LMFDB - Embedded newform 147.7.d.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,7,Mod(97,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("147.97");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	147.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$33.8179502921$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.1
Root			$-6.30797 + 10.9257i$ of defining polynomial
Character	$\chi$	$=$	147.97
Dual form			147.7.d.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.6159 q^{2} -15.5885i q^{3} +70.9299 q^{4} +190.875i q^{5} +181.074i q^{6} -80.4975 q^{8} -243.000 q^{9} +O(q^{10})$	\(q-11.6159 q^{2} -15.5885i q^{3} +70.9299 q^{4} +190.875i q^{5} +181.074i q^{6} -80.4975 q^{8} -243.000 q^{9} -2217.19i q^{10} -2055.10 q^{11} -1105.69i q^{12} -3059.97i q^{13} +2975.44 q^{15} -3604.46 q^{16} +2850.24i q^{17} +2822.67 q^{18} +3949.13i q^{19} +13538.7i q^{20} +23872.0 q^{22} +660.543 q^{23} +1254.83i q^{24} -20808.1 q^{25} +35544.4i q^{26} +3788.00i q^{27} -9282.66 q^{29} -34562.5 q^{30} +2801.72i q^{31} +47021.0 q^{32} +32035.9i q^{33} -33108.2i q^{34} -17236.0 q^{36} -36932.5 q^{37} -45872.8i q^{38} -47700.1 q^{39} -15364.9i q^{40} +67941.3i q^{41} +12336.3 q^{43} -145768. q^{44} -46382.5i q^{45} -7672.83 q^{46} -147613. i q^{47} +56188.0i q^{48} +241705. q^{50} +44430.9 q^{51} -217043. i q^{52} +219635. q^{53} -44001.1i q^{54} -392267. i q^{55} +61560.8 q^{57} +107827. q^{58} +192518. i q^{59} +211048. q^{60} -332836. i q^{61} -32544.5i q^{62} -315508. q^{64} +584069. q^{65} -372127. i q^{66} +349184. q^{67} +202168. i q^{68} -10296.9i q^{69} +305650. q^{71} +19560.9 q^{72} -236498. i q^{73} +429005. q^{74} +324366. i q^{75} +280111. i q^{76} +554082. q^{78} -586437. q^{79} -688000. i q^{80} +59049.0 q^{81} -789201. i q^{82} -106377. i q^{83} -544039. q^{85} -143298. q^{86} +144702. i q^{87} +165431. q^{88} -13057.9i q^{89} +538776. i q^{90} +46852.3 q^{92} +43674.4 q^{93} +1.71466e6i q^{94} -753788. q^{95} -732985. i q^{96} -205209. i q^{97} +499390. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9} + 628 q^{11} + 5292 q^{15} + 25442 q^{16} - 2430 q^{18} + 86106 q^{22} - 7856 q^{23} + 34076 q^{25} - 8300 q^{29} - 61398 q^{30} + 372414 q^{32} - 84078 q^{36} - 129412 q^{37} - 58212 q^{39} + 45740 q^{43} - 185058 q^{44} + 223008 q^{46} + 967216 q^{50} - 99576 q^{51} + 1081948 q^{53} + 328212 q^{57} - 1079598 q^{58} + 292734 q^{60} + 2378626 q^{64} + 828408 q^{65} + 2317804 q^{67} + 1442344 q^{71} - 808218 q^{72} + 865880 q^{74} - 222588 q^{78} - 1222904 q^{79} + 472392 q^{81} - 275112 q^{85} - 1632448 q^{86} + 732882 q^{88} + 678720 q^{92} - 1611144 q^{93} + 1183584 q^{95} - 152604 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9 + 628 * q^11 + 5292 * q^15 + 25442 * q^16 - 2430 * q^18 + 86106 * q^22 - 7856 * q^23 + 34076 * q^25 - 8300 * q^29 - 61398 * q^30 + 372414 * q^32 - 84078 * q^36 - 129412 * q^37 - 58212 * q^39 + 45740 * q^43 - 185058 * q^44 + 223008 * q^46 + 967216 * q^50 - 99576 * q^51 + 1081948 * q^53 + 328212 * q^57 - 1079598 * q^58 + 292734 * q^60 + 2378626 * q^64 + 828408 * q^65 + 2317804 * q^67 + 1442344 * q^71 - 808218 * q^72 + 865880 * q^74 - 222588 * q^78 - 1222904 * q^79 + 472392 * q^81 - 275112 * q^85 - 1632448 * q^86 + 732882 * q^88 + 678720 * q^92 - 1611144 * q^93 + 1183584 * q^95 - 152604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−11.6159	−1.45199	−0.725996	−	0.687699i	$-0.758621\pi$
$2$	−11.6159	−1.45199	−0.725996	+	0.687699i	$0.758621\pi$
$3$	− 15.5885i	− 0.577350i
$3$	− 15.5885i	− 0.577350i
$4$	70.9299	1.10828
$5$	190.875i	1.52700i	0.645810	+	0.763498i	$0.276520\pi$
$5$	190.875i	1.52700i	−0.645810	+	0.763498i	$0.723480\pi$
$6$	181.074i	0.838308i
$7$	0	0
$7$	0	0
$8$	−80.4975	−0.157222
$9$	−243.000	−0.333333
$10$	− 2217.19i	− 2.21719i
$11$	−2055.10	−1.54403	−0.772015	−	0.635604i	$-0.780751\pi$
$11$	−2055.10	−1.54403	−0.772015	+	0.635604i	$0.780751\pi$
$12$	− 1105.69i	− 0.639866i
$13$	− 3059.97i	− 1.39279i	−0.717657	−	0.696396i	$-0.754786\pi$
$13$	− 3059.97i	− 1.39279i	0.717657	−	0.696396i	$-0.245214\pi$
$14$	0	0
$15$	2975.44	0.881612
$16$	−3604.46	−0.879995
$17$	2850.24i	0.580143i	0.957005	+	0.290072i	$0.0936791\pi$
$17$	2850.24i	0.580143i	−0.957005	+	0.290072i	$0.906321\pi$
$18$	2822.67	0.483997
$19$	3949.13i	0.575759i	0.957667	+	0.287879i	$0.0929502\pi$
$19$	3949.13i	0.575759i	−0.957667	+	0.287879i	$0.907050\pi$
$20$	13538.7i	1.69234i
$21$	0	0
$22$	23872.0	2.24192
$23$	660.543	0.0542897	0.0271449	−	0.999632i	$-0.491358\pi$
$23$	660.543	0.0542897	0.0271449	+	0.999632i	$0.491358\pi$
$24$	1254.83i	0.0907720i
$25$	−20808.1	−1.33172
$26$	35544.4i	2.02232i
$27$	3788.00i	0.192450i
$28$	0	0
$29$	−9282.66	−0.380609	−0.190304	−	0.981725i	$-0.560947\pi$
$29$	−9282.66	−0.380609	−0.190304	+	0.981725i	$0.560947\pi$
$30$	−34562.5	−1.28009
$31$	2801.72i	0.0940457i	0.998894	+	0.0470229i	$0.0149734\pi$
$31$	2801.72i	0.0940457i	−0.998894	+	0.0470229i	$0.985027\pi$
$32$	47021.0	1.43497
$33$	32035.9i	0.891446i
$34$	− 33108.2i	− 0.842363i
$35$	0	0
$36$	−17236.0	−0.369427
$37$	−36932.5	−0.729127	−0.364563	−	0.931179i	$-0.618782\pi$
$37$	−36932.5	−0.729127	−0.364563	+	0.931179i	$0.618782\pi$
$38$	− 45872.8i	− 0.835997i
$39$	−47700.1	−0.804129
$40$	− 15364.9i	− 0.240077i
$41$	67941.3i	0.985785i	0.870090	+	0.492892i	$0.164060\pi$
$41$	67941.3i	0.985785i	−0.870090	+	0.492892i	$0.835940\pi$
$42$	0	0
$43$	12336.3	0.155160	0.0775799	−	0.996986i	$-0.475281\pi$
$43$	12336.3	0.155160	0.0775799	+	0.996986i	$0.475281\pi$
$44$	−145768.	−1.71122
$45$	− 46382.5i	− 0.508999i
$46$	−7672.83	−0.0788283
$47$	− 147613.i	− 1.42177i	−0.703308	−	0.710886i	$-0.748294\pi$
$47$	− 147613.i	− 1.42177i	0.703308	−	0.710886i	$-0.251706\pi$
$48$	56188.0i	0.508066i
$49$	0	0
$50$	241705.	1.93364
$51$	44430.9	0.334946
$52$	− 217043.i	− 1.54360i
$53$	219635.	1.47528	0.737641	−	0.675194i	$-0.235940\pi$
$53$	219635.	1.47528	0.737641	+	0.675194i	$0.235940\pi$
$54$	− 44001.1i	− 0.279436i
$55$	− 392267.i	− 2.35773i
$56$	0	0
$57$	61560.8	0.332414
$58$	107827.	0.552641
$59$	192518.i	0.937377i	0.883363	+	0.468689i	$0.155273\pi$
