LMFDB - Embedded newform 201.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.a (trivial)

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:	yes
Analytic conductor:	$11.8593839112$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 38x^{5} + 18x^{4} + 373x^{3} - 151x^{2} - 956x + 498 $ x^7 - x^6 - 38x^5 + 18x^4 + 373x^3 - 151x^2 - 956*x + 498
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.535294$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.535294 q^{2} -3.00000 q^{3} -7.71346 q^{4} +12.7037 q^{5} +1.60588 q^{6} -8.67573 q^{7} +8.41132 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.535294 q^{2} -3.00000 q^{3} -7.71346 q^{4} +12.7037 q^{5} +1.60588 q^{6} -8.67573 q^{7} +8.41132 q^{8} +9.00000 q^{9} -6.80020 q^{10} +52.9021 q^{11} +23.1404 q^{12} -73.3935 q^{13} +4.64407 q^{14} -38.1110 q^{15} +57.2051 q^{16} -23.1557 q^{17} -4.81765 q^{18} -91.6759 q^{19} -97.9892 q^{20} +26.0272 q^{21} -28.3182 q^{22} +7.43454 q^{23} -25.2340 q^{24} +36.3830 q^{25} +39.2871 q^{26} -27.0000 q^{27} +66.9199 q^{28} -234.492 q^{29} +20.4006 q^{30} -304.783 q^{31} -97.9122 q^{32} -158.706 q^{33} +12.3951 q^{34} -110.214 q^{35} -69.4211 q^{36} +227.591 q^{37} +49.0736 q^{38} +220.181 q^{39} +106.855 q^{40} -169.995 q^{41} -13.9322 q^{42} -398.291 q^{43} -408.059 q^{44} +114.333 q^{45} -3.97967 q^{46} +327.644 q^{47} -171.615 q^{48} -267.732 q^{49} -19.4756 q^{50} +69.4672 q^{51} +566.118 q^{52} +21.5803 q^{53} +14.4529 q^{54} +672.051 q^{55} -72.9744 q^{56} +275.028 q^{57} +125.522 q^{58} +76.8494 q^{59} +293.968 q^{60} +639.851 q^{61} +163.148 q^{62} -78.0816 q^{63} -405.229 q^{64} -932.366 q^{65} +84.9546 q^{66} +67.0000 q^{67} +178.611 q^{68} -22.3036 q^{69} +58.9967 q^{70} -1134.80 q^{71} +75.7019 q^{72} +822.973 q^{73} -121.828 q^{74} -109.149 q^{75} +707.138 q^{76} -458.965 q^{77} -117.861 q^{78} -883.380 q^{79} +726.715 q^{80} +81.0000 q^{81} +90.9975 q^{82} -967.641 q^{83} -200.760 q^{84} -294.163 q^{85} +213.203 q^{86} +703.477 q^{87} +444.977 q^{88} +1097.53 q^{89} -61.2018 q^{90} +636.743 q^{91} -57.3460 q^{92} +914.348 q^{93} -175.386 q^{94} -1164.62 q^{95} +293.737 q^{96} +1147.80 q^{97} +143.315 q^{98} +476.119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.535294	−0.189255	−0.0946275	−	0.995513i	$-0.530166\pi$
$2$	−0.535294	−0.189255	−0.0946275	+	0.995513i	$0.530166\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.71346	−0.964183
$5$	12.7037	1.13625	0.568125	−	0.822942i	$-0.307669\pi$
$5$	12.7037	1.13625	0.568125	+	0.822942i	$0.307669\pi$
$6$	1.60588	0.109266
$7$	−8.67573	−0.468446	−0.234223	−	0.972183i	$-0.575255\pi$
$7$	−8.67573	−0.468446	−0.234223	+	0.972183i	$0.575255\pi$
$8$	8.41132	0.371731
$9$	9.00000	0.333333
$10$	−6.80020	−0.215041
$11$	52.9021	1.45005	0.725027	−	0.688720i	$-0.241827\pi$
$11$	52.9021	1.45005	0.725027	+	0.688720i	$0.241827\pi$
$12$	23.1404	0.556671
$13$	−73.3935	−1.56582	−0.782911	−	0.622133i	$-0.786266\pi$
$13$	−73.3935	−1.56582	−0.782911	+	0.622133i	$0.786266\pi$
$14$	4.64407	0.0886557
$15$	−38.1110	−0.656014
$16$	57.2051	0.893830
$17$	−23.1557	−0.330358	−0.165179	−	0.986264i	$-0.552820\pi$
$17$	−23.1557	−0.330358	−0.165179	+	0.986264i	$0.552820\pi$
$18$	−4.81765	−0.0630850
$19$	−91.6759	−1.10694	−0.553471	−	0.832869i	$-0.686697\pi$
$19$	−91.6759	−1.10694	−0.553471	+	0.832869i	$0.686697\pi$
$20$	−97.9892	−1.09555
$21$	26.0272	0.270457
$22$	−28.3182	−0.274430
$23$	7.43454	0.0674004	0.0337002	−	0.999432i	$-0.489271\pi$
$23$	7.43454	0.0674004	0.0337002	+	0.999432i	$0.489271\pi$
$24$	−25.2340	−0.214619
$25$	36.3830	0.291064
$26$	39.2871	0.296340
$27$	−27.0000	−0.192450
$28$	66.9199	0.451667
$29$	−234.492	−1.50152	−0.750761	−	0.660574i	$-0.770313\pi$
$29$	−234.492	−1.50152	−0.750761	+	0.660574i	$0.770313\pi$
$30$	20.4006	0.124154
$31$	−304.783	−1.76583	−0.882913	−	0.469536i	$-0.844421\pi$
$31$	−304.783	−1.76583	−0.882913	+	0.469536i	$0.844421\pi$
$32$	−97.9122	−0.540893
$33$	−158.706	−0.837189
$34$	12.3951	0.0625220
$35$	−110.214	−0.532271
$36$	−69.4211	−0.321394
$37$	227.591	1.01123	0.505617	−	0.862758i	$-0.331265\pi$
$37$	227.591	1.01123	0.505617	+	0.862758i	$0.331265\pi$
$38$	49.0736	0.209494
$39$	220.181	0.904028
$40$	106.855	0.422380
$41$	−169.995	−0.647532	−0.323766	−	0.946137i	$-0.604949\pi$
$41$	−169.995	−0.647532	−0.323766	+	0.946137i	$0.604949\pi$
$42$	−13.9322	−0.0511854
$43$	−398.291	−1.41253	−0.706266	−	0.707947i	$-0.749622\pi$
$43$	−398.291	−1.41253	−0.706266	+	0.707947i	$0.749622\pi$
$44$	−408.059	−1.39812
$45$	114.333	0.378750
$46$	−3.97967	−0.0127559
$47$	327.644	1.01685	0.508423	−	0.861108i	$-0.330229\pi$
$47$	327.644	1.01685	0.508423	+	0.861108i	$0.330229\pi$
$48$	−171.615	−0.516053
$49$	−267.732	−0.780559
$50$	−19.4756	−0.0550853
$51$	69.4672	0.190732
$52$	566.118	1.50974
$53$	21.5803	0.0559298	0.0279649	−	0.999609i	$-0.491097\pi$
$53$	21.5803	0.0559298	0.0279649	+	0.999609i	$0.491097\pi$
$54$	14.4529	0.0364222
$55$	672.051	1.64762
$56$	−72.9744	−0.174136
$57$	275.028	0.639093
$58$	125.522	0.284171
$59$	76.8494	0.169575	0.0847877	−	0.996399i	$-0.472979\pi$
$59$	76.8494	0.169575	0.0847877	+	0.996399i	$0.472979\pi$
$60$	293.968	0.632517
$61$	639.851	1.34302	0.671512	−	0.740994i	$-0.265645\pi$
$61$	639.851	1.34302	0.671512	+	0.740994i	$0.265645\pi$
$62$	163.148	0.334192
$63$	−78.0816	−0.156149
$64$	−405.229	−0.791464
$65$	−932.366	−1.77917
$66$	84.9546	0.158442
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	178.611	0.318526
$69$	−22.3036	−0.0389136
$70$	58.9967	0.100735
$71$	−1134.80	−1.89685	−0.948424	−	0.317005i	$-0.897323\pi$
