LMFDB - Embedded newform 45.4.l.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, 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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27001 - 4.73973i) q^{2} +(-2.23746 + 4.68975i) q^{3} +(-13.9239 + 8.03899i) q^{4} +(1.75298 + 11.0421i) q^{5} +(25.0698 + 4.64896i) q^{6} +(-21.2589 + 5.69629i) q^{7} +(28.0284 + 28.0284i) q^{8} +(-16.9875 - 20.9863i) q^{9} +O(q^{10})$	\(q+(-1.27001 - 4.73973i) q^{2} +(-2.23746 + 4.68975i) q^{3} +(-13.9239 + 8.03899i) q^{4} +(1.75298 + 11.0421i) q^{5} +(25.0698 + 4.64896i) q^{6} +(-21.2589 + 5.69629i) q^{7} +(28.0284 + 28.0284i) q^{8} +(-16.9875 - 20.9863i) q^{9} +(50.1101 - 22.3322i) q^{10} +(30.9441 + 17.8656i) q^{11} +(-6.54654 - 83.2868i) q^{12} +(-38.8149 - 10.4004i) q^{13} +(53.9978 + 93.5270i) q^{14} +(-55.7067 - 16.4852i) q^{15} +(32.9388 - 57.0517i) q^{16} +(-54.1151 + 54.1151i) q^{17} +(-77.8952 + 107.169i) q^{18} +55.2993i q^{19} +(-113.175 - 139.657i) q^{20} +(20.8517 - 112.444i) q^{21} +(45.3788 - 169.356i) q^{22} +(25.9049 - 96.6785i) q^{23} +(-194.159 + 68.7336i) q^{24} +(-118.854 + 38.7131i) q^{25} +197.181i q^{26} +(136.429 - 32.7111i) q^{27} +(250.215 - 250.215i) q^{28} +(74.2482 - 128.602i) q^{29} +(-7.38730 + 284.971i) q^{30} +(102.561 + 177.641i) q^{31} +(-5.94267 - 1.59233i) q^{32} +(-153.021 + 105.146i) q^{33} +(325.217 + 187.764i) q^{34} +(-100.165 - 224.756i) q^{35} +(405.242 + 155.649i) q^{36} +(-151.248 - 151.248i) q^{37} +(262.104 - 70.2305i) q^{38} +(135.622 - 158.762i) q^{39} +(-260.358 + 358.624i) q^{40} +(-38.4281 + 22.1865i) q^{41} +(-559.436 + 43.9730i) q^{42} +(-11.3232 - 42.2588i) q^{43} -574.485 q^{44} +(201.953 - 224.366i) q^{45} -491.130 q^{46} +(126.857 + 473.436i) q^{47} +(193.859 + 282.126i) q^{48} +(122.445 - 70.6935i) q^{49} +(334.435 + 514.171i) q^{50} +(-132.706 - 374.867i) q^{51} +(624.066 - 167.218i) q^{52} +(215.632 + 215.632i) q^{53} +(-328.308 - 605.096i) q^{54} +(-143.028 + 373.005i) q^{55} +(-755.509 - 436.194i) q^{56} +(-259.340 - 123.730i) q^{57} +(-703.833 - 188.591i) q^{58} +(21.8014 + 37.7612i) q^{59} +(908.181 - 218.287i) q^{60} +(-16.1944 + 28.0496i) q^{61} +(711.717 - 711.717i) q^{62} +(480.679 + 349.379i) q^{63} -496.832i q^{64} +(46.8003 - 446.828i) q^{65} +(692.704 + 591.744i) q^{66} +(-268.503 + 1002.07i) q^{67} +(318.464 - 1188.53i) q^{68} +(395.437 + 337.802i) q^{69} +(-938.073 + 760.198i) q^{70} -53.5643i q^{71} +(112.079 - 1064.34i) q^{72} +(23.7710 - 23.7710i) q^{73} +(-524.789 + 908.961i) q^{74} +(84.3773 - 644.015i) q^{75} +(-444.551 - 769.984i) q^{76} +(-759.604 - 203.535i) q^{77} +(-924.730 - 441.185i) q^{78} +(189.055 + 109.151i) q^{79} +(687.710 + 263.702i) q^{80} +(-151.849 + 713.010i) q^{81} +(153.962 + 153.962i) q^{82} +(275.656 - 73.8617i) q^{83} +(613.598 + 1733.29i) q^{84} +(-692.404 - 502.679i) q^{85} +(-185.915 + 107.338i) q^{86} +(436.982 + 635.947i) q^{87} +(366.570 + 1368.06i) q^{88} -870.778 q^{89} +(-1319.92 - 672.258i) q^{90} +884.405 q^{91} +(416.499 + 1554.40i) q^{92} +(-1062.57 + 83.5204i) q^{93} +(2082.85 - 1202.54i) q^{94} +(-610.618 + 96.9387i) q^{95} +(20.7642 - 24.3069i) q^{96} +(127.719 - 34.2222i) q^{97} +(-490.574 - 490.574i) q^{98} +(-150.731 - 952.894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.27001	−	4.73973i	−0.449015	−	1.67575i	−0.705111	−	0.709097i	$-0.749103\pi$
$2$	−1.27001	−	4.73973i	−0.449015	−	1.67575i	0.256096	−	0.966651i	$-0.417564\pi$
$3$	−2.23746	+	4.68975i	−0.430600	+	0.902543i
$3$	−2.23746	+	4.68975i	−0.430600	+	0.902543i
$4$	−13.9239	+	8.03899i	−1.74049	+	1.00487i
$5$	1.75298	+	11.0421i	0.156791	+	0.987632i
$5$	1.75298	+	11.0421i	0.156791	+	0.987632i
$6$	25.0698	+	4.64896i	1.70578	+	0.316322i
$7$	−21.2589	+	5.69629i	−1.14787	+	0.307571i	−0.782111	−	0.623139i	$-0.785857\pi$
$7$	−21.2589	+	5.69629i	−1.14787	+	0.307571i	−0.365759	+	0.930710i	$0.619191\pi$
$8$	28.0284	+	28.0284i	1.23869	+	1.23869i
$9$	−16.9875	−	20.9863i	−0.629167	−	0.777270i
$10$	50.1101	−	22.3322i	1.58462	−	0.706205i
$11$	30.9441	+	17.8656i	0.848181	+	0.489698i	0.860037	−	0.510232i	$-0.170440\pi$
$11$	30.9441	+	17.8656i	0.848181	+	0.489698i	−0.0118554	+	0.999930i	$0.503774\pi$
$12$	−6.54654	−	83.2868i	−0.157485	−	2.00357i
$13$	−38.8149	−	10.4004i	−0.828102	−	0.221889i	−0.180216	−	0.983627i	$-0.557680\pi$
$13$	−38.8149	−	10.4004i	−0.828102	−	0.221889i	−0.647885	+	0.761738i	$0.724346\pi$
$14$	53.9978	+	93.5270i	1.03082	+	1.78544i
$15$	−55.7067	−	16.4852i	−0.958894	−	0.283763i
$16$	32.9388	−	57.0517i	0.514669	−	0.891433i
$17$	−54.1151	+	54.1151i	−0.772049	+	0.772049i	−0.978464	−	0.206415i	$-0.933820\pi$
$17$	−54.1151	+	54.1151i	−0.772049	+	0.772049i	0.206415	+	0.978464i	$0.433820\pi$
$18$	−77.8952	+	107.169i	−1.02000	+	1.40333i
$19$			55.2993i			0.667712i	0.942624	+	0.333856i	$0.108350\pi$
$19$			55.2993i			0.667712i	−0.942624	+	0.333856i	$0.891650\pi$
$20$	−113.175	−	139.657i	−1.26534	−	1.56141i
$21$	20.8517	−	112.444i	0.216677	−	1.16844i
$22$	45.3788	−	169.356i	0.439764	−	1.64122i
$23$	25.9049	−	96.6785i	0.234850	−	0.876472i	−0.743366	−	0.668885i	$-0.766772\pi$
$23$	25.9049	−	96.6785i	0.234850	−	0.876472i	0.978216	−	0.207588i	$-0.0665613\pi$
$24$	−194.159	+	68.7336i	−1.65135	+	0.584591i
$25$	−118.854	+	38.7131i	−0.950833	+	0.309704i
$26$			197.181i			1.48732i
$27$	136.429	−	32.7111i	0.972439	−	0.233157i
$28$	250.215	−	250.215i	1.68879	−	1.68879i
$29$	74.2482	−	128.602i	0.475432	−	0.823473i	−0.524172	−	0.851613i	$-0.675625\pi$
$29$	74.2482	−	128.602i	0.475432	−	0.823473i	0.999604	+	0.0281395i	$0.00895827\pi$
$30$	−7.38730	+	284.971i	−0.0449577	+	1.73428i
$31$	102.561	+	177.641i	0.594210	+	1.02920i	0.993658	+	0.112446i	$0.0358685\pi$
$31$	102.561	+	177.641i	0.594210	+	1.02920i	−0.399448	+	0.916756i	$0.630798\pi$
$32$	−5.94267	−	1.59233i	−0.0328289	−	0.00879649i
$33$	−153.021	+	105.146i	−0.807200	+	0.554656i
$34$	325.217	+	187.764i	1.64042	+	0.947098i
$35$	−100.165	−	224.756i	−0.483743	−	1.08545i
$36$	405.242	+	155.649i	1.87612	+	0.720599i
$37$	−151.248	−	151.248i	−0.672027	−	0.672027i	0.286156	−	0.958183i	$-0.407622\pi$
$37$	−151.248	−	151.248i	−0.672027	−	0.672027i	−0.958183	+	0.286156i	$0.907622\pi$
$38$	262.104	−	70.2305i	1.11892	−	0.299813i
$39$	135.622	−	158.762i	0.556845	−	0.651852i
$40$	−260.358	+	358.624i	−1.02915	+	1.41759i
$41$	−38.4281	+	22.1865i	−0.146377	+	0.0845108i	−0.571400	−	0.820672i	$-0.693599\pi$
$41$	−38.4281	+	22.1865i	−0.146377	+	0.0845108i	0.425023	+	0.905183i	$0.360266\pi$
$42$	−559.436	+	43.9730i	−2.05531	+	0.161552i
$43$	−11.3232	−	42.2588i	−0.0401575	−	0.149870i	0.942936	−	0.332974i	$-0.108052\pi$
$43$	−11.3232	−	42.2588i	−0.0401575	−	0.149870i	−0.983094	+	0.183104i	$0.941385\pi$
$44$	−574.485			−1.96834
$45$	201.953	−	224.366i	0.669009	−	0.743255i
$46$	−491.130			−1.57420
$47$	126.857	+	473.436i	0.393702	+	1.46932i	0.823980	+	0.566619i	$0.191749\pi$
$47$	126.857	+	473.436i	0.393702	+	1.46932i	−0.430278	+	0.902696i	$0.641585\pi$
$48$	193.859	+	282.126i	0.582940	+	0.848362i
$49$	122.445	−	70.6935i	0.356982	−	0.206104i
$50$	334.435	+	514.171i	0.945925	+	1.45429i
$51$	−132.706	−	374.867i	−0.364363	−	1.02925i
$52$	624.066	−	167.218i	1.66428	−	0.445941i
$53$	215.632	+	215.632i	0.558855	+	0.558855i	0.928982	−	0.370126i	$-0.120686\pi$
$53$	215.632	+	215.632i	0.558855	+	0.558855i	−0.370126	+	0.928982i	$0.620686\pi$
$54$	−328.308	−	605.096i	−0.827353	−	1.52487i
$55$	−143.028	+	373.005i	−0.350653	+	0.914471i
$56$	−755.509	−	436.194i	−1.80284	−	1.04087i
$57$	−259.340	−	123.730i	−0.602639	−	0.287517i
$58$	−703.833	−	188.591i	−1.59341	−	0.426953i
$59$	21.8014	+	37.7612i	0.0481069	+	0.0833235i	0.889076	−	0.457759i	$-0.151348\pi$
$59$	21.8014	+	37.7612i	0.0481069	+	0.0833235i	−0.840969	+	0.541083i	$0.818015\pi$
$60$	908.181	−	218.287i	1.95409	−	0.469680i
$61$	−16.1944	+	28.0496i	−0.0339915	+	0.0588751i	−0.882521	−	0.470274i	$-0.844155\pi$
$61$	−16.1944	+	28.0496i	−0.0339915	+	0.0588751i	0.848529	+	0.529149i	$0.177489\pi$
$62$	711.717	−	711.717i	1.45787	−	1.45787i
$63$	480.679	+	349.379i	0.961268	+	0.698692i
$64$		−	496.832i		−	0.970376i
$65$	46.8003	−	446.828i	0.0893055	−	0.852650i
$66$	692.704	+	591.744i	1.29191	+	1.10362i
$67$	−268.503	+	1002.07i	−0.489594	+	1.82719i	0.0688217	+	0.997629i	$0.478076\pi$
$67$	−268.503	+	1002.07i	−0.489594	+	1.82719i	−0.558416	+	0.829561i	$0.688591\pi$
$68$	318.464	−	1188.53i	0.567934	−	2.11956i
$69$	395.437	+	337.802i	0.689927	+	0.589371i
$70$	−938.073	+	760.198i	−1.60173	+	1.29802i
$71$		−	53.5643i		−	0.0895339i	−0.998997	−	0.0447670i	$-0.985745\pi$
$71$		−	53.5643i		−	0.0895339i	0.998997	−	0.0447670i	$-0.0142545\pi$
$72$	112.079	−	1064.34i	0.183454	−	1.74214i
$73$	23.7710	−	23.7710i	0.0381122	−	0.0381122i	−0.687794	−	0.725906i	$-0.741421\pi$
$73$	23.7710	−	23.7710i	0.0381122	−	0.0381122i	0.725906	+	0.687794i	$0.241421\pi$
$74$	−524.789	+	908.961i	−0.824398	+	1.42790i
$75$	84.3773	−	644.015i	0.129907	−	0.991526i
$76$	−444.551	−	769.984i	−0.670967	−	1.16215i
$77$	−759.604	−	203.535i	−1.12422	−	0.301234i
$78$	−924.730	−	441.185i	−1.34237	−	0.640441i