$59$	192518.i	0.937377i	−0.883363	+	0.468689i	$0.844727\pi$
$60$	211048.	0.977073
$61$	− 332836.i	− 1.46636i	−0.680035	−	0.733180i	$-0.738035\pi$
$61$	− 332836.i	− 1.46636i	0.680035	−	0.733180i	$-0.261965\pi$
$62$	− 32544.5i	− 0.136554i
$63$	0	0
$64$	−315508.	−1.20357
$65$	584069.	2.12679
$66$	− 372127.i	− 1.29437i
$67$	349184.	1.16099	0.580496	−	0.814263i	$-0.302859\pi$
$67$	349184.	1.16099	0.580496	+	0.814263i	$0.302859\pi$
$68$	202168.i	0.642961i
$69$	− 10296.9i	− 0.0313442i
$70$	0	0
$71$	305650.	0.853984	0.426992	−	0.904255i	$-0.359573\pi$
$71$	305650.	0.853984	0.426992	+	0.904255i	$0.359573\pi$
$72$	19560.9	0.0524073
$73$	− 236498.i	− 0.607939i	−0.952682	−	0.303969i	$-0.901688\pi$
$73$	− 236498.i	− 0.607939i	0.952682	−	0.303969i	$-0.0983120\pi$
$74$	429005.	1.05869
$75$	324366.i	0.768867i
$76$	280111.i	0.638102i
$77$	0	0
$78$	554082.	1.16759
$79$	−586437.	−1.18943	−0.594716	−	0.803936i	$-0.702736\pi$
$79$	−586437.	−1.18943	−0.594716	+	0.803936i	$0.702736\pi$
$80$	− 688000.i	− 1.34375i
$81$	59049.0	0.111111
$82$	− 789201.i	− 1.43135i
$83$	− 106377.i	− 0.186044i	−0.995664	−	0.0930218i	$-0.970347\pi$
$83$	− 106377.i	− 0.186044i	0.995664	−	0.0930218i	$-0.0296526\pi$
$84$	0	0
$85$	−544039.	−0.885876
$86$	−143298.	−0.225291
$87$	144702.i	0.219744i
$88$	165431.	0.242755
$89$	− 13057.9i	− 0.0185227i	−0.999957	−	0.00926134i	$-0.997052\pi$
$89$	− 13057.9i	− 0.0185227i	0.999957	−	0.00926134i	$-0.00294802\pi$
$90$	538776.i	0.739062i
$91$	0	0
$92$	46852.3	0.0601682
$93$	43674.4	0.0542973
$94$	1.71466e6i	2.06440i
$95$	−753788.	−0.879181
$96$	− 732985.i	− 0.828479i
$97$	− 205209.i	− 0.224844i	−0.993661	−	0.112422i	$-0.964139\pi$
$97$	− 205209.i	− 0.224844i	0.993661	−	0.112422i	$-0.0358609\pi$
$98$	0	0
$99$	499390.	0.514677
$100$	−1.47592e6	−1.47592
$101$	− 1.40110e6i	− 1.35989i	−0.733262	−	0.679946i	$-0.762003\pi$
$101$	− 1.40110e6i	− 1.35989i	0.733262	−	0.679946i	$-0.237997\pi$
$102$	−516106.	−0.486339
$103$	− 517642.i	− 0.473716i	−0.971544	−	0.236858i	$-0.923882\pi$
$103$	− 517642.i	− 0.473716i	0.971544	−	0.236858i	$-0.0761176\pi$
$104$	246320.i	0.218977i
$105$	0	0
$106$	−2.55127e6	−2.14210
$107$	646744.	0.527936	0.263968	−	0.964531i	$-0.414969\pi$
$107$	646744.	0.527936	0.263968	+	0.964531i	$0.414969\pi$
$108$	268682.i	0.213289i
$109$	−687262.	−0.530692	−0.265346	−	0.964153i	$-0.585486\pi$
$109$	−687262.	−0.530692	−0.265346	+	0.964153i	$0.585486\pi$
$110$	4.55655e6i	3.42340i
$111$	575720.i	0.420962i
$112$	0	0
$113$	2.11668e6	1.46697	0.733483	−	0.679708i	$-0.237893\pi$
$113$	2.11668e6	1.46697	0.733483	+	0.679708i	$0.237893\pi$
$114$	−715086.	−0.482663
$115$	126081.i	0.0829002i
$116$	−658419.	−0.421821
$117$	743572.i	0.464264i
$118$	− 2.23627e6i	− 1.36106i
$119$	0	0
$120$	−239516.	−0.138609
$121$	2.45189e6	1.38403
$122$	3.86620e6i	2.12914i
$123$	1.05910e6	0.569143
$124$	198725.i	0.104229i
$125$	− 989318.i	− 0.506531i
$126$	0	0
$127$	3.29012e6	1.60620	0.803102	−	0.595841i	$-0.203181\pi$
$127$	3.29012e6	1.60620	0.803102	+	0.595841i	$0.203181\pi$
$128$	655570.	0.312600
$129$	− 192304.i	− 0.0895816i
$130$	−6.78451e6	−3.08808
$131$	− 223347.i	− 0.0993497i	−0.998765	−	0.0496748i	$-0.984181\pi$
$131$	− 223347.i	− 0.0993497i	0.998765	−	0.0496748i	$-0.0158185\pi$
$132$	2.27230e6i	0.987972i
$133$	0	0
$134$	−4.05609e6	−1.68575
$135$	−723032.	−0.293871
$136$	− 229438.i	− 0.0912111i
$137$	−3.17050e6	−1.23301	−0.616504	−	0.787352i	$-0.711452\pi$
$137$	−3.17050e6	−1.23301	−0.616504	+	0.787352i	$0.711452\pi$
$138$	119608.i	0.0455115i
$139$	− 774740.i	− 0.288477i	−0.989543	−	0.144239i	$-0.953927\pi$
$139$	− 774740.i	− 0.288477i	0.989543	−	0.144239i	$-0.0460733\pi$
$140$	0	0
$141$	−2.30105e6	−0.820860
$142$	−3.55042e6	−1.23998
$143$	6.28855e6i	2.15051i
$144$	875884.	0.293332
$145$	− 1.77182e6i	− 0.581188i
$146$	2.74715e6i	0.882722i
$147$	0	0
$148$	−2.61962e6	−0.808077
$149$	3.50921e6	1.06084	0.530421	−	0.847734i	$-0.322034\pi$
$149$	3.50921e6	1.06084	0.530421	+	0.847734i	$0.322034\pi$
$150$	− 3.76781e6i	− 1.11639i
$151$	6.45201e6	1.87398	0.936989	−	0.349360i	$-0.113601\pi$
$151$	6.45201e6	1.87398	0.936989	+	0.349360i	$0.113601\pi$
$152$	− 317895.i	− 0.0905218i
$153$	− 692609.i	− 0.193381i
$154$	0	0
$155$	−534776.	−0.143607
$156$	−3.38337e6	−0.891200
$157$	− 4.68297e6i	− 1.21010i	−0.796187	−	0.605051i	$-0.793153\pi$
$157$	− 4.68297e6i	− 1.21010i	0.796187	−	0.605051i	$-0.206847\pi$
$158$	6.81201e6	1.72705
$159$	− 3.42378e6i	− 0.851754i
$160$	8.97512e6i	2.19119i
$161$	0	0
$162$	−685909.	−0.161332
$163$	5.18233e6	1.19664	0.598318	−	0.801259i	$-0.295836\pi$
$163$	5.18233e6	1.19664	0.598318	+	0.801259i	$0.295836\pi$
$164$	4.81907e6i	1.09253i
$165$	−6.11484e6	−1.36123
$166$	1.23567e6i	0.270134i
$167$	− 1.56630e6i	− 0.336298i	−0.985762	−	0.168149i	$-0.946221\pi$
$167$	− 1.56630e6i	− 0.336298i	0.985762	−	0.168149i	$-0.0537790\pi$
$168$	0	0
$169$	−4.53658e6	−0.939871
$170$	6.31952e6	1.28629
$171$	− 959638.i	− 0.191920i
$172$	875012.	0.171961
$173$	1.24462e6i	0.240381i	0.992751	+	0.120190i	$0.0383505\pi$
$173$	1.24462e6i	0.240381i	−0.992751	+	0.120190i	$0.961649\pi$
$174$	− 1.68085e6i	− 0.319067i
$175$	0	0
$176$	7.40754e6	1.35874
$177$	3.00105e6	0.541195
$178$	151680.i	0.0268948i
$179$	2.25600e6	0.393350	0.196675	−	0.980469i	$-0.436986\pi$
$179$	2.25600e6	0.393350	0.196675	+	0.980469i	$0.436986\pi$
$180$	− 3.28991e6i	− 0.564113i
$181$	− 7.97198e6i	− 1.34441i	−0.740367	−	0.672203i	$-0.765348\pi$
$181$	− 7.97198e6i	− 1.34441i	0.740367	−	0.672203i	$-0.234652\pi$
$182$	0	0
$183$	−5.18839e6	−0.846603
$184$	−53172.1	−0.00853553
$185$	− 7.04947e6i	− 1.11337i
$186$	−507319.	−0.0788393
$187$	− 5.85755e6i	− 0.895759i
$188$	− 1.04701e7i	− 1.57572i
$189$	0	0
$190$	8.75595e6	1.27656
$191$	4.26174e6	0.611627	0.305814	−	0.952091i	$-0.401072\pi$
$191$	4.26174e6	0.611627	0.305814	+	0.952091i	$0.401072\pi$
$192$	4.91828e6i	0.694879i
$193$	−145773.	−0.0202771	−0.0101386	−	0.999949i	$-0.503227\pi$
$193$	−145773.	−0.0202771	−0.0101386	+	0.999949i	$0.503227\pi$
$194$	2.38370e6i	0.326472i
$195$	− 9.10474e6i	− 1.22790i
$196$	0	0
$197$	−7.21313e6	−0.943463	−0.471732	−	0.881742i	$-0.656371\pi$
