LMFDB - Embedded newform 930.4.d.c.559.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(559,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.d (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:	$54.8717763053$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 $ x^20 + 2763x^18 + 2652899x^16 + 1161420105x^14 + 247831438280x^12 + 26461073949176x^10 + 1433368340491408x^8 + 37536884921183444x^6 + 414170668954972900x^4 + 1987578737873500000*x^2 + 3460065015625000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.16
Root			$7.05659i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.4.d.c.559.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(2.19955 + 10.9618i) q^{5} +6.00000 q^{6} +7.05659i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(2.19955 + 10.9618i) q^{5} +6.00000 q^{6} +7.05659i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-21.9237 + 4.39910i) q^{10} -11.6698 q^{11} +12.0000i q^{12} +71.0038i q^{13} -14.1132 q^{14} +(32.8855 - 6.59865i) q^{15} +16.0000 q^{16} -133.370i q^{17} -18.0000i q^{18} -101.278 q^{19} +(-8.79821 - 43.8474i) q^{20} +21.1698 q^{21} -23.3396i q^{22} -38.2373i q^{23} -24.0000 q^{24} +(-115.324 + 48.2223i) q^{25} -142.008 q^{26} +27.0000i q^{27} -28.2264i q^{28} -24.1642 q^{29} +(13.1973 + 65.7711i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +35.0094i q^{33} +266.740 q^{34} +(-77.3532 + 15.5213i) q^{35} +36.0000 q^{36} +270.467i q^{37} -202.555i q^{38} +213.011 q^{39} +(87.6947 - 17.5964i) q^{40} +64.4183 q^{41} +42.3395i q^{42} -298.699i q^{43} +46.6792 q^{44} +(-19.7960 - 98.6566i) q^{45} +76.4747 q^{46} +166.313i q^{47} -48.0000i q^{48} +293.205 q^{49} +(-96.4445 - 230.648i) q^{50} -400.110 q^{51} -284.015i q^{52} -386.427i q^{53} -54.0000 q^{54} +(-25.6683 - 127.922i) q^{55} +56.4527 q^{56} +303.833i q^{57} -48.3284i q^{58} +796.895 q^{59} +(-131.542 + 26.3946i) q^{60} -671.455 q^{61} -62.0000i q^{62} -63.5093i q^{63} -64.0000 q^{64} +(-778.332 + 156.177i) q^{65} -70.0188 q^{66} -525.664i q^{67} +533.480i q^{68} -114.712 q^{69} +(-31.0427 - 154.706i) q^{70} +19.0477 q^{71} +72.0000i q^{72} -723.007i q^{73} -540.934 q^{74} +(144.667 + 345.972i) q^{75} +405.110 q^{76} -82.3490i q^{77} +426.023i q^{78} -800.140 q^{79} +(35.1928 + 175.389i) q^{80} +81.0000 q^{81} +128.837i q^{82} +826.960i q^{83} -84.6791 q^{84} +(1461.98 - 293.354i) q^{85} +597.399 q^{86} +72.4927i q^{87} +93.3584i q^{88} -166.350 q^{89} +(197.313 - 39.5919i) q^{90} -501.045 q^{91} +152.949i q^{92} +93.0000i q^{93} -332.626 q^{94} +(-222.765 - 1110.19i) q^{95} +96.0000 q^{96} -1590.14i q^{97} +586.409i q^{98} +105.028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.00000			−0.500000
$5$	2.19955	+	10.9618i	0.196734	+	0.980457i
$5$	2.19955	+	10.9618i	0.196734	+	0.980457i
$6$	6.00000			0.408248
$7$			7.05659i			0.381020i	0.981685	+	0.190510i	$0.0610141\pi$
$7$			7.05659i			0.381020i	−0.981685	+	0.190510i	$0.938986\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−9.00000			−0.333333
$10$	−21.9237	+	4.39910i	−0.693288	+	0.139112i
$11$	−11.6698			−0.319871			−0.159935	−	0.987127i	$-0.551129\pi$
$11$	−11.6698			−0.319871			−0.159935	+	0.987127i	$0.551129\pi$
$12$			12.0000i			0.288675i
$13$			71.0038i			1.51484i	0.652928	+	0.757420i	$0.273540\pi$
$13$			71.0038i			1.51484i	−0.652928	+	0.757420i	$0.726460\pi$
$14$	−14.1132			−0.269422
$15$	32.8855	−	6.59865i	0.566067	−	0.113584i
$16$	16.0000			0.250000
$17$		−	133.370i		−	1.90276i	−0.308013	−	0.951382i	$-0.599664\pi$
$17$		−	133.370i		−	1.90276i	0.308013	−	0.951382i	$-0.400336\pi$
$18$		−	18.0000i		−	0.235702i
$19$	−101.278			−1.22288			−0.611439	−	0.791292i	$-0.709409\pi$
$19$	−101.278			−1.22288			−0.611439	+	0.791292i	$0.709409\pi$
$20$	−8.79821	−	43.8474i	−0.0983669	−	0.490228i
$21$	21.1698			0.219982
$22$		−	23.3396i		−	0.226183i
$23$		−	38.2373i		−	0.346654i	−0.984864	−	0.173327i	$-0.944548\pi$
$23$		−	38.2373i		−	0.346654i	0.984864	−	0.173327i	$-0.0554517\pi$
$24$	−24.0000			−0.204124
$25$	−115.324	+	48.2223i	−0.922592	+	0.385778i
$26$	−142.008			−1.07115
$27$			27.0000i			0.192450i
$28$		−	28.2264i		−	0.190510i
$29$	−24.1642			−0.154730			−0.0773652	−	0.997003i	$-0.524651\pi$
$29$	−24.1642			−0.154730			−0.0773652	+	0.997003i	$0.524651\pi$
$30$	13.1973	+	65.7711i	0.0803163	+	0.400270i
$31$	−31.0000			−0.179605
$31$	−31.0000			−0.179605
$32$			32.0000i			0.176777i
$33$			35.0094i			0.184677i
$34$	266.740			1.34546
$35$	−77.3532	+	15.5213i	−0.373574	+	0.0749595i
$36$	36.0000			0.166667
$37$			270.467i			1.20174i	0.799346	+	0.600871i	$0.205180\pi$
$37$			270.467i			1.20174i	−0.799346	+	0.600871i	$0.794820\pi$
$38$		−	202.555i		−	0.864705i
$39$	213.011			0.874593
$40$	87.6947	−	17.5964i	0.346644	−	0.0695559i
$41$	64.4183			0.245377			0.122688	−	0.992445i	$-0.460848\pi$
$41$	64.4183			0.245377			0.122688	+	0.992445i	$0.460848\pi$
$42$			42.3395i			0.155551i
$43$		−	298.699i		−	1.05933i	−0.848207	−	0.529665i	$-0.822317\pi$
$43$		−	298.699i		−	1.05933i	0.848207	−	0.529665i	$-0.177683\pi$
$44$	46.6792			0.159935
$45$	−19.7960	−	98.6566i	−0.0655779	−	0.326819i
$46$	76.4747			0.245121
$47$			166.313i			0.516155i	0.966124	+	0.258077i	$0.0830890\pi$
$47$			166.313i			0.516155i	−0.966124	+	0.258077i	$0.916911\pi$
$48$		−	48.0000i		−	0.144338i
$49$	293.205			0.854824
$50$	−96.4445	−	230.648i	−0.272786	−	0.652371i
$51$	−400.110			−1.09856
$52$		−	284.015i		−	0.757420i
$53$		−	386.427i		−	1.00151i	−0.865590	−	0.500753i	$-0.833056\pi$
$53$		−	386.427i		−	1.00151i	0.865590	−	0.500753i	$-0.166944\pi$
$54$	−54.0000			−0.136083
$55$	−25.6683	−	127.922i	−0.0629294	−	0.313619i
$56$	56.4527			0.134711
$57$			303.833i			0.706029i
$58$		−	48.3284i		−	0.109411i
$59$	796.895			1.75842			0.879211	−	0.476433i	$-0.158070\pi$
$59$	796.895			1.75842			0.879211	+	0.476433i	$0.158070\pi$
$60$	−131.542	+	26.3946i	−0.283034	+	0.0567922i
$61$	−671.455			−1.40936			−0.704681	−	0.709524i	$-0.748910\pi$
$61$	−671.455			−1.40936			−0.704681	+	0.709524i	$0.748910\pi$
$62$		−	62.0000i		−	0.127000i
$63$		−	63.5093i		−	0.127007i
$64$	−64.0000			−0.125000
$65$	−778.332	+	156.177i	−1.48523	+	0.298020i
$66$	−70.0188			−0.130587
$67$		−	525.664i		−	0.958509i	−0.877676	−	0.479255i	$-0.840907\pi$
$67$		−	525.664i		−	0.958509i	0.877676	−	0.479255i	$-0.159093\pi$
$68$			533.480i			0.951382i
$69$	−114.712			−0.200141
$70$	−31.0427	−	154.706i	−0.0530044	−	0.264156i
$71$	19.0477			0.0318387			0.0159193	−	0.999873i	$-0.494933\pi$
$71$	19.0477			0.0318387			0.0159193	+	0.999873i	$0.494933\pi$
$72$			72.0000i			0.117851i
$73$		−	723.007i		−	1.15920i	−0.814901	−	0.579600i	$-0.803209\pi$
$73$		−	723.007i		−	1.15920i	0.814901	−	0.579600i	$-0.196791\pi$
$74$	−540.934			−0.849761
$75$	144.667	+	345.972i	0.222729	+	0.532658i