$71$	−1134.80	−1.89685	−0.948424	+	0.317005i	$0.897323\pi$
$72$	75.7019	0.123910
$73$	822.973	1.31948	0.659738	−	0.751496i	$-0.270667\pi$
$73$	822.973	1.31948	0.659738	+	0.751496i	$0.270667\pi$
$74$	−121.828	−0.191381
$75$	−109.149	−0.168046
$76$	707.138	1.06729
$77$	−458.965	−0.679272
$78$	−117.861	−0.171092
$79$	−883.380	−1.25808	−0.629038	−	0.777375i	$-0.716551\pi$
$79$	−883.380	−1.25808	−0.629038	+	0.777375i	$0.716551\pi$
$80$	726.715	1.01561
$81$	81.0000	0.111111
$82$	90.9975	0.122549
$83$	−967.641	−1.27967	−0.639834	−	0.768514i	$-0.720997\pi$
$83$	−967.641	−1.27967	−0.639834	+	0.768514i	$0.720997\pi$
$84$	−200.760	−0.260770
$85$	−294.163	−0.375370
$86$	213.203	0.267329
$87$	703.477	0.866904
$88$	444.977	0.539031
$89$	1097.53	1.30717	0.653586	−	0.756852i	$-0.273264\pi$
$89$	1097.53	1.30717	0.653586	+	0.756852i	$0.273264\pi$
$90$	−61.2018	−0.0716804
$91$	636.743	0.733503
$92$	−57.3460	−0.0649863
$93$	914.348	1.01950
$94$	−175.386	−0.192443
$95$	−1164.62	−1.25776
$96$	293.737	0.312285
$97$	1147.80	1.20146	0.600731	−	0.799451i	$-0.294876\pi$
$97$	1147.80	1.20146	0.600731	+	0.799451i	$0.294876\pi$
$98$	143.315	0.147725
$99$	476.119	0.483351
$100$	−280.639	−0.280639
$101$	679.304	0.669241	0.334620	−	0.942353i	$-0.391392\pi$
$101$	679.304	0.669241	0.334620	+	0.942353i	$0.391392\pi$
$102$	−37.1854	−0.0360971
$103$	−875.812	−0.837829	−0.418914	−	0.908026i	$-0.637589\pi$
$103$	−875.812	−0.837829	−0.418914	+	0.908026i	$0.637589\pi$
$104$	−617.337	−0.582066
$105$	330.641	0.307307
$106$	−11.5518	−0.0105850
$107$	1038.50	0.938279	0.469139	−	0.883124i	$-0.344564\pi$
$107$	1038.50	0.938279	0.469139	+	0.883124i	$0.344564\pi$
$108$	208.263	0.185557
$109$	−1294.69	−1.13770	−0.568848	−	0.822443i	$-0.692611\pi$
$109$	−1294.69	−1.13770	−0.568848	+	0.822443i	$0.692611\pi$
$110$	−359.745	−0.311821
$111$	−682.772	−0.583836
$112$	−496.297	−0.418711
$113$	2209.80	1.83965	0.919823	−	0.392333i	$-0.128332\pi$
$113$	2209.80	1.83965	0.919823	+	0.392333i	$0.128332\pi$
$114$	−147.221	−0.120952
$115$	94.4459	0.0765837
$116$	1808.75	1.44774
$117$	−660.542	−0.521941
$118$	−41.1371	−0.0320930
$119$	200.893	0.154755
$120$	−320.564	−0.243861
$121$	1467.64	1.10266
$122$	−342.508	−0.254174
$123$	509.986	0.373853
$124$	2350.93	1.70258
$125$	−1125.76	−0.805529
$126$	41.7966	0.0295519
$127$	−1923.32	−1.34383	−0.671917	−	0.740627i	$-0.734529\pi$
$127$	−1923.32	−1.34383	−0.671917	+	0.740627i	$0.734529\pi$
$128$	1000.21	0.690682
$129$	1194.87	0.815525
$130$	499.090	0.336716
$131$	−2201.26	−1.46813	−0.734066	−	0.679078i	$-0.762380\pi$
$131$	−2201.26	−1.46813	−0.734066	+	0.679078i	$0.762380\pi$
$132$	1224.18	0.807203
$133$	795.356	0.518542
$134$	−35.8647	−0.0231212
$135$	−342.999	−0.218671
$136$	−194.770	−0.122805
$137$	−948.243	−0.591342	−0.295671	−	0.955290i	$-0.595543\pi$
$137$	−948.243	−0.591342	−0.295671	+	0.955290i	$0.595543\pi$
$138$	11.9390	0.00736460
$139$	699.873	0.427068	0.213534	−	0.976936i	$-0.431503\pi$
$139$	699.873	0.427068	0.213534	+	0.976936i	$0.431503\pi$
$140$	850.128	0.513207
$141$	−982.931	−0.587076
$142$	607.453	0.358988
$143$	−3882.67	−2.27053
$144$	514.846	0.297943
$145$	−2978.91	−1.70610
$146$	−440.533	−0.249717
$147$	803.195	0.450656
$148$	−1755.51	−0.975014
$149$	600.174	0.329988	0.164994	−	0.986295i	$-0.447240\pi$
$149$	600.174	0.329988	0.164994	+	0.986295i	$0.447240\pi$
$150$	58.4268	0.0318035
$151$	−1694.47	−0.913203	−0.456601	−	0.889671i	$-0.650933\pi$
$151$	−1694.47	−0.913203	−0.456601	+	0.889671i	$0.650933\pi$
$152$	−771.116	−0.411485
$153$	−208.402	−0.110119
$154$	245.681	0.128556
$155$	−3871.86	−2.00642
$156$	−1698.35	−0.871648
$157$	−53.0089	−0.0269463	−0.0134732	−	0.999909i	$-0.504289\pi$
$157$	−53.0089	−0.0269463	−0.0134732	+	0.999909i	$0.504289\pi$
$158$	472.868	0.238097
$159$	−64.7409	−0.0322911
$160$	−1243.84	−0.614590
$161$	−64.5001	−0.0315734
$162$	−43.3588	−0.0210283
$163$	−1711.65	−0.822495	−0.411248	−	0.911524i	$-0.634907\pi$
$163$	−1711.65	−0.822495	−0.411248	+	0.911524i	$0.634907\pi$
$164$	1311.25	0.624339
$165$	−2016.15	−0.951256
$166$	517.972	0.242183
$167$	1474.22	0.683107	0.341554	−	0.939862i	$-0.389047\pi$
$167$	1474.22	0.683107	0.341554	+	0.939862i	$0.389047\pi$
$168$	218.923	0.100537
$169$	3189.61	1.45180
$170$	157.464	0.0710406
$171$	−825.083	−0.368981
$172$	3072.20	1.36194
$173$	80.3940	0.0353309	0.0176654	−	0.999844i	$-0.494377\pi$
$173$	80.3940	0.0353309	0.0176654	+	0.999844i	$0.494377\pi$
$174$	−376.567	−0.164066
$175$	−315.649	−0.136348
$176$	3026.27	1.29610
$177$	−230.548	−0.0979044
$178$	−587.503	−0.247389
$179$	−2425.50	−1.01280	−0.506398	−	0.862300i	$-0.669023\pi$
$179$	−2425.50	−1.01280	−0.506398	+	0.862300i	$0.669023\pi$
$180$	−881.903	−0.365184
$181$	−238.866	−0.0980925	−0.0490463	−	0.998797i	$-0.515618\pi$
$181$	−238.866	−0.0980925	−0.0490463	+	0.998797i	$0.515618\pi$
$182$	−340.845	−0.138819
$183$	−1919.55	−0.775395
$184$	62.5343	0.0250548
$185$	2891.23	1.14901
$186$	−489.445	−0.192946
$187$	−1224.99	−0.479037
$188$	−2527.27	−0.980424
$189$	234.245	0.0901524
$190$	623.414	0.238038
$191$	3908.63	1.48073	0.740363	−	0.672207i	$-0.234654\pi$
$191$	3908.63	1.48073	0.740363	+	0.672207i	$0.234654\pi$
$192$	1215.69	0.456952
$193$	−2322.25	−0.866110	−0.433055	−	0.901367i	$-0.642564\pi$
$193$	−2322.25	−0.866110	−0.433055	+	0.901367i	$0.642564\pi$
$194$	−614.413	−0.227383
$195$	2797.10	1.02720
$196$	2065.14	0.752601
$197$	−1372.13	−0.496244	−0.248122	−	0.968729i	$-0.579813\pi$
$197$	−1372.13	−0.496244	−0.248122	+	0.968729i	$0.579813\pi$
$198$	−254.864	−0.0914767
$199$	2736.38	0.974758	0.487379	−	0.873190i	$-0.337953\pi$