$197$	−7.21313e6	−0.943463	−0.471732	+	0.881742i	$0.656371\pi$
$198$	−5.80089e6	−0.747306
$199$	1.76480e6i	0.223942i	0.993711	+	0.111971i	$0.0357164\pi$
$199$	1.76480e6i	0.223942i	−0.993711	+	0.111971i	$0.964284\pi$
$200$	1.67500e6	0.209375
$201$	− 5.44323e6i	− 0.670299i
$202$	1.62751e7i	1.97455i
$203$	0	0
$204$	3.15148e6	0.371214
$205$	−1.29683e7	−1.50529
$206$	6.01290e6i	0.687832i
$207$	−160512.	−0.0180966
$208$	1.10295e7i	1.22565i
$209$	− 8.11587e6i	− 0.888989i
$210$	0	0
$211$	1.37033e7	1.45874	0.729369	−	0.684121i	$-0.239814\pi$
$211$	1.37033e7	1.45874	0.729369	+	0.684121i	$0.239814\pi$
$212$	1.55787e7	1.63502
$213$	− 4.76462e6i	− 0.493048i
$214$	−7.51254e6	−0.766558
$215$	2.35468e6i	0.236928i
$216$	− 304924.i	− 0.0302573i
$217$	0	0
$218$	7.98318e6	0.770560
$219$	−3.68665e6	−0.350993
$220$	− 2.78235e7i	− 2.61302i
$221$	8.72165e6	0.808019
$222$	− 6.68753e6i	− 0.611233i
$223$	2.15029e7i	1.93902i	0.245055	+	0.969509i	$0.421194\pi$
$223$	2.15029e7i	1.93902i	−0.245055	+	0.969509i	$0.578806\pi$
$224$	0	0
$225$	5.05636e6	0.443906
$226$	−2.45872e7	−2.13002
$227$	3.93130e6i	0.336093i	0.985779	+	0.168046i	$0.0537458\pi$
$227$	3.93130e6i	0.336093i	−0.985779	+	0.168046i	$0.946254\pi$
$228$	4.36650e6	0.368408
$229$	− 562326.i	− 0.0468254i	−0.999726	−	0.0234127i	$-0.992547\pi$
$229$	− 562326.i	− 0.0468254i	0.999726	−	0.0234127i	$-0.00745317\pi$
$230$	− 1.46455e6i	− 0.120370i
$231$	0	0
$232$	747232.	0.0598400
$233$	−1.63331e7	−1.29122	−0.645612	−	0.763666i	$-0.723398\pi$
$233$	−1.63331e7	−1.29122	−0.645612	+	0.763666i	$0.723398\pi$
$234$	− 8.63728e6i	− 0.674108i
$235$	2.81755e7	2.17104
$236$	1.36553e7i	1.03888i
$237$	9.14164e6i	0.686719i
$238$	0	0
$239$	−1.96132e7	−1.43666	−0.718331	−	0.695702i	$-0.755094\pi$
$239$	−1.96132e7	−1.43666	−0.718331	+	0.695702i	$0.755094\pi$
$240$	−1.07249e7	−0.775814
$241$	3.59901e6i	0.257118i	0.991702	+	0.128559i	$0.0410351\pi$
$241$	3.59901e6i	0.257118i	−0.991702	+	0.128559i	$0.958965\pi$
$242$	−2.84810e7	−2.00960
$243$	− 920483.i	− 0.0641500i
$244$	− 2.36080e7i	− 1.62514i
$245$	0	0
$246$	−1.23024e7	−0.826391
$247$	1.20842e7	0.801912
$248$	− 225531.i	− 0.0147860i
$249$	−1.65826e6	−0.107412
$250$	1.14918e7i	0.735478i
$251$	6.49855e6i	0.410956i	0.978662	+	0.205478i	$0.0658749\pi$
$251$	6.49855e6i	0.410956i	−0.978662	+	0.205478i	$0.934125\pi$
$252$	0	0
$253$	−1.35749e6	−0.0838250
$254$	−3.82178e7	−2.33220
$255$	8.48073e6i	0.511461i
$256$	1.25774e7	0.749673
$257$	− 2.85795e6i	− 0.168366i	−0.996450	−	0.0841832i	$-0.973172\pi$
$257$	− 2.85795e6i	− 0.168366i	0.996450	−	0.0841832i	$-0.0268281\pi$
$258$	2.23379e6i	0.130072i
$259$	0	0
$260$	4.14280e7	2.35708
$261$	2.25569e6	0.126870
$262$	2.59439e6i	0.144255i
$263$	−4.99827e6	−0.274759	−0.137380	−	0.990518i	$-0.543868\pi$
$263$	−4.99827e6	−0.274759	−0.137380	+	0.990518i	$0.543868\pi$
$264$	− 2.57881e6i	− 0.140155i
$265$	4.19228e7i	2.25275i
$266$	0	0
$267$	−203553.	−0.0106941
$268$	2.47676e7	1.28670
$269$	− 2.04199e7i	− 1.04905i	−0.851394	−	0.524527i	$-0.824242\pi$
$269$	− 2.04199e7i	− 1.04905i	0.851394	−	0.524527i	$-0.175758\pi$
$270$	8.39869e6	0.426698
$271$	− 1.23420e7i	− 0.620124i	−0.950716	−	0.310062i	$-0.899650\pi$
$271$	− 1.23420e7i	− 0.620124i	0.950716	−	0.310062i	$-0.100350\pi$
$272$	− 1.02736e7i	− 0.510523i
$273$	0	0
$274$	3.68283e7	1.79032
$275$	4.27628e7	2.05621
$276$	− 730355.i	− 0.0347381i
$277$	−2.08302e7	−0.980062	−0.490031	−	0.871705i	$-0.663015\pi$
$277$	−2.08302e7	−0.980062	−0.490031	+	0.871705i	$0.663015\pi$
$278$	8.99933e6i	0.418867i
$279$	− 680817.i	− 0.0313486i
$280$	0	0
$281$	2.10143e7	0.947100	0.473550	−	0.880767i	$-0.342972\pi$
$281$	2.10143e7	0.947100	0.473550	+	0.880767i	$0.342972\pi$
$282$	2.67289e7	1.19188
$283$	1.04239e7i	0.459908i	0.973201	+	0.229954i	$0.0738576\pi$
$283$	1.04239e7i	0.459908i	−0.973201	+	0.229954i	$0.926142\pi$
$284$	2.16798e7	0.946454
$285$	1.17504e7i	0.507595i
$286$	− 7.30474e7i	− 3.12253i
$287$	0	0
$288$	−1.14261e7	−0.478323
$289$	1.60137e7	0.663434
$290$	2.05814e7i	0.843880i
$291$	−3.19890e6	−0.129814
$292$	− 1.67748e7i	− 0.673766i
$293$	− 2.85328e7i	− 1.13433i	−0.823603	−	0.567167i	$-0.808039\pi$
$293$	− 2.85328e7i	− 1.13433i	0.823603	−	0.567167i	$-0.191961\pi$
$294$	0	0
$295$	−3.67467e7	−1.43137
$296$	2.97297e6	0.114635
$297$	− 7.78472e6i	− 0.297149i
$298$	−4.07628e7	−1.54033
$299$	− 2.02124e6i	− 0.0756143i
$300$	2.30072e7i	0.852120i
$301$	0	0
$302$	−7.49461e7	−2.72100
$303$	−2.18410e7	−0.785134
$304$	− 1.42345e7i	− 0.506665i
$305$	6.35299e7	2.23912
$306$	8.04530e6i	0.280788i
$307$	− 1.02269e7i	− 0.353450i	−0.984260	−	0.176725i	$-0.943450\pi$
$307$	− 1.02269e7i	− 0.353450i	0.984260	−	0.176725i	$-0.0565503\pi$
$308$	0	0
$309$	−8.06925e6	−0.273500
$310$	6.21192e6	0.208517
$311$	− 1.57422e7i	− 0.523339i	−0.965158	−	0.261669i	$-0.915727\pi$
$311$	− 1.57422e7i	− 0.523339i	0.965158	−	0.261669i	$-0.0842730\pi$
$312$	3.83974e6	0.126427
$313$	− 5.55274e7i	− 1.81082i	−0.424543	−	0.905408i	$-0.639565\pi$
$313$	− 5.55274e7i	− 1.81082i	0.424543	−	0.905408i	$-0.360435\pi$
$314$	5.43970e7i	1.75706i
$315$	0	0
$316$	−4.15959e7	−1.31822
$317$	−6.03079e6	−0.189320	−0.0946600	−	0.995510i	$-0.530176\pi$
$317$	−6.03079e6	−0.189320	−0.0946600	+	0.995510i	$0.530176\pi$
$318$	3.97704e7i	1.23674i
$319$	1.90768e7	0.587671
$320$	− 6.02224e7i	− 1.83784i
$321$	− 1.00817e7i	− 0.304804i
$322$	0	0
$323$	−1.12560e7	−0.334022
$324$	4.18834e6	0.123142
$325$	6.36720e7i	1.85481i
$326$	−6.01976e7	−1.73750
$327$	1.07133e7i	0.306395i
$328$	− 5.46910e6i	− 0.154987i
$329$	0	0
$330$	7.10295e7	1.97650
$331$	9.76554e6	0.269285	0.134643	−	0.990894i	$-0.457011\pi$
$331$	9.76554e6	0.269285	0.134643	+	0.990894i	$0.457011\pi$
$332$	− 7.54533e6i	− 0.206188i
$333$	8.97459e6	0.243042
$334$	1.81940e7i	0.488302i
$335$	6.66502e7i	1.77283i
$336$	0	0
$337$	−5.70025e7	−1.48938	−0.744688	−	0.667412i	$-0.767402\pi$
$337$	−5.70025e7	−1.48938	−0.744688	+	0.667412i	$0.767402\pi$
$338$	5.26966e7	1.36469
$339$	− 3.29958e7i	− 0.846953i
$340$	−3.85886e7	−0.981799
$341$	− 5.75782e6i	− 0.145209i
$342$	1.11471e7i	0.278666i
$343$	0	0
$344$	−993041.	−0.0243945
