$884$	−42871.6	+	24751.9i	−1.63114	+	0.941739i
$885$		0			0
$886$	−1962.61	+	3399.33i	−0.0744188	+	0.128897i
$887$	−11259.1	−	19501.3i	−0.426203	−	0.738205i	0.570329	−	0.821416i	$-0.306816\pi$
$887$	−11259.1	−	19501.3i	−0.426203	−	0.738205i	−0.996532	+	0.0832111i	$0.973482\pi$
$888$		0			0
$889$	7084.72	−	3484.99i	0.267282	−	0.131477i
$890$			2463.33i			0.0927765i
$891$		0			0
$892$	12532.1	+	7235.42i	0.470411	+	0.271592i
$893$	−32186.7	−	18583.0i	−1.20615	−	0.696369i
$894$		0			0
$895$			15989.1i			0.597160i
$896$	7897.76	−	11794.3i	0.294471	−	0.439754i
$897$		0			0
$898$	15390.8	+	26657.7i	0.571936	+	0.990623i
$899$	281.085	−	486.854i	0.0104279	−	0.0180617i
$900$		0			0
$901$	−38119.5	+	22008.3i	−1.40948	+	0.813766i
$902$	6234.25			0.230131
$903$		0			0
$904$	−41443.1			−1.52475
$905$	−14170.1	+	8181.11i	−0.520475	+	0.300496i
$906$		0			0
$907$	−10298.4	+	17837.3i	−0.377013	+	0.653007i	−0.990626	−	0.136601i	$-0.956382\pi$
$907$	−10298.4	+	17837.3i	−0.377013	+	0.653007i	0.613613	+	0.789607i	$0.289716\pi$
$908$	−3408.58	−	5903.83i	−0.124579	−	0.215777i
$909$		0			0
$910$	997.454	−	14988.5i	0.0363355	−	0.546005i
$911$			27812.7i			1.01150i	0.862680	+	0.505750i	$0.168784\pi$
$911$			27812.7i			1.01150i	−0.862680	+	0.505750i	$0.831216\pi$
$912$		0			0
$913$	−13289.5	−	7672.70i	−0.481729	−	0.278126i
$914$	−16526.1	−	9541.37i	−0.598070	−	0.345296i
$915$		0			0
$916$			15622.9i			0.563534i
$917$	−9333.78	−	6250.14i	−0.336127	−	0.225079i
$918$		0			0
$919$	1992.83	+	3451.67i	0.0715313	+	0.123896i	0.899573	−	0.436771i	$-0.143878\pi$
$919$	1992.83	+	3451.67i	0.0715313	+	0.123896i	−0.828041	+	0.560667i	$0.810545\pi$
$920$	1310.35	−	2269.59i	0.0469575	−	0.0813327i
$921$		0			0
$922$	27143.1	−	15671.1i	0.969533	−	0.559760i
$923$	728.266			0.0259709
$924$		0			0
$925$	2173.11			0.0772449
$926$	2738.65	−	1581.16i	0.0971898	−	0.0561126i
$927$		0			0
$928$	−3411.95	+	5909.68i	−0.120693	+	0.209046i
$929$	2378.61	+	4119.87i	0.0840038	+	0.145499i	0.904966	−	0.425483i	$-0.139896\pi$
$929$	2378.61	+	4119.87i	0.0840038	+	0.145499i	−0.820962	+	0.570982i	$0.806563\pi$
$930$		0			0
$931$	5181.75	−	38760.0i	0.182411	−	1.36446i
$932$			1016.46i			0.0357247i
$933$		0			0
$934$	−16348.8	−	9439.00i	−0.572751	−	0.330678i
$935$	5898.99	+	3405.78i	0.206329	+	0.119124i
$936$		0			0
$937$		−	3069.55i		−	0.107020i	−0.998567	−	0.0535100i	$-0.982959\pi$
$937$		−	3069.55i		−	0.107020i	0.998567	−	0.0535100i	$-0.0170409\pi$
$938$	−12427.4	−	25263.9i	−0.432589	−	0.879420i
$939$		0			0
$940$	3827.97	+	6630.24i	0.132824	+	0.230058i
$941$	6523.89	−	11299.7i	0.226007	−	0.391456i	−0.730614	−	0.682791i	$-0.760766\pi$
$941$	6523.89	−	11299.7i	0.226007	−	0.391456i	0.956621	+	0.291335i	$0.0940994\pi$
$942$		0			0
$943$	5848.54	−	3376.65i	0.201967	−	0.116606i
$944$	22.3553			0.000770766
$945$		0			0
$946$	2432.97			0.0836180
$947$	34079.5	−	19675.8i	1.16941	−	0.675162i	0.215872	−	0.976422i	$-0.430741\pi$
$947$	34079.5	−	19675.8i	1.16941	−	0.675162i	0.953542	+	0.301260i	$0.0974072\pi$
$948$		0			0
$949$	−45744.7	+	79232.1i	−1.56474	+	2.71020i
$950$	−2590.02	−	4486.04i	−0.0884539	−	0.153207i