$199$	2736.38	0.974758	0.487379	+	0.873190i	$0.337953\pi$
$200$	306.029	0.108198
$201$	−201.000	−0.0705346
$202$	−363.628	−0.126657
$203$	2034.39	0.703382
$204$	−535.833	−0.183901
$205$	−2159.56	−0.735758
$206$	468.817	0.158563
$207$	66.9109	0.0224668
$208$	−4198.49	−1.39958
$209$	−4849.85	−1.60513
$210$	−176.990	−0.0581594
$211$	−888.727	−0.289965	−0.144982	−	0.989434i	$-0.546313\pi$
$211$	−888.727	−0.289965	−0.144982	+	0.989434i	$0.546313\pi$
$212$	−166.459	−0.0539266
$213$	3404.40	1.09515
$214$	−555.904	−0.177574
$215$	−5059.76	−1.60499
$216$	−227.106	−0.0715398
$217$	2644.21	0.827193
$218$	693.040	0.215315
$219$	−2468.92	−0.761800
$220$	−5183.84	−1.58861
$221$	1699.48	0.517283
$222$	365.484	0.110494
$223$	4484.78	1.34674	0.673371	−	0.739305i	$-0.264846\pi$
$223$	4484.78	1.34674	0.673371	+	0.739305i	$0.264846\pi$
$224$	849.460	0.253379
$225$	327.447	0.0970213
$226$	−1182.89	−0.348162
$227$	1979.25	0.578711	0.289355	−	0.957222i	$-0.406559\pi$
$227$	1979.25	0.578711	0.289355	+	0.957222i	$0.406559\pi$
$228$	−2121.42	−0.616202
$229$	−1194.73	−0.344760	−0.172380	−	0.985031i	$-0.555146\pi$
$229$	−1194.73	−0.344760	−0.172380	+	0.985031i	$0.555146\pi$
$230$	−50.5563	−0.0144938
$231$	1376.89	0.392178
$232$	−1972.39	−0.558163
$233$	−273.639	−0.0769386	−0.0384693	−	0.999260i	$-0.512248\pi$
$233$	−273.639	−0.0769386	−0.0384693	+	0.999260i	$0.512248\pi$
$234$	353.584	0.0987800
$235$	4162.27	1.15539
$236$	−592.775	−0.163502
$237$	2650.14	0.726350
$238$	−107.537	−0.0292881
$239$	1895.66	0.513056	0.256528	−	0.966537i	$-0.417421\pi$
$239$	1895.66	0.513056	0.256528	+	0.966537i	$0.417421\pi$
$240$	−2180.14	−0.586365
$241$	−1402.20	−0.374787	−0.187394	−	0.982285i	$-0.560004\pi$
$241$	−1402.20	−0.374787	−0.187394	+	0.982285i	$0.560004\pi$
$242$	−785.617	−0.208683
$243$	−243.000	−0.0641500
$244$	−4935.46	−1.29492
$245$	−3401.17	−0.886910
$246$	−272.993	−0.0707536
$247$	6728.42	1.73327
$248$	−2563.63	−0.656413
$249$	2902.92	0.738816
$250$	602.613	0.152450
$251$	6372.79	1.60258	0.801289	−	0.598278i	$-0.204148\pi$
$251$	6372.79	1.60258	0.801289	+	0.598278i	$0.204148\pi$
$252$	602.279	0.150556
$253$	393.303	0.0977342
$254$	1029.54	0.254327
$255$	882.488	0.216720
$256$	2706.43	0.660749
$257$	1114.29	0.270457	0.135229	−	0.990814i	$-0.456823\pi$
$257$	1114.29	0.270457	0.135229	+	0.990814i	$0.456823\pi$
$258$	−639.609	−0.154342
$259$	−1974.52	−0.473708
$260$	7191.77	1.71544
$261$	−2110.43	−0.500508
$262$	1178.32	0.277851
$263$	4189.60	0.982289	0.491145	−	0.871078i	$-0.336579\pi$
$263$	4189.60	0.982289	0.491145	+	0.871078i	$0.336579\pi$
$264$	−1334.93	−0.311210
$265$	274.149	0.0635503
$266$	−425.749	−0.0981367
$267$	−3292.60	−0.754696
$268$	−516.802	−0.117794
$269$	−1890.49	−0.428494	−0.214247	−	0.976779i	$-0.568730\pi$
$269$	−1890.49	−0.428494	−0.214247	+	0.976779i	$0.568730\pi$
$270$	183.605	0.0413847
$271$	−3340.05	−0.748684	−0.374342	−	0.927291i	$-0.622131\pi$
$271$	−3340.05	−0.748684	−0.374342	+	0.927291i	$0.622131\pi$
$272$	−1324.63	−0.295284
$273$	−1910.23	−0.423488
$274$	507.589	0.111915
$275$	1924.74	0.422058
$276$	172.038	0.0375198
$277$	3155.53	0.684468	0.342234	−	0.939615i	$-0.388817\pi$
$277$	3155.53	0.684468	0.342234	+	0.939615i	$0.388817\pi$
$278$	−374.638	−0.0808248
$279$	−2743.05	−0.588609
$280$	−927.042	−0.197862
$281$	152.205	0.0323123	0.0161562	−	0.999869i	$-0.494857\pi$
$281$	152.205	0.0323123	0.0161562	+	0.999869i	$0.494857\pi$
$282$	526.157	0.111107
$283$	−51.8139	−0.0108835	−0.00544173	−	0.999985i	$-0.501732\pi$
$283$	−51.8139	−0.0108835	−0.00544173	+	0.999985i	$0.501732\pi$
$284$	8753.25	1.82891
$285$	3493.86	0.726170
$286$	2078.37	0.429709
$287$	1474.83	0.303334
$288$	−881.210	−0.180298
$289$	−4376.81	−0.890863
$290$	1594.59	0.322889
$291$	−3443.41	−0.693665
$292$	−6347.97	−1.27222
$293$	7055.66	1.40681	0.703407	−	0.710788i	$-0.251661\pi$
$293$	7055.66	1.40681	0.703407	+	0.710788i	$0.251661\pi$
$294$	−429.946	−0.0852889
$295$	976.269	0.192680
$296$	1914.34	0.375908
$297$	−1428.36	−0.279063
$298$	−321.270	−0.0624519
$299$	−545.647	−0.105537
$300$	841.916	0.162027
$301$	3455.47	0.661694
$302$	907.037	0.172828
$303$	−2037.91	−0.386386
$304$	−5244.33	−0.989418
$305$	8128.45	1.52601
$306$	111.556	0.0208407
$307$	4434.84	0.824462	0.412231	−	0.911079i	$-0.364750\pi$
$307$	4434.84	0.824462	0.412231	+	0.911079i	$0.364750\pi$
$308$	3540.21	0.654942
$309$	2627.44	0.483721
$310$	2072.58	0.379725
$311$	6017.09	1.09710	0.548549	−	0.836118i	$-0.315180\pi$
$311$	6017.09	1.09710	0.548549	+	0.836118i	$0.315180\pi$
$312$	1852.01	0.336056
$313$	7443.44	1.34418	0.672089	−	0.740470i	$-0.265397\pi$
$313$	7443.44	1.34418	0.672089	+	0.740470i	$0.265397\pi$
$314$	28.3754	0.00509973
$315$	−991.922	−0.177424
$316$	6813.91	1.21301
$317$	−2333.15	−0.413384	−0.206692	−	0.978406i	$-0.566270\pi$
$317$	−2333.15	−0.413384	−0.206692	+	0.978406i	$0.566270\pi$
$318$	34.6554	0.00611126
$319$	−12405.2	−2.17729
$320$	−5147.90	−0.899300
$321$	−3115.51	−0.541716
$322$	34.5265	0.00597543
$323$	2122.82	0.365687
$324$	−624.790	−0.107131
$325$	−2670.28	−0.455755
$326$	916.236	0.155661
$327$	3884.07	0.656849
$328$	−1429.89	−0.240708
$329$	−2842.55	−0.476337
$330$	1079.23	0.180030
$331$	2030.06	0.337106	0.168553	−	0.985693i	$-0.446091\pi$
$331$	2030.06	0.337106	0.168553	+	0.985693i	$0.446091\pi$
$332$	7463.86	1.23383
$333$	2048.31	0.337078
$334$	−789.144	−0.129282
$335$	851.145	0.138815
$336$	1488.89	0.241743
$337$	1483.82	0.239847	0.119924	−	0.992783i	$-0.461735\pi$
$337$	1483.82	0.239847	0.119924	+	0.992783i	$0.461735\pi$
$338$	−1707.38	−0.274761