$345$	1.96541e6	0.0478625
$346$	− 1.44575e7i	− 0.349031i
$347$	−3.67355e7	−0.879219	−0.439610	−	0.898189i	$-0.644883\pi$
$347$	−3.67355e7	−0.879219	−0.439610	+	0.898189i	$0.644883\pi$
$348$	1.02637e7i	0.243538i
$349$	− 6.58421e7i	− 1.54891i	−0.632626	−	0.774457i	$-0.718023\pi$
$349$	− 6.58421e7i	− 1.54891i	0.632626	−	0.774457i	$-0.281977\pi$
$350$	0	0
$351$	1.15911e7	0.268043
$352$	−9.66331e7	−2.21563
$353$	3.18706e7i	0.724546i	0.932072	+	0.362273i	$0.117999\pi$
$353$	3.18706e7i	0.724546i	−0.932072	+	0.362273i	$0.882001\pi$
$354$	−3.48600e7	−0.785811
$355$	5.83409e7i	1.30403i
$356$	− 926197.i	− 0.0205283i
$357$	0	0
$358$	−2.62055e7	−0.571141
$359$	−3.82257e7	−0.826174	−0.413087	−	0.910691i	$-0.635550\pi$
$359$	−3.82257e7	−0.826174	−0.413087	+	0.910691i	$0.635550\pi$
$360$	3.73368e6i	0.0800257i
$361$	3.14503e7	0.668502
$362$	9.26020e7i	1.95207i
$363$	− 3.82212e7i	− 0.799070i
$364$	0	0
$365$	4.51415e7	0.928320
$366$	6.02681e7	1.22926
$367$	9.73841e7i	1.97011i	0.172249	+	0.985053i	$0.444896\pi$
$367$	9.73841e7i	1.97011i	−0.172249	+	0.985053i	$0.555104\pi$
$368$	−2.38090e6	−0.0477747
$369$	− 1.65097e7i	− 0.328595i
$370$	8.18861e7i	1.61661i
$371$	0	0
$372$	3.09782e6	0.0601766
$373$	2.10427e7	0.405484	0.202742	−	0.979232i	$-0.435015\pi$
$373$	2.10427e7	0.405484	0.202742	+	0.979232i	$0.435015\pi$
$374$	6.80409e7i	1.30063i
$375$	−1.54219e7	−0.292446
$376$	1.18824e7i	0.223533i
$377$	2.84046e7i	0.530109i
$378$	0	0
$379$	−4.11794e7	−0.756418	−0.378209	−	0.925720i	$-0.623460\pi$
$379$	−4.11794e7	−0.756418	−0.378209	+	0.925720i	$0.623460\pi$
$380$	−5.34661e7	−0.974379
$381$	− 5.12879e7i	− 0.927343i
$382$	−4.95041e7	−0.888078
$383$	1.52188e7i	0.270884i	0.990785	+	0.135442i	$0.0432454\pi$
$383$	1.52188e7i	0.270884i	−0.990785	+	0.135442i	$0.956755\pi$
$384$	− 1.02193e7i	− 0.180480i
$385$	0	0
$386$	1.69329e6	0.0294422
$387$	−2.99772e6	−0.0517199
$388$	− 1.45555e7i	− 0.249191i
$389$	−6.74995e7	−1.14671	−0.573353	−	0.819309i	$-0.694357\pi$
$389$	−6.74995e7	−1.14671	−0.573353	+	0.819309i	$0.694357\pi$
$390$	1.05760e8i	1.78290i
$391$	1.88271e6i	0.0314958i
$392$	0	0
$393$	−3.48164e6	−0.0573596
$394$	8.37872e7	1.36990
$395$	− 1.11936e8i	− 1.81626i
$396$	3.54217e7	0.570406
$397$	− 9.40155e6i	− 0.150255i	−0.997174	−	0.0751273i	$-0.976064\pi$
$397$	− 9.40155e6i	− 0.150255i	0.997174	−	0.0751273i	$-0.0239363\pi$
$398$	− 2.04998e7i	− 0.325162i
$399$	0	0
$400$	7.50019e7	1.17190
$401$	−5.54972e7	−0.860673	−0.430336	−	0.902669i	$-0.641605\pi$
$401$	−5.54972e7	−0.860673	−0.430336	+	0.902669i	$0.641605\pi$
$402$	6.32282e7i	0.973269i
$403$	8.57315e6	0.130986
$404$	− 9.93798e7i	− 1.50714i
$405$	1.12709e7i	0.169666i
$406$	0	0
$407$	7.59001e7	1.12579
$408$	−3.57658e6	−0.0526608
$409$	1.63471e7i	0.238931i	0.992838	+	0.119465i	$0.0381180\pi$
$409$	1.63471e7i	0.238931i	−0.992838	+	0.119465i	$0.961882\pi$
$410$	1.50638e8	2.18567
$411$	4.94232e7i	0.711877i
$412$	− 3.67163e7i	− 0.525010i
$413$	0	0
$414$	1.86450e6	0.0262761
$415$	2.03047e7	0.284088
$416$	− 1.43883e8i	− 1.99861i
$417$	−1.20770e7	−0.166552
$418$	9.42734e7i	1.29080i
$419$	− 3.75022e7i	− 0.509818i	−0.966965	−	0.254909i	$-0.917955\pi$
$419$	− 3.75022e7i	− 0.509818i	0.966965	−	0.254909i	$-0.0820455\pi$
$420$	0	0
$421$	9.17501e7	1.22959	0.614795	−	0.788687i	$-0.289239\pi$
$421$	9.17501e7	1.22959	0.614795	+	0.788687i	$0.289239\pi$
$422$	−1.59176e8	−2.11807
$423$	3.58699e7i	0.473924i
$424$	−1.76801e7	−0.231946
$425$	− 5.93081e7i	− 0.772587i
$426$	5.53455e7i	0.715902i
$427$	0	0
$428$	4.58735e7	0.585101
$429$	9.80288e7	1.24160
$430$	− 2.73518e7i	− 0.344018i
$431$	−1.37807e8	−1.72123	−0.860616	−	0.509255i	$-0.829921\pi$
$431$	−1.37807e8	−1.72123	−0.860616	+	0.509255i	$0.829921\pi$
$432$	− 1.36537e7i	− 0.169355i
$433$	2.00324e7i	0.246757i	0.992360	+	0.123378i	$0.0393729\pi$
$433$	2.00324e7i	0.246757i	−0.992360	+	0.123378i	$0.960627\pi$
$434$	0	0
$435$	−2.76200e7	−0.335549
$436$	−4.87474e7	−0.588155
$437$	2.60857e6i	0.0312578i
$438$	4.28238e7	0.509640
$439$	− 8.61025e7i	− 1.01771i	−0.860854	−	0.508853i	$-0.830070\pi$
$439$	− 8.61025e7i	− 1.01771i	0.860854	−	0.508853i	$-0.169930\pi$
$440$	3.15765e7i	0.370686i
$441$	0	0
$442$	−1.01310e8	−1.17324
$443$	−8.07874e6	−0.0929250	−0.0464625	−	0.998920i	$-0.514795\pi$
$443$	−8.07874e6	−0.0929250	−0.0464625	+	0.998920i	$0.514795\pi$
$444$	4.08358e7i	0.466543i
$445$	2.49242e6	0.0282840
$446$	− 2.49776e8i	− 2.81544i
$447$	− 5.47032e7i	− 0.612477i
$448$	0	0
$449$	−5.16486e7	−0.570584	−0.285292	−	0.958441i	$-0.592091\pi$
$449$	−5.16486e7	−0.570584	−0.285292	+	0.958441i	$0.592091\pi$
$450$	−5.87344e7	−0.644547
$451$	− 1.39626e8i	− 1.52208i
$452$	1.50136e8	1.62581
$453$	− 1.00577e8i	− 1.08194i
$454$	− 4.56657e7i	− 0.488004i
$455$	0	0
$456$	−4.95549e6	−0.0522628
$457$	−3.99394e7	−0.418459	−0.209229	−	0.977867i	$-0.567096\pi$
$457$	−3.99394e7	−0.418459	−0.209229	+	0.977867i	$0.567096\pi$
$458$	6.53194e6i	0.0679901i
$459$	−1.07967e7	−0.111649
$460$	8.94291e6i	0.0918767i
$461$	− 1.40914e7i	− 0.143831i	−0.997411	−	0.0719153i	$-0.977089\pi$
$461$	− 1.40914e7i	− 0.143831i	0.997411	−	0.0719153i	$-0.0229111\pi$
$462$	0	0
$463$	1.25200e8	1.26142	0.630712	−	0.776017i	$-0.282763\pi$
$463$	1.25200e8	1.26142	0.630712	+	0.776017i	$0.282763\pi$
$464$	3.34590e7	0.334934
$465$	8.33633e6i	0.0829118i
$466$	1.89725e8	1.87485
$467$	1.03527e8i	1.01649i	0.861214	+	0.508243i	$0.169705\pi$
$467$	1.03527e8i	1.01649i	−0.861214	+	0.508243i	$0.830295\pi$
$468$	5.27415e7i	0.514535i
$469$	0	0
$470$	−3.27284e8	−3.15233
$471$	−7.30002e7	−0.698653
$472$	− 1.54972e7i	− 0.147376i
$473$	−2.53524e7	−0.239571
$474$	− 1.06189e8i	− 0.997111i
$475$	− 8.21738e7i	− 0.766747i
$476$	0	0
$477$	−5.33714e7	−0.491760
$478$	2.27826e8	2.08602
$479$	− 7.79771e7i	− 0.709513i	−0.934959	−	0.354757i	$-0.884564\pi$
$479$	− 7.79771e7i	− 0.709513i	0.934959	−	0.354757i	$-0.115436\pi$
$480$	1.39908e8	1.26508
$481$	1.13012e8i	1.01552i
$482$	− 4.18058e7i	− 0.373333i
$483$	0	0
$484$	1.73913e8	1.53389
$485$	3.91692e7	0.343336
$486$	1.06923e7i	0.0931453i
$487$	1.42798e8	1.23634	0.618168	−	0.786046i	$-0.287875\pi$
$487$	1.42798e8	1.23634	0.618168	+	0.786046i	$0.287875\pi$