$76$	405.110			0.611439
$77$		−	82.3490i		−	0.121877i
$78$			426.023i			0.618431i
$79$	−800.140			−1.13953			−0.569764	−	0.821808i	$-0.692966\pi$
$79$	−800.140			−1.13953			−0.569764	+	0.821808i	$0.692966\pi$
$80$	35.1928	+	175.389i	0.0491835	+	0.245114i
$81$	81.0000			0.111111
$82$			128.837i			0.173508i
$83$			826.960i			1.09362i	0.837256	+	0.546811i	$0.184159\pi$
$83$			826.960i			1.09362i	−0.837256	+	0.546811i	$0.815841\pi$
$84$	−84.6791			−0.109991
$85$	1461.98	−	293.354i	1.86558	−	0.374338i
$86$	597.399			0.749060
$87$			72.4927i			0.0893337i
$88$			93.3584i			0.113091i
$89$	−166.350			−0.198124			−0.0990620	−	0.995081i	$-0.531584\pi$
$89$	−166.350			−0.198124			−0.0990620	+	0.995081i	$0.531584\pi$
$90$	197.313	−	39.5919i	0.231096	−	0.0463706i
$91$	−501.045			−0.577184
$92$			152.949i			0.173327i
$93$			93.0000i			0.103695i
$94$	−332.626			−0.364977
$95$	−222.765	−	1110.19i	−0.240581	−	1.19898i
$96$	96.0000			0.102062
$97$		−	1590.14i		−	1.66448i	−0.554416	−	0.832240i	$-0.687058\pi$
$97$		−	1590.14i		−	1.66448i	0.554416	−	0.832240i	$-0.312942\pi$
$98$			586.409i			0.604452i
$99$	105.028			0.106624
$100$	461.296	−	192.889i	0.461296	−	0.192889i
$101$	−975.101			−0.960656			−0.480328	−	0.877089i	$-0.659482\pi$
$101$	−975.101			−0.960656			−0.480328	+	0.877089i	$0.659482\pi$
$102$		−	800.221i		−	0.776800i
$103$		−	1500.81i		−	1.43572i	−0.696186	−	0.717861i	$-0.745121\pi$
$103$		−	1500.81i		−	1.43572i	0.696186	−	0.717861i	$-0.254879\pi$
$104$	568.030			0.535577
$105$	46.5640	+	232.060i	0.0432779	+	0.215683i
$106$	772.854			0.708172
$107$		−	888.369i		−	0.802634i	−0.915939	−	0.401317i	$-0.868553\pi$
$107$		−	888.369i		−	0.802634i	0.915939	−	0.401317i	$-0.131447\pi$
$108$		−	108.000i		−	0.0962250i
$109$	2150.64			1.88985			0.944927	−	0.327281i	$-0.106132\pi$
$109$	2150.64			1.88985			0.944927	+	0.327281i	$0.106132\pi$
$110$	255.845	−	51.3366i	0.221762	−	0.0444978i
$111$	811.401			0.693827
$112$			112.905i			0.0952550i
$113$			1708.19i			1.42206i	0.703161	+	0.711030i	$0.251771\pi$
$113$			1708.19i			1.42206i	−0.703161	+	0.711030i	$0.748229\pi$
$114$	−607.665			−0.499238
$115$	419.152	−	84.1050i	0.339879	−	0.0681985i
$116$	96.6569			0.0773652
$117$		−	639.034i		−	0.504946i
$118$			1593.79i			1.24339i
$119$	941.138			0.724991
$120$	−52.7892	−	263.084i	−0.0401581	−	0.200135i
$121$	−1194.82			−0.897683
$122$		−	1342.91i		−	0.996569i
$123$		−	193.255i		−	0.141668i
$124$	124.000			0.0898027
$125$	−782.266	−	1158.10i	−0.559744	−	0.828666i
$126$	127.019			0.0898073
$127$		−	2346.53i		−	1.63953i	−0.572698	−	0.819766i	$-0.694103\pi$
$127$		−	2346.53i		−	1.63953i	0.572698	−	0.819766i	$-0.305897\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−896.098			−0.611605
$130$	−312.353	−	1556.66i	−0.210732	−	1.05022i
$131$	−1971.94			−1.31519			−0.657594	−	0.753373i	$-0.728426\pi$
$131$	−1971.94			−1.31519			−0.657594	+	0.753373i	$0.728426\pi$
$132$		−	140.038i		−	0.0923387i
$133$		−	714.674i		−	0.465941i
$134$	1051.33			0.677769
$135$	−295.970	+	59.3879i	−0.188689	+	0.0378614i
$136$	−1066.96			−0.672729
$137$		−	1085.19i		−	0.676743i	−0.941013	−	0.338371i	$-0.890124\pi$
$137$		−	1085.19i		−	0.676743i	0.941013	−	0.338371i	$-0.109876\pi$
$138$		−	229.424i		−	0.141521i
$139$	−1126.51			−0.687404			−0.343702	−	0.939079i	$-0.611681\pi$
$139$	−1126.51			−0.687404			−0.343702	+	0.939079i	$0.611681\pi$
$140$	309.413	−	62.0853i	0.186787	−	0.0374798i
$141$	498.940			0.298002
$142$			38.0954i			0.0225133i
$143$		−	828.600i		−	0.484553i
$144$	−144.000			−0.0833333
$145$	−53.1504	−	264.884i	−0.0304407	−	0.151707i
$146$	1446.01			0.819678
$147$		−	879.614i		−	0.493533i
$148$		−	1081.87i		−	0.600871i
$149$	−1930.17			−1.06124			−0.530622	−	0.847608i	$-0.678042\pi$
$149$	−1930.17			−1.06124			−0.530622	+	0.847608i	$0.678042\pi$
$150$	−691.944	+	289.334i	−0.376646	+	0.157493i
$151$	−302.179			−0.162854			−0.0814272	−	0.996679i	$-0.525948\pi$
$151$	−302.179			−0.162854			−0.0814272	+	0.996679i	$0.525948\pi$
$152$			810.221i			0.432352i
$153$			1200.33i			0.634255i
$154$	164.698			0.0861801
$155$	−68.1861	−	339.817i	−0.0353344	−	0.176095i
$156$	−852.046			−0.437296
$157$		−	251.976i		−	0.128088i	−0.997947	−	0.0640442i	$-0.979600\pi$
$157$		−	251.976i		−	0.128088i	0.997947	−	0.0640442i	$-0.0203999\pi$
$158$		−	1600.28i		−	0.805768i
$159$	−1159.28			−0.578220
$160$	−350.779	+	70.3856i	−0.173322	+	0.0347780i
$161$	269.825			0.132082
$162$			162.000i			0.0785674i
$163$		−	2239.00i		−	1.07590i	−0.842976	−	0.537950i	$-0.819199\pi$
$163$		−	2239.00i		−	1.07590i	0.842976	−	0.537950i	$-0.180801\pi$
$164$	−257.673			−0.122688
$165$	−383.767	+	77.0050i	−0.181068	+	0.0363323i
$166$	−1653.92			−0.773308
$167$		−	4223.87i		−	1.95720i	−0.205766	−	0.978601i	$-0.565969\pi$
$167$		−	4223.87i		−	1.95720i	0.205766	−	0.978601i	$-0.434031\pi$
$168$		−	169.358i		−	0.0777754i
$169$	−2844.54			−1.29474
$170$	586.709	+	2923.96i	0.264697	+	1.31916i
$171$	911.498			0.407626
$172$			1194.80i			0.529665i
$173$			2356.60i			1.03566i	0.855485	+	0.517828i	$0.173259\pi$
$173$			2356.60i			1.03566i	−0.855485	+	0.517828i	$0.826741\pi$
$174$	−144.985			−0.0631684
$175$	−340.285	−	813.794i	−0.146989	−	0.351526i
$176$	−186.717			−0.0799677
$177$		−	2390.68i		−	1.01523i
$178$		−	332.699i		−	0.140095i
$179$	4619.26			1.92883			0.964413	−	0.264402i	$-0.0851744\pi$
$179$	4619.26			1.92883			0.964413	+	0.264402i	$0.0851744\pi$
$180$	79.1838	+	394.626i	0.0327890	+	0.163409i
$181$	1470.53			0.603889			0.301944	−	0.953326i	$-0.402364\pi$
$181$	1470.53			0.603889			0.301944	+	0.953326i	$0.402364\pi$
$182$		−	1002.09i		−	0.408131i
$183$			2014.37i			0.813695i
$184$	−305.899			−0.122561
$185$	−2964.82	+	594.906i	−1.17826	+	0.236424i
$186$	−186.000			−0.0733236
$187$			1556.40i			0.608638i
$188$		−	665.253i		−	0.258077i
$189$	−190.528			−0.0733273
$190$	2220.38	−	445.530i	0.847806	−	0.170117i
$191$	−1459.25			−0.552817			−0.276408	−	0.961040i	$-0.589144\pi$
$191$	−1459.25			−0.552817			−0.276408	+	0.961040i	$0.589144\pi$
$192$			192.000i			0.0721688i
$193$			2164.12i			0.807135i	0.914950	+	0.403567i	$0.132230\pi$
$193$			2164.12i			0.807135i	−0.914950	+	0.403567i	$0.867770\pi$
$194$	3180.29			1.17696
$195$	468.530	+	2335.00i	0.172062	+	0.857501i
$196$	−1172.82			−0.427412
$197$		−	890.792i		−	0.322164i	−0.986941	−	0.161082i	$-0.948502\pi$
$197$		−	890.792i		−	0.322164i	0.986941	−	0.161082i	$-0.0514983\pi$
$198$			210.056i			0.0753942i
$199$	5458.63			1.94448			0.972242	−	0.233979i	$-0.0751748\pi$
$199$	5458.63			1.94448			0.972242	+	0.233979i	$0.0751748\pi$
$200$	385.778	+	922.592i	0.136393	+	0.326185i
$201$	−1576.99			−0.553396
$202$		−	1950.20i		−	0.679286i
$203$		−	170.517i		−	0.0589554i
$204$	1600.44			0.549281
$205$	141.691	+	706.143i	0.0482739	+	0.240581i
