LMFDB - Embedded newform 225.4.h.a.136.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.3
Character	$\chi$	$=$	225.136
Dual form			225.4.h.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +O(q^{10})$	\(q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +(9.34059 - 5.17797i) q^{10} +(-36.1845 + 26.2896i) q^{11} +(5.77338 + 4.19460i) q^{13} +(-9.64726 + 7.00914i) q^{14} +(-34.7339 - 25.2356i) q^{16} +(-8.19254 - 25.2140i) q^{17} +(-14.3353 - 44.1196i) q^{19} +(33.4864 - 71.8179i) q^{20} +(13.2025 - 40.6331i) q^{22} +(117.674 - 85.4955i) q^{23} +(121.289 + 30.2324i) q^{25} -6.81679 q^{26} +(-27.3411 + 84.1473i) q^{28} +(65.9299 - 202.911i) q^{29} +(-45.7598 - 140.834i) q^{31} +156.308 q^{32} +(20.4881 + 14.8855i) q^{34} +(-138.531 - 17.0049i) q^{35} +(-325.478 - 236.473i) q^{37} +(35.8502 + 26.0467i) q^{38} +(30.7505 + 158.170i) q^{40} +(189.031 + 137.339i) q^{41} +87.5080 q^{43} +(-97.9587 - 301.486i) q^{44} +(-42.9353 + 132.141i) q^{46} +(23.4804 - 72.2653i) q^{47} -187.161 q^{49} +(-110.706 + 44.7366i) q^{50} +(-40.9190 + 29.7294i) q^{52} +(-51.6149 + 158.854i) q^{53} +(437.353 - 242.447i) q^{55} +(-55.5964 - 171.108i) q^{56} +(62.9782 + 193.827i) q^{58} +(-481.431 - 349.780i) q^{59} +(700.442 - 508.901i) q^{61} +(114.437 + 83.1435i) q^{62} +(157.077 - 114.123i) q^{64} +(-58.3536 - 54.4121i) q^{65} +(-125.554 - 386.416i) q^{67} +187.902 q^{68} +(116.604 - 64.6395i) q^{70} +(-162.592 + 500.406i) q^{71} +(-810.387 + 588.781i) q^{73} +384.301 q^{74} +328.792 q^{76} +(-451.712 + 328.188i) q^{77} +(-41.3945 + 127.399i) q^{79} +(351.068 + 327.355i) q^{80} -223.195 q^{82} +(-159.651 - 491.355i) q^{83} +(56.5668 + 290.961i) q^{85} +(-67.6259 + 49.1331i) q^{86} +(521.494 + 378.888i) q^{88} +(-494.065 + 358.959i) q^{89} +(72.0723 + 52.3636i) q^{91} +(318.568 + 980.452i) q^{92} +(22.4292 + 69.0300i) q^{94} +(98.9809 + 509.125i) q^{95} +(-506.654 + 1559.32i) q^{97} +(144.637 - 105.085i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.772797	+	0.561470i	−0.273225	+	0.198510i	−0.715957	−	0.698144i	$-0.754009\pi$
$2$	−0.772797	+	0.561470i	−0.273225	+	0.198510i	0.442732	+	0.896654i	$0.354009\pi$
$3$		0			0
$3$		0			0
$4$	−2.19017	+	6.74065i	−0.273771	+	0.842581i
$5$	−11.0970	−	1.36218i	−0.992550	−	0.121837i
$5$	−11.0970	−	1.36218i	−0.992550	−	0.121837i
$6$		0			0
$7$	12.4836			0.674049			0.337024	−	0.941496i	$-0.390580\pi$
$7$	12.4836			0.674049			0.337024	+	0.941496i	$0.390580\pi$
$8$	−4.45357	−	13.7067i	−0.196822	−	0.605756i
$9$		0			0
$10$	9.34059	−	5.17797i	0.295375	−	0.163742i
$11$	−36.1845	+	26.2896i	−0.991823	+	0.720601i	−0.960319	−	0.278902i	$-0.910029\pi$
$11$	−36.1845	+	26.2896i	−0.991823	+	0.720601i	−0.0315032	+	0.999504i	$0.510029\pi$
$12$		0			0
$13$	5.77338	+	4.19460i	0.123173	+	0.0894903i	0.647666	−	0.761924i	$-0.275745\pi$
$13$	5.77338	+	4.19460i	0.123173	+	0.0894903i	−0.524493	+	0.851415i	$0.675745\pi$
$14$	−9.64726	+	7.00914i	−0.184167	+	0.133805i
$15$		0			0
$16$	−34.7339	−	25.2356i	−0.542717	−	0.394307i
$17$	−8.19254	−	25.2140i	−0.116881	−	0.359724i	0.875453	−	0.483302i	$-0.160563\pi$
$17$	−8.19254	−	25.2140i	−0.116881	−	0.359724i	−0.992335	+	0.123579i	$0.960563\pi$
$18$		0			0
$19$	−14.3353	−	44.1196i	−0.173092	−	0.532723i	0.826449	−	0.563012i	$-0.190357\pi$
$19$	−14.3353	−	44.1196i	−0.173092	−	0.532723i	−0.999541	+	0.0302886i	$0.990357\pi$
$20$	33.4864	−	71.8179i	0.374389	−	0.802948i
$21$		0			0
$22$	13.2025	−	40.6331i	0.127945	−	0.393773i
$23$	117.674	−	85.4955i	1.06682	−	0.775089i	0.0914808	−	0.995807i	$-0.470840\pi$
$23$	117.674	−	85.4955i	1.06682	−	0.775089i	0.975338	+	0.220718i	$0.0708400\pi$
$24$		0			0
$25$	121.289	+	30.2324i	0.970311	+	0.241859i
$26$	−6.81679			−0.0514186
$27$		0			0
$28$	−27.3411	+	84.1473i	−0.184535	+	0.567941i
$29$	65.9299	−	202.911i	0.422168	−	1.29930i	−0.483512	−	0.875338i	$-0.660639\pi$
$29$	65.9299	−	202.911i	0.422168	−	1.29930i	0.905680	−	0.423962i	$-0.139361\pi$
$30$		0			0
$31$	−45.7598	−	140.834i	−0.265120	−	0.815954i	−0.991666	−	0.128837i	$-0.958876\pi$
$31$	−45.7598	−	140.834i	−0.265120	−	0.815954i	0.726546	−	0.687118i	$-0.241124\pi$
$32$	156.308			0.863487
$33$		0			0
$34$	20.4881	+	14.8855i	0.103344	+	0.0750835i
$35$	−138.531	−	17.0049i	−0.669027	−	0.0821243i
$36$		0			0
$37$	−325.478	−	236.473i	−1.44617	−	1.05070i	−0.986708	−	0.162503i	$-0.948043\pi$
$37$	−325.478	−	236.473i	−1.44617	−	1.05070i	−0.459459	−	0.888199i	$-0.651957\pi$
$38$	35.8502	+	26.0467i	0.153044	+	0.111193i
$39$		0			0
$40$	30.7505	+	158.170i	0.121552	+	0.625223i
$41$	189.031	+	137.339i	0.720043	+	0.523142i	0.886398	−	0.462924i	$-0.153200\pi$
$41$	189.031	+	137.339i	0.720043	+	0.523142i	−0.166355	+	0.986066i	$0.553200\pi$
$42$		0			0
$43$	87.5080			0.310345			0.155173	−	0.987887i	$-0.450407\pi$
$43$	87.5080			0.310345			0.155173	+	0.987887i	$0.450407\pi$
$44$	−97.9587	−	301.486i	−0.335633	−	1.03297i
$45$		0			0
$46$	−42.9353	+	132.141i	−0.137619	+	0.423548i
$47$	23.4804	−	72.2653i	0.0728717	−	0.224276i	−0.907986	−	0.418999i	$-0.862381\pi$
$47$	23.4804	−	72.2653i	0.0728717	−	0.224276i	0.980858	+	0.194723i	$0.0623809\pi$
$48$		0			0
$49$	−187.161			−0.545658
$50$	−110.706	+	44.7366i	−0.313125	+	0.126534i
$51$		0			0
$52$	−40.9190	+	29.7294i	−0.109124	+	0.0792832i
$53$	−51.6149	+	158.854i	−0.133771	+	0.411704i	−0.995397	−	0.0958396i	$-0.969446\pi$
$53$	−51.6149	+	158.854i	−0.133771	+	0.411704i	0.861626	+	0.507544i	$0.169446\pi$
$54$		0			0
$55$	437.353	−	242.447i	1.07223	−	0.594392i
$56$	−55.5964	−	171.108i	−0.132668	−	0.408309i
$57$		0			0
$58$	62.9782	+	193.827i	0.142577	+	0.438806i
$59$	−481.431	−	349.780i	−1.06232	−	0.771822i	−0.0878053	−	0.996138i	$-0.527985\pi$
$59$	−481.431	−	349.780i	−1.06232	−	0.771822i	−0.974517	+	0.224316i	$0.927985\pi$
$60$		0			0
$61$	700.442	−	508.901i	1.47020	−	1.06817i	0.489649	−	0.871920i	$-0.337125\pi$
$61$	700.442	−	508.901i	1.47020	−	1.06817i	0.980555	−	0.196246i	$-0.0628752\pi$
$62$	114.437	+	83.1435i	0.234412	+	0.170310i
$63$		0			0
$64$	157.077	−	114.123i	0.306791	−	0.222896i
$65$	−58.3536	−	54.4121i	−0.111352	−	0.103831i
$66$		0			0
$67$	−125.554	−	386.416i	−0.228939	−	0.704601i	−0.997868	−	0.0652671i	$-0.979210\pi$
$67$	−125.554	−	386.416i	−0.228939	−	0.704601i	0.768929	−	0.639334i	$-0.220790\pi$
$68$	187.902			0.335095
$69$		0			0
$70$	116.604	−	64.6395i	0.199097	−	0.110370i
$71$	−162.592	+	500.406i	−0.271776	+	0.836441i	0.718278	+	0.695756i	$0.244930\pi$
$71$	−162.592	+	500.406i	−0.271776	+	0.836441i	−0.990054	+	0.140685i	$0.955070\pi$
$72$		0			0
$73$	−810.387	+	588.781i	−1.29930	+	0.943994i	−0.999948	−	0.0101504i	$-0.996769\pi$
$73$	−810.387	+	588.781i	−1.29930	+	0.943994i	−0.299347	+	0.954144i	$0.596769\pi$
$74$	384.301			0.603704
$75$		0			0
$76$	328.792			0.496250
$77$	−451.712	+	328.188i	−0.668537	+	0.485720i
$78$		0			0
$79$	−41.3945	+	127.399i	−0.0589525	+	0.181437i	−0.976196	−	0.216889i	$-0.930409\pi$
$79$	−41.3945	+	127.399i	−0.0589525	+	0.181437i	0.917244	+	0.398327i	$0.130409\pi$
$80$	351.068	+	327.355i	0.490632	+	0.457493i
$81$		0			0
$82$	−223.195			−0.300582
$83$	−159.651	−	491.355i	−0.211132	−	0.649798i	−0.999406	−	0.0344730i	$-0.989025\pi$
$83$	−159.651	−	491.355i	−0.211132	−	0.649798i	0.788273	−	0.615325i	$-0.210975\pi$