$79$	189.055	+	109.151i	0.269244	+	0.155448i	0.628544	−	0.777774i	$-0.283651\pi$
$79$	189.055	+	109.151i	0.269244	+	0.155448i	−0.359300	+	0.933222i	$0.616984\pi$
$80$	687.710	+	263.702i	0.961103	+	0.368535i
$81$	−151.849	+	713.010i	−0.208298	+	0.978065i
$82$	153.962	+	153.962i	0.207344	+	0.207344i
$83$	275.656	−	73.8617i	0.364544	−	0.0976792i	−0.0718973	−	0.997412i	$-0.522905\pi$
$83$	275.656	−	73.8617i	0.364544	−	0.0976792i	0.436441	+	0.899733i	$0.356239\pi$
$84$	613.598	+	1733.29i	0.797012	+	2.25140i
$85$	−692.404	−	502.679i	−0.883551	−	0.641449i
$86$	−185.915	+	107.338i	−0.233113	+	0.134588i
$87$	436.982	+	635.947i	0.538498	+	0.783686i
$88$	366.570	+	1368.06i	0.444050	+	1.65722i
$89$	−870.778			−1.03710			−0.518552	−	0.855046i	$-0.673529\pi$
$89$	−870.778			−1.03710			−0.518552	+	0.855046i	$0.673529\pi$
$90$	−1319.92	−	672.258i	−1.54590	−	0.787357i
$91$	884.405			1.01880
$92$	416.499	+	1554.40i	0.471989	+	1.76149i
$93$	−1062.57	+	83.5204i	−1.18477	+	0.0931254i
$94$	2082.85	−	1202.54i	2.28542	−	1.31949i
$95$	−610.618	+	96.9387i	−0.659454	+	0.104692i
$96$	20.7642	−	24.3069i	0.0220753	−	0.0258417i
$97$	127.719	−	34.2222i	0.133690	−	0.0358220i	−0.191354	−	0.981521i	$-0.561288\pi$
$97$	127.719	−	34.2222i	0.133690	−	0.0358220i	0.325043	+	0.945699i	$0.394621\pi$
$98$	−490.574	−	490.574i	−0.505668	−	0.505668i
$99$	−150.731	−	952.894i	−0.153020	−	0.967368i
$100$	1343.70	−	1494.51i	1.34370	−	1.49451i
$101$	97.7701	+	56.4476i	0.0963217	+	0.0556113i	0.547387	−	0.836880i	$-0.315623\pi$
$101$	97.7701	+	56.4476i	0.0963217	+	0.0556113i	−0.451065	+	0.892491i	$0.648956\pi$
$102$	−1608.23	+	1105.07i	−1.56116	+	1.07273i
$103$	800.791	+	214.571i	0.766061	+	0.205266i	0.620631	−	0.784103i	$-0.286877\pi$
$103$	800.791	+	214.571i	0.766061	+	0.205266i	0.145431	+	0.989368i	$0.453543\pi$
$104$	−796.412	−	1379.43i	−0.750910	−	1.30061i
$105$	1278.17	+	33.1339i	1.18796	+	0.0307956i
$106$	748.184	−	1295.89i	0.685566	−	1.18744i
$107$	841.614	−	841.614i	0.760392	−	0.760392i	−0.216001	−	0.976393i	$-0.569302\pi$
$107$	841.614	−	841.614i	0.760392	−	0.760392i	0.976393	+	0.216001i	$0.0693015\pi$
$108$	−1636.67	+	1552.22i	−1.45823	+	1.38299i
$109$			1008.98i			0.886634i	0.896365	+	0.443317i	$0.146198\pi$
$109$			1008.98i			0.886634i	−0.896365	+	0.443317i	$0.853802\pi$
$110$	1949.59	+	204.198i	1.68987	+	0.176995i
$111$	1047.73	−	370.903i	0.895908	−	0.317158i
$112$	−375.259	+	1400.48i	−0.316595	+	1.18155i
$113$	−502.567	+	1875.61i	−0.418385	+	1.56143i	0.359572	+	0.933117i	$0.382923\pi$
$113$	−502.567	+	1875.61i	−0.418385	+	1.56143i	−0.777957	+	0.628318i	$0.783744\pi$
$114$	−257.085	+	1386.34i	−0.211212	+	1.13897i
$115$	1112.94	+	116.568i	0.902454	+	0.0945220i
$116$			2387.52i			1.91100i
$117$	441.102	+	991.259i	0.348546	+	0.783264i
$118$	151.290	−	151.290i	0.118029	−	0.118029i
$119$	842.169	−	1458.68i	0.648752	−	1.12367i
$120$	−1099.32	−	2023.42i	−0.836279	−	1.53927i
$121$	−27.1419	−	47.0112i	−0.0203921	−	0.0353202i
$122$	153.515	+	41.1341i	0.113923	+	0.0305255i
$123$	−18.0675	−	229.860i	−0.0132447	−	0.168502i
$124$	−2856.11	−	1648.97i	−2.06844	−	1.19421i
$125$	−635.821	−	1244.53i	−0.454956	−	0.890514i
$126$	1045.50	−	2722.00i	0.739208	−	1.92457i
$127$	−1231.81	−	1231.81i	−0.860676	−	0.860676i	0.130741	−	0.991417i	$-0.458264\pi$
$127$	−1231.81	−	1231.81i	−0.860676	−	0.860676i	−0.991417	+	0.130741i	$0.958264\pi$
$128$	−2402.39	+	643.719i	−1.65893	+	0.444510i
$129$	223.518	+	41.4495i	0.152556	+	0.0282901i
$130$	−2177.28	+	345.655i	−1.46893	+	0.233199i
$131$	−1205.79	+	696.162i	−0.804200	+	0.464305i	−0.844938	−	0.534865i	$-0.820362\pi$
$131$	−1205.79	+	696.162i	−0.804200	+	0.464305i	0.0407378	+	0.999170i	$0.487029\pi$
$132$	1285.39	−	2694.19i	0.847567	−	1.77651i
$133$	−315.001	−	1175.60i	−0.205369	−	0.766447i
$134$	5090.52			3.28175
$135$	600.356	+	1449.12i	0.382744	+	0.923855i
$136$	−3033.52			−1.91266
$137$	−301.445	−	1125.01i	−0.187987	−	0.701575i	−0.993971	−	0.109639i	$-0.965030\pi$
$137$	−301.445	−	1125.01i	−0.187987	−	0.701575i	0.805985	−	0.591936i	$-0.201636\pi$
$138$	1098.89	−	2303.28i	0.677850	−	1.42078i
$139$	−1101.52	+	635.962i	−0.672155	+	0.388069i	−0.796893	−	0.604121i	$-0.793524\pi$
$139$	−1101.52	+	635.962i	−0.672155	+	0.388069i	0.124738	+	0.992190i	$0.460191\pi$
$140$	3201.51	+	2324.26i	1.93269	+	1.40312i
$141$	−2504.14	−	464.370i	−1.49565	−	0.277355i
$142$	−253.880	+	68.0270i	−0.150036	+	0.0402021i
$143$	−1015.28	−	1015.28i	−0.593722	−	0.593722i
$144$	−1756.85	+	277.903i	−1.01670	+	0.160823i
$145$	1550.18	+	594.416i	0.887832	+	0.340439i
$146$	−142.858	−	82.4790i	−0.0809794	−	0.0467535i
$147$	57.5691	+	732.409i	0.0323008	+	0.410940i
$148$	3321.85	+	890.087i	1.84496	+	0.494356i
$149$	−499.034	−	864.352i	−0.274379	−	0.475238i	0.695599	−	0.718430i	$-0.255139\pi$
$149$	−499.034	−	864.352i	−0.274379	−	0.475238i	−0.969978	+	0.243192i	$0.921806\pi$
$150$	−3159.62	+	417.978i	−1.71988	+	0.227519i
$151$	1319.57	−	2285.56i	0.711160	−	1.23177i	−0.253262	−	0.967398i	$-0.581503\pi$
$151$	1319.57	−	2285.56i	0.711160	−	1.23177i	0.964422	−	0.264368i	$-0.0851633\pi$
$152$	−1549.95	+	1549.95i	−0.827089	+	0.827089i
$153$	2054.95	+	216.395i	1.08584	+	0.114343i
$154$			3858.81i			2.01917i
$155$	−1781.73	+	1443.89i	−0.923305	+	0.748231i
$156$	−612.114	+	3300.86i	−0.314156	+	1.69410i
$157$	−160.486	+	598.944i	−0.0815810	+	0.304464i	−0.994645	−	0.103352i	$-0.967043\pi$
$157$	−160.486	+	598.944i	−0.0815810	+	0.304464i	0.913064	+	0.407817i	$0.133710\pi$
$158$	277.245	−	1034.69i	0.139597	−	0.520985i
$159$	−1493.73	+	528.791i	−0.745034	+	0.263748i
$160$	7.16525	−	68.4107i	0.00354039	−	0.0338021i
$161$			2202.84i			1.07831i
$162$	3572.32	−	185.804i	1.73252	−	0.0901118i
$163$	1015.96	−	1015.96i	0.488196	−	0.488196i	−0.419540	−	0.907737i	$-0.637809\pi$
$163$	1015.96	−	1015.96i	0.488196	−	0.488196i	0.907737	+	0.419540i	$0.137809\pi$
$164$	356.714	−	617.846i	0.169845	−	0.294181i
$165$	−1429.28	−	1505.35i	−0.674358	−	0.710251i
$166$	−700.169	−	1212.73i	−0.327372	−	0.567024i
$167$	2209.46	+	592.024i	1.02379	+	0.274324i	0.731382	−	0.681968i	$-0.238876\pi$
$167$	2209.46	+	592.024i	1.02379	+	0.274324i	0.292411	+	0.956293i	$0.405543\pi$
$168$	3736.06	−	2567.18i	1.71574	−	1.17894i
$169$	−504.228	−	291.116i	−0.229508	−	0.132506i
$170$	−1503.21	+	3920.22i	−0.678180	+	1.76863i
$171$	1160.53	−	939.398i	0.518993	−	0.420103i
$172$	497.381	+	497.381i	0.220494	+	0.220494i
$173$	2826.92	−	757.471i	1.24235	−	0.332887i	0.422974	−	0.906142i	$-0.360986\pi$
$173$	2826.92	−	757.471i	1.24235	−	0.332887i	0.819377	+	0.573255i	$0.194320\pi$
$174$	2459.25	−	2878.83i	1.07147	−	1.25428i
$175$	2306.18	−	1500.02i	0.996177	−	0.647949i
$176$	2038.52	−	1176.94i	0.873066	−	0.504065i
$177$	−225.870	+	17.7540i	−0.0959179	+	0.00753938i
$178$	1105.89	+	4127.25i	0.465676	+	1.73793i
$179$	−3623.88			−1.51319			−0.756595	−	0.653883i	$-0.773139\pi$
$179$	−3623.88			−1.51319			−0.756595	+	0.653883i	$0.773139\pi$
$180$	−1008.31	+	4747.55i	−0.417527	+	1.96590i
$181$	−3609.03			−1.48208			−0.741042	−	0.671459i	$-0.765668\pi$
$181$	−3609.03			−1.48208			−0.741042	+	0.671459i	$0.765668\pi$
$182$	−1123.20	−	4191.84i	−0.457457	−	1.70725i
$183$	−95.3110	−	138.708i	−0.0385005	−	0.0560304i
$184$	3435.82	−	1983.67i	1.37659	−	0.794772i
$185$	1404.95	−	1935.22i	0.558347	−	0.769084i
$186$	1745.33	+	4930.22i	0.688033	+	1.94355i
$187$	−2641.34	+	707.745i	−1.03291	+	0.276767i
$188$	−5572.30	−	5572.30i	−2.16171	−	2.16171i
$189$	−2714.00	+	1472.54i	−1.04452	+	0.566729i
$190$	1234.95	+	2771.05i	0.471542	+	1.05807i
$191$	1137.14	+	656.527i	0.430788	+	0.248715i	0.699682	−	0.714454i	$-0.253325\pi$
$191$	1137.14	+	656.527i	0.430788	+	0.248715i	−0.268894	+	0.963170i	$0.586658\pi$
$192$	2330.02	+	1111.64i	0.875806	+	0.417844i
$193$	−740.960	−	198.540i	−0.276350	−	0.0740476i	0.117982	−	0.993016i	$-0.462357\pi$
$193$	−740.960	−	198.540i	−0.276350	−	0.0740476i	−0.394332	+	0.918968i	$0.629024\pi$
$194$	−324.408	−	561.891i	−0.120057	−	0.207945i
$195$	1990.80	+	1219.24i	0.731098	+	0.447753i
$196$	−1136.61	+	1968.66i	−0.414216	+	0.717443i
$197$	1124.09	−	1124.09i	0.406537	−	0.406537i	−0.473992	−	0.880529i	$-0.657187\pi$
$197$	1124.09	−	1124.09i	0.406537	−	0.406537i	0.880529	+	0.473992i	$0.157187\pi$
$198$	−4325.03	+	1924.61i	−1.55236	+	0.690787i
$199$			974.029i			0.346970i	0.984836	+	0.173485i	$0.0555028\pi$
$199$			974.029i			0.346970i	−0.984836	+	0.173485i	$0.944497\pi$
$200$	−4416.35	−	2246.22i	−1.56142	−	0.794160i
$201$	−4098.67	−	3501.29i	−1.43830	−	1.22867i
$202$	143.378	−	535.093i	0.0499407	−	0.186381i
$203$	−845.879	+	3156.86i	−0.292458	+	1.09147i
$204$	4861.33	+	4152.80i	1.66844	+	1.42527i
$205$	−312.348	−	385.433i	−0.106416	−	0.131316i
$206$		−	4068.04i		−	1.37589i
$207$	−2468.98	+	1098.68i	−0.829016	+	0.368906i
$208$	−1871.88	+	1871.88i	−0.623998	+	0.623998i
$209$	−987.954	+	1711.19i	−0.326977	+	0.566341i
$210$	−1466.23	−	6100.25i	−0.481809	−	2.00456i
$211$	2371.15	+	4106.94i	0.773632	+	1.33997i	0.935560	+	0.353167i	$0.114895\pi$
$211$	2371.15	+	4106.94i	0.773632	+	1.33997i	−0.161928	+	0.986803i	$0.551771\pi$
