LMFDB - Embedded newform 60.4.h.c.59.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(59,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.h (of order $2$, degree $1$, 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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.6
Character	$\chi$	$=$	60.59
Dual form			60.4.h.c.59.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40208 - 1.49331i) q^{2} +(3.96106 + 3.36304i) q^{3} +(3.54002 + 7.17414i) q^{4} +(-9.10892 + 6.48287i) q^{5} +(-4.49272 - 13.9934i) q^{6} -26.5236 q^{7} +(2.20980 - 22.5193i) q^{8} +(4.37993 + 26.6424i) q^{9} +O(q^{10})$	\(q+(-2.40208 - 1.49331i) q^{2} +(3.96106 + 3.36304i) q^{3} +(3.54002 + 7.17414i) q^{4} +(-9.10892 + 6.48287i) q^{5} +(-4.49272 - 13.9934i) q^{6} -26.5236 q^{7} +(2.20980 - 22.5193i) q^{8} +(4.37993 + 26.6424i) q^{9} +(31.5614 - 1.96993i) q^{10} -17.2030 q^{11} +(-10.1047 + 40.3224i) q^{12} +66.7249i q^{13} +(63.7120 + 39.6081i) q^{14} +(-57.8831 - 4.95463i) q^{15} +(-38.9365 + 50.7932i) q^{16} +87.8981 q^{17} +(29.2645 - 70.5379i) q^{18} -22.3542i q^{19} +(-78.7548 - 42.3991i) q^{20} +(-105.062 - 89.2000i) q^{21} +(41.3231 + 25.6895i) q^{22} +30.5698i q^{23} +(84.4863 - 81.7684i) q^{24} +(40.9447 - 118.104i) q^{25} +(99.6413 - 160.279i) q^{26} +(-72.2502 + 120.262i) q^{27} +(-93.8943 - 190.284i) q^{28} +54.3226i q^{29} +(131.641 + 98.3391i) q^{30} -143.859i q^{31} +(169.379 - 63.8653i) q^{32} +(-68.1420 - 57.8544i) q^{33} +(-211.139 - 131.260i) q^{34} +(241.602 - 171.949i) q^{35} +(-175.631 + 125.737i) q^{36} +285.192i q^{37} +(-33.3819 + 53.6967i) q^{38} +(-224.399 + 264.301i) q^{39} +(125.861 + 219.452i) q^{40} +57.8269i q^{41} +(119.163 + 371.156i) q^{42} +284.756 q^{43} +(-60.8990 - 123.417i) q^{44} +(-212.616 - 214.289i) q^{45} +(45.6503 - 73.4312i) q^{46} -111.229i q^{47} +(-325.049 + 70.2499i) q^{48} +360.503 q^{49} +(-274.719 + 222.552i) q^{50} +(348.169 + 295.605i) q^{51} +(-478.694 + 236.208i) q^{52} -160.655 q^{53} +(353.140 - 180.987i) q^{54} +(156.701 - 111.525i) q^{55} +(-58.6120 + 597.292i) q^{56} +(75.1781 - 88.5462i) q^{57} +(81.1208 - 130.488i) q^{58} -447.420 q^{59} +(-169.362 - 432.801i) q^{60} +559.424 q^{61} +(-214.826 + 345.561i) q^{62} +(-116.172 - 706.653i) q^{63} +(-502.234 - 99.5263i) q^{64} +(-432.569 - 607.792i) q^{65} +(77.2882 + 240.729i) q^{66} +84.2324 q^{67} +(311.161 + 630.593i) q^{68} +(-102.807 + 121.089i) q^{69} +(-837.122 + 52.2498i) q^{70} +119.044 q^{71} +(609.645 - 39.7583i) q^{72} -253.949i q^{73} +(425.881 - 685.054i) q^{74} +(559.372 - 330.117i) q^{75} +(160.372 - 79.1344i) q^{76} +456.286 q^{77} +(933.709 - 299.776i) q^{78} +1184.13i q^{79} +(25.3830 - 715.091i) q^{80} +(-690.632 + 233.383i) q^{81} +(86.3538 - 138.905i) q^{82} +1029.67i q^{83} +(268.013 - 1069.50i) q^{84} +(-800.657 + 569.832i) q^{85} +(-684.009 - 425.231i) q^{86} +(-182.689 + 215.175i) q^{87} +(-38.0153 + 387.399i) q^{88} +859.928i q^{89} +(190.720 + 832.241i) q^{90} -1769.79i q^{91} +(-219.312 + 108.218i) q^{92} +(483.803 - 569.832i) q^{93} +(-166.099 + 267.181i) q^{94} +(144.919 + 203.623i) q^{95} +(885.701 + 316.654i) q^{96} +79.1248i q^{97} +(-865.959 - 538.344i) q^{98} +(-75.3479 - 458.329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9}+O(q^{10}) $ 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9	$ 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9} - 32 q^{10} - 240 q^{16} - 264 q^{21} + 168 q^{24} - 88 q^{25} - 252 q^{30} - 1088 q^{34} - 1104 q^{36} + 704 q^{40} + 456 q^{45} + 3368 q^{46} - 1304 q^{49} + 468 q^{54} + 2496 q^{60} + 2080 q^{61} + 1376 q^{64} - 672 q^{66} + 2568 q^{69} - 2632 q^{70} - 1536 q^{76} - 5112 q^{81} - 2328 q^{84} - 6944 q^{85} - 1152 q^{90} - 4840 q^{94} - 2832 q^{96}+O(q^{100}) $ 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9 - 32 * q^10 - 240 * q^16 - 264 * q^21 + 168 * q^24 - 88 * q^25 - 252 * q^30 - 1088 * q^34 - 1104 * q^36 + 704 * q^40 + 456 * q^45 + 3368 * q^46 - 1304 * q^49 + 468 * q^54 + 2496 * q^60 + 2080 * q^61 + 1376 * q^64 - 672 * q^66 + 2568 * q^69 - 2632 * q^70 - 1536 * q^76 - 5112 * q^81 - 2328 * q^84 - 6944 * q^85 - 1152 * q^90 - 4840 * q^94 - 2832 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.40208	−	1.49331i	−0.849265	−	0.527966i
$2$	−2.40208	−	1.49331i	−0.849265	−	0.527966i
$3$	3.96106	+	3.36304i	0.762306	+	0.647217i
$3$	3.96106	+	3.36304i	0.762306	+	0.647217i
$4$	3.54002	+	7.17414i	0.442503	+	0.896767i
$5$	−9.10892	+	6.48287i	−0.814726	+	0.579846i
$5$	−9.10892	+	6.48287i	−0.814726	+	0.579846i
$6$	−4.49272	−	13.9934i	−0.305691	−	0.952131i
$7$	−26.5236			−1.43214			−0.716071	−	0.698028i	$-0.754061\pi$
$7$	−26.5236			−1.43214			−0.716071	+	0.698028i	$0.754061\pi$
$8$	2.20980	−	22.5193i	0.0976605	−	0.995220i
$9$	4.37993	+	26.6424i	0.162220	+	0.986755i
$10$	31.5614	−	1.96993i	0.998058	−	0.0622948i
$11$	−17.2030			−0.471536			−0.235768	−	0.971809i	$-0.575761\pi$
$11$	−17.2030			−0.471536			−0.235768	+	0.971809i	$0.575761\pi$
$12$	−10.1047	+	40.3224i	−0.243081	+	0.970006i
$13$			66.7249i			1.42355i	0.702407	+	0.711775i	$0.252109\pi$
$13$			66.7249i			1.42355i	−0.702407	+	0.711775i	$0.747891\pi$
$14$	63.7120	+	39.6081i	1.21627	+	0.756123i
$15$	−57.8831	−	4.95463i	−0.996357	−	0.0852852i
$16$	−38.9365	+	50.7932i	−0.608382	+	0.793644i
$17$	87.8981			1.25403			0.627013	−	0.779009i	$-0.284277\pi$
$17$	87.8981			1.25403			0.627013	+	0.779009i	$0.284277\pi$
$18$	29.2645	−	70.5379i	0.383206	−	0.923663i
$19$		−	22.3542i		−	0.269916i	−0.990851	−	0.134958i	$-0.956910\pi$
$19$		−	22.3542i		−	0.269916i	0.990851	−	0.134958i	$-0.0430900\pi$
$20$	−78.7548	−	42.3991i	−0.880505	−	0.474036i
$21$	−105.062	−	89.2000i	−1.09173	−	0.926907i
$22$	41.3231	+	25.6895i	0.400459	+	0.248955i
$23$			30.5698i			0.277141i	0.990353	+	0.138571i	$0.0442508\pi$
$23$			30.5698i			0.277141i	−0.990353	+	0.138571i	$0.955749\pi$
$24$	84.4863	−	81.7684i	0.718571	−	0.695454i
$25$	40.9447	−	118.104i	0.327558	−	0.944831i
$26$	99.6413	−	160.279i	0.751587	−	1.20897i
$27$	−72.2502	+	120.262i	−0.514984	+	0.857200i
$28$	−93.8943	−	190.284i	−0.633727	−	1.28430i
$29$			54.3226i			0.347843i	0.984759	+	0.173922i	$0.0556440\pi$
$29$			54.3226i			0.347843i	−0.984759	+	0.173922i	$0.944356\pi$
$30$	131.641	+	98.3391i	0.801143	+	0.598473i
$31$		−	143.859i		−	0.833477i	−0.909026	−	0.416738i	$-0.863173\pi$
$31$		−	143.859i		−	0.833477i	0.909026	−	0.416738i	$-0.136827\pi$
$32$	169.379	−	63.8653i	0.935695	−	0.352809i
$33$	−68.1420	−	57.8544i	−0.359455	−	0.305186i
$34$	−211.139	−	131.260i	−1.06500	−	0.662083i
$35$	241.602	−	171.949i	1.16680	−	0.830421i
$36$	−175.631	+	125.737i	−0.813106	+	0.582115i
$37$			285.192i			1.26717i	0.773674	+	0.633584i	$0.218417\pi$
$37$			285.192i			1.26717i	−0.773674	+	0.633584i	$0.781583\pi$
$38$	−33.3819	+	53.6967i	−0.142507	+	0.229230i
$39$	−224.399	+	264.301i	−0.921347	+	1.08518i
$40$	125.861	+	219.452i	0.497507	+	0.867460i
$41$			57.8269i			0.220269i	0.993917	+	0.110135i	$0.0351282\pi$
$41$			57.8269i			0.220269i	−0.993917	+	0.110135i	$0.964872\pi$
$42$	119.163	+	371.156i	0.437792	+	1.36359i
$43$	284.756			1.00988			0.504941	−	0.863154i	$-0.331514\pi$
$43$	284.756			1.00988			0.504941	+	0.863154i	$0.331514\pi$
$44$	−60.8990	−	123.417i	−0.208656	−	0.422858i
$45$	−212.616	−	214.289i	−0.704330	−	0.709873i
$46$	45.6503	−	73.4312i	0.146321	−	0.235366i
$47$		−	111.229i		−	0.345199i	−0.984992	−	0.172600i	$-0.944783\pi$
$47$		−	111.229i		−	0.345199i	0.984992	−	0.172600i	$-0.0552167\pi$
$48$	−325.049	+	70.2499i	−0.977433	+	0.211244i
$49$	360.503			1.05103
$50$	−274.719	+	222.552i	−0.777023	+	0.629473i
$51$	348.169	+	295.605i	0.955950	+	0.811627i
$52$	−478.694	+	236.208i	−1.27659	+	0.629926i
$53$	−160.655			−0.416371			−0.208185	−	0.978089i	$-0.566756\pi$
$53$	−160.655			−0.416371			−0.208185	+	0.978089i	$0.566756\pi$
$54$	353.140	−	180.987i	0.889931	−	0.456096i
$55$	156.701	−	111.525i	0.384173	−	0.273418i
$56$	−58.6120	+	597.292i	−0.139864	+	1.42530i
$57$	75.1781	−	88.5462i	0.174694	−	0.205759i
$58$	81.1208	−	130.488i	0.183650	−	0.295411i
$59$	−447.420			−0.987273			−0.493637	−	0.869668i	$-0.664333\pi$
$59$	−447.420			−0.987273			−0.493637	+	0.869668i	$0.664333\pi$
$60$	−169.362	−	432.801i	−0.364410	−	0.931239i
$61$	559.424			1.17421			0.587106	−	0.809510i	$-0.300267\pi$
$61$	559.424			1.17421			0.587106	+	0.809510i	$0.300267\pi$
$62$	−214.826	+	345.561i	−0.440048	+	0.707843i
$63$	−116.172	−	706.653i	−0.232321	−	1.41317i
$64$	−502.234	−	99.5263i	−0.980925	−	0.194387i
$65$	−432.569	−	607.792i	−0.825440	−	1.15980i