$84$		0			0
$85$	56.5668	+	290.961i	0.0721828	+	0.371284i
$86$	−67.6259	+	49.1331i	−0.0847941	+	0.0616065i
$87$		0			0
$88$	521.494	+	378.888i	0.631721	+	0.458972i
$89$	−494.065	+	358.959i	−0.588436	+	0.427524i	−0.841755	−	0.539859i	$-0.818478\pi$
$89$	−494.065	+	358.959i	−0.588436	+	0.427524i	0.253320	+	0.967383i	$0.418478\pi$
$90$		0			0
$91$	72.0723	+	52.3636i	0.0830245	+	0.0603208i
$92$	318.568	+	980.452i	0.361011	+	1.11108i
$93$		0			0
$94$	22.4292	+	69.0300i	0.0246106	+	0.0757436i
$95$	98.9809	+	509.125i	0.106897	+	0.549843i
$96$		0			0
$97$	−506.654	+	1559.32i	−0.530339	+	1.63222i	0.223171	+	0.974779i	$0.428359\pi$
$97$	−506.654	+	1559.32i	−0.530339	+	1.63222i	−0.753510	+	0.657437i	$0.771641\pi$
$98$	144.637	−	105.085i	0.149088	−	0.108318i
$99$		0			0
$100$	−469.429	+	751.352i	−0.469429	+	0.751352i
$101$	433.248			0.426830			0.213415	−	0.976962i	$-0.431541\pi$
$101$	433.248			0.426830			0.213415	+	0.976962i	$0.431541\pi$
$102$		0			0
$103$	25.1306	−	77.3441i	0.0240407	−	0.0739897i	−0.938316	−	0.345778i	$-0.887615\pi$
$103$	25.1306	−	77.3441i	0.0240407	−	0.0739897i	0.962357	+	0.271788i	$0.0876150\pi$
$104$	31.7820	−	97.8148i	0.0299661	−	0.0922263i
$105$		0			0
$106$	−49.3041	−	151.742i	−0.0451777	−	0.139043i
$107$	−391.773			−0.353964			−0.176982	−	0.984214i	$-0.556633\pi$
$107$	−391.773			−0.353964			−0.176982	+	0.984214i	$0.556633\pi$
$108$		0			0
$109$	−1469.11	−	1067.37i	−1.29097	−	0.937943i	−0.291143	−	0.956679i	$-0.594036\pi$
$109$	−1469.11	−	1067.37i	−1.29097	−	0.937943i	−0.999824	+	0.0187366i	$0.994036\pi$
$110$	−201.858	+	432.923i	−0.174968	+	0.375251i
$111$		0			0
$112$	−433.603	−	315.031i	−0.365818	−	0.265782i
$113$	879.567	+	639.043i	0.732236	+	0.532001i	0.890270	−	0.455433i	$-0.150515\pi$
$113$	879.567	+	639.043i	0.732236	+	0.532001i	−0.158034	+	0.987434i	$0.550515\pi$
$114$		0			0
$115$	−1422.30	+	788.454i	−1.15331	+	0.639336i
$116$	1223.36	+	888.820i	0.979188	+	0.711422i
$117$		0			0
$118$	568.440			0.443467
$119$	−102.272	−	314.761i	−0.0787837	−	0.242471i
$120$		0			0
$121$	206.876	−	636.699i	0.155429	−	0.478361i
$122$	−255.567	+	786.555i	−0.189655	+	0.583699i
$123$		0			0
$124$	1049.54			0.760089
$125$	−1304.77	−	500.708i	−0.933615	−	0.358278i
$126$		0			0
$127$	−705.031	+	512.235i	−0.492609	+	0.357902i	−0.806187	−	0.591661i	$-0.798472\pi$
$127$	−705.031	+	512.235i	−0.492609	+	0.357902i	0.313578	+	0.949563i	$0.398472\pi$
$128$	−443.726	+	1365.65i	−0.306408	+	0.943027i
$129$		0			0
$130$	75.6463	+	9.28572i	0.0510355	+	0.00626470i
$131$	−527.849	−	1624.55i	−0.352049	−	1.08349i	−0.957701	−	0.287765i	$-0.907088\pi$
$131$	−527.849	−	1624.55i	−0.352049	−	1.08349i	0.605652	−	0.795729i	$-0.292912\pi$
$132$		0			0
$133$	−178.956	−	550.770i	−0.116673	−	0.359081i
$134$	313.989	+	228.127i	0.202422	+	0.147068i
$135$		0			0
$136$	−309.115	+	224.585i	−0.194900	+	0.141603i
$137$	−1943.14	−	1411.78i	−1.21178	−	0.880409i	−0.216389	−	0.976307i	$-0.569428\pi$
$137$	−1943.14	−	1411.78i	−1.21178	−	0.880409i	−0.995391	+	0.0958978i	$0.969428\pi$
$138$		0			0
$139$	1749.05	−	1270.76i	1.06728	−	0.775427i	0.0918613	−	0.995772i	$-0.470718\pi$
$139$	1749.05	−	1270.76i	1.06728	−	0.775427i	0.975422	+	0.220345i	$0.0707184\pi$
$140$	418.029	−	896.542i	0.252357	−	0.541226i
$141$		0			0
$142$	−155.313	−	478.003i	−0.0917855	−	0.282487i
$143$	−319.181			−0.186652
$144$		0			0
$145$	−1008.03	+	2161.91i	−0.577326	+	1.23818i
$146$	295.682	−	910.016i	0.167608	−	0.515846i
$147$		0			0
$148$	2306.83	−	1676.01i	1.28122	−	0.930861i
$149$	1527.70			0.839959			0.419980	−	0.907534i	$-0.362037\pi$
$149$	1527.70			0.839959			0.419980	+	0.907534i	$0.362037\pi$
$150$		0			0
$151$	2584.71			1.39299			0.696493	−	0.717564i	$-0.254743\pi$
$151$	2584.71			1.39299			0.696493	+	0.717564i	$0.254743\pi$
$152$	−540.891	+	392.980i	−0.288632	+	0.209703i
$153$		0			0
$154$	164.814	−	507.245i	0.0862409	−	0.265422i
$155$	315.957	+	1625.18i	0.163731	+	0.842177i
$156$		0			0
$157$	−692.965			−0.352259			−0.176129	−	0.984367i	$-0.556358\pi$
$157$	−692.965			−0.352259			−0.176129	+	0.984367i	$0.556358\pi$
$158$	−39.5413	−	121.696i	−0.0199097	−	0.0612759i
$159$		0			0
$160$	−1734.56	−	212.920i	−0.857054	−	0.105205i
$161$	1469.00	−	1067.29i	0.719088	−	0.522448i
$162$		0			0
$163$	2929.06	+	2128.09i	1.40750	+	1.02261i	0.993680	+	0.112246i	$0.0358046\pi$
$163$	2929.06	+	2128.09i	1.40750	+	1.02261i	0.413817	+	0.910360i	$0.364195\pi$
$164$	−1339.77	+	973.398i	−0.637916	+	0.463473i
$165$		0			0
$166$	399.259	+	290.079i	0.186678	+	0.135629i
$167$	−480.709	−	1479.47i	−0.222745	−	0.685538i	−0.998513	−	0.0545197i	$-0.982637\pi$
$167$	−480.709	−	1479.47i	−0.222745	−	0.685538i	0.775768	−	0.631018i	$-0.217363\pi$
$168$		0			0
$169$	−663.173	−	2041.04i	−0.301854	−	0.929011i
$170$	−207.081	−	193.093i	−0.0934257	−	0.0871152i
$171$		0			0
$172$	−191.657	+	589.861i	−0.0849636	+	0.261491i
$173$	−1760.35	+	1278.97i	−0.773622	+	0.562070i	−0.903058	−	0.429518i	$-0.858683\pi$
$173$	−1760.35	+	1278.97i	−0.773622	+	0.562070i	0.129436	+	0.991588i	$0.458683\pi$
$174$		0			0
$175$	1514.12	+	377.408i	0.654037	+	0.163025i
$176$	1920.27			0.822417
$177$		0			0
$178$	180.267	−	554.805i	0.0759079	−	0.233620i
$179$	576.453	−	1774.14i	0.240705	−	0.740813i	−0.755609	−	0.655023i	$-0.772659\pi$
$179$	576.453	−	1774.14i	0.240705	−	0.740813i	0.996313	−	0.0857896i	$-0.0273413\pi$
$180$		0			0
$181$	−79.6740	−	245.211i	−0.0327189	−	0.100698i	0.933363	−	0.358933i	$-0.116859\pi$
$181$	−79.6740	−	245.211i	−0.0327189	−	0.100698i	−0.966082	+	0.258234i	$0.916859\pi$
$182$	−85.0978			−0.0346586
$183$		0			0
$184$	−1695.93	−	1232.17i	−0.679488	−	0.493677i
$185$	3289.72	+	3067.52i	1.30738	+	1.21907i
$186$		0			0
$187$	959.311	+	696.980i	0.375143	+	0.272557i
$188$	435.689	+	316.546i	0.169021	+	0.122801i
$189$		0			0
$190$	−362.351	−	337.876i	−0.138356	−	0.129011i
$191$	−3204.41	−	2328.14i	−1.21394	−	0.881982i	−0.218361	−	0.975868i	$-0.570071\pi$
$191$	−3204.41	−	2328.14i	−1.21394	−	0.881982i	−0.995583	+	0.0938864i	$0.970071\pi$
$192$		0			0
$193$	1253.72			0.467590			0.233795	−	0.972286i	$-0.424886\pi$
$193$	1253.72			0.467590			0.233795	+	0.972286i	$0.424886\pi$
$194$	−483.971	−	1489.51i	−0.179109	−	0.551240i
$195$		0			0
$196$	409.914	−	1261.58i	0.149385	−	0.459761i
$197$	1563.58	−	4812.19i	0.565483	−	1.74038i	−0.101027	−	0.994884i	$-0.532213\pi$
$197$	1563.58	−	4812.19i	0.565483	−	1.74038i	0.666511	−	0.745495i	$-0.267787\pi$
$198$		0			0
$199$	−5323.91			−1.89649			−0.948246	−	0.317536i	$-0.897145\pi$
$199$	−5323.91			−1.89649			−0.948246	+	0.317536i	$0.897145\pi$
$200$	−125.783	−	1797.11i	−0.0444709	−	0.635375i
$201$		0			0
$202$	−334.813	+	243.256i	−0.116621	+	0.0847299i
$203$	823.040	−	2533.06i	0.284562	−	0.875791i
$204$		0			0
$205$	−1910.61	−	1781.56i	−0.650940	−	0.606972i
$206$	24.0055	+	73.8814i	0.00811915	+	0.0249882i
$207$		0			0
$208$	−94.6783	−	291.390i	−0.0315613	−	0.0971358i
$209$	1678.61	+	1219.58i	0.555558	+	0.403636i
$210$		0			0
$211$	832.974	−	605.191i	0.271774	−	0.197455i	−0.443548	−	0.896251i	$-0.646280\pi$
$211$	832.974	−	605.191i	0.271774	−	0.197455i	0.715321	+	0.698796i	$0.246280\pi$
$212$	−957.736	−	695.836i	−0.310271	−	0.225425i
$213$		0			0
$214$	302.761	−	219.969i	0.0967118	−	0.0702653i