$212$	−4735.91	−	1268.98i	−1.53426	−	0.411105i
$213$	251.203	+	119.848i	0.0808082	+	0.0385533i
$214$	−5057.88	−	2920.17i	−1.61565	−	0.932798i
$215$	446.774	−	199.110i	0.141720	−	0.0631591i
$216$	4740.73	+	2907.06i	1.49336	+	0.915741i
$217$	−3192.23	−	3192.23i	−0.998629	−	0.998629i
$218$	4782.31	−	1281.42i	1.48578	−	0.398112i
$219$	58.2934	+	164.667i	0.0179868	+	0.0508090i
$220$	−1007.06	−	6343.50i	−0.308619	−	1.94399i
$221$	2663.29	−	1537.65i	0.810645	−	0.468026i
$222$	−3088.60	−	4494.90i	−0.933754	−	1.35891i
$223$	1214.35	+	4532.02i	0.364659	+	1.36093i	0.867882	+	0.496770i	$0.165481\pi$
$223$	1214.35	+	4532.02i	0.364659	+	1.36093i	−0.503223	+	0.864157i	$0.667852\pi$
$224$	135.405			0.0403889
$225$	2831.48	+	1836.67i	0.838957	+	0.544198i
$226$	9528.13			2.80443
$227$	86.7255	+	323.664i	0.0253576	+	0.0946358i	0.977445	−	0.211190i	$-0.0677340\pi$
$227$	86.7255	+	323.664i	0.0253576	+	0.0946358i	−0.952087	+	0.305826i	$0.901067\pi$
$228$	4605.70	−	362.019i	1.33781	−	0.105155i
$229$	1072.94	−	619.462i	0.309615	−	0.178756i	−0.337139	−	0.941455i	$-0.609459\pi$
$229$	1072.94	−	619.462i	0.309615	−	0.178756i	0.646754	+	0.762699i	$0.276126\pi$
$230$	−860.942	−	5423.08i	−0.246821	−	1.55473i
$231$	2654.12	−	3106.95i	0.755965	−	0.884945i
$232$	5685.55	−	1523.44i	1.60894	−	0.431115i
$233$	3854.73	+	3854.73i	1.08383	+	1.08383i	0.996149	+	0.0876793i	$0.0279451\pi$
$233$	3854.73	+	3854.73i	1.08383	+	1.08383i	0.0876793	+	0.996149i	$0.472055\pi$
$234$	4138.10	−	3349.61i	1.15605	−	0.935774i
$235$	−5005.34	+	2230.69i	−1.38941	+	0.619208i
$236$	−607.124	−	350.523i	−0.167459	−	0.0966827i
$237$	−934.893	+	642.398i	−0.256236	+	0.176069i
$238$	−7983.32	−	2139.12i	−2.17429	−	0.582600i
$239$	674.870	+	1168.91i	0.182651	+	0.316362i	0.942783	−	0.333408i	$-0.108199\pi$
$239$	674.870	+	1168.91i	0.182651	+	0.316362i	−0.760131	+	0.649770i	$0.774865\pi$
$240$	−2775.42	+	2635.16i	−0.746469	+	0.708746i
$241$	2347.24	−	4065.54i	0.627381	−	1.08666i	−0.360694	−	0.932684i	$-0.617460\pi$
$241$	2347.24	−	4065.54i	0.627381	−	1.08666i	0.988075	−	0.153972i	$-0.0492066\pi$
$242$	−188.350	+	188.350i	−0.0500314	+	0.0500314i
$243$	−3004.08	−	2307.47i	−0.793053	−	0.609153i
$244$		−	520.747i		−	0.136629i
$245$	995.245	+	1228.12i	0.259526	+	0.320251i
$246$	−1066.53	+	377.559i	−0.276420	+	0.0978547i
$247$	575.137	−	2146.44i	0.148158	−	0.552934i
$248$	−2104.37	+	7853.61i	−0.538821	+	2.01091i
$249$	−270.377	+	1458.02i	−0.0688129	+	0.371077i
$250$	−5091.25	+	4594.18i	−1.28799	+	1.16225i
$251$		−	2822.23i		−	0.709712i	−0.934921	−	0.354856i	$-0.884530\pi$
$251$		−	2822.23i		−	0.709712i	0.934921	−	0.354856i	$-0.115470\pi$
$252$	−9501.60	−	1000.55i	−2.37518	−	0.250115i
$253$	2528.82	−	2528.82i	0.628402	−	0.628402i
$254$	−4274.05	+	7402.88i	−1.05582	+	1.82873i
$255$	3906.67	−	2122.48i	0.959393	−	0.521234i
$256$	4114.79	+	7127.02i	1.00459	+	1.73999i
$257$	7557.21	+	2024.95i	1.83426	+	0.491489i	0.998353	−	0.0573767i	$-0.0182736\pi$
$257$	7557.21	+	2024.95i	1.83426	+	0.491489i	0.835910	+	0.548866i	$0.184940\pi$
$258$	−87.4105	−	1112.06i	−0.0210928	−	0.268348i
$259$	4076.91	+	2353.81i	0.978096	+	0.564704i
$260$	2940.41	+	6597.84i	0.701370	+	1.57377i
$261$	−3960.16	+	626.427i	−0.939188	+	0.148563i
$262$	4830.98	+	4830.98i	1.13916	+	1.13916i
$263$	−324.565	+	86.9668i	−0.0760970	+	0.0203901i	−0.296667	−	0.954981i	$-0.595875\pi$
$263$	−324.565	+	86.9668i	−0.0760970	+	0.0203901i	0.220570	+	0.975371i	$0.429208\pi$
$264$	−7236.03	−	1341.86i	−1.68692	−	0.312824i
$265$	−2003.02	+	2759.02i	−0.464320	+	0.639567i
$266$	−5171.98	+	2986.04i	−1.19216	+	0.688293i
$267$	1948.33	−	4083.73i	0.446577	−	0.936031i
$268$	−4316.98	−	16111.2i	−0.983961	−	3.67219i
$269$	5461.46			1.23789			0.618943	−	0.785436i	$-0.287561\pi$
$269$	5461.46			1.23789			0.618943	+	0.785436i	$0.287561\pi$
$270$	6105.98	−	4685.92i	1.37629	−	1.05621i
$271$	−5112.19			−1.14592			−0.572958	−	0.819585i	$-0.694204\pi$
$271$	−5112.19			−1.14592			−0.572958	+	0.819585i	$0.694204\pi$
$272$	1304.87	+	4869.85i	0.290880	+	1.08558i
$273$	−1978.82	+	4147.64i	−0.438696	+	0.919511i
$274$	−4949.39	+	2857.53i	−1.09125	+	0.630036i
$275$	−4369.46	−	925.457i	−0.958140	−	0.202935i
$276$	−8221.63	−	1524.63i	−1.79306	−	0.332507i
$277$	−145.481	+	38.9814i	−0.0315563	+	0.00845548i	−0.274563	−	0.961569i	$-0.588533\pi$
$277$	−145.481	+	38.9814i	−0.0315563	+	0.00845548i	0.243006	+	0.970025i	$0.421866\pi$
$278$	4413.22	+	4413.22i	0.952114	+	0.952114i
$279$	1985.77	−	5170.05i	0.426111	−	1.10940i
$280$	3492.08	−	9107.02i	0.745328	−	1.94374i
$281$	3550.17	+	2049.69i	0.753684	+	0.435140i	0.827024	−	0.562167i	$-0.190032\pi$
$281$	3550.17	+	2049.69i	0.753684	+	0.435140i	−0.0733392	+	0.997307i	$0.523366\pi$
$282$	979.283	+	12458.7i	0.206792	+	2.63087i
$283$	333.006	+	89.2286i	0.0699475	+	0.0187424i	0.293623	−	0.955921i	$-0.405139\pi$
$283$	333.006	+	89.2286i	0.0699475	+	0.0187424i	−0.223676	+	0.974664i	$0.571806\pi$
$284$	430.603	+	745.826i	0.0899703	+	0.155833i
$285$	911.618	−	3080.54i	0.189472	−	0.640266i
$286$	−3522.75	+	6101.59i	−0.728338	+	1.26152i
$287$	690.557	−	690.557i	0.142029	−	0.142029i
$288$	67.5340	+	151.764i	0.0138176	+	0.0310514i
$289$		−	943.881i		−	0.192119i
$290$	848.632	−	8102.36i	0.171839	−	1.64065i
$291$	−125.273	+	675.540i	−0.0252358	+	0.136085i
$292$	−139.891	+	522.082i	−0.0280360	+	0.104632i
$293$	456.519	−	1703.75i	0.0910243	−	0.339707i	−0.905362	−	0.424640i	$-0.860401\pi$
$293$	456.519	−	1703.75i	0.0910243	−	0.339707i	0.996387	+	0.0849324i	$0.0270674\pi$
$294$	3398.31	−	1203.03i	0.674128	−	0.238646i
$295$	−378.744	+	306.927i	−0.0747502	+	0.0605763i
$296$		−	8478.47i		−	1.66487i
$297$	4806.09	+	1425.18i	0.938981	+	0.278441i
$298$	−3463.02	+	3463.02i	−0.673179	+	0.673179i
$299$	−2011.00	+	3483.15i	−0.388960	+	0.673698i
$300$	4002.37	+	9645.54i	0.770256	+	1.85628i
$301$	481.437	+	833.873i	0.0921912	+	0.159680i
$302$	−12508.8	−	3351.73i	−2.38345	−	0.638644i
$303$	−483.482	+	332.218i	−0.0916678	+	0.0629882i
$304$	3154.92	+	1821.49i	0.595221	+	0.343651i
$305$	−338.114	−	129.649i	−0.0634765	−	0.0243400i
$306$	−1584.16	−	10014.8i	−0.295948	−	1.87093i
$307$	−1654.78	−	1654.78i	−0.307633	−	0.307633i	0.536358	−	0.843991i	$-0.319800\pi$
$307$	−1654.78	−	1654.78i	−0.307633	−	0.307633i	−0.843991	+	0.536358i	$0.819800\pi$
$308$	12212.9	−	3272.44i	2.25940	−	0.605404i
$309$	−2798.03	+	3275.42i	−0.515127	+	0.603016i
$310$	9106.45	+	6611.20i	1.66842	+	1.21126i
$311$	852.679	−	492.295i	0.155469	−	0.0897603i	−0.420247	−	0.907410i	$-0.638057\pi$
$311$	852.679	−	492.295i	0.155469	−	0.0897603i	0.575716	+	0.817649i	$0.304723\pi$
$312$	8251.11	−	648.557i	1.49720	−	0.117684i
$313$	−2270.15	−	8472.33i	−0.409957	−	1.52998i	−0.794726	−	0.606969i	$-0.792385\pi$
$313$	−2270.15	−	8472.33i	−0.409957	−	1.52998i	0.384768	−	0.923013i	$-0.374281\pi$
$314$	3042.65			0.546837
$315$	−3015.24	+	5920.14i	−0.539332	+	1.05893i
$316$	−3509.85			−0.624824
$317$	1329.11	+	4960.32i	0.235490	+	0.878862i	0.977927	+	0.208946i	$0.0670033\pi$
$317$	1329.11	+	4960.32i	0.235490	+	0.878862i	−0.742437	+	0.669916i	$0.766330\pi$
$318$	4403.38	+	6408.31i	0.776507	+	1.13006i
$319$	4595.09	−	2652.97i	0.806506	−	0.465636i
$320$	5486.05	−	870.938i	0.958374	−	0.152147i
$321$	2063.88	+	5830.04i	0.358861	+	1.01371i
$322$	10440.9	−	2797.62i	1.80698	−	0.484178i
$323$	−2992.53	−	2992.53i	−0.515507	−	0.515507i
$324$	−3617.54	−	11148.6i	−0.620292	−	1.91163i
$325$	5015.95	−	266.511i	0.856107	−	0.0454873i
$326$	−6105.64	−	3525.10i	−1.03730	−	0.598886i
$327$	−4731.88	−	2257.56i	−0.800225	−	0.381785i
$328$	−1698.93	−	455.226i	−0.285999	−	0.0766331i
$329$	−5393.67	−	9342.11i	−0.903837	−	1.56549i
$330$	−5319.77	+	8686.20i	−0.887405	+	1.44897i
$331$	−933.056	+	1616.10i	−0.154941	+	0.268365i	−0.933037	−	0.359779i	$-0.882852\pi$
$331$	−933.056	+	1616.10i	−0.154941	+	0.268365i	0.778097	+	0.628145i	$0.216185\pi$
$332$	−3244.44	+	3244.44i	−0.536330	+	0.536330i
$333$	−604.808	+	5743.46i	−0.0995294	+	0.945164i
$334$		−	11224.1i		−	1.83879i
$335$	−11535.5	−	1208.22i	−1.88136	−	0.197051i
$336$	−5728.29	−	4893.40i	−0.930071	−	0.794515i
$337$	549.952	−	2052.45i	0.0888955	−	0.331762i	−0.907128	−	0.420855i	$-0.861730\pi$
$337$	549.952	−	2052.45i	0.0888955	−	0.331762i	0.996023	+	0.0890927i	$0.0283967\pi$
$338$	−739.439	+	2759.63i	−0.118995	+	0.444094i
$339$	−7671.65	−	6553.51i	−1.22911	−	1.04996i
$340$	13682.0	+	1433.04i	2.18239	+	0.228581i
$341$			7329.25i			1.16393i
$342$	−5926.37	−	4307.55i	−0.937022	−	0.681069i
$343$	3137.62	−	3137.62i	0.493922	−	0.493922i
$344$	867.074	−	1501.82i	0.135900	−	0.235385i
$345$	−3036.84	+	4958.60i	−0.473907	+	0.773803i
$346$	−7180.42	−	12436.8i	−1.11567	−	1.93240i
$347$	−3014.63	−	807.768i	−0.466380	−	0.124966i	0.0179736	−	0.999838i	$-0.494279\pi$
$347$	−3014.63	−	807.768i	−0.466380	−	0.124966i	−0.484354	+	0.874872i	$0.660945\pi$
$348$	−11196.9	−	5341.99i	−1.72476	−	0.822876i
$349$	9231.54	+	5329.83i	1.41591	+	0.817477i	0.995936	−	0.0900593i	$-0.0287057\pi$
$349$	9231.54	+	5329.83i	1.41591	+	0.817477i	0.419975	+	0.907536i	$0.362039\pi$