$66$	77.2882	+	240.729i	0.144144	+	0.448964i
$67$	84.2324			0.153591			0.0767957	−	0.997047i	$-0.475531\pi$
$67$	84.2324			0.153591			0.0767957	+	0.997047i	$0.475531\pi$
$68$	311.161	+	630.593i	0.554910	+	1.12457i
$69$	−102.807	+	121.089i	−0.179370	+	0.211266i
$70$	−837.122	+	52.2498i	−1.42936	+	0.0892149i
$71$	119.044			0.198985			0.0994924	−	0.995038i	$-0.468278\pi$
$71$	119.044			0.198985			0.0994924	+	0.995038i	$0.468278\pi$
$72$	609.645	−	39.7583i	0.997880	−	0.0650772i
$73$		−	253.949i		−	0.407157i	−0.979059	−	0.203579i	$-0.934743\pi$
$73$		−	253.949i		−	0.407157i	0.979059	−	0.203579i	$-0.0652572\pi$
$74$	425.881	−	685.054i	0.669022	−	1.07616i
$75$	559.372	−	330.117i	0.861210	−	0.508249i
$76$	160.372	−	79.1344i	0.242052	−	0.119439i
$77$	456.286			0.675307
$78$	933.709	−	299.776i	1.35541	−	0.435166i
$79$			1184.13i			1.68639i	0.537610	+	0.843194i	$0.319327\pi$
$79$			1184.13i			1.68639i	−0.537610	+	0.843194i	$0.680673\pi$
$80$	25.3830	−	715.091i	0.0354738	−	0.999371i
$81$	−690.632	+	233.383i	−0.947370	+	0.320142i
$82$	86.3538	−	138.905i	0.116295	−	0.187067i
$83$			1029.67i			1.36169i	0.732427	+	0.680846i	$0.238388\pi$
$83$			1029.67i			1.36169i	−0.732427	+	0.680846i	$0.761612\pi$
$84$	268.013	−	1069.50i	0.348126	−	1.38919i
$85$	−800.657	+	569.832i	−1.02169	+	0.727141i
$86$	−684.009	−	425.231i	−0.857658	−	0.533184i
$87$	−182.689	+	215.175i	−0.225130	+	0.265163i
$88$	−38.0153	+	387.399i	−0.0460505	+	0.469282i
$89$			859.928i			1.02418i	0.858931	+	0.512091i	$0.171129\pi$
$89$			859.928i			1.02418i	−0.858931	+	0.512091i	$0.828871\pi$
$90$	190.720	+	832.241i	0.223374	+	0.974733i
$91$		−	1769.79i		−	2.03873i
$92$	−219.312	+	108.218i	−0.248531	+	0.122636i
$93$	483.803	−	569.832i	0.539441	−	0.635364i
$94$	−166.099	+	267.181i	−0.182254	+	0.293166i
$95$	144.919	+	203.623i	0.156510	+	0.219908i
$96$	885.701	+	316.654i	0.941630	+	0.336650i
$97$			79.1248i			0.0828238i	0.999142	+	0.0414119i	$0.0131856\pi$
$97$			79.1248i			0.0828238i	−0.999142	+	0.0414119i	$0.986814\pi$
$98$	−865.959	−	538.344i	−0.892603	−	0.554908i
$99$	−75.3479	−	458.329i	−0.0764924	−	0.465291i
$100$	992.239	−	124.348i	0.992239	−	0.124348i
$101$		−	699.590i		−	0.689226i	−0.938745	−	0.344613i	$-0.888010\pi$
$101$		−	699.590i		−	0.689226i	0.938745	−	0.344613i	$-0.111990\pi$
$102$	−394.901	−	1229.99i	−0.383344	−	1.19400i
$103$	−1324.06			−1.26663			−0.633317	−	0.773892i	$-0.718307\pi$
$103$	−1324.06			−1.26663			−0.633317	+	0.773892i	$0.718307\pi$
$104$	1502.60	+	147.449i	1.41675	+	0.139025i
$105$	1535.27	+	131.415i	1.42692	+	0.122141i
$106$	385.907	+	239.908i	0.353609	+	0.219830i
$107$		−	224.641i		−	0.202961i	−0.994838	−	0.101481i	$-0.967642\pi$
$107$		−	224.641i		−	0.202961i	0.994838	−	0.101481i	$-0.0323580\pi$
$108$	−1118.54	−	92.6033i	−0.996590	−	0.0825070i
$109$	541.597			0.475923			0.237962	−	0.971275i	$-0.423521\pi$
$109$	541.597			0.475923			0.237962	+	0.971275i	$0.423521\pi$
$110$	−542.950	+	33.8888i	−0.470621	+	0.0293743i
$111$	−959.111	+	1129.66i	−0.820133	+	0.965969i
$112$	1032.74	−	1347.22i	0.871289	−	1.13661i
$113$	189.054			0.157387			0.0786936	−	0.996899i	$-0.474925\pi$
$113$	189.054			0.157387			0.0786936	+	0.996899i	$0.474925\pi$
$114$	−312.812	+	100.431i	−0.256995	+	0.0825108i
$115$	−198.180	−	278.458i	−0.160699	−	0.225794i
$116$	−389.718	+	192.303i	−0.311935	+	0.153922i
$117$	−1777.71	+	292.250i	−1.40470	+	0.230928i
$118$	1074.74	+	668.139i	0.838457	+	0.521247i
$119$	−2331.38			−1.79594
$120$	−239.485	+	1292.54i	−0.182182	+	0.983265i
$121$	−1035.06			−0.777653
$122$	−1343.78	−	835.396i	−0.997217	−	0.619944i
$123$	−194.474	+	229.056i	−0.142562	+	0.167913i
$124$	1032.06	−	509.263i	0.747435	−	0.368816i
$125$	392.691	+	1341.24i	0.280986	+	0.959712i
$126$	−776.200	+	1870.92i	−0.548805	+	1.32282i
$127$	407.219			0.284527			0.142263	−	0.989829i	$-0.454562\pi$
$127$	407.219			0.284527			0.142263	+	0.989829i	$0.454562\pi$
$128$	1057.78	+	989.063i	0.730435	+	0.682982i
$129$	1127.94	+	957.647i	0.769839	+	0.653613i
$130$	131.444	+	2105.93i	0.0886798	+	1.42079i
$131$	1904.06			1.26991			0.634955	−	0.772549i	$-0.281019\pi$
$131$	1904.06			1.26991			0.634955	+	0.772549i	$0.281019\pi$
$132$	173.831	−	693.666i	0.114621	−	0.457393i
$133$			592.915i			0.386558i
$134$	−202.333	−	125.785i	−0.130440	−	0.0810911i
$135$	−121.521	−	1563.84i	−0.0774729	−	0.996994i
$136$	194.238	−	1979.40i	0.122469	−	1.24803i
$137$	−300.695			−0.187519			−0.0937597	−	0.995595i	$-0.529889\pi$
$137$	−300.695			−0.187519			−0.0937597	+	0.995595i	$0.529889\pi$
$138$	427.776	−	137.341i	0.263875	−	0.0847194i
$139$			1423.64i			0.868716i	0.900740	+	0.434358i	$0.143025\pi$
$139$			1423.64i			0.868716i	−0.900740	+	0.434358i	$0.856975\pi$
$140$	2088.86	+	1124.58i	1.26101	+	0.678887i
$141$	374.067	−	440.583i	0.223419	−	0.263147i
$142$	−285.954	−	177.770i	−0.168991	−	0.105057i
$143$		−	1147.87i		−	0.671256i
$144$	−1523.79	−	814.889i	−0.881824	−	0.471579i
$145$	−352.167	−	494.820i	−0.201696	−	0.283397i
$146$	−379.226	+	610.007i	−0.214965	+	0.345784i
$147$	1427.97	+	1212.39i	0.801205	+	0.680244i
$148$	−2046.00	+	1009.59i	−1.13635	+	0.560726i
$149$		−	287.103i		−	0.157855i	−0.996880	−	0.0789275i	$-0.974850\pi$
$149$		−	287.103i		−	0.157855i	0.996880	−	0.0789275i	$-0.0251496\pi$
$150$	−1836.63	−	42.3488i	−0.999734	−	0.0230518i
$151$			253.776i			0.136768i	0.997659	+	0.0683842i	$0.0217844\pi$
$151$			253.776i			0.136768i	−0.997659	+	0.0683842i	$0.978216\pi$
$152$	−503.400	−	49.3984i	−0.268626	−	0.0263601i
$153$	384.988	+	2341.81i	0.203427	+	1.23742i
$154$	−1096.04	−	681.379i	−0.573515	−	0.356539i
$155$	932.618	+	1310.40i	0.483288	+	0.679056i
$156$	−2690.51	−	674.233i	−1.38085	−	0.346038i
$157$		−	3792.57i		−	1.92790i	−0.266084	−	0.963950i	$-0.585730\pi$
$157$		−	3792.57i		−	1.92790i	0.266084	−	0.963950i	$-0.414270\pi$
$158$	1768.27	−	2844.37i	0.890356	−	1.43219i
$159$	−636.363	−	540.289i	−0.317402	−	0.269482i
$160$	−1128.83	+	1679.81i	−0.557761	+	0.830002i
$161$		−	810.822i		−	0.396905i
$162$	2007.47	+	470.725i	0.973592	+	0.228294i
$163$	2637.73			1.26750			0.633751	−	0.773537i	$-0.281514\pi$
$163$	2637.73			1.26750			0.633751	+	0.773537i	$0.281514\pi$
$164$	−414.858	+	204.709i	−0.197530	+	0.0974699i
$165$	995.763	+	85.2344i	0.469818	+	0.0402151i
$166$	1537.61	−	2473.34i	0.718928	−	1.15644i
$167$		−	3943.77i		−	1.82741i	−0.406373	−	0.913707i	$-0.633207\pi$
$167$		−	3943.77i		−	1.82741i	0.406373	−	0.913707i	$-0.366793\pi$
$168$	−2240.88	+	2168.79i	−1.02909	+	0.995989i
$169$	−2255.21			−1.02650
$170$	2774.18	−	173.154i	1.25159	−	0.0781192i
$171$	595.569	−	97.9098i	0.266341	−	0.0437857i
$172$	1008.04	+	2042.88i	0.446876	+	0.905629i
$173$	−833.359			−0.366238			−0.183119	−	0.983091i	$-0.558619\pi$
$173$	−833.359			−0.366238			−0.183119	+	0.983091i	$0.558619\pi$
$174$	760.159	−	244.056i	0.331192	−	0.106332i
$175$	−1086.00	+	3132.54i	−0.469109	+	1.35313i
$176$	669.824	−	873.796i	0.286874	−	0.374232i
$177$	−1772.26	−	1504.69i	−0.752604	−	0.638980i
$178$	1284.14	−	2065.62i	0.540734	−	0.869802i
$179$	4233.91			1.76792			0.883960	−	0.467563i	$-0.154868\pi$
$179$	4233.91			1.76792			0.883960	+	0.467563i	$0.154868\pi$
$180$	784.672	−	2283.92i	0.324922	−	0.945741i
$181$	692.073			0.284207			0.142103	−	0.989852i	$-0.454613\pi$
$181$	692.073			0.284207			0.142103	+	0.989852i	$0.454613\pi$
$182$	−2642.85	+	4251.18i	−1.07638	+	1.73142i
$183$	2215.91	+	1881.37i	0.895108	+	0.759970i
$184$	688.409	+	67.5533i	0.275816	+	0.0270657i
$185$	−1848.86	−	2597.79i	−0.734762	−	1.03239i
$186$	−2013.07	+	646.316i	−0.793579	+	0.254786i
$187$	−1512.11			−0.591318
$188$	797.970	−	393.752i	0.309563	−	0.152752i
$189$	1916.34	−	3189.78i	0.737530	−	1.22763i
$190$	−44.0363	−	705.529i	−0.0168144	−	0.269392i
$191$	−2424.56			−0.918509			−0.459254	−	0.888305i	$-0.651883\pi$
$191$	−2424.56			−0.918509			−0.459254	+	0.888305i	$0.651883\pi$
$192$	−1654.66	−	2083.26i	−0.621954	−	0.783054i
$193$		−	635.137i		−	0.236882i	−0.992961	−	0.118441i	$-0.962210\pi$
$193$		−	635.137i		−	0.236882i	0.992961	−	0.118441i	$-0.0377896\pi$
$194$	118.158	−	190.065i	0.0437282	−	0.0703394i
$195$	330.597	−	3862.24i	0.121408	−	1.41836i
$196$	1276.19	+	2586.30i	0.465084	+	0.942528i
$197$	4881.45			1.76543			0.882713	−	0.469913i	$-0.155715\pi$
$197$	4881.45			1.76543			0.882713	+	0.469913i	$0.155715\pi$
$198$	−503.437	+	1213.46i	−0.180695	+	0.435541i
$199$		−	739.302i		−	0.263355i	−0.991293	−	0.131678i	$-0.957964\pi$
$199$		−	739.302i		−	0.263355i	0.991293	−	0.131678i	$-0.0420364\pi$