$488$	2.67925e7i	0.230544i
$489$	− 8.07845e7i	− 0.690878i
$490$	0	0
$491$	5.07818e7	0.429006	0.214503	−	0.976723i	$-0.431187\pi$
$491$	5.07818e7	0.429006	0.214503	+	0.976723i	$0.431187\pi$
$492$	7.51218e7	0.630770
$493$	− 2.64578e7i	− 0.220807i
$494$	−1.40369e8	−1.16437
$495$	9.53209e7i	0.785909i
$496$	− 1.00987e7i	− 0.0827598i
$497$	0	0
$498$	1.92622e7	0.155962
$499$	1.26504e8	1.01813	0.509065	−	0.860728i	$-0.329991\pi$
$499$	1.26504e8	1.01813	0.509065	+	0.860728i	$0.329991\pi$
$500$	− 7.01722e7i	− 0.561378i
$501$	−2.44161e7	−0.194162
$502$	− 7.54868e7i	− 0.596705i
$503$	− 7.36652e6i	− 0.0578840i	−0.999581	−	0.0289420i	$-0.990786\pi$
$503$	− 7.36652e6i	− 0.0578840i	0.999581	−	0.0289420i	$-0.00921381\pi$
$504$	0	0
$505$	2.67434e8	2.07655
$506$	1.57685e7	0.121713
$507$	7.07183e7i	0.542635i
$508$	2.33368e8	1.78012
$509$	2.29433e8i	1.73981i	0.493217	+	0.869906i	$0.335821\pi$
$509$	2.29433e8i	1.73981i	−0.493217	+	0.869906i	$0.664179\pi$
$510$	− 9.85116e7i	− 0.742637i
$511$	0	0
$512$	−1.88055e8	−1.40112
$513$	−1.49593e7	−0.110805
$514$	3.31978e7i	0.244466i
$515$	9.88047e7	0.723363
$516$	− 1.36401e7i	− 0.0992814i
$517$	3.03359e8i	2.19526i
$518$	0	0
$519$	1.94018e7	0.138784
$520$	−4.70161e7	−0.334377
$521$	− 1.07368e8i	− 0.759210i	−0.925149	−	0.379605i	$-0.876060\pi$
$521$	− 1.07368e8i	− 0.759210i	0.925149	−	0.379605i	$-0.123940\pi$
$522$	−2.62019e7	−0.184214
$523$	− 1.50523e8i	− 1.05220i	−0.850423	−	0.526099i	$-0.823654\pi$
$523$	− 1.50523e8i	− 1.05220i	0.850423	−	0.526099i	$-0.176346\pi$
$524$	− 1.58420e7i	− 0.110107i
$525$	0	0
$526$	5.80595e7	0.398948
$527$	−7.98557e6	−0.0545600
$528$	− 1.15472e8i	− 0.784469i
$529$	−1.47600e8	−0.997053
$530$	− 4.86973e8i	− 3.27097i
$531$	− 4.67818e7i	− 0.312459i
$532$	0	0
$533$	2.07898e8	1.37299
$534$	2.36445e6	0.0155277
$535$	1.23447e8i	0.806156i
$536$	−2.81084e7	−0.182533
$537$	− 3.51675e7i	− 0.227101i
$538$	2.37197e8i	1.52322i
$539$	0	0
$540$	−5.12846e7	−0.325691
$541$	−6.05747e7	−0.382560	−0.191280	−	0.981535i	$-0.561264\pi$
$541$	−6.05747e7	−0.382560	−0.191280	+	0.981535i	$0.561264\pi$
$542$	1.43364e8i	0.900416i
$543$	−1.24271e8	−0.776193
$544$	1.34021e8i	0.832487i
$545$	− 1.31181e8i	− 0.810365i
$546$	0	0
$547$	−2.68955e8	−1.64330	−0.821651	−	0.569992i	$-0.806946\pi$
$547$	−2.68955e8	−1.64330	−0.821651	+	0.569992i	$0.806946\pi$
$548$	−2.24883e8	−1.36652
$549$	8.08791e7i	0.488786i
$550$	−4.96730e8	−2.98560
$551$	− 3.66584e7i	− 0.219139i
$552$	828871.i	0.00492799i
$553$	0	0
$554$	2.41962e8	1.42304
$555$	−1.09890e8	−0.642807
$556$	− 5.49522e7i	− 0.319714i
$557$	2.01772e8	1.16760	0.583800	−	0.811897i	$-0.301565\pi$
$557$	2.01772e8	1.16760	0.583800	+	0.811897i	$0.301565\pi$
$558$	7.90832e6i	0.0455179i
$559$	− 3.77486e7i	− 0.216105i
$560$	0	0
$561$	−9.13101e7	−0.517166
$562$	−2.44101e8	−1.37518
$563$	1.76315e8i	0.988019i	0.869456	+	0.494010i	$0.164469\pi$
$563$	1.76315e8i	0.988019i	−0.869456	+	0.494010i	$0.835531\pi$
$564$	−1.63213e8	−0.909743
$565$	4.04020e8i	2.24005i
$566$	− 1.21083e8i	− 0.667783i
$567$	0	0
$568$	−2.46041e7	−0.134265
$569$	2.00736e8	1.08966	0.544828	−	0.838548i	$-0.316595\pi$
$569$	2.00736e8	1.08966	0.544828	+	0.838548i	$0.316595\pi$
$570$	− 1.36492e8i	− 0.737024i
$571$	−4.46408e7	−0.239786	−0.119893	−	0.992787i	$-0.538255\pi$
$571$	−4.46408e7	−0.239786	−0.119893	+	0.992787i	$0.538255\pi$
$572$	4.46046e8i	2.38337i
$573$	− 6.64340e7i	− 0.353123i
$574$	0	0
$575$	−1.37446e7	−0.0722986
$576$	7.66683e7	0.401189
$577$	− 2.58790e8i	− 1.34716i	−0.739114	−	0.673581i	$-0.764755\pi$
$577$	− 2.58790e8i	− 1.34716i	0.739114	−	0.673581i	$-0.235245\pi$
$578$	−1.86014e8	−0.963301
$579$	2.27238e6i	0.0117070i
$580$	− 1.25675e8i	− 0.644119i
$581$	0	0
$582$	3.71582e7	0.188489
$583$	−4.51374e8	−2.27788
$584$	1.90375e7i	0.0955812i
$585$	−1.41929e8	−0.708930
$586$	3.31435e8i	1.64704i
$587$	3.41902e8i	1.69039i	0.534457	+	0.845196i	$0.320516\pi$
$587$	3.41902e8i	1.69039i	−0.534457	+	0.845196i	$0.679484\pi$
$588$	0	0
$589$	−1.10643e7	−0.0541476
$590$	4.26847e8	2.07834
$591$	1.12442e8i	0.544709i
$592$	1.33122e8	0.641628
$593$	− 1.47561e8i	− 0.707630i	−0.935315	−	0.353815i	$-0.884884\pi$
$593$	− 1.47561e8i	− 0.707630i	0.935315	−	0.353815i	$-0.115116\pi$
$594$	9.04268e7i	0.431458i
$595$	0	0
$596$	2.48908e8	1.17571
$597$	2.75105e7	0.129293
$598$	2.34786e7i	0.109791i
$599$	−6.64923e7	−0.309379	−0.154690	−	0.987963i	$-0.549438\pi$
$599$	−6.64923e7	−0.309379	−0.154690	+	0.987963i	$0.549438\pi$
$600$	− 2.61107e7i	− 0.120883i
$601$	3.71302e7i	0.171042i	0.996336	+	0.0855212i	$0.0272555\pi$
$601$	3.71302e7i	0.171042i	−0.996336	+	0.0855212i	$0.972744\pi$
$602$	0	0
$603$	−8.48516e7	−0.386998
$604$	4.57641e8	2.07689
$605$	4.68004e8i	2.11341i
$606$	2.53703e8	1.14001
$607$	− 1.27170e8i	− 0.568616i	−0.958733	−	0.284308i	$-0.908236\pi$
$607$	− 1.27170e8i	− 0.568616i	0.958733	−	0.284308i	$-0.0917638\pi$
$608$	1.85692e8i	0.826195i
$609$	0	0
$610$	−7.37959e8	−3.25119
$611$	−4.51689e8	−1.98023
$612$	− 4.91267e7i	− 0.214320i
$613$	−1.42995e8	−0.620783	−0.310391	−	0.950609i	$-0.600460\pi$
$613$	−1.42995e8	−0.620783	−0.310391	+	0.950609i	$0.600460\pi$
$614$	1.18795e8i	0.513206i
$615$	2.02155e8i	0.869079i
$616$	0	0
$617$	−2.96115e8	−1.26068	−0.630339	−	0.776320i	$-0.717084\pi$
$617$	−2.96115e8	−1.26068	−0.630339	+	0.776320i	$0.717084\pi$
$618$	9.37318e7	0.397120
$619$	3.24866e8i	1.36972i	0.728673	+	0.684862i	$0.240137\pi$
$619$	3.24866e8i	1.36972i	−0.728673	+	0.684862i	$0.759863\pi$
$620$	−3.79316e7	−0.159157
$621$	2.50213e6i	0.0104481i
$622$	1.82860e8i	0.759884i
$623$	0	0
$624$	1.71933e8	0.707630
$625$	−1.36291e8	−0.558247
$626$	6.45002e8i	2.62929i
$627$	−1.26514e8	−0.513258
$628$	− 3.32162e8i	− 1.34113i
$629$	− 1.05267e8i	− 0.422998i
$630$	0	0
$631$	−1.40735e8	−0.560163	−0.280082	−	0.959976i	$-0.590362\pi$
$631$	−1.40735e8	−0.560163	−0.280082	+	0.959976i	$0.590362\pi$
$632$	4.72067e7	0.187005
$633$	− 2.13613e8i	− 0.842202i
$634$	7.00533e7	0.274891
$635$	6.28000e8i	2.45267i
$636$	− 2.42848e8i	− 0.943982i
$637$	0	0
$638$	−2.21595e8	−0.853294
$639$	−7.42731e7	−0.284661
$640$	1.25132e8i	0.477339i