$350$	−10038.6	−	9025.65i	−1.53310	−	1.37840i
$351$	−5635.71	−	149.246i	−0.857014	−	0.0226956i
$352$	−155.443	−	155.443i	−0.0235373	−	0.0235373i
$353$	−7290.95	+	1953.60i	−1.09931	+	0.294561i	−0.762486	−	0.647005i	$-0.776021\pi$
$353$	−7290.95	+	1953.60i	−1.09931	+	0.294561i	−0.336829	+	0.941566i	$0.609355\pi$
$354$	371.006	+	1048.02i	0.0557027	+	0.157349i
$355$	591.460	−	93.8972i	0.0884266	−	0.0140382i
$356$	12124.7	−	7000.17i	1.80507	−	1.04216i
$357$	4956.52	+	7213.31i	0.734809	+	1.06938i
$358$	4602.35	+	17176.2i	0.679446	+	2.53573i
$359$	7412.54			1.08975			0.544873	−	0.838519i	$-0.316578\pi$
$359$	7412.54			1.08975			0.544873	+	0.838519i	$0.316578\pi$
$360$	11949.0	−	628.188i	1.74936	−	0.0919678i
$361$	3800.99			0.554160
$362$	4583.49	+	17105.8i	0.665478	+	2.48360i
$363$	281.200	−	22.1030i	0.0406589	−	0.00319589i
$364$	−12314.4	+	7109.73i	−1.77321	+	1.02377i
$365$	304.151	+	220.811i	0.0436165	+	0.0316651i
$366$	−536.392	+	627.909i	−0.0766056	+	0.0896757i
$367$	−11220.0	+	3006.39i	−1.59586	+	0.427609i	−0.943788	−	0.330551i	$-0.892765\pi$
$367$	−11220.0	+	3006.39i	−1.59586	+	0.427609i	−0.652069	+	0.758160i	$0.726099\pi$
$368$	−4662.40	−	4662.40i	−0.660446	−	0.660446i
$369$	1118.41	+	429.570i	0.157783	+	0.0606031i
$370$	−10956.7	−	4201.36i	−1.53950	−	0.590319i
$371$	−5812.40	−	3355.79i	−0.813381	−	0.469606i
$372$	14123.7	−	9704.91i	1.96850	−	1.35262i
$373$	−10312.6	−	2763.24i	−1.43154	−	0.383580i	−0.541978	−	0.840393i	$-0.682324\pi$
$373$	−10312.6	−	2763.24i	−1.43154	−	0.383580i	−0.889563	+	0.456813i	$0.848991\pi$
$374$	6709.04	+	11620.4i	0.927584	+	1.60662i
$375$	7259.16	−	197.248i	0.999631	−	0.0271623i
$376$	−9714.06	+	16825.2i	−1.33235	+	2.30770i
$377$	−4219.45	+	4219.45i	−0.576426	+	0.576426i
$378$	10426.3	+	10993.5i	1.41870	+	1.49589i
$379$			7637.00i			1.03506i	0.855666	+	0.517528i	$0.173148\pi$
$379$			7637.00i			1.03506i	−0.855666	+	0.517528i	$0.826852\pi$
$380$	7722.92	−	6258.52i	1.04257	−	0.844883i
$381$	8533.04	−	3020.76i	1.14740	−	0.406189i
$382$	1667.59	−	6223.53i	0.223354	−	0.833569i
$383$	1250.05	−	4665.26i	0.166775	−	0.622411i	−0.831033	−	0.556224i	$-0.812250\pi$
$383$	1250.05	−	4665.26i	0.166775	−	0.622411i	0.997807	−	0.0661874i	$-0.0210835\pi$
$384$	2356.39	−	12706.9i	0.313148	−	1.68867i
$385$	915.876	−	8744.38i	0.121240	−	1.15755i
$386$			3764.10i			0.496341i
$387$	−694.502	+	955.503i	−0.0912236	+	0.125506i
$388$	−1503.24	+	1503.24i	−0.196689	+	0.196689i
$389$	6965.92	−	12065.3i	0.907934	−	1.57259i	0.0910048	−	0.995850i	$-0.470992\pi$
$389$	6965.92	−	12065.3i	0.907934	−	1.57259i	0.816929	−	0.576738i	$-0.195675\pi$
$390$	3250.56	−	10984.3i	0.422048	−	1.42618i
$391$	3829.92	+	6633.61i	0.495364	+	0.857995i
$392$	5413.35	+	1450.50i	0.697489	+	0.186892i
$393$	−566.918	−	7212.48i	−0.0727665	−	0.925754i
$394$	−6755.47	−	3900.27i	−0.863796	−	0.498713i
$395$	−873.840	+	2278.89i	−0.111311	+	0.290287i
$396$	9759.07	+	12056.3i	1.23841	+	1.52993i
$397$	2730.43	+	2730.43i	0.345179	+	0.345179i	0.858310	−	0.513131i	$-0.171515\pi$
$397$	2730.43	+	2730.43i	0.345179	+	0.345179i	−0.513131	+	0.858310i	$0.671515\pi$
$398$	4616.64	−	1237.02i	0.581435	−	0.155795i
$399$	6218.08	+	1153.09i	0.780183	+	0.144678i
$400$	−1706.27	+	8055.99i	−0.213284	+	1.00700i
$401$	−4840.65	+	2794.75i	−0.602820	+	0.348038i	−0.770150	−	0.637863i	$-0.779819\pi$
$401$	−4840.65	+	2794.75i	−0.602820	+	0.348038i	0.167330	+	0.985901i	$0.446485\pi$
$402$	−11389.9	+	23873.3i	−1.41312	+	2.96192i
$403$	−2133.36	−	7961.80i	−0.263698	−	0.984133i
$404$	−1815.13			−0.223530
$405$	−8139.28	−	426.833i	−0.998628	−	0.0523692i
$406$	16037.0			1.96035
$407$	−1978.10	−	7382.36i	−0.240911	−	0.899091i
$408$	6787.38	−	14226.4i	0.823592	−	1.72626i
$409$	−10223.3	+	5902.44i	−1.23597	+	0.713587i	−0.968268	−	0.249915i	$-0.919597\pi$
$409$	−10223.3	+	5902.44i	−1.23597	+	0.713587i	−0.267701	+	0.963502i	$0.586264\pi$
$410$	−1430.16	+	1969.95i	−0.172270	+	0.237290i
$411$	5950.47	+	1103.46i	0.714149	+	0.132433i
$412$	−12875.1	+	3449.87i	−1.53959	+	0.412532i
$413$	−678.573	−	678.573i	−0.0808484	−	0.0808484i
$414$	8343.07	+	10307.0i	0.990434	+	1.22358i
$415$	1298.80	+	2914.33i	0.153628	+	0.344720i
$416$	214.103	+	123.613i	0.0252339	+	0.0145688i
$417$	−517.894	−	6588.79i	−0.0608187	−	0.773751i
$418$	9365.28	+	2509.42i	1.09586	+	0.293636i
$419$	323.874	+	560.966i	0.0377620	+	0.0654057i	0.884289	−	0.466941i	$-0.154644\pi$
$419$	323.874	+	560.966i	0.0377620	+	0.0654057i	−0.846527	+	0.532346i	$0.821310\pi$
$420$	−18063.5	+	9813.81i	−2.09859	+	1.14015i
$421$	−1424.62	+	2467.51i	−0.164921	+	0.285651i	−0.936627	−	0.350328i	$-0.886070\pi$
$421$	−1424.62	+	2467.51i	−0.164921	+	0.285651i	0.771707	+	0.635979i	$0.219403\pi$
$422$	16454.4	−	16454.4i	1.89808	−	1.89808i
$423$	7780.69	−	10704.8i	0.894351	−	1.23046i
$424$			12087.6i			1.38450i
$425$	4336.84	−	8526.76i	0.494983	−	0.973196i
$426$	249.018	−	1342.84i	0.0283215	−	0.152725i
$427$	184.496	−	688.550i	0.0209096	−	0.0780358i
$428$	−4952.86	+	18484.3i	−0.559358	+	2.08755i
$429$	7033.08	−	2489.76i	0.791516	−	0.280203i
$430$	−1511.14	−	1864.72i	−0.169473	−	0.209127i
$431$		−	134.733i		−	0.0150577i	−0.999972	−	0.00752887i	$-0.997603\pi$
$431$		−	134.733i		−	0.0150577i	0.999972	−	0.00752887i	$-0.00239654\pi$
$432$	2627.60	−	8861.00i	0.292640	−	0.986863i
$433$	−5119.91	+	5119.91i	−0.568238	+	0.568238i	−0.931635	−	0.363396i	$-0.881617\pi$
$433$	−5119.91	+	5119.91i	−0.568238	+	0.568238i	0.363396	+	0.931635i	$0.381617\pi$
$434$	−11076.1	+	19184.5i	−1.22505	+	2.12185i
$435$	−6256.14	+	5939.98i	−0.689561	+	0.654713i
$436$	−8111.21	−	14049.0i	−0.890955	−	1.54318i
$437$	5346.26	+	1432.52i	0.585231	+	0.156812i
$438$	706.445	−	485.424i	0.0770668	−	0.0529553i
$439$	4915.51	+	2837.97i	0.534406	+	0.308540i	0.742809	−	0.669504i	$-0.233493\pi$
$439$	4915.51	+	2837.97i	0.534406	+	0.308540i	−0.208403	+	0.978043i	$0.566826\pi$
$440$	−14463.6	+	6445.86i	−1.56710	+	0.698396i
$441$	−3563.63	−	1368.75i	−0.384799	−	0.147798i
$442$	−10670.5	−	10670.5i	−1.14829	−	1.14829i
$443$	−12550.6	+	3362.93i	−1.34604	+	0.360671i	−0.858673	−	0.512524i	$-0.828711\pi$
$443$	−12550.6	+	3362.93i	−1.34604	+	0.360671i	−0.487371	+	0.873195i	$0.662044\pi$
$444$	−11606.8	+	13587.1i	−1.24062	+	1.45229i
$445$	−1526.46	−	9615.18i	−0.162609	−	1.02428i
$446$	19938.3	−	11511.4i	2.11683	−	1.22215i
$447$	5170.16	−	406.387i	0.547070	−	0.0430010i
$448$	2830.10	+	10562.1i	0.298459	+	1.11387i
$449$	−5699.77			−0.599084			−0.299542	−	0.954083i	$-0.596834\pi$
$449$	−5699.77			−0.599084			−0.299542	+	0.954083i	$0.596834\pi$
$450$	5109.32	−	15753.0i	0.535235	−	1.65023i
$451$	−1585.50			−0.165539
$452$	−8080.26	−	30156.0i	−0.840849	−	3.13809i
$453$	7766.23	+	11302.3i	0.805496	+	1.17225i
$454$	1423.94	−	822.111i	0.147200	−	0.0849859i
$455$	1550.35	+	9765.65i	0.159739	+	1.00620i
$456$	−3800.92	−	10736.8i	−0.390339	−	1.10263i
$457$	16682.5	−	4470.06i	1.70760	−	0.457550i	0.732766	−	0.680480i	$-0.238229\pi$
$457$	16682.5	−	4470.06i	1.70760	−	0.457550i	0.974834	+	0.222930i	$0.0715622\pi$
$458$	−4298.72	−	4298.72i	−0.438572	−	0.438572i
$459$	−5612.72	+	9153.05i	−0.570762	+	0.930779i
$460$	−16433.6	+	7323.83i	−1.66570	+	0.742338i
$461$	5324.34	+	3074.01i	0.537916	+	0.310566i	0.744234	−	0.667919i	$-0.232815\pi$
$461$	5324.34	+	3074.01i	0.537916	+	0.310566i	−0.206318	+	0.978485i	$0.566148\pi$
$462$	−18096.9	−	8633.95i	−1.82239	−	0.869454i
$463$	8781.07	+	2352.88i	0.881405	+	0.236172i	0.671013	−	0.741445i	$-0.265859\pi$
$463$	8781.07	+	2352.88i	0.881405	+	0.236172i	0.210392	+	0.977617i	$0.432526\pi$
$464$	−4891.30	−	8471.97i	−0.489381	−	0.847633i
$465$	−2784.90	−	11586.5i	−0.277735	−	1.15551i
$466$	13374.9	−	23165.9i	1.32957	−	2.30288i
$467$	−5400.86	+	5400.86i	−0.535164	+	0.535164i	−0.922105	−	0.386940i	$-0.873532\pi$
$467$	−5400.86	+	5400.86i	−0.535164	+	0.535164i	0.386940	+	0.922105i	$0.373532\pi$
$468$	−14110.6	−	10256.2i	−1.39372	−	1.01302i
$469$		−	22832.2i		−	2.24796i
$470$	16929.7	+	20891.0i	1.66151	+	2.05027i
$471$	−2449.81	−	2092.76i	−0.239663	−	0.204733i
$472$	−447.326	+	1669.44i	−0.0436226	+	0.162802i
$473$	404.591	−	1509.96i	0.0393301	−	0.146782i
$474$	4232.12	+	3615.29i	0.410100	+	0.350329i
$475$	−2140.81	−	6572.55i	−0.206793	−	0.634883i
$476$			27080.8i			2.60766i
$477$	862.266	−	8188.37i	0.0827683	−	0.785995i
$478$	4683.22	−	4683.22i	0.448129	−	0.448129i
$479$	5938.91	−	10286.5i	0.566504	−	0.981214i	−0.430404	−	0.902637i	$-0.641629\pi$
$479$	5938.91	−	10286.5i	0.566504	−	0.981214i	0.996908	−	0.0785777i	$-0.0250379\pi$
$480$	304.797	+	186.670i	0.0289834	+	0.0177505i
$481$	4297.63	+	7443.72i	0.407391	+	0.705623i
$482$	−22250.6	−	5962.02i	−2.10267	−	0.563408i
$483$	−10330.8	−	4928.77i	−0.973221	−	0.464320i
$484$	755.846	+	436.388i	0.0709848	+	0.0409831i
$485$	601.772	+	1350.29i	0.0563403	+	0.126419i
$486$	−7121.58	+	17169.0i	−0.664694	+	1.60248i
$487$	10315.2	+	10315.2i	0.959807	+	0.959807i	0.999223	−	0.0394159i	$-0.0125497\pi$
$487$	10315.2	+	10315.2i	0.959807	+	0.959807i	−0.0394159	+	0.999223i	$0.512550\pi$
$488$	−1240.09	+	332.280i	−0.115033	+	0.0308230i