$200$	−2569.13	−	1183.03i	−0.908325	−	0.418265i
$201$	333.649	+	283.277i	0.117084	+	0.0994070i
$202$	−1044.71	+	1680.47i	−0.363888	+	0.585335i
$203$		−	1440.83i		−	0.498161i
$204$	−888.182	+	3544.26i	−0.304829	+	1.21641i
$205$	−374.885	−	526.741i	−0.127722	−	0.179459i
$206$	3180.50	+	1977.24i	1.07571	+	0.668740i
$207$	−814.452	+	133.894i	−0.273470	+	0.0449577i
$208$	−3389.17	−	2598.03i	−1.12979	−	0.866063i
$209$			384.559i			0.127275i
$210$	−3491.60	−	2608.31i	−1.14735	−	0.857097i
$211$		−	49.3924i		−	0.0161152i	−0.999968	−	0.00805761i	$-0.997435\pi$
$211$		−	49.3924i		−	0.0161152i	0.999968	−	0.00805761i	$-0.00256485\pi$
$212$	−568.722	−	1152.56i	−0.184245	−	0.373388i
$213$	471.540	+	400.350i	0.151687	+	0.128786i
$214$	−335.460	+	539.607i	−0.107157	+	0.172368i
$215$	−2593.82	+	1846.04i	−0.822778	+	0.585576i
$216$	2548.55	+	1892.78i	0.802809	+	0.596237i
$217$			3815.66i			1.19366i
$218$	−1300.96	−	808.775i	−0.404185	−	0.251271i
$219$	854.040	−	1005.91i	0.263519	−	0.310378i
$220$	1354.82	+	729.391i	0.415190	+	0.223525i
$221$			5865.00i			1.78517i
$222$	3990.80	−	1281.29i	1.20651	−	0.387361i
$223$	−3386.76			−1.01701			−0.508507	−	0.861058i	$-0.669803\pi$
$223$	−3386.76			−1.01701			−0.508507	+	0.861058i	$0.669803\pi$
$224$	−4492.54	+	1693.94i	−1.34005	+	0.505272i
$225$	3325.90	+	573.578i	0.985453	+	0.169949i
$226$	−454.125	−	282.318i	−0.133663	−	0.0830951i
$227$			4323.98i			1.26429i	0.774852	+	0.632143i	$0.217824\pi$
$227$			4323.98i			1.26429i	−0.774852	+	0.632143i	$0.782176\pi$
$228$	901.375	+	225.882i	0.261820	+	0.0656114i
$229$	−2988.79			−0.862466			−0.431233	−	0.902241i	$-0.641921\pi$
$229$	−2988.79			−0.862466			−0.431233	+	0.902241i	$0.641921\pi$
$230$	60.2205	+	964.824i	0.0172644	+	0.276603i
$231$	1807.37	+	1534.51i	0.514790	+	0.437070i
$232$	1223.31	+	120.042i	0.346181	+	0.0339705i
$233$	−3800.60			−1.06861			−0.534304	−	0.845292i	$-0.679426\pi$
$233$	−3800.60			−1.06861			−0.534304	+	0.845292i	$0.679426\pi$
$234$	4706.63	+	1952.67i	1.31488	+	0.545513i
$235$	721.082	+	1013.17i	0.200162	+	0.281243i
$236$	−1583.88	−	3209.85i	−0.436871	−	0.885354i
$237$	−3982.26	+	4690.39i	−1.09146	+	1.28554i
$238$	5600.17	+	3481.48i	1.52523	+	0.948197i
$239$	1907.49			0.516256			0.258128	−	0.966111i	$-0.416894\pi$
$239$	1907.49			0.516256			0.258128	+	0.966111i	$0.416894\pi$
$240$	2505.42	−	2747.15i	0.673852	−	0.738867i
$241$	4625.68			1.23637			0.618187	−	0.786031i	$-0.287867\pi$
$241$	4625.68			1.23637			0.618187	+	0.786031i	$0.287867\pi$
$242$	2486.29	+	1545.67i	0.660434	+	0.410575i
$243$	−3520.51	−	1398.18i	−0.929386	−	0.369108i
$244$	1980.37	+	4013.39i	0.519592	+	1.05299i
$245$	−3283.79	+	2337.10i	−0.856301	+	0.609435i
$246$	809.196	−	259.800i	0.209725	−	0.0673343i
$247$	1491.58			0.384239
$248$	−3239.59	−	317.900i	−0.829493	−	0.0813977i
$249$	−3462.80	+	4078.56i	−0.881311	+	1.03803i
$250$	1059.61	−	3808.18i	0.268064	−	0.963401i
$251$	−5436.89			−1.36722			−0.683612	−	0.729845i	$-0.739592\pi$
$251$	−5436.89			−1.36722			−0.683612	+	0.729845i	$0.739592\pi$
$252$	4658.37	−	3335.00i	1.16448	−	0.833671i
$253$		−	525.892i		−	0.130682i
$254$	−978.176	−	608.107i	−0.241639	−	0.150221i
$255$	−5087.81	−	435.502i	−1.24946	−	0.106950i
$256$	−1063.90	−	3955.42i	−0.259742	−	0.965678i
$257$	4260.69			1.03414			0.517072	−	0.855942i	$-0.327022\pi$
$257$	4260.69			1.03414			0.517072	+	0.855942i	$0.327022\pi$
$258$	−1279.33	−	3984.71i	−0.308712	−	0.961540i
$259$		−	7564.32i		−	1.81476i
$260$	2829.08	−	5254.91i	0.674815	−	1.25344i
$261$	−1447.28	+	237.929i	−0.343236	+	0.0564270i
$262$	−4573.71	−	2843.36i	−1.07849	−	0.670470i
$263$			3516.29i			0.824425i	0.911088	+	0.412212i	$0.135244\pi$
$263$			3516.29i			0.824425i	−0.911088	+	0.412212i	$0.864756\pi$
$264$	−1453.42	+	1406.66i	−0.338832	+	0.327932i
$265$	1463.39	−	1041.51i	0.339228	−	0.241431i
$266$	885.408	−	1424.23i	0.204090	−	0.328290i
$267$	−2891.97	+	3406.22i	−0.662868	+	0.780740i
$268$	298.185	+	604.294i	0.0679646	+	0.137736i
$269$		−	8095.72i		−	1.83496i	−0.397779	−	0.917481i	$-0.630219\pi$
$269$		−	8095.72i		−	1.83496i	0.397779	−	0.917481i	$-0.369781\pi$
$270$	−2043.41	+	3937.95i	−0.460584	+	0.887616i
$271$		−	661.220i		−	0.148215i	−0.997250	−	0.0741075i	$-0.976389\pi$
$271$		−	661.220i		−	0.148215i	0.997250	−	0.0741075i	$-0.0236108\pi$
$272$	−3422.44	+	4464.63i	−0.762927	+	0.995250i
$273$	5951.86	−	7010.23i	1.31950	−	1.55413i
$274$	722.296	+	449.033i	0.159254	+	0.0990039i
$275$	−704.372	+	2031.74i	−0.154455	+	0.445522i
$276$	−1232.65	−	308.898i	−0.268828	−	0.0673676i
$277$			5273.41i			1.14386i	0.820304	+	0.571928i	$0.193804\pi$
$277$			5273.41i			1.14386i	−0.820304	+	0.571928i	$0.806196\pi$
$278$	2125.94	−	3419.70i	0.458653	−	0.737770i
$279$	3832.74	−	630.091i	0.822437	−	0.135206i
$280$	−3338.28	−	5820.66i	−0.712501	−	1.24233i
$281$		−	5265.93i		−	1.11793i	−0.829190	−	0.558966i	$-0.811198\pi$
$281$		−	5265.93i		−	1.11793i	0.829190	−	0.558966i	$-0.188802\pi$
$282$	−1556.47	+	499.719i	−0.328675	+	0.105524i
$283$	1890.66			0.397132			0.198566	−	0.980088i	$-0.436372\pi$
$283$	1890.66			0.397132			0.198566	+	0.980088i	$0.436372\pi$
$284$	421.418	+	854.037i	0.0880513	+	0.178443i
$285$	−110.757	+	1293.93i	−0.0230199	+	0.268933i
$286$	−1714.13	+	2757.28i	−0.354401	+	0.570074i
$287$		−	1533.78i		−	0.315457i
$288$	2443.39	+	4232.93i	0.499924	+	0.866069i
$289$	2813.08			0.572579
$290$	107.012	+	1714.50i	0.0216688	+	0.347168i
$291$	−266.100	+	313.418i	−0.0536050	+	0.0631371i
$292$	1821.86	−	898.985i	0.365125	−	0.180168i
$293$	2352.00			0.468961			0.234481	−	0.972121i	$-0.424661\pi$
$293$	2352.00			0.468961			0.234481	+	0.972121i	$0.424661\pi$
$294$	−1619.64	−	5044.67i	−0.321290	−	1.00072i
$295$	4075.51	−	2900.57i	0.804357	−	0.572466i
$296$	6422.30	+	630.218i	1.26111	+	0.123752i
$297$	1242.92	−	2068.86i	0.242834	−	0.404201i
$298$	−428.735	+	689.646i	−0.0833422	+	0.134061i
$299$	−2039.77			−0.394524
$300$	4348.50	+	2844.39i	0.836869	+	0.547403i
$301$	−7552.77			−1.44629
$302$	378.968	−	609.592i	0.0722091	−	0.116153i
$303$	2352.75	−	2771.11i	0.446079	−	0.525401i
$304$	1135.44	+	870.394i	0.214217	+	0.164212i
$305$	−5095.75	+	3626.68i	−0.956661	+	0.680862i
$306$	2572.29	−	6200.15i	0.480550	−	1.15830i
$307$	−3922.53			−0.729220			−0.364610	−	0.931160i	$-0.618798\pi$
$307$	−3922.53			−0.729220			−0.364610	+	0.931160i	$0.618798\pi$
$308$	1615.26	+	3273.46i	0.298825	+	0.605593i
$309$	−5244.67	−	4452.86i	−0.965563	−	0.819788i
$310$	−283.392	−	4540.38i	−0.0519213	−	0.831858i
$311$	4470.09			0.815034			0.407517	−	0.913198i	$-0.366395\pi$
$311$	4470.09			0.815034			0.407517	+	0.913198i	$0.366395\pi$
$312$	5455.99	+	5637.34i	0.990014	+	1.02292i
$313$		−	156.300i		−	0.0282255i	−0.999900	−	0.0141127i	$-0.995508\pi$
$313$		−	156.300i		−	0.0282255i	0.999900	−	0.0141127i	$-0.00449238\pi$
$314$	−5663.50	+	9110.08i	−1.01787	+	1.63730i
$315$	5639.34	+	5683.71i	1.00870	+	1.01664i
$316$	−8495.08	+	4191.84i	−1.51230	+	0.746232i
$317$	6333.51			1.12216			0.561081	−	0.827761i	$-0.310386\pi$
$317$	6333.51			1.12216			0.561081	+	0.827761i	$0.310386\pi$
$318$	721.777	+	2248.11i	0.127281	+	0.396439i
$319$		−	934.512i		−	0.164021i
$320$	5220.02	−	2349.34i	0.911900	−	0.410413i
$321$	755.476	−	889.815i	0.131360	−	0.154719i
$322$	−1210.81	+	1947.66i	−0.209553	+	0.337078i
$323$		−	1964.89i		−	0.338482i
$324$	−4119.18	−	4128.51i	−0.706307	−	0.707906i
$325$	7880.47	+	2732.03i	1.34502	+	0.466295i
$326$	−6336.05	−	3938.96i	−1.07645	−	0.669199i
$327$	2145.30	+	1821.41i	0.362799	+	0.308026i
$328$	1302.22	+	127.786i	0.219217	+	0.0215116i
$329$			2950.19i			0.494374i
$330$	−2264.62	−	1691.73i	−0.377768	−	0.282202i
$331$			7260.21i			1.20561i	0.797888	+	0.602806i	$0.205951\pi$
$331$			7260.21i			1.20561i	−0.797888	+	0.602806i	$0.794049\pi$
$332$	−7386.96	+	3645.04i	−1.22112	+	0.602553i
$333$	−7598.18	+	1249.12i	−1.25038	+	0.205559i
$334$	−5889.29	+	9473.27i	−0.964813	+	1.55196i
$335$	−767.266	+	546.068i	−0.125135	+	0.0890593i
$336$	8621.48	−	1863.28i	1.39982	−	0.302531i
$337$		−	2013.28i		−	0.325431i	−0.986673	−	0.162716i	$-0.947975\pi$
$337$		−	2013.28i		−	0.325431i	0.986673	−	0.162716i	$-0.0520253\pi$
$338$	5417.22	+	3367.74i	0.871768	+	0.541956i
$339$	748.855	+	635.798i	0.119977	+	0.101864i
$340$	−6922.40	−	3726.80i	−1.10418	−	0.594453i
$341$			2474.80i			0.393015i
$342$	−1576.82	−	654.184i	−0.249312	−	0.103433i
$343$	−464.243			−0.0730810
$344$	629.256	−	6412.50i	0.0986256	−	1.00505i
$345$	151.462	−	1769.47i	0.0236360	−	0.276131i
$346$	2001.80	+	1244.47i	0.311033	+	0.193361i