$206$	3001.62			1.01521
$207$			344.136i			0.115551i
$208$			1136.06i			0.378710i
$209$	1181.89			0.391163
$210$	−464.119	+	93.1280i	−0.152511	+	0.0306021i
$211$	−2732.02			−0.891374			−0.445687	−	0.895189i	$-0.647041\pi$
$211$	−2732.02			−0.891374			−0.445687	+	0.895189i	$0.647041\pi$
$212$			1545.71i			0.500753i
$213$		−	57.1431i		−	0.0183821i
$214$	1776.74			0.567548
$215$	3274.30	−	657.005i	1.03863	−	0.208406i
$216$	216.000			0.0680414
$217$		−	218.754i		−	0.0684332i
$218$			4301.28i			1.33633i
$219$	−2169.02			−0.669264
$220$	102.673	+	511.690i	0.0314647	+	0.156810i
$221$	9469.78			2.88238
$222$			1622.80i			0.490610i
$223$		−	4581.19i		−	1.37569i	−0.725857	−	0.687845i	$-0.758557\pi$
$223$		−	4581.19i		−	1.37569i	0.725857	−	0.687845i	$-0.241443\pi$
$224$	−225.811			−0.0673554
$225$	1037.92	−	434.000i	0.307531	−	0.128593i
$226$	−3416.38			−1.00555
$227$			4065.29i			1.18865i	0.804226	+	0.594324i	$0.202580\pi$
$227$			4065.29i			1.18865i	−0.804226	+	0.594324i	$0.797420\pi$
$228$		−	1215.33i		−	0.353014i
$229$	3431.00			0.990073			0.495036	−	0.868872i	$-0.335155\pi$
$229$	3431.00			0.990073			0.495036	+	0.868872i	$0.335155\pi$
$230$	168.210	+	838.303i	0.0482236	+	0.240331i
$231$	−247.047			−0.0703658
$232$			193.314i			0.0547055i
$233$		−	2165.60i		−	0.608898i	−0.952529	−	0.304449i	$-0.901528\pi$
$233$		−	2165.60i		−	0.608898i	0.952529	−	0.304449i	$-0.0984723\pi$
$234$	1278.07			0.357051
$235$	−1823.10	+	365.814i	−0.506068	+	0.101545i
$236$	−3187.58			−0.879211
$237$			2400.42i			0.657907i
$238$			1882.28i			0.512646i
$239$	633.061			0.171336			0.0856680	−	0.996324i	$-0.472698\pi$
$239$	633.061			0.171336			0.0856680	+	0.996324i	$0.472698\pi$
$240$	526.168	−	105.578i	0.141517	−	0.0283961i
$241$	−4781.34			−1.27798			−0.638990	−	0.769215i	$-0.720648\pi$
$241$	−4781.34			−1.27798			−0.638990	+	0.769215i	$0.720648\pi$
$242$		−	2389.63i		−	0.634758i
$243$		−	243.000i		−	0.0641500i
$244$	2685.82			0.704681
$245$	644.918	+	3214.06i	0.168173	+	0.838118i
$246$	386.510			0.100175
$247$		−	7191.09i		−	1.85246i
$248$			248.000i			0.0635001i
$249$	2480.88			0.631403
$250$	2316.19	−	1564.53i	0.585955	−	0.395799i
$251$	−6159.41			−1.54892			−0.774459	−	0.632624i	$-0.781978\pi$
$251$	−6159.41			−1.54892			−0.774459	+	0.632624i	$0.781978\pi$
$252$			254.037i			0.0635033i
$253$			446.222i			0.110884i
$254$	4693.05			1.15932
$255$	−880.063	−	4385.95i	−0.216124	−	1.07709i
$256$	256.000			0.0625000
$257$			1642.19i			0.398587i	0.979940	+	0.199294i	$0.0638648\pi$
$257$			1642.19i			0.398587i	−0.979940	+	0.199294i	$0.936135\pi$
$258$		−	1792.20i		−	0.432470i
$259$	−1908.57			−0.457888
$260$	3113.33	−	624.706i	0.742617	−	0.149010i
$261$	217.478			0.0515768
$262$		−	3943.89i		−	0.929978i
$263$		−	1264.42i		−	0.296453i	−0.988953	−	0.148227i	$-0.952643\pi$
$263$		−	1264.42i		−	0.296453i	0.988953	−	0.148227i	$-0.0473565\pi$
$264$	280.075			0.0652933
$265$	4235.95	−	849.966i	0.981934	−	0.197030i
$266$	1429.35			0.329470
$267$			499.049i			0.114387i
$268$			2102.66i			0.479255i
$269$	−6887.56			−1.56112			−0.780561	−	0.625079i	$-0.785067\pi$
$269$	−6887.56			−1.56112			−0.780561	+	0.625079i	$0.785067\pi$
$270$	−118.776	−	591.939i	−0.0267721	−	0.133423i
$271$	2673.75			0.599330			0.299665	−	0.954044i	$-0.403125\pi$
$271$	2673.75			0.599330			0.299665	+	0.954044i	$0.403125\pi$
$272$		−	2133.92i		−	0.475691i
$273$			1503.13i			0.333237i
$274$	2170.37			0.478529
$275$	1345.81	−	562.744i	0.295110	−	0.123399i
$276$	458.848			0.100070
$277$			7166.95i			1.55458i	0.629139	+	0.777292i	$0.283407\pi$
$277$			7166.95i			1.55458i	−0.629139	+	0.777292i	$0.716593\pi$
$278$		−	2253.02i		−	0.486068i
$279$	279.000			0.0598684
$280$	124.171	+	618.826i	0.0265022	+	0.132078i
$281$	2475.41			0.525518			0.262759	−	0.964862i	$-0.415368\pi$
$281$	2475.41			0.525518			0.262759	+	0.964862i	$0.415368\pi$
$282$			997.879i			0.210719i
$283$			2511.48i			0.527534i	0.964586	+	0.263767i	$0.0849649\pi$
$283$			2511.48i			0.527534i	−0.964586	+	0.263767i	$0.915035\pi$
$284$	−76.1908			−0.0159193
$285$	−3330.57	+	668.296i	−0.692231	+	0.138900i
$286$	1657.20			0.342630
$287$			454.573i			0.0934934i
$288$		−	288.000i		−	0.0589256i
$289$	−12874.6			−2.62051
$290$	529.769	−	106.301i	0.107273	−	0.0215248i
$291$	−4770.43			−0.960988
$292$			2892.03i			0.579600i
$293$			2119.77i			0.422657i	0.977415	+	0.211329i	$0.0677790\pi$
$293$			2119.77i			0.422657i	−0.977415	+	0.211329i	$0.932221\pi$
$294$	1759.23			0.348980
$295$	1752.81	+	8735.44i	0.345941	+	1.72406i
$296$	2163.74			0.424880
$297$		−	315.085i		−	0.0615591i
$298$		−	3860.33i		−	0.750413i
$299$	2715.00			0.525125
$300$	−578.667	−	1383.89i	−0.111365	−	0.266329i
$301$	2107.80			0.403626
$302$		−	604.359i		−	0.115155i
$303$			2925.30i			0.554635i
$304$	−1620.44			−0.305719
$305$	−1476.90	−	7360.39i	−0.277269	−	1.38182i
$306$	−2400.66			−0.448486
$307$			3082.71i			0.573094i	0.958066	+	0.286547i	$0.0925074\pi$
$307$			3082.71i			0.573094i	−0.958066	+	0.286547i	$0.907493\pi$
$308$			329.396i			0.0609385i
$309$	−4502.43			−0.828914
$310$	679.634	−	136.372i	0.124518	−	0.0249852i
$311$	5571.48			1.01585			0.507925	−	0.861401i	$-0.330413\pi$
$311$	5571.48			1.01585			0.507925	+	0.861401i	$0.330413\pi$
$312$		−	1704.09i		−	0.309215i
$313$			266.469i			0.0481205i	0.999711	+	0.0240602i	$0.00765935\pi$
$313$			266.469i			0.0481205i	−0.999711	+	0.0240602i	$0.992341\pi$
$314$	503.952			0.0905722
$315$	696.179	−	139.692i	0.124525	−	0.0249865i
$316$	3200.56			0.569764
$317$			7339.74i			1.30044i	0.759744	+	0.650222i	$0.225324\pi$
$317$			7339.74i			1.30044i	−0.759744	+	0.650222i	$0.774676\pi$
$318$		−	2318.56i		−	0.408863i
$319$	281.992			0.0494937
$320$	−140.771	−	701.558i	−0.0245917	−	0.122557i
$321$	−2665.11			−0.463401
$322$			539.650i			0.0933961i
$323$			13507.4i			2.32685i
$324$	−324.000			−0.0555556
$325$	−3423.96	−	8188.44i	−0.584392	−	1.39758i
$326$	4478.00			0.760777
$327$		−	6451.92i		−	1.09111i
$328$		−	515.346i		−	0.0867538i
$329$	−1173.60			−0.196665
$330$	−154.010	−	767.535i	−0.0256908	−	0.128035i
$331$	−6092.82			−1.01176			−0.505879	−	0.862604i	$-0.668832\pi$
$331$	−6092.82			−1.01176			−0.505879	+	0.862604i	$0.668832\pi$
$332$		−	3307.84i		−	0.546811i
$333$		−	2434.20i		−	0.400581i
$334$	8447.74			1.38395
$335$	5762.25	−	1156.23i	0.939777	−	0.188571i
$336$	338.716			0.0549955
$337$			4290.95i			0.693600i	0.937939	+	0.346800i	$0.112732\pi$
$337$			4290.95i			0.693600i	−0.937939	+	0.346800i	$0.887268\pi$
$338$		−	5689.08i		−	0.915518i
$339$	5124.57			0.821027
$340$	−5847.93	+	1173.42i	−0.932789	+	0.187169i
$341$	361.764			0.0574505
$342$			1823.00i			0.288235i
$343$			4489.43i			0.706725i
$344$	−2389.60			−0.374530
$345$	−252.315	−	1257.45i	−0.0393744	−	0.196229i