$489$	2491.42	+	7037.76i	0.230401	+	0.650835i
$490$	4556.98	−	6276.91i	0.420129	−	0.578698i
$491$	11050.6	−	6380.07i	1.01570	−	0.586413i	0.102842	−	0.994698i	$-0.467206\pi$
$491$	11050.6	−	6380.07i	1.01570	−	0.586413i	0.912854	+	0.408285i	$0.133873\pi$
$492$	2099.41	+	3055.31i	0.192375	+	0.279967i
$493$	2941.34	+	10977.2i	0.268704	+	1.00282i
$494$	−10904.0			−0.993103
$495$	10257.7	−	3334.78i	0.931411	−	0.302803i
$496$	13513.0			1.22329
$497$	305.118	+	1138.72i	0.0275380	+	0.102773i
$498$	7254.00	−	570.182i	0.652730	−	0.0513061i
$499$	931.016	−	537.522i	0.0835230	−	0.0482221i	−0.457657	−	0.889129i	$-0.651311\pi$
$499$	931.016	−	537.522i	0.0835230	−	0.0482221i	0.541180	+	0.840907i	$0.317978\pi$
$500$	18857.9	+	12217.4i	1.68670	+	1.09276i
$501$	−7720.04	+	9037.19i	−0.688435	+	0.805892i
$502$	−13376.6	+	3584.26i	−1.18930	+	0.318672i
$503$	279.405	+	279.405i	0.0247675	+	0.0247675i	0.719382	−	0.694615i	$-0.244425\pi$
$503$	279.405	+	279.405i	0.0247675	+	0.0247675i	−0.694615	+	0.719382i	$0.744425\pi$
$504$	3680.14	+	23265.2i	0.325251	+	2.05618i
$505$	−451.908	+	1178.53i	−0.0398211	+	0.103850i
$506$	−15197.6	−	8774.32i	−1.33521	−	0.770882i
$507$	2493.45	−	1713.34i	0.218419	−	0.150083i
$508$	27054.2	+	7249.16i	2.36287	+	0.633129i
$509$	−2578.44	−	4465.98i	−0.224533	−	0.388902i	0.731646	−	0.681684i	$-0.238752\pi$
$509$	−2578.44	−	4465.98i	−0.224533	−	0.388902i	−0.956179	+	0.292782i	$0.905419\pi$
$510$	−15021.5	−	15821.0i	−1.30424	−	1.37366i
$511$	−369.938	+	640.752i	−0.0320257	+	0.0554701i
$512$	14485.0	−	14485.0i	1.25029	−	1.25029i
$513$	1808.90	+	7544.45i	0.155682	+	0.649309i
$514$		−	38390.8i		−	3.29445i
$515$	−965.537	+	9218.52i	−0.0826149	+	0.788770i
$516$	−3445.47	+	1219.72i	−0.293950	+	0.104061i
$517$	−4532.75	+	16916.4i	−0.385590	+	1.43904i
$518$	5978.70	−	22312.8i	0.507122	−	1.89260i
$519$	−2772.78	+	14952.4i	−0.234512	+	1.26462i
$520$	13835.6	−	11212.1i	1.16679	−	0.945548i
$521$		−	913.546i		−	0.0768199i	−0.999262	−	0.0384100i	$-0.987771\pi$
$521$		−	913.546i		−	0.0768199i	0.999262	−	0.0384100i	$-0.0122293\pi$
$522$	7998.53	+	17974.5i	0.670663	+	1.50714i
$523$	−9189.64	+	9189.64i	−0.768326	+	0.768326i	−0.977812	−	0.209485i	$-0.932821\pi$
$523$	−9189.64	+	9189.64i	−0.768326	+	0.768326i	0.209485	+	0.977812i	$0.432821\pi$
$524$	11192.9	−	19386.6i	0.933136	−	1.61624i
$525$	1874.74	+	14171.7i	0.155848	+	1.17810i
$526$	824.399	+	1427.90i	0.0683374	+	0.118364i
$527$	−15163.2	−	4062.95i	−1.25335	−	0.335835i
$528$	958.441	+	12193.5i	0.0789977	+	1.00503i
$529$	1861.26	+	1074.60i	0.152976	+	0.0883208i
$530$	15620.9	+	5989.81i	1.28024	+	0.490907i
$531$	422.115	−	1099.00i	0.0344976	−	0.0898164i
$532$	13836.7	+	13836.7i	1.12763	+	1.12763i
$533$	1722.33	−	461.498i	0.139967	−	0.0375041i
$534$	−21830.2	−	4048.21i	−1.76907	−	0.328059i
$535$	10768.5	+	7817.82i	0.870210	+	0.631764i
$536$	−35612.0	+	20560.6i	−2.86978	+	1.65687i
$537$	8108.29	−	16995.1i	0.651580	−	1.36572i
$538$	−6936.10	−	25885.9i	−0.555830	−	2.07439i
$539$	5051.92			0.403714
$540$	−20008.8	−	15351.2i	−1.59452	−	1.22335i
$541$	−23779.3			−1.88975			−0.944873	−	0.327437i	$-0.893815\pi$
$541$	−23779.3			−1.88975			−0.944873	+	0.327437i	$0.893815\pi$
$542$	6492.51	+	24230.4i	0.514534	+	1.92027i
$543$	8075.07	−	16925.4i	0.638185	−	1.33764i
$544$	407.757	−	235.419i	0.0321369	−	0.0185542i
$545$	−11141.3	+	1768.73i	−0.875668	+	0.139017i
$546$	22171.8	+	4111.57i	1.73785	+	0.322269i
$547$	−22174.6	+	5941.66i	−1.73330	+	0.464437i	−0.980940	−	0.194311i	$-0.937753\pi$
$547$	−22174.6	+	5941.66i	−1.73330	+	0.464437i	−0.752364	+	0.658748i	$0.771086\pi$
$548$	13241.2	+	13241.2i	1.03218	+	1.03218i
$549$	863.760	−	136.631i	0.0671482	−	0.0106216i
$550$	1162.83	+	21885.4i	0.0901515	+	1.69672i
$551$	7111.58	+	4105.87i	0.549843	+	0.317452i
$552$	1615.40	+	20551.5i	0.124558	+	1.58466i
$553$	−4640.84	−	1243.51i	−0.356869	−	0.0956228i
$554$	369.523	+	640.033i	0.0283385	+	0.0490837i
$555$	5932.18	+	10918.9i	0.453706	+	0.835100i
$556$	10225.0	−	17710.2i	0.779920	−	1.35086i
$557$	7388.21	−	7388.21i	0.562026	−	0.562026i	−0.367856	−	0.929883i	$-0.619908\pi$
$557$	7388.21	−	7388.21i	0.562026	−	0.562026i	0.929883	+	0.367856i	$0.119908\pi$
$558$	−27026.6	−	2846.00i	−2.05041	−	0.215916i
$559$			1758.04i			0.133018i
$560$	−16122.0	−	1688.60i	−1.21657	−	0.127422i
$561$	2590.76	−	13970.8i	0.194976	−	1.05142i
$562$	5206.25	−	19430.0i	0.390769	−	1.45837i
$563$	1541.08	−	5751.38i	0.115362	−	0.430536i	−0.883952	−	0.467578i	$-0.845127\pi$
$563$	1541.08	−	5751.38i	0.115362	−	0.430536i	0.999314	+	0.0370416i	$0.0117934\pi$
$564$	38600.5	−	13664.9i	2.88187	−	1.02020i
$565$	−21591.5	−	2261.47i	−1.60772	−	0.168391i
$566$		−	1691.68i		−	0.125630i
$567$	−833.375	−	16022.8i	−0.0617257	−	1.18676i
$568$	1501.32	−	1501.32i	0.110905	−	0.110905i
$569$	−5649.04	+	9784.43i	−0.416204	+	0.720887i	−0.995554	−	0.0941921i	$-0.969973\pi$
$569$	−5649.04	+	9784.43i	−0.416204	+	0.720887i	0.579350	+	0.815079i	$0.303307\pi$
$570$	−15758.7	−	408.513i	−1.15800	−	0.0300188i
$571$	−2788.98	−	4830.66i	−0.204405	−	0.354040i	0.745538	−	0.666463i	$-0.232193\pi$
$571$	−2788.98	−	4830.66i	−0.204405	−	0.354040i	−0.949943	+	0.312423i	$0.898859\pi$
$572$	22298.6	+	5974.89i	1.62998	+	0.436753i
$573$	−5623.25	+	3863.94i	−0.409974	+	0.281707i
$574$	−4150.07	−	2396.04i	−0.301778	−	0.174231i
$575$	663.813	+	12493.5i	0.0481442	+	0.906113i
$576$	−10426.7	+	8439.94i	−0.754244	+	0.610528i
$577$	11393.3	+	11393.3i	0.822023	+	0.822023i	0.986398	−	0.164375i	$-0.0525606\pi$
$577$	11393.3	+	11393.3i	0.822023	+	0.822023i	−0.164375	+	0.986398i	$0.552561\pi$
$578$	−4473.74	+	1198.74i	−0.321943	+	0.0862645i
$579$	2588.97	−	3030.69i	0.185827	−	0.217532i
$580$	−26363.2	+	4185.28i	−1.88736	+	0.299628i
$581$	−5439.39	+	3140.43i	−0.388406	+	0.224246i
$582$	3360.98	−	264.181i	0.239376	−	0.0188156i
$583$	2820.15	+	10524.9i	0.200341	+	0.747681i
$584$	1332.53			0.0944185
$585$	−10172.3	+	6608.34i	−0.718928	+	0.467045i
$586$	−8655.11			−0.610135
$587$	3971.91	+	14823.4i	0.279282	+	1.04229i	0.952918	+	0.303230i	$0.0980649\pi$
$587$	3971.91	+	14823.4i	0.279282	+	1.04229i	−0.673636	+	0.739063i	$0.735268\pi$
$588$	−6689.42	−	9735.23i	−0.469162	−	0.682779i
$589$	−9823.42	+	5671.56i	−0.687211	+	0.396761i
$590$	1935.76	+	1405.34i	0.135075	+	0.0980629i
$591$	2756.58	+	7786.79i	0.191862	+	0.541972i
$592$	−13610.9	+	3647.03i	−0.944939	+	0.253196i
$593$	−10431.9	−	10431.9i	−0.722408	−	0.722408i	0.246687	−	0.969095i	$-0.420658\pi$
$593$	−10431.9	−	10431.9i	−0.722408	−	0.722408i	−0.969095	+	0.246687i	$0.920658\pi$
$594$	651.185	−	24589.6i	0.0449805	−	1.69852i
$595$	17583.1	+	6742.24i	1.21149	+	0.464546i
$596$	13897.0	+	8023.46i	0.955108	+	0.551432i
$597$	−4567.95	−	2179.35i	−0.313155	−	0.149405i
$598$	19063.2	+	5107.96i	1.30360	+	0.349298i
$599$	5809.12	+	10061.7i	0.396251	+	0.686326i	0.993260	−	0.115908i	$-0.0369778\pi$
$599$	5809.12	+	10061.7i	0.396251	+	0.686326i	−0.597009	+	0.802234i	$0.703644\pi$
$600$	20415.7	−	15685.7i	1.38911	−	1.06728i
$601$	−7747.92	+	13419.8i	−0.525864	+	0.910823i	0.473682	+	0.880696i	$0.342924\pi$
$601$	−7747.92	+	13419.8i	−0.525864	+	0.910823i	−0.999546	+	0.0301268i	$0.990409\pi$
$602$	3340.91	−	3340.91i	0.226188	−	0.226188i
$603$	25590.8	−	11387.7i	1.72826	−	0.769061i
$604$			42432.1i			2.85851i
$605$	471.521	−	382.113i	0.0316861	−	0.0256778i
$606$	2188.65	+	1869.66i	0.146713	+	0.125329i
$607$	6677.87	−	24922.2i	0.446535	−	1.66649i	−0.265318	−	0.964161i	$-0.585477\pi$
$607$	6677.87	−	24922.2i	0.446535	−	1.66649i	0.711853	−	0.702329i	$-0.247856\pi$
$608$	88.0550	−	328.626i	0.00587352	−	0.0219203i
$609$	−12912.3	−	11030.3i	−0.859166	−	0.733943i
$610$	−185.097	+	1767.22i	−0.0122858	+	0.117300i
$611$		−	19695.8i		−	1.30410i
$612$	−30352.7	+	13506.7i	−2.00479	+	0.892118i
$613$	18273.9	−	18273.9i	1.20404	−	1.20404i	0.231113	−	0.972927i	$-0.425763\pi$
$613$	18273.9	−	18273.9i	1.20404	−	1.20404i	0.972927	−	0.231113i	$-0.0742366\pi$
$614$	−5741.64	+	9944.81i	−0.377384	+	0.653648i
$615$	2506.45	−	602.442i	0.164341	−	0.0395005i
$616$	−15585.7	−	26995.2i	−1.01943	−	1.76570i
$617$	12550.6	+	3362.92i	0.818910	+	0.219426i	0.643870	−	0.765135i	$-0.277328\pi$
$617$	12550.6	+	3362.92i	0.818910	+	0.219426i	0.175040	+	0.984561i	$0.443995\pi$
$618$	19078.1	+	9102.10i	1.24180	+	0.592460i
$619$	10202.6	+	5890.46i	0.662481	+	0.382484i	0.793222	−	0.608933i	$-0.208402\pi$
$619$	10202.6	+	5890.46i	0.662481	+	0.382484i	−0.130740	+	0.991417i	$0.541735\pi$
$620$	13201.4	−	34427.9i	0.855129	−	2.23010i
$621$	371.735	−	14037.2i	0.0240213	−	0.907073i
$622$	−3416.25	−	3416.25i	−0.220224	−	0.220224i
$623$	18511.7	−	4960.21i	1.19046	−	0.318983i
$624$	−4590.39	−	12966.9i	−0.294491	−	0.831878i
$625$	12627.6	−	9202.41i	0.808166	−	0.588954i
$626$	−37273.5	+	21519.8i	−2.37979	+	1.37397i
$627$	−5814.53	−	8461.98i	−0.370351	−	0.538978i
$628$	−2580.30	−	9629.81i	−0.163957	−	0.611897i
$629$	16369.6			1.03768
$630$	31889.3	+	6772.80i	2.01667	+	0.428310i
$631$	1710.76			0.107931			0.0539654	−	0.998543i	$-0.482814\pi$
$631$	1710.76			0.107931			0.0539654	+	0.998543i	$0.482814\pi$