$347$		−	11929.2i		−	1.84551i	−0.385390	−	0.922754i	$-0.625933\pi$
$347$		−	11929.2i		−	1.84551i	0.385390	−	0.922754i	$-0.374067\pi$
$348$	−2190.42	−	548.912i	−0.337410	−	0.0845540i
$349$	8987.66			1.37850			0.689252	−	0.724521i	$-0.257939\pi$
$349$	8987.66			1.37850			0.689252	+	0.724521i	$0.257939\pi$
$350$	7286.54	−	5902.89i	1.11281	−	0.901494i
$351$	−8024.46	−	4820.89i	−1.22027	−	0.733106i
$352$	−2913.83	+	1098.67i	−0.441214	+	0.166362i
$353$	−8127.12			−1.22539			−0.612695	−	0.790319i	$-0.709915\pi$
$353$	−8127.12			−1.22539			−0.612695	+	0.790319i	$0.709915\pi$
$354$	2010.13	+	6260.93i	0.301800	+	0.940013i
$355$	−1084.36	+	771.747i	−0.162118	+	0.115380i
$356$	−6169.24	+	3044.17i	−0.918453	+	0.453204i
$357$	−9234.72	−	7840.51i	−1.36906	−	1.16236i
$358$	−10170.2	−	6322.57i	−1.50143	−	0.933402i
$359$	11792.5			1.73365			0.866827	−	0.498608i	$-0.166155\pi$
$359$	11792.5			1.73365			0.866827	+	0.498608i	$0.166155\pi$
$360$	−5295.46	+	4314.41i	−0.775264	+	0.631637i
$361$	6359.29			0.927145
$362$	−1662.42	−	1033.48i	−0.241367	−	0.150052i
$363$	−4099.92	−	3480.94i	−0.592810	−	0.503311i
$364$	12696.7	−	6265.09i	1.82826	−	0.902142i
$365$	1646.32	+	2313.20i	0.236088	+	0.331722i
$366$	−2513.33	−	7828.25i	−0.358946	−	1.11800i
$367$	11786.7			1.67646			0.838230	−	0.545317i	$-0.183591\pi$
$367$	11786.7			1.67646			0.838230	+	0.545317i	$0.183591\pi$
$368$	−1552.74	−	1190.28i	−0.219951	−	0.168608i
$369$	−1540.65	+	253.278i	−0.217352	+	0.0357320i
$370$	561.809	+	9001.03i	0.0789380	+	1.26471i
$371$	4261.15			0.596302
$372$	5800.73	+	1453.65i	0.808478	+	0.202602i
$373$		−	2406.87i		−	0.334109i	−0.985948	−	0.167055i	$-0.946574\pi$
$373$		−	2406.87i		−	0.334109i	0.985948	−	0.167055i	$-0.0534257\pi$
$374$	3632.22	+	2258.06i	0.502186	+	0.312196i
$375$	−2955.17	+	6633.35i	−0.406944	+	0.913453i
$376$	−2504.79	−	245.794i	−0.343549	−	0.0337123i
$377$	−3624.67			−0.495173
$378$	−9366.55	+	4800.43i	−1.27451	+	0.653194i
$379$			5023.30i			0.680817i	0.940278	+	0.340408i	$0.110565\pi$
$379$			5023.30i			0.680817i	−0.940278	+	0.340408i	$0.889435\pi$
$380$	−947.798	+	1760.50i	−0.127950	+	0.237663i
$381$	1613.02	+	1369.50i	0.216896	+	0.184151i
$382$	5824.00	+	3620.63i	0.780057	+	0.484942i
$383$			7326.45i			0.977452i	0.872437	+	0.488726i	$0.162538\pi$
$383$			7326.45i			0.977452i	−0.872437	+	0.488726i	$0.837462\pi$
$384$	863.681	+	7475.10i	0.114777	+	0.993391i
$385$	−4156.27	+	2958.04i	−0.550190	+	0.391574i
$386$	−948.460	+	1525.65i	−0.125066	+	0.201175i
$387$	1247.21	+	7586.59i	0.163823	+	0.996506i
$388$	−567.652	+	280.104i	−0.0742737	+	0.0366498i
$389$			7611.38i			0.992063i	0.868305	+	0.496031i	$0.165210\pi$
$389$			7611.38i			0.992063i	−0.868305	+	0.496031i	$0.834790\pi$
$390$	−6561.67	+	8783.75i	−0.851956	+	1.14047i
$391$			2687.03i			0.347542i
$392$	796.641	−	8118.26i	0.102644	−	1.04601i
$393$	7542.07	+	6403.42i	0.968059	+	0.821908i
$394$	−11725.7	−	7289.54i	−1.49931	−	0.932085i
$395$	−7676.54	−	10786.1i	−0.977845	−	1.37394i
$396$	3021.38	−	2163.05i	0.383409	−	0.274488i
$397$		−	2312.18i		−	0.292305i	−0.989262	−	0.146152i	$-0.953311\pi$
$397$		−	2312.18i		−	0.292305i	0.989262	−	0.146152i	$-0.0466890\pi$
$398$	−1104.01	+	1775.87i	−0.139043	+	0.223659i
$399$	−1994.00	+	2348.57i	−0.250187	+	0.294675i
$400$	4404.64	+	6678.26i	0.550579	+	0.834783i
$401$		−	7277.89i		−	0.906336i	−0.891425	−	0.453168i	$-0.850294\pi$
$401$		−	7277.89i		−	0.906336i	0.891425	−	0.453168i	$-0.149706\pi$
$402$	−378.432	−	1178.70i	−0.0469514	−	0.146239i
$403$	9598.96			1.18650
$404$	5018.95	−	2476.56i	0.618075	−	0.304984i
$405$	4777.92	−	6603.15i	0.586214	−	0.810156i
$406$	−2151.62	+	3461.00i	−0.263012	+	0.423071i
$407$		−	4906.15i		−	0.597516i
$408$	7426.19	−	7187.29i	0.901106	−	0.872117i
$409$	−9439.22			−1.14117			−0.570586	−	0.821238i	$-0.693284\pi$
$409$	−9439.22			−1.14117			−0.570586	+	0.821238i	$0.693284\pi$
$410$	113.915	+	1825.10i	0.0137216	+	0.219842i
$411$	−1191.07	−	1011.25i	−0.142947	−	0.121366i
$412$	−4687.20	−	9498.98i	−0.560490	−	1.13588i
$413$	11867.2			1.41392
$414$	2156.33	+	894.609i	0.255985	+	0.106202i
$415$	−6675.19	−	9379.13i	−0.789571	−	1.10941i
$416$	4261.40	+	11301.8i	0.502242	+	1.33201i
$417$	−4787.75	+	5639.11i	−0.562248	+	0.662227i
$418$	574.268	−	923.744i	0.0671971	−	0.108090i
$419$	−9466.00			−1.10369			−0.551843	−	0.833948i	$-0.686075\pi$
$419$	−9466.00			−1.10369			−0.551843	+	0.833948i	$0.686075\pi$
$420$	4492.10	+	11479.4i	0.521886	+	1.33367i
$421$	295.101			0.0341623			0.0170811	−	0.999854i	$-0.494563\pi$
$421$	295.101			0.0341623			0.0170811	+	0.999854i	$0.494563\pi$
$422$	−73.7584	+	118.645i	−0.00850830	+	0.0136861i
$423$	2963.40	−	487.174i	0.340627	−	0.0559981i
$424$	−355.016	+	3617.83i	−0.0406630	+	0.414380i
$425$	3598.96	−	10381.1i	0.410766	−	1.18484i
$426$	−534.831	−	1665.83i	−0.0608278	−	0.189460i
$427$	−14838.0			−1.68164
$428$	1611.60	−	795.234i	0.182009	−	0.0898110i
$429$	3860.33	−	4546.77i	0.434448	−	0.511702i
$430$	8987.30	−	560.951i	1.00792	−	0.0629104i
$431$	3224.98			0.360422			0.180211	−	0.983628i	$-0.442322\pi$
$431$	3224.98			0.360422			0.180211	+	0.983628i	$0.442322\pi$
$432$	−3295.32	−	8352.39i	−0.367005	−	0.930219i
$433$			14208.4i			1.57693i	0.615081	+	0.788464i	$0.289123\pi$
$433$			14208.4i			1.57693i	−0.615081	+	0.788464i	$0.710877\pi$
$434$	5697.97	−	9165.53i	0.630211	−	1.01373i
$435$	269.148	−	3144.36i	0.0296659	−	0.346576i
$436$	1917.27	+	3885.49i	0.210597	+	0.426792i
$437$	683.363			0.0748048
$438$	−3553.61	+	1140.92i	−0.387667	+	0.124464i
$439$		−	11992.1i		−	1.30376i	−0.758320	−	0.651882i	$-0.773980\pi$
$439$		−	11992.1i		−	1.30376i	0.758320	−	0.651882i	$-0.226020\pi$
$440$	−2165.18	−	3775.23i	−0.234593	−	0.409039i
$441$	1578.98	+	9604.66i	0.170498	+	1.03711i
$442$	8758.28	−	14088.2i	0.942509	−	1.51608i
$443$			3449.96i			0.370005i	0.982738	+	0.185003i	$0.0592294\pi$
$443$			3449.96i			0.370005i	−0.982738	+	0.185003i	$0.940771\pi$
$444$	−11499.6	−	2881.77i	−1.22916	−	0.308024i
$445$	−5574.81	−	7833.01i	−0.593868	−	0.834428i
$446$	8135.29	+	5057.50i	0.863715	+	0.536950i
$447$	965.539	−	1137.23i	0.102167	−	0.120334i
$448$	13321.1	+	2639.80i	1.40482	+	0.278390i
$449$		−	4937.03i		−	0.518915i	−0.965755	−	0.259458i	$-0.916456\pi$
$449$		−	4937.03i		−	0.518915i	0.965755	−	0.259458i	$-0.0835438\pi$
$450$	−7132.57	−	6344.40i	−0.747183	−	0.664618i
$451$		−	994.796i		−	0.103865i
$452$	669.257	+	1356.30i	0.0696443	+	0.141140i
$453$	−853.460	+	1005.22i	−0.0885189	+	0.104259i
$454$	6457.07	−	10386.6i	0.667500	−	1.07371i
$455$	11473.3	+	16120.8i	1.18215	+	1.66100i
$456$	−1827.87	−	1888.62i	−0.187714	−	0.193954i
$457$		−	14718.6i		−	1.50658i	−0.657686	−	0.753292i	$-0.728465\pi$
$457$		−	14718.6i		−	1.50658i	0.657686	−	0.753292i	$-0.271535\pi$
$458$	7179.32	+	4463.20i	0.732462	+	0.455353i
$459$	−6350.66	+	10570.8i	−0.645803	+	1.07495i
$460$	1296.13	−	2407.52i	0.131375	−	0.244024i
$461$			8999.57i			0.909223i	0.890690	+	0.454611i	$0.150222\pi$
$461$			8999.57i			0.909223i	−0.890690	+	0.454611i	$0.849778\pi$
$462$	−2049.96	−	6385.00i	−0.206435	−	0.642980i
$463$	−13787.6			−1.38394			−0.691972	−	0.721924i	$-0.743258\pi$
$463$	−13787.6			−1.38394			−0.691972	+	0.721924i	$0.743258\pi$
$464$	−2759.22	−	2115.13i	−0.276064	−	0.211622i
$465$	−712.766	+	8326.99i	−0.0710833	+	0.830440i
$466$	9129.37	+	5675.50i	0.907532	+	0.564189i
$467$			13505.3i			1.33823i	0.743160	+	0.669113i	$0.233326\pi$
$467$			13505.3i			1.33823i	−0.743160	+	0.669113i	$0.766674\pi$
$468$	−8389.78	−	11719.0i	−0.828670	−	1.15750i
$469$	−2234.15			−0.219965
$470$	−219.113	−	3510.53i	−0.0215041	−	0.344529i
$471$	12754.6	−	15022.6i	1.24777	−	1.46965i
$472$	−988.711	+	10075.6i	−0.0964176	+	0.982554i
$473$	−4898.66			−0.476196
$474$	16570.0	−	5319.95i	1.60566	−	0.515513i
$475$	−2640.12	−	915.287i	−0.255025	−	0.0884131i
$476$	−8253.13	−	16725.6i	−0.794709	−	1.61054i
$477$	−703.657	−	4280.23i	−0.0675435	−	0.410856i
$478$	−4581.95	−	2848.48i	−0.438438	−	0.272566i
$479$	−16769.0			−1.59957			−0.799785	−	0.600287i	$-0.795053\pi$
$479$	−16769.0			−1.59957			−0.799785	+	0.600287i	$0.795053\pi$
$480$	−10120.6	+	2857.51i	−0.962376	+	0.271723i
$481$	−19029.4			−1.80388
$482$	−11111.3	−	6907.60i	−1.05001	−	0.652764i
$483$	2726.83	−	3211.71i	0.256884	−	0.302563i
$484$	−3664.13	−	7425.64i	−0.344114	−	0.697374i
$485$	−512.956	−	720.742i	−0.0480250	−	0.0674787i
$486$	6368.65	+	8615.78i	0.594419	+	0.804155i
$487$	15310.5			1.42461			0.712305	−	0.701870i	$-0.247651\pi$
$487$	15310.5			1.42461			0.712305	+	0.701870i	$0.247651\pi$