$951$		0			0
$952$	−50352.1	−	3350.83i	−1.71420	−	0.114077i
$953$			5274.34i			0.179279i	0.995974	+	0.0896393i	$0.0285714\pi$
$953$			5274.34i			0.179279i	−0.995974	+	0.0896393i	$0.971429\pi$
$954$		0			0
$955$	9235.37	+	5332.05i	0.312932	+	0.180671i
$956$	29915.6	+	17271.8i	1.01207	+	0.584320i
$957$		0			0
$958$			2418.49i			0.0815635i
$959$	28572.1	+	1901.41i	0.962087	+	0.0640249i
$960$		0			0
$961$	−14789.6	−	25616.3i	−0.496444	−	0.859867i
$962$	7050.39	−	12211.6i	0.236293	−	0.409271i
$963$		0			0
$964$	10836.4	−	6256.37i	0.362049	−	0.209029i
$965$	15346.6			0.511942
$966$		0			0
$967$	−32400.0			−1.07747			−0.538735	−	0.842475i	$-0.681097\pi$
$967$	−32400.0			−1.07747			−0.538735	+	0.842475i	$0.681097\pi$
$968$	−23938.9	+	13821.1i	−0.794861	+	0.458913i
$969$		0			0
$970$	−4307.09	+	7460.11i	−0.142570	+	0.246938i
$971$	−27305.2	−	47294.0i	−0.902436	−	1.56307i	−0.824322	−	0.566121i	$-0.808444\pi$
$971$	−27305.2	−	47294.0i	−0.902436	−	1.56307i	−0.0781136	−	0.996944i	$-0.524890\pi$
$972$		0			0
$973$	7511.96	+	15271.2i	0.247505	+	0.503158i
$974$			12532.7i			0.412294i
$975$		0			0
$976$	2140.58	+	1235.86i	0.0702031	+	0.0405318i
$977$	−43123.3	−	24897.3i	−1.41212	−	0.815286i	−0.416529	−	0.909123i	$-0.636753\pi$
$977$	−43123.3	−	24897.3i	−1.41212	−	0.815286i	−0.995588	+	0.0938369i	$0.970087\pi$
$978$		0			0
$979$			3127.52i			0.102100i
$980$	−4916.54	+	6380.90i	−0.160258	+	0.207990i
$981$		0			0
$982$	9672.81	+	16753.8i	0.314330	+	0.544435i
$983$	−22031.9	+	38160.3i	−0.714861	+	1.23817i	0.248153	+	0.968721i	$0.420176\pi$
$983$	−22031.9	+	38160.3i	−0.714861	+	1.23817i	−0.963013	+	0.269454i	$0.913157\pi$
$984$		0			0
$985$	−2602.42	+	1502.51i	−0.0841828	+	0.0486029i
$986$	8288.61			0.267711
$987$		0			0
$988$	47797.1			1.53910
$989$	2282.44	−	1317.77i	0.0733846	−	0.0423686i
$990$		0			0
$991$	−680.188	+	1178.12i	−0.0218031	+	0.0377641i	−0.876721	−	0.480999i	$-0.840274\pi$
$991$	−680.188	+	1178.12i	−0.0218031	+	0.0377641i	0.854918	+	0.518763i	$0.173607\pi$
$992$	−1285.78	−	2227.04i	−0.0411529	−	0.0712789i
$993$		0			0
$994$	228.193	+	152.804i	0.00728154	+	0.00487591i
$995$			13888.1i			0.442494i
$996$		0			0
$997$	−33757.5	−	19489.9i	−1.07233	−	0.619108i	−0.143510	−	0.989649i	$-0.545839\pi$
$997$	−33757.5	−	19489.9i	−1.07233	−	0.619108i	−0.928816	+	0.370541i	$0.879172\pi$
$998$	−11255.6	−	6498.40i	−0.357003	−	0.206116i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.bj.b.206.6	yes	32
3.2	odd	2		315.4.bj.a.206.11	yes	32
7.5	odd	6		315.4.bj.a.26.11	✓	32
21.5	even	6	inner	315.4.bj.b.26.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.4.bj.a.26.11	✓	32	7.5	odd	6
315.4.bj.a.206.11	yes	32	3.2	odd	2
315.4.bj.b.26.6	yes	32	21.5	even	6	inner