$346$	−4713.19			−0.732320
$347$			12795.7i			1.97957i	0.142573	+	0.989784i	$0.454462\pi$
$347$			12795.7i			1.97957i	−0.142573	+	0.989784i	$0.545538\pi$
$348$		−	289.971i		−	0.0446668i
$349$	−11863.9			−1.81966			−0.909830	−	0.414981i	$-0.863788\pi$
$349$	−11863.9			−1.81966			−0.909830	+	0.414981i	$0.863788\pi$
$350$	1627.59	−	680.569i	0.248566	−	0.103937i
$351$	−1917.10			−0.291531
$352$		−	373.434i		−	0.0565457i
$353$			3605.57i			0.543641i	0.962348	+	0.271820i	$0.0876257\pi$
$353$			3605.57i			0.543641i	−0.962348	+	0.271820i	$0.912374\pi$
$354$	4781.37			0.717873
$355$	41.8964	+	208.798i	0.00626374	+	0.0312164i
$356$	665.399			0.0990620
$357$		−	2823.41i		−	0.418574i
$358$			9238.52i			1.36389i
$359$	10806.2			1.58866			0.794330	−	0.607486i	$-0.207822\pi$
$359$	10806.2			1.58866			0.794330	+	0.607486i	$0.207822\pi$
$360$	−789.253	+	158.368i	−0.115548	+	0.0231853i
$361$	3398.15			0.495429
$362$			2941.07i			0.427014i
$363$			3584.45i			0.518277i
$364$	2004.18			0.288592
$365$	7925.49	−	1590.29i	1.13655	−	0.228054i
$366$	−4028.73			−0.575370
$367$		−	10905.7i		−	1.55115i	−0.631254	−	0.775576i	$-0.717460\pi$
$367$		−	10905.7i		−	1.55115i	0.631254	−	0.775576i	$-0.282540\pi$
$368$		−	611.797i		−	0.0866634i
$369$	−579.765			−0.0817923
$370$	−1189.81	−	5929.63i	−0.167177	−	0.833154i
$371$	2726.86			0.381594
$372$		−	372.000i		−	0.0518476i
$373$		−	4504.91i		−	0.625350i	−0.949860	−	0.312675i	$-0.898775\pi$
$373$		−	4504.91i		−	0.625350i	0.949860	−	0.312675i	$-0.101225\pi$
$374$	−3112.80			−0.430372
$375$	−3474.29	+	2346.80i	−0.478430	+	0.323168i
$376$	1330.51			0.182488
$377$		−	1715.75i		−	0.234392i
$378$		−	381.056i		−	0.0518502i
$379$	−7619.44			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$379$	−7619.44			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$380$	891.061	+	4440.75i	0.120291	+	0.599489i
$381$	−7039.58			−0.946584
$382$		−	2918.51i		−	0.390900i
$383$		−	10575.4i		−	1.41091i	−0.708757	−	0.705453i	$-0.750744\pi$
$383$		−	10575.4i		−	1.41091i	0.708757	−	0.705453i	$-0.249256\pi$
$384$	−384.000			−0.0510310
$385$	902.696	−	181.131i	0.119495	−	0.0239773i
$386$	−4328.25			−0.570730
$387$			2688.29i			0.353110i
$388$			6360.57i			0.832240i
$389$	−15072.9			−1.96459			−0.982295	−	0.187338i	$-0.940014\pi$
$389$	−15072.9			−1.96459			−0.982295	+	0.187338i	$0.940014\pi$
$390$	−4669.99	+	937.059i	−0.606345	+	0.121666i
$391$	−5099.72			−0.659600
$392$		−	2345.64i		−	0.302226i
$393$			5915.83i			0.759324i
$394$	1781.58			0.227804
$395$	−1759.95	−	8771.01i	−0.224184	−	1.11726i
$396$	−420.113			−0.0533118
$397$		−	5453.21i		−	0.689393i	−0.938714	−	0.344696i	$-0.887982\pi$
$397$		−	5453.21i		−	0.689393i	0.938714	−	0.344696i	$-0.112018\pi$
$398$			10917.3i			1.37496i
$399$	−2144.02			−0.269011
$400$	−1845.18	+	771.556i	−0.230648	+	0.0964445i
$401$	−5395.40			−0.671904			−0.335952	−	0.941879i	$-0.609058\pi$
$401$	−5395.40			−0.671904			−0.335952	+	0.941879i	$0.609058\pi$
$402$		−	3153.99i		−	0.391310i
$403$		−	2201.12i		−	0.272073i
$404$	3900.41			0.480328
$405$	178.164	+	887.909i	0.0218593	+	0.108940i
$406$	341.034			0.0416878
$407$		−	3156.29i		−	0.384402i
$408$			3200.88i			0.388400i
$409$	−3217.71			−0.389011			−0.194506	−	0.980901i	$-0.562310\pi$
$409$	−3217.71			−0.389011			−0.194506	+	0.980901i	$0.562310\pi$
$410$	−1412.29	+	283.383i	−0.170117	+	0.0341348i
$411$	−3255.56			−0.390718
$412$			6003.25i			0.717861i
$413$			5623.36i			0.669994i
$414$	−688.272			−0.0817071
$415$	−9065.01	+	1818.94i	−1.07225	+	0.215153i
$416$	−2272.12			−0.267788
$417$			3379.53i			0.396873i
$418$			2363.78i			0.276594i
$419$	4318.46			0.503510			0.251755	−	0.967791i	$-0.418992\pi$
$419$	4318.46			0.503510			0.251755	+	0.967791i	$0.418992\pi$
$420$	−186.256	−	928.238i	−0.0216389	−	0.107841i
$421$	−8292.07			−0.959931			−0.479965	−	0.877287i	$-0.659351\pi$
$421$	−8292.07			−0.959931			−0.479965	+	0.877287i	$0.659351\pi$
$422$		−	5464.04i		−	0.630297i
$423$		−	1496.82i		−	0.172052i
$424$	−3091.42			−0.354086
$425$	6431.41	+	15380.8i	0.734045	+	1.75547i
$426$	114.286			0.0129981
$427$		−	4738.18i		−	0.536995i
$428$			3553.48i			0.401317i
$429$	−2485.80			−0.279757
$430$	1314.01	+	6548.59i	0.147365	+	0.734421i
$431$	−12812.2			−1.43188			−0.715939	−	0.698162i	$-0.754001\pi$
$431$	−12812.2			−1.43188			−0.715939	+	0.698162i	$0.754001\pi$
$432$			432.000i			0.0481125i
$433$			9629.28i			1.06872i	0.845258	+	0.534358i	$0.179447\pi$
$433$			9629.28i			1.06872i	−0.845258	+	0.534358i	$0.820553\pi$
$434$	437.508			0.0483896
$435$	−794.653	+	159.451i	−0.0875878	+	0.0175750i
$436$	−8602.57			−0.944927
$437$			3872.58i			0.423915i
$438$		−	4338.04i		−	0.473241i
$439$	−767.192			−0.0834079			−0.0417039	−	0.999130i	$-0.513279\pi$
$439$	−767.192			−0.0834079			−0.0417039	+	0.999130i	$0.513279\pi$
$440$	−1023.38	+	205.347i	−0.110881	+	0.0222489i
$441$	−2638.84			−0.284941
$442$			18939.6i			2.03815i
$443$			11665.3i			1.25109i	0.780187	+	0.625546i	$0.215124\pi$
$443$			11665.3i			1.25109i	−0.780187	+	0.625546i	$0.784876\pi$
$444$	−3245.60			−0.346913
$445$	−365.895	−	1823.50i	−0.0389777	−	0.194252i
$446$	9162.37			0.972760
$447$			5790.50i			0.612710i
$448$		−	451.622i		−	0.0476275i
$449$	−782.591			−0.0822556			−0.0411278	−	0.999154i	$-0.513095\pi$
$449$	−782.591			−0.0822556			−0.0411278	+	0.999154i	$0.513095\pi$
$450$	868.001	+	2075.83i	0.0909288	+	0.217457i
$451$	−751.749			−0.0784888
$452$		−	6832.75i		−	0.711030i
$453$			906.538i			0.0940240i
$454$	−8130.59			−0.840501
$455$	−1102.07	−	5492.37i	−0.113552	−	0.565904i
$456$	2430.66			0.249619
$457$			1330.18i			0.136156i	0.997680	+	0.0680778i	$0.0216866\pi$
$457$			1330.18i			0.136156i	−0.997680	+	0.0680778i	$0.978313\pi$
$458$			6861.99i			0.700087i
$459$	3600.99			0.366187
$460$	−1676.61	+	336.420i	−0.169940	+	0.0340993i
$461$	15179.9			1.53362			0.766808	−	0.641876i	$-0.221844\pi$
$461$	15179.9			1.53362			0.766808	+	0.641876i	$0.221844\pi$
$462$		−	494.094i		−	0.0497561i
$463$		−	10604.2i		−	1.06440i	−0.846618	−	0.532202i	$-0.821365\pi$
$463$		−	10604.2i		−	1.06440i	0.846618	−	0.532202i	$-0.178635\pi$
$464$	−386.628			−0.0386826
$465$	−1019.45	+	204.558i	−0.101669	+	0.0204003i
$466$	4331.20			0.430556
$467$		−	5879.93i		−	0.582635i	−0.956626	−	0.291317i	$-0.905906\pi$
$467$		−	5879.93i		−	0.582635i	0.956626	−	0.291317i	$-0.0940936\pi$
$468$			2556.14i			0.252473i
$469$	3709.40			0.365211
$470$	−731.629	−	3646.20i	−0.0718032	−	0.357844i
$471$	−755.929			−0.0739519
$472$		−	6375.16i		−	0.621696i
$473$			3485.76i			0.338849i
$474$	−4800.84			−0.465211
$475$	11679.7	−	4883.83i	1.12822	−	0.471759i
$476$	−3764.55			−0.362496
$477$			3477.84i			0.333835i
$478$			1266.12i			0.121153i
$479$	−14811.2			−1.41282			−0.706409	−	0.707804i	$-0.749686\pi$