$488$	1236.22	−	12597.8i	0.114674	−	1.16860i
$489$	10448.2	+	8870.79i	0.966224	+	0.820349i
$490$	11378.0	−	710.167i	1.04899	−	0.0654736i
$491$	−9679.94			−0.889714			−0.444857	−	0.895602i	$-0.646745\pi$
$491$	−9679.94			−0.889714			−0.444857	+	0.895602i	$0.646745\pi$
$492$	−2331.72	−	584.322i	−0.213663	−	0.0535432i
$493$			4774.86i			0.436204i
$494$	−3582.91	−	2227.40i	−0.326321	−	0.202865i
$495$	3657.63	+	3686.41i	0.332117	+	0.334731i
$496$	7307.05	+	5601.35i	0.661484	+	0.507073i
$497$	−3157.48			−0.284974
$498$	14408.5	−	4625.99i	1.29651	−	0.416257i
$499$			13876.2i			1.24486i	0.782676	+	0.622429i	$0.213854\pi$
$499$			13876.2i			1.24486i	−0.782676	+	0.622429i	$0.786146\pi$
$500$	−8232.09	+	7565.23i	−0.736301	+	0.676655i
$501$	13263.1	−	15621.5i	1.18273	−	1.39305i
$502$	13059.9	+	8118.99i	1.16114	+	0.721849i
$503$			5061.48i			0.448669i	0.974512	+	0.224334i	$0.0720208\pi$
$503$			5061.48i			0.448669i	−0.974512	+	0.224334i	$0.927979\pi$
$504$	−16170.0	+	1054.53i	−1.42911	+	0.0931998i
$505$	4535.35	+	6372.50i	0.399645	+	0.561530i
$506$	−785.322	+	1263.24i	−0.0689957	+	0.110984i
$507$	−8933.03	−	7584.38i	−0.782505	−	0.664367i
$508$	1441.57	+	2921.45i	0.125904	+	0.255154i
$509$			8757.04i			0.762572i	0.924457	+	0.381286i	$0.124519\pi$
$509$			8757.04i			0.762572i	−0.924457	+	0.381286i	$0.875481\pi$
$510$	11571.0	+	8643.82i	1.00465	+	0.750500i
$511$			6735.65i			0.583107i
$512$	−3351.10	+	11090.0i	−0.289256	+	0.957252i
$513$	2688.36	+	1615.10i	0.231372	+	0.139002i
$514$	−10234.5	−	6362.56i	−0.878262	−	0.545993i
$515$	12060.7	−	8583.70i	1.03196	−	0.734453i
$516$	−2877.37	+	11482.1i	−0.245483	+	0.979592i
$517$			1913.47i			0.162774i
$518$	−11295.9	+	18170.1i	−0.958134	+	1.54122i
$519$	−3300.98	−	2802.62i	−0.279185	−	0.237035i
$520$	−14642.9	+	8398.03i	−1.23487	+	0.708227i
$521$			7223.90i			0.607456i	0.952759	+	0.303728i	$0.0982314\pi$
$521$			7223.90i			0.607456i	−0.952759	+	0.303728i	$0.901769\pi$
$522$	3831.80	+	1589.72i	0.321290	+	0.133296i
$523$	−3932.76			−0.328810			−0.164405	−	0.986393i	$-0.552570\pi$
$523$	−3932.76			−0.328810			−0.164405	+	0.986393i	$0.552570\pi$
$524$	6740.41	+	13660.0i	0.561939	+	1.13881i
$525$	−14836.6	+	8755.91i	−1.23337	+	0.727884i
$526$	5250.93	−	8446.43i	0.435269	−	0.700155i
$527$		−	12644.9i		−	1.04520i
$528$	5591.82	−	1208.51i	0.460895	−	0.0996092i
$529$	11232.5			0.923193
$530$	−5070.49	+	316.480i	−0.415562	+	0.0259377i
$531$	−1959.67	−	11920.3i	−0.160155	−	0.974197i
$532$	−4253.65	+	2098.93i	−0.346653	+	0.171053i
$533$	−3858.50			−0.313565
$534$	12033.3	−	3863.41i	0.975155	−	0.313083i
$535$	1456.32	+	2046.24i	0.117686	+	0.165358i
$536$	186.137	−	1896.85i	0.0149998	−	0.152857i
$537$	16770.8	+	14238.8i	1.34770	+	1.14423i
$538$	−12089.5	+	19446.6i	−0.968799	+	1.55837i
$539$	−6201.73			−0.495598
$540$	10789.0	−	6407.85i	0.859790	−	0.510648i
$541$	−1221.12			−0.0970427			−0.0485213	−	0.998822i	$-0.515451\pi$
$541$	−1221.12			−0.0970427			−0.0485213	+	0.998822i	$0.515451\pi$
$542$	−987.409	+	1588.31i	−0.0782525	+	0.125874i
$543$	2741.34	+	2327.47i	0.216652	+	0.183943i
$544$	14888.1	−	5613.64i	1.17339	−	0.442431i
$545$	−4933.36	+	3511.11i	−0.387747	+	0.275962i
$546$	−24765.4	+	7951.15i	−1.94113	+	0.623220i
$547$	−14694.1			−1.14858			−0.574290	−	0.818652i	$-0.694722\pi$
$547$	−14694.1			−1.14858			−0.574290	+	0.818652i	$0.694722\pi$
$548$	−1064.47	−	2157.23i	−0.0829779	−	0.168161i
$549$	2450.24	+	14904.4i	0.190480	+	1.15866i
$550$	4725.99	−	3828.57i	0.366394	−	0.296819i
$551$	1214.34			0.0938885
$552$	2499.64	+	2582.73i	0.192739	+	0.199145i
$553$		−	31407.3i		−	2.41515i
$554$	7874.85	−	12667.2i	0.603918	−	0.971438i
$555$	1413.02	−	16507.8i	0.108071	−	1.26255i
$556$	−10213.4	+	5039.72i	−0.779036	+	0.384409i
$557$	139.514			0.0106129			0.00530647	−	0.999986i	$-0.498311\pi$
$557$	139.514			0.0106129			0.00530647	+	0.999986i	$0.498311\pi$
$558$	−10147.5	−	4209.95i	−0.769852	−	0.319393i
$559$			19000.3i			1.43762i
$560$	−673.249	+	18966.8i	−0.0508035	+	1.43124i
$561$	−5989.56	−	5085.29i	−0.450765	−	0.382711i
$562$	−7863.69	+	12649.2i	−0.590231	+	0.949421i
$563$		−	8054.91i		−	0.602974i	−0.953470	−	0.301487i	$-0.902517\pi$
$563$		−	8054.91i		−	0.602974i	0.953470	−	0.301487i	$-0.0974829\pi$
$564$	4485.01	+	1123.93i	0.334846	+	0.0839113i
$565$	−1722.08	+	1225.62i	−0.128227	+	0.0912603i
$566$	−4541.54	−	2823.36i	−0.337270	−	0.209672i
$567$	18318.1	−	6190.18i	1.35677	−	0.458488i
$568$	263.064	−	2680.78i	0.0194329	−	0.198034i
$569$		−	10472.5i		−	0.771578i	−0.922587	−	0.385789i	$-0.873929\pi$
$569$		−	10472.5i		−	0.771578i	0.922587	−	0.385789i	$-0.126071\pi$
$570$	2198.29	−	2942.74i	0.161537	−	0.216241i
$571$			13318.8i			0.976135i	0.872806	+	0.488067i	$0.162298\pi$
$571$			13318.8i			0.976135i	−0.872806	+	0.488067i	$0.837702\pi$
$572$	8234.97	−	4063.48i	0.601960	−	0.297033i
$573$	−9603.82	−	8153.90i	−0.700184	−	0.594475i
$574$	−2290.42	+	3684.27i	−0.166551	+	0.267907i
$575$	3610.41	+	1251.67i	0.261851	+	0.0907797i
$576$	451.869	−	13816.6i	0.0326873	−	0.999466i
$577$			6604.83i			0.476538i	0.971199	+	0.238269i	$0.0765800\pi$
$577$			6604.83i			0.476538i	−0.971199	+	0.238269i	$0.923420\pi$
$578$	−6757.26	−	4200.81i	−0.486271	−	0.302302i
$579$	2135.99	−	2515.81i	0.153314	−	0.180576i
$580$	2303.23	−	4278.17i	0.164890	−	0.306278i
$581$		−	27310.5i		−	1.95014i
$582$	1107.23	−	355.486i	0.0788591	−	0.0253185i
$583$	2763.75			0.196334
$584$	−5718.74	−	561.177i	−0.405211	−	0.0397632i
$585$	14298.4	−	14186.8i	1.01054	−	1.00265i
$586$	−5649.72	−	3512.28i	−0.398272	−	0.247596i
$587$			18372.1i			1.29182i	0.763414	+	0.645909i	$0.223522\pi$
$587$			18372.1i			1.29182i	−0.763414	+	0.645909i	$0.776478\pi$
$588$	−3642.76	+	14536.3i	−0.255485	+	1.01950i
$589$	−3215.85			−0.224969
$590$	−14121.2	+	881.388i	−0.985356	+	0.0615020i
$591$	19335.7	+	16416.5i	1.34579	+	1.14261i
$592$	−14485.8	−	11104.4i	−1.00568	−	0.770922i
$593$	1383.40			0.0958000			0.0479000	−	0.998852i	$-0.484747\pi$
$593$	1383.40			0.0958000			0.0479000	+	0.998852i	$0.484747\pi$
$594$	−6075.07	+	3113.52i	−0.419635	+	0.215066i
$595$	21236.3	−	15114.0i	1.46320	−	1.04137i
$596$	2059.72	−	1016.35i	0.141559	−	0.0698513i
$597$	2486.30	−	2928.42i	0.170448	−	0.200757i
$598$	4899.69	+	3046.01i	0.335056	+	0.208296i
$599$	4488.77			0.306187			0.153094	−	0.988212i	$-0.451076\pi$
$599$	4488.77			0.306187			0.153094	+	0.988212i	$0.451076\pi$
$600$	−6197.89	−	13326.1i	−0.421713	−	0.906729i
$601$	−2648.46			−0.179755			−0.0898775	−	0.995953i	$-0.528648\pi$
$601$	−2648.46			−0.179755			−0.0898775	+	0.995953i	$0.528648\pi$
$602$	18142.4	+	11278.7i	1.22829	+	0.763595i
$603$	368.932	+	2244.15i	0.0249155	+	0.151557i
$604$	−1820.63	+	898.374i	−0.122649	+	0.0605204i
$605$	9428.25	−	6710.14i	0.633575	−	0.450919i
$606$	−9789.65	+	3143.06i	−0.656233	+	0.210690i
$607$	4123.51			0.275730			0.137865	−	0.990451i	$-0.455976\pi$
$607$	4123.51			0.275730			0.137865	+	0.990451i	$0.455976\pi$
$608$	−1427.66	−	3786.33i	−0.0952288	−	0.252559i
$609$	4845.58	−	5707.22i	0.322418	−	0.379751i
$610$	17656.2	−	1102.03i	1.17193	−	0.0731473i
$611$	7421.73			0.491409
$612$	−15437.6	+	11052.0i	−1.01966	+	0.729987i
$613$		−	12312.1i		−	0.811225i	−0.914045	−	0.405613i	$-0.867058\pi$
$613$		−	12312.1i		−	0.811225i	0.914045	−	0.405613i	$-0.132942\pi$
$614$	9422.25	+	5857.57i	0.619301	+	0.385004i
$615$	286.511	−	3347.20i	0.0187857	−	0.219467i
$616$	1008.30	−	10275.2i	0.0659508	−	0.672079i
$617$	−16541.2			−1.07929			−0.539646	−	0.841892i	$-0.681442\pi$
$617$	−16541.2			−1.07929			−0.539646	+	0.841892i	$0.681442\pi$
$618$	5948.62	+	18528.1i	0.387198	+	1.20600i
$619$			2365.55i			0.153601i	0.997046	+	0.0768007i	$0.0244705\pi$
$619$			2365.55i			0.153601i	−0.997046	+	0.0768007i	$0.975529\pi$
$620$	−6099.48	+	11329.6i	−0.395098	+	0.733881i
$621$	−3676.38	−	2208.67i	−0.237565	−	0.142723i
$622$	−10737.5	−	6675.25i	−0.692180	−	0.430310i
$623$		−	22808.4i		−	1.46677i
$624$	−4687.42	−	21688.9i	−0.300716	−	1.39143i
$625$	−12272.1	−	9671.46i	−0.785412	−	0.618974i
$626$	−233.405	+	375.445i	−0.0149021	+	0.0239709i
$627$	−1293.29	+	1523.26i	−0.0823747	+	0.0970226i
$628$	27208.4	−	13425.8i	1.72888	−	0.853101i
$629$			25067.8i			1.58906i
$630$	−5058.59	−	22074.1i	−0.319903	−	1.39596i
$631$		−	28496.5i		−	1.79782i	−0.438129	−	0.898912i	$-0.644359\pi$
$631$		−	28496.5i		−	1.79782i	0.438129	−	0.898912i	$-0.355641\pi$
$632$	26665.6	+	2616.69i	1.67833	+	0.164693i
$633$	166.109	−	195.646i	0.0104301	−	0.0122847i
$634$	−15213.6	−	9457.92i	−0.953013	−	0.592463i