$215$	−971.080	−	119.202i	−0.308033	−	0.0378116i
$216$		0			0
$217$	−571.245	−	1758.11i	−0.178703	−	0.549993i
$218$	1734.62			0.538915
$219$		0			0
$220$	676.373	+	3479.04i	0.207278	+	1.06617i
$221$	58.4643	−	179.935i	0.0177952	−	0.0547679i
$222$		0			0
$223$	−1007.29	+	731.839i	−0.302480	+	0.219765i	−0.728663	−	0.684872i	$-0.759858\pi$
$223$	−1007.29	+	731.839i	−0.302480	+	0.219765i	0.426183	+	0.904637i	$0.359858\pi$
$224$	1951.28			0.582032
$225$		0			0
$226$	−1038.53			−0.305673
$227$	−3720.10	+	2702.81i	−1.08772	+	0.790272i	−0.979012	−	0.203803i	$-0.934670\pi$
$227$	−3720.10	+	2702.81i	−1.08772	+	0.790272i	−0.108704	+	0.994074i	$0.534670\pi$
$228$		0			0
$229$	1963.73	−	6043.74i	0.566668	−	1.74402i	−0.0962760	−	0.995355i	$-0.530693\pi$
$229$	1963.73	−	6043.74i	0.566668	−	1.74402i	0.662944	−	0.748669i	$-0.269307\pi$
$230$	656.456	−	1407.89i	0.188198	−	0.403625i
$231$		0			0
$232$	−3074.87			−0.870150
$233$	−196.524	−	604.840i	−0.0552564	−	0.170062i	0.919620	−	0.392810i	$-0.128497\pi$
$233$	−196.524	−	604.840i	−0.0552564	−	0.170062i	−0.974876	+	0.222749i	$0.928497\pi$
$234$		0			0
$235$	−359.002	+	769.947i	−0.0996541	+	0.213727i
$236$	3412.16	−	2479.08i	0.941156	−	0.683790i
$237$		0			0
$238$	255.764	+	185.824i	0.0696586	+	0.0506099i
$239$	−5224.68	+	3795.95i	−1.41404	+	1.02736i	−0.421326	+	0.906909i	$0.638435\pi$
$239$	−5224.68	+	3795.95i	−1.41404	+	1.02736i	−0.992719	+	0.120454i	$0.961565\pi$
$240$		0			0
$241$	−412.394	−	299.622i	−0.110227	−	0.0800844i	0.531306	−	0.847180i	$-0.321701\pi$
$241$	−412.394	−	299.622i	−0.110227	−	0.0800844i	−0.641533	+	0.767095i	$0.721701\pi$
$242$	197.614	+	608.194i	0.0524922	+	0.161554i
$243$		0			0
$244$	1896.24	+	5836.01i	0.497517	+	1.53120i
$245$	2076.93	+	254.947i	0.541593	+	0.0664816i
$246$		0			0
$247$	102.301	−	314.850i	0.0263533	−	0.0811070i
$248$	−1726.58	+	1254.43i	−0.442088	+	0.321195i
$249$		0			0
$250$	1289.45	−	345.641i	0.326209	−	0.0874411i
$251$	−2645.82			−0.665349			−0.332674	−	0.943042i	$-0.607951\pi$
$251$	−2645.82			−0.665349			−0.332674	+	0.943042i	$0.607951\pi$
$252$		0			0
$253$	−2010.35	+	6187.23i	−0.499565	+	1.53750i
$254$	257.241	−	791.707i	0.0635463	−	0.195575i
$255$		0			0
$256$	56.1236	+	172.731i	0.0137020	+	0.0421706i
$257$	3975.12			0.964829			0.482415	−	0.875943i	$-0.339760\pi$
$257$	3975.12			0.964829			0.482415	+	0.875943i	$0.339760\pi$
$258$		0			0
$259$	−4063.12	−	2952.03i	−0.974787	−	0.708224i
$260$	494.577	−	274.169i	0.117971	−	0.0653972i
$261$		0			0
$262$	1320.06	+	959.078i	0.311273	+	0.226153i
$263$	3899.67	+	2833.27i	0.914311	+	0.664285i	0.942101	−	0.335328i	$-0.108847\pi$
$263$	3899.67	+	2833.27i	0.914311	+	0.664285i	−0.0277908	+	0.999614i	$0.508847\pi$
$264$		0			0
$265$	789.162	−	1692.50i	0.182935	−	0.392339i
$266$	447.538	+	325.155i	0.103159	+	0.0749494i
$267$		0			0
$268$	2879.68			0.656360
$269$	−1296.72	−	3990.91i	−0.293913	−	0.904572i	−0.983584	−	0.180449i	$-0.942245\pi$
$269$	−1296.72	−	3990.91i	−0.293913	−	0.904572i	0.689671	−	0.724123i	$-0.257755\pi$
$270$		0			0
$271$	−630.388	+	1940.13i	−0.141304	+	0.434888i	−0.996517	−	0.0833877i	$-0.973426\pi$
$271$	−630.388	+	1940.13i	−0.141304	+	0.434888i	0.855213	+	0.518276i	$0.173426\pi$
$272$	−351.734	+	1082.53i	−0.0784081	+	0.241315i
$273$		0			0
$274$	2294.32			0.505858
$275$	−5183.58	+	2094.69i	−1.13666	+	0.459326i
$276$		0			0
$277$	3732.32	−	2711.69i	0.809578	−	0.588193i	−0.104130	−	0.994564i	$-0.533206\pi$
$277$	3732.32	−	2711.69i	0.809578	−	0.588193i	0.913708	+	0.406371i	$0.133206\pi$
$278$	−638.167	+	1964.08i	−0.137679	+	0.423732i
$279$		0			0
$280$	383.876	+	1974.53i	0.0819320	+	0.421431i
$281$	776.295	+	2389.19i	0.164804	+	0.507214i	0.999022	−	0.0442208i	$-0.0140805\pi$
$281$	776.295	+	2389.19i	0.164804	+	0.507214i	−0.834218	+	0.551435i	$0.814081\pi$
$282$		0			0
$283$	328.149	+	1009.94i	0.0689274	+	0.212137i	0.979587	−	0.201021i	$-0.0644259\pi$
$283$	328.149	+	1009.94i	0.0689274	+	0.212137i	−0.910660	+	0.413158i	$0.864426\pi$
$284$	−3016.96	−	2191.95i	−0.630365	−	0.457987i
$285$		0			0
$286$	246.663	−	179.211i	0.0509981	−	0.0370523i
$287$	2359.79	+	1714.48i	0.485344	+	0.352623i
$288$		0			0
$289$	3406.07	−	2474.65i	0.693277	−	0.503695i
$290$	−434.844	−	2236.70i	−0.0880515	−	0.452908i
$291$		0			0
$292$	−2193.88	−	6752.06i	−0.439681	−	1.35320i
$293$	7941.52			1.58344			0.791721	−	0.610883i	$-0.209186\pi$
$293$	7941.52			1.58344			0.791721	+	0.610883i	$0.209186\pi$
$294$		0			0
$295$	4866.00	+	4537.32i	0.960371	+	0.895503i
$296$	−1791.73	+	5514.37i	−0.351831	+	1.08283i
$297$		0			0
$298$	−1180.60	+	857.757i	−0.229498	+	0.166740i
$299$	1038.00			0.200766
$300$		0			0
$301$	1092.41			0.209188
$302$	−1997.46	+	1451.24i	−0.380599	+	0.276521i
$303$		0			0
$304$	−615.465	+	1894.21i	−0.116116	+	0.357369i
$305$	−8466.06	+	4693.17i	−1.58939	+	0.881082i
$306$		0			0
$307$	−5405.88			−1.00498			−0.502492	−	0.864582i	$-0.667583\pi$
$307$	−5405.88			−1.00498			−0.502492	+	0.864582i	$0.667583\pi$
$308$	−1222.87	−	3763.62i	−0.226233	−	0.696273i
$309$		0			0
$310$	−1156.66	−	1078.53i	−0.211916	−	0.197602i
$311$	−3742.38	+	2719.00i	−0.682350	+	0.495756i	−0.874136	−	0.485681i	$-0.838572\pi$
$311$	−3742.38	+	2719.00i	−0.682350	+	0.495756i	0.191787	+	0.981437i	$0.438572\pi$
$312$		0			0
$313$	852.150	+	619.123i	0.153886	+	0.111805i	0.662064	−	0.749447i	$-0.269681\pi$
$313$	852.150	+	619.123i	0.153886	+	0.111805i	−0.508178	+	0.861252i	$0.669681\pi$
$314$	535.522	−	389.079i	0.0962460	−	0.0699268i
$315$		0			0
$316$	−768.093	−	558.052i	−0.136736	−	0.0993446i
$317$	−837.437	−	2577.37i	−0.148376	−	0.456654i	0.849054	−	0.528306i	$-0.177173\pi$
$317$	−837.437	−	2577.37i	−0.148376	−	0.456654i	−0.997430	+	0.0716525i	$0.977173\pi$
$318$		0			0
$319$	2948.82	+	9075.53i	0.517561	+	1.59289i
$320$	−1898.55	+	1052.46i	−0.331662	+	0.183857i
$321$		0			0
$322$	−535.986	+	1649.59i	−0.0927619	+	0.285492i
$323$	−994.991	+	722.904i	−0.171402	+	0.124531i
$324$		0			0
$325$	573.433	+	683.302i	0.0978719	+	0.116624i
$326$	−3458.43			−0.587561
$327$		0			0
$328$	1040.60	−	3202.65i	0.175176	−	0.539136i
$329$	293.119	−	902.128i	0.0491191	−	0.151173i
$330$		0			0
$331$	−1355.87	−	4172.95i	−0.225153	−	0.692948i	−0.998276	−	0.0586928i	$-0.981307\pi$
$331$	−1355.87	−	4172.95i	−0.225153	−	0.692948i	0.773124	−	0.634255i	$-0.218693\pi$
$332$	3661.72			0.605309
$333$		0			0
$334$	1202.17	+	873.427i	0.196945	+	0.143089i
$335$	866.912	+	4459.11i	0.141386	+	0.727245i
$336$		0			0
$337$	3133.04	+	2276.28i	0.506431	+	0.367944i	0.811468	−	0.584397i	$-0.198669\pi$
$337$	3133.04	+	2276.28i	0.506431	+	0.367944i	−0.305037	+	0.952341i	$0.598669\pi$
$338$	1658.48	+	1204.96i	0.266892	+	0.193908i
$339$		0			0
$340$	−2085.16	−	255.957i	−0.332599	−	0.0408271i
$341$	5358.28	+	3893.01i	0.850929	+	0.618236i
$342$		0			0
$343$	−6618.29			−1.04185
$344$	−389.723	−	1199.44i	−0.0610828	−	0.187993i
$345$		0			0
$346$	642.289	−	1976.76i	0.0997968	−	0.307143i
$347$	−1787.02	+	5499.89i	−0.276462	+	0.850864i	0.712366	+	0.701808i	$0.247623\pi$
$347$	−1787.02	+	5499.89i	−0.276462	+	0.850864i	−0.988829	+	0.149056i	$0.952377\pi$
$348$		0			0
$349$	−2916.63			−0.447345			−0.223673	−	0.974664i	$-0.571805\pi$