$479$	−14811.2			−1.41282			−0.706409	+	0.707804i	$0.749686\pi$
$480$	211.157	+	1052.34i	0.0200791	+	0.100067i
$481$	−19204.2			−1.82045
$482$		−	9562.68i		−	0.903668i
$483$		−	809.475i		−	0.0762576i
$484$	4779.26			0.448841
$485$	17430.9	−	3497.60i	1.63195	−	0.327459i
$486$	486.000			0.0453609
$487$			4992.29i			0.464522i	0.972653	+	0.232261i	$0.0746124\pi$
$487$			4992.29i			0.464522i	−0.972653	+	0.232261i	$0.925388\pi$
$488$			5371.64i			0.498285i
$489$	−6716.99			−0.621172
$490$	−6428.12	+	1289.84i	−0.592639	+	0.118916i
$491$	−8482.04			−0.779612			−0.389806	−	0.920897i	$-0.627458\pi$
$491$	−8482.04			−0.779612			−0.389806	+	0.920897i	$0.627458\pi$
$492$			773.020i			0.0708342i
$493$			3222.78i			0.294416i
$494$	14382.2			1.30989
$495$	231.015	+	1151.30i	0.0209765	+	0.104540i
$496$	−496.000			−0.0449013
$497$			134.412i			0.0121312i
$498$			4961.76i			0.446470i
$499$	1305.62			0.117129			0.0585645	−	0.998284i	$-0.481348\pi$
$499$	1305.62			0.117129			0.0585645	+	0.998284i	$0.481348\pi$
$500$	3129.06	+	4632.38i	0.279872	+	0.414333i
$501$	−12671.6			−1.12999
$502$		−	12318.8i		−	1.09525i
$503$			12677.7i			1.12380i	0.827207	+	0.561898i	$0.189929\pi$
$503$			12677.7i			1.12380i	−0.827207	+	0.561898i	$0.810071\pi$
$504$	−508.074			−0.0449036
$505$	−2144.79	−	10688.9i	−0.188993	−	0.941882i
$506$	−892.444			−0.0784071
$507$			8533.62i			0.747518i
$508$			9386.11i			0.819766i
$509$	15662.6			1.36392			0.681958	−	0.731392i	$-0.261129\pi$
$509$	15662.6			1.36392			0.681958	+	0.731392i	$0.261129\pi$
$510$	8771.89	−	1760.13i	0.761619	−	0.152823i
$511$	5101.96			0.441678
$512$			512.000i			0.0441942i
$513$		−	2734.49i		−	0.235343i
$514$	−3284.38			−0.281844
$515$	16451.7	−	3301.11i	1.40766	−	0.282455i
$516$	3584.39			0.305802
$517$		−	1940.84i		−	0.165103i
$518$		−	3817.15i		−	0.323776i
$519$	7069.79			0.597937
$520$	1249.41	+	6226.66i	0.105366	+	0.525110i
$521$	−12391.3			−1.04198			−0.520990	−	0.853563i	$-0.674437\pi$
$521$	−12391.3			−1.04198			−0.520990	+	0.853563i	$0.674437\pi$
$522$			434.956i			0.0364703i
$523$		−	4060.63i		−	0.339500i	−0.985487	−	0.169750i	$-0.945704\pi$
$523$		−	4060.63i		−	0.339500i	0.985487	−	0.169750i	$-0.0542961\pi$
$524$	7887.78			0.657594
$525$	−2441.38	+	1020.85i	−0.202954	+	0.0848642i
$526$	2528.83			0.209624
$527$			4134.47i			0.341747i
$528$			560.150i			0.0461693i
$529$	10704.9			0.879831
$530$	1699.93	+	8471.90i	0.139321	+	0.694332i
$531$	−7172.05			−0.586141
$532$			2858.70i			0.232970i
$533$			4573.94i			0.371706i
$534$	−998.098			−0.0808838
$535$	9738.16	−	1954.01i	0.786948	−	0.157905i
$536$	−4205.32			−0.338884
$537$		−	13857.8i		−	1.11361i
$538$		−	13775.1i		−	1.10388i
$539$	−3421.64			−0.273433
$540$	1183.88	−	237.552i	0.0943445	−	0.0189307i
$541$	1397.87			0.111089			0.0555443	−	0.998456i	$-0.482311\pi$
$541$	1397.87			0.111089			0.0555443	+	0.998456i	$0.482311\pi$
$542$			5347.49i			0.423791i
$543$		−	4411.60i		−	0.348655i
$544$	4267.84			0.336364
$545$	4730.45	+	23575.0i	0.371798	+	1.85292i
$546$	−3006.27			−0.235634
$547$			73.9150i			0.00577765i	0.999996	+	0.00288883i	$0.000919543\pi$
$547$			73.9150i			0.00577765i	−0.999996	+	0.00288883i	$0.999080\pi$
$548$			4340.75i			0.338371i
$549$	6043.10			0.469787
$550$	1125.49	+	2691.61i	0.0872563	+	0.208674i
$551$	2447.29			0.189216
$552$			917.696i			0.0707604i
$553$		−	5646.26i		−	0.434183i
$554$	−14333.9			−1.09926
$555$	1784.72	+	8894.45i	0.136499	+	0.680267i
$556$	4506.03			0.343702
$557$		−	1474.09i		−	0.112135i	−0.998427	−	0.0560674i	$-0.982144\pi$
$557$		−	1474.09i		−	0.112135i	0.998427	−	0.0560674i	$-0.0178562\pi$
$558$			558.000i			0.0423334i
$559$	21208.8			1.60472
$560$	−1237.65	+	248.341i	−0.0933934	+	0.0187399i
$561$	4669.21			0.351398
$562$			4950.82i			0.371597i
$563$		−	9466.04i		−	0.708607i	−0.935130	−	0.354304i	$-0.884718\pi$
$563$		−	9466.04i		−	0.708607i	0.935130	−	0.354304i	$-0.115282\pi$
$564$	−1995.76			−0.149001
$565$	−18724.9	+	3757.25i	−1.39427	+	0.279767i
$566$	−5022.96			−0.373023
$567$			571.584i			0.0423355i
$568$		−	152.382i		−	0.0112567i
$569$	−21972.8			−1.61889			−0.809446	−	0.587195i	$-0.800232\pi$
$569$	−21972.8			−1.61889			−0.809446	+	0.587195i	$0.800232\pi$
$570$	−1336.59	−	6661.13i	−0.0982169	−	0.489481i
$571$	2833.86			0.207694			0.103847	−	0.994593i	$-0.466885\pi$
$571$	2833.86			0.207694			0.103847	+	0.994593i	$0.466885\pi$
$572$			3314.40i			0.242276i
$573$			4377.76i			0.319169i
$574$	−909.147			−0.0661099
$575$	1843.89	+	4409.68i	0.133731	+	0.319820i
$576$	576.000			0.0416667
$577$			19806.7i			1.42905i	0.699609	+	0.714525i	$0.253357\pi$
$577$			19806.7i			1.42905i	−0.699609	+	0.714525i	$0.746643\pi$
$578$		−	25749.2i		−	1.85298i
$579$	6492.37			0.465999
$580$	212.602	+	1059.54i	0.0152204	+	0.0758533i
$581$	−5835.52			−0.416692
$582$		−	9540.86i		−	0.679521i
$583$			4509.52i			0.320352i
$584$	−5784.06			−0.409839
$585$	7004.99	−	1405.59i	0.495078	−	0.0993401i
$586$	−4239.55			−0.298864
$587$		−	290.167i		−	0.0204028i	−0.999948	−	0.0102014i	$-0.996753\pi$
$587$		−	290.167i		−	0.0204028i	0.999948	−	0.0102014i	$-0.00324727\pi$
$588$			3518.45i			0.246766i
$589$	3139.60			0.219635
$590$	−17470.9	+	3505.62i	−1.21909	+	0.244617i
$591$	−2672.37			−0.186001
$592$			4327.47i			0.300436i
$593$			12795.1i			0.886058i	0.896507	+	0.443029i	$0.146096\pi$
$593$			12795.1i			0.886058i	−0.896507	+	0.443029i	$0.853904\pi$
$594$	630.169			0.0435289
$595$	2070.08	+	10316.6i	0.142630	+	0.710823i
$596$	7720.67			0.530622
$597$		−	16375.9i		−	1.12265i
$598$			5429.99i			0.371319i
$599$	6339.21			0.432409			0.216205	−	0.976348i	$-0.430632\pi$
$599$	6339.21			0.432409			0.216205	+	0.976348i	$0.430632\pi$
$600$	2767.77	−	1157.33i	0.188323	−	0.0787466i
$601$	−4212.75			−0.285926			−0.142963	−	0.989728i	$-0.545663\pi$
$601$	−4212.75			−0.285926			−0.142963	+	0.989728i	$0.545663\pi$
$602$			4215.60i			0.285407i
$603$			4730.98i			0.319503i
$604$	1208.72			0.0814272
$605$	−2628.06	−	13097.4i	−0.176605	−	0.880139i
$606$	−5850.61			−0.392186
$607$			14923.3i			0.997885i	0.866635	+	0.498943i	$0.166278\pi$
$607$			14923.3i			0.997885i	−0.866635	+	0.498943i	$0.833722\pi$
$608$		−	3240.88i		−	0.216176i
$609$	−511.551			−0.0340379
$610$	14720.8	−	2953.80i	0.977093	−	0.196059i
$611$	−11808.9			−0.781892
$612$		−	4801.32i		−	0.317127i
$613$		−	21526.7i		−	1.41836i	−0.705028	−	0.709179i	$-0.749066\pi$
$613$		−	21526.7i		−	1.41836i	0.705028	−	0.709179i	$-0.250934\pi$
$614$	−6165.43			−0.405238
$615$	2118.43	−	425.074i	0.138900	−	0.0278710i
$616$	−658.792			−0.0430901
$617$			12647.2i			0.825213i	0.910909	+	0.412607i	$0.135382\pi$
$617$			12647.2i			0.825213i	−0.910909	+	0.412607i	$0.864618\pi$
$618$		−	9004.87i		−	0.586131i
$619$	21394.2			1.38918			0.694592	−	0.719404i	$-0.255585\pi$