$632$	2239.58	+	8358.21i	0.140958	+	0.526063i
$633$	−24565.9	+	1930.94i	−1.54251	+	0.121245i
$634$	21822.6	−	12599.3i	1.36701	−	0.789245i
$635$	11442.4	−	15761.1i	0.715084	−	0.984977i
$636$	16547.6	−	19370.9i	1.03169	−	1.20772i
$637$	−5487.93	+	1470.49i	−0.341349	+	0.0914643i
$638$	−18410.2	−	18410.2i	−1.14242	−	1.14242i
$639$	−1124.12	+	909.924i	−0.0695921	+	0.0563318i
$640$	−11319.3	−	25398.9i	−0.699119	−	1.56872i
$641$	11323.2	+	6537.44i	0.697720	+	0.402829i	0.806498	−	0.591237i	$-0.201360\pi$
$641$	11323.2	+	6537.44i	0.697720	+	0.402829i	−0.108778	+	0.994066i	$0.534694\pi$
$642$	25011.7	−	17186.4i	1.53759	−	1.05653i
$643$	−24170.1	−	6476.35i	−1.48239	−	0.397204i	−0.575228	−	0.817993i	$-0.695087\pi$
$643$	−24170.1	−	6476.35i	−1.48239	−	0.397204i	−0.907159	+	0.420789i	$0.861753\pi$
$644$	−17708.6	−	30672.2i	−1.08357	−	1.87679i
$645$	−65.8641	+	2540.76i	−0.00402077	+	0.155105i
$646$	−10383.2	+	17984.3i	−0.632389	+	1.09533i
$647$	−13484.9	+	13484.9i	−0.819392	+	0.819392i	−0.986020	−	0.166628i	$-0.946712\pi$
$647$	−13484.9	+	13484.9i	−0.819392	+	0.819392i	0.166628	+	0.986020i	$0.446712\pi$
$648$	−24240.6	+	15728.4i	−1.46954	+	0.953504i
$649$			1557.98i			0.0942313i
$650$	−7633.48	−	23435.8i	−0.460630	−	1.41419i
$651$	22113.2	−	7828.25i	1.33132	−	0.471296i
$652$	−5978.86	+	22313.4i	−0.359126	+	1.34028i
$653$	−5647.44	+	21076.5i	−0.338440	+	1.26308i	0.561651	+	0.827374i	$0.310166\pi$
$653$	−5647.44	+	21076.5i	−0.338440	+	1.26308i	−0.900091	+	0.435702i	$0.856500\pi$
$654$	−4690.73	+	25295.0i	−0.280462	+	1.51240i
$655$	−9800.78	−	12094.0i	−0.584654	−	0.721454i
$656$			2923.19i			0.173980i
$657$	−902.677	−	95.0553i	−0.0536024	−	0.00564454i
$658$	−37429.1	+	37429.1i	−2.21753	+	2.21753i
$659$	−1324.52	+	2294.14i	−0.0782945	+	0.135610i	−0.902514	−	0.430660i	$-0.858281\pi$
$659$	−1324.52	+	2294.14i	−0.0782945	+	0.135610i	0.824220	+	0.566270i	$0.191614\pi$
$660$	32002.7	+	9470.48i	1.88743	+	0.558542i
$661$	−12790.2	−	22153.2i	−0.752618	−	1.30357i	−0.946550	−	0.322557i	$-0.895458\pi$
$661$	−12790.2	−	22153.2i	−0.752618	−	1.30357i	0.193932	−	0.981015i	$-0.437876\pi$
$662$	8844.87	+	2369.98i	0.519283	+	0.139142i
$663$	1252.19	+	15930.6i	0.0733497	+	0.933173i
$664$	9796.40	+	5655.96i	0.572551	+	0.330563i
$665$	12428.9	−	5539.07i	0.724768	−	0.323001i
$666$	27990.6	−	4427.61i	1.62855	−	0.257607i
$667$	−10509.6	−	10509.6i	−0.610096	−	0.610096i
$668$	−35523.7	+	9518.55i	−2.05756	+	0.551323i
$669$	−23971.1	−	4445.23i	−1.38532	−	0.256895i
$670$	8923.59	+	56209.8i	0.514550	+	3.24116i
$671$	−1002.24	+	578.646i	−0.0576620	+	0.0332912i
$672$	−302.963	+	635.015i	−0.0173915	+	0.0364527i
$673$	8021.88	+	29938.1i	0.459466	+	1.71475i	0.674614	+	0.738170i	$0.264310\pi$
$673$	8021.88	+	29938.1i	0.459466	+	1.71475i	−0.215148	+	0.976581i	$0.569023\pi$
$674$	−10426.5			−0.595866
$675$	−14948.9	+	9169.45i	−0.852417	+	0.522862i
$676$	9361.12			0.532608
$677$	−3786.35	−	14130.9i	−0.214950	−	0.802205i	−0.986184	−	0.165653i	$-0.947027\pi$
$677$	−3786.35	−	14130.9i	−0.214950	−	0.802205i	0.771234	−	0.636552i	$-0.219640\pi$
$678$	−21318.9	+	44684.6i	−1.20759	+	2.53112i
$679$	−2520.22	+	1455.05i	−0.142440	+	0.0822380i
$680$	−5317.70	−	33496.3i	−0.299889	−	1.88900i
$681$	−1711.95	−	317.466i	−0.0963319	−	0.0178639i
$682$	34738.7	−	9308.21i	1.95046	−	0.522624i
$683$	2122.33	+	2122.33i	0.118900	+	0.118900i	0.764053	−	0.645153i	$-0.223206\pi$
$683$	2122.33	+	2122.33i	0.118900	+	0.118900i	−0.645153	+	0.764053i	$0.723206\pi$
$684$	−8607.31	+	22409.6i	−0.481153	+	1.25271i
$685$	11894.0	−	5300.69i	0.663423	−	0.295662i
$686$	−18856.3	−	10886.7i	−1.04947	−	0.605911i
$687$	504.458	+	6417.84i	0.0280149	+	0.356413i
$688$	−2783.91	−	745.946i	−0.154267	−	0.0413357i
$689$	−6127.08	−	10612.4i	−0.338785	−	0.586793i
$690$	27359.2	+	8096.35i	1.50949	+	0.446700i
$691$	5113.37	−	8856.62i	0.281508	−	0.487586i	−0.690249	−	0.723572i	$-0.742499\pi$
$691$	5113.37	−	8856.62i	0.281508	−	0.487586i	0.971756	+	0.235987i	$0.0758321\pi$
$692$	−33272.5	+	33272.5i	−1.82779	+	1.82779i
$693$	8632.33	+	19398.8i	0.473182	+	1.06335i
$694$			15314.4i			0.837647i
$695$	−8953.27	−	11048.2i	−0.488657	−	0.602996i
$696$	−5576.67	+	30072.5i	−0.303711	+	1.63778i
$697$	878.916	−	3280.16i	0.0477638	−	0.178257i
$698$	13537.9	−	50523.9i	0.734119	−	2.73977i
$699$	−26702.6	+	9452.91i	−1.44490	+	0.511505i
$700$	−20052.5	+	39425.6i	−1.08273	+	2.12878i
$701$		−	28820.6i		−	1.55284i	−0.630218	−	0.776419i	$-0.717034\pi$
$701$		−	28820.6i		−	1.55284i	0.630218	−	0.776419i	$-0.282966\pi$
$702$	6450.01	+	26901.3i	0.346780	+	1.44633i
$703$	8363.91	−	8363.91i	0.448721	−	0.448721i
$704$	8876.20	−	15374.0i	0.475191	−	0.823055i
$705$	737.894	−	28464.9i	0.0394194	−	1.52064i
$706$	18519.1	+	32076.1i	0.987219	+	1.70991i
$707$	−2400.02	−	643.084i	−0.127669	−	0.0342089i
$708$	3002.28	−	2062.98i	0.159368	−	0.109508i
$709$	−9674.05	−	5585.32i	−0.512435	−	0.295855i	0.221399	−	0.975183i	$-0.428938\pi$
$709$	−9674.05	−	5585.32i	−0.512435	−	0.295855i	−0.733834	+	0.679329i	$0.762271\pi$
$710$	−1196.21	−	2684.11i	−0.0632293	−	0.141877i
$711$	−920.898	−	5821.76i	−0.0485744	−	0.307079i
$712$	−24406.5	−	24406.5i	−1.28465	−	1.28465i
$713$	19830.9	−	5313.67i	1.04162	−	0.279101i
$714$	27894.3	−	32653.5i	1.46207	−	1.71152i
$715$	9431.04	−	12990.6i	0.493288	−	0.679469i
$716$	50458.6	−	29132.3i	2.63370	−	1.52057i
$717$	−6991.88	+	549.579i	−0.364180	+	0.0286254i
$718$	−9413.98	−	35133.4i	−0.489313	−	1.82614i
$719$	−25908.4			−1.34384			−0.671921	−	0.740623i	$-0.734530\pi$
$719$	−25908.4			−1.34384			−0.671921	+	0.740623i	$0.734530\pi$
$720$	−6148.35	−	18912.1i	−0.318244	−	0.978907i
$721$	−18246.2			−0.942473
$722$	−4827.28	−	18015.7i	−0.248827	−	0.928633i
$723$	13814.5	+	20104.5i	0.710604	+	1.03415i
$724$	50251.9	−	29013.0i	2.57955	−	1.48931i
$725$	−3846.14	+	18159.2i	−0.197024	+	0.930229i
$726$	−461.888	−	1304.74i	−0.0236120	−	0.0666991i
$727$	33234.5	−	8905.15i	1.69546	−	0.454297i	0.723669	−	0.690147i	$-0.242454\pi$
$727$	33234.5	−	8905.15i	1.69546	−	0.454297i	0.971789	+	0.235850i	$0.0757876\pi$
$728$	24788.4	+	24788.4i	1.26198	+	1.26198i
$729$	17543.0	−	8925.51i	0.891275	−	0.453463i
$730$	660.311	−	1722.03i	0.0334783	−	0.0873084i
$731$	2899.59	+	1674.08i	0.146710	+	0.0847033i
$732$	2442.18	+	1165.15i	0.123313	+	0.0588324i
$733$	10615.4	+	2844.39i	0.534909	+	0.143328i	0.516154	−	0.856496i	$-0.327363\pi$
$733$	10615.4	+	2844.39i	0.534909	+	0.143328i	0.0187549	+	0.999824i	$0.494030\pi$
$734$	28499.0	+	49361.7i	1.43313	+	2.48225i
$735$	−7986.39	+	1919.58i	−0.400792	+	0.0963331i
$736$	−307.889	+	533.279i	−0.0154198	+	0.0267078i
$737$	−26211.0	+	26211.0i	−1.31004	+	1.31004i
$738$	615.660	−	5846.52i	0.0307084	−	0.291617i
$739$			19313.7i			0.961390i	0.876888	+	0.480695i	$0.159616\pi$
$739$			19313.7i			0.961390i	−0.876888	+	0.480695i	$0.840384\pi$
$740$	−4005.25	+	38240.3i	−0.198967	+	1.89965i
$741$	8779.41	+	7499.83i	0.435249	+	0.371812i
$742$	−8523.75	+	31811.1i	−0.421721	+	1.57388i
$743$	−1909.67	+	7127.00i	−0.0942922	+	0.351903i	−0.996911	−	0.0785371i	$-0.974975\pi$
$743$	−1909.67	+	7127.00i	−0.0942922	+	0.351903i	0.902619	+	0.430440i	$0.141642\pi$
$744$	−32123.0	−	27441.1i	−1.58291	−	1.35220i
$745$	8669.43	−	7025.55i	0.426340	−	0.345498i
$746$			52388.2i			2.57113i
$747$	−6232.78	−	4530.26i	−0.305282	−	0.221892i
$748$	31088.3	−	31088.3i	1.51965	−	1.51965i
$749$	−13097.7	+	22685.8i	−0.638957	+	1.10671i
$750$	−10154.1	−	34156.0i	−0.494367	−	1.66293i
$751$	13539.4	+	23451.0i	0.657870	+	1.13946i	0.981166	+	0.193167i	$0.0618758\pi$
$751$	13539.4	+	23451.0i	0.657870	+	1.13946i	−0.323296	+	0.946298i	$0.604791\pi$
$752$	31188.9	+	8357.04i	1.51242	+	0.405252i
$753$	13235.6	+	6314.64i	0.640545	+	0.305602i
$754$	25357.8	+	14640.3i	1.22477	+	0.707121i
$755$	27550.5	+	10564.2i	1.32803	+	0.509234i
$756$	25951.8	−	42321.4i	1.24849	−	2.03600i
$757$	5463.06	+	5463.06i	0.262296	+	0.262296i	0.825986	−	0.563690i	$-0.190619\pi$
$757$	5463.06	+	5463.06i	0.262296	+	0.262296i	−0.563690	+	0.825986i	$0.690619\pi$
$758$	36197.3	−	9699.05i	1.73449	−	0.464756i
$759$	6201.40	+	17517.7i	0.296570	+	0.837750i
$760$	−19831.7	−	14397.6i	−0.946540	−	0.687179i
$761$	−15944.4	+	9205.52i	−0.759507	+	0.438502i	−0.829119	−	0.559073i	$-0.811157\pi$
$761$	−15944.4	+	9205.52i	−0.759507	+	0.438502i	0.0696116	+	0.997574i	$0.477824\pi$
$762$	−25154.6	−	36607.9i	−1.19587	−	1.74037i
$763$	−5747.47	−	21449.8i	−0.272703	−	1.01774i
$764$	−21111.3			−0.999710
$765$	1212.86	+	23070.3i	0.0573215	+	1.09034i
$766$	−23699.6			−1.11789
$767$	−453.489	−	1692.44i	−0.0213488	−	0.0796748i
$768$	−42630.6	+	3350.87i	−2.00299	+	0.157440i
$769$	6927.29	−	3999.48i	0.324843	−	0.187548i	−0.328706	−	0.944432i	$-0.606613\pi$
$769$	6927.29	−	3999.48i	0.324843	−	0.187548i	0.653549	+	0.756884i	$0.273279\pi$
$770$	−42609.2	+	6764.42i	−1.99419	+	0.316588i
$771$	−26405.5	+	30910.7i	−1.23342	+	1.44387i
$772$	11913.1	−	3192.12i	0.555393	−	0.148817i
$773$	−20472.9	−	20472.9i	−0.952597	−	0.952597i	0.0463293	−	0.998926i	$-0.485248\pi$