$635$	−3709.33	+	2639.95i	−0.231811	+	0.164982i
$636$	1623.37	−	6477.99i	0.101212	−	0.403882i
$637$			24054.5i			1.49619i
$638$	−1395.52	+	2244.78i	−0.0865975	+	0.139297i
$639$	521.404	+	3171.61i	0.0322792	+	0.196349i
$640$	−16047.2	−	2151.82i	−0.991129	−	0.132903i
$641$			5586.35i			0.344224i	0.985077	+	0.172112i	$0.0550591\pi$
$641$			5586.35i			0.344224i	−0.985077	+	0.172112i	$0.944941\pi$
$642$	−3143.49	+	1009.25i	−0.193246	+	0.0620434i
$643$	9416.10			0.577503			0.288752	−	0.957404i	$-0.406760\pi$
$643$	9416.10			0.577503			0.288752	+	0.957404i	$0.406760\pi$
$644$	5816.95	−	2870.33i	0.355931	−	0.175632i
$645$	−16482.6	−	1410.86i	−1.00620	−	0.0861281i
$646$	−2934.20	+	4719.84i	−0.178707	+	0.287461i
$647$			11061.4i			0.672133i	0.941838	+	0.336067i	$0.109097\pi$
$647$			11061.4i			0.672133i	−0.941838	+	0.336067i	$0.890903\pi$
$648$	3729.46	+	16068.3i	0.226091	+	0.974106i
$649$	7696.97			0.465535
$650$	−14849.8	−	18330.6i	−0.896087	−	1.10613i
$651$	−12832.2	+	15114.0i	−0.772555	+	0.909931i
$652$	9337.62	+	18923.4i	0.560873	+	1.13665i
$653$	8014.73			0.480307			0.240154	−	0.970735i	$-0.422802\pi$
$653$	8014.73			0.480307			0.240154	+	0.970735i	$0.422802\pi$
$654$	−2433.24	−	7578.79i	−0.145485	−	0.453141i
$655$	−17343.9	+	12343.8i	−1.03463	+	0.736352i
$656$	−2937.22	−	2251.58i	−0.174816	−	0.134008i
$657$	6765.80	−	1112.28i	0.401764	−	0.0660489i
$658$	4405.56	−	7086.60i	0.261013	−	0.419855i
$659$	15718.9			0.929166			0.464583	−	0.885530i	$-0.346204\pi$
$659$	15718.9			0.929166			0.464583	+	0.885530i	$0.346204\pi$
$660$	2913.54	+	7445.47i	0.171832	+	0.439113i
$661$	5688.74			0.334745			0.167372	−	0.985894i	$-0.446472\pi$
$661$	5688.74			0.334745			0.167372	+	0.985894i	$0.446472\pi$
$662$	10841.8	−	17439.7i	0.636522	−	1.02388i
$663$	−19724.2	+	23231.6i	−1.15539	+	1.36084i
$664$	23187.3	+	2275.36i	1.35518	+	0.132983i
$665$	−3843.79	−	5400.81i	−0.224144	−	0.314939i
$666$	20116.8	+	8345.99i	1.17044	+	0.485586i
$667$	−1660.63			−0.0964017
$668$	28293.2	−	13961.0i	1.63876	−	0.808636i
$669$	−13415.2	−	11389.8i	−0.775276	−	0.658230i
$670$	2658.49	−	165.932i	0.153293	−	0.00956794i
$671$	−9623.77			−0.553684
$672$	−23492.0	−	8398.82i	−1.34855	−	0.482130i
$673$			11536.1i			0.660751i	0.943850	+	0.330376i	$0.107175\pi$
$673$			11536.1i			0.660751i	−0.943850	+	0.330376i	$0.892825\pi$
$674$	−3006.46	+	4836.07i	−0.171817	+	0.276377i
$675$	11245.1	+	13457.1i	0.641222	+	0.767355i
$676$	−7983.51	−	16179.2i	−0.454228	−	0.920529i
$677$	16537.0			0.938799			0.469399	−	0.882986i	$-0.344470\pi$
$677$	16537.0			0.938799			0.469399	+	0.882986i	$0.344470\pi$
$678$	−849.368	−	2645.52i	−0.0481118	−	0.149853i
$679$		−	2098.68i		−	0.118615i
$680$	11062.9	+	19289.4i	0.623887	+	1.08782i
$681$	−14541.7	+	17127.5i	−0.818268	+	0.963772i
$682$	3695.66	−	5944.68i	0.207499	−	0.333774i
$683$		−	22976.1i		−	1.28720i	−0.765363	−	0.643599i	$-0.777440\pi$
$683$		−	22976.1i		−	1.28720i	0.765363	−	0.643599i	$-0.222560\pi$
$684$	2810.75	+	3926.09i	0.157122	+	0.219471i
$685$	2739.01	−	1949.37i	0.152777	−	0.108732i
$686$	1115.15	+	693.261i	0.0620651	+	0.0385843i
$687$	−11838.8	−	10051.4i	−0.657463	−	0.558203i
$688$	−11087.4	+	14463.7i	−0.614394	+	0.801487i
$689$		−	10719.7i		−	0.592725i
$690$	−3006.21	+	4024.25i	−0.165861	+	0.222030i
$691$		−	28269.3i		−	1.55631i	−0.628070	−	0.778157i	$-0.716155\pi$
$691$		−	28269.3i		−	1.55631i	0.628070	−	0.778157i	$-0.283845\pi$
$692$	−2950.11	−	5978.63i	−0.162061	−	0.328430i
$693$	1998.50	+	12156.5i	0.109548	+	0.666362i
$694$	−17814.0	+	28654.9i	−0.974366	+	1.56733i
$695$	−9229.27	−	12967.8i	−0.503721	−	0.707766i
$696$	4441.87	+	4589.52i	0.241909	+	0.249950i
$697$			5082.88i			0.276223i
$698$	−21589.1	−	13421.4i	−1.17072	−	0.727804i
$699$	−15054.4	−	12781.6i	−0.814606	−	0.691622i
$700$	−26317.8	+	3298.15i	−1.42103	+	0.178083i
$701$			12562.3i			0.676850i	0.940993	+	0.338425i	$0.109894\pi$
$701$			12562.3i			0.676850i	−0.940993	+	0.338425i	$0.890106\pi$
$702$	12076.3	+	23563.2i	0.649276	+	1.26686i
$703$	6375.23			0.342029
$704$	8639.92	+	1712.15i	0.462542	+	0.0916607i
$705$	−551.097	+	6438.26i	−0.0294404	+	0.343942i
$706$	19522.0	+	12136.3i	1.04068	+	0.646965i
$707$			18555.7i			0.987069i
$708$	4521.03	−	18041.0i	0.239987	−	0.957661i
$709$	2330.28			0.123435			0.0617177	−	0.998094i	$-0.480342\pi$
$709$	2330.28			0.123435			0.0617177	+	0.998094i	$0.480342\pi$
$710$	3757.19	−	234.509i	0.198598	−	0.0123957i
$711$	−31547.9	+	5186.39i	−1.66405	+	0.273565i
$712$	19364.9	+	1900.27i	1.01929	+	0.100022i
$713$	4397.73			0.230991
$714$	10474.2	+	32623.9i	0.549003	+	1.70997i
$715$	7441.49	+	10455.8i	0.389225	+	0.546890i
$716$	14988.2	+	30374.7i	0.782310	+	1.58541i
$717$	7555.67	+	6414.96i	0.393545	+	0.334130i
$718$	−28326.5	−	17609.8i	−1.47233	−	0.915311i
$719$	−16633.3			−0.862748			−0.431374	−	0.902173i	$-0.641971\pi$
$719$	−16633.3			−0.862748			−0.431374	+	0.902173i	$0.641971\pi$
$720$	19162.9	−	2455.79i	0.991888	−	0.127114i
$721$	35118.8			1.81400
$722$	−15275.6	−	9496.42i	−0.787392	−	0.489502i
$723$	18322.6	+	15556.4i	0.942495	+	0.800203i
$724$	2449.96	+	4965.03i	0.125762	+	0.254867i
$725$	6415.71	+	2224.22i	0.328653	+	0.113939i
$726$	4650.22	+	14484.0i	0.237721	+	0.740428i
$727$	−3154.28			−0.160916			−0.0804578	−	0.996758i	$-0.525638\pi$
$727$	−3154.28			−0.160916			−0.0804578	+	0.996758i	$0.525638\pi$
$728$	−39854.3	−	3910.88i	−2.02898	−	0.199103i
$729$	−9242.81	−	17377.9i	−0.469583	−	0.882888i
$730$	−500.263	−	8014.97i	−0.0253638	−	0.406366i
$731$	25029.5			1.26642
$732$	−5652.80	+	22557.3i	−0.285428	+	1.13899i
$733$			27541.6i			1.38782i	0.720061	+	0.693911i	$0.244114\pi$
$733$			27541.6i			1.38782i	−0.720061	+	0.693911i	$0.755886\pi$
$734$	−28312.6	−	17601.2i	−1.42376	−	0.885114i
$735$	−20867.0	−	1786.16i	−1.04720	−	0.0896373i
$736$	1952.35	+	5177.88i	0.0977779	+	0.259320i
$737$	−1449.05			−0.0724239
$738$	4078.99	+	1692.28i	0.203455	+	0.0844085i
$739$		−	16151.0i		−	0.803956i	−0.915649	−	0.401978i	$-0.868323\pi$
$739$		−	16151.0i		−	0.803956i	0.915649	−	0.401978i	$-0.131677\pi$
$740$	12091.9	−	22460.2i	0.600683	−	1.11575i
$741$	5908.24	+	5016.25i	0.292908	+	0.248686i
$742$	−10235.6	−	6363.24i	−0.506418	−	0.314827i
$743$			24987.9i			1.23380i	0.787040	+	0.616901i	$0.211612\pi$
$743$			24987.9i			1.23380i	−0.787040	+	0.616901i	$0.788388\pi$
$744$	−11763.1	−	12154.1i	−0.579645	−	0.598912i
$745$	1861.25	+	2615.20i	0.0915316	+	0.128609i
$746$	−3594.21	+	5781.50i	−0.176399	+	0.283748i
$747$	−27432.7	+	4509.86i	−1.34366	+	0.220893i
$748$	−5352.91	−	10848.1i	−0.261660	−	0.530275i
$749$			5958.29i			0.290669i
$750$	17004.2	−	11520.9i	0.827876	−	0.560911i
$751$			15497.5i			0.753012i	0.926414	+	0.376506i	$0.122875\pi$
$751$			15497.5i			0.753012i	−0.926414	+	0.376506i	$0.877125\pi$
$752$	5649.66	+	4330.85i	0.273966	+	0.210013i
$753$	−21535.8	−	18284.5i	−1.04224	−	0.884892i
$754$	8706.77	+	5412.78i	0.420533	+	0.261435i
$755$	−1645.20	−	2311.63i	−0.0793046	−	0.111429i
$756$	29667.8	+	2456.18i	1.42726	+	0.118162i
$757$		−	18262.8i		−	0.876846i	−0.898769	−	0.438423i	$-0.855537\pi$
$757$		−	18262.8i		−	0.876846i	0.898769	−	0.438423i	$-0.144463\pi$
$758$	7501.36	−	12066.4i	0.359448	−	0.578194i
$759$	1768.60	−	2083.09i	0.0845797	−	0.0996197i
$760$	4905.67	−	2813.51i	0.234141	−	0.134285i
$761$			19670.9i			0.937015i	0.883459	+	0.468508i	$0.155208\pi$
$761$			19670.9i			0.937015i	−0.883459	+	0.468508i	$0.844792\pi$
$762$	−1829.52	−	5698.39i	−0.0869771	−	0.270907i
$763$	−14365.1			−0.681589
$764$	−8583.01	−	17394.1i	−0.406443	−	0.823688i
$765$	−18688.5	−	18835.6i	−0.883248	−	0.890198i
$766$	10940.7	−	17598.8i	0.516062	−	0.830116i
$767$		−	29854.1i		−	1.40543i
$768$	9088.04	−	19245.6i	0.427001	−	0.904251i
$769$	−9763.72			−0.457853			−0.228926	−	0.973444i	$-0.573522\pi$
$769$	−9763.72			−0.457853			−0.228926	+	0.973444i	$0.573522\pi$
$770$	14401.0	−	898.853i	0.673995	−	0.0420681i
$771$	16876.8	+	14328.9i	0.788333	+	0.669315i
$772$	4556.56	−	2248.40i	0.212428	−	0.104821i
$773$	−10092.1			−0.469584			−0.234792	−	0.972046i	$-0.575441\pi$
$773$	−10092.1			−0.469584			−0.234792	+	0.972046i	$0.575441\pi$
$774$	8333.25	−	20086.1i	0.386993	−	0.932791i
$775$	−16990.3	−	5890.25i	−0.787495	−	0.273012i
$776$	1781.83	+	174.850i	0.0824279	+	0.00808861i
$777$	25439.1	−	29962.7i	1.17455	−	1.38340i
$778$	11366.2	−	18283.2i	0.523776	−	0.842524i
$779$	1292.67			0.0594543
$780$	28878.6	−	11300.7i	1.32567	−	0.518756i
$781$	−2047.91			−0.0938285
$782$	4012.58	−	6454.47i	0.183490	−	0.295155i