$339$	−6629.39	−1.06212
$340$	2269.01	0.361925
$341$	−16123.7	−2.56054
$342$	441.662	0.0698314
$343$	5298.55	0.834095
$344$	−3350.16	−0.525082
$345$	−283.338	−0.0442156
$346$	−43.0344	−0.00668655
$347$	−8967.67	−1.38735	−0.693674	−	0.720289i	$-0.744009\pi$
$347$	−8967.67	−1.38735	−0.693674	+	0.720289i	$0.744009\pi$
$348$	−5426.24	−0.835854
$349$	9428.05	1.44605	0.723026	−	0.690821i	$-0.242751\pi$
$349$	9428.05	1.44605	0.723026	+	0.690821i	$0.242751\pi$
$350$	168.965	0.0258045
$351$	1981.62	0.301343
$352$	−5179.76	−0.784325
$353$	6028.06	0.908899	0.454449	−	0.890773i	$-0.349836\pi$
$353$	6028.06	0.908899	0.454449	+	0.890773i	$0.349836\pi$
$354$	123.411	0.0185289
$355$	−14416.1	−2.15529
$356$	−8465.78	−1.26035
$357$	−602.679	−0.0893478
$358$	1298.36	0.191677
$359$	−6866.47	−1.00947	−0.504733	−	0.863275i	$-0.668409\pi$
$359$	−6866.47	−1.00947	−0.504733	+	0.863275i	$0.668409\pi$
$360$	961.691	0.140793
$361$	1545.47	0.225320
$362$	127.863	0.0185645
$363$	−4402.91	−0.636619
$364$	−4911.49	−0.707231
$365$	10454.8	1.49925
$366$	1027.53	0.146748
$367$	3301.99	0.469652	0.234826	−	0.972037i	$-0.424548\pi$
$367$	3301.99	0.469652	0.234826	+	0.972037i	$0.424548\pi$
$368$	425.294	0.0602445
$369$	−1529.96	−0.215844
$370$	−1547.66	−0.217457
$371$	−187.225	−0.0262001
$372$	−7052.79	−0.982984
$373$	−12194.2	−1.69274	−0.846371	−	0.532594i	$-0.821217\pi$
$373$	−12194.2	−1.69274	−0.846371	+	0.532594i	$0.821217\pi$
$374$	655.729	0.0906603
$375$	3377.28	0.465072
$376$	2755.92	0.377993
$377$	17210.2	2.35112
$378$	−125.390	−0.0170618
$379$	6314.59	0.855827	0.427914	−	0.903820i	$-0.359249\pi$
$379$	6314.59	0.855827	0.427914	+	0.903820i	$0.359249\pi$
$380$	8983.25	1.21271
$381$	5769.95	0.775863
$382$	−2092.27	−0.280235
$383$	−12648.5	−1.68749	−0.843745	−	0.536745i	$-0.819654\pi$
$383$	−12648.5	−1.68749	−0.843745	+	0.536745i	$0.819654\pi$
$384$	−3000.64	−0.398765
$385$	−5830.53	−0.771822
$386$	1243.09	0.163916
$387$	−3584.62	−0.470844
$388$	−8853.54	−1.15843
$389$	−11169.2	−1.45578	−0.727891	−	0.685693i	$-0.759499\pi$
$389$	−11169.2	−1.45578	−0.727891	+	0.685693i	$0.759499\pi$
$390$	−1497.27	−0.194403
$391$	−172.152	−0.0222663
$392$	−2251.98	−0.290158
$393$	6603.79	0.847627
$394$	734.491	0.0939166
$395$	−11222.2	−1.42949
$396$	−3672.53	−0.466039
$397$	9546.35	1.20685	0.603423	−	0.797421i	$-0.293803\pi$
$397$	9546.35	1.20685	0.603423	+	0.797421i	$0.293803\pi$
$398$	−1464.77	−0.184478
$399$	−2386.07	−0.299380
$400$	2081.29	0.260162
$401$	7271.16	0.905497	0.452749	−	0.891638i	$-0.350443\pi$
$401$	7271.16	0.905497	0.452749	+	0.891638i	$0.350443\pi$
$402$	107.594	0.0133490
$403$	22369.1	2.76497
$404$	−5239.79	−0.645270
$405$	1029.00	0.126250
$406$	−1089.00	−0.133119
$407$	12040.0	1.46634
$408$	584.311	0.0709013
$409$	3162.84	0.382377	0.191189	−	0.981553i	$-0.438766\pi$
$409$	3162.84	0.382377	0.191189	+	0.981553i	$0.438766\pi$
$410$	1156.00	0.139246
$411$	2844.73	0.341412
$412$	6755.54	0.807820
$413$	−666.725	−0.0794368
$414$	−35.8170	−0.00425195
$415$	−12292.6	−1.45402
$416$	7186.12	0.846943
$417$	−2099.62	−0.246568
$418$	2596.10	0.303778
$419$	−13128.7	−1.53074	−0.765369	−	0.643592i	$-0.777443\pi$
$419$	−13128.7	−1.53074	−0.765369	+	0.643592i	$0.777443\pi$
$420$	−2550.38	−0.296300
$421$	−3166.81	−0.366606	−0.183303	−	0.983056i	$-0.558679\pi$
$421$	−3166.81	−0.366606	−0.183303	+	0.983056i	$0.558679\pi$
$422$	475.731	0.0548773
$423$	2948.79	0.338948
$424$	181.519	0.0207909
$425$	−842.475	−0.0961554
$426$	−1822.36	−0.207262
$427$	−5551.17	−0.629134
$428$	−8010.45	−0.904672
$429$	11648.0	1.31089
$430$	2708.46	0.303752
$431$	−9723.09	−1.08665	−0.543323	−	0.839524i	$-0.682834\pi$
$431$	−9723.09	−1.08665	−0.543323	+	0.839524i	$0.682834\pi$
$432$	−1544.54	−0.172018
$433$	−15386.5	−1.70769	−0.853844	−	0.520529i	$-0.825735\pi$
$433$	−15386.5	−1.70769	−0.853844	+	0.520529i	$0.825735\pi$
$434$	−1415.43	−0.156551
$435$	8936.74	0.985020
$436$	9986.55	1.09695
$437$	−681.568	−0.0746083
$438$	1321.60	0.144174
$439$	−6437.90	−0.699919	−0.349959	−	0.936765i	$-0.613805\pi$
$439$	−6437.90	−0.699919	−0.349959	+	0.936765i	$0.613805\pi$
$440$	5652.84	0.612474
$441$	−2409.58	−0.260186
$442$	−909.722	−0.0978983
$443$	−4463.50	−0.478707	−0.239354	−	0.970932i	$-0.576936\pi$
$443$	−4463.50	−0.478707	−0.239354	+	0.970932i	$0.576936\pi$
$444$	5266.53	0.562925
$445$	13942.7	1.48527
$446$	−2400.68	−0.254878
$447$	−1800.52	−0.190519
$448$	3515.66	0.370758
$449$	2954.97	0.310587	0.155293	−	0.987868i	$-0.450368\pi$
$449$	2954.97	0.310587	0.155293	+	0.987868i	$0.450368\pi$
$450$	−175.280	−0.0183618
$451$	−8993.12	−0.938957
$452$	−17045.2	−1.77375
$453$	5083.40	0.527238
$454$	−1059.48	−0.109524
$455$	8088.96	0.833443
$456$	2313.35	0.237571
$457$	−2594.54	−0.265574	−0.132787	−	0.991145i	$-0.542393\pi$
$457$	−2594.54	−0.265574	−0.132787	+	0.991145i	$0.542393\pi$
$458$	639.533	0.0652476
$459$	625.205	0.0635775
$460$	−728.504	−0.0738406
$461$	−14702.4	−1.48538	−0.742689	−	0.669636i	$-0.766450\pi$
$461$	−14702.4	−1.48538	−0.742689	+	0.669636i	$0.766450\pi$
$462$	−737.044	−0.0742216
$463$	−915.553	−0.0918992	−0.0459496	−	0.998944i	$-0.514631\pi$
$463$	−915.553	−0.0918992	−0.0459496	+	0.998944i	$0.514631\pi$
$464$	−13414.2	−1.34211
$465$	11615.6	1.15841
$466$	146.477	0.0145610
$467$	16198.8	1.60512	0.802560	−	0.596571i	$-0.203471\pi$
$467$	16198.8	1.60512	0.802560	+	0.596571i	$0.203471\pi$
$468$	5095.06	0.503246
$469$	−581.274	−0.0572297
$470$	−2228.04	−0.218663
$471$	159.027	0.0155575
$472$	646.406	0.0630365
$473$	−21070.5	−2.04825
$474$	−1418.60	−0.137466
$475$	−3335.44	−0.322191