$619$	21394.2			1.38918			0.694592	+	0.719404i	$0.255585\pi$
$620$	272.744	+	1359.27i	0.0176672	+	0.0880476i
$621$	1032.41			0.0667135
$622$			11143.0i			0.718315i
$623$		−	1173.86i		−	0.0754892i
$624$	3408.18			0.218648
$625$	10974.2	−	11122.4i	0.702350	−	0.711831i
$626$	−532.938			−0.0340263
$627$		−	3545.67i		−	0.225838i
$628$			1007.90i			0.0640442i
$629$	36072.2			2.28663
$630$	279.384	+	1392.36i	0.0176681	+	0.0880521i
$631$	−7949.42			−0.501524			−0.250762	−	0.968049i	$-0.580681\pi$
$631$	−7949.42			−0.501524			−0.250762	+	0.968049i	$0.580681\pi$
$632$			6401.12i			0.402884i
$633$			8196.06i			0.514635i
$634$	−14679.5			−0.919553
$635$	25722.3	−	5161.31i	1.60749	−	0.322552i
$636$	4637.12			0.289110
$637$			20818.6i			1.29492i
$638$			563.983i			0.0349973i
$639$	−171.429			−0.0106129
$640$	1403.12	−	281.543i	0.0866610	−	0.0173890i
$641$	14556.0			0.896921			0.448461	−	0.893803i	$-0.351972\pi$
$641$	14556.0			0.896921			0.448461	+	0.893803i	$0.351972\pi$
$642$		−	5330.21i		−	0.327674i
$643$			8656.33i			0.530906i	0.964124	+	0.265453i	$0.0855215\pi$
$643$			8656.33i			0.530906i	−0.964124	+	0.265453i	$0.914479\pi$
$644$	−1079.30			−0.0660410
$645$	−1971.01	−	9822.89i	−0.120323	−	0.599652i
$646$	−27014.8			−1.64533
$647$		−	12781.6i		−	0.776654i	−0.921522	−	0.388327i	$-0.873053\pi$
$647$		−	12781.6i		−	0.776654i	0.921522	−	0.388327i	$-0.126947\pi$
$648$		−	648.000i		−	0.0392837i
$649$	−9299.60			−0.562467
$650$	16376.9	−	6847.93i	0.988237	−	0.413227i
$651$	−656.263			−0.0395099
$652$			8955.99i			0.537950i
$653$		−	4571.01i		−	0.273932i	−0.990576	−	0.136966i	$-0.956265\pi$
$653$		−	4571.01i		−	0.273932i	0.990576	−	0.136966i	$-0.0437350\pi$
$654$	12903.8			0.771530
$655$	−4337.39	−	21616.1i	−0.258742	−	1.28949i
$656$	1030.69			0.0613442
$657$			6507.06i			0.386400i
$658$		−	2347.21i		−	0.139063i
$659$	6975.85			0.412353			0.206177	−	0.978515i	$-0.433898\pi$
$659$	6975.85			0.412353			0.206177	+	0.978515i	$0.433898\pi$
$660$	1535.07	−	308.020i	0.0905341	−	0.0181661i
$661$	−11554.2			−0.679891			−0.339946	−	0.940445i	$-0.610409\pi$
$661$	−11554.2			−0.679891			−0.339946	+	0.940445i	$0.610409\pi$
$662$		−	12185.6i		−	0.715421i
$663$		−	28409.4i		−	1.66414i
$664$	6615.68			0.386654
$665$	7834.14	−	1571.96i	0.456835	−	0.0916663i
$666$	4868.40			0.283254
$667$			923.975i			0.0536379i
$668$			16895.5i			0.978601i
$669$	−13743.6			−0.794255
$670$	2312.45	+	11524.5i	0.133340	+	0.664523i
$671$	7835.75			0.450813
$672$			677.432i			0.0388877i
$673$		−	31877.5i		−	1.82583i	−0.408146	−	0.912917i	$-0.633825\pi$
$673$		−	31877.5i		−	1.82583i	0.408146	−	0.912917i	$-0.366175\pi$
$674$	−8581.91			−0.490449
$675$	−1302.00	−	3113.75i	−0.0742430	−	0.177553i
$676$	11378.2			0.647369
$677$		−	30683.3i		−	1.74188i	−0.491387	−	0.870942i	$-0.663510\pi$
$677$		−	30683.3i		−	1.74188i	0.491387	−	0.870942i	$-0.336490\pi$
$678$			10249.1i			0.580554i
$679$	11221.0			0.634200
$680$	−2346.83	−	11695.9i	−0.132349	−	0.659582i
$681$	12195.9			0.686266
$682$			723.528i			0.0406236i
$683$		−	5890.61i		−	0.330012i	−0.986293	−	0.165006i	$-0.947236\pi$
$683$		−	5890.61i		−	0.330012i	0.986293	−	0.165006i	$-0.0527643\pi$
$684$	−3645.99			−0.203813
$685$	11895.6	−	2386.92i	0.663517	−	0.133138i
$686$	−8978.87			−0.499730
$687$		−	10293.0i		−	0.571619i
$688$		−	4779.19i		−	0.264833i
$689$	27437.8			1.51712
$690$	2514.91	−	504.630i	0.138755	−	0.0278419i
$691$	23992.5			1.32087			0.660433	−	0.750885i	$-0.270373\pi$
$691$	23992.5			1.32087			0.660433	+	0.750885i	$0.270373\pi$
$692$		−	9426.38i		−	0.517828i
$693$			741.141i			0.0406257i
$694$	−25591.4			−1.39977
$695$	−2477.81	−	12348.6i	−0.135236	−	0.673970i
$696$	579.941			0.0315842
$697$		−	8591.47i		−	0.466894i
$698$		−	23727.9i		−	1.28669i
$699$	−6496.80			−0.351547
$700$	1361.14	+	3255.17i	0.0734946	+	0.175763i
$701$	14115.1			0.760516			0.380258	−	0.924880i	$-0.375835\pi$
$701$	14115.1			0.760516			0.380258	+	0.924880i	$0.375835\pi$
$702$		−	3834.21i		−	0.206144i
$703$		−	27392.2i		−	1.46958i
$704$	746.867			0.0399838
$705$	1097.44	+	5469.30i	0.0586271	+	0.292178i
$706$	−7211.14			−0.384412
$707$		−	6880.89i		−	0.366029i
$708$			9562.74i			0.507613i
$709$	−7705.57			−0.408165			−0.204082	−	0.978954i	$-0.565421\pi$
$709$	−7705.57			−0.408165			−0.204082	+	0.978954i	$0.565421\pi$
$710$	−417.595	+	83.7927i	−0.0220734	+	0.00442913i
$711$	7201.26			0.379843
$712$			1330.80i			0.0700474i
$713$			1185.36i			0.0622608i
$714$	5646.83			0.295976
$715$	9082.98	−	1822.55i	0.475083	−	0.0953279i
$716$	−18477.0			−0.964413
$717$		−	1899.18i		−	0.0989209i
$718$			21612.4i			1.12335i
$719$	−1539.98			−0.0798772			−0.0399386	−	0.999202i	$-0.512716\pi$
$719$	−1539.98			−0.0798772			−0.0399386	+	0.999202i	$0.512716\pi$
$720$	−316.735	−	1578.51i	−0.0163945	−	0.0817047i
$721$	10590.6			0.547039
$722$			6796.29i			0.350321i
$723$			14344.0i			0.737842i
$724$	−5882.13			−0.301944
$725$	2786.71	−	1165.25i	0.142753	−	0.0596916i
$726$	−7168.89			−0.366477
$727$			19658.1i			1.00286i	0.865199	+	0.501429i	$0.167192\pi$
$727$			19658.1i			1.00286i	−0.865199	+	0.501429i	$0.832808\pi$
$728$			4008.36i			0.204065i
$729$	−729.000			−0.0370370
$730$	3180.58	+	15851.0i	0.161258	+	0.803659i
$731$	−39837.6			−2.01566
$732$		−	8057.47i		−	0.406848i
$733$			37244.2i			1.87673i	0.345643	+	0.938366i	$0.387661\pi$
$733$			37244.2i			1.87673i	−0.345643	+	0.938366i	$0.612339\pi$
$734$	21811.4			1.09683
$735$	9642.19	−	1934.76i	0.483888	−	0.0970946i
$736$	1223.59			0.0612803
$737$			6134.40i			0.306599i
$738$		−	1159.53i		−	0.0578359i
$739$	1223.08			0.0608820			0.0304410	−	0.999537i	$-0.490309\pi$
$739$	1223.08			0.0608820			0.0304410	+	0.999537i	$0.490309\pi$
$740$	11859.3	−	2379.62i	0.589129	−	0.118212i
$741$	−21573.3			−1.06952
$742$			5453.71i			0.269828i
$743$		−	15911.3i		−	0.785637i	−0.919616	−	0.392818i	$-0.871500\pi$
$743$		−	15911.3i		−	0.785637i	0.919616	−	0.392818i	$-0.128500\pi$
$744$	744.000			0.0366618
$745$	−4245.50	−	21158.2i	−0.208783	−	1.04050i
$746$	9009.83			0.442189
$747$		−	7442.64i		−	0.364541i
$748$		−	6225.61i		−	0.304319i
$749$	6268.85			0.305820
$750$	−4693.59	−	6948.57i	−0.228514	−	0.338301i
$751$	−11321.9			−0.550121			−0.275061	−	0.961427i	$-0.588698\pi$
$751$	−11321.9			−0.550121			−0.275061	+	0.961427i	$0.588698\pi$
$752$			2661.01i			0.129039i
$753$			18478.2i			0.894268i
$754$	3431.50			0.165740
$755$	−664.659	−	3312.44i	−0.0320390	−	0.159672i
$756$	762.111			0.0366637
$757$		−	19189.0i		−	0.921315i	−0.887578	−	0.460658i	$-0.847614\pi$
$757$		−	19189.0i		−	0.921315i	0.887578	−	0.460658i	$-0.152386\pi$
$758$		−	15238.9i		−	0.730212i
$759$	1338.67			0.0640191
$760$	−8881.51	+	1782.12i	−0.423903	+	0.0850584i
$761$	4934.48			0.235052			0.117526	−	0.993070i	$-0.462504\pi$