$783$	−6532.94	−	3924.82i	−0.298171	−	0.179134i
$784$	−14036.7	+	18311.1i	−0.639427	+	0.834143i
$785$	24586.8	+	34546.2i	1.11788	+	1.57071i
$786$	−8554.39	−	26644.2i	−0.388200	−	1.20912i
$787$	−8470.33			−0.383653			−0.191826	−	0.981429i	$-0.561441\pi$
$787$	−8470.33			−0.383653			−0.191826	+	0.981429i	$0.561441\pi$
$788$	17280.4	+	35020.2i	0.781206	+	1.58318i
$789$	−11825.4	+	13928.2i	−0.533582	+	0.628464i
$790$	2332.65	+	37372.6i	0.105053	+	1.68311i
$791$	−5014.41			−0.225401
$792$	−10487.7	+	683.962i	−0.470537	+	0.0306863i
$793$			37327.5i			1.67155i
$794$	−3452.81	+	5554.05i	−0.154327	+	0.248244i
$795$	9299.20	+	795.985i	0.414854	+	0.0355103i
$796$	5303.85	−	2617.15i	0.236168	−	0.116536i
$797$	−37293.4			−1.65747			−0.828734	−	0.559643i	$-0.810938\pi$
$797$	−37293.4			−1.65747			−0.828734	+	0.559643i	$0.810938\pi$
$798$	8296.90	−	2663.80i	0.368054	−	0.118167i
$799$		−	9776.79i		−	0.432889i
$800$	−607.562	−	22619.3i	−0.0268507	−	0.999639i
$801$	−22910.5	+	3766.42i	−1.01062	+	0.166142i
$802$	−10868.2	+	17482.1i	−0.478515	+	0.769719i
$803$			4368.68i			0.191989i
$804$	−851.141	+	3396.45i	−0.0373351	+	0.148985i
$805$	5256.46	+	7385.71i	0.230144	+	0.323369i
$806$	−23057.5	−	14334.3i	−1.00765	−	0.626430i
$807$	27226.2	−	32067.6i	1.18762	−	1.39880i
$808$	−15754.2	−	1545.96i	−0.685931	−	0.0673101i
$809$		−	35890.7i		−	1.55977i	−0.625925	−	0.779883i	$-0.715278\pi$
$809$		−	35890.7i		−	1.55977i	0.625925	−	0.779883i	$-0.284722\pi$
$810$	−21337.5	+	8726.40i	−0.925586	+	0.378536i
$811$		−	12888.9i		−	0.558064i	−0.960282	−	0.279032i	$-0.909986\pi$
$811$		−	12888.9i		−	0.558064i	0.960282	−	0.279032i	$-0.0900136\pi$
$812$	10336.7	−	5100.58i	0.446734	−	0.220438i
$813$	2223.71	−	2619.13i	0.0959273	−	0.112985i
$814$	−7326.43	+	11785.0i	−0.315468	+	0.507449i
$815$	−24026.9	+	17100.1i	−1.03267	+	0.734956i
$816$	−28571.2	+	6174.84i	−1.22573	+	0.264905i
$817$		−	6365.50i		−	0.272583i
$818$	22673.8	+	14095.7i	0.969157	+	0.602500i
$819$	47151.3	−	7751.54i	2.01172	−	0.330721i
$820$	2451.81	−	4554.15i	0.104416	−	0.193948i
$821$		−	17206.2i		−	0.731428i	−0.930727	−	0.365714i	$-0.880825\pi$
$821$		−	17206.2i		−	0.731428i	0.930727	−	0.365714i	$-0.119175\pi$
$822$	1350.94	+	4207.75i	0.0573229	+	0.178543i
$823$	6503.39			0.275448			0.137724	−	0.990471i	$-0.456021\pi$
$823$	6503.39			0.275448			0.137724	+	0.990471i	$0.456021\pi$
$824$	−2925.91	+	29816.8i	−0.123700	+	1.26058i
$825$	−9622.88	+	5679.01i	−0.406092	+	0.239658i
$826$	−28506.0	−	17721.5i	−1.20079	−	0.746500i
$827$			39962.5i			1.68033i	0.542332	+	0.840164i	$0.317541\pi$
$827$			39962.5i			1.68033i	−0.542332	+	0.840164i	$0.682459\pi$
$828$	−3843.75	−	5369.00i	−0.161328	−	0.225345i
$829$	−13893.1			−0.582060			−0.291030	−	0.956714i	$-0.593998\pi$
$829$	−13893.1			−0.582060			−0.291030	+	0.956714i	$0.593998\pi$
$830$	2028.37	+	32497.6i	0.0848263	+	1.35905i
$831$	−17734.7	+	20888.3i	−0.740324	+	0.871968i
$832$	6640.88	−	33511.5i	0.276720	−	1.39640i
$833$	31687.5			1.31802
$834$	19921.6	−	6396.01i	0.827131	−	0.265558i
$835$	25567.0	+	35923.5i	1.05962	+	1.48884i
$836$	−2758.88	+	1361.35i	−0.114136	+	0.0563197i
$837$	17300.7	+	10393.8i	0.714456	+	0.429227i
$838$	22738.1	+	14135.7i	0.937322	+	0.582709i
$839$	40559.7			1.66898			0.834490	−	0.551023i	$-0.185762\pi$
$839$	40559.7			1.66898			0.834490	+	0.551023i	$0.185762\pi$
$840$	6352.00	−	34282.7i	0.260911	−	1.40817i
$841$	21438.1			0.879005
$842$	−708.857	−	440.678i	−0.0290128	−	0.0180365i
$843$	17709.5	−	20858.6i	0.723545	−	0.852206i
$844$	354.348	−	174.850i	0.0144516	−	0.00713103i
$845$	20542.6	−	14620.3i	0.836314	−	0.595210i
$846$	−7845.83	−	3255.05i	−0.318848	−	0.132282i
$847$	27453.5			1.11371
$848$	6255.33	−	8160.18i	0.253313	−	0.330450i
$849$	7489.03	+	6358.38i	0.302736	+	0.257031i
$850$	−24147.3	+	19561.9i	−0.974406	+	0.789375i
$851$	−8718.25			−0.351184
$852$	−1202.90	+	4800.14i	−0.0483693	+	0.193016i
$853$		−	22168.0i		−	0.889820i	−0.895575	−	0.444910i	$-0.853236\pi$
$853$		−	22168.0i		−	0.889820i	0.895575	−	0.444910i	$-0.146764\pi$
$854$	35642.0	+	22157.7i	1.42816	+	0.887848i
$855$	−4790.25	+	4752.85i	−0.191606	+	0.190110i
$856$	−5058.75	−	496.412i	−0.201991	−	0.0198213i
$857$	−43491.5			−1.73354			−0.866769	−	0.498710i	$-0.833807\pi$
$857$	−43491.5			−1.73354			−0.866769	+	0.498710i	$0.833807\pi$
$858$	−16062.6	+	5157.05i	−0.639124	+	0.205197i
$859$		−	35008.5i		−	1.39054i	−0.718748	−	0.695270i	$-0.755285\pi$
$859$		−	35008.5i		−	1.39054i	0.718748	−	0.695270i	$-0.244715\pi$
$860$	−22425.9	−	12073.4i	−0.889207	−	0.478721i
$861$	5158.16	−	6075.39i	0.204169	−	0.240475i
$862$	−7746.68	−	4815.91i	−0.306094	−	0.190291i
$863$		−	1389.28i		−	0.0547993i	−0.999625	−	0.0273996i	$-0.991277\pi$
$863$		−	1389.28i		−	0.0547993i	0.999625	−	0.0273996i	$-0.00872266\pi$
$864$	−4557.12	+	24984.1i	−0.179440	+	0.983769i
$865$	7591.00	−	5402.56i	0.298384	−	0.212361i
$866$	21217.5	−	34129.7i	0.832565	−	1.33923i
$867$	11142.8	+	9460.50i	0.436480	+	0.370583i
$868$	−27374.0	+	13507.5i	−1.07043	+	0.528197i
$869$		−	20370.5i		−	0.795193i
$870$	−5342.04	+	7151.10i	−0.208175	+	0.278672i
$871$			5620.40i			0.218645i
$872$	1196.82	−	12196.4i	0.0464789	−	0.473648i
$873$	−2108.07	+	346.561i	−0.0817268	+	0.0134356i
$874$	−1641.50	−	1020.48i	−0.0635291	−	0.0394944i
$875$	−10415.6	−	35574.5i	−0.402412	−	1.37444i
$876$	10239.8	+	2566.07i	0.394945	+	0.0989720i
$877$		−	36841.2i		−	1.41852i	−0.704948	−	0.709259i	$-0.749030\pi$
$877$		−	36841.2i		−	1.41852i	0.704948	−	0.709259i	$-0.250970\pi$
$878$	−17908.0	+	28806.1i	−0.688344	+	1.10724i
$879$	9316.42	+	7909.89i	0.357492	+	0.303520i
$880$	−436.663	+	12301.7i	−0.0167272	+	0.471240i
$881$		−	40136.7i		−	1.53489i	−0.641115	−	0.767445i	$-0.721528\pi$
$881$		−	40136.7i		−	1.53489i	0.641115	−	0.767445i	$-0.278472\pi$
$882$	10549.9	−	25429.1i	0.402761	−	0.970797i
$883$	18116.6			0.690457			0.345228	−	0.938519i	$-0.387801\pi$
$883$	18116.6			0.690457			0.345228	+	0.938519i	$0.387801\pi$
$884$	−42076.3	+	20762.2i	−1.60088	+	0.789942i
$885$	25898.1	+	2216.80i	0.983676	+	0.0841998i
$886$	5151.87	−	8287.09i	0.195350	−	0.314233i
$887$		−	16554.1i		−	0.626642i	−0.949647	−	0.313321i	$-0.898559\pi$
$887$		−	16554.1i		−	0.626642i	0.949647	−	0.313321i	$-0.101441\pi$
$888$	23319.7	+	24094.8i	0.881257	+	0.910550i
$889$	−10800.9			−0.407482
$890$	1694.00	+	27140.5i	0.0638012	+	1.02219i
$891$	11881.0	−	4014.90i	0.446719	−	0.150959i
$892$	−11989.2	−	24297.1i	−0.450032	−	0.912025i
$893$	−2486.43			−0.0931749
$894$	−4017.55	+	1289.87i	−0.150299	+	0.0482548i
$895$	−38566.4	+	27447.9i	−1.44037	+	1.02512i
$896$	−28056.3	−	26233.5i	−1.04609	−	0.978126i
$897$	−8079.63	−	6859.82i	−0.300748	−	0.255343i
$898$	−7372.54	+	11859.2i	−0.273970	+	0.440697i
$899$	7814.78			0.289919
$900$	7658.85	+	25891.0i	0.283661	+	0.958925i
$901$	−14121.3			−0.522139
$902$	−1485.54	+	2389.59i	−0.0548373	+	0.0882090i
$903$	−29917.0	−	25400.3i	−1.10252	−	0.936067i
$904$	417.773	−	4257.36i	0.0153705	−	0.156635i
$905$	−6304.04	+	4486.62i	−0.231551	+	0.164796i
$906$	3551.20	−	1140.15i	0.130221	−	0.0418088i
$907$	27715.4			1.01464			0.507319	−	0.861759i	$-0.330637\pi$
$907$	27715.4			1.01464			0.507319	+	0.861759i	$0.330637\pi$
$908$	−31020.8	+	15307.0i	−1.13377	+	0.559450i
$909$	18638.7	−	3064.15i	0.680097	−	0.111806i
$910$	−3486.36	−	55856.9i	−0.127002	−	2.03477i
$911$	−33328.7			−1.21211			−0.606053	−	0.795424i	$-0.707248\pi$
$911$	−33328.7			−1.21211			−0.606053	+	0.795424i	$0.707248\pi$
$912$	1570.38	+	7266.21i	0.0570181	+	0.263825i
$913$		−	17713.3i		−	0.642087i
$914$	−21979.6	+	35355.4i	−0.795426	+	1.27949i
$915$	−32381.2	−	2771.74i	−1.16993	−	0.100143i
$916$	−10580.4	−	21442.0i	−0.381644	−	0.773431i
$917$	−50502.5			−1.81869
$918$	31040.3	−	15908.4i	1.11600	−	0.571956i
$919$			33640.2i			1.20750i	0.797175	+	0.603748i	$0.206327\pi$
$919$			33640.2i			1.20750i	−0.797175	+	0.603748i	$0.793673\pi$
$920$	−6708.60	+	3847.53i	−0.240409	+	0.137880i
$921$	−15537.4	−	13191.6i	−0.555889	−	0.471964i
$922$	13439.2	−	21617.7i	0.480039	−	0.772171i
$923$			7943.20i			0.283265i
$924$	−4610.62	+	18398.5i	−0.164154	+	0.655052i
$925$	33682.2	+	11677.1i	1.19726	+	0.415071i
$926$	33119.1	+	20589.3i	1.17534	+	0.730676i
$927$	−5799.28	−	35276.1i	−0.205473	−	1.24986i
$928$	3469.33	+	9201.11i	0.122722	+	0.325475i
$929$			18425.5i			0.650722i	0.945590	+	0.325361i	$0.105486\pi$
$929$			18425.5i			0.650722i	−0.945590	+	0.325361i	$0.894514\pi$
$930$	14146.9	−	18937.7i	0.498813	−	0.667734i
$931$		−	8058.76i		−	0.283690i