$476$	−1549.58	−0.149212
$477$	194.223	0.0186433
$478$	−1014.74	−0.0970984
$479$	898.316	0.0856892	0.0428446	−	0.999082i	$-0.486358\pi$
$479$	898.316	0.0856892	0.0428446	+	0.999082i	$0.486358\pi$
$480$	3731.53	0.354834
$481$	−16703.7	−1.58341
$482$	750.590	0.0709304
$483$	193.500	0.0182289
$484$	−11320.6	−1.06316
$485$	14581.3	1.36516
$486$	130.076	0.0121407
$487$	4641.28	0.431861	0.215931	−	0.976409i	$-0.430721\pi$
$487$	4641.28	0.431861	0.215931	+	0.976409i	$0.430721\pi$
$488$	5381.99	0.499244
$489$	5134.95	0.474868
$490$	1820.63	0.167852
$491$	−10110.3	−0.929268	−0.464634	−	0.885503i	$-0.653814\pi$
$491$	−10110.3	−0.929268	−0.464634	+	0.885503i	$0.653814\pi$
$492$	−3933.76	−0.360462
$493$	5429.84	0.496040
$494$	−3601.68	−0.328031
$495$	6048.46	0.549208
$496$	−17435.1	−1.57835
$497$	9845.24	0.888570
$498$	−1553.92	−0.139825
$499$	4381.96	0.393113	0.196556	−	0.980493i	$-0.437024\pi$
$499$	4381.96	0.393113	0.196556	+	0.980493i	$0.437024\pi$
$500$	8683.51	0.776677
$501$	−4422.67	−0.394392
$502$	−3411.32	−0.303296
$503$	−8529.13	−0.756054	−0.378027	−	0.925795i	$-0.623397\pi$
$503$	−8529.13	−0.756054	−0.378027	+	0.925795i	$0.623397\pi$
$504$	−656.770	−0.0580453
$505$	8629.65	0.760425
$506$	−210.533	−0.0184967
$507$	−9568.82	−0.838198
$508$	14835.4	1.29570
$509$	−13727.8	−1.19543	−0.597715	−	0.801709i	$-0.703925\pi$
$509$	−13727.8	−1.19543	−0.597715	+	0.801709i	$0.703925\pi$
$510$	−472.391	−0.0410153
$511$	−7139.90	−0.618103
$512$	−9450.45	−0.815732
$513$	2475.25	0.213031
$514$	−596.473	−0.0511854
$515$	−11126.0	−0.951983
$516$	−9216.61	−0.786315
$517$	17333.0	1.47448
$518$	1056.95	0.0896517
$519$	−241.182	−0.0203983
$520$	−7842.43	−0.661372
$521$	−7091.66	−0.596336	−0.298168	−	0.954513i	$-0.596376\pi$
$521$	−7091.66	−0.596336	−0.298168	+	0.954513i	$0.596376\pi$
$522$	1129.70	0.0947236
$523$	−18236.6	−1.52472	−0.762362	−	0.647151i	$-0.775960\pi$
$523$	−18236.6	−1.52472	−0.762362	+	0.647151i	$0.775960\pi$
$524$	16979.4	1.41555
$525$	946.947	0.0787203
$526$	−2242.67	−0.185903
$527$	7057.47	0.583355
$528$	−9078.82	−0.748305
$529$	−12111.7	−0.995457
$530$	−146.750	−0.0120272
$531$	691.645	0.0565251
$532$	−6134.94	−0.499969
$533$	12476.6	1.01392
$534$	1762.51	0.142830
$535$	13192.8	1.06612
$536$	563.559	0.0454142
$537$	7276.50	0.584738
$538$	1011.97	0.0810947
$539$	−14163.6	−1.13185
$540$	2645.71	0.210839
$541$	10414.1	0.827611	0.413805	−	0.910365i	$-0.364199\pi$
$541$	10414.1	0.827611	0.413805	+	0.910365i	$0.364199\pi$
$542$	1787.91	0.141692
$543$	716.597	0.0566337
$544$	2267.23	0.178689
$545$	−16447.3	−1.29271
$546$	1022.53	0.0801473
$547$	12517.3	0.978427	0.489214	−	0.872164i	$-0.337284\pi$
$547$	12517.3	0.978427	0.489214	+	0.872164i	$0.337284\pi$
$548$	7314.24	0.570162
$549$	5758.66	0.447675
$550$	−1030.30	−0.0798767
$551$	21497.3	1.66210
$552$	−187.603	−0.0144654
$553$	7663.97	0.589340
$554$	−1689.14	−0.129539
$555$	−8673.70	−0.663384
$556$	−5398.44	−0.411771
$557$	−2409.29	−0.183276	−0.0916380	−	0.995792i	$-0.529210\pi$
$557$	−2409.29	−0.183276	−0.0916380	+	0.995792i	$0.529210\pi$
$558$	1468.34	0.111397
$559$	29232.0	2.21177
$560$	−6304.78	−0.475760
$561$	3674.96	0.276572
$562$	−81.4743	−0.00611527
$563$	18207.3	1.36296	0.681481	−	0.731836i	$-0.261336\pi$
$563$	18207.3	1.36296	0.681481	+	0.731836i	$0.261336\pi$
$564$	7581.80	0.566048
$565$	28072.5	2.09030
$566$	27.7357	0.00205975
$567$	−702.734	−0.0520495
$568$	−9545.18	−0.705118
$569$	−4017.41	−0.295990	−0.147995	−	0.988988i	$-0.547282\pi$
$569$	−4017.41	−0.295990	−0.147995	+	0.988988i	$0.547282\pi$
$570$	−1870.24	−0.137431
$571$	15369.5	1.12644	0.563218	−	0.826309i	$-0.309563\pi$
$571$	15369.5	1.12644	0.563218	+	0.826309i	$0.309563\pi$
$572$	29948.9	2.18920
$573$	−11725.9	−0.854897
$574$	−789.470	−0.0574074
$575$	270.491	0.0196178
$576$	−3647.06	−0.263821
$577$	−10708.7	−0.772634	−0.386317	−	0.922366i	$-0.626253\pi$
$577$	−10708.7	−0.772634	−0.386317	+	0.922366i	$0.626253\pi$
$578$	2342.88	0.168600
$579$	6966.75	0.500049
$580$	22977.7	1.64500
$581$	8394.99	0.599454
$582$	1843.24	0.131280
$583$	1141.64	0.0811013
$584$	6922.29	0.490491
$585$	−8391.30	−0.593055
$586$	−3776.86	−0.266247
$587$	−2958.04	−0.207992	−0.103996	−	0.994578i	$-0.533163\pi$
$587$	−2958.04	−0.207992	−0.103996	+	0.994578i	$0.533163\pi$
$588$	−6195.41	−0.434514
$589$	27941.2	1.95467
$590$	−522.591	−0.0364657
$591$	4116.38	0.286506
$592$	13019.4	0.903872
$593$	−17016.4	−1.17838	−0.589191	−	0.807994i	$-0.700554\pi$
$593$	−17016.4	−1.17838	−0.589191	+	0.807994i	$0.700554\pi$
$594$	764.592	0.0528141
$595$	2552.08	0.175840
$596$	−4629.42	−0.318169
$597$	−8209.14	−0.562777
$598$	292.082	0.0199734
$599$	−11992.3	−0.818014	−0.409007	−	0.912531i	$-0.634125\pi$
$599$	−11992.3	−0.818014	−0.409007	+	0.912531i	$0.634125\pi$
$600$	−918.087	−0.0624679
$601$	3785.54	0.256931	0.128465	−	0.991714i	$-0.458995\pi$
$601$	3785.54	0.256931	0.128465	+	0.991714i	$0.458995\pi$
$602$	−1849.69	−0.125229
$603$	603.000	0.0407231
$604$	13070.2	0.880494
$605$	18644.4	1.25289
$606$	1090.88	0.0731256
$607$	−14323.5	−0.957784	−0.478892	−	0.877874i	$-0.658961\pi$
$607$	−14323.5	−0.957784	−0.478892	+	0.877874i	$0.658961\pi$
$608$	8976.19	0.598738
$609$	−6103.18	−0.406098
$610$	−4351.11	−0.288805
$611$	−24046.9	−1.59220
$612$	1607.50	0.106175
$613$	4016.78	0.264659	0.132330	−	0.991206i	$-0.457754\pi$
$613$	4016.78	0.264659	0.132330	+	0.991206i	$0.457754\pi$
$614$	−2373.95	−0.156034
$615$	6478.69	0.424790
$616$	−3860.50	−0.252507
$617$	−14275.7	−0.931471	−0.465735	−	0.884924i	$-0.654210\pi$
$617$	−14275.7	−0.931471	−0.465735	+	0.884924i	$0.654210\pi$