$761$	4934.48			0.235052			0.117526	+	0.993070i	$0.462504\pi$
$762$		−	14079.2i		−	0.669336i
$763$			15176.2i			0.720072i
$764$	5837.02			0.276408
$765$	−13157.8	+	2640.19i	−0.621860	+	0.124779i
$766$	21150.8			0.997661
$767$			56582.6i			2.66373i
$768$		−	768.000i		−	0.0360844i
$769$	−21025.6			−0.985958			−0.492979	−	0.870041i	$-0.664092\pi$
$769$	−21025.6			−0.985958			−0.492979	+	0.870041i	$0.664092\pi$
$770$	362.262	+	1805.39i	0.0169545	+	0.0844959i
$771$	4926.57			0.230124
$772$		−	8656.49i		−	0.403567i
$773$		−	2682.13i		−	0.124799i	−0.998051	−	0.0623993i	$-0.980125\pi$
$773$		−	2682.13i		−	0.124799i	0.998051	−	0.0623993i	$-0.0198752\pi$
$774$	−5376.59			−0.249687
$775$	3575.04	−	1494.89i	0.165702	−	0.0692878i
$776$	−12721.1			−0.588482
$777$			5725.72i			0.264362i
$778$		−	30145.8i		−	1.38918i
$779$	−6524.13			−0.300066
$780$	−1874.12	−	9339.99i	−0.0860310	−	0.428750i
$781$	−222.283			−0.0101843
$782$		−	10199.4i		−	0.466408i
$783$		−	652.434i		−	0.0297779i
$784$	4691.27			0.213706
$785$	2762.12	−	554.235i	0.125585	−	0.0251993i
$786$	−11831.7			−0.536923
$787$			25069.2i			1.13548i	0.823210	+	0.567738i	$0.192181\pi$
$787$			25069.2i			1.13548i	−0.823210	+	0.567738i	$0.807819\pi$
$788$			3563.17i			0.161082i
$789$	−3793.25			−0.171157
$790$	17542.0	−	3519.90i	0.790021	−	0.158522i
$791$	−12054.0			−0.541833
$792$		−	840.226i		−	0.0376971i
$793$		−	47675.9i		−	2.13496i
$794$	10906.4			0.487474
$795$	−2549.90	−	12707.9i	−0.113755	−	0.566920i
$796$	−21834.5			−0.972242
$797$		−	14661.6i		−	0.651618i	−0.945436	−	0.325809i	$-0.894363\pi$
$797$		−	14661.6i		−	0.651618i	0.945436	−	0.325809i	$-0.105637\pi$
$798$		−	4288.04i		−	0.190219i
$799$	22181.2			0.982121
$800$	−1543.11	−	3690.37i	−0.0681966	−	0.163093i
$801$	1497.15			0.0660413
$802$		−	10790.8i		−	0.475108i
$803$			8437.35i			0.370794i
$804$	6307.97			0.276698
$805$	593.494	+	2957.78i	0.0259850	+	0.129501i
$806$	4402.24			0.192385
$807$			20662.7i			0.901315i
$808$			7800.81i			0.339643i
$809$	−24396.6			−1.06025			−0.530123	−	0.847921i	$-0.677854\pi$
$809$	−24396.6			−1.06025			−0.530123	+	0.847921i	$0.677854\pi$
$810$	−1775.82	+	356.327i	−0.0770320	+	0.0154569i
$811$	−23803.2			−1.03063			−0.515317	−	0.857000i	$-0.672326\pi$
$811$	−23803.2			−1.03063			−0.515317	+	0.857000i	$0.672326\pi$
$812$			682.068i			0.0294777i
$813$		−	8021.24i		−	0.346023i
$814$	6312.59			0.271813
$815$	24543.5	−	4924.79i	1.05487	−	0.211666i
$816$	−6401.76			−0.274640
$817$			30251.5i			1.29543i
$818$		−	6435.42i		−	0.275072i
$819$	4509.40			0.192395
$820$	−566.765	−	2824.57i	−0.0241370	−	0.120291i
$821$	4846.80			0.206035			0.103017	−	0.994680i	$-0.467150\pi$
$821$	4846.80			0.206035			0.103017	+	0.994680i	$0.467150\pi$
$822$		−	6511.12i		−	0.276279i
$823$			33862.6i			1.43424i	0.696952	+	0.717118i	$0.254539\pi$
$823$			33862.6i			1.43424i	−0.696952	+	0.717118i	$0.745461\pi$
$824$	−12006.5			−0.507604
$825$	−1688.23	−	4037.42i	−0.0712445	−	0.170382i
$826$	−11246.7			−0.473757
$827$			34428.3i			1.44763i	0.689995	+	0.723814i	$0.257613\pi$
$827$			34428.3i			1.44763i	−0.689995	+	0.723814i	$0.742387\pi$
$828$		−	1376.54i		−	0.0577756i
$829$	−34818.1			−1.45872			−0.729361	−	0.684129i	$-0.760183\pi$
$829$	−34818.1			−1.45872			−0.729361	+	0.684129i	$0.760183\pi$
$830$	−3637.88	−	18130.0i	−0.152136	−	0.758195i
$831$	21500.8			0.897540
$832$		−	4544.24i		−	0.189355i
$833$		−	39104.7i		−	1.62653i
$834$	−6759.05			−0.280632
$835$	46301.4	−	9290.62i	1.91895	−	0.385048i
$836$	−4727.56			−0.195581
$837$		−	837.000i		−	0.0345651i
$838$			8636.93i			0.356035i
$839$	6.25571			0.000257415			0.000128707	−	1.00000i	$-0.499959\pi$
$839$	6.25571			0.000257415			0.000128707		1.00000i	$0.499959\pi$
$840$	1856.48	−	372.512i	0.0762554	−	0.0153010i
$841$	−23805.1			−0.976058
$842$		−	16584.1i		−	0.678774i
$843$		−	7426.22i		−	0.303408i
$844$	10928.1			0.445687
$845$	−6256.71	−	31181.4i	−0.254719	−	1.26944i
$846$	2993.64			0.121659
$847$		−	8431.32i		−	0.342035i
$848$		−	6182.83i		−	0.250377i
$849$	7534.44			0.304572
$850$	−30761.5	+	12862.8i	−1.24131	+	0.519048i
$851$	10341.9			0.416589
$852$			228.572i			0.00919103i
$853$		−	8759.58i		−	0.351609i	−0.984425	−	0.175804i	$-0.943747\pi$
$853$		−	8759.58i		−	0.351609i	0.984425	−	0.175804i	$-0.0562526\pi$
$854$	9476.37			0.379713
$855$	2004.89	+	9991.70i	0.0801938	+	0.399660i
$856$	−7106.95			−0.283774
$857$		−	13782.3i		−	0.549352i	−0.961537	−	0.274676i	$-0.911429\pi$
$857$		−	13782.3i		−	0.549352i	0.961537	−	0.274676i	$-0.0885706\pi$
$858$		−	4971.60i		−	0.197818i
$859$	35096.6			1.39404			0.697019	−	0.717052i	$-0.254509\pi$
$859$	35096.6			1.39404			0.697019	+	0.717052i	$0.254509\pi$
$860$	−13097.2	+	2628.02i	−0.519314	+	0.104203i
$861$	1363.72			0.0539785
$862$		−	25624.3i		−	1.01249i
$863$			22809.5i			0.899704i	0.893103	+	0.449852i	$0.148523\pi$
$863$			22809.5i			0.899704i	−0.893103	+	0.449852i	$0.851477\pi$
$864$	−864.000			−0.0340207
$865$	−25832.6	+	5183.45i	−1.01542	+	0.203749i
$866$	−19258.6			−0.755696
$867$			38623.7i			1.51295i
$868$			875.017i			0.0342166i
$869$	9337.47			0.364502
$870$	−318.903	−	1589.31i	−0.0124274	−	0.0619339i
$871$	37324.2			1.45199
$872$		−	17205.1i		−	0.668164i
$873$			14311.3i			0.554827i
$874$	−7745.17			−0.299753
$875$	8172.20	−	5520.13i	0.315738	−	0.213274i
$876$	8676.08			0.334632
$877$		−	16091.9i		−	0.619595i	−0.950803	−	0.309798i	$-0.899739\pi$
$877$		−	16091.9i		−	0.619595i	0.950803	−	0.309798i	$-0.100261\pi$
$878$		−	1534.38i		−	0.0589783i
$879$	6359.32			0.244021
$880$	−410.693	−	2046.76i	−0.0157323	−	0.0784048i
$881$	6546.20			0.250337			0.125169	−	0.992135i	$-0.460053\pi$
$881$	6546.20			0.250337			0.125169	+	0.992135i	$0.460053\pi$
$882$		−	5277.68i		−	0.201484i
$883$		−	24904.3i		−	0.949146i	−0.880216	−	0.474573i	$-0.842603\pi$
$883$		−	24904.3i		−	0.949146i	0.880216	−	0.474573i	$-0.157397\pi$
$884$	−37879.1			−1.44119
$885$	26206.3	−	5258.43i	0.995385	−	0.199729i
$886$	−23330.5			−0.884656
$887$		−	6174.42i		−	0.233728i	−0.993148	−	0.116864i	$-0.962716\pi$
$887$		−	6174.42i		−	0.233728i	0.993148	−	0.116864i	$-0.0372842\pi$
$888$		−	6491.21i		−	0.245305i
$889$	16558.5			0.624695
$890$	3647.00	−	731.789i	0.137357	−	0.0275614i
$891$	−945.254			−0.0355412
$892$			18324.7i			0.687845i
$893$		−	16843.8i		−	0.631194i
$894$	−11581.0			−0.433251
$895$	10160.3	+	50635.6i	0.379465	+	1.89113i
$896$	903.243			0.0336777
$897$		−	8144.99i		−	0.303181i
$898$		−	1565.18i		−	0.0581635i
$899$	749.091			0.0277904
$900$	−4151.66	+	1736.00i	−0.153765	+	0.0642964i
$901$	−51537.8			−1.90563
$902$		−	1503.50i		−	0.0555000i
$903$		−	6323.40i		−	0.233034i
$904$	13665.5			0.502774
$905$	3234.51	+	16119.8i	0.118805	+	0.592087i
$906$	−1813.08			−0.0664850