$773$	−20472.9	−	20472.9i	−0.952597	−	0.952597i	−0.998926	+	0.0463293i	$0.985248\pi$
$774$	5410.85	+	2078.26i	0.251278	+	0.0965134i
$775$	−19066.8	−	17142.9i	−0.883743	−	0.794570i
$776$	4538.94	+	2620.56i	0.209972	+	0.121228i
$777$	−20160.7	+	13853.1i	−0.930838	+	0.639612i
$778$	−66033.2	−	17693.6i	−3.04294	−	0.815353i
$779$	−1226.90	−	2125.05i	−0.0564289	−	0.0977378i
$780$	−37521.3	−	972.663i	−1.72241	−	0.0446499i
$781$	956.957	−	1657.50i	0.0438446	−	0.0759410i
$782$	26577.5	−	26577.5i	1.21536	−	1.21536i
$783$	5922.94	−	19973.8i	0.270330	−	0.911628i
$784$		−	9314.24i		−	0.424301i
$785$	−6894.90	−	722.164i	−0.313490	−	0.0328346i
$786$	−33465.2	+	11846.9i	−1.51866	+	0.537616i
$787$	−1013.69	+	3783.16i	−0.0459140	+	0.171353i	−0.985076	−	0.172122i	$-0.944938\pi$
$787$	−1013.69	+	3783.16i	−0.0459140	+	0.171353i	0.939162	+	0.343476i	$0.111604\pi$
$788$	−6615.19	+	24688.2i	−0.299057	+	1.11609i
$789$	318.349	−	1716.71i	0.0143644	−	0.0774608i
$790$	11911.1	+	1247.56i	0.536429	+	0.0561849i
$791$		−	42736.0i		−	1.92101i
$792$	22483.3	−	30932.8i	1.00872	−	1.38781i
$793$	920.313	−	920.313i	0.0412122	−	0.0412122i
$794$	9473.83	−	16409.2i	0.423443	−	0.733424i
$795$	−8457.43	−	15566.9i	−0.377301	−	0.694466i
$796$	−7830.21	−	13562.3i	−0.348661	−	0.603899i
$797$	25020.6	+	6704.25i	1.11201	+	0.297963i	0.767647	−	0.640872i	$-0.221427\pi$
$797$	25020.6	+	6704.25i	1.11201	+	0.297963i	0.344366	+	0.938835i	$0.388094\pi$
$798$	−2431.68	−	30936.4i	−0.107870	−	1.37235i
$799$	−32484.9	−	18755.2i	−1.43834	−	0.830426i
$800$	767.955	−	40.8035i	0.0339391	−	0.00180328i
$801$	14792.3	+	18274.4i	0.652512	+	0.806110i
$802$	19394.0	+	19394.0i	0.853900	+	0.853900i
$803$	1160.26	−	310.890i	0.0509895	−	0.0136626i
$804$	85216.5	+	15802.6i	3.73800	+	0.693180i
$805$	−24323.9	+	3861.53i	−1.06497	+	0.169070i
$806$	−35027.4	+	20223.1i	−1.53075	+	0.883782i
$807$	−12219.8	+	25612.9i	−0.533034	+	1.11724i
$808$	1158.20	+	4322.47i	0.0504275	+	0.188198i
$809$	1308.93			0.0568846			0.0284423	−	0.999595i	$-0.490945\pi$
$809$	1308.93			0.0568846			0.0284423	+	0.999595i	$0.490945\pi$
$810$	8313.88	+	39120.1i	0.360642	+	1.69696i
$811$	33565.9			1.45334			0.726670	−	0.686987i	$-0.241067\pi$
$811$	33565.9			1.45334			0.726670	+	0.686987i	$0.241067\pi$
$812$	−13600.0	−	50756.0i	−0.587768	−	2.19358i
$813$	11438.3	−	23974.9i	0.493432	−	1.03424i
$814$	−32478.2	+	18751.3i	−1.39848	+	0.807412i
$815$	12999.2	+	9437.31i	0.558703	+	0.405613i
$816$	−25758.0	−	4776.58i	−1.10504	−	0.204919i
$817$	2336.88	−	626.165i	0.100070	−	0.0268137i
$818$	40959.7	+	40959.7i	1.75076	+	1.75076i
$819$	−15023.8	−	18560.4i	−0.640996	−	0.791883i
$820$	7447.61	+	2855.78i	0.317173	+	0.121620i
$821$	−25446.9	−	14691.8i	−1.08173	−	0.624539i	−0.150370	−	0.988630i	$-0.548047\pi$
$821$	−25446.9	−	14691.8i	−1.08173	−	0.624539i	−0.931364	+	0.364090i	$0.881380\pi$
$822$	−2327.03	−	29605.0i	−0.0987402	−	1.25620i
$823$	−20686.7	−	5542.98i	−0.876175	−	0.234770i	−0.207419	−	0.978252i	$-0.566506\pi$
$823$	−20686.7	−	5542.98i	−0.876175	−	0.234770i	−0.668756	+	0.743482i	$0.733173\pi$
$824$	16430.8	+	28459.0i	0.694653	+	1.20317i
$825$	14116.7	−	18421.0i	0.595733	−	0.777379i
$826$	−2354.46	+	4078.04i	−0.0991794	+	0.171784i
$827$	−5587.09	+	5587.09i	−0.234924	+	0.234924i	−0.814744	−	0.579820i	$-0.803123\pi$
$827$	−5587.09	+	5587.09i	−0.234924	+	0.234924i	0.579820	+	0.814744i	$0.303123\pi$
$828$	25545.7	−	35146.1i	1.07219	−	1.47513i
$829$		−	41079.2i		−	1.72104i	−0.509420	−	0.860518i	$-0.670140\pi$
$829$		−	41079.2i		−	1.72104i	0.509420	−	0.860518i	$-0.329860\pi$
$830$	12163.6	−	9857.20i	0.508682	−	0.412227i
$831$	142.695	−	769.488i	0.00595671	−	0.0321218i
$832$	−5167.27	+	19284.5i	−0.215316	+	0.803570i
$833$	−2800.52	+	10451.7i	−0.116485	+	0.434729i
$834$	−30571.3	+	10822.5i	−1.26930	+	0.449343i
$835$	−2664.01	+	25434.8i	−0.110410	+	1.05414i
$836$		−	31768.6i		−	1.31428i
$837$	19803.2	+	20880.6i	0.817799	+	0.862292i
$838$	2247.51	−	2247.51i	0.0926477	−	0.0926477i
$839$	10182.7	−	17636.9i	0.419005	−	0.725738i	−0.576835	−	0.816861i	$-0.695712\pi$
$839$	10182.7	−	17636.9i	0.419005	−	0.725738i	0.995840	+	0.0911228i	$0.0290456\pi$
$840$	34896.2	+	36753.6i	1.43337	+	1.50967i
$841$	1168.91	+	2024.62i	0.0479280	+	0.0830136i
$842$	13504.6	+	3618.55i	0.552731	+	0.148104i
$843$	−17555.9	+	12063.3i	−0.717269	+	0.492861i
$844$	−66031.4	−	38123.2i	−2.69300	−	1.55481i
$845$	2330.62	−	6078.04i	0.0948825	−	0.247445i
$846$	−60619.3	−	23283.3i	−2.46351	−	0.946212i
$847$	844.797	+	844.797i	0.0342710	+	0.0342710i
$848$	19404.8	−	5199.51i	0.785808	−	0.210557i
$849$	−1163.55	+	1362.07i	−0.0470352	+	0.0550601i
$850$	−45922.4	−	9726.41i	−1.85309	−	0.392486i
$851$	−18540.5	+	10704.4i	−0.746839	+	0.431188i
$852$	−4461.19	+	350.661i	−0.179387	+	0.0141003i
$853$	8368.42	+	31231.4i	0.335908	+	1.25362i	0.902882	+	0.429889i	$0.141447\pi$
$853$	8368.42	+	31231.4i	0.335908	+	1.25362i	−0.566974	+	0.823736i	$0.691886\pi$
$854$	−3497.86			−0.140157
$855$	12407.3	+	11167.9i	0.496280	+	0.446705i
$856$	47178.2			1.88378
$857$	−3530.24	−	13175.0i	−0.140712	−	0.525146i	−0.999909	−	0.0135002i	$-0.995703\pi$
$857$	−3530.24	−	13175.0i	−0.140712	−	0.525146i	0.859196	−	0.511646i	$-0.170964\pi$
$858$	−20732.9	−	30172.9i	−0.824952	−	1.20057i
$859$	27930.0	−	16125.4i	1.10938	−	0.640503i	0.170714	−	0.985321i	$-0.445393\pi$
$859$	27930.0	−	16125.4i	1.10938	−	0.640503i	0.938670	+	0.344818i	$0.112059\pi$
$860$	−4620.21	+	6364.02i	−0.183195	+	0.252339i
$861$	1693.44	+	4783.63i	0.0670295	+	0.189345i
$862$	−638.601	+	171.113i	−0.0252330	+	0.00676116i
$863$	25623.9	+	25623.9i	1.01071	+	1.01071i	0.999942	+	0.0107728i	$0.00342915\pi$
$863$	25623.9	+	25623.9i	1.01071	+	1.01071i	0.0107728	+	0.999942i	$0.496571\pi$
$864$	−862.842	−	22.8499i	−0.0339751	−	0.000899735i
$865$	13319.6	+	29887.2i	0.523560	+	1.17479i
$866$	30769.3	+	17764.7i	1.20737	+	0.697076i
$867$	4426.57	+	2111.90i	0.173396	+	0.0827265i
$868$	70110.7	+	18786.1i	2.74160	+	0.734610i
$869$	3900.08	+	6755.14i	0.152245	+	0.263697i
$870$	36099.3	+	22108.6i	1.40676	+	0.861554i
$871$	20843.8	−	36102.5i	0.810868	−	1.40446i
$872$	−28280.2	+	28280.2i	−1.09827	+	1.09827i
$873$	−2887.82	−	2099.00i	−0.111956	−	0.0813748i
$874$		−	27159.1i		−	1.05111i
$875$	20606.0	+	22835.5i	0.796127	+	0.882263i
$876$	−2135.43	−	1824.20i	−0.0823625	−	0.0703583i
$877$	8882.00	−	33148.1i	0.341989	−	1.27632i	−0.554102	−	0.832448i	$-0.686938\pi$
$877$	8882.00	−	33148.1i	0.341989	−	1.27632i	0.896091	−	0.443870i	$-0.146395\pi$
$878$	7208.48	−	26902.4i	0.277078	−	1.03407i
$879$	6968.73	+	5953.04i	0.267405	+	0.228431i
$880$	16569.4	+	20446.3i	0.634720	+	0.783234i
$881$			48843.4i			1.86785i	0.357471	+	0.933924i	$0.383639\pi$
$881$			48843.4i			1.86785i	−0.357471	+	0.933924i	$0.616361\pi$
$882$	−1961.70	+	18629.0i	−0.0748910	+	0.711190i
$883$	1227.15	−	1227.15i	0.0467687	−	0.0467687i	−0.683336	−	0.730104i	$-0.739471\pi$
$883$	1227.15	−	1227.15i	0.0467687	−	0.0467687i	0.730104	+	0.683336i	$0.239471\pi$
$884$	−24722.4	+	42820.4i	−0.940614	+	1.62919i
$885$	−591.987	−	2462.95i	−0.0224852	−	0.0935494i
$886$	31878.7	+	55215.6i	1.20879	+	2.09368i
$887$	14230.9	+	3813.17i	0.538701	+	0.144345i	0.517903	−	0.855439i	$-0.326713\pi$
$887$	14230.9	+	3813.17i	0.538701	+	0.144345i	0.0207980	+	0.999784i	$0.493379\pi$
$888$	39761.9	+	18970.3i	1.50261	+	0.716892i
$889$	33203.7	+	19170.2i	1.25266	+	0.723225i
$890$	−43634.8	+	19446.3i	−1.64342	+	0.732408i
$891$	−17437.2	+	19350.6i	−0.655631	+	0.727574i
$892$	−53341.5	−	53341.5i	−2.00225	−	2.00225i
$893$	−26180.7	+	7015.10i	−0.981080	+	0.262879i
$894$	−8492.31	−	23989.1i	−0.317702	−	0.897444i
$895$	−6352.59	−	40015.0i	−0.237255	−	1.49448i
$896$	47405.3	−	27369.5i	1.76752	−	1.02048i
$897$	−11835.6	−	17224.5i	−0.440555	−	0.641147i
$898$	7238.75	+	27015.4i	0.268998	+	1.00391i
$899$	30459.9			1.13003
$900$	−54190.3	−	2811.44i	−2.00705	−	0.104127i
$901$	−23337.9			−0.862927
$902$	2013.59	+	7514.83i	0.0743296	+	0.277402i
$903$	−4987.85	+	392.057i	−0.183815	+	0.0144483i
$904$	−66656.3	+	38484.0i	−2.45239	+	1.41589i
$905$	−6326.56	−	39851.1i	−0.232378	−	1.46375i
$906$	43706.8	−	51163.9i	1.60272	−	1.87617i
$907$	−38574.2	+	10335.9i	−1.41217	+	0.378389i	−0.882698	−	0.469941i	$-0.844275\pi$
$907$	−38574.2	+	10335.9i	−1.41217	+	0.378389i	−0.529468	+	0.848330i	$0.677608\pi$
$908$	−3809.49	−	3809.49i	−0.139232	−	0.139232i
$909$	−476.245	−	3010.74i	−0.0173774	−	0.109857i
$910$	44317.6	−	19750.7i	1.61441	−	0.719482i
$911$	23676.2	+	13669.5i	0.861062	+	0.497135i	0.864368	−	0.502860i	$-0.167719\pi$
$911$	23676.2	+	13669.5i	0.861062	+	0.497135i	−0.00330562	+	0.999995i	$0.501052\pi$
$912$	−15601.4	+	10720.3i	−0.566462	+	0.389236i
$913$	9849.50	+	2639.16i	0.357033	+	0.0956666i
$914$	−42373.7	−	73393.5i	−1.53348	−	2.65606i
$915$	1364.54	−	1295.58i	0.0493009	−	0.0468094i
$916$	−9959.69	+	17250.7i	−0.359255	+	0.622248i
$917$	21668.1	−	21668.1i	0.780311	−	0.780311i
$918$	50511.2	+	14978.4i	1.81603	+	0.538518i
$919$			25885.5i			0.929144i	0.885535	+	0.464572i	$0.153792\pi$
$919$			25885.5i			0.929144i	−0.885535	+	0.464572i	$0.846208\pi$