$618$	−1406.45	−0.0915466
$619$	20440.8	1.32728	0.663639	−	0.748053i	$-0.269011\pi$
$619$	20440.8	1.32728	0.663639	+	0.748053i	$0.269011\pi$
$620$	29865.4	1.93455
$621$	−200.733	−0.0129712
$622$	−3220.91	−0.207632
$623$	−9521.91	−0.612339
$624$	12595.5	0.808048
$625$	−18849.2	−1.20635
$626$	−3984.43	−0.254393
$627$	14549.6	0.926720
$628$	408.882	0.0259812
$629$	−5270.03	−0.334069
$630$	530.970	0.0335783
$631$	−28737.7	−1.81304	−0.906520	−	0.422163i	$-0.861271\pi$
$631$	−28737.7	−1.81304	−0.906520	+	0.422163i	$0.861271\pi$
$632$	−7430.39	−0.467666
$633$	2666.18	0.167411
$634$	1248.92	0.0782350
$635$	−24433.2	−1.52693
$636$	499.376	0.0311345
$637$	19649.8	1.22222
$638$	6640.41	0.412063
$639$	−10213.2	−0.632282
$640$	12706.4	0.784787
$641$	14139.5	0.871259	0.435629	−	0.900126i	$-0.356526\pi$
$641$	14139.5	0.871259	0.435629	+	0.900126i	$0.356526\pi$
$642$	1667.71	0.102522
$643$	11734.4	0.719687	0.359844	−	0.933013i	$-0.382830\pi$
$643$	11734.4	0.719687	0.359844	+	0.933013i	$0.382830\pi$
$644$	497.519	0.0304425
$645$	15179.3	0.926641
$646$	−1136.33	−0.0692082
$647$	−10527.4	−0.639682	−0.319841	−	0.947471i	$-0.603629\pi$
$647$	−10527.4	−0.639682	−0.319841	+	0.947471i	$0.603629\pi$
$648$	681.317	0.0413035
$649$	4065.50	0.245893
$650$	1429.38	0.0862539
$651$	−7932.64	−0.477580
$652$	13202.7	0.793035
$653$	−6406.31	−0.383918	−0.191959	−	0.981403i	$-0.561484\pi$
$653$	−6406.31	−0.383918	−0.191959	+	0.981403i	$0.561484\pi$
$654$	−2079.12	−0.124312
$655$	−27964.1	−1.66817
$656$	−9724.61	−0.578784
$657$	7406.76	0.439825
$658$	1521.60	0.0901491
$659$	−7432.91	−0.439370	−0.219685	−	0.975571i	$-0.570503\pi$
$659$	−7432.91	−0.439370	−0.219685	+	0.975571i	$0.570503\pi$
$660$	15551.5	0.917185
$661$	−10413.2	−0.612750	−0.306375	−	0.951911i	$-0.599116\pi$
$661$	−10413.2	−0.612750	−0.306375	+	0.951911i	$0.599116\pi$
$662$	−1086.68	−0.0637989
$663$	−5098.44	−0.298653
$664$	−8139.14	−0.475693
$665$	10103.9	0.589193
$666$	−1096.45	−0.0637937
$667$	−1743.34	−0.101203
$668$	−11371.4	−0.658640
$669$	−13454.4	−0.777542
$670$	−455.613	−0.0262714
$671$	33849.5	1.94746
$672$	−2548.38	−0.146289
$673$	−28105.3	−1.60977	−0.804887	−	0.593428i	$-0.797774\pi$
$673$	−28105.3	−1.60977	−0.804887	+	0.593428i	$0.797774\pi$
$674$	−794.278	−0.0453923
$675$	−982.341	−0.0560153
$676$	−24602.9	−1.39980
$677$	16017.7	0.909323	0.454661	−	0.890664i	$-0.349760\pi$
$677$	16017.7	0.909323	0.454661	+	0.890664i	$0.349760\pi$
$678$	3548.67	0.201012
$679$	−9958.04	−0.562820
$680$	−2474.30	−0.139537
$681$	−5937.74	−0.334119
$682$	8630.90	0.484596
$683$	8903.58	0.498808	0.249404	−	0.968400i	$-0.419765\pi$
$683$	8903.58	0.498808	0.249404	+	0.968400i	$0.419765\pi$
$684$	6364.25	0.355765
$685$	−12046.2	−0.671913
$686$	−2836.28	−0.157857
$687$	3584.20	0.199047
$688$	−22784.3	−1.26256
$689$	−1583.85	−0.0875762
$690$	151.669	0.00836803
$691$	3629.10	0.199794	0.0998969	−	0.994998i	$-0.468149\pi$
$691$	3629.10	0.199794	0.0998969	+	0.994998i	$0.468149\pi$
$692$	−620.116	−0.0340654
$693$	−4130.68	−0.226424
$694$	4800.34	0.262563
$695$	8890.95	0.485256
$696$	5917.18	0.322256
$697$	3936.37	0.213918
$698$	−5046.78	−0.273673
$699$	820.918	0.0444205
$700$	2434.75	0.131464
$701$	−7009.71	−0.377679	−0.188840	−	0.982008i	$-0.560473\pi$
$701$	−7009.71	−0.377679	−0.188840	+	0.982008i	$0.560473\pi$
$702$	−1060.75	−0.0570306
$703$	−20864.6	−1.11938
$704$	−21437.5	−1.14767
$705$	−12486.8	−0.667065
$706$	−3226.79	−0.172014
$707$	−5893.46	−0.313503
$708$	1778.33	0.0943977
$709$	18052.8	0.956257	0.478129	−	0.878290i	$-0.341315\pi$
$709$	18052.8	0.956257	0.478129	+	0.878290i	$0.341315\pi$
$710$	7716.87	0.407900
$711$	−7950.42	−0.419359
$712$	9231.71	0.485917
$713$	−2265.92	−0.119017
$714$	322.611	0.0169095
$715$	−49324.2	−2.57989
$716$	18709.0	0.976520
$717$	−5686.99	−0.296213
$718$	3675.58	0.191047
$719$	−29936.7	−1.55278	−0.776390	−	0.630253i	$-0.782951\pi$
$719$	−29936.7	−1.55278	−0.776390	+	0.630253i	$0.782951\pi$
$720$	6540.43	0.338538
$721$	7598.31	0.392477
$722$	−827.282	−0.0426430
$723$	4206.60	0.216384
$724$	1842.48	0.0945791
$725$	−8531.54	−0.437039
$726$	2356.85	0.120483
$727$	18244.1	0.930723	0.465361	−	0.885121i	$-0.345924\pi$
$727$	18244.1	0.930723	0.465361	+	0.885121i	$0.345924\pi$
$728$	5355.85	0.272666
$729$	729.000	0.0370370
$730$	−5596.38	−0.283741
$731$	9222.73	0.466641
$732$	14806.4	0.747623
$733$	36774.2	1.85305	0.926525	−	0.376234i	$-0.122781\pi$
$733$	36774.2	1.85305	0.926525	+	0.376234i	$0.122781\pi$
$734$	−1767.54	−0.0888841
$735$	10203.5	0.512058
$736$	−727.932	−0.0364564
$737$	3544.44	0.177152
$738$	818.978	0.0408496
$739$	−20048.8	−0.997980	−0.498990	−	0.866608i	$-0.666296\pi$
$739$	−20048.8	−0.997980	−0.498990	+	0.866608i	$0.666296\pi$
$740$	−22301.4	−1.10786
$741$	−20185.3	−1.00071
$742$	100.220	0.00495850
$743$	26714.9	1.31908	0.659539	−	0.751671i	$-0.270752\pi$
$743$	26714.9	1.31908	0.659539	+	0.751671i	$0.270752\pi$
$744$	7690.88	0.378980
$745$	7624.41	0.374949
$746$	6527.49	0.320360
$747$	−8708.77	−0.426556
$748$	9448.90	0.461879
$749$	−9009.77	−0.439533
$750$	−1807.84	−0.0880173
$751$	18024.4	0.875790	0.437895	−	0.899026i	$-0.355724\pi$
$751$	18024.4	0.875790	0.437895	+	0.899026i	$0.355724\pi$
$752$	18742.9	0.908887
$753$	−19118.4	−0.925249
$754$	−9212.53	−0.444961
$755$	−21525.9	−1.03763
$756$	−1806.84	−0.0869234
$757$	−1608.70	−0.0772379	−0.0386190	−	0.999254i	$-0.512296\pi$
$757$	−1608.70	−0.0772379	−0.0386190	+	0.999254i	$0.512296\pi$
$758$	−3380.16	−0.161970
$759$	−1179.91	−0.0564269
$760$	−9795.99	−0.467550
$761$	26288.7	1.25225	0.626126	−	0.779722i	$-0.284640\pi$