$641$	−2.16677e8	−0.822696	−0.411348	−	0.911478i	$-0.634942\pi$
$641$	−2.16677e8	−0.822696	−0.411348	+	0.911478i	$0.634942\pi$
$642$	1.17109e8i	0.442573i
$643$	− 2.61645e8i	− 0.984192i	−0.870541	−	0.492096i	$-0.836231\pi$
$643$	− 2.61645e8i	− 0.984192i	0.870541	−	0.492096i	$-0.163769\pi$
$644$	0	0
$645$	3.67059e7	0.136791
$646$	1.30749e8	0.484998
$647$	− 1.07319e8i	− 0.396245i	−0.980177	−	0.198122i	$-0.936516\pi$
$647$	− 1.07319e8i	− 0.396245i	0.980177	−	0.198122i	$-0.0634843\pi$
$648$	−4.75330e6	−0.0174691
$649$	− 3.95644e8i	− 1.44734i
$650$	− 7.39610e8i	− 2.69316i
$651$	0	0
$652$	3.67582e8	1.32621
$653$	4.43953e8	1.59440	0.797200	−	0.603715i	$-0.206313\pi$
$653$	4.43953e8	1.59440	0.797200	+	0.603715i	$0.206313\pi$
$654$	− 1.24446e8i	− 0.444883i
$655$	4.26313e7	0.151707
$656$	− 2.44892e8i	− 0.867486i
$657$	5.74691e7i	0.202646i
$658$	0	0
$659$	−1.87037e7	−0.0653538	−0.0326769	−	0.999466i	$-0.510403\pi$
$659$	−1.87037e7	−0.0653538	−0.0326769	+	0.999466i	$0.510403\pi$
$660$	−4.33725e8	−1.50863
$661$	− 2.14286e7i	− 0.0741976i	−0.999312	−	0.0370988i	$-0.988188\pi$
$661$	− 2.14286e7i	− 0.0741976i	0.999312	−	0.0370988i	$-0.0118116\pi$
$662$	−1.13436e8	−0.391000
$663$	− 1.35957e8i	− 0.466510i
$664$	8.56311e6i	0.0292501i
$665$	0	0
$666$	−1.04248e8	−0.352895
$667$	−6.13160e6	−0.0206631
$668$	− 1.11097e8i	− 0.372712i
$669$	3.35197e8	1.11949
$670$	− 7.74205e8i	− 2.57414i
$671$	6.84012e8i	2.26410i
$672$	0	0
$673$	2.29593e8	0.753205	0.376603	−	0.926375i	$-0.377092\pi$
$673$	2.29593e8	0.753205	0.376603	+	0.926375i	$0.377092\pi$
$674$	6.62138e8	2.16256
$675$	− 7.88209e7i	− 0.256289i
$676$	−3.21779e8	−1.04164
$677$	− 2.26448e7i	− 0.0729798i	−0.999334	−	0.0364899i	$-0.988382\pi$
$677$	− 2.26448e7i	− 0.0729798i	0.999334	−	0.0364899i	$-0.0116177\pi$
$678$	3.83277e8i	1.22977i
$679$	0	0
$680$	4.37938e7	0.139279
$681$	6.12829e7	0.194043
$682$	6.68824e7i	0.210843i
$683$	2.24621e8	0.704998	0.352499	−	0.935812i	$-0.385332\pi$
$683$	2.24621e8	0.704998	0.352499	+	0.935812i	$0.385332\pi$
$684$	− 6.80671e7i	− 0.212701i
$685$	− 6.05167e8i	− 1.88280i
$686$	0	0
$687$	−8.76579e6	−0.0270346
$688$	−4.44657e7	−0.136540
$689$	− 6.72077e8i	− 2.05476i
$690$	−2.28300e7	−0.0694959
$691$	− 2.53201e8i	− 0.767417i	−0.923454	−	0.383709i	$-0.874647\pi$
$691$	− 2.53201e8i	− 0.767417i	0.923454	−	0.383709i	$-0.125353\pi$
$692$	8.82811e7i	0.266409i
$693$	0	0
$694$	4.26717e8	1.27662
$695$	1.47878e8	0.440504
$696$	− 1.16482e7i	− 0.0345486i
$697$	−1.93649e8	−0.571896
$698$	7.64817e8i	2.24901i
$699$	2.54608e8i	0.745489i
$700$	0	0
$701$	3.18180e8	0.923674	0.461837	−	0.886965i	$-0.347191\pi$
$701$	3.18180e8	0.923674	0.461837	+	0.886965i	$0.347191\pi$
$702$	−1.34642e8	−0.389196
$703$	− 1.45851e8i	− 0.419801i
$704$	6.48401e8	1.85834
$705$	− 4.39212e8i	− 1.25345i
$706$	− 3.70207e8i	− 1.05204i
$707$	0	0
$708$	2.12864e8	0.599796
$709$	2.70283e8	0.758369	0.379185	−	0.925321i	$-0.376205\pi$
$709$	2.70283e8	0.758369	0.379185	+	0.925321i	$0.376205\pi$
$710$	− 6.77684e8i	− 1.89344i
$711$	1.42504e8	0.396478
$712$	1.05113e6i	0.00291217i
$713$	1.85065e6i	0.00510572i
$714$	0	0
$715$	−1.20032e9	−3.28383
$716$	1.60018e8	0.435942
$717$	3.05739e8i	0.829457i
$718$	4.44027e8	1.19960
$719$	− 1.05505e8i	− 0.283849i	−0.989877	−	0.141924i	$-0.954671\pi$
$719$	− 1.05505e8i	− 0.283849i	0.989877	−	0.141924i	$-0.0453290\pi$
$720$	1.67184e8i	0.447916i
$721$	0	0
$722$	−3.65324e8	−0.970660
$723$	5.61030e7	0.148447
$724$	− 5.65452e8i	− 1.48998i
$725$	1.93154e8	0.506863
$726$	4.43975e8i	1.16024i
$727$	3.47133e8i	0.903425i	0.892164	+	0.451713i	$0.149187\pi$
$727$	3.47133e8i	0.903425i	−0.892164	+	0.451713i	$0.850813\pi$
$728$	0	0
$729$	−1.43489e7	−0.0370370
$730$	−5.24361e8	−1.34791
$731$	3.51614e7i	0.0900149i
$732$	−3.68012e8	−0.938273
$733$	4.67191e8i	1.18627i	0.805104	+	0.593134i	$0.202110\pi$
$733$	4.67191e8i	1.18627i	−0.805104	+	0.593134i	$0.797890\pi$
$734$	− 1.13121e9i	− 2.86058i
$735$	0	0
$736$	3.10594e7	0.0779040
$737$	−7.17609e8	−1.79261
$738$	1.91776e8i	0.477117i
$739$	3.97629e8	0.985245	0.492623	−	0.870243i	$-0.336038\pi$
$739$	3.97629e8	0.985245	0.492623	+	0.870243i	$0.336038\pi$
$740$	− 5.00018e8i	− 1.23393i
$741$	− 1.88374e8i	− 0.462984i
$742$	0	0
$743$	6.88913e8	1.67957	0.839784	−	0.542920i	$-0.182681\pi$
$743$	6.88913e8	1.67957	0.839784	+	0.542920i	$0.182681\pi$
$744$	−3.51568e6	−0.00853672
$745$	6.69819e8i	1.61990i
$746$	−2.44430e8	−0.588760
$747$	2.58497e7i	0.0620145i
$748$	− 4.15475e8i	− 0.992751i
$749$	0	0
$750$	1.79140e8	0.424629
$751$	3.66564e8	0.865425	0.432712	−	0.901532i	$-0.357557\pi$
$751$	3.66564e8	0.865425	0.432712	+	0.901532i	$0.357557\pi$
$752$	5.32064e8i	1.25115i
$753$	1.01302e8	0.237266
$754$	− 3.29946e8i	− 0.769714i
$755$	1.23152e9i	2.86156i
$756$	0	0
$757$	−2.07241e8	−0.477735	−0.238868	−	0.971052i	$-0.576776\pi$
$757$	−2.07241e8	−0.477735	−0.238868	+	0.971052i	$0.576776\pi$
$758$	4.78337e8	1.09831
$759$	2.11611e7i	0.0483964i
$760$	6.06781e7	0.138226
$761$	6.76679e8i	1.53542i	0.640795	+	0.767712i	$0.278605\pi$
$761$	6.76679e8i	1.53542i	−0.640795	+	0.767712i	$0.721395\pi$
$762$	5.95757e8i	1.34649i
$763$	0	0
$764$	3.02285e8	0.677854
$765$	1.32201e8	0.295292
$766$	− 1.76780e8i	− 0.393321i
$767$	5.89097e8	1.30557
$768$	− 1.96063e8i	− 0.432824i
$769$	− 5.58023e8i	− 1.22708i	−0.789663	−	0.613540i	$-0.789745\pi$
$769$	− 5.58023e8i	− 1.22708i	0.789663	−	0.613540i	$-0.210255\pi$
$770$	0	0
$771$	−4.45510e7	−0.0972063
$772$	−1.03397e7	−0.0224727
$773$	8.28716e7i	0.179419i	0.995968	+	0.0897093i	$0.0285938\pi$
$773$	8.28716e7i	0.179419i	−0.995968	+	0.0897093i	$0.971406\pi$
$774$	3.48213e7	0.0750969
$775$	− 5.82983e7i	− 0.125242i
$776$	1.65188e7i	0.0353504i
$777$	0	0
$778$	7.84070e8	1.66501
$779$	−2.68309e8	−0.567574
$780$	− 6.45799e8i	− 1.36086i
$781$	−6.28143e8	−1.31858
$782$	− 2.18694e7i	− 0.0457317i
$783$	− 3.51627e7i	− 0.0732482i
$784$	0	0
$785$	8.93859e8	1.84782
$786$	4.04425e7	0.0832856
$787$	− 5.30510e8i	− 1.08835i	−0.838971	−	0.544176i	$-0.816842\pi$
$787$	− 5.30510e8i	− 1.08835i	0.838971	−	0.544176i	$-0.183158\pi$
$788$	−5.11627e8	−1.04562
$789$	7.79152e7i	0.158632i
$790$	1.30024e9i	2.63719i