$920$	27926.7	+	34461.1i	1.00078	+	1.23495i
$921$	11463.0	−	4058.00i	0.410119	−	0.145185i
$922$	7808.04	−	29140.0i	0.278898	−	1.04086i
$923$	−557.091	+	2079.09i	−0.0198666	+	0.0741432i
$924$	−11979.0	+	64597.4i	−0.426494	+	2.29989i
$925$	23831.7	+	12121.2i	0.847115	+	0.430856i
$926$		−	44608.1i		−	1.58306i
$927$	−9100.39	−	20450.7i	−0.322434	−	0.724583i
$928$	−646.009	+	646.009i	−0.0228516	+	0.0228516i
$929$	−10617.2	+	18389.5i	−0.374962	+	0.649453i	−0.990321	−	0.138794i	$-0.955677\pi$
$929$	−10617.2	+	18389.5i	−0.374962	+	0.649453i	0.615360	+	0.788247i	$0.289011\pi$
$930$	−51380.2	+	27914.7i	−1.81164	+	0.984256i
$931$	3909.30	+	6771.11i	0.137618	+	0.238361i
$932$	−84661.2	−	22684.9i	−2.97551	−	0.797284i
$933$	400.899	+	5100.34i	0.0140674	+	0.178969i
$934$	32457.7	+	18739.5i	1.13710	+	0.656504i
$935$	−12445.2	−	27925.2i	−0.435295	−	0.976738i
$936$	−15420.0	+	40146.8i	−0.538481	+	1.40196i
$937$	22300.2	+	22300.2i	0.777496	+	0.777496i	0.979404	−	0.201908i	$-0.0647142\pi$
$937$	22300.2	+	22300.2i	0.777496	+	0.777496i	−0.201908	+	0.979404i	$0.564714\pi$
$938$	−108219.	+	28997.1i	−3.76702	+	1.00937i
$939$	44812.5	+	8310.08i	1.55740	+	0.288806i
$940$	51761.5	−	71297.8i	1.79604	−	2.47391i
$941$	23848.9	−	13769.2i	0.826197	−	0.477005i	−0.0263519	−	0.999653i	$-0.508389\pi$
$941$	23848.9	−	13769.2i	0.826197	−	0.477005i	0.852549	+	0.522648i	$0.175056\pi$
$942$	−6807.82	+	14269.3i	−0.235468	+	0.493544i
$943$	1149.48	+	4289.91i	0.0396947	+	0.148143i
$944$	2872.45			0.0990365
$945$	−21017.5	−	27386.8i	−0.723491	−	0.942745i
$946$	−7670.62			−0.263629
$947$	−685.191	−	2557.17i	−0.0235118	−	0.0877474i	0.953173	−	0.302426i	$-0.0977964\pi$
$947$	−685.191	−	2557.17i	−0.0235118	−	0.0877474i	−0.976685	+	0.214678i	$0.931130\pi$
$948$	7853.16	−	16460.3i	0.269049	−	0.563930i
$949$	−1169.90	+	675.442i	−0.0400175	+	0.0231041i
$950$	−28433.3	+	18494.0i	−0.971050	+	0.631606i
$951$	−26236.5	−	4865.33i	−0.894613	−	0.165898i
$952$	64489.1	−	17279.8i	2.19549	−	0.588279i
$953$	−32937.8	−	32937.8i	−1.11958	−	1.11958i	−0.991803	−	0.127777i	$-0.959216\pi$
$953$	−32937.8	−	32937.8i	−1.11958	−	1.11958i	−0.127777	−	0.991803i	$-0.540784\pi$
$954$	−39905.8	+	6312.38i	−1.35429	+	0.214225i
$955$	−5256.03	+	13707.2i	−0.178095	+	0.464456i
$956$	−18793.7	−	10850.5i	−0.635807	−	0.367083i
$957$	2160.45	+	27485.7i	0.0729752	+	0.928409i
$958$	−56297.7	−	15084.9i	−1.89864	−	0.508738i
$959$	12816.7	+	22199.2i	0.431568	+	0.747498i
$960$	−8190.36	+	27676.9i	−0.275357	+	0.930488i
$961$	−6142.04	+	10638.3i	−0.206171	+	0.357099i
$962$	29823.2	−	29823.2i	0.999521	−	0.999521i
$963$	−31959.3	−	3365.43i	−1.06944	−	0.112616i
$964$			75477.7i			2.52176i
$965$	893.397	−	8529.76i	0.0298025	−	0.284542i
$966$	−10240.9	+	55224.6i	−0.341093	+	1.83936i
$967$	−3869.66	+	14441.8i	−0.128686	+	0.480264i	−0.999944	−	0.0105613i	$-0.996638\pi$
$967$	−3869.66	+	14441.8i	−0.128686	+	0.480264i	0.871258	+	0.490826i	$0.163305\pi$
$968$	556.904	−	2078.39i	0.0184913	−	0.0690104i
$969$	20729.9	−	7338.53i	0.687244	−	0.243290i
$970$	5635.75	−	4567.11i	0.186549	−	0.151176i
$971$			20437.6i			0.675462i	0.941243	+	0.337731i	$0.109659\pi$
$971$			20437.6i			0.675462i	−0.941243	+	0.337731i	$0.890341\pi$
$972$	60378.4	+	7979.27i	1.99242	+	0.263308i
$973$	19794.4	−	19794.4i	0.652188	−	0.652188i
$974$	35790.9	−	61991.6i	1.17743	−	2.03936i
$975$	−9973.13	+	24119.8i	−0.327585	+	0.792260i
$976$	1066.85	+	1847.84i	0.0349888	+	0.0606024i
$977$	−39938.1	−	10701.4i	−1.30781	−	0.350427i	−0.463413	−	0.886143i	$-0.653375\pi$
$977$	−39938.1	−	10701.4i	−1.30781	−	0.350427i	−0.844398	+	0.535716i	$0.820042\pi$
$978$	30193.0	−	20746.7i	0.987183	−	0.678329i
$979$	−26945.4	−	15556.9i	−0.879652	−	0.507867i
$980$	−23730.6	−	9099.47i	−0.773515	−	0.296604i
$981$	21174.8	−	17140.1i	0.689154	−	0.557841i
$982$	−44274.2	−	44274.2i	−1.43874	−	1.43874i
$983$	43739.9	−	11720.1i	1.41921	−	0.380277i	0.534008	−	0.845479i	$-0.320685\pi$
$983$	43739.9	−	11720.1i	1.41921	−	0.380277i	0.885204	+	0.465202i	$0.154018\pi$
$984$	5936.19	−	6948.99i	0.192316	−	0.225128i
$985$	14382.7	+	10441.7i	0.465251	+	0.337768i
$986$	48293.6	−	27882.3i	1.55982	−	0.900562i
$987$	55880.3	−	4392.32i	1.80212	−	0.141651i
$988$	9247.04	+	34510.4i	0.297761	+	1.11126i
$989$	−4378.84			−0.140788
$990$	−28833.3	−	44383.5i	−0.925639	−	1.42485i
$991$	−38854.5			−1.24546			−0.622731	−	0.782436i	$-0.713977\pi$
$991$	−38854.5			−1.24546			−0.622731	+	0.782436i	$0.713977\pi$
$992$	−326.623	−	1218.97i	−0.0104539	−	0.0390146i
$993$	−5491.43	−	7991.76i	−0.175494	−	0.255399i
$994$	5009.71	−	2892.35i	0.159857	−	0.0922937i
$995$	−10755.3	+	1707.45i	−0.342679	+	0.0544020i
$996$	−7956.29	−	22474.9i	−0.253117	−	0.715005i
$997$	−29534.8	+	7913.82i	−0.938190	+	0.251387i	−0.695344	−	0.718677i	$-0.744748\pi$
$997$	−29534.8	+	7913.82i	−0.938190	+	0.251387i	−0.242847	+	0.970065i	$0.578081\pi$
$998$	−3730.11	−	3730.11i	−0.118311	−	0.118311i
$999$	−25582.2	−	15687.2i	−0.810194	−	0.496817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.2.2	✓	64
3.2	odd	2		135.4.m.a.62.15		64
5.2	odd	4		225.4.p.b.218.15		64
5.3	odd	4	inner	45.4.l.a.38.2	yes	64
5.4	even	2		225.4.p.b.182.15		64
9.4	even	3		135.4.m.a.17.15		64
9.5	odd	6	inner	45.4.l.a.32.2	yes	64
15.8	even	4		135.4.m.a.8.15		64
45.13	odd	12		135.4.m.a.98.15		64
45.14	odd	6		225.4.p.b.32.15		64
45.23	even	12	inner	45.4.l.a.23.2	yes	64
45.32	even	12		225.4.p.b.68.15		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.2	✓	64	1.1	even	1	trivial
45.4.l.a.23.2	yes	64	45.23	even	12	inner
45.4.l.a.32.2	yes	64	9.5	odd	6	inner
45.4.l.a.38.2	yes	64	5.3	odd	4	inner
135.4.m.a.8.15		64	15.8	even	4
135.4.m.a.17.15		64	9.4	even	3
135.4.m.a.62.15		64	3.2	odd	2
135.4.m.a.98.15		64	45.13	odd	12
225.4.p.b.32.15		64	45.14	odd	6
225.4.p.b.68.15		64	45.32	even	12
225.4.p.b.182.15		64	5.4	even	2
225.4.p.b.218.15		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27001 - 4.73973i) q^{2} +(-2.23746 + 4.68975i) q^{3} +(-13.9239 + 8.03899i) q^{4} +(1.75298 + 11.0421i) q^{5} +(25.0698 + 4.64896i) q^{6} +(-21.2589 + 5.69629i) q^{7} +(28.0284 + 28.0284i) q^{8} +(-16.9875 - 20.9863i) q^{9} +O(q^{10})\)	\(q+(-1.27001 - 4.73973i) q^{2} +(-2.23746 + 4.68975i) q^{3} +(-13.9239 + 8.03899i) q^{4} +(1.75298 + 11.0421i) q^{5} +(25.0698 + 4.64896i) q^{6} +(-21.2589 + 5.69629i) q^{7} +(28.0284 + 28.0284i) q^{8} +(-16.9875 - 20.9863i) q^{9} +(50.1101 - 22.3322i) q^{10} +(30.9441 + 17.8656i) q^{11} +(-6.54654 - 83.2868i) q^{12} +(-38.8149 - 10.4004i) q^{13} +(53.9978 + 93.5270i) q^{14} +(-55.7067 - 16.4852i) q^{15} +(32.9388 - 57.0517i) q^{16} +(-54.1151 + 54.1151i) q^{17} +(-77.8952 + 107.169i) q^{18} +55.2993i q^{19} +(-113.175 - 139.657i) q^{20} +(20.8517 - 112.444i) q^{21} +(45.3788 - 169.356i) q^{22} +(25.9049 - 96.6785i) q^{23} +(-194.159 + 68.7336i) q^{24} +(-118.854 + 38.7131i) q^{25} +197.181i q^{26} +(136.429 - 32.7111i) q^{27} +(250.215 - 250.215i) q^{28} +(74.2482 - 128.602i) q^{29} +(-7.38730 + 284.971i) q^{30} +(102.561 + 177.641i) q^{31} +(-5.94267 - 1.59233i) q^{32} +(-153.021 + 105.146i) q^{33} +(325.217 + 187.764i) q^{34} +(-100.165 - 224.756i) q^{35} +(405.242 + 155.649i) q^{36} +(-151.248 - 151.248i) q^{37} +(262.104 - 70.2305i) q^{38} +(135.622 - 158.762i) q^{39} +(-260.358 + 358.624i) q^{40} +(-38.4281 + 22.1865i) q^{41} +(-559.436 + 43.9730i) q^{42} +(-11.3232 - 42.2588i) q^{43} -574.485 q^{44} +(201.953 - 224.366i) q^{45} -491.130 q^{46} +(126.857 + 473.436i) q^{47} +(193.859 + 282.126i) q^{48} +(122.445 - 70.6935i) q^{49} +(334.435 + 514.171i) q^{50} +(-132.706 - 374.867i) q^{51} +(624.066 - 167.218i) q^{52} +(215.632 + 215.632i) q^{53} +(-328.308 - 605.096i) q^{54} +(-143.028 + 373.005i) q^{55} +(-755.509 - 436.194i) q^{56} +(-259.340 - 123.730i) q^{57} +(-703.833 - 188.591i) q^{58} +(21.8014 + 37.7612i) q^{59} +(908.181 - 218.287i) q^{60} +(-16.1944 + 28.0496i) q^{61} +(711.717 - 711.717i) q^{62} +(480.679 + 349.379i) q^{63} -496.832i q^{64} +(46.8003 - 446.828i) q^{65} +(692.704 + 591.744i) q^{66} +(-268.503 + 1002.07i) q^{67} +(318.464 - 1188.53i) q^{68} +(395.437 + 337.802i) q^{69} +(-938.073 + 760.198i) q^{70} -53.5643i q^{71} +(112.079 - 1064.34i) q^{72} +(23.7710 - 23.7710i) q^{73} +(-524.789 + 908.961i) q^{74} +(84.3773 - 644.015i) q^{75} +(-444.551 - 769.984i) q^{76} +(-759.604 - 203.535i) q^{77} +(-924.730 - 441.185i) q^{78} +(189.055 + 109.151i) q^{79} +(687.710 + 263.702i) q^{80} +(-151.849 + 713.010i) q^{81} +(153.962 + 153.962i) q^{82} +(275.656 - 73.8617i) q^{83} +(613.598 + 1733.29i) q^{84} +(-692.404 - 502.679i) q^{85} +(-185.915 + 107.338i) q^{86} +(436.982 + 635.947i) q^{87} +(366.570 + 1368.06i) q^{88} -870.778 q^{89} +(-1319.92 - 672.258i) q^{90} +884.405 q^{91} +(416.499 + 1554.40i) q^{92} +(-1062.57 + 83.5204i) q^{93} +(2082.85 - 1202.54i) q^{94} +(-610.618 + 96.9387i) q^{95} +(20.7642 - 24.3069i) q^{96} +(127.719 - 34.2222i) q^{97} +(-490.574 - 490.574i) q^{98} +(-150.731 - 952.894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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