$761$	26288.7	1.25225	0.626126	+	0.779722i	$0.284640\pi$
$762$	−3088.62	−0.146836
$763$	11232.4	0.532949
$764$	−30149.1	−1.42769
$765$	−2647.46	−0.125123
$766$	6770.67	0.319366
$767$	−5640.25	−0.265525
$768$	−8119.28	−0.381483
$769$	21924.5	1.02811	0.514056	−	0.857756i	$-0.328142\pi$
$769$	21924.5	1.02811	0.514056	+	0.857756i	$0.328142\pi$
$770$	3121.05	0.146071
$771$	−3342.87	−0.156149
$772$	17912.6	0.835088
$773$	−17859.7	−0.831006	−0.415503	−	0.909592i	$-0.636394\pi$
$773$	−17859.7	−0.831006	−0.415503	+	0.909592i	$0.636394\pi$
$774$	1918.83	0.0891096
$775$	−11088.9	−0.513968
$776$	9654.55	0.446621
$777$	5923.55	0.273495
$778$	5978.79	0.275514
$779$	15584.5	0.716780
$780$	−21575.3	−0.990410
$781$	−60033.4	−2.75053
$782$	92.1521	0.00421400
$783$	6331.30	0.288968
$784$	−15315.6	−0.697687
$785$	−673.407	−0.0306178
$786$	−3534.97	−0.160418
$787$	−14381.2	−0.651378	−0.325689	−	0.945477i	$-0.605596\pi$
$787$	−14381.2	−0.651378	−0.325689	+	0.945477i	$0.605596\pi$
$788$	10583.8	0.478469
$789$	−12568.8	−0.567125
$790$	6007.16	0.270538
$791$	−19171.6	−0.861774
$792$	4004.79	0.179677
$793$	−46960.9	−2.10294
$794$	−5110.11	−0.228402
$795$	−822.446	−0.0366908
$796$	−21107.0	−0.939845
$797$	−18452.7	−0.820111	−0.410056	−	0.912060i	$-0.634491\pi$
$797$	−18452.7	−0.820111	−0.410056	+	0.912060i	$0.634491\pi$
$798$	1277.25	0.0566593
$799$	−7586.83	−0.335923
$800$	−3562.34	−0.157435
$801$	9877.80	0.435724
$802$	−3892.21	−0.171370
$803$	43537.0	1.91331
$804$	1550.41	0.0680082
$805$	−819.387	−0.0358753
$806$	−11974.0	−0.523285
$807$	5671.46	0.247391
$808$	5713.85	0.248778
$809$	29948.2	1.30151	0.650755	−	0.759288i	$-0.274453\pi$
$809$	29948.2	1.30151	0.650755	+	0.759288i	$0.274453\pi$
$810$	−550.816	−0.0238935
$811$	−32219.3	−1.39503	−0.697517	−	0.716568i	$-0.745712\pi$
$811$	−32219.3	−1.39503	−0.697517	+	0.716568i	$0.745712\pi$
$812$	−15692.2	−0.678188
$813$	10020.1	0.432253
$814$	−6444.96	−0.277513
$815$	−21744.2	−0.934560
$816$	3973.88	0.170482
$817$	36513.7	1.56359
$818$	−1693.05	−0.0723668
$819$	5730.68	0.244501
$820$	16657.7	0.709405
$821$	21744.8	0.924360	0.462180	−	0.886786i	$-0.347067\pi$
$821$	21744.8	0.924360	0.462180	+	0.886786i	$0.347067\pi$
$822$	−1522.77	−0.0646139
$823$	−33219.6	−1.40700	−0.703501	−	0.710694i	$-0.748381\pi$
$823$	−33219.6	−1.40700	−0.703501	+	0.710694i	$0.748381\pi$
$824$	−7366.74	−0.311447
$825$	−5774.21	−0.243676
$826$	356.894	0.0150338
$827$	437.889	0.0184122	0.00920611	−	0.999958i	$-0.497070\pi$
$827$	437.889	0.0184122	0.00920611	+	0.999958i	$0.497070\pi$
$828$	−516.114	−0.0216621
$829$	−22201.8	−0.930156	−0.465078	−	0.885270i	$-0.653974\pi$
$829$	−22201.8	−0.930156	−0.465078	+	0.885270i	$0.653974\pi$
$830$	6580.15	0.275181
$831$	−9466.59	−0.395178
$832$	29741.2	1.23929
$833$	6199.52	0.257864
$834$	1123.91	0.0466642
$835$	18728.0	0.776181
$836$	37409.1	1.54763
$837$	8229.14	0.339833
$838$	7027.72	0.289700
$839$	3514.51	0.144618	0.0723089	−	0.997382i	$-0.476963\pi$
$839$	3514.51	0.144618	0.0723089	+	0.997382i	$0.476963\pi$
$840$	2781.13	0.114236
$841$	30597.7	1.25457
$842$	1695.18	0.0693820
$843$	−456.614	−0.0186555
$844$	6855.16	0.279579
$845$	40519.7	1.64961
$846$	−1578.47	−0.0641477
$847$	−12732.8	−0.516535
$848$	1234.50	0.0499918
$849$	155.442	0.00628357
$850$	450.972	0.0181979
$851$	1692.03	0.0681575
$852$	−26259.7	−1.05592
$853$	32360.1	1.29893	0.649465	−	0.760391i	$-0.274993\pi$
$853$	32360.1	1.29893	0.649465	+	0.760391i	$0.274993\pi$
$854$	2971.51	0.119067
$855$	−10481.6	−0.419254
$856$	8735.18	0.348788
$857$	−28152.2	−1.12213	−0.561063	−	0.827773i	$-0.689607\pi$
$857$	−28152.2	−1.12213	−0.561063	+	0.827773i	$0.689607\pi$
$858$	−6235.12	−0.248093
$859$	−42173.5	−1.67513	−0.837567	−	0.546335i	$-0.816023\pi$
$859$	−42173.5	−1.67513	−0.837567	+	0.546335i	$0.816023\pi$
$860$	39028.2	1.54750
$861$	−4424.50	−0.175130
$862$	5204.71	0.205653
$863$	19030.6	0.750650	0.375325	−	0.926893i	$-0.377531\pi$
$863$	19030.6	0.750650	0.375325	+	0.926893i	$0.377531\pi$
$864$	2643.63	0.104095
$865$	1021.30	0.0401447
$866$	8236.32	0.323189
$867$	13130.4	0.514340
$868$	−20396.0	−0.797566
$869$	−46732.7	−1.82428
$870$	−4783.78	−0.186420
$871$	−4917.37	−0.191296
$872$	−10890.1	−0.422918
$873$	10330.2	0.400487
$874$	364.839	0.0141200
$875$	9766.80	0.377346
$876$	19043.9	0.734514
$877$	34239.2	1.31833	0.659165	−	0.751998i	$-0.270910\pi$
$877$	34239.2	1.31833	0.659165	+	0.751998i	$0.270910\pi$
$878$	3446.17	0.132463
$879$	−21167.0	−0.812224
$880$	38444.8	1.47270
$881$	−1053.48	−0.0402866	−0.0201433	−	0.999797i	$-0.506412\pi$
$881$	−1053.48	−0.0402866	−0.0201433	+	0.999797i	$0.506412\pi$
$882$	1289.84	0.0492416
$883$	−24094.6	−0.918288	−0.459144	−	0.888362i	$-0.651844\pi$
$883$	−24094.6	−0.918288	−0.459144	+	0.888362i	$0.651844\pi$
$884$	−13108.9	−0.498755
$885$	−2928.81	−0.111244
$886$	2389.29	0.0905977
$887$	−19109.7	−0.723381	−0.361691	−	0.932298i	$-0.617800\pi$
$887$	−19109.7	−0.723381	−0.361691	+	0.932298i	$0.617800\pi$
$888$	−5743.01	−0.217030
$889$	16686.2	0.629513
$890$	−7463.44	−0.281096
$891$	4285.07	0.161117
$892$	−34593.2	−1.29850
$893$	−30037.0	−1.12559
$894$	963.809	0.0360566
$895$	−30812.7	−1.15079
$896$	−8677.59	−0.323547
$897$	1636.94	0.0609318
$898$	−1581.78	−0.0587801
$899$	71469.3	2.65143
$900$	−2525.75	−0.0935463
$901$	−499.708	−0.0184769
$902$	4813.96	0.177702
$903$	−10366.4	−0.382029
$904$	18587.3	0.683854
$905$	−3034.47	−0.111458
$906$	−2721.11	−0.0997824
$907$	−2899.84	−0.106161	−0.0530803	−	0.998590i	$-0.516904\pi$
$907$	−2899.84	−0.106161	−0.0530803	+	0.998590i	$0.516904\pi$