$932$	−13454.2	−	27266.0i	−0.472862	−	0.958293i
$933$	17706.3	+	15033.1i	0.621305	+	0.527504i
$934$	20167.7	−	32440.9i	0.706539	−	1.13651i
$935$	13773.7	−	9802.83i	0.481763	−	0.342873i
$936$	2652.87	+	40678.5i	0.0926407	+	1.42053i
$937$			36640.8i			1.27748i	0.769421	+	0.638742i	$0.220545\pi$
$937$			36640.8i			1.27748i	−0.769421	+	0.638742i	$0.779455\pi$
$938$	5366.61	+	3336.29i	0.186808	+	0.116134i
$939$	525.642	−	619.112i	0.0182680	−	0.0215164i
$940$	−4716.00	+	8759.79i	−0.163637	+	0.303950i
$941$			39477.2i			1.36761i	0.729666	+	0.683804i	$0.239676\pi$
$941$			39477.2i			1.36761i	−0.729666	+	0.683804i	$0.760324\pi$
$942$	−53071.0	+	17039.0i	−1.83561	+	0.589341i
$943$	−1767.76			−0.0610457
$944$	17421.0	−	22725.9i	0.600640	−	0.783544i
$945$	3223.17	+	41478.8i	0.110952	+	1.42784i
$946$	11767.0	+	7315.25i	0.404417	+	0.251416i
$947$			4299.16i			0.147522i	0.997276	+	0.0737612i	$0.0235003\pi$
$947$			4299.16i			0.147522i	−0.997276	+	0.0737612i	$0.976500\pi$
$948$	−47746.8	−	11965.2i	−1.63581	−	0.409928i
$949$	16944.7			0.579609
$950$	4974.98	+	6141.12i	0.169905	+	0.209731i
$951$	25087.4	+	21299.8i	0.855430	+	0.726282i
$952$	−5151.89	+	52500.9i	−0.175392	+	1.78736i
$953$	−356.972			−0.0121337			−0.00606687	−	0.999982i	$-0.501931\pi$
$953$	−356.972			−0.0121337			−0.00606687	+	0.999982i	$0.501931\pi$
$954$	−4701.48	+	11332.3i	−0.159556	+	0.384586i
$955$	22085.1	−	15718.1i	0.748333	−	0.532593i
$956$	6752.56	+	13684.6i	0.228445	+	0.462961i
$957$	3142.80	−	3701.66i	0.106157	−	0.125034i
$958$	40280.5	+	25041.4i	1.35846	+	0.844519i
$959$	7975.54			0.268554
$960$	28577.7	+	8249.27i	0.960773	+	0.277337i
$961$	9095.67			0.305316
$962$	45710.2	+	28416.9i	1.53197	+	0.952387i
$963$	5984.97	−	983.911i	0.200273	−	0.0329243i
$964$	16375.0	+	33185.3i	0.547100	+	1.10874i
$965$	4117.51	+	5785.41i	0.137355	+	0.192994i
$966$	−11346.2	+	3642.79i	−0.377906	+	0.121330i
$967$	3244.13			0.107884			0.0539422	−	0.998544i	$-0.482821\pi$
$967$	3244.13			0.107884			0.0539422	+	0.998544i	$0.482821\pi$
$968$	−2287.27	+	23308.7i	−0.0759460	+	0.773936i
$969$	6608.01	−	7783.05i	0.219071	−	0.258026i
$970$	155.871	+	2497.29i	0.00515949	+	0.0826630i
$971$	−22274.6			−0.736176			−0.368088	−	0.929791i	$-0.619987\pi$
$971$	−22274.6			−0.736176			−0.368088	+	0.929791i	$0.619987\pi$
$972$	−2431.96	−	30206.2i	−0.0802523	−	0.996775i
$973$		−	37760.1i		−	1.24412i
$974$	−36777.1	−	22863.4i	−1.20987	−	0.752146i
$975$	22027.1	+	37324.1i	0.723518	+	1.22598i
$976$	−21782.0	+	28415.0i	−0.714370	+	0.931906i
$977$	29367.3			0.961662			0.480831	−	0.876813i	$-0.340335\pi$
$977$	29367.3			0.961662			0.480831	+	0.876813i	$0.340335\pi$
$978$	−11850.6	−	36910.8i	−0.387464	−	1.20683i
$979$		−	14793.3i		−	0.482939i
$980$	−28391.3	−	15285.0i	−0.925437	−	0.498226i
$981$	2372.16	+	14429.4i	0.0772040	+	0.469619i
$982$	23252.0	+	14455.2i	0.755603	+	0.469739i
$983$			22189.8i			0.719986i	0.932955	+	0.359993i	$0.117221\pi$
$983$			22189.8i			0.719986i	−0.932955	+	0.359993i	$0.882779\pi$
$984$	4728.41	+	4885.58i	0.153187	+	0.158279i
$985$	−44464.7	+	31645.8i	−1.43834	+	1.02367i
$986$	7130.36	−	11469.6i	0.230301	−	0.370453i
$987$	−9921.60	+	11685.9i	−0.319968	+	0.376864i
$988$	5280.24	+	10700.8i	0.170027	+	0.344573i
$989$			8704.94i			0.279880i
$990$	−3280.96	−	14317.0i	−0.105329	−	0.459622i
$991$			10454.0i			0.335097i	0.985864	+	0.167548i	$0.0535851\pi$
$991$			10454.0i			0.335097i	−0.985864	+	0.167548i	$0.946415\pi$
$992$	−9187.57	−	24366.6i	−0.294058	−	0.779881i
$993$	−24416.4	+	28758.1i	−0.780293	+	0.919045i
$994$	7584.53	+	4715.11i	0.242019	+	0.150457i
$995$	4792.80	+	6734.24i	0.152706	+	0.214563i
$996$	−41518.6	−	10404.4i	−1.32085	−	0.331001i
$997$		−	5030.23i		−	0.159788i	−0.996803	−	0.0798941i	$-0.974542\pi$
$997$		−	5030.23i		−	0.159788i	0.996803	−	0.0798941i	$-0.0254582\pi$
$998$	20721.5	−	33331.8i	0.657243	−	1.05721i
$999$	−34297.7	−	20605.2i	−1.08622	−	0.652571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.h.c.59.6	yes	24
3.2	odd	2	inner	60.4.h.c.59.20	yes	24
4.3	odd	2	inner	60.4.h.c.59.7	yes	24
5.4	even	2	inner	60.4.h.c.59.19	yes	24
12.11	even	2	inner	60.4.h.c.59.17	yes	24
15.14	odd	2	inner	60.4.h.c.59.5	✓	24
20.19	odd	2	inner	60.4.h.c.59.18	yes	24
60.59	even	2	inner	60.4.h.c.59.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.h.c.59.5	✓	24	15.14	odd	2	inner
60.4.h.c.59.6	yes	24	1.1	even	1	trivial
60.4.h.c.59.7	yes	24	4.3	odd	2	inner
60.4.h.c.59.8	yes	24	60.59	even	2	inner
60.4.h.c.59.17	yes	24	12.11	even	2	inner
60.4.h.c.59.18	yes	24	20.19	odd	2	inner
60.4.h.c.59.19	yes	24	5.4	even	2	inner
60.4.h.c.59.20	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.40208 - 1.49331i) q^{2} +(3.96106 + 3.36304i) q^{3} +(3.54002 + 7.17414i) q^{4} +(-9.10892 + 6.48287i) q^{5} +(-4.49272 - 13.9934i) q^{6} -26.5236 q^{7} +(2.20980 - 22.5193i) q^{8} +(4.37993 + 26.6424i) q^{9} +O(q^{10})\)	\(q+(-2.40208 - 1.49331i) q^{2} +(3.96106 + 3.36304i) q^{3} +(3.54002 + 7.17414i) q^{4} +(-9.10892 + 6.48287i) q^{5} +(-4.49272 - 13.9934i) q^{6} -26.5236 q^{7} +(2.20980 - 22.5193i) q^{8} +(4.37993 + 26.6424i) q^{9} +(31.5614 - 1.96993i) q^{10} -17.2030 q^{11} +(-10.1047 + 40.3224i) q^{12} +66.7249i q^{13} +(63.7120 + 39.6081i) q^{14} +(-57.8831 - 4.95463i) q^{15} +(-38.9365 + 50.7932i) q^{16} +87.8981 q^{17} +(29.2645 - 70.5379i) q^{18} -22.3542i q^{19} +(-78.7548 - 42.3991i) q^{20} +(-105.062 - 89.2000i) q^{21} +(41.3231 + 25.6895i) q^{22} +30.5698i q^{23} +(84.4863 - 81.7684i) q^{24} +(40.9447 - 118.104i) q^{25} +(99.6413 - 160.279i) q^{26} +(-72.2502 + 120.262i) q^{27} +(-93.8943 - 190.284i) q^{28} +54.3226i q^{29} +(131.641 + 98.3391i) q^{30} -143.859i q^{31} +(169.379 - 63.8653i) q^{32} +(-68.1420 - 57.8544i) q^{33} +(-211.139 - 131.260i) q^{34} +(241.602 - 171.949i) q^{35} +(-175.631 + 125.737i) q^{36} +285.192i q^{37} +(-33.3819 + 53.6967i) q^{38} +(-224.399 + 264.301i) q^{39} +(125.861 + 219.452i) q^{40} +57.8269i q^{41} +(119.163 + 371.156i) q^{42} +284.756 q^{43} +(-60.8990 - 123.417i) q^{44} +(-212.616 - 214.289i) q^{45} +(45.6503 - 73.4312i) q^{46} -111.229i q^{47} +(-325.049 + 70.2499i) q^{48} +360.503 q^{49} +(-274.719 + 222.552i) q^{50} +(348.169 + 295.605i) q^{51} +(-478.694 + 236.208i) q^{52} -160.655 q^{53} +(353.140 - 180.987i) q^{54} +(156.701 - 111.525i) q^{55} +(-58.6120 + 597.292i) q^{56} +(75.1781 - 88.5462i) q^{57} +(81.1208 - 130.488i) q^{58} -447.420 q^{59} +(-169.362 - 432.801i) q^{60} +559.424 q^{61} +(-214.826 + 345.561i) q^{62} +(-116.172 - 706.653i) q^{63} +(-502.234 - 99.5263i) q^{64} +(-432.569 - 607.792i) q^{65} +(77.2882 + 240.729i) q^{66} +84.2324 q^{67} +(311.161 + 630.593i) q^{68} +(-102.807 + 121.089i) q^{69} +(-837.122 + 52.2498i) q^{70} +119.044 q^{71} +(609.645 - 39.7583i) q^{72} -253.949i q^{73} +(425.881 - 685.054i) q^{74} +(559.372 - 330.117i) q^{75} +(160.372 - 79.1344i) q^{76} +456.286 q^{77} +(933.709 - 299.776i) q^{78} +1184.13i q^{79} +(25.3830 - 715.091i) q^{80} +(-690.632 + 233.383i) q^{81} +(86.3538 - 138.905i) q^{82} +1029.67i q^{83} +(268.013 - 1069.50i) q^{84} +(-800.657 + 569.832i) q^{85} +(-684.009 - 425.231i) q^{86} +(-182.689 + 215.175i) q^{87} +(-38.0153 + 387.399i) q^{88} +859.928i q^{89} +(190.720 + 832.241i) q^{90} -1769.79i q^{91} +(-219.312 + 108.218i) q^{92} +(483.803 - 569.832i) q^{93} +(-166.099 + 267.181i) q^{94} +(144.919 + 203.623i) q^{95} +(885.701 + 316.654i) q^{96} +79.1248i q^{97} +(-865.959 - 538.344i) q^{98} +(-75.3479 - 458.329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9}+O(q^{10}) \) 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9	\( 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9} - 32 q^{10} - 240 q^{16} - 264 q^{21} + 168 q^{24} - 88 q^{25} - 252 q^{30} - 1088 q^{34} - 1104 q^{36} + 704 q^{40} + 456 q^{45} + 3368 q^{46} - 1304 q^{49} + 468 q^{54} + 2496 q^{60} + 2080 q^{61} + 1376 q^{64} - 672 q^{66} + 2568 q^{69} - 2632 q^{70} - 1536 q^{76} - 5112 q^{81} - 2328 q^{84} - 6944 q^{85} - 1152 q^{90} - 4840 q^{94} - 2832 q^{96}+O(q^{100}) \) 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9 - 32 * q^10 - 240 * q^16 - 264 * q^21 + 168 * q^24 - 88 * q^25 - 252 * q^30 - 1088 * q^34 - 1104 * q^36 + 704 * q^40 + 456 * q^45 + 3368 * q^46 - 1304 * q^49 + 468 * q^54 + 2496 * q^60 + 2080 * q^61 + 1376 * q^64 - 672 * q^66 + 2568 * q^69 - 2632 * q^70 - 1536 * q^76 - 5112 * q^81 - 2328 * q^84 - 6944 * q^85 - 1152 * q^90 - 4840 * q^94 - 2832 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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