$349$	−2916.63			−0.447345			−0.223673	+	0.974664i	$0.571805\pi$
$350$	−1382.01	+	558.471i	−0.211061	+	0.0852902i
$351$		0			0
$352$	−5655.93	+	4109.27i	−0.856426	+	0.622230i
$353$	1077.72	−	3316.87i	0.162496	−	0.500111i	−0.836347	−	0.548200i	$-0.815313\pi$
$353$	1077.72	−	3316.87i	0.162496	−	0.500111i	0.998843	+	0.0480894i	$0.0153132\pi$
$354$		0			0
$355$	2485.93	−	5331.55i	0.371661	−	0.797097i
$356$	−1337.53	−	4116.50i	−0.199127	−	0.612848i
$357$		0			0
$358$	550.646	+	1694.71i	0.0812920	+	0.250191i
$359$	8580.85	+	6234.36i	1.26150	+	0.916537i	0.998831	−	0.0483479i	$-0.0153956\pi$
$359$	8580.85	+	6234.36i	1.26150	+	0.916537i	0.262674	+	0.964885i	$0.415396\pi$
$360$		0			0
$361$	3808.01	−	2766.68i	0.555184	−	0.403365i
$362$	199.251	+	144.764i	0.0289292	+	0.0210183i
$363$		0			0
$364$	−510.815	+	371.129i	−0.0735549	+	0.0534407i
$365$	9794.93	−	5429.83i	1.40463	−	0.778658i
$366$		0			0
$367$	−829.748	−	2553.70i	−0.118018	−	0.363221i	0.874547	−	0.484941i	$-0.161159\pi$
$367$	−829.748	−	2553.70i	−0.118018	−	0.363221i	−0.992564	+	0.121720i	$0.961159\pi$
$368$	−6244.83			−0.884604
$369$		0			0
$370$	−4264.61	−	523.488i	−0.599206	−	0.0735537i
$371$	−644.338	+	1983.07i	−0.0901680	+	0.277509i
$372$		0			0
$373$	556.991	−	404.678i	0.0773187	−	0.0561754i	−0.548454	−	0.836180i	$-0.684784\pi$
$373$	556.991	−	404.678i	0.0773187	−	0.0561754i	0.625773	+	0.780005i	$0.284784\pi$
$374$	−1132.69			−0.156604
$375$		0			0
$376$	−1095.09			−0.150199
$377$	1231.77	−	894.934i	0.168274	−	0.122258i
$378$		0			0
$379$	−3780.96	+	11636.6i	−0.512440	+	1.57713i	0.275452	+	0.961315i	$0.411173\pi$
$379$	−3780.96	+	11636.6i	−0.512440	+	1.57713i	−0.787892	+	0.615814i	$0.788827\pi$
$380$	−3648.62	−	447.875i	−0.492553	−	0.0604618i
$381$		0			0
$382$	3783.54			0.506762
$383$	−587.804	−	1809.08i	−0.0784214	−	0.241356i	0.904158	−	0.427197i	$-0.140499\pi$
$383$	−587.804	−	1809.08i	−0.0784214	−	0.241356i	−0.982580	+	0.185841i	$0.940499\pi$
$384$		0			0
$385$	5459.72	−	3026.60i	0.722735	−	0.400649i
$386$	−968.872	+	703.927i	−0.127757	+	0.0928211i
$387$		0			0
$388$	−9401.17	−	6830.35i	−1.23008	−	0.893707i
$389$	152.083	−	110.495i	0.0198224	−	0.0144019i	−0.577830	−	0.816157i	$-0.696100\pi$
$389$	152.083	−	110.495i	0.0198224	−	0.0144019i	0.597652	+	0.801755i	$0.296100\pi$
$390$		0			0
$391$	−3119.74	−	2266.62i	−0.403509	−	0.293167i
$392$	833.534	+	2565.35i	0.107398	+	0.330536i
$393$		0			0
$394$	1493.58	+	4596.75i	0.190978	+	0.587769i
$395$	632.898	−	1357.37i	0.0806192	−	0.172903i
$396$		0			0
$397$	−2332.28	+	7178.01i	−0.294845	+	0.907441i	0.688428	+	0.725305i	$0.258301\pi$
$397$	−2332.28	+	7178.01i	−0.294845	+	0.907441i	−0.983273	+	0.182136i	$0.941699\pi$
$398$	4114.30	−	2989.22i	0.518169	−	0.376472i
$399$		0			0
$400$	−3449.90	−	4110.89i	−0.431238	−	0.513862i
$401$	−5396.95			−0.672097			−0.336049	−	0.941845i	$-0.609091\pi$
$401$	−5396.95			−0.672097			−0.336049	+	0.941845i	$0.609091\pi$
$402$		0			0
$403$	326.555	−	1005.03i	0.0403644	−	0.124229i
$404$	−948.887	+	2920.37i	−0.116854	+	0.359639i
$405$		0			0
$406$	786.192	+	2419.65i	0.0961036	+	0.295776i
$407$	17994.1			2.19148
$408$		0			0
$409$	3309.21	+	2404.29i	0.400074	+	0.290671i	0.769571	−	0.638561i	$-0.220470\pi$
$409$	3309.21	+	2404.29i	0.400074	+	0.290671i	−0.369497	+	0.929232i	$0.620470\pi$
$410$	2476.81	+	304.032i	0.298343	+	0.0366222i
$411$		0			0
$412$	466.309	+	338.793i	0.0557607	+	0.0405125i
$413$	−6009.97	−	4366.50i	−0.716057	−	0.520246i
$414$		0			0
$415$	1102.34	+	5670.07i	0.130390	+	0.670681i
$416$	902.424	+	655.649i	0.106358	+	0.0772737i
$417$		0			0
$418$	−1981.98			−0.231918
$419$	−878.165	−	2702.71i	−0.102389	−	0.315122i	0.886719	−	0.462308i	$-0.152979\pi$
$419$	−878.165	−	2702.71i	−0.102389	−	0.315122i	−0.989109	+	0.147186i	$0.952979\pi$
$420$		0			0
$421$	−5111.07	+	15730.3i	−0.591683	+	1.82101i	−0.0210917	+	0.999778i	$0.506714\pi$
$421$	−5111.07	+	15730.3i	−0.591683	+	1.82101i	−0.570591	+	0.821234i	$0.693286\pi$
$422$	−303.923	+	935.379i	−0.0350586	+	0.107899i
$423$		0			0
$424$	2407.24			0.275721
$425$	−231.383	−	3305.86i	−0.0264087	−	0.377313i
$426$		0			0
$427$	8744.01	−	6352.90i	0.990989	−	0.719996i
$428$	858.049	−	2640.80i	0.0969051	−	0.298243i
$429$		0			0
$430$	817.377	−	453.114i	0.0916684	−	0.0508165i
$431$	711.200	+	2188.85i	0.0794833	+	0.244625i	0.982900	−	0.184139i	$-0.0589495\pi$
$431$	711.200	+	2188.85i	0.0794833	+	0.244625i	−0.903417	+	0.428763i	$0.858950\pi$
$432$		0			0
$433$	−2335.09	−	7186.68i	−0.259163	−	0.797621i	−0.992981	−	0.118275i	$-0.962264\pi$
$433$	−2335.09	−	7186.68i	−0.259163	−	0.797621i	0.733818	−	0.679346i	$-0.237736\pi$
$434$	1428.58	+	1037.93i	0.158005	+	0.114797i
$435$		0			0
$436$	10412.4	−	7565.04i	1.14372	−	0.830963i
$437$	−5458.93	−	3966.15i	−0.597566	−	0.434157i
$438$		0			0
$439$	6737.51	−	4895.09i	0.732492	−	0.532186i	−0.157859	−	0.987462i	$-0.550459\pi$
$439$	6737.51	−	4895.09i	0.732492	−	0.532186i	0.890351	+	0.455275i	$0.150459\pi$
$440$	−5270.93	−	4914.90i	−0.571095	−	0.532520i
$441$		0			0
$442$	55.8468	+	171.879i	0.00600987	+	0.0184965i
$443$	−11675.9			−1.25223			−0.626114	−	0.779731i	$-0.715356\pi$
$443$	−11675.9			−1.25223			−0.626114	+	0.779731i	$0.715356\pi$
$444$		0			0
$445$	5971.63	−	3310.38i	0.636140	−	0.352645i
$446$	367.525	−	1131.13i	0.0390198	−	0.120091i
$447$		0			0
$448$	1960.88	−	1424.66i	0.206792	−	0.150243i
$449$	1034.94			0.108779			0.0543893	−	0.998520i	$-0.482679\pi$
$449$	1034.94			0.108779			0.0543893	+	0.998520i	$0.482679\pi$
$450$		0			0
$451$	−10450.6			−1.09113
$452$	−6233.96	+	4529.24i	−0.648719	+	0.471322i
$453$		0			0
$454$	1357.33	−	4177.44i	0.140315	−	0.431844i
$455$	−728.461	−	679.257i	−0.0750566	−	0.0699869i
$456$		0			0
$457$	15279.9			1.56403			0.782016	−	0.623259i	$-0.214192\pi$
$457$	15279.9			1.56403			0.782016	+	0.623259i	$0.214192\pi$
$458$	1875.81	+	5773.16i	0.191378	+	0.589000i
$459$		0			0
$460$	−2199.61	−	11314.1i	−0.222951	−	1.14679i
$461$	12778.7	−	9284.26i	1.29103	−	0.937985i	0.291200	−	0.956662i	$-0.405946\pi$
$461$	12778.7	−	9284.26i	1.29103	−	0.937985i	0.999826	+	0.0186773i	$0.00594552\pi$
$462$		0			0
$463$	−1434.54	−	1042.25i	−0.143993	−	0.104617i	0.513457	−	0.858115i	$-0.328365\pi$
$463$	−1434.54	−	1042.25i	−0.143993	−	0.104617i	−0.657449	+	0.753499i	$0.728365\pi$
$464$	−7410.60	+	5384.12i	−0.741441	+	0.538688i
$465$		0			0
$466$	491.473	+	357.076i	0.0488563	+	0.0354962i
$467$	−4033.05	−	12412.4i	−0.399630	−	1.22993i	−0.925297	−	0.379244i	$-0.876184\pi$
$467$	−4033.05	−	12412.4i	−0.399630	−	1.22993i	0.525667	−	0.850691i	$-0.323816\pi$
$468$		0			0
$469$	−1567.36	−	4823.85i	−0.154316	−	0.474936i
$470$	−154.866	−	796.582i	−0.0151988	−	0.0781778i
$471$		0			0
$472$	−2650.24	+	8156.60i	−0.258447	+	0.795419i
$473$	−3166.44	+	2300.55i	−0.307807	+	0.223635i
$474$		0			0
$475$	−404.874	−	5784.61i	−0.0391092	−	0.558771i
$476$	2345.69			0.225870
$477$		0			0
$478$	1906.31	−	5867.01i	0.182411	−	0.561403i
$479$	195.645	−	602.132i	0.0186623	−	0.0574366i	−0.941292	−	0.337594i	$-0.890387\pi$
$479$	195.645	−	602.132i	0.0186623	−	0.0574366i	0.959954	+	0.280158i	$0.0903868\pi$
$480$		0			0
$481$	−887.193	−	2730.50i	−0.0841008	−	0.258836i
$482$	486.926			0.0460142
$483$		0			0
$484$	3838.67	+	2788.96i	0.360506	+	0.261923i