$791$	0	0
$792$	−4.01997e7	−0.0809184
$793$	−1.01847e9	−2.04233
$794$	1.09208e8i	0.218169i
$795$	6.53512e8	1.30063
$796$	1.25177e8i	0.248191i
$797$	− 4.96880e8i	− 0.981469i	−0.871309	−	0.490735i	$-0.836728\pi$
$797$	− 4.96880e8i	− 0.981469i	0.871309	−	0.490735i	$-0.163272\pi$
$798$	0	0
$799$	4.20732e8	0.824831
$800$	−9.78417e8	−1.91097
$801$	3.17307e6i	0.00617422i
$802$	6.44652e8	1.24969
$803$	4.86029e8i	0.938675i
$804$	− 3.86088e8i	− 0.742879i
$805$	0	0
$806$	−9.95852e7	−0.190191
$807$	−3.18315e8	−0.605672
$808$	1.12785e8i	0.213805i
$809$	−4.20304e8	−0.793812	−0.396906	−	0.917859i	$-0.629916\pi$
$809$	−4.20304e8	−0.793812	−0.396906	+	0.917859i	$0.629916\pi$
$810$	− 1.30923e8i	− 0.246354i
$811$	4.27809e8i	0.802025i	0.916073	+	0.401012i	$0.131342\pi$
$811$	4.27809e8i	0.802025i	−0.916073	+	0.401012i	$0.868658\pi$
$812$	0	0
$813$	−1.92393e8	−0.358029
$814$	−8.81650e8	−1.63464
$815$	9.89174e8i	1.82726i
$816$	−1.60149e8	−0.294751
$817$	4.87176e7i	0.0893346i
$818$	− 1.89887e8i	− 0.346925i
$819$	0	0
$820$	−9.19837e8	−1.66828
$821$	9.52803e8	1.72176	0.860882	−	0.508805i	$-0.169912\pi$
$821$	9.52803e8	1.72176	0.860882	+	0.508805i	$0.169912\pi$
$822$	− 5.74096e8i	− 1.03364i
$823$	−7.41229e8	−1.32970	−0.664848	−	0.746978i	$-0.731504\pi$
$823$	−7.41229e8	−1.32970	−0.664848	+	0.746978i	$0.731504\pi$
$824$	4.16689e7i	0.0744785i
$825$	− 6.66606e8i	− 1.18715i
$826$	0	0
$827$	−7.61072e8	−1.34558	−0.672790	−	0.739834i	$-0.734904\pi$
$827$	−7.61072e8	−1.34558	−0.672790	+	0.739834i	$0.734904\pi$
$828$	−1.13851e7	−0.0200561
$829$	− 8.15761e8i	− 1.43186i	−0.698174	−	0.715928i	$-0.746004\pi$
$829$	− 8.15761e8i	− 1.43186i	0.698174	−	0.715928i	$-0.253996\pi$
$830$	−2.35858e8	−0.412493
$831$	3.24710e8i	0.565839i
$832$	9.65442e8i	1.67632i
$833$	0	0
$834$	1.40286e8	0.241833
$835$	2.98966e8	0.513526
$836$	− 5.75658e8i	− 0.985248i
$837$	−1.06129e7	−0.0180991
$838$	4.35623e8i	0.740251i
$839$	− 1.07654e9i	− 1.82283i	−0.411491	−	0.911414i	$-0.634992\pi$
$839$	− 1.07654e9i	− 1.82283i	0.411491	−	0.911414i	$-0.365008\pi$
$840$	0	0
$841$	−5.08655e8	−0.855137
$842$	−1.06576e9	−1.78535
$843$	− 3.27581e8i	− 0.546809i
$844$	9.71972e8	1.61669
$845$	− 8.65917e8i	− 1.43518i
$846$	− 4.16662e8i	− 0.688133i
$847$	0	0
$848$	−7.91667e8	−1.29824
$849$	1.62493e8	0.265528
$850$	6.88919e8i	1.12179i
$851$	−2.43955e7	−0.0395841
$852$	− 3.37954e8i	− 0.546435i
$853$	− 9.74565e8i	− 1.57023i	−0.619349	−	0.785116i	$-0.712603\pi$
$853$	− 9.74565e8i	− 1.57023i	0.619349	−	0.785116i	$-0.287397\pi$
$854$	0	0
$855$	1.83170e8	0.293060
$856$	−5.20613e7	−0.0830030
$857$	− 9.60657e8i	− 1.52625i	−0.646251	−	0.763125i	$-0.723664\pi$
$857$	− 9.60657e8i	− 1.52625i	0.646251	−	0.763125i	$-0.276336\pi$
$858$	−1.13870e9	−1.80279
$859$	− 4.88078e8i	− 0.770034i	−0.922910	−	0.385017i	$-0.874196\pi$
$859$	− 4.88078e8i	− 0.770034i	0.922910	−	0.385017i	$-0.125804\pi$
$860$	1.67018e8i	0.262583i
$861$	0	0
$862$	1.60076e9	2.49921
$863$	3.22747e8	0.502146	0.251073	−	0.967968i	$-0.419217\pi$
$863$	3.22747e8	0.502146	0.251073	+	0.967968i	$0.419217\pi$
$864$	1.78115e8i	0.276160i
$865$	−2.37567e8	−0.367061
$866$	− 2.32695e8i	− 0.358289i
$867$	− 2.49629e8i	− 0.383034i
$868$	0	0
$869$	1.20519e9	1.83652
$870$	3.20832e8	0.487214
$871$	− 1.06849e9i	− 1.61702i
$872$	5.53229e7	0.0834363
$873$	4.98659e7i	0.0749481i
$874$	− 3.03010e7i	− 0.0453860i
$875$	0	0
$876$	−2.61494e8	−0.388999
$877$	9.37896e8	1.39045	0.695226	−	0.718791i	$-0.255304\pi$
$877$	9.37896e8	1.39045	0.695226	+	0.718791i	$0.255304\pi$
$878$	1.00016e9i	1.47770i
$879$	−4.44782e8	−0.654908
$880$	1.41391e9i	2.07479i
$881$	9.47337e8i	1.38540i	0.721224	+	0.692702i	$0.243580\pi$
$881$	9.47337e8i	1.38540i	−0.721224	+	0.692702i	$0.756420\pi$
$882$	0	0
$883$	1.52054e8	0.220860	0.110430	−	0.993884i	$-0.464777\pi$
$883$	1.52054e8	0.220860	0.110430	+	0.993884i	$0.464777\pi$
$884$	6.18626e8	0.895511
$885$	5.72824e8i	0.826403i
$886$	9.38422e7	0.134926
$887$	− 1.18390e9i	− 1.69646i	−0.529632	−	0.848228i	$-0.677670\pi$
$887$	− 1.18390e9i	− 1.69646i	0.529632	−	0.848228i	$-0.322330\pi$
$888$	− 4.63441e7i	− 0.0661843i
$889$	0	0
$890$	−2.89518e7	−0.0410682
$891$	−1.21352e8	−0.171559
$892$	1.52520e9i	2.14898i
$893$	5.82941e8	0.818597
$894$	6.35429e8i	0.889312i
$895$	4.30612e8i	0.600644i
$896$	0	0
$897$	−3.15080e7	−0.0436560
$898$	5.99947e8	0.828484
$899$	− 2.60074e7i	− 0.0357946i
$900$	3.58647e8	0.491972
$901$	6.26014e8i	0.855874i
$902$	1.62189e9i	2.21005i
$903$	0	0
$904$	−1.70388e8	−0.230639
$905$	1.52165e9	2.05290
$906$	1.16829e9i	1.57097i
$907$	3.39773e8	0.455372	0.227686	−	0.973735i	$-0.426884\pi$
$907$	3.39773e8	0.455372	0.227686	+	0.973735i	$0.426884\pi$
$908$	2.78847e8i	0.372485i
$909$	3.40467e8i	0.453297i
$910$	0	0
$911$	−9.44286e8	−1.24896	−0.624480	−	0.781041i	$-0.714689\pi$
$911$	−9.44286e8	−1.24896	−0.624480	+	0.781041i	$0.714689\pi$
$912$	−2.21894e8	−0.292523
$913$	2.18616e8i	0.287257i
$914$	4.63933e8	0.607599
$915$	− 9.90332e8i	− 1.29276i
$916$	− 3.98857e7i	− 0.0518956i
$917$	0	0
$918$	1.25414e8	0.162113
$919$	−3.74554e8	−0.482579	−0.241290	−	0.970453i	$-0.577570\pi$
$919$	−3.74554e8	−0.482579	−0.241290	+	0.970453i	$0.577570\pi$
$920$	− 1.01492e7i	− 0.0130337i
$921$	−1.59421e8	−0.204064
$922$	1.63685e8i	0.208841i
$923$	− 9.35280e8i	− 1.18942i
$924$	0	0
$925$	7.68494e8	0.970991
$926$	−1.45431e9	−1.83158
$927$	1.25787e8i	0.157905i
$928$	−4.36480e8	−0.546161
$929$	− 9.11640e8i	− 1.13704i	−0.822669	−	0.568521i	$-0.807516\pi$
$929$	− 9.11640e8i	− 1.13704i	0.822669	−	0.568521i	$-0.192484\pi$
$930$	− 9.68343e7i	− 0.120387i
$931$	0	0
$932$	−1.15851e9	−1.43104
$933$	−2.45396e8	−0.302150
$934$	− 1.20256e9i	− 1.47593i
$935$	1.11806e9	1.36782
$936$	− 5.98557e7i	− 0.0729924i
$937$	− 3.76597e8i	− 0.457781i	−0.973452	−	0.228890i	$-0.926490\pi$
$937$	− 3.76597e8i	− 0.457781i	0.973452	−	0.228890i	$-0.0735097\pi$
$938$	0	0
$939$	−8.65586e8	−1.04547
$940$	1.99848e9	2.40612
$941$	2.51723e8i	0.302103i	0.988526	+	0.151051i	$0.0482659\pi$
$941$	2.51723e8i	0.302103i	−0.988526	+	0.151051i	$0.951734\pi$
$942$	8.47966e8	1.01444
$943$	4.48781e7i	0.0535180i
$944$	− 6.93922e8i	− 0.824888i