$908$	−15266.9	−0.557983
$909$	6113.74	0.223080
$910$	−4329.97	−0.157733
$911$	1336.13	0.0485927	0.0242964	−	0.999705i	$-0.492265\pi$
$911$	1336.13	0.0485927	0.0242964	+	0.999705i	$0.492265\pi$
$912$	15733.0	0.571241
$913$	−51190.3	−1.85559
$914$	1388.84	0.0502613
$915$	−24385.3	−0.881043
$916$	9215.52	0.332412
$917$	19097.6	0.687740
$918$	−334.668	−0.0120324
$919$	−19934.0	−0.715519	−0.357759	−	0.933814i	$-0.616459\pi$
$919$	−19934.0	−0.715519	−0.357759	+	0.933814i	$0.616459\pi$
$920$	794.415	0.0284686
$921$	−13304.5	−0.476003
$922$	7870.11	0.281115
$923$	83287.1	2.97013
$924$	−10620.6	−0.378131
$925$	8280.43	0.294334
$926$	490.090	0.0173924
$927$	−7882.31	−0.279276
$928$	22959.7	0.812164
$929$	−31623.9	−1.11684	−0.558420	−	0.829558i	$-0.688592\pi$
$929$	−31623.9	−1.11684	−0.558420	+	0.829558i	$0.688592\pi$
$930$	−6217.75	−0.219234
$931$	24544.5	0.864033
$932$	2110.71	0.0741829
$933$	−18051.3	−0.633410
$934$	−8671.12	−0.303777
$935$	−15561.8	−0.544306
$936$	−5556.03	−0.194022
$937$	−8025.24	−0.279801	−0.139900	−	0.990166i	$-0.544678\pi$
$937$	−8025.24	−0.279801	−0.139900	+	0.990166i	$0.544678\pi$
$938$	311.153	0.0108310
$939$	−22330.3	−0.776062
$940$	−32105.5	−1.11401
$941$	39004.3	1.35123	0.675613	−	0.737256i	$-0.263879\pi$
$941$	39004.3	1.35123	0.675613	+	0.737256i	$0.263879\pi$
$942$	−85.1261	−0.00294433
$943$	−1263.84	−0.0436439
$944$	4396.18	0.151572
$945$	2975.77	0.102436
$946$	11278.9	0.387641
$947$	48181.0	1.65330	0.826649	−	0.562718i	$-0.190244\pi$
$947$	48181.0	1.65330	0.826649	+	0.562718i	$0.190244\pi$
$948$	−20441.7	−0.700334
$949$	−60400.9	−2.06607
$950$	1785.44	0.0609762
$951$	6999.45	0.238667
$952$	1689.78	0.0575273
$953$	−9236.87	−0.313968	−0.156984	−	0.987601i	$-0.550177\pi$
$953$	−9236.87	−0.313968	−0.156984	+	0.987601i	$0.550177\pi$
$954$	−103.966	−0.00352834
$955$	49653.9	1.68247
$956$	−14622.1	−0.494679
$957$	37215.5	1.25706
$958$	−480.863	−0.0162171
$959$	8226.71	0.277012
$960$	15443.7	0.519211
$961$	63101.6	2.11814
$962$	8941.38	0.299669
$963$	9346.52	0.312760
$964$	10815.8	0.361363
$965$	−29501.1	−0.984118
$966$	−103.580	−0.00344991
$967$	−30501.5	−1.01434	−0.507168	−	0.861847i	$-0.669308\pi$
$967$	−30501.5	−1.01434	−0.507168	+	0.861847i	$0.669308\pi$
$968$	12344.8	0.409892
$969$	−6368.47	−0.211130
$970$	−7805.29	−0.258364
$971$	53413.2	1.76530	0.882652	−	0.470027i	$-0.155756\pi$
$971$	53413.2	1.76530	0.882652	+	0.470027i	$0.155756\pi$
$972$	1874.37	0.0618523
$973$	−6071.91	−0.200058
$974$	−2484.45	−0.0817320
$975$	8010.83	0.263130
$976$	36602.8	1.20044
$977$	28755.2	0.941618	0.470809	−	0.882235i	$-0.343962\pi$
$977$	28755.2	0.941618	0.470809	+	0.882235i	$0.343962\pi$
$978$	−2748.71	−0.0898711
$979$	58061.9	1.89547
$980$	26234.8	0.855143
$981$	−11652.2	−0.379232
$982$	5411.97	0.175869
$983$	−25736.4	−0.835060	−0.417530	−	0.908663i	$-0.637104\pi$
$983$	−25736.4	−0.835060	−0.417530	+	0.908663i	$0.637104\pi$
$984$	4289.66	0.138973
$985$	−17431.0	−0.563857
$986$	−2906.56	−0.0938782
$987$	8527.64	0.275013
$988$	−51899.4	−1.67119
$989$	−2961.11	−0.0952051
$990$	−3237.70	−0.103940
$991$	−31392.1	−1.00626	−0.503130	−	0.864211i	$-0.667818\pi$
$991$	−31392.1	−1.00626	−0.503130	+	0.864211i	$0.667818\pi$
$992$	29841.9	0.955124
$993$	−6090.17	−0.194628
$994$	−5270.10	−0.168166
$995$	34762.1	1.10757
$996$	−22391.6	−0.712354
$997$	34183.0	1.08585	0.542923	−	0.839783i	$-0.317318\pi$
$997$	34183.0	1.08585	0.542923	+	0.839783i	$0.317318\pi$
$998$	−2345.64	−0.0743986
$999$	−6144.94	−0.194612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.c.1.4	✓	7
3.2	odd	2		603.4.a.c.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.c.1.4	✓	7	1.1	even	1	trivial
603.4.a.c.1.4		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q-0.535294 q^{2} -3.00000 q^{3} -7.71346 q^{4} +12.7037 q^{5} +1.60588 q^{6} -8.67573 q^{7} +8.41132 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.535294 q^{2} -3.00000 q^{3} -7.71346 q^{4} +12.7037 q^{5} +1.60588 q^{6} -8.67573 q^{7} +8.41132 q^{8} +9.00000 q^{9} -6.80020 q^{10} +52.9021 q^{11} +23.1404 q^{12} -73.3935 q^{13} +4.64407 q^{14} -38.1110 q^{15} +57.2051 q^{16} -23.1557 q^{17} -4.81765 q^{18} -91.6759 q^{19} -97.9892 q^{20} +26.0272 q^{21} -28.3182 q^{22} +7.43454 q^{23} -25.2340 q^{24} +36.3830 q^{25} +39.2871 q^{26} -27.0000 q^{27} +66.9199 q^{28} -234.492 q^{29} +20.4006 q^{30} -304.783 q^{31} -97.9122 q^{32} -158.706 q^{33} +12.3951 q^{34} -110.214 q^{35} -69.4211 q^{36} +227.591 q^{37} +49.0736 q^{38} +220.181 q^{39} +106.855 q^{40} -169.995 q^{41} -13.9322 q^{42} -398.291 q^{43} -408.059 q^{44} +114.333 q^{45} -3.97967 q^{46} +327.644 q^{47} -171.615 q^{48} -267.732 q^{49} -19.4756 q^{50} +69.4672 q^{51} +566.118 q^{52} +21.5803 q^{53} +14.4529 q^{54} +672.051 q^{55} -72.9744 q^{56} +275.028 q^{57} +125.522 q^{58} +76.8494 q^{59} +293.968 q^{60} +639.851 q^{61} +163.148 q^{62} -78.0816 q^{63} -405.229 q^{64} -932.366 q^{65} +84.9546 q^{66} +67.0000 q^{67} +178.611 q^{68} -22.3036 q^{69} +58.9967 q^{70} -1134.80 q^{71} +75.7019 q^{72} +822.973 q^{73} -121.828 q^{74} -109.149 q^{75} +707.138 q^{76} -458.965 q^{77} -117.861 q^{78} -883.380 q^{79} +726.715 q^{80} +81.0000 q^{81} +90.9975 q^{82} -967.641 q^{83} -200.760 q^{84} -294.163 q^{85} +213.203 q^{86} +703.477 q^{87} +444.977 q^{88} +1097.53 q^{89} -61.2018 q^{90} +636.743 q^{91} -57.3460 q^{92} +914.348 q^{93} -175.386 q^{94} -1164.62 q^{95} +293.737 q^{96} +1147.80 q^{97} +143.315 q^{98} +476.119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * q^99

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