$485$	7746.44	−	16613.7i	0.725253	−	1.55544i
$486$		0			0
$487$	5207.88	+	3783.74i	0.484582	+	0.352069i	0.803097	−	0.595848i	$-0.203184\pi$
$487$	5207.88	+	3783.74i	0.484582	+	0.352069i	−0.318515	+	0.947918i	$0.603184\pi$
$488$	−10094.8	−	7334.32i	−0.936416	−	0.680346i
$489$		0			0
$490$	−1748.19	+	969.113i	−0.161174	+	0.0893470i
$491$	2519.61	+	1830.61i	0.231586	+	0.168257i	0.697526	−	0.716559i	$-0.254284\pi$
$491$	2519.61	+	1830.61i	0.231586	+	0.168257i	−0.465941	+	0.884816i	$0.654284\pi$
$492$		0			0
$493$	−5656.35			−0.516733
$494$	97.7210	+	300.754i	0.00890015	+	0.0273919i
$495$		0			0
$496$	−1964.63	+	6046.50i	−0.177852	+	0.547371i
$497$	−2029.72	+	6246.85i	−0.183190	+	0.563802i
$498$		0			0
$499$	−7664.80			−0.687623			−0.343811	−	0.939039i	$-0.611718\pi$
$499$	−7664.80			−0.687623			−0.343811	+	0.939039i	$0.611718\pi$
$500$	6232.76	−	7698.34i	0.557475	−	0.688560i
$501$		0			0
$502$	2044.68	−	1485.55i	0.181790	−	0.132078i
$503$	−2558.22	+	7873.40i	−0.226770	+	0.697927i	0.771337	+	0.636427i	$0.219588\pi$
$503$	−2558.22	+	7873.40i	−0.226770	+	0.697927i	−0.998107	+	0.0615000i	$0.980412\pi$
$504$		0			0
$505$	−4807.78	−	590.164i	−0.423650	−	0.0520038i
$506$	−1920.35	−	5910.23i	−0.168715	−	0.519252i
$507$		0			0
$508$	−1908.66	−	5874.25i	−0.166699	−	0.513046i
$509$	−5753.10	−	4179.87i	−0.500985	−	0.363987i	0.308408	−	0.951254i	$-0.400204\pi$
$509$	−5753.10	−	4179.87i	−0.500985	−	0.363987i	−0.809393	+	0.587267i	$0.800204\pi$
$510$		0			0
$511$	−10116.5	+	7350.08i	−0.875789	+	0.636298i
$512$	−9433.88	−	6854.11i	−0.814302	−	0.591625i
$513$		0			0
$514$	−3071.96	+	2231.91i	−0.263616	+	0.191528i
$515$	−384.233	+	824.059i	−0.0328763	+	0.0705095i
$516$		0			0
$517$	1050.20	+	3232.18i	0.0893378	+	0.274954i
$518$	4797.44			0.406926
$519$		0			0
$520$	−485.928	+	1042.16i	−0.0409795	+	0.0878882i
$521$	251.088	−	772.770i	0.0211140	−	0.0649821i	−0.939944	−	0.341328i	$-0.889123\pi$
$521$	251.088	−	772.770i	0.0211140	−	0.0649821i	0.961058	+	0.276346i	$0.0891234\pi$
$522$		0			0
$523$	−5215.02	+	3788.93i	−0.436017	+	0.316785i	−0.784050	−	0.620697i	$-0.786850\pi$
$523$	−5215.02	+	3788.93i	−0.436017	+	0.316785i	0.348033	+	0.937482i	$0.386850\pi$
$524$	12106.6			1.00931
$525$		0			0
$526$	−4604.45			−0.381680
$527$	−3176.11	+	2307.58i	−0.262531	+	0.190740i
$528$		0			0
$529$	2777.99	−	8549.77i	0.228322	−	0.702702i
$530$	340.429	+	1751.05i	0.0279005	+	0.143511i
$531$		0			0
$532$	4104.49			0.334497
$533$	515.265	+	1585.82i	0.0418736	+	0.128874i
$534$		0			0
$535$	4347.53	+	533.667i	0.351327	+	0.0431260i
$536$	−4737.33	+	3441.87i	−0.381756	+	0.277362i
$537$		0			0
$538$	3242.88	+	2356.09i	0.259871	+	0.188807i
$539$	6772.33	−	4920.38i	0.541196	−	0.393202i
$540$		0			0
$541$	3683.00	+	2675.86i	0.292689	+	0.212651i	0.724433	−	0.689345i	$-0.242102\pi$
$541$	3683.00	+	2675.86i	0.292689	+	0.212651i	−0.431744	+	0.901996i	$0.642102\pi$
$542$	−602.165	−	1853.27i	−0.0477218	−	0.146873i
$543$		0			0
$544$	−1280.56	−	3941.15i	−0.100926	−	0.310617i
$545$	14848.9	+	13845.9i	1.16707	+	1.08824i
$546$		0			0
$547$	4424.68	−	13617.8i	0.345861	−	1.06445i	−0.615261	−	0.788324i	$-0.710949\pi$
$547$	4424.68	−	13617.8i	0.345861	−	1.06445i	0.961121	−	0.276126i	$-0.0890508\pi$
$548$	13772.1	−	10006.0i	1.07357	−	0.779992i
$549$		0			0
$550$	2829.75	−	4529.20i	0.219384	−	0.351138i
$551$	−9897.50			−0.765241
$552$		0			0
$553$	−516.751	+	1590.40i	−0.0397369	+	0.122298i
$554$	−1361.79	+	4191.17i	−0.104435	+	0.321418i
$555$		0			0
$556$	4735.02	+	14572.9i	0.361168	+	1.11156i
$557$	14882.2			1.13210			0.566050	−	0.824371i	$-0.308471\pi$
$557$	14882.2			1.13210			0.566050	+	0.824371i	$0.308471\pi$
$558$		0			0
$559$	505.217	+	367.061i	0.0382261	+	0.0277729i
$560$	4382.58	+	4086.56i	0.330710	+	0.308372i
$561$		0			0
$562$	−1941.38	−	1410.49i	−0.145715	−	0.105868i
$563$	4575.37	+	3324.20i	0.342502	+	0.248842i	0.745717	−	0.666263i	$-0.232107\pi$
$563$	4575.37	+	3324.20i	0.342502	+	0.248842i	−0.403215	+	0.915105i	$0.632107\pi$
$564$		0			0
$565$	−8890.10	−	8289.62i	−0.661964	−	0.617251i
$566$	−820.644	−	596.233i	−0.0609439	−	0.0442783i
$567$		0			0
$568$	7583.03			0.560170
$569$	3095.34	+	9526.47i	0.228055	+	0.701881i	0.997967	+	0.0637311i	$0.0203000\pi$
$569$	3095.34	+	9526.47i	0.228055	+	0.701881i	−0.769912	+	0.638150i	$0.779700\pi$
$570$		0			0
$571$	−5372.65	+	16535.3i	−0.393763	+	1.21188i	0.536158	+	0.844117i	$0.319875\pi$
$571$	−5372.65	+	16535.3i	−0.393763	+	1.21188i	−0.929921	+	0.367759i	$0.880125\pi$
$572$	699.061	−	2151.49i	0.0511000	−	0.157270i
$573$		0			0
$574$	−2786.27			−0.202607
$575$	16857.3	−	6812.07i	1.22261	−	0.494058i
$576$		0			0
$577$	7189.00	−	5223.12i	0.518686	−	0.376848i	−0.297422	−	0.954746i	$-0.596127\pi$
$577$	7189.00	−	5223.12i	0.518686	−	0.376848i	0.816109	+	0.577898i	$0.196127\pi$
$578$	−1242.76	+	3824.81i	−0.0894323	+	0.275244i
$579$		0			0
$580$	−12364.9	−	11529.7i	−0.885215	−	0.825423i
$581$	−1993.01	−	6133.86i	−0.142313	−	0.437996i
$582$		0			0
$583$	−2308.56	−	7105.01i	−0.163998	−	0.504733i
$584$	11679.3	+	8485.54i	0.827560	+	0.601257i
$585$		0			0
$586$	−6137.18	+	4458.92i	−0.432636	+	0.314328i
$587$	16841.6	+	12236.1i	1.18420	+	0.860372i	0.992639	−	0.121109i	$-0.0386450\pi$
$587$	16841.6	+	12236.1i	1.18420	+	0.860372i	0.191561	+	0.981481i	$0.438645\pi$
$588$		0			0
$589$	−5557.57	+	4037.81i	−0.388787	+	0.282471i
$590$	−6308.00	−	774.319i	−0.440163	−	0.0540309i
$591$		0			0
$592$	5337.55	+	16427.3i	0.370560	+	1.14047i
$593$	−24320.9			−1.68422			−0.842108	−	0.539309i	$-0.818686\pi$
$593$	−24320.9			−1.68422			−0.842108	+	0.539309i	$0.818686\pi$
$594$		0			0
$595$	706.156	+	3632.23i	0.0486547	+	0.250264i
$596$	−3345.92	+	10297.7i	−0.229957	+	0.707734i
$597$		0			0
$598$	−802.163	+	582.805i	−0.0548543	+	0.0398540i
$599$	−18650.6			−1.27219			−0.636096	−	0.771610i	$-0.719452\pi$
$599$	−18650.6			−1.27219			−0.636096	+	0.771610i	$0.719452\pi$
$600$		0			0
$601$	−15558.8			−1.05600			−0.528000	−	0.849245i	$-0.677058\pi$
$601$	−15558.8			−1.05600			−0.528000	+	0.849245i	$0.677058\pi$
$602$	−844.212	+	613.356i	−0.0571554	+	0.0415258i
$603$		0			0
$604$	−5660.96	+	17422.6i	−0.381359	+	1.17370i
$605$	−3163.01	+	6783.67i	−0.212553	+	0.455860i
$606$		0			0
$607$	27620.1			1.84690			0.923448	−	0.383722i	$-0.125358\pi$
$607$	27620.1			1.84690			0.923448	+	0.383722i	$0.125358\pi$
$608$	−2240.73	−	6896.24i	−0.149463	−	0.459999i
$609$		0			0
$610$	3907.47	−	8380.31i	0.259359	−	0.556244i
$611$	438.686	−	318.724i	0.0290463	−	0.0211034i
$612$		0			0
$613$	8560.30	+	6219.42i	0.564025	+	0.409788i	0.832930	−	0.553379i	$-0.186662\pi$
$613$	8560.30	+	6219.42i	0.564025	+	0.409788i	−0.268905	+	0.963167i	$0.586662\pi$
$614$	4177.65	−	3035.24i	0.274587	−	0.199499i
$615$		0			0
$616$	6510.10	+	4729.87i	0.425811	+	0.309370i
$617$	−8162.75	−	25122.4i	−0.532609	−	1.63920i	−0.748759	−	0.662842i	$-0.769350\pi$
$617$	−8162.75	−	25122.4i	−0.532609	−	1.63920i	0.216150	−	0.976360i	$-0.430650\pi$
$618$		0			0
$619$	−1467.19	−	4515.54i	−0.0952686	−	0.293207i	0.892055	−	0.451927i	$-0.149263\pi$
$619$	−1467.19	−	4515.54i	−0.0952686	−	0.293207i	−0.987324	+	0.158720i	$0.949263\pi$
$620$	−11646.7	−	1429.66i	−0.754427	−	0.0926073i
$621$		0			0