$945$	0	0
$946$	2.94491e8	0.347856
$947$	−2.65866e8	−0.313050	−0.156525	−	0.987674i	$-0.550029\pi$
$947$	−2.65866e8	−0.313050	−0.156525	+	0.987674i	$0.550029\pi$
$948$	6.48416e8i	0.761077i
$949$	−7.23677e8	−0.846732
$950$	9.54525e8i	1.11331i
$951$	9.40107e7i	0.109304i
$952$	0	0
$953$	−5.38039e8	−0.621635	−0.310817	−	0.950470i	$-0.600603\pi$
$953$	−5.38039e8	−0.621635	−0.310817	+	0.950470i	$0.600603\pi$
$954$	6.19959e8	0.714032
$955$	8.13458e8i	0.933953i
$956$	−1.39116e9	−1.59222
$957$	− 2.97379e8i	− 0.339292i
$958$	9.05777e8i	1.03021i
$959$	0	0
$960$	−9.38774e8	−1.06108
$961$	8.79654e8	0.991155
$962$	− 1.31274e9i	− 1.47453i
$963$	−1.57159e8	−0.175979
$964$	2.55277e8i	0.284958i
$965$	− 2.78244e7i	− 0.0309631i
$966$	0	0
$967$	−1.16138e9	−1.28439	−0.642194	−	0.766542i	$-0.721976\pi$
$967$	−1.16138e9	−1.28439	−0.642194	+	0.766542i	$0.721976\pi$
$968$	−1.97371e8	−0.217600
$969$	1.75463e8i	0.192848i
$970$	−4.54987e8	−0.498522
$971$	− 1.50850e9i	− 1.64773i	−0.566784	−	0.823866i	$-0.691813\pi$
$971$	− 1.50850e9i	− 1.64773i	0.566784	−	0.823866i	$-0.308187\pi$
$972$	− 6.52898e7i	− 0.0710962i
$973$	0	0
$974$	−1.65874e9	−1.79515
$975$	9.92548e8	1.07087
$976$	1.19969e9i	1.29039i
$977$	−1.20754e8	−0.129485	−0.0647425	−	0.997902i	$-0.520623\pi$
$977$	−1.20754e8	−0.129485	−0.0647425	+	0.997902i	$0.520623\pi$
$978$	9.38387e8i	1.00315i
$979$	2.68354e7i	0.0285996i
$980$	0	0
$981$	1.67005e8	0.176897
$982$	−5.89878e8	−0.622914
$983$	− 2.15159e7i	− 0.0226516i	−0.999936	−	0.0113258i	$-0.996395\pi$
$983$	− 2.15159e7i	− 0.0226516i	0.999936	−	0.0113258i	$-0.00360520\pi$
$984$	−8.52549e7	−0.0894817
$985$	− 1.37680e9i	− 1.44067i
$986$	3.07333e8i	0.320611i
$987$	0	0
$988$	8.57131e8	0.888743
$989$	8.14865e6	0.00842359
$990$	− 1.10724e9i	− 1.14113i
$991$	−6.15881e7	−0.0632813	−0.0316407	−	0.999499i	$-0.510073\pi$
$991$	−6.15881e7	−0.0632813	−0.0316407	+	0.999499i	$0.510073\pi$
$992$	1.31740e8i	0.134953i
$993$	− 1.52230e8i	− 0.155472i
$994$	0	0
$995$	−3.36855e8	−0.341959
$996$	−1.17620e8	−0.119043
$997$	7.76327e8i	0.783356i	0.920102	+	0.391678i	$0.128105\pi$
$997$	7.76327e8i	0.783356i	−0.920102	+	0.391678i	$0.871895\pi$
$998$	−1.46947e9	−1.47832
$999$	− 1.39900e8i	− 0.140321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.7.d.b.97.1		8
3.2	odd	2		441.7.d.c.244.7		8
7.2	even	3		147.7.f.d.31.4		8
7.3	odd	6		147.7.f.d.19.4		8
7.4	even	3		21.7.f.a.19.4	yes	8
7.5	odd	6		21.7.f.a.10.4	✓	8
7.6	odd	2	inner	147.7.d.b.97.2		8
21.5	even	6		63.7.m.d.10.1		8
21.11	odd	6		63.7.m.d.19.1		8
21.20	even	2		441.7.d.c.244.8		8
28.11	odd	6		336.7.bh.d.145.1		8
28.19	even	6		336.7.bh.d.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.4	✓	8	7.5	odd	6
21.7.f.a.19.4	yes	8	7.4	even	3
63.7.m.d.10.1		8	21.5	even	6
63.7.m.d.19.1		8	21.11	odd	6
147.7.d.b.97.1		8	1.1	even	1	trivial
147.7.d.b.97.2		8	7.6	odd	2	inner
147.7.f.d.19.4		8	7.3	odd	6
147.7.f.d.31.4		8	7.2	even	3
336.7.bh.d.145.1		8	28.11	odd	6
336.7.bh.d.241.1		8	28.19	even	6
441.7.d.c.244.7		8	3.2	odd	2
441.7.d.c.244.8		8	21.20	even	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	147.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.6159 q^{2} -15.5885i q^{3} +70.9299 q^{4} +190.875i q^{5} +181.074i q^{6} -80.4975 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q-11.6159 q^{2} -15.5885i q^{3} +70.9299 q^{4} +190.875i q^{5} +181.074i q^{6} -80.4975 q^{8} -243.000 q^{9} -2217.19i q^{10} -2055.10 q^{11} -1105.69i q^{12} -3059.97i q^{13} +2975.44 q^{15} -3604.46 q^{16} +2850.24i q^{17} +2822.67 q^{18} +3949.13i q^{19} +13538.7i q^{20} +23872.0 q^{22} +660.543 q^{23} +1254.83i q^{24} -20808.1 q^{25} +35544.4i q^{26} +3788.00i q^{27} -9282.66 q^{29} -34562.5 q^{30} +2801.72i q^{31} +47021.0 q^{32} +32035.9i q^{33} -33108.2i q^{34} -17236.0 q^{36} -36932.5 q^{37} -45872.8i q^{38} -47700.1 q^{39} -15364.9i q^{40} +67941.3i q^{41} +12336.3 q^{43} -145768. q^{44} -46382.5i q^{45} -7672.83 q^{46} -147613. i q^{47} +56188.0i q^{48} +241705. q^{50} +44430.9 q^{51} -217043. i q^{52} +219635. q^{53} -44001.1i q^{54} -392267. i q^{55} +61560.8 q^{57} +107827. q^{58} +192518. i q^{59} +211048. q^{60} -332836. i q^{61} -32544.5i q^{62} -315508. q^{64} +584069. q^{65} -372127. i q^{66} +349184. q^{67} +202168. i q^{68} -10296.9i q^{69} +305650. q^{71} +19560.9 q^{72} -236498. i q^{73} +429005. q^{74} +324366. i q^{75} +280111. i q^{76} +554082. q^{78} -586437. q^{79} -688000. i q^{80} +59049.0 q^{81} -789201. i q^{82} -106377. i q^{83} -544039. q^{85} -143298. q^{86} +144702. i q^{87} +165431. q^{88} -13057.9i q^{89} +538776. i q^{90} +46852.3 q^{92} +43674.4 q^{93} +1.71466e6i q^{94} -753788. q^{95} -732985. i q^{96} -205209. i q^{97} +499390. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} + 3326 q^{8} - 1944 q^{9} + 628 q^{11} + 5292 q^{15} + 25442 q^{16} - 2430 q^{18} + 86106 q^{22} - 7856 q^{23} + 34076 q^{25} - 8300 q^{29} - 61398 q^{30} + 372414 q^{32} - 84078 q^{36} - 129412 q^{37} - 58212 q^{39} + 45740 q^{43} - 185058 q^{44} + 223008 q^{46} + 967216 q^{50} - 99576 q^{51} + 1081948 q^{53} + 328212 q^{57} - 1079598 q^{58} + 292734 q^{60} + 2378626 q^{64} + 828408 q^{65} + 2317804 q^{67} + 1442344 q^{71} - 808218 q^{72} + 865880 q^{74} - 222588 q^{78} - 1222904 q^{79} + 472392 q^{81} - 275112 q^{85} - 1632448 q^{86} + 732882 q^{88} + 678720 q^{92} - 1611144 q^{93} + 1183584 q^{95} - 152604 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 + 3326 * q^8 - 1944 * q^9 + 628 * q^11 + 5292 * q^15 + 25442 * q^16 - 2430 * q^18 + 86106 * q^22 - 7856 * q^23 + 34076 * q^25 - 8300 * q^29 - 61398 * q^30 + 372414 * q^32 - 84078 * q^36 - 129412 * q^37 - 58212 * q^39 + 45740 * q^43 - 185058 * q^44 + 223008 * q^46 + 967216 * q^50 - 99576 * q^51 + 1081948 * q^53 + 328212 * q^57 - 1079598 * q^58 + 292734 * q^60 + 2378626 * q^64 + 828408 * q^65 + 2317804 * q^67 + 1442344 * q^71 - 808218 * q^72 + 865880 * q^74 - 222588 * q^78 - 1222904 * q^79 + 472392 * q^81 - 275112 * q^85 - 1632448 * q^86 + 732882 * q^88 + 678720 * q^92 - 1611144 * q^93 + 1183584 * q^95 - 152604 * q^99

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