315.4.bj.b.206.6	yes	32	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57393 + 0.908710i) q^{2} +(-2.34849 + 4.06771i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.6185 + 8.17469i) q^{7} -23.0758i q^{8} +O(q^{10})\)	\(q+(-1.57393 + 0.908710i) q^{2} +(-2.34849 + 4.06771i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.6185 + 8.17469i) q^{7} -23.0758i q^{8} +(-7.86966 - 4.54355i) q^{10} +(-9.99156 - 5.76863i) q^{11} -89.2576i q^{13} +(18.7280 - 27.9678i) q^{14} +(2.18125 + 3.77803i) q^{16} +(-59.0397 + 102.260i) q^{17} +(98.7342 - 57.0042i) q^{19} -23.4849 q^{20} +20.9681 q^{22} +(19.6708 - 11.3569i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(81.1093 + 140.486i) q^{26} +(5.77618 - 86.7973i) q^{28} +38.6235i q^{29} +(-12.6051 - 7.27757i) q^{31} +(153.007 + 88.3388i) q^{32} -214.600i q^{34} +(-76.9437 - 51.5235i) q^{35} +(-43.4623 - 75.2789i) q^{37} +(-103.601 + 179.442i) q^{38} +(99.9210 - 57.6894i) q^{40} +297.321 q^{41} +116.032 q^{43} +(46.9302 - 27.0952i) q^{44} +(-20.6403 + 35.7500i) q^{46} +(-162.997 - 282.319i) q^{47} +(209.349 - 271.702i) q^{49} -45.4355i q^{50} +(363.074 + 209.621i) q^{52} +(322.829 + 186.386i) q^{53} -57.6863i q^{55} +(188.637 + 383.484i) q^{56} +(-35.0976 - 60.7908i) q^{58} +(2.56221 - 4.43788i) q^{59} +(490.677 - 283.293i) q^{61} +26.4528 q^{62} -355.997 q^{64} +(386.497 - 223.144i) q^{65} +(418.238 - 724.409i) q^{67} +(-277.309 - 480.313i) q^{68} +(167.924 + 11.1750i) q^{70} +8.15914i q^{71} +(-887.678 - 512.501i) q^{73} +(136.813 + 78.9892i) q^{74} +535.495i q^{76} +(213.202 + 14.1881i) q^{77} +(359.673 + 622.971i) q^{79} +(-10.9062 + 18.8902i) q^{80} +(-467.964 + 270.179i) q^{82} +1330.07 q^{83} -590.397 q^{85} +(-182.627 + 105.440i) q^{86} +(-133.116 + 230.563i) q^{88} +(-135.540 - 234.762i) q^{89} +(729.653 + 1483.33i) q^{91} +106.686i q^{92} +(513.092 + 296.234i) q^{94} +(493.671 + 285.021i) q^{95} -947.958i q^{97} +(-82.6028 + 617.878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 80 q^{5} - 44 q^{7}+O(q^{10}) \) 32 * q + 64 * q^4 + 80 * q^5 - 44 * q^7	\( 32 q + 64 q^{4} + 80 q^{5} - 44 q^{7} + 72 q^{11} - 108 q^{14} - 196 q^{16} + 396 q^{19} + 640 q^{20} - 480 q^{22} + 36 q^{23} - 400 q^{25} - 120 q^{26} - 316 q^{28} - 300 q^{31} + 1620 q^{32} - 20 q^{35} + 980 q^{37} - 888 q^{38} - 1296 q^{41} + 8 q^{43} + 4068 q^{44} + 540 q^{46} - 120 q^{47} - 1396 q^{49} - 4452 q^{52} + 576 q^{53} - 4260 q^{56} + 828 q^{58} - 96 q^{59} + 336 q^{61} - 4152 q^{62} - 5120 q^{64} + 1020 q^{65} + 700 q^{67} + 60 q^{68} + 540 q^{70} - 756 q^{73} + 5796 q^{74} - 2952 q^{77} + 916 q^{79} + 980 q^{80} + 5832 q^{82} - 2352 q^{83} + 3276 q^{86} - 1212 q^{88} + 1608 q^{89} - 960 q^{91} + 5112 q^{94} + 1980 q^{95} - 5184 q^{98}+O(q^{100}) \) 32 * q + 64 * q^4 + 80 * q^5 - 44 * q^7 + 72 * q^11 - 108 * q^14 - 196 * q^16 + 396 * q^19 + 640 * q^20 - 480 * q^22 + 36 * q^23 - 400 * q^25 - 120 * q^26 - 316 * q^28 - 300 * q^31 + 1620 * q^32 - 20 * q^35 + 980 * q^37 - 888 * q^38 - 1296 * q^41 + 8 * q^43 + 4068 * q^44 + 540 * q^46 - 120 * q^47 - 1396 * q^49 - 4452 * q^52 + 576 * q^53 - 4260 * q^56 + 828 * q^58 - 96 * q^59 + 336 * q^61 - 4152 * q^62 - 5120 * q^64 + 1020 * q^65 + 700 * q^67 + 60 * q^68 + 540 * q^70 - 756 * q^73 + 5796 * q^74 - 2952 * q^77 + 916 * q^79 + 980 * q^80 + 5832 * q^82 - 2352 * q^83 + 3276 * q^86 - 1212 * q^88 + 1608 * q^89 - 960 * q^91 + 5112 * q^94 + 1980 * q^95 - 5184 * q^98

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