$622$	1365.46	−	4202.47i	0.0880227	−	0.270906i
$623$	−6167.69	+	4481.09i	−0.396634	+	0.288172i
$624$		0			0
$625$	13797.0	+	7333.72i	0.883008	+	0.469358i
$626$	−1006.16			−0.0642399
$627$		0			0
$628$	1517.71	−	4671.03i	0.0964383	−	0.296807i
$629$	−3295.96	+	10143.9i	−0.208933	+	0.643028i
$630$		0			0
$631$	−7572.56	−	23305.9i	−0.477748	−	1.47036i	−0.842216	−	0.539141i	$-0.818749\pi$
$631$	−7572.56	−	23305.9i	−0.477748	−	1.47036i	0.364468	−	0.931216i	$-0.381251\pi$
$632$	1930.58			0.121510
$633$		0			0
$634$	2094.28	+	1521.59i	0.131190	+	0.0953153i
$635$	8521.52	−	4723.91i	0.532545	−	0.295217i
$636$		0			0
$637$	−1080.55	−	785.065i	−0.0672103	−	0.0488311i
$638$	−7374.48	−	5357.87i	−0.457615	−	0.332477i
$639$		0			0
$640$	6784.31	−	14550.2i	0.419021	−	0.898669i
$641$	−5161.67	−	3750.17i	−0.318055	−	0.231081i	0.417290	−	0.908773i	$-0.362980\pi$
$641$	−5161.67	−	3750.17i	−0.318055	−	0.231081i	−0.735345	+	0.677693i	$0.762980\pi$
$642$		0			0
$643$	−21527.0			−1.32029			−0.660143	−	0.751140i	$-0.729504\pi$
$643$	−21527.0			−1.32029			−0.660143	+	0.751140i	$0.729504\pi$
$644$	3976.86	+	12239.5i	0.243339	+	0.748921i
$645$		0			0
$646$	363.038	−	1117.32i	0.0221107	−	0.0680499i
$647$	−7369.80	+	22681.9i	−0.447816	+	1.37824i	0.431550	+	0.902089i	$0.357967\pi$
$647$	−7369.80	+	22681.9i	−0.447816	+	1.37824i	−0.879366	+	0.476147i	$0.842033\pi$
$648$		0			0
$649$	26615.9			1.60981
$650$	−826.801	−	206.088i	−0.0498920	−	0.0124361i
$651$		0			0
$652$	−20759.8	+	15082.9i	−1.24696	+	0.905970i
$653$	−3660.56	+	11266.1i	−0.219370	+	0.675153i	0.779444	+	0.626472i	$0.215502\pi$
$653$	−3660.56	+	11266.1i	−0.219370	+	0.675153i	−0.998814	+	0.0486808i	$0.984498\pi$
$654$		0			0
$655$	3644.63	+	18746.8i	0.217416	+	1.11832i
$656$	−3099.95	−	9540.66i	−0.184501	−	0.567836i
$657$		0			0
$658$	279.996	+	861.740i	0.0165887	+	0.0510549i
$659$	−10619.8	−	7715.74i	−0.627752	−	0.456089i	0.227869	−	0.973692i	$-0.426824\pi$
$659$	−10619.8	−	7715.74i	−0.627752	−	0.456089i	−0.855621	+	0.517603i	$0.826824\pi$
$660$		0			0
$661$	−19816.4	+	14397.4i	−1.16606	+	0.847195i	−0.990532	−	0.137279i	$-0.956164\pi$
$661$	−19816.4	+	14397.4i	−1.16606	+	0.847195i	−0.175531	+	0.984474i	$0.556164\pi$
$662$	3390.80	+	2463.56i	0.199074	+	0.144636i
$663$		0			0
$664$	−6023.84	+	4376.57i	−0.352064	+	0.255789i
$665$	1235.63	+	6355.69i	0.0720539	+	0.370621i
$666$		0			0
$667$	−9589.75	−	29514.2i	−0.556696	−	1.71333i
$668$	11025.4			0.638602
$669$		0			0
$670$	−3173.60	−	2959.24i	−0.182996	−	0.170635i
$671$	−11966.4	+	36828.7i	−0.688460	+	2.11886i
$672$		0			0
$673$	22718.1	−	16505.7i	1.30122	−	0.945389i	0.301250	−	0.953545i	$-0.402596\pi$
$673$	22718.1	−	16505.7i	1.30122	−	0.945389i	0.999967	+	0.00815586i	$0.00259612\pi$
$674$	−3699.27			−0.211410
$675$		0			0
$676$	15210.4			0.865406
$677$	−5521.73	+	4011.77i	−0.313467	+	0.227747i	−0.733383	−	0.679816i	$-0.762060\pi$
$677$	−5521.73	+	4011.77i	−0.313467	+	0.227747i	0.419916	+	0.907563i	$0.362060\pi$
$678$		0			0
$679$	−6324.84	+	19465.9i	−0.357474	+	1.10019i
$680$	3736.19	−	2071.16i	0.210701	−	0.116802i
$681$		0			0
$682$	−6326.67			−0.355221
$683$	9718.81	+	29911.4i	0.544480	+	1.67574i	0.722223	+	0.691661i	$0.243121\pi$
$683$	9718.81	+	29911.4i	0.544480	+	1.67574i	−0.177742	+	0.984077i	$0.556879\pi$
$684$		0			0
$685$	19640.0	+	18313.5i	1.09549	+	1.02149i
$686$	5114.60	−	3715.97i	0.284659	−	0.206817i
$687$		0			0
$688$	−3039.49	−	2208.32i	−0.168430	−	0.122371i
$689$	−964.323	+	700.622i	−0.0533204	+	0.0387396i
$690$		0			0
$691$	−4964.49	−	3606.92i	−0.273312	−	0.198572i	0.442683	−	0.896678i	$-0.354027\pi$
$691$	−4964.49	−	3606.92i	−0.273312	−	0.198572i	−0.715995	+	0.698106i	$0.754027\pi$
$692$	−4765.61	−	14667.0i	−0.261794	−	0.805718i
$693$		0			0
$694$	−1707.02	−	5253.66i	−0.0933682	−	0.287358i
$695$	−21140.3	+	11719.1i	−1.15381	+	0.639615i
$696$		0			0
$697$	1914.23	−	5891.41i	0.104027	−	0.320162i
$698$	2253.96	−	1637.60i	0.122226	−	0.0888024i
$699$		0			0
$700$	−5860.15	+	9379.54i	−0.316418	+	0.506448i
$701$	−5291.43			−0.285099			−0.142550	−	0.989788i	$-0.545530\pi$
$701$	−5291.43			−0.285099			−0.142550	+	0.989788i	$0.545530\pi$
$702$		0			0
$703$	−5767.28	+	17749.9i	−0.309413	+	0.952275i
$704$	−2683.50	+	8258.98i	−0.143662	+	0.442148i
$705$		0			0
$706$	1029.47	+	3168.37i	0.0548789	+	0.168900i
$707$	5408.48			0.287704
$708$		0			0
$709$	3548.04	+	2577.80i	0.187940	+	0.136546i	0.677777	−	0.735268i	$-0.262944\pi$
$709$	3548.04	+	2577.80i	0.187940	+	0.136546i	−0.489837	+	0.871814i	$0.662944\pi$
$710$	1072.38	+	5515.99i	0.0566843	+	0.291565i
$711$		0			0
$712$	7120.50	+	5173.34i	0.374792	+	0.272302i
$713$	−17425.5	−	12660.3i	−0.915271	−	0.664984i
$714$		0			0
$715$	3541.97	+	434.784i	0.185262	+	0.0227412i
$716$	10696.3	+	7771.34i	0.558297	+	0.405626i
$717$		0			0
$718$	−10131.7			−0.526616
$719$	−1980.88	−	6096.52i	−0.102746	−	0.316219i	0.886449	−	0.462827i	$-0.153165\pi$
$719$	−1980.88	−	6096.52i	−0.102746	−	0.316219i	−0.989195	+	0.146607i	$0.953165\pi$
$720$		0			0
$721$	313.720	−	965.530i	0.0162046	−	0.0498727i
$722$	−1389.41	+	4276.16i	−0.0716184	+	0.220419i
$723$		0			0
$724$	1827.38			0.0938040
$725$	14131.1	−	22617.7i	0.723882	−	1.15862i
$726$		0			0
$727$	−25616.4	+	18611.4i	−1.30682	+	0.949463i	−0.999997	−	0.00230297i	$-0.999267\pi$
$727$	−25616.4	+	18611.4i	−1.30682	+	0.949463i	−0.306826	+	0.951766i	$0.599267\pi$
$728$	396.752	−	1221.08i	0.0201986	−	0.0621650i
$729$		0			0
$730$	−4520.81	+	9695.72i	−0.229209	+	0.491582i
$731$	−716.913	−	2206.43i	−0.0362736	−	0.111639i
$732$		0			0
$733$	7962.64	+	24506.5i	0.401237	+	1.23488i	0.923997	+	0.382401i	$0.124903\pi$
$733$	7962.64	+	24506.5i	0.401237	+	1.23488i	−0.522759	+	0.852480i	$0.675097\pi$
$734$	2075.05	+	1507.61i	0.104348	+	0.0758135i
$735$		0			0
$736$	18393.4	−	13363.6i	0.921184	−	0.669279i
$737$	14701.9	+	10681.5i	0.734803	+	0.533866i
$738$		0			0
$739$	−2741.77	+	1992.01i	−0.136479	+	0.0991575i	−0.653930	−	0.756555i	$-0.726881\pi$
$739$	−2741.77	+	1992.01i	−0.136479	+	0.0991575i	0.517451	+	0.855713i	$0.326881\pi$
$740$	−27882.1	+	15456.5i	−1.38509	+	0.767826i
$741$		0			0
$742$	−615.491	−	1894.29i	−0.0304520	−	0.0937216i
$743$	17203.7			0.849453			0.424727	−	0.905322i	$-0.360370\pi$
$743$	17203.7			0.849453			0.424727	+	0.905322i	$0.360370\pi$
$744$		0			0
$745$	−16952.9	−	2081.01i	−0.833702	−	0.102338i
$746$	−203.227	+	625.467i	−0.00997407	+	0.0306970i
$747$		0			0
$748$	−6799.15	+	4939.87i	−0.332355	+	0.241470i
$749$	−4890.72			−0.238589
$750$		0			0
$751$	17081.3			0.829970			0.414985	−	0.909828i	$-0.363787\pi$
$751$	17081.3			0.829970			0.414985	+	0.909828i	$0.363787\pi$
$752$	−2639.23	+	1917.51i	−0.127982	+	0.0929846i
$753$		0			0
$754$	−449.430	+	1383.20i	−0.0217073	+	0.0668082i
$755$	−28682.7	−	3520.85i	−1.38261	−	0.169718i
$756$		0			0
$757$	4684.65			0.224923			0.112461	−	0.993656i	$-0.464127\pi$
$757$	4684.65			0.224923			0.112461	+	0.993656i	$0.464127\pi$
$758$	−3611.69	−	11115.6i	−0.173064	−	0.532635i
$759$		0			0
$760$	6537.60	−	3624.13i	0.312031	−	0.172975i
$761$	20522.2	−	14910.2i	0.977567	−	0.710244i	0.0204031	−	0.999792i	$-0.493505\pi$
$761$	20522.2	−	14910.2i	0.977567	−	0.710244i	0.957163	+	0.289548i	$0.0935050\pi$
$762$		0			0