$907$			25549.9i			0.935361i	0.883898	+	0.467680i	$0.154910\pi$
$907$			25549.9i			0.935361i	−0.883898	+	0.467680i	$0.845090\pi$
$908$		−	16261.2i		−	0.594324i
$909$	8775.91			0.320219
$910$	10984.7	−	2204.15i	0.400155	−	0.0802931i
$911$	−7410.76			−0.269516			−0.134758	−	0.990879i	$-0.543026\pi$
$911$	−7410.76			−0.269516			−0.134758	+	0.990879i	$0.543026\pi$
$912$			4861.32i			0.176507i
$913$		−	9650.46i		−	0.349818i
$914$	−2660.35			−0.0962765
$915$	−22081.2	+	4430.70i	−0.797793	+	0.160081i
$916$	−13724.0			−0.495036
$917$		−	13915.2i		−	0.501113i
$918$			7201.98i			0.258933i
$919$	−28213.9			−1.01272			−0.506360	−	0.862322i	$-0.669009\pi$
$919$	−28213.9			−1.01272			−0.506360	+	0.862322i	$0.669009\pi$
$920$	−672.840	−	3353.21i	−0.0241118	−	0.120165i
$921$	9248.14			0.330876
$922$			30359.7i			1.08443i
$923$			1352.46i			0.0482305i
$924$	988.188			0.0351829
$925$	−13042.5	−	31191.3i	−0.463606	−	1.10872i
$926$	21208.4			0.752647
$927$			13507.3i			0.478574i
$928$		−	773.255i		−	0.0273527i
$929$	−27026.8			−0.954489			−0.477244	−	0.878771i	$-0.658364\pi$
$929$	−27026.8			−0.954489			−0.477244	+	0.878771i	$0.658364\pi$
$930$	−409.117	−	2038.90i	−0.0144252	−	0.0718906i
$931$	−29695.0			−1.04534
$932$			8662.40i			0.304449i
$933$		−	16714.4i		−	0.586502i
$934$	11759.9			0.411985
$935$	−17061.0	+	3423.39i	−0.596744	+	0.119740i
$936$	−5112.27			−0.178526
$937$			26553.9i			0.925804i	0.886409	+	0.462902i	$0.153192\pi$
$937$			26553.9i			0.925804i	−0.886409	+	0.462902i	$0.846808\pi$
$938$			7418.79i			0.258243i
$939$	799.407			0.0277824
$940$	7292.40	−	1463.26i	0.253034	−	0.0507726i
$941$	−27153.6			−0.940682			−0.470341	−	0.882485i	$-0.655869\pi$
$941$	−27153.6			−0.940682			−0.470341	+	0.882485i	$0.655869\pi$
$942$		−	1511.86i		−	0.0522919i
$943$		−	2463.18i		−	0.0850608i
$944$	12750.3			0.439605
$945$	−419.076	−	2088.54i	−0.0144260	−	0.0718943i
$946$	−6971.52			−0.239602
$947$		−	31212.6i		−	1.07104i	−0.844524	−	0.535518i	$-0.820116\pi$
$947$		−	31212.6i		−	1.07104i	0.844524	−	0.535518i	$-0.179884\pi$
$948$		−	9601.68i		−	0.328954i
$949$	51336.2			1.75600
$950$	9767.67	+	23359.5i	0.333584	+	0.797769i
$951$	22019.2			0.750812
$952$		−	7529.10i		−	0.256323i
$953$		−	44064.7i		−	1.49779i	−0.662688	−	0.748895i	$-0.730585\pi$
$953$		−	44064.7i		−	1.49779i	0.662688	−	0.748895i	$-0.269415\pi$
$954$	−6955.68			−0.236057
$955$	−3209.71	−	15996.1i	−0.108758	−	0.542013i
$956$	−2532.24			−0.0856680
$957$		−	845.975i		−	0.0285752i
$958$		−	29622.4i		−	0.999014i
$959$	7657.71			0.257852
$960$	−2104.67	+	422.314i	−0.0707584	+	0.0141980i
$961$	961.000			0.0322581
$962$		−	38408.4i		−	1.28725i
$963$			7995.32i			0.267545i
$964$	19125.4			0.638990
$965$	−23722.8	+	4760.10i	−0.791361	+	0.158791i
$966$	1618.95			0.0539222
$967$			451.200i			0.0150048i	0.999972	+	0.00750238i	$0.00238810\pi$
$967$			451.200i			0.0150048i	−0.999972	+	0.00750238i	$0.997612\pi$
$968$			9558.53i			0.317379i
$969$	40522.2			1.34341
$970$	6995.20	+	34861.8i	0.231549	+	1.15396i
$971$	17309.0			0.572063			0.286032	−	0.958220i	$-0.407664\pi$
$971$	17309.0			0.572063			0.286032	+	0.958220i	$0.407664\pi$
$972$			972.000i			0.0320750i
$973$		−	7949.31i		−	0.261915i
$974$	−9984.58			−0.328467
$975$	−24565.3	+	10271.9i	−0.806892	+	0.337399i
$976$	−10743.3			−0.352340
$977$		−	19883.0i		−	0.651090i	−0.945527	−	0.325545i	$-0.894452\pi$
$977$		−	19883.0i		−	0.651090i	0.945527	−	0.325545i	$-0.105548\pi$
$978$		−	13434.0i		−	0.439235i
$979$	1941.27			0.0633740
$980$	−2579.67	−	12856.2i	−0.0840864	−	0.419059i
$981$	−19355.8			−0.629951
$982$		−	16964.1i		−	0.551269i
$983$			22574.3i			0.732461i	0.930524	+	0.366231i	$0.119352\pi$
$983$			22574.3i			0.732461i	−0.930524	+	0.366231i	$0.880648\pi$
$984$	−1546.04			−0.0500873
$985$	9764.72	−	1959.34i	0.315868	−	0.0633805i
$986$	−6445.57			−0.208183
$987$			3520.81i			0.113545i
$988$			28764.4i			0.926231i
$989$	−11421.5			−0.367221
$990$	−2302.60	+	462.030i	−0.0739208	+	0.0148326i
$991$	41411.9			1.32744			0.663720	−	0.747981i	$-0.268977\pi$
$991$	41411.9			1.32744			0.663720	+	0.747981i	$0.268977\pi$
$992$		−	992.000i		−	0.0317500i
$993$			18278.5i			0.584139i
$994$	−268.823			−0.00857803
$995$	12006.5	+	59836.7i	0.382546	+	1.90648i
$996$	−9923.52			−0.315702
$997$		−	61836.0i		−	1.96426i	−0.188209	−	0.982129i	$-0.560268\pi$
$997$		−	61836.0i		−	1.96426i	0.188209	−	0.982129i	$-0.439732\pi$
$998$			2611.23i			0.0828227i
$999$	−7302.61			−0.231276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.d.c.559.16	yes	20
5.4	even	2	inner	930.4.d.c.559.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.d.c.559.6	✓	20	5.4	even	2	inner
930.4.d.c.559.16	yes	20	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(2.19955 + 10.9618i) q^{5} +6.00000 q^{6} +7.05659i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(2.19955 + 10.9618i) q^{5} +6.00000 q^{6} +7.05659i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-21.9237 + 4.39910i) q^{10} -11.6698 q^{11} +12.0000i q^{12} +71.0038i q^{13} -14.1132 q^{14} +(32.8855 - 6.59865i) q^{15} +16.0000 q^{16} -133.370i q^{17} -18.0000i q^{18} -101.278 q^{19} +(-8.79821 - 43.8474i) q^{20} +21.1698 q^{21} -23.3396i q^{22} -38.2373i q^{23} -24.0000 q^{24} +(-115.324 + 48.2223i) q^{25} -142.008 q^{26} +27.0000i q^{27} -28.2264i q^{28} -24.1642 q^{29} +(13.1973 + 65.7711i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +35.0094i q^{33} +266.740 q^{34} +(-77.3532 + 15.5213i) q^{35} +36.0000 q^{36} +270.467i q^{37} -202.555i q^{38} +213.011 q^{39} +(87.6947 - 17.5964i) q^{40} +64.4183 q^{41} +42.3395i q^{42} -298.699i q^{43} +46.6792 q^{44} +(-19.7960 - 98.6566i) q^{45} +76.4747 q^{46} +166.313i q^{47} -48.0000i q^{48} +293.205 q^{49} +(-96.4445 - 230.648i) q^{50} -400.110 q^{51} -284.015i q^{52} -386.427i q^{53} -54.0000 q^{54} +(-25.6683 - 127.922i) q^{55} +56.4527 q^{56} +303.833i q^{57} -48.3284i q^{58} +796.895 q^{59} +(-131.542 + 26.3946i) q^{60} -671.455 q^{61} -62.0000i q^{62} -63.5093i q^{63} -64.0000 q^{64} +(-778.332 + 156.177i) q^{65} -70.0188 q^{66} -525.664i q^{67} +533.480i q^{68} -114.712 q^{69} +(-31.0427 - 154.706i) q^{70} +19.0477 q^{71} +72.0000i q^{72} -723.007i q^{73} -540.934 q^{74} +(144.667 + 345.972i) q^{75} +405.110 q^{76} -82.3490i q^{77} +426.023i q^{78} -800.140 q^{79} +(35.1928 + 175.389i) q^{80} +81.0000 q^{81} +128.837i q^{82} +826.960i q^{83} -84.6791 q^{84} +(1461.98 - 293.354i) q^{85} +597.399 q^{86} +72.4927i q^{87} +93.3584i q^{88} -166.350 q^{89} +(197.313 - 39.5919i) q^{90} -501.045 q^{91} +152.949i q^{92} +93.0000i q^{93} -332.626 q^{94} +(-222.765 - 1110.19i) q^{95} +96.0000 q^{96} -1590.14i q^{97} +586.409i q^{98} +105.028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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