$763$	−18339.8	−	13324.6i	−0.870175	−	0.632219i
$764$	22711.4	−	16500.8i	1.07548	−	0.781385i
$765$		0			0
$766$	1470.00	+	1068.01i	0.0693382	+	0.0503772i
$767$	−1312.29	−	4038.82i	−0.0617786	−	0.190135i
$768$		0			0
$769$	−6578.26	−	20245.8i	−0.308476	−	0.949392i	−0.978357	−	0.206923i	$-0.933655\pi$
$769$	−6578.26	−	20245.8i	−0.308476	−	0.949392i	0.669881	−	0.742468i	$-0.266345\pi$
$770$	−2519.91	+	5404.42i	−0.117937	+	0.252937i
$771$		0			0
$772$	−2745.86	+	8450.89i	−0.128013	+	0.393982i
$773$	19212.9	−	13959.0i	0.893970	−	0.649507i	−0.0429404	−	0.999078i	$-0.513673\pi$
$773$	19212.9	−	13959.0i	0.893970	−	0.649507i	0.936910	+	0.349571i	$0.113673\pi$
$774$		0			0
$775$	−1292.40	−	18465.1i	−0.0599023	−	0.855851i
$776$	23629.5			1.09311
$777$		0			0
$778$	−55.4899	+	170.780i	−0.00255708	+	0.00786989i
$779$	3349.53	−	10308.8i	0.154056	−	0.474135i
$780$		0			0
$781$	−7272.17	−	22381.4i	−0.333187	−	1.02544i
$782$	3683.57			0.168445
$783$		0			0
$784$	6500.82	+	4723.12i	0.296138	+	0.215157i
$785$	7689.87	+	943.946i	0.349635	+	0.0429183i
$786$		0			0
$787$	−15525.8	−	11280.2i	−0.703222	−	0.510921i	0.177758	−	0.984074i	$-0.443116\pi$
$787$	−15525.8	−	11280.2i	−0.703222	−	0.510921i	−0.880980	+	0.473153i	$0.843116\pi$
$788$	29012.8	+	21079.0i	1.31160	+	0.952931i
$789$		0			0
$790$	273.020	+	1404.32i	0.0122957	+	0.0632451i
$791$	10980.1	+	7977.53i	0.493563	+	0.358595i
$792$		0			0
$793$	6178.55			0.276680
$794$	−2227.86	−	6856.65i	−0.0995766	−	0.306465i
$795$		0			0
$796$	11660.3	−	35886.6i	0.519205	−	1.59795i
$797$	6243.84	−	19216.6i	0.277501	−	0.854060i	−0.711046	−	0.703146i	$-0.751778\pi$
$797$	6243.84	−	19216.6i	0.277501	−	0.854060i	0.988547	−	0.150915i	$-0.0482218\pi$
$798$		0			0
$799$	−2014.46			−0.0891948
$800$	18958.4	+	4725.57i	0.837851	+	0.208842i
$801$		0			0
$802$	4170.75	−	3030.23i	0.183634	−	0.133418i
$803$	13844.7	−	42609.5i	0.608428	−	1.87255i
$804$		0			0
$805$	−17755.4	+	9842.70i	−0.777384	+	0.430944i
$806$	311.935	+	960.038i	0.0136321	+	0.0419552i
$807$		0			0
$808$	−1929.50	−	5938.40i	−0.0840095	−	0.258555i
$809$	−14738.1	−	10707.8i	−0.640498	−	0.465349i	0.219523	−	0.975607i	$-0.429550\pi$
$809$	−14738.1	−	10707.8i	−0.640498	−	0.465349i	−0.860021	+	0.510258i	$0.829550\pi$
$810$		0			0
$811$	20740.9	−	15069.1i	0.898040	−	0.652464i	−0.0399217	−	0.999203i	$-0.512711\pi$
$811$	20740.9	−	15069.1i	0.898040	−	0.652464i	0.937962	+	0.346738i	$0.112711\pi$
$812$	15271.8	+	11095.6i	0.660020	+	0.479533i
$813$		0			0
$814$	−13905.8	+	10103.1i	−0.598767	+	0.435030i
$815$	−29605.1	−	27605.4i	−1.27242	−	1.18647i
$816$		0			0
$817$	−1254.46	−	3860.82i	−0.0537183	−	0.165328i
$818$	−3907.29			−0.167011
$819$		0			0
$820$	16193.4	−	8976.83i	0.689632	−	0.382298i
$821$	1027.54	−	3162.44i	0.0436800	−	0.134433i	−0.926838	−	0.375461i	$-0.877484\pi$
$821$	1027.54	−	3162.44i	0.0436800	−	0.134433i	0.970518	+	0.241028i	$0.0774844\pi$
$822$		0			0
$823$	−3464.35	+	2517.00i	−0.146731	+	0.106606i	−0.658729	−	0.752380i	$-0.728906\pi$
$823$	−3464.35	+	2517.00i	−0.146731	+	0.106606i	0.511998	+	0.858987i	$0.328906\pi$
$824$	−1172.05			−0.0495515
$825$		0			0
$826$	7096.15			0.298918
$827$	−12542.3	+	9112.50i	−0.527373	+	0.383159i	−0.819374	−	0.573259i	$-0.805679\pi$
$827$	−12542.3	+	9112.50i	−0.527373	+	0.383159i	0.292001	+	0.956418i	$0.405679\pi$
$828$		0			0
$829$	8054.69	−	24789.8i	0.337456	−	1.03858i	−0.628044	−	0.778178i	$-0.716144\pi$
$829$	8054.69	−	24789.8i	0.337456	−	1.03858i	0.965500	−	0.260405i	$-0.0838559\pi$
$830$	−4035.46	−	3762.88i	−0.168762	−	0.157363i
$831$		0			0
$832$	1385.56			0.0577353
$833$	1533.32	+	4719.08i	0.0637773	+	0.196286i
$834$		0			0
$835$	3319.14	+	17072.6i	0.137561	+	0.707570i
$836$	−11897.2	+	8643.80i	−0.492192	+	0.357598i
$837$		0			0
$838$	2196.14	+	1595.59i	0.0905302	+	0.0657740i
$839$	36143.6	−	26259.8i	1.48726	−	1.08056i	0.512140	−	0.858902i	$-0.328853\pi$
$839$	36143.6	−	26259.8i	1.48726	−	1.08056i	0.975124	−	0.221658i	$-0.0711470\pi$
$840$		0			0
$841$	−17095.2	−	12420.4i	−0.700937	−	0.509261i
$842$	−4882.25	−	15026.0i	−0.199826	−	0.615001i
$843$		0			0
$844$	2255.02	+	6940.25i	0.0919682	+	0.283049i
$845$	4579.00	+	23552.8i	0.186417	+	0.958867i
$846$		0			0
$847$	2582.55	−	7948.27i	0.104767	−	0.322439i
$848$	5801.58	−	4215.09i	0.234937	−	0.170692i
$849$		0			0
$850$	2034.96	+	2424.85i	0.0821158	+	0.0978490i
$851$	−58517.8			−2.35719
$852$		0			0
$853$	−5136.91	+	15809.8i	−0.206195	+	0.634603i	0.793467	+	0.608613i	$0.208274\pi$
$853$	−5136.91	+	15809.8i	−0.206195	+	0.634603i	−0.999662	+	0.0259902i	$0.991726\pi$
$854$	−3190.39	+	9819.00i	−0.127837	+	0.393442i
$855$		0			0
$856$	1744.79	+	5369.91i	0.0696679	+	0.214416i
$857$	5804.93			0.231380			0.115690	−	0.993285i	$-0.463092\pi$
$857$	5804.93			0.231380			0.115690	+	0.993285i	$0.463092\pi$
$858$		0			0
$859$	25067.3	+	18212.4i	0.995674	+	0.723399i	0.961156	−	0.276005i	$-0.0890105\pi$
$859$	25067.3	+	18212.4i	0.995674	+	0.723399i	0.0345176	+	0.999404i	$0.489011\pi$
$860$	2930.33	−	6284.64i	0.116190	−	0.249191i
$861$		0			0
$862$	−1778.59	−	1292.22i	−0.0702772	−	0.0510594i
$863$	2841.18	+	2064.24i	0.112068	+	0.0814224i	0.642408	−	0.766363i	$-0.277936\pi$
$863$	2841.18	+	2064.24i	0.112068	+	0.0814224i	−0.530340	+	0.847785i	$0.677936\pi$
$864$		0			0
$865$	21276.8	−	11794.8i	0.836340	−	0.463626i
$866$	5839.66	+	4242.76i	0.229145	+	0.166484i
$867$		0			0
$868$	13101.9			0.512337
$869$	−1851.44	−	5698.13i	−0.0722735	−	0.222435i
$870$		0			0
$871$	895.991	−	2757.58i	0.0348559	−	0.107276i
$872$	−8087.35	+	24890.3i	−0.314074	+	0.966619i
$873$		0			0
$874$	6445.52			0.249454
$875$	−16288.1	−	6250.62i	−0.629302	−	0.241497i
$876$		0			0
$877$	−29710.4	+	21585.9i	−1.14395	+	0.831132i	−0.987665	−	0.156580i	$-0.949953\pi$
$877$	−29710.4	+	21585.9i	−1.14395	+	0.831132i	−0.156289	+	0.987711i	$0.549953\pi$
$878$	−2458.28	+	7565.82i	−0.0944910	+	0.290813i
$879$		0			0
$880$	−21309.3	−	2615.75i	−0.816290	−	0.100201i
$881$	−12745.7	−	39227.1i	−0.487415	−	1.50011i	−0.828453	−	0.560059i	$-0.810779\pi$
$881$	−12745.7	−	39227.1i	−0.487415	−	1.50011i	0.341038	−	0.940049i	$-0.389221\pi$
$882$		0			0
$883$	638.390	+	1964.76i	0.0243302	+	0.0748805i	0.962484	−	0.271337i	$-0.0874658\pi$
$883$	638.390	+	1964.76i	0.0243302	+	0.0748805i	−0.938154	+	0.346218i	$0.887466\pi$
$884$	1084.83	+	788.174i	0.0412746	+	0.0299878i
$885$		0			0
$886$	9023.08	−	6555.65i	0.342140	−	0.248580i
$887$	−8791.16	−	6387.15i	−0.332783	−	0.241781i	0.408828	−	0.912612i	$-0.365938\pi$
$887$	−8791.16	−	6387.15i	−0.332783	−	0.241781i	−0.741610	+	0.670831i	$0.765938\pi$
$888$		0			0
$889$	−8801.29	+	6394.51i	−0.332043	+	0.241243i
$890$	−2756.18	+	5911.15i	−0.103806	+	0.222632i
$891$		0			0
$892$	−2726.93	−	8392.64i	−0.102359	−	0.315029i
$893$	−3524.92			−0.132091
$894$		0			0
$895$	−8813.64	+	18902.5i	−0.329170	+	0.705967i
$896$	−5539.28	+	17048.2i	−0.206534	+	0.635646i
$897$		0			0
$898$	−799.795	+	581.085i	−0.0297211	+	0.0215936i
$899$	−31593.8			−1.17209
$900$		0			0
$901$	4428.22			0.163735
$902$	8076.21	−	5867.71i	0.298124	−	0.216600i
$903$		0			0
$904$	4841.95	−	14902.0i	0.178142	−	0.548266i
$905$	550.123	+	2829.65i	0.0202063	+	0.103935i
$906$		0			0
$907$	12436.5			0.455290			0.227645	−	0.973744i	$-0.426897\pi$
$907$	12436.5			0.455290			0.227645	+	0.973744i	$0.426897\pi$
$908$	−10071.0	−	30995.5i	−0.368083	−	1.13284i
$909$		0			0
$910$	944.335	+	115.919i	0.0344004	+	0.00422272i
$911$	15557.8	−	11303.4i	0.565810	−	0.411085i	−0.267771	−	0.963483i	$-0.586287\pi$
$911$	15557.8	−	11303.4i	0.565810	−	0.411085i	0.833581	+	0.552398i	$0.186287\pi$
$912$		0			0
$913$	18694.4	+	13582.3i	0.677651	+	0.492342i
$914$	−11808.2	+	8579.19i	−0.427333	+	0.310475i
$915$		0			0
$916$	36437.8	+	26473.6i	1.31434	+	0.954927i
$917$	−6589.43	−	20280.2i	−0.237298	−	0.730328i
$918$		0			0
$919$	−7483.00	−	23030.3i	−0.268598	−	0.826659i	−0.990843	−	0.135022i	$-0.956890\pi$
$919$	−7483.00	−	23030.3i	−0.268598	−	0.826659i	0.722245	−	0.691638i	$-0.243110\pi$
$920$	17141.4	+	15983.6i	0.614278	+	0.572786i
$921$		0			0
$922$	−4662.50	+	14349.7i	−0.166542	+	0.512562i
$923$	−3037.71	+	2207.03i	−0.108329	+	0.0787054i
$924$		0			0
$925$	−32327.7	−	38521.6i	−1.14911	−	1.36928i
$926$	1693.80			0.0601098
$927$		0			0
$928$	10305.4	−	31716.6i	0.364537	−	1.12193i
$929$	5931.40	−	18255.0i	0.209476	−	0.644700i	−0.790024	−	0.613076i	$-0.789932\pi$
$929$	5931.40	−	18255.0i	0.209476	−	0.644700i	0.999500	−	0.0316245i	$-0.0100681\pi$
$930$		0			0
$931$	2683.01	+	8257.46i	0.0944492	+	0.290685i
$932$	4507.44			0.158418
$933$		0			0
$934$	10085.9	+	7327.87i	0.353343	+	0.256719i
$935$	−9696.10	−	9041.18i	−0.339141	−	0.316233i
$936$		0			0
$937$	−30092.3	−	21863.3i	−1.04917	−	0.762266i	−0.0771154	−	0.997022i	$-0.524571\pi$
$937$	−30092.3	−	21863.3i	−1.04917	−	0.762266i	−0.972054	+	0.234756i	$0.924571\pi$
$938$	3919.70	+	2847.83i	0.136442	+	0.0991311i
$939$		0			0
$940$	−4403.66	−	4106.22i	−0.152800	−	0.142479i
$941$	27249.7	+	19798.1i	0.944011	+	0.685864i	0.949383	−	0.314121i	$-0.101710\pi$
$941$	27249.7	+	19798.1i	0.944011	+	0.685864i	−0.00537159	+	0.999986i	$0.501710\pi$
$942$		0			0
$943$	33986.1			1.17364
$944$	7895.05	+	24298.5i	0.272205	+	0.837762i
$945$		0			0
$946$	1155.32	−	3555.72i	0.0397070	−	0.122205i
$947$	−13716.2	+	42214.1i	−0.470662	+	1.44855i	0.381059	+	0.924551i	$0.375560\pi$
$947$	−13716.2	+	42214.1i	−0.470662	+	1.44855i	−0.851720	+	0.523997i	$0.824440\pi$
$948$		0			0
$949$	−7148.37			−0.244516
$950$	3560.77	+	4243.01i	0.121607	+	0.144907i
$951$		0			0
$952$	−3858.85	+	2803.62i	−0.131372	+	0.0954474i
$953$	−2365.73	+	7280.97i	−0.0804129	+	0.247486i	−0.983178	−	0.182647i	$-0.941533\pi$
$953$	−2365.73	+	7280.97i	−0.0804129	+	0.247486i	0.902766	+	0.430133i	$0.141533\pi$
$954$		0			0
$955$	32388.2	+	30200.5i	1.09744	+	1.02331i
$956$	−14144.2	−	43531.5i	−0.478512	−	1.47271i
$957$		0			0
$958$	186.886	+	575.175i	0.00630271	+	0.0193978i
$959$	−24257.3	−	17624.0i	−0.816799	−	0.593439i
$960$		0			0
$961$	6361.10	−	4621.61i	0.213524	−	0.155135i
$962$	2218.71	+	1611.99i	0.0743599	+	0.0540256i
$963$		0			0
$964$	2922.86	−	2123.58i	0.0976545	−	0.0709501i
$965$	−13912.6	−	1707.80i	−0.464106	−	0.0569699i
$966$		0			0
$967$	−4525.99	−	13929.6i	−0.150513	−	0.463232i	0.847166	−	0.531329i	$-0.178307\pi$
$967$	−4525.99	−	13929.6i	−0.150513	−	0.463232i	−0.997679	+	0.0680974i	$0.978307\pi$
$968$	−9648.37			−0.320362
$969$		0			0
$970$	3341.66	+	17188.4i	0.110613	+	0.568955i
$971$	13729.5	−	42255.1i	0.453761	−	1.39653i	−0.418824	−	0.908068i	$-0.637557\pi$
$971$	13729.5	−	42255.1i	0.453761	−	1.39653i	0.872584	−	0.488464i	$-0.162443\pi$
$972$		0			0
$973$	21834.4	−	15863.6i	0.719401	−	0.522675i
$974$	−6149.09			−0.202289
$975$		0			0
$976$	−37171.5			−1.21909
$977$	3734.28	−	2713.12i	0.122283	−	0.0888437i	−0.524963	−	0.851125i	$-0.675921\pi$
$977$	3734.28	−	2713.12i	0.122283	−	0.0888437i	0.647246	+	0.762281i	$0.275921\pi$
$978$		0			0
$979$	8440.62	−	25977.6i	0.275550	−	0.848055i
$980$	−6267.34	+	13441.5i	−0.204289	+	0.438135i
$981$		0			0
$982$	−2974.98			−0.0966756
$983$	6207.06	+	19103.4i	0.201398	+	0.619840i	0.999842	+	0.0177707i	$0.00565687\pi$
$983$	6207.06	+	19103.4i	0.201398	+	0.619840i	−0.798444	+	0.602069i	$0.794343\pi$
$984$		0			0
$985$	−23906.2	+	51271.3i	−0.773314	+	1.65852i
$986$	4371.21	−	3175.87i	0.141184	−	0.102576i
$987$		0			0
$988$	1898.24	+	1379.15i	0.0611245	+	0.0444095i
$989$	10297.5	−	7481.54i	0.331082	−	0.240545i
$990$		0			0
$991$	−795.900	−	578.255i	−0.0255122	−	0.0185357i	0.574956	−	0.818184i	$-0.305019\pi$
$991$	−795.900	−	578.255i	−0.0255122	−	0.0185357i	−0.600468	+	0.799649i	$0.705019\pi$
$992$	−7152.62	−	22013.5i	−0.228927	−	0.704566i
$993$		0			0
$994$	−1938.85	−	5967.18i	−0.0618679	−	0.190410i
$995$	59079.7	+	7252.14i	1.88236	+	0.231064i
$996$		0			0
$997$	273.212	−	840.860i	0.00867875	−	0.0267104i	−0.946623	−	0.322342i	$-0.895530\pi$
$997$	273.212	−	840.860i	0.00867875	−	0.0267104i	0.955302	+	0.295631i	$0.0955300\pi$
$998$	5923.34	−	4303.56i	0.187876	−	0.136500i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.136.3		28
3.2	odd	2		75.4.g.b.61.5	yes	28
25.16	even	5	inner	225.4.h.a.91.3		28
75.29	odd	10		1875.4.a.f.1.9		14
75.41	odd	10		75.4.g.b.16.5	✓	28
75.71	odd	10		1875.4.a.g.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.5	✓	28	75.41	odd	10
75.4.g.b.61.5	yes	28	3.2	odd	2
225.4.h.a.91.3		28	25.16	even	5	inner
225.4.h.a.136.3		28	1.1	even	1	trivial
1875.4.a.f.1.9		14	75.29	odd	10
1875.4.a.g.1.6		14	75.71	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +O(q^{10})\)	\(q+(-0.772797 + 0.561470i) q^{2} +(-2.19017 + 6.74065i) q^{4} +(-11.0970 - 1.36218i) q^{5} +12.4836 q^{7} +(-4.45357 - 13.7067i) q^{8} +(9.34059 - 5.17797i) q^{10} +(-36.1845 + 26.2896i) q^{11} +(5.77338 + 4.19460i) q^{13} +(-9.64726 + 7.00914i) q^{14} +(-34.7339 - 25.2356i) q^{16} +(-8.19254 - 25.2140i) q^{17} +(-14.3353 - 44.1196i) q^{19} +(33.4864 - 71.8179i) q^{20} +(13.2025 - 40.6331i) q^{22} +(117.674 - 85.4955i) q^{23} +(121.289 + 30.2324i) q^{25} -6.81679 q^{26} +(-27.3411 + 84.1473i) q^{28} +(65.9299 - 202.911i) q^{29} +(-45.7598 - 140.834i) q^{31} +156.308 q^{32} +(20.4881 + 14.8855i) q^{34} +(-138.531 - 17.0049i) q^{35} +(-325.478 - 236.473i) q^{37} +(35.8502 + 26.0467i) q^{38} +(30.7505 + 158.170i) q^{40} +(189.031 + 137.339i) q^{41} +87.5080 q^{43} +(-97.9587 - 301.486i) q^{44} +(-42.9353 + 132.141i) q^{46} +(23.4804 - 72.2653i) q^{47} -187.161 q^{49} +(-110.706 + 44.7366i) q^{50} +(-40.9190 + 29.7294i) q^{52} +(-51.6149 + 158.854i) q^{53} +(437.353 - 242.447i) q^{55} +(-55.5964 - 171.108i) q^{56} +(62.9782 + 193.827i) q^{58} +(-481.431 - 349.780i) q^{59} +(700.442 - 508.901i) q^{61} +(114.437 + 83.1435i) q^{62} +(157.077 - 114.123i) q^{64} +(-58.3536 - 54.4121i) q^{65} +(-125.554 - 386.416i) q^{67} +187.902 q^{68} +(116.604 - 64.6395i) q^{70} +(-162.592 + 500.406i) q^{71} +(-810.387 + 588.781i) q^{73} +384.301 q^{74} +328.792 q^{76} +(-451.712 + 328.188i) q^{77} +(-41.3945 + 127.399i) q^{79} +(351.068 + 327.355i) q^{80} -223.195 q^{82} +(-159.651 - 491.355i) q^{83} +(56.5668 + 290.961i) q^{85} +(-67.6259 + 49.1331i) q^{86} +(521.494 + 378.888i) q^{88} +(-494.065 + 358.959i) q^{89} +(72.0723 + 52.3636i) q^{91} +(318.568 + 980.452i) q^{92} +(22.4292 + 69.0300i) q^{94} +(98.9809 + 509.125i) q^{95} +(-506.654 + 1559.32i) q^{97} +(144.637 - 105.085i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

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